Finite Group Databasebeta

← #14322823

Subgroups — #14322823

Order 1920.

1632 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
2C2×D5×#217C211yesmaximal, characteristic
3C22×#6665C211yesmaximal, characteristic
4#11751043C211yesmaximal, characteristic, complemented
5C5×#4942C211yesmaximal, characteristic, complemented
6#11749516C211yesmaximal, characteristic, complemented
7#11749513C211yesmaximal, characteristic, complemented
8#11748891C212yesmaximal, complemented
9#11748890C212yesmaximal, complemented
10#11748704C212yesmaximal, complemented
11#11748703C212yesmaximal, complemented
12#10605736—31nomaximal, Hall
13C24×C3×D5C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C22×C3×C4×D5C2212yes—
17C22×D5×Dic3C2212yes—
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×#6719C2211yescharacteristic
20C2×#6712C2212yescomplemented
21C2×C5×#217C2211yescharacteristic
22C2×C5×Dic3⋊C4C2212yescomplemented
23C2×C3×C22⋊Dic5C2211yescharacteristic
24C2×C3×#685C2212yes—
25C3×D5×C22⋊C4—24no—
26D5×#217—24no—
27C2×Dic3⋊Dic5C2212yescomplemented
28C2×#6669C2212yescomplemented
29C2×#6665C418yescomplemented
30C2×#6665C2212yes—
31C2×#6665C2211yescharacteristic
32C2×#6665C2211yescharacteristic
33C2×#6665C2211yescharacteristic
34C2×#6665C2211yescharacteristic
35#91115C2212yescomplemented
36C5×C3⋊#95C2212yescomplemented
37#90994C2212yescomplemented
38#90994C2212yescomplemented
39#82095—51nomaximal, Hall
40C22×#685—31no—
41C2×D5×C22⋊C4—31no—
42C2×D5×C22⋊C4D311yescharacteristic
43C5×#380—31no—
44#65501—31no—
45#65278—32no—
46#65278—32no—
47#65231—31no—
48#65231—31no—
49#64957—32no—
50#64957—32no—
51C24×C3×C5C2311yescharacteristic
52C23×C3×D5—42no—
53C23×C3×D5—42no—
54C23×C3×D5C2×C414yes—
55C23×C3×D5D414yes—
56C23×C3×D5Q814yes—
57C23×C3×D5C2311yescharacteristic
58C23×C3×D5C2311yescharacteristic
59C22×C3×C4×C5C2312yes—
60C22×Dic15—42no—
61C22×Dic15C2×C414yescomplemented
62C22×Dic15C2312yes—
63C22×Dic15C2311yescharacteristic
64C22×Dic15C2311yescharacteristic
65C22×C5×Dic3—42no—
66C22×C5×Dic3C2×C414yescomplemented
67C22×C5×Dic3C2312yes—
68C22×C5×Dic3C2311yescharacteristic
69C22×C5×Dic3C2311yescharacteristic
70C22×C3×Dic5C2312yes—
71C2×C3×C4×D5—24no—
72C2×C3×C4×D5—42no—
73C2×C3×C4×D5—42no—
74C2×D5×Dic3—24no—
75C2×D5×Dic3—42no—
76C2×D5×Dic3—42no—
77C3×C5×C22⋊C4—22no—
78#6719—22no—
79#6712—42no—
80C5×#217—22no—
81C5×Dic3⋊C4—42no—
82C3×C22⋊Dic5—22no—
83C3×#685—24no—
84Dic3⋊Dic5—42no—
85#6669—42no—
86#6665—24no—
87#6665C2×C414yescomplemented
88#6665C2×C414yescomplemented
89#6665C2×C414yescomplemented
90#6665C2×C414yescomplemented
91C22×C3×C22⋊C4—51no—
92C22×#217—51no—
93C22×#217—51no—
94#5210—52no—
95#5210—52no—
96#4946—52no—
97#4946—52no—
98#4942—51no—
99#4942—51no—
100#4942—51no—
101#4942D511yescharacteristic, complemented
102C24×D5C2×D311yescharacteristic
103C23×C4×C5—31no—
104C23×Dic5—31no—
105C22×C4×D5—32no—
106C22×C4×D5C2×D312yes—
107C2×C5×C4⋊C4—32no—
108C2×C5×C22⋊C4—31no—
109C2×C5×C22⋊C4C2×D311yescharacteristic
110C2×C22⋊Dic5—31no—
111C2×C22⋊Dic5C2×D311yescharacteristic
112C2×#685—38no—
113C2×#685—31no—
114C2×#685—31no—
115C2×#685—31no—
116C2×#685—31no—
117C2×#685—32no—
118C2×#685C2×D312yes—
119C2×C4⋊Dic5—32no—
120C2×#683—32no—
121C2×#683—32no—
122D5×C22⋊C4—24no—
123D5×C22⋊C4—64no—
124C5×#95—32no—
125#3963—32no—
126#3963—32no—
127#3963—32no—
128#2315—151noSylow
129C23×C3×C5—22no—
130C23×C3×C5—22no—
131C23×C3×C5C22×C412yes—
132C23×C3×C5C2×D412yes—
133C23×C3×C5C2×Q812yes—
134C23×C3×C5C2411yescharacteristic
135C22×C3×D5—22no—
136C22×C3×D5—22no—
137C22×C3×D5—22no—
138C22×C3×D5—22no—
139C22×C3×D5—44no—
140C22×C3×D5—44no—
141C22×C3×D5—48no—
142C22×C3×D5—48no—
143C22×C3×D5C4⋊C4116yescomplemented
144C22×C3×D5C22×C412yes—
145C22×C3×D5C22×C412yes—
146C22×C3×D5C2×D412yes—
147C22×C3×D5C2×D412yes—
148C22×C3×D5C2×Q812yes—
149C22×C3×D5C2×Q812yes—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—22no—
153C2×Dic15—22no—
154C2×Dic15—22no—
155C2×Dic15—22no—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—44no—
159C2×Dic15C22×C412yes—
160C2×Dic15C22×C412yes—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—44no—
167C2×C5×Dic3C22×C412yes—
168C2×C5×Dic3C22×C412yes—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C3×C4×D5—48no—
173D5×Dic3—48no—
174C25×C3—51no—
175C23×C3×C4—52no—
176C23×Dic3—51no—
177C23×Dic3—52no—
178C23×Dic3C2×D511yescharacteristic
179C2×C3×C22⋊C4—51no—
180C2×C3×C22⋊C4—52no—
181C2×C3×C22⋊C4—104no—
182C2×C3×C22⋊C4C2×D511yescharacteristic
183C2×#217—58no—
184C2×#217—51no—
185C2×#217—51no—
186C2×#217—51no—
187C2×#217—51no—
188C2×#217—51no—
189C2×#217—52no—
190C2×#217—104no—
191C2×#217C2×D511yescharacteristic
192C2×Dic3⋊C4—52no—
193C2×Dic3⋊C4—52no—
194C2×Dic3⋊C4—52no—
195C2×Dic3⋊C4C2×D512yescomplemented
196C3⋊#95—52no—
197C3⋊#95—52no—
198C3⋊#95—52no—
199C3⋊#95C2×D512yescomplemented
200C24×C5C22×D311yescharacteristic
201C23×D5—42no—
202C23×D5—42no—
203C23×D5Dic614yes—
204C23×D5C4×D314yes—
205C23×D5#6714yes—
206C23×D5C22×D311yescharacteristic
207C23×D5C22×D311yescharacteristic
208C22×C4×C5—31no—
209C22×C4×C5—31no—
210C22×C4×C5—34no—
211C22×C4×C5—32no—
212C22×C4×C5—122no—
213C22×C4×C5C22×D312yes—
214C22×Dic5—31no—
215C22×Dic5—31no—
216C22×Dic5—34no—
217C22×Dic5—32no—
218C22×Dic5—122no—
219C22×Dic5C22×D312yes—
220C2×C4×D5—24no—
221C2×C4×D5—42no—
222C2×C4×D5—42no—
223C2×C4×D5—64no—
224C2×C4×D5—122no—
225C2×C4×D5—122no—
226C5×C4⋊C4—122no—
227C5×C22⋊C4—22no—
228C5×C22⋊C4—62no—
229C22⋊Dic5—22no—
230C22⋊Dic5—62no—
231#685—24no—
232#685—34no—
233#685—34no—
234#685—34no—
235#685—34no—
236#685—64no—
237C4⋊Dic5—122no—
238#683—122no—
239#683—122no—
240C22×C22⋊C4—51no—
241C22×C22⋊C4—151no—
242C22×C22⋊C4—151no—
243#385—152no—
244#385—152no—
245#385—152no—
246#385—152no—
247#380—31no—
248#380—151no—
249#380—151no—
250#380—151no—
251C22×C3×C5—22no—
252C22×C3×C5—22no—
253C22×C3×C5—24no—
254C22×C3×C5—24no—
255C22×C3×C5C2×C4⋊C414yes—
256C22×C3×C5C23×C411yescharacteristic
257C22×C3×C5C22×D411yescharacteristic
258C22×C3×C5C22×Q811yescharacteristic
259C22×C3×C5H(5,𝔽2)12yes—
260C22×C3×C5H(5,𝔽2)12yes—
261C2×C3×D5—22no—
262C2×C3×D5—22no—
263C2×C3×D5—22no—
264C2×C3×D5—22no—
265C2×C3×D5—24no—
266C2×C3×D5—24no—
267C2×C3×D5—24no—
268C2×C3×D5—24no—
269C2×C3×D5—416no—
270C2×C3×D5C2×C4⋊C414yes—
271C2×C3×D5C2×C4⋊C414yes—
272C3×C4×C5—42no—
273Dic15—22no—
274Dic15—22no—
275Dic15—42no—
276C3×Dic5—42no—
277C5×Dic3—22no—
278C5×Dic3—22no—
279C5×Dic3—42no—
280C24×C3—51no—
281C24×C3—51no—
282C24×C3—54no—
283C24×C3—54no—
284C24×C3—54no—
285C24×C3—202no—
286C24×C3—202no—
287C24×C3C22×D511yescharacteristic
288C22×C3×C4—52no—
289C22×C3×C4—104no—
290C22×C3×C4—202no—
291C22×C3×C4—202no—
292C22×C3×C4C22×D512yes—
293C22×Dic3—42no—
294C22×Dic3—51no—
295C22×Dic3—51no—
296C22×Dic3—54no—
297C22×Dic3—52no—
298C22×Dic3—104no—
299C22×Dic3—202no—
300C22×Dic3—202no—
301C22×Dic3—202no—
302C22×Dic3C4×D514yescomplemented
303C22×Dic3C22×D512yes—
304C22×Dic3C22×D511yescharacteristic
305C22×Dic3C22×D511yescharacteristic
306C3×C22⋊C4—22no—
307C3×C22⋊C4—104no—
308C3×C22⋊C4—102no—
309#217—22no—
310#217—54no—
311#217—54no—
312#217—54no—
313#217—54no—
314#217—104no—
315#217—102no—
316Dic3⋊C4—42no—
317Dic3⋊C4—202no—
318Dic3⋊C4—202no—
319Dic3⋊C4—202no—
320C23×C5—22no—
321C23×C5—22no—
322C23×C5C2×Dic612yes—
323C23×C5C2×C4×D312yes—
324C23×C5C2×#6712yes—
325C23×C5C23×D311yescharacteristic
326C22×D5—22no—
327C22×D5—22no—
328C22×D5—22no—
329C22×D5—22no—
330C22×D5—48no—
331C22×D5—44no—
332C22×D5—44no—
333C22×D5—48no—
334C22×D5Dic3⋊C4116yescomplemented
335C22×D5C2×Dic612yes—
336C22×D5C2×Dic612yes—
337C22×D5C2×C4×D312yes—
338C22×D5C2×C4×D312yes—
339C22×D5C2×#6712yes—
340C22×D5C2×#6712yes—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—32no—
345C2×C4×C5—32no—
346C2×C4×C5—62no—
347C2×C4×C5—62no—
348C2×C4×C5—62no—
349C2×C4×C5—62no—
350C2×C4×C5—62no—
351C2×C4×C5—124no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—22no—
355C2×Dic5—32no—
356C2×Dic5—32no—
357C2×Dic5—62no—
358C2×Dic5—62no—
359C2×Dic5—62no—
360C2×Dic5—62no—
361C2×Dic5—62no—
362C2×Dic5—124no—
363C4×D5—48no—
364C4×D5—128no—
365C25—51no—
366C23×C4—31no—
367C23×C4—52no—
368C23×C4—152no—
369C23×C4—151no—
370C2×C4⋊C4—32no—
371C2×C4⋊C4—152no—
372C2×C4⋊C4—152no—
373C2×C4⋊C4—152no—
374C2×C22⋊C4—31no—
375C2×C22⋊C4—51no—
376C2×C22⋊C4—52no—
377C2×C22⋊C4—104no—
378C2×C22⋊C4—151no—
379C2×C22⋊C4—151no—
380C2×C22⋊C4—151no—
381C2×C22⋊C4—151no—
382C2×C22⋊C4—158no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—151no—
385C2×C22⋊C4—304no—
386C2×C22⋊C4D3×D511yescharacteristic
387#95—32no—
388#95—152no—
389#95—152no—
390#95—152no—
391C2×C3×C5—24no—
392C2×C3×C5C22×C4⋊C411yescharacteristic
393C2×C3×C5#51811yescharacteristic
394C2×C3×C5#51811yescharacteristic
395C2×C3×C5#53412yes—
396C2×C3×C5#54312yes—
397C3×D5—24no—
398C3×D5—24no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—52no—
402C23×C3—52no—
403C23×C3—52no—
404C23×C3—52no—
405C23×C3—52no—
406C23×C3—52no—
407C23×C3—516no—
408C23×C3—102no—
409C23×C3—102no—
410C23×C3—102no—
411C23×C3—102no—
412C23×C3—204no—
413C23×C3—204no—
414C23×C3—208no—
415C23×C3—208no—
416C23×C3C2×C4×D512yes—
417C23×C3D4×D512yes—
418C23×C3Q8×D512yes—
419C23×C3C23×D511yescharacteristic
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—102no—
424C2×C3×C4—102no—
425C2×C3×C4—102no—
426C2×C3×C4—208no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—44no—
433C2×Dic3—52no—
434C2×Dic3—52no—
435C2×Dic3—102no—
436C2×Dic3—102no—
437C2×Dic3—102no—
438C2×Dic3—102no—
439C2×Dic3—102no—
440C2×Dic3—208no—
441C2×Dic3—204no—
442C2×Dic3C2×C4×D512yes—
443C2×Dic3C2×C4×D512yes—
444C22×C5—24no—
445C22×C5—22no—
446C22×C5—22no—
447C22×C5—24no—
448C22×C5C2×Dic3⋊C414yes—
449C22×C5C22×Dic611yescharacteristic
450C22×C5C22×C4×D311yescharacteristic
451C22×C5#100412yes—
452C22×C5#100412yes—
453C22×C5C22×#6711yescharacteristic
454C2×D5—24no—
455C2×D5—24no—
456C2×D5—22no—
457C2×D5—22no—
458C2×D5—22no—
459C2×D5—22no—
460C2×D5—24no—
461C2×D5—24no—
462C2×D5—416no—
463C2×D5C2×Dic3⋊C414yes—
464C2×D5C2×Dic3⋊C414yes—
465C4×C5—42no—
466C4×C5—62no—
467C4×C5—62no—
468C4×C5—122no—
469Dic5—42no—
470Dic5—62no—
471Dic5—62no—
472Dic5—122no—
473C24—51no—
474C24—51no—
475C24—54no—
476C24—54no—
477C24—54no—
478C24—202no—
479C24—202no—
480C24C2×D3×D511yescharacteristic
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—34no—
484C22×C4—32no—
485C22×C4—52no—
486C22×C4—104no—
487C22×C4—122no—
488C22×C4—151no—
489C22×C4—151no—
490C22×C4—154no—
491C22×C4—152no—
492C22×C4—202no—
493C22×C4—202no—
494C22×C4—304no—
495C22×C4—602no—
496C22×C4—602no—
497C22×C4—602no—
498C22×C4C2×D3×D512yes—
499C4⋊C4—122no—
500C4⋊C4—602no—
501C4⋊C4—602no—
502C4⋊C4—602no—
503C22⋊C4—22no—
504C22⋊C4—62no—
505C22⋊C4—104no—
506C22⋊C4—102no—
507C22⋊C4—154no—
508C22⋊C4—154no—
509C22⋊C4—154no—
510C22⋊C4—154no—
511C22⋊C4—304no—
512C22⋊C4—302no—
513C3×C5#231511yescharacteristic, complemented, Hall
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—24no—
517C22×C3—24no—
518C22×C3—54no—
519C22×C3—54no—
520C22×C3—102no—
521C22×C3—102no—
522C22×C3—102no—
523C22×C3—102no—
524C22×C3—104no—
525C22×C3—104no—
526C22×C3—104no—
527C22×C3—104no—
528C22×C3—2016no—
529C22×C3D5×C4⋊C414yes—
530C22×C3C22×C4×D511yescharacteristic
531C22×C3C2×D4×D511yescharacteristic
532C22×C3#414412yes—
533C22×C3C2×Q8×D511yescharacteristic
534C22×C3#414912yes—
535C3×C4—42no—
536C3×C4—202no—
537Dic3—22no—
538Dic3—22no—
539Dic3—42no—
540Dic3—102no—
541Dic3—102no—
542Dic3—202no—
543C2×C5—24no—
544C2×C5#548312yes—
545C2×C5#548611yescharacteristic
546C2×C5#548611yescharacteristic
547C2×C5C22×Dic3⋊C411yescharacteristic
548C2×C5#580412yes—
549D5—24no—
550D5—24no—
551C23—22no—
552C23—22no—
553C23—52no—
554C23—52no—
555C23—52no—
556C23—52no—
557C23—52no—
558C23—52no—
559C23—516no—
560C23—102no—
561C23—102no—
562C23—102no—
563C23—102no—
564C23—208no—
565C23—208no—
566C23—204no—
567C23—204no—
568C23D5×Dic612yes—
569C23C4×D3×D512yes—
570C23D5×#6712yes—
571C23C22×D3×D511yescharacteristic
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—32no—
576C2×C4—32no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—102no—
583C2×C4—102no—
584C2×C4—102no—
585C2×C4—124no—
586C2×C4—152no—
587C2×C4—152no—
588C2×C4—208no—
589C2×C4—302no—
590C2×C4—302no—
591C2×C4—302no—
592C2×C4—302no—
593C2×C4—302no—
594C2×C4—608no—
595C2×C4—604no—
596C2×C3—24no—
597C2×C3—104no—
598C2×C3—104no—
599C2×C3#6582011yescharacteristic
600C2×C3C2×D5×C4⋊C411yescharacteristic
601C2×C3#6585511yescharacteristic
602C2×C3#6593912yes—
603C2×C3#6596812yes—
604C5#8209511yescharacteristic, complemented, Sylow
605C22—24no—
606C22—24no—
607C22—22no—
608C22—22no—
609C22—54no—
610C22—54no—
611C22—104no—
612C22—104no—
613C22—104no—
614C22—104no—
615C22—102no—
616C22—102no—
617C22—102no—
618C22—102no—
619C22—2016no—
620C22D5×Dic3⋊C414yes—
621C22C2×D5×Dic611yescharacteristic
622C22C2×C4×D3×D511yescharacteristic
623C22#9202512yes—
624C22#9202612yes—
625C22C2×D5×#6711yescharacteristic
626C4—42no—
627C4—62no—
628C4—62no—
629C4—122no—
630C4—202no—
631C4—302no—
632C4—302no—
633C4—602no—
634C3#1060573611yescharacteristic, complemented, Sylow
635C2—24no—
636C2—104no—
637C2—104no—
638C2#1175304412yes—
639C2#1175306511yescharacteristic
640C2#1175306611yescharacteristic
641C2C2×D5×Dic3⋊C411yescharacteristic
642C2#1175506112yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2315
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #11751043C2semidirect
5. C5×#4942C2semidirect
6. #11749516C2semidirect
7. #11749513C2semidirect
8. #11748891C2semidirect
9. #11748890C2semidirect
10. #11748704C2semidirect
11. #11748703C2semidirect
20. C2×#6712C22semidirect
22. C2×C5×Dic3⋊C4C22semidirect
27. C2×Dic3⋊Dic5C22semidirect
28. C2×#6669C22semidirect
29. C2×#6665C4semidirect
35. #91115C22semidirect
36. C5×C3⋊#95C22semidirect
37. #90994C22semidirect
38. #90994C22semidirect
61. C22×Dic15C2×C4semidirect
66. C22×C5×Dic3C2×C4semidirect
87. #6665C2×C4semidirect
88. #6665C2×C4semidirect
89. #6665C2×C4semidirect
90. #6665C2×C4semidirect
101. #4942D5semidirect
143. C22×C3×D5C4⋊C4semidirect
195. C2×Dic3⋊C4C2×D5semidirect
199. C3⋊#95C2×D5semidirect
302. C22×Dic3C4×D5semidirect
334. C22×D5Dic3⋊C4semidirect
513. C3×C5#2315semidirect
604. C5#82095semidirect
634. C3#10605736semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C22⋊C42
C2×D5×#2172
C22×#66652
#117510432
C5×#49422
#117495162
#117495132
#117488912
#117488902
#117487042
#117487032
#106057363
#820955