Finite Group Databasebeta

← C2×#10612197 #12979006

Subgroups — C2×#10612197 #12979006

Order 1280.

1778 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66055C211yesmaximal, characteristic
2C2×#65903C211yesmaximal, characteristic
3C2×C5×#462C211yesmaximal, characteristic
4C2×#65471C211yesmaximal, characteristic
5C2×#65471C211yesmaximal, characteristic
6C2×#65473C211yesmaximal, characteristic
7C2×Q16×Dic5C211yesmaximal, characteristic
8C2×#65371C211yesmaximal, characteristic
9C2×#65319C211yesmaximal, characteristic
10#10612197C2116yesmaximal, direct product factor
11C2×#65118C211yesmaximal, characteristic
12C2×#65117C211yesmaximal, characteristic
13C2×#65086C211yesmaximal, characteristic
14C2×#65081C211yesmaximal, characteristic
15C2×#65085C211yesmaximal, characteristic
16C2×#65080C211yesmaximal, characteristic
17C22×C5×Q16C2211yescharacteristic
18C22×C5×Q16C2211yescharacteristic
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C4×C5×Q8C2211yescharacteristic
21C2×Q8×Dic5C2211yescharacteristic
22C2×Q8×Dic5C2211yescharacteristic
23C2×Q8×Dic5C2211yescharacteristic
24C2×Q8×Dic5C2211yescharacteristic
25C2×#4090C2211yescharacteristic
26C2×#4090C2211yescharacteristic
27C22×#689C2211yescharacteristic
28#66055—24no—
29#66055C2218yes—
30#65903—24no—
31#65903C2218yes—
32C2×#4036—21no—
33C2×#4036—21no—
34C2×#4036C2211yescharacteristic
35C2×#4035—21no—
36C2×#4035—21no—
37C2×#4034—21no—
38C2×#4034C2211yescharacteristic
39C2×#4033—21no—
40C2×#4016—21no—
41C2×#4016C2211yescharacteristic
42C2×C4×Dic10—21no—
43C2×C4×Dic10C2211yescharacteristic
44C2×C4×Dic10C2211yescharacteristic
45C5×#462C2218yes—
46C2×C5×C4⋊C8C2211yescharacteristic
47C2×C5×#103C2211yescharacteristic
48C2×C5×#103C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×#3967C2211yescharacteristic
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54#65473C2218yes—
55Q16×Dic5C2218yes—
56#65471C2218yes—
57#65471C2218yes—
58C2×#3950C2211yescharacteristic
59C2×#3949C2211yescharacteristic
60C2×#3948C2211yescharacteristic
61C2×#3948C2211yescharacteristic
62C2×#3947C2211yescharacteristic
63C2×#3946C2211yescharacteristic
64C2×#3946C2211yescharacteristic
65C2×C8×Dic5C2211yescharacteristic
66#65371C2218yes—
67#65319C2218yes—
68C2×#3942C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3935C2211yescharacteristic
71#65118C2218yes—
72#65117C2218yes—
73#65086C2218yes—
74#65085C2218yes—
75#65081C2218yes—
76#65080C2218yes—
77C2×#3374—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×Q8C2311yescharacteristic
80C22×C5×Q8C2311yescharacteristic
81C22×Dic10—21no—
82C22×Dic10D411yescharacteristic
83C22×Dic10C2311yescharacteristic
84C2×C5×Q16—24no—
85C2×C5×Q16—24no—
86C2×C5×Q16C2314yes—
87C2×C5×Q16C2314yes—
88C22×C5×C8C2311yescharacteristic
89C22×C5×C8C2311yescharacteristic
90C5×C4⋊Q8—22no—
91C5×C4⋊Q8C2314yes—
92C4×C5×Q8—22no—
93C4×C5×Q8C2314yes—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—21no—
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C42×C5—21no—
99C2×C42×C5C2311yescharacteristic
100Q8×Dic5—22no—
101Q8×Dic5—22no—
102Q8×Dic5—22no—
103Q8×Dic5—22no—
104Q8×Dic5C2314yes—
105Q8×Dic5C2314yes—
106Q8×Dic5C2314yes—
107Q8×Dic5C2314yes—
108#4090—22no—
109#4090—22no—
110#4090C2314yes—
111#4090C2314yes—
112C2×#689—24no—
113C2×#689C2314yes—
114C2×C4⋊Dic5—21no—
115C2×C4⋊Dic5—21no—
116C2×C4⋊Dic5—21no—
117C2×C4⋊Dic5—21no—
118C2×C4⋊Dic5—21no—
119C2×C4⋊Dic5D411yescharacteristic
120C2×C4⋊Dic5C2311yescharacteristic
121C2×C4⋊Dic5C2311yescharacteristic
122C2×C4⋊Dic5C2311yescharacteristic
123C2×#683—21no—
124C2×#683—21no—
125C2×#683—21no—
126C2×#683—21no—
127C2×#683—21no—
128C2×#683—21no—
129C2×#683—21no—
130C2×#683—21no—
131C2×#683—21no—
132C2×#683D411yescharacteristic
133C2×#683D411yescharacteristic
134C2×C4×Dic5—21no—
135C2×C4×Dic5—21no—
136C2×C4×Dic5—21no—
137C2×C4×Dic5—21no—
138C2×C4×Dic5—21no—
139C2×C4×Dic5C2311yescharacteristic
140C2×C4×Dic5C2311yescharacteristic
141C22×#168C2311yescharacteristic
142C22×#168C2311yescharacteristic
143#4036—28no—
144#4036—28no—
145#4036—22no—
146#4036C2314yes—
147#4035—28no—
148#4035—28no—
149#4034—28no—
150#4034—22no—
151#4034C2314yes—
152#4033—28no—
153#4016—22no—
154#4016—28no—
155#4016C2314yes—
156C4×Dic10—22no—
157C4×Dic10—28no—
158C4×Dic10D414yes—
159C4×Dic10C2314yes—
160C4×Dic10C2314yes—
161C5×C4⋊C8C2314yes—
162C5×#103C2314yes—
163C5×#103C2314yes—
164#3967C2314yes—
165#3967C2314yes—
166#3967C2314yes—
167#3967C2314yes—
168#3967C2314yes—
169#3950C2314yes—
170#3949C2314yes—
171#3948C2314yes—
172#3948C2314yes—
173#3947C2314yes—
174#3946C2314yes—
175#3946C2314yes—
176C8×Dic5C2314yes—
177#3942C2314yes—
178#3940C2314yes—
179#3935C2314yes—
180C2×#557—51no—
181C2×#557—51no—
182#3374—516no—
183C2×#491—51no—
184C2×#491—51no—
185C2×#487—51no—
186C2×#479—51no—
187C2×#479—51no—
188C2×#475—51no—
189C2×#462—51no—
190C2×#462—51no—
191C2×#462D511yescharacteristic
192C2×#446—51no—
193C2×#441—51no—
194C2×#441—51no—
195C2×C4×Q16—51no—
196C2×C5×Q8—21no—
197C2×C5×Q8—21no—
198C2×C5×Q8—21no—
199C2×C5×Q8—22no—
200C2×C5×Q8—22no—
201C2×C5×Q8—22no—
202C2×C5×Q8—22no—
203C2×C5×Q8—22no—
204C2×C5×Q8#4114yes—
205C2×C5×Q8C2412yes—
206C2×C5×Q8C2412yes—
207C2×C5×Q8C2412yes—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5C2×D411yescharacteristic
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2411yescharacteristic
215C22×Dic5—21no—
216C22×Dic5—21no—
217C22×Dic5—21no—
218C22×Dic5—21no—
219C22×Dic5C2×D411yescharacteristic
220C22×Dic5C2×D411yescharacteristic
221C22×Dic5C2×D411yescharacteristic
222C22×Dic5C2×D411yescharacteristic
223C2×Dic10—24no—
224C2×Dic10—22no—
225C2×Dic10—22no—
226C2×Dic10—21no—
227C2×Dic10—24no—
228C2×Dic10—44no—
229C2×Dic10C2×D414yes—
230C2×Dic10C2412yes—
231C5×Q16—28no—
232C5×Q16—28no—
233C2×C5×C8—22no—
234C2×C5×C8—22no—
235C2×C5×C8C2412yes—
236C2×C5×C8C2412yes—
237C5×C4⋊C4—24no—
238C5×C4⋊C4—24no—
239C5×C4⋊C4—24no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4C2412yes—
242C42×C5—24no—
243C42×C5C2×D412yes—
244C42×C5C2412yes—
245#689—28no—
246C4⋊Dic5—21no—
247C4⋊Dic5—21no—
248C4⋊Dic5—21no—
249C4⋊Dic5—24no—
250C4⋊Dic5—24no—
251C4⋊Dic5—24no—
252C4⋊Dic5—24no—
253C4⋊Dic5—24no—
254C4⋊Dic5C2×D414yes—
255C4⋊Dic5C2412yes—
256C4⋊Dic5C2412yes—
257C4⋊Dic5C2412yes—
258#683—24no—
259#683—24no—
260#683—24no—
261#683—24no—
262#683—24no—
263#683—24no—
264#683—24no—
265#683—24no—
266#683—24no—
267#683C2×D414yes—
268#683C2×D414yes—
269C4×Dic5—24no—
270C4×Dic5—24no—
271C4×Dic5—24no—
272C4×Dic5—24no—
273C4×Dic5—24no—
274C4×Dic5C2×D412yes—
275C4×Dic5C2×D412yes—
276C4×Dic5C2412yes—
277C4×Dic5C2412yes—
278C2×#168—22no—
279C2×#168—22no—
280C2×#168C2412yes—
281C2×#168C2412yes—
282C22×Q16—51no—
283C22×Q16C2×D511yescharacteristic
284C22×Q16C2×D511yescharacteristic
285#557—58no—
286#557—58no—
287#557—104no—
288#557—104no—
289C2×C4⋊Q8—51no—
290C2×C4⋊Q8—51no—
291C2×C4⋊Q8—51no—
292C2×C4⋊Q8—101no—
293C2×C4⋊Q8C2×D511yescharacteristic
294C2×#125—51no—
295C2×#125—51no—
296C2×#125—101no—
297C2×#125—101no—
298C2×#125—101no—
299C2×#125—101no—
300C2×#125—101no—
301C2×C4×Q8—51no—
302C2×C4×Q8—51no—
303C2×C4×Q8—51no—
304C2×C4×Q8—51no—
305C2×C4×Q8—51no—
306C2×C4×Q8—51no—
307C2×C4×Q8—101no—
308C2×C4×Q8—101no—
309C2×C4×Q8C2×D511yescharacteristic
310#491—58no—
311#491—58no—
312#487—58no—
313#479—58no—
314#479—58no—
315#475—58no—
316#462—58no—
317#462—58no—
318#462C2×D518yes—
319#446—58no—
320#441—58no—
321#441—58no—
322C4×Q16—58no—
323C2×#107—51no—
324C2×#106—51no—
325C2×#106—51no—
326C2×C4⋊C8—51no—
327C2×C4⋊C8—51no—
328C2×C4⋊C8C2×D511yescharacteristic
329C2×#103—51no—
330C2×#103—51no—
331C2×#103—51no—
332C2×#103—51no—
333C2×#103—51no—
334C2×#103—51no—
335C2×#103—51no—
336C2×#103—51no—
337C2×#103C2×D511yescharacteristic
338C2×#103C2×D511yescharacteristic
339C2×#97—51no—
340C2×#97—51no—
341C2×C4×C8—51no—
342C23×C5C22×D411yescharacteristic
343C5×Q8—24no—
344C5×Q8—22no—
345C5×Q8—22no—
346C5×Q8—22no—
347C5×Q8—22no—
348C5×Q8—22no—
349C5×Q8—42no—
350C5×Q8—42no—
351C5×Q8C2×#4114yes—
352C2×C4×C5—24no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—42no—
360C2×C4×C5—42no—
361C2×C4×C5—42no—
362C2×C4×C5C22×D412yes—
363C2×C4×C5C22×D412yes—
364C2×C4×C5C22×D411yescharacteristic
365C2×C4×C5C2×#4112yes—
366C2×C4×C52−1+412yes—
367C2×C4×C5C2511yescharacteristic
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—42no—
376C2×Dic5—42no—
377C2×Dic5—42no—
378C2×Dic5—42no—
379C2×Dic5#13714yes—
380C2×Dic5C22×D412yes—
381C2×Dic5C22×D412yes—
382C2×Dic5C22×D412yes—
383C2×Dic5C22×D412yes—
384Dic10—28no—
385Dic10—22no—
386Dic10—22no—
387Dic10—42no—
388Dic10—48no—
389C5×C8—22no—
390C5×C8—22no—
391#168—22no—
392#168—22no—
393C22×Q8—51no—
394C22×Q8—51no—
395C22×Q8—101no—
396C22×Q8C22×D511yescharacteristic
397C22×Q8C22×D511yescharacteristic
398C22×Q8C22×D511yescharacteristic
399C2×Q16—24no—
400C2×Q16—24no—
401C2×Q16—54no—
402C2×Q16—104no—
403C2×Q16C22×D514yes—
404C2×Q16C22×D514yes—
405C22×C8—51no—
406C22×C8—51no—
407C22×C8C22×D511yescharacteristic
408C22×C8C22×D511yescharacteristic
409C4⋊Q8—22no—
410C4⋊Q8—54no—
411C4⋊Q8—54no—
412C4⋊Q8—54no—
413C4⋊Q8—102no—
414C4⋊Q8—102no—
415C4⋊Q8—102no—
416C4⋊Q8—108no—
417C4⋊Q8C22×D514yes—
418#125—54no—
419#125—54no—
420#125—108no—
421#125—102no—
422#125—108no—
423#125—108no—
424#125—108no—
425#125—108no—
426#125—102no—
427C4×Q8—22no—
428C4×Q8—54no—
429C4×Q8—54no—
430C4×Q8—54no—
431C4×Q8—54no—
432C4×Q8—54no—
433C4×Q8—54no—
434C4×Q8—54no—
435C4×Q8—108no—
436C4×Q8—102no—
437C4×Q8—102no—
438C4×Q8—102no—
439C4×Q8—102no—
440C4×Q8—108no—
441C4×Q8—102no—
442C4×Q8C22×D514yes—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—51no—
447C2×C4⋊C4—51no—
448C2×C4⋊C4—51no—
449C2×C4⋊C4—51no—
450C2×C4⋊C4—51no—
451C2×C4⋊C4—51no—
452C2×C4⋊C4—101no—
453C2×C4⋊C4—101no—
454C2×C4⋊C4—101no—
455C2×C4⋊C4—101no—
456C2×C4⋊C4—101no—
457C2×C4⋊C4—101no—
458C2×C4⋊C4—101no—
459C2×C4⋊C4—101no—
460C2×C4⋊C4—101no—
461C2×C4⋊C4—101no—
462C2×C4⋊C4—101no—
463C2×C4⋊C4—101no—
464C2×C4⋊C4—101no—
465C2×C4⋊C4—101no—
466C2×C4⋊C4C22×D511yescharacteristic
467C2×C42—21no—
468C2×C42—51no—
469C2×C42—51no—
470C2×C42—101no—
471C2×C42—101no—
472C2×C42—101no—
473C2×C42—101no—
474C2×C42—101no—
475C2×C42C22×D511yescharacteristic
476#107—54no—
477#106—54no—
478#106—54no—
479C4⋊C8—54no—
480C4⋊C8—54no—
481C4⋊C8C22×D514yes—
482#103—54no—
483#103—54no—
484#103—54no—
485#103—54no—
486#103—54no—
487#103—54no—
488#103—54no—
489#103—54no—
490#103C22×D514yes—
491#103C22×D514yes—
492#97—54no—
493#97—54no—
494C4×C8—54no—
495C22×C5#54812yes—
496C22×C5C2×#13712yes—
497C22×C5#57812yes—
498C22×C5C23×D411yescharacteristic
499C4×C5—24no—
500C4×C5—22no—
501C4×C5—22no—
502C4×C5—42no—
503C4×C5—42no—
504C4×C5—42no—
505C4×C5#54812yes—
506C4×C5C22×#4111yescharacteristic
507C4×C5C2×2−1+411yescharacteristic
508Dic5—22no—
509Dic5—22no—
510Dic5—22no—
511Dic5—42no—
512Dic5—42no—
513Dic5—42no—
514Dic5—42no—
515Dic5C2×#13714yes—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—54no—
525C2×Q8—52no—
526C2×Q8—104no—
527C2×Q8—104no—
528C2×Q8—101no—
529C2×Q8—102no—
530C2×Q8—102no—
531C2×Q8—204no—
532C2×Q8#71114yes—
533C2×Q8C23×D512yes—
534C2×Q8C23×D512yes—
535C2×Q8C23×D512yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—51no—
541C22×C4—51no—
542C22×C4—51no—
543C22×C4—51no—
544C22×C4—101no—
545C22×C4—101no—
546C22×C4—101no—
547C22×C4—101no—
548C22×C4D4×D511yescharacteristic
549C22×C4D4×D511yescharacteristic
550C22×C4C23×D511yescharacteristic
551Q16—28no—
552Q16—28no—
553Q16—108no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—52no—
557C2×C8—52no—
558C2×C8—102no—
559C2×C8—102no—
560C2×C8C23×D512yes—
561C2×C8C23×D512yes—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—21no—
566C4⋊C4—54no—
567C4⋊C4—54no—
568C4⋊C4—54no—
569C4⋊C4—52no—
570C4⋊C4—52no—
571C4⋊C4—52no—
572C4⋊C4—104no—
573C4⋊C4—104no—
574C4⋊C4—104no—
575C4⋊C4—104no—
576C4⋊C4—104no—
577C4⋊C4—104no—
578C4⋊C4—104no—
579C4⋊C4—104no—
580C4⋊C4—104no—
581C4⋊C4—104no—
582C4⋊C4—104no—
583C4⋊C4—101no—
584C4⋊C4—101no—
585C4⋊C4—101no—
586C4⋊C4—104no—
587C4⋊C4—104no—
588C4⋊C4—104no—
589C4⋊C4C23×D512yes—
590C42—24no—
591C42—52no—
592C42—52no—
593C42—52no—
594C42—52no—
595C42—104no—
596C42—104no—
597C42—104no—
598C42—104no—
599C42—104no—
600C42D4×D512yes—
601C42C23×D512yes—
602C2×C5#337414yescomplemented
603C2×C5C2×#54811yescharacteristic
604C2×C5C22×#13711yescharacteristic
605C2×C5C2×#57811yescharacteristic
606C23C2×D4×D511yescharacteristic
607Q8—24no—
608Q8—22no—
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—22no—
613Q8—42no—
614Q8—42no—
615Q8—108no—
616Q8—102no—
617Q8—102no—
618Q8—208no—
619Q8—202no—
620Q8C2×#71114yes—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—54no—
632C2×C4—52no—
633C2×C4—52no—
634C2×C4—52no—
635C2×C4—52no—
636C2×C4—102no—
637C2×C4—102no—
638C2×C4—102no—
639C2×C4—102no—
640C2×C4—102no—
641C2×C4—102no—
642C2×C4—102no—
643C2×C4—202no—
644C2×C4—202no—
645C2×C4—202no—
646C2×C4—202no—
647C2×C4C2×D4×D512yes—
648C2×C4C2×D4×D512yes—
649C2×C4C2×D4×D511yescharacteristic
650C2×C4C2×#71112yes—
651C2×C4#415012yes—
652C2×C4C24×D511yescharacteristic
653C8—22no—
654C8—22no—
655C8—102no—
656C8—102no—
657C5C2×#337411yescharacteristic, complemented, Sylow
658C22#6593212yes—
659C22#6610012yes—
660C22D5×#13712yes—
661C22C22×D4×D511yescharacteristic
662C4—22no—
663C4—22no—
664C4—24no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—54no—
669C4—102no—
670C4—102no—
671C4—102no—
672C4—202no—
673C4—202no—
674C4—202no—
675C4—202no—
676C4#6593212yes—
677C4C22×#71111yescharacteristic
678C4C2×#415011yescharacteristic
679C2#1061219714yesdirect product factor
680C2C2×#6593211yescharacteristic
681C2C2×#6610011yescharacteristic
682C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#462C2
socle, prime radicalC23×C5C22×D4
hypercenterC2×#462D5
hypocenterC5C2×#3374
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
10. #10612197C2direct (N × H)
602. C2×C5#3374semidirect
657. C5C2×#3374semidirect
679. C2#10612197direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660552
C2×#659032
C2×C5×#4622
C2×#654712
C2×#654732
C2×Q16×Dic52
C2×#653712
C2×#653192
#106121972
C2×#651182
C2×#651172
C2×#650862
C2×#650812
C2×#650852
C2×#650802
C2×#33745