Finite Group Databasebeta

← AGL(1,𝔽5)×#2912 #72253184

Subgroups — AGL(1,𝔽5)×#2912 #72253184

Order 2560.

6456 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10617416C211yesmaximal, characteristic
2C2×AGL(1,𝔽5)×#131C211yesmaximal, characteristic
3AGL(1,𝔽5)×#520C212yesmaximal
4#13033586C213yesmaximal, complemented
5#13033585C213yesmaximal, complemented
6#13033583C216yesmaximal, complemented
7AGL(1,𝔽5)×#428C216yesmaximal, complemented
8AGL(1,𝔽5)×#427C213yesmaximal, complemented
9C2×AGL(1,𝔽5)×#106C213yesmaximal, complemented
10#13033172C212yesmaximal
11D5×#2912C211yesmaximal, characteristic
12C2×#66266C2212yes—
13C2×#41×AGL(1,𝔽5)C2211yescharacteristic
14C2×D5⋊#131C2211yescharacteristic
15C2×D5×#131C2211yescharacteristic
16D5×#520C2212yes—
17#10617416C4116yescomplemented
18AGL(1,𝔽5)×#131C4116yescomplemented
19C2×#65727C2216yes—
20C2×#65728C2213yes—
21C2×M16×AGL(1,𝔽5)C2213yes—
22C2×#65721C2213yes—
23C22×#3993C2213yes—
24C2×#65718C2213yes—
25C22×C8×AGL(1,𝔽5)C2213yes—
26#10617208—22no—
27C4×Q8×AGL(1,𝔽5)—22no—
28#10617172—26no—
29C4×D4×AGL(1,𝔽5)—26no—
30#10617127C2216yes—
31AGL(1,𝔽5)×#117C2216yes—
32#10617098C2216yes—
33C2×C4⋊C4×AGL(1,𝔽5)C2216yes—
34C5×#2912C411yescharacteristic, complemented
35#10615515C411yescharacteristic, complemented
36#10614292C412yescomplemented
37#10610940C416yescomplemented
38D5×#428C2216yes—
39#10610909C413yescomplemented
40D5×#427C2213yes—
41#10610847C413yescomplemented
42C2×D5×#106C2213yes—
43#10604379C2216yes—
44#10604378C2216yes—
45#10604285C2216yes—
46C2×#64874C2216yes—
47#10604072C22112yes—
48AGL(1,𝔽5)×#107C2216yes—
49AGL(1,𝔽5)×#107C2216yes—
50#10604048C22112yes—
51AGL(1,𝔽5)×#106C2213yes—
52AGL(1,𝔽5)×#106C2216yes—
53AGL(1,𝔽5)×#106C2216yes—
54AGL(1,𝔽5)×#106C2216yes—
55AGL(1,𝔽5)×#106C2211yescharacteristic
56AGL(1,𝔽5)×#106C2213yes—
57AGL(1,𝔽5)×#106C2213yes—
58C4×#2912—51nomaximal, Sylow
59C2×D5×#41C2311yescharacteristic
60#66266—28no—
61#66266C2×C4116yes—
62#41×AGL(1,𝔽5)C2×C418yes—
63#41×AGL(1,𝔽5)Q818yes—
64D5⋊#131—24no—
65D5⋊#131C2×C418yes—
66C2×Q8×AGL(1,𝔽5)—22no—
67C2×Q8×AGL(1,𝔽5)D411yescharacteristic
68C2×Q8×AGL(1,𝔽5)D411yescharacteristic
69C2×#4133—21no—
70C2×D4×AGL(1,𝔽5)—26no—
71C2×D4×AGL(1,𝔽5)D413yes—
72C2×D4×AGL(1,𝔽5)D413yes—
73C2×#4131—23no—
74C2×#4130C2316yes—
75C2×#4130C2313yes—
76C22×C4⋊AGL(1,𝔽5)C2316yes—
77C22×C4×AGL(1,𝔽5)—26no—
78C22×C4×AGL(1,𝔽5)C2313yes—
79C2×D5⋊M16C2313yes—
80C22×D5⋊C8C2313yes—
81C2×C5×#131C2×C411yescharacteristic
82C5×#520C2×C412yes—
83#66161C2×C412yes—
84C2×#4094C2×C411yescharacteristic
85D5×#131C2×C418yes—
86D5×#131C2×C418yes—
87C2×#4053C2×C413yes—
88C2×D5×M16C2313yes—
89C2×#4047C2×C413yes—
90C22×C8×D5C2313yes—
91#65908—22no—
92C4×Q8×D5—22no—
93#65880—26no—
94C4×D4×D5—26no—
95#65857C2×C416yes—
96D5×#117C2316yes—
97#65838C2×C416yes—
98C2×D5×C4⋊C4C2316yes—
99C4×C22⋊AGL(1,𝔽5)—212no—
100C2×(C2×AGL(1,𝔽5))⋊C4—26no—
101#65728C2×C4124yescomplemented
102#65727C2×C4148yescomplemented
103M16×AGL(1,𝔽5)C2×C4124yescomplemented
104#65721C2×C4124yescomplemented
105C2×#3994C2316yes—
106C2×#3993C2×C4124yescomplemented
107C2×#3993C2313yes—
108C2×#3993C2311yescharacteristic
109C2×#3993C2316yes—
110#65718C2×C4124yescomplemented
111C2×#3992C2316yes—
112C2×C8×AGL(1,𝔽5)C2×C4124yescomplemented
113C2×C8×AGL(1,𝔽5)C2311yescharacteristic
114C2×C8×AGL(1,𝔽5)C2313yes—
115C2×C8×AGL(1,𝔽5)C2313yes—
116C2×C8×AGL(1,𝔽5)C2313yes—
117C4⋊C4×AGL(1,𝔽5)—26no—
118C4⋊C4×AGL(1,𝔽5)—26no—
119C4⋊C4×AGL(1,𝔽5)—26no—
120C4⋊C4×AGL(1,𝔽5)—26no—
121C4⋊C4×AGL(1,𝔽5)C2316yes—
122C4⋊C4×AGL(1,𝔽5)C23112yes—
123C4⋊C4×AGL(1,𝔽5)C2316yes—
124C4⋊C4×AGL(1,𝔽5)C2312yes—
125C4⋊C4×AGL(1,𝔽5)C2316yes—
126C22⋊C4×AGL(1,𝔽5)—26no—
127C22⋊C4×AGL(1,𝔽5)—26no—
128C22⋊C4×AGL(1,𝔽5)—212no—
129C4×C4⋊AGL(1,𝔽5)—26no—
130C4×C4⋊AGL(1,𝔽5)—26no—
131#65686—26no—
132C42×AGL(1,𝔽5)—26no—
133C5×#428C2×C416yescomplemented
134C5×#427C2×C413yescomplemented
135C2×C5×#106C2×C413yescomplemented
136#65410C2×C416yescomplemented
137#65395C2×C413yescomplemented
138C2×#3949C2×C413yescomplemented
139#65287C2×C416yescomplemented
140#65284C2×C416yescomplemented
141#65253C2×C416yescomplemented
142C2×#3940C2×C416yescomplemented
143#65170C2×C4112yescomplemented
144#65169C2×C416yescomplemented
145D5×#107C2316yes—
146#65150C2×C4112yescomplemented
147#65149C2×C413yescomplemented
148#65149C2×C413yescomplemented
149D5×#106C2×C416yescomplemented
150D5×#106C2×C416yescomplemented
151D5×#106C2313yes—
152D5×#106C2311yescharacteristic
153D5×#106C2316yes—
154#64874C2316yes—
155#64874C23112yes—
156#64874C2316yes—
157#64874C2312yes—
158#64874C2316yes—
159C2×#2912—51no—
160C2×#2912—51no—
161C2×C4×#131—51no—
162C4×#520—52no—
163#20454—53no—
164#20454—53no—
165#20453—56no—
166C4×#428—56no—
167C4×#427—53no—
168C2×C4×#106—53no—
169#20348—52no—
170C23×AGL(1,𝔽5)—26no—
171C23×AGL(1,𝔽5)C2×D413yes—
172C23×AGL(1,𝔽5)C2×D413yes—
173C2×C5×#41C22×C411yescharacteristic
174D5×#41C22×C414yes—
175D5×#41C22×C414yes—
176D5×#41C2×Q814yes—
177D5×#41#4114yes—
178C2×#713#4111yescharacteristic
179C2×Q8×D5C2×D411yescharacteristic
180C2×#711#4113yes—
181C2×D4×D5C2×D413yes—
182C2×#709C22×C413yes—
183C22×C4×D5—26no—
184C22×C4×D5C2413yes—
185C2×C22⋊AGL(1,𝔽5)—26no—
186C2×C22⋊AGL(1,𝔽5)C2×D416yes—
187C2×#704—23no—
188C22×#170—23no—
189Q8×AGL(1,𝔽5)—216no—
190Q8×AGL(1,𝔽5)C4⋊C418yes—
191Q8×AGL(1,𝔽5)C4⋊C418yes—
192#4133—28no—
193D4×AGL(1,𝔽5)—248no—
194D4×AGL(1,𝔽5)C4⋊C4124yes—
195D4×AGL(1,𝔽5)C4⋊C4124yes—
196#4131—224no—
197#4130—212no—
198#4130C22×C4124yes—
199#4130C22×C4112yes—
200#4130C2×Q8112yes—
201C2×C4⋊AGL(1,𝔽5)—26no—
202C2×C4⋊AGL(1,𝔽5)—212no—
203C2×C4⋊AGL(1,𝔽5)C22×C4124yes—
204C2×C4⋊AGL(1,𝔽5)C2×D413yes—
205C2×C4⋊AGL(1,𝔽5)C2×D413yes—
206C2×C4⋊AGL(1,𝔽5)C2416yes—
207C2×C4⋊AGL(1,𝔽5)C2412yes—
208C2×C4×AGL(1,𝔽5)—26no—
209C2×C4×AGL(1,𝔽5)—22no—
210C2×C4×AGL(1,𝔽5)—26no—
211C2×C4×AGL(1,𝔽5)—26no—
212C2×C4×AGL(1,𝔽5)—26no—
213C2×C4×AGL(1,𝔽5)—212no—
214C2×C4×AGL(1,𝔽5)—812no—
215C2×C4×AGL(1,𝔽5)C22×C4112yes—
216C2×C4×AGL(1,𝔽5)C2×D413yes—
217C2×C4×AGL(1,𝔽5)C2×D413yes—
218C2×C4×AGL(1,𝔽5)C2×Q8112yes—
219C2×C4×AGL(1,𝔽5)C2411yescharacteristic
220C2×C4×AGL(1,𝔽5)C2413yes—
221D5⋊M16—26no—
222D5⋊M16C22×C4112yes—
223C2×#700—23no—
224C2×D5⋊C8—23no—
225C2×D5⋊C8—26no—
226C2×D5⋊C8C22×C4112yes—
227C2×D5⋊C8C2411yescharacteristic
228C2×D5⋊C8C2413yes—
229C5×#131C4218yescomplemented
230C2×C5×M16C22×C413yes—
231C22×C5×C8C22×C413yes—
232C4×C5×Q8—22no—
233C4×C5×D4—26no—
234C5×#117C22×C416yes—
235C2×C5×C4⋊C4C22×C416yes—
236#4094C4218yescomplemented
237Q8×Dic5—22no—
238D4×Dic5—26no—
239C4×C22⋊D5—212no—
240#4072C22×C416yes—
241C2×C4⋊Dic5C22×C416yes—
242C2×#683—26no—
243C2×#681C22×C413yes—
244C22×#168C22×C413yes—
245#4053C42124yescomplemented
246D5×M16C22×C4112yes—
247D5×M16C22×C4112yes—
248#4047C42124yescomplemented
249C2×#676C22×C416yes—
250C2×C8×D5C22×C413yes—
251C2×C8×D5C22×C413yes—
252C2×C8×D5C22×C4112yes—
253C2×C8×D5C22×C4112yes—
254C2×C8×D5C2411yescharacteristic
255C2×C8×D5C2413yes—
256#4039—26no—
257#4038C22×C416yes—
258#4038C22×C416yes—
259D5×C4⋊C4—26no—
260D5×C4⋊C4—26no—
261D5×C4⋊C4C22×C4112yes—
262D5×C4⋊C4C2416yes—
263D5×C4⋊C4C2412yes—
264#4033—26no—
265#4027—212no—
266D5×C22⋊C4—26no—
267#4023—26no—
268C4×D20—26no—
269#4018—26no—
270C42×D5—26no—
271C4×Dic10—26no—
272(C2×AGL(1,𝔽5))⋊C4—22no—
273(C2×AGL(1,𝔽5))⋊C4—26no—
274(C2×AGL(1,𝔽5))⋊C4—26no—
275(C2×AGL(1,𝔽5))⋊C4—26no—
276(C2×AGL(1,𝔽5))⋊C4—212no—
277#3994C22×C4124yes—
278#3993C22×C4112yes—
279#3993C22×C4124yes—
280#3993C22×C414yes—
281#3992C22×C4124yes—
282C8×AGL(1,𝔽5)C22×C414yes—
283C8×AGL(1,𝔽5)C22×C4112yes—
284C8×AGL(1,𝔽5)C22×C4112yes—
285C8×AGL(1,𝔽5)C22×C4112yes—
286C5×#107C22×C416yes—
287C5×#106C22×C413yes—
288C5×#106C22×C416yes—
289C5×#106C22×C411yescharacteristic
290#3950C22×C416yes—
291#3949C22×C413yes—
292#3949C22×C416yes—
293#3949C22×C411yescharacteristic
294#3940C22×C4112yes—
295#3940C22×C412yes—
296#3940C22×C416yes—
297#3939C22×C416yes—
298#3939C22×C416yes—
299C22×#131—51no—
300C22×#131—51no—
301C2×#520—52no—
302C2×#520—52no—
303C2×C4×#41—51no—
304#2912—516no—
305#2912—56no—
306#2912—53no—
307#2912—53no—
308#2912—51no—
309#2912—52no—
310#2912AGL(1,𝔽5)11yescharacteristic, direct product factor
311C2×#428—56no—
312C2×#428—56no—
313C2×#427—53no—
314C2×#427—53no—
315C22×#106—53no—
316C22×#106—53no—
317C4×#131—516no—
318C2×#405—53no—
319C2×#405—53no—
320C2×C4×M16—53no—
321C22×C4×C8—53no—
322#2276—102no—
323#2275—106no—
324#2274—56no—
325#2274—56no—
326C42×Q8—102no—
327C42×D4—106no—
328C4×#117—56no—
329C2×C4×C4⋊C4—56no—
330#1776—512no—
331#1776—512no—
332C4×#107—56no—
333C4×#107—56no—
334C4×#106—53no—
335C4×#106—56no—
336C4×#106—56no—
337C4×#106—56no—
338C4×#106—51no—
339C4×#106—53no—
340C4×#106—53no—
341#1736—56no—
342#1736—56no—
343#1735—56no—
344C2×#340—56no—
345C23×D5C22×D413yes—
346C22×AGL(1,𝔽5)—212no—
347C22×AGL(1,𝔽5)—22no—
348C22×AGL(1,𝔽5)—26no—
349C22×AGL(1,𝔽5)—224no—
350C22×AGL(1,𝔽5)—46no—
351C22×AGL(1,𝔽5)—86no—
352C22×AGL(1,𝔽5)—86no—
353C22×AGL(1,𝔽5)C2×C4⋊C4112yes—
354C22×AGL(1,𝔽5)C2×C4⋊C4112yes—
355C22×AGL(1,𝔽5)C22×D413yes—
356C22×AGL(1,𝔽5)C22×D413yes—
357C22×AGL(1,𝔽5)C22×D411yescharacteristic
358C22×AGL(1,𝔽5)C22×D411yescharacteristic
359C5×#41C2×C4214yes—
360C5×#41C4×Q814yes—
361C2×C5×Q8C4×D411yescharacteristic
362C2×C5×D4C4×D413yes—
363C22×C4×C5—26no—
364C22×C4×C5C23×C413yes—
365C2×C22⋊D5C4×D416yes—
366C22×Dic5—26no—
367C22×Dic5C2×#4113yes—
368#713#11714yes—
369#713C4×Q814yes—
370Q8×D5C2×C4⋊C414yes—
371Q8×D5C4×D414yes—
372#711#117112yes—
373#711C4×Q8112yes—
374D4×D5C2×C4⋊C4112yes—
375D4×D5C4×D4112yes—
376#709C2×C42112yes—
377#709C4×Q8112yes—
378C2×D20C4×D413yes—
379C2×C4×D5—26no—
380C2×C4×D5—22no—
381C2×C4×D5—212no—
382C2×C4×D5—86no—
383C2×C4×D5—86no—
384C2×C4×D5C23×C416yes—
385C2×C4×D5C23×C416yes—
386C2×C4×D5C23×C413yes—
387C2×C4×D5C22×D413yes—
388C2×C4×D5C22×Q816yes—
389C2×C4×D5C2×#4113yes—
390C2×C4×D5C2×#4116yes—
391C2×C4×D5C2511yescharacteristic
392C2×Dic10C4×D413yes—
393C22⋊AGL(1,𝔽5)—224no—
394C22⋊AGL(1,𝔽5)C2×C4⋊C4124yes—
395#704—212no—
396C2×#170—212no—
397C2×#170—21no—
398C2×#170—23no—
399C4⋊AGL(1,𝔽5)—224no—
400C4⋊AGL(1,𝔽5)—26no—
401C4⋊AGL(1,𝔽5)—22no—
402C4⋊AGL(1,𝔽5)C2×C4⋊C4112yes—
403C4⋊AGL(1,𝔽5)C2×C4⋊C4112yes—
404C4⋊AGL(1,𝔽5)C23×C4112yes—
405C4⋊AGL(1,𝔽5)C23×C414yes—
406C4×AGL(1,𝔽5)—224no—
407C4×AGL(1,𝔽5)—44no—
408C4×AGL(1,𝔽5)—412no—
409C4×AGL(1,𝔽5)—86no—
410C4×AGL(1,𝔽5)—86no—
411C4×AGL(1,𝔽5)—812no—
412C4×AGL(1,𝔽5)C2×C4⋊C4112yes—
413C4×AGL(1,𝔽5)C2×C4⋊C4112yes—
414C4×AGL(1,𝔽5)C23×C412yes—
415C4×AGL(1,𝔽5)C23×C416yes—
416C4×AGL(1,𝔽5)C22×Q812yes—
417C4×AGL(1,𝔽5)C22×Q816yes—
418#700—212no—
419D5⋊C8—212no—
420D5⋊C8—21no—
421D5⋊C8—23no—
422D5⋊C8C23×C412yes—
423D5⋊C8C23×C416yes—
424C5×M16C2×C42112yescomplemented
425C2×C5×C8C2×C42112yescomplemented
426C2×C5×C8C23×C411yescharacteristic
427C2×C5×C8C23×C413yes—
428C5×C4⋊C4—26no—
429C5×C4⋊C4C23×C416yes—
430C5×C4⋊C4C23×C412yes—
431C5×C22⋊C4—26no—
432C42×C5—26no—
433C22⋊Dic5—26no—
434#685—26no—
435#685—26no—
436C4⋊Dic5—26no—
437C4⋊Dic5C23×C412yes—
438C4⋊Dic5C23×C416yes—
439#683—212no—
440#683—22no—
441#683—26no—
442C4×Dic5—26no—
443C4×Dic5—26no—
444C4×Dic5—26no—
445#681C2×C42112yescomplemented
446C2×#168C2×C42112yescomplemented
447C2×#168C23×C413yes—
448C2×#168C23×C411yescharacteristic
449#676C2×C42124yescomplemented
450C8×D5C2×C42112yescomplemented
451C8×D5C2×C42112yescomplemented
452C8×D5C23×C412yes—
453C8×D5C23×C416yes—
454C8×D5C23×C412yes—
455C8×D5C23×C416yes—
456C22×#41—51no—
457C2×#131—51no—
458C2×#131—58no—
459C2×#131—58no—
460C2×#131—58no—
461C2×#131—53no—
462C2×#131—53no—
463C2×#131—103no—
464C2×#131—101no—
465C2×#131—104no—
466C2×#131C2×AGL(1,𝔽5)11yescharacteristic
467C22×M16—53no—
468C22×M16—53no—
469C23×C8—53no—
470C23×C8—53no—
471#520—516no—
472#520—52no—
473#520—56no—
474#520—56no—
475#520—106no—
476#520—102no—
477#520—108no—
478#520C2×AGL(1,𝔽5)12yes—
479C4×#41—58no—
480C4×#41—58no—
481C2×C4×Q8—51no—
482C2×C4×Q8—51no—
483C2×C4×Q8—102no—
484C2×C4×Q8—102no—
485C2×C4×D4—53no—
486C2×C4×D4—53no—
487C2×C4×D4—106no—
488C2×C4×D4—106no—
489C2×#117—53no—
490C2×#117—56no—
491C2×#117—56no—
492C22×C4⋊C4—56no—
493C22×C4⋊C4—56no—
494C22×C42—53no—
495C22×C42—106no—
496#428—548no—
497#428—56no—
498#428—56no—
499#428—56no—
500#428—512no—
501#428—512no—
502#428C2×AGL(1,𝔽5)16yescomplemented
503#427—524no—
504#427—53no—
505#427—56no—
506#427—56no—
507#427—53no—
508#427—53no—
509#427C2×AGL(1,𝔽5)13yescomplemented
510C2×#107—56no—
511C2×#107—56no—
512C2×#106—53no—
513C2×#106—56no—
514C2×#106—524no—
515C2×#106—51no—
516C2×#106—53no—
517C2×#106—56no—
518C2×#106—53no—
519C2×#106—56no—
520C2×#106—56no—
521C2×#106—56no—
522C2×#106—51no—
523C2×#106C2×AGL(1,𝔽5)13yescomplemented
524#405—524no—
525#405—524no—
526C4×M16—524no—
527C2×#97—56no—
528C2×C4×C8—51no—
529C2×C4×C8—53no—
530C2×C4×C8—53no—
531C2×C4×C8—53no—
532C2×C4×C8—524no—
533C4×C4⋊C4—56no—
534C4×C4⋊C4—512no—
535C4×C4⋊C4—52no—
536C4×C4⋊C4—56no—
537C4×C4⋊C4—56no—
538C4×C4⋊C4—106no—
539C4×C4⋊C4—106no—
540C4×C4⋊C4—106no—
541C4×C4⋊C4—106no—
542C4×C4⋊C4—106no—
543C4×C4⋊C4—106no—
544C4×C22⋊C4—1012no—
545C4×C22⋊C4—1012no—
546C4×C22⋊C4—106no—
547C4×C22⋊C4—106no—
548#376—106no—
549C2×#95—106no—
550C43—106no—
551#340—56no—
552#340—512no—
553#340—52no—
554#340—56no—
555#340—56no—
556C23×C5C2×C4×D413yes—
557C22×D5—26no—
558C22×D5—26no—
559C22×D5C22×C4⋊C416yes—
560C22×D5C2×C4×D416yes—
561C22×D5C2×C4×D413yes—
562C22×D5C23×D411yescharacteristic
563C2×AGL(1,𝔽5)—26no—
564C2×AGL(1,𝔽5)—22no—
565C2×AGL(1,𝔽5)—26no—
566C2×AGL(1,𝔽5)—224no—
567C2×AGL(1,𝔽5)—24no—
568C2×AGL(1,𝔽5)—212no—
569C2×AGL(1,𝔽5)—412no—
570C2×AGL(1,𝔽5)—42no—
571C2×AGL(1,𝔽5)—46no—
572C2×AGL(1,𝔽5)—46no—
573C2×AGL(1,𝔽5)—42no—
574C2×AGL(1,𝔽5)—824no—
575C2×AGL(1,𝔽5)C22×C4⋊C412yes—
576C2×AGL(1,𝔽5)C22×C4⋊C416yes—
577C2×AGL(1,𝔽5)C22×C4⋊C416yes—
578C2×AGL(1,𝔽5)C22×C4⋊C412yes—
579C2×AGL(1,𝔽5)#57714yes—
580C5×Q8C4×C4⋊C414yes—
581C5×D4C4×C4⋊C4112yes—
582C2×C4×C5—22no—
583C2×C4×C5—26no—
584C2×C4×C5—86no—
585C2×C4×C5C22×C4216yes—
586C2×C4×C5C2×C4×D413yes—
587C2×C4×C5C2×C4×Q816yes—
588C2×C4×C5C24×C411yescharacteristic
589C22⋊D5C4×C4⋊C4124yes—
590C2×Dic5—22no—
591C2×Dic5—26no—
592C2×Dic5—86no—
593C2×Dic5C2×#11716yes—
594C2×Dic5C2×C4×D413yes—
595C2×Dic5C2×C4×Q816yes—
596C2×Dic5C22×#4111yescharacteristic
597D20C4×C4⋊C4112yes—
598C4×D5—42no—
599C4×D5—46no—
600C4×D5—46no—
601C4×D5—42no—
602C4×D5—812no—
603C4×D5C22×C4216yes—
604C4×D5C22×C4⋊C416yes—
605C4×D5C2×#11716yes—
606C4×D5C2×C4×D416yes—
607C4×D5C2×C4×Q816yes—
608C4×D5C2×C4×Q816yes—
609C4×D5C24×C411yescharacteristic
610C4×D5C24×C411yescharacteristic
611C4×D5C23×Q811yescharacteristic
612C4×D5C22×#4111yescharacteristic
613Dic10C4×C4⋊C4112yes—
614#170—22no—
615#170—26no—
616C5×C8C22×C4212yes—
617C5×C8C22×C4216yes—
618#168C22×C4212yes—
619#168C22×C4216yes—
620C2×#41—54no—
621C2×#41—54no—
622C2×#41—54no—
623C2×#41—54no—
624C2×#41—51no—
625C2×#41—53no—
626C2×#41—53no—
627C2×#41C22×AGL(1,𝔽5)11yescharacteristic
628C22×Q8—51no—
629C22×D4—53no—
630C23×C4—53no—
631C23×C4—53no—
632C23×C4—53no—
633C23×C4—106no—
634C23×C4—106no—
635#131—58no—
636#131—524no—
637#131—524no—
638#131—1024no—
639#131—108no—
640#131C4×AGL(1,𝔽5)18yescomplemented
641C2×M16—53no—
642C2×M16—512no—
643C2×M16—512no—
644C2×M16—512no—
645C2×M16—56no—
646C2×M16—103no—
647C2×M16—106no—
648C2×M16—103no—
649C2×M16C22×AGL(1,𝔽5)13yes—
650C22×C8—53no—
651C22×C8—512no—
652C22×C8—512no—
653C22×C8—51no—
654C22×C8—53no—
655C22×C8—53no—
656C22×C8—53no—
657C22×C8—512no—
658C22×C8—51no—
659C22×C8—53no—
660C22×C8—106no—
661C22×C8—103no—
662C22×C8—103no—
663C22×C8C22×AGL(1,𝔽5)13yes—
664C4×Q8—22no—
665C4×Q8—58no—
666C4×Q8—58no—
667C4×Q8—106no—
668C4×Q8—106no—
669C4×Q8—1016no—
670C4×Q8—102no—
671C4×D4—26no—
672C4×D4—524no—
673C4×D4—524no—
674C4×D4—106no—
675C4×D4—1012no—
676C4×D4—106no—
677C4×D4—1012no—
678C4×D4—1048no—
679C4×D4—106no—
680#117—512no—
681#117—512no—
682#117—524no—
683#117—56no—
684#117—56no—
685#117—56no—
686#117—106no—
687#117—106no—
688#117—1012no—
689#117C22×AGL(1,𝔽5)16yes—
690C2×C4⋊C4—53no—
691C2×C4⋊C4—53no—
692C2×C4⋊C4—56no—
693C2×C4⋊C4—524no—
694C2×C4⋊C4—52no—
695C2×C4⋊C4—56no—
696C2×C4⋊C4—56no—
697C2×C4⋊C4—512no—
698C2×C4⋊C4—52no—
699C2×C4⋊C4—106no—
700C2×C4⋊C4—106no—
701C2×C4⋊C4—106no—
702C2×C4⋊C4—106no—
703C2×C4⋊C4—1012no—
704C2×C4⋊C4C22×AGL(1,𝔽5)16yes—
705C2×C22⋊C4—56no—
706C2×C22⋊C4—106no—
707C2×C22⋊C4—106no—
708C2×C42—53no—
709C2×C42—53no—
710C2×C42—53no—
711C2×C42—512no—
712C2×C42—512no—
713C2×C42—51no—
714C2×C42—106no—
715C2×C42—106no—
716C2×C42—102no—
717C2×C42—106no—
718C2×C42—106no—
719C2×C42—106no—
720C2×C42—1012no—
721C2×C42—4012no—
722#107—524no—
723#107—56no—
724#107—56no—
725#107—56no—
726#107C22×AGL(1,𝔽5)16yes—
727#106—512no—
728#106—524no—
729#106—54no—
730#106—53no—
731#106—56no—
732#106—51no—
733#106—56no—
734#106—512no—
735#106—52no—
736#106C22×AGL(1,𝔽5)13yes—
737#106C22×AGL(1,𝔽5)16yes—
738#106C22×AGL(1,𝔽5)11yescharacteristic
739#97—524no—
740C4×C8—54no—
741C4×C8—512no—
742C4×C8—512no—
743C4×C8—512no—
744#95—106no—
745#95—1012no—
746#95—102no—
747#95—106no—
748#95—106no—
749C22×C5—26no—
750C22×C5C2×C4×C4⋊C416yes—
751C22×C5C22×C4×D411yescharacteristic
752C2×D5—26no—
753C2×D5—212no—
754C2×D5—26no—
755C2×D5—26no—
756C2×D5C2×C4×C4⋊C416yes—
757C2×D5C23×C4⋊C411yescharacteristic
758C2×D5C22×C4×D411yescharacteristic
759C2×D5C2×#57712yes—
760C2×D5#358412yes—
761AGL(1,𝔽5)—26no—
762AGL(1,𝔽5)—22no—
763AGL(1,𝔽5)—26no—
764AGL(1,𝔽5)—44no—
765AGL(1,𝔽5)—412no—
766AGL(1,𝔽5)#291214yesdirect product factor
767C4×C5—46no—
768C4×C5—42no—
769C4×C5C2×C4×C4⋊C416yes—
770C4×C5C23×C4211yescharacteristic
771C4×C5C22×C4×Q811yescharacteristic
772Dic5—46no—
773Dic5—42no—
774Dic5C2×C4×C4⋊C416yes—
775Dic5C22×#11711yescharacteristic
776Dic5C22×C4×Q811yescharacteristic
777C24—53no—
778#41—54no—
779#41—54no—
780#41—512no—
781#41—512no—
782#41—512no—
783#41—512no—
784#41C2×C4×AGL(1,𝔽5)14yes—
785#41Q8×AGL(1,𝔽5)14yes—
786C2×Q8—54no—
787C2×Q8—54no—
788C2×Q8—53no—
789C2×Q8D4×AGL(1,𝔽5)11yescharacteristic
790C2×D4—56no—
791C2×D4—512no—
792C2×D4—512no—
793C2×D4—53no—
794C2×D4D4×AGL(1,𝔽5)13yes—
795C22×C4—26no—
796C22×C4—51no—
797C22×C4—53no—
798C22×C4—56no—
799C22×C4—56no—
800C22×C4—53no—
801C22×C4—53no—
802C22×C4—56no—
803C22×C4—56no—
804C22×C4—51no—
805C22×C4—53no—
806C22×C4—51no—
807C22×C4—53no—
808C22×C4—53no—
809C22×C4—512no—
810C22×C4—512no—
811C22×C4—102no—
812C22×C4—106no—
813C22×C4—1012no—
814C22×C4—1012no—
815C22×C4—102no—
816C22×C4—106no—
817C22×C4—1024no—
818C22×C4—106no—
819C22×C4—206no—
820C22×C4—406no—
821C22×C4—406no—
822C22×C4—406no—
823C22×C4—406no—
824C22×C4C23×AGL(1,𝔽5)13yes—
825M16—512no—
826M16—524no—
827M16—1012no—
828M16—1012no—
829M16C2×C4×AGL(1,𝔽5)112yescomplemented
830C2×C8—512no—
831C2×C8—51no—
832C2×C8—53no—
833C2×C8—52no—
834C2×C8—56no—
835C2×C8—52no—
836C2×C8—56no—
837C2×C8—512no—
838C2×C8—512no—
839C2×C8—52no—
840C2×C8—56no—
841C2×C8—101no—
842C2×C8—101no—
843C2×C8—103no—
844C2×C8—103no—
845C2×C8—1012no—
846C2×C8—1012no—
847C2×C8C2×C4×AGL(1,𝔽5)112yescomplemented
848C2×C8C23×AGL(1,𝔽5)11yescharacteristic
849C2×C8C23×AGL(1,𝔽5)13yes—
850C4⋊C4—26no—
851C4⋊C4—512no—
852C4⋊C4—512no—
853C4⋊C4—512no—
854C4⋊C4—54no—
855C4⋊C4—56no—
856C4⋊C4—52no—
857C4⋊C4—106no—
858C4⋊C4—1012no—
859C4⋊C4—102no—
860C4⋊C4—106no—
861C4⋊C4—1024no—
862C4⋊C4—102no—
863C4⋊C4—106no—
864C4⋊C4C23×AGL(1,𝔽5)16yes—
865C4⋊C4C23×AGL(1,𝔽5)12yes—
866C22⋊C4—26no—
867C22⋊C4—524no—
868C22⋊C4—106no—
869C22⋊C4—106no—
870C22⋊C4—1024no—
871C22⋊C4—106no—
872C42—26no—
873C42—52no—
874C42—56no—
875C42—52no—
876C42—56no—
877C42—512no—
878C42—512no—
879C42—106no—
880C42—106no—
881C42—1024no—
882C42—106no—
883C42—2012no—
884C42—204no—
885C42—4012no—
886C42—406no—
887C42—406no—
888C2×C5—26no—
889C2×C5C22×C4×C4⋊C411yescharacteristic
890C2×C5C4×#57712yes—
891D5—26no—
892D5C2×#291211yescharacteristic
893D5#6010811yescharacteristic
894D5C4×#57712yes—
895C23—51no—
896C23—56no—
897C23—56no—
898C23—53no—
899C23—106no—
900C23—106no—
901C23C2×D4×AGL(1,𝔽5)13yes—
902Q8—512no—
903Q8C4⋊C4×AGL(1,𝔽5)14yes—
904D4—524no—
905D4—512no—
906D4C4⋊C4×AGL(1,𝔽5)112yes—
907C2×C4—22no—
908C2×C4—26no—
909C2×C4—52no—
910C2×C4—54no—
911C2×C4—56no—
912C2×C4—56no—
913C2×C4—53no—
914C2×C4—51no—
915C2×C4—51no—
916C2×C4—51no—
917C2×C4—56no—
918C2×C4—56no—
919C2×C4—56no—
920C2×C4—56no—
921C2×C4—56no—
922C2×C4—51no—
923C2×C4—51no—
924C2×C4—56no—
925C2×C4—52no—
926C2×C4—56no—
927C2×C4—56no—
928C2×C4—86no—
929C2×C4—1024no—
930C2×C4—106no—
931C2×C4—106no—
932C2×C4—102no—
933C2×C4—104no—
934C2×C4—1012no—
935C2×C4—102no—
936C2×C4—106no—
937C2×C4—206no—
938C2×C4—202no—
939C2×C4—202no—
940C2×C4—206no—
941C2×C4—2012no—
942C2×C4—206no—
943C2×C4—202no—
944C2×C4—202no—
945C2×C4—206no—
946C2×C4—4012no—
947C2×C4—406no—
948C2×C4—4024no—
949C2×C4C22×C4×AGL(1,𝔽5)16yes—
950C2×C4C2×D4×AGL(1,𝔽5)13yes—
951C2×C4C2×Q8×AGL(1,𝔽5)16yes—
952C2×C4C24×AGL(1,𝔽5)11yescharacteristic
953C8—52no—
954C8—56no—
955C8—102no—
956C8—106no—
957C8C22×C4×AGL(1,𝔽5)12yes—
958C8C22×C4×AGL(1,𝔽5)16yes—
959C5C4×#291211yescharacteristic, complemented, Sylow
960C22—26no—
961C22—52no—
962C22—52no—
963C22—51no—
964C22—51no—
965C22—56no—
966C22—106no—
967C22—106no—
968C22—1012no—
969C22—106no—
970C22C2×C4⋊C4×AGL(1,𝔽5)16yes—
971C22C22×D4×AGL(1,𝔽5)11yescharacteristic
972C4—46no—
973C4—42no—
974C4—54no—
975C4—51no—
976C4—51no—
977C4—56no—
978C4—106no—
979C4—102no—
980C4—106no—
981C4—2012no—
982C4—204no—
983C4—206no—
984C4—202no—
985C4C2×C4⋊C4×AGL(1,𝔽5)16yes—
986C4C23×C4×AGL(1,𝔽5)11yescharacteristic
987C4C22×Q8×AGL(1,𝔽5)11yescharacteristic
988C2—26no—
989C2—51no—
990C2—51no—
991C2—52no—
992C2—106no—
993C2C22×C4⋊C4×AGL(1,𝔽5)11yescharacteristic
994C2AGL(1,𝔽5)×#57712yes—
subgroupG/H
centerC22C22×D4×AGL(1,𝔽5)
commutatorC4×C5C23×C42
FrattiniC2×C4C24×AGL(1,𝔽5)
FittingC5×#2912C4
socleC22×C5C22×C4×D4
prime radicalC2×D5×#41C23
cosocleC2×C4×D5C25
hypercenter#2912AGL(1,𝔽5)
hypocenterC5C4×#2912
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2912

Complements

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

NH ≅ G/Ntype
4. #13033586C2semidirect
5. #13033585C2semidirect
6. #13033583C2semidirect
7. AGL(1,𝔽5)×#428C2semidirect
8. AGL(1,𝔽5)×#427C2semidirect
9. C2×AGL(1,𝔽5)×#106C2semidirect
17. #10617416C4semidirect
18. AGL(1,𝔽5)×#131C4semidirect
34. C5×#2912C4semidirect
35. #10615515C4semidirect
36. #10614292C4semidirect
37. #10610940C4semidirect
39. #10610909C4semidirect
41. #10610847C4semidirect
101. #65728C2×C4semidirect
102. #65727C2×C4semidirect
103. M16×AGL(1,𝔽5)C2×C4semidirect
104. #65721C2×C4semidirect
106. C2×#3993C2×C4semidirect
110. #65718C2×C4semidirect
112. C2×C8×AGL(1,𝔽5)C2×C4semidirect
133. C5×#428C2×C4semidirect
134. C5×#427C2×C4semidirect
135. C2×C5×#106C2×C4semidirect
136. #65410C2×C4semidirect
137. #65395C2×C4semidirect
138. C2×#3949C2×C4semidirect
139. #65287C2×C4semidirect
140. #65284C2×C4semidirect
141. #65253C2×C4semidirect
142. C2×#3940C2×C4semidirect
143. #65170C2×C4semidirect
144. #65169C2×C4semidirect
146. #65150C2×C4semidirect
147. #65149C2×C4semidirect
148. #65149C2×C4semidirect
149. D5×#106C2×C4semidirect
150. D5×#106C2×C4semidirect
229. C5×#131C42semidirect
236. #4094C42semidirect
245. #4053C42semidirect
248. #4047C42semidirect
310. #2912AGL(1,𝔽5)direct (N × H)
424. C5×M16C2×C42semidirect
425. C2×C5×C8C2×C42semidirect
445. #681C2×C42semidirect
446. C2×#168C2×C42semidirect
449. #676C2×C42semidirect
450. C8×D5C2×C42semidirect
451. C8×D5C2×C42semidirect
502. #428C2×AGL(1,𝔽5)semidirect
509. #427C2×AGL(1,𝔽5)semidirect
523. C2×#106C2×AGL(1,𝔽5)semidirect
640. #131C4×AGL(1,𝔽5)semidirect
766. AGL(1,𝔽5)#2912direct (N × H)
829. M16C2×C4×AGL(1,𝔽5)semidirect
847. C2×C8C2×C4×AGL(1,𝔽5)semidirect
959. C5C4×#2912semidirect

Maximal subgroups

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

subgroupindex
C2×#106174162
C2×AGL(1,𝔽5)×#1312
AGL(1,𝔽5)×#5202
#130335862
#130335852
#130335832
AGL(1,𝔽5)×#4282
AGL(1,𝔽5)×#4272
C2×AGL(1,𝔽5)×#1062
#130331722
D5×#29122
C4×#29125