Subgroups — C₁₁×2₋¹⁺⁴⋊C₅ #13183329

Order 1760.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×2₋¹⁺⁴	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×#41	—	5	2	no	—
3	C₂×Q₈×C₁₁	—	5	1	no	—
4	2₋¹⁺⁴⋊C₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₁	—	16	1	no	maximal
6	Q₈×C₁₁	—	5	2	no	—
7	D₄×C₁₁	—	5	2	no	—
8	C₂×C₄×C₁₁	—	5	1	no	—
9	C₂×C₄×C₁₁	—	5	2	no	—
10	C₅×C₁₁	—	16	1	no	Hall
11	C₂²×C₁₁	—	5	1	no	—
12	C₄×C₁₁	—	5	2	no	—
13	2₋¹⁺⁴	C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₁₁	—	10	1	no	—
15	C₂×C₁₁	C₂⁴⋊C₅	1	1	yes	characteristic
16	#41	—	5	2	no	—
17	C₂×Q₈	—	5	1	no	—
18	C₁₁	2₋¹⁺⁴⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	—	16	1	no	—
20	Q₈	—	5	2	no	—
21	D₄	—	5	2	no	—
22	C₂×C₄	—	5	1	no	—
23	C₂×C₄	—	5	2	no	—
24	C₅	—	16	1	no	Sylow
25	C₂²	—	5	1	no	—
26	C₄	—	5	2	no	—
27	C₂	—	10	1	no	—
28	C₂	C₁₁×C₂⁴⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, socle, hypercenter	C₂×C₁₁	C₂⁴⋊C₅
commutator, cosocle, hypocenter	2₋¹⁺⁴	C₅×C₁₁
Frattini	C₂	C₁₁×C₂⁴⋊C₅
Fitting	C₁₁×2₋¹⁺⁴	C₅
LCS	G ▷ 2₋¹⁺⁴
UCS	C₁ ◁ C₂×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.