Finite Group Databasebeta

← C2×#10611944 #12967366

Subgroups — C2×#10611944 #12967366

Order 1280.

2170 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic5C211yesmaximal, characteristic
2C2×#65956C211yesmaximal, characteristic, complemented
3C2×C5×#452C211yesmaximal, characteristic
4C2×#65528C211yesmaximal, characteristic
5C2×#65471C211yesmaximal, characteristic, complemented
6C2×Q16×Dic5C211yesmaximal, characteristic, complemented
7C2×#65451C211yesmaximal, characteristic, complemented
8C2×SD16×Dic5C211yesmaximal, characteristic, complemented
9C2×#65334C211yesmaximal, characteristic, complemented
10#10611944C2116yesmaximal, direct product factor
11C2×#65080C211yesmaximal, characteristic, complemented
12C2×#65079C211yesmaximal, characteristic, complemented
13C2×#65048C211yesmaximal, characteristic, complemented
14C2×#65047C211yesmaximal, characteristic, complemented
15C2×#65012C211yesmaximal, characteristic, complemented
16C2×#65007C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C22×C5×Q16C2211yescharacteristic
19C22×C5×SD16C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21#41×Dic5—24no—
22#41×Dic5C2218yes—
23C2×Q8×Dic5C2211yescharacteristic
24C2×Q8×Dic5C2211yescharacteristic
25C2×Q8×Dic5C2211yescharacteristic
26C2×#4090C2211yescharacteristic
27C22×#689C2211yescharacteristic
28C2×D4×Dic5—21no—
29C2×D4×Dic5—21no—
30C2×D4×Dic5C2211yescharacteristic
31C2×D4×Dic5C2211yescharacteristic
32C22×#687C2211yescharacteristic
33C2×#4072—21no—
34C2×#4072C2211yescharacteristic
35C2×#4070C2211yescharacteristic
36C22×C4×Dic5—21no—
37C22×C4×Dic5C2211yescharacteristic
38#65956—24no—
39#65956C2218yescomplemented
40C2×#4035—21no—
41C2×#4034C2211yescharacteristic
42C2×#4033—21no—
43C2×#4033C2211yescharacteristic
44C2×#4024—21no—
45C2×#4023—21no—
46C5×#452C2218yes—
47C2×C5×#103C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×C5×C22⋊C8C2211yescharacteristic
50#65528C2218yes—
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3964C2211yescharacteristic
55C2×C22⋊#168C2211yescharacteristic
56Q16×Dic5C2218yescomplemented
57#65471C2218yescomplemented
58#65451C2218yescomplemented
59SD16×Dic5C2218yescomplemented
60C2×#3950C2211yescharacteristic
61C2×#3949C2211yescharacteristic
62C2×#3948C2211yescharacteristic
63C2×#3948C2211yescharacteristic
64C2×#3946C2211yescharacteristic
65C2×#3946C2211yescharacteristic
66C2×C8×Dic5C2211yescharacteristic
67C2×C8×Dic5C2211yescharacteristic
68#65334C2218yescomplemented
69C2×#3940C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71#65080C2218yescomplemented
72#65079C2218yescomplemented
73#65048C2218yescomplemented
74#65047C2218yescomplemented
75#65012C2218yescomplemented
76#65007C2218yescomplemented
77C2×#3107—51nomaximal, Sylow
78C2×C5×#41—24no—
79C2×C5×#41—24no—
80C2×C5×#41—22no—
81C2×C5×#41C2314yes—
82C22×C5×Q8C2311yescharacteristic
83C22×C5×Q8C2311yescharacteristic
84C22×C5×D4—21no—
85C22×C5×D4C2311yescharacteristic
86C23×C4×C5—21no—
87C23×C4×C5C2311yescharacteristic
88C23×Dic5—21no—
89C23×Dic5—21no—
90C23×Dic5D411yescharacteristic
91C23×Dic5D411yescharacteristic
92C22×Dic10—21no—
93C22×Dic10C2311yescharacteristic
94C2×C5×Q16—24no—
95C2×C5×Q16C2314yes—
96C2×C5×SD16—24no—
97C2×C5×SD16C2314yes—
98C22×C5×C8C2311yescharacteristic
99C22×C5×C8C2311yescharacteristic
100C5×C22⋊Q8—22no—
101C5×C22⋊Q8C2314yes—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C22⋊C4—21no—
105C2×C22⋊Dic5—21no—
106C2×C22⋊Dic5—21no—
107C2×C22⋊Dic5—21no—
108C2×C22⋊Dic5—21no—
109Q8×Dic5—22no—
110Q8×Dic5—22no—
111Q8×Dic5—22no—
112Q8×Dic5C2314yes—
113Q8×Dic5C2314yes—
114Q8×Dic5C2314yes—
115#4090—22no—
116#4090C2314yes—
117C2×#689—24no—
118C2×#689C2314yes—
119D4×Dic5—28no—
120D4×Dic5—28no—
121D4×Dic5—22no—
122D4×Dic5—22no—
123D4×Dic5C2314yes—
124D4×Dic5C2314yes—
125C2×#687—24no—
126C2×#687C2314yes—
127#4072—22no—
128#4072—28no—
129#4072C2314yes—
130C2×C4⋊Dic5—21no—
131C2×C4⋊Dic5—21no—
132C2×C4⋊Dic5—21no—
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2311yescharacteristic
135C2×C4⋊Dic5C2311yescharacteristic
136#4070—22no—
137#4070C2314yes—
138C2×#683—21no—
139C2×#683—21no—
140C2×#683—21no—
141C2×#683—21no—
142C2×#683—21no—
143C2×C4×Dic5—21no—
144C2×C4×Dic5—21no—
145C2×C4×Dic5—21no—
146C2×C4×Dic5—21no—
147C2×C4×Dic5—21no—
148C2×C4×Dic5—28no—
149C2×C4×Dic5D411yescharacteristic
150C2×C4×Dic5D411yescharacteristic
151C2×C4×Dic5D414yes—
152C2×C4×Dic5C2311yescharacteristic
153C2×C4×Dic5C2311yescharacteristic
154C2×C4×Dic5C2314yes—
155C22×#168C2311yescharacteristic
156C22×#168C2311yescharacteristic
157#4035—28no—
158#4034—22no—
159#4034C2314yes—
160#4033—28no—
161#4033—22no—
162#4033C2314yes—
163#4024—28no—
164#4023—28no—
165C5×#103C2314yes—
166C5×#102C2314yes—
167C5×C22⋊C8C2314yes—
168#3967C2314yes—
169#3967C2314yes—
170#3967C2314yes—
171#3964C2314yes—
172C22⋊#168C2314yes—
173#3950C2314yes—
174#3949C2314yes—
175#3948C2314yes—
176#3948C2314yes—
177#3946C2314yes—
178#3946C2314yes—
179C8×Dic5C2314yes—
180C8×Dic5C2314yes—
181#3940C2314yes—
182#3939C2314yes—
183C2×#533—51no—
184C2×C4×#41—51no—
185#3107—516no—
186C2×#485—51no—
187C2×#485—51no—
188C2×#475—51no—
189C2×#474—51no—
190C2×#462—51no—
191C2×#461—51no—
192C2×#452—51no—
193C2×#452D511yescharacteristic
194C2×C4×Q16—51no—
195C2×C4×Q16—51no—
196C2×C4×SD16—51no—
197C2×C4×SD16—51no—
198C2×#431—51no—
199C24×C5—21no—
200C24×C5C2×D411yescharacteristic
201C5×#41—216no—
202C5×#41—28no—
203C5×#41—28no—
204C2×C5×Q8—21no—
205C2×C5×Q8—21no—
206C2×C5×Q8—22no—
207C2×C5×Q8—22no—
208C2×C5×Q8—22no—
209C2×C5×Q8#4114yes—
210C2×C5×Q8C2412yes—
211C2×C5×Q8C2412yes—
212C2×C5×D4—28no—
213C2×C5×D4—24no—
214C2×C5×D4—21no—
215C2×C5×D4—22no—
216C2×C5×D4#4114yes—
217C2×C5×D4C2412yes—
218C22×C4×C5—28no—
219C22×C4×C5—21no—
220C22×C4×C5—24no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2411yescharacteristic
229C22×Dic5—24no—
230C22×Dic5—24no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—24no—
236C22×Dic5—24no—
237C22×Dic5—44no—
238C22×Dic5—44no—
239C22×Dic5C2×D411yescharacteristic
240C22×Dic5C2×D411yescharacteristic
241C22×Dic5C2×D414yes—
242C22×Dic5C2×D414yes—
243C22×Dic5C2×D411yescharacteristic
244C22×Dic5C2×D411yescharacteristic
245C2×Dic10—22no—
246C2×Dic10—22no—
247C2×Dic10—21no—
248C2×Dic10—24no—
249C2×Dic10—44no—
250C2×Dic10C2412yes—
251C5×Q16—28no—
252C5×SD16—28no—
253C2×C5×C8—22no—
254C2×C5×C8—22no—
255C2×C5×C8C2412yes—
256C2×C5×C8C2412yes—
257C5×C4⋊C4—24no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4C2412yes—
260C5×C22⋊C4—24no—
261C22⋊Dic5—24no—
262C22⋊Dic5—24no—
263C22⋊Dic5—24no—
264C22⋊Dic5—24no—
265#689—28no—
266#687—28no—
267C4⋊Dic5—21no—
268C4⋊Dic5—21no—
269C4⋊Dic5—21no—
270C4⋊Dic5—24no—
271C4⋊Dic5—24no—
272C4⋊Dic5—24no—
273C4⋊Dic5C2412yes—
274C4⋊Dic5C2412yes—
275C4⋊Dic5C2412yes—
276#683—24no—
277#683—24no—
278#683—24no—
279#683—24no—
280#683—24no—
281C4×Dic5—24no—
282C4×Dic5—24no—
283C4×Dic5—24no—
284C4×Dic5—24no—
285C4×Dic5—24no—
286C4×Dic5C2×D414yes—
287C4×Dic5C2×D412yes—
288C4×Dic5C2×D412yes—
289C4×Dic5C2×D414yes—
290C4×Dic5C2412yes—
291C4×Dic5C2412yes—
292C2×#168—22no—
293C2×#168—22no—
294C2×#168C2412yes—
295C2×#168C2412yes—
296C22×#41C2×D511yescharacteristic
297C22×Q16—51no—
298C22×Q16C2×D511yescharacteristic
299C22×SD16—51no—
300C22×SD16C2×D511yescharacteristic
301#533—58no—
302#533—104no—
303C2×C4⋊Q8—51no—
304C2×C4⋊Q8—51no—
305C2×#125—101no—
306C2×C22⋊Q8—51no—
307C2×C22⋊Q8—101no—
308C2×C22⋊Q8C2×D511yescharacteristic
309C4×#41—58no—
310C4×#41—104no—
311C2×C4×Q8—51no—
312C2×C4×Q8—51no—
313C2×C4×Q8—51no—
314C2×C4×Q8—51no—
315C2×C4×Q8—101no—
316C2×C4×D4—51no—
317C2×C4×D4—51no—
318C2×C4×D4—101no—
319C2×C4×D4—101no—
320C2×#117—51no—
321C2×#117—101no—
322C2×#117—101no—
323C22×C42—51no—
324C22×C42—101no—
325#485—58no—
326#485—58no—
327#475—58no—
328#474—58no—
329#462—58no—
330#461—58no—
331#452—58no—
332#452C2×D518yes—
333C4×Q16—58no—
334C4×Q16—58no—
335C4×SD16—58no—
336C4×SD16—58no—
337#431—58no—
338C2×#107—51no—
339C2×#107—51no—
340C2×#106—51no—
341C2×#106—51no—
342C2×C4⋊C8—51no—
343C2×C4⋊C8—51no—
344C2×#103—51no—
345C2×#103—51no—
346C2×#103—51no—
347C2×#103—51no—
348C2×#103—51no—
349C2×#103C2×D511yescharacteristic
350C2×#102—51no—
351C2×#102C2×D511yescharacteristic
352C2×C22⋊C8—51no—
353C2×C22⋊C8C2×D511yescharacteristic
354C2×C4×C8—51no—
355C2×C4×C8—51no—
356C23×C5—22no—
357C23×C5—24no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—42no—
362C23×C5—42no—
363C23×C5C22×D412yes—
364C23×C5C22×D411yescharacteristic
365C5×Q8—24no—
366C5×Q8—22no—
367C5×Q8—22no—
368C5×Q8—22no—
369C5×Q8—42no—
370C5×Q8C2×#4114yes—
371C5×D4—216no—
372C5×D4—24no—
373C5×D4—22no—
374C5×D4C2×#4114yes—
375C2×C4×C5—216no—
376C2×C4×C5—22no—
377C2×C4×C5—24no—
378C2×C4×C5—22no—
379C2×C4×C5—24no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—42no—
385C2×C4×C5—42no—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D411yescharacteristic
388C2×C4×C5C2×#4112yes—
389C2×C4×C5C2×#4112yes—
390C2×C4×C5C2511yescharacteristic
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—28no—
394C2×Dic5—28no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—42no—
402C2×Dic5—42no—
403C2×Dic5—48no—
404C2×Dic5—48no—
405C2×Dic5#13514yes—
406C2×Dic5#13714yes—
407C2×Dic5C22×D412yes—
408C2×Dic5C22×D412yes—
409C2×Dic5C22×D412yes—
410C2×Dic5C22×D412yes—
411Dic10—22no—
412Dic10—22no—
413Dic10—42no—
414Dic10—48no—
415C5×C8—22no—
416C5×C8—22no—
417#168—22no—
418#168—22no—
419C2×#41—24no—
420C2×#41—24no—
421C2×#41—22no—
422C2×#41C22×D514yes—
423C22×Q8—51no—
424C22×Q8—101no—
425C22×Q8C22×D511yescharacteristic
426C22×Q8C22×D511yescharacteristic
427C22×D4—21no—
428C22×D4C22×D511yescharacteristic
429C23×C4—21no—
430C23×C4—51no—
431C23×C4—51no—
432C23×C4—101no—
433C23×C4—101no—
434C23×C4C22×D511yescharacteristic
435C2×Q16—24no—
436C2×Q16—54no—
437C2×Q16—104no—
438C2×Q16C22×D514yes—
439C2×SD16—24no—
440C2×SD16—54no—
441C2×SD16—104no—
442C2×SD16C22×D514yes—
443C22×C8—51no—
444C22×C8—51no—
445C22×C8C22×D511yescharacteristic
446C22×C8C22×D511yescharacteristic
447C4⋊Q8—54no—
448C4⋊Q8—54no—
449C4⋊Q8—102no—
450C4⋊Q8—102no—
451#125—108no—
452C22⋊Q8—22no—
453C22⋊Q8—54no—
454C22⋊Q8—108no—
455C22⋊Q8—102no—
456C22⋊Q8C22×D514yes—
457C4×Q8—54no—
458C4×Q8—54no—
459C4×Q8—54no—
460C4×Q8—54no—
461C4×Q8—102no—
462C4×Q8—108no—
463C4×Q8—102no—
464C4×Q8—102no—
465C4×Q8—102no—
466C4×D4—54no—
467C4×D4—54no—
468C4×D4—102no—
469C4×D4—102no—
470C4×D4—108no—
471C4×D4—108no—
472#117—54no—
473#117—108no—
474#117—108no—
475#117—102no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—51no—
478C2×C4⋊C4—51no—
479C2×C4⋊C4—51no—
480C2×C4⋊C4—101no—
481C2×C4⋊C4—101no—
482C2×C4⋊C4—101no—
483C2×C4⋊C4—101no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4C22×D511yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4—101no—
493C2×C22⋊C4—101no—
494C2×C42—51no—
495C2×C42—51no—
496C2×C42—54no—
497C2×C42—51no—
498C2×C42—51no—
499C2×C42—54no—
500C2×C42—108no—
501C2×C42—101no—
502C2×C42—101no—
503C2×C42—101no—
504C2×C42—101no—
505C2×C42—101no—
506#107—54no—
507#107—54no—
508#106—54no—
509#106—54no—
510C4⋊C8—54no—
511C4⋊C8—54no—
512#103—54no—
513#103—54no—
514#103—54no—
515#103—54no—
516#103—54no—
517#103C22×D514yes—
518#102—54no—
519#102C22×D514yes—
520C22⋊C8—54no—
521C22⋊C8C22×D514yes—
522C4×C8—54no—
523C4×C8—54no—
524C22×C5—22no—
525C22×C5—24no—
526C22×C5—22no—
527C22×C5—22no—
528C22×C5—44no—
529C22×C5—48no—
530C22×C5—42no—
531C22×C5—42no—
532C22×C5#52512yes—
533C22×C5C2×#13512yes—
534C22×C5C2×#13712yes—
535C22×C5C23×D411yescharacteristic
536C4×C5—22no—
537C4×C5—24no—
538C4×C5—42no—
539C4×C5—42no—
540C4×C5#52512yes—
541C4×C5C22×#4111yescharacteristic
542C4×C5C22×#4111yescharacteristic
543Dic5—22no—
544Dic5—22no—
545Dic5—42no—
546Dic5—42no—
547Dic5—42no—
548Dic5—42no—
549Dic5C2×#13514yes—
550Dic5C2×#13714yes—
551C24—21no—
552C24D4×D511yescharacteristic
553#41—216no—
554#41—28no—
555#41—28no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—52no—
562C2×Q8—104no—
563C2×Q8—101no—
564C2×Q8—102no—
565C2×Q8—102no—
566C2×Q8—204no—
567C2×Q8#71114yes—
568C2×Q8C23×D512yes—
569C2×Q8C23×D512yes—
570C2×D4—28no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4#71114yes—
575C2×D4C23×D512yes—
576C22×C4—28no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—51no—
584C22×C4—51no—
585C22×C4—54no—
586C22×C4—54no—
587C22×C4—51no—
588C22×C4—51no—
589C22×C4—104no—
590C22×C4—104no—
591C22×C4—104no—
592C22×C4—104no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—101no—
596C22×C4—101no—
597C22×C4—204no—
598C22×C4—204no—
599C22×C4D4×D512yes—
600C22×C4D4×D511yescharacteristic
601C22×C4C23×D512yes—
602C22×C4C23×D511yescharacteristic
603Q16—28no—
604Q16—108no—
605SD16—28no—
606SD16—108no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—52no—
610C2×C8—52no—
611C2×C8—102no—
612C2×C8—102no—
613C2×C8C23×D512yes—
614C2×C8C23×D512yes—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—52no—
618C4⋊C4—52no—
619C4⋊C4—52no—
620C4⋊C4—104no—
621C4⋊C4—104no—
622C4⋊C4—104no—
623C4⋊C4—104no—
624C4⋊C4—104no—
625C4⋊C4—104no—
626C4⋊C4—104no—
627C4⋊C4—101no—
628C4⋊C4—101no—
629C4⋊C4—101no—
630C4⋊C4—104no—
631C4⋊C4C23×D512yes—
632C22⋊C4—24no—
633C22⋊C4—104no—
634C22⋊C4—104no—
635C22⋊C4—104no—
636C22⋊C4—104no—
637C42—54no—
638C42—54no—
639C42—52no—
640C42—52no—
641C42—52no—
642C42—52no—
643C42—104no—
644C42—104no—
645C42—104no—
646C42—104no—
647C42—104no—
648C2×C5—42no—
649C2×C5—44no—
650C2×C5#310714yescomplemented
651C2×C5C2×#52511yescharacteristic
652C2×C5C22×#13511yescharacteristic
653C2×C5C22×#13711yescharacteristic
654C23—22no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23C2×D4×D512yes—
662C23C2×D4×D511yescharacteristic
663Q8—24no—
664Q8—22no—
665Q8—22no—
666Q8—22no—
667Q8—42no—
668Q8—102no—
669Q8—102no—
670Q8—208no—
671Q8—202no—
672Q8C2×#71114yes—
673D4—216no—
674D4—24no—
675D4—22no—
676D4C2×#71114yes—
677C2×C4—216no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—54no—
689C2×C4—54no—
690C2×C4—52no—
691C2×C4—52no—
692C2×C4—52no—
693C2×C4—52no—
694C2×C4—108no—
695C2×C4—108no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—208no—
703C2×C4—208no—
704C2×C4—202no—
705C2×C4—202no—
706C2×C4—202no—
707C2×C4—202no—
708C2×C4C2×D4×D512yes—
709C2×C4C2×D4×D511yescharacteristic
710C2×C4C2×#71112yes—
711C2×C4C2×#71112yes—
712C2×C4C24×D511yescharacteristic
713C8—22no—
714C8—22no—
715C8—102no—
716C8—102no—
717C5C2×#310711yescharacteristic, complemented, Sylow
718C22—22no—
719C22—22no—
720C22—24no—
721C22—22no—
722C22—42no—
723C22—42no—
724C22—44no—
725C22—48no—
726C22#6592012yes—
727C22D5×#13512yes—
728C22D5×#13712yes—
729C22C22×D4×D511yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—54no—
735C4—54no—
736C4—102no—
737C4—102no—
738C4—202no—
739C4—202no—
740C4—202no—
741C4—202no—
742C4#6592012yes—
743C4C22×#71111yescharacteristic
744C4C22×#71111yescharacteristic
745C2—42no—
746C2—44no—
747C2#1061194414yesdirect product factor
748C2C2×#6592011yescharacteristic
749C2C2×D5×#13511yescharacteristic
750C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#452C2
socleC23×C5C22×D4
prime radicalC22×C5×#41C22
hypercenterC2×#452D5
hypocenterC5C2×#3107
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#65956C2semidirect
5. C2×#65471C2semidirect
6. C2×Q16×Dic5C2semidirect
7. C2×#65451C2semidirect
8. C2×SD16×Dic5C2semidirect
9. C2×#65334C2semidirect
10. #10611944C2direct (N × H)
11. C2×#65080C2semidirect
12. C2×#65079C2semidirect
13. C2×#65048C2semidirect
14. C2×#65047C2semidirect
15. C2×#65012C2semidirect
16. C2×#65007C2semidirect
39. #65956C22semidirect
56. Q16×Dic5C22semidirect
57. #65471C22semidirect
58. #65451C22semidirect
59. SD16×Dic5C22semidirect
68. #65334C22semidirect
71. #65080C22semidirect
72. #65079C22semidirect
73. #65048C22semidirect
74. #65047C22semidirect
75. #65012C22semidirect
76. #65007C22semidirect
650. C2×C5#3107semidirect
717. C5C2×#3107semidirect
747. C2#10611944direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×Dic52
C2×#659562
C2×C5×#4522
C2×#655282
C2×#654712
C2×Q16×Dic52
C2×#654512
C2×SD16×Dic52
C2×#653342
#106119442
C2×#650802
C2×#650792
C2×#650482
C2×#650472
C2×#650122
C2×#650072
C2×#31075