Subgroups — #64713

Order 320.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#108	C₂	1	1	yes	maximal, characteristic
2	#3951	C₂	1	1	yes	maximal, characteristic
3	C₂×#672	C₂	1	1	yes	maximal, characteristic
4	C₅×M₁₆	—	2	1	no	—
5	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
6	#681	—	2	1	no	—
7	#672	C₄	1	2	yes	—
8	#368	—	5	1	no	maximal, Sylow
9	C₂×C₄×C₅	D₄	1	1	yes	characteristic
10	C₅×C₈	—	4	1	no	—
11	C₅×C₈	C₂×C₄	1	1	yes	characteristic
12	C₅×C₈	Q₈	1	1	yes	characteristic
13	#168	—	4	1	no	—
14	C₂×C₁₆	—	5	1	no	—
15	#108	—	5	1	no	—
16	#108	D₅	1	1	yes	characteristic
17	C₂²×C₅	Q₁₆	1	1	yes	characteristic
18	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₅	D₈	1	1	yes	characteristic
20	M₁₆	—	2	1	no	—
21	M₁₆	—	10	1	no	—
22	C₂×C₈	C₂×D₅	1	1	yes	characteristic
23	C₁₆	—	5	2	no	—
24	C₂×C₅	—	2	1	no	—
25	C₂×C₅	#107	1	1	yes	characteristic
26	C₂×C₄	C₂²⋊D₅	1	1	yes	characteristic
27	C₈	—	4	1	no	—
28	C₈	—	20	1	no	—
29	C₈	Dic₁₀	1	1	yes	characteristic
30	C₈	C₄×D₅	1	1	yes	characteristic
31	C₅	#368	1	1	yes	characteristic, complemented, Sylow
32	C₂²	#689	1	1	yes	characteristic
33	C₄	#683	1	1	yes	characteristic
34	C₄	#686	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#3939	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
31. C₅	#368	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.