Subgroups — C₁₁⋊#15668535 #44542099

Order 31900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₁×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊#10596817	—	5	6	no	maximal
4	C₅×C₁₁×D₂₉	D₅	1	6	yes	—
5	#15668535	—	11	1	no	maximal, Hall
6	C₅×C₁₁×C₂₉	Dic₅	1	6	yes	complemented
7	C₅²×D₂₉	D₁₁	1	1	yes	characteristic
8	C₁₁⋊#1181	—	25	1	no	Hall
9	C₁₁⋊#1039	—	29	1	no	maximal, Hall
10	C₅²×C₂₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
11	C₁₁×D₂₉	C₅⋊D₅	1	1	yes	characteristic
12	#10596817	—	55	6	no	—
13	C₂×C₅²×C₁₁	—	29	1	no	—
14	C₁₁×C₂₉	#1039	1	1	yes	characteristic, complemented, Hall
15	C₅×D₂₉	D₅₅	1	6	yes	—
16	C₅²×C₁₁	#1181	1	1	yes	characteristic, complemented, Hall
17	Dic₅₅	—	145	6	no	—
18	C₅×C₂₉	Dic₅₅	1	6	yes	complemented
19	#1181	—	275	1	no	Hall
20	C₂×C₅×C₁₁	—	29	6	no	—
21	#1039	—	319	1	no	Hall
22	D₂₉	C₅⋊D₅₅	1	1	yes	characteristic
23	C₅×C₁₁	#10596817	1	6	yes	complemented
24	C₂×C₅²	—	29	1	no	—
25	Dic₁₁	—	725	1	no	Hall
26	C₂₉	C₁₁⋊#1039	1	1	yes	characteristic, complemented, Sylow
27	C₅²	C₁₁⋊#1181	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₁₁	—	29	1	no	—
29	Dic₅	—	1595	6	no	—
30	C₁₁	#15668535	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	29	6	no	—
32	C₅	C₁₁⋊#10596817	1	6	yes	complemented
33	C₄	—	7975	1	no	Sylow
34	C₂	—	29	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₁₁×C₂₉	C₄
prime radical, cosocle	C₅²×C₁₁×D₂₉	C₂
LCS	G ▷ C₅²×C₁₁×C₂₉
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.