Subgroups — C₄×D₃×Dic₅ #91397

Order 480.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃×Dic₅	C₂	1	2	yes	maximal
3	C₄×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₃×Dic₅	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×Dic₅	—	3	1	no	maximal, Hall
7	C₂²×C₅×D₃	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₅	C₂²	1	2	yes	—
10	C₂×C₅×Dic₃	C₂²	1	1	yes	characteristic
11	C₄×C₅×D₃	C₄	1	4	yes	complemented
12	C₂×C₃×Dic₅	C₂²	1	2	yes	—
13	D₃×Dic₅	C₄	1	8	yes	direct product factor
14	C₄²×D₃	—	5	1	no	maximal, Hall
15	C₂²×C₄×C₅	—	3	1	no	—
16	C₂²×Dic₅	—	3	2	no	—
17	C₄×Dic₅	—	3	1	no	—
18	C₄×Dic₅	—	3	2	no	—
19	C₄×Dic₅	D₃	1	1	yes	characteristic, direct product factor
20	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
21	C₂×C₅×D₃	C₂×C₄	1	4	yes	—
22	C₂×C₅×D₃	C₂×C₄	1	2	yes	—
23	C₃×C₄×C₅	C₂×C₄	1	2	yes	complemented
24	Dic₁₅	C₂×C₄	1	4	yes	complemented
25	C₃×Dic₅	C₂×C₄	1	4	yes	complemented
26	C₅×Dic₃	C₂×C₄	1	2	yes	complemented
27	C₂×C₄×D₃	—	5	2	no	—
28	C₂×C₄×D₃	D₅	1	1	yes	characteristic
29	C₃×C₄²	—	5	1	no	—
30	C₄×Dic₃	—	5	1	no	—
31	C₄×Dic₃	—	5	2	no	—
32	C₂³×C₅	—	3	1	no	—
33	C₂×C₄×C₅	—	3	1	no	—
34	C₂×C₄×C₅	—	3	4	no	—
35	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
36	C₂×Dic₅	—	3	2	no	—
37	C₂×Dic₅	—	3	8	no	—
38	C₂×Dic₅	C₂×D₃	1	2	yes	—
39	C₂×C₄²	—	15	1	no	Sylow
40	C₂×C₃×C₅	C₂²×C₄	1	2	yes	—
41	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
42	C₅×D₃	C₄²	1	4	yes	complemented
43	C₂²×D₃	C₂×D₅	1	1	yes	characteristic
44	C₂×C₃×C₄	—	5	2	no	—
45	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
46	C₂×Dic₃	—	5	2	no	—
47	C₂×Dic₃	C₂×D₅	1	1	yes	characteristic
48	C₄×D₃	—	5	8	no	—
49	C₄×D₃	Dic₅	1	4	yes	direct product factor
50	C₂²×C₅	—	3	4	no	—
51	C₂²×C₅	—	3	2	no	—
52	C₂²×C₅	C₂²×D₃	1	1	yes	characteristic
53	C₄×C₅	—	3	2	no	—
54	C₄×C₅	C₄×D₃	1	2	yes	complemented
55	Dic₅	—	3	4	no	—
56	Dic₅	C₄×D₃	1	4	yes	direct product factor
57	C₂²×C₄	—	3	1	no	—
58	C₂²×C₄	—	15	2	no	—
59	C₄²	—	5	1	no	—
60	C₄²	—	15	2	no	—
61	C₄²	—	15	1	no	—
62	C₃×C₅	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
63	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
64	C₂×D₃	C₄×D₅	1	4	yes	—
65	C₂×D₃	C₂×Dic₅	1	2	yes	—
66	C₃×C₄	—	5	4	no	—
67	C₃×C₄	C₂×Dic₅	1	2	yes	complemented
68	Dic₃	—	5	4	no	—
69	Dic₃	C₂×Dic₅	1	2	yes	complemented
70	C₂×C₅	—	3	4	no	—
71	C₂×C₅	C₂×C₄×D₃	1	2	yes	—
72	C₂×C₅	C₂×C₄×D₃	1	1	yes	characteristic
73	C₂³	—	3	1	no	—
74	C₂×C₄	—	3	1	no	—
75	C₂×C₄	—	3	4	no	—
76	C₂×C₄	—	5	2	no	—
77	C₂×C₄	—	15	8	no	—
78	C₂×C₄	—	15	2	no	—
79	C₂×C₄	D₃×D₅	1	1	yes	characteristic
80	C₂×C₃	C₂×C₄×D₅	1	2	yes	—
81	C₂×C₃	C₂²×Dic₅	1	1	yes	characteristic
82	D₃	C₄×Dic₅	1	4	yes	direct product factor
83	C₅	C₄²×D₃	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	3	4	no	—
85	C₂²	—	3	2	no	—
86	C₂²	C₂×D₃×D₅	1	1	yes	characteristic
87	C₄	—	3	2	no	—
88	C₄	—	5	4	no	—
89	C₄	—	15	4	no	—
90	C₄	D₃×Dic₅	1	2	yes	direct product factor
91	C₃	C₂×C₄×Dic₅	1	1	yes	characteristic, complemented, Sylow
92	C₂	—	3	4	no	—
93	C₂	C₄×D₃×D₅	1	2	yes	—
94	C₂	C₂×D₃×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂×C₄²
Frattini	C₂²	C₂×D₃×D₅
Fitting	C₂×C₃×C₄×C₅	C₂²
socle, cosocle	C₂²×C₃×C₅	C₂³
prime radical	C₂²×C₅×D₃	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
3. C₄×Dic₁₅	C₂	semidirect
4. C₃×C₄×Dic₅	C₂	semidirect
5. Dic₃×Dic₅	C₂	semidirect
11. C₄×C₅×D₃	C₄	semidirect
13. D₃×Dic₅	C₄	direct (N × H)
19. C₄×Dic₅	D₃	direct (N × H)
23. C₃×C₄×C₅	C₂×C₄	semidirect
24. Dic₁₅	C₂×C₄	semidirect
25. C₃×Dic₅	C₂×C₄	semidirect
26. C₅×Dic₃	C₂×C₄	semidirect
42. C₅×D₃	C₄²	semidirect
49. C₄×D₃	Dic₅	direct (N × H)
54. C₄×C₅	C₄×D₃	semidirect
56. Dic₅	C₄×D₃	direct (N × H)
62. C₃×C₅	C₂×C₄²	semidirect
67. C₃×C₄	C₂×Dic₅	semidirect
69. Dic₃	C₂×Dic₅	semidirect
82. D₃	C₄×Dic₅	direct (N × H)
83. C₅	C₄²×D₃	semidirect
90. C₄	D₃×Dic₅	direct (N × H)
91. C₃	C₂×C₄×Dic₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×D₃	2
C₂×D₃×Dic₅	2
C₄×Dic₁₅	2
C₃×C₄×Dic₅	2
Dic₃×Dic₅	2
C₂×C₄×Dic₅	3
C₄²×D₃	5

Subgroups — C4×D3×Dic5 #91397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₃×Dic₅ #91397