Finite Group Databasebeta

← C2×#10607217 #12258995

Subgroups — C2×#10607217 #12258995

Order 1280.

2726 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4025C211yesmaximal, characteristic
2C2×C5×#388C211yesmaximal, characteristic
3C2×#65261C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
5C2×#65234C211yesmaximal, characteristic
6C2×#65233C211yesmaximal, characteristic
7C2×#65239C211yesmaximal, characteristic
8C2×C22⋊C4×Dic5C211yesmaximal, characteristic
9C2×C22⋊C4×Dic5C211yesmaximal, characteristic
10C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
11C2×C4×#683C211yesmaximal, characteristic, complemented
12#10607217C2116yesmaximal, direct product factor
13C2×#64944C211yesmaximal, characteristic, complemented
14C2×#64944C211yesmaximal, characteristic, complemented
15C2×#64942C211yesmaximal, characteristic, complemented
16C2×#64937C211yesmaximal, characteristic, complemented
17C24×Dic5C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C42×C5C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C4⋊Dic5C2211yescharacteristic
27C22×C4⋊Dic5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C22×#683C2211yescharacteristic
30C22×#683C2211yescharacteristic
31C22×#683C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×C4×Dic5C2211yescharacteristic
34C22×C4×Dic5C2211yescharacteristic
35C22×C4×Dic5C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C2×#4025C4116yescomplemented
41C2×#4025C2218yes—
42C5×#388C2218yes—
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C4⋊C4×Dic5C2218yescomplemented
56#65261C2218yescomplemented
57#65239C2218yes—
58#65234C2218yes—
59#65233C2218yes—
60C22⋊C4×Dic5C2218yes—
61C22⋊C4×Dic5C2218yes—
62C4×C4⋊Dic5C2218yescomplemented
63C4×#683C2218yescomplemented
64#64944C2218yescomplemented
65#64944C2218yescomplemented
66#64942C2218yescomplemented
67#64937C2218yescomplemented
68C2×#2373—51nomaximal, Sylow
69C25×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×Dic5—24no—
77C23×Dic5—24no—
78C23×Dic5—42no—
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2314yes—
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C2×C5×C4⋊C4—24no—
89C2×C5×C4⋊C4C2314yes—
90C2×C5×C22⋊C4—24no—
91C2×C5×C22⋊C4—24no—
92C2×C5×C22⋊C4C2×C418yes—
93C2×C5×C22⋊C4C2314yes—
94C2×C5×C22⋊C4C2314yes—
95C2×C5×C22⋊C4C2314yes—
96C2×C42×C5—24no—
97C2×C42×C5C2314yes—
98C2×C22⋊Dic5—42no—
99C2×C22⋊Dic5C2×C418yes—
100C2×C22⋊Dic5C2×C418yes—
101C2×C22⋊Dic5C2314yes—
102C2×C22⋊Dic5C2314yes—
103C2×C22⋊Dic5C2314yes—
104C2×C4⋊Dic5—24no—
105C2×C4⋊Dic5—24no—
106C2×C4⋊Dic5C2×C418yescomplemented
107C2×C4⋊Dic5C2314yes—
108C2×C4⋊Dic5C2314yes—
109C2×C4⋊Dic5C2314yes—
110C2×#683—24no—
111C2×#683—42no—
112C2×#683C2×C418yescomplemented
113C2×#683C2×C418yescomplemented
114C2×#683C2314yes—
115C2×#683C2314yes—
116C2×#683C2314yes—
117C2×#683C2314yes—
118C2×C4×Dic5—24no—
119C2×C4×Dic5—24no—
120C2×C4×Dic5—24no—
121C2×C4×Dic5—42no—
122C2×C4×Dic5—42no—
123C2×C4×Dic5—42no—
124C2×C4×Dic5C2×C418yescomplemented
125C2×C4×Dic5C2314yes—
126C2×C4×Dic5C2314yes—
127C2×C4×Dic5C2314yes—
128C2×C4×Dic5C2314yes—
129C2×C4×Dic5C2314yes—
130C2×C4×Dic5C2314yes—
131C2×C4×Dic5C2314yes—
132#4025C2×C4164yescomplemented
133C5×#95C2314yes—
134C5×#95C2314yes—
135#3963C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145C22×#126—51no—
146#2373—516no—
147C2×#389—51no—
148C2×#388—51no—
149C2×#388—51no—
150C2×#388D511yescharacteristic
151C2×#387—51no—
152C2×#387—51no—
153C2×#387—51no—
154C2×#385—51no—
155C2×C4×C4⋊C4—51no—
156C2×C4×C4⋊C4—51no—
157C2×C4×C4⋊C4—51no—
158C2×C4×C22⋊C4—51no—
159C2×C4×C22⋊C4—51no—
160C2×#376—51no—
161C24×C5—22no—
162C24×C5—22no—
163C24×C5—22no—
164C24×C5—22no—
165C24×C5—22no—
166C24×C5—22no—
167C24×C5C22×C414yes—
168C24×C5C2412yes—
169C24×C5C2411yescharacteristic
170C22×C4×C5—22no—
171C22×C4×C5—22no—
172C22×C4×C5—22no—
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
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×C5C22×C414yes—
185C22×C4×C5C22×C414yes—
186C22×C4×C5#4114yes—
187C22×C4×C5#4114yes—
188C22×C4×C5C2412yes—
189C22×C4×C5C2412yes—
190C22×C4×C5C2412yes—
191C22×C4×C5C2412yes—
192C22×C4×C5C2412yes—
193C22×C4×C5C2412yes—
194C22×Dic5—22no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
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—28no—
213C22×Dic5—28no—
214C22×Dic5—44no—
215C22×Dic5—416no—
216C22×Dic5C22×C414yes—
217C22×Dic5C22×C414yes—
218C22×Dic5C22×C414yes—
219C22×Dic5C22×C414yes—
220C22×Dic5#4114yes—
221C22×Dic5#4114yes—
222C22×Dic5C2412yes—
223C22×Dic5C2412yes—
224C22×Dic5C2412yes—
225C22×Dic5C2412yes—
226C22×Dic5C2412yes—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C5×C4⋊C4—28no—
231C5×C22⋊C4—28no—
232C5×C22⋊C4—28no—
233C5×C22⋊C4C22×C4116yes—
234C42×C5—28no—
235C22⋊Dic5—44no—
236C22⋊Dic5C22×C4116yes—
237C22⋊Dic5C22×C4116yes—
238C4⋊Dic5—28no—
239C4⋊Dic5—28no—
240C4⋊Dic5C22×C4116yescomplemented
241#683—28no—
242#683—44no—
243#683C22×C4116yescomplemented
244#683C22×C4116yescomplemented
245C4×Dic5—28no—
246C4×Dic5—28no—
247C4×Dic5—28no—
248C4×Dic5—44no—
249C4×Dic5—44no—
250C4×Dic5—44no—
251C4×Dic5C22×C4116yescomplemented
252C24×C4—51no—
253C2×#126—516no—
254C2×#126—58no—
255C22×C4⋊C4—51no—
256C22×C4⋊C4—51no—
257C22×C4⋊C4—51no—
258C22×C4⋊C4—51no—
259C22×C4⋊C4—51no—
260C22×C4⋊C4—51no—
261C22×C4⋊C4—51no—
262C22×C4⋊C4C2×D511yescharacteristic
263C22×C22⋊C4—51no—
264C22×C22⋊C4—51no—
265C22×C22⋊C4—51no—
266C22×C22⋊C4C2×D511yescharacteristic
267C22×C22⋊C4C2×D511yescharacteristic
268C22×C22⋊C4C2×D511yescharacteristic
269C22×C42—51no—
270C22×C42—51no—
271C22×C42—51no—
272C22×C42—51no—
273C22×C42—51no—
274C22×C42—51no—
275C22×C42—51no—
276C22×C42C2×D511yescharacteristic
277#389—58no—
278#388—58no—
279#388—58no—
280#388C2×D518yes—
281#387—58no—
282#387—58no—
283#387—58no—
284#385—58no—
285C4×C4⋊C4—58no—
286C4×C4⋊C4—58no—
287C4×C4⋊C4—58no—
288C4×C22⋊C4—58no—
289C4×C22⋊C4—58no—
290#376—58no—
291C2×#95—51no—
292C2×#95—51no—
293C2×#95—51no—
294C2×#95—51no—
295C2×#95—51no—
296C2×#95—51no—
297C2×#95—51no—
298C2×#95—51no—
299C2×#95—51no—
300C2×#95—51no—
301C2×#95C2×D511yescharacteristic
302C2×#95C2×D511yescharacteristic
303C23×C5—28no—
304C23×C5—28no—
305C23×C5—28no—
306C23×C5—22no—
307C23×C5—22no—
308C23×C5—22no—
309C23×C5—22no—
310C23×C5—22no—
311C23×C5—22no—
312C23×C5—44no—
313C23×C5—44no—
314C23×C5—44no—
315C23×C5—44no—
316C23×C5C23×C414yes—
317C23×C5C23×C412yes—
318C23×C5C2×#4112yes—
319C23×C5C2×#4112yes—
320C23×C5C2×#4112yes—
321C23×C5C2×#4112yes—
322C23×C5H(5,𝔽2)12yes—
323C23×C52−1+412yes—
324C23×C5C2511yescharacteristic
325C2×C4×C5—28no—
326C2×C4×C5—28no—
327C2×C4×C5—28no—
328C2×C4×C5—28no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—44no—
344C2×C4×C5—44no—
345C2×C4×C5C23×C414yes—
346C2×C4×C5C23×C414yes—
347C2×C4×C5C2×#4114yes—
348C2×C4×C5C2×#4114yes—
349C2×Dic5—28no—
350C2×Dic5—28no—
351C2×Dic5—28no—
352C2×Dic5—28no—
353C2×Dic5—28no—
354C2×Dic5—28no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—22no—
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—416no—
374C2×Dic5—44no—
375C2×Dic5—44no—
376C2×Dic5C23×C414yes—
377C2×Dic5C23×C414yes—
378C2×Dic5C23×C414yes—
379C2×Dic5C23×C414yes—
380C2×Dic5C2×#4114yes—
381C2×Dic5C2×#4114yes—
382C25C22×D511yescharacteristic
383C23×C4—51no—
384C23×C4—51no—
385C23×C4—51no—
386C23×C4—51no—
387C23×C4—51no—
388C23×C4—51no—
389C23×C4—51no—
390C23×C4—51no—
391C23×C4—54no—
392C23×C4—104no—
393C23×C4—104no—
394C23×C4—202no—
395C23×C4C22×D511yescharacteristic
396C23×C4C22×D511yescharacteristic
397C23×C4C22×D511yescharacteristic
398C23×C4C22×D511yescharacteristic
399C23×C4C22×D511yescharacteristic
400C23×C4C22×D511yescharacteristic
401#126—564no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—58no—
404C2×C4⋊C4—58no—
405C2×C4⋊C4—58no—
406C2×C4⋊C4—54no—
407C2×C4⋊C4—54no—
408C2×C4⋊C4—54no—
409C2×C4⋊C4—54no—
410C2×C4⋊C4—54no—
411C2×C4⋊C4—54no—
412C2×C4⋊C4—54no—
413C2×C4⋊C4—104no—
414C2×C4⋊C4—104no—
415C2×C4⋊C4—104no—
416C2×C4⋊C4—202no—
417C2×C4⋊C4C22×D514yes—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—58no—
421C2×C22⋊C4—58no—
422C2×C22⋊C4—54no—
423C2×C22⋊C4—54no—
424C2×C22⋊C4—54no—
425C2×C22⋊C4—202no—
426C2×C22⋊C4C4×D518yes—
427C2×C22⋊C4C22×D514yes—
428C2×C22⋊C4C22×D514yes—
429C2×C22⋊C4C22×D514yes—
430C2×C42—24no—
431C2×C42—58no—
432C2×C42—54no—
433C2×C42—54no—
434C2×C42—54no—
435C2×C42—54no—
436C2×C42—54no—
437C2×C42—54no—
438C2×C42—54no—
439C2×C42—104no—
440C2×C42—104no—
441C2×C42—104no—
442C2×C42—202no—
443C2×C42—202no—
444C2×C42—202no—
445C2×C42C22×D514yes—
446#95—54no—
447#95—54no—
448#95—54no—
449#95—54no—
450#95—54no—
451#95—54no—
452#95—54no—
453#95—54no—
454#95—54no—
455#95—54no—
456#95C22×D514yes—
457#95C22×D514yes—
458C22×C5—24no—
459C22×C5—24no—
460C22×C5—24no—
461C22×C5—416no—
462C22×C5—42no—
463C22×C5—42no—
464C22×C5—42no—
465C22×C5—42no—
466C22×C5C4×#4114yes—
467C22×C5C4×#4114yes—
468C22×C5#52014yes—
469C22×C5#55114yes—
470C22×C5#55214yes—
471C22×C5#55314yes—
472C22×C5#55614yes—
473C22×C5C24×C411yescharacteristic
474C22×C5C22×#4111yescharacteristic
475C22×C5C22×#4111yescharacteristic
476C22×C5C22×#4111yescharacteristic
477C22×C5C22×#4111yescharacteristic
478C22×C5C2×H(5,𝔽2)11yescharacteristic
479C22×C5C2×2−1+411yescharacteristic
480C4×C5—24no—
481C4×C5—24no—
482C4×C5—24no—
483C4×C5—24no—
484C4×C5—42no—
485C4×C5—42no—
486Dic5—24no—
487Dic5—24no—
488Dic5—24no—
489Dic5—24no—
490Dic5—24no—
491Dic5—24no—
492Dic5—42no—
493Dic5—42no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24C2×C4×D514yes—
501C24C23×D512yes—
502C24C23×D511yescharacteristic
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—54no—
518C22×C4—54no—
519C22×C4—54no—
520C22×C4—54no—
521C22×C4—54no—
522C22×C4—54no—
523C22×C4—52no—
524C22×C4—52no—
525C22×C4—52no—
526C22×C4—52no—
527C22×C4—52no—
528C22×C4—52no—
529C22×C4—52no—
530C22×C4—52no—
531C22×C4—108no—
532C22×C4—108no—
533C22×C4—102no—
534C22×C4—102no—
535C22×C4—102no—
536C22×C4—102no—
537C22×C4—102no—
538C22×C4—102no—
539C22×C4—102no—
540C22×C4—102no—
541C22×C4—102no—
542C22×C4—102no—
543C22×C4—102no—
544C22×C4—102no—
545C22×C4—102no—
546C22×C4—102no—
547C22×C4—102no—
548C22×C4—102no—
549C22×C4—102no—
550C22×C4—102no—
551C22×C4—204no—
552C22×C4—2016no—
553C22×C4C2×C4×D514yes—
554C22×C4C2×C4×D514yes—
555C22×C4#71114yes—
556C22×C4#71114yes—
557C22×C4C23×D512yes—
558C22×C4C23×D512yes—
559C22×C4C23×D512yes—
560C22×C4C23×D512yes—
561C22×C4C23×D512yes—
562C22×C4C23×D512yes—
563C4⋊C4—28no—
564C4⋊C4—516no—
565C4⋊C4—516no—
566C4⋊C4—516no—
567C4⋊C4—108no—
568C4⋊C4—108no—
569C4⋊C4—108no—
570C4⋊C4—204no—
571C22⋊C4—28no—
572C22⋊C4—28no—
573C22⋊C4—516no—
574C22⋊C4—516no—
575C22⋊C4—204no—
576C22⋊C4C2×C4×D5116yes—
577C42—28no—
578C42—516no—
579C42—108no—
580C42—108no—
581C42—108no—
582C42—204no—
583C42—204no—
584C42—204no—
585C2×C5—44no—
586C2×C5#237318yescomplemented
587C2×C5C2×C4×#4111yescharacteristic
588C2×C5C2×C4×#4111yescharacteristic
589C2×C5C2×#52011yescharacteristic
590C2×C5C2×#55111yescharacteristic
591C2×C5C2×#55211yescharacteristic
592C2×C5C2×#55311yescharacteristic
593C2×C5C2×#55611yescharacteristic
594C23—28no—
595C23—28no—
596C23—28no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23C22×C4×D514yes—
608C23C22×C4×D512yes—
609C23C2×#71112yes—
610C23C2×#71112yes—
611C23D5×#4112yes—
612C23D5×#4112yes—
613C23#414912yes—
614C23#415012yes—
615C23C24×D511yescharacteristic
616C2×C4—28no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—44no—
635C2×C4—44no—
636C2×C4—54no—
637C2×C4—54no—
638C2×C4—54no—
639C2×C4—54no—
640C2×C4—54no—
641C2×C4—54no—
642C2×C4—108no—
643C2×C4—108no—
644C2×C4—108no—
645C2×C4—108no—
646C2×C4—102no—
647C2×C4—102no—
648C2×C4—102no—
649C2×C4—102no—
650C2×C4—102no—
651C2×C4—102no—
652C2×C4—102no—
653C2×C4—102no—
654C2×C4—102no—
655C2×C4—102no—
656C2×C4—102no—
657C2×C4—102no—
658C2×C4—108no—
659C2×C4—108no—
660C2×C4—102no—
661C2×C4—102no—
662C2×C4—102no—
663C2×C4—102no—
664C2×C4—102no—
665C2×C4—102no—
666C2×C4—2016no—
667C2×C4—204no—
668C2×C4—204no—
669C2×C4C22×C4×D514yes—
670C2×C4C22×C4×D514yes—
671C2×C4C2×#71114yes—
672C2×C4C2×#71114yes—
673C5C2×#237311yescharacteristic, complemented, Sylow
674C22—24no—
675C22—24no—
676C22—24no—
677C22—42no—
678C22—42no—
679C22—416no—
680C22—42no—
681C22—42no—
682C22#6585714yes—
683C22C4×#71114yes—
684C22C4×#71114yes—
685C22#6595214yes—
686C22#6598414yes—
687C22#6600514yes—
688C22#6603914yes—
689C22C23×C4×D511yescharacteristic
690C22C22×#71111yescharacteristic
691C22C22×#71111yescharacteristic
692C22C2×D5×#4111yescharacteristic
693C22C2×D5×#4111yescharacteristic
694C22C2×#414911yescharacteristic
695C22C2×#415011yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—42no—
702C4—104no—
703C4—104no—
704C4—104no—
705C4—104no—
706C4—104no—
707C4—104no—
708C4—202no—
709C4—202no—
710C2—44no—
711C2#1060721718yesdirect product factor
712C2C2×#6585711yescharacteristic
713C2C2×C4×#71111yescharacteristic
714C2C2×C4×#71111yescharacteristic
715C2C2×#6595211yescharacteristic
716C2C2×#6598411yescharacteristic
717C2C2×#6600511yescharacteristic
718C2C2×#6603911yescharacteristic
subgroupG/H
centerC24C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC25×C5C23
cosocleC23×C5C25
hypercenterC2×#388D5
hypocenterC5C2×#2373
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×#65261C2semidirect
4. C2×C4⋊C4×Dic5C2semidirect
10. C2×C4×C4⋊Dic5C2semidirect
11. C2×C4×#683C2semidirect
12. #10607217C2direct (N × H)
13. C2×#64944C2semidirect
14. C2×#64944C2semidirect
15. C2×#64942C2semidirect
16. C2×#64937C2semidirect
40. C2×#4025C4semidirect
55. C4⋊C4×Dic5C22semidirect
56. #65261C22semidirect
62. C4×C4⋊Dic5C22semidirect
63. C4×#683C22semidirect
64. #64944C22semidirect
65. #64944C22semidirect
66. #64942C22semidirect
67. #64937C22semidirect
106. C2×C4⋊Dic5C2×C4semidirect
112. C2×#683C2×C4semidirect
113. C2×#683C2×C4semidirect
124. C2×C4×Dic5C2×C4semidirect
132. #4025C2×C4semidirect
240. C4⋊Dic5C22×C4semidirect
243. #683C22×C4semidirect
244. #683C22×C4semidirect
251. C4×Dic5C22×C4semidirect
586. C2×C5#2373semidirect
673. C5C2×#2373semidirect
711. C2#10607217direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40252
C2×C5×#3882
C2×#652612
C2×C4⋊C4×Dic52
C2×#652342
C2×#652332
C2×#652392
C2×C22⋊C4×Dic52
C2×C4×C4⋊Dic52
C2×C4×#6832
#106072172
C2×#649442
C2×#649422
C2×#649372
C2×#23735