Subgroups — C₉×D₇×C₂₅₇ #44569202

Order 32382.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₇×C₂₅₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₂₅₇	C₂×C₃	1	1	yes	characteristic
4	C₂×C₉×C₂₅₇	—	7	1	no	maximal, Hall
5	D₇×C₂₅₇	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₂₅₇	D₇	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₂₅₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₂₅₇	—	7	1	no	—
9	C₃×C₂₅₇	C₃×D₇	1	1	yes	characteristic
10	C₂×C₂₅₇	—	7	1	no	Hall
11	C₂₅₇	C₉×D₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₉×D₇	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₇×C₉	C₂×C₂₅₇	1	1	yes	characteristic, complemented, Hall
14	C₃×D₇	C₃×C₂₅₇	1	1	yes	characteristic
15	C₃×C₇	C₂×C₃×C₂₅₇	1	1	yes	characteristic
16	C₂×C₉	—	7	1	no	Hall
17	D₇	C₉×C₂₅₇	1	1	yes	characteristic, direct product factor, Hall
18	C₉	D₇×C₂₅₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₇	C₂×C₉×C₂₅₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	7	1	no	—
21	C₃	C₃×D₇×C₂₅₇	1	1	yes	characteristic
22	C₂	—	7	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.