Subgroups — C₅×#216 #6702

Order 240.

36 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
2	C₅×Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₅×Q₁₆	—	3	1	no	maximal, Hall
5	C₃×C₄×C₅	—	2	1	no	—
6	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₅×Dic₃	—	2	1	no	—
8	#216	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×Q₈	—	3	1	no	—
10	C₅×Q₈	D₃	1	1	yes	characteristic
11	C₅×C₈	—	3	1	no	—
12	C₂×C₃×C₅	D₄	1	1	yes	characteristic
13	C₃×Q₈	C₂×C₅	1	1	yes	characteristic
14	Dic₆	C₂×C₅	1	1	yes	characteristic
15	C₃⋊C₈	C₂×C₅	1	1	yes	characteristic
16	C₄×C₅	—	2	1	no	—
17	C₄×C₅	—	6	1	no	—
18	C₄×C₅	C₂×D₃	1	1	yes	characteristic
19	Q₁₆	—	3	1	no	Sylow
20	C₃×C₅	Q₁₆	1	1	yes	characteristic, complemented, Hall
21	C₃×C₄	—	2	1	no	—
22	C₃×C₄	C₂²×C₅	1	1	yes	characteristic
23	Dic₃	—	2	1	no	—
24	C₂×C₅	#67	1	1	yes	characteristic
25	Q₈	—	3	1	no	—
26	Q₈	C₅×D₃	1	1	yes	characteristic
27	C₈	—	3	1	no	—
28	C₂×C₃	C₅×D₄	1	1	yes	characteristic
29	C₅	#216	1	1	yes	characteristic, direct product factor, Sylow
30	C₄	—	2	1	no	—
31	C₄	—	6	1	no	—
32	C₄	C₂×C₅×D₃	1	1	yes	characteristic
33	C₃	C₅×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₂	C₅×#67	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.