Subgroups — C₅×(C₂₃⋊C₁₁)⋊Dic₅ #38760713

Order 25300.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₂₃⋊C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
3	(C₂₃⋊C₁₁)⋊Dic₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×Dic₂₃⋊C₁₁	—	5	1	no	maximal
5	C₂×C₅×C₂₃⋊C₁₁	—	2	2	no	—
6	C₂×C₅×C₂₃⋊C₁₁	D₅	1	1	yes	characteristic
7	C₂×C₅×C₂₃⋊C₁₁	C₂×C₅	1	1	yes	characteristic
8	C₅×Dic₁₁₅	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
9	C₅×C₂₃⋊C₁₁	—	2	2	no	—
10	C₅×C₂₃⋊C₁₁	Dic₅	1	1	yes	characteristic, complemented
11	C₅×C₂₃⋊C₁₁	C₄×C₅	1	1	yes	characteristic, complemented
12	C₂×C₅²×C₂₃	C₂×C₁₁	1	1	yes	characteristic
13	C₅×C₁₁×Dic₅	—	23	1	no	maximal, Hall
14	Dic₂₃⋊C₁₁	—	5	1	no	Hall
15	C₅²×C₂₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅²×C₁₁	—	23	1	no	—
17	C₂×C₂₃⋊C₁₁	C₅×D₅	1	1	yes	characteristic
18	Dic₁₁₅	C₅×C₁₁	1	1	yes	characteristic, complemented
19	C₅×Dic₂₃	—	5	1	no	—
20	C₅²×C₁₁	—	23	1	no	Hall
21	C₂₃⋊C₁₁	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₅×C₂₃	—	2	2	no	—
23	C₂×C₅×C₂₃	D₅×C₁₁	1	1	yes	characteristic
24	C₂×C₅×C₂₃	C₂×C₅×C₁₁	1	1	yes	characteristic
25	C₄×C₅×C₁₁	—	115	1	no	—
26	C₁₁×Dic₅	—	23	1	no	—
27	C₅×C₂₃	—	2	2	no	—
28	C₅×C₂₃	C₁₁×Dic₅	1	1	yes	characteristic, complemented
29	C₅×C₂₃	C₄×C₅×C₁₁	1	1	yes	characteristic, complemented
30	C₂×C₅×C₁₁	—	23	1	no	—
31	C₂×C₅×C₁₁	—	23	1	no	—
32	C₂×C₅×C₁₁	—	46	2	no	—
33	C₅×Dic₅	—	253	1	no	Hall
34	Dic₂₃	—	5	1	no	Hall
35	C₅×C₁₁	—	23	1	no	—
36	C₅×C₁₁	—	23	1	no	—
37	C₅×C₁₁	—	46	2	no	—
38	C₂×C₅²	AGL(1,𝔽₂₃)	1	1	yes	characteristic
39	C₂×C₂₃	C₅×D₅×C₁₁	1	1	yes	characteristic
40	C₄×C₁₁	—	115	1	no	Hall
41	C₅²	Dic₂₃⋊C₁₁	1	1	yes	characteristic, complemented, Sylow
42	C₂₃	C₅×C₁₁×Dic₅	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₁₁	—	23	1	no	—
44	C₄×C₅	—	1265	1	no	—
45	Dic₅	—	253	1	no	—
46	C₁₁	—	23	1	no	Sylow
47	C₂×C₅	—	2	2	no	—
48	C₂×C₅	C₅×AGL(1,𝔽₂₃)	1	1	yes	characteristic
49	C₂×C₅	C₅⋊AGL(1,𝔽₂₃)	1	1	yes	characteristic
50	C₅	—	2	2	no	—
51	C₅	C₅×Dic₂₃⋊C₁₁	1	1	yes	characteristic, complemented
52	C₅	(C₂₃⋊C₁₁)⋊Dic₅	1	1	yes	characteristic, direct product factor
53	C₄	—	1265	1	no	Sylow
54	C₂	C₅×C₅⋊AGL(1,𝔽₂₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₅⋊AGL(1,𝔽₂₃)
commutator, hypocenter	C₅×C₂₃	C₄×C₅×C₁₁
Frattini	C₂	C₅×C₅⋊AGL(1,𝔽₂₃)
Fitting, socle	C₂×C₅²×C₂₃	C₂×C₁₁
prime radical	C₂×C₅²×C₂₃⋊C₁₁	C₂
cosocle	C₂×C₅×C₂₃	C₂×C₅×C₁₁
LCS	G ▷ C₅×C₂₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
2. C₅²×C₂₃⋊C₁₁	C₄	semidirect
3. (C₂₃⋊C₁₁)⋊Dic₅	C₅	direct (N × H)
8. C₅×Dic₁₁₅	C₁₁	semidirect
10. C₅×C₂₃⋊C₁₁	Dic₅	semidirect
11. C₅×C₂₃⋊C₁₁	C₄×C₅	semidirect
15. C₅²×C₂₃	C₄×C₁₁	semidirect
18. Dic₁₁₅	C₅×C₁₁	semidirect
21. C₂₃⋊C₁₁	C₅×Dic₅	semidirect
28. C₅×C₂₃	C₁₁×Dic₅	semidirect
29. C₅×C₂₃	C₄×C₅×C₁₁	semidirect
41. C₅²	Dic₂₃⋊C₁₁	semidirect
42. C₂₃	C₅×C₁₁×Dic₅	semidirect
51. C₅	C₅×Dic₂₃⋊C₁₁	semidirect
52. C₅	(C₂₃⋊C₁₁)⋊Dic₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅²×C₂₃⋊C₁₁	2
(C₂₃⋊C₁₁)⋊Dic₅	5
C₅×Dic₂₃⋊C₁₁	5
C₅×Dic₁₁₅	11
C₅×C₁₁×Dic₅	23

Subgroups — C5×(C23⋊C11)⋊Dic5 #38760713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×(C₂₃⋊C₁₁)⋊Dic₅ #38760713