Subgroups — C₂⁵×D₅ #66301

Order 320.

5650 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₅	C₂	1	62	yes	maximal, direct product factor
3	C₂⁴×C₅	C₂²	1	31	yes	complemented
4	C₂³×D₅	C₂²	1	620	yes	direct product factor
5	C₂⁶	—	5	1	no	maximal, Sylow
6	C₂³×C₅	C₂³	1	155	yes	complemented
7	C₂²×D₅	C₂³	1	1240	yes	direct product factor
8	C₂⁵	—	5	62	no	—
9	C₂⁵	D₅	1	1	yes	characteristic, direct product factor
10	C₂²×C₅	C₂⁴	1	155	yes	complemented
11	C₂×D₅	C₂⁴	1	496	yes	direct product factor
12	C₂⁴	—	5	620	no	—
13	C₂⁴	C₂×D₅	1	31	yes	direct product factor
14	C₂×C₅	C₂⁵	1	31	yes	complemented
15	D₅	C₂⁵	1	32	yes	direct product factor
16	C₂³	—	5	1240	no	—
17	C₂³	C₂²×D₅	1	155	yes	direct product factor
18	C₅	C₂⁶	1	1	yes	characteristic, complemented, Sylow
19	C₂²	—	5	496	no	—
20	C₂²	C₂³×D₅	1	155	yes	direct product factor
21	C₂	—	5	32	no	—
22	C₂	C₂⁴×D₅	1	31	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁵	D₅
commutator, cosocle, hypocenter	C₅	C₂⁶
Frattini	C₁	G
Fitting, socle	C₂⁵×C₅	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂⁵

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.