Finite Group Databasebeta

← C2×#10606490 #12269416

Subgroups — C2×#10606490 #12269416

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×#4082C211yesmaximal, characteristic, complemented
2C22×#4029C211yesmaximal, characteristic, complemented
3C2×C5×#386C211yesmaximal, characteristic, complemented
4C2×#65512C211yesmaximal, characteristic
5C2×#65502C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
7C2×#65245C211yesmaximal, characteristic, complemented
8C2×#65241C211yesmaximal, characteristic, complemented
9C2×#65241C211yesmaximal, characteristic, complemented
10C2×#65246C211yesmaximal, characteristic, complemented
11C2×#65240C211yesmaximal, characteristic, complemented
12#10606490C2116yesmaximal, direct product factor
13C2×#64962C211yesmaximal, characteristic, complemented
14C2×#64935C211yesmaximal, characteristic, complemented
15C2×#64944C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C2×#4082—28no—
33C2×#4082C2218yescomplemented
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4029—28no—
45C2×#4029C2218yescomplemented
46C5×#386C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49#65512C2218yes—
50#65502C2218yescomplemented
51C4×C22⋊Dic5C2218yescomplemented
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60#65246C2218yescomplemented
61#65245C2218yescomplemented
62#65241C2218yescomplemented
63#65241C2218yescomplemented
64#65240C2218yescomplemented
65#64962C2218yescomplemented
66#64955C2218yescomplemented
67#64944C2218yescomplemented
68#64935C2218yescomplemented
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×C5—24no—
78C23×C4×C5—42no—
79C23×C4×C5—42no—
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2314yes—
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5—42no—
91C22×C22⋊D5—42no—
92C22×C22⋊D5C2314yes—
93C22×C22⋊D5C2314yes—
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C22×C4×D5—24no—
102C22×C4×D5—24no—
103C22×C4×D5—42no—
104C22×C4×D5C2314yes—
105C22×Dic10—24no—
106C22×Dic10—24no—
107C22×Dic10—42no—
108C22×Dic10C2314yes—
109C2×C5×C22⋊C4—24no—
110C2×C5×C22⋊C4—24no—
111C2×C5×C22⋊C4—42no—
112C2×C5×C22⋊C4C2314yes—
113C2×C5×C22⋊C4C2314yes—
114C2×C5×C22⋊C4C2314yes—
115C2×C22⋊Dic5—24no—
116C2×C22⋊Dic5—24no—
117C2×C22⋊Dic5—24no—
118C2×C22⋊Dic5—24no—
119C2×C22⋊Dic5—42no—
120C2×C22⋊Dic5D418yescomplemented
121C2×C22⋊Dic5C2314yes—
122C2×C22⋊Dic5C2314yes—
123C2×C22⋊Dic5C2314yes—
124C2×C22⋊Dic5C2314yes—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127#4082—232no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—24no—
131C2×#685—42no—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×C4⋊Dic5—24no—
137C2×C4⋊Dic5C2314yes—
138C2×#683—24no—
139C2×#683—24no—
140C2×#683C2314yes—
141C2×#683C2314yes—
142C2×C4×Dic5—24no—
143C2×C4×Dic5—42no—
144C2×C4×Dic5—42no—
145C2×C4×Dic5C2314yes—
146C2×C4×Dic5C2314yes—
147C2×C4×Dic5C2314yes—
148#4029—232no—
149C5×#95C2314yes—
150C5×#95C2314yes—
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×#390—51no—
168C2×#388—51no—
169C2×#387—51no—
170C2×#386—51no—
171C2×#386—51no—
172C2×#386D511yescharacteristic, complemented
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×C5C2×D414yes—
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×D5#4114yes—
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×C5—22no—
217C22×C4×C5—28no—
218C22×C4×C5—44no—
219C22×C4×C5—44no—
220C22×C4×C5—416no—
221C22×C4×C5#4114yes—
222C22×C4×C5#4114yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C2×C22⋊D5—28no—
229C2×C22⋊D5—28no—
230C2×C22⋊D5—28no—
231C2×C22⋊D5—28no—
232C2×C22⋊D5—44no—
233C2×C22⋊D5—44no—
234C2×C22⋊D5—416no—
235C2×C22⋊D5—416no—
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×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5C2×D414yes—
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—28no—
266C2×C4×D5—44no—
267C2×C4×D5—416no—
268C2×Dic10—28no—
269C2×Dic10—28no—
270C2×Dic10—44no—
271C2×Dic10—416no—
272C5×C22⋊C4—28no—
273C5×C22⋊C4—28no—
274C5×C22⋊C4—44no—
275C22⋊Dic5—28no—
276C22⋊Dic5—28no—
277C22⋊Dic5—28no—
278C22⋊Dic5—28no—
279C22⋊Dic5—44no—
280C22⋊Dic5C2×D4116yescomplemented
281#685—28no—
282#685—28no—
283#685—28no—
284#685—44no—
285C4⋊Dic5—28no—
286#683—28no—
287#683—28no—
288C4×Dic5—28no—
289C4×Dic5—44no—
290C4×Dic5—44no—
291C23×Q8—51no—
292C23×D4—51no—
293C23×D4—51no—
294C23×D4C2×D511yescharacteristic
295C24×C4—51no—
296C24×C4C2×D511yescharacteristic
297C2×#124—58no—
298C2×#124—108no—
299C2×#123—58no—
300C2×#123—108no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
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⋊C4—51no—
314C22×C22⋊C4C2×D511yescharacteristic
315C22×C22⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C42—51no—
318C22×C42—51no—
319C22×C42—51no—
320#397—58no—
321#397—58no—
322#393—58no—
323#392—58no—
324#391—58no—
325#390—58no—
326#388—58no—
327#387—58no—
328#386—58no—
329#386—58no—
330#386C2×D518yescomplemented
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×#95C2×D511yescharacteristic
342C2×#95C2×D511yescharacteristic
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×D414yes—
371C23×C5C22×D412yes—
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×D5C2×#4114yes—
393C5×D4—416no—
394C2×C4×C5—28no—
395C2×C4×C5—28no—
396C2×C4×C5—22no—
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—416no—
410C2×C4×C5—44no—
411C2×C4×C5—44no—
412C2×C4×C5—44no—
413C2×C4×C5C2×#4114yes—
414C2×C4×C5C2×#4114yes—
415C22⋊D5—416no—
416C22⋊D5—416no—
417C2×Dic5—28no—
418C2×Dic5—28no—
419C2×Dic5—28no—
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—22no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5C22×D414yes—
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—24no—
467C23×C4—42no—
468C23×C4—42no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
472C23×C4—51no—
473C23×C4—51no—
474C23×C4—51no—
475C23×C4—51no—
476C23×C4—54no—
477C23×C4—104no—
478C23×C4—104no—
479C23×C4—202no—
480C23×C4C22×D511yescharacteristic
481C23×C4C22×D511yescharacteristic
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D511yescharacteristic
485C23×C4C22×D514yes—
486#124—1032no—
487#123—1032no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—104no—
492C2×C4⋊C4—104no—
493C2×C4⋊C4—104no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—58no—
498C2×C22⋊C4—54no—
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—104no—
514C2×C22⋊C4—104no—
515C2×C22⋊C4—202no—
516C2×C22⋊C4—202no—
517C2×C22⋊C4C22×D514yes—
518C2×C22⋊C4C22×D514yes—
519C2×C22⋊C4C22×D514yes—
520C2×C42—54no—
521C2×C42—54no—
522C2×C42—54no—
523C2×C42—104no—
524C2×C42—202no—
525C2×C42—202no—
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#95C22×D514yes—
535#95C22×D514yes—
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—42no—
577C4×C5—42no—
578C4×C5—42no—
579Dic5—24no—
580Dic5—24no—
581Dic5—24no—
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—
607C24D4×D514yes—
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—22no—
640C22×C4—28no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—416no—
644C22×C4—54no—
645C22×C4—54no—
646C22×C4—54no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—52no—
650C22×C4—52no—
651C22×C4—52no—
652C22×C4—52no—
653C22×C4—52no—
654C22×C4—108no—
655C22×C4—108no—
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—102no—
670C22×C4—102no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4—102no—
674C22×C4—204no—
675C22×C4—2016no—
676C22×C4#70914yes—
677C22×C4#71114yes—
678C22×C4C23×D512yes—
679C22×C4C23×D512yes—
680C22×C4C23×D512yes—
681C22×C4C23×D512yes—
682C22×C4C23×D512yes—
683C4⋊C4—108no—
684C4⋊C4—108no—
685C4⋊C4—108no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—44no—
689C22⋊C4—516no—
690C22⋊C4—108no—
691C22⋊C4—108no—
692C22⋊C4—108no—
693C22⋊C4—108no—
694C22⋊C4—108no—
695C22⋊C4—108no—
696C22⋊C4—108no—
697C22⋊C4—204no—
698C22⋊C4—204no—
699C42—108no—
700C42—204no—
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×#70912yes—
755C23C2×D4×D514yes—
756C23C2×D4×D512yes—
757C23C2×#71112yes—
758C23#414412yes—
759C23#414412yes—
760C23D5×#4112yes—
761C23D5×#4112yes—
762C23C24×D511yescharacteristic
763Q8—2016no—
764D4—416no—
765D4—2016no—
766D4—2016no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—22no—
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—416no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—54no—
787C2×C4—54no—
788C2×C4—54no—
789C2×C4—108no—
790C2×C4—108no—
791C2×C4—108no—
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—102no—
808C2×C4—102no—
809C2×C4—102no—
810C2×C4—2016no—
811C2×C4—204no—
812C2×C4—204no—
813C2×C4—204no—
814C2×C4—204no—
815C2×C4C2×#70914yes—
816C2×C4C2×#71114yes—
817C5C2×#255711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—416no—
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—2016no—
839C22—202no—
840C22—202no—
841C22—202no—
842C22#6582414yes—
843C22#6589114yes—
844C22#6589314yes—
845C22#6592714yes—
846C22#6593014yes—
847C22#6594414yes—
848C22#6599314yes—
849C22C22×#70911yescharacteristic
850C22C22×D4×D511yescharacteristic
851C22C22×#71111yescharacteristic
852C22C2×#414411yescharacteristic
853C22C2×#414411yescharacteristic
854C22C2×D5×#4111yescharacteristic
855C22C2×D5×#4111yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—104no—
862C4—104no—
863C4—104no—
864C4—202no—
865C4—202no—
866C4—202no—
867C4—202no—
868C2—44no—
869C2—82no—
870C2—204no—
871C2#1060649018yesdirect product factor
872C2C2×#6582411yescharacteristic
873C2C2×#6589311yescharacteristic
874C2C2×#6589111yescharacteristic
875C2C2×#6592711yescharacteristic
876C2C2×#6593011yescharacteristic
877C2C2×#6594411yescharacteristic
878C2C2×#6599311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#386C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC2×#386D5
hypocenterC5C2×#2557
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#4082C2semidirect
2. C22×#4029C2semidirect
3. C2×C5×#386C2semidirect
5. C2×#65502C2semidirect
6. C2×C4×C22⋊Dic5C2semidirect
7. C2×#65245C2semidirect
8. C2×#65241C2semidirect
9. C2×#65241C2semidirect
10. C2×#65246C2semidirect
11. C2×#65240C2semidirect
12. #10606490C2direct (N × H)
13. C2×#64962C2semidirect
14. C2×#64935C2semidirect
15. C2×#64944C2semidirect
16. C2×#64955C2semidirect
33. C2×#4082C22semidirect
45. C2×#4029C22semidirect
46. C5×#386C22semidirect
50. #65502C22semidirect
51. C4×C22⋊Dic5C22semidirect
60. #65246C22semidirect
61. #65245C22semidirect
62. #65241C22semidirect
63. #65241C22semidirect
64. #65240C22semidirect
65. #64962C22semidirect
66. #64955C22semidirect
67. #64944C22semidirect
68. #64935C22semidirect
120. C2×C22⋊Dic5D4semidirect
172. C2×#386D5semidirect
280. C22⋊Dic5C2×D4semidirect
330. #386C2×D5semidirect
704. C2×C5#2557semidirect
817. C5C2×#2557semidirect
871. C2#10606490direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40822
C22×#40292
C2×C5×#3862
C2×#655122
C2×#655022
C2×C4×C22⋊Dic52
C2×#652452
C2×#652412
C2×#652462
C2×#652402
#106064902
C2×#649622
C2×#649352
C2×#649442
C2×#649552
C2×#25575