Finite Group Databasebeta

← #14317124

Subgroups — #14317124

Order 1920.

332 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 78 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#11751284C211yesmaximal, characteristic, complemented
2C2×C3×#3960C211yesmaximal, characteristic
3#11747809C211yesmaximal, characteristic
4C2×#90942C211yesmaximal, characteristic
5C5×#4564C211yesmaximal, characteristic, complemented
6#11745928C211yesmaximal, characteristic, complemented
7#11745902C211yesmaximal, characteristic, complemented
8#10600027—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10#91833—21no—
11C2×#6718—21no—
12C2×Dic60C2211yescharacteristic
13C2×C3×D40C2211yescharacteristic
14#91434—21no—
15C8×Dic15C2211yescharacteristic
16C5×#818C2211yescharacteristic
17C2×C5×C3⋊C16C2211yescharacteristic
18C3×#3960—22no—
19C2×C3×#672C2211yescharacteristic
20#90964—21no—
21#90942—22no—
22#71476—51nomaximal, Hall
23#65470—31no—
24C2×#3960D311yescharacteristic
25C2×#3932—31no—
26#65161—31no—
27C5×#358—31no—
28#64721—31no—
29#64712—31no—
30C2×C3×C5×Q8—21no—
31C2×Dic30—21no—
32C2×C3×D20—21no—
33C2×D5×Dic3—41no—
34C3×C5×Q16—21no—
35C3×C5×Q16—21no—
36C2×C3×C5×C8C2311yescharacteristic
37#6718—42no—
38#6712—41no—
39#6712—41no—
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×SD32—51no—
51#5183—51no—
52Dic3×D8—51no—
53C2×#827—51no—
54#4564D511yescharacteristic, complemented
55#4503—51no—
56Dic3⋊C16—51no—
57C2×C5×Q16C2×D311yescharacteristic
58#4090—61no—
59C2×#689—61no—
60C2×Dic20—31no—
61C2×D40C2×D311yescharacteristic
62#4039—61no—
63C2×C5×C16—31no—
64C5×#107—31no—
65#3960—22no—
66C8×Dic5—31no—
67C2×#672C2×D311yescharacteristic
68#3941—61no—
69#3932—62no—
70#2208—151noSylow
71C22×C3×D5—41no—
72C3×C5×Q8—41no—
73C3×C5×Q8—41no—
74C2×C3×C4×C5—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×Q16C2×D511yescharacteristic
89C2×C3×D8—51no—
90#944—101no—
91C2×#216—101no—
92D4×Dic3—101no—
93C2×Dic12—51no—
94C3×SD32—102no—
95C2×C3×C16—51no—
96#832—101no—
97#827—102no—
98#818C2×D511yescharacteristic
99C8×Dic3—51no—
100C2×C3⋊C16C2×D511yescharacteristic
101C2×C5×Q8—21no—
102C2×D20—21no—
103C2×C4×D5—121no—
104C2×Dic10—61no—
105C5×Q16—21no—
106C5×Q16—21no—
107C2×C5×C8C22×D311yescharacteristic
108C5×C4⋊C4—61no—
109#689—122no—
110#685—121no—
111#683—121no—
112#683—121no—
113C4×Dic5—31no—
114C2×#168—31no—
115Dic20—61no—
116Dic20—61no—
117D40—21no—
118D40#6712yes—
119C5×C16—61no—
120#672—21no—
121C2×SD32—51no—
122C2×SD32—151no—
123#494—151no—
124C4×D8—151no—
125C4⋊C16—151no—
126#358—31no—
127#358—151no—
128C22×C3×C5C2×D811yescharacteristic
129C2×C3×D5—42no—
130C2×C3×D5—81no—
131C2×C3×D5—81no—
132C3×C4×C5—81no—
133C3×C4×C5#12111yescharacteristic
134C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
135Dic15—21no—
136Dic15—81no—
137Dic15SD3212yescomplemented
138C5×Dic3—81no—
139C2×C3×Q8—21no—
140C2×C3×D4—101no—
141C22×Dic3—201no—
142C2×Dic6—101no—
143C3×Q16—21no—
144C3×Q16—21no—
145C3×D8—52no—
146C3×D8—101no—
147C2×C3×C8C22×D511yescharacteristic
148#217—201no—
149#216—202no—
150C4⋊Dic3—21no—
151Dic3⋊C4—201no—
152Dic3⋊C4—201no—
153C4×Dic3—51no—
154C2×C3⋊C8—51no—
155Dic12—101no—
156Dic12—101no—
157C3×C16—101no—
158C3⋊C16—21no—
159C22×D5—41no—
160C5×Q8—41no—
161C5×Q8—41no—
162C2×C4×C5—41no—
163C2×C4×C5—121no—
164C2×C4×C5D3×D411yescharacteristic
165C2×Dic5—31no—
166C2×Dic5—31no—
167C2×Dic5—121no—
168D20—22no—
169D20—41no—
170C4×D5—242no—
171Dic10—121no—
172Dic10—121no—
173C5×C8#23711yescharacteristic
174C5×C8C2×#6711yescharacteristic
175#168—61no—
176C2×Q16—151no—
177C2×Q16—301no—
178C2×Q16D3×D511yescharacteristic
179C2×D8—51no—
180C4⋊Q8—301no—
181C4×D4—301no—
182SD32—102no—
183SD32—302no—
184C2×C16—31no—
185C2×C16—51no—
186#107—31no—
187#102—301no—
188C4×C8—151no—
189C2×C3×C5#45911yescharacteristic
190C2×C3×C5C2×SD3211yescharacteristic
191C2×C3×C5#51011yescharacteristic
192C3×D5—82no—
193C23×C3—201no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×D4—102no—
197C3×D4—201no—
198C2×C3×C4—41no—
199C2×C3×C4D4×D511yescharacteristic
200C2×Dic3—41no—
201C2×Dic3—51no—
202C2×Dic3—51no—
203C2×Dic3—201no—
204C2×Dic3—402no—
205Dic6—201no—
206Dic6—201no—
207C3×C8#70911yescharacteristic
208C3×C8D4×D511yescharacteristic
209C3⋊C8—101no—
210C22×C5D3×D811yescharacteristic
211C2×D5—42no—
212C2×D5—81no—
213C2×D5—81no—
214C4×C5—81no—
215C4×C5—241no—
216C4×C5#91111yescharacteristic
217C4×C5#93911yescharacteristic
218Dic5—32no—
219Dic5—61no—
220Dic5—241no—
221C2×Q8—21no—
222C2×Q8—301no—
223C2×D4—101no—
224C22×C4—601no—
225Q16—21no—
226Q16—21no—
227Q16—301no—
228Q16—301no—
229Q16—602no—
230D8—52no—
231D8—101no—
232C2×C8—151no—
233C2×C8C2×D3×D511yescharacteristic
234C4⋊C4—61no—
235C4⋊C4—601no—
236C4⋊C4—601no—
237C22⋊C4—601no—
238C42—151no—
239C16—61no—
240C16—101no—
241C3×C5#220811yescharacteristic, complemented, Hall
242C22×C3—202no—
243C22×C3—401no—
244C22×C3—401no—
245C22×C3D5×D811yescharacteristic
246C3×C4—81no—
247C3×C4#403011yescharacteristic
248C3×C4#406011yescharacteristic
249Dic3—52no—
250Dic3—81no—
251Dic3—101no—
252Dic3—401no—
253C2×C5D3×SD3211yescharacteristic
254C2×C5#491511yescharacteristic
255C2×C5#515011yescharacteristic
256D5—82no—
257C23—201no—
258Q8—41no—
259Q8—41no—
260Q8—601no—
261Q8—601no—
262D4—102no—
263D4—201no—
264C2×C4—41no—
265C2×C4—121no—
266C2×C4—151no—
267C2×C4—151no—
268C2×C4—601no—
269C2×C4—1202no—
270C2×C4#679011yescharacteristic
271C8—301no—
272C8#677911yescharacteristic
273C8D5×#6711yescharacteristic
274C2×C3—402no—
275C2×C3#6507511yescharacteristic
276C2×C3D5×SD3211yescharacteristic
277C2×C3#6520711yescharacteristic
278C5#7147611yescharacteristic, complemented, Sylow
279C22—202no—
280C22—401no—
281C22—401no—
282C22#9148111yescharacteristic
283C4—81no—
284C4—152no—
285C4—241no—
286C4—301no—
287C4—1201no—
288C4#9149811yescharacteristic
289C4#9155011yescharacteristic
290C3#1060002711yescharacteristic, complemented, Sylow
291C2—402no—
292C2#1174829211yescharacteristic
293C2#1174830911yescharacteristic
294C2#1174898311yescharacteristic
subgroupG/H
centerC22#91481
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C2×D8
prime radicalC2×C3×D40C22
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2208
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
1. #11751284C2semidirect
5. C5×#4564C2semidirect
6. #11745928C2semidirect
7. #11745902C2semidirect
54. #4564D5semidirect
137. Dic15SD32semidirect
241. C3×C5#2208semidirect
278. C5#71476semidirect
290. C3#10600027semidirect

Maximal subgroups

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

subgroupindex
#117512842
C2×C3×#39602
#117478092
C2×#909422
C5×#45642
#117459282
#117459022
#106000273
#714765