Finite Group Databasebeta

← #12118752

Subgroups — #12118752

Order 1280.

740 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2925C211yesmaximal, characteristic, complemented
2C4×#4096C211yesmaximal, characteristic
3#10610743C211yesmaximal, characteristic, complemented
4#10602439C211yesmaximal, characteristic, complemented
5#10601322C211yesmaximal, characteristic, complemented
6#10601309C211yesmaximal, characteristic, complemented
7#10601259C211yesmaximal, characteristic, complemented
8#10600804C212yesmaximal
9#10600791C212yesmaximal, complemented
10#10600692C212yesmaximal, complemented
11#10600681C212yesmaximal, complemented
12C4×C5×#41C2211yescharacteristic
13C2×#4096C2211yescharacteristic
14C2×#4047C2212yes—
15C4×#709C2211yescharacteristic
16C5×#433—22no—
17C5×#432—21no—
18C5×#431—21no—
19C5×#423C2211yescharacteristic
20C2×C5×C4⋊C8C2211yescharacteristic
21C5×#408C2212yes—
22C5×#405C2212yes—
23C2×#3969C2212yes—
24#65522C2211yescharacteristic
25C2×#3957C2212yes—
26#65391C2212yes—
27C2×#3947C2212yes—
28C4×#689C411yescharacteristic, complemented
29C4×#689C411yescharacteristic, complemented
30C4×#688C411yescharacteristic, complemented
31C4×#688C411yescharacteristic, complemented
32C4×#687C411yescharacteristic, complemented
33C4×#687C411yescharacteristic, complemented
34C4×#686C411yescharacteristic, complemented
35C4×#686C411yescharacteristic, complemented
36#65291C2211yescharacteristic
37#65287C2211yescharacteristic
38C4×C4⋊Dic5C2211yescharacteristic
39#65213C2211yescharacteristic
40C2×C4×#168C2211yescharacteristic
41#65128—22no—
42#65126—21no—
43D5×C4⋊C8—21no—
44#64778C2212yes—
45#64778C2212yes—
46#64775C2212yes—
47#64770C2212yes—
48#64752C2212yes—
49#22782—51nomaximal, Sylow
50C2×C5×#41C2311yescharacteristic
51C2×#709C2311yescharacteristic
52C2×C5×M16C2312yes—
53C22×C5×C8C2312yes—
54C4×C5×Q8C2×C411yescharacteristic
55C4×C5×Q8C2×C411yescharacteristic
56C4×C5×D4—21no—
57C4×C5×D4—21no—
58C4×C5×D4C2×C411yescharacteristic
59C4×C5×D4C2×C411yescharacteristic
60C5×#117—21no—
61C5×#117C2311yescharacteristic
62C2×C42×C5—21no—
63C2×C42×C5C2311yescharacteristic
64#4096—22no—
65#4096—22no—
66C2×#689C2×C411yescharacteristic
67C2×#688C2×C411yescharacteristic
68C2×#687C2×C411yescharacteristic
69C2×#686C2×C411yescharacteristic
70C4×C22⋊D5—21no—
71C4×C22⋊D5—21no—
72#4072C2311yescharacteristic
73C2×C4⋊Dic5—21no—
74C2×C4×Dic5C2312yes—
75C2×#681C2312yes—
76C22×#168C2311yescharacteristic
77C22×#168C2311yescharacteristic
78#4047—24no—
79#4047—42no—
80C2×#676—22no—
81C2×C8×D5—22no—
82C4×D20C2×C411yescharacteristic
83C4×D20C2×C411yescharacteristic
84#4018—21no—
85C42×D5—21no—
86C4×Dic10C2×C411yescharacteristic
87C4×Dic10C2×C411yescharacteristic
88C5×C4⋊C8—21no—
89C5×C4⋊C8—21no—
90C5×C4⋊C8D411yescharacteristic
91C5×C4⋊C8D411yescharacteristic
92C5×C4⋊C8D412yes—
93C5×C22⋊C8—22no—
94C5×C22⋊C8—22no—
95C5×#97—22no—
96C4×C5×C8—22no—
97#3969—42no—
98#3967C2×C411yescharacteristic
99#3967C2×C411yescharacteristic
100#3964C2×C411yescharacteristic
101#3964C2×C411yescharacteristic
102#3963—21no—
103#3957—24no—
104#3947—42no—
105#3946—22no—
106#3946—22no—
107#3942C2×C411yescharacteristic
108#3942C2×C411yescharacteristic
109#3941C2×C411yescharacteristic
110#3941C2×C411yescharacteristic
111#3940C2×C411yescharacteristic
112#3940C2×C411yescharacteristic
113#3939C2×C411yescharacteristic
114#3939C2×C411yescharacteristic
115C4⋊#168—21no—
116C4⋊#168—21no—
117C4×#168C2×C411yescharacteristic
118C4×#168C2×C411yescharacteristic
119C4×#168C2×C411yescharacteristic
120C4×#168C2×C411yescharacteristic
121C4×#135—51no—
122#2925D511yescharacteristic, complemented
123#2906—51no—
124#1938—52no—
125#1922—52no—
126#1876—52no—
127#1837—51no—
128#1806—51no—
129#1806—51no—
130#1770—51no—
131#1765—52no—
132C5×#41—21no—
133C5×#41—21no—
134C5×#41—21no—
135C5×#41—21no—
136C2×C5×Q8C22×C411yescharacteristic
137C2×C5×D4—21no—
138C2×C5×D4C22×C411yescharacteristic
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5#4111yescharacteristic
143C22×C4×C5#4111yescharacteristic
144C22×C4×C5C2411yescharacteristic
145C2×C22⋊D5—21no—
146C22×Dic5—22no—
147#709—21no—
148#709—21no—
149#709#4112yes—
150#709#4112yes—
151C2×D20C22×C411yescharacteristic
152C2×C4×D5—21no—
153C2×C4×D5—21no—
154C2×C4×D5—21no—
155C2×Dic10C22×C411yescharacteristic
156C5×M16—22no—
157C5×M16—22no—
158C2×C5×C8—22no—
159C2×C5×C8—22no—
160C2×C5×C8—22no—
161C2×C5×C8C2×D412yes—
162C2×C5×C8C2×D412yes—
163C5×C4⋊C4—21no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4C22×C411yescharacteristic
166C5×C4⋊C4C22×C411yescharacteristic
167C5×C22⋊C4—21no—
168C5×C22⋊C4—21no—
169C5×C22⋊C4—21no—
170C42×C5—21no—
171C42×C5—21no—
172C42×C5—21no—
173C42×C5C22×C411yescharacteristic
174C42×C5C22×C411yescharacteristic
175C42×C5C2×D411yescharacteristic
176C42×C5C2×D411yescharacteristic
177C22⋊Dic5—21no—
178#689—22no—
179#688—22no—
180#687—22no—
181#686—22no—
182#685—21no—
183#685—21no—
184C4⋊Dic5—42no—
185C4⋊Dic5C22×C411yescharacteristic
186C4⋊Dic5C22×C411yescharacteristic
187#683—21no—
188#683—21no—
189C4×Dic5—21no—
190C4×Dic5—21no—
191C4×Dic5—21no—
192C4×Dic5—22no—
193C4×Dic5—22no—
194#681—22no—
195#681—22no—
196C2×#168—21no—
197C2×#168—21no—
198C2×#168—21no—
199C2×#168—21no—
200C2×#168—22no—
201C2×#168C22×C411yescharacteristic
202C2×#168C22×C411yescharacteristic
203C2×#168C22×C411yescharacteristic
204C2×#168C22×C411yescharacteristic
205#676—44no—
206C8×D5—44no—
207C2×#135—51no—
208C2×#131—52no—
209C4×#41—51no—
210C4×#41C2×D511yescharacteristic
211C4×Q16—51no—
212C4×Q16—51no—
213C4×SD16—51no—
214C4×SD16—51no—
215C4×SD16—51no—
216C4×SD16—51no—
217C4×D8—51no—
218C4×D8—51no—
219#433—22no—
220#432—21no—
221#431—21no—
222#427—51no—
223#424—52no—
224#424—102no—
225#423—51no—
226#423—101no—
227#423C2×D511yescharacteristic
228C2×C4⋊C8—101no—
229C2×C4⋊C8C2×D511yescharacteristic
230C2×#104—52no—
231C2×#104—52no—
232#416—51no—
233#416—51no—
234#408C2×D512yes—
235#405C2×D512yes—
236C2×#97—52no—
237C2×C4×C8—51no—
238C4×C4⋊C4—51no—
239#341—52no—
240#341—52no—
241#339—52no—
242#339—52no—
243#336—52no—
244C23×C5—21no—
245C23×C5C2×#4111yescharacteristic
246C22×D5—21no—
247C5×Q8—21no—
248C5×Q8—21no—
249C5×D4—21no—
250C5×D4—21no—
251C5×D4—41no—
252C5×D4—41no—
253C2×C4×C5—22no—
254C2×C4×C5—21no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—41no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5—42no—
261C2×C4×C5—81no—
262C2×C4×C5C4×D411yescharacteristic
263C2×C4×C5C4×D411yescharacteristic
264C2×C4×C5C4×D411yescharacteristic
265C2×C4×C5C4×D411yescharacteristic
266C2×C4×C5C23×C411yescharacteristic
267C2×C4×C5C22×D411yescharacteristic
268C2×C4×C5C2×#4111yescharacteristic
269C2×C4×C5C2×#4111yescharacteristic
270C2×C4×C5H(5,𝔽2)11yescharacteristic
271C2×C4×C52−1+411yescharacteristic
272C22⋊D5—22no—
273C22⋊D5—22no—
274C2×Dic5—21no—
275C2×Dic5—21no—
276C2×Dic5—21no—
277C2×Dic5—42no—
278C2×Dic5—42no—
279C2×Dic5—42no—
280D20—21no—
281D20#11712yes—
282C4×D5—22no—
283C4×D5—22no—
284C4×D5—42no—
285C4×D5—81no—
286Dic10—21no—
287Dic10#11712yes—
288C5×C8—22no—
289C5×C8—22no—
290C5×C8—42no—
291#168—21no—
292#168—21no—
293#168—21no—
294#168—21no—
295#168—42no—
296C2×#41—51no—
297C2×#41C22×D511yescharacteristic
298#135—102no—
299#135—102no—
300C2×Q16—51no—
301C2×SD16—51no—
302C2×SD16—51no—
303C2×D8—51no—
304#131—104no—
305#131—202no—
306C2×M16—52no—
307C2×M16—102no—
308C2×M16C22×D512yes—
309C22×C8—51no—
310C22×C8—51no—
311C22×C8—102no—
312C22×C8C22×D512yes—
313C4×Q8—51no—
314C4×Q8—51no—
315C4×Q8C4×D511yescharacteristic
316C4×Q8C4×D511yescharacteristic
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—51no—
320C4×D4—51no—
321C4×D4—101no—
322C4×D4—101no—
323C4×D4C4×D511yescharacteristic
324C4×D4C4×D511yescharacteristic
325#117—21no—
326#117—51no—
327#117—101no—
328#117C22×D511yescharacteristic
329C2×C4⋊C4—101no—
330C2×C42—21no—
331C2×C42—52no—
332C2×C42—101no—
333C2×C42C22×D511yescharacteristic
334#107—51no—
335#107—51no—
336#106—51no—
337#106—51no—
338C4⋊C8—21no—
339C4⋊C8—21no—
340C4⋊C8—102no—
341C4⋊C8—102no—
342C4⋊C8—101no—
343C4⋊C8—101no—
344C4⋊C8C22⋊D511yescharacteristic
345C4⋊C8C22⋊D511yescharacteristic
346C4⋊C8C22⋊D512yes—
347#104—104no—
348#104—202no—
349#103—51no—
350#103—51no—
351#103—51no—
352#103—51no—
353#102—51no—
354#102—51no—
355#102—51no—
356#102—51no—
357C22⋊C8—22no—
358C22⋊C8—22no—
359#97—22no—
360#97—202no—
361C4×C8—22no—
362C4×C8—51no—
363C4×C8—51no—
364C4×C8—51no—
365C4×C8—51no—
366#95—101no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5—41no—
370C22×C5—41no—
371C22×C5—41no—
372C22×C5C2×C4×D411yescharacteristic
373C22×C5#55211yescharacteristic
374C22×C5#55311yescharacteristic
375C2×D5—22no—
376C2×D5—41no—
377C2×D5—41no—
378C4×C5—21no—
379C4×C5—21no—
380C4×C5—21no—
381C4×C5—41no—
382C4×C5—41no—
383C4×C5—41no—
384C4×C5#44412yes—
385C4×C5C2×#11711yescharacteristic
386C4×C5#52011yescharacteristic
387C4×C5#54611yescharacteristic
388C4×C5#54811yescharacteristic
389Dic5—22no—
390Dic5—41no—
391Dic5—41no—
392Dic5—82no—
393#41—21no—
394#41—21no—
395#41—21no—
396#41—21no—
397#41—52no—
398#41—52no—
399#41—101no—
400#41—101no—
401C2×Q8—51no—
402C2×Q8C2×C4×D511yescharacteristic
403C2×D4—21no—
404C2×D4—51no—
405C2×D4—101no—
406C2×D4C2×C4×D511yescharacteristic
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—101no—
411C22×C4—101no—
412C22×C4—101no—
413C22×C4—102no—
414C22×C4#70911yescharacteristic
415C22×C4#70911yescharacteristic
416C22×C4C23×D511yescharacteristic
417Q16—102no—
418SD16—102no—
419SD16—102no—
420D8—102no—
421M16—22no—
422M16—22no—
423M16—102no—
424M16—102no—
425M16—204no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—51no—
430C2×C8—51no—
431C2×C8—51no—
432C2×C8—51no—
433C2×C8—101no—
434C2×C8—101no—
435C2×C8—101no—
436C2×C8—101no—
437C2×C8—102no—
438C2×C8—204no—
439C2×C8C2×C22⋊D512yes—
440C2×C8C2×C22⋊D512yes—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—51no—
444C4⋊C4—51no—
445C4⋊C4—101no—
446C4⋊C4—101no—
447C4⋊C4—202no—
448C4⋊C4C2×C4×D511yescharacteristic
449C4⋊C4C2×C4×D511yescharacteristic
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—21no—
453C22⋊C4—101no—
454C22⋊C4—101no—
455C22⋊C4—101no—
456C42—21no—
457C42—21no—
458C42—21no—
459C42—101no—
460C42—101no—
461C42—101no—
462C42—102no—
463C42—102no—
464C42C2×C4×D511yescharacteristic
465C42C2×C4×D511yescharacteristic
466C42C2×C22⋊D511yescharacteristic
467C42C2×C22⋊D511yescharacteristic
468C2×C5—21no—
469C2×C5—21no—
470C2×C5—81no—
471C2×C5#235211yescharacteristic
472C2×C5C2×#44411yescharacteristic
473C2×C5#295711yescharacteristic
474D5—42no—
475C23—21no—
476C23—101no—
477C23C2×#70911yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—52no—
481Q8—101no—
482D4—21no—
483D4—21no—
484D4—41no—
485D4—41no—
486D4—52no—
487D4—102no—
488D4—102no—
489D4—101no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—81no—
499C2×C4—101no—
500C2×C4—102no—
501C2×C4—102no—
502C2×C4—101no—
503C2×C4—101no—
504C2×C4—202no—
505C2×C4—202no—
506C2×C4—202no—
507C2×C4—202no—
508C2×C4—401no—
509C2×C4C4×C22⋊D511yescharacteristic
510C2×C4C4×C22⋊D511yescharacteristic
511C2×C4C4×C22⋊D511yescharacteristic
512C2×C4C4×C22⋊D511yescharacteristic
513C2×C4C22×C4×D511yescharacteristic
514C2×C4D5×#4111yescharacteristic
515C2×C4D5×#4111yescharacteristic
516C2×C4#414911yescharacteristic
517C2×C4#415011yescharacteristic
518C2×C4C22×C22⋊D511yescharacteristic
519C8—22no—
520C8—22no—
521C8—42no—
522C8—101no—
523C8—101no—
524C8—101no—
525C8—101no—
526C8—202no—
527C5#2278211yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—102no—
534C22—201no—
535C22—201no—
536C22#6586311yescharacteristic
537C22#6586411yescharacteristic
538C22C2×C4×C22⋊D511yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—102no—
546C4—201no—
547C4—201no—
548C4—402no—
549C4#6543412yes—
550C4D5×#11711yescharacteristic
551C4#6585711yescharacteristic
552C4#6616311yescharacteristic
553C4#6616511yescharacteristic
554C2—21no—
555C2—21no—
556C2—81no—
557C2—202no—
558C2#1061400311yescharacteristic
559C2C2×#6543411yescharacteristic
560C2#1061554311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#2925C2
socleC22×C5C2×C4×D4
prime radicalC2×#4096C22
cosocleC22×C4×C5C24
hypercenter#2925D5
hypocenterC5#22782
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2925

Complements

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

NH ≅ G/Ntype
1. C5×#2925C2semidirect
3. #10610743C2semidirect
4. #10602439C2semidirect
5. #10601322C2semidirect
6. #10601309C2semidirect
7. #10601259C2semidirect
9. #10600791C2semidirect
10. #10600692C2semidirect
11. #10600681C2semidirect
28. C4×#689C4semidirect
29. C4×#689C4semidirect
30. C4×#688C4semidirect
31. C4×#688C4semidirect
32. C4×#687C4semidirect
33. C4×#687C4semidirect
34. C4×#686C4semidirect
35. C4×#686C4semidirect
122. #2925D5semidirect
527. C5#22782semidirect

Maximal subgroups

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

subgroupindex
C5×#29252
C4×#40962
#106107432
#106024392
#106013222
#106013092
#106012592
#106008042
#106007912
#106006922
#106006812
#227825