Subgroups — C₅×D₃₁₁₅ #44528276

Order 31150.

40 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	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×D₆₂₃	—	5	1	no	maximal
4	C₅×D₄₄₅	—	7	1	no	maximal, Hall
5	C₅×C₇×C₈₉	—	2	2	no	—
6	C₅×C₇×C₈₉	D₅	1	1	yes	characteristic, complemented
7	C₅×C₇×C₈₉	C₂×C₅	1	1	yes	characteristic, complemented
8	C₅²×C₈₉	D₇	1	1	yes	characteristic, complemented, Hall
9	D₆₂₃	—	5	1	no	Hall
10	D₄₄₅	—	7	1	no	—
11	C₅×D₈₉	—	35	1	no	—
12	C₇×C₈₉	C₅×D₅	1	1	yes	characteristic, complemented, Hall
13	C₅×C₈₉	—	2	2	no	—
14	C₅×C₈₉	C₅×D₇	1	1	yes	characteristic, complemented
15	C₅×C₈₉	D₃₅	1	1	yes	characteristic, complemented
16	C₅×D₃₅	—	89	1	no	maximal, Hall
17	D₈₉	—	35	1	no	Hall
18	C₅²×C₇	D₈₉	1	1	yes	characteristic, complemented, Hall
19	C₈₉	C₅×D₃₅	1	1	yes	characteristic, complemented, Sylow
20	D₃₅	—	89	1	no	—
21	C₅×D₇	—	445	1	no	—
22	C₅×D₅	—	623	1	no	Hall
23	C₅×C₇	—	2	2	no	—
24	C₅×C₇	C₅×D₈₉	1	1	yes	characteristic, complemented
25	C₅×C₇	D₄₄₅	1	1	yes	characteristic, complemented
26	C₅²	D₆₂₃	1	1	yes	characteristic, complemented, Sylow
27	D₇	—	445	1	no	Hall
28	C₂×C₅	—	3115	1	no	—
29	D₅	—	623	1	no	—
30	C₇	C₅×D₄₄₅	1	1	yes	characteristic, complemented, Sylow
31	C₅	—	2	2	no	—
32	C₅	C₅×D₆₂₃	1	1	yes	characteristic, complemented
33	C₅	D₃₁₁₅	1	1	yes	characteristic, direct product factor
34	C₂	—	3115	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃₁₁₅
commutator, cosocle, hypocenter	C₅×C₇×C₈₉	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₈₉	C₂
LCS	G ▷ C₅×C₇×C₈₉
UCS	C₁ ◁ C₅

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.