Finite Group Databasebeta

← #12967712

Subgroups — #12967712

Order 1280.

2138 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3444C211yesmaximal, characteristic
2C22×C4×Dic10C211yesmaximal, characteristic, complemented
3#10615100C212yesmaximal, complemented
4#10615099C212yesmaximal, complemented
5#10615098C212yesmaximal, complemented
6#10615047C212yesmaximal, complemented
7#10615046C212yesmaximal, complemented
8#10615045C212yesmaximal, complemented
9#10614884C214yesmaximal, complemented
10#10614883C214yesmaximal, complemented
11#10614664C212yesmaximal, complemented
12#10614645C212yesmaximal, complemented
13C4×#4097C214yesmaximal, complemented
14#10613780C211yesmaximal, characteristic, complemented
15C23×Dic10C2211yescharacteristic
16C5×#533C2211yescharacteristic
17C5×#533C2211yescharacteristic
18C5×#533C2211yescharacteristic
19C5×#532C2211yescharacteristic
20C5×#532C2211yescharacteristic
21C5×#532C2211yescharacteristic
22C5×#529—21no—
23C5×#529—21no—
24C5×#529—21no—
25C5×#529—21no—
26C5×#529C2212yes—
27C5×#529C2212yes—
28C5×#525—21no—
29C5×#525—21no—
30C5×#525C2212yes—
31C4×C5×#41—21no—
32C4×C5×#41—21no—
33C4×C5×#41C2212yes—
34C22×C42×C5C2211yescharacteristic
35C2×#4097C2214yes—
36C22×C4⋊Dic5C2211yescharacteristic
37C22×#683—21no—
38C22×C4×Dic5—21no—
39C2×C4×Dic10—21no—
40C2×C4×Dic10—21no—
41C2×C4×Dic10—21no—
42C2×C4×Dic10—21no—
43C2×C4×Dic10—21no—
44C2×C4×Dic10—21no—
45C2×C4×Dic10C2212yes—
46C2×C4×Dic10C2212yes—
47C2×C4×Dic10C2212yes—
48C2×C4×Dic10C2212yes—
49C2×C4×Dic10C2212yes—
50C2×C4×Dic10C2212yes—
51#65521C2214yes—
52#65496C2212yes—
53#65383C2214yescomplemented
54#65380C2214yescomplemented
55#65379C2214yescomplemented
56#65364C2214yescomplemented
57#65352C2218yescomplemented
58#65343C2218yescomplemented
59#65339C2214yes—
60#65339C2214yes—
61#65333C2214yes—
62#65332C2214yes—
63#65329C2214yes—
64#65329C2214yes—
65#65323C2214yes—
66#65322C2214yes—
67#65319C2218yescomplemented
68C4×#689C2218yescomplemented
69#65307C2218yescomplemented
70C4×#687C2218yescomplemented
71#65293C2214yes—
72#65284C2214yes—
73#65215C2212yes—
74#65215C2212yes—
75#65214C2212yes—
76#65214C2212yes—
77#65213C2212yes—
78C4×#681C2212yes—
79#60560—51nomaximal, Sylow
80C2×C5×#41—21no—
81C2×C5×#41—21no—
82C2×C5×#41C2312yes—
83C23×C4×C5D411yescharacteristic
84C23×C4×C5D411yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×Dic5—21no—
87C23×Dic5—21no—
88C22×Dic10—21no—
89C22×Dic10—21no—
90C22×Dic10—21no—
91C22×Dic10—28no—
92C22×Dic10C2312yes—
93C22×Dic10C2312yes—
94C22×Dic10C2312yes—
95C5×C4⋊Q8C2311yescharacteristic
96C5×C4⋊Q8C2311yescharacteristic
97C5×C4⋊Q8C2311yescharacteristic
98C5×#127C2311yescharacteristic
99C5×#126—22no—
100C5×#126—22no—
101C5×#125—21no—
102C5×#125—21no—
103C5×#125C2312yes—
104C5×#124—21no—
105C5×#124—21no—
106C5×#124C2312yes—
107C5×#123—22no—
108C5×#123—22no—
109C5×#123—22no—
110C5×C22⋊Q8—21no—
111C5×C22⋊Q8—21no—
112C5×C22⋊Q8—21no—
113C5×C22⋊Q8—21no—
114C5×C22⋊Q8C2312yes—
115C5×C22⋊Q8C2312yes—
116C5×#121—21no—
117C5×#121—21no—
118C5×#121—21no—
119C5×#121—21no—
120C5×#121C2312yes—
121C5×#121C2312yes—
122C5×#120—22no—
123C4×C5×Q8—21no—
124C4×C5×Q8—21no—
125C4×C5×Q8—21no—
126C4×C5×Q8—21no—
127C4×C5×Q8C2312yes—
128C4×C5×Q8C2312yes—
129C4×C5×D4—22no—
130C4×C5×D4—22no—
131C4×C5×D4—22no—
132C4×C5×D4—22no—
133C4×C5×D4—22no—
134C4×C5×D4—22no—
135C4×C5×D4—21no—
136C4×C5×D4—21no—
137C4×C5×D4—21no—
138C4×C5×D4—21no—
139C4×C5×D4C2312yes—
140C4×C5×D4C2312yes—
141C5×#117—21no—
142C5×#117—21no—
143C5×#117—22no—
144C5×#117—22no—
145C5×#117—22no—
146C5×#117C2312yes—
147C2×C42×C5—22no—
148C2×C42×C5D411yescharacteristic
149C2×C42×C5D411yescharacteristic
150C2×C42×C5D411yescharacteristic
151C2×C42×C5D411yescharacteristic
152C2×C42×C5D411yescharacteristic
153C2×C42×C5D411yescharacteristic
154C2×C42×C5C2311yescharacteristic
155C2×C42×C5C2311yescharacteristic
156C2×C42×C5C2311yescharacteristic
157C2×C42×C5C2311yescharacteristic
158C2×C42×C5C2311yescharacteristic
159C2×C42×C5C2311yescharacteristic
160#4097—216no—
161C2×#689C2318yes—
162C2×#687C2318yes—
163C2×C4⋊Dic5—21no—
164C2×C4⋊Dic5—21no—
165C2×C4⋊Dic5—21no—
166C2×C4⋊Dic5C2312yes—
167C2×C4⋊Dic5C2312yes—
168C2×C4⋊Dic5C2312yes—
169C2×#683—22no—
170C2×#683—22no—
171C2×#683—22no—
172C2×#683—22no—
173C2×#683—22no—
174C2×#683—22no—
175C2×C4×Dic5—22no—
176C2×C4×Dic5—22no—
177C2×C4×Dic5—22no—
178C2×C4×Dic5—22no—
179C2×C4×Dic5—22no—
180C2×C4×Dic5—22no—
181C2×#681C2314yes—
182C4×Dic10—22no—
183C4×Dic10—22no—
184C4×Dic10—22no—
185C4×Dic10—22no—
186C4×Dic10—22no—
187C4×Dic10—22no—
188C4×Dic10—22no—
189C4×Dic10—22no—
190C4×Dic10—22no—
191C4×Dic10—22no—
192C4×Dic10—22no—
193C4×Dic10—22no—
194C4×Dic10C2314yes—
195C4×Dic10C2314yes—
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—
210#3444D511yescharacteristic
211C22×C4×Q8—51no—
212#3117—54no—
213#3113—52no—
214#3112—52no—
215#3108—54no—
216#3104—52no—
217#3103—52no—
218#3092—52no—
219#3078—52no—
220#3037—52no—
221#3004—52no—
222C4×#137—54no—
223#2920—51no—
224C24×C5C2×D411yescharacteristic
225C5×#41—28no—
226C5×#41—44no—
227C5×#41—44no—
228C2×C5×Q8—21no—
229C2×C5×Q8—21no—
230C2×C5×Q8C2412yes—
231C2×C5×D4—22no—
232C2×C5×D4—22no—
233C2×C5×D4—22no—
234C2×C5×D4—21no—
235C2×C5×D4—21no—
236C2×C5×D4C2412yes—
237C22×C4×C5—24no—
238C22×C4×C5—24no—
239C22×C4×C5—22no—
240C22×C4×C5—22no—
241C22×C4×C5—22no—
242C22×C4×C5—42no—
243C22×C4×C5C2×D411yescharacteristic
244C22×C4×C5C2×D411yescharacteristic
245C22×C4×C5C2×D411yescharacteristic
246C22×C4×C5C2×D411yescharacteristic
247C22×C4×C5C2×D411yescharacteristic
248C22×C4×C5C2×D411yescharacteristic
249C22×C4×C5C2×D411yescharacteristic
250C22×C4×C5C2×D411yescharacteristic
251C22×C4×C5C2×D411yescharacteristic
252C22×C4×C5C2×D411yescharacteristic
253C22×C4×C5C2×D411yescharacteristic
254C22×C4×C5C2×D411yescharacteristic
255C22×C4×C5C2×D411yescharacteristic
256C22×C4×C5C2×D411yescharacteristic
257C22×C4×C5C2×D411yescharacteristic
258C22×C4×C5C2411yescharacteristic
259C22×C4×C5C2411yescharacteristic
260C22×C4×C5C2411yescharacteristic
261C22×Dic5—28no—
262C22×Dic5—22no—
263C22×Dic5—22no—
264C22×Dic5—22no—
265C22×Dic5—22no—
266C22×Dic5—22no—
267C22×Dic5—22no—
268C22×Dic5—44no—
269C2×Dic10—28no—
270C2×Dic10—28no—
271C2×Dic10—28no—
272C2×Dic10—22no—
273C2×Dic10—22no—
274C2×Dic10—22no—
275C2×Dic10—24no—
276C2×Dic10—28no—
277C2×Dic10—28no—
278C2×Dic10#4118yescomplemented
279C2×Dic10C2414yes—
280C5×C4⋊C4—21no—
281C5×C4⋊C4—21no—
282C5×C4⋊C4—21no—
283C5×C4⋊C4—21no—
284C5×C4⋊C4—22no—
285C5×C4⋊C4—22no—
286C5×C4⋊C4—22no—
287C5×C4⋊C4—22no—
288C5×C4⋊C4—22no—
289C5×C4⋊C4—22no—
290C5×C4⋊C4C2412yes—
291C5×C4⋊C4C2412yes—
292C5×C22⋊C4—22no—
293C5×C22⋊C4—22no—
294C5×C22⋊C4—22no—
295C5×C22⋊C4—22no—
296C5×C22⋊C4—22no—
297C5×C22⋊C4—22no—
298C5×C22⋊C4—22no—
299C5×C22⋊C4—22no—
300C5×C22⋊C4—22no—
301C42×C5—22no—
302C42×C5—22no—
303C42×C5—22no—
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×C5C2×D411yescharacteristic
315C42×C5C2×D411yescharacteristic
316C42×C5C2411yescharacteristic
317C42×C5C2411yescharacteristic
318C42×C5C2411yescharacteristic
319C42×C5C2411yescharacteristic
320#689—216no—
321#687—216no—
322C4⋊Dic5—22no—
323C4⋊Dic5—22no—
324C4⋊Dic5—22no—
325C4⋊Dic5C2414yes—
326#683—24no—
327#683—24no—
328#683—24no—
329#683—24no—
330C4×Dic5—24no—
331C4×Dic5—24no—
332C4×Dic5—24no—
333C4×Dic5—24no—
334#681—28no—
335C2×#168C2418yes—
336C23×Q8—51no—
337C2×#137—54no—
338#533C2×D511yescharacteristic
339#533C2×D511yescharacteristic
340#533C2×D511yescharacteristic
341#532C2×D511yescharacteristic
342#532C2×D511yescharacteristic
343#532C2×D511yescharacteristic
344#529—21no—
345#529—21no—
346#529—21no—
347#529—21no—
348#529C2×D512yes—
349#529C2×D512yes—
350#525—21no—
351#525—21no—
352#525C2×D512yes—
353C4×#41—21no—
354C4×#41—21no—
355C4×#41C2×D512yes—
356C2×C4×Q8—52no—
357C2×C4×Q8—52no—
358C2×C4×Q8—52no—
359C2×C4×Q8—52no—
360C2×C4×Q8—52no—
361C2×C4×Q8—52no—
362C2×C4×Q8—101no—
363C2×C4×Q8—101no—
364C2×C4×Q8—101no—
365C2×C4×Q8—101no—
366C2×C4×Q8—101no—
367C2×C4×Q8—101no—
368C22×C4⋊C4—51no—
369C22×C4⋊C4—101no—
370C22×C42—101no—
371C22×C42C2×D511yescharacteristic
372#484—54no—
373#483—54no—
374#481—54no—
375#480—54no—
376#479—58no—
377#477—54no—
378#475—54no—
379#464—58no—
380#462—54no—
381#460—54no—
382#451—54no—
383#451—54no—
384#448—54no—
385#448—54no—
386#441—58no—
387#440—58no—
388C4×Q16—58no—
389C4×SD16—58no—
390#432—52no—
391#432—52no—
392#431—52no—
393#431—52no—
394#428—54no—
395#423—52no—
396#419—54no—
397#417—54no—
398#407—52no—
399C4×M16—52no—
400C23×C5—22no—
401C23×C5—22no—
402C23×C5—22no—
403C23×C5—22no—
404C23×C5C22×D411yescharacteristic
405C23×C5C22×D411yescharacteristic
406C23×C5C22×D411yescharacteristic
407C5×Q8—24no—
408C5×Q8—42no—
409C5×Q8—42no—
410C5×D4—24no—
411C5×D4—42no—
412C5×D4—44no—
413C5×D4—44no—
414C5×D4—44no—
415C5×D4—42no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—22no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—22no—
430C2×C4×C5—22no—
431C2×C4×C5—41no—
432C2×C4×C5—41no—
433C2×C4×C5—41no—
434C2×C4×C5—41no—
435C2×C4×C5—44no—
436C2×C4×C5—44no—
437C2×C4×C5—44no—
438C2×C4×C5#13714yescomplemented
439C2×C4×C5C22×D411yescharacteristic
440C2×C4×C5C22×D411yescharacteristic
441C2×C4×C5C22×D411yescharacteristic
442C2×C4×C5C22×D411yescharacteristic
443C2×C4×C5C22×D411yescharacteristic
444C2×C4×C5C22×D411yescharacteristic
445C2×C4×C5C22×D411yescharacteristic
446C2×C4×C5C22×D411yescharacteristic
447C2×C4×C5C22×D411yescharacteristic
448C2×C4×C5C22×D411yescharacteristic
449C2×C4×C5C22×D411yescharacteristic
450C2×C4×C5C2×#4114yes—
451C2×C4×C5C2511yescharacteristic
452C2×Dic5—28no—
453C2×Dic5—28no—
454C2×Dic5—28no—
455C2×Dic5—24no—
456C2×Dic5—24no—
457C2×Dic5—44no—
458C2×Dic5—44no—
459C2×Dic5—44no—
460Dic10—28no—
461Dic10—28no—
462Dic10—28no—
463Dic10—24no—
464Dic10C2×#4118yes—
465#168—28no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41C22×D512yes—
469C22×Q8—52no—
470C22×Q8—52no—
471C22×Q8—52no—
472C22×Q8—108no—
473C22×Q8—101no—
474C22×Q8—101no—
475C22×Q8—101no—
476C23×C4—101no—
477C23×C4—101no—
478C23×C4C22⋊D511yescharacteristic
479C23×C4C22⋊D511yescharacteristic
480C23×C4C22×D511yescharacteristic
481#137—1016no—
482C2×Q16—58no—
483C2×SD16—58no—
484C2×M16—54no—
485C4⋊Q8C22×D511yescharacteristic
486C4⋊Q8C22×D511yescharacteristic
487C4⋊Q8C22×D511yescharacteristic
488#127C22×D511yescharacteristic
489#126—22no—
490#126—22no—
491#125—21no—
492#125—21no—
493#125C22×D512yes—
494#124—21no—
495#124—21no—
496#124C22×D512yes—
497#123—22no—
498#123—22no—
499#123—22no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8C22×D512yes—
505C22⋊Q8C22×D512yes—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121C22×D512yes—
511#121C22×D512yes—
512#120—22no—
513C4×Q8—21no—
514C4×Q8—21no—
515C4×Q8—21no—
516C4×Q8—21no—
517C4×Q8—54no—
518C4×Q8—54no—
519C4×Q8—54no—
520C4×Q8—54no—
521C4×Q8—102no—
522C4×Q8—102no—
523C4×Q8—102no—
524C4×Q8—102no—
525C4×Q8—102no—
526C4×Q8—102no—
527C4×Q8—102no—
528C4×Q8—102no—
529C4×Q8—102no—
530C4×Q8—102no—
531C4×Q8—102no—
532C4×Q8—102no—
533C4×Q8C22×D512yes—
534C4×Q8C22×D512yes—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4C22×D512yes—
546C4×D4C22×D512yes—
547#117—21no—
548#117—21no—
549#117—22no—
550#117—22no—
551#117—22no—
552#117C22×D512yes—
553C2×C4⋊C4—52no—
554C2×C4⋊C4—52no—
555C2×C4⋊C4—52no—
556C2×C4⋊C4—101no—
557C2×C4⋊C4—101no—
558C2×C4⋊C4—101no—
559C2×C4⋊C4—102no—
560C2×C4⋊C4—102no—
561C2×C4⋊C4—102no—
562C2×C4⋊C4—102no—
563C2×C4⋊C4—102no—
564C2×C4⋊C4—102no—
565C2×C42—22no—
566C2×C42—102no—
567C2×C42—102no—
568C2×C42—102no—
569C2×C42—102no—
570C2×C42—102no—
571C2×C42—102no—
572C2×C42C22⋊D511yescharacteristic
573C2×C42C22⋊D511yescharacteristic
574C2×C42C22⋊D511yescharacteristic
575C2×C42C22⋊D511yescharacteristic
576C2×C42C22⋊D511yescharacteristic
577C2×C42C22⋊D511yescharacteristic
578C2×C42C22×D511yescharacteristic
579C2×C42C22×D511yescharacteristic
580C2×C42C22×D511yescharacteristic
581C2×C42C22×D511yescharacteristic
582C2×C42C22×D511yescharacteristic
583C2×C42C22×D511yescharacteristic
584#107—58no—
585#106—58no—
586C4⋊C8—54no—
587C4⋊C8—54no—
588#103—58no—
589#103—58no—
590#103—58no—
591#102—58no—
592C22⋊C8—54no—
593C22⋊C8—54no—
594#97—54no—
595C4×C8—54no—
596C22×C5—28no—
597C22×C5—21no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—21no—
601C22×C5—21no—
602C22×C5—21no—
603C22×C5—42no—
604C22×C5—42no—
605C22×C5—42no—
606C22×C5#52512yes—
607C22×C5C2×#13712yes—
608C22×C5#57512yes—
609C22×C5C23×D411yescharacteristic
610C4×C5—21no—
611C4×C5—21no—
612C4×C5—21no—
613C4×C5—21no—
614C4×C5—21no—
615C4×C5—21no—
616C4×C5—21no—
617C4×C5—21no—
618C4×C5—42no—
619C4×C5—42no—
620C4×C5—42no—
621C4×C5#52512yes—
622C4×C5C2×#13712yes—
623C4×C5C2×#13712yes—
624C4×C5C22×#4112yes—
625Dic5—28no—
626Dic5—44no—
627C24C2×C22⋊D511yescharacteristic
628#41—28no—
629#41—44no—
630#41—44no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—58no—
634C2×Q8—54no—
635C2×Q8—108no—
636C2×Q8—108no—
637C2×Q8—108no—
638C2×Q8—108no—
639C2×Q8—108no—
640C2×Q8—104no—
641C2×Q8—102no—
642C2×Q8—102no—
643C2×Q8—102no—
644C2×Q8C23×D512yes—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4C23×D512yes—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—42no—
657C22×C4—108no—
658C22×C4—102no—
659C22×C4—102no—
660C22×C4—102no—
661C22×C4—102no—
662C22×C4—102no—
663C22×C4—102no—
664C22×C4—204no—
665C22×C4C2×C22⋊D511yescharacteristic
666C22×C4C2×C22⋊D511yescharacteristic
667C22×C4C2×C22⋊D511yescharacteristic
668C22×C4C2×C22⋊D511yescharacteristic
669C22×C4C2×C22⋊D511yescharacteristic
670C22×C4C2×C22⋊D511yescharacteristic
671C22×C4C2×C22⋊D511yescharacteristic
672C22×C4C2×C22⋊D511yescharacteristic
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×C4C23×D511yescharacteristic
681C22×C4C23×D511yescharacteristic
682C22×C4C23×D511yescharacteristic
683Q16—1016no—
684SD16—1016no—
685M16—108no—
686C2×C8—58no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—54no—
698C4⋊C4—102no—
699C4⋊C4—102no—
700C4⋊C4—102no—
701C4⋊C4—104no—
702C4⋊C4—104no—
703C4⋊C4—104no—
704C4⋊C4—104no—
705C4⋊C4C23×D512yes—
706C4⋊C4C23×D512yes—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—104no—
720C42—104no—
721C42—104no—
722C42—104no—
723C42C2×C22⋊D511yescharacteristic
724C42C2×C22⋊D511yescharacteristic
725C42C2×C22⋊D511yescharacteristic
726C42C2×C22⋊D511yescharacteristic
727C42C2×C22⋊D511yescharacteristic
728C42C2×C22⋊D511yescharacteristic
729C42C2×C22⋊D511yescharacteristic
730C42C2×C22⋊D511yescharacteristic
731C42C2×C22⋊D511yescharacteristic
732C42C2×C22⋊D511yescharacteristic
733C42C2×C22⋊D511yescharacteristic
734C42C2×C22⋊D511yescharacteristic
735C42C23×D511yescharacteristic
736C42C23×D511yescharacteristic
737C42C23×D511yescharacteristic
738C42C23×D511yescharacteristic
739C2×C5—22no—
740C2×C5—22no—
741C2×C5—22no—
742C2×C5—82no—
743C2×C5C2×#52511yescharacteristic
744C2×C5C22×#13711yescharacteristic
745C2×C5C2×#57511yescharacteristic
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23C22×C22⋊D511yescharacteristic
751C23C22×C22⋊D511yescharacteristic
752C23C22×C22⋊D511yescharacteristic
753Q8—24no—
754Q8—42no—
755Q8—42no—
756Q8—58no—
757Q8—108no—
758Q8—108no—
759Q8—108no—
760Q8—104no—
761D4—24no—
762D4—42no—
763D4—44no—
764D4—44no—
765D4—44no—
766D4—42no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—108no—
790C2×C4—108no—
791C2×C4—108no—
792C2×C4—104no—
793C2×C4—104no—
794C2×C4—204no—
795C2×C4—204no—
796C2×C4—204no—
797C2×C4#409714yescomplemented
798C2×C4D5×#4114yes—
799C2×C4C22×C22⋊D511yescharacteristic
800C2×C4C22×C22⋊D511yescharacteristic
801C2×C4C22×C22⋊D511yescharacteristic
802C2×C4C22×C22⋊D511yescharacteristic
803C2×C4C22×C22⋊D511yescharacteristic
804C2×C4C22×C22⋊D511yescharacteristic
805C2×C4C22×C22⋊D511yescharacteristic
806C2×C4C22×C22⋊D511yescharacteristic
807C2×C4C22×C22⋊D511yescharacteristic
808C2×C4C22×C22⋊D511yescharacteristic
809C2×C4C22×C22⋊D511yescharacteristic
810C2×C4C24×D511yescharacteristic
811C8—108no—
812C5#6056011yescharacteristic, complemented, Sylow
813C22—28no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22#6615612yes—
824C22C2×#409712yes—
825C22#6616212yes—
826C22C23×C22⋊D511yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—108no—
839C4—204no—
840C4C2×#409712yes—
841C4C2×#409712yes—
842C4#6616212yes—
843C4C2×D5×#4112yes—
844C2—22no—
845C2—22no—
846C2—22no—
847C2—82no—
848C2C2×#6615611yescharacteristic
849C2C22×#409711yescharacteristic
850C2C2×#6616211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
Fitting, prime radicalC5×#3444C2
socleC22×C5C23×D4
hypercenter#3444D5
hypocenterC5#60560
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic10C2semidirect
3. #10615100C2semidirect
4. #10615099C2semidirect
5. #10615098C2semidirect
6. #10615047C2semidirect
7. #10615046C2semidirect
8. #10615045C2semidirect
9. #10614884C2semidirect
10. #10614883C2semidirect
11. #10614664C2semidirect
12. #10614645C2semidirect
13. C4×#4097C2semidirect
14. #10613780C2semidirect
53. #65383C22semidirect
54. #65380C22semidirect
55. #65379C22semidirect
56. #65364C22semidirect
57. #65352C22semidirect
58. #65343C22semidirect
67. #65319C22semidirect
68. C4×#689C22semidirect
69. #65307C22semidirect
70. C4×#687C22semidirect
278. C2×Dic10#41semidirect
438. C2×C4×C5#137semidirect
797. C2×C4#4097semidirect
812. C5#60560semidirect

Maximal subgroups

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

subgroupindex
C5×#34442
C22×C4×Dic102
#106151002
#106150992
#106150982
#106150472
#106150462
#106150452
#106148842
#106148832
#106146642
#106146452
C4×#40972
#106137802
#605605