Finite Group Databasebeta

← #12270709

Subgroups — #12270709

Order 1280.

2062 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2388C211yesmaximal, characteristic
2#10615817C212yesmaximal, complemented
3#10614079C211yesmaximal, characteristic, complemented
4#10614077C212yesmaximal, complemented
5C4×#4081C211yesmaximal, characteristic, complemented
6C4×D4×Dic5C212yesmaximal, complemented
7#10608926C212yesmaximal, complemented
8#10608691C212yesmaximal, complemented
9#10608689C212yesmaximal, complemented
10#10608685C212yesmaximal, complemented
11#10608538C211yesmaximal, characteristic, complemented
12#10608525C211yesmaximal, characteristic, complemented
13#10608425C212yesmaximal, complemented
14#10608424C211yesmaximal, characteristic, complemented
15#10608415C212yesmaximal, complemented
16#10608412C211yesmaximal, characteristic, complemented
17C4×#4025C212yesmaximal, complemented
18C4×#4024C212yesmaximal, complemented
19#10605171C212yesmaximal, complemented
20C22×C5×#41C2211yescharacteristic
21C2×C4×C5×D4C2212yes—
22C2×C4×C5×D4C2211yescharacteristic
23C2×#4081C2211yescharacteristic
24C2×D4×Dic5C2212yes—
25C2×D4×Dic5C2212yes—
26C2×#4072C2212yes—
27C22×C4×Dic5C2212yes—
28C22×C4×Dic5C2211yescharacteristic
29C2×#4025C2212yes—
30C2×#4024C2212yes—
31C2×C4×Dic10C2211yescharacteristic
32C5×#395C2211yescharacteristic
33C5×#394C2212yes—
34C5×#394C2211yescharacteristic
35C5×#393C2211yescharacteristic
36C5×#392C2211yescharacteristic
37C5×#392C2212yes—
38C4×C5×C22⋊C4C2212yes—
39C4×C5×C22⋊C4C2211yescharacteristic
40#65519C2212yes—
41#65519C2212yes—
42#65511C2212yes—
43#65511C2212yes—
44#65511C2212yes—
45#65510C2212yes—
46#65510C2212yes—
47#65509C2212yes—
48#65509C2212yes—
49#65509C2212yes—
50#65509C2212yes—
51#65509C2211yescharacteristic
52C4×C22⋊Dic5C2212yes—
53C4×C22⋊Dic5C2212yes—
54C4×C22⋊Dic5C2212yes—
55C4×C22⋊Dic5C2212yes—
56C4×C22⋊Dic5C2212yes—
57C4×C22⋊Dic5C2211yescharacteristic
58#65275C2212yes—
59#65272C2212yes—
60#65271C2212yes—
61#65267C2212yes—
62C4⋊C4×Dic5C2212yes—
63C4⋊C4×Dic5C2212yes—
64#65242C2211yescharacteristic
65#65242C2212yes—
66#65242C2211yescharacteristic
67#65241C2212yes—
68#65241C2212yes—
69#65240C2212yes—
70#65239C2212yes—
71#65238C2212yes—
72#65236C2211yescharacteristic
73#65236C2211yescharacteristic
74#65235C2211yescharacteristic
75#65235C2212yes—
76#65234C2212yes—
77#65234C2212yes—
78#65234C2212yes—
79#65233C2212yes—
80#65233C2212yes—
81#65233C2212yes—
82#65233C2212yes—
83#65232C2211yescharacteristic
84#65231C2212yes—
85C22⋊C4×Dic5C2212yes—
86C22⋊C4×Dic5C2212yes—
87C22⋊C4×Dic5C2212yes—
88C22⋊C4×Dic5C2212yes—
89C4×C4⋊Dic5C2212yes—
90#65221C2211yescharacteristic
91C4×#683C2212yes—
92C4×#683C2212yes—
93C4×#683C2212yes—
94C42×Dic5C2212yes—
95#64944C2212yes—
96#64944C2212yes—
97#64943C2212yes—
98#64943C2212yes—
99#64943C2212yes—
100#64942C2212yes—
101#64942C2212yes—
102#64942C2212yes—
103#64941C2212yes—
104#64940C2212yes—
105#64936C2212yes—
106#64935C2212yes—
107#34906—51nomaximal, Sylow
108C2×C5×#41—28no—
109C2×C5×#41—42no—
110C22×C5×Q8C2311yescharacteristic
111C22×C5×D4C2312yes—
112C22×C5×D4C2311yescharacteristic
113C22×C5×D4C2312yes—
114C22×C5×D4C2311yescharacteristic
115C23×C4×C5C2311yescharacteristic
116C23×C4×C5C2311yescharacteristic
117C23×C4×C5C2312yes—
118C23×Dic5C2312yes—
119C23×Dic5C2311yescharacteristic
120C23×Dic5C2312yes—
121C23×Dic5C2311yescharacteristic
122C22×Dic10C2311yescharacteristic
123C4×C5×D4—28no—
124C4×C5×D4—42no—
125C2×C5×C4⋊C4C2312yes—
126C2×C5×C4⋊C4C2311yescharacteristic
127C2×C5×C22⋊C4C2312yes—
128C2×C5×C22⋊C4C2312yes—
129C2×C5×C22⋊C4C2312yes—
130C2×C5×C22⋊C4C2312yes—
131C2×C5×C22⋊C4C2312yes—
132C2×C5×C22⋊C4C2311yescharacteristic
133C2×C5×C22⋊C4C2311yescharacteristic
134C2×C42×C5C2311yescharacteristic
135C2×C42×C5C2312yes—
136C2×C22⋊Dic5C2312yes—
137C2×C22⋊Dic5C2312yes—
138C2×C22⋊Dic5C2312yes—
139C2×C22⋊Dic5C2312yes—
140C2×C22⋊Dic5C2312yes—
141C2×C22⋊Dic5C2312yes—
142C2×C22⋊Dic5C2312yes—
143C2×C22⋊Dic5C2312yes—
144C2×C22⋊Dic5C2312yes—
145C2×C22⋊Dic5C2312yes—
146C2×C22⋊Dic5C2311yescharacteristic
147C2×C22⋊Dic5C2312yes—
148C2×C22⋊Dic5C2311yescharacteristic
149C2×C22⋊Dic5C2312yes—
150#4081—24no—
151D4×Dic5—28no—
152D4×Dic5—28no—
153#4072—28no—
154C2×C4⋊Dic5C2312yes—
155C2×C4⋊Dic5C2312yes—
156C2×C4⋊Dic5C2312yes—
157C2×C4⋊Dic5C2311yescharacteristic
158C2×C4⋊Dic5C2312yes—
159C2×#683C2312yes—
160C2×#683C2312yes—
161C2×#683C2312yes—
162C2×#683C2312yes—
163C2×#683C2312yes—
164C2×#683C2312yes—
165C2×#683C2312yes—
166C2×C4×Dic5—44no—
167C2×C4×Dic5—42no—
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×Dic5C2312yes—
178C2×C4×Dic5C2312yes—
179#4025—28no—
180#4024—28no—
181C4×Dic10—42no—
182C5×#95C2312yes—
183C5×#95C2311yescharacteristic
184C5×#95C2312yes—
185C5×#95C2311yescharacteristic
186#3963C2312yes—
187#3963C2312yes—
188#3963C2312yes—
189#3963C2312yes—
190#3963C2312yes—
191#3963C2312yes—
192#3963C2312yes—
193#3963C2312yes—
194#3963C2312yes—
195#3963C2312yes—
196#3963C2312yes—
197#3963C2311yescharacteristic
198#3963C2312yes—
199#3963C2312yes—
200#3963C2312yes—
201#3963C2312yes—
202#3963C2312yes—
203#3963C2311yescharacteristic
204#3963C2312yes—
205#3963C2312yes—
206#3963C2312yes—
207#3963C2312yes—
208#2607—51no—
209#2602—52no—
210#2600—51no—
211#2595—52no—
212#2588—52no—
213#2578—52no—
214#2560—52no—
215#2523—51no—
216#2467—52no—
217#2463—51no—
218#2398—51no—
219#2395—52no—
220#2388D511yescharacteristic
221C4×#126—52no—
222C4×C22⋊Q8—52no—
223C4×#123—51no—
224#2298—52no—
225#2297—52no—
226C42×D4—52no—
227C24×C5C2411yescharacteristic
228C24×C5C2412yes—
229C24×C5C2411yescharacteristic
230C5×#41—416no—
231C2×C5×Q8—24no—
232C2×C5×Q8—41no—
233C2×C5×D4—24no—
234C2×C5×D4—24no—
235C2×C5×D4—24no—
236C2×C5×D4—24no—
237C2×C5×D4—22no—
238C2×C5×D4—24no—
239C2×C5×D4—24no—
240C2×C5×D4—41no—
241C2×C5×D4—41no—
242C2×C5×D4—42no—
243C2×C5×D4—41no—
244C22×C4×C5—24no—
245C22×C4×C5—24no—
246C22×C4×C5—24no—
247C22×C4×C5—24no—
248C22×C4×C5—22no—
249C22×C4×C5—22no—
250C22×C4×C5#4118yes—
251C22×C4×C5C2411yescharacteristic
252C22×C4×C5C2412yes—
253C22×C4×C5C2411yescharacteristic
254C22×C4×C5C2411yescharacteristic
255C22×C4×C5C2411yescharacteristic
256C22×C4×C5C2412yes—
257C22×C4×C5C2412yes—
258C22×C4×C5C2411yescharacteristic
259C22×Dic5—24no—
260C22×Dic5—24no—
261C22×Dic5—24no—
262C22×Dic5—24no—
263C22×Dic5—41no—
264C22×Dic5—42no—
265C22×Dic5—41no—
266C22×Dic5—41no—
267C22×Dic5—42no—
268C22×Dic5—42no—
269C22×Dic5#4114yescomplemented
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C22×Dic5C2412yes—
273C22×Dic5C2412yes—
274C22×Dic5C2412yes—
275C22×Dic5C2412yes—
276C22×Dic5C2412yes—
277C22×Dic5C2412yes—
278C2×Dic10—24no—
279C2×Dic10—41no—
280C5×C4⋊C4—24no—
281C5×C4⋊C4—41no—
282C5×C22⋊C4—24no—
283C5×C22⋊C4—24no—
284C5×C22⋊C4—24no—
285C5×C22⋊C4—24no—
286C5×C22⋊C4—42no—
287C5×C22⋊C4—41no—
288C5×C22⋊C4—41no—
289C42×C5—24no—
290C42×C5—22no—
291C22⋊Dic5—24no—
292C22⋊Dic5—24no—
293C22⋊Dic5—24no—
294C22⋊Dic5—22no—
295C22⋊Dic5—24no—
296C22⋊Dic5—24no—
297C22⋊Dic5—24no—
298C22⋊Dic5—24no—
299C22⋊Dic5—24no—
300C22⋊Dic5—24no—
301C22⋊Dic5—24no—
302C22⋊Dic5—42no—
303C22⋊Dic5—41no—
304C22⋊Dic5—42no—
305C4⋊Dic5—24no—
306C4⋊Dic5—24no—
307C4⋊Dic5—24no—
308C4⋊Dic5—41no—
309C4⋊Dic5#4118yescomplemented
310#683—24no—
311#683—24no—
312#683—24no—
313#683—24no—
314#683—24no—
315#683—42no—
316#683—42no—
317C4×Dic5—24no—
318C4×Dic5—24no—
319C4×Dic5—24no—
320C4×Dic5—24no—
321C4×Dic5—24no—
322C4×Dic5—24no—
323C4×Dic5—24no—
324C4×Dic5—42no—
325C4×Dic5—42no—
326C4×Dic5—42no—
327C4×Dic5—42no—
328C22×#41C2×D511yescharacteristic
329C2×#126—52no—
330C2×#123—51no—
331C2×C22⋊Q8—52no—
332C2×C4×Q8—51no—
333C2×C4×D4—52no—
334C2×C4×D4—52no—
335C2×C4×D4C2×D512yes—
336C2×C4×D4C2×D511yescharacteristic
337C2×#117—52no—
338C22×C42—51no—
339C22×C42—52no—
340#400—52no—
341#400—52no—
342#399—52no—
343#398—52no—
344#397—52no—
345#397—52no—
346#397—51no—
347#397—51no—
348#397—52no—
349#395C2×D511yescharacteristic
350#394—52no—
351#394—52no—
352#394—52no—
353#394C2×D512yes—
354#394C2×D511yescharacteristic
355#393—51no—
356#393—51no—
357#393C2×D511yescharacteristic
358#392C2×D511yescharacteristic
359#392C2×D512yes—
360#391—52no—
361#391—52no—
362#391—52no—
363#390—52no—
364#390—52no—
365#389—52no—
366#388—52no—
367#388—52no—
368#388—52no—
369#388—52no—
370#388—52no—
371#388—52no—
372#388—52no—
373#388—52no—
374#387—52no—
375#387—52no—
376#387—52no—
377#387—52no—
378#387—52no—
379#387—52no—
380#387—52no—
381#387—52no—
382#387—52no—
383#387—52no—
384#386—52no—
385#386—52no—
386#386—52no—
387#386—52no—
388#386—51no—
389#385—52no—
390#385—52no—
391#385—51no—
392#383—52no—
393#381—51no—
394#380—52no—
395C4×C4⋊C4—52no—
396C4×C4⋊C4—52no—
397C4×C4⋊C4—52no—
398C4×C4⋊C4—52no—
399C4×C4⋊C4—52no—
400C4×C4⋊C4—52no—
401C4×C22⋊C4—52no—
402C4×C22⋊C4—52no—
403C4×C22⋊C4—51no—
404C4×C22⋊C4—52no—
405C4×C22⋊C4—52no—
406C4×C22⋊C4—52no—
407C4×C22⋊C4—52no—
408C4×C22⋊C4—52no—
409C4×C22⋊C4—52no—
410C4×C22⋊C4—52no—
411C4×C22⋊C4C2×D511yescharacteristic
412C4×C22⋊C4C2×D512yes—
413#376—51no—
414C43—52no—
415C23×C5—22no—
416C23×C5—22no—
417C23×C5—22no—
418C23×C5—22no—
419C23×C5—22no—
420C23×C5—22no—
421C23×C5—21no—
422C23×C5—22no—
423C23×C5—22no—
424C23×C5—21no—
425C23×C5—22no—
426C23×C5—21no—
427C23×C5—22no—
428C23×C5—21no—
429C23×C5—21no—
430C23×C5C2×#4114yes—
431C23×C5C2×#4112yes—
432C23×C5C2511yescharacteristic
433C5×Q8—44no—
434C5×D4—216no—
435C5×D4—48no—
436C5×D4—44no—
437C5×D4—44no—
438C2×C4×C5—22no—
439C2×C4×C5—22no—
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5—216no—
443C2×C4×C5—22no—
444C2×C4×C5—21no—
445C2×C4×C5—22no—
446C2×C4×C5—22no—
447C2×C4×C5—22no—
448C2×C4×C5—22no—
449C2×C4×C5—21no—
450C2×C4×C5—21no—
451C2×C4×C5—21no—
452C2×C4×C5—21no—
453C2×C4×C5—22no—
454C2×C4×C5—21no—
455C2×C4×C5—44no—
456C2×C4×C5—44no—
457C2×C4×C5C2×#4114yes—
458C2×C4×C5C2×#4114yes—
459C2×C4×C5C2×#4114yes—
460C2×C4×C5H(5,𝔽2)12yes—
461C2×Dic5—22no—
462C2×Dic5—22no—
463C2×Dic5—22no—
464C2×Dic5—22no—
465C2×Dic5—22no—
466C2×Dic5—22no—
467C2×Dic5—22no—
468C2×Dic5—22no—
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—22no—
479C2×Dic5—22no—
480C2×Dic5—22no—
481C2×Dic5—22no—
482C2×Dic5—44no—
483C2×Dic5—48no—
484C2×Dic5—44no—
485C2×Dic5—48no—
486C2×Dic5C2×#4114yes—
487C2×Dic5C2×#4114yes—
488C2×Dic5C2×#4114yes—
489Dic10—44no—
490C2×#41—28no—
491C2×#41—42no—
492C22×Q8—51no—
493C22×Q8C22×D511yescharacteristic
494C22×D4C22×D512yes—
495C22×D4C22×D511yescharacteristic
496C22×D4C22×D512yes—
497C22×D4C22×D511yescharacteristic
498C23×C4—51no—
499C23×C4—51no—
500C23×C4—52no—
501C23×C4—52no—
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D512yes—
505#126—108no—
506#123—104no—
507C22⋊Q8—108no—
508C4×Q8—202no—
509C4×D4—28no—
510C4×D4—42no—
511C4×D4—108no—
512C4×D4—108no—
513#117—108no—
514C2×C4⋊C4—52no—
515C2×C4⋊C4—52no—
516C2×C4⋊C4—52no—
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—51no—
525C2×C4⋊C4—52no—
526C2×C4⋊C4C22×D512yes—
527C2×C4⋊C4C22×D511yescharacteristic
528C2×C22⋊C4—52no—
529C2×C22⋊C4—52no—
530C2×C22⋊C4—52no—
531C2×C22⋊C4—52no—
532C2×C22⋊C4—52no—
533C2×C22⋊C4—52no—
534C2×C22⋊C4—52no—
535C2×C22⋊C4—51no—
536C2×C22⋊C4—52no—
537C2×C22⋊C4—52no—
538C2×C22⋊C4—52no—
539C2×C22⋊C4—52no—
540C2×C22⋊C4—51no—
541C2×C22⋊C4—52no—
542C2×C22⋊C4C22×D512yes—
543C2×C22⋊C4C22×D512yes—
544C2×C22⋊C4C22×D512yes—
545C2×C22⋊C4C22×D512yes—
546C2×C22⋊C4C22×D511yescharacteristic
547C2×C22⋊C4C22×D511yescharacteristic
548C2×C22⋊C4C22×D512yes—
549C2×C42—52no—
550C2×C42—52no—
551C2×C42—52no—
552C2×C42—52no—
553C2×C42—52no—
554C2×C42—52no—
555C2×C42—52no—
556C2×C42—52no—
557C2×C42—52no—
558C2×C42—52no—
559C2×C42—52no—
560C2×C42—202no—
561C2×C42—204no—
562C2×C42C22×D511yescharacteristic
563C2×C42C22×D512yes—
564#95—51no—
565#95—51no—
566#95—52no—
567#95—52no—
568#95—52no—
569#95—52no—
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#95C22×D511yescharacteristic
587#95C22×D511yescharacteristic
588#95C22×D512yes—
589#95C22×D512yes—
590C22×C5—24no—
591C22×C5—24no—
592C22×C5—22no—
593C22×C5—24no—
594C22×C5—24no—
595C22×C5—42no—
596C22×C5—42no—
597C22×C5—41no—
598C22×C5—42no—
599C22×C5—42no—
600C22×C5—42no—
601C22×C5—41no—
602C22×C5—42no—
603C22×C5—41no—
604C22×C5—41no—
605C22×C5—42no—
606C22×C5—41no—
607C22×C5C22×#4112yes—
608C22×C5C22×#4111yescharacteristic
609C22×C5C22×#4112yes—
610C22×C5C2×H(5,𝔽2)11yescharacteristic
611C22×C5#58511yescharacteristic
612C4×C5—24no—
613C4×C5—24no—
614C4×C5—41no—
615C4×C5—41no—
616C4×C5—41no—
617C4×C5—42no—
618C4×C5—41no—
619C4×C5#55114yes—
620Dic5—24no—
621Dic5—24no—
622Dic5—24no—
623Dic5—42no—
624Dic5—42no—
625Dic5—42no—
626Dic5—42no—
627Dic5—42no—
628C24C23×D511yescharacteristic
629C24C23×D512yes—
630C24C23×D511yescharacteristic
631#41—416no—
632C2×Q8—24no—
633C2×Q8—41no—
634C2×Q8—104no—
635C2×Q8—201no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—22no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—41no—
644C2×D4—42no—
645C2×D4—41no—
646C2×D4—41no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—52no—
654C22×C4—52no—
655C22×C4—52no—
656C22×C4—54no—
657C22×C4—52no—
658C22×C4—52no—
659C22×C4—52no—
660C22×C4—52no—
661C22×C4—52no—
662C22×C4—104no—
663C22×C4—104no—
664C22×C4—104no—
665C22×C4—104no—
666C22×C4—201no—
667C22×C4—201no—
668C22×C4—202no—
669C22×C4—202no—
670C22×C4—201no—
671C22×C4—202no—
672C22×C4#71118yes—
673C22×C4C23×D511yescharacteristic
674C22×C4C23×D511yescharacteristic
675C22×C4C23×D512yes—
676C22×C4C23×D511yescharacteristic
677C22×C4C23×D511yescharacteristic
678C22×C4C23×D512yes—
679C22×C4C23×D512yes—
680C22×C4C23×D511yescharacteristic
681C4⋊C4—24no—
682C4⋊C4—41no—
683C4⋊C4—58no—
684C4⋊C4—104no—
685C4⋊C4—104no—
686C4⋊C4—104no—
687C4⋊C4—104no—
688C4⋊C4—104no—
689C4⋊C4—104no—
690C4⋊C4—104no—
691C4⋊C4—104no—
692C4⋊C4—202no—
693C4⋊C4—201no—
694C4⋊C4—202no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—42no—
702C22⋊C4—104no—
703C22⋊C4—104no—
704C22⋊C4—104no—
705C22⋊C4—104no—
706C22⋊C4—104no—
707C22⋊C4—104no—
708C22⋊C4—104no—
709C22⋊C4—104no—
710C22⋊C4—104no—
711C22⋊C4—104no—
712C22⋊C4—102no—
713C22⋊C4—202no—
714C22⋊C4—201no—
715C22⋊C4—202no—
716C42—24no—
717C42—22no—
718C42—104no—
719C42—104no—
720C42—104no—
721C42—104no—
722C42—104no—
723C42—104no—
724C42—104no—
725C42—202no—
726C42—202no—
727C42—202no—
728C42—202no—
729C2×C5—42no—
730C2×C5—44no—
731C2×C5—81no—
732C2×C5#344412yes—
733C2×C5#345911yescharacteristic
734C2×C5C2×#55111yescharacteristic
735C2×C5#348012yes—
736C2×C5#348111yescharacteristic
737C23—22no—
738C23—22no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—21no—
747C23—22no—
748C23—21no—
749C23—22no—
750C23—21no—
751C23—21no—
752C23C2×#71114yes—
753C23D5×#4112yes—
754C23C24×D511yescharacteristic
755Q8—44no—
756Q8—204no—
757D4—216no—
758D4—48no—
759D4—44no—
760D4—44no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—216no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—54no—
781C2×C4—54no—
782C2×C4—54no—
783C2×C4—102no—
784C2×C4—102no—
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—102no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—204no—
805C2×C4—204no—
806C2×C4—208no—
807C2×C4—208no—
808C2×C4C2×#71114yes—
809C2×C4C2×#71114yes—
810C2×C4#414412yes—
811C2×C4D5×#4114yes—
812C5#3490611yescharacteristic, complemented, Sylow
813C22—24no—
814C22—24no—
815C22—24no—
816C22—22no—
817C22—24no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—41no—
830C22C22×#71112yes—
831C22C2×#414411yescharacteristic
832C22C2×D5×#4112yes—
833C22C2×D5×#4111yescharacteristic
834C22#6628311yescharacteristic
835C4—24no—
836C4—24no—
837C4—42no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—104no—
843C4—104no—
844C4—104no—
845C4—202no—
846C4—202no—
847C4—202no—
848C4—202no—
849C4—202no—
850C4#6592114yes—
851C2—44no—
852C2—42no—
853C2—81no—
854C2C2×#6592111yescharacteristic
855C2#1061791912yes—
856C2#1061793711yescharacteristic
857C2#1061812112yes—
858C2#1061814011yescharacteristic
subgroupG/H
centerC22×C4C23×D5
commutator, socle, cosocleC23×C5C25
FrattiniC23C24×D5
Fitting, prime radicalC5×#2388C2
hypercenter#2388D5
hypocenterC5#34906
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #2388

Complements

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

NH ≅ G/Ntype
2. #10615817C2semidirect
3. #10614079C2semidirect
4. #10614077C2semidirect
5. C4×#4081C2semidirect
6. C4×D4×Dic5C2semidirect
7. #10608926C2semidirect
8. #10608691C2semidirect
9. #10608689C2semidirect
10. #10608685C2semidirect
11. #10608538C2semidirect
12. #10608525C2semidirect
13. #10608425C2semidirect
14. #10608424C2semidirect
15. #10608415C2semidirect
16. #10608412C2semidirect
17. C4×#4025C2semidirect
18. C4×#4024C2semidirect
19. #10605171C2semidirect
269. C22×Dic5#41semidirect
309. C4⋊Dic5#41semidirect
812. C5#34906semidirect

Maximal subgroups

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

subgroupindex
C5×#23882
#106158172
#106140792
#106140772
C4×#40812
C4×D4×Dic52
#106089262
#106086912
#106086892
#106086852
#106085382
#106085252
#106084252
#106084242
#106084152
#106084122
C4×#40252
C4×#40242
#106051712
#349065