Finite Group Databasebeta

← #12121145

Subgroups — #12121145

Order 1280.

846 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2349C211yesmaximal, characteristic
2C2×#65298C211yesmaximal, characteristic
3#10605390C211yesmaximal, characteristic, complemented
4C4×#3964C211yesmaximal, characteristic
5C4×#3964C211yesmaximal, characteristic
6C4×#3964C211yesmaximal, characteristic
7#10602400C211yesmaximal, characteristic
8#10602399C211yesmaximal, characteristic
9#10600412C211yesmaximal, characteristic, complemented
10#10600411C211yesmaximal, characteristic, complemented
11#10600396C211yesmaximal, characteristic, complemented
12#10600395C211yesmaximal, characteristic, complemented
13#10600347C211yesmaximal, characteristic, complemented
14#10600333C211yesmaximal, characteristic, complemented
15C4⋊C4×#168C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17C2×C4×C5×D4C2211yescharacteristic
18C2×C4×C5×D4C2211yescharacteristic
19C2×#4016C2211yescharacteristic
20C5×#389C2211yescharacteristic
21C5×#389C2211yescharacteristic
22C5×#385—21no—
23C5×#385—21no—
24C5×#382C2211yescharacteristic
25C5×#380—21no—
26C4×C5×C4⋊C4C2211yescharacteristic
27C2×C5×#95—21no—
28C2×#3964C2211yescharacteristic
29C2×#3964C2211yescharacteristic
30C2×#3964C2211yescharacteristic
31C2×#3964C2211yescharacteristic
32#65298C418yescomplemented
33#65267—21no—
34#65261—21no—
35C2×#3940C2211yescharacteristic
36C2×#3940C2211yescharacteristic
37C2×#3939C2211yescharacteristic
38C2×#3939C2211yescharacteristic
39C4×C4⋊Dic5C2211yescharacteristic
40C4×C4⋊Dic5C2211yescharacteristic
41C4×C4⋊Dic5C2211yescharacteristic
42#65217C2211yescharacteristic
43#65217C2211yescharacteristic
44C2×C4⋊#168C2211yescharacteristic
45C2×C4×#168C2211yescharacteristic
46C2×C4×#168C2211yescharacteristic
47C2×C4×#168C2211yescharacteristic
48#64941—21no—
49#64938—21no—
50#64749C2211yescharacteristic
51#64749C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64744C2211yescharacteristic
59#64744C2211yescharacteristic
60#22966—51nomaximal, Sylow
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C23×C4×C5—21no—
64C23×C4×C5—21no—
65C4×C5×D4—22no—
66C4×C5×D4—22no—
67C4×C5×D4—22no—
68C4×C5×D4—41no—
69C4×C5×D4—41no—
70C4×C5×D4C2×C414yes—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4D411yescharacteristic
74C2×C5×C4⋊C4D411yescharacteristic
75C2×C5×C4⋊C4C2311yescharacteristic
76C2×C5×C4⋊C4C2311yescharacteristic
77C2×C5×C4⋊C4C2311yescharacteristic
78C2×C5×C22⋊C4—21no—
79C2×C5×C22⋊C4—21no—
80C2×C5×C22⋊C4—21no—
81C2×C42×C5C2311yescharacteristic
82C2×C42×C5C2311yescharacteristic
83C2×C42×C5C2311yescharacteristic
84C2×C4⋊Dic5C2311yescharacteristic
85C2×C4⋊Dic5C2311yescharacteristic
86C2×C4⋊Dic5C2311yescharacteristic
87C2×C4⋊Dic5C2311yescharacteristic
88C2×#683—21no—
89C2×#683—21no—
90C2×#683—21no—
91C2×#683—21no—
92C2×C4×Dic5—21no—
93C2×C4×Dic5—21no—
94C2×C4×Dic5—21no—
95C22×#168C2311yescharacteristic
96C22×#168C2311yescharacteristic
97C22×#168C2311yescharacteristic
98C22×#168C2311yescharacteristic
99#4016—22no—
100#4016C2×C414yescomplemented
101C5×#95—21no—
102C5×#95—21no—
103C5×#95—21no—
104C5×#95—21no—
105C5×#95D411yescharacteristic
106C5×#95D411yescharacteristic
107#3964—22no—
108#3964C2×C414yes—
109#3964C2×C414yes—
110#3964Q814yes—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3963—21no—
115#3963—21no—
116#3940—41no—
117#3940C2×C414yescomplemented
118#3939—41no—
119#3939C2×C414yescomplemented
120C4⋊#168C2×C414yescomplemented
121C4×#168—22no—
122C4×#168—41no—
123C4×#168—41no—
124C2×#478—51no—
125#2370—51no—
126#2349D511yescharacteristic
127#1991—51no—
128#1949—51no—
129#1942—51no—
130#1941—51no—
131#1921—51no—
132#1920—51no—
133#1864—51no—
134#1862—51no—
135C8×C4⋊C4—51no—
136C4×#102—51no—
137C4×#102—51no—
138C4×#102—51no—
139C24×C5—21no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4C22×C412yes—
144C2×C5×D4C2×Q812yes—
145C2×C5×D4#4112yes—
146C22×C4×C5—21no—
147C22×C4×C5—24no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—42no—
151C22×C4×C5—42no—
152C22×C4×C5—42no—
153C22×C4×C5—42no—
154C22×C4×C5—81no—
155C22×C4×C5—81no—
156C22×C4×C5—81no—
157C22×C4×C5—81no—
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2411yescharacteristic
165C22×Dic5—21no—
166C22×Dic5—21no—
167C22×Dic5—21no—
168C22×Dic5—21no—
169C5×C4⋊C4—22no—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—81no—
177C5×C4⋊C4—81no—
178C5×C4⋊C4C22×C412yes—
179C5×C22⋊C4—24no—
180C5×C22⋊C4—42no—
181C5×C22⋊C4—42no—
182C42×C5—21no—
183C42×C5—21no—
184C42×C5—21no—
185C42×C5—21no—
186C42×C5C22×C412yes—
187C42×C5#4112yes—
188C4⋊Dic5—21no—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5C22×C412yes—
194C4⋊Dic5C22×C412yes—
195C4⋊Dic5C2×Q812yes—
196#683—24no—
197#683—24no—
198#683—42no—
199#683—81no—
200C4×Dic5—42no—
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×#168C22×C412yes—
213C2×#168C22×C412yes—
214C2×#168C2×Q812yes—
215C2×#125—51no—
216C2×C4×D4C2×D511yescharacteristic
217C2×C4×D4C2×D511yescharacteristic
218C2×C4×D4C2×D511yescharacteristic
219#478—58no—
220C2×#107—51no—
221C2×#107—51no—
222C2×#106—51no—
223C2×#106—51no—
224C2×C4⋊C8—51no—
225C2×#102—51no—
226C2×#102—51no—
227C2×#102—51no—
228C2×#102—51no—
229C2×C4×C8—51no—
230C2×C4×C8—51no—
231C2×C4×C8—51no—
232#389—51no—
233#389—51no—
234#389—101no—
235#389C2×D511yescharacteristic
236#389C2×D511yescharacteristic
237#387—101no—
238#387—101no—
239#385—21no—
240#385—21no—
241#382C2×D511yescharacteristic
242#380—21no—
243C4×C4⋊C4—51no—
244C4×C4⋊C4—51no—
245C4×C4⋊C4—51no—
246C4×C4⋊C4—101no—
247C4×C4⋊C4C2×D511yescharacteristic
248C2×#95—21no—
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×C5—22no—
260C23×C5—22no—
261C23×C5—22no—
262C23×C5—41no—
263C23×C5—41no—
264C23×C5—41no—
265C23×C5—41no—
266C23×C5C22×D411yescharacteristic
267C5×D4—22no—
268C5×D4—22no—
269C5×D4—22no—
270C5×D4C4×Q814yes—
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—22no—
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—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×C5—84no—
295C2×C4×C5—84no—
296C2×C4×C5—84no—
297C2×C4×C5C4×D412yes—
298C2×C4×C5C4×D412yes—
299C2×C4×C5#13512yes—
300C2×C4×C5#13512yes—
301C2×C4×C5C23×C411yescharacteristic
302C2×C4×C5C22×Q811yescharacteristic
303C2×C4×C5C2×#4111yescharacteristic
304C2×C4×C5C2×#4111yescharacteristic
305C2×C4×C5H(5,𝔽2)11yescharacteristic
306C2×C4×C52−1+411yescharacteristic
307C2×Dic5—22no—
308C2×Dic5—22no—
309C2×Dic5—22no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319#168—22no—
320#168—22no—
321#168—22no—
322#168—41no—
323C22×D4C22×D511yescharacteristic
324C23×C4—21no—
325C23×C4—21no—
326C23×C4—21no—
327C22×C8—51no—
328C22×C8—51no—
329C22×C8—51no—
330C22×C8—51no—
331#125—54no—
332#125—102no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—41no—
337C4×D4—41no—
338C4×D4C4×D514yes—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—51no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—101no—
346C2×C4⋊C4—101no—
347C2×C4⋊C4—101no—
348C2×C4⋊C4—101no—
349C2×C4⋊C4C22⋊D511yescharacteristic
350C2×C4⋊C4C22⋊D511yescharacteristic
351C2×C4⋊C4C22×D511yescharacteristic
352C2×C4⋊C4C22×D511yescharacteristic
353C2×C4⋊C4C22×D511yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C42—101no—
358C2×C42—101no—
359C2×C42—101no—
360C2×C42C22×D511yescharacteristic
361C2×C42C22×D511yescharacteristic
362C2×C42C22×D511yescharacteristic
363#107—54no—
364#107—201no—
365#106—54no—
366#106—201no—
367C4⋊C8—54no—
368#102—54no—
369#102—54no—
370#102—54no—
371#102—102no—
372C4×C8—102no—
373C4×C8—201no—
374C4×C8—201no—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—101no—
380#95—101no—
381#95—101no—
382#95—101no—
383#95—101no—
384#95C22⋊D511yescharacteristic
385#95C22⋊D511yescharacteristic
386C22×C5—24no—
387C22×C5—42no—
388C22×C5—42no—
389C22×C5—42no—
390C22×C5—42no—
391C22×C5—42no—
392C22×C5—42no—
393C22×C5C2×C4×D411yescharacteristic
394C22×C5#54611yescharacteristic
395C22×C5D4×Q811yescharacteristic
396C22×C5C2×#13511yescharacteristic
397C22×C5C2×#13511yescharacteristic
398C22×C5#57611yescharacteristic
399C22×C5#57711yescharacteristic
400C4×C5—22no—
401C4×C5—22no—
402C4×C5—22no—
403C4×C5—22no—
404C4×C5—42no—
405C4×C5—41no—
406C4×C5—41no—
407C4×C5—81no—
408C4×C5—81no—
409C4×C5C2×C4×Q811yescharacteristic
410C4×C5#52011yescharacteristic
411C4×C5#55211yescharacteristic
412C4×C5#55411yescharacteristic
413Dic5—42no—
414Dic5—42no—
415Dic5—42no—
416Dic5—81no—
417C24—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C2×C4×D512yes—
422C2×D4#71112yes—
423C2×D4Q8×D512yes—
424C22×C4—21no—
425C22×C4—24no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—81no—
433C22×C4—81no—
434C22×C4—81no—
435C22×C4—81no—
436C22×C4—101no—
437C22×C4—101no—
438C22×C4—101no—
439C22×C4—101no—
440C22×C4C2×C22⋊D511yescharacteristic
441C22×C4C2×C22⋊D511yescharacteristic
442C22×C4C2×C22⋊D511yescharacteristic
443C22×C4C2×C22⋊D511yescharacteristic
444C22×C4C2×C22⋊D511yescharacteristic
445C22×C4C2×C22⋊D511yescharacteristic
446C22×C4C23×D511yescharacteristic
447C2×C8—52no—
448C2×C8—52no—
449C2×C8—52no—
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—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—52no—
467C4⋊C4—52no—
468C4⋊C4—52no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—101no—
472C4⋊C4—101no—
473C4⋊C4—101no—
474C4⋊C4—104no—
475C4⋊C4—104no—
476C4⋊C4—101no—
477C4⋊C4—101no—
478C4⋊C4—202no—
479C4⋊C4—401no—
480C4⋊C4C2×C4×D512yes—
481C22⋊C4—24no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—202no—
489C42—401no—
490C42—401no—
491C42C2×C4×D512yes—
492C42#70912yes—
493C2×C5—44no—
494C2×C5#236011yescharacteristic
495C2×C5C4×#13511yescharacteristic
496C2×C5#294611yescharacteristic
497C2×C5#329611yescharacteristic
498C2×C5#329711yescharacteristic
499C2×C5#338011yescharacteristic
500C2×C5#338111yescharacteristic
501C23—22no—
502C23—22no—
503C23—22no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23C22×C22⋊D511yescharacteristic
509D4—22no—
510D4—22no—
511D4—22no—
512D4#403314yes—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—84no—
537C2×C4—84no—
538C2×C4—84no—
539C2×C4—102no—
540C2×C4—102no—
541C2×C4—102no—
542C2×C4—201no—
543C2×C4—201no—
544C2×C4—201no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—201no—
551C2×C4C4×C22⋊D512yes—
552C2×C4C4×C22⋊D512yes—
553C2×C4#409612yes—
554C2×C4#409612yes—
555C2×C4C22×C4×D511yescharacteristic
556C2×C4C2×#70911yescharacteristic
557C2×C4C2×#71111yescharacteristic
558C2×C4#414411yescharacteristic
559C2×C4C2×Q8×D511yescharacteristic
560C2×C4#414711yescharacteristic
561C8—102no—
562C8—102no—
563C8—102no—
564C8—201no—
565C5#2296611yescharacteristic, complemented, Sylow
566C22—24no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22C2×C4×C22⋊D511yescharacteristic
574C22#6614011yescharacteristic
575C22Q8×C22⋊D511yescharacteristic
576C22C2×#409611yescharacteristic
577C22C2×#409611yescharacteristic
578C22#6616911yescharacteristic
579C22#6617011yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—42no—
587C4—81no—
588C4—81no—
589C4—202no—
590C4—202no—
591C4—202no—
592C4—401no—
593C4C2×#403311yescharacteristic
594C4#6583811yescharacteristic
595C4#6584511yescharacteristic
596C4#6584711yescharacteristic
597C2—44no—
598C2#1061389311yescharacteristic
599C2C4×#409611yescharacteristic
600C2#1061426811yescharacteristic
601C2#1061522511yescharacteristic
602C2#1061522611yescharacteristic
603C2#1061535911yescharacteristic
604C2#1061536011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#2349C2
socleC23×C5C22×D4
prime radicalC22×C5×D4C23
cosocleC22×C4×C5C24
hypercenter#2349D5
hypocenterC5#22966
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2349

Complements

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

NH ≅ G/Ntype
3. #10605390C2semidirect
9. #10600412C2semidirect
10. #10600411C2semidirect
11. #10600396C2semidirect
12. #10600395C2semidirect
13. #10600347C2semidirect
14. #10600333C2semidirect
15. C4⋊C4×#168C2semidirect
32. #65298C4semidirect
100. #4016C2×C4semidirect
117. #3940C2×C4semidirect
119. #3939C2×C4semidirect
120. C4⋊#168C2×C4semidirect
565. C5#22966semidirect

Maximal subgroups

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

subgroupindex
C5×#23492
C2×#652982
#106053902
C4×#39642
#106024002
#106023992
#106004122
#106004112
#106003962
#106003952
#106003472
#106003332
C4⋊C4×#1682
#229665