Finite Group Databasebeta

← #12121385

Subgroups — #12121385

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
1C5×#2962C211yesmaximal, characteristic, complemented
2#10615080C211yesmaximal, characteristic
3#10610743C211yesmaximal, characteristic
4#10602633C211yesmaximal, characteristic, complemented
5#10601338C211yesmaximal, characteristic
6#10601338C211yesmaximal, characteristic
7#10601331C211yesmaximal, characteristic, complemented
8#10601330C211yesmaximal, characteristic, complemented
9#10601235C211yesmaximal, characteristic, complemented
10#10600692C211yesmaximal, characteristic, complemented
11#10600692C211yesmaximal, characteristic, complemented
12#10600681C211yesmaximal, characteristic
13#10600680C211yesmaximal, characteristic
14#10600668C211yesmaximal, characteristic, complemented
15#10600659C211yesmaximal, characteristic
16C5×#533C2211yescharacteristic
17C2×#4047C2211yescharacteristic
18C2×#4047C2211yescharacteristic
19C4×#709C2211yescharacteristic
20C5×#446—21no—
21C5×#446—21no—
22C5×#446—21no—
23C5×C8×Q8—21no—
24C5×#424C2211yescharacteristic
25C5×#424C2211yescharacteristic
26C2×C5×C4⋊C8C2211yescharacteristic
27C5×#405C2211yescharacteristic
28C5×#405C2211yescharacteristic
29C4×C5×M16C2211yescharacteristic
30C2×#3957C2211yescharacteristic
31C2×#3957C2211yescharacteristic
32C2×#3954C2211yescharacteristic
33C2×#3954C2211yescharacteristic
34#65391C2211yescharacteristic
35#65391C2211yescharacteristic
36C2×#3947C2211yescharacteristic
37C2×C8×Dic5C2211yescharacteristic
38#65383C411yescharacteristic, complemented
39#65380C411yescharacteristic, complemented
40#65376C411yescharacteristic, complemented
41#65373C411yescharacteristic, complemented
42#65355C411yescharacteristic, complemented
43#65355C411yescharacteristic, complemented
44#65352C411yescharacteristic, complemented
45#65352C411yescharacteristic, complemented
46#65291C2211yescharacteristic
47#65291C2211yescharacteristic
48#65287C2211yescharacteristic
49#65287C2211yescharacteristic
50#65221C2211yescharacteristic
51#65213C2211yescharacteristic
52C2×C4⋊#168C2211yescharacteristic
53#65128—21no—
54#65128—21no—
55#65126—21no—
56D5×C4⋊C8—21no—
57#64778C2211yescharacteristic
58#64778C2211yescharacteristic
59#64775C2211yescharacteristic
60#64775C2211yescharacteristic
61#64770C2211yescharacteristic
62#64770C2211yescharacteristic
63#64752C2211yescharacteristic
64#64752C2211yescharacteristic
65#64752C2211yescharacteristic
66#64752C2211yescharacteristic
67#22984—51nomaximal, Sylow
68C2×#709C2311yescharacteristic
69C2×C5×M16C2311yescharacteristic
70C2×C5×M16C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C5×C4⋊Q8C2×C411yescharacteristic
74C5×C4⋊Q8C2×C411yescharacteristic
75C5×#125C2×C411yescharacteristic
76C5×#125C2×C411yescharacteristic
77C5×C22⋊Q8—21no—
78C5×C22⋊Q8—21no—
79C4×C5×Q8—21no—
80C4×C5×Q8—21no—
81C5×#117C2311yescharacteristic
82C5×#117C2311yescharacteristic
83C2×C42×C5C2311yescharacteristic
84C4×C22⋊D5—21no—
85C4×C22⋊D5—21no—
86#4072C2311yescharacteristic
87C2×C4×Dic5C2311yescharacteristic
88C2×C4×Dic5C2311yescharacteristic
89C2×#681C2311yescharacteristic
90C2×#681C2311yescharacteristic
91C22×#168C2311yescharacteristic
92C22×#168C2311yescharacteristic
93#4047—22no—
94#4047—22no—
95#4047—41no—
96#4047—41no—
97C2×#676—21no—
98C2×#676—21no—
99C2×C8×D5—21no—
100C2×C8×D5—21no—
101C4×D20C2×C411yescharacteristic
102C4×D20C2×C411yescharacteristic
103#4018—21no—
104C42×D5—21no—
105C4×Dic10C2×C411yescharacteristic
106C4×Dic10C2×C411yescharacteristic
107C5×C4⋊C8—21no—
108C5×C4⋊C8—21no—
109C5×C4⋊C8—21no—
110C5×C4⋊C8—21no—
111C5×C4⋊C8D411yescharacteristic
112C5×C4⋊C8D411yescharacteristic
113C5×C4⋊C8D411yescharacteristic
114C5×C4⋊C8D411yescharacteristic
115C5×#97—21no—
116C5×#97—21no—
117C5×#97—21no—
118C4×C5×C8—21no—
119C4×C5×C8—21no—
120C4×C5×C8—21no—
121#3963—21no—
122#3963—21no—
123#3957—22no—
124#3957Q814yescomplemented
125#3954—41no—
126#3954—41no—
127#3947—41no—
128#3946—21no—
129#3946—21no—
130#3946—21no—
131#3946—21no—
132C8×Dic5—41no—
133#3942C2×C411yescharacteristic
134#3942C2×C411yescharacteristic
135#3942C2×C411yescharacteristic
136#3942C2×C411yescharacteristic
137#3941C2×C411yescharacteristic
138#3941C2×C411yescharacteristic
139#3941C2×C411yescharacteristic
140#3941C2×C411yescharacteristic
141#3940C2×C411yescharacteristic
142#3940C2×C411yescharacteristic
143#3940C2×C411yescharacteristic
144#3940C2×C411yescharacteristic
145#3939C2×C411yescharacteristic
146#3939C2×C411yescharacteristic
147#3939C2×C411yescharacteristic
148#3939C2×C411yescharacteristic
149C4⋊#168—21no—
150C4⋊#168—21no—
151C4⋊#168C2×C411yescharacteristic
152C4⋊#168C2×C411yescharacteristic
153C4⋊#168C2×C411yescharacteristic
154C4⋊#168C2×C411yescharacteristic
155#3076—51no—
156#2962D511yescharacteristic, complemented
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#1768—51no—
167#1765—51no—
168#1764—51no—
169#1759—51no—
170C2×C5×Q8—21no—
171C2×C5×Q8—21no—
172C22×C4×C5#4111yescharacteristic
173C22×C4×C5#4111yescharacteristic
174C22×C4×C5C2411yescharacteristic
175C2×C22⋊D5—21no—
176C22×Dic5—21no—
177C22×Dic5—21no—
178#709—21no—
179#709—21no—
180#709C2×Q812yes—
181#709#4112yes—
182C2×D20C22×C411yescharacteristic
183C2×C4×D5—21no—
184C2×C4×D5—21no—
185C2×C4×D5—21no—
186C2×Dic10C22×C411yescharacteristic
187C5×M16—21no—
188C5×M16—21no—
189C5×M16—21no—
190C5×M16C2×Q812yes—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8C2×D411yescharacteristic
198C2×C5×C8C2×D411yescharacteristic
199C2×C5×C8C2×D411yescharacteristic
200C2×C5×C8C2×D411yescharacteristic
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4C22×C411yescharacteristic
208C5×C4⋊C4C22×C411yescharacteristic
209C5×C4⋊C4C22×C411yescharacteristic
210C5×C4⋊C4C22×C411yescharacteristic
211C5×C22⋊C4—21no—
212C5×C22⋊C4—21no—
213C42×C5—21no—
214C42×C5—21no—
215C42×C5C22×C411yescharacteristic
216C42×C5C22×C411yescharacteristic
217C42×C5C2×D411yescharacteristic
218C42×C5C2×D411yescharacteristic
219C22⋊Dic5—21no—
220#685—21no—
221#685—21no—
222C4⋊Dic5C22×C411yescharacteristic
223C4⋊Dic5C22×C411yescharacteristic
224#683—21no—
225#683—21no—
226C4×Dic5—21no—
227C4×Dic5—21no—
228C4×Dic5—21no—
229C4×Dic5—21no—
230C4×Dic5—21no—
231C4×Dic5—21no—
232C4×Dic5C2×Q812yes—
233#681—21no—
234#681—21no—
235#681—21no—
236#681—21no—
237C2×#168—21no—
238C2×#168—21no—
239C2×#168—21no—
240C2×#168—21no—
241C2×#168—21no—
242C2×#168—21no—
243C2×#168C22×C411yescharacteristic
244C2×#168C22×C411yescharacteristic
245C2×#168C22×C411yescharacteristic
246C2×#168C22×C411yescharacteristic
247#676—42no—
248#676—42no—
249C8×D5—42no—
250C8×D5—42no—
251C2×#131—51no—
252C2×#131—51no—
253#533C2×D511yescharacteristic
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—21no—
264#446—21no—
265#446—21no—
266C8×Q8—21no—
267C2×#108—51no—
268C2×#108—51no—
269#427—51no—
270#427—51no—
271#424—51no—
272#424—51no—
273#424—101no—
274#424—101no—
275#424C2×D511yescharacteristic
276#424C2×D511yescharacteristic
277#423—51no—
278#423—101no—
279C2×C4⋊C8—51no—
280C2×C4⋊C8—101no—
281C2×C4⋊C8C2×D511yescharacteristic
282C2×#104—51no—
283C2×#104—51no—
284#416—51no—
285#416—51no—
286#405C2×D511yescharacteristic
287#405C2×D511yescharacteristic
288C4×M16C2×D511yescharacteristic
289C2×#97—51no—
290C2×C4×C8—51no—
291#376—51no—
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#336—51no—
301#336—51no—
302C23×C5C2×#4111yescharacteristic
303C22×D5—21no—
304C5×Q8—42no—
305C5×Q8—81no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
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—22no—
328C2×Dic5—41no—
329C2×Dic5—41no—
330C2×Dic5—41no—
331C2×Dic5—41no—
332C2×Dic5—41no—
333D20—21no—
334D20C4×Q812yes—
335C4×D5—22no—
336C4×D5—22no—
337C4×D5—42no—
338C4×D5—81no—
339Dic10—21no—
340Dic10C4×Q812yes—
341C5×C8—21no—
342C5×C8—21no—
343C5×C8—21no—
344C5×C8—21no—
345C5×C8—22no—
346C5×C8—41no—
347#168—21no—
348#168—21no—
349#168—21no—
350#168—21no—
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—101no—
361C2×M16—101no—
362C2×M16C22×D511yescharacteristic
363C2×M16C22×D511yescharacteristic
364C22×C8—51no—
365C22×C8—51no—
366C22×C8—101no—
367C22×C8—101no—
368C22×C8C22×D511yescharacteristic
369C22×C8C22×D511yescharacteristic
370C4⋊Q8C4×D511yescharacteristic
371C4⋊Q8C4×D511yescharacteristic
372#125C4×D511yescharacteristic
373#125C4×D511yescharacteristic
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—51no—
379C4×Q8—51no—
380C4×D4—51no—
381C4×D4—51no—
382C4×D4—101no—
383C4×D4—101no—
384#117—51no—
385#117—101no—
386#117C22×D511yescharacteristic
387#117C22×D511yescharacteristic
388C2×C42—51no—
389C2×C42—51no—
390C2×C42—101no—
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—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—51no—
407C4⋊C8—51no—
408C4⋊C8—51no—
409C4⋊C8—51no—
410C4⋊C8—101no—
411C4⋊C8—101no—
412C4⋊C8—101no—
413C4⋊C8—101no—
414C4⋊C8—101no—
415C4⋊C8—101no—
416C4⋊C8C22⋊D511yescharacteristic
417C4⋊C8C22⋊D511yescharacteristic
418C4⋊C8C22⋊D511yescharacteristic
419C4⋊C8C22⋊D511yescharacteristic
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—21no—
431#97—21no—
432#97—21no—
433#97—201no—
434C4×C8—21no—
435C4×C8—21no—
436C4×C8—21no—
437C4×C8—201no—
438#95—101no—
439#95—101no—
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—41no—
453C4×C5—41no—
454C4×C5—41no—
455C4×C5—41no—
456C4×C5C2×C4×Q811yescharacteristic
457C4×C5#52011yescharacteristic
458C4×C5#54611yescharacteristic
459C4×C5D4×Q811yescharacteristic
460Dic5—22no—
461Dic5—42no—
462Dic5—41no—
463Dic5—41no—
464Dic5—81no—
465#41—52no—
466#41—52no—
467#41—101no—
468#41—101no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—51no—
472C2×D4—51no—
473C2×D4—101no—
474C22×C4—101no—
475C22×C4—101no—
476C22×C4—101no—
477C22×C4—101no—
478C22×C4—101no—
479C22×C4#70911yescharacteristic
480C22×C4#70911yescharacteristic
481C22×C4C23×D511yescharacteristic
482M16—21no—
483M16—21no—
484M16—21no—
485M16—101no—
486M16—101no—
487M16—101no—
488M16—101no—
489M16—202no—
490M16—202no—
491M16Q8×D512yes—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—51no—
499C2×C8—51no—
500C2×C8—51no—
501C2×C8—51no—
502C2×C8—101no—
503C2×C8—101no—
504C2×C8—101no—
505C2×C8—101no—
506C2×C8—101no—
507C2×C8—101no—
508C2×C8—202no—
509C2×C8—202no—
510C2×C8C2×C22⋊D511yescharacteristic
511C2×C8C2×C22⋊D511yescharacteristic
512C2×C8C2×C22⋊D511yescharacteristic
513C2×C8C2×C22⋊D511yescharacteristic
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—51no—
521C4⋊C4—51no—
522C4⋊C4—101no—
523C4⋊C4—101no—
524C4⋊C4C2×C4×D511yescharacteristic
525C4⋊C4C2×C4×D511yescharacteristic
526C4⋊C4C2×C4×D511yescharacteristic
527C4⋊C4C2×C4×D511yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—101no—
531C22⋊C4—101no—
532C22⋊C4—101no—
533C42—21no—
534C42—21no—
535C42—52no—
536C42—101no—
537C42—101no—
538C42—101no—
539C42—101no—
540C42—101no—
541C42—101no—
542C42C2×C4×D511yescharacteristic
543C42C2×C4×D511yescharacteristic
544C42C2×C22⋊D511yescharacteristic
545C42C2×C22⋊D511yescharacteristic
546C2×C5—21no—
547C2×C5—21no—
548C2×C5#236011yescharacteristic
549C2×C5#295511yescharacteristic
550C2×C5#295711yescharacteristic
551D5—42no—
552C23—101no—
553C23C2×#70911yescharacteristic
554Q8—42no—
555Q8—52no—
556Q8—81no—
557Q8—101no—
558D4—52no—
559D4—102no—
560D4—102no—
561D4—101no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—101no—
569C2×C4—102no—
570C2×C4—102no—
571C2×C4—101no—
572C2×C4—101no—
573C2×C4—102no—
574C2×C4—202no—
575C2×C4—201no—
576C2×C4—201no—
577C2×C4—201no—
578C2×C4—201no—
579C2×C4—201no—
580C2×C4—401no—
581C2×C4C4×C22⋊D511yescharacteristic
582C2×C4C4×C22⋊D511yescharacteristic
583C2×C4C4×C22⋊D511yescharacteristic
584C2×C4C4×C22⋊D511yescharacteristic
585C2×C4C22×C4×D511yescharacteristic
586C2×C4C2×Q8×D511yescharacteristic
587C2×C4#414711yescharacteristic
588C2×C4D5×#4111yescharacteristic
589C2×C4#414911yescharacteristic
590C2×C4C22×C22⋊D511yescharacteristic
591C8—22no—
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—101no—
598C8—101no—
599C8—101no—
600C8—101no—
601C8—201no—
602C8—201no—
603C5#2298411yescharacteristic, complemented, Sylow
604C22—21no—
605C22—21no—
606C22—102no—
607C22—201no—
608C22—201no—
609C22#6591311yescharacteristic
610C22#6591511yescharacteristic
611C22C2×C4×C22⋊D511yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—102no—
621C4—202no—
622C4—201no—
623C4—201no—
624C4—401no—
625C4C4×Q8×D511yescharacteristic
626C4#6590811yescharacteristic
627C4Q8×C22⋊D511yescharacteristic
628C4#6616311yescharacteristic
629C2—21no—
630C2—21no—
631C2—202no—
632C2#1061422111yescharacteristic
633C2#1061552311yescharacteristic
634C2#1061554311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#2962C2
socleC22×C5C2×C4×D4
prime radicalC2×#709C23
cosocleC22×C4×C5C24
hypercenter#2962D5
hypocenterC5#22984
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2962

Complements

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

NH ≅ G/Ntype
1. C5×#2962C2semidirect
4. #10602633C2semidirect
7. #10601331C2semidirect
8. #10601330C2semidirect
9. #10601235C2semidirect
10. #10600692C2semidirect
11. #10600692C2semidirect
14. #10600668C2semidirect
38. #65383C4semidirect
39. #65380C4semidirect
40. #65376C4semidirect
41. #65373C4semidirect
42. #65355C4semidirect
43. #65355C4semidirect
44. #65352C4semidirect
45. #65352C4semidirect
124. #3957Q8semidirect
156. #2962D5semidirect
603. C5#22984semidirect

Maximal subgroups

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

subgroupindex
C5×#29622
#106150802
#106107432
#106026332
#106013382
#106013312
#106013302
#106012352
#106006922
#106006812
#106006802
#106006682
#106006592
#229845