Subgroups — C₄₃×Dic₁₈₅ #44541302

Order 31820.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₇×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₇×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄₃×Dic₃₇	—	5	1	no	maximal, Hall
4	C₂×C₃₇×C₄₃	D₅	1	1	yes	characteristic
5	C₃₇×C₄₃	Dic₅	1	1	yes	characteristic, complemented, Hall
6	Dic₅×C₄₃	—	37	1	no	maximal, Hall
7	Dic₁₈₅	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₄₃	D₃₇	1	1	yes	characteristic
9	C₂×C₅×C₃₇	C₂×C₄₃	1	1	yes	characteristic
10	C₅×C₄₃	Dic₃₇	1	1	yes	characteristic, complemented, Hall
11	C₅×C₃₇	C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
12	C₄×C₄₃	—	185	1	no	Hall
13	Dic₃₇	—	5	1	no	Hall
14	C₂×C₄₃	D₁₈₅	1	1	yes	characteristic
15	C₂×C₃₇	D₅×C₄₃	1	1	yes	characteristic
16	C₄₃	Dic₁₈₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₃₇	Dic₅×C₄₃	1	1	yes	characteristic, complemented, Sylow
18	Dic₅	—	37	1	no	Hall
19	C₂×C₅	C₄₃×D₃₇	1	1	yes	characteristic
20	C₅	C₄₃×Dic₃₇	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	185	1	no	Sylow
22	C₂	C₄₃×D₁₈₅	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.