Finite Group Databasebeta

← C2×#10610855 #12977719

Subgroups — C2×#10610855 #12977719

Order 1280.

2158 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×#65841C211yesmaximal, characteristic
2C2×#65845C211yesmaximal, characteristic, complemented
3C22×C5×#106C211yesmaximal, characteristic, complemented
4C2×#65403C211yesmaximal, characteristic, complemented
5C2×C8×C22⋊D5C211yesmaximal, characteristic, complemented
6C2×#65260C211yesmaximal, characteristic, complemented
7C2×#65257C211yesmaximal, characteristic, complemented
8C2×#65143C211yesmaximal, characteristic, complemented
9C2×#65159C211yesmaximal, characteristic, complemented
10#10610855C2116yesmaximal, direct product factor
11C2×#65152C211yesmaximal, characteristic, complemented
12C2×#65151C211yesmaximal, characteristic, complemented
13C2×#65153C211yesmaximal, characteristic, complemented
14C2×D5×#106C211yesmaximal, characteristic, complemented
15C2×#65144C211yesmaximal, characteristic, complemented
16C2×#65141C211yesmaximal, characteristic, complemented
17C22×#709—21no—
18C23×C5×C8C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C2×#4076C2211yescharacteristic
22C2×#4075—21no—
23C2×C4×C22⋊D5—21no—
24C2×C4×C22⋊D5C2211yescharacteristic
25C2×#4070—21no—
26C2×#4070C2211yescharacteristic
27C22×#677C2211yescharacteristic
28C22×C8×D5C2211yescharacteristic
29#65845—24no—
30#65845C2218yescomplemented
31C2×#4043C2211yescharacteristic
32C2×#4042—21no—
33C2×#4042—21no—
34#65841—24no—
35#65841C2218yes—
36C2×#4041C2211yescharacteristic
37C2×#4040—21no—
38C2×#4039C2211yescharacteristic
39C2×D5×C4⋊C4C2211yescharacteristic
40C2×D5×C4⋊C4C2211yescharacteristic
41C2×#4035—21no—
42C2×#4034C2211yescharacteristic
43C2×#4034C2211yescharacteristic
44C2×#4033C2211yescharacteristic
45C2×C5×#106C2211yescharacteristic
46C2×C5×#106C2211yescharacteristic
47C2×C5×#106C2211yescharacteristic
48C2×C5×#106C2211yescharacteristic
49C2×C5×#106C2218yescomplemented
50C2×C22⋊#168C2211yescharacteristic
51#65403C2218yescomplemented
52C2×#3953C2211yescharacteristic
53C8×C22⋊D5C2218yescomplemented
54C2×#3952C2211yescharacteristic
55C2×#3949C2211yescharacteristic
56C2×#3948C2211yescharacteristic
57C2×#3946C2211yescharacteristic
58C2×C8×Dic5C2211yescharacteristic
59#65260C2218yescomplemented
60C2×#3942C2211yescharacteristic
61C2×#3942C2211yescharacteristic
62#65257C2218yescomplemented
63C2×#3941C2211yescharacteristic
64C2×#3941C2211yescharacteristic
65C2×#3940C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69#65159C2218yescomplemented
70#65153C2218yescomplemented
71#65152C2218yescomplemented
72#65151C2218yescomplemented
73D5×#106C2218yescomplemented
74#65144C2218yescomplemented
75#65143C2218yescomplemented
76#65141C2218yescomplemented
77C2×#3335—51nomaximal, Sylow
78C23×C4×C5—21no—
79C23×C4×C5—21no—
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C22×C22⋊D5D411yescharacteristic
83C2×#709—28no—
84C2×#709—48no—
85C22×D20—21no—
86C22×D20C2311yescharacteristic
87C22×C4×D5—21no—
88C22×C4×D5—21no—
89C22×C4×D5—21no—
90C22×C4×D5C2311yescharacteristic
91C22×Dic10—21no—
92C22×Dic10—21no—
93C22×Dic10C2311yescharacteristic
94C22×C5×C8—24no—
95C22×C5×C8C2311yescharacteristic
96C22×C5×C8C2314yes—
97C22×C5×C8C2311yescharacteristic
98C2×C5×C4⋊C4—21no—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—22no—
101C2×C5×C4⋊C4—22no—
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C4⋊C4C2314yes—
108C2×C22⋊Dic5—21no—
109C2×C22⋊Dic5D411yescharacteristic
110#4076—22no—
111#4076C2314yes—
112#4075—28no—
113C4×C22⋊D5—28no—
114C4×C22⋊D5D414yes—
115C4×C22⋊D5C2314yes—
116C2×#685—21no—
117C2×#685—21no—
118C2×#685—21no—
119C2×#685—21no—
120C2×#685D411yescharacteristic
121C2×C4⋊Dic5—21no—
122C2×C4⋊Dic5C2311yescharacteristic
123C2×C4⋊Dic5C2311yescharacteristic
124#4070—22no—
125#4070—28no—
126#4070C2314yes—
127C2×#683—21no—
128C2×#683—21no—
129C2×#683—21no—
130C2×#683—21no—
131C2×#683—21no—
132C2×#683—21no—
133C2×#683D411yescharacteristic
134C2×C4×Dic5—21no—
135C2×C4×Dic5C2311yescharacteristic
136C22×#168C2311yescharacteristic
137C22×#168C2311yescharacteristic
138C2×#677—24no—
139C2×#677C2314yes—
140C2×C8×D5—24no—
141C2×C8×D5C2314yes—
142#4043—22no—
143#4043C2314yes—
144#4042—28no—
145#4042—28no—
146#4041—22no—
147#4041C2314yes—
148#4040—28no—
149#4039—22no—
150#4039C2314yes—
151D5×C4⋊C4—22no—
152D5×C4⋊C4—22no—
153D5×C4⋊C4C2314yes—
154D5×C4⋊C4C2314yes—
155#4035—28no—
156#4034—22no—
157#4034—22no—
158#4034C2314yes—
159#4034C2314yes—
160#4033—22no—
161#4033C2314yes—
162C5×#106C2314yes—
163C5×#106C2314yes—
164C5×#106C2314yes—
165C5×#106C2314yes—
166C22⋊#168C2314yes—
167#3953C2314yes—
168#3952C2314yes—
169#3949C2314yes—
170#3948C2314yes—
171#3946C2314yes—
172C8×Dic5C2314yes—
173#3942C2314yes—
174#3942C2314yes—
175#3941C2314yes—
176#3941C2314yes—
177#3940C2314yes—
178#3940C2314yes—
179#3940C2314yes—
180#3940C2314yes—
181C2×#554—51no—
182C2×#547—51no—
183#3335—516no—
184C2×#498—51no—
185C2×#481—51no—
186C2×#481—51no—
187C2×#483—51no—
188C2×#483—51no—
189C2×#475—51no—
190C2×#476—51no—
191C2×#465—51no—
192C2×#465—51no—
193C2×C4×SD16—51no—
194C2×C8×D4—51no—
195C22×#106—51no—
196C22×#106D511yescharacteristic, complemented
197C24×C5C2×D411yescharacteristic
198C23×D5—21no—
199C23×D5C2×D411yescharacteristic
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—24no—
207C22×C4×C5—24no—
208C22×C4×C5—44no—
209C22×C4×C5—82no—
210C22×C4×C5C2×D411yescharacteristic
211C22×C4×C5C2×D412yes—
212C22×C4×C5C2412yes—
213C22×C4×C5C2411yescharacteristic
214C2×C22⋊D5—24no—
215C2×C22⋊D5—44no—
216C2×C22⋊D5SD1618yescomplemented
217C2×C22⋊D5C2×D414yes—
218C22×Dic5—21no—
219C22×Dic5—21no—
220C22×Dic5—21no—
221C22×Dic5C2×D411yescharacteristic
222C22×Dic5C2×D411yescharacteristic
223C22×Dic5C2×D411yescharacteristic
224#709—432no—
225C2×D20—22no—
226C2×D20—22no—
227C2×D20—24no—
228C2×D20—21no—
229C2×D20—44no—
230C2×D20C2412yes—
231C2×C4×D5—22no—
232C2×C4×D5—22no—
233C2×C4×D5—24no—
234C2×C4×D5—24no—
235C2×C4×D5—24no—
236C2×C4×D5—44no—
237C2×C4×D5—44no—
238C2×C4×D5—82no—
239C2×C4×D5C2×D412yes—
240C2×C4×D5C2412yes—
241C2×Dic10—22no—
242C2×Dic10—22no—
243C2×Dic10—21no—
244C2×Dic10—24no—
245C2×Dic10—24no—
246C2×Dic10—44no—
247C2×Dic10—82no—
248C2×Dic10C2412yes—
249C2×C5×C8—22no—
250C2×C5×C8—28no—
251C2×C5×C8#4114yescomplemented
252C2×C5×C8C2412yes—
253C2×C5×C8C2412yes—
254C5×C4⋊C4—21no—
255C5×C4⋊C4—21no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—24no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4—24no—
260C5×C4⋊C4C2412yes—
261C5×C4⋊C4C2412yes—
262C5×C4⋊C4C2412yes—
263C5×C4⋊C4C2412yes—
264C22⋊Dic5—24no—
265C22⋊Dic5C2×D414yes—
266#685—24no—
267#685—24no—
268#685—24no—
269#685—24no—
270#685C2×D414yes—
271C4⋊Dic5—21no—
272C4⋊Dic5—21no—
273C4⋊Dic5—24no—
274C4⋊Dic5C2412yes—
275C4⋊Dic5C2412yes—
276#683—24no—
277#683—24no—
278#683—24no—
279#683—24no—
280#683—24no—
281#683—24no—
282#683C2×D414yes—
283C4×Dic5—24no—
284C4×Dic5C2×D412yes—
285C4×Dic5C2412yes—
286C2×#168—22no—
287C2×#168—22no—
288C2×#168C2412yes—
289C2×#168C2412yes—
290#677—28no—
291C8×D5—28no—
292C22×#41—101no—
293C22×SD16—51no—
294C23×C8—51no—
295C23×C8C2×D511yescharacteristic
296#554—58no—
297#554—104no—
298#547—58no—
299#547—104no—
300C2×C4⋊Q8—51no—
301C2×C4⋊Q8—51no—
302C2×#125—101no—
303C2×#123—101no—
304C2×#123—101no—
305C2×C22⋊Q8—51no—
306C2×C22⋊Q8—51no—
307C2×C22⋊Q8—101no—
308C2×C22⋊Q8—101no—
309C2×C22⋊Q8—101no—
310C2×#121—51no—
311C2×#121—51no—
312C2×C4×Q8—51no—
313C2×C4×D4—51no—
314C2×C4×D4—51no—
315C2×C4×D4—101no—
316C22×C4⋊C4—51no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4C2×D511yescharacteristic
319C22×C4⋊C4C2×D511yescharacteristic
320#498—58no—
321#483—58no—
322#483—58no—
323#481—58no—
324#481—58no—
325#476—58no—
326#475—58no—
327#465—58no—
328#465—58no—
329C4×SD16—58no—
330C8×D4—58no—
331C2×#106—51no—
332C2×#106—51no—
333C2×#106—51no—
334C2×#106—51no—
335C2×#106—51no—
336C2×#106—58no—
337C2×#106C2×D511yescharacteristic
338C2×#106C2×D511yescharacteristic
339C2×#106C2×D511yescharacteristic
340C2×#106C2×D511yescharacteristic
341C2×#106C2×D518yescomplemented
342C2×C4⋊C8—51no—
343C2×#103—51no—
344C2×#103—51no—
345C2×#103—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102—51no—
349C2×C22⋊C8—51no—
350C2×C22⋊C8—51no—
351C2×C4×C8—51no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5C2×SD1614yes—
355C23×C5C22×D412yes—
356C23×C5C22×D411yescharacteristic
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—22no—
360C22×D5—42no—
361C22×D5—42no—
362C22×D5—42no—
363C22×D5C2×SD1614yes—
364C22×D5C22×D412yes—
365C2×C4×C5—22no—
366C2×C4×C5—24no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—42no—
374C2×C4×C5—42no—
375C2×C4×C5—48no—
376C2×C4×C5—42no—
377C2×C4×C5—42no—
378C2×C4×C5—84no—
379C2×C4×C5C22×D412yes—
380C2×C4×C5C22×D411yescharacteristic
381C2×C4×C5C2×#4112yes—
382C2×C4×C52−1+412yes—
383C2×C4×C5C2511yescharacteristic
384C22⋊D5—48no—
385C22⋊D5C2×SD16116yescomplemented
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—42no—
392C2×Dic5—42no—
393C2×Dic5—42no—
394C2×Dic5C2×SD1614yes—
395C2×Dic5C22×D412yes—
396C2×Dic5C22×D412yes—
397C2×Dic5C22×D412yes—
398D20—22no—
399D20—22no—
400D20—48no—
401D20—42no—
402C4×D5—24no—
403C4×D5—22no—
404C4×D5—22no—
405C4×D5—48no—
406C4×D5—48no—
407C4×D5—84no—
408Dic10—22no—
409Dic10—22no—
410Dic10—42no—
411Dic10—48no—
412Dic10—84no—
413C5×C8—22no—
414C5×C8C2×#4114yescomplemented
415#168—22no—
416#168—22no—
417C2×#41—108no—
418C2×#41—208no—
419C22×Q8—51no—
420C22×Q8—101no—
421C22×Q8—101no—
422C22×D4—51no—
423C22×D4—51no—
424C22×D4—101no—
425C22×D4—101no—
426C23×C4—21no—
427C23×C4—21no—
428C23×C4—51no—
429C23×C4—101no—
430C23×C4—101no—
431C23×C4—101no—
432C23×C4C22×D511yescharacteristic
433C2×SD16—54no—
434C2×SD16—104no—
435C22×C8—24no—
436C22×C8—51no—
437C22×C8—51no—
438C22×C8—54no—
439C22×C8—104no—
440C22×C8C22×D511yescharacteristic
441C22×C8C22×D514yes—
442C22×C8C22×D511yescharacteristic
443C4⋊Q8—54no—
444C4⋊Q8—54no—
445C4⋊Q8—102no—
446C4⋊Q8—102no—
447#125—108no—
448#123—108no—
449#123—108no—
450C22⋊Q8—54no—
451C22⋊Q8—54no—
452C22⋊Q8—108no—
453C22⋊Q8—108no—
454C22⋊Q8—108no—
455C22⋊Q8—102no—
456C22⋊Q8—102no—
457#121—54no—
458#121—54no—
459#121—102no—
460#121—102no—
461C4×Q8—54no—
462C4×Q8—102no—
463C4×D4—54no—
464C4×D4—54no—
465C4×D4—54no—
466C4×D4—102no—
467C4×D4—108no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—51no—
474C2×C4⋊C4—51no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—54no—
477C2×C4⋊C4—102no—
478C2×C4⋊C4—102no—
479C2×C4⋊C4—101no—
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⋊C4C22×D511yescharacteristic
487C2×C4⋊C4C22×D511yescharacteristic
488C2×C4⋊C4C22×D511yescharacteristic
489C2×C4⋊C4C22×D511yescharacteristic
490C2×C4⋊C4C22×D514yes—
491C2×C4⋊C4C22×D514yes—
492C2×C22⋊C4—51no—
493C2×C22⋊C4—51no—
494C2×C22⋊C4—101no—
495C2×C22⋊C4—101no—
496C2×C22⋊C4—101no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C42—51no—
500C2×C42—101no—
501#106—54no—
502#106—54no—
503#106—54no—
504#106—54no—
505#106—54no—
506#106C22×D514yes—
507#106C22×D514yes—
508#106C22×D514yes—
509#106C22×D514yes—
510C4⋊C8—54no—
511#103—54no—
512#103—54no—
513#103—54no—
514#102—54no—
515#102—54no—
516#102—54no—
517C22⋊C8—54no—
518C22⋊C8—54no—
519C4×C8—54no—
520C22×C5—28no—
521C22×C5—22no—
522C22×C5—22no—
523C22×C5#54712yes—
524C22×C5C22×SD1614yes—
525C22×C5C22×SD1612yes—
526C22×C5#57712yes—
527C22×C5C23×D411yescharacteristic
528C2×D5—28no—
529C2×D5—22no—
530C2×D5—22no—
531C2×D5—42no—
532C2×D5—42no—
533C2×D5—42no—
534C2×D5—84no—
535C2×D5C22×SD1614yes—
536C4×C5—22no—
537C4×C5—42no—
538C4×C5—42no—
539C4×C5—42no—
540C4×C5—42no—
541C4×C5#54712yes—
542C4×C5C22×#4111yescharacteristic
543C4×C5C2×2−1+411yescharacteristic
544Dic5—22no—
545Dic5—22no—
546Dic5—42no—
547Dic5—42no—
548Dic5—42no—
549Dic5C22×SD1614yes—
550C24—51no—
551C24—101no—
552C24D4×D511yescharacteristic
553#41—2032no—
554C2×Q8—52no—
555C2×Q8—104no—
556C2×Q8—104no—
557C2×Q8—101no—
558C2×Q8—102no—
559C2×Q8—102no—
560C2×Q8—204no—
561C2×Q8—402no—
562C2×D4—54no—
563C2×D4—58no—
564C2×D4—52no—
565C2×D4—104no—
566C2×D4—104no—
567C2×D4—102no—
568C2×D4—101no—
569C2×D4—102no—
570C2×D4—204no—
571C2×D4—204no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—44no—
581C22×C4—51no—
582C22×C4—51no—
583C22×C4—51no—
584C22×C4—52no—
585C22×C4—52no—
586C22×C4—82no—
587C22×C4—104no—
588C22×C4—104no—
589C22×C4—104no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—204no—
596C22×C4—204no—
597C22×C4—402no—
598C22×C4D4×D512yes—
599C22×C4D4×D511yescharacteristic
600C22×C4C23×D512yes—
601C22×C4C23×D511yescharacteristic
602SD16—108no—
603C2×C8—22no—
604C2×C8—28no—
605C2×C8—52no—
606C2×C8—52no—
607C2×C8—102no—
608C2×C8—102no—
609C2×C8—108no—
610C2×C8#70914yescomplemented
611C2×C8C23×D512yes—
612C2×C8C23×D512yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—54no—
620C4⋊C4—52no—
621C4⋊C4—52no—
622C4⋊C4—104no—
623C4⋊C4—104no—
624C4⋊C4—104no—
625C4⋊C4—104no—
626C4⋊C4—104no—
627C4⋊C4—104no—
628C4⋊C4—101no—
629C4⋊C4—101no—
630C4⋊C4—104no—
631C4⋊C4C23×D512yes—
632C4⋊C4C23×D512yes—
633C4⋊C4C23×D512yes—
634C4⋊C4C23×D512yes—
635C22⋊C4—54no—
636C22⋊C4—54no—
637C22⋊C4—104no—
638C22⋊C4—104no—
639C22⋊C4—104no—
640C22⋊C4—104no—
641C22⋊C4—104no—
642C42—52no—
643C42—52no—
644C42—104no—
645C2×C5—24no—
646C2×C5#333514yescomplemented
647C2×C5C2×#54711yescharacteristic
648C2×C5C23×SD1611yescharacteristic
649C2×C5C2×#57711yescharacteristic
650D5—24no—
651D5—82no—
652C23—22no—
653C23—22no—
654C23—54no—
655C23—52no—
656C23—102no—
657C23—102no—
658C23—102no—
659C23—202no—
660C23—202no—
661C23—202no—
662C23D5×SD1614yes—
663C23C2×D4×D512yes—
664C23C2×D4×D511yescharacteristic
665Q8—102no—
666Q8—102no—
667Q8—208no—
668Q8—202no—
669Q8—404no—
670D4—516no—
671D4—102no—
672D4—102no—
673D4—208no—
674D4—208no—
675D4—202no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—48no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—54no—
690C2×C4—52no—
691C2×C4—52no—
692C2×C4—52no—
693C2×C4—84no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—104no—
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—404no—
708C2×C4C2×#70912yes—
709C2×C4C2×D4×D512yes—
710C2×C4C2×D4×D511yescharacteristic
711C2×C4#414712yes—
712C2×C4C24×D511yescharacteristic
713C8—22no—
714C8—102no—
715C8—102no—
716C8C2×#70914yescomplemented
717C5C2×#333511yescharacteristic, complemented, Sylow
718C22—22no—
719C22—28no—
720C22—22no—
721C22—54no—
722C22—102no—
723C22—108no—
724C22—102no—
725C22—202no—
726C22—202no—
727C22—202no—
728C22—404no—
729C22#6584112yes—
730C22C2×D5×SD1614yes—
731C22C2×D5×SD1612yes—
732C22#6609612yes—
733C22C22×D4×D511yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—54no—
740C4—102no—
741C4—102no—
742C4—202no—
743C4—202no—
744C4—202no—
745C4#6584112yes—
746C4C22×#70911yescharacteristic
747C4C2×#414711yescharacteristic
748C2—24no—
749C2—104no—
750C2—402no—
751C2#1061085514yesdirect product factor
752C2C2×#6584111yescharacteristic
753C2C22×D5×SD1611yescharacteristic
754C2C2×#6609611yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC22×C5×#106C2
socleC23×C5C22×D4
prime radicalC2×#65841C2
hypercenterC22×#106D5
hypocenterC5C2×#3335
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. C2×#65845C2semidirect
3. C22×C5×#106C2semidirect
4. C2×#65403C2semidirect
5. C2×C8×C22⋊D5C2semidirect
6. C2×#65260C2semidirect
7. C2×#65257C2semidirect
8. C2×#65143C2semidirect
9. C2×#65159C2semidirect
10. #10610855C2direct (N × H)
11. C2×#65152C2semidirect
12. C2×#65151C2semidirect
13. C2×#65153C2semidirect
14. C2×D5×#106C2semidirect
15. C2×#65144C2semidirect
16. C2×#65141C2semidirect
30. #65845C22semidirect
49. C2×C5×#106C22semidirect
51. #65403C22semidirect
53. C8×C22⋊D5C22semidirect
59. #65260C22semidirect
62. #65257C22semidirect
69. #65159C22semidirect
70. #65153C22semidirect
71. #65152C22semidirect
72. #65151C22semidirect
73. D5×#106C22semidirect
74. #65144C22semidirect
75. #65143C22semidirect
76. #65141C22semidirect
196. C22×#106D5semidirect
216. C2×C22⋊D5SD16semidirect
251. C2×C5×C8#41semidirect
341. C2×#106C2×D5semidirect
385. C22⋊D5C2×SD16semidirect
414. C5×C8C2×#41semidirect
610. C2×C8#709semidirect
646. C2×C5#3335semidirect
716. C8C2×#709semidirect
717. C5C2×#3335semidirect
751. C2#10610855direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658412
C2×#658452
C22×C5×#1062
C2×#654032
C2×C8×C22⋊D52
C2×#652602
C2×#652572
C2×#651432
C2×#651592
#106108552
C2×#651522
C2×#651512
C2×#651532
C2×D5×#1062
C2×#651442
C2×#651412
C2×#33355