Subgroups — A₅×C₃₇⋊C₃ #20269186

Order 6660.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×A₅	C₃	1	1	yes	maximal, characteristic, complemented
2	A₄×C₃₇⋊C₃	—	5	1	no	maximal, Hall
3	D₅×C₃₇⋊C₃	—	6	1	no	maximal
4	D₃×C₃₇⋊C₃	—	10	1	no	maximal
5	C₅×C₃₇⋊C₃	—	6	1	no	—
6	C₂²⋊(C₃₇⋊C₃)	—	5	2	no	—
7	A₄×C₃₇	—	5	1	no	—
8	C₂²×C₃₇⋊C₃	—	5	1	no	—
9	D₅×C₃₇	—	6	1	no	—
10	C₃×C₃₇⋊C₃	—	10	1	no	Hall
11	D₃×C₃₇	—	10	1	no	—
12	C₂×C₃₇⋊C₃	—	15	1	no	—
13	C₅×C₃₇	—	6	1	no	Hall
14	C₃×A₅	—	37	1	no	maximal, Hall
15	C₂²×C₃₇	—	5	1	no	Hall
16	C₃×C₃₇	—	10	1	no	—
17	C₃₇⋊C₃	—	20	1	no	—
18	C₃₇⋊C₃	A₅	1	1	yes	maximal normal, characteristic, direct product factor
19	C₂×C₃₇	—	15	1	no	—
20	A₅	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
21	C₃₇	C₃×A₅	1	1	yes	characteristic, complemented, Sylow
22	C₃×A₄	—	185	1	no	Hall
23	C₃×D₅	—	222	1	no	—
24	C₃×D₃	—	370	1	no	—
25	C₃×C₅	—	222	1	no	—
26	C₂²×C₃	—	185	1	no	—
27	A₄	—	5	1	no	—
28	A₄	—	185	2	no	—
29	D₅	—	6	1	no	—
30	C₃²	—	370	1	no	Sylow
31	C₂×C₃	—	555	1	no	—
32	D₃	—	10	1	no	—
33	C₅	—	6	1	no	Sylow
34	C₂²	—	5	1	no	Sylow
35	C₃	—	10	1	no	—
36	C₃	—	37	1	no	—
37	C₃	—	740	1	no	—
38	C₂	—	15	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₃₇×A₅	C₃
Fitting	C₃₇	C₃×A₅
LCS	G ▷ C₃₇×A₅
UCS	C₁

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