Finite Group Databasebeta

← C2×#10608416 #12267879

Subgroups — C2×#10608416 #12267879

Order 1280.

3330 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4081C211yesmaximal, characteristic, complemented
2C22×#4023C211yesmaximal, characteristic, complemented
3C2×C5×#392C211yesmaximal, characteristic
4C2×#65510C211yesmaximal, characteristic, complemented
5C2×#65510C211yesmaximal, characteristic, complemented
6C2×#65509C211yesmaximal, characteristic, complemented
7C2×#65509C211yesmaximal, characteristic, complemented
8C2×#65509C211yesmaximal, characteristic, complemented
9C2×#65238C211yesmaximal, characteristic, complemented
10C2×#65241C211yesmaximal, characteristic, complemented
11C2×#65237C211yesmaximal, characteristic, complemented
12C2×#65234C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14#10608416C2116yesmaximal, direct product factor
15C2×#64944C211yesmaximal, characteristic, complemented
16C2×#64942C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C23×C5×D4C2211yescharacteristic
19C23×C5×D4C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×C22⋊Dic5C2211yescharacteristic
35C2×#4081—28no—
36C2×#4081C2218yescomplemented
37C22×C4⋊Dic5C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4023—28no—
47C2×#4023C2218yescomplemented
48C5×#392C2218yes—
49C2×C5×#95C2211yescharacteristic
50#65510C2218yescomplemented
51#65510C2218yescomplemented
52#65509C2218yescomplemented
53#65509C2218yescomplemented
54#65509C2218yescomplemented
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65241C2218yescomplemented
63#65238C2218yescomplemented
64#65237C2218yescomplemented
65#65234C2218yescomplemented
66C22⋊C4×Dic5C2218yescomplemented
67#64944C2218yescomplemented
68#64942C2218yescomplemented
69C2×#2471—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C25×C5C2311yescharacteristic
73C22×C5×D4—24no—
74C22×C5×D4—24no—
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—24no—
78C22×C5×D4—24no—
79C22×C5×D4—42no—
80C22×C5×D4—42no—
81C22×C5×D4—42no—
82C22×C5×D4C2314yes—
83C22×C5×D4C2314yes—
84C22×C5×D4C2314yes—
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×Dic5—24no—
90C23×Dic5—24no—
91C23×Dic5—24no—
92C23×Dic5—24no—
93C23×Dic5—24no—
94C23×Dic5—42no—
95C23×Dic5C2314yes—
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2314yes—
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C2×C5×C22⋊C4—24no—
106C2×C5×C22⋊C4—24no—
107C2×C5×C22⋊C4—42no—
108C2×C5×C22⋊C4C2314yes—
109C2×C5×C22⋊C4C2314yes—
110C2×C5×C22⋊C4C2314yes—
111C2×C22⋊Dic5—24no—
112C2×C22⋊Dic5—24no—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5—24no—
115C2×C22⋊Dic5—24no—
116C2×C22⋊Dic5—24no—
117C2×C22⋊Dic5—42no—
118C2×C22⋊Dic5—42no—
119C2×C22⋊Dic5—42no—
120C2×C22⋊Dic5—42no—
121C2×C22⋊Dic5C2314yes—
122C2×C22⋊Dic5C2314yes—
123C2×C22⋊Dic5C2314yes—
124C2×C22⋊Dic5C2314yes—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130C2×C22⋊Dic5C2314yes—
131#4081—232no—
132C2×C4⋊Dic5—24no—
133C2×C4⋊Dic5—42no—
134C2×C4⋊Dic5C2314yes—
135C2×C4⋊Dic5C2314yes—
136C2×#683—24no—
137C2×#683—24no—
138C2×#683—42no—
139C2×#683D418yescomplemented
140C2×#683C2314yes—
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×C4×Dic5—24no—
145C2×C4×Dic5—24no—
146C2×C4×Dic5—42no—
147C2×C4×Dic5C2314yes—
148C2×C4×Dic5C2314yes—
149C2×C4×Dic5C2314yes—
150#4023—232no—
151C5×#95C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#123—51no—
160C22×#117—51no—
161#2471—516no—
162C2×#399—51no—
163C2×#397—51no—
164C2×#396—51no—
165C2×#392D511yescharacteristic
166C2×#390—51no—
167C2×#390—51no—
168C2×#388—51no—
169C2×#387—51no—
170C2×#387—51no—
171C2×#386—51no—
172C2×#386—51no—
173C2×#386—51no—
174C2×C4×C22⋊C4—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5—22no—
182C24×C5—22no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5—22no—
190C24×C5—22no—
191C24×C5—22no—
192C24×C5—22no—
193C24×C5—22no—
194C24×C5#4114yes—
195C24×C5#4114yes—
196C24×C5C2412yes—
197C24×C5C2412yes—
198C24×C5C2412yes—
199C24×C5C2411yescharacteristic
200C2×C5×D4—28no—
201C2×C5×D4—28no—
202C2×C5×D4—28no—
203C2×C5×D4—28no—
204C2×C5×D4—28no—
205C2×C5×D4—28no—
206C2×C5×D4—44no—
207C2×C5×D4—44no—
208C2×C5×D4—44no—
209C2×C5×D4—416no—
210C2×C5×D4—416no—
211C2×C5×D4—416no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5C2×D414yes—
223C22×C4×C5#4114yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C22×Dic5—232no—
229C22×Dic5—22no—
230C22×Dic5—28no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—28no—
237C22×Dic5—28no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—28no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—28no—
255C22×Dic5—44no—
256C22×Dic5—416no—
257C22×Dic5C2×D414yes—
258C22×Dic5C2×D414yes—
259C22×Dic5#4114yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C5×C22⋊C4—28no—
269C5×C22⋊C4—28no—
270C5×C22⋊C4—44no—
271C22⋊Dic5—28no—
272C22⋊Dic5—28no—
273C22⋊Dic5—28no—
274C22⋊Dic5—28no—
275C22⋊Dic5—28no—
276C22⋊Dic5—28no—
277C22⋊Dic5—44no—
278C22⋊Dic5—44no—
279C22⋊Dic5—44no—
280C22⋊Dic5—44no—
281C4⋊Dic5—28no—
282C4⋊Dic5—44no—
283#683—28no—
284#683—28no—
285#683—44no—
286#683C2×D4116yescomplemented
287C4×Dic5—28no—
288C4×Dic5—28no—
289C4×Dic5—44no—
290C23×D4C2×D511yescharacteristic
291C23×D4C2×D511yescharacteristic
292C23×D4C2×D511yescharacteristic
293C24×C4—51no—
294C24×C4—51no—
295C2×#123—58no—
296C2×#123—108no—
297C2×#117—58no—
298C2×#117—108no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4—51no—
305C22×C22⋊C4—51no—
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C22⋊C4—51no—
311C22×C22⋊C4—51no—
312C22×C22⋊C4—51no—
313C22×C22⋊C4—51no—
314C22×C22⋊C4—51no—
315C22×C22⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42—51no—
320C22×C42—51no—
321#399—58no—
322#397—58no—
323#396—58no—
324#392C2×D518yes—
325#390—58no—
326#390—58no—
327#388—58no—
328#387—58no—
329#387—58no—
330#386—58no—
331#386—58no—
332#386—58no—
333C4×C22⋊C4—58no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95C2×D511yescharacteristic
342C23×C5—28no—
343C23×C5—28no—
344C23×C5—28no—
345C23×C5—28no—
346C23×C5—28no—
347C23×C5—28no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5—44no—
371C23×C5—44no—
372C23×C5—44no—
373C23×C5—44no—
374C23×C5—44no—
375C23×C5—44no—
376C23×C5—44no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5C22×D412yes—
383C23×C5C2×#4114yes—
384C23×C5C2×#4114yes—
385C23×C5C2×#4112yes—
386C23×C5C2×#4112yes—
387C23×C5C2×#4112yes—
388C23×C5C2×#4112yes—
389C23×C5H(5,𝔽2)12yes—
390C23×C5H(5,𝔽2)12yes—
391C23×C5C2511yescharacteristic
392C5×D4—416no—
393C5×D4—416no—
394C5×D4—416no—
395C2×C4×C5—28no—
396C2×C4×C5—28no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—44no—
408C2×C4×C5—44no—
409C2×C4×C5C22×D414yes—
410C2×C4×C5C2×#4114yes—
411C2×Dic5—232no—
412C2×Dic5—28no—
413C2×Dic5—28no—
414C2×Dic5—28no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5—22no—
419C2×Dic5—22no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—416no—
437C2×Dic5—44no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5C22×D414yes—
443C2×Dic5C22×D414yes—
444C2×Dic5C2×#4114yes—
445C25C22×D511yescharacteristic
446C25C22×D511yescharacteristic
447C25C22×D511yescharacteristic
448C22×D4—24no—
449C22×D4—24no—
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—24no—
454C22×D4—42no—
455C22×D4—42no—
456C22×D4—42no—
457C22×D4C22×D514yes—
458C22×D4C22×D514yes—
459C22×D4C22×D514yes—
460C23×C4—51no—
461C23×C4—51no—
462C23×C4—51no—
463C23×C4—54no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—54no—
470C23×C4—104no—
471C23×C4—104no—
472C23×C4—104no—
473C23×C4—104no—
474C23×C4—104no—
475C23×C4—202no—
476C23×C4C22×D511yescharacteristic
477C23×C4C22×D511yescharacteristic
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D511yescharacteristic
480#123—1032no—
481#117—1032no—
482C2×C4⋊C4—58no—
483C2×C4⋊C4—54no—
484C2×C4⋊C4—54no—
485C2×C4⋊C4—54no—
486C2×C4⋊C4—54no—
487C2×C4⋊C4—54no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—104no—
490C2×C4⋊C4—104no—
491C2×C4⋊C4—104no—
492C2×C4⋊C4—202no—
493C2×C4⋊C4—202no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—54no—
498C2×C22⋊C4—54no—
499C2×C22⋊C4—54no—
500C2×C22⋊C4—54no—
501C2×C22⋊C4—54no—
502C2×C22⋊C4—54no—
503C2×C22⋊C4—54no—
504C2×C22⋊C4—54no—
505C2×C22⋊C4—54no—
506C2×C22⋊C4—54no—
507C2×C22⋊C4—104no—
508C2×C22⋊C4—104no—
509C2×C22⋊C4—104no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—104no—
513C2×C22⋊C4—202no—
514C2×C22⋊C4—202no—
515C2×C22⋊C4—202no—
516C2×C22⋊C4—202no—
517C2×C22⋊C4C22×D514yes—
518C2×C22⋊C4C22×D514yes—
519C2×C22⋊C4C22×D514yes—
520C2×C42—54no—
521C2×C42—54no—
522C2×C42—54no—
523C2×C42—104no—
524C2×C42—104no—
525C2×C42—202no—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532#95—54no—
533#95C22×D514yes—
534C22×C5—24no—
535C22×C5—24no—
536C22×C5—24no—
537C22×C5—24no—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—416no—
549C22×C5—416no—
550C22×C5—42no—
551C22×C5—42no—
552C22×C5—42no—
553C22×C5—42no—
554C22×C5—42no—
555C22×C5—42no—
556C22×C5—42no—
557C22×C5—88no—
558C22×C5#52514yes—
559C22×C5#52914yes—
560C22×C5#54014yes—
561C22×C5#54614yes—
562C22×C5#55014yes—
563C22×C5#55114yes—
564C22×C5#55114yes—
565C22×C5C23×D411yescharacteristic
566C22×C5C22×#4111yescharacteristic
567C22×C5C22×#4111yescharacteristic
568C22×C5C22×#4111yescharacteristic
569C22×C5C22×#4111yescharacteristic
570C22×C5C2×H(5,𝔽2)11yescharacteristic
571C22×C5C2×H(5,𝔽2)11yescharacteristic
572C4×C5—24no—
573C4×C5—24no—
574C4×C5—42no—
575C4×C5—42no—
576Dic5—24no—
577Dic5—24no—
578Dic5—24no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582Dic5—42no—
583Dic5—42no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24#71114yes—
604C24#71114yes—
605C24C23×D512yes—
606C24C23×D512yes—
607C24C23×D512yes—
608C24C23×D511yescharacteristic
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—416no—
619C2×D4—416no—
620C2×D4—416no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—54no—
632C22×C4—54no—
633C22×C4—54no—
634C22×C4—52no—
635C22×C4—52no—
636C22×C4—52no—
637C22×C4—52no—
638C22×C4—52no—
639C22×C4—52no—
640C22×C4—52no—
641C22×C4—52no—
642C22×C4—108no—
643C22×C4—108no—
644C22×C4—108no—
645C22×C4—1032no—
646C22×C4—102no—
647C22×C4—108no—
648C22×C4—102no—
649C22×C4—102no—
650C22×C4—102no—
651C22×C4—102no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—108no—
659C22×C4—102no—
660C22×C4—102no—
661C22×C4—102no—
662C22×C4—102no—
663C22×C4—102no—
664C22×C4—102no—
665C22×C4—102no—
666C22×C4—102no—
667C22×C4—102no—
668C22×C4—102no—
669C22×C4—204no—
670C22×C4—2016no—
671C22×C4D4×D514yes—
672C22×C4#71114yes—
673C22×C4C23×D512yes—
674C22×C4C23×D512yes—
675C22×C4C23×D512yes—
676C22×C4C23×D512yes—
677C4⋊C4—516no—
678C4⋊C4—108no—
679C4⋊C4—108no—
680C4⋊C4—108no—
681C4⋊C4—204no—
682C4⋊C4—204no—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—44no—
686C22⋊C4—108no—
687C22⋊C4—108no—
688C22⋊C4—108no—
689C22⋊C4—108no—
690C22⋊C4—108no—
691C22⋊C4—108no—
692C22⋊C4—204no—
693C22⋊C4—204no—
694C22⋊C4—204no—
695C22⋊C4—204no—
696C42—108no—
697C42—108no—
698C42—204no—
699C2×C5—44no—
700C2×C5—44no—
701C2×C5—82no—
702C2×C5#247118yescomplemented
703C2×C5C2×#52511yescharacteristic
704C2×C5C2×#52911yescharacteristic
705C2×C5C2×#54011yescharacteristic
706C2×C5C2×#54611yescharacteristic
707C2×C5C2×#55011yescharacteristic
708C2×C5C2×#55111yescharacteristic
709C2×C5C2×#55111yescharacteristic
710C23—28no—
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23C2×D4×D512yes—
751C23C2×#71114yes—
752C23C2×#71114yes—
753C23C2×#71112yes—
754C23C2×#71112yes—
755C23C2×#71112yes—
756C23#414412yes—
757C23#414412yes—
758C23D5×#4112yes—
759C23C24×D511yescharacteristic
760D4—416no—
761D4—416no—
762D4—416no—
763C2×C4—28no—
764C2×C4—28no—
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—22no—
774C2×C4—22no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—54no—
778C2×C4—54no—
779C2×C4—54no—
780C2×C4—1032no—
781C2×C4—108no—
782C2×C4—108no—
783C2×C4—108no—
784C2×C4—102no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—102no—
791C2×C4—102no—
792C2×C4—102no—
793C2×C4—102no—
794C2×C4—102no—
795C2×C4—102no—
796C2×C4—102no—
797C2×C4—102no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—102no—
805C2×C4—2016no—
806C2×C4—204no—
807C2×C4—204no—
808C2×C4—204no—
809C2×C4—204no—
810C2×C4—204no—
811C2×C4C2×D4×D514yes—
812C2×C4C2×#71114yes—
813C5C2×#247111yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—416no—
821C22—416no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—88no—
838C22#6592114yes—
839C22#6592114yes—
840C22#6592514yes—
841C22#6593414yes—
842C22#6594014yes—
843C22#6594914yes—
844C22#6605214yes—
845C22C22×D4×D511yescharacteristic
846C22C22×#71111yescharacteristic
847C22C22×#71111yescharacteristic
848C22C22×#71111yescharacteristic
849C22C2×#414411yescharacteristic
850C22C2×#414411yescharacteristic
851C22C2×D5×#4111yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—104no—
857C4—104no—
858C4—104no—
859C4—202no—
860C4—202no—
861C4—202no—
862C4—202no—
863C4—202no—
864C2—44no—
865C2—44no—
866C2—82no—
867C2#1060841618yesdirect product factor
868C2C2×#6592111yescharacteristic
869C2C2×#6592111yescharacteristic
870C2C2×#6592511yescharacteristic
871C2C2×#6594011yescharacteristic
872C2C2×#6593411yescharacteristic
873C2C2×#6594911yescharacteristic
874C2C2×#6605211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
Fitting, prime radicalC2×C5×#392C2
socleC24×C5C24
hypercenterC2×#392D5
hypocenterC5C2×#2471
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#4081C2semidirect
2. C22×#4023C2semidirect
4. C2×#65510C2semidirect
5. C2×#65510C2semidirect
6. C2×#65509C2semidirect
7. C2×#65509C2semidirect
8. C2×#65509C2semidirect
9. C2×#65238C2semidirect
10. C2×#65241C2semidirect
11. C2×#65237C2semidirect
12. C2×#65234C2semidirect
13. C2×C22⋊C4×Dic5C2semidirect
14. #10608416C2direct (N × H)
15. C2×#64944C2semidirect
16. C2×#64942C2semidirect
36. C2×#4081C22semidirect
47. C2×#4023C22semidirect
50. #65510C22semidirect
51. #65510C22semidirect
52. #65509C22semidirect
53. #65509C22semidirect
54. #65509C22semidirect
62. #65241C22semidirect
63. #65238C22semidirect
64. #65237C22semidirect
65. #65234C22semidirect
66. C22⋊C4×Dic5C22semidirect
67. #64944C22semidirect
68. #64942C22semidirect
139. C2×#683D4semidirect
286. #683C2×D4semidirect
702. C2×C5#2471semidirect
813. C5C2×#2471semidirect
867. C2#10608416direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40812
C22×#40232
C2×C5×#3922
C2×#655102
C2×#655092
C2×#652382
C2×#652412
C2×#652372
C2×#652342
C2×C22⋊C4×Dic52
#106084162
C2×#649442
C2×#649422
C2×#24715