Subgroups — #49137555

Order 36300.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊C₃×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	#27130990	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅²×C₁₁⋊D₁₁	C₂×C₃	1	1	yes	characteristic
5	C₅²×C₁₁²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	#14559102	—	15	2	no	—
7	D₁₁×C₅²⋊C₃	—	22	6	no	—
8	C₃×#92150	—	25	1	no	maximal, Hall
9	C₅×C₁₁⋊D₁₁	—	3	2	no	—
10	C₁₁×C₅²⋊C₃	—	2	6	no	—
11	C₃×C₁₁⋊D₁₁	—	50	1	no	—
12	C₅×C₁₁²	—	3	2	no	—
13	C₅²×D₁₁	—	22	6	no	—
14	#92150	—	25	1	no	Hall
15	C₃×C₁₁²	—	50	1	no	Hall
16	#1039⋊C₃	—	121	1	no	maximal, Hall
17	C₅²×C₁₁	—	2	6	no	—
18	C₁₁⋊D₁₁	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
19	C₂×C₅²⋊C₃	—	121	1	no	—
20	C₁₁²	#1039⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₅×D₁₁	—	66	12	no	—
22	#1039	—	121	1	no	Hall
23	C₅²⋊C₃	#92150	1	1	yes	characteristic, complemented, Hall
24	C₃×D₁₁	—	550	6	no	—
25	C₅×C₁₁	—	6	12	no	—
26	C₂×C₅²	—	121	1	no	—
27	C₃×C₁₁	—	50	6	no	—
28	C₅²	C₃×#92150	1	1	yes	characteristic, complemented, Sylow
29	D₁₁	—	22	6	no	—
30	Dic₅	—	1815	2	no	—
31	C₃×C₄	—	3025	1	no	Hall
32	C₁₁	—	2	6	no	—
33	C₂×C₅	—	363	2	no	—
34	C₂×C₃	—	6050	1	no	—
35	C₅	—	3	2	no	—
36	C₄	—	3025	1	no	Sylow
37	C₃	—	50	1	no	Sylow
38	C₂	—	121	1	no	—

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