Finite Group Databasebeta

← #13041357

Subgroups — #13041357

Order 1280.

788 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×#65788C211yesmaximal, characteristic, complemented
2C2×#65696C211yesmaximal, characteristic
3#10608509C211yesmaximal, characteristic
4#10604985C211yesmaximal, characteristic, complemented
5#10604232C211yesmaximal, characteristic
6#10604230C211yesmaximal, characteristic
7#10604227C211yesmaximal, characteristic
8#10604226C211yesmaximal, characteristic
9#10604224C211yesmaximal, characteristic
10#10603797C211yesmaximal, characteristic, complemented
11#10603796C211yesmaximal, characteristic, complemented
12#10603796C211yesmaximal, characteristic, complemented
13#10603791C211yesmaximal, characteristic, complemented
14#10603790C211yesmaximal, characteristic, complemented
15#10603781C211yesmaximal, characteristic, complemented
16C22×#704C2211yescharacteristic
17C23×#170C2211yescharacteristic
18C2×Q8×Dic5C2211yescharacteristic
19C2×#4023C2211yescharacteristic
20C2×C22⋊#170C2211yescharacteristic
21C2×C22⋊#170C2211yescharacteristic
22#65788—24no—
23C2×#4004C2211yescharacteristic
24C2×#4004C2211yescharacteristic
25C2×#4004C2211yescharacteristic
26C2×#4004C2211yescharacteristic
27C2×#4004C2211yescharacteristic
28C2×#4002C2211yescharacteristic
29C2×#4002C2211yescharacteristic
30C2×#4002C2211yescharacteristic
31C2×#4002C2211yescharacteristic
32C2×C4⋊#170C2211yescharacteristic
33C2×C4⋊#170C2211yescharacteristic
34C2×C4⋊#170C2211yescharacteristic
35C2×C4×#170C2211yescharacteristic
36C2×C4×#170C2211yescharacteristic
37#65696—24no—
38C5×#393C411yescharacteristic
39#65518C411yescharacteristic
40#65238C411yescharacteristic
41#65237C411yescharacteristic
42#65237C411yescharacteristic
43C22⋊C4×Dic5C2211yescharacteristic
44C22⋊C4×Dic5C2211yescharacteristic
45#64948C411yescharacteristic
46#64946C411yescharacteristic
47#64946C411yescharacteristic
48#64938C2211yescharacteristic
49#64938C2211yescharacteristic
50#64938C2211yescharacteristic
51#64918C2211yescharacteristic
52#64918C2211yescharacteristic
53#64918C2211yescharacteristic
54#64918C2211yescharacteristic
55#64918C2211yescharacteristic
56#64918C2211yescharacteristic
57#64918C2211yescharacteristic
58#64918C2211yescharacteristic
59#64918C2211yescharacteristic
60#64918C2211yescharacteristic
61#22961—51nomaximal, Sylow
62C22×C5×Q8C2×C411yescharacteristic
63C23×Dic5C2311yescharacteristic
64C2×#704—22no—
65C2×#704—22no—
66C2×#704—41no—
67C22×#170—22no—
68C22×#170—22no—
69C22×#170—41no—
70C22×#170C2311yescharacteristic
71C22×#170C2311yescharacteristic
72C22×#170C2311yescharacteristic
73C22×#170C2311yescharacteristic
74C22×#170C2311yescharacteristic
75C22×#170C2311yescharacteristic
76C22×#170C2311yescharacteristic
77C22×#170C2311yescharacteristic
78C2×C5×C22⋊C4C2×C411yescharacteristic
79C2×C5×C22⋊C4C2×C411yescharacteristic
80C2×C5×C22⋊C4C2×C411yescharacteristic
81C2×C22⋊Dic5C2×C411yescharacteristic
82C2×C22⋊Dic5C2×C411yescharacteristic
83C2×C22⋊Dic5C2×C411yescharacteristic
84Q8×Dic5—22no—
85Q8×Dic5—22no—
86C2×C4⋊Dic5C2×C411yescharacteristic
87C2×C4⋊Dic5C2×C411yescharacteristic
88C2×C4⋊Dic5C2×C411yescharacteristic
89C2×#683C2×C411yescharacteristic
90C2×#683C2×C411yescharacteristic
91C2×#683C2×C411yescharacteristic
92C2×#683C2×C411yescharacteristic
93C2×#683C2×C411yescharacteristic
94C2×#683C2×C411yescharacteristic
95C2×#683C2×C411yescharacteristic
96C2×#683C2×C411yescharacteristic
97C2×C4×Dic5C2311yescharacteristic
98C2×C4×Dic5C2311yescharacteristic
99C2×C4×Dic5C2311yescharacteristic
100C2×C4×Dic5C2311yescharacteristic
101C2×C4×Dic5C2311yescharacteristic
102C2×C4×Dic5C2311yescharacteristic
103#4023—22no—
104#4023—22no—
105C22⋊#170—22no—
106C22⋊#170Q814yescomplemented
107#4004—22no—
108#4004—22no—
109#4004—22no—
110#4004—22no—
111#4004—41no—
112#4002—22no—
113#4002—22no—
114#4002—22no—
115#4002—41no—
116C4⋊#170—22no—
117C4⋊#170—41no—
118C4⋊#170D414yes—
119C4×#170—22no—
120C4×#170—41no—
121C5×#95C2×C411yescharacteristic
122C5×#95C2×C411yescharacteristic
123C5×#95C2×C411yescharacteristic
124#3963C2×C411yescharacteristic
125#3963C2×C411yescharacteristic
126#3963C2×C411yescharacteristic
127#3963C2×C411yescharacteristic
128#3963C2×C411yescharacteristic
129#3963C2×C411yescharacteristic
130#3963C2×C411yescharacteristic
131C2×#446—51no—
132C2×#424—51no—
133#2396—51no—
134#1985—51no—
135#1940—51no—
136#1939—51no—
137#1939—51no—
138#1917—51no—
139#1917—51no—
140#1851—51no—
141#1850—51no—
142#1771—51no—
143#1753—51no—
144#1752—51no—
145#1750—51no—
146C24×C5C22×C411yescharacteristic
147C2×C5×Q8—22no—
148C2×C5×Q8—41no—
149C2×C5×Q8—41no—
150C22×C4×C5C22×C411yescharacteristic
151C22×C4×C5C22×C411yescharacteristic
152C22×C4×C5C22×C411yescharacteristic
153C22×C4×C5C22×C411yescharacteristic
154C22×C4×C5C22×C411yescharacteristic
155C22×C4×C5C22×C411yescharacteristic
156C22×Dic5—21no—
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5C22×C411yescharacteristic
161C22×Dic5C22×C411yescharacteristic
162C22×Dic5C22×C411yescharacteristic
163C22×Dic5C22×C411yescharacteristic
164C22×Dic5C22×C411yescharacteristic
165C22×Dic5C22×C411yescharacteristic
166C22×Dic5C22×C411yescharacteristic
167C22×Dic5C2×Q812yes—
168C22×Dic5#4112yes—
169C22×Dic5C2411yescharacteristic
170#704—44no—
171C2×#170—21no—
172C2×#170—21no—
173C2×#170—21no—
174C2×#170—21no—
175C2×#170—21no—
176C2×#170—21no—
177C2×#170—21no—
178C2×#170—21no—
179C2×#170—21no—
180C2×#170—21no—
181C2×#170—21no—
182C2×#170—21no—
183C2×#170—21no—
184C2×#170—21no—
185C2×#170—21no—
186C2×#170—21no—
187C2×#170—21no—
188C2×#170—21no—
189C2×#170—21no—
190C2×#170—21no—
191C2×#170—44no—
192C2×#170C2×D412yes—
193C2×#170C2×D412yes—
194C2×#170C2×Q812yes—
195C2×#170C2×Q812yes—
196C5×C22⋊C4—22no—
197C5×C22⋊C4—41no—
198C5×C22⋊C4—41no—
199C22⋊Dic5—22no—
200C22⋊Dic5—22no—
201C22⋊Dic5—41no—
202C4⋊Dic5—22no—
203C4⋊Dic5—22no—
204C4⋊Dic5—22no—
205#683—22no—
206#683—22no—
207#683—22no—
208#683—22no—
209#683—41no—
210#683—41no—
211#683—41no—
212#683—41no—
213C4×Dic5—21no—
214C4×Dic5—21no—
215C4×Dic5—21no—
216C4×Dic5—21no—
217C4×Dic5—21no—
218C4×Dic5—21no—
219C4×Dic5—21no—
220C4×Dic5—21no—
221C4×Dic5—21no—
222C4×Dic5—21no—
223C4×Dic5C2×D412yes—
224C4×Dic5#4112yes—
225C22×M16—51no—
226C23×C8—51no—
227C2×C4×Q8—51no—
228C2×#117—51no—
229#446—104no—
230#424—104no—
231C2×C4⋊C8—51no—
232C2×C4⋊C8—51no—
233C2×C4⋊C8—51no—
234C2×C4⋊C8—51no—
235C2×C4⋊C8—51no—
236C2×C4⋊C8—51no—
237C2×C4⋊C8—51no—
238C2×C4⋊C8—51no—
239C2×C22⋊C8—51no—
240C2×C22⋊C8—51no—
241C2×#97—51no—
242C2×#97—51no—
243C2×#97—51no—
244C2×#97—51no—
245C2×C4×C8—51no—
246C2×C4×C8—51no—
247#400—51no—
248#399—51no—
249#398—51no—
250#398—51no—
251#396—51no—
252#396—51no—
253#395—51no—
254#393AGL(1,𝔽5)11yescharacteristic
255C4×C4⋊C4—51no—
256C4×C4⋊C4—51no—
257C4×C4⋊C4—51no—
258C4×C22⋊C4—51no—
259C4×C22⋊C4—51no—
260#336—51no—
261#336—51no—
262#336—51no—
263#336—51no—
264#336—51no—
265#336—51no—
266#336—51no—
267#336—51no—
268#336—51no—
269#336—51no—
270C23×C5—21no—
271C23×C5—21no—
272C23×C5—21no—
273C23×C5—21no—
274C23×C5—21no—
275C23×C5—21no—
276C23×C5C4×Q812yes—
277C23×C5C23×C411yescharacteristic
278C5×Q8—44no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5C4×D412yes—
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5—21no—
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—21no—
318C2×Dic5—21no—
319C2×Dic5C4×D412yes—
320C2×Dic5C4×Q812yes—
321C2×Dic5#13112yes—
322C2×Dic5C22×D411yescharacteristic
323C2×Dic5C22×Q811yescharacteristic
324C2×Dic5C2×#4111yescharacteristic
325C2×Dic5C2×#4111yescharacteristic
326C2×Dic5H(5,𝔽2)11yescharacteristic
327C2×Dic52−1+411yescharacteristic
328#170—22no—
329#170—22no—
330#170—22no—
331#170—22no—
332#170—41no—
333#170—41no—
334#170—41no—
335#170—41no—
336C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
337C23×C4—51no—
338C2×M16—102no—
339C2×M16—102no—
340C2×M16—201no—
341C22×C8—51no—
342C22×C8—51no—
343C22×C8—51no—
344C22×C8—51no—
345C22×C8—51no—
346C22×C8—51no—
347C22×C8—51no—
348C22×C8—51no—
349C22×C8—102no—
350C22×C8—102no—
351C22×C8—201no—
352C4×Q8—102no—
353C4×Q8—102no—
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—51no—
363C2×C4⋊C4—51no—
364C2×C4⋊C4—51no—
365C2×C4⋊C4—51no—
366C2×C4⋊C4—51no—
367C2×C22⋊C4—51no—
368C2×C22⋊C4—51no—
369C2×C22⋊C4—51no—
370C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
371C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
372C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
373C2×C42—51no—
374C2×C42—51no—
375C2×C42—51no—
376C2×C42—51no—
377C2×C42—51no—
378C2×C42—51no—
379C4⋊C8—54no—
380C4⋊C8—102no—
381C4⋊C8—102no—
382C4⋊C8—102no—
383C4⋊C8—102no—
384C4⋊C8—102no—
385C4⋊C8—201no—
386C4⋊C8—201no—
387C22⋊C8—54no—
388C22⋊C8—102no—
389#97—102no—
390#97—102no—
391#97—102no—
392#97—201no—
393C4×C8—102no—
394C4×C8—201no—
395#95—51no—
396#95—51no—
397#95—51no—
398#95—51no—
399#95—51no—
400#95—51no—
401#95—51no—
402#95C2×AGL(1,𝔽5)11yescharacteristic
403#95C2×AGL(1,𝔽5)11yescharacteristic
404#95C2×AGL(1,𝔽5)11yescharacteristic
405C22×C5—22no—
406C22×C5—22no—
407C22×C5—22no—
408C22×C5—41no—
409C22×C5—41no—
410C22×C5—41no—
411C22×C5—41no—
412C22×C5C2×C4×D411yescharacteristic
413C22×C5C2×C4×Q811yescharacteristic
414C22×C5#52011yescharacteristic
415C22×C5C2×#13111yescharacteristic
416C22×C5#56811yescharacteristic
417C22×C5#56811yescharacteristic
418C22×C5#56811yescharacteristic
419C4×C5—22no—
420C4×C5—41no—
421C4×C5—41no—
422C4×C5—41no—
423C4×C5—41no—
424C4×C5—41no—
425Dic5—22no—
426Dic5—22no—
427Dic5—22no—
428Dic5—41no—
429Dic5—41no—
430Dic5—41no—
431Dic5—41no—
432Dic5#54611yescharacteristic
433Dic5D4×Q811yescharacteristic
434Dic5#55211yescharacteristic
435Dic5#55411yescharacteristic
436C24C22×AGL(1,𝔽5)11yescharacteristic
437C2×Q8—22no—
438C2×Q8—41no—
439C2×Q8—41no—
440C22×C4—51no—
441C22×C4—52no—
442C22×C4—52no—
443C22×C4—51no—
444C22×C4—51no—
445C22×C4—51no—
446C22×C4—51no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—51no—
450C22×C4—101no—
451C22×C4—101no—
452C22×C4—101no—
453C22×C4—101no—
454C22×C4C22×AGL(1,𝔽5)11yescharacteristic
455C22×C4C22×AGL(1,𝔽5)11yescharacteristic
456C22×C4C22×AGL(1,𝔽5)11yescharacteristic
457C22×C4C22×AGL(1,𝔽5)11yescharacteristic
458C22×C4C22×AGL(1,𝔽5)11yescharacteristic
459C22×C4C22×AGL(1,𝔽5)11yescharacteristic
460M16—204no—
461C2×C8—52no—
462C2×C8—52no—
463C2×C8—52no—
464C2×C8—52no—
465C2×C8—101no—
466C2×C8—101no—
467C2×C8—101no—
468C2×C8—101no—
469C2×C8—101no—
470C2×C8—101no—
471C2×C8—101no—
472C2×C8—101no—
473C2×C8—101no—
474C2×C8—101no—
475C2×C8—101no—
476C2×C8—101no—
477C2×C8—101no—
478C2×C8—101no—
479C2×C8—101no—
480C2×C8—101no—
481C2×C8—101no—
482C2×C8—101no—
483C2×C8—101no—
484C2×C8—101no—
485C2×C8—204no—
486C4⋊C4—102no—
487C4⋊C4—102no—
488C4⋊C4—102no—
489C4⋊C4—102no—
490C4⋊C4—102no—
491C4⋊C4—102no—
492C4⋊C4—102no—
493C4⋊C4—201no—
494C4⋊C4—201no—
495C4⋊C4—201no—
496C4⋊C4—201no—
497C22⋊C4—22no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—102no—
501C22⋊C4—102no—
502C22⋊C4—201no—
503C42—52no—
504C42—52no—
505C42—101no—
506C42—101no—
507C42—101no—
508C42—101no—
509C42—101no—
510C42—101no—
511C42—101no—
512C42—101no—
513C42—101no—
514C42—101no—
515C2×C5—42no—
516C2×C5#236011yescharacteristic
517C2×C5#293011yescharacteristic
518C2×C5#293511yescharacteristic
519C2×C5#296111yescharacteristic
520C2×C5#296211yescharacteristic
521C2×C5#299211yescharacteristic
522C2×C5#299511yescharacteristic
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23Q8×AGL(1,𝔽5)12yes—
530C23C23×AGL(1,𝔽5)11yescharacteristic
531Q8—44no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—51no—
550C2×C4—51no—
551C2×C4—51no—
552C2×C4—51no—
553C2×C4—51no—
554C2×C4—51no—
555C2×C4—52no—
556C2×C4—52no—
557C2×C4—52no—
558C2×C4—102no—
559C2×C4—102no—
560C2×C4—102no—
561C2×C4—102no—
562C2×C4—101no—
563C2×C4—101no—
564C2×C4—101no—
565C2×C4—101no—
566C2×C4—101no—
567C2×C4—101no—
568C2×C4—101no—
569C2×C4—101no—
570C2×C4—101no—
571C2×C4—101no—
572C2×C4—101no—
573C2×C4—101no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—101no—
579C2×C4—101no—
580C2×C4D4×AGL(1,𝔽5)12yes—
581C8—102no—
582C8—102no—
583C8—102no—
584C8—102no—
585C8—201no—
586C8—201no—
587C8—201no—
588C8—201no—
589C5#2296111yescharacteristic, complemented, Sylow
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22#6625611yescharacteristic
598C22#6625611yescharacteristic
599C22C2×D4×AGL(1,𝔽5)11yescharacteristic
600C22C2×Q8×AGL(1,𝔽5)11yescharacteristic
601C22D5⋊#13111yescharacteristic
602C22#6626411yescharacteristic
603C22#6626611yescharacteristic
604C4—22no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—51no—
611C4—51no—
612C4—51no—
613C4—51no—
614C4—102no—
615C4—102no—
616C4—102no—
617C4—201no—
618C4—201no—
619C4—201no—
620C4—201no—
621C2—42no—
622C2#1061721611yescharacteristic
623C2#1061726211yescharacteristic
624C2#1061726411yescharacteristic
625C2#1061728511yescharacteristic
626C2#1061731111yescharacteristic
627C2#1061731911yescharacteristic
628C2#1061732211yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutator, socleC23×C5C23×C4
FittingC5×#393C4
prime radicalC24×C5C22×C4
cosocleC22×Dic5C24
hypercenter#393AGL(1,𝔽5)
hypocenterC5#22961
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#65788C2semidirect
4. #10604985C2semidirect
10. #10603797C2semidirect
11. #10603796C2semidirect
12. #10603796C2semidirect
13. #10603791C2semidirect
14. #10603790C2semidirect
15. #10603781C2semidirect
106. C22⋊#170Q8semidirect
589. C5#22961semidirect

Maximal subgroups

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

subgroupindex
C2×#657882
C2×#656962
#106085092
#106049852
#106042322
#106042302
#106042272
#106042262
#106042242
#106037972
#106037962
#106037912
#106037902
#106037812
#229615