Subgroups — #44538197

Order 31460.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#10597245	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#10597245	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊(C₁₁⋊#261)	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁²×D₁₃	C₂×C₅	1	1	yes	characteristic
5	(C₁₁⋊C₅)⋊#261	—	11	2	no	maximal
6	#14559052	—	13	1	no	maximal, Hall
7	C₁₁²×C₁₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	D₁₃×C₁₁⋊C₅	—	11	2	no	—
9	C₂×#10597245	—	13	1	no	—
10	C₁₃×C₁₁⋊C₅	—	11	2	no	—
11	#10597245	#261	1	1	yes	characteristic, complemented, Hall
12	C₁₁⋊#261	—	11	2	no	—
13	C₁₁⋊#261	—	55	2	no	—
14	C₁₁⋊Dic₁₁	—	13	1	no	Hall
15	C₁₁×D₁₃	—	5	2	no	—
16	C₁₁×D₁₃	AGL(1,𝔽₁₁)	1	2	yes	—
17	C₅×#261	—	121	1	no	Hall
18	C₂×C₁₁²	—	13	1	no	—
19	Dic₁₁⋊C₅	—	143	2	no	—
20	C₁₁×C₁₃	—	5	2	no	—
21	C₁₁×C₁₃	Dic₁₁⋊C₅	1	2	yes	complemented
22	C₅×D₁₃	—	121	1	no	—
23	C₁₁²	C₅×#261	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₁₁⋊C₅	—	143	2	no	—
25	C₅×C₁₃	—	121	1	no	Hall
26	C₁₁⋊C₅	—	11	2	no	—
27	#261	—	121	1	no	Hall
28	Dic₁₁	—	143	2	no	—
29	Dic₁₁	—	715	2	no	—
30	D₁₃	#11925893	1	1	yes	characteristic
31	C₂×C₁₁	—	13	2	no	—
32	C₂×C₁₁	—	65	2	no	—
33	C₄×C₅	—	1573	1	no	Hall
34	C₁₃	#14559052	1	1	yes	characteristic, complemented, Sylow
35	C₁₁	—	5	2	no	—
36	C₁₁	(C₁₁⋊C₅)⋊#261	1	2	yes	complemented
37	C₂×C₅	—	1573	1	no	—
38	C₅	—	121	1	no	Sylow
39	C₄	—	1573	1	no	Sylow
40	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁²×C₁₃	C₄×C₅
prime radical	D₁₃×#10597245	C₂
cosocle	C₁₁²×D₁₃	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.