Finite Group Databasebeta

← C5×#71128 #14289940

Subgroups — C5×#71128 #14289940

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5585C211yesmaximal, characteristic
2C3×C5×#475C211yesmaximal, characteristic, complemented
3C5×#5090C211yesmaximal, characteristic, complemented
4C5×#5088C211yesmaximal, characteristic
5C5×#4535C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic
7C5×#4484C211yesmaximal, characteristic, complemented
8C5×#1640—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×Q8C2211yescharacteristic
11C5×#947—21no—
12C2×C5×#216—21no—
13C5×#894—22no—
14C5×#893—21no—
15C5×#875—21no—
16C5×#874C2211yescharacteristic
17C4×C5×D12—21no—
18C4×C5×Dic6C2211yescharacteristic
19C3×C5×#106—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#103—21no—
22C5×#835—21no—
23C5×#809—22no—
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#71128C511yesmaximal, characteristic, direct product factor, Hall
27C5×#559—31no—
28C5×#486—31no—
29C5×#475D311yescharacteristic, complemented
30C5×#462—31no—
31C5×#331—31no—
32C5×Q8⋊C8—31no—
33C5×Q8⋊C8—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×D12D412yes—
39C2×C4×C5×D3—22no—
40C2×C5×Dic6D411yescharacteristic
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C42×C5—21no—
47C3×C42×C5C2311yescharacteristic
48C5×#216—42no—
49C5×(C2×D3)⋊C4—22no—
50C5×(C2×D3)⋊C4—22no—
51C5×(C2×D3)⋊C4—22no—
52C5×C4⋊Dic3D411yescharacteristic
53C5×Dic3⋊C4—21no—
54C4×C5×Dic3—21no—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8—21no—
57#5585C2×C511yescharacteristic
58C3×#475C2×C511yescharacteristic, complemented
59#5090C2×C511yescharacteristic, complemented
60#5088C2×C511yescharacteristic
61#4535C2×C511yescharacteristic, complemented
62#4485C2×C511yescharacteristic
63#4484C2×C511yescharacteristic, complemented
64C2×C5×Q16—61no—
65C5×C4⋊Q8C2×D311yescharacteristic
66C5×#127—31no—
67C5×#124—61no—
68C5×#124—61no—
69C5×#123—62no—
70C4×C5×Q8—31no—
71C4×C5×Q8C2×D311yescharacteristic
72C4×C5×D4—61no—
73C4×C5×D4—61no—
74C5×#106—21no—
75C5×C4⋊C8—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77C5×#103—21no—
78C5×#103—61no—
79C5×#102—62no—
80C4×C5×C8—31no—
81#1640—31noSylow
82C22×C5×D3—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C5×Dic3—21no—
94C2×C5×Dic3—21no—
95C5×D12—42no—
96C5×D12—41no—
97C5×D12—41no—
98C5×D12—41no—
99C5×D12—41no—
100C4×C5×D3—82no—
101C5×Dic6—21no—
102C5×Dic6—21no—
103C3×C5×C8—41no—
104C5×C3⋊C8—41no—
105C5×C3⋊C8—41no—
106C3×C4⋊Q8C22×C511yescharacteristic
107C3×C4×Q8C22×C511yescharacteristic
108#947—21no—
109C2×#216—21no—
110#894—22no—
111#893—21no—
112#875—21no—
113#874C22×C511yescharacteristic
114C4×D12—21no—
115C4×Dic6C22×C511yescharacteristic
116C3×#106—21no—
117C3×C4⋊C8C22×C511yescharacteristic
118C3×#103—21no—
119#835—21no—
120#809—22no—
121C4⋊(C3⋊C8)C22×C511yescharacteristic
122C4×C3⋊C8C22×C511yescharacteristic
123C2×C5×Q8—21no—
124C2×C5×Q8—31no—
125C2×C5×Q8#6711yescharacteristic
126C2×C5×D4—32no—
127C2×C5×D4—61no—
128C2×C5×D4—61no—
129C22×C4×C5—62no—
130C5×Q16—122no—
131C2×C5×C8—21no—
132C2×C5×C8—61no—
133C2×C5×C8—61no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—31no—
138C5×C4⋊C4—61no—
139C5×C4⋊C4#6711yescharacteristic
140C5×C22⋊C4—62no—
141C5×C22⋊C4—62no—
142C5×C22⋊C4—62no—
143C42×C5—21no—
144C42×C5—61no—
145C42×C5C22×D311yescharacteristic
146#559—31no—
147#486—31no—
148#475C5×D311yescharacteristic, complemented
149#462—31no—
150#331—31no—
151Q8⋊C8—31no—
152Q8⋊C8—31no—
153C22×C3×C5#12011yescharacteristic
154C2×C5×D3—42no—
155C2×C5×D3—42no—
156C2×C5×D3—42no—
157C3×C4×C5—21no—
158C3×C4×C5—41no—
159C3×C4×C5—41no—
160C3×C4×C5—81no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165C5×Dic3—41no—
166C5×Dic3—41no—
167C2×C3×Q8—21no—
168C2×C3×Q8C5×D411yescharacteristic
169C2×D12—21no—
170C2×D12—21no—
171C2×D12C5×D412yes—
172C2×C4×D3—22no—
173C2×Dic6C5×D411yescharacteristic
174C2×C3×C8—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4C5×D411yescharacteristic
179C3×C42—21no—
180C3×C42C23×C511yescharacteristic
181#216—42no—
182(C2×D3)⋊C4—22no—
183(C2×D3)⋊C4—22no—
184(C2×D3)⋊C4—22no—
185C4⋊Dic3C5×D411yescharacteristic
186Dic3⋊C4—21no—
187C4×Dic3—21no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190C23×C5—62no—
191C5×Q8—21no—
192C5×Q8—21no—
193C5×Q8—41no—
194C5×Q8—41no—
195C5×Q8—61no—
196C5×Q8—61no—
197C5×D4—122no—
198C5×D4—121no—
199C5×D4—121no—
200C5×D4—121no—
201C5×D4—121no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—41no—
205C2×C4×C5—61no—
206C2×C4×C5—61no—
207C2×C4×C5—242no—
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C5×C8—41no—
212C5×C8—121no—
213C5×C8—121no—
214C2×Q16—61no—
215C4⋊Q8C2×C5×D311yescharacteristic
216#127—31no—
217#124—61no—
218#124—61no—
219#123—62no—
220C4×Q8—31no—
221C4×Q8C2×C5×D311yescharacteristic
222C4×D4—61no—
223C4×D4—61no—
224#106—21no—
225C4⋊C8—31no—
226C4⋊C8C2×C5×D311yescharacteristic
227#103—21no—
228#103—61no—
229#102—62no—
230C4×C8—31no—
231C2×C3×C5#44911yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45511yescharacteristic
234C5×D3—82no—
235C22×D3—22no—
236C3×Q8—21no—
237C3×Q8—21no—
238C3×Q8—41no—
239C3×Q8—41no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—41no—
243C2×C3×C4C2×C5×D411yescharacteristic
244C2×C3×C4C2×C5×D411yescharacteristic
245C2×C3×C4C2×C5×D411yescharacteristic
246C2×Dic3—21no—
247C2×Dic3—21no—
248D12—42no—
249D12—41no—
250D12—41no—
251D12—41no—
252D12—41no—
253C4×D3—82no—
254Dic6—21no—
255Dic6—21no—
256C3×C8—41no—
257C3⋊C8—41no—
258C3⋊C8—41no—
259C22×C5—122no—
260C22×C5—122no—
261C22×C5—122no—
262C22×C5#93711yescharacteristic
263C4×C5—21no—
264C4×C5—41no—
265C4×C5—41no—
266C4×C5—81no—
267C4×C5—121no—
268C4×C5—121no—
269C4×C5#91411yescharacteristic
270C4×C5#91611yescharacteristic
271C4×C5#94211yescharacteristic
272C4×C5#95011yescharacteristic
273C2×Q8—21no—
274C2×Q8—31no—
275C2×Q8C5×#6711yescharacteristic
276C2×D4—32no—
277C2×D4—61no—
278C2×D4—61no—
279C22×C4—62no—
280Q16—122no—
281C2×C8—21no—
282C2×C8—61no—
283C2×C8—61no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—31no—
288C4⋊C4—61no—
289C4⋊C4C5×#6711yescharacteristic
290C22⋊C4—62no—
291C22⋊C4—62no—
292C22⋊C4—62no—
293C42—21no—
294C42—61no—
295C42C22×C5×D311yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3C5×#12011yescharacteristic
298C2×D3—42no—
299C2×D3—42no—
300C2×D3—42no—
301C3×C4—21no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—81no—
305C3×C4C5×#13511yescharacteristic
306C3×C4C5×#13511yescharacteristic
307C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
308C3×C4C5×#13711yescharacteristic
309Dic3—41no—
310Dic3—41no—
311C2×C5—242no—
312C2×C5#504711yescharacteristic
313C2×C5#517211yescharacteristic
314C2×C5#520211yescharacteristic
315C23—62no—
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—41no—
320Q8—61no—
321Q8—61no—
322D4—122no—
323D4—121no—
324D4—121no—
325D4—121no—
326D4—121no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—61no—
331C2×C4—61no—
332C2×C4—242no—
333C2×C4C5×D3×D411yescharacteristic
334C2×C4C5×D3×D411yescharacteristic
335C2×C4C2×C5×#6711yescharacteristic
336C8—41no—
337C8—121no—
338C8—121no—
339C2×C3C5×#44911yescharacteristic
340C2×C3C5×#45211yescharacteristic
341C2×C3C5×#45511yescharacteristic
342D3—82no—
343C5#7112811yescharacteristic, direct product factor, Sylow
344C22—122no—
345C22—122no—
346C22—122no—
347C22C5×#93711yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—121no—
353C4—121no—
354C4C5×#91411yescharacteristic
355C4C5×#91611yescharacteristic
356C4C5×#94211yescharacteristic
357C4C5×#95011yescharacteristic
358C3C5×#164011yescharacteristic, complemented, Sylow
359C2—242no—
360C2C5×#504711yescharacteristic
361C2C5×#517211yescharacteristic
362C2C5×#520211yescharacteristic
subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#475C2
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenterC5×#475D3
hypocenterC3C5×#1640
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#475

Complements

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

NH ≅ G/Ntype
2. C3×C5×#475C2semidirect
3. C5×#5090C2semidirect
5. C5×#4535C2semidirect
7. C5×#4484C2semidirect
26. #71128C5direct (N × H)
29. C5×#475D3semidirect
58. C3×#475C2×C5semidirect
59. #5090C2×C5semidirect
61. #4535C2×C5semidirect
63. #4484C2×C5semidirect
148. #475C5×D3semidirect
296. C3×C5#1640semidirect
343. C5#71128direct (N × H)
358. C3C5×#1640semidirect

Maximal subgroups

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

subgroupindex
C5×#55852
C3×C5×#4752
C5×#50902
C5×#50882
C5×#45352
C5×#44852
C5×#44842
C5×#16403
#711285