Subgroups — C₂×C₃×C₂²⋊Dic₅ #91669

Order 480.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×Dic₅	C₂	1	2	yes	maximal, complemented
3	C₃×C₂²⋊Dic₅	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₂²⋊Dic₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₃×C₅	—	2	4	no	—
6	C₂³×C₃×C₅	C₄	1	4	yes	complemented
7	C₂³×C₃×C₅	C₂²	1	2	yes	—
8	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×Dic₅	—	2	4	no	—
10	C₂×C₃×Dic₅	C₂²	1	4	yes	complemented
11	C₂×C₃×C₂²⋊C₄	—	5	1	no	maximal, Hall
12	C₂⁴×C₅	C₂×C₃	1	1	yes	characteristic
13	C₂²×Dic₅	C₂×C₃	1	2	yes	complemented
14	C₂²⋊Dic₅	C₂×C₃	1	4	yes	direct product factor
15	C₂²×C₃×C₅	—	2	8	no	—
16	C₂²×C₃×C₅	—	2	4	no	—
17	C₂²×C₃×C₅	C₂×C₄	1	2	yes	—
18	C₂²×C₃×C₅	C₂×C₄	1	4	yes	complemented
19	C₂²×C₃×C₅	D₄	1	4	yes	—
20	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
21	C₃×Dic₅	—	2	4	no	—
22	C₂⁴×C₃	D₅	1	1	yes	characteristic
23	C₂²×C₃×C₄	—	5	2	no	—
24	C₃×C₂²⋊C₄	—	5	4	no	—
25	C₂³×C₅	—	2	4	no	—
26	C₂³×C₅	C₃×C₄	1	4	yes	complemented
27	C₂³×C₅	C₂²×C₃	1	2	yes	—
28	C₂³×C₅	C₂²×C₃	1	1	yes	characteristic
29	C₂×Dic₅	—	2	4	no	—
30	C₂×Dic₅	C₂²×C₃	1	4	yes	complemented
31	C₂×C₂²⋊C₄	—	5	1	no	Sylow
32	C₂×C₃×C₅	—	2	4	no	—
33	C₂×C₃×C₅	C₂²⋊C₄	1	4	yes	complemented
34	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₃×C₅	C₂×D₄	1	2	yes	—
36	C₂³×C₃	—	2	4	no	—
37	C₂³×C₃	Dic₅	1	4	yes	complemented
38	C₂³×C₃	C₂×D₅	1	2	yes	—
39	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
40	C₂×C₃×C₄	—	5	4	no	—
41	C₂×C₃×C₄	—	10	4	no	—
42	C₂²×C₅	—	2	8	no	—
43	C₂²×C₅	—	2	4	no	—
44	C₂²×C₅	C₂×C₃×C₄	1	2	yes	—
45	C₂²×C₅	C₂×C₃×C₄	1	4	yes	complemented
46	C₂²×C₅	C₃×D₄	1	4	yes	—
47	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
48	Dic₅	—	2	4	no	—
49	C₂⁴	C₃×D₅	1	1	yes	characteristic
50	C₂²×C₄	—	5	2	no	—
51	C₂²⋊C₄	—	5	4	no	—
52	C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
53	C₂²×C₃	—	2	8	no	—
54	C₂²×C₃	—	2	4	no	—
55	C₂²×C₃	C₂×Dic₅	1	2	yes	—
56	C₂²×C₃	C₂×Dic₅	1	4	yes	complemented
57	C₂²×C₃	C₂²⋊D₅	1	4	yes	—
58	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
59	C₃×C₄	—	10	4	no	—
60	C₂×C₅	—	2	4	no	—
61	C₂×C₅	C₃×C₂²⋊C₄	1	4	yes	complemented
62	C₂×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
63	C₂×C₅	C₂×C₃×D₄	1	2	yes	—
64	C₂³	—	2	4	no	—
65	C₂³	C₃×Dic₅	1	4	yes	complemented
66	C₂³	C₂×C₃×D₅	1	2	yes	—
67	C₂³	C₂×C₃×D₅	1	1	yes	characteristic
68	C₂×C₄	—	5	4	no	—
69	C₂×C₄	—	10	4	no	—
70	C₂×C₃	—	2	4	no	—
71	C₂×C₃	C₂²⋊Dic₅	1	4	yes	direct product factor
72	C₂×C₃	C₂²×Dic₅	1	1	yes	characteristic
73	C₂×C₃	C₂×C₂²⋊D₅	1	2	yes	—
74	C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	2	8	no	—
76	C₂²	—	2	4	no	—
77	C₂²	C₂×C₃×Dic₅	1	2	yes	—
78	C₂²	C₂×C₃×Dic₅	1	4	yes	complemented
79	C₂²	C₃×C₂²⋊D₅	1	4	yes	—
80	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
81	C₄	—	10	4	no	—
82	C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic, direct product factor, Sylow
83	C₂	—	2	4	no	—
84	C₂	C₃×C₂²⋊Dic₅	1	4	yes	direct product factor
85	C₂	C₂²×C₃×Dic₅	1	1	yes	characteristic
86	C₂	C₂×C₃×C₂²⋊D₅	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂×D₅
commutator	C₂×C₅	C₂²×C₃×C₄
Frattini	C₂²	C₂²×C₃×D₅
Fitting, prime radical	C₂⁴×C₃×C₅	C₂
socle	C₂³×C₃×C₅	C₂²
cosocle	C₂²×C₅	C₂³×C₃
hypercenter	C₂⁴×C₃	D₅
hypocenter	C₅	C₂×C₃×C₂²⋊C₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂⁴×C₃

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×Dic₅	C₂	semidirect
3. C₃×C₂²⋊Dic₅	C₂	direct (N × H)
4. C₂×C₂²⋊Dic₅	C₃	direct (N × H)
6. C₂³×C₃×C₅	C₄	semidirect
10. C₂×C₃×Dic₅	C₂²	semidirect
13. C₂²×Dic₅	C₂×C₃	semidirect
14. C₂²⋊Dic₅	C₂×C₃	direct (N × H)
18. C₂²×C₃×C₅	C₂×C₄	semidirect
26. C₂³×C₅	C₃×C₄	semidirect
30. C₂×Dic₅	C₂²×C₃	semidirect
33. C₂×C₃×C₅	C₂²⋊C₄	semidirect
37. C₂³×C₃	Dic₅	semidirect
45. C₂²×C₅	C₂×C₃×C₄	semidirect
52. C₃×C₅	C₂×C₂²⋊C₄	semidirect
56. C₂²×C₃	C₂×Dic₅	semidirect
61. C₂×C₅	C₃×C₂²⋊C₄	semidirect
65. C₂³	C₃×Dic₅	semidirect
71. C₂×C₃	C₂²⋊Dic₅	direct (N × H)
74. C₅	C₂×C₃×C₂²⋊C₄	semidirect
78. C₂²	C₂×C₃×Dic₅	semidirect
82. C₃	C₂×C₂²⋊Dic₅	direct (N × H)
84. C₂	C₃×C₂²⋊Dic₅	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×C₃×C₅	2
C₂²×C₃×Dic₅	2
C₃×C₂²⋊Dic₅	2
C₂×C₂²⋊Dic₅	3
C₂×C₃×C₂²⋊C₄	5

Subgroups — C2×C3×C22⋊Dic5 #91669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₂²⋊Dic₅ #91669