Subgroups — C₁₁⋊#13049918 #28384694

Order 14300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₁₅	—	5	6	no	maximal
4	C₂×C₅×C₁₁×C₁₃	D₅	1	6	yes	—
5	#13049918	—	11	1	no	maximal, Hall
6	C₁₁⋊#1039	—	13	1	no	maximal, Hall
7	C₅×C₁₁×C₁₃	Dic₅	1	6	yes	complemented
8	C₂×C₅²×C₁₃	D₁₁	1	1	yes	characteristic
9	Dic₁₄₃	—	25	1	no	Hall
10	C₂×C₅²×C₁₁	D₁₃	1	1	yes	characteristic
11	C₅²×C₁₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₁₃	C₅⋊D₅	1	1	yes	characteristic
13	C₅²×C₁₁	Dic₁₃	1	1	yes	characteristic, complemented, Hall
14	Dic₆₅	—	55	6	no	—
15	Dic₅₅	—	65	6	no	—
16	C₁₁×C₁₃	#1039	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₁₃	D₅₅	1	6	yes	—
18	C₂×C₅×C₁₁	D₆₅	1	6	yes	—
19	#1039	—	143	1	no	Hall
20	C₅×C₁₃	Dic₅₅	1	6	yes	complemented
21	C₅×C₁₁	Dic₆₅	1	6	yes	complemented
22	Dic₁₃	—	275	1	no	Hall
23	C₂×C₅²	D₁₄₃	1	1	yes	characteristic
24	Dic₁₁	—	325	1	no	Hall
25	C₂×C₁₃	C₅⋊D₅₅	1	1	yes	characteristic
26	C₅²	Dic₁₄₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₁	C₅⋊D₆₅	1	1	yes	characteristic
28	Dic₅	—	715	6	no	—
29	C₁₃	C₁₁⋊#1039	1	1	yes	characteristic, complemented, Sylow
30	C₁₁	#13049918	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	D₇₁₅	1	6	yes	—
32	C₅	Dic₇₁₅	1	6	yes	complemented
33	C₄	—	3575	1	no	Sylow
34	C₂	C₅⋊D₇₁₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊D₇₁₅
commutator, hypocenter	C₅²×C₁₁×C₁₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅²×C₁₁×C₁₃	C₂
LCS	G ▷ C₅²×C₁₁×C₁₃
UCS	C₁ ◁ C₂

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.