Subgroups — #64885

Order 320.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#674	C₂	1	2	yes	maximal
2	C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₈	C₄	1	1	yes	characteristic
4	C₄×Dic₅	C₄	1	1	yes	characteristic
5	C₂×#168	C₂²	1	1	yes	characteristic
6	#674	C₄	1	4	yes	complemented
7	C₄×C₁₆	—	5	1	no	maximal, Sylow
8	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
9	C₂×Dic₅	C₈	1	2	yes	—
10	C₅×C₈	C₈	1	2	yes	—
11	#168	C₂×C₄	1	2	yes	—
12	C₂×C₁₆	—	5	2	no	—
13	C₄×C₈	—	5	1	no	—
14	C₂²×C₅	C₂×C₈	1	1	yes	characteristic
15	C₄×C₅	C₄²	1	1	yes	characteristic
16	C₄×C₅	C₂×C₈	1	1	yes	characteristic
17	Dic₅	C₁₆	1	4	yes	complemented
18	C₂×C₈	—	5	1	no	—
19	C₂×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
20	C₄²	—	5	1	no	—
21	C₁₆	—	5	4	no	—
22	C₂×C₅	C₄×C₈	1	1	yes	characteristic
23	C₂×C₅	C₂×C₁₆	1	2	yes	—
24	C₂×C₄	—	5	2	no	—
25	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
26	C₈	—	5	2	no	—
27	C₈	#170	1	2	yes	—
28	C₅	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₂²	D₅⋊C₈	1	1	yes	characteristic
30	C₄	—	5	4	no	—
31	C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
32	C₄	C₂×#170	1	1	yes	characteristic
33	C₂	D₅⋊C₁₆	1	2	yes	—
34	C₂	C₄×#170	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.