Subgroups — C₅⋊D₃₁₁₅ #44528280

Order 31150.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₁₁₅	—	5	6	no	maximal
3	C₅⋊D₄₄₅	—	7	1	no	maximal, Hall
4	C₅×C₇×C₈₉	D₅	1	6	yes	complemented
5	C₅²×C₈₉	D₇	1	1	yes	characteristic, complemented, Hall
6	D₆₂₃	—	25	1	no	Hall
7	D₄₄₅	—	35	6	no	—
8	C₇×C₈₉	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
9	C₅×C₈₉	D₃₅	1	6	yes	complemented
10	C₅⋊D₃₅	—	89	1	no	maximal, Hall
11	D₈₉	—	175	1	no	Hall
12	C₅²×C₇	D₈₉	1	1	yes	characteristic, complemented, Hall
13	C₈₉	C₅⋊D₃₅	1	1	yes	characteristic, complemented, Sylow
14	D₃₅	—	445	6	no	—
15	C₅⋊D₅	—	623	1	no	Hall
16	C₅×C₇	D₄₄₅	1	6	yes	complemented
17	C₅²	D₆₂₃	1	1	yes	characteristic, complemented, Sylow
18	D₇	—	2225	1	no	Hall
19	D₅	—	3115	6	no	—
20	C₇	C₅⋊D₄₄₅	1	1	yes	characteristic, complemented, Sylow
21	C₅	D₃₁₁₅	1	6	yes	complemented
22	C₂	—	15575	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₇×C₈₉	C₂
LCS	G ▷ C₅²×C₇×C₈₉
UCS	C₁

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.