Subgroups — #64884

Order 320.

54 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	—	2	2	no	—
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	#335	—	5	1	no	maximal, Sylow
8	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
9	C₂×Dic₅	D₄	1	1	yes	characteristic
10	C₂×Dic₅	Q₈	1	1	yes	characteristic
11	#170	—	4	2	no	—
12	C₅×C₈	—	2	1	no	—
13	#168	C₈	1	2	yes	complemented
14	C₄⋊C₈	—	5	2	no	—
15	C₄×C₈	—	5	1	no	—
16	C₂²×C₅	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₅	C₂×C₈	1	1	yes	characteristic
18	C₄×C₅	M₁₆	1	1	yes	characteristic
19	Dic₅	—	2	1	no	—
20	Dic₅	D₈	1	1	yes	characteristic
21	Dic₅	Q₁₆	1	1	yes	characteristic
22	C₂×C₈	—	5	1	no	—
23	C₂×C₈	—	10	2	no	—
24	C₂×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₄²	—	5	1	no	—
26	C₂×C₅	C₄⋊C₈	1	1	yes	characteristic
27	C₂×C₅	#107	1	1	yes	characteristic
28	C₂×C₅	#108	1	1	yes	characteristic
29	C₂×C₄	—	5	1	no	—
30	C₂×C₄	—	5	1	no	—
31	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	5	2	no	—
34	C₈	—	20	2	no	—
35	C₅	#335	1	1	yes	characteristic, complemented, Sylow
36	C₂²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
37	C₄	—	5	1	no	—
38	C₄	—	5	1	no	—
39	C₄	—	10	1	no	—
40	C₄	D₅⋊C₈	1	1	yes	characteristic
41	C₄	#704	1	1	yes	characteristic
42	C₂	#3994	1	1	yes	characteristic
43	C₂	#3995	1	1	yes	characteristic
44	C₂	#4004	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
13. #168	C₈	semidirect
35. C₅	#335	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.