Subgroups — C₃₇×D₁₅⋊D₅ #26012923

Order 11100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₅×C₃₇	C₂	1	2	yes	maximal, complemented
2	C₃×C₃₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	D₅²×C₃₇	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃×D₅×C₃₇	—	5	2	no	maximal
6	C₃₇×C₅⋊D₅	D₃	1	1	yes	characteristic, complemented
7	C₅×D₅×C₃₇	—	3	2	no	—
8	D₁₅×C₃₇	D₅	1	2	yes	complemented
9	C₅×D₃×C₃₇	—	5	2	no	—
10	C₃×D₅×C₃₇	—	5	2	no	—
11	C₃×D₅×C₃₇	—	10	2	no	—
12	C₅²×C₃₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
13	C₂×D₅×C₃₇	—	15	2	no	—
14	C₃×C₅×C₃₇	—	2	2	no	—
15	C₃×C₅×C₃₇	C₂×D₅	1	2	yes	complemented
16	C₂×D₃×C₃₇	—	25	1	no	Hall
17	C₂×C₅×C₃₇	—	15	2	no	—
18	D₅×C₃₇	—	3	2	no	—
19	D₅×C₃₇	—	5	2	no	—
20	D₅×C₃₇	—	10	2	no	—
21	D₁₅⋊D₅	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₃×C₃₇	—	25	1	no	—
23	D₃×C₃₇	—	5	2	no	—
24	C₅×C₃₇	—	2	2	no	—
25	C₅×C₃₇	D₃×D₅	1	2	yes	complemented
26	C₅×D₁₅	C₂×C₃₇	1	2	yes	complemented
27	C₃×C₅⋊D₅	C₂×C₃₇	1	1	yes	characteristic, complemented
28	C₂²×C₃₇	—	75	1	no	Hall
29	C₃×C₃₇	D₅²	1	1	yes	characteristic, complemented, Hall
30	D₅²	—	3	1	no	Hall
31	C₃×C₅²	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃₇	—	15	2	no	—
33	C₂×C₃₇	—	25	1	no	—
34	D₃×D₅	—	5	2	no	—
35	C₅⋊D₅	D₃×C₃₇	1	1	yes	characteristic, complemented
36	C₅×D₅	—	3	2	no	—
37	C₃₇	D₁₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
38	D₁₅	D₅×C₃₇	1	2	yes	complemented
39	C₃×D₅	—	5	2	no	—
40	C₃×D₅	—	10	2	no	—
41	C₅×D₃	—	5	2	no	—
42	C₅²	C₂×D₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₅	—	15	2	no	—
44	C₃×C₅	—	2	2	no	—
45	C₃×C₅	C₂×D₅×C₃₇	1	2	yes	complemented
46	C₂×D₃	—	25	1	no	Hall
47	C₂×C₅	—	15	2	no	—
48	D₅	—	3	2	no	—
49	D₅	—	5	2	no	—
50	D₅	—	10	2	no	—
51	C₂×C₃	—	25	1	no	—
52	D₃	—	5	2	no	—
53	C₅	—	2	2	no	—
54	C₅	D₃×D₅×C₃₇	1	2	yes	complemented
55	C₂²	—	75	1	no	Sylow
56	C₃	D₅²×C₃₇	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	15	2	no	—
58	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃₇	D₁₅⋊D₅
commutator, cosocle, hypocenter	C₃×C₅²	C₂²×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₇	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₃₇

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₅×C₃₇	C₂	semidirect
2. C₃×C₃₇×C₅⋊D₅	C₂	semidirect
4. C₃×C₅²×C₃₇	C₂²	semidirect
6. C₃₇×C₅⋊D₅	D₃	semidirect
8. D₁₅×C₃₇	D₅	semidirect
12. C₅²×C₃₇	C₂×D₃	semidirect
15. C₃×C₅×C₃₇	C₂×D₅	semidirect
21. D₁₅⋊D₅	C₃₇	direct (N × H)
25. C₅×C₃₇	D₃×D₅	semidirect
26. C₅×D₁₅	C₂×C₃₇	semidirect
27. C₃×C₅⋊D₅	C₂×C₃₇	semidirect
29. C₃×C₃₇	D₅²	semidirect
31. C₃×C₅²	C₂²×C₃₇	semidirect
35. C₅⋊D₅	D₃×C₃₇	semidirect
37. C₃₇	D₁₅⋊D₅	direct (N × H)
38. D₁₅	D₅×C₃₇	semidirect
42. C₅²	C₂×D₃×C₃₇	semidirect
45. C₃×C₅	C₂×D₅×C₃₇	semidirect
54. C₅	D₃×D₅×C₃₇	semidirect
56. C₃	D₅²×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₁₅×C₃₇	2
C₃×C₃₇×C₅⋊D₅	2
D₅²×C₃₇	3
D₃×D₅×C₃₇	5
D₁₅⋊D₅	37

Subgroups — C37×D15⋊D5 #26012923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×D₁₅⋊D₅ #26012923