Subgroups — C₂×C₃×C₄×Dic₅ #91639

Order 480.

216 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	C₄	1	8	yes	direct product factor
9	C₂×C₃×Dic₅	C₂²	1	4	yes	—
10	C₂×C₃×C₄²	—	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	4	yes	—
15	C₂²×C₃×C₅	C₂×C₄	1	2	yes	—
16	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
17	C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
18	C₃×Dic₅	C₂×C₄	1	8	yes	direct product factor
19	C₂²×C₃×C₄	—	5	2	no	—
20	C₂²×C₃×C₄	D₅	1	1	yes	characteristic
21	C₃×C₄²	—	5	4	no	—
22	C₂³×C₅	C₂²×C₃	1	1	yes	characteristic
23	C₂×C₄×C₅	C₃×C₄	1	4	yes	complemented
24	C₂×C₄×C₅	C₂²×C₃	1	2	yes	—
25	C₂×Dic₅	C₃×C₄	1	8	yes	direct product factor
26	C₂×Dic₅	C₂²×C₃	1	4	yes	—
27	C₂×C₄²	—	5	1	no	Sylow
28	C₂×C₃×C₅	C₄²	1	4	yes	complemented
29	C₂×C₃×C₅	C₂²×C₄	1	2	yes	—
30	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
31	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
32	C₂×C₃×C₄	—	5	8	no	—
33	C₂×C₃×C₄	—	5	4	no	—
34	C₂×C₃×C₄	Dic₅	1	4	yes	direct product factor
35	C₂×C₃×C₄	C₂×D₅	1	2	yes	—
36	C₂²×C₅	C₂×C₃×C₄	1	4	yes	—
37	C₂²×C₅	C₂×C₃×C₄	1	2	yes	—
38	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
39	C₄×C₅	C₂×C₃×C₄	1	4	yes	complemented
40	Dic₅	C₂×C₃×C₄	1	8	yes	direct product factor
41	C₂²×C₄	—	5	2	no	—
42	C₂²×C₄	C₃×D₅	1	1	yes	characteristic
43	C₄²	—	5	4	no	—
44	C₃×C₅	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₃	C₄×D₅	1	4	yes	—
46	C₂²×C₃	C₂×Dic₅	1	2	yes	—
47	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
48	C₃×C₄	—	5	8	no	—
49	C₃×C₄	C₂×Dic₅	1	4	yes	direct product factor
50	C₂×C₅	C₃×C₄²	1	4	yes	complemented
51	C₂×C₅	C₂²×C₃×C₄	1	2	yes	—
52	C₂×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
53	C₂³	C₂×C₃×D₅	1	1	yes	characteristic
54	C₂×C₄	—	5	8	no	—
55	C₂×C₄	—	5	4	no	—
56	C₂×C₄	C₃×Dic₅	1	4	yes	direct product factor
57	C₂×C₄	C₂×C₃×D₅	1	2	yes	—
58	C₂×C₃	C₄×Dic₅	1	4	yes	direct product factor
59	C₂×C₃	C₂×C₄×D₅	1	2	yes	—
60	C₂×C₃	C₂²×Dic₅	1	1	yes	characteristic
61	C₅	C₂×C₃×C₄²	1	1	yes	characteristic, complemented, Sylow
62	C₂²	C₃×C₄×D₅	1	4	yes	—
63	C₂²	C₂×C₃×Dic₅	1	2	yes	—
64	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
65	C₄	—	5	8	no	—
66	C₄	C₂×C₃×Dic₅	1	4	yes	direct product factor
67	C₃	C₂×C₄×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	C₃×C₄×Dic₅	1	4	yes	direct product factor
69	C₂	C₂×C₃×C₄×D₅	1	2	yes	—
70	C₂	C₂²×C₃×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₄	D₅
commutator, hypocenter	C₅	C₂×C₃×C₄²
Frattini	C₂²	C₂²×C₃×D₅
Fitting	C₂²×C₃×C₄×C₅	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²
cosocle	C₂²×C₅	C₂³×C₃
LCS	G ▷ C₅
UCS	C₁ ◁ 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
8. C₂×C₃×Dic₅	C₄	direct (N × H)
13. C₄×Dic₅	C₂×C₃	direct (N × H)
17. C₃×C₄×C₅	C₂×C₄	semidirect
18. C₃×Dic₅	C₂×C₄	direct (N × H)
23. C₂×C₄×C₅	C₃×C₄	semidirect
25. C₂×Dic₅	C₃×C₄	direct (N × H)
28. C₂×C₃×C₅	C₄²	semidirect
34. C₂×C₃×C₄	Dic₅	direct (N × H)
39. C₄×C₅	C₂×C₃×C₄	semidirect
40. Dic₅	C₂×C₃×C₄	direct (N × H)
44. C₃×C₅	C₂×C₄²	semidirect
49. C₃×C₄	C₂×Dic₅	direct (N × H)
50. C₂×C₅	C₃×C₄²	semidirect
56. C₂×C₄	C₃×Dic₅	direct (N × H)
58. C₂×C₃	C₄×Dic₅	direct (N × H)
61. C₅	C₂×C₃×C₄²	semidirect
66. C₄	C₂×C₃×Dic₅	direct (N × H)
67. C₃	C₂×C₄×Dic₅	direct (N × H)
68. 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×C₄²	5

Subgroups — C2×C3×C4×Dic5 #91639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×Dic₅ #91639