Finite Group Databasebeta

← C2×#10618854 #13006983

Subgroups — C2×#10618854 #13006983

Order 1280.

7086 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#554C211yesmaximal, characteristic, complemented
2#10618854C2132yesmaximal, direct product factor
3C2×#66064C211yesmaximal, characteristic, complemented
4C2×D5×C4⋊Q8C211yesmaximal, characteristic, complemented
5C2×#66028C212yesmaximal, complemented
6C2×#66023C212yesmaximal, complemented
7C2×#65973C212yesmaximal, complemented
8C2×#65962C214yesmaximal, complemented
9C2×#65980C214yesmaximal, complemented
10C2×#65977C212yesmaximal, complemented
11C2×#65914C211yesmaximal, characteristic, complemented
12C2×Q8×Dic10C211yesmaximal, characteristic, complemented
13C2×#65885C212yesmaximal, complemented
14C2×#65895C212yesmaximal, complemented
15C2×#65891C211yesmaximal, characteristic, complemented
16C2×#65897C211yesmaximal, characteristic, complemented
17C2×#65841C212yesmaximal, complemented
18C2×#65834C212yesmaximal, complemented
19C22×Q8×D5C2212yes—
20C22×#709C2214yes—
21C5×#554C22116yescomplemented
22C2×C5×C4⋊Q8C2211yescharacteristic
23C2×C5×#125C2212yes—
24C2×C5×C22⋊Q8C2212yes—
25C2×C5×C22⋊Q8C2214yes—
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C4×C5×D4C2212yes—
29C22×C5×C4⋊C4C2212yes—
30C2×#4093C2211yescharacteristic
31C2×#4092C2214yes—
32C2×#4092C2211yescharacteristic
33C2×Q8×Dic5C2212yes—
34C2×#4090C2212yes—
35C2×#4084C2212yes—
36C2×#4084C2211yescharacteristic
37C2×#4082C2211yescharacteristic
38C2×#4076C2212yes—
39C2×#4075C2214yes—
40C2×C4×C22⋊D5C2212yes—
41C2×#4072C2212yes—
42C2×#4072C2212yes—
43C2×#4070C2214yes—
44C2×#4070C2214yes—
45#66064C22116yescomplemented
46D5×C4⋊Q8C22116yescomplemented
47#66028C22132yescomplemented
48#66023C22132yescomplemented
49#65980C22164yescomplemented
50#65977C22132yescomplemented
51#65973C22132yescomplemented
52#65962C22164yescomplemented
53#65914C22116yescomplemented
54Q8×Dic10C22116yescomplemented
55#65897C22116yescomplemented
56#65895C22132yescomplemented
57#65891C22116yescomplemented
58#65885C22132yescomplemented
59C2×#4044C2214yes—
60C2×#4044C2212yes—
61C2×#4043C2212yes—
62C2×#4043C2214yes—
63C2×#4043C2211yescharacteristic
64C2×#4042C2214yes—
65#65841C22132yescomplemented
66C2×#4041C2211yescharacteristic
67C2×#4040C2214yes—
68C2×#4040C2212yes—
69C2×#4039C2212yes—
70C2×#4038C2214yes—
71C2×#4038C2212yes—
72C2×D5×C4⋊C4C2212yes—
73C2×D5×C4⋊C4C2212yes—
74C2×D5×C4⋊C4C2212yes—
75#65834C22132yescomplemented
76C2×#4036C2212yes—
77C2×#4036C2211yescharacteristic
78C2×#4036C2214yes—
79C2×#4036C2211yescharacteristic
80C2×#4035C2214yes—
81C2×#4034C2212yes—
82C2×#4034C2212yes—
83C2×#4034C2214yes—
84C2×#4034C2214yes—
85C2×#4034C2212yes—
86C2×#4031C2214yes—
87C2×#4031C2214yes—
88C2×#4029C2214yes—
89C2×#4029C2212yes—
90C2×#4029C2214yes—
91C2×#4025C2212yes—
92C2×#4025C2214yes—
93C2×C4×D20C2211yescharacteristic
94C2×C4×D20C2212yes—
95C2×#4018C2212yes—
96C2×C42×D5C2211yescharacteristic
97C2×#4015C2211yescharacteristic
98C2×#4015C2212yes—
99C2×C4×Dic10C2211yescharacteristic
100C2×C4×Dic10C2212yes—
101C2×#3544—51nomaximal, Sylow
102C22×C5×Q8C2311yescharacteristic
103C22×C5×Q8C2312yes—
104C22×C5×D4C2311yescharacteristic
105C23×C4×C5C2312yes—
106C23×C4×C5C2314yes—
107C22×C22⋊D5C2312yes—
108C22×C22⋊D5C2314yes—
109C2×Q8×D5—48no—
110C2×Q8×D5C23116yes—
111C2×#709—416no—
112C2×#709C23132yes—
113C22×D20C2311yescharacteristic
114C22×D20C2312yes—
115C22×C4×D5C2311yescharacteristic
116C22×C4×D5C2311yescharacteristic
117C22×C4×D5C2311yescharacteristic
118C22×C4×D5C2312yes—
119C22×C4×D5C2314yes—
120C22×C4×D5C2314yes—
121C22×Dic10C2311yescharacteristic
122C22×Dic10C2312yes—
123C22×Dic10C2314yes—
124C22×Dic10C2314yes—
125C5×C4⋊Q8C2318yes—
126C5×#125C23116yes—
127C5×C22⋊Q8C23132yes—
128C5×C22⋊Q8C23116yes—
129C4×C5×Q8C2318yes—
130C4×C5×D4C23116yes—
131C4×C5×D4C2318yes—
132C2×C5×C4⋊C4C2311yescharacteristic
133C2×C5×C4⋊C4C2312yes—
134C2×C5×C4⋊C4C2312yes—
135C2×C5×C4⋊C4C2314yes—
136C2×C5×C4⋊C4C2312yes—
137C2×C5×C4⋊C4C2314yes—
138C2×C5×C4⋊C4C2311yescharacteristic
139C2×C5×C4⋊C4C23116yes—
140C2×C5×C22⋊C4C2314yes—
141C2×C5×C22⋊C4C2312yes—
142C2×C42×C5C2311yescharacteristic
143C2×C42×C5C2312yes—
144C2×C22⋊Dic5C2312yes—
145C2×C22⋊Dic5C2312yes—
146C2×C22⋊Dic5C2314yes—
147C2×C22⋊Dic5C2312yes—
148#4093C2318yes—
149#4092C23132yes—
150#4092C2318yes—
151Q8×Dic5C23116yes—
152#4090C23116yes—
153#4084C2318yes—
154#4084C23116yes—
155#4082C2318yes—
156#4076C23116yes—
157#4075C23132yes—
158C4×C22⋊D5C23116yes—
159C2×#685C2312yes—
160C2×#685C2312yes—
161C2×#685C2312yes—
162C2×#685C2312yes—
163C2×#685C2312yes—
164C2×#685C2312yes—
165C2×#685C2314yes—
166C2×#685C2314yes—
167#4072C23116yes—
168#4072C23116yes—
169C2×C4⋊Dic5C2312yes—
170C2×C4⋊Dic5C2311yescharacteristic
171C2×C4⋊Dic5C2314yes—
172C2×C4⋊Dic5C2312yes—
173C2×C4⋊Dic5C2312yes—
174C2×C4⋊Dic5C2311yescharacteristic
175C2×C4⋊Dic5C2314yes—
176C2×C4⋊Dic5C2312yes—
177C2×C4⋊Dic5C2312yes—
178#4070C23132yes—
179#4070C23132yes—
180C2×#683C2312yes—
181C2×#683C2314yes—
182C2×#683C2312yes—
183C2×#683C2312yes—
184C2×#683C2314yes—
185C2×#683C2312yes—
186C2×#683C2314yes—
187C2×#683C2314yes—
188C2×C4×Dic5C2314yes—
189C2×C4×Dic5C2312yes—
190C2×C4×Dic5C2311yescharacteristic
191C2×C4×Dic5C2311yescharacteristic
192C2×C4×Dic5C2311yescharacteristic
193C2×C4×Dic5C2314yes—
194#4044C23116yes—
195#4044C23132yes—
196#4043C23116yes—
197#4043C2318yes—
198#4043C23132yes—
199#4042C23132yes—
200#4041C2318yes—
201#4040C23132yes—
202#4040C23116yes—
203#4039C23116yes—
204#4038C23116yes—
205#4038C23132yes—
206D5×C4⋊C4C23116yes—
207D5×C4⋊C4C23116yes—
208D5×C4⋊C4C23116yes—
209#4036C23116yes—
210#4036C2318yes—
211#4036C23132yes—
212#4036C2318yes—
213#4035C23132yes—
214#4034C23116yes—
215#4034C23116yes—
216#4034C23116yes—
217#4034C23132yes—
218#4034C23132yes—
219#4031C23132yes—
220#4031C23132yes—
221#4029C23132yes—
222#4029C23132yes—
223#4029C23116yes—
224#4025C23116yes—
225#4025C23132yes—
226C4×D20C2318yes—
227C4×D20C23116yes—
228#4018C23116yes—
229C42×D5C2318yes—
230#4015C2318yes—
231#4015C23116yes—
232C4×Dic10C2318yes—
233C4×Dic10C23116yes—
234#3544—532no—
235C2×#563—54no—
236C2×Q82—51no—
237C2×#555—51no—
238C2×#554—51no—
239C2×#554D511yescharacteristic, complemented
240C2×#552—52no—
241C2×#552—52no—
242C2×#547—52no—
243C2×#547—52no—
244C2×#544—52no—
245C2×#544—52no—
246C2×#542—52no—
247C2×#542—52no—
248C2×#536—54no—
249C22×C4⋊Q8—51no—
250C2×#529—51no—
251C2×#529—51no—
252C24×C5C2412yes—
253C23×D5C2412yes—
254C23×D5C2411yescharacteristic
255C2×C5×Q8—24no—
256C2×C5×Q8—44no—
257C2×C5×Q8C2414yes—
258C2×C5×Q8C2418yes—
259C2×C5×D4—24no—
260C2×C5×D4C2414yes—
261C22×C4×C5—28no—
262C22×C4×C5—48no—
263C22×C4×C5C2412yes—
264C22×C4×C5C2411yescharacteristic
265C22×C4×C5C2412yes—
266C22×C4×C5C2412yes—
267C22×C4×C5C2414yes—
268C22×C4×C5C2418yes—
269C22×C4×C5C24116yes—
270C22×C4×C5C2411yescharacteristic
271C22×C4×C5C2411yescharacteristic
272C2×C22⋊D5—28no—
273C2×C22⋊D5—48no—
274C2×C22⋊D5C2418yes—
275C2×C22⋊D5C24116yes—
276C22×Dic5C2411yescharacteristic
277C22×Dic5C2412yes—
278C22×Dic5C2411yescharacteristic
279C22×Dic5C2411yescharacteristic
280C22×Dic5C2412yes—
281C22×Dic5C2414yes—
282C22×Dic5C2412yes—
283Q8×D5—432no—
284#709—464no—
285C2×D20—28no—
286C2×D20—24no—
287C2×D20C2418yes—
288C2×D20C2414yes—
289C2×C4×D5—216no—
290C2×C4×D5—24no—
291C2×C4×D5—24no—
292C2×C4×D5—28no—
293C2×C4×D5—24no—
294C2×C4×D5—48no—
295C2×C4×D5C24116yes—
296C2×C4×D5C2414yes—
297C2×C4×D5C2414yes—
298C2×C4×D5C2414yes—
299C2×C4×D5C2418yes—
300C2×C4×D5C24116yes—
301C2×Dic10—24no—
302C2×Dic10—48no—
303C2×Dic10—48no—
304C2×Dic10—44no—
305C2×Dic10C2414yes—
306C2×Dic10C24116yes—
307C2×Dic10C2418yes—
308C2×Dic10C24116yes—
309C5×C4⋊C4C2414yes—
310C5×C4⋊C4C24116yes—
311C5×C4⋊C4C2418yes—
312C5×C4⋊C4C2414yes—
313C5×C4⋊C4C2418yes—
314C5×C4⋊C4C2418yes—
315C5×C4⋊C4C24116yes—
316C5×C22⋊C4C24116yes—
317C5×C22⋊C4C2418yes—
318C42×C5C2418yes—
319C42×C5C2414yes—
320C22⋊Dic5C2418yes—
321C22⋊Dic5C2418yes—
322C22⋊Dic5C24116yes—
323C22⋊Dic5C2418yes—
324#685C2418yes—
325#685C2418yes—
326#685C2418yes—
327#685C2418yes—
328#685C2418yes—
329#685C2418yes—
330#685C24116yes—
331#685C24116yes—
332C4⋊Dic5C2418yes—
333C4⋊Dic5C2414yes—
334C4⋊Dic5C24116yes—
335C4⋊Dic5C2418yes—
336C4⋊Dic5C2418yes—
337C4⋊Dic5C2414yes—
338C4⋊Dic5C24116yes—
339C4⋊Dic5C2418yes—
340C4⋊Dic5C2418yes—
341#683C2418yes—
342#683C24116yes—
343#683C2418yes—
344#683C2418yes—
345#683C24116yes—
346#683C2418yes—
347#683C24116yes—
348#683C24116yes—
349C4×Dic5C24116yes—
350C4×Dic5C2418yes—
351C4×Dic5C2414yes—
352C4×Dic5C2414yes—
353C4×Dic5C2414yes—
354C4×Dic5C24116yes—
355C22×#41—54no—
356C23×Q8—52no—
357#563—564no—
358Q82—516no—
359#555—516no—
360#554—516no—
361#554C2×D5116yescomplemented
362#552—532no—
363#552—532no—
364#547—532no—
365#547—532no—
366#544—532no—
367#544—532no—
368#542—532no—
369#542—532no—
370#536—564no—
371C2×C4⋊Q8—52no—
372C2×C4⋊Q8—516no—
373C2×C4⋊Q8—52no—
374C2×C4⋊Q8—52no—
375C2×C4⋊Q8—54no—
376C2×C4⋊Q8—54no—
377C2×C4⋊Q8—52no—
378C2×C4⋊Q8—51no—
379C2×C4⋊Q8—52no—
380C2×C4⋊Q8C2×D511yescharacteristic
381#529—516no—
382#529—516no—
383C2×#126—52no—
384C2×#126—54no—
385C2×#126—52no—
386C2×#126—54no—
387C2×#125—54no—
388C2×#125—51no—
389C2×#125—51no—
390C2×#125—52no—
391C2×#125—54no—
392C2×#125C2×D512yes—
393C2×#124—51no—
394C2×#124—51no—
395C2×#124—54no—
396C2×#124—54no—
397C2×#123—54no—
398C2×#123—52no—
399C2×#123—54no—
400C2×#123—52no—
401C2×#123—54no—
402C2×#123—54no—
403C2×C22⋊Q8—51no—
404C2×C22⋊Q8—54no—
405C2×C22⋊Q8—54no—
406C2×C22⋊Q8—54no—
407C2×C22⋊Q8—54no—
408C2×C22⋊Q8—51no—
409C2×C22⋊Q8—54no—
410C2×C22⋊Q8—52no—
411C2×C22⋊Q8C2×D514yes—
412C2×C22⋊Q8C2×D512yes—
413C2×#121—51no—
414C2×#121—52no—
415C2×#121—52no—
416C2×#121—51no—
417C2×C4×Q8—52no—
418C2×C4×Q8—51no—
419C2×C4×Q8—52no—
420C2×C4×Q8C2×D511yescharacteristic
421C2×C4×D4—52no—
422C2×C4×D4—52no—
423C2×C4×D4—52no—
424C2×C4×D4—51no—
425C2×C4×D4C2×D511yescharacteristic
426C2×C4×D4C2×D512yes—
427C2×#117—52no—
428C2×#117—52no—
429C2×#117—54no—
430C2×#117—52no—
431C2×#117—52no—
432C22×C4⋊C4—52no—
433C22×C4⋊C4—52no—
434C22×C4⋊C4—52no—
435C22×C4⋊C4C2×D512yes—
436C22×C42—51no—
437C23×C5—24no—
438C23×C5—24no—
439C23×C5—24no—
440C23×C5C2514yes—
441C23×C5C2511yescharacteristic
442C22×D5—22no—
443C22×D5—22no—
444C22×D5—24no—
445C22×D5—24no—
446C22×D5—24no—
447C22×D5H(5,𝔽2)14yes—
448C22×D5C2514yes—
449C22×D5C2512yes—
450C5×Q8—28no—
451C5×Q8—48no—
452C5×D4—28no—
453C2×C4×C5—22no—
454C2×C4×C5—24no—
455C2×C4×C5—28no—
456C2×C4×C5—24no—
457C2×C4×C5—24no—
458C2×C4×C5—216no—
459C2×C4×C5—416no—
460C2×C4×C52−1+414yes—
461C2×C4×C52−1+414yes—
462C2×C4×C5C2514yes—
463C2×C4×C5C2514yes—
464C2×C4×C5C2512yes—
465C2×C4×C5C2514yes—
466C2×C4×C5C2518yes—
467C2×C4×C5C2512yes—
468C2×C4×C5C2512yes—
469C22⋊D5—216no—
470C22⋊D5—416no—
471C2×Dic5—22no—
472C2×Dic5—28no—
473C2×Dic5—24no—
474C2×Dic5—24no—
475C2×Dic5—22no—
476C2×Dic5—24no—
477C2×Dic5—22no—
478C2×Dic5C2514yes—
479C2×Dic5C2512yes—
480C2×Dic5C2512yes—
481C2×Dic5C2514yes—
482C2×Dic5C2518yes—
483C2×Dic5C2512yes—
484C2×Dic5C2514yes—
485D20—216no—
486D20—28no—
487C4×D5—232no—
488C4×D5—28no—
489C4×D5—28no—
490C4×D5—216no—
491C4×D5—28no—
492C4×D5—416no—
493Dic10—28no—
494Dic10—416no—
495Dic10—416no—
496Dic10—48no—
497C2×#41—532no—
498C2×#41—2016no—
499C22×Q8—516no—
500C22×Q8—51no—
501C22×Q8—54no—
502C22×Q8—54no—
503C22×Q8—52no—
504C22×Q8—208no—
505C22×Q8C22×D511yescharacteristic
506C22×Q8C22×D512yes—
507C22×D4—52no—
508C22×D4—54no—
509C22×D4—51no—
510C22×D4—52no—
511C22×D4C22×D511yescharacteristic
512C23×C4—54no—
513C23×C4—51no—
514C23×C4—51no—
515C23×C4—52no—
516C23×C4—51no—
517C23×C4—54no—
518C23×C4C22×D512yes—
519C23×C4C22×D514yes—
520C4⋊Q8—516no—
521C4⋊Q8—516no—
522C4⋊Q8—516no—
523C4⋊Q8—532no—
524C4⋊Q8—532no—
525C4⋊Q8—516no—
526C4⋊Q8—58no—
527C4⋊Q8—516no—
528C4⋊Q8C22×D518yes—
529#126—516no—
530#126—532no—
531#126—516no—
532#126—532no—
533#125—58no—
534#125—58no—
535#125—516no—
536#125—532no—
537#125—532no—
538#125C22×D5116yes—
539#124—58no—
540#124—58no—
541#124—532no—
542#124—532no—
543#123—532no—
544#123—516no—
545#123—532no—
546#123—516no—
547#123—532no—
548#123—532no—
549C22⋊Q8—58no—
550C22⋊Q8—532no—
551C22⋊Q8—532no—
552C22⋊Q8—532no—
553C22⋊Q8—58no—
554C22⋊Q8—532no—
555C22⋊Q8—516no—
556C22⋊Q8—532no—
557C22⋊Q8C22×D5132yes—
558C22⋊Q8C22×D5116yes—
559#121—58no—
560#121—516no—
561#121—516no—
562#121—58no—
563C4×Q8—516no—
564C4×Q8—58no—
565C4×Q8—516no—
566C4×Q8C22×D518yes—
567C4×D4—516no—
568C4×D4—516no—
569C4×D4—516no—
570C4×D4—58no—
571C4×D4C22×D518yes—
572C4×D4C22×D5116yes—
573#117—516no—
574#117—516no—
575#117—532no—
576#117—516no—
577#117—516no—
578C2×C4⋊C4—51no—
579C2×C4⋊C4—52no—
580C2×C4⋊C4—52no—
581C2×C4⋊C4—54no—
582C2×C4⋊C4—54no—
583C2×C4⋊C4—54no—
584C2×C4⋊C4—51no—
585C2×C4⋊C4—54no—
586C2×C4⋊C4—52no—
587C2×C4⋊C4—52no—
588C2×C4⋊C4—52no—
589C2×C4⋊C4—52no—
590C2×C4⋊C4—52no—
591C2×C4⋊C4—52no—
592C2×C4⋊C4—52no—
593C2×C4⋊C4—54no—
594C2×C4⋊C4—54no—
595C2×C4⋊C4—516no—
596C2×C4⋊C4—516no—
597C2×C4⋊C4—516no—
598C2×C4⋊C4C22×D512yes—
599C2×C4⋊C4C22×D512yes—
600C2×C4⋊C4C22×D511yescharacteristic
601C2×C4⋊C4C22×D514yes—
602C2×C4⋊C4C22×D5116yes—
603C2×C4⋊C4C22×D511yescharacteristic
604C2×C4⋊C4C22×D514yes—
605C2×C4⋊C4C22×D512yes—
606C2×C22⋊C4—52no—
607C2×C22⋊C4—54no—
608C2×C22⋊C4—52no—
609C2×C22⋊C4—52no—
610C2×C22⋊C4—52no—
611C2×C22⋊C4—52no—
612C2×C22⋊C4—52no—
613C2×C22⋊C4—54no—
614C2×C22⋊C4—52no—
615C2×C22⋊C4—54no—
616C2×C22⋊C4—52no—
617C2×C22⋊C4—52no—
618C2×C22⋊C4C22×D514yes—
619C2×C22⋊C4C22×D512yes—
620C2×C42—54no—
621C2×C42—51no—
622C2×C42—51no—
623C2×C42—52no—
624C2×C42—54no—
625C2×C42—51no—
626C2×C42—58no—
627C2×C42C22×D512yes—
628C2×C42C22×D511yescharacteristic
629C22×C5—24no—
630C22×C5—24no—
631C22×C5—24no—
632C22×C5—48no—
633C22×C5C2×H(5,𝔽2)12yes—
634C22×C5C2×2−1+412yes—
635C22×C5C2×2−1+412yes—
636C22×C5C2611yescharacteristic
637C2×D5—22no—
638C2×D5—22no—
639C2×D5—28no—
640C2×D5—24no—
641C2×D5—24no—
642C2×D5—24no—
643C2×D5—48no—
644C2×D5C2×H(5,𝔽2)14yes—
645C4×C5—22no—
646C4×C5—24no—
647C4×C5—28no—
648C4×C5—24no—
649C4×C5—24no—
650C4×C5C2×2−1+414yes—
651C4×C5C2×2−1+414yes—
652Dic5—22no—
653Dic5—28no—
654Dic5—24no—
655Dic5—24no—
656Dic5—22no—
657Dic5—24no—
658Dic5—22no—
659C24—51no—
660C24—52no—
661C24C23×D512yes—
662#41—2064no—
663C2×Q8—24no—
664C2×Q8—44no—
665C2×Q8—54no—
666C2×Q8—516no—
667C2×Q8—516no—
668C2×Q8—58no—
669C2×Q8—104no—
670C2×Q8—208no—
671C2×Q8—204no—
672C2×Q8—208no—
673C2×Q8—2032no—
674C2×Q8C23×D514yes—
675C2×Q8C23×D518yes—
676C2×D4—24no—
677C2×D4—58no—
678C2×D4—516no—
679C2×D4—54no—
680C2×D4—58no—
681C2×D4—108no—
682C2×D4—108no—
683C2×D4—104no—
684C2×D4—208no—
685C2×D4C23×D514yes—
686C22×C4—28no—
687C22×C4—48no—
688C22×C4—52no—
689C22×C4—52no—
690C22×C4—51no—
691C22×C4—51no—
692C22×C4—51no—
693C22×C4—54no—
694C22×C4—52no—
695C22×C4—54no—
696C22×C4—54no—
697C22×C4—54no—
698C22×C4—516no—
699C22×C4—58no—
700C22×C4—516no—
701C22×C4—104no—
702C22×C4—1016no—
703C22×C4—104no—
704C22×C4—108no—
705C22×C4—104no—
706C22×C4—208no—
707C22×C4C23×D518yes—
708C22×C4C23×D512yes—
709C22×C4C23×D512yes—
710C22×C4C23×D511yescharacteristic
711C22×C4C23×D512yes—
712C22×C4C23×D514yes—
713C22×C4C23×D5116yes—
714C22×C4C23×D511yescharacteristic
715C22×C4C23×D511yescharacteristic
716C4⋊C4—54no—
717C4⋊C4—58no—
718C4⋊C4—58no—
719C4⋊C4—516no—
720C4⋊C4—516no—
721C4⋊C4—516no—
722C4⋊C4—54no—
723C4⋊C4—516no—
724C4⋊C4—58no—
725C4⋊C4—58no—
726C4⋊C4—58no—
727C4⋊C4—58no—
728C4⋊C4—58no—
729C4⋊C4—58no—
730C4⋊C4—58no—
731C4⋊C4—516no—
732C4⋊C4—516no—
733C4⋊C4C23×D518yes—
734C4⋊C4C23×D518yes—
735C4⋊C4C23×D514yes—
736C4⋊C4C23×D5116yes—
737C4⋊C4C23×D514yes—
738C4⋊C4C23×D5116yes—
739C4⋊C4C23×D518yes—
740C22⋊C4—58no—
741C22⋊C4—516no—
742C22⋊C4—58no—
743C22⋊C4—58no—
744C22⋊C4—58no—
745C22⋊C4—58no—
746C22⋊C4—58no—
747C22⋊C4—516no—
748C22⋊C4—58no—
749C22⋊C4—516no—
750C22⋊C4—58no—
751C22⋊C4—58no—
752C22⋊C4C23×D5116yes—
753C22⋊C4C23×D518yes—
754C42—54no—
755C42—54no—
756C42—54no—
757C42—516no—
758C42—58no—
759C42—516no—
760C42C23×D514yes—
761C42C23×D518yes—
762C2×C5—44no—
763C2×C5#354414yescomplemented
764C2×C5C22×H(5,𝔽2)11yescharacteristic
765C2×C5C22×2−1+411yescharacteristic
766C2×C5C22×2−1+411yescharacteristic
767D5—24no—
768D5—44no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—54no—
773C23—52no—
774C23—54no—
775C23—102no—
776C23—102no—
777C23—104no—
778C23—104no—
779C23—104no—
780C23C24×D514yes—
781C23C24×D511yescharacteristic
782Q8—28no—
783Q8—48no—
784Q8—108no—
785Q8—2016no—
786Q8—208no—
787Q8—2016no—
788D4—28no—
789D4—1016no—
790D4—1016no—
791D4—108no—
792D4—2016no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—28no—
797C2×C4—22no—
798C2×C4—216no—
799C2×C4—416no—
800C2×C4—54no—
801C2×C4—52no—
802C2×C4—54no—
803C2×C4—52no—
804C2×C4—52no—
805C2×C4—58no—
806C2×C4—54no—
807C2×C4—108no—
808C2×C4—1032no—
809C2×C4—104no—
810C2×C4—102no—
811C2×C4—104no—
812C2×C4—102no—
813C2×C4—108no—
814C2×C4—102no—
815C2×C4—104no—
816C2×C4—108no—
817C2×C4—1016no—
818C2×C4—108no—
819C2×C4—2016no—
820C2×C4#414714yes—
821C2×C4#415014yes—
822C2×C4C24×D514yes—
823C2×C4C24×D514yes—
824C2×C4C24×D512yes—
825C2×C4C24×D514yes—
826C2×C4C24×D518yes—
827C2×C4C24×D512yes—
828C2×C4C24×D512yes—
829C5C2×#354411yescharacteristic, complemented, Sylow
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—54no—
835C22—102no—
836C22—102no—
837C22—108no—
838C22—104no—
839C22—104no—
840C22—104no—
841C22—208no—
842C22C2×#414712yes—
843C22C2×#415012yes—
844C22D5×H(5,𝔽2)12yes—
845C22C25×D511yescharacteristic
846C4—24no—
847C4—24no—
848C4—24no—
849C4—28no—
850C4—22no—
851C4—102no—
852C4—104no—
853C4—104no—
854C4—102no—
855C4—108no—
856C4—102no—
857C4—104no—
858C4C2×#414714yes—
859C4C2×#415014yes—
860C2—44no—
861C2—104no—
862C2—204no—
863C2#1061885414yesdirect product factor
864C2C22×#414711yescharacteristic
865C2C22×#415011yescharacteristic
866C2C2×D5×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#554C2
socleC23×C5C25
hypercenterC2×#554D5
hypocenterC5C2×#3544
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×C5×#554C2semidirect
2. #10618854C2direct (N × H)
3. C2×#66064C2semidirect
4. C2×D5×C4⋊Q8C2semidirect
5. C2×#66028C2semidirect
6. C2×#66023C2semidirect
7. C2×#65973C2semidirect
8. C2×#65962C2semidirect
9. C2×#65980C2semidirect
10. C2×#65977C2semidirect
11. C2×#65914C2semidirect
12. C2×Q8×Dic10C2semidirect
13. C2×#65885C2semidirect
14. C2×#65895C2semidirect
15. C2×#65891C2semidirect
16. C2×#65897C2semidirect
17. C2×#65841C2semidirect
18. C2×#65834C2semidirect
21. C5×#554C22semidirect
45. #66064C22semidirect
46. D5×C4⋊Q8C22semidirect
47. #66028C22semidirect
48. #66023C22semidirect
49. #65980C22semidirect
50. #65977C22semidirect
51. #65973C22semidirect
52. #65962C22semidirect
53. #65914C22semidirect
54. Q8×Dic10C22semidirect
55. #65897C22semidirect
56. #65895C22semidirect
57. #65891C22semidirect
58. #65885C22semidirect
65. #65841C22semidirect
75. #65834C22semidirect
239. C2×#554D5semidirect
361. #554C2×D5semidirect
763. C2×C5#3544semidirect
829. C5C2×#3544semidirect
863. C2#10618854direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5542
#106188542
C2×#660642
C2×D5×C4⋊Q82
C2×#660282
C2×#660232
C2×#659732
C2×#659622
C2×#659802
C2×#659772
C2×#659142
C2×Q8×Dic102
C2×#658852
C2×#658952
C2×#658912
C2×#658972
C2×#658412
C2×#658342
C2×#35445