Finite Group Databasebeta

← #14317160

Subgroups — #14317160

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×C5×#829C211yesmaximal, characteristic
2C3×#65470C211yesmaximal, characteristic
3Dic5×Dic12C211yesmaximal, characteristic
4C2×#90946C211yesmaximal, characteristic
5#11746385C211yesmaximal, characteristic
6#11745927C211yesmaximal, characteristic
7#11745898C211yesmaximal, characteristic
8#10602290—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10C2×C5×Dic12C2211yescharacteristic
11C3×#4090—21no—
12C2×C3×#689—21no—
13C2×C3×Dic20C2211yescharacteristic
14Dic5×Dic6—21no—
15#91102C2211yescharacteristic
16C2×C3⋊#672C2211yescharacteristic
17C5×#829—22no—
18C2×C5×C3⋊C16C2211yescharacteristic
19C3×C8×Dic5C2211yescharacteristic
20#90973—21no—
21#90946—22no—
22#71316—51nomaximal, Hall
23C2×C5×Q32—31no—
24Q16×Dic5—31no—
25#65470D311yescharacteristic
26C2×#3961—31no—
27#64784—31no—
28#64723—31no—
29#64721—31no—
30C2×C3×C5×Q8—21no—
31C2×C5×Dic6—21no—
32C2×C3×Dic10—21no—
33C3×C5×Q16—21no—
34C3×C5×Q16—21no—
35C2×C3×C5×C8C2311yescharacteristic
36C4⋊Dic15—21no—
37C5×Dic12—21no—
38C5×Dic12D412yes—
39C3×#689—42no—
40C3×#683—41no—
41C3×#683—41no—
42C3×C4×Dic5D411yescharacteristic
43C2×C3×#168D411yescharacteristic
44C3×Dic20—21no—
45C3×Dic20—21no—
46Dic3⋊Dic5—41no—
47Dic3×Dic5—41no—
48C3⋊#672—21no—
49C5×C3⋊C16—21no—
50C3×#494—51no—
51C2×#829—51no—
52C2×#829D511yescharacteristic
53C4×Dic12—51no—
54#4564—51no—
55#4564—51no—
56C4⋊(C3⋊C16)—51no—
57C2×C5×Q16—31no—
58C2×C5×Q16C2×D311yescharacteristic
59Q8×Dic5—61no—
60#4090—21no—
61C2×#689—21no—
62C2×Dic20C2×D311yescharacteristic
63C5×Q32—62no—
64C2×C5×C16—31no—
65#3967—61no—
66#3961—62no—
67#3950—31no—
68C8×Dic5C2×D311yescharacteristic
69C2×#672—31no—
70#2209—151noSylow
71C3×C5×Q8—41no—
72C3×C5×Q8—41no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×Dic15—41no—
76C2×C5×Dic3—41no—
77C5×Dic6—22no—
78C5×Dic6—41no—
79C2×C3×Dic5—41no—
80C2×C3×Dic5D811yescharacteristic
81C2×C3×Dic5D811yescharacteristic
82C3×Dic10—41no—
83C3×Dic10—41no—
84C3×C5×C8C2×D411yescharacteristic
85C3×C5×C8#4111yescharacteristic
86C3×#168—21no—
87C2×C3×Q16—51no—
88C2×C3×Q16—101no—
89C2×C3×Q16C2×D511yescharacteristic
90C3×C4⋊Q8—101no—
91C2×Dic12C2×D511yescharacteristic
92C4×Dic6—101no—
93C3×C4×C8—51no—
94#829—22no—
95#829—102no—
96#818—51no—
97#816—101no—
98C2×C3⋊C16—51no—
99C2×C3⋊C16C2×D511yescharacteristic
100C2×C5×Q8—21no—
101C2×C5×Q8—61no—
102C2×Dic10—21no—
103C5×Q16—21no—
104C5×Q16—21no—
105C5×Q16—32no—
106C5×Q16—61no—
107C2×C5×C8C22×D311yescharacteristic
108#689—42no—
109C4⋊Dic5—61no—
110C4⋊Dic5—121no—
111#683—41no—
112#683—41no—
113C4×Dic5—121no—
114C4×Dic5#6711yescharacteristic
115C2×#168#6711yescharacteristic
116Dic20—21no—
117Dic20—21no—
118C5×C16—61no—
119#672—61no—
120C2×Q32—31no—
121C2×Q32—151no—
122#494—51no—
123C4×Q16—151no—
124C4⋊C16—151no—
125#358—151no—
126#358—151no—
127C22×C3×C5C2×D811yescharacteristic
128C3×C4×C5—81no—
129C3×C4×C5#12111yescharacteristic
130C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
131Dic15—81no—
132C3×Dic5—21no—
133C3×Dic5—81no—
134C3×Dic5Q3212yescomplemented
135C5×Dic3—42no—
136C2×C3×Q8—21no—
137C2×C3×Q8—101no—
138C2×Dic6—21no—
139C3×Q16—21no—
140C3×Q16—21no—
141C3×Q16—101no—
142C3×Q16—101no—
143C3×Q16—202no—
144C2×C3×C8—51no—
145C2×C3×C8C22×D511yescharacteristic
146C3×C4⋊C4—201no—
147C3×C4⋊C4—201no—
148C3×C42—51no—
149C4⋊Dic3—101no—
150Dic3⋊C4—201no—
151C4×Dic3—201no—
152Dic12—21no—
153Dic12C22⋊D512yes—
154C3⋊C16—21no—
155C3⋊C16—101no—
156C5×Q8—41no—
157C5×Q8—41no—
158C5×Q8—62no—
159C5×Q8—121no—
160C2×C4×C5—41no—
161C2×C4×C5—121no—
162C2×C4×C5C2×#6711yescharacteristic
163C2×Dic5—41no—
164C2×Dic5—121no—
165C2×Dic5#21311yescharacteristic
166C2×Dic5#21311yescharacteristic
167Dic10—41no—
168Dic10—41no—
169C5×C8D3×D411yescharacteristic
170C5×C8#23711yescharacteristic
171#168—21no—
172C2×Q16—31no—
173C2×Q16—51no—
174C2×Q16—101no—
175C2×Q16D3×D511yescharacteristic
176C4⋊Q8—101no—
177C4×Q8—301no—
178Q32—62no—
179Q32—302no—
180C2×C16—31no—
181C2×C16—151no—
182#107—151no—
183#103—301no—
184C4×C8—51no—
185C2×C3×C5#45911yescharacteristic
186C2×C3×C5C2×Q3211yescharacteristic
187C2×C3×C5#51011yescharacteristic
188C3×Q8—41no—
189C3×Q8—41no—
190C3×Q8—201no—
191C3×Q8—201no—
192C2×C3×C4—41no—
193C2×C3×C4—51no—
194C2×C3×C4—51no—
195C2×C3×C4—201no—
196C2×C3×C4D4×D511yescharacteristic
197C2×Dic3—41no—
198C2×Dic3—201no—
199Dic6—22no—
200Dic6—41no—
201C3×C8—101no—
202C3×C8#71111yescharacteristic
203C3×C8C2×C22⋊D511yescharacteristic
204C22×C5C2×#21311yescharacteristic
205C4×C5—81no—
206C4×C5—122no—
207C4×C5#93211yescharacteristic
208C4×C5#93811yescharacteristic
209Dic5—21no—
210Dic5—81no—
211Dic5—241no—
212Dic5#82912yescomplemented
213C2×Q8—21no—
214C2×Q8—61no—
215C2×Q8—101no—
216Q16—21no—
217Q16—21no—
218Q16—32no—
219Q16—61no—
220Q16—101no—
221Q16—101no—
222Q16—202no—
223C2×C8—51no—
224C2×C8C2×D3×D511yescharacteristic
225C4⋊C4—201no—
226C4⋊C4—201no—
227C4⋊C4—301no—
228C4⋊C4—601no—
229C42—51no—
230C42—601no—
231C16—61no—
232C16—301no—
233C3×C5#220911yescharacteristic, complemented, Hall
234C22×C3D5×D811yescharacteristic
235C3×C4—52no—
236C3×C4—81no—
237C3×C4—101no—
238C3×C4—401no—
239C3×C4#405711yescharacteristic
240C3×C4#408511yescharacteristic
241Dic3—42no—
242Dic3—401no—
243C2×C5#507211yescharacteristic
244C2×C5#517911yescharacteristic
245C2×C5C2×#82911yescharacteristic
246Q8—41no—
247Q8—41no—
248Q8—62no—
249Q8—121no—
250Q8—201no—
251Q8—201no—
252C2×C4—41no—
253C2×C4—51no—
254C2×C4—51no—
255C2×C4—121no—
256C2×C4—201no—
257C2×C4—601no—
258C2×C4D5×#6711yescharacteristic
259C8—101no—
260C8#678011yescharacteristic
261C8D3×C22⋊D511yescharacteristic
262C2×C3D5×Q3211yescharacteristic
263C2×C3#6520711yescharacteristic
264C2×C3#6543911yescharacteristic
265C5#7131611yescharacteristic, complemented, Sylow
266C22D5×#21311yescharacteristic
267C4—52no—
268C4—81no—
269C4—101no—
270C4—122no—
271C4—401no—
272C4—1201no—
273C4#9148911yescharacteristic
274C4#9156511yescharacteristic
275C3#1060229011yescharacteristic, complemented, Sylow
276C2D5×#82911yescharacteristic
277C2#1174830211yescharacteristic
278C2#1174897411yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socle, prime radicalC22×C3×C5C2×D8
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2209
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
134. C3×Dic5Q32semidirect
212. Dic5#829semidirect
233. C3×C5#2209semidirect
265. C5#71316semidirect
275. C3#10602290semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8292
C3×#654702
Dic5×Dic122
C2×#909462
#117463852
#117459272
#117458982
#106022903
#713165