Subgroups — Q₈×#170 #65786

Order 320.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#170	C₂	1	3	yes	maximal
3	C₄×#170	C₂	1	3	yes	maximal
4	C₂×C₅×Q₈	C₄	1	1	yes	characteristic
5	C₂×#170	C₂²	1	3	yes	—
6	C₂×#170	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₅	C₄	1	3	yes	—
8	C₄×Dic₅	C₂²	1	3	yes	—
9	C₈×Q₈	—	5	1	no	maximal, Sylow
10	C₅×Q₈	C₈	1	4	yes	complemented
11	C₂×C₄×C₅	C₂×C₄	1	3	yes	—
12	C₂×Dic₅	C₂×C₄	1	3	yes	—
13	C₂×Dic₅	C₂³	1	1	yes	characteristic
14	#170	—	2	3	no	—
15	#170	Q₈	1	2	yes	direct product factor
16	C₄×Q₈	—	5	1	no	—
17	C₄⋊C₈	—	5	3	no	—
18	C₄×C₈	—	5	3	no	—
19	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
20	C₄×C₅	C₂×C₈	1	6	yes	—
21	Dic₅	—	2	3	no	—
22	Dic₅	C₂×Q₈	1	1	yes	characteristic
23	Dic₅	#41	1	1	yes	characteristic
24	C₂×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₂×C₈	—	5	1	no	—
26	C₂×C₈	—	5	3	no	—
27	C₄⋊C₄	—	5	3	no	—
28	C₄²	—	5	3	no	—
29	C₂×C₅	C₄×Q₈	1	1	yes	characteristic
30	C₂×C₅	C₂²×C₈	1	1	yes	characteristic
31	C₂×C₅	#131	1	1	yes	characteristic
32	Q₈	#170	1	4	yes	direct product factor
33	C₂×C₄	—	5	1	no	—
34	C₂×C₄	—	5	3	no	—
35	C₂×C₄	C₂×AGL(1,𝔽₅)	1	3	yes	—
36	C₈	—	5	2	no	—
37	C₈	—	10	3	no	—
38	C₅	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
39	C₂²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
40	C₄	—	5	1	no	—
41	C₄	—	5	1	no	—
42	C₄	—	10	3	no	—
43	C₄	C₂×#170	1	6	yes	—
44	C₂	#4133	1	1	yes	characteristic
45	C₂	Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
46	C₂	C₂²×#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.