Subgroups — C₅×#87718 #14522176

Order 2000.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×Dic₂₅	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₅×C₂₅	C₂²	1	1	yes	characteristic
5	C₄×C₅×C₂₅	—	2	1	no	—
6	C₅×Dic₂₅	—	2	1	no	—
7	C₅×Dic₂₅	C₄	1	2	yes	complemented
8	C₅×#683	—	5	1	no	maximal
9	#87718	C₅	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₅×C₂₅	C₂×C₄	1	1	yes	characteristic
11	C₂×C₅×C₂₅	D₄	1	1	yes	characteristic
12	C₂×C₅×C₂₅	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₅²	D₅	1	1	yes	characteristic
14	C₂×C₅×Dic₅	—	5	1	no	—
15	C₂×C₅×Dic₅	—	5	1	no	—
16	C₂×C₄×C₂₅	—	2	2	no	—
17	C₂×C₄×C₂₅	C₂×C₅	1	1	yes	characteristic
18	C₂×Dic₂₅	C₂×C₅	1	1	yes	characteristic
19	C₂×Dic₂₅	C₂×C₅	1	1	yes	characteristic
20	C₅×C₂₅	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₅²	C₂×D₅	1	1	yes	characteristic
22	C₄×C₅²	—	2	1	no	—
23	C₅×Dic₅	—	5	2	no	—
24	C₅×Dic₅	—	10	1	no	—
25	C₂²×C₂₅	—	2	2	no	—
26	C₂²×C₂₅	C₂²×C₅	1	1	yes	characteristic
27	C₄×C₂₅	—	2	4	no	—
28	C₄×C₂₅	—	2	1	no	—
29	Dic₂₅	—	2	1	no	—
30	Dic₂₅	C₄×C₅	1	2	yes	complemented
31	C₅×C₄⋊C₄	—	25	1	no	—
32	#683	—	5	1	no	—
33	C₂×C₅²	Dic₁₀	1	1	yes	characteristic
34	C₂×C₅²	C₄×D₅	1	1	yes	characteristic
35	C₂×C₅²	C₂²⋊D₅	1	1	yes	characteristic
36	C₂×C₂₅	—	2	2	no	—
37	C₂×C₂₅	—	2	2	no	—
38	C₂×C₂₅	—	2	2	no	—
39	C₂×C₂₅	C₂×C₄×C₅	1	1	yes	characteristic
40	C₂×C₂₅	C₅×D₄	1	1	yes	characteristic
41	C₂×C₂₅	C₅×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₅	—	2	2	no	—
43	C₂×C₄×C₅	—	25	1	no	—
44	C₂×C₄×C₅	—	25	1	no	—
45	C₂×C₄×C₅	D₂₅	1	1	yes	characteristic
46	C₂×C₄×C₅	C₅×D₅	1	1	yes	characteristic
47	C₂×Dic₅	—	5	1	no	—
48	C₂×Dic₅	—	5	1	no	—
49	C₅²	#683	1	1	yes	characteristic
50	C₂₅	—	2	2	no	—
51	C₂₅	C₅×C₄⋊C₄	1	1	yes	characteristic, complemented
52	C₂²×C₅	—	2	2	no	—
53	C₂²×C₅	C₂×D₂₅	1	1	yes	characteristic
54	C₂²×C₅	C₂×C₅×D₅	1	1	yes	characteristic
55	C₄×C₅	—	2	4	no	—
56	C₄×C₅	—	2	1	no	—
57	C₄×C₅	—	2	1	no	—
58	C₄×C₅	—	25	2	no	—
59	C₄×C₅	—	50	1	no	—
60	Dic₅	—	5	2	no	—
61	Dic₅	—	10	1	no	—
62	C₄⋊C₄	—	25	1	no	Sylow
63	C₂×C₅	—	2	2	no	—
64	C₂×C₅	—	2	2	no	—
65	C₂×C₅	—	2	2	no	—
66	C₂×C₅	Dic₅₀	1	1	yes	characteristic
67	C₂×C₅	C₄×D₂₅	1	1	yes	characteristic
68	C₂×C₅	C₂²⋊D₂₅	1	1	yes	characteristic
69	C₂×C₅	C₅×Dic₁₀	1	1	yes	characteristic
70	C₂×C₅	C₄×C₅×D₅	1	1	yes	characteristic
71	C₂×C₅	C₅×C₂²⋊D₅	1	1	yes	characteristic
72	C₂×C₄	—	25	1	no	—
73	C₂×C₄	—	25	1	no	—
74	C₂×C₄	C₅×D₂₅	1	1	yes	characteristic
75	C₅	—	2	2	no	—
76	C₅	#87718	1	1	yes	characteristic, direct product factor
77	C₅	C₅×#683	1	1	yes	characteristic
78	C₂²	C₂×C₅×D₂₅	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	—	25	2	no	—
81	C₄	—	50	1	no	—
82	C₂	C₅×Dic₅₀	1	1	yes	characteristic
83	C₂	C₄×C₅×D₂₅	1	1	yes	characteristic
84	C₂	C₅×C₂²⋊D₂₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
7. C₅×Dic₂₅	C₄	semidirect
9. #87718	C₅	direct (N × H)
20. C₅×C₂₅	C₄⋊C₄	semidirect
30. Dic₂₅	C₄×C₅	semidirect
51. C₂₅	C₅×C₄⋊C₄	semidirect
76. C₅	#87718	direct (N × H)

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
C₂×C₅×Dic₂₅	2
C₅×#683	5
#87718	5

Subgroups — C5×#87718 #14522176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#87718 #14522176