Subgroups — C₇×C₄⋊Dic₁₅ #13132346

Order 1680.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×Dic₁₅	C₂	1	2	yes	maximal
3	C₇×C₄⋊Dic₅	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₅×C₇	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₅×C₇	C₄	1	2	yes	complemented
6	C₇×Dic₁₅	—	2	2	no	—
7	C₇×C₄⋊Dic₃	—	5	1	no	maximal, Hall
8	C₂×C₄×C₅×C₇	D₃	1	1	yes	characteristic
9	C₂×C₇×Dic₅	—	3	2	no	—
10	C₄⋊Dic₁₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×C₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₅×C₇	D₄	1	1	yes	characteristic
13	C₂×C₃×C₅×C₇	Q₈	1	1	yes	characteristic
14	C₂×C₃×C₄×C₇	D₅	1	1	yes	characteristic
15	C₂×C₇×Dic₃	—	5	2	no	—
16	C₂²×C₅×C₇	C₂×D₃	1	1	yes	characteristic
17	C₄×C₅×C₇	Dic₃	1	2	yes	complemented
18	C₇×Dic₅	—	6	2	no	—
19	C₂×C₃×C₄×C₅	C₂×C₇	1	1	yes	characteristic
20	C₂×Dic₁₅	C₂×C₇	1	2	yes	—
21	C₇×C₄⋊C₄	—	15	1	no	Hall
22	C₃×C₅×C₇	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
23	C₂²×C₃×C₇	C₂×D₅	1	1	yes	characteristic
24	C₃×C₄×C₇	Dic₅	1	2	yes	complemented
25	C₇×Dic₃	—	10	2	no	—
26	C₄⋊Dic₅	—	3	1	no	Hall
27	C₂×C₅×C₇	Dic₆	1	1	yes	characteristic
28	C₂×C₅×C₇	D₁₂	1	1	yes	characteristic
29	C₂×C₅×C₇	C₂×Dic₃	1	1	yes	characteristic
30	C₂²×C₃×C₅	C₂²×C₇	1	1	yes	characteristic
31	C₃×C₄×C₅	C₄×C₇	1	2	yes	complemented
32	Dic₁₅	—	2	2	no	—
33	C₂×C₄×C₇	—	15	2	no	—
34	C₂×C₄×C₇	D₁₅	1	1	yes	characteristic
35	C₄⋊Dic₃	—	5	1	no	Hall
36	C₂×C₃×C₇	Dic₁₀	1	1	yes	characteristic
37	C₂×C₃×C₇	D₂₀	1	1	yes	characteristic
38	C₂×C₃×C₇	C₂×Dic₅	1	1	yes	characteristic
39	C₂×C₄×C₅	D₃×C₇	1	1	yes	characteristic
40	C₂×Dic₅	—	3	2	no	—
41	C₅×C₇	C₄⋊Dic₃	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×C₅	C₂×C₄×C₇	1	1	yes	characteristic
43	C₂×C₃×C₅	C₇×D₄	1	1	yes	characteristic
44	C₂×C₃×C₅	C₇×Q₈	1	1	yes	characteristic
45	C₂²×C₇	C₂×D₁₅	1	1	yes	characteristic
46	C₄×C₇	—	30	2	no	—
47	C₄×C₇	Dic₁₅	1	2	yes	complemented
48	C₂×C₃×C₄	C₇×D₅	1	1	yes	characteristic
49	C₂×Dic₃	—	5	2	no	—
50	C₃×C₇	C₄⋊Dic₅	1	1	yes	characteristic, complemented, Hall
51	C₂²×C₅	C₂×D₃×C₇	1	1	yes	characteristic
52	C₄×C₅	C₇×Dic₃	1	2	yes	complemented
53	Dic₅	—	6	2	no	—
54	C₄⋊C₄	—	15	1	no	Sylow
55	C₃×C₅	C₇×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
56	C₂×C₇	Dic₃₀	1	1	yes	characteristic
57	C₂×C₇	D₆₀	1	1	yes	characteristic
58	C₂×C₇	C₂×Dic₁₅	1	1	yes	characteristic
59	C₂²×C₃	C₂×C₇×D₅	1	1	yes	characteristic
60	C₃×C₄	C₇×Dic₅	1	2	yes	complemented
61	Dic₃	—	10	2	no	—
62	C₂×C₅	C₇×Dic₆	1	1	yes	characteristic
63	C₂×C₅	C₇×D₁₂	1	1	yes	characteristic
64	C₂×C₅	C₂×C₇×Dic₃	1	1	yes	characteristic
65	C₂×C₄	—	15	2	no	—
66	C₂×C₄	C₇×D₁₅	1	1	yes	characteristic
67	C₇	C₄⋊Dic₁₅	1	1	yes	characteristic, direct product factor, Sylow
68	C₂×C₃	C₇×Dic₁₀	1	1	yes	characteristic
69	C₂×C₃	C₇×D₂₀	1	1	yes	characteristic
70	C₂×C₃	C₂×C₇×Dic₅	1	1	yes	characteristic
71	C₅	C₇×C₄⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
72	C₂²	C₂×C₇×D₁₅	1	1	yes	characteristic
73	C₄	—	30	2	no	—
74	C₄	C₇×Dic₁₅	1	2	yes	complemented
75	C₃	C₇×C₄⋊Dic₅	1	1	yes	characteristic, complemented, Sylow
76	C₂	C₇×Dic₃₀	1	1	yes	characteristic
77	C₂	C₇×D₆₀	1	1	yes	characteristic
78	C₂	C₂×C₇×Dic₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₇	C₂×D₁₅
commutator	C₂×C₃×C₅	C₂×C₄×C₇
Frattini	C₂²	C₂×C₇×D₁₅
Fitting	C₂×C₃×C₄×C₅×C₇	C₂
socle, prime radical	C₂²×C₃×C₅×C₇	C₂²
cosocle	C₂²×C₃×C₅	C₂²×C₇
hypercenter	C₂×C₄×C₇	D₁₅
hypocenter	C₃×C₅	C₇×C₄⋊C₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇

Complements

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

N	H ≅ G/N	type
5. C₃×C₄×C₅×C₇	C₄	semidirect
10. C₄⋊Dic₁₅	C₇	direct (N × H)
17. C₄×C₅×C₇	Dic₃	semidirect
22. C₃×C₅×C₇	C₄⋊C₄	semidirect
24. C₃×C₄×C₇	Dic₅	semidirect
31. C₃×C₄×C₅	C₄×C₇	semidirect
41. C₅×C₇	C₄⋊Dic₃	semidirect
47. C₄×C₇	Dic₁₅	semidirect
50. C₃×C₇	C₄⋊Dic₅	semidirect
52. C₄×C₅	C₇×Dic₃	semidirect
55. C₃×C₅	C₇×C₄⋊C₄	semidirect
60. C₃×C₄	C₇×Dic₅	semidirect
67. C₇	C₄⋊Dic₁₅	direct (N × H)
71. C₅	C₇×C₄⋊Dic₃	semidirect
74. C₄	C₇×Dic₁₅	semidirect
75. C₃	C₇×C₄⋊Dic₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅×C₇	2
C₂×C₇×Dic₁₅	2
C₇×C₄⋊Dic₅	3
C₇×C₄⋊Dic₃	5
C₄⋊Dic₁₅	7

Subgroups — C7×C4⋊Dic15 #13132346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₄⋊Dic₁₅ #13132346