Subgroups — C₂×C₅×C₂²⋊Dic₇ #11765110

Order 1120.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×Dic₇	C₂	1	2	yes	maximal, complemented
3	C₅×C₂²⋊Dic₇	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₅×C₇	—	2	4	no	—
5	C₂³×C₅×C₇	C₄	1	4	yes	complemented
6	C₂³×C₅×C₇	C₂²	1	2	yes	—
7	C₂³×C₅×C₇	C₂²	1	1	yes	characteristic
8	C₂×C₅×Dic₇	—	2	4	no	—
9	C₂×C₅×Dic₇	C₂²	1	4	yes	complemented
10	C₂×C₂²⋊Dic₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₅×C₂²⋊C₄	—	7	1	no	maximal, Hall
12	C₂²×C₅×C₇	—	2	8	no	—
13	C₂²×C₅×C₇	—	2	4	no	—
14	C₂²×C₅×C₇	C₂×C₄	1	2	yes	—
15	C₂²×C₅×C₇	C₂×C₄	1	4	yes	complemented
16	C₂²×C₅×C₇	D₄	1	4	yes	—
17	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
18	C₅×Dic₇	—	2	4	no	—
19	C₂⁴×C₇	C₂×C₅	1	1	yes	characteristic
20	C₂²×Dic₇	C₂×C₅	1	2	yes	complemented
21	C₂²⋊Dic₇	C₂×C₅	1	4	yes	direct product factor
22	C₂⁴×C₅	D₇	1	1	yes	characteristic
23	C₂²×C₄×C₅	—	7	2	no	—
24	C₅×C₂²⋊C₄	—	7	4	no	—
25	C₂×C₅×C₇	—	2	4	no	—
26	C₂×C₅×C₇	C₂²⋊C₄	1	4	yes	complemented
27	C₂×C₅×C₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₅×C₇	C₂×D₄	1	2	yes	—
29	C₂³×C₇	—	2	4	no	—
30	C₂³×C₇	C₄×C₅	1	4	yes	complemented
31	C₂³×C₇	C₂²×C₅	1	2	yes	—
32	C₂³×C₇	C₂²×C₅	1	1	yes	characteristic
33	C₂×Dic₇	—	2	4	no	—
34	C₂×Dic₇	C₂²×C₅	1	4	yes	complemented
35	C₂³×C₅	—	2	4	no	—
36	C₂³×C₅	Dic₇	1	4	yes	complemented
37	C₂³×C₅	C₂×D₇	1	2	yes	—
38	C₂³×C₅	C₂×D₇	1	1	yes	characteristic
39	C₂×C₄×C₅	—	7	4	no	—
40	C₂×C₄×C₅	—	14	4	no	—
41	C₅×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
42	C₂×C₂²⋊C₄	—	7	1	no	Sylow
43	C₂²×C₇	—	2	8	no	—
44	C₂²×C₇	—	2	4	no	—
45	C₂²×C₇	C₂×C₄×C₅	1	2	yes	—
46	C₂²×C₇	C₂×C₄×C₅	1	4	yes	complemented
47	C₂²×C₇	C₅×D₄	1	4	yes	—
48	C₂²×C₇	C₂³×C₅	1	1	yes	characteristic
49	Dic₇	—	2	4	no	—
50	C₂²×C₅	—	2	8	no	—
51	C₂²×C₅	—	2	4	no	—
52	C₂²×C₅	C₂×Dic₇	1	2	yes	—
53	C₂²×C₅	C₂×Dic₇	1	4	yes	complemented
54	C₂²×C₅	C₂²⋊D₇	1	4	yes	—
55	C₂²×C₅	C₂²×D₇	1	1	yes	characteristic
56	C₄×C₅	—	14	4	no	—
57	C₂⁴	C₅×D₇	1	1	yes	characteristic
58	C₂²×C₄	—	7	2	no	—
59	C₂²⋊C₄	—	7	4	no	—
60	C₂×C₇	—	2	4	no	—
61	C₂×C₇	C₅×C₂²⋊C₄	1	4	yes	complemented
62	C₂×C₇	C₂²×C₄×C₅	1	1	yes	characteristic
63	C₂×C₇	C₂×C₅×D₄	1	2	yes	—
64	C₂×C₅	—	2	4	no	—
65	C₂×C₅	C₂²⋊Dic₇	1	4	yes	direct product factor
66	C₂×C₅	C₂²×Dic₇	1	1	yes	characteristic
67	C₂×C₅	C₂×C₂²⋊D₇	1	2	yes	—
68	C₂³	—	2	4	no	—
69	C₂³	C₅×Dic₇	1	4	yes	complemented
70	C₂³	C₂×C₅×D₇	1	2	yes	—
71	C₂³	C₂×C₅×D₇	1	1	yes	characteristic
72	C₂×C₄	—	7	4	no	—
73	C₂×C₄	—	14	4	no	—
74	C₇	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
75	C₅	C₂×C₂²⋊Dic₇	1	1	yes	characteristic, direct product factor, Sylow
76	C₂²	—	2	4	no	—
77	C₂²	—	2	8	no	—
78	C₂²	C₂×C₅×Dic₇	1	2	yes	—
79	C₂²	C₂×C₅×Dic₇	1	4	yes	complemented
80	C₂²	C₅×C₂²⋊D₇	1	4	yes	—
81	C₂²	C₂²×C₅×D₇	1	1	yes	characteristic
82	C₄	—	14	4	no	—
83	C₂	—	2	4	no	—
84	C₂	C₅×C₂²⋊Dic₇	1	4	yes	direct product factor
85	C₂	C₂²×C₅×Dic₇	1	1	yes	characteristic
86	C₂	C₂×C₅×C₂²⋊D₇	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂×D₇
commutator	C₂×C₇	C₂²×C₄×C₅
Frattini	C₂²	C₂²×C₅×D₇
Fitting, prime radical	C₂⁴×C₅×C₇	C₂
socle	C₂³×C₅×C₇	C₂²
cosocle	C₂²×C₇	C₂³×C₅
hypercenter	C₂⁴×C₅	D₇
hypocenter	C₇	C₂×C₅×C₂²⋊C₄
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³×C₅ ◁ C₂⁴×C₅

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×Dic₇	C₂	semidirect
3. C₅×C₂²⋊Dic₇	C₂	direct (N × H)
5. C₂³×C₅×C₇	C₄	semidirect
9. C₂×C₅×Dic₇	C₂²	semidirect
10. C₂×C₂²⋊Dic₇	C₅	direct (N × H)
15. C₂²×C₅×C₇	C₂×C₄	semidirect
20. C₂²×Dic₇	C₂×C₅	semidirect
21. C₂²⋊Dic₇	C₂×C₅	direct (N × H)
26. C₂×C₅×C₇	C₂²⋊C₄	semidirect
30. C₂³×C₇	C₄×C₅	semidirect
34. C₂×Dic₇	C₂²×C₅	semidirect
36. C₂³×C₅	Dic₇	semidirect
41. C₅×C₇	C₂×C₂²⋊C₄	semidirect
46. C₂²×C₇	C₂×C₄×C₅	semidirect
53. C₂²×C₅	C₂×Dic₇	semidirect
61. C₂×C₇	C₅×C₂²⋊C₄	semidirect
65. C₂×C₅	C₂²⋊Dic₇	direct (N × H)
69. C₂³	C₅×Dic₇	semidirect
74. C₇	C₂×C₅×C₂²⋊C₄	semidirect
75. C₅	C₂×C₂²⋊Dic₇	direct (N × H)
79. C₂²	C₂×C₅×Dic₇	semidirect
84. C₂	C₅×C₂²⋊Dic₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₅×C₇	2
C₂²×C₅×Dic₇	2
C₅×C₂²⋊Dic₇	2
C₂×C₂²⋊Dic₇	5
C₂×C₅×C₂²⋊C₄	7

Subgroups — C2×C5×C22⋊Dic7 #11765110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₂²⋊Dic₇ #11765110