Subgroups — C₃²×C₁₉×D₉₅ #44570624

Order 32490.

204 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₉×D₉₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₉×D₁₉	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₉²	C₂×C₃	1	4	yes	complemented
5	C₁₉×D₉₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₁₉²	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₉×D₁₉	—	5	4	no	—
8	C₅×C₁₉²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×D₉₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor
10	C₃²×D₅×C₁₉	—	19	1	no	maximal
11	C₃×C₁₉²	C₃×D₅	1	4	yes	complemented
12	C₃²×C₅×C₁₉	—	2	9	no	—
13	C₃²×C₅×C₁₉	D₁₉	1	1	yes	characteristic, complemented
14	C₃²×C₅×C₁₉	C₂×C₁₉	1	1	yes	characteristic, complemented
15	C₁₉×D₁₉	—	5	1	no	Hall
16	C₃×D₉₅	C₃×C₁₉	1	4	yes	direct product factor
17	C₃×D₅×C₁₉	—	19	4	no	—
18	C₁₉²	C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃²×C₁₉	—	95	1	no	—
20	C₃²×D₁₉	—	5	1	no	—
21	C₃×C₅×C₁₉	—	2	36	no	—
22	C₃×C₅×C₁₉	C₃×D₁₉	1	4	yes	complemented
23	C₃×C₅×C₁₉	C₂×C₃×C₁₉	1	4	yes	complemented
24	D₉₅	C₃²×C₁₉	1	1	yes	characteristic, direct product factor
25	D₅×C₁₉	—	19	1	no	—
26	C₃²×C₁₉	—	2	9	no	—
27	C₃²×C₁₉	D₅×C₁₉	1	1	yes	characteristic, complemented
28	C₃²×C₁₉	D₉₅	1	1	yes	characteristic, direct product factor
29	C₂×C₃×C₁₉	—	95	4	no	—
30	C₃×D₁₉	—	5	4	no	—
31	C₅×C₁₉	—	2	9	no	—
32	C₅×C₁₉	C₃²×D₁₉	1	1	yes	characteristic, complemented
33	C₅×C₁₉	C₂×C₃²×C₁₉	1	1	yes	characteristic, complemented
34	C₃²×D₅	—	19	1	no	Hall
35	C₃×C₁₉	—	2	36	no	—
36	C₃×C₁₉	C₃×D₅×C₁₉	1	4	yes	complemented
37	C₃×C₁₉	C₃×D₉₅	1	4	yes	direct product factor
38	C₃²×C₅	C₁₉×D₁₉	1	1	yes	characteristic, complemented, Hall
39	C₂×C₁₉	—	95	1	no	—
40	D₁₉	—	5	1	no	—
41	C₃×D₅	—	19	4	no	—
42	C₁₉	—	2	9	no	—
43	C₁₉	C₃²×D₅×C₁₉	1	1	yes	characteristic, complemented
44	C₁₉	C₃²×D₉₅	1	1	yes	characteristic, direct product factor
45	C₂×C₃²	—	95	1	no	Hall
46	C₃×C₅	C₃×C₁₉×D₁₉	1	4	yes	complemented
47	D₅	—	19	1	no	Hall
48	C₃²	C₁₉×D₉₅	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₃	—	95	4	no	—
50	C₅	C₃²×C₁₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
51	C₃	C₃×C₁₉×D₉₅	1	4	yes	direct product factor
52	C₂	—	95	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₁₉	D₉₅
commutator, cosocle, hypocenter	C₅×C₁₉	C₂×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₉²	C₂
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₃²×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₉²	C₂	semidirect
2. C₃×C₁₉×D₉₅	C₃	direct (N × H)
4. C₃×C₅×C₁₉²	C₂×C₃	semidirect
5. C₁₉×D₉₅	C₃²	direct (N × H)
6. C₃²×C₁₉²	D₅	semidirect
8. C₅×C₁₉²	C₂×C₃²	semidirect
9. C₃²×D₉₅	C₁₉	direct (N × H)
11. C₃×C₁₉²	C₃×D₅	semidirect
13. C₃²×C₅×C₁₉	D₁₉	semidirect
14. C₃²×C₅×C₁₉	C₂×C₁₉	semidirect
16. C₃×D₉₅	C₃×C₁₉	direct (N × H)
18. C₁₉²	C₃²×D₅	semidirect
22. C₃×C₅×C₁₉	C₃×D₁₉	semidirect
23. C₃×C₅×C₁₉	C₂×C₃×C₁₉	semidirect
24. D₉₅	C₃²×C₁₉	direct (N × H)
27. C₃²×C₁₉	D₅×C₁₉	semidirect
28. C₃²×C₁₉	D₉₅	direct (N × H)
32. C₅×C₁₉	C₃²×D₁₉	semidirect
33. C₅×C₁₉	C₂×C₃²×C₁₉	semidirect
36. C₃×C₁₉	C₃×D₅×C₁₉	semidirect
37. C₃×C₁₉	C₃×D₉₅	direct (N × H)
38. C₃²×C₅	C₁₉×D₁₉	semidirect
43. C₁₉	C₃²×D₅×C₁₉	semidirect
44. C₁₉	C₃²×D₉₅	direct (N × H)
46. C₃×C₅	C₃×C₁₉×D₁₉	semidirect
48. C₃²	C₁₉×D₉₅	direct (N × H)
50. C₅	C₃²×C₁₉×D₁₉	semidirect
51. C₃	C₃×C₁₉×D₉₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₉²	2
C₃×C₁₉×D₉₅	3
C₃²×C₁₉×D₁₉	5
C₃²×D₉₅	19
C₃²×D₅×C₁₉	19

Subgroups — C32×C19×D95 #44570624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₁₉×D₉₅ #44570624