Subgroups — D₁₃×D₁₁⋊C₂₅ #28384643

Order 14300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊(D₁₁⋊C₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₁₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₃×C₁₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×C₁₁⋊C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅×D₁₁×D₁₃	C₅	1	1	yes	maximal, characteristic
6	C₅×D₁₄₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₃×D₁₁	C₂×C₅	1	1	yes	characteristic
8	C₅×C₁₁×D₁₃	C₂×C₅	1	1	yes	characteristic
9	C₂×C₂₅×D₁₃	—	11	1	no	maximal, Hall
10	C₂×D₁₁⋊C₂₅	—	13	1	no	maximal, Hall
11	C₅×C₁₁×C₁₃	C₂²×C₅	1	1	yes	characteristic
12	C₂×C₁₃×C₂₅	—	11	1	no	—
13	C₂₅×D₁₃	—	11	1	no	—
14	C₂₅×D₁₃	—	11	1	no	—
15	D₁₁×D₁₃	C₂₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁⋊C₂₅	—	13	1	no	—
17	D₁₁⋊C₂₅	—	13	1	no	—
18	D₁₁⋊C₂₅	D₁₃	1	1	yes	characteristic, direct product factor
19	C₁₃×C₂₅	—	11	1	no	Hall
20	D₁₄₃	C₂×C₂₅	1	1	yes	characteristic, complemented
21	C₁₁×D₁₃	C₂×C₂₅	1	1	yes	characteristic, complemented
22	C₁₃×D₁₁	C₂×C₂₅	1	1	yes	characteristic, complemented
23	C₁₁⋊C₂₅	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×D₁₃	—	11	1	no	—
25	C₂×C₅×D₁₁	—	13	1	no	—
26	C₁₁×C₁₃	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×C₁₃	—	55	1	no	—
28	C₅×D₁₃	—	55	1	no	—
29	C₅×D₁₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic
30	C₂×C₅×C₁₁	—	13	1	no	—
31	C₅×D₁₁	—	13	1	no	—
32	C₅×D₁₁	C₅×D₁₃	1	1	yes	characteristic
33	C₂²×C₂₅	—	143	1	no	Hall
34	C₅×C₁₃	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic
35	C₅×C₁₁	C₂×C₅×D₁₃	1	1	yes	characteristic
36	C₂×D₁₃	—	11	1	no	Hall
37	C₂×C₂₅	—	11	1	no	—
38	C₂×C₂₅	—	143	1	no	—
39	C₂×C₂₅	—	143	1	no	—
40	C₂×D₁₁	—	13	1	no	Hall
41	C₂×C₁₃	—	55	1	no	—
42	D₁₃	—	55	1	no	—
43	D₁₃	D₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor
44	C₂₅	—	11	1	no	Sylow
45	C₂×C₁₁	—	13	1	no	—
46	D₁₁	—	13	1	no	—
47	D₁₁	C₂₅×D₁₃	1	1	yes	characteristic, complemented
48	C₂²×C₅	—	715	1	no	—
49	C₁₃	C₂×D₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
50	C₁₁	C₂×C₂₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₅	—	13	1	no	—
52	C₂×C₅	—	55	1	no	—
53	C₂×C₅	—	715	1	no	—
54	C₅	D₁₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
55	C₂²	—	715	1	no	Sylow
56	C₂	—	13	1	no	—
57	C₂	—	55	1	no	—
58	C₂	—	715	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₅	D₁₃×AGL(1,𝔽₁₁)
commutator, hypocenter	C₁₁×C₁₃	C₂²×C₂₅
Fitting, socle, cosocle	C₅×C₁₁×C₁₃	C₂²×C₅
prime radical	C₅×D₁₁×D₁₃	C₅
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊(D₁₁⋊C₂₅)	C₂	semidirect
2. C₁₃×D₁₁⋊C₂₅	C₂	semidirect
3. D₁₃×C₁₁⋊C₂₅	C₂	semidirect
4. C₁₃×C₁₁⋊C₂₅	C₂²	semidirect
15. D₁₁×D₁₃	C₂₅	semidirect
18. D₁₁⋊C₂₅	D₁₃	direct (N × H)
20. D₁₄₃	C₂×C₂₅	semidirect
21. C₁₁×D₁₃	C₂×C₂₅	semidirect
22. C₁₃×D₁₁	C₂×C₂₅	semidirect
23. C₁₁⋊C₂₅	C₂×D₁₃	semidirect
26. C₁₁×C₁₃	C₂²×C₂₅	semidirect
43. D₁₃	D₁₁⋊C₂₅	direct (N × H)
47. D₁₁	C₂₅×D₁₃	semidirect
49. C₁₃	C₂×D₁₁⋊C₂₅	semidirect
50. C₁₁	C₂×C₂₅×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₃⋊(D₁₁⋊C₂₅)	2
C₁₃×D₁₁⋊C₂₅	2
D₁₃×C₁₁⋊C₂₅	2
C₅×D₁₁×D₁₃	5
C₂×C₂₅×D₁₃	11
C₂×D₁₁⋊C₂₅	13

Subgroups — D13×D11⋊C25 #28384643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×D₁₁⋊C₂₅ #28384643