Subgroups — #49137619

Order 36300.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(C₅⋊((C₁₁⋊D₁₁)⋊C₃))	C₂	1	1	yes	maximal, characteristic
2	#27130977	—	3	1	no	maximal, Hall
3	C₅²×C₁₁²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	#20300038	—	5	6	no	maximal
5	C₅⋊(C₅⋊(C₁₁⋊D₁₁))	D₃	1	1	yes	characteristic
6	C₅⋊((C₁₁⋊D₁₁)⋊C₃)	—	5	6	no	—
7	C₅²×C₁₁²	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#14559097	—	15	6	no	—
9	C₅×C₁₁²⋊C₃	AGL(1,𝔽₅)	1	6	yes	complemented
10	#13089721	—	25	1	no	Hall
11	C₅⋊(C₁₁⋊D₁₁)	—	5	6	no	—
12	(C₁₁⋊D₁₁)⋊C₃	—	25	1	no	—
13	C₅×C₁₁²	ΓL(1,𝔽₁₆)	1	6	yes	complemented
14	C₅⋊D₅₅	—	66	2	no	—
15	#92150	—	75	1	no	Hall
16	C₁₁²⋊C₃	#1043	1	1	yes	characteristic, complemented, Hall
17	C₃⋊#1043	—	121	1	no	maximal, Hall
18	C₅²×C₁₁	—	6	2	no	—
19	C₁₁⋊D₁₁	—	25	1	no	—
20	C₃×C₅⋊D₅	—	121	1	no	—
21	C₁₁²	C₃⋊#1043	1	1	yes	characteristic, complemented, Sylow
22	D₅₅	—	330	12	no	—
23	#1043	—	363	1	no	Hall
24	C₃×C₅²	—	484	1	no	Hall
25	ΓL(1,𝔽₁₆)	—	605	6	no	—
26	C₅×C₁₁	—	6	12	no	—
27	C₅⋊D₅	—	121	1	no	—
28	C₃×D₅	—	605	6	no	—
29	C₅²	#13089721	1	1	yes	characteristic, complemented, Sylow
30	D₁₁	—	1650	2	no	—
31	AGL(1,𝔽₅)	—	1815	6	no	—
32	C₃×C₅	—	484	6	no	—
33	Dic₃	—	3025	1	no	Hall
34	C₁₁	—	6	2	no	—
35	D₅	—	605	6	no	—
36	C₂×C₃	—	3025	1	no	—
37	C₅	#20300038	1	6	yes	complemented
38	C₄	—	9075	1	no	Sylow
39	C₃	—	484	1	no	Sylow
40	C₂	—	3025	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₅²×C₁₁²⋊C₃	C₄
Fitting, socle	C₅²×C₁₁²	Dic₃
prime radical, cosocle	C₅⋊(C₅⋊((C₁₁⋊D₁₁)⋊C₃))	C₂
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.