Finite Group Databasebeta

← #12099225

Subgroups — #12099225

Order 1280.

1350 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65856C211yesmaximal, characteristic
2C2×#64994C211yesmaximal, characteristic, complemented
3C2×#64974C211yesmaximal, characteristic, complemented
4C5×#1750C211yesmaximal, characteristic, complemented
5#10602375C211yesmaximal, characteristic, complemented
6#10600749C212yesmaximal
7#10600701C212yesmaximal, complemented
8#10600623C211yesmaximal, characteristic, complemented
9#10600546C211yesmaximal, characteristic, complemented
10#10599458C212yesmaximal, complemented
11#10599455C212yesmaximal, complemented
12C22×#709C2211yescharacteristic
13C2×C5×#117C2211yescharacteristic
14C22×C4×Dic5C2211yescharacteristic
15#65856—24no—
16#65856—24no—
17C2×#4039C411yescharacteristic
18C2×#4039C411yescharacteristic
19C2×#4033C411yescharacteristic
20C2×#4033C411yescharacteristic
21C2×#4027C411yescharacteristic
22C2×#4027C411yescharacteristic
23C2×#4027C411yescharacteristic
24C2×#4027C411yescharacteristic
25C2×#4018C2211yescharacteristic
26C2×#4018C2211yescharacteristic
27C2×C42×D5C2211yescharacteristic
28C2×C42×D5C2211yescharacteristic
29C2×C5×C22⋊C8C2212yes—
30C2×C5×#97C2211yescharacteristic
31C2×C4×C5×C8C2211yescharacteristic
32C2×C22⋊#168C2212yes—
33C2×#3952C2212yes—
34C2×#3952C2212yes—
35C2×#3952C2212yes—
36C2×#3952C2212yes—
37C2×#3946C2212yes—
38C2×#3946C2212yes—
39C2×#3935C2211yescharacteristic
40C2×C4×#168C2211yescharacteristic
41#64994—24no—
42#64974—24no—
43C5×#336C2212yes—
44#64770C2212yes—
45#64770C2212yes—
46#64744C2212yes—
47#20721—51nomaximal, Sylow
48C23×C4×C5C2311yescharacteristic
49C22×C22⋊D5C2×C411yescharacteristic
50C22×C22⋊D5C2×C411yescharacteristic
51C23×Dic5C2×C411yescharacteristic
52C23×Dic5C2×C411yescharacteristic
53C2×#709—24no—
54C2×#709—22no—
55C2×#709—22no—
56C2×#709—24no—
57C22×D20C2×C411yescharacteristic
58C22×C4×D5C2×C411yescharacteristic
59C22×C4×D5C2×C411yescharacteristic
60C22×C4×D5C2×C411yescharacteristic
61C22×C4×D5C2×C411yescharacteristic
62C22×C4×D5C2311yescharacteristic
63C22×C4×D5C2311yescharacteristic
64C22×Dic10C2×C411yescharacteristic
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×#685C2×C411yescharacteristic
76C2×#685C2×C411yescharacteristic
77C2×#685C2×C411yescharacteristic
78C2×#685C2×C411yescharacteristic
79C2×#683C2×C411yescharacteristic
80C2×#683C2×C411yescharacteristic
81C2×#683C2×C411yescharacteristic
82C2×#683C2×C411yescharacteristic
83C2×C4×Dic5—22no—
84C2×C4×Dic5—22no—
85C2×C4×Dic5C2×C411yescharacteristic
86C2×C4×Dic5C2×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#4039—24no—
96#4039—24no—
97#4033—24no—
98#4033—24no—
99#4027—24no—
100#4027—24no—
101#4027—24no—
102#4027—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—
123C2×C4×#41—51no—
124C2×#432—51no—
125C2×#431—51no—
126#1818—52no—
127#1797—52no—
128#1797—52no—
129#1780—52no—
130#1750—51no—
131#1750—51no—
132#1750—51no—
133#1750D511yescharacteristic, complemented
134C24×C5C22×C411yescharacteristic
135C23×D5C22×C411yescharacteristic
136C23×D5C22×C411yescharacteristic
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—22no—
140C22×C4×C5C22×C411yescharacteristic
141C22×C4×C5C22×C411yescharacteristic
142C22×C4×C5C22×C411yescharacteristic
143C22×C4×C5C22×C411yescharacteristic
144C22×C4×C5C22×C411yescharacteristic
145C22×C4×C5#4114yes—
146C22×C4×C5C2411yescharacteristic
147C2×C22⋊D5—22no—
148C2×C22⋊D5—22no—
149C2×C22⋊D5—22no—
150C2×C22⋊D5—22no—
151C2×C22⋊D5—22no—
152C2×C22⋊D5—22no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—24no—
156C22×Dic5—42no—
157C22×Dic5C22×C411yescharacteristic
158C22×Dic5C22×C411yescharacteristic
159C22×Dic5C22×C411yescharacteristic
160C22×Dic5C22×C411yescharacteristic
161C22×Dic5C22×C411yescharacteristic
162C22×Dic5C22×C411yescharacteristic
163#709—216no—
164#709—216no—
165C2×D20—22no—
166C2×D20—22no—
167C2×D20—22no—
168C2×C4×D5—21no—
169C2×C4×D5—21no—
170C2×C4×D5—22no—
171C2×C4×D5—22no—
172C2×C4×D5—22no—
173C2×C4×D5—24no—
174C2×C4×D5—22no—
175C2×C4×D5—22no—
176C2×C4×D5—24no—
177C2×C4×D5—42no—
178C2×C4×D5—42no—
179C2×C4×D5C22⋊C414yes—
180C2×C4×D5C22⋊C414yes—
181C2×C4×D5C2×D412yes—
182C2×C4×D5C2×D412yes—
183C2×C4×D5#4114yes—
184C2×Dic10—22no—
185C2×Dic10—22no—
186C2×Dic10—22no—
187C2×C5×C8—22no—
188C2×C5×C8—22no—
189C2×C5×C8—22no—
190C2×C5×C8—22no—
191C2×C5×C8—22no—
192C2×C5×C8—22no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—22no—
195C5×C22⋊C4—22no—
196C5×C22⋊C4—22no—
197C42×C5—21no—
198C42×C5—21no—
199C42×C5C2×D412yes—
200C42×C5C2×D412yes—
201#685—22no—
202#685—22no—
203#685—22no—
204#685—22no—
205#683—22no—
206#683—22no—
207#683—22no—
208#683—22no—
209C4×Dic5—21no—
210C4×Dic5—21no—
211C4×Dic5—22no—
212C4×Dic5—22no—
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—
225C22×#41—51no—
226C4×#41—104no—
227C4×#41—104no—
228C2×C4×Q8—51no—
229C2×C4×Q8—51no—
230C2×C4×D4—51no—
231C2×C4×D4—51no—
232C2×C4×D4—51no—
233C2×C4×D4—51no—
234C2×C4×D4—51no—
235C2×C4×D4—51no—
236C2×#117—51no—
237C2×#117—51no—
238C2×#117C2×D511yescharacteristic
239C22×C42—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
254C2×C4×C8—51no—
255C2×C4×C8C2×D511yescharacteristic
256#336—52no—
257#336—52no—
258#336—52no—
259#336C2×D512yes—
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—21no—
269C22×D5—21no—
270C22×D5—22no—
271C22×D5—22no—
272C22×D5—22no—
273C22×D5—22no—
274C22×D5C2×C22⋊C412yes—
275C22×D5#11712yes—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
280C2×C4×C5—24no—
281C2×C4×C5—24no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5C2×C22⋊C412yes—
287C2×C4×C5C2×C22⋊C412yes—
288C2×C4×C5#11712yes—
289C2×C4×C5C22×D411yescharacteristic
290C2×C4×C5C22×D411yescharacteristic
291C2×C4×C5C2×#4112yes—
292C2×C4×C5C2×#4112yes—
293C22⋊D5—28no—
294C22⋊D5—28no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—22no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—44no—
305C2×Dic5—44no—
306C2×Dic5C2×C22⋊C412yes—
307C2×Dic5C2×C22⋊C412yes—
308C2×Dic5C2×C22⋊C412yes—
309C2×Dic5#11712yes—
310C2×Dic5#13114yes—
311D20—28no—
312C4×D5—24no—
313C4×D5—24no—
314C4×D5—24no—
315C4×D5—24no—
316C4×D5—28no—
317C4×D5—44no—
318C4×D5—44no—
319C4×D5—44no—
320Dic10—28no—
321C5×C8—42no—
322C5×C8—42no—
323#168—42no—
324#168—42no—
325C2×#41—102no—
326C2×#41—102no—
327C2×#41—104no—
328C2×#41—104no—
329C22×Q8—51no—
330C22×D4—51no—
331C22×D4—51no—
332C22×D4—51no—
333C23×C4—51no—
334C23×C4—51no—
335C23×C4—51no—
336C23×C4—51no—
337C23×C4—51no—
338C23×C4—51no—
339C23×C4—51no—
340C23×C4—51no—
341C23×C4C22×D511yescharacteristic
342C22×C8—52no—
343C22×C8—52no—
344C22×C8C22×D512yes—
345C22×C8C22×D512yes—
346C4×Q8—104no—
347C4×Q8—104no—
348C4×D4—104no—
349C4×D4—104no—
350C4×D4—104no—
351C4×D4—104no—
352C4×D4—104no—
353C4×D4—104no—
354#117—22no—
355#117—22no—
356#117—102no—
357#117—102no—
358#117—102no—
359#117—102no—
360C2×C4⋊C4—51no—
361C2×C4⋊C4—51no—
362C2×C4⋊C4—51no—
363C2×C4⋊C4—51no—
364C2×C4⋊C4C4×D511yescharacteristic
365C2×C4⋊C4C4×D511yescharacteristic
366C2×C22⋊C4—51no—
367C2×C22⋊C4—51no—
368C2×C22⋊C4—51no—
369C2×C22⋊C4—51no—
370C2×C22⋊C4C4×D511yescharacteristic
371C2×C22⋊C4C4×D511yescharacteristic
372C2×C42—51no—
373C2×C42—51no—
374C2×C42—51no—
375C2×C42—54no—
376C2×C42—54no—
377C2×C42—51no—
378C2×C42—51no—
379C2×C42—51no—
380C2×C42—51no—
381C2×C42—51no—
382C2×C42—102no—
383C2×C42—102no—
384C2×C42—102no—
385C2×C42—102no—
386C2×C42C22×D511yescharacteristic
387C2×C42C22×D511yescharacteristic
388C4⋊C8—104no—
389C4⋊C8—104no—
390C22⋊C8—24no—
391C22⋊C8—104no—
392C22⋊C8—104no—
393C22⋊C8—104no—
394C22⋊C8—104no—
395C22⋊C8—104no—
396#97—22no—
397#97—102no—
398C4×C8—22no—
399C4×C8—102no—
400C22×C5—24no—
401C22×C5—22no—
402C22×C5—41no—
403C22×C5—41no—
404C22×C5—42no—
405C22×C5C22×C22⋊C411yescharacteristic
406C22×C5C2×#11711yescharacteristic
407C22×C5C2×#11711yescharacteristic
408C22×C5C2×#13112yes—
409C22×C5#56812yes—
410C2×D5—22no—
411C2×D5—22no—
412C2×D5—24no—
413C2×D5—22no—
414C2×D5—22no—
415C2×D5—41no—
416C2×D5—41no—
417C2×D5—42no—
418C2×D5—42no—
419C2×D5—42no—
420C4×C5—22no—
421C4×C5—22no—
422C4×C5—22no—
423C4×C5—41no—
424C4×C5—41no—
425C4×C5#52512yes—
426C4×C5#52512yes—
427Dic5—22no—
428Dic5—22no—
429Dic5—22no—
430Dic5—41no—
431Dic5—41no—
432Dic5#40814yes—
433C24—51no—
434C24—51no—
435C24C2×C4×D511yescharacteristic
436#41—1016no—
437#41—1016no—
438C2×Q8—102no—
439C2×Q8—102no—
440C2×Q8—102no—
441C2×D4—102no—
442C2×D4—102no—
443C2×D4—102no—
444C2×D4—102no—
445C2×D4—102no—
446C2×D4—102no—
447C2×D4—102no—
448C2×D4—102no—
449C2×D4—102no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—51no—
454C22×C4—51no—
455C22×C4—51no—
456C22×C4—51no—
457C22×C4—52no—
458C22×C4—52no—
459C22×C4—54no—
460C22×C4—54no—
461C22×C4—54no—
462C22×C4—51no—
463C22×C4—51no—
464C22×C4—104no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—104no—
468C22×C4—102no—
469C22×C4—102no—
470C22×C4—104no—
471C22×C4—102no—
472C22×C4—102no—
473C22×C4—101no—
474C22×C4—101no—
475C22×C4—102no—
476C22×C4—202no—
477C22×C4—202no—
478C22×C4—202no—
479C22×C4C2×C4×D511yescharacteristic
480C22×C4C2×C4×D511yescharacteristic
481C22×C4C2×C4×D511yescharacteristic
482C22×C4C2×C4×D511yescharacteristic
483C22×C4C2×C4×D511yescharacteristic
484C22×C4#70914yes—
485C22×C4C23×D511yescharacteristic
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—102no—
493C2×C8—102no—
494C2×C8—102no—
495C2×C8—102no—
496C2×C8—102no—
497C2×C8—102no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—102no—
501C4⋊C4—102no—
502C4⋊C4—102no—
503C4⋊C4—102no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—102no—
507C22⋊C4—102no—
508C22⋊C4—102no—
509C22⋊C4—102no—
510C42—21no—
511C42—21no—
512C42—52no—
513C42—52no—
514C42—54no—
515C42—54no—
516C42—102no—
517C42—102no—
518C42—102no—
519C42—102no—
520C42—101no—
521C42—101no—
522C42D4×D512yes—
523C42D4×D512yes—
524C2×C5—42no—
525C2×C5#228011yescharacteristic
526C2×C5C2×#40811yescharacteristic
527C2×C5#287911yescharacteristic
528C2×C5#292512yes—
529C2×C5#292512yes—
530D5—42no—
531D5—42no—
532C23—21no—
533C23—22no—
534C23—22no—
535C23—21no—
536C23—52no—
537C23—52no—
538C23—101no—
539C23—101no—
540C23—101no—
541C23—102no—
542C23—102no—
543C23—102no—
544C23—102no—
545C23—101no—
546C23#401812yes—
547C23C22×C4×D511yescharacteristic
548Q8—108no—
549D4—108no—
550D4—108no—
551D4—108no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—52no—
563C2×C4—54no—
564C2×C4—52no—
565C2×C4—52no—
566C2×C4—52no—
567C2×C4—108no—
568C2×C4—101no—
569C2×C4—101no—
570C2×C4—101no—
571C2×C4—102no—
572C2×C4—101no—
573C2×C4—104no—
574C2×C4—104no—
575C2×C4—104no—
576C2×C4—104no—
577C2×C4—101no—
578C2×C4—101no—
579C2×C4—102no—
580C2×C4—102no—
581C2×C4—204no—
582C2×C4—204no—
583C2×C4—204no—
584C2×C4—204no—
585C2×C4—204no—
586C2×C4#401812yes—
587C2×C4D5×C22⋊C412yes—
588C2×C4D5×C22⋊C412yes—
589C2×C4C2×#70912yes—
590C2×C4C2×D4×D511yescharacteristic
591C2×C4C2×D4×D511yescharacteristic
592C2×C4D5×#4112yes—
593C8—42no—
594C8—42no—
595C8—202no—
596C8—202no—
597C5#2072111yescharacteristic, complemented, Sylow
598C22—24no—
599C22—22no—
600C22—42no—
601C22—41no—
602C22—41no—
603C22—104no—
604C22—102no—
605C22—102no—
606C22—102no—
607C22—102no—
608C22—202no—
609C22—202no—
610C22—202no—
611C22—201no—
612C22—201no—
613C22C2×#401811yescharacteristic
614C22C2×D5×C22⋊C411yescharacteristic
615C22D5×#11711yescharacteristic
616C22D5×#13112yes—
617C22#6608412yes—
618C4—22no—
619C4—22no—
620C4—22no—
621C4—41no—
622C4—41no—
623C4—54no—
624C4—102no—
625C4—102no—
626C4—102no—
627C4—201no—
628C4—201no—
629C4#6588112yes—
630C4#6588112yes—
631C2—42no—
632C2—202no—
633C2—202no—
634C2#1060529211yescharacteristic
635C2#1061028312yes—
636C2D5×#40811yescharacteristic
637C2#1061039311yescharacteristic
638C2#1061110612yes—
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1750C2
prime radicalC22×#709C22
cosocleC22×C4×C5C24
hypercenter#1750D5
hypocenterC5#20721
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. #10600701C2semidirect
8. #10600623C2semidirect
9. #10600546C2semidirect
10. #10599458C2semidirect
11. #10599455C2semidirect
133. #1750D5semidirect
597. C5#20721semidirect

Maximal subgroups

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

subgroupindex
C2×#658562
C2×#649942
C2×#649742
C5×#17502
#106023752
#106007492
#106007012
#106006232
#106005462
#105994582
#105994552
#207215