Finite Group Databasebeta

← AGL(1,𝔽5)×#541 #13043938

Subgroups — AGL(1,𝔽5)×#541 #13043938

Order 1280.

2070 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#541C211yesmaximal, characteristic
2#10617386C211yesmaximal, characteristic, complemented
3AGL(1,𝔽5)×C4⋊Q8C211yesmaximal, characteristic, complemented
4#10617358C214yesmaximal
5AGL(1,𝔽5)×#126C214yesmaximal
6#10617345C214yesmaximal, complemented
7#10617344C211yesmaximal, characteristic, complemented
8AGL(1,𝔽5)×#125C214yesmaximal, complemented
9AGL(1,𝔽5)×#125C211yesmaximal, characteristic, complemented
10#10617282C212yesmaximal
11AGL(1,𝔽5)×C22⋊Q8C212yesmaximal
12#10617210C212yesmaximal, complemented
13C4×Q8×AGL(1,𝔽5)C212yesmaximal, complemented
14#10617130C211yesmaximal, characteristic
15AGL(1,𝔽5)×#117C211yesmaximal, characteristic
16C2×Q8×AGL(1,𝔽5)C2212yes—
17C2×Q8×AGL(1,𝔽5)C2212yes—
18C2×#4130C2211yescharacteristic
19C22×C4×AGL(1,𝔽5)C2211yescharacteristic
20C5×#541C411yescharacteristic, complemented
21#66065C411yescharacteristic, complemented
22D5×C4⋊Q8C2211yescharacteristic
23D5×#126C2214yes—
24#66035C414yescomplemented
25#66031C411yescharacteristic, complemented
26#66030C414yescomplemented
27D5×#125C2211yescharacteristic
28D5×#125C2214yes—
29D5×C22⋊Q8C2212yes—
30#65959C412yescomplemented
31#65917C412yescomplemented
32C4×Q8×D5C2212yes—
33D5×#117C2211yescharacteristic
34#65852C411yescharacteristic, complemented
35(C2×AGL(1,𝔽5))⋊Q8C2212yes—
36(C2×AGL(1,𝔽5))⋊Q8C2212yes—
37#65765C2212yes—
38#65712C2214yes—
39#65712C2212yes—
40#65712C2214yes—
41#65712C2214yes—
42#65712C2212yes—
43#65711C2214yes—
44#65711C2214yes—
45#65711C2214yes—
46#65711C2214yes—
47#65711C2214yes—
48#65711C2214yes—
49#65711C2214yes—
50#65711C2214yes—
51#65711C2214yes—
52C4⋊C4×AGL(1,𝔽5)C2212yes—
53C4⋊C4×AGL(1,𝔽5)C2212yes—
54C4⋊C4×AGL(1,𝔽5)C2214yes—
55C4⋊C4×AGL(1,𝔽5)C2214yes—
56C4⋊C4×AGL(1,𝔽5)C2214yes—
57C4⋊C4×AGL(1,𝔽5)C2214yes—
58C4⋊C4×AGL(1,𝔽5)C2212yes—
59C4⋊C4×AGL(1,𝔽5)C2212yes—
60C4⋊C4×AGL(1,𝔽5)C2214yes—
61#65700C2214yes—
62#65700C2214yes—
63#65700C2214yes—
64#65699C2214yes—
65C22⋊C4×AGL(1,𝔽5)C2212yes—
66C22⋊C4×AGL(1,𝔽5)C2214yes—
67C22⋊C4×AGL(1,𝔽5)C2212yes—
68#65690C2214yes—
69#65689C2214yes—
70#65689C2211yescharacteristic
71#65688C2211yescharacteristic
72C4×C4⋊AGL(1,𝔽5)C2214yes—
73C4×C4⋊AGL(1,𝔽5)C2212yes—
74#65686C2211yescharacteristic
75#65686C2211yescharacteristic
76C42×AGL(1,𝔽5)C2214yes—
77C42×AGL(1,𝔽5)C2211yescharacteristic
78C42×AGL(1,𝔽5)C2211yescharacteristic
79C4×#541—51nomaximal, Sylow
80C23×AGL(1,𝔽5)C2311yescharacteristic
81C23×AGL(1,𝔽5)C2311yescharacteristic
82C2×Q8×D5C2312yes—
83C22×C4×D5C2311yescharacteristic
84C2×C22⋊AGL(1,𝔽5)C2312yes—
85C2×C22⋊AGL(1,𝔽5)C2314yes—
86Q8×AGL(1,𝔽5)—28no—
87Q8×AGL(1,𝔽5)—28no—
88#4130—24no—
89C2×C4⋊AGL(1,𝔽5)C2312yes—
90C2×C4⋊AGL(1,𝔽5)C2312yes—
91C2×C4⋊AGL(1,𝔽5)C2314yes—
92C2×C4⋊AGL(1,𝔽5)C2314yes—
93C2×C4⋊AGL(1,𝔽5)C2312yes—
94C2×C4⋊AGL(1,𝔽5)C2314yes—
95C2×C4⋊AGL(1,𝔽5)C2314yes—
96C2×C4⋊AGL(1,𝔽5)C2314yes—
97C2×C4×AGL(1,𝔽5)—24no—
98C2×C4×AGL(1,𝔽5)C2312yes—
99C2×C4×AGL(1,𝔽5)C2311yescharacteristic
100C2×C4×AGL(1,𝔽5)C2314yes—
101C2×C4×AGL(1,𝔽5)C2312yes—
102C2×C4×AGL(1,𝔽5)C2314yes—
103C2×C4×AGL(1,𝔽5)C2314yes—
104C2×C4×AGL(1,𝔽5)C2311yescharacteristic
105C2×C4×AGL(1,𝔽5)C2311yescharacteristic
106C2×C4×AGL(1,𝔽5)C2311yescharacteristic
107C2×C4×AGL(1,𝔽5)C2312yes—
108C2×C4×AGL(1,𝔽5)C2314yes—
109C2×C4×AGL(1,𝔽5)C2312yes—
110C2×C4×AGL(1,𝔽5)C2314yes—
111C2×C4×AGL(1,𝔽5)C2311yescharacteristic
112C2×C4×AGL(1,𝔽5)C2311yescharacteristic
113C5×C4⋊Q8C2×C411yescharacteristic, complemented
114C5×#126C2×C414yes—
115C5×#125C2×C414yescomplemented
116C5×#125C2×C411yescharacteristic, complemented
117C5×C22⋊Q8C2×C412yes—
118C4×C5×Q8C2×C412yescomplemented
119C5×#117C2×C411yescharacteristic
120#4092C2×C412yes—
121Q8×Dic5C2×C412yescomplemented
122#4090C2×C412yescomplemented
123#4072C2×C411yescharacteristic
124#4070C2×C412yes—
125#4044C2×C414yes—
126#4044C2×C414yes—
127#4044C2×C414yes—
128#4043C2×C412yes—
129#4042C2×C414yes—
130#4038C2×C412yes—
131D5×C4⋊C4C2314yes—
132D5×C4⋊C4C2312yes—
133D5×C4⋊C4C2312yes—
134D5×C4⋊C4C2314yes—
135D5×C4⋊C4C2314yes—
136D5×C4⋊C4C2314yes—
137#4036C2×C412yescomplemented
138#4036C2×C414yescomplemented
139#4036C2×C414yescomplemented
140#4035C2×C414yescomplemented
141#4035C2×C414yescomplemented
142#4035C2×C414yescomplemented
143#4035C2×C414yescomplemented
144#4035C2×C414yescomplemented
145#4034C2×C414yescomplemented
146#4033C2×C412yescomplemented
147#4033C2×C414yescomplemented
148D5×C22⋊C4C2312yes—
149D5×C22⋊C4C2314yes—
150#4025C2×C414yes—
151#4025C2×C414yes—
152#4025C2×C414yes—
153#4024C2×C414yes—
154#4023C2×C412yes—
155#4022C2×C414yes—
156#4018C2×C411yescharacteristic
157#4018C2×C411yescharacteristic
158C42×D5C2311yescharacteristic
159C42×D5C2311yescharacteristic
160C42×D5C2314yes—
161#4016C2×C411yescharacteristic, complemented
162#4016C2×C414yescomplemented
163#4015C2×C411yescharacteristic, complemented
164C4×Dic10C2×C412yescomplemented
165C4×Dic10C2×C414yescomplemented
166(C2×AGL(1,𝔽5))⋊C4C2312yes—
167(C2×AGL(1,𝔽5))⋊C4C2312yes—
168(C2×AGL(1,𝔽5))⋊C4C2312yes—
169(C2×AGL(1,𝔽5))⋊C4C2312yes—
170(C2×AGL(1,𝔽5))⋊C4C2314yes—
171(C2×AGL(1,𝔽5))⋊C4C2314yes—
172(C2×AGL(1,𝔽5))⋊C4C2314yes—
173(C2×AGL(1,𝔽5))⋊C4C2314yes—
174(C2×AGL(1,𝔽5))⋊C4C2314yes—
175(C2×AGL(1,𝔽5))⋊C4C2314yes—
176(C2×AGL(1,𝔽5))⋊C4C2314yes—
177(C2×AGL(1,𝔽5))⋊C4C2314yes—
178(C2×AGL(1,𝔽5))⋊C4C2314yes—
179(C2×AGL(1,𝔽5))⋊C4C2314yes—
180(C2×AGL(1,𝔽5))⋊C4C2314yes—
181C2×#541—51no—
182#2336—54no—
183#2334—54no—
184#2330—51no—
185#2327—51no—
186#2323—52no—
187#2320—52no—
188#2314—51no—
189C4×C4⋊Q8—51no—
190C4×#125—51no—
191C4×#125—54no—
192C4×#126—54no—
193C4×C22⋊Q8—52no—
194C42×Q8—52no—
195C4×#117—51no—
196C23×D5C2411yescharacteristic
197C22×AGL(1,𝔽5)—22no—
198C22×AGL(1,𝔽5)—22no—
199C22×AGL(1,𝔽5)—24no—
200C22×AGL(1,𝔽5)—42no—
201C22×AGL(1,𝔽5)C2414yes—
202C22×AGL(1,𝔽5)C2414yes—
203C22×AGL(1,𝔽5)C2412yes—
204C22×AGL(1,𝔽5)C2411yescharacteristic
205C22×AGL(1,𝔽5)C2411yescharacteristic
206C22×AGL(1,𝔽5)C2412yes—
207C22×AGL(1,𝔽5)C2411yescharacteristic
208C22×AGL(1,𝔽5)C2411yescharacteristic
209C2×C5×Q8C22×C412yes—
210C22×C4×C5C22×C411yescharacteristic
211C22×Dic5C22×C411yescharacteristic
212Q8×D5—24no—
213Q8×D5—24no—
214C2×C4×D5—22no—
215C2×C4×D5—22no—
216C2×C4×D5C22×C411yescharacteristic
217C2×C4×D5C22×C411yescharacteristic
218C2×C4×D5C2412yes—
219C2×C4×D5C2411yescharacteristic
220C2×C4×D5C2414yes—
221C2×C4×D5C2412yes—
222C2×C4×D5C2414yes—
223C2×C4×D5C2411yescharacteristic
224C2×Dic10C22×C412yes—
225C2×Dic10C22×C414yes—
226C22⋊AGL(1,𝔽5)—24no—
227C22⋊AGL(1,𝔽5)—44no—
228C4⋊AGL(1,𝔽5)—24no—
229C4⋊AGL(1,𝔽5)—28no—
230C4⋊AGL(1,𝔽5)—28no—
231C4⋊AGL(1,𝔽5)—24no—
232C4⋊AGL(1,𝔽5)—24no—
233C4⋊AGL(1,𝔽5)—44no—
234C4⋊AGL(1,𝔽5)—44no—
235C4⋊AGL(1,𝔽5)—44no—
236C4×AGL(1,𝔽5)—22no—
237C4×AGL(1,𝔽5)—22no—
238C4×AGL(1,𝔽5)—28no—
239C4×AGL(1,𝔽5)—28no—
240C4×AGL(1,𝔽5)—24no—
241C4×AGL(1,𝔽5)—28no—
242C4×AGL(1,𝔽5)—24no—
243C4×AGL(1,𝔽5)—22no—
244C4×AGL(1,𝔽5)—22no—
245C4×AGL(1,𝔽5)—42no—
246C4×AGL(1,𝔽5)—44no—
247C4×AGL(1,𝔽5)—44no—
248C4×AGL(1,𝔽5)—42no—
249C4×AGL(1,𝔽5)#4114yes—
250C4×AGL(1,𝔽5)#4114yes—
251C5×C4⋊C4C22×C412yes—
252C5×C4⋊C4C22×C412yes—
253C5×C4⋊C4C22×C414yes—
254C5×C4⋊C4C22×C414yes—
255C5×C4⋊C4C22×C414yes—
256C5×C4⋊C4C22×C414yes—
257C5×C22⋊C4C22×C412yes—
258C5×C22⋊C4C22×C414yes—
259C42×C5C22×C411yescharacteristic
260C42×C5C22×C411yescharacteristic
261C42×C5C22×C414yes—
262C22⋊Dic5C22×C412yes—
263C22⋊Dic5C22×C414yes—
264#685C22×C412yes—
265#685C22×C412yes—
266#685C22×C414yes—
267#685C22×C414yes—
268C4⋊Dic5C22×C412yes—
269C4⋊Dic5C22×C414yes—
270C4⋊Dic5C22×C414yes—
271C4⋊Dic5C22×C414yes—
272C4⋊Dic5C22×C414yes—
273C4⋊Dic5C22×C412yes—
274#683C22×C414yes—
275#683C22×C414yes—
276#683C22×C414yes—
277#683C22×C412yes—
278#683C22×C414yes—
279#683C22×C414yes—
280#683C22×C414yes—
281#683C22×C412yes—
282#683C22×C414yes—
283#683C22×C414yes—
284#683C22×C414yes—
285C4×Dic5C22×C412yes—
286C4×Dic5C22×C414yes—
287C4×Dic5C22×C411yescharacteristic
288C4×Dic5C22×C411yescharacteristic
289C4×Dic5C22×C412yes—
290C4×Dic5C22×C414yes—
291C4×Dic5C22×C414yes—
292#541—51no—
293#541—54no—
294#541—54no—
295#541—51no—
296#541—52no—
297#541—52no—
298#541—51no—
299#541AGL(1,𝔽5)11yescharacteristic, direct product factor
300C2×C4⋊Q8—51no—
301C2×#126—54no—
302C2×#125—51no—
303C2×#125—54no—
304C2×C22⋊Q8—52no—
305C2×C4×Q8—52no—
306C2×C4×Q8—52no—
307C2×C4×Q8—52no—
308C2×#117—51no—
309C2×#117—51no—
310C22×C42—51no—
311#391—52no—
312#391—52no—
313#389—52no—
314#389—54no—
315#389—54no—
316#389—54no—
317#389—52no—
318#388—54no—
319#388—54no—
320#388—54no—
321#387—54no—
322#387—54no—
323#387—54no—
324#387—54no—
325#387—54no—
326#387—54no—
327#387—54no—
328#387—54no—
329#387—54no—
330#385—54no—
331#384—51no—
332#383—54no—
333#382—51no—
334#382—54no—
335#380—52no—
336C4×C4⋊C4—54no—
337C4×C4⋊C4—54no—
338C4×C4⋊C4—54no—
339C4×C4⋊C4—52no—
340C4×C4⋊C4—54no—
341C4×C4⋊C4—52no—
342C4×C4⋊C4—52no—
343C4×C4⋊C4—52no—
344C4×C4⋊C4—54no—
345C4×C4⋊C4—54no—
346C4×C4⋊C4—52no—
347C4×C22⋊C4—52no—
348C4×C22⋊C4—54no—
349C4×C22⋊C4—52no—
350#376—51no—
351#376—51no—
352C43—54no—
353C43—51no—
354C43—51no—
355C23×C5C23×C411yescharacteristic
356C22×D5—21no—
357C22×D5—21no—
358C22×D5—22no—
359C22×D5—22no—
360C22×D5C23×C411yescharacteristic
361C22×D5C2511yescharacteristic
362C2×AGL(1,𝔽5)—22no—
363C2×AGL(1,𝔽5)—22no—
364C2×AGL(1,𝔽5)—22no—
365C2×AGL(1,𝔽5)—21no—
366C2×AGL(1,𝔽5)—21no—
367C2×AGL(1,𝔽5)—24no—
368C2×AGL(1,𝔽5)—24no—
369C2×AGL(1,𝔽5)—22no—
370C2×AGL(1,𝔽5)—24no—
371C2×AGL(1,𝔽5)—22no—
372C2×AGL(1,𝔽5)—22no—
373C2×AGL(1,𝔽5)—24no—
374C2×AGL(1,𝔽5)—22no—
375C2×AGL(1,𝔽5)—24no—
376C2×AGL(1,𝔽5)—24no—
377C2×AGL(1,𝔽5)—22no—
378C2×AGL(1,𝔽5)—44no—
379C2×AGL(1,𝔽5)—44no—
380C2×AGL(1,𝔽5)C2×#4114yes—
381C2×AGL(1,𝔽5)C2×#4112yes—
382C2×AGL(1,𝔽5)C2×#4112yes—
383C2×AGL(1,𝔽5)2−1+414yes—
384C5×Q8—24no—
385C2×C4×C5—22no—
386C2×C4×C5C23×C412yes—
387C2×C4×C5C23×C412yes—
388C2×C4×C5C23×C414yes—
389C2×C4×C5C23×C414yes—
390C2×C4×C5C23×C411yescharacteristic
391C2×C4×C5C23×C411yescharacteristic
392C2×Dic5—22no—
393C2×Dic5C23×C412yes—
394C2×Dic5C23×C414yes—
395C2×Dic5C23×C412yes—
396C2×Dic5C23×C414yes—
397C2×Dic5C23×C411yescharacteristic
398C2×Dic5C23×C411yescharacteristic
399C4×D5—21no—
400C4×D5—24no—
401C4×D5—24no—
402C4×D5—21no—
403C4×D5—22no—
404C4×D5—22no—
405C4×D5—24no—
406C4×D5—22no—
407C4×D5—24no—
408C4×D5—22no—
409C4×D5—22no—
410C4×D5—22no—
411C4×D5C2×#4112yes—
412C4×D5C2×#4112yes—
413Dic10—24no—
414Dic10—28no—
415C22×Q8—52no—
416C23×C4—51no—
417C23×C4—51no—
418C23×C4—51no—
419C4⋊Q8—52no—
420C4⋊Q8—54no—
421C4⋊Q8—51no—
422C4⋊Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
423#126—54no—
424#126—54no—
425#126—54no—
426#126—54no—
427#126—54no—
428#126—54no—
429#126—54no—
430#126C2×AGL(1,𝔽5)14yes—
431#125—54no—
432#125—54no—
433#125—54no—
434#125—54no—
435#125—54no—
436#125—52no—
437#125—54no—
438#125—54no—
439#125—51no—
440#125—54no—
441#125C2×AGL(1,𝔽5)11yescharacteristic, complemented
442#125C2×AGL(1,𝔽5)14yescomplemented
443C22⋊Q8—52no—
444C22⋊Q8—52no—
445C22⋊Q8—54no—
446C22⋊Q8—52no—
447C22⋊Q8—54no—
448C22⋊Q8C2×AGL(1,𝔽5)12yes—
449C4×Q8—52no—
450C4×Q8—54no—
451C4×Q8—52no—
452C4×Q8—54no—
453C4×Q8—52no—
454C4×Q8—108no—
455C4×Q8—108no—
456C4×Q8C2×AGL(1,𝔽5)12yescomplemented
457#117—51no—
458#117—52no—
459#117—52no—
460#117—51no—
461#117—51no—
462#117—104no—
463#117C2×AGL(1,𝔽5)11yescharacteristic
464C2×C4⋊C4—52no—
465C2×C4⋊C4—52no—
466C2×C4⋊C4—54no—
467C2×C4⋊C4—54no—
468C2×C4⋊C4—54no—
469C2×C4⋊C4—54no—
470C2×C4⋊C4—52no—
471C2×C4⋊C4—52no—
472C2×C4⋊C4—52no—
473C2×C4⋊C4—54no—
474C2×C4⋊C4—54no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—54no—
477C2×C4⋊C4—54no—
478C2×C22⋊C4—52no—
479C2×C22⋊C4—54no—
480C2×C22⋊C4—52no—
481C2×C22⋊C4—54no—
482C2×C42—51no—
483C2×C42—51no—
484C2×C42—51no—
485C2×C42—51no—
486C2×C42—54no—
487C2×C42—51no—
488C2×C42—54no—
489C2×C42—54no—
490C2×C42—52no—
491C2×C42—54no—
492C2×C42—52no—
493C2×C42—51no—
494C2×C42—51no—
495C2×C42—51no—
496C2×C42—52no—
497C2×C42—52no—
498C2×C42—54no—
499C2×C42—54no—
500C2×C42—104no—
501#95—52no—
502#95—52no—
503#95—52no—
504#95—52no—
505#95—54no—
506#95—54no—
507#95—54no—
508#95—54no—
509#95—54no—
510#95—54no—
511#95—54no—
512#95—54no—
513#95—54no—
514#95—54no—
515#95—54no—
516C22×C5—21no—
517C22×C5—22no—
518C22×C5C24×C411yescharacteristic
519C2×D5—21no—
520C2×D5—22no—
521C2×D5—41no—
522C2×D5—41no—
523C2×D5—42no—
524C2×D5C22×#4111yescharacteristic
525C2×D5C22×#4111yescharacteristic
526C2×D5C2×2−1+412yes—
527C2×D5#58512yes—
528AGL(1,𝔽5)—22no—
529AGL(1,𝔽5)—24no—
530AGL(1,𝔽5)—41no—
531AGL(1,𝔽5)—44no—
532AGL(1,𝔽5)—41no—
533AGL(1,𝔽5)—44no—
534AGL(1,𝔽5)—42no—
535AGL(1,𝔽5)#54114yesdirect product factor
536C4×C5—24no—
537C4×C5—21no—
538C4×C5—22no—
539C4×C5—22no—
540C4×C5—24no—
541C4×C5C4×#4112yes—
542Dic5—24no—
543Dic5—21no—
544Dic5—22no—
545Dic5—24no—
546Dic5—22no—
547Dic5C4×#4112yes—
548C24—51no—
549C2×Q8—54no—
550C2×Q8—52no—
551C2×Q8—104no—
552C2×Q8—104no—
553C2×Q8C22×AGL(1,𝔽5)12yes—
554C22×C4—51no—
555C22×C4—51no—
556C22×C4—52no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—52no—
560C22×C4—52no—
561C22×C4—54no—
562C22×C4—54no—
563C22×C4—51no—
564C22×C4—51no—
565C22×C4—51no—
566C22×C4—51no—
567C22×C4—52no—
568C22×C4—54no—
569C22×C4—51no—
570C22×C4—54no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—104no—
576C22×C4—202no—
577C22×C4C22×AGL(1,𝔽5)11yescharacteristic
578C4⋊C4—52no—
579C4⋊C4—52no—
580C4⋊C4—52no—
581C4⋊C4—54no—
582C4⋊C4—52no—
583C4⋊C4—54no—
584C4⋊C4—54no—
585C4⋊C4—54no—
586C4⋊C4—54no—
587C4⋊C4—54no—
588C4⋊C4—54no—
589C4⋊C4—54no—
590C4⋊C4—54no—
591C4⋊C4—54no—
592C4⋊C4—54no—
593C4⋊C4—54no—
594C4⋊C4—54no—
595C4⋊C4—104no—
596C4⋊C4—104no—
597C4⋊C4—104no—
598C4⋊C4—108no—
599C4⋊C4—108no—
600C4⋊C4—204no—
601C4⋊C4—204no—
602C4⋊C4—204no—
603C4⋊C4C22×AGL(1,𝔽5)12yes—
604C4⋊C4C22×AGL(1,𝔽5)12yes—
605C4⋊C4C22×AGL(1,𝔽5)14yes—
606C4⋊C4C22×AGL(1,𝔽5)14yes—
607C4⋊C4C22×AGL(1,𝔽5)14yes—
608C4⋊C4C22×AGL(1,𝔽5)14yes—
609C22⋊C4—52no—
610C22⋊C4—54no—
611C22⋊C4—52no—
612C22⋊C4—52no—
613C22⋊C4—54no—
614C22⋊C4—54no—
615C22⋊C4—104no—
616C22⋊C4—204no—
617C22⋊C4C22×AGL(1,𝔽5)12yes—
618C22⋊C4C22×AGL(1,𝔽5)14yes—
619C42—54no—
620C42—54no—
621C42—52no—
622C42—51no—
623C42—52no—
624C42—51no—
625C42—54no—
626C42—54no—
627C42—54no—
628C42—102no—
629C42—102no—
630C42—102no—
631C42—102no—
632C42—108no—
633C42—108no—
634C42—104no—
635C42—108no—
636C42—104no—
637C42—202no—
638C42—204no—
639C42—204no—
640C42—202no—
641C42C22×AGL(1,𝔽5)11yescharacteristic
642C42C22×AGL(1,𝔽5)11yescharacteristic
643C42C22×AGL(1,𝔽5)14yes—
644C2×C5—41no—
645C2×C5C2×C4×#4111yescharacteristic
646C2×C5C4×2−1+412yes—
647D5—41no—
648D5C2×#54111yescharacteristic
649D5#345511yescharacteristic
650D5#346112yes—
651C23—51no—
652C23—51no—
653C23—101no—
654C23—102no—
655C23—101no—
656C23—102no—
657C23C23×AGL(1,𝔽5)11yescharacteristic
658Q8—24no—
659Q8—108no—
660Q8—104no—
661C2×C4—22no—
662C2×C4—52no—
663C2×C4—54no—
664C2×C4—51no—
665C2×C4—52no—
666C2×C4—52no—
667C2×C4—54no—
668C2×C4—52no—
669C2×C4—52no—
670C2×C4—52no—
671C2×C4—54no—
672C2×C4—54no—
673C2×C4—51no—
674C2×C4—102no—
675C2×C4—101no—
676C2×C4—104no—
677C2×C4—104no—
678C2×C4—102no—
679C2×C4—102no—
680C2×C4—104no—
681C2×C4—102no—
682C2×C4—104no—
683C2×C4—102no—
684C2×C4—101no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—101no—
691C2×C4—101no—
692C2×C4—102no—
693C2×C4—104no—
694C2×C4—104no—
695C2×C4—102no—
696C2×C4—104no—
697C2×C4—104no—
698C2×C4—104no—
699C2×C4—102no—
700C2×C4—104no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—204no—
704C2×C4—204no—
705C2×C4C23×AGL(1,𝔽5)12yes—
706C2×C4C23×AGL(1,𝔽5)12yes—
707C2×C4C23×AGL(1,𝔽5)14yes—
708C2×C4C23×AGL(1,𝔽5)14yes—
709C2×C4C23×AGL(1,𝔽5)11yescharacteristic
710C2×C4C23×AGL(1,𝔽5)11yescharacteristic
711C5C4×#54111yescharacteristic, complemented, Sylow
712C22—21no—
713C22—22no—
714C22—51no—
715C22—51no—
716C22—52no—
717C22—52no—
718C22—101no—
719C22—102no—
720C22—201no—
721C22—201no—
722C22—202no—
723C22C24×AGL(1,𝔽5)11yescharacteristic
724C4—21no—
725C4—24no—
726C4—22no—
727C4—22no—
728C4—24no—
729C4—54no—
730C4—52no—
731C4—102no—
732C4—104no—
733C4—101no—
734C4—104no—
735C4—102no—
736C4—102no—
737C4—104no—
738C4—201no—
739C4—201no—
740C4—204no—
741C4—202no—
742C4—204no—
743C4#41×AGL(1,𝔽5)12yes—
744C2—41no—
745C2—51no—
746C2—51no—
747C2—52no—
748C2—201no—
749C2C2×#41×AGL(1,𝔽5)11yescharacteristic
750C2AGL(1,𝔽5)×2−1+412yes—
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#541C4
prime radicalC23×D5C24
cosocleC22×D5C25
hypercenter#541AGL(1,𝔽5)
hypocenterC5C4×#541
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #10617386C2semidirect
3. AGL(1,𝔽5)×C4⋊Q8C2semidirect
6. #10617345C2semidirect
7. #10617344C2semidirect
8. AGL(1,𝔽5)×#125C2semidirect
9. AGL(1,𝔽5)×#125C2semidirect
12. #10617210C2semidirect
13. C4×Q8×AGL(1,𝔽5)C2semidirect
20. C5×#541C4semidirect
21. #66065C4semidirect
24. #66035C4semidirect
25. #66031C4semidirect
26. #66030C4semidirect
30. #65959C4semidirect
31. #65917C4semidirect
34. #65852C4semidirect
113. C5×C4⋊Q8C2×C4semidirect
115. C5×#125C2×C4semidirect
116. C5×#125C2×C4semidirect
118. C4×C5×Q8C2×C4semidirect
121. Q8×Dic5C2×C4semidirect
122. #4090C2×C4semidirect
137. #4036C2×C4semidirect
138. #4036C2×C4semidirect
139. #4036C2×C4semidirect
140. #4035C2×C4semidirect
141. #4035C2×C4semidirect
142. #4035C2×C4semidirect
143. #4035C2×C4semidirect
144. #4035C2×C4semidirect
145. #4034C2×C4semidirect
146. #4033C2×C4semidirect
147. #4033C2×C4semidirect
161. #4016C2×C4semidirect
162. #4016C2×C4semidirect
163. #4015C2×C4semidirect
164. C4×Dic10C2×C4semidirect
165. C4×Dic10C2×C4semidirect
299. #541AGL(1,𝔽5)direct (N × H)
422. C4⋊Q8C2×AGL(1,𝔽5)semidirect
441. #125C2×AGL(1,𝔽5)semidirect
442. #125C2×AGL(1,𝔽5)semidirect
456. C4×Q8C2×AGL(1,𝔽5)semidirect
535. AGL(1,𝔽5)#541direct (N × H)
711. C5C4×#541semidirect

Maximal subgroups

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

subgroupindex
D5×#5412
#106173862
AGL(1,𝔽5)×C4⋊Q82
#106173582
AGL(1,𝔽5)×#1262
#106173452
#106173442
AGL(1,𝔽5)×#1252
#106172822
AGL(1,𝔽5)×C22⋊Q82
#106172102
C4×Q8×AGL(1,𝔽5)2
#106171302
AGL(1,𝔽5)×#1172
C4×#5415