Subgroups — D₂₅×D₃₁₉ #44542003

Order 31900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₉₇₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₂₉×D₂₅	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	D₅×D₃₁₉	—	5	1	no	maximal
6	D₁₅₉₅	—	5	1	no	—
7	D₅×C₁₁×C₂₉	—	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	—	11	1	no	—
12	C₂₅×D₂₉	—	11	1	no	—
13	C₂₉×D₂₅	D₁₁	1	1	yes	characteristic, complemented
14	C₂×D₃₁₉	—	25	1	no	Hall
15	D₁₁×D₂₅	—	29	1	no	maximal, Hall
16	C₂₅×C₂₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁×C₂₉	—	25	1	no	—
18	D₃₁₉	—	25	1	no	—
19	D₃₁₉	D₂₅	1	1	yes	characteristic, direct product factor
20	D₅×D₂₉	—	55	1	no	—
21	D₂₇₅	—	29	1	no	—
22	D₁₁×C₂₅	—	29	1	no	—
23	C₁₁×D₂₅	D₂₉	1	1	yes	characteristic, complemented
24	C₁₁×C₂₉	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
25	D₁₄₅	—	55	1	no	—
26	C₅×D₂₉	—	11	1	no	—
27	D₅×C₂₉	—	5	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	—	145	1	no	—
33	C₅×D₁₁	—	29	1	no	—
34	D₅×C₁₁	—	5	1	no	—
35	C₂×D₂₅	—	319	1	no	Hall
36	C₂×C₂₉	—	25	1	no	—
37	D₂₉	—	11	1	no	—
38	D₂₉	—	275	1	no	—
39	C₅×C₁₁	D₅×D₂₉	1	1	yes	characteristic
40	C₂×C₂₅	—	319	1	no	—
41	D₂₅	—	319	1	no	—
42	D₂₅	D₃₁₉	1	1	yes	characteristic, direct product factor
43	C₂×D₁₁	—	725	1	no	Hall
44	C₂₉	D₁₁×D₂₅	1	1	yes	characteristic, complemented, Sylow
45	C₂₅	C₂×D₃₁₉	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₁₁	—	25	1	no	—
47	D₁₁	—	29	1	no	—
48	D₁₁	—	725	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	—	5	1	no	—
53	D₅	—	1595	1	no	—
54	C₅	D₅×D₃₁₉	1	1	yes	characteristic
55	C₂²	—	7975	1	no	Sylow
56	C₂	—	25	1	no	—
57	C₂	—	7975	1	no	—
58	C₂	—	319	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₁×C₂₅×C₂₉	C₂²
Frattini	C₅	D₅×D₃₁₉
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. D₇₉₇₅	C₂	semidirect
2. C₁₁×C₂₉×D₂₅	C₂	semidirect
3. C₂₅×D₃₁₉	C₂	semidirect
4. C₁₁×C₂₅×C₂₉	C₂²	semidirect
13. C₂₉×D₂₅	D₁₁	semidirect
16. C₂₅×C₂₉	C₂×D₁₁	semidirect
19. D₃₁₉	D₂₅	direct (N × H)
23. C₁₁×D₂₅	D₂₉	semidirect
24. C₁₁×C₂₉	C₂×D₂₅	semidirect
28. C₁₁×C₂₅	C₂×D₂₉	semidirect
42. D₂₅	D₃₁₉	direct (N × H)
44. C₂₉	D₁₁×D₂₅	semidirect
45. C₂₅	C₂×D₃₁₉	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
D₇₉₇₅	2
C₁₁×C₂₉×D₂₅	2
C₂₅×D₃₁₉	2
D₅×D₃₁₉	5
D₂₅×D₂₉	11
D₁₁×D₂₅	29

Subgroups — D25×D319 #44542003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₅×D₃₁₉ #44542003