Finite Group Databasebeta

← C2×#10608640 #12267408

Subgroups — C2×#10608640 #12267408

Order 1280.

3438 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×D4×Dic5C211yesmaximal, characteristic, complemented
2C22×#4029C211yesmaximal, characteristic, complemented
3C2×C5×#394C211yesmaximal, characteristic, complemented
4C2×#65512C211yesmaximal, characteristic
5C2×#65283C211yesmaximal, characteristic, complemented
6C2×#65270C211yesmaximal, characteristic, complemented
7C2×#65245C211yesmaximal, characteristic, complemented
8C2×#65233C211yesmaximal, characteristic, complemented
9C2×#65240C211yesmaximal, characteristic, complemented
10C2×#65247C211yesmaximal, characteristic, complemented
11C2×#65247C211yesmaximal, characteristic, complemented
12C2×#65232C211yesmaximal, characteristic, complemented
13C2×#65231C211yesmaximal, characteristic, complemented
14#10608640C2116yesmaximal, direct product factor
15C2×#64949C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C2×D4×Dic5—28no—
33C2×D4×Dic5C2218yescomplemented
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4029—28no—
45C2×#4029C2218yescomplemented
46C5×#394C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48#65512C2218yes—
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58#65283C2218yescomplemented
59#65270C2218yescomplemented
60#65247C2218yescomplemented
61#65247C2218yescomplemented
62#65245C2218yescomplemented
63#65240C2218yescomplemented
64#65233C2218yescomplemented
65#65232C2218yescomplemented
66#65231C2218yescomplemented
67#64955C2218yescomplemented
68#64949C2218yescomplemented
69C2×#2457—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C22×C5×D4—24no—
74C22×C5×D4—24no—
75C22×C5×D4—24no—
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—24no—
93C23×Dic5—24no—
94C23×Dic5—42no—
95C23×Dic5—42no—
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2314yes—
101C23×Dic5C2314yes—
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C22×C4×D5—24no—
106C22×C4×D5—24no—
107C22×C4×D5—42no—
108C22×C4×D5C2314yes—
109C2×C5×C4⋊C4—24no—
110C2×C5×C4⋊C4C2314yes—
111C2×C5×C22⋊C4—24no—
112C2×C5×C22⋊C4—24no—
113C2×C5×C22⋊C4—42no—
114C2×C5×C22⋊C4—42no—
115C2×C5×C22⋊C4C2314yes—
116C2×C5×C22⋊C4C2314yes—
117C2×C5×C22⋊C4C2314yes—
118C2×C5×C22⋊C4C2314yes—
119C2×C22⋊Dic5—24no—
120C2×C22⋊Dic5—42no—
121C2×C22⋊Dic5—42no—
122C2×C22⋊Dic5D418yescomplemented
123C2×C22⋊Dic5C2314yes—
124C2×C22⋊Dic5C2314yes—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127D4×Dic5—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⋊Dic5—24no—
138C2×C4⋊Dic5C2314yes—
139C2×C4⋊Dic5C2314yes—
140C2×#683—24no—
141C2×#683—42no—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×C4×Dic5—24no—
145C2×C4×Dic5—42no—
146C2×C4×Dic5C2314yes—
147C2×C4×Dic5C2314yes—
148#4029—232no—
149C5×#95C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#123—51no—
160C22×C4×D4—51no—
161#2457—516no—
162C2×#400—51no—
163C2×#396—51no—
164C2×#394D511yescharacteristic, complemented
165C2×#392—51no—
166C2×#388—51no—
167C2×#388—51no—
168C2×#387—51no—
169C2×#386—51no—
170C2×#386—51no—
171C2×#386—51no—
172C2×#381—51no—
173C2×#380—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×C5C2×D414yes—
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×D5#4114yes—
199C23×D5C2412yes—
200C2×C5×D4—232no—
201C2×C5×D4—28no—
202C2×C5×D4—28no—
203C2×C5×D4—28no—
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—22no—
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—28no—
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—28no—
252C22×Dic5—28no—
253C22×Dic5—28no—
254C22×Dic5—44no—
255C22×Dic5—44no—
256C22×Dic5—416no—
257C22×Dic5—416no—
258C22×Dic5C2×D414yes—
259C22×Dic5C2×D414yes—
260C22×Dic5#4114yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C2×C4×D5—28no—
269C2×C4×D5—28no—
270C2×C4×D5—44no—
271C2×C4×D5—416no—
272C5×C4⋊C4—28no—
273C5×C22⋊C4—28no—
274C5×C22⋊C4—28no—
275C5×C22⋊C4—44no—
276C5×C22⋊C4—44no—
277C22⋊Dic5—28no—
278C22⋊Dic5—44no—
279C22⋊Dic5—44no—
280C22⋊Dic5C2×D4116yescomplemented
281#685—28no—
282#685—28no—
283#685—28no—
284#685—44no—
285C4⋊Dic5—28no—
286C4⋊Dic5—28no—
287#683—28no—
288#683—44no—
289C4×Dic5—28no—
290C4×Dic5—44no—
291C23×D4—51no—
292C23×D4—51no—
293C23×D4C2×D511yescharacteristic
294C24×C4—51no—
295C24×C4—51no—
296C24×C4—51no—
297C2×#123—58no—
298C2×#123—108no—
299C2×C4×D4—58no—
300C2×C4×D4—108no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4—51no—
305C22×C4⋊C4C2×D511yescharacteristic
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×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42—51no—
320#400—58no—
321#396—58no—
322#394C2×D518yescomplemented
323#392—58no—
324#388—58no—
325#388—58no—
326#387—58no—
327#386—58no—
328#386—58no—
329#386—58no—
330#381—58no—
331#380—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×#95C2×D511yescharacteristic
343C23×C5—28no—
344C23×C5—28no—
345C23×C5—28no—
346C23×C5—28no—
347C23×C5—28no—
348C23×C5—28no—
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—22no—
360C23×C5—22no—
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×C5C22×D414yes—
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×D5C2×#4114yes—
393C5×D4—232no—
394C2×C4×C5—28no—
395C2×C4×C5—22no—
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—44no—
410C2×C4×C5—44no—
411C2×C4×C5—44no—
412C2×C4×C5—44no—
413C2×C4×C5C2×#4114yes—
414C22⋊D5—416no—
415C22⋊D5—416no—
416C2×Dic5—28no—
417C2×Dic5—28no—
418C2×Dic5—28no—
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—416no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5—44no—
443C2×Dic5C22×D414yes—
444C2×Dic5C22×D414yes—
445C2×Dic5C2×#4114yes—
446C4×D5—416no—
447C25—51no—
448C25C22×D511yescharacteristic
449C25C22×D511yescharacteristic
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—54no—
454C22×D4—54no—
455C22×D4—104no—
456C22×D4—104no—
457C22×D4—104no—
458C22×D4—104no—
459C22×D4—202no—
460C22×D4—202no—
461C22×D4C22×D514yes—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—54no—
470C23×C4—54no—
471C23×C4—54no—
472C23×C4—104no—
473C23×C4—104no—
474C23×C4—104no—
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#123—1032no—
487C4×D4—1032no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—54no—
492C2×C4⋊C4—54no—
493C2×C4⋊C4—104no—
494C2×C4⋊C4—104no—
495C2×C4⋊C4—104no—
496C2×C4⋊C4—202no—
497C2×C4⋊C4C22×D514yes—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—58no—
503C2×C22⋊C4—54no—
504C2×C22⋊C4—54no—
505C2×C22⋊C4—54no—
506C2×C22⋊C4—54no—
507C2×C22⋊C4—54no—
508C2×C22⋊C4—54no—
509C2×C22⋊C4—54no—
510C2×C22⋊C4—54no—
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⋊C4—202no—
518C2×C22⋊C4C22×D514yes—
519C2×C22⋊C4C22×D514yes—
520C2×C22⋊C4C22×D514yes—
521C2×C22⋊C4C22×D514yes—
522C2×C42—54no—
523C2×C42—54no—
524C2×C42—104no—
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#95—54no—
535#95C22×D514yes—
536C22×C5—24no—
537C22×C5—24no—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—24no—
541C22×C5—24no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—416no—
551C22×C5—416no—
552C22×C5#52514yes—
553C22×C5#52914yes—
554C22×C5#54014yes—
555C22×C5#54614yes—
556C22×C5#54614yes—
557C22×C5#55114yes—
558C22×C5#55314yes—
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—42no—
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—54no—
599C24—52no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24—102no—
606C24D4×D514yes—
607C24#71114yes—
608C24C23×D512yes—
609C24C23×D512yes—
610C24C23×D511yescharacteristic
611C2×D4—232no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—108no—
616C2×D4—108no—
617C2×D4—108no—
618C2×D4—108no—
619C2×D4—204no—
620C2×D4—204no—
621C2×D4—2016no—
622C2×D4—2016no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
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—54no—
638C22×C4—54no—
639C22×C4—54no—
640C22×C4—52no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—108no—
648C22×C4—108no—
649C22×C4—108no—
650C22×C4—108no—
651C22×C4—108no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—102no—
659C22×C4—102no—
660C22×C4—108no—
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—204no—
672C22×C4—2016no—
673C22×C4—204no—
674C22×C4—204no—
675C22×C4—2016no—
676C22×C4—2016no—
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—
686C4⋊C4—108no—
687C4⋊C4—204no—
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—516no—
693C22⋊C4—108no—
694C22⋊C4—108no—
695C22⋊C4—108no—
696C22⋊C4—108no—
697C22⋊C4—204no—
698C22⋊C4—204no—
699C22⋊C4—204no—
700C42—108no—
701C42—204no—
702C2×C5—44no—
703C2×C5—44no—
704C2×C5#245718yescomplemented
705C2×C5C2×#52511yescharacteristic
706C2×C5C2×#52911yescharacteristic
707C2×C5C2×#54011yescharacteristic
708C2×C5C2×#54611yescharacteristic
709C2×C5C2×#54611yescharacteristic
710C2×C5C2×#55111yescharacteristic
711C2×C5C2×#55311yescharacteristic
712D5—44no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—54no—
740C23—108no—
741C23—108no—
742C23—108no—
743C23—102no—
744C23—102no—
745C23—102no—
746C23—102no—
747C23—102no—
748C23—102no—
749C23—204no—
750C23—204no—
751C23—204no—
752C23—204no—
753C23C2×D4×D514yes—
754C23C2×D4×D512yes—
755C23C2×#71114yes—
756C23C2×#71112yes—
757C23C2×#71112yes—
758C23#414412yes—
759C23D5×#4112yes—
760C23D5×#4112yes—
761C23#414912yes—
762C23C24×D511yescharacteristic
763D4—232no—
764D4—2016no—
765D4—2016no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
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—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—54no—
786C2×C4—54no—
787C2×C4—54no—
788C2×C4—108no—
789C2×C4—108no—
790C2×C4—108no—
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—102no—
808C2×C4—102no—
809C2×C4—2016no—
810C2×C4—2016no—
811C2×C4—2016no—
812C2×C4—204no—
813C2×C4—204no—
814C2×C4—204no—
815C2×C4—204no—
816C2×C4C2×#71114yes—
817C5C2×#245711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—416no—
825C22—416no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—104no—
835C22—104no—
836C22—104no—
837C22—2016no—
838C22—202no—
839C22—202no—
840C22—202no—
841C22—202no—
842C22#6592014yes—
843C22#6593514yes—
844C22#6594414yes—
845C22#6595314yes—
846C22#6598814yes—
847C22#6599214yes—
848C22#6601414yes—
849C22C22×D4×D511yescharacteristic
850C22C22×#71111yescharacteristic
851C22C22×#71111yescharacteristic
852C22C2×#414411yescharacteristic
853C22C2×D5×#4111yescharacteristic
854C22C2×D5×#4111yescharacteristic
855C22C2×#414911yescharacteristic
856C4—24no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—104no—
862C4—104no—
863C4—104no—
864C4—202no—
865C4—202no—
866C4—202no—
867C4—202no—
868C2—44no—
869C2—44no—
870C2—204no—
871C2#1060864018yesdirect product factor
872C2C2×#6592011yescharacteristic
873C2C2×#6595311yescharacteristic
874C2C2×#6593511yescharacteristic
875C2C2×#6594411yescharacteristic
876C2C2×#6598811yescharacteristic
877C2C2×#6599211yescharacteristic
878C2C2×#6601411yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#394C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC2×#394D5
hypocenterC5C2×#2457
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic5C2semidirect
2. C22×#4029C2semidirect
3. C2×C5×#394C2semidirect
5. C2×#65283C2semidirect
6. C2×#65270C2semidirect
7. C2×#65245C2semidirect
8. C2×#65233C2semidirect
9. C2×#65240C2semidirect
10. C2×#65247C2semidirect
11. C2×#65247C2semidirect
12. C2×#65232C2semidirect
13. C2×#65231C2semidirect
14. #10608640C2direct (N × H)
15. C2×#64949C2semidirect
16. C2×#64955C2semidirect
33. C2×D4×Dic5C22semidirect
45. C2×#4029C22semidirect
46. C5×#394C22semidirect
58. #65283C22semidirect
59. #65270C22semidirect
60. #65247C22semidirect
61. #65247C22semidirect
62. #65245C22semidirect
63. #65240C22semidirect
64. #65233C22semidirect
65. #65232C22semidirect
66. #65231C22semidirect
67. #64955C22semidirect
68. #64949C22semidirect
122. C2×C22⋊Dic5D4semidirect
164. C2×#394D5semidirect
280. C22⋊Dic5C2×D4semidirect
322. #394C2×D5semidirect
704. C2×C5#2457semidirect
817. C5C2×#2457semidirect
871. C2#10608640direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic52
C22×#40292
C2×C5×#3942
C2×#655122
C2×#652832
C2×#652702
C2×#652452
C2×#652332
C2×#652402
C2×#652472
C2×#652322
C2×#652312
#106086402
C2×#649492
C2×#649552
C2×#24575