Finite Group Databasebeta

← #12097378

Subgroups — #12097378

Order 1280.

1126 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65170C211yesmaximal, characteristic
2C2×#65150C211yesmaximal, characteristic
3C2×#64997C211yesmaximal, characteristic
4#10605481C211yesmaximal, characteristic
5#10605481C211yesmaximal, characteristic
6C5×#1776C211yesmaximal, characteristic, complemented
7Dic5×#107C211yesmaximal, characteristic, complemented
8Dic5×#106C211yesmaximal, characteristic, complemented
9#10600607C211yesmaximal, characteristic, complemented
10C4×#3939C211yesmaximal, characteristic, complemented
11C4×#3940C211yesmaximal, characteristic, complemented
12#10599659C211yesmaximal, characteristic
13D5×#340C211yesmaximal, characteristic
14#10599579C211yesmaximal, characteristic, complemented
15#10599579C211yesmaximal, characteristic, complemented
16C22×#676C2211yescharacteristic
17C22×C8×D5C2211yescharacteristic
18C2×#4038C2211yescharacteristic
19C2×#4038C2211yescharacteristic
20C2×D5×C4⋊C4C2211yescharacteristic
21C2×D5×C4⋊C4C2211yescharacteristic
22C2×#4018C2211yescharacteristic
23C2×C5×#107C2211yescharacteristic
24C2×C5×#106C2211yescharacteristic
25C2×C5×#97C2211yescharacteristic
26C4×C5×C4⋊C4C2211yescharacteristic
27C4×C5×C4⋊C4C2211yescharacteristic
28C2×#3950C2211yescharacteristic
29C2×#3949C2211yescharacteristic
30C2×#3947C2211yescharacteristic
31C2×C8×Dic5C2211yescharacteristic
32C4⋊C4×Dic5C2211yescharacteristic
33C4⋊C4×Dic5C2211yescharacteristic
34C4⋊C4×Dic5C2211yescharacteristic
35C4⋊C4×Dic5C2211yescharacteristic
36C2×#3940C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3939C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C4×#685—21no—
41C4×#685—21no—
42C4×C4⋊Dic5C2211yescharacteristic
43C4×C4⋊Dic5C2211yescharacteristic
44C4×#683—21no—
45C4×#683—21no—
46C2×C4×#168C2211yescharacteristic
47#65170C418yescomplemented
48#65150C418yescomplemented
49#64997C418yescomplemented
50#64955—21no—
51#64955—21no—
52#64938—21no—
53#64938—21no—
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56#64771C2211yescharacteristic
57#64771C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#64749C2211yescharacteristic
61#64749C2211yescharacteristic
62#20453—51nomaximal, Sylow
63C22×C4×D5—21no—
64C22×C4×D5—21no—
65C22×C4×D5C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C5×C4⋊C4C2311yescharacteristic
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C42×C5—21no—
73C2×C42×C5—21no—
74C2×C42×C5C2311yescharacteristic
75C2×#685—21no—
76C2×#685—21no—
77C2×#685D411yescharacteristic
78C2×#685D411yescharacteristic
79C2×C4⋊Dic5C2311yescharacteristic
80C2×C4⋊Dic5C2311yescharacteristic
81C2×C4⋊Dic5C2311yescharacteristic
82C2×C4⋊Dic5C2311yescharacteristic
83C2×#683—21no—
84C2×#683—21no—
85C2×#683D411yescharacteristic
86C2×#683D411yescharacteristic
87C2×C4×Dic5—21no—
88C2×C4×Dic5—21no—
89C2×C4×Dic5—21no—
90C2×C4×Dic5—21no—
91C2×C4×Dic5—21no—
92C2×C4×Dic5—21no—
93C2×C4×Dic5—21no—
94C2×C4×Dic5—21no—
95C2×C4×Dic5C2311yescharacteristic
96C22×#168C2311yescharacteristic
97C22×#168C2311yescharacteristic
98C2×#676C2×C414yes—
99C2×#676C2×C414yes—
100C2×#676C2×C414yes—
101C2×C8×D5—22no—
102C2×C8×D5—22no—
103C2×C8×D5C2×C414yes—
104#4038—22no—
105#4038—22no—
106#4038C2×C414yes—
107#4038C2×C414yes—
108D5×C4⋊C4—22no—
109D5×C4⋊C4—22no—
110D5×C4⋊C4C2×C414yes—
111D5×C4⋊C4C2×C414yes—
112#4018C2×C414yes—
113#4018Q814yes—
114C5×#107C2×C414yescomplemented
115C5×#106C2×C414yescomplemented
116C5×#97C2×C414yescomplemented
117C5×#95—21no—
118C5×#95—21no—
119#3963—21no—
120#3963—21no—
121#3963—21no—
122#3963—21no—
123#3963—21no—
124#3963—21no—
125#3950C2×C414yescomplemented
126#3949C2×C414yescomplemented
127#3947C2×C414yescomplemented
128C8×Dic5C2×C414yescomplemented
129#3940C2×C414yescomplemented
130#3940C2×C414yescomplemented
131#3939C2×C414yescomplemented
132#3939C2×C414yescomplemented
133C4×#168C2×C414yescomplemented
134C2×#428—51no—
135C2×#428—51no—
136C2×#405—51no—
137#2274—51no—
138#2274—51no—
139#1776—51no—
140#1776—51no—
141#1776—51no—
142#1776D511yescharacteristic, complemented
143C4×#107—51no—
144C4×#107—51no—
145C4×#106—51no—
146C4×#106—51no—
147#1735—51no—
148C2×#340—51no—
149C23×D5C2×D411yescharacteristic
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2411yescharacteristic
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5—21no—
161C22×Dic5C2×D411yescharacteristic
162C22×Dic5C2×D411yescharacteristic
163C22×Dic5C2×D411yescharacteristic
164C2×C4×D5—24no—
165C2×C4×D5—24no—
166C2×C4×D5—81no—
167C2×C4×D5—81no—
168C2×C4×D5—81no—
169C2×C4×D5—81no—
170C2×C4×D5C22×C412yes—
171C2×C4×D5C22×C412yes—
172C2×C4×D5C22×C412yes—
173C2×C4×D5C2×Q812yes—
174C2×C4×D5#4112yes—
175C2×C4×D5#4112yes—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8C22×C412yes—
179C2×C5×C8C22×C412yes—
180C2×C5×C8C22×C412yes—
181C2×C5×C8C22×C412yes—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4C22×C412yes—
187C5×C4⋊C4C22×C412yes—
188C5×C4⋊C4C22×C412yes—
189C5×C4⋊C4C22×C412yes—
190C42×C5—81no—
191C42×C5—81no—
192C42×C5C22×C412yes—
193C42×C5C2×Q812yes—
194#685—24no—
195#685—24no—
196#685C4⋊C414yes—
197#685C4⋊C414yes—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5C22×C412yes—
203C4⋊Dic5C22×C412yes—
204C4⋊Dic5C22×C412yes—
205C4⋊Dic5C22×C412yes—
206#683—24no—
207#683—24no—
208#683C4⋊C414yes—
209#683C4⋊C414yes—
210C4×Dic5—24no—
211C4×Dic5—24no—
212C4×Dic5—81no—
213C4×Dic5—81no—
214C4×Dic5—81no—
215C4×Dic5—81no—
216C4×Dic5—81no—
217C4×Dic5—81no—
218C4×Dic5C22×C412yes—
219C4×Dic5C2×Q812yes—
220C2×#168—21no—
221C2×#168—21no—
222C2×#168C22×C412yes—
223C2×#168C22×C412yes—
224C2×#168C22×C412yes—
225C2×#168C22×C412yes—
226#676C42116yescomplemented
227C8×D5—28no—
228C22×M16—51no—
229C23×C8—51no—
230C2×#117—51no—
231C2×#117—51no—
232C2×#117—51no—
233C22×C4⋊C4—51no—
234C22×C4⋊C4—51no—
235#428—58no—
236#428—58no—
237C2×#107—51no—
238C2×#107—51no—
239C2×#107—51no—
240C2×#107C2×D511yescharacteristic
241C2×#106—51no—
242C2×#106—51no—
243C2×#106—51no—
244C2×#106C2×D511yescharacteristic
245#405—58no—
246C2×#97—51no—
247C2×#97C2×D511yescharacteristic
248C2×C4×C8—51no—
249C2×C4×C8—51no—
250C4×C4⋊C4—51no—
251C4×C4⋊C4—51no—
252C4×C4⋊C4—51no—
253C4×C4⋊C4—51no—
254C4×C4⋊C4—51no—
255C4×C4⋊C4—51no—
256C4×C4⋊C4—101no—
257C4×C4⋊C4—101no—
258C4×C4⋊C4—101no—
259C4×C4⋊C4—101no—
260C4×C4⋊C4C2×D511yescharacteristic
261C4×C4⋊C4C2×D511yescharacteristic
262C4×C22⋊C4—101no—
263C4×C22⋊C4—101no—
264C4×C22⋊C4—101no—
265C4×C22⋊C4—101no—
266#340—51no—
267#340—51no—
268#340—51no—
269#340—51no—
270#340—51no—
271#340—51no—
272#340C2×D511yescharacteristic
273#340C2×D511yescharacteristic
274C23×C5C22×D411yescharacteristic
275C22×D5—21no—
276C22×D5—21no—
277C22×D5—21no—
278C22×D5—21no—
279C22×D5C2×C4⋊C412yes—
280C22×D5C4×D412yes—
281C22×D5C4×D412yes—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5C2×C4⋊C412yes—
299C2×C4×C5C2×C4⋊C412yes—
300C2×C4×C5C23×C411yescharacteristic
301C2×C4×C5C23×C411yescharacteristic
302C2×C4×C5C23×C411yescharacteristic
303C2×C4×C5C22×Q811yescharacteristic
304C2×C4×C5C2×#4111yescharacteristic
305C2×C4×C5C2×#4111yescharacteristic
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5—21no—
310C2×Dic5—22no—
311C2×Dic5—22no—
312C2×Dic5—22no—
313C2×Dic5—22no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320C2×Dic5—41no—
321C2×Dic5—41no—
322C2×Dic5C2×C4⋊C412yes—
323C2×Dic5C2×C4⋊C412yes—
324C2×Dic5C2×C4⋊C412yes—
325C2×Dic5C4×D412yes—
326C2×Dic5C4×D412yes—
327C4×D5—84no—
328C4×D5—84no—
329C4×D5C2×C4214yes—
330C4×D5#11714yes—
331C4×D5C4×Q814yes—
332C4×D5C4×Q814yes—
333C5×C8—22no—
334C5×C8C2×C4214yes—
335#168—22no—
336#168C2×C4214yes—
337C23×C4—51no—
338C23×C4—101no—
339C23×C4—101no—
340C2×M16—54no—
341C2×M16—54no—
342C2×M16—54no—
343C22×C8—51no—
344C22×C8—51no—
345C22×C8—54no—
346C22×C8—102no—
347C22×C8—102no—
348C22×C8C22×D511yescharacteristic
349C22×C8C22×D511yescharacteristic
350#117—54no—
351#117—54no—
352#117—54no—
353#117—54no—
354#117—102no—
355#117—102no—
356C2×C4⋊C4—51no—
357C2×C4⋊C4—51no—
358C2×C4⋊C4—51no—
359C2×C4⋊C4—51no—
360C2×C4⋊C4—51no—
361C2×C4⋊C4—51no—
362C2×C4⋊C4—54no—
363C2×C4⋊C4—54no—
364C2×C4⋊C4—102no—
365C2×C4⋊C4—102no—
366C2×C4⋊C4—101no—
367C2×C4⋊C4—101no—
368C2×C4⋊C4C22×D511yescharacteristic
369C2×C4⋊C4C22×D511yescharacteristic
370C2×C4⋊C4C22×D511yescharacteristic
371C2×C4⋊C4C22×D511yescharacteristic
372C2×C22⋊C4—51no—
373C2×C22⋊C4—51no—
374C2×C22⋊C4—101no—
375C2×C22⋊C4—101no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—51no—
379C2×C42—101no—
380C2×C42—101no—
381C2×C42—101no—
382C2×C42—101no—
383C2×C42—101no—
384C2×C42—101no—
385C2×C42—101no—
386C2×C42—101no—
387C2×C42C22×D511yescharacteristic
388#107—54no—
389#107—54no—
390#107—54no—
391#107C4×D514yescomplemented
392#106—54no—
393#106—54no—
394#106—54no—
395#106C4×D514yescomplemented
396#97—54no—
397#97C4×D514yescomplemented
398C4×C8—54no—
399C4×C8—54no—
400#95—21no—
401#95—21no—
402#95—101no—
403#95—101no—
404#95—101no—
405#95—101no—
406#95—101no—
407#95—101no—
408C22×C5C22×C4⋊C411yescharacteristic
409C22×C5C2×C4×D411yescharacteristic
410C22×C5C2×C4×D411yescharacteristic
411C22×C5#57611yescharacteristic
412C22×C5#57711yescharacteristic
413C22×C5#57711yescharacteristic
414C22×C5#57811yescharacteristic
415C2×D5—22no—
416C2×D5—22no—
417C2×D5—22no—
418C2×D5—22no—
419C2×D5—22no—
420C2×D5—22no—
421C2×D5C4×C4⋊C414yes—
422C4×C5—22no—
423C4×C5—22no—
424C4×C5—42no—
425C4×C5—42no—
426C4×C5—42no—
427C4×C5—42no—
428C4×C5C22×C4211yescharacteristic
429C4×C5C2×#11711yescharacteristic
430C4×C5C2×C4×Q811yescharacteristic
431C4×C5C2×C4×Q811yescharacteristic
432Dic5—22no—
433Dic5—22no—
434Dic5—42no—
435Dic5—42no—
436Dic5—42no—
437Dic5—42no—
438Dic5C4×C4⋊C414yes—
439C24—51no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—51no—
445C22×C4—52no—
446C22×C4—52no—
447C22×C4—52no—
448C22×C4—52no—
449C22×C4—52no—
450C22×C4—52no—
451C22×C4—51no—
452C22×C4—51no—
453C22×C4—104no—
454C22×C4—104no—
455C22×C4—101no—
456C22×C4—101no—
457C22×C4—101no—
458C22×C4—101no—
459C22×C4—401no—
460C22×C4—401no—
461C22×C4—401no—
462C22×C4—401no—
463C22×C4D4×D511yescharacteristic
464C22×C4D4×D511yescharacteristic
465C22×C4C23×D511yescharacteristic
466M16—516no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—52no—
470C2×C8—52no—
471C2×C8—52no—
472C2×C8—52no—
473C2×C8—108no—
474C2×C8—101no—
475C2×C8—101no—
476C2×C8C2×C4×D512yes—
477C2×C8C2×C4×D512yes—
478C2×C8C2×C4×D512yes—
479C2×C8C2×C4×D512yes—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—54no—
485C4⋊C4—54no—
486C4⋊C4—52no—
487C4⋊C4—52no—
488C4⋊C4—52no—
489C4⋊C4—52no—
490C4⋊C4—104no—
491C4⋊C4—104no—
492C4⋊C4—101no—
493C4⋊C4—101no—
494C4⋊C4—101no—
495C4⋊C4—101no—
496C4⋊C4C2×C4×D512yes—
497C4⋊C4C2×C4×D512yes—
498C4⋊C4C2×C4×D512yes—
499C4⋊C4C2×C4×D512yes—
500C22⋊C4—54no—
501C22⋊C4—54no—
502C22⋊C4—104no—
503C22⋊C4—104no—
504C42—52no—
505C42—52no—
506C42—81no—
507C42—81no—
508C42—104no—
509C42—104no—
510C42—401no—
511C42—401no—
512C42—401no—
513C42—401no—
514C42—401no—
515C42—401no—
516C42C2×C4×D512yes—
517C42Q8×D512yes—
518C2×C5C2×C4×C4⋊C411yescharacteristic
519C2×C5#291211yescharacteristic
520C2×C5#291311yescharacteristic
521C2×C5#294611yescharacteristic
522C2×C5#294611yescharacteristic
523C2×C5#294711yescharacteristic
524C2×C5#294711yescharacteristic
525D5—24no—
526C23—52no—
527C23—52no—
528C23—52no—
529C23—101no—
530C23—101no—
531C23—101no—
532C23—101no—
533C23C2×D4×D511yescharacteristic
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—52no—
551C2×C4—52no—
552C2×C4—52no—
553C2×C4—54no—
554C2×C4—54no—
555C2×C4—54no—
556C2×C4—54no—
557C2×C4—52no—
558C2×C4—52no—
559C2×C4—101no—
560C2×C4—101no—
561C2×C4—101no—
562C2×C4—101no—
563C2×C4—102no—
564C2×C4—102no—
565C2×C4—102no—
566C2×C4—102no—
567C2×C4—201no—
568C2×C4—201no—
569C2×C4—201no—
570C2×C4—201no—
571C2×C4—201no—
572C2×C4—201no—
573C2×C4—201no—
574C2×C4—201no—
575C2×C4—404no—
576C2×C4—404no—
577C2×C4D5×C4⋊C412yes—
578C2×C4D5×C4⋊C412yes—
579C2×C4C22×C4×D511yescharacteristic
580C2×C4C22×C4×D511yescharacteristic
581C2×C4C22×C4×D511yescharacteristic
582C2×C4C2×Q8×D511yescharacteristic
583C2×C4D5×#4111yescharacteristic
584C2×C4D5×#4111yescharacteristic
585C8—22no—
586C8—54no—
587C8—102no—
588C8C42×D514yes—
589C5#2045311yescharacteristic, complemented, Sylow
590C22—54no—
591C22—102no—
592C22—102no—
593C22—102no—
594C22—102no—
595C22—102no—
596C22—102no—
597C22C2×D5×C4⋊C411yescharacteristic
598C22C4×D4×D511yescharacteristic
599C22C4×D4×D511yescharacteristic
600C22#6610811yescharacteristic
601C22#6610911yescharacteristic
602C22#6611211yescharacteristic
603C22#6611311yescharacteristic
604C4—22no—
605C4—22no—
606C4—42no—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—54no—
611C4—102no—
612C4—102no—
613C4—202no—
614C4—202no—
615C4—202no—
616C4—202no—
617C4C2×C42×D511yescharacteristic
618C4D5×#11711yescharacteristic
619C4C4×Q8×D511yescharacteristic
620C4C4×Q8×D511yescharacteristic
621C2—104no—
622C2C4×D5×C4⋊C411yescharacteristic
623C2#1061094011yescharacteristic
624C2#1061094111yescharacteristic
625C2#1061150611yescharacteristic
626C2#1061150711yescharacteristic
627C2#1061156111yescharacteristic
628C2#1061159711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC4×C5C22×C42
FrattiniC22×C4C23×D5
FittingC5×#1776C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1776D5
hypocenterC5#20453
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
6. C5×#1776C2semidirect
7. Dic5×#107C2semidirect
8. Dic5×#106C2semidirect
9. #10600607C2semidirect
10. C4×#3939C2semidirect
11. C4×#3940C2semidirect
14. #10599579C2semidirect
15. #10599579C2semidirect
47. #65170C4semidirect
48. #65150C4semidirect
49. #64997C4semidirect
114. C5×#107C2×C4semidirect
115. C5×#106C2×C4semidirect
116. C5×#97C2×C4semidirect
125. #3950C2×C4semidirect
126. #3949C2×C4semidirect
127. #3947C2×C4semidirect
128. C8×Dic5C2×C4semidirect
129. #3940C2×C4semidirect
130. #3940C2×C4semidirect
131. #3939C2×C4semidirect
132. #3939C2×C4semidirect
133. C4×#168C2×C4semidirect
142. #1776D5semidirect
226. #676C42semidirect
391. #107C4×D5semidirect
395. #106C4×D5semidirect
397. #97C4×D5semidirect
589. C5#20453semidirect

Maximal subgroups

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

subgroupindex
C2×#651702
C2×#651502
C2×#649972
#106054812
C5×#17762
Dic5×#1072
Dic5×#1062
#106006072
C4×#39392
C4×#39402
#105996592
D5×#3402
#105995792
#204535