Subgroups — Q₈×A₅ #91882

Order 480.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×A₅	C₂	1	3	yes	maximal
2	C₂×A₅	C₂²	1	1	yes	characteristic
3	Q₈×A₄	—	5	1	no	maximal, Hall
4	Q₈×D₅	—	6	1	no	maximal
5	A₅	Q₈	1	1	yes	characteristic, direct product factor
6	D₃×Q₈	—	10	1	no	maximal
7	C₄×A₄	—	5	3	no	—
8	C₅×Q₈	—	6	1	no	—
9	C₄×D₅	—	6	3	no	—
10	Dic₁₀	—	6	3	no	—
11	C₂²×Q₈	—	5	1	no	Sylow
12	C₂×A₄	—	5	1	no	—
13	C₃×Q₈	—	10	1	no	—
14	C₄×D₃	—	10	3	no	—
15	Dic₆	—	10	3	no	—
16	C₂×D₅	—	6	1	no	—
17	C₄×C₅	—	6	3	no	—
18	Dic₅	—	6	3	no	—
19	C₂×Q₈	—	15	3	no	—
20	C₂×Q₈	—	15	1	no	—
21	C₂²×C₄	—	5	3	no	—
22	C₂×D₃	—	10	1	no	—
23	A₄	—	5	1	no	—
24	C₃×C₄	—	10	3	no	—
25	Dic₃	—	10	3	no	—
26	C₂×C₅	—	6	1	no	—
27	D₅	—	6	1	no	—
28	D₅	—	6	1	no	—
29	C₂³	—	5	1	no	—
30	Q₈	—	15	2	no	—
31	Q₈	—	15	3	no	—
32	Q₈	A₅	1	1	yes	maximal normal, characteristic, direct product factor
33	C₂×C₄	—	15	3	no	—
34	C₂×C₄	—	15	3	no	—
35	C₂×C₃	—	10	1	no	—
36	D₃	—	10	1	no	—
37	D₃	—	10	1	no	—
38	C₅	—	6	1	no	Sylow
39	C₂²	—	5	1	no	—
40	C₂²	—	15	1	no	—
41	C₂²	—	15	1	no	—
42	C₄	—	15	3	no	—
43	C₄	C₂×A₅	1	3	yes	—
44	C₃	—	10	1	no	Sylow
45	C₂	—	15	1	no	—
46	C₂	—	15	1	no	—
47	C₂	C₂²×A₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂	C₂²×A₅
commutator, socle, prime radical	C₂×A₅	C₂²
Fitting, hypercenter	Q₈	A₅
hypocenter	A₅	Q₈
LCS	G ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ Q₈

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

N	H ≅ G/N	type
5. A₅	Q₈	direct (N × H)
32. Q₈	A₅	direct (N × H)

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