Finite Group Databasebeta

← #14424183

Subgroups — #14424183

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#235C211yesmaximal, characteristic
2C3×D5×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×#91515C211yesmaximal, characteristic, complemented
4C2×#91513C211yesmaximal, characteristic, complemented
5#11751148C211yesmaximal, characteristic, complemented
6C5×#5047C211yesmaximal, characteristic, complemented
7#11749400C211yesmaximal, characteristic, complemented
8#11749397C211yesmaximal, characteristic, complemented
9#11748552C211yesmaximal, characteristic, complemented
10#11748538C211yesmaximal, characteristic, complemented
11#11748499C211yesmaximal, characteristic, complemented
12#11747500C211yesmaximal, characteristic, complemented
13#11747498C211yesmaximal, characteristic, complemented
14#11747492C211yesmaximal, characteristic, complemented
15#11747481C211yesmaximal, characteristic, complemented
16#10611959—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C2×C5×#235C2211yescharacteristic
19C2×C3×Q8×D5C2211yescharacteristic, complemented
20C22×C3×C4×D5C2211yescharacteristic
21C2×D5×#67—21no—
22C2×#6782—21no—
23D5×#235—24no—
24D5×#235—24no—
25C2×D5×D12C2211yescharacteristic
26C2×C4×D3×D5—21no—
27C2×#6773C2211yescharacteristic
28C2×#6772C2211yescharacteristic
29C2×#6771—21no—
30C2×D5×Dic6C2211yescharacteristic
31C3×C5×C22⋊Q8C2211yescharacteristic, complemented
32C2×#6718C2211yescharacteristic, complemented
33C2×#6717C2211yescharacteristic, complemented
34C2×C5×#216C2211yescharacteristic, complemented
35C2×C5×#215C2211yescharacteristic, complemented
36C3×#4092C2211yescharacteristic
37C3×#4070C2211yescharacteristic, complemented
38C3×#4043C2211yescharacteristic
39C3×#4042—21no—
40C3×D5×C4⋊C4—21no—
41C3×D5×C4⋊C4C2211yescharacteristic, complemented
42C3×D5×C22⋊C4—21no—
43C3×#4024—21no—
44#91515—24no—
45#91513—24no—
46C2×#6662C2211yescharacteristic, complemented
47C2×#6661C2211yescharacteristic, complemented
48C2×#6658C2211yescharacteristic, complemented
49C2×#6656C2211yescharacteristic, complemented
50C2×#6649C2211yescharacteristic, complemented
51C2×#6649C2211yescharacteristic, complemented
52#91114C2211yescharacteristic, complemented
53#91094C2211yescharacteristic, complemented
54#91093C2211yescharacteristic, complemented
55C5×#830C2211yescharacteristic, complemented
56C5×#810C2211yescharacteristic, complemented
57C5×#809C2211yescharacteristic, complemented
58#90974C2211yescharacteristic, complemented
59#90972C2211yescharacteristic, complemented
60#90968C2211yescharacteristic, complemented
61#90966C2211yescharacteristic, complemented
62#90955C2211yescharacteristic
63#90955C2211yescharacteristic
64#82735—51nomaximal, Hall
65C2×D5×#41—31no—
66C2×#4064—31no—
67C2×#4061—31no—
68D5×C22⋊Q8D311yescharacteristic, complemented
69C5×#452—31no—
70#65528—31no—
71#65475—31no—
72#65458—31no—
73#65336—31no—
74#65097—31no—
75#65092—31no—
76#65065—31no—
77#65060—31no—
78#65022—31no—
79#65015—31no—
80C23×C3×D5D411yescharacteristic
81C22×D3×D5—21no—
82C2×C3×C5×Q8C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C2×#1220—21no—
85#6817—22no—
86#6817—22no—
87C2×D60C2311yescharacteristic
88C2×C4×D15—21no—
89C2×Dic30C2311yescharacteristic
90C2×C5×#67—21no—
91C5×#235—22no—
92C5×#235—22no—
93C2×C5×D12C2311yescharacteristic
94C2×C4×C5×D3—21no—
95C2×C5×Dic6C2311yescharacteristic
96C22×C3×Dic5D411yescharacteristic
97C3×Q8×D5—22no—
98C3×Q8×D5—22no—
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—22no—
101C2×C3×C4×D5—21no—
102C2×C3×C4×D5—21no—
103C2×C3×C4×D5D411yescharacteristic
104C2×C3×C4×D5D411yescharacteristic
105C2×C3×C4×D5C2311yescharacteristic
106C2×C3×C4×D5C2311yescharacteristic
107C2×C3×Dic10—21no—
108C2×C3×Dic10C2311yescharacteristic
109D5×#67—28no—
110C2×#1204—21no—
111C2×#1203—21no—
112C2×#1202—21no—
113C2×#1201—21no—
114C2×#1200—21no—
115#6782—28no—
116C2×D3×Dic5—21no—
117C2×D5×Dic3—21no—
118D5×D12—22no—
119D5×D12—22no—
120C4×D3×D5—28no—
121#6773—22no—
122#6773D414yes—
123#6772—22no—
124#6772D414yes—
125#6771—28no—
126D5×Dic6—22no—
127D5×Dic6—22no—
128C3×C5×C4⋊C4—21no—
129C3×C5×C4⋊C4C2311yescharacteristic
130C3×C5×C22⋊C4—21no—
131#6718—22no—
132#6717—22no—
133C2×C3⋊#168C2311yescharacteristic
134C2×C3⋊#168C2311yescharacteristic
135C5×#216—22no—
136C5×#215—22no—
137C2×C5×C3⋊C8C2311yescharacteristic
138C2×C5×C3⋊C8C2311yescharacteristic
139C3×C22⋊Dic5—21no—
140C3×#685—21no—
141C3×#685—21no—
142C3×C4⋊Dic5—21no—
143C3×C4⋊Dic5C2311yescharacteristic
144C3×#683—21no—
145C3×#683—21no—
146C3×#683—21no—
147#6662—22no—
148#6661—22no—
149#6658—22no—
150#6656—22no—
151#6649—22no—
152#6649—22no—
153C22×#235—51no—
154C2×C3×C22⋊Q8—51no—
155C2×#942—51no—
156C2×#942—51no—
157#5207—51no—
158#5050—51no—
159#5050—51no—
160#5047—51no—
161#5047—51no—
162#5047—51no—
163#5047D511yescharacteristic, complemented
164#5046—51no—
165#5046—51no—
166#4966—51no—
167#4966—51no—
168C2×C5×#41—31no—
169D5×#41—64no—
170D5×#41—64no—
171C2×#713—31no—
172C2×Q8×D5—31no—
173C2×Q8×D5C2×D311yescharacteristic, complemented
174C2×#711—31no—
175C2×#711—61no—
176C2×D4×D5—31no—
177C2×D4×D5—61no—
178C2×#709—31no—
179C2×#709—61no—
180C22×C4×D5—61no—
181C22×C4×D5C2×D311yescharacteristic
182C2×C5×Q16—31no—
183C2×C5×SD16—31no—
184C5×C22⋊Q8C2×D311yescharacteristic, complemented
185#4092C2×D311yescharacteristic
186C2×#689—31no—
187C2×#689—31no—
188C2×#688—31no—
189C2×#687—31no—
190#4070C2×D311yescharacteristic, complemented
191#4064—64no—
192#4061—64no—
193C2×Dic20—31no—
194C2×#677—31no—
195C2×#676—31no—
196C2×#676—31no—
197#4043C2×D311yescharacteristic
198#4042—21no—
199D5×C4⋊C4—21no—
200D5×C4⋊C4C2×D311yescharacteristic, complemented
201D5×C22⋊C4—21no—
202#4024—21no—
203C5×#103—31no—
204C5×#102—31no—
205C5×C22⋊C8—31no—
206#3967—31no—
207#3964—31no—
208C22⋊#168—31no—
209#3953—31no—
210#3952—31no—
211#3952—31no—
212#3948—31no—
213#3942—31no—
214#3941—31no—
215#3007—151noSylow
216C23×C3×C5C2×D411yescharacteristic
217C22×D15—21no—
218C22×C5×D3—21no—
219C22×C3×D5—22no—
220C22×C3×D5—22no—
221C22×C3×D5—41no—
222C22×C3×D5C2×D411yescharacteristic
223C22×C3×D5C2×D411yescharacteristic
224C2×D3×D5—24no—
225C2×D3×D5—42no—
226C2×D3×D5—42no—
227C3×C5×Q8—21no—
228C3×C5×Q8—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5C2×D411yescharacteristic
234C2×C3×C4×C5C2411yescharacteristic
235#1220—24no—
236C2×Dic15—21no—
237D60—21no—
238D60C2×D412yes—
239C4×D15—24no—
240Dic30—21no—
241Dic30C2×D412yes—
242C5×#67—24no—
243C2×C5×Dic3—21no—
244C5×D12—21no—
245C5×D12C2×D412yes—
246C4×C5×D3—24no—
247C5×Dic6—21no—
248C5×Dic6C2×D412yes—
249C2×C3×Dic5—22no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5C2×D411yescharacteristic
253C2×C3×Dic5C2×D411yescharacteristic
254C3×C4×D5—22no—
255C3×C4×D5—21no—
256C3×C4×D5—21no—
257C3×C4×D5—22no—
258C3×C4×D5—42no—
259C3×C4×D5—42no—
260C3×C4×D5C2×D412yes—
261C3×C4×D5C2×D412yes—
262C3×Dic10—21no—
263C3×Dic10—21no—
264C3×Dic10—42no—
265#1204—24no—
266#1203—24no—
267#1202—24no—
268#1201—24no—
269#1200—24no—
270D3×Dic5—24no—
271D5×Dic3—24no—
272C3⋊#168—21no—
273C3⋊#168—21no—
274C5×C3⋊C8—21no—
275C5×C3⋊C8—21no—
276C22×C3×Q8—51no—
277C23×C3×C4—51no—
278C22×#67—101no—
279C2×#235—51no—
280C2×#235—51no—
281C2×#235—51no—
282C2×#235—101no—
283C2×#235—104no—
284C2×#235—104no—
285C2×#235—101no—
286C2×#235C2×D511yescharacteristic
287C22×D12—51no—
288C22×C4×D3—101no—
289C22×Dic6—51no—
290C3×C22⋊Q8—51no—
291C3×C22⋊Q8—51no—
292C3×C22⋊Q8—51no—
293C3×C22⋊Q8—101no—
294C3×C22⋊Q8—101no—
295C3×C22⋊Q8C2×D511yescharacteristic, complemented
296C2×C3×C4⋊C4—51no—
297C2×C3×C4⋊C4—101no—
298C2×C3×C22⋊C4—101no—
299C2×#216—51no—
300C2×#216—51no—
301C2×#216—51no—
302C2×#216C2×D511yescharacteristic, complemented
303#942—104no—
304#942—104no—
305C2×#215—51no—
306C2×#215—51no—
307C2×#215—51no—
308C2×#215C2×D511yescharacteristic, complemented
309C2×#208—51no—
310C2×#208—51no—
311#830—51no—
312#830—51no—
313#830—51no—
314#830C2×D511yescharacteristic, complemented
315#810—51no—
316#810—51no—
317#810—51no—
318#810C2×D511yescharacteristic, complemented
319#809—51no—
320#809—51no—
321#809—51no—
322#809C2×D511yescharacteristic, complemented
323C23×D5—61no—
324C23×D5#6711yescharacteristic
325C5×#41—62no—
326C5×#41—62no—
327C2×C5×Q8—31no—
328C2×C5×Q8C22×D311yescharacteristic
329C2×C5×D4—31no—
330C2×C5×D4—61no—
331C22×C4×C5—61no—
332C22×C4×C5C22×D311yescharacteristic
333C2×C22⋊D5—61no—
334C2×C22⋊D5—61no—
335C2×C22⋊D5—61no—
336C22×Dic5—61no—
337C22×Dic5#6711yescharacteristic
338#713—34no—
339#713—62no—
340Q8×D5—22no—
341Q8×D5—22no—
342Q8×D5—62no—
343Q8×D5—62no—
344#711—34no—
345#711—68no—
346#711—62no—
347D4×D5—62no—
348D4×D5—62no—
349D4×D5—68no—
350#709—62no—
351#709—68no—
352#709—62no—
353C2×D20—31no—
354C2×D20—61no—
355C2×C4×D5—22no—
356C2×C4×D5—22no—
357C2×C4×D5—21no—
358C2×C4×D5—21no—
359C2×C4×D5—68no—
360C2×C4×D5—61no—
361C2×C4×D5—61no—
362C2×C4×D5—61no—
363C2×C4×D5#6711yescharacteristic
364C2×C4×D5#6711yescharacteristic
365C2×C4×D5C22×D311yescharacteristic
366C2×C4×D5C22×D311yescharacteristic
367C2×Dic10—21no—
368C2×Dic10—31no—
369C2×Dic10—61no—
370C2×Dic10C22×D311yescharacteristic
371C5×Q16—62no—
372C5×SD16—62no—
373C2×C5×C8—31no—
374C2×C5×C8—31no—
375C5×C4⋊C4—21no—
376C5×C4⋊C4C22×D311yescharacteristic
377C5×C22⋊C4—21no—
378C22⋊Dic5—21no—
379#689—62no—
380#689—62no—
381#688—62no—
382#687—62no—
383#685—21no—
384#685—21no—
385C4⋊Dic5—21no—
386C4⋊Dic5C22×D311yescharacteristic
387#683—21no—
388#683—21no—
389#683—21no—
390C2×#168—31no—
391C2×#168—31no—
392Dic20—62no—
393#677—62no—
394#676—62no—
395#676—62no—
396C22×#41—151no—
397C2×#137—151no—
398C2×#137—151no—
399C2×C22⋊Q8—51no—
400#452—31no—
401#452—151no—
402#452—151no—
403#452—151no—
404#451—151no—
405#451—151no—
406#450—151no—
407#450—151no—
408#417—151no—
409#417—151no—
410#407—151no—
411C22×C3×C5—21no—
412C22×C3×C5—21no—
413C22×C3×C5—21no—
414C22×C3×C5C22×D411yescharacteristic
415C2×D15—22no—
416C2×D15—41no—
417C2×D15—41no—
418C2×C5×D3—22no—
419C2×C5×D3—41no—
420C2×C5×D3—41no—
421C2×C3×D5—21no—
422C2×C3×D5—21no—
423C2×C3×D5—21no—
424C2×C3×D5—21no—
425C2×C3×D5—44no—
426C2×C3×D5#12012yes—
427C2×C3×D5#13712yescomplemented
428D3×D5—48no—
429C3×C4×C5—21no—
430C3×C4×C5—41no—
431C3×C4×C5—41no—
432C3×C4×C5C22×D411yescharacteristic
433C3×C4×C5C22×D411yescharacteristic
434Dic15—22no—
435C3×Dic5—21no—
436C3×Dic5—41no—
437C3×Dic5—41no—
438C3×Dic5#12012yes—
439C5×Dic3—22no—
440C24×C3—51no—
441C23×D3—101no—
442C2×C3×Q8—51no—
443C2×C3×Q8—101no—
444C2×C3×Q8—102no—
445C2×C3×Q8—102no—
446C2×C3×Q8C22×D511yescharacteristic
447C22×C3×C4—51no—
448C22×C3×C4—51no—
449C22×C3×C4—51no—
450C22×C3×C4—51no—
451C22×C3×C4—51no—
452C22×C3×C4—102no—
453C22×C3×C4—102no—
454C22×C3×C4—101no—
455C22×C3×C4—101no—
456C22×C3×C4C22×D511yescharacteristic
457C2×#67—21no—
458C2×#67—101no—
459C2×#67—108no—
460C2×#67—101no—
461C2×#67—101no—
462C22×Dic3—101no—
463#235—22no—
464#235—22no—
465#235—54no—
466#235—54no—
467#235—102no—
468#235—102no—
469#235—108no—
470#235—102no—
471#235—102no—
472#235—108no—
473C2×D12—51no—
474C2×D12—102no—
475C2×D12—101no—
476C2×D12—102no—
477C2×D12C22×D511yescharacteristic
478C2×C4×D3—21no—
479C2×C4×D3—108no—
480C2×C4×D3—101no—
481C2×C4×D3—101no—
482C2×C4×D3—101no—
483C2×Dic6—51no—
484C2×Dic6—102no—
485C2×Dic6—101no—
486C2×Dic6—102no—
487C2×Dic6C22×D511yescharacteristic
488C3×C4⋊C4—21no—
489C3×C4⋊C4—51no—
490C3×C4⋊C4—101no—
491C3×C4⋊C4—101no—
492C3×C4⋊C4—101no—
493C3×C4⋊C4—101no—
494C3×C4⋊C4C22×D511yescharacteristic
495C3×C22⋊C4—21no—
496C3×C22⋊C4—101no—
497C3×C22⋊C4—101no—
498C3×C22⋊C4—101no—
499#216—22no—
500#216—102no—
501#216—102no—
502#216—102no—
503#215—22no—
504#215—102no—
505#215—102no—
506#215—102no—
507#208—102no—
508#208—102no—
509C2×C3⋊C8—51no—
510C2×C3⋊C8—51no—
511C2×C3⋊C8C22×D511yescharacteristic
512C2×C3⋊C8C22×D511yescharacteristic
513C23×C5—61no—
514C23×C5C2×#6711yescharacteristic
515C22×D5—22no—
516C22×D5—22no—
517C22×D5—41no—
518C22×D5—64no—
519C22×D5—61no—
520C22×D5—122no—
521C22×D5—122no—
522C22×D5C2×#6711yescharacteristic
523C22×D5C2×#6711yescharacteristic
524C5×Q8—21no—
525C5×Q8—21no—
526C5×Q8—32no—
527C5×Q8—61no—
528C5×D4—32no—
529C5×D4—64no—
530C5×D4—61no—
531C2×C4×C5—21no—
532C2×C4×C5—21no—
533C2×C4×C5—21no—
534C2×C4×C5—21no—
535C2×C4×C5—64no—
536C2×C4×C5—61no—
537C2×C4×C5C2×#6711yescharacteristic
538C2×C4×C5C23×D311yescharacteristic
539C22⋊D5—64no—
540C22⋊D5—64no—
541C22⋊D5—64no—
542C2×Dic5—22no—
543C2×Dic5—21no—
544C2×Dic5—21no—
545C2×Dic5—61no—
546C2×Dic5—64no—
547C2×Dic5C2×#6711yescharacteristic
548C2×Dic5C2×#6711yescharacteristic
549D20—32no—
550D20—64no—
551D20—61no—
552C4×D5—22no—
553C4×D5—21no—
554C4×D5—21no—
555C4×D5—22no—
556C4×D5—42no—
557C4×D5—42no—
558C4×D5—64no—
559C4×D5—64no—
560C4×D5—64no—
561C4×D5D3×D412yes—
562C4×D5D3×D412yes—
563Dic10—21no—
564Dic10—21no—
565Dic10—32no—
566Dic10—42no—
567Dic10—64no—
568Dic10—61no—
569C5×C8—61no—
570C5×C8—61no—
571#168—61no—
572#168—61no—
573C2×#41—31no—
574C2×#41—151no—
575C2×#41—151no—
576C2×#41—151no—
577C2×#41—301no—
578C2×#41—301no—
579C2×#41—304no—
580C2×#41—304no—
581C22×Q8—51no—
582C22×Q8—151no—
583C22×D4—151no—
584C22×D4—301no—
585C23×C4—51no—
586C23×C4—301no—
587#137—304no—
588#137—304no—
589C2×Q16—31no—
590C2×Q16—151no—
591C2×Q16—151no—
592C2×Q16—151no—
593C2×SD16—31no—
594C2×SD16—151no—
595C2×SD16—151no—
596C2×SD16—151no—
597C2×M16—151no—
598C2×M16—151no—
599C22⋊Q8—51no—
600C22⋊Q8—51no—
601C22⋊Q8—51no—
602C22⋊Q8—101no—
603C22⋊Q8—101no—
604C22⋊Q8D3×D511yescharacteristic, complemented
605C2×C4⋊C4—51no—
606C2×C4⋊C4—101no—
607C2×C22⋊C4—101no—
608#103—31no—
609#103—151no—
610#103—151no—
611#103—151no—
612#102—31no—
613#102—151no—
614#102—151no—
615#102—151no—
616C22⋊C8—31no—
617C22⋊C8—151no—
618C22⋊C8—151no—
619C22⋊C8—151no—
620C2×C3×C5—41no—
621C2×C3×C5C2×#12011yescharacteristic
622C2×C3×C5C2×#13711yescharacteristic
623C2×C3×C5#57511yescharacteristic
624D15—42no—
625C3×D5—22no—
626C3×D5—22no—
627C5×D3—42no—
628C23×C3—51no—
629C23×C3—51no—
630C23×C3—102no—
631C23×C3—102no—
632C23×C3—201no—
633C23×C3D4×D511yescharacteristic
634C22×D3—21no—
635C22×D3—104no—
636C22×D3—101no—
637C22×D3—202no—
638C22×D3—202no—
639C3×Q8—21no—
640C3×Q8—21no—
641C3×Q8—101no—
642C3×Q8—101no—
643C3×Q8—202no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—51no—
649C2×C3×C4—52no—
650C2×C3×C4—52no—
651C2×C3×C4—51no—
652C2×C3×C4—102no—
653C2×C3×C4—102no—
654C2×C3×C4—102no—
655C2×C3×C4—101no—
656C2×C3×C4—101no—
657C2×C3×C4—101no—
658C2×C3×C4—101no—
659C2×C3×C4—202no—
660C2×C3×C4—202no—
661C2×C3×C4D4×D511yescharacteristic
662C2×C3×C4C23×D511yescharacteristic
663#67—24no—
664#67—104no—
665#67—104no—
666#67—104no—
667C2×Dic3—21no—
668C2×Dic3—104no—
669C2×Dic3—101no—
670D12—21no—
671D12—52no—
672D12—104no—
673D12—101no—
674D12D4×D512yes—
675C4×D3—24no—
676C4×D3—104no—
677C4×D3—104no—
678C4×D3—104no—
679Dic6—21no—
680Dic6—52no—
681Dic6—104no—
682Dic6—101no—
683Dic6D4×D512yes—
684C3⋊C8—21no—
685C3⋊C8—21no—
686C3⋊C8—101no—
687C3⋊C8—101no—
688C22×C5—21no—
689C22×C5—21no—
690C22×C5—21no—
691C22×C5—62no—
692C22×C5—121no—
693C22×C5—121no—
694C22×C5C22×#6711yescharacteristic
695C2×D5—21no—
696C2×D5—21no—
697C2×D5—21no—
698C2×D5—21no—
699C2×D5—44no—
700C2×D5—62no—
701C2×D5—128no—
702C2×D5—121no—
703C2×D5—121no—
704C2×D5#93712yes—
705C2×D5#94212yescomplemented
706C4×C5—21no—
707C4×C5—41no—
708C4×C5—41no—
709C4×C5—62no—
710C4×C5C2×D3×D411yescharacteristic
711C4×C5C2×D3×D411yescharacteristic
712Dic5—21no—
713Dic5—41no—
714Dic5—41no—
715Dic5—62no—
716Dic5#93712yes—
717C24—51no—
718C24—301no—
719#41—62no—
720#41—62no—
721#41—154no—
722#41—154no—
723#41—302no—
724#41—302no—
725#41—302no—
726#41—302no—
727#41—308no—
728#41—308no—
729C2×Q8—31no—
730C2×Q8—51no—
731C2×Q8—101no—
732C2×Q8—102no—
733C2×Q8—102no—
734C2×Q8—151no—
735C2×Q8—301no—
736C2×Q8—302no—
737C2×Q8—302no—
738C2×Q8C2×D3×D511yescharacteristic
739C2×D4—31no—
740C2×D4—61no—
741C2×D4—151no—
742C2×D4—301no—
743C2×D4—301no—
744C2×D4—302no—
745C2×D4—302no—
746C2×D4—308no—
747C2×D4—301no—
748C2×D4—301no—
749C22×C4—51no—
750C22×C4—51no—
751C22×C4—51no—
752C22×C4—51no—
753C22×C4—51no—
754C22×C4—61no—
755C22×C4—102no—
756C22×C4—102no—
757C22×C4—101no—
758C22×C4—101no—
759C22×C4—301no—
760C22×C4—301no—
761C22×C4—308no—
762C22×C4—301no—
763C22×C4—301no—
764C22×C4C2×D3×D511yescharacteristic
765Q16—62no—
766Q16—302no—
767Q16—302no—
768Q16—302no—
769SD16—62no—
770SD16—302no—
771SD16—302no—
772SD16—302no—
773M16—302no—
774M16—302no—
775C2×C8—31no—
776C2×C8—31no—
777C2×C8—151no—
778C2×C8—151no—
779C4⋊C4—21no—
780C4⋊C4—51no—
781C4⋊C4—101no—
782C4⋊C4—101no—
783C4⋊C4—101no—
784C4⋊C4—101no—
785C4⋊C4C2×D3×D511yescharacteristic
786C22⋊C4—21no—
787C22⋊C4—101no—
788C22⋊C4—101no—
789C22⋊C4—101no—
790C3×C5#300711yescharacteristic, complemented, Hall
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—52no—
795C22×C3—52no—
796C22×C3—101no—
797C22×C3—101no—
798C22×C3—101no—
799C22×C3—101no—
800C22×C3—204no—
801C22×C3C2×D4×D511yescharacteristic
802C2×D3—22no—
803C2×D3—41no—
804C2×D3—41no—
805C2×D3—102no—
806C2×D3—208no—
807C2×D3—201no—
808C2×D3—201no—
809C3×C4—21no—
810C3×C4—41no—
811C3×C4—41no—
812C3×C4—52no—
813C3×C4—101no—
814C3×C4—201no—
815C3×C4—201no—
816C3×C4C2×D4×D511yescharacteristic
817C3×C4C2×D4×D511yescharacteristic
818Dic3—22no—
819Dic3—102no—
820C2×C5—41no—
821C2×C5—122no—
822C2×C5C2×#93711yescharacteristic
823C2×C5C2×#94211yescharacteristic
824C2×C5#582211yescharacteristic
825D5—22no—
826D5—22no—
827D5—122no—
828C23—51no—
829C23—51no—
830C23—61no—
831C23—102no—
832C23—102no—
833C23—201no—
834C23—304no—
835C23—301no—
836C23—602no—
837C23—602no—
838C23D5×#6711yescharacteristic
839Q8—21no—
840Q8—21no—
841Q8—32no—
842Q8—61no—
843Q8—101no—
844Q8—101no—
845Q8—152no—
846Q8—202no—
847Q8—304no—
848Q8—301no—
849D4—32no—
850D4—64no—
851D4—61no—
852D4—152no—
853D4—304no—
854D4—304no—
855D4—304no—
856D4—304no—
857D4—301no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—51no—
863C2×C4—52no—
864C2×C4—52no—
865C2×C4—51no—
866C2×C4—64no—
867C2×C4—61no—
868C2×C4—102no—
869C2×C4—102no—
870C2×C4—102no—
871C2×C4—101no—
872C2×C4—101no—
873C2×C4—101no—
874C2×C4—101no—
875C2×C4—202no—
876C2×C4—202no—
877C2×C4—304no—
878C2×C4—304no—
879C2×C4—304no—
880C2×C4—304no—
881C2×C4—301no—
882C2×C4D5×#6711yescharacteristic
883C2×C4C22×D3×D511yescharacteristic
884C8—61no—
885C8—61no—
886C8—301no—
887C8—301no—
888C2×C3—41no—
889C2×C3—102no—
890C2×C3—102no—
891C2×C3D5×#12011yescharacteristic
892C2×C3#6610211yescharacteristic
893C2×C3D5×#13711yescharacteristic
894D3—42no—
895D3—202no—
896C5#8273511yescharacteristic, complemented, Sylow
897C22—21no—
898C22—21no—
899C22—21no—
900C22—52no—
901C22—52no—
902C22—62no—
903C22—101no—
904C22—101no—
905C22—101no—
906C22—101no—
907C22—121no—
908C22—121no—
909C22—204no—
910C22—302no—
911C22—608no—
912C22—601no—
913C22—601no—
914C22C2×D5×#6711yescharacteristic
915C4—21no—
916C4—41no—
917C4—41no—
918C4—52no—
919C4—62no—
920C4—101no—
921C4—201no—
922C4—201no—
923C4—302no—
924C4D3×D4×D511yescharacteristic
925C4D3×D4×D511yescharacteristic
926C3#1061195911yescharacteristic, complemented, Sylow
927C2—41no—
928C2—102no—
929C2—102no—
930C2—122no—
931C2—602no—
932C2D5×#93711yescharacteristic
933C2D5×#94211yescharacteristic
934C2#1175531511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×#235C2
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×D5×C22⋊Q8C2semidirect
3. C2×#91515C2semidirect
4. C2×#91513C2semidirect
5. #11751148C2semidirect
6. C5×#5047C2semidirect
7. #11749400C2semidirect
8. #11749397C2semidirect
9. #11748552C2semidirect
10. #11748538C2semidirect
11. #11748499C2semidirect
12. #11747500C2semidirect
13. #11747498C2semidirect
14. #11747492C2semidirect
15. #11747481C2semidirect
19. C2×C3×Q8×D5C22semidirect
31. C3×C5×C22⋊Q8C22semidirect
32. C2×#6718C22semidirect
33. C2×#6717C22semidirect
34. C2×C5×#216C22semidirect
35. C2×C5×#215C22semidirect
37. C3×#4070C22semidirect
41. C3×D5×C4⋊C4C22semidirect
46. C2×#6662C22semidirect
47. C2×#6661C22semidirect
48. C2×#6658C22semidirect
49. C2×#6656C22semidirect
50. C2×#6649C22semidirect
51. C2×#6649C22semidirect
52. #91114C22semidirect
53. #91094C22semidirect
54. #91093C22semidirect
55. C5×#830C22semidirect
56. C5×#810C22semidirect
57. C5×#809C22semidirect
58. #90974C22semidirect
59. #90972C22semidirect
60. #90968C22semidirect
61. #90966C22semidirect
68. D5×C22⋊Q8D3semidirect
163. #5047D5semidirect
173. C2×Q8×D5C2×D3semidirect
184. C5×C22⋊Q8C2×D3semidirect
190. #4070C2×D3semidirect
200. D5×C4⋊C4C2×D3semidirect
295. C3×C22⋊Q8C2×D5semidirect
302. C2×#216C2×D5semidirect
308. C2×#215C2×D5semidirect
314. #830C2×D5semidirect
318. #810C2×D5semidirect
322. #809C2×D5semidirect
427. C2×C3×D5#137semidirect
604. C22⋊Q8D3×D5semidirect
705. C2×D5#942semidirect
790. C3×C5#3007semidirect
896. C5#82735semidirect
926. C3#10611959semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2352
C3×D5×C22⋊Q82
C2×#915152
C2×#915132
#117511482
C5×#50472
#117494002
#117493972
#117485522
#117485382
#117484992
#117475002
#117474982
#117474922
#117474812
#106119593
#827355