Subgroups — C₅×C₁₁×D₃₄₁ #49176014

Order 37510.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₃₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁²×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₃₄₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor
5	C₅×C₁₁×D₃₁	—	11	1	no	maximal
6	C₅×C₁₁×C₃₁	—	2	5	no	—
7	C₅×C₁₁×C₃₁	D₁₁	1	1	yes	characteristic, complemented
8	C₅×C₁₁×C₃₁	C₂×C₁₁	1	1	yes	characteristic, complemented
9	C₅×C₁₁×D₁₁	—	31	1	no	maximal, Hall
10	D₃₄₁	C₅×C₁₁	1	1	yes	characteristic, direct product factor
11	C₁₁×D₃₁	—	11	1	no	—
12	C₅×C₁₁²	D₃₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁×C₃₁	—	2	5	no	—
14	C₁₁×C₃₁	C₅×D₁₁	1	1	yes	characteristic, complemented
15	C₁₁×C₃₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
16	C₅×D₃₁	—	11	1	no	Hall
17	C₁₁×D₁₁	—	31	1	no	Hall
18	C₅×C₃₁	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
19	C₁₁²	C₅×D₃₁	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅×C₁₁	—	341	1	no	—
21	C₅×D₁₁	—	31	1	no	—
22	D₃₁	—	11	1	no	Hall
23	C₅×C₁₁	—	2	5	no	—
24	C₅×C₁₁	C₁₁×D₃₁	1	1	yes	characteristic, complemented
25	C₅×C₁₁	D₃₄₁	1	1	yes	characteristic, direct product factor
26	C₃₁	C₅×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₁	—	341	1	no	—
28	D₁₁	—	31	1	no	—
29	C₁₁	—	2	5	no	—
30	C₁₁	C₅×C₁₁×D₃₁	1	1	yes	characteristic, complemented
31	C₁₁	C₅×D₃₄₁	1	1	yes	characteristic, direct product factor
32	C₂×C₅	—	341	1	no	Hall
33	C₅	C₁₁×D₃₄₁	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	341	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁	D₃₄₁
commutator, cosocle, hypocenter	C₁₁×C₃₁	C₂×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₃₁	C₂
LCS	G ▷ C₁₁×C₃₁
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁²×C₃₁	C₂	semidirect
2. C₁₁×D₃₄₁	C₅	direct (N × H)
3. C₁₁²×C₃₁	C₂×C₅	semidirect
4. C₅×D₃₄₁	C₁₁	direct (N × H)
7. C₅×C₁₁×C₃₁	D₁₁	semidirect
8. C₅×C₁₁×C₃₁	C₂×C₁₁	semidirect
10. D₃₄₁	C₅×C₁₁	direct (N × H)
12. C₅×C₁₁²	D₃₁	semidirect
14. C₁₁×C₃₁	C₅×D₁₁	semidirect
15. C₁₁×C₃₁	C₂×C₅×C₁₁	semidirect
18. C₅×C₃₁	C₁₁×D₁₁	semidirect
19. C₁₁²	C₅×D₃₁	semidirect
24. C₅×C₁₁	C₁₁×D₃₁	semidirect
25. C₅×C₁₁	D₃₄₁	direct (N × H)
26. C₃₁	C₅×C₁₁×D₁₁	semidirect
30. C₁₁	C₅×C₁₁×D₃₁	semidirect
31. C₁₁	C₅×D₃₄₁	direct (N × H)
33. C₅	C₁₁×D₃₄₁	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×C₁₁²×C₃₁	2
C₁₁×D₃₄₁	5
C₅×D₃₄₁	11
C₅×C₁₁×D₃₁	11
C₅×C₁₁×D₁₁	31

Subgroups — C5×C11×D341 #49176014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×D₃₄₁ #49176014