Finite Group Databasebeta

← #12097117

Subgroups — #12097117

Order 1280.

1522 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65906C211yesmaximal, characteristic
2C2×#65091C211yesmaximal, characteristic
3C2×D5×#103C211yesmaximal, characteristic
4C2×#64978C211yesmaximal, characteristic
5#10605481C211yesmaximal, characteristic
6C4×C5×#103C211yesmaximal, characteristic, complemented
7#10602424C211yesmaximal, characteristic, complemented
8#10601013C211yesmaximal, characteristic, complemented
9Dic5×#103C211yesmaximal, characteristic, complemented
10C4×#3948C211yesmaximal, characteristic, complemented
11#10600268C211yesmaximal, characteristic, complemented
12#10599660C211yesmaximal, characteristic
13#10599659C211yesmaximal, characteristic
14#10599576C211yesmaximal, characteristic, complemented
15#10599574C211yesmaximal, characteristic, complemented
16C22×Q8×D5C2211yescharacteristic
17C2×C4×C5×Q8C2211yescharacteristic
18C2×Q8×Dic5C2211yescharacteristic
19C22×#676C2211yescharacteristic
20C22×C8×D5C2211yescharacteristic
21#65906—24no—
22#65906C418yescomplemented
23C2×#4038—21no—
24C2×#4038C2211yescharacteristic
25C2×#4038C2211yescharacteristic
26C2×D5×C4⋊C4C2211yescharacteristic
27C2×#4033—21no—
28C2×#4033C2211yescharacteristic
29C2×#4018—21no—
30C2×#4018C2211yescharacteristic
31C2×C4×Dic10—21no—
32C2×C4×Dic10C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C4×C5×C8C2211yescharacteristic
36C4×C5×C4⋊C4C2211yescharacteristic
37C2×#3967C2211yescharacteristic
38C2×#3967C2211yescharacteristic
39C2×#3948C2211yescharacteristic
40C2×#3948C2211yescharacteristic
41C2×#3947C2211yescharacteristic
42C2×C8×Dic5C2211yescharacteristic
43C4⋊C4×Dic5C2211yescharacteristic
44C4⋊C4×Dic5C2211yescharacteristic
45C2×#3942C2211yescharacteristic
46C2×#3942C2211yescharacteristic
47C4×#685—21no—
48C4×C4⋊Dic5C2211yescharacteristic
49C4×#683—21no—
50C2×#3935C2211yescharacteristic
51#65091C418yescomplemented
52D5×#103C418yescomplemented
53#64978—24no—
54#64955—21no—
55#64938—21no—
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58#64771C2211yescharacteristic
59#64771C2211yescharacteristic
60#64749C2211yescharacteristic
61#64749C2211yescharacteristic
62#64749C2211yescharacteristic
63#64749C2211yescharacteristic
64#20417—51nomaximal, Sylow
65C22×C5×Q8C2311yescharacteristic
66C2×Q8×D5—22no—
67C2×Q8×D5—22no—
68C2×Q8×D5—22no—
69C2×Q8×D5C2×C414yes—
70C2×Q8×D5C2×C414yes—
71C2×Q8×D5C2×C414yes—
72C22×C4×D5—21no—
73C22×C4×D5—21no—
74C22×C4×D5C2311yescharacteristic
75C22×Dic10—21no—
76C22×Dic10C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C4×C5×Q8—22no—
80C4×C5×Q8C2×C414yescomplemented
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4C2311yescharacteristic
83C2×C5×C4⋊C4C2311yescharacteristic
84C2×C5×C4⋊C4C2311yescharacteristic
85C2×C42×C5—21no—
86C2×C42×C5—21no—
87C2×C42×C5C2311yescharacteristic
88Q8×Dic5—22no—
89Q8×Dic5C2×C414yescomplemented
90C2×#685—21no—
91C2×#685—21no—
92C2×#685D411yescharacteristic
93C2×#685D411yescharacteristic
94C2×C4⋊Dic5—21no—
95C2×C4⋊Dic5C2311yescharacteristic
96C2×C4⋊Dic5C2311yescharacteristic
97C2×C4⋊Dic5C2311yescharacteristic
98C2×#683—21no—
99C2×#683—21no—
100C2×#683—21no—
101C2×#683D411yescharacteristic
102C2×#683D411yescharacteristic
103C2×C4×Dic5—21no—
104C2×C4×Dic5—21no—
105C2×C4×Dic5—21no—
106C2×C4×Dic5—21no—
107C2×C4×Dic5—21no—
108C2×C4×Dic5—21no—
109C2×C4×Dic5—21no—
110C2×C4×Dic5—21no—
111C2×C4×Dic5C2311yescharacteristic
112C22×#168C2311yescharacteristic
113C22×#168C2311yescharacteristic
114C2×#676—22no—
115C2×#676—22no—
116C2×#676C2×C414yes—
117C2×C8×D5—22no—
118C2×C8×D5—22no—
119C2×C8×D5C2×C414yes—
120#4038—22no—
121#4038—22no—
122#4038—28no—
123#4038C2×C414yes—
124#4038C2×C414yes—
125D5×C4⋊C4—22no—
126D5×C4⋊C4C2×C414yes—
127#4033—28no—
128#4033—22no—
129#4033C2×C414yescomplemented
130#4018—28no—
131#4018C2×C414yes—
132#4018D414yes—
133C4×Dic10—22no—
134C4×Dic10—28no—
135C4×Dic10C2×C414yescomplemented
136C5×#103C2×C414yes—
137C5×#103C2×C414yescomplemented
138C4×C5×C8—22no—
139C5×#95—21no—
140#3967C2×C414yes—
141#3967C2×C414yescomplemented
142#3963—21no—
143#3963—21no—
144#3963—21no—
145#3948C2×C414yes—
146#3948C2×C414yescomplemented
147#3947—22no—
148C8×Dic5—22no—
149#3942C2×C414yes—
150#3942C2×C414yescomplemented
151#3935—22no—
152C2×#519—51no—
153C2×#419—51no—
154C22×#103—51no—
155C2×#405—51no—
156#2274—51no—
157#1763—51no—
158#1763—51no—
159#1763—51no—
160#1763—51no—
161C4×#103—51no—
162C4×#103—51no—
163C4×#103—51no—
164C4×#103D511yescharacteristic, complemented
165#1736—51no—
166#1735—51no—
167C23×D5C2×D411yescharacteristic
168C2×C5×Q8—21no—
169C2×C5×Q8—21no—
170C2×C5×Q8—21no—
171C2×C5×Q8C22×C412yes—
172C2×C5×Q8C22×C412yes—
173C2×C5×Q8C22×C412yes—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5C2×D411yescharacteristic
179C22×C4×C5C2×D411yescharacteristic
180C22×C4×C5C2411yescharacteristic
181C22×Dic5—21no—
182C22×Dic5—21no—
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5C2×D411yescharacteristic
186C22×Dic5C2×D411yescharacteristic
187C22×Dic5C2×D411yescharacteristic
188Q8×D5—28no—
189Q8×D5—28no—
190Q8×D5—28no—
191Q8×D5C42116yescomplemented
192C2×C4×D5—24no—
193C2×C4×D5—24no—
194C2×C4×D5—24no—
195C2×C4×D5—24no—
196C2×C4×D5—81no—
197C2×C4×D5—81no—
198C2×C4×D5C22×C412yes—
199C2×C4×D5C22×C412yes—
200C2×C4×D5C22×C412yes—
201C2×C4×D5C2×D412yes—
202C2×C4×D5#4112yes—
203C2×C4×D5#4112yes—
204C2×Dic10—21no—
205C2×Dic10—21no—
206C2×Dic10—21no—
207C2×Dic10—24no—
208C2×Dic10—24no—
209C2×Dic10—24no—
210C2×Dic10C22×C412yes—
211C2×Dic10C22×C412yes—
212C2×Dic10C22×C412yes—
213C2×C5×C8—21no—
214C2×C5×C8—21no—
215C2×C5×C8—21no—
216C2×C5×C8—21no—
217C2×C5×C8C22×C412yes—
218C2×C5×C8C22×C412yes—
219C5×C4⋊C4—24no—
220C5×C4⋊C4—21no—
221C5×C4⋊C4—21no—
222C5×C4⋊C4—21no—
223C5×C4⋊C4C22×C412yes—
224C5×C4⋊C4C22×C412yes—
225C5×C4⋊C4C22×C412yes—
226C42×C5—24no—
227C42×C5—81no—
228C42×C5C22×C412yes—
229C42×C5C2×D412yes—
230#685—24no—
231#685—24no—
232#685C22⋊C414yes—
233#685C22⋊C414yes—
234C4⋊Dic5—21no—
235C4⋊Dic5—21no—
236C4⋊Dic5—21no—
237C4⋊Dic5—24no—
238C4⋊Dic5C22×C412yes—
239C4⋊Dic5C22×C412yes—
240C4⋊Dic5C22×C412yes—
241#683—24no—
242#683—24no—
243#683—24no—
244#683C22⋊C414yes—
245#683C22⋊C414yes—
246C4×Dic5—24no—
247C4×Dic5—24no—
248C4×Dic5—24no—
249C4×Dic5—24no—
250C4×Dic5—24no—
251C4×Dic5—81no—
252C4×Dic5—81no—
253C4×Dic5—81no—
254C4×Dic5C22×C412yes—
255C4×Dic5C2×D412yes—
256C2×#168—21no—
257C2×#168—21no—
258C2×#168—21no—
259C2×#168—21no—
260C2×#168C22×C412yes—
261C2×#168C22×C412yes—
262#676—28no—
263C8×D5—28no—
264C23×Q8—51no—
265C22×M16—51no—
266C23×C8—51no—
267#519—58no—
268#519—104no—
269C2×C4×Q8—51no—
270C2×C4×Q8—51no—
271C2×C4×Q8—51no—
272C2×C4×Q8—101no—
273C2×C4×Q8—101no—
274C2×C4×Q8C2×D511yescharacteristic
275C2×#117—51no—
276C2×#117—51no—
277C2×#117—51no—
278C2×#117—101no—
279C2×#117—101no—
280C22×C4⋊C4—51no—
281#419—58no—
282C2×#103—51no—
283C2×#103—51no—
284C2×#103—51no—
285C2×#103—51no—
286C2×#103—51no—
287C2×#103—51no—
288C2×#103—58no—
289C2×#103C2×D511yescharacteristic
290C2×#103C2×D511yescharacteristic
291#405—104no—
292C2×#97—51no—
293C2×#97—51no—
294C2×C4×C8—51no—
295C2×C4×C8C2×D511yescharacteristic
296C4×C4⋊C4—51no—
297C4×C4⋊C4—51no—
298C4×C4⋊C4—51no—
299C4×C4⋊C4—101no—
300C4×C4⋊C4—101no—
301C4×C4⋊C4C2×D511yescharacteristic
302C4×C22⋊C4—101no—
303C4×C22⋊C4—101no—
304#340—51no—
305#340—51no—
306#340—51no—
307#340—51no—
308#340—51no—
309#340—51no—
310#340C2×D511yescharacteristic
311#340C2×D511yescharacteristic
312C23×C5C22×D411yescharacteristic
313C22×D5—21no—
314C22×D5—21no—
315C22×D5—21no—
316C22×D5—21no—
317C22×D5C2×C22⋊C412yes—
318C22×D5C4×D412yes—
319C22×D5C4×D412yes—
320C5×Q8—22no—
321C5×Q8—22no—
322C5×Q8—22no—
323C5×Q8C2×C4214yes—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5C2×C22⋊C412yes—
341C2×C4×C5C2×C22⋊C412yes—
342C2×C4×C5C23×C411yescharacteristic
343C2×C4×C5C23×C411yescharacteristic
344C2×C4×C5C23×C411yescharacteristic
345C2×C4×C5C22×D411yescharacteristic
346C2×C4×C5C2×#4111yescharacteristic
347C2×C4×C5C2×#4111yescharacteristic
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—21no—
352C2×Dic5—21no—
353C2×Dic5—21no—
354C2×Dic5—21no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—41no—
359C2×Dic5—41no—
360C2×Dic5—41no—
361C2×Dic5—41no—
362C2×Dic5—41no—
363C2×Dic5—41no—
364C2×Dic5C2×C22⋊C412yes—
365C2×Dic5C2×C22⋊C412yes—
366C2×Dic5C2×C22⋊C412yes—
367C2×Dic5C4×D412yes—
368C2×Dic5C4×D412yes—
369C4×D5—216no—
370C4×D5—84no—
371C4×D5C2×C4214yes—
372C4×D5#11714yes—
373C4×D5C4×D414yes—
374C4×D5C4×D414yes—
375Dic10—22no—
376Dic10—22no—
377Dic10—22no—
378Dic10—216no—
379Dic10C2×C4214yes—
380C5×C8—22no—
381C5×C8—22no—
382#168—22no—
383#168—22no—
384C22×Q8—54no—
385C22×Q8—54no—
386C22×Q8—54no—
387C22×Q8—51no—
388C22×Q8—101no—
389C22×Q8—102no—
390C22×Q8—102no—
391C22×Q8—102no—
392C22×Q8C22×D511yescharacteristic
393C23×C4—51no—
394C23×C4—101no—
395C23×C4—101no—
396C2×M16—54no—
397C2×M16—102no—
398C2×M16—102no—
399C22×C8—51no—
400C22×C8—51no—
401C22×C8—54no—
402C22×C8—102no—
403C22×C8—102no—
404C22×C8C22×D511yescharacteristic
405C22×C8C22×D511yescharacteristic
406C4×Q8—22no—
407C4×Q8—54no—
408C4×Q8—54no—
409C4×Q8—54no—
410C4×Q8—108no—
411C4×Q8—102no—
412C4×Q8—102no—
413C4×Q8—108no—
414C4×Q8—102no—
415C4×Q8C4×D514yescomplemented
416#117—54no—
417#117—54no—
418#117—54no—
419#117—54no—
420#117—108no—
421#117—108no—
422#117—102no—
423#117—102no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—51no—
426C2×C4⋊C4—51no—
427C2×C4⋊C4—51no—
428C2×C4⋊C4—51no—
429C2×C4⋊C4—51no—
430C2×C4⋊C4—54no—
431C2×C4⋊C4—102no—
432C2×C4⋊C4—101no—
433C2×C4⋊C4—101no—
434C2×C4⋊C4—101no—
435C2×C4⋊C4—101no—
436C2×C4⋊C4C22×D511yescharacteristic
437C2×C4⋊C4C22×D511yescharacteristic
438C2×C4⋊C4C22×D511yescharacteristic
439C2×C22⋊C4—51no—
440C2×C22⋊C4—51no—
441C2×C22⋊C4—101no—
442C2×C22⋊C4—101no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—51no—
446C2×C42—101no—
447C2×C42—101no—
448C2×C42—101no—
449C2×C42—101no—
450C2×C42—101no—
451C2×C42—101no—
452C2×C42—101no—
453C2×C42—101no—
454C2×C42C22×D511yescharacteristic
455#103—54no—
456#103—54no—
457#103—54no—
458#103—54no—
459#103—54no—
460#103—54no—
461#103C4×D514yes—
462#103C4×D514yescomplemented
463#97—102no—
464#97—102no—
465C4×C8—22no—
466C4×C8—102no—
467#95—21no—
468#95—101no—
469#95—101no—
470#95—101no—
471C22×C5C22×C22⋊C411yescharacteristic
472C22×C5C2×C4×D411yescharacteristic
473C22×C5C2×C4×D411yescharacteristic
474C22×C5#57711yescharacteristic
475C22×C5#57711yescharacteristic
476C22×C5#57811yescharacteristic
477C22×C5#57811yescharacteristic
478C2×D5—22no—
479C2×D5—22no—
480C2×D5—22no—
481C2×D5—22no—
482C2×D5—22no—
483C2×D5—22no—
484C2×D5C4×C22⋊C414yes—
485C4×C5—22no—
486C4×C5—22no—
487C4×C5—24no—
488C4×C5—42no—
489C4×C5—42no—
490C4×C5—42no—
491C4×C5C22×C4211yescharacteristic
492C4×C5C2×#11711yescharacteristic
493C4×C5C2×C4×D411yescharacteristic
494C4×C5C2×C4×D411yescharacteristic
495Dic5—22no—
496Dic5—22no—
497Dic5—24no—
498Dic5—42no—
499Dic5—42no—
500Dic5—42no—
501Dic5C4×C22⋊C414yes—
502C24—51no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—516no—
507C2×Q8—52no—
508C2×Q8—52no—
509C2×Q8—52no—
510C2×Q8—104no—
511C2×Q8—104no—
512C2×Q8—104no—
513C2×Q8—108no—
514C2×Q8—108no—
515C2×Q8—108no—
516C2×Q8—101no—
517C2×Q8—101no—
518C2×Q8—101no—
519C2×Q8C2×C4×D512yes—
520C2×Q8C2×C4×D512yes—
521C2×Q8C2×C4×D512yes—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—51no—
527C22×C4—52no—
528C22×C4—52no—
529C22×C4—52no—
530C22×C4—52no—
531C22×C4—52no—
532C22×C4—52no—
533C22×C4—51no—
534C22×C4—51no—
535C22×C4—104no—
536C22×C4—104no—
537C22×C4—104no—
538C22×C4—104no—
539C22×C4—101no—
540C22×C4—101no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4—401no—
544C22×C4—401no—
545C22×C4D4×D511yescharacteristic
546C22×C4D4×D511yescharacteristic
547C22×C4C23×D511yescharacteristic
548M16—108no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—52no—
554C2×C8—52no—
555C2×C8—108no—
556C2×C8—101no—
557C2×C8—101no—
558C2×C8—101no—
559C2×C8—101no—
560C2×C8C2×C4×D512yes—
561C2×C8C2×C4×D512yes—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—24no—
566C4⋊C4—54no—
567C4⋊C4—54no—
568C4⋊C4—52no—
569C4⋊C4—52no—
570C4⋊C4—52no—
571C4⋊C4—104no—
572C4⋊C4—104no—
573C4⋊C4—104no—
574C4⋊C4—101no—
575C4⋊C4—101no—
576C4⋊C4—101no—
577C4⋊C4—104no—
578C4⋊C4C2×C4×D512yes—
579C4⋊C4C2×C4×D512yes—
580C4⋊C4C2×C4×D512yes—
581C22⋊C4—54no—
582C22⋊C4—54no—
583C22⋊C4—104no—
584C22⋊C4—104no—
585C42—24no—
586C42—52no—
587C42—52no—
588C42—81no—
589C42—104no—
590C42—104no—
591C42—104no—
592C42—104no—
593C42—104no—
594C42—401no—
595C42—401no—
596C42—401no—
597C42C2×C4×D512yes—
598C42D4×D512yes—
599C2×C5C2×C4×C22⋊C411yescharacteristic
600C2×C5#289811yescharacteristic
601C2×C5#289811yescharacteristic
602C2×C5#294711yescharacteristic
603C2×C5#294711yescharacteristic
604C2×C5#294911yescharacteristic
605C2×C5#295011yescharacteristic
606D5—24no—
607C23—52no—
608C23—52no—
609C23—52no—
610C23—101no—
611C23—101no—
612C23—101no—
613C23—101no—
614C23C2×D4×D511yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—22no—
618Q8—54no—
619Q8—1016no—
620Q8—102no—
621Q8—102no—
622Q8—102no—
623Q8C42×D514yes—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—52no—
641C2×C4—52no—
642C2×C4—52no—
643C2×C4—54no—
644C2×C4—54no—
645C2×C4—54no—
646C2×C4—54no—
647C2×C4—52no—
648C2×C4—52no—
649C2×C4—1016no—
650C2×C4—102no—
651C2×C4—101no—
652C2×C4—101no—
653C2×C4—101no—
654C2×C4—101no—
655C2×C4—102no—
656C2×C4—102no—
657C2×C4—102no—
658C2×C4—102no—
659C2×C4—102no—
660C2×C4—201no—
661C2×C4—201no—
662C2×C4—201no—
663C2×C4—201no—
664C2×C4—201no—
665C2×C4—201no—
666C2×C4—404no—
667C2×C4D5×C22⋊C412yes—
668C2×C4D5×C22⋊C412yes—
669C2×C4C22×C4×D511yescharacteristic
670C2×C4C22×C4×D511yescharacteristic
671C2×C4C22×C4×D511yescharacteristic
672C2×C4C2×D4×D511yescharacteristic
673C2×C4D5×#4111yescharacteristic
674C2×C4D5×#4111yescharacteristic
675C8—22no—
676C8—22no—
677C8—102no—
678C8—102no—
679C5#2041711yescharacteristic, complemented, Sylow
680C22—54no—
681C22—102no—
682C22—102no—
683C22—102no—
684C22—102no—
685C22—102no—
686C22—102no—
687C22C2×D5×C22⋊C411yescharacteristic
688C22C4×D4×D511yescharacteristic
689C22C4×D4×D511yescharacteristic
690C22#6609611yescharacteristic
691C22#6610011yescharacteristic
692C22#6610411yescharacteristic
693C22#6610511yescharacteristic
694C4—22no—
695C4—22no—
696C4—24no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—54no—
701C4—102no—
702C4—102no—
703C4—104no—
704C4—202no—
705C4—202no—
706C4—202no—
707C4C2×C42×D511yescharacteristic
708C4D5×#11711yescharacteristic
709C4C4×D4×D511yescharacteristic
710C4C4×D4×D511yescharacteristic
711C2—104no—
712C2C4×D5×C22⋊C411yescharacteristic
713C2#1061052111yescharacteristic
714C2#1061056311yescharacteristic
715C2#1061137911yescharacteristic
716C2#1061138011yescharacteristic
717C2#1061145011yescharacteristic
718C2#1061145111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC4×C5C22×C42
FrattiniC22×C4C23×D5
FittingC4×C5×#103C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenterC4×#103D5
hypocenterC5#20417
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
6. C4×C5×#103C2semidirect
7. #10602424C2semidirect
8. #10601013C2semidirect
9. Dic5×#103C2semidirect
10. C4×#3948C2semidirect
11. #10600268C2semidirect
14. #10599576C2semidirect
15. #10599574C2semidirect
22. #65906C4semidirect
51. #65091C4semidirect
52. D5×#103C4semidirect
80. C4×C5×Q8C2×C4semidirect
89. Q8×Dic5C2×C4semidirect
129. #4033C2×C4semidirect
135. C4×Dic10C2×C4semidirect
137. C5×#103C2×C4semidirect
141. #3967C2×C4semidirect
146. #3948C2×C4semidirect
150. #3942C2×C4semidirect
164. C4×#103D5semidirect
191. Q8×D5C42semidirect
415. C4×Q8C4×D5semidirect
462. #103C4×D5semidirect
679. C5#20417semidirect

Maximal subgroups

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

subgroupindex
C2×#659062
C2×#650912
C2×D5×#1032
C2×#649782
#106054812
C4×C5×#1032
#106024242
#106010132
Dic5×#1032
C4×#39482
#106002682
#105996602
#105996592
#105995762
#105995742
#204175