Subgroups — #64707

Order 320.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#106	C₂	1	1	yes	maximal, characteristic
2	#3951	C₂	1	1	yes	maximal, characteristic
3	#3944	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
5	C₅×C₄⋊C₄	—	2	1	no	—
6	#681	—	2	1	no	—
7	#672	C₄	1	2	yes	complemented
8	#365	—	5	1	no	maximal, Sylow
9	C₂×C₄×C₅	—	4	1	no	—
10	C₂×C₄×C₅	D₄	1	1	yes	characteristic
11	C₅×C₈	C₂×C₄	1	1	yes	characteristic
12	C₅×C₈	Q₈	1	1	yes	characteristic
13	#168	—	4	1	no	—
14	M₃₂	—	5	1	no	—
15	#108	—	5	1	no	—
16	#106	D₅	1	1	yes	characteristic
17	C₂²×C₅	SD₁₆	1	1	yes	characteristic
18	C₄×C₅	—	8	1	no	—
19	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
20	C₄×C₅	SD₁₆	1	1	yes	characteristic
21	M₁₆	—	10	1	no	—
22	C₂×C₈	C₂×D₅	1	1	yes	characteristic
23	C₄⋊C₄	—	2	1	no	—
24	C₁₆	—	5	2	no	—
25	C₂×C₅	—	2	1	no	—
26	C₂×C₅	#106	1	1	yes	characteristic
27	C₂×C₄	—	4	1	no	—
28	C₂×C₄	C₂²⋊D₅	1	1	yes	characteristic
29	C₈	—	20	1	no	—
30	C₈	Dic₁₀	1	1	yes	characteristic
31	C₈	C₄×D₅	1	1	yes	characteristic
32	C₅	#365	1	1	yes	characteristic, complemented, Sylow
33	C₂²	#687	1	1	yes	characteristic
34	C₄	—	8	1	no	—
35	C₄	#683	1	1	yes	characteristic
36	C₄	#688	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#3940	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. #672	C₄	semidirect
32. C₅	#365	semidirect

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