Subgroups — C₅×C₇×Dic₂₂₇ #44541000

Order 31780.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×C₂₂₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₂₂₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×Dic₂₂₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×Dic₂₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₂₂₇	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅×C₂₂₇	C₂×C₇	1	1	yes	characteristic
7	C₇×C₂₂₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₂₂₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
9	Dic₂₂₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₂₂₇	C₂×C₅×C₇	1	1	yes	characteristic
11	C₂₂₇	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
12	C₄×C₅×C₇	—	227	1	no	maximal, Hall
13	C₂×C₅×C₇	D₂₂₇	1	1	yes	characteristic
14	C₅×C₇	Dic₂₂₇	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₇	—	227	1	no	Hall
16	C₄×C₅	—	227	1	no	Hall
17	C₂×C₇	C₅×D₂₂₇	1	1	yes	characteristic
18	C₂×C₅	C₇×D₂₂₇	1	1	yes	characteristic
19	C₇	C₅×Dic₂₂₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₅	C₇×Dic₂₂₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	227	1	no	Sylow
22	C₂	C₅×C₇×D₂₂₇	1	1	yes	characteristic

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.