Subgroups — C₂×Q₈×D₃₅ #11765458

Order 1120.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×D₃₅	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×D₃₅	C₂	1	3	yes	maximal
4	C₂×Dic₇₀	C₂	1	3	yes	maximal, complemented
5	C₂²×D₃₅	C₂²	1	1	yes	characteristic
6	C₅×C₇×Q₈	C₂²	1	4	yes	complemented
7	C₂×C₄×C₅×C₇	C₂²	1	3	yes	—
8	C₂×Dic₃₅	C₂²	1	3	yes	—
9	C₄×D₃₅	C₂²	1	12	yes	—
10	Dic₇₀	C₂²	1	12	yes	complemented
11	C₂×Q₈×D₇	—	5	1	no	maximal, Hall
12	C₂×Q₈×D₅	—	7	1	no	maximal, Hall
13	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
14	C₂×D₃₅	Q₈	1	4	yes	direct product factor
15	C₂×D₃₅	C₂³	1	2	yes	—
16	C₄×C₅×C₇	C₂³	1	6	yes	—
17	Dic₃₅	C₂³	1	6	yes	—
18	C₂×C₇×Q₈	D₅	1	1	yes	characteristic, complemented
19	Q₈×D₇	—	5	8	no	—
20	C₂×C₄×D₇	—	5	3	no	—
21	C₂×Dic₁₄	—	5	3	no	—
22	C₂×C₅×Q₈	D₇	1	1	yes	characteristic, complemented
23	Q₈×D₅	—	7	8	no	—
24	C₂×C₄×D₅	—	7	3	no	—
25	C₂×Dic₁₀	—	7	3	no	—
26	C₂×C₅×C₇	C₂×Q₈	1	2	yes	complemented
27	C₂×C₅×C₇	C₂⁴	1	1	yes	characteristic
28	D₃₅	C₂×Q₈	1	4	yes	direct product factor
29	C₂²×D₇	—	5	1	no	—
30	C₇×Q₈	C₂×D₅	1	4	yes	complemented
31	C₂×C₄×C₇	C₂×D₅	1	3	yes	—
32	C₂×Dic₇	—	5	3	no	—
33	C₄×D₇	—	5	12	no	—
34	Dic₁₄	—	5	12	no	—
35	C₂²×D₅	—	7	1	no	—
36	C₅×Q₈	C₂×D₇	1	4	yes	complemented
37	C₂×C₄×C₅	C₂×D₇	1	3	yes	—
38	C₂×Dic₅	—	7	3	no	—
39	C₄×D₅	—	7	12	no	—
40	Dic₁₀	—	7	12	no	—
41	C₅×C₇	C₂²×Q₈	1	1	yes	characteristic, complemented, Hall
42	C₂²×Q₈	—	35	1	no	Sylow
43	C₂²×C₇	C₂²×D₅	1	1	yes	characteristic
44	C₂×D₇	—	5	4	no	—
45	C₂×D₇	—	5	2	no	—
46	C₄×C₇	C₂²×D₅	1	6	yes	—
47	Dic₇	—	5	6	no	—
48	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
49	C₂×D₅	—	7	4	no	—
50	C₂×D₅	—	7	2	no	—
51	C₄×C₅	C₂²×D₇	1	6	yes	—
52	Dic₅	—	7	6	no	—
53	C₂×Q₈	—	35	8	no	—
54	C₂×Q₈	—	35	3	no	—
55	C₂×Q₈	D₃₅	1	1	yes	characteristic, direct product factor
56	C₂²×C₄	—	35	3	no	—
57	C₂×C₇	Q₈×D₅	1	2	yes	complemented
58	C₂×C₇	C₂³×D₅	1	1	yes	characteristic
59	D₇	—	5	4	no	—
60	C₂×C₅	Q₈×D₇	1	2	yes	complemented
61	C₂×C₅	C₂³×D₇	1	1	yes	characteristic
62	D₅	—	7	4	no	—
63	C₂³	—	35	1	no	—
64	Q₈	—	35	12	no	—
65	Q₈	C₂×D₃₅	1	4	yes	direct product factor
66	C₂×C₄	—	35	3	no	—
67	C₂×C₄	—	35	12	no	—
68	C₂×C₄	C₂×D₃₅	1	3	yes	—
69	C₇	C₂×Q₈×D₅	1	1	yes	characteristic, complemented, Sylow
70	C₅	C₂×Q₈×D₇	1	1	yes	characteristic, complemented, Sylow
71	C₂²	—	35	4	no	—
72	C₂²	—	35	2	no	—
73	C₂²	C₂²×D₃₅	1	1	yes	characteristic
74	C₄	—	35	6	no	—
75	C₄	C₂²×D₃₅	1	6	yes	—
76	C₂	—	35	4	no	—
77	C₂	Q₈×D₃₅	1	2	yes	direct product factor
78	C₂	C₂³×D₃₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₃₅
commutator, cosocle	C₂×C₅×C₇	C₂⁴
Frattini	C₂	C₂³×D₃₅
Fitting	C₂×C₅×C₇×Q₈	C₂
socle	C₂²×C₅×C₇	C₂³
prime radical	C₂²×D₃₅	C₂²
hypercenter	C₂×Q₈	D₃₅
hypocenter	C₅×C₇	C₂²×Q₈
LCS	G ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₇×Q₈	C₂	semidirect
2. Q₈×D₃₅	C₂	direct (N × H)
4. C₂×Dic₇₀	C₂	semidirect
6. C₅×C₇×Q₈	C₂²	semidirect
10. Dic₇₀	C₂²	semidirect
14. C₂×D₃₅	Q₈	direct (N × H)
18. C₂×C₇×Q₈	D₅	semidirect
22. C₂×C₅×Q₈	D₇	semidirect
26. C₂×C₅×C₇	C₂×Q₈	semidirect
28. D₃₅	C₂×Q₈	direct (N × H)
30. C₇×Q₈	C₂×D₅	semidirect
36. C₅×Q₈	C₂×D₇	semidirect
41. C₅×C₇	C₂²×Q₈	semidirect
55. C₂×Q₈	D₃₅	direct (N × H)
57. C₂×C₇	Q₈×D₅	semidirect
60. C₂×C₅	Q₈×D₇	semidirect
65. Q₈	C₂×D₃₅	direct (N × H)
69. C₇	C₂×Q₈×D₅	semidirect
70. C₅	C₂×Q₈×D₇	semidirect
77. C₂	Q₈×D₃₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₇×Q₈	2
Q₈×D₃₅	2
C₂×C₄×D₃₅	2
C₂×Dic₇₀	2
C₂×Q₈×D₇	5
C₂×Q₈×D₅	7

Subgroups — C2×Q8×D35 #11765458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×D₃₅ #11765458