Finite Group Databasebeta

← C2×#10615139 #12969986

Subgroups — C2×#10615139 #12969986

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×#536C211yesmaximal, characteristic, complemented
2C2×#66167C211yesmaximal, characteristic
3C2×#65523C211yesmaximal, characteristic, complemented
4C2×#65517C211yesmaximal, characteristic, complemented
5C2×#65516C211yesmaximal, characteristic, complemented
6#10615139C2116yesmaximal, direct product factor
7C2×#65336C211yesmaximal, characteristic, complemented
8C2×#65336C211yesmaximal, characteristic, complemented
9C2×#65341C211yesmaximal, characteristic, complemented
10C2×#65338C211yesmaximal, characteristic, complemented
11C2×#65340C211yesmaximal, characteristic, complemented
12C2×#65337C211yesmaximal, characteristic, complemented
13C2×#65333C211yesmaximal, characteristic, complemented
14C2×#65332C211yesmaximal, characteristic, complemented
15C2×#65285C211yesmaximal, characteristic, complemented
16C2×#65292C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C23×C5×Q8C2211yescharacteristic
19C22×#709C2211yescharacteristic
20C5×#536—24no—
21C5×#536C2218yescomplemented
22C2×C5×C4⋊Q8—21no—
23C2×C5×#124—21no—
24C2×C5×#123—21no—
25C2×C5×#123—21no—
26C2×C5×C22⋊Q8C2211yescharacteristic
27C2×C5×C22⋊Q8C2211yescharacteristic
28C2×C5×C22⋊Q8C2211yescharacteristic
29C2×C5×C22⋊Q8C2211yescharacteristic
30C2×C5×#117C2211yescharacteristic
31#66167—24no—
32#66167C2218yes—
33C2×#4092—21no—
34C22×#689C2211yescharacteristic
35C22×#689C2211yescharacteristic
36C22×#688C2211yescharacteristic
37C22×#688C2211yescharacteristic
38C2×#4085—21no—
39C2×#4085—21no—
40C2×#4084—21no—
41C2×#4076C2211yescharacteristic
42C2×#4076C2211yescharacteristic
43C22×C4⋊Dic5C2211yescharacteristic
44C2×#4070C2211yescharacteristic
45C2×#4070C2211yescharacteristic
46C22×#681C2211yescharacteristic
47C23×#168C2211yescharacteristic
48#65523C2218yescomplemented
49#65517C2218yescomplemented
50#65516C2218yescomplemented
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3967C2211yescharacteristic
55C2×C22⋊#168C2211yescharacteristic
56C2×C22⋊#168C2211yescharacteristic
57C2×C22⋊#168C2211yescharacteristic
58C2×C22⋊#168C2211yescharacteristic
59#65341C2218yescomplemented
60#65340C2218yescomplemented
61#65338C2218yescomplemented
62#65337C2218yescomplemented
63#65336C2218yescomplemented
64#65336C2218yescomplemented
65#65333C2218yescomplemented
66#65332C2218yescomplemented
67#65292C2218yescomplemented
68#65285C2218yescomplemented
69C2×#3942C2211yescharacteristic
70C2×#3942C2211yescharacteristic
71C2×#3941C2211yescharacteristic
72C2×#3941C2211yescharacteristic
73C2×#3940C2211yescharacteristic
74C2×#3940C2211yescharacteristic
75C2×#3939C2211yescharacteristic
76C2×#3939C2211yescharacteristic
77C2×#3201—51nomaximal, Sylow
78C2×C5×#41—42no—
79C2×C5×#41—42no—
80C2×C5×#41D414yes—
81C2×C5×#41C2314yes—
82C22×C5×Q8—21no—
83C22×C5×Q8—22no—
84C22×C5×Q8—42no—
85C22×C5×Q8—42no—
86C22×C5×Q8D411yescharacteristic
87C22×C5×Q8C2311yescharacteristic
88C22×C5×Q8C2311yescharacteristic
89C22×C5×Q8C2314yes—
90C22×C5×D4D411yescharacteristic
91C22×C5×D4D411yescharacteristic
92C22×C5×D4D411yescharacteristic
93C23×C4×C5—21no—
94C23×C4×C5C2311yescharacteristic
95C23×C4×C5C2311yescharacteristic
96C23×C4×C5C2311yescharacteristic
97C22×C22⋊D5—21no—
98C22×C22⋊D5—21no—
99C22×C22⋊D5—21no—
100C23×Dic5—21no—
101C2×#709—22no—
102C2×#709—42no—
103C2×#709—42no—
104C2×#709C2314yes—
105C22×D20C2311yescharacteristic
106C22×C4×D5—21no—
107C22×Dic10C2311yescharacteristic
108C5×C4⋊Q8—28no—
109C5×#124—28no—
110C5×#123—28no—
111C5×#123—28no—
112C5×C22⋊Q8—22no—
113C5×C22⋊Q8—22no—
114C5×C22⋊Q8—22no—
115C5×C22⋊Q8—22no—
116C5×C22⋊Q8C2314yes—
117C5×C22⋊Q8C2314yes—
118C5×C22⋊Q8C2314yes—
119C5×C22⋊Q8C2314yes—
120C5×#117—22no—
121C5×#117C2314yes—
122C2×C5×C4⋊C4—21no—
123C2×C5×C4⋊C4—21no—
124C2×C5×C4⋊C4—21no—
125C2×C5×C4⋊C4—21no—
126C2×C5×C4⋊C4C2311yescharacteristic
127C2×C5×C4⋊C4C2311yescharacteristic
128C2×C5×C22⋊C4—21no—
129C2×C5×C22⋊C4—21no—
130C2×C5×C22⋊C4—21no—
131C2×C5×C22⋊C4—21no—
132C2×C5×C22⋊C4—21no—
133C2×C42×C5—21no—
134C2×C22⋊Dic5—21no—
135C2×C22⋊Dic5—21no—
136#4092—28no—
137C2×#689—42no—
138C2×#689—42no—
139C2×#689C2314yes—
140C2×#689C2314yes—
141C2×#688—42no—
142C2×#688—42no—
143C2×#688C2314yes—
144C2×#688C2314yes—
145#4085—28no—
146#4085—28no—
147#4084—28no—
148#4076—22no—
149#4076—22no—
150#4076C2314yes—
151#4076C2314yes—
152C2×#685—21no—
153C2×#685—21no—
154C2×C4⋊Dic5—21no—
155C2×C4⋊Dic5—22no—
156C2×C4⋊Dic5C2314yes—
157C2×C4⋊Dic5C2311yescharacteristic
158C2×C4⋊Dic5C2311yescharacteristic
159#4070—22no—
160#4070—22no—
161#4070C2314yes—
162#4070C2314yes—
163C2×#683—21no—
164C2×#683—21no—
165C2×#681—42no—
166C2×#681C2314yes—
167C22×#168—42no—
168C22×#168C2311yescharacteristic
169C22×#168C2311yescharacteristic
170C22×#168C2311yescharacteristic
171C22×#168C2311yescharacteristic
172C22×#168C2314yes—
173#3967C2314yes—
174#3967C2314yes—
175#3967C2314yes—
176#3967C2314yes—
177C22⋊#168C2314yes—
178C22⋊#168C2314yes—
179C22⋊#168C2314yes—
180C22⋊#168C2314yes—
181#3942C2314yes—
182#3942C2314yes—
183#3941C2314yes—
184#3941C2314yes—
185#3940C2314yes—
186#3940C2314yes—
187#3939C2314yes—
188#3939C2314yes—
189C2×#537—51no—
190C2×#536D511yescharacteristic, complemented
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×C5C2×D411yescharacteristic
206C24×C5C2×D411yescharacteristic
207C24×C5C2×D411yescharacteristic
208C23×D5—21no—
209C5×#41—48no—
210C5×#41—44no—
211C5×#41—44no—
212C2×C5×Q8—21no—
213C2×C5×Q8—21no—
214C2×C5×Q8—24no—
215C2×C5×Q8—22no—
216C2×C5×Q8—22no—
217C2×C5×Q8—22no—
218C2×C5×Q8—22no—
219C2×C5×Q8—42no—
220C2×C5×Q8—44no—
221C2×C5×Q8—44no—
222C2×C5×Q8—44no—
223C2×C5×Q8—48no—
224C2×C5×Q8C2×D414yes—
225C2×C5×Q8C2412yes—
226C2×C5×Q8C2412yes—
227C2×C5×D4—42no—
228C2×C5×D4—42no—
229C2×C5×D4—42no—
230C2×C5×D4C2×D414yes—
231C2×C5×D4C2×D414yes—
232C2×C5×D4C2×D414yes—
233C22×C4×C5—22no—
234C22×C4×C5—22no—
235C22×C4×C5—22no—
236C22×C4×C5—22no—
237C22×C4×C5—22no—
238C22×C4×C5—22no—
239C22×C4×C5—21no—
240C22×C4×C5—21no—
241C22×C4×C5—21no—
242C22×C4×C5—21no—
243C22×C4×C5—24no—
244C22×C4×C5—44no—
245C22×C4×C5C2×D411yescharacteristic
246C22×C4×C5C2×D411yescharacteristic
247C22×C4×C5C2×D411yescharacteristic
248C22×C4×C5C2×D412yes—
249C22×C4×C5C2×D412yes—
250C22×C4×C5C2×D412yes—
251C22×C4×C5C2412yes—
252C22×C4×C5C2412yes—
253C22×C4×C5C2412yes—
254C22×C4×C5C2411yescharacteristic
255C2×C22⋊D5—24no—
256C2×C22⋊D5—24no—
257C2×C22⋊D5—24no—
258C2×C22⋊D5—44no—
259C2×C22⋊D5—82no—
260C2×C22⋊D5—82no—
261C22×Dic5—21no—
262C22×Dic5—21no—
263C22×Dic5—21no—
264C22×Dic5—24no—
265C22×Dic5—82no—
266#709—44no—
267#709—44no—
268#709—48no—
269C2×D20—22no—
270C2×D20—22no—
271C2×D20—21no—
272C2×D20C2412yes—
273C2×C4×D5—24no—
274C2×C4×D5—44no—
275C2×Dic10—22no—
276C2×Dic10—22no—
277C2×Dic10—21no—
278C2×Dic10C2412yes—
279C5×C4⋊C4—24no—
280C5×C4⋊C4—24no—
281C5×C4⋊C4—24no—
282C5×C4⋊C4—24no—
283C5×C4⋊C4—21no—
284C5×C4⋊C4—21no—
285C5×C4⋊C4C2412yes—
286C5×C4⋊C4C2412yes—
287C5×C22⋊C4—24no—
288C5×C22⋊C4—24no—
289C5×C22⋊C4—24no—
290C5×C22⋊C4—24no—
291C5×C22⋊C4—24no—
292C42×C5—24no—
293C22⋊Dic5—24no—
294C22⋊Dic5—24no—
295#689—44no—
296#689—44no—
297#688—44no—
298#688—44no—
299#685—24no—
300#685—24no—
301C4⋊Dic5—21no—
302C4⋊Dic5—21no—
303C4⋊Dic5—24no—
304C4⋊Dic5C2412yes—
305C4⋊Dic5C2412yes—
306#683—24no—
307#683—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×#41—51no—
319C22×#41C2×D511yescharacteristic
320C23×Q8C2×D511yescharacteristic
321C22×Q16—51no—
322C22×Q16—51no—
323C22×SD16—51no—
324C22×SD16—51no—
325C22×M16—51no—
326C23×C8—51no—
327#537—58no—
328#537—104no—
329#536—24no—
330#536C2×D518yescomplemented
331C2×C4⋊Q8—21no—
332C2×#124—21no—
333C2×#123—21no—
334C2×#123—21no—
335C2×C22⋊Q8—51no—
336C2×C22⋊Q8—51no—
337C2×C22⋊Q8—101no—
338C2×C22⋊Q8C2×D511yescharacteristic
339C2×C22⋊Q8C2×D511yescharacteristic
340C2×C22⋊Q8C2×D511yescharacteristic
341C2×C22⋊Q8C2×D511yescharacteristic
342C2×#121—51no—
343C2×#121—51no—
344C2×#121—101no—
345C2×#121—101no—
346C2×#121—101no—
347C2×#117C2×D511yescharacteristic
348C22×C4⋊C4—51no—
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×C5C22×D412yes—
388C23×C5C22×D412yes—
389C23×C5C22×D412yes—
390C23×C5C22×D411yescharacteristic
391C22×D5—22no—
392C22×D5—42no—
393C22×D5—42no—
394C22×D5—42no—
395C5×Q8—22no—
396C5×Q8—22no—
397C5×Q8—22no—
398C5×Q8—22no—
399C5×Q8—44no—
400C5×Q8—48no—
401C5×Q8—42no—
402C5×Q8—42no—
403C5×D4—44no—
404C5×D4—44no—
405C5×D4—44no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—24no—
410C2×C4×C5—24no—
411C2×C4×C5—24no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
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—48no—
423C2×C4×C5—42no—
424C2×C4×C5—42no—
425C2×C4×C5—42no—
426C2×C4×C5—42no—
427C2×C4×C5C22×D412yes—
428C2×C4×C5C22×D412yes—
429C2×C4×C5C22×D412yes—
430C2×C4×C5C22×D411yescharacteristic
431C2×C4×C5H(5,𝔽2)12yes—
432C2×C4×C5H(5,𝔽2)12yes—
433C2×C4×C5C2511yescharacteristic
434C22⋊D5—48no—
435C22⋊D5—84no—
436C22⋊D5—84no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—42no—
441C2×Dic5—42no—
442C2×Dic5—42no—
443C2×Dic5—84no—
444D20—22no—
445D20—22no—
446D20—42no—
447C4×D5—48no—
448Dic10—22no—
449Dic10—22no—
450Dic10—42no—
451#168—22no—
452#168—22no—
453#168—22no—
454#168—22no—
455C2×#41—42no—
456C2×#41—42no—
457C2×#41—54no—
458C2×#41—102no—
459C2×#41—202no—
460C2×#41—202no—
461C2×#41C22⋊D514yes—
462C2×#41C22×D514yes—
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8—42no—
466C22×Q8—42no—
467C22×Q8—51no—
468C22×Q8C22⋊D511yescharacteristic
469C22×Q8C22×D511yescharacteristic
470C22×Q8C22×D511yescharacteristic
471C22×Q8C22×D514yes—
472C22×D4—51no—
473C22×D4—101no—
474C22×D4—101no—
475C22×D4—101no—
476C22×D4C22⋊D511yescharacteristic
477C22×D4C22⋊D511yescharacteristic
478C22×D4C22⋊D511yescharacteristic
479C23×C4—21no—
480C23×C4—101no—
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—28no—
502#124—28no—
503#123—28no—
504#123—28no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509C22⋊Q8—54no—
510C22⋊Q8—54no—
511C22⋊Q8—108no—
512C22⋊Q8—102no—
513C22⋊Q8—102no—
514C22⋊Q8C22×D514yes—
515C22⋊Q8C22×D514yes—
516C22⋊Q8C22×D514yes—
517C22⋊Q8C22×D514yes—
518#121—54no—
519#121—54no—
520#121—108no—
521#121—108no—
522#121—108no—
523#121—102no—
524#121—102no—
525#117—22no—
526#117C22×D514yes—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—51no—
532C2×C4⋊C4—51no—
533C2×C4⋊C4—54no—
534C2×C4⋊C4—101no—
535C2×C4⋊C4—102no—
536C2×C4⋊C4—101no—
537C2×C4⋊C4—101no—
538C2×C4⋊C4C22×D511yescharacteristic
539C2×C4⋊C4C22×D511yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—101no—
546C2×C22⋊C4—101no—
547C2×C22⋊C4—101no—
548C2×C22⋊C4—101no—
549C2×C42—21no—
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#53412yes—
579C22×C5#57712yes—
580C22×C5#57812yes—
581C22×C5C23×D411yescharacteristic
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—84no—
586C4×C5—22no—
587C4×C5—22no—
588C4×C5—22no—
589C4×C5—42no—
590C4×C5—42no—
591C4×C5—42no—
592C4×C5—42no—
593C4×C5#53412yes—
594C4×C5C2×H(5,𝔽2)11yescharacteristic
595C4×C5C2×H(5,𝔽2)11yescharacteristic
596Dic5—42no—
597Dic5—42no—
598Dic5—42no—
599C24—101no—
600C24C2×C22⋊D511yescharacteristic
601C24C2×C22⋊D511yescharacteristic
602C24C2×C22⋊D511yescharacteristic
603#41—48no—
604#41—44no—
605#41—44no—
606#41—204no—
607#41—204no—
608#41—208no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—24no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—22no—
616C2×Q8—42no—
617C2×Q8—44no—
618C2×Q8—44no—
619C2×Q8—44no—
620C2×Q8—48no—
621C2×Q8—52no—
622C2×Q8—101no—
623C2×Q8—102no—
624C2×Q8—102no—
625C2×Q8C2×C22⋊D514yes—
626C2×Q8C23×D512yes—
627C2×Q8C23×D512yes—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—52no—
632C2×D4—104no—
633C2×D4—104no—
634C2×D4—104no—
635C2×D4—102no—
636C2×D4—102no—
637C2×D4—101no—
638C2×D4—204no—
639C2×D4—402no—
640C2×D4—402no—
641C2×D4C2×C22⋊D514yes—
642C2×D4C2×C22⋊D514yes—
643C2×D4C2×C22⋊D514yes—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—24no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—44no—
656C22×C4—101no—
657C22×C4—101no—
658C22×C4—101no—
659C22×C4—104no—
660C22×C4—104no—
661C22×C4—204no—
662C22×C4—402no—
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—24no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—52no—
694C4⋊C4—52no—
695C4⋊C4—104no—
696C4⋊C4—101no—
697C4⋊C4—101no—
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—24no—
707C22⋊C4—104no—
708C22⋊C4—104no—
709C22⋊C4—104no—
710C22⋊C4—104no—
711C42—24no—
712C2×C5—42no—
713C2×C5—42no—
714C2×C5—42no—
715C2×C5#320114yescomplemented
716C2×C5C2×#53411yescharacteristic
717C2×C5C2×#57711yescharacteristic
718C2×C5C2×#57811yescharacteristic
719D5—82no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—102no—
730C23—202no—
731C23—202no—
732C23—202no—
733C23C22×C22⋊D512yes—
734C23C22×C22⋊D512yes—
735C23C22×C22⋊D512yes—
736C23C22×C22⋊D511yescharacteristic
737Q8—22no—
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—48no—
743Q8—42no—
744Q8—42no—
745Q8—102no—
746Q8—102no—
747Q8—202no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—102no—
752D4—102no—
753D4—208no—
754D4—202no—
755D4—404no—
756D4—404no—
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—22no—
773C2×C4—48no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—102no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—208no—
782C2×C4—202no—
783C2×C4—202no—
784C2×C4—202no—
785C2×C4—404no—
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—202no—
811C22—202no—
812C22—202no—
813C22—404no—
814C22#6613812yes—
815C22#6617112yes—
816C22#6617212yes—
817C22C23×C22⋊D511yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—202no—
826C4—202no—
827C4—202no—
828C4#6613812yes—
829C4C2×#414411yescharacteristic
830C4C2×#414411yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—402no—
835C2#1061513914yesdirect product factor
836C2C2×#6613811yescharacteristic
837C2C2×#6617111yescharacteristic
838C2C2×#6617211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#536C2
socleC23×C5C22×D4
prime radicalC2×#66167C2
hypercenterC2×#536D5
hypocenterC5C2×#3201
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×C5×#536C2semidirect
3. C2×#65523C2semidirect
4. C2×#65517C2semidirect
5. C2×#65516C2semidirect
6. #10615139C2direct (N × H)
7. C2×#65336C2semidirect
8. C2×#65336C2semidirect
9. C2×#65341C2semidirect
10. C2×#65338C2semidirect
11. C2×#65340C2semidirect
12. C2×#65337C2semidirect
13. C2×#65333C2semidirect
14. C2×#65332C2semidirect
15. C2×#65285C2semidirect
16. C2×#65292C2semidirect
21. C5×#536C22semidirect
48. #65523C22semidirect
49. #65517C22semidirect
50. #65516C22semidirect
59. #65341C22semidirect
60. #65340C22semidirect
61. #65338C22semidirect
62. #65337C22semidirect
63. #65336C22semidirect
64. #65336C22semidirect
65. #65333C22semidirect
66. #65332C22semidirect
67. #65292C22semidirect
68. #65285C22semidirect
190. C2×#536D5semidirect
330. #536C2×D5semidirect
715. C2×C5#3201semidirect
797. C5C2×#3201semidirect
835. C2#10615139direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5362
C2×#661672
C2×#655232
C2×#655172
C2×#655162
#106151392
C2×#653362
C2×#653412
C2×#653382
C2×#653402
C2×#653372
C2×#653332
C2×#653322
C2×#652852
C2×#652922
C2×#32015