Subgroups — ΓL(2,𝔽₄) #67190

Order 360.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×A₅	C₂	1	1	yes	maximal, characteristic, complemented
2	S₅	—	3	1	no	maximal
3	C₃⋊S₄	—	5	1	no	maximal, Hall
4	ΓL(1,𝔽₁₆)	—	6	1	no	maximal
5	A₅	D₃	1	1	yes	characteristic, complemented
6	C₃×A₄	—	5	1	no	—
7	D₃²	—	10	1	no	maximal
8	C₃×D₅	—	6	1	no	—
9	S₄	—	15	1	no	—
10	S₄	—	15	2	no	—
11	#67	—	15	1	no	—
12	AGL(1,𝔽₅)	—	18	1	no	—
13	C₃⋊D₃	—	10	1	no	—
14	C₃×D₃	—	10	1	no	—
15	C₃×D₃	—	10	1	no	—
16	C₃×C₅	—	6	1	no	—
17	C₂²×C₃	—	5	1	no	—
18	C₂×D₃	—	15	1	no	—
19	C₂×D₃	—	30	1	no	—
20	A₄	—	5	1	no	—
21	A₄	—	5	2	no	—
22	Dic₃	—	15	1	no	—
23	D₅	—	6	1	no	—
24	C₃²	—	10	1	no	Sylow
25	D₄	—	45	1	no	Sylow
26	C₂×C₃	—	15	1	no	—
27	C₂×C₃	—	30	1	no	—
28	D₃	—	10	1	no	—
29	D₃	—	10	1	no	—
30	D₃	—	30	1	no	—
31	D₃	—	60	1	no	—
32	C₅	—	6	1	no	Sylow
33	C₂²	—	5	1	no	—
34	C₂²	—	45	1	no	—
35	C₄	—	45	1	no	—
36	C₃	—	10	1	no	—
37	C₃	—	20	1	no	—
38	C₃	S₅	1	1	yes	characteristic, complemented
39	C₂	—	15	1	no	—
40	C₂	—	30	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, cosocle, hypocenter	C₃×A₅	C₂
Fitting	C₃	S₅
LCS	G ▷ C₃×A₅
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.