Finite Group Databasebeta

← #14317287

Subgroups — #14317287

Order 1920.

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

normal subgroups only

This group has 316 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#11751292C211yesmaximal, characteristic
2C2×C5×#829C211yesmaximal, characteristic, complemented
3#11747886C211yesmaximal, characteristic, complemented
4C2×#90945C211yesmaximal, characteristic
5C3×#64784C211yesmaximal, characteristic, complemented
6#11745928C211yesmaximal, characteristic, complemented
7#11745895C211yesmaximal, characteristic
8#10602291—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10#91836—21no—
11C2×#6717—21no—
12C2×D120C2211yescharacteristic
13C2×C5×Dic12C2211yescharacteristic
14#91344—21no—
15C8×Dic15C2211yescharacteristic
16C5×#829—22no—
17C2×C5×C3⋊C16C2211yescharacteristic
18C3×#3950C2211yescharacteristic
19C2×C3×#672C2211yescharacteristic
20#90972—21no—
21#90945—22no—
22#69237—51nomaximal, Hall
23C2×C5×Q32—31no—
24#65480—31no—
25Q16×Dic5—31no—
26C2×#3960—31no—
27#64784D311yescharacteristic, complemented
28#64729—31no—
29#64721—31no—
30C2×C3×C5×Q8—21no—
31C2×D60—21no—
32C2×C5×Dic6—21no—
33C3×C5×Q16—21no—
34C3×C5×Q16—21no—
35C2×C3×C5×C8C2311yescharacteristic
36#6717—42no—
37#6714—41no—
38#6714—41no—
39C4×Dic15D411yescharacteristic
40C2×C3⋊#168D411yescharacteristic
41D120—21no—
42D120—21no—
43C5×Dic12—21no—
44C5×Dic12D412yes—
45C3×C4⋊Dic5—21no—
46Dic3⋊Dic5—41no—
47Dic3×Dic5—41no—
48C3×#672—21no—
49C5×C3⋊C16—21no—
50#5191—51no—
51C2×#829D511yescharacteristic, complemented
52C2×#800—51no—
53#4873—51no—
54C3×#358—51no—
55Dic3⋊C16—51no—
56#4491—51no—
57C2×C5×Q16—31no—
58C2×C5×Q16C2×D311yescharacteristic
59#4093—61no—
60Q8×Dic5—61no—
61C2×#688—61no—
62C2×D40—31no—
63C5×Q32—62no—
64C2×C5×C16—31no—
65#3967—61no—
66#3960—62no—
67#3950C2×D311yescharacteristic
68C8×Dic5—31no—
69C2×#672C2×D311yescharacteristic
70#2211—151noSylow
71C22×D15—41no—
72C3×C5×Q8—41no—
73C3×C5×Q8—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×Dic15D811yescharacteristic
77C2×Dic15D811yescharacteristic
78D60—41no—
79D60—41no—
80C2×C5×Dic3—41no—
81C5×Dic6—22no—
82C5×Dic6—41no—
83C2×C3×Dic5—41no—
84C3×C5×C8C2×D411yescharacteristic
85C3×C5×C8#4111yescharacteristic
86C3⋊#168—21no—
87C2×C3×Q16C2×D511yescharacteristic
88#947—101no—
89C2×#215—101no—
90C2×Dic12C2×D511yescharacteristic
91C2×D24—51no—
92#887—101no—
93C2×C3×C16—51no—
94C3×#107—51no—
95#829—22no—
96C8×Dic3—51no—
97C2×C3⋊C16C2×D511yescharacteristic
98#810—101no—
99#800—102no—
100C2×C5×Q8—21no—
101C2×C5×Q8—61no—
102C2×D20—61no—
103C5×Q16—21no—
104C5×Q16—21no—
105C5×Q16—32no—
106C5×Q16—61no—
107C2×C5×C8C22×D311yescharacteristic
108#688—122no—
109#685—121no—
110#685—121no—
111C4⋊Dic5—21no—
112C4⋊Dic5—121no—
113C4×Dic5—31no—
114C4×Dic5—121no—
115C2×#168—31no—
116D40—61no—
117D40—61no—
118C5×C16—61no—
119#672—21no—
120C2×Q32—31no—
121C2×SD32—151no—
122#495—151no—
123C4×Q16—151no—
124C4⋊C16—151no—
125#358—51no—
126#357—151no—
127C22×C3×C5C2×D811yescharacteristic
128C2×D15—81no—
129C2×D15—81no—
130C2×D15—81no—
131C3×C4×C5—81no—
132C3×C4×C5#12111yescharacteristic
133C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
134Dic15—21no—
135Dic15—21no—
136C3×Dic5—81no—
137C5×Dic3—42no—
138C2×C3×Q8—21no—
139C2×D12—101no—
140C2×Dic6—21no—
141C3×Q16—21no—
142C3×Q16—21no—
143C2×C3×C8C22×D511yescharacteristic
144C3×C4⋊C4—101no—
145#215—202no—
146(C2×D3)⋊C4—201no—
147(C2×D3)⋊C4—201no—
148Dic3⋊C4—201no—
149C4×Dic3—51no—
150C4×Dic3—201no—
151C2×C3⋊C8—51no—
152Dic12—21no—
153Dic12C22⋊D512yes—
154D24—101no—
155D24—101no—
156C3×C16—101no—
157C3⋊C16—21no—
158C22×D5—121no—
159C5×Q8—41no—
160C5×Q8—41no—
161C5×Q8—62no—
162C5×Q8—121no—
163C2×C4×C5—41no—
164C2×C4×C5—121no—
165C2×C4×C5D3×D411yescharacteristic
166C2×Dic5—31no—
167C2×Dic5—31no—
168C2×Dic5—41no—
169D20—121no—
170D20—121no—
171C5×C8#23511yescharacteristic
172C5×C8D3×D411yescharacteristic
173#168—61no—
174C2×Q16—31no—
175C2×Q16D3×D511yescharacteristic
176C2×SD16—301no—
177C2×D8—151no—
178#124—301no—
179C4×Q8—301no—
180Q32—62no—
181SD32—302no—
182C2×C16—31no—
183C2×C16—51no—
184#107—51no—
185#103—301no—
186C4×C8—151no—
187C2×C3×C5#45911yescharacteristic
188C2×C3×C5#50811yescharacteristic
189C2×C3×C5#51011yescharacteristic
190D15—161no—
191C22×D3—201no—
192C3×Q8—41no—
193C3×Q8—41no—
194C2×C3×C4—41no—
195C2×C3×C4—201no—
196C2×C3×C4D4×D511yescharacteristic
197C2×Dic3—41no—
198C2×Dic3—51no—
199C2×Dic3—51no—
200D12—201no—
201D12—201no—
202Dic6—22no—
203Dic6—41no—
204C3×C8#71111yescharacteristic
205C3×C8C2×C22⋊D511yescharacteristic
206C3⋊C8—101no—
207C22×C5D3×D811yescharacteristic
208C2×D5—241no—
209C2×D5—241no—
210C2×D5—241no—
211C4×C5—81no—
212C4×C5—122no—
213C4×C5#88411yescharacteristic
214C4×C5#91411yescharacteristic
215Dic5—61no—
216Dic5—61no—
217Dic5—81no—
218C2×Q8—21no—
219C2×Q8—61no—
220C2×D4—301no—
221Q16—21no—
222Q16—21no—
223Q16—32no—
224Q16—61no—
225SD16—602no—
226D8—301no—
227D8—301no—
228C2×C8—151no—
229C2×C8C2×D3×D511yescharacteristic
230C4⋊C4—101no—
231C4⋊C4—601no—
232C22⋊C4—601no—
233C22⋊C4—601no—
234C42—151no—
235C42—601no—
236C16—61no—
237C16—101no—
238C3×C5#221111yescharacteristic, complemented, Hall
239C22×C3D5×D811yescharacteristic
240C2×D3—401no—
241C2×D3—401no—
242C2×D3—401no—
243C3×C4—81no—
244C3×C4—401no—
245C3×C4#405711yescharacteristic
246C3×C4#408511yescharacteristic
247Dic3—42no—
248Dic3—101no—
249Dic3—101no—
250C2×C5#478611yescharacteristic
251C2×C5#491611yescharacteristic
252C2×C5#491811yescharacteristic
253D5—481no—
254C23—601no—
255Q8—41no—
256Q8—41no—
257Q8—62no—
258Q8—121no—
259D4—601no—
260D4—601no—
261C2×C4—41no—
262C2×C4—121no—
263C2×C4—151no—
264C2×C4—151no—
265C2×C4—201no—
266C2×C4#679011yescharacteristic
267C8—301no—
268C8#678211yescharacteristic
269C8D3×C22⋊D511yescharacteristic
270C2×C3#6520711yescharacteristic
271C2×C3#6520811yescharacteristic
272C2×C3#6543911yescharacteristic
273D3—801no—
274C5#6923711yescharacteristic, complemented, Sylow
275C22—1201no—
276C22—1201no—
277C22—1201no—
278C22#9148111yescharacteristic
279C4—81no—
280C4—122no—
281C4—301no—
282C4—301no—
283C4—401no—
284C4#9150011yescharacteristic
285C4#9155811yescharacteristic
286C3#1060229111yescharacteristic, complemented, Sylow
287C2—2401no—
288C2#1174829911yescharacteristic
289C2#1174830811yescharacteristic
290C2#1174899111yescharacteristic
subgroupG/H
centerC22#91481
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C2×D8
prime radicalC2×D120C22
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2211
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C2×C5×#829C2semidirect
3. #11747886C2semidirect
5. C3×#64784C2semidirect
6. #11745928C2semidirect
27. #64784D3semidirect
51. C2×#829D5semidirect
238. C3×C5#2211semidirect
274. C5#69237semidirect
286. C3#10602291semidirect

Maximal subgroups

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

subgroupindex
#117512922
C2×C5×#8292
#117478862
C2×#909452
C3×#647842
#117459282
#117458952
#106022913
#692375