Finite Group Databasebeta

← #12107079

Subgroups — #12107079

Order 1280.

876 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2331C211yesmaximal, characteristic, complemented
2C2×#65376C211yesmaximal, characteristic
3#10605143C211yesmaximal, characteristic
4#10602572C211yesmaximal, characteristic, complemented
5#10600419C211yesmaximal, characteristic
6#10600418C211yesmaximal, characteristic
7#10600396C211yesmaximal, characteristic, complemented
8#10600393C211yesmaximal, characteristic, complemented
9#10600349C211yesmaximal, characteristic
10#10600333C211yesmaximal, characteristic, complemented
11#10600274C211yesmaximal, characteristic, complemented
12C4×#3939C211yesmaximal, characteristic, complemented
13#10600267C211yesmaximal, characteristic
14C4×#3941C211yesmaximal, characteristic
15#10600229C211yesmaximal, characteristic, complemented
16C2×C5×C4⋊Q8C2211yescharacteristic
17C2×C4×D20C2211yescharacteristic
18C2×C4×D20C2211yescharacteristic
19C2×C4×D20C2211yescharacteristic
20C5×#391—21no—
21C5×#391—21no—
22C5×#389C2211yescharacteristic
23C5×#389C2211yescharacteristic
24C5×#387—21no—
25C5×#387—21no—
26C5×#382C2211yescharacteristic
27C4×C5×C4⋊C4C2211yescharacteristic
28C4×C5×C4⋊C4C2211yescharacteristic
29C5×#376C2211yescharacteristic
30#65376C418yescomplemented
31C2×#3941C2211yescharacteristic
32C2×#3941C2211yescharacteristic
33C2×#3941C2211yescharacteristic
34C2×#3941C2211yescharacteristic
35C2×#3940C2211yescharacteristic
36C2×#3939C2211yescharacteristic
37C2×#3939C2211yescharacteristic
38C2×#3939C2211yescharacteristic
39C4×C4⋊Dic5C2211yescharacteristic
40C4×C4⋊Dic5C2211yescharacteristic
41C4×C4⋊Dic5C2211yescharacteristic
42C2×C4⋊#168C2211yescharacteristic
43C2×C4⋊#168C2211yescharacteristic
44C2×#3935C2211yescharacteristic
45C2×C4×#168C2211yescharacteristic
46#64955—21no—
47#64955—21no—
48#64955—21no—
49D5×#95—21no—
50#64749C2211yescharacteristic
51#64749C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64744C2211yescharacteristic
59#64744C2211yescharacteristic
60#21624—51nomaximal, Sylow
61C22×C5×Q8—21no—
62C22×D20C2311yescharacteristic
63C22×C4×D5—21no—
64C22×C4×D5—21no—
65C22×C4×D5—21no—
66C5×C4⋊Q8—22no—
67C5×C4⋊Q8C2×C414yescomplemented
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C5×C4⋊C4C2311yescharacteristic
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C42×C5—21no—
76C2×C42×C5—21no—
77C2×C42×C5C2311yescharacteristic
78C2×C42×C5C2311yescharacteristic
79C2×C42×C5C2311yescharacteristic
80C2×#685—21no—
81C2×#685—21no—
82C2×#685—21no—
83C2×C4⋊Dic5C2311yescharacteristic
84C2×C4⋊Dic5C2311yescharacteristic
85C2×C4⋊Dic5C2311yescharacteristic
86C2×C4×Dic5—21no—
87C2×C4×Dic5—21no—
88C2×C4×Dic5—21no—
89C22×#168C2311yescharacteristic
90C22×#168C2311yescharacteristic
91C22×#168C2311yescharacteristic
92C22×#168C2311yescharacteristic
93C4×D20—22no—
94C4×D20—22no—
95C4×D20—22no—
96C4×D20—22no—
97C4×D20C2×C414yes—
98C4×D20Q814yescomplemented
99C5×#95—21no—
100C5×#95—21no—
101C5×#95—21no—
102C5×#95—21no—
103C5×#95—21no—
104C5×#95—21no—
105C5×#95D411yescharacteristic
106C5×#95D411yescharacteristic
107C5×#95D411yescharacteristic
108C5×#95D411yescharacteristic
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3941—22no—
113#3941—22no—
114#3941C2×C414yes—
115#3941C2×C414yes—
116#3940—22no—
117#3939—22no—
118#3939C2×C414yescomplemented
119#3939C2×C414yescomplemented
120C4⋊#168—22no—
121C4⋊#168C2×C414yescomplemented
122#3935—22no—
123C4×#168—22no—
124C2×#474—51no—
125#2331D511yescharacteristic, complemented
126#2275—51no—
127#1987—51no—
128#1949—51no—
129#1921—51no—
130#1918—51no—
131#1864—51no—
132#1862—51no—
133#1804—51no—
134#1776—51no—
135C4×#107—51no—
136#1768—51no—
137#1762—51no—
138C4×#102—51no—
139C23×D5—21no—
140C2×C5×Q8—24no—
141C2×C5×Q8—81no—
142C2×C5×Q8—81no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5C2×D411yescharacteristic
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2411yescharacteristic
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5—21no—
157C2×D20—21no—
158C2×D20—21no—
159C2×D20—21no—
160C2×D20C22×C412yes—
161C2×D20C2×Q812yes—
162C2×D20#4112yes—
163C2×C4×D5—24no—
164C2×C4×D5—24no—
165C2×C4×D5—24no—
166C2×C4×D5—81no—
167C2×C4×D5—81no—
168C2×C4×D5—81no—
169C2×C4×D5—81no—
170C2×C4×D5—81no—
171C2×C4×D5—81no—
172C5×C4⋊C4—24no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—81no—
180C5×C4⋊C4—81no—
181C5×C4⋊C4C22×C412yes—
182C5×C4⋊C4C22×C412yes—
183C42×C5—21no—
184C42×C5—21no—
185C42×C5—81no—
186C42×C5—81no—
187C42×C5C22×C412yes—
188C42×C5C2×Q812yes—
189C42×C5#4112yes—
190C42×C5#4112yes—
191#685—24no—
192#685—24no—
193#685—24no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5C22×C412yes—
198C4⋊Dic5C2×Q812yes—
199C4⋊Dic5#4112yes—
200C4×Dic5—81no—
201C4×Dic5—81no—
202C4×Dic5—81no—
203C2×#168—21no—
204C2×#168—21no—
205C2×#168—21no—
206C2×#168—21no—
207C2×#168—21no—
208C2×#168—21no—
209C2×#168—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168C22×C412yes—
214C2×#168C22×C412yes—
215C2×C4⋊Q8C2×D511yescharacteristic
216C2×C4×D4—51no—
217C2×C4×D4—51no—
218C2×C4×D4—51no—
219#474—58no—
220C2×#107—51no—
221C2×#107—51no—
222C2×#107—51no—
223C2×#106—51no—
224C2×C4⋊C8—51no—
225C2×C4⋊C8—51no—
226C2×#102—51no—
227C2×#102—51no—
228C2×#102—51no—
229C2×#102—51no—
230C2×#97—51no—
231C2×C4×C8—51no—
232#391—21no—
233#391—21no—
234#389C2×D511yescharacteristic
235#389C2×D511yescharacteristic
236#387—21no—
237#387—21no—
238#382C2×D511yescharacteristic
239C4×C4⋊C4—51no—
240C4×C4⋊C4—51no—
241C4×C4⋊C4—51no—
242C4×C4⋊C4C2×D511yescharacteristic
243C4×C4⋊C4C2×D511yescharacteristic
244C4×C22⋊C4—101no—
245C4×C22⋊C4—101no—
246C4×C22⋊C4—101no—
247#376C2×D511yescharacteristic
248C2×#95—101no—
249#340—51no—
250#340—51no—
251#340—51no—
252#340—51no—
253#340—51no—
254#340—51no—
255#340—51no—
256#340—51no—
257#336—51no—
258#336—51no—
259C23×C5C22×D411yescharacteristic
260C22×D5—22no—
261C22×D5—22no—
262C22×D5—22no—
263C22×D5—41no—
264C22×D5—41no—
265C22×D5—41no—
266C22×D5—41no—
267C5×Q8—84no—
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—22no—
277C2×C4×C5—22no—
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—41no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5C4×D412yes—
295C2×C4×C5C4×D412yes—
296C2×C4×C5C22⋊Q812yes—
297C2×C4×C5C22⋊Q812yes—
298C2×C4×C5C23×C411yescharacteristic
299C2×C4×C5C22×Q811yescharacteristic
300C2×C4×C5C2×#4111yescharacteristic
301C2×C4×C5C2×#4111yescharacteristic
302C2×C4×C5C2×#4111yescharacteristic
303C2×C4×C5C2×#4111yescharacteristic
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313D20—22no—
314D20—22no—
315D20—22no—
316D20C4×Q814yes—
317C4×D5—84no—
318C4×D5—84no—
319C4×D5—84no—
320#168—22no—
321#168—22no—
322#168—41no—
323#168—41no—
324C22×Q8—21no—
325C22×D4—51no—
326C23×C4—101no—
327C23×C4—101no—
328C23×C4—101no—
329C22×C8—51no—
330C22×C8—51no—
331C22×C8—51no—
332C22×C8—51no—
333C4⋊Q8—22no—
334C4⋊Q8C4×D514yescomplemented
335C4×D4—54no—
336C4×D4—54no—
337C4×D4—102no—
338C4×D4—102no—
339C4×D4—102no—
340C4×D4—102no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—51no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4C22×D511yescharacteristic
348C2×C4⋊C4C22×D511yescharacteristic
349C2×C4⋊C4C22×D511yescharacteristic
350C2×C4⋊C4C22×D511yescharacteristic
351C2×C22⋊C4—101no—
352C2×C22⋊C4—101no—
353C2×C22⋊C4—101no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—101no—
357C2×C42—101no—
358C2×C42—101no—
359C2×C42C22×D511yescharacteristic
360C2×C42C22×D511yescharacteristic
361C2×C42C22×D511yescharacteristic
362#107—54no—
363#107—54no—
364#107—102no—
365#106—102no—
366C4⋊C8—54no—
367C4⋊C8—102no—
368#102—54no—
369#102—54no—
370#102—102no—
371#102—102no—
372#97—102no—
373C4×C8—102no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—101no—
381#95—101no—
382#95—101no—
383#95C22⋊D511yescharacteristic
384#95C22⋊D511yescharacteristic
385#95C22⋊D511yescharacteristic
386#95C22⋊D511yescharacteristic
387C22×C5C2×C4×D411yescharacteristic
388C22×C5C2×C22⋊Q811yescharacteristic
389C22×C5#52511yescharacteristic
390C22×C5#57611yescharacteristic
391C22×C5#57611yescharacteristic
392C22×C5#57711yescharacteristic
393C22×C5#57811yescharacteristic
394C2×D5—24no—
395C2×D5—42no—
396C2×D5—42no—
397C2×D5—42no—
398C2×D5—42no—
399C2×D5—42no—
400C2×D5—42no—
401C4×C5—22no—
402C4×C5—22no—
403C4×C5—22no—
404C4×C5—22no—
405C4×C5—41no—
406C4×C5—41no—
407C4×C5—42no—
408C4×C5—42no—
409C4×C5—81no—
410C4×C5—81no—
411C4×C5C2×C4×Q811yescharacteristic
412C4×C5C4×#4111yescharacteristic
413C4×C5#52911yescharacteristic
414C4×C5#53311yescharacteristic
415Dic5—42no—
416Dic5—42no—
417Dic5—42no—
418C24—101no—
419C2×Q8—24no—
420C2×Q8—81no—
421C2×Q8—81no—
422C2×D4—52no—
423C2×D4—52no—
424C2×D4—52no—
425C2×D4—101no—
426C2×D4—101no—
427C2×D4—101no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—104no—
433C22×C4—101no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—104no—
437C22×C4—104no—
438C22×C4—401no—
439C22×C4—401no—
440C22×C4—401no—
441C22×C4—401no—
442C22×C4—401no—
443C22×C4—401no—
444C22×C4C2×C22⋊D511yescharacteristic
445C22×C4C2×C22⋊D511yescharacteristic
446C22×C4C2×C22⋊D511yescharacteristic
447C22×C4C2×C22⋊D511yescharacteristic
448C22×C4C2×C22⋊D511yescharacteristic
449C22×C4C2×C22⋊D511yescharacteristic
450C22×C4C23×D511yescharacteristic
451C2×C8—52no—
452C2×C8—52no—
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—
462C2×C8—101no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—52no—
471C4⋊C4—52no—
472C4⋊C4—52no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—101no—
476C4⋊C4—101no—
477C4⋊C4—101no—
478C4⋊C4C2×C4×D512yes—
479C4⋊C4C2×C4×D512yes—
480C22⋊C4—104no—
481C22⋊C4—104no—
482C22⋊C4—104no—
483C42—21no—
484C42—21no—
485C42—81no—
486C42—81no—
487C42—401no—
488C42—401no—
489C42—401no—
490C42C2×C4×D512yes—
491C42#70912yes—
492C42Q8×D512yes—
493C42#71312yes—
494C2×C5C4×C22⋊Q811yescharacteristic
495C2×C5#294711yescharacteristic
496C2×C5#294811yescharacteristic
497C2×C5#308111yescharacteristic
498C2×C5#308311yescharacteristic
499C2×C5#311811yescharacteristic
500C2×C5#312411yescharacteristic
501D5—44no—
502C23—102no—
503C23—102no—
504C23—102no—
505C23—201no—
506C23—201no—
507C23—201no—
508C23—201no—
509C23C22×C22⋊D511yescharacteristic
510Q8—84no—
511D4—54no—
512D4—102no—
513D4—102no—
514D4—102no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—201no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—404no—
551C2×C4—404no—
552C2×C4—404no—
553C2×C4C4×C22⋊D512yes—
554C2×C4C4×C22⋊D512yes—
555C2×C4#409212yes—
556C2×C4#409212yes—
557C2×C4C22×C4×D511yescharacteristic
558C2×C4C2×#70911yescharacteristic
559C2×C4C2×Q8×D511yescharacteristic
560C2×C4C2×#71311yescharacteristic
561C2×C4D5×#4111yescharacteristic
562C2×C4D5×#4111yescharacteristic
563C8—102no—
564C8—102no—
565C8—201no—
566C8—201no—
567C5#2162411yescharacteristic, complemented, Sylow
568C22—104no—
569C22—202no—
570C22—202no—
571C22—202no—
572C22—202no—
573C22—202no—
574C22—202no—
575C22C2×C4×C22⋊D511yescharacteristic
576C22C2×#409211yescharacteristic
577C22#6616211yescharacteristic
578C22#6616911yescharacteristic
579C22#6616911yescharacteristic
580C22#6617111yescharacteristic
581C22#6617211yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—42no—
589C4—42no—
590C4—81no—
591C4—81no—
592C4—202no—
593C4—202no—
594C4—202no—
595C4C4×Q8×D511yescharacteristic
596C4C4×#71311yescharacteristic
597C4#6591211yescharacteristic
598C4#6591411yescharacteristic
599C2—204no—
600C2C4×#409211yescharacteristic
601C2#1061426911yescharacteristic
602C2#1061427811yescharacteristic
603C2#1061519111yescharacteristic
604C2#1061519211yescharacteristic
605C2#1061520511yescharacteristic
606C2#1061520611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#2331C2
socleC23×C5C22×D4
prime radicalC22×D20C23
cosocleC22×C4×C5C24
hypercenter#2331D5
hypocenterC5#21624
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ #376 ◁ #2331

Complements

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

NH ≅ G/Ntype
1. C5×#2331C2semidirect
4. #10602572C2semidirect
7. #10600396C2semidirect
8. #10600393C2semidirect
10. #10600333C2semidirect
11. #10600274C2semidirect
12. C4×#3939C2semidirect
15. #10600229C2semidirect
30. #65376C4semidirect
67. C5×C4⋊Q8C2×C4semidirect
98. C4×D20Q8semidirect
118. #3939C2×C4semidirect
119. #3939C2×C4semidirect
121. C4⋊#168C2×C4semidirect
125. #2331D5semidirect
334. C4⋊Q8C4×D5semidirect
567. C5#21624semidirect

Maximal subgroups

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

subgroupindex
C5×#23312
C2×#653762
#106051432
#106025722
#106004192
#106004182
#106003962
#106003932
#106003492
#106003332
#106002742
C4×#39392
#106002672
C4×#39412
#106002292
#216245