Finite Group Databasebeta

← #14307349

Subgroups — #14307349

Order 1920.

520 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C3×D5×#125C211yesmaximal, characteristic
2#11752347C211yesmaximal, characteristic
3#11752335C211yesmaximal, characteristic
4#11746745C214yesmaximal
5#10604591—31nomaximal, Hall
6C2×C4⋊ΓL(1,𝔽16)—22no—
7C2×C4⋊ΓL(1,𝔽16)C2212yes—
8C2×D5⋊(C3⋊C8)C2212yes—
9C3×C5×#125C411yescharacteristic, complemented
10C3×D5×C4⋊C4—22no—
11C3×D5×C4⋊C4C2212yes—
12C3×#4036C412yescomplemented
13C3×#4035—22no—
14C3×C42×D5C2211yescharacteristic
15C3×#4016C411yescharacteristic, complemented
16#91231—22no—
17#71741—51nomaximal, Hall
18D5×#125D311yescharacteristic
19#65688—31no—
20#65676—31no—
21#64874—34no—
22C22×ΓL(1,𝔽16)—22no—
23C2×C3×C4×D5—22no—
24C2×C3×C4×D5D412yes—
25C2×C3×C4×D5C2311yescharacteristic
26C2×C3⋊#170—22no—
27C4⋊ΓL(1,𝔽16)—24no—
28C4⋊ΓL(1,𝔽16)—44no—
29D5⋊(C3⋊C8)—22no—
30D5⋊(C3⋊C8)Q814yes—
31C3×C5×C4⋊C4—22no—
32C3×C5×C4⋊C4C2×C412yes—
33C3×C42×C5C2×C411yescharacteristic
34C3×C4⋊Dic5—22no—
35C3×C4⋊Dic5C2×C412yes—
36C3×#683—22no—
37C3×#683—22no—
38C3×#683—22no—
39C3×C4×Dic5C2×C411yescharacteristic
40C3×C4×Dic5D412yes—
41C2×C3×#125—51no—
42#4935—51no—
43C2×#803—51no—
44#4529—54no—
45C2×C4⋊AGL(1,𝔽5)—32no—
46C2×C4⋊AGL(1,𝔽5)—62no—
47C2×D5⋊C8—32no—
48C5×#125Dic311yescharacteristic, complemented
49D5×C4⋊C4—22no—
50D5×C4⋊C4C2×D312yes—
51#4036Dic312yescomplemented
52#4035—22no—
53C42×D5C2×D311yescharacteristic
54#4016Dic311yescharacteristic, complemented
55#4002—62no—
56#1992—151noSylow
57C22×C3×D5C2×D411yescharacteristic
58C2×ΓL(1,𝔽16)—42no—
59C2×ΓL(1,𝔽16)—44no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5C22⋊C412yes—
62C2×C3×C4×C5C22×C411yescharacteristic
63C2×C3×Dic5—22no—
64C2×C3×Dic5C22⋊C412yes—
65C2×C3×Dic5C2×D411yescharacteristic
66C3×C4×D5—22no—
67C3×C4×D5—22no—
68C3×C4×D5—42no—
69C3×C4×D5—42no—
70C3×C4×D5C2×Q812yes—
71C3×C4×D5#4112yes—
72C3⋊#170—24no—
73C3×#125—52no—
74C3×#125—51no—
75C3×#125—102no—
76C3×#125AGL(1,𝔽5)11yescharacteristic, complemented
77C2×C3×C4⋊C4—52no—
78C2×C3×C4⋊C4—102no—
79C2×C3×C42—51no—
80C2×C4⋊Dic3—52no—
81C2×C4⋊Dic3—102no—
82C22×C3⋊C8—52no—
83#803—102no—
84C22×AGL(1,𝔽5)—62no—
85C2×C4×D5—22no—
86C2×C4×D5#6712yes—
87C2×C4×D5C22×D311yescharacteristic
88C2×#170—62no—
89C4⋊AGL(1,𝔽5)—64no—
90C4⋊AGL(1,𝔽5)—124no—
91D5⋊C8—34no—
92D5⋊C8—62no—
93C5×C4⋊C4—22no—
94C5×C4⋊C4C2×Dic312yes—
95C42×C5C2×Dic311yescharacteristic
96C4⋊Dic5—22no—
97C4⋊Dic5C2×Dic312yes—
98#683—22no—
99#683—22no—
100#683—22no—
101C4×Dic5C2×Dic311yescharacteristic
102C4×Dic5#6712yes—
103C2×#125—51no—
104C2×#97—151no—
105#384—151no—
106#340—154no—
107C22×C3×C5C2×C22⋊C411yescharacteristic
108C2×C3×D5#12411yescharacteristic
109C2×C3×D5C4⋊Q811yescharacteristic
110C2×C3×D5AGL(1,ℤ/8)12yes—
111C2×C3×D5#13712yes—
112ΓL(1,𝔽16)—82no—
113C3×C4×C5—22no—
114C3×C4×C5—42no—
115C3×C4×C5C4×Q812yes—
116C3×Dic5—22no—
117C3×Dic5—42no—
118C3×Dic5C22⋊Q812yes—
119C22×C3×C4—51no—
120C22×C3×C4—52no—
121C22×C3×C4—102no—
122C22×Dic3—102no—
123C3×C4⋊C4—22no—
124C3×C4⋊C4—52no—
125C3×C4⋊C4—102no—
126C3×C4⋊C4—102no—
127C3×C4⋊C4—102no—
128C3×C4⋊C4—102no—
129C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
130C3×C42—52no—
131C3×C42—51no—
132C3×C42C2×AGL(1,𝔽5)11yescharacteristic
133C4⋊Dic3—104no—
134C4⋊Dic3—204no—
135C2×C3⋊C8—54no—
136C2×C3⋊C8—102no—
137C2×C3⋊C8—102no—
138C22×D5C2×#6711yescharacteristic
139C2×AGL(1,𝔽5)—122no—
140C2×AGL(1,𝔽5)—124no—
141C2×C4×C5—22no—
142C2×C4×C5#21712yes—
143C2×C4×C5C22×Dic311yescharacteristic
144C2×Dic5—22no—
145C2×Dic5#21712yes—
146C2×Dic5C2×#6711yescharacteristic
147C4×D5—22no—
148C4×D5—22no—
149C4×D5—42no—
150C4×D5—42no—
151C4×D5D3×Q812yes—
152C4×D5#23912yes—
153#170—64no—
154C22×C8—152no—
155#125—52no—
156#125—51no—
157#125—102no—
158#125ΓL(1,𝔽16)11yescharacteristic, complemented
159C2×C4⋊C4—52no—
160C2×C4⋊C4—102no—
161C2×C4⋊C4—152no—
162C2×C4⋊C4—302no—
163C2×C42—51no—
164#97—302no—
165C2×C3×C5#39111yescharacteristic
166C2×C3×C5#41712yes—
167C3×D5#49011yescharacteristic
168C3×D5#49111yescharacteristic
169C3×D5#50112yes—
170C23×C3—51no—
171C2×C3×C4—22no—
172C2×C3×C4—51no—
173C2×C3×C4—52no—
174C2×C3×C4—52no—
175C2×C3×C4—52no—
176C2×C3×C4—102no—
177C2×C3×C4—102no—
178C2×C3×C4—102no—
179C2×C3×C4—202no—
180C2×C3×C4—202no—
181C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
182C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
183C2×Dic3—202no—
184C2×Dic3—204no—
185C3⋊C8—104no—
186C22×C5C2×#21711yescharacteristic
187C2×D5#94411yescharacteristic
188C2×D5#94711yescharacteristic
189C2×D5#94912yes—
190C2×D5#95112yes—
191AGL(1,𝔽5)—242no—
192C4×C5—22no—
193C4×C5—42no—
194C4×C5Q8×Dic312yes—
195Dic5—22no—
196Dic5—42no—
197Dic5#94612yes—
198C22×C4—51no—
199C22×C4—52no—
200C22×C4—102no—
201C22×C4—302no—
202C2×C8—154no—
203C2×C8—302no—
204C2×C8—302no—
205C4⋊C4—22no—
206C4⋊C4—52no—
207C4⋊C4—102no—
208C4⋊C4—102no—
209C4⋊C4—102no—
210C4⋊C4—102no—
211C4⋊C4—304no—
212C4⋊C4—604no—
213C4⋊C4C2×ΓL(1,𝔽16)12yes—
214C42—52no—
215C42—51no—
216C42C2×ΓL(1,𝔽16)11yescharacteristic
217C3×C5#199211yescharacteristic, complemented, Hall
218C22×C3—52no—
219C22×C3—52no—
220C22×C3—51no—
221C22×C3—51no—
222C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
223C3×C4—22no—
224C3×C4—42no—
225C3×C4—52no—
226C3×C4—102no—
227C3×C4—202no—
228C3×C4Q8×AGL(1,𝔽5)12yes—
229Dic3—402no—
230C2×C5#522911yescharacteristic
231C2×C5#523212yes—
232D5#506412yes—
233D5#506711yescharacteristic
234D5#506911yescharacteristic
235C23—51no—
236C2×C4—22no—
237C2×C4—51no—
238C2×C4—52no—
239C2×C4—52no—
240C2×C4—52no—
241C2×C4—102no—
242C2×C4—102no—
243C2×C4—102no—
244C2×C4—202no—
245C2×C4—202no—
246C2×C4—602no—
247C2×C4—604no—
248C2×C4#676312yes—
249C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
250C8—304no—
251C2×C3—51no—
252C2×C3—51no—
253C2×C3—52no—
254C2×C3(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
255C2×C3#6579312yes—
256C5#7174111yescharacteristic, complemented, Sylow
257C22—51no—
258C22—51no—
259C22—52no—
260C22—52no—
261C22C2×#676311yescharacteristic
262C4—22no—
263C4—42no—
264C4—52no—
265C4—102no—
266C4—202no—
267C4—1202no—
268C4Q8×ΓL(1,𝔽16)12yes—
269C3#1060459111yescharacteristic, complemented, Sylow
270C2—51no—
271C2—52no—
272C2—51no—
273C2#1175244911yescharacteristic
274C2#1175245212yes—
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#125C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenter#125ΓL(1,𝔽16)
hypocenterC3×C5#1992
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
9. C3×C5×#125C4semidirect
12. C3×#4036C4semidirect
15. C3×#4016C4semidirect
48. C5×#125Dic3semidirect
51. #4036Dic3semidirect
54. #4016Dic3semidirect
76. C3×#125AGL(1,𝔽5)semidirect
158. #125ΓL(1,𝔽16)semidirect
217. C3×C5#1992semidirect
256. C5#71741semidirect
269. C3#10604591semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1252
#117523472
#117523352
#117467452
#106045913
#717415