Subgroups — C₄⋊Dic₁₅ #6713

Order 240.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₅	C₂	1	2	yes	maximal
3	C₄⋊Dic₅	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₅	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₅	C₄	1	2	yes	complemented
6	Dic₁₅	—	2	2	no	—
7	C₄⋊Dic₃	—	5	1	no	maximal, Hall
8	C₂×C₄×C₅	D₃	1	1	yes	characteristic
9	C₂×Dic₅	—	3	2	no	—
10	C₂×C₃×C₅	C₂×C₄	1	1	yes	characteristic
11	C₂×C₃×C₅	D₄	1	1	yes	characteristic
12	C₂×C₃×C₅	Q₈	1	1	yes	characteristic
13	C₂×C₃×C₄	D₅	1	1	yes	characteristic
14	C₂×Dic₃	—	5	2	no	—
15	C₂²×C₅	C₂×D₃	1	1	yes	characteristic
16	C₄×C₅	Dic₃	1	2	yes	complemented
17	Dic₅	—	6	2	no	—
18	C₄⋊C₄	—	15	1	no	Sylow
19	C₃×C₅	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₃	C₂×D₅	1	1	yes	characteristic
21	C₃×C₄	Dic₅	1	2	yes	complemented
22	Dic₃	—	10	2	no	—
23	C₂×C₅	Dic₆	1	1	yes	characteristic
24	C₂×C₅	D₁₂	1	1	yes	characteristic
25	C₂×C₅	C₂×Dic₃	1	1	yes	characteristic
26	C₂×C₄	—	15	2	no	—
27	C₂×C₄	D₁₅	1	1	yes	characteristic
28	C₂×C₃	Dic₁₀	1	1	yes	characteristic
29	C₂×C₃	D₂₀	1	1	yes	characteristic
30	C₂×C₃	C₂×Dic₅	1	1	yes	characteristic
31	C₅	C₄⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
32	C₂²	C₂×D₁₅	1	1	yes	characteristic
33	C₄	—	30	2	no	—
34	C₄	Dic₁₅	1	2	yes	complemented
35	C₃	C₄⋊Dic₅	1	1	yes	characteristic, complemented, Sylow
36	C₂	Dic₃₀	1	1	yes	characteristic
37	C₂	D₆₀	1	1	yes	characteristic
38	C₂	C₂×Dic₁₅	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.