Finite Group Databasebeta

← C2×#10611245 #12976020

Subgroups — C2×#10611245 #12976020

Order 1280.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65875C211yesmaximal, characteristic, complemented
2C2×#65887C211yesmaximal, characteristic
3C2×C5×#435C211yesmaximal, characteristic, complemented
4C2×#65423C211yesmaximal, characteristic, complemented
5C2×#65422C211yesmaximal, characteristic, complemented
6C2×#65403C211yesmaximal, characteristic, complemented
7C2×#65402C211yesmaximal, characteristic, complemented
8#10611245C2116yesmaximal, direct product factor
9C2×#65118C211yesmaximal, characteristic, complemented
10C2×#65137C211yesmaximal, characteristic, complemented
11C2×#65022C211yesmaximal, characteristic, complemented
12C2×#65022C211yesmaximal, characteristic, complemented
13C2×#65024C211yesmaximal, characteristic, complemented
14C2×#65026C211yesmaximal, characteristic, complemented
15C2×#65005C211yesmaximal, characteristic, complemented
16C2×#65002C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C22×#709C2211yescharacteristic
19C22×C5×M16C2211yescharacteristic
20C23×C5×C8C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C2×#4086—21no—
23C2×#4081—21no—
24C2×#4076C2211yescharacteristic
25C2×#4076C2211yescharacteristic
26C2×#4072C2211yescharacteristic
27C22×C4⋊Dic5C2211yescharacteristic
28C2×#4070C2211yescharacteristic
29C2×#4070C2211yescharacteristic
30C22×Dic20C2211yescharacteristic
31C22×#677C2211yescharacteristic
32C22×#677C2211yescharacteristic
33#65887—24no—
34#65887C2218yes—
35#65875—24no—
36#65875C2218yescomplemented
37C2×#4039—21no—
38C2×#4035—21no—
39C2×#4030—21no—
40C2×#4030—21no—
41C2×#4025—21no—
42C2×#4023—21no—
43C2×#4020C2211yescharacteristic
44C2×#4016C2211yescharacteristic
45C2×C4×Dic10C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47C5×#435C2218yescomplemented
48C2×C5×C4⋊C8C2211yescharacteristic
49C2×C5×C22⋊C8C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51C2×C5×#97C2211yescharacteristic
52#65423C2218yescomplemented
53#65422C2218yescomplemented
54#65403C2218yescomplemented
55#65402C2218yescomplemented
56C2×#3953C2211yescharacteristic
57C2×#3953C2211yescharacteristic
58C2×#3953C2211yescharacteristic
59C2×#3953C2211yescharacteristic
60C2×#3953C2211yescharacteristic
61C2×#3953C2211yescharacteristic
62C2×#3950C2211yescharacteristic
63C2×#3949C2211yescharacteristic
64C2×#3949C2211yescharacteristic
65C2×#3948C2211yescharacteristic
66C2×#3948C2211yescharacteristic
67C2×#3948C2211yescharacteristic
68C2×#3948C2211yescharacteristic
69#65137C2218yescomplemented
70#65118C2218yescomplemented
71#65026C2218yescomplemented
72#65024C2218yescomplemented
73#65022C2218yescomplemented
74#65022C2218yescomplemented
75#65005C2218yescomplemented
76#65002C2218yescomplemented
77C2×#3317—51nomaximal, Sylow
78C22×C5×D4D411yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C23×Dic5—21no—
86C2×#709—22no—
87C2×#709—22no—
88C2×#709—24no—
89C2×#709—24no—
90C2×#709—42no—
91C2×#709—42no—
92C2×#709C2314yes—
93C2×#709C2314yes—
94C22×D20—21no—
95C22×D20—21no—
96C22×D20C2311yescharacteristic
97C22×D20C2311yescharacteristic
98C22×C4×D5—21no—
99C22×C4×D5—21no—
100C22×Dic10C2311yescharacteristic
101C22×Dic10C2311yescharacteristic
102C2×C5×M16—42no—
103C2×C5×M16C2314yes—
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#4086—28no—
120#4081—28no—
121#4076—22no—
122#4076—22no—
123#4076C2314yes—
124#4076C2314yes—
125C2×#685—21no—
126C2×#685—21no—
127#4072—22no—
128#4072C2314yes—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5—22no—
131C2×C4⋊Dic5C2314yes—
132C2×C4⋊Dic5C2311yescharacteristic
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2311yescharacteristic
135C2×C4⋊Dic5C2311yescharacteristic
136#4070—22no—
137#4070—22no—
138#4070C2314yes—
139#4070C2314yes—
140C2×#683—21no—
141C2×#683—21no—
142C2×#683—21no—
143C2×#683—21no—
144C2×#683—21no—
145C2×#683—21no—
146C2×C4×Dic5—21no—
147C2×C4×Dic5—21no—
148C2×C4×Dic5—21no—
149C2×Dic20—24no—
150C2×Dic20C2314yes—
151C2×#677—42no—
152C2×#677—42no—
153C2×#677C2314yes—
154C2×#677C2314yes—
155#4039—28no—
156#4035—28no—
157#4030—28no—
158#4030—28no—
159#4025—28no—
160#4023—28no—
161#4020—22no—
162#4020C2314yes—
163#4016—22no—
164#4016C2314yes—
165C4×Dic10—22no—
166C4×Dic10—22no—
167C4×Dic10C2314yes—
168C4×Dic10C2314yes—
169C5×C4⋊C8C2314yes—
170C5×C22⋊C8C2314yes—
171C5×C22⋊C8C2314yes—
172C5×#97C2314yes—
173#3953C2314yes—
174#3953C2314yes—
175#3953C2314yes—
176#3953C2314yes—
177#3953C2314yes—
178#3953C2314yes—
179#3950C2314yes—
180#3949C2314yes—
181#3949C2314yes—
182#3948C2314yes—
183#3948C2314yes—
184#3948C2314yes—
185#3948C2314yes—
186C2×#552—51no—
187C2×#550—51no—
188#3317—516no—
189C2×#490—51no—
190C2×#481—51no—
191C2×#482—51no—
192C2×#479—51no—
193C2×#468—51no—
194C2×#465—51no—
195C2×#460—51no—
196C2×#452—51no—
197C2×#452—51no—
198C2×#441—51no—
199C2×#435D511yescharacteristic, complemented
200C2×#417—51no—
201C2×#416—51no—
202C24×C5C2×D411yescharacteristic
203C24×C5C2×D411yescharacteristic
204C23×D5—21no—
205C23×D5—21no—
206C2×C5×D4—42no—
207C2×C5×D4C2×D414yes—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5C2×D411yescharacteristic
213C22×C4×C5C2×D411yescharacteristic
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D412yes—
217C22×C4×C5C2×D412yes—
218C22×C4×C5C2412yes—
219C22×C4×C5C2412yes—
220C22×C4×C5C2411yescharacteristic
221C2×C22⋊D5—24no—
222C2×C22⋊D5—24no—
223C2×C22⋊D5—24no—
224C2×C22⋊D5—24no—
225C2×C22⋊D5—44no—
226C2×C22⋊D5—44no—
227C2×C22⋊D5—82no—
228C2×C22⋊D5—82no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—24no—
235C22×Dic5—21no—
236C22×Dic5—44no—
237#709—28no—
238#709—28no—
239#709—44no—
240#709—44no—
241#709—48no—
242#709—48no—
243C2×D20—22no—
244C2×D20—22no—
245C2×D20—22no—
246C2×D20—22no—
247C2×D20—24no—
248C2×D20—21no—
249C2×D20—21no—
250C2×D20—24no—
251C2×D20—44no—
252C2×D20—82no—
253C2×D20C2412yes—
254C2×D20C2412yes—
255C2×C4×D5—24no—
256C2×C4×D5—24no—
257C2×C4×D5—44no—
258C2×C4×D5—44no—
259C2×Dic10—21no—
260C2×Dic10—22no—
261C2×Dic10—22no—
262C2×Dic10—22no—
263C2×Dic10—21no—
264C2×Dic10#4114yes—
265C2×Dic10C2412yes—
266C2×Dic10C2412yes—
267C5×M16—44no—
268C2×C5×C8—22no—
269C2×C5×C8—22no—
270C2×C5×C8—22no—
271C2×C5×C8—22no—
272C2×C5×C8—44no—
273C2×C5×C8C2412yes—
274C2×C5×C8C2412yes—
275C2×C5×C8C2412yes—
276C2×C5×C8C2412yes—
277C5×C4⋊C4C2×D414yes—
278C5×C22⋊C4C2×D414yes—
279C5×C22⋊C4C2×D414yes—
280C42×C5C2×D412yes—
281C42×C5C2412yes—
282C22⋊Dic5—24no—
283C22⋊Dic5—24no—
284C22⋊Dic5—24no—
285#685—24no—
286#685—24no—
287C4⋊Dic5—21no—
288C4⋊Dic5—21no—
289C4⋊Dic5—21no—
290C4⋊Dic5—21no—
291C4⋊Dic5—24no—
292C4⋊Dic5C2412yes—
293C4⋊Dic5C2412yes—
294C4⋊Dic5C2412yes—
295C4⋊Dic5C2412yes—
296#683—24no—
297#683—24no—
298#683—24no—
299#683—24no—
300#683—24no—
301#683—24no—
302C4×Dic5—24no—
303C4×Dic5—24no—
304C4×Dic5—24no—
305Dic20—28no—
306#677—44no—
307#677—44no—
308C22×#41—51no—
309C22×#41—51no—
310C22×Q16—51no—
311C22×SD16—51no—
312C22×SD16—51no—
313C22×M16C2×D511yescharacteristic
314C23×C8C2×D511yescharacteristic
315#552—58no—
316#552—104no—
317#550—58no—
318#550—104no—
319C2×#127—51no—
320C2×#127—101no—
321C2×#126—101no—
322C2×#125—51no—
323C2×#125—101no—
324C2×#123—101no—
325C2×C22⋊Q8—51no—
326C2×C22⋊Q8—51no—
327C2×#121—51no—
328C2×#121—51no—
329C2×#121—101no—
330C2×#121—101no—
331C2×C4×Q8—51no—
332C2×C4×Q8—51no—
333C2×C4×D4—101no—
334C2×C4×D4C2×D511yescharacteristic
335C2×#117—51no—
336C2×#117—101no—
337C22×C4⋊C4—51no—
338#490—58no—
339#482—58no—
340#481—58no—
341#479—58no—
342#468—58no—
343#465—58no—
344#460—58no—
345#452—58no—
346#452—58no—
347#441—58no—
348#435C2×D518yescomplemented
349C2×#107—51no—
350C2×#106—51no—
351C2×#106—51no—
352C2×C4⋊C8C2×D511yescharacteristic
353#417—58no—
354#416—58no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—51no—
359C2×#102—51no—
360C2×#102—51no—
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×C22⋊C8C2×D511yescharacteristic
366C2×C22⋊C8C2×D511yescharacteristic
367C2×#97C2×D511yescharacteristic
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5C22×D412yes—
375C23×C5C22×D412yes—
376C23×C5C22×D411yescharacteristic
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—42no—
380C22×D5—42no—
381C22×D5—42no—
382C22×D5—42no—
383C22×D5—42no—
384C22×D5—42no—
385C5×D4—44no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—24no—
391C2×C4×C5—24no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5C22×D412yes—
397C2×C4×C5C22×D412yes—
398C2×C4×C5C22×D412yes—
399C2×C4×C5C22×D412yes—
400C2×C4×C5C22×D411yescharacteristic
401C2×C4×C5C2×#4112yes—
402C2×C4×C5H(5,𝔽2)12yes—
403C2×C4×C5C2511yescharacteristic
404C22⋊D5—48no—
405C22⋊D5—48no—
406C22⋊D5—84no—
407C22⋊D5—84no—
408C2×Dic5—24no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—48no—
416C2×Dic5—42no—
417C2×Dic5—42no—
418C2×Dic5—42no—
419C2×Dic5—42no—
420C2×Dic5—42no—
421D20—22no—
422D20—22no—
423D20—22no—
424D20—22no—
425D20—48no—
426D20—42no—
427D20—42no—
428D20—84no—
429C4×D5—48no—
430C4×D5—48no—
431Dic10—24no—
432Dic10—22no—
433Dic10—22no—
434Dic10—22no—
435Dic10—42no—
436Dic10C2×#4114yes—
437C5×C8—22no—
438C5×C8—22no—
439C5×C8—22no—
440C5×C8—22no—
441C2×#41—54no—
442C2×#41—54no—
443C2×#41—104no—
444C2×#41—104no—
445C2×#41—102no—
446C2×#41—102no—
447C2×#41—202no—
448C2×#41—202no—
449C22×Q8—51no—
450C22×Q8—51no—
451C22×D4—51no—
452C22×D4—51no—
453C22×D4—101no—
454C22×D4—101no—
455C22×D4—101no—
456C22×D4—101no—
457C22×D4—101no—
458C22×D4—101no—
459C22×D4D2011yescharacteristic
460C23×C4—101no—
461C23×C4—101no—
462C23×C4—101no—
463C23×C4C22×D511yescharacteristic
464C23×C4C22×D511yescharacteristic
465C2×Q16—54no—
466C2×Q16—104no—
467C2×SD16—54no—
468C2×SD16—54no—
469C2×SD16—202no—
470C2×SD16—202no—
471C2×M16—42no—
472C2×M16C22×D514yes—
473C22×C8—42no—
474C22×C8C22×D511yescharacteristic
475C22×C8C22×D511yescharacteristic
476C22×C8C22×D511yescharacteristic
477C22×C8C22×D511yescharacteristic
478C22×C8C22×D514yes—
479#127—54no—
480#127—108no—
481#127—102no—
482#126—108no—
483#125—54no—
484#125—108no—
485#125—102no—
486#123—108no—
487C22⋊Q8—54no—
488C22⋊Q8—54no—
489C22⋊Q8—102no—
490C22⋊Q8—102no—
491#121—54no—
492#121—54no—
493#121—102no—
494#121—102no—
495#121—108no—
496#121—108no—
497C4×Q8—54no—
498C4×Q8—54no—
499C4×Q8—102no—
500C4×Q8—102no—
501C4×D4—108no—
502C4×D4D2014yes—
503C4×D4C22×D514yes—
504#117—54no—
505#117—102no—
506#117—108no—
507C2×C4⋊C4—51no—
508C2×C4⋊C4—51no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—51no—
511C2×C4⋊C4—51no—
512C2×C4⋊C4—101no—
513C2×C4⋊C4—102no—
514C2×C4⋊C4—101no—
515C2×C4⋊C4—101no—
516C2×C4⋊C4—101no—
517C2×C4⋊C4—101no—
518C2×C4⋊C4—101no—
519C2×C4⋊C4—101no—
520C2×C4⋊C4D2011yescharacteristic
521C2×C22⋊C4—101no—
522C2×C22⋊C4—101no—
523C2×C22⋊C4—101no—
524C2×C22⋊C4—101no—
525C2×C22⋊C4—101no—
526C2×C22⋊C4D2011yescharacteristic
527C2×C22⋊C4D2011yescharacteristic
528C2×C42—101no—
529C2×C42—101no—
530C2×C42—101no—
531C2×C42C22×D511yescharacteristic
532#107—54no—
533#106—54no—
534#106—54no—
535C4⋊C8C22×D514yes—
536#103—54no—
537#103—54no—
538#103—54no—
539#103—54no—
540#102—54no—
541#102—54no—
542#102—54no—
543#102—54no—
544#102—54no—
545#102—54no—
546C22⋊C8C22×D514yes—
547C22⋊C8C22×D514yes—
548#97C22×D514yes—
549C22×C5—22no—
550C22×C5—22no—
551C22×C5—22no—
552C22×C5—22no—
553C22×C5—22no—
554C22×C5—22no—
555C22×C5—44no—
556C22×C5—44no—
557C22×C5#54612yes—
558C22×C5#57512yes—
559C22×C5#57712yes—
560C22×C5C23×D411yescharacteristic
561C2×D5—42no—
562C2×D5—42no—
563C2×D5—42no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—84no—
568C2×D5—84no—
569C4×C5—22no—
570C4×C5—22no—
571C4×C5—22no—
572C4×C5—22no—
573C4×C5#54612yes—
574C4×C5C22×#4111yescharacteristic
575C4×C5C2×H(5,𝔽2)11yescharacteristic
576Dic5—24no—
577Dic5—42no—
578Dic5—42no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582C24—101no—
583C24—101no—
584C24C2×D2011yescharacteristic
585C24C2×D2011yescharacteristic
586#41—108no—
587#41—108no—
588#41—204no—
589#41—204no—
590#41—208no—
591#41—208no—
592C2×Q8—54no—
593C2×Q8—52no—
594C2×Q8—52no—
595C2×Q8—101no—
596C2×Q8—101no—
597C2×Q8—102no—
598C2×Q8—102no—
599C2×Q8—102no—
600C2×D4—42no—
601C2×D4—52no—
602C2×D4—52no—
603C2×D4—104no—
604C2×D4—104no—
605C2×D4—104no—
606C2×D4—104no—
607C2×D4—104no—
608C2×D4—101no—
609C2×D4—101no—
610C2×D4—104no—
611C2×D4—102no—
612C2×D4—102no—
613C2×D4—102no—
614C2×D4—102no—
615C2×D4—204no—
616C2×D4—204no—
617C2×D4—204no—
618C2×D4—402no—
619C2×D4—402no—
620C2×D4—402no—
621C2×D4C2×D2014yes—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—101no—
627C22×C4—104no—
628C22×C4—101no—
629C22×C4—101no—
630C22×C4—101no—
631C22×C4—101no—
632C22×C4—101no—
633C22×C4—104no—
634C22×C4—104no—
635C22×C4—204no—
636C22×C4—204no—
637C22×C4—204no—
638C22×C4C2×D2012yes—
639C22×C4C2×D2012yes—
640C22×C4C2×D2011yescharacteristic
641C22×C4C2×D2011yescharacteristic
642C22×C4C2×D2011yescharacteristic
643C22×C4C2×D2011yescharacteristic
644C22×C4C23×D512yes—
645C22×C4C23×D512yes—
646C22×C4C23×D511yescharacteristic
647Q16—108no—
648SD16—204no—
649SD16—204no—
650M16—44no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—44no—
656C2×C8C23×D512yes—
657C2×C8C23×D512yes—
658C2×C8C23×D512yes—
659C2×C8C23×D512yes—
660C4⋊C4—52no—
661C4⋊C4—52no—
662C4⋊C4—52no—
663C4⋊C4—52no—
664C4⋊C4—101no—
665C4⋊C4—101no—
666C4⋊C4—104no—
667C4⋊C4—101no—
668C4⋊C4—101no—
669C4⋊C4—104no—
670C4⋊C4—104no—
671C4⋊C4—104no—
672C4⋊C4—104no—
673C4⋊C4—104no—
674C4⋊C4—104no—
675C4⋊C4C2×D2014yes—
676C22⋊C4—104no—
677C22⋊C4—104no—
678C22⋊C4—104no—
679C22⋊C4—104no—
680C22⋊C4—104no—
681C22⋊C4C2×D2014yes—
682C22⋊C4C2×D2014yes—
683C42—104no—
684C42—104no—
685C42—104no—
686C42C2×D2012yes—
687C42C23×D512yes—
688C2×C5—42no—
689C2×C5—42no—
690C2×C5#331714yescomplemented
691C2×C5C2×#54611yescharacteristic
692C2×C5C2×#57511yescharacteristic
693C2×C5C2×#57711yescharacteristic
694D5—82no—
695D5—82no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—102no—
703C23—102no—
704C23—202no—
705C23—202no—
706C23—202no—
707C23—202no—
708C23—202no—
709C23—202no—
710C23C22×D2012yes—
711C23C22×D2012yes—
712C23C22×D2011yescharacteristic
713Q8—54no—
714Q8—104no—
715Q8—102no—
716Q8—102no—
717Q8—102no—
718Q8—202no—
719D4—44no—
720D4—102no—
721D4—102no—
722D4—102no—
723D4—102no—
724D4—208no—
725D4—208no—
726D4—208no—
727D4—202no—
728D4—202no—
729D4—404no—
730D4—404no—
731D4—404no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—104no—
743C2×C4—102no—
744C2×C4—102no—
745C2×C4—102no—
746C2×C4—102no—
747C2×C4—102no—
748C2×C4—102no—
749C2×C4—208no—
750C2×C4—208no—
751C2×C4—208no—
752C2×C4—202no—
753C2×C4—202no—
754C2×C4—202no—
755C2×C4—202no—
756C2×C4—202no—
757C2×C4C22×D2012yes—
758C2×C4C22×D2012yes—
759C2×C4C22×D2012yes—
760C2×C4C22×D2012yes—
761C2×C4C22×D2011yescharacteristic
762C2×C4#414412yes—
763C2×C4D5×#4112yes—
764C2×C4C24×D511yescharacteristic
765C8—22no—
766C8—22no—
767C8—22no—
768C8—22no—
769C5C2×#331711yescharacteristic, complemented, Sylow
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—202no—
779C22—202no—
780C22—202no—
781C22—202no—
782C22—202no—
783C22—202no—
784C22—404no—
785C22—404no—
786C22#6588812yes—
787C22#6608212yes—
788C22#6608512yes—
789C22C23×D2011yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—104no—
795C4—202no—
796C4—202no—
797C4—202no—
798C4—202no—
799C4—202no—
800C4#6588812yes—
801C4C2×#414411yescharacteristic
802C4C2×D5×#4111yescharacteristic
803C2—42no—
804C2—42no—
805C2—402no—
806C2—402no—
807C2#1061124514yesdirect product factor
808C2C2×#6588811yescharacteristic
809C2C2×#6608211yescharacteristic
810C2C2×#6608511yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#435C2
socleC23×C5C22×D4
prime radicalC2×#65887C2
hypercenterC2×#435D5
hypocenterC5C2×#3317
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×#65422C2semidirect
6. C2×#65403C2semidirect
7. C2×#65402C2semidirect
8. #10611245C2direct (N × H)
9. C2×#65118C2semidirect
10. C2×#65137C2semidirect
11. C2×#65022C2semidirect
12. C2×#65022C2semidirect
13. C2×#65024C2semidirect
14. C2×#65026C2semidirect
15. C2×#65005C2semidirect
16. C2×#65002C2semidirect
36. #65875C22semidirect
47. C5×#435C22semidirect
52. #65423C22semidirect
53. #65422C22semidirect
54. #65403C22semidirect
55. #65402C22semidirect
69. #65137C22semidirect
70. #65118C22semidirect
71. #65026C22semidirect
72. #65024C22semidirect
73. #65022C22semidirect
74. #65022C22semidirect
75. #65005C22semidirect
76. #65002C22semidirect
199. C2×#435D5semidirect
348. #435C2×D5semidirect
690. C2×C5#3317semidirect
769. C5C2×#3317semidirect
807. C2#10611245direct (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×#658872
C2×C5×#4352
C2×#654232
C2×#654222
C2×#654032
C2×#654022
#106112452
C2×#651182
C2×#651372
C2×#650222
C2×#650242
C2×#650262
C2×#650052
C2×#650022
C2×#33175