Finite Group Databasebeta

← AGL(1,𝔽5)×#912 #14416301

Subgroups — AGL(1,𝔽5)×#912 #14416301

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1AGL(1,𝔽5)×#237C212yesmaximal, complemented
2D5×#912C211yesmaximal, characteristic
3D8×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
4C3×D8×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
5#11751947C212yesmaximal, complemented
6#11751945C212yesmaximal, complemented
7AGL(1,𝔽5)×#214C212yesmaximal, complemented
8#11751669C211yesmaximal, characteristic, complemented
9AGL(1,𝔽5)×Dic12C211yesmaximal, characteristic, complemented
10#11751658C211yesmaximal, characteristic, complemented
11D3×C8×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
12AGL(1,𝔽5)×#135—31nomaximal, Hall
13D5×#237C2212yes—
14D4×ΓL(1,𝔽16)C2212yes—
15C3×D4×AGL(1,𝔽5)C2212yes—
16#67⋊AGL(1,𝔽5)—22no—
17AGL(1,𝔽5)×#67—22no—
18#91923—22no—
19C2×Dic3×AGL(1,𝔽5)—22no—
20C4×D3×AGL(1,𝔽5)C2211yescharacteristic
21D3×D5⋊C8C2211yescharacteristic
22ΓL(1,𝔽16)⋊Q8C2212yes—
23#91907C2212yes—
24AGL(1,𝔽5)×Dic6C2212yes—
25#91801C411yescharacteristic, complemented
26C5×#912C411yescharacteristic, complemented
27C3×D5×D8C2211yescharacteristic
28#91497C412yescomplemented
29#91493C412yescomplemented
30D5×#214C2212yes—
31#91277C411yescharacteristic, complemented
32#91273C411yescharacteristic, complemented
33D5×Dic12C2211yescharacteristic
34D3×C8×D5C2211yescharacteristic
35#91236C2212yes—
36#91223C2211yescharacteristic
37C8×ΓL(1,𝔽16)C2211yescharacteristic
38C3×#4007C2212yes—
39C3×#3994C2211yescharacteristic
40C3×C8×AGL(1,𝔽5)C2211yescharacteristic
41#91159C2212yes—
42#91154C2212yes—
43#91153C2212yes—
44ΓL(1,𝔽16)⋊C8C2211yescharacteristic
45AGL(1,𝔽5)×C3⋊C8C2211yescharacteristic
46C4×#912—51nomaximal, Hall
47#41×AGL(1,𝔽5)—32no—
48D5×#135—31no—
49#65794—32no—
50Q16×AGL(1,𝔽5)—31no—
51Q16×AGL(1,𝔽5)—31no—
52SD16×AGL(1,𝔽5)—32no—
53SD16×AGL(1,𝔽5)—32no—
54D8×AGL(1,𝔽5)—31no—
55D8×AGL(1,𝔽5)D311yescharacteristic, complemented
56#65721—31no—
57C2×C8×AGL(1,𝔽5)—31no—
58C22×ΓL(1,𝔽16)—22no—
59C22×C3×AGL(1,𝔽5)—22no—
60C2×D3×AGL(1,𝔽5)D411yescharacteristic
61C2×D3×AGL(1,𝔽5)D411yescharacteristic
62#6819C2×C412yescomplemented
63C5×#237C2×C412yescomplemented
64C3×D4×D5C2312yes—
65D5×#67—22no—
66#6780—22no—
67#6779—22no—
68C2×D5×Dic3—22no—
69C4×D3×D5C2311yescharacteristic
70#6766C2×C412yescomplemented
71#6765C2×C412yescomplemented
72D5×Dic6C2312yes—
73#6763—22no—
74C4⋊ΓL(1,𝔽16)C2312yes—
75C4×ΓL(1,𝔽16)C2311yescharacteristic
76D5⋊(C3⋊C8)C2311yescharacteristic
77C3×C22⋊AGL(1,𝔽5)—22no—
78C3×C4⋊AGL(1,𝔽5)C2312yes—
79C3×C4×AGL(1,𝔽5)C2311yescharacteristic
80C3×D5⋊C8C2311yescharacteristic
81#6738—21no—
82D3×#170—21no—
83Dic3⋊AGL(1,𝔽5)—22no—
84Dic3⋊AGL(1,𝔽5)—22no—
85(C2×D3)⋊AGL(1,𝔽5)—22no—
86Dic3×AGL(1,𝔽5)—22no—
87Dic3×AGL(1,𝔽5)—22no—
88Dic3×AGL(1,𝔽5)—22no—
89Dic3×AGL(1,𝔽5)D411yescharacteristic
90Dic3×AGL(1,𝔽5)D411yescharacteristic
91C3×C5×D8C2×C411yescharacteristic, complemented
92#6716C2×C412yescomplemented
93Dic60C2×C411yescharacteristic, complemented
94C8×D15C2×C411yescharacteristic, complemented
95C5×#214C2×C412yescomplemented
96C5×Dic12C2×C411yescharacteristic, complemented
97C5×D3×C8C2×C411yescharacteristic, complemented
98C3×#686C2×C412yescomplemented
99C3×D40C2×C411yescharacteristic, complemented
100C3×C8×D5C2311yescharacteristic
101#6663C2×C412yescomplemented
102#6657C2×C412yescomplemented
103#6655C2×C412yescomplemented
104#6648C2×C411yescharacteristic, complemented
105D3×#168C2×C411yescharacteristic, complemented
106D5×C3⋊C8C2311yescharacteristic
107C2×#912—51no—
108C4×#237—52no—
109C3×C4×D8—51no—
110Dic3×D8—51no—
111C4×#214—52no—
112#4880—51no—
113#4873—51no—
114#4772—52no—
115#4758—52no—
116C4×Dic12—51no—
117C4×D3×C8—51no—
118D5×#41—32no—
119Q8×AGL(1,𝔽5)—32no—
120Q8×AGL(1,𝔽5)—32no—
121D4×AGL(1,𝔽5)—32no—
122D4×AGL(1,𝔽5)—62no—
123D4×AGL(1,𝔽5)—62no—
124D4×AGL(1,𝔽5)C2×D312yes—
125#4130—32no—
126#4130—62no—
127C2×C4×AGL(1,𝔽5)—31no—
128C2×C4×AGL(1,𝔽5)—62no—
129C2×D5⋊C8—31no—
130C5×#135—31no—
131#4096—32no—
132#4065—31no—
133D5×Q16—31no—
134#4062—32no—
135D5×SD16—32no—
136#4058—31no—
137D5×D8C2×D311yescharacteristic
138#4050—31no—
139C2×C8×D5—31no—
140#4009—32no—
141#4009—32no—
142#4007—32no—
143#4007C2×D312yes—
144#3994—31no—
145#3994C2×D311yescharacteristic
146#3993—32no—
147C8×AGL(1,𝔽5)—31no—
148C8×AGL(1,𝔽5)—31no—
149C8×AGL(1,𝔽5)—31no—
150C8×AGL(1,𝔽5)C2×D311yescharacteristic
151C4×#135—151noSylow
152C22×C3×D5—22no—
153C2×D3×D5C2×D411yescharacteristic
154C2×ΓL(1,𝔽16)—22no—
155C2×ΓL(1,𝔽16)—44no—
156C2×ΓL(1,𝔽16)C2×D411yescharacteristic
157C2×ΓL(1,𝔽16)C2×D411yescharacteristic
158C2×C3×AGL(1,𝔽5)—22no—
159C2×C3×AGL(1,𝔽5)—44no—
160C2×C3×AGL(1,𝔽5)C2×D411yescharacteristic
161C2×C3×AGL(1,𝔽5)C2×D411yescharacteristic
162D3×AGL(1,𝔽5)—22no—
163D3×AGL(1,𝔽5)—22no—
164C3×C5×D4C22×C412yes—
165#1220—22no—
166C2×Dic15—22no—
167C4×D15C22×C411yescharacteristic
168Dic30C22×C412yes—
169C5×#67—22no—
170C2×C5×Dic3—22no—
171C4×C5×D3C22×C411yescharacteristic
172C5×Dic6C22×C412yes—
173C3×C22⋊D5—22no—
174C3×D20C22×C412yes—
175C3×C4×D5C2411yescharacteristic
176#1204—22no—
177#1202—22no—
178#1201—22no—
179#1200#4111yescharacteristic
180D3×Dic5#4111yescharacteristic
181D5×Dic3—22no—
182D5×Dic3—22no—
183D5×Dic3—22no—
184D5×Dic3C2×D411yescharacteristic
185C3⋊#170—21no—
186C3×#170—21no—
187C3×C5×C8C22×C411yescharacteristic
188C3⋊#168C22×C411yescharacteristic
189C3×#168C22×C411yescharacteristic
190C5×C3⋊C8C22×C411yescharacteristic
191C2×#237—52no—
192C2×C3×D8—51no—
193C3×C4×D4—52no—
194D4×Dic3—52no—
195C2×#214—52no—
196C4×#67—102no—
197C2×C4×Dic3—102no—
198#912—52no—
199#912—51no—
200#912—52no—
201#912—51no—
202#912—51no—
203#912AGL(1,𝔽5)11yescharacteristic, direct product factor
204C2×Dic12—51no—
205C2×D3×C8—51no—
206C2×D3×C8—51no—
207#892—52no—
208#887—52no—
209#67⋊C4—102no—
210#877—102no—
211C42×D3—51no—
212C4×Dic6—52no—
213C3×#107—51no—
214C3×#102—52no—
215C3×C4×C8—51no—
216#832—52no—
217#818—51no—
218#816—52no—
219C8×Dic3—51no—
220C8×Dic3—51no—
221#810—52no—
222#808—52no—
223C4×C3⋊C8—51no—
224C22×AGL(1,𝔽5)—22no—
225C22×AGL(1,𝔽5)—31no—
226C22×AGL(1,𝔽5)—31no—
227C22×AGL(1,𝔽5)—62no—
228C5×#41—32no—
229#713—32no—
230Q8×D5—32no—
231#711—32no—
232#711—62no—
233D4×D5—62no—
234D4×D5C22×D312yes—
235#709—32no—
236#709—62no—
237C2×C4×D5—31no—
238C2×C4×D5—62no—
239C22⋊AGL(1,𝔽5)—22no—
240C22⋊AGL(1,𝔽5)—62no—
241C22⋊AGL(1,𝔽5)—62no—
242C2×#170—61no—
243C4⋊AGL(1,𝔽5)—32no—
244C4⋊AGL(1,𝔽5)—62no—
245C4⋊AGL(1,𝔽5)—62no—
246C4⋊AGL(1,𝔽5)C22×D312yes—
247C4×AGL(1,𝔽5)—31no—
248C4×AGL(1,𝔽5)—31no—
249C4×AGL(1,𝔽5)—31no—
250C4×AGL(1,𝔽5)—62no—
251C4×AGL(1,𝔽5)—62no—
252C4×AGL(1,𝔽5)—62no—
253C4×AGL(1,𝔽5)C22×D311yescharacteristic
254D5⋊C8—31no—
255D5⋊C8—61no—
256D5⋊C8C22×D311yescharacteristic
257C5×Q16—31no—
258C5×SD16—32no—
259C5×D8C4×D311yescharacteristic, complemented
260C2×C5×C8—31no—
261#689—32no—
262#688—32no—
263#687—32no—
264#686C4×D312yescomplemented
265C2×#168—31no—
266Dic20—31no—
267D40C4×D311yescharacteristic, complemented
268#677—32no—
269C8×D5—31no—
270C8×D5—31no—
271C8×D5—31no—
272C8×D5C22×D311yescharacteristic
273C2×#135—151no—
274C4×#41—152no—
275C4×Q16—151no—
276C4×Q16—151no—
277C4×SD16—152no—
278C4×SD16—152no—
279C4×D8—51no—
280C4×D8—151no—
281#427—151no—
282#416—152no—
283C2×C4×C8—151no—
284C22×C3×C5—22no—
285C2×D15C4×D411yescharacteristic
286C2×C5×D3C4×D411yescharacteristic
287C2×C3×D5—22no—
288C2×C3×D5—42no—
289C2×C3×D5—42no—
290C2×C3×D5C22×D411yescharacteristic
291D3×D5—21no—
292D3×D5—21no—
293ΓL(1,𝔽16)—21no—
294ΓL(1,𝔽16)—42no—
295ΓL(1,𝔽16)#13512yescomplemented
296C3×AGL(1,𝔽5)—21no—
297C3×AGL(1,𝔽5)—42no—
298C3×AGL(1,𝔽5)#13512yescomplemented
299C3×C4×C5C23×C411yescharacteristic
300Dic15—22no—
301Dic15C4×D411yescharacteristic
302C3×Dic5C2×#4111yescharacteristic
303C5×Dic3—22no—
304C5×Dic3C4×D411yescharacteristic
305C2×C3×D4—52no—
306C22×C3×C4—102no—
307C2×#67—102no—
308C22×Dic3—102no—
309C22×Dic3—102no—
310#237—52no—
311#237—52no—
312#237—52no—
313#237—102no—
314#237—102no—
315#237C2×AGL(1,𝔽5)12yescomplemented
316C2×C4×D3—51no—
317C2×C4×D3—51no—
318C2×C4×D3—51no—
319C2×Dic6—52no—
320C3×D8—52no—
321C3×D8—51no—
322C3×D8C2×AGL(1,𝔽5)11yescharacteristic, complemented
323C2×C3×C8—51no—
324C2×C3×C8—51no—
325C3×C4⋊C4—52no—
326C3×C22⋊C4—102no—
327C3×C42—51no—
328#217—102no—
329#214—52no—
330#214—52no—
331#214—52no—
332#214C2×AGL(1,𝔽5)12yescomplemented
333(C2×D3)⋊C4—102no—
334C4⋊Dic3—52no—
335Dic3⋊C4—102no—
336Dic3⋊C4—102no—
337C4×Dic3—51no—
338C4×Dic3—51no—
339C4×Dic3—51no—
340C4×Dic3—102no—
341C4×Dic3—102no—
342C4×Dic3—102no—
343C2×C3⋊C8—51no—
344C2×C3⋊C8—51no—
345Dic12—52no—
346Dic12—51no—
347Dic12C2×AGL(1,𝔽5)11yescharacteristic, complemented
348D3×C8—51no—
349D3×C8—51no—
350D3×C8—51no—
351D3×C8—101no—
352D3×C8—101no—
353D3×C8C2×AGL(1,𝔽5)11yescharacteristic, complemented
354C22×D5—22no—
355C22×D5—31no—
356C2×AGL(1,𝔽5)—22no—
357C2×AGL(1,𝔽5)—31no—
358C2×AGL(1,𝔽5)—31no—
359C2×AGL(1,𝔽5)—44no—
360C2×AGL(1,𝔽5)—62no—
361C2×AGL(1,𝔽5)—62no—
362C2×AGL(1,𝔽5)—62no—
363C2×AGL(1,𝔽5)—124no—
364C2×AGL(1,𝔽5)D3×D411yescharacteristic
365C2×AGL(1,𝔽5)D3×D411yescharacteristic
366C5×Q8—32no—
367C5×D4—62no—
368C5×D4C2×C4×D312yes—
369C2×C4×C5—31no—
370C2×C4×C5—62no—
371C22⋊D5—22no—
372C22⋊D5—62no—
373C22⋊D5—62no—
374C2×Dic5—31no—
375C2×Dic5—62no—
376D20—62no—
377D20C2×C4×D312yes—
378C4×D5—31no—
379C4×D5—31no—
380C4×D5—31no—
381C4×D5—62no—
382C4×D5—62no—
383C4×D5—62no—
384C4×D5C23×D311yescharacteristic
385Dic10—32no—
386Dic10—62no—
387#170—21no—
388#170—61no—
389C5×C8—31no—
390C5×C8C2×C4×D311yescharacteristic
391#168—31no—
392#168C2×C4×D311yescharacteristic
393C2×#41—152no—
394#135—31no—
395#135—151no—
396#135—152no—
397#135—151no—
398#135—152no—
399#135—151no—
400C2×Q16—151no—
401C2×SD16—152no—
402C2×D8—51no—
403C22×C8—151no—
404C22×C8—151no—
405C4×Q8—152no—
406C4×Q8—152no—
407C4×D4—52no—
408C4×D4—152no—
409C4×D4—302no—
410C4×D4—302no—
411#117—152no—
412#117—302no—
413C2×C42—151no—
414C2×C42—302no—
415#107—51no—
416#107—151no—
417#106—152no—
418#103—152no—
419#103—152no—
420#102—52no—
421#102—152no—
422C4×C8—51no—
423C4×C8—151no—
424C4×C8—151no—
425C4×C8—151no—
426C2×C3×C5—42no—
427C2×C3×C5C2×C4×D411yescharacteristic
428D15—21no—
429C3×D5—42no—
430C3×D5C2×#13511yescharacteristic
431C3×D5C2×#13511yescharacteristic
432C5×D3—21no—
433C23×C3—102no—
434C22×D3—51no—
435C3×D4—52no—
436C3×D4—102no—
437C3×D4C22×AGL(1,𝔽5)12yes—
438C2×C3×C4—51no—
439C2×C3×C4—51no—
440C2×C3×C4—51no—
441C2×C3×C4—102no—
442C2×C3×C4—204no—
443#67—22no—
444#67—102no—
445#67—102no—
446#67—102no—
447C2×Dic3—22no—
448C2×Dic3—51no—
449C2×Dic3—51no—
450C2×Dic3—51no—
451C2×Dic3—102no—
452C2×Dic3—102no—
453C2×Dic3—102no—
454C2×Dic3—102no—
455C2×Dic3—102no—
456C2×Dic3—204no—
457C4×D3—51no—
458C4×D3—51no—
459C4×D3—51no—
460C4×D3—102no—
461C4×D3—102no—
462C4×D3C22×AGL(1,𝔽5)11yescharacteristic
463Dic6—52no—
464Dic6—102no—
465Dic6C22×AGL(1,𝔽5)12yes—
466C3×C8—51no—
467C3×C8—101no—
468C3×C8C22×AGL(1,𝔽5)11yescharacteristic
469C3⋊C8—51no—
470C3⋊C8—101no—
471C3⋊C8C22×AGL(1,𝔽5)11yescharacteristic
472C22×C5—22no—
473C22×C5—31no—
474C2×D5—22no—
475C2×D5—31no—
476C2×D5—42no—
477C2×D5—42no—
478C2×D5—61no—
479C2×D5—61no—
480C2×D5C2×D3×D411yescharacteristic
481AGL(1,𝔽5)—21no—
482AGL(1,𝔽5)—32no—
483AGL(1,𝔽5)—42no—
484AGL(1,𝔽5)—61no—
485AGL(1,𝔽5)—122no—
486AGL(1,𝔽5)#91212yesdirect product factor
487C4×C5—31no—
488C4×C5—62no—
489C4×C5C22×C4×D311yescharacteristic
490Dic5—31no—
491Dic5—62no—
492Dic5D3×#4111yescharacteristic
493#41—32no—
494#41—152no—
495#41—152no—
496#41—152no—
497#41—302no—
498#41—302no—
499C2×Q8—152no—
500C2×D4—52no—
501C2×D4—302no—
502C22×C4—102no—
503C22×C4—151no—
504C22×C4—151no—
505C22×C4—151no—
506C22×C4—302no—
507C22×C4—302no—
508Q16—31no—
509Q16—152no—
510Q16—151no—
511SD16—32no—
512SD16—152no—
513SD16—152no—
514SD16—152no—
515D8—52no—
516D8—51no—
517D8D3×AGL(1,𝔽5)11yescharacteristic, complemented
518C2×C8—31no—
519C2×C8—51no—
520C2×C8—51no—
521C2×C8—151no—
522C2×C8—151no—
523C2×C8—151no—
524C2×C8—151no—
525C2×C8—151no—
526C2×C8—301no—
527C2×C8—301no—
528C4⋊C4—52no—
529C4⋊C4—152no—
530C4⋊C4—302no—
531C4⋊C4—302no—
532C22⋊C4—102no—
533C22⋊C4—302no—
534C22⋊C4—302no—
535C42—51no—
536C42—151no—
537C42—151no—
538C42—151no—
539C42—302no—
540C42—302no—
541C42—302no—
542C3×C5C4×#13511yescharacteristic, complemented, Hall
543C22×C3—22no—
544C22×C3—51no—
545C22×C3—102no—
546C22×C3—202no—
547C22×C3—202no—
548C2×D3—51no—
549C2×D3—101no—
550C2×D3—101no—
551C2×D3D4×AGL(1,𝔽5)11yescharacteristic
552C3×C4—52no—
553C3×C4—51no—
554C3×C4—101no—
555C3×C4—202no—
556C3×C4C23×AGL(1,𝔽5)11yescharacteristic
557Dic3—22no—
558Dic3—52no—
559Dic3—51no—
560Dic3—101no—
561Dic3—102no—
562Dic3—202no—
563Dic3D4×AGL(1,𝔽5)11yescharacteristic
564C2×C5—42no—
565C2×C5—61no—
566C2×C5C4×D3×D411yescharacteristic
567D5—42no—
568D5—61no—
569D5C2×#91211yescharacteristic
570D5D3×#13511yescharacteristic
571C23—102no—
572C23—151no—
573Q8—32no—
574Q8—152no—
575Q8—302no—
576D4—52no—
577D4—62no—
578D4—102no—
579D4—302no—
580D4—302no—
581D4—302no—
582D4C2×D3×AGL(1,𝔽5)12yes—
583C2×C4—31no—
584C2×C4—51no—
585C2×C4—51no—
586C2×C4—51no—
587C2×C4—62no—
588C2×C4—102no—
589C2×C4—151no—
590C2×C4—151no—
591C2×C4—151no—
592C2×C4—151no—
593C2×C4—151no—
594C2×C4—151no—
595C2×C4—204no—
596C2×C4—302no—
597C2×C4—302no—
598C2×C4—302no—
599C2×C4—302no—
600C2×C4—302no—
601C2×C4—302no—
602C2×C4—302no—
603C2×C4—604no—
604C8—31no—
605C8—51no—
606C8—101no—
607C8—151no—
608C8—301no—
609C8C2×D3×AGL(1,𝔽5)11yescharacteristic
610C2×C3—42no—
611C2×C3—51no—
612C2×C3—51no—
613C2×C3—202no—
614C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
615D3—21no—
616D3—101no—
617C5C4×#91211yescharacteristic, complemented, Sylow
618C22—22no—
619C22—31no—
620C22—51no—
621C22—102no—
622C22—151no—
623C22—202no—
624C22—202no—
625C22—301no—
626C22—301no—
627C4—31no—
628C4—52no—
629C4—51no—
630C4—62no—
631C4—101no—
632C4—152no—
633C4—151no—
634C4—202no—
635C4—301no—
636C4—302no—
637C4—602no—
638C4C22×D3×AGL(1,𝔽5)11yescharacteristic
639C3AGL(1,𝔽5)×#13511yescharacteristic, complemented, Sylow
640C2—42no—
641C2—51no—
642C2—51no—
643C2—61no—
644C2—202no—
645C2—301no—
646C2D3×D4×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2D3×D4×AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC3×C5×D8C2×C4
socleC2×C3×C5C2×C4×D4
prime radicalD5×#912C2
cosocleC3×C4×D5C24
hypercenterD8D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ D8

Complements

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

NH ≅ G/Ntype
1. AGL(1,𝔽5)×#237C2semidirect
3. D8×ΓL(1,𝔽16)C2semidirect
4. C3×D8×AGL(1,𝔽5)C2semidirect
5. #11751947C2semidirect
6. #11751945C2semidirect
7. AGL(1,𝔽5)×#214C2semidirect
8. #11751669C2semidirect
9. AGL(1,𝔽5)×Dic12C2semidirect
10. #11751658C2semidirect
11. D3×C8×AGL(1,𝔽5)C2semidirect
25. #91801C4semidirect
26. C5×#912C4semidirect
28. #91497C4semidirect
29. #91493C4semidirect
31. #91277C4semidirect
32. #91273C4semidirect
55. D8×AGL(1,𝔽5)D3semidirect
62. #6819C2×C4semidirect
63. C5×#237C2×C4semidirect
70. #6766C2×C4semidirect
71. #6765C2×C4semidirect
91. C3×C5×D8C2×C4semidirect
92. #6716C2×C4semidirect
93. Dic60C2×C4semidirect
94. C8×D15C2×C4semidirect
95. C5×#214C2×C4semidirect
96. C5×Dic12C2×C4semidirect
97. C5×D3×C8C2×C4semidirect
98. C3×#686C2×C4semidirect
99. C3×D40C2×C4semidirect
101. #6663C2×C4semidirect
102. #6657C2×C4semidirect
103. #6655C2×C4semidirect
104. #6648C2×C4semidirect
105. D3×#168C2×C4semidirect
203. #912AGL(1,𝔽5)direct (N × H)
259. C5×D8C4×D3semidirect
264. #686C4×D3semidirect
267. D40C4×D3semidirect
295. ΓL(1,𝔽16)#135semidirect
298. C3×AGL(1,𝔽5)#135semidirect
315. #237C2×AGL(1,𝔽5)semidirect
322. C3×D8C2×AGL(1,𝔽5)semidirect
332. #214C2×AGL(1,𝔽5)semidirect
347. Dic12C2×AGL(1,𝔽5)semidirect
353. D3×C8C2×AGL(1,𝔽5)semidirect
486. AGL(1,𝔽5)#912direct (N × H)
517. D8D3×AGL(1,𝔽5)semidirect
542. C3×C5C4×#135semidirect
617. C5C4×#912semidirect
639. C3AGL(1,𝔽5)×#135semidirect

Maximal subgroups

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

subgroupindex
AGL(1,𝔽5)×#2372
D5×#9122
D8×ΓL(1,𝔽16)2
C3×D8×AGL(1,𝔽5)2
#117519472
#117519452
AGL(1,𝔽5)×#2142
#117516692
AGL(1,𝔽5)×Dic122
#117516582
D3×C8×AGL(1,𝔽5)2
AGL(1,𝔽5)×#1353
C4×#9125