Finite Group Databasebeta

← C5×#71049 #14290567

Subgroups — C5×#71049 #14290567

Order 1920.

400 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5542C211yesmaximal, characteristic
2C3×C5×#461C211yesmaximal, characteristic
3C5×#5094C211yesmaximal, characteristic, complemented
4C5×#5078C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic
6C5×#4484C211yesmaximal, characteristic, complemented
7C5×#4482C211yesmaximal, characteristic, complemented
8C5×#1650—31nomaximal, Hall
9C2×C3×C5×SD16—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C4×C5×D4C2211yescharacteristic
12C5×#936—21no—
13C5×#926—21no—
14C5×#924—21no—
15C5×#887—21no—
16C5×#879—22no—
17C5×#869C2211yescharacteristic
18C4×C5×Dic6C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×#103—21no—
21C5×#810—21no—
22C5×#808—21no—
23C5×#807—22no—
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#71049C511yesmaximal, characteristic, direct product factor, Hall
27C5×#556—31no—
28C5×#500—31no—
29C5×#475—31no—
30C5×#461D311yescharacteristic
31C5×#332—31no—
32C5×Q8⋊C8—31no—
33C5×D4⋊C8—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C2×C5×Dic6—21no—
38C2×C5×Dic6D411yescharacteristic
39C3×C5×SD16—42no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C5×#217—22no—
47C5×#217—22no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×C4⋊Dic3D412yes—
51C5×Dic3⋊C4—22no—
52C5×Dic3⋊C4—21no—
53C4×C5×Dic3—22no—
54C4×C5×Dic3—21no—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8—21no—
57#5542C2×C511yescharacteristic
58C3×#461C2×C511yescharacteristic
59#5094C2×C511yescharacteristic, complemented
60#5078C2×C511yescharacteristic, complemented
61D4⋊(C3⋊C8)C2×C511yescharacteristic
62#4484C2×C511yescharacteristic, complemented
63#4482C2×C511yescharacteristic, complemented
64C2×C5×SD16—21no—
65C5×C4⋊Q8—31no—
66C5×C4⋊Q8C2×D311yescharacteristic
67C5×#126—62no—
68C5×#124—61no—
69C5×C22⋊Q8—61no—
70C4×C5×Q8—31no—
71C4×C5×Q8—61no—
72C4×C5×D4C2×D311yescharacteristic
73C5×#117—61no—
74C5×#107—62no—
75C5×#106—61no—
76C5×C4⋊C8—31no—
77C5×C4⋊C8C2×D311yescharacteristic
78C5×#103—21no—
79C5×#103—61no—
80C4×C5×C8—31no—
81#1650—31noSylow
82C23×C3×C5—21no—
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C3×C5×D4—21no—
86C3×C5×D4—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C5×Dic3—21no—
95C2×C5×Dic3—21no—
96C2×C5×Dic3—22no—
97C5×Dic6—21no—
98C5×Dic6—21no—
99C5×Dic6—41no—
100C5×Dic6—41no—
101C3×C5×C8—41no—
102C5×C3⋊C8—22no—
103C5×C3⋊C8—41no—
104C2×C3×SD16—21no—
105C3×C4⋊Q8C22×C511yescharacteristic
106C3×C4×D4C22×C511yescharacteristic
107#936—21no—
108#926—21no—
109#924—21no—
110#887—21no—
111#879—22no—
112#869C22×C511yescharacteristic
113C4×Dic6C22×C511yescharacteristic
114C3×C4⋊C8C22×C511yescharacteristic
115C3×#103—21no—
116#810—21no—
117#808—21no—
118#807—22no—
119C4⋊(C3⋊C8)C22×C511yescharacteristic
120C4×C3⋊C8C22×C511yescharacteristic
121C2×C5×Q8—21no—
122C2×C5×Q8—31no—
123C2×C5×Q8—61no—
124C2×C5×D4#6711yescharacteristic
125C22×C4×C5—21no—
126C5×SD16—42no—
127C2×C5×C8—21no—
128C2×C5×C8—61no—
129C2×C5×C8—61no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—31no—
133C5×C4⋊C4—32no—
134C5×C4⋊C4—62no—
135C5×C4⋊C4—61no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4#6711yescharacteristic
138C5×C22⋊C4—21no—
139C5×C22⋊C4—62no—
140C5×C22⋊C4—62no—
141C42×C5—62no—
142C42×C5—61no—
143C42×C5C22×D311yescharacteristic
144#556—31no—
145#500—31no—
146#475—31no—
147#461C5×D311yescharacteristic
148#332—31no—
149Q8⋊C8—31no—
150D4⋊C8—31no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5#12011yescharacteristic
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5—81no—
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C5×Dic3—42no—
163C5×Dic3—41no—
164C5×Dic3—41no—
165C2×C3×Q8—21no—
166C2×C3×D4C5×D411yescharacteristic
167C22×C3×C4—21no—
168C2×Dic6—21no—
169C2×Dic6C5×D411yescharacteristic
170C3×SD16—42no—
171C2×C3×C8—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4C5×D411yescharacteristic
175C3×C22⋊C4—21no—
176C3×C42C23×C511yescharacteristic
177#217—22no—
178#217—22no—
179C4⋊Dic3—21no—
180C4⋊Dic3C5×D412yes—
181C4⋊Dic3C5×D411yescharacteristic
182Dic3⋊C4—22no—
183Dic3⋊C4—21no—
184C4×Dic3—22no—
185C4×Dic3—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C23×C5—21no—
189C5×Q8—41no—
190C5×Q8—41no—
191C5×Q8—61no—
192C5×Q8—61no—
193C5×Q8—121no—
194C5×Q8—121no—
195C5×D4—21no—
196C5×D4—21no—
197C2×C4×C5—21no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5—61no—
202C2×C4×C5—62no—
203C2×C4×C5—61no—
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5D3×D411yescharacteristic
206C2×C4×C5C2×#6711yescharacteristic
207C5×C8—41no—
208C5×C8—62no—
209C5×C8—121no—
210C2×SD16—21no—
211C4⋊Q8—31no—
212C4⋊Q8C2×C5×D311yescharacteristic
213#126—62no—
214#124—61no—
215C22⋊Q8—61no—
216C4×Q8—31no—
217C4×Q8—61no—
218C4×D4C2×C5×D311yescharacteristic
219#117—61no—
220#107—62no—
221#106—61no—
222C4⋊C8—31no—
223C4⋊C8C2×C5×D311yescharacteristic
224#103—21no—
225#103—61no—
226C4×C8—31no—
227C2×C3×C5—81no—
228C2×C3×C5#44911yescharacteristic
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45611yescharacteristic
231C23×C3—21no—
232C3×Q8—41no—
233C3×Q8—41no—
234C3×D4—21no—
235C3×D4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4C2×C5×D411yescharacteristic
241C2×C3×C4C2×C5×D411yescharacteristic
242C2×C3×C4C2×C5×D411yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—22no—
246Dic6—21no—
247Dic6—21no—
248Dic6—41no—
249Dic6—41no—
250C3×C8—41no—
251C3⋊C8—22no—
252C3⋊C8—41no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—41no—
256C22×C5#93711yescharacteristic
257C4×C5—21no—
258C4×C5—41no—
259C4×C5—81no—
260C4×C5—121no—
261C4×C5—121no—
262C4×C5—122no—
263C4×C5#91511yescharacteristic
264C4×C5#91611yescharacteristic
265C4×C5#93211yescharacteristic
266C4×C5#95011yescharacteristic
267C2×Q8—21no—
268C2×Q8—31no—
269C2×Q8—61no—
270C2×D4C5×#6711yescharacteristic
271C22×C4—21no—
272SD16—42no—
273C2×C8—21no—
274C2×C8—61no—
275C2×C8—61no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—31no—
279C4⋊C4—32no—
280C4⋊C4—62no—
281C4⋊C4—61no—
282C4⋊C4—61no—
283C4⋊C4C5×#6711yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—62no—
286C22⋊C4—62no—
287C42—62no—
288C42—61no—
289C42C22×C5×D311yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3—41no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3C5×#12011yescharacteristic
295C3×C4—21no—
296C3×C4—41no—
297C3×C4—81no—
298C3×C4C5×#13511yescharacteristic
299C3×C4C5×#13511yescharacteristic
300C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
301C3×C4C5×#13711yescharacteristic
302Dic3—42no—
303Dic3—41no—
304Dic3—41no—
305C2×C5—81no—
306C2×C5#503711yescharacteristic
307C2×C5#517311yescharacteristic
308C2×C5#520511yescharacteristic
309C23—21no—
310Q8—41no—
311Q8—41no—
312Q8—61no—
313Q8—61no—
314Q8—121no—
315Q8—121no—
316D4—21no—
317D4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—61no—
323C2×C4—62no—
324C2×C4—61no—
325C2×C4C5×D3×D411yescharacteristic
326C2×C4C5×D3×D411yescharacteristic
327C2×C4C2×C5×#6711yescharacteristic
328C8—41no—
329C8—62no—
330C8—121no—
331C2×C3—81no—
332C2×C3C5×#44911yescharacteristic
333C2×C3C5×#45211yescharacteristic
334C2×C3C5×#45611yescharacteristic
335C5#7104911yescharacteristic, direct product factor, Sylow
336C22—41no—
337C22—41no—
338C22—41no—
339C22C5×#93711yescharacteristic
340C4—21no—
341C4—41no—
342C4—81no—
343C4—121no—
344C4—121no—
345C4—122no—
346C4C5×#91511yescharacteristic
347C4C5×#91611yescharacteristic
348C4C5×#93211yescharacteristic
349C4C5×#95011yescharacteristic
350C3C5×#165011yescharacteristic, complemented, Sylow
351C2—81no—
352C2C5×#503711yescharacteristic
353C2C5×#517311yescharacteristic
354C2C5×#520511yescharacteristic
subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#461C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC5×#461D3
hypocenterC3C5×#1650
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#461

Complements

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

NH ≅ G/Ntype
3. C5×#5094C2semidirect
4. C5×#5078C2semidirect
6. C5×#4484C2semidirect
7. C5×#4482C2semidirect
26. #71049C5direct (N × H)
59. #5094C2×C5semidirect
60. #5078C2×C5semidirect
62. #4484C2×C5semidirect
63. #4482C2×C5semidirect
290. C3×C5#1650semidirect
335. C5#71049direct (N × H)
350. C3C5×#1650semidirect

Maximal subgroups

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

subgroupindex
C5×#55422
C3×C5×#4612
C5×#50942
C5×#50782
C5×D4⋊(C3⋊C8)2
C5×#44842
C5×#44822
C5×#16503
#710495