Subgroups — C₃×D₅×D₈ #91627

Order 480.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×D₅	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#686	C₂	1	2	yes	maximal, complemented
4	C₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	D₅×D₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×D₅	—	2	2	no	—
8	C₃×C₅×D₄	C₂²	1	2	yes	complemented
9	C₃×C₂²⋊D₅	—	2	2	no	—
10	C₃×D₂₀	C₂²	1	2	yes	complemented
11	C₃×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
13	C₃×#168	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×D₈	—	5	1	no	maximal, Hall
15	D₄×D₅	C₂×C₃	1	2	yes	complemented
16	C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
17	#686	C₂×C₃	1	2	yes	complemented
18	D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
19	C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
20	C₂²×C₃×C₅	—	2	2	no	—
21	C₂×C₃×D₅	—	2	2	no	—
22	C₂×C₃×D₅	—	4	4	no	—
23	C₂×C₃×D₅	D₄	1	1	yes	characteristic
24	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₃×Dic₅	D₄	1	1	yes	characteristic
26	C₂×C₃×D₄	—	5	2	no	—
27	C₃×D₈	—	5	2	no	—
28	C₃×D₈	—	5	1	no	—
29	C₃×D₈	D₅	1	1	yes	characteristic, direct product factor
30	C₂×C₃×C₈	—	5	1	no	—
31	C₂²×D₅	—	2	2	no	—
32	C₅×D₄	C₂²×C₃	1	2	yes	complemented
33	C₂²⋊D₅	—	2	2	no	—
34	D₂₀	C₂²×C₃	1	2	yes	complemented
35	C₄×D₅	C₂²×C₃	1	1	yes	characteristic
36	C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
37	#168	C₂²×C₃	1	1	yes	characteristic, complemented
38	C₂×D₈	—	5	1	no	Sylow
39	C₂×C₃×C₅	—	4	2	no	—
40	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
41	C₃×D₅	—	4	2	no	—
42	C₃×D₅	D₈	1	2	yes	direct product factor
43	C₂³×C₃	—	10	2	no	—
44	C₃×D₄	—	5	2	no	—
45	C₃×D₄	—	10	2	no	—
46	C₃×D₄	C₂×D₅	1	2	yes	complemented
47	C₂×C₃×C₄	—	5	1	no	—
48	C₃×C₈	—	5	1	no	—
49	C₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
50	C₂²×C₅	—	2	2	no	—
51	C₂×D₅	—	2	2	no	—
52	C₂×D₅	—	4	4	no	—
53	C₂×D₅	C₃×D₄	1	1	yes	characteristic
54	C₄×C₅	C₂³×C₃	1	1	yes	characteristic
55	Dic₅	C₃×D₄	1	1	yes	characteristic
56	C₂×D₄	—	5	2	no	—
57	D₈	—	5	2	no	—
58	D₈	—	5	1	no	—
59	D₈	C₃×D₅	1	1	yes	characteristic, direct product factor
60	C₂×C₈	—	5	1	no	—
61	C₃×C₅	C₂×D₈	1	1	yes	characteristic, complemented, Hall
62	C₂²×C₃	—	2	2	no	—
63	C₂²×C₃	—	5	1	no	—
64	C₂²×C₃	—	10	2	no	—
65	C₂²×C₃	—	20	4	no	—
66	C₃×C₄	—	5	1	no	—
67	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
68	C₂×C₅	—	4	2	no	—
69	C₂×C₅	C₂×C₃×D₄	1	1	yes	characteristic
70	D₅	—	4	2	no	—
71	D₅	C₃×D₈	1	2	yes	direct product factor
72	C₂³	—	10	2	no	—
73	D₄	—	5	2	no	—
74	D₄	—	10	2	no	—
75	D₄	C₂×C₃×D₅	1	2	yes	complemented
76	C₂×C₄	—	5	1	no	—
77	C₈	—	5	1	no	—
78	C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
79	C₂×C₃	—	4	2	no	—
80	C₂×C₃	—	5	2	no	—
81	C₂×C₃	—	20	2	no	—
82	C₂×C₃	D₄×D₅	1	1	yes	characteristic
83	C₅	C₂×C₃×D₈	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	2	2	no	—
85	C₂²	—	5	1	no	—
86	C₂²	—	10	2	no	—
87	C₂²	—	20	4	no	—
88	C₄	—	5	1	no	—
89	C₄	C₂²×C₃×D₅	1	1	yes	characteristic
90	C₃	D₅×D₈	1	1	yes	characteristic, direct product factor, Sylow
91	C₂	—	4	2	no	—
92	C₂	—	5	2	no	—
93	C₂	—	20	2	no	—
94	C₂	C₃×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₄×D₅
commutator, cosocle	C₄×C₅	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×D₈	C₂
socle	C₂×C₃×C₅	C₂×D₄
hypercenter	C₃×D₈	D₅
hypocenter	C₅	C₂×C₃×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×D₈

Complements

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

N	H ≅ G/N	type
1. C₃×D₄×D₅	C₂	semidirect
2. C₃×C₅×D₈	C₂	semidirect
3. C₃×#686	C₂	semidirect
4. C₃×D₄₀	C₂	semidirect
5. C₃×C₈×D₅	C₂	semidirect
6. D₅×D₈	C₃	direct (N × H)
8. C₃×C₅×D₄	C₂²	semidirect
10. C₃×D₂₀	C₂²	semidirect
12. C₃×C₅×C₈	C₂²	semidirect
13. C₃×#168	C₂²	semidirect
15. D₄×D₅	C₂×C₃	semidirect
16. C₅×D₈	C₂×C₃	semidirect
17. #686	C₂×C₃	semidirect
18. D₄₀	C₂×C₃	semidirect
19. C₈×D₅	C₂×C₃	semidirect
29. C₃×D₈	D₅	direct (N × H)
32. C₅×D₄	C₂²×C₃	semidirect
34. D₂₀	C₂²×C₃	semidirect
36. C₅×C₈	C₂²×C₃	semidirect
37. #168	C₂²×C₃	semidirect
42. C₃×D₅	D₈	direct (N × H)
46. C₃×D₄	C₂×D₅	semidirect
49. C₃×C₈	C₂×D₅	semidirect
59. D₈	C₃×D₅	direct (N × H)
61. C₃×C₅	C₂×D₈	semidirect
71. D₅	C₃×D₈	direct (N × H)
75. D₄	C₂×C₃×D₅	semidirect
78. C₈	C₂×C₃×D₅	semidirect
83. C₅	C₂×C₃×D₈	semidirect
90. C₃	D₅×D₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₄×D₅	2
C₃×C₅×D₈	2
C₃×#686	2
C₃×D₄₀	2
C₃×C₈×D₅	2
D₅×D₈	3
C₂×C₃×D₈	5

Subgroups — C3×D5×D8 #91627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×D₈ #91627