Subgroups — #11761914

Order 1080.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×A₅	—	6	2	no	maximal
2	#1088	—	10	1	no	maximal
3	C₃×S₄	—	15	2	no	maximal
4	A₅	—	6	2	no	—
5	#272	—	10	1	no	—
6	C₃×A₄	—	15	2	no	—
7	C₃×D₅	—	36	1	no	—
8	H(3,𝔽₃)	—	10	1	no	Sylow
9	S₄	—	15	2	no	—
10	C₃×D₄	—	45	1	no	—
11	C₃×D₃	—	60	2	no	—
12	C₃×C₅	—	36	1	no	—
13	C₂²×C₃	—	15	2	no	—
14	A₄	—	15	2	no	—
15	A₄	—	30	2	no	—
16	C₃×C₄	—	45	1	no	—
17	D₅	—	36	1	no	—
18	C₃²	—	20	2	no	—
19	D₄	—	45	1	no	Sylow
20	C₂×C₃	—	45	1	no	—
21	D₃	—	60	2	no	—
22	C₅	—	36	1	no	Sylow
23	C₂²	—	15	2	no	—
24	C₄	—	45	1	no	—
25	C₃	—	60	2	no	—
26	C₃	A₆	1	1	yes	maximal normal, characteristic
27	C₂	—	45	1	no	—

	subgroup	G/H
center, Frattini, Fitting, socle, cosocle, hypercenter	C₃	A₆
commutator, hypocenter	G	C₁
LCS	G
UCS	C₁ ◁ C₃

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.