Subgroups — C₁₁×C₂₅×#261 #28384649

Order 14300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₅×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₃×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×C₁₁×#261	C₅	1	1	yes	maximal, characteristic
4	C₅×C₁₁×D₁₃	C₂×C₅	1	1	yes	characteristic
5	C₂₅×#261	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₄×C₁₁×C₂₅	—	13	1	no	maximal, Hall
7	C₅×C₁₁×C₁₃	C₄×C₅	1	1	yes	characteristic
8	C₂₅×D₁₃	C₂×C₁₁	1	1	yes	characteristic
9	C₁₁×#261	C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₁×C₂₅	—	13	1	no	—
11	C₁₃×C₂₅	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×D₁₃	C₂×C₂₅	1	1	yes	characteristic
13	C₁₁×C₂₅	#261	1	1	yes	characteristic, direct product factor, Hall
14	C₅×#261	C₅×C₁₁	1	1	yes	characteristic
15	C₄×C₅×C₁₁	—	13	1	no	—
16	C₁₁×C₁₃	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
17	C₅×D₁₃	C₂×C₅×C₁₁	1	1	yes	characteristic
18	C₂×C₅×C₁₁	—	13	1	no	—
19	C₄×C₂₅	—	13	1	no	Hall
20	C₅×C₁₃	C₄×C₅×C₁₁	1	1	yes	characteristic
21	C₅×C₁₁	C₅×#261	1	1	yes	characteristic
22	#261	C₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₂₅	—	13	1	no	—
24	C₄×C₁₁	—	13	1	no	Hall
25	D₁₃	C₂×C₁₁×C₂₅	1	1	yes	characteristic
26	C₂₅	C₁₁×#261	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₁	—	13	1	no	—
28	C₄×C₅	—	13	1	no	—
29	C₁₃	C₄×C₁₁×C₂₅	1	1	yes	characteristic, complemented, Sylow
30	C₁₁	C₂₅×#261	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₅	—	13	1	no	—
32	C₅	C₅×C₁₁×#261	1	1	yes	characteristic
33	C₄	—	13	1	no	Sylow
34	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₂₅	#261
commutator, hypocenter	C₁₃	C₄×C₁₁×C₂₅
Frattini	C₅	C₅×C₁₁×#261
Fitting	C₁₁×C₁₃×C₂₅	C₄
socle	C₅×C₁₁×C₁₃	C₄×C₅
prime radical	C₅×C₁₁×D₁₃	C₂×C₅
cosocle	C₅×D₁₃	C₂×C₅×C₁₁
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₁×C₂₅

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₁₃×C₂₅	C₄	semidirect
5. C₂₅×#261	C₁₁	direct (N × H)
9. C₁₁×#261	C₂₅	direct (N × H)
11. C₁₃×C₂₅	C₄×C₁₁	semidirect
13. C₁₁×C₂₅	#261	direct (N × H)
16. C₁₁×C₁₃	C₄×C₂₅	semidirect
22. #261	C₁₁×C₂₅	direct (N × H)
26. C₂₅	C₁₁×#261	direct (N × H)
29. C₁₃	C₄×C₁₁×C₂₅	semidirect
30. C₁₁	C₂₅×#261	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₂₅×D₁₃	2
C₅×C₁₁×#261	5
C₂₅×#261	11
C₄×C₁₁×C₂₅	13

Subgroups — C11×C25×#261 #28384649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₂₅×#261 #28384649