Finite Group Databasebeta

← C2×#10615343 #12977972

Subgroups — C2×#10615343 #12977972

Order 1280.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#553C211yesmaximal, characteristic
2C2×#65875C211yesmaximal, characteristic, complemented
3#10615343C2116yesmaximal, direct product factor
4C2×#65352C211yesmaximal, characteristic, complemented
5C2×#65353C211yesmaximal, characteristic, complemented
6C2×#65331C211yesmaximal, characteristic, complemented
7C2×#65331C211yesmaximal, characteristic, complemented
8C2×#65323C211yesmaximal, characteristic, complemented
9C2×#65324C211yesmaximal, characteristic, complemented
10C2×C4×#687C211yesmaximal, characteristic, complemented
11C2×#65301C211yesmaximal, characteristic, complemented
12C2×#65298C211yesmaximal, characteristic, complemented
13C2×#65285C211yesmaximal, characteristic, complemented
14C2×#65284C211yesmaximal, characteristic, complemented
15C2×#65260C211yesmaximal, characteristic, complemented
16C2×#65253C211yesmaximal, characteristic, complemented
17C5×#553—24no—
18C5×#553C2218yes—
19C2×C5×#126—21no—
20C2×C5×#125C2211yescharacteristic
21C2×C5×#123—21no—
22C2×C5×#121—21no—
23C2×C5×#121C2211yescharacteristic
24C2×C5×#121C2211yescharacteristic
25C2×C4×C5×D4—21no—
26C2×C4×C5×D4C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C5×#117C2211yescharacteristic
29C22×C5×C4⋊C4C2211yescharacteristic
30C2×#4081—21no—
31C22×#687C2211yescharacteristic
32C2×#4072C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C2×#4070C2211yescharacteristic
35C2×#4070C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C22×#681C2211yescharacteristic
38#65875—24no—
39#65875C2218yescomplemented
40C2×#4035—21no—
41C2×#4025—21no—
42C2×#4023—21no—
43C2×#4016C2211yescharacteristic
44C2×C4×Dic10C2211yescharacteristic
45C2×#3964C2211yescharacteristic
46C2×#3964C2211yescharacteristic
47C2×#3964C2211yescharacteristic
48C2×C22⋊#168C2211yescharacteristic
49C2×C22⋊#168C2211yescharacteristic
50#65353C2218yescomplemented
51#65352C2218yescomplemented
52#65331C2218yescomplemented
53#65331C2218yescomplemented
54#65324C2218yescomplemented
55#65323C2218yescomplemented
56C4×#687C2218yescomplemented
57#65301C2218yescomplemented
58#65298C2218yescomplemented
59#65285C2218yescomplemented
60#65284C2218yescomplemented
61#65260C2218yescomplemented
62C2×#3942C2211yescharacteristic
63C2×#3942C2211yescharacteristic
64C2×#3942C2211yescharacteristic
65#65253C2218yescomplemented
66C2×#3940C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71C2×#3939C2211yescharacteristic
72C2×#3939C2211yescharacteristic
73C2×#3939C2211yescharacteristic
74C2×#3939C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3351—51nomaximal, Sylow
78C22×C5×D4—21no—
79C22×C5×D4—21no—
80C22×C5×D4D411yescharacteristic
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5—21no—
83C23×C4×C5—21no—
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×Dic5—21no—
87C22×Dic10C2311yescharacteristic
88C5×#126—28no—
89C5×#125—22no—
90C5×#125C2314yes—
91C5×#123—28no—
92C5×#121—28no—
93C5×#121—22no—
94C5×#121—22no—
95C5×#121C2314yes—
96C5×#121C2314yes—
97C4×C5×D4—28no—
98C4×C5×D4—22no—
99C4×C5×D4D414yes—
100C4×C5×D4C2314yes—
101C4×C5×D4C2314yes—
102C5×#117—22no—
103C5×#117C2314yes—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—22no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4D411yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2314yes—
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C22⋊C4—21no—
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4D411yescharacteristic
118C2×C5×C22⋊C4D411yescharacteristic
119C2×C42×C5—21no—
120C2×C42×C5C2311yescharacteristic
121C2×C22⋊Dic5—21no—
122C2×C22⋊Dic5—21no—
123C2×C22⋊Dic5—21no—
124#4081—28no—
125C2×#687—24no—
126C2×#687C2314yes—
127#4072—22no—
128#4072C2314yes—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5—22no—
131C2×C4⋊Dic5C2314yes—
132C2×C4⋊Dic5C2311yescharacteristic
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2311yescharacteristic
135#4070—22no—
136#4070—22no—
137#4070C2314yes—
138#4070C2314yes—
139C2×#683—21no—
140C2×#683—21no—
141C2×#683—21no—
142C2×#683—21no—
143C2×#683—21no—
144C2×C4×Dic5—21no—
145C2×C4×Dic5—21no—
146C2×#681—24no—
147C2×#681—24no—
148C2×#681C2314yes—
149C2×#681C2314yes—
150C22×#168C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C22×#168C2311yescharacteristic
154#4035—28no—
155#4025—28no—
156#4023—28no—
157#4016—22no—
158#4016C2314yes—
159C4×Dic10—22no—
160C4×Dic10C2314yes—
161#3964C2314yes—
162#3964C2314yes—
163#3964C2314yes—
164C22⋊#168C2314yes—
165C22⋊#168C2314yes—
166#3942C2314yes—
167#3942C2314yes—
168#3942C2314yes—
169#3940C2314yes—
170#3940C2314yes—
171#3940C2314yes—
172#3940C2314yes—
173#3940C2314yes—
174#3939C2314yes—
175#3939C2314yes—
176#3939C2314yes—
177#3939C2314yes—
178C4⋊#168C2314yes—
179C4×#168C2314yes—
180C2×#553D511yescharacteristic
181C2×#552—51no—
182#3351—516no—
183C2×#499—51no—
184C2×#481—51no—
185C2×#485—51no—
186C2×#482—51no—
187C2×#483—51no—
188C2×#479—51no—
189C2×#478—51no—
190C2×#468—51no—
191C2×#468—51no—
192C2×C4×SD16—51no—
193C2×#436—51no—
194C2×#428—51no—
195C2×#428—51no—
196C24×C5—21no—
197C24×C5C2×D411yescharacteristic
198C24×C5C2×D411yescharacteristic
199C2×C5×D4—24no—
200C2×C5×D4—24no—
201C2×C5×D4—21no—
202C2×C5×D4—22no—
203C2×C5×D4—22no—
204C2×C5×D4—42no—
205C2×C5×D4—44no—
206C2×C5×D4—82no—
207C2×C5×D4C2×D414yes—
208C2×C5×D4C2412yes—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—24no—
217C22×C4×C5—24no—
218C22×C4×C5—82no—
219C22×C4×C5—82no—
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D412yes—
225C22×C4×C5C2×D412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2411yescharacteristic
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—24no—
234C22×Dic5—44no—
235C2×Dic10—22no—
236C2×Dic10—22no—
237C2×Dic10—21no—
238C2×Dic10C2412yes—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—24no—
242C5×C4⋊C4—24no—
243C5×C4⋊C4—24no—
244C5×C4⋊C4—21no—
245C5×C4⋊C4C2×D414yes—
246C5×C4⋊C4C2412yes—
247C5×C4⋊C4C2412yes—
248C5×C4⋊C4C2412yes—
249C5×C22⋊C4—24no—
250C5×C22⋊C4—24no—
251C5×C22⋊C4—24no—
252C5×C22⋊C4—24no—
253C5×C22⋊C4C2×D414yes—
254C5×C22⋊C4C2×D414yes—
255C42×C5—24no—
256C42×C5C2×D412yes—
257C42×C5C2412yes—
258C22⋊Dic5—24no—
259C22⋊Dic5—24no—
260C22⋊Dic5—24no—
261#687—28no—
262C4⋊Dic5—21no—
263C4⋊Dic5—21no—
264C4⋊Dic5—21no—
265C4⋊Dic5—24no—
266C4⋊Dic5C2412yes—
267C4⋊Dic5C2412yes—
268C4⋊Dic5C2412yes—
269#683—24no—
270#683—24no—
271#683—24no—
272#683—24no—
273#683—24no—
274C4×Dic5—24no—
275C4×Dic5—24no—
276#681—28no—
277#681—28no—
278C2×#168—22no—
279C2×#168—22no—
280C2×#168—22no—
281C2×#168#4114yes—
282C2×#168C2412yes—
283C2×#168C2412yes—
284C2×#168C2412yes—
285C2×#168C2412yes—
286C22×SD16—51no—
287C22×M16—51no—
288C22×M16—51no—
289#553—24no—
290#553C2×D518yes—
291#552—58no—
292#552—104no—
293C2×#126—21no—
294C2×#126—101no—
295C2×#125—51no—
296C2×#125—101no—
297C2×#125C2×D511yescharacteristic
298C2×#123—21no—
299C2×#123—101no—
300C2×C22⋊Q8—51no—
301C2×C22⋊Q8—51no—
302C2×#121—21no—
303C2×#121C2×D511yescharacteristic
304C2×#121C2×D511yescharacteristic
305C2×C4×Q8—51no—
306C2×C4×D4—21no—
307C2×C4×D4C2×D511yescharacteristic
308C2×C4×D4C2×D511yescharacteristic
309C2×#117—51no—
310C2×#117—101no—
311C2×#117C2×D511yescharacteristic
312C22×C4⋊C4—51no—
313C22×C4⋊C4C2×D511yescharacteristic
314#499—58no—
315#485—58no—
316#483—58no—
317#482—58no—
318#481—58no—
319#479—58no—
320#478—58no—
321#468—58no—
322#468—58no—
323C4×SD16—58no—
324#436—58no—
325#428—58no—
326#428—58no—
327C2×#107—51no—
328C2×#107—51no—
329C2×#107—51no—
330C2×#107—51no—
331C2×#106—51no—
332C2×#106—51no—
333C2×#106—51no—
334C2×#106—51no—
335C2×#106—51no—
336C2×C4⋊C8—51no—
337C2×#103—51no—
338C2×#103—51no—
339C2×#103—51no—
340C2×#102—51no—
341C2×#102—51no—
342C2×#102—51no—
343C2×C22⋊C8—51no—
344C2×C22⋊C8—51no—
345C2×C4×C8—51no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—42no—
354C23×C5—42no—
355C23×C5—42no—
356C23×C5C22×D412yes—
357C23×C5C22×D412yes—
358C23×C5C22×D411yescharacteristic
359C5×D4—22no—
360C5×D4—22no—
361C5×D4—44no—
362C5×D4—48no—
363C5×D4—42no—
364C5×D4—84no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—24no—
370C2×C4×C5—24no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5—42no—
381C2×C4×C5—84no—
382C2×C4×C5—84no—
383C2×C4×C5C22×D412yes—
384C2×C4×C5C22×D412yes—
385C2×C4×C5C22×D412yes—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D411yescharacteristic
388C2×C4×C5C2×#4112yes—
389C2×C4×C52−1+412yes—
390C2×C4×C5C2511yescharacteristic
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—48no—
396C2×Dic5—42no—
397C2×Dic5—42no—
398C2×Dic5—42no—
399C2×Dic5—42no—
400Dic10—22no—
401Dic10—22no—
402Dic10—42no—
403#168—22no—
404#168—22no—
405#168—22no—
406#168C2×#4114yes—
407C22×Q8—51no—
408C22×D4—21no—
409C22×D4—21no—
410C22×D4C22⋊D511yescharacteristic
411C22×D4C22×D511yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—101no—
415C23×C4C22×D511yescharacteristic
416C23×C4C22×D511yescharacteristic
417C2×SD16—54no—
418C2×SD16—104no—
419C2×M16—54no—
420C2×M16—54no—
421C2×M16—104no—
422C2×M16—104no—
423C22×C8—51no—
424C22×C8—51no—
425C22×C8—51no—
426C22×C8—51no—
427#126—28no—
428#126—108no—
429#125—22no—
430#125—54no—
431#125—108no—
432#125—102no—
433#125C22×D514yes—
434#123—28no—
435#123—108no—
436C22⋊Q8—54no—
437C22⋊Q8—54no—
438C22⋊Q8—102no—
439C22⋊Q8—102no—
440#121—28no—
441#121—22no—
442#121—22no—
443#121C22×D514yes—
444#121C22×D514yes—
445C4×Q8—54no—
446C4×Q8—102no—
447C4×D4—28no—
448C4×D4—22no—
449C4×D4C22⋊D514yes—
450C4×D4C22×D514yes—
451C4×D4C22×D514yes—
452#117—22no—
453#117—54no—
454#117—102no—
455#117—108no—
456#117C22×D514yes—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—51no—
462C2×C4⋊C4—51no—
463C2×C4⋊C4—54no—
464C2×C4⋊C4—51no—
465C2×C4⋊C4—101no—
466C2×C4⋊C4—102no—
467C2×C4⋊C4—101no—
468C2×C4⋊C4—101no—
469C2×C4⋊C4—101no—
470C2×C4⋊C4—101no—
471C2×C4⋊C4—101no—
472C2×C4⋊C4C22⋊D511yescharacteristic
473C2×C4⋊C4C22×D511yescharacteristic
474C2×C4⋊C4C22×D511yescharacteristic
475C2×C4⋊C4C22×D514yes—
476C2×C4⋊C4C22×D511yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—101no—
482C2×C22⋊C4—101no—
483C2×C22⋊C4—101no—
484C2×C22⋊C4C22⋊D511yescharacteristic
485C2×C22⋊C4C22⋊D511yescharacteristic
486C2×C42—21no—
487C2×C42—101no—
488C2×C42—101no—
489C2×C42C22×D511yescharacteristic
490#107—54no—
491#107—54no—
492#107—54no—
493#107—54no—
494#106—54no—
495#106—54no—
496#106—54no—
497#106—54no—
498#106—54no—
499C4⋊C8—54no—
500#103—54no—
501#103—54no—
502#103—54no—
503#102—54no—
504#102—54no—
505#102—54no—
506C22⋊C8—54no—
507C22⋊C8—54no—
508C4×C8—54no—
509C22×C5—22no—
510C22×C5—22no—
511C22×C5—22no—
512C22×C5—22no—
513C22×C5—22no—
514C22×C5—22no—
515C22×C5—44no—
516C22×C5—44no—
517C22×C5—42no—
518C22×C5—42no—
519C22×C5—42no—
520C22×C5—84no—
521C22×C5#54712yes—
522C22×C5#57512yes—
523C22×C5#57712yes—
524C22×C5C23×D411yescharacteristic
525C4×C5—22no—
526C4×C5—22no—
527C4×C5—22no—
528C4×C5—22no—
529C4×C5—42no—
530C4×C5—42no—
531C4×C5—42no—
532C4×C5#54712yes—
533C4×C5C22×#4111yescharacteristic
534C4×C5C2×2−1+411yescharacteristic
535Dic5—42no—
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539C24—21no—
540C24C2×C22⋊D511yescharacteristic
541C24C2×C22⋊D511yescharacteristic
542C2×Q8—52no—
543C2×Q8—101no—
544C2×Q8—102no—
545C2×Q8—102no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—44no—
553C2×D4—82no—
554C2×D4C2×C22⋊D514yes—
555C2×D4C23×D512yes—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—82no—
566C22×C4—82no—
567C22×C4—104no—
568C22×C4—101no—
569C22×C4—101no—
570C22×C4—101no—
571C22×C4—101no—
572C22×C4—204no—
573C22×C4C2×C22⋊D512yes—
574C22×C4C2×C22⋊D512yes—
575C22×C4C2×C22⋊D511yescharacteristic
576C22×C4C2×C22⋊D511yescharacteristic
577C22×C4C2×C22⋊D511yescharacteristic
578C22×C4C2×C22⋊D511yescharacteristic
579C22×C4C23×D512yes—
580C22×C4C23×D512yes—
581C22×C4C23×D511yescharacteristic
582SD16—108no—
583M16—108no—
584M16—108no—
585C2×C8—54no—
586C2×C8—52no—
587C2×C8—52no—
588C2×C8—52no—
589C2×C8—52no—
590C2×C8—102no—
591C2×C8—102no—
592C2×C8—102no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—21no—
599C4⋊C4—52no—
600C4⋊C4—52no—
601C4⋊C4—52no—
602C4⋊C4—101no—
603C4⋊C4—101no—
604C4⋊C4—104no—
605C4⋊C4—101no—
606C4⋊C4—104no—
607C4⋊C4—104no—
608C4⋊C4—104no—
609C4⋊C4—104no—
610C4⋊C4—104no—
611C4⋊C4C2×C22⋊D514yes—
612C4⋊C4C23×D512yes—
613C4⋊C4C23×D512yes—
614C4⋊C4C23×D512yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—104no—
620C22⋊C4—104no—
621C22⋊C4—104no—
622C22⋊C4C2×C22⋊D514yes—
623C22⋊C4C2×C22⋊D514yes—
624C42—24no—
625C42—104no—
626C42—104no—
627C42C2×C22⋊D512yes—
628C42C23×D512yes—
629C2×C5—42no—
630C2×C5—42no—
631C2×C5—82no—
632C2×C5#335114yescomplemented
633C2×C5C2×#54711yescharacteristic
634C2×C5C2×#57511yescharacteristic
635C2×C5C2×#57711yescharacteristic
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23C22×C22⋊D512yes—
647C23C22×C22⋊D512yes—
648C23C22×C22⋊D511yescharacteristic
649Q8—102no—
650Q8—102no—
651Q8—202no—
652D4—22no—
653D4—22no—
654D4—44no—
655D4—48no—
656D4—42no—
657D4—84no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—84no—
675C2×C4—84no—
676C2×C4—102no—
677C2×C4—102no—
678C2×C4—102no—
679C2×C4—102no—
680C2×C4—208no—
681C2×C4—202no—
682C2×C4—202no—
683C2×C4—202no—
684C2×C4—202no—
685C2×C4D5×#4112yes—
686C2×C4#415012yes—
687C2×C4C22×C22⋊D512yes—
688C2×C4C22×C22⋊D512yes—
689C2×C4C22×C22⋊D512yes—
690C2×C4C22×C22⋊D512yes—
691C2×C4C22×C22⋊D511yescharacteristic
692C2×C4C24×D511yescharacteristic
693C8—54no—
694C8—102no—
695C8—102no—
696C8—102no—
697C5C2×#335111yescharacteristic, complemented, Sylow
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22#6615612yes—
711C22#6615812yes—
712C22#6617012yes—
713C22C23×C22⋊D511yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—202no—
722C4—202no—
723C4—202no—
724C4—202no—
725C4#6615812yes—
726C4C2×D5×#4111yescharacteristic
727C4C2×#415011yescharacteristic
728C2—42no—
729C2—42no—
730C2—82no—
731C2#1061534314yesdirect product factor
732C2C2×#6615611yescharacteristic
733C2C2×#6615811yescharacteristic
734C2C2×#6617011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
Fitting, prime radicalC2×C5×#553C2
socleC23×C5C22×D4
hypercenterC2×#553D5
hypocenterC5C2×#3351
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
2. C2×#65875C2semidirect
3. #10615343C2direct (N × H)
4. C2×#65352C2semidirect
5. C2×#65353C2semidirect
6. C2×#65331C2semidirect
7. C2×#65331C2semidirect
8. C2×#65323C2semidirect
9. C2×#65324C2semidirect
10. C2×C4×#687C2semidirect
11. C2×#65301C2semidirect
12. C2×#65298C2semidirect
13. C2×#65285C2semidirect
14. C2×#65284C2semidirect
15. C2×#65260C2semidirect
16. C2×#65253C2semidirect
39. #65875C22semidirect
50. #65353C22semidirect
51. #65352C22semidirect
52. #65331C22semidirect
53. #65331C22semidirect
54. #65324C22semidirect
55. #65323C22semidirect
56. C4×#687C22semidirect
57. #65301C22semidirect
58. #65298C22semidirect
59. #65285C22semidirect
60. #65284C22semidirect
61. #65260C22semidirect
65. #65253C22semidirect
632. C2×C5#3351semidirect
697. C5C2×#3351semidirect
731. C2#10615343direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5532
C2×#658752
#106153432
C2×#653522
C2×#653532
C2×#653312
C2×#653232
C2×#653242
C2×C4×#6872
C2×#653012
C2×#652982
C2×#652852
C2×#652842
C2×#652602
C2×#652532
C2×#33515