Subgroups — #31827688

Order 18150.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊(C₁₁²⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×D₅₅	—	3	1	no	maximal, Hall
3	C₅²×C₁₁²	D₃	1	1	yes	characteristic, complemented, Hall
4	C₁₁×D₅₅	—	3	1	no	—
5	C₅×C₁₁×D₁₁	—	15	1	no	—
6	#10624391	—	25	1	no	maximal, Hall
7	C₅×C₁₁²	—	3	1	no	—
8	C₅×C₁₁²	—	3	1	no	—
9	C₅×D₅₅	—	3	1	no	—
10	C₅×D₅×C₁₁	—	33	1	no	—
11	C₁₁²⋊C₃	—	50	1	no	Hall
12	C₅²×C₁₁	—	3	1	no	—
13	C₅²×C₁₁	—	6	1	no	—
14	C₅²×C₁₁	—	6	1	no	—
15	C₁₁×D₁₁	—	15	1	no	Hall
16	#3874	—	121	1	no	maximal, Hall
17	C₁₁²	#3874	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₅×C₁₁	—	165	1	no	—
19	D₅₅	—	3	1	no	—
20	C₅×D₁₁	—	15	1	no	—
21	D₅×C₁₁	—	33	1	no	—
22	C₅²⋊C₃	—	242	1	no	Hall
23	C₅×C₁₁	—	6	1	no	—
24	C₅×C₁₁	—	6	1	no	—
25	C₅×C₁₁	—	6	1	no	—
26	C₅×C₁₁	—	6	1	no	—
27	C₅×C₁₁	—	6	1	no	—
28	C₅×C₁₁	—	6	1	no	—
29	C₅×C₁₁	—	6	3	no	—
30	C₅×C₁₁	—	6	1	no	—
31	C₅×C₁₁	—	6	3	no	—
32	C₅×C₁₁	—	6	1	no	—
33	C₅×D₅	—	33	1	no	Hall
34	C₅²	#10624391	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₁₁	—	165	1	no	—
36	D₁₁	—	15	1	no	—
37	C₁₁	—	6	1	no	—
38	C₁₁	—	6	1	no	—
39	C₁₁	—	6	1	no	—
40	C₂×C₅	—	165	1	no	—
41	D₅	—	33	1	no	—
42	D₃	—	3025	1	no	Hall
43	C₅	—	6	1	no	—
44	C₅	—	6	1	no	—
45	C₃	—	6050	1	no	Sylow
46	C₂	—	165	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅²⋊(C₁₁²⋊C₃)	C₂
Fitting, socle	C₅²×C₁₁²	D₃
LCS	G ▷ C₅²⋊(C₁₁²⋊C₃)
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.