Subgroups — C₅×C₂²⋊#66526 #20269111

Order 6660.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₅×#66526	—	4	1	no	maximal, Hall
3	C₂²⋊#66526	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₅×C₃₇⋊C₃	—	3	1	no	—
5	C₂²×C₅×C₃₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₅×C₃₇⋊C₃	A₄	1	1	yes	characteristic
7	C₂²×C₃₇⋊C₃	C₃×C₅	1	1	yes	characteristic
8	C₂×C₅×C₃₇	—	3	1	no	—
9	#66526	—	4	1	no	Hall
10	C₂×C₃₇⋊C₃	—	3	1	no	—
11	C₅×C₃₇	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
12	C₅×C₂²⋊C₉	—	37	1	no	maximal, Hall
13	C₂²×C₃₇	C₅×C₉	1	1	yes	characteristic, complemented, Hall
14	C₃₇⋊C₃	C₅×A₄	1	1	yes	characteristic
15	C₂×C₃₇	—	3	1	no	—
16	C₂²×C₃×C₅	—	37	1	no	—
17	C₅×C₉	—	148	1	no	Hall
18	C₃₇	C₅×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
19	C₂²⋊C₉	—	37	1	no	Hall
20	C₂×C₃×C₅	—	111	1	no	—
21	C₂²×C₅	#66526	1	1	yes	characteristic, complemented, Hall
22	C₃×C₅	—	37	1	no	—
23	C₂²×C₃	—	37	1	no	—
24	C₂×C₅	—	3	1	no	—
25	C₉	—	148	1	no	Sylow
26	C₂×C₃	—	111	1	no	—
27	C₅	C₂²⋊#66526	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	C₅×#66526	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	37	1	no	—
30	C₂	—	3	1	no	—

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