Subgroups — C₂×C₁₁×D₂₃₅ #23780296

Order 10340.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₂₃₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₁×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₁×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×D₄₇	—	5	1	no	maximal, Hall
5	C₂×C₁₁×C₄₇	D₅	1	1	yes	characteristic, complemented
6	C₁₁×D₄₇	—	5	2	no	—
7	C₂×D₂₃₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁×C₄₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₄₇	C₂×C₁₁	1	1	yes	characteristic, complemented
10	D₂₃₅	C₂×C₁₁	1	2	yes	direct product factor
11	C₅×C₄₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×D₅×C₁₁	—	47	1	no	maximal, Hall
13	C₂×D₄₇	—	5	1	no	Hall
14	C₂×C₅×C₁₁	D₄₇	1	1	yes	characteristic, complemented
15	D₅×C₁₁	—	47	2	no	—
16	C₂×C₄₇	D₅×C₁₁	1	1	yes	characteristic, complemented
17	D₄₇	—	5	2	no	—
18	C₅×C₁₁	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
19	C₄₇	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₁₁	—	235	1	no	Hall
21	C₂×C₁₁	—	235	2	no	—
22	C₂×C₁₁	D₂₃₅	1	1	yes	characteristic, direct product factor
23	C₂×D₅	—	47	1	no	Hall
24	C₁₁	C₂×D₂₃₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₅	C₁₁×D₄₇	1	1	yes	characteristic, complemented
26	D₅	—	47	2	no	—
27	C₅	C₂×C₁₁×D₄₇	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	235	1	no	Sylow
29	C₂	—	235	2	no	—
30	C₂	C₁₁×D₂₃₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₂₃₅
commutator, cosocle, hypocenter	C₅×C₄₇	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁×C₄₇	C₂
LCS	G ▷ C₅×C₄₇
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₂₃₅	C₂	direct (N × H)
2. C₂×C₅×C₁₁×C₄₇	C₂	semidirect
3. C₅×C₁₁×C₄₇	C₂²	semidirect
5. C₂×C₁₁×C₄₇	D₅	semidirect
7. C₂×D₂₃₅	C₁₁	direct (N × H)
8. C₁₁×C₄₇	C₂×D₅	semidirect
9. C₂×C₅×C₄₇	C₂×C₁₁	semidirect
10. D₂₃₅	C₂×C₁₁	direct (N × H)
11. C₅×C₄₇	C₂²×C₁₁	semidirect
14. C₂×C₅×C₁₁	D₄₇	semidirect
16. C₂×C₄₇	D₅×C₁₁	semidirect
18. C₅×C₁₁	C₂×D₄₇	semidirect
19. C₄₇	C₂×D₅×C₁₁	semidirect
22. C₂×C₁₁	D₂₃₅	direct (N × H)
24. C₁₁	C₂×D₂₃₅	direct (N × H)
25. C₂×C₅	C₁₁×D₄₇	semidirect
27. C₅	C₂×C₁₁×D₄₇	semidirect
30. C₂	C₁₁×D₂₃₅	direct (N × H)

Subgroups — C2×C11×D235 #23780296

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₁×D₂₃₅ #23780296