Finite Group Databasebeta

← C2×#10615323 #12977831

Subgroups — C2×#10615323 #12977831

Order 1280.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#552C211yesmaximal, characteristic, complemented
2C2×#65889C211yesmaximal, characteristic
3#10615323C2116yesmaximal, direct product factor
4C2×#65355C211yesmaximal, characteristic, complemented
5C2×#65354C211yesmaximal, characteristic, complemented
6C2×#65338C211yesmaximal, characteristic, complemented
7C2×#65337C211yesmaximal, characteristic, complemented
8C2×#65333C211yesmaximal, characteristic, complemented
9C2×#65332C211yesmaximal, characteristic, complemented
10C2×#65315C211yesmaximal, characteristic, complemented
11C2×#65310C211yesmaximal, characteristic, complemented
12C2×#65300C211yesmaximal, characteristic, complemented
13C2×#65292C211yesmaximal, characteristic, complemented
14C2×#65284C211yesmaximal, characteristic, complemented
15C2×#65256C211yesmaximal, characteristic, complemented
16C22×#3939C211yesmaximal, characteristic, complemented
17C22×#711—21no—
18C5×#552—24no—
19C5×#552C2218yescomplemented
20C2×C5×#126—21no—
21C2×C5×#125—21no—
22C2×C5×#125C2211yescharacteristic
23C2×C5×#123—21no—
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C5×#117—21no—
29C2×C5×#117C2211yescharacteristic
30C22×C5×C4⋊C4C2211yescharacteristic
31C22×#688C2211yescharacteristic
32C2×#4076C2211yescharacteristic
33C2×#4076C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C23×#168C2211yescharacteristic
38#65889—24no—
39#65889C2218yes—
40C2×#4043—21no—
41C2×#4032—21no—
42C2×#4032—21no—
43C2×C4×D20C2211yescharacteristic
44C2×#4015C2211yescharacteristic
45C2×#3967C2211yescharacteristic
46C2×#3967C2211yescharacteristic
47C2×#3967C2211yescharacteristic
48C2×C22⋊#168C2211yescharacteristic
49C2×C22⋊#168C2211yescharacteristic
50#65355C2218yescomplemented
51#65354C2218yescomplemented
52#65338C2218yescomplemented
53#65337C2218yescomplemented
54#65333C2218yescomplemented
55#65332C2218yescomplemented
56#65315C2218yescomplemented
57#65310C2218yescomplemented
58#65300C2218yescomplemented
59#65292C2218yescomplemented
60#65284C2218yescomplemented
61#65256C2218yescomplemented
62C2×#3941C2211yescharacteristic
63C2×#3941C2211yescharacteristic
64C2×#3941C2211yescharacteristic
65C2×#3940C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×#3939C2211yescharacteristic
69C2×#3939C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71C2×#3939C2211yescharacteristic
72C2×#3939C2211yescharacteristic
73C2×#3939C2211yescharacteristic
74C2×#3939C2218yescomplemented
75C2×C4⋊#168C2211yescharacteristic
76C2×#3935C2211yescharacteristic
77C2×#3343—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4D411yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C23×Dic5—21no—
86C23×Dic5—21no—
87C2×#711—28no—
88C2×#711—48no—
89C22×D20C2311yescharacteristic
90C22×C4×D5—21no—
91C22×Dic10—21no—
92C5×#126—28no—
93C5×#125—28no—
94C5×#125—22no—
95C5×#125C2314yes—
96C5×#123—28no—
97C5×C22⋊Q8—22no—
98C5×C22⋊Q8—22no—
99C5×C22⋊Q8C2314yes—
100C5×C22⋊Q8C2314yes—
101C4×C5×Q8—22no—
102C4×C5×Q8C2314yes—
103C4×C5×D4D414yes—
104C4×C5×D4C2314yes—
105C5×#117—22no—
106C5×#117—28no—
107C5×#117C2314yes—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—22no—
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⋊C4D411yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C4⋊C4C2311yescharacteristic
118C2×C5×C4⋊C4C2314yes—
119C2×C5×C4⋊C4C2311yescharacteristic
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4D411yescharacteristic
124C2×C5×C22⋊C4D411yescharacteristic
125C2×C42×C5—21no—
126C2×C42×C5—21no—
127C2×C42×C5C2311yescharacteristic
128C2×#688—24no—
129C2×#688C2314yes—
130#4076—22no—
131#4076—22no—
132#4076C2314yes—
133#4076C2314yes—
134C2×#685—21no—
135C2×#685—21no—
136C2×#685—21no—
137C2×C4⋊Dic5—21no—
138C2×C4⋊Dic5—21no—
139C2×C4⋊Dic5—21no—
140C2×C4⋊Dic5—22no—
141C2×C4⋊Dic5—22no—
142C2×C4⋊Dic5C2314yes—
143C2×C4⋊Dic5C2311yescharacteristic
144C2×C4⋊Dic5C2311yescharacteristic
145C2×C4⋊Dic5C2311yescharacteristic
146C2×C4⋊Dic5C2314yes—
147C2×#681—24no—
148C2×#681C2314yes—
149C22×#168—24no—
150C22×#168C2314yes—
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C22×#168C2311yescharacteristic
154C22×#168C2311yescharacteristic
155#4043—28no—
156#4032—28no—
157#4032—28no—
158C4×D20—22no—
159C4×D20C2314yes—
160#4015—22no—
161#4015C2314yes—
162#3967C2314yes—
163#3967C2314yes—
164#3967C2314yes—
165C22⋊#168C2314yes—
166C22⋊#168C2314yes—
167#3941C2314yes—
168#3941C2314yes—
169#3941C2314yes—
170#3940C2314yes—
171#3940C2314yes—
172#3940C2314yes—
173#3939C2314yes—
174#3939C2314yes—
175#3939C2314yes—
176#3939C2314yes—
177#3939C2314yes—
178#3939C2314yes—
179C4⋊#168C2314yes—
180#3935C2314yes—
181C2×#552D511yescharacteristic, complemented
182C2×#547—51no—
183#3343—516no—
184C2×#501—51no—
185C2×#484—51no—
186C2×#482—51no—
187C2×#483—51no—
188C2×#480—51no—
189C2×#477—51no—
190C2×#478—51no—
191C2×#468—51no—
192C2×#465—51no—
193C2×#440—51no—
194C2×#435—51no—
195C2×#428—51no—
196C22×#107—51no—
197C24×C5C2×D411yescharacteristic
198C24×C5C2×D411yescharacteristic
199C23×D5—21no—
200C2×C5×Q8—21no—
201C2×C5×Q8—22no—
202C2×C5×Q8—22no—
203C2×C5×Q8C2412yes—
204C2×C5×D4—24no—
205C2×C5×D4C2×D414yes—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—24no—
215C22×C4×C5—44no—
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D412yes—
221C22×C4×C5C2×D412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2411yescharacteristic
225C2×C22⋊D5—24no—
226C2×C22⋊D5—24no—
227C2×C22⋊D5—44no—
228C2×C22⋊D5—44no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—24no—
233C22×Dic5—24no—
234C22×Dic5—44no—
235C22×Dic5—44no—
236#711—432no—
237C2×D20—22no—
238C2×D20—22no—
239C2×D20—21no—
240C2×D20C2412yes—
241C2×C4×D5—24no—
242C2×C4×D5—44no—
243C2×Dic10—24no—
244C2×Dic10—44no—
245C5×C4⋊C4—21no—
246C5×C4⋊C4—21no—
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—21no—
254C5×C4⋊C4C2×D414yes—
255C5×C4⋊C4C2412yes—
256C5×C4⋊C4C2412yes—
257C5×C4⋊C4C2412yes—
258C5×C22⋊C4—24no—
259C5×C22⋊C4—24no—
260C5×C22⋊C4—24no—
261C5×C22⋊C4C2×D414yes—
262C5×C22⋊C4C2×D414yes—
263C42×C5—24no—
264C42×C5—24no—
265C42×C5C2×D412yes—
266C42×C5C2412yes—
267#688—28no—
268#685—24no—
269#685—24no—
270#685—24no—
271C4⋊Dic5—21no—
272C4⋊Dic5—21no—
273C4⋊Dic5—24no—
274C4⋊Dic5—21no—
275C4⋊Dic5—24no—
276C4⋊Dic5—24no—
277C4⋊Dic5C2412yes—
278C4⋊Dic5C2412yes—
279C4⋊Dic5C2412yes—
280#681—28no—
281C2×#168—22no—
282C2×#168—22no—
283C2×#168—22no—
284C2×#168—28no—
285C2×#168#4114yescomplemented
286C2×#168C2412yes—
287C2×#168C2412yes—
288C2×#168C2412yes—
289C2×#168C2412yes—
290C22×#41—101no—
291C22×SD16—51no—
292C22×M16—51no—
293C23×C8—51no—
294#552—24no—
295#552C2×D518yescomplemented
296#547—58no—
297#547—104no—
298C2×C4⋊Q8—51no—
299C2×#126—21no—
300C2×#125—21no—
301C2×#125C2×D511yescharacteristic
302C2×#123—21no—
303C2×#123—101no—
304C2×#123—101no—
305C2×C22⋊Q8—101no—
306C2×C22⋊Q8C2×D511yescharacteristic
307C2×C22⋊Q8C2×D511yescharacteristic
308C2×#121—51no—
309C2×#121—51no—
310C2×C4×Q8C2×D511yescharacteristic
311C2×C4×D4—51no—
312C2×C4×D4C2×D511yescharacteristic
313C2×#117—21no—
314C2×#117C2×D511yescharacteristic
315C22×C4⋊C4—51no—
316C22×C4⋊C4—51no—
317C22×C4⋊C4C2×D511yescharacteristic
318#501—58no—
319#484—58no—
320#483—58no—
321#482—58no—
322#480—58no—
323#478—58no—
324#477—58no—
325#468—58no—
326#465—58no—
327#440—58no—
328#435—58no—
329#428—58no—
330C2×#107—51no—
331C2×#107—51no—
332C2×#107—51no—
333C2×#107—51no—
334C2×#107—58no—
335C2×#107—51no—
336C2×#107—51no—
337C2×#106—51no—
338C2×#106—51no—
339C2×#106—51no—
340C2×C4⋊C8—51no—
341C2×#103—51no—
342C2×#103—51no—
343C2×#103—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×C22⋊C8—51no—
348C2×C22⋊C8—51no—
349C2×#97—51no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5AGL(1,ℤ/8)14yes—
356C23×C5C22×D412yes—
357C23×C5C22×D412yes—
358C23×C5C22×D411yescharacteristic
359C22×D5—22no—
360C22×D5—42no—
361C22×D5—42no—
362C22×D5—42no—
363C5×Q8—22no—
364C5×Q8—22no—
365C5×Q8—42no—
366C5×D4—28no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—24no—
372C2×C4×C5—24no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
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—48no—
383C2×C4×C5—42no—
384C2×C4×C5—42no—
385C2×C4×C5—42no—
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×C52−1+412yes—
393C2×C4×C5C2511yescharacteristic
394C22⋊D5—48no—
395C22⋊D5—48no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—48no—
400C2×Dic5—42no—
401C2×Dic5—42no—
402C2×Dic5—42no—
403C2×Dic5—48no—
404D20—22no—
405D20—22no—
406D20—42no—
407C4×D5—48no—
408Dic10—48no—
409#168—22no—
410#168—22no—
411#168—22no—
412#168C2×#4114yescomplemented
413C2×#41—108no—
414C2×#41—208no—
415C22×Q8—101no—
416C22×Q8C22×D511yescharacteristic
417C22×D4—51no—
418C22×D4—101no—
419C22×D4—101no—
420C22×D4C22⋊D511yescharacteristic
421C23×C4—21no—
422C23×C4—101no—
423C23×C4—101no—
424C23×C4—101no—
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D511yescharacteristic
427C2×SD16—54no—
428C2×SD16—104no—
429C2×M16—54no—
430C2×M16—104no—
431C22×C8—51no—
432C22×C8—51no—
433C22×C8—54no—
434C22×C8—51no—
435C22×C8—51no—
436C22×C8—104no—
437C4⋊Q8—54no—
438C4⋊Q8—102no—
439#126—28no—
440#125—28no—
441#125—22no—
442#125C22×D514yes—
443#123—28no—
444#123—108no—
445#123—108no—
446C22⋊Q8—22no—
447C22⋊Q8—22no—
448C22⋊Q8—108no—
449C22⋊Q8C22×D514yes—
450C22⋊Q8C22×D514yes—
451#121—54no—
452#121—54no—
453#121—102no—
454#121—102no—
455C4×Q8—22no—
456C4×Q8C22×D514yes—
457C4×D4—54no—
458C4×D4—102no—
459C4×D4C22⋊D514yes—
460C4×D4C22×D514yes—
461#117—22no—
462#117—28no—
463#117C22×D514yes—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—51no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—51no—
474C2×C4⋊C4—54no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—101no—
477C2×C4⋊C4—101no—
478C2×C4⋊C4—102no—
479C2×C4⋊C4—102no—
480C2×C4⋊C4—101no—
481C2×C4⋊C4C22⋊D511yescharacteristic
482C2×C4⋊C4C22×D511yescharacteristic
483C2×C4⋊C4C22×D511yescharacteristic
484C2×C4⋊C4C22×D514yes—
485C2×C4⋊C4C22×D511yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—101no—
490C2×C22⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4C22⋊D511yescharacteristic
493C2×C22⋊C4C22⋊D511yescharacteristic
494C2×C42—21no—
495C2×C42—21no—
496C2×C42C22×D511yescharacteristic
497#107—54no—
498#107—54no—
499#107—54no—
500#107—54no—
501#107—54no—
502#107—54no—
503#106—54no—
504#106—54no—
505#106—54no—
506C4⋊C8—54no—
507#103—54no—
508#103—54no—
509#103—54no—
510#102—54no—
511#102—54no—
512#102—54no—
513C22⋊C8—54no—
514C22⋊C8—54no—
515#97—54no—
516C22×C5—28no—
517C22×C5—22no—
518C22×C5—22no—
519C22×C5—22no—
520C22×C5—22no—
521C22×C5—22no—
522C22×C5—44no—
523C22×C5#54712yes—
524C22×C5C2×AGL(1,ℤ/8)14yes—
525C22×C5C2×AGL(1,ℤ/8)12yes—
526C22×C5#57812yes—
527C22×C5C23×D411yescharacteristic
528C2×D5—42no—
529C2×D5—42no—
530C2×D5—42no—
531C2×D5—84no—
532C4×C5—22no—
533C4×C5—22no—
534C4×C5—22no—
535C4×C5—22no—
536C4×C5—42no—
537C4×C5—42no—
538C4×C5—42no—
539C4×C5—42no—
540C4×C5#54712yes—
541C4×C5C22×#4111yescharacteristic
542C4×C5C2×2−1+411yescharacteristic
543Dic5—42no—
544Dic5—42no—
545Dic5—42no—
546C24—101no—
547C24C2×C22⋊D511yescharacteristic
548C24C2×C22⋊D511yescharacteristic
549#41—2032no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—104no—
554C2×Q8—204no—
555C2×Q8C23×D512yes—
556C2×D4—24no—
557C2×D4—52no—
558C2×D4—104no—
559C2×D4—104no—
560C2×D4—102no—
561C2×D4—102no—
562C2×D4—101no—
563C2×D4—204no—
564C2×D4—204no—
565C2×D4C2×C22⋊D514yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—44no—
576C22×C4—104no—
577C22×C4—104no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—104no—
582C22×C4—204no—
583C22×C4—204no—
584C22×C4—204no—
585C22×C4C2×C22⋊D512yes—
586C22×C4C2×C22⋊D512yes—
587C22×C4C2×C22⋊D511yescharacteristic
588C22×C4C2×C22⋊D511yescharacteristic
589C22×C4C2×C22⋊D511yescharacteristic
590C22×C4C2×C22⋊D511yescharacteristic
591C22×C4C23×D512yes—
592C22×C4C23×D512yes—
593C22×C4C23×D511yescharacteristic
594SD16—108no—
595M16—108no—
596C2×C8—54no—
597C2×C8—52no—
598C2×C8—52no—
599C2×C8—52no—
600C2×C8—52no—
601C2×C8—108no—
602C2×C8—102no—
603C2×C8—102no—
604C2×C8—102no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—52no—
615C4⋊C4—52no—
616C4⋊C4—52no—
617C4⋊C4—101no—
618C4⋊C4—101no—
619C4⋊C4—101no—
620C4⋊C4—104no—
621C4⋊C4—104no—
622C4⋊C4—104no—
623C4⋊C4C2×C22⋊D514yes—
624C4⋊C4C23×D512yes—
625C4⋊C4C23×D512yes—
626C4⋊C4C23×D512yes—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—104no—
631C22⋊C4—104no—
632C22⋊C4—104no—
633C22⋊C4C2×C22⋊D514yes—
634C22⋊C4C2×C22⋊D514yes—
635C42—24no—
636C42—24no—
637C42C2×C22⋊D512yes—
638C42C23×D512yes—
639C2×C5—24no—
640C2×C5—42no—
641C2×C5#334314yescomplemented
642C2×C5C2×#54711yescharacteristic
643C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
644C2×C5C2×#57811yescharacteristic
645D5—82no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—102no—
652C23—202no—
653C23—202no—
654C23—202no—
655C23#409514yes—
656C23C22×C22⋊D512yes—
657C23C22×C22⋊D512yes—
658C23C22×C22⋊D511yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—208no—
663D4—28no—
664D4—102no—
665D4—102no—
666D4—208no—
667D4—208no—
668D4—202no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—48no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—208no—
692C2×C4—208no—
693C2×C4—202no—
694C2×C4—202no—
695C2×C4—202no—
696C2×C4—208no—
697C2×C4D5×#4112yes—
698C2×C4#415012yes—
699C2×C4C22×C22⋊D512yes—
700C2×C4C22×C22⋊D512yes—
701C2×C4C22×C22⋊D512yes—
702C2×C4C22×C22⋊D512yes—
703C2×C4C22×C22⋊D511yescharacteristic
704C2×C4C24×D511yescharacteristic
705C8—54no—
706C8—102no—
707C8—102no—
708C8—102no—
709C5C2×#334311yescharacteristic, complemented, Sylow
710C22—28no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—202no—
718C22—202no—
719C22—202no—
720C22—404no—
721C22C2×#409514yes—
722C22C2×#409512yes—
723C22#6615812yes—
724C22#6617212yes—
725C22C23×C22⋊D511yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—202no—
735C4—202no—
736C4—202no—
737C4#6615812yes—
738C4C2×D5×#4111yescharacteristic
739C4C2×#415011yescharacteristic
740C2—24no—
741C2—42no—
742C2—402no—
743C2#1061532314yesdirect product factor
744C2C22×#409511yescharacteristic
745C2C2×#6615811yescharacteristic
746C2C2×#6617211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#552C2
socleC23×C5C22×D4
prime radicalC2×#65889C2
hypercenterC2×#552D5
hypocenterC5C2×#3343
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×C5×#552C2semidirect
3. #10615323C2direct (N × H)
4. C2×#65355C2semidirect
5. C2×#65354C2semidirect
6. C2×#65338C2semidirect
7. C2×#65337C2semidirect
8. C2×#65333C2semidirect
9. C2×#65332C2semidirect
10. C2×#65315C2semidirect
11. C2×#65310C2semidirect
12. C2×#65300C2semidirect
13. C2×#65292C2semidirect
14. C2×#65284C2semidirect
15. C2×#65256C2semidirect
16. C22×#3939C2semidirect
19. C5×#552C22semidirect
50. #65355C22semidirect
51. #65354C22semidirect
52. #65338C22semidirect
53. #65337C22semidirect
54. #65333C22semidirect
55. #65332C22semidirect
56. #65315C22semidirect
57. #65310C22semidirect
58. #65300C22semidirect
59. #65292C22semidirect
60. #65284C22semidirect
61. #65256C22semidirect
74. C2×#3939C22semidirect
181. C2×#552D5semidirect
285. C2×#168#41semidirect
295. #552C2×D5semidirect
412. #168C2×#41semidirect
641. C2×C5#3343semidirect
709. C5C2×#3343semidirect
743. C2#10615323direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5522
C2×#658892
#106153232
C2×#653552
C2×#653542
C2×#653382
C2×#653372
C2×#653332
C2×#653322
C2×#653152
C2×#653102
C2×#653002
C2×#652922
C2×#652842
C2×#652562
C22×#39392
C2×#33435