Subgroups — C₂×C₃²×C₃⋊D₁₅ #13108566

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×C₃⋊D₁₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₃⋊D₁₅	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃²×D₁₅	—	3	4	no	maximal
5	C₃⁴×C₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃²×C₃⋊D₃	—	5	1	no	maximal, 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×C₃⋊D₁₅	C₂×C₃	1	8	yes	direct product factor
11	C₃²×D₁₅	—	3	8	no	—
12	C₂×C₃⋊D₁₅	C₃²	1	1	yes	characteristic, direct product factor
13	C₂×C₃×D₁₅	—	3	16	no	—
14	C₂×C₃²×D₅	—	9	1	no	—
15	C₂×C₃⁴	D₅	1	1	yes	characteristic, complemented
16	C₃²×C₃⋊D₃	—	5	2	no	—
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	—	5	4	no	—
21	C₂×C₃²×D₃	—	15	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	C₃×D₃	1	16	yes	complemented
26	C₂×C₃²×C₅	C₃⋊D₃	1	1	yes	characteristic, complemented
27	C₂×C₃²×C₅	C₂×C₃²	1	1	yes	characteristic, complemented
28	C₃⋊D₁₅	C₂×C₃²	1	2	yes	direct product factor
29	C₃×D₁₅	—	3	32	no	—
30	C₃²×D₅	—	9	2	no	—
31	C₃⁴	C₂×D₅	1	1	yes	characteristic, complemented, Sylow
32	C₂×D₁₅	—	3	4	no	—
33	C₂×C₃×D₅	—	9	4	no	—
34	C₂×C₃³	—	2	16	no	—
35	C₂×C₃³	C₃×D₅	1	4	yes	complemented
36	C₂×C₃³	D₁₅	1	4	yes	complemented
37	C₃×C₃⋊D₃	—	5	8	no	—
38	C₃²×D₃	—	15	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, complemented
44	C₃²×C₅	C₂²×C₃²	1	1	yes	characteristic, complemented
45	C₂²×C₃²	—	45	1	no	—
46	C₂×C₃⋊D₃	—	5	1	no	—
47	C₂×C₃×D₃	—	15	16	no	—
48	C₂×C₃×C₅	—	2	16	no	—
49	C₂×C₃×C₅	C₃²×D₃	1	4	yes	complemented
50	C₂×C₃×C₅	C₃×C₃⋊D₃	1	4	yes	complemented
51	D₁₅	—	3	8	no	—
52	C₃×D₅	—	9	8	no	—
53	C₃³	—	2	16	no	—
54	C₃³	C₂×C₃×D₅	1	4	yes	complemented
55	C₃³	C₂×D₁₅	1	4	yes	complemented
56	C₂×D₅	—	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	—	45	2	no	—
61	C₂×C₃²	C₃²×D₅	1	1	yes	characteristic, complemented
62	C₂×C₃²	C₃×D₁₅	1	16	yes	complemented
63	C₂×C₃²	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
64	C₃⋊D₃	—	5	2	no	—
65	C₃×D₃	—	15	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	complemented
69	C₂²×C₃	—	45	4	no	—
70	C₂×D₃	—	15	4	no	—
71	C₂×C₅	C₃²×C₃⋊D₃	1	1	yes	characteristic, complemented
72	D₅	—	9	2	no	—
73	C₃²	—	2	24	no	—
74	C₃²	—	2	16	no	—
75	C₃²	—	2	16	no	—
76	C₃²	C₂×C₃²×D₅	1	1	yes	characteristic, complemented
77	C₃²	C₂×C₃×D₁₅	1	16	yes	complemented
78	C₃²	C₂×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
79	C₂×C₃	—	2	16	no	—
80	C₂×C₃	—	45	8	no	—
81	C₂×C₃	C₃²×D₁₅	1	4	yes	complemented
82	C₂×C₃	C₃×C₃⋊D₁₅	1	4	yes	direct product factor
83	D₃	—	15	8	no	—
84	C₅	C₂×C₃²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
85	C₂²	—	45	1	no	Sylow
86	C₃	—	2	16	no	—
87	C₃	C₂×C₃²×D₁₅	1	4	yes	complemented
88	C₃	C₂×C₃×C₃⋊D₁₅	1	4	yes	direct product factor
89	C₂	—	45	2	no	—
90	C₂	C₃²×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃⁴×C₅	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃⁴×C₅	C₂	semidirect
2. C₃²×C₃⋊D₁₅	C₂	direct (N × H)
3. C₂×C₃×C₃⋊D₁₅	C₃	direct (N × H)
5. C₃⁴×C₅	C₂²	semidirect
8. C₂×C₃³×C₅	D₃	semidirect
9. C₂×C₃³×C₅	C₂×C₃	semidirect
10. C₃×C₃⋊D₁₅	C₂×C₃	direct (N × H)
12. C₂×C₃⋊D₁₅	C₃²	direct (N × H)
15. C₂×C₃⁴	D₅	semidirect
18. C₃³×C₅	C₂×D₃	semidirect
19. C₃³×C₅	C₂²×C₃	semidirect
25. C₂×C₃²×C₅	C₃×D₃	semidirect
26. C₂×C₃²×C₅	C₃⋊D₃	semidirect
27. C₂×C₃²×C₅	C₂×C₃²	semidirect
28. C₃⋊D₁₅	C₂×C₃²	direct (N × H)
31. C₃⁴	C₂×D₅	semidirect
35. C₂×C₃³	C₃×D₅	semidirect
36. C₂×C₃³	D₁₅	semidirect
42. C₃²×C₅	C₂×C₃×D₃	semidirect
43. C₃²×C₅	C₂×C₃⋊D₃	semidirect
44. C₃²×C₅	C₂²×C₃²	semidirect
49. C₂×C₃×C₅	C₃²×D₃	semidirect
50. C₂×C₃×C₅	C₃×C₃⋊D₃	semidirect
54. C₃³	C₂×C₃×D₅	semidirect
55. C₃³	C₂×D₁₅	semidirect
61. C₂×C₃²	C₃²×D₅	semidirect
62. C₂×C₃²	C₃×D₁₅	semidirect
63. C₂×C₃²	C₃⋊D₁₅	direct (N × H)
67. C₃×C₅	C₂×C₃²×D₃	semidirect
68. C₃×C₅	C₂×C₃×C₃⋊D₃	semidirect
71. C₂×C₅	C₃²×C₃⋊D₃	semidirect
76. C₃²	C₂×C₃²×D₅	semidirect
77. C₃²	C₂×C₃×D₁₅	semidirect
78. C₃²	C₂×C₃⋊D₁₅	direct (N × H)
81. C₂×C₃	C₃²×D₁₅	semidirect
82. C₂×C₃	C₃×C₃⋊D₁₅	direct (N × H)
84. C₅	C₂×C₃²×C₃⋊D₃	semidirect
87. C₃	C₂×C₃²×D₁₅	semidirect
88. C₃	C₂×C₃×C₃⋊D₁₅	direct (N × H)
90. C₂	C₃²×C₃⋊D₁₅	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×C₃⋊D₁₅	2
C₂×C₃×C₃⋊D₁₅	3
C₂×C₃²×D₁₅	3
C₂×C₃²×C₃⋊D₃	5

Subgroups — C2×C32×C3⋊D15 #13108566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₃⋊D₁₅ #13108566