Finite Group Databasebeta

← #14438625

Subgroups — #14438625

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756236C211yesmaximal, characteristic
2C2×C3×#4015C211yesmaximal, characteristic, complemented
3C4×C5×#208C211yesmaximal, characteristic, complemented
4#11748413C214yesmaximal, complemented
5#11746935C214yesmaximal, complemented
6#11746921C212yesmaximal, complemented
7#11746910C212yesmaximal, complemented
8#10610259—31nomaximal, Hall
9C2×#6817C2212yes—
10C22×C3×Dic10—21no—
11C2×C3×C42×C5C2211yescharacteristic
12#91819—21no—
13#91819—21no—
14#91764C2212yes—
15#91763C2211yescharacteristic
16C4×D60—21no—
17C4×D60—21no—
18#91758C2211yescharacteristic
19C2×C5×#208C2212yes—
20C2×C3×C4⋊Dic5—21no—
21C2×C3×C4⋊Dic5C2212yes—
22C3×#4015—21no—
23C3×#4015—21no—
24C3×#4015C2212yes—
25C3×#4015C2212yes—
26C5×#803C2212yes—
27C4×C5×C3⋊C8C2212yes—
28#90974C2218yes—
29#90968C2218yes—
30#83199—51nomaximal, Hall
31#65811—31no—
32C2×#4015D311yescharacteristic, complemented
33C4×C5×M16—31no—
34#65422—34no—
35#65003—34no—
36#64983—32no—
37#64970—32no—
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5C2311yescharacteristic
41C2×#1220—22no—
42#6817—28no—
43C2×D60—21no—
44C2×D60—21no—
45C2×D60C2312yes—
46C2×C4×D15—22no—
47C2×Dic30C2312yes—
48C22×C3×Dic5—22no—
49C2×C3×Dic10—22no—
50C2×C3×Dic10—22no—
51C2×C3×Dic10—44no—
52C3×C42×C5D411yescharacteristic
53C3×C42×C5D411yescharacteristic
54C3×C42×C5C2311yescharacteristic
55C3×C42×C5C2311yescharacteristic
56#6714—22no—
57#6714—22no—
58C4⋊Dic15—21no—
59C4⋊Dic15—21no—
60C5×#208—24no—
61C2×C5×C3⋊C8C2314yes—
62C3×C4⋊Dic5—22no—
63C3×C4⋊Dic5—22no—
64C3×C4⋊Dic5—22no—
65C3×C4⋊Dic5C2314yes—
66C2×C3×C4⋊Q8—51no—
67#5477—51no—
68#5093—52no—
69#5089—54no—
70#5088—52no—
71#4966—54no—
72C4×#208D511yescharacteristic, complemented
73C2×#709—32no—
74C22×Dic10—21no—
75C2×C5×M16—32no—
76C2×C42×C5C2×D311yescharacteristic
77#4076—61no—
78#4076—61no—
79C2×C4⋊Dic5—21no—
80C2×C4⋊Dic5C2×D312yes—
81#4021—32no—
82#4020—31no—
83C4×D20—61no—
84C4×D20—61no—
85#4015—21no—
86#4015—21no—
87#4015—31no—
88#4015C2×D312yes—
89#4015C2×D312yes—
90C5×#97—32no—
91C4×C5×C8—32no—
92#3953—38no—
93#3948—38no—
94#3141—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×D15—22no—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5#4114yes—
105C2×C3×C4×C5C2411yescharacteristic
106#1220—44no—
107C2×Dic15—22no—
108D60—24no—
109D60—42no—
110D60—42no—
111C4×D15—44no—
112Dic30—24no—
113C2×C3×Dic5—24no—
114C2×C3×Dic5—44no—
115C3×Dic10—44no—
116C3×Dic10—44no—
117C5×C3⋊C8—24no—
118C22×C3×Q8—101no—
119C2×#235—52no—
120C3×C4⋊Q8—52no—
121C3×C4⋊Q8—52no—
122C3×C4⋊Q8—101no—
123C3×C4⋊Q8—101no—
124C2×C3×C4⋊C4—52no—
125C2×C3×C4⋊C4—101no—
126C2×C3×C42C2×D511yescharacteristic
127#930—101no—
128#930—101no—
129C2×#208C2×D512yes—
130#875—52no—
131#874—51no—
132C4×D12—101no—
133C4×D12—101no—
134#869—51no—
135#810—58no—
136#809—58no—
137#803C2×D512yes—
138C4×C3⋊C8C2×D512yes—
139C22×C4×C5#6711yescharacteristic
140C22×C4×C5#6711yescharacteristic
141C22×C4×C5C22×D311yescharacteristic
142C2×C22⋊D5—62no—
143C22×Dic5—22no—
144#709—68no—
145C2×D20—32no—
146C2×D20—61no—
147C2×D20—61no—
148C2×C4×D5—62no—
149C2×Dic10—22no—
150C2×Dic10—22no—
151C2×Dic10—32no—
152C2×Dic10—44no—
153C5×M16—64no—
154C2×C5×C8—34no—
155C42×C5#6711yescharacteristic
156C42×C5#6711yescharacteristic
157C42×C5C22×D311yescharacteristic
158C42×C5C22×D311yescharacteristic
159#685—62no—
160#685—62no—
161C4⋊Dic5—22no—
162C4⋊Dic5—22no—
163C4⋊Dic5—22no—
164C4⋊Dic5—61no—
165C4⋊Dic5—61no—
166C4⋊Dic5C22×D314yes—
167#532—151no—
168C2×C4⋊Q8—51no—
169#489—154no—
170#487—152no—
171#486—152no—
172#417—154no—
173C4×M16—31no—
174C22×C3×C5—21no—
175C22×C3×C5—21no—
176C22×C3×C5#12412yes—
177C22×C3×C5C22×D411yescharacteristic
178C2×D15—42no—
179C2×D15—42no—
180C2×D15—42no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183C3×C4×C5#12412yes—
184C3×C4×C5AGL(1,ℤ/8)12yes—
185C3×C4×C5#13712yes—
186C3×C4×C5C2×#4112yes—
187Dic15—42no—
188C3×Dic5—44no—
189C2×C3×Q8—102no—
190C2×C3×Q8—102no—
191C2×C3×Q8—204no—
192C22×C3×C4—102no—
193C22×C3×C4D2011yescharacteristic
194C22×C3×C4D2011yescharacteristic
195C22×C3×C4C22×D511yescharacteristic
196C2×#67—102no—
197#235—108no—
198C2×D12—52no—
199C2×D12—101no—
200C2×D12—101no—
201C2×C4×D3—102no—
202C2×Dic6—52no—
203C3×C4⋊C4—54no—
204C3×C4⋊C4—102no—
205C3×C4⋊C4—102no—
206C3×C4⋊C4—102no—
207C3×C42D2011yescharacteristic
208C3×C42D2011yescharacteristic
209C3×C42C22×D511yescharacteristic
210C3×C42C22×D511yescharacteristic
211(C2×D3)⋊C4—102no—
212(C2×D3)⋊C4—102no—
213C4⋊Dic3—101no—
214C4⋊Dic3—101no—
215#208—24no—
216C2×C3⋊C8C22×D514yes—
217C23×C5C2×#6711yescharacteristic
218C22×D5—62no—
219C2×C4×C5—22no—
220C2×C4×C5—22no—
221C2×C4×C5#23914yes—
222C2×C4×C5C2×#6711yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C2×C4×C5C2×#6711yescharacteristic
225C2×C4×C5C2×#6711yescharacteristic
226C2×C4×C5C2×#6711yescharacteristic
227C2×C4×C5C23×D311yescharacteristic
228C22⋊D5—124no—
229C2×Dic5—24no—
230C2×Dic5—44no—
231C2×Dic5—62no—
232D20—64no—
233D20—122no—
234D20—122no—
235C4×D5—124no—
236Dic10—44no—
237Dic10—44no—
238Dic10—64no—
239C5×C8—64no—
240C2×#41—152no—
241C22×Q8—101no—
242C2×M16—32no—
243C4⋊Q8—52no—
244C4⋊Q8—52no—
245C4⋊Q8—101no—
246C4⋊Q8—101no—
247C4⋊Q8—151no—
248#127—151no—
249#124—152no—
250#121—301no—
251#121—301no—
252C4×D4—301no—
253C4×D4—301no—
254C2×C4⋊C4—52no—
255C2×C4⋊C4—101no—
256C2×C42D3×D511yescharacteristic
257#103—158no—
258#102—158no—
259#97—32no—
260C4×C8—32no—
261C2×C3×C5—22no—
262C2×C3×C5C2×#12411yescharacteristic
263C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
264C2×C3×C5C2×#13711yescharacteristic
265D15—82no—
266C23×C3C2×D2011yescharacteristic
267C22×D3—102no—
268C3×Q8—204no—
269C3×Q8—204no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—104no—
273C2×C3×C4—204no—
274C2×C3×C4C2×D2011yescharacteristic
275C2×C3×C4C2×D2011yescharacteristic
276C2×C3×C4C2×D2011yescharacteristic
277C2×C3×C4C2×D2011yescharacteristic
278C2×C3×C4C2×D2011yescharacteristic
279C2×C3×C4#70914yes—
280C2×C3×C4C23×D511yescharacteristic
281#67—204no—
282C2×Dic3—102no—
283D12—104no—
284D12—202no—
285D12—202no—
286C4×D3—204no—
287Dic6—104no—
288C3⋊C8—24no—
289C22×C5—21no—
290C22×C5—21no—
291C22×C5#94712yes—
292C22×C5C22×#6711yescharacteristic
293C2×D5—122no—
294C2×D5—122no—
295C2×D5—122no—
296C4×C5—21no—
297C4×C5—21no—
298C4×C5#93212yes—
299C4×C5#94212yes—
300C4×C5#94712yes—
301C4×C5C2×#23912yes—
302Dic5—44no—
303Dic5—122no—
304#41—308no—
305C2×Q8—102no—
306C2×Q8—102no—
307C2×Q8—152no—
308C2×Q8—204no—
309C2×D4—152no—
310C2×D4—302no—
311C2×D4—301no—
312C2×D4—301no—
313C22×C4—102no—
314C22×C4—302no—
315C22×C4#120211yescharacteristic
316C22×C4#120211yescharacteristic
317C22×C4C2×D3×D511yescharacteristic
318M16—64no—
319C2×C8—34no—
320C4⋊C4—54no—
321C4⋊C4—102no—
322C4⋊C4—102no—
323C4⋊C4—102no—
324C4⋊C4—301no—
325C4⋊C4—301no—
326C22⋊C4—302no—
327C22⋊C4—302no—
328C42#120211yescharacteristic
329C42#120211yescharacteristic
330C42C2×D3×D511yescharacteristic
331C42C2×D3×D511yescharacteristic
332C3×C5#314111yescharacteristic, complemented, Hall
333C22×C3—21no—
334C22×C3—21no—
335C22×C3#402112yes—
336C22×C3C22×D2011yescharacteristic
337C2×D3—202no—
338C2×D3—202no—
339C2×D3—202no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—204no—
343C3×C4#402112yes—
344C3×C4#405412yes—
345C3×C4#405512yes—
346C3×C4C2×#70912yes—
347Dic3—202no—
348C2×C5—22no—
349C2×C5C2×#93211yescharacteristic
350C2×C5C2×#94211yescharacteristic
351C2×C5C2×#94711yescharacteristic
352D5—242no—
353C23—302no—
354C23C2×#120211yescharacteristic
355Q8—204no—
356Q8—204no—
357Q8—304no—
358D4—304no—
359D4—604no—
360D4—602no—
361D4—602no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—104no—
365C2×C4—204no—
366C2×C4—302no—
367C2×C4—604no—
368C2×C4#676914yes—
369C2×C4C2×#120211yescharacteristic
370C2×C4C2×#120211yescharacteristic
371C2×C4C2×#120211yescharacteristic
372C2×C4C2×#120211yescharacteristic
373C2×C4C2×#120211yescharacteristic
374C2×C4C22×D3×D511yescharacteristic
375C8—64no—
376C2×C3—22no—
377C2×C3C2×#402111yescharacteristic
378C2×C3C2×#405411yescharacteristic
379C2×C3C2×#405511yescharacteristic
380D3—402no—
381C5#8319911yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—602no—
385C22—602no—
386C22—602no—
387C22#9137412yes—
388C22C22×#120211yescharacteristic
389C4—21no—
390C4—21no—
391C4—204no—
392C4—602no—
393C4#9131212yes—
394C4#9131512yes—
395C4#9137412yes—
396C4C2×#676912yes—
397C3#1061025911yescharacteristic, complemented, Sylow
398C2—22no—
399C2—1202no—
400C2C2×#9131211yescharacteristic
401C2C2×#9131511yescharacteristic
402C2C2×#9137411yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C22×D4
prime radical#11756236C2
hypercenterC2×C42D3×D5
hypocenterC3×C5#3141
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4015C2semidirect
3. C4×C5×#208C2semidirect
4. #11748413C2semidirect
5. #11746935C2semidirect
6. #11746921C2semidirect
7. #11746910C2semidirect
32. C2×#4015D3semidirect
72. C4×#208D5semidirect
332. C3×C5#3141semidirect
381. C5#83199semidirect
397. C3#10610259semidirect

Maximal subgroups

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

subgroupindex
#117562362
C2×C3×#40152
C4×C5×#2082
#117484132
#117469352
#117469212
#117469102
#106102593
#831995