Subgroups — C₅×C₄⋊C₄×C₂₅ #14522253

Order 2000.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₂₅	C₂	1	2	yes	maximal
2	C₂×C₄×C₅×C₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×C₂₅	C₂²	1	1	yes	characteristic
4	C₄×C₅×C₂₅	—	2	2	no	—
5	C₄×C₅×C₂₅	C₄	1	2	yes	complemented
6	C₅²×C₄⋊C₄	C₅	1	1	yes	maximal, characteristic
7	C₄⋊C₄×C₂₅	C₅	1	5	yes	maximal, direct product factor
8	C₂×C₅×C₂₅	C₂×C₄	1	1	yes	characteristic
9	C₂×C₅×C₂₅	D₄	1	1	yes	characteristic
10	C₂×C₅×C₂₅	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₅²	C₂×C₅	1	2	yes	—
12	C₂×C₄×C₅²	C₂×C₅	1	1	yes	characteristic
13	C₂×C₄×C₂₅	C₂×C₅	1	10	yes	—
14	C₂×C₄×C₂₅	C₂×C₅	1	5	yes	—
15	C₅×C₂₅	C₄⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
16	C₂²×C₅²	C₂²×C₅	1	1	yes	characteristic
17	C₄×C₅²	—	2	2	no	—
18	C₄×C₅²	C₄×C₅	1	2	yes	—
19	C₂²×C₂₅	C₂²×C₅	1	5	yes	—
20	C₄×C₂₅	—	2	10	no	—
21	C₄×C₂₅	C₄×C₅	1	10	yes	complemented
22	C₅×C₄⋊C₄	C₂₅	1	5	yes	direct product factor
23	C₅×C₄⋊C₄	C₅²	1	1	yes	characteristic
24	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
25	C₂×C₅²	C₅×D₄	1	1	yes	characteristic
26	C₂×C₅²	C₅×Q₈	1	1	yes	characteristic
27	C₂×C₂₅	C₂×C₄×C₅	1	5	yes	—
28	C₂×C₂₅	C₅×D₄	1	5	yes	—
29	C₂×C₂₅	C₅×Q₈	1	5	yes	—
30	C₂×C₄×C₅	C₂×C₂₅	1	10	yes	—
31	C₂×C₄×C₅	C₂×C₂₅	1	5	yes	—
32	C₂×C₄×C₅	C₂×C₅²	1	2	yes	—
33	C₂×C₄×C₅	C₂×C₅²	1	1	yes	characteristic
34	C₅²	C₅×C₄⋊C₄	1	1	yes	characteristic
35	C₂₅	C₅×C₄⋊C₄	1	5	yes	direct product factor
36	C₂²×C₅	C₂²×C₂₅	1	5	yes	—
37	C₂²×C₅	C₂²×C₅²	1	1	yes	characteristic
38	C₄×C₅	—	2	10	no	—
39	C₄×C₅	—	2	2	no	—
40	C₄×C₅	C₄×C₂₅	1	10	yes	complemented
41	C₄×C₅	C₄×C₅²	1	2	yes	—
42	C₄⋊C₄	C₅×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₅	C₂×C₄×C₂₅	1	5	yes	—
44	C₂×C₅	D₄×C₂₅	1	5	yes	—
45	C₂×C₅	Q₈×C₂₅	1	5	yes	—
46	C₂×C₅	C₂×C₄×C₅²	1	1	yes	characteristic
47	C₂×C₅	C₅²×D₄	1	1	yes	characteristic
48	C₂×C₅	C₅²×Q₈	1	1	yes	characteristic
49	C₂×C₄	C₂×C₅×C₂₅	1	2	yes	—
50	C₂×C₄	C₂×C₅×C₂₅	1	1	yes	characteristic
51	C₅	C₄⋊C₄×C₂₅	1	5	yes	direct product factor
52	C₅	C₅²×C₄⋊C₄	1	1	yes	characteristic
53	C₂²	C₂²×C₅×C₂₅	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	C₄×C₅×C₂₅	1	2	yes	complemented
56	C₂	C₂×C₄×C₅×C₂₅	1	1	yes	characteristic
57	C₂	C₅×D₄×C₂₅	1	1	yes	characteristic
58	C₂	C₅×Q₈×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅×C₂₅	C₂²
commutator	C₂	C₂×C₄×C₅×C₂₅
Frattini, cosocle	C₂²×C₅	C₂²×C₅²
socle, prime radical	C₂²×C₅²	C₂²×C₅
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₄×C₅×C₂₅	C₄	semidirect
7. C₄⋊C₄×C₂₅	C₅	direct (N × H)
15. C₅×C₂₅	C₄⋊C₄	direct (N × H)
21. C₄×C₂₅	C₄×C₅	semidirect
22. C₅×C₄⋊C₄	C₂₅	direct (N × H)
35. C₂₅	C₅×C₄⋊C₄	direct (N × H)
40. C₄×C₅	C₄×C₂₅	semidirect
42. C₄⋊C₄	C₅×C₂₅	direct (N × H)
51. C₅	C₄⋊C₄×C₂₅	direct (N × H)
55. C₄	C₄×C₅×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×C₂₅	2
C₅²×C₄⋊C₄	5
C₄⋊C₄×C₂₅	5

Subgroups — C5×C4⋊C4×C25 #14522253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₄⋊C₄×C₂₅ #14522253