Subgroups — D₅×C₂²⋊A₄ #92127

Order 480.

296 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂²⋊A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	D₅×A₄	—	4	5	no	maximal
4	C₂×C₂²⋊A₄	—	5	1	no	maximal, Hall
5	C₂⁴×C₅	C₂×C₃	1	1	yes	characteristic, complemented
6	C₂³×D₅	—	3	5	no	—
7	C₂³×D₅	—	3	5	no	—
8	C₅×A₄	—	4	5	no	—
9	C₂²⋊A₄	D₅	1	1	yes	characteristic, direct product factor
10	C₂³×C₅	—	3	5	no	—
11	C₂²×D₅	—	3	30	no	—
12	C₂²×D₅	—	3	10	no	—
13	C₂²×D₅	—	3	5	no	—
14	C₂²×D₅	A₄	1	5	yes	complemented
15	C₂⁵	—	5	1	no	Sylow
16	C₃×D₅	—	16	1	no	—
17	C₂×A₄	—	20	5	no	—
18	C₂²×C₅	—	3	10	no	—
19	C₂²×C₅	C₂×A₄	1	5	yes	complemented
20	C₂×D₅	—	3	30	no	—
21	C₂×D₅	—	3	5	no	—
22	C₂×D₅	—	3	5	no	—
23	C₂⁴	—	15	5	no	—
24	C₂⁴	—	15	5	no	—
25	C₂⁴	C₃×D₅	1	1	yes	characteristic, complemented
26	C₃×C₅	—	16	1	no	Hall
27	A₄	—	4	5	no	—
28	C₂×C₅	—	3	5	no	—
29	D₅	—	3	5	no	—
30	D₅	C₂²⋊A₄	1	1	yes	characteristic, direct product factor
31	C₂³	—	3	5	no	—
32	C₂³	—	5	5	no	—
33	C₂³	—	15	10	no	—
34	C₂³	—	15	30	no	—
35	C₂³	—	15	5	no	—
36	C₂×C₃	—	80	1	no	—
37	C₅	C₂×C₂²⋊A₄	1	1	yes	characteristic, complemented, Sylow
38	C₂²	—	3	10	no	—
39	C₂²	—	15	5	no	—
40	C₂²	—	15	5	no	—
41	C₂²	—	15	30	no	—
42	C₂²	D₅×A₄	1	5	yes	complemented
43	C₃	—	16	1	no	Sylow
44	C₂	—	3	5	no	—
45	C₂	—	5	1	no	—
46	C₂	—	15	5	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂⁴×C₅	C₂×C₃
LCS	G ▷ C₂⁴×C₅
UCS	C₁

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

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