Finite Group Databasebeta

← C5×#68260 #14289388

Subgroups — C5×#68260 #14289388

Order 1920.

436 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5585C211yesmaximal, characteristic
2C5×#5021C211yesmaximal, characteristic, complemented
3C5×#4850C211yesmaximal, characteristic, complemented
4C5×#4693C211yesmaximal, characteristic
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic
7C5×#4456C211yesmaximal, characteristic, complemented
8C5×#1630—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×#947—21no—
11C2×C5×#204—22no—
12C5×#894—22no—
13C5×#893—21no—
14C5×#875—21no—
15C5×#874C2211yescharacteristic
16C4×C5×D12—21no—
17C5×#869C2211yescharacteristic
18C4×C5×Dic6C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21C5×#835—21no—
22C5×#818—21no—
23C5×#816—21no—
24C5×#807—21no—
25C5×C4⋊(C3⋊C8)C2211yescharacteristic
26#68260C511yesmaximal, characteristic, direct product factor, Hall
27C5×#559—31no—
28C5×#492—31no—
29C5×#477—31no—
30C5×#477—31no—
31C5×#331—31no—
32C5×Q8⋊C8—31no—
33C5×Q8⋊C8D311yescharacteristic, complemented
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12D412yes—
38C2×C4×C5×D3—22no—
39C2×C5×Dic6—21no—
40C2×C5×Dic6D411yescharacteristic
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2311yescharacteristic
47C5×(C2×D3)⋊C4—22no—
48C5×(C2×D3)⋊C4—22no—
49C5×(C2×D3)⋊C4—22no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3D411yescharacteristic
53C5×Dic3⋊C4—21no—
54C4×C5×Dic3—21no—
55C2×C5×C3⋊C8—21no—
56C5×#204—44no—
57#5585C2×C511yescharacteristic
58#5021C2×C511yescharacteristic, complemented
59#4850C2×C511yescharacteristic, complemented
60#4693C2×C511yescharacteristic
61C3×Q8⋊C8C2×C511yescharacteristic, complemented
62#4485C2×C511yescharacteristic
63#4456C2×C511yescharacteristic, complemented
64C2×C5×SD16—62no—
65C5×C4⋊Q8—31no—
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×#107—61no—
75C5×#107—61no—
76C5×C4⋊C8—31no—
77C5×C4⋊C8C2×D311yescharacteristic
78C5×#103—61no—
79C5×#103—61no—
80C4×C5×C8C2×D311yescharacteristic
81#1630—31noSylow
82C22×C5×D3—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—41no—
93C5×D12—42no—
94C5×D12—41no—
95C5×D12—41no—
96C5×D12—41no—
97C5×D12—41no—
98C4×C5×D3—82no—
99C5×Dic6—21no—
100C5×Dic6—21no—
101C5×Dic6—42no—
102C3×C5×C8—22no—
103C3×C5×C8—41no—
104C5×C3⋊C8—41no—
105C3×C4×Q8C22×C511yescharacteristic
106#947—21no—
107C2×#204—22no—
108#894—22no—
109#893—21no—
110#875—21no—
111#874C22×C511yescharacteristic
112C4×D12—21no—
113#869C22×C511yescharacteristic
114C4×Dic6C22×C511yescharacteristic
115C3×C4⋊C8C22×C511yescharacteristic
116C3×C4×C8C22×C511yescharacteristic
117#835—21no—
118#818—21no—
119#816—21no—
120#807—21no—
121C4⋊(C3⋊C8)C22×C511yescharacteristic
122C2×C5×Q8—31no—
123C2×C5×Q8—61no—
124C2×C5×Q8D1211yescharacteristic
125C2×C5×D4—32no—
126C2×C5×D4—61no—
127C2×C5×D4—61no—
128C22×C4×C5—62no—
129C5×SD16—124no—
130C2×C5×C8—21no—
131C2×C5×C8—21no—
132C2×C5×C8—61no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—31no—
135C5×C4⋊C4—61no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4D1211yescharacteristic
139C5×C22⋊C4—62no—
140C5×C22⋊C4—62no—
141C5×C22⋊C4—62no—
142C42×C5—21no—
143C42×C5—61no—
144C42×C5C22×D311yescharacteristic
145#559—31no—
146#492—31no—
147#477—31no—
148#477—31no—
149#331—31no—
150Q8⋊C8—31no—
151Q8⋊C8C5×D311yescharacteristic, complemented
152C22×C3×C5#12011yescharacteristic
153C2×C5×D3—42no—
154C2×C5×D3—42no—
155C2×C5×D3—42no—
156C3×C4×C5—21no—
157C3×C4×C5—41no—
158C3×C4×C5—41no—
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×C4×C5#13711yescharacteristic
163C5×Dic3—41no—
164C5×Dic3—41no—
165C5×Dic3—81no—
166C2×C3×Q8C5×D411yescharacteristic
167C2×D12—21no—
168C2×D12—21no—
169C2×D12C5×D412yes—
170C2×C4×D3—22no—
171C2×Dic6—21no—
172C2×Dic6C5×D411yescharacteristic
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4C5×D411yescharacteristic
177C3×C42—21no—
178C3×C42C23×C511yescharacteristic
179(C2×D3)⋊C4—22no—
180(C2×D3)⋊C4—22no—
181(C2×D3)⋊C4—22no—
182C4⋊Dic3—21no—
183C4⋊Dic3—21no—
184C4⋊Dic3C5×D411yescharacteristic
185Dic3⋊C4—21no—
186C4×Dic3—21no—
187C2×C3⋊C8—21no—
188#204—44no—
189C23×C5—62no—
190C5×Q8—21no—
191C5×Q8—21no—
192C5×Q8—61no—
193C5×Q8—61no—
194C5×Q8—122no—
195C5×D4—122no—
196C5×D4—121no—
197C5×D4—121no—
198C5×D4—121no—
199C5×D4—121no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—61no—
203C2×C4×C5—61no—
204C2×C4×C5—121no—
205C2×C4×C5—242no—
206C2×C4×C5C2×D1211yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C5×C8—22no—
210C5×C8—41no—
211C5×C8—121no—
212C2×SD16—62no—
213C4⋊Q8—31no—
214#127—31no—
215#124—61no—
216#124—61no—
217#123—62no—
218C4×Q8—31no—
219C4×Q8C2×C5×D311yescharacteristic
220C4×D4—61no—
221C4×D4—61no—
222#107—61no—
223#107—61no—
224C4⋊C8—31no—
225C4⋊C8C2×C5×D311yescharacteristic
226#103—61no—
227#103—61no—
228C4×C8C2×C5×D311yescharacteristic
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45211yescharacteristic
231C2×C3×C5#45311yescharacteristic
232C5×D3—82no—
233C22×D3—22no—
234C3×Q8—21no—
235C3×Q8—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4C2×C5×D411yescharacteristic
239C2×C3×C4C2×C5×D411yescharacteristic
240C2×C3×C4C2×C5×D411yescharacteristic
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—41no—
244D12—42no—
245D12—41no—
246D12—41no—
247D12—41no—
248D12—41no—
249C4×D3—82no—
250Dic6—21no—
251Dic6—21no—
252Dic6—42no—
253C3×C8—22no—
254C3×C8—41no—
255C3⋊C8—41no—
256C22×C5—122no—
257C22×C5—122no—
258C22×C5—122no—
259C22×C5#88211yescharacteristic
260C4×C5—21no—
261C4×C5—41no—
262C4×C5—41no—
263C4×C5—121no—
264C4×C5—121no—
265C4×C5—241no—
266C4×C5#90411yescharacteristic
267C4×C5#90911yescharacteristic
268C4×C5#91611yescharacteristic
269C4×C5#91811yescharacteristic
270C2×Q8—31no—
271C2×Q8—61no—
272C2×Q8C5×D1211yescharacteristic
273C2×D4—32no—
274C2×D4—61no—
275C2×D4—61no—
276C22×C4—62no—
277SD16—124no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—61no—
281C4⋊C4—21no—
282C4⋊C4—31no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C4⋊C4C5×D1211yescharacteristic
287C22⋊C4—62no—
288C22⋊C4—62no—
289C22⋊C4—62no—
290C42—21no—
291C42—61no—
292C42C22×C5×D311yescharacteristic
293C3×C5#163011yescharacteristic, complemented, Hall
294C22×C3C5×#12011yescharacteristic
295C2×D3—42no—
296C2×D3—42no—
297C2×D3—42no—
298C3×C4—21no—
299C3×C4—41no—
300C3×C4—41no—
301C3×C4C5×#13511yescharacteristic
302C3×C4C5×#13511yescharacteristic
303C3×C4C5×#13711yescharacteristic
304C3×C4C5×#13711yescharacteristic
305Dic3—41no—
306Dic3—41no—
307Dic3—81no—
308C2×C5—242no—
309C2×C5#473311yescharacteristic
310C2×C5#480811yescharacteristic
311C2×C5#482211yescharacteristic
312C23—62no—
313Q8—21no—
314Q8—21no—
315Q8—61no—
316Q8—61no—
317Q8—122no—
318D4—122no—
319D4—121no—
320D4—121no—
321D4—121no—
322D4—121no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—121no—
328C2×C4—242no—
329C2×C4C2×C5×D1211yescharacteristic
330C2×C4C5×D3×D411yescharacteristic
331C2×C4C5×D3×D411yescharacteristic
332C8—22no—
333C8—41no—
334C8—121no—
335C2×C3C5×#45211yescharacteristic
336C2×C3C5×#45211yescharacteristic
337C2×C3C5×#45311yescharacteristic
338D3—82no—
339C5#6826011yescharacteristic, direct product factor, Sylow
340C22—122no—
341C22—122no—
342C22—122no—
343C22C5×#88211yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—121no—
348C4—121no—
349C4—241no—
350C4C5×#90411yescharacteristic
351C4C5×#90911yescharacteristic
352C4C5×#91611yescharacteristic
353C4C5×#91811yescharacteristic
354C3C5×#163011yescharacteristic, complemented, Sylow
355C2—242no—
356C2C5×#473311yescharacteristic
357C2C5×#480811yescharacteristic
358C2C5×#482211yescharacteristic
subgroupG/H
centerC22×C5#882
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenterC5×Q8⋊C8D3
hypocenterC3C5×#1630
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C5×#5021C2semidirect
3. C5×#4850C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
7. C5×#4456C2semidirect
26. #68260C5direct (N × H)
33. C5×Q8⋊C8D3semidirect
58. #5021C2×C5semidirect
59. #4850C2×C5semidirect
61. C3×Q8⋊C8C2×C5semidirect
63. #4456C2×C5semidirect
151. Q8⋊C8C5×D3semidirect
293. C3×C5#1630semidirect
339. C5#68260direct (N × H)
354. C3C5×#1630semidirect

Maximal subgroups

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

subgroupindex
C5×#55852
C5×#50212
C5×#48502
C5×#46932
C3×C5×Q8⋊C82
C5×#44852
C5×#44562
C5×#16303
#682605