Subgroups — C₂×C₃×AGL(1,𝔽₅) #1230

Order 120.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, direct product factor
3	C₂×AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₅	C₄	1	1	yes	characteristic, complemented
5	C₃×D₅	C₄	1	1	yes	characteristic, complemented
6	C₃×D₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄	—	5	1	no	maximal, Hall
8	C₂×D₅	C₂×C₃	1	1	yes	characteristic
9	AGL(1,𝔽₅)	C₂×C₃	1	2	yes	direct product factor
10	C₃×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₃	—	5	1	no	—
12	C₃×C₄	—	5	2	no	—
13	C₂×C₅	C₃×C₄	1	1	yes	characteristic, complemented
14	D₅	C₃×C₄	1	1	yes	characteristic, complemented
15	D₅	C₂²×C₃	1	1	yes	characteristic
16	C₂×C₄	—	5	1	no	Sylow
17	C₂×C₃	—	5	1	no	—
18	C₂×C₃	—	5	1	no	—
19	C₂×C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
20	C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
21	C₂²	—	5	1	no	—
22	C₄	—	5	2	no	—
23	C₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
24	C₂	—	5	1	no	—
25	C₂	—	5	1	no	—
26	C₂	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor

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.