Finite Group Databasebeta

← C2×#10607229 #12267302

Subgroups — C2×#10607229 #12267302

Order 1280.

2790 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
1C22×#4024C211yesmaximal, characteristic
2C22×C4×Dic10C211yesmaximal, characteristic, complemented
3C2×C5×#388C211yesmaximal, characteristic
4C2×#65273C211yesmaximal, characteristic, complemented
5C2×#65265C211yesmaximal, characteristic, complemented
6C2×#65238C211yesmaximal, characteristic
7C2×#65238C211yesmaximal, characteristic
8C2×#65240C211yesmaximal, characteristic
9C2×#65231C211yesmaximal, characteristic
10C2×C22⋊C4×Dic5C211yesmaximal, characteristic
11C2×#65222C211yesmaximal, characteristic, complemented
12#10607229C2116yesmaximal, direct product factor
13C2×#64950C211yesmaximal, characteristic, complemented
14C2×#64935C211yesmaximal, characteristic, complemented
15C2×#64936C211yesmaximal, characteristic, complemented
16C2×#64944C211yesmaximal, characteristic, complemented
17C24×Dic5C2211yescharacteristic
18C23×Dic10C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C42×C5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C4⋊Dic5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C22×C4⋊Dic5C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×#683C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4024—28no—
43C2×#4024C2218yes—
44C2×C4×Dic10—28no—
45C2×C4×Dic10C2218yescomplemented
46C5×#388C2218yes—
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65273C2218yescomplemented
58#65265C2218yescomplemented
59#65240C2218yes—
60#65238C2218yes—
61#65238C2218yes—
62#65231C2218yes—
63C22⋊C4×Dic5C2218yes—
64#65222C2218yescomplemented
65#64950C2218yescomplemented
66#64944C2218yescomplemented
67#64936C2218yescomplemented
68#64935C2218yescomplemented
69C2×#2423—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×Dic5—24no—
78C23×Dic5—24no—
79C23×Dic5—24no—
80C23×Dic5C2314yes—
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C22×Dic10—24no—
90C22×Dic10—24no—
91C22×Dic10D418yes—
92C22×Dic10C2314yes—
93C2×C5×C4⋊C4—42no—
94C2×C5×C4⋊C4C2314yes—
95C2×C5×C22⋊C4—24no—
96C2×C5×C22⋊C4—42no—
97C2×C5×C22⋊C4Q818yescomplemented
98C2×C5×C22⋊C4C2314yes—
99C2×C5×C22⋊C4C2314yes—
100C2×C5×C22⋊C4C2314yes—
101C2×C42×C5—24no—
102C2×C42×C5C2314yes—
103C2×C22⋊Dic5—24no—
104C2×C22⋊Dic5—24no—
105C2×C22⋊Dic5—42no—
106C2×C22⋊Dic5C2314yes—
107C2×C22⋊Dic5C2314yes—
108C2×C22⋊Dic5C2314yes—
109C2×C4⋊Dic5—24no—
110C2×C4⋊Dic5—24no—
111C2×C4⋊Dic5—42no—
112C2×C4⋊Dic5—42no—
113C2×C4⋊Dic5C2314yes—
114C2×C4⋊Dic5C2314yes—
115C2×C4⋊Dic5C2314yes—
116C2×C4⋊Dic5C2314yes—
117C2×#683—24no—
118C2×#683—24no—
119C2×#683—24no—
120C2×#683—24no—
121C2×#683—24no—
122C2×#683—24no—
123C2×#683—24no—
124C2×#683—42no—
125C2×#683C2314yes—
126C2×#683C2314yes—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×C4×Dic5—24no—
134C2×C4×Dic5—24no—
135C2×C4×Dic5—24no—
136C2×C4×Dic5C2314yes—
137C2×C4×Dic5C2314yes—
138C2×C4×Dic5C2314yes—
139#4024—232no—
140C4×Dic10—232no—
141C5×#95C2314yes—
142C5×#95C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151C22×C22⋊Q8—51no—
152C22×C4×Q8—51no—
153#2423—516no—
154C2×#399—51no—
155C2×#399—51no—
156C2×#398—51no—
157C2×#398—51no—
158C2×#391—51no—
159C2×#389—51no—
160C2×#388—51no—
161C2×#388D511yescharacteristic
162C2×#387—51no—
163C2×#387—51no—
164C2×#384—51no—
165C2×#380—51no—
166C2×C4×C22⋊C4—51no—
167C24×C5—22no—
168C24×C5—22no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5C2×Q814yes—
174C24×C5C2412yes—
175C24×C5C2411yescharacteristic
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5C2×D414yes—
192C22×C4×C5C2×Q814yes—
193C22×C4×C5C2×Q814yes—
194C22×C4×C5C2412yes—
195C22×C4×C5C2412yes—
196C22×C4×C5C2412yes—
197C22×C4×C5C2412yes—
198C22×C4×C5C2412yes—
199C22×C4×C5C2412yes—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5—22no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—28no—
220C22×Dic5—28no—
221C22×Dic5—28no—
222C22×Dic5—416no—
223C22×Dic5C2×D414yes—
224C22×Dic5C2×D414yes—
225C22×Dic5#4114yes—
226C22×Dic5#4114yes—
227C22×Dic5#4114yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C22×Dic5C2412yes—
235C22×Dic5C2412yes—
236C2×Dic10—232no—
237C2×Dic10—28no—
238C2×Dic10—28no—
239C2×Dic10C2×D4116yes—
240C5×C4⋊C4—44no—
241C5×C22⋊C4—28no—
242C5×C22⋊C4—44no—
243C5×C22⋊C4C2×Q8116yescomplemented
244C42×C5—28no—
245C22⋊Dic5—28no—
246C22⋊Dic5—28no—
247C22⋊Dic5—44no—
248C4⋊Dic5—28no—
249C4⋊Dic5—28no—
250C4⋊Dic5—44no—
251C4⋊Dic5—44no—
252#683—28no—
253#683—28no—
254#683—28no—
255#683—28no—
256#683—28no—
257#683—28no—
258#683—28no—
259#683—44no—
260C4×Dic5—28no—
261C4×Dic5—28no—
262C4×Dic5—28no—
263C23×Q8—51no—
264C24×C4—51no—
265C2×C22⋊Q8—58no—
266C2×C22⋊Q8—108no—
267C2×C4×Q8—58no—
268C2×C4×Q8—108no—
269C22×C4⋊C4—51no—
270C22×C4⋊C4—51no—
271C22×C4⋊C4—51no—
272C22×C4⋊C4—51no—
273C22×C4⋊C4—51no—
274C22×C4⋊C4—51no—
275C22×C4⋊C4—51no—
276C22×C4⋊C4—51no—
277C22×C4⋊C4—51no—
278C22×C4⋊C4—51no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4C2×D511yescharacteristic
282C22×C22⋊C4—51no—
283C22×C22⋊C4—51no—
284C22×C22⋊C4—51no—
285C22×C22⋊C4C2×D511yescharacteristic
286C22×C22⋊C4C2×D511yescharacteristic
287C22×C22⋊C4C2×D511yescharacteristic
288C22×C42—51no—
289C22×C42—51no—
290C22×C42—51no—
291C22×C42C2×D511yescharacteristic
292#399—58no—
293#399—58no—
294#398—58no—
295#398—58no—
296#391—58no—
297#389—58no—
298#388—58no—
299#388C2×D518yes—
300#387—58no—
301#387—58no—
302#384—58no—
303#380—58no—
304C4×C22⋊C4—58no—
305C2×#95—51no—
306C2×#95—51no—
307C2×#95—51no—
308C2×#95—51no—
309C2×#95—51no—
310C2×#95—51no—
311C2×#95—51no—
312C2×#95—51no—
313C2×#95C2×D511yescharacteristic
314C2×#95C2×D511yescharacteristic
315C23×C5—28no—
316C23×C5—28no—
317C23×C5—28no—
318C23×C5—22no—
319C23×C5—22no—
320C23×C5—22no—
321C23×C5—22no—
322C23×C5—22no—
323C23×C5—22no—
324C23×C5—44no—
325C23×C5—44no—
326C23×C5—44no—
327C23×C5—44no—
328C23×C5C22×D412yes—
329C23×C5C22×Q814yes—
330C23×C5C22×Q812yes—
331C23×C5C2×#4112yes—
332C23×C5C2×#4112yes—
333C23×C5C2×#4112yes—
334C23×C5H(5,𝔽2)12yes—
335C23×C52−1+412yes—
336C23×C5C2511yescharacteristic
337C2×C4×C5—28no—
338C2×C4×C5—28no—
339C2×C4×C5—28no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—44no—
356C2×C4×C5—44no—
357C2×C4×C5—44no—
358C2×C4×C5C22×D414yes—
359C2×C4×C5C22×Q814yes—
360C2×C4×C5C22×Q814yes—
361C2×Dic5—28no—
362C2×Dic5—28no—
363C2×Dic5—22no—
364C2×Dic5—22no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—44no—
383C2×Dic5—44no—
384C2×Dic5—44no—
385C2×Dic5—44no—
386C2×Dic5—44no—
387C2×Dic5—416no—
388C2×Dic5#123116yes—
389C2×Dic5C22×D414yes—
390C2×Dic5C22×D414yes—
391C2×Dic5C2×#4114yes—
392C2×Dic5C2×#4114yes—
393C2×Dic5C2×#4114yes—
394Dic10—232no—
395C25C22×D511yescharacteristic
396C22×Q8—58no—
397C22×Q8—54no—
398C22×Q8—104no—
399C22×Q8—104no—
400C23×C4—51no—
401C23×C4—51no—
402C23×C4—51no—
403C23×C4—54no—
404C23×C4—51no—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—104no—
410C23×C4—104no—
411C23×C4—104no—
412C23×C4C22×D511yescharacteristic
413C23×C4C22×D511yescharacteristic
414C23×C4C22×D511yescharacteristic
415C23×C4C22×D511yescharacteristic
416C23×C4C22×D511yescharacteristic
417C23×C4C22×D511yescharacteristic
418C22⋊Q8—1032no—
419C4×Q8—1032no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—54no—
422C2×C4⋊C4—54no—
423C2×C4⋊C4—54no—
424C2×C4⋊C4—54no—
425C2×C4⋊C4—54no—
426C2×C4⋊C4—54no—
427C2×C4⋊C4—54no—
428C2×C4⋊C4—54no—
429C2×C4⋊C4—54no—
430C2×C4⋊C4—54no—
431C2×C4⋊C4—54no—
432C2×C4⋊C4—54no—
433C2×C4⋊C4—104no—
434C2×C4⋊C4—104no—
435C2×C4⋊C4—104no—
436C2×C4⋊C4—104no—
437C2×C4⋊C4—104no—
438C2×C4⋊C4—104no—
439C2×C4⋊C4—104no—
440C2×C4⋊C4—104no—
441C2×C4⋊C4—104no—
442C2×C4⋊C4—202no—
443C2×C4⋊C4—202no—
444C2×C4⋊C4—202no—
445C2×C4⋊C4C22×D514yes—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—54no—
449C2×C22⋊C4—54no—
450C2×C22⋊C4—54no—
451C2×C22⋊C4—104no—
452C2×C22⋊C4—104no—
453C2×C22⋊C4—202no—
454C2×C22⋊C4Dic1018yescomplemented
455C2×C22⋊C4C22×D514yes—
456C2×C22⋊C4C22×D514yes—
457C2×C22⋊C4C22×D514yes—
458C2×C42—24no—
459C2×C42—54no—
460C2×C42—54no—
461C2×C42—54no—
462C2×C42—104no—
463C2×C42—104no—
464C2×C42—104no—
465C2×C42C22×D514yes—
466#95—54no—
467#95—54no—
468#95—54no—
469#95—54no—
470#95—54no—
471#95—54no—
472#95—54no—
473#95—54no—
474#95C22×D514yes—
475#95C22×D514yes—
476C22×C5—24no—
477C22×C5—24no—
478C22×C5—24no—
479C22×C5—42no—
480C22×C5—416no—
481C22×C5—42no—
482C22×C5—42no—
483C22×C5—42no—
484C22×C5C2×#12314yes—
485C22×C5#53314yes—
486C22×C5#54214yes—
487C22×C5D4×Q814yes—
488C22×C5#55014yes—
489C22×C5#55214yes—
490C22×C5#55414yes—
491C22×C5C23×D411yescharacteristic
492C22×C5C23×Q811yescharacteristic
493C22×C5C22×#4111yescharacteristic
494C22×C5C22×#4111yescharacteristic
495C22×C5C22×#4111yescharacteristic
496C22×C5C2×H(5,𝔽2)11yescharacteristic
497C22×C5C2×2−1+411yescharacteristic
498C4×C5—24no—
499C4×C5—24no—
500C4×C5—24no—
501C4×C5—42no—
502C4×C5—42no—
503C4×C5—42no—
504Dic5—24no—
505Dic5—24no—
506Dic5—42no—
507Dic5—42no—
508Dic5—42no—
509Dic5—42no—
510Dic5—42no—
511Dic5C2×#12318yes—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24C2×Dic1014yes—
519C24C23×D512yes—
520C24C23×D511yescharacteristic
521C2×Q8—516no—
522C2×Q8—1032no—
523C2×Q8—108no—
524C2×Q8—108no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—54no—
541C22×C4—54no—
542C22×C4—54no—
543C22×C4—52no—
544C22×C4—54no—
545C22×C4—54no—
546C22×C4—52no—
547C22×C4—52no—
548C22×C4—52no—
549C22×C4—52no—
550C22×C4—52no—
551C22×C4—52no—
552C22×C4—52no—
553C22×C4—108no—
554C22×C4—108no—
555C22×C4—108no—
556C22×C4—102no—
557C22×C4—102no—
558C22×C4—102no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—102no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—2016no—
576C22×C4C2×Dic1014yes—
577C22×C4C2×Dic1014yes—
578C22×C4D4×D514yes—
579C22×C4C23×D512yes—
580C22×C4C23×D512yes—
581C22×C4C23×D512yes—
582C22×C4C23×D512yes—
583C22×C4C23×D512yes—
584C22×C4C23×D512yes—
585C4⋊C4—44no—
586C4⋊C4—108no—
587C4⋊C4—108no—
588C4⋊C4—108no—
589C4⋊C4—108no—
590C4⋊C4—108no—
591C4⋊C4—108no—
592C4⋊C4—108no—
593C4⋊C4—108no—
594C4⋊C4—108no—
595C4⋊C4—204no—
596C4⋊C4—204no—
597C4⋊C4—204no—
598C22⋊C4—28no—
599C22⋊C4—44no—
600C22⋊C4—108no—
601C22⋊C4—108no—
602C22⋊C4—204no—
603C22⋊C4C2×Dic10116yescomplemented
604C42—28no—
605C42—108no—
606C42—108no—
607C42—108no—
608C2×C5—44no—
609C2×C5#242318yescomplemented
610C2×C5C22×#12311yescharacteristic
611C2×C5C2×#53311yescharacteristic
612C2×C5C2×#54211yescharacteristic
613C2×C5C2×D4×Q811yescharacteristic
614C2×C5C2×#55011yescharacteristic
615C2×C5C2×#55211yescharacteristic
616C2×C5C2×#55411yescharacteristic
617C23—28no—
618C23—28no—
619C23—28no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23C22×Dic1014yes—
631C23C22×Dic1012yes—
632C23C2×D4×D512yes—
633C23#414412yes—
634C23D5×#4112yes—
635C23D5×#4112yes—
636C23D5×#4112yes—
637C23#415012yes—
638C23C24×D511yescharacteristic
639Q8—1032no—
640C2×C4—28no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—516no—
662C2×C4—54no—
663C2×C4—54no—
664C2×C4—54no—
665C2×C4—54no—
666C2×C4—54no—
667C2×C4—108no—
668C2×C4—102no—
669C2×C4—102no—
670C2×C4—102no—
671C2×C4—102no—
672C2×C4—108no—
673C2×C4—102no—
674C2×C4—102no—
675C2×C4—102no—
676C2×C4—102no—
677C2×C4—102no—
678C2×C4—102no—
679C2×C4—102no—
680C2×C4—102no—
681C2×C4—102no—
682C2×C4—102no—
683C2×C4—102no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—2016no—
689C2×C4—204no—
690C2×C4—204no—
691C2×C4—204no—
692C2×C4—204no—
693C2×C4—204no—
694C2×C4C22×Dic1014yes—
695C2×C4C22×Dic1014yes—
696C2×C4C2×D4×D514yes—
697C5C2×#242311yescharacteristic, complemented, Sylow
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—416no—
704C22—42no—
705C22—42no—
706C22#6585114yes—
707C22D4×Dic1014yes—
708C22#6587314yes—
709C22#6593314yes—
710C22D5×#12314yes—
711C22#6600314yes—
712C22#6604214yes—
713C22C23×Dic1011yescharacteristic
714C22C22×D4×D511yescharacteristic
715C22C2×#414411yescharacteristic
716C22C2×D5×#4111yescharacteristic
717C22C2×D5×#4111yescharacteristic
718C22C2×D5×#4111yescharacteristic
719C22C2×#415011yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—58no—
727C4—104no—
728C4—104no—
729C4—202no—
730C4—202no—
731C4—202no—
732C4—202no—
733C4—202no—
734C2—44no—
735C2#1060722918yesdirect product factor
736C2C2×#6585111yescharacteristic
737C2C2×D4×Dic1011yescharacteristic
738C2C2×#6587311yescharacteristic
739C2C2×#6593311yescharacteristic
740C2C2×D5×#12311yescharacteristic
741C2C2×#6600311yescharacteristic
742C2C2×#6604211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#388D5
hypocenterC5C2×#2423
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic10C2semidirect
4. C2×#65273C2semidirect
5. C2×#65265C2semidirect
11. C2×#65222C2semidirect
12. #10607229C2direct (N × H)
13. C2×#64950C2semidirect
14. C2×#64935C2semidirect
15. C2×#64936C2semidirect
16. C2×#64944C2semidirect
45. C2×C4×Dic10C22semidirect
57. #65273C22semidirect
58. #65265C22semidirect
64. #65222C22semidirect
65. #64950C22semidirect
66. #64944C22semidirect
67. #64936C22semidirect
68. #64935C22semidirect
97. C2×C5×C22⋊C4Q8semidirect
243. C5×C22⋊C4C2×Q8semidirect
454. C2×C22⋊C4Dic10semidirect
603. C22⋊C4C2×Dic10semidirect
609. C2×C5#2423semidirect
697. C5C2×#2423semidirect
735. C2#10607229direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40242
C22×C4×Dic102
C2×C5×#3882
C2×#652732
C2×#652652
C2×#652382
C2×#652402
C2×#652312
C2×C22⋊C4×Dic52
C2×#652222
#106072292
C2×#649502
C2×#649352
C2×#649362
C2×#649442
C2×#24235