Finite Group Databasebeta

← C5×#18148 #11940868

Subgroups — C5×#18148 #11940868

Order 1280.

930 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#544C211yesmaximal, characteristic
2C5×#3095C212yesmaximal
3C5×#2484C211yesmaximal, characteristic
4C5×#1617C214yesmaximal, complemented
5C5×#1611C214yesmaximal, complemented
6C5×#1511C212yesmaximal
7C5×#1463C211yesmaximal, characteristic
8C5×#544—24no—
9C5×#544—22no—
10C5×#544C2214yes—
11C2×C5×C4⋊Q8—22no—
12C2×C5×#125—22no—
13C2×C5×C22⋊Q8—21no—
14C2×C5×C22⋊Q8C2212yes—
15C2×C5×#117—21no—
16C2×C5×#117C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C5×#485—24no—
19C5×#484C2214yes—
20C5×#483C2214yes—
21C5×#428—22no—
22C5×#419—22no—
23C5×#407C2212yes—
24C5×#400C2212yes—
25C5×#398C2212yes—
26C5×#387—22no—
27C5×#385—21no—
28C5×#381—21no—
29C5×#381C2211yescharacteristic
30C5×#328C2218yes—
31C5×#324C2214yes—
32#18148C511yesmaximal, characteristic, direct product factor, Sylow
33C22×C5×Q8—21no—
34C22×C5×Q8D412yes—
35C23×C4×C5D411yescharacteristic
36C23×C4×C5D411yescharacteristic
37C23×C4×C5C2311yescharacteristic
38C2×C5×M16—22no—
39C5×C4⋊Q8—28no—
40C5×C4⋊Q8—28no—
41C5×#125—28no—
42C5×#125—28no—
43C5×C22⋊Q8—24no—
44C5×C22⋊Q8—24no—
45C5×C22⋊Q8—22no—
46C5×C22⋊Q8—22no—
47C5×C22⋊Q8D414yes—
48C5×C22⋊Q8C2314yes—
49C5×#117—24no—
50C5×#117—24no—
51C5×#117—22no—
52C5×#117—22no—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4—22no—
57C2×C5×C4⋊C4—22no—
58C2×C5×C4⋊C4—22no—
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4D412yes—
62C2×C5×C4⋊C4D412yes—
63C2×C5×C4⋊C4C2311yescharacteristic
64C2×C5×C4⋊C4C2311yescharacteristic
65C2×C5×C4⋊C4C2312yes—
66C2×C5×C22⋊C4—22no—
67C2×C5×C22⋊C4—21no—
68C2×C5×C22⋊C4—21no—
69C2×C42×C5—22no—
70C2×C42×C5—21no—
71C5×#107—24no—
72C5×#106—24no—
73C5×#103—24no—
74C5×#103—24no—
75C5×C22⋊C8—22no—
76C5×C22⋊C8C2314yes—
77C5×#95—22no—
78C5×#95—22no—
79C5×#95—21no—
80C5×#95—22no—
81C5×#95C2312yes—
82C2×#544C2×C511yescharacteristic
83#3095C2×C512yes—
84#2484C2×C511yescharacteristic
85#1617C2×C514yescomplemented
86#1611C2×C514yescomplemented
87#1511C2×C512yes—
88#1463C2×C511yescharacteristic
89C24×C5C2×D411yescharacteristic
90C2×C5×Q8—24no—
91C2×C5×Q8—22no—
92C2×C5×Q8—44no—
93C2×C5×Q8—82no—
94C2×C5×Q8C2×D414yes—
95C22×C4×C5—21no—
96C22×C4×C5—21no—
97C22×C4×C5—24no—
98C22×C4×C5—22no—
99C22×C4×C5—22no—
100C22×C4×C5—21no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—22no—
105C22×C4×C5—42no—
106C22×C4×C5—42no—
107C22×C4×C5C2×D412yes—
108C22×C4×C5C2×D412yes—
109C22×C4×C5C2×D412yes—
110C22×C4×C5C2×D411yescharacteristic
111C22×C4×C5C2×D412yes—
112C22×C4×C5C2411yescharacteristic
113C5×M16—44no—
114C2×C5×C8—24no—
115C5×C4⋊C4—24no—
116C5×C4⋊C4—24no—
117C5×C4⋊C4—24no—
118C5×C4⋊C4—28no—
119C5×C4⋊C4—24no—
120C5×C4⋊C4—24no—
121C5×C4⋊C4—22no—
122C5×C4⋊C4—24no—
123C5×C4⋊C4—24no—
124C5×C4⋊C4—22no—
125C5×C4⋊C4—22no—
126C5×C4⋊C4—44no—
127C5×C4⋊C4C2×D414yes—
128C5×C22⋊C4—24no—
129C5×C22⋊C4—24no—
130C5×C22⋊C4—42no—
131C5×C22⋊C4—41no—
132C5×C22⋊C4—41no—
133C42×C5—28no—
134C42×C5—42no—
135#544—24no—
136#544—22no—
137#544C22×C514yes—
138C2×C4⋊Q8—22no—
139C2×#125—22no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8C22×C512yes—
142C2×#117—21no—
143C2×#117C22×C511yescharacteristic
144C22×C4⋊C4C22×C511yescharacteristic
145#485—24no—
146#484C22×C514yes—
147#483C22×C514yes—
148#428—22no—
149#419—22no—
150#407C22×C512yes—
151#400C22×C512yes—
152#398C22×C512yes—
153#387—22no—
154#385—21no—
155#381—21no—
156#381C22×C511yescharacteristic
157#328C22×C518yes—
158#324C22×C514yes—
159C23×C5—22no—
160C23×C5—22no—
161C23×C5—41no—
162C23×C5#12011yescharacteristic
163C23×C5#12011yescharacteristic
164C23×C5C22×D411yescharacteristic
165C5×Q8—44no—
166C5×Q8—82no—
167C5×Q8—84no—
168C2×C4×C5—24no—
169C2×C4×C5—24no—
170C2×C4×C5—22no—
171C2×C4×C5—22no—
172C2×C4×C5—24no—
173C2×C4×C5—24no—
174C2×C4×C5—24no—
175C2×C4×C5—22no—
176C2×C4×C5—42no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—44no—
180C2×C4×C5—42no—
181C2×C4×C5—44no—
182C2×C4×C5—42no—
183C2×C4×C5—42no—
184C2×C4×C5—42no—
185C2×C4×C5—42no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—42no—
189C2×C4×C5—42no—
190C2×C4×C5—81no—
191C2×C4×C5#12012yes—
192C2×C4×C5#13714yes—
193C2×C4×C5C22×D412yes—
194C5×C8—44no—
195C22×Q8—21no—
196C22×Q8C5×D412yes—
197C23×C4C5×D411yescharacteristic
198C23×C4C5×D411yescharacteristic
199C23×C4C23×C511yescharacteristic
200C2×M16—22no—
201C4⋊Q8—28no—
202C4⋊Q8—28no—
203#125—28no—
204#125—28no—
205C22⋊Q8—24no—
206C22⋊Q8—24no—
207C22⋊Q8—22no—
208C22⋊Q8—22no—
209C22⋊Q8C5×D414yes—
210C22⋊Q8C23×C514yes—
211#117—24no—
212#117—24no—
213#117—22no—
214#117—22no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4C5×D412yes—
224C2×C4⋊C4C5×D412yes—
225C2×C4⋊C4C23×C511yescharacteristic
226C2×C4⋊C4C23×C511yescharacteristic
227C2×C4⋊C4C23×C512yes—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C42—22no—
232C2×C42—21no—
233#107—24no—
234#106—24no—
235#103—24no—
236#103—24no—
237C22⋊C8—22no—
238C22⋊C8C23×C514yes—
239#95—22no—
240#95—22no—
241#95—21no—
242#95—22no—
243#95C23×C512yes—
244C22×C5—21no—
245C22×C5—21no—
246C22×C5—21no—
247C22×C5—21no—
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—44no—
252C22×C5#45812yes—
253C22×C5C2×#12011yescharacteristic
254C22×C5C2×#13712yes—
255C4×C5—24no—
256C4×C5—22no—
257C4×C5—22no—
258C4×C5—44no—
259C4×C5—42no—
260C4×C5—44no—
261C4×C5—82no—
262C4×C5—81no—
263C4×C5—81no—
264C24C2×C5×D411yescharacteristic
265C2×Q8—24no—
266C2×Q8—22no—
267C2×Q8—44no—
268C2×Q8—82no—
269C2×Q8C2×C5×D414yes—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—24no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4C2×C5×D412yes—
283C22×C4C2×C5×D412yes—
284C22×C4C2×C5×D412yes—
285C22×C4C2×C5×D411yescharacteristic
286C22×C4C2×C5×D412yes—
287C22×C4C24×C511yescharacteristic
288M16—44no—
289C2×C8—24no—
290C4⋊C4—24no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—28no—
294C4⋊C4—24no—
295C4⋊C4—24no—
296C4⋊C4—22no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—44no—
302C4⋊C4C2×C5×D414yes—
303C22⋊C4—24no—
304C22⋊C4—24no—
305C22⋊C4—42no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42—28no—
309C42—42no—
310C2×C5—22no—
311C2×C5—22no—
312C2×C5—41no—
313C2×C5#300411yescharacteristic
314C2×C5#302011yescharacteristic
315C2×C5C2×#45811yescharacteristic
316C23—22no—
317C23—22no—
318C23—41no—
319C23C5×#12011yescharacteristic
320C23C5×#12011yescharacteristic
321C23C22×C5×D411yescharacteristic
322Q8—44no—
323Q8—82no—
324Q8—84no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—22no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4C5×#12012yes—
349C2×C4C5×#13714yes—
350C2×C4C22×C5×D412yes—
351C8—44no—
352C5#1814811yescharacteristic, direct product factor, Sylow
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22C5×#45812yes—
362C22C2×C5×#12011yescharacteristic
363C22C2×C5×#13712yes—
364C4—24no—
365C4—22no—
366C4—22no—
367C4—44no—
368C4—42no—
369C4—44no—
370C4—82no—
371C4—81no—
372C4—81no—
373C2—22no—
374C2—22no—
375C2—41no—
376C2C5×#300411yescharacteristic
377C2C5×#302011yescharacteristic
378C2C2×C5×#45811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
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
4. C5×#1617C2semidirect
5. C5×#1611C2semidirect
32. #18148C5direct (N × H)
85. #1617C2×C5semidirect
86. #1611C2×C5semidirect
352. C5#18148direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5442
C5×#30952
C5×#24842
C5×#16172
C5×#16112
C5×#15112
C5×#14632
#181485