Finite Group Databasebeta

← #14318531

Subgroups — #14318531

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#11751260C211yesmaximal, characteristic
2#11748061C211yesmaximal, characteristic, complemented
3C5×#4563C211yesmaximal, characteristic, complemented
4C3×#64783C211yesmaximal, characteristic, complemented
5#11745938C211yesmaximal, characteristic, complemented
6#11745934C211yesmaximal, characteristic, complemented
7#11745884C211yesmaximal, characteristic, complemented
8#10600050—31nomaximal, Hall
9C2×C3×C5×D8C2211yescharacteristic
10#91827—21no—
11C2×#6705C2211yescharacteristic
12#91292—21no—
13#91116—21no—
14#91101C2211yescharacteristic
15C5×#819C2211yescharacteristic
16C5×#812C2211yescharacteristic
17C3×#3951C2211yescharacteristic
18C3×#3944C2211yescharacteristic
19#90992—21no—
20#69257—51nomaximal, Hall
21#65448—31no—
22#65182—31no—
23C5×#361—31no—
24#64783D311yescharacteristic, complemented
25#64734—31no—
26#64733—31no—
27#64714—31no—
28C2×C3×C5×D4—21no—
29C2×#1220—41no—
30C2×C4×D15D411yescharacteristic
31C3×C5×D8—21no—
32C3×C5×D8—21no—
33C2×C3×C5×C8C2311yescharacteristic
34#6719—41no—
35C4⋊Dic15—21no—
36C2×C3⋊#168D411yescharacteristic
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#5159—51no—
46#4893—51no—
47C3×#361—51no—
48#4563D511yescharacteristic, complemented
49#4514—51no—
50#4513—51no—
51#4494—51no—
52C2×C5×D8C2×D311yescharacteristic
53#4084—61no—
54D5×M16—61no—
55C2×#676—31no—
56C5×M32—31no—
57C5×#108—31no—
58#3964—61no—
59#3954—61no—
60#3951C2×D311yescharacteristic
61#3949—31no—
62#3944C2×D311yescharacteristic
63#2238—151noSylow
64C23×C3×C5—41no—
65C22×D15SD1611yescharacteristic
66C3×C5×D4—41no—
67C3×C5×D4—41no—
68C2×C3×C4×C5C2×D411yescharacteristic
69#1220—82no—
70C2×Dic15—41no—
71C2×Dic15SD1611yescharacteristic
72C4×D15—21no—
73C4×D15—21no—
74C3×C5×C8#4111yescharacteristic
75C3×C5×C8#4111yescharacteristic
76C3⋊#168—21no—
77C3×#168—41no—
78C5×C3⋊C8—41no—
79C2×C3×D8C2×D511yescharacteristic
80#938—101no—
81D3×M16—101no—
82C2×ΓL(1,𝔽25)—51no—
83C3×M32—51no—
84C3×#108—51no—
85#832—101no—
86#822—101no—
87#819C2×D511yescharacteristic
88#817—51no—
89#812C2×D511yescharacteristic
90C2×C5×D4—21no—
91C2×C22⋊D5—121no—
92C2×C4×D5—31no—
93C5×D8—21no—
94C5×D8—21no—
95C5×M16—61no—
96C2×C5×C8C22×D311yescharacteristic
97C22⋊Dic5—121no—
98C4⋊Dic5—61no—
99#681—21no—
100C2×#168—31no—
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—151no—
110#365—151no—
111#361—31no—
112#361—51no—
113#349—151no—
114C22×C3×C5—81no—
115C22×C3×C5—81no—
116C22×C3×C5—81no—
117C22×C3×C5C2×SD1611yescharacteristic
118C2×D15—21no—
119C2×D15—41no—
120C3×C4×C5#12311yescharacteristic
121C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
122Dic15—21no—
123Dic15—81no—
124C2×C3×D4—21no—
125C2×#67—201no—
126C2×C4×D3—51no—
127C3×D8—21no—
128C3×D8—21no—
129C3×M16—101no—
130C2×C3×C8C22×D511yescharacteristic
131#217—201no—
132C4⋊Dic3—101no—
133#208—21no—
134C2×C3⋊C8—51no—
135ΓL(1,𝔽25)—101no—
136ΓL(1,𝔽25)—101no—
137ΓL(1,𝔽25)—201no—
138D3×C8—201no—
139C3×C16—101no—
140C3⋊C16—21no—
141C23×C5—41no—
142C22×D5—31no—
143C5×D4—41no—
144C5×D4—41no—
145C2×C4×C5D3×D411yescharacteristic
146C22⋊D5—242no—
147C2×Dic5—31no—
148C2×Dic5—121no—
149C4×D5—61no—
150C4×D5—61no—
151C5×C8—121no—
152C5×C8#23511yescharacteristic
153C5×C8#23711yescharacteristic
154#168—41no—
155#168—61no—
156C2×D8D3×D511yescharacteristic
157C2×M16—151no—
158C2×M16—301no—
159#121—301no—
160M32—31no—
161M32—51no—
162#108—31no—
163#108—51no—
164#108—301no—
165#106—151no—
166#102—301no—
167C2×C3×C5—21no—
168C2×C3×C5—161no—
169C2×C3×C5#48111yescharacteristic
170D15—41no—
171C23×C3—41no—
172C22×D3—51no—
173C3×D4—41no—
174C3×D4—41no—
175C2×C3×C4D4×D511yescharacteristic
176#67—402no—
177C2×Dic3—51no—
178C2×Dic3—201no—
179C4×D3—101no—
180C4×D3—101no—
181C3×C8—201no—
182C3×C8#70911yescharacteristic
183C3×C8#71111yescharacteristic
184C3⋊C8—41no—
185C3⋊C8—101no—
186C22×C5—81no—
187C22×C5—81no—
188C22×C5—81no—
189C22×C5D3×SD1611yescharacteristic
190C2×D5—61no—
191C2×D5—121no—
192C4×C5#88311yescharacteristic
193C4×C5#91111yescharacteristic
194Dic5—61no—
195Dic5—241no—
196C2×D4—21no—
197C2×D4—601no—
198C22×C4—151no—
199D8—21no—
200D8—21no—
201M16—61no—
202M16—101no—
203M16—301no—
204M16—301no—
205M16—601no—
206C2×C8—151no—
207C2×C8—601no—
208C2×C8C2×D3×D511yescharacteristic
209C4⋊C4—301no—
210C22⋊C4—601no—
211C16—61no—
212C16—101no—
213C3×C5#223811yescharacteristic, complemented, Hall
214C22×C3—81no—
215C22×C3—81no—
216C22×C3—81no—
217C22×C3D5×SD1611yescharacteristic
218C2×D3—101no—
219C2×D3—201no—
220C3×C4#402911yescharacteristic
221C3×C4#405711yescharacteristic
222Dic3—101no—
223Dic3—401no—
224C2×C5—21no—
225C2×C5—161no—
226C2×C5#477711yescharacteristic
227D5—121no—
228C23—41no—
229C23—151no—
230D4—41no—
231D4—41no—
232D4—1202no—
233C2×C4—151no—
234C2×C4—301no—
235C2×C4—301no—
236C2×C4—601no—
237C2×C4#679011yescharacteristic
238C8—121no—
239C8—201no—
240C8—301no—
241C8#677911yescharacteristic
242C8#678211yescharacteristic
243C2×C3—21no—
244C2×C3—161no—
245C2×C3#6506611yescharacteristic
246D3—201no—
247C5#6925711yescharacteristic, complemented, Sylow
248C22—81no—
249C22—81no—
250C22—81no—
251C22—301no—
252C22—601no—
253C22#9148711yescharacteristic
254C4—301no—
255C4—1201no—
256C4#9148211yescharacteristic
257C4#9156211yescharacteristic
258C3#1060005011yescharacteristic, complemented, Sylow
259C2—21no—
260C2—161no—
261C2—601no—
262C2#1174896011yescharacteristic
subgroupG/H
centerC2#11748960
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×D8C22
socleC2×C3×C5#481
prime radical#11751260C2
hypercenterC2×D8D3×D5
hypocenterC3×C5#2238
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #11748061C2semidirect
3. C5×#4563C2semidirect
4. C3×#64783C2semidirect
5. #11745938C2semidirect
6. #11745934C2semidirect
7. #11745884C2semidirect
24. #64783D3semidirect
48. #4563D5semidirect
213. C3×C5#2238semidirect
247. C5#69257semidirect
258. C3#10600050semidirect

Maximal subgroups

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

subgroupindex
#117512602
#117480612
C5×#45632
C3×#647832
#117459382
#117459342
#117458842
#106000503
#692575