Finite Group Databasebeta

← #14318546

Subgroups — #14318546

Order 1920.

268 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 64 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#11750966C211yesmaximal, characteristic
2#11748061C211yesmaximal, characteristic, complemented
3C5×#4487C211yesmaximal, characteristic, complemented
4C3×#64707C211yesmaximal, characteristic, complemented
5#11745920C211yesmaximal, characteristic, complemented
6#11745919C211yesmaximal, characteristic, complemented
7#11745884C211yesmaximal, characteristic, complemented
8#10600106—31nomaximal, Hall
9C2×D120C2211yescharacteristic
10C2×#6705C2211yescharacteristic
11#91784—21no—
12#91292—21no—
13C3×C5×#106C2211yescharacteristic
14#91093—21no—
15C5×#819C2211yescharacteristic
16C5×#812C2211yescharacteristic
17C3×#3951C2211yescharacteristic
18C3×#3944C2211yescharacteristic
19#90992—21no—
20#69313—51nomaximal, Hall
21#65182—31no—
22#65154—31no—
23C5×#365—31no—
24#64736—31no—
25#64734—31no—
26#64715—31no—
27#64707D311yescharacteristic, complemented
28C2×D60—21no—
29C2×D60—41no—
30C2×C4×D15D411yescharacteristic
31C2×C3×C5×C8C2311yescharacteristic
32C3×C5×C4⋊C4—21no—
33#6714—41no—
34C2×C3⋊#168D411yescharacteristic
35D120—21no—
36D120—21no—
37#6705—21no—
38#6705—21no—
39C5×#208—21no—
40C3×#681—21no—
41#6651—41no—
42#6648—41no—
43C3×#672—21no—
44C5×C3⋊C16—21no—
45#4893—51no—
46#4865—51no—
47C3×#365—51no—
48#4516—51no—
49#4514—51no—
50#4495—51no—
51#4487D511yescharacteristic, complemented
52D5×M16—61no—
53C2×D40—31no—
54C2×#676—31no—
55#4041—61no—
56C5×M32—31no—
57C5×#108—31no—
58C5×#106C2×D311yescharacteristic
59#3954—61no—
60#3951C2×D311yescharacteristic
61#3944C2×D311yescharacteristic
62#3941—61no—
63#2238—151noSylow
64C22×D15—41no—
65C22×D15SD1611yescharacteristic
66C2×C3×C4×C5—41no—
67C2×C3×C4×C5C2×D411yescharacteristic
68C2×Dic15SD1611yescharacteristic
69D60—41no—
70D60—41no—
71D60—82no—
72C4×D15—21no—
73C4×D15—21no—
74C3×C5×C8#4111yescharacteristic
75C3×C5×C8#4111yescharacteristic
76C3⋊#168—21no—
77C3×#168—41no—
78C5×C3⋊C8—41no—
79D3×M16—101no—
80C2×D24—51no—
81C2×ΓL(1,𝔽25)—51no—
82#895—101no—
83C3×M32—51no—
84C3×#108—51no—
85C3×#106C2×D511yescharacteristic
86#822—101no—
87#819C2×D511yescharacteristic
88#812C2×D511yescharacteristic
89#809—101no—
90C2×D20—61no—
91C2×D20—121no—
92C2×C4×D5—31no—
93C5×M16—61no—
94C2×C5×C8C22×D311yescharacteristic
95C5×C4⋊C4—21no—
96#685—121no—
97#681—21no—
98C2×#168—31no—
99D40—61no—
100D40—61no—
101#676—61no—
102#676—61no—
103#676—121no—
104C8×D5—121no—
105C5×C16—61no—
106#672—21no—
107#469—151no—
108#430—151no—
109#365—31no—
110#365—51no—
111#361—151no—
112#361—151no—
113#349—151no—
114C22×C3×C5C2×SD1611yescharacteristic
115C2×D15—21no—
116C2×D15—41no—
117C2×D15—81no—
118C2×D15—81no—
119C2×D15—81no—
120C3×C4×C5—81no—
121C3×C4×C5#12311yescharacteristic
122C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
123Dic15—21no—
124C2×D12—101no—
125C2×D12—201no—
126C2×C4×D3—51no—
127C3×M16—101no—
128C2×C3×C8C22×D511yescharacteristic
129C3×C4⋊C4—21no—
130(C2×D3)⋊C4—201no—
131#208—21no—
132C2×C3⋊C8—51no—
133D24—101no—
134D24—101no—
135ΓL(1,𝔽25)—101no—
136ΓL(1,𝔽25)—101no—
137ΓL(1,𝔽25)—201no—
138D3×C8—201no—
139C3×C16—101no—
140C3⋊C16—21no—
141C22×D5—31no—
142C22×D5—121no—
143C2×C4×C5—41no—
144C2×C4×C5D3×D411yescharacteristic
145C2×Dic5—31no—
146D20—121no—
147D20—121no—
148D20—242no—
149C4×D5—61no—
150C4×D5—61no—
151C5×C8—121no—
152C5×C8#23511yescharacteristic
153C5×C8#23911yescharacteristic
154#168—41no—
155#168—61no—
156C2×D8—151no—
157C2×M16—151no—
158C2×M16—301no—
159#121—301no—
160M32—31no—
161M32—51no—
162#108—31no—
163#108—51no—
164#108—301no—
165#106D3×D511yescharacteristic
166#102—301no—
167C2×C3×C5—21no—
168C2×C3×C5#48111yescharacteristic
169D15—41no—
170D15—161no—
171C22×D3—51no—
172C22×D3—201no—
173C2×C3×C4—41no—
174C2×C3×C4D4×D511yescharacteristic
175C2×Dic3—51no—
176D12—201no—
177D12—201no—
178D12—402no—
179C4×D3—101no—
180C4×D3—101no—
181C3×C8—201no—
182C3×C8#70911yescharacteristic
183C3×C8#71311yescharacteristic
184C3⋊C8—41no—
185C3⋊C8—101no—
186C22×C5D3×SD1611yescharacteristic
187C2×D5—61no—
188C2×D5—121no—
189C2×D5—241no—
190C2×D5—241no—
191C2×D5—241no—
192C4×C5—81no—
193C4×C5#89411yescharacteristic
194C4×C5#91411yescharacteristic
195Dic5—61no—
196C2×D4—301no—
197C2×D4—601no—
198C22×C4—151no—
199D8—301no—
200D8—301no—
201M16—61no—
202M16—101no—
203M16—301no—
204M16—301no—
205M16—601no—
206C2×C8—151no—
207C2×C8—601no—
208C2×C8C2×D3×D511yescharacteristic
209C4⋊C4—21no—
210C22⋊C4—601no—
211C16—61no—
212C16—101no—
213C3×C5#223811yescharacteristic, complemented, Hall
214C22×C3D5×SD1611yescharacteristic
215C2×D3—101no—
216C2×D3—201no—
217C2×D3—401no—
218C2×D3—401no—
219C2×D3—401no—
220C3×C4—81no—
221C3×C4#404011yescharacteristic
222C3×C4#406011yescharacteristic
223Dic3—101no—
224C2×C5—21no—
225C2×C5#486311yescharacteristic
226D5—121no—
227D5—481no—
228C23—151no—
229C23—601no—
230D4—601no—
231D4—601no—
232D4—1202no—
233C2×C4—41no—
234C2×C4—151no—
235C2×C4—301no—
236C2×C4—301no—
237C2×C4#679011yescharacteristic
238C8—121no—
239C8—201no—
240C8—301no—
241C8#676911yescharacteristic
242C8#677311yescharacteristic
243C2×C3—21no—
244C2×C3#6515211yescharacteristic
245D3—201no—
246D3—801no—
247C5#6931311yescharacteristic, complemented, Sylow
248C22—301no—
249C22—601no—
250C22—1201no—
251C22—1201no—
252C22—1201no—
253C22#9148711yescharacteristic
254C4—81no—
255C4—301no—
256C4#9143311yescharacteristic
257C4#9150611yescharacteristic
258C3#1060010611yescharacteristic, complemented, Sylow
259C2—21no—
260C2—601no—
261C2—2401no—
262C2#1174720311yescharacteristic
subgroupG/H
centerC2#11747203
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#106C22
socleC2×C3×C5#481
prime radical#11750966C2
hypercenter#106D3×D5
hypocenterC3×C5#2238
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #11748061C2semidirect
3. C5×#4487C2semidirect
4. C3×#64707C2semidirect
5. #11745920C2semidirect
6. #11745919C2semidirect
7. #11745884C2semidirect
27. #64707D3semidirect
51. #4487D5semidirect
213. C3×C5#2238semidirect
247. C5#69313semidirect
258. C3#10600106semidirect

Maximal subgroups

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

subgroupindex
#117509662
#117480612
C5×#44872
C3×#647072
#117459202
#117459192
#117458842
#106001063
#693135