Subgroups — C₃×Q₈×Dic₅ #91662

Order 480.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊Dic₅	C₂	1	3	yes	maximal
3	C₃×C₄×Dic₅	C₂	1	3	yes	maximal
4	Q₈×Dic₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×Q₈	C₄	1	4	yes	complemented
6	C₂×C₃×C₄×C₅	C₂²	1	3	yes	—
7	C₂×C₃×Dic₅	C₂²	1	3	yes	—
8	C₂×C₃×Dic₅	C₂²	1	1	yes	characteristic
9	C₃×C₄×Q₈	—	5	1	no	maximal, Hall
10	C₂×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
11	C₄⋊Dic₅	C₂×C₃	1	3	yes	—
12	C₄×Dic₅	C₂×C₃	1	3	yes	—
13	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
14	C₃×C₄×C₅	C₂×C₄	1	6	yes	—
15	C₃×Dic₅	—	2	3	no	—
16	C₃×Dic₅	Q₈	1	2	yes	direct product factor
17	C₂×C₃×Q₈	D₅	1	1	yes	characteristic
18	C₃×C₄⋊C₄	—	5	3	no	—
19	C₃×C₄²	—	5	3	no	—
20	C₅×Q₈	C₃×C₄	1	4	yes	complemented
21	C₂×C₄×C₅	C₂²×C₃	1	3	yes	—
22	C₂×Dic₅	C₂²×C₃	1	3	yes	—
23	C₂×Dic₅	C₂²×C₃	1	1	yes	characteristic
24	C₄×Q₈	—	5	1	no	Sylow
25	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
27	C₂×C₃×C₅	#41	1	1	yes	characteristic
28	C₃×Q₈	Dic₅	1	4	yes	direct product factor
29	C₂×C₃×C₄	—	5	1	no	—
30	C₂×C₃×C₄	—	5	3	no	—
31	C₂×C₃×C₄	C₂×D₅	1	3	yes	—
32	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
33	C₄×C₅	C₂×C₃×C₄	1	6	yes	—
34	Dic₅	—	2	3	no	—
35	Dic₅	C₃×Q₈	1	2	yes	direct product factor
36	C₂×Q₈	C₃×D₅	1	1	yes	characteristic
37	C₄⋊C₄	—	5	3	no	—
38	C₄²	—	5	3	no	—
39	C₃×C₅	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
40	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
41	C₃×C₄	—	5	2	no	—
42	C₃×C₄	—	10	3	no	—
43	C₃×C₄	C₂×Dic₅	1	6	yes	—
44	C₂×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
45	C₂×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
46	C₂×C₅	C₃×#41	1	1	yes	characteristic
47	Q₈	C₃×Dic₅	1	4	yes	direct product factor
48	C₂×C₄	—	5	1	no	—
49	C₂×C₄	—	5	3	no	—
50	C₂×C₄	C₂×C₃×D₅	1	3	yes	—
51	C₂×C₃	Q₈×D₅	1	1	yes	characteristic
52	C₂×C₃	#713	1	1	yes	characteristic
53	C₂×C₃	C₂²×Dic₅	1	1	yes	characteristic
54	C₅	C₃×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
55	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
56	C₄	—	5	2	no	—
57	C₄	—	10	3	no	—
58	C₄	C₂×C₃×Dic₅	1	6	yes	—
59	C₃	Q₈×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
60	C₂	C₃×Q₈×D₅	1	1	yes	characteristic
61	C₂	C₃×#713	1	1	yes	characteristic
62	C₂	C₂²×C₃×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₅
commutator	C₂×C₅	C₂²×C₃×C₄
Frattini	C₂²	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×Q₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₂³
cosocle	C₂²×C₅	C₂³×C₃
hypercenter	C₂×C₃×Q₈	D₅
hypocenter	C₅	C₃×C₄×Q₈
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×Q₈

Complements

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

N	H ≅ G/N	type
4. Q₈×Dic₅	C₃	direct (N × H)
5. C₃×C₅×Q₈	C₄	semidirect
16. C₃×Dic₅	Q₈	direct (N × H)
20. C₅×Q₈	C₃×C₄	semidirect
28. C₃×Q₈	Dic₅	direct (N × H)
35. Dic₅	C₃×Q₈	direct (N × H)
39. C₃×C₅	C₄×Q₈	semidirect
47. Q₈	C₃×Dic₅	direct (N × H)
54. C₅	C₃×C₄×Q₈	semidirect
59. C₃	Q₈×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
C₂×C₃×C₅×Q₈	2
C₃×C₄⋊Dic₅	2
C₃×C₄×Dic₅	2
Q₈×Dic₅	3
C₃×C₄×Q₈	5

Subgroups — C3×Q8×Dic5 #91662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Q₈×Dic₅ #91662