Finite Group Databasebeta

← #14297010

Subgroups — #14297010

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×Q8×D15C211yesmaximal, characteristic
2C2×C3×C5×#103C211yesmaximal, characteristic, complemented
3C2×#91119C211yesmaximal, characteristic, complemented
4C2×#91104C211yesmaximal, characteristic
5C2×#91100C211yesmaximal, characteristic, complemented
6#11751088C211yesmaximal, characteristic
7C2×#91094C211yesmaximal, characteristic, complemented
8#10601059—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×Q8×D15—22no—
11C2×Q8×D15—22no—
12C2×Q8×D15—22no—
13C2×Q8×D15—22no—
14C2×Q8×D15—22no—
15C2×Q8×D15C414yescomplemented
16C22×C4×D15—21no—
17C22×C4×D15C2211yescharacteristic
18C22×Dic30—21no—
19C22×Dic30C2211yescharacteristic
20C22×C3×C5×C8C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×#6714—21no—
23C2×C4⋊Dic15C2211yescharacteristic
24C22×C3⋊#168C2211yescharacteristic
25C3×C5×#103—22no—
26#91119—22no—
27#91115—21no—
28#91104—22no—
29#91100—22no—
30#91094—22no—
31#70266—51nomaximal, Hall
32C22×Q8×D5—31no—
33C2×C5×#103D311yescharacteristic, complemented
34C2×#3967—31no—
35C2×#3952—31no—
36C2×#3948—31no—
37#65276—31no—
38C2×#3942—31no—
39C23×D15D411yescharacteristic
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×C5—21no—
48C22×C3×C4×C5C2311yescharacteristic
49C22×Dic15—21no—
50C22×Dic15—21no—
51C22×Dic15D411yescharacteristic
52Q8×D15—28no—
53Q8×D15—28no—
54Q8×D15—28no—
55Q8×D15—28no—
56C2×C4×D15—24no—
57C2×C4×D15—24no—
58C2×C4×D15—24no—
59C2×C4×D15—21no—
60C2×C4×D15—21no—
61C2×C4×D15—21no—
62C2×C4×D15—21no—
63C2×C4×D15C2×C412yes—
64C2×C4×D15D412yes—
65C2×Dic30—24no—
66C2×Dic30—24no—
67C2×Dic30—21no—
68C2×Dic30—21no—
69C2×Dic30—21no—
70C2×Dic30—24no—
71C2×Dic30C2×C412yes—
72C2×Dic30D412yes—
73C2×Dic30D412yes—
74C2×C3×C5×C8—21no—
75C2×C3×C5×C8—21no—
76C2×C3×C5×C8—21no—
77C3×C5×C4⋊C4—21no—
78C3×C5×C4⋊C4—21no—
79#6714—42no—
80C4⋊Dic15—21no—
81C4⋊Dic15—21no—
82C2×C3⋊#168—21no—
83C2×C3⋊#168—21no—
84C2×C3⋊#168—21no—
85C22×D3×Q8—51no—
86C2×C3×#103D511yescharacteristic, complemented
87C2×#835—51no—
88C2×(C2×D3)⋊C8—51no—
89C2×#816—51no—
90#4987—51no—
91C2×#810—51no—
92C22×C5×Q8C2×D311yescharacteristic
93C2×Q8×D5—34no—
94C2×Q8×D5—62no—
95C2×Q8×D5—62no—
96C2×Q8×D5—62no—
97C2×Q8×D5—62no—
98C2×Q8×D5—62no—
99C22×C4×D5—31no—
100C22×C4×D5—61no—
101C22×Dic10—31no—
102C22×Dic10—61no—
103C22×C5×C8C2×D311yescharacteristic
104C2×C5×C4⋊C4C2×D311yescharacteristic
105C2×#685—61no—
106C2×C4⋊Dic5—31no—
107C22×#168—31no—
108C5×#103—22no—
109#3967—62no—
110#3963—61no—
111#3952—62no—
112#3948—62no—
113#3942—62no—
114#1787—151noSylow
115C23×C3×C5C2×D411yescharacteristic
116C22×D15—21no—
117C22×D15—21no—
118C22×D15—21no—
119C22×D15—21no—
120C22×D15C22⋊C412yes—
121C22×D15SD1612yes—
122C22×D15Q1612yes—
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×C5—41no—
131C2×C3×C4×C5—41no—
132C2×C3×C4×C5—41no—
133C2×C3×C4×C5C22×C411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×Dic15—22no—
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—41no—
145C2×Dic15—41no—
146C2×Dic15—41no—
147C2×Dic15C22⋊C412yes—
148C4×D15—216no—
149C4×D15—22no—
150C4×D15—22no—
151C4×D15—22no—
152C4×D15—22no—
153Dic30—216no—
154Dic30—22no—
155Dic30—22no—
156Dic30—22no—
157Dic30C22⋊C414yescomplemented
158C3×C5×C8—41no—
159C3⋊#168—41no—
160C22×C3×Q8C2×D511yescharacteristic
161C2×D3×Q8—54no—
162C2×D3×Q8—102no—
163C2×D3×Q8—102no—
164C2×D3×Q8—102no—
165C2×D3×Q8—102no—
166C2×D3×Q8—102no—
167C22×C4×D3—51no—
168C22×C4×D3—101no—
169C22×Dic6—51no—
170C22×Dic6—101no—
171C22×C3×C8C2×D511yescharacteristic
172C2×C3×C4⋊C4C2×D511yescharacteristic
173C2×(C2×D3)⋊C4—101no—
174C2×C4⋊Dic3—51no—
175C22×C3⋊C8—51no—
176C3×#103—22no—
177#835—102no—
178C3⋊#95—101no—
179(C2×D3)⋊C8—102no—
180#816—102no—
181#810—102no—
182C23×D5—31no—
183C2×C5×Q8—21no—
184C2×C5×Q8—21no—
185C2×C5×Q8—21no—
186C2×C5×Q8C4×D312yes—
187C2×C5×Q8D1212yes—
188C2×C5×Q8#6712yes—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5C22×D311yescharacteristic
192C22×Dic5—31no—
193C22×Dic5—61no—
194C22×Dic5—61no—
195Q8×D5—68no—
196Q8×D5—68no—
197Q8×D5—68no—
198Q8×D5—68no—
199C2×C4×D5—32no—
200C2×C4×D5—32no—
201C2×C4×D5—64no—
202C2×C4×D5—64no—
203C2×C4×D5—64no—
204C2×C4×D5—61no—
205C2×C4×D5—61no—
206C2×C4×D5—61no—
207C2×C4×D5—61no—
208C2×Dic10—32no—
209C2×Dic10—32no—
210C2×Dic10—32no—
211C2×Dic10—64no—
212C2×Dic10—64no—
213C2×Dic10—64no—
214C2×Dic10—61no—
215C2×Dic10—61no—
216C2×Dic10—61no—
217C2×C5×C8—21no—
218C2×C5×C8—21no—
219C2×C5×C8—21no—
220C5×C4⋊C4—21no—
221C5×C4⋊C4—21no—
222#685—122no—
223C4⋊Dic5—61no—
224C4⋊Dic5—61no—
225C2×#168—61no—
226C2×#168—61no—
227C2×#168—61no—
228C23×Q8—151no—
229C2×#103—151no—
230C2×#103—151no—
231C2×#103—151no—
232C2×#103D1511yescharacteristic, complemented
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×D15—22no—
243C2×D15—22no—
244C2×D15—22no—
245C2×D15—22no—
246C2×D15—22no—
247C2×D15—22no—
248C2×D15#10314yescomplemented
249C3×C4×C5—24no—
250C3×C4×C5—81no—
251C3×C4×C5C2×C22⋊C411yescharacteristic
252C3×C4×C5C2×C22⋊C411yescharacteristic
253C3×C4×C5#12011yescharacteristic
254C3×C4×C5#12011yescharacteristic
255Dic15—22no—
256Dic15—24no—
257Dic15—81no—
258C23×D3—51no—
259C2×C3×Q8—21no—
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8C4×D512yes—
263C2×C3×Q8D2012yes—
264C2×C3×Q8C22⋊D512yes—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4C22×D511yescharacteristic
268C22×Dic3—51no—
269C22×Dic3—101no—
270C22×Dic3—101no—
271D3×Q8—108no—
272D3×Q8—108no—
273D3×Q8—108no—
274D3×Q8—108no—
275C2×C4×D3—52no—
276C2×C4×D3—52no—
277C2×C4×D3—104no—
278C2×C4×D3—104no—
279C2×C4×D3—104no—
280C2×C4×D3—101no—
281C2×C4×D3—101no—
282C2×C4×D3—101no—
283C2×C4×D3—101no—
284C2×Dic6—52no—
285C2×Dic6—52no—
286C2×Dic6—52no—
287C2×Dic6—104no—
288C2×Dic6—104no—
289C2×Dic6—104no—
290C2×Dic6—101no—
291C2×Dic6—101no—
292C2×Dic6—101no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298(C2×D3)⋊C4—202no—
299C4⋊Dic3—101no—
300C4⋊Dic3—101no—
301C2×C3⋊C8—101no—
302C2×C3⋊C8—101no—
303C2×C3⋊C8—101no—
304C23×C5D3×D411yescharacteristic
305C22×D5—32no—
306C22×D5—32no—
307C22×D5—32no—
308C22×D5—61no—
309C22×D5—61no—
310C22×D5—61no—
311C22×D5—61no—
312C5×Q8—22no—
313C5×Q8—22no—
314C5×Q8—22no—
315C5×Q8(C2×D3)⋊C414yescomplemented
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5C2×C4×D311yescharacteristic
323C2×C4×C5C2×D1211yescharacteristic
324C2×C4×C5D3×D411yescharacteristic
325C2×C4×C5D3×D411yescharacteristic
326C2×C4×C5D3×D411yescharacteristic
327C2×C4×C5C2×#6711yescharacteristic
328C2×Dic5—32no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5—61no—
332C2×Dic5—62no—
333C2×Dic5—61no—
334C2×Dic5—121no—
335C2×Dic5—121no—
336C2×Dic5—121no—
337C4×D5—616no—
338C4×D5—62no—
339C4×D5—62no—
340C4×D5—62no—
341C4×D5—62no—
342Dic10—34no—
343Dic10—616no—
344Dic10—62no—
345Dic10—62no—
346Dic10—62no—
347C5×C8—41no—
348#168—121no—
349C22×Q8—154no—
350C22×Q8—151no—
351C22×Q8—301no—
352C22×Q8—302no—
353C22×Q8—302no—
354C22×Q8—302no—
355C22×Q8—302no—
356C22×Q8—302no—
357C22×Q8C2×D1511yescharacteristic
358C23×C4—151no—
359C23×C4—301no—
360C22×C8—151no—
361C22×C8C2×D1511yescharacteristic
362C2×C4⋊C4—151no—
363C2×C4⋊C4C2×D1511yescharacteristic
364C2×C22⋊C4—301no—
365#103—22no—
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
378D15—24no—
379C23×C3D4×D511yescharacteristic
380C22×D3—52no—
381C22×D3—52no—
382C22×D3—52no—
383C22×D3—101no—
384C22×D3—101no—
385C22×D3—101no—
386C22×D3—101no—
387C3×Q8—22no—
388C3×Q8—22no—
389C3×Q8—22no—
390C3×Q8#68514yescomplemented
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4C2×C4×D511yescharacteristic
398C2×C3×C4C2×D2011yescharacteristic
399C2×C3×C4D4×D511yescharacteristic
400C2×C3×C4D4×D511yescharacteristic
401C2×C3×C4D4×D511yescharacteristic
402C2×C3×C4C2×C22⋊D511yescharacteristic
403C2×Dic3—52no—
404C2×Dic3—102no—
405C2×Dic3—102no—
406C2×Dic3—101no—
407C2×Dic3—102no—
408C2×Dic3—101no—
409C2×Dic3—201no—
410C2×Dic3—201no—
411C2×Dic3—201no—
412C4×D3—1016no—
413C4×D3—102no—
414C4×D3—102no—
415C4×D3—102no—
416C4×D3—102no—
417Dic6—54no—
418Dic6—1016no—
419Dic6—102no—
420Dic6—102no—
421Dic6—102no—
422C3×C8—41no—
423C3⋊C8—201no—
424C22×C5D3×C22⋊C411yescharacteristic
425C22×C5#88211yescharacteristic
426C22×C5D3×SD1611yescharacteristic
427C22×C5#91511yescharacteristic
428C22×C5D3×Q1611yescharacteristic
429C22×C5#91811yescharacteristic
430C22×C5#93711yescharacteristic
431C2×D5—34no—
432C2×D5—62no—
433C2×D5—62no—
434C2×D5—62no—
435C2×D5—62no—
436C2×D5—62no—
437C2×D5—62no—
438C4×C5—24no—
439C4×C5—81no—
440C4×C5D3×C22⋊C411yescharacteristic
441C4×C5#88211yescharacteristic
442C4×C5C2×(C2×D3)⋊C411yescharacteristic
443C4×C5#93711yescharacteristic
444Dic5—64no—
445Dic5—62no—
446Dic5—241no—
447C24—151no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—152no—
452C2×Q8—152no—
453C2×Q8—152no—
454C2×Q8—304no—
455C2×Q8—304no—
456C2×Q8—304no—
457C2×Q8—308no—
458C2×Q8—308no—
459C2×Q8—308no—
460C2×Q8—308no—
461C2×Q8—301no—
462C2×Q8—301no—
463C2×Q8—301no—
464C2×Q8C4×D1512yes—
465C2×Q8D6012yes—
466C2×Q8#122012yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—151no—
470C22×C4—152no—
471C22×C4—152no—
472C22×C4—304no—
473C22×C4—304no—
474C22×C4—304no—
475C22×C4—301no—
476C22×C4—301no—
477C22×C4—301no—
478C22×C4—301no—
479C22×C4—301no—
480C22×C4—301no—
481C22×C4C22×D1511yescharacteristic
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—301no—
486C2×C8—301no—
487C2×C8—301no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—301no—
491C4⋊C4—301no—
492C22⋊C4—602no—
493C3×C5#178711yescharacteristic, complemented, Hall
494C22×C3D5×C22⋊C411yescharacteristic
495C22×C3#402811yescharacteristic
496C22×C3D5×SD1611yescharacteristic
497C22×C3#406111yescharacteristic
498C22×C3D5×Q1611yescharacteristic
499C22×C3#406411yescharacteristic
500C22×C3#408311yescharacteristic
501C2×D3—54no—
502C2×D3—102no—
503C2×D3—102no—
504C2×D3—102no—
505C2×D3—102no—
506C2×D3—102no—
507C2×D3—102no—
508C3×C4—24no—
509C3×C4—81no—
510C3×C4D5×C22⋊C411yescharacteristic
511C3×C4#402811yescharacteristic
512C3×C4C2×#68511yescharacteristic
513C3×C4#408311yescharacteristic
514Dic3—104no—
515Dic3—102no—
516Dic3—401no—
517C2×C5D3×#10311yescharacteristic
518C2×C5#480211yescharacteristic
519C2×C5#480611yescharacteristic
520C2×C5#480911yescharacteristic
521C2×C5#495511yescharacteristic
522C2×C5#517011yescharacteristic
523C2×C5#518611yescharacteristic
524D5—64no—
525C23—152no—
526C23—152no—
527C23—152no—
528C23—301no—
529C23—301no—
530C23—301no—
531C23—301no—
532C23D4×D1511yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—154no—
537Q8—3016no—
538Q8—302no—
539Q8—302no—
540Q8—302no—
541Q8#671414yescomplemented
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—152no—
549C2×C4—3016no—
550C2×C4—302no—
551C2×C4—301no—
552C2×C4—302no—
553C2×C4—301no—
554C2×C4—302no—
555C2×C4—302no—
556C2×C4—302no—
557C2×C4—302no—
558C2×C4—302no—
559C2×C4—601no—
560C2×C4—601no—
561C2×C4—601no—
562C2×C4C2×C4×D1511yescharacteristic
563C2×C4C2×D6011yescharacteristic
564C2×C4D4×D1511yescharacteristic
565C2×C4D4×D1511yescharacteristic
566C2×C4D4×D1511yescharacteristic
567C2×C4C2×#122011yescharacteristic
568C8—41no—
569C8—601no—
570C2×C3D5×#10311yescharacteristic
571C2×C3#6509111yescharacteristic
572C2×C3#6509511yescharacteristic
573C2×C3#6509711yescharacteristic
574C2×C3#6524411yescharacteristic
575C2×C3#6545911yescharacteristic
576C2×C3#6547511yescharacteristic
577D3—104no—
578C5#7026611yescharacteristic, complemented, Sylow
579C22—154no—
580C22—302no—
581C22—302no—
582C22—302no—
583C22—302no—
584C22—302no—
585C22—302no—
586C22C22⋊C4×D1511yescharacteristic
587C22#9177111yescharacteristic
588C22SD16×D1511yescharacteristic
589C22#9180411yescharacteristic
590C22Q16×D1511yescharacteristic
591C22#9180711yescharacteristic
592C22#9182611yescharacteristic
593C4—24no—
594C4—81no—
595C4—302no—
596C4—304no—
597C4—1201no—
598C4C22⋊C4×D1511yescharacteristic
599C4#9177111yescharacteristic
600C4C2×#671411yescharacteristic
601C4#9182611yescharacteristic
602C3#1060105911yescharacteristic, complemented, Sylow
603C2—304no—
604C2D15×#10311yescharacteristic
605C2#1175090311yescharacteristic
606C2#1175090711yescharacteristic
607C2#1175091011yescharacteristic
608C2#1175105611yescharacteristic
609C2#1175127111yescharacteristic
610C2#1175128711yescharacteristic
subgroupG/H
centerC23D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#103C2
socleC23×C3×C5C2×D4
prime radicalC23×D15D4
cosocleC22×C3×C4×C5C23
hypercenterC2×#103D15
hypocenterC3×C5#1787
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#103C2semidirect
3. C2×#91119C2semidirect
5. C2×#91100C2semidirect
7. C2×#91094C2semidirect
15. C2×Q8×D15C4semidirect
33. C2×C5×#103D3semidirect
86. C2×C3×#103D5semidirect
126. C3×C5×Q8C22⋊C4semidirect
157. Dic30C22⋊C4semidirect
232. C2×#103D15semidirect
248. C2×D15#103semidirect
315. C5×Q8(C2×D3)⋊C4semidirect
390. C3×Q8#685semidirect
493. C3×C5#1787semidirect
541. Q8#6714semidirect
578. C5#70266semidirect
602. C3#10601059semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D152
C2×C3×C5×#1032
C2×#911192
C2×#911042
C2×#911002
#117510882
C2×#910942
#106010593
#702665