Subgroups — C₁₃×D₅₅⋊D₁₁ #44538271

Order 31460.

120 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	C₁₁×C₁₃×D₅₅	C₂	1	2	yes	maximal, complemented
3	C₅×C₁₁²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₁₁²	—	5	1	no	maximal, Hall
5	C₁₃×C₁₁⋊D₁₁	D₅	1	1	yes	characteristic, complemented
6	C₁₁×C₁₃×D₁₁	—	5	2	no	—
7	D₅×C₁₃×D₁₁	—	11	2	no	maximal
8	D₅₅⋊D₁₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₁²×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
10	C₁₃×D₅₅	D₁₁	1	2	yes	complemented
11	D₅×C₁₁×C₁₃	—	11	2	no	—
12	C₅×C₁₃×D₁₁	—	11	2	no	—
13	C₅×C₁₃×D₁₁	—	22	5	no	—
14	C₁₁×D₅₅	C₂×C₁₃	1	2	yes	complemented
15	C₅×C₁₁⋊D₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
16	C₅×C₁₁×C₁₃	—	2	5	no	—
17	C₅×C₁₁×C₁₃	C₂×D₁₁	1	2	yes	complemented
18	C₅×C₁₁²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₁₃×D₁₁	—	55	2	no	—
20	D₁₁²	—	5	1	no	Hall
21	C₂×C₁₁×C₁₃	—	55	2	no	—
22	C₁₃×D₁₁	—	5	2	no	—
23	C₁₃×D₁₁	—	11	2	no	—
24	C₁₃×D₁₁	—	22	5	no	—
25	C₂×D₅×C₁₃	—	121	1	no	Hall
26	C₁₁⋊D₁₁	D₅×C₁₃	1	1	yes	characteristic, complemented
27	C₁₁×D₁₁	—	5	2	no	—
28	D₅×D₁₁	—	11	2	no	—
29	C₁₁×C₁₃	—	2	5	no	—
30	C₁₁×C₁₃	D₅×D₁₁	1	2	yes	complemented
31	C₂×C₅×C₁₃	—	121	1	no	—
32	D₅×C₁₃	—	11	2	no	—
33	C₁₁²	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
34	D₅₅	C₁₃×D₁₁	1	2	yes	complemented
35	C₅×D₁₁	—	11	2	no	—
36	C₅×D₁₁	—	22	5	no	—
37	D₅×C₁₁	—	11	2	no	—
38	C₅×C₁₃	D₁₁²	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₁	—	2	5	no	—
40	C₅×C₁₁	C₂×C₁₃×D₁₁	1	2	yes	complemented
41	C₂²×C₁₃	—	605	1	no	Hall
42	C₂×D₁₁	—	55	2	no	—
43	C₂×C₁₃	—	55	2	no	—
44	C₂×C₁₃	—	121	1	no	—
45	C₂×C₁₁	—	55	2	no	—
46	D₁₁	—	5	2	no	—
47	D₁₁	—	11	2	no	—
48	D₁₁	—	22	5	no	—
49	C₂×D₅	—	121	1	no	Hall
50	C₁₃	D₅₅⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
51	C₁₁	—	2	5	no	—
52	C₁₁	D₅×C₁₃×D₁₁	1	2	yes	complemented
53	C₂×C₅	—	121	1	no	—
54	D₅	—	11	2	no	—
55	C₅	C₁₃×D₁₁²	1	1	yes	characteristic, complemented, Sylow
56	C₂²	—	605	1	no	Sylow
57	C₂	—	55	2	no	—
58	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₅₅⋊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. C₁₁×C₁₃×D₅₅	C₂	semidirect
3. C₅×C₁₁²×C₁₃	C₂²	semidirect
5. C₁₃×C₁₁⋊D₁₁	D₅	semidirect
8. D₅₅⋊D₁₁	C₁₃	direct (N × H)
9. C₁₁²×C₁₃	C₂×D₅	semidirect
10. C₁₃×D₅₅	D₁₁	semidirect
14. C₁₁×D₅₅	C₂×C₁₃	semidirect
15. C₅×C₁₁⋊D₁₁	C₂×C₁₃	semidirect
17. C₅×C₁₁×C₁₃	C₂×D₁₁	semidirect
18. C₅×C₁₁²	C₂²×C₁₃	semidirect
26. C₁₁⋊D₁₁	D₅×C₁₃	semidirect
30. C₁₁×C₁₃	D₅×D₁₁	semidirect
33. C₁₁²	C₂×D₅×C₁₃	semidirect
34. D₅₅	C₁₃×D₁₁	semidirect
38. C₅×C₁₃	D₁₁²	semidirect
40. C₅×C₁₁	C₂×C₁₃×D₁₁	semidirect
50. C₁₃	D₅₅⋊D₁₁	direct (N × H)
52. C₁₁	D₅×C₁₃×D₁₁	semidirect
55. C₅	C₁₃×D₁₁²	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
C₁₁×C₁₃×D₅₅	2
C₁₃×D₁₁²	5
D₅×C₁₃×D₁₁	11
D₅₅⋊D₁₁	13

Subgroups — C13×D55⋊D11 #44538271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₅₅⋊D₁₁ #44538271