Subgroups — C₁₁×D₁₅×D₃₇ #37567607

Order 24420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₅₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₁₅×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₁₁×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₁₁×D₃₇	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₁×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₁₁×D₃₇	—	5	1	no	maximal, Hall
7	C₁₁×D₁₈₅	—	3	1	no	—
8	D₅×C₁₁×C₃₇	—	3	1	no	—
9	C₅×C₁₁×D₃₇	D₃	1	1	yes	characteristic, complemented
10	C₁₁×D₁₁₁	—	5	1	no	—
11	D₃×C₁₁×C₃₇	—	5	1	no	—
12	C₃×C₁₁×D₃₇	D₅	1	1	yes	characteristic, complemented
13	D₁₅×D₃₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₅×C₁₁×C₃₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₁×D₃₇	—	15	1	no	Hall
16	C₃×C₁₁×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	D₅₅₅	C₂×C₁₁	1	1	yes	characteristic, complemented
18	D₁₅×C₃₇	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₃×C₅×D₃₇	C₂×C₁₁	1	1	yes	characteristic, complemented
20	C₂×C₁₁×C₃₇	—	15	1	no	—
21	C₁₁×D₃₇	—	15	1	no	—
22	C₁₁×D₃₇	D₁₅	1	1	yes	characteristic, direct product factor
23	D₅×D₃₇	—	3	1	no	Hall
24	C₂×C₁₁×D₁₅	—	37	1	no	maximal, Hall
25	C₃×C₅×C₃₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
26	D₃×D₃₇	—	5	1	no	Hall
27	C₁₁×C₃₇	C₂×D₁₅	1	1	yes	characteristic, complemented, Hall
28	D₁₈₅	—	3	1	no	—
29	C₅×D₃₇	D₃×C₁₁	1	1	yes	characteristic, complemented
30	D₅×C₃₇	—	3	1	no	—
31	C₂×C₃×C₅×C₁₁	—	37	1	no	—
32	C₁₁×D₁₅	—	37	1	no	—
33	C₁₁×D₁₅	D₃₇	1	1	yes	characteristic, direct product factor
34	D₁₁₁	—	5	1	no	—
35	C₃×D₃₇	D₅×C₁₁	1	1	yes	characteristic, complemented
36	D₃×C₃₇	—	5	1	no	—
37	C₂×D₅×C₁₁	—	111	1	no	Hall
38	C₅×C₃₇	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅×C₁₁	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
40	C₂×D₃₇	—	15	1	no	Hall
41	C₂×D₃×C₁₁	—	185	1	no	Hall
42	C₃×C₃₇	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
43	C₂×C₅×C₁₁	—	37	1	no	—
44	D₅×C₁₁	—	3	1	no	—
45	D₅×C₁₁	—	111	1	no	—
46	C₂×C₃₇	—	15	1	no	—
47	D₃₇	—	15	1	no	—
48	D₃₇	C₁₁×D₁₅	1	1	yes	characteristic, direct product factor
49	C₂×C₃×C₁₁	—	37	1	no	—
50	D₃×C₁₁	—	5	1	no	—
51	D₃×C₁₁	—	185	1	no	—
52	C₂×D₁₅	—	37	1	no	Hall
53	C₅×C₁₁	D₃×D₃₇	1	1	yes	characteristic, complemented, Hall
54	C₂²×C₁₁	—	555	1	no	Hall
55	C₃₇	C₂×C₁₁×D₁₅	1	1	yes	characteristic, complemented, Sylow
56	C₃×C₁₁	D₅×D₃₇	1	1	yes	characteristic, complemented, Hall
57	C₂×C₃×C₅	—	37	1	no	—
58	D₁₅	—	37	1	no	—
59	D₁₅	C₁₁×D₃₇	1	1	yes	characteristic, direct product factor
60	C₂×C₁₁	—	15	1	no	—
61	C₂×C₁₁	—	37	1	no	—
62	C₂×C₁₁	—	555	1	no	—
63	C₂×D₅	—	111	1	no	Hall
64	C₃×C₅	C₂×C₁₁×D₃₇	1	1	yes	characteristic, complemented, Hall
65	C₂×D₃	—	185	1	no	Hall
66	C₁₁	D₁₅×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×C₅	—	37	1	no	—
68	D₅	—	3	1	no	—
69	D₅	—	111	1	no	—
70	C₂×C₃	—	37	1	no	—
71	D₃	—	5	1	no	—
72	D₃	—	185	1	no	—
73	C₅	D₃×C₁₁×D₃₇	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	555	1	no	Sylow
75	C₃	D₅×C₁₁×D₃₇	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	15	1	no	—
77	C₂	—	37	1	no	—
78	C₂	—	555	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₁₅×D₃₇
commutator, cosocle, hypocenter	C₃×C₅×C₃₇	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₃₇	C₂²
LCS	G ▷ C₃×C₅×C₃₇
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₅₅₅	C₂	semidirect
2. C₁₁×D₁₅×C₃₇	C₂	semidirect
3. C₃×C₅×C₁₁×D₃₇	C₂	semidirect
5. C₃×C₅×C₁₁×C₃₇	C₂²	semidirect
9. C₅×C₁₁×D₃₇	D₃	semidirect
12. C₃×C₁₁×D₃₇	D₅	semidirect
13. D₁₅×D₃₇	C₁₁	direct (N × H)
14. C₅×C₁₁×C₃₇	C₂×D₃	semidirect
16. C₃×C₁₁×C₃₇	C₂×D₅	semidirect
17. D₅₅₅	C₂×C₁₁	semidirect
18. D₁₅×C₃₇	C₂×C₁₁	semidirect
19. C₃×C₅×D₃₇	C₂×C₁₁	semidirect
22. C₁₁×D₃₇	D₁₅	direct (N × H)
25. C₃×C₅×C₃₇	C₂²×C₁₁	semidirect
27. C₁₁×C₃₇	C₂×D₁₅	semidirect
29. C₅×D₃₇	D₃×C₁₁	semidirect
33. C₁₁×D₁₅	D₃₇	direct (N × H)
35. C₃×D₃₇	D₅×C₁₁	semidirect
38. C₅×C₃₇	C₂×D₃×C₁₁	semidirect
39. C₃×C₅×C₁₁	C₂×D₃₇	semidirect
42. C₃×C₃₇	C₂×D₅×C₁₁	semidirect
48. D₃₇	C₁₁×D₁₅	direct (N × H)
53. C₅×C₁₁	D₃×D₃₇	semidirect
55. C₃₇	C₂×C₁₁×D₁₅	semidirect
56. C₃×C₁₁	D₅×D₃₇	semidirect
59. D₁₅	C₁₁×D₃₇	direct (N × H)
64. C₃×C₅	C₂×C₁₁×D₃₇	semidirect
66. C₁₁	D₁₅×D₃₇	direct (N × H)
73. C₅	D₃×C₁₁×D₃₇	semidirect
75. C₃	D₅×C₁₁×D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×D₅₅₅	2
C₁₁×D₁₅×C₃₇	2
C₃×C₅×C₁₁×D₃₇	2
D₅×C₁₁×D₃₇	3
D₃×C₁₁×D₃₇	5
D₁₅×D₃₇	11
C₂×C₁₁×D₁₅	37

Subgroups — C11×D15×D37 #37567607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₁₅×D₃₇ #37567607