Finite Group Databasebeta

← C2×#10612571 #12976103

Subgroups — C2×#10612571 #12976103

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×#65964C211yesmaximal, characteristic, complemented
2C2×#65948C211yesmaximal, characteristic, complemented
3C2×C5×#468C211yesmaximal, characteristic, complemented
4C2×#65461C211yesmaximal, characteristic, complemented
5C2×#65454C211yesmaximal, characteristic, complemented
6C2×#65420C211yesmaximal, characteristic, complemented
7C2×#65417C211yesmaximal, characteristic, complemented
8C2×#65334C211yesmaximal, characteristic, complemented
9C2×#65325C211yesmaximal, characteristic, complemented
10#10612571C2116yesmaximal, direct product factor
11C2×#65180C211yesmaximal, characteristic, complemented
12C2×#65171C211yesmaximal, characteristic, complemented
13C2×#65092C211yesmaximal, characteristic, complemented
14C2×#65089C211yesmaximal, characteristic, complemented
15C2×#65071C211yesmaximal, characteristic, complemented
16C2×#65045C211yesmaximal, characteristic, complemented
17C22×#713C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C22×C5×SD16C2211yescharacteristic, complemented
20C22×C5×M16C2211yescharacteristic
21C2×C5×C22⋊Q8C2211yescharacteristic
22C2×C5×#121C2211yescharacteristic
23C2×#4093C2211yescharacteristic
24C2×#4084—21no—
25C2×#4084C2211yescharacteristic, complemented
26C2×#4081—21no—
27C2×D4×Dic5C2211yescharacteristic, complemented
28C22×#686C2211yescharacteristic
29C22×#686C2211yescharacteristic
30C2×C4×C22⋊D5C2211yescharacteristic
31C2×#4072C2211yescharacteristic
32C22×#676C2211yescharacteristic, complemented
33#65964—24no—
34#65964C2218yescomplemented
35#65948—24no—
36#65948C2218yescomplemented
37C2×#4041—21no—
38C2×#4041C2211yescharacteristic
39C2×#4040—21no—
40C2×#4039C2211yescharacteristic
41C2×D5×C4⋊C4C2211yescharacteristic, complemented
42C2×#4036C2211yescharacteristic, complemented
43C2×#4028—21no—
44C2×#4027—21no—
45C2×D5×C22⋊C4—21no—
46C2×#4025—21no—
47C5×#468C2218yescomplemented
48C2×C5×#107C2211yescharacteristic, complemented
49C2×C5×#103C2211yescharacteristic, complemented
50C2×C5×#102C2211yescharacteristic, complemented
51C2×#3967C2211yescharacteristic, complemented
52C2×#3967C2211yescharacteristic, complemented
53C2×C22⋊#168C2211yescharacteristic
54#65461C2218yescomplemented
55#65454C2218yescomplemented
56#65420C2218yescomplemented
57#65417C2218yescomplemented
58C2×#3953C2211yescharacteristic
59C2×#3953C2211yescharacteristic
60C2×#3953C2211yescharacteristic
61C2×#3953C2211yescharacteristic
62C2×#3952C2211yescharacteristic, complemented
63C2×#3946C2211yescharacteristic, complemented
64C2×C8×Dic5C2211yescharacteristic, complemented
65#65334C2218yescomplemented
66#65325C2218yescomplemented
67C2×#3941C2211yescharacteristic
68C2×#3941C2211yescharacteristic
69C2×#3940C2211yescharacteristic, complemented
70C2×#3939C2211yescharacteristic, complemented
71#65180C2218yescomplemented
72#65171C2218yescomplemented
73#65092C2218yescomplemented
74#65089C2218yescomplemented
75#65071C2218yescomplemented
76#65045C2218yescomplemented
77C2×#3322—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4—21no—
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C22×C22⋊D5—21no—
84C22×C22⋊D5D411yescharacteristic
85C23×Dic5—21no—
86C2×#713—22no—
87C2×#713—24no—
88C2×#713—42no—
89C2×#713C2314yes—
90C22×D20—24no—
91C22×D20—21no—
92C22×D20—21no—
93C22×D20—22no—
94C22×D20—21no—
95C22×D20—42no—
96C22×D20C2311yescharacteristic
97C22×D20C2314yes—
98C22×D20C2311yescharacteristic
99C22×C4×D5—21no—
100C22×C4×D5—21no—
101C22×C4×D5—21no—
102C22×C4×D5C2311yescharacteristic
103C2×C5×SD16—42no—
104C2×C5×SD16C2314yescomplemented
105C2×C5×M16—42no—
106C2×C5×M16C2314yes—
107C22×C5×C8C2311yescharacteristic
108C22×C5×C8C2311yescharacteristic
109C5×C22⋊Q8—22no—
110C5×C22⋊Q8C2314yes—
111C5×#121—22no—
112C5×#121C2314yes—
113C2×C5×C4⋊C4—21no—
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C22⋊Dic5—21no—
119C2×C22⋊Dic5—21no—
120C2×C22⋊Dic5—21no—
121C2×C22⋊Dic5D411yescharacteristic
122#4093—22no—
123#4093C2314yes—
124#4084—28no—
125#4084—22no—
126#4084C2314yescomplemented
127#4081—28no—
128D4×Dic5—22no—
129D4×Dic5C2314yescomplemented
130C2×#686—24no—
131C2×#686—42no—
132C2×#686C2314yes—
133C2×#686C2314yes—
134C4×C22⋊D5D414yes—
135C4×C22⋊D5C2314yes—
136C2×#685—21no—
137C2×#685—21no—
138C2×#685—21no—
139C2×#685—21no—
140C2×#685D411yescharacteristic
141#4072—22no—
142#4072C2314yes—
143C2×C4⋊Dic5—21no—
144C2×C4⋊Dic5C2311yescharacteristic
145C2×C4⋊Dic5C2311yescharacteristic
146C2×#683—21no—
147C2×#683—21no—
148C2×#683D411yescharacteristic
149C2×C4×Dic5—21no—
150C2×C4×Dic5C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C2×#676—42no—
154C2×#676C2314yescomplemented
155#4041—22no—
156#4041—28no—
157#4041C2314yes—
158#4040—28no—
159#4039—22no—
160#4039C2314yes—
161D5×C4⋊C4—22no—
162D5×C4⋊C4C2314yescomplemented
163#4036—22no—
164#4036C2314yescomplemented
165#4028—28no—
166#4027—28no—
167D5×C22⋊C4—28no—
168#4025—28no—
169C5×#107C2314yescomplemented
170C5×#103C2314yescomplemented
171C5×#102C2314yescomplemented
172#3967C2314yescomplemented
173#3967C2314yescomplemented
174C22⋊#168C2314yes—
175#3953C2314yes—
176#3953C2314yes—
177#3953C2314yes—
178#3953C2314yes—
179#3952C2314yescomplemented
180#3946C2314yescomplemented
181C8×Dic5C2314yescomplemented
182#3941C2314yes—
183#3941C2314yes—
184#3940C2314yescomplemented
185#3939C2314yescomplemented
186C2×#553—51no—
187C2×#546—51no—
188#3322—516no—
189C2×#488—51no—
190C2×#485—51no—
191C2×#480—51no—
192C2×#478—51no—
193C2×#469—51no—
194C2×#468D511yescharacteristic, complemented
195C2×#463—51no—
196C2×#449—51no—
197C2×#447—51no—
198C2×C4×D8—51no—
199C2×#436—51no—
200C2×#417—51no—
201C2×#418—51no—
202C24×C5—21no—
203C24×C5C2×D411yescharacteristic
204C23×D5—21no—
205C23×D5—21no—
206C23×D5—24no—
207C23×D5—44no—
208C23×D5—44no—
209C23×D5—82no—
210C23×D5C2×D411yescharacteristic
211C2×C5×Q8—21no—
212C2×C5×Q8—22no—
213C2×C5×Q8—22no—
214C2×C5×Q8C2412yes—
215C2×C5×D4—24no—
216C2×C5×D4—21no—
217C2×C5×D4—22no—
218C2×C5×D4—22no—
219C2×C5×D4—82no—
220C2×C5×D4C2412yes—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2411yescharacteristic
230C2×C22⋊D5—24no—
231C2×C22⋊D5—42no—
232C2×C22⋊D5—44no—
233C2×C22⋊D5C2×D414yes—
234C22×Dic5—21no—
235C22×Dic5—21no—
236C22×Dic5—24no—
237C22×Dic5—82no—
238C22×Dic5C2×D411yescharacteristic
239C22×Dic5C2×D411yescharacteristic
240C22×Dic5C2×D411yescharacteristic
241#713—28no—
242#713—44no—
243#713—48no—
244C2×D20—21no—
245C2×D20—22no—
246C2×D20—22no—
247C2×D20—22no—
248C2×D20—28no—
249C2×D20—24no—
250C2×D20—24no—
251C2×D20—21no—
252C2×D20—24no—
253C2×D20—44no—
254C2×D20—48no—
255C2×D20—44no—
256C2×D20—44no—
257C2×D20—82no—
258C2×D20#4114yes—
259C2×D20C2412yes—
260C2×D20C2412yes—
261C2×C4×D5—22no—
262C2×C4×D5—22no—
263C2×C4×D5—24no—
264C2×C4×D5—24no—
265C2×C4×D5—24no—
266C2×C4×D5—44no—
267C2×C4×D5—82no—
268C2×C4×D5—82no—
269C2×C4×D5C2×D412yes—
270C2×C4×D5C2412yes—
271C5×SD16—44no—
272C5×M16—44no—
273C2×C5×C8—22no—
274C2×C5×C8—22no—
275C2×C5×C8C2412yes—
276C2×C5×C8C2412yes—
277C5×C4⋊C4—24no—
278C5×C4⋊C4—21no—
279C5×C4⋊C4—21no—
280C5×C4⋊C4C2412yes—
281C5×C4⋊C4C2412yes—
282C5×C22⋊C4—24no—
283C5×C22⋊C4—24no—
284C22⋊Dic5—24no—
285C22⋊Dic5—24no—
286C22⋊Dic5—24no—
287C22⋊Dic5C2×D414yes—
288#686—28no—
289#686—44no—
290#685—24no—
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#683—24no—
302#683C2×D414yes—
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×SD16C2×D511yescharacteristic, complemented
314C22×D8—51no—
315C22×D8—51no—
316C22×M16—51no—
317C22×M16C2×D511yescharacteristic
318#553—58no—
319#553—104no—
320#546—58no—
321#546—104no—
322C2×#126—101no—
323C2×#125—51no—
324C2×#124—51no—
325C2×#123—101no—
326C2×#123—101no—
327C2×C22⋊Q8C2×D511yescharacteristic
328C2×#121—51no—
329C2×#121—51no—
330C2×#121—101no—
331C2×#121—101no—
332C2×#121C2×D511yescharacteristic
333C2×#120—101no—
334C2×C4×D4—51no—
335C2×C4×D4—51no—
336C2×C4×D4—51no—
337C2×C4×D4—101no—
338C2×#117—51no—
339C22×C4⋊C4—51no—
340C22×C22⋊C4—101no—
341#488—58no—
342#485—58no—
343#480—58no—
344#478—58no—
345#469—58no—
346#468C2×D518yescomplemented
347#463—58no—
348#449—58no—
349#447—58no—
350C4×D8—58no—
351#436—58no—
352C2×#107—51no—
353C2×#107C2×D511yescharacteristic, complemented
354C2×#106—51no—
355C2×C4⋊C8—51no—
356#418—58no—
357#417—58no—
358C2×#103—51no—
359C2×#103—51no—
360C2×#103C2×D511yescharacteristic, complemented
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×#102—51no—
366C2×#102—51no—
367C2×#102C2×D511yescharacteristic, complemented
368C2×C22⋊C8—51no—
369C2×C22⋊C8—51no—
370C2×C4×C8—51no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—42no—
376C23×C5—42no—
377C23×C5—42no—
378C23×C5C22×D412yes—
379C23×C5C22×D411yescharacteristic
380C22×D5—22no—
381C22×D5—24no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—48no—
387C22×D5—42no—
388C22×D5—42no—
389C22×D5—48no—
390C22×D5—42no—
391C22×D5—42no—
392C22×D5—42no—
393C22×D5—84no—
394C22×D5—816no—
395C22×D5C22×D412yes—
396C5×Q8—22no—
397C5×Q8—22no—
398C5×Q8—42no—
399C5×D4—22no—
400C5×D4—22no—
401C5×D4—42no—
402C5×D4—84no—
403C2×C4×C5—22no—
404C2×C4×C5—24no—
405C2×C4×C5—22no—
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×C5—42no—
413C2×C4×C5C22×D412yes—
414C2×C4×C5C22×D411yescharacteristic
415C2×C4×C5C2×#4112yes—
416C2×C4×C5H(5,𝔽2)12yes—
417C2×C4×C5C2511yescharacteristic
418C22⋊D5—44no—
419C22⋊D5—48no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—42no—
426C2×Dic5—42no—
427C2×Dic5—84no—
428C2×Dic5C22×D412yes—
429C2×Dic5C22×D412yes—
430C2×Dic5C22×D412yes—
431D20—24no—
432D20—22no—
433D20—22no—
434D20—22no—
435D20—48no—
436D20—48no—
437D20—42no—
438D20—84no—
439D20C2×#4114yes—
440C4×D5—24no—
441C4×D5—22no—
442C4×D5—22no—
443C4×D5—48no—
444C4×D5—84no—
445C4×D5—84no—
446C5×C8—22no—
447C5×C8—22no—
448#168—22no—
449#168—22no—
450C25—101no—
451C2×#41—54no—
452C2×#41—102no—
453C2×#41—104no—
454C2×#41—202no—
455C22×Q8C22×D511yescharacteristic
456C22×D4—21no—
457C22×D4—51no—
458C22×D4—51no—
459C22×D4—51no—
460C22×D4—54no—
461C22×D4—104no—
462C22×D4—101no—
463C22×D4—101no—
464C22×D4—101no—
465C22×D4—101no—
466C22×D4—102no—
467C22×D4—202no—
468C22×D4C22×D511yescharacteristic
469C23×C4—51no—
470C23×C4—101no—
471C23×C4—101no—
472C23×C4—101no—
473C23×C4—101no—
474C23×C4C22×D511yescharacteristic
475C2×SD16—42no—
476C2×SD16C22×D514yescomplemented
477C2×D8—54no—
478C2×D8—54no—
479C2×D8—104no—
480C2×D8—202no—
481C2×M16—42no—
482C2×M16—54no—
483C2×M16—202no—
484C2×M16C22×D514yes—
485C22×C8—51no—
486C22×C8—51no—
487C22×C8C22×D511yescharacteristic
488C22×C8C22×D511yescharacteristic
489#126—108no—
490#125—54no—
491#125—102no—
492#124—54no—
493#124—102no—
494#123—108no—
495#123—108no—
496C22⋊Q8—22no—
497C22⋊Q8C22×D514yes—
498#121—22no—
499#121—54no—
500#121—54no—
501#121—108no—
502#121—102no—
503#121—102no—
504#121—108no—
505#121C22×D514yes—
506#120—108no—
507C4×D4—54no—
508C4×D4—54no—
509C4×D4—54no—
510C4×D4—54no—
511C4×D4—102no—
512C4×D4—102no—
513C4×D4—108no—
514#117—54no—
515#117—102no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—51no—
518C2×C4⋊C4—51no—
519C2×C4⋊C4—51no—
520C2×C4⋊C4—54no—
521C2×C4⋊C4—102no—
522C2×C4⋊C4—101no—
523C2×C4⋊C4—101no—
524C2×C4⋊C4—101no—
525C2×C4⋊C4C22×D511yescharacteristic
526C2×C4⋊C4C22×D511yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—51no—
530C2×C22⋊C4—51no—
531C2×C22⋊C4—108no—
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×C22⋊C4—101no—
539C2×C42—51no—
540C2×C42—101no—
541#107—54no—
542#107C22×D514yescomplemented
543#106—54no—
544C4⋊C8—54no—
545#103—54no—
546#103—54no—
547#103C22×D514yescomplemented
548#102—54no—
549#102—54no—
550#102—54no—
551#102—54no—
552#102—54no—
553#102—54no—
554#102C22×D514yescomplemented
555C22⋊C8—54no—
556C22⋊C8—54no—
557C4×C8—54no—
558C22×C5—22no—
559C22×C5—22no—
560C22×C5—22no—
561C22×C5—44no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5—84no—
566C22×C5#54612yes—
567C22×C5#57512yes—
568C22×C5#57612yes—
569C22×C5C23×D411yescharacteristic
570C2×D5—22no—
571C2×D5—24no—
572C2×D5—22no—
573C2×D5—22no—
574C2×D5—44no—
575C2×D5—48no—
576C2×D5—42no—
577C2×D5—42no—
578C2×D5—42no—
579C2×D5—42no—
580C2×D5—42no—
581C2×D5—816no—
582C2×D5—84no—
583C4×C5—22no—
584C4×C5—42no—
585C4×C5—42no—
586C4×C5—42no—
587C4×C5#54612yes—
588C4×C5C22×#4111yescharacteristic
589C4×C5C2×H(5,𝔽2)11yescharacteristic
590Dic5—22no—
591Dic5—22no—
592Dic5—22no—
593Dic5—42no—
594Dic5—42no—
595C24—21no—
596C24—51no—
597C24—101no—
598C24—101no—
599C24—104no—
600C24—204no—
601C24—204no—
602C24—402no—
603C24D4×D511yescharacteristic
604#41—108no—
605#41—204no—
606#41—208no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8C23×D512yes—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—54no—
616C2×D4—54no—
617C2×D4—52no—
618C2×D4—52no—
619C2×D4—82no—
620C2×D4—108no—
621C2×D4—104no—
622C2×D4—104no—
623C2×D4—104no—
624C2×D4—101no—
625C2×D4—104no—
626C2×D4—101no—
627C2×D4—102no—
628C2×D4—102no—
629C2×D4—102no—
630C2×D4—204no—
631C2×D4—208no—
632C2×D4—204no—
633C2×D4—204no—
634C2×D4—202no—
635C2×D4—204no—
636C2×D4—402no—
637C2×D4C23×D512yes—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—51no—
644C22×C4—51no—
645C22×C4—51no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—104no—
649C22×C4—104no—
650C22×C4—104no—
651C22×C4—104no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—101no—
655C22×C4—101no—
656C22×C4—204no—
657C22×C4—402no—
658C22×C4—402no—
659C22×C4—402no—
660C22×C4D4×D512yes—
661C22×C4D4×D511yescharacteristic
662C22×C4C23×D512yes—
663C22×C4C23×D511yescharacteristic
664SD16—44no—
665D8—108no—
666D8—204no—
667M16—44no—
668M16—204no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—52no—
672C2×C8—52no—
673C2×C8—102no—
674C2×C8—102no—
675C2×C8C23×D512yes—
676C2×C8C23×D512yes—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—54no—
681C4⋊C4—52no—
682C4⋊C4—52no—
683C4⋊C4—104no—
684C4⋊C4—104no—
685C4⋊C4—104no—
686C4⋊C4—101no—
687C4⋊C4—101no—
688C4⋊C4C23×D512yes—
689C4⋊C4C23×D512yes—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—54no—
693C22⋊C4—54no—
694C22⋊C4—104no—
695C22⋊C4—104no—
696C22⋊C4—104no—
697C22⋊C4—104no—
698C22⋊C4—104no—
699C22⋊C4—104no—
700C22⋊C4—104no—
701C42—52no—
702C42—52no—
703C42—104no—
704C2×C5—42no—
705C2×C5—82no—
706C2×C5#332214yescomplemented
707C2×C5C2×#54611yescharacteristic
708C2×C5C2×#57511yescharacteristic
709C2×C5C2×#57611yescharacteristic
710D5—42no—
711D5—44no—
712D5—82no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—52no—
721C23—102no—
722C23—102no—
723C23—102no—
724C23—104no—
725C23—102no—
726C23—102no—
727C23—208no—
728C23—208no—
729C23—202no—
730C23—202no—
731C23—202no—
732C23—202no—
733C23—202no—
734C23—404no—
735C23—4016no—
736C23C2×D4×D512yes—
737C23C2×D4×D511yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—42no—
741D4—22no—
742D4—22no—
743D4—42no—
744D4—54no—
745D4—84no—
746D4—104no—
747D4—102no—
748D4—102no—
749D4—102no—
750D4—208no—
751D4—208no—
752D4—204no—
753D4—208no—
754D4—202no—
755D4—404no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—52no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—102no—
770C2×C4—102no—
771C2×C4—102no—
772C2×C4—104no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—208no—
778C2×C4—202no—
779C2×C4—202no—
780C2×C4—404no—
781C2×C4—404no—
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×#332211yescharacteristic, complemented, Sylow
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—102no—
802C22—102no—
803C22—102no—
804C22—104no—
805C22—204no—
806C22—208no—
807C22—202no—
808C22—202no—
809C22—202no—
810C22—202no—
811C22—202no—
812C22—4016no—
813C22—404no—
814C22#6594412yes—
815C22#6610812yes—
816C22#6611112yes—
817C22C22×D4×D511yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—102no—
823C4—102no—
824C4—102no—
825C4—202no—
826C4—202no—
827C4#6594412yes—
828C4C2×#414411yescharacteristic
829C4C2×D5×#4111yescharacteristic
830C2—42no—
831C2—82no—
832C2—202no—
833C2—204no—
834C2—402no—
835C2#1061257114yesdirect product factor
836C2C2×#6594411yescharacteristic
837C2C2×#6610811yescharacteristic
838C2C2×#6611111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#468C2
socleC23×C5C22×D4
hypercenterC2×#468D5
hypocenterC5C2×#3322
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#65964C2semidirect
2. C2×#65948C2semidirect
3. C2×C5×#468C2semidirect
4. C2×#65461C2semidirect
5. C2×#65454C2semidirect
6. C2×#65420C2semidirect
7. C2×#65417C2semidirect
8. C2×#65334C2semidirect
9. C2×#65325C2semidirect
10. #10612571C2direct (N × H)
11. C2×#65180C2semidirect
12. C2×#65171C2semidirect
13. C2×#65092C2semidirect
14. C2×#65089C2semidirect
15. C2×#65071C2semidirect
16. C2×#65045C2semidirect
19. C22×C5×SD16C22semidirect
25. C2×#4084C22semidirect
27. C2×D4×Dic5C22semidirect
32. C22×#676C22semidirect
34. #65964C22semidirect
36. #65948C22semidirect
41. C2×D5×C4⋊C4C22semidirect
42. C2×#4036C22semidirect
47. C5×#468C22semidirect
48. C2×C5×#107C22semidirect
49. C2×C5×#103C22semidirect
50. C2×C5×#102C22semidirect
51. C2×#3967C22semidirect
52. C2×#3967C22semidirect
54. #65461C22semidirect
55. #65454C22semidirect
56. #65420C22semidirect
57. #65417C22semidirect
62. C2×#3952C22semidirect
63. C2×#3946C22semidirect
64. C2×C8×Dic5C22semidirect
65. #65334C22semidirect
66. #65325C22semidirect
69. C2×#3940C22semidirect
70. C2×#3939C22semidirect
71. #65180C22semidirect
72. #65171C22semidirect
73. #65092C22semidirect
74. #65089C22semidirect
75. #65071C22semidirect
76. #65045C22semidirect
104. C2×C5×SD16C23semidirect
126. #4084C23semidirect
129. D4×Dic5C23semidirect
154. C2×#676C23semidirect
162. D5×C4⋊C4C23semidirect
164. #4036C23semidirect
169. C5×#107C23semidirect
170. C5×#103C23semidirect
171. C5×#102C23semidirect
172. #3967C23semidirect
173. #3967C23semidirect
179. #3952C23semidirect
180. #3946C23semidirect
181. C8×Dic5C23semidirect
184. #3940C23semidirect
185. #3939C23semidirect
194. C2×#468D5semidirect
313. C22×SD16C2×D5semidirect
346. #468C2×D5semidirect
353. C2×#107C2×D5semidirect
360. C2×#103C2×D5semidirect
367. C2×#102C2×D5semidirect
476. C2×SD16C22×D5semidirect
542. #107C22×D5semidirect
547. #103C22×D5semidirect
554. #102C22×D5semidirect
706. C2×C5#3322semidirect
792. C5C2×#3322semidirect
835. C2#10612571direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659642
C2×#659482
C2×C5×#4682
C2×#654612
C2×#654542
C2×#654202
C2×#654172
C2×#653342
C2×#653252
#106125712
C2×#651802
C2×#651712
C2×#650922
C2×#650892
C2×#650712
C2×#650452
C2×#33225