Subgroups — C₃×C₁₃×D₁₁⋊C₂₅ #36339697

Order 21450.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₁₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₁₁⋊C₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₃×D₁₁	C₅	1	1	yes	maximal, characteristic
4	C₁₃×C₁₁⋊C₂₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₁×C₁₃	C₂×C₅	1	1	yes	characteristic
6	C₂×C₃×C₁₃×C₂₅	—	11	1	no	maximal, Hall
7	C₃×D₁₁⋊C₂₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₃×D₁₁	C₃×C₅	1	1	yes	characteristic
9	C₃×C₁₃×C₂₅	—	11	1	no	Hall
10	C₃×C₁₃×D₁₁	C₂₅	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₁⋊C₂₅	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₅×C₁₁×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic
13	C₂×C₁₃×C₂₅	—	11	1	no	Hall
14	D₁₁⋊C₂₅	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₁×C₁₃	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₅×C₁₃	—	55	1	no	—
17	C₃×C₅×D₁₁	C₅×C₁₃	1	1	yes	characteristic
18	C₁₃×C₂₅	—	11	1	no	Hall
19	C₁₃×D₁₁	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
20	C₁₁⋊C₂₅	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic
22	C₃×C₅×C₁₁	C₂×C₅×C₁₃	1	1	yes	characteristic
23	C₂×C₃×C₂₅	—	11	1	no	Hall
24	C₁₁×C₁₃	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅×C₁₃	—	55	1	no	—
26	C₅×D₁₁	C₃×C₅×C₁₃	1	1	yes	characteristic
27	C₂×C₃×C₁₃	—	55	1	no	Hall
28	C₃×C₂₅	—	11	1	no	Hall
29	C₃×D₁₁	C₁₃×C₂₅	1	1	yes	characteristic, complemented, Hall
30	C₅×C₁₃	C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
31	C₅×C₁₁	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic
32	C₂×C₂₅	—	11	1	no	Hall
33	C₃×C₁₃	D₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
34	C₃×C₁₁	C₂×C₁₃×C₂₅	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	—	55	1	no	—
36	C₂×C₁₃	—	55	1	no	Hall
37	C₂₅	—	11	1	no	Sylow
38	D₁₁	C₃×C₁₃×C₂₅	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅	C₁₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
40	C₁₃	C₃×D₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow
41	C₁₁	C₂×C₃×C₁₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₅	—	11	1	no	—
43	C₂×C₃	—	55	1	no	Hall
44	C₅	C₃×C₁₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
45	C₃	C₁₃×D₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₃	AGL(1,𝔽₁₁)
commutator, hypocenter	C₁₁	C₂×C₃×C₁₃×C₂₅
Frattini	C₅	C₃×C₁₃×AGL(1,𝔽₁₁)
Fitting, socle	C₃×C₅×C₁₁×C₁₃	C₂×C₅
prime radical	C₃×C₅×C₁₃×D₁₁	C₅
cosocle	C₅×C₁₁	C₂×C₃×C₅×C₁₃
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃×C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×C₁₁⋊C₂₅	C₂	semidirect
2. C₁₃×D₁₁⋊C₂₅	C₃	direct (N × H)
4. C₁₃×C₁₁⋊C₂₅	C₂×C₃	semidirect
7. C₃×D₁₁⋊C₂₅	C₁₃	direct (N × H)
10. C₃×C₁₃×D₁₁	C₂₅	semidirect
11. C₃×C₁₁⋊C₂₅	C₂×C₁₃	semidirect
14. D₁₁⋊C₂₅	C₃×C₁₃	direct (N × H)
15. C₃×C₁₁×C₁₃	C₂×C₂₅	semidirect
19. C₁₃×D₁₁	C₃×C₂₅	semidirect
20. C₁₁⋊C₂₅	C₂×C₃×C₁₃	semidirect
24. C₁₁×C₁₃	C₂×C₃×C₂₅	semidirect
29. C₃×D₁₁	C₁₃×C₂₅	semidirect
33. C₃×C₁₃	D₁₁⋊C₂₅	direct (N × H)
34. C₃×C₁₁	C₂×C₁₃×C₂₅	semidirect
38. D₁₁	C₃×C₁₃×C₂₅	semidirect
40. C₁₃	C₃×D₁₁⋊C₂₅	direct (N × H)
41. C₁₁	C₂×C₃×C₁₃×C₂₅	semidirect
45. C₃	C₁₃×D₁₁⋊C₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₃×C₁₁⋊C₂₅	2
C₁₃×D₁₁⋊C₂₅	3
C₃×C₅×C₁₃×D₁₁	5
C₂×C₃×C₁₃×C₂₅	11
C₃×D₁₁⋊C₂₅	13

Subgroups — C3×C13×D11⋊C25 #36339697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×D₁₁⋊C₂₅ #36339697