Subgroups — #64889

Order 320.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3998	C₂	1	2	yes	maximal
2	C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₈	C₄	1	1	yes	characteristic
4	C₄×Dic₅	C₄	1	1	yes	characteristic
5	C₂×#168	C₂²	1	1	yes	characteristic
6	#674	—	2	2	no	—
7	#364	—	5	1	no	maximal, Sylow
8	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
9	C₂×Dic₅	—	2	1	no	—
10	C₅×C₈	C₈	1	2	yes	—
11	#168	D₄	1	1	yes	characteristic
12	#168	Q₈	1	1	yes	characteristic
13	M₃₂	—	5	2	no	—
14	C₄×C₈	—	5	1	no	—
15	C₂²×C₅	M₁₆	1	1	yes	characteristic
16	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₅	C₂×C₈	1	1	yes	characteristic
18	Dic₅	—	2	2	no	—
19	C₂×C₈	—	5	1	no	—
20	C₂×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
21	C₄²	—	5	1	no	—
22	C₁₆	—	10	2	no	—
23	C₂×C₅	—	2	1	no	—
24	C₂×C₅	C₄⋊C₈	1	1	yes	characteristic
25	C₂×C₄	—	10	1	no	—
26	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
27	C₈	—	5	1	no	—
28	C₈	—	5	1	no	—
29	C₈	#170	1	2	yes	—
30	C₅	#364	1	1	yes	characteristic, complemented, Sylow
31	C₂²	#700	1	1	yes	characteristic
32	C₄	—	10	2	no	—
33	C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
34	C₄	C₂×#170	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	C₄⋊#170	1	1	yes	characteristic

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

N	H ≅ G/N	type
30. C₅	#364	semidirect

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