Subgroups — C₂×C₅⋊(C₇⋊D₇₇) #24924791

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	2	yes	maximal, direct product factor
2	C₂×C₅×C₇²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇⋊D₇₇	—	5	1	no	maximal, Hall
5	C₂×D₃₈₅	—	7	8	no	maximal
6	C₂×C₇²×C₁₁	D₅	1	1	yes	characteristic, complemented
7	C₇⋊D₇₇	—	5	2	no	—
8	C₂×C₅⋊(C₇⋊D₇)	—	11	1	no	maximal, Hall
9	C₂×C₅×C₇×C₁₁	D₇	1	8	yes	complemented
10	D₃₈₅	—	7	16	no	—
11	C₇²×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₇²	D₁₁	1	1	yes	characteristic, complemented
13	C₅⋊(C₇⋊D₇)	—	11	2	no	—
14	C₅×C₇×C₁₁	C₂×D₇	1	8	yes	complemented
15	C₂×D₇₇	—	35	8	no	—
16	C₅×C₇²	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×D₅₅	—	49	1	no	Hall
18	C₂×C₇⋊D₇	—	55	1	no	Hall
19	C₂×C₇×C₁₁	D₃₅	1	8	yes	complemented
20	D₇₇	—	35	16	no	—
21	C₂×D₃₅	—	77	8	no	—
22	C₂×C₅×C₁₁	C₇⋊D₇	1	1	yes	characteristic, complemented
23	D₅₅	—	49	2	no	—
24	C₂×C₇²	D₅₅	1	1	yes	characteristic, complemented
25	C₇⋊D₇	—	55	2	no	—
26	C₇×C₁₁	C₂×D₃₅	1	8	yes	complemented
27	C₂×C₅×C₇	D₇₇	1	8	yes	complemented
28	D₃₅	—	77	16	no	—
29	C₅×C₁₁	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
30	C₇²	C₂×D₅₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₁	—	245	1	no	Hall
32	C₅×C₇	C₂×D₇₇	1	8	yes	complemented
33	C₂×D₇	—	385	8	no	—
34	C₂×C₁₁	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented
35	D₁₁	—	245	2	no	—
36	C₂×D₅	—	539	1	no	Hall
37	C₂×C₇	D₃₈₅	1	8	yes	complemented
38	D₇	—	385	16	no	—
39	C₁₁	C₂×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₅	C₇⋊D₇₇	1	1	yes	characteristic, complemented
41	D₅	—	539	2	no	—
42	C₇	C₂×D₃₈₅	1	8	yes	complemented
43	C₅	C₂×C₇⋊D₇₇	1	1	yes	characteristic, complemented, Sylow
44	C₂²	—	2695	1	no	Sylow
45	C₂	—	2695	2	no	—
46	C₂	C₅⋊(C₇⋊D₇₇)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊(C₇⋊D₇₇)
commutator, cosocle, hypocenter	C₅×C₇²×C₁₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₁	C₂
LCS	G ▷ C₅×C₇²×C₁₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₅⋊(C₇⋊D₇₇)	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₁₁	C₂	semidirect
3. C₅×C₇²×C₁₁	C₂²	semidirect
6. C₂×C₇²×C₁₁	D₅	semidirect
9. C₂×C₅×C₇×C₁₁	D₇	semidirect
11. C₇²×C₁₁	C₂×D₅	semidirect
12. C₂×C₅×C₇²	D₁₁	semidirect
14. C₅×C₇×C₁₁	C₂×D₇	semidirect
16. C₅×C₇²	C₂×D₁₁	semidirect
19. C₂×C₇×C₁₁	D₃₅	semidirect
22. C₂×C₅×C₁₁	C₇⋊D₇	semidirect
24. C₂×C₇²	D₅₅	semidirect
26. C₇×C₁₁	C₂×D₃₅	semidirect
27. C₂×C₅×C₇	D₇₇	semidirect
29. C₅×C₁₁	C₂×C₇⋊D₇	semidirect
30. C₇²	C₂×D₅₅	semidirect
32. C₅×C₇	C₂×D₇₇	semidirect
34. C₂×C₁₁	C₅⋊(C₇⋊D₇)	semidirect
37. C₂×C₇	D₃₈₅	semidirect
39. C₁₁	C₂×C₅⋊(C₇⋊D₇)	semidirect
40. C₂×C₅	C₇⋊D₇₇	semidirect
42. C₇	C₂×D₃₈₅	semidirect
43. C₅	C₂×C₇⋊D₇₇	semidirect
46. C₂	C₅⋊(C₇⋊D₇₇)	direct (N × H)

Subgroups — C2×C5⋊(C7⋊D77) #24924791

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅⋊(C₇⋊D₇₇) #24924791