Subgroups — C₅×D₃×Q₈ #6810

Order 240.

76 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	C₄×C₅×D₃	C₂	1	3	yes	maximal
3	C₅×Dic₆	C₂	1	3	yes	maximal, complemented
4	C₂×C₅×Q₈	—	3	1	no	maximal, Hall
5	C₂×C₅×D₃	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₅	C₂²	1	3	yes	—
7	C₅×Dic₃	C₂²	1	3	yes	—
8	D₃×Q₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×Q₈	—	3	3	no	—
10	C₅×Q₈	D₃	1	1	yes	characteristic, direct product factor
11	C₂×C₄×C₅	—	3	3	no	—
12	C₂×C₃×C₅	C₂³	1	1	yes	characteristic
13	C₅×D₃	Q₈	1	2	yes	direct product factor
14	C₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
15	C₄×D₃	C₂×C₅	1	3	yes	—
16	Dic₆	C₂×C₅	1	3	yes	complemented
17	C₂²×C₅	—	3	1	no	—
18	C₄×C₅	—	3	3	no	—
19	C₄×C₅	C₂×D₃	1	3	yes	—
20	C₂×Q₈	—	3	1	no	Sylow
21	C₃×C₅	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
22	C₂×D₃	C₂²×C₅	1	1	yes	characteristic
23	C₃×C₄	C₂²×C₅	1	3	yes	—
24	Dic₃	C₂²×C₅	1	3	yes	—
25	C₂×C₅	—	3	2	no	—
26	C₂×C₅	C₂²×D₃	1	1	yes	characteristic
27	Q₈	—	3	3	no	—
28	Q₈	C₅×D₃	1	1	yes	characteristic, direct product factor
29	C₂×C₄	—	3	3	no	—
30	C₂×C₃	C₂³×C₅	1	1	yes	characteristic
31	D₃	C₅×Q₈	1	2	yes	direct product factor
32	C₅	D₃×Q₈	1	1	yes	characteristic, direct product factor, Sylow
33	C₂²	—	3	1	no	—
34	C₄	—	3	3	no	—
35	C₄	C₂×C₅×D₃	1	3	yes	—
36	C₃	C₂×C₅×Q₈	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	3	2	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.