Finite Group Databasebeta

← C2×#10614769 #12269399

Subgroups — C2×#10614769 #12269399

Order 1280.

2726 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×C5×#125C211yesmaximal, characteristic, complemented
2C22×#4042C211yesmaximal, characteristic
3#10614769C2116yesmaximal, direct product factor
4C2×#65281C211yesmaximal, characteristic
5C2×#65283C211yesmaximal, characteristic
6C2×#65278C211yesmaximal, characteristic
7C2×#65273C211yesmaximal, characteristic, complemented
8C2×#65268C211yesmaximal, characteristic, complemented
9C2×#65263C211yesmaximal, characteristic, complemented
10C2×#65261C211yesmaximal, characteristic, complemented
11C2×#65261C211yesmaximal, characteristic, complemented
12C2×#65279C211yesmaximal, characteristic
13C2×#65279C211yesmaximal, characteristic
14C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
15C2×#65222C211yesmaximal, characteristic, complemented
16C2×C4×#685C211yesmaximal, characteristic
17C23×C4×D5C2211yescharacteristic
18C23×Dic10C2211yescharacteristic
19C2×C5×#125—28no—
20C2×C5×#125C2218yescomplemented
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4042—28no—
45C2×#4042C2218yes—
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56#65283C2218yes—
57#65281C2218yes—
58#65279C2218yes—
59#65279C2218yes—
60#65278C2218yes—
61#65273C2218yescomplemented
62#65268C2218yescomplemented
63C4⋊C4×Dic5C2218yescomplemented
64#65263C2218yescomplemented
65#65261C2218yescomplemented
66#65261C2218yescomplemented
67C4×#685C2218yes—
68#65222C2218yescomplemented
69C2×#2556—51nomaximal, Sylow
70C24×D5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C22×C4×D5—24no—
86C22×C4×D5—24no—
87C22×C4×D5—42no—
88C22×C4×D5C2314yes—
89C22×Dic10—24no—
90C22×Dic10—24no—
91C22×Dic10—42no—
92C22×Dic10C2314yes—
93C5×#125—232no—
94C2×C5×C4⋊C4—24no—
95C2×C5×C4⋊C4—24no—
96C2×C5×C4⋊C4—24no—
97C2×C5×C4⋊C4—24no—
98C2×C5×C4⋊C4—24no—
99C2×C5×C4⋊C4D418yes—
100C2×C5×C4⋊C4C2314yes—
101C2×C5×C4⋊C4C2314yes—
102C2×C5×C4⋊C4C2314yes—
103C2×C5×C4⋊C4C2314yes—
104C2×C5×C4⋊C4C2314yes—
105C2×C5×C4⋊C4C2314yes—
106C2×C42×C5—24no—
107C2×C42×C5C2314yes—
108C2×#685—24no—
109C2×#685—24no—
110C2×#685—24no—
111C2×#685—24no—
112C2×#685—42no—
113C2×#685Q818yescomplemented
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×C4⋊Dic5—24no—
121C2×C4⋊Dic5C2314yes—
122C2×#683—24no—
123C2×#683—24no—
124C2×#683—24no—
125C2×#683—24no—
126C2×#683—24no—
127C2×#683—42no—
128C2×#683C2314yes—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×C4×Dic5—24no—
135C2×C4×Dic5—42no—
136C2×C4×Dic5—42no—
137C2×C4×Dic5C2314yes—
138C2×C4×Dic5C2314yes—
139C2×C4×Dic5C2314yes—
140#4042—232no—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151C22×#125D511yescharacteristic, complemented
152C22×C22⋊Q8—51no—
153#2556—516no—
154C2×#399—51no—
155C2×#398—51no—
156C2×#396—51no—
157C2×#395—51no—
158C2×#391—51no—
159C2×#389—51no—
160C2×#389—51no—
161C2×#388—51no—
162C2×#388—51no—
163C2×#387—51no—
164C2×#385—51no—
165C2×C4×C4⋊C4—51no—
166C2×C4×C22⋊C4—51no—
167C24×C5C2411yescharacteristic
168C23×D5—22no—
169C23×D5—22no—
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5C2×Q814yes—
175C23×D5C2412yes—
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×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5C2×D414yes—
194C22×C4×C5C2×D414yes—
195C22×C4×C5C2×D414yes—
196C22×C4×C5C2×Q814yes—
197C22×C4×C5C2412yes—
198C22×C4×C5C2412yes—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2412yes—
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—22no—
220C22×Dic5—22no—
221C22×Dic5C2×Q814yes—
222C22×Dic5#4114yes—
223C22×Dic5#4114yes—
224C22×Dic5#4114yes—
225C22×Dic5C2412yes—
226C22×Dic5C2412yes—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C2×C4×D5—28no—
233C2×C4×D5—28no—
234C2×C4×D5—44no—
235C2×C4×D5—416no—
236C2×Dic10—28no—
237C2×Dic10—28no—
238C2×Dic10—44no—
239C2×Dic10—416no—
240C5×C4⋊C4—28no—
241C5×C4⋊C4—28no—
242C5×C4⋊C4—28no—
243C5×C4⋊C4—28no—
244C5×C4⋊C4—28no—
245C5×C4⋊C4C2×D4116yes—
246C42×C5—28no—
247#685—28no—
248#685—28no—
249#685—28no—
250#685—28no—
251#685—44no—
252#685C2×Q8116yescomplemented
253C4⋊Dic5—28no—
254#683—28no—
255#683—28no—
256#683—28no—
257#683—28no—
258#683—28no—
259#683—44no—
260C4×Dic5—28no—
261C4×Dic5—44no—
262C4×Dic5—44no—
263C23×Q8—51no—
264C24×C4—51no—
265C2×#125—28no—
266C2×#125C2×D518yescomplemented
267C2×C22⋊Q8—58no—
268C2×C22⋊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⋊C4C2×D511yescharacteristic
277C22×C4⋊C4C2×D511yescharacteristic
278C22×C4⋊C4C2×D511yescharacteristic
279C22×C4⋊C4C2×D511yescharacteristic
280C22×C4⋊C4C2×D511yescharacteristic
281C22×C4⋊C4C2×D511yescharacteristic
282C22×C22⋊C4—51no—
283C22×C22⋊C4—51no—
284C22×C22⋊C4—51no—
285C22×C22⋊C4—51no—
286C22×C22⋊C4—51no—
287C22×C22⋊C4—51no—
288C22×C42—51no—
289C22×C42—51no—
290C22×C42—51no—
291C22×C42C2×D511yescharacteristic
292#399—58no—
293#398—58no—
294#396—58no—
295#395—58no—
296#391—58no—
297#389—58no—
298#389—58no—
299#388—58no—
300#388—58no—
301#387—58no—
302#385—58no—
303C4×C4⋊C4—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×#95—51no—
314C2×#95—51no—
315C23×C5C22×D412yes—
316C23×C5C22×Q812yes—
317C23×C5C2×#4112yes—
318C23×C5C2×#4112yes—
319C23×C5C2×#4112yes—
320C23×C5H(5,𝔽2)12yes—
321C23×C52−1+412yes—
322C23×C5C2511yescharacteristic
323C22×D5—28no—
324C22×D5—28no—
325C22×D5—28no—
326C22×D5—22no—
327C22×D5—22no—
328C22×D5—22no—
329C22×D5—22no—
330C22×D5—22no—
331C22×D5—22no—
332C22×D5—44no—
333C22×D5—44no—
334C22×D5—44no—
335C22×D5—44no—
336C22×D5C22×Q814yes—
337C2×C4×C5—28no—
338C2×C4×C5—28no—
339C2×C4×C5—28no—
340C2×C4×C5—28no—
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—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—44no—
359C2×C4×C5—44no—
360C2×C4×C5—44no—
361C2×C4×C5C22×D414yes—
362C2×C4×C5C22×D414yes—
363C2×C4×C5C22×D414yes—
364C2×C4×C5C22×Q814yes—
365C2×Dic5—28no—
366C2×Dic5—28no—
367C2×Dic5—28no—
368C2×Dic5—28no—
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—22no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—44no—
387C2×Dic5—44no—
388C2×Dic5—44no—
389C2×Dic5C22×Q814yes—
390C2×Dic5C2×#4114yes—
391C2×Dic5C2×#4114yes—
392C2×Dic5C2×#4114yes—
393C4×D5—416no—
394Dic10—416no—
395C25—51no—
396C22×Q8—54no—
397C22×Q8—104no—
398C22×Q8—104no—
399C22×Q8—202no—
400C23×C4—51no—
401C23×C4—51no—
402C23×C4—51no—
403C23×C4—51no—
404C23×C4—51no—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—54no—
408C23×C4—104no—
409C23×C4—104no—
410C23×C4—202no—
411C23×C4C22×D511yescharacteristic
412C23×C4C22×D511yescharacteristic
413C23×C4C22×D511yescharacteristic
414C23×C4C22×D511yescharacteristic
415C23×C4C22×D511yescharacteristic
416C23×C4C22×D511yescharacteristic
417C23×C4C22×D511yescharacteristic
418#125—232no—
419C22⋊Q8—1032no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
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—104no—
433C2×C4⋊C4—104no—
434C2×C4⋊C4—104no—
435C2×C4⋊C4—104no—
436C2×C4⋊C4—104no—
437C2×C4⋊C4—104no—
438C2×C4⋊C4—202no—
439C2×C4⋊C4C22⋊D518yes—
440C2×C4⋊C4C22×D514yes—
441C2×C4⋊C4C22×D514yes—
442C2×C4⋊C4C22×D514yes—
443C2×C4⋊C4C22×D514yes—
444C2×C4⋊C4C22×D514yes—
445C2×C4⋊C4C22×D514yes—
446C2×C22⋊C4—58no—
447C2×C22⋊C4—54no—
448C2×C22⋊C4—54no—
449C2×C22⋊C4—54no—
450C2×C22⋊C4—54no—
451C2×C22⋊C4—54no—
452C2×C22⋊C4—54no—
453C2×C22⋊C4—104no—
454C2×C22⋊C4—104no—
455C2×C22⋊C4—104no—
456C2×C22⋊C4—104no—
457C2×C22⋊C4—202no—
458C2×C42—24no—
459C2×C42—54no—
460C2×C42—54no—
461C2×C42—54no—
462C2×C42—104no—
463C2×C42—202no—
464C2×C42—202no—
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#95—54no—
475#95—54no—
476C22×C5#53214yes—
477C22×C5#53314yes—
478C22×C5#53914yes—
479C22×C5#54614yes—
480C22×C5D4×Q814yes—
481C22×C5#55214yes—
482C22×C5#55414yes—
483C22×C5C23×D411yescharacteristic
484C22×C5C23×Q811yescharacteristic
485C22×C5C22×#4111yescharacteristic
486C22×C5C22×#4111yescharacteristic
487C22×C5C22×#4111yescharacteristic
488C22×C5C2×H(5,𝔽2)11yescharacteristic
489C22×C5C2×2−1+411yescharacteristic
490C2×D5—24no—
491C2×D5—24no—
492C2×D5—24no—
493C2×D5—42no—
494C2×D5—42no—
495C2×D5—42no—
496C2×D5—42no—
497C2×D5—416no—
498C4×C5—24no—
499C4×C5—24no—
500C4×C5—24no—
501C4×C5—24no—
502C4×C5—42no—
503C4×C5—42no—
504C4×C5—42no—
505Dic5—24no—
506Dic5—24no—
507Dic5—24no—
508Dic5—24no—
509Dic5—42no—
510Dic5—42no—
511Dic5—42no—
512C24—54no—
513C24—52no—
514C24—102no—
515C24—102no—
516C24—102no—
517C24—102no—
518C24—102no—
519C24—102no—
520C24C23×D511yescharacteristic
521C2×Q8—108no—
522C2×Q8—108no—
523C2×Q8—204no—
524C2×Q8—2016no—
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—22no—
541C22×C4—22no—
542C22×C4—54no—
543C22×C4—54no—
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—102no—
555C22×C4—102no—
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—108no—
572C22×C4—204no—
573C22×C4—2016no—
574C22×C4Q8×D514yes—
575C22×C4C2×C22⋊D514yes—
576C22×C4C2×C22⋊D514yes—
577C22×C4C2×C22⋊D514yes—
578C22×C4C23×D512yes—
579C22×C4C23×D512yes—
580C22×C4C23×D512yes—
581C22×C4C23×D512yes—
582C22×C4C23×D512yes—
583C22×C4C23×D512yes—
584C22×C4C23×D512yes—
585C4⋊C4—28no—
586C4⋊C4—28no—
587C4⋊C4—28no—
588C4⋊C4—28no—
589C4⋊C4—28no—
590C4⋊C4—108no—
591C4⋊C4—108no—
592C4⋊C4—108no—
593C4⋊C4—108no—
594C4⋊C4—108no—
595C4⋊C4—108no—
596C4⋊C4—204no—
597C4⋊C4C2×C22⋊D5116yes—
598C22⋊C4—516no—
599C22⋊C4—108no—
600C22⋊C4—108no—
601C22⋊C4—108no—
602C22⋊C4—108no—
603C22⋊C4—204no—
604C42—28no—
605C42—108no—
606C42—204no—
607C42—204no—
608C2×C5#255618yescomplemented
609C2×C5C2×#53211yescharacteristic
610C2×C5C2×#53311yescharacteristic
611C2×C5C2×#53911yescharacteristic
612C2×C5C2×#54611yescharacteristic
613C2×C5C2×D4×Q811yescharacteristic
614C2×C5C2×#55211yescharacteristic
615C2×C5C2×#55411yescharacteristic
616D5—44no—
617C23—54no—
618C23—108no—
619C23—108no—
620C23—102no—
621C23—108no—
622C23—102no—
623C23—102no—
624C23—102no—
625C23—102no—
626C23—102no—
627C23—204no—
628C23—204no—
629C23—204no—
630C23—204no—
631C23C2×Q8×D512yes—
632C23#414712yes—
633C23D5×#4112yes—
634C23D5×#4112yes—
635C23D5×#4112yes—
636C23#414912yes—
637C23C22×C22⋊D512yes—
638C23C24×D511yescharacteristic
639Q8—2016no—
640C2×C4—28no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—28no—
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—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—54no—
665C2×C4—54no—
666C2×C4—54no—
667C2×C4—54no—
668C2×C4—108no—
669C2×C4—102no—
670C2×C4—102no—
671C2×C4—108no—
672C2×C4—102no—
673C2×C4—102no—
674C2×C4—102no—
675C2×C4—102no—
676C2×C4—102no—
677C2×C4—108no—
678C2×C4—108no—
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—102no—
689C2×C4—2016no—
690C2×C4—204no—
691C2×C4—204no—
692C2×C4—204no—
693C2×C4C2×Q8×D514yes—
694C2×C4C22×C22⋊D514yes—
695C2×C4C22×C22⋊D514yes—
696C2×C4C22×C22⋊D514yes—
697C5C2×#255611yescharacteristic, complemented, Sylow
698C22—104no—
699C22—104no—
700C22—104no—
701C22—202no—
702C22—202no—
703C22—202no—
704C22—202no—
705C22—2016no—
706C22#6602214yes—
707C22#6602414yes—
708C22#6602614yes—
709C22#6602714yes—
710C22Q8×C22⋊D514yes—
711C22#6616314yes—
712C22#6616614yes—
713C22C22×Q8×D511yescharacteristic
714C22C2×#414711yescharacteristic
715C22C2×D5×#4111yescharacteristic
716C22C2×D5×#4111yescharacteristic
717C22C2×D5×#4111yescharacteristic
718C22C2×#414911yescharacteristic
719C22C23×C22⋊D511yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—104no—
728C4—104no—
729C4—104no—
730C4—104no—
731C4—202no—
732C4—202no—
733C4—202no—
734C2—204no—
735C2#1061476918yesdirect product factor
736C2C2×#6602211yescharacteristic
737C2C2×#6602411yescharacteristic
738C2C2×#6602611yescharacteristic
739C2C2×#6602711yescharacteristic
740C2C2×Q8×C22⋊D511yescharacteristic
741C2C2×#6616611yescharacteristic
742C2C2×#6616311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#125C2
socleC24×C5C24
prime radicalC24×D5C23
hypercenterC22×#125D5
hypocenterC5C2×#2556
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. C22×C5×#125C2semidirect
3. #10614769C2direct (N × H)
7. C2×#65273C2semidirect
8. C2×#65268C2semidirect
9. C2×#65263C2semidirect
10. C2×#65261C2semidirect
11. C2×#65261C2semidirect
14. C2×C4⋊C4×Dic5C2semidirect
15. C2×#65222C2semidirect
20. C2×C5×#125C22semidirect
61. #65273C22semidirect
62. #65268C22semidirect
63. C4⋊C4×Dic5C22semidirect
64. #65263C22semidirect
65. #65261C22semidirect
66. #65261C22semidirect
68. #65222C22semidirect
113. C2×#685Q8semidirect
151. C22×#125D5semidirect
252. #685C2×Q8semidirect
266. C2×#125C2×D5semidirect
608. C2×C5#2556semidirect
697. C5C2×#2556semidirect
735. C2#10614769direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1252
C22×#40422
#106147692
C2×#652812
C2×#652832
C2×#652782
C2×#652732
C2×#652682
C2×#652632
C2×#652612
C2×#652792
C2×C4⋊C4×Dic52
C2×#652222
C2×C4×#6852
C2×#25565