Subgroups — D₁₁×C₂₉×D₂₅ #44542001

Order 31900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×D₂₇₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₂₉×D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₁×C₂₅×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₂₅×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₁₁×C₂₉	—	5	1	no	maximal
6	C₂₉×D₅₅	—	5	1	no	—
7	D₅×C₁₁×C₂₉	—	5	1	no	—
8	C₅×D₁₁×C₂₉	D₅	1	1	yes	characteristic
9	C₂×C₂₉×D₂₅	—	11	1	no	maximal, Hall
10	C₅×C₁₁×C₂₉	C₂×D₅	1	1	yes	characteristic
11	C₂×C₂₅×C₂₉	—	11	1	no	—
12	C₂₉×D₂₅	—	11	1	no	—
13	C₂₉×D₂₅	D₁₁	1	1	yes	characteristic, direct product factor
14	C₂×D₁₁×C₂₉	—	25	1	no	Hall
15	D₁₁×D₂₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂₅×C₂₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁×C₂₉	—	25	1	no	—
18	D₁₁×C₂₉	—	25	1	no	—
19	D₁₁×C₂₉	D₂₅	1	1	yes	characteristic, direct product factor
20	C₂×D₅×C₂₉	—	55	1	no	—
21	D₂₇₅	C₂×C₂₉	1	1	yes	characteristic, complemented
22	D₁₁×C₂₅	C₂×C₂₉	1	1	yes	characteristic, complemented
23	C₁₁×D₂₅	C₂×C₂₉	1	1	yes	characteristic, complemented
24	C₁₁×C₂₉	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅×C₂₉	—	11	1	no	—
26	D₅×C₂₉	—	5	1	no	—
27	D₅×C₂₉	—	55	1	no	—
28	C₁₁×C₂₅	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
29	D₅×D₁₁	—	5	1	no	—
30	C₅×C₂₉	D₅×D₁₁	1	1	yes	characteristic
31	C₂²×C₂₉	—	275	1	no	Hall
32	D₅₅	—	5	1	no	—
33	C₅×D₁₁	D₅×C₂₉	1	1	yes	characteristic
34	D₅×C₁₁	—	5	1	no	—
35	C₂×D₂₅	—	11	1	no	Hall
36	C₂×C₂₉	—	11	1	no	—
37	C₂×C₂₉	—	275	1	no	—
38	C₂×C₂₉	—	25	1	no	—
39	C₅×C₁₁	C₂×D₅×C₂₉	1	1	yes	characteristic
40	C₂×C₂₅	—	11	1	no	—
41	D₂₅	—	11	1	no	—
42	D₂₅	D₁₁×C₂₉	1	1	yes	characteristic, direct product factor
43	C₂×D₁₁	—	25	1	no	Hall
44	C₂₉	D₁₁×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
45	C₂₅	C₂×D₁₁×C₂₉	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₁₁	—	25	1	no	—
47	D₁₁	—	25	1	no	—
48	D₁₁	C₂₉×D₂₅	1	1	yes	characteristic, direct product factor
49	C₂×D₅	—	55	1	no	—
50	C₁₁	C₂×C₂₉×D₂₅	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₅	—	11	1	no	—
52	D₅	—	5	1	no	—
53	D₅	—	55	1	no	—
54	C₅	D₅×D₁₁×C₂₉	1	1	yes	characteristic
55	C₂²	—	275	1	no	Sylow
56	C₂	—	11	1	no	—
57	C₂	—	275	1	no	—
58	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	D₁₁×D₂₅
commutator, cosocle, hypocenter	C₁₁×C₂₅	C₂²×C₂₉
Frattini	C₅	D₅×D₁₁×C₂₉
Fitting	C₁₁×C₂₅×C₂₉	C₂²
socle	C₅×C₁₁×C₂₉	C₂×D₅
LCS	G ▷ C₁₁×C₂₅
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×D₂₇₅	C₂	semidirect
2. C₁₁×C₂₉×D₂₅	C₂	semidirect
3. D₁₁×C₂₅×C₂₉	C₂	semidirect
4. C₁₁×C₂₅×C₂₉	C₂²	semidirect
13. C₂₉×D₂₅	D₁₁	direct (N × H)
15. D₁₁×D₂₅	C₂₉	direct (N × H)
16. C₂₅×C₂₉	C₂×D₁₁	semidirect
19. D₁₁×C₂₉	D₂₅	direct (N × H)
21. D₂₇₅	C₂×C₂₉	semidirect
22. D₁₁×C₂₅	C₂×C₂₉	semidirect
23. C₁₁×D₂₅	C₂×C₂₉	semidirect
24. C₁₁×C₂₉	C₂×D₂₅	semidirect
28. C₁₁×C₂₅	C₂²×C₂₉	semidirect
42. D₂₅	D₁₁×C₂₉	direct (N × H)
44. C₂₉	D₁₁×D₂₅	direct (N × H)
45. C₂₅	C₂×D₁₁×C₂₉	semidirect
48. D₁₁	C₂₉×D₂₅	direct (N × H)
50. C₁₁	C₂×C₂₉×D₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×D₂₇₅	2
C₁₁×C₂₉×D₂₅	2
D₁₁×C₂₅×C₂₉	2
D₅×D₁₁×C₂₉	5
C₂×C₂₉×D₂₅	11
D₁₁×D₂₅	29

Subgroups — D11×C29×D25 #44542001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×C₂₉×D₂₅ #44542001