Finite Group Databasebeta

← C2×#10607957 #12266803

Subgroups — C2×#10607957 #12266803

Order 1280.

3894 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×#4040C211yesmaximal, characteristic, complemented
2C22×#4040C211yesmaximal, characteristic, complemented
3C22×#4039C211yesmaximal, characteristic, complemented
4C22×C4×D20C211yesmaximal, characteristic, complemented
5C2×C5×#389C211yesmaximal, characteristic, complemented
6C2×#65281C211yesmaximal, characteristic, complemented
7C2×#65280C211yesmaximal, characteristic, complemented
8C2×#65278C211yesmaximal, characteristic, complemented
9C2×#65278C211yesmaximal, characteristic, complemented
10C2×#65279C211yesmaximal, characteristic, complemented
11C2×#65229C211yesmaximal, characteristic, complemented
12#10607957C2116yesmaximal, direct product factor
13C2×#64960C211yesmaximal, characteristic
14C2×#64957C211yesmaximal, characteristic, complemented
15C2×#64961C211yesmaximal, characteristic, complemented
16C2×#64936C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4040—28no—
47C2×#4040—28no—
48C2×#4040C2218yescomplemented
49C2×#4040C2218yescomplemented
50C2×#4039—28no—
51C2×#4039C2218yescomplemented
52C2×C4×D20—28no—
53C2×C4×D20C2218yescomplemented
54C5×#389C2218yescomplemented
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65281C2218yescomplemented
62#65280C2218yescomplemented
63#65279C2218yescomplemented
64#65278C2218yescomplemented
65#65278C2218yescomplemented
66#65229C2218yescomplemented
67#64961C2218yescomplemented
68#64960C2218yes—
69#64957C2218yescomplemented
70#64936C2218yescomplemented
71C2×#2455—51nomaximal, Sylow
72C24×D5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C22×D20—24no—
88C22×D20—24no—
89C22×D20—24no—
90C22×D20—24no—
91C22×D20—24no—
92C22×D20—24no—
93C22×D20—24no—
94C22×D20—24no—
95C22×D20—42no—
96C22×D20C2314yes—
97C22×D20C2314yes—
98C22×D20C2314yes—
99C22×C4×D5—24no—
100C22×C4×D5—24no—
101C22×C4×D5—24no—
102C22×C4×D5—24no—
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—42no—
106C22×C4×D5—42no—
107C22×C4×D5—42no—
108C22×C4×D5C2314yes—
109C22×C4×D5C2314yes—
110C22×C4×D5C2314yes—
111C2×C5×C4⋊C4—24no—
112C2×C5×C4⋊C4—24no—
113C2×C5×C4⋊C4—24no—
114C2×C5×C4⋊C4—24no—
115C2×C5×C4⋊C4C2314yes—
116C2×C5×C4⋊C4C2314yes—
117C2×C5×C4⋊C4C2314yes—
118C2×C5×C4⋊C4C2314yes—
119C2×C42×C5—24no—
120C2×C42×C5C2314yes—
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—42no—
131C2×#685D418yescomplemented
132C2×#685D418yescomplemented
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×#683—24no—
150C2×#683—42no—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×C4×Dic5—24no—
156C2×C4×Dic5C2314yes—
157#4040—232no—
158#4040—232no—
159#4039—232no—
160C4×D20—232no—
161C5×#95C2314yes—
162C5×#95C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#123—51no—
168C22×#123—51no—
169C22×C4×D4—51no—
170C22×C4×D4—51no—
171#2455—516no—
172C2×#399—51no—
173C2×#394—51no—
174C2×#394—51no—
175C2×#392—51no—
176C2×#389—51no—
177C2×#389D511yescharacteristic, complemented
178C2×#388—51no—
179C2×#388—51no—
180C2×#385—51no—
181C2×#385—51no—
182C2×#385—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×D5C2×D414yes—
203C23×D5C2×D414yes—
204C23×D5#4114yes—
205C23×D5C2412yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
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×C5C2×D414yes—
226C22×C4×C5C2×D414yes—
227C22×C4×C5#4114yes—
228C22×C4×C5#4114yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
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×Dic5C2×D414yes—
250C22×Dic5C2×D414yes—
251C22×Dic5C2412yes—
252C22×Dic5C2412yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C2×D20—232no—
257C2×D20—232no—
258C2×D20—28no—
259C2×D20—28no—
260C2×D20—28no—
261C2×D20—28no—
262C2×D20—28no—
263C2×D20—28no—
264C2×D20—28no—
265C2×D20—28no—
266C2×D20—44no—
267C2×D20—416no—
268C2×C4×D5—28no—
269C2×C4×D5—28no—
270C2×C4×D5—28no—
271C2×C4×D5—28no—
272C2×C4×D5—28no—
273C2×C4×D5—28no—
274C2×C4×D5—44no—
275C2×C4×D5—44no—
276C2×C4×D5—44no—
277C2×C4×D5—416no—
278C2×C4×D5—416no—
279C2×C4×D5—416no—
280C5×C4⋊C4—28no—
281C5×C4⋊C4—28no—
282C5×C4⋊C4—28no—
283C5×C4⋊C4—28no—
284C42×C5—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—44no—
295#685C2×D4116yescomplemented
296#685C2×D4116yescomplemented
297C4⋊Dic5—28no—
298#683—28no—
299#683—28no—
300#683—28no—
301#683—44no—
302C4×Dic5—28no—
303C23×D4—51no—
304C23×D4—51no—
305C23×D4—51no—
306C24×C4—51no—
307C24×C4—51no—
308C24×C4—51no—
309C2×#123—58no—
310C2×#123—58no—
311C2×#123—108no—
312C2×#123—108no—
313C2×C4×D4—58no—
314C2×C4×D4—58no—
315C2×C4×D4—108no—
316C2×C4×D4—108no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4C2×D511yescharacteristic
323C22×C4⋊C4C2×D511yescharacteristic
324C22×C4⋊C4C2×D511yescharacteristic
325C22×C4⋊C4C2×D511yescharacteristic
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×C22⋊C4—51no—
338C22×C42—51no—
339C22×C42C2×D511yescharacteristic
340#399—58no—
341#394—58no—
342#394—58no—
343#392—58no—
344#389—58no—
345#389C2×D518yescomplemented
346#388—58no—
347#388—58no—
348#385—58no—
349#385—58no—
350#385—58no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
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—28no—
372C22×D5—28no—
373C22×D5—28no—
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—22no—
391C22×D5—22no—
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×D5C22×D414yes—
405C22×D5C22×D414yes—
406C22×D5C2×#4114yes—
407C2×C4×C5—28no—
408C2×C4×C5—28no—
409C2×C4×C5—28no—
410C2×C4×C5—28no—
411C2×C4×C5—22no—
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—44no—
429C2×C4×C5—44no—
430C2×C4×C5—44no—
431C2×C4×C5C22×D414yes—
432C2×C4×C5C22×D414yes—
433C2×C4×C5C2×#4114yes—
434C2×C4×C5C2×#4114yes—
435C2×Dic5—28no—
436C2×Dic5—28no—
437C2×Dic5—22no—
438C2×Dic5—22no—
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—44no—
451C2×Dic5—44no—
452C2×Dic5—44no—
453C2×Dic5C22×D414yes—
454C2×Dic5C22×D414yes—
455D20—232no—
456D20—232no—
457D20—416no—
458C4×D5—416no—
459C4×D5—416no—
460C4×D5—416no—
461C25—51no—
462C25—51no—
463C25—51no—
464C22×D4—54no—
465C22×D4—54no—
466C22×D4—54no—
467C22×D4—104no—
468C22×D4—104no—
469C22×D4—104no—
470C22×D4—104no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—202no—
476C23×C4—51no—
477C23×C4—51no—
478C23×C4—51no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—54no—
482C23×C4—54no—
483C23×C4—54no—
484C23×C4—104no—
485C23×C4—104no—
486C23×C4—104no—
487C23×C4—104no—
488C23×C4—104no—
489C23×C4—104no—
490C23×C4—202no—
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#123—1032no—
501#123—1032no—
502C4×D4—1032no—
503C4×D4—1032no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—54no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—54no—
511C2×C4⋊C4—54no—
512C2×C4⋊C4—54no—
513C2×C4⋊C4—104no—
514C2×C4⋊C4—104no—
515C2×C4⋊C4—104no—
516C2×C4⋊C4—104no—
517C2×C4⋊C4—202no—
518C2×C4⋊C4C22×D514yes—
519C2×C4⋊C4C22×D514yes—
520C2×C4⋊C4C22×D514yes—
521C2×C4⋊C4C22×D514yes—
522C2×C22⋊C4—58no—
523C2×C22⋊C4—58no—
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—54no—
533C2×C22⋊C4—54no—
534C2×C22⋊C4—54no—
535C2×C22⋊C4—54no—
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×C22⋊C4—104no—
545C2×C22⋊C4—202no—
546C2×C42—24no—
547C2×C42—54no—
548C2×C42—104no—
549C2×C42C22×D514yes—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95C22×D514yes—
555#95C22×D514yes—
556C22×C5#52514yes—
557C22×C5#52514yes—
558C22×C5#53914yes—
559C22×C5D4214yes—
560C22×C5#54714yes—
561C22×C5#54714yes—
562C22×C5#55914yes—
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—24no—
577C2×D5—24no—
578C2×D5—24no—
579C2×D5—42no—
580C2×D5—42no—
581C2×D5—42no—
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—42no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—416no—
589C2×D5—416no—
590C2×D5—416no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—42no—
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—42no—
604Dic5—42no—
605Dic5—42no—
606C24—54no—
607C24—54no—
608C24—54no—
609C24—52no—
610C24—52no—
611C24—52no—
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×D4—108no—
632C2×D4—108no—
633C2×D4—108no—
634C2×D4—108no—
635C2×D4—1032no—
636C2×D4—1032no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—204no—
642C2×D4—2016no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
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—54no—
661C22×C4—54no—
662C22×C4—52no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—108no—
668C22×C4—108no—
669C22×C4—108no—
670C22×C4—108no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4—102no—
674C22×C4—102no—
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—108no—
685C22×C4—108no—
686C22×C4—204no—
687C22×C4—204no—
688C22×C4—204no—
689C22×C4—2016no—
690C22×C4—2016no—
691C22×C4—2016no—
692C22×C4#70914yes—
693C22×C4D4×D514yes—
694C22×C4D4×D514yes—
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—28no—
706C4⋊C4—28no—
707C4⋊C4—108no—
708C4⋊C4—108no—
709C4⋊C4—108no—
710C4⋊C4—108no—
711C4⋊C4—204no—
712C22⋊C4—516no—
713C22⋊C4—516no—
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—
723C22⋊C4—204no—
724C42—28no—
725C42—108no—
726C2×C5#245518yescomplemented
727C2×C5C2×#52511yescharacteristic
728C2×C5C2×#52511yescharacteristic
729C2×C5C2×#53911yescharacteristic
730C2×C5C2×D4211yescharacteristic
731C2×C5C2×#54711yescharacteristic
732C2×C5C2×#54711yescharacteristic
733C2×C5C2×#55911yescharacteristic
734D5—44no—
735D5—44no—
736D5—44no—
737C23—54no—
738C23—54no—
739C23—54no—
740C23—108no—
741C23—108no—
742C23—108no—
743C23—108no—
744C23—108no—
745C23—108no—
746C23—108no—
747C23—108no—
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—102no—
765C23—102no—
766C23—108no—
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×#70912yes—
780C23C2×D4×D512yes—
781C23C2×D4×D512yes—
782C23C2×#71312yes—
783C23#414712yes—
784C23D5×#4112yes—
785C23#414912yes—
786C23C24×D511yescharacteristic
787D4—1032no—
788D4—1032no—
789D4—2016no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—22no—
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—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—54no—
815C2×C4—54no—
816C2×C4—108no—
817C2×C4—108no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
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—2016no—
832C2×C4—2016no—
833C2×C4—2016no—
834C2×C4—204no—
835C2×C4—204no—
836C2×C4—204no—
837C2×C4C2×#70914yes—
838C2×C4C2×D4×D514yes—
839C2×C4C2×D4×D514yes—
840C2×C4C2×#71314yes—
841C5C2×#245511yescharacteristic, complemented, Sylow
842C22—104no—
843C22—104no—
844C22—104no—
845C22—104no—
846C22—104no—
847C22—104no—
848C22—104no—
849C22—104no—
850C22—104no—
851C22—202no—
852C22—202no—
853C22—202no—
854C22—202no—
855C22—202no—
856C22—202no—
857C22—2016no—
858C22—2016no—
859C22—2016no—
860C22—202no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—202no—
866C22#6584114yes—
867C22#6588114yes—
868C22#6591914yes—
869C22#6594314yes—
870C22#6596114yes—
871C22#6602614yes—
872C22#6606014yes—
873C22C22×#70911yescharacteristic
874C22C22×D4×D511yescharacteristic
875C22C22×D4×D511yescharacteristic
876C22C22×#71311yescharacteristic
877C22C2×#414711yescharacteristic
878C22C2×D5×#4111yescharacteristic
879C22C2×#414911yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—104no—
888C4—104no—
889C4—202no—
890C4—202no—
891C4—202no—
892C2—204no—
893C2—204no—
894C2—204no—
895C2#1060795718yesdirect product factor
896C2C2×#6584111yescharacteristic
897C2C2×#6588111yescharacteristic
898C2C2×#6591911yescharacteristic
899C2C2×#6594311yescharacteristic
900C2C2×#6596111yescharacteristic
901C2C2×#6602611yescharacteristic
902C2C2×#6606011yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#389C2
socleC24×C5C24
prime radicalC2×#64960C2
hypercenterC2×#389D5
hypocenterC5C2×#2455
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#4040C2semidirect
2. C22×#4040C2semidirect
3. C22×#4039C2semidirect
4. C22×C4×D20C2semidirect
5. C2×C5×#389C2semidirect
6. C2×#65281C2semidirect
7. C2×#65280C2semidirect
8. C2×#65278C2semidirect
9. C2×#65278C2semidirect
10. C2×#65279C2semidirect
11. C2×#65229C2semidirect
12. #10607957C2direct (N × H)
14. C2×#64957C2semidirect
15. C2×#64961C2semidirect
16. C2×#64936C2semidirect
48. C2×#4040C22semidirect
49. C2×#4040C22semidirect
51. C2×#4039C22semidirect
53. C2×C4×D20C22semidirect
54. C5×#389C22semidirect
61. #65281C22semidirect
62. #65280C22semidirect
63. #65279C22semidirect
64. #65278C22semidirect
65. #65278C22semidirect
66. #65229C22semidirect
67. #64961C22semidirect
69. #64957C22semidirect
70. #64936C22semidirect
131. C2×#685D4semidirect
132. C2×#685D4semidirect
177. C2×#389D5semidirect
295. #685C2×D4semidirect
296. #685C2×D4semidirect
345. #389C2×D5semidirect
726. C2×C5#2455semidirect
841. C5C2×#2455semidirect
895. C2#10607957direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40402
C22×#40392
C22×C4×D202
C2×C5×#3892
C2×#652812
C2×#652802
C2×#652782
C2×#652792
C2×#652292
#106079572
C2×#649602
C2×#649572
C2×#649612
C2×#649362
C2×#24555