Finite Group Databasebeta

← C5×#9301 #11932021

Subgroups — C5×#9301 #11932021

Order 1280.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3206C211yesmaximal, characteristic
2C5×#2331C211yesmaximal, characteristic, complemented
3C5×#1963C211yesmaximal, characteristic
4C5×#1548C211yesmaximal, characteristic, complemented
5C5×#1517C211yesmaximal, characteristic
6C5×#1286C211yesmaximal, characteristic, complemented
7C5×#1274C211yesmaximal, characteristic, complemented
8C5×#532C2211yescharacteristic
9C2×C5×C4⋊Q8C2211yescharacteristic
10C5×#492C412yescomplemented
11C5×#487C412yescomplemented
12C5×#461—22no—
13C5×#448—22no—
14C5×#431C2211yescharacteristic
15C5×#431C2211yescharacteristic
16C5×#423C2211yescharacteristic
17C2×C5×#104—21no—
18C2×C5×#104—21no—
19C5×#391—22no—
20C5×#389—21no—
21C5×#387—22no—
22C5×#382C2211yescharacteristic
23C4×C5×C4⋊C4—21no—
24C5×#376C2211yescharacteristic
25C5×#333—22no—
26C5×#327—22no—
27#9301C511yesmaximal, characteristic, direct product factor, Sylow
28C2×C5×#41—21no—
29C22×C5×Q8D412yes—
30C2×C5×SD16—24no—
31C2×C5×M16—21no—
32C5×C4⋊Q8—21no—
33C5×C4⋊Q8—21no—
34C5×C4⋊Q8C2×C411yescharacteristic
35C5×C4⋊Q8C2×C412yes—
36C5×C4⋊Q8D412yes—
37C5×#127C2×C411yescharacteristic
38C5×#124—21no—
39C5×#121—21no—
40C5×#121—21no—
41C4×C5×D4—21no—
42C4×C5×D4—21no—
43C2×C5×C4⋊C4—21no—
44C2×C5×C4⋊C4—21no—
45C2×C5×C4⋊C4—21no—
46C2×C5×C4⋊C4—22no—
47C2×C42×C5—22no—
48C2×C42×C5D411yescharacteristic
49C2×C42×C5D411yescharacteristic
50C2×C42×C5C2311yescharacteristic
51C5×C4⋊C8—21no—
52C5×C4⋊C8—21no—
53C5×C4⋊C8—21no—
54C5×C4⋊C8—21no—
55C5×#104—42no—
56C5×#104—42no—
57C5×#103—24no—
58C5×C22⋊C8—21no—
59C5×C22⋊C8—21no—
60C4×C5×C8—21no—
61C4×C5×C8C2×C412yes—
62C5×#95—22no—
63C5×#95—22no—
64C5×#95—21no—
65C5×#95—21no—
66C5×#95—21no—
67C5×#95D412yes—
68#3206C2×C511yescharacteristic
69#2331C2×C511yescharacteristic, complemented
70#1963C2×C511yescharacteristic
71#1548C2×C511yescharacteristic, complemented
72#1517C2×C511yescharacteristic
73#1286C2×C511yescharacteristic, complemented
74#1274C2×C511yescharacteristic, complemented
75C5×#41—41no—
76C5×#41—41no—
77C5×#41—41no—
78C5×#41—41no—
79C2×C5×Q8—22no—
80C2×C5×Q8—21no—
81C2×C5×Q8—82no—
82C2×C5×Q8C22⋊C414yes—
83C2×C5×D4—21no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4—41no—
87C22×C4×C5—21no—
88C22×C4×C5—22no—
89C22×C4×C5—22no—
90C22×C4×C5—21no—
91C22×C4×C5—41no—
92C22×C4×C5C2×D411yescharacteristic
93C22×C4×C5C2×D411yescharacteristic
94C22×C4×C5C2×D411yescharacteristic
95C5×SD16—84no—
96C5×M16—41no—
97C5×M16—41no—
98C2×C5×C8—22no—
99C2×C5×C8—41no—
100C2×C5×C8—41no—
101C5×C4⋊C4—22no—
102C5×C4⋊C4—22no—
103C5×C4⋊C4—22no—
104C5×C4⋊C4—22no—
105C5×C4⋊C4—21no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—41no—
108C5×C4⋊C4—41no—
109C5×C4⋊C4—82no—
110C5×C22⋊C4—41no—
111C5×C22⋊C4—41no—
112C42×C5—21no—
113C42×C5—21no—
114C42×C5—21no—
115C42×C5—82no—
116C42×C5SD1612yescomplemented
117C42×C5C22×C411yescharacteristic
118C42×C5C2×D411yescharacteristic
119C42×C5#4111yescharacteristic
120C42×C5#4111yescharacteristic
121#532C22×C511yescharacteristic
122C2×C4⋊Q8C22×C511yescharacteristic
123#492C4×C512yescomplemented
124#487C4×C512yescomplemented
125#461—22no—
126#448—22no—
127#431C22×C511yescharacteristic
128#431C22×C511yescharacteristic
129#423C22×C511yescharacteristic
130C2×#104—21no—
131C2×#104—21no—
132#391—22no—
133#389—21no—
134#387—22no—
135#382C22×C511yescharacteristic
136C4×C4⋊C4—21no—
137#376C22×C511yescharacteristic
138#333—22no—
139#327—22no—
140C23×C5—41no—
141C23×C5#12011yescharacteristic
142C5×Q8—44no—
143C5×Q8—41no—
144C5×Q8—41no—
145C5×Q8—82no—
146C5×D4—42no—
147C5×D4—41no—
148C5×D4—41no—
149C5×D4—81no—
150C5×D4—81no—
151C5×D4—81no—
152C2×C4×C5—24no—
153C2×C4×C5—22no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—42no—
158C2×C4×C5—42no—
159C2×C4×C5—41no—
160C2×C4×C5—42no—
161C2×C4×C5—41no—
162C2×C4×C5—42no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—42no—
167C2×C4×C5—81no—
168C2×C4×C5—81no—
169C2×C4×C5C2×C22⋊C411yescharacteristic
170C2×C4×C5C4×D411yescharacteristic
171C2×C4×C5C4×D411yescharacteristic
172C2×C4×C5#12111yescharacteristic
173C2×C4×C5#12111yescharacteristic
174C2×C4×C5#12311yescharacteristic
175C2×C4×C5C2×SD1611yescharacteristic
176C2×C4×C5#13511yescharacteristic
177C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C5#13711yescharacteristic
179C5×C8—42no—
180C5×C8—81no—
181C5×C8—81no—
182C2×#41—21no—
183C22×Q8C5×D412yes—
184C2×SD16—24no—
185C2×M16—21no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8C2×C4×C511yescharacteristic
189C4⋊Q8C2×C4×C512yes—
190C4⋊Q8C5×D412yes—
191#127C2×C4×C511yescharacteristic
192#124—21no—
193#121—21no—
194#121—21no—
195C4×D4—21no—
196C4×D4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—22no—
201C2×C42—22no—
202C2×C42C5×D411yescharacteristic
203C2×C42C5×D411yescharacteristic
204C2×C42C23×C511yescharacteristic
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209#104—42no—
210#104—42no—
211#103—24no—
212C22⋊C8—21no—
213C22⋊C8—21no—
214C4×C8—21no—
215C4×C8C2×C4×C512yes—
216#95—22no—
217#95—22no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95C5×D412yes—
222C22×C5—21no—
223C22×C5—21no—
224C22×C5—81no—
225C22×C5—81no—
226C22×C5—81no—
227C22×C5#38611yescharacteristic
228C22×C5#44811yescharacteristic
229C22×C5#44911yescharacteristic
230C4×C5—21no—
231C4×C5—21no—
232C4×C5—21no—
233C4×C5—21no—
234C4×C5—42no—
235C4×C5—44no—
236C4×C5—82no—
237C4×C5—81no—
238C4×C5—81no—
239C4×C5C4×SD1611yescharacteristic
240C4×C5#44011yescharacteristic
241C4×C5#46011yescharacteristic
242C4×C5#46411yescharacteristic
243#41—41no—
244#41—41no—
245#41—41no—
246#41—41no—
247C2×Q8—22no—
248C2×Q8—21no—
249C2×Q8—82no—
250C2×Q8C5×C22⋊C414yes—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4C2×C5×D411yescharacteristic
261C22×C4C2×C5×D411yescharacteristic
262C22×C4C2×C5×D411yescharacteristic
263SD16—84no—
264M16—41no—
265M16—41no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—82no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C42—21no—
281C42—21no—
282C42—21no—
283C42—82no—
284C42C5×SD1612yescomplemented
285C42C22×C4×C511yescharacteristic
286C42C2×C5×D411yescharacteristic
287C42C5×#4111yescharacteristic
288C42C5×#4111yescharacteristic
289C2×C5—21no—
290C2×C5—21no—
291C2×C5—161no—
292C2×C5#188011yescharacteristic
293C2×C5#190511yescharacteristic
294C2×C5#191111yescharacteristic
295C23—41no—
296C23C5×#12011yescharacteristic
297Q8—44no—
298Q8—41no—
299Q8—41no—
300Q8—82no—
301D4—42no—
302D4—41no—
303D4—41no—
304D4—81no—
305D4—81no—
306D4—81no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4C2×C5×C22⋊C411yescharacteristic
325C2×C4C4×C5×D411yescharacteristic
326C2×C4C4×C5×D411yescharacteristic
327C2×C4C5×#12111yescharacteristic
328C2×C4C5×#12111yescharacteristic
329C2×C4C5×#12311yescharacteristic
330C2×C4C2×C5×SD1611yescharacteristic
331C2×C4C5×#13511yescharacteristic
332C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
333C2×C4C5×#13711yescharacteristic
334C8—42no—
335C8—81no—
336C8—81no—
337C5#930111yescharacteristic, direct product factor, Sylow
338C22—21no—
339C22—21no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22C5×#38611yescharacteristic
344C22C5×#44811yescharacteristic
345C22C5×#44911yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—44no—
352C4—82no—
353C4—81no—
354C4—81no—
355C4C4×C5×SD1611yescharacteristic
356C4C5×#44011yescharacteristic
357C4C5×#46011yescharacteristic
358C4C5×#46411yescharacteristic
359C2—21no—
360C2—21no—
361C2—161no—
362C2C5×#188011yescharacteristic
363C2C5×#190511yescharacteristic
364C2C5×#191111yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC5×#532C22
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×#2331C2semidirect
4. C5×#1548C2semidirect
6. C5×#1286C2semidirect
7. C5×#1274C2semidirect
10. C5×#492C4semidirect
11. C5×#487C4semidirect
27. #9301C5direct (N × H)
69. #2331C2×C5semidirect
71. #1548C2×C5semidirect
73. #1286C2×C5semidirect
74. #1274C2×C5semidirect
116. C42×C5SD16semidirect
123. #492C4×C5semidirect
124. #487C4×C5semidirect
284. C42C5×SD16semidirect
337. C5#9301direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32062
C5×#23312
C5×#19632
C5×#15482
C5×#15172
C5×#12862
C5×#12742
#93015