Finite Group Databasebeta

← C2×#10617295 #13044869

Subgroups — C2×#10617295 #13044869

Order 1280.

2014 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65983C211yesmaximal, characteristic
2C2×#65774C211yesmaximal, characteristic, complemented
3C2×#65773C211yesmaximal, characteristic, complemented
4C2×#65754C211yesmaximal, characteristic, complemented
5C2×C4×#704C211yesmaximal, characteristic, complemented
6#10617295C2116yesmaximal, direct product factor
7C2×#65707C211yesmaximal, characteristic, complemented
8C2×#65703C211yesmaximal, characteristic, complemented
9C2×#65706C211yesmaximal, characteristic, complemented
10C2×#65701C211yesmaximal, characteristic, complemented
11C2×#65695C211yesmaximal, characteristic, complemented
12C2×#65695C211yesmaximal, characteristic, complemented
13C2×#65694C211yesmaximal, characteristic, complemented
14C2×#65692C211yesmaximal, characteristic, complemented
15C2×#65697C211yesmaximal, characteristic, complemented
16C2×#65691C211yesmaximal, characteristic, complemented
17C22×#704C2211yescharacteristic
18C22×#704C2211yescharacteristic
19C22×#704C2211yescharacteristic
20C23×#170C2211yescharacteristic
21C22×#700C2211yescharacteristic
22C22×D5⋊C8C2211yescharacteristic
23C2×C5×#123C411yescharacteristic
24C2×#4085C411yescharacteristic
25C2×D4×Dic5C2211yescharacteristic
26C2×#4075C411yescharacteristic
27C22×C4×Dic5C2211yescharacteristic
28#65983C418yes—
29#65983C2218yes—
30C2×#4044C411yescharacteristic
31C2×#4038C2211yescharacteristic
32C2×#4035C411yescharacteristic
33C2×#4033C2211yescharacteristic
34C2×#4031C411yescharacteristic
35C2×#4027C2211yescharacteristic
36C2×#4027C2211yescharacteristic
37C2×#4025C411yescharacteristic
38C2×#4024C411yescharacteristic
39C2×#4023C2211yescharacteristic
40C2×C22⋊#170C2211yescharacteristic
41C2×C22⋊#170C2211yescharacteristic
42C2×C22⋊#170C2211yescharacteristic
43C2×C22⋊#170C2211yescharacteristic
44#65774C2218yescomplemented
45#65773C2218yescomplemented
46#65754C2218yescomplemented
47C2×#4004C2211yescharacteristic
48C2×#4004C2211yescharacteristic
49C2×#4004C2211yescharacteristic
50C2×#4004C2211yescharacteristic
51C2×#4003C2211yescharacteristic
52C2×#4003C2211yescharacteristic
53C4×#704C2218yescomplemented
54C2×#4002C2211yescharacteristic
55C2×#4002C2211yescharacteristic
56C2×#4002C2211yescharacteristic
57C2×#4002C2211yescharacteristic
58C2×C4⋊#170C2211yescharacteristic
59C2×C4⋊#170C2211yescharacteristic
60C2×C4×#170C2211yescharacteristic
61C2×C4×#170C2211yescharacteristic
62C2×C4×#170C2211yescharacteristic
63C2×C4×#170C2211yescharacteristic
64C2×C4×#170C2211yescharacteristic
65C2×C4×#170C2211yescharacteristic
66#65707C2218yescomplemented
67#65706C2218yescomplemented
68#65703C2218yescomplemented
69#65701C2218yescomplemented
70#65697C2218yescomplemented
71#65695C2218yescomplemented
72#65695C2218yescomplemented
73#65694C2218yescomplemented
74#65692C2218yescomplemented
75#65691C2218yescomplemented
76C2×#2969—51nomaximal, Sylow
77C22×C5×D4C2×C411yescharacteristic
78C23×C4×C5C2×C411yescharacteristic
79C22×C22⋊D5C2×C411yescharacteristic
80C22×C22⋊D5C2×C411yescharacteristic
81C23×Dic5C2×C411yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C22×C4×D5C2311yescharacteristic
85C22×Dic10C2×C411yescharacteristic
86C2×#704—24no—
87C2×#704—24no—
88C2×#704—24no—
89C2×#704C2314yes—
90C2×#704C2314yes—
91C2×#704C2314yes—
92C22×#170—24no—
93C22×#170C2311yescharacteristic
94C22×#170C2311yescharacteristic
95C22×#170C2311yescharacteristic
96C22×#170C2311yescharacteristic
97C22×#170C2311yescharacteristic
98C22×#170C2311yescharacteristic
99C22×#170C2314yes—
100C22×#170C2311yescharacteristic
101C22×#170C2311yescharacteristic
102C2×#700—24no—
103C2×#700C2314yes—
104C2×D5⋊C8—24no—
105C2×D5⋊C8C2314yes—
106C5×#123C2×C418yes—
107C2×C5×C4⋊C4C2×C411yescharacteristic
108C2×C5×C4⋊C4C2×C411yescharacteristic
109C2×C5×C22⋊C4C2×C411yescharacteristic
110C2×C5×C22⋊C4C2×C411yescharacteristic
111C2×C5×C22⋊C4C2×C411yescharacteristic
112C2×C22⋊Dic5C2×C411yescharacteristic
113C2×C22⋊Dic5C2×C411yescharacteristic
114C2×C22⋊Dic5C2×C411yescharacteristic
115#4085C2×C418yes—
116D4×Dic5C2×C414yes—
117D4×Dic5C2314yes—
118#4075C2×C418yes—
119C2×#685C2×C411yescharacteristic
120C2×#685C2×C411yescharacteristic
121C2×#685C2×C411yescharacteristic
122C2×#685C2×C411yescharacteristic
123C2×C4⋊Dic5C2×C411yescharacteristic
124C2×C4⋊Dic5C2×C411yescharacteristic
125C2×#683C2×C411yescharacteristic
126C2×#683C2×C411yescharacteristic
127C2×#683C2×C411yescharacteristic
128C2×#683C2×C411yescharacteristic
129C2×#683C2×C411yescharacteristic
130C2×#683C2×C411yescharacteristic
131C2×C4×Dic5C2×C411yescharacteristic
132C2×C4×Dic5C2×C411yescharacteristic
133C2×C4×Dic5C2×C414yes—
134C2×C4×Dic5C2311yescharacteristic
135C2×C4×Dic5C2311yescharacteristic
136C2×C4×Dic5C2311yescharacteristic
137C2×C4×Dic5C2311yescharacteristic
138C2×C4×Dic5C2314yes—
139#4044C2×C418yes—
140#4038C2×C414yes—
141#4038C2314yes—
142#4035C2×C418yes—
143#4033C2×C414yes—
144#4033C2314yes—
145#4031C2×C418yes—
146#4027C2×C414yes—
147#4027C2×C414yes—
148#4027C2314yes—
149#4027C2314yes—
150#4025C2×C418yes—
151#4024C2×C418yes—
152#4023C2×C414yes—
153#4023C2314yes—
154C22⋊#170C2314yes—
155C22⋊#170C2314yes—
156C22⋊#170C2314yes—
157C22⋊#170C2314yes—
158#4004C2314yes—
159#4004C2314yes—
160#4004C2314yes—
161#4004C2314yes—
162#4003C2314yes—
163#4003C2314yes—
164#4002C2314yes—
165#4002C2314yes—
166#4002C2314yes—
167#4002C2314yes—
168C4⋊#170C2314yes—
169C4⋊#170C2314yes—
170C4×#170C2314yes—
171C4×#170C2314yes—
172C4×#170C2314yes—
173C4×#170C2314yes—
174C4×#170C2314yes—
175C4×#170C2314yes—
176C2×#529—51no—
177#2969—516no—
178C2×#446—51no—
179C2×C8×Q8—51no—
180C2×#436—51no—
181C2×#436—51no—
182C2×#436—51no—
183C2×#435—51no—
184C2×#435—51no—
185C2×C8×D4—51no—
186C2×#433—51no—
187C2×#433—51no—
188C2×#431—51no—
189C2×#405—51no—
190C2×#405—51no—
191C2×C4×M16—51no—
192C24×C5C22×C411yescharacteristic
193C24×C5C22×C411yescharacteristic
194C23×D5C22×C411yescharacteristic
195C2×C5×D4—42no—
196C2×C5×D4C22×C414yes—
197C22×C4×C5—42no—
198C22×C4×C5C22×C411yescharacteristic
199C22×C4×C5C22×C411yescharacteristic
200C22×C4×C5C22×C411yescharacteristic
201C22×C4×C5C22×C411yescharacteristic
202C22×C4×C5C22×C411yescharacteristic
203C22×C4×C5C22×C414yes—
204C2×C22⋊D5—24no—
205C2×C22⋊D5—42no—
206C2×C22⋊D5C22×C414yes—
207C2×C22⋊D5C22×C414yes—
208C22×Dic5—24no—
209C22×Dic5—22no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5C22×C411yescharacteristic
214C22×Dic5C22×C411yescharacteristic
215C22×Dic5C22×C411yescharacteristic
216C22×Dic5C22×C411yescharacteristic
217C22×Dic5C22×C411yescharacteristic
218C22×Dic5C22×C414yes—
219C22×Dic5C22×C412yes—
220C22×Dic5C22×C412yes—
221C22×Dic5C22×C411yescharacteristic
222C22×Dic5C2412yes—
223C22×Dic5C2412yes—
224C22×Dic5C2411yescharacteristic
225C2×C4×D5—22no—
226C2×C4×D5—22no—
227C2×C4×D5C22×C412yes—
228C2×C4×D5C2412yes—
229C2×Dic10—24no—
230C2×Dic10C22×C414yes—
231#704—28no—
232#704—28no—
233#704—28no—
234C2×#170—22no—
235C2×#170—22no—
236C2×#170—22no—
237C2×#170—22no—
238C2×#170—22no—
239C2×#170—22no—
240C2×#170—28no—
241C2×#170#4114yes—
242C2×#170#4114yes—
243C2×#170C2412yes—
244C2×#170C2412yes—
245C2×#170C2412yes—
246C2×#170C2412yes—
247C2×#170C2412yes—
248C2×#170C2412yes—
249C2×#170C2412yes—
250C2×#170C2412yes—
251#700—28no—
252D5⋊C8—28no—
253C5×C4⋊C4C22×C414yes—
254C5×C4⋊C4C22×C414yes—
255C5×C22⋊C4C22×C414yes—
256C5×C22⋊C4C22×C414yes—
257C5×C22⋊C4C22×C414yes—
258C22⋊Dic5C22×C414yes—
259C22⋊Dic5C22×C414yes—
260C22⋊Dic5C22×C414yes—
261#685C22×C414yes—
262#685C22×C414yes—
263#685C22×C414yes—
264#685C22×C414yes—
265C4⋊Dic5C22×C414yes—
266C4⋊Dic5C22×C414yes—
267#683C22×C414yes—
268#683C22×C414yes—
269#683C22×C414yes—
270#683C22×C414yes—
271#683C22×C414yes—
272#683C22×C414yes—
273C4×Dic5C22×C412yes—
274C4×Dic5C22×C412yes—
275C4×Dic5C22×C414yes—
276C4×Dic5C22×C412yes—
277C4×Dic5C22×C414yes—
278C4×Dic5C22×C412yes—
279C4×Dic5C2412yes—
280C4×Dic5C2412yes—
281C4×Dic5C2412yes—
282C4×Dic5C2412yes—
283C22×M16—51no—
284C22×M16—51no—
285C22×M16—51no—
286C22×M16—51no—
287C23×C8—51no—
288C23×C8—51no—
289#529—58no—
290#529—58no—
291C2×#126—51no—
292C2×#126—51no—
293C2×#125—51no—
294C2×#124—51no—
295C2×#123—51no—
296C2×#123AGL(1,𝔽5)11yescharacteristic
297C2×C22⋊Q8—51no—
298C2×#121—51no—
299C2×C4×Q8—51no—
300C2×C4×D4—51no—
301C2×C4×D4—51no—
302C2×C4×D4—51no—
303C2×#117—51no—
304C2×#117—51no—
305C22×C42—51no—
306#446—58no—
307C8×Q8—58no—
308#436—58no—
309#436—58no—
310#436—58no—
311#435—58no—
312#435—58no—
313C8×D4—58no—
314#433—58no—
315#433—58no—
316#431—58no—
317C2×C4⋊C8—51no—
318C2×C4⋊C8—51no—
319C2×C4⋊C8—51no—
320C2×C4⋊C8—51no—
321C2×C4⋊C8—51no—
322C2×C4⋊C8—51no—
323C2×C22⋊C8—51no—
324C2×C22⋊C8—51no—
325C2×C22⋊C8—51no—
326C2×C22⋊C8—51no—
327C2×C22⋊C8—51no—
328C2×C22⋊C8—51no—
329#405—58no—
330#405—58no—
331C4×M16—58no—
332C2×#97—51no—
333C2×#97—51no—
334C2×#97—51no—
335C2×#97—51no—
336C2×C4×C8—51no—
337C2×C4×C8—51no—
338C2×C4×C8—51no—
339C2×C4×C8—51no—
340C2×C4×C8—51no—
341C2×C4×C8—51no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5C23×C412yes—
349C23×C5C23×C412yes—
350C23×C5C23×C411yescharacteristic
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5C23×C412yes—
355C5×D4—44no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—44no—
362C2×C4×C5C23×C412yes—
363C2×C4×C5C23×C412yes—
364C2×C4×C5C23×C412yes—
365C2×C4×C5C23×C412yes—
366C2×C4×C5C23×C412yes—
367C22⋊D5—28no—
368C22⋊D5—44no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—24no—
375C2×Dic5—24no—
376C2×Dic5—28no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5#13114yes—
382C2×Dic5C23×C412yes—
383C2×Dic5C23×C412yes—
384C2×Dic5C23×C412yes—
385C2×Dic5C23×C412yes—
386C2×Dic5C23×C412yes—
387C2×Dic5C23×C411yescharacteristic
388C2×Dic5C23×C412yes—
389C2×Dic5C2×#4112yes—
390C2×Dic5C2×#4112yes—
391C2×Dic5C2511yescharacteristic
392C4×D5—24no—
393C4×D5—22no—
394C4×D5—22no—
395Dic10—28no—
396#170—22no—
397#170—22no—
398#170—22no—
399#170—22no—
400#170—22no—
401#170—22no—
402#170C2×#4114yes—
403#170C2×#4114yes—
404C22×Q8—51no—
405C22×D4—51no—
406C22×D4—51no—
407C22×D4C2×AGL(1,𝔽5)11yescharacteristic
408C23×C4—51no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4C2×AGL(1,𝔽5)11yescharacteristic
413C2×M16—54no—
414C2×M16—54no—
415C2×M16—54no—
416C2×M16—54no—
417C2×M16—104no—
418C2×M16—104no—
419C2×M16—104no—
420C2×M16—104no—
421C22×C8—51no—
422C22×C8—51no—
423C22×C8—54no—
424C22×C8—51no—
425C22×C8—51no—
426C22×C8—54no—
427C22×C8—51no—
428C22×C8—51no—
429C22×C8—51no—
430C22×C8—51no—
431C22×C8—104no—
432C22×C8—104no—
433#126—58no—
434#126—58no—
435#125—58no—
436#124—58no—
437#123—58no—
438#123C2×AGL(1,𝔽5)18yes—
439C22⋊Q8—58no—
440#121—58no—
441C4×Q8—54no—
442C4×Q8—54no—
443C4×D4—54no—
444C4×D4—54no—
445C4×D4—54no—
446C4×D4—54no—
447C4×D4—54no—
448C4×D4—54no—
449#117—54no—
450#117—54no—
451#117—54no—
452#117—54no—
453C2×C4⋊C4—51no—
454C2×C4⋊C4—51no—
455C2×C4⋊C4—51no—
456C2×C4⋊C4—51no—
457C2×C4⋊C4—51no—
458C2×C4⋊C4—51no—
459C2×C4⋊C4—51no—
460C2×C4⋊C4—51no—
461C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
462C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
463C2×C22⋊C4—51no—
464C2×C22⋊C4—51no—
465C2×C22⋊C4—51no—
466C2×C22⋊C4—51no—
467C2×C22⋊C4—51no—
468C2×C22⋊C4—51no—
469C2×C22⋊C4—51no—
470C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
471C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
472C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
473C2×C42—51no—
474C2×C42—51no—
475C2×C42—51no—
476C2×C42—51no—
477C2×C42—51no—
478C2×C42—51no—
479C2×C42—54no—
480C2×C42—54no—
481C4⋊C8—54no—
482C4⋊C8—54no—
483C4⋊C8—54no—
484C4⋊C8—54no—
485C4⋊C8—54no—
486C4⋊C8—54no—
487C22⋊C8—54no—
488C22⋊C8—54no—
489C22⋊C8—54no—
490C22⋊C8—54no—
491C22⋊C8—54no—
492C22⋊C8—54no—
493#97—54no—
494#97—54no—
495#97—54no—
496#97—54no—
497C4×C8—54no—
498C4×C8—54no—
499C4×C8—54no—
500C4×C8—54no—
501C4×C8—54no—
502C4×C8—54no—
503C22×C5—22no—
504C22×C5—22no—
505C22×C5—22no—
506C22×C5—22no—
507C22×C5—22no—
508C22×C5—22no—
509C22×C5—44no—
510C22×C5—44no—
511C22×C5C4×#4112yes—
512C22×C5C2×#13112yes—
513C22×C5#56812yes—
514C22×C5C24×C411yescharacteristic
515C2×D5—22no—
516C2×D5—22no—
517C2×D5—22no—
518C2×D5—44no—
519C4×C5—22no—
520C4×C5—22no—
521C4×C5—22no—
522C4×C5—22no—
523C4×C5—22no—
524Dic5—22no—
525Dic5—22no—
526Dic5—22no—
527Dic5—22no—
528Dic5—22no—
529Dic5C4×#4112yes—
530Dic5C2×#13114yes—
531Dic5C22×#4111yescharacteristic
532Dic5C22×#4111yescharacteristic
533C24—51no—
534C24C22×AGL(1,𝔽5)11yescharacteristic
535C24C22×AGL(1,𝔽5)11yescharacteristic
536C2×Q8—54no—
537C2×Q8—104no—
538C2×D4—42no—
539C2×D4—54no—
540C2×D4—54no—
541C2×D4—104no—
542C2×D4—202no—
543C2×D4C22×AGL(1,𝔽5)14yes—
544C22×C4—42no—
545C22×C4—51no—
546C22×C4—51no—
547C22×C4—52no—
548C22×C4—52no—
549C22×C4—52no—
550C22×C4—54no—
551C22×C4—52no—
552C22×C4—51no—
553C22×C4—51no—
554C22×C4—51no—
555C22×C4—51no—
556C22×C4—51no—
557C22×C4—52no—
558C22×C4—52no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—102no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—104no—
566C22×C4C22×AGL(1,𝔽5)11yescharacteristic
567C22×C4C22×AGL(1,𝔽5)11yescharacteristic
568C22×C4C22×AGL(1,𝔽5)11yescharacteristic
569C22×C4C22×AGL(1,𝔽5)11yescharacteristic
570C22×C4C22×AGL(1,𝔽5)11yescharacteristic
571C22×C4C22×AGL(1,𝔽5)14yes—
572M16—108no—
573M16—108no—
574M16—108no—
575M16—108no—
576C2×C8—52no—
577C2×C8—52no—
578C2×C8—54no—
579C2×C8—54no—
580C2×C8—52no—
581C2×C8—52no—
582C2×C8—52no—
583C2×C8—52no—
584C2×C8—52no—
585C2×C8—52no—
586C2×C8—108no—
587C2×C8—108no—
588C2×C8—102no—
589C2×C8—102no—
590C2×C8—102no—
591C2×C8—102no—
592C2×C8—102no—
593C2×C8—102no—
594C4⋊C4—54no—
595C4⋊C4—54no—
596C4⋊C4—54no—
597C4⋊C4—54no—
598C4⋊C4—54no—
599C4⋊C4—54no—
600C4⋊C4—54no—
601C4⋊C4—54no—
602C4⋊C4C22×AGL(1,𝔽5)14yes—
603C4⋊C4C22×AGL(1,𝔽5)14yes—
604C22⋊C4—54no—
605C22⋊C4—54no—
606C22⋊C4—54no—
607C22⋊C4—54no—
608C22⋊C4—54no—
609C22⋊C4—54no—
610C22⋊C4—54no—
611C22⋊C4C22×AGL(1,𝔽5)14yes—
612C22⋊C4C22×AGL(1,𝔽5)14yes—
613C22⋊C4C22×AGL(1,𝔽5)14yes—
614C42—52no—
615C42—52no—
616C42—52no—
617C42—52no—
618C42—52no—
619C42—52no—
620C42—54no—
621C42—54no—
622C42—52no—
623C42—52no—
624C2×C5—42no—
625C2×C5—42no—
626C2×C5#296914yescomplemented
627C2×C5C2×C4×#4111yescharacteristic
628C2×C5C22×#13111yescharacteristic
629C2×C5C2×#56811yescharacteristic
630D5—42no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—52no—
638C23—102no—
639C23—102no—
640C23—102no—
641C23C23×AGL(1,𝔽5)12yes—
642C23C23×AGL(1,𝔽5)12yes—
643C23C23×AGL(1,𝔽5)11yescharacteristic
644Q8—108no—
645D4—44no—
646D4—108no—
647D4—204no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—44no—
654C2×C4—54no—
655C2×C4—52no—
656C2×C4—52no—
657C2×C4—51no—
658C2×C4—51no—
659C2×C4—52no—
660C2×C4—52no—
661C2×C4—52no—
662C2×C4—52no—
663C2×C4—52no—
664C2×C4—52no—
665C2×C4—102no—
666C2×C4—102no—
667C2×C4—104no—
668C2×C4—102no—
669C2×C4—102no—
670C2×C4—102no—
671C2×C4—102no—
672C2×C4—108no—
673C2×C4—104no—
674C2×C4—104no—
675C2×C4—102no—
676C2×C4—102no—
677C2×C4—102no—
678C2×C4—102no—
679C2×C4—102no—
680C2×C4C23×AGL(1,𝔽5)12yes—
681C2×C4C23×AGL(1,𝔽5)12yes—
682C2×C4C23×AGL(1,𝔽5)12yes—
683C2×C4C23×AGL(1,𝔽5)12yes—
684C2×C4C23×AGL(1,𝔽5)12yes—
685C8—54no—
686C8—54no—
687C8—102no—
688C8—102no—
689C8—102no—
690C8—102no—
691C8—102no—
692C8—102no—
693C5C2×#296911yescharacteristic, complemented, Sylow
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—44no—
702C22—102no—
703C22—102no—
704C22—102no—
705C22—204no—
706C22#6625612yes—
707C22D5⋊#13112yes—
708C22#41×AGL(1,𝔽5)12yes—
709C22C24×AGL(1,𝔽5)11yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—54no—
716C4—51no—
717C4—51no—
718C4—52no—
719C4—102no—
720C4—102no—
721C4—102no—
722C4—102no—
723C4—102no—
724C2—42no—
725C2—42no—
726C2—202no—
727C2#1061729514yesdirect product factor
728C2C2×#6625611yescharacteristic
729C2C2×D5⋊#13111yescharacteristic
730C2C2×#41×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC23C23×AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC2×C5×#123C4
socleC23×C5C23×C4
prime radicalC2×#4085C4
cosocleC2×Dic5C25
hypercenterC2×#123AGL(1,𝔽5)
hypocenterC5C2×#2969
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#65774C2semidirect
3. C2×#65773C2semidirect
4. C2×#65754C2semidirect
5. C2×C4×#704C2semidirect
6. #10617295C2direct (N × H)
7. C2×#65707C2semidirect
8. C2×#65703C2semidirect
9. C2×#65706C2semidirect
10. C2×#65701C2semidirect
11. C2×#65695C2semidirect
12. C2×#65695C2semidirect
13. C2×#65694C2semidirect
14. C2×#65692C2semidirect
15. C2×#65697C2semidirect
16. C2×#65691C2semidirect
44. #65774C22semidirect
45. #65773C22semidirect
46. #65754C22semidirect
53. C4×#704C22semidirect
66. #65707C22semidirect
67. #65706C22semidirect
68. #65703C22semidirect
69. #65701C22semidirect
70. #65697C22semidirect
71. #65695C22semidirect
72. #65695C22semidirect
73. #65694C22semidirect
74. #65692C22semidirect
75. #65691C22semidirect
626. C2×C5#2969semidirect
693. C5C2×#2969semidirect
727. C2#10617295direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659832
C2×#657742
C2×#657732
C2×#657542
C2×C4×#7042
#106172952
C2×#657072
C2×#657032
C2×#657062
C2×#657012
C2×#656952
C2×#656942
C2×#656922
C2×#656972
C2×#656912
C2×#29695