Finite Group Databasebeta

← C2×#10607242 #12267162

Subgroups — C2×#10607242 #12267162

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×#4040C211yesmaximal, characteristic, complemented
2C22×#4024C211yesmaximal, characteristic, complemented
3C22×#4027C211yesmaximal, characteristic, complemented
4C22×#4021C211yesmaximal, characteristic, complemented
5C2×C5×#388C211yesmaximal, characteristic, complemented
6C2×#65268C211yesmaximal, characteristic, complemented
7C2×#65248C211yesmaximal, characteristic, complemented
8C2×#65249C211yesmaximal, characteristic
9C2×#65246C211yesmaximal, characteristic, complemented
10C2×#65247C211yesmaximal, characteristic, complemented
11C2×C4×#683C211yesmaximal, characteristic, complemented
12#10607242C2116yesmaximal, direct product factor
13C2×#64965C211yesmaximal, characteristic, complemented
14C2×#64957C211yesmaximal, characteristic, complemented
15C2×#64959C211yesmaximal, characteristic, complemented
16C2×#64958C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C24×Dic5C2211yescharacteristic
20C23×D20C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4040—28no—
47C2×#4040C2218yescomplemented
48C2×#4027—28no—
49C2×#4027C2218yescomplemented
50C2×#4024—28no—
51C2×#4024C2218yescomplemented
52C2×#4021—28no—
53C2×#4021C2218yescomplemented
54C5×#388C2218yescomplemented
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65268C2218yescomplemented
62#65249C2218yes—
63#65248C2218yescomplemented
64#65247C2218yescomplemented
65#65246C2218yescomplemented
66C4×#683C2218yescomplemented
67#64965C2218yescomplemented
68#64959C2218yescomplemented
69#64958C2218yescomplemented
70#64957C2218yescomplemented
71C2×#2461—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—24no—
82C22×C22⋊D5—24no—
83C22×C22⋊D5—24no—
84C22×C22⋊D5—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—42no—
87C22×C22⋊D5C2314yes—
88C22×C22⋊D5C2314yes—
89C23×Dic5—24no—
90C23×Dic5—24no—
91C23×Dic5—42no—
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2314yes—
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C22×D20—24no—
100C22×D20—24no—
101C22×D20—42no—
102C22×D20C2314yes—
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—42no—
106C22×C4×D5C2314yes—
107C22×Dic10—24no—
108C22×Dic10—24no—
109C22×Dic10—42no—
110C22×Dic10C2314yes—
111C2×C5×C4⋊C4—24no—
112C2×C5×C4⋊C4C2314yes—
113C2×C5×C22⋊C4—24no—
114C2×C5×C22⋊C4—24no—
115C2×C5×C22⋊C4—24no—
116C2×C5×C22⋊C4C2314yes—
117C2×C5×C22⋊C4C2314yes—
118C2×C5×C22⋊C4C2314yes—
119C2×C42×C5—24no—
120C2×C42×C5C2314yes—
121C2×C22⋊Dic5—24no—
122C2×C22⋊Dic5C2314yes—
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×C4⋊Dic5—24no—
142C2×C4⋊Dic5C2314yes—
143C2×#683—24no—
144C2×#683—24no—
145C2×#683—24no—
146C2×#683—42no—
147C2×#683D418yescomplemented
148C2×#683C2314yes—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×C4×Dic5—24no—
154C2×C4×Dic5—24no—
155C2×C4×Dic5C2314yes—
156C2×C4×Dic5C2314yes—
157#4040—232no—
158#4027—232no—
159#4024—232no—
160#4021—232no—
161C5×#95C2314yes—
162C5×#95C2314yes—
163#3963C2314yes—
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×#395—51no—
174C2×#394—51no—
175C2×#392—51no—
176C2×#390—51no—
177C2×#388—51no—
178C2×#388—51no—
179C2×#388D511yescharacteristic, complemented
180C2×#386—51no—
181C2×#385—51no—
182C2×C4×C4⋊C4—51no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5#4114yes—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
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×D5—22no—
204C23×D5—22no—
205C23×D5C2×D414yes—
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×C5C2×D414yes—
225C22×C4×C5C2×D414yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C2×C22⋊D5—232no—
233C2×C22⋊D5—28no—
234C2×C22⋊D5—28no—
235C2×C22⋊D5—28no—
236C2×C22⋊D5—28no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—44no—
239C2×C22⋊D5—416no—
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×Dic5—22no—
253C22×Dic5—28no—
254C22×Dic5—28no—
255C22×Dic5—44no—
256C22×Dic5—416no—
257C22×Dic5C2×D414yes—
258C22×Dic5C2×D414yes—
259C22×Dic5C2×D414yes—
260C22×Dic5#4114yes—
261C22×Dic5#4114yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C2×D20—28no—
269C2×D20—28no—
270C2×D20—44no—
271C2×D20—416no—
272C2×C4×D5—28no—
273C2×C4×D5—28no—
274C2×C4×D5—44no—
275C2×C4×D5—416no—
276C2×Dic10—28no—
277C2×Dic10—28no—
278C2×Dic10—44no—
279C2×Dic10—416no—
280C5×C4⋊C4—28no—
281C5×C22⋊C4—28no—
282C5×C22⋊C4—28no—
283C5×C22⋊C4—28no—
284C42×C5—28no—
285C22⋊Dic5—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#685C2×D4116yescomplemented
295C4⋊Dic5—28no—
296#683—28no—
297#683—28no—
298#683—28no—
299#683—44no—
300#683C2×D4116yescomplemented
301C4×Dic5—28no—
302C4×Dic5—28no—
303C23×Q8—51no—
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⋊C4—51no—
322C22×C4⋊C4—51no—
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⋊C4C2×D511yescharacteristic
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C42—51no—
338C22×C42—51no—
339C22×C42C2×D511yescharacteristic
340#396—58no—
341#395—58no—
342#394—58no—
343#392—58no—
344#390—58no—
345#388—58no—
346#388—58no—
347#388C2×D518yescomplemented
348#386—58no—
349#385—58no—
350C4×C4⋊C4—58no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95C2×D511yescharacteristic
356C2×#95C2×D511yescharacteristic
357C23×C5—28no—
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5C22×D412yes—
371C23×C5C22×D412yes—
372C23×C5C2×#4114yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4112yes—
376C23×C5H(5,𝔽2)12yes—
377C23×C52−1+412yes—
378C23×C5C2511yescharacteristic
379C22×D5—28no—
380C22×D5—28no—
381C22×D5—28no—
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—22no—
393C22×D5—22no—
394C22×D5—22no—
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×D5—44no—
406C22×D5C22×D414yes—
407C2×C4×C5—28no—
408C2×C4×C5—28no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
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—44no—
426C2×C4×C5—44no—
427C2×C4×C5—44no—
428C2×C4×C5—44no—
429C2×C4×C5C22×D414yes—
430C2×C4×C5C22×D414yes—
431C22⋊D5—232no—
432C22⋊D5—416no—
433C2×Dic5—28no—
434C2×Dic5—28no—
435C2×Dic5—28no—
436C2×Dic5—28no—
437C2×Dic5—28no—
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—22no—
451C2×Dic5—416no—
452C2×Dic5—44no—
453C2×Dic5C22×D414yes—
454C2×Dic5C22×D414yes—
455C2×Dic5C22×D414yes—
456C2×Dic5C2×#4114yes—
457C2×Dic5C2×#4114yes—
458D20—416no—
459C4×D5—416no—
460Dic10—416no—
461C25—51no—
462C25—51no—
463C25C22×D511yescharacteristic
464C22×Q8—54no—
465C22×Q8—104no—
466C22×Q8—104no—
467C22×Q8—202no—
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—51no—
486C23×C4—54no—
487C23×C4—54no—
488C23×C4—104no—
489C23×C4—104no—
490C23×C4—104no—
491C23×C4—104no—
492C23×C4—202no—
493C23×C4—202no—
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—58no—
506C2×C4⋊C4—54no—
507C2×C4⋊C4—54no—
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⋊C4—104no—
516C2×C4⋊C4—202no—
517C2×C4⋊C4C22×D514yes—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—58no—
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⋊C4C22×D514yes—
542C2×C22⋊C4C22×D514yes—
543C2×C22⋊C4C22×D514yes—
544C2×C42—24no—
545C2×C42—54no—
546C2×C42—54no—
547C2×C42—104no—
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—24no—
557C22×C5—24no—
558C22×C5—24no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—416no—
564C22×C5#52514yes—
565C22×C5#53214yes—
566C22×C5#54214yes—
567C22×C5D4214yes—
568C22×C5#54714yes—
569C22×C5#54814yes—
570C22×C5#55114yes—
571C22×C5C23×D411yescharacteristic
572C22×C5C23×D411yescharacteristic
573C22×C5C22×#4111yescharacteristic
574C22×C5C22×#4111yescharacteristic
575C22×C5C22×#4111yescharacteristic
576C22×C5C2×H(5,𝔽2)11yescharacteristic
577C22×C5C2×2−1+411yescharacteristic
578C2×D5—24no—
579C2×D5—24no—
580C2×D5—24no—
581C2×D5—42no—
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—42no—
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—42no—
597C4×C5—42no—
598C4×C5—42no—
599C4×C5—42no—
600Dic5—24no—
601Dic5—24no—
602Dic5—24no—
603Dic5—24no—
604Dic5—24no—
605Dic5—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—54no—
613C24—52no—
614C24—52no—
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#70914yes—
629C24C23×D512yes—
630C24C23×D511yescharacteristic
631C2×Q8—108no—
632C2×Q8—108no—
633C2×Q8—204no—
634C2×Q8—2016no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—1032no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—108no—
643C2×D4—204no—
644C2×D4—2016no—
645C2×D4—204no—
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—54no—
664C22×C4—54no—
665C22×C4—54no—
666C22×C4—54no—
667C22×C4—54no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—52no—
672C22×C4—52no—
673C22×C4—52no—
674C22×C4—108no—
675C22×C4—108no—
676C22×C4—108no—
677C22×C4—108no—
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—102no—
688C22×C4—102no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—204no—
692C22×C4—2016no—
693C22×C4—204no—
694C22×C4—2016no—
695C22×C4D4×D514yes—
696C22×C4D4×D514yes—
697C22×C4C23×D512yes—
698C22×C4C23×D512yes—
699C22×C4C23×D512yes—
700C22×C4C23×D512yes—
701C22×C4C23×D512yes—
702C22×C4C23×D512yes—
703C4⋊C4—28no—
704C4⋊C4—516no—
705C4⋊C4—108no—
706C4⋊C4—108no—
707C4⋊C4—108no—
708C4⋊C4—108no—
709C4⋊C4—204no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—28no—
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—
723C42—28no—
724C42—108no—
725C42—108no—
726C2×C5—44no—
727C2×C5#246118yescomplemented
728C2×C5C2×#52511yescharacteristic
729C2×C5C2×#53211yescharacteristic
730C2×C5C2×#54211yescharacteristic
731C2×C5C2×D4211yescharacteristic
732C2×C5C2×#54711yescharacteristic
733C2×C5C2×#54811yescharacteristic
734C2×C5C2×#55111yescharacteristic
735D5—44no—
736D5—82no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—54no—
751C23—108no—
752C23—108no—
753C23—108no—
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—102no—
767C23—204no—
768C23—204no—
769C23—204no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23C2×#70914yes—
779C23C2×#70912yes—
780C23C2×D4×D512yes—
781C23C2×D4×D512yes—
782C23D5×#4112yes—
783C23D5×#4112yes—
784C23#414912yes—
785C23#415012yes—
786C23C24×D511yescharacteristic
787Q8—2016no—
788D4—1032no—
789D4—2016no—
790D4—2016no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—22no—
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—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—54no—
814C2×C4—54no—
815C2×C4—54no—
816C2×C4—54no—
817C2×C4—54no—
818C2×C4—108no—
819C2×C4—108no—
820C2×C4—108no—
821C2×C4—108no—
822C2×C4—108no—
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—102no—
834C2×C4—102no—
835C2×C4—102no—
836C2×C4—2016no—
837C2×C4—2016no—
838C2×C4—204no—
839C2×C4C2×D4×D514yes—
840C2×C4C2×D4×D514yes—
841C5C2×#246111yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—416no—
848C22—42no—
849C22—42no—
850C22—104no—
851C22—104no—
852C22—104no—
853C22—202no—
854C22—202no—
855C22—202no—
856C22—2016no—
857C22—202no—
858C22—202no—
859C22—202no—
860C22—202no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—408no—
866C22#6586114yes—
867C22#6588114yes—
868C22#6588614yes—
869C22#6594314yes—
870C22#6598914yes—
871C22#6600214yes—
872C22#6604414yes—
873C22C22×#70911yescharacteristic
874C22C22×D4×D511yescharacteristic
875C22C22×D4×D511yescharacteristic
876C22C2×D5×#4111yescharacteristic
877C22C2×D5×#4111yescharacteristic
878C22C2×#414911yescharacteristic
879C22C2×#415011yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—104no—
887C4—104no—
888C4—104no—
889C4—104no—
890C4—104no—
891C4—202no—
892C2—44no—
893C2—204no—
894C2—402no—
895C2#1060724218yesdirect product factor
896C2C2×#6586111yescharacteristic
897C2C2×#6588611yescharacteristic
898C2C2×#6588111yescharacteristic
899C2C2×#6594311yescharacteristic
900C2C2×#6598911yescharacteristic
901C2C2×#6600211yescharacteristic
902C2C2×#6604411yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC2×#65249C2
hypercenterC2×#388D5
hypocenterC5C2×#2461
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#4040C2semidirect
2. C22×#4024C2semidirect
3. C22×#4027C2semidirect
4. C22×#4021C2semidirect
5. C2×C5×#388C2semidirect
6. C2×#65268C2semidirect
7. C2×#65248C2semidirect
9. C2×#65246C2semidirect
10. C2×#65247C2semidirect
11. C2×C4×#683C2semidirect
12. #10607242C2direct (N × H)
13. C2×#64965C2semidirect
14. C2×#64957C2semidirect
15. C2×#64959C2semidirect
16. C2×#64958C2semidirect
47. C2×#4040C22semidirect
49. C2×#4027C22semidirect
51. C2×#4024C22semidirect
53. C2×#4021C22semidirect
54. C5×#388C22semidirect
61. #65268C22semidirect
63. #65248C22semidirect
64. #65247C22semidirect
65. #65246C22semidirect
66. C4×#683C22semidirect
67. #64965C22semidirect
68. #64959C22semidirect
69. #64958C22semidirect
70. #64957C22semidirect
131. C2×#685D4semidirect
147. C2×#683D4semidirect
179. C2×#388D5semidirect
294. #685C2×D4semidirect
300. #683C2×D4semidirect
347. #388C2×D5semidirect
727. C2×C5#2461semidirect
841. C5C2×#2461semidirect
895. C2#10607242direct (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×#40242
C22×#40272
C22×#40212
C2×C5×#3882
C2×#652682
C2×#652482
C2×#652492
C2×#652462
C2×#652472
C2×C4×#6832
#106072422
C2×#649652
C2×#649572
C2×#649592
C2×#649582
C2×#24615