Subgroups — C₅×(C₂⁴⋊C₅)⋊C₂ #11717536

Order 800.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂⁴⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₂⁴⋊C₅)⋊C₂	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×#120	—	5	1	no	maximal
4	C₂⁴×C₅	D₅	1	1	yes	characteristic, complemented
5	C₂⁴⋊C₅	—	2	2	no	—
6	C₂⁴⋊C₅	C₂×C₅	1	1	yes	characteristic, complemented
7	C₂×C₅×D₄	—	5	3	no	—
8	C₅×C₂²⋊C₄	—	5	3	no	—
9	C₅×D₅	—	16	1	no	maximal
10	C₂³×C₅	—	5	3	no	—
11	C₂³×C₅	—	5	1	no	—
12	C₅×D₄	—	10	6	no	—
13	C₂×C₄×C₅	—	5	3	no	—
14	#120	—	5	1	no	Sylow
15	C₅²	—	16	1	no	Sylow
16	C₂²×C₅	—	5	6	no	—
17	C₂²×C₅	—	5	1	no	—
18	C₂²×C₅	—	10	3	no	—
19	C₄×C₅	—	10	3	no	—
20	C₂⁴	C₅×D₅	1	1	yes	characteristic, complemented
21	C₂×D₄	—	5	3	no	—
22	C₂²⋊C₄	—	5	3	no	—
23	C₂×C₅	—	5	3	no	—
24	C₂×C₅	—	20	1	no	—
25	D₅	—	16	1	no	—
26	C₂³	—	5	3	no	—
27	C₂³	—	5	1	no	—
28	D₄	—	10	6	no	—
29	C₂×C₄	—	5	3	no	—
30	C₅	—	16	1	no	—
31	C₅	—	32	2	no	—
32	C₅	(C₂⁴⋊C₅)⋊C₂	1	1	yes	characteristic, direct product factor
33	C₂²	—	5	6	no	—
34	C₂²	—	5	1	no	—
35	C₂²	—	10	3	no	—
36	C₄	—	10	3	no	—
37	C₂	—	5	3	no	—
38	C₂	—	20	1	no	—

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

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.