Subgroups — C₃×ΓL(1,𝔽₁₆) #4376

Order 180.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₅	C₂	1	1	yes	maximal, characteristic
2	ΓL(1,𝔽₁₆)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×AGL(1,𝔽₅)	—	3	1	no	maximal
4	C₃²×C₅	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×Dic₃	—	5	1	no	maximal, Hall
6	C₃×D₅	—	2	1	no	—
7	C₃×D₅	D₃	1	1	yes	characteristic
8	C₃×D₅	C₂×C₃	1	1	yes	characteristic
9	AGL(1,𝔽₅)	—	3	1	no	Hall
10	C₂×C₃²	—	5	1	no	—
11	C₃×C₅	—	2	1	no	—
12	C₃×C₅	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅	C₃×C₄	1	1	yes	characteristic, complemented
14	C₃×C₄	—	15	1	no	—
15	Dic₃	—	5	1	no	—
16	D₅	C₃×D₃	1	1	yes	characteristic
17	C₃²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃	—	5	1	no	—
19	C₂×C₃	—	5	1	no	—
20	C₂×C₃	—	10	1	no	—
21	C₅	C₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
22	C₄	—	15	1	no	Sylow
23	C₃	—	2	1	no	—
24	C₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
25	C₃	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor
26	C₂	—	5	1	no	—

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.