Subgroups — D₅×C₁₃×C₁₁⋊D₁₁ #44538276

Order 31460.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₁²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₅⋊(C₁₁⋊D₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₁²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₁₁⋊D₁₁	—	5	1	no	maximal, Hall
6	C₁₃×C₁₁⋊D₁₁	—	5	1	no	—
7	C₁₃×C₁₁⋊D₁₁	D₅	1	1	yes	characteristic, direct product factor
8	C₂×C₁₁²×C₁₃	—	5	1	no	—
9	D₅×C₁₃×D₁₁	—	11	12	no	maximal
10	D₅×C₁₁⋊D₁₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₁²×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
12	C₁₃×D₅₅	—	11	12	no	—
13	D₅×C₁₁×C₁₃	D₁₁	1	12	yes	complemented
14	C₅×C₁₃×D₁₁	—	11	12	no	—
15	C₅⋊(C₁₁⋊D₁₁)	C₂×C₁₃	1	1	yes	characteristic, complemented
16	D₅×C₁₁²	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₅×C₁₁⋊D₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₅×C₁₁×C₁₃	C₂×D₁₁	1	12	yes	complemented
19	C₅×C₁₁²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₃×D₁₁	—	55	12	no	—
21	C₂×C₁₁⋊D₁₁	—	5	1	no	Hall
22	C₂×C₁₁×C₁₃	—	5	12	no	—
23	C₁₃×D₁₁	—	11	12	no	—
24	C₁₃×D₁₁	—	55	12	no	—
25	C₂×D₅×C₁₃	—	121	1	no	Hall
26	C₂×C₁₁²	—	5	1	no	—
27	C₁₁⋊D₁₁	—	5	1	no	—
28	C₁₁⋊D₁₁	D₅×C₁₃	1	1	yes	characteristic, direct product factor
29	D₅×D₁₁	—	11	12	no	—
30	C₁₁×C₁₃	D₅×D₁₁	1	12	yes	complemented
31	C₂×C₅×C₁₃	—	121	1	no	—
32	D₅×C₁₃	—	121	1	no	—
33	D₅×C₁₃	C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
34	C₁₁²	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
35	D₅₅	—	11	12	no	—
36	C₅×D₁₁	—	11	12	no	—
37	D₅×C₁₁	C₁₃×D₁₁	1	12	yes	complemented
38	C₅×C₁₃	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₁	C₂×C₁₃×D₁₁	1	12	yes	complemented
40	C₂²×C₁₃	—	605	1	no	Hall
41	C₂×D₁₁	—	55	12	no	—
42	C₂×C₁₃	—	5	1	no	—
43	C₂×C₁₃	—	605	1	no	—
44	C₂×C₁₃	—	121	1	no	—
45	C₂×C₁₁	—	5	12	no	—
46	D₁₁	—	11	12	no	—
47	D₁₁	—	55	12	no	—
48	C₂×D₅	—	121	1	no	Hall
49	C₁₃	D₅×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
50	C₁₁	D₅×C₁₃×D₁₁	1	12	yes	complemented
51	C₂×C₅	—	121	1	no	—
52	D₅	—	121	1	no	—
53	D₅	C₁₃×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
54	C₅	C₂×C₁₃×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
55	C₂²	—	605	1	no	Sylow
56	C₂	—	5	1	no	—
57	C₂	—	605	1	no	—
58	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₅×C₁₁⋊D₁₁
commutator, cosocle, hypocenter	C₅×C₁₁²	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₁₃	C₂²
LCS	G ▷ C₅×C₁₁²
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×C₁₁⋊D₁₁	C₂	semidirect
2. D₅×C₁₁²×C₁₃	C₂	semidirect
3. C₁₃×C₅⋊(C₁₁⋊D₁₁)	C₂	semidirect
4. C₅×C₁₁²×C₁₃	C₂²	semidirect
7. C₁₃×C₁₁⋊D₁₁	D₅	direct (N × H)
10. D₅×C₁₁⋊D₁₁	C₁₃	direct (N × H)
11. C₁₁²×C₁₃	C₂×D₅	semidirect
13. D₅×C₁₁×C₁₃	D₁₁	semidirect
15. C₅⋊(C₁₁⋊D₁₁)	C₂×C₁₃	semidirect
16. D₅×C₁₁²	C₂×C₁₃	semidirect
17. C₅×C₁₁⋊D₁₁	C₂×C₁₃	semidirect
18. C₅×C₁₁×C₁₃	C₂×D₁₁	semidirect
19. C₅×C₁₁²	C₂²×C₁₃	semidirect
28. C₁₁⋊D₁₁	D₅×C₁₃	direct (N × H)
30. C₁₁×C₁₃	D₅×D₁₁	semidirect
33. D₅×C₁₃	C₁₁⋊D₁₁	direct (N × H)
34. C₁₁²	C₂×D₅×C₁₃	semidirect
37. D₅×C₁₁	C₁₃×D₁₁	semidirect
38. C₅×C₁₃	C₂×C₁₁⋊D₁₁	semidirect
39. C₅×C₁₁	C₂×C₁₃×D₁₁	semidirect
49. C₁₃	D₅×C₁₁⋊D₁₁	direct (N × H)
50. C₁₁	D₅×C₁₃×D₁₁	semidirect
53. D₅	C₁₃×C₁₁⋊D₁₁	direct (N × H)
54. C₅	C₂×C₁₃×C₁₁⋊D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃×C₁₁⋊D₁₁	2
D₅×C₁₁²×C₁₃	2
C₁₃×C₅⋊(C₁₁⋊D₁₁)	2
C₂×C₁₃×C₁₁⋊D₁₁	5
D₅×C₁₃×D₁₁	11
D₅×C₁₁⋊D₁₁	13

Subgroups — D5×C13×C11⋊D11 #44538276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₃×C₁₁⋊D₁₁ #44538276