Finite Group Databasebeta

← #14299994

Subgroups — #14299994

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×#91236C211yesmaximal, characteristic
3#11751859C211yesmaximal, characteristic, complemented
4C2×#91160C211yesmaximal, characteristic, complemented
5D5×#832C211yesmaximal, characteristic
6#11746528C211yesmaximal, characteristic, complemented
7(C2×AGL(1,𝔽5))⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10603957—31nomaximal, Hall
9C23×C3×AGL(1,𝔽5)—21no—
10C2×C3×D4×D5C2211yescharacteristic
11C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
12C2×D5⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×C22⋊AGL(1,𝔽5)—21no—
14C3×D4×AGL(1,𝔽5)—22no—
15C3×D4×AGL(1,𝔽5)—22no—
16C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
17C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
18C2×Dic3⋊AGL(1,𝔽5)—21no—
19D5×C4⋊Dic3C2211yescharacteristic
20C2×D5×C3⋊C8C2211yescharacteristic
21#91236—22no—
22(C2×AGL(1,𝔽5))⋊Dic3—21no—
23#91160—22no—
24#91116C411yescharacteristic, complemented
25C5×#832C411yescharacteristic, complemented
26#90965C411yescharacteristic, complemented
27#90964C411yescharacteristic, complemented
28#71606—51nomaximal, Hall
29C2×D4×AGL(1,𝔽5)D311yescharacteristic
30C2×#4007—31no—
31C2×#3994—31no—
32#65712—31no—
33D5×#102—31no—
34(C2×AGL(1,𝔽5))⋊C8—31no—
35#64874—31no—
36C23×C3×D5—21no—
37C22×ΓL(1,𝔽16)—21no—
38C22×C3×AGL(1,𝔽5)—24no—
39C22×C3×AGL(1,𝔽5)—21no—
40C22×C3×AGL(1,𝔽5)—42no—
41C22×C3×AGL(1,𝔽5)—42no—
42C22×C3×AGL(1,𝔽5)D411yescharacteristic
43C22×C3×AGL(1,𝔽5)D411yescharacteristic
44C2×C3×C5×D4C2×C411yescharacteristic
45C2×C3×C22⋊D5—21no—
46C3×D4×D5—21no—
47C3×D4×D5—21no—
48C3×D4×D5D412yes—
49C3×D4×D5Q812yes—
50C2×C3×D20C2×C411yescharacteristic
51C2×C3×C4×D5C2311yescharacteristic
52C2×D5×Dic3—21no—
53C2×C3⋊#170—21no—
54C4⋊ΓL(1,𝔽16)—21no—
55C4⋊ΓL(1,𝔽16)—21no—
56D5⋊(C3⋊C8)—21no—
57D5⋊(C3⋊C8)—21no—
58C3×C22⋊AGL(1,𝔽5)—24no—
59C3×C4⋊AGL(1,𝔽5)—21no—
60C3×C4⋊AGL(1,𝔽5)D412yes—
61C3×C4×AGL(1,𝔽5)—21no—
62C3×C4×AGL(1,𝔽5)—21no—
63Dic3⋊AGL(1,𝔽5)—42no—
64C4⋊Dic15C2×C411yescharacteristic, complemented
65C2×C3⋊#168C2×C411yescharacteristic, complemented
66C5×C4⋊Dic3C2×C411yescharacteristic, complemented
67C2×C5×C3⋊C8C2×C411yescharacteristic, complemented
68#6668—21no—
69D5×C3⋊C8—21no—
70D5×C3⋊C8—21no—
71C2×C3×C4×D4—51no—
72C2×#832—51no—
73C2×#832—51no—
74C2×#807—51no—
75#4928—51no—
76#4529—51no—
77#4524—51no—
78C23×AGL(1,𝔽5)—21no—
79C2×D4×D5C2×D311yescharacteristic
80C2×C22⋊AGL(1,𝔽5)—21no—
81D4×AGL(1,𝔽5)—22no—
82D4×AGL(1,𝔽5)—22no—
83C2×C4⋊AGL(1,𝔽5)—31no—
84C2×C4⋊AGL(1,𝔽5)—61no—
85C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
86C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
87C2×D5⋊C8—31no—
88C2×C8×D5—31no—
89D5×C4⋊C4—31no—
90#4007—62no—
91(C2×AGL(1,𝔽5))⋊C4—61no—
92#3994—62no—
93C5×#102—31no—
94#3964—31no—
95#3953—31no—
96#3941—31no—
97#1862—151noSylow
98C23×C3×C5—21no—
99C22×C3×D5—21no—
100C22×C3×D5—22no—
101C22×C3×D5—22no—
102C22×C3×D5—41no—
103C22×C3×D5—41no—
104C22×C3×D5—41no—
105C22×C3×D5—41no—
106C22×C3×D5C2×D411yescharacteristic
107C2×ΓL(1,𝔽16)—41no—
108C2×ΓL(1,𝔽16)—41no—
109C2×ΓL(1,𝔽16)—41no—
110C2×C3×AGL(1,𝔽5)—21no—
111C2×C3×AGL(1,𝔽5)—21no—
112C2×C3×AGL(1,𝔽5)—21no—
113C2×C3×AGL(1,𝔽5)—22no—
114C2×C3×AGL(1,𝔽5)—21no—
115C2×C3×AGL(1,𝔽5)—21no—
116C2×C3×AGL(1,𝔽5)—48no—
117C2×C3×AGL(1,𝔽5)—41no—
118C2×C3×AGL(1,𝔽5)—41no—
119C2×C3×AGL(1,𝔽5)D812yes—
120C3×C5×D4—21no—
121C3×C5×D4C4⋊C412yescomplemented
122C2×C3×C4×C5C22×C411yescharacteristic
123C2×Dic15—21no—
124C2×C5×Dic3—21no—
125C3×C22⋊D5—22no—
126C3×C22⋊D5—22no—
127C2×C3×Dic5#4111yescharacteristic
128C3×D20—21no—
129C3×D20C4⋊C412yescomplemented
130C3×C4×D5C2×D411yescharacteristic
131C3×C4×D5C2×D411yescharacteristic
132C3×C4×D5C2×Q811yescharacteristic
133C3×C4×D5#4111yescharacteristic
134D5×Dic3—41no—
135D5×Dic3—41no—
136C3⋊#170—41no—
137C3⋊#168—21no—
138C5×C3⋊C8—21no—
139C22×C3×D4—51no—
140C23×C3×C4—101no—
141C3×C4×D4—102no—
142C3×C4×D4—102no—
143C2×C3×C4⋊C4—51no—
144C2×C3×C22⋊C4—101no—
145C2×C3×C42—51no—
146C2×C4⋊Dic3—51no—
147C2×C4⋊Dic3—51no—
148C2×Dic3⋊C4—101no—
149C22×C3⋊C8—51no—
150C22×C3⋊C8—51no—
151#832—51no—
152#832—51no—
153#832—51no—
154#832—102no—
155#832AGL(1,𝔽5)11yescharacteristic, complemented
156C3⋊#95—101no—
157#807—102no—
158C23×D5—21no—
159C22×AGL(1,𝔽5)—24no—
160C22×AGL(1,𝔽5)—21no—
161C22×AGL(1,𝔽5)—42no—
162C22×AGL(1,𝔽5)—42no—
163C22×AGL(1,𝔽5)—61no—
164C22×AGL(1,𝔽5)#6711yescharacteristic
165C22×AGL(1,𝔽5)#6711yescharacteristic
166C2×C5×D4C4×D311yescharacteristic
167C2×C22⋊D5—21no—
168D4×D5—21no—
169D4×D5—21no—
170D4×D5Dic612yes—
171D4×D5#6712yes—
172C2×D20C4×D311yescharacteristic
173C2×C4×D5—61no—
174C2×C4×D5C22×D311yescharacteristic
175C22⋊AGL(1,𝔽5)—24no—
176C2×#170—61no—
177C4⋊AGL(1,𝔽5)—21no—
178C4⋊AGL(1,𝔽5)—61no—
179C4⋊AGL(1,𝔽5)—61no—
180C4⋊AGL(1,𝔽5)—122no—
181C4⋊AGL(1,𝔽5)#6712yes—
182C4×AGL(1,𝔽5)—21no—
183C4×AGL(1,𝔽5)—21no—
184D5⋊C8—61no—
185D5⋊C8—61no—
186C2×C5×C8—31no—
187C5×C4⋊C4—31no—
188C4⋊Dic5—31no—
189#683—61no—
190C2×#168—31no—
191C8×D5—61no—
192C8×D5—61no—
193C2×C4×D4—51no—
194C2×#107—151no—
195C2×#102—151no—
196C2×#102—151no—
197#389—151no—
198#340—151no—
199#336—151no—
200C22×C3×C5—22no—
201C22×C3×C5—41no—
202C22×C3×C5—41no—
203C22×C3×C5C4×D411yescharacteristic
204C2×C3×D5—22no—
205C2×C3×D5—41no—
206C2×C3×D5—41no—
207C2×C3×D5—42no—
208C2×C3×D5—42no—
209C2×C3×D5—42no—
210C2×C3×D5—42no—
211C2×C3×D5#12011yescharacteristic
212C2×C3×D5C22⋊Q811yescharacteristic
213C2×C3×D5C2×D811yescharacteristic
214C2×C3×D5#13511yescharacteristic
215C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
216C2×C3×D5#13711yescharacteristic
217ΓL(1,𝔽16)—81no—
218C3×AGL(1,𝔽5)—22no—
219C3×AGL(1,𝔽5)—42no—
220C3×AGL(1,𝔽5)—41no—
221C3×C4×C5C2×C4⋊C411yescharacteristic
222C3×C4×C5C4×D411yescharacteristic
223Dic15—41no—
224C3×Dic5C22⋊Q811yescharacteristic
225C3×Dic5#12311yescharacteristic
226C5×Dic3—41no—
227C24×C3—101no—
228C2×C3×D4—52no—
229C2×C3×D4—52no—
230C2×C3×D4—51no—
231C2×C3×D4—101no—
232C2×C3×D4—101no—
233C2×C3×D4—101no—
234C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
235C22×C3×C4—51no—
236C22×C3×C4—51no—
237C22×C3×C4—51no—
238C22×C3×C4—101no—
239C22×C3×C4—104no—
240C22×C3×C4—202no—
241C22×C3×C4—202no—
242C22×Dic3—101no—
243C22×Dic3—101no—
244C3×C4⋊C4—52no—
245C3×C4⋊C4—101no—
246C3×C22⋊C4—104no—
247C3×C42—101no—
248C3×C42—101no—
249C4⋊Dic3—51no—
250C4⋊Dic3—101no—
251C4⋊Dic3—101no—
252C4⋊Dic3—101no—
253C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
254Dic3⋊C4—202no—
255C2×C3⋊C8—51no—
256C2×C3⋊C8—101no—
257C2×C3⋊C8—101no—
258C2×C3⋊C8—101no—
259C2×C3⋊C8—101no—
260C2×C3⋊C8—101no—
261C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic, complemented
262C23×C5—21no—
263C22×D5—21no—
264C22×D5—22no—
265C22×D5—22no—
266C22×D5—41no—
267C22×D5—41no—
268C22×D5—41no—
269C22×D5—41no—
270C22×D5C2×#6711yescharacteristic
271C2×AGL(1,𝔽5)—21no—
272C2×AGL(1,𝔽5)—21no—
273C2×AGL(1,𝔽5)—21no—
274C2×AGL(1,𝔽5)—21no—
275C2×AGL(1,𝔽5)—21no—
276C2×AGL(1,𝔽5)—22no—
277C2×AGL(1,𝔽5)—48no—
278C2×AGL(1,𝔽5)—41no—
279C2×AGL(1,𝔽5)—41no—
280C2×AGL(1,𝔽5)—121no—
281C2×AGL(1,𝔽5)—121no—
282C2×AGL(1,𝔽5)—121no—
283C2×AGL(1,𝔽5)#21312yes—
284C5×D4—21no—
285C5×D4Dic3⋊C412yescomplemented
286C2×C4×C5—61no—
287C2×C4×C5C2×C4×D311yescharacteristic
288C22⋊D5—22no—
289C22⋊D5—22no—
290C2×Dic5—61no—
291C2×Dic5#23511yescharacteristic
292D20—21no—
293D20Dic3⋊C412yescomplemented
294C4×D5—121no—
295C4×D5—121no—
296C4×D5C2×Dic611yescharacteristic
297C4×D5#23511yescharacteristic
298C4×D5C2×#6711yescharacteristic
299C4×D5C2×#6711yescharacteristic
300#170—121no—
301C5×C8—61no—
302#168—61no—
303C22×D4—51no—
304C23×C4—101no—
305C22×C8—151no—
306C22×C8—151no—
307C4×D4—102no—
308C4×D4—102no—
309C2×C4⋊C4—51no—
310C2×C4⋊C4—151no—
311C2×C4⋊C4—151no—
312C2×C4⋊C4—301no—
313C2×C22⋊C4—101no—
314C2×C42—51no—
315#107—302no—
316#102—31no—
317#102—151no—
318#102—151no—
319#102—151no—
320#102—302no—
321#95—301no—
322C2×C3×C5—42no—
323C2×C3×C5#38511yescharacteristic
324C2×C3×C5C4×D811yescharacteristic
325C2×C3×C5#44011yescharacteristic
326C3×D5—42no—
327C3×D5#44711yescharacteristic
328C3×D5#45211yescharacteristic
329C3×D5#47411yescharacteristic
330C3×D5#47811yescharacteristic
331C23×C3—21no—
332C23×C3—51no—
333C23×C3—102no—
334C23×C3—102no—
335C23×C3—101no—
336C23×C3—201no—
337C23×C3—201no—
338C23×C3—201no—
339C23×C3—201no—
340C3×D4—21no—
341C3×D4—52no—
342C3×D4—102no—
343C3×D4—102no—
344C3×D4—101no—
345C3×D4C4⋊AGL(1,𝔽5)12yescomplemented
346C2×C3×C4—51no—
347C2×C3×C4—51no—
348C2×C3×C4—51no—
349C2×C3×C4—51no—
350C2×C3×C4—51no—
351C2×C3×C4—52no—
352C2×C3×C4—101no—
353C2×C3×C4—101no—
354C2×C3×C4—101no—
355C2×C3×C4—102no—
356C2×C3×C4—101no—
357C2×C3×C4—101no—
358C2×C3×C4—208no—
359C2×C3×C4—201no—
360C2×C3×C4—201no—
361C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
362C2×Dic3—21no—
363C2×Dic3—101no—
364C2×Dic3—201no—
365C2×Dic3—201no—
366C2×Dic3—201no—
367C2×Dic3—201no—
368C2×Dic3—201no—
369C3⋊C8—21no—
370C3⋊C8—101no—
371C3⋊C8—201no—
372C22×C5—22no—
373C22×C5—41no—
374C22×C5—41no—
375C22×C5C4×#6711yescharacteristic
376C2×D5—22no—
377C2×D5—41no—
378C2×D5—41no—
379C2×D5—42no—
380C2×D5—42no—
381C2×D5—42no—
382C2×D5—42no—
383C2×D5#92411yescharacteristic
384C2×D5C2×#21311yescharacteristic
385C2×D5#93211yescharacteristic
386C2×D5#95011yescharacteristic
387C2×D5#95111yescharacteristic
388C2×D5#95311yescharacteristic
389AGL(1,𝔽5)—22no—
390AGL(1,𝔽5)—42no—
391AGL(1,𝔽5)—41no—
392AGL(1,𝔽5)—241no—
393C4×C5—121no—
394C4×C5C2×Dic3⋊C411yescharacteristic
395C4×C5C4×#6711yescharacteristic
396Dic5—121no—
397Dic5#92411yescharacteristic
398Dic5#92911yescharacteristic
399C24—101no—
400C2×D4—52no—
401C2×D4—52no—
402C2×D4—51no—
403C2×D4—101no—
404C2×D4—101no—
405C2×D4—101no—
406C2×D4D3×AGL(1,𝔽5)11yescharacteristic
407C22×C4—51no—
408C22×C4—51no—
409C22×C4—51no—
410C22×C4—101no—
411C22×C4—104no—
412C22×C4—202no—
413C22×C4—202no—
414C22×C4—301no—
415C22×C4—301no—
416C2×C8—31no—
417C2×C8—151no—
418C2×C8—301no—
419C2×C8—301no—
420C2×C8—301no—
421C2×C8—301no—
422C2×C8—301no—
423C4⋊C4—31no—
424C4⋊C4—52no—
425C4⋊C4—101no—
426C4⋊C4—151no—
427C4⋊C4—301no—
428C4⋊C4—301no—
429C4⋊C4—301no—
430C4⋊C4—602no—
431C22⋊C4—104no—
432C42—101no—
433C42—101no—
434C3×C5#186211yescharacteristic, complemented, Hall
435C22×C3—22no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—51no—
439C22×C3—51no—
440C22×C3—51no—
441C22×C3—51no—
442C22×C3—51no—
443C22×C3—51no—
444C22×C3—102no—
445C22×C3—202no—
446C22×C3—202no—
447C22×C3—202no—
448C22×C3—202no—
449C22×C3—201no—
450C22×C3—201no—
451C22×C3D4×AGL(1,𝔽5)11yescharacteristic
452C3×C4—51no—
453C3×C4—51no—
454C3×C4—102no—
455C3×C4—201no—
456C3×C4—202no—
457C3×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
458C3×C4D4×AGL(1,𝔽5)11yescharacteristic
459Dic3—41no—
460Dic3—201no—
461Dic3—401no—
462C2×C5—42no—
463C2×C5C4×#21311yescharacteristic
464C2×C5#501811yescharacteristic
465C2×C5#521011yescharacteristic
466D5—42no—
467D5#500711yescharacteristic
468D5#500911yescharacteristic
469D5#521711yescharacteristic
470D5#523911yescharacteristic
471C23—21no—
472C23—51no—
473C23—102no—
474C23—102no—
475C23—101no—
476C23—201no—
477C23—201no—
478C23—201no—
479C23—201no—
480D4—21no—
481D4—52no—
482D4—102no—
483D4—102no—
484D4—101no—
485D4Dic3⋊AGL(1,𝔽5)12yescomplemented
486C2×C4—51no—
487C2×C4—51no—
488C2×C4—51no—
489C2×C4—51no—
490C2×C4—51no—
491C2×C4—52no—
492C2×C4—61no—
493C2×C4—101no—
494C2×C4—101no—
495C2×C4—101no—
496C2×C4—102no—
497C2×C4—101no—
498C2×C4—101no—
499C2×C4—208no—
500C2×C4—201no—
501C2×C4—201no—
502C2×C4—301no—
503C2×C4—601no—
504C2×C4—601no—
505C2×C4—601no—
506C2×C4—601no—
507C2×C4—601no—
508C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
509C8—61no—
510C8—301no—
511C8—601no—
512C2×C3—42no—
513C2×C3—51no—
514C2×C3—51no—
515C2×C3—51no—
516C2×C3—51no—
517C2×C3—202no—
518C2×C3#6569911yescharacteristic
519C2×C3D8×AGL(1,𝔽5)11yescharacteristic
520C2×C3#6573511yescharacteristic
521C5#7160611yescharacteristic, complemented, Sylow
522C22—22no—
523C22—41no—
524C22—41no—
525C22—51no—
526C22—51no—
527C22—51no—
528C22—51no—
529C22—51no—
530C22—51no—
531C22—102no—
532C22—202no—
533C22—202no—
534C22—202no—
535C22—202no—
536C22—201no—
537C22—201no—
538C22AGL(1,𝔽5)×#6711yescharacteristic
539C4—51no—
540C4—51no—
541C4—102no—
542C4—121no—
543C4—201no—
544C4—202no—
545C4—601no—
546C4—1201no—
547C4C2×Dic3⋊AGL(1,𝔽5)11yescharacteristic
548C4AGL(1,𝔽5)×#6711yescharacteristic
549C3#1060395711yescharacteristic, complemented, Sylow
550C2—42no—
551C2—51no—
552C2—51no—
553C2—51no—
554C2—51no—
555C2—202no—
556C2AGL(1,𝔽5)×#21311yescharacteristic
557C2#1175194411yescharacteristic
558C2#1175202711yescharacteristic
subgroupG/H
centerC22AGL(1,𝔽5)×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×D4×D5C22
cosocleC2×C3×C4×D5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1862
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
3. #11751859C2semidirect
4. C2×#91160C2semidirect
6. #11746528C2semidirect
7. (C2×AGL(1,𝔽5))⋊(C3⋊C8)C2semidirect
24. #91116C4semidirect
25. C5×#832C4semidirect
26. #90965C4semidirect
27. #90964C4semidirect
64. C4⋊Dic15C2×C4semidirect
65. C2×C3⋊#168C2×C4semidirect
66. C5×C4⋊Dic3C2×C4semidirect
67. C2×C5×C3⋊C8C2×C4semidirect
121. C3×C5×D4C4⋊C4semidirect
129. C3×D20C4⋊C4semidirect
155. #832AGL(1,𝔽5)semidirect
253. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
261. C2×C3⋊C8C2×AGL(1,𝔽5)semidirect
285. C5×D4Dic3⋊C4semidirect
293. D20Dic3⋊C4semidirect
345. C3×D4C4⋊AGL(1,𝔽5)semidirect
434. C3×C5#1862semidirect
485. D4Dic3⋊AGL(1,𝔽5)semidirect
521. C5#71606semidirect
549. C3#10603957semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×AGL(1,𝔽5)2
C2×#912362
#117518592
C2×#911602
D5×#8322
#117465282
(C2×AGL(1,𝔽5))⋊(C3⋊C8)2
#106039573
#716065