Subgroups — C₂×C₃×#170 #6754

Order 240.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₃×#170	C₂	1	2	yes	maximal, direct product factor
3	C₂×#170	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₅	C₄	1	1	yes	characteristic
5	C₃×Dic₅	C₄	1	1	yes	characteristic
6	C₃×Dic₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₈	—	5	1	no	maximal, Hall
8	C₂×Dic₅	C₂×C₃	1	1	yes	characteristic
9	#170	C₂×C₃	1	2	yes	direct product factor
10	C₂×C₃×C₅	C₈	1	2	yes	complemented
11	C₂×C₃×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₄	—	5	1	no	—
13	C₃×C₈	—	5	2	no	—
14	C₂²×C₅	C₃×C₄	1	1	yes	characteristic
15	Dic₅	C₃×C₄	1	1	yes	characteristic
16	Dic₅	C₂²×C₃	1	1	yes	characteristic
17	C₂×C₈	—	5	1	no	Sylow
18	C₃×C₅	C₂×C₈	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₃	AGL(1,𝔽₅)	1	1	yes	characteristic
20	C₃×C₄	—	5	1	no	—
21	C₃×C₄	—	5	1	no	—
22	C₂×C₅	C₃×C₈	1	2	yes	complemented
23	C₂×C₅	C₂×C₃×C₄	1	1	yes	characteristic
24	C₂×C₄	—	5	1	no	—
25	C₈	—	5	2	no	—
26	C₂×C₃	#170	1	2	yes	direct product factor
27	C₂×C₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₅	C₂×C₃×C₈	1	1	yes	characteristic, complemented, Sylow
29	C₂²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
30	C₄	—	5	1	no	—
31	C₄	—	5	1	no	—
32	C₃	C₂×#170	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	C₃×#170	1	2	yes	direct product factor
34	C₂	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic

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.