Finite Group Databasebeta

← #14301792

Subgroups — #14301792

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D5⋊C8C211yesmaximal, characteristic
2D5×#924C211yesmaximal, characteristic
3#11752424C211yesmaximal, characteristic
4C2×#91154C212yesmaximal, complemented
5#11746530C212yesmaximal, complemented
6#10604525—31nomaximal, Hall
7C22×C3×C4×D5C2211yescharacteristic
8C2×D5×Dic6C2211yescharacteristic
9C2×#6763—21no—
10C2×C4⋊ΓL(1,𝔽16)C2212yes—
11C22×C3×#170—21no—
12C2×C3×D5⋊C8—21no—
13C2×C3×D5⋊C8—24no—
14C2×C3×D5⋊C8C2212yes—
15#91813C411yescharacteristic, complemented
16C5×#924C411yescharacteristic, complemented
17#91574—21no—
18D5×#217—21no—
19D5×C4⋊Dic3C2211yescharacteristic
20D5×Dic3⋊C4—21no—
21#91360C411yescharacteristic, complemented
22#91359C411yescharacteristic, complemented
23#91349—21no—
24#91235—21no—
25#91154—24no—
26#71972—51nomaximal, Hall
27C22×D5⋊C8D311yescharacteristic
28D5×C22⋊Q8—31no—
29C2×#4009—32no—
30#65765—31no—
31#64874—32no—
32C23×C3×D5D411yescharacteristic
33C22×ΓL(1,𝔽16)—22no—
34C22×C3×C4×C5C2×C411yescharacteristic
35C2×Dic30C2×C411yescharacteristic
36C2×C5×Dic6C2×C411yescharacteristic
37C22×C3×Dic5D411yescharacteristic
38C2×C3×C4×D5—22no—
39C2×C3×C4×D5—22no—
40C2×C3×C4×D5C2×C411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×C4×D5C2311yescharacteristic
44C2×#1204—21no—
45C2×D5×Dic3—21no—
46C2×D5×Dic3—21no—
47D5×Dic6—22no—
48D5×Dic6—22no—
49#6763—42no—
50C4⋊ΓL(1,𝔽16)—22no—
51C4⋊ΓL(1,𝔽16)—22no—
52C2×C3×#170—24no—
53C2×C3×#170—22no—
54C3×D5⋊C8—24no—
55C3×D5⋊C8—22no—
56C3×D5⋊C8D414yes—
57#6719—21no—
58C4⋊Dic15C2×C411yescharacteristic
59#6712—21no—
60C5×#217—21no—
61C5×C4⋊Dic3C2×C411yescharacteristic
62C5×Dic3⋊C4—21no—
63Dic3⋊Dic5—21no—
64#6669—21no—
65#6668—21no—
66#6665—21no—
67#6665—21no—
68C23×C3×C8—51no—
69C2×#924—51no—
70#5212—51no—
71C2×#816—52no—
72#4551—52no—
73C2×Q8×D5—31no—
74C22×C4×D5C2×D311yescharacteristic
75C2×C22⋊AGL(1,𝔽5)—61no—
76C22×#170—21no—
77C2×C4⋊AGL(1,𝔽5)—32no—
78C2×D5⋊C8—21no—
79C2×D5⋊C8—24no—
80C2×D5⋊C8C2×D312yes—
81C5×C22⋊Q8—31no—
82#4092—31no—
83#4070—31no—
84#4043—31no—
85#4042—61no—
86D5×C4⋊C4—31no—
87D5×C4⋊C4—61no—
88D5×C22⋊C4—61no—
89#4024—61no—
90#4009—64no—
91(C2×AGL(1,𝔽5))⋊C4—61no—
92#1892—151noSylow
93C23×C3×C5C22⋊C411yescharacteristic
94C22×C3×D5—22no—
95C22×C3×D5—22no—
96C22×C3×D5C22⋊C411yescharacteristic
97C22×C3×D5SD1612yes—
98C22×C3×D5Q1612yes—
99C22×C3×D5C2×D411yescharacteristic
100C2×ΓL(1,𝔽16)—42no—
101C2×ΓL(1,𝔽16)—42no—
102C2×ΓL(1,𝔽16)—42no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5C22⋊C411yescharacteristic
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×Dic15—21no—
107C2×Dic15—21no—
108Dic30—22no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—21no—
111C5×Dic6—22no—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5C22⋊C411yescharacteristic
115C2×C3×Dic5C2×D411yescharacteristic
116C3×C4×D5—22no—
117C3×C4×D5—22no—
118C3×C4×D5—21no—
119C3×C4×D5—21no—
120C3×C4×D5C2×D412yes—
121C3×C4×D5#4112yes—
122#1204—41no—
123#1204—41no—
124D5×Dic3—42no—
125D5×Dic3—42no—
126C3×#170—24no—
127C23×C3×C4—51no—
128C22×Dic6—51no—
129C22×C3×C8—52no—
130C22×C3×C8—104no—
131C22×C3×C8—101no—
132C22×C3×C8—101no—
133C2×#217—101no—
134C2×#217—101no—
135C2×C4⋊Dic3—51no—
136C2×C4⋊Dic3—52no—
137#924—51no—
138#924—51no—
139#924—51no—
140#924—101no—
141#924—101no—
142#924AGL(1,𝔽5)11yescharacteristic, complemented
143C2×Dic3⋊C4—101no—
144C3⋊#95—101no—
145#816—104no—
146C23×D5D1211yescharacteristic
147C22×AGL(1,𝔽5)—62no—
148C2×C5×Q8—31no—
149C22×C4×C5C4×D311yescharacteristic
150C22×Dic5#6711yescharacteristic
151Q8×D5—62no—
152Q8×D5—62no—
153C2×C4×D5—22no—
154C2×C4×D5—22no—
155C2×C4×D5—61no—
156C2×C4×D5—61no—
157C2×C4×D5C4×D311yescharacteristic
158C2×C4×D5D1211yescharacteristic
159C2×C4×D5#6711yescharacteristic
160C2×C4×D5C22×D311yescharacteristic
161C2×Dic10—31no—
162C2×Dic10—61no—
163C22⋊AGL(1,𝔽5)—122no—
164C2×#170—24no—
165C2×#170—22no—
166C4⋊AGL(1,𝔽5)—62no—
167C4⋊AGL(1,𝔽5)—62no—
168D5⋊C8—24no—
169D5⋊C8—22no—
170D5⋊C8#6714yes—
171C5×C4⋊C4—31no—
172C5×C4⋊C4—61no—
173C5×C22⋊C4—61no—
174C22⋊Dic5—61no—
175#685—61no—
176#685—61no—
177C4⋊Dic5—31no—
178C4⋊Dic5—61no—
179#683—61no—
180#683—61no—
181#683—61no—
182C23×C8—51no—
183C2×C22⋊Q8—151no—
184C2×#103—152no—
185#380—151no—
186#340—152no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5#10312yescomplemented
190C22×C3×C5C2×C22⋊C411yescharacteristic
191C2×C3×D5—21no—
192C2×C3×D5—21no—
193C2×C3×D5—24no—
194C2×C3×D5—24no—
195C2×C3×D5#10312yescomplemented
196C2×C3×D5#12112yes—
197C2×C3×D5C2×SD1611yescharacteristic
198C2×C3×D5C2×Q1611yescharacteristic
199C2×C3×D5#13512yes—
200ΓL(1,𝔽16)—82no—
201C3×C4×C5—21no—
202C3×C4×C5C4×D412yes—
203Dic15—41no—
204Dic15—41no—
205C3×Dic5—21no—
206C3×Dic5#12011yescharacteristic
207C3×Dic5#12311yescharacteristic
208C5×Dic3—41no—
209C5×Dic3—41no—
210C24×C3—51no—
211C22×C3×C4—51no—
212C22×C3×C4—51no—
213C22×C3×C4—51no—
214C22×C3×C4—51no—
215C22×C3×C4—51no—
216C22×C3×C4—102no—
217C22×C3×C4—102no—
218C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
219C22×Dic3—101no—
220C22×Dic3—101no—
221C22×Dic3—102no—
222C2×Dic6—51no—
223C2×Dic6—102no—
224C2×Dic6—102no—
225C2×Dic6—101no—
226C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
227C2×C3×C8—54no—
228C2×C3×C8—102no—
229C2×C3×C8—102no—
230C2×C3×C8—104no—
231C2×C3×C8—104no—
232#217—21no—
233#217—101no—
234#217—101no—
235#217—101no—
236#217—202no—
237C4⋊Dic3—51no—
238C4⋊Dic3—101no—
239C4⋊Dic3—102no—
240C4⋊Dic3—102no—
241C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
242Dic3⋊C4—21no—
243Dic3⋊C4—101no—
244Dic3⋊C4—101no—
245Dic3⋊C4—101no—
246C23×C5(C2×D3)⋊C411yescharacteristic
247C22×D5—22no—
248C22×D5—22no—
249C22×D5#20412yes—
250C22×D5Dic1212yes—
251C22×D5(C2×D3)⋊C411yescharacteristic
252C22×D5C2×D1211yescharacteristic
253C2×AGL(1,𝔽5)—122no—
254C2×AGL(1,𝔽5)—122no—
255C2×AGL(1,𝔽5)—122no—
256C5×Q8—62no—
257C2×C4×C5—22no—
258C2×C4×C5—61no—
259C2×C4×C5—61no—
260C2×C4×C5(C2×D3)⋊C411yescharacteristic
261C2×C4×C5C2×C4×D311yescharacteristic
262C2×Dic5—21no—
263C2×Dic5—21no—
264C2×Dic5—61no—
265C2×Dic5—61no—
266C2×Dic5(C2×D3)⋊C411yescharacteristic
267C2×Dic5C2×#6711yescharacteristic
268C4×D5—22no—
269C4×D5—22no—
270C4×D5—21no—
271C4×D5—21no—
272C4×D5—122no—
273C4×D5—122no—
274C4×D5#23512yes—
275C4×D5C2×#6712yes—
276Dic10—62no—
277Dic10—121no—
278Dic10—121no—
279#170—24no—
280C22×Q8—151no—
281C23×C4—51no—
282C22×C8—52no—
283C22×C8—104no—
284C22×C8—101no—
285C22×C8—101no—
286C22⋊Q8—31no—
287C22⋊Q8—151no—
288C22⋊Q8—151no—
289C22⋊Q8—151no—
290C22⋊Q8—301no—
291C22⋊Q8—301no—
292C2×C4⋊C4—151no—
293C2×C4⋊C4—152no—
294C2×C4⋊C4—301no—
295C2×C22⋊C4—301no—
296C2×C22⋊C4—301no—
297#103—304no—
298#95—301no—
299C2×C3×C5—22no—
300C2×C3×C5#38611yescharacteristic
301C2×C3×C5C2×#10311yescharacteristic
302C2×C3×C5#41611yescharacteristic
303C3×D5—22no—
304C3×D5#46512yes—
305C3×D5#46712yes—
306C23×C3—51no—
307C23×C3—51no—
308C23×C3—52no—
309C23×C3—52no—
310C23×C3—102no—
311C23×C3—102no—
312C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
313C2×C3×C4—22no—
314C2×C3×C4—51no—
315C2×C3×C4—52no—
316C2×C3×C4—52no—
317C2×C3×C4—51no—
318C2×C3×C4—101no—
319C2×C3×C4—101no—
320C2×C3×C4—102no—
321C2×C3×C4—101no—
322C2×C3×C4—101no—
323C2×C3×C4—102no—
324C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
325C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
326C2×Dic3—21no—
327C2×Dic3—21no—
328C2×Dic3—101no—
329C2×Dic3—101no—
330C2×Dic3—202no—
331C2×Dic3—202no—
332C2×Dic3—202no—
333C2×Dic3—202no—
334C2×Dic3—202no—
335Dic6—22no—
336Dic6—102no—
337Dic6—201no—
338Dic6—201no—
339C3×C8—104no—
340C22×C5—21no—
341C22×C5—21no—
342C22×C5#81612yescomplemented
343C22×C5C2×(C2×D3)⋊C411yescharacteristic
344C2×D5—21no—
345C2×D5—21no—
346C2×D5—24no—
347C2×D5—24no—
348C2×D5#81612yescomplemented
349C2×D5C2×#20411yescharacteristic
350C2×D5#90412yes—
351C2×D5C2×Dic1211yescharacteristic
352C2×D5#93012yes—
353AGL(1,𝔽5)—242no—
354C4×C5—21no—
355C4×C5—121no—
356C4×C5—121no—
357C4×C5C4×#6712yes—
358Dic5—21no—
359Dic5—121no—
360Dic5—121no—
361Dic5#92911yescharacteristic
362Dic5#95311yescharacteristic
363C24—51no—
364C2×Q8—31no—
365C2×Q8—151no—
366C2×Q8—301no—
367C2×Q8—302no—
368C2×Q8—302no—
369C22×C4—51no—
370C22×C4—51no—
371C22×C4—51no—
372C22×C4—51no—
373C22×C4—51no—
374C22×C4—102no—
375C22×C4—102no—
376C22×C4—301no—
377C22×C4—301no—
378C22×C4—302no—
379C22×C4D3×AGL(1,𝔽5)11yescharacteristic
380C2×C8—54no—
381C2×C8—102no—
382C2×C8—102no—
383C2×C8—104no—
384C2×C8—104no—
385C4⋊C4—31no—
386C4⋊C4—61no—
387C4⋊C4—151no—
388C4⋊C4—301no—
389C4⋊C4—301no—
390C4⋊C4—301no—
391C4⋊C4—302no—
392C4⋊C4—302no—
393C4⋊C4—301no—
394C22⋊C4—61no—
395C22⋊C4—301no—
396C22⋊C4—301no—
397C22⋊C4—301no—
398C22⋊C4—602no—
399C3×C5#189211yescharacteristic, complemented, Hall
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—52no—
403C22×C3—52no—
404C22×C3—51no—
405C22×C3—51no—
406C22×C3—52no—
407C22×C3—104no—
408C22×C3—104no—
409C22×C3—101no—
410C22×C3—101no—
411C22×C3#400912yescomplemented
412C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
413C3×C4—21no—
414C3×C4—51no—
415C3×C4—51no—
416C3×C4—101no—
417C3×C4D4×AGL(1,𝔽5)12yes—
418Dic3—41no—
419Dic3—41no—
420Dic3—201no—
421Dic3—201no—
422Dic3—402no—
423C2×C5—22no—
424C2×C5C2×#81611yescharacteristic
425C2×C5#511311yescharacteristic
426C2×C5#521311yescharacteristic
427D5—22no—
428D5#511412yes—
429D5#511612yes—
430C23—51no—
431C23—52no—
432C23—52no—
433C23—51no—
434C23—102no—
435C23—102no—
436C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
437Q8—62no—
438Q8—302no—
439Q8—601no—
440Q8—601no—
441C2×C4—22no—
442C2×C4—51no—
443C2×C4—52no—
444C2×C4—52no—
445C2×C4—51no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—101no—
449C2×C4—101no—
450C2×C4—102no—
451C2×C4—101no—
452C2×C4—101no—
453C2×C4—102no—
454C2×C4—301no—
455C2×C4—301no—
456C2×C4—602no—
457C2×C4—602no—
458C2×C4—602no—
459C2×C4—602no—
460C2×C4—602no—
461C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
462C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
463C8—104no—
464C2×C3—22no—
465C2×C3—52no—
466C2×C3—52no—
467C2×C3—102no—
468C2×C3#6577911yescharacteristic
469C2×C3C2×#400911yescharacteristic
470C2×C3#6579411yescharacteristic
471C5#7197211yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—52no—
475C22—51no—
476C22—51no—
477C22—52no—
478C22—52no—
479C22—104no—
480C22—104no—
481C22—101no—
482C22—101no—
483C22#9115412yescomplemented
484C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
485C4—21no—
486C4—51no—
487C4—51no—
488C4—101no—
489C4—121no—
490C4—121no—
491C4—601no—
492C4—601no—
493C4—1202no—
494C4AGL(1,𝔽5)×#6712yes—
495C3#1060452511yescharacteristic, complemented, Sylow
496C2—22no—
497C2—52no—
498C2—52no—
499C2—102no—
500C2#1175170411yescharacteristic
501C2C2×#9115411yescharacteristic
502C2#1175202211yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5D4
cosocleC2×C3×C4×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1892
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. C2×#91154C2semidirect
5. #11746530C2semidirect
15. #91813C4semidirect
16. C5×#924C4semidirect
21. #91360C4semidirect
22. #91359C4semidirect
142. #924AGL(1,𝔽5)semidirect
189. C22×C3×C5#103semidirect
195. C2×C3×D5#103semidirect
342. C22×C5#816semidirect
348. C2×D5#816semidirect
399. C3×C5#1892semidirect
411. C22×C3#4009semidirect
471. C5#71972semidirect
483. C22#91154semidirect
495. C3#10604525semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D5⋊C82
D5×#9242
#117524242
C2×#911542
#117465302
#106045253
#719725