Subgroups — #64890

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	#3947	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	C₄	1	4	yes	complemented
7	#347	—	5	1	no	maximal, Sylow
8	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
9	C₂×Dic₅	—	2	1	no	—
10	C₅×C₈	—	2	1	no	—
11	#168	C₂×C₄	1	2	yes	—
12	M₃₂	—	5	2	no	—
13	#97	—	5	1	no	—
14	C₂²×C₅	M₁₆	1	1	yes	characteristic
15	C₄×C₅	C₄²	1	1	yes	characteristic
16	C₄×C₅	M₁₆	1	1	yes	characteristic
17	Dic₅	—	4	1	no	—
18	C₂×C₈	—	5	1	no	—
19	C₂×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
20	C₄²	—	5	1	no	—
21	C₁₆	—	5	4	no	—
22	C₂×C₅	—	2	1	no	—
23	C₂×C₅	#97	1	1	yes	characteristic
24	C₂×C₄	—	10	1	no	—
25	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
26	C₈	—	2	1	no	—
27	C₈	—	5	2	no	—
28	C₅	#347	1	1	yes	characteristic, complemented, Sylow
29	C₂²	#700	1	1	yes	characteristic
30	C₄	—	20	1	no	—
31	C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
32	C₄	#704	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#4002	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. #674	C₄	semidirect
28. C₅	#347	semidirect

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