Finite Group Databasebeta

← C2×#10617871 #13007720

Subgroups — C2×#10617871 #13007720

Order 1280.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#66150C211yesmaximal, characteristic, complemented
3C2×#66146C211yesmaximal, characteristic, complemented
4C2×#66125C211yesmaximal, characteristic
5C22×#4072C211yesmaximal, characteristic, complemented
6C2×#65973C212yesmaximal, complemented
7#10617871C2132yesmaximal, direct product factor
8C2×#65975C212yesmaximal, complemented
9C2×#65969C212yesmaximal, complemented
10C2×#65976C212yesmaximal, complemented
11C2×#65977C212yesmaximal, complemented
12C2×#65959C212yesmaximal, complemented
13C2×#65956C212yesmaximal, complemented
14C2×#65958C212yesmaximal, complemented
15C2×#65838C211yesmaximal, characteristic, complemented
16C2×#65847C214yesmaximal, complemented
17C2×#65834C211yesmaximal, characteristic, complemented
18C2×#65829C214yesmaximal, complemented
19C23×C5×Q8C2211yescharacteristic
20C24×C4×C5C2211yescharacteristic
21C22×#709C2211yescharacteristic
22C2×C5×C22⋊Q8C2212yes—
23C2×C5×C22⋊Q8C2212yes—
24C2×C5×C22⋊Q8C2212yes—
25C2×C5×C22⋊Q8C2212yes—
26C2×C5×C22⋊Q8C22116yescomplemented
27C22×C5×C4⋊C4C2211yescharacteristic
28C22×C5×C4⋊C4C2212yes—
29C22×C5×C22⋊C4C2212yes—
30C2×#4099C2212yes—
31C22×C22⋊Dic5C2212yes—
32#66150C22116yescomplemented
33C2×#4093C2212yescomplemented
34C2×#4092C2212yescomplemented
35C2×#4092C2212yescomplemented
36#66146C22116yescomplemented
37C2×Q8×Dic5C2212yescomplemented
38C2×Q8×Dic5C2212yescomplemented
39C2×Q8×Dic5C2212yescomplemented
40C2×Q8×Dic5C2212yescomplemented
41C2×#4090C2212yescomplemented
42#66125C22116yes—
43C2×#4076C2211yescharacteristic
44C2×#4076C2211yescharacteristic
45C2×#4075C2212yes—
46C2×#4075C2214yes—
47C2×C4×C22⋊D5C2214yes—
48C2×C4×C22⋊D5C2212yes—
49C2×C4×C22⋊D5C2212yes—
50C2×#4072C2211yescharacteristic
51C2×#4072C2211yescharacteristic
52C2×#4072C2212yes—
53C2×#4072C2212yes—
54C2×#4072C2214yes—
55C2×#4072C2211yescharacteristic
56C2×#4072C2211yescharacteristic
57C2×#4072C2211yescharacteristic
58C2×#4072C22116yescomplemented
59C22×C4⋊Dic5C2211yescharacteristic
60C22×C4⋊Dic5C2211yescharacteristic
61C2×#4070C2211yescharacteristic
62C2×#4070C2214yes—
63C2×#4070C2211yescharacteristic
64C22×C4×Dic5C2212yes—
65#65977C22132yescomplemented
66#65976C22132yescomplemented
67#65975C22132yescomplemented
68#65973C22132yescomplemented
69#65969C22132yescomplemented
70#65959C22132yescomplemented
71#65958C22132yescomplemented
72#65956C22132yescomplemented
73#65847C22164yescomplemented
74C2×#4044C2214yescomplemented
75C2×#4044C2214yescomplemented
76C2×#4043C2214yescomplemented
77#65838C22116yescomplemented
78C2×#4039C2212yescomplemented
79C2×#4038C2214yescomplemented
80C2×#4038C2212yescomplemented
81C2×D5×C4⋊C4C2212yescomplemented
82#65834C22116yescomplemented
83C2×#4036C2212yescomplemented
84C2×#4036C2212yescomplemented
85C2×#4036C2214yescomplemented
86C2×#4035C2214yescomplemented
87C2×#4035C2214yescomplemented
88C2×#4034C2212yescomplemented
89C2×#4034C2212yescomplemented
90C2×#4033C2212yescomplemented
91C2×#4033C2214yescomplemented
92#65829C22164yescomplemented
93C2×#4032C2214yes—
94C2×#4031C2214yes—
95C2×#4029C2214yes—
96C2×#4027C2214yes—
97C2×#4025C2214yes—
98C2×#4025C2214yes—
99C2×#4024C2214yes—
100C2×#4023C2214yes—
101C2×#3495—51nomaximal, Sylow
102C25×C5C2311yescharacteristic
103C22×C5×Q8—28no—
104C22×C5×Q8C2312yes—
105C22×C5×Q8C2312yes—
106C22×C5×Q8C2318yes—
107C23×C4×C5—28no—
108C23×C4×C5C2311yescharacteristic
109C23×C4×C5C2311yescharacteristic
110C23×C4×C5C2311yescharacteristic
111C23×C4×C5C2311yescharacteristic
112C23×C4×C5C2312yes—
113C23×C4×C5C2311yescharacteristic
114C23×C4×C5C2318yes—
115C23×C4×C5C2312yes—
116C23×C4×C5C2311yescharacteristic
117C22×C22⋊D5C2312yes—
118C22×C22⋊D5C2312yes—
119C22×C22⋊D5C2312yes—
120C23×Dic5C2312yes—
121C23×Dic5C2312yes—
122C2×#709—28no—
123C2×#709C2318yes—
124C22×D20C2311yescharacteristic
125C22×C4×D5C2312yes—
126C22×C4×D5C2314yes—
127C22×Dic10C2311yescharacteristic
128C22×Dic10C2314yes—
129C5×C22⋊Q8C23116yes—
130C5×C22⋊Q8C23116yes—
131C5×C22⋊Q8C23116yes—
132C5×C22⋊Q8C23116yes—
133C2×C5×C4⋊C4C2312yes—
134C2×C5×C4⋊C4C2314yes—
135C2×C5×C4⋊C4C2312yes—
136C2×C5×C4⋊C4C2314yes—
137C2×C5×C4⋊C4C2318yes—
138C2×C5×C4⋊C4C23116yes—
139C2×C5×C22⋊C4C2314yes—
140C2×C5×C22⋊C4C2314yes—
141C2×C5×C22⋊C4C23116yes—
142#4099C23116yes—
143C2×C22⋊Dic5C2312yes—
144C2×C22⋊Dic5C2312yes—
145C2×C22⋊Dic5C2312yes—
146C2×C22⋊Dic5C2312yes—
147C2×C22⋊Dic5C23116yes—
148C2×C22⋊Dic5C2312yes—
149C2×C22⋊Dic5C2312yes—
150C2×C22⋊Dic5C2312yes—
151#4093C23116yescomplemented
152#4092C23116yescomplemented
153#4092C23116yescomplemented
154Q8×Dic5C23116yescomplemented
155Q8×Dic5C23116yescomplemented
156Q8×Dic5C23116yescomplemented
157Q8×Dic5C23116yescomplemented
158#4090C23116yescomplemented
159#4076C2318yes—
160#4076C2318yes—
161#4075C23132yes—
162#4075C23116yes—
163C4×C22⋊D5C23132yes—
164C4×C22⋊D5C23116yes—
165C4×C22⋊D5C23116yes—
166C2×#685C2314yes—
167C2×#685C2314yes—
168C2×#685C2314yes—
169C2×#685C2312yes—
170C2×#685C2312yes—
171#4072C23132yes—
172#4072C2318yes—
173#4072C2318yes—
174#4072C2318yes—
175#4072C23116yes—
176#4072C23116yes—
177#4072C2318yes—
178#4072C2318yes—
179C2×C4⋊Dic5C2314yes—
180C2×C4⋊Dic5C2314yes—
181C2×C4⋊Dic5C2314yes—
182C2×C4⋊Dic5C2311yescharacteristic
183C2×C4⋊Dic5C2311yescharacteristic
184C2×C4⋊Dic5C2312yes—
185C2×C4⋊Dic5C2312yes—
186C2×C4⋊Dic5C2311yescharacteristic
187C2×C4⋊Dic5C2311yescharacteristic
188C2×C4⋊Dic5C2311yescharacteristic
189C2×C4⋊Dic5C2311yescharacteristic
190C2×C4⋊Dic5C2318yes—
191C2×C4⋊Dic5C2318yes—
192#4070C23132yes—
193#4070C2318yes—
194#4070C2318yes—
195C2×#683C2314yes—
196C2×#683C2314yes—
197C2×#683C2314yes—
198C2×#683C2314yes—
199C2×#683C2314yes—
200C2×#683C2312yes—
201C2×#683C2312yes—
202C2×C4×Dic5C2314yes—
203C2×C4×Dic5C2314yes—
204C2×C4×Dic5C2314yes—
205C2×C4×Dic5C2312yes—
206C2×C4×Dic5C2312yes—
207C2×C4×Dic5C2312yes—
208C2×C4×Dic5C2312yes—
209C2×C4×Dic5C2312yes—
210C2×C4×Dic5C23116yes—
211#4044C23132yescomplemented
212#4044C23132yescomplemented
213#4043C23132yescomplemented
214#4039C23116yescomplemented
215#4038C23116yescomplemented
216#4038C23132yescomplemented
217D5×C4⋊C4C23116yescomplemented
218#4036C23116yescomplemented
219#4036C23116yescomplemented
220#4036C23132yescomplemented
221#4035C23132yescomplemented
222#4035C23132yescomplemented
223#4034C23116yescomplemented
224#4034C23116yescomplemented
225#4033C23116yescomplemented
226#4033C23132yescomplemented
227#4032C23132yes—
228#4031C23132yes—
229#4029C23132yes—
230#4027C23132yes—
231#4025C23132yes—
232#4025C23132yes—
233#4024C23132yes—
234#4023C23132yes—
235#3495—532no—
236C2×#556—52no—
237C2×#554—52no—
238C2×#552—52no—
239C2×#552—52no—
240C2×#552—54no—
241C2×#551—54no—
242C2×#544—51no—
243C2×#542—52no—
244C2×#541—52no—
245C2×#536—51no—
246C2×#533—52no—
247C2×#529—52no—
248C2×#525—51no—
249C22×C22⋊Q8D511yescharacteristic, complemented
250C2×#520—51no—
251C2×#519—51no—
252C22×#117—51no—
253C24×C5—24no—
254C24×C5—24no—
255C24×C5—42no—
256C24×C5C2411yescharacteristic
257C24×C5C2414yes—
258C24×C5C2411yescharacteristic
259C24×C5C2411yescharacteristic
260C23×D5C2412yes—
261C2×C5×Q8—28no—
262C2×C5×Q8—28no—
263C2×C5×Q8—232no—
264C2×C5×Q8C2418yes—
265C2×C5×Q8C2418yes—
266C22×C4×C5—24no—
267C22×C4×C5—28no—
268C22×C4×C5—24no—
269C22×C4×C5—24no—
270C22×C4×C5—24no—
271C22×C4×C5—24no—
272C22×C4×C5—232no—
273C22×C4×C5—44no—
274C22×C4×C5#4118yes—
275C22×C4×C5C2414yes—
276C22×C4×C5C2414yes—
277C22×C4×C5C2418yes—
278C22×C4×C5C2411yescharacteristic
279C22×C4×C5C2411yescharacteristic
280C22×C4×C5C2414yes—
281C22×C4×C5C2414yes—
282C22×C4×C5C2414yes—
283C22×C4×C5C2414yes—
284C22×C4×C5C2414yes—
285C22×C4×C5C2418yes—
286C22×C4×C5C2411yescharacteristic
287C22×C4×C5C2411yescharacteristic
288C22×C4×C5C2414yes—
289C2×C22⋊D5—28no—
290C2×C22⋊D5—28no—
291C2×C22⋊D5—44no—
292C2×C22⋊D5C2418yes—
293C2×C22⋊D5C2418yes—
294C2×C22⋊D5C2418yes—
295C22×Dic5—28no—
296C22×Dic5—44no—
297C22×Dic5C2412yes—
298C22×Dic5C2412yes—
299C22×Dic5C2412yes—
300C22×Dic5C2412yes—
301C22×Dic5C2418yes—
302C22×Dic5C2412yes—
303C22×Dic5C2412yes—
304C22×Dic5C2412yes—
305C22×Dic5C2418yes—
306#709—232no—
307C2×D20—24no—
308C2×D20C2414yes—
309C2×C4×D5—28no—
310C2×C4×D5—48no—
311C2×C4×D5C2418yes—
312C2×C4×D5C24116yes—
313C2×Dic10—24no—
314C2×Dic10—48no—
315C2×Dic10C2414yes—
316C2×Dic10C24116yes—
317C5×C4⋊C4C2418yes—
318C5×C4⋊C4C24116yes—
319C5×C4⋊C4C2418yes—
320C5×C4⋊C4C24116yes—
321C5×C22⋊C4C24116yes—
322C5×C22⋊C4C24116yes—
323C22⋊Dic5C2418yes—
324C22⋊Dic5C2418yes—
325C22⋊Dic5C2418yes—
326C22⋊Dic5C2418yes—
327C22⋊Dic5C2418yes—
328C22⋊Dic5C2418yes—
329C22⋊Dic5C2418yes—
330#685C24116yes—
331#685C24116yes—
332#685C24116yes—
333#685C2418yes—
334#685C2418yes—
335C4⋊Dic5C24116yes—
336C4⋊Dic5C24116yes—
337C4⋊Dic5C24116yes—
338C4⋊Dic5C2414yes—
339C4⋊Dic5C2414yes—
340C4⋊Dic5C2418yes—
341C4⋊Dic5C2418yes—
342C4⋊Dic5C2414yes—
343C4⋊Dic5C2414yes—
344C4⋊Dic5C2414yes—
345C4⋊Dic5C2414yes—
346#683C24116yes—
347#683C24116yes—
348#683C24116yes—
349#683C24116yes—
350#683C24116yes—
351#683C2418yes—
352#683C2418yes—
353C4×Dic5C24116yes—
354C4×Dic5C24116yes—
355C4×Dic5C24116yes—
356C4×Dic5C2418yes—
357C4×Dic5C2418yes—
358C4×Dic5C2418yes—
359C4×Dic5C2418yes—
360C4×Dic5C2418yes—
361C22×#41—51no—
362C23×Q8C2×D511yescharacteristic
363C24×C4C2×D511yescharacteristic
364#556—532no—
365#554—532no—
366#552—532no—
367#552—532no—
368#552—564no—
369#551—564no—
370#544—516no—
371#542—532no—
372#541—532no—
373#536—516no—
374#533—532no—
375C2×C4⋊Q8—52no—
376C2×C4⋊Q8—52no—
377C2×C4⋊Q8—52no—
378#529—532no—
379C2×#126—54no—
380C2×#126—54no—
381C2×#126—54no—
382C2×#126—54no—
383C2×#125—54no—
384C2×#125—54no—
385C2×#125—52no—
386C2×#125—54no—
387C2×#125—52no—
388C2×#124—52no—
389C2×#124—54no—
390#525—516no—
391C2×#123—52no—
392C2×#123—54no—
393C2×#123—54no—
394C2×#123—54no—
395C2×C22⋊Q8—52no—
396C2×C22⋊Q8—52no—
397C2×C22⋊Q8—51no—
398C2×C22⋊Q8—51no—
399C2×C22⋊Q8—54no—
400C2×C22⋊Q8—54no—
401C2×C22⋊Q8—54no—
402C2×C22⋊Q8C2×D512yes—
403C2×C22⋊Q8C2×D512yes—
404C2×C22⋊Q8C2×D512yes—
405C2×C22⋊Q8C2×D512yes—
406C2×C22⋊Q8C2×D5116yescomplemented
407C2×#121—51no—
408C2×#121—51no—
409C2×#120—52no—
410#520—516no—
411#519—516no—
412C2×C4×Q8—52no—
413C2×C4×Q8—52no—
414C2×C4×Q8—52no—
415C2×C4×Q8—52no—
416C2×C4×Q8—52no—
417C2×C4×Q8—54no—
418C2×C4×D4—54no—
419C2×C4×D4—52no—
420C2×C4×D4—52no—
421C2×C4×D4—52no—
422C2×C4×D4—54no—
423C2×#117—51no—
424C2×#117—51no—
425C2×#117—52no—
426C2×#117—51no—
427C2×#117—52no—
428C2×#117—51no—
429C2×#117—51no—
430C2×#117—54no—
431C2×#117—516no—
432C2×#117—52no—
433C2×#117—54no—
434C2×#117—54no—
435C22×C4⋊C4—51no—
436C22×C4⋊C4—51no—
437C22×C4⋊C4—52no—
438C22×C4⋊C4C2×D511yescharacteristic
439C22×C4⋊C4C2×D512yes—
440C22×C22⋊C4—52no—
441C22×C22⋊C4C2×D512yes—
442C22×C42—52no—
443C23×C5—22no—
444C23×C5—22no—
445C23×C5—22no—
446C23×C5—22no—
447C23×C5—28no—
448C23×C5—22no—
449C23×C5—28no—
450C23×C5—22no—
451C23×C5—22no—
452C23×C5—44no—
453C23×C5—416no—
454C23×C5C2×#4114yes—
455C23×C52−1+414yes—
456C23×C5C2512yes—
457C23×C5C2512yes—
458C23×C5C2512yes—
459C23×C5C2511yescharacteristic
460C22×D5—24no—
461C22×D5—24no—
462C22×D5—24no—
463C22×D5C2514yes—
464C5×Q8—216no—
465C5×Q8—216no—
466C2×C4×C5—28no—
467C2×C4×C5—22no—
468C2×C4×C5—22no—
469C2×C4×C5—216no—
470C2×C4×C5—28no—
471C2×C4×C5—28no—
472C2×C4×C5—28no—
473C2×C4×C5—28no—
474C2×C4×C5—28no—
475C2×C4×C5—28no—
476C2×C4×C5—48no—
477C2×C4×C5C2×#4114yes—
478C2×C4×C5C2×#4114yes—
479C2×C4×C5C2×#41116yes—
480C2×C4×C5C2512yes—
481C2×C4×C5C2518yes—
482C2×C4×C5C2518yes—
483C2×C4×C5C2512yes—
484C2×C4×C5C2512yes—
485C2×C4×C5C2512yes—
486C22⋊D5—216no—
487C22⋊D5—216no—
488C22⋊D5—48no—
489C2×Dic5—24no—
490C2×Dic5—216no—
491C2×Dic5—24no—
492C2×Dic5—24no—
493C2×Dic5—24no—
494C2×Dic5—24no—
495C2×Dic5—24no—
496C2×Dic5—24no—
497C2×Dic5—48no—
498C2×Dic5C2514yes—
499C2×Dic5C2514yes—
500C2×Dic5C2514yes—
501C2×Dic5C2514yes—
502C2×Dic5C2514yes—
503C2×Dic5C2514yes—
504C2×Dic5C2514yes—
505D20—28no—
506C4×D5—216no—
507C4×D5—416no—
508Dic10—28no—
509Dic10—416no—
510C25C22×D511yescharacteristic
511C2×#41—58no—
512C2×#41—108no—
513C22×Q8—28no—
514C22×Q8—51no—
515C22×Q8—54no—
516C22×Q8C22×D512yes—
517C22×Q8C22×D512yes—
518C22×Q8C22×D518yes—
519C22×D4—52no—
520C22×D4—52no—
521C22×D4—52no—
522C22×D4—51no—
523C23×C4—28no—
524C23×C4—52no—
525C23×C4—52no—
526C23×C4—52no—
527C23×C4—54no—
528C23×C4C22×D512yes—
529C23×C4C22×D511yescharacteristic
530C23×C4C22×D511yescharacteristic
531C23×C4C22×D511yescharacteristic
532C23×C4C22×D511yescharacteristic
533C23×C4C22×D518yes—
534C23×C4C22×D511yescharacteristic
535C23×C4C22×D512yes—
536C23×C4C22×D511yescharacteristic
537C4⋊Q8—516no—
538C4⋊Q8—516no—
539C4⋊Q8—516no—
540#126—532no—
541#126—532no—
542#126—532no—
543#126—532no—
544#125—516no—
545#125—532no—
546#125—532no—
547#125—532no—
548#125—516no—
549#124—516no—
550#124—532no—
551#123—516no—
552#123—532no—
553#123—532no—
554#123—532no—
555C22⋊Q8—516no—
556C22⋊Q8—516no—
557C22⋊Q8—58no—
558C22⋊Q8—58no—
559C22⋊Q8—532no—
560C22⋊Q8—532no—
561C22⋊Q8—532no—
562C22⋊Q8C22×D5116yes—
563C22⋊Q8C22×D5116yes—
564C22⋊Q8C22×D5116yes—
565C22⋊Q8C22×D5116yes—
566#121—58no—
567#121—58no—
568#120—516no—
569C4×Q8—516no—
570C4×Q8—516no—
571C4×Q8—516no—
572C4×Q8—516no—
573C4×Q8—516no—
574C4×Q8—532no—
575C4×D4—532no—
576C4×D4—516no—
577C4×D4—516no—
578C4×D4—516no—
579C4×D4—532no—
580#117—58no—
581#117—58no—
582#117—516no—
583#117—58no—
584#117—516no—
585#117—58no—
586#117—58no—
587#117—532no—
588#117—516no—
589#117—532no—
590#117—532no—
591C2×C4⋊C4—51no—
592C2×C4⋊C4—51no—
593C2×C4⋊C4—52no—
594C2×C4⋊C4—51no—
595C2×C4⋊C4—51no—
596C2×C4⋊C4—52no—
597C2×C4⋊C4—58no—
598C2×C4⋊C4—58no—
599C2×C4⋊C4—54no—
600C2×C4⋊C4—51no—
601C2×C4⋊C4—51no—
602C2×C4⋊C4—54no—
603C2×C4⋊C4—54no—
604C2×C4⋊C4—54no—
605C2×C4⋊C4—54no—
606C2×C4⋊C4—54no—
607C2×C4⋊C4—52no—
608C2×C4⋊C4—52no—
609C2×C4⋊C4—54no—
610C2×C4⋊C4—54no—
611C2×C4⋊C4—516no—
612C2×C4⋊C4C22×D512yes—
613C2×C4⋊C4C22×D514yes—
614C2×C4⋊C4C22×D512yes—
615C2×C4⋊C4C22×D518yes—
616C2×C4⋊C4C22×D514yes—
617C2×C4⋊C4C22×D5116yes—
618C2×C22⋊C4—52no—
619C2×C22⋊C4—52no—
620C2×C22⋊C4—52no—
621C2×C22⋊C4—52no—
622C2×C22⋊C4—516no—
623C2×C22⋊C4—52no—
624C2×C22⋊C4—52no—
625C2×C22⋊C4—52no—
626C2×C22⋊C4—52no—
627C2×C22⋊C4—54no—
628C2×C22⋊C4—54no—
629C2×C22⋊C4—52no—
630C2×C22⋊C4—54no—
631C2×C22⋊C4C22×D514yes—
632C2×C22⋊C4C22×D514yes—
633C2×C22⋊C4C22×D5116yes—
634C2×C42—52no—
635C2×C42—52no—
636C2×C42—54no—
637C2×C42—54no—
638C2×C42—54no—
639C2×C42—52no—
640C2×C42—52no—
641C2×C42—516no—
642C2×C42—52no—
643C22×C5—22no—
644C22×C5—22no—
645C22×C5—22no—
646C22×C5—22no—
647C22×C5—28no—
648C22×C5—28no—
649C22×C5—22no—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—416no—
653C22×C5—44no—
654C22×C5C22×#4114yes—
655C22×C5C22×#4112yes—
656C22×C5C2×2−1+414yes—
657C22×C5C2×2−1+412yes—
658C22×C5#58512yes—
659C22×C5C2611yescharacteristic
660C2×D5—24no—
661C2×D5—24no—
662C2×D5—24no—
663C2×D5—48no—
664C4×C5—22no—
665C4×C5—22no—
666C4×C5—28no—
667C4×C5—28no—
668C4×C5C22×#4114yes—
669C4×C5C22×#4114yes—
670Dic5—24no—
671Dic5—24no—
672Dic5—24no—
673Dic5—24no—
674Dic5—24no—
675Dic5—24no—
676Dic5—24no—
677C24—24no—
678C24—24no—
679C24—42no—
680C24—52no—
681C24C23×D511yescharacteristic
682C24C23×D514yes—
683C24C23×D511yescharacteristic
684C24C23×D511yescharacteristic
685#41—1032no—
686C2×Q8—28no—
687C2×Q8—28no—
688C2×Q8—232no—
689C2×Q8—54no—
690C2×Q8—516no—
691C2×Q8—104no—
692C2×Q8—208no—
693C2×Q8C23×D518yes—
694C2×Q8C23×D518yes—
695C2×D4—58no—
696C2×D4—58no—
697C2×D4—58no—
698C2×D4—54no—
699C2×D4—108no—
700C2×D4—108no—
701C2×D4—104no—
702C2×D4—204no—
703C22×C4—24no—
704C22×C4—28no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—232no—
710C22×C4—44no—
711C22×C4—58no—
712C22×C4—52no—
713C22×C4—52no—
714C22×C4—52no—
715C22×C4—52no—
716C22×C4—52no—
717C22×C4—52no—
718C22×C4—52no—
719C22×C4—58no—
720C22×C4—58no—
721C22×C4—516no—
722C22×C4—108no—
723C22×C4—108no—
724C22×C4—208no—
725C22×C4—204no—
726C22×C4#71118yes—
727C22×C4C23×D514yes—
728C22×C4C23×D518yes—
729C22×C4C23×D514yes—
730C22×C4C23×D514yes—
731C22×C4C23×D514yes—
732C22×C4C23×D514yes—
733C22×C4C23×D511yescharacteristic
734C22×C4C23×D514yes—
735C22×C4C23×D514yes—
736C22×C4C23×D511yescharacteristic
737C22×C4C23×D518yes—
738C22×C4C23×D514yes—
739C22×C4C23×D511yescharacteristic
740C22×C4C23×D511yescharacteristic
741C4⋊C4—54no—
742C4⋊C4—54no—
743C4⋊C4—58no—
744C4⋊C4—54no—
745C4⋊C4—54no—
746C4⋊C4—58no—
747C4⋊C4—516no—
748C4⋊C4—54no—
749C4⋊C4—54no—
750C4⋊C4—516no—
751C4⋊C4—516no—
752C4⋊C4—516no—
753C4⋊C4—516no—
754C4⋊C4—516no—
755C4⋊C4—58no—
756C4⋊C4—58no—
757C4⋊C4—516no—
758C4⋊C4—516no—
759C4⋊C4C23×D518yes—
760C4⋊C4C23×D5116yes—
761C4⋊C4C23×D518yes—
762C4⋊C4C23×D5116yes—
763C22⋊C4—58no—
764C22⋊C4—58no—
765C22⋊C4—58no—
766C22⋊C4—58no—
767C22⋊C4—58no—
768C22⋊C4—58no—
769C22⋊C4—58no—
770C22⋊C4—58no—
771C22⋊C4—516no—
772C22⋊C4—516no—
773C22⋊C4—58no—
774C22⋊C4—516no—
775C22⋊C4C23×D5116yes—
776C22⋊C4C23×D5116yes—
777C42—58no—
778C42—58no—
779C42—58no—
780C42—58no—
781C42—516no—
782C42—516no—
783C42—516no—
784C42—58no—
785C2×C5—24no—
786C2×C5—24no—
787C2×C5—42no—
788C2×C5#349514yescomplemented
789C2×C5C23×#4111yescharacteristic
790C2×C5C22×2−1+411yescharacteristic
791C2×C5C2×#58511yescharacteristic
792D5—44no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—28no—
798C23—22no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—44no—
803C23—416no—
804C23—54no—
805C23—104no—
806C23—104no—
807C23—104no—
808C23C2×#71114yes—
809C23#414714yes—
810C23C24×D512yes—
811C23C24×D512yes—
812C23C24×D512yes—
813C23C24×D511yescharacteristic
814Q8—216no—
815Q8—216no—
816Q8—108no—
817Q8—2016no—
818D4—1016no—
819D4—1016no—
820D4—108no—
821D4—208no—
822C2×C4—28no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—216no—
826C2×C4—28no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—48no—
833C2×C4—54no—
834C2×C4—54no—
835C2×C4—54no—
836C2×C4—54no—
837C2×C4—54no—
838C2×C4—54no—
839C2×C4—54no—
840C2×C4—104no—
841C2×C4—1016no—
842C2×C4—104no—
843C2×C4—104no—
844C2×C4—104no—
845C2×C4—104no—
846C2×C4—104no—
847C2×C4—104no—
848C2×C4—1016no—
849C2×C4—2016no—
850C2×C4—208no—
851C2×C4C2×#71114yes—
852C2×C4C2×#71114yes—
853C2×C4C2×#711116yes—
854C2×C4C24×D512yes—
855C2×C4C24×D518yes—
856C2×C4C24×D518yes—
857C2×C4C24×D512yes—
858C2×C4C24×D512yes—
859C2×C4C24×D512yes—
860C5C2×#349511yescharacteristic, complemented, Sylow
861C22—28no—
862C22—28no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—416no—
871C22—44no—
872C22—104no—
873C22—104no—
874C22—104no—
875C22—208no—
876C22C22×#71114yes—
877C22C22×#71112yes—
878C22C2×#414714yes—
879C22C2×#414712yes—
880C22#6628312yes—
881C22C25×D511yescharacteristic
882C4—22no—
883C4—22no—
884C4—28no—
885C4—28no—
886C4—104no—
887C4—104no—
888C4—104no—
889C4—104no—
890C4—104no—
891C4—104no—
892C4—104no—
893C4C22×#71114yes—
894C4C22×#71114yes—
895C2—24no—
896C2—24no—
897C2—42no—
898C2—204no—
899C2#1061787114yesdirect product factor
900C2C23×#71111yescharacteristic
901C2C22×#414711yescharacteristic
902C2C2×#6628311yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC22×C5×C22⋊Q8C2
socleC23×C5C25
prime radicalC2×#66125C2
hypercenterC22×C22⋊Q8D5
hypocenterC5C2×#3495
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C5×C22⋊Q8C2semidirect
2. C2×#66150C2semidirect
3. C2×#66146C2semidirect
5. C22×#4072C2semidirect
6. C2×#65973C2semidirect
7. #10617871C2direct (N × H)
8. C2×#65975C2semidirect
9. C2×#65969C2semidirect
10. C2×#65976C2semidirect
11. C2×#65977C2semidirect
12. C2×#65959C2semidirect
13. C2×#65956C2semidirect
14. C2×#65958C2semidirect
15. C2×#65838C2semidirect
16. C2×#65847C2semidirect
17. C2×#65834C2semidirect
18. C2×#65829C2semidirect
26. C2×C5×C22⋊Q8C22semidirect
32. #66150C22semidirect
33. C2×#4093C22semidirect
34. C2×#4092C22semidirect
35. C2×#4092C22semidirect
36. #66146C22semidirect
37. C2×Q8×Dic5C22semidirect
38. C2×Q8×Dic5C22semidirect
39. C2×Q8×Dic5C22semidirect
40. C2×Q8×Dic5C22semidirect
41. C2×#4090C22semidirect
58. C2×#4072C22semidirect
65. #65977C22semidirect
66. #65976C22semidirect
67. #65975C22semidirect
68. #65973C22semidirect
69. #65969C22semidirect
70. #65959C22semidirect
71. #65958C22semidirect
72. #65956C22semidirect
73. #65847C22semidirect
74. C2×#4044C22semidirect
75. C2×#4044C22semidirect
76. C2×#4043C22semidirect
77. #65838C22semidirect
78. C2×#4039C22semidirect
79. C2×#4038C22semidirect
80. C2×#4038C22semidirect
81. C2×D5×C4⋊C4C22semidirect
82. #65834C22semidirect
83. C2×#4036C22semidirect
84. C2×#4036C22semidirect
85. C2×#4036C22semidirect
86. C2×#4035C22semidirect
87. C2×#4035C22semidirect
88. C2×#4034C22semidirect
89. C2×#4034C22semidirect
90. C2×#4033C22semidirect
91. C2×#4033C22semidirect
92. #65829C22semidirect
151. #4093C23semidirect
152. #4092C23semidirect
153. #4092C23semidirect
154. Q8×Dic5C23semidirect
155. Q8×Dic5C23semidirect
156. Q8×Dic5C23semidirect
157. Q8×Dic5C23semidirect
158. #4090C23semidirect
211. #4044C23semidirect
212. #4044C23semidirect
213. #4043C23semidirect
214. #4039C23semidirect
215. #4038C23semidirect
216. #4038C23semidirect
217. D5×C4⋊C4C23semidirect
218. #4036C23semidirect
219. #4036C23semidirect
220. #4036C23semidirect
221. #4035C23semidirect
222. #4035C23semidirect
223. #4034C23semidirect
224. #4034C23semidirect
225. #4033C23semidirect
226. #4033C23semidirect
249. C22×C22⋊Q8D5semidirect
406. C2×C22⋊Q8C2×D5semidirect
788. C2×C5#3495semidirect
860. C5C2×#3495semidirect
899. C2#10617871direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C22⋊Q82
C2×#661502
C2×#661462
C2×#661252
C22×#40722
C2×#659732
#106178712
C2×#659752
C2×#659692
C2×#659762
C2×#659772
C2×#659592
C2×#659562
C2×#659582
C2×#658382
C2×#658472
C2×#658342
C2×#658292
C2×#34955