Finite Group Databasebeta

← C2×#10615168 #12972204

Subgroups — C2×#10615168 #12972204

Order 1280.

1946 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×#540C211yesmaximal, characteristic, complemented
2C2×#65868C211yesmaximal, characteristic, complemented
3#10615168C2116yesmaximal, direct product factor
4C2×#65364C211yesmaximal, characteristic, complemented
5C2×#65361C211yesmaximal, characteristic, complemented
6C2×#65352C211yesmaximal, characteristic, complemented
7C2×#65355C211yesmaximal, characteristic, complemented
8C2×#65328C211yesmaximal, characteristic, complemented
9C2×#65331C211yesmaximal, characteristic, complemented
10C2×#65327C211yesmaximal, characteristic, complemented
11C2×#65330C211yesmaximal, characteristic, complemented
12C2×#65305C211yesmaximal, characteristic, complemented
13C2×#65305C211yesmaximal, characteristic, complemented
14C2×#65297C211yesmaximal, characteristic, complemented
15C2×#65296C211yesmaximal, characteristic, complemented
16C2×#65288C211yesmaximal, characteristic, complemented
17C5×#540—24no—
18C5×#540C2218yescomplemented
19C2×C5×#127C2211yescharacteristic
20C2×C5×#125C2211yescharacteristic
21C2×C5×#123—21no—
22C2×C5×#123—21no—
23C2×C5×#121—21no—
24C2×C5×#121—21no—
25C2×C5×#121C2211yescharacteristic
26C2×C5×#121C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C22×#687C2211yescharacteristic
31C22×#687C2211yescharacteristic
32C22×#686C2211yescharacteristic
33C22×#686C2211yescharacteristic
34C2×#4076C2211yescharacteristic
35C2×#4070C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C23×#168C2211yescharacteristic
38#65868—24no—
39#65868C2218yescomplemented
40C2×#4044—21no—
41C2×#4042—21no—
42C2×#4031—21no—
43C2×#4029—21no—
44C2×#4021C2211yescharacteristic
45C2×C4×D20C2211yescharacteristic
46C2×#4015C2211yescharacteristic
47C2×C4×Dic10C2211yescharacteristic
48C2×#3964C2211yescharacteristic
49C2×#3964C2211yescharacteristic
50C2×#3964C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52#65364C2218yescomplemented
53#65361C2218yescomplemented
54#65355C2218yescomplemented
55#65352C2218yescomplemented
56#65331C2218yescomplemented
57#65330C2218yescomplemented
58#65328C2218yescomplemented
59#65327C2218yescomplemented
60#65305C2218yescomplemented
61#65305C2218yescomplemented
62#65297C2218yescomplemented
63#65296C2218yescomplemented
64#65288C2218yescomplemented
65C2×#3942C2211yescharacteristic
66C2×#3942C2211yescharacteristic
67C2×#3941C2211yescharacteristic
68C2×#3941C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71C2×#3939C2211yescharacteristic
72C2×#3939C2211yescharacteristic
73C2×C4⋊#168C2211yescharacteristic
74C2×C4⋊#168C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×C4⋊#168C2211yescharacteristic
77C2×#3257—51nomaximal, Sylow
78C22×C5×D4—21no—
79C22×C5×D4—21no—
80C22×C5×D4—21no—
81C22×C5×D4—21no—
82C22×C5×D4C2311yescharacteristic
83C22×C5×D4C2311yescharacteristic
84C23×C4×C5—21no—
85C23×C4×C5—21no—
86C23×C4×C5C2311yescharacteristic
87C22×C22⋊D5—21no—
88C22×D20C2311yescharacteristic
89C22×C4×D5—21no—
90C22×Dic10—21no—
91C22×Dic10C2311yescharacteristic
92C5×#127—22no—
93C5×#127C2314yes—
94C5×#125—22no—
95C5×#125C2314yes—
96C5×#123—28no—
97C5×#123—28no—
98C5×#121—22no—
99C5×#121—22no—
100C5×#121—28no—
101C5×#121—28no—
102C5×#121C2314yes—
103C5×#121C2314yes—
104C4×C5×D4—22no—
105C4×C5×D4—22no—
106C4×C5×D4C2314yes—
107C4×C5×D4C2314yes—
108C5×#117D414yes—
109C5×#117C2314yes—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4D411yescharacteristic
113C2×C5×C4⋊C4D411yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4D411yescharacteristic
121C2×C5×C22⋊C4D411yescharacteristic
122C2×C42×C5C2311yescharacteristic
123C2×C42×C5C2311yescharacteristic
124C2×C22⋊Dic5—21no—
125C2×#687—42no—
126C2×#687—42no—
127C2×#687C2314yes—
128C2×#687C2314yes—
129C2×#686—42no—
130C2×#686—42no—
131C2×#686C2314yes—
132C2×#686C2314yes—
133#4076—22no—
134#4076C2314yes—
135C2×#685—21no—
136C2×#685—21no—
137C2×#685—21no—
138C2×#685—21no—
139C2×C4⋊Dic5—21no—
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142#4070—22no—
143#4070C2314yes—
144C2×#683—21no—
145C2×#683—21no—
146C2×C4×Dic5—21no—
147C2×#681—42no—
148C2×#681C2314yes—
149C22×#168—42no—
150C22×#168C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C22×#168C2311yescharacteristic
154C22×#168C2314yes—
155#4044—28no—
156#4042—28no—
157#4031—28no—
158#4029—28no—
159#4021—22no—
160#4021C2314yes—
161C4×D20—22no—
162C4×D20C2314yes—
163#4015—22no—
164#4015C2314yes—
165C4×Dic10—22no—
166C4×Dic10C2314yes—
167#3964C2314yes—
168#3964C2314yes—
169#3964C2314yes—
170#3964C2314yes—
171#3942C2314yes—
172#3942C2314yes—
173#3941C2314yes—
174#3941C2314yes—
175#3940C2314yes—
176#3940C2314yes—
177#3939C2314yes—
178#3939C2314yes—
179C4⋊#168C2314yes—
180C4⋊#168C2314yes—
181C4⋊#168C2314yes—
182C4⋊#168C2314yes—
183C2×#542—51no—
184C2×#540D511yescharacteristic, complemented
185#3257—516no—
186C2×#479—51no—
187C2×#478—51no—
188C2×#476—51no—
189C2×#474—51no—
190C2×#469—51no—
191C2×#468—51no—
192C2×#466—51no—
193C2×#465—51no—
194C2×#460—51no—
195C2×#463—51no—
196C2×#463—51no—
197C2×#459—51no—
198C2×#424—51no—
199C24×C5—21no—
200C24×C5—21no—
201C24×C5C2×D411yescharacteristic
202C23×D5—21no—
203C2×C5×D4—24no—
204C2×C5×D4—24no—
205C2×C5×D4—21no—
206C2×C5×D4—21no—
207C2×C5×D4—24no—
208C2×C5×D4—24no—
209C2×C5×D4—22no—
210C2×C5×D4—22no—
211C2×C5×D4—22no—
212C2×C5×D4—22no—
213C2×C5×D4—82no—
214C2×C5×D4—82no—
215C2×C5×D4—82no—
216C2×C5×D4—82no—
217C2×C5×D4C2412yes—
218C2×C5×D4C2412yes—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—24no—
224C22×C4×C5—24no—
225C22×C4×C5—82no—
226C22×C4×C5—82no—
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2×D411yescharacteristic
232C22×C4×C5C2×D412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2411yescharacteristic
235C2×C22⋊D5—24no—
236C2×C22⋊D5—82no—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—21no—
240C2×D20—22no—
241C2×D20—22no—
242C2×D20—21no—
243C2×D20C2412yes—
244C2×C4×D5—24no—
245C2×C4×D5—82no—
246C2×Dic10—22no—
247C2×Dic10—22no—
248C2×Dic10—21no—
249C2×Dic10—24no—
250C2×Dic10—82no—
251C2×Dic10C2412yes—
252C5×C4⋊C4—24no—
253C5×C4⋊C4—24no—
254C5×C4⋊C4—21no—
255C5×C4⋊C4—21no—
256C5×C4⋊C4C2×D414yes—
257C5×C4⋊C4C2×D414yes—
258C5×C4⋊C4C2412yes—
259C5×C4⋊C4C2412yes—
260C5×C22⋊C4—24no—
261C5×C22⋊C4—24no—
262C5×C22⋊C4—24no—
263C5×C22⋊C4—24no—
264C5×C22⋊C4C2×D414yes—
265C5×C22⋊C4C2×D414yes—
266C42×C5C2×D412yes—
267C42×C5C2×D412yes—
268C42×C5C2412yes—
269C42×C5C2412yes—
270C22⋊Dic5—24no—
271#687—44no—
272#687—44no—
273#686—44no—
274#686—44no—
275#685—24no—
276#685—24no—
277#685—24no—
278#685—24no—
279C4⋊Dic5—21no—
280C4⋊Dic5—21no—
281C4⋊Dic5—24no—
282C4⋊Dic5C2412yes—
283C4⋊Dic5C2412yes—
284#683—24no—
285#683—24no—
286C4×Dic5—24no—
287#681—44no—
288C2×#168—22no—
289C2×#168—22no—
290C2×#168—22no—
291C2×#168—22no—
292C2×#168—44no—
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—58no—
304#542—104no—
305#540—24no—
306#540C2×D518yescomplemented
307C2×C4⋊Q8—51no—
308C2×#127C2×D511yescharacteristic
309C2×#126—101no—
310C2×#125C2×D511yescharacteristic
311C2×#124—51no—
312C2×#124—101no—
313C2×#123—21no—
314C2×#123—21no—
315C2×#123—101no—
316C2×C22⋊Q8—51no—
317C2×C22⋊Q8—101no—
318C2×#121—21no—
319C2×#121—21no—
320C2×#121—51no—
321C2×#121C2×D511yescharacteristic
322C2×#121C2×D511yescharacteristic
323C2×C4×Q8—51no—
324C2×C4×D4—51no—
325C2×C4×D4C2×D511yescharacteristic
326C2×C4×D4C2×D511yescharacteristic
327C2×#117C2×D511yescharacteristic
328#479—58no—
329#478—58no—
330#476—58no—
331#474—58no—
332#469—58no—
333#468—58no—
334#466—58no—
335#465—58no—
336#463—58no—
337#463—58no—
338#460—58no—
339#459—58no—
340C2×#107—51no—
341C2×#107—51no—
342C2×#106—51no—
343C2×#106—51no—
344#424—58no—
345C2×C4⋊C8—51no—
346C2×C4⋊C8—51no—
347C2×C4⋊C8—51no—
348C2×C4⋊C8—51no—
349C2×#103—51no—
350C2×#103—51no—
351C2×#102—51no—
352C2×#102—51no—
353C2×#102—51no—
354C2×#102—51no—
355C2×#102—51no—
356C2×#102—51no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—42no—
363C23×C5—42no—
364C23×C5—42no—
365C23×C5—42no—
366C23×C5—42no—
367C23×C5—42no—
368C23×C5C22×D412yes—
369C23×C5C22×D411yescharacteristic
370C22×D5—22no—
371C22×D5—42no—
372C22×D5—42no—
373C22×D5—42no—
374C5×D4—22no—
375C5×D4—22no—
376C5×D4—22no—
377C5×D4—22no—
378C5×D4—42no—
379C5×D4—42no—
380C5×D4—84no—
381C5×D4—84no—
382C5×D4—84no—
383C5×D4—84no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—24no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—42no—
395C2×C4×C5—42no—
396C2×C4×C5—84no—
397C2×C4×C5—84no—
398C2×C4×C5C22×D412yes—
399C2×C4×C5C22×D412yes—
400C2×C4×C5C22×D412yes—
401C2×C4×C5C22×D412yes—
402C2×C4×C5C22×D412yes—
403C2×C4×C5C22×D411yescharacteristic
404C2×C4×C5H(5,𝔽2)12yes—
405C2×C4×C52−1+412yes—
406C2×C4×C5C2511yescharacteristic
407C22⋊D5—84no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—42no—
412C2×Dic5—42no—
413C2×Dic5—42no—
414D20—22no—
415D20—22no—
416D20—42no—
417C4×D5—84no—
418Dic10—22no—
419Dic10—22no—
420Dic10—42no—
421Dic10—84no—
422#168—22no—
423#168—22no—
424#168—22no—
425#168—22no—
426C22×Q8—51no—
427C22×Q8—101no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—21no—
432C22×D4—51no—
433C22×D4—101no—
434C22×D4C22×D511yescharacteristic
435C22×D4C22×D511yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—101no—
439C23×C4C22×D511yescharacteristic
440C2×SD16—54no—
441C2×SD16—54no—
442C2×SD16—202no—
443C2×SD16—202no—
444C2×D8—54no—
445C2×D8—54no—
446C2×D8—202no—
447C2×D8—202no—
448C2×M16—54no—
449C2×M16—202no—
450C22×C8—51no—
451C22×C8—51no—
452C22×C8—51no—
453C22×C8—51no—
454C22×C8—54no—
455C22×C8—202no—
456C4⋊Q8—54no—
457C4⋊Q8—102no—
458#127—22no—
459#127C22×D514yes—
460#126—108no—
461#125—22no—
462#125C22×D514yes—
463#124—54no—
464#124—108no—
465#124—102no—
466#123—28no—
467#123—28no—
468#123—108no—
469C22⋊Q8—54no—
470C22⋊Q8—102no—
471C22⋊Q8—108no—
472#121—22no—
473#121—22no—
474#121—28no—
475#121—28no—
476#121—54no—
477#121—102no—
478#121C22×D514yes—
479#121C22×D514yes—
480C4×Q8—54no—
481C4×Q8—102no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—54no—
485C4×D4—102no—
486C4×D4C22×D514yes—
487C4×D4C22×D514yes—
488#117C22⋊D514yes—
489#117C22×D514yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—51no—
493C2×C4⋊C4—51no—
494C2×C4⋊C4—101no—
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—101no—
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—101no—
513C2×C42C22×D511yescharacteristic
514C2×C42C22×D511yescharacteristic
515#107—54no—
516#107—54no—
517#106—54no—
518#106—54no—
519C4⋊C8—54no—
520C4⋊C8—54no—
521C4⋊C8—54no—
522C4⋊C8—54no—
523#103—54no—
524#103—54no—
525#102—54no—
526#102—54no—
527#102—54no—
528#102—54no—
529#102—54no—
530#102—54no—
531C22×C5—22no—
532C22×C5—22no—
533C22×C5—22no—
534C22×C5—44no—
535C22×C5—42no—
536C22×C5—42no—
537C22×C5—42no—
538C22×C5—42no—
539C22×C5—42no—
540C22×C5—42no—
541C22×C5—84no—
542C22×C5—84no—
543C22×C5#53712yes—
544C22×C5#57612yes—
545C22×C5#57712yes—
546C22×C5C23×D411yescharacteristic
547C2×D5—42no—
548C2×D5—42no—
549C2×D5—42no—
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#53712yes—
559C4×C5C2×H(5,𝔽2)11yescharacteristic
560C4×C5C2×2−1+411yescharacteristic
561Dic5—42no—
562Dic5—42no—
563Dic5—42no—
564C24—21no—
565C24—21no—
566C24—101no—
567C24C2×C22⋊D511yescharacteristic
568C2×Q8—52no—
569C2×Q8—101no—
570C2×Q8—104no—
571C2×Q8—102no—
572C2×Q8—102no—
573C2×Q8—402no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—52no—
585C2×D4—82no—
586C2×D4—82no—
587C2×D4—82no—
588C2×D4—82no—
589C2×D4—104no—
590C2×D4—102no—
591C2×D4—102no—
592C2×D4—101no—
593C2×D4—402no—
594C2×D4C23×D512yes—
595C2×D4C23×D512yes—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—104no—
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—204no—
618SD16—204no—
619D8—204no—
620D8—204no—
621M16—204no—
622C2×C8—52no—
623C2×C8—52no—
624C2×C8—52no—
625C2×C8—52no—
626C2×C8—102no—
627C2×C8—102no—
628C2×C8—102no—
629C2×C8—102no—
630C2×C8—204no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—52no—
636C4⋊C4—52no—
637C4⋊C4—101no—
638C4⋊C4—101no—
639C4⋊C4—104no—
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—104no—
651C22⋊C4—104no—
652C22⋊C4—104no—
653C22⋊C4—104no—
654C22⋊C4—104no—
655C22⋊C4C2×C22⋊D514yes—
656C22⋊C4C2×C22⋊D514yes—
657C42—104no—
658C42C2×C22⋊D512yes—
659C42C2×C22⋊D512yes—
660C42C23×D512yes—
661C42C23×D512yes—
662C2×C5—42no—
663C2×C5—82no—
664C2×C5—82no—
665C2×C5#325714yescomplemented
666C2×C5C2×#53711yescharacteristic
667C2×C5C2×#57611yescharacteristic
668C2×C5C2×#57711yescharacteristic
669D5—82no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—102no—
682C23—202no—
683C23—202no—
684C23—202no—
685C23C22×C22⋊D512yes—
686C23C22×C22⋊D511yescharacteristic
687Q8—102no—
688Q8—102no—
689Q8—202no—
690Q8—404no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—42no—
697D4—84no—
698D4—84no—
699D4—84no—
700D4—84no—
701D4—102no—
702D4—102no—
703D4—202no—
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—42no—
716C2×C4—42no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4—102no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—202no—
723C2×C4—202no—
724C2×C4—202no—
725C2×C4—404no—
726C2×C4#414912yes—
727C2×C4#415012yes—
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—102no—
736C8—102no—
737C8—102no—
738C8—102no—
739C5C2×#325711yescharacteristic, complemented, Sylow
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—84no—
751C22—84no—
752C22—202no—
753C22—202no—
754C22—202no—
755C22—404no—
756C22#6616712yes—
757C22#6616912yes—
758C22#6617012yes—
759C22C23×C22⋊D511yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—202no—
768C4—202no—
769C4—202no—
770C4#6616712yes—
771C4C2×#414911yescharacteristic
772C4C2×#415011yescharacteristic
773C2—42no—
774C2—82no—
775C2—82no—
776C2—402no—
777C2#1061516814yesdirect product factor
778C2C2×#6616711yescharacteristic
779C2C2×#6616911yescharacteristic
780C2C2×#6617011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#540C2
socleC23×C5C22×D4
hypercenterC2×#540D5
hypocenterC5C2×#3257
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×C5×#540C2semidirect
2. C2×#65868C2semidirect
3. #10615168C2direct (N × H)
4. C2×#65364C2semidirect
5. C2×#65361C2semidirect
6. C2×#65352C2semidirect
7. C2×#65355C2semidirect
8. C2×#65328C2semidirect
9. C2×#65331C2semidirect
10. C2×#65327C2semidirect
11. C2×#65330C2semidirect
12. C2×#65305C2semidirect
13. C2×#65305C2semidirect
14. C2×#65297C2semidirect
15. C2×#65296C2semidirect
16. C2×#65288C2semidirect
18. C5×#540C22semidirect
39. #65868C22semidirect
52. #65364C22semidirect
53. #65361C22semidirect
54. #65355C22semidirect
55. #65352C22semidirect
56. #65331C22semidirect
57. #65330C22semidirect
58. #65328C22semidirect
59. #65327C22semidirect
60. #65305C22semidirect
61. #65305C22semidirect
62. #65297C22semidirect
63. #65296C22semidirect
64. #65288C22semidirect
184. C2×#540D5semidirect
306. #540C2×D5semidirect
665. C2×C5#3257semidirect
739. C5C2×#3257semidirect
777. C2#10615168direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5402
C2×#658682
#106151682
C2×#653642
C2×#653612
C2×#653522
C2×#653552
C2×#653282
C2×#653312
C2×#653272
C2×#653302
C2×#653052
C2×#652972
C2×#652962
C2×#652882
C2×#32575