Subgroups — C₂×C₇²×D₅₅ #24924795

Order 10780.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₅₅	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×C₇²×D₁₁	—	5	1	no	maximal, Hall
5	C₂×C₇×D₅₅	C₇	1	8	yes	maximal, direct product factor
6	C₂×C₇²×C₁₁	D₅	1	1	yes	characteristic, complemented
7	C₇²×D₁₁	—	5	2	no	—
8	C₂×C₇²×D₅	—	11	1	no	maximal, Hall
9	C₂×C₅×C₇×C₁₁	C₂×C₇	1	8	yes	complemented
10	C₇×D₅₅	C₂×C₇	1	16	yes	direct product factor
11	C₇²×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₇²	D₁₁	1	1	yes	characteristic, complemented
13	C₇²×D₅	—	11	2	no	—
14	C₅×C₇×C₁₁	C₂²×C₇	1	8	yes	complemented
15	C₂×C₇×D₁₁	—	5	8	no	—
16	C₅×C₇²	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×D₅₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
18	C₂²×C₇²	—	55	1	no	Hall
19	C₂×C₇×C₁₁	C₇×D₅	1	8	yes	complemented
20	C₇×D₁₁	—	5	16	no	—
21	C₂×C₇×D₅	—	11	8	no	—
22	C₂×C₅×C₁₁	C₂×C₇²	1	1	yes	characteristic, complemented
23	D₅₅	C₂×C₇²	1	2	yes	direct product factor
24	C₂×C₇²	—	55	2	no	—
25	C₂×C₇²	D₅₅	1	1	yes	characteristic, direct product factor
26	C₇×C₁₁	C₂×C₇×D₅	1	8	yes	complemented
27	C₂×C₅×C₇	C₇×D₁₁	1	8	yes	complemented
28	C₇×D₅	—	11	16	no	—
29	C₅×C₁₁	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
30	C₇²	C₂×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×D₁₁	—	5	1	no	Hall
32	C₅×C₇	C₂×C₇×D₁₁	1	8	yes	complemented
33	C₂²×C₇	—	55	8	no	—
34	C₂×C₁₁	C₇²×D₅	1	1	yes	characteristic, complemented
35	D₁₁	—	5	2	no	—
36	C₂×D₅	—	11	1	no	Hall
37	C₂×C₇	—	55	16	no	—
38	C₂×C₇	C₇×D₅₅	1	8	yes	direct product factor
39	C₁₁	C₂×C₇²×D₅	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₅	C₇²×D₁₁	1	1	yes	characteristic, complemented
41	D₅	—	11	2	no	—
42	C₇	C₂×C₇×D₅₅	1	8	yes	direct product factor
43	C₅	C₂×C₇²×D₁₁	1	1	yes	characteristic, complemented, Sylow
44	C₂²	—	55	1	no	Sylow
45	C₂	—	55	2	no	—
46	C₂	C₇²×D₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇²	D₅₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂²×C₇²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₁	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂×C₇²

Complements

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

N	H ≅ G/N	type
1. C₇²×D₅₅	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₁₁	C₂	semidirect
3. C₅×C₇²×C₁₁	C₂²	semidirect
5. C₂×C₇×D₅₅	C₇	direct (N × H)
6. C₂×C₇²×C₁₁	D₅	semidirect
9. C₂×C₅×C₇×C₁₁	C₂×C₇	semidirect
10. C₇×D₅₅	C₂×C₇	direct (N × H)
11. C₇²×C₁₁	C₂×D₅	semidirect
12. C₂×C₅×C₇²	D₁₁	semidirect
14. C₅×C₇×C₁₁	C₂²×C₇	semidirect
16. C₅×C₇²	C₂×D₁₁	semidirect
17. C₂×D₅₅	C₇²	direct (N × H)
19. C₂×C₇×C₁₁	C₇×D₅	semidirect
22. C₂×C₅×C₁₁	C₂×C₇²	semidirect
23. D₅₅	C₂×C₇²	direct (N × H)
25. C₂×C₇²	D₅₅	direct (N × H)
26. C₇×C₁₁	C₂×C₇×D₅	semidirect
27. C₂×C₅×C₇	C₇×D₁₁	semidirect
29. C₅×C₁₁	C₂²×C₇²	semidirect
30. C₇²	C₂×D₅₅	direct (N × H)
32. C₅×C₇	C₂×C₇×D₁₁	semidirect
34. C₂×C₁₁	C₇²×D₅	semidirect
38. C₂×C₇	C₇×D₅₅	direct (N × H)
39. C₁₁	C₂×C₇²×D₅	semidirect
40. C₂×C₅	C₇²×D₁₁	semidirect
42. C₇	C₂×C₇×D₅₅	direct (N × H)
43. C₅	C₂×C₇²×D₁₁	semidirect
46. C₂	C₇²×D₅₅	direct (N × H)

Subgroups — C2×C72×D55 #24924795

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇²×D₅₅ #24924795