Subgroups — C₅×D₃₃⋊D₃₇ #37567597

Order 24420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₇×D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₁×D₁₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₄₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₁₁×D₃₇	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₁×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃₃⋊D₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₄₀₇	D₃	1	1	yes	characteristic, complemented
8	C₅×D₁₁×C₃₇	—	3	1	no	—
9	C₅×C₁₁×D₃₇	—	3	1	no	—
10	C₃₇×D₃₃	C₂×C₅	1	1	yes	characteristic, complemented
11	C₁₁×D₁₁₁	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×D₄₀₇	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×D₃×D₃₇	—	11	1	no	maximal, Hall
14	C₅×C₁₁×C₃₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	D₁₁×D₃₇	—	3	1	no	Hall
16	C₃×C₁₁×C₃₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₅×D₁₁₁	D₁₁	1	1	yes	characteristic, complemented
18	C₅×D₃×C₃₇	—	11	1	no	—
19	C₃×C₅×D₃₇	—	11	1	no	—
20	D₄₀₇	C₅×D₃	1	1	yes	characteristic, complemented
21	C₁₁×D₃₇	—	3	1	no	—
22	D₁₁×C₃₇	—	3	1	no	—
23	C₂×C₅×D₃₇	—	33	1	no	Hall
24	C₅×D₃×D₁₁	—	37	1	no	maximal, Hall
25	C₃×C₅×C₃₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
26	D₃×D₃₇	—	11	1	no	Hall
27	C₁₁×C₃₇	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
28	C₂×C₅×C₃₇	—	33	1	no	—
29	C₅×D₃₇	—	3	1	no	—
30	C₅×D₃₇	—	11	1	no	—
31	C₅×D₃₃	D₃₇	1	1	yes	characteristic, complemented
32	C₅×D₃×C₁₁	—	37	1	no	—
33	C₃×C₅×D₁₁	—	37	1	no	—
34	D₁₁₁	C₅×D₁₁	1	1	yes	characteristic, complemented
35	C₃×D₃₇	—	11	1	no	—
36	D₃×C₃₇	—	11	1	no	—
37	C₂×C₅×D₁₁	—	111	1	no	Hall
38	C₅×C₃₇	D₃×D₁₁	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅×C₁₁	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
40	C₂×D₃₇	—	33	1	no	Hall
41	D₃×D₁₁	—	37	1	no	Hall
42	C₃×C₃₇	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
43	C₂×C₅×C₁₁	—	111	1	no	—
44	C₅×D₁₁	—	3	1	no	—
45	C₅×D₁₁	—	37	1	no	—
46	C₂×C₃₇	—	33	1	no	—
47	D₃₇	—	3	1	no	—
48	D₃₇	—	11	1	no	—
49	D₃₃	C₅×D₃₇	1	1	yes	characteristic, complemented
50	C₃×D₁₁	—	37	1	no	—
51	D₃×C₁₁	—	37	1	no	—
52	C₂×C₅×D₃	—	407	1	no	Hall
53	C₅×C₁₁	D₃×D₃₇	1	1	yes	characteristic, complemented, Hall
54	C₂×D₁₁	—	111	1	no	Hall
55	C₃₇	C₅×D₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
56	C₃×C₁₁	C₂×C₅×D₃₇	1	1	yes	characteristic, complemented, Hall
57	C₂×C₃×C₅	—	407	1	no	—
58	C₅×D₃	—	11	1	no	—
59	C₅×D₃	—	37	1	no	—
60	C₂×C₁₁	—	111	1	no	—
61	D₁₁	—	3	1	no	—
62	D₁₁	—	37	1	no	—
63	C₂²×C₅	—	1221	1	no	Hall
64	C₃×C₅	D₁₁×D₃₇	1	1	yes	characteristic, complemented, Hall
65	C₂×D₃	—	407	1	no	Hall
66	C₁₁	C₅×D₃×D₃₇	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₅	—	33	1	no	—
68	C₂×C₅	—	111	1	no	—
69	C₂×C₅	—	407	1	no	—
70	C₂×C₃	—	407	1	no	—
71	D₃	—	11	1	no	—
72	D₃	—	37	1	no	—
73	C₅	D₃₃⋊D₃₇	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	1221	1	no	Sylow
75	C₃	C₅×D₁₁×D₃₇	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	33	1	no	—
77	C₂	—	111	1	no	—
78	C₂	—	407	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₃₃⋊D₃₇
commutator, cosocle, hypocenter	C₃×C₁₁×C₃₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₃₇	C₂²
LCS	G ▷ C₃×C₁₁×C₃₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₇×D₃₃	C₂	semidirect
2. C₅×C₁₁×D₁₁₁	C₂	semidirect
3. C₃×C₅×D₄₀₇	C₂	semidirect
5. C₃×C₅×C₁₁×C₃₇	C₂²	semidirect
6. D₃₃⋊D₃₇	C₅	direct (N × H)
7. C₅×D₄₀₇	D₃	semidirect
10. C₃₇×D₃₃	C₂×C₅	semidirect
11. C₁₁×D₁₁₁	C₂×C₅	semidirect
12. C₃×D₄₀₇	C₂×C₅	semidirect
14. C₅×C₁₁×C₃₇	C₂×D₃	semidirect
16. C₃×C₁₁×C₃₇	C₂²×C₅	semidirect
17. C₅×D₁₁₁	D₁₁	semidirect
20. D₄₀₇	C₅×D₃	semidirect
25. C₃×C₅×C₃₇	C₂×D₁₁	semidirect
27. C₁₁×C₃₇	C₂×C₅×D₃	semidirect
31. C₅×D₃₃	D₃₇	semidirect
34. D₁₁₁	C₅×D₁₁	semidirect
38. C₅×C₃₇	D₃×D₁₁	semidirect
39. C₃×C₅×C₁₁	C₂×D₃₇	semidirect
42. C₃×C₃₇	C₂×C₅×D₁₁	semidirect
49. D₃₃	C₅×D₃₇	semidirect
53. C₅×C₁₁	D₃×D₃₇	semidirect
55. C₃₇	C₅×D₃×D₁₁	semidirect
56. C₃×C₁₁	C₂×C₅×D₃₇	semidirect
64. C₃×C₅	D₁₁×D₃₇	semidirect
66. C₁₁	C₅×D₃×D₃₇	semidirect
73. C₅	D₃₃⋊D₃₇	direct (N × H)
75. C₃	C₅×D₁₁×D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₃₇×D₃₃	2
C₅×C₁₁×D₁₁₁	2
C₃×C₅×D₄₀₇	2
C₅×D₁₁×D₃₇	3
D₃₃⋊D₃₇	5
C₅×D₃×D₃₇	11
C₅×D₃×D₁₁	37

Subgroups — C5×D33⋊D37 #37567597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃₃⋊D₃₇ #37567597