Subgroups — C₁₃×C₂₅×Dic₁₁ #28384635

Order 14300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₃×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₃×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×C₁₃×Dic₁₁	C₅	1	1	yes	maximal, characteristic
4	C₂×C₅×C₁₁×C₁₃	C₂×C₅	1	1	yes	characteristic
5	C₄×C₁₃×C₂₅	—	11	1	no	maximal, Hall
6	C₂₅×Dic₁₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₁×C₁₃	C₄×C₅	1	1	yes	characteristic
8	C₂×C₁₃×C₂₅	D₁₁	1	1	yes	characteristic
9	C₁₃×Dic₁₁	C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₁×C₂₅	C₂×C₁₃	1	1	yes	characteristic
11	C₁₃×C₂₅	Dic₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₁₁×C₁₃	C₂×C₂₅	1	1	yes	characteristic
13	C₁₁×C₂₅	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₄×C₅×C₁₃	—	11	1	no	—
15	C₅×Dic₁₁	C₅×C₁₃	1	1	yes	characteristic
16	C₁₁×C₁₃	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₁₃	C₅×D₁₁	1	1	yes	characteristic
18	C₂×C₅×C₁₁	C₂×C₅×C₁₃	1	1	yes	characteristic
19	C₄×C₂₅	—	11	1	no	Hall
20	C₅×C₁₃	C₅×Dic₁₁	1	1	yes	characteristic
21	C₅×C₁₁	C₄×C₅×C₁₃	1	1	yes	characteristic
22	C₄×C₁₃	—	11	1	no	Hall
23	C₂×C₂₅	C₁₃×D₁₁	1	1	yes	characteristic
24	Dic₁₁	C₁₃×C₂₅	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₁₃	D₁₁×C₂₅	1	1	yes	characteristic
26	C₂₅	C₁₃×Dic₁₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₁	C₂×C₁₃×C₂₅	1	1	yes	characteristic
28	C₄×C₅	—	11	1	no	—
29	C₁₃	C₂₅×Dic₁₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₁₁	C₄×C₁₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	C₅×C₁₃×D₁₁	1	1	yes	characteristic
32	C₅	C₅×C₁₃×Dic₁₁	1	1	yes	characteristic
33	C₄	—	11	1	no	Sylow
34	C₂	C₁₃×D₁₁×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₂₅	D₁₁
commutator, hypocenter	C₁₁	C₄×C₁₃×C₂₅
Frattini	C₂×C₅	C₅×C₁₃×D₁₁
Fitting	C₂×C₁₁×C₁₃×C₂₅	C₂
socle, prime radical	C₂×C₅×C₁₁×C₁₃	C₂×C₅
cosocle	C₂×C₅×C₁₁	C₂×C₅×C₁₃
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₃×C₂₅

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₁₃×C₂₅	C₄	semidirect
6. C₂₅×Dic₁₁	C₁₃	direct (N × H)
9. C₁₃×Dic₁₁	C₂₅	direct (N × H)
11. C₁₃×C₂₅	Dic₁₁	direct (N × H)
13. C₁₁×C₂₅	C₄×C₁₃	semidirect
16. C₁₁×C₁₃	C₄×C₂₅	semidirect
24. Dic₁₁	C₁₃×C₂₅	direct (N × H)
26. C₂₅	C₁₃×Dic₁₁	direct (N × H)
29. C₁₃	C₂₅×Dic₁₁	direct (N × H)
30. C₁₁	C₄×C₁₃×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×C₁₃×C₂₅	2
C₅×C₁₃×Dic₁₁	5
C₄×C₁₃×C₂₅	11
C₂₅×Dic₁₁	13

Subgroups — C13×C25×Dic11 #28384635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₂₅×Dic₁₁ #28384635