Finite Group Databasebeta

← #12971393

Subgroups — #12971393

Order 1280.

1800 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#533C211yesmaximal, characteristic, complemented
2#10617581C211yesmaximal, characteristic
3#10615102C212yesmaximal, complemented
4#10615091C214yesmaximal, complemented
5#10615090C212yesmaximal, complemented
6#10615080C214yesmaximal, complemented
7#10615070C212yesmaximal, complemented
8#10615065C212yesmaximal, complemented
9#10614955C211yesmaximal, characteristic, complemented
10#10614954C211yesmaximal, characteristic, complemented
11#10614947C211yesmaximal, characteristic, complemented
12#10614946C211yesmaximal, characteristic, complemented
13#10614749C214yesmaximal, complemented
14#10613946C214yesmaximal, complemented
15C2×#65214C211yesmaximal, characteristic, complemented
16C5×#533—21no—
17C5×#533—21no—
18C5×#533—21no—
19C5×#533—21no—
20C5×#533C2212yes—
21C5×#533C2212yes—
22C5×#533C2212yes—
23C5×#533C2212yes—
24C2×C5×C4⋊Q8C2211yescharacteristic
25C2×C5×C4⋊Q8C2211yescharacteristic
26C2×C5×#125C2212yes—
27C2×C5×C22⋊Q8—21no—
28C2×C5×C22⋊Q8—21no—
29C2×C4×C5×Q8—21no—
30C2×C4×C5×Q8—21no—
31C2×C5×#117C2212yes—
32C22×C42×C5C2211yescharacteristic
33#66125—21no—
34#66125—21no—
35#66125C2212yes—
36#65813—21no—
37#65813—21no—
38#65813—21no—
39#65813—21no—
40#65813C2212yes—
41#65813C2212yes—
42#65811C2211yescharacteristic
43#65811C2211yescharacteristic
44#65811C2211yescharacteristic
45C4×#709—21no—
46C4×#709—21no—
47C4×#709C2212yes—
48#65804C2211yescharacteristic
49#65804C2211yescharacteristic
50#65804C2211yescharacteristic
51C2×C22⋊#168C2212yes—
52#65383C2214yescomplemented
53#65382C2212yescomplemented
54#65382C2212yescomplemented
55#65380C2214yescomplemented
56#65377C2212yescomplemented
57#65377C2212yescomplemented
58#65376C2214yescomplemented
59#65373C2214yescomplemented
60#65368C2212yescomplemented
61#65368C2212yescomplemented
62#65367C2212yescomplemented
63#65367C2212yescomplemented
64#65357C2218yescomplemented
65#65355C2218yescomplemented
66#65353C2218yescomplemented
67#65352C2218yescomplemented
68#65292C2218yes—
69#65291C2218yes—
70#65287C2218yes—
71#65285C2218yes—
72#65260C2214yes—
73#65259C2214yes—
74#65257C2214yes—
75#65256C2214yes—
76#65214C2212yes—
77#65214C2212yes—
78#65214C2211yescharacteristic
79#65214C2211yescharacteristic
80#65214C2212yes—
81C2×C4⋊#168C2212yes—
82C2×C4×#168C2212yes—
83#60846—51nomaximal, Sylow
84C22×C5×Q8—21no—
85C22×C5×Q8—21no—
86C23×C4×C5D411yescharacteristic
87C23×C4×C5D411yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C2×#709—21no—
90C2×#709—21no—
91C2×#709C2312yes—
92C5×C4⋊Q8—21no—
93C5×C4⋊Q8—21no—
94C5×C4⋊Q8—21no—
95C5×C4⋊Q8—21no—
96C5×C4⋊Q8C2312yes—
97C5×C4⋊Q8C2312yes—
98C5×C4⋊Q8C2312yes—
99C5×C4⋊Q8C2312yes—
100C5×#125—22no—
101C5×#125—22no—
102C5×#125C2314yes—
103C5×#125C2314yes—
104C5×C22⋊Q8—22no—
105C5×C22⋊Q8—22no—
106C5×C22⋊Q8—22no—
107C5×C22⋊Q8—22no—
108C5×C22⋊Q8—22no—
109C5×C22⋊Q8—22no—
110C5×C22⋊Q8—22no—
111C5×C22⋊Q8—22no—
112C4×C5×Q8—22no—
113C4×C5×Q8—22no—
114C4×C5×Q8—22no—
115C4×C5×Q8—22no—
116C4×C5×Q8—22no—
117C4×C5×Q8—22no—
118C4×C5×Q8—22no—
119C4×C5×Q8—22no—
120C5×#117—22no—
121C5×#117—22no—
122C5×#117C2314yes—
123C5×#117C2314yes—
124C2×C5×C4⋊C4—22no—
125C2×C5×C4⋊C4—22no—
126C2×C5×C4⋊C4—21no—
127C2×C5×C4⋊C4—21no—
128C2×C5×C4⋊C4C2312yes—
129C2×C5×C4⋊C4C2312yes—
130C2×C5×C22⋊C4—22no—
131C2×C42×C5—22no—
132C2×C42×C5D411yescharacteristic
133C2×C42×C5D411yescharacteristic
134C2×C42×C5D411yescharacteristic
135C2×C42×C5D411yescharacteristic
136C2×C42×C5D411yescharacteristic
137C2×C42×C5D411yescharacteristic
138C2×C42×C5C2311yescharacteristic
139C2×C42×C5C2311yescharacteristic
140C2×C42×C5C2311yescharacteristic
141C2×C42×C5C2311yescharacteristic
142C2×C42×C5C2311yescharacteristic
143C2×C42×C5C2311yescharacteristic
144#4099—22no—
145#4076—21no—
146#4076—21no—
147#4076—21no—
148#4076—21no—
149#4076C2312yes—
150#4076C2312yes—
151#4075—22no—
152#4075—22no—
153#4075—22no—
154C4×C22⋊D5—22no—
155C4×C22⋊D5—22no—
156C4×C22⋊D5—22no—
157C4×C22⋊D5—22no—
158C4×C22⋊D5—22no—
159C4×C22⋊D5—22no—
160#4072—21no—
161#4072—21no—
162#4072C2312yes—
163#4070—21no—
164#4070—21no—
165#4070—21no—
166#4070—21no—
167#4070C2312yes—
168#4070C2312yes—
169C22×#168C2314yes—
170#4022—22no—
171#4022—22no—
172#4021—21no—
173#4021—21no—
174#4021C2312yes—
175#4020C2311yescharacteristic
176C4×D20—21no—
177C4×D20—21no—
178C4×D20—21no—
179C4×D20—21no—
180C4×D20C2312yes—
181C4×D20C2312yes—
182#4018—22no—
183#4018—22no—
184#4018—22no—
185C42×D5—22no—
186#4016—21no—
187#4016—21no—
188#4016C2312yes—
189#4015C2311yescharacteristic
190#4015C2311yescharacteristic
191#4015C2311yescharacteristic
192C4×Dic10—21no—
193C4×Dic10—21no—
194C4×Dic10—21no—
195C4×Dic10—21no—
196C4×Dic10C2312yes—
197C4×Dic10C2312yes—
198C22⋊#168C2314yes—
199C22⋊#168C2312yes—
200C22⋊#168C2312yes—
201#3942C2318yes—
202#3942C2318yes—
203#3941C2318yes—
204#3941C2318yes—
205#3940C2318yes—
206#3940C2318yes—
207#3939C2318yes—
208#3939C2318yes—
209C4⋊#168C2314yes—
210C4⋊#168C2312yes—
211C4⋊#168C2312yes—
212C4×#168C2314yes—
213C4×#168C2312yes—
214C4×#168C2312yes—
215#3444—51no—
216C2×#533D511yescharacteristic, complemented
217#3233—54no—
218#3232—54no—
219#3231—52no—
220#3230—51no—
221#3229—51no—
222#3228—52no—
223#3227—51no—
224#3226—51no—
225#3160—52no—
226#3131—52no—
227#3091—54no—
228#3076—54no—
229C2×#431—51no—
230C24×C5C2×D411yescharacteristic
231C2×C5×Q8—22no—
232C2×C5×Q8—22no—
233C2×C5×Q8—22no—
234C2×C5×Q8—22no—
235C2×C5×Q8—44no—
236C2×C5×Q8—44no—
237C22×C4×C5—24no—
238C22×C4×C5—24no—
239C22×C4×C5—22no—
240C22×C4×C5—22no—
241C22×C4×C5—42no—
242C22×C4×C5C2×D411yescharacteristic
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×C5C2411yescharacteristic
258C22×C4×C5C2411yescharacteristic
259C22×C4×C5C2411yescharacteristic
260C2×C22⋊D5—22no—
261C2×C22⋊D5—22no—
262C2×C22⋊D5—22no—
263#709—28no—
264#709—44no—
265#709—44no—
266C2×D20—21no—
267C2×D20—21no—
268C2×D20C2412yes—
269C2×C4×D5—22no—
270C2×C4×D5—22no—
271C2×C4×D5—22no—
272C2×Dic10—21no—
273C2×Dic10—21no—
274C2×Dic10C2412yes—
275C5×C4⋊C4—24no—
276C5×C4⋊C4—24no—
277C5×C4⋊C4—24no—
278C5×C4⋊C4—24no—
279C5×C4⋊C4—22no—
280C5×C4⋊C4—22no—
281C5×C4⋊C4—22no—
282C5×C4⋊C4—22no—
283C5×C4⋊C4—22no—
284C5×C4⋊C4—22no—
285C5×C4⋊C4C2414yes—
286C5×C4⋊C4C2414yes—
287C5×C22⋊C4—24no—
288C5×C22⋊C4—24no—
289C42×C5—24no—
290C42×C5—24no—
291C42×C5C2×D411yescharacteristic
292C42×C5C2×D411yescharacteristic
293C42×C5C2×D411yescharacteristic
294C42×C5C2×D411yescharacteristic
295C42×C5C2×D411yescharacteristic
296C42×C5C2×D411yescharacteristic
297C42×C5C2×D411yescharacteristic
298C42×C5C2×D411yescharacteristic
299C42×C5C2×D411yescharacteristic
300C42×C5C2×D411yescharacteristic
301C42×C5C2×D411yescharacteristic
302C42×C5C2×D411yescharacteristic
303C42×C5C2411yescharacteristic
304C42×C5C2411yescharacteristic
305C42×C5C2411yescharacteristic
306C42×C5C2411yescharacteristic
307C22⋊Dic5—22no—
308C22⋊Dic5—22no—
309C22⋊Dic5—22no—
310#685—22no—
311#685—22no—
312#685—22no—
313#685—22no—
314#685—22no—
315#685—22no—
316C4⋊Dic5—21no—
317C4⋊Dic5—21no—
318C4⋊Dic5—21no—
319C4⋊Dic5—21no—
320C4⋊Dic5C2412yes—
321C4⋊Dic5C2412yes—
322#683—22no—
323#683—22no—
324#683—22no—
325#683—22no—
326#683—22no—
327#683—22no—
328C4×Dic5—22no—
329C4×Dic5—22no—
330C4×Dic5—22no—
331C2×#168—28no—
332C2×#168C2414yes—
333C2×#168C2414yes—
334#533—21no—
335#533—21no—
336#533—21no—
337#533—21no—
338#533—51no—
339#533—51no—
340#533—51no—
341#533C2×D512yes—
342#533C2×D512yes—
343#533C2×D512yes—
344#533C2×D512yes—
345#532—51no—
346#532—51no—
347#532—51no—
348C2×C4⋊Q8C2×D511yescharacteristic
349C2×C4⋊Q8C2×D511yescharacteristic
350#529—52no—
351#529—52no—
352#529—101no—
353#529—101no—
354#529—101no—
355#529—101no—
356C2×#125C2×D512yes—
357#525—52no—
358#525—101no—
359#525—101no—
360C2×C22⋊Q8—21no—
361C2×C22⋊Q8—21no—
362C4×#41—52no—
363C4×#41—101no—
364C4×#41—101no—
365C2×C4×Q8—21no—
366C2×C4×Q8—21no—
367C2×#117C2×D512yes—
368C22×C42C2×D511yescharacteristic
369#500—52no—
370#500—52no—
371#499—58no—
372#498—52no—
373#498—52no—
374#488—58no—
375#487—52no—
376#487—52no—
377#486—52no—
378#486—52no—
379#485—58no—
380#484—54no—
381#483—54no—
382#482—58no—
383#481—54no—
384#480—54no—
385#479—58no—
386#478—58no—
387#477—54no—
388#476—54no—
389#475—54no—
390#474—54no—
391#431—51no—
392#431—51no—
393#431—52no—
394#431—52no—
395#431—52no—
396#427—58no—
397C2×C4⋊C8—52no—
398#416—58no—
399C2×C22⋊C8—52no—
400C2×C4×C8—52no—
401C23×C5—22no—
402C23×C5—22no—
403C23×C5—41no—
404C23×C5C22×D411yescharacteristic
405C23×C5C22×D411yescharacteristic
406C23×C5C22×D411yescharacteristic
407C22×D5—22no—
408C5×Q8—44no—
409C5×Q8—44no—
410C5×Q8—44no—
411C5×Q8—44no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
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—24no—
426C2×C4×C5—24no—
427C2×C4×C5—41no—
428C2×C4×C5—41no—
429C2×C4×C5—41no—
430C2×C4×C5—44no—
431C2×C4×C5—44no—
432C2×C4×C5#13514yes—
433C2×C4×C5C22×D411yescharacteristic
434C2×C4×C5C22×D411yescharacteristic
435C2×C4×C5C22×D411yescharacteristic
436C2×C4×C5C22×D411yescharacteristic
437C2×C4×C5C22×D411yescharacteristic
438C2×C4×C5C22×D411yescharacteristic
439C2×C4×C5C22×D411yescharacteristic
440C2×C4×C5C22×D411yescharacteristic
441C2×C4×C5C22×D411yescharacteristic
442C2×C4×C5C22×D411yescharacteristic
443C2×C4×C5C22×D411yescharacteristic
444C2×C4×C52−1+414yes—
445C2×C4×C5C2511yescharacteristic
446C22⋊D5—44no—
447C22⋊D5—44no—
448C22⋊D5—44no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—22no—
452D20—24no—
453D20—42no—
454D20—42no—
455C4×D5—44no—
456C4×D5—44no—
457C4×D5—44no—
458Dic10—24no—
459Dic10—42no—
460Dic10—42no—
461#168—24no—
462#168—24no—
463C2×#41—52no—
464C2×#41—101no—
465C2×#41—101no—
466C22×Q8—21no—
467C22×Q8—21no—
468C23×C4C22⋊D511yescharacteristic
469C23×C4C22⋊D511yescharacteristic
470C23×C4C22×D511yescharacteristic
471C22×C8—54no—
472C4⋊Q8—21no—
473C4⋊Q8—21no—
474C4⋊Q8—21no—
475C4⋊Q8—21no—
476C4⋊Q8—51no—
477C4⋊Q8—51no—
478C4⋊Q8—51no—
479C4⋊Q8C22×D512yes—
480C4⋊Q8C22×D512yes—
481C4⋊Q8C22×D512yes—
482C4⋊Q8C22×D512yes—
483#127—51no—
484#126—102no—
485#126—102no—
486#125—22no—
487#125—22no—
488#125—52no—
489#125—101no—
490#125—101no—
491#125C22×D514yes—
492#125C22×D514yes—
493#124—52no—
494#124—101no—
495#124—101no—
496#123—102no—
497#123—102no—
498#123—102no—
499C22⋊Q8—22no—
500C22⋊Q8—22no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8—22no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—52no—
508C22⋊Q8—52no—
509C22⋊Q8—101no—
510C22⋊Q8—101no—
511C22⋊Q8—101no—
512C22⋊Q8—101no—
513#121—52no—
514#121—52no—
515#121—101no—
516#121—101no—
517#121—101no—
518#121—101no—
519#120—102no—
520C4×Q8—22no—
521C4×Q8—22no—
522C4×Q8—22no—
523C4×Q8—22no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—52no—
529C4×Q8—52no—
530C4×Q8—101no—
531C4×Q8—101no—
532C4×Q8—101no—
533C4×Q8—101no—
534C4×D4—52no—
535C4×D4—52no—
536C4×D4—102no—
537C4×D4—102no—
538C4×D4—102no—
539C4×D4—102no—
540C4×D4—102no—
541C4×D4—102no—
542C4×D4—101no—
543C4×D4—101no—
544C4×D4—101no—
545C4×D4—101no—
546#117—22no—
547#117—22no—
548#117—52no—
549#117—101no—
550#117—101no—
551#117—102no—
552#117—102no—
553#117—102no—
554#117C22×D514yes—
555#117C22×D514yes—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4C22×D512yes—
561C2×C4⋊C4C22×D512yes—
562C2×C22⋊C4—22no—
563C2×C42—22no—
564C2×C42—102no—
565C2×C42C22⋊D511yescharacteristic
566C2×C42C22⋊D511yescharacteristic
567C2×C42C22⋊D511yescharacteristic
568C2×C42C22⋊D511yescharacteristic
569C2×C42C22⋊D511yescharacteristic
570C2×C42C22⋊D511yescharacteristic
571C2×C42C22×D511yescharacteristic
572C2×C42C22×D511yescharacteristic
573C2×C42C22×D511yescharacteristic
574C2×C42C22×D511yescharacteristic
575C2×C42C22×D511yescharacteristic
576C2×C42C22×D511yescharacteristic
577#107—58no—
578#107—58no—
579#106—58no—
580#106—58no—
581C4⋊C8—52no—
582C4⋊C8—52no—
583C4⋊C8—54no—
584#103—58no—
585#103—58no—
586#102—58no—
587#102—58no—
588C22⋊C8—52no—
589C22⋊C8—52no—
590C22⋊C8—54no—
591C4×C8—52no—
592C4×C8—52no—
593C4×C8—54no—
594C22×C5—21no—
595C22×C5—21no—
596C22×C5—21no—
597C22×C5—21no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—21no—
601C22×C5—44no—
602C22×C5#53612yes—
603C22×C5C2×#13512yes—
604C22×C5C23×D411yescharacteristic
605C2×D5—42no—
606C2×D5—42no—
607C2×D5—42no—
608C4×C5—21no—
609C4×C5—21no—
610C4×C5—21no—
611C4×C5—21no—
612C4×C5—21no—
613C4×C5—21no—
614C4×C5—21no—
615C4×C5—44no—
616C4×C5—44no—
617C4×C5#53612yes—
618C4×C5C2×#13512yes—
619C4×C5C2×#13512yes—
620C4×C5#57512yes—
621C4×C5C2×2−1+412yes—
622Dic5—42no—
623Dic5—42no—
624Dic5—42no—
625C24C2×C22⋊D511yescharacteristic
626#41—108no—
627#41—204no—
628#41—204no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—22no—
633C2×Q8—44no—
634C2×Q8—44no—
635C2×Q8—52no—
636C2×Q8—101no—
637C2×Q8—101no—
638C2×D4—52no—
639C2×D4—102no—
640C2×D4—102no—
641C2×D4—102no—
642C2×D4—101no—
643C2×D4—101no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—42no—
649C22×C4—102no—
650C22×C4—102no—
651C22×C4—102no—
652C22×C4C2×C22⋊D511yescharacteristic
653C22×C4C2×C22⋊D511yescharacteristic
654C22×C4C2×C22⋊D511yescharacteristic
655C22×C4C2×C22⋊D511yescharacteristic
656C22×C4C2×C22⋊D511yescharacteristic
657C22×C4C2×C22⋊D511yescharacteristic
658C22×C4C2×C22⋊D511yescharacteristic
659C22×C4C2×C22⋊D511yescharacteristic
660C22×C4C2×C22⋊D511yescharacteristic
661C22×C4C2×C22⋊D511yescharacteristic
662C22×C4C2×C22⋊D511yescharacteristic
663C22×C4C2×C22⋊D511yescharacteristic
664C22×C4C2×C22⋊D511yescharacteristic
665C22×C4C2×C22⋊D511yescharacteristic
666C22×C4C2×C22⋊D511yescharacteristic
667C22×C4C23×D511yescharacteristic
668C22×C4C23×D511yescharacteristic
669C22×C4C23×D511yescharacteristic
670C2×C8—54no—
671C2×C8—54no—
672C2×C8—108no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—52no—
684C4⋊C4—52no—
685C4⋊C4—102no—
686C4⋊C4—102no—
687C4⋊C4—101no—
688C4⋊C4—101no—
689C4⋊C4—101no—
690C4⋊C4—101no—
691C4⋊C4—102no—
692C4⋊C4—102no—
693C4⋊C4—102no—
694C4⋊C4—102no—
695C4⋊C4C23×D514yes—
696C4⋊C4C23×D514yes—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—102no—
700C22⋊C4—102no—
701C22⋊C4—102no—
702C22⋊C4—102no—
703C22⋊C4—102no—
704C22⋊C4—102no—
705C22⋊C4—102no—
706C22⋊C4—102no—
707C22⋊C4—102no—
708C42—24no—
709C42—24no—
710C42—102no—
711C42—102no—
712C42—102no—
713C42C2×C22⋊D511yescharacteristic
714C42C2×C22⋊D511yescharacteristic
715C42C2×C22⋊D511yescharacteristic
716C42C2×C22⋊D511yescharacteristic
717C42C2×C22⋊D511yescharacteristic
718C42C2×C22⋊D511yescharacteristic
719C42C2×C22⋊D511yescharacteristic
720C42C2×C22⋊D511yescharacteristic
721C42C2×C22⋊D511yescharacteristic
722C42C2×C22⋊D511yescharacteristic
723C42C2×C22⋊D511yescharacteristic
724C42C2×C22⋊D511yescharacteristic
725C42C23×D511yescharacteristic
726C42C23×D511yescharacteristic
727C42C23×D511yescharacteristic
728C42C23×D511yescharacteristic
729C2×C5—22no—
730C2×C5—22no—
731C2×C5—41no—
732C2×C5C2×#53611yescharacteristic
733C2×C5C22×#13511yescharacteristic
734C2×C5C2×#57511yescharacteristic
735D5—82no—
736C23—22no—
737C23—22no—
738C23—41no—
739C23—102no—
740C23C22×C22⋊D511yescharacteristic
741C23C22×C22⋊D511yescharacteristic
742C23C22×C22⋊D511yescharacteristic
743Q8—44no—
744Q8—44no—
745Q8—44no—
746Q8—44no—
747Q8—104no—
748Q8—202no—
749Q8—202no—
750D4—104no—
751D4—204no—
752D4—204no—
753D4—204no—
754D4—202no—
755D4—202no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—102no—
777C2×C4—102no—
778C2×C4—102no—
779C2×C4—204no—
780C2×C4—204no—
781C2×C4—204no—
782C2×C4#409614yes—
783C2×C4#414714yes—
784C2×C4C22×C22⋊D511yescharacteristic
785C2×C4C22×C22⋊D511yescharacteristic
786C2×C4C22×C22⋊D511yescharacteristic
787C2×C4C22×C22⋊D511yescharacteristic
788C2×C4C22×C22⋊D511yescharacteristic
789C2×C4C22×C22⋊D511yescharacteristic
790C2×C4C22×C22⋊D511yescharacteristic
791C2×C4C22×C22⋊D511yescharacteristic
792C2×C4C22×C22⋊D511yescharacteristic
793C2×C4C22×C22⋊D511yescharacteristic
794C2×C4C22×C22⋊D511yescharacteristic
795C2×C4C24×D511yescharacteristic
796C8—104no—
797C8—104no—
798C5#6084611yescharacteristic, complemented, Sylow
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—44no—
807C22—202no—
808C22—202no—
809C22—202no—
810C22#6615012yes—
811C22C2×#409612yes—
812C22C23×C22⋊D511yescharacteristic
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—44no—
821C4—44no—
822C4—202no—
823C4—202no—
824C4—202no—
825C4#6615012yes—
826C4C2×#409612yes—
827C4C2×#409612yes—
828C4#6615612yes—
829C4C2×#414712yes—
830C2—22no—
831C2—22no—
832C2—41no—
833C2—402no—
834C2C2×#6615011yescharacteristic
835C2C22×#409611yescharacteristic
836C2C2×#6615611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#533C2
socleC22×C5C23×D4
prime radical#10617581C2
hypercenterC2×#533D5
hypocenterC5#60846
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C5×#533C2semidirect
3. #10615102C2semidirect
4. #10615091C2semidirect
5. #10615090C2semidirect
6. #10615080C2semidirect
7. #10615070C2semidirect
8. #10615065C2semidirect
9. #10614955C2semidirect
10. #10614954C2semidirect
11. #10614947C2semidirect
12. #10614946C2semidirect
13. #10614749C2semidirect
14. #10613946C2semidirect
15. C2×#65214C2semidirect
52. #65383C22semidirect
53. #65382C22semidirect
54. #65382C22semidirect
55. #65380C22semidirect
56. #65377C22semidirect
57. #65377C22semidirect
58. #65376C22semidirect
59. #65373C22semidirect
60. #65368C22semidirect
61. #65368C22semidirect
62. #65367C22semidirect
63. #65367C22semidirect
64. #65357C22semidirect
65. #65355C22semidirect
66. #65353C22semidirect
67. #65352C22semidirect
216. C2×#533D5semidirect
798. C5#60846semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5332
#106175812
#106151022
#106150912
#106150902
#106150802
#106150702
#106150652
#106149552
#106149542
#106149472
#106149462
#106147492
#106139462
C2×#652142
#608465