Subgroups — #6758

Order 240.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#170	C₂	1	2	yes	maximal, complemented
3	#700	—	3	1	no	maximal, Hall
4	C₂×C₃×D₅	C₄	1	1	yes	characteristic
5	C₃×C₄×C₅	C₄	1	1	yes	characteristic
6	C₃×Dic₅	C₂²	1	1	yes	characteristic
7	#208	—	5	1	no	maximal, Hall
8	C₄×D₅	D₃	1	1	yes	characteristic
9	#170	—	3	2	no	—
10	C₂×C₃×C₅	C₂×C₄	1	1	yes	characteristic
11	C₃×D₅	—	2	1	no	—
12	C₂×C₃×C₄	—	5	1	no	—
13	C₃⋊C₈	—	5	2	no	—
14	C₂×D₅	Dic₃	1	1	yes	characteristic
15	C₄×C₅	Dic₃	1	1	yes	characteristic
16	Dic₅	C₂×D₃	1	1	yes	characteristic
17	M₁₆	—	15	1	no	Sylow
18	C₃×C₅	M₁₆	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₃	—	5	1	no	—
20	C₃×C₄	—	5	1	no	—
21	C₃×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
22	C₂×C₅	C₂×Dic₃	1	1	yes	characteristic
23	D₅	—	2	1	no	—
24	C₂×C₄	—	5	1	no	—
25	C₈	—	15	2	no	—
26	C₂×C₃	—	10	1	no	—
27	C₂×C₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₅	#208	1	1	yes	characteristic, complemented, Sylow
29	C₂²	—	5	1	no	—
30	C₄	—	5	1	no	—
31	C₄	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
32	C₃	#700	1	1	yes	characteristic, complemented, Sylow
33	C₂	—	10	1	no	—
34	C₂	C₂×ΓL(1,𝔽₁₆)	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.