Finite Group Databasebeta

← C2×#10612464 #12975992

Subgroups — C2×#10612464 #12975992

Order 1280.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65946C211yesmaximal, characteristic, complemented
2C2×#65950C211yesmaximal, characteristic, complemented
3C2×C5×#466C211yesmaximal, characteristic, complemented
4C2×#65445C211yesmaximal, characteristic, complemented
5C2×#65442C211yesmaximal, characteristic, complemented
6C2×#65402C211yesmaximal, characteristic, complemented
7C2×#65400C211yesmaximal, characteristic, complemented
8C2×#65326C211yesmaximal, characteristic, complemented
9C2×#65324C211yesmaximal, characteristic, complemented
10#10612464C2116yesmaximal, direct product factor
11C2×#65179C211yesmaximal, characteristic, complemented
12C2×#65177C211yesmaximal, characteristic, complemented
13C2×#65069C211yesmaximal, characteristic, complemented
14C2×#65059C211yesmaximal, characteristic, complemented
15C2×#65054C211yesmaximal, characteristic, complemented
16C2×#65074C211yesmaximal, characteristic, complemented
17C22×D4×D5C2211yescharacteristic
18C22×#709C2211yescharacteristic
19C22×C5×D8C2211yescharacteristic
20C23×C5×C8C2211yescharacteristic, complemented
21C2×C5×#121C2211yescharacteristic
22C2×C5×#121C2211yescharacteristic, complemented
23C2×#4085—21no—
24C2×#4084—21no—
25C2×#4084C2211yescharacteristic
26C2×#4083—21no—
27C2×#4082—21no—
28C2×#4082C2211yescharacteristic
29C2×D4×Dic5C2211yescharacteristic, complemented
30C22×#687C2211yescharacteristic, complemented
31C22×#686C2211yescharacteristic
32C2×C4×C22⋊D5C2211yescharacteristic
33C2×#4072C2211yescharacteristic, complemented
34C22×#676C2211yescharacteristic
35#65950—24no—
36#65950C2218yescomplemented
37#65946—24no—
38#65946C2218yescomplemented
39C2×#4043C2211yescharacteristic
40C2×#4039C2211yescharacteristic
41C2×#4038C2211yescharacteristic
42C2×#4034C2211yescharacteristic, complemented
43C2×#4031—21no—
44C2×#4029—21no—
45C2×D5×C22⋊C4—21no—
46C2×#4023—21no—
47C5×#466C2218yescomplemented
48C2×C5×#107C2211yescharacteristic, complemented
49C2×C5×#102C2211yescharacteristic
50C2×C5×#102C2211yescharacteristic, complemented
51C2×#3964C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53C2×C22⋊#168C2211yescharacteristic, complemented
54#65445C2218yescomplemented
55#65442C2218yescomplemented
56#65402C2218yescomplemented
57C2×#3953C2211yescharacteristic
58C2×#3953C2211yescharacteristic
59#65400C2218yescomplemented
60C2×#3952C2211yescharacteristic
61C2×#3948C2211yescharacteristic, complemented
62C2×#3948C2211yescharacteristic, complemented
63C2×#3947C2211yescharacteristic, complemented
64C2×#3946C2211yescharacteristic, complemented
65#65326C2218yescomplemented
66#65324C2218yescomplemented
67C2×#3942C2211yescharacteristic, complemented
68C2×#3941C2211yescharacteristic
69C2×#3940C2211yescharacteristic, complemented
70C2×#3939C2211yescharacteristic, complemented
71#65179C2218yescomplemented
72#65177C2218yescomplemented
73#65074C2218yescomplemented
74#65069C2218yescomplemented
75#65059C2218yescomplemented
76#65054C2218yescomplemented
77C2×#3319—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×D4—21no—
80C22×C5×D4—21no—
81C22×C5×D4C2311yescharacteristic
82C22×C5×D4C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C22×C22⋊D5—21no—
85C22×C22⋊D5—21no—
86C22×C22⋊D5—21no—
87C22×C22⋊D5D411yescharacteristic
88C23×Dic5—21no—
89C2×D4×D5—24no—
90C2×D4×D5—22no—
91C2×D4×D5—42no—
92C2×D4×D5C2314yes—
93C2×#709—22no—
94C2×#709—24no—
95C2×#709—42no—
96C2×#709C2314yes—
97C22×D20C2311yescharacteristic
98C22×C4×D5—21no—
99C22×C4×D5—21no—
100C22×C4×D5C2311yescharacteristic
101C22×Dic10—21no—
102C22×Dic10C2311yescharacteristic
103C2×C5×D8—42no—
104C2×C5×D8C2314yes—
105C22×C5×C8—42no—
106C22×C5×C8C2311yescharacteristic
107C22×C5×C8C2311yescharacteristic
108C22×C5×C8C2314yescomplemented
109C5×#121—22no—
110C5×#121—22no—
111C5×#121C2314yes—
112C5×#121C2314yescomplemented
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C22⋊Dic5—21no—
118C2×C22⋊Dic5—21no—
119C2×C22⋊Dic5—21no—
120C2×C22⋊Dic5—21no—
121C2×C22⋊Dic5—21no—
122C2×C22⋊Dic5D411yescharacteristic
123#4085—28no—
124#4084—22no—
125#4084—28no—
126#4084C2314yes—
127#4083—28no—
128#4082—28no—
129#4082—22no—
130#4082C2314yes—
131D4×Dic5—22no—
132D4×Dic5C2314yescomplemented
133C2×#687—42no—
134C2×#687C2314yescomplemented
135C2×#686—24no—
136C2×#686C2314yes—
137C4×C22⋊D5D414yes—
138C4×C22⋊D5C2314yes—
139C2×#685—21no—
140C2×#685—21no—
141C2×#685—21no—
142C2×#685D411yescharacteristic
143#4072—22no—
144#4072C2314yescomplemented
145C2×C4⋊Dic5—21no—
146C2×C4⋊Dic5C2311yescharacteristic
147C2×C4⋊Dic5C2311yescharacteristic
148C2×#683—21no—
149C2×#683D411yescharacteristic
150C2×C4×Dic5—21no—
151C2×C4×Dic5—21no—
152C2×C4×Dic5C2311yescharacteristic
153C22×#168C2311yescharacteristic
154C22×#168C2311yescharacteristic
155C2×#676—42no—
156C2×#676C2314yes—
157#4043—22no—
158#4043C2314yes—
159#4039—22no—
160#4039C2314yes—
161#4038—22no—
162#4038C2314yes—
163#4034—22no—
164#4034C2314yescomplemented
165#4031—28no—
166#4029—28no—
167D5×C22⋊C4—28no—
168#4023—28no—
169C5×#107C2314yescomplemented
170C5×#102C2314yes—
171C5×#102C2314yescomplemented
172#3964C2314yes—
173#3964C2314yes—
174C22⋊#168C2314yescomplemented
175#3953C2314yes—
176#3953C2314yes—
177#3952C2314yes—
178#3948C2314yescomplemented
179#3948C2314yescomplemented
180#3947C2314yescomplemented
181#3946C2314yescomplemented
182#3942C2314yescomplemented
183#3941C2314yes—
184#3940C2314yescomplemented
185#3939C2314yescomplemented
186C2×#555—51no—
187C2×#546—51no—
188#3319—516no—
189C2×#489—51no—
190C2×#485—51no—
191C2×#482—51no—
192C2×#474—51no—
193C2×#468—51no—
194C2×#466D511yescharacteristic, complemented
195C2×#463—51no—
196C2×#449—51no—
197C2×#447—51no—
198C2×#442—51no—
199C2×#435—51no—
200C2×#418—51no—
201C2×#416—51no—
202C24×C5—21no—
203C24×C5—21no—
204C24×C5C2×D411yescharacteristic
205C23×D5—21no—
206C23×D5—24no—
207C23×D5—44no—
208C23×D5—44no—
209C23×D5—82no—
210C23×D5C2×D411yescharacteristic
211C2×C5×D4—24no—
212C2×C5×D4—24no—
213C2×C5×D4—21no—
214C2×C5×D4—21no—
215C2×C5×D4—22no—
216C2×C5×D4—22no—
217C2×C5×D4—22no—
218C2×C5×D4—22no—
219C2×C5×D4—82no—
220C2×C5×D4—82no—
221C2×C5×D4C2412yes—
222C2×C5×D4C2412yes—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2411yescharacteristic
231C2×C22⋊D5—24no—
232C2×C22⋊D5—24no—
233C2×C22⋊D5—24no—
234C2×C22⋊D5—42no—
235C2×C22⋊D5—44no—
236C2×C22⋊D5—44no—
237C2×C22⋊D5—82no—
238C2×C22⋊D5C2×D414yes—
239C22×Dic5—21no—
240C22×Dic5—21no—
241C22×Dic5—21no—
242C22×Dic5—24no—
243C22×Dic5—44no—
244C22×Dic5C2×D411yescharacteristic
245C22×Dic5C2×D411yescharacteristic
246C22×Dic5C2×D411yescharacteristic
247D4×D5—28no—
248D4×D5—44no—
249D4×D5—48no—
250#709—28no—
251#709—44no—
252#709—48no—
253C2×D20—21no—
254C2×D20—22no—
255C2×D20#4114yes—
256C2×D20C2412yes—
257C2×C4×D5—22no—
258C2×C4×D5—22no—
259C2×C4×D5—24no—
260C2×C4×D5—24no—
261C2×C4×D5—44no—
262C2×C4×D5—82no—
263C2×C4×D5C2×D412yes—
264C2×C4×D5C2412yes—
265C2×Dic10—22no—
266C2×Dic10—22no—
267C2×Dic10—21no—
268C2×Dic10—24no—
269C2×Dic10—82no—
270C2×Dic10C2412yes—
271C5×D8—44no—
272C2×C5×C8—22no—
273C2×C5×C8—22no—
274C2×C5×C8—44no—
275C2×C5×C8C2412yes—
276C2×C5×C8C2412yes—
277C5×C4⋊C4—21no—
278C5×C4⋊C4—21no—
279C5×C4⋊C4C2412yes—
280C5×C4⋊C4C2412yes—
281C5×C22⋊C4—24no—
282C5×C22⋊C4—24no—
283C22⋊Dic5—24no—
284C22⋊Dic5—24no—
285C22⋊Dic5—24no—
286C22⋊Dic5—24no—
287C22⋊Dic5—24no—
288C22⋊Dic5C2×D414yes—
289#687—44no—
290#686—28no—
291#685—24no—
292#685—24no—
293#685—24no—
294#685C2×D414yes—
295C4⋊Dic5—21no—
296C4⋊Dic5—21no—
297C4⋊Dic5—24no—
298C4⋊Dic5C2412yes—
299C4⋊Dic5C2412yes—
300#683—24no—
301#683C2×D414yes—
302C4×Dic5—24no—
303C4×Dic5—24no—
304C4×Dic5C2×D412yes—
305C4×Dic5C2412yes—
306C2×#168—22no—
307C2×#168—22no—
308C2×#168C2412yes—
309C2×#168C2412yes—
310#676—44no—
311C22×#41—51no—
312C23×D4—51no—
313C22×SD16—51no—
314C22×D8—51no—
315C22×D8C2×D511yescharacteristic
316C22×M16—51no—
317C23×C8C2×D511yescharacteristic, complemented
318#555—58no—
319#555—104no—
320#546—58no—
321#546—104no—
322C2×C4⋊Q8—51no—
323C2×#124—51no—
324C2×#124—101no—
325C2×#124—101no—
326C2×#123—101no—
327C2×C22⋊Q8—51no—
328C2×#121—51no—
329C2×#121—101no—
330C2×#121—101no—
331C2×#121C2×D511yescharacteristic
332C2×#121C2×D511yescharacteristic, complemented
333C2×#120—101no—
334C2×C4×D4—51no—
335C2×C4×D4—51no—
336C2×C4×D4—51no—
337C2×#117—51no—
338C2×#117—51no—
339C2×#117—101no—
340C22×C22⋊C4—101no—
341#489—58no—
342#485—58no—
343#482—58no—
344#474—58no—
345#468—58no—
346#466C2×D518yescomplemented
347#463—58no—
348#449—58no—
349#447—58no—
350#442—58no—
351#435—58no—
352C2×#107—51no—
353C2×#107C2×D511yescharacteristic, complemented
354C2×#106—51no—
355C2×C4⋊C8—51no—
356#418—58no—
357#416—58no—
358C2×#103—51no—
359C2×#103—51no—
360C2×#103—51no—
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×#102—51no—
366C2×#102C2×D511yescharacteristic
367C2×#102C2×D511yescharacteristic, complemented
368C2×C22⋊C8—51no—
369C2×C22⋊C8—51no—
370C2×#97—51no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—42no—
377C23×C5—42no—
378C23×C5—42no—
379C23×C5—42no—
380C23×C5—42no—
381C23×C5—42no—
382C23×C5C22×D412yes—
383C23×C5C22×D411yescharacteristic
384C22×D5—22no—
385C22×D5—24no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—48no—
390C22×D5—48no—
391C22×D5—42no—
392C22×D5—42no—
393C22×D5—84no—
394C22×D5—816no—
395C22×D5C22×D412yes—
396C5×D4—22no—
397C5×D4—22no—
398C5×D4—22no—
399C5×D4—22no—
400C5×D4—42no—
401C5×D4—42no—
402C5×D4—84no—
403C5×D4—84no—
404C2×C4×C5—22no—
405C2×C4×C5—24no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—42no—
411C2×C4×C5—42no—
412C2×C4×C5C22×D412yes—
413C2×C4×C5C22×D411yescharacteristic
414C2×C4×C5C2×#4112yes—
415C2×C4×C5H(5,𝔽2)12yes—
416C2×C4×C5C2511yescharacteristic
417C22⋊D5—44no—
418C22⋊D5—48no—
419C22⋊D5—48no—
420C22⋊D5—84no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—48no—
428C2×Dic5—42no—
429C2×Dic5—42no—
430C2×Dic5—42no—
431C2×Dic5C22×D412yes—
432C2×Dic5C22×D412yes—
433C2×Dic5C22×D412yes—
434D20—24no—
435D20—22no—
436D20C2×#4114yes—
437C4×D5—24no—
438C4×D5—22no—
439C4×D5—22no—
440C4×D5—48no—
441C4×D5—84no—
442Dic10—22no—
443Dic10—22no—
444Dic10—42no—
445Dic10—84no—
446C5×C8—22no—
447C5×C8—22no—
448#168—22no—
449#168—22no—
450C25—101no—
451C2×#41—54no—
452C2×#41—104no—
453C2×#41—102no—
454C2×#41—202no—
455C22×Q8—51no—
456C22×Q8—101no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—51no—
460C22×D4—54no—
461C22×D4—51no—
462C22×D4—102no—
463C22×D4—101no—
464C22×D4—104no—
465C22×D4—101no—
466C22×D4—101no—
467C22×D4—202no—
468C22×D4C22×D511yescharacteristic
469C22×D4C22×D511yescharacteristic
470C23×C4—51no—
471C23×C4—101no—
472C23×C4—101no—
473C23×C4—101no—
474C23×C4C22×D511yescharacteristic
475C2×SD16—54no—
476C2×SD16—202no—
477C2×D8—42no—
478C2×D8—54no—
479C2×D8—104no—
480C2×D8C22×D514yes—
481C2×M16—54no—
482C2×M16—202no—
483C22×C8—42no—
484C22×C8—51no—
485C22×C8—51no—
486C22×C8C22×D511yescharacteristic
487C22×C8C22×D511yescharacteristic
488C22×C8C22×D514yescomplemented
489C4⋊Q8—54no—
490C4⋊Q8—102no—
491#124—54no—
492#124—102no—
493#124—108no—
494#124—108no—
495#123—108no—
496C22⋊Q8—54no—
497C22⋊Q8—102no—
498#121—22no—
499#121—22no—
500#121—54no—
501#121—108no—
502#121—102no—
503#121—108no—
504#121C22×D514yes—
505#121C22×D514yescomplemented
506#120—108no—
507C4×D4—54no—
508C4×D4—54no—
509C4×D4—54no—
510C4×D4—54no—
511C4×D4—102no—
512C4×D4—102no—
513#117—54no—
514#117—54no—
515#117—108no—
516#117—102no—
517#117—102no—
518C2×C4⋊C4—51no—
519C2×C4⋊C4—51no—
520C2×C4⋊C4—51no—
521C2×C4⋊C4—101no—
522C2×C4⋊C4—101no—
523C2×C4⋊C4C22×D511yescharacteristic
524C2×C4⋊C4C22×D511yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—51no—
528C2×C22⋊C4—51no—
529C2×C22⋊C4—108no—
530C2×C22⋊C4—101no—
531C2×C22⋊C4—101no—
532C2×C22⋊C4—101no—
533C2×C22⋊C4—101no—
534C2×C22⋊C4—101no—
535C2×C22⋊C4—101no—
536C2×C22⋊C4—101no—
537C2×C22⋊C4—101no—
538C2×C42—51no—
539C2×C42—101no—
540C2×C42—101no—
541#107—54no—
542#107C22×D514yescomplemented
543#106—54no—
544C4⋊C8—54no—
545#103—54no—
546#103—54no—
547#103—54no—
548#102—54no—
549#102—54no—
550#102—54no—
551#102—54no—
552#102—54no—
553#102C22×D514yes—
554#102C22×D514yescomplemented
555C22⋊C8—54no—
556C22⋊C8—54no—
557#97—54no—
558C22×C5—22no—
559C22×C5—22no—
560C22×C5—22no—
561C22×C5—44no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—84no—
569C22×C5—84no—
570C22×C5#54612yes—
571C22×C5#57512yes—
572C22×C5#57612yes—
573C22×C5C23×D411yescharacteristic
574C2×D5—22no—
575C2×D5—24no—
576C2×D5—22no—
577C2×D5—22no—
578C2×D5—44no—
579C2×D5—48no—
580C2×D5—42no—
581C2×D5—42no—
582C2×D5—816no—
583C4×C5—22no—
584C4×C5—42no—
585C4×C5—42no—
586C4×C5#54612yes—
587C4×C5C22×#4111yescharacteristic
588C4×C5C2×H(5,𝔽2)11yescharacteristic
589Dic5—22no—
590Dic5—22no—
591Dic5—22no—
592Dic5—42no—
593Dic5—42no—
594Dic5—42no—
595C24—21no—
596C24—21no—
597C24—51no—
598C24—104no—
599C24—101no—
600C24—204no—
601C24—204no—
602C24—402no—
603C24D4×D511yescharacteristic
604#41—108no—
605#41—204no—
606#41—208no—
607C2×Q8—52no—
608C2×Q8—104no—
609C2×Q8—101no—
610C2×Q8—102no—
611C2×Q8—102no—
612C2×Q8—402no—
613C2×D4—24no—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—54no—
622C2×D4—54no—
623C2×D4—52no—
624C2×D4—82no—
625C2×D4—82no—
626C2×D4—104no—
627C2×D4—108no—
628C2×D4—104no—
629C2×D4—104no—
630C2×D4—101no—
631C2×D4—102no—
632C2×D4—204no—
633C2×D4—208no—
634C2×D4—202no—
635C2×D4—204no—
636C2×D4—204no—
637C2×D4—402no—
638C2×D4C23×D512yes—
639C2×D4C23×D512yes—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—51no—
645C22×C4—51no—
646C22×C4—51no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—104no—
650C22×C4—104no—
651C22×C4—102no—
652C22×C4—102no—
653C22×C4—101no—
654C22×C4—101no—
655C22×C4—101no—
656C22×C4—104no—
657C22×C4—204no—
658C22×C4—204no—
659C22×C4—402no—
660C22×C4D4×D512yes—
661C22×C4D4×D511yescharacteristic
662C22×C4C23×D512yes—
663C22×C4C23×D511yescharacteristic
664SD16—204no—
665D8—44no—
666D8—108no—
667M16—204no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—44no—
671C2×C8—52no—
672C2×C8—52no—
673C2×C8—102no—
674C2×C8—102no—
675C2×C8C23×D512yes—
676C2×C8C23×D512yes—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—54no—
680C4⋊C4—52no—
681C4⋊C4—52no—
682C4⋊C4—104no—
683C4⋊C4—104no—
684C4⋊C4—101no—
685C4⋊C4—101no—
686C4⋊C4C23×D512yes—
687C4⋊C4C23×D512yes—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—54no—
691C22⋊C4—54no—
692C22⋊C4—104no—
693C22⋊C4—104no—
694C22⋊C4—104no—
695C22⋊C4—104no—
696C22⋊C4—104no—
697C22⋊C4—104no—
698C22⋊C4—104no—
699C22⋊C4—104no—
700C42—52no—
701C42—52no—
702C42—104no—
703C42—104no—
704C2×C5—42no—
705C2×C5—82no—
706C2×C5—82no—
707C2×C5#331914yescomplemented
708C2×C5C2×#54611yescharacteristic
709C2×C5C2×#57511yescharacteristic
710C2×C5C2×#57611yescharacteristic
711D5—42no—
712D5—44no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—52no—
725C23—102no—
726C23—102no—
727C23—102no—
728C23—104no—
729C23—102no—
730C23—208no—
731C23—208no—
732C23—202no—
733C23—202no—
734C23—404no—
735C23—4016no—
736C23C2×D4×D512yes—
737C23C2×D4×D511yescharacteristic
738Q8—102no—
739Q8—102no—
740Q8—202no—
741Q8—404no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—42no—
747D4—42no—
748D4—54no—
749D4—84no—
750D4—84no—
751D4—104no—
752D4—102no—
753D4—204no—
754D4—208no—
755D4—208no—
756D4—404no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—52no—
766C2×C4—52no—
767C2×C4—52no—
768C2×C4—102no—
769C2×C4—102no—
770C2×C4—102no—
771C2×C4—104no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—208no—
778C2×C4—208no—
779C2×C4—202no—
780C2×C4—202no—
781C2×C4—202no—
782C2×C4—404no—
783C2×C4C2×D4×D512yes—
784C2×C4C2×D4×D511yescharacteristic
785C2×C4#414412yes—
786C2×C4D5×#4112yes—
787C2×C4C24×D511yescharacteristic
788C8—22no—
789C8—22no—
790C8—102no—
791C8—102no—
792C5C2×#331911yescharacteristic, complemented, Sylow
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—84no—
804C22—84no—
805C22—102no—
806C22—102no—
807C22—102no—
808C22—104no—
809C22—202no—
810C22—202no—
811C22—204no—
812C22—208no—
813C22—4016no—
814C22#6594412yes—
815C22#6609112yes—
816C22#6610212yes—
817C22C22×D4×D511yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—102no—
822C4—102no—
823C4—102no—
824C4—202no—
825C4—202no—
826C4—202no—
827C4#6594412yes—
828C4C2×#414411yescharacteristic
829C4C2×D5×#4111yescharacteristic
830C2—42no—
831C2—82no—
832C2—82no—
833C2—202no—
834C2—204no—
835C2#1061246414yesdirect product factor
836C2C2×#6594411yescharacteristic
837C2C2×#6609111yescharacteristic
838C2C2×#6610211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#466C2
socleC23×C5C22×D4
hypercenterC2×#466D5
hypocenterC5C2×#3319
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#65946C2semidirect
2. C2×#65950C2semidirect
3. C2×C5×#466C2semidirect
4. C2×#65445C2semidirect
5. C2×#65442C2semidirect
6. C2×#65402C2semidirect
7. C2×#65400C2semidirect
8. C2×#65326C2semidirect
9. C2×#65324C2semidirect
10. #10612464C2direct (N × H)
11. C2×#65179C2semidirect
12. C2×#65177C2semidirect
13. C2×#65069C2semidirect
14. C2×#65059C2semidirect
15. C2×#65054C2semidirect
16. C2×#65074C2semidirect
20. C23×C5×C8C22semidirect
22. C2×C5×#121C22semidirect
29. C2×D4×Dic5C22semidirect
30. C22×#687C22semidirect
33. C2×#4072C22semidirect
36. #65950C22semidirect
38. #65946C22semidirect
42. C2×#4034C22semidirect
47. C5×#466C22semidirect
48. C2×C5×#107C22semidirect
50. C2×C5×#102C22semidirect
53. C2×C22⋊#168C22semidirect
54. #65445C22semidirect
55. #65442C22semidirect
56. #65402C22semidirect
59. #65400C22semidirect
61. C2×#3948C22semidirect
62. C2×#3948C22semidirect
63. C2×#3947C22semidirect
64. C2×#3946C22semidirect
65. #65326C22semidirect
66. #65324C22semidirect
67. C2×#3942C22semidirect
69. C2×#3940C22semidirect
70. C2×#3939C22semidirect
71. #65179C22semidirect
72. #65177C22semidirect
73. #65074C22semidirect
74. #65069C22semidirect
75. #65059C22semidirect
76. #65054C22semidirect
108. C22×C5×C8C23semidirect
112. C5×#121C23semidirect
132. D4×Dic5C23semidirect
134. C2×#687C23semidirect
144. #4072C23semidirect
164. #4034C23semidirect
169. C5×#107C23semidirect
171. C5×#102C23semidirect
174. C22⋊#168C23semidirect
178. #3948C23semidirect
179. #3948C23semidirect
180. #3947C23semidirect
181. #3946C23semidirect
182. #3942C23semidirect
184. #3940C23semidirect
185. #3939C23semidirect
194. C2×#466D5semidirect
317. C23×C8C2×D5semidirect
332. C2×#121C2×D5semidirect
346. #466C2×D5semidirect
353. C2×#107C2×D5semidirect
367. C2×#102C2×D5semidirect
488. C22×C8C22×D5semidirect
505. #121C22×D5semidirect
542. #107C22×D5semidirect
554. #102C22×D5semidirect
707. C2×C5#3319semidirect
792. C5C2×#3319semidirect
835. C2#10612464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659462
C2×#659502
C2×C5×#4662
C2×#654452
C2×#654422
C2×#654022
C2×#654002
C2×#653262
C2×#653242
#106124642
C2×#651792
C2×#651772
C2×#650692
C2×#650592
C2×#650542
C2×#650742
C2×#33195