Subgroups — #66245

Order 320.

111 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂⁴⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₂⁴⋊C₅	C₄	1	1	yes	characteristic, complemented
3	#379	—	5	1	no	maximal, Sylow
4	C₂⁵	D₅	1	1	yes	characteristic
5	C₂×C₂²⋊C₄	—	5	3	no	—
6	C₂×C₂²⋊C₄	—	5	3	no	—
7	Dic₅	—	16	1	no	maximal
8	C₂⁴	—	5	3	no	—
9	C₂⁴	—	5	3	no	—
10	C₂⁴	Dic₅	1	1	yes	characteristic, complemented
11	C₂²×C₄	—	5	3	no	—
12	C₂²×C₄	—	5	1	no	—
13	C₂²⋊C₄	—	10	6	no	—
14	C₂²⋊C₄	—	10	6	no	—
15	C₂×C₅	—	16	1	no	—
16	C₂³	—	5	3	no	—
17	C₂³	—	5	1	no	—
18	C₂³	—	5	6	no	—
19	C₂³	—	5	6	no	—
20	C₂³	—	5	3	no	—
21	C₂³	—	10	6	no	—
22	C₂×C₄	—	10	6	no	—
23	C₂×C₄	—	10	3	no	—
24	C₂×C₄	—	10	3	no	—
25	C₅	—	16	1	no	Sylow
26	C₂²	—	5	6	no	—
27	C₂²	—	5	6	no	—
28	C₂²	—	5	3	no	—
29	C₂²	—	5	1	no	—
30	C₂²	—	5	3	no	—
31	C₂²	—	10	6	no	—
32	C₄	—	20	3	no	—
33	C₄	—	20	1	no	—
34	C₂	—	5	3	no	—
35	C₂	—	5	3	no	—
36	C₂	(C₂⁴⋊C₅)⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	(C₂⁴⋊C₅)⋊C₂
commutator, hypocenter	C₂⁴⋊C₅	C₄
Fitting, socle	C₂⁵	D₅
prime radical, cosocle	C₂×C₂⁴⋊C₅	C₂
LCS	G ▷ C₂⁴⋊C₅
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
2. C₂⁴⋊C₅	C₄	semidirect
10. C₂⁴	Dic₅	semidirect

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