Finite Group Databasebeta

← #12121393

Subgroups — #12121393

Order 1280.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10610756C211yesmaximal, characteristic
2#10610743C211yesmaximal, characteristic
3#10610739C211yesmaximal, characteristic, complemented
4C5×#1768C211yesmaximal, characteristic, complemented
5#10601267C211yesmaximal, characteristic, complemented
6#10600637C211yesmaximal, characteristic, complemented
7#10600632C211yesmaximal, characteristic
8#10600587C211yesmaximal, characteristic, complemented
9#10600582C211yesmaximal, characteristic
10#10600234C211yesmaximal, characteristic, complemented
11#10600223C211yesmaximal, characteristic
12#10599487C211yesmaximal, characteristic
13#10599487C211yesmaximal, characteristic
14#10599438C211yesmaximal, characteristic, complemented
15#10599438C211yesmaximal, characteristic, complemented
16C2×#4047C2211yescharacteristic
17C2×#4047C2211yescharacteristic
18C4×#709C2211yescharacteristic
19#65804C2211yescharacteristic
20C2×C5×C4⋊C8C2211yescharacteristic
21C2×C5×C4⋊C8C2211yescharacteristic
22C2×C5×#97C2211yescharacteristic
23C2×C4×C5×C8C2211yescharacteristic
24C5×#376C2211yescharacteristic
25#65402C2211yescharacteristic
26#65402C2211yescharacteristic
27C2×#3951C2211yescharacteristic
28C2×#3951C2211yescharacteristic
29#65395C2211yescharacteristic
30#65395C2211yescharacteristic
31#65391C2211yescharacteristic
32#65391C2211yescharacteristic
33#65391C2211yescharacteristic
34#65391C2211yescharacteristic
35#65390C2211yescharacteristic
36#65390C2211yescharacteristic
37C2×#3937C2211yescharacteristic
38C2×#3937C2211yescharacteristic
39#65213C2211yescharacteristic
40C4×#681C2211yescharacteristic
41#65140C411yescharacteristic, complemented
42#65139C411yescharacteristic, complemented
43#65136C411yescharacteristic, complemented
44#65136C411yescharacteristic, complemented
45#65135C411yescharacteristic, complemented
46#65131C411yescharacteristic, complemented
47#65128—21no—
48#65128—21no—
49#65126—21no—
50D5×C4⋊C8—21no—
51#65120—21no—
52#65119—21no—
53#65118C411yescharacteristic, complemented
54#65118C411yescharacteristic, complemented
55#65117—21no—
56#65117—21no—
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#64772C2211yescharacteristic
60#64772C2211yescharacteristic
61#64743C2211yescharacteristic
62#64743C2211yescharacteristic
63#64743C2211yescharacteristic
64#64743C2211yescharacteristic
65#64743C2211yescharacteristic
66#64743C2211yescharacteristic
67#22984—51nomaximal, Sylow
68C2×#709C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C2×C42×C5C2311yescharacteristic
74C2×C42×C5C2311yescharacteristic
75C2×C42×C5C2311yescharacteristic
76C4×C22⋊D5—21no—
77C4×C22⋊D5—21no—
78#4072C2311yescharacteristic
79#4072C2311yescharacteristic
80#4072C2311yescharacteristic
81#4070—21no—
82#4070—21no—
83C2×#681C2311yescharacteristic
84C2×#681C2311yescharacteristic
85C2×#681C2311yescharacteristic
86C2×#681C2311yescharacteristic
87#4047—22no—
88#4047—22no—
89#4047—41no—
90#4047—41no—
91C2×#676—21no—
92C2×#676—21no—
93C2×C8×D5—21no—
94C2×C8×D5—21no—
95C4×D20C2×C411yescharacteristic
96C4×D20C2×C411yescharacteristic
97#4018—21no—
98C42×D5—21no—
99#4016C2×C411yescharacteristic
100#4016C2×C411yescharacteristic
101#4015C2×C411yescharacteristic
102#4015C2×C411yescharacteristic
103C4×Dic10—21no—
104C4×Dic10—21no—
105C4×Dic10C2×C411yescharacteristic
106C4×Dic10C2×C411yescharacteristic
107C5×C4⋊C8C2×C411yescharacteristic
108C5×C4⋊C8C2×C411yescharacteristic
109C5×C4⋊C8C2×C411yescharacteristic
110C5×C4⋊C8C2×C411yescharacteristic
111C5×C4⋊C8D411yescharacteristic
112C5×C4⋊C8D411yescharacteristic
113C5×C4⋊C8D411yescharacteristic
114C5×C4⋊C8D411yescharacteristic
115C5×#97—41no—
116C4×C5×C8—41no—
117C5×#95—21no—
118C5×#95—21no—
119#3953C2×C411yescharacteristic
120#3953C2×C411yescharacteristic
121#3953C2×C411yescharacteristic
122#3953C2×C411yescharacteristic
123#3951—41no—
124#3951—41no—
125#3950C2×C411yescharacteristic
126#3950C2×C411yescharacteristic
127#3950C2×C411yescharacteristic
128#3950C2×C411yescharacteristic
129#3949C2×C411yescharacteristic
130#3949C2×C411yescharacteristic
131#3949C2×C411yescharacteristic
132#3949C2×C411yescharacteristic
133#3948C2×C411yescharacteristic
134#3948C2×C411yescharacteristic
135#3948C2×C411yescharacteristic
136#3948C2×C411yescharacteristic
137#3947—21no—
138#3947—21no—
139#3946—21no—
140#3946—21no—
141#3946—21no—
142#3946—21no—
143#3946—21no—
144#3946—21no—
145#3946—21no—
146#3946—21no—
147C8×Dic5—21no—
148C8×Dic5—21no—
149#3937—22no—
150#3937Q814yescomplemented
151C4⋊#168—21no—
152C4⋊#168—21no—
153#3935—21no—
154C4×#168—21no—
155#3076—51no—
156#2962—51no—
157#2906—51no—
158#1995—51no—
159#1950—51no—
160#1946—51no—
161#1945—51no—
162#1922—51no—
163#1922—51no—
164#1866—51no—
165#1866—51no—
166#1768D511yescharacteristic, complemented
167#1765—51no—
168#1764—51no—
169#1759—51no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5#4111yescharacteristic
173C22×C4×C5#4111yescharacteristic
174C22×C4×C5C2411yescharacteristic
175C2×C22⋊D5—21no—
176#709—21no—
177#709—21no—
178#709C2×Q812yes—
179#709#4112yes—
180C2×D20C22×C411yescharacteristic
181C2×C4×D5—21no—
182C2×C4×D5—21no—
183C2×C4×D5—21no—
184C2×Dic10—21no—
185C2×Dic10—21no—
186C2×Dic10C22×C411yescharacteristic
187C2×C5×C8—21no—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8C22×C411yescharacteristic
196C2×C5×C8C22×C411yescharacteristic
197C2×C5×C8C22×C411yescharacteristic
198C2×C5×C8C22×C411yescharacteristic
199C2×C5×C8C2×D411yescharacteristic
200C2×C5×C8C2×D411yescharacteristic
201C2×C5×C8C2×D411yescharacteristic
202C2×C5×C8C2×D411yescharacteristic
203C42×C5—21no—
204C42×C5—21no—
205C42×C5—21no—
206C42×C5C22×C411yescharacteristic
207C42×C5C22×C411yescharacteristic
208C42×C5C2×D411yescharacteristic
209C42×C5C2×D411yescharacteristic
210C42×C5C2×Q812yes—
211C22⋊Dic5—21no—
212C22⋊Dic5—21no—
213C22⋊Dic5—21no—
214#685—21no—
215#685—21no—
216C4⋊Dic5—21no—
217C4⋊Dic5—21no—
218C4⋊Dic5C22×C411yescharacteristic
219C4⋊Dic5C22×C411yescharacteristic
220C4⋊Dic5C22×C411yescharacteristic
221C4⋊Dic5C22×C411yescharacteristic
222C4⋊Dic5C22×C411yescharacteristic
223C4⋊Dic5C22×C411yescharacteristic
224#683—21no—
225#683—21no—
226#683—21no—
227#683—21no—
228#683—21no—
229#683—21no—
230C4×Dic5—21no—
231C4×Dic5—21no—
232C4×Dic5—21no—
233C4×Dic5—21no—
234C4×Dic5—21no—
235#681—21no—
236#681—21no—
237#681—21no—
238#681—21no—
239#681—21no—
240#681—21no—
241#681—21no—
242#681C2×Q812yes—
243C2×#168—21no—
244C2×#168—21no—
245C2×#168—21no—
246C2×#168—21no—
247#676—42no—
248#676—42no—
249C8×D5—42no—
250C8×D5—42no—
251C2×#131—51no—
252C2×#131—51no—
253#533—51no—
254C4×#41—51no—
255#479—51no—
256#479—51no—
257#478—51no—
258#478—51no—
259#477—51no—
260#476—51no—
261#475—51no—
262#474—51no—
263#446—101no—
264#446—101no—
265#446—101no—
266C8×Q8—101no—
267C2×#108—51no—
268C2×#108—51no—
269#427—51no—
270#427—51no—
271#424—51no—
272#424—51no—
273#424—51no—
274#424—51no—
275#424—101no—
276#424—101no—
277#423—51no—
278#423—101no—
279C2×C4⋊C8—101no—
280C2×C4⋊C8C2×D511yescharacteristic
281C2×C4⋊C8C2×D511yescharacteristic
282C2×#104—51no—
283C2×#104—51no—
284#416—51no—
285#416—51no—
286#405—51no—
287#405—51no—
288C4×M16—51no—
289C2×#97C2×D511yescharacteristic
290C2×C4×C8C2×D511yescharacteristic
291#376C2×D511yescharacteristic
292#341—51no—
293#341—51no—
294#339—51no—
295#339—51no—
296#339—51no—
297#339—51no—
298#339—51no—
299#339—51no—
300#336C2×D511yescharacteristic
301#336C2×D511yescharacteristic
302C23×C5C2×#4111yescharacteristic
303C22×D5—21no—
304C2×C4×C5—22no—
305C2×C4×C5—41no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5C4×D411yescharacteristic
313C2×C4×C5C4×D411yescharacteristic
314C2×C4×C5C4×D411yescharacteristic
315C2×C4×C5C4×D411yescharacteristic
316C2×C4×C5C23×C411yescharacteristic
317C2×C4×C5C22×D411yescharacteristic
318C2×C4×C5C22×Q811yescharacteristic
319C2×C4×C5C2×#4111yescharacteristic
320C2×C4×C5H(5,𝔽2)11yescharacteristic
321C2×C4×C52−1+411yescharacteristic
322C22⋊D5—22no—
323C22⋊D5—22no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—21no—
328C2×Dic5—21no—
329C2×Dic5—21no—
330C2×Dic5—21no—
331D20—21no—
332D20C4×Q812yes—
333C4×D5—22no—
334C4×D5—22no—
335C4×D5—42no—
336C4×D5—81no—
337Dic10—21no—
338Dic10—42no—
339Dic10—81no—
340Dic10C4×Q812yes—
341C5×C8—21no—
342C5×C8—21no—
343C5×C8—21no—
344C5×C8—21no—
345C5×C8—21no—
346C5×C8—21no—
347C5×C8—21no—
348C5×C8—21no—
349#168—22no—
350#168—41no—
351#168—41no—
352#168—41no—
353C2×#41—51no—
354#131—102no—
355#131—102no—
356#131—201no—
357#131—201no—
358C2×M16—51no—
359C2×M16—51no—
360C2×M16—51no—
361C2×M16—51no—
362C2×M16—101no—
363C2×M16—101no—
364C22×C8—101no—
365C22×C8—101no—
366C22×C8C22×D511yescharacteristic
367C22×C8C22×D511yescharacteristic
368C22×C8C22×D511yescharacteristic
369C22×C8C22×D511yescharacteristic
370C4⋊Q8—51no—
371C4⋊Q8—51no—
372#125—51no—
373#125—51no—
374C22⋊Q8—101no—
375C22⋊Q8—101no—
376C4×Q8—51no—
377C4×Q8—51no—
378C4×Q8—101no—
379C4×Q8—101no—
380C4×D4—51no—
381C4×D4—51no—
382C4×D4—101no—
383C4×D4—101no—
384#117—51no—
385#117—51no—
386#117—51no—
387#117—101no—
388C2×C42—101no—
389C2×C42C22×D511yescharacteristic
390C2×C42C22×D511yescharacteristic
391C2×C42C22×D511yescharacteristic
392#108—201no—
393#108—201no—
394#107—51no—
395#107—51no—
396#107—51no—
397#107—51no—
398#106—51no—
399#106—51no—
400#106—51no—
401#106—51no—
402C4⋊C8—101no—
403C4⋊C8—101no—
404C4⋊C8—101no—
405C4⋊C8—101no—
406C4⋊C8—101no—
407C4⋊C8—101no—
408C4⋊C8—101no—
409C4⋊C8—101no—
410C4⋊C8—101no—
411C4⋊C8—101no—
412C4⋊C8C4×D511yescharacteristic
413C4⋊C8C4×D511yescharacteristic
414C4⋊C8C4×D511yescharacteristic
415C4⋊C8C4×D511yescharacteristic
416C4⋊C8D2011yescharacteristic
417C4⋊C8D2011yescharacteristic
418C4⋊C8D2011yescharacteristic
419C4⋊C8D2011yescharacteristic
420#104—54no—
421#104—102no—
422#103—51no—
423#103—51no—
424#103—51no—
425#103—51no—
426#102—51no—
427#102—51no—
428#102—51no—
429#102—51no—
430#97—41no—
431#97—101no—
432#97—101no—
433#97—101no—
434C4×C8—41no—
435C4×C8—101no—
436C4×C8—101no—
437C4×C8—101no—
438#95—21no—
439#95—21no—
440C22×C5—21no—
441C22×C5—21no—
442C22×C5C2×C4×D411yescharacteristic
443C22×C5#55211yescharacteristic
444C22×C5#55411yescharacteristic
445C2×D5—22no—
446C2×D5—41no—
447C2×D5—41no—
448C4×C5—21no—
449C4×C5—21no—
450C4×C5—21no—
451C4×C5—21no—
452C4×C5—42no—
453C4×C5—81no—
454C4×C5C2×C4×Q811yescharacteristic
455C4×C5#52011yescharacteristic
456C4×C5#54611yescharacteristic
457C4×C5D4×Q811yescharacteristic
458Dic5—22no—
459Dic5—41no—
460Dic5—41no—
461Dic5—41no—
462Dic5—41no—
463Dic5—41no—
464Dic5—41no—
465#41—52no—
466#41—52no—
467#41—101no—
468#41—101no—
469C2×Q8—51no—
470C2×Q8—101no—
471C2×Q8—101no—
472C2×D4—51no—
473C2×D4—101no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—101no—
477C22×C4—101no—
478C22×C4—101no—
479C22×C4#70911yescharacteristic
480C22×C4#70911yescharacteristic
481C22×C4C23×D511yescharacteristic
482M16—52no—
483M16—101no—
484M16—101no—
485M16—101no—
486M16—101no—
487M16—101no—
488M16—101no—
489M16—101no—
490M16—202no—
491M16—202no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—101no—
501C2×C8—101no—
502C2×C8—101no—
503C2×C8—101no—
504C2×C8—202no—
505C2×C8—202no—
506C2×C8C2×C4×D511yescharacteristic
507C2×C8C2×C4×D511yescharacteristic
508C2×C8C2×C4×D511yescharacteristic
509C2×C8C2×C4×D511yescharacteristic
510C2×C8C2×D2011yescharacteristic
511C2×C8C2×D2011yescharacteristic
512C2×C8C2×D2011yescharacteristic
513C2×C8C2×D2011yescharacteristic
514C4⋊C4—51no—
515C4⋊C4—51no—
516C4⋊C4—51no—
517C4⋊C4—51no—
518C4⋊C4—51no—
519C4⋊C4—51no—
520C4⋊C4—101no—
521C4⋊C4—101no—
522C4⋊C4—101no—
523C4⋊C4—101no—
524C4⋊C4—101no—
525C4⋊C4—101no—
526C4⋊C4—101no—
527C4⋊C4—101no—
528C22⋊C4—101no—
529C22⋊C4—101no—
530C22⋊C4—101no—
531C22⋊C4—101no—
532C22⋊C4—101no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—101no—
537C42—101no—
538C42—101no—
539C42—101no—
540C42—101no—
541C42C2×C4×D511yescharacteristic
542C42C2×C4×D511yescharacteristic
543C42C2×D2011yescharacteristic
544C42C2×D2011yescharacteristic
545C42Q8×D512yes—
546C2×C5—21no—
547C2×C5—21no—
548C2×C5#236011yescharacteristic
549C2×C5#295511yescharacteristic
550C2×C5#295711yescharacteristic
551D5—42no—
552C23—101no—
553C23C2×#70911yescharacteristic
554Q8—52no—
555Q8—101no—
556Q8—202no—
557Q8—401no—
558D4—52no—
559D4—102no—
560D4—102no—
561D4—101no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—101no—
571C2×C4—102no—
572C2×C4—102no—
573C2×C4—101no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—101no—
579C2×C4—202no—
580C2×C4—401no—
581C2×C4C4×D2011yescharacteristic
582C2×C4C4×D2011yescharacteristic
583C2×C4C4×D2011yescharacteristic
584C2×C4C4×D2011yescharacteristic
585C2×C4C22×C4×D511yescharacteristic
586C2×C4C22×D2011yescharacteristic
587C2×C4#414411yescharacteristic
588C2×C4C2×Q8×D511yescharacteristic
589C2×C4D5×#4111yescharacteristic
590C2×C4#415011yescharacteristic
591C8—21no—
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—21no—
599C8—102no—
600C8—201no—
601C8—201no—
602C8—201no—
603C5#2298411yescharacteristic, complemented, Sylow
604C22—21no—
605C22—21no—
606C22—102no—
607C22—201no—
608C22—201no—
609C22C2×C4×D2011yescharacteristic
610C22#6584511yescharacteristic
611C22#6586311yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—81no—
618C4—102no—
619C4—201no—
620C4—201no—
621C4—201no—
622C4—201no—
623C4—201no—
624C4—201no—
625C4#6588011yescharacteristic
626C4#6588811yescharacteristic
627C4C4×Q8×D511yescharacteristic
628C4Q8×D2011yescharacteristic
629C2—21no—
630C2—21no—
631C2—202no—
632C2#1060550411yescharacteristic
633C2#1061031011yescharacteristic
634C2#1061031111yescharacteristic
subgroupG/H
centerC2×C4C22×D20
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1768C2
socleC22×C5C2×C4×D4
prime radicalC2×#709C23
cosocleC22×C4×C5C24
hypercenter#1768D5
hypocenterC5#22984
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #1768

Complements

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

NH ≅ G/Ntype
3. #10610739C2semidirect
4. C5×#1768C2semidirect
5. #10601267C2semidirect
6. #10600637C2semidirect
8. #10600587C2semidirect
10. #10600234C2semidirect
14. #10599438C2semidirect
15. #10599438C2semidirect
41. #65140C4semidirect
42. #65139C4semidirect
43. #65136C4semidirect
44. #65136C4semidirect
45. #65135C4semidirect
46. #65131C4semidirect
53. #65118C4semidirect
54. #65118C4semidirect
150. #3937Q8semidirect
166. #1768D5semidirect
603. C5#22984semidirect

Maximal subgroups

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

subgroupindex
#106107562
#106107432
#106107392
C5×#17682
#106012672
#106006372
#106006322
#106005872
#106005822
#106002342
#106002232
#105994872
#105994382
#229845