Subgroups — C₅×C₂²⋊Dic₂₅ #14522211

Order 2000.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₂₅	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅×C₂₅	—	2	2	no	—
4	C₂²×C₅×C₂₅	C₄	1	2	yes	complemented
5	C₂²×C₅×C₂₅	C₂²	1	1	yes	characteristic
6	C₅×Dic₂₅	—	2	2	no	—
7	C₅×C₂²⋊Dic₅	—	5	1	no	maximal
8	C₂²⋊Dic₂₅	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₅×C₂₅	—	2	2	no	—
10	C₂×C₅×C₂₅	C₂×C₄	1	1	yes	characteristic
11	C₂×C₅×C₂₅	D₄	1	2	yes	—
12	C₂³×C₅²	D₅	1	1	yes	characteristic
13	C₂×C₅×Dic₅	—	5	2	no	—
14	C₂³×C₂₅	—	2	2	no	—
15	C₂³×C₂₅	C₂×C₅	1	1	yes	characteristic
16	C₂×Dic₂₅	C₂×C₅	1	2	yes	complemented
17	C₅×C₂₅	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₅²	—	2	2	no	—
19	C₂²×C₅²	Dic₅	1	2	yes	—
20	C₂²×C₅²	C₂×D₅	1	1	yes	characteristic
21	C₅×Dic₅	—	10	2	no	—
22	C₂²×C₂₅	—	2	8	no	—
23	C₂²×C₂₅	—	2	2	no	—
24	C₂²×C₂₅	—	2	4	no	—
25	C₂²×C₂₅	—	2	2	no	—
26	C₂²×C₂₅	C₄×C₅	1	2	yes	complemented
27	C₂²×C₂₅	C₂²×C₅	1	1	yes	characteristic
28	Dic₂₅	—	2	2	no	—
29	C₅×C₂²⋊C₄	—	25	1	no	—
30	C₂²⋊Dic₅	—	5	1	no	—
31	C₂×C₅²	—	2	2	no	—
32	C₂×C₅²	C₂×Dic₅	1	1	yes	characteristic
33	C₂×C₅²	C₂²⋊D₅	1	2	yes	—
34	C₂×C₂₅	—	2	8	no	—
35	C₂×C₂₅	—	2	2	no	—
36	C₂×C₂₅	—	2	2	no	—
37	C₂×C₂₅	—	2	4	no	—
38	C₂×C₂₅	C₂×C₄×C₅	1	1	yes	characteristic
39	C₂×C₂₅	C₅×D₄	1	2	yes	—
40	C₂³×C₅	—	2	2	no	—
41	C₂³×C₅	D₂₅	1	1	yes	characteristic
42	C₂³×C₅	C₅×D₅	1	1	yes	characteristic
43	C₂×C₄×C₅	—	25	2	no	—
44	C₂×Dic₅	—	5	2	no	—
45	C₅²	C₂²⋊Dic₅	1	1	yes	characteristic
46	C₂₅	—	2	2	no	—
47	C₂₅	C₅×C₂²⋊C₄	1	1	yes	characteristic, complemented
48	C₂²×C₅	—	2	8	no	—
49	C₂²×C₅	—	2	2	no	—
50	C₂²×C₅	—	2	2	no	—
51	C₂²×C₅	—	2	4	no	—
52	C₂²×C₅	—	2	2	no	—
53	C₂²×C₅	Dic₂₅	1	2	yes	complemented
54	C₂²×C₅	C₂×D₂₅	1	1	yes	characteristic
55	C₂²×C₅	C₅×Dic₅	1	2	yes	—
56	C₂²×C₅	C₂×C₅×D₅	1	1	yes	characteristic
57	C₄×C₅	—	50	2	no	—
58	Dic₅	—	10	2	no	—
59	C₂²⋊C₄	—	25	1	no	Sylow
60	C₂×C₅	—	2	8	no	—
61	C₂×C₅	—	2	2	no	—
62	C₂×C₅	—	2	2	no	—
63	C₂×C₅	—	2	2	no	—
64	C₂×C₅	—	2	4	no	—
65	C₂×C₅	C₂×Dic₂₅	1	1	yes	characteristic
66	C₂×C₅	C₂²⋊D₂₅	1	2	yes	—
67	C₂×C₅	C₂×C₅×Dic₅	1	1	yes	characteristic
68	C₂×C₅	C₅×C₂²⋊D₅	1	2	yes	—
69	C₂³	C₅×D₂₅	1	1	yes	characteristic
70	C₂×C₄	—	25	2	no	—
71	C₅	—	2	2	no	—
72	C₅	C₂²⋊Dic₂₅	1	1	yes	characteristic, direct product factor
73	C₅	C₅×C₂²⋊Dic₅	1	1	yes	characteristic
74	C₂²	—	2	2	no	—
75	C₂²	C₅×Dic₂₅	1	2	yes	complemented
76	C₂²	C₂×C₅×D₂₅	1	1	yes	characteristic
77	C₄	—	50	2	no	—
78	C₂	—	2	2	no	—
79	C₂	C₂×C₅×Dic₂₅	1	1	yes	characteristic
80	C₂	C₅×C₂²⋊D₂₅	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₂₅
commutator	C₂×C₂₅	C₂×C₄×C₅
Frattini	C₂²×C₅	C₂×C₅×D₅
Fitting	C₂³×C₅×C₂₅	C₂
socle	C₂²×C₅²	C₂×D₅
prime radical	C₂³×C₅²	D₅
cosocle	C₂²×C₂₅	C₂²×C₅
hypercenter	C₂³×C₅	D₂₅
hypocenter	C₂₅	C₅×C₂²⋊C₄
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₅

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Dic₂₅	C₂	semidirect
4. C₂²×C₅×C₂₅	C₄	semidirect
8. C₂²⋊Dic₂₅	C₅	direct (N × H)
16. C₂×Dic₂₅	C₂×C₅	semidirect
17. C₅×C₂₅	C₂²⋊C₄	semidirect
26. C₂²×C₂₅	C₄×C₅	semidirect
47. C₂₅	C₅×C₂²⋊C₄	semidirect
53. C₂²×C₅	Dic₂₅	semidirect
72. C₅	C₂²⋊Dic₂₅	direct (N × H)
75. C₂²	C₅×Dic₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅×C₂₅	2
C₂×C₅×Dic₂₅	2
C₅×C₂²⋊Dic₅	5
C₂²⋊Dic₂₅	5

Subgroups — C5×C22⋊Dic25 #14522211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂²⋊Dic₂₅ #14522211