Subgroups — C₂×D₃×D₁₅ #67224

Order 360.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₅	C₂	1	4	yes	maximal, direct product factor
5	C₂²×D₁₅	—	3	1	no	maximal
6	C₂×D₃×D₅	—	3	1	no	maximal
7	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic, complemented
8	C₃⋊D₁₅	C₂²	1	2	yes	complemented
9	C₃×D₁₅	C₂²	1	2	yes	complemented
10	C₃×C₅×D₃	C₂²	1	2	yes	complemented
11	C₂×D₃²	—	5	1	no	maximal, Hall
12	C₂²×C₃×C₅	—	3	1	no	—
13	C₂×D₁₅	—	3	1	no	—
14	C₂×D₁₅	—	3	1	no	—
15	C₂×D₁₅	—	3	4	no	—
16	C₂×D₁₅	—	6	1	no	—
17	C₂×D₁₅	D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₅×D₃	D₃	1	1	yes	characteristic, complemented
19	C₂×C₃×D₅	—	3	1	no	—
20	D₃×D₅	—	3	4	no	—
21	C₃²×C₅	C₂³	1	1	yes	characteristic, complemented, Hall
22	C₂²×D₅	—	9	1	no	Hall
23	C₂×C₃⋊D₃	—	5	1	no	—
24	C₂×C₃×D₃	—	5	1	no	—
25	C₂×C₃×D₃	D₅	1	1	yes	characteristic, complemented
26	D₃²	—	5	4	no	—
27	C₂×C₃×C₅	—	2	1	no	—
28	C₂×C₃×C₅	—	3	2	no	—
29	C₂×C₃×C₅	C₂×D₃	1	1	yes	characteristic, complemented
30	C₂×C₃×C₅	C₂×D₃	1	1	yes	characteristic, complemented
31	D₁₅	—	3	2	no	—
32	D₁₅	—	3	2	no	—
33	D₁₅	—	6	2	no	—
34	D₁₅	C₂×D₃	1	2	yes	direct product factor
35	C₃×D₅	—	3	2	no	—
36	C₅×D₃	C₂×D₃	1	2	yes	complemented
37	C₂²×D₃	—	15	1	no	—
38	C₂²×D₃	—	15	1	no	—
39	C₂²×C₅	—	3	1	no	—
40	C₂×D₅	—	3	1	no	—
41	C₂×D₅	—	9	4	no	—
42	C₂×D₅	—	9	1	no	—
43	C₂×C₃²	C₂×D₅	1	1	yes	characteristic, complemented
44	C₃⋊D₃	—	5	2	no	—
45	C₃×D₃	—	5	2	no	—
46	C₃×D₃	C₂×D₅	1	2	yes	complemented
47	C₃×C₅	—	2	1	no	—
48	C₃×C₅	C₂²×D₃	1	1	yes	characteristic, complemented
49	C₃×C₅	C₂²×D₃	1	1	yes	characteristic, complemented
50	C₂²×C₃	—	3	1	no	—
51	C₂²×C₃	—	15	1	no	—
52	C₂×D₃	—	5	1	no	—
53	C₂×D₃	—	15	4	no	—
54	C₂×D₃	—	15	1	no	—
55	C₂×D₃	—	15	1	no	—
56	C₂×D₃	—	15	4	no	—
57	C₂×D₃	—	30	1	no	—
58	C₂×D₃	D₁₅	1	1	yes	characteristic, direct product factor
59	C₂×C₅	—	3	2	no	—
60	C₂×C₅	D₃²	1	1	yes	characteristic, complemented
61	D₅	—	3	2	no	—
62	D₅	—	9	2	no	—
63	C₃²	C₂²×D₅	1	1	yes	characteristic, complemented, Sylow
64	C₂³	—	45	1	no	Sylow
65	C₂×C₃	—	2	1	no	—
66	C₂×C₃	—	3	2	no	—
67	C₂×C₃	—	15	2	no	—
68	C₂×C₃	D₃×D₅	1	1	yes	characteristic, complemented
69	C₂×C₃	C₂×D₁₅	1	1	yes	characteristic, complemented
70	D₃	—	5	2	no	—
71	D₃	—	15	2	no	—
72	D₃	—	15	2	no	—
73	D₃	—	30	2	no	—
74	D₃	C₂×D₁₅	1	2	yes	direct product factor
75	C₅	C₂×D₃²	1	1	yes	characteristic, complemented, Sylow
76	C₂²	—	3	1	no	—
77	C₂²	—	15	1	no	—
78	C₂²	—	45	4	no	—
79	C₂²	—	45	1	no	—
80	C₃	—	2	1	no	—
81	C₃	C₂×D₃×D₅	1	1	yes	characteristic, complemented
82	C₃	C₂²×D₁₅	1	1	yes	characteristic, complemented
83	C₂	—	3	2	no	—
84	C₂	—	15	2	no	—
85	C₂	—	45	2	no	—
86	C₂	D₃×D₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃×D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃⋊D₁₅	C₂	semidirect
2. C₂×C₃×D₁₅	C₂	semidirect
3. C₂×C₃×C₅×D₃	C₂	semidirect
4. D₃×D₁₅	C₂	direct (N × H)
7. C₂×C₃²×C₅	C₂²	semidirect
8. C₃⋊D₁₅	C₂²	semidirect
9. C₃×D₁₅	C₂²	semidirect
10. C₃×C₅×D₃	C₂²	semidirect
17. C₂×D₁₅	D₃	direct (N × H)
18. C₂×C₅×D₃	D₃	semidirect
21. C₃²×C₅	C₂³	semidirect
25. C₂×C₃×D₃	D₅	semidirect
29. C₂×C₃×C₅	C₂×D₃	semidirect
30. C₂×C₃×C₅	C₂×D₃	semidirect
34. D₁₅	C₂×D₃	direct (N × H)
36. C₅×D₃	C₂×D₃	semidirect
43. C₂×C₃²	C₂×D₅	semidirect
46. C₃×D₃	C₂×D₅	semidirect
48. C₃×C₅	C₂²×D₃	semidirect
49. C₃×C₅	C₂²×D₃	semidirect
58. C₂×D₃	D₁₅	direct (N × H)
60. C₂×C₅	D₃²	semidirect
63. C₃²	C₂²×D₅	semidirect
68. C₂×C₃	D₃×D₅	semidirect
69. C₂×C₃	C₂×D₁₅	semidirect
74. D₃	C₂×D₁₅	direct (N × H)
75. C₅	C₂×D₃²	semidirect
81. C₃	C₂×D₃×D₅	semidirect
82. C₃	C₂²×D₁₅	semidirect
86. C₂	D₃×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×C₃⋊D₁₅	2
C₂×C₃×D₁₅	2
C₂×C₃×C₅×D₃	2
D₃×D₁₅	2
C₂²×D₁₅	3
C₂×D₃×D₅	3
C₂×D₃²	5

Subgroups — C2×D3×D15 #67224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×D₁₅ #67224