Finite Group Databasebeta

← C2×#10608088 #12269412

Subgroups — C2×#10608088 #12269412

Order 1280.

3330 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4031C211yesmaximal, characteristic, complemented
2C22×#4032C211yesmaximal, characteristic, complemented
3C2×C5×#390C211yesmaximal, characteristic, complemented
4C2×#65512C211yesmaximal, characteristic
5C2×#65509C211yesmaximal, characteristic, complemented
6C2×#65282C211yesmaximal, characteristic, complemented
7C2×#65270C211yesmaximal, characteristic, complemented
8C2×#65245C211yesmaximal, characteristic, complemented
9C2×#65245C211yesmaximal, characteristic, complemented
10C2×#65242C211yesmaximal, characteristic, complemented
11C2×#65236C211yesmaximal, characteristic, complemented
12C2×#65240C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14C2×#65218C211yesmaximal, characteristic, complemented
15C2×C4×#685C211yesmaximal, characteristic, complemented
16#10608088C2116yesmaximal, direct product factor
17C23×C5×D4C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C42×C5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4032—28no—
43C2×#4032C2218yescomplemented
44C2×#4031—28no—
45C2×#4031C2218yescomplemented
46C5×#390C2218yescomplemented
47#65512C2218yes—
48#65509C2218yescomplemented
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59#65282C2218yescomplemented
60#65270C2218yescomplemented
61#65245C2218yescomplemented
62#65245C2218yescomplemented
63#65242C2218yescomplemented
64#65240C2218yescomplemented
65#65236C2218yescomplemented
66C22⋊C4×Dic5C2218yescomplemented
67C4×#685C2218yescomplemented
68#65218C2218yescomplemented
69C2×#2557—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C22×C5×D4—24no—
74C22×C5×D4—24no—
75C22×C5×D4—42no—
76C22×C5×D4C2314yes—
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—24no—
83C22×C22⋊D5—24no—
84C22×C22⋊D5—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—42no—
87C22×C22⋊D5—42no—
88C22×C22⋊D5C2314yes—
89C22×C22⋊D5C2314yes—
90C23×Dic5—24no—
91C23×Dic5—24no—
92C23×Dic5—42no—
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2314yes—
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C22×C4×D5—24no—
102C22×C4×D5—42no—
103C22×C4×D5—42no—
104C22×C4×D5C2314yes—
105C22×Dic10—24no—
106C22×Dic10—24no—
107C22×Dic10—42no—
108C22×Dic10C2314yes—
109C2×C5×C4⋊C4—24no—
110C2×C5×C4⋊C4C2314yes—
111C2×C5×C22⋊C4—24no—
112C2×C5×C22⋊C4—24no—
113C2×C5×C22⋊C4—24no—
114C2×C5×C22⋊C4—24no—
115C2×C5×C22⋊C4C2314yes—
116C2×C5×C22⋊C4C2314yes—
117C2×C5×C22⋊C4C2314yes—
118C2×C5×C22⋊C4C2314yes—
119C2×C42×C5—42no—
120C2×C42×C5C2314yes—
121C2×C22⋊Dic5—24no—
122C2×C22⋊Dic5—24no—
123C2×C22⋊Dic5—42no—
124C2×C22⋊Dic5—42no—
125C2×C22⋊Dic5—42no—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130C2×C22⋊Dic5C2314yes—
131C2×#685—24no—
132C2×#685—24no—
133C2×#685—24no—
134C2×#685D418yescomplemented
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×C4⋊Dic5—24no—
140C2×C4⋊Dic5—24no—
141C2×C4⋊Dic5C2314yes—
142C2×C4⋊Dic5C2314yes—
143C2×C4×Dic5—24no—
144C2×C4×Dic5—42no—
145C2×C4×Dic5C2314yes—
146C2×C4×Dic5C2314yes—
147#4032—232no—
148#4031—232no—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#124—51no—
160C22×#123—51no—
161#2557—516no—
162C2×#397—51no—
163C2×#397—51no—
164C2×#393—51no—
165C2×#392—51no—
166C2×#391—51no—
167C2×#390D511yescharacteristic, complemented
168C2×#388—51no—
169C2×#387—51no—
170C2×#386—51no—
171C2×#386—51no—
172C2×#386—51no—
173C2×C4×C22⋊C4—51no—
174C2×C4×C22⋊C4—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5—22no—
182C24×C5—22no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5#4114yes—
189C24×C5C2412yes—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5C2×D414yes—
199C23×D5C2412yes—
200C2×C5×D4—28no—
201C2×C5×D4—28no—
202C2×C5×D4—44no—
203C2×C5×D4—416no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
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×C5C2×D414yes—
217C22×C4×C5#4114yes—
218C22×C4×C5#4114yes—
219C22×C4×C5C2412yes—
220C22×C4×C5C2412yes—
221C22×C4×C5C2412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C2×C22⋊D5—28no—
225C2×C22⋊D5—28no—
226C2×C22⋊D5—28no—
227C2×C22⋊D5—28no—
228C2×C22⋊D5—44no—
229C2×C22⋊D5—44no—
230C2×C22⋊D5—416no—
231C2×C22⋊D5—416no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—28no—
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—28no—
253C22×Dic5—44no—
254C22×Dic5—416no—
255C22×Dic5C2×D414yes—
256C22×Dic5#4114yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C2×C4×D5—28no—
265C2×C4×D5—44no—
266C2×C4×D5—44no—
267C2×C4×D5—416no—
268C2×Dic10—28no—
269C2×Dic10—28no—
270C2×Dic10—44no—
271C2×Dic10—416no—
272C5×C4⋊C4—28no—
273C5×C22⋊C4—28no—
274C5×C22⋊C4—28no—
275C5×C22⋊C4—28no—
276C5×C22⋊C4—28no—
277C42×C5—44no—
278C22⋊Dic5—28no—
279C22⋊Dic5—28no—
280C22⋊Dic5—44no—
281C22⋊Dic5—44no—
282C22⋊Dic5—44no—
283#685—28no—
284#685—28no—
285#685—28no—
286#685C2×D4116yescomplemented
287C4⋊Dic5—28no—
288C4⋊Dic5—28no—
289C4×Dic5—28no—
290C4×Dic5—44no—
291C23×Q8—51no—
292C23×D4—51no—
293C23×D4—51no—
294C23×D4C2×D511yescharacteristic
295C24×C4—51no—
296C24×C4—51no—
297C2×#124—58no—
298C2×#124—108no—
299C2×#123—58no—
300C2×#123—108no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4C2×D511yescharacteristic
304C22×C22⋊C4—51no—
305C22×C22⋊C4—51no—
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C22⋊C4—51no—
311C22×C22⋊C4—51no—
312C22×C22⋊C4—51no—
313C22×C22⋊C4C2×D511yescharacteristic
314C22×C22⋊C4C2×D511yescharacteristic
315C22×C22⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C42—51no—
318C22×C42—51no—
319C22×C42C2×D511yescharacteristic
320#397—58no—
321#397—58no—
322#393—58no—
323#392—58no—
324#391—58no—
325#390C2×D518yescomplemented
326#388—58no—
327#387—58no—
328#386—58no—
329#386—58no—
330#386—58no—
331C4×C22⋊C4—58no—
332C4×C22⋊C4—58no—
333C2×#95—51no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95—51no—
342C2×#95—51no—
343C23×C5—28no—
344C23×C5—28no—
345C23×C5—28no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—44no—
360C23×C5—44no—
361C23×C5—44no—
362C23×C5—44no—
363C23×C5—44no—
364C23×C5—44no—
365C23×C5—44no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5C22×D412yes—
371C23×C5C2×#4114yes—
372C23×C5C2×#4112yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4112yes—
376C23×C5H(5,𝔽2)12yes—
377C23×C5H(5,𝔽2)12yes—
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—44no—
389C22×D5—44no—
390C22×D5—44no—
391C22×D5—44no—
392C22×D5C22×D414yes—
393C5×D4—416no—
394C2×C4×C5—28no—
395C2×C4×C5—28no—
396C2×C4×C5—28no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—44no—
410C2×C4×C5—44no—
411C2×C4×C5C22×D414yes—
412C2×C4×C5C2×#4114yes—
413C2×C4×C5C2×#4114yes—
414C22⋊D5—416no—
415C22⋊D5—416no—
416C2×Dic5—28no—
417C2×Dic5—28no—
418C2×Dic5—22no—
419C2×Dic5—22no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—416no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5—44no—
443C2×Dic5C22×D414yes—
444C2×Dic5C2×#4114yes—
445C4×D5—416no—
446Dic10—416no—
447C25—51no—
448C25C22×D511yescharacteristic
449C25C22×D511yescharacteristic
450C22×Q8—54no—
451C22×Q8—104no—
452C22×Q8—104no—
453C22×Q8—202no—
454C22×D4—24no—
455C22×D4—24no—
456C22×D4—42no—
457C22×D4—54no—
458C22×D4—54no—
459C22×D4—104no—
460C22×D4—104no—
461C22×D4—104no—
462C22×D4—104no—
463C22×D4—202no—
464C22×D4—202no—
465C22×D4C22×D514yes—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
472C23×C4—51no—
473C23×C4—54no—
474C23×C4—54no—
475C23×C4—104no—
476C23×C4—104no—
477C23×C4—104no—
478C23×C4—202no—
479C23×C4—202no—
480C23×C4—202no—
481C23×C4C22×D511yescharacteristic
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D511yescharacteristic
485C23×C4C22×D511yescharacteristic
486#124—1032no—
487#123—1032no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—104no—
492C2×C4⋊C4—104no—
493C2×C4⋊C4C22×D514yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—58no—
499C2×C22⋊C4—54no—
500C2×C22⋊C4—54no—
501C2×C22⋊C4—54no—
502C2×C22⋊C4—54no—
503C2×C22⋊C4—54no—
504C2×C22⋊C4—54no—
505C2×C22⋊C4—54no—
506C2×C22⋊C4—54no—
507C2×C22⋊C4—54no—
508C2×C22⋊C4—104no—
509C2×C22⋊C4—104no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—104no—
513C2×C22⋊C4—202no—
514C2×C22⋊C4—202no—
515C2×C22⋊C4—202no—
516C2×C22⋊C4C22×D514yes—
517C2×C22⋊C4C22×D514yes—
518C2×C22⋊C4C22×D514yes—
519C2×C22⋊C4C22×D514yes—
520C2×C42—42no—
521C2×C42—54no—
522C2×C42—54no—
523C2×C42—104no—
524C2×C42—202no—
525C2×C42C22×D514yes—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532#95—54no—
533#95—54no—
534#95—54no—
535#95—54no—
536C22×C5—24no—
537C22×C5—24no—
538C22×C5—24no—
539C22×C5—42no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—416no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—88no—
552C22×C5#52914yes—
553C22×C5#53214yes—
554C22×C5#53814yes—
555C22×C5#54614yes—
556C22×C5#54614yes—
557C22×C5#55114yes—
558C22×C5#55914yes—
559C22×C5C23×D411yescharacteristic
560C22×C5C22×#4111yescharacteristic
561C22×C5C22×#4111yescharacteristic
562C22×C5C22×#4111yescharacteristic
563C22×C5C22×#4111yescharacteristic
564C22×C5C2×H(5,𝔽2)11yescharacteristic
565C22×C5C2×H(5,𝔽2)11yescharacteristic
566C2×D5—24no—
567C2×D5—24no—
568C2×D5—24no—
569C2×D5—42no—
570C2×D5—42no—
571C2×D5—42no—
572C2×D5—42no—
573C2×D5—416no—
574C4×C5—24no—
575C4×C5—24no—
576C4×C5—24no—
577C4×C5—42no—
578C4×C5—42no—
579Dic5—24no—
580Dic5—24no—
581Dic5—42no—
582Dic5—42no—
583Dic5—42no—
584Dic5—42no—
585Dic5—42no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—54no—
600C24—52no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24—102no—
606C24—102no—
607C24#70914yes—
608C24C23×D512yes—
609C24C23×D512yes—
610C24C23×D511yescharacteristic
611C2×Q8—108no—
612C2×Q8—108no—
613C2×Q8—204no—
614C2×Q8—2016no—
615C2×D4—28no—
616C2×D4—28no—
617C2×D4—44no—
618C2×D4—416no—
619C2×D4—108no—
620C2×D4—108no—
621C2×D4—108no—
622C2×D4—108no—
623C2×D4—204no—
624C2×D4—204no—
625C2×D4—2016no—
626C2×D4—2016no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—54no—
640C22×C4—54no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—108no—
649C22×C4—102no—
650C22×C4—102no—
651C22×C4—102no—
652C22×C4—102no—
653C22×C4—108no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—102no—
659C22×C4—102no—
660C22×C4—102no—
661C22×C4—102no—
662C22×C4—102no—
663C22×C4—102no—
664C22×C4—102no—
665C22×C4—102no—
666C22×C4—102no—
667C22×C4—102no—
668C22×C4—102no—
669C22×C4—108no—
670C22×C4—204no—
671C22×C4—204no—
672C22×C4—2016no—
673C22×C4—204no—
674C22×C4—2016no—
675C22×C4D4×D514yes—
676C22×C4#71114yes—
677C22×C4#71114yes—
678C22×C4C23×D512yes—
679C22×C4C23×D512yes—
680C22×C4C23×D512yes—
681C22×C4C23×D512yes—
682C22×C4C23×D512yes—
683C4⋊C4—28no—
684C4⋊C4—108no—
685C4⋊C4—108no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—516no—
691C22⋊C4—108no—
692C22⋊C4—108no—
693C22⋊C4—108no—
694C22⋊C4—108no—
695C22⋊C4—108no—
696C22⋊C4—204no—
697C22⋊C4—204no—
698C22⋊C4—204no—
699C42—44no—
700C42—108no—
701C42—204no—
702C2×C5—44no—
703C2×C5—82no—
704C2×C5#255718yescomplemented
705C2×C5C2×#52911yescharacteristic
706C2×C5C2×#53211yescharacteristic
707C2×C5C2×#53811yescharacteristic
708C2×C5C2×#54611yescharacteristic
709C2×C5C2×#54611yescharacteristic
710C2×C5C2×#55111yescharacteristic
711C2×C5C2×#55911yescharacteristic
712D5—44no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—54no—
741C23—108no—
742C23—108no—
743C23—108no—
744C23—102no—
745C23—102no—
746C23—102no—
747C23—102no—
748C23—102no—
749C23—102no—
750C23—204no—
751C23—204no—
752C23—204no—
753C23—204no—
754C23C2×#70914yes—
755C23C2×#70912yes—
756C23C2×D4×D512yes—
757C23C2×#71112yes—
758C23C2×#71112yes—
759C23#414412yes—
760C23D5×#4112yes—
761C23#414912yes—
762C23C24×D511yescharacteristic
763Q8—2016no—
764D4—416no—
765D4—2016no—
766D4—2016no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—54no—
785C2×C4—54no—
786C2×C4—108no—
787C2×C4—108no—
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—102no—
801C2×C4—102no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—2016no—
808C2×C4—2016no—
809C2×C4—204no—
810C2×C4—204no—
811C2×C4—204no—
812C2×C4—204no—
813C2×C4—204no—
814C2×C4C2×D4×D514yes—
815C2×C4C2×#71114yes—
816C2×C4C2×#71114yes—
817C5C2×#255711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—416no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—88no—
834C22—104no—
835C22—104no—
836C22—104no—
837C22—202no—
838C22—202no—
839C22—2016no—
840C22—202no—
841C22—202no—
842C22#6582914yes—
843C22#6587214yes—
844C22#6588414yes—
845C22#6594414yes—
846C22#6595114yes—
847C22#6601514yes—
848C22#6605014yes—
849C22C22×#70911yescharacteristic
850C22C22×D4×D511yescharacteristic
851C22C22×#71111yescharacteristic
852C22C22×#71111yescharacteristic
853C22C2×#414411yescharacteristic
854C22C2×D5×#4111yescharacteristic
855C22C2×#414911yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—42no—
860C4—42no—
861C4—104no—
862C4—104no—
863C4—202no—
864C4—202no—
865C4—202no—
866C4—202no—
867C4—202no—
868C2—44no—
869C2—82no—
870C2—204no—
871C2#1060808818yesdirect product factor
872C2C2×#6582911yescharacteristic
873C2C2×#6587211yescharacteristic
874C2C2×#6588411yescharacteristic
875C2C2×#6595111yescharacteristic
876C2C2×#6594411yescharacteristic
877C2C2×#6601511yescharacteristic
878C2C2×#6605011yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#390C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC2×#390D5
hypocenterC5C2×#2557
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#4031C2semidirect
2. C22×#4032C2semidirect
3. C2×C5×#390C2semidirect
5. C2×#65509C2semidirect
6. C2×#65282C2semidirect
7. C2×#65270C2semidirect
8. C2×#65245C2semidirect
9. C2×#65245C2semidirect
10. C2×#65242C2semidirect
11. C2×#65236C2semidirect
12. C2×#65240C2semidirect
13. C2×C22⋊C4×Dic5C2semidirect
14. C2×#65218C2semidirect
15. C2×C4×#685C2semidirect
16. #10608088C2direct (N × H)
43. C2×#4032C22semidirect
45. C2×#4031C22semidirect
46. C5×#390C22semidirect
48. #65509C22semidirect
59. #65282C22semidirect
60. #65270C22semidirect
61. #65245C22semidirect
62. #65245C22semidirect
63. #65242C22semidirect
64. #65240C22semidirect
65. #65236C22semidirect
66. C22⋊C4×Dic5C22semidirect
67. C4×#685C22semidirect
68. #65218C22semidirect
134. C2×#685D4semidirect
167. C2×#390D5semidirect
286. #685C2×D4semidirect
325. #390C2×D5semidirect
704. C2×C5#2557semidirect
817. C5C2×#2557semidirect
871. C2#10608088direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40312
C22×#40322
C2×C5×#3902
C2×#655122
C2×#655092
C2×#652822
C2×#652702
C2×#652452
C2×#652422
C2×#652362
C2×#652402
C2×C22⋊C4×Dic52
C2×#652182
C2×C4×#6852
#106080882
C2×#25575