Subgroups — C₃₇×(C₅⋊D₅)⋊D₇ #39906013

Order 25900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₇×D₃₅	C₂	1	2	yes	maximal, complemented
2	C₇×C₃₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₇×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₅×D₇×C₃₇	—	5	2	no	maximal
5	D₅²×C₃₇	—	7	1	no	maximal, Hall
6	C₃₇×D₃₅	D₅	1	2	yes	complemented
7	C₇×D₅×C₃₇	—	5	2	no	—
8	C₇×D₅×C₃₇	—	10	2	no	—
9	C₅×D₇×C₃₇	—	5	2	no	—
10	C₃₇×C₅⋊D₅	D₇	1	1	yes	characteristic, complemented
11	C₅×D₅×C₃₇	—	7	2	no	—
12	C₅×C₇×C₃₇	—	2	2	no	—
13	C₅×C₇×C₃₇	C₂×D₅	1	2	yes	complemented
14	C₂×D₇×C₃₇	—	25	1	no	Hall
15	C₅²×C₃₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₂×D₅×C₃₇	—	35	2	no	—
17	(C₅⋊D₅)⋊D₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂×C₇×C₃₇	—	25	1	no	—
19	D₇×C₃₇	—	5	2	no	—
20	C₂×C₅×C₃₇	—	35	2	no	—
21	D₅×C₃₇	—	5	2	no	—
22	D₅×C₃₇	—	7	2	no	—
23	D₅×C₃₇	—	10	2	no	—
24	C₇×C₅⋊D₅	C₂×C₃₇	1	1	yes	characteristic, complemented
25	C₅×D₃₅	C₂×C₃₇	1	2	yes	complemented
26	C₇×C₃₇	D₅²	1	1	yes	characteristic, complemented, Hall
27	C₅×C₃₇	—	2	2	no	—
28	C₅×C₃₇	D₅×D₇	1	2	yes	complemented
29	C₅²×C₇	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃₇	—	175	1	no	Hall
31	D₅×D₇	—	5	2	no	—
32	D₅²	—	7	1	no	Hall
33	C₂×C₃₇	—	25	1	no	—
34	C₂×C₃₇	—	35	2	no	—
35	D₃₅	D₅×C₃₇	1	2	yes	complemented
36	C₅×D₇	—	5	2	no	—
37	C₇×D₅	—	5	2	no	—
38	C₇×D₅	—	10	2	no	—
39	C₅⋊D₅	D₇×C₃₇	1	1	yes	characteristic, complemented
40	C₅×D₅	—	7	2	no	—
41	C₃₇	(C₅⋊D₅)⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₅×C₇	—	2	2	no	—
43	C₅×C₇	C₂×D₅×C₃₇	1	2	yes	complemented
44	C₂×D₇	—	25	1	no	Hall
45	C₅²	C₂×D₇×C₃₇	1	1	yes	characteristic, complemented, Sylow
46	C₂×D₅	—	35	2	no	—
47	C₂×C₇	—	25	1	no	—
48	D₇	—	5	2	no	—
49	C₂×C₅	—	35	2	no	—
50	D₅	—	5	2	no	—
51	D₅	—	7	2	no	—
52	D₅	—	10	2	no	—
53	C₇	D₅²×C₃₇	1	1	yes	characteristic, complemented, Sylow
54	C₅	—	2	2	no	—
55	C₅	D₅×D₇×C₃₇	1	2	yes	complemented
56	C₂²	—	175	1	no	Sylow
57	C₂	—	25	1	no	—
58	C₂	—	35	2	no	—

	subgroup	G/H
center, hypercenter	C₃₇	(C₅⋊D₅)⋊D₇
commutator, cosocle, hypocenter	C₅²×C₇	C₂²×C₃₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₃₇	C₂²
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₃₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₇×D₃₅	C₂	semidirect
2. C₇×C₃₇×C₅⋊D₅	C₂	semidirect
3. C₅²×C₇×C₃₇	C₂²	semidirect
6. C₃₇×D₃₅	D₅	semidirect
10. C₃₇×C₅⋊D₅	D₇	semidirect
13. C₅×C₇×C₃₇	C₂×D₅	semidirect
15. C₅²×C₃₇	C₂×D₇	semidirect
17. (C₅⋊D₅)⋊D₇	C₃₇	direct (N × H)
24. C₇×C₅⋊D₅	C₂×C₃₇	semidirect
25. C₅×D₃₅	C₂×C₃₇	semidirect
26. C₇×C₃₇	D₅²	semidirect
28. C₅×C₃₇	D₅×D₇	semidirect
29. C₅²×C₇	C₂²×C₃₇	semidirect
35. D₃₅	D₅×C₃₇	semidirect
39. C₅⋊D₅	D₇×C₃₇	semidirect
41. C₃₇	(C₅⋊D₅)⋊D₇	direct (N × H)
43. C₅×C₇	C₂×D₅×C₃₇	semidirect
45. C₅²	C₂×D₇×C₃₇	semidirect
53. C₇	D₅²×C₃₇	semidirect
55. C₅	D₅×D₇×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₃₇×D₃₅	2
C₇×C₃₇×C₅⋊D₅	2
D₅×D₇×C₃₇	5
D₅²×C₃₇	7
(C₅⋊D₅)⋊D₇	37

Subgroups — C37×(C5⋊D5)⋊D7 #39906013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×(C₅⋊D₅)⋊D₇ #39906013