Finite Group Databasebeta

← AGL(1,𝔽5)×#550 #13044003

Subgroups — AGL(1,𝔽5)×#550 #13044003

Order 1280.

3420 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×AGL(1,𝔽5)C212yesmaximal, complemented
2D5×#550C211yesmaximal, characteristic
3#10617558C212yesmaximal, complemented
4#10617369C213yesmaximal, complemented
5AGL(1,𝔽5)×#127C213yesmaximal, complemented
6#10617254C216yesmaximal, complemented
7AGL(1,𝔽5)×#121C216yesmaximal, complemented
8Q8×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
9C4×Q8×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
10#10617181C213yesmaximal, complemented
11C4×D4×AGL(1,𝔽5)C213yesmaximal, complemented
12C2×D5×#41C2212yes—
13#41×AGL(1,𝔽5)—216no—
14C2×Q8×AGL(1,𝔽5)C2212yes—
15C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
16C2×Q8×AGL(1,𝔽5)C2211yescharacteristic
17C2×D4×AGL(1,𝔽5)C2216yes—
18C2×D4×AGL(1,𝔽5)C2216yes—
19C2×D4×AGL(1,𝔽5)C2213yes—
20C2×D4×AGL(1,𝔽5)C2213yes—
21C2×D4×AGL(1,𝔽5)C2216yes—
22C2×#4130C2216yes—
23C22×C4×AGL(1,𝔽5)C2216yes—
24C5×#550C411yescharacteristic, complemented
25#66168C412yescomplemented
26#66052C413yescomplemented
27D5×#127C2213yes—
28D5×#121C2216yes—
29#65933C416yescomplemented
30#65911C411yescharacteristic, complemented
31C4×Q8×D5C2211yescharacteristic
32#65887C413yescomplemented
33C4×D4×D5C2213yes—
34#65780C2216yes—
35#65780C2216yes—
36#65780C2216yes—
37#65780C2216yes—
38#65779C22112yes—
39#65765C2216yes—
40C4×C22⋊AGL(1,𝔽5)C2216yes—
41#65712C2216yes—
42C4⋊C4×AGL(1,𝔽5)C2211yescharacteristic
43C4⋊C4×AGL(1,𝔽5)C2213yes—
44C4⋊C4×AGL(1,𝔽5)C2213yes—
45C4⋊C4×AGL(1,𝔽5)C2213yes—
46#65700C22112yes—
47C22⋊C4×AGL(1,𝔽5)C2216yes—
48C22⋊C4×AGL(1,𝔽5)C2216yes—
49#65688C2213yes—
50C4×C4⋊AGL(1,𝔽5)C2213yes—
51C4×C4⋊AGL(1,𝔽5)C2213yes—
52C42×AGL(1,𝔽5)C2213yes—
53C4×#550—51nomaximal, Sylow
54C23×AGL(1,𝔽5)C2316yes—
55C23×AGL(1,𝔽5)C2316yes—
56C2×C5×#41C2×C412yescomplemented
57D5×#41—28no—
58D5×#41—28no—
59C2×#713C2×C412yescomplemented
60C2×Q8×D5C2311yescharacteristic
61C2×#711C2×C416yescomplemented
62C2×D4×D5C2313yes—
63C2×D4×D5C2316yes—
64C2×D4×D5C2316yes—
65C2×#709C2×C416yescomplemented
66C22×C4×D5C2316yes—
67C2×C22⋊AGL(1,𝔽5)C2316yes—
68C2×C22⋊AGL(1,𝔽5)C2316yes—
69C2×C22⋊AGL(1,𝔽5)C23112yes—
70C2×C22⋊AGL(1,𝔽5)C23112yes—
71Q8×AGL(1,𝔽5)—28no—
72Q8×AGL(1,𝔽5)—24no—
73Q8×AGL(1,𝔽5)D418yescomplemented
74D4×AGL(1,𝔽5)—224no—
75D4×AGL(1,𝔽5)—212no—
76D4×AGL(1,𝔽5)—224no—
77D4×AGL(1,𝔽5)—212no—
78D4×AGL(1,𝔽5)—412no—
79#4130—224no—
80C2×C4⋊AGL(1,𝔽5)C2313yes—
81C2×C4⋊AGL(1,𝔽5)C2313yes—
82C2×C4⋊AGL(1,𝔽5)C2316yes—
83C2×C4⋊AGL(1,𝔽5)C2316yes—
84C2×C4⋊AGL(1,𝔽5)C2313yes—
85C2×C4⋊AGL(1,𝔽5)C2311yescharacteristic
86C2×C4×AGL(1,𝔽5)—224no—
87C2×C4×AGL(1,𝔽5)C2313yes—
88C2×C4×AGL(1,𝔽5)C2313yes—
89C2×C4×AGL(1,𝔽5)C2313yes—
90C2×C4×AGL(1,𝔽5)C2316yes—
91C2×C4×AGL(1,𝔽5)C2312yes—
92C2×C4×AGL(1,𝔽5)C2316yes—
93C2×C4×AGL(1,𝔽5)C2313yes—
94C2×C4×AGL(1,𝔽5)C2313yes—
95C2×C4×AGL(1,𝔽5)C2311yescharacteristic
96C5×#127C2×C413yescomplemented
97C5×#121C2×C416yescomplemented
98C4×C5×Q8C2×C411yescharacteristic, complemented
99C4×C5×D4C2×C413yescomplemented
100Q8×Dic5C2×C411yescharacteristic, complemented
101#4086C2×C416yescomplemented
102#4086C2×C416yescomplemented
103#4086C2×C416yescomplemented
104#4085C2×C4112yescomplemented
105#4084C2×C416yescomplemented
106D4×Dic5C2×C413yescomplemented
107#4076C2×C416yescomplemented
108C4×C22⋊D5C2×C416yescomplemented
109#4041C2×C416yescomplemented
110#4039C2×C413yescomplemented
111D5×C4⋊C4C2311yescharacteristic
112D5×C4⋊C4C2313yes—
113#4033C2×C413yescomplemented
114#4030C2×C4112yescomplemented
115#4027C2×C416yescomplemented
116D5×C22⋊C4C2316yes—
117#4020C2×C413yescomplemented
118C4×D20C2×C413yescomplemented
119C42×D5C2313yes—
120C4×Dic10C2×C413yescomplemented
121(C2×AGL(1,𝔽5))⋊C4C2316yes—
122(C2×AGL(1,𝔽5))⋊C4C2316yes—
123(C2×AGL(1,𝔽5))⋊C4C2312yes—
124(C2×AGL(1,𝔽5))⋊C4C2316yes—
125C2×#550—51no—
126C2×C4×#41—52no—
127#2366—53no—
128#2363—56no—
129#2354—53no—
130Q8×C4⋊C4—51no—
131#2341—52no—
132C4×#127—53no—
133C4×#121—56no—
134C42×Q8—51no—
135C42×D4—53no—
136C23×D5C2416yes—
137C22×AGL(1,𝔽5)—212no—
138C22×AGL(1,𝔽5)—212no—
139C22×AGL(1,𝔽5)—212no—
140C22×AGL(1,𝔽5)—212no—
141C22×AGL(1,𝔽5)—212no—
142C22×AGL(1,𝔽5)—46no—
143C22×AGL(1,𝔽5)C2413yes—
144C22×AGL(1,𝔽5)C2416yes—
145C22×AGL(1,𝔽5)C2413yes—
146C22×AGL(1,𝔽5)C2411yescharacteristic
147C22×AGL(1,𝔽5)C2412yes—
148C22×AGL(1,𝔽5)C2411yescharacteristic
149C5×#41—28no—
150C2×C5×Q8C22×C411yescharacteristic
151C2×C5×D4C22×C413yes—
152C2×C5×D4C22×C416yes—
153C2×C5×D4C22×C416yes—
154C22×C4×C5C22×C416yes—
155C2×C22⋊D5C22×C4112yes—
156C2×C22⋊D5C22×C416yes—
157C2×C22⋊D5C22×C4112yes—
158C22×Dic5C22×C416yes—
159#713—28no—
160Q8×D5C2×D414yes—
161Q8×D5#4114yes—
162#711—224no—
163D4×D5—212no—
164D4×D5—26no—
165D4×D5—26no—
166D4×D5—212no—
167D4×D5—46no—
168D4×D5—46no—
169#709—224no—
170C2×D20C22×C416yes—
171C2×D20C22×C413yes—
172C2×D20C22×C416yes—
173C2×C4×D5—212no—
174C2×C4×D5—212no—
175C2×C4×D5C22×C416yes—
176C2×C4×D5C22×C416yes—
177C2×C4×D5C2412yes—
178C2×C4×D5C2413yes—
179C2×C4×D5C2413yes—
180C2×C4×D5C2411yescharacteristic
181C2×Dic10C22×C413yes—
182C22⋊AGL(1,𝔽5)—224no—
183C22⋊AGL(1,𝔽5)—212no—
184C22⋊AGL(1,𝔽5)—212no—
185C22⋊AGL(1,𝔽5)—412no—
186C4⋊AGL(1,𝔽5)—212no—
187C4⋊AGL(1,𝔽5)—26no—
188C4⋊AGL(1,𝔽5)—26no—
189C4⋊AGL(1,𝔽5)—46no—
190C4⋊AGL(1,𝔽5)C2×D4112yes—
191C4⋊AGL(1,𝔽5)#4114yescomplemented
192C4×AGL(1,𝔽5)—24no—
193C4×AGL(1,𝔽5)—212no—
194C4×AGL(1,𝔽5)—26no—
195C4×AGL(1,𝔽5)—212no—
196C4×AGL(1,𝔽5)—26no—
197C4×AGL(1,𝔽5)—26no—
198C4×AGL(1,𝔽5)—43no—
199C4×AGL(1,𝔽5)C2×D4112yes—
200C4×AGL(1,𝔽5)#4114yescomplemented
201C5×C4⋊C4C22×C411yescharacteristic
202C5×C4⋊C4C22×C413yes—
203C5×C22⋊C4C22×C416yes—
204C42×C5C22×C413yes—
205C22⋊Dic5C22×C416yes—
206#685C22×C416yes—
207#685C22×C416yes—
208C4⋊Dic5C22×C413yes—
209C4⋊Dic5C22×C411yescharacteristic
210#683C22×C416yes—
211#683C22×C412yes—
212C4×Dic5C22×C413yes—
213C4×Dic5C22×C413yes—
214C4×Dic5C22×C413yes—
215C22×#41—52no—
216#550—52no—
217#550—53no—
218#550—56no—
219#550—51no—
220#550—53no—
221#550AGL(1,𝔽5)11yescharacteristic, direct product factor
222C2×#127—53no—
223C2×#121—56no—
224C4×#41—1016no—
225C2×C4×Q8—51no—
226C2×C4×Q8—51no—
227C2×C4×Q8—51no—
228C2×C4×Q8—52no—
229C2×C4×D4—53no—
230C2×C4×D4—53no—
231C2×C4×D4—56no—
232C2×C4×D4—56no—
233C2×C4×D4—53no—
234C2×C4×D4—56no—
235C2×#117—56no—
236C22×C42—56no—
237#390—56no—
238#390—56no—
239#390—56no—
240#390—56no—
241#389—56no—
242#388—512no—
243#386—512no—
244#384—53no—
245#380—56no—
246C4×C4⋊C4—53no—
247C4×C4⋊C4—53no—
248C4×C4⋊C4—53no—
249C4×C4⋊C4—53no—
250C4×C4⋊C4—51no—
251C4×C4⋊C4—53no—
252C4×C22⋊C4—56no—
253C4×C22⋊C4—56no—
254C4×C22⋊C4—56no—
255C43—53no—
256C23×C5C23×C416yes—
257C22×D5—26no—
258C22×D5—26no—
259C22×D5—26no—
260C22×D5—26no—
261C22×D5—26no—
262C22×D5—26no—
263C22×D5C23×C416yes—
264C22×D5C2511yescharacteristic
265C2×AGL(1,𝔽5)—22no—
266C2×AGL(1,𝔽5)—21no—
267C2×AGL(1,𝔽5)—23no—
268C2×AGL(1,𝔽5)—21no—
269C2×AGL(1,𝔽5)—23no—
270C2×AGL(1,𝔽5)—22no—
271C2×AGL(1,𝔽5)—26no—
272C2×AGL(1,𝔽5)—23no—
273C2×AGL(1,𝔽5)—23no—
274C2×AGL(1,𝔽5)—26no—
275C2×AGL(1,𝔽5)—23no—
276C2×AGL(1,𝔽5)—26no—
277C2×AGL(1,𝔽5)—424no—
278C2×AGL(1,𝔽5)—424no—
279C2×AGL(1,𝔽5)C22×D416yes—
280C2×AGL(1,𝔽5)C22×D412yes—
281C2×AGL(1,𝔽5)C2×#4112yes—
282C2×AGL(1,𝔽5)C2×#4114yes—
283C2×AGL(1,𝔽5)C2×#4112yes—
284C2×AGL(1,𝔽5)H(5,𝔽2)12yes—
285C5×Q8C4×D414yescomplemented
286C5×D4—212no—
287C5×D4—26no—
288C5×D4—46no—
289C2×C4×C5—212no—
290C2×C4×C5C23×C413yes—
291C2×C4×C5C23×C412yes—
292C2×C4×C5C23×C413yes—
293C2×C4×C5C23×C411yescharacteristic
294C22⋊D5—224no—
295C22⋊D5—212no—
296C22⋊D5—412no—
297C2×Dic5—212no—
298C2×Dic5C23×C413yes—
299C2×Dic5C23×C412yes—
300C2×Dic5C23×C413yes—
301C2×Dic5C23×C411yescharacteristic
302D20—212no—
303D20—26no—
304D20—46no—
305C4×D5—22no—
306C4×D5—22no—
307C4×D5—23no—
308C4×D5—23no—
309C4×D5—212no—
310C4×D5—212no—
311C4×D5C22×D416yes—
312C4×D5C2×#4116yes—
313C4×D5C2×#4112yes—
314C4×D5C2×#4112yes—
315Dic10C4×D4112yescomplemented
316C2×#41—52no—
317C2×#41—56no—
318C2×#41—56no—
319C2×#41—108no—
320C2×#41—108no—
321C2×#41C2×AGL(1,𝔽5)12yescomplemented
322C22×Q8—51no—
323C22×D4—53no—
324C22×D4—56no—
325C22×D4—56no—
326C23×C4—56no—
327C23×C4—56no—
328C23×C4—56no—
329#127—56no—
330#127—56no—
331#127—56no—
332#127—53no—
333#127C2×AGL(1,𝔽5)13yescomplemented
334#121—56no—
335#121—512no—
336#121—56no—
337#121—56no—
338#121—512no—
339#121C2×AGL(1,𝔽5)16yescomplemented
340C4×Q8—58no—
341C4×Q8—51no—
342C4×Q8—53no—
343C4×Q8—53no—
344C4×Q8—108no—
345C4×Q8—104no—
346C4×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
347C4×D4—53no—
348C4×D4—56no—
349C4×D4—53no—
350C4×D4—56no—
351C4×D4—53no—
352C4×D4—1024no—
353C4×D4—1012no—
354C4×D4—1024no—
355C4×D4—1012no—
356C4×D4—2012no—
357C4×D4C2×AGL(1,𝔽5)13yescomplemented
358#117—1024no—
359C2×C4⋊C4—53no—
360C2×C4⋊C4—51no—
361C2×C4⋊C4—51no—
362C2×C4⋊C4—53no—
363C2×C4⋊C4—56no—
364C2×C4⋊C4—53no—
365C2×C4⋊C4—53no—
366C2×C4⋊C4—56no—
367C2×C22⋊C4—56no—
368C2×C22⋊C4—512no—
369C2×C22⋊C4—56no—
370C2×C22⋊C4—56no—
371C2×C22⋊C4—512no—
372C2×C42—51no—
373C2×C42—53no—
374C2×C42—53no—
375C2×C42—56no—
376C2×C42—53no—
377C2×C42—56no—
378C2×C42—53no—
379C2×C42—53no—
380C2×C42—52no—
381C2×C42—53no—
382C2×C42—1024no—
383#95—52no—
384#95—56no—
385#95—56no—
386#95—56no—
387C22×C5—26no—
388C22×C5—26no—
389C22×C5—26no—
390C22×C5C24×C411yescharacteristic
391C2×D5—26no—
392C2×D5—26no—
393C2×D5—26no—
394C2×D5—46no—
395C2×D5—46no—
396C2×D5—46no—
397C2×D5—46no—
398C2×D5C23×D411yescharacteristic
399C2×D5C22×#4111yescharacteristic
400C2×D5C22×#4111yescharacteristic
401C2×D5C22×#4111yescharacteristic
402C2×D5C2×H(5,𝔽2)11yescharacteristic
403C2×D5#58511yescharacteristic
404AGL(1,𝔽5)—24no—
405AGL(1,𝔽5)—26no—
406AGL(1,𝔽5)—22no—
407AGL(1,𝔽5)—46no—
408AGL(1,𝔽5)—43no—
409AGL(1,𝔽5)#55014yesdirect product factor
410C4×C5—22no—
411C4×C5—23no—
412C4×C5C2×C4×D416yes—
413C4×C5C4×#4112yescomplemented
414Dic5—22no—
415Dic5—23no—
416Dic5C2×C4×D416yes—
417Dic5C4×#4112yescomplemented
418C24—56no—
419#41—28no—
420#41—1024no—
421#41—1024no—
422#41—108no—
423C2×Q8—54no—
424C2×Q8—54no—
425C2×Q8—53no—
426C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
427C2×D4—56no—
428C2×D4—512no—
429C2×D4—512no—
430C2×D4—53no—
431C2×D4—56no—
432C2×D4—56no—
433C2×D4—1012no—
434C2×D4—106no—
435C2×D4—106no—
436C2×D4—1012no—
437C2×D4—206no—
438C2×D4—206no—
439C2×D4C22×AGL(1,𝔽5)13yes—
440C2×D4C22×AGL(1,𝔽5)16yes—
441C2×D4C22×AGL(1,𝔽5)16yes—
442C22×C4—51no—
443C22×C4—51no—
444C22×C4—53no—
445C22×C4—52no—
446C22×C4—51no—
447C22×C4—53no—
448C22×C4—56no—
449C22×C4—52no—
450C22×C4—53no—
451C22×C4—56no—
452C22×C4—56no—
453C22×C4—53no—
454C22×C4—56no—
455C22×C4—1012no—
456C22×C4—1012no—
457C22×C4—1012no—
458C22×C4—1012no—
459C22×C4—1012no—
460C22×C4—1012no—
461C22×C4—1012no—
462C22×C4—206no—
463C22×C4C22×AGL(1,𝔽5)16yes—
464C4⋊C4—512no—
465C4⋊C4—54no—
466C4⋊C4—52no—
467C4⋊C4—51no—
468C4⋊C4—56no—
469C4⋊C4—53no—
470C4⋊C4—1012no—
471C4⋊C4—106no—
472C4⋊C4—106no—
473C4⋊C4—206no—
474C4⋊C4C22×AGL(1,𝔽5)11yescharacteristic
475C4⋊C4C22×AGL(1,𝔽5)13yes—
476C22⋊C4—56no—
477C22⋊C4—56no—
478C22⋊C4—56no—
479C22⋊C4—1024no—
480C22⋊C4—1012no—
481C22⋊C4—1012no—
482C22⋊C4—2012no—
483C22⋊C4C22×AGL(1,𝔽5)16yes—
484C42—512no—
485C42—54no—
486C42—53no—
487C42—53no—
488C42—53no—
489C42—104no—
490C42—1012no—
491C42—1012no—
492C42—106no—
493C42—106no—
494C42—106no—
495C42—203no—
496C42C22×AGL(1,𝔽5)13yes—
497C2×C5—46no—
498C2×C5C22×C4×D411yescharacteristic
499C2×C5C2×C4×#4111yescharacteristic
500C2×C5C4×H(5,𝔽2)11yescharacteristic
501D5—46no—
502D5C2×#55011yescharacteristic
503D5D4×#4111yescharacteristic
504D5#348011yescharacteristic
505D5#348311yescharacteristic
506C23—51no—
507C23—56no—
508C23—106no—
509C23—106no—
510C23—106no—
511C23—106no—
512C23—106no—
513C23—106no—
514C23C23×AGL(1,𝔽5)16yes—
515Q8—512no—
516Q8D4×AGL(1,𝔽5)14yescomplemented
517D4—212no—
518D4—26no—
519D4—46no—
520D4—1024no—
521D4—1012no—
522D4—1012no—
523D4—106no—
524D4—206no—
525D4—2012no—
526C2×C4—212no—
527C2×C4—52no—
528C2×C4—52no—
529C2×C4—52no—
530C2×C4—51no—
531C2×C4—53no—
532C2×C4—56no—
533C2×C4—56no—
534C2×C4—52no—
535C2×C4—52no—
536C2×C4—56no—
537C2×C4—52no—
538C2×C4—54no—
539C2×C4—53no—
540C2×C4—52no—
541C2×C4—1012no—
542C2×C4—102no—
543C2×C4—103no—
544C2×C4—103no—
545C2×C4—102no—
546C2×C4—1012no—
547C2×C4—102no—
548C2×C4—101no—
549C2×C4—103no—
550C2×C4—101no—
551C2×C4—103no—
552C2×C4—102no—
553C2×C4—1012no—
554C2×C4—106no—
555C2×C4—103no—
556C2×C4—103no—
557C2×C4—103no—
558C2×C4—106no—
559C2×C4—106no—
560C2×C4—2024no—
561C2×C4—2024no—
562C2×C4C23×AGL(1,𝔽5)13yes—
563C2×C4C23×AGL(1,𝔽5)12yes—
564C2×C4C23×AGL(1,𝔽5)13yes—
565C2×C4C23×AGL(1,𝔽5)11yescharacteristic
566C5C4×#55011yescharacteristic, complemented, Sylow
567C22—26no—
568C22—26no—
569C22—26no—
570C22—51no—
571C22—51no—
572C22—51no—
573C22—51no—
574C22—51no—
575C22—51no—
576C22—106no—
577C22—106no—
578C22—106no—
579C22—206no—
580C22—206no—
581C22—206no—
582C22—206no—
583C22C24×AGL(1,𝔽5)11yescharacteristic
584C4—22no—
585C4—23no—
586C4—54no—
587C4—56no—
588C4—52no—
589C4—104no—
590C4—106no—
591C4—102no—
592C4—102no—
593C4—103no—
594C4—206no—
595C4—203no—
596C4C2×D4×AGL(1,𝔽5)16yes—
597C4#41×AGL(1,𝔽5)12yescomplemented
598C2—46no—
599C2—51no—
600C2—51no—
601C2—51no—
602C2—51no—
603C2—206no—
604C2C22×D4×AGL(1,𝔽5)11yescharacteristic
605C2C2×#41×AGL(1,𝔽5)11yescharacteristic
606C2AGL(1,𝔽5)×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#550C4
prime radicalD5×#550C2
cosocleC22×D5C25
hypercenter#550AGL(1,𝔽5)
hypocenterC5C4×#550
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#41×AGL(1,𝔽5)C2semidirect
3. #10617558C2semidirect
4. #10617369C2semidirect
5. AGL(1,𝔽5)×#127C2semidirect
6. #10617254C2semidirect
7. AGL(1,𝔽5)×#121C2semidirect
8. Q8×C4⋊AGL(1,𝔽5)C2semidirect
9. C4×Q8×AGL(1,𝔽5)C2semidirect
10. #10617181C2semidirect
11. C4×D4×AGL(1,𝔽5)C2semidirect
24. C5×#550C4semidirect
25. #66168C4semidirect
26. #66052C4semidirect
29. #65933C4semidirect
30. #65911C4semidirect
32. #65887C4semidirect
56. C2×C5×#41C2×C4semidirect
59. C2×#713C2×C4semidirect
61. C2×#711C2×C4semidirect
65. C2×#709C2×C4semidirect
73. Q8×AGL(1,𝔽5)D4semidirect
96. C5×#127C2×C4semidirect
97. C5×#121C2×C4semidirect
98. C4×C5×Q8C2×C4semidirect
99. C4×C5×D4C2×C4semidirect
100. Q8×Dic5C2×C4semidirect
101. #4086C2×C4semidirect
102. #4086C2×C4semidirect
103. #4086C2×C4semidirect
104. #4085C2×C4semidirect
105. #4084C2×C4semidirect
106. D4×Dic5C2×C4semidirect
107. #4076C2×C4semidirect
108. C4×C22⋊D5C2×C4semidirect
109. #4041C2×C4semidirect
110. #4039C2×C4semidirect
113. #4033C2×C4semidirect
114. #4030C2×C4semidirect
115. #4027C2×C4semidirect
117. #4020C2×C4semidirect
118. C4×D20C2×C4semidirect
120. C4×Dic10C2×C4semidirect
191. C4⋊AGL(1,𝔽5)#41semidirect
200. C4×AGL(1,𝔽5)#41semidirect
221. #550AGL(1,𝔽5)direct (N × H)
285. C5×Q8C4×D4semidirect
315. Dic10C4×D4semidirect
321. C2×#41C2×AGL(1,𝔽5)semidirect
333. #127C2×AGL(1,𝔽5)semidirect
339. #121C2×AGL(1,𝔽5)semidirect
346. C4×Q8C2×AGL(1,𝔽5)semidirect
357. C4×D4C2×AGL(1,𝔽5)semidirect
409. AGL(1,𝔽5)#550direct (N × H)
413. C4×C5C4×#41semidirect
417. Dic5C4×#41semidirect
516. Q8D4×AGL(1,𝔽5)semidirect
566. C5C4×#550semidirect
597. 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
D5×#5502
#106175582
#106173692
AGL(1,𝔽5)×#1272
#106172542
AGL(1,𝔽5)×#1212
Q8×C4⋊AGL(1,𝔽5)2
C4×Q8×AGL(1,𝔽5)2
#106171812
C4×D4×AGL(1,𝔽5)2
C4×#5505