Subgroups — #64847

Order 320.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3995	C₂	1	1	yes	maximal, characteristic
2	#3993	C₂	1	1	yes	maximal, characteristic
3	#3930	C₂	1	1	yes	maximal, characteristic
4	C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
5	#700	—	2	1	no	—
6	C₈×D₅	C₂²	1	1	yes	characteristic
7	C₅×C₁₆	C₄	1	1	yes	characteristic, complemented
8	#672	C₄	1	1	yes	characteristic, complemented
9	#365	—	5	1	no	maximal, Sylow
10	C₂×AGL(1,𝔽₅)	—	4	1	no	—
11	C₄×D₅	D₄	1	1	yes	characteristic
12	#170	—	4	1	no	—
13	C₅×C₈	C₂×C₄	1	1	yes	characteristic
14	#168	Q₈	1	1	yes	characteristic
15	M₃₂	—	5	1	no	—
16	#108	—	5	1	no	—
17	#106	—	5	1	no	—
18	C₂×D₅	SD₁₆	1	1	yes	characteristic
19	AGL(1,𝔽₅)	—	8	1	no	—
20	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
21	Dic₅	SD₁₆	1	1	yes	characteristic
22	M₁₆	—	10	1	no	—
23	C₂×C₈	—	5	1	no	—
24	C₄⋊C₄	—	10	1	no	—
25	C₁₆	—	5	1	no	—
26	C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
27	C₂×C₅	#106	1	1	yes	characteristic
28	D₅	—	2	1	no	—
29	C₂×C₄	—	5	1	no	—
30	C₂×C₄	—	20	1	no	—
31	C₈	—	5	1	no	—
32	C₈	—	20	1	no	—
33	C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
34	C₅	#365	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	5	1	no	—
36	C₄	—	5	1	no	—
37	C₄	—	40	1	no	—
38	C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
39	C₂	—	10	1	no	—
40	C₂	#3993	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.