Table of number of groups for small orders

This page contains a table for the number of groups up to isomorphism of order $n$ for $n$ small.

Order	page link	prime factorisation	Number of groups
1	groups of order 1		1
2	groups of order 2	2	1
3	groups of order 3	3	1
4	groups of order 4	2^2	2
5	groups of order 5	5	1
6	groups of order 6	2 x 3	2
7	groups of order 7	7	1
8	groups of order 8	2^3	5
9	groups of order 9	3^2	2
10	groups of order 10	2 x 5	2
11	groups of order 11	11	1
12	groups of order 12	2^2 x 3	5
13	groups of order 13	13	1
14	groups of order 14	2 x 7	2
15	groups of order 15	3 x 5	1
16	groups of order 16	2^4	14
17	groups of order 17	17	1
18	groups of order 18	2 x 3^2	5
19	groups of order 19	19	1
20	groups of order 20	2^2 x 5	5
21	groups of order 21	3 x 7	2
22	groups of order 22	2 x 11	2
23	groups of order 23	23	1
24	groups of order 24	2^3 x 3	15
25	groups of order 25	5^2	2
26	groups of order 26	2 x 13	2
27	groups of order 27	3^3	5
28	groups of order 28	2^2 x 7	4
29	groups of order 29	29	1
30	groups of order 30	2 x 3 x 5	4
31	groups of order 31	31	1
32	groups of order 32	2^5	51
33	groups of order 33	3 x 11	1
34	groups of order 34	2 x 17	2
35	groups of order 35	5 x 7	1
36	groups of order 36	2^2 x 3^2	14
37	groups of order 37	37	1
38	groups of order 38	2 x 19	2
39	groups of order 39	3 x 13	2
40	groups of order 40	2^3 x 5	14
41	groups of order 41	41	1
42	groups of order 42	2 x 3 x 7	6
43	groups of order 43	43	1
44	groups of order 44	2^2 x 11	4
45	groups of order 45	3^2 x 5	2
46	groups of order 46	2 x 23	2
47	groups of order 47	47	1
48	groups of order 48	2^4 x 3	52
49	groups of order 49	7^2	2
50	groups of order 50	2 x 5^2	5
51	groups of order 51	3 x 17	1
52	groups of order 52	2^2 x 13	5
53	groups of order 53	53	1
54	groups of order 54	2 x 3^3	15
55	groups of order 55	5 x 11	2
56	groups of order 56	2^3 x 7	13
57	groups of order 57	3 x 19	2
58	groups of order 58	2 x 29	2
59	groups of order 59	59	1
60	groups of order 60	2^2 x 3 x 5	13
61	groups of order 61	61	1
62	groups of order 62	2 x 31	2
63	groups of order 63	3^2 x 7	4
64	groups of order 64	2^6	267
65	groups of order 65	5 x 13	1
66	groups of order 66	2 x 3 x 11	4
67	groups of order 67	67	1
68	groups of order 68	2^2 x 17	5
69	groups of order 69	3 x 23	1
70	groups of order 70	2 x 5 x 7	4
71	groups of order 71	71	1
72	groups of order 72	2^3 x 3^2	50
73	groups of order 73	73	1
74	groups of order 74	2 x 37	2
75	groups of order 75	3 x 5^2	3
76	groups of order 76	2^2 x 19	4
77	groups of order 77	7 x 11	1
78	groups of order 78	2 x 3 x 13	6
79	groups of order 79	79	1
80	groups of order 80	2^4 x 5	52
81	groups of order 81	3^4	15
82	groups of order 82	2 x 41	2
83	groups of order 83	83	1
84	groups of order 84	2^2 x 3 x 7	15
85	groups of order 85	5 x 17	1
86	groups of order 86	2 x 43	2
87	groups of order 87	3 x 29	1
88	groups of order 88	2^3 x 11	12
89	groups of order 89	89	1
90	groups of order 90	2 x 3^2 x 5	10
91	groups of order 91	7 x 13	1
92	groups of order 92	2^2 x 23	4
93	groups of order 93	3 x 31	2
94	groups of order 94	2 x 47	2
95	groups of order 95	5 x 19	1
96	groups of order 96	2^5 x 3	231
97	groups of order 97	97	1
98	groups of order 98	2 x 7^2	5
99	groups of order 99	3^2 x 11	2
100	groups of order 100	2^2 x 5^2	16