Subgroups — C₅×#1711 #10603219

Order 640.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#487	C₂	1	3	yes	maximal, complemented
2	C₅×#486	C₂	1	3	yes	maximal
3	C₅×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₄⋊Q₈	C₂²	1	3	yes	—
5	C₅×#127	C₂²	1	1	yes	characteristic
6	C₅×#103	—	2	6	no	—
7	C₅×#102	—	2	6	no	—
8	C₄×C₅×C₈	C₂²	1	3	yes	—
9	#1711	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₅×Q₈	—	2	3	no	—
11	C₂×C₅×D₄	—	2	3	no	—
12	C₂×C₅×C₈	D₄	1	6	yes	—
13	C₅×C₄⋊C₄	—	2	3	no	—
14	C₅×C₄⋊C₄	—	2	3	no	—
15	C₄²×C₅	C₂³	1	1	yes	characteristic
16	#487	C₂×C₅	1	3	yes	complemented
17	#486	C₂×C₅	1	3	yes	—
18	C₈²	C₂×C₅	1	1	yes	characteristic, complemented
19	C₂³×C₅	—	4	1	no	—
20	C₅×Q₈	—	4	6	no	—
21	C₅×D₄	—	4	6	no	—
22	C₂×C₄×C₅	—	4	3	no	—
23	C₂×C₄×C₅	C₂×D₄	1	3	yes	—
24	C₅×C₈	—	2	6	no	—
25	C₄⋊Q₈	C₂²×C₅	1	3	yes	—
26	#127	C₂²×C₅	1	1	yes	characteristic
27	#103	—	2	6	no	—
28	#102	—	2	6	no	—
29	C₄×C₈	C₂²×C₅	1	3	yes	—
30	C₂²×C₅	—	8	3	no	—
31	C₂²×C₅	#127	1	1	yes	characteristic
32	C₄×C₅	—	8	3	no	—
33	C₄×C₅	#135	1	6	yes	—
34	C₂×Q₈	—	2	3	no	—
35	C₂×D₄	—	2	3	no	—
36	C₂×C₈	C₅×D₄	1	6	yes	—
37	C₄⋊C₄	—	2	3	no	—
38	C₄⋊C₄	—	2	3	no	—
39	C₄²	C₂³×C₅	1	1	yes	characteristic
40	C₂×C₅	—	16	1	no	—
41	C₂×C₅	#495	1	3	yes	—
42	C₂³	—	4	1	no	—
43	Q₈	—	4	6	no	—
44	D₄	—	4	6	no	—
45	C₂×C₄	—	4	3	no	—
46	C₂×C₄	C₂×C₅×D₄	1	3	yes	—
47	C₈	—	2	6	no	—
48	C₅	#1711	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²	—	8	3	no	—
50	C₂²	C₅×#127	1	1	yes	characteristic
51	C₄	—	8	3	no	—
52	C₄	C₅×#135	1	6	yes	—
53	C₂	—	16	1	no	—
54	C₂	C₅×#495	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₅
prime radical	C₅×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#487	C₂	semidirect
3. C₅×C₈²	C₂	semidirect
9. #1711	C₅	direct (N × H)
16. #487	C₂×C₅	semidirect
18. C₈²	C₂×C₅	semidirect
48. C₅	#1711	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#487	2
C₅×#486	2
C₅×C₈²	2
#1711	5

Subgroups — C5×#1711 #10603219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#1711 #10603219