Finite Group Databasebeta

← #12306925

Subgroups — #12306925

Order 1280.

1858 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2626C211yesmaximal, characteristic
2#10614512C212yesmaximal, complemented
3#10613848C211yesmaximal, characteristic
4C2×#65235C211yesmaximal, characteristic
5#10609820C211yesmaximal, characteristic, complemented
6#10609799C212yesmaximal, complemented
7#10609792C211yesmaximal, characteristic, complemented
8#10609125C212yesmaximal, complemented
9#10609114C212yesmaximal, complemented
10#10609100C212yesmaximal, complemented
11#10609083C212yesmaximal, complemented
12#10608580C212yesmaximal, complemented
13#10608574C211yesmaximal, characteristic, complemented
14#10608567C211yesmaximal, characteristic, complemented
15#10606148C212yesmaximal, complemented
16#10606147C212yesmaximal, complemented
17#10605675C212yesmaximal, complemented
18#10605577C212yesmaximal
19#10605551C212yesmaximal
20C24×Dic5C2211yescharacteristic
21C2×C5×C22⋊Q8C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C2×#4070C2211yescharacteristic
25C22×#683C2212yes—
26C2×#4035C2212yescomplemented
27C2×#4034C2212yescomplemented
28C2×#4024C2212yes—
29C2×#4024C2212yes—
30C2×#4024C2212yes—
31C5×#399C2211yescharacteristic
32C5×#399C2211yescharacteristic
33C5×#396C2212yes—
34C5×#396C2212yes—
35C5×#393C2211yescharacteristic
36C5×#393C2211yescharacteristic
37C5×#385C2212yes—
38C5×#380C2211yescharacteristic
39C5×#379C2212yes—
40#65536C2212yes—
41#65519C2212yescomplemented
42#65518C2212yescomplemented
43#65501C2211yescharacteristic
44#65499C2212yes—
45C2×#3963C2212yes—
46#65273C2212yescomplemented
47#65273C2212yescomplemented
48#65273C2212yescomplemented
49#65272C2212yescomplemented
50#65270C2212yescomplemented
51#65269C2212yescomplemented
52#65269C2212yescomplemented
53#65269C2212yescomplemented
54#65268C2212yescomplemented
55#65268C2212yescomplemented
56#65267C2212yescomplemented
57#65265C2212yescomplemented
58#65263C2212yescomplemented
59#65261C2212yescomplemented
60#65261C2212yescomplemented
61#65261C2212yescomplemented
62#65239C2212yes—
63#65239C2212yes—
64#65239C2212yes—
65#65238C2211yescharacteristic
66#65238C2211yescharacteristic
67#65237C2212yes—
68#65237C2212yes—
69#65236C2211yescharacteristic
70#65236C2211yescharacteristic
71#65235C2212yes—
72#65235C2212yes—
73#65235C2212yes—
74#65235C2211yescharacteristic
75#65235C2212yes—
76#65235C2211yescharacteristic
77#65235C2211yescharacteristic
78#65235C2212yes—
79#65235C2211yescharacteristic
80#65234C2212yes—
81#65234C2212yes—
82#65234C2212yes—
83#65234C2212yes—
84#65233C2212yes—
85#65233C2212yes—
86#65233C2212yes—
87#65233C2212yes—
88#65231C2212yes—
89#65231C2212yes—
90#65231C2212yes—
91#65231C2212yes—
92#65231C2212yes—
93C22⋊C4×Dic5C2212yes—
94C22⋊C4×Dic5C2212yes—
95#64948C2212yescomplemented
96#64948C2212yescomplemented
97#64947C2212yescomplemented
98#64947C2212yescomplemented
99#64946C2212yescomplemented
100#64945C2212yescomplemented
101#64942C2212yescomplemented
102#64941C2212yescomplemented
103#64939C2212yescomplemented
104#64936C2212yescomplemented
105#64936C2212yescomplemented
106#64936C2212yescomplemented
107#36748—51nomaximal, Sylow
108C25×C5C2311yescharacteristic
109C22×C5×Q8C2311yescharacteristic
110C23×C4×C5C2311yescharacteristic
111C23×C4×C5C2311yescharacteristic
112C23×Dic5—44no—
113C23×Dic5—42no—
114C23×Dic5C2311yescharacteristic
115C23×Dic5C2312yes—
116C23×Dic5C2312yes—
117C23×Dic5C2311yescharacteristic
118C23×Dic5C2312yes—
119C22×Dic10C2312yes—
120C22×Dic10C2311yescharacteristic
121C5×C22⋊Q8—42no—
122C2×C5×C4⋊C4C2312yes—
123C2×C5×C4⋊C4C2312yes—
124C2×C5×C4⋊C4C2312yes—
125C2×C5×C4⋊C4C2312yes—
126C2×C5×C4⋊C4C2311yescharacteristic
127C2×C5×C22⋊C4—42no—
128C2×C5×C22⋊C4C2312yes—
129C2×C5×C22⋊C4C2312yes—
130C2×C5×C22⋊C4C2312yes—
131C2×C5×C22⋊C4C2312yes—
132C2×C5×C22⋊C4C2312yes—
133C2×C5×C22⋊C4C2312yes—
134C2×C5×C22⋊C4C2311yescharacteristic
135C2×C5×C22⋊C4C2311yescharacteristic
136C2×C5×C22⋊C4C2311yescharacteristic
137C2×C5×C22⋊C4C2311yescharacteristic
138C2×C22⋊Dic5Q818yescomplemented
139C2×C22⋊Dic5C2312yes—
140C2×C22⋊Dic5C2312yes—
141C2×C22⋊Dic5C2312yes—
142C2×C22⋊Dic5C2312yes—
143C2×C22⋊Dic5C2312yes—
144C2×C22⋊Dic5C2312yes—
145C2×C22⋊Dic5C2311yescharacteristic
146C2×C22⋊Dic5C2311yescharacteristic
147C2×C22⋊Dic5C2312yes—
148C2×C4⋊Dic5C2312yes—
149C2×C4⋊Dic5C2312yes—
150C2×C4⋊Dic5C2312yes—
151C2×C4⋊Dic5C2312yes—
152C2×C4⋊Dic5C2311yescharacteristic
153#4070—42no—
154C2×#683—44no—
155C2×#683C2312yes—
156C2×#683C2312yes—
157C2×#683C2312yes—
158C2×#683C2312yes—
159C2×#683C2312yes—
160C2×#683C2312yes—
161C2×#683C2312yes—
162C2×#683C2312yes—
163C2×#683C2312yes—
164C2×#683C2312yes—
165C2×#683C2312yes—
166C2×#683C2312yes—
167C2×#683C2312yes—
168C2×#683C2312yes—
169C2×#683C2312yes—
170C2×#683C2312yes—
171C2×#683C2312yes—
172C2×C4×Dic5C2312yes—
173C2×C4×Dic5C2312yes—
174C2×C4×Dic5C2312yes—
175C2×C4×Dic5C2312yes—
176#4035—44no—
177#4034—44no—
178#4024—44no—
179#4024—44no—
180#4024—44no—
181C5×#95C2311yescharacteristic
182C5×#95C2311yescharacteristic
183C5×#95C2312yes—
184C5×#95C2312yes—
185#3963C2312yes—
186#3963C2312yes—
187#3963C2312yes—
188#3963C2311yescharacteristic
189#3963C2312yes—
190#3963C2312yes—
191#3963C2312yes—
192#3963C2312yes—
193#3963C2312yes—
194#3963C2312yes—
195#3963C2312yes—
196#3963C2312yes—
197#3963C2312yes—
198#3963C2311yescharacteristic
199#3963C2312yes—
200#3963C2312yes—
201#3963C2312yes—
202#3963C2312yes—
203#3963C2312yes—
204#3963C2312yes—
205#3963C2312yes—
206#3963C2312yes—
207#2848—52no—
208#2807—51no—
209#2790—52no—
210#2788—52no—
211#2768—52no—
212#2763—51no—
213#2742—51no—
214#2729—52no—
215#2720—52no—
216#2704—52no—
217#2677—51no—
218#2626—51no—
219#2626D511yescharacteristic
220#2569—52no—
221#2549—52no—
222#2442—52no—
223#2440—52no—
224#2312—52no—
225C2×#385—51no—
226C24×C5—22no—
227C24×C5—22no—
228C24×C5—42no—
229C24×C5—42no—
230C24×C5C2×Q814yes—
231C24×C5C2411yescharacteristic
232C24×C5C2411yescharacteristic
233C24×C5C2411yescharacteristic
234C2×C5×Q8—41no—
235C2×C5×Q8—42no—
236C22×C4×C5—22no—
237C22×C4×C5—22no—
238C22×C4×C5—42no—
239C22×C4×C5—42no—
240C22×C4×C5C2412yes—
241C22×C4×C5C2412yes—
242C22×C4×C5C2412yes—
243C22×C4×C5C2412yes—
244C22×C4×C5C2411yescharacteristic
245C22×C4×C5C2411yescharacteristic
246C22×C4×C5C2411yescharacteristic
247C22×C4×C5C2411yescharacteristic
248C22×Dic5—24no—
249C22×Dic5—24no—
250C22×Dic5—24no—
251C22×Dic5—24no—
252C22×Dic5—41no—
253C22×Dic5—42no—
254C22×Dic5—42no—
255C22×Dic5—42no—
256C22×Dic5—42no—
257C22×Dic5—41no—
258C22×Dic5—42no—
259C22×Dic5—42no—
260C22×Dic5—416no—
261C22×Dic5C2×Q818yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C2×Dic10—24no—
271C2×Dic10—42no—
272C2×Dic10—42no—
273C2×Dic10—42no—
274C2×Dic10—41no—
275C5×C4⋊C4—42no—
276C5×C4⋊C4—42no—
277C5×C4⋊C4—41no—
278C5×C4⋊C4—42no—
279C5×C4⋊C4—42no—
280C5×C22⋊C4—24no—
281C5×C22⋊C4—24no—
282C5×C22⋊C4—41no—
283C5×C22⋊C4—41no—
284C5×C22⋊C4—41no—
285C5×C22⋊C4—41no—
286C5×C22⋊C4—42no—
287C5×C22⋊C4—42no—
288C5×C22⋊C4—42no—
289C5×C22⋊C4—42no—
290C22⋊Dic5—24no—
291C22⋊Dic5—24no—
292C22⋊Dic5—42no—
293C22⋊Dic5—42no—
294C22⋊Dic5—42no—
295C22⋊Dic5—42no—
296C22⋊Dic5C2×Q814yes—
297C22⋊Dic5C2×Q814yes—
298C22⋊Dic5C2×Q818yes—
299C4⋊Dic5—24no—
300C4⋊Dic5—42no—
301C4⋊Dic5—42no—
302C4⋊Dic5—42no—
303C4⋊Dic5—41no—
304#683—24no—
305#683—24no—
306#683—24no—
307#683—24no—
308#683—42no—
309#683—42no—
310#683—42no—
311#683—42no—
312#683—42no—
313#683—42no—
314#683—42no—
315#683—42no—
316#683—42no—
317#683—42no—
318#683—42no—
319#683—42no—
320#683—42no—
321C4×Dic5—42no—
322C4×Dic5—42no—
323C4×Dic5—42no—
324C4×Dic5—42no—
325C24×C4—51no—
326C2×C4⋊Q8—52no—
327C2×#125—52no—
328C2×C22⋊Q8—51no—
329C2×C22⋊Q8—52no—
330C2×C22⋊Q8—52no—
331C2×C22⋊Q8—52no—
332C2×C22⋊Q8C2×D511yescharacteristic
333C22×C4⋊C4—52no—
334C22×C22⋊C4—51no—
335C22×C22⋊C4C2×D511yescharacteristic
336#400—52no—
337#400—52no—
338#400—52no—
339#400—52no—
340#399—51no—
341#399—51no—
342#399C2×D511yescharacteristic
343#399C2×D511yescharacteristic
344#398—52no—
345#398—52no—
346#398—52no—
347#398—52no—
348#398—52no—
349#398—52no—
350#398—52no—
351#398—52no—
352#396—52no—
353#396—52no—
354#396C2×D512yes—
355#396C2×D512yes—
356#395—52no—
357#395—52no—
358#395—52no—
359#395—52no—
360#393—51no—
361#393—51no—
362#393C2×D511yescharacteristic
363#393C2×D511yescharacteristic
364#391—52no—
365#391—52no—
366#389—52no—
367#389—52no—
368#389—52no—
369#389—52no—
370#389—52no—
371#389—52no—
372#388—52no—
373#388—52no—
374#388—52no—
375#388—52no—
376#388—52no—
377#388—52no—
378#388—52no—
379#388—52no—
380#387—52no—
381#387—52no—
382#387—52no—
383#387—52no—
384#385—52no—
385#385—52no—
386#385—52no—
387#385—52no—
388#385—52no—
389#385—52no—
390#385—52no—
391#385—51no—
392#385—51no—
393#385—52no—
394#385—52no—
395#385—51no—
396#385—51no—
397#385C2×D512yes—
398#384—52no—
399#382—52no—
400#380—51no—
401#380—52no—
402#380—52no—
403#380—52no—
404#380—52no—
405#380—52no—
406#380C2×D511yescharacteristic
407#379—52no—
408#379C2×D512yes—
409C4×C22⋊C4—52no—
410C4×C22⋊C4—52no—
411C2×#95—52no—
412C23×C5—22no—
413C23×C5—22no—
414C23×C5—28no—
415C23×C5—22no—
416C23×C5—22no—
417C23×C5—21no—
418C23×C5—21no—
419C23×C5—21no—
420C23×C5—21no—
421C23×C5—22no—
422C23×C5—22no—
423C23×C5—48no—
424C23×C5—44no—
425C23×C5—44no—
426C23×C5—48no—
427C23×C5C22×Q812yes—
428C23×C5C22×Q812yes—
429C23×C5C22×Q812yes—
430C23×C5H(5,𝔽2)12yes—
431C23×C52−1+412yes—
432C23×C5C2511yescharacteristic
433C5×Q8—82no—
434C2×C4×C5—22no—
435C2×C4×C5—22no—
436C2×C4×C5—22no—
437C2×C4×C5—22no—
438C2×C4×C5—22no—
439C2×C4×C5—21no—
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5—22no—
443C2×C4×C5—21no—
444C2×C4×C5—21no—
445C2×C4×C5—21no—
446C2×C4×C5—22no—
447C2×C4×C5—22no—
448C2×C4×C5—22no—
449C2×C4×C5—22no—
450C2×C4×C5—22no—
451C2×C4×C5—22no—
452C2×C4×C5—22no—
453C2×C4×C5—22no—
454C2×C4×C5—82no—
455C2×C4×C5—82no—
456C2×Dic5—22no—
457C2×Dic5—22no—
458C2×Dic5—22no—
459C2×Dic5—22no—
460C2×Dic5—22no—
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—48no—
478C2×Dic5—44no—
479C2×Dic5—48no—
480C2×Dic5—48no—
481C2×Dic5—44no—
482C2×Dic5C22×Q814yes—
483C2×Dic5C22×Q814yes—
484C2×Dic5H(5,𝔽2)14yes—
485Dic10—84no—
486Dic10—82no—
487C25C22×D511yescharacteristic
488C22×Q8—52no—
489C22×Q8—51no—
490C22×Q8C22×D511yescharacteristic
491C23×C4—52no—
492C23×C4—52no—
493C23×C4—51no—
494C23×C4—52no—
495C23×C4—51no—
496C23×C4—204no—
497C23×C4—202no—
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500C4⋊Q8—204no—
501#125—204no—
502C22⋊Q8—42no—
503C22⋊Q8—204no—
504C22⋊Q8—204no—
505C22⋊Q8—204no—
506C22⋊Q8—202no—
507C2×C4⋊C4—52no—
508C2×C4⋊C4—52no—
509C2×C4⋊C4—52no—
510C2×C4⋊C4—52no—
511C2×C4⋊C4—52no—
512C2×C4⋊C4—52no—
513C2×C4⋊C4—52no—
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—51no—
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—204no—
530C2×C4⋊C4C22×D511yescharacteristic
531C2×C4⋊C4C22×D512yes—
532C2×C4⋊C4C22×D512yes—
533C2×C4⋊C4C22×D512yes—
534C2×C4⋊C4C22×D512yes—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—58no—
537C2×C22⋊C4—51no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—52no—
540C2×C22⋊C4—52no—
541C2×C22⋊C4—52no—
542C2×C22⋊C4—52no—
543C2×C22⋊C4—52no—
544C2×C22⋊C4—52no—
545C2×C22⋊C4—52no—
546C2×C22⋊C4C22×D512yes—
547C2×C22⋊C4C22×D512yes—
548C2×C22⋊C4C22×D511yescharacteristic
549C2×C22⋊C4C22×D511yescharacteristic
550C2×C22⋊C4C22×D511yescharacteristic
551C2×C22⋊C4C22×D511yescharacteristic
552C2×C22⋊C4C22×D512yes—
553C2×C22⋊C4C22×D512yes—
554C2×C22⋊C4C22×D512yes—
555C2×C22⋊C4C22×D512yes—
556C2×C42—52no—
557C2×C42—52no—
558C2×C42—52no—
559C2×C42—52no—
560#95—52no—
561#95—52no—
562#95—52no—
563#95—52no—
564#95—52no—
565#95—52no—
566#95—52no—
567#95—52no—
568#95—51no—
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—51no—
580#95—52no—
581#95—52no—
582#95C22×D511yescharacteristic
583#95C22×D511yescharacteristic
584#95C22×D512yes—
585#95C22×D512yes—
586C22×C5—24no—
587C22×C5—22no—
588C22×C5—22no—
589C22×C5—24no—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5—24no—
593C22×C5—24no—
594C22×C5—416no—
595C22×C5—41no—
596C22×C5—41no—
597C22×C5—41no—
598C22×C5—41no—
599C22×C5—42no—
600C22×C5—42no—
601C22×C5#54414yes—
602C22×C5C23×Q811yescharacteristic
603C22×C5C2×H(5,𝔽2)11yescharacteristic
604C22×C5C2×H(5,𝔽2)12yes—
605C22×C5C2×2−1+411yescharacteristic
606C22×C5#58512yes—
607C4×C5—42no—
608C4×C5—41no—
609C4×C5—41no—
610C4×C5—41no—
611C4×C5—41no—
612C4×C5—42no—
613C4×C5—42no—
614C4×C5—42no—
615Dic5—24no—
616Dic5—24no—
617Dic5—24no—
618Dic5—42no—
619Dic5—42no—
620Dic5—42no—
621Dic5—42no—
622Dic5—42no—
623C24—22no—
624C24—22no—
625C24—42no—
626C24—42no—
627C24Q8×D514yes—
628C24C23×D511yescharacteristic
629C24C23×D511yescharacteristic
630C24C23×D511yescharacteristic
631C2×Q8—41no—
632C2×Q8—42no—
633C2×Q8—104no—
634C2×Q8—202no—
635C2×Q8—201no—
636C2×Q8—202no—
637C2×Q8—202no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—58no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—52no—
650C22×C4—52no—
651C22×C4—104no—
652C22×C4—104no—
653C22×C4—104no—
654C22×C4—104no—
655C22×C4—202no—
656C22×C4—201no—
657C22×C4—202no—
658C22×C4—202no—
659C22×C4—202no—
660C22×C4—201no—
661C22×C4—202no—
662C22×C4—202no—
663C22×C4—2016no—
664C22×C4C23×D511yescharacteristic
665C22×C4C23×D511yescharacteristic
666C22×C4C23×D512yes—
667C22×C4C23×D512yes—
668C22×C4C23×D512yes—
669C22×C4C23×D511yescharacteristic
670C22×C4C23×D512yes—
671C22×C4C23×D511yescharacteristic
672C4⋊C4—41no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—104no—
678C4⋊C4—104no—
679C4⋊C4—104no—
680C4⋊C4—104no—
681C4⋊C4—104no—
682C4⋊C4—202no—
683C4⋊C4—202no—
684C4⋊C4—202no—
685C4⋊C4—202no—
686C4⋊C4—202no—
687C4⋊C4—202no—
688C4⋊C4—202no—
689C4⋊C4—202no—
690C4⋊C4—201no—
691C4⋊C4—202no—
692C4⋊C4—202no—
693C4⋊C4—202no—
694C4⋊C4—202no—
695C4⋊C4—202no—
696C4⋊C4—202no—
697C4⋊C4—202no—
698C4⋊C4—202no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—41no—
704C22⋊C4—41no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—54no—
710C22⋊C4—54no—
711C22⋊C4—58no—
712C22⋊C4—104no—
713C22⋊C4—104no—
714C22⋊C4—202no—
715C22⋊C4—202no—
716C22⋊C4—202no—
717C22⋊C4—202no—
718C42—202no—
719C42—202no—
720C42—202no—
721C42—202no—
722C2×C5—24no—
723C2×C5—42no—
724C2×C5—42no—
725C2×C5C2×#54411yescharacteristic
726C2×C5#350112yes—
727C2×C5#353211yescharacteristic
728C2×C5#353311yescharacteristic
729C2×C5#354112yes—
730C23—22no—
731C23—22no—
732C23—28no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—48no—
742C23—44no—
743C23—44no—
744C23—48no—
745C23#414412yes—
746C23C2×Q8×D512yes—
747C23C2×Q8×D512yes—
748C23C2×Q8×D512yes—
749C23#415012yes—
750C23C24×D511yescharacteristic
751Q8—82no—
752Q8—404no—
753Q8—402no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—54no—
775C2×C4—54no—
776C2×C4—54no—
777C2×C4—82no—
778C2×C4—82no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—102no—
782C2×C4—102no—
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—208no—
801C2×C4—204no—
802C2×C4—208no—
803C2×C4—208no—
804C2×C4—204no—
805C5#3674811yescharacteristic, complemented, Sylow
806C22—22no—
807C22—24no—
808C22—22no—
809C22—24no—
810C22—22no—
811C22—22no—
812C22—24no—
813C22—24no—
814C22—416no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22#6595714yes—
822C22C2×#414411yescharacteristic
823C22C22×Q8×D511yescharacteristic
824C22C2×#415011yescharacteristic
825C22D5×H(5,𝔽2)12yes—
826C22#6628512yes—
827C4—41no—
828C4—41no—
829C4—42no—
830C4—41no—
831C4—41no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—104no—
836C4—104no—
837C4—104no—
838C4—202no—
839C4—202no—
840C4—202no—
841C4—202no—
842C4—202no—
843C2—24no—
844C2—42no—
845C2—42no—
846C2C2×#6595711yescharacteristic
847C2#1061820111yescharacteristic
848C2#1061823411yescharacteristic
849C2#1061830012yes—
850C2#1061847512yes—
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2626C2
prime radicalC25×C5C23
hypercenter#2626D5
hypocenterC5#36748
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2626

Complements

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

NH ≅ G/Ntype
2. #10614512C2semidirect
5. #10609820C2semidirect
6. #10609799C2semidirect
7. #10609792C2semidirect
8. #10609125C2semidirect
9. #10609114C2semidirect
10. #10609100C2semidirect
11. #10609083C2semidirect
12. #10608580C2semidirect
13. #10608574C2semidirect
14. #10608567C2semidirect
15. #10606148C2semidirect
16. #10606147C2semidirect
17. #10605675C2semidirect
26. C2×#4035C22semidirect
27. C2×#4034C22semidirect
41. #65519C22semidirect
42. #65518C22semidirect
46. #65273C22semidirect
47. #65273C22semidirect
48. #65273C22semidirect
49. #65272C22semidirect
50. #65270C22semidirect
51. #65269C22semidirect
52. #65269C22semidirect
53. #65269C22semidirect
54. #65268C22semidirect
55. #65268C22semidirect
56. #65267C22semidirect
57. #65265C22semidirect
58. #65263C22semidirect
59. #65261C22semidirect
60. #65261C22semidirect
61. #65261C22semidirect
95. #64948C22semidirect
96. #64948C22semidirect
97. #64947C22semidirect
98. #64947C22semidirect
99. #64946C22semidirect
100. #64945C22semidirect
101. #64942C22semidirect
102. #64941C22semidirect
103. #64939C22semidirect
104. #64936C22semidirect
105. #64936C22semidirect
106. #64936C22semidirect
138. C2×C22⋊Dic5Q8semidirect
805. C5#36748semidirect

Maximal subgroups

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

subgroupindex
C5×#26262
#106145122
#106138482
C2×#652352
#106098202
#106097992
#106097922
#106091252
#106091142
#106091002
#106090832
#106085802
#106085742
#106085672
#106061482
#106061472
#106056752
#106055772
#106055512
#367485