Finite Group Databasebeta

← C2×#10615403 #12980306

Subgroups — C2×#10615403 #12980306

Order 1280.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#556C211yesmaximal, characteristic, complemented
2C2×#65919C211yesmaximal, characteristic, complemented
3#10615403C2116yesmaximal, direct product factor
4C2×#65372C211yesmaximal, characteristic, complemented
5C2×#65375C211yesmaximal, characteristic, complemented
6C2×#65343C211yesmaximal, characteristic, complemented
7C2×#65346C211yesmaximal, characteristic, complemented
8C2×#65347C211yesmaximal, characteristic
9C2×#65348C211yesmaximal, characteristic, complemented
10C2×#65317C211yesmaximal, characteristic, complemented
11C2×#65316C211yesmaximal, characteristic, complemented
12C2×#65313C211yesmaximal, characteristic, complemented
13C2×#65319C211yesmaximal, characteristic, complemented
14C2×C4×#688C211yesmaximal, characteristic, complemented
15C2×#65305C211yesmaximal, characteristic, complemented
16C2×#65303C211yesmaximal, characteristic, complemented
17C5×#556—24no—
18C5×#556C2218yescomplemented
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×#126—21no—
21C2×C5×#126—21no—
22C2×C5×#124C2211yescharacteristic
23C2×C5×#124C2211yescharacteristic
24C2×C5×C22⋊Q8—21no—
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C5×#117—21no—
30C2×#4093—21no—
31C22×#689C2211yescharacteristic
32C22×#689C2211yescharacteristic
33C22×#688C2211yescharacteristic
34C22×#688C2211yescharacteristic
35C22×#688C2211yescharacteristic
36C22×#688C2211yescharacteristic
37C22×#687C2211yescharacteristic
38C22×#686C2211yescharacteristic
39C22×#686C2211yescharacteristic
40#65919—24no—
41#65919C2218yescomplemented
42C2×#4040—21no—
43C2×#4040—21no—
44C2×#4039—21no—
45C2×#4021C2211yescharacteristic
46C2×#4021C2211yescharacteristic
47C2×#4020C2211yescharacteristic
48C2×C4×D20C2211yescharacteristic
49C2×C4×D20C2211yescharacteristic
50C2×C4×Dic10C2211yescharacteristic
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54#65375C2218yescomplemented
55#65372C2218yescomplemented
56#65348C2218yescomplemented
57#65347C2218yes—
58#65346C2218yescomplemented
59#65343C2218yescomplemented
60#65319C2218yescomplemented
61#65317C2218yescomplemented
62#65316C2218yescomplemented
63C4×#688C2218yescomplemented
64#65313C2218yescomplemented
65#65305C2218yescomplemented
66#65303C2218yescomplemented
67C2×#3942C2211yescharacteristic
68C2×#3941C2211yescharacteristic
69C2×#3941C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71C2×C4⋊#168C2211yescharacteristic
72C2×C4⋊#168C2211yescharacteristic
73C2×C4⋊#168C2211yescharacteristic
74C2×#3935C2211yescharacteristic
75C2×#3935C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3401—51nomaximal, Sylow
78C22×C5×Q8D411yescharacteristic
79C22×C5×Q8C2311yescharacteristic
80C22×C5×Q8C2311yescharacteristic
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5—21no—
83C22×D20—21no—
84C22×D20—21no—
85C22×D20C2311yescharacteristic
86C22×D20C2311yescharacteristic
87C22×C4×D5—21no—
88C22×C4×D5—21no—
89C22×Dic10C2311yescharacteristic
90C5×C4⋊Q8—22no—
91C5×C4⋊Q8C2314yes—
92C5×#126—28no—
93C5×#126—28no—
94C5×#124—22no—
95C5×#124—22no—
96C5×#124C2314yes—
97C5×#124C2314yes—
98C5×C22⋊Q8—28no—
99C4×C5×Q8—22no—
100C4×C5×Q8—22no—
101C4×C5×Q8D414yes—
102C4×C5×Q8C2314yes—
103C4×C5×Q8C2314yes—
104C4×C5×Q8C2314yes—
105C4×C5×D4—22no—
106C4×C5×D4C2314yes—
107C5×#117—28no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4D411yescharacteristic
113C2×C5×C4⋊C4D411yescharacteristic
114C2×C5×C4⋊C4D411yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C42×C5—21no—
122C2×C42×C5—21no—
123C2×C42×C5C2311yescharacteristic
124C2×C42×C5C2311yescharacteristic
125C2×C42×C5C2311yescharacteristic
126#4093—28no—
127C2×#689—24no—
128C2×#689—42no—
129C2×#689C2314yes—
130C2×#689C2314yes—
131C2×#688—24no—
132C2×#688—42no—
133C2×#688—42no—
134C2×#688—42no—
135C2×#688C2314yes—
136C2×#688C2314yes—
137C2×#688C2314yes—
138C2×#688C2314yes—
139C2×#687—42no—
140C2×#687C2314yes—
141C2×#686—24no—
142C2×#686—42no—
143C2×#686C2314yes—
144C2×#686C2314yes—
145C2×#685—21no—
146C2×#685—21no—
147C2×#685—21no—
148C2×#685—21no—
149C2×#685—21no—
150C2×#685—21no—
151C2×C4⋊Dic5C2311yescharacteristic
152C2×#683—21no—
153C2×C4×Dic5—21no—
154C22×#168C2311yescharacteristic
155C22×#168C2311yescharacteristic
156C22×#168C2311yescharacteristic
157C22×#168C2311yescharacteristic
158#4040—28no—
159#4040—28no—
160#4039—28no—
161#4021—22no—
162#4021—22no—
163#4021C2314yes—
164#4021C2314yes—
165#4020—22no—
166#4020C2314yes—
167C4×D20—22no—
168C4×D20—22no—
169C4×D20C2314yes—
170C4×D20C2314yes—
171C4×Dic10—22no—
172C4×Dic10C2314yes—
173#3967C2314yes—
174#3967C2314yes—
175#3964C2314yes—
176#3942C2314yes—
177#3941C2314yes—
178#3941C2314yes—
179#3940C2314yes—
180C4⋊#168C2314yes—
181C4⋊#168C2314yes—
182C4⋊#168C2314yes—
183#3935C2314yes—
184#3935C2314yes—
185C4×#168C2314yes—
186C2×#559—51no—
187C2×#556D511yescharacteristic, complemented
188#3401—516no—
189C2×#497—51no—
190C2×#496—51no—
191C2×#495—51no—
192C2×#464—51no—
193C2×#464—51no—
194C2×#460—51no—
195C2×#463—51no—
196C2×#463—51no—
197C2×#461—51no—
198C2×#446—51no—
199C2×#442—51no—
200C2×#441—51no—
201C2×C4×SD16—51no—
202C24×C5—21no—
203C23×D5—21no—
204C23×D5—21no—
205C2×C5×Q8—21no—
206C2×C5×Q8—21no—
207C2×C5×Q8—22no—
208C2×C5×Q8—22no—
209C2×C5×Q8—22no—
210C2×C5×Q8—22no—
211C2×C5×Q8—42no—
212C2×C5×Q8C2×D414yes—
213C2×C5×Q8C2412yes—
214C2×C5×Q8C2412yes—
215C2×C5×D4—21no—
216C2×C5×D4—22no—
217C2×C5×D4—22no—
218C2×C5×D4C2412yes—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—24no—
223C22×C4×C5—44no—
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2411yescharacteristic
231C22×Dic5—21no—
232C22×Dic5—21no—
233C2×D20—22no—
234C2×D20—22no—
235C2×D20—22no—
236C2×D20—22no—
237C2×D20—24no—
238C2×D20—21no—
239C2×D20—21no—
240C2×D20—24no—
241C2×D20—44no—
242C2×D20—82no—
243C2×D20C2412yes—
244C2×D20C2412yes—
245C2×C4×D5—24no—
246C2×C4×D5—24no—
247C2×C4×D5—82no—
248C2×C4×D5—82no—
249C2×Dic10—22no—
250C2×Dic10—22no—
251C2×Dic10—21no—
252C2×Dic10C2412yes—
253C5×C4⋊C4—24no—
254C5×C4⋊C4—24no—
255C5×C4⋊C4—24no—
256C5×C4⋊C4—24no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4C2×D414yes—
259C5×C4⋊C4C2×D414yes—
260C5×C4⋊C4C2×D414yes—
261C5×C4⋊C4C2412yes—
262C5×C22⋊C4—24no—
263C5×C22⋊C4—24no—
264C5×C22⋊C4—24no—
265C5×C22⋊C4—24no—
266C5×C22⋊C4—24no—
267C42×C5—24no—
268C42×C5—24no—
269C42×C5C2×D412yes—
270C42×C5C2×D412yes—
271C42×C5C2×D412yes—
272C42×C5C2412yes—
273C42×C5C2412yes—
274C42×C5C2412yes—
275#689—28no—
276#689—44no—
277#688—28no—
278#688—44no—
279#688—44no—
280#688—44no—
281#687—44no—
282#686—28no—
283#686—44no—
284#685—24no—
285#685—24no—
286#685—24no—
287#685—24no—
288#685—24no—
289#685—24no—
290C4⋊Dic5—21no—
291C4⋊Dic5C2412yes—
292#683—24no—
293C4×Dic5—24no—
294C2×#168—22no—
295C2×#168—22no—
296C2×#168—22no—
297C2×#168#4114yes—
298C2×#168C2412yes—
299C2×#168C2412yes—
300C2×#168C2412yes—
301C2×#168C2412yes—
302C22×Q16—51no—
303C22×Q16—51no—
304C22×SD16—51no—
305C22×SD16—51no—
306C22×SD16—51no—
307C22×SD16—51no—
308C22×SD16—51no—
309C22×D8—51no—
310C22×D8—51no—
311#559—58no—
312#559—104no—
313#556—24no—
314#556C2×D518yescomplemented
315C2×C4⋊Q8C2×D511yescharacteristic
316C2×#127—51no—
317C2×#126—21no—
318C2×#126—21no—
319C2×#124—51no—
320C2×#124—51no—
321C2×#124—101no—
322C2×#124C2×D511yescharacteristic
323C2×#124C2×D511yescharacteristic
324C2×#123—101no—
325C2×#123—101no—
326C2×C22⋊Q8—21no—
327C2×C4×Q8—51no—
328C2×C4×Q8C2×D511yescharacteristic
329C2×C4×Q8C2×D511yescharacteristic
330C2×C4×Q8C2×D511yescharacteristic
331C2×C4×D4—51no—
332C2×C4×D4—51no—
333C2×C4×D4—101no—
334C2×C4×D4C2×D511yescharacteristic
335C2×#117—21no—
336#497—58no—
337#496—58no—
338#495—58no—
339#464—58no—
340#464—58no—
341#463—58no—
342#463—58no—
343#461—58no—
344#460—58no—
345#446—58no—
346#442—58no—
347#441—58no—
348C4×SD16—58no—
349C2×#106—51no—
350C2×C4⋊C8—51no—
351C2×C4⋊C8—51no—
352C2×C4⋊C8—51no—
353C2×#103—51no—
354C2×#103—51no—
355C2×#103—51no—
356C2×#102—51no—
357C2×#102—51no—
358C2×#102—51no—
359C2×#97—51no—
360C2×#97—51no—
361C2×C4×C8—51no—
362C23×C5—22no—
363C23×C5—42no—
364C23×C5—42no—
365C23×C5—42no—
366C23×C5C22×D411yescharacteristic
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—42no—
370C22×D5—42no—
371C22×D5—42no—
372C22×D5—42no—
373C22×D5—42no—
374C22×D5—42no—
375C5×Q8—22no—
376C5×Q8—22no—
377C5×Q8—22no—
378C5×Q8—22no—
379C5×Q8—44no—
380C5×Q8—42no—
381C5×Q8—42no—
382C5×D4—22no—
383C5×D4—22no—
384C5×D4—42no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—48no—
395C2×C4×C5—42no—
396C2×C4×C5—42no—
397C2×C4×C5—42no—
398C2×C4×C5C22×D412yes—
399C2×C4×C5C22×D412yes—
400C2×C4×C5C22×D412yes—
401C2×C4×C5C22×D412yes—
402C2×C4×C5C22×D412yes—
403C2×C4×C5C22×D412yes—
404C2×C4×C5C22×D411yescharacteristic
405C2×C4×C5C2×#4112yes—
406C2×C4×C5H(5,𝔽2)12yes—
407C2×C4×C5C2511yescharacteristic
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—42no—
411C2×Dic5—42no—
412D20—22no—
413D20—22no—
414D20—22no—
415D20—22no—
416D20—48no—
417D20—42no—
418D20—42no—
419D20—84no—
420C4×D5—84no—
421C4×D5—84no—
422Dic10—22no—
423Dic10—22no—
424Dic10—42no—
425#168—22no—
426#168—22no—
427#168—22no—
428#168C2×#4114yes—
429C22×Q8—51no—
430C22×Q8C22⋊D511yescharacteristic
431C22×Q8C22×D511yescharacteristic
432C22×Q8C22×D511yescharacteristic
433C22×D4—51no—
434C22×D4—51no—
435C22×D4—101no—
436C22×D4—101no—
437C22×D4C22×D511yescharacteristic
438C23×C4—21no—
439C23×C4—101no—
440C23×C4—101no—
441C2×Q16—54no—
442C2×Q16—54no—
443C2×Q16—104no—
444C2×Q16—202no—
445C2×SD16—54no—
446C2×SD16—54no—
447C2×SD16—54no—
448C2×SD16—54no—
449C2×SD16—54no—
450C2×SD16—104no—
451C2×SD16—202no—
452C2×SD16—202no—
453C2×SD16—202no—
454C2×SD16—202no—
455C2×D8—54no—
456C2×D8—54no—
457C2×D8—104no—
458C2×D8—202no—
459C22×C8—51no—
460C22×C8—51no—
461C22×C8—51no—
462C22×C8—51no—
463C4⋊Q8—22no—
464C4⋊Q8C22×D514yes—
465#127—54no—
466#127—102no—
467#126—28no—
468#126—28no—
469#124—22no—
470#124—22no—
471#124—54no—
472#124—54no—
473#124—108no—
474#124—102no—
475#124—102no—
476#124C22×D514yes—
477#124C22×D514yes—
478#123—108no—
479#123—108no—
480C22⋊Q8—28no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—54no—
484C4×Q8—102no—
485C4×Q8C22⋊D514yes—
486C4×Q8C22×D514yes—
487C4×Q8C22×D514yes—
488C4×Q8C22×D514yes—
489C4×D4—22no—
490C4×D4—54no—
491C4×D4—54no—
492C4×D4—108no—
493C4×D4—102no—
494C4×D4—102no—
495C4×D4C22×D514yes—
496#117—28no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—51no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4C22⋊D511yescharacteristic
504C2×C4⋊C4C22⋊D511yescharacteristic
505C2×C4⋊C4C22⋊D511yescharacteristic
506C2×C4⋊C4C22×D511yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—101no—
513C2×C22⋊C4—101no—
514C2×C22⋊C4—101no—
515C2×C22⋊C4—101no—
516C2×C22⋊C4—101no—
517C2×C22⋊C4—101no—
518C2×C42—21no—
519C2×C42—21no—
520C2×C42—101no—
521C2×C42C22×D511yescharacteristic
522C2×C42C22×D511yescharacteristic
523C2×C42C22×D511yescharacteristic
524#106—54no—
525C4⋊C8—54no—
526C4⋊C8—54no—
527C4⋊C8—54no—
528#103—54no—
529#103—54no—
530#103—54no—
531#102—54no—
532#102—54no—
533#102—54no—
534#97—54no—
535#97—54no—
536C4×C8—54no—
537C22×C5—42no—
538C22×C5—42no—
539C22×C5—42no—
540C22×C5—84no—
541C22×C5#55012yes—
542C22×C5#57512yes—
543C22×C5#57712yes—
544C22×C5C23×D411yescharacteristic
545C2×D5—42no—
546C2×D5—42no—
547C2×D5—42no—
548C2×D5—42no—
549C2×D5—42no—
550C2×D5—42no—
551C2×D5—84no—
552C2×D5—84no—
553C4×C5—22no—
554C4×C5—22no—
555C4×C5—22no—
556C4×C5—22no—
557C4×C5—22no—
558C4×C5—22no—
559C4×C5—42no—
560C4×C5—42no—
561C4×C5—42no—
562C4×C5#55012yes—
563C4×C5C22×#4111yescharacteristic
564C4×C5C2×H(5,𝔽2)11yescharacteristic
565Dic5—42no—
566Dic5—42no—
567C24—21no—
568C24—101no—
569C24—101no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—42no—
577C2×Q8—52no—
578C2×Q8—101no—
579C2×Q8—102no—
580C2×Q8—102no—
581C2×Q8C2×C22⋊D514yes—
582C2×Q8C23×D512yes—
583C2×Q8C23×D512yes—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—52no—
588C2×D4—52no—
589C2×D4—102no—
590C2×D4—102no—
591C2×D4—102no—
592C2×D4—102no—
593C2×D4—104no—
594C2×D4—101no—
595C2×D4—101no—
596C2×D4—104no—
597C2×D4—204no—
598C2×D4—402no—
599C2×D4C23×D512yes—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—44no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—104no—
608C22×C4—104no—
609C22×C4—402no—
610C22×C4—402no—
611C22×C4C2×C22⋊D511yescharacteristic
612C22×C4C2×C22⋊D511yescharacteristic
613C22×C4C2×C22⋊D511yescharacteristic
614C22×C4C2×C22⋊D511yescharacteristic
615C22×C4C2×C22⋊D511yescharacteristic
616C22×C4C2×C22⋊D511yescharacteristic
617C22×C4C23×D511yescharacteristic
618Q16—108no—
619Q16—204no—
620SD16—108no—
621SD16—204no—
622SD16—204no—
623SD16—204no—
624SD16—204no—
625D8—108no—
626D8—204no—
627C2×C8—54no—
628C2×C8—52no—
629C2×C8—52no—
630C2×C8—52no—
631C2×C8—52no—
632C2×C8—102no—
633C2×C8—102no—
634C2×C8—102no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—21no—
640C4⋊C4—52no—
641C4⋊C4—101no—
642C4⋊C4—104no—
643C4⋊C4C2×C22⋊D514yes—
644C4⋊C4C2×C22⋊D514yes—
645C4⋊C4C2×C22⋊D514yes—
646C4⋊C4C23×D512yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—104no—
653C22⋊C4—104no—
654C22⋊C4—104no—
655C22⋊C4—104no—
656C22⋊C4—104no—
657C22⋊C4—104no—
658C42—24no—
659C42—24no—
660C42—104no—
661C42C2×C22⋊D512yes—
662C42C2×C22⋊D512yes—
663C42C2×C22⋊D512yes—
664C42C23×D512yes—
665C42C23×D512yes—
666C42C23×D512yes—
667C2×C5—82no—
668C2×C5#340114yescomplemented
669C2×C5C2×#55011yescharacteristic
670C2×C5C2×#57511yescharacteristic
671C2×C5C2×#57711yescharacteristic
672D5—82no—
673D5—82no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—102no—
679C23—102no—
680C23—202no—
681C23—202no—
682C23—202no—
683C23—202no—
684C23—202no—
685C23—202no—
686C23C22×C22⋊D511yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—44no—
692Q8—42no—
693Q8—42no—
694Q8—102no—
695Q8—102no—
696Q8—202no—
697D4—22no—
698D4—22no—
699D4—42no—
700D4—102no—
701D4—102no—
702D4—102no—
703D4—102no—
704D4—208no—
705D4—202no—
706D4—202no—
707D4—404no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—202no—
724C2×C4—202no—
725C2×C4—404no—
726C2×C4—404no—
727C2×C4D5×#4112yes—
728C2×C4#414912yes—
729C2×C4C22×C22⋊D512yes—
730C2×C4C22×C22⋊D512yes—
731C2×C4C22×C22⋊D512yes—
732C2×C4C22×C22⋊D512yes—
733C2×C4C22×C22⋊D512yes—
734C2×C4C22×C22⋊D512yes—
735C2×C4C22×C22⋊D511yescharacteristic
736C2×C4C24×D511yescharacteristic
737C8—54no—
738C8—102no—
739C8—102no—
740C8—102no—
741C5C2×#340111yescharacteristic, complemented, Sylow
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22—202no—
747C22—202no—
748C22—202no—
749C22—202no—
750C22—202no—
751C22—202no—
752C22—404no—
753C22—404no—
754C22#6615612yes—
755C22#6616812yes—
756C22#6617112yes—
757C22C23×C22⋊D511yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—42no—
767C4—202no—
768C4—202no—
769C4#6616812yes—
770C4C2×D5×#4111yescharacteristic
771C4C2×#414911yescharacteristic
772C2—82no—
773C2—402no—
774C2—402no—
775C2#1061540314yesdirect product factor
776C2C2×#6615611yescharacteristic
777C2C2×#6616811yescharacteristic
778C2C2×#6617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#556C2
socleC23×C5C22×D4
prime radicalC2×#65347C2
hypercenterC2×#556D5
hypocenterC5C2×#3401
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×C5×#556C2semidirect
2. C2×#65919C2semidirect
3. #10615403C2direct (N × H)
4. C2×#65372C2semidirect
5. C2×#65375C2semidirect
6. C2×#65343C2semidirect
7. C2×#65346C2semidirect
9. C2×#65348C2semidirect
10. C2×#65317C2semidirect
11. C2×#65316C2semidirect
12. C2×#65313C2semidirect
13. C2×#65319C2semidirect
14. C2×C4×#688C2semidirect
15. C2×#65305C2semidirect
16. C2×#65303C2semidirect
18. C5×#556C22semidirect
41. #65919C22semidirect
54. #65375C22semidirect
55. #65372C22semidirect
56. #65348C22semidirect
58. #65346C22semidirect
59. #65343C22semidirect
60. #65319C22semidirect
61. #65317C22semidirect
62. #65316C22semidirect
63. C4×#688C22semidirect
64. #65313C22semidirect
65. #65305C22semidirect
66. #65303C22semidirect
187. C2×#556D5semidirect
314. #556C2×D5semidirect
668. C2×C5#3401semidirect
741. C5C2×#3401semidirect
775. C2#10615403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5562
C2×#659192
#106154032
C2×#653722
C2×#653752
C2×#653432
C2×#653462
C2×#653472
C2×#653482
C2×#653172
C2×#653162
C2×#653132
C2×#653192
C2×C4×#6882
C2×#653052
C2×#653032
C2×#34015