Finite Group Databasebeta

← #13036109

Subgroups — #13036109

Order 1280.

710 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#10605878C211yesmaximal, characteristic
2#10604323C211yesmaximal, characteristic, complemented
3#10604323C211yesmaximal, characteristic, complemented
4#10604322C211yesmaximal, characteristic, complemented
5#10604322C211yesmaximal, characteristic, complemented
6#10604177C211yesmaximal, characteristic
7C4×#4003C211yesmaximal, characteristic
8#10603795C211yesmaximal, characteristic
9#10603794C211yesmaximal, characteristic
10#10603793C211yesmaximal, characteristic
11#10603792C211yesmaximal, characteristic
12#10603778C211yesmaximal, characteristic, complemented
13#10603778C211yesmaximal, characteristic, complemented
14#10603774C211yesmaximal, characteristic, complemented
15#10603773C211yesmaximal, characteristic, complemented
16C2×C42×D5C2211yescharacteristic
17C2×#4004C2211yescharacteristic
18C2×#4004C2211yescharacteristic
19C2×#4003C2211yescharacteristic
20C2×#4003C2211yescharacteristic
21C2×#4003C2211yescharacteristic
22C2×#4003C2211yescharacteristic
23C2×#4002C2211yescharacteristic
24C2×#4002C2211yescharacteristic
25C2×#4002C2211yescharacteristic
26C2×#4002C2211yescharacteristic
27C2×C4⋊#170C2211yescharacteristic
28C2×C4⋊#170C2211yescharacteristic
29C2×C4×#170C2211yescharacteristic
30C2×C4×#170C2211yescharacteristic
31C2×C4×#170C2211yescharacteristic
32C2×C4×#170C2211yescharacteristic
33C5×#382C411yescharacteristic
34#65276C411yescharacteristic
35#65276C411yescharacteristic
36C4⋊C4×Dic5C2211yescharacteristic
37C4⋊C4×Dic5C2211yescharacteristic
38#65225C411yescharacteristic
39#64955C2211yescharacteristic
40#64955C2211yescharacteristic
41#64953C411yescharacteristic
42#64953C411yescharacteristic
43#64940C411yescharacteristic
44#64940C411yescharacteristic
45#64937C2211yescharacteristic
46#64937C2211yescharacteristic
47#64918C2211yescharacteristic
48#64918C2211yescharacteristic
49#64918C2211yescharacteristic
50#64918C2211yescharacteristic
51#64918C2211yescharacteristic
52#64918C2211yescharacteristic
53#64918C2211yescharacteristic
54#64918C2211yescharacteristic
55#64918C2211yescharacteristic
56#64918C2211yescharacteristic
57#64918C2211yescharacteristic
58#64918C2211yescharacteristic
59#21437—51nomaximal, Sylow
60C22×C4×D5C2×C411yescharacteristic
61C22×C4×D5C2×C411yescharacteristic
62C22×C4×D5C2311yescharacteristic
63C22×#170C2311yescharacteristic
64C22×#170C2311yescharacteristic
65C22×#170C2311yescharacteristic
66C22×#170C2311yescharacteristic
67C22×#170C2311yescharacteristic
68C22×#170C2311yescharacteristic
69C22×#170C2311yescharacteristic
70C22×#170C2311yescharacteristic
71C2×C5×C4⋊C4C2×C411yescharacteristic
72C2×C5×C4⋊C4C2×C411yescharacteristic
73C2×C42×C5C2×C411yescharacteristic
74C2×#685C2×C411yescharacteristic
75C2×#685C2×C411yescharacteristic
76C2×#685C2×C411yescharacteristic
77C2×#685C2×C411yescharacteristic
78C2×C4⋊Dic5C2×C411yescharacteristic
79C2×C4⋊Dic5C2×C411yescharacteristic
80C2×C4×Dic5C2×C411yescharacteristic
81C2×C4×Dic5C2311yescharacteristic
82C2×C4×Dic5C2311yescharacteristic
83C2×C4×Dic5C2311yescharacteristic
84C2×C4×Dic5C2311yescharacteristic
85C2×C4×Dic5C2311yescharacteristic
86C2×C4×Dic5C2311yescharacteristic
87C42×D5—22no—
88C42×D5—22no—
89#4004—22no—
90#4004—22no—
91#4003—22no—
92#4003—22no—
93#4003—22no—
94#4003—22no—
95#4002—22no—
96#4002—22no—
97#4002—22no—
98#4002—22no—
99C4⋊#170—22no—
100C4⋊#170—22no—
101C4×#170—22no—
102C4×#170—22no—
103C4×#170—22no—
104C4×#170—22no—
105C5×#95C2×C411yescharacteristic
106C5×#95C2×C411yescharacteristic
107C5×#95C2×C411yescharacteristic
108C5×#95C2×C411yescharacteristic
109#3963C2×C411yescharacteristic
110#3963C2×C411yescharacteristic
111#3963C2×C411yescharacteristic
112#3963C2×C411yescharacteristic
113#3963C2×C411yescharacteristic
114#3963C2×C411yescharacteristic
115#3963C2×C411yescharacteristic
116#3963C2×C411yescharacteristic
117#3963C2×C411yescharacteristic
118#3963C2×C411yescharacteristic
119#3963C2×C411yescharacteristic
120#3963C2×C411yescharacteristic
121#2283—51no—
122#1924—51no—
123#1924—51no—
124#1923—51no—
125#1923—51no—
126#1917—51no—
127#1917—51no—
128#1916—51no—
129#1916—51no—
130#1768—51no—
131#1768—51no—
132#1749—51no—
133C4×C22⋊C8—51no—
134#1746—51no—
135#1726—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×C5C22×C411yescharacteristic
144C22×Dic5C22×C411yescharacteristic
145C22×Dic5C22×C411yescharacteristic
146C22×Dic5C22×C411yescharacteristic
147C22×Dic5C22×C411yescharacteristic
148C22×Dic5C22×C411yescharacteristic
149C22×Dic5C22×C411yescharacteristic
150C22×Dic5C2411yescharacteristic
151C2×C4×D5—22no—
152C2×C4×D5—22no—
153C2×C4×D5—22no—
154C2×C4×D5—22no—
155C2×C4×D5—21no—
156C2×C4×D5—21no—
157C2×C4×D5—21no—
158C2×C4×D5—21no—
159C2×C4×D5—21no—
160C2×C4×D5—21no—
161C2×C4×D5—41no—
162C2×C4×D5—41no—
163C2×#170—21no—
164C2×#170—21no—
165C2×#170—21no—
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#4112yes—
184C2×#170#4112yes—
185C2×#170#4112yes—
186C2×#170#4112yes—
187C5×C4⋊C4—41no—
188C5×C4⋊C4—41no—
189C42×C5—22no—
190#685—22no—
191#685—22no—
192#685—41no—
193#685—41no—
194C4⋊Dic5—22no—
195C4⋊Dic5—22no—
196C4×Dic5—22no—
197C4×Dic5—21no—
198C4×Dic5—21no—
199C4×Dic5—21no—
200C4×Dic5—21no—
201C4×Dic5—21no—
202C4×Dic5—21no—
203C4×Dic5—21no—
204C4×Dic5—21no—
205C4×Dic5—21no—
206C4×Dic5—21no—
207C4×Dic5#4112yes—
208C4×Dic5#4112yes—
209C22×C42—51no—
210C2×C4⋊C8—51no—
211C2×C4⋊C8—51no—
212C2×C4⋊C8—51no—
213C2×C4⋊C8—51no—
214C2×C22⋊C8—51no—
215C2×C22⋊C8—51no—
216C2×C22⋊C8—51no—
217C2×C22⋊C8—51no—
218C2×#97—51no—
219C2×#97—51no—
220C2×#97—51no—
221C2×#97—51no—
222C2×C4×C8—51no—
223C2×C4×C8—51no—
224C2×C4×C8—51no—
225C2×C4×C8—51no—
226#383—51no—
227#383—51no—
228#382—51no—
229#382AGL(1,𝔽5)11yescharacteristic
230#381—51no—
231#381—51no—
232#380—51no—
233#380—51no—
234C4×C4⋊C4—51no—
235C4×C4⋊C4—51no—
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#336—51no—
249#336—51no—
250#336—51no—
251#336—51no—
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—21no—
278C2×C4×C5—21no—
279C2×C4×C5#11712yes—
280C2×C4×C5#13112yes—
281C2×Dic5—21no—
282C2×Dic5—21no—
283C2×Dic5—21no—
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#11712yes—
299C2×Dic5C2×#4111yescharacteristic
300C2×Dic5C2×#4111yescharacteristic
301C2×Dic5C2×#4111yescharacteristic
302C2×Dic5C2×#4111yescharacteristic
303C2×Dic5C2×#4111yescharacteristic
304C2×Dic5C2×#4111yescharacteristic
305C4×D5—44no—
306C4×D5—44no—
307C4×D5—41no—
308C4×D5—41no—
309C4×D5—41no—
310C4×D5—41no—
311#170—22no—
312#170—22no—
313#170—22no—
314#170—22no—
315#170—41no—
316#170—41no—
317#170—41no—
318#170—41no—
319C23×C4—51no—
320C23×C4—51no—
321C23×C4—51no—
322C22×C8—51no—
323C22×C8—51no—
324C22×C8—51no—
325C22×C8—51no—
326C22×C8—51no—
327C22×C8—51no—
328C22×C8—51no—
329C22×C8—51no—
330C2×C4⋊C4—51no—
331C2×C4⋊C4—51no—
332C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
333C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
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—51no—
344C2×C42—51no—
345C2×C42—102no—
346C2×C42—102no—
347C2×C42C2×AGL(1,𝔽5)11yescharacteristic
348C4⋊C8—102no—
349C4⋊C8—102no—
350C4⋊C8—102no—
351C4⋊C8—102no—
352C22⋊C8—102no—
353C22⋊C8—102no—
354C22⋊C8—102no—
355C22⋊C8—102no—
356#97—102no—
357#97—102no—
358#97—102no—
359#97—102no—
360C4×C8—102no—
361C4×C8—102no—
362C4×C8—102no—
363C4×C8—102no—
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#95C2×AGL(1,𝔽5)11yescharacteristic
377#95C2×AGL(1,𝔽5)11yescharacteristic
378#95C2×AGL(1,𝔽5)11yescharacteristic
379#95C2×AGL(1,𝔽5)11yescharacteristic
380C22×C5C2×#11711yescharacteristic
381C22×C5C4×#4111yescharacteristic
382C22×C5C4×#4111yescharacteristic
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—22no—
396C4×C5—41no—
397C4×C5—41no—
398C4×C5—41no—
399C4×C5—41no—
400C4×C5—41no—
401Dic5—22no—
402Dic5—41no—
403Dic5—41no—
404Dic5—41no—
405Dic5—41no—
406Dic5—41no—
407Dic5#52911yescharacteristic
408Dic5#52911yescharacteristic
409Dic5#52911yescharacteristic
410Dic5#52911yescharacteristic
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—101no—
420C22×C4—101no—
421C22×C4—101no—
422C22×C4—101no—
423C22×C4—102no—
424C22×C4—101no—
425C22×C4—101no—
426C22×C4—102no—
427C22×C4—102no—
428C22×C4—102no—
429C22×C4—201no—
430C22×C4—201no—
431C22×C4C22×AGL(1,𝔽5)11yescharacteristic
432C22×C4C22×AGL(1,𝔽5)11yescharacteristic
433C22×C4C22×AGL(1,𝔽5)11yescharacteristic
434C22×C4C22×AGL(1,𝔽5)11yescharacteristic
435C22×C4C22×AGL(1,𝔽5)11yescharacteristic
436C22×C4C22×AGL(1,𝔽5)11yescharacteristic
437C22×C4C22×AGL(1,𝔽5)11yescharacteristic
438C2×C8—52no—
439C2×C8—52no—
440C2×C8—52no—
441C2×C8—52no—
442C2×C8—101no—
443C2×C8—101no—
444C2×C8—101no—
445C2×C8—101no—
446C2×C8—101no—
447C2×C8—101no—
448C2×C8—101no—
449C2×C8—101no—
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—41no—
463C4⋊C4—41no—
464C4⋊C4—102no—
465C4⋊C4—102no—
466C22⋊C4—102no—
467C22⋊C4—102no—
468C22⋊C4—201no—
469C22⋊C4—201no—
470C42—22no—
471C42—52no—
472C42—52no—
473C42—101no—
474C42—101no—
475C42—101no—
476C42—101no—
477C42—101no—
478C42—101no—
479C42—101no—
480C42—101no—
481C42—101no—
482C42—101no—
483C42—102no—
484C2×C5#229811yescharacteristic
485C2×C5#292411yescharacteristic
486C2×C5#292411yescharacteristic
487C2×C5#296611yescharacteristic
488C2×C5#296711yescharacteristic
489C2×C5#296811yescharacteristic
490C2×C5#296911yescharacteristic
491D5—42no—
492C23—52no—
493C23—101no—
494C23—101no—
495C23—101no—
496C23—101no—
497C23—101no—
498C23—101no—
499C23C23×AGL(1,𝔽5)11yescharacteristic
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—21no—
518C2×C4—21no—
519C2×C4—51no—
520C2×C4—51no—
521C2×C4—51no—
522C2×C4—51no—
523C2×C4—51no—
524C2×C4—51no—
525C2×C4—52no—
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—101no—
539C2×C4—101no—
540C2×C4—101no—
541C2×C4—101no—
542C2×C4—101no—
543C2×C4—204no—
544C2×C4—204no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4#413012yes—
550C2×C4#413312yes—
551C8—102no—
552C8—102no—
553C8—102no—
554C8—102no—
555C8—201no—
556C8—201no—
557C8—201no—
558C8—201no—
559C5#2143711yescharacteristic, complemented, Sylow
560C22—102no—
561C22—102no—
562C22—102no—
563C22—201no—
564C22—201no—
565C22—201no—
566C22—201no—
567C22C2×#413011yescharacteristic
568C22#6625611yescharacteristic
569C22C2×#413311yescharacteristic
570C22D5⋊#13111yescharacteristic
571C22#6626411yescharacteristic
572C22#41×AGL(1,𝔽5)11yescharacteristic
573C22#41×AGL(1,𝔽5)11yescharacteristic
574C4—22no—
575C4—22no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—51no—
582C4—51no—
583C4—51no—
584C4—51no—
585C4—102no—
586C4—201no—
587C4—201no—
588C4—201no—
589C4—201no—
590C4—201no—
591C2—202no—
592C2#1061708011yescharacteristic
593C2#1061711111yescharacteristic
594C2#1061712911yescharacteristic
595C2#1061731311yescharacteristic
596C2#1061731411yescharacteristic
597C2#1061733211yescharacteristic
598C2#1061733511yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutator, socleC23×C5C23×C4
FittingC5×#382C4
prime radicalC23×D5C22×C4
cosocleC22×Dic5C24
hypercenter#382AGL(1,𝔽5)
hypocenterC5#21437
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #10604323C2semidirect
3. #10604323C2semidirect
4. #10604322C2semidirect
5. #10604322C2semidirect
12. #10603778C2semidirect
13. #10603778C2semidirect
14. #10603774C2semidirect
15. #10603773C2semidirect
559. C5#21437semidirect

Maximal subgroups

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

subgroupindex
#106058782
#106043232
#106043222
#106041772
C4×#40032
#106037952
#106037942
#106037932
#106037922
#106037782
#106037742
#106037732
#214375