Subgroups — C₂₅×D₆₂₃ #44528264

Order 31150.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₅×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₆₂₃	C₅	1	1	yes	maximal, characteristic
3	C₂₅×D₈₉	—	7	1	no	maximal, Hall
4	C₅×C₇×C₈₉	C₂×C₅	1	1	yes	characteristic
5	C₂₅×C₈₉	D₇	1	1	yes	characteristic, complemented, Hall
6	D₆₂₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
7	C₅×D₈₉	—	7	1	no	—
8	C₇×C₈₉	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
9	C₅×C₈₉	C₅×D₇	1	1	yes	characteristic
10	D₇×C₂₅	—	89	1	no	maximal, Hall
11	D₈₉	—	7	1	no	Hall
12	C₇×C₂₅	D₈₉	1	1	yes	characteristic, complemented, Hall
13	C₈₉	D₇×C₂₅	1	1	yes	characteristic, complemented, Sylow
14	C₅×D₇	—	89	1	no	—
15	C₂×C₂₅	—	623	1	no	Hall
16	C₅×C₇	C₅×D₈₉	1	1	yes	characteristic
17	C₂₅	D₆₂₃	1	1	yes	characteristic, direct product factor, Sylow
18	D₇	—	89	1	no	Hall
19	C₂×C₅	—	623	1	no	—
20	C₇	C₂₅×D₈₉	1	1	yes	characteristic, complemented, Sylow
21	C₅	C₅×D₆₂₃	1	1	yes	characteristic
22	C₂	—	623	1	no	Sylow

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.