Subgroups — #11765463

Order 1120.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×D₃₅	C₂	1	2	yes	maximal, complemented
3	#10587989	C₂	1	6	yes	maximal, complemented
4	#10587987	C₂	1	3	yes	maximal, complemented
5	C₂×Dic₇₀	C₂	1	3	yes	maximal, complemented
6	C₅×C₇×Q₈	C₂²	1	1	yes	characteristic
7	C₅×C₇×D₄	C₂²	1	3	yes	—
8	C₂×C₄×C₅×C₇	C₂²	1	3	yes	—
9	C₂²⋊D₃₅	C₂²	1	6	yes	—
10	C₂×Dic₃₅	C₂²	1	6	yes	—
11	D₁₄₀	C₂²	1	1	yes	characteristic
12	C₄×D₃₅	C₂²	1	6	yes	—
13	Dic₇₀	C₂²	1	3	yes	—
14	Dic₇₀	C₂²	1	6	yes	—
15	#6554	—	5	1	no	maximal, Hall
16	#4150	—	7	1	no	maximal, Hall
17	C₂²×C₅×C₇	C₂³	1	3	yes	—
18	C₂×D₃₅	C₂³	1	2	yes	—
19	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
20	C₄×C₅×C₇	C₂³	1	3	yes	—
21	Dic₃₅	C₂³	1	6	yes	—
22	C₇×#41	D₅	1	1	yes	characteristic, complemented
23	Q₈×D₇	—	5	2	no	—
24	#1159	—	5	6	no	—
25	#1157	—	5	3	no	—
26	C₂×Dic₁₄	—	5	3	no	—
27	C₅×#41	D₇	1	1	yes	characteristic, complemented
28	Q₈×D₅	—	7	2	no	—
29	#711	—	7	6	no	—
30	#709	—	7	3	no	—
31	C₂×Dic₁₀	—	7	3	no	—
32	C₂×C₅×C₇	—	2	3	no	—
33	C₂×C₅×C₇	C₂⁴	1	1	yes	characteristic
34	D₃₅	—	2	2	no	—
35	C₇×Q₈	C₂×D₅	1	1	yes	characteristic
36	C₇×D₄	C₂×D₅	1	3	yes	—
37	C₂×C₄×C₇	C₂×D₅	1	3	yes	—
38	C₂²⋊D₇	—	5	6	no	—
39	C₂×Dic₇	—	5	6	no	—
40	D₂₈	—	5	1	no	—
41	C₄×D₇	—	5	6	no	—
42	Dic₁₄	—	5	3	no	—
43	Dic₁₄	—	5	6	no	—
44	C₅×Q₈	C₂×D₇	1	1	yes	characteristic
45	C₅×D₄	C₂×D₇	1	3	yes	—
46	C₂×C₄×C₅	C₂×D₇	1	3	yes	—
47	C₂²⋊D₅	—	7	6	no	—
48	C₂×Dic₅	—	7	6	no	—
49	D₂₀	—	7	1	no	—
50	C₄×D₅	—	7	6	no	—
51	Dic₁₀	—	7	3	no	—
52	Dic₁₀	—	7	6	no	—
53	C₅×C₇	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Hall
54	2₋¹⁺⁴	—	35	1	no	Sylow
55	C₂²×C₇	C₂²×D₅	1	3	yes	—
56	C₂×D₇	—	5	2	no	—
57	C₄×C₇	C₂²×D₅	1	1	yes	characteristic
58	C₄×C₇	C₂²×D₅	1	3	yes	—
59	Dic₇	—	5	6	no	—
60	C₂²×C₅	C₂²×D₇	1	3	yes	—
61	C₂×D₅	—	7	2	no	—
62	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
63	C₄×C₅	C₂²×D₇	1	3	yes	—
64	Dic₅	—	7	6	no	—
65	#41	—	35	6	no	—
66	#41	—	35	3	no	—
67	#41	D₃₅	1	1	yes	characteristic, complemented
68	C₂×Q₈	—	35	2	no	—
69	C₂×Q₈	—	35	3	no	—
70	C₂×C₇	—	2	3	no	—
71	C₂×C₇	C₂³×D₅	1	1	yes	characteristic
72	D₇	—	10	2	no	—
73	C₂×C₅	—	2	3	no	—
74	C₂×C₅	C₂³×D₇	1	1	yes	characteristic
75	D₅	—	14	2	no	—
76	Q₈	—	35	6	no	—
77	Q₈	—	35	3	no	—
78	Q₈	C₂×D₃₅	1	1	yes	characteristic
79	D₄	—	35	6	no	—
80	D₄	—	35	1	no	—
81	D₄	C₂×D₃₅	1	3	yes	—
82	C₂×C₄	—	35	6	no	—
83	C₂×C₄	—	35	6	no	—
84	C₂×C₄	C₂×D₃₅	1	3	yes	—
85	C₇	#4150	1	1	yes	characteristic, complemented, Sylow
86	C₅	#6554	1	1	yes	characteristic, complemented, Sylow
87	C₂²	—	35	2	no	—
88	C₂²	C₂²×D₃₅	1	3	yes	—
89	C₄	—	35	6	no	—
90	C₄	C₂²×D₃₅	1	3	yes	—
91	C₄	C₂²×D₃₅	1	1	yes	characteristic
92	C₂	—	2	3	no	—
93	C₂	—	70	2	no	—
94	C₂	C₂³×D₃₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×D₃₅
commutator, socle, cosocle	C₂×C₅×C₇	C₂⁴
Fitting	C₅×C₇×#41	C₂
hypercenter	#41	D₃₅
hypocenter	C₅×C₇	2₋¹⁺⁴
LCS	G ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂ ◁ #41

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×#41	C₂	semidirect
2. Q₈×D₃₅	C₂	semidirect
3. #10587989	C₂	semidirect
4. #10587987	C₂	semidirect
5. C₂×Dic₇₀	C₂	semidirect
22. C₇×#41	D₅	semidirect
27. C₅×#41	D₇	semidirect
53. C₅×C₇	2₋¹⁺⁴	semidirect
67. #41	D₃₅	semidirect
85. C₇	#4150	semidirect
86. C₅	#6554	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×#41	2
Q₈×D₃₅	2
#10587989	2
#10587987	2
C₂×Dic₇₀	2
#6554	5
#4150	7