Finite Group Databasebeta

← C2×#10615177 #12967557

Subgroups — C2×#10615177 #12967557

Order 1280.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#541C211yesmaximal, characteristic, complemented
2C2×#65857C211yesmaximal, characteristic
3#10615177C2116yesmaximal, direct product factor
4C2×#65379C211yesmaximal, characteristic, complemented
5C2×#65372C211yesmaximal, characteristic, complemented
6C2×#65352C211yesmaximal, characteristic, complemented
7C2×#65355C211yesmaximal, characteristic, complemented
8C2×#65336C211yesmaximal, characteristic
9C2×#65336C211yesmaximal, characteristic
10C2×#65333C211yesmaximal, characteristic, complemented
11C2×#65332C211yesmaximal, characteristic, complemented
12C2×#65315C211yesmaximal, characteristic, complemented
13C2×#65319C211yesmaximal, characteristic, complemented
14C2×C4×#689C211yesmaximal, characteristic, complemented
15C2×C4×#688C211yesmaximal, characteristic, complemented
16C2×#65289C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C5×#541—24no—
19C5×#541C2218yescomplemented
20C2×C5×C4⋊Q8C2211yescharacteristic
21C2×C5×#126—21no—
22C2×C5×#126—21no—
23C2×C5×#125—21no—
24C2×C5×#125—21no—
25C2×C5×#125C2211yescharacteristic
26C2×C5×C22⋊Q8C2211yescharacteristic
27C2×C5×C22⋊Q8C2211yescharacteristic
28C2×C4×C5×Q8C2211yescharacteristic
29C2×C4×C5×Q8C2211yescharacteristic
30C2×C5×#117C2211yescharacteristic
31C22×#689C2211yescharacteristic
32C22×#689C2211yescharacteristic
33C22×#688C2211yescharacteristic
34C22×#688C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36#65857—24no—
37#65857C2218yes—
38C2×#4038—21no—
39C2×D5×C4⋊C4—21no—
40C2×#4027—21no—
41C2×#4027—21no—
42C2×C4×D20C2211yescharacteristic
43C2×C4×D20C2211yescharacteristic
44C2×C4×Dic10C2211yescharacteristic
45C2×C4×Dic10C2211yescharacteristic
46C2×#3967C2211yescharacteristic
47C2×#3967C2211yescharacteristic
48C2×#3967C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×C22⋊#168C2211yescharacteristic
51C2×C22⋊#168C2211yescharacteristic
52#65379C2218yescomplemented
53#65372C2218yescomplemented
54#65355C2218yescomplemented
55#65352C2218yescomplemented
56#65336C2218yes—
57#65336C2218yes—
58#65333C2218yescomplemented
59#65332C2218yescomplemented
60#65319C2218yescomplemented
61C4×#689C2218yescomplemented
62#65315C2218yescomplemented
63C4×#688C2218yescomplemented
64#65289C2218yescomplemented
65C2×#3942C2211yescharacteristic
66C2×#3942C2211yescharacteristic
67C2×#3941C2211yescharacteristic
68C2×#3941C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71C2×#3939C2211yescharacteristic
72C2×#3939C2211yescharacteristic
73C2×C4⋊#168C2211yescharacteristic
74C2×C4⋊#168C2211yescharacteristic
75C2×#3935C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3120—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×Q8C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C23×Dic5—21no—
83C2×#709—22no—
84C2×#709—24no—
85C2×#709—24no—
86C2×#709C2314yes—
87C22×D20C2311yescharacteristic
88C22×C4×D5—21no—
89C22×C4×D5—21no—
90C22×C4×D5—21no—
91C22×Dic10C2311yescharacteristic
92C5×C4⋊Q8—22no—
93C5×C4⋊Q8C2314yes—
94C5×#126—28no—
95C5×#126—28no—
96C5×#125—28no—
97C5×#125—28no—
98C5×#125—22no—
99C5×#125C2314yes—
100C5×C22⋊Q8—22no—
101C5×C22⋊Q8—22no—
102C5×C22⋊Q8C2314yes—
103C5×C22⋊Q8C2314yes—
104C4×C5×Q8—22no—
105C4×C5×Q8—22no—
106C4×C5×Q8C2314yes—
107C4×C5×Q8C2314yes—
108C5×#117D414yes—
109C5×#117C2314yes—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4—21no—
114C2×C5×C4⋊C4—21no—
115C2×C5×C4⋊C4—21no—
116C2×C5×C4⋊C4—21no—
117C2×C5×C4⋊C4—21no—
118C2×C5×C4⋊C4D411yescharacteristic
119C2×C5×C4⋊C4D411yescharacteristic
120C2×C5×C4⋊C4C2311yescharacteristic
121C2×C5×C4⋊C4C2311yescharacteristic
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4D411yescharacteristic
125C2×C5×C22⋊C4D411yescharacteristic
126C2×C42×C5—21no—
127C2×C42×C5—21no—
128C2×C42×C5C2311yescharacteristic
129C2×C42×C5C2311yescharacteristic
130C2×#689—24no—
131C2×#689—24no—
132C2×#689C2314yes—
133C2×#689C2314yes—
134C2×#688—24no—
135C2×#688—24no—
136C2×#688C2314yes—
137C2×#688C2314yes—
138C2×#685—21no—
139C2×#685—21no—
140C2×C4⋊Dic5—21no—
141C2×C4⋊Dic5—22no—
142C2×C4⋊Dic5C2311yescharacteristic
143C2×C4⋊Dic5C2311yescharacteristic
144C2×C4⋊Dic5C2314yes—
145C2×#683—21no—
146C2×#683—21no—
147C2×C4×Dic5—21no—
148C2×C4×Dic5—21no—
149C22×#168C2311yescharacteristic
150C22×#168C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153#4038—28no—
154D5×C4⋊C4—28no—
155#4027—28no—
156#4027—28no—
157C4×D20—22no—
158C4×D20—22no—
159C4×D20C2314yes—
160C4×D20C2314yes—
161C4×Dic10—22no—
162C4×Dic10—22no—
163C4×Dic10C2314yes—
164C4×Dic10C2314yes—
165#3967C2314yes—
166#3967C2314yes—
167#3967C2314yes—
168#3967C2314yes—
169C22⋊#168C2314yes—
170C22⋊#168C2314yes—
171#3942C2314yes—
172#3942C2314yes—
173#3941C2314yes—
174#3941C2314yes—
175#3940C2314yes—
176#3940C2314yes—
177#3939C2314yes—
178#3939C2314yes—
179C4⋊#168C2314yes—
180C4⋊#168C2314yes—
181#3935C2314yes—
182C4×#168C2314yes—
183C2×#541D511yescharacteristic, complemented
184C2×#520—51no—
185#3120—516no—
186C2×#484—51no—
187C2×#483—51no—
188C2×#479—51no—
189C2×#478—51no—
190C2×#462—51no—
191C2×#461—51no—
192C2×#452—51no—
193C2×#452—51no—
194C2×#441—51no—
195C2×#440—51no—
196C2×C4×Q16—51no—
197C2×C4×SD16—51no—
198C2×#433—51no—
199C24×C5C2×D411yescharacteristic
200C23×D5—21no—
201C2×C5×Q8—21no—
202C2×C5×Q8—21no—
203C2×C5×Q8—22no—
204C2×C5×Q8—22no—
205C2×C5×Q8—22no—
206C2×C5×Q8—22no—
207C2×C5×Q8C2412yes—
208C2×C5×Q8C2412yes—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D412yes—
221C22×C4×C5C2412yes—
222C22×C4×C5C2411yescharacteristic
223C2×C22⋊D5—28no—
224C2×C22⋊D5—24no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—24no—
229C22×Dic5—82no—
230#709—216no—
231#709—28no—
232#709—28no—
233C2×D20—21no—
234C2×D20—22no—
235C2×D20#4114yes—
236C2×D20C2412yes—
237C2×C4×D5—28no—
238C2×C4×D5—24no—
239C2×C4×D5—24no—
240C2×C4×D5—24no—
241C2×C4×D5—82no—
242C2×C4×D5—82no—
243C2×Dic10—21no—
244C2×Dic10—22no—
245C2×Dic10#4114yes—
246C2×Dic10C2412yes—
247C5×C4⋊C4—24no—
248C5×C4⋊C4—24no—
249C5×C4⋊C4—24no—
250C5×C4⋊C4—24no—
251C5×C4⋊C4—24no—
252C5×C4⋊C4—24no—
253C5×C4⋊C4—24no—
254C5×C4⋊C4—24no—
255C5×C4⋊C4—21no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4C2×D414yes—
258C5×C4⋊C4C2×D414yes—
259C5×C4⋊C4C2412yes—
260C5×C4⋊C4C2412yes—
261C5×C22⋊C4—24no—
262C5×C22⋊C4—24no—
263C5×C22⋊C4C2×D414yes—
264C5×C22⋊C4C2×D414yes—
265C42×C5—24no—
266C42×C5—24no—
267C42×C5C2×D412yes—
268C42×C5C2×D412yes—
269C42×C5C2412yes—
270C42×C5C2412yes—
271#689—28no—
272#689—28no—
273#688—28no—
274#688—28no—
275#685—24no—
276#685—24no—
277C4⋊Dic5—21no—
278C4⋊Dic5—21no—
279C4⋊Dic5—24no—
280C4⋊Dic5C2412yes—
281C4⋊Dic5C2412yes—
282#683—24no—
283#683—24no—
284C4×Dic5—24no—
285C4×Dic5—24no—
286C2×#168—22no—
287C2×#168—22no—
288C2×#168—22no—
289C2×#168—22no—
290C2×#168C2412yes—
291C2×#168C2412yes—
292C2×#168C2412yes—
293C2×#168C2412yes—
294C22×#41—51no—
295C22×Q16—51no—
296C22×Q16—51no—
297C22×SD16—51no—
298C22×SD16—51no—
299#541—24no—
300#541C2×D518yescomplemented
301C2×C4⋊Q8C2×D511yescharacteristic
302C2×#126—21no—
303C2×#126—21no—
304C2×#125—21no—
305C2×#125—21no—
306C2×#125C2×D511yescharacteristic
307C2×C22⋊Q8C2×D511yescharacteristic
308C2×C22⋊Q8C2×D511yescharacteristic
309#520—58no—
310#520—104no—
311C2×C4×Q8—51no—
312C2×C4×Q8—51no—
313C2×C4×Q8C2×D511yescharacteristic
314C2×C4×Q8C2×D511yescharacteristic
315C2×C4×D4—51no—
316C2×C4×D4—51no—
317C2×C4×D4—101no—
318C2×C4×D4—101no—
319C2×#117—101no—
320C2×#117C2×D511yescharacteristic
321C22×C4⋊C4—51no—
322C22×C4⋊C4—101no—
323#484—58no—
324#483—58no—
325#479—58no—
326#478—58no—
327#462—58no—
328#461—58no—
329#452—58no—
330#452—58no—
331#441—58no—
332#440—58no—
333C4×Q16—58no—
334C4×SD16—58no—
335#433—58no—
336C2×#107—51no—
337C2×#107—51no—
338C2×#106—51no—
339C2×#106—51no—
340C2×C4⋊C8—51no—
341C2×C4⋊C8—51no—
342C2×#103—51no—
343C2×#103—51no—
344C2×#103—51no—
345C2×#103—51no—
346C2×#103—51no—
347C2×#103—51no—
348C2×#102—51no—
349C2×#102—51no—
350C2×C22⋊C8—51no—
351C2×C22⋊C8—51no—
352C2×#97—51no—
353C2×C4×C8—51no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5C22×D412yes—
358C23×C5C22×D411yescharacteristic
359C22×D5—24no—
360C22×D5—22no—
361C22×D5—42no—
362C22×D5—42no—
363C5×Q8—22no—
364C5×Q8—22no—
365C5×Q8—22no—
366C5×Q8—22no—
367C5×Q8—42no—
368C5×Q8—42no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—24no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—42no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5—42no—
385C2×C4×C5C22×D412yes—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D412yes—
388C2×C4×C5C22×D412yes—
389C2×C4×C5C22×D412yes—
390C2×C4×C5C22×D411yescharacteristic
391C2×C4×C5C2×#4112yes—
392C2×C4×C5C2×#4112yes—
393C2×C4×C5C2511yescharacteristic
394C22⋊D5—216no—
395C2×Dic5—24no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—84no—
402D20—24no—
403D20—22no—
404D20C2×#4114yes—
405C4×D5—216no—
406C4×D5—84no—
407C4×D5—84no—
408Dic10—24no—
409Dic10—22no—
410Dic10C2×#4114yes—
411#168—22no—
412#168—22no—
413#168—22no—
414#168—22no—
415C2×#41—54no—
416C2×#41—104no—
417C2×#41—104no—
418C2×#41—102no—
419C22×Q8—51no—
420C22×Q8C22×D511yescharacteristic
421C22×Q8C22×D511yescharacteristic
422C22×D4—51no—
423C22×D4—101no—
424C23×C4—101no—
425C23×C4—101no—
426C23×C4—101no—
427C23×C4—101no—
428C23×C4C22×D511yescharacteristic
429C2×Q16—54no—
430C2×Q16—54no—
431C2×Q16—104no—
432C2×Q16—104no—
433C2×SD16—54no—
434C2×SD16—54no—
435C2×SD16—104no—
436C2×SD16—104no—
437C22×C8—51no—
438C22×C8—51no—
439C22×C8—51no—
440C22×C8—51no—
441C4⋊Q8—22no—
442C4⋊Q8C22×D514yes—
443#126—28no—
444#126—28no—
445#125—28no—
446#125—28no—
447#125—22no—
448#125C22×D514yes—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8C22×D514yes—
452C22⋊Q8C22×D514yes—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8—54no—
456C4×Q8—54no—
457C4×Q8—102no—
458C4×Q8—102no—
459C4×Q8C22×D514yes—
460C4×Q8C22×D514yes—
461C4×D4—54no—
462C4×D4—54no—
463C4×D4—108no—
464C4×D4—108no—
465C4×D4—102no—
466C4×D4—102no—
467#117—108no—
468#117C22⋊D514yes—
469#117C22×D514yes—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—51no—
479C2×C4⋊C4—51no—
480C2×C4⋊C4—54no—
481C2×C4⋊C4—101no—
482C2×C4⋊C4—102no—
483C2×C4⋊C4—101no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—108no—
486C2×C4⋊C4C22⋊D511yescharacteristic
487C2×C4⋊C4C22⋊D511yescharacteristic
488C2×C4⋊C4C22×D511yescharacteristic
489C2×C4⋊C4C22×D511yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—101no—
493C2×C22⋊C4—101no—
494C2×C22⋊C4C22⋊D511yescharacteristic
495C2×C22⋊C4C22⋊D511yescharacteristic
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—101no—
499C2×C42—101no—
500C2×C42C22×D511yescharacteristic
501C2×C42C22×D511yescharacteristic
502#107—54no—
503#107—54no—
504#106—54no—
505#106—54no—
506C4⋊C8—54no—
507C4⋊C8—54no—
508#103—54no—
509#103—54no—
510#103—54no—
511#103—54no—
512#103—54no—
513#103—54no—
514#102—54no—
515#102—54no—
516C22⋊C8—54no—
517C22⋊C8—54no—
518#97—54no—
519C4×C8—54no—
520C22×C5—22no—
521C22×C5—22no—
522C22×C5—22no—
523C22×C5—44no—
524C22×C5#52512yes—
525C22×C5#57712yes—
526C22×C5#57812yes—
527C22×C5C23×D411yescharacteristic
528C2×D5—24no—
529C2×D5—48no—
530C2×D5—42no—
531C2×D5—42no—
532C4×C5—22no—
533C4×C5—22no—
534C4×C5—22no—
535C4×C5—22no—
536C4×C5—22no—
537C4×C5—42no—
538C4×C5—42no—
539C4×C5—42no—
540C4×C5—42no—
541C4×C5#52512yes—
542C4×C5C22×#4111yescharacteristic
543C4×C5C22×#4111yescharacteristic
544Dic5—24no—
545Dic5—42no—
546Dic5—42no—
547C24—101no—
548C24C2×C22⋊D511yescharacteristic
549#41—108no—
550#41—108no—
551#41—1016no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—54no—
559C2×Q8—52no—
560C2×Q8—102no—
561C2×Q8—101no—
562C2×Q8C23×D512yes—
563C2×Q8C23×D512yes—
564C2×D4—54no—
565C2×D4—52no—
566C2×D4—108no—
567C2×D4—104no—
568C2×D4—102no—
569C2×D4—101no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—108no—
577C22×C4—101no—
578C22×C4—104no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—104no—
582C22×C4—104no—
583C22×C4—104no—
584C22×C4—402no—
585C22×C4—402no—
586C22×C4—402no—
587C22×C4C2×C22⋊D512yes—
588C22×C4C2×C22⋊D511yescharacteristic
589C22×C4C2×C22⋊D511yescharacteristic
590C22×C4C2×C22⋊D511yescharacteristic
591C22×C4C2×C22⋊D511yescharacteristic
592C22×C4C2×C22⋊D511yescharacteristic
593C22×C4C23×D512yes—
594C22×C4C23×D511yescharacteristic
595Q16—108no—
596Q16—108no—
597SD16—108no—
598SD16—108no—
599C2×C8—52no—
600C2×C8—52no—
601C2×C8—52no—
602C2×C8—52no—
603C2×C8—102no—
604C2×C8—102no—
605C2×C8—102no—
606C2×C8—102no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—52no—
618C4⋊C4—52no—
619C4⋊C4—104no—
620C4⋊C4—101no—
621C4⋊C4—101no—
622C4⋊C4—104no—
623C4⋊C4—104no—
624C4⋊C4C2×C22⋊D514yes—
625C4⋊C4C2×C22⋊D514yes—
626C4⋊C4C23×D512yes—
627C4⋊C4C23×D512yes—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—104no—
631C22⋊C4—104no—
632C22⋊C4C2×C22⋊D514yes—
633C22⋊C4C2×C22⋊D514yes—
634C42—24no—
635C42—24no—
636C42—104no—
637C42—104no—
638C42C2×C22⋊D512yes—
639C42C2×C22⋊D512yes—
640C42C23×D512yes—
641C42C23×D512yes—
642C2×C5—42no—
643C2×C5#312014yescomplemented
644C2×C5C2×#52511yescharacteristic
645C2×C5C2×#57711yescharacteristic
646C2×C5C2×#57811yescharacteristic
647D5—44no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—104no—
652C23—102no—
653C23—202no—
654C23—202no—
655C23C22×C22⋊D512yes—
656C23C22×C22⋊D511yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—42no—
663Q8—54no—
664Q8—104no—
665Q8—102no—
666D4—54no—
667D4—1016no—
668D4—104no—
669D4—102no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—1016no—
687C2×C4—104no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—202no—
692C2×C4—202no—
693C2×C4—404no—
694C2×C4—404no—
695C2×C4—404no—
696C2×C4D5×#4112yes—
697C2×C4D5×#4112yes—
698C2×C4C22×C22⋊D512yes—
699C2×C4C22×C22⋊D512yes—
700C2×C4C22×C22⋊D512yes—
701C2×C4C22×C22⋊D512yes—
702C2×C4C22×C22⋊D512yes—
703C2×C4C22×C22⋊D511yescharacteristic
704C2×C4C24×D511yescharacteristic
705C8—102no—
706C8—102no—
707C8—102no—
708C8—102no—
709C5C2×#312011yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—104no—
715C22—202no—
716C22—202no—
717C22—208no—
718C22#6616212yes—
719C22#6617112yes—
720C22#6617212yes—
721C22C23×C22⋊D511yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—104no—
732C4—202no—
733C4—202no—
734C4#6616212yes—
735C4C2×D5×#4111yescharacteristic
736C4C2×D5×#4111yescharacteristic
737C2—42no—
738C2—204no—
739C2#1061517714yesdirect product factor
740C2C2×#6616211yescharacteristic
741C2C2×#6617111yescharacteristic
742C2C2×#6617211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#541C2
socleC23×C5C22×D4
prime radicalC22×#709C22
hypercenterC2×#541D5
hypocenterC5C2×#3120
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. C2×C5×#541C2semidirect
3. #10615177C2direct (N × H)
4. C2×#65379C2semidirect
5. C2×#65372C2semidirect
6. C2×#65352C2semidirect
7. C2×#65355C2semidirect
10. C2×#65333C2semidirect
11. C2×#65332C2semidirect
12. C2×#65315C2semidirect
13. C2×#65319C2semidirect
14. C2×C4×#689C2semidirect
15. C2×C4×#688C2semidirect
16. C2×#65289C2semidirect
19. C5×#541C22semidirect
52. #65379C22semidirect
53. #65372C22semidirect
54. #65355C22semidirect
55. #65352C22semidirect
58. #65333C22semidirect
59. #65332C22semidirect
60. #65319C22semidirect
61. C4×#689C22semidirect
62. #65315C22semidirect
63. C4×#688C22semidirect
64. #65289C22semidirect
183. C2×#541D5semidirect
300. #541C2×D5semidirect
643. C2×C5#3120semidirect
709. C5C2×#3120semidirect
739. C2#10615177direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5412
C2×#658572
#106151772
C2×#653792
C2×#653722
C2×#653522
C2×#653552
C2×#653362
C2×#653332
C2×#653322
C2×#653152
C2×#653192
C2×C4×#6892
C2×C4×#6882
C2×#652892
C2×#31205