Subgroups — C₅²×Dic₇×C₃₇ #39905976

Order 25900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₇×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₇×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×Dic₇×C₃₇	C₅	1	6	yes	maximal, direct product factor
4	C₄×C₅²×C₃₇	—	7	1	no	maximal, Hall
5	C₂×C₅×C₇×C₃₇	C₂×C₅	1	6	yes	—
6	C₂×C₅²×C₃₇	D₇	1	1	yes	characteristic
7	C₅×C₇×C₃₇	C₄×C₅	1	6	yes	complemented
8	Dic₇×C₃₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
9	C₅²×C₃₇	Dic₇	1	1	yes	characteristic, direct product factor, Hall
10	C₄×C₅×C₃₇	—	7	6	no	—
11	C₅²×Dic₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₇×C₃₇	C₂×C₅²	1	1	yes	characteristic
13	C₂×C₅×C₃₇	C₅×D₇	1	6	yes	—
14	C₂×C₅²×C₇	C₂×C₃₇	1	1	yes	characteristic
15	C₇×C₃₇	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
16	C₅×C₃₇	C₅×Dic₇	1	6	yes	direct product factor
17	C₅²×C₇	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
18	C₄×C₃₇	—	7	1	no	Hall
19	C₅×Dic₇	C₅×C₃₇	1	6	yes	direct product factor
20	C₄×C₅²	—	7	1	no	Hall
21	C₂×C₃₇	C₅²×D₇	1	1	yes	characteristic
22	C₂×C₅×C₇	C₂×C₅×C₃₇	1	6	yes	—
23	C₂×C₅²	D₇×C₃₇	1	1	yes	characteristic
24	C₃₇	C₅²×Dic₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₅×C₇	C₄×C₅×C₃₇	1	6	yes	complemented
26	Dic₇	C₅²×C₃₇	1	1	yes	characteristic, direct product factor, Hall
27	C₅²	Dic₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₄×C₅	—	7	6	no	—
29	C₂×C₇	C₂×C₅²×C₃₇	1	1	yes	characteristic
30	C₂×C₅	C₅×D₇×C₃₇	1	6	yes	—
31	C₇	C₄×C₅²×C₃₇	1	1	yes	characteristic, complemented, Sylow
32	C₅	C₅×Dic₇×C₃₇	1	6	yes	direct product factor
33	C₄	—	7	1	no	Sylow
34	C₂	C₅²×D₇×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₃₇	D₇
commutator, hypocenter	C₇	C₄×C₅²×C₃₇
Frattini	C₂	C₅²×D₇×C₃₇
Fitting, socle, prime radical	C₂×C₅²×C₇×C₃₇	C₂
cosocle	C₂×C₇	C₂×C₅²×C₃₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₅²×C₃₇

Complements

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

N	H ≅ G/N	type
2. C₅²×C₇×C₃₇	C₄	semidirect
3. C₅×Dic₇×C₃₇	C₅	direct (N × H)
7. C₅×C₇×C₃₇	C₄×C₅	semidirect
8. Dic₇×C₃₇	C₅²	direct (N × H)
9. C₅²×C₃₇	Dic₇	direct (N × H)
11. C₅²×Dic₇	C₃₇	direct (N × H)
15. C₇×C₃₇	C₄×C₅²	semidirect
16. C₅×C₃₇	C₅×Dic₇	direct (N × H)
17. C₅²×C₇	C₄×C₃₇	semidirect
19. C₅×Dic₇	C₅×C₃₇	direct (N × H)
24. C₃₇	C₅²×Dic₇	direct (N × H)
25. C₅×C₇	C₄×C₅×C₃₇	semidirect
26. Dic₇	C₅²×C₃₇	direct (N × H)
27. C₅²	Dic₇×C₃₇	direct (N × H)
31. C₇	C₄×C₅²×C₃₇	semidirect
32. C₅	C₅×Dic₇×C₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅²×C₇×C₃₇	2
C₅×Dic₇×C₃₇	5
C₄×C₅²×C₃₇	7
C₅²×Dic₇	37

Subgroups — C52×Dic7×C37 #39905976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×Dic₇×C₃₇ #39905976