Finite Group Databasebeta

← #14317173

Subgroups — #14317173

Order 1920.

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

normal subgroups only

This group has 308 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
1C2×C3×Dic40C211yesmaximal, characteristic
2#11748033C211yesmaximal, characteristic
3Dic3×Dic20C211yesmaximal, characteristic
4C2×#90947C211yesmaximal, characteristic
5#11746324C211yesmaximal, characteristic
6C5×Dic3⋊C16C211yesmaximal, characteristic
7#11745898C211yesmaximal, characteristic
8#10600086—31nomaximal, Hall
9C2×Dic60C2211yescharacteristic
10C2×C3×Dic20C2211yescharacteristic
11C2×C3×Dic20C2211yescharacteristic
12#91389—21no—
13Dic3×Dic10—21no—
14C2×#6662—21no—
15C2×C3×C5×C16C2211yescharacteristic
16#91102C2211yescharacteristic
17C5×C8×Dic3C2211yescharacteristic
18C2×C5×C3⋊C16C2211yescharacteristic
19C3×Dic40—22no—
20#90971—21no—
21#90947—22no—
22#71497—51nomaximal, Hall
23C2×Dic40—31no—
24C2×Dic40D311yescharacteristic
25#64988—31no—
26C4×Dic20—31no—
27C5×C4⋊C16—31no—
28#64723—31no—
29#64723—31no—
30C2×Dic30—21no—
31C2×C3×Dic10—21no—
32C2×C3×Dic10—21no—
33C2×C3×C5×C8C2311yescharacteristic
34C4⋊Dic15—21no—
35Dic60—21no—
36Dic60—21no—
37C4×C5×Dic3D411yescharacteristic
38C2×C5×C3⋊C8D411yescharacteristic
39C3×Dic20—21no—
40C3×Dic20—21no—
41C3×Dic20—21no—
42C3×Dic20D412yes—
43Dic3⋊Dic5—41no—
44Dic3⋊Dic5—41no—
45#6668—41no—
46Dic3×Dic5—41no—
47#6662—42no—
48C3×C5×C16—21no—
49C5×C3⋊C16—21no—
50C2×C3×Q32—51no—
51#5183—51no—
52Dic3×Q16—51no—
53C2×#829—51no—
54#4564—51no—
55#4503—51no—
56Dic3⋊C16D511yescharacteristic
57C2×Dic20—31no—
58C2×Dic20—61no—
59C2×Dic20C2×D311yescharacteristic
60C2×Dic20C2×D311yescharacteristic
61#4015—61no—
62C4×Dic10—61no—
63C2×C5×C16—31no—
64C2×C5×C16C2×D311yescharacteristic
65C4×C5×C8—31no—
66#3950—31no—
67#3948—61no—
68Dic40—22no—
69Dic40—62no—
70#2209—151noSylow
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×Dic15—41no—
73C2×Dic15—41no—
74Dic30—41no—
75Dic30—41no—
76C2×C5×Dic3D811yescharacteristic
77C2×C5×Dic3D811yescharacteristic
78C2×C3×Dic5—41no—
79C2×C3×Dic5—41no—
80C3×Dic10—22no—
81C3×Dic10—41no—
82C3×Dic10—41no—
83C3×Dic10—41no—
84C3×C5×C8C2×D411yescharacteristic
85C3×C5×C8#4111yescharacteristic
86C5×C3⋊C8—21no—
87C2×C3×Q16—51no—
88C2×C3×Q16—51no—
89Q8×Dic3—101no—
90#944—101no—
91C2×#216—101no—
92C2×Dic12—51no—
93C3×Q32—102no—
94C2×C3×C16C2×D511yescharacteristic
95#835—101no—
96#829—102no—
97#818—51no—
98C8×Dic3C2×D511yescharacteristic
99C2×C3⋊C16C2×D511yescharacteristic
100C2×Dic10—21no—
101C2×Dic10—21no—
102C2×Dic10—61no—
103C2×C5×C8—31no—
104C2×C5×C8C22×D311yescharacteristic
105C42×C5—31no—
106C4⋊Dic5—61no—
107C4⋊Dic5—121no—
108C4⋊Dic5—121no—
109#683—121no—
110C4×Dic5—121no—
111Dic20—21no—
112Dic20—21no—
113Dic20—21no—
114Dic20—61no—
115Dic20—61no—
116Dic20—122no—
117Dic20#6712yes—
118C5×C16—21no—
119C5×C16—61no—
120C2×Q32—51no—
121C2×Q32—151no—
122#494—151no—
123C4×Q16—151no—
124C4⋊C16—31no—
125#358—151no—
126#358—151no—
127C22×C3×C5C2×D811yescharacteristic
128C3×C4×C5#12111yescharacteristic
129C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
130Dic15—81no—
131Dic15—81no—
132C3×Dic5—42no—
133C3×Dic5—81no—
134C5×Dic3—21no—
135C5×Dic3Q3212yescomplemented
136C2×C3×Q8—101no—
137C2×C3×Q8—101no—
138C2×Dic6—101no—
139C3×Q16—52no—
140C3×Q16—101no—
141C3×Q16—101no—
142C3×Q16—101no—
143C2×C3×C8C22×D511yescharacteristic
144#216—202no—
145C4⋊Dic3—101no—
146C4⋊Dic3—201no—
147Dic3⋊C4—201no—
148Dic3⋊C4—201no—
149C4×Dic3—201no—
150C4×Dic3D2011yescharacteristic
151C2×C3⋊C8D2011yescharacteristic
152Dic12—101no—
153Dic12—101no—
154C3×C16—21no—
155C3⋊C16—21no—
156C2×C4×C5—31no—
157C2×C4×C5—31no—
158C2×C4×C5D3×D411yescharacteristic
159C2×Dic5—41no—
160C2×Dic5—41no—
161C2×Dic5—121no—
162C2×Dic5—121no—
163Dic10—22no—
164Dic10—41no—
165Dic10—41no—
166Dic10—41no—
167Dic10—121no—
168Dic10—121no—
169C5×C8—61no—
170C5×C8#23711yescharacteristic
171C5×C8C2×#6711yescharacteristic
172C2×Q16—51no—
173C2×Q16—51no—
174C2×Q16—151no—
175C2×Q16—301no—
176C4⋊Q8—301no—
177C4×Q8—301no—
178Q32—102no—
179Q32—302no—
180C2×C16—31no—
181C2×C16D3×D511yescharacteristic
182#107—151no—
183#103—301no—
184C4×C8—31no—
185C2×C3×C5#45911yescharacteristic
186C2×C3×C5C2×Q3211yescharacteristic
187C2×C3×C5#51011yescharacteristic
188C3×Q8—102no—
189C3×Q8—201no—
190C3×Q8—201no—
191C3×Q8—201no—
192C2×C3×C4—201no—
193C2×C3×C4—201no—
194C2×C3×C4C2×D2011yescharacteristic
195C2×Dic3—201no—
196C2×Dic3—201no—
197C2×Dic3D4011yescharacteristic
198C2×Dic3D4011yescharacteristic
199Dic6—201no—
200Dic6—201no—
201C3×C8D4×D511yescharacteristic
202C3×C8#71311yescharacteristic
203C3⋊C8—21no—
204C22×C5D3×D811yescharacteristic
205C4×C5—32no—
206C4×C5—61no—
207C4×C5#91111yescharacteristic
208C4×C5#93911yescharacteristic
209Dic5—42no—
210Dic5—81no—
211Dic5—241no—
212Dic5—241no—
213C2×Q8—101no—
214C2×Q8—101no—
215C2×Q8—301no—
216Q16—52no—
217Q16—101no—
218Q16—101no—
219Q16—101no—
220Q16—301no—
221Q16—301no—
222Q16—602no—
223C2×C8—31no—
224C2×C8C2×D3×D511yescharacteristic
225C4⋊C4—301no—
226C4⋊C4—601no—
227C4⋊C4—601no—
228C4⋊C4—601no—
229C42—31no—
230C42—601no—
231C16—21no—
232C16—61no—
233C3×C5#220911yescharacteristic, complemented, Hall
234C22×C3C2×D4011yescharacteristic
235C3×C4—202no—
236C3×C4—401no—
237C3×C4#404111yescharacteristic
238C3×C4#405411yescharacteristic
239Dic3—21no—
240Dic3—401no—
241Dic3—401no—
242Dic3Dic4012yescomplemented
243C2×C5D3×Q3211yescharacteristic
244C2×C5#491811yescharacteristic
245C2×C5#515011yescharacteristic
246Q8—102no—
247Q8—201no—
248Q8—201no—
249Q8—201no—
250Q8—601no—
251Q8—601no—
252C2×C4—31no—
253C2×C4—31no—
254C2×C4—201no—
255C2×C4—201no—
256C2×C4—601no—
257C2×C4—601no—
258C2×C4D3×D2011yescharacteristic
259C8—61no—
260C8#676611yescharacteristic
261C8D5×#6711yescharacteristic
262C2×C3#6513211yescharacteristic
263C2×C3C2×Dic4011yescharacteristic
264C2×C3#6519811yescharacteristic
265C5#7149711yescharacteristic, complemented, Sylow
266C22D3×D4011yescharacteristic
267C4—32no—
268C4—61no—
269C4—202no—
270C4—401no—
271C4—1201no—
272C4—1201no—
273C4#9125411yescharacteristic
274C4#9140911yescharacteristic
275C3#1060008611yescharacteristic, complemented, Sylow
276C2D3×Dic4011yescharacteristic
277C2#1174683011yescharacteristic
278C2#1174775411yescharacteristic
subgroupG/H
centerC22D3×D40
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×C16C22
socle, prime radicalC22×C3×C5C2×D8
hypercenterC2×C16D3×D5
hypocenterC3×C5#2209
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
135. C5×Dic3Q32semidirect
233. C3×C5#2209semidirect
242. Dic3Dic40semidirect
265. C5#71497semidirect
275. C3#10600086semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Dic402
#117480332
Dic3×Dic202
C2×#909472
#117463242
C5×Dic3⋊C162
#117458982
#106000863
#714975