Subgroups — C₂×C₅×D₇×C₂₃⋊C₁₁ #47978413

Order 35420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₇×C₂₃⋊C₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₂₃⋊C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₇×C₂₃⋊C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₅×C₂₃⋊C₁₁	—	7	1	no	maximal, Hall
6	D₇×C₂₃⋊C₁₁	C₂×C₅	1	2	yes	direct product factor
7	C₂×C₇×C₂₃⋊C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
8	C₂×C₅×D₇×C₂₃	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
9	C₂×C₅×C₂₃⋊C₁₁	—	7	2	no	—
10	C₂×C₅×C₂₃⋊C₁₁	D₇	1	1	yes	characteristic, direct product factor
11	C₇×C₂₃⋊C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₇×C₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented
13	C₅×D₇×C₂₃	C₂×C₁₁	1	2	yes	complemented
14	C₂×C₅×C₁₁×D₇	—	23	1	no	maximal, Hall
15	C₅×C₂₃⋊C₁₁	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂²×C₂₃⋊C₁₁	—	7	1	no	Hall
17	C₅×C₇×C₂₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₇×C₁₁	—	23	1	no	—
19	C₅×C₁₁×D₇	—	23	2	no	—
20	C₂×D₇×C₂₃	C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₂₃⋊C₁₁	—	7	2	no	—
22	C₂×C₂₃⋊C₁₁	C₅×D₇	1	1	yes	characteristic, direct product factor
23	C₂²×C₅×C₂₃	—	7	1	no	Hall
24	C₅×C₇×C₁₁	—	23	1	no	Hall
25	C₂×C₇×C₂₃	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
26	D₇×C₂₃	C₂×C₅×C₁₁	1	2	yes	complemented
27	C₂×C₁₁×D₇	—	23	1	no	Hall
28	C₂₃⋊C₁₁	C₂×C₅×D₇	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₅×C₂₃	—	7	2	no	—
30	C₂×C₅×C₂₃	C₁₁×D₇	1	1	yes	characteristic, complemented
31	C₂²×C₅×C₁₁	—	161	1	no	Hall
32	C₇×C₂₃	C₂²×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
33	C₂×C₇×C₁₁	—	23	1	no	—
34	C₁₁×D₇	—	23	2	no	—
35	C₂×C₅×D₇	C₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor, Hall
36	C₅×C₂₃	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
37	C₂×C₅×C₁₁	—	23	1	no	—
38	C₂×C₅×C₁₁	—	161	2	no	—
39	C₂²×C₂₃	—	7	1	no	Hall
40	C₇×C₁₁	—	23	1	no	Hall
41	C₂×C₅×C₇	C₂×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented
42	C₅×D₇	C₂×C₂₃⋊C₁₁	1	2	yes	direct product factor
43	C₅×C₁₁	—	23	1	no	Hall
44	C₂×C₂₃	—	7	2	no	—
45	C₂×C₂₃	C₅×C₁₁×D₇	1	1	yes	characteristic, complemented
46	C₂²×C₁₁	—	161	1	no	Hall
47	C₅×C₇	C₂²×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented, Hall
48	C₂×D₇	C₅×C₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor, Hall
49	C₂₃	C₂×C₅×C₁₁×D₇	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₁₁	—	23	1	no	—
51	C₂×C₁₁	—	161	2	no	—
52	C₂²×C₅	—	7	1	no	Hall
53	C₂×C₇	C₂×C₅×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented
54	D₇	C₂×C₅×C₂₃⋊C₁₁	1	2	yes	direct product factor
55	C₁₁	—	23	1	no	Sylow
56	C₂×C₅	—	7	2	no	—
57	C₂×C₅	D₇×C₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor
58	C₇	C₂²×C₅×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented, Sylow
59	C₅	C₂×D₇×C₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor, Sylow
60	C₂²	—	7	1	no	Sylow
61	C₂	—	7	2	no	—
62	C₂	C₅×D₇×C₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₇×C₂₃⋊C₁₁
commutator, cosocle, hypocenter	C₇×C₂₃	C₂²×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₂₃	C₂×C₁₁
LCS	G ▷ C₇×C₂₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₇×C₂₃⋊C₁₁	C₂	direct (N × H)
2. C₂×C₅×C₇×C₂₃⋊C₁₁	C₂	semidirect
3. C₅×C₇×C₂₃⋊C₁₁	C₂²	semidirect
4. C₂×D₇×C₂₃⋊C₁₁	C₅	direct (N × H)
6. D₇×C₂₃⋊C₁₁	C₂×C₅	direct (N × H)
7. C₂×C₇×C₂₃⋊C₁₁	C₂×C₅	semidirect
8. C₂×C₅×D₇×C₂₃	C₁₁	semidirect
10. C₂×C₅×C₂₃⋊C₁₁	D₇	direct (N × H)
11. C₇×C₂₃⋊C₁₁	C₂²×C₅	semidirect
12. C₂×C₅×C₇×C₂₃	C₂×C₁₁	semidirect
13. C₅×D₇×C₂₃	C₂×C₁₁	semidirect
15. C₅×C₂₃⋊C₁₁	C₂×D₇	direct (N × H)
17. C₅×C₇×C₂₃	C₂²×C₁₁	semidirect
20. C₂×D₇×C₂₃	C₅×C₁₁	semidirect
22. C₂×C₂₃⋊C₁₁	C₅×D₇	direct (N × H)
25. C₂×C₇×C₂₃	C₂×C₅×C₁₁	semidirect
26. D₇×C₂₃	C₂×C₅×C₁₁	semidirect
28. C₂₃⋊C₁₁	C₂×C₅×D₇	direct (N × H)
30. C₂×C₅×C₂₃	C₁₁×D₇	semidirect
32. C₇×C₂₃	C₂²×C₅×C₁₁	semidirect
35. C₂×C₅×D₇	C₂₃⋊C₁₁	direct (N × H)
36. C₅×C₂₃	C₂×C₁₁×D₇	semidirect
41. C₂×C₅×C₇	C₂×C₂₃⋊C₁₁	semidirect
42. C₅×D₇	C₂×C₂₃⋊C₁₁	direct (N × H)
45. C₂×C₂₃	C₅×C₁₁×D₇	semidirect
47. C₅×C₇	C₂²×C₂₃⋊C₁₁	semidirect
48. C₂×D₇	C₅×C₂₃⋊C₁₁	direct (N × H)
49. C₂₃	C₂×C₅×C₁₁×D₇	semidirect
53. C₂×C₇	C₂×C₅×C₂₃⋊C₁₁	semidirect
54. D₇	C₂×C₅×C₂₃⋊C₁₁	direct (N × H)
57. C₂×C₅	D₇×C₂₃⋊C₁₁	direct (N × H)
58. C₇	C₂²×C₅×C₂₃⋊C₁₁	semidirect
59. C₅	C₂×D₇×C₂₃⋊C₁₁	direct (N × H)
62. C₂	C₅×D₇×C₂₃⋊C₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₇×C₂₃⋊C₁₁	2
C₂×C₅×C₇×C₂₃⋊C₁₁	2
C₂×D₇×C₂₃⋊C₁₁	5
C₂²×C₅×C₂₃⋊C₁₁	7
C₂×C₅×D₇×C₂₃	11
C₂×C₅×C₁₁×D₇	23

Subgroups — C2×C5×D7×C23⋊C11 #47978413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₇×C₂₃⋊C₁₁ #47978413