Finite Group Databasebeta

← C5×#9379 #11932099

Subgroups — C5×#9379 #11932099

Order 1280.

492 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3215C211yesmaximal, characteristic
2C5×#2337C211yesmaximal, characteristic
3C5×#1986C211yesmaximal, characteristic, complemented
4C5×#1527C211yesmaximal, characteristic
5C5×#1515C211yesmaximal, characteristic, complemented
6C5×#1288C211yesmaximal, characteristic, complemented
7C5×#1285C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C2×C5×#124C2211yescharacteristic
10C5×#497C412yescomplemented
11C5×#489C412yescomplemented
12C5×#464—22no—
13C5×#451—21no—
14C5×#450—21no—
15C5×#432C2211yescharacteristic
16C5×#432C2211yescharacteristic
17C4×C5×M16C2211yescharacteristic
18C5×#391—21no—
19C5×#388—21no—
20C5×#388—21no—
21C5×#386—21no—
22C5×#385—21no—
23C5×#383C2211yescharacteristic
24C4×C5×C4⋊C4C2211yescharacteristic
25C4×C5×C22⋊C4—21no—
26C5×#339—21no—
27C5×#339—21no—
28C5×#329—22no—
29C5×#328—21no—
30C5×#328—21no—
31#9379C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×Q8D411yescharacteristic
33C22×C5×D4D411yescharacteristic
34C23×C4×C5—21no—
35C2×C5×Q16—22no—
36C2×C5×SD16—22no—
37C2×C5×M16—21no—
38C5×C4⋊Q8C2×C411yescharacteristic, complemented
39C5×C4⋊Q8C2×C411yescharacteristic, complemented
40C5×#125—21no—
41C5×#124—21no—
42C5×#124—21no—
43C5×#124C2×C412yes—
44C5×#124D412yes—
45C5×C22⋊Q8—21no—
46C5×C22⋊Q8—21no—
47C4×C5×Q8—21no—
48C4×C5×Q8—21no—
49C5×#117—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×#103—22no—
64C5×#102—22no—
65C5×C22⋊C8—21no—
66C5×C22⋊C8—21no—
67C5×#97—21no—
68C5×#97—21no—
69C5×#97C2×C412yescomplemented
70C4×C5×C8—21no—
71C5×#95—21no—
72C5×#95—21no—
73C5×#95—21no—
74C5×#95—21no—
75C5×#95—21no—
76C5×#95D411yescharacteristic
77C5×#95D411yescharacteristic
78#3215C2×C511yescharacteristic
79#2337C2×C511yescharacteristic
80#1986C2×C511yescharacteristic, complemented
81#1527C2×C511yescharacteristic
82#1515C2×C511yescharacteristic, complemented
83#1288C2×C511yescharacteristic, complemented
84#1285C2×C511yescharacteristic, complemented
85C24×C5—21no—
86C2×C5×Q8—21no—
87C2×C5×Q8—21no—
88C2×C5×Q8—21no—
89C2×C5×Q8—81no—
90C2×C5×Q8C22⋊C412yes—
91C2×C5×D4—21no—
92C2×C5×D4—81no—
93C2×C5×D4C22⋊C412yes—
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—21no—
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5—42no—
100C22×C4×C5—81no—
101C22×C4×C5—81no—
102C22×C4×C5C2×D411yescharacteristic
103C22×C4×C5C2×D411yescharacteristic
104C22×C4×C5C2×D411yescharacteristic
105C5×Q16—82no—
106C5×SD16—82no—
107C5×M16—22no—
108C5×M16—41no—
109C2×C5×C8—22no—
110C2×C5×C8—41no—
111C2×C5×C8—41no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—42no—
117C5×C4⋊C4—41no—
118C5×C4⋊C4—41no—
119C5×C4⋊C4—81no—
120C5×C22⋊C4—22no—
121C5×C22⋊C4—22no—
122C5×C22⋊C4—22no—
123C5×C22⋊C4—22no—
124C5×C22⋊C4—42no—
125C5×C22⋊C4—41no—
126C5×C22⋊C4—81no—
127C5×C22⋊C4—81no—
128C42×C5—41no—
129C42×C5—41no—
130C42×C5—41no—
131C42×C5—81no—
132C42×C5C22×C411yescharacteristic
133C42×C5C2×D411yescharacteristic
134C42×C5#4111yescharacteristic
135C42×C5#4111yescharacteristic
136#533C22×C511yescharacteristic
137C2×#124C22×C511yescharacteristic
138#497C4×C512yescomplemented
139#489C4×C512yescomplemented
140#464—22no—
141#451—21no—
142#450—21no—
143#432C22×C511yescharacteristic
144#432C22×C511yescharacteristic
145C4×M16C22×C511yescharacteristic
146#391—21no—
147#388—21no—
148#388—21no—
149#386—21no—
150#385—21no—
151#383C22×C511yescharacteristic
152C4×C4⋊C4C22×C511yescharacteristic
153C4×C22⋊C4—21no—
154#339—21no—
155#339—21no—
156#329—22no—
157#328—21no—
158#328—21no—
159C23×C5—22no—
160C23×C5—41no—
161C23×C5—41no—
162C23×C5—41no—
163C23×C5—41no—
164C23×C5—41no—
165C23×C5—41no—
166C23×C5#12011yescharacteristic
167C5×Q8—42no—
168C5×Q8—42no—
169C5×Q8—81no—
170C5×Q8—81no—
171C5×D4—42no—
172C5×D4—81no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5—22no—
176C2×C4×C5—22no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
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—84no—
195C2×C4×C5C2×C22⋊C411yescharacteristic
196C2×C4×C5C4×D411yescharacteristic
197C2×C4×C5C4×D411yescharacteristic
198C2×C4×C5#12111yescharacteristic
199C2×C4×C5#12111yescharacteristic
200C2×C4×C5#12311yescharacteristic
201C5×C8—42no—
202C5×C8—42no—
203C5×C8—81no—
204C22×Q8C5×D411yescharacteristic
205C22×D4C5×D411yescharacteristic
206C23×C4—21no—
207C2×Q16—22no—
208C2×SD16—22no—
209C2×M16—21no—
210C4⋊Q8C2×C4×C511yescharacteristic, complemented
211C4⋊Q8C2×C4×C511yescharacteristic, complemented
212#125—21no—
213#124—21no—
214#124—21no—
215#124C2×C4×C512yes—
216#124C5×D412yes—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221#117—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C42—21no—
230C2×C42C5×D411yescharacteristic
231C2×C42C5×D411yescharacteristic
232C2×C42C23×C511yescharacteristic
233C4⋊C8—21no—
234C4⋊C8—21no—
235#103—22no—
236#102—22no—
237C22⋊C8—21no—
238C22⋊C8—21no—
239#97—21no—
240#97—21no—
241#97C2×C4×C512yescomplemented
242C4×C8—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95C5×D411yescharacteristic
249#95C5×D411yescharacteristic
250C22×C5—21no—
251C22×C5—21no—
252C22×C5—42no—
253C22×C5—42no—
254C22×C5—42no—
255C22×C5—81no—
256C22×C5—81no—
257C22×C5—81no—
258C22×C5—81no—
259C22×C5#38611yescharacteristic
260C22×C5#45511yescharacteristic
261C22×C5#45611yescharacteristic
262C4×C5—21no—
263C4×C5—21no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—21no—
268C4×C5—42no—
269C4×C5—42no—
270C4×C5—81no—
271C4×C5—81no—
272C4×C5—81no—
273C4×C5—81no—
274C4×C5—81no—
275C24—21no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—81no—
280C2×Q8C5×C22⋊C412yes—
281C2×D4—21no—
282C2×D4—81no—
283C2×D4C5×C22⋊C412yes—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—42no—
290C22×C4—81no—
291C22×C4—81no—
292C22×C4C2×C5×D411yescharacteristic
293C22×C4C2×C5×D411yescharacteristic
294C22×C4C2×C5×D411yescharacteristic
295Q16—82no—
296SD16—82no—
297M16—22no—
298M16—41no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—42no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—81no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—42no—
315C22⋊C4—41no—
316C22⋊C4—81no—
317C22⋊C4—81no—
318C42—41no—
319C42—41no—
320C42—41no—
321C42—81no—
322C42C22×C4×C511yescharacteristic
323C42C2×C5×D411yescharacteristic
324C42C5×#4111yescharacteristic
325C42C5×#4111yescharacteristic
326C2×C5—21no—
327C2×C5—21no—
328C2×C5—82no—
329C2×C5#188211yescharacteristic
330C2×C5#190611yescharacteristic
331C2×C5#191111yescharacteristic
332C23—22no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23C5×#12011yescharacteristic
340Q8—42no—
341Q8—42no—
342Q8—81no—
343Q8—81no—
344D4—42no—
345D4—81no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—84no—
368C2×C4C2×C5×C22⋊C411yescharacteristic
369C2×C4C4×C5×D411yescharacteristic
370C2×C4C4×C5×D411yescharacteristic
371C2×C4C5×#12111yescharacteristic
372C2×C4C5×#12111yescharacteristic
373C2×C4C5×#12311yescharacteristic
374C8—42no—
375C8—42no—
376C8—81no—
377C5#937911yescharacteristic, direct product factor, Sylow
378C22—21no—
379C22—21no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22C5×#38611yescharacteristic
388C22C5×#45511yescharacteristic
389C22C5×#45611yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—42no—
398C4—81no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C2—21no—
404C2—21no—
405C2—82no—
406C2C5×#188211yescharacteristic
407C2C5×#190611yescharacteristic
408C2C5×#191111yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4D4
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
3. C5×#1986C2semidirect
5. C5×#1515C2semidirect
6. C5×#1288C2semidirect
7. C5×#1285C2semidirect
10. C5×#497C4semidirect
11. C5×#489C4semidirect
31. #9379C5direct (N × H)
38. C5×C4⋊Q8C2×C4semidirect
39. C5×C4⋊Q8C2×C4semidirect
69. C5×#97C2×C4semidirect
80. #1986C2×C5semidirect
82. #1515C2×C5semidirect
83. #1288C2×C5semidirect
84. #1285C2×C5semidirect
138. #497C4×C5semidirect
139. #489C4×C5semidirect
210. C4⋊Q8C2×C4×C5semidirect
211. C4⋊Q8C2×C4×C5semidirect
241. #97C2×C4×C5semidirect
377. C5#9379direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32152
C5×#23372
C5×#19862
C5×#15272
C5×#15152
C5×#12882
C5×#12852
#93795