Subgroups — C₂×C₇×D₁₁×C₂₅ #21440366

Order 7700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₁×C₂₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₁×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₁×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₇×D₁₁	C₅	1	1	yes	maximal, characteristic
5	C₂×D₁₁×C₂₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₁₁	C₂×C₅	1	1	yes	characteristic
7	C₅×C₇×D₁₁	C₂×C₅	1	2	yes	—
8	C₂²×C₇×C₂₅	—	11	1	no	maximal, Hall
9	C₂×C₁₁×C₂₅	C₂×C₇	1	1	yes	characteristic, complemented
10	D₁₁×C₂₅	C₂×C₇	1	2	yes	direct product factor
11	C₅×C₇×C₁₁	C₂²×C₅	1	1	yes	characteristic
12	C₂×C₇×C₂₅	—	11	2	no	—
13	C₂×C₇×C₂₅	D₁₁	1	1	yes	characteristic, direct product factor
14	C₂×C₇×D₁₁	C₂₅	1	1	yes	characteristic, direct product factor, Hall
15	C₁₁×C₂₅	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×D₁₁	C₅×C₇	1	1	yes	characteristic
17	C₇×C₂₅	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₇×C₁₁	C₂×C₂₅	1	1	yes	characteristic, complemented
19	C₇×D₁₁	C₂×C₂₅	1	2	yes	direct product factor
20	C₂²×C₅×C₇	—	11	1	no	—
21	C₂×C₅×C₁₁	C₂×C₅×C₇	1	1	yes	characteristic
22	C₅×D₁₁	C₂×C₅×C₇	1	2	yes	—
23	C₂²×C₂₅	—	11	1	no	Hall
24	C₇×C₁₁	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅×C₇	—	11	2	no	—
26	C₂×C₅×C₇	C₅×D₁₁	1	1	yes	characteristic
27	C₅×C₁₁	C₂²×C₅×C₇	1	1	yes	characteristic
28	C₂×C₂₅	—	11	2	no	—
29	C₂×C₂₅	C₇×D₁₁	1	1	yes	characteristic, direct product factor
30	C₂×D₁₁	C₇×C₂₅	1	1	yes	characteristic, direct product factor, Hall
31	C₅×C₇	C₂×C₅×D₁₁	1	1	yes	characteristic
32	C₂²×C₇	—	11	1	no	Hall
33	C₂₅	C₂×C₇×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₁₁	C₂×C₇×C₂₅	1	1	yes	characteristic, complemented
35	D₁₁	C₂×C₇×C₂₅	1	2	yes	direct product factor
36	C₂²×C₅	—	11	1	no	—
37	C₂×C₇	—	11	2	no	—
38	C₂×C₇	D₁₁×C₂₅	1	1	yes	characteristic, direct product factor
39	C₁₁	C₂²×C₇×C₂₅	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₅	—	11	2	no	—
41	C₂×C₅	C₅×C₇×D₁₁	1	1	yes	characteristic
42	C₇	C₂×D₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₅	C₂×C₅×C₇×D₁₁	1	1	yes	characteristic
44	C₂²	—	11	1	no	Sylow
45	C₂	—	11	2	no	—
46	C₂	C₇×D₁₁×C₂₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₂₅	D₁₁
commutator, hypocenter	C₁₁	C₂²×C₇×C₂₅
Frattini	C₅	C₂×C₅×C₇×D₁₁
Fitting	C₂×C₇×C₁₁×C₂₅	C₂
socle	C₂×C₅×C₇×C₁₁	C₂×C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₇×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₁×C₂₅	C₂	direct (N × H)
2. C₂×C₇×C₁₁×C₂₅	C₂	semidirect
3. C₇×C₁₁×C₂₅	C₂²	semidirect
5. C₂×D₁₁×C₂₅	C₇	direct (N × H)
9. C₂×C₁₁×C₂₅	C₂×C₇	semidirect
10. D₁₁×C₂₅	C₂×C₇	direct (N × H)
13. C₂×C₇×C₂₅	D₁₁	direct (N × H)
14. C₂×C₇×D₁₁	C₂₅	direct (N × H)
15. C₁₁×C₂₅	C₂²×C₇	semidirect
17. C₇×C₂₅	C₂×D₁₁	direct (N × H)
18. C₂×C₇×C₁₁	C₂×C₂₅	semidirect
19. C₇×D₁₁	C₂×C₂₅	direct (N × H)
24. C₇×C₁₁	C₂²×C₂₅	semidirect
29. C₂×C₂₅	C₇×D₁₁	direct (N × H)
30. C₂×D₁₁	C₇×C₂₅	direct (N × H)
33. C₂₅	C₂×C₇×D₁₁	direct (N × H)
34. C₂×C₁₁	C₂×C₇×C₂₅	semidirect
35. D₁₁	C₂×C₇×C₂₅	direct (N × H)
38. C₂×C₇	D₁₁×C₂₅	direct (N × H)
39. C₁₁	C₂²×C₇×C₂₅	semidirect
42. C₇	C₂×D₁₁×C₂₅	direct (N × H)
46. C₂	C₇×D₁₁×C₂₅	direct (N × H)

Subgroups — C2×C7×D11×C25 #21440366

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇×D₁₁×C₂₅ #21440366