Subgroups — C₃²×C₅×D₉₅ #22555578

Order 8550.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×D₉₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₉₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₃²×C₅×D₁₉	—	5	1	no	maximal
5	C₃×C₅²×C₁₉	C₂×C₃	1	4	yes	complemented
6	C₅×D₉₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅×C₁₉	—	2	2	no	—
8	C₃²×C₅×C₁₉	D₅	1	1	yes	characteristic, complemented
9	C₃²×C₅×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×D₉₅	C₃×C₅	1	4	yes	direct product factor
11	C₃×C₅×D₁₉	—	5	4	no	—
12	C₅²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₅×D₅	—	19	1	no	maximal, Hall
14	C₃²×D₁₉	—	5	1	no	Hall
15	C₃×C₅×C₁₉	—	2	8	no	—
16	C₃×C₅×C₁₉	C₃×D₅	1	4	yes	complemented
17	C₃×C₅×C₁₉	C₂×C₃×C₅	1	4	yes	complemented
18	C₃²×C₅²	D₁₉	1	1	yes	characteristic, complemented, Hall
19	D₉₅	C₃²×C₅	1	1	yes	characteristic, direct product factor
20	C₅×D₁₉	—	5	1	no	—
21	C₃²×C₁₉	C₅×D₅	1	1	yes	characteristic, complemented, Hall
22	C₃×C₅×D₅	—	19	4	no	—
23	C₃×D₁₉	—	5	4	no	—
24	C₅×C₁₉	—	2	2	no	—
25	C₅×C₁₉	C₃²×D₅	1	1	yes	characteristic, complemented
26	C₅×C₁₉	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
27	C₂×C₃²×C₅	—	95	1	no	—
28	C₃²×D₅	—	19	1	no	—
29	C₃×C₅²	C₃×D₁₉	1	4	yes	complemented
30	C₃×C₁₉	C₃×C₅×D₅	1	4	yes	complemented
31	C₅×D₅	—	19	1	no	Hall
32	C₃²×C₅	—	2	2	no	—
33	C₃²×C₅	C₅×D₁₉	1	1	yes	characteristic, complemented
34	C₃²×C₅	D₉₅	1	1	yes	characteristic, direct product factor
35	D₁₉	—	5	1	no	Hall
36	C₂×C₃×C₅	—	95	4	no	—
37	C₃×D₅	—	19	4	no	—
38	C₅²	C₃²×D₁₉	1	1	yes	characteristic, complemented, Sylow
39	C₁₉	C₃²×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃²	—	95	1	no	Hall
41	C₃×C₅	—	2	8	no	—
42	C₃×C₅	C₃×C₅×D₁₉	1	4	yes	complemented
43	C₃×C₅	C₃×D₉₅	1	4	yes	direct product factor
44	C₂×C₅	—	95	1	no	—
45	D₅	—	19	1	no	—
46	C₃²	C₅×D₉₅	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₃	—	95	4	no	—
48	C₅	—	2	2	no	—
49	C₅	C₃²×C₅×D₁₉	1	1	yes	characteristic, complemented
50	C₅	C₃²×D₉₅	1	1	yes	characteristic, direct product factor
51	C₃	C₃×C₅×D₉₅	1	4	yes	direct product factor
52	C₂	—	95	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₅	D₉₅
commutator, hypocenter	C₅×C₁₉	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₉	C₂
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₃²×C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₁₉	C₂	semidirect
2. C₃×C₅×D₉₅	C₃	direct (N × H)
3. C₃²×D₉₅	C₅	direct (N × H)
5. C₃×C₅²×C₁₉	C₂×C₃	semidirect
6. C₅×D₉₅	C₃²	direct (N × H)
8. C₃²×C₅×C₁₉	D₅	semidirect
9. C₃²×C₅×C₁₉	C₂×C₅	semidirect
10. C₃×D₉₅	C₃×C₅	direct (N × H)
12. C₅²×C₁₉	C₂×C₃²	semidirect
16. C₃×C₅×C₁₉	C₃×D₅	semidirect
17. C₃×C₅×C₁₉	C₂×C₃×C₅	semidirect
18. C₃²×C₅²	D₁₉	semidirect
19. D₉₅	C₃²×C₅	direct (N × H)
21. C₃²×C₁₉	C₅×D₅	semidirect
25. C₅×C₁₉	C₃²×D₅	semidirect
26. C₅×C₁₉	C₂×C₃²×C₅	semidirect
29. C₃×C₅²	C₃×D₁₉	semidirect
30. C₃×C₁₉	C₃×C₅×D₅	semidirect
33. C₃²×C₅	C₅×D₁₉	semidirect
34. C₃²×C₅	D₉₅	direct (N × H)
38. C₅²	C₃²×D₁₉	semidirect
39. C₁₉	C₃²×C₅×D₅	semidirect
42. C₃×C₅	C₃×C₅×D₁₉	semidirect
43. C₃×C₅	C₃×D₉₅	direct (N × H)
46. C₃²	C₅×D₉₅	direct (N × H)
49. C₅	C₃²×C₅×D₁₉	semidirect
50. C₅	C₃²×D₉₅	direct (N × H)
51. C₃	C₃×C₅×D₉₅	direct (N × H)

Subgroups — C32×C5×D95 #22555578

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₅×D₉₅ #22555578