Finite Group Databasebeta

← C4×C5×AΣL(1,𝔽16) #11935339

Subgroups — C4×C5×AΣL(1,𝔽16) #11935339

Order 1280.

844 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#120C211yesmaximal, characteristic
2C2×C5×AΣL(1,𝔽16)C212yesmaximal
3C4×C5×#100C211yesmaximal, characteristic, complemented
4C4×C5×#99C211yesmaximal, characteristic, complemented
5C5×#1390C212yesmaximal, complemented
6C24×C4×C5C411yescharacteristic, complemented
7C2×C5×#120C2211yescharacteristic
8C2×C4×C5×D4—21no—
9C2×C4×C5×D4C2211yescharacteristic
10C2×C5×#100C2212yes—
11C2×C5×#99C2212yes—
12C4×C5×M16—21no—
13C5×#386—21no—
14C5×#386C2211yescharacteristic
15C5×#385—21no—
16C5×#385C411yescharacteristic, complemented
17C5×#379C411yescharacteristic, complemented
18C4×C5×C22⋊C4—21no—
19C4×C5×C22⋊C4—21no—
20C4×C5×C22⋊C4C411yescharacteristic, complemented
21C5×AΣL(1,𝔽16)C418yesdirect product factor
22C5×#343—21no—
23C5×#342—21no—
24C4×AΣL(1,𝔽16)C511yesmaximal, characteristic, direct product factor, Sylow
25C25×C5C2×C411yescharacteristic
26C22×C5×D4—21no—
27C22×C5×D4C2311yescharacteristic
28C23×C4×C5—21no—
29C23×C4×C5—21no—
30C23×C4×C5—44no—
31C23×C4×C5—41no—
32C23×C4×C5—41no—
33C23×C4×C5C2×C411yescharacteristic
34C23×C4×C5C2×C411yescharacteristic
35C23×C4×C5D411yescharacteristic
36C2×C5×M16—22no—
37C5×#120—22no—
38C5×#120C2×C414yes—
39C4×C5×D4—41no—
40C4×C5×D4—41no—
41C4×C5×D4—44no—
42C2×C5×C4⋊C4—21no—
43C2×C5×C4⋊C4D411yescharacteristic
44C2×C5×C22⋊C4—21no—
45C2×C5×C22⋊C4—22no—
46C2×C5×C22⋊C4—21no—
47C2×C5×C22⋊C4—21no—
48C2×C5×C22⋊C4—21no—
49C2×C5×C22⋊C4C2×C411yescharacteristic
50C2×C5×C22⋊C4C2×C411yescharacteristic
51C2×C5×C22⋊C4C2×C411yescharacteristic
52C2×C5×C22⋊C4D411yescharacteristic
53C2×C42×C5—21no—
54C2×C42×C5—41no—
55C2×C42×C5D411yescharacteristic
56C5×#100—22no—
57C5×#100C2×C414yescomplemented
58C5×#99—22no—
59C5×#99C2×C414yescomplemented
60C5×#97—41no—
61C4×C5×C8—41no—
62C5×#95—21no—
63C5×#95—21no—
64C5×#95—21no—
65C5×#95—41no—
66C4×#120C2×C511yescharacteristic
67C2×AΣL(1,𝔽16)C2×C512yes—
68C4×#100C2×C511yescharacteristic, complemented
69C4×#99C2×C511yescharacteristic, complemented
70#1390C2×C512yescomplemented
71C24×C5—21no—
72C24×C5—21no—
73C24×C5—42no—
74C24×C5—41no—
75C24×C5—42no—
76C24×C5—41no—
77C24×C5C4212yescomplemented
78C24×C5C22×C411yescharacteristic
79C24×C5C2×D411yescharacteristic
80C2×C5×D4—24no—
81C2×C5×D4—41no—
82C2×C5×D4—41no—
83C2×C5×D4—42no—
84C2×C5×D4—42no—
85C2×C5×D4C22×C412yes—
86C2×C5×D4#4112yes—
87C22×C4×C5—24no—
88C22×C4×C5—21no—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—21no—
92C22×C4×C5—21no—
93C22×C4×C5—21no—
94C22×C4×C5—21no—
95C22×C4×C5—42no—
96C22×C4×C5—42no—
97C22×C4×C5—42no—
98C22×C4×C5—42no—
99C22×C4×C5—42no—
100C22×C4×C5—42no—
101C22×C4×C5—42no—
102C22×C4×C5—44no—
103C22×C4×C5—44no—
104C22×C4×C5—44no—
105C22×C4×C5—41no—
106C22×C4×C5—41no—
107C22×C4×C5—41no—
108C22×C4×C5—44no—
109C22×C4×C5—42no—
110C22×C4×C5C22⋊C411yescharacteristic
111C22×C4×C5C22⋊C411yescharacteristic
112C22×C4×C5C22⋊C411yescharacteristic
113C22×C4×C5C22⋊C411yescharacteristic
114C22×C4×C5C2×D411yescharacteristic
115C5×M16—24no—
116C5×M16—42no—
117C2×C5×C8—42no—
118C5×C4⋊C4—41no—
119C5×C4⋊C4—42no—
120C5×C22⋊C4—21no—
121C5×C22⋊C4—24no—
122C5×C22⋊C4—24no—
123C5×C22⋊C4—41no—
124C5×C22⋊C4—41no—
125C5×C22⋊C4—42no—
126C5×C22⋊C4—42no—
127C5×C22⋊C4—42no—
128C5×C22⋊C4—42no—
129C5×C22⋊C4—41no—
130C5×C22⋊C4C4212yescomplemented
131C42×C5—21no—
132C42×C5—21no—
133C42×C5—42no—
134C42×C5—82no—
135C24×C4C4×C511yescharacteristic, complemented
136C2×#120C22×C511yescharacteristic
137C2×C4×D4—21no—
138C2×C4×D4C22×C511yescharacteristic
139C2×#100C22×C512yes—
140C2×#99C22×C512yes—
141C4×M16—21no—
142#386—21no—
143#386C22×C511yescharacteristic
144#385—21no—
145#385C4×C511yescharacteristic, complemented
146#379C4×C511yescharacteristic, complemented
147C4×C22⋊C4—21no—
148C4×C22⋊C4—21no—
149C4×C22⋊C4C4×C511yescharacteristic, complemented
150AΣL(1,𝔽16)C4×C518yesdirect product factor
151#343—21no—
152#342—21no—
153C23×C5—22no—
154C23×C5—22no—
155C23×C5—22no—
156C23×C5—21no—
157C23×C5—21no—
158C23×C5—21no—
159C23×C5—21no—
160C23×C5—41no—
161C23×C5—44no—
162C23×C5—42no—
163C23×C5—41no—
164C23×C5—41no—
165C23×C5—41no—
166C23×C5—44no—
167C23×C5—42no—
168C23×C5—41no—
169C23×C5—41no—
170C23×C5—42no—
171C23×C5—42no—
172C23×C5—42no—
173C23×C5—48no—
174C23×C5—42no—
175C23×C5—41no—
176C23×C5—41no—
177C23×C5C2×C4211yescharacteristic
178C23×C5C2×C22⋊C411yescharacteristic
179C23×C5#11711yescharacteristic
180C23×C5C4×D412yes—
181C5×D4—42no—
182C5×D4—42no—
183C5×D4—48no—
184C2×C4×C5—21no—
185C2×C4×C5—21no—
186C2×C4×C5—22no—
187C2×C4×C5—22no—
188C2×C4×C5—22no—
189C2×C4×C5—21no—
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5—44no—
193C2×C4×C5—42no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—48no—
198C2×C4×C5—42no—
199C2×C4×C5—41no—
200C2×C4×C5—42no—
201C2×C4×C5—44no—
202C2×C4×C5—42no—
203C2×C4×C5—41no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—42no—
207C2×C4×C5—41no—
208C2×C4×C5—44no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—81no—
212C2×C4×C5—82no—
213C2×C4×C5—82no—
214C2×C4×C5#9911yescharacteristic
215C2×C4×C5#9911yescharacteristic
216C2×C4×C5C4×D412yes—
217C5×C8—44no—
218C25C2×C4×C511yescharacteristic
219C22×D4—21no—
220C22×D4C23×C511yescharacteristic
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—44no—
224C23×C4—41no—
225C23×C4—41no—
226C23×C4C2×C4×C511yescharacteristic
227C23×C4C2×C4×C511yescharacteristic
228C23×C4C5×D411yescharacteristic
229C2×M16—22no—
230#120—22no—
231#120C2×C4×C514yes—
232C4×D4—41no—
233C4×D4—41no—
234C4×D4—44no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C5×D411yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4C2×C4×C511yescharacteristic
243C2×C22⋊C4C2×C4×C511yescharacteristic
244C2×C22⋊C4C2×C4×C511yescharacteristic
245C2×C22⋊C4C5×D411yescharacteristic
246C2×C42—21no—
247C2×C42—41no—
248C2×C42C5×D411yescharacteristic
249#100—22no—
250#100C2×C4×C514yescomplemented
251#99—22no—
252#99C2×C4×C514yescomplemented
253#97—41no—
254C4×C8—41no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—41no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5—24no—
262C22×C5—22no—
263C22×C5—21no—
264C22×C5—21no—
265C22×C5—42no—
266C22×C5—41no—
267C22×C5—41no—
268C22×C5—42no—
269C22×C5—42no—
270C22×C5—42no—
271C22×C5—42no—
272C22×C5—44no—
273C22×C5—44no—
274C22×C5—44no—
275C22×C5—44no—
276C22×C5—42no—
277C22×C5—41no—
278C22×C5—41no—
279C22×C5—41no—
280C22×C5—42no—
281C22×C5—41no—
282C22×C5—42no—
283C22×C5—81no—
284C22×C5C4×C22⋊C411yescharacteristic
285C22×C5C2×#9911yescharacteristic
286C22×C5#41011yescharacteristic
287C4×C5—21no—
288C4×C5—22no—
289C4×C5—42no—
290C4×C5—42no—
291C4×C5—41no—
292C4×C5—41no—
293C4×C5—41no—
294C4×C5—81no—
295C4×C5—84no—
296C4×C5AΣL(1,𝔽16)12yesdirect product factor
297C24—21no—
298C24—21no—
299C24—42no—
300C24—41no—
301C24—42no—
302C24—41no—
303C24C42×C512yescomplemented
304C24C22×C4×C511yescharacteristic
305C24C2×C5×D411yescharacteristic
306C2×D4—24no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—42no—
310C2×D4—42no—
311C2×D4C22×C4×C512yes—
312C2×D4C5×#4112yes—
313C22×C4—24no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—44no—
329C22×C4—44no—
330C22×C4—44no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—44no—
335C22×C4—42no—
336C22×C4C5×C22⋊C411yescharacteristic
337C22×C4C5×C22⋊C411yescharacteristic
338C22×C4C5×C22⋊C411yescharacteristic
339C22×C4C5×C22⋊C411yescharacteristic
340C22×C4C2×C5×D411yescharacteristic
341M16—24no—
342M16—42no—
343C2×C8—42no—
344C4⋊C4—41no—
345C4⋊C4—42no—
346C22⋊C4—21no—
347C22⋊C4—24no—
348C22⋊C4—24no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—42no—
352C22⋊C4—42no—
353C22⋊C4—42no—
354C22⋊C4—42no—
355C22⋊C4—41no—
356C22⋊C4C42×C512yescomplemented
357C42—21no—
358C42—21no—
359C42—42no—
360C42—82no—
361C2×C5—21no—
362C2×C5—21no—
363C2×C5—42no—
364C2×C5—44no—
365C2×C5—41no—
366C2×C5—41no—
367C2×C5C4×#9911yescharacteristic
368C2×C5C2×AΣL(1,𝔽16)11yescharacteristic
369C2×C5#212011yescharacteristic
370C23—22no—
371C23—22no—
372C23—22no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—44no—
379C23—42no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—44no—
384C23—42no—
385C23—41no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—48no—
391C23—42no—
392C23—41no—
393C23—41no—
394C23C2×C42×C511yescharacteristic
395C23C2×C5×C22⋊C411yescharacteristic
396C23C5×#11711yescharacteristic
397C23C4×C5×D412yes—
398D4—42no—
399D4—42no—
400D4—48no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—48no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—44no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—44no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—81no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4C5×#9911yescharacteristic
432C2×C4C5×#9911yescharacteristic
433C2×C4C4×C5×D412yes—
434C8—44no—
435C5C4×AΣL(1,𝔽16)11yescharacteristic, direct product factor, Sylow
436C22—21no—
437C22—21no—
438C22—24no—
439C22—22no—
440C22—21no—
441C22—21no—
442C22—42no—
443C22—41no—
444C22—41no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—44no—
450C22—44no—
451C22—44no—
452C22—44no—
453C22—42no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—42no—
458C22—41no—
459C22—42no—
460C22—81no—
461C22C4×C5×C22⋊C411yescharacteristic
462C22C2×C5×#9911yescharacteristic
463C22C5×#41011yescharacteristic
464C4—21no—
465C4—22no—
466C4—42no—
467C4—42no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—81no—
472C4—84no—
473C4C5×AΣL(1,𝔽16)12yesdirect product factor
474C2—21no—
475C2—21no—
476C2—42no—
477C2—44no—
478C2—41no—
479C2—41no—
480C2C4×C5×#9911yescharacteristic
481C2C2×C5×AΣL(1,𝔽16)11yescharacteristic
482C2C5×#212011yescharacteristic
subgroupG/H
centerC2×C4×C5#99
commutatorC23C2×C42×C5
Frattini, cosocleC22×D4C23×C5
socleC22×C5C2×#99
prime radicalC2×C5×#120C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C4×C5×#100C2semidirect
4. C4×C5×#99C2semidirect
5. C5×#1390C2semidirect
6. C24×C4×C5C4semidirect
16. C5×#385C4semidirect
17. C5×#379C4semidirect
20. C4×C5×C22⋊C4C4semidirect
21. C5×AΣL(1,𝔽16)C4direct (N × H)
24. C4×AΣL(1,𝔽16)C5direct (N × H)
57. C5×#100C2×C4semidirect
59. C5×#99C2×C4semidirect
68. C4×#100C2×C5semidirect
69. C4×#99C2×C5semidirect
70. #1390C2×C5semidirect
77. C24×C5C42semidirect
130. C5×C22⋊C4C42semidirect
135. C24×C4C4×C5semidirect
145. #385C4×C5semidirect
146. #379C4×C5semidirect
149. C4×C22⋊C4C4×C5semidirect
150. AΣL(1,𝔽16)C4×C5direct (N × H)
250. #100C2×C4×C5semidirect
252. #99C2×C4×C5semidirect
296. C4×C5AΣL(1,𝔽16)direct (N × H)
303. C24C42×C5semidirect
356. C22⋊C4C42×C5semidirect
435. C5C4×AΣL(1,𝔽16)direct (N × H)
473. C4C5×AΣL(1,𝔽16)direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×#1202
C2×C5×AΣL(1,𝔽16)2
C4×C5×#1002
C4×C5×#992
C5×#13902
C4×AΣL(1,𝔽16)5