Subgroups — C₇×C₁₁×Dic₅×C₂₃ #47978377

Order 35420.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×C₁₁×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₁×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₇×C₁₁×C₂₃	—	5	1	no	maximal, Hall
4	C₁₁×Dic₅×C₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₁₁×C₂₃	D₅	1	1	yes	characteristic
6	C₇×Dic₅×C₂₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₁₁×C₂₃	C₂×C₇	1	1	yes	characteristic
8	C₇×C₁₁×C₂₃	Dic₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₇×C₂₃	C₂×C₁₁	1	1	yes	characteristic
10	C₇×C₁₁×Dic₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁×C₂₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₄×C₁₁×C₂₃	—	5	1	no	Hall
13	C₅×C₇×C₂₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₇×C₁₁	C₂×C₂₃	1	1	yes	characteristic
15	C₄×C₇×C₂₃	—	5	1	no	Hall
16	C₂×C₁₁×C₂₃	C₇×D₅	1	1	yes	characteristic
17	Dic₅×C₂₃	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₇×C₁₁	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇×C₂₃	D₅×C₁₁	1	1	yes	characteristic
20	C₄×C₇×C₁₁	—	5	1	no	Hall
21	C₁₁×C₂₃	C₇×Dic₅	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₅×C₂₃	C₂×C₇×C₁₁	1	1	yes	characteristic
23	C₁₁×Dic₅	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
24	C₇×C₂₃	C₁₁×Dic₅	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇×C₁₁	D₅×C₂₃	1	1	yes	characteristic
26	C₇×Dic₅	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
27	C₅×C₂₃	C₄×C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
28	C₂×C₅×C₁₁	C₂×C₇×C₂₃	1	1	yes	characteristic
29	C₄×C₂₃	—	5	1	no	Hall
30	C₇×C₁₁	Dic₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₅×C₇	C₂×C₁₁×C₂₃	1	1	yes	characteristic
32	C₅×C₁₁	C₄×C₇×C₂₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₂₃	C₇×D₅×C₁₁	1	1	yes	characteristic
34	C₄×C₁₁	—	5	1	no	Hall
35	C₅×C₇	C₄×C₁₁×C₂₃	1	1	yes	characteristic, complemented, Hall
36	C₄×C₇	—	5	1	no	Hall
37	C₂₃	C₇×C₁₁×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₁₁	C₇×D₅×C₂₃	1	1	yes	characteristic
39	Dic₅	C₇×C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₇	D₅×C₁₁×C₂₃	1	1	yes	characteristic
41	C₁₁	C₇×Dic₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₅	C₂×C₇×C₁₁×C₂₃	1	1	yes	characteristic
43	C₇	C₁₁×Dic₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₅	C₄×C₇×C₁₁×C₂₃	1	1	yes	characteristic, complemented, Sylow
45	C₄	—	5	1	no	Sylow
46	C₂	C₇×D₅×C₁₁×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₁×C₂₃	D₅
commutator, hypocenter	C₅	C₄×C₇×C₁₁×C₂₃
Frattini	C₂	C₇×D₅×C₁₁×C₂₃
Fitting, socle, prime radical	C₂×C₅×C₇×C₁₁×C₂₃	C₂
cosocle	C₂×C₅	C₂×C₇×C₁₁×C₂₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₇×C₁₁×C₂₃

Complements

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

N	H ≅ G/N	type
2. C₅×C₇×C₁₁×C₂₃	C₄	semidirect
4. C₁₁×Dic₅×C₂₃	C₇	direct (N × H)
6. C₇×Dic₅×C₂₃	C₁₁	direct (N × H)
8. C₇×C₁₁×C₂₃	Dic₅	direct (N × H)
10. C₇×C₁₁×Dic₅	C₂₃	direct (N × H)
11. C₅×C₁₁×C₂₃	C₄×C₇	semidirect
13. C₅×C₇×C₂₃	C₄×C₁₁	semidirect
17. Dic₅×C₂₃	C₇×C₁₁	direct (N × H)
18. C₅×C₇×C₁₁	C₄×C₂₃	semidirect
21. C₁₁×C₂₃	C₇×Dic₅	direct (N × H)
23. C₁₁×Dic₅	C₇×C₂₃	direct (N × H)
24. C₇×C₂₃	C₁₁×Dic₅	direct (N × H)
26. C₇×Dic₅	C₁₁×C₂₃	direct (N × H)
27. C₅×C₂₃	C₄×C₇×C₁₁	semidirect
30. C₇×C₁₁	Dic₅×C₂₃	direct (N × H)
32. C₅×C₁₁	C₄×C₇×C₂₃	semidirect
35. C₅×C₇	C₄×C₁₁×C₂₃	semidirect
37. C₂₃	C₇×C₁₁×Dic₅	direct (N × H)
39. Dic₅	C₇×C₁₁×C₂₃	direct (N × H)
41. C₁₁	C₇×Dic₅×C₂₃	direct (N × H)
43. C₇	C₁₁×Dic₅×C₂₃	direct (N × H)
44. C₅	C₄×C₇×C₁₁×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₇×C₁₁×C₂₃	2
C₄×C₇×C₁₁×C₂₃	5
C₁₁×Dic₅×C₂₃	7
C₇×Dic₅×C₂₃	11
C₇×C₁₁×Dic₅	23

Subgroups — C7×C11×Dic5×C23 #47978377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₁×Dic₅×C₂₃ #47978377