Subgroups — C₂×C₇×C₄⋊Dic₅ #11765169

Order 1120.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇×Dic₅	C₂	1	2	yes	maximal
3	C₇×C₄⋊Dic₅	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₅×C₇	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅×C₇	C₄	1	4	yes	complemented
6	C₂×C₄×C₅×C₇	C₂²	1	2	yes	—
7	C₂×C₇×Dic₅	—	2	4	no	—
8	C₂×C₇×Dic₅	C₂²	1	4	yes	—
9	C₂×C₇×C₄⋊C₄	—	5	1	no	maximal, Hall
10	C₂×C₄⋊Dic₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₅×C₇	C₂×C₄	1	2	yes	—
12	C₂²×C₅×C₇	D₄	1	2	yes	—
13	C₂²×C₅×C₇	Q₈	1	2	yes	—
14	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
15	C₄×C₅×C₇	C₂×C₄	1	4	yes	complemented
16	C₇×Dic₅	—	2	4	no	—
17	C₂²×C₄×C₇	—	5	2	no	—
18	C₂²×C₄×C₇	D₅	1	1	yes	characteristic
19	C₇×C₄⋊C₄	—	5	4	no	—
20	C₂²×C₄×C₅	C₂×C₇	1	1	yes	characteristic
21	C₂²×Dic₅	C₂×C₇	1	2	yes	—
22	C₄⋊Dic₅	C₂×C₇	1	4	yes	direct product factor
23	C₂×C₅×C₇	C₄⋊C₄	1	4	yes	complemented
24	C₂×C₅×C₇	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
26	C₂×C₅×C₇	C₂×Q₈	1	1	yes	characteristic
27	C₂³×C₇	C₂×D₅	1	1	yes	characteristic
28	C₂×C₄×C₇	—	5	4	no	—
29	C₂×C₄×C₇	—	10	4	no	—
30	C₂×C₄×C₇	Dic₅	1	4	yes	complemented
31	C₂×C₄×C₇	C₂×D₅	1	2	yes	—
32	C₂³×C₅	C₂²×C₇	1	1	yes	characteristic
33	C₂×C₄×C₅	C₄×C₇	1	4	yes	complemented
34	C₂×C₄×C₅	C₂²×C₇	1	2	yes	—
35	C₂×Dic₅	—	2	4	no	—
36	C₂×Dic₅	C₂²×C₇	1	4	yes	—
37	C₅×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
38	C₂×C₄⋊C₄	—	5	1	no	Sylow
39	C₂²×C₇	Dic₁₀	1	2	yes	—
40	C₂²×C₇	D₂₀	1	2	yes	—
41	C₂²×C₇	C₂×Dic₅	1	2	yes	—
42	C₂²×C₇	C₂²×D₅	1	1	yes	characteristic
43	C₄×C₇	—	10	4	no	—
44	C₄×C₇	C₂×Dic₅	1	4	yes	complemented
45	C₂²×C₅	C₂×C₄×C₇	1	2	yes	—
46	C₂²×C₅	C₇×D₄	1	2	yes	—
47	C₂²×C₅	C₇×Q₈	1	2	yes	—
48	C₂²×C₅	C₂³×C₇	1	1	yes	characteristic
49	C₄×C₅	C₂×C₄×C₇	1	4	yes	complemented
50	Dic₅	—	2	4	no	—
51	C₂²×C₄	—	5	2	no	—
52	C₂²×C₄	C₇×D₅	1	1	yes	characteristic
53	C₄⋊C₄	—	5	4	no	—
54	C₂×C₇	C₄⋊Dic₅	1	4	yes	direct product factor
55	C₂×C₇	C₂×Dic₁₀	1	1	yes	characteristic
56	C₂×C₇	C₂×D₂₀	1	1	yes	characteristic
57	C₂×C₇	C₂²×Dic₅	1	1	yes	characteristic
58	C₂×C₅	C₇×C₄⋊C₄	1	4	yes	complemented
59	C₂×C₅	C₂²×C₄×C₇	1	1	yes	characteristic
60	C₂×C₅	C₂×C₇×D₄	1	1	yes	characteristic
61	C₂×C₅	C₂×C₇×Q₈	1	1	yes	characteristic
62	C₂³	C₂×C₇×D₅	1	1	yes	characteristic
63	C₂×C₄	—	5	4	no	—
64	C₂×C₄	—	10	4	no	—
65	C₂×C₄	C₇×Dic₅	1	4	yes	complemented
66	C₂×C₄	C₂×C₇×D₅	1	2	yes	—
67	C₇	C₂×C₄⋊Dic₅	1	1	yes	characteristic, direct product factor, Sylow
68	C₅	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
69	C₂²	C₇×Dic₁₀	1	2	yes	—
70	C₂²	C₇×D₂₀	1	2	yes	—
71	C₂²	C₂×C₇×Dic₅	1	2	yes	—
72	C₂²	C₂²×C₇×D₅	1	1	yes	characteristic
73	C₄	—	10	4	no	—
74	C₄	C₂×C₇×Dic₅	1	4	yes	complemented
75	C₂	C₇×C₄⋊Dic₅	1	4	yes	direct product factor
76	C₂	C₂×C₇×Dic₁₀	1	1	yes	characteristic
77	C₂	C₂×C₇×D₂₀	1	1	yes	characteristic
78	C₂	C₂²×C₇×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₇	C₂×D₅
commutator	C₂×C₅	C₂²×C₄×C₇
Frattini	C₂²	C₂²×C₇×D₅
Fitting	C₂²×C₄×C₅×C₇	C₂
socle, prime radical	C₂³×C₅×C₇	C₂²
cosocle	C₂²×C₅	C₂³×C₇
hypercenter	C₂²×C₄×C₇	D₅
hypocenter	C₅	C₂×C₇×C₄⋊C₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₇ ◁ C₂²×C₄×C₇

Complements

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

N	H ≅ G/N	type
3. C₇×C₄⋊Dic₅	C₂	direct (N × H)
5. C₂×C₄×C₅×C₇	C₄	semidirect
10. C₂×C₄⋊Dic₅	C₇	direct (N × H)
15. C₄×C₅×C₇	C₂×C₄	semidirect
22. C₄⋊Dic₅	C₂×C₇	direct (N × H)
23. C₂×C₅×C₇	C₄⋊C₄	semidirect
30. C₂×C₄×C₇	Dic₅	semidirect
33. C₂×C₄×C₅	C₄×C₇	semidirect
37. C₅×C₇	C₂×C₄⋊C₄	semidirect
44. C₄×C₇	C₂×Dic₅	semidirect
49. C₄×C₅	C₂×C₄×C₇	semidirect
54. C₂×C₇	C₄⋊Dic₅	direct (N × H)
58. C₂×C₅	C₇×C₄⋊C₄	semidirect
65. C₂×C₄	C₇×Dic₅	semidirect
67. C₇	C₂×C₄⋊Dic₅	direct (N × H)
68. C₅	C₂×C₇×C₄⋊C₄	semidirect
74. C₄	C₂×C₇×Dic₅	semidirect
75. C₂	C₇×C₄⋊Dic₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₅×C₇	2
C₂²×C₇×Dic₅	2
C₇×C₄⋊Dic₅	2
C₂×C₇×C₄⋊C₄	5
C₂×C₄⋊Dic₅	7

Subgroups — C2×C7×C4⋊Dic5 #11765169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₄⋊Dic₅ #11765169