Subgroups — C₂²×Dic₁₅ #6822

Order 240.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₅	C₂	1	6	yes	maximal, direct product factor
3	C₂²×Dic₅	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₅	C₄	1	4	yes	complemented
5	C₂²×C₃×C₅	C₂²	1	3	yes	—
6	Dic₁₅	C₂²	1	4	yes	direct product factor
7	C₂²×Dic₃	—	5	1	no	maximal, Hall
8	C₂³×C₅	D₃	1	1	yes	characteristic
9	C₂×Dic₅	—	3	6	no	—
10	C₂×C₃×C₅	C₂×C₄	1	6	yes	complemented
11	C₂×C₃×C₅	C₂³	1	1	yes	characteristic
12	C₂³×C₃	D₅	1	1	yes	characteristic
13	C₂×Dic₃	—	5	6	no	—
14	C₂²×C₅	Dic₃	1	4	yes	complemented
15	C₂²×C₅	C₂×D₃	1	3	yes	—
16	Dic₅	—	3	4	no	—
17	C₂²×C₄	—	15	1	no	Sylow
18	C₃×C₅	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₃	Dic₅	1	4	yes	complemented
20	C₂²×C₃	C₂×D₅	1	3	yes	—
21	Dic₃	—	5	4	no	—
22	C₂×C₅	C₂×Dic₃	1	6	yes	complemented
23	C₂×C₅	C₂²×D₃	1	1	yes	characteristic
24	C₂³	D₁₅	1	1	yes	characteristic
25	C₂×C₄	—	15	6	no	—
26	C₂×C₃	C₂×Dic₅	1	6	yes	complemented
27	C₂×C₃	C₂²×D₅	1	1	yes	characteristic
28	C₅	C₂²×Dic₃	1	1	yes	characteristic, complemented, Sylow
29	C₂²	Dic₁₅	1	4	yes	direct product factor
30	C₂²	C₂×D₁₅	1	3	yes	—
31	C₄	—	15	4	no	—
32	C₃	C₂²×Dic₅	1	1	yes	characteristic, complemented, Sylow
33	C₂	C₂×Dic₁₅	1	6	yes	direct product factor
34	C₂	C₂²×D₁₅	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.