Finite Group Databasebeta

← C5×#81791 #14458173

Subgroups — C5×#81791 #14458173

Order 1920.

952 conjugacy classes of subgroups; only the 234 normal subgroups are shown.

normal subgroups only

This group has 952 conjugacy classes of subgroups — too many to draw. Only its 234 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5757C214yesmaximal, complemented
2C3×C5×#493C211yesmaximal, characteristic, complemented
3C5×#5160C214yesmaximal, complemented
4C5×#5077C214yesmaximal, complemented
5C5×#4700C212yesmaximal, complemented
6C5×#3292—31nomaximal, Hall
7C5×#1004C2214yescomplemented
8C2×C3×C5×D8C2214yescomplemented
9C3×C5×#127C2212yescomplemented
10C5×#932C2218yescomplemented
11C5×#912—24no—
12C5×#911—28no—
13C5×D3×D8—24no—
14C5×#904C2212yes—
15C5×#901C2214yescomplemented
16C3×C4×C5×C8C2211yescharacteristic, complemented
17C5×#833C2214yescomplemented
18C5×#819C2212yescomplemented
19C5×#805C2214yescomplemented
20#81791C511yesmaximal, characteristic, direct product factor, Hall
21C5×#576—34no—
22C5×#493D311yescharacteristic, complemented
23C5×#472—34no—
24C5×#453—34no—
25C5×#443—32no—
26C2×C3×C5×D4—42no—
27C2×C3×C5×D4C2314yes—
28C2×C5×#67—44no—
29C5×#237—28no—
30C5×D3×D4—28no—
31C5×#235C2314yes—
32C3×C5×D8—24no—
33C3×C5×D8—24no—
34C2×C3×C5×C8C2312yes—
35C3×C42×C5C2311yescharacteristic
36C5×#214—28no—
37C5×#213—28no—
38C5×#208C2314yes—
39C5×Dic12D412yescomplemented
40C5×D24D412yescomplemented
41C5×#204D414yescomplemented
42C5×ΓL(1,𝔽25)—24no—
43C5×D3×C8—24no—
44#5757C2×C514yescomplemented
45C3×#493C2×C511yescharacteristic, complemented
46#5160C2×C514yescomplemented
47#5077C2×C514yescomplemented
48#4700C2×C512yescomplemented
49C5×H(5,𝔽2)—34no—
50C5×AGL(1,ℤ/8)—38no—
51C5×AGL(1,ℤ/8)—68no—
52C5×#135—32no—
53C5×#135—64no—
54C2×C5×D8—64no—
55C2×C5×D8C2×D314yescomplemented
56C5×#131—34no—
57C5×#127C2×D312yescomplemented
58C5×#108—32no—
59C5×#104—34no—
60C5×#100—34no—
61C4×C5×C8C2×D311yescharacteristic, complemented
62#3292—31noSylow
63C23×C3×C5—24no—
64C22×C5×D3—44no—
65C3×C5×D4—28no—
66C3×C5×D4—84no—
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5C2411yescharacteristic
69C5×#67—24no—
70C5×#67—48no—
71C2×C5×Dic3—44no—
72C5×D12C2×D414yes—
73C4×C5×D3—24no—
74C5×Dic6C2×D414yes—
75C3×C5×C8C2×D412yes—
76C3×C5×C8C2×D412yes—
77C5×C3⋊C8—24no—
78#1004C22×C514yescomplemented
79C2×C3×D8C22×C514yescomplemented
80C3×#127C22×C512yescomplemented
81#932C22×C518yescomplemented
82#912—24no—
83#911—28no—
84D3×D8—24no—
85#904C22×C512yes—
86#901C22×C514yescomplemented
87C3×C4×C8C22×C511yescharacteristic, complemented
88#833C22×C514yescomplemented
89#819C22×C512yescomplemented
90#805C22×C514yescomplemented
91C5×#41—34no—
92C5×#41—68no—
93C2×C5×D4—42no—
94C2×C5×D4—68no—
95C2×C5×D4—124no—
96C2×C5×D4C22×D314yes—
97C5×Q16—32no—
98C5×SD16—34no—
99C5×SD16—68no—
100C5×D8—24no—
101C5×D8—24no—
102C5×D8—32no—
103C5×D8—68no—
104C5×M16—34no—
105C5×M16—64no—
106C2×C5×C8—64no—
107C2×C5×C8C22×D312yes—
108C42×C5C22×D311yescharacteristic
109#576—34no—
110#493C5×D311yescharacteristic, complemented
111#472—34no—
112#453—34no—
113#443—32no—
114C22×C3×C5—44no—
115C22×C3×C5—84no—
116C22×C3×C5H(5,𝔽2)11yescharacteristic
117C2×C5×D3—24no—
118C2×C5×D3—164no—
119C3×C4×C5—22no—
120C3×C4×C5C22×D412yes—
121C5×Dic3—24no—
122C2×C3×D4—42no—
123C2×C3×D4C23×C514yes—
124C2×#67—44no—
125#237—28no—
126D3×D4—28no—
127#235C23×C514yes—
128C3×D8—24no—
129C3×D8—24no—
130C2×C3×C8C23×C512yes—
131C3×C42C23×C511yescharacteristic
132#214—28no—
133#213—28no—
134#208C23×C514yes—
135Dic12C5×D412yescomplemented
136D24C5×D412yescomplemented
137#204C5×D414yescomplemented
138ΓL(1,𝔽25)—24no—
139D3×C8—24no—
140C23×C5—24no—
141C23×C5—124no—
142C5×Q8—34no—
143C5×D4—28no—
144C5×D4—34no—
145C5×D4—64no—
146C5×D4—84no—
147C5×D4—128no—
148C2×C4×C5—21no—
149C2×C4×C5—64no—
150C2×C4×C5—124no—
151C2×C4×C5C23×D311yescharacteristic
152C5×C8—64no—
153C5×C8D3×D412yes—
154C5×C8D3×D412yes—
155H(5,𝔽2)—34no—
156AGL(1,ℤ/8)—38no—
157AGL(1,ℤ/8)—68no—
158#135—32no—
159#135—64no—
160C2×D8—64no—
161C2×D8C2×C5×D314yescomplemented
162#131—34no—
163#127C2×C5×D312yescomplemented
164#108—32no—
165#104—34no—
166#100—34no—
167C4×C8C2×C5×D311yescharacteristic, complemented
168C2×C3×C5—21no—
169C2×C3×C5—84no—
170C2×C3×C5D4211yescharacteristic
171C5×D3—44no—
172C23×C3—24no—
173C22×D3—44no—
174C3×D4—28no—
175C3×D4—84no—
176C2×C3×C4—21no—
177C2×C3×C4C24×C511yescharacteristic
178#67—24no—
179#67—48no—
180C2×Dic3—44no—
181D12C2×C5×D414yes—
182C4×D3—24no—
183Dic6C2×C5×D414yes—
184C3×C8C2×C5×D412yes—
185C3×C8C2×C5×D412yes—
186C3⋊C8—24no—
187C22×C5—44no—
188C22×C5—64no—
189C22×C5—84no—
190C22×C5—484no—
191C22×C5#100411yescharacteristic
192C4×C5—22no—
193C4×C5—64no—
194C4×C5C2×D3×D412yes—
195#41—34no—
196#41—68no—
197C2×D4—42no—
198C2×D4—68no—
199C2×D4—124no—
200C2×D4C22×C5×D314yes—
201Q16—32no—
202SD16—34no—
203SD16—68no—
204D8—24no—
205D8—24no—
206D8—32no—
207D8—68no—
208M16—34no—
209M16—64no—
210C2×C8—64no—
211C2×C8C22×C5×D312yes—
212C42C22×C5×D311yescharacteristic
213C3×C5#329211yescharacteristic, complemented, Hall
214C22×C3—44no—
215C22×C3—84no—
216C22×C3C5×H(5,𝔽2)11yescharacteristic
217C2×D3—24no—
218C2×D3—164no—
219C3×C4—22no—
220C3×C4C22×C5×D412yes—
221Dic3—24no—
222C2×C5—21no—
223C2×C5—84no—
224C2×C5—124no—
225C2×C5#571711yescharacteristic
226C23—24no—
227C23—124no—
228Q8—34no—
229D4—28no—
230D4—34no—
231D4—64no—
232D4—84no—
233D4—128no—
234C2×C4—21no—
235C2×C4—64no—
236C2×C4—124no—
237C2×C4C23×C5×D311yescharacteristic
238C8—64no—
239C8C5×D3×D412yes—
240C8C5×D3×D412yes—
241C2×C3—21no—
242C2×C3—84no—
243C2×C3C5×D4211yescharacteristic
244D3—44no—
245C5#8179111yescharacteristic, direct product factor, Sylow
246C22—44no—
247C22—64no—
248C22—84no—
249C22—484no—
250C22C5×#100411yescharacteristic
251C4—22no—
252C4—64no—
253C4C2×C5×D3×D412yes—
254C3C5×#329211yescharacteristic, complemented, Sylow
255C2—21no—
256C2—84no—
257C2—124no—
258C2C5×#571711yescharacteristic
subgroupG/H
centerC2×C5#5717
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#493C2
socleC2×C3×C5D42
hypercenterC5×#493D3
hypocenterC3C5×#3292
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#493

Complements

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

NH ≅ G/Ntype
1. C5×#5757C2semidirect
2. C3×C5×#493C2semidirect
3. C5×#5160C2semidirect
4. C5×#5077C2semidirect
5. C5×#4700C2semidirect
7. C5×#1004C22semidirect
8. C2×C3×C5×D8C22semidirect
9. C3×C5×#127C22semidirect
10. C5×#932C22semidirect
15. C5×#901C22semidirect
16. C3×C4×C5×C8C22semidirect
17. C5×#833C22semidirect
18. C5×#819C22semidirect
19. C5×#805C22semidirect
20. #81791C5direct (N × H)
22. C5×#493D3semidirect
39. C5×Dic12D4semidirect
40. C5×D24D4semidirect
41. C5×#204D4semidirect
44. #5757C2×C5semidirect
45. C3×#493C2×C5semidirect
46. #5160C2×C5semidirect
47. #5077C2×C5semidirect
48. #4700C2×C5semidirect
55. C2×C5×D8C2×D3semidirect
57. C5×#127C2×D3semidirect
61. C4×C5×C8C2×D3semidirect
78. #1004C22×C5semidirect
79. C2×C3×D8C22×C5semidirect
80. C3×#127C22×C5semidirect
81. #932C22×C5semidirect
86. #901C22×C5semidirect
87. C3×C4×C8C22×C5semidirect
88. #833C22×C5semidirect
89. #819C22×C5semidirect
90. #805C22×C5semidirect
110. #493C5×D3semidirect
135. Dic12C5×D4semidirect
136. D24C5×D4semidirect
137. #204C5×D4semidirect
161. C2×D8C2×C5×D3semidirect
163. #127C2×C5×D3semidirect
167. C4×C8C2×C5×D3semidirect
213. C3×C5#3292semidirect
245. C5#81791direct (N × H)
254. C3C5×#3292semidirect

Maximal subgroups

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

subgroupindex
C5×#57572
C3×C5×#4932
C5×#51602
C5×#50772
C5×#47002
C5×#32923
#817915