Subgroups — C₅×#204 #6690

Order 240.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×SD₁₆	—	3	1	no	maximal, Hall
5	C₂×C₅×D₃	—	2	1	no	—
6	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₅×Dic₃	—	2	1	no	—
8	#204	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×Q₈	—	3	1	no	—
10	C₅×D₄	—	3	1	no	—
11	C₅×C₈	D₃	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅	D₄	1	1	yes	characteristic
13	C₅×D₃	—	4	1	no	—
14	D₁₂	C₂×C₅	1	1	yes	characteristic
15	Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
16	C₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
17	C₂²×C₅	—	6	1	no	—
18	C₄×C₅	—	6	1	no	—
19	C₄×C₅	C₂×D₃	1	1	yes	characteristic
20	SD₁₆	—	3	1	no	Sylow
21	C₃×C₅	SD₁₆	1	1	yes	characteristic, complemented, Hall
22	C₂×D₃	—	2	1	no	—
23	C₃×C₄	C₂²×C₅	1	1	yes	characteristic
24	Dic₃	—	2	1	no	—
25	C₂×C₅	—	12	1	no	—
26	C₂×C₅	D₁₂	1	1	yes	characteristic
27	Q₈	—	3	1	no	—
28	D₄	—	3	1	no	—
29	C₈	C₅×D₃	1	1	yes	characteristic, complemented
30	C₂×C₃	C₅×D₄	1	1	yes	characteristic
31	D₃	—	4	1	no	—
32	C₅	#204	1	1	yes	characteristic, direct product factor, Sylow
33	C₂²	—	6	1	no	—
34	C₄	—	6	1	no	—
35	C₄	C₂×C₅×D₃	1	1	yes	characteristic
36	C₃	C₅×SD₁₆	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	12	1	no	—
38	C₂	C₅×D₁₂	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.