Subgroups — C₅×D₃×D₈ #91713

Order 480.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×D₄	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#213	C₂	1	2	yes	maximal, complemented
4	C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×D₈	—	3	1	no	maximal, Hall
7	C₂²×C₅×D₃	—	2	2	no	—
8	C₃×C₅×D₄	C₂²	1	2	yes	complemented
9	C₅×#67	—	2	2	no	—
10	C₅×D₁₂	C₂²	1	2	yes	complemented
11	C₄×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
13	C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
14	D₃×D₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₅×D₄	—	3	2	no	—
16	C₅×D₈	—	3	2	no	—
17	C₅×D₈	—	3	1	no	—
18	C₅×D₈	D₃	1	1	yes	characteristic, direct product factor
19	C₂×C₅×C₈	—	3	1	no	—
20	C₂²×C₃×C₅	—	2	2	no	—
21	C₂×C₅×D₃	—	2	2	no	—
22	C₂×C₅×D₃	—	4	4	no	—
23	C₂×C₅×D₃	D₄	1	1	yes	characteristic
24	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₅×Dic₃	D₄	1	1	yes	characteristic
26	D₃×D₄	C₂×C₅	1	2	yes	complemented
27	C₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
28	#213	C₂×C₅	1	2	yes	complemented
29	D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
30	D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
31	C₂³×C₅	—	6	2	no	—
32	C₅×D₄	—	3	2	no	—
33	C₅×D₄	—	6	2	no	—
34	C₅×D₄	C₂×D₃	1	2	yes	complemented
35	C₂×C₄×C₅	—	3	1	no	—
36	C₅×C₈	—	3	1	no	—
37	C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
38	C₂×D₈	—	3	1	no	Sylow
39	C₂×C₃×C₅	—	4	2	no	—
40	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
41	C₅×D₃	—	4	2	no	—
42	C₅×D₃	D₈	1	2	yes	direct product factor
43	C₂²×D₃	—	2	2	no	—
44	C₃×D₄	C₂²×C₅	1	2	yes	complemented
45	#67	—	2	2	no	—
46	D₁₂	C₂²×C₅	1	2	yes	complemented
47	C₄×D₃	C₂²×C₅	1	1	yes	characteristic
48	C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
49	C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
50	C₂²×C₅	—	2	2	no	—
51	C₂²×C₅	—	3	1	no	—
52	C₂²×C₅	—	6	2	no	—
53	C₂²×C₅	—	12	4	no	—
54	C₄×C₅	—	3	1	no	—
55	C₄×C₅	C₂²×D₃	1	1	yes	characteristic
56	C₂×D₄	—	3	2	no	—
57	D₈	—	3	2	no	—
58	D₈	—	3	1	no	—
59	D₈	C₅×D₃	1	1	yes	characteristic, direct product factor
60	C₂×C₈	—	3	1	no	—
61	C₃×C₅	C₂×D₈	1	1	yes	characteristic, complemented, Hall
62	C₂²×C₃	—	2	2	no	—
63	C₂×D₃	—	2	2	no	—
64	C₂×D₃	—	4	4	no	—
65	C₂×D₃	C₅×D₄	1	1	yes	characteristic
66	C₃×C₄	C₂³×C₅	1	1	yes	characteristic
67	Dic₃	C₅×D₄	1	1	yes	characteristic
68	C₂×C₅	—	3	2	no	—
69	C₂×C₅	—	4	2	no	—
70	C₂×C₅	—	12	2	no	—
71	C₂×C₅	D₃×D₄	1	1	yes	characteristic
72	C₂³	—	6	2	no	—
73	D₄	—	3	2	no	—
74	D₄	—	6	2	no	—
75	D₄	C₂×C₅×D₃	1	2	yes	complemented
76	C₂×C₄	—	3	1	no	—
77	C₈	—	3	1	no	—
78	C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
79	C₂×C₃	—	4	2	no	—
80	C₂×C₃	C₂×C₅×D₄	1	1	yes	characteristic
81	D₃	—	4	2	no	—
82	D₃	C₅×D₈	1	2	yes	direct product factor
83	C₅	D₃×D₈	1	1	yes	characteristic, direct product factor, Sylow
84	C₂²	—	2	2	no	—
85	C₂²	—	3	1	no	—
86	C₂²	—	6	2	no	—
87	C₂²	—	12	4	no	—
88	C₄	—	3	1	no	—
89	C₄	C₂²×C₅×D₃	1	1	yes	characteristic
90	C₃	C₂×C₅×D₈	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	3	2	no	—
92	C₂	—	4	2	no	—
93	C₂	—	12	2	no	—
94	C₂	C₅×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	D₃×D₄
commutator, cosocle	C₃×C₄	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×D₈	C₂
socle	C₂×C₃×C₅	C₂×D₄
hypercenter	C₅×D₈	D₃
hypocenter	C₃	C₂×C₅×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×D₈

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×D₄	C₂	semidirect
2. C₃×C₅×D₈	C₂	semidirect
3. C₅×#213	C₂	semidirect
4. C₅×D₂₄	C₂	semidirect
5. C₅×D₃×C₈	C₂	semidirect
8. C₃×C₅×D₄	C₂²	semidirect
10. C₅×D₁₂	C₂²	semidirect
12. C₃×C₅×C₈	C₂²	semidirect
13. C₅×C₃⋊C₈	C₂²	semidirect
14. D₃×D₈	C₅	direct (N × H)
18. C₅×D₈	D₃	direct (N × H)
26. D₃×D₄	C₂×C₅	semidirect
27. C₃×D₈	C₂×C₅	semidirect
28. #213	C₂×C₅	semidirect
29. D₂₄	C₂×C₅	semidirect
30. D₃×C₈	C₂×C₅	semidirect
34. C₅×D₄	C₂×D₃	semidirect
37. C₅×C₈	C₂×D₃	semidirect
42. C₅×D₃	D₈	direct (N × H)
44. C₃×D₄	C₂²×C₅	semidirect
46. D₁₂	C₂²×C₅	semidirect
48. C₃×C₈	C₂²×C₅	semidirect
49. C₃⋊C₈	C₂²×C₅	semidirect
59. D₈	C₅×D₃	direct (N × H)
61. C₃×C₅	C₂×D₈	semidirect
75. D₄	C₂×C₅×D₃	semidirect
78. C₈	C₂×C₅×D₃	semidirect
82. D₃	C₅×D₈	direct (N × H)
83. C₅	D₃×D₈	direct (N × H)
90. C₃	C₂×C₅×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×D₄	2
C₃×C₅×D₈	2
C₅×#213	2
C₅×D₂₄	2
C₅×D₃×C₈	2
C₂×C₅×D₈	3
D₃×D₈	5

Subgroups — C5×D3×D8 #91713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×D₈ #91713