Subgroups — C₂²×C₅×C₂²⋊D₇ #11765435

Order 1120.

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

	subgroup	G/H
center	C₂³×C₅	C₂×D₇
commutator, cosocle	C₂×C₇	C₂⁴×C₅
Frattini	C₂	C₂³×C₅×D₇
Fitting	C₂⁴×C₅×C₇	C₂
socle	C₂³×C₅×C₇	C₂²
hypercenter	C₂⁴×C₅	D₇
hypocenter	C₇	C₂²×C₅×D₄
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
1. C₂⁴×C₅×C₇	C₂	semidirect
2. C₂³×C₅×D₇	C₂	semidirect
3. C₂×C₅×C₂²⋊D₇	C₂	direct (N × H)
4. C₂²×C₅×Dic₇	C₂	semidirect
7. C₂³×C₅×C₇	C₂²	semidirect
9. C₂²×C₅×D₇	C₂²	semidirect
10. C₅×C₂²⋊D₇	C₂²	direct (N × H)
11. C₂×C₅×Dic₇	C₂²	semidirect
12. C₂²×C₂²⋊D₇	C₅	direct (N × H)
15. C₂²×C₅×C₇	D₄	semidirect
17. C₂²×C₅×C₇	C₂³	semidirect
19. C₂×C₅×D₇	C₂³	semidirect
20. C₅×Dic₇	C₂³	semidirect
21. C₂⁴×C₇	C₂×C₅	semidirect
22. C₂³×D₇	C₂×C₅	semidirect
23. C₂×C₂²⋊D₇	C₂×C₅	direct (N × H)
24. C₂²×Dic₇	C₂×C₅	semidirect
26. C₂⁴×C₅	D₇	semidirect
30. C₂×C₅×C₇	C₂×D₄	semidirect
35. C₂³×C₇	C₂²×C₅	semidirect
37. C₂²×D₇	C₂²×C₅	semidirect
38. C₂²⋊D₇	C₂²×C₅	direct (N × H)
39. C₂×Dic₇	C₂²×C₅	semidirect
44. C₂³×C₅	C₂×D₇	semidirect
47. C₅×C₇	C₂²×D₄	semidirect
50. C₂²×C₇	C₅×D₄	semidirect
52. C₂²×C₇	C₂³×C₅	semidirect
54. C₂×D₇	C₂³×C₅	semidirect
55. Dic₇	C₂³×C₅	semidirect
59. C₂²×C₅	C₂²⋊D₇	direct (N × H)
61. C₂²×C₅	C₂²×D₇	semidirect
64. C₂⁴	C₅×D₇	semidirect
68. C₂×C₇	C₂×C₅×D₄	semidirect
73. C₂×C₅	C₂×C₂²⋊D₇	direct (N × H)
79. C₂³	C₂×C₅×D₇	semidirect
82. C₇	C₂²×C₅×D₄	semidirect
83. C₅	C₂²×C₂²⋊D₇	direct (N × H)
87. C₂²	C₅×C₂²⋊D₇	direct (N × H)
89. C₂²	C₂²×C₅×D₇	semidirect
93. C₂	C₂×C₅×C₂²⋊D₇	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
C₂³×C₅×D₇	2
C₂×C₅×C₂²⋊D₇	2
C₂²×C₅×Dic₇	2
C₂²×C₂²⋊D₇	5
C₂²×C₅×D₄	7

Subgroups — C22×C5×C22⋊D7 #11765435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₂²⋊D₇ #11765435