Subgroups — C₅×#2866 #10616461

Order 640.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#388	C₂	1	7	yes	maximal
2	C₅×#387	C₂	1	7	yes	maximal, complemented
3	C₄³×C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₄⋊C₄	C₂²	1	7	yes	—
5	C₂×C₅×C₂²⋊C₄	C₂²	1	7	yes	—
6	C₂×C₄²×C₅	C₂²	1	7	yes	—
7	C₅×#95	C₂²	1	14	yes	—
8	#2866	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂⁴×C₅	C₂³	1	1	yes	characteristic
10	C₂²×C₄×C₅	C₂³	1	7	yes	—
11	C₂²×C₄×C₅	C₂³	1	7	yes	—
12	C₅×C₄⋊C₄	—	2	14	no	—
13	C₅×C₂²⋊C₄	—	2	14	no	—
14	C₄²×C₅	—	2	14	no	—
15	#388	C₂×C₅	1	7	yes	—
16	#387	C₂×C₅	1	7	yes	complemented
17	C₄³	C₂×C₅	1	1	yes	characteristic, complemented
18	C₂³×C₅	—	2	7	no	—
19	C₂³×C₅	C₂⁴	1	1	yes	characteristic
20	C₂×C₄×C₅	—	2	14	no	—
21	C₂×C₄×C₅	—	2	7	no	—
22	C₂×C₄×C₅	—	2	14	no	—
23	C₂×C₄×C₅	#41	1	14	yes	—
24	C₂×C₄⋊C₄	C₂²×C₅	1	7	yes	—
25	C₂×C₂²⋊C₄	C₂²×C₅	1	7	yes	—
26	C₂×C₄²	C₂²×C₅	1	7	yes	—
27	#95	C₂²×C₅	1	14	yes	—
28	C₂²×C₅	—	4	7	no	—
29	C₂²×C₅	C₂×#41	1	7	yes	—
30	C₄×C₅	—	2	14	no	—
31	C₄×C₅	—	4	7	no	—
32	C₂⁴	C₂³×C₅	1	1	yes	characteristic
33	C₂²×C₄	C₂³×C₅	1	7	yes	—
34	C₂²×C₄	C₂³×C₅	1	7	yes	—
35	C₄⋊C₄	—	2	14	no	—
36	C₂²⋊C₄	—	2	14	no	—
37	C₄²	—	2	14	no	—
38	C₂×C₅	—	8	1	no	—
39	C₂×C₅	#529	1	7	yes	—
40	C₂³	—	2	7	no	—
41	C₂³	C₂⁴×C₅	1	1	yes	characteristic
42	C₂×C₄	—	2	14	no	—
43	C₂×C₄	—	2	7	no	—
44	C₂×C₄	—	2	14	no	—
45	C₂×C₄	C₅×#41	1	14	yes	—
46	C₅	#2866	1	1	yes	characteristic, direct product factor, Sylow
47	C₂²	—	4	7	no	—
48	C₂²	C₂×C₅×#41	1	7	yes	—
49	C₄	—	2	14	no	—
50	C₄	—	4	7	no	—
51	C₂	—	8	1	no	—
52	C₂	C₅×#529	1	7	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#387	C₂	semidirect
3. C₄³×C₅	C₂	semidirect
8. #2866	C₅	direct (N × H)
16. #387	C₂×C₅	semidirect
17. C₄³	C₂×C₅	semidirect
46. C₅	#2866	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×#388	2
C₅×#387	2
C₄³×C₅	2
#2866	5

Subgroups — C5×#2866 #10616461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#2866 #10616461