Finite Group Databasebeta

← #14315441

Subgroups — #14315441

Order 1920.

300 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 98 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
1Q16×Dic15C211yesmaximal, characteristic
2C2×C5×#829C211yesmaximal, characteristic
3#11747886C211yesmaximal, characteristic
4C3×#64784C211yesmaximal, characteristic
5#11745941C211yesmaximal, characteristic
6#11745900C211yesmaximal, characteristic
7#11745872C211yesmaximal, characteristic
8Dic5×Q32—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10Q8×Dic15—21no—
11C2×C5×Dic12C2211yescharacteristic
12#91344—21no—
13#91119—21no—
14#91102C2211yescharacteristic
15C8×Dic15C2211yescharacteristic
16C5×#829C414yescomplemented
17C2×C5×C3⋊C16C2211yescharacteristic
18C3×#3950C2211yescharacteristic
19C2×C3×#672C2211yescharacteristic
20#90972—21no—
21#69207—51nomaximal, Hall
22C2×C5×Q32—31no—
23Q16×Dic5—31no—
24Q16×Dic5—31no—
25#64784—31no—
26#64784D311yescharacteristic
27#64724—31no—
28C16×Dic5—31no—
29C2×C3×C5×Q8—21no—
30C2×C5×Dic6—21no—
31C3×C5×Q16—21no—
32C3×C5×Q16C2×C412yes—
33C2×C3×C5×C8C2311yescharacteristic
34C4⋊Dic15—21no—
35C4⋊Dic15—41no—
36C4×Dic15—41no—
37C4×Dic15D411yescharacteristic
38C2×C3⋊#168D411yescharacteristic
39C5×Dic12—21no—
40C5×Dic12C2×C412yes—
41C3×C4⋊Dic5—21no—
42Dic3⋊Dic5—41no—
43Dic3×Dic5—41no—
44C3×#672—21no—
45C5×C3⋊C16C2×C412yes—
46Dic3×Q16—51no—
47C2×#829D511yescharacteristic
48#4873—51no—
49C3×#358—51no—
50#4503—51no—
51Dic3×C16—51no—
52#4489—51no—
53C2×C5×Q16—31no—
54C2×C5×Q16C2×D311yescharacteristic
55Q8×Dic5—61no—
56Q8×Dic5—61no—
57C5×Q32—34no—
58C2×C5×C16—31no—
59#3967—61no—
60#3967—61no—
61#3950—31no—
62#3950C2×D311yescharacteristic
63C8×Dic5—31no—
64C2×#672C2×D311yescharacteristic
65C4×Q32—151noSylow
66C3×C5×Q8—22no—
67C3×C5×Q8—41no—
68C2×C3×C4×C5—41no—
69C2×C3×C4×C5C2×D411yescharacteristic
70C2×Dic15—41no—
71C2×Dic15D811yescharacteristic
72C2×Dic15D811yescharacteristic
73C2×C5×Dic3—41no—
74C5×Dic6—22no—
75C5×Dic6—41no—
76C2×C3×Dic5—41no—
77C3×C5×C8C22×C411yescharacteristic
78C3×C5×C8#4111yescharacteristic
79C3⋊#168—21no—
80C2×C3×Q16C2×D511yescharacteristic
81Q8×Dic3—101no—
82C2×Dic12C2×D511yescharacteristic
83#887—101no—
84C2×C3×C16—51no—
85C3×#107—51no—
86#835—101no—
87#829Dic514yescomplemented
88#818—51no—
89C8×Dic3—51no—
90C2×C3⋊C16C2×D511yescharacteristic
91#810—101no—
92C2×C5×Q8—21no—
93C2×C5×Q8—61no—
94C5×Q16—21no—
95C5×Q16—32no—
96C5×Q16—61no—
97C5×Q16C4×D312yes—
98C2×C5×C8C22×D311yescharacteristic
99C4⋊Dic5—21no—
100C4⋊Dic5—61no—
101C4⋊Dic5—121no—
102C4⋊Dic5—121no—
103C4×Dic5—31no—
104C4×Dic5—121no—
105C4×Dic5—121no—
106C2×#168—31no—
107C5×C16—32no—
108#672—21no—
109C2×Q32—31no—
110C4×Q16—151no—
111C4×Q16—151no—
112#366—151no—
113#358—51no—
114#358—151no—
115C4×C16—151no—
116C22×C3×C5C2×D811yescharacteristic
117C3×C4×C5—42no—
118C3×C4×C5C4×D411yescharacteristic
119C3×C4×C5#13511yescharacteristic
120Dic15—21no—
121Dic15—81no—
122Dic15Q3212yescomplemented
123C3×Dic5—81no—
124C5×Dic3—42no—
125C2×C3×Q8—21no—
126C2×Dic6—21no—
127C3×Q16—21no—
128C3×Q16C2×Dic512yes—
129C2×C3×C8C22×D511yescharacteristic
130C3×C4⋊C4—101no—
131C4⋊Dic3—101no—
132C4⋊Dic3—201no—
133Dic3⋊C4—201no—
134C4×Dic3—51no—
135C4×Dic3—201no—
136C4×Dic3—201no—
137C2×C3⋊C8—51no—
138Dic12—21no—
139Dic12C2×Dic512yes—
140C3×C16—101no—
141C3⋊C16C2×Dic512yes—
142C5×Q8—22no—
143C5×Q8—41no—
144C5×Q8—62no—
145C5×Q8—121no—
146C2×C4×C5—41no—
147C2×C4×C5—121no—
148C2×C4×C5D3×D411yescharacteristic
149C2×Dic5—31no—
150C2×Dic5—31no—
151C2×Dic5—41no—
152C2×Dic5—121no—
153C5×C8C2×C4×D311yescharacteristic
154C5×C8#23711yescharacteristic
155#168—61no—
156C2×Q16—31no—
157C2×Q16D3×D511yescharacteristic
158C4×Q8—301no—
159C4×Q8—301no—
160Q32—34no—
161C2×C16—31no—
162C2×C16—51no—
163#107—51no—
164#107—151no—
165#103—301no—
166#103—301no—
167C4×C8—151no—
168C2×C3×C5C4×D811yescharacteristic
169C2×C3×C5C2×Q3211yescharacteristic
170C2×C3×C5#50811yescharacteristic
171C3×Q8—22no—
172C3×Q8—41no—
173C2×C3×C4—41no—
174C2×C3×C4—201no—
175C2×C3×C4D4×D511yescharacteristic
176C2×Dic3—41no—
177C2×Dic3—51no—
178C2×Dic3—51no—
179C2×Dic3—201no—
180Dic6—22no—
181Dic6—41no—
182C3×C8#71111yescharacteristic
183C3×C8C22×Dic511yescharacteristic
184C3⋊C8—101no—
185C22×C5D3×D811yescharacteristic
186C4×C5—42no—
187C4×C5—122no—
188C4×C5#67⋊C411yescharacteristic
189C4×C5#91611yescharacteristic
190Dic5—32no—
191Dic5—61no—
192Dic5—81no—
193Dic5—241no—
194C2×Q8—21no—
195C2×Q8—61no—
196Q16—21no—
197Q16—32no—
198Q16—61no—
199Q16D3×Dic512yes—
200C2×C8—151no—
201C2×C8C2×D3×D511yescharacteristic
202C4⋊C4—101no—
203C4⋊C4—301no—
204C4⋊C4—601no—
205C4⋊C4—601no—
206C42—151no—
207C42—601no—
208C42—601no—
209C16—32no—
210C16—101no—
211C3×C5C4×Q3211yescharacteristic, complemented, Hall
212C22×C3D5×D811yescharacteristic
213C3×C4—42no—
214C3×C4—401no—
215C3×C4#405811yescharacteristic
216C3×C4D4×Dic511yescharacteristic
217Dic3—42no—
218Dic3—52no—
219Dic3—101no—
220Dic3—401no—
221C2×C5#475611yescharacteristic
222C2×C5#491611yescharacteristic
223C2×C5D3×Q3211yescharacteristic
224Q8—22no—
225Q8—41no—
226Q8—62no—
227Q8—121no—
228C2×C4—41no—
229C2×C4—121no—
230C2×C4—151no—
231C2×C4—151no—
232C2×C4—201no—
233C2×C4—601no—
234C2×C4#679011yescharacteristic
235C8—301no—
236C8#678011yescharacteristic
237C8C2×D3×Dic511yescharacteristic
238C2×C3D5×Q3211yescharacteristic
239C2×C3#6520811yescharacteristic
240C2×C3D8×Dic511yescharacteristic
241C5#6920711yescharacteristic, complemented, Sylow
242C22#9148111yescharacteristic
243C4—42no—
244C4—122no—
245C4—152no—
246C4—301no—
247C4—401no—
248C4—1201no—
249C4#9149911yescharacteristic
250C4#67⋊Dic511yescharacteristic
251C3Dic5×Q3211yescharacteristic, complemented, Sylow
252C2#1174829811yescharacteristic
253C2#1174830811yescharacteristic
254C2#1174899411yescharacteristic
subgroupG/H
centerC22#91481
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socle, prime radicalC22×C3×C5C2×D8
cosocleC2×C3×C5×C8C23
hypercenterC2×Q16D3×D5
hypocenterC3×C5C4×Q32
LCSG ▷ 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
16. C5×#829C4semidirect
87. #829Dic5semidirect
122. Dic15Q32semidirect
211. C3×C5C4×Q32semidirect
241. C5#69207semidirect
251. C3Dic5×Q32semidirect

Maximal subgroups

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

subgroupindex
Q16×Dic152
C2×C5×#8292
#117478862
C3×#647842
#117459412
#117459002
#117458722
Dic5×Q323
#692075