Finite Group Databasebeta

← C2×#10617732 #13007414

Subgroups — C2×#10617732 #13007414

Order 1280.

7142 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×C4×C5×#41C211yesmaximal, characteristic, complemented
2C2×#66158C212yesmaximal, complemented
3#10617732C2132yesmaximal, direct product factor
4C2×#65913C211yesmaximal, characteristic, complemented
5C2×#65917C212yesmaximal, complemented
6C2×#65901C211yesmaximal, characteristic, complemented
7C2×#65877C211yesmaximal, characteristic, complemented
8C2×#65899C212yesmaximal, complemented
9C2×#65875C212yesmaximal, complemented
10C2×#65889C211yesmaximal, characteristic, complemented
11C2×#65898C214yesmaximal, complemented
12C2×#65880C212yesmaximal, complemented
13C2×#65863C212yesmaximal, complemented
14C2×#65865C214yesmaximal, complemented
15C2×#65813C212yesmaximal, complemented
16C2×#65813C211yesmaximal, characteristic, complemented
17C2×#65804C211yesmaximal, characteristic, complemented
18C22×#4016C212yesmaximal, complemented
19C22×C5×#41C2211yescharacteristic
20C22×#711C2212yes—
21C4×C5×#41C22116yescomplemented
22C2×C4×C5×Q8C2211yescharacteristic
23C2×C4×C5×Q8C2211yescharacteristic
24C2×C4×C5×D4C2211yescharacteristic
25C2×C4×C5×D4C2212yes—
26C2×C4×C5×D4C2211yescharacteristic
27C2×C4×C5×D4C2212yes—
28C2×C5×#117C2212yes—
29C2×C5×#117C2211yescharacteristic
30C22×C42×C5C2212yes—
31C22×C42×C5C2211yescharacteristic
32#66158C22132yescomplemented
33C2×#4092C2212yes—
34C2×#4090C2212yes—
35C2×#4085C2214yes—
36C2×#4081C2214yes—
37C2×D4×Dic5C2212yes—
38C2×#4076C2212yes—
39C2×#4076C2211yescharacteristic
40C2×#4075C2214yes—
41C2×#4075C2212yes—
42C2×C4×C22⋊D5C2212yes—
43C2×C4×C22⋊D5C2214yes—
44C2×#4072C2212yes—
45C22×C4⋊Dic5C2212yes—
46C22×C4⋊Dic5C2212yes—
47C2×#4070C2212yes—
48C2×#4070C2212yes—
49C2×#4070C2211yescharacteristic
50C2×#4070C2212yes—
51C22×#683C2214yes—
52C22×#683C2214yes—
53#65917C22132yescomplemented
54#65913C22116yescomplemented
55#65901C22116yescomplemented
56#65899C22132yescomplemented
57#65898C22164yescomplemented
58#65889C22116yescomplemented
59#65880C22132yescomplemented
60#65877C22116yescomplemented
61#65875C22132yescomplemented
62#65865C22164yescomplemented
63#65863C22132yescomplemented
64C2×#4044C2214yes—
65C2×#4043C2212yes—
66C2×#4042C2214yes—
67C2×D5×C4⋊C4C2212yes—
68C2×#4036C2212yes—
69C2×#4035C2214yes—
70C2×#4035C2214yes—
71C2×#4033C2212yes—
72C2×#4032C2214yes—
73C2×#4029C2214yes—
74C2×#4027C2214yes—
75C2×#4025C2214yes—
76C2×#4024C2214yes—
77C2×#4023C2214yes—
78#65813C22132yescomplemented
79#65813C22116yescomplemented
80C2×#4022C2212yes—
81C2×#4022C2214yes—
82C2×#4021C2211yescharacteristic
83C2×C4×D20C2211yescharacteristic
84C2×C4×D20C2212yes—
85C2×#4018C2214yes—
86C2×#4018C2212yes—
87#65804C22116yescomplemented
88C2×#4016C2214yes—
89C2×#4016C2214yes—
90C2×#4016C2212yes—
91C2×#4016C2212yes—
92C2×#4016C2211yescharacteristic
93C2×#4016C2212yes—
94C2×#4016C22132yescomplemented
95C2×#4015C2211yescharacteristic
96C2×#4015C2211yescharacteristic
97C2×C4×Dic10C2212yes—
98C2×C4×Dic10C2212yes—
99C2×C4×Dic10C2212yes—
100C2×C4×Dic10C2211yescharacteristic
101C2×#3515—51nomaximal, Sylow
102C2×C5×#41—28no—
103C2×C5×#41C2318yes—
104C22×C5×Q8C2311yescharacteristic
105C22×C5×D4C2312yes—
106C22×C5×D4C2311yescharacteristic
107C23×C4×C5C2312yes—
108C23×C4×C5C2311yescharacteristic
109C23×C4×C5C2312yes—
110C23×C4×C5C2311yescharacteristic
111C23×C4×C5C2312yes—
112C23×C4×C5C2311yescharacteristic
113C22×C22⋊D5C2314yes—
114C22×C22⋊D5C2312yes—
115C23×Dic5C2314yes—
116C23×Dic5C2314yes—
117C2×#711—216no—
118C2×#711C23116yes—
119C22×D20C2311yescharacteristic
120C22×C4×D5C2312yes—
121C22×C4×D5C2314yes—
122C22×Dic10C2311yescharacteristic
123C22×Dic10C2312yes—
124C22×Dic10C2312yes—
125C4×C5×Q8C2318yes—
126C4×C5×Q8C2318yes—
127C4×C5×D4C23116yes—
128C4×C5×D4C2318yes—
129C4×C5×D4C2318yes—
130C4×C5×D4C23116yes—
131C5×#117C2318yes—
132C5×#117C23116yes—
133C2×C5×C4⋊C4C2311yescharacteristic
134C2×C5×C4⋊C4C2312yes—
135C2×C5×C4⋊C4C2312yes—
136C2×C5×C4⋊C4C2311yescharacteristic
137C2×C5×C22⋊C4C2312yes—
138C2×C5×C22⋊C4C2312yes—
139C2×C5×C22⋊C4C2312yes—
140C2×C42×C5C2311yescharacteristic
141C2×C42×C5C2311yescharacteristic
142C2×C42×C5C2311yescharacteristic
143C2×C42×C5C2312yes—
144C2×C42×C5C2311yescharacteristic
145C2×C42×C5C2312yes—
146C2×C42×C5C2312yes—
147C2×C42×C5C23116yes—
148C2×C42×C5C2318yes—
149C2×C22⋊Dic5C2314yes—
150C2×C22⋊Dic5C2312yes—
151C2×C22⋊Dic5C2314yes—
152#4092C23116yes—
153#4090C23116yes—
154#4085C23132yes—
155#4081C23132yes—
156D4×Dic5C23116yes—
157#4076C23116yes—
158#4076C2318yes—
159#4075C23132yes—
160#4075C23116yes—
161C4×C22⋊D5C23116yes—
162C4×C22⋊D5C23132yes—
163C2×#685C2312yes—
164C2×#685C2312yes—
165C2×#685C2312yes—
166C2×#685C2314yes—
167C2×#685C2312yes—
168C2×#685C2314yes—
169#4072C23116yes—
170C2×C4⋊Dic5C2312yes—
171C2×C4⋊Dic5C2312yes—
172C2×C4⋊Dic5C2312yes—
173C2×C4⋊Dic5C2311yescharacteristic
174C2×C4⋊Dic5C2312yes—
175C2×C4⋊Dic5C2311yescharacteristic
176C2×C4⋊Dic5C2314yes—
177C2×C4⋊Dic5C2314yes—
178C2×C4⋊Dic5C23116yes—
179C2×C4⋊Dic5C23116yes—
180#4070C23116yes—
181#4070C23116yes—
182#4070C2318yes—
183#4070C23116yes—
184C2×#683C2314yes—
185C2×#683C2314yes—
186C2×#683C2312yes—
187C2×#683C2314yes—
188C2×#683C2312yes—
189C2×#683C2312yes—
190C2×#683C2314yes—
191C2×#683C2314yes—
192C2×#683C2314yes—
193C2×#683C2314yes—
194C2×#683C23132yes—
195C2×#683C23132yes—
196C2×#683C2312yes—
197C2×#683C2314yes—
198C2×C4×Dic5C2314yes—
199C2×C4×Dic5C2314yes—
200C2×C4×Dic5C2312yes—
201#4044C23132yes—
202#4043C23116yes—
203#4042C23132yes—
204D5×C4⋊C4C23116yes—
205#4036C23116yes—
206#4035C23132yes—
207#4035C23132yes—
208#4033C23116yes—
209#4032C23132yes—
210#4029C23132yes—
211#4027C23132yes—
212#4025C23132yes—
213#4024C23132yes—
214#4023C23132yes—
215#4022C23116yes—
216#4022C23132yes—
217#4021C2318yes—
218C4×D20C2318yes—
219C4×D20C23116yes—
220#4018C23132yes—
221#4018C23116yes—
222#4016C2318yes—
223#4016C23116yes—
224#4016C23132yes—
225#4016C23116yes—
226#4016C23132yes—
227#4016C23116yes—
228#4015C2318yes—
229#4015C2318yes—
230C4×Dic10C23116yes—
231C4×Dic10C23116yes—
232C4×Dic10C23116yes—
233C4×Dic10C2318yes—
234#3515—532no—
235C2×#557—51no—
236C2×#554—51no—
237C2×#554—51no—
238C2×#553—52no—
239C2×#552—52no—
240C2×#552—54no—
241C2×#552—52no—
242C2×#547—52no—
243C2×#547—51no—
244C2×#541—52no—
245C2×#539—54no—
246C2×#533—51no—
247C2×#529—51no—
248C2×#529—52no—
249C22×#125—52no—
250C2×#520—52no—
251C2×C4×#41D511yescharacteristic, complemented
252C24×C5C2411yescharacteristic
253C24×C5C2412yes—
254C23×D5C2412yes—
255C5×#41—232no—
256C2×C5×Q8—24no—
257C2×C5×Q8C2414yes—
258C2×C5×D4—28no—
259C2×C5×D4#4118yes—
260C2×C5×D4C2418yes—
261C2×C5×D4C2414yes—
262C22×C4×C5—28no—
263C22×C4×C5—24no—
264C22×C4×C5—28no—
265C22×C4×C5—24no—
266C22×C4×C5—42no—
267C22×C4×C5—44no—
268C22×C4×C5C2411yescharacteristic
269C22×C4×C5C2411yescharacteristic
270C22×C4×C5C2411yescharacteristic
271C22×C4×C5C2412yes—
272C22×C4×C5C2411yescharacteristic
273C22×C4×C5C2412yes—
274C22×C4×C5C2412yes—
275C22×C4×C5C2418yes—
276C22×C4×C5C2414yes—
277C22×C4×C5C2418yes—
278C22×C4×C5C2414yes—
279C22×C4×C5C2418yes—
280C22×C4×C5C2414yes—
281C22×C4×C5C2411yescharacteristic
282C22×C4×C5C2411yescharacteristic
283C2×C22⋊D5—216no—
284C2×C22⋊D5—44no—
285C2×C22⋊D5C24116yes—
286C2×C22⋊D5C2418yes—
287C22×Dic5—216no—
288C22×Dic5—48no—
289C22×Dic5C2412yes—
290C22×Dic5C2414yes—
291C22×Dic5C2414yes—
292C22×Dic5C2412yes—
293C22×Dic5C24116yes—
294C22×Dic5C2412yes—
295C22×Dic5C24116yes—
296#711—264no—
297C2×D20—24no—
298C2×D20C2414yes—
299C2×C4×D5—28no—
300C2×C4×D5—48no—
301C2×C4×D5C2418yes—
302C2×C4×D5C24116yes—
303C2×Dic10—28no—
304C2×Dic10—24no—
305C2×Dic10—44no—
306C2×Dic10C2418yes—
307C2×Dic10C2414yes—
308C2×Dic10C2418yes—
309C5×C4⋊C4C2414yes—
310C5×C4⋊C4C2418yes—
311C5×C4⋊C4C2418yes—
312C5×C4⋊C4C2414yes—
313C5×C22⋊C4C2418yes—
314C5×C22⋊C4C2418yes—
315C5×C22⋊C4C2418yes—
316C42×C5C2414yes—
317C42×C5C2414yes—
318C42×C5C2418yes—
319C42×C5C2414yes—
320C42×C5C2414yes—
321C42×C5C2418yes—
322C42×C5C2418yes—
323C22⋊Dic5C24116yes—
324C22⋊Dic5C2418yes—
325C22⋊Dic5C24116yes—
326#685C2418yes—
327#685C2418yes—
328#685C2418yes—
329#685C24116yes—
330#685C2418yes—
331#685C24116yes—
332C4⋊Dic5C2418yes—
333C4⋊Dic5C2418yes—
334C4⋊Dic5C2418yes—
335C4⋊Dic5C2414yes—
336C4⋊Dic5C2418yes—
337C4⋊Dic5C2414yes—
338C4⋊Dic5C24116yes—
339C4⋊Dic5C24116yes—
340#683C24116yes—
341#683C24116yes—
342#683C2418yes—
343#683C24116yes—
344#683C2418yes—
345#683C2418yes—
346#683C24116yes—
347#683C24116yes—
348#683C24116yes—
349#683C24116yes—
350#683C2418yes—
351#683C24116yes—
352C4×Dic5C24116yes—
353C4×Dic5C24116yes—
354C4×Dic5C2418yes—
355C22×#41—52no—
356C22×#41C2×D511yescharacteristic
357#557—516no—
358#554—516no—
359#554—516no—
360#553—532no—
361#552—532no—
362#552—532no—
363#552—564no—
364#547—532no—
365#547—516no—
366#541—532no—
367#539—564no—
368#533—516no—
369C2×C4⋊Q8—52no—
370C2×C4⋊Q8—51no—
371C2×C4⋊Q8—51no—
372#529—532no—
373#529—516no—
374C2×#126—54no—
375C2×#126—54no—
376C2×#126—54no—
377C2×#126—52no—
378C2×#125—54no—
379C2×#125—54no—
380C2×#125—52no—
381C2×#125—51no—
382C2×#125—52no—
383C2×#125—54no—
384C2×#125—54no—
385C2×#125—52no—
386C2×#125—52no—
387C2×#125—532no—
388C2×#124—51no—
389C2×#123—54no—
390C2×#123—52no—
391C2×#123—54no—
392C2×#123—54no—
393C2×#123—54no—
394C2×C22⋊Q8—52no—
395C2×C22⋊Q8—51no—
396C2×C22⋊Q8—52no—
397C2×C22⋊Q8—52no—
398C2×C22⋊Q8—52no—
399C2×C22⋊Q8—54no—
400C2×C22⋊Q8—52no—
401C2×C22⋊Q8—54no—
402C2×#121—54no—
403C2×#121—52no—
404C2×#121—51no—
405#520—532no—
406C4×#41C2×D5116yescomplemented
407C2×C4×Q8—52no—
408C2×C4×Q8—52no—
409C2×C4×Q8—52no—
410C2×C4×Q8—51no—
411C2×C4×Q8—52no—
412C2×C4×Q8C2×D511yescharacteristic
413C2×C4×Q8C2×D511yescharacteristic
414C2×C4×D4—52no—
415C2×C4×D4—54no—
416C2×C4×D4—52no—
417C2×C4×D4—54no—
418C2×C4×D4—51no—
419C2×C4×D4—52no—
420C2×C4×D4C2×D511yescharacteristic
421C2×C4×D4C2×D512yes—
422C2×C4×D4C2×D511yescharacteristic
423C2×C4×D4C2×D512yes—
424C2×#117—52no—
425C2×#117—54no—
426C2×#117—52no—
427C2×#117—54no—
428C2×#117C2×D511yescharacteristic
429C2×#117C2×D512yes—
430C22×C4⋊C4—54no—
431C22×C4⋊C4—54no—
432C22×C4⋊C4—52no—
433C22×C4⋊C4—52no—
434C22×C4⋊C4—52no—
435C22×C42C2×D512yes—
436C22×C42C2×D511yescharacteristic
437C23×C5—24no—
438C23×C5—24no—
439C23×C5—22no—
440C23×C5—22no—
441C23×C5—22no—
442C23×C5C2×#4118yes—
443C23×C5C2512yes—
444C23×C5C2514yes—
445C23×C5C2511yescharacteristic
446C22×D5—24no—
447C22×D5—24no—
448C22×D5—24no—
449C22×D5C2514yes—
450C5×Q8—28no—
451C5×D4—216no—
452C5×D4C2×#41116yes—
453C2×C4×C5—22no—
454C2×C4×C5—24no—
455C2×C4×C5—216no—
456C2×C4×C5—22no—
457C2×C4×C5—24no—
458C2×C4×C5—22no—
459C2×C4×C5—24no—
460C2×C4×C5—22no—
461C2×C4×C5—28no—
462C2×C4×C5—216no—
463C2×C4×C5—28no—
464C2×C4×C5—44no—
465C2×C4×C5—48no—
466C2×C4×C5C2×#4114yes—
467C2×C4×C52−1+414yes—
468C2×C4×C5C2512yes—
469C2×C4×C5C2514yes—
470C2×C4×C5C2512yes—
471C2×C4×C5C2512yes—
472C2×C4×C5C2514yes—
473C2×C4×C5C2514yes—
474C2×C4×C5C2512yes—
475C2×C4×C5C2512yes—
476C2×C4×C5C2512yes—
477C22⋊D5—232no—
478C22⋊D5—48no—
479C2×Dic5—28no—
480C2×Dic5—24no—
481C2×Dic5—232no—
482C2×Dic5—24no—
483C2×Dic5—28no—
484C2×Dic5—24no—
485C2×Dic5—416no—
486C2×Dic5C2514yes—
487C2×Dic5C2518yes—
488C2×Dic5C2514yes—
489C2×Dic5C2518yes—
490C2×Dic5C2514yes—
491D20—28no—
492C4×D5—216no—
493C4×D5—416no—
494Dic10—216no—
495Dic10—28no—
496Dic10—48no—
497C2×#41—28no—
498C2×#41—516no—
499C2×#41—1016no—
500C2×#41C22×D518yes—
501C22×Q8—51no—
502C22×Q8—52no—
503C22×Q8—52no—
504C22×Q8C22×D511yescharacteristic
505C22×D4—54no—
506C22×D4—52no—
507C22×D4—51no—
508C22×D4C22×D512yes—
509C22×D4C22×D511yescharacteristic
510C23×C4—54no—
511C23×C4—54no—
512C23×C4—52no—
513C23×C4—54no—
514C23×C4C22×D512yes—
515C23×C4C22×D512yes—
516C23×C4C22×D511yescharacteristic
517C23×C4C22×D511yescharacteristic
518C23×C4C22×D512yes—
519C23×C4C22×D511yescharacteristic
520C4⋊Q8—516no—
521C4⋊Q8—58no—
522C4⋊Q8—58no—
523#126—532no—
524#126—532no—
525#126—532no—
526#126—516no—
527#125—532no—
528#125—532no—
529#125—516no—
530#125—58no—
531#125—516no—
532#125—532no—
533#125—532no—
534#125—516no—
535#125—516no—
536#124—58no—
537#123—532no—
538#123—516no—
539#123—532no—
540#123—532no—
541#123—532no—
542C22⋊Q8—516no—
543C22⋊Q8—58no—
544C22⋊Q8—516no—
545C22⋊Q8—516no—
546C22⋊Q8—516no—
547C22⋊Q8—532no—
548C22⋊Q8—516no—
549C22⋊Q8—532no—
550#121—532no—
551#121—516no—
552#121—58no—
553C4×Q8—516no—
554C4×Q8—516no—
555C4×Q8—516no—
556C4×Q8—58no—
557C4×Q8—516no—
558C4×Q8C22×D518yes—
559C4×Q8C22×D518yes—
560C4×D4—516no—
561C4×D4—532no—
562C4×D4—516no—
563C4×D4—532no—
564C4×D4—58no—
565C4×D4—516no—
566C4×D4C22×D518yes—
567C4×D4C22×D5116yes—
568C4×D4C22×D518yes—
569C4×D4C22×D5116yes—
570#117—516no—
571#117—532no—
572#117—516no—
573#117—532no—
574#117C22×D518yes—
575#117C22×D5116yes—
576C2×C4⋊C4—54no—
577C2×C4⋊C4—52no—
578C2×C4⋊C4—51no—
579C2×C4⋊C4—52no—
580C2×C4⋊C4—51no—
581C2×C4⋊C4—52no—
582C2×C4⋊C4—52no—
583C2×C4⋊C4—54no—
584C2×C4⋊C4—52no—
585C2×C4⋊C4—54no—
586C2×C4⋊C4—54no—
587C2×C4⋊C4—532no—
588C2×C4⋊C4—54no—
589C2×C4⋊C4—54no—
590C2×C4⋊C4—54no—
591C2×C4⋊C4—54no—
592C2×C4⋊C4—532no—
593C2×C4⋊C4—516no—
594C2×C4⋊C4—516no—
595C2×C4⋊C4—52no—
596C2×C4⋊C4—54no—
597C2×C4⋊C4—52no—
598C2×C4⋊C4—52no—
599C2×C4⋊C4—54no—
600C2×C4⋊C4—516no—
601C2×C4⋊C4C22×D511yescharacteristic
602C2×C4⋊C4C22×D512yes—
603C2×C4⋊C4C22×D511yescharacteristic
604C2×C4⋊C4C22×D512yes—
605C2×C22⋊C4—54no—
606C2×C22⋊C4—54no—
607C2×C22⋊C4—52no—
608C2×C22⋊C4—52no—
609C2×C22⋊C4—52no—
610C2×C22⋊C4—52no—
611C2×C22⋊C4—54no—
612C2×C22⋊C4—54no—
613C2×C22⋊C4—52no—
614C2×C22⋊C4C22×D512yes—
615C2×C22⋊C4C22×D512yes—
616C2×C22⋊C4C22×D512yes—
617C2×C42—54no—
618C2×C42—54no—
619C2×C42—52no—
620C2×C42C22×D512yes—
621C2×C42C22×D511yescharacteristic
622C2×C42C22×D511yescharacteristic
623C2×C42C22×D512yes—
624C2×C42C22×D511yescharacteristic
625C2×C42C22×D512yes—
626C2×C42C22×D5116yes—
627C2×C42C22×D518yes—
628C2×C42C22×D511yescharacteristic
629C22×C5—24no—
630C22×C5—24no—
631C22×C5—216no—
632C22×C5—22no—
633C22×C5—22no—
634C22×C5—22no—
635C22×C5—44no—
636C22×C5C22×#4118yes—
637C22×C5C22×#4112yes—
638C22×C5C2×2−1+412yes—
639C22×C5#58512yes—
640C22×C5C2611yescharacteristic
641C2×D5—24no—
642C2×D5—24no—
643C2×D5—24no—
644C2×D5—48no—
645C4×C5—22no—
646C4×C5—24no—
647C4×C5—22no—
648C4×C5—24no—
649C4×C5—22no—
650C4×C5—24no—
651C4×C5—22no—
652C4×C5C22×#4114yes—
653C4×C5C2×2−1+414yes—
654Dic5—28no—
655Dic5—24no—
656Dic5—24no—
657Dic5—28no—
658Dic5—24no—
659C24—52no—
660C24C23×D511yescharacteristic
661C24C23×D512yes—
662#41—232no—
663#41—1064no—
664C2×Q8—24no—
665C2×Q8—54no—
666C2×Q8—58no—
667C2×Q8—58no—
668C2×Q8—108no—
669C2×Q8—104no—
670C2×Q8—204no—
671C2×Q8C23×D514yes—
672C2×D4—28no—
673C2×D4—516no—
674C2×D4—58no—
675C2×D4—54no—
676C2×D4—1016no—
677C2×D4—104no—
678C2×D4—204no—
679C2×D4#70918yes—
680C2×D4C23×D518yes—
681C2×D4C23×D514yes—
682C22×C4—28no—
683C22×C4—24no—
684C22×C4—28no—
685C22×C4—24no—
686C22×C4—44no—
687C22×C4—42no—
688C22×C4—516no—
689C22×C4—52no—
690C22×C4—54no—
691C22×C4—54no—
692C22×C4—52no—
693C22×C4—52no—
694C22×C4—516no—
695C22×C4—58no—
696C22×C4—516no—
697C22×C4—1016no—
698C22×C4—108no—
699C22×C4—208no—
700C22×C4—208no—
701C22×C4C23×D518yes—
702C22×C4C23×D518yes—
703C22×C4C23×D514yes—
704C22×C4C23×D514yes—
705C22×C4C23×D511yescharacteristic
706C22×C4C23×D512yes—
707C22×C4C23×D511yescharacteristic
708C22×C4C23×D511yescharacteristic
709C22×C4C23×D512yes—
710C22×C4C23×D511yescharacteristic
711C22×C4C23×D512yes—
712C22×C4C23×D518yes—
713C22×C4C23×D514yes—
714C22×C4C23×D511yescharacteristic
715C22×C4C23×D511yescharacteristic
716C4⋊C4—516no—
717C4⋊C4—58no—
718C4⋊C4—54no—
719C4⋊C4—58no—
720C4⋊C4—54no—
721C4⋊C4—58no—
722C4⋊C4—58no—
723C4⋊C4—516no—
724C4⋊C4—58no—
725C4⋊C4—516no—
726C4⋊C4—516no—
727C4⋊C4—516no—
728C4⋊C4—516no—
729C4⋊C4—516no—
730C4⋊C4—516no—
731C4⋊C4—58no—
732C4⋊C4—516no—
733C4⋊C4—58no—
734C4⋊C4—58no—
735C4⋊C4—516no—
736C4⋊C4C23×D514yes—
737C4⋊C4C23×D518yes—
738C4⋊C4C23×D514yes—
739C4⋊C4C23×D518yes—
740C22⋊C4—516no—
741C22⋊C4—516no—
742C22⋊C4—58no—
743C22⋊C4—58no—
744C22⋊C4—58no—
745C22⋊C4—58no—
746C22⋊C4—516no—
747C22⋊C4—516no—
748C22⋊C4—58no—
749C22⋊C4C23×D518yes—
750C22⋊C4C23×D518yes—
751C22⋊C4C23×D518yes—
752C42—516no—
753C42—516no—
754C42—58no—
755C42C23×D514yes—
756C42C23×D518yes—
757C42C23×D514yes—
758C42C23×D514yes—
759C42C23×D518yes—
760C42C23×D514yes—
761C42C23×D518yes—
762C2×C5—28no—
763C2×C5—42no—
764C2×C5#351514yescomplemented
765C2×C5C23×#4111yescharacteristic
766C2×C5C22×2−1+411yescharacteristic
767C2×C5C2×#58511yescharacteristic
768D5—44no—
769C23—24no—
770C23—24no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—54no—
775C23—104no—
776C23—104no—
777C23—104no—
778C23C2×#70918yes—
779C23C24×D512yes—
780C23C24×D514yes—
781C23C24×D511yescharacteristic
782Q8—28no—
783Q8—1016no—
784Q8—108no—
785Q8—208no—
786D4—216no—
787D4—1032no—
788D4—108no—
789D4—208no—
790D4C2×#709116yes—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—216no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—28no—
800C2×C4—216no—
801C2×C4—28no—
802C2×C4—48no—
803C2×C4—44no—
804C2×C4—54no—
805C2×C4—58no—
806C2×C4—58no—
807C2×C4—54no—
808C2×C4—54no—
809C2×C4—104no—
810C2×C4—108no—
811C2×C4—1032no—
812C2×C4—104no—
813C2×C4—104no—
814C2×C4—108no—
815C2×C4—1016no—
816C2×C4—2016no—
817C2×C4—2016no—
818C2×C4C2×#70914yes—
819C2×C4#415014yes—
820C2×C4C24×D512yes—
821C2×C4C24×D514yes—
822C2×C4C24×D512yes—
823C2×C4C24×D512yes—
824C2×C4C24×D514yes—
825C2×C4C24×D512yes—
826C2×C4C24×D514yes—
827C2×C4C24×D512yes—
828C2×C4C24×D512yes—
829C5C2×#351511yescharacteristic, complemented, Sylow
830C22—24no—
831C22—24no—
832C22—216no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—44no—
837C22—104no—
838C22—104no—
839C22—104no—
840C22—208no—
841C22C22×#70918yes—
842C22C22×#70912yes—
843C22C2×#415012yes—
844C22#6628312yes—
845C22C25×D511yescharacteristic
846C4—22no—
847C4—24no—
848C4—22no—
849C4—24no—
850C4—22no—
851C4—24no—
852C4—22no—
853C4—104no—
854C4—108no—
855C4—104no—
856C4—104no—
857C4—108no—
858C4C22×#70914yes—
859C4C2×#415014yes—
860C2—28no—
861C2—42no—
862C2—204no—
863C2#1061773214yesdirect product factor
864C2C23×#70911yescharacteristic
865C2C22×#415011yescharacteristic
866C2C2×#6628311yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C4×C5×#41C2
socleC23×C5C25
hypercenterC2×C4×#41D5
hypocenterC5C2×#3515
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×#41C2semidirect
2. C2×#66158C2semidirect
3. #10617732C2direct (N × H)
4. C2×#65913C2semidirect
5. C2×#65917C2semidirect
6. C2×#65901C2semidirect
7. C2×#65877C2semidirect
8. C2×#65899C2semidirect
9. C2×#65875C2semidirect
10. C2×#65889C2semidirect
11. C2×#65898C2semidirect
12. C2×#65880C2semidirect
13. C2×#65863C2semidirect
14. C2×#65865C2semidirect
15. C2×#65813C2semidirect
16. C2×#65813C2semidirect
17. C2×#65804C2semidirect
18. C22×#4016C2semidirect
21. C4×C5×#41C22semidirect
32. #66158C22semidirect
53. #65917C22semidirect
54. #65913C22semidirect
55. #65901C22semidirect
56. #65899C22semidirect
57. #65898C22semidirect
58. #65889C22semidirect
59. #65880C22semidirect
60. #65877C22semidirect
61. #65875C22semidirect
62. #65865C22semidirect
63. #65863C22semidirect
78. #65813C22semidirect
79. #65813C22semidirect
87. #65804C22semidirect
94. C2×#4016C22semidirect
251. C2×C4×#41D5semidirect
406. C4×#41C2×D5semidirect
764. C2×C5#3515semidirect
829. C5C2×#3515semidirect
863. C2#10617732direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C5×#412
C2×#661582
#106177322
C2×#659132
C2×#659172
C2×#659012
C2×#658772
C2×#658992
C2×#658752
C2×#658892
C2×#658982
C2×#658802
C2×#658632
C2×#658652
C2×#658132
C2×#658042
C22×#40162
C2×#35155