Finite Group Databasebeta

← #14315448

Subgroups — #14315448

Order 1920.

300 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 94 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#11747873C211yesmaximal, characteristic
2Dic3×Dic20C211yesmaximal, characteristic
3C2×#90947C211yesmaximal, characteristic
4#11746324C211yesmaximal, characteristic
5C5×Dic3×C16C211yesmaximal, characteristic
6C3×#64723C211yesmaximal, characteristic
7#11745941C211yesmaximal, characteristic
8C4×Dic40—31nomaximal, Hall
9C2×Dic60C2211yescharacteristic
10C2×C3×Dic20C2211yescharacteristic
11#91340—21no—
12Dic3×Dic10—21no—
13C2×C3×C5×C16C2211yescharacteristic
14#91102C2211yescharacteristic
15C5×C8×Dic3C2211yescharacteristic
16C2×C5×C3⋊C16C2211yescharacteristic
17C3×#3950C2211yescharacteristic
18#90974—21no—
19#90971—21no—
20#90947C414yescomplemented
21#69207—51nomaximal, Hall
22C2×Dic40—31no—
23C4×Dic20—31no—
24C4×Dic20—31no—
25C4×C5×C16—31no—
26#64724—31no—
27#64723—31no—
28#64723D311yescharacteristic
29C2×Dic30—21no—
30C2×C3×Dic10—21no—
31C2×C3×C5×C8C2311yescharacteristic
32C4⋊Dic15—21no—
33Dic60—21no—
34Dic60C2×C412yes—
35C4×C5×Dic3D411yescharacteristic
36C2×C5×C3⋊C8D411yescharacteristic
37C3×C4⋊Dic5—21no—
38C3×Dic20—21no—
39C3×Dic20C2×C412yes—
40#6669—41no—
41#6668—41no—
42Dic3×Dic5—41no—
43Dic3×Dic5—41no—
44C3×C5×C16—21no—
45C5×C3⋊C16C2×C412yes—
46Dic3×Q16—51no—
47C2×#829—51no—
48#4873—51no—
49C3×#358—51no—
50#4503—51no—
51Dic3×C16D511yescharacteristic
52#4489—51no—
53C2×Dic20—31no—
54C2×Dic20C2×D311yescharacteristic
55C4×Dic10—61no—
56C4×Dic10—61no—
57C2×C5×C16—31no—
58C2×C5×C16C2×D311yescharacteristic
59C4×C5×C8—31no—
60#3950—31no—
61#3950C2×D311yescharacteristic
62#3948—61no—
63#3948—61no—
64Dic40—34no—
65C4×Q32—151noSylow
66C2×C3×C4×C5C2×D411yescharacteristic
67C2×Dic15—41no—
68C2×Dic15—41no—
69Dic30—22no—
70Dic30—41no—
71C2×C5×Dic3D811yescharacteristic
72C2×C5×Dic3D811yescharacteristic
73C2×C3×Dic5—41no—
74C2×C3×Dic5—41no—
75C3×Dic10—22no—
76C3×Dic10—41no—
77C3×C5×C8C22×C411yescharacteristic
78C3×C5×C8#4111yescharacteristic
79C5×C3⋊C8—21no—
80C2×C3×Q16—51no—
81Q8×Dic3—101no—
82C2×Dic12—51no—
83#887—101no—
84C2×C3×C16C2×D511yescharacteristic
85C3×#107—51no—
86#835—101no—
87#829—54no—
88#818—51no—
89C8×Dic3C2×D511yescharacteristic
90C2×C3⋊C16C2×D511yescharacteristic
91#810—101no—
92C2×Dic10—21no—
93C2×Dic10—61no—
94C2×C5×C8—31no—
95C2×C5×C8C22×D311yescharacteristic
96C42×C5—31no—
97C4⋊Dic5—21no—
98C4⋊Dic5—61no—
99#683—121no—
100#683—121no—
101C4×Dic5—121no—
102C4×Dic5—121no—
103Dic20—21no—
104Dic20—32no—
105Dic20—61no—
106Dic20C4×D312yes—
107C5×C16—21no—
108C5×C16—32no—
109C2×Q32—151no—
110C4×Q16—151no—
111C4×Q16—151no—
112#366—151no—
113#358—51no—
114#358—151no—
115C4×C16—31no—
116C22×C3×C5C2×D811yescharacteristic
117C3×C4×C5C4×D411yescharacteristic
118C3×C4×C5#13511yescharacteristic
119Dic15—42no—
120Dic15—81no—
121C3×Dic5—42no—
122C3×Dic5—81no—
123C5×Dic3—21no—
124C5×Dic3Q3212yescomplemented
125C2×C3×Q8—101no—
126C2×Dic6—101no—
127C3×Q16—52no—
128C3×Q16—101no—
129C2×C3×C8C22×D511yescharacteristic
130C3×C4⋊C4—101no—
131C4⋊Dic3—101no—
132C4⋊Dic3—201no—
133Dic3⋊C4—201no—
134C4×Dic3—201no—
135C4×Dic3—201no—
136C4×Dic3D2011yescharacteristic
137C2×C3⋊C8D2011yescharacteristic
138Dic12—52no—
139Dic12—101no—
140C3×C16—21no—
141C3⋊C16C4×D512yes—
142C2×C4×C5—31no—
143C2×C4×C5—31no—
144C2×C4×C5D3×D411yescharacteristic
145C2×Dic5—41no—
146C2×Dic5—41no—
147C2×Dic5—121no—
148C2×Dic5—121no—
149Dic10—22no—
150Dic10—41no—
151Dic10—62no—
152Dic10—121no—
153C5×C8—61no—
154C5×C8C2×C4×D311yescharacteristic
155C5×C8#23711yescharacteristic
156C2×Q16—51no—
157C2×Q16—151no—
158C4×Q8—301no—
159C4×Q8—301no—
160Q32—154no—
161C2×C16—31no—
162C2×C16D3×D511yescharacteristic
163#107—51no—
164#107—151no—
165#103—301no—
166#103—301no—
167C4×C8—31no—
168C2×C3×C5C4×D811yescharacteristic
169C2×C3×C5C2×Q3211yescharacteristic
170C2×C3×C5#50811yescharacteristic
171C3×Q8—102no—
172C3×Q8—201no—
173C2×C3×C4—201no—
174C2×C3×C4—201no—
175C2×C3×C4C2×D2011yescharacteristic
176C2×Dic3—201no—
177C2×Dic3—201no—
178C2×Dic3D4011yescharacteristic
179C2×Dic3D4011yescharacteristic
180Dic6—102no—
181Dic6—201no—
182C3×C8C2×C4×D511yescharacteristic
183C3×C8#70911yescharacteristic
184C3⋊C8—21no—
185C22×C5D3×D811yescharacteristic
186C4×C5—32no—
187C4×C5—61no—
188C4×C5#67⋊C411yescharacteristic
189C4×C5#91611yescharacteristic
190Dic5—42no—
191Dic5—81no—
192Dic5—122no—
193Dic5—241no—
194C2×Q8—101no—
195C2×Q8—301no—
196Q16—52no—
197Q16—101no—
198Q16—152no—
199Q16—301no—
200C2×C8—31no—
201C2×C8C2×D3×D511yescharacteristic
202C4⋊C4—101no—
203C4⋊C4—301no—
204C4⋊C4—601no—
205C4⋊C4—601no—
206C42—31no—
207C42—601no—
208C42—601no—
209C16—21no—
210C16—32no—
211C3×C5C4×Q3211yescharacteristic, complemented, Hall
212C22×C3C2×D4011yescharacteristic
213C3×C4—202no—
214C3×C4—401no—
215C3×C4C4×D2011yescharacteristic
216C3×C4#405011yescharacteristic
217Dic3—21no—
218Dic3—202no—
219Dic3—401no—
220Dic3Dic4012yescomplemented
221C2×C5#475611yescharacteristic
222C2×C5#491611yescharacteristic
223C2×C5D3×Q3211yescharacteristic
224Q8—102no—
225Q8—201no—
226Q8—302no—
227Q8—601no—
228C2×C4—31no—
229C2×C4—31no—
230C2×C4—201no—
231C2×C4—201no—
232C2×C4—601no—
233C2×C4—601no—
234C2×C4D3×D2011yescharacteristic
235C8—61no—
236C8C4×D3×D511yescharacteristic
237C8#677911yescharacteristic
238C2×C3C4×D4011yescharacteristic
239C2×C3#6519311yescharacteristic
240C2×C3C2×Dic4011yescharacteristic
241C5#6920711yescharacteristic, complemented, Sylow
242C22D3×D4011yescharacteristic
243C4—32no—
244C4—61no—
245C4—202no—
246C4—401no—
247C4—602no—
248C4—1201no—
249C4#9127211yescharacteristic
250C4#9139511yescharacteristic
251C3C4×Dic4011yescharacteristic, complemented, Sylow
252C2D3×Dic4011yescharacteristic
253C2#1174683611yescharacteristic
254C2#1174774011yescharacteristic
subgroupG/H
centerC22D3×D40
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×C16C22
socle, prime radicalC22×C3×C5C2×D8
cosocleC2×C3×C5×C8C23
hypercenterC2×C16D3×D5
hypocenterC3×C5C4×Q32
LCSG ▷ 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
20. #90947C4semidirect
124. C5×Dic3Q32semidirect
211. C3×C5C4×Q32semidirect
220. Dic3Dic40semidirect
241. C5#69207semidirect
251. C3C4×Dic40semidirect

Maximal subgroups

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

subgroupindex
#117478732
Dic3×Dic202
C2×#909472
#117463242
C5×Dic3×C162
C3×#647232
#117459412
C4×Dic403
#692075