Subgroups — C₃×#681 #6678

Order 240.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₃×#168	C₂	1	2	yes	maximal, complemented
3	#681	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₅	C₄	1	1	yes	characteristic
5	C₃×C₄×C₅	C₄	1	1	yes	characteristic
6	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₃×M₁₆	—	5	1	no	maximal, Hall
8	C₂×C₄×C₅	C₂×C₃	1	1	yes	characteristic
9	#168	C₂×C₃	1	2	yes	complemented
10	C₂×C₃×C₅	—	2	1	no	—
11	C₂×C₃×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₄	D₅	1	1	yes	characteristic
13	C₃×C₈	—	5	2	no	—
14	C₂²×C₅	C₃×C₄	1	1	yes	characteristic
15	C₄×C₅	C₃×C₄	1	1	yes	characteristic
16	C₄×C₅	C₂²×C₃	1	1	yes	characteristic
17	M₁₆	—	5	1	no	Sylow
18	C₃×C₅	M₁₆	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₃	Dic₅	1	1	yes	characteristic
20	C₃×C₄	Dic₅	1	1	yes	characteristic
21	C₃×C₄	C₂×D₅	1	1	yes	characteristic
22	C₂×C₅	—	2	1	no	—
23	C₂×C₅	C₂×C₃×C₄	1	1	yes	characteristic
24	C₂×C₄	C₃×D₅	1	1	yes	characteristic
25	C₈	—	5	2	no	—
26	C₂×C₃	—	2	1	no	—
27	C₂×C₃	C₂×Dic₅	1	1	yes	characteristic
28	C₅	C₃×M₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₂²	C₃×Dic₅	1	1	yes	characteristic
30	C₄	C₃×Dic₅	1	1	yes	characteristic
31	C₄	C₂×C₃×D₅	1	1	yes	characteristic
32	C₃	#681	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	—	2	1	no	—
34	C₂	C₂×C₃×Dic₅	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.