Finite Group Databasebeta

← #12260129

Subgroups — #12260129

Order 1280.

2330 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65934C211yesmaximal, characteristic
2C5×#2364C211yesmaximal, characteristic
3#10614369C211yesmaximal, characteristic
4D4×#683C212yesmaximal, complemented
5C4×#4081C212yesmaximal, complemented
6#10607216C212yesmaximal, complemented
7#10607187C212yesmaximal, complemented
8#10606694C212yesmaximal, complemented
9#10606691C212yesmaximal, complemented
10#10606404C212yesmaximal, complemented
11#10606404C212yesmaximal, complemented
12#10606402C212yesmaximal, complemented
13#10606392C212yesmaximal, complemented
14#10605208C212yesmaximal, complemented
15#10605204C211yesmaximal, characteristic, complemented
16#10605168C211yesmaximal, characteristic, complemented
17#10605166C212yesmaximal, complemented
18#10605070C211yesmaximal, characteristic, complemented
19C2×#64938C211yesmaximal, characteristic, complemented
20C2×C5×#121C2211yescharacteristic
21C2×C4×C5×D4C2212yes—
22C2×#4082C2211yescharacteristic
23C2×#4081C2212yes—
24C2×D4×Dic5C2212yes—
25C2×D4×Dic5C2212yes—
26C2×D4×Dic5C2211yescharacteristic
27C2×#4070C2211yescharacteristic
28C22×#683C2212yes—
29C22×#683C2212yes—
30C22×C4×Dic5C2212yes—
31C22×C4×Dic5C2211yescharacteristic
32#65934C4116yescomplemented
33C2×#4036C2211yescharacteristic
34C2×#4033C2211yescharacteristic
35C2×#4025C2212yes—
36C2×#4023C2212yes—
37C2×#4023C2212yes—
38C5×#388C2212yes—
39C5×#387C2212yes—
40C5×#386C2212yes—
41C5×#386C2212yes—
42C4×C5×C22⋊C4C2212yes—
43C4×C5×C22⋊C4C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45#65509C2212yes—
46#65509C2212yes—
47#65499C2212yes—
48#65499C2212yes—
49C4×C22⋊Dic5C2212yes—
50C4×C22⋊Dic5C2211yescharacteristic
51C4×C22⋊Dic5C2212yes—
52C4×C22⋊Dic5C2212yes—
53C2×#3963C2211yescharacteristic
54#65270C2212yes—
55#65267C2212yes—
56#65267C2212yes—
57#65265C2212yes—
58#65262C2212yes—
59#65240C2212yes—
60#65235C2212yes—
61#65235C2212yes—
62#65234C2212yes—
63#65234C2212yes—
64#65234C2212yes—
65#65233C2212yes—
66#65233C2212yes—
67#65233C2212yes—
68#65232C2211yescharacteristic
69#65232C2211yescharacteristic
70#65231C2211yescharacteristic
71#65231C2212yes—
72#65231C2212yes—
73#65231C2211yescharacteristic
74C22⋊C4×Dic5C2212yes—
75C22⋊C4×Dic5C2212yes—
76C22⋊C4×Dic5C2212yes—
77C22⋊C4×Dic5C2212yes—
78#65222C2212yes—
79#65221C2212yes—
80C4×#683C2212yes—
81C4×#683C2212yes—
82C4×#683C2212yes—
83C4×#683C2212yes—
84C4×#683C2212yes—
85#65217C2212yes—
86#64944C2212yes—
87#64944C2212yes—
88#64943C2212yes—
89#64943C2212yes—
90#64942C2212yes—
91#64942C2212yes—
92#64941C2212yes—
93#64940C2212yes—
94#64939C2212yes—
95#64939C2212yes—
96#64938C2212yes—
97#64938C2212yes—
98#64938C2212yes—
99#64938C2212yes—
100#64938C2212yes—
101#64938C2212yes—
102#64938C2211yescharacteristic
103#64938C2211yescharacteristic
104#64938C2211yescharacteristic
105#64938C2211yescharacteristic
106#64935C2212yes—
107#64935C2212yes—
108#34241—51nomaximal, Sylow
109C22×C5×D4C2312yes—
110C22×C5×D4C2311yescharacteristic
111C23×C4×C5C2312yes—
112C23×C4×C5C2312yes—
113C23×C4×C5C2311yescharacteristic
114C23×Dic5C2312yes—
115C23×Dic5C2312yes—
116C23×Dic5C2311yescharacteristic
117C23×Dic5C2311yescharacteristic
118C23×Dic5C2312yes—
119C22×Dic10C2311yescharacteristic
120C5×#121C2×C418yes—
121C4×C5×D4—44no—
122C2×C5×C4⋊C4C2312yes—
123C2×C5×C4⋊C4C2311yescharacteristic
124C2×C5×C22⋊C4C2312yes—
125C2×C5×C22⋊C4C2311yescharacteristic
126C2×C5×C22⋊C4C2311yescharacteristic
127C2×C5×C22⋊C4C2312yes—
128C2×C5×C22⋊C4C2312yes—
129C2×C5×C22⋊C4C2312yes—
130C2×C42×C5C2312yes—
131C2×C42×C5C2312yes—
132C2×C22⋊Dic5C2312yes—
133C2×C22⋊Dic5C2311yescharacteristic
134C2×C22⋊Dic5C2311yescharacteristic
135C2×C22⋊Dic5C2312yes—
136C2×C22⋊Dic5C2312yes—
137C2×C22⋊Dic5C2312yes—
138C2×C22⋊Dic5C2312yes—
139C2×C22⋊Dic5C2312yes—
140C2×C22⋊Dic5C2312yes—
141#4082C2×C418yescomplemented
142#4081C2×C4116yescomplemented
143D4×Dic5—44no—
144D4×Dic5C2×C4116yescomplemented
145D4×Dic5C2×C418yescomplemented
146C2×C4⋊Dic5C2312yes—
147C2×C4⋊Dic5C2312yes—
148C2×C4⋊Dic5C2311yescharacteristic
149#4070C2×C418yescomplemented
150C2×#683—28no—
151C2×#683—28no—
152C2×#683C2312yes—
153C2×#683C2312yes—
154C2×#683C2312yes—
155C2×#683C2312yes—
156C2×#683C2312yes—
157C2×#683C2312yes—
158C2×#683C2312yes—
159C2×#683C2312yes—
160C2×#683C2312yes—
161C2×#683C2312yes—
162C2×#683C2312yes—
163C2×#683C2312yes—
164C2×#683C2312yes—
165C2×C4×Dic5—44no—
166C2×C4×Dic5C2×C418yescomplemented
167C2×C4×Dic5C2312yes—
168C2×C4×Dic5C2312yes—
169C2×C4×Dic5C2312yes—
170C2×C4×Dic5C2312yes—
171C2×C4×Dic5C2312yes—
172C2×C4×Dic5C2312yes—
173C2×C4×Dic5C2312yes—
174C2×C4×Dic5C2312yes—
175C2×C4×Dic5C2312yes—
176C2×C4×Dic5C2312yes—
177C2×C4×Dic5C2311yescharacteristic
178C2×C4×Dic5C2312yes—
179C2×C4×Dic5C2311yescharacteristic
180C2×C4×Dic5C2311yescharacteristic
181C2×C4×Dic5C2311yescharacteristic
182#4036C2×C418yescomplemented
183#4033C2×C418yescomplemented
184#4025C2×C4116yescomplemented
185#4023—28no—
186#4023C2×C4116yescomplemented
187C5×#95C2311yescharacteristic
188C5×#95C2312yes—
189C5×#95C2311yescharacteristic
190C5×#95C2312yes—
191C5×#95C2312yes—
192C5×#95C2312yes—
193#3963C2312yes—
194#3963C2312yes—
195#3963C2312yes—
196#3963C2312yes—
197#3963C2312yes—
198#3963C2312yes—
199#3963C2311yescharacteristic
200#3963C2311yescharacteristic
201#3963C2312yes—
202#3963C2312yes—
203#3963C2312yes—
204#3963C2312yes—
205#3963C2312yes—
206#3963C2312yes—
207#3963C2312yes—
208#3963C2312yes—
209#3963C2312yes—
210#3963C2312yes—
211#3963C2312yes—
212#3963C2312yes—
213C2×#529—51no—
214#2373—52no—
215#2373—52no—
216#2368—51no—
217#2368—51no—
218#2364—51no—
219#2364D511yescharacteristic
220#2355—52no—
221#2352—52no—
222#2352—52no—
223D4×C4⋊C4—52no—
224#2337—52no—
225#2336—52no—
226#2314—52no—
227C4×#123—52no—
228C4×#123—52no—
229#2283—51no—
230#2274—52no—
231C2×C4×C4⋊C4—51no—
232C24×C5C2412yes—
233C24×C5C2411yescharacteristic
234C2×C5×D4—24no—
235C2×C5×D4—24no—
236C2×C5×D4—42no—
237C2×C5×D4C22×C418yes—
238C2×C5×D4C22×C414yes—
239C22×C4×C5—24no—
240C22×C4×C5—24no—
241C22×C4×C5—24no—
242C22×C4×C5—42no—
243C22×C4×C5—42no—
244C22×C4×C5—42no—
245C22×C4×C5—42no—
246C22×C4×C5C22×C414yes—
247C22×C4×C5C2412yes—
248C22×C4×C5C2412yes—
249C22×C4×C5C2412yes—
250C22×C4×C5C2411yescharacteristic
251C22×C4×C5C2412yes—
252C22×C4×C5C2411yescharacteristic
253C22×C4×C5C2412yes—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5—24no—
257C22×Dic5—24no—
258C22×Dic5—24no—
259C22×Dic5—24no—
260C22×Dic5—24no—
261C22×Dic5—24no—
262C22×Dic5—42no—
263C22×Dic5—42no—
264C22×Dic5—42no—
265C22×Dic5C22×C418yes—
266C22×Dic5C22×C414yes—
267C22×Dic5C22×C414yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C22×Dic5C2411yescharacteristic
273C22×Dic5C2411yescharacteristic
274C22×Dic5C2412yes—
275C22×Dic5C2411yescharacteristic
276C22×Dic5C2412yes—
277C22×Dic5C2411yescharacteristic
278C2×Dic10—42no—
279C2×Dic10C22×C414yes—
280C5×C4⋊C4—42no—
281C5×C4⋊C4C22×C414yes—
282C5×C22⋊C4—22no—
283C5×C22⋊C4—22no—
284C5×C22⋊C4—24no—
285C5×C22⋊C4—42no—
286C5×C22⋊C4—42no—
287C5×C22⋊C4C22×C418yes—
288C42×C5—42no—
289C42×C5—42no—
290C22⋊Dic5—22no—
291C22⋊Dic5—22no—
292C22⋊Dic5—24no—
293C22⋊Dic5—42no—
294C22⋊Dic5—42no—
295C22⋊Dic5C22×C418yes—
296C22⋊Dic5C22×C418yes—
297C22⋊Dic5C22×C418yes—
298C22⋊Dic5C22×C418yes—
299C4⋊Dic5—42no—
300C4⋊Dic5C22×C418yes—
301C4⋊Dic5C22×C414yes—
302#683—24no—
303#683—24no—
304#683—24no—
305#683—24no—
306#683—24no—
307#683—24no—
308#683—24no—
309#683—42no—
310#683—42no—
311#683C22×C418yes—
312#683C22×C418yes—
313#683C22×C418yes—
314#683#4118yes—
315C4×Dic5—24no—
316C4×Dic5—24no—
317C4×Dic5—42no—
318C4×Dic5—42no—
319C4×Dic5—42no—
320C4×Dic5—42no—
321C4×Dic5—42no—
322C4×Dic5—42no—
323C4×Dic5—42no—
324C4×Dic5—42no—
325C4×Dic5C22×C414yes—
326C4×Dic5C22×C418yes—
327C4×Dic5C22×C414yes—
328C4×Dic5C22×C414yes—
329C4×Dic5C22×C414yes—
330#529—516no—
331C2×#126—52no—
332C2×#125—51no—
333C2×#124—51no—
334C2×#123—52no—
335C2×C22⋊Q8—51no—
336C2×#121C2×D511yescharacteristic
337C2×C4×Q8—51no—
338C2×C4×D4—52no—
339C2×C4×D4—51no—
340C2×C4×D4—52no—
341C2×C4×D4C2×D512yes—
342C2×#117—52no—
343C2×#117—52no—
344C22×C4⋊C4—52no—
345C22×C4⋊C4—52no—
346C22×C42—51no—
347C22×C42—52no—
348#391—52no—
349#391—52no—
350#389—52no—
351#389—52no—
352#388—52no—
353#388—52no—
354#388—52no—
355#388—52no—
356#388—52no—
357#388—52no—
358#388—52no—
359#388C2×D512yes—
360#387—52no—
361#387—52no—
362#387—52no—
363#387—52no—
364#387—52no—
365#387—52no—
366#387—52no—
367#387—52no—
368#387—52no—
369#387—52no—
370#387—52no—
371#387C2×D512yes—
372#386—52no—
373#386—52no—
374#386C2×D512yes—
375#386C2×D512yes—
376#385—52no—
377#385—52no—
378#385—52no—
379#385—52no—
380#384—52no—
381#383—52no—
382#382—52no—
383#382—52no—
384#381—51no—
385#381—51no—
386#380—52no—
387#380—52no—
388#380—51no—
389#380—51no—
390C4×C4⋊C4—52no—
391C4×C4⋊C4—52no—
392C4×C4⋊C4—52no—
393C4×C4⋊C4—52no—
394C4×C4⋊C4—52no—
395C4×C4⋊C4—51no—
396C4×C4⋊C4—52no—
397C4×C4⋊C4—52no—
398C4×C4⋊C4—52no—
399C4×C4⋊C4—52no—
400C4×C4⋊C4—52no—
401C4×C4⋊C4—52no—
402C4×C4⋊C4—51no—
403C4×C4⋊C4—51no—
404C4×C4⋊C4—51no—
405C4×C22⋊C4—52no—
406C4×C22⋊C4—52no—
407C4×C22⋊C4—52no—
408C4×C22⋊C4—51no—
409C4×C22⋊C4—52no—
410C4×C22⋊C4—52no—
411C4×C22⋊C4—52no—
412C4×C22⋊C4—52no—
413C4×C22⋊C4C2×D511yescharacteristic
414C4×C22⋊C4C2×D512yes—
415#376—52no—
416C2×#95—51no—
417C2×#95C2×D511yescharacteristic
418C23×C5—22no—
419C23×C5—22no—
420C23×C5—22no—
421C23×C5—22no—
422C23×C5—22no—
423C23×C5—22no—
424C23×C5—22no—
425C23×C5—22no—
426C23×C5C23×C414yes—
427C23×C5C23×C412yes—
428C23×C5H(5,𝔽2)12yes—
429C23×C52−1+412yes—
430C23×C5C2511yescharacteristic
431C5×D4—216no—
432C5×D4—44no—
433C2×C4×C5—22no—
434C2×C4×C5—22no—
435C2×C4×C5—22no—
436C2×C4×C5—22no—
437C2×C4×C5—22no—
438C2×C4×C5—22no—
439C2×C4×C5—22no—
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5—22no—
443C2×C4×C5—22no—
444C2×C4×C5—22no—
445C2×C4×C5—22no—
446C2×C4×C5—22no—
447C2×C4×C5—22no—
448C2×C4×C5—44no—
449C2×C4×C5—48no—
450C2×C4×C5—84no—
451C2×C4×C5C23×C412yes—
452C2×C4×C5C23×C412yes—
453C2×C4×C5C23×C414yes—
454C2×C4×C5C2×#4114yes—
455C2×Dic5—28no—
456C2×Dic5—22no—
457C2×Dic5—22no—
458C2×Dic5—22no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—22no—
462C2×Dic5—21no—
463C2×Dic5—21no—
464C2×Dic5—22no—
465C2×Dic5—22no—
466C2×Dic5—22no—
467C2×Dic5—28no—
468C2×Dic5—216no—
469C2×Dic5—22no—
470C2×Dic5—22no—
471C2×Dic5—22no—
472C2×Dic5—22no—
473C2×Dic5—22no—
474C2×Dic5—22no—
475C2×Dic5—22no—
476C2×Dic5—22no—
477C2×Dic5—22no—
478C2×Dic5—48no—
479C2×Dic5—84no—
480C2×Dic5C23×C412yes—
481C2×Dic5C23×C412yes—
482C2×Dic5C23×C412yes—
483C2×Dic5C23×C414yes—
484C2×Dic5C23×C414yes—
485C2×Dic5C23×C412yes—
486C2×Dic5C2×#4114yes—
487C2×Dic5C2×#4114yes—
488Dic10—44no—
489C22×Q8—51no—
490C22×D4C22×D512yes—
491C22×D4C22×D511yescharacteristic
492C23×C4—51no—
493C23×C4—52no—
494C23×C4—51no—
495C23×C4—52no—
496C23×C4—52no—
497C23×C4C22×D512yes—
498C23×C4C22×D512yes—
499C23×C4C22×D511yescharacteristic
500#126—516no—
501#125—58no—
502#124—58no—
503#123—516no—
504C22⋊Q8—58no—
505#121C4×D518yes—
506C4×Q8—58no—
507C4×D4—44no—
508C4×D4—58no—
509C4×D4—516no—
510C4×D4—204no—
511#117—516no—
512#117—108no—
513C2×C4⋊C4—52no—
514C2×C4⋊C4—52no—
515C2×C4⋊C4—52no—
516C2×C4⋊C4—51no—
517C2×C4⋊C4—52no—
518C2×C4⋊C4—52no—
519C2×C4⋊C4—52no—
520C2×C4⋊C4—52no—
521C2×C4⋊C4—52no—
522C2×C4⋊C4—52no—
523C2×C4⋊C4—52no—
524C2×C4⋊C4—52no—
525C2×C4⋊C4—52no—
526C2×C4⋊C4—52no—
527C2×C4⋊C4—52no—
528C2×C4⋊C4—52no—
529C2×C4⋊C4—108no—
530C2×C4⋊C4—108no—
531C2×C4⋊C4C22×D512yes—
532C2×C4⋊C4C22×D511yescharacteristic
533C2×C22⋊C4—52no—
534C2×C22⋊C4—52no—
535C2×C22⋊C4—52no—
536C2×C22⋊C4—52no—
537C2×C22⋊C4—52no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—51no—
540C2×C22⋊C4—52no—
541C2×C22⋊C4—52no—
542C2×C22⋊C4C22×D512yes—
543C2×C22⋊C4C22×D511yescharacteristic
544C2×C22⋊C4C22×D511yescharacteristic
545C2×C22⋊C4C22×D512yes—
546C2×C22⋊C4C22×D512yes—
547C2×C22⋊C4C22×D512yes—
548C2×C42—58no—
549C2×C42—51no—
550C2×C42—52no—
551C2×C42—51no—
552C2×C42—51no—
553C2×C42—51no—
554C2×C42—52no—
555C2×C42—52no—
556C2×C42—52no—
557C2×C42—52no—
558C2×C42—52no—
559C2×C42—52no—
560C2×C42—52no—
561C2×C42—52no—
562C2×C42—52no—
563C2×C42—52no—
564C2×C42—204no—
565C2×C42C22×D512yes—
566C2×C42C22×D512yes—
567#95—51no—
568#95—52no—
569#95—51no—
570#95—52no—
571#95—52no—
572#95—52no—
573#95—52no—
574#95—52no—
575#95—52no—
576#95—52no—
577#95—52no—
578#95—52no—
579#95—52no—
580#95—52no—
581#95—52no—
582#95—52no—
583#95—52no—
584#95—52no—
585#95—52no—
586#95—52no—
587#95C22×D511yescharacteristic
588#95C22×D512yes—
589#95C22×D511yescharacteristic
590#95C22×D512yes—
591#95C22×D512yes—
592#95C22×D512yes—
593C22×C5—22no—
594C22×C5—22no—
595C22×C5—24no—
596C22×C5—24no—
597C22×C5—24no—
598C22×C5—24no—
599C22×C5—24no—
600C22×C5—42no—
601C22×C5—42no—
602C22×C5—42no—
603C22×C5—42no—
604C22×C5#52014yes—
605C22×C5C24×C411yescharacteristic
606C22×C5C22×#4112yes—
607C22×C5C2×H(5,𝔽2)11yescharacteristic
608C22×C5C2×2−1+411yescharacteristic
609C22×C5#58512yes—
610C4×C5—24no—
611C4×C5—22no—
612C4×C5—22no—
613C4×C5—24no—
614C4×C5—42no—
615C4×C5—42no—
616C4×C5—42no—
617Dic5—24no—
618Dic5—22no—
619Dic5—22no—
620Dic5—22no—
621Dic5—24no—
622Dic5—24no—
623Dic5—42no—
624Dic5—42no—
625Dic5—42no—
626Dic5C4×#4114yes—
627C24C23×D512yes—
628C24C23×D511yescharacteristic
629C2×Q8—54no—
630C2×Q8—202no—
631C2×D4—24no—
632C2×D4—24no—
633C2×D4—42no—
634C2×D4C2×C4×D518yes—
635C2×D4C2×C4×D514yes—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—51no—
644C22×C4—54no—
645C22×C4—54no—
646C22×C4—58no—
647C22×C4—51no—
648C22×C4—51no—
649C22×C4—52no—
650C22×C4—52no—
651C22×C4—51no—
652C22×C4—52no—
653C22×C4—52no—
654C22×C4—52no—
655C22×C4—52no—
656C22×C4—104no—
657C22×C4—104no—
658C22×C4—104no—
659C22×C4—104no—
660C22×C4—104no—
661C22×C4—102no—
662C22×C4—102no—
663C22×C4—104no—
664C22×C4—202no—
665C22×C4—202no—
666C22×C4—202no—
667C22×C4C2×C4×D514yes—
668C22×C4C23×D512yes—
669C22×C4C23×D512yes—
670C22×C4C23×D512yes—
671C22×C4C23×D511yescharacteristic
672C22×C4C23×D511yescharacteristic
673C22×C4C23×D512yes—
674C22×C4C23×D512yes—
675C4⋊C4—42no—
676C4⋊C4—58no—
677C4⋊C4—58no—
678C4⋊C4—54no—
679C4⋊C4—58no—
680C4⋊C4—58no—
681C4⋊C4—58no—
682C4⋊C4—104no—
683C4⋊C4—104no—
684C4⋊C4—104no—
685C4⋊C4—104no—
686C4⋊C4—104no—
687C4⋊C4—104no—
688C4⋊C4—104no—
689C4⋊C4—202no—
690C4⋊C4—202no—
691C4⋊C4—202no—
692C4⋊C4C2×C4×D514yes—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—58no—
699C22⋊C4—58no—
700C22⋊C4—58no—
701C22⋊C4—58no—
702C22⋊C4—104no—
703C22⋊C4—102no—
704C22⋊C4—102no—
705C22⋊C4—202no—
706C22⋊C4—202no—
707C22⋊C4C2×C4×D518yes—
708C42—42no—
709C42—42no—
710C42—54no—
711C42—54no—
712C42—54no—
713C42—54no—
714C42—58no—
715C42—104no—
716C42—104no—
717C42—202no—
718C42—202no—
719C42—202no—
720C42—202no—
721C42—202no—
722C42—202no—
723C42—202no—
724C42—202no—
725C2×C5—24no—
726C2×C5—44no—
727C2×C5C2×C4×#4111yescharacteristic
728C2×C5C2×#52011yescharacteristic
729C2×C5#342811yescharacteristic
730C2×C5#351312yes—
731C2×C5#351612yes—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23C22×C4×D514yes—
741C23C22×C4×D512yes—
742C23#414412yes—
743C23#415012yes—
744C23C24×D511yescharacteristic
745Q8—204no—
746D4—216no—
747D4—44no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—44no—
764C2×C4—48no—
765C2×C4—52no—
766C2×C4—54no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—52no—
770C2×C4—54no—
771C2×C4—54no—
772C2×C4—54no—
773C2×C4—84no—
774C2×C4—108no—
775C2×C4—1016no—
776C2×C4—108no—
777C2×C4—101no—
778C2×C4—101no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—102no—
782C2×C4—102no—
783C2×C4—101no—
784C2×C4—101no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—102no—
791C2×C4—102no—
792C2×C4—102no—
793C2×C4—102no—
794C2×C4—102no—
795C2×C4—102no—
796C2×C4—102no—
797C2×C4—208no—
798C2×C4—404no—
799C2×C4C22×C4×D512yes—
800C2×C4C22×C4×D512yes—
801C2×C4C22×C4×D514yes—
802C2×C4D5×#4114yes—
803C5#3424111yescharacteristic, complemented, Sylow
804C22—22no—
805C22—22no—
806C22—24no—
807C22—24no—
808C22—24no—
809C22—24no—
810C22—24no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22#6588014yes—
816C22C23×C4×D511yescharacteristic
817C22C2×#414411yescharacteristic
818C22C2×D5×#4112yes—
819C22C2×#415011yescharacteristic
820C22#6628512yes—
821C4—24no—
822C4—22no—
823C4—22no—
824C4—24no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—54no—
829C4—102no—
830C4—102no—
831C4—102no—
832C4—104no—
833C4—104no—
834C4—104no—
835C4—202no—
836C4—202no—
837C4—202no—
838C2—24no—
839C2—44no—
840C2C2×#6588011yescharacteristic
841C2C4×D5×#4111yescharacteristic
842C2#1061775711yescharacteristic
843C2#1061853612yes—
844C2#1061878612yes—
subgroupG/H
center, FrattiniC23C24×D5
commutatorC22×C5C24×C4
FittingC5×#2364C2
socle, cosocleC23×C5C25
prime radicalC2×C5×#121C22
hypercenter#2364D5
hypocenterC5#34241
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2364

Complements

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

NH ≅ G/Ntype
4. D4×#683C2semidirect
5. C4×#4081C2semidirect
6. #10607216C2semidirect
7. #10607187C2semidirect
8. #10606694C2semidirect
9. #10606691C2semidirect
10. #10606404C2semidirect
11. #10606404C2semidirect
12. #10606402C2semidirect
13. #10606392C2semidirect
14. #10605208C2semidirect
15. #10605204C2semidirect
16. #10605168C2semidirect
17. #10605166C2semidirect
18. #10605070C2semidirect
19. C2×#64938C2semidirect
32. #65934C4semidirect
141. #4082C2×C4semidirect
142. #4081C2×C4semidirect
144. D4×Dic5C2×C4semidirect
145. D4×Dic5C2×C4semidirect
149. #4070C2×C4semidirect
166. C2×C4×Dic5C2×C4semidirect
182. #4036C2×C4semidirect
183. #4033C2×C4semidirect
184. #4025C2×C4semidirect
186. #4023C2×C4semidirect
803. C5#34241semidirect

Maximal subgroups

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

subgroupindex
C2×#659342
C5×#23642
#106143692
D4×#6832
C4×#40812
#106072162
#106071872
#106066942
#106066912
#106064042
#106064022
#106063922
#106052082
#106052042
#106051682
#106051662
#106050702
C2×#649382
#342415