Finite Group Databasebeta

← AGL(1,𝔽5)×#555 #13044008

Subgroups — AGL(1,𝔽5)×#555 #13044008

Order 1280.

2564 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#555C211yesmaximal, characteristic
2#10617389C211yesmaximal, characteristic, complemented
3AGL(1,𝔽5)×C4⋊Q8C211yesmaximal, characteristic, complemented
4#10617327C214yesmaximal, complemented
5AGL(1,𝔽5)×#124C214yesmaximal, complemented
6#10617254C214yesmaximal, complemented
7AGL(1,𝔽5)×#121C214yesmaximal, complemented
8#10617181C212yesmaximal, complemented
9C4×D4×AGL(1,𝔽5)C212yesmaximal, complemented
10#10617133C214yesmaximal, complemented
11AGL(1,𝔽5)×#117C214yesmaximal, complemented
12C2×Q8×AGL(1,𝔽5)C2212yes—
13C2×D4×AGL(1,𝔽5)C2212yes—
14C2×D4×AGL(1,𝔽5)C2212yes—
15C2×D4×AGL(1,𝔽5)C2214yes—
16C2×#4130C2214yes—
17C22×C4×AGL(1,𝔽5)C2214yes—
18C5×#555C411yescharacteristic, complemented
19#66068C411yescharacteristic, complemented
20D5×C4⋊Q8C2211yescharacteristic
21D5×#124C2214yes—
22#66004C414yescomplemented
23#65950C414yescomplemented
24D5×#121C2214yes—
25#65897C412yescomplemented
26C4×D4×D5C2212yes—
27#65866C414yescomplemented
28D5×#117C2214yes—
29(C2×AGL(1,𝔽5))⋊Q8C2212yes—
30(C2×AGL(1,𝔽5))⋊Q8C2214yes—
31#65780C2214yes—
32#65780C2214yes—
33#65779C2218yes—
34#65765C2214yes—
35C4×C22⋊AGL(1,𝔽5)C2214yes—
36#65712C2214yes—
37#65712C2214yes—
38C4⋊C4×AGL(1,𝔽5)C2212yes—
39C4⋊C4×AGL(1,𝔽5)C2214yes—
40C4⋊C4×AGL(1,𝔽5)C2214yes—
41C4⋊C4×AGL(1,𝔽5)C2214yes—
42C4⋊C4×AGL(1,𝔽5)C2212yes—
43#65700C2218yes—
44#65700C2218yes—
45#65700C2218yes—
46C22⋊C4×AGL(1,𝔽5)C2218yes—
47C22⋊C4×AGL(1,𝔽5)C2218yes—
48C22⋊C4×AGL(1,𝔽5)C2214yes—
49C22⋊C4×AGL(1,𝔽5)C2214yes—
50#65689C2214yes—
51#65688C2211yescharacteristic
52C4×C4⋊AGL(1,𝔽5)C2212yes—
53#65686C2218yes—
54C42×AGL(1,𝔽5)C2214yes—
55C42×AGL(1,𝔽5)C2211yescharacteristic
56C4×#555—51nomaximal, Sylow
57C23×AGL(1,𝔽5)C2314yes—
58C23×AGL(1,𝔽5)C2314yes—
59C2×Q8×D5C2312yes—
60C2×D4×D5C2312yes—
61C2×D4×D5C2314yes—
62C22×C4×D5C2314yes—
63C2×C22⋊AGL(1,𝔽5)C2318yes—
64C2×C22⋊AGL(1,𝔽5)C2314yes—
65C2×C22⋊AGL(1,𝔽5)C2314yes—
66C2×C22⋊AGL(1,𝔽5)C2318yes—
67Q8×AGL(1,𝔽5)—44no—
68D4×AGL(1,𝔽5)—28no—
69D4×AGL(1,𝔽5)—28no—
70D4×AGL(1,𝔽5)—48no—
71#4130—216no—
72C2×C4⋊AGL(1,𝔽5)C2312yes—
73C2×C4⋊AGL(1,𝔽5)C2314yes—
74C2×C4⋊AGL(1,𝔽5)C2312yes—
75C2×C4⋊AGL(1,𝔽5)C2314yes—
76C2×C4⋊AGL(1,𝔽5)C2314yes—
77C2×C4⋊AGL(1,𝔽5)C2312yes—
78C2×C4×AGL(1,𝔽5)—216no—
79C2×C4×AGL(1,𝔽5)C2314yes—
80C2×C4×AGL(1,𝔽5)C2318yes—
81C2×C4×AGL(1,𝔽5)C2311yescharacteristic
82C2×C4×AGL(1,𝔽5)C2314yes—
83C2×C4×AGL(1,𝔽5)C2312yes—
84C2×C4×AGL(1,𝔽5)C2314yes—
85C2×C4×AGL(1,𝔽5)C2314yes—
86C2×C4×AGL(1,𝔽5)C2311yescharacteristic
87C2×C4×AGL(1,𝔽5)C2314yes—
88C2×C4×AGL(1,𝔽5)C2312yes—
89C5×C4⋊Q8C2×C411yescharacteristic, complemented
90C5×#124C2×C414yescomplemented
91C5×#121C2×C414yescomplemented
92C4×C5×D4C2×C412yescomplemented
93C5×#117C2×C414yescomplemented
94#4093C2×C414yescomplemented
95#4090C2×C412yescomplemented
96#4085C2×C418yescomplemented
97#4084C2×C414yescomplemented
98#4082C2×C414yescomplemented
99D4×Dic5C2×C412yescomplemented
100#4076C2×C414yescomplemented
101C4×C22⋊D5C2×C414yescomplemented
102#4072C2×C414yescomplemented
103#4041C2×C414yescomplemented
104#4039C2×C412yescomplemented
105#4038C2×C414yescomplemented
106#4038C2×C414yescomplemented
107D5×C4⋊C4C2314yes—
108D5×C4⋊C4C2312yes—
109#4034C2×C414yescomplemented
110#4031C2×C418yescomplemented
111#4031C2×C418yescomplemented
112#4030C2×C418yescomplemented
113#4027C2×C414yescomplemented
114D5×C22⋊C4C2318yes—
115D5×C22⋊C4C2314yes—
116#4023C2×C418yescomplemented
117#4021C2×C414yescomplemented
118C4×D20C2×C412yescomplemented
119#4018C2×C418yescomplemented
120C42×D5C2311yescharacteristic
121C42×D5C2314yes—
122#4015C2×C411yescharacteristic, complemented
123(C2×AGL(1,𝔽5))⋊C4C2314yes—
124(C2×AGL(1,𝔽5))⋊C4C2318yes—
125(C2×AGL(1,𝔽5))⋊C4C2318yes—
126(C2×AGL(1,𝔽5))⋊C4C2318yes—
127(C2×AGL(1,𝔽5))⋊C4C2314yes—
128(C2×AGL(1,𝔽5))⋊C4C2314yes—
129C2×#555—51no—
130#2372—54no—
131#2369—51no—
132#2363—54no—
133#2354—52no—
134#2346—54no—
135C4×C4⋊Q8—51no—
136C4×#124—54no—
137C4×#121—54no—
138C42×D4—52no—
139C4×#117—54no—
140C23×D5C2414yes—
141C22×AGL(1,𝔽5)—28no—
142C22×AGL(1,𝔽5)—28no—
143C22×AGL(1,𝔽5)—28no—
144C22×AGL(1,𝔽5)—28no—
145C22×AGL(1,𝔽5)—28no—
146C22×AGL(1,𝔽5)—44no—
147C22×AGL(1,𝔽5)C2414yes—
148C22×AGL(1,𝔽5)C2411yescharacteristic
149C22×AGL(1,𝔽5)C2414yes—
150C22×AGL(1,𝔽5)C2414yes—
151C22×AGL(1,𝔽5)C2412yes—
152C22×AGL(1,𝔽5)C2411yescharacteristic
153C2×C5×Q8C22×C412yes—
154C2×C5×D4C22×C412yes—
155C2×C5×D4C22×C414yes—
156C22×C4×C5C22×C414yes—
157C2×C22⋊D5C22×C414yes—
158C2×C22⋊D5C22×C418yes—
159C22×Dic5C22×C414yes—
160Q8×D5—42no—
161Q8×D5—42no—
162D4×D5—24no—
163D4×D5—24no—
164D4×D5—44no—
165D4×D5—44no—
166C2×D20C22×C412yes—
167C2×D20C22×C414yes—
168C2×C4×D5—28no—
169C2×C4×D5—28no—
170C2×C4×D5C22×C414yes—
171C2×C4×D5C22×C414yes—
172C2×C4×D5C2414yes—
173C2×C4×D5C2414yes—
174C2×C4×D5C2411yescharacteristic
175C2×C4×D5C2412yes—
176C2×Dic10C22×C412yes—
177C2×Dic10C22×C414yes—
178C22⋊AGL(1,𝔽5)—216no—
179C22⋊AGL(1,𝔽5)—28no—
180C22⋊AGL(1,𝔽5)—28no—
181C22⋊AGL(1,𝔽5)—48no—
182C4⋊AGL(1,𝔽5)—28no—
183C4⋊AGL(1,𝔽5)—24no—
184C4⋊AGL(1,𝔽5)—44no—
185C4⋊AGL(1,𝔽5)—44no—
186C4⋊AGL(1,𝔽5)—42no—
187C4⋊AGL(1,𝔽5)#4118yes—
188C4×AGL(1,𝔽5)—28no—
189C4×AGL(1,𝔽5)—28no—
190C4×AGL(1,𝔽5)—216no—
191C4×AGL(1,𝔽5)—28no—
192C4×AGL(1,𝔽5)—22no—
193C4×AGL(1,𝔽5)—28no—
194C4×AGL(1,𝔽5)—24no—
195C4×AGL(1,𝔽5)—44no—
196C4×AGL(1,𝔽5)—41no—
197C4×AGL(1,𝔽5)#4118yes—
198C5×C4⋊C4C22×C412yes—
199C5×C4⋊C4C22×C414yes—
200C5×C22⋊C4C22×C418yes—
201C5×C22⋊C4C22×C414yes—
202C42×C5C22×C414yes—
203C42×C5C22×C411yescharacteristic
204C22⋊Dic5C22×C418yes—
205C22⋊Dic5C22×C414yes—
206#685C22×C418yes—
207#685C22×C418yes—
208#685C22×C414yes—
209#685C22×C414yes—
210C4⋊Dic5C22×C414yes—
211C4⋊Dic5C22×C412yes—
212#683C22×C414yes—
213#683C22×C418yes—
214C4×Dic5C22×C418yes—
215C4×Dic5C22×C414yes—
216C4×Dic5C22×C411yescharacteristic
217C4×Dic5C22×C412yes—
218#555—51no—
219#555—54no—
220#555—54no—
221#555—52no—
222#555—54no—
223#555AGL(1,𝔽5)11yescharacteristic, direct product factor
224C2×C4⋊Q8—51no—
225C2×#124—54no—
226C2×#121—54no—
227C2×C4×Q8—52no—
228C2×C4×D4—52no—
229C2×C4×D4—52no—
230C2×C4×D4—52no—
231C2×C4×D4—54no—
232C2×#117—54no—
233C2×#117—54no—
234C22×C42—54no—
235#391—52no—
236#391—54no—
237#390—54no—
238#390—54no—
239#389—54no—
240#389—54no—
241#388—58no—
242#388—58no—
243#388—58no—
244#386—58no—
245#384—51no—
246#382—54no—
247#380—54no—
248C4×C4⋊C4—54no—
249C4×C4⋊C4—52no—
250C4×C4⋊C4—54no—
251C4×C4⋊C4—52no—
252C4×C4⋊C4—54no—
253C4×C4⋊C4—52no—
254C4×C22⋊C4—54no—
255C4×C22⋊C4—58no—
256C4×C22⋊C4—54no—
257C4×C22⋊C4—58no—
258C4×C22⋊C4—54no—
259#376—58no—
260C43—51no—
261C43—54no—
262C23×C5C23×C414yes—
263C22×D5—24no—
264C22×D5—24no—
265C22×D5—24no—
266C22×D5—24no—
267C22×D5—24no—
268C22×D5—24no—
269C22×D5C23×C414yes—
270C22×D5C2511yescharacteristic
271C2×AGL(1,𝔽5)—24no—
272C2×AGL(1,𝔽5)—22no—
273C2×AGL(1,𝔽5)—24no—
274C2×AGL(1,𝔽5)—22no—
275C2×AGL(1,𝔽5)—24no—
276C2×AGL(1,𝔽5)—28no—
277C2×AGL(1,𝔽5)—22no—
278C2×AGL(1,𝔽5)—24no—
279C2×AGL(1,𝔽5)—21no—
280C2×AGL(1,𝔽5)—24no—
281C2×AGL(1,𝔽5)—24no—
282C2×AGL(1,𝔽5)—416no—
283C2×AGL(1,𝔽5)—416no—
284C2×AGL(1,𝔽5)C2×#4114yes—
285C2×AGL(1,𝔽5)C2×#4118yes—
286C2×AGL(1,𝔽5)C2×#4114yes—
287C2×AGL(1,𝔽5)H(5,𝔽2)12yes—
288C5×Q8—42no—
289C5×D4—24no—
290C5×D4—44no—
291C2×C4×C5—28no—
292C2×C4×C5C23×C414yes—
293C2×C4×C5C23×C414yes—
294C2×C4×C5C23×C411yescharacteristic
295C2×C4×C5C23×C412yes—
296C22⋊D5—28no—
297C22⋊D5—48no—
298C2×Dic5—28no—
299C2×Dic5C23×C414yes—
300C2×Dic5C23×C414yes—
301C2×Dic5C23×C411yescharacteristic
302C2×Dic5C23×C412yes—
303D20—24no—
304D20—44no—
305C4×D5—24no—
306C4×D5—24no—
307C4×D5—24no—
308C4×D5—21no—
309C4×D5—24no—
310C4×D5—21no—
311C4×D5—28no—
312C4×D5—28no—
313C4×D5C2×#4114yes—
314C4×D5C2×#4114yes—
315Dic10—44no—
316Dic10—42no—
317C22×Q8—52no—
318C22×D4—52no—
319C22×D4—54no—
320C23×C4—54no—
321C23×C4—54no—
322C23×C4—54no—
323C4⋊Q8—52no—
324C4⋊Q8—54no—
325C4⋊Q8—51no—
326C4⋊Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
327#124—54no—
328#124—54no—
329#124—58no—
330#124—58no—
331#124—54no—
332#124C2×AGL(1,𝔽5)14yescomplemented
333#121—54no—
334#121—58no—
335#121—54no—
336#121—54no—
337#121—58no—
338#121C2×AGL(1,𝔽5)14yescomplemented
339C4×Q8—204no—
340C4×D4—52no—
341C4×D4—54no—
342C4×D4—52no—
343C4×D4—54no—
344C4×D4—52no—
345C4×D4—108no—
346C4×D4—108no—
347C4×D4—208no—
348C4×D4C2×AGL(1,𝔽5)12yescomplemented
349#117—54no—
350#117—54no—
351#117—54no—
352#117—58no—
353#117—58no—
354#117—1016no—
355#117C2×AGL(1,𝔽5)14yescomplemented
356C2×C4⋊C4—52no—
357C2×C4⋊C4—52no—
358C2×C4⋊C4—54no—
359C2×C4⋊C4—54no—
360C2×C4⋊C4—52no—
361C2×C4⋊C4—54no—
362C2×C4⋊C4—54no—
363C2×C4⋊C4—52no—
364C2×C22⋊C4—58no—
365C2×C22⋊C4—54no—
366C2×C22⋊C4—58no—
367C2×C22⋊C4—54no—
368C2×C22⋊C4—54no—
369C2×C22⋊C4—58no—
370C2×C42—52no—
371C2×C42—54no—
372C2×C42—51no—
373C2×C42—58no—
374C2×C42—54no—
375C2×C42—52no—
376C2×C42—51no—
377C2×C42—54no—
378C2×C42—54no—
379C2×C42—54no—
380C2×C42—51no—
381C2×C42—54no—
382C2×C42—1016no—
383#95—54no—
384#95—58no—
385#95—58no—
386#95—58no—
387#95—54no—
388#95—54no—
389C22×C5—24no—
390C22×C5—24no—
391C22×C5—24no—
392C22×C5C24×C411yescharacteristic
393C2×D5—24no—
394C2×D5—24no—
395C2×D5—24no—
396C2×D5—44no—
397C2×D5—44no—
398C2×D5—44no—
399C2×D5—44no—
400C2×D5C22×#4112yes—
401C2×D5C22×#4112yes—
402C2×D5C2×H(5,𝔽2)11yescharacteristic
403C2×D5#58511yescharacteristic
404AGL(1,𝔽5)—24no—
405AGL(1,𝔽5)—28no—
406AGL(1,𝔽5)—44no—
407AGL(1,𝔽5)—44no—
408AGL(1,𝔽5)—41no—
409AGL(1,𝔽5)#55514yesdirect product factor
410C4×C5—24no—
411C4×C5—21no—
412C4×C5—24no—
413C4×C5C4×#4114yes—
414Dic5—24no—
415Dic5—21no—
416Dic5—24no—
417Dic5C4×#4114yes—
418C24—54no—
419C2×Q8—54no—
420C2×Q8—52no—
421C2×Q8—202no—
422C2×Q8—202no—
423C2×Q8C22×AGL(1,𝔽5)12yes—
424C2×D4—54no—
425C2×D4—58no—
426C2×D4—52no—
427C2×D4—54no—
428C2×D4—104no—
429C2×D4—104no—
430C2×D4—204no—
431C2×D4—204no—
432C2×D4C22×AGL(1,𝔽5)12yes—
433C2×D4C22×AGL(1,𝔽5)14yes—
434C22×C4—51no—
435C22×C4—52no—
436C22×C4—52no—
437C22×C4—54no—
438C22×C4—54no—
439C22×C4—54no—
440C22×C4—51no—
441C22×C4—54no—
442C22×C4—54no—
443C22×C4—54no—
444C22×C4—54no—
445C22×C4—51no—
446C22×C4—54no—
447C22×C4—108no—
448C22×C4—108no—
449C22×C4—108no—
450C22×C4—108no—
451C22×C4—108no—
452C22×C4—108no—
453C22×C4—108no—
454C22×C4—204no—
455C22×C4C22×AGL(1,𝔽5)14yes—
456C4⋊C4—58no—
457C4⋊C4—54no—
458C4⋊C4—52no—
459C4⋊C4—58no—
460C4⋊C4—54no—
461C4⋊C4—108no—
462C4⋊C4—104no—
463C4⋊C4—204no—
464C4⋊C4—204no—
465C4⋊C4—202no—
466C4⋊C4C22×AGL(1,𝔽5)12yes—
467C4⋊C4C22×AGL(1,𝔽5)14yes—
468C22⋊C4—58no—
469C22⋊C4—54no—
470C22⋊C4—58no—
471C22⋊C4—58no—
472C22⋊C4—54no—
473C22⋊C4—54no—
474C22⋊C4—1016no—
475C22⋊C4—108no—
476C22⋊C4—108no—
477C22⋊C4—208no—
478C22⋊C4C22×AGL(1,𝔽5)18yes—
479C22⋊C4C22×AGL(1,𝔽5)14yes—
480C42—58no—
481C42—54no—
482C42—58no—
483C42—51no—
484C42—52no—
485C42—108no—
486C42—108no—
487C42—108no—
488C42—1016no—
489C42—104no—
490C42—108no—
491C42—102no—
492C42—204no—
493C42—201no—
494C42C22×AGL(1,𝔽5)14yes—
495C42C22×AGL(1,𝔽5)11yescharacteristic
496C2×C5—44no—
497C2×C5C2×C4×#4112yes—
498C2×C5C4×H(5,𝔽2)11yescharacteristic
499D5—44no—
500D5C2×#55511yescharacteristic
501D5#347512yes—
502D5#348311yescharacteristic
503C23—51no—
504C23—54no—
505C23—104no—
506C23—104no—
507C23—104no—
508C23—104no—
509C23—104no—
510C23—104no—
511C23C23×AGL(1,𝔽5)14yes—
512Q8—42no—
513Q8—204no—
514Q8—202no—
515D4—24no—
516D4—44no—
517D4—108no—
518D4—104no—
519D4—204no—
520D4—208no—
521C2×C4—28no—
522C2×C4—54no—
523C2×C4—52no—
524C2×C4—52no—
525C2×C4—54no—
526C2×C4—54no—
527C2×C4—54no—
528C2×C4—58no—
529C2×C4—54no—
530C2×C4—51no—
531C2×C4—54no—
532C2×C4—108no—
533C2×C4—104no—
534C2×C4—104no—
535C2×C4—104no—
536C2×C4—101no—
537C2×C4—104no—
538C2×C4—101no—
539C2×C4—108no—
540C2×C4—104no—
541C2×C4—102no—
542C2×C4—104no—
543C2×C4—102no—
544C2×C4—108no—
545C2×C4—104no—
546C2×C4—102no—
547C2×C4—108no—
548C2×C4—104no—
549C2×C4—101no—
550C2×C4—104no—
551C2×C4—104no—
552C2×C4—2016no—
553C2×C4—2016no—
554C2×C4C23×AGL(1,𝔽5)14yes—
555C2×C4C23×AGL(1,𝔽5)11yescharacteristic
556C2×C4C23×AGL(1,𝔽5)14yes—
557C2×C4C23×AGL(1,𝔽5)12yes—
558C5C4×#55511yescharacteristic, complemented, Sylow
559C22—24no—
560C22—24no—
561C22—24no—
562C22—52no—
563C22—52no—
564C22—51no—
565C22—51no—
566C22—104no—
567C22—104no—
568C22—104no—
569C22—204no—
570C22—204no—
571C22—204no—
572C22—204no—
573C22C24×AGL(1,𝔽5)11yescharacteristic
574C4—24no—
575C4—24no—
576C4—21no—
577C4—54no—
578C4—54no—
579C4—104no—
580C4—108no—
581C4—104no—
582C4—104no—
583C4—101no—
584C4—204no—
585C4—201no—
586C4—204no—
587C4#41×AGL(1,𝔽5)14yes—
588C2—44no—
589C2—51no—
590C2—52no—
591C2—51no—
592C2—204no—
593C2C2×#41×AGL(1,𝔽5)12yes—
594C2AGL(1,𝔽5)×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#555C4
prime radicalD5×#555C2
cosocleC22×D5C25
hypercenter#555AGL(1,𝔽5)
hypocenterC5C4×#555
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #555

Complements

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

NH ≅ G/Ntype
2. #10617389C2semidirect
3. AGL(1,𝔽5)×C4⋊Q8C2semidirect
4. #10617327C2semidirect
5. AGL(1,𝔽5)×#124C2semidirect
6. #10617254C2semidirect
7. AGL(1,𝔽5)×#121C2semidirect
8. #10617181C2semidirect
9. C4×D4×AGL(1,𝔽5)C2semidirect
10. #10617133C2semidirect
11. AGL(1,𝔽5)×#117C2semidirect
18. C5×#555C4semidirect
19. #66068C4semidirect
22. #66004C4semidirect
23. #65950C4semidirect
25. #65897C4semidirect
27. #65866C4semidirect
89. C5×C4⋊Q8C2×C4semidirect
90. C5×#124C2×C4semidirect
91. C5×#121C2×C4semidirect
92. C4×C5×D4C2×C4semidirect
93. C5×#117C2×C4semidirect
94. #4093C2×C4semidirect
95. #4090C2×C4semidirect
96. #4085C2×C4semidirect
97. #4084C2×C4semidirect
98. #4082C2×C4semidirect
99. D4×Dic5C2×C4semidirect
100. #4076C2×C4semidirect
101. C4×C22⋊D5C2×C4semidirect
102. #4072C2×C4semidirect
103. #4041C2×C4semidirect
104. #4039C2×C4semidirect
105. #4038C2×C4semidirect
106. #4038C2×C4semidirect
109. #4034C2×C4semidirect
110. #4031C2×C4semidirect
111. #4031C2×C4semidirect
112. #4030C2×C4semidirect
113. #4027C2×C4semidirect
116. #4023C2×C4semidirect
117. #4021C2×C4semidirect
118. C4×D20C2×C4semidirect
119. #4018C2×C4semidirect
122. #4015C2×C4semidirect
223. #555AGL(1,𝔽5)direct (N × H)
326. C4⋊Q8C2×AGL(1,𝔽5)semidirect
332. #124C2×AGL(1,𝔽5)semidirect
338. #121C2×AGL(1,𝔽5)semidirect
348. C4×D4C2×AGL(1,𝔽5)semidirect
355. #117C2×AGL(1,𝔽5)semidirect
409. AGL(1,𝔽5)#555direct (N × H)
558. C5C4×#555semidirect

Maximal subgroups

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

subgroupindex
D5×#5552
#106173892
AGL(1,𝔽5)×C4⋊Q82
#106173272
AGL(1,𝔽5)×#1242
#106172542
AGL(1,𝔽5)×#1212
#106171812
C4×D4×AGL(1,𝔽5)2
#106171332
AGL(1,𝔽5)×#1172
C4×#5555