Finite Group Databasebeta

← #14299502

Subgroups — #14299502

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4130C211yesmaximal, characteristic
2#11752424C211yesmaximal, characteristic
3C2×#91160C211yesmaximal, characteristic, complemented
4C2×#91159C211yesmaximal, characteristic, complemented
5D5×#830C211yesmaximal, characteristic
6#11746529C211yesmaximal, characteristic, complemented
7#11746529C211yesmaximal, characteristic, complemented
8#10603912—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×#6763—21no—
11C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
12C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
13C2×C3×C22⋊AGL(1,𝔽5)—21no—
14C3×#4130—22no—
15C3×#4130—22no—
16C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
17C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
18C2×C3×C4×AGL(1,𝔽5)—21no—
19C2×D5×C3⋊C8C2211yescharacteristic
20C2×D5×C3⋊C8C2211yescharacteristic
21#91235—21no—
22#91160—22no—
23#91159—22no—
24#91114C411yescharacteristic, complemented
25C5×#830C411yescharacteristic, complemented
26#90955C411yescharacteristic, complemented
27#90955C411yescharacteristic, complemented
28#71576—51nomaximal, Hall
29C2×#4130D311yescharacteristic
30#65765—31no—
31C2×#3994—31no—
32C2×#3993—31no—
33D5×C22⋊C8—31no—
34#64893—31no—
35#64893—31no—
36C23×C3×D5D411yescharacteristic
37C22×ΓL(1,𝔽16)—21no—
38C22×ΓL(1,𝔽16)—21no—
39C22×C3×AGL(1,𝔽5)—21no—
40C22×C3×AGL(1,𝔽5)—21no—
41C22×C3×C4×C5C2×C411yescharacteristic
42C22×C3×Dic5Q811yescharacteristic
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—21no—
46C2×C3×C4×D5—21no—
47C2×C3×C4×D5C2×C411yescharacteristic
48C2×C3×C4×D5D411yescharacteristic
49C2×C3×C4×D5Q811yescharacteristic
50C2×C3×C4×D5C2311yescharacteristic
51#6763—42no—
52C4⋊ΓL(1,𝔽16)—21no—
53C4⋊ΓL(1,𝔽16)—21no—
54C4⋊ΓL(1,𝔽16)—21no—
55C4⋊ΓL(1,𝔽16)—21no—
56C3×C22⋊AGL(1,𝔽5)—24no—
57C3×C4⋊AGL(1,𝔽5)—21no—
58C3×C4⋊AGL(1,𝔽5)—21no—
59C3×C4⋊AGL(1,𝔽5)D412yes—
60C3×C4⋊AGL(1,𝔽5)D412yes—
61C3×C4×AGL(1,𝔽5)—24no—
62C2×C3⋊#168C2×C411yescharacteristic
63C2×C3⋊#168C2×C411yescharacteristic
64C2×C5×C3⋊C8C2×C411yescharacteristic
65C2×C5×C3⋊C8C2×C411yescharacteristic
66D5×C3⋊C8—21no—
67D5×C3⋊C8—21no—
68D5×C3⋊C8—21no—
69D5×C3⋊C8—21no—
70C2×C3×#117—51no—
71#5212—51no—
72C2×#830—51no—
73C2×#808—51no—
74C2×#807—51no—
75#4529—51no—
76#4529—51no—
77C22×C4×D5C2×D311yescharacteristic
78C2×C22⋊AGL(1,𝔽5)—21no—
79C2×C22⋊AGL(1,𝔽5)—61no—
80#4130—22no—
81#4130—22no—
82C2×C4⋊AGL(1,𝔽5)—31no—
83C2×C4⋊AGL(1,𝔽5)—31no—
84C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
85C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
86C2×C4×AGL(1,𝔽5)—21no—
87C2×C8×D5—31no—
88C2×C8×D5—31no—
89(C2×AGL(1,𝔽5))⋊C4—61no—
90#3994—62no—
91#3993—62no—
92C5×C22⋊C8—31no—
93C22⋊#168—31no—
94#3952—31no—
95#3952—31no—
96#1854—151noSylow
97C23×C3×C5C4⋊C411yescharacteristic
98C22×C3×D5—21no—
99C22×C3×D5—21no—
100C22×C3×D5—21no—
101C22×C3×D5—21no—
102C22×C3×D5—21no—
103C22×C3×D5—21no—
104C22×C3×D5C4⋊C411yescharacteristic
105C22×C3×D5C2×D411yescharacteristic
106C2×ΓL(1,𝔽16)—41no—
107C2×ΓL(1,𝔽16)—41no—
108C2×ΓL(1,𝔽16)—41no—
109C2×ΓL(1,𝔽16)—41no—
110C2×ΓL(1,𝔽16)—41no—
111C2×ΓL(1,𝔽16)—41no—
112C2×C3×AGL(1,𝔽5)—22no—
113C2×C3×AGL(1,𝔽5)—22no—
114C2×C3×AGL(1,𝔽5)—41no—
115C2×C3×AGL(1,𝔽5)—41no—
116C2×C3×AGL(1,𝔽5)—41no—
117C2×C3×AGL(1,𝔽5)—41no—
118C2×C3×C4×C5—21no—
119C2×C3×C4×C5—21no—
120C2×C3×C4×C5C4⋊C411yescharacteristic
121C2×C3×C4×C5C22×C411yescharacteristic
122C2×C3×Dic5—21no—
123C2×C3×Dic5—21no—
124C2×C3×Dic5C4⋊C411yescharacteristic
125C2×C3×Dic5C2×Q811yescharacteristic
126C3×C4×D5—21no—
127C3×C4×D5—21no—
128C3×C4×D5—21no—
129C3×C4×D5—21no—
130C3×C4×D5—21no—
131C3×C4×D5—21no—
132C3×C4×D5C2×D411yescharacteristic
133C3×C4×D5C2×D411yescharacteristic
134C3×C4×D5#4111yescharacteristic
135C3×C4×D5#4111yescharacteristic
136C3⋊#168—21no—
137C3⋊#168—21no—
138C5×C3⋊C8—21no—
139C5×C3⋊C8—21no—
140C23×C3×C4—51no—
141C3×#117—102no—
142C3×#117—102no—
143C2×C3×C4⋊C4—51no—
144C2×C3×C4⋊C4—51no—
145C2×C3×C22⋊C4—101no—
146C2×C3×C42—101no—
147C2×#217—101no—
148C2×C4⋊Dic3—51no—
149C2×C4⋊Dic3—51no—
150C22×C3⋊C8—51no—
151C22×C3⋊C8—51no—
152C3⋊#95—101no—
153#830—51no—
154#830—51no—
155#830—51no—
156#830AGL(1,𝔽5)11yescharacteristic, complemented
157#808—102no—
158#807—102no—
159C23×D5#6711yescharacteristic
160C22×AGL(1,𝔽5)—21no—
161C22×AGL(1,𝔽5)—21no—
162C22×AGL(1,𝔽5)—61no—
163C22×AGL(1,𝔽5)—61no—
164C22×C4×C5C4×D311yescharacteristic
165C22×Dic5Dic611yescharacteristic
166C2×C4×D5—21no—
167C2×C4×D5—21no—
168C2×C4×D5—21no—
169C2×C4×D5—21no—
170C2×C4×D5Dic611yescharacteristic
171C2×C4×D5C4×D311yescharacteristic
172C2×C4×D5#6711yescharacteristic
173C2×C4×D5C22×D311yescharacteristic
174C22⋊AGL(1,𝔽5)—24no—
175C22⋊AGL(1,𝔽5)—122no—
176C4⋊AGL(1,𝔽5)—21no—
177C4⋊AGL(1,𝔽5)—21no—
178C4⋊AGL(1,𝔽5)—61no—
179C4⋊AGL(1,𝔽5)—61no—
180C4⋊AGL(1,𝔽5)—61no—
181C4⋊AGL(1,𝔽5)—61no—
182C4⋊AGL(1,𝔽5)#6712yes—
183C4⋊AGL(1,𝔽5)#6712yes—
184C4×AGL(1,𝔽5)—24no—
185C2×C5×C8—31no—
186C2×C5×C8—31no—
187C2×#168—31no—
188C2×#168—31no—
189C8×D5—61no—
190C8×D5—61no—
191C8×D5—61no—
192C8×D5—61no—
193C2×#117—51no—
194C2×#107—151no—
195C2×#106—151no—
196C2×C22⋊C8—151no—
197#380—151no—
198#340—151no—
199#340—151no—
200C22×C3×C5—21no—
201C22×C3×C5—21no—
202C22×C3×C5—21no—
203C22×C3×C5C2×C4⋊C411yescharacteristic
204C2×C3×D5—21no—
205C2×C3×D5—21no—
206C2×C3×D5—21no—
207C2×C3×D5—41no—
208C2×C3×D5—41no—
209C2×C3×D5—41no—
210C2×C3×D5—41no—
211C2×C3×D5#12011yescharacteristic
212C2×C3×D5#12311yescharacteristic
213C2×C3×D5#13511yescharacteristic
214C2×C3×D5#13511yescharacteristic
215C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
216C2×C3×D5#13711yescharacteristic
217ΓL(1,𝔽16)—81no—
218ΓL(1,𝔽16)—81no—
219C3×AGL(1,𝔽5)—42no—
220C3×AGL(1,𝔽5)—42no—
221C3×C4×C5—21no—
222C3×C4×C5C4×D411yescharacteristic
223C3×C4×C5C4×D411yescharacteristic
224C3×Dic5—21no—
225C3×Dic5C22⋊Q811yescharacteristic
226C3×Dic5C22⋊Q811yescharacteristic
227C24×C3—51no—
228C22×C3×C4—51no—
229C22×C3×C4—51no—
230C22×C3×C4—51no—
231C22×C3×C4—51no—
232C22×C3×C4—51no—
233C22×C3×C4—101no—
234C22×C3×C4—101no—
235C22×C3×C4—101no—
236C22×C3×C4—101no—
237C22×C3×C4—101no—
238C22×C3×C4—101no—
239C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
240C22×Dic3—101no—
241C22×Dic3—101no—
242C3×C4⋊C4—52no—
243C3×C4⋊C4—52no—
244C3×C4⋊C4—101no—
245C3×C4⋊C4—101no—
246C3×C22⋊C4—104no—
247C3×C42—104no—
248#217—202no—
249C4⋊Dic3—101no—
250C4⋊Dic3—101no—
251C4⋊Dic3—101no—
252C4⋊Dic3—101no—
253C2×C3⋊C8—51no—
254C2×C3⋊C8—51no—
255C2×C3⋊C8—101no—
256C2×C3⋊C8—101no—
257C2×C3⋊C8—101no—
258C2×C3⋊C8—101no—
259C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
260C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
261C23×C5Dic3⋊C411yescharacteristic
262C22×D5—21no—
263C22×D5—21no—
264C22×D5—21no—
265C22×D5—21no—
266C22×D5—21no—
267C22×D5—21no—
268C22×D5Dic3⋊C411yescharacteristic
269C22×D5C2×#6711yescharacteristic
270C2×AGL(1,𝔽5)—22no—
271C2×AGL(1,𝔽5)—22no—
272C2×AGL(1,𝔽5)—41no—
273C2×AGL(1,𝔽5)—41no—
274C2×AGL(1,𝔽5)—41no—
275C2×AGL(1,𝔽5)—41no—
276C2×AGL(1,𝔽5)—121no—
277C2×AGL(1,𝔽5)—121no—
278C2×AGL(1,𝔽5)—121no—
279C2×AGL(1,𝔽5)—121no—
280C2×AGL(1,𝔽5)—121no—
281C2×AGL(1,𝔽5)—121no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5Dic3⋊C411yescharacteristic
285C2×C4×C5C2×C4×D311yescharacteristic
286C2×Dic5—21no—
287C2×Dic5—21no—
288C2×Dic5Dic3⋊C411yescharacteristic
289C2×Dic5C2×Dic611yescharacteristic
290C4×D5—21no—
291C4×D5—21no—
292C4×D5—21no—
293C4×D5—21no—
294C4×D5—21no—
295C4×D5—21no—
296C4×D5#23511yescharacteristic
297C4×D5#23511yescharacteristic
298C4×D5C2×#6711yescharacteristic
299C4×D5C2×#6711yescharacteristic
300C5×C8—61no—
301C5×C8—61no—
302#168—61no—
303#168—61no—
304C23×C4—51no—
305C22×C8—151no—
306C22×C8—151no—
307#117—102no—
308#117—102no—
309C2×C4⋊C4—51no—
310C2×C4⋊C4—51no—
311C2×C4⋊C4—151no—
312C2×C4⋊C4—151no—
313C2×C22⋊C4—101no—
314C2×C22⋊C4—301no—
315C2×C42—101no—
316#107—302no—
317#106—302no—
318C22⋊C8—31no—
319C22⋊C8—151no—
320C22⋊C8—151no—
321C22⋊C8—151no—
322#95—301no—
323C2×C3×C5—41no—
324C2×C3×C5#38511yescharacteristic
325C2×C3×C5#42711yescharacteristic
326C2×C3×C5#42811yescharacteristic
327C3×D5—41no—
328C3×D5#44911yescharacteristic
329C3×D5#45211yescharacteristic
330C3×D5#48211yescharacteristic
331C3×D5#48511yescharacteristic
332C23×C3—51no—
333C23×C3—51no—
334C23×C3—101no—
335C23×C3—101no—
336C23×C3—101no—
337C23×C3—101no—
338C23×C3—101no—
339C23×C3—101no—
340C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—51no—
344C2×C3×C4—51no—
345C2×C3×C4—51no—
346C2×C3×C4—51no—
347C2×C3×C4—51no—
348C2×C3×C4—51no—
349C2×C3×C4—101no—
350C2×C3×C4—101no—
351C2×C3×C4—101no—
352C2×C3×C4—101no—
353C2×C3×C4—101no—
354C2×C3×C4—101no—
355C2×C3×C4—101no—
356C2×C3×C4—101no—
357C2×C3×C4—102no—
358C2×C3×C4—102no—
359C2×C3×C4—201no—
360C2×C3×C4—201no—
361C2×C3×C4—201no—
362C2×C3×C4—201no—
363C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
364C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
365C2×Dic3—201no—
366C2×Dic3—201no—
367C2×Dic3—201no—
368C2×Dic3—201no—
369C2×Dic3—201no—
370C2×Dic3—201no—
371C3⋊C8—21no—
372C3⋊C8—21no—
373C3⋊C8—101no—
374C3⋊C8—101no—
375C22×C5—21no—
376C22×C5—21no—
377C22×C5—21no—
378C22×C5C2×Dic3⋊C411yescharacteristic
379C2×D5—21no—
380C2×D5—21no—
381C2×D5—21no—
382C2×D5—41no—
383C2×D5—41no—
384C2×D5—41no—
385C2×D5—41no—
386C2×D5#92911yescharacteristic
387C2×D5#94911yescharacteristic
388C2×D5#95011yescharacteristic
389C2×D5#95011yescharacteristic
390C2×D5#95111yescharacteristic
391C2×D5#95311yescharacteristic
392AGL(1,𝔽5)—42no—
393AGL(1,𝔽5)—42no—
394AGL(1,𝔽5)—241no—
395AGL(1,𝔽5)—241no—
396C4×C5—21no—
397C4×C5C4×#6711yescharacteristic
398C4×C5C4×#6711yescharacteristic
399Dic5—21no—
400Dic5#92411yescharacteristic
401Dic5#92411yescharacteristic
402C24—51no—
403C22×C4—51no—
404C22×C4—51no—
405C22×C4—51no—
406C22×C4—51no—
407C22×C4—51no—
408C22×C4—101no—
409C22×C4—101no—
410C22×C4—101no—
411C22×C4—101no—
412C22×C4—101no—
413C22×C4—101no—
414C22×C4—301no—
415C22×C4—301no—
416C22×C4D3×AGL(1,𝔽5)11yescharacteristic
417C2×C8—31no—
418C2×C8—31no—
419C2×C8—151no—
420C2×C8—151no—
421C2×C8—301no—
422C2×C8—301no—
423C2×C8—301no—
424C2×C8—301no—
425C4⋊C4—52no—
426C4⋊C4—52no—
427C4⋊C4—101no—
428C4⋊C4—101no—
429C4⋊C4—301no—
430C4⋊C4—301no—
431C4⋊C4—301no—
432C4⋊C4—301no—
433C22⋊C4—104no—
434C22⋊C4—602no—
435C42—104no—
436C3×C5#185411yescharacteristic, complemented, Hall
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—51no—
441C22×C3—51no—
442C22×C3—51no—
443C22×C3—51no—
444C22×C3—51no—
445C22×C3—51no—
446C22×C3—101no—
447C22×C3—101no—
448C22×C3—101no—
449C22×C3—201no—
450C22×C3—201no—
451C22×C3—201no—
452C22×C3—201no—
453C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
454C3×C4—21no—
455C3×C4—51no—
456C3×C4—51no—
457C3×C4—101no—
458C3×C4—202no—
459C3×C4—202no—
460C3×C4D4×AGL(1,𝔽5)11yescharacteristic
461C3×C4D4×AGL(1,𝔽5)11yescharacteristic
462Dic3—401no—
463Dic3—401no—
464C2×C5—41no—
465C2×C5#499511yescharacteristic
466C2×C5#499811yescharacteristic
467C2×C5#521011yescharacteristic
468D5—41no—
469D5#499611yescharacteristic
470D5#500311yescharacteristic
471D5#523811yescharacteristic
472D5#523911yescharacteristic
473C23—51no—
474C23—51no—
475C23—101no—
476C23—101no—
477C23—101no—
478C23—101no—
479C23—101no—
480C23—101no—
481C23Dic3⋊AGL(1,𝔽5)11yescharacteristic
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—51no—
485C2×C4—51no—
486C2×C4—51no—
487C2×C4—51no—
488C2×C4—51no—
489C2×C4—51no—
490C2×C4—101no—
491C2×C4—101no—
492C2×C4—101no—
493C2×C4—101no—
494C2×C4—101no—
495C2×C4—101no—
496C2×C4—101no—
497C2×C4—101no—
498C2×C4—102no—
499C2×C4—102no—
500C2×C4—201no—
501C2×C4—201no—
502C2×C4—201no—
503C2×C4—201no—
504C2×C4—601no—
505C2×C4—601no—
506C2×C4—601no—
507C2×C4—601no—
508C2×C4—601no—
509C2×C4—601no—
510C2×C4Dic3⋊AGL(1,𝔽5)11yescharacteristic
511C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
512C8—61no—
513C8—61no—
514C8—301no—
515C8—301no—
516C2×C3—41no—
517C2×C3—51no—
518C2×C3—51no—
519C2×C3—51no—
520C2×C3—51no—
521C2×C3—201no—
522C2×C3#6569911yescharacteristic
523C2×C3#6572111yescharacteristic
524C2×C3#6572711yescharacteristic
525C5#7157611yescharacteristic, complemented, Sylow
526C22—21no—
527C22—21no—
528C22—21no—
529C22—51no—
530C22—51no—
531C22—51no—
532C22—51no—
533C22—51no—
534C22—51no—
535C22—101no—
536C22—101no—
537C22—101no—
538C22—201no—
539C22—201no—
540C22—201no—
541C22—201no—
542C22C2×Dic3⋊AGL(1,𝔽5)11yescharacteristic
543C4—21no—
544C4—51no—
545C4—51no—
546C4—101no—
547C4—202no—
548C4—202no—
549C4—1201no—
550C4—1201no—
551C4AGL(1,𝔽5)×#6711yescharacteristic
552C4AGL(1,𝔽5)×#6711yescharacteristic
553C3#1060391211yescharacteristic, complemented, Sylow
554C2—41no—
555C2—51no—
556C2—51no—
557C2—51no—
558C2—51no—
559C2—201no—
560C2#1175172611yescharacteristic
561C2#1175172811yescharacteristic
562C2#1175202711yescharacteristic
subgroupG/H
centerC22C2×Dic3⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C3×D5D4
cosocleC2×C3×C4×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1854
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
3. C2×#91160C2semidirect
4. C2×#91159C2semidirect
6. #11746529C2semidirect
7. #11746529C2semidirect
24. #91114C4semidirect
25. C5×#830C4semidirect
26. #90955C4semidirect
27. #90955C4semidirect
156. #830AGL(1,𝔽5)semidirect
436. C3×C5#1854semidirect
525. C5#71576semidirect
553. C3#10603912semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41302
#117524242
C2×#911602
C2×#911592
D5×#8302
#117465292
#106039123
#715765