Finite Group Databasebeta

← C2×#10609024 #12267420

Subgroups — C2×#10609024 #12267420

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×#4039C211yesmaximal, characteristic, complemented
2C22×#4032C211yesmaximal, characteristic, complemented
3C2×C5×#396C211yesmaximal, characteristic, complemented
4C2×#65280C211yesmaximal, characteristic, complemented
5C2×#65276C211yesmaximal, characteristic, complemented
6C2×#65275C211yesmaximal, characteristic, complemented
7C2×#65279C211yesmaximal, characteristic, complemented
8C2×#65270C211yesmaximal, characteristic, complemented
9C2×#65249C211yesmaximal, characteristic
10C2×#65245C211yesmaximal, characteristic, complemented
11C2×#65245C211yesmaximal, characteristic, complemented
12C2×#65247C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14#10609024C2116yesmaximal, direct product factor
15C2×#64953C211yesmaximal, characteristic, complemented
16C2×#64959C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C24×Dic5C2211yescharacteristic
20C23×D20C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4039—28no—
43C2×#4039C2218yescomplemented
44C2×#4032—28no—
45C2×#4032C2218yescomplemented
46C5×#396C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65280C2218yescomplemented
58#65279C2218yescomplemented
59#65276C2218yescomplemented
60#65275C2218yescomplemented
61#65270C2218yescomplemented
62#65249C2218yes—
63#65247C2218yescomplemented
64#65245C2218yescomplemented
65#65245C2218yescomplemented
66C22⋊C4×Dic5C2218yescomplemented
67#64959C2218yescomplemented
68#64953C2218yescomplemented
69C2×#2457—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C22×C22⋊D5—24no—
80C22×C22⋊D5—24no—
81C22×C22⋊D5—24no—
82C22×C22⋊D5—24no—
83C22×C22⋊D5—42no—
84C22×C22⋊D5—42no—
85C22×C22⋊D5C2314yes—
86C22×C22⋊D5C2314yes—
87C23×Dic5—24no—
88C23×Dic5—24no—
89C23×Dic5—42no—
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2314yes—
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C22×D20—24no—
98C22×D20—24no—
99C22×D20—24no—
100C22×D20C2314yes—
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×D5C2314yes—
108C22×C4×D5C2314yes—
109C2×C5×C4⋊C4—24no—
110C2×C5×C4⋊C4—24no—
111C2×C5×C4⋊C4—42no—
112C2×C5×C4⋊C4C2314yes—
113C2×C5×C4⋊C4C2314yes—
114C2×C5×C4⋊C4C2314yes—
115C2×C5×C22⋊C4—24no—
116C2×C5×C22⋊C4—24no—
117C2×C5×C22⋊C4—42no—
118C2×C5×C22⋊C4C2314yes—
119C2×C5×C22⋊C4C2314yes—
120C2×C5×C22⋊C4C2314yes—
121C2×C22⋊Dic5—24no—
122C2×C22⋊Dic5C2314yes—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—42no—
127C2×#685—42no—
128C2×#685—42no—
129C2×#685—42no—
130C2×#685D418yescomplemented
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
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#4039—232no—
148#4032—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×#396D511yescharacteristic, complemented
164C2×#394—51no—
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#4114yes—
182C24×C5C2412yes—
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×D5C2×D414yes—
197C23×D5#4114yes—
198C23×D5C2412yes—
199C23×D5C2412yes—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
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×C5C2412yes—
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—28no—
250C22×Dic5—44no—
251C22×Dic5—416no—
252C22×Dic5C2×D414yes—
253C22×Dic5#4114yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C22×Dic5C2412yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C2×D20—232no—
261C2×D20—28no—
262C2×D20—28no—
263C2×D20—28no—
264C2×C4×D5—28no—
265C2×C4×D5—28no—
266C2×C4×D5—28no—
267C2×C4×D5—28no—
268C2×C4×D5—44no—
269C2×C4×D5—44no—
270C2×C4×D5—416no—
271C2×C4×D5—416no—
272C5×C4⋊C4—28no—
273C5×C4⋊C4—28no—
274C5×C4⋊C4—44no—
275C5×C22⋊C4—28no—
276C5×C22⋊C4—28no—
277C5×C22⋊C4—44no—
278C22⋊Dic5—28no—
279#685—28no—
280#685—28no—
281#685—28no—
282#685—44no—
283#685—44no—
284#685—44no—
285#685—44no—
286#685C2×D4116yescomplemented
287C4⋊Dic5—28no—
288C4⋊Dic5—28no—
289C4×Dic5—28no—
290C4×Dic5—44no—
291C23×D4—51no—
292C23×D4—51no—
293C23×D4—51no—
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⋊C4C2×D511yescharacteristic
304C22×C4⋊C4C2×D511yescharacteristic
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⋊C4—51no—
315C22×C22⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42—51no—
320#400—58no—
321#396C2×D518yescomplemented
322#394—58no—
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—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—44no—
353C23×C5—44no—
354C23×C5—44no—
355C23×C5—44no—
356C23×C5C22×D412yes—
357C23×C5C2×#4112yes—
358C23×C5C2×#4114yes—
359C23×C5C2×#4112yes—
360C23×C5C2×#4112yes—
361C23×C5C2×#4112yes—
362C23×C5H(5,𝔽2)12yes—
363C23×C5H(5,𝔽2)12yes—
364C23×C5C2511yescharacteristic
365C22×D5—28no—
366C22×D5—28no—
367C22×D5—28no—
368C22×D5—28no—
369C22×D5—28no—
370C22×D5—28no—
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—22no—
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—44no—
384C22×D5—44no—
385C22×D5—44no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5—44no—
391C22×D5C22×D414yes—
392C22×D5C2×#4114yes—
393C2×C4×C5—28no—
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—22no—
410C2×C4×C5—22no—
411C2×C4×C5—44no—
412C2×C4×C5—44no—
413C2×C4×C5—44no—
414C2×C4×C5—44no—
415C2×C4×C5C22×D414yes—
416C2×C4×C5C2×#4114yes—
417C22⋊D5—416no—
418C22⋊D5—416no—
419C2×Dic5—28no—
420C2×Dic5—28no—
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×Dic5C22×D414yes—
443C2×Dic5C2×#4114yes—
444D20—232no—
445C4×D5—416no—
446C4×D5—416no—
447C25—51no—
448C25—51no—
449C25C22×D511yescharacteristic
450C22×D4—54no—
451C22×D4—54no—
452C22×D4—54no—
453C22×D4—104no—
454C22×D4—104no—
455C22×D4—104no—
456C22×D4—104no—
457C22×D4—104no—
458C22×D4—104no—
459C22×D4—104no—
460C22×D4—202no—
461C22×D4—202no—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—54no—
469C23×C4—54no—
470C23×C4—54no—
471C23×C4—104no—
472C23×C4—104no—
473C23×C4—104no—
474C23×C4—104no—
475C23×C4—104no—
476C23×C4—104no—
477C23×C4—202no—
478C23×C4—202no—
479C23×C4—202no—
480C23×C4C22×D511yescharacteristic
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—24no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—54no—
492C2×C4⋊C4—54no—
493C2×C4⋊C4—104no—
494C2×C4⋊C4—104no—
495C2×C4⋊C4C22×D514yes—
496C2×C4⋊C4C22×D514yes—
497C2×C4⋊C4C22×D514yes—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—58no—
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—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⋊C4—202no—
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—42no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—416no—
544C22×C5#52514yes—
545C22×C5#52914yes—
546C22×C5#54014yes—
547C22×C5#54614yes—
548C22×C5#54614yes—
549C22×C5#55114yes—
550C22×C5#55314yes—
551C22×C5C23×D411yescharacteristic
552C22×C5C22×#4111yescharacteristic
553C22×C5C22×#4111yescharacteristic
554C22×C5C22×#4111yescharacteristic
555C22×C5C22×#4111yescharacteristic
556C22×C5C2×H(5,𝔽2)11yescharacteristic
557C22×C5C2×H(5,𝔽2)11yescharacteristic
558C2×D5—24no—
559C2×D5—24no—
560C2×D5—24no—
561C2×D5—24no—
562C2×D5—24no—
563C2×D5—24no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—42no—
569C2×D5—42no—
570C2×D5—42no—
571C2×D5—42no—
572C2×D5—416no—
573C2×D5—416no—
574C4×C5—24no—
575C4×C5—24no—
576C4×C5—42no—
577C4×C5—42no—
578C4×C5—42no—
579C4×C5—42no—
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—54no—
593C24—54no—
594C24—52no—
595C24—52no—
596C24—102no—
597C24—102no—
598C24—102no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24—102no—
606C24—102no—
607C24—102no—
608C24#71314yes—
609C24C23×D512yes—
610C24C23×D511yescharacteristic
611C2×D4—108no—
612C2×D4—108no—
613C2×D4—1032no—
614C2×D4—108no—
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—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—108no—
648C22×C4—108no—
649C22×C4—108no—
650C22×C4—108no—
651C22×C4—102no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—108no—
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—108no—
669C22×C4—204no—
670C22×C4—204no—
671C22×C4—2016no—
672C22×C4—2016no—
673C22×C4—204no—
674C22×C4—2016no—
675C22×C4D4×D514yes—
676C22×C4#71114yes—
677C22×C4C23×D512yes—
678C22×C4C23×D512yes—
679C22×C4C23×D512yes—
680C22×C4C23×D512yes—
681C22×C4C23×D512yes—
682C22×C4C23×D512yes—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—44no—
686C4⋊C4—108no—
687C4⋊C4—108no—
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—44no—
691C22⋊C4—516no—
692C22⋊C4—108no—
693C22⋊C4—108no—
694C22⋊C4—108no—
695C22⋊C4—108no—
696C22⋊C4—204no—
697C22⋊C4—204no—
698C22⋊C4—204no—
699C22⋊C4—204no—
700C42—108no—
701C42—204no—
702C2×C5—44no—
703C2×C5#245718yescomplemented
704C2×C5C2×#52511yescharacteristic
705C2×C5C2×#52911yescharacteristic
706C2×C5C2×#54011yescharacteristic
707C2×C5C2×#54611yescharacteristic
708C2×C5C2×#54611yescharacteristic
709C2×C5C2×#55111yescharacteristic
710C2×C5C2×#55311yescharacteristic
711D5—44no—
712D5—44no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—54no—
727C23—54no—
728C23—108no—
729C23—108no—
730C23—108no—
731C23—108no—
732C23—108no—
733C23—102no—
734C23—102no—
735C23—102no—
736C23—102no—
737C23—102no—
738C23—102no—
739C23—102no—
740C23—102no—
741C23—102no—
742C23—102no—
743C23—102no—
744C23—102no—
745C23—108no—
746C23—204no—
747C23—204no—
748C23—204no—
749C23—204no—
750C23—204no—
751C23—204no—
752C23—204no—
753C23—204no—
754C23C2×D4×D512yes—
755C23C2×#71112yes—
756C23#414412yes—
757C23C2×#71314yes—
758C23C2×#71312yes—
759C23D5×#4112yes—
760C23D5×#4112yes—
761C23#414912yes—
762C23C24×D511yescharacteristic
763D4—1032no—
764D4—2016no—
765D4—2016no—
766C2×C4—28no—
767C2×C4—28no—
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—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—54no—
789C2×C4—54no—
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—2016no—
809C2×C4—2016no—
810C2×C4—2016no—
811C2×C4—204no—
812C2×C4—204no—
813C2×C4—204no—
814C2×C4—204no—
815C2×C4C2×D4×D514yes—
816C2×C4C2×#71114yes—
817C5C2×#245711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—416no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—104no—
827C22—104no—
828C22—104no—
829C22—104no—
830C22—104no—
831C22—104no—
832C22—202no—
833C22—202no—
834C22—202no—
835C22—202no—
836C22—2016no—
837C22—2016no—
838C22—202no—
839C22—202no—
840C22—202no—
841C22—202no—
842C22#6594014yes—
843C22#6594414yes—
844C22#6595314yes—
845C22#6595814yes—
846C22#6596414yes—
847C22#6597114yes—
848C22#6604314yes—
849C22C22×D4×D511yescharacteristic
850C22C22×#71111yescharacteristic
851C22C2×#414411yescharacteristic
852C22C22×#71311yescharacteristic
853C22C2×D5×#4111yescharacteristic
854C22C2×D5×#4111yescharacteristic
855C22C2×#414911yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—104no—
863C4—104no—
864C4—202no—
865C4—202no—
866C4—202no—
867C4—202no—
868C2—44no—
869C2—204no—
870C2—204no—
871C2#1060902418yesdirect product factor
872C2C2×#6594011yescharacteristic
873C2C2×#6595311yescharacteristic
874C2C2×#6594411yescharacteristic
875C2C2×#6595811yescharacteristic
876C2C2×#6596411yescharacteristic
877C2C2×#6597111yescharacteristic
878C2C2×#6604311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#396C2
socleC24×C5C24
prime radicalC2×#65249C2
hypercenterC2×#396D5
hypocenterC5C2×#2457
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#4039C2semidirect
2. C22×#4032C2semidirect
3. C2×C5×#396C2semidirect
4. C2×#65280C2semidirect
5. C2×#65276C2semidirect
6. C2×#65275C2semidirect
7. C2×#65279C2semidirect
8. C2×#65270C2semidirect
10. C2×#65245C2semidirect
11. C2×#65245C2semidirect
12. C2×#65247C2semidirect
13. C2×C22⋊C4×Dic5C2semidirect
14. #10609024C2direct (N × H)
15. C2×#64953C2semidirect
16. C2×#64959C2semidirect
43. C2×#4039C22semidirect
45. C2×#4032C22semidirect
46. C5×#396C22semidirect
57. #65280C22semidirect
58. #65279C22semidirect
59. #65276C22semidirect
60. #65275C22semidirect
61. #65270C22semidirect
63. #65247C22semidirect
64. #65245C22semidirect
65. #65245C22semidirect
66. C22⋊C4×Dic5C22semidirect
67. #64959C22semidirect
68. #64953C22semidirect
130. C2×#685D4semidirect
163. C2×#396D5semidirect
286. #685C2×D4semidirect
321. #396C2×D5semidirect
703. C2×C5#2457semidirect
817. C5C2×#2457semidirect
871. C2#10609024direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40392
C22×#40322
C2×C5×#3962
C2×#652802
C2×#652762
C2×#652752
C2×#652792
C2×#652702
C2×#652492
C2×#652452
C2×#652472
C2×C22⋊C4×Dic52
#106090242
C2×#649532
C2×#649592
C2×#24575