Subgroups — C₃×#687 #6684

Order 240.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#687	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₅	—	2	1	no	—
6	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₃×Dic₅	—	2	1	no	—
8	C₃×SD₁₆	—	5	1	no	maximal, Hall
9	C₅×D₄	C₂×C₃	1	1	yes	characteristic
10	Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
11	#168	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅	—	4	1	no	—
13	C₂×C₃×C₅	D₄	1	1	yes	characteristic
14	C₃×Q₈	—	5	1	no	—
15	C₃×D₄	D₅	1	1	yes	characteristic
16	C₃×C₈	—	5	1	no	—
17	C₂²×C₅	—	2	1	no	—
18	C₄×C₅	C₂²×C₃	1	1	yes	characteristic
19	Dic₅	—	2	1	no	—
20	SD₁₆	—	5	1	no	Sylow
21	C₃×C₅	SD₁₆	1	1	yes	characteristic, complemented, Hall
22	C₂²×C₃	—	2	1	no	—
23	C₃×C₄	—	10	1	no	—
24	C₃×C₄	C₂×D₅	1	1	yes	characteristic
25	C₂×C₅	—	4	1	no	—
26	C₂×C₅	C₃×D₄	1	1	yes	characteristic
27	Q₈	—	5	1	no	—
28	D₄	C₃×D₅	1	1	yes	characteristic
29	C₈	—	5	1	no	—
30	C₂×C₃	—	4	1	no	—
31	C₂×C₃	C₂²⋊D₅	1	1	yes	characteristic
32	C₅	C₃×SD₁₆	1	1	yes	characteristic, complemented, Sylow
33	C₂²	—	2	1	no	—
34	C₄	—	10	1	no	—
35	C₄	C₂×C₃×D₅	1	1	yes	characteristic
36	C₃	#687	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	4	1	no	—
38	C₂	C₃×C₂²⋊D₅	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.