Subgroups — C₁₃⋊#11925898 #30628513

Order 15730.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#10597244	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₁₄₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₁₃⋊AGL(1,𝔽₁₁)	—	11	1	no	maximal
5	D₁₃×C₁₁⋊C₅	—	11	1	no	maximal
6	#11925898	—	13	1	no	maximal, Hall
7	C₁₃×C₁₁⋊C₅	—	11	1	no	—
8	C₁₃×C₁₁⋊C₅	—	11	1	no	—
9	#10597244	D₁₃	1	1	yes	characteristic, complemented, Hall
10	D₁₄₃	C₁₁⋊C₅	1	1	yes	characteristic, complemented
11	C₁₁×D₁₃	—	55	1	no	—
12	C₁₁×D₁₁	—	13	1	no	Hall
13	C₁₁×C₁₃	—	10	1	no	—
14	C₁₁×C₁₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
15	C₁₁×C₁₃	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
16	C₅×D₁₃	—	121	1	no	Hall
17	C₁₁²	C₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₁⋊C₅	—	143	1	no	—
19	AGL(1,𝔽₁₁)	—	143	1	no	—
20	C₅×C₁₃	—	121	1	no	Hall
21	C₁₁⋊C₅	—	11	1	no	—
22	C₁₁⋊C₅	—	11	1	no	—
23	D₁₃	—	55	1	no	Hall
24	C₂×C₁₁	—	143	1	no	—
25	D₁₁	—	13	1	no	—
26	C₁₃	#11925898	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	—	10	1	no	—
28	C₁₁	D₁₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
29	C₁₁	C₁₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
30	C₂×C₅	—	1573	1	no	Hall
31	C₅	—	121	1	no	Sylow
32	C₂	—	715	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₁₃	C₂×C₅
LCS	G ▷ C₁₁²×C₁₃
UCS	C₁

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.