Finite Group Databasebeta

← #14317142

Subgroups — #14317142

Order 1920.

332 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C5×#4872C211yesmaximal, characteristic
2#11748033C211yesmaximal, characteristic, complemented
3C2×#90944C211yesmaximal, characteristic
4C2×#90941C211yesmaximal, characteristic
5#11746313C211yesmaximal, characteristic, complemented
6C3×#64712C211yesmaximal, characteristic, complemented
7Dic3⋊#672C211yesmaximal, characteristic, complemented
8#10601685—31nomaximal, Hall
9C2×Dic60C2211yescharacteristic
10C2×C5×D24C2211yescharacteristic
11C5×#893—21no—
12C2×C3×Dic20C2211yescharacteristic
13#91389—21no—
14C2×#6662—21no—
15C3×C5×#107C2211yescharacteristic
16C2×C3⋊#672C2211yescharacteristic
17C5×C8×Dic3C2211yescharacteristic
18C5×#809—21no—
19C2×C3×#672C2211yescharacteristic
20#90944—22no—
21#90941—22no—
22#69234—51nomaximal, Hall
23C4×C5×D8—31no—
24C2×#3959—31no—
25C2×#3959—31no—
26#64988—31no—
27#64712—31no—
28#64712D311yescharacteristic, complemented
29C4⋊#672—31no—
30C2×Dic30—21no—
31C2×C5×D12—21no—
32C2×C4×C5×D3—41no—
33C2×C3×Dic10—21no—
34C2×C3×C5×C8C2311yescharacteristic
35C3×C5×C4⋊C4—21no—
36Dic60—21no—
37Dic60—21no—
38C5×(C2×D3)⋊C4—41no—
39C4×C5×Dic3D411yescharacteristic
40C2×C5×C3⋊C8D411yescharacteristic
41C5×D24—21no—
42C5×D24D412yes—
43C3×Dic20—21no—
44C3×Dic20—21no—
45Dic3⋊Dic5—41no—
46Dic3⋊Dic5—41no—
47#6662—42no—
48C3⋊#672—21no—
49C3×#672—21no—
50#5183—51no—
51C2×#828—51no—
52C2×#800—51no—
53#4872D511yescharacteristic
54C3×#358—51no—
55Dic3⋊C16—51no—
56#4492—51no—
57C2×C5×D8—31no—
58C4×C5×D4—61no—
59C2×Dic20—31no—
60C2×Dic20—61no—
61C2×Dic20C2×D311yescharacteristic
62#4015—61no—
63C5×#107C2×D311yescharacteristic
64C5×#102—61no—
65C4×C5×C8—31no—
66#3959—62no—
67#3959—62no—
68C2×#672—31no—
69C2×#672C2×D311yescharacteristic
70#2208—151noSylow
71C22×C5×D3—41no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×Dic15—41no—
75Dic30—41no—
76Dic30—41no—
77C2×C5×Dic3D811yescharacteristic
78C2×C5×Dic3D811yescharacteristic
79C5×D12—22no—
80C5×D12—41no—
81C4×C5×D3—82no—
82C2×C3×Dic5—41no—
83C3×Dic10—41no—
84C3×Dic10—41no—
85C3×C5×C8C2×D411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C5×C3⋊C8—21no—
88C2×C3×Q16—51no—
89#944—101no—
90C2×#216—101no—
91C2×Dic12—51no—
92C2×D24C2×D511yescharacteristic
93#893—21no—
94C2×C3×C16—51no—
95C3×#107C2×D511yescharacteristic
96#828—102no—
97C8×Dic3C2×D511yescharacteristic
98C2×C3⋊C16—51no—
99#809—21no—
100#800—102no—
101C2×C5×D4—61no—
102C22×C4×C5—121no—
103C2×Dic10—21no—
104C2×Dic10—61no—
105C5×D8—32no—
106C5×D8—61no—
107C2×C5×C8—31no—
108C2×C5×C8C22×D311yescharacteristic
109C5×C4⋊C4—21no—
110C5×C22⋊C4—121no—
111C42×C5—31no—
112C4⋊Dic5—121no—
113C4⋊Dic5—121no—
114Dic20—21no—
115Dic20—21no—
116Dic20—61no—
117Dic20—61no—
118Dic20—122no—
119#672—21no—
120#672—61no—
121C2×SD32—151no—
122C2×SD32—151no—
123#494—151no—
124C4×D8—31no—
125C4⋊C16—151no—
126#358—51no—
127#358—151no—
128C22×C3×C5C2×D811yescharacteristic
129C2×C5×D3—42no—
130C2×C5×D3—81no—
131C2×C5×D3—81no—
132C3×C4×C5—81no—
133C3×C4×C5#12111yescharacteristic
134C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
135Dic15—81no—
136C3×Dic5—81no—
137C5×Dic3—21no—
138C5×Dic3SD3212yescomplemented
139C2×C3×Q8—101no—
140C2×D12—21no—
141C2×C4×D3—41no—
142C2×Dic6—101no—
143C3×Q16—101no—
144C3×Q16—101no—
145C2×C3×C8C22×D511yescharacteristic
146C3×C4⋊C4—21no—
147#216—202no—
148(C2×D3)⋊C4—41no—
149Dic3⋊C4—201no—
150Dic3⋊C4—201no—
151C4×Dic3C22⋊D511yescharacteristic
152C2×C3⋊C8C22⋊D511yescharacteristic
153Dic12—101no—
154Dic12—101no—
155D24—21no—
156D24D2012yes—
157C3×C16—101no—
158C3⋊C16—101no—
159C23×C5—121no—
160C5×D4—62no—
161C5×D4—121no—
162C2×C4×C5—31no—
163C2×C4×C5—31no—
164C2×C4×C5—41no—
165C2×C4×C5—242no—
166C2×C4×C5D3×D411yescharacteristic
167C2×Dic5—41no—
168C2×Dic5—121no—
169Dic10—41no—
170Dic10—41no—
171Dic10—121no—
172Dic10—121no—
173C5×C8—61no—
174C5×C8#23511yescharacteristic
175C5×C8D3×D411yescharacteristic
176C2×Q16—51no—
177C2×Q16—151no—
178C2×Q16—301no—
179C2×D8—31no—
180C4⋊Q8—301no—
181C4×D4—61no—
182SD32—302no—
183SD32—302no—
184C2×C16—51no—
185C2×C16—151no—
186#107D3×D511yescharacteristic
187#102—61no—
188C4×C8—31no—
189C2×C3×C5#45911yescharacteristic
190C2×C3×C5C2×SD3211yescharacteristic
191C2×C3×C5#51011yescharacteristic
192C5×D3—82no—
193C22×D3—41no—
194C3×Q8—201no—
195C3×Q8—201no—
196C2×C3×C4—41no—
197C2×C3×C4—201no—
198C2×C3×C4C2×C22⋊D511yescharacteristic
199C2×Dic3—201no—
200C2×Dic3#68611yescharacteristic
201C2×Dic3#68611yescharacteristic
202D12—22no—
203D12—41no—
204C4×D3—82no—
205Dic6—201no—
206Dic6—201no—
207C3×C8C2×D2011yescharacteristic
208C3×C8#70911yescharacteristic
209C3⋊C8—21no—
210C22×C5—122no—
211C22×C5—241no—
212C22×C5—241no—
213C22×C5D3×D811yescharacteristic
214C4×C5—32no—
215C4×C5—61no—
216C4×C5—81no—
217C4×C5#88411yescharacteristic
218C4×C5#91411yescharacteristic
219Dic5—81no—
220Dic5—241no—
221C2×Q8—101no—
222C2×Q8—301no—
223C2×D4—61no—
224C22×C4—121no—
225Q16—101no—
226Q16—101no—
227Q16—301no—
228Q16—301no—
229Q16—602no—
230D8—32no—
231D8—61no—
232C2×C8—31no—
233C2×C8C2×D3×D511yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—601no—
236C4⋊C4—601no—
237C22⋊C4—121no—
238C42—31no—
239C16—101no—
240C16—301no—
241C3×C5#220811yescharacteristic, complemented, Hall
242C22×C3C2×#68611yescharacteristic
243C2×D3—42no—
244C2×D3—81no—
245C2×D3—81no—
246C3×C4—81no—
247C3×C4—401no—
248C3×C4#407611yescharacteristic
249C3×C4#409511yescharacteristic
250Dic3—21no—
251Dic3—401no—
252Dic3#395912yescomplemented
253C2×C5—242no—
254C2×C5#478611yescharacteristic
255C2×C5D3×SD3211yescharacteristic
256C2×C5#491811yescharacteristic
257C23—121no—
258Q8—201no—
259Q8—201no—
260Q8—601no—
261Q8—601no—
262D4—62no—
263D4—121no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—41no—
267C2×C4—201no—
268C2×C4—242no—
269C2×C4—601no—
270C2×C4D3×C22⋊D511yescharacteristic
271C8—61no—
272C8#677111yescharacteristic
273C8D3×D2011yescharacteristic
274C2×C3#6530411yescharacteristic
275C2×C3C2×#395911yescharacteristic
276C2×C3#6548411yescharacteristic
277D3—82no—
278C5#6923411yescharacteristic, complemented, Sylow
279C22—122no—
280C22—241no—
281C22—241no—
282C22D3×#68611yescharacteristic
283C4—32no—
284C4—61no—
285C4—81no—
286C4—401no—
287C4—1201no—
288C4#9145411yescharacteristic
289C4#9150411yescharacteristic
290C3#1060168511yescharacteristic, complemented, Sylow
291C2—242no—
292C2#1174740211yescharacteristic
293C2D3×#395911yescharacteristic
294C2#1174829711yescharacteristic
subgroupG/H
centerC22D3×#686
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
prime radicalC2×C5×D24C22
hypercenter#107D3×D5
hypocenterC3×C5#2208
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #11748033C2semidirect
5. #11746313C2semidirect
6. C3×#64712C2semidirect
7. Dic3⋊#672C2semidirect
28. #64712D3semidirect
138. C5×Dic3SD32semidirect
241. C3×C5#2208semidirect
252. Dic3#3959semidirect
278. C5#69234semidirect
290. C3#10601685semidirect

Maximal subgroups

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

subgroupindex
C5×#48722
#117480332
C2×#909442
C2×#909412
#117463132
C3×#647122
Dic3⋊#6722
#106016853
#692345