Subgroups — A₅×C₆₇⋊C₃ #27130461

Order 12060.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₅×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented
2	A₄×C₆₇⋊C₃	—	5	1	no	maximal, Hall
3	D₅×C₆₇⋊C₃	—	6	1	no	maximal
4	D₃×C₆₇⋊C₃	—	10	1	no	maximal
5	C₅×C₆₇⋊C₃	—	6	1	no	—
6	C₂²⋊(C₆₇⋊C₃)	—	5	2	no	—
7	A₄×C₆₇	—	5	1	no	—
8	C₂²×C₆₇⋊C₃	—	5	1	no	—
9	D₅×C₆₇	—	6	1	no	—
10	C₃×C₆₇⋊C₃	—	10	1	no	Hall
11	D₃×C₆₇	—	10	1	no	—
12	C₂×C₆₇⋊C₃	—	15	1	no	—
13	C₅×C₆₇	—	6	1	no	Hall
14	C₂²×C₆₇	—	5	1	no	Hall
15	C₃×C₆₇	—	10	1	no	—
16	C₆₇⋊C₃	—	20	1	no	—
17	C₆₇⋊C₃	A₅	1	1	yes	maximal normal, characteristic, direct product factor
18	C₃×A₅	—	67	1	no	maximal, Hall
19	C₂×C₆₇	—	15	1	no	—
20	C₆₇	C₃×A₅	1	1	yes	characteristic, complemented, Sylow
21	A₅	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
22	C₃×A₄	—	335	1	no	Hall
23	C₃×D₅	—	402	1	no	—
24	C₃×D₃	—	670	1	no	—
25	C₃×C₅	—	402	1	no	—
26	C₂²×C₃	—	335	1	no	—
27	A₄	—	5	1	no	—
28	A₄	—	335	2	no	—
29	D₅	—	6	1	no	—
30	C₃²	—	670	1	no	Sylow
31	C₂×C₃	—	1005	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	—	1340	1	no	—
37	C₃	—	67	1	no	—
38	C₂	—	15	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	A₅×C₆₇	C₃
Fitting, cosocle	C₆₇	C₃×A₅
LCS	G ▷ A₅×C₆₇
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.