Subgroups — D₁₁×C₅⋊(C₇⋊D₇) #24924777

Order 10780.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(C₇⋊D₇₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₅⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×C₇⋊D₇	—	5	1	no	maximal, Hall
6	D₁₁×D₃₅	—	7	8	no	maximal
7	C₇⋊D₇₇	—	5	1	no	—
8	C₁₁×C₇⋊D₇	—	5	1	no	—
9	C₇²×D₁₁	D₅	1	1	yes	characteristic, complemented
10	C₂×C₅⋊(C₇⋊D₇)	—	11	1	no	maximal, Hall
11	D₃₈₅	—	7	8	no	—
12	C₁₁×D₃₅	—	7	8	no	—
13	C₅×C₇×D₁₁	D₇	1	8	yes	complemented
14	C₇²×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₇²	—	11	1	no	—
16	C₅⋊(C₇⋊D₇)	—	11	1	no	—
17	C₅⋊(C₇⋊D₇)	D₁₁	1	1	yes	characteristic, direct product factor
18	C₅×C₇×C₁₁	C₂×D₇	1	8	yes	complemented
19	D₇×D₁₁	—	35	8	no	—
20	C₅×C₇²	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
21	D₅×D₁₁	—	49	1	no	Hall
22	C₂×C₇⋊D₇	—	55	1	no	Hall
23	D₇₇	—	35	8	no	—
24	C₇×D₁₁	D₃₅	1	8	yes	complemented
25	C₁₁×D₇	—	35	8	no	—
26	C₂×D₃₅	—	77	8	no	—
27	D₅₅	—	49	1	no	—
28	C₅×D₁₁	C₇⋊D₇	1	1	yes	characteristic, complemented
29	D₅×C₁₁	—	49	1	no	—
30	C₂×C₇²	—	11	1	no	—
31	C₇⋊D₇	—	5	1	no	—
32	C₇⋊D₇	—	55	1	no	—
33	C₇×C₁₁	C₂×D₃₅	1	8	yes	complemented
34	C₂×C₅×C₇	—	11	8	no	—
35	D₃₅	—	7	8	no	—
36	D₃₅	—	77	8	no	—
37	C₅×C₁₁	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
38	C₇²	D₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₁₁	—	245	1	no	Hall
40	C₅×C₇	D₇×D₁₁	1	8	yes	complemented
41	C₂×D₇	—	385	8	no	—
42	C₂×C₁₁	—	245	1	no	—
43	D₁₁	—	245	1	no	—
44	D₁₁	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor
45	C₂×D₅	—	539	1	no	Hall
46	C₂×C₇	—	11	8	no	—
47	D₇	—	35	8	no	—
48	D₇	—	385	8	no	—
49	C₁₁	C₂×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₅	—	11	1	no	—
51	D₅	—	539	1	no	—
52	D₅	—	49	1	no	—
53	C₇	D₁₁×D₃₅	1	8	yes	complemented
54	C₅	D₁₁×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
55	C₂²	—	2695	1	no	Sylow
56	C₂	—	11	1	no	—
57	C₂	—	2695	1	no	—
58	C₂	—	245	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇²×C₁₁	C₂²
LCS	G ▷ C₅×C₇²×C₁₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅⋊(C₇⋊D₇₇)	C₂	semidirect
2. C₁₁×C₅⋊(C₇⋊D₇)	C₂	semidirect
3. C₅×C₇²×D₁₁	C₂	semidirect
4. C₅×C₇²×C₁₁	C₂²	semidirect
9. C₇²×D₁₁	D₅	semidirect
13. C₅×C₇×D₁₁	D₇	semidirect
14. C₇²×C₁₁	C₂×D₅	semidirect
17. C₅⋊(C₇⋊D₇)	D₁₁	direct (N × H)
18. C₅×C₇×C₁₁	C₂×D₇	semidirect
20. C₅×C₇²	C₂×D₁₁	semidirect
24. C₇×D₁₁	D₃₅	semidirect
28. C₅×D₁₁	C₇⋊D₇	semidirect
33. C₇×C₁₁	C₂×D₃₅	semidirect
37. C₅×C₁₁	C₂×C₇⋊D₇	semidirect
38. C₇²	D₅×D₁₁	semidirect
40. C₅×C₇	D₇×D₁₁	semidirect
44. D₁₁	C₅⋊(C₇⋊D₇)	direct (N × H)
49. C₁₁	C₂×C₅⋊(C₇⋊D₇)	semidirect
53. C₇	D₁₁×D₃₅	semidirect
54. C₅	D₁₁×C₇⋊D₇	semidirect

Subgroups — D11×C5⋊(C7⋊D7) #24924777

Conjugacy classes of subgroups

Complements

Subgroups — D₁₁×C₅⋊(C₇⋊D₇) #24924777