Finite Group Databasebeta

← C2×#10613107 #12967146

Subgroups — C2×#10613107 #12967146

Order 1280.

2234 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65942C211yesmaximal, characteristic
2C2×#65857C211yesmaximal, characteristic, complemented
3C2×C5×#482C211yesmaximal, characteristic, complemented
4C2×#65322C211yesmaximal, characteristic, complemented
5C2×#65285C211yesmaximal, characteristic, complemented
6#10613107C2116yesmaximal, direct product factor
7C2×#65173C211yesmaximal, characteristic, complemented
8C2×D5×#107C211yesmaximal, characteristic, complemented
9C2×#65150C211yesmaximal, characteristic, complemented
10C2×#65156C211yesmaximal, characteristic, complemented
11C2×#65073C211yesmaximal, characteristic, complemented
12C2×#65063C211yesmaximal, characteristic, complemented
13C2×#65060C211yesmaximal, characteristic, complemented
14C2×#65061C211yesmaximal, characteristic, complemented
15C2×#65016C211yesmaximal, characteristic, complemented
16C2×#65011C211yesmaximal, characteristic, complemented
17C22×#711C2211yescharacteristic
18C22×#709C2211yescharacteristic
19C2×C5×#121C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C2×#4085—21no—
22C2×#4084—21no—
23C2×#4084C2211yescharacteristic
24C22×C4⋊Dic5C2211yescharacteristic
25C2×#4070C2211yescharacteristic
26C22×#676C2211yescharacteristic
27C22×C8×D5C2211yescharacteristic
28#65942—24no—
29#65942C2218yes—
30#65857—24no—
31#65857C2218yescomplemented
32C2×#4043C2211yescharacteristic
33C2×#4038C2211yescharacteristic
34C2×#4038C2211yescharacteristic
35C2×D5×C4⋊C4C2211yescharacteristic
36C2×D5×C4⋊C4C2211yescharacteristic
37C2×D5×C4⋊C4C2211yescharacteristic
38C2×#4030—21no—
39C2×#4027—21no—
40C2×#4027—21no—
41C2×#4024—21no—
42C2×C4×D20—21no—
43C2×C4×Dic10—21no—
44C5×#482C2218yescomplemented
45C2×C5×#107C2211yescharacteristic
46C2×C5×#106C2211yescharacteristic
47C2×C5×#102C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×C5×C22⋊C8C2211yescharacteristic
50C2×#3964C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×C22⋊#168C2211yescharacteristic
53C2×#3952C2211yescharacteristic
54C2×#3952C2211yescharacteristic
55C2×#3950C2211yescharacteristic
56C2×#3950C2211yescharacteristic
57C2×#3948C2211yescharacteristic
58C2×#3948C2211yescharacteristic
59#65322C2218yescomplemented
60#65285C2218yescomplemented
61C2×#3942C2211yescharacteristic
62C2×#3942C2211yescharacteristic
63C2×#3940C2211yescharacteristic
64C2×#3939C2211yescharacteristic
65C2×#3939C2211yescharacteristic
66C2×#3939C2211yescharacteristic
67#65173C2218yescomplemented
68D5×#107C2218yescomplemented
69#65156C2218yescomplemented
70#65150C2218yescomplemented
71#65073C2218yescomplemented
72#65063C2218yescomplemented
73#65061C2218yescomplemented
74#65060C2218yescomplemented
75#65016C2218yescomplemented
76#65011C2218yescomplemented
77C2×#3098—51nomaximal, Sylow
78C22×C5×D4—21no—
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C22×C22⋊D5—21no—
83C22×C22⋊D5D411yescharacteristic
84C22×C22⋊D5D411yescharacteristic
85C23×Dic5—21no—
86C23×Dic5—21no—
87C2×#711—22no—
88C2×#711—24no—
89C2×#711—24no—
90C2×#711C2314yes—
91C2×#709—24no—
92C2×#709—24no—
93C2×#709D414yes—
94C2×#709C2314yes—
95C22×D20D411yescharacteristic
96C22×C4×D5—21no—
97C22×C4×D5—21no—
98C22×C4×D5—21no—
99C22×C4×D5C2311yescharacteristic
100C22×C4×D5C2311yescharacteristic
101C22×Dic10D411yescharacteristic
102C22×Dic10C2311yescharacteristic
103C22×C5×C8C2311yescharacteristic
104C22×C5×C8C2311yescharacteristic
105C5×#121—22no—
106C5×#121C2314yes—
107C5×#117—22no—
108C5×#117C2314yes—
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C22⋊C4—21no—
113C2×C5×C22⋊C4—21no—
114C2×C42×C5—21no—
115C2×C22⋊Dic5—21no—
116C2×C22⋊Dic5—21no—
117#4085—28no—
118#4084—28no—
119#4084—22no—
120#4084C2314yes—
121C2×#685—21no—
122C2×#685—21no—
123C2×#685—21no—
124C2×C4⋊Dic5—21no—
125C2×C4⋊Dic5—22no—
126C2×C4⋊Dic5—21no—
127C2×C4⋊Dic5C2314yes—
128C2×C4⋊Dic5C2311yescharacteristic
129C2×C4⋊Dic5C2311yescharacteristic
130C2×C4⋊Dic5C2311yescharacteristic
131#4070—22no—
132#4070C2314yes—
133C2×#683—21no—
134C2×#683—21no—
135C2×#683—21no—
136C2×#683—21no—
137C2×C4×Dic5—21no—
138C2×C4×Dic5—21no—
139C22×#168C2311yescharacteristic
140C22×#168C2311yescharacteristic
141C2×#676—24no—
142C2×#676C2314yes—
143C2×C8×D5—24no—
144C2×C8×D5C2314yes—
145#4043—22no—
146#4043C2314yes—
147#4038—22no—
148#4038—22no—
149#4038C2314yes—
150#4038C2314yes—
151D5×C4⋊C4—22no—
152D5×C4⋊C4—22no—
153D5×C4⋊C4—22no—
154D5×C4⋊C4C2314yes—
155D5×C4⋊C4C2314yes—
156D5×C4⋊C4C2314yes—
157#4030—28no—
158#4027—28no—
159#4027—28no—
160#4024—28no—
161C4×D20—28no—
162C4×Dic10—28no—
163C5×#107C2314yes—
164C5×#106C2314yes—
165C5×#102C2314yes—
166C5×#102C2314yes—
167C5×C22⋊C8C2314yes—
168#3964C2314yes—
169#3964C2314yes—
170C22⋊#168C2314yes—
171#3952C2314yes—
172#3952C2314yes—
173#3950C2314yes—
174#3950C2314yes—
175#3948C2314yes—
176#3948C2314yes—
177#3942C2314yes—
178#3942C2314yes—
179#3940C2314yes—
180#3939C2314yes—
181#3939C2314yes—
182#3939C2314yes—
183C2×#537—51no—
184C2×#520—51no—
185#3098—516no—
186C2×#484—51no—
187C2×#484—51no—
188C2×#485—51no—
189C2×#485—51no—
190C2×#482—51no—
191C2×#482D511yescharacteristic, complemented
192C2×#480—51no—
193C2×#480—51no—
194C2×#428—51no—
195C22×#107—51no—
196C2×#417—51no—
197C2×#416—51no—
198C2×#408—51no—
199C24×C5—21no—
200C24×C5C2×D411yescharacteristic
201C23×D5C2×D411yescharacteristic
202C23×D5C2×D411yescharacteristic
203C2×C5×D4—24no—
204C2×C5×D4—21no—
205C2×C5×D4—22no—
206C2×C5×D4—22no—
207C2×C5×D4—82no—
208C2×C5×D4C2412yes—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D412yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2411yescharacteristic
218C2×C22⋊D5—24no—
219C2×C22⋊D5—24no—
220C2×C22⋊D5—24no—
221C2×C22⋊D5—24no—
222C2×C22⋊D5—44no—
223C2×C22⋊D5—82no—
224C2×C22⋊D5C2×D414yes—
225C2×C22⋊D5C2×D414yes—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—24no—
231C22×Dic5—24no—
232C22×Dic5—44no—
233C22×Dic5—82no—
234C22×Dic5C2×D411yescharacteristic
235C22×Dic5C2×D411yescharacteristic
236#711—28no—
237#711—28no—
238#711—48no—
239#709—216no—
240#709—28no—
241#709—28no—
242C2×D20—24no—
243C2×D20C2×D414yes—
244C2×C4×D5—22no—
245C2×C4×D5—22no—
246C2×C4×D5—24no—
247C2×C4×D5—24no—
248C2×C4×D5—24no—
249C2×C4×D5—82no—
250C2×C4×D5—82no—
251C2×C4×D5—82no—
252C2×C4×D5C2×D412yes—
253C2×C4×D5C2×D412yes—
254C2×C4×D5#4114yes—
255C2×C4×D5#4114yes—
256C2×C4×D5C2412yes—
257C2×C4×D5C2412yes—
258C2×Dic10—24no—
259C2×Dic10—22no—
260C2×Dic10—22no—
261C2×Dic10—21no—
262C2×Dic10C2×D414yes—
263C2×Dic10C2412yes—
264C2×C5×C8—22no—
265C2×C5×C8—22no—
266C2×C5×C8C2412yes—
267C2×C5×C8C2412yes—
268C5×C4⋊C4—21no—
269C5×C4⋊C4—21no—
270C5×C4⋊C4—21no—
271C5×C4⋊C4C2412yes—
272C5×C4⋊C4C2412yes—
273C5×C4⋊C4C2412yes—
274C5×C22⋊C4—24no—
275C5×C22⋊C4—24no—
276C42×C5—24no—
277C22⋊Dic5—24no—
278C22⋊Dic5—24no—
279#685—24no—
280#685—24no—
281#685—24no—
282C4⋊Dic5—24no—
283C4⋊Dic5—21no—
284C4⋊Dic5—21no—
285C4⋊Dic5—21no—
286C4⋊Dic5—24no—
287C4⋊Dic5C2412yes—
288C4⋊Dic5C2412yes—
289C4⋊Dic5C2412yes—
290#683—24no—
291#683—24no—
292#683—24no—
293#683—24no—
294C4×Dic5—24no—
295C4×Dic5—24no—
296C2×#168—22no—
297C2×#168—22no—
298C2×#168C2412yes—
299C2×#168C2412yes—
300#676—28no—
301C8×D5—28no—
302C22×#41—51no—
303C22×#41—51no—
304C22×M16—51no—
305C23×C8—51no—
306#537—58no—
307#537—104no—
308C2×C22⋊Q8—51no—
309C2×C22⋊Q8—51no—
310C2×C22⋊Q8—101no—
311C2×#121—51no—
312C2×#121—101no—
313C2×#121—101no—
314C2×#121—101no—
315C2×#121C2×D511yescharacteristic
316#520—58no—
317#520—104no—
318C2×C4×Q8—101no—
319C2×C4×D4—101no—
320C2×C4×D4—101no—
321C2×C4×D4—101no—
322C2×#117—51no—
323C2×#117—51no—
324C2×#117C2×D511yescharacteristic
325C22×C4⋊C4—51no—
326C22×C4⋊C4—51no—
327C22×C4⋊C4—51no—
328C22×C4⋊C4—51no—
329#485—58no—
330#485—58no—
331#484—58no—
332#484—58no—
333#482—58no—
334#482C2×D518yescomplemented
335#480—58no—
336#480—58no—
337#428—58no—
338C2×#107—51no—
339C2×#107—51no—
340C2×#107—51no—
341C2×#107—51no—
342C2×#107—51no—
343C2×#107—58no—
344C2×#107C2×D511yescharacteristic
345C2×#106—51no—
346C2×#106C2×D511yescharacteristic
347#417—58no—
348#416—58no—
349C2×#103—51no—
350C2×#103—51no—
351C2×#103—51no—
352C2×#103—51no—
353C2×#102—51no—
354C2×#102—51no—
355C2×#102C2×D511yescharacteristic
356C2×#102C2×D511yescharacteristic
357#408—58no—
358C2×C22⋊C8—51no—
359C2×C22⋊C8—51no—
360C2×C22⋊C8—51no—
361C2×C22⋊C8C2×D511yescharacteristic
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—42no—
367C23×C5—42no—
368C23×C5—42no—
369C23×C5C22×D412yes—
370C23×C5C22×D411yescharacteristic
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5#12314yes—
377C22×D5C22×D412yes—
378C22×D5C22×D412yes—
379C5×D4—22no—
380C5×D4—22no—
381C5×D4—42no—
382C5×D4—84no—
383C2×C4×C5—22no—
384C2×C4×C5—24no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—42no—
391C2×C4×C5—42no—
392C2×C4×C5—42no—
393C2×C4×C5C22×D412yes—
394C2×C4×C5C22×D411yescharacteristic
395C2×C4×C5C2×#4112yes—
396C2×C4×C5C2×#4112yes—
397C2×C4×C5C2511yescharacteristic
398C22⋊D5—28no—
399C22⋊D5—28no—
400C22⋊D5—48no—
401C22⋊D5—84no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—42no—
408C2×Dic5—42no—
409C2×Dic5—42no—
410C2×Dic5—42no—
411C2×Dic5—48no—
412C2×Dic5—84no—
413C2×Dic5#12314yes—
414C2×Dic5C22×D412yes—
415C2×Dic5C22×D412yes—
416D20—28no—
417C4×D5—24no—
418C4×D5—22no—
419C4×D5—22no—
420C4×D5—84no—
421C4×D5—84no—
422C4×D5—84no—
423C4×D5#12318yes—
424C4×D5C2×#4114yes—
425C4×D5C2×#4114yes—
426Dic10—28no—
427Dic10—22no—
428Dic10—22no—
429Dic10—42no—
430C5×C8—22no—
431C5×C8—22no—
432#168—22no—
433#168—22no—
434C2×#41—54no—
435C2×#41—54no—
436C2×#41—54no—
437C2×#41—104no—
438C2×#41—104no—
439C2×#41—102no—
440C2×#41—104no—
441C2×#41—104no—
442C22×Q8—51no—
443C22×Q8—51no—
444C22×D4—21no—
445C22×D4—51no—
446C22×D4—51no—
447C22×D4—51no—
448C22×D4—101no—
449C22×D4—101no—
450C22×D4C22×D511yescharacteristic
451C23×C4—51no—
452C23×C4—51no—
453C23×C4—101no—
454C23×C4—101no—
455C23×C4—101no—
456C23×C4—101no—
457C23×C4—101no—
458C23×C4C22×D511yescharacteristic
459C2×M16—54no—
460C2×M16—104no—
461C22×C8—51no—
462C22×C8—51no—
463C22×C8—54no—
464C22×C8—104no—
465C22×C8C22×D511yescharacteristic
466C22×C8C22×D511yescharacteristic
467C22⋊Q8—54no—
468C22⋊Q8—54no—
469C22⋊Q8—108no—
470C22⋊Q8—102no—
471C22⋊Q8—102no—
472#121—22no—
473#121—54no—
474#121—108no—
475#121—102no—
476#121—108no—
477#121—108no—
478#121C22×D514yes—
479C4×Q8—108no—
480C4×D4—108no—
481C4×D4—108no—
482C4×D4—108no—
483#117—22no—
484#117—54no—
485#117—54no—
486#117—102no—
487#117—102no—
488#117C22×D514yes—
489C2×C4⋊C4—51no—
490C2×C4⋊C4—51no—
491C2×C4⋊C4—54no—
492C2×C4⋊C4—51no—
493C2×C4⋊C4—54no—
494C2×C4⋊C4—54no—
495C2×C4⋊C4—54no—
496C2×C4⋊C4—102no—
497C2×C4⋊C4—102no—
498C2×C4⋊C4—102no—
499C2×C4⋊C4—101no—
500C2×C4⋊C4—101no—
501C2×C4⋊C4—101no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4—101no—
504C2×C4⋊C4—102no—
505C2×C4⋊C4—101no—
506C2×C4⋊C4C22×D511yescharacteristic
507C2×C4⋊C4C22×D511yescharacteristic
508C2×C4⋊C4C22×D511yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—101no—
512C2×C22⋊C4—101no—
513C2×C22⋊C4—101no—
514C2×C22⋊C4—101no—
515C2×C22⋊C4—101no—
516C2×C42—21no—
517C2×C42—101no—
518C2×C42—101no—
519#107—54no—
520#107—54no—
521#107—54no—
522#107—54no—
523#107—54no—
524#107C22×D514yes—
525#106—54no—
526#106C22×D514yes—
527#103—54no—
528#103—54no—
529#103—54no—
530#103—54no—
531#102—54no—
532#102—54no—
533#102C22×D514yes—
534#102C22×D514yes—
535C22⋊C8—54no—
536C22⋊C8—54no—
537C22⋊C8—54no—
538C22⋊C8C22×D514yes—
539C22×C5—22no—
540C22×C5—22no—
541C22×C5—22no—
542C22×C5—44no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—84no—
547C22×C5C2×#12312yes—
548C22×C5#57612yes—
549C22×C5#57812yes—
550C22×C5C23×D411yescharacteristic
551C2×D5—28no—
552C2×D5—22no—
553C2×D5—22no—
554C2×D5—22no—
555C2×D5—22no—
556C2×D5—22no—
557C2×D5—44no—
558C2×D5C2×#12314yes—
559C4×C5—22no—
560C4×C5—42no—
561C4×C5—42no—
562C4×C5—42no—
563C4×C5C2×#12312yes—
564C4×C5C22×#4111yescharacteristic
565C4×C5C22×#4111yescharacteristic
566Dic5—22no—
567Dic5—42no—
568Dic5—42no—
569Dic5—42no—
570Dic5—42no—
571Dic5C2×#12314yes—
572C24—21no—
573C24—51no—
574C24—51no—
575C24D4×D511yescharacteristic
576#41—1016no—
577#41—108no—
578#41—108no—
579#41—108no—
580#41—108no—
581#41—208no—
582C2×Q8—54no—
583C2×Q8—52no—
584C2×Q8—104no—
585C2×Q8—101no—
586C2×Q8—102no—
587C2×Q8—102no—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—54no—
593C2×D4—54no—
594C2×D4—54no—
595C2×D4—82no—
596C2×D4—104no—
597C2×D4—104no—
598C2×D4—104no—
599C2×D4—104no—
600C2×D4—104no—
601C2×D4—204no—
602C2×D4—402no—
603C2×D4C23×D512yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—51no—
610C22×C4—52no—
611C22×C4—54no—
612C22×C4—54no—
613C22×C4—52no—
614C22×C4—51no—
615C22×C4—52no—
616C22×C4—52no—
617C22×C4—104no—
618C22×C4—104no—
619C22×C4—104no—
620C22×C4—104no—
621C22×C4—102no—
622C22×C4—102no—
623C22×C4—101no—
624C22×C4—101no—
625C22×C4—101no—
626C22×C4—101no—
627C22×C4—104no—
628C22×C4—204no—
629C22×C4—402no—
630C22×C4—402no—
631C22×C4—402no—
632C22×C4—402no—
633C22×C4D4×D512yes—
634C22×C4D4×D511yescharacteristic
635C22×C4C23×D512yes—
636C22×C4C23×D511yescharacteristic
637M16—108no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—52no—
641C2×C8—52no—
642C2×C8—108no—
643C2×C8—102no—
644C2×C8—102no—
645C2×C8C23×D512yes—
646C2×C8C23×D512yes—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—52no—
651C4⋊C4—52no—
652C4⋊C4—52no—
653C4⋊C4—104no—
654C4⋊C4—104no—
655C4⋊C4—104no—
656C4⋊C4—104no—
657C4⋊C4—101no—
658C4⋊C4—101no—
659C4⋊C4—104no—
660C4⋊C4—101no—
661C4⋊C4—104no—
662C4⋊C4C23×D512yes—
663C4⋊C4C23×D512yes—
664C4⋊C4C23×D512yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—104no—
668C22⋊C4—104no—
669C22⋊C4—104no—
670C22⋊C4—104no—
671C22⋊C4—104no—
672C42—24no—
673C42—104no—
674C42—104no—
675C2×C5—42no—
676C2×C5—82no—
677C2×C5#309814yescomplemented
678C2×C5C22×#12311yescharacteristic
679C2×C5C2×#57611yescharacteristic
680C2×C5C2×#57811yescharacteristic
681D5—24no—
682D5—42no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—54no—
691C23—52no—
692C23—52no—
693C23—102no—
694C23—102no—
695C23—102no—
696C23—102no—
697C23—102no—
698C23C2×D4×D512yes—
699C23C2×D4×D511yescharacteristic
700Q8—108no—
701Q8—102no—
702Q8—102no—
703Q8—202no—
704D4—22no—
705D4—22no—
706D4—42no—
707D4—84no—
708D4—108no—
709D4—108no—
710D4—108no—
711D4—208no—
712D4—404no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—54no—
724C2×C4—52no—
725C2×C4—58no—
726C2×C4—54no—
727C2×C4—54no—
728C2×C4—52no—
729C2×C4—102no—
730C2×C4—104no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—208no—
738C2×C4—202no—
739C2×C4—202no—
740C2×C4—202no—
741C2×C4—202no—
742C2×C4—404no—
743C2×C4—404no—
744C2×C4—404no—
745C2×C4—404no—
746C2×C4C2×D4×D512yes—
747C2×C4C2×D4×D511yescharacteristic
748C2×C4D5×#4112yes—
749C2×C4D5×#4112yes—
750C2×C4C24×D511yescharacteristic
751C8—22no—
752C8—22no—
753C8—102no—
754C8—102no—
755C5C2×#309811yescharacteristic, complemented, Sylow
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—54no—
764C22—84no—
765C22—108no—
766C22—102no—
767C22—102no—
768C22—102no—
769C22—102no—
770C22—102no—
771C22—204no—
772C22D5×#12312yes—
773C22#6610512yes—
774C22#6610812yes—
775C22C22×D4×D511yescharacteristic
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—54no—
781C4—102no—
782C4—202no—
783C4—202no—
784C4—202no—
785C4—202no—
786C4D5×#12312yes—
787C4C2×D5×#4111yescharacteristic
788C4C2×D5×#4111yescharacteristic
789C2—42no—
790C2—82no—
791C2—104no—
792C2—202no—
793C2#1061310714yesdirect product factor
794C2C2×D5×#12311yescharacteristic
795C2C2×#6610511yescharacteristic
796C2C2×#6610811yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#482C2
socleC23×C5C22×D4
prime radicalC2×#65942C2
hypercenterC2×#482D5
hypocenterC5C2×#3098
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#65857C2semidirect
3. C2×C5×#482C2semidirect
4. C2×#65322C2semidirect
5. C2×#65285C2semidirect
6. #10613107C2direct (N × H)
7. C2×#65173C2semidirect
8. C2×D5×#107C2semidirect
9. C2×#65150C2semidirect
10. C2×#65156C2semidirect
11. C2×#65073C2semidirect
12. C2×#65063C2semidirect
13. C2×#65060C2semidirect
14. C2×#65061C2semidirect
15. C2×#65016C2semidirect
16. C2×#65011C2semidirect
31. #65857C22semidirect
44. C5×#482C22semidirect
59. #65322C22semidirect
60. #65285C22semidirect
67. #65173C22semidirect
68. D5×#107C22semidirect
69. #65156C22semidirect
70. #65150C22semidirect
71. #65073C22semidirect
72. #65063C22semidirect
73. #65061C22semidirect
74. #65060C22semidirect
75. #65016C22semidirect
76. #65011C22semidirect
191. C2×#482D5semidirect
334. #482C2×D5semidirect
677. C2×C5#3098semidirect
755. C5C2×#3098semidirect
793. C2#10613107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659422
C2×#658572
C2×C5×#4822
C2×#653222
C2×#652852
#106131072
C2×#651732
C2×D5×#1072
C2×#651502
C2×#651562
C2×#650732
C2×#650632
C2×#650602
C2×#650612
C2×#650162
C2×#650112
C2×#30985