Subgroups — #27130990

Order 12100.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
3	#14559102	—	5	6	no	maximal
4	C₅×C₁₁⋊D₁₁	D₅	1	6	yes	—
5	C₅×C₁₁²	Dic₅	1	6	yes	complemented
6	C₅²×D₁₁	—	22	6	no	—
7	#92150	—	25	1	no	Hall
8	C₅²×C₁₁	—	2	6	no	—
9	C₁₁⋊D₁₁	C₅⋊D₅	1	1	yes	characteristic
10	C₁₁²	#1039	1	1	yes	characteristic, complemented, Sylow
11	C₅×D₁₁	—	22	36	no	—
12	#1039	—	121	1	no	maximal, Hall
13	C₅×C₁₁	—	2	36	no	—
14	C₂×C₅²	—	121	1	no	—
15	C₅²	#92150	1	1	yes	characteristic, complemented, Sylow
16	D₁₁	—	22	6	no	—
17	Dic₅	—	605	6	no	—
18	C₁₁	—	2	6	no	—
19	C₂×C₅	—	121	6	no	—
20	C₅	#14559102	1	6	yes	complemented
21	C₄	—	3025	1	no	Sylow
22	C₂	—	121	1	no	—

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