Subgroups — C₈×#168 #64673

Order 320.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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