Subgroups — D₅×#401 #10610160

Order 640.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#401	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×#95	C₂	1	7	yes	maximal
3	C₅⋊#401	C₂	1	7	yes	maximal, complemented
4	C₂²×C₄×D₅	C₂²	1	7	yes	—
5	C₅×#95	C₂²	1	7	yes	—
6	#3963	C₂²	1	21	yes	—
7	C₂×#401	—	5	1	no	maximal, Sylow
8	C₂³×D₅	C₂³	1	1	yes	characteristic
9	C₂²×C₄×C₅	C₂³	1	7	yes	—
10	C₂²×Dic₅	C₂³	1	7	yes	—
11	C₂×C₄×D₅	—	2	42	no	—
12	#401	—	5	7	no	—
13	#401	D₅	1	1	yes	characteristic, direct product factor
14	C₂×#95	—	5	7	no	—
15	C₂³×C₅	C₂⁴	1	1	yes	characteristic
16	C₂²×D₅	#41	1	14	yes	—
17	C₂×C₄×C₅	—	2	21	no	—
18	C₂×Dic₅	—	2	21	no	—
19	C₄×D₅	—	4	28	no	—
20	C₂³×C₄	—	5	7	no	—
21	#95	—	5	21	no	—
22	#95	C₂×D₅	1	7	yes	—
23	C₂²×C₅	C₂×#41	1	7	yes	—
24	C₂×D₅	#126	1	28	yes	—
25	C₄×C₅	—	4	7	no	—
26	Dic₅	—	4	7	no	—
27	C₂⁴	—	5	1	no	—
28	C₂²×C₄	—	5	7	no	—
29	C₂²×C₄	—	10	42	no	—
30	C₂²×C₄	C₂²×D₅	1	7	yes	—
31	C₂×C₅	C₂×#126	1	7	yes	—
32	D₅	#401	1	8	yes	direct product factor
33	C₂³	—	5	14	no	—
34	C₂³	C₂³×D₅	1	1	yes	characteristic
35	C₂×C₄	—	2	21	no	—
36	C₂×C₄	—	10	21	no	—
37	C₂×C₄	—	20	28	no	—
38	C₅	C₂×#401	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	5	28	no	—
40	C₂²	D₅×#41	1	7	yes	—
41	C₄	—	4	7	no	—
42	C₄	—	20	7	no	—
43	C₂	—	5	8	no	—
44	C₂	D₅×#126	1	7	yes	—

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.