Finite Group Databasebeta

← #12265987

Subgroups — #12265987

Order 1280.

1774 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2618C211yesmaximal, characteristic
2#10614597C212yesmaximal, complemented
3Dic5×#123C212yesmaximal, complemented
4#10614410C211yesmaximal, characteristic
5Dic5×#121C211yesmaximal, characteristic
6#10613914C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
8#10609565C212yesmaximal, complemented
9#10609472C212yesmaximal, complemented
10#10609074C212yesmaximal, complemented
11#10609071C212yesmaximal, complemented
12#10609014C212yesmaximal, complemented
13#10609013C212yesmaximal, complemented
14#10608721C212yesmaximal, complemented
15#10608623C212yesmaximal, complemented
16#10606517C212yesmaximal, complemented
17#10606388C212yesmaximal, complemented
18#10605687C211yesmaximal, characteristic, complemented
19#10605597C211yesmaximal, characteristic, complemented
20C2×C5×#123C2212yes—
21C2×C5×#121C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C2×D4×Dic5C2212yes—
24C2×D4×Dic5C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C2×#4070C2211yescharacteristic
27C22×C4×Dic5C2211yescharacteristic
28C22×C4×Dic5C2211yescharacteristic
29C22×C4×Dic5C2211yescharacteristic
30C2×#4033C2211yescharacteristic
31C2×#4023C2212yes—
32C5×#398C2212yes—
33C5×#396C2212yes—
34C5×#396C2212yes—
35C5×#394C2212yes—
36C5×#386C2212yes—
37C5×#380C2211yescharacteristic
38#65511C2212yes—
39#65510C2211yescharacteristic
40#65509C2212yes—
41#65509C2212yes—
42#65509C2212yes—
43#65501C2211yescharacteristic
44#65500C2212yes—
45#65499C2212yes—
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48#65275C2212yes—
49#65275C2212yes—
50#65275C2212yes—
51#65275C2212yes—
52#65274C2211yescharacteristic
53#65273C2212yes—
54#65273C2212yes—
55#65273C2212yes—
56#65272C2212yes—
57#65272C2212yes—
58#65271C2212yes—
59#65270C2212yes—
60#65270C2212yes—
61#65268C2212yes—
62C4⋊C4×Dic5C2211yescharacteristic
63C4⋊C4×Dic5C2212yes—
64C4⋊C4×Dic5C2212yes—
65C4⋊C4×Dic5C2211yescharacteristic
66C4⋊C4×Dic5C2212yes—
67C4⋊C4×Dic5C2212yes—
68C4⋊C4×Dic5C2212yes—
69C4⋊C4×Dic5C2212yes—
70#65263C2211yescharacteristic
71#65262C2211yescharacteristic
72#65242C2212yes—
73#65242C2212yes—
74#65242C2212yes—
75#65242C2212yes—
76#65241C2212yes—
77#65241C2212yes—
78#65240C2212yes—
79#65240C2212yes—
80#65240C2212yes—
81#65239C2212yes—
82#65238C2212yes—
83#65238C2212yes—
84#65237C2212yes—
85#65236C2212yes—
86#65235C2212yes—
87#65235C2212yes—
88#65234C2212yes—
89#65233C2212yes—
90C22⋊C4×Dic5C2212yes—
91C22⋊C4×Dic5C2212yes—
92C22⋊C4×Dic5C2212yes—
93C22⋊C4×Dic5C2212yes—
94C22⋊C4×Dic5C2212yes—
95C5⋊#401C2212yes—
96#64950C2212yes—
97#64949C2212yes—
98#64949C2212yes—
99#64948C2212yes—
100#64947C2212yes—
101#64943C2212yes—
102#64942C2212yes—
103#64941C2212yes—
104#64938C2212yes—
105#64938C2212yes—
106#64937C2212yes—
107#34584—51nomaximal, Sylow
108C22×C5×D4C2312yes—
109C22×C5×D4C2311yescharacteristic
110C23×C4×C5C2311yescharacteristic
111C23×C4×C5C2311yescharacteristic
112C23×C4×C5C2311yescharacteristic
113C23×Dic5C2312yes—
114C23×Dic5C2311yescharacteristic
115C23×Dic5C2311yescharacteristic
116C23×Dic5C2311yescharacteristic
117C23×Dic5C2311yescharacteristic
118C22×Dic10C2311yescharacteristic
119C5×#123—28no—
120C5×#121—24no—
121C2×C5×C4⋊C4—24no—
122C2×C5×C4⋊C4C2312yes—
123C2×C5×C4⋊C4C2312yes—
124C2×C5×C4⋊C4C2312yes—
125C2×C5×C4⋊C4C2312yes—
126C2×C5×C4⋊C4C2311yescharacteristic
127C2×C5×C4⋊C4C2311yescharacteristic
128C2×C5×C4⋊C4C2311yescharacteristic
129C2×C5×C22⋊C4C2312yes—
130C2×C5×C22⋊C4C2312yes—
131C2×C5×C22⋊C4C2312yes—
132C2×C5×C22⋊C4C2312yes—
133C2×C5×C22⋊C4C2312yes—
134C2×C5×C22⋊C4C2312yes—
135C2×C22⋊Dic5C2312yes—
136C2×C22⋊Dic5C2312yes—
137C2×C22⋊Dic5C2312yes—
138C2×C22⋊Dic5C2312yes—
139C2×C22⋊Dic5C2312yes—
140C2×C22⋊Dic5C2312yes—
141C2×C22⋊Dic5C2312yes—
142C2×C22⋊Dic5C2312yes—
143C2×C22⋊Dic5C2312yes—
144D4×Dic5—28no—
145D4×Dic5—42no—
146C2×C4⋊Dic5—24no—
147C2×C4⋊Dic5C2311yescharacteristic
148C2×C4⋊Dic5C2312yes—
149C2×C4⋊Dic5C2312yes—
150C2×C4⋊Dic5C2312yes—
151C2×C4⋊Dic5C2311yescharacteristic
152C2×C4⋊Dic5C2312yes—
153C2×C4⋊Dic5C2312yes—
154C2×C4⋊Dic5C2311yescharacteristic
155#4070—24no—
156C2×#683C2312yes—
157C2×#683C2312yes—
158C2×#683C2312yes—
159C2×#683C2312yes—
160C2×#683C2312yes—
161C2×#683C2312yes—
162C2×#683C2312yes—
163C2×C4×Dic5—24no—
164C2×C4×Dic5—42no—
165C2×C4×Dic5—42no—
166C2×C4×Dic5C2312yes—
167C2×C4×Dic5C2312yes—
168C2×C4×Dic5C2311yescharacteristic
169C2×C4×Dic5C2311yescharacteristic
170C2×C4×Dic5C2312yes—
171C2×C4×Dic5C2312yes—
172C2×C4×Dic5C2312yes—
173C2×C4×Dic5C2312yes—
174C2×C4×Dic5C2311yescharacteristic
175C2×C4×Dic5C2312yes—
176C2×C4×Dic5C2311yescharacteristic
177#4033—42no—
178#4023—44no—
179C5×#95C2312yes—
180C5×#95C2312yes—
181C5×#95C2312yes—
182#3963C2312yes—
183#3963C2312yes—
184#3963C2312yes—
185#3963C2312yes—
186#3963C2312yes—
187#3963C2312yes—
188#3963C2312yes—
189#3963C2312yes—
190#3963C2312yes—
191#3963C2312yes—
192#3963C2312yes—
193#3963C2312yes—
194#3963C2312yes—
195#3963C2312yes—
196#3963C2312yes—
197#3963C2312yes—
198#3963C2312yes—
199#3963C2312yes—
200#3963C2312yes—
201#3963C2312yes—
202#3963C2312yes—
203#3963C2312yes—
204#3963C2312yes—
205#3963C2312yes—
206#3963C2312yes—
207#2655—52no—
208#2654—52no—
209#2651—52no—
210#2650—52no—
211#2646—51no—
212#2643—52no—
213#2639—51no—
214#2627—51no—
215#2623—52no—
216#2618D511yescharacteristic
217#2402—52no—
218#2401—52no—
219#2396—52no—
220#2395—52no—
221C4×C22⋊Q8—51no—
222C4×#123—52no—
223C4×#121—51no—
224#2290—52no—
225C2×C4×C4⋊C4—51no—
226C24×C5C2412yes—
227C24×C5C2411yescharacteristic
228C2×C5×D4—24no—
229C2×C5×D4—24no—
230C2×C5×D4—24no—
231C2×C5×D4—22no—
232C2×C5×D4—41no—
233C2×C5×D4—41no—
234C22×C4×C5—22no—
235C22×C4×C5—22no—
236C22×C4×C5—22no—
237C22×C4×C5—41no—
238C22×C4×C5—41no—
239C22×C4×C5—41no—
240C22×C4×C5—41no—
241C22×C4×C5#4114yes—
242C22×C4×C5#4114yes—
243C22×C4×C5C2412yes—
244C22×C4×C5C2412yes—
245C22×C4×C5C2412yes—
246C22×C4×C5C2412yes—
247C22×C4×C5C2411yescharacteristic
248C22×C4×C5C2412yes—
249C22×C4×C5C2411yescharacteristic
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—24no—
256C22×Dic5—24no—
257C22×Dic5—24no—
258C22×Dic5—41no—
259C22×Dic5—41no—
260C22×Dic5—41no—
261C22×Dic5—41no—
262C22×Dic5—41no—
263C22×Dic5—41no—
264C22×Dic5#4114yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C22×Dic5C2411yescharacteristic
271C22×Dic5C2412yes—
272C22×Dic5C2411yescharacteristic
273C22×Dic5C2411yescharacteristic
274C22×Dic5C2411yescharacteristic
275C2×Dic10—22no—
276C2×Dic10—41no—
277C2×Dic10—41no—
278C5×C4⋊C4—24no—
279C5×C4⋊C4—24no—
280C5×C4⋊C4—22no—
281C5×C4⋊C4—24no—
282C5×C4⋊C4—24no—
283C5×C4⋊C4—41no—
284C5×C4⋊C4—41no—
285C5×C22⋊C4—24no—
286C5×C22⋊C4—24no—
287C5×C22⋊C4—24no—
288C5×C22⋊C4—24no—
289C5×C22⋊C4—42no—
290C5×C22⋊C4—42no—
291C22⋊Dic5—24no—
292C22⋊Dic5—24no—
293C22⋊Dic5—24no—
294C22⋊Dic5—42no—
295C22⋊Dic5—42no—
296C22⋊Dic5—42no—
297C22⋊Dic5—42no—
298C22⋊Dic5—42no—
299C22⋊Dic5—42no—
300C4⋊Dic5—22no—
301C4⋊Dic5—24no—
302C4⋊Dic5—24no—
303C4⋊Dic5—24no—
304C4⋊Dic5—41no—
305C4⋊Dic5—42no—
306C4⋊Dic5—42no—
307C4⋊Dic5—41no—
308#683—24no—
309#683—42no—
310#683—42no—
311#683—42no—
312#683—42no—
313#683—42no—
314#683—42no—
315C4×Dic5—24no—
316C4×Dic5—24no—
317C4×Dic5—24no—
318C4×Dic5—24no—
319C4×Dic5—24no—
320C4×Dic5—22no—
321C4×Dic5—22no—
322C4×Dic5—24no—
323C4×Dic5—41no—
324C4×Dic5—42no—
325C4×Dic5—41no—
326C2×#123C2×D512yes—
327C2×C22⋊Q8—51no—
328C2×#121C2×D511yescharacteristic
329C2×C4×Q8—51no—
330C2×C4×D4—52no—
331C2×C4×D4—51no—
332C2×#117—52no—
333C22×C4⋊C4—51no—
334C22×C4⋊C4C2×D511yescharacteristic
335C22×C42—51no—
336C22×C42—51no—
337C22×C42—51no—
338#401—52no—
339#400—52no—
340#400—52no—
341#400—52no—
342#400—52no—
343#400—52no—
344#400—52no—
345#400—52no—
346#400—52no—
347#400—52no—
348#399—52no—
349#399—52no—
350#398—52no—
351#398—52no—
352#398—52no—
353#398—52no—
354#398—52no—
355#398—52no—
356#398C2×D512yes—
357#397—52no—
358#397—52no—
359#397—52no—
360#397—52no—
361#397—52no—
362#397—52no—
363#396—52no—
364#396C2×D512yes—
365#396C2×D512yes—
366#395—52no—
367#394—52no—
368#394C2×D512yes—
369#393—52no—
370#391—51no—
371#390—51no—
372#389—51no—
373#389—51no—
374#388—52no—
375#388—52no—
376#388—52no—
377#388—52no—
378#388—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#386C2×D512yes—
388#385—52no—
389#385—52no—
390#385—52no—
391#385—52no—
392#381—52no—
393#380—51no—
394#380C2×D511yescharacteristic
395C4×C4⋊C4—52no—
396C4×C4⋊C4—52no—
397C4×C4⋊C4—52no—
398C4×C4⋊C4—52no—
399C4×C4⋊C4—52no—
400C4×C4⋊C4—51no—
401C4×C4⋊C4—52no—
402C4×C4⋊C4—51no—
403C4×C4⋊C4—52no—
404C4×C4⋊C4—52no—
405C4×C22⋊C4—52no—
406C4×C22⋊C4—52no—
407C4×C22⋊C4—52no—
408C4×C22⋊C4—52no—
409C4×C22⋊C4—52no—
410#376—52no—
411C2×#95—51no—
412C2×#95—51no—
413C23×C5—21no—
414C23×C5—21no—
415C23×C5—21no—
416C23×C5—21no—
417C23×C5—22no—
418C23×C5—22no—
419C23×C5—22no—
420C23×C5—22no—
421C23×C5—22no—
422C23×C5—22no—
423C23×C5—22no—
424C23×C5C2×#4112yes—
425C23×C5C2×#4112yes—
426C23×C5C2×#4112yes—
427C23×C5C2511yescharacteristic
428C5×D4—44no—
429C5×D4—48no—
430C2×C4×C5—28no—
431C2×C4×C5—22no—
432C2×C4×C5—22no—
433C2×C4×C5—21no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
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—22no—
449C2×C4×C5—44no—
450C2×C4×C5—44no—
451C2×C4×C5C2×#4112yes—
452C2×C4×C5C2×#4114yes—
453C2×C4×C5C2×#4112yes—
454C2×Dic5—21no—
455C2×Dic5—21no—
456C2×Dic5—28no—
457C2×Dic5—22no—
458C2×Dic5—22no—
459C2×Dic5—22no—
460C2×Dic5—22no—
461C2×Dic5—21no—
462C2×Dic5—22no—
463C2×Dic5—21no—
464C2×Dic5—22no—
465C2×Dic5—21no—
466C2×Dic5—22no—
467C2×Dic5—21no—
468C2×Dic5—22no—
469C2×Dic5—22no—
470C2×Dic5—22no—
471C2×Dic5—22no—
472C2×Dic5—21no—
473C2×Dic5—22no—
474C2×Dic5—22no—
475C2×Dic5—22no—
476C2×Dic5—22no—
477C2×Dic5—22no—
478C2×Dic5—22no—
479C2×Dic5—22no—
480C2×Dic5—21no—
481C2×Dic5—44no—
482C2×Dic5—44no—
483C2×Dic5—44no—
484C2×Dic5—48no—
485C2×Dic5C2×#4112yes—
486C2×Dic5C2×#4112yes—
487C2×Dic5H(5,𝔽2)12yes—
488C2×Dic52−1+412yes—
489Dic10—44no—
490C22×Q8—51no—
491C22×D4C22×D512yes—
492C22×D4C22×D511yescharacteristic
493C23×C4—51no—
494C23×C4—52no—
495C23×C4—51no—
496C23×C4—51no—
497C23×C4—51no—
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500C23×C4C22×D511yescharacteristic
501#123—28no—
502C22⋊Q8—104no—
503#121—24no—
504C4×Q8—202no—
505C4×D4—108no—
506C4×D4—202no—
507#117—204no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—52no—
510C2×C4⋊C4—52no—
511C2×C4⋊C4—52no—
512C2×C4⋊C4—52no—
513C2×C4⋊C4—51no—
514C2×C4⋊C4—52no—
515C2×C4⋊C4—52no—
516C2×C4⋊C4—51no—
517C2×C4⋊C4—52no—
518C2×C4⋊C4—51no—
519C2×C4⋊C4—52no—
520C2×C4⋊C4—52no—
521C2×C4⋊C4—52no—
522C2×C4⋊C4—52no—
523C2×C4⋊C4—52no—
524C2×C4⋊C4—104no—
525C2×C4⋊C4C22×D512yes—
526C2×C4⋊C4C22×D512yes—
527C2×C4⋊C4C22×D511yescharacteristic
528C2×C4⋊C4C22×D512yes—
529C2×C4⋊C4C22×D512yes—
530C2×C4⋊C4C22×D511yescharacteristic
531C2×C4⋊C4C22×D511yescharacteristic
532C2×C22⋊C4—52no—
533C2×C22⋊C4—52no—
534C2×C22⋊C4—52no—
535C2×C22⋊C4—52no—
536C2×C22⋊C4—52no—
537C2×C22⋊C4—52no—
538C2×C22⋊C4—52no—
539C2×C22⋊C4—52no—
540C2×C22⋊C4—52no—
541C2×C22⋊C4C22×D512yes—
542C2×C22⋊C4C22×D512yes—
543C2×C22⋊C4C22×D512yes—
544C2×C22⋊C4C22×D512yes—
545C2×C22⋊C4C22×D512yes—
546C2×C22⋊C4C22×D512yes—
547C2×C42—52no—
548C2×C42—52no—
549C2×C42—52no—
550C2×C42—51no—
551C2×C42—51no—
552C2×C42—52no—
553C2×C42—52no—
554C2×C42—52no—
555C2×C42—52no—
556C2×C42—51no—
557C2×C42—51no—
558C2×C42—104no—
559C2×C42—202no—
560C2×C42—202no—
561#95—52no—
562#95—52no—
563#95—52no—
564#95—52no—
565#95—52no—
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×D512yes—
587#95C22×D512yes—
588#95C22×D512yes—
589C22×C5—22no—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5—22no—
593C22×C5—22no—
594C22×C5—22no—
595C22×C5—42no—
596C22×C5—42no—
597C22×C5—42no—
598C22×C5—42no—
599C22×C5—42no—
600C22×C5—42no—
601C22×C5—42no—
602C22×C5#52914yes—
603C22×C5C22×#4111yescharacteristic
604C22×C5C22×#4111yescharacteristic
605C22×C5C22×#4111yescharacteristic
606C22×C5C2×H(5,𝔽2)11yescharacteristic
607C22×C5C2×2−1+411yescharacteristic
608C22×C5#58511yescharacteristic
609C22×C5#58511yescharacteristic
610C4×C5—24no—
611C4×C5—22no—
612C4×C5—22no—
613C4×C5—42no—
614C4×C5—42no—
615C4×C5—42no—
616C4×C5—42no—
617Dic5—22no—
618Dic5—42no—
619Dic5—42no—
620Dic5—42no—
621Dic5—42no—
622Dic5—41no—
623Dic5—42no—
624Dic5—41no—
625Dic5—42no—
626Dic5#53914yes—
627C24C23×D512yes—
628C24C23×D511yescharacteristic
629C2×Q8—102no—
630C2×Q8—201no—
631C2×Q8—201no—
632C2×D4—24no—
633C2×D4—24no—
634C2×D4—24no—
635C2×D4—22no—
636C2×D4—41no—
637C2×D4—41no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—51no—
646C22×C4—54no—
647C22×C4—51no—
648C22×C4—52no—
649C22×C4—52no—
650C22×C4—52no—
651C22×C4—51no—
652C22×C4—52no—
653C22×C4—51no—
654C22×C4—52no—
655C22×C4—52no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—104no—
659C22×C4—104no—
660C22×C4—104no—
661C22×C4—102no—
662C22×C4—102no—
663C22×C4—102no—
664C22×C4—201no—
665C22×C4—201no—
666C22×C4—201no—
667C22×C4—201no—
668C22×C4—201no—
669C22×C4—201no—
670C22×C4#71114yes—
671C22×C4#71114yes—
672C22×C4C23×D512yes—
673C22×C4C23×D512yes—
674C22×C4C23×D512yes—
675C22×C4C23×D512yes—
676C22×C4C23×D512yes—
677C22×C4C23×D511yescharacteristic
678C22×C4C23×D511yescharacteristic
679C4⋊C4—24no—
680C4⋊C4—24no—
681C4⋊C4—22no—
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4—104no—
687C4⋊C4—104no—
688C4⋊C4—104no—
689C4⋊C4—104no—
690C4⋊C4—102no—
691C4⋊C4—202no—
692C4⋊C4—202no—
693C4⋊C4—201no—
694C4⋊C4—202no—
695C4⋊C4—202no—
696C4⋊C4—202no—
697C4⋊C4—202no—
698C4⋊C4—201no—
699C4⋊C4—202no—
700C4⋊C4—202no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—104no—
708C22⋊C4—104no—
709C22⋊C4—104no—
710C22⋊C4—202no—
711C22⋊C4—202no—
712C22⋊C4—202no—
713C22⋊C4—202no—
714C22⋊C4—202no—
715C22⋊C4—202no—
716C42—104no—
717C42—104no—
718C42—104no—
719C42—102no—
720C42—102no—
721C42—104no—
722C42—104no—
723C42—104no—
724C42—201no—
725C42—201no—
726C42—202no—
727C2×C5—24no—
728C2×C5—82no—
729C2×C5C2×#52911yescharacteristic
730C2×C5C2×#53911yescharacteristic
731C2×C5#345511yescharacteristic
732C2×C5#345911yescharacteristic
733C2×C5#346011yescharacteristic
734C2×C5#346111yescharacteristic
735C2×C5#346111yescharacteristic
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23C2×#71112yes—
748C23C2×#71112yes—
749C23D5×#4112yes—
750C23C24×D511yescharacteristic
751Q8—204no—
752D4—44no—
753D4—48no—
754C2×C4—28no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
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—44no—
774C2×C4—44no—
775C2×C4—52no—
776C2×C4—52no—
777C2×C4—52no—
778C2×C4—52no—
779C2×C4—108no—
780C2×C4—101no—
781C2×C4—101no—
782C2×C4—102no—
783C2×C4—102no—
784C2×C4—101no—
785C2×C4—102no—
786C2×C4—101no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—101no—
791C2×C4—102no—
792C2×C4—101no—
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—101no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—102no—
805C2×C4—101no—
806C2×C4—208no—
807C2×C4—204no—
808C2×C4—204no—
809C2×C4—204no—
810C2×C4C2×#71114yes—
811C2×C4C2×#71112yes—
812C2×C4C2×#71112yes—
813C5#3458411yescharacteristic, complemented, Sylow
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22#6593414yes—
828C22C22×#71111yescharacteristic
829C22C22×#71111yescharacteristic
830C22C2×D5×#4111yescharacteristic
831C22D5×H(5,𝔽2)11yescharacteristic
832C22#6628511yescharacteristic
833C22D5×2−1+411yescharacteristic
834C22#6628711yescharacteristic
835C4—22no—
836C4—22no—
837C4—24no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—54no—
843C4—102no—
844C4—202no—
845C4—202no—
846C4—201no—
847C4—202no—
848C4—201no—
849C4—202no—
850C4—202no—
851C4—202no—
852C2—24no—
853C2—82no—
854C2C2×#6593411yescharacteristic
855C2#1061819611yescharacteristic
856C2#1061824011yescharacteristic
857C2#1061826511yescharacteristic
858C2#1061826611yescharacteristic
859C2#1061832811yescharacteristic
860C2D5×#53911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2618C2
prime radicalC2×C5×#121C22
hypercenter#2618D5
hypocenterC5#34584
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2618

Complements

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

NH ≅ G/Ntype
2. #10614597C2semidirect
3. Dic5×#123C2semidirect
6. #10613914C2semidirect
7. C2×C4⋊C4×Dic5C2semidirect
8. #10609565C2semidirect
9. #10609472C2semidirect
10. #10609074C2semidirect
11. #10609071C2semidirect
12. #10609014C2semidirect
13. #10609013C2semidirect
14. #10608721C2semidirect
15. #10608623C2semidirect
16. #10606517C2semidirect
17. #10606388C2semidirect
18. #10605687C2semidirect
19. #10605597C2semidirect
813. C5#34584semidirect

Maximal subgroups

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

subgroupindex
C5×#26182
#106145972
Dic5×#1232
#106144102
Dic5×#1212
#106139142
C2×C4⋊C4×Dic52
#106095652
#106094722
#106090742
#106090712
#106090142
#106090132
#106087212
#106086232
#106065172
#106063882
#106056872
#106055972
#345845