Finite Group Databasebeta

← C2×#10618646 #13007700

Subgroups — C2×#10618646 #13007700

Order 1280.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4147C211yesmaximal, characteristic, complemented
2C23×#713C211yesmaximal, characteristic, complemented
3C2×C5×D4×Q8C211yesmaximal, characteristic, complemented
4C2×#66151C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D5C211yesmaximal, characteristic, complemented
6#10618646C2132yesmaximal, direct product factor
7C2×#66060C213yesmaximal, complemented
8C2×#66058C213yesmaximal, complemented
9C2×#65965C213yesmaximal, complemented
10C2×#65964C213yesmaximal, complemented
11C2×#65963C213yesmaximal, complemented
12C2×D5×C22⋊Q8C213yesmaximal, complemented
13C2×#65910C211yesmaximal, characteristic, complemented
14C2×#65908C211yesmaximal, characteristic, complemented
15C2×#65884C213yesmaximal, complemented
16C2×#65881C213yesmaximal, complemented
17C23×C5×Q8C2211yescharacteristic
18C23×C5×Q8C2211yescharacteristic, complemented
19C2×#4147—216no—
20C2×#4147C22116yescomplemented
21C22×#713—216no—
22C22×#713C2213yes—
23C22×#713C2211yescharacteristic
24C22×#713C2213yes—
25C22×#713C2211yescharacteristic
26C22×#713C22116yescomplemented
27C22×#713C2213yescomplemented
28C22×Q8×D5C2211yescharacteristic, complemented
29C22×Q8×D5C2213yescomplemented
30C22×#709C2213yescomplemented
31C22×#709C2213yescomplemented
32C23×D20C2213yes—
33C23×C4×D5C2213yes—
34C5×D4×Q8C22116yescomplemented
35C2×C5×C4⋊Q8C2213yescomplemented
36C2×C5×C22⋊Q8C2213yes—
37C2×C5×C22⋊Q8C2213yescomplemented
38C2×C4×C5×Q8C2211yescharacteristic, complemented
39C2×C4×C5×D4C2213yes—
40#66151C22116yescomplemented
41Q8×C22⋊D5C22116yescomplemented
42C2×#4093C2213yescomplemented
43C2×#4092C2213yescomplemented
44C2×#4092C2213yescomplemented
45C2×Q8×Dic5C2211yescharacteristic, complemented
46C2×#4090C2213yescomplemented
47C2×#4085C2211yescharacteristic
48C2×#4083C2213yes—
49C2×#4076C2213yescomplemented
50C2×C4×C22⋊D5C2213yes—
51C2×C4×C22⋊D5C2213yescomplemented
52C2×#4070C2213yes—
53#66060C22148yescomplemented
54#66058C22148yescomplemented
55#65965C22148yescomplemented
56#65964C22148yescomplemented
57#65963C22148yescomplemented
58D5×C22⋊Q8C22148yescomplemented
59#65910C22116yescomplemented
60#65908C22116yescomplemented
61#65884C22148yescomplemented
62#65881C22148yescomplemented
63C2×#4043C2213yescomplemented
64C2×#4042C2216yescomplemented
65C2×#4042C2213yescomplemented
66C2×#4041C2216yescomplemented
67C2×#4041C2213yescomplemented
68C2×#4040C2213yescomplemented
69C2×#4040C2216yescomplemented
70C2×#4040C2216yescomplemented
71C2×#4039C2213yescomplemented
72C2×D5×C4⋊C4C2216yescomplemented
73C2×D5×C4⋊C4C2213yescomplemented
74C2×#4030C2213yescomplemented
75C2×#4030C2216yescomplemented
76C2×#4029C2213yescomplemented
77C2×#4028C2213yes—
78C2×D5×C22⋊C4C2216yes—
79C2×#4024C2213yes—
80C2×#4021C2213yescomplemented
81C2×C4×D20C2213yescomplemented
82C2×C4×D20C2213yescomplemented
83C2×#4018C2213yescomplemented
84C2×#3489—51nomaximal, Sylow
85C24×D5C2313yes—
86C22×C5×Q8—28no—
87C22×C5×Q8—28no—
88C22×C5×Q8C2313yes—
89C22×C5×Q8C2313yes—
90C22×C5×Q8C2318yes—
91C22×C5×Q8C2311yescharacteristic
92C22×C5×Q8C2318yescomplemented
93C22×C5×D4C2311yescharacteristic
94C23×C4×C5C2313yes—
95C23×C4×C5C2313yes—
96C22×C22⋊D5C2311yescharacteristic
97C22×C22⋊D5C2313yes—
98C22×C22⋊D5C2311yescharacteristic
99C22×C22⋊D5C2313yes—
100C23×Dic5C2311yescharacteristic
101#4147—2128no—
102C2×#713—28no—
103C2×#713—2128no—
104C2×#713—224no—
105C2×#713—224no—
106C2×#713—224no—
107C2×#713D4116yescomplemented
108C2×#713C23124yes—
109C2×#713C23124yes—
110C2×#713C2318yes—
111C2×#713C2318yes—
112C2×#713C23124yescomplemented
113C2×Q8×D5—28no—
114C2×Q8×D5—224no—
115C2×Q8×D5C23124yescomplemented
116C2×Q8×D5C2318yescomplemented
117C2×#709—224no—
118C2×#709—224no—
119C2×#709C23124yescomplemented
120C2×#709C23124yescomplemented
121C22×D20—224no—
122C22×D20C2313yes—
123C22×D20C2313yes—
124C22×D20C2316yes—
125C22×D20C23124yes—
126C22×D20C2313yes—
127C22×D20C2313yes—
128C22×C4×D5—224no—
129C22×C4×D5C2313yes—
130C22×C4×D5C2313yes—
131C22×C4×D5C2316yes—
132C22×C4×D5C2313yes—
133C22×C4×D5C2313yes—
134C22×C4×D5C23124yes—
135C22×C4×D5C2316yes—
136C22×C4×D5C2313yes—
137C22×Dic10C2313yes—
138C22×Dic10C2313yes—
139C5×C4⋊Q8C23124yescomplemented
140C5×C22⋊Q8C23124yes—
141C5×C22⋊Q8C23124yescomplemented
142C4×C5×Q8C2318yescomplemented
143C4×C5×D4C23124yes—
144C2×C5×C4⋊C4C2313yes—
145C2×C5×C4⋊C4C2316yes—
146C2×C5×C4⋊C4C2313yes—
147C2×C5×C22⋊C4C2313yes—
148C2×C5×C22⋊C4C2313yes—
149C2×C42×C5C2313yes—
150C2×C22⋊Dic5C2313yes—
151C2×C22⋊Dic5C2311yescharacteristic
152#4093C23124yescomplemented
153#4092C23124yescomplemented
154#4092C23124yescomplemented
155Q8×Dic5C2318yescomplemented
156#4090C23124yescomplemented
157#4085C2318yes—
158#4083C23124yes—
159#4076C23124yescomplemented
160C4×C22⋊D5C23124yes—
161C4×C22⋊D5C23124yescomplemented
162C2×#685C2313yes—
163C2×#685C2313yes—
164C2×#685C2311yescharacteristic
165C2×#685C2313yes—
166C2×#685C2316yes—
167C2×#685C2316yes—
168C2×#685C2313yes—
169C2×#685C2313yes—
170C2×C4⋊Dic5C2313yes—
171C2×C4⋊Dic5C2313yes—
172#4070C23124yes—
173C2×#683C2311yescharacteristic
174C2×#683C2313yes—
175C2×#683C2313yes—
176C2×#683C2313yes—
177C2×#683C2316yes—
178C2×C4×Dic5C2313yes—
179#4043C23124yescomplemented
180#4042C23124yescomplemented
181#4042C23148yescomplemented
182#4041C23148yescomplemented
183#4041C23124yescomplemented
184#4040C23148yescomplemented
185#4040C23148yescomplemented
186#4040C23124yescomplemented
187#4039C23124yescomplemented
188D5×C4⋊C4C23148yescomplemented
189D5×C4⋊C4C23124yescomplemented
190#4030C23124yescomplemented
191#4030C23148yescomplemented
192#4029C23124yescomplemented
193#4028C23124yes—
194D5×C22⋊C4C23148yes—
195#4024C23124yes—
196#4021C23124yescomplemented
197C4×D20C23124yescomplemented
198C4×D20C23124yescomplemented
199#4018C23124yescomplemented
200C22×2−1+4—51no—
201C23×#41—51no—
202#3489—532no—
203C2×D4×Q8—51no—
204C2×D4×Q8D511yescharacteristic, complemented
205C2×#548—51no—
206C2×#548—51no—
207C2×#547—53no—
208C2×#547—53no—
209C2×#546—53no—
210C2×#546—53no—
211C2×#537—53no—
212C2×#536—53no—
213C2×#525—53no—
214C22×C22⋊Q8—53no—
215C2×#520—51no—
216C24×C5C2411yescharacteristic
217C24×C5C2411yescharacteristic
218C23×D5—212no—
219C23×D5—212no—
220C23×D5—46no—
221C23×D5C2411yescharacteristic
222C23×D5C2413yes—
223C23×D5C24112yes—
224C23×D5C2413yes—
225C2×C5×Q8—232no—
226C2×C5×Q8—232no—
227C2×C5×Q8—212no—
228C2×C5×Q8—212no—
229C2×C5×Q8C2×D418yes—
230C2×C5×Q8C24112yes—
231C2×C5×Q8C24112yes—
232C2×C5×Q8C2414yes—
233C2×C5×D4—24no—
234C2×C5×D4C2414yes—
235C22×C4×C5—212no—
236C22×C4×C5—212no—
237C22×C4×C5C2411yescharacteristic
238C22×C4×C5C2413yes—
239C22×C4×C5C2413yes—
240C22×C4×C5C2413yes—
241C22×C4×C5C24112yes—
242C22×C4×C5C24112yes—
243C22×C4×C5C2413yes—
244C2×C22⋊D5—24no—
245C2×C22⋊D5—212no—
246C2×C22⋊D5—24no—
247C2×C22⋊D5—46no—
248C2×C22⋊D5C24112yes—
249C2×C22⋊D5C2414yes—
250C2×C22⋊D5C2414yes—
251C2×C22⋊D5C24112yes—
252C22×Dic5—24no—
253C22×Dic5C2413yes—
254C22×Dic5C2411yescharacteristic
255C22×Dic5C2413yes—
256C22×Dic5C2411yescharacteristic
257C22×Dic5C2414yes—
258C22×Dic5C2411yescharacteristic
259#713—232no—
260#713—296no—
261#713—296no—
262#713—296no—
263#713C2×D4164yescomplemented
264Q8×D5—232no—
265Q8×D5—296no—
266#709—296no—
267#709—296no—
268C2×D20—224no—
269C2×D20—212no—
270C2×D20—212no—
271C2×D20—296no—
272C2×D20—46no—
273C2×D20C2×D4124yes—
274C2×D20C24112yes—
275C2×D20C24124yes—
276C2×D20C24112yes—
277C2×D20C24112yes—
278C2×D20C24112yes—
279C2×C4×D5—212no—
280C2×C4×D5—224no—
281C2×C4×D5—212no—
282C2×C4×D5—212no—
283C2×C4×D5—212no—
284C2×C4×D5—296no—
285C2×C4×D5—412no—
286C2×C4×D5C2×D4124yes—
287C2×C4×D5C24112yes—
288C2×C4×D5C24112yes—
289C2×C4×D5C24112yes—
290C2×C4×D5C24112yes—
291C2×C4×D5C24124yes—
292C2×C4×D5C24124yes—
293C2×C4×D5C24112yes—
294C2×Dic10—212no—
295C2×Dic10—212no—
296C2×Dic10C24112yes—
297C2×Dic10C24112yes—
298C5×C4⋊C4C24112yes—
299C5×C4⋊C4C24112yes—
300C5×C4⋊C4C24124yes—
301C5×C22⋊C4C24112yes—
302C5×C22⋊C4C24112yes—
303C42×C5C24112yes—
304C22⋊Dic5C24112yes—
305C22⋊Dic5C2414yes—
306#685C24112yes—
307#685C24112yes—
308#685C2414yes—
309#685C24112yes—
310#685C24124yes—
311#685C24124yes—
312#685C24112yes—
313#685C24112yes—
314C4⋊Dic5C24112yes—
315C4⋊Dic5C24112yes—
316#683C2414yes—
317#683C24112yes—
318#683C24112yes—
319#683C24112yes—
320#683C24124yes—
321C4×Dic5C24112yes—
322C2×2−1+4—516no—
323C2×2−1+4—1016no—
324C22×#41—51no—
325C22×#41—53no—
326C22×#41—53no—
327C22×#41—51no—
328C22×#41—516no—
329C22×#41—53no—
330C22×#41—53no—
331C22×#41—53no—
332C22×#41—1016no—
333C23×Q8—53no—
334C23×Q8—51no—
335C23×Q8C2×D511yescharacteristic
336C23×Q8C2×D511yescharacteristic, complemented
337C23×D4—53no—
338C24×C4—53no—
339D4×Q8—516no—
340D4×Q8C2×D5116yescomplemented
341#548—516no—
342#548—516no—
343#547—548no—
344#547—548no—
345#546—548no—
346#546—548no—
347#537—548no—
348#536—548no—
349C2×C4⋊Q8—53no—
350C2×C4⋊Q8C2×D513yescomplemented
351C2×#124—53no—
352C2×#124—53no—
353#525—548no—
354C2×#123—53no—
355C2×#123—56no—
356C2×#123—56no—
357C2×#123—53no—
358C2×C22⋊Q8—53no—
359C2×C22⋊Q8—53no—
360C2×C22⋊Q8—53no—
361C2×C22⋊Q8—548no—
362C2×C22⋊Q8—56no—
363C2×C22⋊Q8—53no—
364C2×C22⋊Q8—53no—
365C2×C22⋊Q8—53no—
366C2×C22⋊Q8C2×D513yes—
367C2×C22⋊Q8C2×D513yescomplemented
368C2×#121—51no—
369C2×#121—53no—
370C2×#121—56no—
371C2×#121—53no—
372C2×#121—53no—
373C2×#121—56no—
374C2×#120—53no—
375C2×#120—53no—
376#520—516no—
377C2×C4×Q8—51no—
378C2×C4×Q8C2×D511yescharacteristic, complemented
379C2×C4×D4—53no—
380C2×C4×D4—53no—
381C2×C4×D4—53no—
382C2×C4×D4—53no—
383C2×C4×D4—53no—
384C2×C4×D4C2×D513yes—
385C2×#117—53no—
386C22×C4⋊C4—53no—
387C22×C4⋊C4—56no—
388C22×C22⋊C4—56no—
389C23×C5—22no—
390C23×C5—22no—
391C23×C5—22no—
392C23×C5—22no—
393C23×C5—22no—
394C23×C52−1+414yescomplemented
395C23×C5C2512yes—
396C23×C5C2512yes—
397C23×C5C2511yescharacteristic
398C22×D5—26no—
399C22×D5—26no—
400C22×D5—22no—
401C22×D5—26no—
402C22×D5—22no—
403C22×D5—26no—
404C22×D5—224no—
405C22×D5—22no—
406C22×D5—26no—
407C22×D5—224no—
408C22×D5—412no—
409C22×D5—448no—
410C22×D5C22×D4112yes—
411C22×D5C2516yes—
412C22×D5C2512yes—
413C22×D5C2516yes—
414C5×Q8—224no—
415C5×Q8—224no—
416C5×Q8C22×D4116yes—
417C5×D4—28no—
418C2×C4×C5—26no—
419C2×C4×C5—26no—
420C2×C4×C5—22no—
421C2×C4×C5—26no—
422C2×C4×C5—224no—
423C2×C4×C5—224no—
424C2×C4×C5C22×D4112yes—
425C2×C4×C5C2516yes—
426C2×C4×C5C2516yes—
427C2×C4×C5C2512yes—
428C2×C4×C5C2516yes—
429C2×C4×C5C2516yes—
430C22⋊D5—28no—
431C22⋊D5—224no—
432C22⋊D5—28no—
433C22⋊D5—412no—
434C2×Dic5—26no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—26no—
438C2×Dic5—28no—
439C2×Dic5C22×D414yes—
440C2×Dic5C2512yes—
441C2×Dic5C2516yes—
442C2×Dic5C2512yes—
443C2×Dic5C2516yes—
444C2×Dic5C2512yes—
445D20—248no—
446D20—224no—
447D20—224no—
448D20—412no—
449D20C22×D4148yes—
450C4×D5—224no—
451C4×D5—248no—
452C4×D5—224no—
453C4×D5—224no—
454C4×D5—224no—
455C4×D5—424no—
456C4×D5C22×D4148yes—
457Dic10—224no—
458Dic10—224no—
459C25—53no—
4602−1+4—10128no—
461C2×#41—516no—
462C2×#41—58no—
463C2×#41—524no—
464C2×#41—524no—
465C2×#41—524no—
466C2×#41—58no—
467C2×#41—524no—
468C2×#41—524no—
469C2×#41—1024no—
470C2×#41—1024no—
471C2×#41—1024no—
472C2×#41—1024no—
473C2×#41—1024no—
474C2×#41—10128no—
475C2×#41—108no—
476C22×Q8—28no—
477C22×Q8—28no—
478C22×Q8—524no—
479C22×Q8—58no—
480C22×Q8—53no—
481C22×Q8—53no—
482C22×Q8—1024no—
483C22×Q8—108no—
484C22×Q8C22×D513yes—
485C22×Q8C22×D513yes—
486C22×Q8C22×D518yes—
487C22×Q8C22×D511yescharacteristic
488C22×Q8C22×D518yescomplemented
489C22×D4—51no—
490C22×D4—53no—
491C22×D4—51no—
492C22×D4—53no—
493C22×D4—53no—
494C22×D4—53no—
495C22×D4—56no—
496C22×D4—53no—
497C22×D4—524no—
498C22×D4—53no—
499C22×D4—1024no—
500C22×D4C22×D511yescharacteristic
501C23×C4—53no—
502C23×C4—51no—
503C23×C4—56no—
504C23×C4—53no—
505C23×C4—53no—
506C23×C4—53no—
507C23×C4—53no—
508C23×C4—524no—
509C23×C4—56no—
510C23×C4—1024no—
511C23×C4C22×D513yes—
512C23×C4C22×D513yes—
513C4⋊Q8—524no—
514C4⋊Q8C22×D5124yescomplemented
515#124—524no—
516#124—524no—
517#123—524no—
518#123—548no—
519#123—548no—
520#123—524no—
521C22⋊Q8—524no—
522C22⋊Q8—524no—
523C22⋊Q8—524no—
524C22⋊Q8—548no—
525C22⋊Q8—524no—
526C22⋊Q8—524no—
527C22⋊Q8—524no—
528C22⋊Q8C22×D5124yes—
529C22⋊Q8C22×D5124yescomplemented
530#121—58no—
531#121—524no—
532#121—548no—
533#121—524no—
534#121—524no—
535#121—548no—
536#120—524no—
537#120—524no—
538C4×Q8—58no—
539C4×Q8C22×D518yescomplemented
540C4×D4—524no—
541C4×D4—524no—
542C4×D4—524no—
543C4×D4—524no—
544C4×D4—524no—
545C4×D4C22×D5124yes—
546#117—524no—
547C2×C4⋊C4—53no—
548C2×C4⋊C4—53no—
549C2×C4⋊C4—53no—
550C2×C4⋊C4—53no—
551C2×C4⋊C4—56no—
552C2×C4⋊C4—51no—
553C2×C4⋊C4—53no—
554C2×C4⋊C4—524no—
555C2×C4⋊C4—548no—
556C2×C4⋊C4C22×D513yes—
557C2×C4⋊C4C22×D516yes—
558C2×C4⋊C4C22×D513yes—
559C2×C22⋊C4—53no—
560C2×C22⋊C4—51no—
561C2×C22⋊C4—56no—
562C2×C22⋊C4—56no—
563C2×C22⋊C4—53no—
564C2×C22⋊C4—53no—
565C2×C22⋊C4—51no—
566C2×C22⋊C4—53no—
567C2×C22⋊C4—53no—
568C2×C22⋊C4—53no—
569C2×C22⋊C4—548no—
570C2×C22⋊C4C22×D513yes—
571C2×C22⋊C4C22×D513yes—
572C2×C42—53no—
573C2×C42C22×D513yes—
574C22×C5—22no—
575C22×C5—22no—
576C22×C5—28no—
577C22×C5—22no—
578C22×C5—22no—
579C22×C5—22no—
580C22×C5—44no—
581C22×C5C23×D412yes—
582C22×C5C2×2−1+412yes—
583C22×C5C2×2−1+414yescomplemented
584C22×C5#58512yes—
585C22×C5C2611yescharacteristic
586C2×D5—26no—
587C2×D5—26no—
588C2×D5—224no—
589C2×D5—22no—
590C2×D5—26no—
591C2×D5—22no—
592C2×D5—26no—
593C2×D5—22no—
594C2×D5—26no—
595C2×D5—448no—
596C2×D5—44no—
597C2×D5—412no—
598C2×D5C23×D4112yes—
599C4×C5—26no—
600C4×C5—26no—
601C4×C5—22no—
602C4×C5—26no—
603C4×C5C23×D4112yes—
604Dic5—26no—
605Dic5—22no—
606Dic5—22no—
607Dic5—26no—
608Dic5C23×D414yes—
609C24—53no—
610C24—53no—
611C24—51no—
612C24—512no—
613C24—1012no—
614C24—1012no—
615C24—206no—
616C24C23×D511yescharacteristic
617C24C23×D511yescharacteristic
618#41—564no—
619#41—1096no—
620#41—1096no—
621#41—1096no—
622#41—1096no—
623#41—1096no—
624#41—1032no—
625C2×Q8—232no—
626C2×Q8—232no—
627C2×Q8—212no—
628C2×Q8—212no—
629C2×Q8—512no—
630C2×Q8—512no—
631C2×Q8—1012no—
632C2×Q8—1096no—
633C2×Q8—1032no—
634C2×Q8—1012no—
635C2×Q8D4×D518yes—
636C2×Q8C23×D5112yes—
637C2×Q8C23×D5112yes—
638C2×Q8C23×D514yes—
639C2×D4—24no—
640C2×D4—54no—
641C2×D4—512no—
642C2×D4—54no—
643C2×D4—512no—
644C2×D4—524no—
645C2×D4—512no—
646C2×D4—512no—
647C2×D4—524no—
648C2×D4—512no—
649C2×D4—512no—
650C2×D4—1096no—
651C2×D4—1024no—
652C2×D4—1012no—
653C2×D4—104no—
654C2×D4—1012no—
655C2×D4—104no—
656C2×D4—1012no—
657C2×D4—206no—
658C2×D4—206no—
659C2×D4C23×D514yes—
660C22×C4—212no—
661C22×C4—212no—
662C22×C4—51no—
663C22×C4—524no—
664C22×C4—512no—
665C22×C4—54no—
666C22×C4—51no—
667C22×C4—53no—
668C22×C4—53no—
669C22×C4—51no—
670C22×C4—524no—
671C22×C4—512no—
672C22×C4—512no—
673C22×C4—512no—
674C22×C4—512no—
675C22×C4—524no—
676C22×C4—1012no—
677C22×C4—1096no—
678C22×C4—1012no—
679C22×C4—1024no—
680C22×C4—104no—
681C22×C4—1012no—
682C22×C4—1012no—
683C22×C4—2012no—
684C22×C4C23×D5112yes—
685C22×C4C23×D5112yes—
686C22×C4C23×D511yescharacteristic
687C22×C4C23×D513yes—
688C22×C4C23×D513yes—
689C22×C4C23×D513yes—
690C22×C4C23×D513yes—
691C4⋊C4—512no—
692C4⋊C4—512no—
693C4⋊C4—512no—
694C4⋊C4—512no—
695C4⋊C4—524no—
696C4⋊C4—54no—
697C4⋊C4—512no—
698C4⋊C4C23×D5112yes—
699C4⋊C4C23×D5124yes—
700C4⋊C4C23×D5112yes—
701C22⋊C4—512no—
702C22⋊C4—54no—
703C22⋊C4—524no—
704C22⋊C4—524no—
705C22⋊C4—512no—
706C22⋊C4—512no—
707C22⋊C4—54no—
708C22⋊C4—512no—
709C22⋊C4—512no—
710C22⋊C4—512no—
711C22⋊C4C23×D5112yes—
712C22⋊C4C23×D5112yes—
713C42—512no—
714C42C23×D5112yes—
715C2×C5—24no—
716C2×C5—42no—
717C2×C5#348914yescomplemented
718C2×C5C24×D411yescharacteristic
719C2×C5C22×2−1+411yescharacteristic
720C2×C5C2×#58511yescharacteristic
721D5—212no—
722D5—42no—
723D5—46no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—512no—
730C23—56no—
731C23—56no—
732C23—52no—
733C23—1024no—
734C23—106no—
735C23—106no—
736C23—102no—
737C23—106no—
738C23—102no—
739C23—106no—
740C23—1024no—
741C23—102no—
742C23—106no—
743C23—2012no—
744C23—2048no—
745C23#414714yescomplemented
746C23C24×D512yes—
747C23C24×D512yes—
748C23C24×D511yescharacteristic
749Q8—224no—
750Q8—224no—
751Q8—1024no—
752Q8—1024no—
753Q8C2×D4×D5116yes—
754D4—28no—
755D4—548no—
756D4—1048no—
757D4—1024no—
758D4—108no—
759D4—1024no—
760D4—108no—
761D4—1024no—
762D4—2012no—
763D4—2012no—
764C2×C4—26no—
765C2×C4—26no—
766C2×C4—22no—
767C2×C4—26no—
768C2×C4—224no—
769C2×C4—224no—
770C2×C4—54no—
771C2×C4—52no—
772C2×C4—548no—
773C2×C4—52no—
774C2×C4—56no—
775C2×C4—56no—
776C2×C4—52no—
777C2×C4—1024no—
778C2×C4—1024no—
779C2×C4—1048no—
780C2×C4—108no—
781C2×C4—102no—
782C2×C4—106no—
783C2×C4—102no—
784C2×C4—106no—
785C2×C4—1024no—
786C2×C4—1024no—
787C2×C4—2024no—
788C2×C4C2×D4×D5112yes—
789C2×C4C24×D512yes—
790C2×C4C24×D516yes—
791C2×C4C24×D516yes—
792C2×C4C24×D516yes—
793C2×C4C24×D516yes—
794C5C2×#348911yescharacteristic, complemented, Sylow
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—512no—
803C22—1024no—
804C22—106no—
805C22—106no—
806C22—102no—
807C22—106no—
808C22—102no—
809C22—106no—
810C22—102no—
811C22—106no—
812C22—2048no—
813C22—2012no—
814C22—204no—
815C22C22×D4×D512yes—
816C22C2×#414712yes—
817C22C2×#414714yescomplemented
818C22#6628712yes—
819C22C25×D511yescharacteristic
820C4—26no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—54no—
825C4—102no—
826C4—106no—
827C4—102no—
828C4—106no—
829C4C22×D4×D5112yes—
830C2—24no—
831C2—42no—
832C2—1012no—
833C2—206no—
834C2—202no—
835C2#1061864614yesdirect product factor
836C2C23×D4×D511yescharacteristic
837C2C22×#414711yescharacteristic
838C2C2×#6628711yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×D4×Q8C2
socleC23×C5C25
hypercenterC2×D4×Q8D5
hypocenterC5C2×#3489
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#4147C2semidirect
2. C23×#713C2semidirect
3. C2×C5×D4×Q8C2semidirect
4. C2×#66151C2semidirect
5. C2×Q8×C22⋊D5C2semidirect
6. #10618646C2direct (N × H)
7. C2×#66060C2semidirect
8. C2×#66058C2semidirect
9. C2×#65965C2semidirect
10. C2×#65964C2semidirect
11. C2×#65963C2semidirect
12. C2×D5×C22⋊Q8C2semidirect
13. C2×#65910C2semidirect
14. C2×#65908C2semidirect
15. C2×#65884C2semidirect
16. C2×#65881C2semidirect
18. C23×C5×Q8C22semidirect
20. C2×#4147C22semidirect
26. C22×#713C22semidirect
27. C22×#713C22semidirect
28. C22×Q8×D5C22semidirect
29. C22×Q8×D5C22semidirect
30. C22×#709C22semidirect
31. C22×#709C22semidirect
34. C5×D4×Q8C22semidirect
35. C2×C5×C4⋊Q8C22semidirect
37. C2×C5×C22⋊Q8C22semidirect
38. C2×C4×C5×Q8C22semidirect
40. #66151C22semidirect
41. Q8×C22⋊D5C22semidirect
42. C2×#4093C22semidirect
43. C2×#4092C22semidirect
44. C2×#4092C22semidirect
45. C2×Q8×Dic5C22semidirect
46. C2×#4090C22semidirect
49. C2×#4076C22semidirect
51. C2×C4×C22⋊D5C22semidirect
53. #66060C22semidirect
54. #66058C22semidirect
55. #65965C22semidirect
56. #65964C22semidirect
57. #65963C22semidirect
58. D5×C22⋊Q8C22semidirect
59. #65910C22semidirect
60. #65908C22semidirect
61. #65884C22semidirect
62. #65881C22semidirect
63. C2×#4043C22semidirect
64. C2×#4042C22semidirect
65. C2×#4042C22semidirect
66. C2×#4041C22semidirect
67. C2×#4041C22semidirect
68. C2×#4040C22semidirect
69. C2×#4040C22semidirect
70. C2×#4040C22semidirect
71. C2×#4039C22semidirect
72. C2×D5×C4⋊C4C22semidirect
73. C2×D5×C4⋊C4C22semidirect
74. C2×#4030C22semidirect
75. C2×#4030C22semidirect
76. C2×#4029C22semidirect
80. C2×#4021C22semidirect
81. C2×C4×D20C22semidirect
82. C2×C4×D20C22semidirect
83. C2×#4018C22semidirect
92. C22×C5×Q8C23semidirect
107. C2×#713D4semidirect
112. C2×#713C23semidirect
115. C2×Q8×D5C23semidirect
116. C2×Q8×D5C23semidirect
119. C2×#709C23semidirect
120. C2×#709C23semidirect
139. C5×C4⋊Q8C23semidirect
141. C5×C22⋊Q8C23semidirect
142. C4×C5×Q8C23semidirect
152. #4093C23semidirect
153. #4092C23semidirect
154. #4092C23semidirect
155. Q8×Dic5C23semidirect
156. #4090C23semidirect
159. #4076C23semidirect
161. C4×C22⋊D5C23semidirect
179. #4043C23semidirect
180. #4042C23semidirect
181. #4042C23semidirect
182. #4041C23semidirect
183. #4041C23semidirect
184. #4040C23semidirect
185. #4040C23semidirect
186. #4040C23semidirect
187. #4039C23semidirect
188. D5×C4⋊C4C23semidirect
189. D5×C4⋊C4C23semidirect
190. #4030C23semidirect
191. #4030C23semidirect
192. #4029C23semidirect
196. #4021C23semidirect
197. C4×D20C23semidirect
198. C4×D20C23semidirect
199. #4018C23semidirect
204. C2×D4×Q8D5semidirect
263. #713C2×D4semidirect
336. C23×Q8C2×D5semidirect
340. D4×Q8C2×D5semidirect
350. C2×C4⋊Q8C2×D5semidirect
367. C2×C22⋊Q8C2×D5semidirect
378. C2×C4×Q8C2×D5semidirect
394. C23×C52−1+4semidirect
488. C22×Q8C22×D5semidirect
514. C4⋊Q8C22×D5semidirect
529. C22⋊Q8C22×D5semidirect
539. C4×Q8C22×D5semidirect
583. C22×C5C2×2−1+4semidirect
717. C2×C5#3489semidirect
745. C23#4147semidirect
794. C5C2×#3489semidirect
817. C22C2×#4147semidirect
835. C2#10618646direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41472
C23×#7132
C2×C5×D4×Q82
C2×#661512
C2×Q8×C22⋊D52
#106186462
C2×#660602
C2×#660582
C2×#659652
C2×#659642
C2×#659632
C2×D5×C22⋊Q82
C2×#659102
C2×#659082
C2×#658842
C2×#658812
C2×#34895