Subgroups — #64855

Order 320.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4015	C₂	1	1	yes	maximal, characteristic
2	#4005	C₂	1	2	yes	maximal
3	C₂×Dic₁₀	C₄	1	1	yes	characteristic
4	C₂×Dic₁₀	C₂²	1	1	yes	characteristic
5	#704	—	2	2	no	—
6	C₄²×C₅	C₄	1	1	yes	characteristic
7	C₄⋊Dic₅	—	2	2	no	—
8	#356	—	5	1	no	maximal, Sylow
9	C₂×C₄×C₅	—	2	1	no	—
10	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₅	—	2	1	no	—
12	C₂×Dic₅	D₄	1	2	yes	—
13	Dic₁₀	—	4	1	no	—
14	Dic₁₀	—	4	1	no	—
15	#170	—	4	2	no	—
16	C₄⋊Q₈	—	5	1	no	—
17	#101	—	5	2	no	—
18	C₂²×C₅	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₅	—	2	2	no	—
20	C₄×C₅	—	2	1	no	—
21	Dic₅	—	2	2	no	—
22	Dic₅	—	4	1	no	—
23	C₂×Q₈	—	5	1	no	—
24	C₂×Q₈	—	5	1	no	—
25	M₁₆	—	10	2	no	—
26	C₄⋊C₄	—	10	2	no	—
27	C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₂×C₅	—	2	1	no	—
29	C₂×C₅	#99	1	1	yes	characteristic
30	Q₈	—	20	1	no	—
31	Q₈	—	20	1	no	—
32	C₂×C₄	—	2	1	no	—
33	C₂×C₄	—	5	2	no	—
34	C₂×C₄	—	10	1	no	—
35	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
36	C₈	—	20	2	no	—
37	C₅	#356	1	1	yes	characteristic, complemented, Sylow
38	C₂²	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	2	1	no	—
41	C₄	—	10	2	no	—
42	C₄	—	20	1	no	—
43	C₂	—	2	1	no	—
44	C₂	#3999	1	1	yes	characteristic

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

N	H ≅ G/N	type
37. C₅	#356	semidirect

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