Finite Group Databasebeta

← C2×#10612698 #12966852

Subgroups — C2×#10612698 #12966852

Order 1280.

2234 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66063C211yesmaximal, characteristic, complemented
2C2×#65879C211yesmaximal, characteristic
3C2×C5×#474C211yesmaximal, characteristic, complemented
4C2×#65373C211yesmaximal, characteristic, complemented
5C2×#65298C211yesmaximal, characteristic, complemented
6#10612698C2116yesmaximal, direct product factor
7C2×#65180C211yesmaximal, characteristic, complemented
8C2×#65179C211yesmaximal, characteristic, complemented
9C2×#65170C211yesmaximal, characteristic, complemented
10C2×#65169C211yesmaximal, characteristic, complemented
11C2×#65136C211yesmaximal, characteristic, complemented
12C2×#65128C211yesmaximal, characteristic, complemented
13C2×#65059C211yesmaximal, characteristic
14C2×D5×#102C211yesmaximal, characteristic
15C2×#65055C211yesmaximal, characteristic, complemented
16C2×#65050C211yesmaximal, characteristic, complemented
17C22×D4×D5C2211yescharacteristic
18C2×C5×C4⋊Q8C2211yescharacteristic, complemented
19C2×C4×C5×D4C2211yescharacteristic
20C2×#4092—21no—
21C2×#4090—21no—
22C2×D4×Dic5C2211yescharacteristic
23C2×C4×C22⋊D5—21no—
24C22×#685—21no—
25C22×#676C2211yescharacteristic
26C22×C8×D5C2211yescharacteristic
27#66063—24no—
28#66063C2218yescomplemented
29#65879—24no—
30#65879C2218yes—
31C2×#4042—21no—
32C2×#4039C2211yescharacteristic
33C2×#4038C2211yescharacteristic
34C2×#4038C2211yescharacteristic
35C2×D5×C4⋊C4C2211yescharacteristic
36C2×#4036C2211yescharacteristic, complemented
37C2×#4035—21no—
38C2×#4034C2211yescharacteristic, complemented
39C2×#4027—21no—
40C2×D5×C22⋊C4—21no—
41C2×C4×D20C2211yescharacteristic
42C2×#4018C2211yescharacteristic
43C2×#4016C2211yescharacteristic, complemented
44C5×#474C2218yescomplemented
45C2×C5×#107C2211yescharacteristic, complemented
46C2×C5×#107C2211yescharacteristic, complemented
47C2×C5×C4⋊C8C2211yescharacteristic, complemented
48C2×C5×#102C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic
50C2×#3964C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3953C2211yescharacteristic
53C2×#3953C2211yescharacteristic
54C2×#3950C2211yescharacteristic, complemented
55C2×#3949C2211yescharacteristic, complemented
56C2×#3946C2211yescharacteristic, complemented
57C2×#3946C2211yescharacteristic, complemented
58#65373C2218yescomplemented
59#65298C2218yescomplemented
60C2×#3941C2211yescharacteristic
61C2×#3941C2211yescharacteristic
62C2×#3940C2211yescharacteristic, complemented
63C2×#3940C2211yescharacteristic, complemented
64C2×#3940C2211yescharacteristic, complemented
65C2×#3939C2211yescharacteristic, complemented
66C2×C4⋊#168C2211yescharacteristic, complemented
67#65180C2218yescomplemented
68#65179C2218yescomplemented
69#65170C2218yescomplemented
70#65169C2218yescomplemented
71#65136C2218yescomplemented
72#65128C2218yescomplemented
73#65059C2218yes—
74D5×#102C2218yes—
75#65055C2218yescomplemented
76#65050C2218yescomplemented
77C2×#3081—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×Q8—21no—
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5—21no—
82C22×C22⋊D5—21no—
83C23×Dic5—21no—
84C2×D4×D5—22no—
85C2×D4×D5—24no—
86C2×D4×D5Q818yescomplemented
87C2×D4×D5C2314yes—
88C22×D20C2311yescharacteristic
89C22×C4×D5—21no—
90C22×C4×D5—21no—
91C22×C4×D5—21no—
92C22×C4×D5C2311yescharacteristic
93C22×Dic10—21no—
94C22×C5×C8C2311yescharacteristic
95C22×C5×C8C2311yescharacteristic
96C5×C4⋊Q8—22no—
97C5×C4⋊Q8C2314yescomplemented
98C4×C5×D4—22no—
99C4×C5×D4C2314yes—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C22⋊C4—21no—
105C2×C42×C5C2311yescharacteristic
106C2×C22⋊Dic5—21no—
107#4092—28no—
108#4090—28no—
109D4×Dic5—22no—
110D4×Dic5C2314yes—
111C4×C22⋊D5—28no—
112C2×#685—21no—
113C2×#685—21no—
114C2×#685—21no—
115C2×#685—21no—
116C2×#685—28no—
117C2×#685D411yescharacteristic
118C2×#685D411yescharacteristic
119C2×C4⋊Dic5—21no—
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×#683D411yescharacteristic
129C2×#683D411yescharacteristic
130C2×C4×Dic5—21no—
131C2×C4×Dic5—21no—
132C2×C4×Dic5C2311yescharacteristic
133C22×#168C2311yescharacteristic
134C22×#168C2311yescharacteristic
135C2×#676—24no—
136C2×#676C2314yes—
137C2×C8×D5—24no—
138C2×C8×D5C2314yes—
139#4042—28no—
140#4039—22no—
141#4039C2314yes—
142#4038—22no—
143#4038—22no—
144#4038C2314yes—
145#4038C2314yes—
146D5×C4⋊C4—22no—
147D5×C4⋊C4C2314yes—
148#4036—22no—
149#4036C2314yescomplemented
150#4035—28no—
151#4034—22no—
152#4034C2314yescomplemented
153#4027—28no—
154D5×C22⋊C4—28no—
155C4×D20—22no—
156C4×D20C2314yes—
157#4018D414yes—
158#4018C2314yes—
159#4016—22no—
160#4016C2314yescomplemented
161C5×#107C2314yescomplemented
162C5×#107C2314yescomplemented
163C5×C4⋊C8C2314yescomplemented
164C5×#102C2314yes—
165C5×#102C2314yes—
166#3964C2314yes—
167#3964C2314yes—
168#3953C2314yes—
169#3953C2314yes—
170#3950C2314yescomplemented
171#3949C2314yescomplemented
172#3946C2314yescomplemented
173#3946C2314yescomplemented
174#3941C2314yes—
175#3941C2314yes—
176#3940C2314yescomplemented
177#3940C2314yescomplemented
178#3940C2314yescomplemented
179#3939C2314yescomplemented
180C4⋊#168C2314yescomplemented
181C2×#544—51no—
182C2×#518—51no—
183#3081—516no—
184C2×#478—51no—
185C2×#478—51no—
186C2×#478—51no—
187C2×#478—51no—
188C2×#476—51no—
189C2×#476—51no—
190C2×#474—51no—
191C2×#474D511yescharacteristic, complemented
192C2×#428—51no—
193C2×#427—51no—
194C2×#424—51no—
195C2×#418—51no—
196C22×#102—51no—
197C24×C5—21no—
198C23×D5—21no—
199C23×D5—28no—
200C23×D5—24no—
201C23×D5—82no—
202C23×D5—82no—
203C23×D5C2×D411yescharacteristic
204C2×C5×Q8—24no—
205C2×C5×Q8—82no—
206C2×C5×D4—21no—
207C2×C5×D4—22no—
208C2×C5×D4C2×Q814yes—
209C2×C5×D4C2412yes—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—24no—
214C22×C4×C5—82no—
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2411yescharacteristic
218C2×C22⋊D5—28no—
219C2×C22⋊D5—24no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—24no—
224C22×Dic5—82no—
225C22×Dic5C2×D411yescharacteristic
226C22×Dic5C2×D411yescharacteristic
227C22×Dic5C2×D411yescharacteristic
228D4×D5—216no—
229D4×D5—28no—
230D4×D5C2×Q8116yescomplemented
231C2×D20—21no—
232C2×D20—22no—
233C2×D20C2×Q814yes—
234C2×D20C2412yes—
235C2×C4×D5—24no—
236C2×C4×D5—24no—
237C2×C4×D5—24no—
238C2×C4×D5—82no—
239C2×C4×D5—82no—
240C2×C4×D5—82no—
241C2×C4×D5C2×D412yes—
242C2×C4×D5C2×Q814yes—
243C2×C4×D5#4114yes—
244C2×C4×D5C2412yes—
245C2×Dic10—24no—
246C2×Dic10—82no—
247C2×C5×C8—22no—
248C2×C5×C8—22no—
249C2×C5×C8C2412yes—
250C2×C5×C8C2412yes—
251C5×C4⋊C4—24no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4—21no—
255C5×C4⋊C4C2412yes—
256C5×C4⋊C4C2412yes—
257C5×C4⋊C4C2412yes—
258C5×C22⋊C4—24no—
259C42×C5C2×D412yes—
260C42×C5C2412yes—
261C22⋊Dic5—24no—
262#685—24no—
263#685—24no—
264#685—24no—
265#685—24no—
266#685C2×D414yes—
267#685C2×D414yes—
268C4⋊Dic5—21no—
269C4⋊Dic5—21no—
270C4⋊Dic5—21no—
271C4⋊Dic5—24no—
272C4⋊Dic5C2412yes—
273C4⋊Dic5C2412yes—
274C4⋊Dic5C2412yes—
275#683—24no—
276#683—24no—
277#683—24no—
278#683—24no—
279#683—24no—
280#683C2×D414yes—
281#683C2×D414yes—
282C4×Dic5—24no—
283C4×Dic5—24no—
284C4×Dic5C2×D412yes—
285C4×Dic5C2412yes—
286C2×#168—22no—
287C2×#168—22no—
288C2×#168C2412yes—
289C2×#168C2412yes—
290#676—28no—
291C8×D5—28no—
292C23×D4—51no—
293C22×M16—51no—
294C23×C8—51no—
295#544—58no—
296#544—104no—
297C2×C4⋊Q8—51no—
298C2×C4⋊Q8—101no—
299C2×C4⋊Q8C2×D511yescharacteristic, complemented
300C2×#125—51no—
301C2×#125—51no—
302C2×#125—101no—
303C2×C22⋊Q8—101no—
304C2×C22⋊Q8—101no—
305#518—58no—
306#518—104no—
307C2×C4×D4—51no—
308C2×C4×D4—51no—
309C2×C4×D4—51no—
310C2×C4×D4—101no—
311C2×C4×D4—101no—
312C2×C4×D4C2×D511yescharacteristic
313C2×#117—51no—
314C2×#117—51no—
315C2×#117—51no—
316C22×C4⋊C4—51no—
317C22×C22⋊C4—101no—
318C22×C22⋊C4—101no—
319#478—58no—
320#478—58no—
321#478—58no—
322#478—58no—
323#476—58no—
324#476—58no—
325#474—58no—
326#474C2×D518yescomplemented
327#428—58no—
328#427—58no—
329C2×#107—51no—
330C2×#107—51no—
331C2×#107C2×D511yescharacteristic, complemented
332C2×#107C2×D511yescharacteristic, complemented
333C2×#106—51no—
334C2×#106—51no—
335C2×#106—51no—
336C2×#106—51no—
337#424—58no—
338C2×C4⋊C8—51no—
339C2×C4⋊C8—51no—
340C2×C4⋊C8—51no—
341C2×C4⋊C8C2×D511yescharacteristic, complemented
342#418—58no—
343C2×#102—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102—51no—
349C2×#102—58no—
350C2×#102C2×D511yescharacteristic
351C2×#102C2×D511yescharacteristic
352C23×C5—24no—
353C23×C5—22no—
354C23×C5—42no—
355C23×C5—42no—
356C23×C5C22×D411yescharacteristic
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—24no—
360C22×D5—22no—
361C22×D5—216no—
362C22×D5—42no—
363C22×D5—42no—
364C22×D5—816no—
365C22×D5—84no—
366C22×D5—84no—
367C22×D5C22⋊Q814yes—
368C22×D5C22×D412yes—
369C5×Q8—84no—
370C5×D4—24no—
371C5×D4—22no—
372C5×D4C22×Q814yes—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5—42no—
381C2×C4×C5—84no—
382C2×C4×C5C22×D412yes—
383C2×C4×C5C22×D412yes—
384C2×C4×C5C22×D411yescharacteristic
385C2×C4×C5C22×Q812yes—
386C2×C4×C5C2×#4112yes—
387C2×C4×C5C2511yescharacteristic
388C22⋊D5—216no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—42no—
395C2×Dic5—42no—
396C2×Dic5—42no—
397C2×Dic5—84no—
398C2×Dic5C22⋊Q814yes—
399C2×Dic5C22×D412yes—
400C2×Dic5C22×D412yes—
401C2×Dic5C22×D412yes—
402D20—24no—
403D20—22no—
404D20C22×Q814yes—
405C4×D5—84no—
406C4×D5—84no—
407C4×D5—84no—
408C4×D5C22⋊Q818yes—
409C4×D5C22×Q814yes—
410C4×D5C2×#4114yes—
411Dic10—84no—
412C5×C8—22no—
413C5×C8—22no—
414#168—22no—
415#168—22no—
416C25—101no—
417C22×Q8—21no—
418C22×Q8—101no—
419C22×D4—58no—
420C22×D4—54no—
421C22×D4—51no—
422C22×D4—102no—
423C22×D4—104no—
424C22×D4—101no—
425C22×D4C22×D511yescharacteristic
426C23×C4—21no—
427C23×C4—51no—
428C23×C4—101no—
429C23×C4—101no—
430C23×C4—101no—
431C23×C4—101no—
432C2×M16—54no—
433C2×M16—104no—
434C22×C8—51no—
435C22×C8—51no—
436C22×C8—54no—
437C22×C8—104no—
438C22×C8C22×D511yescharacteristic
439C22×C8C22×D511yescharacteristic
440C4⋊Q8—22no—
441C4⋊Q8—54no—
442C4⋊Q8—102no—
443C4⋊Q8—108no—
444C4⋊Q8C22×D514yescomplemented
445#125—54no—
446#125—54no—
447#125—102no—
448#125—108no—
449#125—102no—
450C22⋊Q8—108no—
451C22⋊Q8—108no—
452C4×D4—22no—
453C4×D4—54no—
454C4×D4—54no—
455C4×D4—54no—
456C4×D4—102no—
457C4×D4—102no—
458C4×D4—108no—
459C4×D4—108no—
460C4×D4—102no—
461C4×D4C22×D514yes—
462#117—54no—
463#117—54no—
464#117—54no—
465#117—54no—
466#117—102no—
467#117—102no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—51no—
470C2×C4⋊C4—51no—
471C2×C4⋊C4—51no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—51no—
474C2×C4⋊C4—54no—
475C2×C4⋊C4—102no—
476C2×C4⋊C4—101no—
477C2×C4⋊C4—101no—
478C2×C4⋊C4—101no—
479C2×C4⋊C4—101no—
480C2×C4⋊C4—101no—
481C2×C4⋊C4—101no—
482C2×C4⋊C4C22×D511yescharacteristic
483C2×C4⋊C4C22×D511yescharacteristic
484C2×C4⋊C4C22×D511yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—51no—
487C2×C22⋊C4—51no—
488C2×C22⋊C4—108no—
489C2×C22⋊C4—108no—
490C2×C22⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4—101no—
493C2×C22⋊C4—101no—
494C2×C22⋊C4—101no—
495C2×C42—51no—
496C2×C42—101no—
497C2×C42—101no—
498C2×C42C22×D511yescharacteristic
499#107—54no—
500#107—54no—
501#107C22×D514yescomplemented
502#107C22×D514yescomplemented
503#106—54no—
504#106—54no—
505#106—54no—
506#106—54no—
507C4⋊C8—54no—
508C4⋊C8—54no—
509C4⋊C8—54no—
510C4⋊C8C22×D514yescomplemented
511#102—54no—
512#102—54no—
513#102—54no—
514#102—54no—
515#102—54no—
516#102—54no—
517#102C22×D514yes—
518#102C22×D514yes—
519C22×C5—24no—
520C22×C5—48no—
521C22×C5—42no—
522C22×C5—42no—
523C22×C5C2×C22⋊Q812yes—
524C22×C5#57612yes—
525C22×C5#57712yes—
526C22×C5C23×D411yescharacteristic
527C2×D5—28no—
528C2×D5—22no—
529C2×D5—22no—
530C2×D5—24no—
531C2×D5—48no—
532C2×D5—42no—
533C2×D5—42no—
534C2×D5—816no—
535C2×D5C2×C22⋊Q814yes—
536C4×C5—22no—
537C4×C5—22no—
538C4×C5—42no—
539C4×C5—42no—
540C4×C5—42no—
541C4×C5C2×C22⋊Q812yes—
542C4×C5C23×Q811yescharacteristic
543C4×C5C22×#4111yescharacteristic
544Dic5—22no—
545Dic5—22no—
546Dic5—42no—
547Dic5—42no—
548Dic5—42no—
549Dic5C2×C22⋊Q814yes—
550C24—21no—
551C24—51no—
552C24—104no—
553C24—108no—
554C24—101no—
555C24—402no—
556C24—402no—
557C2×Q8—24no—
558C2×Q8—82no—
559C2×Q8—104no—
560C2×Q8—402no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—516no—
564C2×D4—54no—
565C2×D4—52no—
566C2×D4—1016no—
567C2×D4—108no—
568C2×D4—104no—
569C2×D4—108no—
570C2×D4—101no—
571C2×D4—102no—
572C2×D4Q8×D514yes—
573C2×D4C23×D512yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—51no—
579C22×C4—52no—
580C22×C4—54no—
581C22×C4—54no—
582C22×C4—52no—
583C22×C4—51no—
584C22×C4—51no—
585C22×C4—82no—
586C22×C4—104no—
587C22×C4—104no—
588C22×C4—104no—
589C22×C4—101no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—104no—
593C22×C4—402no—
594C22×C4—402no—
595C22×C4—402no—
596C22×C4—402no—
597C22×C4D4×D511yescharacteristic
598C22×C4D4×D511yescharacteristic
599C22×C4C23×D511yescharacteristic
600M16—108no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—52no—
604C2×C8—52no—
605C2×C8—108no—
606C2×C8—102no—
607C2×C8—102no—
608C2×C8C23×D512yes—
609C2×C8C23×D512yes—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—54no—
615C4⋊C4—54no—
616C4⋊C4—52no—
617C4⋊C4—52no—
618C4⋊C4—52no—
619C4⋊C4—104no—
620C4⋊C4—104no—
621C4⋊C4—104no—
622C4⋊C4—104no—
623C4⋊C4—101no—
624C4⋊C4—101no—
625C4⋊C4—101no—
626C4⋊C4—104no—
627C4⋊C4—104no—
628C4⋊C4C23×D512yes—
629C4⋊C4C23×D512yes—
630C4⋊C4C23×D512yes—
631C22⋊C4—24no—
632C22⋊C4—54no—
633C22⋊C4—54no—
634C22⋊C4—104no—
635C22⋊C4—104no—
636C22⋊C4—104no—
637C22⋊C4—104no—
638C22⋊C4—104no—
639C42—52no—
640C42—52no—
641C42—104no—
642C42—104no—
643C42D4×D512yes—
644C42C23×D512yes—
645C2×C5—44no—
646C2×C5#308114yescomplemented
647C2×C5C22×C22⋊Q811yescharacteristic
648C2×C5C2×#57611yescharacteristic
649C2×C5C2×#57711yescharacteristic
650D5—24no—
651D5—44no—
652C23—24no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23—54no—
657C23—52no—
658C23—1016no—
659C23—102no—
660C23—102no—
661C23—104no—
662C23—102no—
663C23—202no—
664C23—202no—
665C23—404no—
666C23—404no—
667C23—4016no—
668C23C2×D4×D511yescharacteristic
669Q8—84no—
670Q8—404no—
671D4—24no—
672D4—22no—
673D4—54no—
674D4—1016no—
675D4—104no—
676D4—102no—
677D4C2×Q8×D514yes—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—54no—
687C2×C4—52no—
688C2×C4—58no—
689C2×C4—54no—
690C2×C4—54no—
691C2×C4—52no—
692C2×C4—52no—
693C2×C4—84no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—202no—
700C2×C4—202no—
701C2×C4—202no—
702C2×C4—404no—
703C2×C4—404no—
704C2×C4—404no—
705C2×C4—404no—
706C2×C4C2×D4×D512yes—
707C2×C4C2×D4×D512yes—
708C2×C4C2×D4×D511yescharacteristic
709C2×C4C2×Q8×D512yes—
710C2×C4D5×#4112yes—
711C2×C4C24×D511yescharacteristic
712C8—22no—
713C8—22no—
714C8—102no—
715C8—102no—
716C5C2×#308111yescharacteristic, complemented, Sylow
717C22—24no—
718C22—42no—
719C22—42no—
720C22—48no—
721C22—54no—
722C22—102no—
723C22—102no—
724C22—108no—
725C22—104no—
726C22—202no—
727C22—202no—
728C22—208no—
729C22—4016no—
730C22D5×C22⋊Q812yes—
731C22#6609112yes—
732C22#6611212yes—
733C22C22×D4×D511yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—54no—
740C4—102no—
741C4—102no—
742C4—202no—
743C4—202no—
744C4—202no—
745C4D5×C22⋊Q812yes—
746C4C22×Q8×D511yescharacteristic
747C4C2×D5×#4111yescharacteristic
748C2—44no—
749C2—104no—
750C2—204no—
751C2#1061269814yesdirect product factor
752C2C2×D5×C22⋊Q811yescharacteristic
753C2C2×#6609111yescharacteristic
754C2C2×#6611211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#474C2
socleC23×C5C22×D4
prime radicalC22×D4×D5C22
hypercenterC2×#474D5
hypocenterC5C2×#3081
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#66063C2semidirect
3. C2×C5×#474C2semidirect
4. C2×#65373C2semidirect
5. C2×#65298C2semidirect
6. #10612698C2direct (N × H)
7. C2×#65180C2semidirect
8. C2×#65179C2semidirect
9. C2×#65170C2semidirect
10. C2×#65169C2semidirect
11. C2×#65136C2semidirect
12. C2×#65128C2semidirect
15. C2×#65055C2semidirect
16. C2×#65050C2semidirect
18. C2×C5×C4⋊Q8C22semidirect
28. #66063C22semidirect
36. C2×#4036C22semidirect
38. C2×#4034C22semidirect
43. C2×#4016C22semidirect
44. C5×#474C22semidirect
45. C2×C5×#107C22semidirect
46. C2×C5×#107C22semidirect
47. C2×C5×C4⋊C8C22semidirect
54. C2×#3950C22semidirect
55. C2×#3949C22semidirect
56. C2×#3946C22semidirect
57. C2×#3946C22semidirect
58. #65373C22semidirect
59. #65298C22semidirect
62. C2×#3940C22semidirect
63. C2×#3940C22semidirect
64. C2×#3940C22semidirect
65. C2×#3939C22semidirect
66. C2×C4⋊#168C22semidirect
67. #65180C22semidirect
68. #65179C22semidirect
69. #65170C22semidirect
70. #65169C22semidirect
71. #65136C22semidirect
72. #65128C22semidirect
75. #65055C22semidirect
76. #65050C22semidirect
86. C2×D4×D5Q8semidirect
97. C5×C4⋊Q8C23semidirect
149. #4036C23semidirect
152. #4034C23semidirect
160. #4016C23semidirect
161. C5×#107C23semidirect
162. C5×#107C23semidirect
163. C5×C4⋊C8C23semidirect
170. #3950C23semidirect
171. #3949C23semidirect
172. #3946C23semidirect
173. #3946C23semidirect
176. #3940C23semidirect
177. #3940C23semidirect
178. #3940C23semidirect
179. #3939C23semidirect
180. C4⋊#168C23semidirect
191. C2×#474D5semidirect
230. D4×D5C2×Q8semidirect
299. C2×C4⋊Q8C2×D5semidirect
326. #474C2×D5semidirect
331. C2×#107C2×D5semidirect
332. C2×#107C2×D5semidirect
341. C2×C4⋊C8C2×D5semidirect
444. C4⋊Q8C22×D5semidirect
501. #107C22×D5semidirect
502. #107C22×D5semidirect
510. C4⋊C8C22×D5semidirect
646. C2×C5#3081semidirect
716. C5C2×#3081semidirect
751. C2#10612698direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660632
C2×#658792
C2×C5×#4742
C2×#653732
C2×#652982
#106126982
C2×#651802
C2×#651792
C2×#651702
C2×#651692
C2×#651362
C2×#651282
C2×#650592
C2×D5×#1022
C2×#650552
C2×#650502
C2×#30815