Finite Group Databasebeta

← C2×#10617351 #13044864

Subgroups — C2×#10617351 #13044864

Order 1280.

2026 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×#66040C211yesmaximal, characteristic
2#10617351C2116yesmaximal, direct product factor
3C2×#65707C211yesmaximal, characteristic, complemented
4C2×#65709C211yesmaximal, characteristic, complemented
5C2×#65704C211yesmaximal, characteristic, complemented
6C2×#65702C211yesmaximal, characteristic, complemented
7C2×#65706C211yesmaximal, characteristic, complemented
8C2×#65701C211yesmaximal, characteristic, complemented
9C2×#65694C211yesmaximal, characteristic, complemented
10C2×#65694C211yesmaximal, characteristic, complemented
11C2×#65693C211yesmaximal, characteristic, complemented
12C2×#65692C211yesmaximal, characteristic, complemented
13C2×#65697C211yesmaximal, characteristic, complemented
14C2×#65691C211yesmaximal, characteristic, complemented
15C2×#65680C211yesmaximal, characteristic, complemented
16C2×#65676C211yesmaximal, characteristic, complemented
17C22×#704C2211yescharacteristic
18C23×#170C2211yescharacteristic
19C22×#700C2211yescharacteristic
20C22×D5⋊C8C2211yescharacteristic
21C22×D5⋊C8C2211yescharacteristic
22C22×D5⋊C8C2211yescharacteristic
23C2×C5×#126C411yescharacteristic
24#66040C418yes—
25#66040C2218yes—
26C2×#4042C411yescharacteristic
27C2×#4040C411yescharacteristic
28C2×#4039C2211yescharacteristic
29C2×#4038C2211yescharacteristic
30C2×#4035C411yescharacteristic
31C2×#4033C2211yescharacteristic
32C2×#4031C411yescharacteristic
33C2×#4030C411yescharacteristic
34C2×#4029C411yescharacteristic
35C2×#4027C2211yescharacteristic
36C2×#4027C2211yescharacteristic
37C2×#4023C2211yescharacteristic
38C2×#4022C411yescharacteristic
39C2×C42×D5C2211yescharacteristic
40C2×C22⋊#170C2211yescharacteristic
41C2×C22⋊#170C2211yescharacteristic
42C2×#4004C2211yescharacteristic
43C2×#4004C2211yescharacteristic
44C2×#4003C2211yescharacteristic
45C2×#4003C2211yescharacteristic
46C2×#4003C2211yescharacteristic
47C2×#4003C2211yescharacteristic
48C2×#4002C2211yescharacteristic
49C2×#4002C2211yescharacteristic
50C2×#4002C2211yescharacteristic
51C2×#4002C2211yescharacteristic
52C2×#4002C2211yescharacteristic
53C2×#4002C2211yescharacteristic
54C2×C4⋊#170C2211yescharacteristic
55C2×C4⋊#170C2211yescharacteristic
56C2×C4⋊#170C2211yescharacteristic
57C2×C4⋊#170C2211yescharacteristic
58C2×C4×#170C2211yescharacteristic
59C2×C4×#170C2211yescharacteristic
60C2×C4×#170C2211yescharacteristic
61C2×C4×#170C2211yescharacteristic
62#65709C2218yescomplemented
63#65707C2218yescomplemented
64#65706C2218yescomplemented
65#65704C2218yescomplemented
66#65702C2218yescomplemented
67#65701C2218yescomplemented
68#65697C2218yescomplemented
69#65694C2218yescomplemented
70#65694C2218yescomplemented
71#65693C2218yescomplemented
72#65692C2218yescomplemented
73#65691C2218yescomplemented
74#65680C2218yescomplemented
75#65676C2218yescomplemented
76C2×#2968—51nomaximal, Sylow
77C22×C22⋊D5C2×C411yescharacteristic
78C22×C22⋊D5C2×C411yescharacteristic
79C23×Dic5C2311yescharacteristic
80C22×D20C2×C411yescharacteristic
81C22×C4×D5C2×C411yescharacteristic
82C22×C4×D5C2×C411yescharacteristic
83C22×C4×D5C2311yescharacteristic
84C22×C4×D5C2311yescharacteristic
85C22×Dic10C2×C411yescharacteristic
86C2×#704—24no—
87C2×#704C2314yes—
88C22×#170—24no—
89C22×#170C2311yescharacteristic
90C22×#170C2311yescharacteristic
91C22×#170C2311yescharacteristic
92C22×#170C2311yescharacteristic
93C22×#170C2314yes—
94C22×#170C2311yescharacteristic
95C22×#170C2311yescharacteristic
96C22×#170C2311yescharacteristic
97C22×#170C2311yescharacteristic
98C2×#700—24no—
99C2×#700C2314yes—
100C2×D5⋊C8—24no—
101C2×D5⋊C8—24no—
102C2×D5⋊C8—24no—
103C2×D5⋊C8C2314yes—
104C2×D5⋊C8C2314yes—
105C2×D5⋊C8C2314yes—
106C5×#126C2×C418yes—
107C2×C5×C4⋊C4C2×C411yescharacteristic
108C2×C5×C4⋊C4C2×C411yescharacteristic
109C2×C5×C4⋊C4C2×C411yescharacteristic
110C2×C5×C22⋊C4C2×C411yescharacteristic
111C2×C5×C22⋊C4C2×C411yescharacteristic
112C2×C5×C22⋊C4C2×C411yescharacteristic
113C2×C42×C5C2×C411yescharacteristic
114C2×C22⋊Dic5C2×C411yescharacteristic
115C2×#685C2×C411yescharacteristic
116C2×#685C2×C411yescharacteristic
117C2×#685C2×C411yescharacteristic
118C2×#685C2×C411yescharacteristic
119C2×#685C2×C411yescharacteristic
120C2×#685C2×C411yescharacteristic
121C2×C4⋊Dic5C2×C411yescharacteristic
122C2×#683C2×C411yescharacteristic
123C2×#683C2×C411yescharacteristic
124C2×#683C2×C411yescharacteristic
125C2×#683C2×C411yescharacteristic
126C2×#683C2×C411yescharacteristic
127C2×#683C2×C411yescharacteristic
128C2×C4×Dic5C2×C411yescharacteristic
129C2×C4×Dic5C2311yescharacteristic
130C2×C4×Dic5C2311yescharacteristic
131C2×C4×Dic5C2311yescharacteristic
132C2×C4×Dic5C2311yescharacteristic
133#4042C2×C418yes—
134#4040C2×C418yes—
135#4039C2×C414yes—
136#4039C2314yes—
137#4038C2×C414yes—
138#4038C2314yes—
139#4035C2×C418yes—
140#4033C2×C414yes—
141#4033C2314yes—
142#4031C2×C418yes—
143#4030C2×C418yes—
144#4029C2×C418yes—
145#4027C2×C414yes—
146#4027C2×C414yes—
147#4027C2314yes—
148#4027C2314yes—
149#4023C2×C414yes—
150#4023C2314yes—
151#4022C2×C418yes—
152C42×D5C2×C414yes—
153C42×D5C2314yes—
154C22⋊#170C2314yes—
155C22⋊#170C2314yes—
156#4004C2314yes—
157#4004C2314yes—
158#4003C2314yes—
159#4003C2314yes—
160#4003C2314yes—
161#4003C2314yes—
162#4002C2314yes—
163#4002C2314yes—
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#2968—516no—
178C2×#446—51no—
179C2×#446—51no—
180C2×#435—51no—
181C2×#435—51no—
182C2×#435—51no—
183C2×#435—51no—
184C2×C8×D4—51no—
185C2×C8×D4—51no—
186C2×#433—51no—
187C2×#433—51no—
188C2×#431—51no—
189C2×#405—51no—
190C2×#405—51no—
191C22×#97—51no—
192C24×C5C22×C411yescharacteristic
193C23×D5C22×C411yescharacteristic
194C23×D5C22×C411yescharacteristic
195C22×C4×C5C22×C411yescharacteristic
196C22×C4×C5C22×C411yescharacteristic
197C22×C4×C5C22×C411yescharacteristic
198C22×C4×C5C22×C411yescharacteristic
199C22×C4×C5C22×C411yescharacteristic
200C22×C4×C5C22×C411yescharacteristic
201C2×C22⋊D5—24no—
202C2×C22⋊D5—42no—
203C2×C22⋊D5C22×C414yes—
204C2×C22⋊D5C22×C414yes—
205C22×Dic5—22no—
206C22×Dic5—22no—
207C22×Dic5C22×C411yescharacteristic
208C22×Dic5C22×C411yescharacteristic
209C22×Dic5C22×C411yescharacteristic
210C22×Dic5C22×C412yes—
211C22×Dic5C22×C411yescharacteristic
212C22×Dic5C22×C411yescharacteristic
213C22×Dic5C2412yes—
214C22×Dic5C2411yescharacteristic
215C2×D20—24no—
216C2×D20C22×C414yes—
217C2×C4×D5—24no—
218C2×C4×D5—22no—
219C2×C4×D5—22no—
220C2×C4×D5—22no—
221C2×C4×D5—22no—
222C2×C4×D5—42no—
223C2×C4×D5C22×C414yes—
224C2×C4×D5C22×C412yes—
225C2×C4×D5C22×C412yes—
226C2×C4×D5C22×C414yes—
227C2×C4×D5C2412yes—
228C2×C4×D5C2412yes—
229C2×Dic10—42no—
230C2×Dic10C22×C414yes—
231#704—28no—
232C2×#170—22no—
233C2×#170—22no—
234C2×#170—22no—
235C2×#170—22no—
236C2×#170—22no—
237C2×#170—22no—
238C2×#170—28no—
239C2×#170#4114yes—
240C2×#170#4114yes—
241C2×#170C2412yes—
242C2×#170C2412yes—
243C2×#170C2412yes—
244C2×#170C2412yes—
245C2×#170C2412yes—
246C2×#170C2412yes—
247C2×#170C2412yes—
248C2×#170C2412yes—
249#700—28no—
250D5⋊C8—28no—
251D5⋊C8—28no—
252D5⋊C8—28no—
253C5×C4⋊C4C22×C414yes—
254C5×C4⋊C4C22×C414yes—
255C5×C4⋊C4C22×C414yes—
256C5×C22⋊C4C22×C414yes—
257C5×C22⋊C4C22×C414yes—
258C5×C22⋊C4C22×C414yes—
259C42×C5C22×C414yes—
260C22⋊Dic5C22×C414yes—
261#685C22×C414yes—
262#685C22×C414yes—
263#685C22×C414yes—
264#685C22×C414yes—
265#685C22×C414yes—
266#685C22×C414yes—
267C4⋊Dic5C22×C414yes—
268#683C22×C414yes—
269#683C22×C414yes—
270#683C22×C414yes—
271#683C22×C414yes—
272#683C22×C414yes—
273#683C22×C414yes—
274C4×Dic5C22×C412yes—
275C4×Dic5C22×C412yes—
276C4×Dic5C22×C414yes—
277C4×Dic5C22×C412yes—
278C4×Dic5C22×C412yes—
279C4×Dic5C2412yes—
280C4×Dic5C2412yes—
281C4×Dic5C2412yes—
282C4×Dic5C2412yes—
283C22×M16—51no—
284C22×M16—51no—
285C23×C8—51no—
286C23×C8—51no—
287C23×C8—51no—
288C23×C8—51no—
289#529—58no—
290#529—58no—
291C2×#126—51no—
292C2×#126AGL(1,𝔽5)11yescharacteristic
293C2×#125—51no—
294C2×#124—51no—
295C2×#123—51no—
296C2×#123—51no—
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—
307#446—58no—
308#435—58no—
309#435—58no—
310#435—58no—
311#435—58no—
312C8×D4—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—
331C2×#97—51no—
332C2×#97—51no—
333C2×#97—51no—
334C2×#97—51no—
335C2×#97—58no—
336C2×#97—51no—
337C2×#97—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×C5C23×C412yes—
346C23×C5C23×C411yescharacteristic
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5#13114yes—
353C22×D5C23×C412yes—
354C22×D5C23×C412yes—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5C23×C412yes—
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—22no—
376C2×Dic5—22no—
377C2×Dic5C23×C412yes—
378C2×Dic5C23×C412yes—
379C2×Dic5C23×C412yes—
380C2×Dic5C23×C412yes—
381C2×Dic5C23×C412yes—
382C2×Dic5C23×C411yescharacteristic
383C2×Dic5C2×#4112yes—
384C2×Dic5C2×#4112yes—
385C2×Dic5C2511yescharacteristic
386D20—28no—
387C4×D5—28no—
388C4×D5—24no—
389C4×D5—24no—
390C4×D5—22no—
391C4×D5—22no—
392C4×D5—22no—
393C4×D5—22no—
394C4×D5—44no—
395Dic10—44no—
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×D4—51no—
408C23×C4—51no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4—51no—
413C2×M16—54no—
414C2×M16—54no—
415C2×M16—104no—
416C2×M16—104no—
417C22×C8—51no—
418C22×C8—51no—
419C22×C8—54no—
420C22×C8—54no—
421C22×C8—54no—
422C22×C8—51no—
423C22×C8—51no—
424C22×C8—51no—
425C22×C8—51no—
426C22×C8—54no—
427C22×C8—51no—
428C22×C8—51no—
429C22×C8—104no—
430C22×C8—104no—
431C22×C8—104no—
432C22×C8—104no—
433#126—58no—
434#126C2×AGL(1,𝔽5)18yes—
435#125—58no—
436#124—58no—
437#123—58no—
438#123—58no—
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⋊C4C2×AGL(1,𝔽5)11yescharacteristic
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—54no—
479C2×C42—54no—
480C2×C42C2×AGL(1,𝔽5)11yescharacteristic
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—
497#97—54no—
498#97—54no—
499C4×C8—54no—
500C4×C8—54no—
501C4×C8—54no—
502C4×C8—54no—
503C22×C5—22no—
504C22×C5—22no—
505C22×C5—22no—
506C22×C5—44no—
507C22×C5C4×#4112yes—
508C22×C5C2×#13112yes—
509C22×C5#56812yes—
510C22×C5C24×C411yescharacteristic
511C2×D5—22no—
512C2×D5—28no—
513C2×D5—22no—
514C2×D5—22no—
515C2×D5—22no—
516C2×D5—22no—
517C2×D5—44no—
518C2×D5C2×#13114yes—
519C4×C5—22no—
520C4×C5—22no—
521C4×C5—22no—
522C4×C5—22no—
523C4×C5—22no—
524C4×C5—22no—
525Dic5—22no—
526Dic5—22no—
527Dic5—22no—
528Dic5—22no—
529Dic5—22no—
530Dic5C4×#4112yes—
531Dic5C22×#4111yescharacteristic
532Dic5C22×#4111yescharacteristic
533C24—51no—
534C24—51no—
535C24C22×AGL(1,𝔽5)11yescharacteristic
536C2×Q8—54no—
537C2×Q8—202no—
538C2×D4—54no—
539C2×D4—54no—
540C2×D4—54no—
541C2×D4—104no—
542C2×D4—104no—
543C2×D4—202no—
544C22×C4—51no—
545C22×C4—52no—
546C22×C4—52no—
547C22×C4—51no—
548C22×C4—51no—
549C22×C4—51no—
550C22×C4—51no—
551C22×C4—51no—
552C22×C4—52no—
553C22×C4—52no—
554C22×C4—52no—
555C22×C4—54no—
556C22×C4—52no—
557C22×C4—54no—
558C22×C4—102no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—104no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—202no—
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)11yescharacteristic
572M16—108no—
573M16—108no—
574C2×C8—52no—
575C2×C8—52no—
576C2×C8—54no—
577C2×C8—54no—
578C2×C8—52no—
579C2×C8—52no—
580C2×C8—52no—
581C2×C8—52no—
582C2×C8—52no—
583C2×C8—52no—
584C2×C8—108no—
585C2×C8—108no—
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⋊C4C22×AGL(1,𝔽5)14yes—
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—52no—
622C42—52no—
623C42C22×AGL(1,𝔽5)14yes—
624C2×C5—42no—
625C2×C5#296814yescomplemented
626C2×C5C2×C4×#4111yescharacteristic
627C2×C5C22×#13111yescharacteristic
628C2×C5C2×#56811yescharacteristic
629D5—24no—
630D5—42no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—54no—
635C23—52no—
636C23—52no—
637C23—102no—
638C23—102no—
639C23—102no—
640C23—102no—
641C23—102no—
642C23C23×AGL(1,𝔽5)12yes—
643C23C23×AGL(1,𝔽5)11yescharacteristic
644Q8—204no—
645D4—108no—
646D4—108no—
647D4—204no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—52no—
655C2×C4—52no—
656C2×C4—51no—
657C2×C4—51no—
658C2×C4—52no—
659C2×C4—52no—
660C2×C4—52no—
661C2×C4—52no—
662C2×C4—52no—
663C2×C4—102no—
664C2×C4—102no—
665C2×C4—102no—
666C2×C4—102no—
667C2×C4—104no—
668C2×C4—104no—
669C2×C4—108no—
670C2×C4—102no—
671C2×C4—102no—
672C2×C4—104no—
673C2×C4—102no—
674C2×C4—102no—
675C2×C4—102no—
676C2×C4—102no—
677C2×C4—102no—
678C2×C4—204no—
679C2×C4C23×AGL(1,𝔽5)12yes—
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×#296811yescharacteristic, complemented, Sylow
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—54no—
699C22—108no—
700C22—102no—
701C22—102no—
702C22—102no—
703C22—102no—
704C22—102no—
705C22—204no—
706C22D5⋊#13112yes—
707C22#6626412yes—
708C22#41×AGL(1,𝔽5)12yes—
709C22C24×AGL(1,𝔽5)11yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—51no—
717C4—51no—
718C4—52no—
719C4—102no—
720C4—102no—
721C4—102no—
722C4—102no—
723C4—102no—
724C2—42no—
725C2—104no—
726C2—202no—
727C2#1061735114yesdirect product factor
728C2C2×D5⋊#13111yescharacteristic
729C2C2×#6626411yescharacteristic
730C2C2×#41×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC23C23×AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC2×C5×#126C4
socleC23×C5C23×C4
prime radicalC2×#4030C4
cosocleC2×Dic5C25
hypercenterC2×#126AGL(1,𝔽5)
hypocenterC5C2×#2968
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
2. #10617351C2direct (N × H)
3. C2×#65707C2semidirect
4. C2×#65709C2semidirect
5. C2×#65704C2semidirect
6. C2×#65702C2semidirect
7. C2×#65706C2semidirect
8. C2×#65701C2semidirect
9. C2×#65694C2semidirect
10. C2×#65694C2semidirect
11. C2×#65693C2semidirect
12. C2×#65692C2semidirect
13. C2×#65697C2semidirect
14. C2×#65691C2semidirect
15. C2×#65680C2semidirect
16. C2×#65676C2semidirect
62. #65709C22semidirect
63. #65707C22semidirect
64. #65706C22semidirect
65. #65704C22semidirect
66. #65702C22semidirect
67. #65701C22semidirect
68. #65697C22semidirect
69. #65694C22semidirect
70. #65694C22semidirect
71. #65693C22semidirect
72. #65692C22semidirect
73. #65691C22semidirect
74. #65680C22semidirect
75. #65676C22semidirect
625. C2×C5#2968semidirect
693. C5C2×#2968semidirect
727. C2#10617351direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660402
#106173512
C2×#657072
C2×#657092
C2×#657042
C2×#657022
C2×#657062
C2×#657012
C2×#656942
C2×#656932
C2×#656922
C2×#656972
C2×#656912
C2×#656802
C2×#656762
C2×#29685