Finite Group Databasebeta

← C2×#10609520 #12269382

Subgroups — C2×#10609520 #12269382

Order 1280.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4040C211yesmaximal, characteristic, complemented
2C22×#4044C211yesmaximal, characteristic, complemented
3C2×C5×#398C211yesmaximal, characteristic, complemented
4C2×#65283C211yesmaximal, characteristic, complemented
5C2×#65277C211yesmaximal, characteristic, complemented
6C2×#65277C211yesmaximal, characteristic, complemented
7C2×#65277C211yesmaximal, characteristic, complemented
8C2×#65279C211yesmaximal, characteristic, complemented
9C2×#65279C211yesmaximal, characteristic, complemented
10#10609520C2116yesmaximal, direct product factor
11C2×#64960C211yesmaximal, characteristic
12C2×#64954C211yesmaximal, characteristic, complemented
13C2×#64961C211yesmaximal, characteristic, complemented
14C2×#64959C211yesmaximal, characteristic, complemented
15C2×#64938C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4044—28no—
47C2×#4044C2218yescomplemented
48C2×#4040—28no—
49C2×#4040C2218yescomplemented
50C5×#398C2218yescomplemented
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×C5×#95C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65283C2218yescomplemented
58#65279C2218yescomplemented
59#65279C2218yescomplemented
60#65277C2218yescomplemented
61#65277C2218yescomplemented
62#65277C2218yescomplemented
63#64961C2218yescomplemented
64#64960C2218yes—
65#64959C2218yescomplemented
66#64955C2218yescomplemented
67#64954C2218yescomplemented
68#64938C2218yescomplemented
69C2×#2554—51nomaximal, Sylow
70C24×D5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C22×D20—24no—
86C22×D20—24no—
87C22×D20—24no—
88C22×D20—24no—
89C22×D20—24no—
90C22×D20—42no—
91C22×D20—42no—
92C22×D20—42no—
93C22×D20—42no—
94C22×D20C2314yes—
95C22×D20C2314yes—
96C22×D20C2314yes—
97C22×C4×D5—24no—
98C22×C4×D5—24no—
99C22×C4×D5—42no—
100C22×C4×D5C2314yes—
101C2×C5×C4⋊C4—24no—
102C2×C5×C4⋊C4—24no—
103C2×C5×C4⋊C4—42no—
104C2×C5×C4⋊C4—42no—
105C2×C5×C4⋊C4C2314yes—
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C4⋊C4C2314yes—
108C2×C5×C4⋊C4C2314yes—
109C2×#685—24no—
110C2×#685—24no—
111C2×#685—24no—
112C2×#685—24no—
113C2×#685—24no—
114C2×#685—24no—
115C2×#685—24no—
116C2×#685—24no—
117C2×#685—24no—
118C2×#685—24no—
119C2×#685—24no—
120C2×#685—42no—
121C2×#685—42no—
122C2×#685—42no—
123C2×#685C2314yes—
124C2×#685C2314yes—
125C2×#685C2314yes—
126C2×#685C2314yes—
127C2×#685C2314yes—
128C2×#685C2314yes—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×C4⋊Dic5—24no—
138C2×C4⋊Dic5C2314yes—
139C2×#683—24no—
140C2×#683D418yescomplemented
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×C4×Dic5—24no—
144C2×C4×Dic5—24no—
145C2×C4×Dic5—42no—
146C2×C4×Dic5—42no—
147C2×C4×Dic5C2314yes—
148C2×C4×Dic5C2314yes—
149C2×C4×Dic5C2314yes—
150C2×C4×Dic5C2314yes—
151#4044—232no—
152#4040—232no—
153C5×#95C2314yes—
154C5×#95C2314yes—
155C5×#95C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#126—51no—
160C22×#123—51no—
161#2554—516no—
162C2×#398D511yescharacteristic, complemented
163C2×#396—51no—
164C2×#394—51no—
165C2×#392—51no—
166C2×#390—51no—
167C2×#390—51no—
168C2×#390—51no—
169C2×#388—51no—
170C2×#388—51no—
171C2×#388—51no—
172C2×#386—51no—
173C2×C4×C4⋊C4—51no—
174C2×C4×C22⋊C4—51no—
175C24×C5C2411yescharacteristic
176C23×D5—22no—
177C23×D5—22no—
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5—22no—
183C23×D5—22no—
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×D5#4114yes—
197C23×D5C2412yes—
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×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5C2×D414yes—
219C22×C4×C5#4114yes—
220C22×C4×C5#4114yes—
221C22×C4×C5C2412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
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×Dic5C2×D414yes—
241C22×Dic5C2×D414yes—
242C22×Dic5#4114yes—
243C22×Dic5C2412yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C22×Dic5C2412yes—
247C22×Dic5C2412yes—
248C2×D20—28no—
249C2×D20—28no—
250C2×D20—28no—
251C2×D20—28no—
252C2×D20—28no—
253C2×D20—44no—
254C2×D20—44no—
255C2×D20—44no—
256C2×D20—44no—
257C2×D20—416no—
258C2×D20—416no—
259C2×D20—416no—
260C2×C4×D5—28no—
261C2×C4×D5—28no—
262C2×C4×D5—44no—
263C2×C4×D5—416no—
264C5×C4⋊C4—28no—
265C5×C4⋊C4—28no—
266C5×C4⋊C4—44no—
267C5×C4⋊C4—44no—
268#685—28no—
269#685—28no—
270#685—28no—
271#685—28no—
272#685—28no—
273#685—28no—
274#685—28no—
275#685—28no—
276#685—28no—
277#685—28no—
278#685—28no—
279#685—44no—
280#685—44no—
281#685—44no—
282C4⋊Dic5—28no—
283#683—28no—
284#683C2×D4116yescomplemented
285C4×Dic5—28no—
286C4×Dic5—28no—
287C4×Dic5—44no—
288C4×Dic5—44no—
289C23×D4—51no—
290C23×D4—51no—
291C23×D4—51no—
292C24×C4—51no—
293C2×#126—58no—
294C2×#126—108no—
295C2×#123—58no—
296C2×#123—108no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4C2×D511yescharacteristic
301C22×C4⋊C4C2×D511yescharacteristic
302C22×C4⋊C4C2×D511yescharacteristic
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⋊C4—51no—
314C22×C22⋊C4—51no—
315C22×C22⋊C4—51no—
316C22×C22⋊C4—51no—
317C22×C22⋊C4—51no—
318C22×C42—51no—
319C22×C42—51no—
320C22×C42—51no—
321C22×C42—51no—
322#398C2×D518yescomplemented
323#396—58no—
324#394—58no—
325#392—58no—
326#390—58no—
327#390—58no—
328#390—58no—
329#388—58no—
330#388—58no—
331#388—58no—
332#386—58no—
333C4×C4⋊C4—58no—
334C4×C22⋊C4—58no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95C2×D511yescharacteristic
339C2×#95C2×D511yescharacteristic
340C2×#95C2×D511yescharacteristic
341C23×C5C22×D412yes—
342C23×C5C2×#4112yes—
343C23×C5C2×#4112yes—
344C23×C5C2×#4112yes—
345C23×C5C2×#4112yes—
346C23×C5H(5,𝔽2)12yes—
347C23×C5H(5,𝔽2)12yes—
348C23×C5C2511yescharacteristic
349C22×D5—28no—
350C22×D5—28no—
351C22×D5—28no—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—22no—
360C22×D5—22no—
361C22×D5—22no—
362C22×D5—22no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—22no—
370C22×D5—22no—
371C22×D5—22no—
372C22×D5—44no—
373C22×D5—44no—
374C22×D5—44no—
375C22×D5—44no—
376C22×D5—44no—
377C22×D5—44no—
378C22×D5—44no—
379C22×D5—44no—
380C22×D5—44no—
381C22×D5—44no—
382C22×D5—44no—
383C22×D5—44no—
384C22×D5—44no—
385C22×D5—44no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5C2×#4114yes—
391C2×C4×C5—28no—
392C2×C4×C5—28no—
393C2×C4×C5—28no—
394C2×C4×C5—22no—
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—22no—
412C2×C4×C5—44no—
413C2×C4×C5—44no—
414C2×C4×C5—44no—
415C2×C4×C5—44no—
416C2×C4×C5C22×D414yes—
417C2×C4×C5C2×#4114yes—
418C2×C4×C5C2×#4114yes—
419C2×Dic5—28no—
420C2×Dic5—28no—
421C2×Dic5—28no—
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—44no—
435C2×Dic5—44no—
436C2×Dic5C22×D414yes—
437C2×Dic5C22×D414yes—
438C2×Dic5C2×#4114yes—
439D20—416no—
440D20—416no—
441D20—416no—
442C4×D5—416no—
443C25—51no—
444C25—51no—
445C25—51no—
446C22×D4—54no—
447C22×D4—54no—
448C22×D4—54no—
449C22×D4—104no—
450C22×D4—104no—
451C22×D4—104no—
452C22×D4—104no—
453C22×D4—104no—
454C22×D4—202no—
455C22×D4—202no—
456C22×D4—202no—
457C22×D4—202no—
458C23×C4—51no—
459C23×C4—51no—
460C23×C4—51no—
461C23×C4—51no—
462C23×C4—51no—
463C23×C4—54no—
464C23×C4—104no—
465C23×C4—104no—
466C23×C4—202no—
467C23×C4C22×D511yescharacteristic
468C23×C4C22×D511yescharacteristic
469C23×C4C22×D511yescharacteristic
470C23×C4C22×D511yescharacteristic
471C23×C4C22×D511yescharacteristic
472C23×C4C22×D511yescharacteristic
473C23×C4C22×D511yescharacteristic
474#126—1032no—
475#123—1032no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—58no—
481C2×C4⋊C4—54no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—54no—
484C2×C4⋊C4—104no—
485C2×C4⋊C4—104no—
486C2×C4⋊C4C22×D514yes—
487C2×C4⋊C4C22×D514yes—
488C2×C4⋊C4C22×D514yes—
489C2×C4⋊C4C22×D514yes—
490C2×C22⋊C4—54no—
491C2×C22⋊C4—54no—
492C2×C22⋊C4—54no—
493C2×C22⋊C4—54no—
494C2×C22⋊C4—54no—
495C2×C22⋊C4—54no—
496C2×C22⋊C4—54no—
497C2×C22⋊C4—54no—
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—104no—
505C2×C22⋊C4—104no—
506C2×C22⋊C4—104no—
507C2×C22⋊C4—104no—
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⋊C4—202no—
518C2×C42—54no—
519C2×C42—54no—
520C2×C42—54no—
521C2×C42—54no—
522C2×C42—104no—
523C2×C42—104no—
524C2×C42—202no—
525C2×C42—202no—
526#95—54no—
527#95—54no—
528#95—54no—
529#95C22×D514yes—
530#95C22×D514yes—
531#95C22×D514yes—
532C22×C5#52914yes—
533C22×C5#53214yes—
534C22×C5#53814yes—
535C22×C5#54614yes—
536C22×C5#55014yes—
537C22×C5#55114yes—
538C22×C5#55314yes—
539C22×C5C23×D411yescharacteristic
540C22×C5C22×#4111yescharacteristic
541C22×C5C22×#4111yescharacteristic
542C22×C5C22×#4111yescharacteristic
543C22×C5C22×#4111yescharacteristic
544C22×C5C2×H(5,𝔽2)11yescharacteristic
545C22×C5C2×H(5,𝔽2)11yescharacteristic
546C2×D5—24no—
547C2×D5—24no—
548C2×D5—24no—
549C2×D5—42no—
550C2×D5—42no—
551C2×D5—42no—
552C2×D5—42no—
553C2×D5—416no—
554C2×D5—42no—
555C2×D5—42no—
556C2×D5—42no—
557C2×D5—42no—
558C2×D5—42no—
559C2×D5—42no—
560C2×D5—42no—
561C2×D5—42no—
562C2×D5—42no—
563C2×D5—42no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—88no—
569C2×D5—88no—
570C4×C5—24no—
571C4×C5—24no—
572C4×C5—24no—
573C4×C5—42no—
574C4×C5—42no—
575C4×C5—42no—
576C4×C5—42no—
577Dic5—24no—
578Dic5—24no—
579Dic5—24no—
580Dic5—42no—
581Dic5—42no—
582C24—54no—
583C24—52no—
584C24—52no—
585C24—52no—
586C24—102no—
587C24—102no—
588C24—102no—
589C24—102no—
590C24—102no—
591C24—102no—
592C24—102no—
593C24—102no—
594C24—102no—
595C24—102no—
596C24—102no—
597C24—102no—
598C24—102no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24—102no—
606C24C23×D511yescharacteristic
607C2×D4—108no—
608C2×D4—108no—
609C2×D4—108no—
610C2×D4—108no—
611C2×D4—108no—
612C2×D4—204no—
613C2×D4—204no—
614C2×D4—204no—
615C2×D4—204no—
616C2×D4—2016no—
617C2×D4—2016no—
618C2×D4—2016no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
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—108no—
646C22×C4—108no—
647C22×C4—102no—
648C22×C4—102no—
649C22×C4—102no—
650C22×C4—102no—
651C22×C4—102no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—102no—
659C22×C4—204no—
660C22×C4—2016no—
661C22×C4D4×D514yes—
662C22×C4#71314yes—
663C22×C4#71314yes—
664C22×C4C23×D512yes—
665C22×C4C23×D512yes—
666C22×C4C23×D512yes—
667C22×C4C23×D512yes—
668C22×C4C23×D512yes—
669C22×C4C23×D512yes—
670C22×C4C23×D512yes—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—516no—
676C4⋊C4—108no—
677C4⋊C4—108no—
678C22⋊C4—108no—
679C22⋊C4—108no—
680C22⋊C4—108no—
681C22⋊C4—108no—
682C22⋊C4—108no—
683C22⋊C4—108no—
684C22⋊C4—108no—
685C22⋊C4—108no—
686C22⋊C4—108no—
687C22⋊C4—108no—
688C22⋊C4—108no—
689C22⋊C4—204no—
690C22⋊C4—204no—
691C22⋊C4—204no—
692C42—108no—
693C42—108no—
694C42—204no—
695C42—204no—
696C2×C5#255418yescomplemented
697C2×C5C2×#52911yescharacteristic
698C2×C5C2×#53211yescharacteristic
699C2×C5C2×#53811yescharacteristic
700C2×C5C2×#54611yescharacteristic
701C2×C5C2×#55011yescharacteristic
702C2×C5C2×#55111yescharacteristic
703C2×C5C2×#55311yescharacteristic
704D5—44no—
705D5—82no—
706D5—82no—
707C23—54no—
708C23—108no—
709C23—108no—
710C23—102no—
711C23—102no—
712C23—102no—
713C23—102no—
714C23—102no—
715C23—108no—
716C23—102no—
717C23—102no—
718C23—102no—
719C23—102no—
720C23—102no—
721C23—102no—
722C23—102no—
723C23—102no—
724C23—102no—
725C23—102no—
726C23—102no—
727C23—102no—
728C23—102no—
729C23—102no—
730C23—102no—
731C23—204no—
732C23—204no—
733C23—204no—
734C23—204no—
735C23—204no—
736C23—204no—
737C23—204no—
738C23—204no—
739C23—204no—
740C23—204no—
741C23—204no—
742C23—204no—
743C23—204no—
744C23—204no—
745C23—204no—
746C23—204no—
747C23—204no—
748C23—204no—
749C23C2×D4×D512yes—
750C23#414412yes—
751C23C2×#71312yes—
752C23C2×#71312yes—
753C23D5×#4112yes—
754C23D5×#4112yes—
755C23#414912yes—
756C23C24×D511yescharacteristic
757D4—2016no—
758D4—2016no—
759D4—2016no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
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—102no—
791C2×C4—102no—
792C2×C4—102no—
793C2×C4—102no—
794C2×C4—102no—
795C2×C4—102no—
796C2×C4—108no—
797C2×C4—102no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—102no—
803C2×C4—2016no—
804C2×C4—204no—
805C2×C4—204no—
806C2×C4C2×D4×D514yes—
807C2×C4C2×#71314yes—
808C2×C4C2×#71314yes—
809C5C2×#255411yescharacteristic, complemented, Sylow
810C22—104no—
811C22—104no—
812C22—104no—
813C22—202no—
814C22—2016no—
815C22—202no—
816C22—202no—
817C22—202no—
818C22—202no—
819C22—202no—
820C22—202no—
821C22—202no—
822C22—202no—
823C22—202no—
824C22—202no—
825C22—202no—
826C22—202no—
827C22—202no—
828C22—202no—
829C22—202no—
830C22—202no—
831C22—202no—
832C22—408no—
833C22—408no—
834C22#6593314yes—
835C22#6597114yes—
836C22#6597814yes—
837C22#6598814yes—
838C22#6602514yes—
839C22#6602914yes—
840C22#6605914yes—
841C22C22×D4×D511yescharacteristic
842C22C2×#414411yescharacteristic
843C22C22×#71311yescharacteristic
844C22C22×#71311yescharacteristic
845C22C2×D5×#4111yescharacteristic
846C22C2×D5×#4111yescharacteristic
847C22C2×#414911yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—104no—
856C4—104no—
857C4—104no—
858C4—202no—
859C4—202no—
860C2—204no—
861C2—402no—
862C2—402no—
863C2#1060952018yesdirect product factor
864C2C2×#6593311yescharacteristic
865C2C2×#6597811yescharacteristic
866C2C2×#6597111yescharacteristic
867C2C2×#6598811yescharacteristic
868C2C2×#6602511yescharacteristic
869C2C2×#6602911yescharacteristic
870C2C2×#6605911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#398C2
socleC24×C5C24
prime radicalC2×#64960C2
hypercenterC2×#398D5
hypocenterC5C2×#2554
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#4040C2semidirect
2. C22×#4044C2semidirect
3. C2×C5×#398C2semidirect
4. C2×#65283C2semidirect
5. C2×#65277C2semidirect
6. C2×#65277C2semidirect
7. C2×#65277C2semidirect
8. C2×#65279C2semidirect
9. C2×#65279C2semidirect
10. #10609520C2direct (N × H)
12. C2×#64954C2semidirect
13. C2×#64961C2semidirect
14. C2×#64959C2semidirect
15. C2×#64938C2semidirect
16. C2×#64955C2semidirect
47. C2×#4044C22semidirect
49. C2×#4040C22semidirect
50. C5×#398C22semidirect
57. #65283C22semidirect
58. #65279C22semidirect
59. #65279C22semidirect
60. #65277C22semidirect
61. #65277C22semidirect
62. #65277C22semidirect
63. #64961C22semidirect
65. #64959C22semidirect
66. #64955C22semidirect
67. #64954C22semidirect
68. #64938C22semidirect
140. C2×#683D4semidirect
162. C2×#398D5semidirect
284. #683C2×D4semidirect
322. #398C2×D5semidirect
696. C2×C5#2554semidirect
809. C5C2×#2554semidirect
863. C2#10609520direct (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×#40442
C2×C5×#3982
C2×#652832
C2×#652772
C2×#652792
#106095202
C2×#649602
C2×#649542
C2×#649612
C2×#649592
C2×#649382
C2×#649552
C2×#25545