Subgroups — D₅²×C₁₁×C₂₉ #44542087

Order 31900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×C₁₁×C₂₉	C₂	1	2	yes	maximal, complemented
2	C₁₁×C₂₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₁₁×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₅×C₁₁×C₂₉	—	5	2	no	maximal
5	D₅×C₁₁×C₂₉	—	5	2	no	—
6	D₅×C₁₁×C₂₉	—	10	2	no	—
7	D₅×C₁₁×C₂₉	D₅	1	2	yes	direct product factor
8	C₂×C₅×C₁₁×C₂₉	—	5	2	no	—
9	D₅²×C₂₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×C₁₁×C₂₉	—	2	2	no	—
11	C₅×C₁₁×C₂₉	C₂×D₅	1	2	yes	complemented
12	C₂₉×C₅⋊D₅	C₂×C₁₁	1	1	yes	characteristic, complemented
13	C₅×D₅×C₂₉	C₂×C₁₁	1	2	yes	complemented
14	C₂²×C₁₁×C₂₉	—	25	1	no	Hall
15	D₅²×C₁₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₅²×C₂₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁×C₂₉	—	5	2	no	—
18	C₂×C₁₁×C₂₉	—	25	1	no	—
19	C₂×D₅×C₂₉	—	5	2	no	—
20	C₁₁×C₅⋊D₅	C₂×C₂₉	1	1	yes	characteristic, complemented
21	C₅×D₅×C₁₁	C₂×C₂₉	1	2	yes	complemented
22	C₁₁×C₂₉	D₅²	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₅×C₂₉	—	5	2	no	—
24	D₅×C₂₉	—	5	2	no	—
25	D₅×C₂₉	—	10	2	no	—
26	D₅×C₂₉	D₅×C₁₁	1	2	yes	direct product factor
27	C₅²×C₁₁	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
28	C₂×D₅×C₁₁	—	5	2	no	—
29	C₅×C₂₉	—	2	2	no	—
30	C₅×C₂₉	C₂×D₅×C₁₁	1	2	yes	complemented
31	C₂²×C₂₉	—	25	1	no	Hall
32	C₂×C₅×C₁₁	—	5	2	no	—
33	D₅×C₁₁	—	5	2	no	—
34	D₅×C₁₁	—	10	2	no	—
35	D₅×C₁₁	D₅×C₂₉	1	2	yes	direct product factor
36	D₅²	C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₂₉	—	5	2	no	—
38	C₂×C₂₉	—	25	1	no	—
39	C₅×C₁₁	—	2	2	no	—
40	C₅×C₁₁	C₂×D₅×C₂₉	1	2	yes	complemented
41	C₅⋊D₅	C₂×C₁₁×C₂₉	1	1	yes	characteristic, complemented
42	C₅×D₅	C₂×C₁₁×C₂₉	1	2	yes	complemented
43	C₂²×C₁₁	—	25	1	no	Hall
44	C₂₉	D₅²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₅²	C₂²×C₁₁×C₂₉	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₁₁	—	5	2	no	—
47	C₂×C₁₁	—	25	1	no	—
48	C₂×D₅	—	5	2	no	—
49	C₁₁	D₅²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₅	—	5	2	no	—
51	D₅	—	5	2	no	—
52	D₅	—	10	2	no	—
53	D₅	D₅×C₁₁×C₂₉	1	2	yes	direct product factor
54	C₅	—	2	2	no	—
55	C₅	C₂×D₅×C₁₁×C₂₉	1	2	yes	complemented
56	C₂²	—	25	1	no	Sylow
57	C₂	—	5	2	no	—
58	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₂₉	D₅²
commutator, cosocle, hypocenter	C₅²	C₂²×C₁₁×C₂₉
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₂₉	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₁₁×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₅×D₅×C₁₁×C₂₉	C₂	semidirect
2. C₁₁×C₂₉×C₅⋊D₅	C₂	semidirect
3. C₅²×C₁₁×C₂₉	C₂²	semidirect
7. D₅×C₁₁×C₂₉	D₅	direct (N × H)
9. D₅²×C₂₉	C₁₁	direct (N × H)
11. C₅×C₁₁×C₂₉	C₂×D₅	semidirect
12. C₂₉×C₅⋊D₅	C₂×C₁₁	semidirect
13. C₅×D₅×C₂₉	C₂×C₁₁	semidirect
15. D₅²×C₁₁	C₂₉	direct (N × H)
16. C₅²×C₂₉	C₂²×C₁₁	semidirect
20. C₁₁×C₅⋊D₅	C₂×C₂₉	semidirect
21. C₅×D₅×C₁₁	C₂×C₂₉	semidirect
22. C₁₁×C₂₉	D₅²	direct (N × H)
26. D₅×C₂₉	D₅×C₁₁	direct (N × H)
27. C₅²×C₁₁	C₂²×C₂₉	semidirect
30. C₅×C₂₉	C₂×D₅×C₁₁	semidirect
35. D₅×C₁₁	D₅×C₂₉	direct (N × H)
36. D₅²	C₁₁×C₂₉	direct (N × H)
40. C₅×C₁₁	C₂×D₅×C₂₉	semidirect
41. C₅⋊D₅	C₂×C₁₁×C₂₉	semidirect
42. C₅×D₅	C₂×C₁₁×C₂₉	semidirect
44. C₂₉	D₅²×C₁₁	direct (N × H)
45. C₅²	C₂²×C₁₁×C₂₉	semidirect
49. C₁₁	D₅²×C₂₉	direct (N × H)
53. D₅	D₅×C₁₁×C₂₉	direct (N × H)
55. C₅	C₂×D₅×C₁₁×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₅×C₁₁×C₂₉	2
C₁₁×C₂₉×C₅⋊D₅	2
C₂×D₅×C₁₁×C₂₉	5
D₅²×C₂₉	11
D₅²×C₁₁	29

Subgroups — D52×C11×C29 #44542087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅²×C₁₁×C₂₉ #44542087