Subgroups — C₁₉×D₁₁×D₂₅ #35229844

Order 20900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₂₇₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₁₉×D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×D₁₁×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₁₉×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×C₁₉×D₁₁	—	5	1	no	maximal
6	C₁₉×D₅₅	—	5	1	no	—
7	D₅×C₁₁×C₁₉	—	5	1	no	—
8	C₅×C₁₉×D₁₁	D₅	1	1	yes	characteristic
9	C₂×C₁₉×D₂₅	—	11	1	no	maximal, Hall
10	D₁₁×D₂₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁×C₁₉	C₂×D₅	1	1	yes	characteristic
12	C₂×C₁₉×C₂₅	—	11	1	no	—
13	C₁₉×D₂₅	—	11	1	no	—
14	C₁₉×D₂₅	D₁₁	1	1	yes	characteristic, direct product factor
15	C₂×C₁₉×D₁₁	—	25	1	no	Hall
16	D₂₇₅	C₂×C₁₉	1	1	yes	characteristic, complemented
17	D₁₁×C₂₅	C₂×C₁₉	1	1	yes	characteristic, complemented
18	C₁₁×D₂₅	C₂×C₁₉	1	1	yes	characteristic, complemented
19	C₁₉×C₂₅	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₁×C₁₉	—	25	1	no	—
21	C₁₉×D₁₁	—	25	1	no	—
22	C₁₉×D₁₁	D₂₅	1	1	yes	characteristic, direct product factor
23	C₂×D₅×C₁₉	—	55	1	no	—
24	C₁₁×C₂₅	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
25	D₅×D₁₁	—	5	1	no	—
26	C₁₁×C₁₉	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×C₁₉	—	11	1	no	—
28	D₅×C₁₉	—	5	1	no	—
29	D₅×C₁₉	—	55	1	no	—
30	D₅₅	—	5	1	no	—
31	C₅×D₁₁	D₅×C₁₉	1	1	yes	characteristic
32	D₅×C₁₁	—	5	1	no	—
33	C₂×D₂₅	—	11	1	no	Hall
34	C₅×C₁₉	D₅×D₁₁	1	1	yes	characteristic
35	C₂²×C₁₉	—	275	1	no	Hall
36	C₅×C₁₁	C₂×D₅×C₁₉	1	1	yes	characteristic
37	C₂×C₂₅	—	11	1	no	—
38	D₂₅	—	11	1	no	—
39	D₂₅	C₁₉×D₁₁	1	1	yes	characteristic, direct product factor
40	C₂×D₁₁	—	25	1	no	Hall
41	C₂×C₁₉	—	11	1	no	—
42	C₂×C₁₉	—	275	1	no	—
43	C₂×C₁₉	—	25	1	no	—
44	C₂₅	C₂×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₁	—	25	1	no	—
46	D₁₁	—	25	1	no	—
47	D₁₁	C₁₉×D₂₅	1	1	yes	characteristic, direct product factor
48	C₂×D₅	—	55	1	no	—
49	C₁₉	D₁₁×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
50	C₁₁	C₂×C₁₉×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×C₁₉×D₁₁	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	C₁₉	D₁₁×D₂₅
commutator, cosocle, hypocenter	C₁₁×C₂₅	C₂²×C₁₉
Frattini	C₅	D₅×C₁₉×D₁₁
Fitting	C₁₁×C₁₉×C₂₅	C₂²
socle	C₅×C₁₁×C₁₉	C₂×D₅
LCS	G ▷ C₁₁×C₂₅
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×D₂₇₅	C₂	semidirect
2. C₁₁×C₁₉×D₂₅	C₂	semidirect
3. C₁₉×D₁₁×C₂₅	C₂	semidirect
4. C₁₁×C₁₉×C₂₅	C₂²	semidirect
10. D₁₁×D₂₅	C₁₉	direct (N × H)
14. C₁₉×D₂₅	D₁₁	direct (N × H)
16. D₂₇₅	C₂×C₁₉	semidirect
17. D₁₁×C₂₅	C₂×C₁₉	semidirect
18. C₁₁×D₂₅	C₂×C₁₉	semidirect
19. C₁₉×C₂₅	C₂×D₁₁	semidirect
22. C₁₉×D₁₁	D₂₅	direct (N × H)
24. C₁₁×C₂₅	C₂²×C₁₉	semidirect
26. C₁₁×C₁₉	C₂×D₂₅	semidirect
39. D₂₅	C₁₉×D₁₁	direct (N × H)
44. C₂₅	C₂×C₁₉×D₁₁	semidirect
47. D₁₁	C₁₉×D₂₅	direct (N × H)
49. C₁₉	D₁₁×D₂₅	direct (N × H)
50. C₁₁	C₂×C₁₉×D₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×D₂₇₅	2
C₁₁×C₁₉×D₂₅	2
C₁₉×D₁₁×C₂₅	2
D₅×C₁₉×D₁₁	5
C₂×C₁₉×D₂₅	11
D₁₁×D₂₅	19

Subgroups — C19×D11×D25 #35229844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×D₁₁×D₂₅ #35229844