Subgroups — C₃⋊C₈×D₃₅ #13132197

Order 1680.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₃₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₃₅	—	3	1	no	maximal, Hall
5	C₂×C₃×D₃₅	C₄	1	1	yes	characteristic
6	C₃×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
7	C₃×Dic₃₅	C₄	1	1	yes	characteristic
8	D₇×C₃⋊C₈	—	5	1	no	maximal, Hall
9	C₄×D₃₅	D₃	1	1	yes	characteristic
10	C₅×C₇×C₈	—	3	1	no	—
11	C₇⋊#168	—	3	1	no	—
12	D₅×C₃⋊C₈	—	7	1	no	maximal, Hall
13	C₂×C₃×C₅×C₇	C₂×C₄	1	1	yes	characteristic
14	C₃×D₃₅	C₈	1	2	yes	complemented
15	C₃×C₄×D₇	—	5	1	no	—
16	C₃⋊(C₇⋊C₈)	—	5	1	no	—
17	C₇×C₃⋊C₈	D₅	1	1	yes	characteristic, complemented
18	C₂×D₃₅	Dic₃	1	1	yes	characteristic
19	C₄×C₅×C₇	C₂×D₃	1	1	yes	characteristic
20	Dic₃₅	Dic₃	1	1	yes	characteristic
21	C₃×C₄×D₅	—	7	1	no	—
22	C₃⋊#168	—	7	1	no	—
23	C₅×C₃⋊C₈	D₇	1	1	yes	characteristic, complemented
24	C₈×D₇	—	15	1	no	Hall
25	C₃×C₅×C₇	C₂×C₈	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×D₇	—	5	1	no	—
27	C₃×C₄×C₇	C₂×D₅	1	1	yes	characteristic
28	C₃×Dic₇	—	5	1	no	—
29	C₈×D₅	—	21	1	no	Hall
30	C₂×C₅×C₇	C₂×Dic₃	1	1	yes	characteristic
31	D₃₅	C₃⋊C₈	1	2	yes	direct product factor
32	C₂×C₃×D₅	—	7	1	no	—
33	C₃×C₄×C₅	C₂×D₇	1	1	yes	characteristic
34	C₃×Dic₅	—	7	1	no	—
35	C₄×D₇	—	5	1	no	—
36	C₇×C₈	—	3	1	no	—
37	C₇⋊C₈	—	15	1	no	—
38	C₂×C₃⋊C₈	—	35	1	no	Hall
39	C₂×C₃×C₇	C₄×D₅	1	1	yes	characteristic
40	C₃×D₇	—	5	2	no	—
41	C₄×D₅	—	7	1	no	—
42	C₅×C₈	—	3	1	no	—
43	#168	—	21	1	no	—
44	C₅×C₇	C₂×C₃⋊C₈	1	1	yes	characteristic, complemented, Hall
45	C₂×C₃×C₅	C₄×D₇	1	1	yes	characteristic
46	C₃×D₅	—	7	2	no	—
47	C₂×D₇	—	5	1	no	—
48	C₄×C₇	D₃×D₅	1	1	yes	characteristic
49	Dic₇	—	5	1	no	—
50	C₂×C₃×C₄	—	35	1	no	—
51	C₃⋊C₈	—	35	1	no	—
52	C₃⋊C₈	D₃₅	1	1	yes	characteristic, direct product factor
53	C₃×C₇	C₈×D₅	1	1	yes	characteristic, complemented, Hall
54	C₂×D₅	—	7	1	no	—
55	C₄×C₅	D₃×D₇	1	1	yes	characteristic
56	Dic₅	—	7	1	no	—
57	C₂×C₈	—	105	1	no	Sylow
58	C₃×C₅	C₈×D₇	1	1	yes	characteristic, complemented, Hall
59	C₂×C₇	D₅×Dic₃	1	1	yes	characteristic
60	D₇	—	5	2	no	—
61	C₂²×C₃	—	35	1	no	—
62	C₃×C₄	—	35	1	no	—
63	C₃×C₄	C₂×D₃₅	1	1	yes	characteristic
64	C₂×C₅	Dic₃×D₇	1	1	yes	characteristic
65	D₅	—	7	2	no	—
66	C₂×C₄	—	35	1	no	—
67	C₈	—	3	1	no	—
68	C₈	—	105	1	no	—
69	C₇	D₅×C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	35	2	no	—
71	C₂×C₃	C₄×D₃₅	1	1	yes	characteristic
72	C₅	D₇×C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
73	C₂²	—	35	1	no	—
74	C₄	—	35	1	no	—
75	C₄	D₃×D₃₅	1	1	yes	characteristic
76	C₃	C₈×D₃₅	1	1	yes	characteristic, complemented, Sylow
77	C₂	—	35	2	no	—
78	C₂	Dic₃×D₃₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃×D₃₅
commutator, hypocenter	C₃×C₅×C₇	C₂×C₈
Fitting, cosocle	C₃×C₄×C₅×C₇	C₂²
socle	C₂×C₃×C₅×C₇	C₂×C₄
prime radical	C₂×C₃×D₃₅	C₄
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₇⋊#168)	C₂	semidirect
3. C₅×C₇×C₃⋊C₈	C₂	semidirect
14. C₃×D₃₅	C₈	semidirect
17. C₇×C₃⋊C₈	D₅	semidirect
23. C₅×C₃⋊C₈	D₇	semidirect
25. C₃×C₅×C₇	C₂×C₈	semidirect
31. D₃₅	C₃⋊C₈	direct (N × H)
44. C₅×C₇	C₂×C₃⋊C₈	semidirect
52. C₃⋊C₈	D₃₅	direct (N × H)
53. C₃×C₇	C₈×D₅	semidirect
58. C₃×C₅	C₈×D₇	semidirect
69. C₇	D₅×C₃⋊C₈	semidirect
72. C₅	D₇×C₃⋊C₈	semidirect
76. C₃	C₈×D₃₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×D₃₅	2
C₃⋊(C₇⋊#168)	2
C₅×C₇×C₃⋊C₈	2
C₈×D₃₅	3
D₇×C₃⋊C₈	5
D₅×C₃⋊C₈	7

Subgroups — C3⋊C8×D35 #13132197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊C₈×D₃₅ #13132197