Subgroups — #6719

Order 240.

68 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	2	yes	maximal, complemented
3	C₂²⋊Dic₅	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₅	—	2	2	no	—
5	C₂²×C₃×C₅	C₄	1	2	yes	complemented
6	C₂²×C₃×C₅	C₂²	1	1	yes	characteristic
7	Dic₁₅	—	2	2	no	—
8	#217	—	5	1	no	maximal, Hall
9	C₂³×C₅	D₃	1	1	yes	characteristic
10	C₂×Dic₅	—	3	2	no	—
11	C₂×C₃×C₅	—	2	2	no	—
12	C₂×C₃×C₅	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₅	D₄	1	2	yes	—
14	C₂³×C₃	D₅	1	1	yes	characteristic
15	C₂×Dic₃	—	5	2	no	—
16	C₂²×C₅	—	2	2	no	—
17	C₂²×C₅	Dic₃	1	2	yes	complemented
18	C₂²×C₅	C₂×D₃	1	1	yes	characteristic
19	Dic₅	—	6	2	no	—
20	C₂²⋊C₄	—	15	1	no	Sylow
21	C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
22	C₂²×C₃	—	2	2	no	—
23	C₂²×C₃	Dic₅	1	2	yes	complemented
24	C₂²×C₃	C₂×D₅	1	1	yes	characteristic
25	Dic₃	—	10	2	no	—
26	C₂×C₅	—	2	2	no	—
27	C₂×C₅	C₂×Dic₃	1	1	yes	characteristic
28	C₂×C₅	#67	1	2	yes	—
29	C₂³	D₁₅	1	1	yes	characteristic
30	C₂×C₄	—	15	2	no	—
31	C₂×C₃	—	2	2	no	—
32	C₂×C₃	C₂×Dic₅	1	1	yes	characteristic
33	C₂×C₃	C₂²⋊D₅	1	2	yes	—
34	C₅	#217	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	2	2	no	—
36	C₂²	Dic₁₅	1	2	yes	complemented
37	C₂²	C₂×D₁₅	1	1	yes	characteristic
38	C₄	—	30	2	no	—
39	C₃	C₂²⋊Dic₅	1	1	yes	characteristic, complemented, Sylow
40	C₂	—	2	2	no	—
41	C₂	C₂×Dic₁₅	1	1	yes	characteristic
42	C₂	#1220	1	2	yes	—

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.