Subgroups — C₃×C₅×D₁₉₅ #19154392

Order 5850.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₉₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅×D₆₅	—	3	1	no	maximal
4	C₃×D₁₉₅	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₅×D₃₉	—	5	1	no	maximal
6	C₃×C₅²×C₁₃	—	2	1	no	—
7	C₃×C₅²×C₁₃	D₃	1	1	yes	characteristic, complemented
8	C₃×C₅²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₆₅	—	3	1	no	Hall
10	C₃²×C₅×C₁₃	—	2	2	no	—
11	C₃²×C₅×C₁₃	D₅	1	1	yes	characteristic, complemented
12	C₃²×C₅×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃×C₅×D₁₅	—	13	1	no	maximal, Hall
14	D₁₉₅	C₃×C₅	1	1	yes	characteristic, direct product factor
15	C₅×D₃₉	—	5	1	no	—
16	C₃×D₆₅	—	3	1	no	—
17	C₃×C₅×D₁₃	—	15	1	no	—
18	C₅²×C₁₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
19	C₃×D₃₉	—	5	1	no	Hall
20	C₃²×C₅²	D₁₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₃	—	2	4	no	—
22	C₃×C₅×C₁₃	—	2	2	no	—
23	C₃×C₅×C₁₃	—	2	2	no	—
24	C₃×C₅×C₁₃	—	2	1	no	—
25	C₃×C₅×C₁₃	—	2	1	no	—
26	C₃×C₅×C₁₃	C₅×D₃	1	1	yes	characteristic, complemented
27	C₃×C₅×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented
28	C₃×C₅×C₁₃	D₁₅	1	1	yes	characteristic, complemented
29	C₃×C₅×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
30	C₅×D₁₅	—	13	1	no	—
31	C₃×C₅×D₅	—	39	1	no	—
32	D₆₅	—	3	1	no	—
33	C₅×D₁₃	—	15	1	no	—
34	C₃²×C₁₃	C₅×D₅	1	1	yes	characteristic, complemented, Hall
35	C₃×D₁₅	—	13	1	no	—
36	C₃×C₅×D₃	—	65	1	no	—
37	D₃₉	—	5	1	no	—
38	C₃×D₁₃	—	15	1	no	—
39	C₃×C₅²	—	2	1	no	—
40	C₃×C₅²	C₃×D₁₃	1	1	yes	characteristic, complemented
41	C₃×C₅²	D₃₉	1	1	yes	characteristic, complemented
42	C₅×C₁₃	—	2	2	no	—
43	C₅×C₁₃	C₃×C₅×D₃	1	1	yes	characteristic, complemented
44	C₅×C₁₃	C₃×D₁₅	1	1	yes	characteristic, complemented
45	C₅×D₅	—	39	1	no	Hall
46	C₃²×C₅	—	2	2	no	—
47	C₃²×C₅	C₅×D₁₃	1	1	yes	characteristic, complemented
48	C₃²×C₅	D₆₅	1	1	yes	characteristic, complemented
49	C₃×C₁₃	—	2	1	no	—
50	C₃×C₁₃	C₃×C₅×D₅	1	1	yes	characteristic, complemented
51	C₃×C₁₃	C₅×D₁₅	1	1	yes	characteristic, complemented
52	C₂×C₃×C₅	—	195	1	no	—
53	D₁₅	—	13	1	no	—
54	C₃×D₅	—	39	1	no	—
55	C₅×D₃	—	65	1	no	—
56	D₁₃	—	15	1	no	Hall
57	C₅²	C₃×D₃₉	1	1	yes	characteristic, complemented, Sylow
58	C₃×D₃	—	65	1	no	Hall
59	C₃×C₅	—	2	4	no	—
60	C₃×C₅	—	2	1	no	—
61	C₃×C₅	—	2	1	no	—
62	C₃×C₅	—	2	2	no	—
63	C₃×C₅	—	2	2	no	—
64	C₃×C₅	C₃×C₅×D₁₃	1	1	yes	characteristic, complemented
65	C₃×C₅	C₃×D₆₅	1	1	yes	characteristic, complemented
66	C₃×C₅	C₅×D₃₉	1	1	yes	characteristic, complemented
67	C₃×C₅	D₁₉₅	1	1	yes	characteristic, direct product factor
68	C₁₃	C₃×C₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
69	C₂×C₅	—	195	1	no	—
70	D₅	—	39	1	no	—
71	C₃²	C₅×D₆₅	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	195	1	no	—
73	D₃	—	65	1	no	—
74	C₅	—	2	2	no	—
75	C₅	C₃×C₅×D₃₉	1	1	yes	characteristic, complemented
76	C₅	C₃×D₁₉₅	1	1	yes	characteristic, direct product factor
77	C₃	—	2	1	no	—
78	C₃	C₃×C₅×D₆₅	1	1	yes	characteristic, complemented
79	C₃	C₅×D₁₉₅	1	1	yes	characteristic, direct product factor
80	C₂	—	195	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	D₁₉₅
commutator, hypocenter	C₃×C₅×C₁₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₃	C₂
LCS	G ▷ C₃×C₅×C₁₃
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₁₃	C₂	semidirect
2. C₅×D₁₉₅	C₃	direct (N × H)
4. C₃×D₁₉₅	C₅	direct (N × H)
7. C₃×C₅²×C₁₃	D₃	semidirect
8. C₃×C₅²×C₁₃	C₂×C₃	semidirect
11. C₃²×C₅×C₁₃	D₅	semidirect
12. C₃²×C₅×C₁₃	C₂×C₅	semidirect
14. D₁₉₅	C₃×C₅	direct (N × H)
18. C₅²×C₁₃	C₃×D₃	semidirect
20. C₃²×C₅²	D₁₃	semidirect
26. C₃×C₅×C₁₃	C₅×D₃	semidirect
27. C₃×C₅×C₁₃	C₃×D₅	semidirect
28. C₃×C₅×C₁₃	D₁₅	semidirect
29. C₃×C₅×C₁₃	C₂×C₃×C₅	semidirect
34. C₃²×C₁₃	C₅×D₅	semidirect
40. C₃×C₅²	C₃×D₁₃	semidirect
41. C₃×C₅²	D₃₉	semidirect
43. C₅×C₁₃	C₃×C₅×D₃	semidirect
44. C₅×C₁₃	C₃×D₁₅	semidirect
47. C₃²×C₅	C₅×D₁₃	semidirect
48. C₃²×C₅	D₆₅	semidirect
50. C₃×C₁₃	C₃×C₅×D₅	semidirect
51. C₃×C₁₃	C₅×D₁₅	semidirect
57. C₅²	C₃×D₃₉	semidirect
64. C₃×C₅	C₃×C₅×D₁₃	semidirect
65. C₃×C₅	C₃×D₆₅	semidirect
66. C₃×C₅	C₅×D₃₉	semidirect
67. C₃×C₅	D₁₉₅	direct (N × H)
68. C₁₃	C₃×C₅×D₁₅	semidirect
71. C₃²	C₅×D₆₅	semidirect
75. C₅	C₃×C₅×D₃₉	semidirect
76. C₅	C₃×D₁₉₅	direct (N × H)
78. C₃	C₃×C₅×D₆₅	semidirect
79. C₃	C₅×D₁₉₅	direct (N × H)

Subgroups — C3×C5×D195 #19154392

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₅×D₁₉₅ #19154392