Finite Group Databasebeta

← #12099198

Subgroups — #12099198

Order 1280.

1426 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#117C211yesmaximal, characteristic
2C2×#65124C211yesmaximal, characteristic, complemented
3C2×#65122C211yesmaximal, characteristic, complemented
4C5×#1798C211yesmaximal, characteristic, complemented
5#10602376C211yesmaximal, characteristic, complemented
6#10601269C211yesmaximal, characteristic, complemented
7#10601269C211yesmaximal, characteristic, complemented
8#10600748C212yesmaximal
9#10600700C212yesmaximal, complemented
10#10599457C212yesmaximal, complemented
11#10599394C212yesmaximal, complemented
12C23×C4×D5C2211yescharacteristic
13C2×C5×#117C2211yescharacteristic
14C2×#4072C2211yescharacteristic
15D5×#117—24no—
16D5×#117—24no—
17C2×#4038C411yescharacteristic
18C2×#4038C411yescharacteristic
19C2×D5×C4⋊C4C411yescharacteristic
20C2×D5×C4⋊C4C411yescharacteristic
21C2×D5×C22⋊C4C411yescharacteristic
22C2×D5×C22⋊C4C411yescharacteristic
23C2×#4023C411yescharacteristic
24C2×#4023C411yescharacteristic
25C2×#4018C2211yescharacteristic
26C2×#4018C2211yescharacteristic
27C2×C42×D5C2211yescharacteristic
28C2×C42×D5C2211yescharacteristic
29C2×C5×C4⋊C8C2211yescharacteristic, complemented
30C2×C5×C4⋊C8C2211yescharacteristic, complemented
31C2×C5×C22⋊C8C2212yes—
32C2×C22⋊#168C2212yes—
33C2×#3952C2212yes—
34C2×#3952C2212yes—
35C2×#3952C2212yes—
36C2×#3952C2212yes—
37C2×#3947C2212yescomplemented
38C2×C8×Dic5C2212yescomplemented
39C2×C4⋊#168C2211yescharacteristic, complemented
40C2×C4⋊#168C2211yescharacteristic, complemented
41#65124—24no—
42#65122—24no—
43C5×#336C2212yescomplemented
44#64770C2212yescomplemented
45#64770C2212yescomplemented
46#64744C2212yescomplemented
47#20717—51nomaximal, Sylow
48C24×D5C2×C411yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C23×Dic5C2×C411yescharacteristic
51C22×C4×D5—22no—
52C22×C4×D5—22no—
53C22×C4×D5—22no—
54C22×C4×D5—22no—
55C22×C4×D5—22no—
56C22×C4×D5—22no—
57C22×C4×D5C2×C411yescharacteristic
58C22×C4×D5C2×C411yescharacteristic
59C22×C4×D5C2×C411yescharacteristic
60C22×C4×D5C2×C411yescharacteristic
61C22×C4×D5C2×C411yescharacteristic
62C22×C4×D5C2×C411yescharacteristic
63C22×C4×D5C2311yescharacteristic
64C22×C4×D5C2311yescharacteristic
65C22×C5×C8C2312yes—
66C22×C5×C8C2312yes—
67C5×#117—22no—
68C5×#117—22no—
69C2×C5×C4⋊C4C2×C411yescharacteristic
70C2×C5×C4⋊C4C2×C411yescharacteristic
71C2×C5×C22⋊C4C2×C411yescharacteristic
72C2×C5×C22⋊C4C2×C411yescharacteristic
73C2×C42×C5C2311yescharacteristic
74C2×C42×C5C2311yescharacteristic
75C2×C22⋊Dic5C2×C411yescharacteristic
76C2×C22⋊Dic5C2×C411yescharacteristic
77C2×#685C2×C411yescharacteristic
78C2×#685C2×C411yescharacteristic
79C2×#685C2×C411yescharacteristic
80C2×#685C2×C411yescharacteristic
81#4072—22no—
82#4072—22no—
83C2×C4⋊Dic5C2×C411yescharacteristic
84C2×C4⋊Dic5C2×C411yescharacteristic
85C2×#683C2×C411yescharacteristic
86C2×#683C2×C411yescharacteristic
87C2×#683C2×C411yescharacteristic
88C2×#683C2×C411yescharacteristic
89C2×C4×Dic5C2×C411yescharacteristic
90C2×C4×Dic5C2×C411yescharacteristic
91C2×C4×Dic5C2×C411yescharacteristic
92C2×C4×Dic5C2×C411yescharacteristic
93C2×C4×Dic5C2311yescharacteristic
94C2×C4×Dic5C2311yescharacteristic
95C22×#168C2312yes—
96C22×#168C2312yes—
97#4038—24no—
98#4038—24no—
99D5×C4⋊C4—24no—
100D5×C4⋊C4—24no—
101D5×C22⋊C4—24no—
102D5×C22⋊C4—24no—
103#4023—24no—
104#4023—24no—
105#4018—22no—
106#4018—22no—
107#4018—22no—
108#4018—22no—
109C42×D5—22no—
110C42×D5—22no—
111C42×D5D414yes—
112C42×D5D414yes—
113C5×C4⋊C8—22no—
114C5×C4⋊C8—22no—
115C5×C22⋊C8—24no—
116C22⋊#168—24no—
117#3952—24no—
118#3952—24no—
119#3952—24no—
120#3952—24no—
121#3947—24no—
122C8×Dic5—24no—
123C4⋊#168—22no—
124C4⋊#168—22no—
125C22×#117—51no—
126C2×#432—51no—
127C2×#431—51no—
128#1817—52no—
129#1798—51no—
130#1798—51no—
131#1798—51no—
132#1798D511yescharacteristic, complemented
133#1779—52no—
134#1750—52no—
135#1750—52no—
136C24×C5C22×C411yescharacteristic
137C23×D5—22no—
138C23×D5—22no—
139C23×D5—22no—
140C23×D5—24no—
141C23×D5—42no—
142C23×D5C22×C411yescharacteristic
143C23×D5C22×C411yescharacteristic
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5C22×C411yescharacteristic
149C22×C4×C5C22×C411yescharacteristic
150C22×C4×C5C22×C411yescharacteristic
151C22×C4×C5C22×C411yescharacteristic
152C22×C4×C5C22×C411yescharacteristic
153C22×C4×C5#4112yes—
154C22×C4×C5#4112yes—
155C22×C4×C5C2411yescharacteristic
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5C22×C411yescharacteristic
160C22×Dic5C22×C411yescharacteristic
161C22×Dic5C22×C411yescharacteristic
162C22×Dic5C22×C411yescharacteristic
163C22×Dic5C22×C411yescharacteristic
164C22×Dic5C22×C411yescharacteristic
165C2×C4×D5—28no—
166C2×C4×D5—28no—
167C2×C4×D5—28no—
168C2×C4×D5—28no—
169C2×C4×D5—22no—
170C2×C4×D5—22no—
171C2×C4×D5—24no—
172C2×C4×D5—22no—
173C2×C4×D5—22no—
174C2×C4×D5—21no—
175C2×C4×D5—21no—
176C2×C4×D5—21no—
177C2×C4×D5—21no—
178C2×C4×D5—21no—
179C2×C4×D5—21no—
180C2×C4×D5—21no—
181C2×C4×D5—21no—
182C2×C4×D5—22no—
183C2×C4×D5—22no—
184C2×C4×D5—22no—
185C2×C4×D5—22no—
186C2×C4×D5—24no—
187C2×C4×D5—42no—
188C2×C4×D5—42no—
189C2×C4×D5C22⋊C414yes—
190C2×C4×D5C22⋊C414yes—
191C2×C4×D5C2×D412yes—
192C2×C4×D5C2×D412yes—
193C2×C4×D5#4112yes—
194C2×C4×D5#4112yes—
195C2×C5×C8—22no—
196C2×C5×C8—22no—
197C2×C5×C8—22no—
198C2×C5×C8—22no—
199C2×C5×C8—22no—
200C2×C5×C8—22no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—22no—
203C5×C22⋊C4—22no—
204C5×C22⋊C4—22no—
205C42×C5—21no—
206C42×C5—21no—
207C42×C5C2×D412yes—
208C42×C5C2×D412yes—
209C22⋊Dic5—22no—
210C22⋊Dic5—22no—
211#685—22no—
212#685—22no—
213#685—22no—
214#685—22no—
215C4⋊Dic5—22no—
216C4⋊Dic5—22no—
217#683—22no—
218#683—22no—
219#683—22no—
220#683—22no—
221C4×Dic5—21no—
222C4×Dic5—21no—
223C4×Dic5—22no—
224C4×Dic5—22no—
225C4×Dic5C22⋊C414yes—
226C4×Dic5C22⋊C414yes—
227C4×Dic5C2×D412yes—
228C4×Dic5C2×D412yes—
229C2×#168—22no—
230C2×#168—22no—
231C2×#168—22no—
232C2×#168—22no—
233C2×#168—22no—
234C2×#168—22no—
235C24×C4—51no—
236C2×#117—51no—
237C2×#117—51no—
238C2×#117—51no—
239C2×#117—51no—
240C2×#117—51no—
241C2×#117—51no—
242C2×#117—51no—
243C2×#117—104no—
244C2×#117—104no—
245C2×#117C2×D511yescharacteristic
246C22×C4⋊C4—51no—
247C22×C4⋊C4—51no—
248C22×C22⋊C4—51no—
249C22×C22⋊C4—51no—
250C22×C42—51no—
251C22×C42—51no—
252#432—104no—
253#431—104no—
254C2×C4⋊C8—51no—
255C2×C4⋊C8—51no—
256C2×C4⋊C8C2×D511yescharacteristic, complemented
257C2×C4⋊C8C2×D511yescharacteristic, complemented
258C2×C22⋊C8—52no—
259C2×C22⋊C8—52no—
260C2×C22⋊C8—52no—
261C2×C22⋊C8—52no—
262C2×C22⋊C8—52no—
263C2×C22⋊C8C2×D512yes—
264C2×#97—52no—
265C2×C4×C8—52no—
266#336—52no—
267#336—52no—
268#336—52no—
269#336C2×D512yescomplemented
270C23×C5—21no—
271C23×C5—21no—
272C23×C5—22no—
273C23×C5—22no—
274C23×C5#11712yes—
275C23×C5C23×C411yescharacteristic
276C22×D5—21no—
277C22×D5—21no—
278C22×D5—22no—
279C22×D5—28no—
280C22×D5—21no—
281C22×D5—21no—
282C22×D5—22no—
283C22×D5—22no—
284C22×D5—48no—
285C22×D5—48no—
286C22×D5—44no—
287C22×D5—44no—
288C22×D5C2×C22⋊C412yes—
289C22×D5#11712yes—
290C22×D5#13114yes—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—22no—
294C2×C4×C5—22no—
295C2×C4×C5—22no—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—22no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5C2×C22⋊C412yes—
304C2×C4×C5C2×C22⋊C412yes—
305C2×C4×C5#11712yes—
306C2×C4×C5C22×D411yescharacteristic
307C2×C4×C5C22×D411yescharacteristic
308C2×C4×C5C2×#4111yescharacteristic
309C2×C4×C5C2×#4111yescharacteristic
310C2×C4×C5C2×#4111yescharacteristic
311C2×C4×C5C2×#4111yescharacteristic
312C2×Dic5—28no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—22no—
318C2×Dic5—22no—
319C2×Dic5—21no—
320C2×Dic5—21no—
321C2×Dic5—22no—
322C2×Dic5—22no—
323C2×Dic5C2×C22⋊C412yes—
324C2×Dic5C2×C22⋊C412yes—
325C2×Dic5C2×C22⋊C412yes—
326C2×Dic5#11712yes—
327C4×D5—28no—
328C4×D5—28no—
329C4×D5—28no—
330C4×D5—22no—
331C4×D5—22no—
332C4×D5—22no—
333C4×D5—22no—
334C4×D5—22no—
335C4×D5—22no—
336C4×D5—22no—
337C4×D5—22no—
338C4×D5—44no—
339C4×D5—44no—
340C4×D5—44no—
341C5×C8—42no—
342C5×C8—42no—
343#168—42no—
344#168—42no—
345C25—51no—
346C23×C4—51no—
347C23×C4—51no—
348C23×C4—51no—
349C23×C4—51no—
350C23×C4—51no—
351C23×C4—51no—
352C23×C4—51no—
353C23×C4—51no—
354C23×C4—51no—
355C23×C4—102no—
356C23×C4—102no—
357C23×C4—102no—
358C23×C4—102no—
359C23×C4—102no—
360C23×C4—102no—
361C23×C4C22×D511yescharacteristic
362C22×C8—52no—
363C22×C8—52no—
364C22×C8C22×D512yes—
365C22×C8C22×D512yes—
366#117—22no—
367#117—22no—
368#117—102no—
369#117—102no—
370#117—104no—
371#117—104no—
372#117—104no—
373#117—104no—
374#117—102no—
375#117—102no—
376#117—102no—
377#117—102no—
378C2×C4⋊C4—51no—
379C2×C4⋊C4—51no—
380C2×C4⋊C4—51no—
381C2×C4⋊C4—51no—
382C2×C4⋊C4—51no—
383C2×C4⋊C4—51no—
384C2×C4⋊C4—104no—
385C2×C4⋊C4—104no—
386C2×C4⋊C4C4×D511yescharacteristic
387C2×C4⋊C4C4×D511yescharacteristic
388C2×C22⋊C4—51no—
389C2×C22⋊C4—51no—
390C2×C22⋊C4—51no—
391C2×C22⋊C4—51no—
392C2×C22⋊C4—51no—
393C2×C22⋊C4—51no—
394C2×C22⋊C4—104no—
395C2×C22⋊C4—104no—
396C2×C22⋊C4C4×D511yescharacteristic
397C2×C22⋊C4C4×D511yescharacteristic
398C2×C42—51no—
399C2×C42—51no—
400C2×C42—51no—
401C2×C42—54no—
402C2×C42—54no—
403C2×C42—51no—
404C2×C42—51no—
405C2×C42—51no—
406C2×C42—102no—
407C2×C42—102no—
408C2×C42C22×D511yescharacteristic
409C2×C42C22×D511yescharacteristic
410C4⋊C8—22no—
411C4⋊C8—22no—
412C4⋊C8—102no—
413C4⋊C8—102no—
414C22⋊C8—24no—
415C22⋊C8—104no—
416C22⋊C8—104no—
417C22⋊C8—104no—
418C22⋊C8—104no—
419C22⋊C8—104no—
420#97—104no—
421C4×C8—104no—
422C22×C5—24no—
423C22×C5—22no—
424C22×C5—41no—
425C22×C5—41no—
426C22×C5—42no—
427C22×C5C22×C22⋊C411yescharacteristic
428C22×C5C2×#11711yescharacteristic
429C22×C5C2×#11711yescharacteristic
430C22×C5C2×#13112yes—
431C22×C5#56812yes—
432C2×D5—22no—
433C2×D5—24no—
434C2×D5—24no—
435C2×D5—22no—
436C2×D5—24no—
437C2×D5—22no—
438C2×D5—416no—
439C2×D5—41no—
440C2×D5—41no—
441C2×D5—42no—
442C2×D5#40814yes—
443C4×C5—22no—
444C4×C5—22no—
445C4×C5—22no—
446C4×C5—41no—
447C4×C5—41no—
448C4×C5#52511yescharacteristic
449C4×C5#52511yescharacteristic
450C4×C5#52511yescharacteristic
451C4×C5#52511yescharacteristic
452Dic5—22no—
453Dic5—22no—
454Dic5—22no—
455Dic5—22no—
456Dic5—41no—
457Dic5—41no—
458C24—51no—
459C24—51no—
460C24—102no—
461C24—102no—
462C24—104no—
463C24—102no—
464C24—202no—
465C24C2×C4×D511yescharacteristic
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—51no—
471C22×C4—51no—
472C22×C4—51no—
473C22×C4—51no—
474C22×C4—52no—
475C22×C4—52no—
476C22×C4—52no—
477C22×C4—52no—
478C22×C4—54no—
479C22×C4—54no—
480C22×C4—51no—
481C22×C4—51no—
482C22×C4—102no—
483C22×C4—102no—
484C22×C4—102no—
485C22×C4—102no—
486C22×C4—104no—
487C22×C4—108no—
488C22×C4—108no—
489C22×C4—108no—
490C22×C4—108no—
491C22×C4—102no—
492C22×C4—102no—
493C22×C4—104no—
494C22×C4—102no—
495C22×C4—102no—
496C22×C4—102no—
497C22×C4—101no—
498C22×C4—101no—
499C22×C4—101no—
500C22×C4—101no—
501C22×C4—101no—
502C22×C4—101no—
503C22×C4—101no—
504C22×C4—101no—
505C22×C4—102no—
506C22×C4—102no—
507C22×C4—202no—
508C22×C4—202no—
509C22×C4C2×C4×D511yescharacteristic
510C22×C4C2×C4×D511yescharacteristic
511C22×C4C2×C4×D511yescharacteristic
512C22×C4C2×C4×D511yescharacteristic
513C22×C4C2×C4×D511yescharacteristic
514C22×C4#71112yes—
515C22×C4#71312yes—
516C22×C4C23×D511yescharacteristic
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—102no—
524C2×C8—102no—
525C2×C8—102no—
526C2×C8—102no—
527C2×C8—102no—
528C2×C8—102no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—102no—
532C4⋊C4—102no—
533C4⋊C4—102no—
534C4⋊C4—102no—
535C4⋊C4—102no—
536C4⋊C4—102no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—102no—
540C22⋊C4—102no—
541C22⋊C4—102no—
542C22⋊C4—102no—
543C22⋊C4—102no—
544C22⋊C4—102no—
545C42—21no—
546C42—21no—
547C42—52no—
548C42—52no—
549C42—54no—
550C42—54no—
551C42—102no—
552C42—102no—
553C42—101no—
554C42—101no—
555C42D4×D512yes—
556C42D4×D512yes—
557C2×C5—42no—
558C2×C5#228011yescharacteristic
559C2×C5C2×#40811yescharacteristic
560C2×C5#287911yescharacteristic
561C2×C5#292412yes—
562C2×C5#292412yes—
563D5—24no—
564D5—42no—
565C23—21no—
566C23—22no—
567C23—22no—
568C23—21no—
569C23—52no—
570C23—54no—
571C23—52no—
572C23—108no—
573C23—102no—
574C23—101no—
575C23—101no—
576C23—101no—
577C23—102no—
578C23—102no—
579C23—101no—
580C23—208no—
581C23—204no—
582C23—208no—
583C23—204no—
584C23#403812yes—
585C23C22×C4×D511yescharacteristic
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—52no—
599C2×C4—52no—
600C2×C4—52no—
601C2×C4—52no—
602C2×C4—108no—
603C2×C4—108no—
604C2×C4—108no—
605C2×C4—108no—
606C2×C4—101no—
607C2×C4—102no—
608C2×C4—102no—
609C2×C4—101no—
610C2×C4—101no—
611C2×C4—101no—
612C2×C4—102no—
613C2×C4—102no—
614C2×C4—102no—
615C2×C4—102no—
616C2×C4—102no—
617C2×C4—102no—
618C2×C4—102no—
619C2×C4—102no—
620C2×C4—101no—
621C2×C4—101no—
622C2×C4—102no—
623C2×C4—102no—
624C2×C4—204no—
625C2×C4—204no—
626C2×C4—204no—
627C2×C4D5×C22⋊C412yes—
628C2×C4D5×C22⋊C412yes—
629C2×C4#403812yes—
630C2×C4C2×D4×D511yescharacteristic
631C2×C4C2×D4×D511yescharacteristic
632C2×C4C2×#71111yescharacteristic
633C2×C4C2×#71311yescharacteristic
634C2×C4D5×#4111yescharacteristic
635C2×C4D5×#4111yescharacteristic
636C8—42no—
637C8—42no—
638C8—202no—
639C8—202no—
640C5#2071711yescharacteristic, complemented, Sylow
641C22—22no—
642C22—24no—
643C22—42no—
644C22—41no—
645C22—41no—
646C22—54no—
647C22—102no—
648C22—104no—
649C22—104no—
650C22—102no—
651C22—102no—
652C22—104no—
653C22—2016no—
654C22—202no—
655C22—201no—
656C22—201no—
657C22C2×D5×C22⋊C411yescharacteristic
658C22C2×#403811yescharacteristic
659C22D5×#11711yescharacteristic
660C22D5×#13112yes—
661C22#6608412yes—
662C4—22no—
663C4—22no—
664C4—22no—
665C4—41no—
666C4—41no—
667C4—102no—
668C4—102no—
669C4—102no—
670C4—102no—
671C4—201no—
672C4—201no—
673C4#6594011yescharacteristic
674C4#6594011yescharacteristic
675C4#6596111yescharacteristic
676C4#6596111yescharacteristic
677C2—42no—
678C2—104no—
679C2—202no—
680C2#1060559311yescharacteristic
681C2D5×#40811yescharacteristic
682C2#1061039311yescharacteristic
683C2#1061080312yes—
684C2#1061110512yes—
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1798C2
prime radicalC24×D5C2×C4
cosocleC22×C4×C5C24
hypercenter#1798D5
hypocenterC5#20717
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. C2×#65124C2semidirect
3. C2×#65122C2semidirect
4. C5×#1798C2semidirect
5. #10602376C2semidirect
6. #10601269C2semidirect
7. #10601269C2semidirect
9. #10600700C2semidirect
10. #10599457C2semidirect
11. #10599394C2semidirect
29. C2×C5×C4⋊C8C22semidirect
30. C2×C5×C4⋊C8C22semidirect
37. C2×#3947C22semidirect
38. C2×C8×Dic5C22semidirect
39. C2×C4⋊#168C22semidirect
40. C2×C4⋊#168C22semidirect
43. C5×#336C22semidirect
44. #64770C22semidirect
45. #64770C22semidirect
46. #64744C22semidirect
132. #1798D5semidirect
256. C2×C4⋊C8C2×D5semidirect
257. C2×C4⋊C8C2×D5semidirect
269. #336C2×D5semidirect
640. C5#20717semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#1172
C2×#651242
C2×#651222
C5×#17982
#106023762
#106012692
#106007482
#106007002
#105994572
#105993942
#207175