Subgroups — C₅×#13050652 #20269162

Order 6660.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₁₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#13050652	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×D₁₁₁	—	6	2	no	—
5	C₅×#3866	—	9	1	no	maximal, Hall
6	C₃⋊D₁₁₁	C₂×C₅	1	1	yes	characteristic
7	C₃×C₅×C₃₇	—	2	2	no	—
8	C₅×D₃₇	—	9	1	no	—
9	C₃²×C₃₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	D₁₁₁	—	6	2	no	—
11	C₅×C₃₇	#157	1	1	yes	characteristic, complemented, Hall
12	C₅×#157	—	37	1	no	maximal, Hall
13	#3866	—	9	1	no	Hall
14	C₃×C₃₇	—	2	2	no	—
15	C₅×C₃⋊D₃	—	37	1	no	—
16	D₃₇	—	9	1	no	—
17	C₃²×C₅	#3866	1	1	yes	characteristic, complemented, Hall
18	C₃₇	C₅×#157	1	1	yes	characteristic, complemented, Sylow
19	#157	—	37	1	no	Hall
20	C₅×D₃	—	222	2	no	—
21	C₄×C₅	—	333	1	no	Hall
22	C₃⋊D₃	—	37	1	no	—
23	C₃×C₅	—	2	2	no	—
24	C₂×C₅	—	333	1	no	—
25	C₃²	C₅×#3866	1	1	yes	characteristic, complemented, Sylow
26	D₃	—	222	2	no	—
27	C₅	#13050652	1	1	yes	characteristic, direct product factor, Sylow
28	C₄	—	333	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	333	1	no	—

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