Finite Group Databasebeta

← #14317208

Subgroups — #14317208

Order 1920.

340 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11751256C211yesmaximal, characteristic, complemented
2C2×C3×#3958C211yesmaximal, characteristic
3#11747809C211yesmaximal, characteristic, complemented
4C2×#90942C211yesmaximal, characteristic, complemented
5C5×#4562C211yesmaximal, characteristic, complemented
6#11745928C211yesmaximal, characteristic, complemented
7#11745902C211yesmaximal, characteristic, complemented
8#10599996—31nomaximal, Hall
9C2×C3×C5×D8C2211yescharacteristic
10#91825—21no—
11C2×#6716—21no—
12C2×Dic60C2211yescharacteristic
13C2×C3×D40C2211yescharacteristic
14#91434—21no—
15C8×Dic15C2211yescharacteristic
16C5×#818C2211yescharacteristic
17C2×C5×C3⋊C16C2211yescharacteristic
18C3×#3958—22no—
19C2×C3×#672C2211yescharacteristic
20#90964—21no—
21#90942—22no—
22#71463—51nomaximal, Hall
23#65444—31no—
24C2×#3958D311yescharacteristic
25C2×#3932—31no—
26#65161—31no—
27C5×#357—31no—
28#64721—31no—
29#64712—31no—
30C2×C3×C5×D4—21no—
31C2×Dic30—21no—
32C2×C3×D20—21no—
33C2×D5×Dic3—41no—
34C3×C5×D8—21no—
35C3×C5×D8—21no—
36C2×C3×C5×C8C2311yescharacteristic
37#6719—41no—
38#6719—41no—
39#6716—42no—
40C4×Dic15D411yescharacteristic
41C2×C3⋊#168D411yescharacteristic
42Dic60—21no—
43Dic60—21no—
44C5×C4⋊Dic3—21no—
45C3×D40—21no—
46C3×D40D412yes—
47#6665—41no—
48C3×#672—21no—
49C5×C3⋊C16—21no—
50C2×C3×D16—51no—
51#5155—51no—
52Dic3×D8—51no—
53C2×#827—51no—
54#4562D511yescharacteristic, complemented
55#4503—51no—
56Dic3⋊C16—51no—
57C2×C5×D8C2×D311yescharacteristic
58#4082—61no—
59C2×#687—61no—
60C2×Dic20—31no—
61C2×D40C2×D311yescharacteristic
62#4039—61no—
63C2×C5×C16—31no—
64C5×#107—31no—
65#3958—22no—
66C8×Dic5—31no—
67C2×#672C2×D311yescharacteristic
68#3941—61no—
69#3932—62no—
70#2210—151noSylow
71C23×C3×C5—41no—
72C22×C3×D5—41no—
73C3×C5×D4—41no—
74C3×C5×D4—41no—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×Dic15—41no—
77C2×Dic15D811yescharacteristic
78C2×Dic15D811yescharacteristic
79Dic30—41no—
80Dic30—41no—
81C2×C5×Dic3—41no—
82C3×D20—22no—
83C3×D20—41no—
84D5×Dic3—82no—
85C3×C5×C8C2×D411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C3⋊#168—21no—
88C2×C3×D8—51no—
89C2×C3×D8C2×D511yescharacteristic
90#936—101no—
91D4×Dic3—101no—
92C2×#214—101no—
93C2×Dic12—51no—
94C3×D16—102no—
95C2×C3×C16—51no—
96#832—101no—
97#827—102no—
98#818C2×D511yescharacteristic
99C8×Dic3—51no—
100C2×C3⋊C16C2×D511yescharacteristic
101C2×C5×D4—21no—
102C2×D20—21no—
103C2×C4×D5—121no—
104C2×Dic10—61no—
105C5×D8—21no—
106C5×D8—21no—
107C2×C5×C8C22×D311yescharacteristic
108C5×C4⋊C4—61no—
109C22⋊Dic5—121no—
110C22⋊Dic5—121no—
111#687—122no—
112#685—121no—
113C4×Dic5—31no—
114C2×#168—31no—
115Dic20—61no—
116Dic20—61no—
117D40—21no—
118D40#6712yes—
119C5×C16—61no—
120#672—21no—
121C2×SD32—151no—
122C2×D16—51no—
123#495—151no—
124C4×D8—151no—
125C4⋊C16—151no—
126#358—151no—
127#357—31no—
128C22×C3×C5—81no—
129C22×C3×C5—81no—
130C22×C3×C5—81no—
131C22×C3×C5C2×D811yescharacteristic
132C2×C3×D5—42no—
133C2×C3×D5—81no—
134C2×C3×D5—81no—
135C3×C4×C5#12111yescharacteristic
136C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
137Dic15—21no—
138Dic15—21no—
139Dic15—81no—
140C5×Dic3—81no—
141C2×C3×D4—21no—
142C2×C3×D4—101no—
143C22×Dic3—201no—
144C2×Dic6—101no—
145C3×D8—21no—
146C3×D8—21no—
147C3×D8—52no—
148C3×D8—101no—
149C2×C3×C8C22×D511yescharacteristic
150#217—201no—
151#217—201no—
152#217—201no—
153#214—202no—
154C4⋊Dic3—21no—
155C4×Dic3—51no—
156C2×C3⋊C8—51no—
157Dic12—101no—
158Dic12—101no—
159C3×C16—101no—
160C3⋊C16—21no—
161C23×C5—41no—
162C22×D5—41no—
163C5×D4—41no—
164C5×D4—41no—
165C2×C4×C5—121no—
166C2×C4×C5D3×D411yescharacteristic
167C2×Dic5—31no—
168C2×Dic5—31no—
169C2×Dic5—121no—
170D20—22no—
171D20—41no—
172C4×D5—242no—
173Dic10—121no—
174Dic10—121no—
175C5×C8#23711yescharacteristic
176C5×C8C2×#6711yescharacteristic
177#168—61no—
178C2×Q16—151no—
179C2×SD16—301no—
180C2×D8—51no—
181C2×D8D3×D511yescharacteristic
182#124—301no—
183C4×D4—301no—
184SD32—302no—
185D16—102no—
186C2×C16—31no—
187C2×C16—51no—
188#107—31no—
189#102—301no—
190C4×C8—151no—
191C2×C3×C5—161no—
192C2×C3×C5#45911yescharacteristic
193C2×C3×C5#50811yescharacteristic
194C2×C3×C5#50911yescharacteristic
195C3×D5—82no—
196C23×C3—41no—
197C23×C3—201no—
198C3×D4—41no—
199C3×D4—41no—
200C3×D4—102no—
201C3×D4—201no—
202C2×C3×C4D4×D511yescharacteristic
203C2×Dic3—41no—
204C2×Dic3—51no—
205C2×Dic3—51no—
206C2×Dic3—201no—
207C2×Dic3—402no—
208Dic6—201no—
209Dic6—201no—
210C3×C8#70911yescharacteristic
211C3×C8D4×D511yescharacteristic
212C3⋊C8—101no—
213C22×C5—81no—
214C22×C5—81no—
215C22×C5—81no—
216C22×C5D3×D811yescharacteristic
217C2×D5—42no—
218C2×D5—81no—
219C2×D5—81no—
220C4×C5—241no—
221C4×C5#91111yescharacteristic
222C4×C5#93911yescharacteristic
223Dic5—61no—
224Dic5—61no—
225Dic5—241no—
226C2×Q8—301no—
227C2×D4—21no—
228C2×D4—101no—
229C22×C4—601no—
230Q16—301no—
231Q16—301no—
232SD16—602no—
233D8—21no—
234D8—21no—
235D8—52no—
236D8—101no—
237C2×C8—151no—
238C2×C8C2×D3×D511yescharacteristic
239C4⋊C4—61no—
240C22⋊C4—601no—
241C22⋊C4—601no—
242C22⋊C4—601no—
243C42—151no—
244C16—61no—
245C16—101no—
246C3×C5#221011yescharacteristic, complemented, Hall
247C22×C3—81no—
248C22×C3—81no—
249C22×C3—81no—
250C22×C3—202no—
251C22×C3—401no—
252C22×C3—401no—
253C22×C3D5×D811yescharacteristic
254C3×C4#403011yescharacteristic
255C3×C4#406011yescharacteristic
256Dic3—81no—
257Dic3—101no—
258Dic3—101no—
259Dic3—401no—
260C2×C5—161no—
261C2×C5#491111yescharacteristic
262C2×C5#491211yescharacteristic
263C2×C5#515011yescharacteristic
264D5—82no—
265C23—41no—
266C23—201no—
267Q8—601no—
268Q8—601no—
269D4—41no—
270D4—41no—
271D4—102no—
272D4—201no—
273C2×C4—121no—
274C2×C4—151no—
275C2×C4—151no—
276C2×C4—601no—
277C2×C4—1202no—
278C2×C4#679011yescharacteristic
279C8—301no—
280C8#677911yescharacteristic
281C8D5×#6711yescharacteristic
282C2×C3—161no—
283C2×C3—402no—
284C2×C3#6507511yescharacteristic
285C2×C3#6520011yescharacteristic
286C2×C3#6520511yescharacteristic
287C5#7146311yescharacteristic, complemented, Sylow
288C22—81no—
289C22—81no—
290C22—81no—
291C22—202no—
292C22—401no—
293C22—401no—
294C22#9148111yescharacteristic
295C4—241no—
296C4—301no—
297C4—301no—
298C4—1201no—
299C4#9149811yescharacteristic
300C4#9155011yescharacteristic
301C3#1059999611yescharacteristic, complemented, Sylow
302C2—161no—
303C2—402no—
304C2#1174826911yescharacteristic
305C2#1174828411yescharacteristic
306C2#1174898311yescharacteristic
subgroupG/H
centerC22#91481
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C2×D8
prime radicalC2×C3×#3958C2
hypercenterC2×D8D3×D5
hypocenterC3×C5#2210
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #11751256C2semidirect
3. #11747809C2semidirect
4. C2×#90942C2semidirect
5. C5×#4562C2semidirect
6. #11745928C2semidirect
7. #11745902C2semidirect
54. #4562D5semidirect
246. C3×C5#2210semidirect
287. C5#71463semidirect
301. C3#10599996semidirect

Maximal subgroups

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

subgroupindex
#117512562
C2×C3×#39582
#117478092
C2×#909422
C5×#45622
#117459282
#117459022
#105999963
#714635