Finite Group Databasebeta

← #14318587

Subgroups — #14318587

Order 1920.

248 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 68 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#11748059C211yesmaximal, characteristic
2#11747951C211yesmaximal, characteristic
3#11746338C211yesmaximal, characteristic, complemented
4C5×#4514C211yesmaximal, characteristic
5C3×#64733C211yesmaximal, characteristic, complemented
6#11745937C211yesmaximal, characteristic, complemented
7#11745925C211yesmaximal, characteristic, complemented
8#10599910—31nomaximal, Hall
9C2×Dic60C2211yescharacteristic
10C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
11#91365—21no—
12D3×#681—21no—
13C3×C5×M32C2211yescharacteristic
14#91103C2211yescharacteristic
15C5×#812C2211yescharacteristic
16C3×#3951C2211yescharacteristic
17C3×#3949C2211yescharacteristic
18#90993—21no—
19#90974—21no—
20#69314—51nomaximal, Hall
21#65426—31no—
22#65414—31no—
23C5×#349—31no—
24#64737—31no—
25#64737—31no—
26#64733—31no—
27#64733D311yescharacteristic, complemented
28C2×Dic30—21no—
29C2×C4×C5×D3D411yescharacteristic
30C2×C3×C5×C8C2311yescharacteristic
31#6710—21no—
32Dic60—21no—
33Dic60—21no—
34C2×C5×C3⋊C8D411yescharacteristic
35C5×ΓL(1,𝔽25)—21no—
36C5×ΓL(1,𝔽25)—21no—
37C3×C4⋊Dic5—21no—
38C3×#681—21no—
39#6668—41no—
40(C2×D3)⋊Dic5—41no—
41#6650—41no—
42D3×#168—41no—
43C3×C5×C16—21no—
44C5×C3⋊C16—21no—
45#4893—51no—
46#4867—51no—
47C3×#365—51no—
48#4517—51no—
49#4514D511yescharacteristic
50#4496—51no—
51#4487—51no—
52C2×C5×M16—31no—
53#4070—61no—
54C2×#681—61no—
55C2×Dic20—31no—
56C5×M32—31no—
57C5×M32C2×D311yescharacteristic
58#3951—31no—
59#3951—61no—
60#3951C2×D311yescharacteristic
61#3949C2×D311yescharacteristic
62#3948—61no—
63#2239—151noSylow
64C22×C5×D3SD1611yescharacteristic
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×Dic15—41no—
67Dic30—41no—
68Dic30—41no—
69C2×C5×Dic3SD1611yescharacteristic
70C4×C5×D3—21no—
71C4×C5×D3—21no—
72C2×C3×Dic5—41no—
73C3×C5×C8#4111yescharacteristic
74C3×C5×C8#4111yescharacteristic
75C3⋊#168—41no—
76C3×#168—41no—
77C5×C3⋊C8—21no—
78D3×M16—101no—
79C2×Dic12—51no—
80C2×ΓL(1,𝔽25)C2×D511yescharacteristic
81#897—101no—
82C3×M32C2×D511yescharacteristic
83C3×#108—51no—
84C3×#106—51no—
85#822—101no—
86#819—51no—
87#812C2×D511yescharacteristic
88#810—101no—
89C22×C4×C5—31no—
90C2×Dic10—61no—
91C5×M16—61no—
92C5×M16—61no—
93C2×C5×C8—31no—
94C2×C5×C8C22×D311yescharacteristic
95C22⋊Dic5—121no—
96C4⋊Dic5—21no—
97#683—121no—
98#681—21no—
99#681—61no—
100#681—121no—
101C2×#168—121no—
102Dic20—61no—
103Dic20—61no—
104C5×C16—21no—
105C5×C16—61no—
106#470—151no—
107#430—151no—
108#365—51no—
109#365—151no—
110#362—151no—
111#362—151no—
112#349—31no—
113C22×C3×C5C2×SD1611yescharacteristic
114C2×C5×D3—21no—
115C2×C5×D3—41no—
116C3×C4×C5#12311yescharacteristic
117C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
118Dic15—81no—
119C3×Dic5—81no—
120C5×Dic3—21no—
121C2×C4×D3D2011yescharacteristic
122C2×Dic6—101no—
123C3×M16—101no—
124C2×C3×C8C22×D511yescharacteristic
125C3×C4⋊C4—101no—
126(C2×D3)⋊C4—201no—
127C4⋊Dic3—201no—
128#208—101no—
129C2×C3⋊C8D2011yescharacteristic
130Dic12—101no—
131Dic12—101no—
132ΓL(1,𝔽25)—21no—
133ΓL(1,𝔽25)—21no—
134ΓL(1,𝔽25)—201no—
135D3×C8—201no—
136C3×C16—21no—
137C3⋊C16—21no—
138C23×C5—31no—
139C2×C4×C5—31no—
140C2×C4×C5—61no—
141C2×C4×C5—61no—
142C2×C4×C5D3×D411yescharacteristic
143C2×Dic5—41no—
144C2×Dic5—121no—
145Dic10—121no—
146Dic10—121no—
147C5×C8—61no—
148C5×C8#23511yescharacteristic
149C5×C8#23911yescharacteristic
150#168—41no—
151#168—121no—
152C2×Q16—151no—
153C2×M16—31no—
154C2×M16—301no—
155C22⋊Q8—301no—
156M32—31no—
157M32D3×D511yescharacteristic
158#108—51no—
159#108—151no—
160#108—301no—
161#106—51no—
162#103—301no—
163C2×C3×C5—21no—
164C2×C3×C5#48111yescharacteristic
165C5×D3—41no—
166C22×D3#67711yescharacteristic
167C2×C3×C4—201no—
168C2×C3×C4C2×D2011yescharacteristic
169C2×Dic3—201no—
170C2×Dic3#67711yescharacteristic
171C4×D3—21no—
172C4×D3—21no—
173Dic6—201no—
174Dic6—201no—
175C3×C8—201no—
176C3×C8#71111yescharacteristic
177C3×C8#71111yescharacteristic
178C3⋊C8—21no—
179C3⋊C8—201no—
180C22×C5—61no—
181C22×C5—121no—
182C22×C5D3×SD1611yescharacteristic
183C4×C5—61no—
184C4×C5#89411yescharacteristic
185C4×C5#91411yescharacteristic
186Dic5—81no—
187Dic5—241no—
188C2×Q8—301no—
189C22×C4—31no—
190Q16—301no—
191Q16—301no—
192M16—61no—
193M16—61no—
194M16—101no—
195M16—301no—
196M16—601no—
197C2×C8—31no—
198C2×C8—601no—
199C2×C8C2×D3×D511yescharacteristic
200C4⋊C4—101no—
201C4⋊C4—601no—
202C22⋊C4—601no—
203C16—21no—
204C16—61no—
205C3×C5#223911yescharacteristic, complemented, Hall
206C22×C3C2×#67711yescharacteristic
207C2×D3—21no—
208C2×D3—41no—
209C3×C4—401no—
210C3×C4#403211yescharacteristic
211C3×C4#405411yescharacteristic
212Dic3—21no—
213Dic3—401no—
214C2×C5—21no—
215C2×C5—121no—
216C2×C5#486311yescharacteristic
217C23—31no—
218Q8—601no—
219Q8—601no—
220C2×C4—31no—
221C2×C4—61no—
222C2×C4—61no—
223C2×C4—201no—
224C2×C4—601no—
225C2×C4D3×D2011yescharacteristic
226C8—61no—
227C8—201no—
228C8—601no—
229C8#676811yescharacteristic
230C8#678211yescharacteristic
231C2×C3—21no—
232C2×C3#6502411yescharacteristic
233D3—41no—
234C5#6931411yescharacteristic, complemented, Sylow
235C22—61no—
236C22—121no—
237C22D3×#67711yescharacteristic
238C4—61no—
239C4—401no—
240C4—1201no—
241C4#9125311yescharacteristic
242C4#9142711yescharacteristic
243C3#1059991011yescharacteristic, complemented, Sylow
244C2—21no—
245C2—121no—
246C2#1174762511yescharacteristic
subgroupG/H
centerC2#11747625
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×M32C22
socleC2×C3×C5#481
prime radicalC22×C5×D3SD16
hypercenterM32D3×D5
hypocenterC3×C5#2239
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
3. #11746338C2semidirect
5. C3×#64733C2semidirect
6. #11745937C2semidirect
7. #11745925C2semidirect
27. #64733D3semidirect
205. C3×C5#2239semidirect
234. C5#69314semidirect
243. C3#10599910semidirect

Maximal subgroups

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

subgroupindex
#117480592
#117479512
#117463382
C5×#45142
C3×#647332
#117459372
#117459252
#105999103
#693145