Subgroups — C₂×C₅×C₃₇×D₃₁ #37525751

Order 22940.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₇×D₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₃₁×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃₁×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₇×D₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃₁×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented
6	C₃₇×D₃₁	C₂×C₅	1	2	yes	direct product factor
7	C₃₁×C₃₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₅×C₃₇	—	31	1	no	maximal, Hall
9	C₂×C₅×D₃₁	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅×C₃₇	—	31	2	no	—
11	C₂×C₅×C₃₇	D₃₁	1	1	yes	characteristic, direct product factor
12	C₂×C₅×C₃₁	C₂×C₃₇	1	1	yes	characteristic, complemented
13	C₅×D₃₁	C₂×C₃₇	1	2	yes	direct product factor
14	C₅×C₃₇	C₂×D₃₁	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₃₁	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₃₇	—	31	1	no	Hall
17	C₂×D₃₁	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃₇	—	31	2	no	—
19	C₂×C₃₇	C₅×D₃₁	1	1	yes	characteristic, direct product factor
20	C₂×C₃₁	C₂×C₅×C₃₇	1	1	yes	characteristic, complemented
21	D₃₁	C₂×C₅×C₃₇	1	2	yes	direct product factor
22	C₃₇	C₂×C₅×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
23	C₃₁	C₂²×C₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₅	—	31	1	no	Hall
25	C₂×C₅	—	31	2	no	—
26	C₂×C₅	C₃₇×D₃₁	1	1	yes	characteristic, direct product factor
27	C₅	C₂×C₃₇×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	31	1	no	Sylow
29	C₂	—	31	2	no	—
30	C₂	C₅×C₃₇×D₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₃₇	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂²×C₅×C₃₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₃₁×C₃₇	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₅×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₇×D₃₁	C₂	direct (N × H)
2. C₂×C₅×C₃₁×C₃₇	C₂	semidirect
3. C₅×C₃₁×C₃₇	C₂²	semidirect
4. C₂×C₃₇×D₃₁	C₅	direct (N × H)
5. C₂×C₃₁×C₃₇	C₂×C₅	semidirect
6. C₃₇×D₃₁	C₂×C₅	direct (N × H)
7. C₃₁×C₃₇	C₂²×C₅	semidirect
9. C₂×C₅×D₃₁	C₃₇	direct (N × H)
11. C₂×C₅×C₃₇	D₃₁	direct (N × H)
12. C₂×C₅×C₃₁	C₂×C₃₇	semidirect
13. C₅×D₃₁	C₂×C₃₇	direct (N × H)
14. C₅×C₃₇	C₂×D₃₁	direct (N × H)
15. C₅×C₃₁	C₂²×C₃₇	semidirect
17. C₂×D₃₁	C₅×C₃₇	direct (N × H)
19. C₂×C₃₇	C₅×D₃₁	direct (N × H)
20. C₂×C₃₁	C₂×C₅×C₃₇	semidirect
21. D₃₁	C₂×C₅×C₃₇	direct (N × H)
22. C₃₇	C₂×C₅×D₃₁	direct (N × H)
23. C₃₁	C₂²×C₅×C₃₇	semidirect
26. C₂×C₅	C₃₇×D₃₁	direct (N × H)
27. C₅	C₂×C₃₇×D₃₁	direct (N × H)
30. C₂	C₅×C₃₇×D₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₃₇×D₃₁	2
C₂×C₅×C₃₁×C₃₇	2
C₂×C₃₇×D₃₁	5
C₂²×C₅×C₃₇	31
C₂×C₅×D₃₁	37

Subgroups — C2×C5×C37×D31 #37525751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₃₇×D₃₁ #37525751