Subgroups — C₂×C₃×C₄⋊Dic₅ #91642

Order 480.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×Dic₅	C₂	1	2	yes	maximal
3	C₃×C₄⋊Dic₅	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊Dic₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₅	C₄	1	4	yes	complemented
7	C₂×C₃×C₄×C₅	C₂²	1	2	yes	—
8	C₂×C₃×Dic₅	—	2	4	no	—
9	C₂×C₃×Dic₅	C₂²	1	4	yes	—
10	C₂×C₃×C₄⋊C₄	—	5	1	no	maximal, Hall
11	C₂²×C₄×C₅	C₂×C₃	1	1	yes	characteristic
12	C₂²×Dic₅	C₂×C₃	1	2	yes	—
13	C₄⋊Dic₅	C₂×C₃	1	4	yes	direct product factor
14	C₂²×C₃×C₅	C₂×C₄	1	2	yes	—
15	C₂²×C₃×C₅	D₄	1	2	yes	—
16	C₂²×C₃×C₅	Q₈	1	2	yes	—
17	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
18	C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
19	C₃×Dic₅	—	2	4	no	—
20	C₂²×C₃×C₄	—	5	2	no	—
21	C₂²×C₃×C₄	D₅	1	1	yes	characteristic
22	C₃×C₄⋊C₄	—	5	4	no	—
23	C₂³×C₅	C₂²×C₃	1	1	yes	characteristic
24	C₂×C₄×C₅	C₃×C₄	1	4	yes	complemented
25	C₂×C₄×C₅	C₂²×C₃	1	2	yes	—
26	C₂×Dic₅	—	2	4	no	—
27	C₂×Dic₅	C₂²×C₃	1	4	yes	—
28	C₂×C₄⋊C₄	—	5	1	no	Sylow
29	C₂×C₃×C₅	C₄⋊C₄	1	4	yes	complemented
30	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
32	C₂×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
33	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
34	C₂×C₃×C₄	—	5	4	no	—
35	C₂×C₃×C₄	—	10	4	no	—
36	C₂×C₃×C₄	Dic₅	1	4	yes	complemented
37	C₂×C₃×C₄	C₂×D₅	1	2	yes	—
38	C₂²×C₅	C₂×C₃×C₄	1	2	yes	—
39	C₂²×C₅	C₃×D₄	1	2	yes	—
40	C₂²×C₅	C₃×Q₈	1	2	yes	—
41	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
42	C₄×C₅	C₂×C₃×C₄	1	4	yes	complemented
43	Dic₅	—	2	4	no	—
44	C₂²×C₄	—	5	2	no	—
45	C₂²×C₄	C₃×D₅	1	1	yes	characteristic
46	C₄⋊C₄	—	5	4	no	—
47	C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₃	Dic₁₀	1	2	yes	—
49	C₂²×C₃	D₂₀	1	2	yes	—
50	C₂²×C₃	C₂×Dic₅	1	2	yes	—
51	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
52	C₃×C₄	—	10	4	no	—
53	C₃×C₄	C₂×Dic₅	1	4	yes	complemented
54	C₂×C₅	C₃×C₄⋊C₄	1	4	yes	complemented
55	C₂×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
56	C₂×C₅	C₂×C₃×D₄	1	1	yes	characteristic
57	C₂×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
58	C₂³	C₂×C₃×D₅	1	1	yes	characteristic
59	C₂×C₄	—	5	4	no	—
60	C₂×C₄	—	10	4	no	—
61	C₂×C₄	C₃×Dic₅	1	4	yes	complemented
62	C₂×C₄	C₂×C₃×D₅	1	2	yes	—
63	C₂×C₃	C₄⋊Dic₅	1	4	yes	direct product factor
64	C₂×C₃	C₂×Dic₁₀	1	1	yes	characteristic
65	C₂×C₃	C₂×D₂₀	1	1	yes	characteristic
66	C₂×C₃	C₂²×Dic₅	1	1	yes	characteristic
67	C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
68	C₂²	C₃×Dic₁₀	1	2	yes	—
69	C₂²	C₃×D₂₀	1	2	yes	—
70	C₂²	C₂×C₃×Dic₅	1	2	yes	—
71	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
72	C₄	—	10	4	no	—
73	C₄	C₂×C₃×Dic₅	1	4	yes	complemented
74	C₃	C₂×C₄⋊Dic₅	1	1	yes	characteristic, direct product factor, Sylow
75	C₂	C₃×C₄⋊Dic₅	1	4	yes	direct product factor
76	C₂	C₂×C₃×Dic₁₀	1	1	yes	characteristic
77	C₂	C₂×C₃×D₂₀	1	1	yes	characteristic
78	C₂	C₂²×C₃×Dic₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₄⋊Dic₅	C₂	direct (N × H)
4. C₂×C₄⋊Dic₅	C₃	direct (N × H)
6. C₂×C₃×C₄×C₅	C₄	semidirect
13. C₄⋊Dic₅	C₂×C₃	direct (N × H)
18. C₃×C₄×C₅	C₂×C₄	semidirect
24. C₂×C₄×C₅	C₃×C₄	semidirect
29. C₂×C₃×C₅	C₄⋊C₄	semidirect
36. C₂×C₃×C₄	Dic₅	semidirect
42. C₄×C₅	C₂×C₃×C₄	semidirect
47. C₃×C₅	C₂×C₄⋊C₄	semidirect
53. C₃×C₄	C₂×Dic₅	semidirect
54. C₂×C₅	C₃×C₄⋊C₄	semidirect
61. C₂×C₄	C₃×Dic₅	semidirect
63. C₂×C₃	C₄⋊Dic₅	direct (N × H)
67. C₅	C₂×C₃×C₄⋊C₄	semidirect
73. C₄	C₂×C₃×Dic₅	semidirect
74. C₃	C₂×C₄⋊Dic₅	direct (N × H)
75. C₂	C₃×C₄⋊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
C₂²×C₃×C₄×C₅	2
C₂²×C₃×Dic₅	2
C₃×C₄⋊Dic₅	2
C₂×C₄⋊Dic₅	3
C₂×C₃×C₄⋊C₄	5

Subgroups — C2×C3×C4⋊Dic5 #91642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄⋊Dic₅ #91642