Subgroups — #20269166

Order 6660.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₅₅₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#13050652	—	5	1	no	maximal, Hall
4	D₅₅₅	—	6	2	no	—
5	#10625192	—	9	1	no	maximal, Hall
6	C₃⋊D₁₁₁	—	5	1	no	—
7	C₃×C₅×C₃₇	—	2	2	no	—
8	D₁₈₅	—	9	1	no	—
9	C₃²×C₃₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	D₁₁₁	—	30	2	no	—
11	C₅×C₃₇	#157	1	1	yes	characteristic, complemented, Hall
12	#4380	—	37	1	no	maximal, Hall
13	#3866	—	45	1	no	Hall
14	C₃×C₃₇	—	2	2	no	—
15	C₃⋊D₁₅	—	37	1	no	—
16	D₃₇	—	45	1	no	—
17	C₃²×C₅	#3866	1	1	yes	characteristic, complemented, Hall
18	C₃₇	#4380	1	1	yes	characteristic, complemented, Sylow
19	#157	—	185	1	no	Hall
20	D₁₅	—	222	2	no	—
21	AGL(1,𝔽₅)	—	333	1	no	Hall
22	C₃⋊D₃	—	185	1	no	—
23	C₃×C₅	—	2	2	no	—
24	D₅	—	333	1	no	—
25	C₃²	#10625192	1	1	yes	characteristic, complemented, Sylow
26	D₃	—	1110	2	no	—
27	C₅	#13050652	1	1	yes	characteristic, complemented, Sylow
28	C₄	—	1665	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	1665	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₃₇	C₄
LCS	G ▷ C₃²×C₅×C₃₇
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.