Subgroups — C₁₁×(C₂⁴⋊C₅)⋊C₂ #13183461

Order 1760.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂⁴⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#120	—	5	1	no	maximal, Hall
3	C₂⁴×C₁₁	D₅	1	1	yes	characteristic, complemented
4	C₂×D₄×C₁₁	—	5	3	no	—
5	C₁₁×C₂²⋊C₄	—	5	3	no	—
6	(C₂⁴⋊C₅)⋊C₂	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₅×C₁₁	—	16	1	no	maximal
8	C₂³×C₁₁	—	5	3	no	—
9	C₂³×C₁₁	—	5	1	no	—
10	D₄×C₁₁	—	10	6	no	—
11	C₂×C₄×C₁₁	—	5	3	no	—
12	C₂⁴⋊C₅	C₂×C₁₁	1	1	yes	characteristic, complemented
13	C₅×C₁₁	—	16	1	no	Hall
14	C₂²×C₁₁	—	5	6	no	—
15	C₂²×C₁₁	—	5	1	no	—
16	C₂²×C₁₁	—	10	3	no	—
17	C₄×C₁₁	—	10	3	no	—
18	#120	—	5	1	no	Sylow
19	C₂×C₁₁	—	5	3	no	—
20	C₂×C₁₁	—	20	1	no	—
21	C₂⁴	D₅×C₁₁	1	1	yes	characteristic, complemented
22	C₂×D₄	—	5	3	no	—
23	C₂²⋊C₄	—	5	3	no	—
24	C₁₁	(C₂⁴⋊C₅)⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
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	Sylow
31	C₂²	—	5	6	no	—
32	C₂²	—	5	1	no	—
33	C₂²	—	10	3	no	—
34	C₄	—	10	3	no	—
35	C₂	—	5	3	no	—
36	C₂	—	20	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	(C₂⁴⋊C₅)⋊C₂
commutator, cosocle, hypocenter	C₂⁴⋊C₅	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₂⁴×C₁₁	D₅
LCS	G ▷ C₂⁴⋊C₅
UCS	C₁ ◁ C₁₁

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.