Subgroups — C₂×C₅×D₁₁×C₁₀₇ #37555342

Order 23540.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₁×C₁₀₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₁×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₁×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁×C₁₀₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×C₁₀₇	C₂×C₅	1	1	yes	characteristic, complemented
6	D₁₁×C₁₀₇	C₂×C₅	1	2	yes	direct product factor
7	C₂²×C₅×C₁₀₇	—	11	1	no	maximal, Hall
8	C₁₁×C₁₀₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₁₀₇	—	11	2	no	—
10	C₂×C₅×C₁₀₇	D₁₁	1	1	yes	characteristic, direct product factor
11	C₅×C₁₀₇	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₁₀₇	—	11	1	no	Hall
13	C₂×C₅×D₁₁	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₁₀₇	—	11	2	no	—
15	C₂×C₁₀₇	C₅×D₁₁	1	1	yes	characteristic, direct product factor
16	C₂×C₅×C₁₁	C₂×C₁₀₇	1	1	yes	characteristic, complemented
17	C₅×D₁₁	C₂×C₁₀₇	1	2	yes	direct product factor
18	C₁₀₇	C₂×C₅×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₅×C₁₁	C₂²×C₁₀₇	1	1	yes	characteristic, complemented, Hall
20	C₂×D₁₁	C₅×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₁₁	C₂×C₅×C₁₀₇	1	1	yes	characteristic, complemented
22	D₁₁	C₂×C₅×C₁₀₇	1	2	yes	direct product factor
23	C₂²×C₅	—	11	1	no	Hall
24	C₁₁	C₂²×C₅×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅	—	11	2	no	—
26	C₂×C₅	D₁₁×C₁₀₇	1	1	yes	characteristic, direct product factor
27	C₅	C₂×D₁₁×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	11	1	no	Sylow
29	C₂	—	11	2	no	—
30	C₂	C₅×D₁₁×C₁₀₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₀₇	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂²×C₅×C₁₀₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁×C₁₀₇	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₅×C₁₀₇

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₁×C₁₀₇	C₂	direct (N × H)
2. C₂×C₅×C₁₁×C₁₀₇	C₂	semidirect
3. C₅×C₁₁×C₁₀₇	C₂²	semidirect
4. C₂×D₁₁×C₁₀₇	C₅	direct (N × H)
5. C₂×C₁₁×C₁₀₇	C₂×C₅	semidirect
6. D₁₁×C₁₀₇	C₂×C₅	direct (N × H)
8. C₁₁×C₁₀₇	C₂²×C₅	semidirect
10. C₂×C₅×C₁₀₇	D₁₁	direct (N × H)
11. C₅×C₁₀₇	C₂×D₁₁	direct (N × H)
13. C₂×C₅×D₁₁	C₁₀₇	direct (N × H)
15. C₂×C₁₀₇	C₅×D₁₁	direct (N × H)
16. C₂×C₅×C₁₁	C₂×C₁₀₇	semidirect
17. C₅×D₁₁	C₂×C₁₀₇	direct (N × H)
18. C₁₀₇	C₂×C₅×D₁₁	direct (N × H)
19. C₅×C₁₁	C₂²×C₁₀₇	semidirect
20. C₂×D₁₁	C₅×C₁₀₇	direct (N × H)
21. C₂×C₁₁	C₂×C₅×C₁₀₇	semidirect
22. D₁₁	C₂×C₅×C₁₀₇	direct (N × H)
24. C₁₁	C₂²×C₅×C₁₀₇	semidirect
26. C₂×C₅	D₁₁×C₁₀₇	direct (N × H)
27. C₅	C₂×D₁₁×C₁₀₇	direct (N × H)
30. C₂	C₅×D₁₁×C₁₀₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×D₁₁×C₁₀₇	2
C₂×C₅×C₁₁×C₁₀₇	2
C₂×D₁₁×C₁₀₇	5
C₂²×C₅×C₁₀₇	11
C₂×C₅×D₁₁	107

Subgroups — C2×C5×D11×C107 #37555342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₁₁×C₁₀₇ #37555342