Subgroups — C₂×C₁₉×D₂₇₅ #35229849

Order 20900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₂₇₅
commutator, cosocle, hypocenter	C₁₁×C₂₅	C₂²×C₁₉
Frattini	C₅	C₂×C₁₉×D₅₅
Fitting	C₂×C₁₁×C₁₉×C₂₅	C₂
socle	C₂×C₅×C₁₁×C₁₉	D₅
LCS	G ▷ C₁₁×C₂₅
UCS	C₁ ◁ C₂×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×D₂₇₅	C₂	direct (N × H)
2. C₂×C₁₁×C₁₉×C₂₅	C₂	semidirect
3. C₁₁×C₁₉×C₂₅	C₂²	semidirect
8. C₂×D₂₇₅	C₁₉	direct (N × H)
10. C₂×C₁₉×C₂₅	D₁₁	semidirect
13. C₂×C₁₁×C₂₅	C₂×C₁₉	semidirect
14. D₂₇₅	C₂×C₁₉	direct (N × H)
15. C₁₉×C₂₅	C₂×D₁₁	semidirect
16. C₂×C₁₁×C₁₉	D₂₅	semidirect
19. C₁₁×C₂₅	C₂²×C₁₉	semidirect
21. C₁₁×C₁₉	C₂×D₂₅	semidirect
30. C₂×C₂₅	C₁₉×D₁₁	semidirect
34. C₂×C₁₉	D₂₇₅	direct (N × H)
35. C₂₅	C₂×C₁₉×D₁₁	semidirect
36. C₂×C₁₁	C₁₉×D₂₅	semidirect
39. C₁₉	C₂×D₂₇₅	direct (N × H)
40. C₁₁	C₂×C₁₉×D₂₅	semidirect
46. C₂	C₁₉×D₂₇₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×D₂₇₅	2
C₂×C₁₁×C₁₉×C₂₅	2
C₂×C₁₉×D₅₅	5
C₂×C₁₉×D₂₅	11
C₂×D₂₇₅	19

Subgroups — C2×C19×D275 #35229849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×D₂₇₅ #35229849