Finite Group Databasebeta

← #12964339

Subgroups — #12964339

Order 1280.

1658 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic10C211yesmaximal, characteristic
2C5×#2922C211yesmaximal, characteristic
3#10614246C211yesmaximal, characteristic
4#10611092C214yesmaximal, complemented
5#10611090C214yesmaximal, complemented
6#10610998C212yesmaximal, complemented
7#10610997C212yesmaximal, complemented
8#10610996C212yesmaximal, complemented
9#10610995C212yesmaximal, complemented
10#10610809C212yesmaximal, complemented
11#10610808C212yesmaximal, complemented
12#10610381C212yesmaximal
13#10610380C212yesmaximal
14M16×Dic10C211yesmaximal, characteristic, complemented
15#10610239C211yesmaximal, characteristic, complemented
16#10610176C211yesmaximal, characteristic, complemented
17C2×#64968C211yesmaximal, characteristic, complemented
18C4×C5×#41C2211yescharacteristic
19#41×Dic5C2212yes—
20#65904C411yescharacteristic
21#65903C412yes—
22Q8×Dic10C411yescharacteristic
23#65877C412yes—
24#65877C411yescharacteristic
25#65873C414yes—
26#65873C412yes—
27D4×Dic10C411yescharacteristic
28D4×Dic10C412yes—
29#65851C2212yes—
30#65851C2214yes—
31#65804C2211yescharacteristic
32#65804C2212yes—
33C2×C4×Dic10C2212yes—
34C2×C4×Dic10C2211yescharacteristic
35C5×#433C2212yes—
36C5×#433C2212yes—
37C5×#431C2212yes—
38C5×#431C2212yes—
39C5×#424C2211yescharacteristic
40C5×#424C2211yescharacteristic
41C5×#408C2211yescharacteristic
42C5×#408C2211yescharacteristic
43C4×C5×M16C2211yescharacteristic
44C2×C4×C5×C8C2211yescharacteristic
45#65523C2212yes—
46#65411C2212yes—
47#65408C2212yes—
48#65407C2212yes—
49M16×Dic5C2212yes—
50#65391C2212yes—
51#65390C2212yes—
52C2×#3947C2212yes—
53C2×#3946C2212yes—
54#65289C2214yes—
55#65286C2212yes—
56#65215C2212yes—
57#65214C2212yes—
58#65213C2211yescharacteristic
59C2×C4⋊#168C2211yescharacteristic
60#65120C2214yes—
61#65120C2214yes—
62#65120C2214yes—
63#65119C2214yes—
64#65117C2214yes—
65#65117C2214yes—
66#65117C2214yes—
67#65117C2214yes—
68#65009C2214yes—
69#65009C2214yes—
70#65009C2214yes—
71#65009C2214yes—
72#65008C2214yes—
73#65008C2214yes—
74#65008C2214yes—
75#65007C2214yes—
76#64990C2214yes—
77#64990C2214yes—
78#64968C2212yes—
79#64968C2212yes—
80#64968C2211yescharacteristic
81#64968C2212yes—
82#64968C2212yes—
83#64968C2211yescharacteristic
84#64968C2211yescharacteristic
85#64968C2211yescharacteristic
86#64968C2212yes—
87#64968C2212yes—
88C8×Dic10C2212yes—
89C8×Dic10C2212yes—
90C8×Dic10C2212yes—
91C8×Dic10C2212yes—
92#60254—51nomaximal, Sylow
93C2×C5×#41C2311yescharacteristic
94C22×Dic10C2×C412yes—
95C22×Dic10C2×C411yescharacteristic
96C2×C5×M16C2311yescharacteristic
97C2×C5×M16C2311yescharacteristic
98C22×C5×C8C2311yescharacteristic
99C22×C5×C8C2311yescharacteristic
100C4×C5×Q8C2×C411yescharacteristic
101C4×C5×Q8C2×C411yescharacteristic
102C4×C5×D4C2×C412yes—
103C4×C5×D4C2×C411yescharacteristic
104C4×C5×D4C2×C412yes—
105C4×C5×D4C2×C411yescharacteristic
106C5×#117C2311yescharacteristic
107C5×#117C2312yes—
108C2×C42×C5C2311yescharacteristic
109C2×C42×C5C2312yes—
110Q8×Dic5C2×C412yes—
111Q8×Dic5C2×C412yes—
112D4×Dic5C2×C414yes—
113D4×Dic5C2×C412yes—
114D4×Dic5C2×C414yes—
115D4×Dic5C2×C412yes—
116#4072C2312yes—
117#4072C2314yes—
118C2×C4⋊Dic5C2×C412yes—
119C2×C4⋊Dic5C2×C411yescharacteristic
120#4070C2×C412yes—
121#4070C2×C412yes—
122#4070C2×C412yes—
123#4070C2×C412yes—
124#4070C2×C414yes—
125C2×#683C2×C414yes—
126C2×#683C2×C412yes—
127C2×C4×Dic5C2312yes—
128C2×C4×Dic5C2314yes—
129C2×#681C2312yes—
130C22×#168C2312yes—
131#4036C2×C412yes—
132#4036C2×C414yes—
133#4036C2×C412yes—
134#4036C2×C414yes—
135#4034C2×C412yes—
136#4034C2×C414yes—
137#4034C2×C412yes—
138#4034C2×C414yes—
139#4024C2×C414yes—
140#4024C2×C414yes—
141#4024C2×C414yes—
142#4024C2×C414yes—
143#4024C2×C414yes—
144#4024C2×C414yes—
145#4016C2×C412yes—
146#4016C2×C414yes—
147#4015C2×C411yescharacteristic
148#4015C2×C412yes—
149#4015C2×C411yescharacteristic
150#4015C2×C412yes—
151C4×Dic10C2×C412yes—
152C4×Dic10C2×C411yescharacteristic
153C4×Dic10C2×C414yes—
154C4×Dic10C2×C412yes—
155C4×Dic10C2×C412yes—
156C4×Dic10C2×C411yescharacteristic
157C4×Dic10C2311yescharacteristic
158C4×Dic10C2312yes—
159C4×Dic10C2311yescharacteristic
160C4×Dic10C2314yes—
161C4×Dic10C2312yes—
162C4×Dic10C2314yes—
163C4×Dic10C2312yes—
164C5×C4⋊C8C2312yes—
165C5×C4⋊C8C2312yes—
166C5×C4⋊C8C2312yes—
167C5×C4⋊C8C2312yes—
168C5×C22⋊C8C2312yes—
169C5×C22⋊C8C2312yes—
170C5×C22⋊C8C2312yes—
171C5×C22⋊C8C2312yes—
172C5×#97C2312yes—
173C4×C5×C8C2311yescharacteristic
174C4×C5×C8C2311yescharacteristic
175C4×C5×C8C2311yescharacteristic
176C4×C5×C8C2311yescharacteristic
177C4×C5×C8C2312yes—
178C22⋊#168C2314yes—
179C22⋊#168C2314yes—
180#3947C2312yes—
181#3947C2312yes—
182#3947C2314yes—
183#3947C2314yes—
184#3947C2312yes—
185#3947C2312yes—
186#3947C2314yes—
187#3946C2312yes—
188#3946C2312yes—
189#3946C2314yes—
190#3946C2314yes—
191#3946C2314yes—
192#3946C2314yes—
193#3946C2314yes—
194#3946C2312yes—
195#3946C2314yes—
196#3946C2312yes—
197C8×Dic5C2314yes—
198C8×Dic5C2314yes—
199C8×Dic5C2314yes—
200C4⋊#168C2312yes—
201C4⋊#168C2312yes—
202C4⋊#168C2311yescharacteristic
203C4⋊#168C2311yescharacteristic
204C4⋊#168C2312yes—
205#3935C2314yes—
206C4×#168C2314yes—
207Q8×#41—51no—
208#2987—54no—
209#2986—52no—
210#2985—54no—
211#2985—52no—
212#2984—52no—
213#2983—52no—
214Q8×M16—51no—
215#2962—52no—
216#2962—51no—
217#2961—52no—
218#2960—51no—
219C2×#446—51no—
220#2925—52no—
221#2925—51no—
222#2923—52no—
223#2922D511yescharacteristic
224C5×#41—22no—
225C5×#41—22no—
226C2×C5×Q8C22×C411yescharacteristic
227C2×C5×D4C22×C412yes—
228C2×C5×D4C22×C411yescharacteristic
229C22×C4×C5C22×C412yes—
230C22×C4×C5C22×C411yescharacteristic
231C22×C4×C5C22×C412yes—
232C22×C4×C5C22×C411yescharacteristic
233C22×C4×C5C2412yes—
234C22×C4×C5C2411yescharacteristic
235C22×Dic5C22×C414yes—
236C22×Dic5C22×C412yes—
237C22×Dic5C22×C414yes—
238C22×Dic5C22×C412yes—
239C2×Dic10—42no—
240C2×Dic10—44no—
241C2×Dic10C22×C411yescharacteristic
242C2×Dic10C22×C412yes—
243C2×Dic10C22×C411yescharacteristic
244C2×Dic10C22×C414yes—
245C2×Dic10C22×C412yes—
246C2×Dic10C22×C414yes—
247C2×Dic10C22×C412yes—
248C5×M16—22no—
249C5×M16—22no—
250C2×C5×C8—22no—
251C2×C5×C8—22no—
252C2×C5×C8C2411yescharacteristic
253C2×C5×C8C2411yescharacteristic
254C2×C5×C8C2411yescharacteristic
255C2×C5×C8C2411yescharacteristic
256C2×C5×C8C2412yes—
257C2×C5×C8C2412yes—
258C5×C4⋊C4C22×C412yes—
259C5×C4⋊C4C22×C412yes—
260C5×C4⋊C4C22×C411yescharacteristic
261C5×C4⋊C4C22×C411yescharacteristic
262C5×C22⋊C4C22×C412yes—
263C5×C22⋊C4C22×C412yes—
264C5×C22⋊C4C22×C412yes—
265C42×C5C22×C412yes—
266C42×C5C22×C411yescharacteristic
267C42×C5C22×C412yes—
268C42×C5C22×C411yescharacteristic
269C42×C5C2411yescharacteristic
270C42×C5C2412yes—
271C42×C5C2411yescharacteristic
272C22⋊Dic5C22×C414yes—
273C22⋊Dic5C22×C414yes—
274C22⋊Dic5C22×C414yes—
275C4⋊Dic5C22×C411yescharacteristic
276C4⋊Dic5C22×C412yes—
277C4⋊Dic5C22×C411yescharacteristic
278C4⋊Dic5C22×C414yes—
279C4⋊Dic5C22×C412yes—
280C4⋊Dic5C22×C414yes—
281C4⋊Dic5C22×C412yes—
282C4⋊Dic5C22×C414yes—
283C4⋊Dic5C22×C414yes—
284C4⋊Dic5C22×C412yes—
285C4⋊Dic5C22×C412yes—
286#683C22×C412yes—
287#683C22×C414yes—
288#683C22×C412yes—
289#683C22×C414yes—
290#683C22×C412yes—
291#683C22×C414yes—
292#683C22×C412yes—
293#683C22×C414yes—
294#683C22×C414yes—
295#683C22×C414yes—
296C4×Dic5C22×C414yes—
297C4×Dic5C22×C412yes—
298C4×Dic5C22×C414yes—
299C4×Dic5C22×C412yes—
300C4×Dic5C2414yes—
301C4×Dic5C2412yes—
302C4×Dic5C2412yes—
303#681—24no—
304C2×#168—24no—
305C2×#168C2412yes—
306C2×#168C2414yes—
307C2×#168C2412yes—
308Q82—51no—
309#557—52no—
310#557—51no—
311#554—54no—
312#554—52no—
313#554—52no—
314#554—51no—
315D4×Q8—51no—
316D4×Q8—52no—
317#533—52no—
318#533—54no—
319#533—51no—
320#533—52no—
321C4×#41—52no—
322C4×#41C2×D511yescharacteristic
323C2×C4×Q8—51no—
324C2×C4×Q8—52no—
325#446—54no—
326#446—54no—
327#446—54no—
328#446—54no—
329#446—54no—
330#446—54no—
331#446—54no—
332#446—54no—
333#446—54no—
334#446—51no—
335#446—51no—
336#446—51no—
337#446—52no—
338#446—51no—
339#446—52no—
340#446—52no—
341#446—52no—
342#446—52no—
343#446—52no—
344C8×Q8—54no—
345C8×Q8—52no—
346C8×Q8—52no—
347C8×Q8—52no—
348C8×Q8—52no—
349#433—54no—
350#433—54no—
351#433—54no—
352#433—54no—
353#433—54no—
354#433C2×D512yes—
355#433C2×D512yes—
356#432—52no—
357#432—54no—
358#432—54no—
359#432—54no—
360#431—52no—
361#431—54no—
362#431C2×D512yes—
363#431C2×D512yes—
364#424—52no—
365#424—52no—
366#424C2×D511yescharacteristic
367#424C2×D511yescharacteristic
368#423—52no—
369#423—51no—
370C2×C4⋊C8—52no—
371C2×C4⋊C8—51no—
372#408—52no—
373#408C2×D511yescharacteristic
374#408C2×D511yescharacteristic
375#405—52no—
376#405—52no—
377#405—52no—
378C4×M16—52no—
379C4×M16C2×D511yescharacteristic
380C2×#97—52no—
381C2×C4×C8C2×D511yescharacteristic
382C23×C5C23×C412yes—
383C23×C5C23×C411yescharacteristic
384C5×Q8—22no—
385C5×D4—24no—
386C5×D4—22no—
387C2×C4×C5—22no—
388C2×C4×C5—24no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—41no—
392C2×C4×C5—42no—
393C2×C4×C5C23×C412yes—
394C2×C4×C5C23×C411yescharacteristic
395C2×C4×C5C23×C412yes—
396C2×C4×C5C23×C411yescharacteristic
397C2×C4×C5C23×C412yes—
398C2×C4×C5C23×C411yescharacteristic
399C2×C4×C5C23×C411yescharacteristic
400C2×C4×C5C23×C411yescharacteristic
401C2×C4×C52−1+412yes—
402C2×C4×C52−1+412yes—
403C2×C4×C5C2511yescharacteristic
404C2×Dic5—42no—
405C2×Dic5—44no—
406C2×Dic5—42no—
407C2×Dic5—44no—
408C2×Dic5C23×C412yes—
409C2×Dic5C23×C412yes—
410C2×Dic5C23×C414yes—
411C2×Dic5C23×C412yes—
412C2×Dic5C23×C414yes—
413C2×Dic5C23×C412yes—
414Dic10—22no—
415Dic10—22no—
416Dic10—24no—
417Dic10—44no—
418Dic10—42no—
419Dic10—44no—
420Dic10—42no—
421C5×C8—21no—
422C5×C8—21no—
423C5×C8—21no—
424C5×C8—21no—
425C5×C8—22no—
426C5×C8—22no—
427#168—22no—
428#168—22no—
429#168—24no—
430C2×#41C22×D511yescharacteristic
431C22×Q8—51no—
432C22×Q8—52no—
433C2×M16—52no—
434C2×M16C22×D511yescharacteristic
435C2×M16C22×D511yescharacteristic
436C22×C8—52no—
437C22×C8C22×D511yescharacteristic
438C22×C8C22×D511yescharacteristic
439C4⋊Q8—52no—
440C4⋊Q8—54no—
441C4⋊Q8—52no—
442C4⋊Q8—54no—
443C4⋊Q8—51no—
444C4⋊Q8—52no—
445C4⋊Q8—51no—
446C4⋊Q8—52no—
447#125—52no—
448#125—54no—
449#125—52no—
450#125—54no—
451#125—52no—
452#125—54no—
453C22⋊Q8—52no—
454C22⋊Q8—52no—
455C22⋊Q8—52no—
456C22⋊Q8—52no—
457C22⋊Q8—54no—
458C22⋊Q8—54no—
459C22⋊Q8—54no—
460C22⋊Q8—54no—
461C22⋊Q8—54no—
462C22⋊Q8—54no—
463C22⋊Q8—54no—
464C4×Q8—52no—
465C4×Q8—52no—
466C4×Q8—51no—
467C4×Q8—52no—
468C4×Q8—51no—
469C4×Q8—52no—
470C4×Q8—52no—
471C4×Q8—54no—
472C4×Q8—51no—
473C4×Q8—51no—
474C4×Q8—52no—
475C4×Q8—54no—
476C4×Q8—52no—
477C4×Q8—54no—
478C4×Q8—52no—
479C4×Q8C4×D511yescharacteristic
480C4×Q8C4×D511yescharacteristic
481C4×D4—54no—
482C4×D4—52no—
483C4×D4—54no—
484C4×D4—52no—
485C4×D4C4×D512yes—
486C4×D4C4×D511yescharacteristic
487C4×D4C4×D512yes—
488C4×D4C4×D511yescharacteristic
489#117—52no—
490#117—54no—
491#117C22×D511yescharacteristic
492#117C22×D512yes—
493C2×C4⋊C4—52no—
494C2×C4⋊C4—54no—
495C2×C4⋊C4—51no—
496C2×C4⋊C4—52no—
497C2×C42—52no—
498C2×C42—54no—
499C2×C42C22×D511yescharacteristic
500C2×C42C22×D512yes—
501C4⋊C8—52no—
502C4⋊C8—52no—
503C4⋊C8—52no—
504C4⋊C8—52no—
505C4⋊C8—54no—
506C4⋊C8—54no—
507C4⋊C8—54no—
508C4⋊C8—54no—
509C4⋊C8—54no—
510C4⋊C8—54no—
511C4⋊C8—51no—
512C4⋊C8—51no—
513C4⋊C8—52no—
514C4⋊C8—52no—
515C4⋊C8—52no—
516C4⋊C8C22×D512yes—
517C4⋊C8C22×D512yes—
518C4⋊C8C22×D512yes—
519C4⋊C8C22×D512yes—
520C22⋊C8—54no—
521C22⋊C8—54no—
522C22⋊C8C22×D512yes—
523C22⋊C8C22×D512yes—
524C22⋊C8C22×D512yes—
525C22⋊C8C22×D512yes—
526#97—52no—
527#97—52no—
528#97—52no—
529#97—52no—
530#97—54no—
531#97—54no—
532#97—54no—
533#97—54no—
534#97C22×D512yes—
535C4×C8—54no—
536C4×C8—54no—
537C4×C8—54no—
538C4×C8—54no—
539C4×C8C22×D511yescharacteristic
540C4×C8C22×D511yescharacteristic
541C4×C8C22×D511yescharacteristic
542C4×C8C22×D511yescharacteristic
543C4×C8C22×D512yes—
544C22×C5—21no—
545C22×C5—21no—
546C22×C5—22no—
547C22×C5—22no—
548C22×C5—22no—
549C22×C5#51912yes—
550C22×C5C24×C411yescharacteristic
551C4×C5—22no—
552C4×C5—21no—
553C4×C5—22no—
554C4×C5—21no—
555C4×C5—22no—
556C4×C5—21no—
557C4×C5#51912yes—
558C4×C5#56812yes—
559C4×C5C2×2−1+411yescharacteristic
560C4×C5C2×2−1+411yescharacteristic
561Dic5—22no—
562Dic5—22no—
563Dic5—24no—
564Dic5—22no—
565Dic5—24no—
566Dic5—22no—
567#41—22no—
568#41—22no—
569C2×Q8—51no—
570C2×Q8—51no—
571C2×Q8—52no—
572C2×Q8—54no—
573C2×Q8—52no—
574C2×Q8—54no—
575C2×Q8—52no—
576C2×Q8—202no—
577C2×Q8—204no—
578C2×Q8C2×C4×D511yescharacteristic
579C2×D4C2×C4×D512yes—
580C2×D4C2×C4×D511yescharacteristic
581C22×C4—54no—
582C22×C4—52no—
583C22×C4—54no—
584C22×C4—52no—
585C22×C4C2×C4×D512yes—
586C22×C4C2×C4×D511yescharacteristic
587C22×C4C2×C4×D512yes—
588C22×C4C2×C4×D511yescharacteristic
589C22×C4C23×D512yes—
590C22×C4C23×D511yescharacteristic
591M16—22no—
592M16—22no—
593M16—104no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—54no—
597C2×C8—52no—
598C2×C8—52no—
599C2×C8—104no—
600C2×C8C23×D511yescharacteristic
601C2×C8C23×D512yes—
602C2×C8C23×D512yes—
603C2×C8C23×D511yescharacteristic
604C2×C8C23×D511yescharacteristic
605C2×C8C23×D511yescharacteristic
606C4⋊C4—52no—
607C4⋊C4—51no—
608C4⋊C4—54no—
609C4⋊C4—52no—
610C4⋊C4—52no—
611C4⋊C4—54no—
612C4⋊C4—54no—
613C4⋊C4—52no—
614C4⋊C4—54no—
615C4⋊C4—52no—
616C4⋊C4—51no—
617C4⋊C4—52no—
618C4⋊C4—54no—
619C4⋊C4—54no—
620C4⋊C4—52no—
621C4⋊C4—52no—
622C4⋊C4—54no—
623C4⋊C4—54no—
624C4⋊C4—54no—
625C4⋊C4—54no—
626C4⋊C4—52no—
627C4⋊C4C2×C4×D512yes—
628C4⋊C4C2×C4×D512yes—
629C4⋊C4C2×C4×D511yescharacteristic
630C4⋊C4C2×C4×D511yescharacteristic
631C22⋊C4—54no—
632C22⋊C4—54no—
633C22⋊C4—54no—
634C22⋊C4C2×C4×D512yes—
635C22⋊C4C2×C4×D512yes—
636C22⋊C4C2×C4×D512yes—
637C42—54no—
638C42—52no—
639C42—54no—
640C42—52no—
641C42—52no—
642C42—54no—
643C42—52no—
644C42C2×C4×D512yes—
645C42C2×C4×D511yescharacteristic
646C42C2×C4×D512yes—
647C42C2×C4×D511yescharacteristic
648C42C23×D512yes—
649C42C23×D511yescharacteristic
650C42C23×D511yescharacteristic
651C2×C5—22no—
652C2×C5—42no—
653C2×C5C2×#51911yescharacteristic
654C2×C5C2×#56811yescharacteristic
655C2×C5#357311yescharacteristic
656C23C22×C4×D512yes—
657C23C22×C4×D511yescharacteristic
658Q8—22no—
659Q8—102no—
660Q8—102no—
661Q8—104no—
662Q8—202no—
663Q8—204no—
664Q8—202no—
665Q8—204no—
666D4—24no—
667D4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—52no—
675C2×C4—52no—
676C2×C4—54no—
677C2×C4—52no—
678C2×C4—54no—
679C2×C4—52no—
680C2×C4—202no—
681C2×C4—204no—
682C2×C4—202no—
683C2×C4—204no—
684C2×C4C22×C4×D512yes—
685C2×C4C22×C4×D511yescharacteristic
686C2×C4C22×C4×D512yes—
687C2×C4C22×C4×D511yescharacteristic
688C2×C4C22×C4×D512yes—
689C2×C4C22×C4×D511yescharacteristic
690C2×C4C22×C4×D511yescharacteristic
691C2×C4C22×C4×D511yescharacteristic
692C2×C4#415012yes—
693C2×C4#415012yes—
694C2×C4C24×D511yescharacteristic
695C8—21no—
696C8—21no—
697C8—21no—
698C8—21no—
699C8—22no—
700C8—22no—
701C8—102no—
702C8—102no—
703C8—104no—
704C5#6025411yescharacteristic, complemented, Sylow
705C22—21no—
706C22—21no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22#6585012yes—
711C22C23×C4×D511yescharacteristic
712C4—22no—
713C4—21no—
714C4—22no—
715C4—21no—
716C4—21no—
717C4—22no—
718C4—102no—
719C4—102no—
720C4—104no—
721C4—102no—
722C4—102no—
723C4—104no—
724C4#6585012yes—
725C4#6608412yes—
726C4C2×#415011yescharacteristic
727C4C2×#415011yescharacteristic
728C2—22no—
729C2—42no—
730C2C2×#6585011yescharacteristic
731C2C2×#6608411yescharacteristic
732C2#1061906111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D5
commutator, socleC22×C5C24×C4
FittingC5×#2922C2
prime radicalC2×C5×#41C23
cosocleC2×C4×C5C25
hypercenter#2922D5
hypocenterC5#60254
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #2922

Complements

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

NH ≅ G/Ntype
4. #10611092C2semidirect
5. #10611090C2semidirect
6. #10610998C2semidirect
7. #10610997C2semidirect
8. #10610996C2semidirect
9. #10610995C2semidirect
10. #10610809C2semidirect
11. #10610808C2semidirect
14. M16×Dic10C2semidirect
15. #10610239C2semidirect
16. #10610176C2semidirect
17. C2×#64968C2semidirect
704. C5#60254semidirect

Maximal subgroups

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

subgroupindex
#41×Dic102
C5×#29222
#106142462
#106110922
#106110902
#106109982
#106109972
#106109962
#106109952
#106108092
#106108082
#106103812
#106103802
M16×Dic102
#106102392
#106101762
C2×#649682
#602545