Subgroups — D₂₇₅⋊D₂₉ #44542004

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×D₇₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₅×D₃₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₂₅×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅₅⋊D₂₉	—	5	1	no	maximal
6	C₂₉×D₅₅	—	5	1	no	—
7	C₁₁×D₁₄₅	—	5	1	no	—
8	C₅×D₃₁₉	D₅	1	1	yes	characteristic
9	D₂₅×D₂₉	—	11	1	no	maximal, Hall
10	C₅×C₁₁×C₂₉	C₂×D₅	1	1	yes	characteristic
11	D₇₂₅	D₁₁	1	1	yes	characteristic, complemented
12	C₂₅×D₂₉	—	11	1	no	—
13	C₂₉×D₂₅	—	11	1	no	—
14	D₁₁×D₂₉	—	25	1	no	Hall
15	D₁₁×D₂₅	—	29	1	no	maximal, Hall
16	C₂₅×C₂₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
17	D₃₁₉	D₂₅	1	1	yes	characteristic, complemented
18	C₁₁×D₂₉	—	25	1	no	—
19	D₁₁×C₂₉	—	25	1	no	—
20	D₅×D₂₉	—	55	1	no	—
21	D₂₇₅	D₂₉	1	1	yes	characteristic, complemented
22	D₁₁×C₂₅	—	29	1	no	—
23	C₁₁×D₂₅	—	29	1	no	—
24	C₁₁×C₂₉	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
25	D₁₄₅	—	5	1	no	—
26	C₅×D₂₉	—	11	1	no	—
27	D₅×C₂₉	—	55	1	no	—
28	C₁₁×C₂₅	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
29	D₅×D₁₁	—	145	1	no	—
30	C₅×C₂₉	D₅×D₁₁	1	1	yes	characteristic
31	C₂×D₂₉	—	275	1	no	Hall
32	D₅₅	—	5	1	no	—
33	C₅×D₁₁	—	29	1	no	—
34	D₅×C₁₁	—	145	1	no	—
35	C₂×D₂₅	—	319	1	no	Hall
36	C₂×C₂₉	—	275	1	no	—
37	D₂₉	—	11	1	no	—
38	D₂₉	—	25	1	no	—
39	C₅×C₁₁	D₅×D₂₉	1	1	yes	characteristic
40	C₂×C₂₅	—	319	1	no	—
41	D₂₅	—	11	1	no	—
42	D₂₅	—	29	1	no	—
43	C₂×D₁₁	—	725	1	no	Hall
44	C₂₉	D₁₁×D₂₅	1	1	yes	characteristic, complemented, Sylow
45	C₂₅	D₁₁×D₂₉	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₁₁	—	725	1	no	—
47	D₁₁	—	25	1	no	—
48	D₁₁	—	29	1	no	—
49	C₂×D₅	—	1595	1	no	—
50	C₁₁	D₂₅×D₂₉	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₅	—	319	1	no	—
52	D₅	—	55	1	no	—
53	D₅	—	145	1	no	—
54	C₅	D₅₅⋊D₂₉	1	1	yes	characteristic
55	C₂²	—	7975	1	no	Sylow
56	C₂	—	275	1	no	—
57	C₂	—	319	1	no	—
58	C₂	—	725	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₁×C₂₅×C₂₉	C₂²
Frattini	C₅	D₅₅⋊D₂₉
socle	C₅×C₁₁×C₂₉	C₂×D₅
LCS	G ▷ C₁₁×C₂₅×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₉×D₂₇₅	C₂	semidirect
2. C₁₁×D₇₂₅	C₂	semidirect
3. C₂₅×D₃₁₉	C₂	semidirect
4. C₁₁×C₂₅×C₂₉	C₂²	semidirect
11. D₇₂₅	D₁₁	semidirect
16. C₂₅×C₂₉	C₂×D₁₁	semidirect
17. D₃₁₉	D₂₅	semidirect
21. D₂₇₅	D₂₉	semidirect
24. C₁₁×C₂₉	C₂×D₂₅	semidirect
28. C₁₁×C₂₅	C₂×D₂₉	semidirect
44. C₂₉	D₁₁×D₂₅	semidirect
45. C₂₅	D₁₁×D₂₉	semidirect
50. C₁₁	D₂₅×D₂₉	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×D₇₂₅	2
C₂₅×D₃₁₉	2
D₅₅⋊D₂₉	5
D₂₅×D₂₉	11
D₁₁×D₂₅	29

Subgroups — D275⋊D29 #44542004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₇₅⋊D₂₉ #44542004