Finite Group Databasebeta

← #14297024

Subgroups — #14297024

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×D3×Dic10C211yesmaximal, characteristic
2C2×#91094C211yesmaximal, characteristic, complemented
3C5×#4987C211yesmaximal, characteristic
4C2×C3×#3942C211yesmaximal, characteristic, complemented
5C2×#90975C211yesmaximal, characteristic, complemented
6C2×#90970C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊#168C211yesmaximal, characteristic
8#10600318—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C22×C4×C5×D3C2211yescharacteristic
11C22×C3×Dic10C2211yescharacteristic
12C22×#1204—21no—
13C22×D3×Dic5—21no—
14C2×D3×Dic10—22no—
15C2×D3×Dic10—22no—
16C2×D3×Dic10—22no—
17C2×D3×Dic10—22no—
18C2×D3×Dic10—22no—
19C2×D3×Dic10C414yescomplemented
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C2×C5×(C2×D3)⋊C4—21no—
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25#91094—22no—
26C5×C3⋊#95—21no—
27C3×#3942—22no—
28#90975—22no—
29#90970—22no—
30(C2×D3)⋊#168—22no—
31#70266—51nomaximal, Hall
32C23×Dic10—31no—
33C5×#380—31no—
34C2×C22⋊#168—31no—
35C2×#3942—31no—
36C2×#3942—31no—
37C2×#3942—31no—
38C2×#3942D311yescharacteristic, complemented
39C23×C5×D3D411yescharacteristic
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15—21no—
43C2×Dic30—21no—
44C2×Dic30—21no—
45C2×Dic30—21no—
46C2×Dic30C2×C412yes—
47C2×Dic30D412yes—
48C2×Dic30D412yes—
49C22×C5×Dic3—21no—
50C22×C5×Dic3D411yescharacteristic
51C2×C4×C5×D3—21no—
52C2×C4×C5×D3—21no—
53C2×C4×C5×D3—21no—
54C2×C4×C5×D3—21no—
55C2×C4×C5×D3C2×C412yes—
56C2×C4×C5×D3D412yes—
57C22×C3×Dic5—21no—
58C2×C3×Dic10—21no—
59C2×C3×Dic10—21no—
60C2×C3×Dic10—21no—
61C2×C3×Dic10C2×C412yes—
62C2×C3×Dic10D412yes—
63C2×C3×Dic10D412yes—
64C2×#1204—24no—
65C2×#1204—24no—
66C2×#1204—24no—
67C2×D3×Dic5—24no—
68C2×D3×Dic5—24no—
69C2×D3×Dic5—24no—
70D3×Dic10—28no—
71D3×Dic10—28no—
72D3×Dic10—28no—
73D3×Dic10—28no—
74C3×C5×C4⋊C4—21no—
75C3×C5×C4⋊C4—21no—
76C2×C3⋊#168—21no—
77C2×C3⋊#168—21no—
78C2×C3⋊#168—21no—
79C5×(C2×D3)⋊C4—42no—
80C5×C4⋊Dic3—21no—
81C5×C4⋊Dic3—21no—
82C2×C3×#168—21no—
83C2×C3×#168—21no—
84C2×C3×#168—21no—
85C22×D3×Q8—51no—
86C2×C3×#103—51no—
87C2×#835—51no—
88C2×(C2×D3)⋊C8—51no—
89C2×#816—51no—
90#4987D511yescharacteristic
91C2×#810—51no—
92C23×C4×C5—31no—
93C23×Dic5—61no—
94C22×Dic10—31no—
95C22×Dic10—34no—
96C22×Dic10—62no—
97C22×Dic10—62no—
98C22×Dic10—62no—
99C22×Dic10—61no—
100C22×Dic10—62no—
101C22×Dic10—62no—
102C22×Dic10C2×D311yescharacteristic
103C2×C5×C4⋊C4—31no—
104C2×C5×C4⋊C4C2×D311yescharacteristic
105C2×C5×C22⋊C4—61no—
106C22×#168—31no—
107C22×#168C2×D311yescharacteristic
108C5×#95—61no—
109C22⋊#168—62no—
110#3942—22no—
111#3942—62no—
112#3942—62no—
113#3942—62no—
114#1787—151noSylow
115C23×C3×C5C2×D411yescharacteristic
116C22×C5×D3—21no—
117C22×C5×D3—21no—
118C22×C5×D3—21no—
119C22×C5×D3—21no—
120C22×C5×D3C22⋊C412yes—
121C22×C5×D3SD1612yes—
122C22×C5×D3Q1612yes—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5—41no—
125C2×C3×C4×C5—41no—
126C2×C3×C4×C5C22×C411yescharacteristic
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135Dic30—22no—
136Dic30—22no—
137Dic30—22no—
138Dic30C22⋊C414yescomplemented
139C2×C5×Dic3—21no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—41no—
142C2×C5×Dic3—41no—
143C2×C5×Dic3—41no—
144C2×C5×Dic3C22⋊C412yes—
145C4×C5×D3—22no—
146C4×C5×D3—22no—
147C4×C5×D3—22no—
148C4×C5×D3—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C3×Dic10—22no—
153C3×Dic10—22no—
154C3×Dic10—22no—
155C3×Dic10C22⋊C414yescomplemented
156#1204—216no—
157D3×Dic5—216no—
158C3⋊#168—41no—
159C3×#168—41no—
160C22×C3×Q8—51no—
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—101no—
168C22×C4×D3C2×D511yescharacteristic
169C22×Dic6—51no—
170C22×Dic6—101no—
171C22×C3×C8—51no—
172C2×C3×C4⋊C4C2×D511yescharacteristic
173C2×(C2×D3)⋊C4—21no—
174C2×C4⋊Dic3C2×D511yescharacteristic
175C22×C3⋊C8—51no—
176C3×#103—102no—
177#835—102no—
178C3⋊#95—21no—
179(C2×D3)⋊C8—102no—
180#816—102no—
181#810—102no—
182C24×C5—31no—
183C22×C4×C5—21no—
184C22×C4×C5—31no—
185C22×C4×C5—32no—
186C22×C4×C5—32no—
187C22×C4×C5—61no—
188C22×C4×C5—61no—
189C22×C4×C5—61no—
190C22×C4×C5—61no—
191C22×C4×C5—61no—
192C22×C4×C5C22×D311yescharacteristic
193C22×Dic5—21no—
194C22×Dic5—64no—
195C22×Dic5—64no—
196C22×Dic5—64no—
197C22×Dic5—61no—
198C2×Dic10—21no—
199C2×Dic10—21no—
200C2×Dic10—21no—
201C2×Dic10—32no—
202C2×Dic10—32no—
203C2×Dic10—32no—
204C2×Dic10—68no—
205C2×Dic10—68no—
206C2×Dic10—68no—
207C2×Dic10—64no—
208C2×Dic10—64no—
209C2×Dic10—64no—
210C2×Dic10—61no—
211C2×Dic10—61no—
212C2×Dic10—61no—
213C2×Dic10—68no—
214C2×Dic10C4×D312yes—
215C2×Dic10D1212yes—
216C2×Dic10#6712yes—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4—61no—
220C5×C4⋊C4—61no—
221C5×C22⋊C4—122no—
222C2×#168—21no—
223C2×#168—21no—
224C2×#168—21no—
225C2×#168—61no—
226C2×#168—61no—
227C2×#168—61no—
228C23×Q8—151no—
229C2×#103—51no—
230C2×#103—151no—
231C2×#103—151no—
232C2×#103—151no—
233C2×C22⋊C8—151no—
234#380—31no—
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×C5×D3—22no—
243C2×C5×D3—22no—
244C2×C5×D3—22no—
245C2×C5×D3—22no—
246C2×C5×D3—22no—
247C2×C5×D3—22no—
248C2×C5×D3#10314yescomplemented
249C3×C4×C5—81no—
250C3×C4×C5C2×C22⋊C411yescharacteristic
251C3×C4×C5C2×C22⋊C411yescharacteristic
252C3×C4×C5#12011yescharacteristic
253C3×C4×C5#12011yescharacteristic
254Dic15—24no—
255C3×Dic5—24no—
256C5×Dic3—22no—
257C5×Dic3—81no—
258C23×D3C22⋊D511yescharacteristic
259C2×C3×Q8—52no—
260C2×C3×Q8—52no—
261C2×C3×Q8—52no—
262C2×C3×Q8—101no—
263C2×C3×Q8—101no—
264C2×C3×Q8—101no—
265C22×C3×C4—21no—
266C22×C3×C4—101no—
267C22×C3×C4C22×D511yescharacteristic
268C22×Dic3—21no—
269C22×Dic3—101no—
270C22×Dic3C22⋊D511yescharacteristic
271D3×Q8—108no—
272D3×Q8—108no—
273D3×Q8—108no—
274D3×Q8—108no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—104no—
280C2×C4×D3—104no—
281C2×C4×D3—104no—
282C2×C4×D3C4×D512yes—
283C2×C4×D3D2012yes—
284C2×Dic6—52no—
285C2×Dic6—52no—
286C2×Dic6—52no—
287C2×Dic6—104no—
288C2×Dic6—104no—
289C2×Dic6—101no—
290C2×Dic6—101no—
291C2×Dic6—101no—
292C2×Dic6—104no—
293C2×C3×C8—101no—
294C2×C3×C8—101no—
295C2×C3×C8—101no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298(C2×D3)⋊C4—42no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C2×C3⋊C8—101no—
302C2×C3⋊C8—101no—
303C2×C3⋊C8—101no—
304C23×C5—32no—
305C23×C5—32no—
306C23×C5—32no—
307C23×C5—61no—
308C23×C5—61no—
309C23×C5—61no—
310C23×C5—61no—
311C23×C5D3×D411yescharacteristic
312C2×C4×C5—32no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—61no—
317C2×C4×C5—61no—
318C2×C4×C5—62no—
319C2×C4×C5—62no—
320C2×C4×C5—62no—
321C2×C4×C5—62no—
322C2×C4×C5—121no—
323C2×C4×C5—121no—
324C2×C4×C5—121no—
325C2×C4×C5C2×C4×D311yescharacteristic
326C2×C4×C5C2×D1211yescharacteristic
327C2×C4×C5D3×D411yescharacteristic
328C2×C4×C5D3×D411yescharacteristic
329C2×C4×C5D3×D411yescharacteristic
330C2×C4×C5C2×#6711yescharacteristic
331C2×Dic5—22no—
332C2×Dic5—22no—
333C2×Dic5—22no—
334C2×Dic5—616no—
335C2×Dic5—62no—
336C2×Dic5—62no—
337C2×Dic5—62no—
338Dic10—22no—
339Dic10—22no—
340Dic10—22no—
341Dic10—34no—
342Dic10—616no—
343Dic10—62no—
344Dic10—62no—
345Dic10—62no—
346Dic10(C2×D3)⋊C414yescomplemented
347#168—41no—
348#168—121no—
349C22×Q8—51no—
350C22×Q8—154no—
351C22×Q8—151no—
352C22×Q8—301no—
353C22×Q8—302no—
354C22×Q8—302no—
355C22×Q8—302no—
356C22×Q8—302no—
357C22×Q8—302no—
358C23×C4—31no—
359C23×C4—301no—
360C22×C8—51no—
361C22×C8—151no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4D3×D511yescharacteristic
364C2×C22⋊C4—61no—
365#103—102no—
366#103—302no—
367#103—302no—
368#103—302no—
369C22⋊C8—302no—
370#95—61no—
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
378C5×D3—24no—
379C23×C3C2×C22⋊D511yescharacteristic
380C22×D3—21no—
381C22×D3—21no—
382C22×D3—21no—
383C22×D3—21no—
384C22×D3#68512yes—
385C22×D3#68712yes—
386C22×D3#68912yes—
387C3×Q8—54no—
388C3×Q8—102no—
389C3×Q8—102no—
390C3×Q8—102no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—102no—
395C2×C3×C4—102no—
396C2×C3×C4—102no—
397C2×C3×C4C2×C4×D511yescharacteristic
398C2×C3×C4C2×D2011yescharacteristic
399C2×C3×C4D4×D511yescharacteristic
400C2×C3×C4D4×D511yescharacteristic
401C2×C3×C4D4×D511yescharacteristic
402C2×C3×C4D4×D511yescharacteristic
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—41no—
406C2×Dic3—41no—
407C2×Dic3—41no—
408C2×Dic3—102no—
409C2×Dic3—102no—
410C2×Dic3—102no—
411C2×Dic3#68512yes—
412C4×D3—22no—
413C4×D3—22no—
414C4×D3—22no—
415C4×D3—22no—
416C4×D3—1016no—
417Dic6—54no—
418Dic6—1016no—
419Dic6—102no—
420Dic6—102no—
421Dic6—102no—
422C3×C8—201no—
423C3⋊C8—201no—
424C22×C5—34no—
425C22×C5—62no—
426C22×C5—62no—
427C22×C5—62no—
428C22×C5—62no—
429C22×C5—62no—
430C22×C5—62no—
431C22×C5D3×C22⋊C411yescharacteristic
432C22×C5#88211yescharacteristic
433C22×C5D3×SD1611yescharacteristic
434C22×C5#91511yescharacteristic
435C22×C5D3×Q1611yescharacteristic
436C22×C5#91811yescharacteristic
437C22×C5#93711yescharacteristic
438C4×C5—62no—
439C4×C5—81no—
440C4×C5—241no—
441C4×C5D3×C22⋊C411yescharacteristic
442C4×C5#88211yescharacteristic
443C4×C5C2×(C2×D3)⋊C411yescharacteristic
444C4×C5#93711yescharacteristic
445Dic5—24no—
446Dic5—64no—
447C24—31no—
448C2×Q8—52no—
449C2×Q8—52no—
450C2×Q8—52no—
451C2×Q8—101no—
452C2×Q8—101no—
453C2×Q8—101no—
454C2×Q8—152no—
455C2×Q8—152no—
456C2×Q8—152no—
457C2×Q8—304no—
458C2×Q8—304no—
459C2×Q8—304no—
460C2×Q8—308no—
461C2×Q8—308no—
462C2×Q8—308no—
463C2×Q8—308no—
464C2×Q8—301no—
465C2×Q8—301no—
466C2×Q8—301no—
467C22×C4—21no—
468C22×C4—31no—
469C22×C4—32no—
470C22×C4—32no—
471C22×C4—61no—
472C22×C4—61no—
473C22×C4—61no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4—101no—
477C22×C4—304no—
478C22×C4—304no—
479C22×C4—304no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482C2×C8—101no—
483C2×C8—101no—
484C2×C8—101no—
485C2×C8—301no—
486C2×C8—301no—
487C2×C8—301no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—61no—
491C4⋊C4—61no—
492C22⋊C4—122no—
493C3×C5#178711yescharacteristic, complemented, Hall
494C22×C3C2×#68511yescharacteristic
495C22×C3C2×#68711yescharacteristic
496C22×C3#408311yescharacteristic
497C22×C3#408311yescharacteristic
498C22×C3C2×#68911yescharacteristic
499C22×C3#409711yescharacteristic
500C22×C3#409711yescharacteristic
501C2×D3—22no—
502C2×D3—22no—
503C2×D3—22no—
504C2×D3—22no—
505C2×D3—22no—
506C2×D3—22no—
507C2×D3#394214yescomplemented
508C3×C4—81no—
509C3×C4—104no—
510C3×C4D5×C22⋊C411yescharacteristic
511C3×C4D5×C22⋊C411yescharacteristic
512C3×C4#402811yescharacteristic
513C3×C4#402811yescharacteristic
514Dic3—22no—
515Dic3—81no—
516Dic3—104no—
517C2×C5—64no—
518C2×C5D3×#10311yescharacteristic
519C2×C5#480211yescharacteristic
520C2×C5#480611yescharacteristic
521C2×C5#480911yescharacteristic
522C2×C5#495511yescharacteristic
523C2×C5#517011yescharacteristic
524C2×C5#518611yescharacteristic
525C23—32no—
526C23—32no—
527C23—32no—
528C23—61no—
529C23—61no—
530C23—61no—
531C23—61no—
532C23D3×C22⋊D511yescharacteristic
533Q8—54no—
534Q8—102no—
535Q8—102no—
536Q8—102no—
537Q8—154no—
538Q8—3016no—
539Q8—302no—
540Q8—302no—
541Q8—302no—
542C2×C4—32no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—61no—
547C2×C4—61no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—102no—
553C2×C4—102no—
554C2×C4—102no—
555C2×C4—121no—
556C2×C4—121no—
557C2×C4—121no—
558C2×C4—3016no—
559C2×C4—302no—
560C2×C4—302no—
561C2×C4—302no—
562C2×C4C4×D3×D511yescharacteristic
563C2×C4D5×D1211yescharacteristic
564C2×C4D3×D2011yescharacteristic
565C2×C4#677711yescharacteristic
566C2×C4D5×#6711yescharacteristic
567C2×C4#679011yescharacteristic
568C8—201no—
569C8—601no—
570C2×C3#6524411yescharacteristic
571C2×C3C2×#394211yescharacteristic
572C2×C3#6529311yescharacteristic
573C2×C3#6532911yescharacteristic
574C2×C3#6532911yescharacteristic
575C2×C3#6533911yescharacteristic
576C2×C3#6533911yescharacteristic
577D3—24no—
578C5#7026611yescharacteristic, complemented, Sylow
579C22—34no—
580C22—62no—
581C22—62no—
582C22—62no—
583C22—62no—
584C22—62no—
585C22—62no—
586C22D3×#68511yescharacteristic
587C22#9147511yescharacteristic
588C22D3×#68711yescharacteristic
589C22#9148611yescharacteristic
590C22D3×#68911yescharacteristic
591C22#9151011yescharacteristic
592C22#9157711yescharacteristic
593C4—62no—
594C4—81no—
595C4—104no—
596C4—241no—
597C4—304no—
598C4D5×(C2×D3)⋊C411yescharacteristic
599C4#9147311yescharacteristic
600C4#9147411yescharacteristic
601C4#9147611yescharacteristic
602C3#1060031811yescharacteristic, complemented, Sylow
603C2—64no—
604C2D3×#394211yescharacteristic
605C2#1174748911yescharacteristic
606C2#1174749411yescharacteristic
607C2#1174749511yescharacteristic
608C2#1174894011yescharacteristic
609C2#1174915511yescharacteristic
610C2#1174940111yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×C5×D3D4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1787
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91094C2semidirect
4. C2×C3×#3942C2semidirect
5. C2×#90975C2semidirect
6. C2×#90970C2semidirect
19. C2×D3×Dic10C4semidirect
38. C2×#3942D3semidirect
138. Dic30C22⋊C4semidirect
155. C3×Dic10C22⋊C4semidirect
248. C2×C5×D3#103semidirect
346. Dic10(C2×D3)⋊C4semidirect
493. C3×C5#1787semidirect
507. C2×D3#3942semidirect
578. C5#70266semidirect
602. C3#10600318semidirect

Maximal subgroups

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

subgroupindex
C22×D3×Dic102
C2×#910942
C5×#49872
C2×C3×#39422
C2×#909752
C2×#909702
C2×(C2×D3)⋊#1682
#106003183
#702665