Subgroups — C₂²×C₂⁴⋊C₅ #66299

Order 320.

583 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂⁴⋊C₅	C₂	1	3	yes	maximal, direct product factor
2	C₂⁴⋊C₅	C₂²	1	1	yes	characteristic, direct product factor
3	C₂⁶	C₅	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂⁵	—	5	3	no	—
5	C₂⁵	—	5	9	no	—
6	C₂⁵	C₂×C₅	1	3	yes	complemented
7	C₂²×C₅	—	16	1	no	maximal
8	C₂⁴	—	5	9	no	—
9	C₂⁴	—	5	9	no	—
10	C₂⁴	—	5	6	no	—
11	C₂⁴	—	5	18	no	—
12	C₂⁴	—	5	36	no	—
13	C₂⁴	—	5	9	no	—
14	C₂⁴	—	5	36	no	—
15	C₂⁴	—	5	6	no	—
16	C₂⁴	—	5	1	no	—
17	C₂⁴	C₂²×C₅	1	1	yes	characteristic, complemented
18	C₂×C₅	—	16	3	no	—
19	C₂³	—	5	3	no	—
20	C₂³	—	5	18	no	—
21	C₂³	—	5	18	no	—
22	C₂³	—	5	18	no	—
23	C₂³	—	5	36	no	—
24	C₂³	—	5	9	no	—
25	C₂³	—	5	18	no	—
26	C₂³	—	5	72	no	—
27	C₂³	—	5	36	no	—
28	C₂³	—	5	3	no	—
29	C₂³	—	5	36	no	—
30	C₂³	—	5	9	no	—
31	C₂³	—	5	3	no	—
32	C₅	—	16	1	no	Sylow
33	C₂²	—	5	6	no	—
34	C₂²	—	5	18	no	—
35	C₂²	—	5	1	no	—
36	C₂²	—	5	9	no	—
37	C₂²	—	5	36	no	—
38	C₂²	—	5	36	no	—
39	C₂²	—	5	6	no	—
40	C₂²	—	5	9	no	—
41	C₂²	—	5	9	no	—
42	C₂²	C₂⁴⋊C₅	1	1	yes	characteristic, direct product factor
43	C₂	—	5	3	no	—
44	C₂	—	5	9	no	—
45	C₂	C₂×C₂⁴⋊C₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	C₂⁴⋊C₅
commutator, cosocle, hypocenter	C₂⁴	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂⁶	C₅
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₂²

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.