Finite Group Databasebeta

← #12109502

Subgroups — #12109502

Order 1280.

670 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10605483C211yesmaximal, characteristic
2C5×#1917C211yesmaximal, characteristic, complemented
3#10601243C211yesmaximal, characteristic
4#10601239C211yesmaximal, characteristic, complemented
5#10600628C211yesmaximal, characteristic
6#10600625C211yesmaximal, characteristic, complemented
7#10600275C211yesmaximal, characteristic, complemented
8#10599455C211yesmaximal, characteristic
9#10599455C211yesmaximal, characteristic
10#10599450C211yesmaximal, characteristic
11#10599408C211yesmaximal, characteristic
12#10599405C211yesmaximal, characteristic, complemented
13#10599403C211yesmaximal, characteristic, complemented
14#10599399C211yesmaximal, characteristic, complemented
15#10599397C211yesmaximal, characteristic, complemented
16C2×C42×D5C2211yescharacteristic
17C2×C5×C4⋊C8C2211yescharacteristic
18C2×C5×#97C2211yescharacteristic
19C4×C5×C4⋊C4C2211yescharacteristic
20C2×#3952C2211yescharacteristic
21C2×#3952C2211yescharacteristic
22C2×#3952C2211yescharacteristic
23C2×#3952C2211yescharacteristic
24C2×#3947C2211yescharacteristic
25C2×#3946C2211yescharacteristic
26C2×#3946C2211yescharacteristic
27C2×#3946C2211yescharacteristic
28C2×#3946C2211yescharacteristic
29C2×#3946C2211yescharacteristic
30C2×#3946C2211yescharacteristic
31C2×C8×Dic5C2211yescharacteristic
32#65276C411yescharacteristic
33#65276C411yescharacteristic
34#65266C411yescharacteristic
35#65266C411yescharacteristic
36C4×#685C2211yescharacteristic
37C4×#685C2211yescharacteristic
38C4×C4⋊Dic5C2211yescharacteristic
39#65221C2211yescharacteristic
40#65221C2211yescharacteristic
41C2×C4⋊#168C2211yescharacteristic
42C2×C4×#168C2211yescharacteristic
43#64953C411yescharacteristic
44#64953C411yescharacteristic
45#64940C411yescharacteristic
46#64940C411yescharacteristic
47C5×#336C2211yescharacteristic
48C5×#336C2211yescharacteristic
49C5×#336C2211yescharacteristic
50C5×#336C2211yescharacteristic
51#64770C2211yescharacteristic
52#64770C2211yescharacteristic
53#64770C2211yescharacteristic
54#64770C2211yescharacteristic
55#64744C2211yescharacteristic
56#64744C2211yescharacteristic
57#64744C2211yescharacteristic
58#64744C2211yescharacteristic
59#21928—51nomaximal, Sylow
60C22×C4×D5C2×C411yescharacteristic
61C22×C4×D5C2×C411yescharacteristic
62C22×C4×D5C2311yescharacteristic
63C22×C5×C8C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C2×C5×C4⋊C4C2×C411yescharacteristic
68C2×C5×C4⋊C4C2×C411yescharacteristic
69C2×C42×C5C2311yescharacteristic
70C2×C42×C5C2311yescharacteristic
71C2×C42×C5C2311yescharacteristic
72C2×#685C2×C411yescharacteristic
73C2×#685C2×C411yescharacteristic
74C2×#685C2×C411yescharacteristic
75C2×#685C2×C411yescharacteristic
76C2×C4⋊Dic5C2×C411yescharacteristic
77C2×C4⋊Dic5C2×C411yescharacteristic
78C2×C4×Dic5C2×C411yescharacteristic
79C2×C4×Dic5C2×C411yescharacteristic
80C2×C4×Dic5C2311yescharacteristic
81C2×C4×Dic5C2311yescharacteristic
82C2×C4×Dic5C2311yescharacteristic
83C22×#168C2311yescharacteristic
84C22×#168C2311yescharacteristic
85C22×#168C2311yescharacteristic
86C22×#168C2311yescharacteristic
87C42×D5—22no—
88C42×D5—22no—
89C5×C4⋊C8—41no—
90C5×#97—41no—
91C5×#95C2×C411yescharacteristic
92C5×#95C2×C411yescharacteristic
93#3963C2×C411yescharacteristic
94#3963C2×C411yescharacteristic
95#3963C2×C411yescharacteristic
96#3963C2×C411yescharacteristic
97#3963C2×C411yescharacteristic
98#3963C2×C411yescharacteristic
99#3963C2×C411yescharacteristic
100#3963C2×C411yescharacteristic
101#3963C2×C411yescharacteristic
102#3963C2×C411yescharacteristic
103#3963C2×C411yescharacteristic
104#3963C2×C411yescharacteristic
105#3963C2×C411yescharacteristic
106#3963C2×C411yescharacteristic
107#3952—41no—
108#3952—41no—
109#3952—41no—
110#3952—41no—
111#3947—41no—
112#3946—22no—
113#3946—22no—
114#3946—22no—
115#3946—22no—
116#3946—41no—
117#3946—41no—
118C8×Dic5—41no—
119C4⋊#168—41no—
120C4×#168—41no—
121#2283—51no—
122#1924—51no—
123#1924—51no—
124#1923—51no—
125#1923—51no—
126#1917—51no—
127#1917D511yescharacteristic, complemented
128#1916—51no—
129#1916—51no—
130#1843—51no—
131#1832—51no—
132#1797—51no—
133#1797—51no—
134#1768—51no—
135#1768—51no—
136C23×D5C22×C411yescharacteristic
137C22×C4×C5C22×C411yescharacteristic
138C22×C4×C5C22×C411yescharacteristic
139C22×C4×C5C22×C411yescharacteristic
140C22×C4×C5C22×C411yescharacteristic
141C22×C4×C5C22×C411yescharacteristic
142C22×C4×C5C22×C411yescharacteristic
143C22×C4×C5C2411yescharacteristic
144C22×Dic5C22×C411yescharacteristic
145C22×Dic5C22×C411yescharacteristic
146C22×Dic5C22×C411yescharacteristic
147C22×Dic5C22×C411yescharacteristic
148C22×Dic5C22×C411yescharacteristic
149C22×Dic5C22×C411yescharacteristic
150C22×Dic5C22×C411yescharacteristic
151C2×C4×D5—22no—
152C2×C4×D5—22no—
153C2×C4×D5—21no—
154C2×C4×D5—21no—
155C2×C4×D5—21no—
156C2×C4×D5—21no—
157C2×C4×D5—21no—
158C2×C4×D5—21no—
159C2×C4×D5—22no—
160C2×C4×D5—22no—
161C2×C4×D5—41no—
162C2×C4×D5—41no—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C2×C5×C8—21no—
166C2×C5×C8—21no—
167C2×C5×C8—21no—
168C2×C5×C8—21no—
169C2×C5×C8—21no—
170C2×C5×C8—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C5×C4⋊C4—22no—
176C5×C4⋊C4—41no—
177C42×C5—21no—
178C42×C5—21no—
179C42×C5—21no—
180C42×C5—21no—
181C42×C5—21no—
182C42×C5—21no—
183#685—22no—
184#685—22no—
185#685—41no—
186#685—41no—
187C4⋊Dic5—22no—
188C4⋊Dic5—41no—
189C4×Dic5—21no—
190C4×Dic5—21no—
191C4×Dic5—21no—
192C4×Dic5—21no—
193C4×Dic5—22no—
194C4×Dic5—22no—
195C4×Dic5#4112yes—
196C4×Dic5#4112yes—
197C2×#168—21no—
198C2×#168—21no—
199C2×#168—21no—
200C2×#168—21no—
201C2×#168—21no—
202C2×#168—21no—
203C2×#168—21no—
204C2×#168—21no—
205C2×#168—21no—
206C2×#168—21no—
207C2×#168—21no—
208C2×#168—21no—
209C22×C42—51no—
210C2×C4⋊C8—51no—
211C2×C4⋊C8—51no—
212C2×C4⋊C8—51no—
213C2×C4⋊C8—51no—
214C2×C4⋊C8—51no—
215C2×C4⋊C8—51no—
216C2×C4⋊C8—51no—
217C2×C4⋊C8C2×D511yescharacteristic
218C2×C22⋊C8—51no—
219C2×C22⋊C8—51no—
220C2×C22⋊C8—51no—
221C2×C22⋊C8—51no—
222C2×#97—51no—
223C2×#97C2×D511yescharacteristic
224C2×C4×C8—51no—
225C2×C4×C8—51no—
226#383—51no—
227#383—51no—
228#382—51no—
229#382—51no—
230#381—51no—
231#381—51no—
232#380—51no—
233#380—51no—
234C4×C4⋊C4—51no—
235C4×C4⋊C4C2×D511yescharacteristic
236C4×C22⋊C4—51no—
237C4×C22⋊C4—51no—
238#376—51no—
239#376—51no—
240#336—51no—
241#336—51no—
242#336—51no—
243#336—51no—
244#336—51no—
245#336—51no—
246#336—51no—
247#336—51no—
248#336C2×D511yescharacteristic
249#336C2×D511yescharacteristic
250#336C2×D511yescharacteristic
251#336C2×D511yescharacteristic
252C23×C5C23×C411yescharacteristic
253C22×D5—21no—
254C22×D5—21no—
255C22×D5—21no—
256C22×D5—21no—
257C22×D5—21no—
258C22×D5—21no—
259C22×D5#13112yes—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5#13112yes—
278C2×C4×C5C2×#4111yescharacteristic
279C2×C4×C5C2×#4111yescharacteristic
280C2×C4×C5H(5,𝔽2)11yescharacteristic
281C2×C4×C5H(5,𝔽2)11yescharacteristic
282C2×C4×C52−1+411yescharacteristic
283C2×C4×C52−1+411yescharacteristic
284C2×Dic5—21no—
285C2×Dic5—21no—
286C2×Dic5—21no—
287C2×Dic5—21no—
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5#11712yes—
304C2×Dic5#11712yes—
305C4×D5—44no—
306C4×D5—44no—
307C4×D5—41no—
308C4×D5—41no—
309C4×D5—41no—
310C4×D5—41no—
311C5×C8—41no—
312C5×C8—41no—
313C5×C8—41no—
314C5×C8—41no—
315#168—41no—
316#168—41no—
317#168—41no—
318#168—41no—
319C23×C4—51no—
320C23×C4—51no—
321C23×C4—51no—
322C22×C8—51no—
323C22×C8—51no—
324C22×C8—51no—
325C22×C8—51no—
326C22×C8C22×D511yescharacteristic
327C22×C8C22×D511yescharacteristic
328C22×C8C22×D511yescharacteristic
329C22×C8C22×D511yescharacteristic
330C2×C4⋊C4—51no—
331C2×C4⋊C4—51no—
332C2×C4⋊C4C4×D511yescharacteristic
333C2×C4⋊C4C4×D511yescharacteristic
334C2×C22⋊C4—51no—
335C2×C22⋊C4—51no—
336C2×C22⋊C4—51no—
337C2×C22⋊C4—51no—
338C2×C42—51no—
339C2×C42—51no—
340C2×C42—51no—
341C2×C42—51no—
342C2×C42—51no—
343C2×C42—102no—
344C2×C42—102no—
345C2×C42C22×D511yescharacteristic
346C2×C42C22×D511yescharacteristic
347C2×C42C22×D511yescharacteristic
348C4⋊C8—41no—
349C4⋊C8—102no—
350C4⋊C8—102no—
351C4⋊C8—102no—
352C4⋊C8—102no—
353C4⋊C8—201no—
354C4⋊C8—201no—
355C4⋊C8—201no—
356C22⋊C8—201no—
357C22⋊C8—201no—
358C22⋊C8—201no—
359C22⋊C8—201no—
360#97—41no—
361#97—201no—
362C4×C8—201no—
363C4×C8—201no—
364#95—51no—
365#95—51no—
366#95—51no—
367#95—51no—
368#95—51no—
369#95—51no—
370#95—51no—
371#95—51no—
372#95—51no—
373#95—51no—
374#95—51no—
375#95—51no—
376#95—51no—
377#95—51no—
378#95C4×D511yescharacteristic
379#95C4×D511yescharacteristic
380C22×C5C2×#11711yescharacteristic
381C22×C5#52011yescharacteristic
382C22×C5#52011yescharacteristic
383C22×C5C2×#13111yescharacteristic
384C22×C5C2×#13111yescharacteristic
385C22×C5#56811yescharacteristic
386C22×C5#56811yescharacteristic
387C2×D5—22no—
388C2×D5—22no—
389C2×D5—22no—
390C2×D5—41no—
391C2×D5—41no—
392C2×D5—41no—
393C2×D5—41no—
394C4×C5—22no—
395C4×C5—41no—
396C4×C5—41no—
397C4×C5—41no—
398C4×C5—41no—
399C4×C5—41no—
400C4×C5#54011yescharacteristic
401C4×C5#54111yescharacteristic
402C4×C5#54211yescharacteristic
403C4×C5#54211yescharacteristic
404Dic5—22no—
405Dic5—22no—
406Dic5—41no—
407Dic5—41no—
408Dic5—41no—
409Dic5—41no—
410Dic5—41no—
411C24—51no—
412C22×C4—51no—
413C22×C4—51no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—51no—
417C22×C4—51no—
418C22×C4—51no—
419C22×C4—102no—
420C22×C4—102no—
421C22×C4—102no—
422C22×C4—101no—
423C22×C4—101no—
424C22×C4—101no—
425C22×C4—101no—
426C22×C4—101no—
427C22×C4—101no—
428C22×C4—102no—
429C22×C4—201no—
430C22×C4—201no—
431C22×C4C2×C4×D511yescharacteristic
432C22×C4C2×C4×D511yescharacteristic
433C22×C4C2×C4×D511yescharacteristic
434C22×C4C2×C4×D511yescharacteristic
435C22×C4C2×C4×D511yescharacteristic
436C22×C4C2×C4×D511yescharacteristic
437C22×C4C23×D511yescharacteristic
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—101no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8—101no—
454C2×C8—101no—
455C2×C8—101no—
456C2×C8—101no—
457C2×C8—101no—
458C2×C8—101no—
459C2×C8—101no—
460C2×C8—101no—
461C2×C8—101no—
462C4⋊C4—22no—
463C4⋊C4—41no—
464C4⋊C4—102no—
465C4⋊C4—201no—
466C22⋊C4—102no—
467C22⋊C4—102no—
468C22⋊C4—201no—
469C22⋊C4—201no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—52no—
477C42—52no—
478C42—102no—
479C42—102no—
480C42—101no—
481C42—101no—
482C42—101no—
483C42—101no—
484C2×C5#231411yescharacteristic
485C2×C5#292411yescharacteristic
486C2×C5#292411yescharacteristic
487C2×C5#299211yescharacteristic
488C2×C5#299311yescharacteristic
489C2×C5#299411yescharacteristic
490C2×C5#299511yescharacteristic
491D5—42no—
492C23—52no—
493C23—101no—
494C23—101no—
495C23—101no—
496C23—101no—
497C23—101no—
498C23—101no—
499C23C22×C4×D511yescharacteristic
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—52no—
518C2×C4—52no—
519C2×C4—101no—
520C2×C4—101no—
521C2×C4—101no—
522C2×C4—101no—
523C2×C4—101no—
524C2×C4—101no—
525C2×C4—101no—
526C2×C4—101no—
527C2×C4—101no—
528C2×C4—101no—
529C2×C4—101no—
530C2×C4—101no—
531C2×C4—101no—
532C2×C4—101no—
533C2×C4—101no—
534C2×C4—101no—
535C2×C4—101no—
536C2×C4—101no—
537C2×C4—101no—
538C2×C4—204no—
539C2×C4—204no—
540C2×C4—201no—
541C2×C4—201no—
542C2×C4—201no—
543C2×C4—201no—
544C2×C4#405312yes—
545C2×C4#414411yescharacteristic
546C2×C4#414711yescharacteristic
547C2×C4D5×#4111yescharacteristic
548C2×C4D5×#4111yescharacteristic
549C2×C4#414911yescharacteristic
550C2×C4#415011yescharacteristic
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—201no—
556C8—201no—
557C8—201no—
558C8—201no—
559C5#2192811yescharacteristic, complemented, Sylow
560C22—102no—
561C22—102no—
562C22—102no—
563C22—201no—
564C22—201no—
565C22—201no—
566C22—201no—
567C22D5×#11711yescharacteristic
568C22#6588011yescharacteristic
569C22#6590811yescharacteristic
570C22C2×#405311yescharacteristic
571C22#6607911yescharacteristic
572C22D5×#13111yescharacteristic
573C22#6608411yescharacteristic
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—102no—
581C4—102no—
582C4—201no—
583C4—201no—
584C4—201no—
585C4—201no—
586C4—201no—
587C4#6597411yescharacteristic
588C4#6599711yescharacteristic
589C4#6603011yescharacteristic
590C4#6604411yescharacteristic
591C2—202no—
592C2#1060667511yescharacteristic
593C2#1061106411yescharacteristic
594C2#1061110511yescharacteristic
595C2#1061119911yescharacteristic
596C2#1061125811yescharacteristic
597C2#1061167711yescharacteristic
598C2#1061167811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1917C2
prime radicalC23×D5C22×C4
cosocleC22×C4×C5C24
hypercenter#1917D5
hypocenterC5#21928
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
2. C5×#1917C2semidirect
4. #10601239C2semidirect
6. #10600625C2semidirect
7. #10600275C2semidirect
12. #10599405C2semidirect
13. #10599403C2semidirect
14. #10599399C2semidirect
15. #10599397C2semidirect
127. #1917D5semidirect
559. C5#21928semidirect

Maximal subgroups

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

subgroupindex
#106054832
C5×#19172
#106012432
#106012392
#106006282
#106006252
#106002752
#105994552
#105994502
#105994082
#105994052
#105994032
#105993992
#105993972
#219285