Subgroups — D₅×C₁₁×C₇⋊D₇ #24924778

Order 10780.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₁₁	D₅×C₇⋊D₇
commutator, cosocle, hypocenter	C₅×C₇²	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₁	C₂²
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₅⋊(C₇⋊D₇)	C₂	semidirect
2. C₇²×D₅×C₁₁	C₂	semidirect
3. C₅×C₁₁×C₇⋊D₇	C₂	semidirect
4. C₅×C₇²×C₁₁	C₂²	semidirect
9. C₁₁×C₇⋊D₇	D₅	direct (N × H)
10. D₅×C₇⋊D₇	C₁₁	direct (N × H)
12. C₇×D₅×C₁₁	D₇	semidirect
14. C₇²×C₁₁	C₂×D₅	semidirect
15. C₅⋊(C₇⋊D₇)	C₂×C₁₁	semidirect
16. C₇²×D₅	C₂×C₁₁	semidirect
17. C₅×C₇⋊D₇	C₂×C₁₁	semidirect
18. C₅×C₇×C₁₁	C₂×D₇	semidirect
20. C₅×C₇²	C₂²×C₁₁	semidirect
29. D₅×C₁₁	C₇⋊D₇	direct (N × H)
32. C₇⋊D₇	D₅×C₁₁	direct (N × H)
33. C₇×C₁₁	D₅×D₇	semidirect
36. C₇×D₅	C₁₁×D₇	semidirect
37. C₅×C₁₁	C₂×C₇⋊D₇	semidirect
38. C₇²	C₂×D₅×C₁₁	semidirect
40. C₅×C₇	C₂×C₁₁×D₇	semidirect
49. C₁₁	D₅×C₇⋊D₇	direct (N × H)
52. D₅	C₁₁×C₇⋊D₇	direct (N × H)
53. C₇	D₅×C₁₁×D₇	semidirect
54. C₅	C₂×C₁₁×C₇⋊D₇	semidirect

Subgroups — D5×C11×C7⋊D7 #24924778

Conjugacy classes of subgroups

Complements

Subgroups — D₅×C₁₁×C₇⋊D₇ #24924778