Finite Group Databasebeta

← #14297025

Subgroups — #14297025

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Q8×D5C211yesmaximal, characteristic
2C2×#91119C211yesmaximal, characteristic, complemented
3C2×C5×#835C211yesmaximal, characteristic, complemented
4#11748759C211yesmaximal, characteristic
5C2×#90971C211yesmaximal, characteristic, complemented
6C2×#90970C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic
8#10601059—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×C3×Q8×D5—22no—
11C2×C3×Q8×D5—22no—
12C2×C3×Q8×D5—22no—
13C2×C3×Q8×D5—22no—
14C2×C3×Q8×D5—22no—
15C2×C3×Q8×D5C414yescomplemented
16C22×C3×C4×D5—21no—
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×Dic10—21no—
19C22×C3×Dic10C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C2×#6665—21no—
25#91119—22no—
26C5×#835—22no—
27#90994—21no—
28#90971—22no—
29#90970—22no—
30#90955—22no—
31#72132—51nomaximal, Hall
32C22×Q8×D5D311yescharacteristic
33C2×C5×#103—31no—
34C2×#3967—31no—
35C2×#3952—31no—
36C2×#3948—31no—
37#65276—31no—
38C2×#3942—31no—
39C23×C3×D5D411yescharacteristic
40C2×C3×C5×Q8—21no—
41C2×C3×C5×Q8—21no—
42C2×C3×C5×Q8—21no—
43C2×C3×C5×Q8C2×C412yes—
44C2×C3×C5×Q8D412yes—
45C2×C3×C5×Q8D412yes—
46C22×C3×C4×C5—21no—
47C22×C3×C4×C5C2311yescharacteristic
48C22×Dic15—21no—
49C22×C5×Dic3—21no—
50C22×C3×Dic5—21no—
51C22×C3×Dic5D411yescharacteristic
52C3×Q8×D5—28no—
53C3×Q8×D5—28no—
54C3×Q8×D5—28no—
55C3×Q8×D5—28no—
56C2×C3×C4×D5—24no—
57C2×C3×C4×D5—24no—
58C2×C3×C4×D5—24no—
59C2×C3×C4×D5—21no—
60C2×C3×C4×D5—21no—
61C2×C3×C4×D5—21no—
62C2×C3×C4×D5—21no—
63C2×C3×C4×D5C2×C412yes—
64C2×C3×C4×D5D412yes—
65C2×C3×Dic10—24no—
66C2×C3×Dic10—24no—
67C2×C3×Dic10—21no—
68C2×C3×Dic10—21no—
69C2×C3×Dic10—21no—
70C2×C3×Dic10—24no—
71C2×C3×Dic10C2×C412yes—
72C2×C3×Dic10D412yes—
73C2×C3×Dic10D412yes—
74C4⋊Dic15—21no—
75C4⋊Dic15—21no—
76C2×C3⋊#168—21no—
77C2×C3⋊#168—21no—
78C2×C3⋊#168—21no—
79C5×C4⋊Dic3—21no—
80C5×C4⋊Dic3—21no—
81C2×C5×C3⋊C8—21no—
82C2×C5×C3⋊C8—21no—
83C2×C5×C3⋊C8—21no—
84#6665—42no—
85C23×C3×Q8—51no—
86C2×#835—51no—
87C2×#835—51no—
88C2×#835—51no—
89C2×#835D511yescharacteristic, complemented
90#5212—51no—
91C2×#830—51no—
92C22×C5×Q8C2×D311yescharacteristic
93C2×Q8×D5—22no—
94C2×Q8×D5—22no—
95C2×Q8×D5—22no—
96C2×Q8×D5—22no—
97C2×Q8×D5—22no—
98C2×Q8×D5Dic314yescomplemented
99C22×C4×D5—21no—
100C22×C4×D5C2×D311yescharacteristic
101C22×Dic10—21no—
102C22×Dic10C2×D311yescharacteristic
103C22×C5×C8—31no—
104C2×C5×C4⋊C4—31no—
105C2×#685—61no—
106C2×C4⋊Dic5—31no—
107C22×#168—31no—
108C5×#103—62no—
109#3967—62no—
110#3963—61no—
111#3952—62no—
112#3948—62no—
113#3942—62no—
114#1787—151noSylow
115C23×C3×C5C2×D411yescharacteristic
116C22×C3×D5—21no—
117C22×C3×D5—21no—
118C22×C3×D5—21no—
119C22×C3×D5—21no—
120C22×C3×D5C22⋊C412yes—
121C22×C3×D5SD1612yes—
122C22×C3×D5Q1612yes—
123C3×C5×Q8—22no—
124C3×C5×Q8—22no—
125C3×C5×Q8—22no—
126C3×C5×Q8C22⋊C414yescomplemented
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5C22×C411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×Dic15—41no—
137C2×Dic15—41no—
138C2×Dic15—41no—
139C2×C5×Dic3—41no—
140C2×C5×Dic3—41no—
141C2×C5×Dic3—41no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5C22⋊C412yes—
148C3×C4×D5—216no—
149C3×C4×D5—22no—
150C3×C4×D5—22no—
151C3×C4×D5—22no—
152C3×C4×D5—22no—
153C3×Dic10—216no—
154C3×Dic10—22no—
155C3×Dic10—22no—
156C3×Dic10—22no—
157C3×Dic10C22⋊C414yescomplemented
158C3⋊#168—41no—
159C5×C3⋊C8—41no—
160C22×C3×Q8—54no—
161C22×C3×Q8—51no—
162C22×C3×Q8—101no—
163C22×C3×Q8—102no—
164C22×C3×Q8—102no—
165C22×C3×Q8—102no—
166C22×C3×Q8—102no—
167C22×C3×Q8—102no—
168C22×C3×Q8C2×D511yescharacteristic
169C23×C3×C4—51no—
170C23×C3×C4—101no—
171C2×#217—101no—
172C2×C4⋊Dic3—51no—
173C2×C4⋊Dic3C2×D511yescharacteristic
174C22×C3⋊C8—51no—
175C22×C3⋊C8C2×D511yescharacteristic
176#835—22no—
177#835—102no—
178#835—102no—
179#835—102no—
180C3⋊#95—101no—
181#830—102no—
182C23×D5#6711yescharacteristic
183C2×C5×Q8—21no—
184C2×C5×Q8—21no—
185C2×C5×Q8—21no—
186C2×C5×Q8C2×Dic312yes—
187C2×C5×Q8#6712yes—
188C2×C5×Q8#6712yes—
189C22×C4×C5—21no—
190C22×C4×C5—61no—
191C22×C4×C5C22×D311yescharacteristic
192C22×Dic5—21no—
193C22×Dic5—61no—
194C22×Dic5#6711yescharacteristic
195Q8×D5—28no—
196Q8×D5—28no—
197Q8×D5—28no—
198Q8×D5—28no—
199C2×C4×D5—24no—
200C2×C4×D5—24no—
201C2×C4×D5—24no—
202C2×C4×D5—21no—
203C2×C4×D5—21no—
204C2×C4×D5—21no—
205C2×C4×D5—21no—
206C2×C4×D5C2×Dic312yes—
207C2×C4×D5#6712yes—
208C2×Dic10—24no—
209C2×Dic10—24no—
210C2×Dic10—21no—
211C2×Dic10—21no—
212C2×Dic10—21no—
213C2×Dic10—24no—
214C2×Dic10C2×Dic312yes—
215C2×Dic10#6712yes—
216C2×Dic10#6712yes—
217C2×C5×C8—61no—
218C2×C5×C8—61no—
219C2×C5×C8—61no—
220C5×C4⋊C4—61no—
221C5×C4⋊C4—61no—
222#685—122no—
223C4⋊Dic5—61no—
224C4⋊Dic5—61no—
225C2×#168—61no—
226C2×#168—61no—
227C2×#168—61no—
228C23×Q8—51no—
229C2×#103—31no—
230C2×#103—151no—
231C2×#103—151no—
232C2×#103—151no—
233C2×C22⋊C8—151no—
234#380—151no—
235C22×C3×C5C2×C22⋊C411yescharacteristic
236C22×C3×C5#12011yescharacteristic
237C22×C3×C5#12011yescharacteristic
238C22×C3×C5C2×SD1611yescharacteristic
239C22×C3×C5C2×Q1611yescharacteristic
240C22×C3×C5#13711yescharacteristic
241C22×C3×C5#13711yescharacteristic
242C2×C3×D5—22no—
243C2×C3×D5—22no—
244C2×C3×D5—22no—
245C2×C3×D5—22no—
246C2×C3×D5—22no—
247C2×C3×D5—22no—
248C2×C3×D5#10314yescomplemented
249C3×C4×C5—24no—
250C3×C4×C5C2×C22⋊C411yescharacteristic
251C3×C4×C5C2×C22⋊C411yescharacteristic
252C3×C4×C5#12011yescharacteristic
253C3×C4×C5#12011yescharacteristic
254Dic15—81no—
255C3×Dic5—22no—
256C3×Dic5—24no—
257C5×Dic3—81no—
258C24×C3—51no—
259C2×C3×Q8—21no—
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8—52no—
263C2×C3×Q8—52no—
264C2×C3×Q8—52no—
265C2×C3×Q8—104no—
266C2×C3×Q8—104no—
267C2×C3×Q8—104no—
268C2×C3×Q8—108no—
269C2×C3×Q8—108no—
270C2×C3×Q8—108no—
271C2×C3×Q8—108no—
272C2×C3×Q8—101no—
273C2×C3×Q8—101no—
274C2×C3×Q8—101no—
275C2×C3×Q8C4×D512yes—
276C2×C3×Q8D2012yes—
277C2×C3×Q8C22⋊D512yes—
278C22×C3×C4—21no—
279C22×C3×C4—51no—
280C22×C3×C4—52no—
281C22×C3×C4—52no—
282C22×C3×C4—104no—
283C22×C3×C4—104no—
284C22×C3×C4—104no—
285C22×C3×C4—101no—
286C22×C3×C4—101no—
287C22×C3×C4—101no—
288C22×C3×C4—101no—
289C22×C3×C4—101no—
290C22×C3×C4C22×D511yescharacteristic
291C22×Dic3—21no—
292C22×Dic3—101no—
293#217—202no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—101no—
297C4⋊Dic3—101no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—101no—
302C2×C3⋊C8—101no—
303C2×C3⋊C8—101no—
304C23×C5C2×#6711yescharacteristic
305C22×D5—21no—
306C22×D5—21no—
307C22×D5—21no—
308C22×D5—21no—
309C22×D5#21512yes—
310C22×D5#21612yes—
311C22×D5#21712yes—
312C5×Q8—22no—
313C5×Q8—22no—
314C5×Q8—22no—
315C5×Q8#21714yescomplemented
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—121no—
320C2×C4×C5—121no—
321C2×C4×C5—121no—
322C2×C4×C5C22×Dic311yescharacteristic
323C2×C4×C5C2×#6711yescharacteristic
324C2×C4×C5C2×#6711yescharacteristic
325C2×C4×C5C2×#6711yescharacteristic
326C2×C4×C5C2×#6711yescharacteristic
327C2×C4×C5C2×#6711yescharacteristic
328C2×Dic5—22no—
329C2×Dic5—21no—
330C2×Dic5—21no—
331C2×Dic5—22no—
332C2×Dic5—22no—
333C2×Dic5—121no—
334C2×Dic5—121no—
335C2×Dic5—121no—
336C2×Dic5#21712yes—
337C4×D5—216no—
338C4×D5—22no—
339C4×D5—22no—
340C4×D5—22no—
341C4×D5—22no—
342Dic10—216no—
343Dic10—22no—
344Dic10—22no—
345Dic10—22no—
346Dic10#21714yescomplemented
347C5×C8—121no—
348#168—121no—
349C22×Q8—54no—
350C22×Q8—51no—
351C22×Q8—101no—
352C22×Q8—102no—
353C22×Q8—102no—
354C22×Q8—102no—
355C22×Q8—102no—
356C22×Q8—102no—
357C22×Q8D3×D511yescharacteristic
358C23×C4—51no—
359C23×C4—101no—
360C22×C8—31no—
361C22×C8—151no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—151no—
364C2×C22⋊C4—301no—
365#103—62no—
366#103—302no—
367#103—302no—
368#103—302no—
369C22⋊C8—302no—
370#95—301no—
371C2×C3×C5#37911yescharacteristic
372C2×C3×C5C2×#10311yescharacteristic
373C2×C3×C5#41911yescharacteristic
374C2×C3×C5#44811yescharacteristic
375C2×C3×C5#44811yescharacteristic
376C2×C3×C5#45111yescharacteristic
377C2×C3×C5#45111yescharacteristic
378C3×D5—24no—
379C23×C3—52no—
380C23×C3—52no—
381C23×C3—52no—
382C23×C3—101no—
383C23×C3—101no—
384C23×C3—101no—
385C23×C3—101no—
386C23×C3D4×D511yescharacteristic
387C3×Q8—22no—
388C3×Q8—22no—
389C3×Q8—22no—
390C3×Q8—54no—
391C3×Q8—1016no—
392C3×Q8—102no—
393C3×Q8—102no—
394C3×Q8—102no—
395C3×Q8#68514yescomplemented
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—52no—
400C2×C3×C4—1016no—
401C2×C3×C4—102no—
402C2×C3×C4—101no—
403C2×C3×C4—102no—
404C2×C3×C4—101no—
405C2×C3×C4—102no—
406C2×C3×C4—102no—
407C2×C3×C4—102no—
408C2×C3×C4—102no—
409C2×C3×C4—102no—
410C2×C3×C4C2×C4×D511yescharacteristic
411C2×C3×C4C2×D2011yescharacteristic
412C2×C3×C4D4×D511yescharacteristic
413C2×C3×C4D4×D511yescharacteristic
414C2×C3×C4D4×D511yescharacteristic
415C2×C3×C4C2×C22⋊D511yescharacteristic
416C2×Dic3—41no—
417C2×Dic3—41no—
418C2×Dic3—41no—
419C2×Dic3—201no—
420C2×Dic3—201no—
421C2×Dic3—201no—
422C3⋊C8—41no—
423C3⋊C8—201no—
424C22×C5C2×#21511yescharacteristic
425C22×C5#94211yescharacteristic
426C22×C5#94211yescharacteristic
427C22×C5C2×#21611yescharacteristic
428C22×C5C2×#21711yescharacteristic
429C22×C5#95311yescharacteristic
430C22×C5#95311yescharacteristic
431C2×D5—22no—
432C2×D5—22no—
433C2×D5—22no—
434C2×D5—22no—
435C2×D5—22no—
436C2×D5—22no—
437C2×D5#83514yescomplemented
438C4×C5—24no—
439C4×C5—241no—
440C4×C5C2×#21711yescharacteristic
441C4×C5C2×#21711yescharacteristic
442C4×C5#95311yescharacteristic
443C4×C5#95311yescharacteristic
444Dic5—22no—
445Dic5—24no—
446Dic5—241no—
447C24—51no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—52no—
452C2×Q8—52no—
453C2×Q8—52no—
454C2×Q8—104no—
455C2×Q8—104no—
456C2×Q8—104no—
457C2×Q8—108no—
458C2×Q8—108no—
459C2×Q8—108no—
460C2×Q8—108no—
461C2×Q8—101no—
462C2×Q8—101no—
463C2×Q8—101no—
464C2×Q8D5×Dic312yes—
465C2×Q8#120112yes—
466C2×Q8#120212yes—
467C22×C4—21no—
468C22×C4—51no—
469C22×C4—52no—
470C22×C4—52no—
471C22×C4—61no—
472C22×C4—104no—
473C22×C4—104no—
474C22×C4—104no—
475C22×C4—101no—
476C22×C4—101no—
477C22×C4—101no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482C2×C8—61no—
483C2×C8—61no—
484C2×C8—61no—
485C2×C8—301no—
486C2×C8—301no—
487C2×C8—301no—
488C4⋊C4—61no—
489C4⋊C4—61no—
490C4⋊C4—301no—
491C4⋊C4—301no—
492C22⋊C4—602no—
493C3×C5#178711yescharacteristic, complemented, Hall
494C22×C3—54no—
495C22×C3—102no—
496C22×C3—102no—
497C22×C3—102no—
498C22×C3—102no—
499C22×C3—102no—
500C22×C3—102no—
501C22×C3D5×C22⋊C411yescharacteristic
502C22×C3#402811yescharacteristic
503C22×C3D5×SD1611yescharacteristic
504C22×C3#406111yescharacteristic
505C22×C3D5×Q1611yescharacteristic
506C22×C3#406411yescharacteristic
507C22×C3#408311yescharacteristic
508C3×C4—24no—
509C3×C4—102no—
510C3×C4—104no—
511C3×C4D5×C22⋊C411yescharacteristic
512C3×C4#402811yescharacteristic
513C3×C4C2×#68511yescharacteristic
514C3×C4#408311yescharacteristic
515Dic3—81no—
516Dic3—401no—
517C2×C5C2×#83511yescharacteristic
518C2×C5#522511yescharacteristic
519C2×C5#522711yescharacteristic
520C2×C5#522711yescharacteristic
521C2×C5#522811yescharacteristic
522C2×C5#522811yescharacteristic
523C2×C5#524711yescharacteristic
524D5—24no—
525C23—52no—
526C23—52no—
527C23—52no—
528C23—101no—
529C23—101no—
530C23—101no—
531C23—101no—
532C23D5×#6711yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—54no—
537Q8—1016no—
538Q8—102no—
539Q8—102no—
540Q8—102no—
541Q8#666514yescomplemented
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—52no—
546C2×C4—1016no—
547C2×C4—102no—
548C2×C4—101no—
549C2×C4—102no—
550C2×C4—101no—
551C2×C4—102no—
552C2×C4—102no—
553C2×C4—102no—
554C2×C4—102no—
555C2×C4—102no—
556C2×C4—121no—
557C2×C4—121no—
558C2×C4—121no—
559C2×C4—601no—
560C2×C4—601no—
561C2×C4—601no—
562C2×C4C2×D5×Dic311yescharacteristic
563C2×C4C2×#120111yescharacteristic
564C2×C4C2×#120211yescharacteristic
565C2×C4D5×#6711yescharacteristic
566C2×C4D5×#6711yescharacteristic
567C2×C4D5×#6711yescharacteristic
568C8—121no—
569C8—601no—
570C2×C3—104no—
571C2×C3D5×#10311yescharacteristic
572C2×C3#6509111yescharacteristic
573C2×C3#6509511yescharacteristic
574C2×C3#6509711yescharacteristic
575C2×C3#6524411yescharacteristic
576C2×C3#6545911yescharacteristic
577C2×C3#6547511yescharacteristic
578C5#7213211yescharacteristic, complemented, Sylow
579C22—54no—
580C22—102no—
581C22—102no—
582C22—102no—
583C22—102no—
584C22—102no—
585C22—102no—
586C22D5×#21511yescharacteristic
587C22D5×#21611yescharacteristic
588C22#9151311yescharacteristic
589C22#9151511yescharacteristic
590C22D5×#21711yescharacteristic
591C22#9156311yescharacteristic
592C22#9156411yescharacteristic
593C4—24no—
594C4—102no—
595C4—104no—
596C4—241no—
597C4—1201no—
598C4C2×#666511yescharacteristic
599C4D5×#21711yescharacteristic
600C4#9156311yescharacteristic
601C4#9156411yescharacteristic
602C3#1060105911yescharacteristic, complemented, Sylow
603C2—104no—
604C2D5×#83511yescharacteristic
605C2#1174920811yescharacteristic
606C2#1174926711yescharacteristic
607C2#1174926811yescharacteristic
608C2#1174929011yescharacteristic
609C2#1174929111yescharacteristic
610C2#1174948811yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
cosocleC22×C3×C4×C5C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5#1787
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#91119C2semidirect
3. C2×C5×#835C2semidirect
5. C2×#90971C2semidirect
6. C2×#90970C2semidirect
15. C2×C3×Q8×D5C4semidirect
89. C2×#835D5semidirect
98. C2×Q8×D5Dic3semidirect
126. C3×C5×Q8C22⋊C4semidirect
157. C3×Dic10C22⋊C4semidirect
248. C2×C3×D5#103semidirect
315. C5×Q8#217semidirect
346. Dic10#217semidirect
395. C3×Q8#685semidirect
437. C2×D5#835semidirect
493. C3×C5#1787semidirect
541. Q8#6665semidirect
578. C5#72132semidirect
602. C3#10601059semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Q8×D52
C2×#911192
C2×C5×#8352
#117487592
C2×#909712
C2×#909702
C2×#909552
#106010593
#721325