Finite Group Databasebeta

← #14301625

Subgroups — #14301625

Order 1920.

1156 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756987C211yesmaximal, characteristic, complemented
2C3×D5×#120C211yesmaximal, characteristic
3#11752459C212yesmaximal, complemented
4D5⋊#834C211yesmaximal, characteristic, complemented
5#11746737C212yesmaximal, complemented
6#10604461—31nomaximal, Hall
7C24×C3×D5C2211yescharacteristic
8C2×C3×D4×D5—21no—
9C2×C3×D4×D5C2211yescharacteristic
10C2×#6763—21no—
11C2×#6763—24no—
12C2×#6763C2212yes—
13C2×#6763C2212yes—
14D4×ΓL(1,𝔽16)—24no—
15#91989—21no—
16C3×C5×#120C411yescharacteristic, complemented
17C3×#4099C411yescharacteristic, complemented
18C3×#4083—21no—
19C3×#4083C411yescharacteristic, complemented
20C3×#4028—21no—
21C3×#4028C411yescharacteristic, complemented
22C3×D5×C22⋊C4—21no—
23C3×D5×C22⋊C4C2211yescharacteristic
24#91240—21no—
25#91228—21no—
26#71669—51nomaximal, Hall
27#66258—31no—
28D5×#120D311yescharacteristic
29#65800—32no—
30D5⋊#99—31no—
31#64866—32no—
32C24×C3×C5C2×C411yescharacteristic, complemented
33C23×C3×D5—22no—
34C23×C3×D5—21no—
35C23×C3×D5—21no—
36C23×C3×D5—22no—
37C23×C3×D5—44no—
38C23×C3×D5C2×C411yescharacteristic, complemented
39C23×C3×D5D411yescharacteristic
40C23×C3×D5C2311yescharacteristic
41C22×ΓL(1,𝔽16)—22no—
42C22×ΓL(1,𝔽16)—22no—
43C22×ΓL(1,𝔽16)D414yescomplemented
44C2×C3×C5×D4—21no—
45C2×C3×C5×D4C2×C411yescharacteristic
46C2×C3×C22⋊D5—21no—
47C2×C3×C22⋊D5—21no—
48C2×C3×C22⋊D5C2×C411yescharacteristic
49C2×C3×C22⋊D5D411yescharacteristic
50C3×D4×D5—22no—
51C3×D4×D5—22no—
52C3×D4×D5—44no—
53C2×C3×D20—21no—
54C2×C3×D20D411yescharacteristic
55C2×C3×C4×D5—21no—
56C2×C3×C4×D5D411yescharacteristic
57#6763—22no—
58#6763—22no—
59#6763—22no—
60#6763—22no—
61#6763—22no—
62#6763—48no—
63C4⋊ΓL(1,𝔽16)—22no—
64C4×ΓL(1,𝔽16)—22no—
65C3×C5×C22⋊C4—21no—
66C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
67C3×C22⋊Dic5—21no—
68C3×C22⋊Dic5C2×C411yescharacteristic, complemented
69C3×#685—21no—
70C3×#685—21no—
71C3×#685—21no—
72C2×C3×#120—51no—
73#5798—51no—
74#5247—52no—
75C2×#834—51no—
76#4527—52no—
77C24×D5C2×D311yescharacteristic
78C2×D4×D5—21no—
79C2×D4×D5C2×D311yescharacteristic
80C2×C22⋊AGL(1,𝔽5)—32no—
81C2×C22⋊AGL(1,𝔽5)—32no—
82C2×C22⋊AGL(1,𝔽5)—61no—
83C2×C22⋊AGL(1,𝔽5)—64no—
84D4×AGL(1,𝔽5)—64no—
85#4130—61no—
86C5×#120Dic311yescharacteristic, complemented
87#4099Dic311yescharacteristic, complemented
88#4083—21no—
89#4083Dic311yescharacteristic, complemented
90#4028—21no—
91#4028Dic311yescharacteristic, complemented
92D5×C22⋊C4—21no—
93D5×C22⋊C4C2×D311yescharacteristic
94#4011—61no—
95#3999—61no—
96#1889—151noSylow
97C23×C3×C5—21no—
98C23×C3×C5—22no—
99C23×C3×C5—42no—
100C23×C3×C5C22⋊C411yescharacteristic, complemented
101C23×C3×C5C22×C411yescharacteristic
102C22×C3×D5—28no—
103C22×C3×D5—24no—
104C22×C3×D5—21no—
105C22×C3×D5—22no—
106C22×C3×D5—21no—
107C22×C3×D5—21no—
108C22×C3×D5—42no—
109C22×C3×D5—42no—
110C22×C3×D5—42no—
111C22×C3×D5—44no—
112C22×C3×D5—42no—
113C22×C3×D5—44no—
114C22×C3×D5—42no—
115C22×C3×D5—42no—
116C22×C3×D5—44no—
117C22×C3×D5—41no—
118C22×C3×D5—42no—
119C22×C3×D5—41no—
120C22×C3×D5C22⋊C411yescharacteristic, complemented
121C22×C3×D5C2×D412yes—
122C22×C3×D5C2×D411yescharacteristic
123C22×C3×D5C2×D411yescharacteristic
124C22×C3×D5#4112yes—
125C2×ΓL(1,𝔽16)—24no—
126C2×ΓL(1,𝔽16)—44no—
127C2×ΓL(1,𝔽16)—44no—
128C2×ΓL(1,𝔽16)—42no—
129C2×ΓL(1,𝔽16)—82no—
130C3×C5×D4—22no—
131C3×C5×D4—42no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5C22⋊C411yescharacteristic, complemented
134C3×C22⋊D5—22no—
135C3×C22⋊D5—22no—
136C3×C22⋊D5—42no—
137C3×C22⋊D5—42no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5C22⋊C411yescharacteristic, complemented
140C3×D20—22no—
141C3×D20—42no—
142C3×C4×D5—21no—
143C3×C4×D5—21no—
144C3×C4×D5—42no—
145C25×C3—51no—
146C22×C3×D4—51no—
147C22×C3×D4—101no—
148C3×#120—51no—
149C3×#120—51no—
150C3×#120—51no—
151C3×#120—101no—
152C3×#120—101no—
153C3×#120AGL(1,𝔽5)11yescharacteristic, complemented
154C2×C3×C22⋊C4—51no—
155C2×C3×C22⋊C4—101no—
156C2×#217—52no—
157C2×#217—52no—
158C2×#217—101no—
159C2×#217—104no—
160D4×Dic3—104no—
161#926—101no—
162#834—101no—
163#834—101no—
164C24×C5C2×Dic311yescharacteristic, complemented
165C23×D5—22no—
166C23×D5—21no—
167C23×D5—22no—
168C23×D5—21no—
169C23×D5—44no—
170C23×D5C2×Dic311yescharacteristic, complemented
171C23×D5#6711yescharacteristic
172C23×D5C22×D311yescharacteristic
173C22×AGL(1,𝔽5)—34no—
174C22×AGL(1,𝔽5)—62no—
175C22×AGL(1,𝔽5)—62no—
176C2×C5×D4—21no—
177C2×C5×D4C2×Dic311yescharacteristic
178C2×C22⋊D5—21no—
179C2×C22⋊D5—21no—
180C2×C22⋊D5C2×Dic311yescharacteristic
181C2×C22⋊D5#6711yescharacteristic
182D4×D5—22no—
183D4×D5—22no—
184D4×D5—44no—
185C2×D20—21no—
186C2×D20#6711yescharacteristic
187C2×C4×D5—21no—
188C2×C4×D5#6711yescharacteristic
189C22⋊AGL(1,𝔽5)—62no—
190C22⋊AGL(1,𝔽5)—62no—
191C22⋊AGL(1,𝔽5)—62no—
192C22⋊AGL(1,𝔽5)—62no—
193C22⋊AGL(1,𝔽5)—62no—
194C22⋊AGL(1,𝔽5)—128no—
195C4⋊AGL(1,𝔽5)—62no—
196C4×AGL(1,𝔽5)—62no—
197C5×C22⋊C4—21no—
198C5×C22⋊C4C2×Dic311yescharacteristic, complemented
199C22⋊Dic5—21no—
200C22⋊Dic5C2×Dic311yescharacteristic, complemented
201#685—21no—
202#685—21no—
203#685—21no—
204C2×#120—51no—
205#518—151no—
206C2×#99—151no—
207#379—152no—
208#342—152no—
209C22×C3×C5—22no—
210C22×C3×C5—24no—
211C22×C3×C5—21no—
212C22×C3×C5—41no—
213C22×C3×C5—41no—
214C22×C3×C5—41no—
215C22×C3×C5—42no—
216C22×C3×C5—41no—
217C22×C3×C5C2×C22⋊C411yescharacteristic
218C22×C3×C5C4×D412yes—
219C2×C3×D5—22no—
220C2×C3×D5—24no—
221C2×C3×D5—22no—
222C2×C3×D5—24no—
223C2×C3×D5—21no—
224C2×C3×D5—41no—
225C2×C3×D5—42no—
226C2×C3×D5—48no—
227C2×C3×D5—44no—
228C2×C3×D5—41no—
229C2×C3×D5—42no—
230C2×C3×D5—41no—
231C2×C3×D5—42no—
232C2×C3×D5—44no—
233C2×C3×D5—41no—
234C2×C3×D5—81no—
235C2×C3×D5#12011yescharacteristic
236C2×C3×D5#12112yes—
237C2×C3×D5#12311yescharacteristic
238ΓL(1,𝔽16)—44no—
239ΓL(1,𝔽16)—82no—
240C3×C4×C5—21no—
241C3×C4×C5—41no—
242C3×Dic5—21no—
243C3×Dic5—41no—
244C24×C3—51no—
245C24×C3—51no—
246C24×C3—51no—
247C24×C3—102no—
248C24×C3—101no—
249C24×C3—102no—
250C24×C3—101no—
251C24×C3—204no—
252C24×C3C2×AGL(1,𝔽5)11yescharacteristic, complemented
253C2×C3×D4—21no—
254C2×C3×D4—51no—
255C2×C3×D4—51no—
256C2×C3×D4—51no—
257C2×C3×D4—101no—
258C2×C3×D4—102no—
259C2×C3×D4—102no—
260C2×C3×D4—101no—
261C2×C3×D4—101no—
262C2×C3×D4—204no—
263C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
264C22×C3×C4—51no—
265C22×C3×C4—101no—
266C22×Dic3—54no—
267C22×Dic3—102no—
268C22×Dic3—102no—
269C3×C22⋊C4—21no—
270C3×C22⋊C4—51no—
271C3×C22⋊C4—101no—
272C3×C22⋊C4—101no—
273C3×C22⋊C4—101no—
274C3×C22⋊C4—101no—
275C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
276#217—102no—
277#217—102no—
278#217—102no—
279#217—102no—
280#217—102no—
281#217—208no—
282C4⋊Dic3—102no—
283C4×Dic3—102no—
284C23×C5—22no—
285C23×C5—21no—
286C23×C5—42no—
287C23×C5#21711yescharacteristic, complemented
288C23×C5C22×Dic311yescharacteristic
289C22×D5—28no—
290C22×D5—24no—
291C22×D5—22no—
292C22×D5—21no—
293C22×D5—21no—
294C22×D5—21no—
295C22×D5—42no—
296C22×D5—42no—
297C22×D5—42no—
298C22×D5—44no—
299C22×D5—42no—
300C22×D5—44no—
301C22×D5—42no—
302C22×D5—44no—
303C22×D5—42no—
304C22×D5—41no—
305C22×D5—41no—
306C22×D5—42no—
307C22×D5#21711yescharacteristic, complemented
308C22×D5D3×D412yes—
309C22×D5#23712yes—
310C22×D5C2×#6711yescharacteristic
311C22×D5C2×#6711yescharacteristic
312C2×AGL(1,𝔽5)—64no—
313C2×AGL(1,𝔽5)—124no—
314C2×AGL(1,𝔽5)—124no—
315C2×AGL(1,𝔽5)—122no—
316C2×AGL(1,𝔽5)—242no—
317C5×D4—22no—
318C5×D4—42no—
319C2×C4×C5—21no—
320C2×C4×C5#21711yescharacteristic, complemented
321C22⋊D5—22no—
322C22⋊D5—22no—
323C22⋊D5—42no—
324C22⋊D5—42no—
325C2×Dic5—21no—
326C2×Dic5#21711yescharacteristic, complemented
327D20—22no—
328D20—42no—
329C4×D5—21no—
330C4×D5—21no—
331C4×D5—42no—
332C25—51no—
333C22×D4—51no—
334C22×D4—101no—
335#120—51no—
336#120—51no—
337#120—51no—
338#120—101no—
339#120—101no—
340#120ΓL(1,𝔽16)11yescharacteristic, complemented
341C4×D4—304no—
342#117—301no—
343C2×C22⋊C4—51no—
344C2×C22⋊C4—101no—
345C2×C22⋊C4—152no—
346C2×C22⋊C4—152no—
347C2×C22⋊C4—301no—
348C2×C22⋊C4—304no—
349#99—301no—
350#99—301no—
351C2×C3×C5—21no—
352C2×C3×C5—22no—
353C2×C3×C5—42no—
354C2×C3×C5—41no—
355C2×C3×C5#38611yescharacteristic
356C3×D5—22no—
357C3×D5—21no—
358C3×D5—42no—
359C3×D5—41no—
360C3×D5B(4,𝔽2)12yes—
361C23×C3—22no—
362C23×C3—21no—
363C23×C3—42no—
364C23×C3—52no—
365C23×C3—51no—
366C23×C3—52no—
367C23×C3—51no—
368C23×C3—51no—
369C23×C3—101no—
370C23×C3—101no—
371C23×C3—108no—
372C23×C3—104no—
373C23×C3—102no—
374C23×C3—101no—
375C23×C3—202no—
376C23×C3—204no—
377C23×C3—201no—
378C23×C3—202no—
379C23×C3—201no—
380C23×C3—202no—
381C23×C3—202no—
382C23×C3—204no—
383C23×C3—202no—
384C23×C3—202no—
385C23×C3—204no—
386C23×C3—202no—
387C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic, complemented
388C23×C3C22×AGL(1,𝔽5)11yescharacteristic
389C3×D4—22no—
390C3×D4—42no—
391C3×D4—102no—
392C3×D4—102no—
393C3×D4—102no—
394C3×D4—202no—
395C3×D4—202no—
396C3×D4—202no—
397C2×C3×C4—21no—
398C2×C3×C4—51no—
399C2×C3×C4—101no—
400C2×C3×C4—101no—
401C2×C3×C4—101no—
402C2×C3×C4—202no—
403C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic, complemented
404C2×Dic3—104no—
405C2×Dic3—204no—
406C2×Dic3—202no—
407C2×Dic3—204no—
408C2×Dic3—402no—
409C22×C5—22no—
410C22×C5—24no—
411C22×C5—21no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5—41no—
415C22×C5—42no—
416C22×C5—41no—
417C22×C5D4×Dic312yes—
418C22×C5C2×#21711yescharacteristic
419C2×D5—22no—
420C2×D5—24no—
421C2×D5—22no—
422C2×D5—24no—
423C2×D5—21no—
424C2×D5—42no—
425C2×D5—41no—
426C2×D5—48no—
427C2×D5—44no—
428C2×D5—41no—
429C2×D5—42no—
430C2×D5—41no—
431C2×D5—42no—
432C2×D5—44no—
433C2×D5—41no—
434C2×D5—81no—
435C2×D5#93511yescharacteristic
436C2×D5#93711yescharacteristic
437C2×D5#93912yes—
438AGL(1,𝔽5)—124no—
439AGL(1,𝔽5)—242no—
440C4×C5—21no—
441C4×C5—41no—
442Dic5—21no—
443Dic5—41no—
444C24—51no—
445C24—51no—
446C24—51no—
447C24—101no—
448C24—102no—
449C24—101no—
450C24—102no—
451C24—204no—
452C24C2×ΓL(1,𝔽16)11yescharacteristic, complemented
453C2×D4—21no—
454C2×D4—51no—
455C2×D4—51no—
456C2×D4—51no—
457C2×D4—101no—
458C2×D4—102no—
459C2×D4—102no—
460C2×D4—101no—
461C2×D4—101no—
462C2×D4—204no—
463C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
464C22×C4—51no—
465C22×C4—101no—
466C22×C4—154no—
467C22×C4—302no—
468C22×C4—302no—
469C4⋊C4—302no—
470C22⋊C4—21no—
471C22⋊C4—51no—
472C22⋊C4—101no—
473C22⋊C4—101no—
474C22⋊C4—101no—
475C22⋊C4—101no—
476C22⋊C4—302no—
477C22⋊C4—302no—
478C22⋊C4—302no—
479C22⋊C4—302no—
480C22⋊C4—302no—
481C22⋊C4—608no—
482C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic, complemented
483C42—302no—
484C3×C5#188911yescharacteristic, complemented, Hall
485C22×C3—22no—
486C22×C3—24no—
487C22×C3—21no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—42no—
492C22×C3—41no—
493C22×C3—51no—
494C22×C3—52no—
495C22×C3—51no—
496C22×C3—104no—
497C22×C3—102no—
498C22×C3—102no—
499C22×C3—104no—
500C22×C3—101no—
501C22×C3—201no—
502C22×C3—202no—
503C22×C3—201no—
504C22×C3—201no—
505C22×C3—202no—
506C22×C3—202no—
507C22×C3—204no—
508C22×C3—208no—
509C22×C3—204no—
510C22×C3—201no—
511C22×C3—401no—
512C22×C3D4×AGL(1,𝔽5)12yes—
513C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
514C3×C4—21no—
515C3×C4—41no—
516C3×C4—101no—
517C3×C4—201no—
518Dic3—204no—
519Dic3—402no—
520C2×C5—21no—
521C2×C5—22no—
522C2×C5—42no—
523C2×C5—41no—
524C2×C5#522011yescharacteristic
525D5—22no—
526D5—21no—
527D5—42no—
528D5—41no—
529D5#503212yes—
530C23—22no—
531C23—21no—
532C23—42no—
533C23—52no—
534C23—51no—
535C23—52no—
536C23—51no—
537C23—51no—
538C23—101no—
539C23—101no—
540C23—108no—
541C23—104no—
542C23—102no—
543C23—101no—
544C23—202no—
545C23—204no—
546C23—201no—
547C23—201no—
548C23—202no—
549C23—202no—
550C23—202no—
551C23—202no—
552C23—204no—
553C23—202no—
554C23—204no—
555C23—202no—
556C23#676311yescharacteristic, complemented
557C23C22×ΓL(1,𝔽16)11yescharacteristic
558D4—22no—
559D4—42no—
560D4—102no—
561D4—102no—
562D4—102no—
563D4—202no—
564D4—202no—
565D4—202no—
566C2×C4—21no—
567C2×C4—51no—
568C2×C4—101no—
569C2×C4—101no—
570C2×C4—101no—
571C2×C4—202no—
572C2×C4—304no—
573C2×C4—604no—
574C2×C4—602no—
575C2×C4—604no—
576C2×C4—1202no—
577C2×C4#676311yescharacteristic, complemented
578C2×C3—21no—
579C2×C3—22no—
580C2×C3—42no—
581C2×C3—41no—
582C2×C3—52no—
583C2×C3—102no—
584C2×C3—101no—
585C2×C3—202no—
586C2×C3—201no—
587C2×C3#6577911yescharacteristic
588C5#7166911yescharacteristic, complemented, Sylow
589C22—22no—
590C22—24no—
591C22—21no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—42no—
596C22—41no—
597C22—51no—
598C22—51no—
599C22—52no—
600C22—102no—
601C22—104no—
602C22—102no—
603C22—104no—
604C22—101no—
605C22—201no—
606C22—202no—
607C22—201no—
608C22—201no—
609C22—202no—
610C22—202no—
611C22—204no—
612C22—208no—
613C22—204no—
614C22—201no—
615C22—401no—
616C22D4×ΓL(1,𝔽16)12yes—
617C22C2×#676311yescharacteristic
618C4—21no—
619C4—41no—
620C4—101no—
621C4—201no—
622C4—604no—
623C4—1202no—
624C3#1060446111yescharacteristic, complemented, Sylow
625C2—21no—
626C2—22no—
627C2—42no—
628C2—41no—
629C2—52no—
630C2—102no—
631C2—101no—
632C2—202no—
633C2—201no—
634C2#1175243811yescharacteristic
subgroupG/H
centerC2#11752438
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC3×C5×#120C4
socleC2×C3×C5#386
prime radicalC3×D5×#120C2
cosocleC23×C3×D5C23
hypercenter#120ΓL(1,𝔽16)
hypocenterC3×C5#1889
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #11756987C2semidirect
3. #11752459C2semidirect
4. D5⋊#834C2semidirect
5. #11746737C2semidirect
16. C3×C5×#120C4semidirect
17. C3×#4099C4semidirect
19. C3×#4083C4semidirect
21. C3×#4028C4semidirect
32. C24×C3×C5C2×C4semidirect
38. C23×C3×D5C2×C4semidirect
43. C22×ΓL(1,𝔽16)D4semidirect
66. C3×C5×C22⋊C4C2×C4semidirect
68. C3×C22⋊Dic5C2×C4semidirect
86. C5×#120Dic3semidirect
87. #4099Dic3semidirect
89. #4083Dic3semidirect
91. #4028Dic3semidirect
100. C23×C3×C5C22⋊C4semidirect
120. C22×C3×D5C22⋊C4semidirect
133. C2×C3×C4×C5C22⋊C4semidirect
139. C2×C3×Dic5C22⋊C4semidirect
153. C3×#120AGL(1,𝔽5)semidirect
164. C24×C5C2×Dic3semidirect
170. C23×D5C2×Dic3semidirect
198. C5×C22⋊C4C2×Dic3semidirect
200. C22⋊Dic5C2×Dic3semidirect
252. C24×C3C2×AGL(1,𝔽5)semidirect
275. C3×C22⋊C4C2×AGL(1,𝔽5)semidirect
287. C23×C5#217semidirect
307. C22×D5#217semidirect
320. C2×C4×C5#217semidirect
326. C2×Dic5#217semidirect
340. #120ΓL(1,𝔽16)semidirect
387. C23×C3C22⋊AGL(1,𝔽5)semidirect
403. C2×C3×C4C22⋊AGL(1,𝔽5)semidirect
452. C24C2×ΓL(1,𝔽16)semidirect
482. C22⋊C4C2×ΓL(1,𝔽16)semidirect
484. C3×C5#1889semidirect
556. C23#6763semidirect
577. C2×C4#6763semidirect
588. C5#71669semidirect
624. C3#10604461semidirect

Maximal subgroups

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

subgroupindex
#117569872
C3×D5×#1202
#117524592
D5⋊#8342
#117467372
#106044613
#716695