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# Category:Subgroup property implications in finite groups

From Groupprops

## Pages in category "Subgroup property implications in finite groups"

The following 19 pages are in this category, out of 19 total. The count *includes* redirect pages that have been included in the category. Redirect pages are shown in italics.

### C

- Central implies finite-pi-potentially verbal in finite
- Central implies potentially fully invariant in finite
- Central implies potentially verbal in finite
- Conjugate-permutable implies subnormal in finite
- Cyclic normal implies finite-pi-potentially verbal in finite
- Cyclic normal implies potentially verbal in finite

### H

### S

- Subgroup of index equal to least prime divisor of group order is normal
- Sylow implies intermediately isomorph-conjugate
- Sylow implies order-dominating
- Sylow implies pronormal
- Sylow normalizer implies abnormal
- Sylow normalizer implies weakly abnormal
- Sylow of normal implies pronormal
- Sylow-permutable implies subnormal in finite