Subgroups — C₁₃×(C₁₁⋊C₅)⋊Dic₅ #28384679

Order 14300.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₃×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃×Dic₅₅	C₅	1	1	yes	maximal, characteristic, complemented
4	C₁₃×Dic₁₁⋊C₅	—	5	1	no	maximal
5	C₂×C₅×C₁₁×C₁₃	C₂×C₅	1	1	yes	characteristic
6	C₂×C₁₃×C₁₁⋊C₅	—	2	2	no	—
7	C₂×C₁₃×C₁₁⋊C₅	D₅	1	1	yes	characteristic
8	C₅×C₁₃×Dic₅	—	11	1	no	maximal, Hall
9	(C₁₁⋊C₅)⋊Dic₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×C₁₁×C₁₃	C₄×C₅	1	1	yes	characteristic, complemented
11	C₁₃×C₁₁⋊C₅	—	2	2	no	—
12	C₁₃×C₁₁⋊C₅	Dic₅	1	1	yes	characteristic, complemented
13	C₂×C₅²×C₁₃	—	11	1	no	—
14	C₁₃×Dic₁₁	—	5	1	no	Hall
15	C₂×C₅×C₁₁⋊C₅	C₂×C₁₃	1	1	yes	characteristic
16	C₅²×C₁₃	—	11	1	no	Hall
17	C₂×C₁₁×C₁₃	C₅×D₅	1	1	yes	characteristic
18	C₅×C₁₁⋊C₅	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
19	C₄×C₅×C₁₃	—	55	1	no	—
20	C₁₃×Dic₅	—	11	1	no	—
21	Dic₅₅	C₅×C₁₃	1	1	yes	characteristic, complemented
22	Dic₁₁⋊C₅	—	5	1	no	—
23	C₁₁×C₁₃	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×C₁₃	—	11	1	no	—
25	C₂×C₅×C₁₃	—	22	2	no	—
26	C₂×C₅×C₁₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic
27	C₂×C₅×C₁₁	C₂×C₅×C₁₃	1	1	yes	characteristic
28	C₂×C₁₁⋊C₅	—	2	2	no	—
29	C₂×C₁₁⋊C₅	D₅×C₁₃	1	1	yes	characteristic
30	C₅×Dic₅	—	11	1	no	Hall
31	C₅×C₁₃	—	11	1	no	—
32	C₅×C₁₃	—	22	2	no	—
33	C₅×C₁₃	Dic₁₁⋊C₅	1	1	yes	characteristic, complemented
34	C₅×C₁₁	C₄×C₅×C₁₃	1	1	yes	characteristic, complemented
35	C₁₁⋊C₅	—	2	2	no	—
36	C₁₁⋊C₅	C₁₃×Dic₅	1	1	yes	characteristic, complemented
37	C₄×C₁₃	—	55	1	no	Hall
38	C₂×C₅²	—	11	1	no	—
39	Dic₁₁	—	5	1	no	Hall
40	C₂×C₁₃	C₅⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
41	C₅²	—	11	1	no	Sylow
42	C₂×C₁₁	C₅×D₅×C₁₃	1	1	yes	characteristic
43	C₄×C₅	—	55	1	no	—
44	Dic₅	—	11	1	no	—
45	C₁₃	(C₁₁⋊C₅)⋊Dic₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₁₁	C₅×C₁₃×Dic₅	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₅	—	11	1	no	—
48	C₂×C₅	—	22	2	no	—
49	C₂×C₅	C₁₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
50	C₅	—	11	1	no	—
51	C₅	—	22	2	no	—
52	C₅	C₁₃×Dic₁₁⋊C₅	1	1	yes	characteristic, complemented
53	C₄	—	55	1	no	Sylow
54	C₂	C₁₃×C₅⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₅⋊AGL(1,𝔽₁₁)
commutator, hypocenter	C₅×C₁₁	C₄×C₅×C₁₃
Frattini	C₂	C₁₃×C₅⋊AGL(1,𝔽₁₁)
Fitting, socle	C₂×C₅×C₁₁×C₁₃	C₂×C₅
prime radical	C₂×C₅×C₁₃×C₁₁⋊C₅	C₂
cosocle	C₂×C₅×C₁₁	C₂×C₅×C₁₃
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₃×C₁₁⋊C₅	C₄	semidirect
3. C₁₃×Dic₅₅	C₅	semidirect
9. (C₁₁⋊C₅)⋊Dic₅	C₁₃	direct (N × H)
10. C₅×C₁₁×C₁₃	C₄×C₅	semidirect
12. C₁₃×C₁₁⋊C₅	Dic₅	semidirect
18. C₅×C₁₁⋊C₅	C₄×C₁₃	semidirect
21. Dic₅₅	C₅×C₁₃	semidirect
23. C₁₁×C₁₃	C₅×Dic₅	semidirect
33. C₅×C₁₃	Dic₁₁⋊C₅	semidirect
34. C₅×C₁₁	C₄×C₅×C₁₃	semidirect
36. C₁₁⋊C₅	C₁₃×Dic₅	semidirect
45. C₁₃	(C₁₁⋊C₅)⋊Dic₅	direct (N × H)
46. C₁₁	C₅×C₁₃×Dic₅	semidirect
52. C₅	C₁₃×Dic₁₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₁₃×C₁₁⋊C₅	2
C₁₃×Dic₅₅	5
C₁₃×Dic₁₁⋊C₅	5
C₅×C₁₃×Dic₅	11
(C₁₁⋊C₅)⋊Dic₅	13

Subgroups — C13×(C11⋊C5)⋊Dic5 #28384679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×(C₁₁⋊C₅)⋊Dic₅ #28384679