Finite Group Databasebeta

← #13044365

Subgroups — #13044365

Order 1280.

2216 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#562C211yesmaximal, characteristic
2#10617348C211yesmaximal, characteristic, complemented
3AGL(1,𝔽5)×#125C211yesmaximal, characteristic, complemented
4#10617328C212yesmaximal, complemented
5AGL(1,𝔽5)×#124C212yesmaximal, complemented
6#10617306C214yesmaximal, complemented
7#10617305C214yesmaximal, complemented
8#10617287C214yesmaximal, complemented
9#10617282C214yesmaximal, complemented
10#10617254C214yesmaximal, complemented
11#10617251C214yesmaximal, complemented
12C2×Q8×AGL(1,𝔽5)C2212yes—
13C2×D4×AGL(1,𝔽5)C2212yes—
14C2×D4×AGL(1,𝔽5)C2214yes—
15C2×#4130C2214yes—
16C5×#562C411yescharacteristic, complemented
17#66034C411yescharacteristic, complemented
18D5×#125C2211yescharacteristic
19#66018C412yescomplemented
20D5×#124C2212yes—
21#66001C414yescomplemented
22D5×#123C2214yes—
23#65981C414yescomplemented
24D5×C22⋊Q8C2214yes—
25#65955C414yescomplemented
26D5×#121C2214yes—
27(C2×AGL(1,𝔽5))⋊Q8C2214yes—
28(C2×AGL(1,𝔽5))⋊Q8C2212yes—
29#65780C2214yes—
30#65780C2212yes—
31#65779C2214yes—
32#65779C2214yes—
33#65779C2214yes—
34#65765C2214yes—
35C4×C22⋊AGL(1,𝔽5)C2214yes—
36C2×(C2×AGL(1,𝔽5))⋊C4C2214yes—
37#65712C2214yes—
38#65712C2214yes—
39#65712C2212yes—
40#65711C2214yes—
41#65711C2214yes—
42#65711C2214yes—
43#65711C2214yes—
44#65711C2214yes—
45C4⋊C4×AGL(1,𝔽5)C2214yes—
46C4⋊C4×AGL(1,𝔽5)C2214yes—
47C4⋊C4×AGL(1,𝔽5)C2212yes—
48#65700C2214yes—
49#65700C2214yes—
50#65700C2214yes—
51#65700C2214yes—
52#65700C2214yes—
53#65700C2214yes—
54#65699C2214yes—
55#65699C2214yes—
56#65699C2214yes—
57C22⋊C4×AGL(1,𝔽5)C2214yes—
58C22⋊C4×AGL(1,𝔽5)C2214yes—
59C22⋊C4×AGL(1,𝔽5)C2214yes—
60#65689C2212yes—
61#65689C2211yescharacteristic
62C42×AGL(1,𝔽5)C2211yescharacteristic
63#34522—51nomaximal, Sylow
64C23×AGL(1,𝔽5)C2314yes—
65C23×AGL(1,𝔽5)C2314yes—
66C2×Q8×D5C2312yes—
67C2×D4×D5C2314yes—
68C2×D4×D5C2312yes—
69C22×C4×D5C2314yes—
70C2×C22⋊AGL(1,𝔽5)C2314yes—
71C2×C22⋊AGL(1,𝔽5)C2314yes—
72C2×C22⋊AGL(1,𝔽5)C2314yes—
73C2×C22⋊AGL(1,𝔽5)C2314yes—
74C2×C22⋊AGL(1,𝔽5)C2314yes—
75C2×C22⋊AGL(1,𝔽5)C2314yes—
76Q8×AGL(1,𝔽5)—44no—
77D4×AGL(1,𝔽5)—44no—
78D4×AGL(1,𝔽5)—48no—
79#4130—48no—
80C2×C4⋊AGL(1,𝔽5)C2314yes—
81C2×C4⋊AGL(1,𝔽5)C2312yes—
82C2×C4⋊AGL(1,𝔽5)C2312yes—
83C2×C4⋊AGL(1,𝔽5)C2312yes—
84C2×C4⋊AGL(1,𝔽5)C2314yes—
85C2×C4⋊AGL(1,𝔽5)C2314yes—
86C2×C4⋊AGL(1,𝔽5)C2314yes—
87C2×C4×AGL(1,𝔽5)C2311yescharacteristic
88C2×C4×AGL(1,𝔽5)C2312yes—
89C2×C4×AGL(1,𝔽5)C2314yes—
90C2×C4×AGL(1,𝔽5)C2311yescharacteristic
91C2×C4×AGL(1,𝔽5)C2312yes—
92C2×C4×AGL(1,𝔽5)C2314yes—
93C2×C4×AGL(1,𝔽5)C2314yes—
94C2×C4×AGL(1,𝔽5)C2314yes—
95C5×#125C2×C411yescharacteristic, complemented
96C5×#124C2×C412yescomplemented
97C5×#123C2×C414yescomplemented
98C5×C22⋊Q8C2×C414yescomplemented
99C5×#121C2×C414yescomplemented
100#4093C2×C412yescomplemented
101#4092C2×C414yescomplemented
102#4085C2×C414yescomplemented
103#4085C2×C414yescomplemented
104#4084C2×C414yescomplemented
105#4082C2×C412yescomplemented
106#4081C2×C414yescomplemented
107#4076C2×C414yescomplemented
108#4075C2×C414yescomplemented
109#4070C2×C414yescomplemented
110#4043C2×C414yescomplemented
111#4042C2×C414yescomplemented
112#4042C2×C414yescomplemented
113#4041C2×C414yescomplemented
114#4040C2×C414yescomplemented
115#4040C2×C414yescomplemented
116D5×C4⋊C4C2314yes—
117D5×C4⋊C4C2314yes—
118D5×C4⋊C4C2312yes—
119#4036C2×C412yescomplemented
120#4035C2×C414yescomplemented
121#4032C2×C414yescomplemented
122#4031C2×C414yescomplemented
123#4031C2×C414yescomplemented
124#4030C2×C414yescomplemented
125#4030C2×C414yescomplemented
126#4029C2×C414yescomplemented
127#4029C2×C414yescomplemented
128D5×C22⋊C4C2314yes—
129D5×C22⋊C4C2314yes—
130D5×C22⋊C4C2314yes—
131#4024C2×C414yescomplemented
132#4024C2×C414yescomplemented
133#4021C2×C412yescomplemented
134C42×D5C2311yescharacteristic
135#4016C2×C411yescharacteristic, complemented
136(C2×AGL(1,𝔽5))⋊C4C2314yes—
137(C2×AGL(1,𝔽5))⋊C4C2314yes—
138(C2×AGL(1,𝔽5))⋊C4C2314yes—
139(C2×AGL(1,𝔽5))⋊C4C2314yes—
140(C2×AGL(1,𝔽5))⋊C4C2314yes—
141(C2×AGL(1,𝔽5))⋊C4C2314yes—
142(C2×AGL(1,𝔽5))⋊C4C2314yes—
143(C2×AGL(1,𝔽5))⋊C4C2314yes—
144(C2×AGL(1,𝔽5))⋊C4C2314yes—
145(C2×AGL(1,𝔽5))⋊C4C2314yes—
146(C2×AGL(1,𝔽5))⋊C4C2314yes—
147C2×#562—51no—
148#2382—51no—
149#2379—52no—
150#2368—54no—
151#2363—54no—
152#2359—54no—
153#2335—54no—
154#2325—54no—
155#2323—54no—
156C4×#125—51no—
157C4×#124—52no—
158C23×D5C2414yes—
159C22×AGL(1,𝔽5)—28no—
160C22×AGL(1,𝔽5)—44no—
161C22×AGL(1,𝔽5)—44no—
162C22×AGL(1,𝔽5)—44no—
163C22×AGL(1,𝔽5)—44no—
164C22×AGL(1,𝔽5)—44no—
165C22×AGL(1,𝔽5)C2414yes—
166C22×AGL(1,𝔽5)C2411yescharacteristic
167C22×AGL(1,𝔽5)C2414yes—
168C22×AGL(1,𝔽5)C2414yes—
169C22×AGL(1,𝔽5)C2412yes—
170C22×AGL(1,𝔽5)C2411yescharacteristic
171C2×C5×Q8C22×C412yes—
172C2×C5×D4C22×C414yes—
173C2×C5×D4C22×C412yes—
174C22×C4×C5C22×C414yes—
175C2×C22⋊D5C22×C414yes—
176C2×C22⋊D5C22×C414yes—
177C2×C22⋊D5C22×C414yes—
178C22×Dic5C22×C414yes—
179Q8×D5—42no—
180Q8×D5—42no—
181D4×D5—42no—
182D4×D5—44no—
183D4×D5—44no—
184D4×D5—42no—
185C2×D20C22×C412yes—
186C2×D20C22×C414yes—
187C2×C4×D5—44no—
188C2×C4×D5—44no—
189C2×C4×D5C22×C414yes—
190C2×C4×D5C22×C414yes—
191C2×C4×D5C2414yes—
192C2×C4×D5C2414yes—
193C2×C4×D5C2412yes—
194C2×C4×D5C2411yescharacteristic
195C2×Dic10C22×C412yes—
196C2×Dic10C22×C414yes—
197C22⋊AGL(1,𝔽5)—28no—
198C22⋊AGL(1,𝔽5)—28no—
199C22⋊AGL(1,𝔽5)—44no—
200C22⋊AGL(1,𝔽5)—44no—
201C22⋊AGL(1,𝔽5)—44no—
202C22⋊AGL(1,𝔽5)—44no—
203C4⋊AGL(1,𝔽5)—28no—
204C4⋊AGL(1,𝔽5)—42no—
205C4⋊AGL(1,𝔽5)—44no—
206C4⋊AGL(1,𝔽5)—44no—
207C4⋊AGL(1,𝔽5)—42no—
208C4⋊AGL(1,𝔽5)—44no—
209C4⋊AGL(1,𝔽5)—42no—
210C4×AGL(1,𝔽5)—28no—
211C4×AGL(1,𝔽5)—24no—
212C4×AGL(1,𝔽5)—22no—
213C4×AGL(1,𝔽5)—41no—
214C4×AGL(1,𝔽5)—44no—
215C4×AGL(1,𝔽5)—42no—
216C4×AGL(1,𝔽5)—44no—
217C4×AGL(1,𝔽5)—44no—
218C5×C4⋊C4C22×C414yes—
219C5×C4⋊C4C22×C414yes—
220C5×C4⋊C4C22×C412yes—
221C5×C22⋊C4C22×C414yes—
222C5×C22⋊C4C22×C414yes—
223C5×C22⋊C4C22×C414yes—
224C42×C5C22×C411yescharacteristic
225C22⋊Dic5C22×C414yes—
226C22⋊Dic5C22×C414yes—
227C22⋊Dic5C22×C414yes—
228#685C22×C414yes—
229#685C22×C414yes—
230#685C22×C414yes—
231#685C22×C414yes—
232#685C22×C414yes—
233#685C22×C414yes—
234C4⋊Dic5C22×C412yes—
235C4⋊Dic5C22×C414yes—
236C4⋊Dic5C22×C414yes—
237#683C22×C414yes—
238#683C22×C414yes—
239#683C22×C414yes—
240#683C22×C414yes—
241#683C22×C414yes—
242C4×Dic5C22×C411yescharacteristic
243C4×Dic5C22×C412yes—
244#562—51no—
245#562—52no—
246#562—54no—
247#562—54no—
248#562—54no—
249#562AGL(1,𝔽5)11yescharacteristic, complemented
250C2×#125—51no—
251C2×#124—52no—
252C2×#123—54no—
253C2×C22⋊Q8—54no—
254C2×#121—54no—
255C2×C4×Q8—52no—
256C2×C4×D4—52no—
257C2×C4×D4—54no—
258C2×#117—54no—
259#391—54no—
260#391—52no—
261#390—54no—
262#390—52no—
263#389—52no—
264#389—54no—
265#389—54no—
266#388—54no—
267#388—54no—
268#388—54no—
269#388—54no—
270#388—54no—
271#388—54no—
272#387—54no—
273#387—54no—
274#387—54no—
275#387—54no—
276#387—54no—
277#386—54no—
278#386—54no—
279#386—54no—
280#385—54no—
281#385—54no—
282#385—54no—
283#382—51no—
284#382—52no—
285#380—54no—
286C4×C4⋊C4—52no—
287C4×C4⋊C4—54no—
288C4×C4⋊C4—54no—
289C4×C22⋊C4—54no—
290C4×C22⋊C4—54no—
291C4×C22⋊C4—54no—
292C4×C22⋊C4—54no—
293C2×#95—54no—
294C43—51no—
295C23×C5C23×C414yes—
296C22×D5—24no—
297C22×D5—24no—
298C22×D5—24no—
299C22×D5—24no—
300C22×D5—24no—
301C22×D5—24no—
302C22×D5C23×C414yes—
303C22×D5C2511yescharacteristic
304C2×AGL(1,𝔽5)—22no—
305C2×AGL(1,𝔽5)—22no—
306C2×AGL(1,𝔽5)—22no—
307C2×AGL(1,𝔽5)—24no—
308C2×AGL(1,𝔽5)—22no—
309C2×AGL(1,𝔽5)—24no—
310C2×AGL(1,𝔽5)—24no—
311C2×AGL(1,𝔽5)—24no—
312C2×AGL(1,𝔽5)—21no—
313C2×AGL(1,𝔽5)—24no—
314C2×AGL(1,𝔽5)—24no—
315C2×AGL(1,𝔽5)—24no—
316C2×AGL(1,𝔽5)—24no—
317C2×AGL(1,𝔽5)—24no—
318C2×AGL(1,𝔽5)—88no—
319C2×AGL(1,𝔽5)—88no—
320C2×AGL(1,𝔽5)H(5,𝔽2)14yes—
321C2×AGL(1,𝔽5)2−1+412yes—
322C5×Q8—42no—
323C5×D4—42no—
324C5×D4—44no—
325C2×C4×C5—44no—
326C2×C4×C5C23×C412yes—
327C2×C4×C5C23×C411yescharacteristic
328C2×C4×C5C23×C414yes—
329C2×C4×C5C23×C414yes—
330C22⋊D5—44no—
331C22⋊D5—44no—
332C22⋊D5—44no—
333C2×Dic5—44no—
334C2×Dic5C23×C411yescharacteristic
335C2×Dic5C23×C412yes—
336C2×Dic5C23×C414yes—
337C2×Dic5C23×C414yes—
338D20—42no—
339D20—44no—
340C4×D5—24no—
341C4×D5—22no—
342C4×D5—24no—
343C4×D5—21no—
344C4×D5—21no—
345C4×D5—24no—
346C4×D5—22no—
347C4×D5—24no—
348C4×D5—44no—
349C4×D5—44no—
350Dic10—42no—
351Dic10—44no—
352C22×Q8—52no—
353C22×D4—54no—
354C22×D4—52no—
355C23×C4—54no—
356C23×C4—54no—
357C23×C4—54no—
358#125—54no—
359#125—52no—
360#125—51no—
361#125C2×AGL(1,𝔽5)11yescharacteristic, complemented
362#124—52no—
363#124—52no—
364#124—54no—
365#124—54no—
366#124—52no—
367#124C2×AGL(1,𝔽5)12yescomplemented
368#123—54no—
369#123—54no—
370#123—54no—
371#123—54no—
372#123—54no—
373#123—54no—
374#123—54no—
375#123C2×AGL(1,𝔽5)14yescomplemented
376C22⋊Q8—54no—
377C22⋊Q8—54no—
378C22⋊Q8—54no—
379C22⋊Q8—54no—
380C22⋊Q8—54no—
381C22⋊Q8—54no—
382C22⋊Q8—54no—
383C22⋊Q8C2×AGL(1,𝔽5)14yescomplemented
384#121—54no—
385#121—54no—
386#121—54no—
387#121—54no—
388#121—54no—
389#121—54no—
390#121—54no—
391#121C2×AGL(1,𝔽5)14yescomplemented
392C4×Q8—204no—
393C4×D4—204no—
394C4×D4—208no—
395#117—208no—
396C2×C4⋊C4—54no—
397C2×C4⋊C4—54no—
398C2×C4⋊C4—52no—
399C2×C4⋊C4—54no—
400C2×C4⋊C4—54no—
401C2×C4⋊C4—52no—
402C2×C4⋊C4—54no—
403C2×C4⋊C4—52no—
404C2×C4⋊C4—54no—
405C2×C4⋊C4—52no—
406C2×C22⋊C4—54no—
407C2×C22⋊C4—54no—
408C2×C22⋊C4—54no—
409C2×C22⋊C4—54no—
410C2×C22⋊C4—54no—
411C2×C22⋊C4—54no—
412C2×C22⋊C4—54no—
413C2×C22⋊C4—54no—
414C2×C22⋊C4—54no—
415C2×C42—51no—
416C2×C42—54no—
417C2×C42—52no—
418C2×C42—51no—
419C2×C42—54no—
420C2×C42—54no—
421C2×C42—51no—
422C2×C42—52no—
423C2×C42—54no—
424#95—54no—
425#95—54no—
426#95—54no—
427#95—54no—
428#95—54no—
429#95—54no—
430#95—54no—
431#95—54no—
432#95—54no—
433#95—54no—
434#95—54no—
435C22×C5—24no—
436C22×C5—24no—
437C22×C5—24no—
438C22×C5C24×C411yescharacteristic
439C2×D5—24no—
440C2×D5—24no—
441C2×D5—24no—
442C2×D5—44no—
443C2×D5—44no—
444C2×D5—44no—
445C2×D5—44no—
446C2×D5C2×H(5,𝔽2)12yes—
447C2×D5C2×2−1+411yescharacteristic
448C2×D5#58511yescharacteristic
449C2×D5#58512yes—
450AGL(1,𝔽5)—24no—
451AGL(1,𝔽5)—22no—
452AGL(1,𝔽5)—44no—
453AGL(1,𝔽5)—44no—
454AGL(1,𝔽5)—44no—
455AGL(1,𝔽5)—41no—
456C4×C5—24no—
457C4×C5—22no—
458C4×C5—24no—
459C4×C5—21no—
460Dic5—24no—
461Dic5—22no—
462Dic5—24no—
463Dic5—21no—
464C24—54no—
465C2×Q8—54no—
466C2×Q8—52no—
467C2×Q8—202no—
468C2×Q8—202no—
469C2×Q8C22×AGL(1,𝔽5)12yes—
470C2×D4—54no—
471C2×D4—54no—
472C2×D4—54no—
473C2×D4—54no—
474C2×D4—52no—
475C2×D4—202no—
476C2×D4—204no—
477C2×D4—204no—
478C2×D4—202no—
479C2×D4C22×AGL(1,𝔽5)14yes—
480C2×D4C22×AGL(1,𝔽5)12yes—
481C22×C4—51no—
482C22×C4—52no—
483C22×C4—54no—
484C22×C4—51no—
485C22×C4—52no—
486C22×C4—54no—
487C22×C4—54no—
488C22×C4—54no—
489C22×C4—54no—
490C22×C4—54no—
491C22×C4—54no—
492C22×C4—51no—
493C22×C4—54no—
494C22×C4—108no—
495C22×C4—204no—
496C22×C4—204no—
497C22×C4—204no—
498C22×C4—204no—
499C22×C4—204no—
500C22×C4—204no—
501C22×C4—204no—
502C22×C4C22×AGL(1,𝔽5)14yes—
503C4⋊C4—54no—
504C4⋊C4—54no—
505C4⋊C4—54no—
506C4⋊C4—54no—
507C4⋊C4—54no—
508C4⋊C4—54no—
509C4⋊C4—54no—
510C4⋊C4—52no—
511C4⋊C4—108no—
512C4⋊C4—204no—
513C4⋊C4—202no—
514C4⋊C4—204no—
515C4⋊C4—202no—
516C4⋊C4—202no—
517C4⋊C4—204no—
518C4⋊C4C22×AGL(1,𝔽5)14yes—
519C4⋊C4C22×AGL(1,𝔽5)14yes—
520C4⋊C4C22×AGL(1,𝔽5)12yes—
521C22⋊C4—54no—
522C22⋊C4—54no—
523C22⋊C4—54no—
524C22⋊C4—54no—
525C22⋊C4—54no—
526C22⋊C4—54no—
527C22⋊C4—54no—
528C22⋊C4—54no—
529C22⋊C4—54no—
530C22⋊C4—108no—
531C22⋊C4—108no—
532C22⋊C4—204no—
533C22⋊C4—204no—
534C22⋊C4—204no—
535C22⋊C4—204no—
536C22⋊C4C22×AGL(1,𝔽5)14yes—
537C22⋊C4C22×AGL(1,𝔽5)14yes—
538C22⋊C4C22×AGL(1,𝔽5)14yes—
539C42—52no—
540C42—51no—
541C42—108no—
542C42—104no—
543C42—102no—
544C42—204no—
545C42—204no—
546C42—201no—
547C42—204no—
548C42—202no—
549C42C22×AGL(1,𝔽5)11yescharacteristic
550C2×C5—44no—
551C2×C5C4×H(5,𝔽2)12yes—
552C2×C5C4×2−1+411yescharacteristic
553D5—44no—
554D5#354512yes—
555D5#354811yescharacteristic
556D5#355311yescharacteristic
557C23—51no—
558C23—54no—
559C23—104no—
560C23—104no—
561C23—104no—
562C23—104no—
563C23—104no—
564C23—104no—
565C23C23×AGL(1,𝔽5)14yes—
566Q8—42no—
567Q8—204no—
568Q8—202no—
569D4—44no—
570D4—42no—
571D4—204no—
572D4—202no—
573D4—204no—
574D4—204no—
575D4—204no—
576C2×C4—44no—
577C2×C4—54no—
578C2×C4—52no—
579C2×C4—51no—
580C2×C4—52no—
581C2×C4—54no—
582C2×C4—54no—
583C2×C4—104no—
584C2×C4—102no—
585C2×C4—101no—
586C2×C4—104no—
587C2×C4—101no—
588C2×C4—104no—
589C2×C4—102no—
590C2×C4—104no—
591C2×C4—102no—
592C2×C4—102no—
593C2×C4—102no—
594C2×C4—102no—
595C2×C4—104no—
596C2×C4—101no—
597C2×C4—104no—
598C2×C4—104no—
599C2×C4—104no—
600C2×C4—104no—
601C2×C4—104no—
602C2×C4—104no—
603C2×C4—104no—
604C2×C4—104no—
605C2×C4—204no—
606C2×C4—204no—
607C2×C4—204no—
608C2×C4—408no—
609C2×C4—408no—
610C2×C4C23×AGL(1,𝔽5)11yescharacteristic
611C2×C4C23×AGL(1,𝔽5)12yes—
612C2×C4C23×AGL(1,𝔽5)14yes—
613C2×C4C23×AGL(1,𝔽5)14yes—
614C5#3452211yescharacteristic, complemented, Sylow
615C22—24no—
616C22—24no—
617C22—24no—
618C22—52no—
619C22—52no—
620C22—51no—
621C22—51no—
622C22—104no—
623C22—104no—
624C22—104no—
625C22—204no—
626C22—204no—
627C22—204no—
628C22—204no—
629C22C24×AGL(1,𝔽5)11yescharacteristic
630C4—24no—
631C4—24no—
632C4—22no—
633C4—21no—
634C4—104no—
635C4—102no—
636C4—104no—
637C4—104no—
638C4—102no—
639C4—101no—
640C4—204no—
641C4—204no—
642C4—201no—
643C4—204no—
644C2—44no—
645C2—52no—
646C2—51no—
647C2—51no—
648C2—204no—
649C2AGL(1,𝔽5)×H(5,𝔽2)12yes—
650C2AGL(1,𝔽5)×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#562C4
prime radicalD5×#562C2
cosocleC22×D5C25
hypercenter#562AGL(1,𝔽5)
hypocenterC5#34522
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #562

Complements

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

NH ≅ G/Ntype
2. #10617348C2semidirect
3. AGL(1,𝔽5)×#125C2semidirect
4. #10617328C2semidirect
5. AGL(1,𝔽5)×#124C2semidirect
6. #10617306C2semidirect
7. #10617305C2semidirect
8. #10617287C2semidirect
9. #10617282C2semidirect
10. #10617254C2semidirect
11. #10617251C2semidirect
16. C5×#562C4semidirect
17. #66034C4semidirect
19. #66018C4semidirect
21. #66001C4semidirect
23. #65981C4semidirect
25. #65955C4semidirect
95. C5×#125C2×C4semidirect
96. C5×#124C2×C4semidirect
97. C5×#123C2×C4semidirect
98. C5×C22⋊Q8C2×C4semidirect
99. C5×#121C2×C4semidirect
100. #4093C2×C4semidirect
101. #4092C2×C4semidirect
102. #4085C2×C4semidirect
103. #4085C2×C4semidirect
104. #4084C2×C4semidirect
105. #4082C2×C4semidirect
106. #4081C2×C4semidirect
107. #4076C2×C4semidirect
108. #4075C2×C4semidirect
109. #4070C2×C4semidirect
110. #4043C2×C4semidirect
111. #4042C2×C4semidirect
112. #4042C2×C4semidirect
113. #4041C2×C4semidirect
114. #4040C2×C4semidirect
115. #4040C2×C4semidirect
119. #4036C2×C4semidirect
120. #4035C2×C4semidirect
121. #4032C2×C4semidirect
122. #4031C2×C4semidirect
123. #4031C2×C4semidirect
124. #4030C2×C4semidirect
125. #4030C2×C4semidirect
126. #4029C2×C4semidirect
127. #4029C2×C4semidirect
131. #4024C2×C4semidirect
132. #4024C2×C4semidirect
133. #4021C2×C4semidirect
135. #4016C2×C4semidirect
249. #562AGL(1,𝔽5)semidirect
361. #125C2×AGL(1,𝔽5)semidirect
367. #124C2×AGL(1,𝔽5)semidirect
375. #123C2×AGL(1,𝔽5)semidirect
383. C22⋊Q8C2×AGL(1,𝔽5)semidirect
391. #121C2×AGL(1,𝔽5)semidirect
614. C5#34522semidirect

Maximal subgroups

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

subgroupindex
D5×#5622
#106173482
AGL(1,𝔽5)×#1252
#106173282
AGL(1,𝔽5)×#1242
#106173062
#106173052
#106172872
#106172822
#106172542
#106172512
#345225