Finite Group Databasebeta

← #12099197

Subgroups — #12099197

Order 1280.

1426 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#117C211yesmaximal, characteristic
2C2×#64994C211yesmaximal, characteristic, complemented
3C2×#64974C211yesmaximal, characteristic, complemented
4C5×#1750C211yesmaximal, characteristic, complemented
5#10602375C211yesmaximal, characteristic, complemented
6#10600748C212yesmaximal
7#10600702C212yesmaximal, complemented
8#10600623C211yesmaximal, characteristic, complemented
9#10600546C211yesmaximal, characteristic, complemented
10#10599457C212yesmaximal, complemented
11#10599456C212yesmaximal, 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×C22⋊C8C2212yes—
30C2×C5×#97C2211yescharacteristic, complemented
31C2×C4×C5×C8C2211yescharacteristic, complemented
32C2×C22⋊#168C2212yes—
33C2×#3952C2212yes—
34C2×#3952C2212yes—
35C2×#3952C2212yes—
36C2×#3952C2212yes—
37C2×#3946C2212yescomplemented
38C2×#3946C2212yescomplemented
39C2×#3935C2211yescharacteristic, complemented
40C2×C4×#168C2211yescharacteristic, complemented
41#64994—24no—
42#64974—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—24no—
52C22×C4×D5—22no—
53C22×C4×D5—22no—
54C22×C4×D5—24no—
55C22×C4×D5C2×C411yescharacteristic
56C22×C4×D5C2×C411yescharacteristic
57C22×C4×D5C2×C411yescharacteristic
58C22×C4×D5C2×C411yescharacteristic
59C22×C4×D5C2×C411yescharacteristic
60C22×C4×D5C2×C411yescharacteristic
61C22×C4×D5C2311yescharacteristic
62C22×C4×D5C2311yescharacteristic
63C22×C5×C8C2312yes—
64C22×C5×C8C2312yes—
65C5×#117—22no—
66C5×#117—22no—
67C2×C5×C4⋊C4C2×C411yescharacteristic
68C2×C5×C4⋊C4C2×C411yescharacteristic
69C2×C5×C22⋊C4C2×C411yescharacteristic
70C2×C5×C22⋊C4C2×C411yescharacteristic
71C2×C42×C5C2311yescharacteristic
72C2×C42×C5C2311yescharacteristic
73C2×C22⋊Dic5C2×C411yescharacteristic
74C2×C22⋊Dic5C2×C411yescharacteristic
75C2×#685C2×C411yescharacteristic
76C2×#685C2×C411yescharacteristic
77C2×#685C2×C411yescharacteristic
78C2×#685C2×C411yescharacteristic
79#4072—22no—
80#4072—22no—
81C2×C4⋊Dic5C2×C411yescharacteristic
82C2×C4⋊Dic5C2×C411yescharacteristic
83C2×#683C2×C411yescharacteristic
84C2×#683C2×C411yescharacteristic
85C2×#683C2×C411yescharacteristic
86C2×#683C2×C411yescharacteristic
87C2×C4×Dic5C2×C411yescharacteristic
88C2×C4×Dic5C2×C411yescharacteristic
89C2×C4×Dic5C2×C411yescharacteristic
90C2×C4×Dic5C2×C411yescharacteristic
91C2×C4×Dic5C2311yescharacteristic
92C2×C4×Dic5C2311yescharacteristic
93C22×#168C2312yes—
94C22×#168C2312yes—
95#4038—24no—
96#4038—24no—
97D5×C4⋊C4—24no—
98D5×C4⋊C4—24no—
99D5×C22⋊C4—24no—
100D5×C22⋊C4—24no—
101#4023—24no—
102#4023—24no—
103#4018—22no—
104#4018—22no—
105#4018—22no—
106#4018—22no—
107C42×D5—22no—
108C42×D5—22no—
109C42×D5D414yes—
110C42×D5D414yes—
111C5×C22⋊C8—24no—
112C5×#97—22no—
113C4×C5×C8—22no—
114C22⋊#168—24no—
115#3952—24no—
116#3952—24no—
117#3952—24no—
118#3952—24no—
119#3946—24no—
120#3946—24no—
121#3935—22no—
122C4×#168—22no—
123C22×#117—51no—
124C2×#432—51no—
125C2×#431—51no—
126#1817—52no—
127#1798—52no—
128#1798—52no—
129#1779—52no—
130#1750—51no—
131#1750—51no—
132#1750—51no—
133#1750D511yescharacteristic, complemented
134C24×C5C22×C411yescharacteristic
135C23×D5—22no—
136C23×D5—22no—
137C23×D5—22no—
138C23×D5—24no—
139C23×D5—42no—
140C23×D5C22×C411yescharacteristic
141C23×D5C22×C411yescharacteristic
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—22no—
145C22×C4×C5C22×C411yescharacteristic
146C22×C4×C5C22×C411yescharacteristic
147C22×C4×C5C22×C411yescharacteristic
148C22×C4×C5C22×C411yescharacteristic
149C22×C4×C5C22×C411yescharacteristic
150C22×C4×C5#4114yes—
151C22×C4×C5C2411yescharacteristic
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5C22×C411yescharacteristic
156C22×Dic5C22×C411yescharacteristic
157C22×Dic5C22×C411yescharacteristic
158C22×Dic5C22×C411yescharacteristic
159C22×Dic5C22×C411yescharacteristic
160C22×Dic5C22×C411yescharacteristic
161C2×C4×D5—216no—
162C2×C4×D5—216no—
163C2×C4×D5—22no—
164C2×C4×D5—22no—
165C2×C4×D5—24no—
166C2×C4×D5—22no—
167C2×C4×D5—22no—
168C2×C4×D5—21no—
169C2×C4×D5—21no—
170C2×C4×D5—22no—
171C2×C4×D5—22no—
172C2×C4×D5—22no—
173C2×C4×D5—22no—
174C2×C4×D5—22no—
175C2×C4×D5—22no—
176C2×C4×D5—22no—
177C2×C4×D5—24no—
178C2×C4×D5—42no—
179C2×C4×D5—42no—
180C2×C4×D5C22⋊C414yes—
181C2×C4×D5C22⋊C414yes—
182C2×C4×D5C2×D412yes—
183C2×C4×D5C2×D412yes—
184C2×C4×D5#4114yes—
185C2×C5×C8—22no—
186C2×C5×C8—22no—
187C2×C5×C8—22no—
188C2×C5×C8—22no—
189C2×C5×C8—22no—
190C2×C5×C8—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C22⋊C4—22no—
194C5×C22⋊C4—22no—
195C42×C5—21no—
196C42×C5—21no—
197C42×C5C2×D412yes—
198C42×C5C2×D412yes—
199C22⋊Dic5—22no—
200C22⋊Dic5—22no—
201#685—22no—
202#685—22no—
203#685—22no—
204#685—22no—
205C4⋊Dic5—22no—
206C4⋊Dic5—22no—
207#683—22no—
208#683—22no—
209#683—22no—
210#683—22no—
211C4×Dic5—21no—
212C4×Dic5—21no—
213C4×Dic5—22no—
214C4×Dic5—22no—
215C4×Dic5C22⋊C414yes—
216C4×Dic5C22⋊C414yes—
217C4×Dic5C2×D412yes—
218C4×Dic5C2×D412yes—
219C2×#168—22no—
220C2×#168—22no—
221C2×#168—22no—
222C2×#168—22no—
223C2×#168—22no—
224C2×#168—22no—
225C24×C4—51no—
226C2×#117—51no—
227C2×#117—51no—
228C2×#117—51no—
229C2×#117—51no—
230C2×#117—51no—
231C2×#117—51no—
232C2×#117—51no—
233C2×#117—104no—
234C2×#117—104no—
235C2×#117C2×D511yescharacteristic
236C22×C4⋊C4—51no—
237C22×C4⋊C4—51no—
238C22×C22⋊C4—51no—
239C22×C22⋊C4—51no—
240C22×C42—51no—
241C22×C42—51no—
242#432—104no—
243#431—104no—
244C2×C4⋊C8—52no—
245C2×C4⋊C8—52no—
246C2×C22⋊C8—52no—
247C2×C22⋊C8—52no—
248C2×C22⋊C8—52no—
249C2×C22⋊C8—52no—
250C2×C22⋊C8—52no—
251C2×C22⋊C8C2×D512yes—
252C2×#97—51no—
253C2×#97C2×D511yescharacteristic, complemented
254C2×C4×C8—51no—
255C2×C4×C8C2×D511yescharacteristic, complemented
256#336—52no—
257#336—52no—
258#336—52no—
259#336C2×D512yescomplemented
260C23×C5—21no—
261C23×C5—21no—
262C23×C5—22no—
263C23×C5—22no—
264C23×C5#11712yes—
265C23×C5C23×C411yescharacteristic
266C22×D5—21no—
267C22×D5—21no—
268C22×D5—22no—
269C22×D5—28no—
270C22×D5—21no—
271C22×D5—21no—
272C22×D5—22no—
273C22×D5—22no—
274C22×D5—48no—
275C22×D5—48no—
276C22×D5—44no—
277C22×D5—44no—
278C22×D5C2×C22⋊C412yes—
279C22×D5#11712yes—
280C22×D5#13114yes—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—24no—
286C2×C4×C5—24no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5C2×C22⋊C412yes—
292C2×C4×C5C2×C22⋊C412yes—
293C2×C4×C5#11712yes—
294C2×C4×C5C22×D411yescharacteristic
295C2×C4×C5C22×D411yescharacteristic
296C2×C4×C5C2×#4112yes—
297C2×C4×C5C2×#4112yes—
298C2×Dic5—28no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—22no—
308C2×Dic5—22no—
309C2×Dic5C2×C22⋊C412yes—
310C2×Dic5C2×C22⋊C412yes—
311C2×Dic5C2×C22⋊C412yes—
312C2×Dic5#11712yes—
313C4×D5—28no—
314C4×D5—28no—
315C4×D5—28no—
316C4×D5—24no—
317C4×D5—24no—
318C4×D5—24no—
319C4×D5—24no—
320C4×D5—44no—
321C4×D5—44no—
322C4×D5—44no—
323C5×C8—42no—
324C5×C8—42no—
325#168—42no—
326#168—42no—
327C25—51no—
328C23×C4—51no—
329C23×C4—51no—
330C23×C4—51no—
331C23×C4—51no—
332C23×C4—51no—
333C23×C4—51no—
334C23×C4—51no—
335C23×C4—51no—
336C23×C4—51no—
337C23×C4—102no—
338C23×C4—102no—
339C23×C4—104no—
340C23×C4—104no—
341C23×C4C22×D511yescharacteristic
342C22×C8—52no—
343C22×C8—52no—
344C22×C8C22×D512yes—
345C22×C8C22×D512yes—
346#117—22no—
347#117—22no—
348#117—102no—
349#117—102no—
350#117—104no—
351#117—104no—
352#117—104no—
353#117—104no—
354#117—102no—
355#117—102no—
356#117—102no—
357#117—102no—
358C2×C4⋊C4—51no—
359C2×C4⋊C4—51no—
360C2×C4⋊C4—51no—
361C2×C4⋊C4—51no—
362C2×C4⋊C4—51no—
363C2×C4⋊C4—51no—
364C2×C4⋊C4—104no—
365C2×C4⋊C4—104no—
366C2×C4⋊C4C4×D511yescharacteristic
367C2×C4⋊C4C4×D511yescharacteristic
368C2×C22⋊C4—51no—
369C2×C22⋊C4—51no—
370C2×C22⋊C4—51no—
371C2×C22⋊C4—51no—
372C2×C22⋊C4—51no—
373C2×C22⋊C4—51no—
374C2×C22⋊C4—104no—
375C2×C22⋊C4—104no—
376C2×C22⋊C4C4×D511yescharacteristic
377C2×C22⋊C4C4×D511yescharacteristic
378C2×C42—51no—
379C2×C42—51no—
380C2×C42—51no—
381C2×C42—54no—
382C2×C42—54no—
383C2×C42—51no—
384C2×C42—51no—
385C2×C42—51no—
386C2×C42—102no—
387C2×C42—102no—
388C2×C42C22×D511yescharacteristic
389C2×C42C22×D511yescharacteristic
390C4⋊C8—104no—
391C4⋊C8—104no—
392C22⋊C8—24no—
393C22⋊C8—104no—
394C22⋊C8—104no—
395C22⋊C8—104no—
396C22⋊C8—104no—
397C22⋊C8—104no—
398#97—22no—
399#97—102no—
400C4×C8—22no—
401C4×C8—102no—
402C22×C5—24no—
403C22×C5—22no—
404C22×C5—41no—
405C22×C5—41no—
406C22×C5—42no—
407C22×C5C22×C22⋊C411yescharacteristic
408C22×C5C2×#11711yescharacteristic
409C22×C5C2×#11711yescharacteristic
410C22×C5C2×#13112yes—
411C22×C5#56812yes—
412C2×D5—22no—
413C2×D5—24no—
414C2×D5—24no—
415C2×D5—22no—
416C2×D5—24no—
417C2×D5—22no—
418C2×D5—416no—
419C2×D5—41no—
420C2×D5—41no—
421C2×D5—42no—
422C2×D5#40814yes—
423C4×C5—22no—
424C4×C5—22no—
425C4×C5—22no—
426C4×C5—41no—
427C4×C5—41no—
428C4×C5#52512yes—
429C4×C5#52512yes—
430Dic5—22no—
431Dic5—22no—
432Dic5—22no—
433Dic5—22no—
434Dic5—41no—
435Dic5—41no—
436C24—51no—
437C24—51no—
438C24—102no—
439C24—102no—
440C24—104no—
441C24—102no—
442C24—202no—
443C24C2×C4×D511yescharacteristic
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—51no—
450C22×C4—51no—
451C22×C4—52no—
452C22×C4—52no—
453C22×C4—54no—
454C22×C4—54no—
455C22×C4—54no—
456C22×C4—51no—
457C22×C4—51no—
458C22×C4—102no—
459C22×C4—102no—
460C22×C4—102no—
461C22×C4—102no—
462C22×C4—104no—
463C22×C4—1016no—
464C22×C4—1016no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—104no—
468C22×C4—102no—
469C22×C4—102no—
470C22×C4—102no—
471C22×C4—102no—
472C22×C4—102no—
473C22×C4—101no—
474C22×C4—101no—
475C22×C4—102no—
476C22×C4—102no—
477C22×C4—102no—
478C22×C4—202no—
479C22×C4—202no—
480C22×C4C2×C4×D511yescharacteristic
481C22×C4C2×C4×D511yescharacteristic
482C22×C4C2×C4×D511yescharacteristic
483C22×C4C2×C4×D511yescharacteristic
484C22×C4C2×C4×D511yescharacteristic
485C22×C4#70914yes—
486C22×C4C23×D511yescharacteristic
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—102no—
494C2×C8—102no—
495C2×C8—102no—
496C2×C8—102no—
497C2×C8—102no—
498C2×C8—102no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—102no—
502C4⋊C4—102no—
503C4⋊C4—102no—
504C4⋊C4—102no—
505C4⋊C4—102no—
506C4⋊C4—102no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—102no—
510C22⋊C4—102no—
511C22⋊C4—102no—
512C22⋊C4—102no—
513C22⋊C4—102no—
514C22⋊C4—102no—
515C42—21no—
516C42—21no—
517C42—52no—
518C42—52no—
519C42—54no—
520C42—54no—
521C42—102no—
522C42—102no—
523C42—101no—
524C42—101no—
525C42D4×D512yes—
526C42D4×D512yes—
527C2×C5—42no—
528C2×C5#228011yescharacteristic
529C2×C5C2×#40811yescharacteristic
530C2×C5#287911yescharacteristic
531C2×C5#292412yes—
532C2×C5#292412yes—
533D5—24no—
534D5—42no—
535C23—21no—
536C23—22no—
537C23—22no—
538C23—21no—
539C23—52no—
540C23—54no—
541C23—52no—
542C23—108no—
543C23—101no—
544C23—102no—
545C23—101no—
546C23—101no—
547C23—101no—
548C23—102no—
549C23—102no—
550C23—208no—
551C23—204no—
552C23—208no—
553C23—204no—
554C23#401812yes—
555C23C22×C4×D511yescharacteristic
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—52no—
567C2×C4—52no—
568C2×C4—52no—
569C2×C4—52no—
570C2×C4—108no—
571C2×C4—108no—
572C2×C4—108no—
573C2×C4—108no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—102no—
578C2×C4—102no—
579C2×C4—101no—
580C2×C4—104no—
581C2×C4—104no—
582C2×C4—104no—
583C2×C4—104no—
584C2×C4—101no—
585C2×C4—101no—
586C2×C4—102no—
587C2×C4—102no—
588C2×C4—204no—
589C2×C4—204no—
590C2×C4—204no—
591C2×C4#401812yes—
592C2×C4D5×C22⋊C412yes—
593C2×C4D5×C22⋊C412yes—
594C2×C4C2×#70912yes—
595C2×C4C2×D4×D511yescharacteristic
596C2×C4C2×D4×D511yescharacteristic
597C2×C4D5×#4112yes—
598C8—42no—
599C8—42no—
600C8—202no—
601C8—202no—
602C5#2071711yescharacteristic, complemented, Sylow
603C22—24no—
604C22—22no—
605C22—42no—
606C22—41no—
607C22—41no—
608C22—54no—
609C22—104no—
610C22—104no—
611C22—102no—
612C22—102no—
613C22—104no—
614C22—102no—
615C22—2016no—
616C22—202no—
617C22—201no—
618C22—201no—
619C22C2×#401811yescharacteristic
620C22C2×D5×C22⋊C411yescharacteristic
621C22D5×#11711yescharacteristic
622C22D5×#13112yes—
623C22#6608412yes—
624C4—22no—
625C4—22no—
626C4—22no—
627C4—41no—
628C4—41no—
629C4—102no—
630C4—102no—
631C4—102no—
632C4—102no—
633C4—201no—
634C4—201no—
635C4#6588112yes—
636C4#6588112yes—
637C2—42no—
638C2—104no—
639C2—202no—
640C2#1060529211yescharacteristic
641C2#1061028212yes—
642C2D5×#40811yescharacteristic
643C2#1061039311yescharacteristic
644C2#1061110512yes—
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1750C2
prime radicalC24×D5C2×C4
cosocleC22×C4×C5C24
hypercenter#1750D5
hypocenterC5#20717
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#64994C2semidirect
3. C2×#64974C2semidirect
4. C5×#1750C2semidirect
5. #10602375C2semidirect
7. #10600702C2semidirect
8. #10600623C2semidirect
9. #10600546C2semidirect
10. #10599457C2semidirect
11. #10599456C2semidirect
30. C2×C5×#97C22semidirect
31. C2×C4×C5×C8C22semidirect
37. C2×#3946C22semidirect
38. C2×#3946C22semidirect
39. C2×#3935C22semidirect
40. C2×C4×#168C22semidirect
43. C5×#336C22semidirect
44. #64770C22semidirect
45. #64770C22semidirect
46. #64744C22semidirect
133. #1750D5semidirect
253. C2×#97C2×D5semidirect
255. C2×C4×C8C2×D5semidirect
259. #336C2×D5semidirect
602. 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×#649942
C2×#649742
C5×#17502
#106023752
#106007482
#106007022
#106006232
#106005462
#105994572
#105994562
#207175