Finite Group Databasebeta

← C2×#10615159 #12969980

Subgroups — C2×#10615159 #12969980

Order 1280.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#537C211yesmaximal, characteristic
2C2×#66159C211yesmaximal, characteristic, complemented
3C2×#65528C211yesmaximal, characteristic, complemented
4C2×#65528C211yesmaximal, characteristic, complemented
5C2×#65523C211yesmaximal, characteristic, complemented
6#10615159C2116yesmaximal, direct product factor
7C2×#65339C211yesmaximal, characteristic, complemented
8C2×#65341C211yesmaximal, characteristic, complemented
9C2×#65340C211yesmaximal, characteristic, complemented
10C2×#65334C211yesmaximal, characteristic, complemented
11C2×#65329C211yesmaximal, characteristic, complemented
12C2×#65331C211yesmaximal, characteristic, complemented
13C2×#65330C211yesmaximal, characteristic, complemented
14C2×#65324C211yesmaximal, characteristic, complemented
15C2×#65259C211yesmaximal, characteristic, complemented
16C2×#65260C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C22×C5×#41C2211yescharacteristic
19C23×Dic10C2211yescharacteristic
20C5×#537—24no—
21C5×#537C2218yes—
22C2×C5×C22⋊Q8—21no—
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C5×#121—21no—
26C2×C5×#121—21no—
27C2×C5×#121—21no—
28C2×C5×#121C2211yescharacteristic
29C2×C5×#121C2211yescharacteristic
30C22×C5×C4⋊C4C2211yescharacteristic
31#66159—24no—
32#66159C2218yescomplemented
33C2×#4090—21no—
34C22×#689C2211yescharacteristic
35C22×#689C2211yescharacteristic
36C2×#4082—21no—
37C2×#4081—21no—
38C2×#4081—21no—
39C22×#687C2211yescharacteristic
40C22×#687C2211yescharacteristic
41C2×#4072C2211yescharacteristic
42C2×#4070C2211yescharacteristic
43C2×#4070C2211yescharacteristic
44C2×#4070C2211yescharacteristic
45C2×#4070C2211yescharacteristic
46C22×#681C2211yescharacteristic
47C23×#168C2211yescharacteristic
48#65528C2218yescomplemented
49#65528C2218yescomplemented
50#65523C2218yescomplemented
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54C2×#3964C2211yescharacteristic
55C2×C22⋊#168C2211yescharacteristic
56C2×C22⋊#168C2211yescharacteristic
57C2×C22⋊#168C2211yescharacteristic
58C2×C22⋊#168C2211yescharacteristic
59#65341C2218yescomplemented
60#65340C2218yescomplemented
61#65339C2218yescomplemented
62#65334C2218yescomplemented
63#65331C2218yescomplemented
64#65330C2218yescomplemented
65#65329C2218yescomplemented
66#65324C2218yescomplemented
67#65260C2218yescomplemented
68#65259C2218yescomplemented
69C2×#3942C2211yescharacteristic
70C2×#3942C2211yescharacteristic
71C2×#3942C2211yescharacteristic
72C2×#3942C2211yescharacteristic
73C2×#3940C2211yescharacteristic
74C2×#3940C2211yescharacteristic
75C2×#3939C2211yescharacteristic
76C2×#3939C2211yescharacteristic
77C2×#3201—51nomaximal, Sylow
78C2×C5×#41—22no—
79C2×C5×#41—42no—
80C2×C5×#41—42no—
81C2×C5×#41—42no—
82C2×C5×#41—42no—
83C2×C5×#41D414yes—
84C2×C5×#41C2314yes—
85C2×C5×#41C2314yes—
86C22×C5×Q8D411yescharacteristic
87C22×C5×Q8C2311yescharacteristic
88C22×C5×D4—21no—
89C22×C5×D4—21no—
90C22×C5×D4—21no—
91C22×C5×D4D411yescharacteristic
92C22×C5×D4D411yescharacteristic
93C22×C5×D4D411yescharacteristic
94C22×C5×D4C2311yescharacteristic
95C23×C4×C5—21no—
96C23×C4×C5—21no—
97C23×C4×C5C2311yescharacteristic
98C23×C4×C5C2311yescharacteristic
99C23×C4×C5C2311yescharacteristic
100C23×Dic5—21no—
101C22×Dic10—21no—
102C22×Dic10—22no—
103C22×Dic10—42no—
104C22×Dic10—42no—
105C22×Dic10C2311yescharacteristic
106C22×Dic10C2311yescharacteristic
107C22×Dic10C2314yes—
108C5×C22⋊Q8—28no—
109C5×C22⋊Q8—22no—
110C5×C22⋊Q8—22no—
111C5×C22⋊Q8C2314yes—
112C5×C22⋊Q8C2314yes—
113C5×#121—28no—
114C5×#121—28no—
115C5×#121—28no—
116C5×#121—22no—
117C5×#121—22no—
118C5×#121C2314yes—
119C5×#121C2314yes—
120C2×C5×C4⋊C4—21no—
121C2×C5×C4⋊C4—22no—
122C2×C5×C4⋊C4—21no—
123C2×C5×C4⋊C4—21no—
124C2×C5×C4⋊C4C2311yescharacteristic
125C2×C5×C4⋊C4C2311yescharacteristic
126C2×C5×C4⋊C4C2314yes—
127C2×C5×C22⋊C4—21no—
128C2×C5×C22⋊C4—21no—
129C2×C5×C22⋊C4—21no—
130C2×C5×C22⋊C4—21no—
131C2×C22⋊Dic5—21no—
132C2×C22⋊Dic5—21no—
133C2×C22⋊Dic5—21no—
134C2×C22⋊Dic5—21no—
135C2×C22⋊Dic5—21no—
136#4090—28no—
137C2×#689—42no—
138C2×#689—42no—
139C2×#689C2314yes—
140C2×#689C2314yes—
141#4082—28no—
142#4081—28no—
143#4081—28no—
144C2×#687—42no—
145C2×#687—42no—
146C2×#687C2314yes—
147C2×#687C2314yes—
148#4072—22no—
149#4072C2314yes—
150C2×C4⋊Dic5C2311yescharacteristic
151C2×C4⋊Dic5C2311yescharacteristic
152#4070—22no—
153#4070—22no—
154#4070—22no—
155#4070—22no—
156#4070C2314yes—
157#4070C2314yes—
158#4070C2314yes—
159#4070C2314yes—
160C2×#683—21no—
161C2×#683—21no—
162C2×#683—21no—
163C2×#683—21no—
164C2×C4×Dic5—21no—
165C2×#681—42no—
166C2×#681C2314yes—
167C22×#168—42no—
168C22×#168C2311yescharacteristic
169C22×#168C2311yescharacteristic
170C22×#168C2311yescharacteristic
171C22×#168C2311yescharacteristic
172C22×#168C2314yes—
173#3967C2314yes—
174#3967C2314yes—
175#3964C2314yes—
176#3964C2314yes—
177C22⋊#168C2314yes—
178C22⋊#168C2314yes—
179C22⋊#168C2314yes—
180C22⋊#168C2314yes—
181#3942C2314yes—
182#3942C2314yes—
183#3942C2314yes—
184#3942C2314yes—
185#3940C2314yes—
186#3940C2314yes—
187#3939C2314yes—
188#3939C2314yes—
189C2×#537D511yescharacteristic
190C2×#536—51no—
191#3201—516no—
192C2×#484—51no—
193C2×#485—51no—
194C2×#482—51no—
195C2×#483—51no—
196C2×#470—51no—
197C2×#468—51no—
198C2×#467—51no—
199C2×#465—51no—
200C2×#452—51no—
201C2×#452—51no—
202C2×#451—51no—
203C2×#448—51no—
204C2×#408—51no—
205C24×C5—21no—
206C24×C5C2×D411yescharacteristic
207C24×C5C2×D411yescharacteristic
208C24×C5C2×D411yescharacteristic
209C5×#41—48no—
210C5×#41—44no—
211C5×#41—44no—
212C5×#41—44no—
213C5×#41—44no—
214C5×#41—48no—
215C2×C5×Q8—21no—
216C2×C5×Q8—22no—
217C2×C5×Q8—22no—
218C2×C5×Q8—42no—
219C2×C5×Q8C2×D414yes—
220C2×C5×Q8C2412yes—
221C2×C5×D4—24no—
222C2×C5×D4—24no—
223C2×C5×D4—24no—
224C2×C5×D4—21no—
225C2×C5×D4—22no—
226C2×C5×D4—22no—
227C2×C5×D4—42no—
228C2×C5×D4—42no—
229C2×C5×D4—42no—
230C2×C5×D4—44no—
231C2×C5×D4—82no—
232C2×C5×D4—82no—
233C2×C5×D4C2×D414yes—
234C2×C5×D4C2×D414yes—
235C2×C5×D4C2×D414yes—
236C2×C5×D4C2412yes—
237C22×C4×C5—22no—
238C22×C4×C5—22no—
239C22×C4×C5—22no—
240C22×C4×C5—22no—
241C22×C4×C5—22no—
242C22×C4×C5—22no—
243C22×C4×C5—21no—
244C22×C4×C5—21no—
245C22×C4×C5—21no—
246C22×C4×C5—24no—
247C22×C4×C5—24no—
248C22×C4×C5—44no—
249C22×C4×C5—82no—
250C22×C4×C5C2×D411yescharacteristic
251C22×C4×C5C2×D411yescharacteristic
252C22×C4×C5C2×D411yescharacteristic
253C22×C4×C5C2×D412yes—
254C22×C4×C5C2×D412yes—
255C22×C4×C5C2×D412yes—
256C22×C4×C5C2412yes—
257C22×C4×C5C2412yes—
258C22×C4×C5C2412yes—
259C22×C4×C5C2411yescharacteristic
260C22×Dic5—21no—
261C22×Dic5—21no—
262C22×Dic5—21no—
263C22×Dic5—21no—
264C22×Dic5—24no—
265C22×Dic5—44no—
266C2×Dic10—22no—
267C2×Dic10—22no—
268C2×Dic10—22no—
269C2×Dic10—22no—
270C2×Dic10—21no—
271C2×Dic10—21no—
272C2×Dic10—24no—
273C2×Dic10—44no—
274C2×Dic10—44no—
275C2×Dic10—44no—
276C2×Dic10—48no—
277C2×Dic10C2412yes—
278C2×Dic10C2412yes—
279C5×C4⋊C4—24no—
280C5×C4⋊C4—21no—
281C5×C4⋊C4—21no—
282C5×C4⋊C4—24no—
283C5×C4⋊C4—24no—
284C5×C4⋊C4C2412yes—
285C5×C4⋊C4C2412yes—
286C5×C22⋊C4—24no—
287C5×C22⋊C4—24no—
288C5×C22⋊C4—24no—
289C5×C22⋊C4—24no—
290C22⋊Dic5—24no—
291C22⋊Dic5—24no—
292C22⋊Dic5—24no—
293C22⋊Dic5—24no—
294C22⋊Dic5—24no—
295#689—44no—
296#689—44no—
297#687—44no—
298#687—44no—
299C4⋊Dic5—21no—
300C4⋊Dic5—21no—
301C4⋊Dic5C2412yes—
302C4⋊Dic5C2412yes—
303#683—24no—
304#683—24no—
305#683—24no—
306#683—24no—
307C4×Dic5—24no—
308#681—44no—
309C2×#168—22no—
310C2×#168—22no—
311C2×#168—22no—
312C2×#168—22no—
313C2×#168—44no—
314C2×#168C2412yes—
315C2×#168C2412yes—
316C2×#168C2412yes—
317C2×#168C2412yes—
318C22×#41C2×D511yescharacteristic
319C22×#41C2×D511yescharacteristic
320C23×Q8—51no—
321C22×Q16—51no—
322C22×Q16—51no—
323C22×SD16—51no—
324C22×SD16—51no—
325C22×M16—51no—
326C23×C8—51no—
327#537—24no—
328#537C2×D518yes—
329#536—58no—
330#536—104no—
331C2×C4⋊Q8—101no—
332C2×#124—101no—
333C2×#123—101no—
334C2×#123—101no—
335C2×C22⋊Q8—21no—
336C2×C22⋊Q8—51no—
337C2×C22⋊Q8—51no—
338C2×C22⋊Q8—51no—
339C2×C22⋊Q8—51no—
340C2×C22⋊Q8C2×D511yescharacteristic
341C2×C22⋊Q8C2×D511yescharacteristic
342C2×#121—21no—
343C2×#121—21no—
344C2×#121—21no—
345C2×#121C2×D511yescharacteristic
346C2×#121C2×D511yescharacteristic
347C2×#117—51no—
348C22×C4⋊C4C2×D511yescharacteristic
349#485—58no—
350#484—58no—
351#483—58no—
352#482—58no—
353#470—58no—
354#468—58no—
355#467—58no—
356#465—58no—
357#452—58no—
358#452—58no—
359#451—58no—
360#448—58no—
361C2×#107—51no—
362C2×#107—51no—
363C2×#106—51no—
364C2×#106—51no—
365C2×#103—51no—
366C2×#103—51no—
367C2×#103—51no—
368C2×#103—51no—
369C2×#103—51no—
370C2×#103—51no—
371C2×#102—51no—
372C2×#102—51no—
373#408—58no—
374C2×C22⋊C8—51no—
375C2×C22⋊C8—51no—
376C2×C22⋊C8—51no—
377C2×C22⋊C8—51no—
378C23×C5—22no—
379C23×C5—22no—
380C23×C5—22no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5—22no—
386C23×C5—22no—
387C23×C5—22no—
388C23×C5—42no—
389C23×C5—42no—
390C23×C5—42no—
391C23×C5C22×D412yes—
392C23×C5C22×D412yes—
393C23×C5C22×D412yes—
394C23×C5C22×D411yescharacteristic
395C5×Q8—22no—
396C5×Q8—22no—
397C5×Q8—44no—
398C5×Q8—42no—
399C5×D4—22no—
400C5×D4—22no—
401C5×D4—44no—
402C5×D4—44no—
403C5×D4—44no—
404C5×D4—48no—
405C5×D4—42no—
406C5×D4—84no—
407C5×D4—84no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—24no—
412C2×C4×C5—24no—
413C2×C4×C5—24no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—48no—
424C2×C4×C5—42no—
425C2×C4×C5—42no—
426C2×C4×C5—42no—
427C2×C4×C5—84no—
428C2×C4×C5C22×D412yes—
429C2×C4×C5C22×D412yes—
430C2×C4×C5C22×D412yes—
431C2×C4×C5C22×D411yescharacteristic
432C2×C4×C5H(5,𝔽2)12yes—
433C2×C4×C5H(5,𝔽2)12yes—
434C2×C4×C5C2511yescharacteristic
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—48no—
440C2×Dic5—42no—
441C2×Dic5—42no—
442C2×Dic5—42no—
443C2×Dic5—42no—
444Dic10—22no—
445Dic10—22no—
446Dic10—22no—
447Dic10—22no—
448Dic10—48no—
449Dic10—42no—
450Dic10—42no—
451#168—22no—
452#168—22no—
453#168—22no—
454#168—22no—
455C2×#41—22no—
456C2×#41—42no—
457C2×#41—42no—
458C2×#41—42no—
459C2×#41—42no—
460C2×#41C22⋊D514yes—
461C2×#41C22×D514yes—
462C2×#41C22×D514yes—
463C22×Q8—51no—
464C22×Q8—51no—
465C22×Q8—54no—
466C22×Q8—101no—
467C22×Q8—102no—
468C22×Q8—202no—
469C22×Q8—202no—
470C22×Q8C22⋊D511yescharacteristic
471C22×Q8C22×D511yescharacteristic
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4C22⋊D511yescharacteristic
476C22×D4C22⋊D511yescharacteristic
477C22×D4C22⋊D511yescharacteristic
478C22×D4C22×D511yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—101no—
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D511yescharacteristic
485C2×Q16—54no—
486C2×Q16—54no—
487C2×Q16—202no—
488C2×Q16—202no—
489C2×SD16—54no—
490C2×SD16—54no—
491C2×SD16—202no—
492C2×SD16—202no—
493C2×M16—54no—
494C2×M16—202no—
495C22×C8—51no—
496C22×C8—51no—
497C22×C8—51no—
498C22×C8—51no—
499C22×C8—54no—
500C22×C8—202no—
501C4⋊Q8—108no—
502#124—108no—
503#123—108no—
504#123—108no—
505C22⋊Q8—28no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—54no—
509C22⋊Q8—54no—
510C22⋊Q8—54no—
511C22⋊Q8—54no—
512C22⋊Q8—102no—
513C22⋊Q8—102no—
514C22⋊Q8—102no—
515C22⋊Q8—102no—
516C22⋊Q8C22×D514yes—
517C22⋊Q8C22×D514yes—
518#121—28no—
519#121—28no—
520#121—28no—
521#121—22no—
522#121—22no—
523#121C22×D514yes—
524#121C22×D514yes—
525#117—54no—
526#117—102no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—51no—
532C2×C4⋊C4—51no—
533C2×C4⋊C4—101no—
534C2×C4⋊C4—101no—
535C2×C4⋊C4—101no—
536C2×C4⋊C4—101no—
537C2×C4⋊C4C22×D511yescharacteristic
538C2×C4⋊C4C22×D511yescharacteristic
539C2×C4⋊C4C22×D514yes—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—101no—
545C2×C22⋊C4—101no—
546C2×C22⋊C4—101no—
547C2×C22⋊C4—101no—
548C2×C22⋊C4—101no—
549C2×C42—101no—
550#107—54no—
551#107—54no—
552#106—54no—
553#106—54no—
554#103—54no—
555#103—54no—
556#103—54no—
557#103—54no—
558#103—54no—
559#103—54no—
560#102—54no—
561#102—54no—
562C22⋊C8—54no—
563C22⋊C8—54no—
564C22⋊C8—54no—
565C22⋊C8—54no—
566C22×C5—22no—
567C22×C5—22no—
568C22×C5—22no—
569C22×C5—22no—
570C22×C5—22no—
571C22×C5—22no—
572C22×C5—22no—
573C22×C5—22no—
574C22×C5—22no—
575C22×C5—44no—
576C22×C5—44no—
577C22×C5—44no—
578C22×C5—42no—
579C22×C5—42no—
580C22×C5—42no—
581C22×C5—84no—
582C22×C5#53412yes—
583C22×C5#57712yes—
584C22×C5#57812yes—
585C22×C5C23×D411yescharacteristic
586C4×C5—22no—
587C4×C5—22no—
588C4×C5—22no—
589C4×C5—42no—
590C4×C5—42no—
591C4×C5—42no—
592C4×C5#53412yes—
593C4×C5C2×H(5,𝔽2)11yescharacteristic
594C4×C5C2×H(5,𝔽2)11yescharacteristic
595Dic5—42no—
596Dic5—42no—
597Dic5—42no—
598Dic5—42no—
599C24—21no—
600C24C2×C22⋊D511yescharacteristic
601C24C2×C22⋊D511yescharacteristic
602C24C2×C22⋊D511yescharacteristic
603#41—48no—
604#41—44no—
605#41—44no—
606#41—44no—
607#41—44no—
608#41—48no—
609C2×Q8—21no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—42no—
613C2×Q8—52no—
614C2×Q8—52no—
615C2×Q8—101no—
616C2×Q8—101no—
617C2×Q8—104no—
618C2×Q8—102no—
619C2×Q8—102no—
620C2×Q8—102no—
621C2×Q8—102no—
622C2×Q8—204no—
623C2×Q8—204no—
624C2×Q8—204no—
625C2×Q8—208no—
626C2×Q8C2×C22⋊D514yes—
627C2×Q8C23×D512yes—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—24no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—21no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—44no—
638C2×D4—82no—
639C2×D4—82no—
640C2×D4C2×C22⋊D514yes—
641C2×D4C2×C22⋊D514yes—
642C2×D4C2×C22⋊D514yes—
643C2×D4C23×D512yes—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—44no—
656C22×C4—82no—
657C22×C4—104no—
658C22×C4—101no—
659C22×C4—101no—
660C22×C4—101no—
661C22×C4—101no—
662C22×C4—204no—
663C22×C4C2×C22⋊D512yes—
664C22×C4C2×C22⋊D512yes—
665C22×C4C2×C22⋊D512yes—
666C22×C4C2×C22⋊D511yescharacteristic
667C22×C4C2×C22⋊D511yescharacteristic
668C22×C4C2×C22⋊D511yescharacteristic
669C22×C4C23×D512yes—
670C22×C4C23×D512yes—
671C22×C4C23×D512yes—
672C22×C4C23×D511yescharacteristic
673Q16—204no—
674Q16—204no—
675SD16—204no—
676SD16—204no—
677M16—204no—
678C2×C8—52no—
679C2×C8—52no—
680C2×C8—52no—
681C2×C8—52no—
682C2×C8—102no—
683C2×C8—102no—
684C2×C8—102no—
685C2×C8—102no—
686C2×C8—204no—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—52no—
693C4⋊C4—52no—
694C4⋊C4—101no—
695C4⋊C4—101no—
696C4⋊C4—104no—
697C4⋊C4—104no—
698C4⋊C4—104no—
699C4⋊C4—104no—
700C4⋊C4C23×D512yes—
701C4⋊C4C23×D512yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—104no—
707C22⋊C4—104no—
708C22⋊C4—104no—
709C22⋊C4—104no—
710C22⋊C4—104no—
711C42—104no—
712C2×C5—42no—
713C2×C5—42no—
714C2×C5—42no—
715C2×C5—82no—
716C2×C5#320114yescomplemented
717C2×C5C2×#53411yescharacteristic
718C2×C5C2×#57711yescharacteristic
719C2×C5C2×#57811yescharacteristic
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23C22×C22⋊D512yes—
734C23C22×C22⋊D512yes—
735C23C22×C22⋊D512yes—
736C23C22×C22⋊D511yescharacteristic
737Q8—22no—
738Q8—22no—
739Q8—44no—
740Q8—42no—
741Q8—102no—
742Q8—102no—
743Q8—102no—
744Q8—102no—
745Q8—208no—
746Q8—202no—
747Q8—202no—
748D4—22no—
749D4—22no—
750D4—44no—
751D4—44no—
752D4—44no—
753D4—48no—
754D4—42no—
755D4—84no—
756D4—84no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—48no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—84no—
777C2×C4—102no—
778C2×C4—102no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—208no—
782C2×C4—202no—
783C2×C4—202no—
784C2×C4—202no—
785C2×C4—202no—
786C2×C4#414412yes—
787C2×C4#414412yes—
788C2×C4C22×C22⋊D512yes—
789C2×C4C22×C22⋊D512yes—
790C2×C4C22×C22⋊D512yes—
791C2×C4C22×C22⋊D511yescharacteristic
792C2×C4C24×D511yescharacteristic
793C8—102no—
794C8—102no—
795C8—102no—
796C8—102no—
797C5C2×#320111yescharacteristic, complemented, Sylow
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—84no—
814C22#6613812yes—
815C22#6617012yes—
816C22#6617212yes—
817C22C23×C22⋊D511yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—202no—
825C4—202no—
826C4—202no—
827C4—202no—
828C4#6613812yes—
829C4C2×#414411yescharacteristic
830C4C2×#414411yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—82no—
835C2#1061515914yesdirect product factor
836C2C2×#6613811yescharacteristic
837C2C2×#6617011yescharacteristic
838C2C2×#6617211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
Fitting, prime radicalC2×C5×#537C2
socleC23×C5C22×D4
hypercenterC2×#537D5
hypocenterC5C2×#3201
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
2. C2×#66159C2semidirect
3. C2×#65528C2semidirect
4. C2×#65528C2semidirect
5. C2×#65523C2semidirect
6. #10615159C2direct (N × H)
7. C2×#65339C2semidirect
8. C2×#65341C2semidirect
9. C2×#65340C2semidirect
10. C2×#65334C2semidirect
11. C2×#65329C2semidirect
12. C2×#65331C2semidirect
13. C2×#65330C2semidirect
14. C2×#65324C2semidirect
15. C2×#65259C2semidirect
16. C2×#65260C2semidirect
32. #66159C22semidirect
48. #65528C22semidirect
49. #65528C22semidirect
50. #65523C22semidirect
59. #65341C22semidirect
60. #65340C22semidirect
61. #65339C22semidirect
62. #65334C22semidirect
63. #65331C22semidirect
64. #65330C22semidirect
65. #65329C22semidirect
66. #65324C22semidirect
67. #65260C22semidirect
68. #65259C22semidirect
716. C2×C5#3201semidirect
797. C5C2×#3201semidirect
835. C2#10615159direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5372
C2×#661592
C2×#655282
C2×#655232
#106151592
C2×#653392
C2×#653412
C2×#653402
C2×#653342
C2×#653292
C2×#653312
C2×#653302
C2×#653242
C2×#652592
C2×#652602
C2×#32015