Finite Group Databasebeta

← #14317180

Subgroups — #14317180

Order 1920.

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

normal subgroups only

This group has 308 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#11750974C211yesmaximal, characteristic
2#11748041C211yesmaximal, characteristic
3C2×#90948C211yesmaximal, characteristic
4C2×#90947C211yesmaximal, characteristic
5C5×#4492C211yesmaximal, characteristic
6C3×#64712C211yesmaximal, characteristic
7#11745928C211yesmaximal, characteristic
8#10600029—31nomaximal, Hall
9C2×Dic60C2211yescharacteristic
10#91776—21no—
11C2×C5×Dic12C2211yescharacteristic
12C2×C3×Dic20C2211yescharacteristic
13#91385—21no—
14C2×#6661—21no—
15C3×C5×#107C2211yescharacteristic
16C8×Dic15C2211yescharacteristic
17#91094—21no—
18C2×C5×C3⋊C16C2211yescharacteristic
19C2×C3×#672C2211yescharacteristic
20#90948—22no—
21#90947—22no—
22#69236—51nomaximal, Hall
23#65470—31no—
24C2×#3961—31no—
25C2×Dic40—31no—
26#65162—31no—
27C5×#358—31no—
28#64721—31no—
29#64712D311yescharacteristic
30C2×Dic30—21no—
31C2×C5×Dic6—21no—
32C2×C3×Dic10—21no—
33C2×C3×C5×C8C2311yescharacteristic
34C3×C5×C4⋊C4—21no—
35#6712—41no—
36C4×Dic15—41no—
37C4×Dic15D411yescharacteristic
38C2×C3⋊#168D411yescharacteristic
39Dic60—21no—
40Dic60D412yes—
41C5×Dic12—21no—
42C5×Dic12—21no—
43C3×Dic20—21no—
44C3×Dic20—21no—
45#6669—41no—
46#6669—41no—
47#6661—42no—
48C3×#672—21no—
49C5×C3⋊C16—21no—
50#5183—51no—
51C2×#829—51no—
52C2×Dic24—51no—
53#4873—51no—
54C3×#358—51no—
55Dic3⋊C16—51no—
56#4492D511yescharacteristic
57C2×C5×Q16—31no—
58#4090—61no—
59C2×#689—61no—
60C2×Dic20—31no—
61C2×Dic20C2×D311yescharacteristic
62#4033—61no—
63C2×C5×C16—31no—
64C5×#107C2×D311yescharacteristic
65#3961—62no—
66C8×Dic5—31no—
67C2×#672C2×D311yescharacteristic
68#3942—61no—
69Dic40—62no—
70#2209—151noSylow
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×Dic15—41no—
74C2×Dic15D811yescharacteristic
75C2×Dic15D811yescharacteristic
76Dic30—22no—
77Dic30—41no—
78C2×C5×Dic3—41no—
79C5×Dic6—41no—
80C5×Dic6—41no—
81C2×C3×Dic5—41no—
82C3×Dic10—41no—
83C3×Dic10—41no—
84C3×C5×C8C2×D411yescharacteristic
85C3×C5×C8#4111yescharacteristic
86C3⋊#168—21no—
87C2×C3×Q16—51no—
88#944—101no—
89C2×#216—101no—
90C2×Dic12—51no—
91C2×Dic12C2×D511yescharacteristic
92#887—101no—
93C2×C3×C16—51no—
94C3×#107C2×D511yescharacteristic
95#829—102no—
96C8×Dic3—51no—
97C2×C3⋊C16C2×D511yescharacteristic
98#810—101no—
99Dic24—102no—
100C2×C5×Q8—61no—
101C2×Dic10—21no—
102C2×Dic10—61no—
103C5×Q16—61no—
104C5×Q16—61no—
105C2×C5×C8C22×D311yescharacteristic
106C5×C4⋊C4—21no—
107#689—122no—
108#683—121no—
109#683—121no—
110#683—121no—
111C4×Dic5—31no—
112C4×Dic5—121no—
113C2×#168—31no—
114Dic20—21no—
115Dic20—21no—
116Dic20—32no—
117Dic20—61no—
118C5×C16—61no—
119#672—21no—
120C2×Q32—151no—
121C2×Q32—151no—
122#494—151no—
123C4×Q16—151no—
124C4⋊C16—151no—
125#358—31no—
126#358—51no—
127C22×C3×C5C2×D811yescharacteristic
128C3×C4×C5—81no—
129C3×C4×C5#12111yescharacteristic
130C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
131Dic15—21no—
132Dic15—42no—
133Dic15Q3212yescomplemented
134C3×Dic5—81no—
135C5×Dic3—81no—
136C2×C3×Q8—101no—
137C2×Dic6—21no—
138C2×Dic6—101no—
139C3×Q16—101no—
140C3×Q16—101no—
141C2×C3×C8C22×D511yescharacteristic
142C3×C4⋊C4—21no—
143#216—202no—
144Dic3⋊C4—201no—
145Dic3⋊C4—201no—
146Dic3⋊C4—201no—
147C4×Dic3—51no—
148C4×Dic3—201no—
149C2×C3⋊C8—51no—
150Dic12—21no—
151Dic12—21no—
152Dic12—52no—
153Dic12—101no—
154C3×C16—101no—
155C3⋊C16—21no—
156C5×Q8—121no—
157C5×Q8—121no—
158C2×C4×C5—41no—
159C2×C4×C5—121no—
160C2×C4×C5D3×D411yescharacteristic
161C2×Dic5—31no—
162C2×Dic5—31no—
163C2×Dic5—41no—
164C2×Dic5—121no—
165Dic10—41no—
166Dic10—41no—
167Dic10—62no—
168Dic10—121no—
169C5×C8#23511yescharacteristic
170C5×C8D3×D411yescharacteristic
171#168—61no—
172C2×Q16—31no—
173C2×Q16—51no—
174C2×Q16—151no—
175C2×Q16—301no—
176C4⋊Q8—301no—
177C4×Q8—301no—
178Q32—302no—
179Q32—302no—
180C2×C16—31no—
181C2×C16—51no—
182#107D3×D511yescharacteristic
183#103—301no—
184C4×C8—151no—
185C2×C3×C5#45911yescharacteristic
186C2×C3×C5C2×Q3211yescharacteristic
187C2×C3×C5#51011yescharacteristic
188C3×Q8—201no—
189C3×Q8—201no—
190C2×C3×C4—41no—
191C2×C3×C4—201no—
192C2×C3×C4D4×D511yescharacteristic
193C2×Dic3—41no—
194C2×Dic3—51no—
195C2×Dic3—51no—
196C2×Dic3—201no—
197Dic6—41no—
198Dic6—41no—
199Dic6—102no—
200Dic6—201no—
201C3×C8#70911yescharacteristic
202C3×C8D4×D511yescharacteristic
203C3⋊C8—101no—
204C22×C5D3×D811yescharacteristic
205C4×C5—81no—
206C4×C5—241no—
207C4×C5#88411yescharacteristic
208C4×C5#91411yescharacteristic
209Dic5—32no—
210Dic5—61no—
211Dic5—81no—
212Dic5—122no—
213C2×Q8—61no—
214C2×Q8—101no—
215C2×Q8—301no—
216Q16—61no—
217Q16—61no—
218Q16—101no—
219Q16—101no—
220Q16—152no—
221Q16—301no—
222Q16—602no—
223C2×C8—151no—
224C2×C8C2×D3×D511yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—601no—
227C4⋊C4—601no—
228C4⋊C4—601no—
229C42—151no—
230C42—601no—
231C16—61no—
232C16—101no—
233C3×C5#220911yescharacteristic, complemented, Hall
234C22×C3D5×D811yescharacteristic
235C3×C4—81no—
236C3×C4—401no—
237C3×C4#403011yescharacteristic
238C3×C4#406011yescharacteristic
239Dic3—52no—
240Dic3—81no—
241Dic3—101no—
242Dic3—202no—
243C2×C5#478611yescharacteristic
244C2×C5#491511yescharacteristic
245C2×C5D3×Q3211yescharacteristic
246Q8—121no—
247Q8—121no—
248Q8—201no—
249Q8—201no—
250Q8—302no—
251Q8—601no—
252C2×C4—41no—
253C2×C4—121no—
254C2×C4—151no—
255C2×C4—151no—
256C2×C4—201no—
257C2×C4—601no—
258C2×C4#679011yescharacteristic
259C8—301no—
260C8#677111yescharacteristic
261C8#677711yescharacteristic
262C2×C3#6507511yescharacteristic
263C2×C3#6520411yescharacteristic
264C2×C3D5×Q3211yescharacteristic
265C5#6923611yescharacteristic, complemented, Sylow
266C22#9148111yescharacteristic
267C4—81no—
268C4—152no—
269C4—241no—
270C4—301no—
271C4—401no—
272C4—602no—
273C4#9146111yescharacteristic
274C4#9150611yescharacteristic
275C3#1060002911yescharacteristic, complemented, Sylow
276C2#1174740611yescharacteristic
277C2#1174827511yescharacteristic
278C2#1174829811yescharacteristic
subgroupG/H
centerC22#91481
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socle, prime radicalC22×C3×C5C2×D8
hypercenter#107D3×D5
hypocenterC3×C5#2209
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
133. Dic15Q32semidirect
233. C3×C5#2209semidirect
265. C5#69236semidirect
275. C3#10600029semidirect

Maximal subgroups

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

subgroupindex
#117509742
#117480412
C2×#909482
C2×#909472
C5×#44922
C3×#647122
#117459282
#106000293
#692365