Subgroups — #64849

Order 320.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3994	C₂	1	2	yes	maximal
2	D₅×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
4	C₈×D₅	C₂²	1	1	yes	characteristic
5	C₅×C₁₆	C₄	1	1	yes	characteristic, complemented
6	#672	C₄	1	1	yes	characteristic, complemented
7	#366	—	5	1	no	maximal, Sylow
8	C₂×AGL(1,𝔽₅)	—	4	2	no	—
9	C₄×D₅	D₄	1	1	yes	characteristic
10	C₅×C₈	C₂×C₄	1	1	yes	characteristic
11	#168	Q₈	1	1	yes	characteristic
12	C₂×C₁₆	—	5	1	no	—
13	#107	—	5	2	no	—
14	C₂×D₅	D₈	1	1	yes	characteristic
15	AGL(1,𝔽₅)	—	8	2	no	—
16	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
17	Dic₅	Q₁₆	1	1	yes	characteristic
18	C₂×C₈	—	5	1	no	—
19	C₄⋊C₄	—	10	2	no	—
20	C₁₆	—	5	1	no	—
21	C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
22	C₂×C₅	#107	1	1	yes	characteristic
23	D₅	D₁₆	1	1	yes	characteristic
24	D₅	Q₃₂	1	1	yes	characteristic
25	C₂×C₄	—	5	1	no	—
26	C₂×C₄	—	20	2	no	—
27	C₈	—	5	1	no	—
28	C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
29	C₅	#366	1	1	yes	characteristic, complemented, Sylow
30	C₂²	—	5	1	no	—
31	C₄	—	5	1	no	—
32	C₄	—	40	2	no	—
33	C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
34	C₂	—	5	1	no	—
35	C₂	—	5	1	no	—
36	C₂	#3994	1	1	yes	characteristic

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

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