Finite Group Databasebeta

← C2×#10615327 #12977978

Subgroups — C2×#10615327 #12977978

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×#552C211yesmaximal, characteristic, complemented
2C2×#65899C211yesmaximal, characteristic
3#10615327C2116yesmaximal, direct product factor
4C2×#65355C211yesmaximal, characteristic, complemented
5C2×#65353C211yesmaximal, characteristic, complemented
6C2×#65338C211yesmaximal, characteristic, complemented
7C2×#65338C211yesmaximal, characteristic, complemented
8C2×#65334C211yesmaximal, characteristic, complemented
9C2×#65332C211yesmaximal, characteristic, complemented
10C2×#65311C211yesmaximal, characteristic, complemented
11C2×C4×#688C211yesmaximal, characteristic, complemented
12C2×#65301C211yesmaximal, characteristic, complemented
13C2×#65292C211yesmaximal, characteristic, complemented
14C2×#65284C211yesmaximal, characteristic, complemented
15C2×#65257C211yesmaximal, characteristic, complemented
16C2×#65253C211yesmaximal, characteristic, complemented
17C5×#552—24no—
18C5×#552C2218yescomplemented
19C2×C5×#126—21no—
20C2×C5×#125—21no—
21C2×C5×#125C2211yescharacteristic
22C2×C5×#123—21no—
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×D4C2211yescharacteristic
27C2×C5×#117—21no—
28C2×C5×#117C2211yescharacteristic
29C22×C5×C4⋊C4C2211yescharacteristic
30C22×#688C2211yescharacteristic
31C2×#4085—21no—
32C2×#4076C2211yescharacteristic
33C2×#4076C2211yescharacteristic
34C2×#4072C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C22×#681C2211yescharacteristic
38#65899—24no—
39#65899C2218yes—
40C2×#4044—21no—
41C2×#4029—21no—
42C2×#4027—21no—
43C2×C4×D20C2211yescharacteristic
44C2×#4016C2211yescharacteristic
45C2×#3967C2211yescharacteristic
46C2×#3967C2211yescharacteristic
47C2×#3967C2211yescharacteristic
48C2×C22⋊#168C2211yescharacteristic
49C2×C22⋊#168C2211yescharacteristic
50#65355C2218yescomplemented
51#65353C2218yescomplemented
52#65338C2218yescomplemented
53#65338C2218yescomplemented
54#65334C2218yescomplemented
55#65332C2218yescomplemented
56C4×#688C2218yescomplemented
57#65311C2218yescomplemented
58#65301C2218yescomplemented
59#65292C2218yescomplemented
60#65284C2218yescomplemented
61#65257C2218yescomplemented
62C2×#3941C2211yescharacteristic
63C2×#3941C2211yescharacteristic
64C2×#3941C2211yescharacteristic
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×Q8C2311yescharacteristic
79C22×C5×D4D411yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C23×Dic5—21no—
86C22×D20C2311yescharacteristic
87C22×C4×D5—21no—
88C5×#126—28no—
89C5×#125—28no—
90C5×#125—22no—
91C5×#125C2314yes—
92C5×#123—28no—
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8—22no—
95C5×C22⋊Q8C2314yes—
96C5×C22⋊Q8C2314yes—
97C4×C5×Q8—22no—
98C4×C5×Q8C2314yes—
99C4×C5×D4D414yes—
100C4×C5×D4C2314yes—
101C5×#117—22no—
102C5×#117—28no—
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⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4D411yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2314yes—
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4D411yescharacteristic
120C2×C5×C22⋊C4D411yescharacteristic
121C2×C42×C5—21no—
122C2×C42×C5—21no—
123C2×C42×C5C2311yescharacteristic
124C2×C22⋊Dic5—21no—
125C2×#688—24no—
126C2×#688C2314yes—
127#4085—28no—
128#4076—22no—
129#4076—22no—
130#4076C2314yes—
131#4076C2314yes—
132C2×#685—21no—
133C2×#685—21no—
134C2×#685—21no—
135#4072—22no—
136#4072C2314yes—
137C2×C4⋊Dic5—21no—
138C2×C4⋊Dic5—22no—
139C2×C4⋊Dic5C2314yes—
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2311yescharacteristic
143C2×#683—21no—
144C2×#683—21no—
145C2×C4×Dic5—21no—
146C2×#681—24no—
147C2×#681—24no—
148C2×#681C2314yes—
149C2×#681C2314yes—
150C22×#168C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C22×#168C2311yescharacteristic
154#4044—28no—
155#4029—28no—
156#4027—28no—
157C4×D20—22no—
158C4×D20C2314yes—
159#4016—22no—
160#4016C2314yes—
161#3967C2314yes—
162#3967C2314yes—
163#3967C2314yes—
164C22⋊#168C2314yes—
165C22⋊#168C2314yes—
166#3941C2314yes—
167#3941C2314yes—
168#3941C2314yes—
169#3940C2314yes—
170#3940C2314yes—
171#3940C2314yes—
172#3940C2314yes—
173#3940C2314yes—
174#3939C2314yes—
175#3939C2314yes—
176#3939C2314yes—
177#3939C2314yes—
178C4⋊#168C2314yes—
179C4×#168C2314yes—
180C2×#553—51no—
181C2×#552D511yescharacteristic, complemented
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×C5C2×D411yescharacteristic
197C24×C5C2×D411yescharacteristic
198C23×D5—21no—
199C2×C5×Q8—21no—
200C2×C5×Q8—22no—
201C2×C5×Q8—22no—
202C2×C5×Q8C2412yes—
203C2×C5×D4—42no—
204C2×C5×D4C2×D414yes—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—24no—
214C22×C4×C5—44no—
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D412yes—
220C22×C4×C5C2×D412yes—
221C22×C4×C5C2412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2411yescharacteristic
224C2×C22⋊D5—24no—
225C2×C22⋊D5—24no—
226C2×C22⋊D5—44no—
227C2×C22⋊D5—82no—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—24no—
232C22×Dic5—82no—
233C2×D20—22no—
234C2×D20—22no—
235C2×D20—21no—
236C2×D20C2412yes—
237C2×C4×D5—24no—
238C2×C4×D5—82no—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—24no—
242C5×C4⋊C4—24no—
243C5×C4⋊C4—24no—
244C5×C4⋊C4—24no—
245C5×C4⋊C4—24no—
246C5×C4⋊C4—24no—
247C5×C4⋊C4—21no—
248C5×C4⋊C4C2×D414yes—
249C5×C4⋊C4C2412yes—
250C5×C4⋊C4C2412yes—
251C5×C4⋊C4C2412yes—
252C5×C22⋊C4—24no—
253C5×C22⋊C4—24no—
254C5×C22⋊C4—24no—
255C5×C22⋊C4C2×D414yes—
256C5×C22⋊C4C2×D414yes—
257C42×C5—24no—
258C42×C5—24no—
259C42×C5C2×D412yes—
260C42×C5C2412yes—
261C22⋊Dic5—24no—
262#688—28no—
263#685—24no—
264#685—24no—
265#685—24no—
266C4⋊Dic5—21no—
267C4⋊Dic5—21no—
268C4⋊Dic5—21no—
269C4⋊Dic5—24no—
270C4⋊Dic5C2412yes—
271C4⋊Dic5C2412yes—
272C4⋊Dic5C2412yes—
273#683—24no—
274#683—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—58no—
290#553—104no—
291#552—24no—
292#552C2×D518yescomplemented
293C2×#126—21no—
294C2×#126—101no—
295C2×#125—21no—
296C2×#125—51no—
297C2×#125C2×D511yescharacteristic
298C2×#123—21no—
299C2×#123—101no—
300C2×C22⋊Q8C2×D511yescharacteristic
301C2×C22⋊Q8C2×D511yescharacteristic
302C2×#121—51no—
303C2×#121—51no—
304C2×#121—101no—
305C2×C4×Q8C2×D511yescharacteristic
306C2×C4×D4—51no—
307C2×C4×D4—101no—
308C2×C4×D4C2×D511yescharacteristic
309C2×#117—21no—
310C2×#117—51no—
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×C5C22×D412yes—
353C23×C5C22×D412yes—
354C23×C5C22×D411yescharacteristic
355C22×D5—22no—
356C22×D5—42no—
357C22×D5—42no—
358C22×D5—42no—
359C5×Q8—22no—
360C5×Q8—22no—
361C5×Q8—42no—
362C5×D4—44no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—24no—
368C2×C4×C5—24no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
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—48no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5—42no—
381C2×C4×C5—42no—
382C2×C4×C5C22×D412yes—
383C2×C4×C5C22×D412yes—
384C2×C4×C5C22×D412yes—
385C2×C4×C5C22×D412yes—
386C2×C4×C5C22×D411yescharacteristic
387C2×C4×C5C2×#4112yes—
388C2×C4×C52−1+412yes—
389C2×C4×C5C2511yescharacteristic
390C22⋊D5—48no—
391C22⋊D5—84no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—42no—
396C2×Dic5—42no—
397C2×Dic5—42no—
398C2×Dic5—84no—
399D20—22no—
400D20—22no—
401D20—42no—
402C4×D5—84no—
403#168—22no—
404#168—22no—
405#168—22no—
406#168C2×#4114yes—
407C22×Q8C22×D511yescharacteristic
408C22×D4—51no—
409C22×D4—101no—
410C22×D4—101no—
411C22×D4C22⋊D511yescharacteristic
412C23×C4—21no—
413C23×C4—101no—
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—28no—
430#125—22no—
431#125—54no—
432#125—102no—
433#125C22×D514yes—
434#123—28no—
435#123—108no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8C22×D514yes—
439C22⋊Q8C22×D514yes—
440#121—54no—
441#121—54no—
442#121—108no—
443#121—102no—
444#121—102no—
445C4×Q8—22no—
446C4×Q8C22×D514yes—
447C4×D4—54no—
448C4×D4—108no—
449C4×D4—102no—
450C4×D4C22⋊D514yes—
451C4×D4C22×D514yes—
452#117—22no—
453#117—28no—
454#117—54no—
455#117—102no—
456#117C22×D514yes—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—51no—
465C2×C4⋊C4—51no—
466C2×C4⋊C4—54no—
467C2×C4⋊C4—51no—
468C2×C4⋊C4—101no—
469C2×C4⋊C4—102no—
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—101no—
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—21no—
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#54712yes—
518C22×C5#57512yes—
519C22×C5#57712yes—
520C22×C5C23×D411yescharacteristic
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—84no—
525C4×C5—22no—
526C4×C5—22no—
527C4×C5—22no—
528C4×C5—22no—
529C4×C5—42no—
530C4×C5—42no—
531C4×C5—42no—
532C4×C5—42no—
533C4×C5#54712yes—
534C4×C5C22×#4111yescharacteristic
535C4×C5C2×2−1+411yescharacteristic
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539C24—101no—
540C24C2×C22⋊D511yescharacteristic
541C24C2×C22⋊D511yescharacteristic
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8C23×D512yes—
546C2×D4—42no—
547C2×D4—52no—
548C2×D4—104no—
549C2×D4—104no—
550C2×D4—102no—
551C2×D4—102no—
552C2×D4—101no—
553C2×D4—204no—
554C2×D4—402no—
555C2×D4C2×C22⋊D514yes—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—44no—
566C22×C4—101no—
567C22×C4—101no—
568C22×C4—101no—
569C22×C4—104no—
570C22×C4—104no—
571C22×C4—402no—
572C22×C4—402no—
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—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—52no—
603C4⋊C4—52no—
604C4⋊C4—52no—
605C4⋊C4—101no—
606C4⋊C4—101no—
607C4⋊C4—104no—
608C4⋊C4—101no—
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—104no—
619C22⋊C4—104no—
620C22⋊C4—104no—
621C22⋊C4—104no—
622C22⋊C4C2×C22⋊D514yes—
623C22⋊C4C2×C22⋊D514yes—
624C42—24no—
625C42—24no—
626C42—104no—
627C42C2×C22⋊D512yes—
628C42C23×D512yes—
629C2×C5—42no—
630C2×C5—42no—
631C2×C5#335114yescomplemented
632C2×C5C2×#54711yescharacteristic
633C2×C5C2×#57511yescharacteristic
634C2×C5C2×#57711yescharacteristic
635D5—82no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—102no—
643C23—202no—
644C23—202no—
645C23—202no—
646C23C22×C22⋊D512yes—
647C23C22×C22⋊D512yes—
648C23C22×C22⋊D511yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—42no—
652D4—44no—
653D4—102no—
654D4—102no—
655D4—208no—
656D4—202no—
657D4—404no—
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—22no—
672C2×C4—48no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—102no—
678C2×C4—102no—
679C2×C4—102no—
680C2×C4—202no—
681C2×C4—202no—
682C2×C4—202no—
683C2×C4—404no—
684C2×C4—404no—
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—202no—
707C22—202no—
708C22—202no—
709C22—404no—
710C22#6615612yes—
711C22#6615812yes—
712C22#6617112yes—
713C22C23×C22⋊D511yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—202no—
723C4—202no—
724C4—202no—
725C4#6615812yes—
726C4C2×D5×#4111yescharacteristic
727C4C2×#415011yescharacteristic
728C2—42no—
729C2—42no—
730C2—402no—
731C2#1061532714yesdirect product factor
732C2C2×#6615611yescharacteristic
733C2C2×#6615811yescharacteristic
734C2C2×#6617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#552C2
socleC23×C5C22×D4
prime radicalC2×#65899C2
hypercenterC2×#552D5
hypocenterC5C2×#3351
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×C5×#552C2semidirect
3. #10615327C2direct (N × H)
4. C2×#65355C2semidirect
5. C2×#65353C2semidirect
6. C2×#65338C2semidirect
7. C2×#65338C2semidirect
8. C2×#65334C2semidirect
9. C2×#65332C2semidirect
10. C2×#65311C2semidirect
11. C2×C4×#688C2semidirect
12. C2×#65301C2semidirect
13. C2×#65292C2semidirect
14. C2×#65284C2semidirect
15. C2×#65257C2semidirect
16. C2×#65253C2semidirect
18. C5×#552C22semidirect
50. #65355C22semidirect
51. #65353C22semidirect
52. #65338C22semidirect
53. #65338C22semidirect
54. #65334C22semidirect
55. #65332C22semidirect
56. C4×#688C22semidirect
57. #65311C22semidirect
58. #65301C22semidirect
59. #65292C22semidirect
60. #65284C22semidirect
61. #65257C22semidirect
65. #65253C22semidirect
181. C2×#552D5semidirect
292. #552C2×D5semidirect
631. C2×C5#3351semidirect
697. C5C2×#3351semidirect
731. C2#10615327direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5522
C2×#658992
#106153272
C2×#653552
C2×#653532
C2×#653382
C2×#653342
C2×#653322
C2×#653112
C2×C4×#6882
C2×#653012
C2×#652922
C2×#652842
C2×#652572
C2×#652532
C2×#33515