Subgroups — C₂×C₇²×D₅×C₁₁ #24924796

Order 10780.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₇²×C₁₁	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₇²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₇²×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₇²×D₅×C₁₁	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₁₁	C₂	semidirect
3. C₅×C₇²×C₁₁	C₂²	semidirect
5. C₂×C₇×D₅×C₁₁	C₇	direct (N × H)
7. C₂×C₇²×C₁₁	D₅	direct (N × H)
8. C₂×C₇²×D₅	C₁₁	direct (N × H)
9. C₂×C₅×C₇×C₁₁	C₂×C₇	semidirect
10. C₇×D₅×C₁₁	C₂×C₇	direct (N × H)
11. C₇²×C₁₁	C₂×D₅	direct (N × H)
12. C₂×C₅×C₇²	C₂×C₁₁	semidirect
13. C₇²×D₅	C₂×C₁₁	direct (N × H)
14. C₅×C₇×C₁₁	C₂²×C₇	semidirect
16. C₅×C₇²	C₂²×C₁₁	semidirect
17. C₂×D₅×C₁₁	C₇²	direct (N × H)
20. C₂×C₇×C₁₁	C₇×D₅	direct (N × H)
21. C₂×C₇×D₅	C₇×C₁₁	direct (N × H)
22. C₂×C₅×C₁₁	C₂×C₇²	semidirect
23. D₅×C₁₁	C₂×C₇²	direct (N × H)
25. C₂×C₇²	D₅×C₁₁	direct (N × H)
26. C₇×C₁₁	C₂×C₇×D₅	direct (N × H)
27. C₂×C₅×C₇	C₂×C₇×C₁₁	semidirect
28. C₇×D₅	C₂×C₇×C₁₁	direct (N × H)
29. C₅×C₁₁	C₂²×C₇²	semidirect
30. C₇²	C₂×D₅×C₁₁	direct (N × H)
32. C₅×C₇	C₂²×C₇×C₁₁	semidirect
35. C₂×C₁₁	C₇²×D₅	direct (N × H)
36. C₂×D₅	C₇²×C₁₁	direct (N × H)
38. C₂×C₇	C₇×D₅×C₁₁	direct (N × H)
39. C₁₁	C₂×C₇²×D₅	direct (N × H)
40. C₂×C₅	C₂×C₇²×C₁₁	semidirect
41. D₅	C₂×C₇²×C₁₁	direct (N × H)
42. C₇	C₂×C₇×D₅×C₁₁	direct (N × H)
43. C₅	C₂²×C₇²×C₁₁	semidirect
46. C₂	C₇²×D₅×C₁₁	direct (N × H)

Subgroups — C2×C72×D5×C11 #24924796

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇²×D₅×C₁₁ #24924796