Subgroups — C₅×#261×C₁₁⋊C₅ #28384698

Order 14300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₃×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×C₁₁×#261	C₅	1	1	yes	maximal, characteristic, complemented
4	#261×C₁₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
5	C₅×C₁₁×D₁₃	C₂×C₅	1	1	yes	characteristic
6	D₁₃×C₁₁⋊C₅	C₂×C₅	1	5	yes	—
7	C₅²×#261	—	11	1	no	maximal, Hall
8	C₄×C₅×C₁₁⋊C₅	—	13	1	no	maximal, Hall
9	C₅×C₁₁×C₁₃	C₄×C₅	1	1	yes	characteristic, complemented
10	C₁₃×C₁₁⋊C₅	C₄×C₅	1	5	yes	complemented
11	C₅²×D₁₃	—	11	1	no	—
12	C₁₁×#261	C₅²	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₁₁⋊C₅	—	13	1	no	—
14	C₅²×C₁₃	—	11	1	no	Hall
15	C₁₁×D₁₃	C₂×C₅²	1	1	yes	characteristic
16	C₅×C₁₁⋊C₅	#261	1	1	yes	characteristic, direct product factor, Hall
17	C₅×#261	—	11	5	no	—
18	C₅×#261	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
19	C₄×C₅×C₁₁	—	13	1	no	—
20	C₄×C₁₁⋊C₅	—	13	5	no	—
21	C₁₁×C₁₃	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
22	C₅×D₁₃	—	11	5	no	—
23	C₅×D₁₃	C₂×C₁₁⋊C₅	1	1	yes	characteristic
24	C₂×C₅×C₁₁	—	13	1	no	—
25	C₂×C₁₁⋊C₅	—	13	5	no	—
26	C₄×C₅²	—	143	1	no	Hall
27	C₅×C₁₃	—	11	5	no	—
28	C₅×C₁₃	C₄×C₁₁⋊C₅	1	1	yes	characteristic, complemented
29	C₅×C₁₁	C₅×#261	1	1	yes	characteristic, complemented
30	C₁₁⋊C₅	C₅×#261	1	5	yes	direct product factor
31	#261	C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
32	C₂×C₅²	—	143	1	no	—
33	C₄×C₁₁	—	13	1	no	Hall
34	D₁₃	C₂×C₅×C₁₁⋊C₅	1	1	yes	characteristic
35	C₅²	—	11	1	no	Sylow
36	C₂×C₁₁	—	13	1	no	—
37	C₄×C₅	—	13	1	no	—
38	C₄×C₅	—	143	5	no	—
39	C₁₃	C₄×C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
40	C₁₁	C₅²×#261	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	13	1	no	—
42	C₂×C₅	—	143	5	no	—
43	C₅	—	11	5	no	—
44	C₅	#261×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
45	C₄	—	13	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#261×C₁₁⋊C₅
commutator, hypocenter	C₁₁×C₁₃	C₄×C₅²
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₃	C₄×C₅
prime radical	C₅×D₁₃×C₁₁⋊C₅	C₂
cosocle	C₁₁×D₁₃	C₂×C₅²
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₃×C₁₁⋊C₅	C₄	semidirect
3. C₅×C₁₁×#261	C₅	semidirect
4. #261×C₁₁⋊C₅	C₅	direct (N × H)
9. C₅×C₁₁×C₁₃	C₄×C₅	semidirect
10. C₁₃×C₁₁⋊C₅	C₄×C₅	semidirect
12. C₁₁×#261	C₅²	semidirect
16. C₅×C₁₁⋊C₅	#261	direct (N × H)
18. C₅×#261	C₁₁⋊C₅	direct (N × H)
21. C₁₁×C₁₃	C₄×C₅²	semidirect
28. C₅×C₁₃	C₄×C₁₁⋊C₅	semidirect
29. C₅×C₁₁	C₅×#261	semidirect
30. C₁₁⋊C₅	C₅×#261	direct (N × H)
31. #261	C₅×C₁₁⋊C₅	direct (N × H)
39. C₁₃	C₄×C₅×C₁₁⋊C₅	semidirect
40. C₁₁	C₅²×#261	semidirect
44. C₅	#261×C₁₁⋊C₅	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×D₁₃×C₁₁⋊C₅	2
C₅×C₁₁×#261	5
#261×C₁₁⋊C₅	5
C₅²×#261	11
C₄×C₅×C₁₁⋊C₅	13

Subgroups — C5×#261×C11⋊C5 #28384698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#261×C₁₁⋊C₅ #28384698