Finite Group Databasebeta

← C2×#10613022 #12977707

Subgroups — C2×#10613022 #12977707

Order 1280.

2374 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65945C211yesmaximal, characteristic, complemented
2C2×#65841C211yesmaximal, characteristic, complemented
3C2×C5×#480C211yesmaximal, characteristic, complemented
4C2×#65327C211yesmaximal, characteristic, complemented
5C22×#3939C211yesmaximal, characteristic, complemented
6#10613022C2116yesmaximal, direct product factor
7C2×#65179C211yesmaximal, characteristic, complemented
8C2×#65171C211yesmaximal, characteristic, complemented
9C2×D5×#107C211yesmaximal, characteristic, complemented
10C2×#65163C211yesmaximal, characteristic, complemented
11C2×#65063C211yesmaximal, characteristic, complemented
12C2×#65064C211yesmaximal, characteristic, complemented
13C2×#65048C211yesmaximal, characteristic, complemented
14C2×#65045C211yesmaximal, characteristic, complemented
15C2×#65014C211yesmaximal, characteristic, complemented
16C2×#65025C211yesmaximal, characteristic, complemented
17C22×#711—21no—
18C22×#709—21no—
19C2×C5×#121C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C2×#4084C2211yescharacteristic
22C2×#4081—21no—
23C2×D4×Dic5C2211yescharacteristic
24C22×#686C2211yescharacteristic
25C2×#4076C2211yescharacteristic
26C2×#4075—21no—
27C2×C4×C22⋊D5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C23×#168C2211yescharacteristic
30C22×C8×D5C2211yescharacteristic
31#65945—24no—
32#65945C2218yescomplemented
33C2×#4042—21no—
34#65841—24no—
35#65841C2218yescomplemented
36C2×#4041C2211yescharacteristic
37C2×#4040—21no—
38C2×#4039C2211yescharacteristic
39C2×D5×C4⋊C4C2211yescharacteristic
40C2×D5×C4⋊C4C2211yescharacteristic
41C2×#4034C2211yescharacteristic
42C2×#4034C2211yescharacteristic
43C2×#4029—21no—
44C2×#4024—21no—
45C5×#480C2218yescomplemented
46C2×C5×#107C2211yescharacteristic
47C2×C5×#107C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3953C2211yescharacteristic
53C2×#3953C2211yescharacteristic
54C2×#3952C2211yescharacteristic
55C2×#3950C2211yescharacteristic
56C2×#3950C2211yescharacteristic
57C2×#3946C2211yescharacteristic
58C2×C8×Dic5C2211yescharacteristic
59#65327C2218yescomplemented
60C2×#3941C2211yescharacteristic
61C2×#3939C2211yescharacteristic
62C2×#3939C2211yescharacteristic
63C2×#3939C2211yescharacteristic
64C2×#3939C2211yescharacteristic
65C2×#3939C2211yescharacteristic
66C2×#3939C2218yescomplemented
67#65179C2218yescomplemented
68#65171C2218yescomplemented
69D5×#107C2218yescomplemented
70#65163C2218yescomplemented
71#65064C2218yescomplemented
72#65063C2218yescomplemented
73#65048C2218yescomplemented
74#65045C2218yescomplemented
75#65025C2218yescomplemented
76#65014C2218yescomplemented
77C2×#3334—51nomaximal, Sylow
78C22×C5×D4—21no—
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C22×C22⋊D5D411yescharacteristic
85C23×Dic5—21no—
86C23×Dic5—21no—
87C2×#711—28no—
88C2×#711—48no—
89C2×#709—28no—
90C2×#709—48no—
91C22×D20—21no—
92C22×D20C2311yescharacteristic
93C22×C4×D5—21no—
94C22×C4×D5—21no—
95C22×C4×D5—21no—
96C22×C4×D5C2311yescharacteristic
97C22×Dic10—21no—
98C22×Dic10—21no—
99C22×C5×C8C2311yescharacteristic
100C22×C5×C8C2311yescharacteristic
101C5×#121—22no—
102C5×#121C2314yes—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—22no—
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C4⋊C4C2314yes—
109C2×C5×C22⋊C4—21no—
110C2×C22⋊Dic5—21no—
111C2×C22⋊Dic5—21no—
112C2×C22⋊Dic5D411yescharacteristic
113#4084—22no—
114#4084C2314yes—
115#4081—28no—
116D4×Dic5—22no—
117D4×Dic5C2314yes—
118C2×#686—24no—
119C2×#686C2314yes—
120#4076—22no—
121#4076C2314yes—
122#4075—28no—
123C4×C22⋊D5D414yes—
124C4×C22⋊D5C2314yes—
125C2×#685—21no—
126C2×#685—21no—
127C2×#685—21no—
128C2×#685D411yescharacteristic
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5—22no—
131C2×C4⋊Dic5C2314yes—
132C2×C4⋊Dic5C2311yescharacteristic
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2311yescharacteristic
135C2×#683—21no—
136C2×#683—21no—
137C2×#683—21no—
138C2×#683—21no—
139C2×#683D411yescharacteristic
140C2×C4×Dic5C2311yescharacteristic
141C22×#168—24no—
142C22×#168C2314yes—
143C22×#168C2311yescharacteristic
144C22×#168C2311yescharacteristic
145C2×C8×D5—24no—
146C2×C8×D5C2314yes—
147#4042—28no—
148#4041—22no—
149#4041C2314yes—
150#4040—28no—
151#4039—22no—
152#4039C2314yes—
153D5×C4⋊C4—22no—
154D5×C4⋊C4—22no—
155D5×C4⋊C4C2314yes—
156D5×C4⋊C4C2314yes—
157#4034—22no—
158#4034—22no—
159#4034C2314yes—
160#4034C2314yes—
161#4029—28no—
162#4024—28no—
163C5×#107C2314yes—
164C5×#107C2314yes—
165C5×#102C2314yes—
166C5×#102C2314yes—
167C5×C22⋊C8C2314yes—
168#3964C2314yes—
169#3953C2314yes—
170#3953C2314yes—
171#3952C2314yes—
172#3950C2314yes—
173#3950C2314yes—
174#3946C2314yes—
175C8×Dic5C2314yes—
176#3941C2314yes—
177#3939C2314yes—
178#3939C2314yes—
179#3939C2314yes—
180#3939C2314yes—
181#3939C2314yes—
182C2×#547—51no—
183C2×#547—51no—
184#3334—516no—
185C2×#500—51no—
186C2×#480—51no—
187C2×#480—51no—
188C2×#480—51no—
189C2×#480D511yescharacteristic, complemented
190C2×#474—51no—
191C2×#474—51no—
192C2×#466—51no—
193C2×#466—51no—
194C2×C4×D8—51no—
195C2×C8×D4—51no—
196C22×#107—51no—
197C22×#107—51no—
198C24×C5—21no—
199C24×C5C2×D411yescharacteristic
200C23×D5—21no—
201C23×D5C2×D411yescharacteristic
202C2×C5×D4—24no—
203C2×C5×D4—21no—
204C2×C5×D4—22no—
205C2×C5×D4—22no—
206C2×C5×D4—44no—
207C2×C5×D4C2412yes—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—24no—
214C22×C4×C5—44no—
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D412yes—
217C22×C4×C5C2412yes—
218C22×C4×C5C2411yescharacteristic
219C2×C22⋊D5—24no—
220C2×C22⋊D5—24no—
221C2×C22⋊D5—44no—
222C2×C22⋊D5—44no—
223C2×C22⋊D5D818yescomplemented
224C2×C22⋊D5C2×D414yes—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—24no—
229C22×Dic5—24no—
230C22×Dic5—44no—
231C22×Dic5—44no—
232C22×Dic5C2×D411yescharacteristic
233C22×Dic5C2×D411yescharacteristic
234C22×Dic5C2×D411yescharacteristic
235#711—432no—
236#709—432no—
237C2×D20—22no—
238C2×D20—22no—
239C2×D20—24no—
240C2×D20—21no—
241C2×D20—44no—
242C2×D20C2412yes—
243C2×C4×D5—22no—
244C2×C4×D5—22no—
245C2×C4×D5—24no—
246C2×C4×D5—24no—
247C2×C4×D5—24no—
248C2×C4×D5—44no—
249C2×C4×D5—44no—
250C2×C4×D5—44no—
251C2×C4×D5C2×D412yes—
252C2×C4×D5C2412yes—
253C2×Dic10—24no—
254C2×Dic10—24no—
255C2×Dic10—44no—
256C2×Dic10—44no—
257C2×C5×C8—22no—
258C2×C5×C8—22no—
259C2×C5×C8C2412yes—
260C2×C5×C8C2412yes—
261C5×C4⋊C4—21no—
262C5×C4⋊C4—21no—
263C5×C4⋊C4—24no—
264C5×C4⋊C4—21no—
265C5×C4⋊C4C2412yes—
266C5×C4⋊C4C2412yes—
267C5×C4⋊C4C2412yes—
268C5×C22⋊C4—24no—
269C22⋊Dic5—24no—
270C22⋊Dic5—24no—
271C22⋊Dic5C2×D414yes—
272#686—28no—
273#685—24no—
274#685—24no—
275#685—24no—
276#685C2×D414yes—
277C4⋊Dic5—24no—
278C4⋊Dic5—21no—
279C4⋊Dic5—21no—
280C4⋊Dic5—21no—
281C4⋊Dic5C2412yes—
282C4⋊Dic5C2412yes—
283C4⋊Dic5C2412yes—
284#683—24no—
285#683—24no—
286#683—24no—
287#683—24no—
288#683C2×D414yes—
289C4×Dic5C2×D412yes—
290C4×Dic5C2412yes—
291C2×#168—22no—
292C2×#168—28no—
293C2×#168#4114yescomplemented
294C2×#168C2412yes—
295C2×#168C2412yes—
296C8×D5—28no—
297C22×#41—101no—
298C22×#41—101no—
299C22×D8—51no—
300C23×C8—51no—
301C23×C8—51no—
302#547—58no—
303#547—58no—
304#547—104no—
305#547—104no—
306C2×C4⋊Q8—51no—
307C2×C4⋊Q8—51no—
308C2×#123—101no—
309C2×#123—101no—
310C2×#123—101no—
311C2×#123—101no—
312C2×C22⋊Q8—101no—
313C2×C22⋊Q8—101no—
314C2×#121—51no—
315C2×#121—51no—
316C2×#121—51no—
317C2×#121C2×D511yescharacteristic
318C2×C4×D4—51no—
319C2×C4×D4—51no—
320C2×C4×D4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4—51no—
324C22×C4⋊C4C2×D511yescharacteristic
325#500—58no—
326#480—58no—
327#480—58no—
328#480—58no—
329#480C2×D518yescomplemented
330#474—58no—
331#474—58no—
332#466—58no—
333#466—58no—
334C4×D8—58no—
335C8×D4—58no—
336C2×#107—51no—
337C2×#107—51no—
338C2×#107—58no—
339C2×#107—51no—
340C2×#107—51no—
341C2×#107—51no—
342C2×#107—51no—
343C2×#107—51no—
344C2×#107—58no—
345C2×#107C2×D511yescharacteristic
346C2×#107C2×D511yescharacteristic
347C2×C4⋊C8—51no—
348C2×#102—51no—
349C2×#102—51no—
350C2×#102—51no—
351C2×#102—51no—
352C2×#102C2×D511yescharacteristic
353C2×#102C2×D511yescharacteristic
354C2×C22⋊C8—51no—
355C2×C22⋊C8C2×D511yescharacteristic
356C2×C4×C8—51no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—42no—
361C23×C5—42no—
362C23×C5—42no—
363C23×C5C2×D814yes—
364C23×C5C22×D412yes—
365C23×C5C22×D411yescharacteristic
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—42no—
370C22×D5—42no—
371C22×D5—42no—
372C22×D5C2×D814yes—
373C22×D5C22×D412yes—
374C5×D4—22no—
375C5×D4—22no—
376C5×D4—48no—
377C5×D4—42no—
378C2×C4×C5—22no—
379C2×C4×C5—24no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—42no—
386C2×C4×C5—42no—
387C2×C4×C5—42no—
388C2×C4×C5—48no—
389C2×C4×C5C22×D412yes—
390C2×C4×C5C22×D411yescharacteristic
391C2×C4×C5C2×#4112yes—
392C2×C4×C52−1+412yes—
393C2×C4×C5C2511yescharacteristic
394C22⋊D5—48no—
395C22⋊D5—48no—
396C22⋊D5C2×D8116yescomplemented
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—42no—
403C2×Dic5—42no—
404C2×Dic5—42no—
405C2×Dic5—48no—
406C2×Dic5—48no—
407C2×Dic5C2×D814yes—
408C2×Dic5C22×D412yes—
409C2×Dic5C22×D412yes—
410C2×Dic5C22×D412yes—
411D20—22no—
412D20—22no—
413D20—48no—
414D20—42no—
415C4×D5—24no—
416C4×D5—22no—
417C4×D5—22no—
418C4×D5—48no—
419C4×D5—48no—
420C4×D5—48no—
421Dic10—48no—
422Dic10—48no—
423C5×C8—22no—
424C5×C8—22no—
425#168—22no—
426#168C2×#4114yescomplemented
427C2×#41—108no—
428C2×#41—108no—
429C2×#41—208no—
430C2×#41—208no—
431C22×Q8—101no—
432C22×Q8—101no—
433C22×D4—21no—
434C22×D4—51no—
435C22×D4—51no—
436C22×D4—101no—
437C22×D4—101no—
438C22×D4—101no—
439C22×D4C22×D511yescharacteristic
440C23×C4—21no—
441C23×C4—51no—
442C23×C4—101no—
443C23×C4—101no—
444C23×C4—101no—
445C23×C4—101no—
446C23×C4—101no—
447C23×C4C22×D511yescharacteristic
448C2×D8—54no—
449C2×D8—104no—
450C22×C8—51no—
451C22×C8—51no—
452C22×C8—54no—
453C22×C8—54no—
454C22×C8—104no—
455C22×C8—104no—
456C22×C8C22×D511yescharacteristic
457C22×C8C22×D511yescharacteristic
458C4⋊Q8—54no—
459C4⋊Q8—54no—
460C4⋊Q8—102no—
461C4⋊Q8—102no—
462#123—108no—
463#123—108no—
464#123—108no—
465#123—108no—
466C22⋊Q8—108no—
467C22⋊Q8—108no—
468#121—22no—
469#121—54no—
470#121—54no—
471#121—54no—
472#121—102no—
473#121—102no—
474#121—102no—
475#121C22×D514yes—
476C4×D4—54no—
477C4×D4—54no—
478C4×D4—54no—
479C4×D4—54no—
480C4×D4—102no—
481C4×D4—102no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—51no—
485C2×C4⋊C4—51no—
486C2×C4⋊C4—51no—
487C2×C4⋊C4—51no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—102no—
492C2×C4⋊C4—102no—
493C2×C4⋊C4—101no—
494C2×C4⋊C4—101no—
495C2×C4⋊C4—101no—
496C2×C4⋊C4—101no—
497C2×C4⋊C4—101no—
498C2×C4⋊C4—102no—
499C2×C4⋊C4C22×D511yescharacteristic
500C2×C4⋊C4C22×D511yescharacteristic
501C2×C4⋊C4C22×D511yescharacteristic
502C2×C4⋊C4C22×D514yes—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—51no—
505C2×C22⋊C4—51no—
506C2×C22⋊C4—101no—
507C2×C22⋊C4—101no—
508C2×C22⋊C4—101no—
509C2×C22⋊C4—101no—
510C2×C22⋊C4—101no—
511C2×C42—51no—
512#107—54no—
513#107—54no—
514#107—54no—
515#107—54no—
516#107—54no—
517#107—54no—
518#107—54no—
519#107C22×D514yes—
520#107C22×D514yes—
521C4⋊C8—54no—
522#102—54no—
523#102—54no—
524#102—54no—
525#102—54no—
526#102C22×D514yes—
527#102C22×D514yes—
528C22⋊C8—54no—
529C22⋊C8C22×D514yes—
530C4×C8—54no—
531C22×C5—28no—
532C22×C5—22no—
533C22×C5—22no—
534C22×C5—42no—
535C22×C5—42no—
536C22×C5—42no—
537C22×C5—84no—
538C22×C5#54712yes—
539C22×C5C22×D814yes—
540C22×C5C22×D812yes—
541C22×C5#57812yes—
542C22×C5C23×D411yescharacteristic
543C2×D5—28no—
544C2×D5—22no—
545C2×D5—22no—
546C2×D5—42no—
547C2×D5—42no—
548C2×D5—42no—
549C2×D5—84no—
550C2×D5C22×D814yes—
551C4×C5—22no—
552C4×C5—42no—
553C4×C5—42no—
554C4×C5—42no—
555C4×C5#54712yes—
556C4×C5C22×#4111yescharacteristic
557C4×C5C2×2−1+411yescharacteristic
558Dic5—22no—
559Dic5—22no—
560Dic5—42no—
561Dic5—42no—
562Dic5—42no—
563Dic5C22×D814yes—
564C24—21no—
565C24—51no—
566C24—101no—
567C24D4×D511yescharacteristic
568#41—2032no—
569#41—2032no—
570C2×Q8—104no—
571C2×Q8—104no—
572C2×Q8—204no—
573C2×Q8—204no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—44no—
579C2×D4—54no—
580C2×D4—58no—
581C2×D4—52no—
582C2×D4—104no—
583C2×D4—104no—
584C2×D4—104no—
585C2×D4—101no—
586C2×D4—102no—
587C2×D4—102no—
588C2×D4—204no—
589C2×D4—204no—
590C2×D4—204no—
591C2×D4C23×D512yes—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—44no—
599C22×C4—51no—
600C22×C4—51no—
601C22×C4—51no—
602C22×C4—52no—
603C22×C4—52no—
604C22×C4—104no—
605C22×C4—104no—
606C22×C4—104no—
607C22×C4—104no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—104no—
611C22×C4—101no—
612C22×C4—101no—
613C22×C4—101no—
614C22×C4—204no—
615C22×C4—204no—
616C22×C4—204no—
617C22×C4—204no—
618C22×C4—204no—
619C22×C4D4×D512yes—
620C22×C4D4×D511yescharacteristic
621C22×C4C23×D512yes—
622C22×C4C23×D511yescharacteristic
623D8—108no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—54no—
627C2×C8—52no—
628C2×C8—52no—
629C2×C8—108no—
630C2×C8—108no—
631C2×C8—102no—
632C2×C8C23×D512yes—
633C2×C8C23×D512yes—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—24no—
637C4⋊C4—21no—
638C4⋊C4—54no—
639C4⋊C4—52no—
640C4⋊C4—52no—
641C4⋊C4—52no—
642C4⋊C4—104no—
643C4⋊C4—104no—
644C4⋊C4—104no—
645C4⋊C4—104no—
646C4⋊C4—101no—
647C4⋊C4—101no—
648C4⋊C4—101no—
649C4⋊C4—104no—
650C4⋊C4C23×D512yes—
651C4⋊C4C23×D512yes—
652C4⋊C4C23×D512yes—
653C22⋊C4—24no—
654C22⋊C4—54no—
655C22⋊C4—54no—
656C22⋊C4—104no—
657C22⋊C4—104no—
658C22⋊C4—104no—
659C22⋊C4—104no—
660C22⋊C4—104no—
661C42—52no—
662C42—52no—
663C2×C5—24no—
664C2×C5—82no—
665C2×C5#333414yescomplemented
666C2×C5C2×#54711yescharacteristic
667C2×C5C23×D811yescharacteristic
668C2×C5C2×#57811yescharacteristic
669D5—24no—
670D5—82no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—54no—
678C23—52no—
679C23—102no—
680C23—102no—
681C23—102no—
682C23—202no—
683C23—202no—
684C23—202no—
685C23D5×D814yes—
686C23C2×D4×D512yes—
687C23C2×D4×D511yescharacteristic
688Q8—208no—
689Q8—208no—
690D4—22no—
691D4—22no—
692D4—48no—
693D4—42no—
694D4—516no—
695D4—102no—
696D4—102no—
697D4—208no—
698D4—208no—
699D4—208no—
700D4—202no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—48no—
711C2×C4—42no—
712C2×C4—54no—
713C2×C4—52no—
714C2×C4—52no—
715C2×C4—52no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—104no—
719C2×C4—102no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—208no—
725C2×C4—208no—
726C2×C4—208no—
727C2×C4—208no—
728C2×C4—202no—
729C2×C4—202no—
730C2×C4—202no—
731C2×C4—208no—
732C2×C4C2×D4×D512yes—
733C2×C4C2×D4×D511yescharacteristic
734C2×C4D5×#4112yes—
735C2×C4#415012yes—
736C2×C4C24×D511yescharacteristic
737C8—22no—
738C8—22no—
739C8—54no—
740C8—102no—
741C5C2×#333411yescharacteristic, complemented, Sylow
742C22—28no—
743C22—22no—
744C22—22no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—54no—
749C22—84no—
750C22—108no—
751C22—102no—
752C22—102no—
753C22—202no—
754C22—202no—
755C22—202no—
756C22—404no—
757C22#6598912yes—
758C22C2×D5×D814yes—
759C22C2×D5×D812yes—
760C22#6611312yes—
761C22C22×D4×D511yescharacteristic
762C4—22no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—54no—
767C4—102no—
768C4—102no—
769C4—202no—
770C4—202no—
771C4—202no—
772C4#6598912yes—
773C4C2×D5×#4111yescharacteristic
774C4C2×#415011yescharacteristic
775C2—24no—
776C2—82no—
777C2—104no—
778C2—402no—
779C2#1061302214yesdirect product factor
780C2C2×#6598911yescharacteristic
781C2C22×D5×D811yescharacteristic
782C2C2×#6611311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#480C2
socleC23×C5C22×D4
hypercenterC2×#480D5
hypocenterC5C2×#3334
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#65945C2semidirect
2. C2×#65841C2semidirect
3. C2×C5×#480C2semidirect
4. C2×#65327C2semidirect
5. C22×#3939C2semidirect
6. #10613022C2direct (N × H)
7. C2×#65179C2semidirect
8. C2×#65171C2semidirect
9. C2×D5×#107C2semidirect
10. C2×#65163C2semidirect
11. C2×#65063C2semidirect
12. C2×#65064C2semidirect
13. C2×#65048C2semidirect
14. C2×#65045C2semidirect
15. C2×#65014C2semidirect
16. C2×#65025C2semidirect
32. #65945C22semidirect
35. #65841C22semidirect
45. C5×#480C22semidirect
59. #65327C22semidirect
66. C2×#3939C22semidirect
67. #65179C22semidirect
68. #65171C22semidirect
69. D5×#107C22semidirect
70. #65163C22semidirect
71. #65064C22semidirect
72. #65063C22semidirect
73. #65048C22semidirect
74. #65045C22semidirect
75. #65025C22semidirect
76. #65014C22semidirect
189. C2×#480D5semidirect
223. C2×C22⋊D5D8semidirect
293. C2×#168#41semidirect
329. #480C2×D5semidirect
396. C22⋊D5C2×D8semidirect
426. #168C2×#41semidirect
665. C2×C5#3334semidirect
741. C5C2×#3334semidirect
779. C2#10613022direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659452
C2×#658412
C2×C5×#4802
C2×#653272
C22×#39392
#106130222
C2×#651792
C2×#651712
C2×D5×#1072
C2×#651632
C2×#650632
C2×#650642
C2×#650482
C2×#650452
C2×#650142
C2×#650252
C2×#33345