Finite Group Databasebeta

← C2×#10615190 #12969178

Subgroups — C2×#10615190 #12969178

Order 1280.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#542C211yesmaximal, characteristic, complemented
2C2×#65869C211yesmaximal, characteristic, complemented
3#10615190C2116yesmaximal, direct product factor
4C2×#65369C211yesmaximal, characteristic, complemented
5C2×#65377C211yesmaximal, characteristic, complemented
6C2×#65347C211yesmaximal, characteristic, complemented
7C2×#65345C211yesmaximal, characteristic, complemented
8C2×#65338C211yesmaximal, characteristic, complemented
9C2×#65337C211yesmaximal, characteristic, complemented
10C2×#65328C211yesmaximal, characteristic, complemented
11C2×#65327C211yesmaximal, characteristic, complemented
12C2×#65315C211yesmaximal, characteristic, complemented
13C2×C4×#688C211yesmaximal, characteristic, complemented
14C2×#65303C211yesmaximal, characteristic, complemented
15C2×C4×#686C211yesmaximal, characteristic, complemented
16C2×#65286C211yesmaximal, characteristic, complemented
17C5×#542—24no—
18C5×#542C2218yescomplemented
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×#126—21no—
21C2×C5×#124—21no—
22C2×C5×#124C2211yescharacteristic
23C2×C5×#123—21no—
24C2×C5×C22⋊Q8—21no—
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C5×#121C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C22×#688C2211yescharacteristic
31C22×#688C2211yescharacteristic
32C22×#686C2211yescharacteristic
33C22×#686C2211yescharacteristic
34C2×#4076C2211yescharacteristic
35C2×#4076C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C23×#168C2211yescharacteristic
38#65869—24no—
39#65869C2218yescomplemented
40C2×#4040—21no—
41C2×#4040—21no—
42C2×#4030—21no—
43C2×#4030—21no—
44C2×#4020C2211yescharacteristic
45C2×C4×D20C2211yescharacteristic
46C2×C4×D20C2211yescharacteristic
47C2×#4016C2211yescharacteristic
48C2×#3967C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×#3964C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52#65377C2218yescomplemented
53#65369C2218yescomplemented
54#65347C2218yescomplemented
55#65345C2218yescomplemented
56#65338C2218yescomplemented
57#65337C2218yescomplemented
58#65328C2218yescomplemented
59#65327C2218yescomplemented
60#65315C2218yescomplemented
61C4×#688C2218yescomplemented
62#65303C2218yescomplemented
63C4×#686C2218yescomplemented
64#65286C2218yescomplemented
65C2×#3941C2211yescharacteristic
66C2×#3941C2211yescharacteristic
67C2×#3941C2211yescharacteristic
68C2×#3941C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71C2×#3939C2211yescharacteristic
72C2×#3939C2211yescharacteristic
73C2×#3935C2211yescharacteristic
74C2×#3935C2211yescharacteristic
75C2×C4×#168C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3179—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4—21no—
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5—21no—
83C23×C4×C5C2311yescharacteristic
84C22×C22⋊D5—21no—
85C22×C22⋊D5—21no—
86C22×D20—21no—
87C22×D20—21no—
88C22×D20C2311yescharacteristic
89C22×D20C2311yescharacteristic
90C22×C4×D5—21no—
91C22×C4×D5—21no—
92C5×C4⋊Q8—22no—
93C5×C4⋊Q8C2314yes—
94C5×#126—28no—
95C5×#124—28no—
96C5×#124—22no—
97C5×#124C2314yes—
98C5×#123—28no—
99C5×C22⋊Q8—22no—
100C5×C22⋊Q8—28no—
101C5×C22⋊Q8C2314yes—
102C5×#121—22no—
103C5×#121C2314yes—
104C4×C5×Q8—22no—
105C4×C5×Q8C2314yes—
106C4×C5×D4—22no—
107C4×C5×D4C2314yes—
108C5×#117D414yes—
109C5×#117C2314yes—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4D411yescharacteristic
114C2×C5×C4⋊C4D411yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4D411yescharacteristic
123C2×C5×C22⋊C4D411yescharacteristic
124C2×C42×C5—21no—
125C2×C42×C5C2311yescharacteristic
126C2×C42×C5C2311yescharacteristic
127C2×#688—24no—
128C2×#688—24no—
129C2×#688C2314yes—
130C2×#688C2314yes—
131C2×#686—24no—
132C2×#686—24no—
133C2×#686C2314yes—
134C2×#686C2314yes—
135#4076—22no—
136#4076—22no—
137#4076C2314yes—
138#4076C2314yes—
139C2×#685—21no—
140C2×#685—21no—
141C2×#685—21no—
142C2×#685—21no—
143C2×C4⋊Dic5C2311yescharacteristic
144C2×C4⋊Dic5C2311yescharacteristic
145C2×#683—21no—
146C2×#683—21no—
147C2×#681—24no—
148C2×#681C2314yes—
149C22×#168—24no—
150C22×#168C2314yes—
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C22×#168C2311yescharacteristic
154C22×#168C2311yescharacteristic
155#4040—28no—
156#4040—28no—
157#4030—28no—
158#4030—28no—
159#4020—22no—
160#4020C2314yes—
161C4×D20—22no—
162C4×D20—22no—
163C4×D20C2314yes—
164C4×D20C2314yes—
165#4016—22no—
166#4016C2314yes—
167#3967C2314yes—
168#3967C2314yes—
169#3964C2314yes—
170#3964C2314yes—
171#3941C2314yes—
172#3941C2314yes—
173#3941C2314yes—
174#3941C2314yes—
175#3940C2314yes—
176#3940C2314yes—
177#3939C2314yes—
178#3939C2314yes—
179#3935C2314yes—
180#3935C2314yes—
181C4×#168C2314yes—
182C4×#168C2314yes—
183C2×#542D511yescharacteristic, complemented
184C2×#540—51no—
185#3179—516no—
186C2×#501—51no—
187C2×#496—51no—
188C2×#488—51no—
189C2×#486—51no—
190C2×#469—51no—
191C2×#468—51no—
192C2×#466—51no—
193C2×#465—51no—
194C2×#442—51no—
195C2×#440—51no—
196C2×C4×SD16—51no—
197C2×C4×D8—51no—
198C2×#405—51no—
199C24×C5—21no—
200C24×C5C2×D411yescharacteristic
201C23×D5—21no—
202C23×D5—21no—
203C2×C5×Q8—21no—
204C2×C5×Q8—24no—
205C2×C5×Q8—22no—
206C2×C5×Q8—22no—
207C2×C5×Q8—82no—
208C2×C5×Q8C2412yes—
209C2×C5×D4—24no—
210C2×C5×D4—21no—
211C2×C5×D4—22no—
212C2×C5×D4—22no—
213C2×C5×D4—82no—
214C2×C5×D4C2412yes—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—24no—
221C22×C4×C5—82no—
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2411yescharacteristic
230C2×C22⋊D5—24no—
231C2×C22⋊D5—24no—
232C2×C22⋊D5—82no—
233C2×C22⋊D5—82no—
234C22×Dic5—21no—
235C22×Dic5—21no—
236C2×D20—22no—
237C2×D20—22no—
238C2×D20—22no—
239C2×D20—22no—
240C2×D20—21no—
241C2×D20—21no—
242C2×D20—24no—
243C2×D20—24no—
244C2×D20—82no—
245C2×D20—82no—
246C2×D20C2412yes—
247C2×D20C2412yes—
248C2×C4×D5—24no—
249C2×C4×D5—24no—
250C2×C4×D5—82no—
251C2×C4×D5—82no—
252C5×C4⋊C4—24no—
253C5×C4⋊C4—24no—
254C5×C4⋊C4—24no—
255C5×C4⋊C4—21no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4C2×D414yes—
258C5×C4⋊C4C2×D414yes—
259C5×C4⋊C4C2412yes—
260C5×C4⋊C4C2412yes—
261C5×C22⋊C4—24no—
262C5×C22⋊C4—24no—
263C5×C22⋊C4—24no—
264C5×C22⋊C4—24no—
265C5×C22⋊C4—24no—
266C5×C22⋊C4C2×D414yes—
267C5×C22⋊C4C2×D414yes—
268C42×C5—24no—
269C42×C5C2×D412yes—
270C42×C5C2×D412yes—
271C42×C5C2412yes—
272C42×C5C2412yes—
273#688—28no—
274#688—28no—
275#686—28no—
276#686—28no—
277#685—24no—
278#685—24no—
279#685—24no—
280#685—24no—
281C4⋊Dic5—21no—
282C4⋊Dic5—21no—
283C4⋊Dic5C2412yes—
284C4⋊Dic5C2412yes—
285#683—24no—
286#683—24no—
287#681—28no—
288C2×#168—22no—
289C2×#168—22no—
290C2×#168—28no—
291C2×#168#4114yes—
292C2×#168#4114yes—
293C2×#168C2412yes—
294C2×#168C2412yes—
295C2×#168C2412yes—
296C2×#168C2412yes—
297C22×SD16—51no—
298C22×SD16—51no—
299C22×D8—51no—
300C22×D8—51no—
301C22×M16—51no—
302C23×C8—51no—
303#542—24no—
304#542C2×D518yescomplemented
305#540—58no—
306#540—104no—
307C2×C4⋊Q8C2×D511yescharacteristic
308C2×#127—51no—
309C2×#126—21no—
310C2×#125—51no—
311C2×#124—21no—
312C2×#124C2×D511yescharacteristic
313C2×#123—21no—
314C2×#123—101no—
315C2×#123—101no—
316C2×C22⋊Q8—21no—
317C2×C22⋊Q8C2×D511yescharacteristic
318C2×#121—51no—
319C2×#121—51no—
320C2×#121—101no—
321C2×#121—101no—
322C2×#121C2×D511yescharacteristic
323C2×C4×Q8C2×D511yescharacteristic
324C2×C4×D4—51no—
325C2×C4×D4—51no—
326C2×C4×D4C2×D511yescharacteristic
327C2×#117C2×D511yescharacteristic
328#501—58no—
329#496—58no—
330#488—58no—
331#486—58no—
332#469—58no—
333#468—58no—
334#466—58no—
335#465—58no—
336#442—58no—
337#440—58no—
338C4×SD16—58no—
339C4×D8—58no—
340C2×#107—51no—
341C2×#107—51no—
342C2×#106—51no—
343C2×#106—51no—
344C2×#103—51no—
345C2×#103—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102—51no—
349C2×#102—51no—
350C2×#102—51no—
351C2×#102—51no—
352#405—58no—
353C2×#97—51no—
354C2×#97—51no—
355C2×C4×C8—51no—
356C2×C4×C8—51no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—42no—
362C23×C5—42no—
363C23×C5—42no—
364C23×C5C22×D412yes—
365C23×C5C22×D411yescharacteristic
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—42no—
369C22×D5—42no—
370C22×D5—42no—
371C22×D5—42no—
372C22×D5—42no—
373C22×D5—42no—
374C5×Q8—22no—
375C5×Q8—22no—
376C5×Q8—42no—
377C5×Q8—84no—
378C5×D4—22no—
379C5×D4—22no—
380C5×D4—42no—
381C5×D4—84no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—24no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—42no—
394C2×C4×C5—42no—
395C2×C4×C5—42no—
396C2×C4×C5—84no—
397C2×C4×C5C22×D412yes—
398C2×C4×C5C22×D412yes—
399C2×C4×C5C22×D412yes—
400C2×C4×C5C22×D412yes—
401C2×C4×C5C22×D412yes—
402C2×C4×C5C22×D411yescharacteristic
403C2×C4×C5C2×#4112yes—
404C2×C4×C5C2×#4112yes—
405C2×C4×C5C2511yescharacteristic
406C22⋊D5—84no—
407C22⋊D5—84no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—42no—
411C2×Dic5—42no—
412D20—22no—
413D20—22no—
414D20—22no—
415D20—22no—
416D20—42no—
417D20—42no—
418D20—84no—
419D20—84no—
420C4×D5—84no—
421C4×D5—84no—
422#168—22no—
423#168—22no—
424#168C2×#4114yes—
425#168C2×#4114yes—
426C22×Q8—21no—
427C22×Q8C22×D511yescharacteristic
428C22×D4—21no—
429C22×D4—51no—
430C22×D4—51no—
431C22×D4—101no—
432C22×D4—101no—
433C22×D4—101no—
434C22×D4—101no—
435C22×D4C22×D511yescharacteristic
436C23×C4—21no—
437C23×C4—101no—
438C23×C4—101no—
439C23×C4C22×D511yescharacteristic
440C2×SD16—54no—
441C2×SD16—54no—
442C2×SD16—104no—
443C2×SD16—104no—
444C2×D8—54no—
445C2×D8—54no—
446C2×D8—104no—
447C2×D8—104no—
448C2×M16—54no—
449C2×M16—104no—
450C22×C8—51no—
451C22×C8—51no—
452C22×C8—51no—
453C22×C8—54no—
454C22×C8—51no—
455C22×C8—104no—
456C4⋊Q8—22no—
457C4⋊Q8C22×D514yes—
458#127—54no—
459#127—102no—
460#126—28no—
461#125—54no—
462#125—102no—
463#124—28no—
464#124—22no—
465#124C22×D514yes—
466#123—28no—
467#123—108no—
468#123—108no—
469C22⋊Q8—22no—
470C22⋊Q8—28no—
471C22⋊Q8C22×D514yes—
472#121—22no—
473#121—54no—
474#121—54no—
475#121—102no—
476#121—102no—
477#121—108no—
478#121—108no—
479#121C22×D514yes—
480C4×Q8—22no—
481C4×Q8C22×D514yes—
482C4×D4—22no—
483C4×D4—54no—
484C4×D4—54no—
485C4×D4—102no—
486C4×D4—102no—
487C4×D4C22×D514yes—
488#117C22⋊D514yes—
489#117C22×D514yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—51no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—101no—
496C2×C4⋊C4—101no—
497C2×C4⋊C4C22⋊D511yescharacteristic
498C2×C4⋊C4C22⋊D511yescharacteristic
499C2×C4⋊C4C22×D511yescharacteristic
500C2×C4⋊C4C22×D511yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—101no—
507C2×C22⋊C4—101no—
508C2×C22⋊C4—101no—
509C2×C22⋊C4—101no—
510C2×C22⋊C4C22⋊D511yescharacteristic
511C2×C22⋊C4C22⋊D511yescharacteristic
512C2×C42—21no—
513C2×C42C22×D511yescharacteristic
514C2×C42C22×D511yescharacteristic
515#107—54no—
516#107—54no—
517#106—54no—
518#106—54no—
519#103—54no—
520#103—54no—
521#102—54no—
522#102—54no—
523#102—54no—
524#102—54no—
525#102—54no—
526#102—54no—
527#97—54no—
528#97—54no—
529C4×C8—54no—
530C4×C8—54no—
531C22×C5—22no—
532C22×C5—22no—
533C22×C5—22no—
534C22×C5—44no—
535C22×C5—42no—
536C22×C5—42no—
537C22×C5—42no—
538C22×C5—84no—
539C22×C5#53212yes—
540C22×C5#57612yes—
541C22×C5#57712yes—
542C22×C5C23×D411yescharacteristic
543C2×D5—42no—
544C2×D5—42no—
545C2×D5—42no—
546C2×D5—42no—
547C2×D5—42no—
548C2×D5—42no—
549C2×D5—84no—
550C2×D5—84no—
551C4×C5—22no—
552C4×C5—22no—
553C4×C5—22no—
554C4×C5—22no—
555C4×C5—22no—
556C4×C5—42no—
557C4×C5—42no—
558C4×C5—42no—
559C4×C5#53212yes—
560C4×C5C22×#4111yescharacteristic
561C4×C5C22×#4111yescharacteristic
562Dic5—42no—
563Dic5—42no—
564C24—21no—
565C24—101no—
566C24—101no—
567C24C2×C22⋊D511yescharacteristic
568C2×Q8—21no—
569C2×Q8—24no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—82no—
573C2×Q8C23×D512yes—
574C2×D4—24no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—52no—
579C2×D4—52no—
580C2×D4—82no—
581C2×D4—104no—
582C2×D4—104no—
583C2×D4—102no—
584C2×D4—102no—
585C2×D4—102no—
586C2×D4—102no—
587C2×D4—101no—
588C2×D4—101no—
589C2×D4—104no—
590C2×D4—104no—
591C2×D4—402no—
592C2×D4—402no—
593C2×D4—402no—
594C2×D4—402no—
595C2×D4C23×D512yes—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—82no—
603C22×C4—101no—
604C22×C4—101no—
605C22×C4—104no—
606C22×C4—104no—
607C22×C4—402no—
608C22×C4—402no—
609C22×C4C2×C22⋊D512yes—
610C22×C4C2×C22⋊D511yescharacteristic
611C22×C4C2×C22⋊D511yescharacteristic
612C22×C4C2×C22⋊D511yescharacteristic
613C22×C4C2×C22⋊D511yescharacteristic
614C22×C4C2×C22⋊D511yescharacteristic
615C22×C4C23×D512yes—
616C22×C4C23×D511yescharacteristic
617SD16—108no—
618SD16—108no—
619D8—108no—
620D8—108no—
621M16—108no—
622C2×C8—54no—
623C2×C8—54no—
624C2×C8—52no—
625C2×C8—52no—
626C2×C8—52no—
627C2×C8—52no—
628C2×C8—108no—
629C2×C8—102no—
630C2×C8—102no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—52no—
637C4⋊C4—52no—
638C4⋊C4—101no—
639C4⋊C4—101no—
640C4⋊C4—104no—
641C4⋊C4—104no—
642C4⋊C4C2×C22⋊D514yes—
643C4⋊C4C2×C22⋊D514yes—
644C4⋊C4C23×D512yes—
645C4⋊C4C23×D512yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—104no—
652C22⋊C4—104no—
653C22⋊C4—104no—
654C22⋊C4—104no—
655C22⋊C4C2×C22⋊D514yes—
656C22⋊C4C2×C22⋊D514yes—
657C42—24no—
658C42C2×C22⋊D512yes—
659C42C2×C22⋊D512yes—
660C42C23×D512yes—
661C42C23×D512yes—
662C2×C5—42no—
663C2×C5—82no—
664C2×C5#317914yescomplemented
665C2×C5C2×#53211yescharacteristic
666C2×C5C2×#57611yescharacteristic
667C2×C5C2×#57711yescharacteristic
668D5—82no—
669D5—82no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—102no—
678C23—102no—
679C23—202no—
680C23—202no—
681C23—202no—
682C23—202no—
683C23—202no—
684C23—202no—
685C23C22×C22⋊D512yes—
686C23C22×C22⋊D511yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—42no—
690Q8—84no—
691D4—22no—
692D4—22no—
693D4—42no—
694D4—84no—
695D4—102no—
696D4—102no—
697D4—102no—
698D4—102no—
699D4—202no—
700D4—202no—
701D4—404no—
702D4—404no—
703D4—404no—
704D4—404no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—84no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—202no—
723C2×C4—202no—
724C2×C4—404no—
725C2×C4—404no—
726C2×C4D5×#4112yes—
727C2×C4D5×#4112yes—
728C2×C4C22×C22⋊D512yes—
729C2×C4C22×C22⋊D512yes—
730C2×C4C22×C22⋊D512yes—
731C2×C4C22×C22⋊D512yes—
732C2×C4C22×C22⋊D512yes—
733C2×C4C22×C22⋊D511yescharacteristic
734C2×C4C24×D511yescharacteristic
735C8—54no—
736C8—54no—
737C8—102no—
738C8—102no—
739C5C2×#317911yescharacteristic, complemented, Sylow
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—202no—
749C22—202no—
750C22—202no—
751C22—202no—
752C22—202no—
753C22—202no—
754C22—404no—
755C22—404no—
756C22#6616612yes—
757C22#6616912yes—
758C22#6617112yes—
759C22C23×C22⋊D511yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—202no—
769C4—202no—
770C4#6616612yes—
771C4C2×D5×#4111yescharacteristic
772C4C2×D5×#4111yescharacteristic
773C2—42no—
774C2—82no—
775C2—402no—
776C2—402no—
777C2#1061519014yesdirect product factor
778C2C2×#6616611yescharacteristic
779C2C2×#6616911yescharacteristic
780C2C2×#6617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#542C2
socleC23×C5C22×D4
hypercenterC2×#542D5
hypocenterC5C2×#3179
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×C5×#542C2semidirect
2. C2×#65869C2semidirect
3. #10615190C2direct (N × H)
4. C2×#65369C2semidirect
5. C2×#65377C2semidirect
6. C2×#65347C2semidirect
7. C2×#65345C2semidirect
8. C2×#65338C2semidirect
9. C2×#65337C2semidirect
10. C2×#65328C2semidirect
11. C2×#65327C2semidirect
12. C2×#65315C2semidirect
13. C2×C4×#688C2semidirect
14. C2×#65303C2semidirect
15. C2×C4×#686C2semidirect
16. C2×#65286C2semidirect
18. C5×#542C22semidirect
39. #65869C22semidirect
52. #65377C22semidirect
53. #65369C22semidirect
54. #65347C22semidirect
55. #65345C22semidirect
56. #65338C22semidirect
57. #65337C22semidirect
58. #65328C22semidirect
59. #65327C22semidirect
60. #65315C22semidirect
61. C4×#688C22semidirect
62. #65303C22semidirect
63. C4×#686C22semidirect
64. #65286C22semidirect
183. C2×#542D5semidirect
304. #542C2×D5semidirect
664. C2×C5#3179semidirect
739. C5C2×#3179semidirect
777. C2#10615190direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5422
C2×#658692
#106151902
C2×#653692
C2×#653772
C2×#653472
C2×#653452
C2×#653382
C2×#653372
C2×#653282
C2×#653272
C2×#653152
C2×C4×#6882
C2×#653032
C2×C4×#6862
C2×#652862
C2×#31795