Subgroups — C₃²×C₃⋊Dic₁₅ #13108506

Order 1620.

568 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
2	C₃×C₃⋊Dic₁₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×Dic₁₅	—	3	4	no	maximal
4	C₃⁴×C₅	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃²×C₃⋊Dic₃	—	5	1	no	maximal, Hall
6	C₂×C₃³×C₅	—	2	16	no	—
7	C₂×C₃³×C₅	D₃	1	4	yes	—
8	C₂×C₃³×C₅	C₂×C₃	1	4	yes	—
9	C₃⋊Dic₁₅	C₃²	1	1	yes	characteristic, direct product factor
10	C₃×Dic₁₅	—	3	16	no	—
11	C₃²×Dic₅	—	9	1	no	—
12	C₂×C₃⁴	D₅	1	1	yes	characteristic
13	C₃³×C₅	—	2	16	no	—
14	C₃³×C₅	Dic₃	1	4	yes	complemented
15	C₃³×C₅	C₃×C₄	1	4	yes	complemented
16	C₃×C₃⋊Dic₃	—	5	4	no	—
17	C₃²×Dic₃	—	15	4	no	—
18	C₂×C₃²×C₅	—	2	24	no	—
19	C₂×C₃²×C₅	—	2	16	no	—
20	C₂×C₃²×C₅	—	2	16	no	—
21	C₂×C₃²×C₅	C₃×D₃	1	16	yes	—
22	C₂×C₃²×C₅	C₃⋊D₃	1	1	yes	characteristic
23	C₂×C₃²×C₅	C₂×C₃²	1	1	yes	characteristic
24	C₃⁴	Dic₅	1	1	yes	characteristic, complemented, Sylow
25	Dic₁₅	—	3	4	no	—
26	C₃×Dic₅	—	9	4	no	—
27	C₂×C₃³	—	2	16	no	—
28	C₂×C₃³	C₃×D₅	1	4	yes	—
29	C₂×C₃³	D₁₅	1	4	yes	—
30	C₃²×C₅	—	2	24	no	—
31	C₃²×C₅	—	2	16	no	—
32	C₃²×C₅	—	2	16	no	—
33	C₃²×C₅	C₃×Dic₃	1	16	yes	complemented
34	C₃²×C₅	C₃⋊Dic₃	1	1	yes	characteristic, complemented
35	C₃²×C₅	C₃²×C₄	1	1	yes	characteristic, complemented
36	C₃²×C₄	—	45	1	no	—
37	C₃⋊Dic₃	—	5	1	no	—
38	C₃×Dic₃	—	15	16	no	—
39	C₂×C₃×C₅	—	2	16	no	—
40	C₂×C₃×C₅	C₃²×D₃	1	4	yes	—
41	C₂×C₃×C₅	C₃×C₃⋊D₃	1	4	yes	—
42	C₃³	—	2	16	no	—
43	C₃³	C₃×Dic₅	1	4	yes	complemented
44	C₃³	Dic₁₅	1	4	yes	complemented
45	Dic₅	—	9	1	no	Hall
46	C₂×C₃²	—	2	24	no	—
47	C₂×C₃²	—	2	16	no	—
48	C₂×C₃²	—	2	16	no	—
49	C₂×C₃²	C₃²×D₅	1	1	yes	characteristic
50	C₂×C₃²	C₃×D₁₅	1	16	yes	—
51	C₂×C₃²	C₃⋊D₁₅	1	1	yes	characteristic
52	C₃×C₅	—	2	16	no	—
53	C₃×C₅	C₃²×Dic₃	1	4	yes	complemented
54	C₃×C₅	C₃×C₃⋊Dic₃	1	4	yes	complemented
55	C₃×C₄	—	45	4	no	—
56	Dic₃	—	15	4	no	—
57	C₂×C₅	C₃²×C₃⋊D₃	1	1	yes	characteristic
58	C₃²	—	2	24	no	—
59	C₃²	—	2	16	no	—
60	C₃²	—	2	16	no	—
61	C₃²	C₃²×Dic₅	1	1	yes	characteristic, complemented
62	C₃²	C₃×Dic₁₅	1	16	yes	complemented
63	C₃²	C₃⋊Dic₁₅	1	1	yes	characteristic, direct product factor
64	C₂×C₃	—	2	16	no	—
65	C₂×C₃	C₃²×D₁₅	1	4	yes	—
66	C₂×C₃	C₃×C₃⋊D₁₅	1	4	yes	—
67	C₅	C₃²×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	45	1	no	Sylow
69	C₃	—	2	16	no	—
70	C₃	C₃²×Dic₁₅	1	4	yes	complemented
71	C₃	C₃×C₃⋊Dic₁₅	1	4	yes	direct product factor
72	C₂	C₃²×C₃⋊D₁₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²	C₃⋊D₁₅
commutator, hypocenter	C₃²×C₅	C₃²×C₄
Frattini	C₂	C₃²×C₃⋊D₁₅
Fitting, socle, prime radical	C₂×C₃⁴×C₅	C₂
cosocle	C₂×C₃²×C₅	C₂×C₃²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
2. C₃×C₃⋊Dic₁₅	C₃	direct (N × H)
4. C₃⁴×C₅	C₄	semidirect
9. C₃⋊Dic₁₅	C₃²	direct (N × H)
14. C₃³×C₅	Dic₃	semidirect
15. C₃³×C₅	C₃×C₄	semidirect
24. C₃⁴	Dic₅	semidirect
33. C₃²×C₅	C₃×Dic₃	semidirect
34. C₃²×C₅	C₃⋊Dic₃	semidirect
35. C₃²×C₅	C₃²×C₄	semidirect
43. C₃³	C₃×Dic₅	semidirect
44. C₃³	Dic₁₅	semidirect
53. C₃×C₅	C₃²×Dic₃	semidirect
54. C₃×C₅	C₃×C₃⋊Dic₃	semidirect
61. C₃²	C₃²×Dic₅	semidirect
62. C₃²	C₃×Dic₁₅	semidirect
63. C₃²	C₃⋊Dic₁₅	direct (N × H)
67. C₅	C₃²×C₃⋊Dic₃	semidirect
70. C₃	C₃²×Dic₁₅	semidirect
71. C₃	C₃×C₃⋊Dic₁₅	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
C₃×C₃⋊Dic₁₅	3
C₃²×Dic₁₅	3
C₃²×C₃⋊Dic₃	5

Subgroups — C32×C3⋊Dic15 #13108506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₃⋊Dic₁₅ #13108506