Finite Group Databasebeta

← #13041612

Subgroups — #13041612

Order 1280.

758 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65709C211yesmaximal, characteristic, complemented
2C2×#65706C211yesmaximal, characteristic
3#10609470C211yesmaximal, characteristic
4#10604331C211yesmaximal, characteristic, complemented
5#10604327C211yesmaximal, characteristic, complemented
6#10604321C211yesmaximal, characteristic, complemented
7#10604315C211yesmaximal, characteristic, complemented
8C4⋊C4×#170C211yesmaximal, characteristic, complemented
9#10604313C211yesmaximal, characteristic
10#10603795C211yesmaximal, characteristic
11#10603793C211yesmaximal, characteristic
12#10603793C211yesmaximal, characteristic
13#10603793C211yesmaximal, characteristic
14#10603791C211yesmaximal, characteristic, complemented
15#10603779C211yesmaximal, characteristic, complemented
16C2×#4038C2211yescharacteristic
17C2×#4033C2211yescharacteristic
18C2×#4004C2211yescharacteristic
19C2×#4004C2211yescharacteristic
20C2×#4003C2211yescharacteristic
21C2×#4003C2211yescharacteristic
22C2×#4003C2211yescharacteristic
23C2×#4003C2211yescharacteristic
24C2×#4002C2211yescharacteristic
25C2×#4002C2211yescharacteristic
26C2×#4002C2211yescharacteristic
27C2×C4⋊#170C2211yescharacteristic
28C2×C4⋊#170C2211yescharacteristic
29C2×C4⋊#170C2211yescharacteristic
30C2×C4⋊#170C2211yescharacteristic
31C2×C4×#170C2211yescharacteristic
32C2×C4×#170C2211yescharacteristic
33C2×C4×#170C2211yescharacteristic
34C2×C4×#170C2211yescharacteristic
35C2×C4×#170C2211yescharacteristic
36#65709—24no—
37#65706—24no—
38C5×#398C411yescharacteristic
39#65283C411yescharacteristic
40#65283C411yescharacteristic
41#65281C411yescharacteristic
42#65273C411yescharacteristic
43C4⋊C4×Dic5C2211yescharacteristic
44C4⋊C4×Dic5C2211yescharacteristic
45#64962C411yescharacteristic
46#64955C2211yescharacteristic
47#64955C2211yescharacteristic
48#64949C411yescharacteristic
49#64945C411yescharacteristic
50#64938C2211yescharacteristic
51#64918C2211yescharacteristic
52#64918C2211yescharacteristic
53#64918C2211yescharacteristic
54#64918C2211yescharacteristic
55#64918C2211yescharacteristic
56#64918C2211yescharacteristic
57#64918C2211yescharacteristic
58#64918C2211yescharacteristic
59#64918C2211yescharacteristic
60#64918C2211yescharacteristic
61#23057—51nomaximal, Sylow
62C22×C4×D5C2311yescharacteristic
63C22×Dic10C2×C411yescharacteristic
64C22×#170C2311yescharacteristic
65C22×#170C2311yescharacteristic
66C22×#170C2311yescharacteristic
67C22×#170C2311yescharacteristic
68C22×#170C2311yescharacteristic
69C22×#170C2311yescharacteristic
70C22×#170C2311yescharacteristic
71C22×#170C2311yescharacteristic
72C2×C5×C4⋊C4C2×C411yescharacteristic
73C2×C5×C4⋊C4C2×C411yescharacteristic
74C2×C5×C4⋊C4C2×C411yescharacteristic
75C2×C5×C4⋊C4C2×C411yescharacteristic
76C2×#685C2×C411yescharacteristic
77C2×#685C2×C411yescharacteristic
78C2×#685C2×C411yescharacteristic
79C2×#685C2×C411yescharacteristic
80C2×#685C2×C411yescharacteristic
81C2×#685C2×C411yescharacteristic
82C2×C4⋊Dic5C2×C411yescharacteristic
83C2×C4⋊Dic5C2×C411yescharacteristic
84C2×C4⋊Dic5C2×C411yescharacteristic
85C2×#683C2×C411yescharacteristic
86C2×#683C2×C411yescharacteristic
87C2×#683C2×C411yescharacteristic
88C2×#683C2×C411yescharacteristic
89C2×C4×Dic5C2311yescharacteristic
90C2×C4×Dic5C2311yescharacteristic
91C2×C4×Dic5C2311yescharacteristic
92C2×C4×Dic5C2311yescharacteristic
93C2×C4×Dic5C2311yescharacteristic
94C2×C4×Dic5C2311yescharacteristic
95#4038—22no—
96#4038—22no—
97#4033—22no—
98#4033—22no—
99#4004—22no—
100#4004—22no—
101#4003—22no—
102#4003—22no—
103#4003—22no—
104#4003—22no—
105#4002—22no—
106#4002—22no—
107#4002—22no—
108C4⋊#170—22no—
109C4⋊#170—22no—
110C4⋊#170—22no—
111C4⋊#170D414yes—
112C4×#170—22no—
113C4×#170—22no—
114C4×#170—22no—
115C4×#170—22no—
116C4×#170—22no—
117C5×#95C2×C411yescharacteristic
118C5×#95C2×C411yescharacteristic
119C5×#95C2×C411yescharacteristic
120#3963C2×C411yescharacteristic
121#3963C2×C411yescharacteristic
122#3963C2×C411yescharacteristic
123#3963C2×C411yescharacteristic
124#3963C2×C411yescharacteristic
125#3963C2×C411yescharacteristic
126#3963C2×C411yescharacteristic
127C2×#446—51no—
128C2×#433—51no—
129#2396—51no—
130#1984—51no—
131#1940—51no—
132#1924—51no—
133#1923—51no—
134#1923—51no—
135#1923—51no—
136#1917—51no—
137#1916—51no—
138#1770—51no—
139C8×C4⋊C4—51no—
140C8×C4⋊C4—51no—
141#1750—51no—
142C23×D5C22×C411yescharacteristic
143C22×C4×C5C22×C411yescharacteristic
144C22×C4×C5C22×C411yescharacteristic
145C22×C4×C5C22×C411yescharacteristic
146C22×C4×C5C22×C411yescharacteristic
147C22×C4×C5C22×C411yescharacteristic
148C22×C4×C5C22×C411yescharacteristic
149C22×C4×C5C22×C411yescharacteristic
150C22×Dic5C22×C411yescharacteristic
151C22×Dic5C22×C411yescharacteristic
152C22×Dic5C22×C411yescharacteristic
153C22×Dic5C22×C411yescharacteristic
154C22×Dic5C22×C411yescharacteristic
155C22×Dic5C22×C411yescharacteristic
156C22×Dic5C2411yescharacteristic
157C2×C4×D5—21no—
158C2×C4×D5—21no—
159C2×C4×D5—21no—
160C2×C4×D5—21no—
161C2×C4×D5—21no—
162C2×C4×D5—21no—
163C2×Dic10—22no—
164C2×Dic10—22no—
165C2×Dic10—41no—
166C2×#170—21no—
167C2×#170—21no—
168C2×#170—21no—
169C2×#170—21no—
170C2×#170—21no—
171C2×#170—21no—
172C2×#170—21no—
173C2×#170—21no—
174C2×#170—21no—
175C2×#170—21no—
176C2×#170—21no—
177C2×#170—21no—
178C2×#170—21no—
179C2×#170—21no—
180C2×#170—21no—
181C2×#170—21no—
182C2×#170—21no—
183C2×#170—21no—
184C2×#170—21no—
185C2×#170—21no—
186C2×#170C2×D412yes—
187C2×#170C2×D412yes—
188C2×#170#4112yes—
189C2×#170#4112yes—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—22no—
194#685—22no—
195#685—22no—
196#685—22no—
197#685—22no—
198#685—22no—
199#685—41no—
200C4⋊Dic5—22no—
201C4⋊Dic5—22no—
202C4⋊Dic5—41no—
203#683—22no—
204#683—22no—
205#683—22no—
206#683—22no—
207C4×Dic5—21no—
208C4×Dic5—21no—
209C4×Dic5—21no—
210C4×Dic5—21no—
211C4×Dic5—21no—
212C4×Dic5—21no—
213C4×Dic5—21no—
214C4×Dic5—21no—
215C4×Dic5—21no—
216C4×Dic5—21no—
217C4×Dic5C2×D412yes—
218C4×Dic5#4112yes—
219C2×C4×Q8—51no—
220C2×#117—51no—
221#446—104no—
222#433—104no—
223C2×C4⋊C8—51no—
224C2×C4⋊C8—51no—
225C2×C4⋊C8—51no—
226C2×C4⋊C8—51no—
227C2×C4⋊C8—51no—
228C2×C4⋊C8—51no—
229C2×C22⋊C8—51no—
230C2×C22⋊C8—51no—
231C2×C22⋊C8—51no—
232C2×C22⋊C8—51no—
233C2×#97—51no—
234C2×#97—51no—
235C2×#97—51no—
236C2×C4×C8—51no—
237C2×C4×C8—51no—
238C2×C4×C8—51no—
239C2×C4×C8—51no—
240C2×C4×C8—51no—
241#400—51no—
242#399—51no—
243#398—51no—
244#398AGL(1,𝔽5)11yescharacteristic
245#396—51no—
246#396—51no—
247#395—51no—
248#393—51no—
249C4×C4⋊C4—51no—
250C4×C4⋊C4—51no—
251C4×C4⋊C4—51no—
252C4×C22⋊C4—51no—
253C4×C22⋊C4—51no—
254#336—51no—
255#336—51no—
256#336—51no—
257#336—51no—
258#336—51no—
259#336—51no—
260#336—51no—
261#336—51no—
262#336—51no—
263#336—51no—
264C23×C5C23×C411yescharacteristic
265C22×D5—21no—
266C22×D5—21no—
267C22×D5—21no—
268C22×D5—21no—
269C22×D5—21no—
270C22×D5—21no—
271C22×D5—21no—
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—21no—
290C2×C4×C5C4×D412yes—
291C2×C4×C5#13112yes—
292C2×C4×C5#13112yes—
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—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5C4×D412yes—
310C2×Dic5#13112yes—
311C2×Dic5C22×D411yescharacteristic
312C2×Dic5C2×#4111yescharacteristic
313C2×Dic5C2×#4111yescharacteristic
314C2×Dic5C2×#4111yescharacteristic
315C2×Dic52−1+411yescharacteristic
316C2×Dic52−1+411yescharacteristic
317C4×D5—41no—
318C4×D5—41no—
319C4×D5—41no—
320C4×D5—41no—
321Dic10—44no—
322#170—22no—
323#170—22no—
324#170—22no—
325#170—22no—
326#170—41no—
327#170—41no—
328#170—41no—
329#170—41no—
330C22×Q8—51no—
331C23×C4—51no—
332C22×C8—51no—
333C22×C8—51no—
334C22×C8—51no—
335C22×C8—51no—
336C22×C8—51no—
337C22×C8—51no—
338C22×C8—51no—
339C22×C8—51no—
340C4×Q8—102no—
341C4×Q8—102no—
342#117—102no—
343#117—102no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—51no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4—51no—
348C2×C4⋊C4—51no—
349C2×C4⋊C4—51no—
350C2×C4⋊C4—51no—
351C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
352C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
353C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
354C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
355C2×C22⋊C4—51no—
356C2×C22⋊C4—51no—
357C2×C22⋊C4—51no—
358C2×C22⋊C4—51no—
359C2×C22⋊C4—51no—
360C2×C22⋊C4—51no—
361C2×C42—51no—
362C2×C42—51no—
363C2×C42—51no—
364C2×C42—51no—
365C2×C42—51no—
366C2×C42—51no—
367C4⋊C8—54no—
368C4⋊C8—102no—
369C4⋊C8—102no—
370C4⋊C8—102no—
371C4⋊C8—102no—
372C4⋊C8—102no—
373C22⋊C8—102no—
374C22⋊C8—102no—
375C22⋊C8—102no—
376C22⋊C8—102no—
377#97—102no—
378#97—102no—
379#97—102no—
380C4×C8—102no—
381C4×C8—102no—
382C4×C8—102no—
383C4×C8—102no—
384C4×C8—102no—
385#95—51no—
386#95—51no—
387#95—51no—
388#95—51no—
389#95—51no—
390#95—51no—
391#95—51no—
392#95C2×AGL(1,𝔽5)11yescharacteristic
393#95C2×AGL(1,𝔽5)11yescharacteristic
394#95C2×AGL(1,𝔽5)11yescharacteristic
395C22×C5C2×C4×D411yescharacteristic
396C22×C5C4×#4111yescharacteristic
397C22×C5#51911yescharacteristic
398C22×C5C2×#13111yescharacteristic
399C22×C5C2×#13111yescharacteristic
400C22×C5C2×#13111yescharacteristic
401C22×C5#56811yescharacteristic
402C2×D5—41no—
403C2×D5—41no—
404C2×D5—41no—
405C2×D5—41no—
406C2×D5—41no—
407C2×D5—41no—
408C2×D5—41no—
409C4×C5—22no—
410C4×C5—22no—
411C4×C5—22no—
412C4×C5—41no—
413C4×C5—41no—
414C4×C5—41no—
415C4×C5—41no—
416Dic5—22no—
417Dic5—22no—
418Dic5—41no—
419Dic5—41no—
420Dic5—41no—
421Dic5—41no—
422Dic5#54711yescharacteristic
423Dic5#54811yescharacteristic
424Dic5#55211yescharacteristic
425Dic5#55611yescharacteristic
426C24—51no—
427C2×Q8—102no—
428C2×Q8—102no—
429C2×Q8—201no—
430C22×C4—51no—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—51no—
437C22×C4—101no—
438C22×C4—101no—
439C22×C4—101no—
440C22×C4—101no—
441C22×C4—101no—
442C22×C4—101no—
443C22×C4C22×AGL(1,𝔽5)11yescharacteristic
444C22×C4C22×AGL(1,𝔽5)11yescharacteristic
445C22×C4C22×AGL(1,𝔽5)11yescharacteristic
446C22×C4C22×AGL(1,𝔽5)11yescharacteristic
447C22×C4C22×AGL(1,𝔽5)11yescharacteristic
448C22×C4C22×AGL(1,𝔽5)11yescharacteristic
449C22×C4C22×AGL(1,𝔽5)11yescharacteristic
450C2×C8—52no—
451C2×C8—52no—
452C2×C8—52no—
453C2×C8—52no—
454C2×C8—101no—
455C2×C8—101no—
456C2×C8—101no—
457C2×C8—101no—
458C2×C8—101no—
459C2×C8—101no—
460C2×C8—101no—
461C2×C8—101no—
462C2×C8—101no—
463C2×C8—101no—
464C2×C8—101no—
465C2×C8—101no—
466C2×C8—101no—
467C2×C8—101no—
468C2×C8—101no—
469C2×C8—101no—
470C2×C8—101no—
471C2×C8—101no—
472C2×C8—101no—
473C2×C8—101no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—102no—
479C4⋊C4—102no—
480C4⋊C4—102no—
481C4⋊C4—102no—
482C4⋊C4—102no—
483C4⋊C4—102no—
484C4⋊C4—201no—
485C22⋊C4—102no—
486C22⋊C4—102no—
487C22⋊C4—102no—
488C22⋊C4—102no—
489C22⋊C4—102no—
490C22⋊C4—201no—
491C42—52no—
492C42—52no—
493C42—101no—
494C42—101no—
495C42—101no—
496C42—101no—
497C42—101no—
498C42—101no—
499C42—101no—
500C42—101no—
501C42—101no—
502C42—101no—
503C2×C5#236211yescharacteristic
504C2×C5#293111yescharacteristic
505C2×C5#293311yescharacteristic
506C2×C5#296611yescharacteristic
507C2×C5#296811yescharacteristic
508C2×C5#298511yescharacteristic
509C2×C5#298611yescharacteristic
510D5—81no—
511C23—101no—
512C23—101no—
513C23—101no—
514C23—101no—
515C23—101no—
516C23—101no—
517C23—101no—
518C23C23×AGL(1,𝔽5)11yescharacteristic
519Q8—204no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
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—51no—
539C2×C4—51no—
540C2×C4—51no—
541C2×C4—51no—
542C2×C4—51no—
543C2×C4—51no—
544C2×C4—52no—
545C2×C4—52no—
546C2×C4—101no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—101no—
550C2×C4—101no—
551C2×C4—101no—
552C2×C4—101no—
553C2×C4—101no—
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—201no—
563C2×C4—201no—
564C2×C4—201no—
565C2×C4—201no—
566C2×C4#413112yes—
567C2×C4D4×AGL(1,𝔽5)12yes—
568C2×C4#413312yes—
569C8—102no—
570C8—102no—
571C8—102no—
572C8—102no—
573C8—201no—
574C8—201no—
575C8—201no—
576C8—201no—
577C5#2305711yescharacteristic, complemented, Sylow
578C22—201no—
579C22—201no—
580C22—201no—
581C22—201no—
582C22—201no—
583C22—201no—
584C22—201no—
585C22C2×#413111yescharacteristic
586C22C2×D4×AGL(1,𝔽5)11yescharacteristic
587C22C2×#413311yescharacteristic
588C22#6626211yescharacteristic
589C22D5⋊#13111yescharacteristic
590C22#6626411yescharacteristic
591C22#41×AGL(1,𝔽5)11yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—51no—
600C4—51no—
601C4—51no—
602C4—51no—
603C4—102no—
604C4—102no—
605C4—201no—
606C4—201no—
607C4—201no—
608C4—201no—
609C2—401no—
610C2#1061722711yescharacteristic
611C2#1061725911yescharacteristic
612C2#1061728611yescharacteristic
613C2#1061729411yescharacteristic
614C2#1061733211yescharacteristic
615C2#1061733611yescharacteristic
616C2#1061738311yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutator, socleC23×C5C23×C4
FittingC5×#398C4
prime radicalC23×D5C22×C4
cosocleC22×Dic5C24
hypercenter#398AGL(1,𝔽5)
hypocenterC5#23057
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#65709C2semidirect
4. #10604331C2semidirect
5. #10604327C2semidirect
6. #10604321C2semidirect
7. #10604315C2semidirect
8. C4⋊C4×#170C2semidirect
14. #10603791C2semidirect
15. #10603779C2semidirect
577. C5#23057semidirect

Maximal subgroups

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

subgroupindex
C2×#657092
C2×#657062
#106094702
#106043312
#106043272
#106043212
#106043152
C4⋊C4×#1702
#106043132
#106037952
#106037932
#106037912
#106037792
#230575