Subgroups — C₃×D₉₅⋊D₂₉ #45683306

Order 33060.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×D₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₉×D₁₄₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₅₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₉₅⋊D₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₉×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₁₉×D₂₉	—	5	1	no	maximal, Hall
7	C₂₉×D₉₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₉×D₁₄₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₅₅₁	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₅₅₁	D₅	1	1	yes	characteristic, complemented
11	C₃×C₂₉×D₁₉	—	5	1	no	—
12	C₃×C₁₉×D₂₉	—	5	1	no	—
13	C₅×C₁₉×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	D₁₉×D₂₉	—	5	1	no	Hall
15	C₃×D₅×D₂₉	—	19	1	no	maximal, Hall
16	C₃×C₁₉×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₃×D₅×D₁₉	—	29	1	no	maximal, Hall
18	D₅₅₁	C₃×D₅	1	1	yes	characteristic, complemented
19	C₁₉×D₂₉	—	5	1	no	—
20	C₂₉×D₁₉	—	5	1	no	—
21	C₃×D₁₄₅	D₁₉	1	1	yes	characteristic, complemented
22	C₃×D₅×C₂₉	—	19	1	no	—
23	C₃×C₅×D₂₉	—	19	1	no	—
24	D₅×D₂₉	—	19	1	no	Hall
25	C₃×D₉₅	D₂₉	1	1	yes	characteristic, complemented
26	C₃×D₅×C₁₉	—	29	1	no	—
27	C₃×C₅×D₁₉	—	29	1	no	—
28	C₁₉×C₂₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
29	C₃×C₅×C₂₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
30	D₅×D₁₉	—	29	1	no	Hall
31	C₂×C₃×D₂₉	—	95	1	no	Hall
32	D₁₄₅	C₃×D₁₉	1	1	yes	characteristic, complemented
33	C₅×D₂₉	—	19	1	no	—
34	D₅×C₂₉	—	19	1	no	—
35	C₃×C₅×C₁₉	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×D₁₉	—	145	1	no	Hall
37	D₉₅	C₃×D₂₉	1	1	yes	characteristic, complemented
38	C₅×D₁₉	—	29	1	no	—
39	D₅×C₁₉	—	29	1	no	—
40	C₂×C₃×C₂₉	—	95	1	no	—
41	C₃×D₂₉	—	5	1	no	—
42	C₃×D₂₉	—	19	1	no	—
43	C₅×C₂₉	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented, Hall
44	C₂×D₂₉	—	95	1	no	Hall
45	C₂×C₃×C₁₉	—	145	1	no	—
46	C₃×D₁₉	—	5	1	no	—
47	C₃×D₁₉	—	29	1	no	—
48	C₅×C₁₉	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
49	C₃×C₂₉	D₅×D₁₉	1	1	yes	characteristic, complemented, Hall
50	C₂×D₁₉	—	145	1	no	Hall
51	C₂×C₃×D₅	—	551	1	no	Hall
52	C₂×C₂₉	—	95	1	no	—
53	D₂₉	—	5	1	no	—
54	D₂₉	—	19	1	no	—
55	C₃×C₁₉	D₅×D₂₉	1	1	yes	characteristic, complemented, Hall
56	C₂×C₁₉	—	145	1	no	—
57	D₁₉	—	5	1	no	—
58	D₁₉	—	29	1	no	—
59	C₂×C₃×C₅	—	551	1	no	—
60	C₃×D₅	—	19	1	no	—
61	C₃×D₅	—	29	1	no	—
62	C₂₉	C₃×D₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	551	1	no	Hall
64	C₁₉	C₃×D₅×D₂₉	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	D₁₉×D₂₉	1	1	yes	characteristic, complemented, Hall
66	C₂²×C₃	—	2755	1	no	Hall
67	C₂×C₅	—	551	1	no	—
68	D₅	—	19	1	no	—
69	D₅	—	29	1	no	—
70	C₂×C₃	—	551	1	no	—
71	C₂×C₃	—	95	1	no	—
72	C₂×C₃	—	145	1	no	—
73	C₅	C₃×D₁₉×D₂₉	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	2755	1	no	Sylow
75	C₃	D₉₅⋊D₂₉	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	551	1	no	—
77	C₂	—	95	1	no	—
78	C₂	—	145	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₉₅⋊D₂₉
commutator, cosocle, hypocenter	C₅×C₁₉×C₂₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉×C₂₉	C₂²
LCS	G ▷ C₅×C₁₉×C₂₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₉×D₉₅	C₂	semidirect
2. C₃×C₁₉×D₁₄₅	C₂	semidirect
3. C₃×C₅×D₅₅₁	C₂	semidirect
4. D₉₅⋊D₂₉	C₃	direct (N × H)
5. C₃×C₅×C₁₉×C₂₉	C₂²	semidirect
7. C₂₉×D₉₅	C₂×C₃	semidirect
8. C₁₉×D₁₄₅	C₂×C₃	semidirect
9. C₅×D₅₅₁	C₂×C₃	semidirect
10. C₃×D₅₅₁	D₅	semidirect
13. C₅×C₁₉×C₂₉	C₂²×C₃	semidirect
16. C₃×C₁₉×C₂₉	C₂×D₅	semidirect
18. D₅₅₁	C₃×D₅	semidirect
21. C₃×D₁₄₅	D₁₉	semidirect
25. C₃×D₉₅	D₂₉	semidirect
28. C₁₉×C₂₉	C₂×C₃×D₅	semidirect
29. C₃×C₅×C₂₉	C₂×D₁₉	semidirect
32. D₁₄₅	C₃×D₁₉	semidirect
35. C₃×C₅×C₁₉	C₂×D₂₉	semidirect
37. D₉₅	C₃×D₂₉	semidirect
43. C₅×C₂₉	C₂×C₃×D₁₉	semidirect
48. C₅×C₁₉	C₂×C₃×D₂₉	semidirect
49. C₃×C₂₉	D₅×D₁₉	semidirect
55. C₃×C₁₉	D₅×D₂₉	semidirect
62. C₂₉	C₃×D₅×D₁₉	semidirect
64. C₁₉	C₃×D₅×D₂₉	semidirect
65. C₃×C₅	D₁₉×D₂₉	semidirect
73. C₅	C₃×D₁₉×D₂₉	semidirect
75. C₃	D₉₅⋊D₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₂₉×D₉₅	2
C₃×C₁₉×D₁₄₅	2
C₃×C₅×D₅₅₁	2
D₉₅⋊D₂₉	3
C₃×D₁₉×D₂₉	5
C₃×D₅×D₂₉	19
C₃×D₅×D₁₉	29

Subgroups — C3×D95⋊D29 #45683306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₉₅⋊D₂₉ #45683306