Finite Group Databasebeta

← #12117095

Subgroups — #12117095

Order 1280.

744 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10605484C211yesmaximal, characteristic
2C5×#1917C211yesmaximal, characteristic, complemented
3#10601269C211yesmaximal, characteristic
4#10601244C211yesmaximal, characteristic, complemented
5#10600626C211yesmaximal, characteristic, complemented
6#10600623C211yesmaximal, characteristic
7#10600275C211yesmaximal, characteristic, complemented
8#10599456C211yesmaximal, characteristic
9#10599455C211yesmaximal, characteristic
10#10599444C211yesmaximal, characteristic, complemented
11#10599410C211yesmaximal, characteristic, complemented
12#10599406C211yesmaximal, characteristic, complemented
13#10599402C211yesmaximal, characteristic, complemented
14#10599394C211yesmaximal, characteristic
15#10599392C211yesmaximal, characteristic
16C2×#4018C2211yescharacteristic
17C2×#4018C2211yescharacteristic
18C2×C42×D5C2211yescharacteristic
19C2×C5×C4⋊C8C2211yescharacteristic
20C2×C5×#97C2211yescharacteristic
21C4×C5×C4⋊C4C2211yescharacteristic
22C2×#3952C2211yescharacteristic
23C2×#3952C2211yescharacteristic
24C2×#3952C2211yescharacteristic
25C2×#3952C2211yescharacteristic
26C2×#3947C2211yescharacteristic
27C2×#3946C2211yescharacteristic
28C2×#3946C2211yescharacteristic
29C2×#3946C2211yescharacteristic
30C2×#3946C2211yescharacteristic
31C2×C8×Dic5C2211yescharacteristic
32C2×C8×Dic5C2211yescharacteristic
33C2×C8×Dic5C2211yescharacteristic
34#65276C411yescharacteristic
35#65276C411yescharacteristic
36#65265C411yescharacteristic
37#65265C411yescharacteristic
38C4×C4⋊Dic5C2211yescharacteristic
39C4×#683C2211yescharacteristic
40C4×#683C2211yescharacteristic
41C2×C4⋊#168C2211yescharacteristic
42C2×C4×#168C2211yescharacteristic
43#64956C411yescharacteristic
44#64956C411yescharacteristic
45#64939C411yescharacteristic
46#64939C411yescharacteristic
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#22626—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×#683C2×C411yescharacteristic
79C2×#683C2×C411yescharacteristic
80C2×#683C2×C411yescharacteristic
81C2×#683C2×C411yescharacteristic
82C2×#683C2×C411yescharacteristic
83C2×#683C2×C411yescharacteristic
84C2×#683C2×C411yescharacteristic
85C2×#683C2×C411yescharacteristic
86C2×C4×Dic5C2×C411yescharacteristic
87C2×C4×Dic5C2×C411yescharacteristic
88C2×C4×Dic5C2311yescharacteristic
89C2×C4×Dic5C2311yescharacteristic
90C2×C4×Dic5C2311yescharacteristic
91C22×#168C2311yescharacteristic
92C22×#168C2311yescharacteristic
93C22×#168C2311yescharacteristic
94C22×#168C2311yescharacteristic
95#4018—41no—
96#4018—41no—
97#4018—41no—
98#4018—41no—
99C42×D5—22no—
100C42×D5—22no—
101C5×C4⋊C8—41no—
102C5×#97—41no—
103C5×#95C2×C411yescharacteristic
104C5×#95C2×C411yescharacteristic
105#3963C2×C411yescharacteristic
106#3963C2×C411yescharacteristic
107#3963C2×C411yescharacteristic
108#3963C2×C411yescharacteristic
109#3963C2×C411yescharacteristic
110#3963C2×C411yescharacteristic
111#3952—22no—
112#3952—22no—
113#3952—22no—
114#3952Q814yes—
115#3947—41no—
116#3946—22no—
117#3946—22no—
118#3946—41no—
119#3946—41no—
120C8×Dic5—22no—
121C8×Dic5—22no—
122C8×Dic5—41no—
123C4⋊#168—41no—
124C4×#168—41no—
125#2285—51no—
126#1939—51no—
127#1939—51no—
128#1917—51no—
129#1917D511yescharacteristic, complemented
130#1916—51no—
131#1916—51no—
132#1798—51no—
133#1798—51no—
134#1797—51no—
135#1770—51no—
136C8×C4⋊C4—51no—
137#1750—51no—
138#1750—51no—
139C4×C22⋊C8—51no—
140C23×D5C22×C411yescharacteristic
141C22×C4×C5C22×C411yescharacteristic
142C22×C4×C5C22×C411yescharacteristic
143C22×C4×C5C22×C411yescharacteristic
144C22×C4×C5C22×C411yescharacteristic
145C22×C4×C5C22×C411yescharacteristic
146C22×C4×C5C22×C411yescharacteristic
147C22×C4×C5C2411yescharacteristic
148C22×Dic5C22×C411yescharacteristic
149C22×Dic5C22×C411yescharacteristic
150C22×Dic5C22×C411yescharacteristic
151C22×Dic5C22×C411yescharacteristic
152C22×Dic5C22×C411yescharacteristic
153C22×Dic5C22×C411yescharacteristic
154C22×Dic5C22×C411yescharacteristic
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—22no—
162C2×C4×D5—22no—
163C2×C4×D5—22no—
164C2×C4×D5—41no—
165C2×C4×D5C2×Q812yes—
166C2×C4×D5#4112yes—
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—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8C2×Q812yes—
179C5×C4⋊C4—22no—
180C5×C4⋊C4—41no—
181C42×C5—21no—
182C42×C5—21no—
183C42×C5—21no—
184C42×C5—21no—
185C42×C5—21no—
186C42×C5—21no—
187#685—41no—
188#685—41no—
189#685—41no—
190#685—41no—
191C4⋊Dic5—22no—
192C4⋊Dic5—41no—
193#683—22no—
194#683—22no—
195#683—22no—
196#683—22no—
197#683—41no—
198#683—41no—
199#683—41no—
200#683—41no—
201C4×Dic5—21no—
202C4×Dic5—21no—
203C4×Dic5—21no—
204C4×Dic5—21no—
205C4×Dic5—22no—
206C4×Dic5—22no—
207C4×Dic5#4112yes—
208C4×Dic5#4112yes—
209C2×#168—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168—21no—
219C2×#168—21no—
220C2×#168C2×Q812yes—
221C2×#117—51no—
222C2×#117—51no—
223C22×C42—51no—
224C2×C4⋊C8—51no—
225C2×C4⋊C8—51no—
226C2×C4⋊C8—51no—
227C2×C4⋊C8—51no—
228C2×C4⋊C8—51no—
229C2×C4⋊C8C2×D511yescharacteristic
230C2×C22⋊C8—51no—
231C2×C22⋊C8—51no—
232C2×C22⋊C8—51no—
233C2×C22⋊C8—51no—
234C2×#97—51no—
235C2×#97C2×D511yescharacteristic
236C2×C4×C8—51no—
237C2×C4×C8—51no—
238C2×C4×C8—51no—
239C2×C4×C8—51no—
240#384—51no—
241#384—51no—
242#382—51no—
243#382—51no—
244#380—51no—
245#380—51no—
246#380—51no—
247#380—51no—
248C4×C4⋊C4—51no—
249C4×C4⋊C4—51no—
250C4×C4⋊C4—51no—
251C4×C4⋊C4C2×D511yescharacteristic
252#336—51no—
253#336—51no—
254#336—51no—
255#336—51no—
256#336—51no—
257#336—51no—
258#336—51no—
259#336—51no—
260#336C2×D511yescharacteristic
261#336C2×D511yescharacteristic
262#336C2×D511yescharacteristic
263#336C2×D511yescharacteristic
264C23×C5C23×C411yescharacteristic
265C22×D5—21no—
266C22×D5—21no—
267C22×D5—21no—
268C22×D5—21no—
269C22×D5—21no—
270C22×D5—21no—
271C22×D5C4×Q812yes—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
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#13112yes—
290C2×C4×C5C22×Q811yescharacteristic
291C2×C4×C5C2×#4111yescharacteristic
292C2×C4×C5C2×#4111yescharacteristic
293C2×C4×C5C2×#4111yescharacteristic
294C2×C4×C5H(5,𝔽2)11yescharacteristic
295C2×C4×C5H(5,𝔽2)11yescharacteristic
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5—21no—
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5#11712yes—
313C2×Dic5#11712yes—
314C2×Dic5C4×Q812yes—
315C2×Dic5#13112yes—
316C2×Dic5#13112yes—
317C4×D5—22no—
318C4×D5—22no—
319C4×D5—22no—
320C4×D5—22no—
321C4×D5—44no—
322C4×D5—44no—
323C5×C8—22no—
324C5×C8—41no—
325C5×C8—41no—
326C5×C8—41no—
327#168—22no—
328#168—41no—
329#168—41no—
330#168—41no—
331C23×C4—51no—
332C23×C4—51no—
333C23×C4—51no—
334C22×C8—51no—
335C22×C8—51no—
336C22×C8—51no—
337C22×C8—51no—
338C22×C8C22×D511yescharacteristic
339C22×C8C22×D511yescharacteristic
340C22×C8C22×D511yescharacteristic
341C22×C8C22×D511yescharacteristic
342#117—201no—
343#117—201no—
344#117—201no—
345#117—201no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4—51no—
348C2×C4⋊C4—51no—
349C2×C4⋊C4—51no—
350C2×C4⋊C4—51no—
351C2×C4⋊C4—51no—
352C2×C4⋊C4—51no—
353C2×C4⋊C4—51no—
354C2×C4⋊C4—51no—
355C2×C4⋊C4—51no—
356C2×C4⋊C4C4×D511yescharacteristic
357C2×C4⋊C4C4×D511yescharacteristic
358C2×C22⋊C4—51no—
359C2×C22⋊C4—51no—
360C2×C22⋊C4—51no—
361C2×C22⋊C4—51no—
362C2×C42—51no—
363C2×C42—51no—
364C2×C42—51no—
365C2×C42—51no—
366C2×C42—51no—
367C2×C42—102no—
368C2×C42—102no—
369C2×C42C22×D511yescharacteristic
370C2×C42C22×D511yescharacteristic
371C2×C42C22×D511yescharacteristic
372C4⋊C8—41no—
373C4⋊C8—102no—
374C4⋊C8—102no—
375C4⋊C8—201no—
376C4⋊C8—201no—
377C4⋊C8—201no—
378C22⋊C8—54no—
379C22⋊C8—102no—
380C22⋊C8—102no—
381C22⋊C8—102no—
382#97—41no—
383#97—201no—
384C4×C8—102no—
385C4×C8—102no—
386C4×C8—201no—
387C4×C8—201no—
388#95—51no—
389#95—51no—
390#95—51no—
391#95—51no—
392#95—51no—
393#95—51no—
394#95C4×D511yescharacteristic
395#95C4×D511yescharacteristic
396C22×C5C2×#11711yescharacteristic
397C22×C5C2×C4×Q811yescharacteristic
398C22×C5#51811yescharacteristic
399C22×C5C2×#13111yescharacteristic
400C22×C5C2×#13111yescharacteristic
401C22×C5C2×#13111yescharacteristic
402C22×C5#56811yescharacteristic
403C2×D5—22no—
404C2×D5—22no—
405C2×D5—22no—
406C2×D5—41no—
407C2×D5—41no—
408C2×D5—41no—
409C2×D5—41no—
410C4×C5—22no—
411C4×C5—41no—
412C4×C5—41no—
413C4×C5—41no—
414C4×C5—41no—
415C4×C5—41no—
416C4×C5#55311yescharacteristic
417C4×C5#55311yescharacteristic
418C4×C5#55411yescharacteristic
419C4×C5#55411yescharacteristic
420Dic5—22no—
421Dic5—22no—
422Dic5—41no—
423Dic5—41no—
424Dic5—41no—
425Dic5—41no—
426Dic5#43314yes—
427C24—51no—
428C22×C4—51no—
429C22×C4—51no—
430C22×C4—51no—
431C22×C4—52no—
432C22×C4—52no—
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—51no—
437C22×C4—102no—
438C22×C4—102no—
439C22×C4—102no—
440C22×C4—102no—
441C22×C4—101no—
442C22×C4—101no—
443C22×C4—101no—
444C22×C4—101no—
445C22×C4—102no—
446C22×C4—201no—
447C22×C4C2×C4×D511yescharacteristic
448C22×C4C2×C4×D511yescharacteristic
449C22×C4C2×C4×D511yescharacteristic
450C22×C4C2×C4×D511yescharacteristic
451C22×C4C2×C4×D511yescharacteristic
452C22×C4C2×C4×D511yescharacteristic
453C22×C4C23×D511yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—52no—
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×C8Q8×D512yes—
478C4⋊C4—22no—
479C4⋊C4—41no—
480C4⋊C4—102no—
481C4⋊C4—102no—
482C4⋊C4—102no—
483C4⋊C4—102no—
484C4⋊C4—102no—
485C4⋊C4—201no—
486C4⋊C4—201no—
487C4⋊C4—201no—
488C4⋊C4—201no—
489C4⋊C4—201no—
490C22⋊C4—201no—
491C22⋊C4—201no—
492C22⋊C4—201no—
493C22⋊C4—201no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—52no—
501C42—52no—
502C42—102no—
503C42—102no—
504C42—101no—
505C42—101no—
506C42—101no—
507C42—101no—
508C2×C5#234511yescharacteristic
509C2×C5C2×#43311yescharacteristic
510C2×C5#292411yescharacteristic
511C2×C5#296011yescharacteristic
512C2×C5#296211yescharacteristic
513C2×C5#297911yescharacteristic
514C2×C5#298111yescharacteristic
515D5—42no—
516C23—52no—
517C23—101no—
518C23—101no—
519C23—101no—
520C23—101no—
521C23—101no—
522C23—101no—
523C23C22×C4×D511yescharacteristic
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
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—52no—
542C2×C4—52no—
543C2×C4—52no—
544C2×C4—52no—
545C2×C4—52no—
546C2×C4—101no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—101no—
550C2×C4—102no—
551C2×C4—102no—
552C2×C4—102no—
553C2×C4—102no—
554C2×C4—101no—
555C2×C4—101no—
556C2×C4—101no—
557C2×C4—101no—
558C2×C4—101no—
559C2×C4—101no—
560C2×C4—101no—
561C2×C4—101no—
562C2×C4—101no—
563C2×C4—101no—
564C2×C4—101no—
565C2×C4—101no—
566C2×C4—204no—
567C2×C4—204no—
568C2×C4#405312yes—
569C2×C4#414411yescharacteristic
570C2×C4C2×Q8×D511yescharacteristic
571C2×C4D5×#4111yescharacteristic
572C2×C4D5×#4111yescharacteristic
573C2×C4D5×#4111yescharacteristic
574C2×C4#414911yescharacteristic
575C8—22no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8—102no—
580C8—201no—
581C8—201no—
582C8—201no—
583C5#2262611yescharacteristic, complemented, Sylow
584C22—102no—
585C22—102no—
586C22—102no—
587C22—201no—
588C22—201no—
589C22—201no—
590C22—201no—
591C22D5×#11711yescharacteristic
592C22#6587911yescharacteristic
593C22C4×Q8×D511yescharacteristic
594C22C2×#405311yescharacteristic
595C22#6607911yescharacteristic
596C22D5×#13111yescharacteristic
597C22D5×#13111yescharacteristic
598C4—22no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—54no—
605C4—102no—
606C4—102no—
607C4—201no—
608C4—201no—
609C4—201no—
610C4—201no—
611C4#6597011yescharacteristic
612C4#6599511yescharacteristic
613C4#6602411yescharacteristic
614C4#6604311yescharacteristic
615C2—202no—
616C2#1060669311yescharacteristic
617C2#1061106411yescharacteristic
618C2D5×#43311yescharacteristic
619C2#1061122311yescharacteristic
620C2#1061127711yescharacteristic
621C2#1061168911yescharacteristic
622C2#1061169211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1917C2
prime radicalC23×D5C22×C4
cosocleC22×C4×C5C24
hypercenter#1917D5
hypocenterC5#22626
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. #10601244C2semidirect
5. #10600626C2semidirect
7. #10600275C2semidirect
10. #10599444C2semidirect
11. #10599410C2semidirect
12. #10599406C2semidirect
13. #10599402C2semidirect
129. #1917D5semidirect
583. C5#22626semidirect

Maximal subgroups

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

subgroupindex
#106054842
C5×#19172
#106012692
#106012442
#106006262
#106006232
#106002752
#105994562
#105994552
#105994442
#105994102
#105994062
#105994022
#105993942
#105993922
#226265