Finite Group Databasebeta

← C2×#10611234 #12975828

Subgroups — C2×#10611234 #12975828

Order 1280.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65884C211yesmaximal, characteristic
2C2×#65877C211yesmaximal, characteristic, complemented
3C2×C5×#435C211yesmaximal, characteristic, complemented
4C2×#65423C211yesmaximal, characteristic, complemented
5C2×#65422C211yesmaximal, characteristic, complemented
6C2×#65405C211yesmaximal, characteristic, complemented
7C22×#3953C211yesmaximal, characteristic, complemented
8#10611234C2116yesmaximal, direct product factor
9C2×#65134C211yesmaximal, characteristic, complemented
10C2×#65135C211yesmaximal, characteristic, complemented
11C2×#65022C211yesmaximal, characteristic, complemented
12C2×#65020C211yesmaximal, characteristic, complemented
13C2×#65011C211yesmaximal, characteristic, complemented
14C2×#65025C211yesmaximal, characteristic, complemented
15C2×#65003C211yesmaximal, characteristic, complemented
16C2×#64999C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C22×C5×M16C2211yescharacteristic, complemented
20C23×C5×C8C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C2×#4083—21no—
23C2×D4×Dic5—21no—
24C2×#4076C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C22×C4⋊Dic5C2211yescharacteristic, complemented
27C2×#4070C2211yescharacteristic
28C2×#4070C2211yescharacteristic
29C2×#4070C2211yescharacteristic, complemented
30C22×Dic20C2211yescharacteristic, complemented
31C22×#677C2211yescharacteristic
32C22×#677C2211yescharacteristic
33#65884—24no—
34#65884C2218yes—
35#65877—24no—
36#65877C2218yescomplemented
37C2×#4040—21no—
38C2×#4036—21no—
39C2×#4030—21no—
40C2×D5×C22⋊C4—21no—
41C2×#4024—21no—
42C2×#4024—21no—
43C2×#4021C2211yescharacteristic
44C2×C4×D20C2211yescharacteristic
45C2×#4015C2211yescharacteristic, complemented
46C2×C4×Dic10C2211yescharacteristic, complemented
47C5×#435C2218yescomplemented
48C2×C5×C4⋊C8C2211yescharacteristic, complemented
49C2×C5×C22⋊C8C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic, complemented
51C2×C5×#97C2211yescharacteristic, complemented
52#65423C2218yescomplemented
53#65422C2218yescomplemented
54#65405C2218yescomplemented
55C2×#3953C2211yescharacteristic
56C2×#3953C2211yescharacteristic
57C2×#3953C2211yescharacteristic
58C2×#3953C2211yescharacteristic
59C2×#3953C2211yescharacteristic
60C2×#3953C2211yescharacteristic
61C2×#3953C2218yescomplemented
62C2×#3950C2211yescharacteristic, complemented
63C2×#3950C2211yescharacteristic, complemented
64C2×#3950C2211yescharacteristic, complemented
65C2×#3948C2211yescharacteristic, complemented
66C2×#3948C2211yescharacteristic, complemented
67C2×#3948C2211yescharacteristic, complemented
68C2×#3948C2211yescharacteristic, complemented
69#65135C2218yescomplemented
70#65134C2218yescomplemented
71#65025C2218yescomplemented
72#65022C2218yescomplemented
73#65020C2218yescomplemented
74#65011C2218yescomplemented
75#65003C2218yescomplemented
76#64999C2218yescomplemented
77C2×#3314—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×D4D411yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C23×Dic5—21no—
85C23×Dic5—21no—
86C2×#709—22no—
87C2×#709—24no—
88C2×#709—42no—
89C2×#709C2314yes—
90C22×D20—24no—
91C22×D20—21no—
92C22×D20—22no—
93C22×D20—42no—
94C22×D20C2311yescharacteristic
95C22×D20C2314yes—
96C22×D20C2311yescharacteristic
97C22×C4×D5—21no—
98C22×C4×D5—21no—
99C22×Dic10—21no—
100C22×Dic10C2311yescharacteristic
101C22×Dic10C2311yescharacteristic
102C2×C5×M16—42no—
103C2×C5×M16C2314yescomplemented
104C22×C5×C8—42no—
105C22×C5×C8C2311yescharacteristic
106C22×C5×C8C2311yescharacteristic
107C22×C5×C8C2311yescharacteristic
108C22×C5×C8C2311yescharacteristic
109C22×C5×C8C2314yes—
110C4×C5×D4D414yes—
111C4×C5×D4C2314yes—
112C2×C5×C4⋊C4D411yescharacteristic
113C2×C5×C22⋊C4D411yescharacteristic
114C2×C5×C22⋊C4D411yescharacteristic
115C2×C42×C5C2311yescharacteristic
116C2×C22⋊Dic5—21no—
117C2×C22⋊Dic5—21no—
118C2×C22⋊Dic5—21no—
119#4083—28no—
120D4×Dic5—28no—
121#4076—22no—
122#4076C2314yes—
123C2×#685—21no—
124C2×#685—21no—
125C2×#685—21no—
126C2×#685—21no—
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5—21no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5—22no—
131C2×C4⋊Dic5—22no—
132C2×C4⋊Dic5C2311yescharacteristic
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2311yescharacteristic
135C2×C4⋊Dic5C2311yescharacteristic
136C2×C4⋊Dic5C2314yes—
137C2×C4⋊Dic5C2314yescomplemented
138#4070—22no—
139#4070—22no—
140#4070—22no—
141#4070C2314yes—
142#4070C2314yes—
143#4070C2314yescomplemented
144C2×#683—21no—
145C2×#683—21no—
146C2×#683—21no—
147C2×#683—21no—
148C2×C4×Dic5—21no—
149C2×Dic20—42no—
150C2×Dic20C2314yescomplemented
151C2×#677—24no—
152C2×#677—42no—
153C2×#677C2314yes—
154C2×#677C2314yes—
155#4040—28no—
156#4036—28no—
157#4030—28no—
158D5×C22⋊C4—28no—
159#4024—28no—
160#4024—28no—
161#4021—22no—
162#4021C2314yes—
163C4×D20—22no—
164C4×D20C2314yes—
165#4015—22no—
166#4015C2314yescomplemented
167C4×Dic10—22no—
168C4×Dic10C2314yescomplemented
169C5×C4⋊C8C2314yescomplemented
170C5×C22⋊C8C2314yes—
171C5×C22⋊C8C2314yescomplemented
172C5×#97C2314yescomplemented
173#3953C2314yes—
174#3953C2314yes—
175#3953C2314yes—
176#3953C2314yes—
177#3953C2314yes—
178#3953C2314yes—
179#3950C2314yescomplemented
180#3950C2314yescomplemented
181#3950C2314yescomplemented
182#3948C2314yescomplemented
183#3948C2314yescomplemented
184#3948C2314yescomplemented
185#3948C2314yescomplemented
186C2×#554—51no—
187C2×#546—51no—
188#3314—516no—
189C2×#489—51no—
190C2×#484—51no—
191C2×#480—51no—
192C2×#474—51no—
193C2×#468—51no—
194C2×#467—51no—
195C2×#464—51no—
196C2×#452—51no—
197C2×#450—51no—
198C2×#440—51no—
199C2×#435D511yescharacteristic, complemented
200C2×#417—51no—
201C22×#102—51no—
202C24×C5C2×D411yescharacteristic
203C24×C5C2×D411yescharacteristic
204C23×D5—21no—
205C23×D5—21no—
206C23×D5—24no—
207C23×D5—44no—
208C23×D5—44no—
209C23×D5—82no—
210C2×C5×D4—24no—
211C2×C5×D4C2×D414yes—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D412yes—
221C22×C4×C5C2×D412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2411yescharacteristic
225C2×C22⋊D5—24no—
226C2×C22⋊D5—24no—
227C2×C22⋊D5—44no—
228C2×C22⋊D5—82no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—24no—
236C22×Dic5—24no—
237C22×Dic5—82no—
238C22×Dic5—82no—
239#709—28no—
240#709—44no—
241#709—48no—
242C2×D20—21no—
243C2×D20—22no—
244C2×D20—22no—
245C2×D20—22no—
246C2×D20—28no—
247C2×D20—21no—
248C2×D20—24no—
249C2×D20—44no—
250C2×D20—48no—
251C2×D20—44no—
252C2×D20#4114yes—
253C2×D20C2412yes—
254C2×D20C2412yes—
255C2×C4×D5—24no—
256C2×C4×D5—24no—
257C2×C4×D5—44no—
258C2×C4×D5—82no—
259C2×Dic10—22no—
260C2×Dic10—22no—
261C2×Dic10—22no—
262C2×Dic10—22no—
263C2×Dic10—21no—
264C2×Dic10—21no—
265C2×Dic10—24no—
266C2×Dic10—82no—
267C2×Dic10C2412yes—
268C2×Dic10C2412yes—
269C5×M16—44no—
270C2×C5×C8—22no—
271C2×C5×C8—22no—
272C2×C5×C8—22no—
273C2×C5×C8—22no—
274C2×C5×C8—44no—
275C2×C5×C8C2412yes—
276C2×C5×C8C2412yes—
277C2×C5×C8C2412yes—
278C2×C5×C8C2412yes—
279C5×C4⋊C4C2×D414yes—
280C5×C22⋊C4C2×D414yes—
281C5×C22⋊C4C2×D414yes—
282C42×C5C2×D412yes—
283C42×C5C2412yes—
284C22⋊Dic5—24no—
285C22⋊Dic5—24no—
286C22⋊Dic5—24no—
287#685—24no—
288#685—24no—
289#685—24no—
290#685—24no—
291C4⋊Dic5—21no—
292C4⋊Dic5—21no—
293C4⋊Dic5—21no—
294C4⋊Dic5—24no—
295C4⋊Dic5—21no—
296C4⋊Dic5—24no—
297C4⋊Dic5—24no—
298C4⋊Dic5C2412yes—
299C4⋊Dic5C2412yes—
300C4⋊Dic5C2412yes—
301C4⋊Dic5C2412yes—
302#683—24no—
303#683—24no—
304#683—24no—
305#683—24no—
306C4×Dic5—24no—
307Dic20—44no—
308#677—28no—
309#677—44no—
310C22×#41—51no—
311C23×D4—51no—
312C22×Q16—51no—
313C22×SD16—51no—
314C22×SD16—51no—
315C22×M16C2×D511yescharacteristic, complemented
316C23×C8C2×D511yescharacteristic
317#554—58no—
318#554—104no—
319#546—58no—
320#546—104no—
321C2×C4⋊Q8—51no—
322C2×#125—101no—
323C2×#124—51no—
324C2×#123—101no—
325C2×C22⋊Q8—51no—
326C2×C22⋊Q8—51no—
327C2×C22⋊Q8—51no—
328C2×C22⋊Q8—101no—
329C2×C22⋊Q8—101no—
330C2×#121—51no—
331C2×#121—101no—
332C2×#120—101no—
333C2×C4×Q8—51no—
334C2×C4×D4—51no—
335C2×C4×D4—101no—
336C2×C4×D4C2×D511yescharacteristic
337C22×C4⋊C4—51no—
338C22×C4⋊C4—51no—
339C22×C22⋊C4—101no—
340#489—58no—
341#484—58no—
342#480—58no—
343#474—58no—
344#468—58no—
345#467—58no—
346#464—58no—
347#452—58no—
348#450—58no—
349#440—58no—
350#435C2×D518yescomplemented
351C2×#107—51no—
352C2×#107—51no—
353C2×#107—51no—
354C2×C4⋊C8C2×D511yescharacteristic, complemented
355#417—58no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—51no—
359C2×#103—51no—
360C2×#102—51no—
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×#102—58no—
366C2×#102—51no—
367C2×C22⋊C8C2×D511yescharacteristic
368C2×C22⋊C8C2×D511yescharacteristic, complemented
369C2×#97C2×D511yescharacteristic, complemented
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5#13714yes—
376C23×C5C22×D412yes—
377C23×C5C22×D412yes—
378C23×C5C22×D411yescharacteristic
379C22×D5—24no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—48no—
383C22×D5—42no—
384C22×D5—42no—
385C22×D5—42no—
386C22×D5—48no—
387C22×D5—42no—
388C22×D5—42no—
389C22×D5—84no—
390C22×D5—816no—
391C5×D4—28no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—24no—
397C2×C4×C5—24no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5C22×D412yes—
403C2×C4×C5C22×D412yes—
404C2×C4×C5C22×D412yes—
405C2×C4×C5C22×D412yes—
406C2×C4×C5C22×D411yescharacteristic
407C2×C4×C5C2×#4112yes—
408C2×C4×C5H(5,𝔽2)12yes—
409C2×C4×C5C2511yescharacteristic
410C22⋊D5—48no—
411C22⋊D5—84no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5—42no—
419C2×Dic5—42no—
420C2×Dic5—42no—
421C2×Dic5—42no—
422C2×Dic5—42no—
423C2×Dic5—42no—
424C2×Dic5—84no—
425C2×Dic5—84no—
426D20—24no—
427D20—22no—
428D20—22no—
429D20—22no—
430D20—48no—
431D20—42no—
432D20C2×#4114yes—
433C4×D5—48no—
434C4×D5—84no—
435Dic10—22no—
436Dic10—22no—
437Dic10—22no—
438Dic10—22no—
439Dic10—42no—
440Dic10—42no—
441Dic10—84no—
442C5×C8—22no—
443C5×C8—22no—
444C5×C8—22no—
445C5×C8—22no—
446C25—101no—
447C2×#41—54no—
448C2×#41—104no—
449C2×#41—102no—
450C2×#41—202no—
451C22×Q8—51no—
452C22×Q8—51no—
453C22×Q8—101no—
454C22×D4—51no—
455C22×D4—51no—
456C22×D4—54no—
457C22×D4—104no—
458C22×D4—101no—
459C22×D4—101no—
460C22×D4—101no—
461C22×D4—102no—
462C22×D4—202no—
463C22×D4D2011yescharacteristic
464C23×C4—101no—
465C23×C4—101no—
466C23×C4—101no—
467C23×C4—101no—
468C23×C4C22×D511yescharacteristic
469C23×C4C22×D511yescharacteristic
470C2×Q16—54no—
471C2×Q16—202no—
472C2×SD16—54no—
473C2×SD16—54no—
474C2×SD16—104no—
475C2×SD16—202no—
476C2×M16—42no—
477C2×M16C22×D514yescomplemented
478C22×C8—42no—
479C22×C8C22×D511yescharacteristic
480C22×C8C22×D511yescharacteristic
481C22×C8C22×D511yescharacteristic
482C22×C8C22×D511yescharacteristic
483C22×C8C22×D514yes—
484C4⋊Q8—54no—
485C4⋊Q8—102no—
486#125—108no—
487#124—54no—
488#124—102no—
489#123—108no—
490C22⋊Q8—54no—
491C22⋊Q8—54no—
492C22⋊Q8—54no—
493C22⋊Q8—102no—
494C22⋊Q8—102no—
495C22⋊Q8—102no—
496C22⋊Q8—108no—
497C22⋊Q8—108no—
498#121—54no—
499#121—102no—
500#121—108no—
501#120—108no—
502C4×Q8—54no—
503C4×Q8—102no—
504C4×D4—54no—
505C4×D4—108no—
506C4×D4—102no—
507C4×D4D2014yes—
508C4×D4C22×D514yes—
509C2×C4⋊C4—51no—
510C2×C4⋊C4—51no—
511C2×C4⋊C4—51no—
512C2×C4⋊C4—54no—
513C2×C4⋊C4—54no—
514C2×C4⋊C4—51no—
515C2×C4⋊C4—101no—
516C2×C4⋊C4—101no—
517C2×C4⋊C4—102no—
518C2×C4⋊C4—102no—
519C2×C4⋊C4—101no—
520C2×C4⋊C4—101no—
521C2×C4⋊C4—101no—
522C2×C4⋊C4—101no—
523C2×C4⋊C4—101no—
524C2×C4⋊C4D2011yescharacteristic
525C2×C22⋊C4—101no—
526C2×C22⋊C4—101no—
527C2×C22⋊C4—101no—
528C2×C22⋊C4—101no—
529C2×C22⋊C4—101no—
530C2×C22⋊C4—101no—
531C2×C22⋊C4—101no—
532C2×C22⋊C4—108no—
533C2×C22⋊C4D2011yescharacteristic
534C2×C22⋊C4D2011yescharacteristic
535C2×C42—101no—
536C2×C42C22×D511yescharacteristic
537#107—54no—
538#107—54no—
539#107—54no—
540C4⋊C8C22×D514yescomplemented
541#103—54no—
542#103—54no—
543#103—54no—
544#103—54no—
545#102—54no—
546#102—54no—
547#102—54no—
548#102—54no—
549#102—54no—
550#102—54no—
551C22⋊C8C22×D514yes—
552C22⋊C8C22×D514yescomplemented
553#97C22×D514yescomplemented
554C22×C5—22no—
555C22×C5—28no—
556C22×C5—22no—
557C22×C5—22no—
558C22×C5—22no—
559C22×C5—22no—
560C22×C5—44no—
561C22×C5#54612yes—
562C22×C5C2×#13714yes—
563C22×C5C2×#13712yes—
564C22×C5#57612yes—
565C22×C5C23×D411yescharacteristic
566C2×D5—24no—
567C2×D5—48no—
568C2×D5—42no—
569C2×D5—42no—
570C2×D5—42no—
571C2×D5—42no—
572C2×D5—42no—
573C2×D5—816no—
574C2×D5—84no—
575C4×C5—22no—
576C4×C5—22no—
577C4×C5—22no—
578C4×C5—22no—
579C4×C5#54612yes—
580C4×C5C22×#4111yescharacteristic
581C4×C5C2×H(5,𝔽2)11yescharacteristic
582Dic5—42no—
583Dic5—42no—
584Dic5—42no—
585Dic5—42no—
586Dic5—42no—
587Dic5—42no—
588C24—101no—
589C24—101no—
590C24—104no—
591C24—204no—
592C24—204no—
593C24—402no—
594C24C2×D2011yescharacteristic
595C24C2×D2011yescharacteristic
596#41—108no—
597#41—204no—
598#41—208no—
599C2×Q8—52no—
600C2×Q8—52no—
601C2×Q8—101no—
602C2×Q8—101no—
603C2×Q8—104no—
604C2×Q8—102no—
605C2×Q8—102no—
606C2×Q8—102no—
607C2×Q8—102no—
608C2×Q8—402no—
609C2×D4—24no—
610C2×D4—54no—
611C2×D4—52no—
612C2×D4—52no—
613C2×D4—108no—
614C2×D4—104no—
615C2×D4—104no—
616C2×D4—101no—
617C2×D4—104no—
618C2×D4—101no—
619C2×D4—102no—
620C2×D4—102no—
621C2×D4—102no—
622C2×D4—204no—
623C2×D4—208no—
624C2×D4—204no—
625C2×D4—204no—
626C2×D4—402no—
627C2×D4C2×D2014yes—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—101no—
633C22×C4—101no—
634C22×C4—101no—
635C22×C4—101no—
636C22×C4—101no—
637C22×C4—101no—
638C22×C4—104no—
639C22×C4—104no—
640C22×C4—104no—
641C22×C4—104no—
642C22×C4—204no—
643C22×C4—402no—
644C22×C4—402no—
645C22×C4—402no—
646C22×C4C2×D2012yes—
647C22×C4C2×D2012yes—
648C22×C4C2×D2011yescharacteristic
649C22×C4C2×D2011yescharacteristic
650C22×C4C2×D2011yescharacteristic
651C22×C4C2×D2011yescharacteristic
652C22×C4C23×D512yes—
653C22×C4C23×D512yes—
654C22×C4C23×D511yescharacteristic
655Q16—204no—
656SD16—108no—
657SD16—204no—
658M16—44no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8C23×D512yes—
665C2×C8C23×D512yes—
666C2×C8C23×D512yes—
667C2×C8C23×D512yes—
668C4⋊C4—52no—
669C4⋊C4—52no—
670C4⋊C4—52no—
671C4⋊C4—52no—
672C4⋊C4—101no—
673C4⋊C4—104no—
674C4⋊C4—104no—
675C4⋊C4—101no—
676C4⋊C4—101no—
677C4⋊C4—101no—
678C4⋊C4—104no—
679C4⋊C4—104no—
680C4⋊C4—104no—
681C4⋊C4—104no—
682C4⋊C4—104no—
683C4⋊C4C2×D2014yes—
684C22⋊C4—104no—
685C22⋊C4—104no—
686C22⋊C4—104no—
687C22⋊C4—104no—
688C22⋊C4—104no—
689C22⋊C4—104no—
690C22⋊C4—104no—
691C22⋊C4C2×D2014yes—
692C22⋊C4C2×D2014yes—
693C42—104no—
694C42C2×D2012yes—
695C42C23×D512yes—
696C2×C5—24no—
697C2×C5—42no—
698C2×C5#331414yescomplemented
699C2×C5C2×#54611yescharacteristic
700C2×C5C22×#13711yescharacteristic
701C2×C5C2×#57611yescharacteristic
702D5—44no—
703D5—82no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—104no—
710C23—102no—
711C23—102no—
712C23—208no—
713C23—202no—
714C23—202no—
715C23—208no—
716C23—202no—
717C23—202no—
718C23—202no—
719C23—404no—
720C23—4016no—
721C23#405514yes—
722C23C22×D2012yes—
723C23C22×D2012yes—
724C23C22×D2011yescharacteristic
725Q8—102no—
726Q8—102no—
727Q8—102no—
728Q8—102no—
729Q8—202no—
730Q8—202no—
731Q8—404no—
732D4—28no—
733D4—54no—
734D4—104no—
735D4—102no—
736D4—102no—
737D4—102no—
738D4—208no—
739D4—208no—
740D4—202no—
741D4—404no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—102no—
753C2×C4—102no—
754C2×C4—102no—
755C2×C4—102no—
756C2×C4—102no—
757C2×C4—102no—
758C2×C4—208no—
759C2×C4—202no—
760C2×C4—202no—
761C2×C4—202no—
762C2×C4—202no—
763C2×C4—202no—
764C2×C4—202no—
765C2×C4—404no—
766C2×C4—404no—
767C2×C4—404no—
768C2×C4C22×D2012yes—
769C2×C4C22×D2012yes—
770C2×C4C22×D2012yes—
771C2×C4C22×D2012yes—
772C2×C4C22×D2011yescharacteristic
773C2×C4#414412yes—
774C2×C4D5×#4112yes—
775C2×C4C24×D511yescharacteristic
776C8—22no—
777C8—22no—
778C8—22no—
779C8—22no—
780C5C2×#331411yescharacteristic, complemented, Sylow
781C22—28no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—44no—
788C22—104no—
789C22—208no—
790C22—202no—
791C22—202no—
792C22—202no—
793C22—202no—
794C22—202no—
795C22—4016no—
796C22—404no—
797C22#6588812yes—
798C22C2×#405514yes—
799C22C2×#405512yes—
800C22#6608612yes—
801C22C23×D2011yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—202no—
807C4—202no—
808C4—202no—
809C4—202no—
810C4—202no—
811C4—202no—
812C4#6588812yes—
813C4C2×#414411yescharacteristic
814C4C2×D5×#4111yescharacteristic
815C2—24no—
816C2—42no—
817C2—204no—
818C2—402no—
819C2#1061123414yesdirect product factor
820C2C2×#6588811yescharacteristic
821C2C22×#405511yescharacteristic
822C2C2×#6608611yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#435C2
socleC23×C5C22×D4
prime radicalC2×#65884C2
hypercenterC2×#435D5
hypocenterC5C2×#3314
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
2. C2×#65877C2semidirect
3. C2×C5×#435C2semidirect
4. C2×#65423C2semidirect
5. C2×#65422C2semidirect
6. C2×#65405C2semidirect
7. C22×#3953C2semidirect
8. #10611234C2direct (N × H)
9. C2×#65134C2semidirect
10. C2×#65135C2semidirect
11. C2×#65022C2semidirect
12. C2×#65020C2semidirect
13. C2×#65011C2semidirect
14. C2×#65025C2semidirect
15. C2×#65003C2semidirect
16. C2×#64999C2semidirect
19. C22×C5×M16C22semidirect
26. C22×C4⋊Dic5C22semidirect
29. C2×#4070C22semidirect
30. C22×Dic20C22semidirect
36. #65877C22semidirect
45. C2×#4015C22semidirect
46. C2×C4×Dic10C22semidirect
47. C5×#435C22semidirect
48. C2×C5×C4⋊C8C22semidirect
50. C2×C5×C22⋊C8C22semidirect
51. C2×C5×#97C22semidirect
52. #65423C22semidirect
53. #65422C22semidirect
54. #65405C22semidirect
61. C2×#3953C22semidirect
62. C2×#3950C22semidirect
63. C2×#3950C22semidirect
64. C2×#3950C22semidirect
65. C2×#3948C22semidirect
66. C2×#3948C22semidirect
67. C2×#3948C22semidirect
68. C2×#3948C22semidirect
69. #65135C22semidirect
70. #65134C22semidirect
71. #65025C22semidirect
72. #65022C22semidirect
73. #65020C22semidirect
74. #65011C22semidirect
75. #65003C22semidirect
76. #64999C22semidirect
103. C2×C5×M16C23semidirect
137. C2×C4⋊Dic5C23semidirect
143. #4070C23semidirect
150. C2×Dic20C23semidirect
166. #4015C23semidirect
168. C4×Dic10C23semidirect
169. C5×C4⋊C8C23semidirect
171. C5×C22⋊C8C23semidirect
172. C5×#97C23semidirect
179. #3950C23semidirect
180. #3950C23semidirect
181. #3950C23semidirect
182. #3948C23semidirect
183. #3948C23semidirect
184. #3948C23semidirect
185. #3948C23semidirect
199. C2×#435D5semidirect
315. C22×M16C2×D5semidirect
350. #435C2×D5semidirect
354. C2×C4⋊C8C2×D5semidirect
368. C2×C22⋊C8C2×D5semidirect
369. C2×#97C2×D5semidirect
477. C2×M16C22×D5semidirect
540. C4⋊C8C22×D5semidirect
552. C22⋊C8C22×D5semidirect
553. #97C22×D5semidirect
698. C2×C5#3314semidirect
780. C5C2×#3314semidirect
819. C2#10611234direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658842
C2×#658772
C2×C5×#4352
C2×#654232
C2×#654222
C2×#654052
C22×#39532
#106112342
C2×#651342
C2×#651352
C2×#650222
C2×#650202
C2×#650112
C2×#650252
C2×#650032
C2×#649992
C2×#33145