Subgroups — C₅×Dic₁₅₆₁ #44530229

Order 31220.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×C₂₂₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₂₂₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₅₆₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×Dic₂₂₃	—	7	1	no	maximal, Hall
5	C₂×C₇×C₂₂₃	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅×C₂₂₃	D₇	1	1	yes	characteristic
7	C₇×C₂₂₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₂₂₃	Dic₇	1	1	yes	characteristic, complemented, Hall
9	Dic₂₂₃	—	7	1	no	Hall
10	C₂×C₂₂₃	C₅×D₇	1	1	yes	characteristic
11	C₂₂₃	C₅×Dic₇	1	1	yes	characteristic, complemented, Sylow
12	C₅×Dic₇	—	223	1	no	maximal, Hall
13	C₂×C₅×C₇	D₂₂₃	1	1	yes	characteristic
14	C₅×C₇	Dic₂₂₃	1	1	yes	characteristic, complemented, Hall
15	Dic₇	—	223	1	no	Hall
16	C₄×C₅	—	1561	1	no	Hall
17	C₂×C₇	C₅×D₂₂₃	1	1	yes	characteristic
18	C₂×C₅	D₁₅₆₁	1	1	yes	characteristic
19	C₇	C₅×Dic₂₂₃	1	1	yes	characteristic, complemented, Sylow
20	C₅	Dic₁₅₆₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	1561	1	no	Sylow
22	C₂	C₅×D₁₅₆₁	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.