Finite Group Databasebeta

← #12066961

Subgroups — #12066961

Order 1280.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10617628C211yesmaximal, characteristic
2C5×#2343C211yesmaximal, characteristic, complemented
3#10613941C211yesmaximal, characteristic, complemented
4#10600359C211yesmaximal, characteristic, complemented
5#10600358C211yesmaximal, characteristic, complemented
6#10600339C211yesmaximal, characteristic, complemented
7#10600337C211yesmaximal, characteristic, complemented
8#10600326C211yesmaximal, characteristic, complemented
9#10600325C211yesmaximal, characteristic
10#10600264C211yesmaximal, characteristic, complemented
11#10600263C211yesmaximal, characteristic, complemented
12#10600226C211yesmaximal, characteristic, complemented
13#10600224C211yesmaximal, characteristic, complemented
14C2×#64672C211yesmaximal, characteristic, complemented
15#10600191C211yesmaximal, characteristic
16C2×C5×#117C2211yescharacteristic
17#66125C2211yescharacteristic
18C2×#4070C2211yescharacteristic
19#65868C411yescharacteristic, complemented
20#65868C411yescharacteristic, complemented
21#65867—21no—
22#65865—21no—
23#65865—21no—
24#65863—21no—
25#65860C411yescharacteristic, complemented
26#65857C411yescharacteristic, complemented
27#65853C411yescharacteristic, complemented
28#65852C411yescharacteristic, complemented
29#65852C411yescharacteristic, complemented
30#65850C411yescharacteristic, complemented
31#65847—21no—
32#65845—21no—
33#65829—21no—
34#65829—21no—
35#65813C2211yescharacteristic
36#65813C2211yescharacteristic
37#65804C2211yescharacteristic
38#65804C2211yescharacteristic
39C5×#387—21no—
40C5×#387—21no—
41C5×#385—21no—
42C5×#383C2211yescharacteristic
43C5×#382C2211yescharacteristic
44C5×#381C2211yescharacteristic
45C4×C5×C4⋊C4C2211yescharacteristic
46C4×C5×C22⋊C4—21no—
47C5×#376C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49#65496C2211yescharacteristic
50C2×C22⋊#168C2211yescharacteristic
51#65289—21no—
52#65289—21no—
53#65288—21no—
54#65286—21no—
55#65215C2211yescharacteristic
56#65215C2211yescharacteristic
57#65214C2211yescharacteristic
58#65214C2211yescharacteristic
59#64672C2211yescharacteristic
60#64672C2211yescharacteristic
61#64672C2211yescharacteristic
62#64672C2211yescharacteristic
63#64672C2211yescharacteristic
64#64672C2211yescharacteristic
65#64672C2211yescharacteristic
66#64672C2211yescharacteristic
67#64672C2211yescharacteristic
68#64672C2211yescharacteristic
69#64672C2211yescharacteristic
70#64672C2211yescharacteristic
71#64671C2211yescharacteristic
72#64671C2211yescharacteristic
73#64671C2211yescharacteristic
74#64671C2211yescharacteristic
75#17609—51nomaximal, Sylow
76C23×C4×C5—21no—
77C23×C4×C5C2311yescharacteristic
78C2×#709C2×C411yescharacteristic
79C22×Dic10C2×C411yescharacteristic
80C5×#117C2×C411yescharacteristic
81C5×#117C2×C411yescharacteristic
82C5×#117C2×C411yescharacteristic
83C5×#117C2×C411yescharacteristic
84C5×#117D411yescharacteristic
85C5×#117D411yescharacteristic
86C5×#117D411yescharacteristic
87C5×#117D411yescharacteristic
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4D411yescharacteristic
91C2×C5×C4⋊C4D411yescharacteristic
92C2×C5×C22⋊C4—21no—
93C2×C5×C22⋊C4D411yescharacteristic
94C2×C5×C22⋊C4D411yescharacteristic
95C2×C42×C5—21no—
96C2×C42×C5—21no—
97C2×C42×C5C2311yescharacteristic
98C2×C42×C5C2311yescharacteristic
99#4099—21no—
100C2×C22⋊Dic5—21no—
101#4076C2×C411yescharacteristic
102#4076C2311yescharacteristic
103#4075—21no—
104#4075—21no—
105#4075—21no—
106C4×C22⋊D5—21no—
107C4×C22⋊D5—21no—
108C4×C22⋊D5—21no—
109C4×C22⋊D5—21no—
110#4072—21no—
111#4072—21no—
112#4072C2×C411yescharacteristic
113C2×C4⋊Dic5C2×C411yescharacteristic
114#4070—21no—
115#4070—21no—
116#4070—21no—
117#4070—21no—
118#4070C2×C411yescharacteristic
119#4070C2×C411yescharacteristic
120#4070C2×C411yescharacteristic
121#4070C2311yescharacteristic
122#4070C2311yescharacteristic
123#4070C2311yescharacteristic
124C2×#683—21no—
125C2×#681—21no—
126C22×#168—21no—
127#4044—21no—
128#4044—21no—
129#4043—21no—
130#4043—21no—
131#4042—21no—
132#4042—21no—
133#4038—21no—
134D5×C4⋊C4—21no—
135#4036—21no—
136#4035—21no—
137#4035—21no—
138#4035—21no—
139#4035—21no—
140#4034—21no—
141#4033—21no—
142#4033—21no—
143#4032—21no—
144#4032—21no—
145#4031—21no—
146#4031—21no—
147#4029—21no—
148#4029—21no—
149#4027—21no—
150#4027—21no—
151#4025—21no—
152#4025—21no—
153#4025—21no—
154#4025—21no—
155#4024—21no—
156#4024—21no—
157#4023—21no—
158#4023—21no—
159#4022—21no—
160#4022—21no—
161#4021C2×C411yescharacteristic, complemented
162#4021C2×C411yescharacteristic, complemented
163C4×D20C2×C411yescharacteristic, complemented
164C4×D20C2×C411yescharacteristic, complemented
165#4018—21no—
166#4018—21no—
167#4016—21no—
168#4016—21no—
169#4016C2×C411yescharacteristic, complemented
170#4016C2×C411yescharacteristic, complemented
171#4015C2×C411yescharacteristic, complemented
172#4015C2×C411yescharacteristic, complemented
173#4015C2×C411yescharacteristic, complemented
174#4015C2×C411yescharacteristic, complemented
175C4×Dic10—21no—
176C4×Dic10—21no—
177C4×Dic10C2×C411yescharacteristic, complemented
178C4×Dic10C2×C411yescharacteristic, complemented
179C4×Dic10C2×C411yescharacteristic, complemented
180C4×Dic10C2×C411yescharacteristic, complemented
181C4×Dic10C2×C411yescharacteristic, complemented
182C4×Dic10C2×C411yescharacteristic, complemented
183C5×#95—21no—
184C5×#95—21no—
185C5×#95—21no—
186C5×#95—21no—
187C5×#95—21no—
188C5×#95—21no—
189C5×#95C2311yescharacteristic
190C5×#95C2311yescharacteristic
191C5×#95C2311yescharacteristic
192C5×#95C2311yescharacteristic
193C22⋊#168—21no—
194C22⋊#168—21no—
195C22⋊#168C2311yescharacteristic
196C22⋊#168C2311yescharacteristic
197C22⋊#168C2311yescharacteristic
198C22⋊#168C2311yescharacteristic
199C4⋊#168—21no—
200C4⋊#168—21no—
201C4⋊#168—21no—
202C4⋊#168—21no—
203#3935—21no—
204#3935—21no—
205C4×#168—21no—
206C4×#168—21no—
207#3495—51no—
208#2924—51no—
209#2343D511yescharacteristic, complemented
210#1521—51no—
211#1518—51no—
212#1516—51no—
213#1515—51no—
214#1512—51no—
215#1511—51no—
216#1509—51no—
217#1506—51no—
218#1504—51no—
219#1503—51no—
220#1500—51no—
221C2×#328—51no—
222C24×C5C2×D411yescharacteristic
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—42no—
228C22×C4×C5—42no—
229C22×C4×C5—42no—
230C22×C4×C5—81no—
231C22×C4×C5C22×C411yescharacteristic
232C22×C4×C5C22×C411yescharacteristic
233C22×C4×C5C2×D411yescharacteristic
234C22×C4×C5C2×D411yescharacteristic
235C22×C4×C5C2×D411yescharacteristic
236C22×C4×C5C2×D411yescharacteristic
237C22×C4×C5C2×D411yescharacteristic
238C22×C4×C5C2×D411yescharacteristic
239C22×C4×C5C2×D411yescharacteristic
240C22×C4×C5C2411yescharacteristic
241C2×C22⋊D5—21no—
242C2×C22⋊D5—21no—
243C2×C22⋊D5—21no—
244C22×Dic5—21no—
245C22×Dic5—21no—
246#709—42no—
247C2×D20C22×C411yescharacteristic
248C2×C4×D5—21no—
249C2×C4×D5—21no—
250C2×C4×D5—21no—
251C2×Dic10—21no—
252C2×Dic10—21no—
253C2×Dic10—21no—
254C2×Dic10—42no—
255C2×Dic10C22×C411yescharacteristic
256C2×Dic10C22×C411yescharacteristic
257C2×Dic10C22×C411yescharacteristic
258C5×C4⋊C4—42no—
259C5×C4⋊C4—81no—
260C5×C4⋊C4C22⋊C411yescharacteristic
261C5×C4⋊C4C22⋊C411yescharacteristic
262C5×C4⋊C4C22⋊C411yescharacteristic
263C5×C4⋊C4C22⋊C411yescharacteristic
264C5×C4⋊C4C22⋊C411yescharacteristic
265C5×C4⋊C4C22⋊C411yescharacteristic
266C5×C4⋊C4C22⋊C411yescharacteristic
267C5×C4⋊C4C22⋊C411yescharacteristic
268C5×C22⋊C4—42no—
269C5×C22⋊C4C22⋊C411yescharacteristic
270C5×C22⋊C4C22⋊C411yescharacteristic
271C5×C22⋊C4C22⋊C411yescharacteristic
272C5×C22⋊C4C22⋊C411yescharacteristic
273C5×C22⋊C4C22⋊C411yescharacteristic
274C5×C22⋊C4C22⋊C411yescharacteristic
275C5×C22⋊C4C22⋊C411yescharacteristic
276C5×C22⋊C4C22⋊C411yescharacteristic
277C42×C5—42no—
278C42×C5—81no—
279C42×C5C22×C411yescharacteristic
280C42×C5C22×C411yescharacteristic
281C42×C5C22×C411yescharacteristic
282C42×C5C22×C411yescharacteristic
283C42×C5C2×D411yescharacteristic
284C42×C5C2×D411yescharacteristic
285C42×C5C2×D411yescharacteristic
286C42×C5C2×D411yescharacteristic
287C22⋊Dic5—21no—
288C22⋊Dic5—21no—
289C22⋊Dic5—21no—
290C22⋊Dic5—21no—
291C22⋊Dic5—21no—
292C22⋊Dic5—21no—
293C22⋊Dic5—21no—
294#685—21no—
295#685—21no—
296#685—21no—
297#685—21no—
298#685—21no—
299#685—21no—
300#685—21no—
301#685—21no—
302C4⋊Dic5—21no—
303C4⋊Dic5—21no—
304C4⋊Dic5—21no—
305C4⋊Dic5—21no—
306C4⋊Dic5—21no—
307C4⋊Dic5—21no—
308C4⋊Dic5—21no—
309C4⋊Dic5C22×C411yescharacteristic
310C4⋊Dic5C22×C411yescharacteristic
311C4⋊Dic5C22×C411yescharacteristic
312C4⋊Dic5C22×C411yescharacteristic
313#683—21no—
314#683—21no—
315#683—21no—
316#683—21no—
317#683—21no—
318#683—21no—
319#683—21no—
320#683—21no—
321#683—21no—
322#683—21no—
323#683—21no—
324#683—21no—
325#683—21no—
326#683—21no—
327#683—21no—
328#683—21no—
329C4×Dic5—21no—
330C4×Dic5—21no—
331C4×Dic5—21no—
332C4×Dic5—21no—
333C4×Dic5—21no—
334C4×Dic5—21no—
335C4×Dic5—21no—
336#681—42no—
337C2×#168—21no—
338C2×#168—21no—
339C2×#168—21no—
340C2×#168—21no—
341C2×#168—42no—
342#556—101no—
343#554—101no—
344#552—101no—
345#552—101no—
346#552—101no—
347#552—101no—
348#551—101no—
349#551—101no—
350#544—51no—
351#542—51no—
352#542—51no—
353#541—51no—
354#541—51no—
355#536—51no—
356#533—51no—
357#533—51no—
358#529—51no—
359#529—51no—
360#525—51no—
361C2×C22⋊Q8—51no—
362#520—51no—
363#519—51no—
364C2×#117C2×D511yescharacteristic
365#433—101no—
366#433—101no—
367#432—51no—
368#432—51no—
369#431—51no—
370#431—51no—
371#424—101no—
372#407—51no—
373C2×C22⋊C8—51no—
374#405—101no—
375#387—21no—
376#387—21no—
377#385—21no—
378#383C2×D511yescharacteristic
379#382C2×D511yescharacteristic
380#381C2×D511yescharacteristic
381C4×C4⋊C4C2×D511yescharacteristic
382C4×C22⋊C4—21no—
383#376C2×D511yescharacteristic
384C2×#95C2×D511yescharacteristic
385#328—51no—
386#328—51no—
387#328—51no—
388#328—51no—
389#328—51no—
390#328—51no—
391#328—51no—
392#328—51no—
393#328—51no—
394#328—51no—
395#328—51no—
396#328—51no—
397#327—51no—
398#327—51no—
399#327—51no—
400#327—51no—
401C23×C5—21no—
402C23×C5—21no—
403C23×C5—22no—
404C23×C5—41no—
405C23×C5C2×C22⋊C411yescharacteristic
406C23×C5C2×C22⋊C411yescharacteristic
407C23×C5C22×D411yescharacteristic
408C22×D5—21no—
409C2×C4×C5—21no—
410C2×C4×C5—21no—
411C2×C4×C5—21no—
412C2×C4×C5—21no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—41no—
417C2×C4×C5—41no—
418C2×C4×C5—41no—
419C2×C4×C5—41no—
420C2×C4×C5—41no—
421C2×C4×C5—41no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5—41no—
428C2×C4×C5—41no—
429C2×C4×C5—41no—
430C2×C4×C5—41no—
431C2×C4×C5—41no—
432C2×C4×C5—41no—
433C2×C4×C5—84no—
434C2×C4×C5C2×C22⋊C411yescharacteristic
435C2×C4×C5C2×C22⋊C411yescharacteristic
436C2×C4×C5C2×C22⋊C411yescharacteristic
437C2×C4×C5C2×C22⋊C411yescharacteristic
438C2×C4×C5C2×C22⋊C411yescharacteristic
439C2×C4×C5C2×C22⋊C411yescharacteristic
440C2×C4×C5C2×C22⋊C411yescharacteristic
441C2×C4×C5C2×C22⋊C411yescharacteristic
442C2×C4×C5C2×C22⋊C411yescharacteristic
443C2×C4×C5C2×C22⋊C411yescharacteristic
444C2×C4×C5C23×C411yescharacteristic
445C2×C4×C5C22×D411yescharacteristic
446C22⋊D5—41no—
447C22⋊D5—41no—
448C22⋊D5—42no—
449C22⋊D5—81no—
450C2×Dic5—21no—
451C2×Dic5—21no—
452C2×Dic5—21no—
453C2×Dic5—21no—
454C2×Dic5—21no—
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5—42no—
458C2×Dic5—81no—
459D20—41no—
460C4×D5—42no—
461C4×D5—81no—
462C4×D5—81no—
463Dic10—42no—
464Dic10—41no—
465Dic10—41no—
466Dic10—41no—
467Dic10—81no—
468Dic10—81no—
469#168—41no—
470#168—41no—
471#168—41no—
472#168—41no—
473C2×#41—51no—
474C22×Q8—51no—
475C23×C4—21no—
476C23×C4C22×D511yescharacteristic
477C2×M16—101no—
478C22×C8—101no—
479C4⋊Q8—51no—
480C4⋊Q8—51no—
481C4⋊Q8—51no—
482C4⋊Q8—51no—
483C4⋊Q8—101no—
484#126—101no—
485#126—101no—
486#126—101no—
487#126—101no—
488#126—101no—
489#126—101no—
490#126—101no—
491#126—101no—
492#125—51no—
493#125—51no—
494#125—101no—
495#125—101no—
496#125—101no—
497#125—101no—
498#125—101no—
499#125—101no—
500#125—101no—
501#124—51no—
502#124—51no—
503#124—101no—
504#124—101no—
505#123—101no—
506#123—101no—
507#123—101no—
508#123—101no—
509#123—101no—
510#123—101no—
511#123—101no—
512C22⋊Q8—51no—
513C22⋊Q8—51no—
514C22⋊Q8—51no—
515C22⋊Q8—51no—
516C22⋊Q8—51no—
517C22⋊Q8—51no—
518C22⋊Q8—101no—
519C22⋊Q8—101no—
520C22⋊Q8—101no—
521C22⋊Q8—101no—
522C22⋊Q8—101no—
523C22⋊Q8—101no—
524C22⋊Q8—101no—
525C22⋊Q8—101no—
526C22⋊Q8—101no—
527C22⋊Q8—101no—
528#121—51no—
529#121—51no—
530#120—101no—
531C4×Q8—51no—
532C4×Q8—51no—
533C4×Q8—51no—
534C4×Q8—51no—
535C4×Q8—51no—
536C4×Q8—51no—
537C4×Q8—101no—
538C4×Q8—101no—
539C4×Q8—101no—
540C4×Q8—101no—
541C4×D4—51no—
542C4×D4—51no—
543C4×D4—101no—
544C4×D4—101no—
545C4×D4—101no—
546C4×D4—101no—
547C4×D4—101no—
548C4×D4—101no—
549#117—51no—
550#117—101no—
551#117—101no—
552#117—101no—
553#117—101no—
554#117—101no—
555#117—101no—
556#117—101no—
557#117C4×D511yescharacteristic
558#117C4×D511yescharacteristic
559#117C4×D511yescharacteristic
560#117C4×D511yescharacteristic
561#117D2011yescharacteristic
562#117D2011yescharacteristic
563#117D2011yescharacteristic
564#117D2011yescharacteristic
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—51no—
568C2×C4⋊C4—101no—
569C2×C4⋊C4—101no—
570C2×C4⋊C4C22⋊D511yescharacteristic
571C2×C4⋊C4C22⋊D511yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—101no—
574C2×C22⋊C4C22⋊D511yescharacteristic
575C2×C22⋊C4C22⋊D511yescharacteristic
576C2×C42—21no—
577C2×C42—21no—
578C2×C42C22×D511yescharacteristic
579C2×C42C22×D511yescharacteristic
580C4⋊C8—101no—
581C4⋊C8—101no—
582C4⋊C8—101no—
583C4⋊C8—101no—
584C22⋊C8—51no—
585C22⋊C8—51no—
586C22⋊C8—51no—
587C22⋊C8—51no—
588C22⋊C8—101no—
589C22⋊C8—101no—
590#97—101no—
591#97—101no—
592C4×C8—101no—
593C4×C8—101no—
594#95—21no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—21no—
599#95—21no—
600#95C22×D511yescharacteristic
601#95C22×D511yescharacteristic
602#95C22×D511yescharacteristic
603#95C22×D511yescharacteristic
604C22×C5—21no—
605C22×C5—21no—
606C22×C5—21no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—21no—
611C22×C5—42no—
612C22×C5—42no—
613C22×C5#41012yes—
614C22×C5C22×C22⋊C411yescharacteristic
615C22×C5#57711yescharacteristic
616C22×C5#57811yescharacteristic
617C2×D5—41no—
618C2×D5—41no—
619C2×D5—41no—
620C4×C5—21no—
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—21no—
624C4×C5—21no—
625C4×C5—21no—
626C4×C5—21no—
627C4×C5—21no—
628C4×C5—21no—
629C4×C5—21no—
630C4×C5—21no—
631C4×C5—21no—
632C4×C5—42no—
633C4×C5—81no—
634C4×C5—81no—
635C4×C5—81no—
636Dic5—41no—
637Dic5—41no—
638Dic5—41no—
639Dic5—41no—
640Dic5—41no—
641Dic5—41no—
642Dic5—41no—
643C24C2×C22⋊D511yescharacteristic
644#41—202no—
645C2×Q8—51no—
646C2×Q8—51no—
647C2×Q8—51no—
648C2×Q8—101no—
649C2×Q8—101no—
650C2×Q8—101no—
651C2×Q8—202no—
652C2×D4—51no—
653C2×D4—101no—
654C2×D4—101no—
655C2×D4—101no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—81no—
664C22×C4—101no—
665C22×C4—101no—
666C22×C4—101no—
667C22×C4—101no—
668C22×C4—101no—
669C22×C4C2×C4×D511yescharacteristic
670C22×C4C2×C4×D511yescharacteristic
671C22×C4C2×D2011yescharacteristic
672C22×C4C2×D2011yescharacteristic
673C22×C4C2×C22⋊D511yescharacteristic
674C22×C4C2×C22⋊D511yescharacteristic
675C22×C4C2×C22⋊D511yescharacteristic
676C22×C4C2×C22⋊D511yescharacteristic
677C22×C4C2×C22⋊D511yescharacteristic
678C22×C4C23×D511yescharacteristic
679M16—202no—
680C2×C8—101no—
681C2×C8—101no—
682C2×C8—101no—
683C2×C8—101no—
684C2×C8—202no—
685C4⋊C4—42no—
686C4⋊C4—51no—
687C4⋊C4—51no—
688C4⋊C4—51no—
689C4⋊C4—51no—
690C4⋊C4—81no—
691C4⋊C4—101no—
692C4⋊C4—101no—
693C4⋊C4—101no—
694C4⋊C4—101no—
695C4⋊C4—101no—
696C4⋊C4—101no—
697C4⋊C4—101no—
698C4⋊C4—101no—
699C4⋊C4—101no—
700C4⋊C4—101no—
701C4⋊C4—101no—
702C4⋊C4—101no—
703C4⋊C4—101no—
704C4⋊C4—101no—
705C4⋊C4—101no—
706C4⋊C4—101no—
707C4⋊C4—101no—
708C4⋊C4—101no—
709C4⋊C4—101no—
710C4⋊C4—101no—
711C4⋊C4—101no—
712C4⋊C4—101no—
713C4⋊C4—101no—
714C4⋊C4#68511yescharacteristic
715C4⋊C4#68511yescharacteristic
716C4⋊C4#68511yescharacteristic
717C4⋊C4#68511yescharacteristic
718C4⋊C4#68511yescharacteristic
719C4⋊C4#68511yescharacteristic
720C4⋊C4#68511yescharacteristic
721C4⋊C4#68511yescharacteristic
722C22⋊C4—42no—
723C22⋊C4—101no—
724C22⋊C4—101no—
725C22⋊C4—101no—
726C22⋊C4—101no—
727C22⋊C4—101no—
728C22⋊C4—101no—
729C22⋊C4—101no—
730C22⋊C4—101no—
731C22⋊C4—101no—
732C22⋊C4—101no—
733C22⋊C4—101no—
734C22⋊C4—101no—
735C22⋊C4—101no—
736C22⋊C4—101no—
737C22⋊C4—101no—
738C22⋊C4#68511yescharacteristic
739C22⋊C4#68511yescharacteristic
740C22⋊C4#68511yescharacteristic
741C22⋊C4#68511yescharacteristic
742C22⋊C4#68511yescharacteristic
743C22⋊C4#68511yescharacteristic
744C22⋊C4#68511yescharacteristic
745C22⋊C4#68511yescharacteristic
746C42—42no—
747C42—81no—
748C42—101no—
749C42—101no—
750C42—101no—
751C42—101no—
752C42—101no—
753C42—101no—
754C42—101no—
755C42C2×C4×D511yescharacteristic
756C42C2×C4×D511yescharacteristic
757C42C2×C4×D511yescharacteristic
758C42C2×C4×D511yescharacteristic
759C42C2×D2011yescharacteristic
760C42C2×D2011yescharacteristic
761C42C2×D2011yescharacteristic
762C42C2×D2011yescharacteristic
763C2×C5—21no—
764C2×C5—21no—
765C2×C5—22no—
766C2×C5—41no—
767C2×C5C2×#41011yescharacteristic
768C2×C5#289811yescharacteristic
769C2×C5#290111yescharacteristic
770D5—81no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—41no—
775C23—101no—
776C23C2×#68511yescharacteristic
777C23C2×#68511yescharacteristic
778C23C22×C22⋊D511yescharacteristic
779Q8—201no—
780Q8—201no—
781Q8—201no—
782Q8—202no—
783Q8—401no—
784Q8—401no—
785D4—201no—
786D4—202no—
787D4—201no—
788D4—201no—
789D4—401no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—101no—
816C2×C4—101no—
817C2×C4—101no—
818C2×C4—101no—
819C2×C4—101no—
820C2×C4—101no—
821C2×C4—101no—
822C2×C4—202no—
823C2×C4—202no—
824C2×C4—401no—
825C2×C4—401no—
826C2×C4—401no—
827C2×C4C2×#68511yescharacteristic
828C2×C4C2×#68511yescharacteristic
829C2×C4C2×#68511yescharacteristic
830C2×C4C2×#68511yescharacteristic
831C2×C4C2×#68511yescharacteristic
832C2×C4C2×#68511yescharacteristic
833C2×C4C2×#68511yescharacteristic
834C2×C4C2×#68511yescharacteristic
835C2×C4C2×#68511yescharacteristic
836C2×C4C2×#68511yescharacteristic
837C2×C4C22×C4×D511yescharacteristic
838C2×C4C22×D2011yescharacteristic
839C8—201no—
840C8—201no—
841C8—201no—
842C8—201no—
843C5#1760911yescharacteristic, complemented, Sylow
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—201no—
854C22—201no—
855C22—201no—
856C22#6529512yes—
857C22C22×#68511yescharacteristic
858C22#6617011yescharacteristic
859C22#6617211yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4—201no—
877C4—201no—
878C4—201no—
879C4—201no—
880C4—201no—
881C4—201no—
882C4—201no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—401no—
888C2C2×#6529511yescharacteristic
889C2#1061426711yescharacteristic
890C2#1061430111yescharacteristic
subgroupG/H
centerC22C22×#685
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#2343C2
socleC22×C5C22×C22⋊C4
prime radical#66125C22
cosocleC22×C4×C5C24
hypercenter#2343D5
hypocenterC5#17609
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2343

Complements

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

NH ≅ G/Ntype
2. C5×#2343C2semidirect
3. #10613941C2semidirect
4. #10600359C2semidirect
5. #10600358C2semidirect
6. #10600339C2semidirect
7. #10600337C2semidirect
8. #10600326C2semidirect
10. #10600264C2semidirect
11. #10600263C2semidirect
12. #10600226C2semidirect
13. #10600224C2semidirect
14. C2×#64672C2semidirect
19. #65868C4semidirect
20. #65868C4semidirect
25. #65860C4semidirect
26. #65857C4semidirect
27. #65853C4semidirect
28. #65852C4semidirect
29. #65852C4semidirect
30. #65850C4semidirect
161. #4021C2×C4semidirect
162. #4021C2×C4semidirect
163. C4×D20C2×C4semidirect
164. C4×D20C2×C4semidirect
169. #4016C2×C4semidirect
170. #4016C2×C4semidirect
171. #4015C2×C4semidirect
172. #4015C2×C4semidirect
173. #4015C2×C4semidirect
174. #4015C2×C4semidirect
177. C4×Dic10C2×C4semidirect
178. C4×Dic10C2×C4semidirect
179. C4×Dic10C2×C4semidirect
180. C4×Dic10C2×C4semidirect
181. C4×Dic10C2×C4semidirect
182. C4×Dic10C2×C4semidirect
209. #2343D5semidirect
843. C5#17609semidirect

Maximal subgroups

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

subgroupindex
#106176282
C5×#23432
#106139412
#106003592
#106003582
#106003392
#106003372
#106003262
#106003252
#106002642
#106002632
#106002262
#106002242
C2×#646722
#106001912
#176095