Subgroups — C₃×#713 #6801

Order 240.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₀	C₂	1	3	yes	maximal, complemented
3	C₃×C₄×D₅	C₂	1	3	yes	maximal, complemented
4	#713	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×D₅	C₂²	1	3	yes	—
6	C₃×C₄×C₅	C₂²	1	3	yes	—
7	C₃×Dic₅	C₂²	1	1	yes	characteristic
8	C₃×#41	—	5	1	no	maximal, Hall
9	C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
10	D₂₀	C₂×C₃	1	3	yes	complemented
11	C₄×D₅	C₂×C₃	1	3	yes	complemented
12	C₂×C₃×C₅	C₂³	1	1	yes	characteristic
13	C₃×D₅	—	2	3	no	—
14	C₃×Q₈	D₅	1	1	yes	characteristic, complemented
15	C₃×D₄	—	5	3	no	—
16	C₂×C₃×C₄	—	5	3	no	—
17	C₂×D₅	C₂²×C₃	1	3	yes	—
18	C₄×C₅	C₂²×C₃	1	3	yes	—
19	Dic₅	C₂²×C₃	1	1	yes	characteristic
20	#41	—	5	1	no	Sylow
21	C₃×C₅	#41	1	1	yes	characteristic, complemented, Hall
22	C₂²×C₃	—	5	3	no	—
23	C₃×C₄	—	5	1	no	—
24	C₃×C₄	C₂×D₅	1	3	yes	—
25	C₂×C₅	C₂³×C₃	1	1	yes	characteristic
26	D₅	—	2	3	no	—
27	Q₈	C₃×D₅	1	1	yes	characteristic, complemented
28	D₄	—	5	3	no	—
29	C₂×C₄	—	5	3	no	—
30	C₂×C₃	—	10	3	no	—
31	C₂×C₃	C₂²×D₅	1	1	yes	characteristic
32	C₅	C₃×#41	1	1	yes	characteristic, complemented, Sylow
33	C₂²	—	5	3	no	—
34	C₄	—	5	1	no	—
35	C₄	C₂×C₃×D₅	1	3	yes	—
36	C₃	#713	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	10	3	no	—
38	C₂	C₂²×C₃×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.