Subgroups — #64731

Order 320.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
3	#3944	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
5	C₄×Dic₅	C₄	1	1	yes	characteristic
6	C₂×#168	C₄	1	1	yes	characteristic
7	C₅×C₁₆	—	2	1	no	—
8	#672	—	2	1	no	—
9	#364	—	5	1	no	maximal, Sylow
10	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₅	—	2	1	no	—
12	C₅×C₈	D₄	1	1	yes	characteristic
13	C₅×C₈	Q₈	1	1	yes	characteristic
14	#168	C₈	1	2	yes	—
15	M₃₂	—	5	1	no	—
16	M₃₂	D₅	1	1	yes	characteristic
17	C₄×C₈	—	5	1	no	—
18	C₂²×C₅	M₁₆	1	1	yes	characteristic
19	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
20	C₄×C₅	C₂×C₈	1	1	yes	characteristic
21	Dic₅	—	2	2	no	—
22	C₂×C₈	—	5	1	no	—
23	C₂×C₈	C₂×D₅	1	1	yes	characteristic
24	C₄²	—	5	1	no	—
25	C₁₆	—	2	1	no	—
26	C₁₆	—	10	1	no	—
27	C₂×C₅	—	2	1	no	—
28	C₂×C₅	C₄⋊C₈	1	1	yes	characteristic
29	C₂×C₄	—	10	1	no	—
30	C₂×C₄	C₄×D₅	1	1	yes	characteristic
31	C₈	—	5	2	no	—
32	C₈	Dic₁₀	1	1	yes	characteristic
33	C₈	C₂²⋊D₅	1	1	yes	characteristic
34	C₅	#364	1	1	yes	characteristic, complemented, Sylow
35	C₂²	#676	1	1	yes	characteristic
36	C₄	—	10	2	no	—
37	C₄	C₈×D₅	1	1	yes	characteristic
38	C₄	#683	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	#3946	1	1	yes	characteristic

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

N	H ≅ G/N	type
34. C₅	#364	semidirect

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