Finite Group Databasebeta

← C5×#9344 #11932064

Subgroups — C5×#9344 #11932064

Order 1280.

520 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3193C211yesmaximal, characteristic
2C5×#2378C211yesmaximal, characteristic, complemented
3C5×#1964C211yesmaximal, characteristic
4C5×#1510C211yesmaximal, characteristic
5C5×#1508C211yesmaximal, characteristic, complemented
6C5×#1305C211yesmaximal, characteristic, complemented
7C5×#1284C211yesmaximal, characteristic, complemented
8C2×C5×C22⋊Q8C2211yescharacteristic
9C2×C5×#121C2211yescharacteristic
10C5×#484C412yescomplemented
11C5×#480—21no—
12C5×#468—22no—
13C5×#450C412yescomplemented
14C5×#448—21no—
15C2×C5×#99—21no—
16C2×C5×#99—21no—
17C5×#407C2211yescharacteristic
18C5×#407C2211yescharacteristic
19C5×#391—21no—
20C5×#389—21no—
21C5×#388—21no—
22C5×#388—21no—
23C5×#387—21no—
24C5×#387—21no—
25C5×#381C2211yescharacteristic
26C5×#380C2211yescharacteristic
27C4×C5×C22⋊C4C2211yescharacteristic
28C5×#328—22no—
29C5×#327—21no—
30C5×#327—21no—
31#9344C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×Q8D411yescharacteristic
33C22×C5×D4—21no—
34C22×C5×D4C2×C411yescharacteristic
35C23×C4×C5C2311yescharacteristic
36C2×C5×SD16—22no—
37C2×C5×M16—21no—
38C2×C5×M16—21no—
39C5×C22⋊Q8—21no—
40C5×C22⋊Q8—21no—
41C5×C22⋊Q8C2×C412yes—
42C5×C22⋊Q8D412yes—
43C5×#121—21no—
44C5×#121—21no—
45C5×#121—21no—
46C5×#121—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4C2×C411yescharacteristic
52C2×C5×C4⋊C4D411yescharacteristic
53C2×C5×C22⋊C4—21no—
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4D411yescharacteristic
58C2×C5×C22⋊C4D411yescharacteristic
59C2×C42×C5—21no—
60C2×C42×C5—21no—
61C2×C42×C5—21no—
62C5×#107—22no—
63C5×#103—22no—
64C5×#102—22no—
65C5×#99—42no—
66C5×#99—42no—
67C5×C22⋊C8—21no—
68C5×C22⋊C8—21no—
69C5×C22⋊C8—21no—
70C5×C22⋊C8C2×C412yes—
71C5×#95—21no—
72C5×#95—21no—
73C5×#95—21no—
74C5×#95—21no—
75C5×#95—21no—
76C5×#95—21no—
77C5×#95—21no—
78C5×#95D411yescharacteristic
79C5×#95D411yescharacteristic
80#3193C2×C511yescharacteristic
81#2378C2×C511yescharacteristic, complemented
82#1964C2×C511yescharacteristic
83#1510C2×C511yescharacteristic
84#1508C2×C511yescharacteristic, complemented
85#1305C2×C511yescharacteristic, complemented
86#1284C2×C511yescharacteristic, complemented
87C24×C5—21no—
88C24×C5C2×D411yescharacteristic
89C2×C5×Q8—21no—
90C2×C5×Q8—81no—
91C2×C5×Q8C22⋊C412yes—
92C2×C5×D4—21no—
93C2×C5×D4—21no—
94C2×C5×D4—41no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—41no—
99C2×C5×D4—41no—
100C2×C5×D4—81no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5—21no—
108C22×C4×C5—41no—
109C22×C4×C5—81no—
110C22×C4×C5C22×C411yescharacteristic
111C22×C4×C5C2×D411yescharacteristic
112C22×C4×C5C2×D411yescharacteristic
113C22×C4×C5C2×D411yescharacteristic
114C22×C4×C5#4111yescharacteristic
115C22×C4×C5#4111yescharacteristic
116C5×SD16—82no—
117C5×M16—81no—
118C5×M16—81no—
119C2×C5×C8—22no—
120C2×C5×C8—41no—
121C5×C4⋊C4—22no—
122C5×C4⋊C4—22no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—81no—
127C5×C4⋊C4—81no—
128C5×C4⋊C4—81no—
129C5×C4⋊C4C22⋊C412yes—
130C5×C22⋊C4—22no—
131C5×C22⋊C4—22no—
132C5×C22⋊C4—22no—
133C5×C22⋊C4—41no—
134C5×C22⋊C4—41no—
135C5×C22⋊C4—41no—
136C5×C22⋊C4—41no—
137C5×C22⋊C4—41no—
138C5×C22⋊C4—81no—
139C42×C5—81no—
140C42×C5—81no—
141C42×C5—81no—
142C2×C22⋊Q8C22×C511yescharacteristic
143C2×#121C22×C511yescharacteristic
144#484C4×C512yescomplemented
145#480—21no—
146#468—22no—
147#450C4×C512yescomplemented
148#448—21no—
149C2×#99—21no—
150C2×#99—21no—
151#407C22×C511yescharacteristic
152#407C22×C511yescharacteristic
153#391—21no—
154#389—21no—
155#388—21no—
156#388—21no—
157#387—21no—
158#387—21no—
159#381C22×C511yescharacteristic
160#380C22×C511yescharacteristic
161C4×C22⋊C4C22×C511yescharacteristic
162#328—22no—
163#327—21no—
164#327—21no—
165C23×C5—21no—
166C23×C5—21no—
167C23×C5—41no—
168C23×C5—41no—
169C23×C5—41no—
170C23×C5—41no—
171C23×C5—41no—
172C23×C5—81no—
173C23×C5—81no—
174C23×C5C4×D411yescharacteristic
175C23×C5#12011yescharacteristic
176C23×C5#12111yescharacteristic
177C5×Q8—42no—
178C5×Q8—81no—
179C5×D4—42no—
180C5×D4—81no—
181C5×D4—81no—
182C5×D4—81no—
183C5×D4—81no—
184C5×D4—81no—
185C2×C4×C5—22no—
186C2×C4×C5—22no—
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—41no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—42no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5—81no—
214C2×C4×C5—81no—
215C2×C4×C5C2×C22⋊C411yescharacteristic
216C2×C4×C5C4×D411yescharacteristic
217C2×C4×C5#12111yescharacteristic
218C2×C4×C5#12311yescharacteristic
219C5×C8—42no—
220C5×C8—81no—
221C22×Q8C5×D411yescharacteristic
222C22×D4—21no—
223C22×D4C2×C4×C511yescharacteristic
224C23×C4C23×C511yescharacteristic
225C2×SD16—22no—
226C2×M16—21no—
227C2×M16—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C22⋊Q8C2×C4×C512yes—
231C22⋊Q8C5×D412yes—
232#121—21no—
233#121—21no—
234#121—21no—
235#121—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4C2×C4×C511yescharacteristic
241C2×C4⋊C4C5×D411yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4C5×D411yescharacteristic
247C2×C22⋊C4C5×D411yescharacteristic
248C2×C42—21no—
249C2×C42—21no—
250C2×C42—21no—
251#107—22no—
252#103—22no—
253#102—22no—
254#99—42no—
255#99—42no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8C2×C4×C512yes—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95C5×D411yescharacteristic
268#95C5×D411yescharacteristic
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—81no—
278C22×C5—81no—
279C22×C5—81no—
280C22×C5—81no—
281C22×C5—81no—
282C22×C5—161no—
283C22×C5—161no—
284C22×C5#38611yescharacteristic
285C22×C5#45311yescharacteristic
286C22×C5#45411yescharacteristic
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—42no—
292C4×C5—42no—
293C4×C5—81no—
294C4×C5—81no—
295C4×C5—81no—
296C4×C5—81no—
297C4×C5—82no—
298C4×C5—81no—
299C24—21no—
300C24C2×C5×D411yescharacteristic
301C2×Q8—21no—
302C2×Q8—81no—
303C2×Q8C5×C22⋊C412yes—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—81no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—81no—
322C22×C4C22×C4×C511yescharacteristic
323C22×C4C2×C5×D411yescharacteristic
324C22×C4C2×C5×D411yescharacteristic
325C22×C4C2×C5×D411yescharacteristic
326C22×C4C5×#4111yescharacteristic
327C22×C4C5×#4111yescharacteristic
328SD16—82no—
329M16—81no—
330M16—81no—
331C2×C8—22no—
332C2×C8—41no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—81no—
339C4⋊C4—81no—
340C4⋊C4—81no—
341C4⋊C4C5×C22⋊C412yes—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—81no—
351C42—81no—
352C42—81no—
353C42—81no—
354C2×C5—21no—
355C2×C5—21no—
356C2×C5—41no—
357C2×C5—41no—
358C2×C5—161no—
359C2×C5#188311yescharacteristic
360C2×C5#190511yescharacteristic
361C2×C5#191311yescharacteristic
362C23—21no—
363C23—21no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—81no—
370C23—81no—
371C23C4×C5×D411yescharacteristic
372C23C5×#12011yescharacteristic
373C23C5×#12111yescharacteristic
374Q8—42no—
375Q8—81no—
376D4—42no—
377D4—81no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—81no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—41no—
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—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4C2×C5×C22⋊C411yescharacteristic
413C2×C4C4×C5×D411yescharacteristic
414C2×C4C5×#12111yescharacteristic
415C2×C4C5×#12311yescharacteristic
416C8—42no—
417C8—81no—
418C5#934411yescharacteristic, direct product factor, Sylow
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—161no—
433C22—161no—
434C22C5×#38611yescharacteristic
435C22C5×#45311yescharacteristic
436C22C5×#45411yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—42no—
443C4—81no—
444C4—81no—
445C4—81no—
446C4—81no—
447C4—82no—
448C4—81no—
449C2—21no—
450C2—21no—
451C2—41no—
452C2—41no—
453C2—161no—
454C2C5×#188311yescharacteristic
455C2C5×#190511yescharacteristic
456C2C5×#191311yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC2×C5×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2378C2semidirect
5. C5×#1508C2semidirect
6. C5×#1305C2semidirect
7. C5×#1284C2semidirect
10. C5×#484C4semidirect
13. C5×#450C4semidirect
31. #9344C5direct (N × H)
81. #2378C2×C5semidirect
84. #1508C2×C5semidirect
85. #1305C2×C5semidirect
86. #1284C2×C5semidirect
144. #484C4×C5semidirect
147. #450C4×C5semidirect
418. C5#9344direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31932
C5×#23782
C5×#19642
C5×#15102
C5×#15082
C5×#13052
C5×#12842
#93445