Subgroups — C₃×D₃×D₅×C₁₀₁ #32911468

Order 18180.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₅×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₃×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₅×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₅×C₁₀₁	—	3	1	no	maximal
5	D₃×D₅×C₁₀₁	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₅×C₁₀₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×D₃×C₁₀₁	—	5	1	no	maximal, Hall
8	D₁₅×C₁₀₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₃×C₁₀₁	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₅×C₁₀₁	—	2	1	no	—
11	C₃×D₅×C₁₀₁	—	3	1	no	—
12	C₃×D₅×C₁₀₁	D₃	1	1	yes	characteristic, direct product factor
13	C₃×D₅×C₁₀₁	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅×C₁₀₁	—	3	1	no	—
15	C₂×D₅×C₁₀₁	—	3	1	no	Hall
16	C₂×C₃²×C₁₀₁	—	5	1	no	—
17	C₃×D₃×C₁₀₁	—	5	1	no	—
18	C₃×D₃×C₁₀₁	D₅	1	1	yes	characteristic, direct product factor
19	C₃×C₅×C₁₀₁	—	2	1	no	—
20	C₃×C₅×C₁₀₁	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅×C₁₀₁	C₂²×C₃	1	1	yes	characteristic, complemented
22	C₂²×C₃×C₁₀₁	—	15	1	no	—
23	C₂×D₃×C₁₀₁	—	5	1	no	—
24	C₂×C₅×C₁₀₁	—	3	1	no	—
25	D₅×C₁₀₁	—	3	1	no	—
26	D₅×C₁₀₁	C₃×D₃	1	1	yes	characteristic, direct product factor
27	C₃²×C₁₀₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₀₁	—	3	1	no	—
29	C₂×C₃×C₁₀₁	—	5	1	no	—
30	C₂×C₃×C₁₀₁	—	5	1	no	—
31	C₂×C₃×C₁₀₁	—	10	1	no	—
32	C₂×C₃×C₁₀₁	—	15	1	no	—
33	D₃×C₁₀₁	—	5	1	no	—
34	D₃×C₁₀₁	C₃×D₅	1	1	yes	characteristic, direct product factor
35	C₅×C₁₀₁	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₁₀₁	—	15	1	no	Hall
37	C₃×C₁₀₁	—	2	1	no	—
38	C₃×C₁₀₁	D₃×D₅	1	1	yes	characteristic, direct product factor
39	C₃×C₁₀₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented
40	C₂×C₁₀₁	—	3	1	no	—
41	C₂×C₁₀₁	—	5	1	no	—
42	C₂×C₁₀₁	—	15	1	no	—
43	C₃×D₃×D₅	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₁₀₁	C₃×D₃×D₅	1	1	yes	characteristic, direct product factor, Sylow
45	C₃×D₁₅	C₂×C₁₀₁	1	1	yes	characteristic, complemented
46	C₃×C₅×D₃	C₂×C₁₀₁	1	1	yes	characteristic, complemented
47	C₃²×D₅	C₂×C₁₀₁	1	1	yes	characteristic, complemented
48	C₂×C₃×D₅	—	3	1	no	—
49	D₃×D₅	C₃×C₁₀₁	1	1	yes	characteristic, direct product factor
50	C₃²×C₅	C₂²×C₁₀₁	1	1	yes	characteristic, complemented, Hall
51	C₂×C₃×D₃	—	5	1	no	Hall
52	C₂×C₃×C₅	—	3	1	no	—
53	D₁₅	C₂×C₃×C₁₀₁	1	1	yes	characteristic, complemented
54	C₃×D₅	—	2	1	no	—
55	C₃×D₅	—	3	1	no	—
56	C₃×D₅	D₃×C₁₀₁	1	1	yes	characteristic, direct product factor
57	C₃×D₅	C₂×C₃×C₁₀₁	1	1	yes	characteristic, complemented
58	C₅×D₃	C₂×C₃×C₁₀₁	1	1	yes	characteristic, complemented
59	C₂×D₅	—	3	1	no	Hall
60	C₂×C₃²	—	5	1	no	—
61	C₃×D₃	—	5	1	no	—
62	C₃×D₃	D₅×C₁₀₁	1	1	yes	characteristic, direct product factor
63	C₃×C₅	—	2	1	no	—
64	C₃×C₅	C₂×D₃×C₁₀₁	1	1	yes	characteristic, complemented
65	C₃×C₅	C₂²×C₃×C₁₀₁	1	1	yes	characteristic, complemented
66	C₂²×C₃	—	15	1	no	—
67	C₂×D₃	—	5	1	no	—
68	C₂×C₅	—	3	1	no	—
69	D₅	—	3	1	no	—
70	D₅	C₃×D₃×C₁₀₁	1	1	yes	characteristic, direct product factor
71	C₃²	C₂×D₅×C₁₀₁	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	3	1	no	—
73	C₂×C₃	—	5	1	no	—
74	C₂×C₃	—	5	1	no	—
75	C₂×C₃	—	10	1	no	—
76	C₂×C₃	—	15	1	no	—
77	D₃	—	5	1	no	—
78	D₃	C₃×D₅×C₁₀₁	1	1	yes	characteristic, direct product factor
79	C₅	C₂×C₃×D₃×C₁₀₁	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	15	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×D₅×C₁₀₁	1	1	yes	characteristic, direct product factor
83	C₃	C₂×C₃×D₅×C₁₀₁	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	5	1	no	—
86	C₂	—	15	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₀₁	D₃×D₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₃×C₁₀₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₀₁	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₃×C₁₀₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₅×C₁₀₁	C₂	semidirect
2. C₃×C₅×D₃×C₁₀₁	C₂	semidirect
3. C₃²×D₅×C₁₀₁	C₂	semidirect
5. D₃×D₅×C₁₀₁	C₃	direct (N × H)
6. C₃²×C₅×C₁₀₁	C₂²	semidirect
8. D₁₅×C₁₀₁	C₂×C₃	semidirect
9. C₅×D₃×C₁₀₁	C₂×C₃	semidirect
12. C₃×D₅×C₁₀₁	D₃	direct (N × H)
13. C₃×D₅×C₁₀₁	C₂×C₃	semidirect
18. C₃×D₃×C₁₀₁	D₅	direct (N × H)
20. C₃×C₅×C₁₀₁	C₂×D₃	semidirect
21. C₃×C₅×C₁₀₁	C₂²×C₃	semidirect
26. D₅×C₁₀₁	C₃×D₃	direct (N × H)
27. C₃²×C₁₀₁	C₂×D₅	semidirect
34. D₃×C₁₀₁	C₃×D₅	direct (N × H)
35. C₅×C₁₀₁	C₂×C₃×D₃	semidirect
38. C₃×C₁₀₁	D₃×D₅	direct (N × H)
39. C₃×C₁₀₁	C₂×C₃×D₅	semidirect
43. C₃×D₃×D₅	C₁₀₁	direct (N × H)
44. C₁₀₁	C₃×D₃×D₅	direct (N × H)
45. C₃×D₁₅	C₂×C₁₀₁	semidirect
46. C₃×C₅×D₃	C₂×C₁₀₁	semidirect
47. C₃²×D₅	C₂×C₁₀₁	semidirect
49. D₃×D₅	C₃×C₁₀₁	direct (N × H)
50. C₃²×C₅	C₂²×C₁₀₁	semidirect
53. D₁₅	C₂×C₃×C₁₀₁	semidirect
56. C₃×D₅	D₃×C₁₀₁	direct (N × H)
57. C₃×D₅	C₂×C₃×C₁₀₁	semidirect
58. C₅×D₃	C₂×C₃×C₁₀₁	semidirect
62. C₃×D₃	D₅×C₁₀₁	direct (N × H)
64. C₃×C₅	C₂×D₃×C₁₀₁	semidirect
65. C₃×C₅	C₂²×C₃×C₁₀₁	semidirect
70. D₅	C₃×D₃×C₁₀₁	direct (N × H)
71. C₃²	C₂×D₅×C₁₀₁	semidirect
78. D₃	C₃×D₅×C₁₀₁	direct (N × H)
79. C₅	C₂×C₃×D₃×C₁₀₁	semidirect
82. C₃	D₃×D₅×C₁₀₁	direct (N × H)
83. C₃	C₂×C₃×D₅×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₁₅×C₁₀₁	2
C₃×C₅×D₃×C₁₀₁	2
C₃²×D₅×C₁₀₁	2
C₂×C₃×D₅×C₁₀₁	3
D₃×D₅×C₁₀₁	3
C₂×C₃×D₃×C₁₀₁	5
C₃×D₃×D₅	101

Subgroups — C3×D3×D5×C101 #32911468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×D₅×C₁₀₁ #32911468