Finite Group Databasebeta

← C2×#10611200 #12977833

Subgroups — C2×#10611200 #12977833

Order 1280.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65875C211yesmaximal, characteristic, complemented
2C2×#65889C211yesmaximal, characteristic
3C2×C5×#435C211yesmaximal, characteristic, complemented
4C2×#65423C211yesmaximal, characteristic, complemented
5C2×#65410C211yesmaximal, characteristic, complemented
6C2×#65403C211yesmaximal, characteristic, complemented
7C22×#3950C211yesmaximal, characteristic, complemented
8#10611200C2116yesmaximal, direct product factor
9C2×#65139C211yesmaximal, characteristic, complemented
10C2×#65136C211yesmaximal, characteristic, complemented
11C2×#65011C211yesmaximal, characteristic, complemented
12C2×#65026C211yesmaximal, characteristic, complemented
13C2×#65010C211yesmaximal, characteristic, complemented
14C2×#65025C211yesmaximal, characteristic, complemented
15C2×#64999C211yesmaximal, characteristic, complemented
16C2×#64991C211yesmaximal, characteristic, complemented
17C22×#711—21no—
18C22×C5×M16C2211yescharacteristic
19C23×C5×C8C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×#4081—21no—
22C2×#4076C2211yescharacteristic
23C2×#4076C2211yescharacteristic
24C2×#4072C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C22×C4⋊Dic5C2211yescharacteristic
27C22×C4⋊Dic5C2211yescharacteristic
28C2×#4070C2211yescharacteristic
29C2×#4070C2211yescharacteristic
30C22×#677C2211yescharacteristic
31#65889—24no—
32#65889C2218yes—
33#65875—24no—
34#65875C2218yescomplemented
35C2×#4043—21no—
36C2×#4035—21no—
37C2×#4032—21no—
38C2×#4032—21no—
39C2×#4025—21no—
40C2×#4023—21no—
41C2×C4×D20C2211yescharacteristic
42C2×#4016C2211yescharacteristic
43C2×#4015C2211yescharacteristic
44C2×C4×Dic10C2211yescharacteristic
45C5×#435C2218yescomplemented
46C2×C5×C4⋊C8C2211yescharacteristic
47C2×C5×C22⋊C8C2211yescharacteristic
48C2×C5×C22⋊C8C2211yescharacteristic
49C2×C5×#97C2211yescharacteristic
50#65423C2218yescomplemented
51#65410C2218yescomplemented
52#65403C2218yescomplemented
53C2×#3953C2211yescharacteristic
54C2×#3953C2211yescharacteristic
55C2×#3953C2211yescharacteristic
56C2×#3950C2211yescharacteristic
57C2×#3950C2211yescharacteristic
58C2×#3950C2211yescharacteristic
59C2×#3950C2211yescharacteristic
60C2×#3950C2211yescharacteristic
61C2×#3950C2211yescharacteristic
62C2×#3950C2218yescomplemented
63C2×#3949C2211yescharacteristic
64C2×#3949C2211yescharacteristic
65C2×#3949C2211yescharacteristic
66C2×#3948C2211yescharacteristic
67C2×#3948C2211yescharacteristic
68C2×#3948C2211yescharacteristic
69#65139C2218yescomplemented
70#65136C2218yescomplemented
71#65026C2218yescomplemented
72#65025C2218yescomplemented
73#65011C2218yescomplemented
74#65010C2218yescomplemented
75#64999C2218yescomplemented
76#64991C2218yescomplemented
77C2×#3343—51nomaximal, Sylow
78C22×C5×D4D411yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C22×C22⋊D5—21no—
83C23×Dic5—21no—
84C23×Dic5—21no—
85C23×Dic5—21no—
86C2×#711—28no—
87C2×#711—48no—
88C22×D20C2311yescharacteristic
89C22×C4×D5—21no—
90C22×Dic10—21no—
91C22×Dic10C2311yescharacteristic
92C2×C5×M16—24no—
93C2×C5×M16C2314yes—
94C22×C5×C8—24no—
95C22×C5×C8C2311yescharacteristic
96C22×C5×C8C2311yescharacteristic
97C22×C5×C8C2311yescharacteristic
98C22×C5×C8C2314yes—
99C22×C5×C8C2311yescharacteristic
100C4×C5×D4D414yes—
101C4×C5×D4C2314yes—
102C2×C5×C4⋊C4D411yescharacteristic
103C2×C5×C22⋊C4D411yescharacteristic
104C2×C5×C22⋊C4D411yescharacteristic
105C2×C42×C5C2311yescharacteristic
106C2×C22⋊Dic5—21no—
107C2×C22⋊Dic5—21no—
108C2×C22⋊Dic5—21no—
109#4081—28no—
110#4076—22no—
111#4076—22no—
112#4076C2314yes—
113#4076C2314yes—
114C2×#685—21no—
115C2×#685—21no—
116C2×#685—21no—
117#4072—22no—
118#4072C2314yes—
119C2×C4⋊Dic5—21no—
120C2×C4⋊Dic5—21no—
121C2×C4⋊Dic5—21no—
122C2×C4⋊Dic5—21no—
123C2×C4⋊Dic5—22no—
124C2×C4⋊Dic5—22no—
125C2×C4⋊Dic5—22no—
126C2×C4⋊Dic5C2314yes—
127C2×C4⋊Dic5C2311yescharacteristic
128C2×C4⋊Dic5C2311yescharacteristic
129C2×C4⋊Dic5C2311yescharacteristic
130C2×C4⋊Dic5C2311yescharacteristic
131C2×C4⋊Dic5C2311yescharacteristic
132C2×C4⋊Dic5C2311yescharacteristic
133C2×C4⋊Dic5C2314yes—
134C2×C4⋊Dic5C2314yes—
135#4070—22no—
136#4070—22no—
137#4070C2314yes—
138#4070C2314yes—
139C2×#683—21no—
140C2×#683—21no—
141C2×#683—21no—
142C2×#683—21no—
143C2×#683—21no—
144C2×C4×Dic5—21no—
145C2×C4×Dic5—21no—
146C2×#677—24no—
147C2×#677C2314yes—
148#4043—28no—
149#4035—28no—
150#4032—28no—
151#4032—28no—
152#4025—28no—
153#4023—28no—
154C4×D20—22no—
155C4×D20C2314yes—
156#4016—22no—
157#4016C2314yes—
158#4015—22no—
159#4015C2314yes—
160C4×Dic10—22no—
161C4×Dic10C2314yes—
162C5×C4⋊C8C2314yes—
163C5×C22⋊C8C2314yes—
164C5×C22⋊C8C2314yes—
165C5×#97C2314yes—
166#3953C2314yes—
167#3953C2314yes—
168#3953C2314yes—
169#3950C2314yes—
170#3950C2314yes—
171#3950C2314yes—
172#3950C2314yes—
173#3950C2314yes—
174#3950C2314yes—
175#3949C2314yes—
176#3949C2314yes—
177#3949C2314yes—
178#3948C2314yes—
179#3948C2314yes—
180#3948C2314yes—
181C2×#552—51no—
182C2×#547—51no—
183#3343—516no—
184C2×#501—51no—
185C2×#484—51no—
186C2×#482—51no—
187C2×#483—51no—
188C2×#480—51no—
189C2×#477—51no—
190C2×#478—51no—
191C2×#468—51no—
192C2×#465—51no—
193C2×#440—51no—
194C2×#435D511yescharacteristic, complemented
195C2×#428—51no—
196C22×#107—51no—
197C24×C5C2×D411yescharacteristic
198C24×C5C2×D411yescharacteristic
199C23×D5—21no—
200C2×C5×D4—24no—
201C2×C5×D4C2×D414yes—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5C2×D411yescharacteristic
207C22×C4×C5C2×D411yescharacteristic
208C22×C4×C5C2×D411yescharacteristic
209C22×C4×C5C2×D411yescharacteristic
210C22×C4×C5C2×D412yes—
211C22×C4×C5C2×D412yes—
212C22×C4×C5C2412yes—
213C22×C4×C5C2412yes—
214C22×C4×C5C2411yescharacteristic
215C2×C22⋊D5—24no—
216C2×C22⋊D5—24no—
217C2×C22⋊D5—44no—
218C2×C22⋊D5—44no—
219C22×Dic5—21no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—24no—
227C22×Dic5—24no—
228C22×Dic5—24no—
229C22×Dic5—44no—
230C22×Dic5—44no—
231C22×Dic5—44no—
232#711—432no—
233C2×D20—22no—
234C2×D20—22no—
235C2×D20—21no—
236C2×D20C2412yes—
237C2×C4×D5—24no—
238C2×C4×D5—44no—
239C2×Dic10—22no—
240C2×Dic10—22no—
241C2×Dic10—24no—
242C2×Dic10—21no—
243C2×Dic10—44no—
244C2×Dic10C2412yes—
245C5×M16—28no—
246C2×C5×C8—22no—
247C2×C5×C8—22no—
248C2×C5×C8—22no—
249C2×C5×C8—28no—
250C2×C5×C8#4114yescomplemented
251C2×C5×C8C2412yes—
252C2×C5×C8C2412yes—
253C2×C5×C8C2412yes—
254C2×C5×C8C2412yes—
255C5×C4⋊C4C2×D414yes—
256C5×C22⋊C4C2×D414yes—
257C5×C22⋊C4C2×D414yes—
258C42×C5C2×D412yes—
259C42×C5C2412yes—
260C22⋊Dic5—24no—
261C22⋊Dic5—24no—
262C22⋊Dic5—24no—
263#685—24no—
264#685—24no—
265#685—24no—
266C4⋊Dic5—21no—
267C4⋊Dic5—21no—
268C4⋊Dic5—21no—
269C4⋊Dic5—24no—
270C4⋊Dic5—21no—
271C4⋊Dic5—21no—
272C4⋊Dic5—21no—
273C4⋊Dic5—24no—
274C4⋊Dic5—24no—
275C4⋊Dic5—24no—
276C4⋊Dic5C2412yes—
277C4⋊Dic5C2412yes—
278C4⋊Dic5C2412yes—
279C4⋊Dic5C2412yes—
280C4⋊Dic5C2412yes—
281C4⋊Dic5C2412yes—
282#683—24no—
283#683—24no—
284#683—24no—
285#683—24no—
286#683—24no—
287C4×Dic5—24no—
288C4×Dic5—24no—
289#677—28no—
290C22×#41—101no—
291C22×SD16—51no—
292C22×M16C2×D511yescharacteristic
293C23×C8C2×D511yescharacteristic
294#552—58no—
295#552—104no—
296#547—58no—
297#547—104no—
298C2×C4⋊Q8—51no—
299C2×#126—101no—
300C2×#125—51no—
301C2×#125—101no—
302C2×#123—101no—
303C2×#123—101no—
304C2×#123—101no—
305C2×C22⋊Q8—51no—
306C2×C22⋊Q8—51no—
307C2×C22⋊Q8—101no—
308C2×#121—51no—
309C2×#121—51no—
310C2×C4×Q8—51no—
311C2×C4×D4—51no—
312C2×C4×D4C2×D511yescharacteristic
313C2×#117—51no—
314C2×#117—101no—
315C22×C4⋊C4—51no—
316C22×C4⋊C4—51no—
317C22×C4⋊C4—51no—
318#501—58no—
319#484—58no—
320#483—58no—
321#482—58no—
322#480—58no—
323#478—58no—
324#477—58no—
325#468—58no—
326#465—58no—
327#440—58no—
328#435C2×D518yescomplemented
329#428—58no—
330C2×#107—51no—
331C2×#107—51no—
332C2×#107—51no—
333C2×#107—51no—
334C2×#107—58no—
335C2×#107—51no—
336C2×#107—51no—
337C2×#106—51no—
338C2×#106—51no—
339C2×#106—51no—
340C2×C4⋊C8C2×D511yescharacteristic
341C2×#103—51no—
342C2×#103—51no—
343C2×#103—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×C22⋊C8C2×D511yescharacteristic
348C2×C22⋊C8C2×D511yescharacteristic
349C2×#97C2×D511yescharacteristic
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5AGL(1,ℤ/8)14yes—
356C23×C5C22×D412yes—
357C23×C5C22×D412yes—
358C23×C5C22×D411yescharacteristic
359C22×D5—22no—
360C22×D5—42no—
361C22×D5—42no—
362C22×D5—42no—
363C5×D4—28no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—24no—
369C2×C4×C5—24no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5C22×D412yes—
375C2×C4×C5C22×D412yes—
376C2×C4×C5C22×D412yes—
377C2×C4×C5C22×D412yes—
378C2×C4×C5C22×D411yescharacteristic
379C2×C4×C5C2×#4112yes—
380C2×C4×C52−1+412yes—
381C2×C4×C5C2511yescharacteristic
382C22⋊D5—48no—
383C22⋊D5—48no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—48no—
392C2×Dic5—42no—
393C2×Dic5—42no—
394C2×Dic5—42no—
395C2×Dic5—42no—
396C2×Dic5—48no—
397C2×Dic5—48no—
398C2×Dic5—42no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401D20—22no—
402D20—22no—
403D20—42no—
404C4×D5—48no—
405Dic10—22no—
406Dic10—22no—
407Dic10—48no—
408Dic10—42no—
409C5×C8—22no—
410C5×C8—22no—
411C5×C8—22no—
412C5×C8C2×#4114yescomplemented
413C2×#41—108no—
414C2×#41—208no—
415C22×Q8—51no—
416C22×Q8—101no—
417C22×D4—51no—
418C22×D4—101no—
419C22×D4—101no—
420C22×D4D2011yescharacteristic
421C23×C4—101no—
422C23×C4—101no—
423C23×C4—101no—
424C23×C4—101no—
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D511yescharacteristic
427C2×SD16—54no—
428C2×SD16—104no—
429C2×M16—24no—
430C2×M16C22×D514yes—
431C22×C8—24no—
432C22×C8C22×D511yescharacteristic
433C22×C8C22×D514yes—
434C22×C8C22×D511yescharacteristic
435C22×C8C22×D511yescharacteristic
436C22×C8C22×D511yescharacteristic
437C4⋊Q8—54no—
438C4⋊Q8—102no—
439#126—108no—
440#125—54no—
441#125—108no—
442#125—102no—
443#123—108no—
444#123—108no—
445#123—108no—
446C22⋊Q8—54no—
447C22⋊Q8—54no—
448C22⋊Q8—102no—
449C22⋊Q8—102no—
450C22⋊Q8—108no—
451#121—54no—
452#121—54no—
453#121—102no—
454#121—102no—
455C4×Q8—54no—
456C4×Q8—102no—
457C4×D4—54no—
458C4×D4—102no—
459C4×D4D2014yes—
460C4×D4C22×D514yes—
461#117—54no—
462#117—102no—
463#117—108no—
464C2×C4⋊C4—51no—
465C2×C4⋊C4—51no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—51no—
468C2×C4⋊C4—51no—
469C2×C4⋊C4—54no—
470C2×C4⋊C4—54no—
471C2×C4⋊C4—54no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—101no—
474C2×C4⋊C4—101no—
475C2×C4⋊C4—101no—
476C2×C4⋊C4—102no—
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⋊C4D2011yescharacteristic
486C2×C22⋊C4—101no—
487C2×C22⋊C4—101no—
488C2×C22⋊C4—101no—
489C2×C22⋊C4—101no—
490C2×C22⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4D2011yescharacteristic
493C2×C22⋊C4D2011yescharacteristic
494C2×C42—101no—
495C2×C42—101no—
496C2×C42C22×D511yescharacteristic
497#107—54no—
498#107—54no—
499#107—54no—
500#107—54no—
501#107—54no—
502#107—54no—
503#106—54no—
504#106—54no—
505#106—54no—
506C4⋊C8C22×D514yes—
507#103—54no—
508#103—54no—
509#103—54no—
510#102—54no—
511#102—54no—
512#102—54no—
513C22⋊C8C22×D514yes—
514C22⋊C8C22×D514yes—
515#97C22×D514yes—
516C22×C5—28no—
517C22×C5—22no—
518C22×C5—22no—
519C22×C5—22no—
520C22×C5—22no—
521C22×C5—22no—
522C22×C5—44no—
523C22×C5#54712yes—
524C22×C5C2×AGL(1,ℤ/8)14yes—
525C22×C5C2×AGL(1,ℤ/8)12yes—
526C22×C5#57812yes—
527C22×C5C23×D411yescharacteristic
528C2×D5—42no—
529C2×D5—42no—
530C2×D5—42no—
531C2×D5—84no—
532C4×C5—22no—
533C4×C5—22no—
534C4×C5—22no—
535C4×C5—22no—
536C4×C5#54712yes—
537C4×C5C22×#4111yescharacteristic
538C4×C5C2×2−1+411yescharacteristic
539Dic5—42no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543Dic5—42no—
544Dic5—42no—
545Dic5—42no—
546C24—101no—
547C24C2×D2011yescharacteristic
548C24C2×D2011yescharacteristic
549#41—2032no—
550C2×Q8—52no—
551C2×Q8—101no—
552C2×Q8—104no—
553C2×Q8—102no—
554C2×Q8—102no—
555C2×Q8—204no—
556C2×D4—24no—
557C2×D4—52no—
558C2×D4—104no—
559C2×D4—104no—
560C2×D4—101no—
561C2×D4—102no—
562C2×D4—102no—
563C2×D4—204no—
564C2×D4—204no—
565C2×D4C2×D2014yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—104no—
571C22×C4—104no—
572C22×C4—104no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—101no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—104no—
581C22×C4—204no—
582C22×C4—204no—
583C22×C4—204no—
584C22×C4—204no—
585C22×C4C2×D2012yes—
586C22×C4C2×D2012yes—
587C22×C4C2×D2011yescharacteristic
588C22×C4C2×D2011yescharacteristic
589C22×C4C2×D2011yescharacteristic
590C22×C4C2×D2011yescharacteristic
591C22×C4C23×D512yes—
592C22×C4C23×D512yes—
593C22×C4C23×D511yescharacteristic
594SD16—108no—
595M16—28no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—28no—
600C2×C8#71114yescomplemented
601C2×C8C23×D512yes—
602C2×C8C23×D512yes—
603C2×C8C23×D512yes—
604C2×C8C23×D512yes—
605C4⋊C4—52no—
606C4⋊C4—52no—
607C4⋊C4—52no—
608C4⋊C4—52no—
609C4⋊C4—52no—
610C4⋊C4—52no—
611C4⋊C4—101no—
612C4⋊C4—101no—
613C4⋊C4—101no—
614C4⋊C4—101no—
615C4⋊C4—104no—
616C4⋊C4—104no—
617C4⋊C4—101no—
618C4⋊C4—104no—
619C4⋊C4—101no—
620C4⋊C4—104no—
621C4⋊C4—104no—
622C4⋊C4—104no—
623C4⋊C4—104no—
624C4⋊C4—104no—
625C4⋊C4—104no—
626C4⋊C4C2×D2014yes—
627C22⋊C4—104no—
628C22⋊C4—104no—
629C22⋊C4—104no—
630C22⋊C4—104no—
631C22⋊C4—104no—
632C22⋊C4—104no—
633C22⋊C4C2×D2014yes—
634C22⋊C4C2×D2014yes—
635C42—104no—
636C42—104no—
637C42C2×D2012yes—
638C42C23×D512yes—
639C2×C5—24no—
640C2×C5—42no—
641C2×C5#334314yescomplemented
642C2×C5C2×#54711yescharacteristic
643C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
644C2×C5C2×#57811yescharacteristic
645D5—82no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—102no—
652C23—202no—
653C23—202no—
654C23—202no—
655C23#405414yes—
656C23C22×D2012yes—
657C23C22×D2012yes—
658C23C22×D2011yescharacteristic
659Q8—102no—
660Q8—102no—
661Q8—208no—
662Q8—202no—
663D4—28no—
664D4—102no—
665D4—102no—
666D4—208no—
667D4—208no—
668D4—202no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—102no—
680C2×C4—102no—
681C2×C4—102no—
682C2×C4—102no—
683C2×C4—102no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—208no—
687C2×C4—208no—
688C2×C4—202no—
689C2×C4—202no—
690C2×C4—202no—
691C2×C4—208no—
692C2×C4—208no—
693C2×C4—202no—
694C2×C4—202no—
695C2×C4—202no—
696C2×C4—202no—
697C2×C4C22×D2012yes—
698C2×C4C22×D2012yes—
699C2×C4C22×D2012yes—
700C2×C4C22×D2012yes—
701C2×C4C22×D2011yescharacteristic
702C2×C4C2×#71112yes—
703C2×C4#415012yes—
704C2×C4C24×D511yescharacteristic
705C8—22no—
706C8—22no—
707C8—22no—
708C8C2×#71114yescomplemented
709C5C2×#334311yescharacteristic, complemented, Sylow
710C22—28no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—202no—
718C22—202no—
719C22—202no—
720C22—404no—
721C22#6588912yes—
722C22C2×#405414yes—
723C22C2×#405412yes—
724C22#6608712yes—
725C22C23×D2011yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—202no—
731C4—202no—
732C4—202no—
733C4—202no—
734C4—202no—
735C4—202no—
736C4—202no—
737C4#6588912yes—
738C4C22×#71111yescharacteristic
739C4C2×#415011yescharacteristic
740C2—24no—
741C2—42no—
742C2—402no—
743C2#1061120014yesdirect product factor
744C2C2×#6588911yescharacteristic
745C2C22×#405411yescharacteristic
746C2C2×#6608711yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#435C2
socleC23×C5C22×D4
prime radicalC2×#65889C2
hypercenterC2×#435D5
hypocenterC5C2×#3343
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#65875C2semidirect
3. C2×C5×#435C2semidirect
4. C2×#65423C2semidirect
5. C2×#65410C2semidirect
6. C2×#65403C2semidirect
7. C22×#3950C2semidirect
8. #10611200C2direct (N × H)
9. C2×#65139C2semidirect
10. C2×#65136C2semidirect
11. C2×#65011C2semidirect
12. C2×#65026C2semidirect
13. C2×#65010C2semidirect
14. C2×#65025C2semidirect
15. C2×#64999C2semidirect
16. C2×#64991C2semidirect
34. #65875C22semidirect
45. C5×#435C22semidirect
50. #65423C22semidirect
51. #65410C22semidirect
52. #65403C22semidirect
62. C2×#3950C22semidirect
69. #65139C22semidirect
70. #65136C22semidirect
71. #65026C22semidirect
72. #65025C22semidirect
73. #65011C22semidirect
74. #65010C22semidirect
75. #64999C22semidirect
76. #64991C22semidirect
194. C2×#435D5semidirect
250. C2×C5×C8#41semidirect
328. #435C2×D5semidirect
412. C5×C8C2×#41semidirect
600. C2×C8#711semidirect
641. C2×C5#3343semidirect
708. C8C2×#711semidirect
709. C5C2×#3343semidirect
743. C2#10611200direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658752
C2×#658892
C2×C5×#4352
C2×#654232
C2×#654102
C2×#654032
C22×#39502
#106112002
C2×#651392
C2×#651362
C2×#650112
C2×#650262
C2×#650102
C2×#650252
C2×#649992
C2×#649912
C2×#33435