Subgroups — C₂×C₁₁×C₂₉×C₅⋊D₅ #44542126

Order 31900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₉×C₅⋊D₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₁₁×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₁₁×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₅×C₁₁×C₂₉	—	5	6	no	maximal
5	D₅×C₁₁×C₂₉	—	5	12	no	—
6	C₂×C₅×C₁₁×C₂₉	D₅	1	6	yes	complemented
7	C₂×C₂₉×C₅⋊D₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×C₂₉	C₂×D₅	1	6	yes	complemented
9	C₂×C₅²×C₂₉	C₂×C₁₁	1	1	yes	characteristic, complemented
10	C₂₉×C₅⋊D₅	C₂×C₁₁	1	2	yes	direct product factor
11	C₂²×C₁₁×C₂₉	—	25	1	no	Hall
12	C₂×C₁₁×C₅⋊D₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅²×C₂₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₁×C₂₉	—	25	2	no	—
15	C₂×C₁₁×C₂₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor
16	C₂×D₅×C₂₉	—	5	6	no	—
17	C₂×C₅²×C₁₁	C₂×C₂₉	1	1	yes	characteristic, complemented
18	C₁₁×C₅⋊D₅	C₂×C₂₉	1	2	yes	direct product factor
19	C₁₁×C₂₉	C₂×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₂₉	D₅×C₁₁	1	6	yes	complemented
21	D₅×C₂₉	—	5	12	no	—
22	C₅²×C₁₁	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
23	C₂×D₅×C₁₁	—	5	6	no	—
24	C₅×C₂₉	C₂×D₅×C₁₁	1	6	yes	complemented
25	C₂²×C₂₉	—	25	1	no	Hall
26	C₂×C₅×C₁₁	D₅×C₂₉	1	6	yes	complemented
27	D₅×C₁₁	—	5	12	no	—
28	C₂×C₅⋊D₅	C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₂₉	—	25	2	no	—
30	C₂×C₂₉	C₁₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor
31	C₅×C₁₁	C₂×D₅×C₂₉	1	6	yes	complemented
32	C₂×C₅²	C₂×C₁₁×C₂₉	1	1	yes	characteristic, complemented
33	C₅⋊D₅	C₂×C₁₁×C₂₉	1	2	yes	direct product factor
34	C₂²×C₁₁	—	25	1	no	Hall
35	C₂₉	C₂×C₁₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
36	C₅²	C₂²×C₁₁×C₂₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₁	—	25	2	no	—
38	C₂×C₁₁	C₂₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor
39	C₂×D₅	—	5	6	no	—
40	C₁₁	C₂×C₂₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	D₅×C₁₁×C₂₉	1	6	yes	complemented
42	D₅	—	5	12	no	—
43	C₅	C₂×D₅×C₁₁×C₂₉	1	6	yes	complemented
44	C₂²	—	25	1	no	Sylow
45	C₂	—	25	2	no	—
46	C₂	C₁₁×C₂₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₂₉	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₁₁×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₁×C₂₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₁₁×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₂₉×C₅⋊D₅	C₂	direct (N × H)
2. C₂×C₅²×C₁₁×C₂₉	C₂	semidirect
3. C₅²×C₁₁×C₂₉	C₂²	semidirect
6. C₂×C₅×C₁₁×C₂₉	D₅	semidirect
7. C₂×C₂₉×C₅⋊D₅	C₁₁	direct (N × H)
8. C₅×C₁₁×C₂₉	C₂×D₅	semidirect
9. C₂×C₅²×C₂₉	C₂×C₁₁	semidirect
10. C₂₉×C₅⋊D₅	C₂×C₁₁	direct (N × H)
12. C₂×C₁₁×C₅⋊D₅	C₂₉	direct (N × H)
13. C₅²×C₂₉	C₂²×C₁₁	semidirect
15. C₂×C₁₁×C₂₉	C₅⋊D₅	direct (N × H)
17. C₂×C₅²×C₁₁	C₂×C₂₉	semidirect
18. C₁₁×C₅⋊D₅	C₂×C₂₉	direct (N × H)
19. C₁₁×C₂₉	C₂×C₅⋊D₅	direct (N × H)
20. C₂×C₅×C₂₉	D₅×C₁₁	semidirect
22. C₅²×C₁₁	C₂²×C₂₉	semidirect
24. C₅×C₂₉	C₂×D₅×C₁₁	semidirect
26. C₂×C₅×C₁₁	D₅×C₂₉	semidirect
28. C₂×C₅⋊D₅	C₁₁×C₂₉	direct (N × H)
30. C₂×C₂₉	C₁₁×C₅⋊D₅	direct (N × H)
31. C₅×C₁₁	C₂×D₅×C₂₉	semidirect
32. C₂×C₅²	C₂×C₁₁×C₂₉	semidirect
33. C₅⋊D₅	C₂×C₁₁×C₂₉	direct (N × H)
35. C₂₉	C₂×C₁₁×C₅⋊D₅	direct (N × H)
36. C₅²	C₂²×C₁₁×C₂₉	semidirect
38. C₂×C₁₁	C₂₉×C₅⋊D₅	direct (N × H)
40. C₁₁	C₂×C₂₉×C₅⋊D₅	direct (N × H)
41. C₂×C₅	D₅×C₁₁×C₂₉	semidirect
43. C₅	C₂×D₅×C₁₁×C₂₉	semidirect
46. C₂	C₁₁×C₂₉×C₅⋊D₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₂₉×C₅⋊D₅	2
C₂×C₅²×C₁₁×C₂₉	2
C₂×D₅×C₁₁×C₂₉	5
C₂×C₂₉×C₅⋊D₅	11
C₂×C₁₁×C₅⋊D₅	29

Subgroups — C2×C11×C29×C5⋊D5 #44542126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₂₉×C₅⋊D₅ #44542126