Subgroups — C₈×#170 #64878

Order 320.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#170	C₂	1	2	yes	maximal
2	C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×#170	C₄	1	4	yes	—
4	C₂×C₅×C₈	C₄	1	1	yes	characteristic
5	C₄×Dic₅	C₂²	1	1	yes	characteristic
6	C₂×#168	C₄	1	1	yes	characteristic
7	C₈²	—	5	1	no	maximal, Sylow
8	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
9	C₂×Dic₅	C₂×C₄	1	2	yes	—
10	#170	C₈	1	8	yes	direct product factor
11	C₅×C₈	C₈	1	2	yes	complemented
12	#168	C₈	1	2	yes	complemented
13	C₄×C₈	—	5	2	no	—
14	C₄×C₈	—	5	1	no	—
15	C₂²×C₅	C₄²	1	1	yes	characteristic
16	C₄×C₅	C₂×C₈	1	1	yes	characteristic
17	C₄×C₅	C₂×C₈	1	1	yes	characteristic
18	Dic₅	C₂×C₈	1	4	yes	—
19	C₂×C₈	—	5	4	no	—
20	C₂×C₈	—	5	1	no	—
21	C₂×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
22	C₄²	—	5	1	no	—
23	C₂×C₅	C₄×C₈	1	2	yes	—
24	C₂×C₅	C₄×C₈	1	1	yes	characteristic
25	C₂×C₄	—	5	2	no	—
26	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
27	C₈	—	5	8	no	—
28	C₈	—	5	2	no	—
29	C₈	#170	1	2	yes	direct product factor
30	C₅	C₈²	1	1	yes	characteristic, complemented, Sylow
31	C₂²	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
32	C₄	—	5	4	no	—
33	C₄	D₅⋊C₈	1	1	yes	characteristic
34	C₄	C₂×#170	1	1	yes	characteristic
35	C₂	C₈×AGL(1,𝔽₅)	1	2	yes	—
36	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.