Subgroups — C₅×D₃₅⋊D₅₃ #49150697

Order 37100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₃₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₇×D₂₆₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₅₃×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₇×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₅⋊D₅₃	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₅×D₇×D₅₃	—	5	1	no	maximal
7	C₅×D₅×D₅₃	—	7	1	no	maximal, Hall
8	C₅₃×D₃₅	C₂×C₅	1	1	yes	characteristic, complemented
9	C₇×D₂₆₅	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅×D₃₇₁	—	2	2	no	—
11	C₅×D₃₇₁	D₅	1	1	yes	characteristic, complemented
12	C₅×D₃₇₁	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×D₇×C₅₃	—	5	1	no	—
14	C₅×C₇×D₅₃	—	5	1	no	—
15	C₅×D₂₆₅	D₇	1	1	yes	characteristic, complemented
16	C₅×D₅×C₅₃	—	7	1	no	—
17	C₅²×D₅₃	—	7	1	no	—
18	C₅×C₇×C₅₃	—	2	2	no	—
19	C₅×C₇×C₅₃	C₂×D₅	1	1	yes	characteristic, complemented
20	C₅×C₇×C₅₃	C₂²×C₅	1	1	yes	characteristic, complemented
21	D₇×D₅₃	—	5	1	no	Hall
22	C₅²×C₅₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×D₅₃	—	35	1	no	—
24	D₅×D₅₃	—	7	1	no	—
25	D₃₇₁	C₅×D₅	1	1	yes	characteristic, complemented
26	C₇×D₅₃	—	5	1	no	—
27	D₇×C₅₃	—	5	1	no	—
28	C₅×D₅×D₇	—	53	1	no	maximal, Hall
29	C₂×C₅×C₅₃	—	35	1	no	—
30	D₂₆₅	C₅×D₇	1	1	yes	characteristic, complemented
31	C₅×D₅₃	—	5	1	no	—
32	C₅×D₅₃	—	7	1	no	—
33	C₅×D₅₃	—	7	1	no	—
34	C₅×D₅₃	—	14	2	no	—
35	D₅×C₅₃	—	7	1	no	—
36	C₇×C₅₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
37	C₅×D₃₅	D₅₃	1	1	yes	characteristic, complemented
38	C₅×C₇×D₅	—	53	1	no	—
39	C₅²×D₇	—	53	1	no	—
40	C₅×C₅₃	—	2	2	no	—
41	C₅×C₅₃	D₅×D₇	1	1	yes	characteristic, complemented
42	C₅×C₅₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented
43	C₂×D₅₃	—	35	1	no	Hall
44	C₅²×C₇	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
45	C₂×C₅×D₇	—	265	1	no	—
46	D₅×D₇	—	53	1	no	—
47	C₂×C₅₃	—	35	1	no	—
48	D₅₃	—	5	1	no	—
49	D₅₃	—	7	1	no	—
50	C₂×C₅×D₅	—	371	1	no	Hall
51	C₂×C₅×C₇	—	265	1	no	—
52	D₃₅	C₅×D₅₃	1	1	yes	characteristic, complemented
53	C₅×D₇	—	5	1	no	—
54	C₅×D₇	—	53	1	no	—
55	C₅×D₇	—	53	1	no	—
56	C₅×D₇	—	106	2	no	—
57	C₇×D₅	—	53	1	no	—
58	C₅₃	C₅×D₅×D₇	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₅²	—	371	1	no	—
60	C₅×D₅	—	7	1	no	—
61	C₅×D₅	—	53	1	no	—
62	C₅×C₇	—	2	2	no	—
63	C₅×C₇	D₅×D₅₃	1	1	yes	characteristic, complemented
64	C₅×C₇	C₂×C₅×D₅₃	1	1	yes	characteristic, complemented
65	C₂×D₇	—	265	1	no	Hall
66	C₅²	D₇×D₅₃	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₅	—	1855	1	no	—
68	C₂×D₅	—	371	1	no	—
69	C₂×C₇	—	265	1	no	—
70	D₇	—	5	1	no	—
71	D₇	—	53	1	no	—
72	C₂×C₅	—	265	1	no	—
73	C₂×C₅	—	35	1	no	—
74	C₂×C₅	—	371	1	no	—
75	C₂×C₅	—	371	1	no	—
76	C₂×C₅	—	742	2	no	—
77	D₅	—	7	1	no	—
78	D₅	—	53	1	no	—
79	C₇	C₅×D₅×D₅₃	1	1	yes	characteristic, complemented, Sylow
80	C₅	—	2	2	no	—
81	C₅	C₅×D₇×D₅₃	1	1	yes	characteristic, complemented
82	C₅	D₃₅⋊D₅₃	1	1	yes	characteristic, direct product factor
83	C₂²	—	1855	1	no	Sylow
84	C₂	—	265	1	no	—
85	C₂	—	35	1	no	—
86	C₂	—	371	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₃₅⋊D₅₃
commutator, cosocle, hypocenter	C₅×C₇×C₅₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₅₃	C₂²
LCS	G ▷ C₅×C₇×C₅₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅²×D₃₇₁	C₂	semidirect
2. C₅×C₇×D₂₆₅	C₂	semidirect
3. C₅×C₅₃×D₃₅	C₂	semidirect
4. C₅²×C₇×C₅₃	C₂²	semidirect
5. D₃₅⋊D₅₃	C₅	direct (N × H)
8. C₅₃×D₃₅	C₂×C₅	semidirect
9. C₇×D₂₆₅	C₂×C₅	semidirect
11. C₅×D₃₇₁	D₅	semidirect
12. C₅×D₃₇₁	C₂×C₅	semidirect
15. C₅×D₂₆₅	D₇	semidirect
19. C₅×C₇×C₅₃	C₂×D₅	semidirect
20. C₅×C₇×C₅₃	C₂²×C₅	semidirect
22. C₅²×C₅₃	C₂×D₇	semidirect
25. D₃₇₁	C₅×D₅	semidirect
30. D₂₆₅	C₅×D₇	semidirect
36. C₇×C₅₃	C₂×C₅×D₅	semidirect
37. C₅×D₃₅	D₅₃	semidirect
41. C₅×C₅₃	D₅×D₇	semidirect
42. C₅×C₅₃	C₂×C₅×D₇	semidirect
44. C₅²×C₇	C₂×D₅₃	semidirect
52. D₃₅	C₅×D₅₃	semidirect
58. C₅₃	C₅×D₅×D₇	semidirect
63. C₅×C₇	D₅×D₅₃	semidirect
64. C₅×C₇	C₂×C₅×D₅₃	semidirect
66. C₅²	D₇×D₅₃	semidirect
79. C₇	C₅×D₅×D₅₃	semidirect
81. C₅	C₅×D₇×D₅₃	semidirect
82. C₅	D₃₅⋊D₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×D₃₇₁	2
C₅×C₇×D₂₆₅	2
C₅×C₅₃×D₃₅	2
D₃₅⋊D₅₃	5
C₅×D₇×D₅₃	5
C₅×D₅×D₅₃	7
C₅×D₅×D₇	53

Subgroups — C5×D35⋊D53 #49150697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃₅⋊D₅₃ #49150697