Finite Group Databasebeta

← #14322695

Subgroups — #14322695

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×Dic3⋊C4C211yesmaximal, characteristic
2C4×#6763C211yesmaximal, characteristic
3C3×C4×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
4#11752028C212yesmaximal
5#11751984C212yesmaximal
6#11751747C214yesmaximal, complemented
7#11751745C214yesmaximal, complemented
8#10617101—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×D5×Dic3C2211yescharacteristic
11C22×D5×Dic3C2211yescharacteristic
12C2×#6763C2212yes—
13C2×C4×ΓL(1,𝔽16)C2212yes—
14C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
15C2×C3×C4×AGL(1,𝔽5)C2212yes—
16C2×Dic3⋊AGL(1,𝔽5)C2214yes—
17C2×#6712C411yescharacteristic, complemented
18C2×C5×Dic3⋊C4C411yescharacteristic, complemented
19C2×Dic3⋊Dic5C411yescharacteristic, complemented
20C2×#6669C411yescharacteristic, complemented
21D5×Dic3⋊C4C412yescomplemented
22D5×Dic3⋊C4C412yescomplemented
23D5×Dic3⋊C4C2212yes—
24D5×Dic3⋊C4C2212yes—
25#91235C2212yes—
26C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
27(C2×AGL(1,𝔽5))⋊Dic3C2218yes—
28(C2×AGL(1,𝔽5))⋊Dic3C2214yes—
29#73445—51nomaximal, Hall
30C2×D5×C4⋊C4—31no—
31#65765—32no—
32#65764—32no—
33C4×C22⋊AGL(1,𝔽5)—31no—
34C4×C22⋊AGL(1,𝔽5)D311yescharacteristic
35#65711—34no—
36#65711—34no—
37C23×C3×D5C2311yescharacteristic
38C22×ΓL(1,𝔽16)C2314yes—
39C22×C3×AGL(1,𝔽5)C2314yes—
40C22×C3×C4×C5C2×C411yescharacteristic
41C22×Dic15C2×C411yescharacteristic
42C22×Dic15C2×C411yescharacteristic
43C22×C5×Dic3C2×C411yescharacteristic
44C22×C5×Dic3C2×C411yescharacteristic
45C22×C3×Dic5C2×C411yescharacteristic
46C2×C3×C4×D5—42no—
47C2×C3×C4×D5C2×C411yescharacteristic
48C2×C3×C4×D5C2×C411yescharacteristic
49C2×C3×C4×D5C2311yescharacteristic
50C2×C3×C4×D5C2311yescharacteristic
51C2×D5×Dic3—24no—
52C2×D5×Dic3—42no—
53C2×D5×Dic3C2×C412yes—
54C2×D5×Dic3C2×C412yes—
55C2×D5×Dic3C2312yes—
56C2×D5×Dic3C2312yes—
57#6763—24no—
58C4×ΓL(1,𝔽16)—42no—
59C3×C22⋊AGL(1,𝔽5)—24no—
60C3×C4×AGL(1,𝔽5)—42no—
61Dic3⋊AGL(1,𝔽5)—44no—
62#6712C2×C412yes—
63#6712C2×C412yes—
64C5×Dic3⋊C4C2×C412yes—
65C5×Dic3⋊C4C2×C412yes—
66Dic3⋊Dic5C2×C412yes—
67Dic3⋊Dic5C2×C412yes—
68#6669C2×C412yes—
69#6669C2×C412yes—
70C22×Dic3⋊C4—51no—
71C3×C4×C22⋊C4—51no—
72C4×#217—51no—
73#4943—52no—
74#4942—52no—
75#4933—54no—
76#4652—54no—
77C22×C4×D5—31no—
78C22×C4×D5—31no—
79C22×C4×D5C2×D311yescharacteristic
80C2×C22⋊AGL(1,𝔽5)—32no—
81C2×C22⋊AGL(1,𝔽5)C2×D312yes—
82C2×C4⋊AGL(1,𝔽5)—34no—
83C2×C4×AGL(1,𝔽5)—32no—
84C2×C4×AGL(1,𝔽5)C2×D312yes—
85C2×C5×C4⋊C4—31no—
86C2×C4⋊Dic5—31no—
87C2×#683—31no—
88C2×#683—31no—
89D5×C4⋊C4—32no—
90D5×C4⋊C4—32no—
91D5×C4⋊C4—32no—
92D5×C4⋊C4—32no—
93(C2×AGL(1,𝔽5))⋊C4—38no—
94(C2×AGL(1,𝔽5))⋊C4—34no—
95(C2×AGL(1,𝔽5))⋊C4—32no—
96(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
97#2313—151noSylow
98C23×C3×C5C22×C411yescharacteristic
99C22×C3×D5—22no—
100C22×C3×D5—22no—
101C22×C3×D5C22×C411yescharacteristic
102C22×C3×D5#4114yes—
103C22×C3×D5C2411yescharacteristic
104C2×ΓL(1,𝔽16)—24no—
105C2×ΓL(1,𝔽16)—24no—
106C2×ΓL(1,𝔽16)—24no—
107C2×C3×AGL(1,𝔽5)—24no—
108C2×C3×AGL(1,𝔽5)—24no—
109C2×C3×AGL(1,𝔽5)—24no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×Dic15—22no—
114C2×Dic15—41no—
115C2×Dic15C22×C412yes—
116C2×Dic15C22×C412yes—
117C2×C5×Dic3—22no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3C22×C412yes—
120C2×C5×Dic3C22×C412yes—
121C2×C3×Dic5—41no—
122C2×C3×Dic5C22×C411yescharacteristic
123C2×C3×Dic5C22×C411yescharacteristic
124C3×C4×D5—22no—
125C3×C4×D5—22no—
126C3×C4×D5—41no—
127C3×C4×D5—41no—
128D5×Dic3—24no—
129D5×Dic3—24no—
130D5×Dic3—24no—
131D5×Dic3—42no—
132C23×C3×C4—51no—
133C23×Dic3—51no—
134C23×Dic3—51no—
135C2×C3×C22⋊C4—52no—
136C2×C3×C42—52no—
137C2×#217—52no—
138C2×Dic3⋊C4—51no—
139C2×Dic3⋊C4—51no—
140C2×Dic3⋊C4—51no—
141C2×Dic3⋊C4—52no—
142C2×Dic3⋊C4—52no—
143C2×Dic3⋊C4—52no—
144C2×Dic3⋊C4—52no—
145C2×Dic3⋊C4—54no—
146C2×Dic3⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
147C2×C4×Dic3—52no—
148C3×#95—52no—
149C3⋊#95—54no—
150C3⋊#95—58no—
151C3⋊#95—52no—
152C23×D5C22×D311yescharacteristic
153C22×AGL(1,𝔽5)—34no—
154C22×AGL(1,𝔽5)C22×D314yes—
155C22×C4×C5—31no—
156C22×C4×C5—31no—
157C22×C4×C5C4×D311yescharacteristic
158C22×Dic5—31no—
159C22×Dic5—31no—
160C22×Dic5C4×D311yescharacteristic
161C2×C4×D5—32no—
162C2×C4×D5—32no—
163C2×C4×D5—32no—
164C2×C4×D5—32no—
165C2×C4×D5—42no—
166C2×C4×D5—64no—
167C2×C4×D5—122no—
168C2×C4×D5C4×D311yescharacteristic
169C2×C4×D5C4×D311yescharacteristic
170C2×C4×D5C22×D311yescharacteristic
171C2×C4×D5C22×D311yescharacteristic
172C22⋊AGL(1,𝔽5)—24no—
173C22⋊AGL(1,𝔽5)—64no—
174C4⋊AGL(1,𝔽5)—124no—
175C4×AGL(1,𝔽5)—42no—
176C4×AGL(1,𝔽5)—122no—
177C5×C4⋊C4—32no—
178C5×C4⋊C4—32no—
179C4⋊Dic5—32no—
180C4⋊Dic5—32no—
181#683—32no—
182#683—32no—
183#683—32no—
184#683—32no—
185C22×C4⋊C4—151no—
186#387—154no—
187#387—154no—
188#381—152no—
189#380—152no—
190C4×C22⋊C4—51no—
191C4×C22⋊C4—151no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5#11712yes—
195C22×C3×C5C23×C411yescharacteristic
196C2×C3×D5—21no—
197C2×C3×D5—21no—
198C2×C3×D5—28no—
199C2×C3×D5#11712yes—
200C2×C3×D5C2×#4112yes—
201C2×C3×D5H(5,𝔽2)12yes—
202C2×C3×D52−1+412yes—
203ΓL(1,𝔽16)—44no—
204C3×AGL(1,𝔽5)—44no—
205C3×C4×C5—21no—
206C3×C4×C5—21no—
207Dic15—22no—
208Dic15—22no—
209C3×Dic5—21no—
210C3×Dic5—21no—
211C5×Dic3—22no—
212C5×Dic3—22no—
213C24×C3—51no—
214C22×C3×C4—51no—
215C22×C3×C4—51no—
216C22×C3×C4—51no—
217C22×C3×C4—51no—
218C22×C3×C4—51no—
219C22×C3×C4—54no—
220C22×C3×C4—202no—
221C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
222C22×Dic3—51no—
223C22×Dic3—51no—
224C22×Dic3—52no—
225C22×Dic3—52no—
226C22×Dic3—52no—
227C22×Dic3—52no—
228C22×Dic3—54no—
229C22×Dic3—104no—
230C22×Dic3—202no—
231C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
232C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
233C3×C22⋊C4—104no—
234C3×C42—202no—
235#217—104no—
236Dic3⋊C4—52no—
237Dic3⋊C4—52no—
238Dic3⋊C4—52no—
239Dic3⋊C4—52no—
240Dic3⋊C4—52no—
241Dic3⋊C4—52no—
242Dic3⋊C4—204no—
243Dic3⋊C4C2×AGL(1,𝔽5)12yes—
244Dic3⋊C4C2×AGL(1,𝔽5)12yes—
245C4×Dic3—202no—
246C23×C5C2×C4×D311yescharacteristic
247C22×D5—22no—
248C22×D5—22no—
249C22×D5C2×C4×D311yescharacteristic
250C22×D5#23514yes—
251C22×D5C23×D311yescharacteristic
252C2×AGL(1,𝔽5)—24no—
253C2×AGL(1,𝔽5)—24no—
254C2×AGL(1,𝔽5)—24no—
255C2×AGL(1,𝔽5)—64no—
256C2×AGL(1,𝔽5)—64no—
257C2×AGL(1,𝔽5)—64no—
258C2×C4×C5—32no—
259C2×C4×C5—32no—
260C2×C4×C5—41no—
261C2×C4×C5—62no—
262C2×C4×C5—121no—
263C2×C4×C5C2×C4×D311yescharacteristic
264C2×C4×C5C2×C4×D311yescharacteristic
265C2×Dic5—32no—
266C2×Dic5—32no—
267C2×Dic5—41no—
268C2×Dic5—62no—
269C2×Dic5—121no—
270C2×Dic5C2×C4×D311yescharacteristic
271C2×Dic5C2×C4×D311yescharacteristic
272C4×D5—22no—
273C4×D5—22no—
274C4×D5—41no—
275C4×D5—41no—
276C4×D5—64no—
277C4×D5—64no—
278C4×D5—64no—
279C4×D5—122no—
280C23×C4—51no—
281C23×C4—151no—
282C23×C4—151no—
283C2×C4⋊C4—31no—
284C2×C4⋊C4—152no—
285C2×C4⋊C4—152no—
286C2×C4⋊C4—152no—
287C2×C4⋊C4—152no—
288C2×C4⋊C4—151no—
289C2×C4⋊C4—151no—
290C2×C4⋊C4—151no—
291C2×C4⋊C4—154no—
292C2×C22⋊C4—52no—
293C2×C22⋊C4—152no—
294C2×C42—52no—
295C2×C42—152no—
296#95—52no—
297#95—152no—
298#95—154no—
299#95—158no—
300C2×C3×C5—22no—
301C2×C3×C5C2×#11711yescharacteristic
302C2×C3×C5#51811yescharacteristic
303C2×C3×C5#51911yescharacteristic
304C3×D5—22no—
305C3×D5#53914yes—
306C23×C3—51no—
307C23×C3—54no—
308C23×C3—51no—
309C23×C3—102no—
310C23×C3—102no—
311C23×C3C22×AGL(1,𝔽5)11yescharacteristic
312C2×C3×C4—41no—
313C2×C3×C4—51no—
314C2×C3×C4—51no—
315C2×C3×C4—102no—
316C2×C3×C4—102no—
317C2×C3×C4—104no—
318C2×C3×C4—104no—
319C2×C3×C4—104no—
320C2×C3×C4—201no—
321C2×C3×C4—201no—
322C2×C3×C4—201no—
323C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
324C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
325C2×Dic3—22no—
326C2×Dic3—41no—
327C2×Dic3—52no—
328C2×Dic3—52no—
329C2×Dic3—104no—
330C2×Dic3—104no—
331C2×Dic3—104no—
332C2×Dic3—102no—
333C2×Dic3—104no—
334C2×Dic3—104no—
335C2×Dic3—104no—
336C2×Dic3—202no—
337C2×Dic3—201no—
338C2×Dic3C22×AGL(1,𝔽5)12yes—
339C2×Dic3C22×AGL(1,𝔽5)12yes—
340C22×C5—21no—
341C22×C5—21no—
342C22×C5#87212yes—
343C22×C5C22×C4×D311yescharacteristic
344C2×D5—21no—
345C2×D5—21no—
346C2×D5—28no—
347C2×D5#87212yes—
348C2×D5C2×#23512yes—
349C2×D5#100412yes—
350C2×D5#101012yes—
351AGL(1,𝔽5)—44no—
352AGL(1,𝔽5)—124no—
353C4×C5—21no—
354C4×C5—21no—
355C4×C5—62no—
356C4×C5—62no—
357Dic5—21no—
358Dic5—21no—
359Dic5—62no—
360Dic5—62no—
361C24—51no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—51no—
365C22×C4—51no—
366C22×C4—51no—
367C22×C4—51no—
368C22×C4—51no—
369C22×C4—54no—
370C22×C4—152no—
371C22×C4—152no—
372C22×C4—152no—
373C22×C4—152no—
374C22×C4—151no—
375C22×C4—151no—
376C22×C4—154no—
377C22×C4—202no—
378C22×C4—304no—
379C22×C4—602no—
380C22×C4D3×AGL(1,𝔽5)11yescharacteristic
381C4⋊C4—32no—
382C4⋊C4—32no—
383C4⋊C4—152no—
384C4⋊C4—152no—
385C4⋊C4—152no—
386C4⋊C4—152no—
387C4⋊C4—152no—
388C4⋊C4—152no—
389C4⋊C4—604no—
390C22⋊C4—104no—
391C22⋊C4—304no—
392C42—202no—
393C42—602no—
394C3×C5#231311yescharacteristic, complemented, Hall
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—52no—
398C22×C3—52no—
399C22×C3—52no—
400C22×C3—52no—
401C22×C3—108no—
402C22×C3—101no—
403C22×C3—101no—
404C22×C3#413012yes—
405C22×C3C23×AGL(1,𝔽5)11yescharacteristic
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—101no—
409C3×C4—101no—
410C3×C4—204no—
411Dic3—22no—
412Dic3—22no—
413Dic3—102no—
414Dic3—102no—
415Dic3—204no—
416C2×C5—22no—
417C2×C5C2×#87211yescharacteristic
418C2×C5#548611yescharacteristic
419C2×C5#551611yescharacteristic
420D5—22no—
421D5#556414yes—
422C23—51no—
423C23—54no—
424C23—51no—
425C23—102no—
426C23—102no—
427C23C2×D3×AGL(1,𝔽5)11yescharacteristic
428C2×C4—32no—
429C2×C4—32no—
430C2×C4—41no—
431C2×C4—51no—
432C2×C4—51no—
433C2×C4—62no—
434C2×C4—102no—
435C2×C4—102no—
436C2×C4—104no—
437C2×C4—104no—
438C2×C4—104no—
439C2×C4—121no—
440C2×C4—152no—
441C2×C4—152no—
442C2×C4—201no—
443C2×C4—201no—
444C2×C4—201no—
445C2×C4—304no—
446C2×C4—304no—
447C2×C4—304no—
448C2×C4—302no—
449C2×C4—304no—
450C2×C4—304no—
451C2×C4—304no—
452C2×C4—602no—
453C2×C4—601no—
454C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
455C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
456C2×C3—22no—
457C2×C3—54no—
458C2×C3—102no—
459C2×C3C2×#413011yescharacteristic
460C2×C3#6625811yescharacteristic
461C2×C3#6626211yescharacteristic
462C5#7344511yescharacteristic, complemented, Sylow
463C22—21no—
464C22—21no—
465C22—52no—
466C22—52no—
467C22—52no—
468C22—52no—
469C22—108no—
470C22—101no—
471C22—101no—
472C22#9190912yes—
473C22C22×D3×AGL(1,𝔽5)11yescharacteristic
474C4—21no—
475C4—21no—
476C4—62no—
477C4—62no—
478C4—101no—
479C4—101no—
480C4—204no—
481C4—302no—
482C4—302no—
483C4—604no—
484C3#1061710111yescharacteristic, complemented, Sylow
485C2—22no—
486C2—54no—
487C2—102no—
488C2#1175681211yescharacteristic
489C2C2×#9190911yescharacteristic
490C2#1175687111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2313
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #11751747C2semidirect
7. #11751745C2semidirect
17. C2×#6712C4semidirect
18. C2×C5×Dic3⋊C4C4semidirect
19. C2×Dic3⋊Dic5C4semidirect
20. C2×#6669C4semidirect
21. D5×Dic3⋊C4C4semidirect
22. D5×Dic3⋊C4C4semidirect
146. C2×Dic3⋊C4AGL(1,𝔽5)semidirect
394. C3×C5#2313semidirect
462. C5#73445semidirect
484. C3#10617101semidirect

Maximal subgroups

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

subgroupindex
C2×D5×Dic3⋊C42
C4×#67632
C3×C4×C22⋊AGL(1,𝔽5)2
#117520282
#117519842
#117517472
#117517452
#106171013
#734455