Subgroups — C₂³×C₃⋊Dic₁₅ #13089516

Order 1440.

1416 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃²×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃⋊Dic₁₅	C₂	1	14	yes	maximal, direct product factor
3	C₂³×Dic₁₅	—	3	4	no	maximal
4	C₂³×C₃²×C₅	C₄	1	8	yes	complemented
5	C₂³×C₃²×C₅	C₂²	1	7	yes	—
6	C₂×C₃⋊Dic₁₅	C₂²	1	28	yes	direct product factor
7	C₂³×C₃⋊Dic₃	—	5	1	no	maximal, Hall
8	C₂⁴×C₃×C₅	D₃	1	4	yes	—
9	C₂²×Dic₁₅	—	3	56	no	—
10	C₂²×C₃²×C₅	C₂×C₄	1	28	yes	complemented
11	C₂²×C₃²×C₅	C₂³	1	7	yes	—
12	C₃⋊Dic₁₅	C₂³	1	8	yes	direct product factor
13	C₂³×Dic₅	—	9	1	no	Hall
14	C₂⁴×C₃²	D₅	1	1	yes	characteristic
15	C₂²×C₃⋊Dic₃	—	5	14	no	—
16	C₂³×C₃×C₅	Dic₃	1	32	yes	complemented
17	C₂³×C₃×C₅	C₂×D₃	1	28	yes	—
18	C₂×Dic₁₅	—	3	112	no	—
19	C₂³×Dic₃	—	15	4	no	—
20	C₂×C₃²×C₅	C₂²×C₄	1	14	yes	complemented
21	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
22	C₂⁴×C₅	C₃⋊D₃	1	1	yes	characteristic
23	C₂²×Dic₅	—	9	14	no	—
24	C₂³×C₃²	Dic₅	1	8	yes	complemented
25	C₂³×C₃²	C₂×D₅	1	7	yes	—
26	C₂×C₃⋊Dic₃	—	5	28	no	—
27	C₂²×C₃×C₅	C₂×Dic₃	1	112	yes	complemented
28	C₂²×C₃×C₅	C₂²×D₃	1	28	yes	—
29	Dic₁₅	—	3	32	no	—
30	C₂⁴×C₃	D₁₅	1	4	yes	—
31	C₂²×Dic₃	—	15	56	no	—
32	C₃²×C₅	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
33	C₂³×C₅	C₃⋊Dic₃	1	8	yes	complemented
34	C₂³×C₅	C₂×C₃⋊D₃	1	7	yes	—
35	C₂×Dic₅	—	9	28	no	—
36	C₂²×C₃²	C₂×Dic₅	1	28	yes	complemented
37	C₂²×C₃²	C₂²×D₅	1	7	yes	—
38	C₃⋊Dic₃	—	5	8	no	—
39	C₂³×C₄	—	45	1	no	Sylow
40	C₂×C₃×C₅	C₂²×Dic₃	1	56	yes	complemented
41	C₂×C₃×C₅	C₂³×D₃	1	4	yes	—
42	C₂³×C₃	Dic₁₅	1	32	yes	complemented
43	C₂³×C₃	C₂×D₁₅	1	28	yes	—
44	C₂×Dic₃	—	15	112	no	—
45	C₂²×C₅	C₂×C₃⋊Dic₃	1	28	yes	complemented
46	C₂²×C₅	C₂²×C₃⋊D₃	1	7	yes	—
47	Dic₅	—	9	8	no	—
48	C₂×C₃²	C₂²×Dic₅	1	14	yes	complemented
49	C₂×C₃²	C₂³×D₅	1	1	yes	characteristic
50	C₂⁴	C₃⋊D₁₅	1	1	yes	characteristic
51	C₂²×C₄	—	45	14	no	—
52	C₃×C₅	C₂³×Dic₃	1	4	yes	complemented
53	C₂²×C₃	C₂×Dic₁₅	1	112	yes	complemented
54	C₂²×C₃	C₂²×D₁₅	1	28	yes	—
55	Dic₃	—	15	32	no	—
56	C₂×C₅	C₂²×C₃⋊Dic₃	1	14	yes	complemented
57	C₂×C₅	C₂³×C₃⋊D₃	1	1	yes	characteristic
58	C₃²	C₂³×Dic₅	1	1	yes	characteristic, complemented, Sylow
59	C₂³	C₃⋊Dic₁₅	1	8	yes	direct product factor
60	C₂³	C₂×C₃⋊D₁₅	1	7	yes	—
61	C₂×C₄	—	45	28	no	—
62	C₂×C₃	C₂²×Dic₁₅	1	56	yes	complemented
63	C₂×C₃	C₂³×D₁₅	1	4	yes	—
64	C₅	C₂³×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
65	C₂²	C₂×C₃⋊Dic₁₅	1	28	yes	direct product factor
66	C₂²	C₂²×C₃⋊D₁₅	1	7	yes	—
67	C₄	—	45	8	no	—
68	C₃	C₂³×Dic₁₅	1	4	yes	complemented
69	C₂	C₂²×C₃⋊Dic₁₅	1	14	yes	direct product factor
70	C₂	C₂³×C₃⋊D₁₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴	C₃⋊D₁₅
commutator, hypocenter	C₃²×C₅	C₂³×C₄
Frattini	C₂	C₂³×C₃⋊D₁₅
Fitting, socle, prime radical	C₂⁴×C₃²×C₅	C₂
cosocle	C₂×C₃²×C₅	C₂⁴
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃⋊Dic₁₅	C₂	direct (N × H)
4. C₂³×C₃²×C₅	C₄	semidirect
6. C₂×C₃⋊Dic₁₅	C₂²	direct (N × H)
10. C₂²×C₃²×C₅	C₂×C₄	semidirect
12. C₃⋊Dic₁₅	C₂³	direct (N × H)
16. C₂³×C₃×C₅	Dic₃	semidirect
20. C₂×C₃²×C₅	C₂²×C₄	semidirect
24. C₂³×C₃²	Dic₅	semidirect
27. C₂²×C₃×C₅	C₂×Dic₃	semidirect
32. C₃²×C₅	C₂³×C₄	semidirect
33. C₂³×C₅	C₃⋊Dic₃	semidirect
36. C₂²×C₃²	C₂×Dic₅	semidirect
40. C₂×C₃×C₅	C₂²×Dic₃	semidirect
42. C₂³×C₃	Dic₁₅	semidirect
45. C₂²×C₅	C₂×C₃⋊Dic₃	semidirect
48. C₂×C₃²	C₂²×Dic₅	semidirect
52. C₃×C₅	C₂³×Dic₃	semidirect
53. C₂²×C₃	C₂×Dic₁₅	semidirect
56. C₂×C₅	C₂²×C₃⋊Dic₃	semidirect
58. C₃²	C₂³×Dic₅	semidirect
59. C₂³	C₃⋊Dic₁₅	direct (N × H)
62. C₂×C₃	C₂²×Dic₁₅	semidirect
64. C₅	C₂³×C₃⋊Dic₃	semidirect
65. C₂²	C₂×C₃⋊Dic₁₅	direct (N × H)
68. C₃	C₂³×Dic₁₅	semidirect
69. C₂	C₂²×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
C₂⁴×C₃²×C₅	2
C₂²×C₃⋊Dic₁₅	2
C₂³×Dic₁₅	3
C₂³×C₃⋊Dic₃	5

Subgroups — C23×C3⋊Dic15 #13089516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃⋊Dic₁₅ #13089516