Finite Group Databasebeta

← C2×#10613445 #12968537

Subgroups — C2×#10613445 #12968537

Order 1280.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66049C211yesmaximal, characteristic
2C2×#66023C211yesmaximal, characteristic, complemented
3C2×C5×#490C211yesmaximal, characteristic, complemented
4C2×#65359C211yesmaximal, characteristic, complemented
5C2×#65357C211yesmaximal, characteristic, complemented
6#10613445C2116yesmaximal, direct product factor
7C2×#65060C211yesmaximal, characteristic, complemented
8C2×#65059C211yesmaximal, characteristic, complemented
9C2×#65061C211yesmaximal, characteristic, complemented
10C2×D5×#102C211yesmaximal, characteristic, complemented
11C2×#65053C211yesmaximal, characteristic, complemented
12C2×#65054C211yesmaximal, characteristic, complemented
13C2×#65057C211yesmaximal, characteristic, complemented
14C2×#65049C211yesmaximal, characteristic, complemented
15C2×#65003C211yesmaximal, characteristic, complemented
16C2×#64997C211yesmaximal, characteristic, complemented
17C22×#711C2211yescharacteristic
18C22×D4×D5C2211yescharacteristic
19C2×C5×#127C2211yescharacteristic
20C2×C5×#125C2211yescharacteristic, complemented
21C2×#4086C2211yescharacteristic
22C2×#4085—21no—
23C2×#4085—21no—
24C2×#4083—21no—
25C2×#4083—21no—
26C2×#4082C2211yescharacteristic
27C22×#676C2211yescharacteristic
28C22×C8×D5C2211yescharacteristic
29#66049—24no—
30#66049C2218yes—
31#66023—24no—
32#66023C2218yescomplemented
33C2×#4043—21no—
34C2×#4042—21no—
35C2×#4038C2211yescharacteristic
36C2×D5×C4⋊C4C2211yescharacteristic
37C2×#4036C2211yescharacteristic, complemented
38C2×#4035—21no—
39C2×#4034—21no—
40C2×#4034C2211yescharacteristic, complemented
41C2×#4021C2211yescharacteristic
42C2×#4018C2211yescharacteristic
43C2×#4015C2211yescharacteristic, complemented
44C5×#490C2218yescomplemented
45C2×C5×#102C2211yescharacteristic
46C2×C5×#102C2211yescharacteristic
47C2×C5×#102C2211yescharacteristic, complemented
48C2×C5×#102C2211yescharacteristic, complemented
49C2×C5×#97C2211yescharacteristic, complemented
50C2×#3964C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3964C2211yescharacteristic, complemented
53C2×#3964C2211yescharacteristic, complemented
54C2×#3953C2211yescharacteristic
55C2×#3953C2211yescharacteristic
56C2×#3948C2211yescharacteristic, complemented
57C2×#3948C2211yescharacteristic, complemented
58C2×#3947C2211yescharacteristic, complemented
59C2×C8×Dic5C2211yescharacteristic, complemented
60#65359C2218yescomplemented
61#65357C2218yescomplemented
62C2×#3942C2211yescharacteristic, complemented
63C2×#3942C2211yescharacteristic, complemented
64C2×#3941C2211yescharacteristic
65C2×#3941C2211yescharacteristic
66C2×C4×#168C2211yescharacteristic, complemented
67#65061C2218yescomplemented
68#65060C2218yescomplemented
69#65059C2218yescomplemented
70D5×#102C2218yescomplemented
71#65057C2218yescomplemented
72#65054C2218yescomplemented
73#65053C2218yescomplemented
74#65049C2218yescomplemented
75#65003C2218yescomplemented
76#64997C2218yescomplemented
77C2×#3136—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×D4—21no—
80C22×C5×D4—21no—
81C22×C5×D4C2311yescharacteristic
82C22×C5×D4C2311yescharacteristic
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C22×C22⋊D5—21no—
86C22×C22⋊D5—21no—
87C23×Dic5—21no—
88C2×#711—22no—
89C2×#711—24no—
90C2×#711—24no—
91C2×#711C2314yes—
92C2×D4×D5—22no—
93C2×D4×D5—24no—
94C2×D4×D5—24no—
95C2×D4×D5C2314yes—
96C22×D20C2311yescharacteristic
97C22×C4×D5—21no—
98C22×C4×D5C2311yescharacteristic
99C22×Dic10—21no—
100C22×Dic10—21no—
101C22×Dic10C2311yescharacteristic
102C22×C5×C8C2311yescharacteristic
103C22×C5×C8C2311yescharacteristic
104C5×#127—22no—
105C5×#127C2314yes—
106C5×#125—22no—
107C5×#125C2314yescomplemented
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C42×C5C2311yescharacteristic
113C2×C22⋊Dic5—21no—
114C2×C22⋊Dic5—21no—
115#4086—22no—
116#4086C2314yes—
117#4085—28no—
118#4085—28no—
119#4083—28no—
120#4083—28no—
121#4082—22no—
122#4082C2314yes—
123C2×#685—21no—
124C2×#685—21no—
125C2×#685—21no—
126C2×#685D411yescharacteristic
127C2×#685D411yescharacteristic
128C2×C4⋊Dic5—21no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5C2311yescharacteristic
131C2×C4⋊Dic5C2311yescharacteristic
132C2×#683—21no—
133C2×#683—21no—
134C2×#683—21no—
135C2×#683D411yescharacteristic
136C2×#683D411yescharacteristic
137C2×C4×Dic5—21no—
138C2×C4×Dic5C2311yescharacteristic
139C22×#168C2311yescharacteristic
140C22×#168C2311yescharacteristic
141C2×#676—24no—
142C2×#676C2314yes—
143C2×C8×D5—24no—
144C2×C8×D5C2314yes—
145#4043—28no—
146#4042—28no—
147#4038—22no—
148#4038C2314yes—
149D5×C4⋊C4—22no—
150D5×C4⋊C4C2314yes—
151#4036—22no—
152#4036C2314yescomplemented
153#4035—28no—
154#4034—28no—
155#4034—22no—
156#4034C2314yescomplemented
157#4021—22no—
158#4021C2314yes—
159#4018D414yes—
160#4018C2314yes—
161#4015—22no—
162#4015C2314yescomplemented
163C5×#102C2314yes—
164C5×#102C2314yes—
165C5×#102C2314yescomplemented
166C5×#102C2314yescomplemented
167C5×#97C2314yescomplemented
168#3964C2314yes—
169#3964C2314yes—
170#3964C2314yescomplemented
171#3964C2314yescomplemented
172#3953C2314yes—
173#3953C2314yes—
174#3948C2314yescomplemented
175#3948C2314yescomplemented
176#3947C2314yescomplemented
177C8×Dic5C2314yescomplemented
178#3942C2314yescomplemented
179#3942C2314yescomplemented
180#3941C2314yes—
181#3941C2314yes—
182C4×#168C2314yescomplemented
183C2×#544—51no—
184C2×#535—51no—
185#3136—516no—
186C2×#490—51no—
187C2×#490D511yescharacteristic, complemented
188C2×#489—51no—
189C2×#489—51no—
190C2×#488—51no—
191C2×#488—51no—
192C2×#486—51no—
193C2×#486—51no—
194C2×#417—51no—
195C2×#418—51no—
196C2×#416—51no—
197C22×#102—51no—
198C2×#405—51no—
199C24×C5—21no—
200C24×C5—21no—
201C23×D5—21no—
202C23×D5—24no—
203C23×D5—44no—
204C23×D5—82no—
205C23×D5—82no—
206C23×D5C2×D411yescharacteristic
207C2×C5×D4—21no—
208C2×C5×D4—21no—
209C2×C5×D4—24no—
210C2×C5×D4—24no—
211C2×C5×D4—22no—
212C2×C5×D4—22no—
213C2×C5×D4—22no—
214C2×C5×D4—22no—
215C2×C5×D4—82no—
216C2×C5×D4—82no—
217C2×C5×D4C2412yes—
218C2×C5×D4C2412yes—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2411yescharacteristic
224C2×C22⋊D5—24no—
225C2×C22⋊D5—24no—
226C2×C22⋊D5—24no—
227C2×C22⋊D5—24no—
228C2×C22⋊D5—44no—
229C2×C22⋊D5—44no—
230C2×C22⋊D5—82no—
231C2×C22⋊D5—82no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—24no—
236C22×Dic5—44no—
237C22×Dic5C2×D411yescharacteristic
238C22×Dic5C2×D411yescharacteristic
239C22×Dic5C2×D411yescharacteristic
240#711—28no—
241#711—28no—
242#711—48no—
243D4×D5—28no—
244D4×D5—28no—
245D4×D5—48no—
246C2×D20—22no—
247C2×D20—22no—
248C2×D20—21no—
249C2×D20C2412yes—
250C2×C4×D5—24no—
251C2×C4×D5—82no—
252C2×C4×D5C2×D412yes—
253C2×C4×D5#4114yes—
254C2×C4×D5#4114yes—
255C2×C4×D5C2412yes—
256C2×Dic10—22no—
257C2×Dic10—22no—
258C2×Dic10—21no—
259C2×Dic10—24no—
260C2×Dic10—24no—
261C2×Dic10—82no—
262C2×Dic10—82no—
263C2×Dic10C2412yes—
264C2×C5×C8—22no—
265C2×C5×C8—22no—
266C2×C5×C8C2412yes—
267C2×C5×C8C2412yes—
268C5×C4⋊C4—24no—
269C5×C4⋊C4—24no—
270C5×C4⋊C4—21no—
271C5×C4⋊C4—21no—
272C5×C4⋊C4C2412yes—
273C5×C4⋊C4C2412yes—
274C42×C5C2×D412yes—
275C42×C5C2412yes—
276C22⋊Dic5—24no—
277C22⋊Dic5—24no—
278#685—24no—
279#685—24no—
280#685—24no—
281#685C2×D414yes—
282#685C2×D414yes—
283C4⋊Dic5—21no—
284C4⋊Dic5—21no—
285C4⋊Dic5—24no—
286C4⋊Dic5—24no—
287C4⋊Dic5C2412yes—
288C4⋊Dic5C2412yes—
289#683—24no—
290#683—24no—
291#683—24no—
292#683C2×D414yes—
293#683C2×D414yes—
294C4×Dic5—24no—
295C4×Dic5C2×D412yes—
296C4×Dic5C2412yes—
297C2×#168—22no—
298C2×#168—22no—
299C2×#168C2412yes—
300C2×#168C2412yes—
301#676—28no—
302C8×D5—28no—
303C22×#41—51no—
304C23×D4—51no—
305C22×M16—51no—
306C23×C8—51no—
307#544—58no—
308#544—104no—
309#535—58no—
310#535—104no—
311C2×C4⋊Q8—51no—
312C2×C4⋊Q8—51no—
313C2×C4⋊Q8—101no—
314C2×#127—51no—
315C2×#127C2×D511yescharacteristic
316C2×#125—51no—
317C2×#125—101no—
318C2×#125C2×D511yescharacteristic, complemented
319C2×#124—51no—
320C2×#124—51no—
321C2×C22⋊Q8—101no—
322C2×C22⋊Q8—101no—
323C2×#121—101no—
324C2×#121—101no—
325C2×#120—101no—
326C2×#120—101no—
327C2×#117—51no—
328C2×#117—51no—
329C22×C4⋊C4—51no—
330#490—58no—
331#490C2×D518yescomplemented
332#489—58no—
333#489—58no—
334#488—58no—
335#488—58no—
336#486—58no—
337#486—58no—
338#418—58no—
339#417—58no—
340#416—58no—
341C2×#103—51no—
342C2×#103—51no—
343C2×#103—51no—
344C2×#103—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102—51no—
349C2×#102—51no—
350C2×#102—51no—
351C2×#102—51no—
352C2×#102—51no—
353C2×#102—58no—
354C2×#102C2×D511yescharacteristic
355C2×#102C2×D511yescharacteristic
356C2×#102C2×D511yescharacteristic, complemented
357C2×#102C2×D511yescharacteristic, complemented
358#405—58no—
359C2×#97—51no—
360C2×#97C2×D511yescharacteristic, complemented
361C2×C4×C8—51no—
362C2×C4×C8—51no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—42no—
366C23×C5—42no—
367C23×C5—42no—
368C23×C5—42no—
369C23×C5—42no—
370C23×C5—42no—
371C23×C5C22×D411yescharacteristic
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—42no—
376C22×D5—42no—
377C22×D5—42no—
378C22×D5—48no—
379C22×D5—84no—
380C22×D5—84no—
381C22×D5—816no—
382C22×D5#12414yes—
383C22×D5C22×D412yes—
384C5×D4—22no—
385C5×D4—22no—
386C5×D4—22no—
387C5×D4—22no—
388C5×D4—42no—
389C5×D4—42no—
390C5×D4—84no—
391C5×D4—84no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—42no—
397C2×C4×C5—42no—
398C2×C4×C5C22×D412yes—
399C2×C4×C5C22×D412yes—
400C2×C4×C5C22×D411yescharacteristic
401C2×C4×C5C2×#4112yes—
402C2×C4×C5C2×#4112yes—
403C2×C4×C5C2511yescharacteristic
404C22⋊D5—48no—
405C22⋊D5—48no—
406C22⋊D5—84no—
407C22⋊D5—84no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—42no—
414C2×Dic5—42no—
415C2×Dic5—42no—
416C2×Dic5—48no—
417C2×Dic5#12414yes—
418C2×Dic5C22×D412yes—
419C2×Dic5C22×D412yes—
420C2×Dic5C22×D412yes—
421D20—22no—
422D20—22no—
423D20—42no—
424C4×D5—84no—
425C4×D5#12418yes—
426C4×D5C2×#4114yes—
427C4×D5C2×#4114yes—
428Dic10—22no—
429Dic10—22no—
430Dic10—42no—
431Dic10—84no—
432Dic10—84no—
433C5×C8—22no—
434C5×C8—22no—
435#168—22no—
436#168—22no—
437C25—101no—
438C2×#41—54no—
439C2×#41—102no—
440C2×#41—104no—
441C2×#41—104no—
442C22×Q8—51no—
443C22×Q8—101no—
444C22×Q8—101no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—54no—
448C22×D4—51no—
449C22×D4—104no—
450C22×D4—104no—
451C22×D4—102no—
452C22×D4—101no—
453C22×D4—101no—
454C22×D4—101no—
455C22×D4—101no—
456C22×D4C22×D511yescharacteristic
457C22×D4C22×D511yescharacteristic
458C23×C4—51no—
459C23×C4—101no—
460C23×C4—101no—
461C2×M16—54no—
462C2×M16—104no—
463C22×C8—51no—
464C22×C8—51no—
465C22×C8—54no—
466C22×C8—104no—
467C22×C8C22×D511yescharacteristic
468C22×C8C22×D511yescharacteristic
469C4⋊Q8—54no—
470C4⋊Q8—54no—
471C4⋊Q8—102no—
472C4⋊Q8—108no—
473C4⋊Q8—102no—
474#127—22no—
475#127—54no—
476#127—102no—
477#127C22×D514yes—
478#125—22no—
479#125—54no—
480#125—102no—
481#125—108no—
482#125C22×D514yescomplemented
483#124—54no—
484#124—54no—
485#124—102no—
486#124—102no—
487C22⋊Q8—108no—
488C22⋊Q8—108no—
489#121—108no—
490#121—108no—
491#120—108no—
492#120—108no—
493#117—54no—
494#117—54no—
495#117—54no—
496#117—102no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—51no—
500C2×C4⋊C4—51no—
501C2×C4⋊C4—51no—
502C2×C4⋊C4—51no—
503C2×C4⋊C4—54no—
504C2×C4⋊C4—102no—
505C2×C4⋊C4—101no—
506C2×C4⋊C4—101no—
507C2×C4⋊C4—101no—
508C2×C4⋊C4—101no—
509C2×C4⋊C4—101no—
510C2×C4⋊C4C22×D511yescharacteristic
511C2×C4⋊C4C22×D511yescharacteristic
512C2×C22⋊C4—51no—
513C2×C22⋊C4—51no—
514C2×C22⋊C4—101no—
515C2×C22⋊C4—101no—
516C2×C22⋊C4—101no—
517C2×C22⋊C4—101no—
518C2×C22⋊C4—101no—
519C2×C42—51no—
520C2×C42—101no—
521C2×C42C22×D511yescharacteristic
522#103—54no—
523#103—54no—
524#103—54no—
525#103—54no—
526#102—54no—
527#102—54no—
528#102—54no—
529#102—54no—
530#102—54no—
531#102—54no—
532#102—54no—
533#102—54no—
534#102C22×D514yes—
535#102C22×D514yes—
536#102C22×D514yescomplemented
537#102C22×D514yescomplemented
538#97—54no—
539#97C22×D514yescomplemented
540C4×C8—54no—
541C4×C8—54no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—84no—
549C22×C5—84no—
550C22×C5C2×#12412yes—
551C22×C5#57612yes—
552C22×C5#57712yes—
553C22×C5C23×D411yescharacteristic
554C2×D5—28no—
555C2×D5—22no—
556C2×D5—22no—
557C2×D5—42no—
558C2×D5—42no—
559C2×D5—42no—
560C2×D5—816no—
561C2×D5—84no—
562C2×D5C2×#12414yes—
563C4×C5—22no—
564C4×C5—22no—
565C4×C5—42no—
566C4×C5—42no—
567C4×C5C2×#12412yes—
568C4×C5C22×#4111yescharacteristic
569C4×C5C22×#4111yescharacteristic
570Dic5—22no—
571Dic5—22no—
572Dic5—42no—
573Dic5—42no—
574Dic5—42no—
575Dic5C2×#12414yes—
576C24—21no—
577C24—21no—
578C24—51no—
579C24—104no—
580C24—101no—
581C24—204no—
582C24—402no—
583C24—402no—
584#41—108no—
585#41—108no—
586#41—208no—
587C2×Q8—52no—
588C2×Q8—104no—
589C2×Q8—101no—
590C2×Q8—104no—
591C2×Q8—102no—
592C2×Q8—102no—
593C2×Q8—402no—
594C2×Q8—402no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—24no—
598C2×D4—24no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—52no—
604C2×D4—82no—
605C2×D4—82no—
606C2×D4—108no—
607C2×D4—108no—
608C2×D4—104no—
609C2×D4—104no—
610C2×D4—104no—
611C2×D4—104no—
612C2×D4—101no—
613C2×D4—102no—
614C2×D4—102no—
615C2×D4—208no—
616C2×D4—204no—
617C2×D4—204no—
618C2×D4—402no—
619C2×D4—402no—
620C2×D4C23×D512yes—
621C2×D4C23×D512yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—51no—
625C22×C4—52no—
626C22×C4—54no—
627C22×C4—54no—
628C22×C4—52no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—104no—
632C22×C4—104no—
633C22×C4—101no—
634C22×C4—101no—
635C22×C4—101no—
636C22×C4—204no—
637C22×C4—402no—
638C22×C4D4×D511yescharacteristic
639C22×C4D4×D511yescharacteristic
640C22×C4C23×D511yescharacteristic
641M16—108no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—52no—
645C2×C8—52no—
646C2×C8—108no—
647C2×C8—102no—
648C2×C8—102no—
649C2×C8C23×D512yes—
650C2×C8C23×D512yes—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—54no—
656C4⋊C4—54no—
657C4⋊C4—52no—
658C4⋊C4—52no—
659C4⋊C4—104no—
660C4⋊C4—104no—
661C4⋊C4—104no—
662C4⋊C4—104no—
663C4⋊C4—101no—
664C4⋊C4—101no—
665C4⋊C4—104no—
666C4⋊C4C23×D512yes—
667C4⋊C4C23×D512yes—
668C22⋊C4—54no—
669C22⋊C4—54no—
670C22⋊C4—104no—
671C22⋊C4—104no—
672C22⋊C4—104no—
673C22⋊C4—104no—
674C22⋊C4—104no—
675C42—52no—
676C42—52no—
677C42—104no—
678C42D4×D512yes—
679C42C23×D512yes—
680C2×C5—82no—
681C2×C5—82no—
682C2×C5#313614yescomplemented
683C2×C5C22×#12411yescharacteristic
684C2×C5C2×#57611yescharacteristic
685C2×C5C2×#57711yescharacteristic
686D5—24no—
687D5—82no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—54no—
697C23—52no—
698C23—102no—
699C23—102no—
700C23—102no—
701C23—208no—
702C23—202no—
703C23—202no—
704C23—202no—
705C23—404no—
706C23—404no—
707C23—4016no—
708C23C2×D4×D511yescharacteristic
709Q8—102no—
710Q8—102no—
711Q8—202no—
712Q8—404no—
713Q8—404no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—42no—
719D4—42no—
720D4—84no—
721D4—84no—
722D4—102no—
723D4—102no—
724D4—208no—
725D4—208no—
726D4—202no—
727D4—404no—
728D4—404no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—54no—
736C2×C4—52no—
737C2×C4—58no—
738C2×C4—54no—
739C2×C4—54no—
740C2×C4—52no—
741C2×C4—52no—
742C2×C4—102no—
743C2×C4—102no—
744C2×C4—102no—
745C2×C4—102no—
746C2×C4—102no—
747C2×C4—208no—
748C2×C4—202no—
749C2×C4—202no—
750C2×C4—202no—
751C2×C4—404no—
752C2×C4C2×D4×D512yes—
753C2×C4C2×D4×D512yes—
754C2×C4C2×D4×D511yescharacteristic
755C2×C4D5×#4112yes—
756C2×C4D5×#4112yes—
757C2×C4C24×D511yescharacteristic
758C8—22no—
759C8—22no—
760C8—102no—
761C8—102no—
762C5C2×#313611yescharacteristic, complemented, Sylow
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—54no—
770C22—84no—
771C22—84no—
772C22—108no—
773C22—102no—
774C22—102no—
775C22—202no—
776C22—202no—
777C22—202no—
778C22—4016no—
779C22—404no—
780C22D5×#12412yes—
781C22#6610812yes—
782C22#6610912yes—
783C22C22×D4×D511yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—54no—
789C4—102no—
790C4—102no—
791C4—202no—
792C4—202no—
793C4—202no—
794C4D5×#12412yes—
795C4C2×D5×#4111yescharacteristic
796C4C2×D5×#4111yescharacteristic
797C2—82no—
798C2—82no—
799C2—104no—
800C2—402no—
801C2#1061344514yesdirect product factor
802C2C2×D5×#12411yescharacteristic
803C2C2×#6610811yescharacteristic
804C2C2×#6610911yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#490C2
socleC23×C5C22×D4
prime radicalC2×#66049C2
hypercenterC2×#490D5
hypocenterC5C2×#3136
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
2. C2×#66023C2semidirect
3. C2×C5×#490C2semidirect
4. C2×#65359C2semidirect
5. C2×#65357C2semidirect
6. #10613445C2direct (N × H)
7. C2×#65060C2semidirect
8. C2×#65059C2semidirect
9. C2×#65061C2semidirect
10. C2×D5×#102C2semidirect
11. C2×#65053C2semidirect
12. C2×#65054C2semidirect
13. C2×#65057C2semidirect
14. C2×#65049C2semidirect
15. C2×#65003C2semidirect
16. C2×#64997C2semidirect
20. C2×C5×#125C22semidirect
32. #66023C22semidirect
37. C2×#4036C22semidirect
40. C2×#4034C22semidirect
43. C2×#4015C22semidirect
44. C5×#490C22semidirect
47. C2×C5×#102C22semidirect
48. C2×C5×#102C22semidirect
49. C2×C5×#97C22semidirect
52. C2×#3964C22semidirect
53. C2×#3964C22semidirect
56. C2×#3948C22semidirect
57. C2×#3948C22semidirect
58. C2×#3947C22semidirect
59. C2×C8×Dic5C22semidirect
60. #65359C22semidirect
61. #65357C22semidirect
62. C2×#3942C22semidirect
63. C2×#3942C22semidirect
66. C2×C4×#168C22semidirect
67. #65061C22semidirect
68. #65060C22semidirect
69. #65059C22semidirect
70. D5×#102C22semidirect
71. #65057C22semidirect
72. #65054C22semidirect
73. #65053C22semidirect
74. #65049C22semidirect
75. #65003C22semidirect
76. #64997C22semidirect
107. C5×#125C23semidirect
152. #4036C23semidirect
156. #4034C23semidirect
162. #4015C23semidirect
165. C5×#102C23semidirect
166. C5×#102C23semidirect
167. C5×#97C23semidirect
170. #3964C23semidirect
171. #3964C23semidirect
174. #3948C23semidirect
175. #3948C23semidirect
176. #3947C23semidirect
177. C8×Dic5C23semidirect
178. #3942C23semidirect
179. #3942C23semidirect
182. C4×#168C23semidirect
187. C2×#490D5semidirect
318. C2×#125C2×D5semidirect
331. #490C2×D5semidirect
356. C2×#102C2×D5semidirect
357. C2×#102C2×D5semidirect
360. C2×#97C2×D5semidirect
482. #125C22×D5semidirect
536. #102C22×D5semidirect
537. #102C22×D5semidirect
539. #97C22×D5semidirect
682. C2×C5#3136semidirect
762. C5C2×#3136semidirect
801. C2#10613445direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660492
C2×#660232
C2×C5×#4902
C2×#653592
C2×#653572
#106134452
C2×#650602
C2×#650592
C2×#650612
C2×D5×#1022
C2×#650532
C2×#650542
C2×#650572
C2×#650492
C2×#650032
C2×#649972
C2×#31365