Subgroups — #64851

Order 320.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3996	C₂	1	2	yes	maximal
2	D₅×C₁₆	C₂	1	1	yes	maximal, characteristic
3	#700	—	2	2	no	—
4	C₈×D₅	C₂²	1	1	yes	characteristic
5	C₅×C₁₆	C₄	1	1	yes	characteristic
6	#672	C₄	1	1	yes	characteristic
7	#368	—	5	1	no	maximal, Sylow
8	C₄×D₅	D₄	1	1	yes	characteristic
9	#170	—	4	2	no	—
10	C₅×C₈	C₂×C₄	1	1	yes	characteristic
11	#168	Q₈	1	1	yes	characteristic
12	C₂×C₁₆	—	5	1	no	—
13	#108	—	5	2	no	—
14	C₂×D₅	Q₁₆	1	1	yes	characteristic
15	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
16	Dic₅	D₈	1	1	yes	characteristic
17	M₁₆	—	10	2	no	—
18	C₂×C₈	—	5	1	no	—
19	C₁₆	—	5	1	no	—
20	C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic
21	C₂×C₅	#107	1	1	yes	characteristic
22	D₅	—	2	1	no	—
23	C₂×C₄	—	5	1	no	—
24	C₈	—	5	1	no	—
25	C₈	—	20	2	no	—
26	C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
27	C₅	#368	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	5	1	no	—
29	C₄	—	5	1	no	—
30	C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
31	C₂	—	10	1	no	—
32	C₂	#3994	1	1	yes	characteristic

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

N	H ≅ G/N	type
27. C₅	#368	semidirect

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