Subgroups — C₂³×#168 #66114

Order 320.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×#168	C₂	1	14	yes	maximal, direct product factor
3	C₂⁴×C₅	C₄	1	1	yes	characteristic
4	C₂²×C₄×C₅	C₄	1	7	yes	—
5	C₂²×C₄×C₅	C₂²	1	7	yes	—
6	C₂×#168	C₂²	1	28	yes	direct product factor
7	C₂³×C₈	—	5	1	no	maximal, Sylow
8	C₂³×C₅	C₈	1	8	yes	complemented
9	C₂³×C₅	C₂×C₄	1	7	yes	—
10	C₂×C₄×C₅	C₂×C₄	1	21	yes	—
11	C₂×C₄×C₅	C₂³	1	7	yes	—
12	#168	C₂³	1	8	yes	direct product factor
13	C₂³×C₄	D₅	1	1	yes	characteristic
14	C₂²×C₈	—	5	14	no	—
15	C₂²×C₅	C₂×C₈	1	28	yes	complemented
16	C₂²×C₅	C₂²×C₄	1	7	yes	—
17	C₄×C₅	C₂²×C₄	1	7	yes	—
18	C₄×C₅	C₂⁴	1	1	yes	characteristic
19	C₂⁴	Dic₅	1	1	yes	characteristic
20	C₂²×C₄	Dic₅	1	7	yes	—
21	C₂²×C₄	C₂×D₅	1	7	yes	—
22	C₂×C₈	—	5	28	no	—
23	C₂×C₅	C₂²×C₈	1	14	yes	complemented
24	C₂×C₅	C₂³×C₄	1	1	yes	characteristic
25	C₂³	#168	1	8	yes	direct product factor
26	C₂³	C₂×Dic₅	1	7	yes	—
27	C₂×C₄	C₂×Dic₅	1	21	yes	—
28	C₂×C₄	C₂²×D₅	1	7	yes	—
29	C₈	—	5	8	no	—
30	C₅	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
31	C₂²	C₂×#168	1	28	yes	direct product factor
32	C₂²	C₂²×Dic₅	1	7	yes	—
33	C₄	C₂²×Dic₅	1	7	yes	—
34	C₄	C₂³×D₅	1	1	yes	characteristic
35	C₂	C₂²×#168	1	14	yes	direct product factor
36	C₂	C₂³×Dic₅	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.