Finite Group Databasebeta

← #41×C4⋊AGL(1,𝔽5) #13043957

Subgroups — #41×C4⋊AGL(1,𝔽5) #13043957

Order 1280.

3250 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×AGL(1,𝔽5)C212yesmaximal
2C4×D5×#41C211yesmaximal, characteristic
3#10617212C212yesmaximal, complemented
4Q8×C4⋊AGL(1,𝔽5)C212yesmaximal, complemented
5#10617178C216yesmaximal, complemented
6D4×C4⋊AGL(1,𝔽5)C216yesmaximal, complemented
7#10617128C216yesmaximal, complemented
8#10617048C213yesmaximal, complemented
9C2×C4×C4⋊AGL(1,𝔽5)C213yesmaximal, complemented
10C2×D5×#41C2211yescharacteristic
11#41×AGL(1,𝔽5)—216no—
12C2×Q8×AGL(1,𝔽5)C2214yes—
13C2×D4×AGL(1,𝔽5)C22112yes—
14C2×#4130C2216yes—
15C22×C4⋊AGL(1,𝔽5)C2216yes—
16C22×C4×AGL(1,𝔽5)C2216yes—
17C4×C5×#41C411yescharacteristic, complemented
18#41×Dic5C411yescharacteristic, complemented
19C4×#713C411yescharacteristic, complemented
20C4×#713C411yescharacteristic, complemented
21C4×Q8×D5C2211yescharacteristic
22C4×Q8×D5C2211yescharacteristic
23C4×D4×D5C2213yes—
24C4×D4×D5C2213yes—
25C4×#711C413yescomplemented
26C4×#711C413yescomplemented
27#65856C413yescomplemented
28D5×#117C2213yes—
29C4×#709C413yescomplemented
30C2×C42×D5C2213yes—
31#65765C2216yes—
32#65765C2216yes—
33C2×(C2×AGL(1,𝔽5))⋊C4C2216yes—
34#65712C22112yes—
35#65712C22112yes—
36#65699C22124yes—
37#65689C2216yes—
38#65688C2216yes—
39C4×C4⋊AGL(1,𝔽5)C2216yes—
40C4×C4⋊AGL(1,𝔽5)C2216yes—
41C4×C4⋊AGL(1,𝔽5)C2216yes—
42C4×C4⋊AGL(1,𝔽5)C2216yes—
43C4×C4⋊AGL(1,𝔽5)C2211yescharacteristic
44C4×C4⋊AGL(1,𝔽5)C2213yes—
45C4⋊C4×#41—51nomaximal, Sylow
46C23×AGL(1,𝔽5)C23112yes—
47C2×C5×#41C2×C411yescharacteristic
48D5×#41D418yes—
49D5×#41Q818yes—
50C2×#713C2×C411yescharacteristic
51C2×Q8×D5C2311yescharacteristic
52C2×#711C2×C413yes—
53C2×D4×D5C2313yes—
54C2×#709C2×C413yes—
55C22×C4×D5C2313yes—
56C22×C4×D5C2313yes—
57C22×C4×D5C2313yes—
58C2×C22⋊AGL(1,𝔽5)C23112yes—
59Q8×AGL(1,𝔽5)—216no—
60D4×AGL(1,𝔽5)—248no—
61#4130—224no—
62C2×C4⋊AGL(1,𝔽5)—224no—
63C2×C4⋊AGL(1,𝔽5)C2316yes—
64C2×C4⋊AGL(1,𝔽5)C23112yes—
65C2×C4⋊AGL(1,𝔽5)C23112yes—
66C2×C4⋊AGL(1,𝔽5)C23112yes—
67C2×C4⋊AGL(1,𝔽5)C2312yes—
68C2×C4×AGL(1,𝔽5)—224no—
69C2×C4×AGL(1,𝔽5)C2312yes—
70C2×C4×AGL(1,𝔽5)C2316yes—
71C2×C4×AGL(1,𝔽5)C23112yes—
72C4×C5×Q8C2×C411yescharacteristic, complemented
73C4×C5×Q8C2×C411yescharacteristic, complemented
74C4×C5×D4C2×C413yescomplemented
75C4×C5×D4C2×C413yescomplemented
76C5×#117C2×C413yescomplemented
77C2×C42×C5C2×C413yescomplemented
78Q8×Dic5C2×C411yescharacteristic, complemented
79Q8×Dic5C2×C411yescharacteristic, complemented
80D4×Dic5C2×C413yescomplemented
81D4×Dic5C2×C413yescomplemented
82C4×C22⋊D5C2×C416yescomplemented
83C4×C22⋊D5C2×C416yescomplemented
84#4072C2×C413yescomplemented
85C2×C4×Dic5C2×C413yescomplemented
86C2×C4×Dic5C2×C413yescomplemented
87C2×C4×Dic5C2×C413yescomplemented
88#4039C2×C413yescomplemented
89#4039C2×C413yescomplemented
90#4038C2×C413yescomplemented
91#4038C2×C413yescomplemented
92D5×C4⋊C4C2313yes—
93D5×C4⋊C4C2313yes—
94#4033C2×C413yescomplemented
95#4033C2×C413yescomplemented
96#4027C2×C416yescomplemented
97#4027C2×C416yescomplemented
98D5×C22⋊C4C2316yes—
99#4023C2×C416yescomplemented
100C4×D20C2×C413yescomplemented
101C4×D20C2×C413yescomplemented
102#4018C2×C416yescomplemented
103C42×D5C2×C413yescomplemented
104C42×D5C2×C413yescomplemented
105C42×D5C2×C413yescomplemented
106C42×D5C2×C413yescomplemented
107C42×D5C2311yescharacteristic
108C42×D5C2313yes—
109C42×D5C2313yes—
110C42×D5C2313yes—
111C4×Dic10C2×C413yescomplemented
112C4×Dic10C2×C413yescomplemented
113(C2×AGL(1,𝔽5))⋊C4C2312yes—
114(C2×AGL(1,𝔽5))⋊C4C2316yes—
115(C2×AGL(1,𝔽5))⋊C4C23112yes—
116(C2×AGL(1,𝔽5))⋊C4C23112yes—
117C2×C4×#41—51no—
118C2×C4×#41—52no—
119#2351—52no—
120Q8×C4⋊C4—52no—
121#2349—56no—
122D4×C4⋊C4—56no—
123#2296—56no—
124#2285—53no—
125C2×C4×C4⋊C4—53no—
126C23×D5C2413yes—
127C22×AGL(1,𝔽5)—224no—
128C22×AGL(1,𝔽5)—224no—
129C22×AGL(1,𝔽5)—412no—
130C22×AGL(1,𝔽5)C24112yes—
131C22×AGL(1,𝔽5)C2414yes—
132C5×#41C4⋊C418yescomplemented
133C2×C5×Q8C22×C411yescharacteristic
134C2×C5×D4C22×C413yes—
135C22×C4×C5C22×C413yes—
136C22×C4×C5C22×C413yes—
137C22×C4×C5C22×C413yes—
138C2×C22⋊D5C22×C416yes—
139C22×Dic5C22×C413yes—
140C22×Dic5C22×C413yes—
141C22×Dic5C22×C413yes—
142#713C4⋊C418yescomplemented
143Q8×D5C2×D414yes—
144Q8×D5C2×Q814yes—
145#711C4⋊C4124yescomplemented
146D4×D5C2×D4112yes—
147D4×D5C2×Q8112yes—
148#709C4⋊C4124yescomplemented
149C2×D20C22×C413yes—
150C2×C4×D5—212no—
151C2×C4×D5—46no—
152C2×C4×D5C22×C413yes—
153C2×C4×D5C22×C413yes—
154C2×C4×D5C22×C413yes—
155C2×C4×D5C22×C413yes—
156C2×C4×D5C22×C413yes—
157C2×C4×D5C22×C413yes—
158C2×C4×D5C2×D4112yes—
159C2×C4×D5C2×Q8112yes—
160C2×C4×D5C2413yes—
161C2×C4×D5C2413yes—
162C2×C4×D5C2411yescharacteristic
163C2×C4×D5C2411yescharacteristic
164C2×C4×D5C2413yes—
165C2×C4×D5C2411yescharacteristic
166C2×Dic10C22×C413yes—
167C22⋊AGL(1,𝔽5)—224no—
168C4⋊AGL(1,𝔽5)—224no—
169C4⋊AGL(1,𝔽5)—224no—
170C4⋊AGL(1,𝔽5)—212no—
171C4⋊AGL(1,𝔽5)—412no—
172C4⋊AGL(1,𝔽5)#4118yesdirect product factor
173C4×AGL(1,𝔽5)—24no—
174C4×AGL(1,𝔽5)—212no—
175C4×AGL(1,𝔽5)—224no—
176C5×C4⋊C4C22×C413yes—
177C5×C4⋊C4C22×C413yes—
178C5×C22⋊C4C22×C416yes—
179C42×C5C22×C411yescharacteristic
180C42×C5C22×C413yes—
181C42×C5C22×C413yes—
182C42×C5C22×C413yes—
183C22⋊Dic5C22×C416yes—
184#685C22×C416yes—
185#685C22×C416yes—
186C4⋊Dic5C22×C413yes—
187C4⋊Dic5C22×C413yes—
188#683C22×C416yes—
189#683C22×C416yes—
190C4×Dic5C22×C413yes—
191C4×Dic5C22×C413yes—
192C4×Dic5C22×C411yescharacteristic
193C4×Dic5C22×C411yescharacteristic
194C4×Dic5C22×C411yescharacteristic
195C4×Dic5C22×C413yes—
196C4×Dic5C22×C413yes—
197C4×Dic5C22×C413yes—
198C4×Dic5C22×C413yes—
199C4×Dic5C22×C413yes—
200C4×Dic5C22×C413yes—
201C4×Dic5C22×C413yes—
202C22×#41—51no—
203C4×#41—51no—
204C4×#41—51no—
205C4×#41—51no—
206C4×#41—53no—
207C4×#41—53no—
208C4×#41—53no—
209C4×#41—53no—
210C4×#41—1016no—
211C4×#41AGL(1,𝔽5)11yescharacteristic, complemented
212C2×C4×Q8—51no—
213C2×C4×Q8—51no—
214C2×C4×Q8—54no—
215C2×C4×D4—53no—
216C2×C4×D4—53no—
217C2×C4×D4—512no—
218C2×#117—53no—
219C2×#117—56no—
220C22×C4⋊C4—56no—
221C22×C42—53no—
222C22×C42—56no—
223#389—512no—
224#389—512no—
225#385—524no—
226#384—56no—
227#382—56no—
228#380—56no—
229#380—56no—
230C4×C4⋊C4—56no—
231C4×C4⋊C4—56no—
232C4×C4⋊C4—51no—
233C4×C4⋊C4—53no—
234C4×C4⋊C4—56no—
235C4×C4⋊C4—56no—
236C2×#95—56no—
237C23×C5C23×C413yes—
238C22×D5—26no—
239C22×D5—26no—
240C22×D5C23×C413yes—
241C22×D5C22×D416yes—
242C22×D5C22×Q816yes—
243C22×D5C2511yescharacteristic
244C2×AGL(1,𝔽5)—24no—
245C2×AGL(1,𝔽5)—24no—
246C2×AGL(1,𝔽5)—212no—
247C2×AGL(1,𝔽5)—212no—
248C2×AGL(1,𝔽5)—212no—
249C2×AGL(1,𝔽5)—448no—
250C2×AGL(1,𝔽5)C2×#4118yes—
251C5×Q8C2×C4⋊C414yescomplemented
252C5×D4C2×C4⋊C4112yescomplemented
253C2×C4×C5—26no—
254C2×C4×C5—43no—
255C2×C4×C5C2×C4⋊C4112yescomplemented
256C2×C4×C5C23×C411yescharacteristic
257C2×C4×C5C23×C413yes—
258C2×C4×C5C23×C413yes—
259C2×C4×C5C23×C413yes—
260C2×C4×C5C23×C411yescharacteristic
261C2×C4×C5C23×C411yescharacteristic
262C22⋊D5C2×C4⋊C4124yescomplemented
263C2×Dic5—26no—
264C2×Dic5—43no—
265C2×Dic5C2×C4⋊C4112yescomplemented
266C2×Dic5C23×C411yescharacteristic
267C2×Dic5C23×C413yes—
268C2×Dic5C23×C413yes—
269C2×Dic5C23×C411yescharacteristic
270C2×Dic5C23×C413yes—
271C2×Dic5C23×C411yescharacteristic
272D20C2×C4⋊C4112yescomplemented
273C4×D5—26no—
274C4×D5—26no—
275C4×D5—22no—
276C4×D5—26no—
277C4×D5—26no—
278C4×D5—43no—
279C4×D5—43no—
280C4×D5C2×C4⋊C4112yescomplemented
281C4×D5C2×C4⋊C4112yescomplemented
282C4×D5C22×D412yes—
283C4×D5C22×D416yes—
284C4×D5C22×Q812yes—
285C4×D5C22×Q816yes—
286C4×D5C2×#4114yes—
287Dic10C2×C4⋊C4112yescomplemented
288C2×#41—58no—
289C2×#41—58no—
290C2×#41—51no—
291C2×#41—53no—
292C2×#41—53no—
293C2×#41C2×AGL(1,𝔽5)11yescharacteristic
294C22×Q8—51no—
295C22×D4—53no—
296C23×C4—53no—
297C23×C4—53no—
298C23×C4—53no—
299C23×C4—512no—
300C4×Q8—51no—
301C4×Q8—51no—
302C4×Q8—53no—
303C4×Q8—53no—
304C4×Q8—53no—
305C4×Q8—53no—
306C4×Q8—1016no—
307C4×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
308C4×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
309C4×D4—53no—
310C4×D4—53no—
311C4×D4—56no—
312C4×D4—56no—
313C4×D4—53no—
314C4×D4—53no—
315C4×D4—56no—
316C4×D4—56no—
317C4×D4—53no—
318C4×D4—53no—
319C4×D4—1048no—
320C4×D4C2×AGL(1,𝔽5)13yescomplemented
321C4×D4C2×AGL(1,𝔽5)13yescomplemented
322#117—53no—
323#117—53no—
324#117—53no—
325#117—56no—
326#117—56no—
327#117—1024no—
328#117C2×AGL(1,𝔽5)13yescomplemented
329C2×C4⋊C4—52no—
330C2×C4⋊C4—53no—
331C2×C4⋊C4—53no—
332C2×C4⋊C4—56no—
333C2×C4⋊C4—512no—
334C2×C4⋊C4—512no—
335C2×C4⋊C4—512no—
336C2×C4⋊C4—1024no—
337C2×C22⋊C4—56no—
338C2×C22⋊C4—512no—
339C2×C42—53no—
340C2×C42—53no—
341C2×C42—53no—
342C2×C42—53no—
343C2×C42—53no—
344C2×C42—53no—
345C2×C42—53no—
346C2×C42—53no—
347C2×C42—53no—
348C2×C42—53no—
349C2×C42—51no—
350C2×C42—56no—
351C2×C42—512no—
352C2×C42—52no—
353C2×C42—1024no—
354C2×C42C2×AGL(1,𝔽5)13yescomplemented
355#95—52no—
356#95—56no—
357#95—512no—
358#95—512no—
359C22×C5—23no—
360C22×C5—23no—
361C22×C5C22×C4⋊C416yes—
362C22×C5C24×C411yescharacteristic
363C2×D5—23no—
364C2×D5—23no—
365C2×D5—212no—
366C2×D5—212no—
367C2×D5C22×C4⋊C416yes—
368C2×D5C23×D411yescharacteristic
369C2×D5C23×Q811yescharacteristic
370C2×D5C22×#4112yes—
371C2×D5#58512yes—
372AGL(1,𝔽5)—28no—
373AGL(1,𝔽5)—412no—
374C4×C5—23no—
375C4×C5—21no—
376C4×C5—23no—
377C4×C5C22×C4⋊C416yes—
378C4×C5C22×C4⋊C412yes—
379C4×C5C4×#4112yescomplemented
380Dic5—23no—
381Dic5—21no—
382Dic5—23no—
383Dic5C22×C4⋊C416yes—
384Dic5C22×C4⋊C412yes—
385Dic5C4×#4112yescomplemented
386C24—53no—
387#41—58no—
388#41—524no—
389#41—524no—
390#41C4⋊AGL(1,𝔽5)18yesdirect product factor
391C2×Q8—54no—
392C2×Q8—54no—
393C2×Q8—53no—
394C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
395C2×D4—56no—
396C2×D4—512no—
397C2×D4—512no—
398C2×D4—53no—
399C2×D4C22×AGL(1,𝔽5)13yes—
400C22×C4—53no—
401C22×C4—512no—
402C22×C4—512no—
403C22×C4—53no—
404C22×C4—51no—
405C22×C4—53no—
406C22×C4—51no—
407C22×C4—53no—
408C22×C4—54no—
409C22×C4—53no—
410C22×C4—53no—
411C22×C4—51no—
412C22×C4—53no—
413C22×C4—53no—
414C22×C4—53no—
415C22×C4—53no—
416C22×C4—53no—
417C22×C4—53no—
418C22×C4—512no—
419C22×C4—1012no—
420C22×C4—1024no—
421C22×C4—1024no—
422C22×C4—206no—
423C22×C4—2012no—
424C22×C4C22×AGL(1,𝔽5)13yes—
425C22×C4C22×AGL(1,𝔽5)13yes—
426C22×C4C22×AGL(1,𝔽5)13yes—
427C4⋊C4—58no—
428C4⋊C4—56no—
429C4⋊C4—56no—
430C4⋊C4—53no—
431C4⋊C4—53no—
432C4⋊C4—1012no—
433C4⋊C4—1024no—
434C4⋊C4—1024no—
435C4⋊C4—2012no—
436C4⋊C4C22×AGL(1,𝔽5)13yes—
437C4⋊C4C22×AGL(1,𝔽5)13yes—
438C22⋊C4—56no—
439C22⋊C4—56no—
440C22⋊C4—56no—
441C22⋊C4—1024no—
442C22⋊C4C22×AGL(1,𝔽5)16yes—
443C42—51no—
444C42—51no—
445C42—53no—
446C42—53no—
447C42—53no—
448C42—53no—
449C42—53no—
450C42—53no—
451C42—53no—
452C42—53no—
453C42—51no—
454C42—53no—
455C42—104no—
456C42—1012no—
457C42—1024no—
458C42C22×AGL(1,𝔽5)13yes—
459C42C22×AGL(1,𝔽5)13yes—
460C42C22×AGL(1,𝔽5)11yescharacteristic
461C42C22×AGL(1,𝔽5)13yes—
462C2×C5—26no—
463C2×C5C23×C4⋊C411yescharacteristic
464C2×C5C2×C4×#4111yescharacteristic
465C2×C5#342811yescharacteristic
466D5—26no—
467D5D4×#4112yes—
468D5Q8×#4112yes—
469C23—51no—
470C23—56no—
471C23—56no—
472C23—53no—
473C23—106no—
474C23—106no—
475C23C23×AGL(1,𝔽5)13yes—
476Q8—512no—
477Q8C2×C4⋊AGL(1,𝔽5)14yescomplemented
478D4—524no—
479D4—512no—
480D4C2×C4⋊AGL(1,𝔽5)112yescomplemented
481C2×C4—26no—
482C2×C4—43no—
483C2×C4—512no—
484C2×C4—51no—
485C2×C4—51no—
486C2×C4—53no—
487C2×C4—52no—
488C2×C4—56no—
489C2×C4—52no—
490C2×C4—56no—
491C2×C4—512no—
492C2×C4—512no—
493C2×C4—54no—
494C2×C4—58no—
495C2×C4—51no—
496C2×C4—53no—
497C2×C4—53no—
498C2×C4—106no—
499C2×C4—106no—
500C2×C4—106no—
501C2×C4—102no—
502C2×C4—106no—
503C2×C4—104no—
504C2×C4—104no—
505C2×C4—106no—
506C2×C4—1012no—
507C2×C4—1012no—
508C2×C4—1012no—
509C2×C4—203no—
510C2×C4—203no—
511C2×C4—203no—
512C2×C4—2048no—
513C2×C4C2×C4⋊AGL(1,𝔽5)112yescomplemented
514C2×C4C23×AGL(1,𝔽5)11yescharacteristic
515C2×C4C23×AGL(1,𝔽5)13yes—
516C2×C4C23×AGL(1,𝔽5)13yes—
517C2×C4C23×AGL(1,𝔽5)13yes—
518C2×C4C23×AGL(1,𝔽5)11yescharacteristic
519C2×C4C23×AGL(1,𝔽5)11yescharacteristic
520C5C4⋊C4×#4111yescharacteristic, complemented, Sylow
521C22—23no—
522C22—23no—
523C22—51no—
524C22—51no—
525C22—52no—
526C22—52no—
527C22—56no—
528C22—1012no—
529C22—1012no—
530C22—103no—
531C22—103no—
532C22C22×C4⋊AGL(1,𝔽5)16yes—
533C22C24×AGL(1,𝔽5)11yescharacteristic
534C4—23no—
535C4—21no—
536C4—23no—
537C4—52no—
538C4—56no—
539C4—52no—
540C4—108no—
541C4—103no—
542C4—101no—
543C4—103no—
544C4—2012no—
545C4C22×C4⋊AGL(1,𝔽5)12yes—
546C4C22×C4⋊AGL(1,𝔽5)16yes—
547C4#41×AGL(1,𝔽5)12yescomplemented
548C2—26no—
549C2—52no—
550C2—52no—
551C2—106no—
552C2C23×C4⋊AGL(1,𝔽5)11yescharacteristic
553C2C2×#41×AGL(1,𝔽5)11yescharacteristic
554C2#1061941211yescharacteristic
subgroupG/H
centerC2×C4C23×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC4×C5×#41C4
prime radicalC2×D5×#41C22
cosocleC22×D5C25
hypercenterC4×#41AGL(1,𝔽5)
hypocenterC5C4⋊C4×#41
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
3. #10617212C2semidirect
4. Q8×C4⋊AGL(1,𝔽5)C2semidirect
5. #10617178C2semidirect
6. D4×C4⋊AGL(1,𝔽5)C2semidirect
7. #10617128C2semidirect
8. #10617048C2semidirect
9. C2×C4×C4⋊AGL(1,𝔽5)C2semidirect
17. C4×C5×#41C4semidirect
18. #41×Dic5C4semidirect
19. C4×#713C4semidirect
20. C4×#713C4semidirect
25. C4×#711C4semidirect
26. C4×#711C4semidirect
27. #65856C4semidirect
29. C4×#709C4semidirect
72. C4×C5×Q8C2×C4semidirect
73. C4×C5×Q8C2×C4semidirect
74. C4×C5×D4C2×C4semidirect
75. C4×C5×D4C2×C4semidirect
76. C5×#117C2×C4semidirect
77. C2×C42×C5C2×C4semidirect
78. Q8×Dic5C2×C4semidirect
79. Q8×Dic5C2×C4semidirect
80. D4×Dic5C2×C4semidirect
81. D4×Dic5C2×C4semidirect
82. C4×C22⋊D5C2×C4semidirect
83. C4×C22⋊D5C2×C4semidirect
84. #4072C2×C4semidirect
85. C2×C4×Dic5C2×C4semidirect
86. C2×C4×Dic5C2×C4semidirect
87. C2×C4×Dic5C2×C4semidirect
88. #4039C2×C4semidirect
89. #4039C2×C4semidirect
90. #4038C2×C4semidirect
91. #4038C2×C4semidirect
94. #4033C2×C4semidirect
95. #4033C2×C4semidirect
96. #4027C2×C4semidirect
97. #4027C2×C4semidirect
99. #4023C2×C4semidirect
100. C4×D20C2×C4semidirect
101. C4×D20C2×C4semidirect
102. #4018C2×C4semidirect
103. C42×D5C2×C4semidirect
104. C42×D5C2×C4semidirect
105. C42×D5C2×C4semidirect
106. C42×D5C2×C4semidirect
111. C4×Dic10C2×C4semidirect
112. C4×Dic10C2×C4semidirect
132. C5×#41C4⋊C4semidirect
142. #713C4⋊C4semidirect
145. #711C4⋊C4semidirect
148. #709C4⋊C4semidirect
172. C4⋊AGL(1,𝔽5)#41direct (N × H)
211. C4×#41AGL(1,𝔽5)semidirect
251. C5×Q8C2×C4⋊C4semidirect
252. C5×D4C2×C4⋊C4semidirect
255. C2×C4×C5C2×C4⋊C4semidirect
262. C22⋊D5C2×C4⋊C4semidirect
265. C2×Dic5C2×C4⋊C4semidirect
272. D20C2×C4⋊C4semidirect
280. C4×D5C2×C4⋊C4semidirect
281. C4×D5C2×C4⋊C4semidirect
287. Dic10C2×C4⋊C4semidirect
307. C4×Q8C2×AGL(1,𝔽5)semidirect
308. C4×Q8C2×AGL(1,𝔽5)semidirect
320. C4×D4C2×AGL(1,𝔽5)semidirect
321. C4×D4C2×AGL(1,𝔽5)semidirect
328. #117C2×AGL(1,𝔽5)semidirect
354. C2×C42C2×AGL(1,𝔽5)semidirect
379. C4×C5C4×#41semidirect
385. Dic5C4×#41semidirect
390. #41C4⋊AGL(1,𝔽5)direct (N × H)
477. Q8C2×C4⋊AGL(1,𝔽5)semidirect
480. D4C2×C4⋊AGL(1,𝔽5)semidirect
513. C2×C4C2×C4⋊AGL(1,𝔽5)semidirect
520. C5C4⋊C4×#41semidirect
547. C4#41×AGL(1,𝔽5)semidirect

Maximal subgroups

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

subgroupindex
C2×#41×AGL(1,𝔽5)2
C4×D5×#412
#106172122
Q8×C4⋊AGL(1,𝔽5)2
#106171782
D4×C4⋊AGL(1,𝔽5)2
#106171282
#106170482
C2×C4×C4⋊AGL(1,𝔽5)2
C4⋊C4×#415