Finite Group Databasebeta

← C5×#9381 #11932101

Subgroups — C5×#9381 #11932101

Order 1280.

530 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3213C211yesmaximal, characteristic
2C5×#2337C211yesmaximal, characteristic, complemented
3C5×#1980C211yesmaximal, characteristic, complemented
4C5×#1527C211yesmaximal, characteristic, complemented
5C5×#1514C211yesmaximal, characteristic, complemented
6C5×#1288C211yesmaximal, characteristic, complemented
7C5×#1285C211yesmaximal, characteristic, complemented
8C5×#532C2211yescharacteristic
9C2×C5×#124C2211yescharacteristic
10C5×#496C412yescomplemented
11C5×#489C412yescomplemented
12C5×#463—22no—
13C5×#448—21no—
14C5×#447—21no—
15C5×#432C2211yescharacteristic
16C5×#432C2211yescharacteristic
17C2×C5×#104—21no—
18C2×C5×#104—21no—
19C4×C5×M16C2211yescharacteristic
20C5×#391—21no—
21C5×#388—21no—
22C5×#388—21no—
23C5×#386—21no—
24C5×#385—21no—
25C5×#383C2211yescharacteristic
26C4×C5×C4⋊C4C2211yescharacteristic
27C4×C5×C22⋊C4—21no—
28C5×#329—22no—
29C5×#327—21no—
30C5×#327—21no—
31#9381C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41—21no—
33C22×C5×Q8D411yescharacteristic
34C22×C5×D4D411yescharacteristic
35C23×C4×C5—21no—
36C2×C5×SD16—22no—
37C2×C5×D8—22no—
38C2×C5×M16—21no—
39C5×C4⋊Q8C2×C411yescharacteristic, complemented
40C5×#127C2×C411yescharacteristic, complemented
41C5×#124—21no—
42C5×#124—21no—
43C5×#124—21no—
44C5×#124C2×C412yes—
45C5×#124D412yes—
46C5×#121—21no—
47C5×#121—21no—
48C4×C5×D4—21no—
49C4×C5×D4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—21no—
52C2×C5×C22⋊C4—21no—
53C2×C5×C22⋊C4—21no—
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×C42×C5—21no—
58C2×C42×C5D411yescharacteristic
59C2×C42×C5D411yescharacteristic
60C2×C42×C5C2311yescharacteristic
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×#104—42no—
64C5×#104—42no—
65C5×#103—22no—
66C5×#102—22no—
67C5×C22⋊C8—21no—
68C5×C22⋊C8—21no—
69C5×#97—21no—
70C5×#97—21no—
71C5×#97C2×C412yescomplemented
72C4×C5×C8—21no—
73C5×#95—21no—
74C5×#95—21no—
75C5×#95—21no—
76C5×#95—21no—
77C5×#95—21no—
78C5×#95D411yescharacteristic
79C5×#95D411yescharacteristic
80#3213C2×C511yescharacteristic
81#2337C2×C511yescharacteristic, complemented
82#1980C2×C511yescharacteristic, complemented
83#1527C2×C511yescharacteristic, complemented
84#1514C2×C511yescharacteristic, complemented
85#1288C2×C511yescharacteristic, complemented
86#1285C2×C511yescharacteristic, complemented
87C24×C5—21no—
88C5×#41—41no—
89C5×#41—41no—
90C5×#41—41no—
91C5×#41—41no—
92C2×C5×Q8—21no—
93C2×C5×Q8—21no—
94C2×C5×Q8—81no—
95C2×C5×Q8C22⋊C412yes—
96C2×C5×D4—21no—
97C2×C5×D4—21no—
98C2×C5×D4—21no—
99C2×C5×D4—21no—
100C2×C5×D4—41no—
101C2×C5×D4—81no—
102C2×C5×D4C22⋊C412yes—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5—21no—
108C22×C4×C5—42no—
109C22×C4×C5—41no—
110C22×C4×C5—81no—
111C22×C4×C5—81no—
112C22×C4×C5C2×D411yescharacteristic
113C22×C4×C5C2×D411yescharacteristic
114C22×C4×C5C2×D411yescharacteristic
115C5×SD16—82no—
116C5×D8—82no—
117C5×M16—22no—
118C5×M16—41no—
119C2×C5×C8—22no—
120C2×C5×C8—41no—
121C2×C5×C8—41no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—42no—
125C5×C4⋊C4—81no—
126C5×C22⋊C4—22no—
127C5×C22⋊C4—22no—
128C5×C22⋊C4—22no—
129C5×C22⋊C4—22no—
130C5×C22⋊C4—42no—
131C5×C22⋊C4—41no—
132C5×C22⋊C4—41no—
133C5×C22⋊C4—81no—
134C5×C22⋊C4—81no—
135C42×C5—41no—
136C42×C5—41no—
137C42×C5—81no—
138C42×C5C22×C411yescharacteristic
139C42×C5C2×D411yescharacteristic
140C42×C5#4111yescharacteristic
141C42×C5#4111yescharacteristic
142#532C22×C511yescharacteristic
143C2×#124C22×C511yescharacteristic
144#496C4×C512yescomplemented
145#489C4×C512yescomplemented
146#463—22no—
147#448—21no—
148#447—21no—
149#432C22×C511yescharacteristic
150#432C22×C511yescharacteristic
151C2×#104—21no—
152C2×#104—21no—
153C4×M16C22×C511yescharacteristic
154#391—21no—
155#388—21no—
156#388—21no—
157#386—21no—
158#385—21no—
159#383C22×C511yescharacteristic
160C4×C4⋊C4C22×C511yescharacteristic
161C4×C22⋊C4—21no—
162#329—22no—
163#327—21no—
164#327—21no—
165C23×C5—22no—
166C23×C5—41no—
167C23×C5—41no—
168C23×C5—41no—
169C23×C5—41no—
170C23×C5—41no—
171C23×C5—41no—
172C23×C5—41no—
173C23×C5#12011yescharacteristic
174C5×Q8—42no—
175C5×Q8—41no—
176C5×Q8—41no—
177C5×Q8—81no—
178C5×D4—42no—
179C5×D4—42no—
180C5×D4—41no—
181C5×D4—41no—
182C5×D4—81no—
183C5×D4—81no—
184C5×D4—81no—
185C5×D4—81no—
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—22no—
189C2×C4×C5—22no—
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—41no—
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—81no—
207C2×C4×C5—81no—
208C2×C4×C5—84no—
209C2×C4×C5C2×C22⋊C411yescharacteristic
210C2×C4×C5C4×D411yescharacteristic
211C2×C4×C5C4×D411yescharacteristic
212C2×C4×C5#12111yescharacteristic
213C2×C4×C5#12111yescharacteristic
214C2×C4×C5#12311yescharacteristic
215C5×C8—42no—
216C5×C8—42no—
217C5×C8—81no—
218C2×#41—21no—
219C22×Q8C5×D411yescharacteristic
220C22×D4C5×D411yescharacteristic
221C23×C4—21no—
222C2×SD16—22no—
223C2×D8—22no—
224C2×M16—21no—
225C4⋊Q8C2×C4×C511yescharacteristic, complemented
226#127C2×C4×C511yescharacteristic, complemented
227#124—21no—
228#124—21no—
229#124—21no—
230#124C2×C4×C512yes—
231#124C5×D412yes—
232#121—21no—
233#121—21no—
234C4×D4—21no—
235C4×D4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C42—21no—
244C2×C42C5×D411yescharacteristic
245C2×C42C5×D411yescharacteristic
246C2×C42C23×C511yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—21no—
249#104—42no—
250#104—42no—
251#103—22no—
252#102—22no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255#97—21no—
256#97—21no—
257#97C2×C4×C512yescomplemented
258C4×C8—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95C5×D411yescharacteristic
265#95C5×D411yescharacteristic
266C22×C5—21no—
267C22×C5—21no—
268C22×C5—42no—
269C22×C5—42no—
270C22×C5—42no—
271C22×C5—81no—
272C22×C5—81no—
273C22×C5—81no—
274C22×C5—81no—
275C22×C5—81no—
276C22×C5—81no—
277C22×C5—81no—
278C22×C5#38611yescharacteristic
279C22×C5#45311yescharacteristic
280C22×C5#45411yescharacteristic
281C4×C5—21no—
282C4×C5—21no—
283C4×C5—21no—
284C4×C5—21no—
285C4×C5—21no—
286C4×C5—21no—
287C4×C5—42no—
288C4×C5—42no—
289C4×C5—81no—
290C4×C5—81no—
291C4×C5—81no—
292C4×C5—81no—
293C24—21no—
294#41—41no—
295#41—41no—
296#41—41no—
297#41—41no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—81no—
301C2×Q8C5×C22⋊C412yes—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—81no—
308C2×D4C5×C22⋊C412yes—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—42no—
315C22×C4—41no—
316C22×C4—81no—
317C22×C4—81no—
318C22×C4C2×C5×D411yescharacteristic
319C22×C4C2×C5×D411yescharacteristic
320C22×C4C2×C5×D411yescharacteristic
321SD16—82no—
322D8—82no—
323M16—22no—
324M16—41no—
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—42no—
331C4⋊C4—81no—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—42no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—81no—
340C22⋊C4—81no—
341C42—41no—
342C42—41no—
343C42—81no—
344C42C22×C4×C511yescharacteristic
345C42C2×C5×D411yescharacteristic
346C42C5×#4111yescharacteristic
347C42C5×#4111yescharacteristic
348C2×C5—21no—
349C2×C5—21no—
350C2×C5—82no—
351C2×C5—161no—
352C2×C5#188311yescharacteristic
353C2×C5#190611yescharacteristic
354C2×C5#191111yescharacteristic
355C23—22no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23C5×#12011yescharacteristic
364Q8—42no—
365Q8—41no—
366Q8—41no—
367Q8—81no—
368D4—42no—
369D4—42no—
370D4—41no—
371D4—41no—
372D4—81no—
373D4—81no—
374D4—81no—
375D4—81no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
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—81no—
397C2×C4—81no—
398C2×C4—84no—
399C2×C4C2×C5×C22⋊C411yescharacteristic
400C2×C4C4×C5×D411yescharacteristic
401C2×C4C4×C5×D411yescharacteristic
402C2×C4C5×#12111yescharacteristic
403C2×C4C5×#12111yescharacteristic
404C2×C4C5×#12311yescharacteristic
405C8—42no—
406C8—42no—
407C8—81no—
408C5#938111yescharacteristic, direct product factor, Sylow
409C22—21no—
410C22—21no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22C5×#38611yescharacteristic
422C22C5×#45311yescharacteristic
423C22C5×#45411yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—42no—
431C4—42no—
432C4—81no—
433C4—81no—
434C4—81no—
435C4—81no—
436C2—21no—
437C2—21no—
438C2—82no—
439C2—161no—
440C2C5×#188311yescharacteristic
441C2C5×#190611yescharacteristic
442C2C5×#191111yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC5×#3213C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2337C2semidirect
3. C5×#1980C2semidirect
4. C5×#1527C2semidirect
5. C5×#1514C2semidirect
6. C5×#1288C2semidirect
7. C5×#1285C2semidirect
10. C5×#496C4semidirect
11. C5×#489C4semidirect
31. #9381C5direct (N × H)
39. C5×C4⋊Q8C2×C4semidirect
40. C5×#127C2×C4semidirect
71. C5×#97C2×C4semidirect
81. #2337C2×C5semidirect
82. #1980C2×C5semidirect
83. #1527C2×C5semidirect
84. #1514C2×C5semidirect
85. #1288C2×C5semidirect
86. #1285C2×C5semidirect
144. #496C4×C5semidirect
145. #489C4×C5semidirect
225. C4⋊Q8C2×C4×C5semidirect
226. #127C2×C4×C5semidirect
257. #97C2×C4×C5semidirect
408. C5#9381direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32132
C5×#23372
C5×#19802
C5×#15272
C5×#15142
C5×#12882
C5×#12852
#93815