Subgroups — C₂×C₃²×C₅×C₃⋊D₃ #13108565

Order 1620.

712 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⁴×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₅×C₃⋊D₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₅×C₃⋊D₃	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₅×D₃	—	3	4	no	maximal
5	C₃⁴×C₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃²×C₃⋊D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃³×C₅	—	2	16	no	—
8	C₂×C₃³×C₅	D₃	1	4	yes	complemented
9	C₂×C₃³×C₅	C₂×C₃	1	4	yes	complemented
10	C₃×C₅×C₃⋊D₃	C₂×C₃	1	8	yes	direct product factor
11	C₃²×C₅×D₃	—	3	8	no	—
12	C₂²×C₃²×C₅	—	9	1	no	—
13	C₂×C₅×C₃⋊D₃	C₃²	1	1	yes	characteristic, direct product factor
14	C₂×C₃×C₅×D₃	—	3	16	no	—
15	C₂×C₃⁴	C₂×C₅	1	1	yes	characteristic, complemented
16	C₃²×C₃⋊D₃	C₂×C₅	1	2	yes	direct product factor
17	C₃³×C₅	—	2	16	no	—
18	C₃³×C₅	C₂×D₃	1	4	yes	complemented
19	C₃³×C₅	C₂²×C₃	1	4	yes	complemented
20	C₂×C₃×C₃⋊D₃	C₃×C₅	1	4	yes	direct product factor
21	C₂×C₃²×D₃	—	3	4	no	—
22	C₂×C₃²×C₅	—	2	24	no	—
23	C₂×C₃²×C₅	—	2	16	no	—
24	C₂×C₃²×C₅	—	2	16	no	—
25	C₂×C₃²×C₅	—	9	2	no	—
26	C₂×C₃²×C₅	C₃×D₃	1	16	yes	complemented
27	C₂×C₃²×C₅	C₃⋊D₃	1	1	yes	characteristic, direct product factor
28	C₂×C₃²×C₅	C₂×C₃²	1	1	yes	characteristic, complemented
29	C₅×C₃⋊D₃	C₂×C₃²	1	2	yes	direct product factor
30	C₃×C₅×D₃	—	3	32	no	—
31	C₃⁴	C₂²×C₅	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₃×C₅	—	9	4	no	—
33	C₂×C₅×D₃	—	3	4	no	—
34	C₂×C₃³	—	2	16	no	—
35	C₂×C₃³	C₅×D₃	1	4	yes	complemented
36	C₂×C₃³	C₂×C₃×C₅	1	4	yes	complemented
37	C₃×C₃⋊D₃	C₂×C₃×C₅	1	8	yes	direct product factor
38	C₃²×D₃	—	3	8	no	—
39	C₃²×C₅	—	2	24	no	—
40	C₃²×C₅	—	2	16	no	—
41	C₃²×C₅	—	2	16	no	—
42	C₃²×C₅	C₂×C₃×D₃	1	16	yes	complemented
43	C₃²×C₅	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor
44	C₃²×C₅	C₂²×C₃²	1	1	yes	characteristic, complemented
45	C₂²×C₃²	—	9	1	no	—
46	C₂×C₃⋊D₃	C₃²×C₅	1	1	yes	characteristic, direct product factor
47	C₂×C₃×D₃	—	3	16	no	—
48	C₂×C₃×C₅	—	2	16	no	—
49	C₂×C₃×C₅	—	9	8	no	—
50	C₂×C₃×C₅	C₃²×D₃	1	4	yes	complemented
51	C₂×C₃×C₅	C₃×C₃⋊D₃	1	4	yes	direct product factor
52	C₅×D₃	—	3	8	no	—
53	C₃³	—	2	16	no	—
54	C₃³	C₂×C₅×D₃	1	4	yes	complemented
55	C₃³	C₂²×C₃×C₅	1	4	yes	complemented
56	C₂²×C₅	—	9	1	no	Hall
57	C₂×C₃²	—	2	24	no	—
58	C₂×C₃²	—	2	16	no	—
59	C₂×C₃²	—	2	16	no	—
60	C₂×C₃²	—	9	2	no	—
61	C₂×C₃²	C₃×C₅×D₃	1	16	yes	complemented
62	C₂×C₃²	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor
63	C₂×C₃²	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
64	C₃⋊D₃	C₂×C₃²×C₅	1	2	yes	direct product factor
65	C₃×D₃	—	3	32	no	—
66	C₃×C₅	—	2	16	no	—
67	C₃×C₅	C₂×C₃²×D₃	1	4	yes	complemented
68	C₃×C₅	C₂×C₃×C₃⋊D₃	1	4	yes	direct product factor
69	C₂²×C₃	—	9	4	no	—
70	C₂×D₃	—	3	4	no	—
71	C₂×C₅	—	9	2	no	—
72	C₂×C₅	C₃²×C₃⋊D₃	1	1	yes	characteristic, direct product factor
73	C₃²	—	2	24	no	—
74	C₃²	—	2	16	no	—
75	C₃²	—	2	16	no	—
76	C₃²	C₂×C₃×C₅×D₃	1	16	yes	complemented
77	C₃²	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor
78	C₃²	C₂²×C₃²×C₅	1	1	yes	characteristic, complemented
79	C₂×C₃	—	2	16	no	—
80	C₂×C₃	—	9	8	no	—
81	C₂×C₃	C₃²×C₅×D₃	1	4	yes	complemented
82	C₂×C₃	C₃×C₅×C₃⋊D₃	1	4	yes	direct product factor
83	D₃	—	3	8	no	—
84	C₅	C₂×C₃²×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
85	C₂²	—	9	1	no	Sylow
86	C₃	—	2	16	no	—
87	C₃	C₂×C₃²×C₅×D₃	1	4	yes	complemented
88	C₃	C₂×C₃×C₅×C₃⋊D₃	1	4	yes	direct product factor
89	C₂	—	9	2	no	—
90	C₂	C₃²×C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃⁴×C₅	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₃²×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₃⁴×C₅	C₂	semidirect
2. C₃²×C₅×C₃⋊D₃	C₂	direct (N × H)
3. C₂×C₃×C₅×C₃⋊D₃	C₃	direct (N × H)
5. C₃⁴×C₅	C₂²	semidirect
6. C₂×C₃²×C₃⋊D₃	C₅	direct (N × H)
8. C₂×C₃³×C₅	D₃	semidirect
9. C₂×C₃³×C₅	C₂×C₃	semidirect
10. C₃×C₅×C₃⋊D₃	C₂×C₃	direct (N × H)
13. C₂×C₅×C₃⋊D₃	C₃²	direct (N × H)
15. C₂×C₃⁴	C₂×C₅	semidirect
16. C₃²×C₃⋊D₃	C₂×C₅	direct (N × H)
18. C₃³×C₅	C₂×D₃	semidirect
19. C₃³×C₅	C₂²×C₃	semidirect
20. C₂×C₃×C₃⋊D₃	C₃×C₅	direct (N × H)
26. C₂×C₃²×C₅	C₃×D₃	semidirect
27. C₂×C₃²×C₅	C₃⋊D₃	direct (N × H)
28. C₂×C₃²×C₅	C₂×C₃²	semidirect
29. C₅×C₃⋊D₃	C₂×C₃²	direct (N × H)
31. C₃⁴	C₂²×C₅	semidirect
35. C₂×C₃³	C₅×D₃	semidirect
36. C₂×C₃³	C₂×C₃×C₅	semidirect
37. C₃×C₃⋊D₃	C₂×C₃×C₅	direct (N × H)
42. C₃²×C₅	C₂×C₃×D₃	semidirect
43. C₃²×C₅	C₂×C₃⋊D₃	direct (N × H)
44. C₃²×C₅	C₂²×C₃²	semidirect
46. C₂×C₃⋊D₃	C₃²×C₅	direct (N × H)
50. C₂×C₃×C₅	C₃²×D₃	semidirect
51. C₂×C₃×C₅	C₃×C₃⋊D₃	direct (N × H)
54. C₃³	C₂×C₅×D₃	semidirect
55. C₃³	C₂²×C₃×C₅	semidirect
61. C₂×C₃²	C₃×C₅×D₃	semidirect
62. C₂×C₃²	C₅×C₃⋊D₃	direct (N × H)
63. C₂×C₃²	C₂×C₃²×C₅	semidirect
64. C₃⋊D₃	C₂×C₃²×C₅	direct (N × H)
67. C₃×C₅	C₂×C₃²×D₃	semidirect
68. C₃×C₅	C₂×C₃×C₃⋊D₃	direct (N × H)
72. C₂×C₅	C₃²×C₃⋊D₃	direct (N × H)
76. C₃²	C₂×C₃×C₅×D₃	semidirect
77. C₃²	C₂×C₅×C₃⋊D₃	direct (N × H)
78. C₃²	C₂²×C₃²×C₅	semidirect
81. C₂×C₃	C₃²×C₅×D₃	semidirect
82. C₂×C₃	C₃×C₅×C₃⋊D₃	direct (N × H)
84. C₅	C₂×C₃²×C₃⋊D₃	direct (N × H)
87. C₃	C₂×C₃²×C₅×D₃	semidirect
88. C₃	C₂×C₃×C₅×C₃⋊D₃	direct (N × H)
90. C₂	C₃²×C₅×C₃⋊D₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃⁴×C₅	2
C₃²×C₅×C₃⋊D₃	2
C₂×C₃×C₅×C₃⋊D₃	3
C₂×C₃²×C₅×D₃	3
C₂×C₃²×C₃⋊D₃	5

Subgroups — C2×C32×C5×C3⋊D3 #13108565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅×C₃⋊D₃ #13108565