Subgroups — C₂³×Dic₅₀ #13099682

Order 1600.

1275 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₂₅	C₂	1	2	yes	maximal
3	C₂²×Dic₅₀	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₂₅	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₂₅	C₂²	1	14	yes	—
6	C₂²×Dic₂₅	C₂²	1	28	yes	—
7	C₂×Dic₅₀	C₂²	1	112	yes	direct product factor
8	C₂³×Dic₁₀	—	5	1	no	maximal
9	C₂³×C₂₅	Q₈	1	8	yes	complemented
10	C₂³×C₂₅	C₂³	1	7	yes	—
11	C₂×C₄×C₂₅	C₂³	1	28	yes	—
12	C₂×Dic₂₅	C₂³	1	56	yes	—
13	Dic₅₀	C₂³	1	64	yes	direct product factor
14	C₂³×C₄×C₅	D₅	1	1	yes	characteristic
15	C₂³×Dic₅	—	5	2	no	—
16	C₂²×Dic₁₀	—	5	28	no	—
17	C₂²×C₂₅	C₂×Q₈	1	28	yes	complemented
18	C₂²×C₂₅	C₂⁴	1	7	yes	—
19	C₄×C₂₅	C₂⁴	1	8	yes	—
20	Dic₂₅	C₂⁴	1	16	yes	—
21	C₂⁴×C₅	C₂×D₅	1	1	yes	characteristic
22	C₂²×C₄×C₅	C₂×D₅	1	14	yes	—
23	C₂²×Dic₅	—	5	28	no	—
24	C₂×Dic₁₀	—	5	112	no	—
25	C₂³×Q₈	—	25	1	no	Sylow
26	C₂×C₂₅	C₂²×Q₈	1	14	yes	complemented
27	C₂×C₂₅	C₂⁵	1	1	yes	characteristic
28	C₂³×C₅	Dic₁₀	1	8	yes	—
29	C₂³×C₅	C₂²×D₅	1	7	yes	—
30	C₂×C₄×C₅	C₂²×D₅	1	28	yes	—
31	C₂×Dic₅	—	5	56	no	—
32	Dic₁₀	—	5	64	no	—
33	C₂²×Q₈	—	25	28	no	—
34	C₂³×C₄	—	25	2	no	—
35	C₂³×C₄	D₂₅	1	1	yes	characteristic
36	C₂₅	C₂³×Q₈	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₅	C₂×Dic₁₀	1	28	yes	—
38	C₂²×C₅	C₂³×D₅	1	7	yes	—
39	C₄×C₅	C₂³×D₅	1	8	yes	—
40	Dic₅	—	5	16	no	—
41	C₂⁴	C₂×D₂₅	1	1	yes	characteristic
42	C₂×Q₈	—	25	112	no	—
43	C₂²×C₄	—	25	28	no	—
44	C₂²×C₄	C₂×D₂₅	1	14	yes	—
45	C₂×C₅	C₂²×Dic₁₀	1	14	yes	—
46	C₂×C₅	C₂⁴×D₅	1	1	yes	characteristic
47	C₂³	Dic₅₀	1	8	yes	direct product factor
48	C₂³	C₂²×D₂₅	1	7	yes	—
49	Q₈	—	25	64	no	—
50	C₂×C₄	—	25	56	no	—
51	C₂×C₄	C₂²×D₂₅	1	28	yes	—
52	C₅	C₂³×Dic₁₀	1	1	yes	characteristic
53	C₂²	C₂×Dic₅₀	1	28	yes	direct product factor
54	C₂²	C₂³×D₂₅	1	7	yes	—
55	C₄	—	25	16	no	—
56	C₄	C₂³×D₂₅	1	8	yes	—
57	C₂	C₂²×Dic₅₀	1	14	yes	direct product factor
58	C₂	C₂⁴×D₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₂₅
commutator, cosocle	C₂×C₂₅	C₂⁵
Frattini	C₂×C₅	C₂⁴×D₅
Fitting	C₂³×C₄×C₂₅	C₂
socle, prime radical	C₂⁴×C₅	C₂×D₅
hypercenter	C₂³×C₄	D₂₅
hypocenter	C₂₅	C₂³×Q₈
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. C₂²×Dic₅₀	C₂	direct (N × H)
7. C₂×Dic₅₀	C₂²	direct (N × H)
9. C₂³×C₂₅	Q₈	semidirect
13. Dic₅₀	C₂³	direct (N × H)
17. C₂²×C₂₅	C₂×Q₈	semidirect
26. C₂×C₂₅	C₂²×Q₈	semidirect
36. C₂₅	C₂³×Q₈	semidirect
47. C₂³	Dic₅₀	direct (N × H)
53. C₂²	C₂×Dic₅₀	direct (N × H)
57. C₂	C₂²×Dic₅₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₂₅	2
C₂³×Dic₂₅	2
C₂²×Dic₅₀	2
C₂³×Dic₁₀	5

Subgroups — C23×Dic50 #13099682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×Dic₅₀ #13099682