Finite Group Databasebeta

← #14305872

Subgroups — #14305872

Order 1920.

672 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 134 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
1D5×#875C211yesmaximal, characteristic
2#11752348C211yesmaximal, characteristic, complemented
3C3×C4×D5⋊C8C211yesmaximal, characteristic, complemented
4C2×#91154C212yesmaximal, complemented
5C2×#91152C212yesmaximal
6#10604566—31nomaximal, Hall
7C2×D5×D12C2211yescharacteristic
8C2×D5×Dic6C2211yescharacteristic
9C2×C4⋊ΓL(1,𝔽16)C2212yes—
10C2×C3×D5⋊C8C2212yes—
11#91764C411yescharacteristic, complemented
12C5×#875C411yescharacteristic, complemented
13C3×C42×D5C2211yescharacteristic
14D5×(C2×D3)⋊C4—22no—
15#91375C411yescharacteristic, complemented
16#91373C411yescharacteristic, complemented
17#91350—22no—
18#91235—22no—
19C3×C4×#170—22no—
20#91154—24no—
21#91152—24no—
22#69773—51nomaximal, Hall
23D5×#124—31no—
24C2×#4009—32no—
25C2×#4007—32no—
26#65689—31no—
27C4×D5⋊C8D311yescharacteristic, complemented
28C22×D3×D5—21no—
29C22×ΓL(1,𝔽16)—22no—
30C2×D60C2×C411yescharacteristic
31C2×Dic30C2×C411yescharacteristic
32C2×C5×D12C2×C411yescharacteristic
33C2×C5×Dic6C2×C411yescharacteristic
34C2×C3×C4×D5D412yes—
35C2×C3×C4×D5C2311yescharacteristic
36C2×#1204—21no—
37C2×#1203—21no—
38C2×D5×Dic3—21no—
39D5×D12—22no—
40D5×D12—22no—
41D5×Dic6—22no—
42D5×Dic6—22no—
43C4⋊ΓL(1,𝔽16)—22no—
44C4⋊ΓL(1,𝔽16)—22no—
45C2×C3×#170—22no—
46C3×D5⋊C8—22no—
47C3×D5⋊C8D414yes—
48C3×C42×C5C2×C411yescharacteristic
49#6714—22no—
50C5×(C2×D3)⋊C4—22no—
51C3×C4×Dic5C2×C411yescharacteristic
52C3×C4×Dic5D412yes—
53#6667—22no—
54(C2×D3)⋊Dic5—22no—
55C2×#875—51no—
56C2×C3×C4×C8—51no—
57C2×#821—52no—
58C2×#816—52no—
59#4936—51no—
60C2×Q8×D5—31no—
61C2×D4×D5—31no—
62C2×C4⋊AGL(1,𝔽5)—32no—
63C2×D5⋊C8C2×D312yes—
64C5×#124—31no—
65#4093—31no—
66#4082—31no—
67#4031—62no—
68D5×C22⋊C4—62no—
69#4021—31no—
70C42×D5C2×D311yescharacteristic
71#4009—64no—
72#4007—64no—
73(C2×AGL(1,𝔽5))⋊C4—62no—
74C4×#170—22no—
75#1958—151noSylow
76C22×D15—21no—
77C22×C5×D3—21no—
78C22×C3×D5C2×D411yescharacteristic
79C2×D3×D5—41no—
80C2×D3×D5—41no—
81C2×D3×D5—44no—
82C2×ΓL(1,𝔽16)—42no—
83C2×ΓL(1,𝔽16)—44no—
84C2×C3×C4×C5C22⋊C412yes—
85C2×C3×C4×C5C22×C411yescharacteristic
86C2×Dic15—21no—
87D60—22no—
88Dic30—22no—
89C2×C5×Dic3—21no—
90C5×D12—22no—
91C5×Dic6—22no—
92C2×C3×Dic5C22⋊C412yes—
93C2×C3×Dic5C2×D411yescharacteristic
94C3×C4×D5—24no—
95C3×C4×D5C2×D412yes—
96C3×C4×D5#4112yes—
97#1204—42no—
98#1203—42no—
99D5×Dic3—41no—
100D5×Dic3—41no—
101C3×#170—24no—
102C22×D12—51no—
103C22×Dic6—51no—
104C22×C3×C8—52no—
105C2×C3×C42—51no—
106C2×(C2×D3)⋊C4—102no—
107C2×C4⋊Dic3—52no—
108#875—51no—
109#875—51no—
110#875—51no—
111#875—102no—
112#875AGL(1,𝔽5)11yescharacteristic, complemented
113C3×C4×C8—102no—
114C3⋊#95—102no—
115#821—104no—
116#816—104no—
117C23×D5—61no—
118C22×AGL(1,𝔽5)—62no—
119C2×C5×Q8—31no—
120C2×C5×D4—31no—
121C2×C22⋊D5—61no—
122Q8×D5—62no—
123Q8×D5—62no—
124D4×D5—62no—
125D4×D5—62no—
126C2×D20—31no—
127C2×C4×D5—61no—
128C2×C4×D5D1212yes—
129C2×C4×D5C22×D311yescharacteristic
130C2×Dic10—31no—
131C2×Dic10—61no—
132C2×#170—22no—
133C4⋊AGL(1,𝔽5)—62no—
134C4⋊AGL(1,𝔽5)—62no—
135D5⋊C8—22no—
136D5⋊C8D1214yes—
137C5×C22⋊C4—62no—
138C42×C5C4×D311yescharacteristic
139C22⋊Dic5—62no—
140#685—62no—
141#685—62no—
142C4×Dic5C4×D311yescharacteristic
143C4×Dic5#6712yes—
144C2×#124—151no—
145C2×#103—152no—
146C2×#102—152no—
147C2×C4×C8—51no—
148#382—151no—
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C2×D15—41no—
151C2×D15—42no—
152C2×C5×D3—41no—
153C2×C5×D3—42no—
154C2×C3×D5#12411yescharacteristic
155C2×C3×D5#12711yescharacteristic
156C2×C3×D5#13514yes—
157D3×D5—82no—
158D3×D5—82no—
159ΓL(1,𝔽16)—82no—
160C3×C4×C5—22no—
161C3×C4×C5C4×D412yes—
162Dic15—41no—
163C3×Dic5—22no—
164C3×Dic5#12112yes—
165C5×Dic3—41no—
166C23×D3—101no—
167C22×C3×C4—51no—
168C22×C3×C4—52no—
169C22×Dic3—101no—
170C22×Dic3—102no—
171C2×D12—51no—
172C2×D12—102no—
173C2×D12—102no—
174C2×D12—101no—
175C2×D12C2×AGL(1,𝔽5)11yescharacteristic
176C2×Dic6—51no—
177C2×Dic6—102no—
178C2×Dic6—102no—
179C2×Dic6—101no—
180C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
181C2×C3×C8—54no—
182C2×C3×C8—102no—
183C2×C3×C8—102no—
184C3×C42—52no—
185C3×C42—51no—
186C3×C42C2×AGL(1,𝔽5)11yescharacteristic
187(C2×D3)⋊C4—22no—
188(C2×D3)⋊C4—102no—
189(C2×D3)⋊C4—102no—
190(C2×D3)⋊C4—102no—
191C4⋊Dic3—102no—
192C4⋊Dic3—102no—
193C23×C5—61no—
194C22×D5—61no—
195C22×D5—121no—
196C22×D5—121no—
197C22×D5—124no—
198C22×D5C2×D1211yescharacteristic
199C2×AGL(1,𝔽5)—122no—
200C2×AGL(1,𝔽5)—124no—
201C5×Q8—62no—
202C5×D4—62no—
203C2×C4×C5—61no—
204C2×C4×C5(C2×D3)⋊C412yes—
205C2×C4×C5C2×C4×D311yescharacteristic
206C22⋊D5—122no—
207C2×Dic5—61no—
208C2×Dic5(C2×D3)⋊C412yes—
209C2×Dic5C2×#6711yescharacteristic
210D20—62no—
211C4×D5—24no—
212C4×D5—121no—
213C4×D5—121no—
214C4×D5C2×D1212yes—
215C4×D5#23512yes—
216Dic10—62no—
217Dic10—122no—
218#170—24no—
219C22×Q8—151no—
220C22×D4—151no—
221C22×C8—52no—
222#124—31no—
223#124—151no—
224#124—151no—
225#124—151no—
226#124—302no—
227C2×C4⋊C4—152no—
228C2×C22⋊C4—302no—
229C2×C42—51no—
230#103—304no—
231#102—304no—
232C4×C8—102no—
233#95—302no—
234C2×C3×C5#39011yescharacteristic
235C2×C3×C5#41612yes—
236D15—81no—
237C3×D5#48812yes—
238C3×D5#49512yes—
239C5×D3—81no—
240C23×C3—51no—
241C22×D3—21no—
242C22×D3—101no—
243C22×D3—201no—
244C22×D3—201no—
245C22×D3—204no—
246C2×C3×C4—51no—
247C2×C3×C4—52no—
248C2×C3×C4—52no—
249C2×C3×C4—52no—
250C2×C3×C4—104no—
251C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
252C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
253C2×Dic3—21no—
254C2×Dic3—101no—
255C2×Dic3—201no—
256C2×Dic3—201no—
257C2×Dic3—202no—
258C2×Dic3—204no—
259D12—22no—
260D12—102no—
261D12—202no—
262Dic6—22no—
263Dic6—102no—
264Dic6—202no—
265C3×C8—104no—
266C22×C5—121no—
267C22×C5—122no—
268C22×C5C2×(C2×D3)⋊C411yescharacteristic
269C2×D5—121no—
270C2×D5—122no—
271C2×D5—242no—
272C2×D5—242no—
273C2×D5#87411yescharacteristic
274C2×D5#87511yescharacteristic
275C2×D5#90414yes—
276AGL(1,𝔽5)—242no—
277C4×C5—22no—
278C4×C5—121no—
279C4×C5C4×D1212yes—
280Dic5—22no—
281Dic5—121no—
282Dic5#93012yes—
283C24—301no—
284C2×Q8—31no—
285C2×Q8—151no—
286C2×Q8—301no—
287C2×Q8—302no—
288C2×Q8—302no—
289C2×D4—31no—
290C2×D4—151no—
291C2×D4—302no—
292C2×D4—302no—
293C2×D4—301no—
294C22×C4—51no—
295C22×C4—52no—
296C22×C4—301no—
297C22×C4—302no—
298C2×C8—54no—
299C2×C8—102no—
300C2×C8—102no—
301C4⋊C4—302no—
302C4⋊C4—302no—
303C22⋊C4—62no—
304C22⋊C4—302no—
305C22⋊C4—302no—
306C22⋊C4—302no—
307C42—52no—
308C42—51no—
309C42D3×AGL(1,𝔽5)11yescharacteristic
310C3×C5#195811yescharacteristic, complemented, Hall
311C22×C3—54no—
312C22×C3—51no—
313C22×C3—51no—
314C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
315C2×D3—42no—
316C2×D3—41no—
317C2×D3—202no—
318C2×D3—201no—
319C2×D3—402no—
320C2×D3—402no—
321C3×C4—22no—
322C3×C4—52no—
323C3×C4—102no—
324C3×C4D4×AGL(1,𝔽5)12yes—
325Dic3—41no—
326Dic3—201no—
327Dic3—402no—
328C2×C5—241no—
329C2×C5#493911yescharacteristic
330C2×C5#511312yes—
331D5—241no—
332D5#469612yes—
333D5#469712yes—
334C23—51no—
335C23—61no—
336C23—301no—
337C23—601no—
338C23—601no—
339C23—604no—
340Q8—62no—
341Q8—302no—
342Q8—602no—
343D4—62no—
344D4—302no—
345D4—602no—
346C2×C4—51no—
347C2×C4—52no—
348C2×C4—52no—
349C2×C4—52no—
350C2×C4—61no—
351C2×C4—104no—
352C2×C4—301no—
353C2×C4—601no—
354C2×C4—601no—
355C2×C4—602no—
356C2×C4—604no—
357C2×C4(C2×D3)⋊AGL(1,𝔽5)12yes—
358C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
359C8—104no—
360C2×C3—52no—
361C2×C3—52no—
362C2×C3#6578011yescharacteristic
363C2×C3#6579412yes—
364D3—81no—
365D3—401no—
366C5#6977311yescharacteristic, complemented, Sylow
367C22—54no—
368C22—51no—
369C22—51no—
370C22—122no—
371C22—121no—
372C22—602no—
373C22—601no—
374C22—1202no—
375C22—1202no—
376C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
377C4—22no—
378C4—52no—
379C4—102no—
380C4—121no—
381C4—601no—
382C4—1202no—
383C4AGL(1,𝔽5)×D1212yes—
384C3#1060456611yescharacteristic, complemented, Sylow
385C2—52no—
386C2—52no—
387C2—241no—
388C2—1201no—
389C2#1175170412yes—
390C2#1175185011yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×D5×D12C22
cosocleC2×C3×C4×D5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1958
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11752348C2semidirect
3. C3×C4×D5⋊C8C2semidirect
4. C2×#91154C2semidirect
11. #91764C4semidirect
12. C5×#875C4semidirect
15. #91375C4semidirect
16. #91373C4semidirect
27. C4×D5⋊C8D3semidirect
112. #875AGL(1,𝔽5)semidirect
310. C3×C5#1958semidirect
366. C5#69773semidirect
384. C3#10604566semidirect

Maximal subgroups

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

subgroupindex
D5×#8752
#117523482
C3×C4×D5⋊C82
C2×#911542
C2×#911522
#106045663
#697735