Subgroups — C₅×D₃₁₄₅ #44537797

Order 31450.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₇×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₁₄₅	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×D₆₂₉	—	5	1	no	maximal
4	C₅×C₁₇×C₃₇	—	2	2	no	—
5	C₅×C₁₇×C₃₇	D₅	1	1	yes	characteristic, complemented
6	C₅×C₁₇×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented
7	C₅×D₁₈₅	—	17	1	no	maximal, Hall
8	D₆₂₉	—	5	1	no	Hall
9	C₅²×C₃₇	D₁₇	1	1	yes	characteristic, complemented, Hall
10	C₅×D₈₅	—	37	1	no	maximal, Hall
11	C₁₇×C₃₇	C₅×D₅	1	1	yes	characteristic, complemented, Hall
12	C₅²×C₁₇	D₃₇	1	1	yes	characteristic, complemented, Hall
13	D₁₈₅	—	17	1	no	—
14	C₅×D₃₇	—	85	1	no	—
15	C₅×C₃₇	—	2	2	no	—
16	C₅×C₃₇	C₅×D₁₇	1	1	yes	characteristic, complemented
17	C₅×C₃₇	D₈₅	1	1	yes	characteristic, complemented
18	D₈₅	—	37	1	no	—
19	C₅×D₁₇	—	185	1	no	—
20	C₅×C₁₇	—	2	2	no	—
21	C₅×C₁₇	C₅×D₃₇	1	1	yes	characteristic, complemented
22	C₅×C₁₇	D₁₈₅	1	1	yes	characteristic, complemented
23	D₃₇	—	85	1	no	Hall
24	C₅×D₅	—	629	1	no	Hall
25	C₃₇	C₅×D₈₅	1	1	yes	characteristic, complemented, Sylow
26	D₁₇	—	185	1	no	Hall
27	C₅²	D₆₂₉	1	1	yes	characteristic, complemented, Sylow
28	C₁₇	C₅×D₁₈₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅	—	3145	1	no	—
30	D₅	—	629	1	no	—
31	C₅	—	2	2	no	—
32	C₅	C₅×D₆₂₉	1	1	yes	characteristic, complemented
33	C₅	D₃₁₄₅	1	1	yes	characteristic, direct product factor
34	C₂	—	3145	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃₁₄₅
commutator, cosocle, hypocenter	C₅×C₁₇×C₃₇	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₁₇×C₃₇	C₂
LCS	G ▷ C₅×C₁₇×C₃₇
UCS	C₁ ◁ C₅

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅²×C₁₇×C₃₇	C₂	semidirect
2. D₃₁₄₅	C₅	direct (N × H)
5. C₅×C₁₇×C₃₇	D₅	semidirect
6. C₅×C₁₇×C₃₇	C₂×C₅	semidirect
9. C₅²×C₃₇	D₁₇	semidirect
11. C₁₇×C₃₇	C₅×D₅	semidirect
12. C₅²×C₁₇	D₃₇	semidirect
16. C₅×C₃₇	C₅×D₁₇	semidirect
17. C₅×C₃₇	D₈₅	semidirect
21. C₅×C₁₇	C₅×D₃₇	semidirect
22. C₅×C₁₇	D₁₈₅	semidirect
25. C₃₇	C₅×D₈₅	semidirect
27. C₅²	D₆₂₉	semidirect
28. C₁₇	C₅×D₁₈₅	semidirect
32. C₅	C₅×D₆₂₉	semidirect
33. C₅	D₃₁₄₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅²×C₁₇×C₃₇	2
D₃₁₄₅	5
C₅×D₆₂₉	5
C₅×D₁₈₅	17
C₅×D₈₅	37

Subgroups — C5×D3145 #44537797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃₁₄₅ #44537797