Subgroups — #32913039

Order 18300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#20259124	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₆₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	#11927415⋊C₃	—	5	6	no	maximal
5	C₅²×D₆₁	C₂×C₃	1	1	yes	characteristic
6	C₅×D₆₁⋊C₃	D₅	1	6	yes	—
7	C₅²×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#11927415	—	5	6	no	—
9	C₅×C₆₁⋊C₃	Dic₅	1	6	yes	complemented
10	#6923⋊C₃	—	25	1	no	Hall
11	C₅×D₆₁	C₃×D₅	1	6	yes	—
12	D₆₁⋊C₃	C₅⋊D₅	1	1	yes	characteristic
13	C₅×C₆₁	C₃×Dic₅	1	6	yes	complemented
14	C₃×#1039	—	61	1	no	maximal, Hall
15	#6923	—	25	1	no	Hall
16	C₆₁⋊C₃	#1039	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₅²	—	61	1	no	—
18	D₆₁	C₃×C₅⋊D₅	1	1	yes	characteristic
19	#1039	—	61	1	no	Hall
20	C₃×C₅²	—	61	1	no	Hall
21	C₆₁	C₃×#1039	1	1	yes	characteristic, complemented, Sylow
22	C₃×Dic₅	—	305	6	no	—
23	C₂×C₅²	—	61	1	no	—
24	C₂×C₃×C₅	—	61	6	no	—
25	C₅²	#6923⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	Dic₅	—	305	6	no	—
27	C₃×C₅	—	244	6	no	—
28	C₃×C₄	—	1525	1	no	Hall
29	C₂×C₅	—	61	6	no	—
30	C₂×C₃	—	61	1	no	—
31	C₅	#11927415⋊C₃	1	6	yes	complemented
32	C₄	—	1525	1	no	Sylow
33	C₃	—	244	1	no	Sylow
34	C₂	—	61	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₆₁	C₃×C₄
prime radical	C₅²×D₆₁⋊C₃	C₂
cosocle	C₅²×D₆₁	C₂×C₃
LCS	G ▷ C₅²×C₆₁
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.