Subgroups — C₂×C₅×Dic₇⋊C₄ #11765081

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×C₅×Dic₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×Dic₇	C₂	1	1	yes	maximal, characteristic
4	C₅×Dic₇⋊C₄	C₂	1	4	yes	maximal, direct product factor
5	C₂³×C₅×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₅×C₇	—	2	2	no	—
7	C₂×C₄×C₅×C₇	C₂²	1	2	yes	—
8	C₂×C₅×Dic₇	—	2	2	no	—
9	C₂×C₅×Dic₇	C₄	1	4	yes	complemented
10	C₂×C₅×Dic₇	C₂²	1	2	yes	—
11	C₂×C₅×Dic₇	C₂²	1	2	yes	—
12	C₂×Dic₇⋊C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₅×C₄⋊C₄	—	7	1	no	maximal, Hall
14	C₂²×C₅×C₇	C₂×C₄	1	2	yes	—
15	C₂²×C₅×C₇	D₄	1	2	yes	—
16	C₂²×C₅×C₇	Q₈	1	2	yes	—
17	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
18	C₄×C₅×C₇	—	2	2	no	—
19	C₅×Dic₇	—	2	2	no	—
20	C₅×Dic₇	C₂×C₄	1	4	yes	complemented
21	C₂²×C₄×C₇	C₂×C₅	1	1	yes	characteristic
22	C₂²×Dic₇	C₂×C₅	1	1	yes	characteristic
23	C₂²×Dic₇	C₂×C₅	1	1	yes	characteristic
24	Dic₇⋊C₄	C₂×C₅	1	4	yes	direct product factor
25	C₂²×C₄×C₅	—	7	1	no	—
26	C₂²×C₄×C₅	—	7	1	no	—
27	C₂²×C₄×C₅	D₇	1	1	yes	characteristic
28	C₅×C₄⋊C₄	—	7	4	no	—
29	C₂×C₅×C₇	C₄⋊C₄	1	4	yes	complemented
30	C₂×C₅×C₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₅×C₇	C₂×Q₈	1	1	yes	characteristic
33	C₂³×C₇	C₂²×C₅	1	1	yes	characteristic
34	C₂×C₄×C₇	—	2	2	no	—
35	C₂×C₄×C₇	C₂²×C₅	1	2	yes	—
36	C₂×Dic₇	—	2	2	no	—
37	C₂×Dic₇	C₄×C₅	1	4	yes	complemented
38	C₂×Dic₇	C₂²×C₅	1	2	yes	—
39	C₂×Dic₇	C₂²×C₅	1	2	yes	—
40	C₂³×C₅	C₂×D₇	1	1	yes	characteristic
41	C₂×C₄×C₅	—	2	2	no	—
42	C₂×C₄×C₅	—	7	4	no	—
43	C₂×C₄×C₅	—	7	2	no	—
44	C₂×C₄×C₅	—	7	2	no	—
45	C₂×C₄×C₅	—	14	2	no	—
46	C₂×C₄×C₅	C₂×D₇	1	2	yes	—
47	C₅×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
48	C₂×C₄⋊C₄	—	7	1	no	Sylow
49	C₂²×C₇	C₂×C₄×C₅	1	2	yes	—
50	C₂²×C₇	C₅×D₄	1	2	yes	—
51	C₂²×C₇	C₅×Q₈	1	2	yes	—
52	C₂²×C₇	C₂³×C₅	1	1	yes	characteristic
53	C₄×C₇	—	2	2	no	—
54	Dic₇	—	2	2	no	—
55	Dic₇	C₂×C₄×C₅	1	4	yes	complemented
56	C₂²×C₅	Dic₁₄	1	2	yes	—
57	C₂²×C₅	C₄×D₇	1	2	yes	—
58	C₂²×C₅	C₂²⋊D₇	1	2	yes	—
59	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
60	C₄×C₅	—	2	2	no	—
61	C₄×C₅	—	7	4	no	—
62	C₄×C₅	—	14	2	no	—
63	C₂²×C₄	—	7	1	no	—
64	C₂²×C₄	—	7	1	no	—
65	C₂²×C₄	C₅×D₇	1	1	yes	characteristic
66	C₄⋊C₄	—	7	4	no	—
67	C₂×C₇	C₅×C₄⋊C₄	1	4	yes	complemented
68	C₂×C₇	C₂²×C₄×C₅	1	1	yes	characteristic
69	C₂×C₇	C₂×C₅×D₄	1	1	yes	characteristic
70	C₂×C₇	C₂×C₅×Q₈	1	1	yes	characteristic
71	C₂×C₅	Dic₇⋊C₄	1	4	yes	direct product factor
72	C₂×C₅	C₂×Dic₁₄	1	1	yes	characteristic
73	C₂×C₅	C₂×C₄×D₇	1	1	yes	characteristic
74	C₂×C₅	C₂×C₂²⋊D₇	1	1	yes	characteristic
75	C₂³	C₂×C₅×D₇	1	1	yes	characteristic
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	7	4	no	—
78	C₂×C₄	—	7	2	no	—
79	C₂×C₄	—	7	2	no	—
80	C₂×C₄	—	14	2	no	—
81	C₂×C₄	C₂×C₅×D₇	1	2	yes	—
82	C₇	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
83	C₅	C₂×Dic₇⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
84	C₂²	C₅×Dic₁₄	1	2	yes	—
85	C₂²	C₄×C₅×D₇	1	2	yes	—
86	C₂²	C₅×C₂²⋊D₇	1	2	yes	—
87	C₂²	C₂²×C₅×D₇	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	7	4	no	—
90	C₄	—	14	2	no	—
91	C₂	C₅×Dic₇⋊C₄	1	4	yes	direct product factor
92	C₂	C₂×C₅×Dic₁₄	1	1	yes	characteristic
93	C₂	C₂×C₄×C₅×D₇	1	1	yes	characteristic
94	C₂	C₂×C₅×C₂²⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×D₇
commutator	C₂×C₇	C₂²×C₄×C₅
Frattini	C₂²	C₂²×C₅×D₇
Fitting	C₂²×C₄×C₅×C₇	C₂
socle, prime radical	C₂³×C₅×C₇	C₂²
cosocle	C₂²×C₇	C₂³×C₅
hypercenter	C₂²×C₄×C₅	D₇
hypocenter	C₇	C₂×C₅×C₄⋊C₄
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅

Complements

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

N	H ≅ G/N	type
4. C₅×Dic₇⋊C₄	C₂	direct (N × H)
9. C₂×C₅×Dic₇	C₄	semidirect
12. C₂×Dic₇⋊C₄	C₅	direct (N × H)
20. C₅×Dic₇	C₂×C₄	semidirect
24. Dic₇⋊C₄	C₂×C₅	direct (N × H)
29. C₂×C₅×C₇	C₄⋊C₄	semidirect
37. C₂×Dic₇	C₄×C₅	semidirect
47. C₅×C₇	C₂×C₄⋊C₄	semidirect
55. Dic₇	C₂×C₄×C₅	semidirect
67. C₂×C₇	C₅×C₄⋊C₄	semidirect
71. C₂×C₅	Dic₇⋊C₄	direct (N × H)
82. C₇	C₂×C₅×C₄⋊C₄	semidirect
83. C₅	C₂×Dic₇⋊C₄	direct (N × H)
91. C₂	C₅×Dic₇⋊C₄	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×C₅×Dic₇	2
C₅×Dic₇⋊C₄	2
C₂×Dic₇⋊C₄	5
C₂×C₅×C₄⋊C₄	7

Subgroups — C2×C5×Dic7⋊C4 #11765081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×Dic₇⋊C₄ #11765081