Finite Group Databasebeta

← C2×#10608907 #12267160

Subgroups — C2×#10608907 #12267160

Order 1280.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4092C211yesmaximal, characteristic, complemented
2C22×#4093C211yesmaximal, characteristic, complemented
3C22×#4040C211yesmaximal, characteristic, complemented
4C22×#4039C211yesmaximal, characteristic, complemented
5C2×C5×#395C211yesmaximal, characteristic, complemented
6C2×#65283C211yesmaximal, characteristic, complemented
7C2×#65278C211yesmaximal, characteristic, complemented
8C2×#65277C211yesmaximal, characteristic, complemented
9C2×#65279C211yesmaximal, characteristic, complemented
10#10608907C2116yesmaximal, direct product factor
11C2×#64960C211yesmaximal, characteristic
12C2×#64954C211yesmaximal, characteristic, complemented
13C2×#64961C211yesmaximal, characteristic, complemented
14C2×#64959C211yesmaximal, characteristic, complemented
15C2×#64958C211yesmaximal, characteristic, complemented
16C2×#64938C211yesmaximal, characteristic, complemented
17C23×C5×Q8C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C23×D20C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C2×#4093—28no—
27C2×#4093C2218yescomplemented
28C2×#4092—28no—
29C2×#4092C2218yescomplemented
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×#685C2211yescharacteristic
42C22×#685C2211yescharacteristic
43C22×C4⋊Dic5C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C22×C4×Dic5C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C2×#4040—28no—
51C2×#4040C2218yescomplemented
52C2×#4039—28no—
53C2×#4039C2218yescomplemented
54C5×#395C2218yescomplemented
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×C5×#95C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65283C2218yescomplemented
62#65279C2218yescomplemented
63#65278C2218yescomplemented
64#65277C2218yescomplemented
65#64961C2218yescomplemented
66#64960C2218yes—
67#64959C2218yescomplemented
68#64958C2218yescomplemented
69#64954C2218yescomplemented
70#64938C2218yescomplemented
71C2×#2461—51nomaximal, Sylow
72C24×D5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×Q8—24no—
76C22×C5×Q8—24no—
77C22×C5×Q8—42no—
78C22×C5×Q8C2314yes—
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C22×D20—24no—
92C22×D20—24no—
93C22×D20—24no—
94C22×D20—24no—
95C22×D20—24no—
96C22×D20—24no—
97C22×D20—24no—
98C22×D20—42no—
99C22×D20—42no—
100C22×D20C2314yes—
101C22×D20C2314yes—
102C22×D20C2314yes—
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—24no—
106C22×C4×D5—24no—
107C22×C4×D5—42no—
108C22×C4×D5—42no—
109C22×C4×D5C2314yes—
110C22×C4×D5C2314yes—
111C2×C5×C4⋊C4—24no—
112C2×C5×C4⋊C4—24no—
113C2×C5×C4⋊C4—42no—
114C2×C5×C4⋊C4C2314yes—
115C2×C5×C4⋊C4C2314yes—
116C2×C5×C4⋊C4C2314yes—
117#4093—232no—
118#4092—232no—
119C2×#685—24no—
120C2×#685—24no—
121C2×#685—24no—
122C2×#685—24no—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—24no—
131C2×#685D418yescomplemented
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×#685C2314yes—
143C2×#685C2314yes—
144C2×#685C2314yes—
145C2×C4⋊Dic5—24no—
146C2×C4⋊Dic5C2314yes—
147C2×#683—24no—
148C2×#683—24no—
149C2×#683D418yescomplemented
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×C4×Dic5—24no—
154C2×C4×Dic5—24no—
155C2×C4×Dic5—24no—
156C2×C4×Dic5C2314yes—
157C2×C4×Dic5C2314yes—
158C2×C4×Dic5C2314yes—
159#4040—232no—
160#4039—232no—
161C5×#95C2314yes—
162C5×#95C2314yes—
163C5×#95C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#124—51no—
168C22×#123—51no—
169C22×C22⋊Q8—51no—
170C22×C4×D4—51no—
171#2461—516no—
172C2×#396—51no—
173C2×#395D511yescharacteristic, complemented
174C2×#394—51no—
175C2×#392—51no—
176C2×#390—51no—
177C2×#388—51no—
178C2×#388—51no—
179C2×#388—51no—
180C2×#386—51no—
181C2×#385—51no—
182C2×C4×C4⋊C4—51no—
183C24×C5C2411yescharacteristic
184C23×D5—22no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—22no—
189C23×D5—22no—
190C23×D5—22no—
191C23×D5—22no—
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5—22no—
199C23×D5—22no—
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5C2×D414yes—
204C23×D5#4114yes—
205C23×D5C2412yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
208C2×C5×Q8—28no—
209C2×C5×Q8—28no—
210C2×C5×Q8—44no—
211C2×C5×Q8—416no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—22no—
227C22×C4×C5—22no—
228C22×C4×C5—22no—
229C22×C4×C5C2×D414yes—
230C22×C4×C5C2×D414yes—
231C22×C4×C5#4114yes—
232C22×C4×C5#4114yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C22×C4×C5C2412yes—
237C22×C4×C5C2412yes—
238C22×C4×C5C2412yes—
239C22×C4×C5C2412yes—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5C2×D414yes—
253C22×Dic5C2×D414yes—
254C22×Dic5C2×D414yes—
255C22×Dic5C2412yes—
256C22×Dic5C2412yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C2×D20—232no—
261C2×D20—28no—
262C2×D20—28no—
263C2×D20—28no—
264C2×D20—28no—
265C2×D20—28no—
266C2×D20—28no—
267C2×D20—28no—
268C2×D20—44no—
269C2×D20—44no—
270C2×D20—416no—
271C2×D20—416no—
272C2×C4×D5—28no—
273C2×C4×D5—28no—
274C2×C4×D5—28no—
275C2×C4×D5—28no—
276C2×C4×D5—44no—
277C2×C4×D5—44no—
278C2×C4×D5—416no—
279C2×C4×D5—416no—
280C5×C4⋊C4—28no—
281C5×C4⋊C4—28no—
282C5×C4⋊C4—44no—
283#685—28no—
284#685—28no—
285#685—28no—
286#685—28no—
287#685—28no—
288#685—28no—
289#685—28no—
290#685—28no—
291#685—28no—
292#685—28no—
293#685—28no—
294#685—28no—
295#685C2×D4116yescomplemented
296C4⋊Dic5—28no—
297#683—28no—
298#683—28no—
299#683C2×D4116yescomplemented
300C4×Dic5—28no—
301C4×Dic5—28no—
302C4×Dic5—28no—
303C23×Q8C2×D511yescharacteristic
304C23×D4—51no—
305C23×D4—51no—
306C23×D4—51no—
307C24×C4—51no—
308C24×C4—51no—
309C2×#124—58no—
310C2×#124—108no—
311C2×#123—58no—
312C2×#123—108no—
313C2×C22⋊Q8—58no—
314C2×C22⋊Q8—108no—
315C2×C4×D4—58no—
316C2×C4×D4—108no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4C2×D511yescharacteristic
322C22×C4⋊C4C2×D511yescharacteristic
323C22×C4⋊C4C2×D511yescharacteristic
324C22×C22⋊C4—51no—
325C22×C22⋊C4—51no—
326C22×C22⋊C4—51no—
327C22×C22⋊C4—51no—
328C22×C22⋊C4—51no—
329C22×C22⋊C4—51no—
330C22×C22⋊C4—51no—
331C22×C22⋊C4—51no—
332C22×C22⋊C4—51no—
333C22×C22⋊C4—51no—
334C22×C22⋊C4—51no—
335C22×C22⋊C4—51no—
336C22×C22⋊C4—51no—
337C22×C42—51no—
338C22×C42—51no—
339C22×C42—51no—
340#396—58no—
341#395C2×D518yescomplemented
342#394—58no—
343#392—58no—
344#390—58no—
345#388—58no—
346#388—58no—
347#388—58no—
348#386—58no—
349#385—58no—
350C4×C4⋊C4—58no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95C2×D511yescharacteristic
355C2×#95C2×D511yescharacteristic
356C2×#95C2×D511yescharacteristic
357C23×C5C22×D412yes—
358C23×C5C22×D412yes—
359C23×C5C2×#4112yes—
360C23×C5C2×#4112yes—
361C23×C5C2×#4112yes—
362C23×C5H(5,𝔽2)12yes—
363C23×C52−1+412yes—
364C23×C5C2511yescharacteristic
365C22×D5—28no—
366C22×D5—28no—
367C22×D5—28no—
368C22×D5—28no—
369C22×D5—28no—
370C22×D5—28no—
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—44no—
391C22×D5—44no—
392C22×D5—44no—
393C22×D5—44no—
394C22×D5—44no—
395C22×D5—44no—
396C22×D5—44no—
397C22×D5—44no—
398C22×D5—44no—
399C22×D5—44no—
400C22×D5—44no—
401C22×D5—44no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5C22×D414yes—
406C22×D5C2×#4114yes—
407C5×Q8—416no—
408C2×C4×C5—28no—
409C2×C4×C5—28no—
410C2×C4×C5—28no—
411C2×C4×C5—28no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—22no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—44no—
430C2×C4×C5—44no—
431C2×C4×C5—44no—
432C2×C4×C5C22×D414yes—
433C2×C4×C5C22×D414yes—
434C2×C4×C5C2×#4114yes—
435C2×C4×C5C2×#4114yes—
436C2×Dic5—28no—
437C2×Dic5—28no—
438C2×Dic5—28no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—44no—
452C2×Dic5—44no—
453C2×Dic5C22×D414yes—
454C2×Dic5C22×D414yes—
455C2×Dic5C22×D414yes—
456D20—232no—
457D20—416no—
458D20—416no—
459C4×D5—416no—
460C4×D5—416no—
461C25—51no—
462C25—51no—
463C25—51no—
464C22×Q8—24no—
465C22×Q8—24no—
466C22×Q8—42no—
467C22×Q8C22×D514yes—
468C22×D4—54no—
469C22×D4—54no—
470C22×D4—54no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—104no—
478C22×D4—202no—
479C22×D4—202no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—54no—
486C23×C4—54no—
487C23×C4—104no—
488C23×C4—104no—
489C23×C4—104no—
490C23×C4—104no—
491C23×C4—202no—
492C23×C4—202no—
493C23×C4C22×D511yescharacteristic
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D511yescharacteristic
496C23×C4C22×D511yescharacteristic
497C23×C4C22×D511yescharacteristic
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500#124—1032no—
501#123—1032no—
502C22⋊Q8—1032no—
503C4×D4—1032no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—58no—
508C2×C4⋊C4—54no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—54no—
511C2×C4⋊C4—54no—
512C2×C4⋊C4—104no—
513C2×C4⋊C4—104no—
514C2×C4⋊C4—104no—
515C2×C4⋊C4C22×D514yes—
516C2×C4⋊C4C22×D514yes—
517C2×C4⋊C4C22×D514yes—
518C2×C22⋊C4—58no—
519C2×C22⋊C4—54no—
520C2×C22⋊C4—54no—
521C2×C22⋊C4—54no—
522C2×C22⋊C4—54no—
523C2×C22⋊C4—54no—
524C2×C22⋊C4—54no—
525C2×C22⋊C4—54no—
526C2×C22⋊C4—54no—
527C2×C22⋊C4—54no—
528C2×C22⋊C4—54no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—104no—
533C2×C22⋊C4—104no—
534C2×C22⋊C4—104no—
535C2×C22⋊C4—104no—
536C2×C22⋊C4—104no—
537C2×C22⋊C4—104no—
538C2×C22⋊C4—104no—
539C2×C22⋊C4—104no—
540C2×C22⋊C4—104no—
541C2×C22⋊C4—104no—
542C2×C22⋊C4—104no—
543C2×C22⋊C4—104no—
544C2×C42—54no—
545C2×C42—54no—
546C2×C42—54no—
547C2×C42—104no—
548C2×C42—104no—
549C2×C42—104no—
550#95—54no—
551#95—54no—
552#95—54no—
553#95C22×D514yes—
554#95C22×D514yes—
555#95C22×D514yes—
556C22×C5#52514yes—
557C22×C5#53214yes—
558C22×C5#54214yes—
559C22×C5D4214yes—
560C22×C5#54714yes—
561C22×C5#54814yes—
562C22×C5#55114yes—
563C22×C5C23×D411yescharacteristic
564C22×C5C23×D411yescharacteristic
565C22×C5C22×#4111yescharacteristic
566C22×C5C22×#4111yescharacteristic
567C22×C5C22×#4111yescharacteristic
568C22×C5C2×H(5,𝔽2)11yescharacteristic
569C22×C5C2×2−1+411yescharacteristic
570C2×D5—24no—
571C2×D5—24no—
572C2×D5—24no—
573C2×D5—24no—
574C2×D5—24no—
575C2×D5—24no—
576C2×D5—42no—
577C2×D5—42no—
578C2×D5—42no—
579C2×D5—42no—
580C2×D5—42no—
581C2×D5—42no—
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—416no—
585C2×D5—416no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—88no—
594C4×C5—24no—
595C4×C5—24no—
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—42no—
599C4×C5—42no—
600C4×C5—42no—
601Dic5—24no—
602Dic5—24no—
603Dic5—24no—
604Dic5—42no—
605Dic5—42no—
606C24—54no—
607C24—54no—
608C24—52no—
609C24—52no—
610C24—52no—
611C24—102no—
612C24—102no—
613C24—102no—
614C24—102no—
615C24—102no—
616C24—102no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24—102no—
629C24—102no—
630C24C23×D511yescharacteristic
631C2×Q8—28no—
632C2×Q8—28no—
633C2×Q8—44no—
634C2×Q8—416no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—1032no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—108no—
643C2×D4—204no—
644C2×D4—204no—
645C2×D4—2016no—
646C2×D4—2016no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—54no—
665C22×C4—54no—
666C22×C4—54no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—52no—
672C22×C4—108no—
673C22×C4—108no—
674C22×C4—108no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—108no—
688C22×C4—204no—
689C22×C4—204no—
690C22×C4—2016no—
691C22×C4—2016no—
692C22×C4D4×D514yes—
693C22×C4D4×D514yes—
694C22×C4#71314yes—
695C22×C4#71314yes—
696C22×C4C23×D512yes—
697C22×C4C23×D512yes—
698C22×C4C23×D512yes—
699C22×C4C23×D512yes—
700C22×C4C23×D512yes—
701C22×C4C23×D512yes—
702C22×C4C23×D512yes—
703C4⋊C4—28no—
704C4⋊C4—28no—
705C4⋊C4—44no—
706C4⋊C4—516no—
707C4⋊C4—108no—
708C4⋊C4—108no—
709C4⋊C4—108no—
710C22⋊C4—516no—
711C22⋊C4—108no—
712C22⋊C4—108no—
713C22⋊C4—108no—
714C22⋊C4—108no—
715C22⋊C4—108no—
716C22⋊C4—108no—
717C22⋊C4—108no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C42—108no—
724C42—108no—
725C42—108no—
726C2×C5#246118yescomplemented
727C2×C5C2×#52511yescharacteristic
728C2×C5C2×#53211yescharacteristic
729C2×C5C2×#54211yescharacteristic
730C2×C5C2×D4211yescharacteristic
731C2×C5C2×#54711yescharacteristic
732C2×C5C2×#54811yescharacteristic
733C2×C5C2×#55111yescharacteristic
734D5—44no—
735D5—44no—
736D5—82no—
737C23—54no—
738C23—54no—
739C23—108no—
740C23—108no—
741C23—108no—
742C23—108no—
743C23—108no—
744C23—108no—
745C23—102no—
746C23—102no—
747C23—102no—
748C23—102no—
749C23—102no—
750C23—102no—
751C23—102no—
752C23—102no—
753C23—102no—
754C23—102no—
755C23—102no—
756C23—102no—
757C23—102no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—204no—
765C23—204no—
766C23—204no—
767C23—204no—
768C23—204no—
769C23—204no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23—204no—
779C23C2×D4×D512yes—
780C23C2×D4×D512yes—
781C23#414412yes—
782C23C2×#71312yes—
783C23C2×#71312yes—
784C23#414712yes—
785C23D5×#4112yes—
786C23C24×D511yescharacteristic
787Q8—416no—
788D4—1032no—
789D4—2016no—
790D4—2016no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—54no—
816C2×C4—54no—
817C2×C4—54no—
818C2×C4—108no—
819C2×C4—108no—
820C2×C4—108no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—2016no—
834C2×C4—2016no—
835C2×C4—204no—
836C2×C4—204no—
837C2×C4C2×D4×D514yes—
838C2×C4C2×D4×D514yes—
839C2×C4C2×#71314yes—
840C2×C4C2×#71314yes—
841C5C2×#246111yescharacteristic, complemented, Sylow
842C22—104no—
843C22—104no—
844C22—104no—
845C22—104no—
846C22—104no—
847C22—104no—
848C22—202no—
849C22—2016no—
850C22—2016no—
851C22—202no—
852C22—202no—
853C22—202no—
854C22—202no—
855C22—202no—
856C22—202no—
857C22—202no—
858C22—202no—
859C22—202no—
860C22—202no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—408no—
866C22#6592414yes—
867C22#6596114yes—
868C22#6596714yes—
869C22#6597114yes—
870C22#6605914yes—
871C22#6606014yes—
872C22#6606714yes—
873C22C22×D4×D511yescharacteristic
874C22C22×D4×D511yescharacteristic
875C22C2×#414411yescharacteristic
876C22C22×#71311yescharacteristic
877C22C22×#71311yescharacteristic
878C22C2×#414711yescharacteristic
879C22C2×D5×#4111yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—104no—
888C4—104no—
889C4—104no—
890C4—202no—
891C4—202no—
892C2—204no—
893C2—204no—
894C2—402no—
895C2#1060890718yesdirect product factor
896C2C2×#6592411yescharacteristic
897C2C2×#6596111yescharacteristic
898C2C2×#6596711yescharacteristic
899C2C2×#6597111yescharacteristic
900C2C2×#6605911yescharacteristic
901C2C2×#6606711yescharacteristic
902C2C2×#6606011yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#395C2
socleC24×C5C24
prime radicalC2×#64960C2
hypercenterC2×#395D5
hypocenterC5C2×#2461
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. C22×#4092C2semidirect
2. C22×#4093C2semidirect
3. C22×#4040C2semidirect
4. C22×#4039C2semidirect
5. C2×C5×#395C2semidirect
6. C2×#65283C2semidirect
7. C2×#65278C2semidirect
8. C2×#65277C2semidirect
9. C2×#65279C2semidirect
10. #10608907C2direct (N × H)
12. C2×#64954C2semidirect
13. C2×#64961C2semidirect
14. C2×#64959C2semidirect
15. C2×#64958C2semidirect
16. C2×#64938C2semidirect
27. C2×#4093C22semidirect
29. C2×#4092C22semidirect
51. C2×#4040C22semidirect
53. C2×#4039C22semidirect
54. C5×#395C22semidirect
61. #65283C22semidirect
62. #65279C22semidirect
63. #65278C22semidirect
64. #65277C22semidirect
65. #64961C22semidirect
67. #64959C22semidirect
68. #64958C22semidirect
69. #64954C22semidirect
70. #64938C22semidirect
131. C2×#685D4semidirect
149. C2×#683D4semidirect
173. C2×#395D5semidirect
295. #685C2×D4semidirect
299. #683C2×D4semidirect
341. #395C2×D5semidirect
726. C2×C5#2461semidirect
841. C5C2×#2461semidirect
895. C2#10608907direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40922
C22×#40932
C22×#40402
C22×#40392
C2×C5×#3952
C2×#652832
C2×#652782
C2×#652772
C2×#652792
#106089072
C2×#649602
C2×#649542
C2×#649612
C2×#649592
C2×#649582
C2×#649382
C2×#24615