Finite Group Databasebeta

← C5×#13222 #11935942

Subgroups — C5×#13222 #11935942

Order 1280.

628 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2534C211yesmaximal, characteristic
2C2×C5×#352C212yesmaximal, complemented
3C2×C5×AΣL(1,𝔽16)C212yesmaximal
4C5×#1800C211yesmaximal, characteristic, complemented
5C4×C5×#99C211yesmaximal, characteristic, complemented
6C2×C5×#123C2211yescharacteristic
7C2×C5×#120C2211yescharacteristic
8C2×C4×C5×D4C2211yescharacteristic
9C22×C5×C22⋊C4C411yescharacteristic, complemented
10C5×#423—21no—
11C2×C5×#100C2212yes—
12C2×C5×#99C2212yes—
13C5×#396—21no—
14C5×#394—21no—
15C5×#388—21no—
16C5×#386—21no—
17C5×#381C411yescharacteristic, complemented
18C5×#380C411yescharacteristic, complemented
19C5×#379C411yescharacteristic, complemented
20C4×C5×C22⋊C4—21no—
21C5×#352—24no—
22C5×AΣL(1,𝔽16)—24no—
23C5×#343—21no—
24C5×#342—21no—
25#13222C511yesmaximal, characteristic, direct product factor, Sylow
26C25×C5C2×C411yescharacteristic
27C22×C5×D4—21no—
28C22×C5×D4C2311yescharacteristic
29C23×C4×C5C2×C411yescharacteristic
30C23×C4×C5C2×C411yescharacteristic
31C23×C4×C5D411yescharacteristic
32C2×C5×M16—22no—
33C5×#123—22no—
34C5×#123—22no—
35C5×#120—22no—
36C5×#120—22no—
37C4×C5×D4—41no—
38C4×C5×D4—41no—
39C2×C5×C4⋊C4—21no—
40C2×C5×C4⋊C4—21no—
41C2×C5×C4⋊C4D411yescharacteristic
42C2×C5×C22⋊C4—22no—
43C2×C5×C22⋊C4—21no—
44C2×C5×C22⋊C4—21no—
45C2×C5×C22⋊C4—21no—
46C2×C5×C22⋊C4—21no—
47C2×C5×C22⋊C4—21no—
48C2×C5×C22⋊C4—21no—
49C2×C5×C22⋊C4—41no—
50C2×C5×C22⋊C4—41no—
51C2×C5×C22⋊C4C2×C411yescharacteristic
52C2×C5×C22⋊C4C2×C411yescharacteristic
53C2×C5×C22⋊C4C2×C411yescharacteristic
54C2×C5×C22⋊C4D411yescharacteristic
55C2×C42×C5—41no—
56C2×C42×C5D411yescharacteristic
57C5×C4⋊C8—41no—
58C5×C4⋊C8—41no—
59C5×#100—22no—
60C5×#100—22no—
61C5×#99—22no—
62C5×#99D414yes—
63C5×#95—21no—
64C5×#95—21no—
65C5×#95—21no—
66C5×#95—41no—
67#2534C2×C511yescharacteristic
68C2×#352C2×C512yescomplemented
69C2×AΣL(1,𝔽16)C2×C512yes—
70#1800C2×C511yescharacteristic, complemented
71C4×#99C2×C511yescharacteristic, complemented
72C24×C5—21no—
73C24×C5—22no—
74C24×C5—41no—
75C24×C5—42no—
76C24×C5—41no—
77C24×C5—81no—
78C24×C5C22×C411yescharacteristic
79C24×C5C2×D411yescharacteristic
80C2×C5×D4—41no—
81C2×C5×D4—41no—
82C2×C5×D4—42no—
83C2×C5×D4—42no—
84C2×C5×D4—81no—
85C2×C5×D4C2×D412yes—
86C2×C5×D4#4112yes—
87C22×C4×C5—21no—
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—22no—
95C22×C4×C5—42no—
96C22×C4×C5—41no—
97C22×C4×C5—41no—
98C22×C4×C5—81no—
99C22×C4×C5—81no—
100C22×C4×C5C22⋊C411yescharacteristic
101C22×C4×C5C22⋊C411yescharacteristic
102C22×C4×C5C22⋊C411yescharacteristic
103C22×C4×C5C22⋊C411yescharacteristic
104C22×C4×C5C2×D411yescharacteristic
105C5×M16—42no—
106C5×M16—42no—
107C2×C5×C8—42no—
108C5×C4⋊C4—41no—
109C5×C4⋊C4—41no—
110C5×C4⋊C4—41no—
111C5×C4⋊C4—81no—
112C5×C22⋊C4—22no—
113C5×C22⋊C4—22no—
114C5×C22⋊C4—24no—
115C5×C22⋊C4—41no—
116C5×C22⋊C4—41no—
117C5×C22⋊C4—42no—
118C5×C22⋊C4—42no—
119C5×C22⋊C4—42no—
120C5×C22⋊C4—42no—
121C5×C22⋊C4—41no—
122C5×C22⋊C4—41no—
123C5×C22⋊C4—41no—
124C5×C22⋊C4—41no—
125C5×C22⋊C4—81no—
126C42×C5—21no—
127C42×C5—21no—
128C42×C5—82no—
129C2×#123C22×C511yescharacteristic
130C2×#120C22×C511yescharacteristic
131C2×C4×D4C22×C511yescharacteristic
132C22×C22⋊C4C4×C511yescharacteristic, complemented
133#423—21no—
134C2×#100C22×C512yes—
135C2×#99C22×C512yes—
136#396—21no—
137#394—21no—
138#388—21no—
139#386—21no—
140#381C4×C511yescharacteristic, complemented
141#380C4×C511yescharacteristic, complemented
142#379C4×C511yescharacteristic, complemented
143C4×C22⋊C4—21no—
144#352—24no—
145AΣL(1,𝔽16)—24no—
146#343—21no—
147#342—21no—
148C23×C5—21no—
149C23×C5—21no—
150C23×C5—21no—
151C23×C5—21no—
152C23×C5—22no—
153C23×C5—41no—
154C23×C5—41no—
155C23×C5—41no—
156C23×C5—41no—
157C23×C5—41no—
158C23×C5—41no—
159C23×C5—41no—
160C23×C5—42no—
161C23×C5—42no—
162C23×C5—41no—
163C23×C5—41no—
164C23×C5—41no—
165C23×C5—82no—
166C23×C5—84no—
167C23×C5—84no—
168C23×C5—82no—
169C23×C5C2×C22⋊C411yescharacteristic
170C23×C5C4×D412yes—
171C23×C5#12112yes—
172C5×D4—42no—
173C5×D4—42no—
174C5×D4—84no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—21no—
178C2×C4×C5—21no—
179C2×C4×C5—21no—
180C2×C4×C5—41no—
181C2×C4×C5—42no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—44no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5—81no—
196C2×C4×C5—81no—
197C2×C4×C5—81no—
198C2×C4×C5—82no—
199C2×C4×C5—82no—
200C2×C4×C5—82no—
201C2×C4×C5#9911yescharacteristic
202C2×C4×C5#9911yescharacteristic
203C2×C4×C5#12411yescharacteristic
204C2×C4×C5#12711yescharacteristic
205C5×C8—82no—
206C25C2×C4×C511yescharacteristic
207C22×D4—21no—
208C22×D4C23×C511yescharacteristic
209C23×C4C2×C4×C511yescharacteristic
210C23×C4C2×C4×C511yescharacteristic
211C23×C4C5×D411yescharacteristic
212C2×M16—22no—
213#123—22no—
214#123—22no—
215#120—22no—
216#120—22no—
217C4×D4—41no—
218C4×D4—41no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C5×D411yescharacteristic
222C2×C22⋊C4—22no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—41no—
230C2×C22⋊C4—41no—
231C2×C22⋊C4C2×C4×C511yescharacteristic
232C2×C22⋊C4C2×C4×C511yescharacteristic
233C2×C22⋊C4C2×C4×C511yescharacteristic
234C2×C22⋊C4C5×D411yescharacteristic
235C2×C42—41no—
236C2×C42C5×D411yescharacteristic
237C4⋊C8—41no—
238C4⋊C8—41no—
239#100—22no—
240#100—22no—
241#99—22no—
242#99C5×D414yes—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—41no—
247C22×C5—21no—
248C22×C5—21no—
249C22×C5—22no—
250C22×C5—22no—
251C22×C5—42no—
252C22×C5—42no—
253C22×C5—42no—
254C22×C5—42no—
255C22×C5—42no—
256C22×C5—41no—
257C22×C5—41no—
258C22×C5—41no—
259C22×C5—41no—
260C22×C5—42no—
261C22×C5—81no—
262C22×C5—81no—
263C22×C5—81no—
264C22×C5—84no—
265C22×C5—84no—
266C22×C5—81no—
267C22×C5—81no—
268C22×C5#39011yescharacteristic
269C22×C5C2×#9911yescharacteristic
270C22×C5#41011yescharacteristic
271C4×C5—21no—
272C4×C5—21no—
273C4×C5—21no—
274C4×C5—21no—
275C4×C5—41no—
276C4×C5—41no—
277C4×C5—41no—
278C4×C5—81no—
279C4×C5—81no—
280C4×C5—84no—
281C4×C5—81no—
282C24—21no—
283C24—22no—
284C24—41no—
285C24—42no—
286C24—41no—
287C24—81no—
288C24C22×C4×C511yescharacteristic
289C24C2×C5×D411yescharacteristic
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—81no—
295C2×D4C2×C5×D412yes—
296C2×D4C5×#4112yes—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—42no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—81no—
309C22×C4—81no—
310C22×C4C5×C22⋊C411yescharacteristic
311C22×C4C5×C22⋊C411yescharacteristic
312C22×C4C5×C22⋊C411yescharacteristic
313C22×C4C5×C22⋊C411yescharacteristic
314C22×C4C2×C5×D411yescharacteristic
315M16—42no—
316M16—42no—
317C2×C8—42no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—81no—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—24no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—42no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—81no—
336C42—21no—
337C42—21no—
338C42—82no—
339C2×C5—21no—
340C2×C5—21no—
341C2×C5—42no—
342C2×C5—42no—
343C2×C5—82no—
344C2×C5#196411yescharacteristic
345C2×C5#212011yescharacteristic
346C2×C5#212111yescharacteristic
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—22no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—42no—
360C23—42no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—82no—
365C23—84no—
366C23—84no—
367C23—82no—
368C23C2×C5×C22⋊C411yescharacteristic
369C23C4×C5×D412yes—
370C23C5×#12112yes—
371D4—42no—
372D4—42no—
373D4—84no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—44no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—82no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4C5×#9911yescharacteristic
401C2×C4C5×#9911yescharacteristic
402C2×C4C5×#12411yescharacteristic
403C2×C4C5×#12711yescharacteristic
404C8—82no—
405C5#1322211yescharacteristic, direct product factor, Sylow
406C22—21no—
407C22—21no—
408C22—22no—
409C22—22no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—42no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—84no—
424C22—84no—
425C22—81no—
426C22—81no—
427C22C5×#39011yescharacteristic
428C22C2×C5×#9911yescharacteristic
429C22C5×#41011yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—81no—
438C4—81no—
439C4—84no—
440C4—81no—
441C2—21no—
442C2—21no—
443C2—42no—
444C2—42no—
445C2—82no—
446C2C5×#196411yescharacteristic
447C2C5×#212011yescharacteristic
448C2C5×#212111yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC24C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC2×C5×#120C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#352C2semidirect
4. C5×#1800C2semidirect
5. C4×C5×#99C2semidirect
9. C22×C5×C22⋊C4C4semidirect
17. C5×#381C4semidirect
18. C5×#380C4semidirect
19. C5×#379C4semidirect
25. #13222C5direct (N × H)
68. C2×#352C2×C5semidirect
70. #1800C2×C5semidirect
71. C4×#99C2×C5semidirect
132. C22×C22⋊C4C4×C5semidirect
140. #381C4×C5semidirect
141. #380C4×C5semidirect
142. #379C4×C5semidirect
405. C5#13222direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25342
C2×C5×#3522
C2×C5×AΣL(1,𝔽16)2
C5×#18002
C4×C5×#992
#132225