Subgroups — C₂³×D₃×D₅ #92131

Order 480.

1496 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₃×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₃×D₅	C₂	1	28	yes	maximal, direct product factor
5	C₂⁴×D₅	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic, complemented
7	C₂²×D₁₅	C₂²	1	14	yes	complemented
8	C₂²×C₅×D₃	C₂²	1	14	yes	complemented
9	C₂²×C₃×D₅	C₂²	1	14	yes	complemented
10	C₂×D₃×D₅	C₂²	1	112	yes	direct product factor
11	C₂⁴×D₃	—	5	1	no	maximal, Hall
12	C₂⁴×C₅	—	3	1	no	—
13	C₂³×D₅	—	3	1	no	—
14	C₂³×D₅	—	3	28	no	—
15	C₂³×D₅	D₃	1	1	yes	characteristic, direct product factor
16	C₂²×C₃×C₅	C₂³	1	7	yes	complemented
17	C₂×D₁₅	C₂³	1	28	yes	complemented
18	C₂×C₅×D₃	C₂³	1	28	yes	complemented
19	C₂×C₃×D₅	C₂³	1	28	yes	complemented
20	D₃×D₅	C₂³	1	64	yes	direct product factor
21	C₂⁴×C₃	—	5	1	no	—
22	C₂³×D₃	—	5	1	no	—
23	C₂³×D₃	—	5	28	no	—
24	C₂³×D₃	D₅	1	1	yes	characteristic, direct product factor
25	C₂³×C₅	—	3	14	no	—
26	C₂³×C₅	C₂×D₃	1	1	yes	characteristic, complemented
27	C₂²×D₅	—	3	14	no	—
28	C₂²×D₅	—	3	112	no	—
29	C₂²×D₅	C₂×D₃	1	14	yes	direct product factor
30	C₂⁵	—	15	1	no	Sylow
31	C₂×C₃×C₅	C₂⁴	1	7	yes	complemented
32	D₁₅	C₂⁴	1	8	yes	complemented
33	C₃×D₅	C₂⁴	1	8	yes	complemented
34	C₅×D₃	C₂⁴	1	8	yes	complemented
35	C₂³×C₃	—	5	14	no	—
36	C₂³×C₃	C₂×D₅	1	1	yes	characteristic, complemented
37	C₂²×D₃	—	5	14	no	—
38	C₂²×D₃	—	5	112	no	—
39	C₂²×D₃	C₂×D₅	1	14	yes	direct product factor
40	C₂²×C₅	—	3	28	no	—
41	C₂²×C₅	C₂²×D₃	1	7	yes	complemented
42	C₂×D₅	—	3	28	no	—
43	C₂×D₅	—	3	64	no	—
44	C₂×D₅	C₂²×D₃	1	28	yes	direct product factor
45	C₂⁴	—	3	1	no	—
46	C₂⁴	—	5	1	no	—
47	C₂⁴	—	15	28	no	—
48	C₂⁴	—	15	1	no	—
49	C₃×C₅	C₂⁵	1	1	yes	characteristic, complemented, Hall
50	C₂²×C₃	—	5	28	no	—
51	C₂²×C₃	C₂²×D₅	1	7	yes	complemented
52	C₂×D₃	—	5	28	no	—
53	C₂×D₃	—	5	64	no	—
54	C₂×D₃	C₂²×D₅	1	28	yes	direct product factor
55	C₂×C₅	—	3	8	no	—
56	C₂×C₅	C₂³×D₃	1	7	yes	complemented
57	D₅	—	3	8	no	—
58	D₅	C₂³×D₃	1	8	yes	direct product factor
59	C₂³	—	3	14	no	—
60	C₂³	—	5	14	no	—
61	C₂³	—	15	112	no	—
62	C₂³	—	15	14	no	—
63	C₂³	D₃×D₅	1	1	yes	characteristic, direct product factor
64	C₂×C₃	—	5	8	no	—
65	C₂×C₃	C₂³×D₅	1	7	yes	complemented
66	D₃	—	5	8	no	—
67	D₃	C₂³×D₅	1	8	yes	direct product factor
68	C₅	C₂⁴×D₃	1	1	yes	characteristic, complemented, Sylow
69	C₂²	—	3	28	no	—
70	C₂²	—	5	28	no	—
71	C₂²	—	15	64	no	—
72	C₂²	—	15	28	no	—
73	C₂²	C₂×D₃×D₅	1	7	yes	direct product factor
74	C₃	C₂⁴×D₅	1	1	yes	characteristic, complemented, Sylow
75	C₂	—	3	8	no	—
76	C₂	—	5	8	no	—
77	C₂	—	15	8	no	—
78	C₂	C₂²×D₃×D₅	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	D₃×D₅
commutator, cosocle, hypocenter	C₃×C₅	C₂⁵
Frattini	C₁	G
Fitting, socle	C₂³×C₃×C₅	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂³×D₁₅	C₂	semidirect
2. C₂³×C₅×D₃	C₂	semidirect
3. C₂³×C₃×D₅	C₂	semidirect
4. C₂²×D₃×D₅	C₂	direct (N × H)
6. C₂³×C₃×C₅	C₂²	semidirect
7. C₂²×D₁₅	C₂²	semidirect
8. C₂²×C₅×D₃	C₂²	semidirect
9. C₂²×C₃×D₅	C₂²	semidirect
10. C₂×D₃×D₅	C₂²	direct (N × H)
15. C₂³×D₅	D₃	direct (N × H)
16. C₂²×C₃×C₅	C₂³	semidirect
17. C₂×D₁₅	C₂³	semidirect
18. C₂×C₅×D₃	C₂³	semidirect
19. C₂×C₃×D₅	C₂³	semidirect
20. D₃×D₅	C₂³	direct (N × H)
24. C₂³×D₃	D₅	direct (N × H)
26. C₂³×C₅	C₂×D₃	semidirect
29. C₂²×D₅	C₂×D₃	direct (N × H)
31. C₂×C₃×C₅	C₂⁴	semidirect
32. D₁₅	C₂⁴	semidirect
33. C₃×D₅	C₂⁴	semidirect
34. C₅×D₃	C₂⁴	semidirect
36. C₂³×C₃	C₂×D₅	semidirect
39. C₂²×D₃	C₂×D₅	direct (N × H)
41. C₂²×C₅	C₂²×D₃	semidirect
44. C₂×D₅	C₂²×D₃	direct (N × H)
49. C₃×C₅	C₂⁵	semidirect
51. C₂²×C₃	C₂²×D₅	semidirect
54. C₂×D₃	C₂²×D₅	direct (N × H)
56. C₂×C₅	C₂³×D₃	semidirect
58. D₅	C₂³×D₃	direct (N × H)
63. C₂³	D₃×D₅	direct (N × H)
65. C₂×C₃	C₂³×D₅	semidirect
67. D₃	C₂³×D₅	direct (N × H)
68. C₅	C₂⁴×D₃	semidirect
73. C₂²	C₂×D₃×D₅	direct (N × H)
74. C₃	C₂⁴×D₅	semidirect
78. C₂	C₂²×D₃×D₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₁₅	2
C₂³×C₅×D₃	2
C₂³×C₃×D₅	2
C₂²×D₃×D₅	2
C₂⁴×D₅	3
C₂⁴×D₃	5

Subgroups — C23×D3×D5 #92131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×D₃×D₅ #92131