Finite Group Databasebeta

← #12115708

Subgroups — #12115708

Order 1280.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#552C211yesmaximal, characteristic
2#10614066C211yesmaximal, characteristic
3C2×#65301C211yesmaximal, characteristic
4#10602533C211yesmaximal, characteristic, complemented
5#10602531C211yesmaximal, characteristic, complemented
6#10602490C211yesmaximal, characteristic, complemented
7#10602490C211yesmaximal, characteristic, complemented
8#10602486C211yesmaximal, characteristic, complemented
9#10602485C211yesmaximal, characteristic, complemented
10C4×#3967C211yesmaximal, characteristic, complemented
11#10602420C211yesmaximal, characteristic, complemented
12#10602374C211yesmaximal, characteristic, complemented
13#10602368C211yesmaximal, characteristic, complemented
14#10602351C211yesmaximal, characteristic, complemented
15#10602347C211yesmaximal, characteristic, complemented
16C5×#552—24no—
17C5×#552C418yescomplemented
18C2×C5×#126—21no—
19C2×C5×#125—21no—
20C2×C5×#125C2211yescharacteristic
21C2×C5×#123—21no—
22C2×C5×C22⋊Q8C2211yescharacteristic
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C4×C5×Q8C2211yescharacteristic
25C2×C4×C5×D4C2211yescharacteristic
26C2×C5×#117—21no—
27C2×C5×#117C2211yescharacteristic
28C22×C5×C4⋊C4C2211yescharacteristic
29C2×#4072C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×#681C2211yescharacteristic
32C22×#681C2211yescharacteristic
33C2×#3967C2211yescharacteristic
34C2×#3967C2211yescharacteristic
35C2×#3967C2211yescharacteristic
36C2×#3967C2211yescharacteristic
37#65509—21no—
38#65501C2211yescharacteristic
39#65501C2211yescharacteristic
40C2×C22⋊#168C2211yescharacteristic
41C2×C22⋊#168C2211yescharacteristic
42#65301—24no—
43#65270—21no—
44#65240—21no—
45C22⋊C4×Dic5—21no—
46#65225C2211yescharacteristic
47C4×C4⋊Dic5C2211yescharacteristic
48C2×C4⋊#168C2211yescharacteristic
49C2×C4×#168C2211yescharacteristic
50#64749C2211yescharacteristic
51#64749C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#64749C2211yescharacteristic
61#64749C2211yescharacteristic
62#22499—51nomaximal, Sylow
63C22×C5×Q8C2311yescharacteristic
64C22×C5×D4D411yescharacteristic
65C23×C4×C5—21no—
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×Dic5—21no—
69C5×#126—28no—
70C5×#125—28no—
71C5×#125—22no—
72C5×#125C2×C414yescomplemented
73C5×#123—28no—
74C5×C22⋊Q8—22no—
75C5×C22⋊Q8—22no—
76C5×C22⋊Q8C2×C414yes—
77C5×C22⋊Q8C2×C414yescomplemented
78C4×C5×Q8—22no—
79C4×C5×Q8C2×C414yescomplemented
80C4×C5×D4C2×C414yes—
81C4×C5×D4D414yes—
82C5×#117—22no—
83C5×#117—28no—
84C5×#117C2×C414yes—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4—21no—
92C2×C5×C4⋊C4C2×C414yescomplemented
93C2×C5×C4⋊C4D411yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4D411yescharacteristic
101C2×C5×C22⋊C4D411yescharacteristic
102C2×C42×C5—21no—
103C2×C42×C5—21no—
104C2×C42×C5C2311yescharacteristic
105C2×C22⋊Dic5—21no—
106C2×C22⋊Dic5—21no—
107C2×C22⋊Dic5—21no—
108#4072—22no—
109#4072—41no—
110C2×C4⋊Dic5—22no—
111C2×C4⋊Dic5—21no—
112C2×C4⋊Dic5—41no—
113C2×C4⋊Dic5C2311yescharacteristic
114C2×C4⋊Dic5C2311yescharacteristic
115C2×C4⋊Dic5C2311yescharacteristic
116C2×C4⋊Dic5C2311yescharacteristic
117C2×C4×Dic5—21no—
118C2×C4×Dic5—21no—
119C2×#681—22no—
120C2×#681—22no—
121C2×#681—22no—
122C2×#681—22no—
123C2×#681—41no—
124C2×#681—41no—
125C22×#168C2311yescharacteristic
126C22×#168C2311yescharacteristic
127C22×#168C2311yescharacteristic
128C22×#168C2311yescharacteristic
129#3967—22no—
130#3967—22no—
131#3967—41no—
132#3967—41no—
133#3963—21no—
134#3963—21no—
135#3963—21no—
136#3963—21no—
137#3963—21no—
138C22⋊#168—22no—
139C22⋊#168—22no—
140C4⋊#168—22no—
141C4×#168—22no—
142C2×#552D511yescharacteristic
143C2×#436—51no—
144#2352—51no—
145#1991—51no—
146#1989—51no—
147#1894—51no—
148#1894—51no—
149#1873—51no—
150#1872—51no—
151#1825—51no—
152#1824—51no—
153#1805—51no—
154C4×#103—51no—
155#1736—51no—
156#1736—51no—
157C24×C5C2×D411yescharacteristic
158C24×C5C2×D411yescharacteristic
159C2×C5×Q8—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8C22×C412yes—
165C2×C5×D4—41no—
166C2×C5×D4—41no—
167C2×C5×D4C22⋊C414yes—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—24no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—42no—
182C22×C4×C5—42no—
183C22×C4×C5C22×C412yes—
184C22×C4×C5C22×C412yes—
185C22×C4×C5C2×D411yescharacteristic
186C22×C4×C5C2×D411yescharacteristic
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×D412yes—
190C22×C4×C5C2×D412yes—
191C22×C4×C5C2411yescharacteristic
192C22×Dic5—21no—
193C22×Dic5—21no—
194C22×Dic5—21no—
195C22×Dic5—21no—
196C22×Dic5—42no—
197C22×Dic5—42no—
198C22×Dic5—81no—
199C5×C4⋊C4—24no—
200C5×C4⋊C4—24no—
201C5×C4⋊C4—24no—
202C5×C4⋊C4—24no—
203C5×C4⋊C4—24no—
204C5×C4⋊C4—24no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4C22⋊C414yes—
209C5×C4⋊C4C22×C412yes—
210C5×C4⋊C4C22×C412yes—
211C5×C4⋊C4C22×C412yes—
212C5×C22⋊C4—24no—
213C5×C22⋊C4—24no—
214C5×C22⋊C4—24no—
215C5×C22⋊C4C22⋊C414yes—
216C5×C22⋊C4C22⋊C414yes—
217C42×C5—24no—
218C42×C5—24no—
219C42×C5C22×C412yes—
220C42×C5C2×D412yes—
221C22⋊Dic5—42no—
222C22⋊Dic5—42no—
223C22⋊Dic5—81no—
224C4⋊Dic5—21no—
225C4⋊Dic5—21no—
226C4⋊Dic5—21no—
227C4⋊Dic5—21no—
228C4⋊Dic5—21no—
229C4⋊Dic5—21no—
230C4⋊Dic5—21no—
231C4⋊Dic5—42no—
232C4⋊Dic5#4112yes—
233C4×Dic5—42no—
234C4×Dic5—81no—
235#681—44no—
236#681—44no—
237C2×#168—21no—
238C2×#168—21no—
239C2×#168—21no—
240C2×#168—21no—
241C2×#168—21no—
242C2×#168—21no—
243C2×#168—21no—
244C2×#168—21no—
245C2×#168—21no—
246C2×#168—21no—
247C2×#168—21no—
248C2×#168#4112yes—
249C22×M16—51no—
250C22×M16—51no—
251#552—24no—
252#552Dic518yescomplemented
253C2×#126—21no—
254C2×#125—21no—
255C2×#125C2×D511yescharacteristic
256C2×#123—21no—
257C2×C22⋊Q8C2×D511yescharacteristic
258C2×C22⋊Q8C2×D511yescharacteristic
259C2×C4×Q8C2×D511yescharacteristic
260C2×C4×D4C2×D511yescharacteristic
261C2×#117—21no—
262C2×#117—51no—
263C2×#117C2×D511yescharacteristic
264C22×C4⋊C4—51no—
265C22×C4⋊C4C2×D511yescharacteristic
266#436—104no—
267C2×C4⋊C8—51no—
268C2×#103—51no—
269C2×#103—51no—
270C2×#103—51no—
271C2×#103—51no—
272C2×C22⋊C8—51no—
273C2×C22⋊C8—51no—
274C2×C4×C8—51no—
275#388—101no—
276#387—101no—
277#386—101no—
278#382—51no—
279#380—51no—
280#380—51no—
281C4×C4⋊C4—51no—
282C4×C22⋊C4—101no—
283#340—51no—
284#340—51no—
285#340—51no—
286#340—51no—
287#340—51no—
288#340—51no—
289#340—51no—
290#340—51no—
291#340—51no—
292#340—51no—
293#340—51no—
294#340—51no—
295C23×C5—21no—
296C23×C5—21no—
297C23×C5—21no—
298C23×C5—21no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—21no—
302C23×C5—21no—
303C23×C5—21no—
304C23×C5—21no—
305C23×C5—21no—
306C23×C5—21no—
307C23×C5C2×C22⋊C412yes—
308C23×C5C2×C22⋊C412yes—
309C23×C5C22×D411yescharacteristic
310C5×Q8—22no—
311C5×Q8—22no—
312C5×Q8—41no—
313C5×Q8—41no—
314C5×D4—44no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—48no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5—41no—
341C2×C4×C5—41no—
342C2×C4×C5—41no—
343C2×C4×C5—41no—
344C2×C4×C5C2×C22⋊C412yes—
345C2×C4×C5C2×C22⋊C412yes—
346C2×C4×C5C2×C22⋊C412yes—
347C2×C4×C5C2×C22⋊C412yes—
348C2×C4×C5C23×C411yescharacteristic
349C2×C4×C5C22×D411yescharacteristic
350C2×C4×C5C2×#4111yescharacteristic
351C2×C4×C5C2×#4111yescharacteristic
352C2×C4×C5H(5,𝔽2)11yescharacteristic
353C2×C4×C52−1+411yescharacteristic
354C2×Dic5—22no—
355C2×Dic5—41no—
356C2×Dic5—41no—
357C2×Dic5—41no—
358C2×Dic5—41no—
359C2×Dic5—41no—
360C2×Dic5—41no—
361C2×Dic5—41no—
362C2×Dic5—41no—
363C2×Dic5—41no—
364C2×Dic5—41no—
365C2×Dic5—41no—
366C2×Dic5—84no—
367#168—22no—
368#168—41no—
369#168—41no—
370#168—41no—
371C22×Q8C22×D511yescharacteristic
372C22×D4C22⋊D511yescharacteristic
373C23×C4—21no—
374C23×C4—101no—
375C23×C4C22×D511yescharacteristic
376C23×C4C22×D511yescharacteristic
377C2×M16—102no—
378C2×M16—102no—
379C2×M16—102no—
380C2×M16—102no—
381C2×M16—201no—
382C2×M16—201no—
383C22×C8—51no—
384C22×C8—51no—
385C22×C8—51no—
386C22×C8—51no—
387#126—28no—
388#125—28no—
389#125—22no—
390#125C2×Dic514yescomplemented
391#123—28no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8C2×Dic514yes—
395C22⋊Q8C2×Dic514yescomplemented
396C4×Q8—22no—
397C4×Q8C2×Dic514yescomplemented
398C4×D4C2×Dic514yes—
399C4×D4C22⋊D514yes—
400#117—22no—
401#117—28no—
402#117—102no—
403#117—201no—
404#117C2×Dic514yes—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—51no—
413C2×C4⋊C4—51no—
414C2×C4⋊C4—51no—
415C2×C4⋊C4—51no—
416C2×C4⋊C4—102no—
417C2×C4⋊C4—101no—
418C2×C4⋊C4—201no—
419C2×C4⋊C4C2×Dic514yescomplemented
420C2×C4⋊C4C22⋊D511yescharacteristic
421C2×C4⋊C4C22×D511yescharacteristic
422C2×C4⋊C4C22×D511yescharacteristic
423C2×C4⋊C4C22×D511yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—101no—
428C2×C22⋊C4—101no—
429C2×C22⋊C4—101no—
430C2×C22⋊C4C22⋊D511yescharacteristic
431C2×C22⋊C4C22⋊D511yescharacteristic
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—101no—
435C2×C42—101no—
436C2×C42C22×D511yescharacteristic
437C4⋊C8—102no—
438#103—102no—
439#103—102no—
440#103—201no—
441#103—201no—
442C22⋊C8—102no—
443C22⋊C8—102no—
444C4×C8—102no—
445#95—101no—
446#95—101no—
447#95—101no—
448#95—101no—
449#95—101no—
450C22×C5—22no—
451C22×C5—22no—
452C22×C5—22no—
453C22×C5—22no—
454C22×C5—22no—
455C22×C5—22no—
456C22×C5—41no—
457C22×C5—41no—
458C22×C5—41no—
459C22×C5—41no—
460C22×C5—41no—
461C22×C5—41no—
462C22×C5—41no—
463C22×C5—41no—
464C22×C5C22×C22⋊C411yescharacteristic
465C22×C5#54611yescharacteristic
466C22×C5#54711yescharacteristic
467C22×C5#57511yescharacteristic
468C22×C5#57511yescharacteristic
469C22×C5#57711yescharacteristic
470C22×C5#57811yescharacteristic
471C4×C5—22no—
472C4×C5—22no—
473C4×C5—22no—
474C4×C5—22no—
475C4×C5—42no—
476C4×C5—42no—
477C4×C5—42no—
478C4×C5—42no—
479C4×C5C4×#4111yescharacteristic
480C4×C5#52011yescharacteristic
481C4×C5#54611yescharacteristic
482C4×C5#54711yescharacteristic
483Dic5—42no—
484Dic5—81no—
485Dic5—81no—
486Dic5—81no—
487C24C2×C22⋊D511yescharacteristic
488C24C2×C22⋊D511yescharacteristic
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C22×Dic512yes—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4C22⋊Dic514yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—101no—
514C22×C4—101no—
515C22×C4—101no—
516C22×C4—101no—
517C22×C4—202no—
518C22×C4—202no—
519C22×C4—401no—
520C22×C4C22×Dic512yes—
521C22×C4C22×Dic512yes—
522C22×C4C2×C22⋊D511yescharacteristic
523C22×C4C2×C22⋊D511yescharacteristic
524C22×C4C2×C22⋊D511yescharacteristic
525C22×C4C2×C22⋊D511yescharacteristic
526C22×C4C2×C22⋊D512yes—
527C22×C4C2×C22⋊D512yes—
528C22×C4C23×D511yescharacteristic
529M16—204no—
530M16—204no—
531C2×C8—52no—
532C2×C8—101no—
533C2×C8—101no—
534C2×C8—101no—
535C2×C8—101no—
536C2×C8—101no—
537C2×C8—101no—
538C2×C8—101no—
539C2×C8—101no—
540C2×C8—101no—
541C2×C8—101no—
542C2×C8—101no—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—24no—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—52no—
553C4⋊C4—101no—
554C4⋊C4—101no—
555C4⋊C4—101no—
556C4⋊C4—101no—
557C4⋊C4—101no—
558C4⋊C4—101no—
559C4⋊C4—101no—
560C4⋊C4—202no—
561C4⋊C4C22⋊Dic514yes—
562C4⋊C4C22×Dic512yes—
563C4⋊C4C22×Dic512yes—
564C4⋊C4C22×Dic512yes—
565C22⋊C4—24no—
566C22⋊C4—24no—
567C22⋊C4—24no—
568C22⋊C4—202no—
569C22⋊C4—202no—
570C22⋊C4—401no—
571C22⋊C4C22⋊Dic514yes—
572C22⋊C4C22⋊Dic514yes—
573C42—24no—
574C42—24no—
575C42—202no—
576C42—401no—
577C42C22×Dic512yes—
578C42C2×C22⋊D512yes—
579C2×C5—42no—
580C2×C5—42no—
581C2×C5#233911yescharacteristic
582C2×C5#289611yescharacteristic
583C2×C5#289811yescharacteristic
584C2×C5#332311yescharacteristic
585C2×C5#332711yescharacteristic
586C2×C5#335111yescharacteristic
587C2×C5#335211yescharacteristic
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23C2×C22⋊Dic512yes—
601C23C2×C22⋊Dic512yes—
602C23C22×C22⋊D511yescharacteristic
603Q8—22no—
604Q8—22no—
605Q8—41no—
606Q8—41no—
607D4—44no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—48no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—102no—
638C2×C4—201no—
639C2×C4—201no—
640C2×C4—201no—
641C2×C4—201no—
642C2×C4—201no—
643C2×C4—201no—
644C2×C4—201no—
645C2×C4—201no—
646C2×C4—201no—
647C2×C4—201no—
648C2×C4—201no—
649C2×C4—404no—
650C2×C4C2×C22⋊Dic512yes—
651C2×C4C2×C22⋊Dic512yes—
652C2×C4C2×C22⋊Dic512yes—
653C2×C4C2×C22⋊Dic512yes—
654C2×C4D5×#4111yescharacteristic
655C2×C4D5×#4111yescharacteristic
656C2×C4#414911yescharacteristic
657C2×C4#415011yescharacteristic
658C2×C4C23×Dic511yescharacteristic
659C2×C4C22×C22⋊D511yescharacteristic
660C8—102no—
661C8—201no—
662C8—201no—
663C8—201no—
664C5#2249911yescharacteristic, complemented, Sylow
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22#6615611yescharacteristic
680C22#6615611yescharacteristic
681C22#6615811yescharacteristic
682C22#6616311yescharacteristic
683C22#6617111yescharacteristic
684C22#6617211yescharacteristic
685C22C22×C22⋊Dic511yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—202no—
695C4—401no—
696C4—401no—
697C4—401no—
698C4#6615811yescharacteristic
699C4#41×Dic511yescharacteristic
700C4#6616111yescharacteristic
701C4#6616311yescharacteristic
702C2—42no—
703C2—42no—
704C2#1061532711yescharacteristic
705C2#1061532811yescharacteristic
706C2#1061533211yescharacteristic
707C2#1061533611yescharacteristic
708C2#1061580311yescharacteristic
709C2#1061581911yescharacteristic
710C2#1061584211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#552C2
socleC23×C5C22×D4
prime radicalC22×C5×D4D4
cosocleC22×C4×C5C24
hypercenterC2×#552D5
hypocenterC5#22499
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
4. #10602533C2semidirect
5. #10602531C2semidirect
6. #10602490C2semidirect
7. #10602490C2semidirect
8. #10602486C2semidirect
9. #10602485C2semidirect
10. C4×#3967C2semidirect
11. #10602420C2semidirect
12. #10602374C2semidirect
13. #10602368C2semidirect
14. #10602351C2semidirect
15. #10602347C2semidirect
17. C5×#552C4semidirect
72. C5×#125C2×C4semidirect
77. C5×C22⋊Q8C2×C4semidirect
79. C4×C5×Q8C2×C4semidirect
92. C2×C5×C4⋊C4C2×C4semidirect
252. #552Dic5semidirect
390. #125C2×Dic5semidirect
395. C22⋊Q8C2×Dic5semidirect
397. C4×Q8C2×Dic5semidirect
419. C2×C4⋊C4C2×Dic5semidirect
664. C5#22499semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5522
#106140662
C2×#653012
#106025332
#106025312
#106024902
#106024862
#106024852
C4×#39672
#106024202
#106023742
#106023682
#106023512
#106023472
#224995