Finite Group Databasebeta

← #14299506

Subgroups — #14299506

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×#91907C211yesmaximal, characteristic
2C2×C3×#3993C211yesmaximal, characteristic, complemented
3#11751855C211yesmaximal, characteristic
4C2×#91160C211yesmaximal, characteristic, complemented
5D5×(C2×D3)⋊C8C211yesmaximal, characteristic
6#11746764C211yesmaximal, characteristic, complemented
7#11746529C211yesmaximal, characteristic, complemented
8#10603912—31nomaximal, Hall
9C2×C4×D3×D5C2211yescharacteristic
10C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
11C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
12C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
13C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
14C2×(C2×D3)⋊AGL(1,𝔽5)—21no—
15C2×(C2×D3)⋊AGL(1,𝔽5)—21no—
16C2×Dic3×AGL(1,𝔽5)—21no—
17#91907—22no—
18#91907—22no—
19C2×C3×C8×D5C2211yescharacteristic
20C2×D5×C3⋊C8C2211yescharacteristic
21C3×#3993—22no—
22(C2×AGL(1,𝔽5))⋊Dic3—21no—
23#91160—22no—
24#91104C411yescharacteristic, complemented
25C5×(C2×D3)⋊C8C411yescharacteristic, complemented
26#90957C411yescharacteristic, complemented
27(C2×D3)⋊#168C411yescharacteristic, complemented
28#70580—51nomaximal, Hall
29C2×#4130—31no—
30#65765—31no—
31C2×#3994—31no—
32C2×#3993D311yescharacteristic, complemented
33D5×C22⋊C8—31no—
34#64893—31no—
35#64893—31no—
36C22×D3×D5D411yescharacteristic
37C22×ΓL(1,𝔽16)—21no—
38C22×ΓL(1,𝔽16)—21no—
39C22×C3×AGL(1,𝔽5)—21no—
40C22×C3×AGL(1,𝔽5)—21no—
41C2×C4×D15C2×C411yescharacteristic
42C2×C4×C5×D3C2×C411yescharacteristic
43C2×C3×C4×D5C2311yescharacteristic
44C2×#1200Q811yescharacteristic
45C2×D3×Dic5Q811yescharacteristic
46C2×D5×Dic3D411yescharacteristic
47C4×D3×D5—21no—
48C4×D3×D5—21no—
49C4×D3×D5—21no—
50C4×D3×D5—21no—
51C4⋊ΓL(1,𝔽16)—21no—
52C4⋊ΓL(1,𝔽16)—21no—
53C4⋊ΓL(1,𝔽16)—21no—
54C4⋊ΓL(1,𝔽16)D412yes—
55C3×C4⋊AGL(1,𝔽5)—21no—
56C3×C4⋊AGL(1,𝔽5)—21no—
57C3×C4⋊AGL(1,𝔽5)—21no—
58C3×C4⋊AGL(1,𝔽5)D412yes—
59(C2×D3)⋊AGL(1,𝔽5)—24no—
60(C2×D3)⋊AGL(1,𝔽5)—42no—
61Dic3×AGL(1,𝔽5)—24no—
62C2×C3×C5×C8C2×C411yescharacteristic
63C2×C3⋊#168C2×C411yescharacteristic
64C2×C5×C3⋊C8C2×C411yescharacteristic
65C2×C3×#168C2×C411yescharacteristic
66C3×C8×D5—21no—
67C3×C8×D5—21no—
68D5×C3⋊C8—21no—
69D5×C3⋊C8—21no—
70C2×#892—51no—
71C2×C3×#106—51no—
72C2×(C2×D3)⋊C8—51no—
73#4987—51no—
74C2×#807—51no—
75#4551—51no—
76#4529—51no—
77C22×C4×D5—31no—
78C2×C22⋊AGL(1,𝔽5)—61no—
79C2×C22⋊AGL(1,𝔽5)—61no—
80#4130—62no—
81#4130—62no—
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)—61no—
87C2×C8×D5—31no—
88C2×C8×D5C2×D311yescharacteristic
89(C2×AGL(1,𝔽5))⋊C4—61no—
90#3994—62no—
91#3993—22no—
92C5×C22⋊C8—31no—
93C22⋊#168—31no—
94#3952—31no—
95#3952—31no—
96#1854—151noSylow
97C22×D15C4⋊C411yescharacteristic
98C22×C5×D3C4⋊C411yescharacteristic
99C22×C3×D5C2×D411yescharacteristic
100C2×D3×D5—21no—
101C2×D3×D5—21no—
102C2×D3×D5—21no—
103C2×D3×D5—21no—
104C2×D3×D5—21no—
105C2×D3×D5—21no—
106C2×ΓL(1,𝔽16)—22no—
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)—41no—
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×C5C22×C411yescharacteristic
119C2×Dic15C4⋊C411yescharacteristic
120C4×D15—21no—
121C4×D15—21no—
122C2×C5×Dic3C4⋊C411yescharacteristic
123C4×C5×D3—21no—
124C4×C5×D3—21no—
125C2×C3×Dic5C2×Q811yescharacteristic
126C3×C4×D5C2×D411yescharacteristic
127C3×C4×D5C2×D411yescharacteristic
128C3×C4×D5#4111yescharacteristic
129C3×C4×D5#4111yescharacteristic
130#1200—21no—
131#1200—21no—
132D3×Dic5—21no—
133D3×Dic5—21no—
134D5×Dic3—21no—
135D5×Dic3—21no—
136C3×C5×C8—21no—
137C3⋊#168—21no—
138C3×#168—21no—
139C5×C3⋊C8—21no—
140C22×C4×D3—51no—
141C22×C3×C8—51no—
142C2×C3×C4⋊C4—51no—
143C2×C3×C4⋊C4—51no—
144C2×(C2×D3)⋊C4—101no—
145C2×(C2×D3)⋊C4—101no—
146C2×C4⋊Dic3—51no—
147C2×C4⋊Dic3—51no—
148C2×C4×Dic3—101no—
149C22×C3⋊C8—51no—
150#892—102no—
151#892—102no—
152C3×#106—102no—
153C3⋊#95—101no—
154(C2×D3)⋊C8—51no—
155(C2×D3)⋊C8—51no—
156(C2×D3)⋊C8—51no—
157(C2×D3)⋊C8AGL(1,𝔽5)11yescharacteristic, complemented
158#807—102no—
159C23×D5—31no—
160C22×AGL(1,𝔽5)—21no—
161C22×AGL(1,𝔽5)—21no—
162C22×AGL(1,𝔽5)—61no—
163C22×AGL(1,𝔽5)—61no—
164C22×C4×C5—31no—
165C22×Dic5—31no—
166C2×C4×D5—31no—
167C2×C4×D5—31no—
168C2×C4×D5—31no—
169C2×C4×D5—61no—
170C2×C4×D5—61no—
171C2×C4×D5—61no—
172C2×C4×D5—61no—
173C2×C4×D5C22×D311yescharacteristic
174C22⋊AGL(1,𝔽5)—64no—
175C22⋊AGL(1,𝔽5)—122no—
176C4⋊AGL(1,𝔽5)—21no—
177C4⋊AGL(1,𝔽5)—21no—
178C4⋊AGL(1,𝔽5)—21no—
179C4⋊AGL(1,𝔽5)—32no—
180C4⋊AGL(1,𝔽5)—61no—
181C4⋊AGL(1,𝔽5)—61no—
182C4⋊AGL(1,𝔽5)—61no—
183C4⋊AGL(1,𝔽5)#6712yes—
184C4×AGL(1,𝔽5)—64no—
185C2×C5×C8—31no—
186C2×C5×C8C4×D311yescharacteristic
187C2×#168—31no—
188C2×#168C4×D311yescharacteristic
189C8×D5—21no—
190C8×D5—21no—
191C8×D5—61no—
192C8×D5—61no—
193C2×#117—151no—
194C2×#107—151no—
195C2×#106—51no—
196C2×C22⋊C8—151no—
197#380—151no—
198#340—151no—
199#340—151no—
200C22×C3×C5C2×C4⋊C411yescharacteristic
201C2×D15—21no—
202C2×D15—21no—
203C2×D15—21no—
204C2×C5×D3—21no—
205C2×C5×D3—21no—
206C2×C5×D3—21no—
207C2×C3×D5#12011yescharacteristic
208C2×C3×D5#12311yescharacteristic
209C2×C3×D5#13511yescharacteristic
210C2×C3×D5#13511yescharacteristic
211C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
212C2×C3×D5#13711yescharacteristic
213D3×D5—41no—
214D3×D5—41no—
215D3×D5—41no—
216D3×D5—41no—
217ΓL(1,𝔽16)—42no—
218ΓL(1,𝔽16)—81no—
219C3×AGL(1,𝔽5)—42no—
220C3×AGL(1,𝔽5)—81no—
221C3×C4×C5C4×D411yescharacteristic
222C3×C4×C5C4×D411yescharacteristic
223Dic15—21no—
224C3×Dic5C22⋊Q811yescharacteristic
225C3×Dic5C22⋊Q811yescharacteristic
226C5×Dic3—21no—
227C23×D3—51no—
228C22×C3×C4—51no—
229C22×C3×C4—101no—
230C22×C3×C4—101no—
231C22×Dic3—51no—
232C22×Dic3—101no—
233C22×Dic3—101no—
234C2×C4×D3—51no—
235C2×C4×D3—51no—
236C2×C4×D3—51no—
237C2×C4×D3—101no—
238C2×C4×D3—101no—
239C2×C4×D3—101no—
240C2×C4×D3—101no—
241C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
242C2×C3×C8—51no—
243C2×C3×C8—101no—
244C2×C3×C8—101no—
245C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
246C3×C4⋊C4—52no—
247C3×C4⋊C4—101no—
248C3×C4⋊C4—101no—
249C3×C4⋊C4—101no—
250(C2×D3)⋊C4—104no—
251(C2×D3)⋊C4—202no—
252C4⋊Dic3—52no—
253C4⋊Dic3—101no—
254C4⋊Dic3—101no—
255C4⋊Dic3—101no—
256C4×Dic3—104no—
257C2×C3⋊C8—51no—
258C2×C3⋊C8—101no—
259C2×C3⋊C8—101no—
260C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
261C23×C5—31no—
262C22×D5—31no—
263C22×D5—61no—
264C22×D5—61no—
265C22×D5—61no—
266C22×D5—61no—
267C22×D5—61no—
268C22×D5—61no—
269C22×D5D3×D411yescharacteristic
270C2×AGL(1,𝔽5)—22no—
271C2×AGL(1,𝔽5)—41no—
272C2×AGL(1,𝔽5)—41no—
273C2×AGL(1,𝔽5)—41no—
274C2×AGL(1,𝔽5)—41no—
275C2×AGL(1,𝔽5)—41no—
276C2×AGL(1,𝔽5)—62no—
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—31no—
283C2×C4×C5—61no—
284C2×C4×C5—61no—
285C2×C4×C5C2×C4×D311yescharacteristic
286C2×Dic5—31no—
287C2×Dic5—61no—
288C2×Dic5—61no—
289C2×Dic5D3×Q811yescharacteristic
290C4×D5—61no—
291C4×D5—61no—
292C4×D5—61no—
293C4×D5—61no—
294C4×D5—61no—
295C4×D5—61no—
296C4×D5#23511yescharacteristic
297C4×D5D3×D411yescharacteristic
298C4×D5#23911yescharacteristic
299C4×D5C2×#6711yescharacteristic
300C5×C8—21no—
301C5×C8—61no—
302#168—21no—
303#168—61no—
304C23×C4—151no—
305C22×C8—51no—
306C22×C8—151no—
307#117—302no—
308#117—302no—
309C2×C4⋊C4—51no—
310C2×C4⋊C4—51no—
311C2×C4⋊C4—151no—
312C2×C4⋊C4—151no—
313C2×C22⋊C4—301no—
314C2×C22⋊C4—301no—
315C2×C42—301no—
316#107—302no—
317#106—102no—
318C22⋊C8—31no—
319C22⋊C8—151no—
320C22⋊C8—151no—
321C22⋊C8—151no—
322#95—301no—
323C2×C3×C5#38511yescharacteristic
324C2×C3×C5#42711yescharacteristic
325C2×C3×C5#42811yescharacteristic
326D15—41no—
327C3×D5#44911yescharacteristic
328C3×D5#45211yescharacteristic
329C3×D5#48211yescharacteristic
330C3×D5#48511yescharacteristic
331C5×D3—41no—
332C23×C3—51no—
333C22×D3—51no—
334C22×D3—101no—
335C22×D3—101no—
336C22×D3—101no—
337C22×D3—101no—
338C22×D3—101no—
339C22×D3—101no—
340C22×D3C4⋊AGL(1,𝔽5)11yescharacteristic
341C2×C3×C4—51no—
342C2×C3×C4—51no—
343C2×C3×C4—51no—
344C2×C3×C4—51no—
345C2×C3×C4—51no—
346C2×C3×C4—102no—
347C2×C3×C4—201no—
348C2×C3×C4—201no—
349C2×C3×C4—201no—
350C2×C3×C4—201no—
351C2×C3×C4—201no—
352C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
353C2×Dic3—51no—
354C2×Dic3—101no—
355C2×Dic3—101no—
356C2×Dic3—102no—
357C2×Dic3—201no—
358C2×Dic3—201no—
359C2×Dic3—201no—
360C2×Dic3—201no—
361C2×Dic3—201no—
362C2×Dic3C4⋊AGL(1,𝔽5)11yescharacteristic
363C4×D3—21no—
364C4×D3—21no—
365C4×D3—101no—
366C4×D3—101no—
367C4×D3—101no—
368C4×D3—101no—
369C4×D3—101no—
370C4×D3—101no—
371C3×C8—21no—
372C3×C8—101no—
373C3⋊C8—21no—
374C3⋊C8—101no—
375C22×C5—61no—
376C22×C5—61no—
377C22×C5—61no—
378C22×C5D3×C4⋊C411yescharacteristic
379C2×D5—61no—
380C2×D5—61no—
381C2×D5—61no—
382C2×D5—121no—
383C2×D5—121no—
384C2×D5—121no—
385C2×D5—121no—
386C2×D5#89411yescharacteristic
387C2×D5#91411yescharacteristic
388C2×D5#91511yescharacteristic
389C2×D5#91611yescharacteristic
390C2×D5#91611yescharacteristic
391C2×D5#93711yescharacteristic
392AGL(1,𝔽5)—42no—
393AGL(1,𝔽5)—81no—
394AGL(1,𝔽5)—122no—
395AGL(1,𝔽5)—241no—
396C4×C5—61no—
397C4×C5#89311yescharacteristic
398C4×C5C4×#6711yescharacteristic
399Dic5—61no—
400Dic5#89611yescharacteristic
401Dic5#94611yescharacteristic
402C24—151no—
403C22×C4—31no—
404C22×C4—51no—
405C22×C4—101no—
406C22×C4—101no—
407C22×C4—151no—
408C22×C4—151no—
409C22×C4—151no—
410C22×C4—151no—
411C22×C4—301no—
412C22×C4—301no—
413C22×C4—301no—
414C22×C4—301no—
415C22×C4—301no—
416C22×C4—301no—
417C2×C8—31no—
418C2×C8—51no—
419C2×C8—101no—
420C2×C8—101no—
421C2×C8—151no—
422C2×C8—301no—
423C2×C8—301no—
424C2×C8D3×AGL(1,𝔽5)11yescharacteristic
425C4⋊C4—52no—
426C4⋊C4—101no—
427C4⋊C4—101no—
428C4⋊C4—101no—
429C4⋊C4—152no—
430C4⋊C4—301no—
431C4⋊C4—301no—
432C4⋊C4—301no—
433C22⋊C4—304no—
434C22⋊C4—602no—
435C42—304no—
436C3×C5#185411yescharacteristic, complemented, Hall
437C22×C3—51no—
438C22×C3—51no—
439C22×C3—51no—
440C22×C3—51no—
441C22×C3—51no—
442C22×C3—51no—
443C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
444C2×D3—21no—
445C2×D3—21no—
446C2×D3—21no—
447C2×D3—101no—
448C2×D3—101no—
449C2×D3—101no—
450C2×D3—201no—
451C2×D3—201no—
452C2×D3—201no—
453C2×D3—201no—
454C3×C4—51no—
455C3×C4—51no—
456C3×C4—202no—
457C3×C4—401no—
458C3×C4D4×AGL(1,𝔽5)11yescharacteristic
459C3×C4D4×AGL(1,𝔽5)11yescharacteristic
460Dic3—21no—
461Dic3—101no—
462Dic3—202no—
463Dic3—401no—
464C2×C5—121no—
465C2×C5#486011yescharacteristic
466C2×C5#486111yescharacteristic
467C2×C5#498911yescharacteristic
468D5—121no—
469D5#486611yescharacteristic
470D5#486811yescharacteristic
471D5#517211yescharacteristic
472D5#517311yescharacteristic
473C23—31no—
474C23—51no—
475C23—151no—
476C23—301no—
477C23—301no—
478C23—301no—
479C23—301no—
480C23—301no—
481C23—301no—
482C2×C4—31no—
483C2×C4—51no—
484C2×C4—51no—
485C2×C4—51no—
486C2×C4—51no—
487C2×C4—51no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—102no—
491C2×C4—151no—
492C2×C4—201no—
493C2×C4—201no—
494C2×C4—201no—
495C2×C4—201no—
496C2×C4—201no—
497C2×C4—301no—
498C2×C4—301no—
499C2×C4—301no—
500C2×C4—301no—
501C2×C4—301no—
502C2×C4—301no—
503C2×C4—301no—
504C2×C4—301no—
505C2×C4—302no—
506C2×C4—601no—
507C2×C4—601no—
508C2×C4—601no—
509C2×C4—601no—
510C2×C4—601no—
511C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
512C8—21no—
513C8—61no—
514C8—101no—
515C8—301no—
516C2×C3—51no—
517C2×C3—51no—
518C2×C3—51no—
519C2×C3—51no—
520C2×C3#6569911yescharacteristic
521C2×C3#6572111yescharacteristic
522C2×C3#6572711yescharacteristic
523D3—41no—
524D3—201no—
525C5#7058011yescharacteristic, complemented, Sylow
526C22—51no—
527C22—51no—
528C22—51no—
529C22—51no—
530C22—51no—
531C22—51no—
532C22—61no—
533C22—61no—
534C22—61no—
535C22—301no—
536C22—301no—
537C22—301no—
538C22—601no—
539C22—601no—
540C22—601no—
541C22—601no—
542C22D3×C4⋊AGL(1,𝔽5)11yescharacteristic
543C4—51no—
544C4—51no—
545C4—61no—
546C4—202no—
547C4—301no—
548C4—401no—
549C4—602no—
550C4—1201no—
551C4#9192111yescharacteristic
552C4AGL(1,𝔽5)×#6711yescharacteristic
553C3#1060391211yescharacteristic, complemented, Sylow
554C2—51no—
555C2—51no—
556C2—51no—
557C2—51no—
558C2—121no—
559C2—601no—
560C2#1175165311yescharacteristic
561C2#1175165711yescharacteristic
562C2#1175193211yescharacteristic
subgroupG/H
centerC22D3×C4⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC22×D3×D5D4
cosocleC2×C3×C4×D5C23
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5#1854
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3993C2semidirect
4. C2×#91160C2semidirect
6. #11746764C2semidirect
7. #11746529C2semidirect
24. #91104C4semidirect
25. C5×(C2×D3)⋊C8C4semidirect
26. #90957C4semidirect
27. (C2×D3)⋊#168C4semidirect
32. C2×#3993D3semidirect
157. (C2×D3)⋊C8AGL(1,𝔽5)semidirect
436. C3×C5#1854semidirect
525. C5#70580semidirect
553. C3#10603912semidirect

Maximal subgroups

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

subgroupindex
C2×#919072
C2×C3×#39932
#117518552
C2×#911602
D5×(C2×D3)⋊C82
#117467642
#117465292
#106039123
#705805