Finite Group Databasebeta

← #12967748

Subgroups — #12967748

Order 1280.

2148 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×#41C211yesmaximal, characteristic
2C2×#65804C211yesmaximal, characteristic, complemented
3#10615815C212yesmaximal
4#10614266C214yesmaximal, complemented
5#10614265C214yesmaximal, complemented
6#10614264C212yesmaximal, complemented
7C4×#4097C214yesmaximal, complemented
8#10614239C212yesmaximal, complemented
9#10614179C212yesmaximal, complemented
10#10614178C212yesmaximal, complemented
11#10614046C212yesmaximal, complemented
12#10614045C212yesmaximal, complemented
13#10613951C212yesmaximal, complemented
14#10613780C211yesmaximal, characteristic, complemented
15C22×C5×#41C2211yescharacteristic
16C4×C5×#41—21no—
17C4×C5×#41—21no—
18C4×C5×#41—21no—
19C4×C5×#41—21no—
20C4×C5×#41C2212yes—
21C4×C5×#41C2212yes—
22C4×C5×#41C2212yes—
23C4×C5×#41C2212yes—
24C2×C4×C5×Q8C2211yescharacteristic
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×D4—21no—
27C2×C4×C5×D4—21no—
28C2×C4×C5×D4C2211yescharacteristic
29C2×C4×C5×D4C2211yescharacteristic
30C2×C5×#117—21no—
31C2×C5×#117C2211yescharacteristic
32C22×C42×C5—21no—
33C22×C42×C5C2211yescharacteristic
34C2×#4097C2214yes—
35C2×#4072—21no—
36C2×#4070—21no—
37C2×#4070C2212yes—
38#65804—21no—
39#65804—21no—
40#65804—21no—
41#65804—21no—
42#65804C2212yes—
43#65804C2212yes—
44#65804C2212yescomplemented
45#65804C2212yescomplemented
46C2×#4016—21no—
47C2×#4015C2211yescharacteristic, complemented
48C2×#4015C2211yescharacteristic, complemented
49C2×C4×Dic10—21no—
50C2×C4×Dic10C2212yescomplemented
51#65528C2218yes—
52#65521C2214yes—
53#65517C2214yes—
54#65507C2214yes—
55#65496C2212yes—
56#65320C2214yescomplemented
57#65320C2214yescomplemented
58#65319C2218yescomplemented
59C4×#689C2218yescomplemented
60#65310C2214yescomplemented
61#65309C2214yescomplemented
62#65308C2214yescomplemented
63#65308C2214yescomplemented
64#65307C2218yescomplemented
65C4×#687C2218yescomplemented
66#65297C2214yescomplemented
67#65296C2214yescomplemented
68#65293C2214yescomplemented
69#65285C2218yescomplemented
70#65284C2214yescomplemented
71#65260C2214yes—
72#65259C2214yes—
73#65215C2212yes—
74#65215C2212yescomplemented
75#65214C2212yes—
76#65214C2212yescomplemented
77#65213C2212yescomplemented
78C4×#681C2212yescomplemented
79#60562—51nomaximal, Sylow
80C2×C5×#41—28no—
81C2×C5×#41—21no—
82C2×C5×#41—21no—
83C2×C5×#41C2312yes—
84C2×C5×#41C2312yes—
85C22×C5×Q8C2311yescharacteristic
86C22×C5×D4—21no—
87C22×C5×D4C2311yescharacteristic
88C23×C4×C5—21no—
89C23×C4×C5—21no—
90C23×C4×C5—21no—
91C23×C4×C5D411yescharacteristic
92C23×C4×C5D411yescharacteristic
93C23×C4×C5C2311yescharacteristic
94C22×Dic10—21no—
95C22×Dic10C2312yes—
96C4×C5×Q8—21no—
97C4×C5×Q8—21no—
98C4×C5×Q8—21no—
99C4×C5×Q8—21no—
100C4×C5×Q8C2312yes—
101C4×C5×Q8C2312yes—
102C4×C5×Q8C2312yes—
103C4×C5×Q8C2312yes—
104C4×C5×D4—22no—
105C4×C5×D4—22no—
106C4×C5×D4—22no—
107C4×C5×D4—22no—
108C4×C5×D4—22no—
109C4×C5×D4—22no—
110C4×C5×D4—22no—
111C4×C5×D4—22no—
112C4×C5×D4—21no—
113C4×C5×D4—21no—
114C4×C5×D4—21no—
115C4×C5×D4—21no—
116C4×C5×D4C2312yes—
117C4×C5×D4C2312yes—
118C4×C5×D4C2312yes—
119C4×C5×D4C2312yes—
120C5×#117—21no—
121C5×#117—21no—
122C5×#117—22no—
123C5×#117—22no—
124C5×#117—22no—
125C5×#117—22no—
126C5×#117C2312yes—
127C5×#117C2312yes—
128C2×C5×C4⋊C4—21no—
129C2×C5×C4⋊C4—21no—
130C2×C5×C4⋊C4C2311yescharacteristic
131C2×C5×C4⋊C4C2311yescharacteristic
132C2×C5×C22⋊C4—21no—
133C2×C5×C22⋊C4—21no—
134C2×C5×C22⋊C4—21no—
135C2×C42×C5—21no—
136C2×C42×C5—21no—
137C2×C42×C5—21no—
138C2×C42×C5—22no—
139C2×C42×C5—22no—
140C2×C42×C5—22no—
141C2×C42×C5—22no—
142C2×C42×C5D411yescharacteristic
143C2×C42×C5D411yescharacteristic
144C2×C42×C5D411yescharacteristic
145C2×C42×C5D411yescharacteristic
146C2×C42×C5D411yescharacteristic
147C2×C42×C5D411yescharacteristic
148C2×C42×C5C2311yescharacteristic
149C2×C42×C5C2311yescharacteristic
150C2×C42×C5C2311yescharacteristic
151C2×C42×C5C2311yescharacteristic
152C2×C42×C5C2311yescharacteristic
153C2×C42×C5C2311yescharacteristic
154C2×C22⋊Dic5—22no—
155#4097—216no—
156C2×#689C2318yes—
157C2×#687C2318yes—
158#4072—22no—
159#4072—22no—
160#4072—22no—
161#4072—22no—
162C2×C4⋊Dic5—21no—
163C2×C4⋊Dic5—21no—
164C2×C4⋊Dic5—21no—
165C2×C4⋊Dic5C2312yes—
166#4070—22no—
167#4070—22no—
168#4070—22no—
169#4070—22no—
170#4070—22no—
171#4070—22no—
172#4070C2314yes—
173#4070C2314yes—
174C2×#683—22no—
175C2×#683—22no—
176C2×C4×Dic5—22no—
177C2×#681C2314yes—
178#4016—22no—
179#4016—22no—
180#4016—22no—
181#4016—22no—
182#4015—21no—
183#4015—21no—
184#4015—21no—
185#4015—21no—
186#4015C2312yes—
187#4015C2312yes—
188#4015C2312yes—
189#4015C2312yes—
190C4×Dic10—22no—
191C4×Dic10—22no—
192C4×Dic10—22no—
193C4×Dic10—22no—
194C4×Dic10—22no—
195C4×Dic10—22no—
196C4×Dic10C2314yes—
197C4×Dic10C2314yes—
198#3967C2318yes—
199#3964C2318yes—
200C22⋊#168C2314yes—
201C22⋊#168C2314yes—
202#3942C2318yes—
203#3942C2318yes—
204#3940C2318yes—
205#3939C2318yes—
206C4⋊#168C2314yes—
207C4⋊#168C2314yes—
208#3935C2314yes—
209C4×#168C2314yes—
210C2×#533—51no—
211C2×C4×#41D511yescharacteristic
212#3116—54no—
213#3113—52no—
214#3110—52no—
215#3107—54no—
216#3104—52no—
217#3101—52no—
218#3095—52no—
219#3079—52no—
220#3039—52no—
221#3007—52no—
222C4×#137—54no—
223#2920—51no—
224C24×C5—21no—
225C24×C5C2×D411yescharacteristic
226C5×#41—28no—
227C5×#41—28no—
228C5×#41—24no—
229C5×#41—24no—
230C5×#41—24no—
231C5×#41#4118yes—
232C2×C5×Q8—24no—
233C2×C5×Q8—21no—
234C2×C5×Q8C2412yes—
235C2×C5×D4—28no—
236C2×C5×D4—22no—
237C2×C5×D4—22no—
238C2×C5×D4—24no—
239C2×C5×D4—21no—
240C2×C5×D4C2412yes—
241C22×C4×C5—28no—
242C22×C4×C5—21no—
243C22×C4×C5—24no—
244C22×C4×C5—22no—
245C22×C4×C5—22no—
246C22×C4×C5—24no—
247C22×C4×C5—21no—
248C22×C4×C5—21no—
249C22×C4×C5—22no—
250C22×C4×C5—22no—
251C22×C4×C5—22no—
252C22×C4×C5—22no—
253C22×C4×C5—42no—
254C22×C4×C5—44no—
255C22×C4×C5—44no—
256C22×C4×C5C2×D411yescharacteristic
257C22×C4×C5C2×D411yescharacteristic
258C22×C4×C5C2×D411yescharacteristic
259C22×C4×C5C2×D411yescharacteristic
260C22×C4×C5C2×D411yescharacteristic
261C22×C4×C5C2×D411yescharacteristic
262C22×C4×C5C2×D411yescharacteristic
263C22×C4×C5C2×D411yescharacteristic
264C22×C4×C5C2×D411yescharacteristic
265C22×C4×C5C2×D411yescharacteristic
266C22×C4×C5C2×D411yescharacteristic
267C22×C4×C5C2×D411yescharacteristic
268C22×C4×C5C2×D411yescharacteristic
269C22×C4×C5C2×D411yescharacteristic
270C22×C4×C5C2×D411yescharacteristic
271C22×C4×C5C2411yescharacteristic
272C22×C4×C5C2411yescharacteristic
273C22×C4×C5C2411yescharacteristic
274C22×Dic5—22no—
275C22×Dic5—22no—
276C2×Dic10—28no—
277C2×Dic10—22no—
278C2×Dic10—22no—
279C2×Dic10—22no—
280C2×Dic10—44no—
281C2×Dic10C2414yes—
282C5×C4⋊C4—22no—
283C5×C4⋊C4—22no—
284C5×C4⋊C4—22no—
285C5×C4⋊C4—22no—
286C5×C4⋊C4—21no—
287C5×C4⋊C4—21no—
288C5×C4⋊C4C2412yes—
289C5×C4⋊C4C2412yes—
290C5×C22⋊C4—22no—
291C5×C22⋊C4—22no—
292C5×C22⋊C4—22no—
293C5×C22⋊C4—22no—
294C5×C22⋊C4—22no—
295C5×C22⋊C4—22no—
296C42×C5—22no—
297C42×C5—22no—
298C42×C5—22no—
299C42×C5—22no—
300C42×C5—22no—
301C42×C5—22no—
302C42×C5C2×D411yescharacteristic
303C42×C5C2×D411yescharacteristic
304C42×C5C2×D411yescharacteristic
305C42×C5C2×D411yescharacteristic
306C42×C5C2×D411yescharacteristic
307C42×C5C2×D411yescharacteristic
308C42×C5C2×D411yescharacteristic
309C42×C5C2×D411yescharacteristic
310C42×C5C2×D411yescharacteristic
311C42×C5C2×D411yescharacteristic
312C42×C5C2×D411yescharacteristic
313C42×C5C2×D411yescharacteristic
314C42×C5C2411yescharacteristic
315C42×C5C2411yescharacteristic
316C42×C5C2411yescharacteristic
317C42×C5C2411yescharacteristic
318C22⋊Dic5—24no—
319C22⋊Dic5—24no—
320#689—216no—
321#687—216no—
322C4⋊Dic5—22no—
323C4⋊Dic5—22no—
324C4⋊Dic5—22no—
325C4⋊Dic5—22no—
326C4⋊Dic5—22no—
327C4⋊Dic5—22no—
328C4⋊Dic5—22no—
329C4⋊Dic5C2414yes—
330#683—24no—
331#683—24no—
332#683—24no—
333#683—24no—
334C4×Dic5—24no—
335C4×Dic5—24no—
336#681—28no—
337C2×#168C2418yes—
338C22×#41C2×D511yescharacteristic
339C2×#137—54no—
340#533—52no—
341#533—52no—
342#533—52no—
343#533—52no—
344#533—101no—
345#533—101no—
346#533—101no—
347#533—101no—
348C2×C4⋊Q8—51no—
349C2×C4⋊Q8—51no—
350C2×#125—101no—
351C2×C22⋊Q8—52no—
352C2×C22⋊Q8—101no—
353C4×#41—21no—
354C4×#41—21no—
355C4×#41—21no—
356C4×#41—21no—
357C4×#41C2×D512yes—
358C4×#41C2×D512yes—
359C4×#41C2×D512yes—
360C4×#41C2×D512yes—
361C2×C4×Q8—52no—
362C2×C4×Q8—101no—
363C2×C4×Q8C2×D511yescharacteristic
364C2×C4×Q8C2×D511yescharacteristic
365C2×C4×D4—21no—
366C2×C4×D4—21no—
367C2×C4×D4C2×D511yescharacteristic
368C2×C4×D4C2×D511yescharacteristic
369C2×#117—21no—
370C2×#117—101no—
371C2×#117C2×D511yescharacteristic
372C22×C42—21no—
373C22×C42C2×D511yescharacteristic
374#485—58no—
375#484—54no—
376#483—54no—
377#477—54no—
378#476—54no—
379#475—54no—
380#474—54no—
381#462—54no—
382#462—54no—
383#461—54no—
384#461—54no—
385#452—58no—
386#451—54no—
387#450—54no—
388#441—58no—
389#440—58no—
390C4×Q16—58no—
391C4×SD16—58no—
392#432—52no—
393#432—52no—
394#431—52no—
395#431—52no—
396#428—54no—
397#423—52no—
398#419—54no—
399#417—54no—
400#407—52no—
401C4×M16—52no—
402C23×C5—24no—
403C23×C5—22no—
404C23×C5—22no—
405C23×C5—22no—
406C23×C5—41no—
407C23×C5—42no—
408C23×C5—42no—
409C23×C5C22×D411yescharacteristic
410C23×C5C22×D411yescharacteristic
411C23×C5C22×D411yescharacteristic
412C5×Q8—24no—
413C5×Q8—22no—
414C5×Q8C2×#4114yes—
415C5×D4—28no—
416C5×D4—24no—
417C5×D4—28no—
418C5×D4—22no—
419C5×D4C2×#4114yes—
420C2×C4×C5—24no—
421C2×C4×C5—28no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—28no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—22no—
430C2×C4×C5—22no—
431C2×C4×C5—22no—
432C2×C4×C5—22no—
433C2×C4×C5—22no—
434C2×C4×C5—22no—
435C2×C4×C5—22no—
436C2×C4×C5—22no—
437C2×C4×C5—22no—
438C2×C4×C5—22no—
439C2×C4×C5—41no—
440C2×C4×C5—41no—
441C2×C4×C5—41no—
442C2×C4×C5—44no—
443C2×C4×C5—42no—
444C2×C4×C5—42no—
445C2×C4×C5—44no—
446C2×C4×C5—44no—
447C2×C4×C5—44no—
448C2×C4×C5#13714yescomplemented
449C2×C4×C5C22×D411yescharacteristic
450C2×C4×C5C22×D411yescharacteristic
451C2×C4×C5C22×D411yescharacteristic
452C2×C4×C5C22×D411yescharacteristic
453C2×C4×C5C22×D411yescharacteristic
454C2×C4×C5C22×D411yescharacteristic
455C2×C4×C5C22×D411yescharacteristic
456C2×C4×C5C22×D411yescharacteristic
457C2×C4×C5C22×D411yescharacteristic
458C2×C4×C5C22×D411yescharacteristic
459C2×C4×C5C22×D411yescharacteristic
460C2×C4×C5C2×#4114yes—
461C2×C4×C5C2511yescharacteristic
462C2×Dic5—24no—
463C2×Dic5—24no—
464C2×Dic5—44no—
465C2×Dic5—44no—
466Dic10—28no—
467Dic10—44no—
468Dic10—44no—
469Dic10—44no—
470#168—28no—
471C2×#41—28no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41C22×D512yes—
475C2×#41C22×D512yes—
476C22×Q8—52no—
477C22×Q8—101no—
478C22×Q8C22×D511yescharacteristic
479C22×D4—21no—
480C22×D4C22×D511yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C22⋊D511yescharacteristic
485C23×C4C22⋊D511yescharacteristic
486C23×C4C22×D511yescharacteristic
487#137—1016no—
488C2×Q16—58no—
489C2×SD16—58no—
490C2×M16—54no—
491C4⋊Q8—52no—
492C4⋊Q8—52no—
493C4⋊Q8—52no—
494C4⋊Q8—52no—
495C4⋊Q8—101no—
496C4⋊Q8—101no—
497C4⋊Q8—101no—
498C4⋊Q8—101no—
499#125—102no—
500#125—102no—
501#125—102no—
502#125—102no—
503C22⋊Q8—54no—
504C22⋊Q8—54no—
505C22⋊Q8—102no—
506C22⋊Q8—102no—
507C22⋊Q8—102no—
508C22⋊Q8—102no—
509C22⋊Q8—102no—
510C22⋊Q8—102no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8—21no—
514C4×Q8—21no—
515C4×Q8—54no—
516C4×Q8—54no—
517C4×Q8—102no—
518C4×Q8—102no—
519C4×Q8—102no—
520C4×Q8—102no—
521C4×Q8—102no—
522C4×Q8—102no—
523C4×Q8C22×D512yes—
524C4×Q8C22×D512yes—
525C4×Q8C22×D512yes—
526C4×Q8C22×D512yes—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4C22×D512yes—
540C4×D4C22×D512yes—
541C4×D4C22×D512yes—
542C4×D4C22×D512yes—
543#117—21no—
544#117—21no—
545#117—22no—
546#117—22no—
547#117—22no—
548#117—22no—
549#117—102no—
550#117—102no—
551#117—102no—
552#117—102no—
553#117C22×D512yes—
554#117C22×D512yes—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—52no—
558C2×C4⋊C4—101no—
559C2×C4⋊C4—101no—
560C2×C4⋊C4—102no—
561C2×C4⋊C4—102no—
562C2×C4⋊C4—101no—
563C2×C4⋊C4C22×D511yescharacteristic
564C2×C4⋊C4C22×D511yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—102no—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42—21no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—102no—
577C2×C42C22⋊D511yescharacteristic
578C2×C42C22⋊D511yescharacteristic
579C2×C42C22⋊D511yescharacteristic
580C2×C42C22⋊D511yescharacteristic
581C2×C42C22⋊D511yescharacteristic
582C2×C42C22⋊D511yescharacteristic
583C2×C42C22×D511yescharacteristic
584C2×C42C22×D511yescharacteristic
585C2×C42C22×D511yescharacteristic
586C2×C42C22×D511yescharacteristic
587C2×C42C22×D511yescharacteristic
588C2×C42C22×D511yescharacteristic
589#107—58no—
590#106—58no—
591C4⋊C8—54no—
592C4⋊C8—54no—
593#103—58no—
594#103—58no—
595#103—58no—
596#102—58no—
597C22⋊C8—54no—
598C22⋊C8—54no—
599#97—54no—
600C4×C8—54no—
601C22×C5—21no—
602C22×C5—21no—
603C22×C5—21no—
604C22×C5—21no—
605C22×C5—21no—
606C22×C5—24no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—44no—
610C22×C5—48no—
611C22×C5—42no—
612C22×C5—42no—
613C22×C5#52512yes—
614C22×C5C2×#13712yes—
615C22×C5C23×D411yescharacteristic
616C4×C5—21no—
617C4×C5—24no—
618C4×C5—21no—
619C4×C5—21no—
620C4×C5—21no—
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—21no—
624C4×C5—42no—
625C4×C5—42no—
626C4×C5#52512yes—
627C4×C5C2×#13712yes—
628C4×C5C2×#13712yes—
629C4×C5#57512yes—
630C4×C5C22×#4112yes—
631Dic5—44no—
632Dic5—44no—
633C24—21no—
634C24C2×C22⋊D511yescharacteristic
635#41—28no—
636#41—28no—
637#41—24no—
638#41—24no—
639#41—24no—
640#41#70918yes—
641C2×Q8—24no—
642C2×Q8—21no—
643C2×Q8—54no—
644C2×Q8—102no—
645C2×Q8—102no—
646C2×Q8—102no—
647C2×Q8—108no—
648C2×Q8—204no—
649C2×Q8C23×D512yes—
650C2×D4—28no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—24no—
654C2×D4—21no—
655C2×D4C23×D512yes—
656C22×C4—28no—
657C22×C4—21no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—42no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4C2×C22⋊D511yescharacteristic
674C22×C4C2×C22⋊D511yescharacteristic
675C22×C4C2×C22⋊D511yescharacteristic
676C22×C4C2×C22⋊D511yescharacteristic
677C22×C4C2×C22⋊D511yescharacteristic
678C22×C4C2×C22⋊D511yescharacteristic
679C22×C4C2×C22⋊D511yescharacteristic
680C22×C4C2×C22⋊D511yescharacteristic
681C22×C4C2×C22⋊D511yescharacteristic
682C22×C4C2×C22⋊D511yescharacteristic
683C22×C4C2×C22⋊D511yescharacteristic
684C22×C4C2×C22⋊D511yescharacteristic
685C22×C4C2×C22⋊D511yescharacteristic
686C22×C4C2×C22⋊D511yescharacteristic
687C22×C4C2×C22⋊D511yescharacteristic
688C22×C4C23×D511yescharacteristic
689C22×C4C23×D511yescharacteristic
690C22×C4C23×D511yescharacteristic
691Q16—1016no—
692SD16—1016no—
693M16—108no—
694C2×C8—58no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—54no—
702C4⋊C4—102no—
703C4⋊C4—102no—
704C4⋊C4—102no—
705C4⋊C4—102no—
706C4⋊C4—102no—
707C4⋊C4—104no—
708C4⋊C4—104no—
709C4⋊C4—104no—
710C4⋊C4—104no—
711C4⋊C4—102no—
712C4⋊C4—102no—
713C4⋊C4C23×D512yes—
714C4⋊C4C23×D512yes—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—104no—
722C22⋊C4—104no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—22no—
728C42—22no—
729C42—104no—
730C42—104no—
731C42C2×C22⋊D511yescharacteristic
732C42C2×C22⋊D511yescharacteristic
733C42C2×C22⋊D511yescharacteristic
734C42C2×C22⋊D511yescharacteristic
735C42C2×C22⋊D511yescharacteristic
736C42C2×C22⋊D511yescharacteristic
737C42C2×C22⋊D511yescharacteristic
738C42C2×C22⋊D511yescharacteristic
739C42C2×C22⋊D511yescharacteristic
740C42C2×C22⋊D511yescharacteristic
741C42C2×C22⋊D511yescharacteristic
742C42C2×C22⋊D511yescharacteristic
743C42C23×D511yescharacteristic
744C42C23×D511yescharacteristic
745C42C23×D511yescharacteristic
746C42C23×D511yescharacteristic
747C2×C5—22no—
748C2×C5—22no—
749C2×C5—41no—
750C2×C5—44no—
751C2×C5C2×#52511yescharacteristic
752C2×C5C22×#13711yescharacteristic
753C2×C5C2×#57511yescharacteristic
754C23—24no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—41no—
759C23—42no—
760C23—42no—
761C23C22×C22⋊D511yescharacteristic
762C23C22×C22⋊D511yescharacteristic
763C23C22×C22⋊D511yescharacteristic
764Q8—24no—
765Q8—22no—
766Q8—108no—
767Q8—204no—
768Q8—204no—
769Q8—204no—
770Q8C2×#70914yes—
771D4—28no—
772D4—24no—
773D4—28no—
774D4—22no—
775D4C2×#70914yes—
776C2×C4—24no—
777C2×C4—28no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—28no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—104no—
805C2×C4—104no—
806C2×C4—204no—
807C2×C4—204no—
808C2×C4#409714yescomplemented
809C2×C4C2×#70914yes—
810C2×C4C22×C22⋊D511yescharacteristic
811C2×C4C22×C22⋊D511yescharacteristic
812C2×C4C22×C22⋊D511yescharacteristic
813C2×C4C22×C22⋊D511yescharacteristic
814C2×C4C22×C22⋊D511yescharacteristic
815C2×C4C22×C22⋊D511yescharacteristic
816C2×C4C22×C22⋊D511yescharacteristic
817C2×C4C22×C22⋊D511yescharacteristic
818C2×C4C22×C22⋊D511yescharacteristic
819C2×C4C22×C22⋊D511yescharacteristic
820C2×C4C22×C22⋊D511yescharacteristic
821C2×C4C24×D511yescharacteristic
822C8—108no—
823C5#6056211yescharacteristic, complemented, Sylow
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—24no—
832C22—44no—
833C22—48no—
834C22—42no—
835C22—42no—
836C22#6612512yes—
837C22C2×#409712yes—
838C22C23×C22⋊D511yescharacteristic
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—24no—
846C4—21no—
847C4—42no—
848C4—42no—
849C4—204no—
850C4—204no—
851C4#6612512yes—
852C4#6615612yes—
853C4C2×#409712yes—
854C4C2×#409712yes—
855C4C22×#70912yes—
856C2—22no—
857C2—22no—
858C2—41no—
859C2—44no—
860C2C2×#6612511yescharacteristic
861C2C2×#6615611yescharacteristic
862C2C22×#409711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C4×C5×#41C2
socleC22×C5C23×D4
prime radicalC22×C5×#41C22
hypercenterC2×C4×#41D5
hypocenterC5#60562
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×#65804C2semidirect
4. #10614266C2semidirect
5. #10614265C2semidirect
6. #10614264C2semidirect
7. C4×#4097C2semidirect
8. #10614239C2semidirect
9. #10614179C2semidirect
10. #10614178C2semidirect
11. #10614046C2semidirect
12. #10614045C2semidirect
13. #10613951C2semidirect
14. #10613780C2semidirect
44. #65804C22semidirect
45. #65804C22semidirect
47. C2×#4015C22semidirect
48. C2×#4015C22semidirect
50. C2×C4×Dic10C22semidirect
56. #65320C22semidirect
57. #65320C22semidirect
58. #65319C22semidirect
59. C4×#689C22semidirect
60. #65310C22semidirect
61. #65309C22semidirect
62. #65308C22semidirect
63. #65308C22semidirect
64. #65307C22semidirect
65. C4×#687C22semidirect
66. #65297C22semidirect
67. #65296C22semidirect
68. #65293C22semidirect
69. #65285C22semidirect
70. #65284C22semidirect
74. #65215C22semidirect
76. #65214C22semidirect
77. #65213C22semidirect
78. C4×#681C22semidirect
448. C2×C4×C5#137semidirect
808. C2×C4#4097semidirect
823. C5#60562semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×#412
C2×#658042
#106158152
#106142662
#106142652
#106142642
C4×#40972
#106142392
#106141792
#106141782
#106140462
#106140452
#106139512
#106137802
#605625