Subgroups — C₅×#239 #6811

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	C₅×D₁₂	C₂	1	3	yes	maximal, complemented
3	C₄×C₅×D₃	C₂	1	3	yes	maximal, complemented
4	C₅×#41	—	3	1	no	maximal, Hall
5	C₂×C₅×D₃	C₂²	1	3	yes	—
6	C₃×C₄×C₅	C₂²	1	3	yes	—
7	C₅×Dic₃	C₂²	1	1	yes	characteristic
8	#239	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×Q₈	D₃	1	1	yes	characteristic, complemented
10	C₅×D₄	—	3	3	no	—
11	C₂×C₄×C₅	—	3	3	no	—
12	C₂×C₃×C₅	C₂³	1	1	yes	characteristic
13	C₅×D₃	—	2	3	no	—
14	C₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
15	D₁₂	C₂×C₅	1	3	yes	complemented
16	C₄×D₃	C₂×C₅	1	3	yes	complemented
17	C₂²×C₅	—	3	3	no	—
18	C₄×C₅	—	3	1	no	—
19	C₄×C₅	C₂×D₃	1	3	yes	—
20	#41	—	3	1	no	Sylow
21	C₃×C₅	#41	1	1	yes	characteristic, complemented, Hall
22	C₂×D₃	C₂²×C₅	1	3	yes	—
23	C₃×C₄	C₂²×C₅	1	3	yes	—
24	Dic₃	C₂²×C₅	1	1	yes	characteristic
25	C₂×C₅	—	6	3	no	—
26	C₂×C₅	C₂²×D₃	1	1	yes	characteristic
27	Q₈	C₅×D₃	1	1	yes	characteristic, complemented
28	D₄	—	3	3	no	—
29	C₂×C₄	—	3	3	no	—
30	C₂×C₃	C₂³×C₅	1	1	yes	characteristic
31	D₃	—	2	3	no	—
32	C₅	#239	1	1	yes	characteristic, direct product factor, Sylow
33	C₂²	—	3	3	no	—
34	C₄	—	3	1	no	—
35	C₄	C₂×C₅×D₃	1	3	yes	—
36	C₃	C₅×#41	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	6	3	no	—
38	C₂	C₂²×C₅×D₃	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.