Subgroups — C₂×C₃×C₂⁴⋊C₅ #92128

Order 480.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃	C₂⁴⋊C₅
commutator, cosocle, hypocenter	C₂⁴	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂⁵×C₃	C₅
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₂×C₃

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.