Finite Group Databasebeta

← #14318512

Subgroups — #14318512

Order 1920.

264 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 76 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#11747942C211yesmaximal, characteristic
2#11747672C211yesmaximal, characteristic
3#11746325C211yesmaximal, characteristic, complemented
4C5×#4503C211yesmaximal, characteristic, complemented
5C3×#64727C211yesmaximal, characteristic
6#11745942C211yesmaximal, characteristic, complemented
7#11745900C211yesmaximal, characteristic, complemented
8#10600007—31nomaximal, Hall
9C2×C5×Dic12C2211yescharacteristic
10C2×C3×C8×D5C2211yescharacteristic
11#91359—21no—
12#91358—21no—
13C2×C3×C5×C16C2211yescharacteristic
14#91102C2211yescharacteristic
15#91102C2211yescharacteristic
16C5×#818C2211yescharacteristic
17C2×C3×#672C2211yescharacteristic
18#90985—21no—
19#90973—21no—
20#69100—51nomaximal, Hall
21#65477—31no—
22#65169—31no—
23C5×#358—31no—
24#64784—31no—
25#64727D311yescharacteristic
26#64724—31no—
27#64710—31no—
28C2×C5×Dic6—21no—
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×C5×C8C2311yescharacteristic
31C4⋊Dic15—21no—
32C4⋊Dic15—21no—
33C5×C4⋊Dic3—21no—
34C5×Dic12—21no—
35C5×Dic12—21no—
36C2×C3×#168D411yescharacteristic
37C3×C8×D5—21no—
38C3×C8×D5—21no—
39#6669—41no—
40#6665—41no—
41#6665—41no—
42Dic3×Dic5—41no—
43C3×C5×C16—21no—
44C3×#672—21no—
45#5116—51no—
46#5106—51no—
47C3×C22⋊C16—51no—
48#4505—51no—
49#4504—51no—
50#4503—51no—
51#4503D511yescharacteristic, complemented
52C2×C5×Q16—31no—
53#4092—61no—
54C2×C8×D5C2×D311yescharacteristic
55#4038—61no—
56C2×C5×C16C2×D311yescharacteristic
57C5×#107—31no—
58#3967—61no—
59#3950—31no—
60#3950—31no—
61C2×#672C2×D311yescharacteristic
62#3940—61no—
63#2237—151noSylow
64C22×C3×D5D811yescharacteristic
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×Dic15—41no—
67C2×Dic15—41no—
68C2×C5×Dic3—41no—
69C2×C5×Dic3—41no—
70C5×Dic6—41no—
71C5×Dic6—41no—
72C2×C3×Dic5D811yescharacteristic
73C3×C4×D5—21no—
74C3×C4×D5—21no—
75C3×C5×C8#4111yescharacteristic
76C3×C5×C8#4111yescharacteristic
77C3×#168—21no—
78C22×C3×C8—51no—
79#926—101no—
80#924—101no—
81C2×Dic12C2×D511yescharacteristic
82C2×C3×C16—51no—
83C2×C3×C16C2×D511yescharacteristic
84#818—51no—
85#818—51no—
86#818C2×D511yescharacteristic
87#817—101no—
88#816—101no—
89C2×C5×Q8—61no—
90C2×C4×D5D1211yescharacteristic
91C5×Q16—61no—
92C5×Q16—61no—
93C2×C5×C8C22×D311yescharacteristic
94C5×C4⋊C4—61no—
95#685—121no—
96#685—121no—
97C4⋊Dic5—61no—
98C4⋊Dic5—61no—
99#683—121no—
100C4×Dic5—121no—
101C2×#168D1211yescharacteristic
102C8×D5—21no—
103C8×D5—21no—
104C5×C16—21no—
105#672—21no—
106#467—151no—
107#427—151no—
108#367—151no—
109#366—151no—
110#358—31no—
111#358—151no—
112C22⋊C16—51no—
113C22×C3×C5C2×D811yescharacteristic
114C2×C3×D5—21no—
115C2×C3×D5—21no—
116C2×C3×D5—21no—
117C3×C4×C5#12311yescharacteristic
118C3×C4×C5#13711yescharacteristic
119Dic15—81no—
120Dic15—81no—
121C3×Dic5—21no—
122C5×Dic3—81no—
123C5×Dic3—81no—
124C22×C3×C4—51no—
125C2×Dic6—21no—
126C2×C3×C8—51no—
127C2×C3×C8—101no—
128C2×C3×C8—101no—
129C2×C3×C8C22×D511yescharacteristic
130#217—201no—
131#217—201no—
132C4⋊Dic3—21no—
133C4⋊Dic3—101no—
134C4⋊Dic3—101no—
135Dic3⋊C4—201no—
136C4×Dic3—201no—
137Dic12—21no—
138Dic12—21no—
139C3×C16—21no—
140C3×C16—101no—
141C22×D5D2411yescharacteristic
142C5×Q8—121no—
143C5×Q8—121no—
144C2×C4×C5—121no—
145C2×C4×C5—121no—
146C2×C4×C5C2×D1211yescharacteristic
147C2×Dic5—121no—
148C2×Dic5—121no—
149C2×Dic5D2411yescharacteristic
150C4×D5—21no—
151C4×D5—21no—
152C5×C8#23711yescharacteristic
153C5×C8#23711yescharacteristic
154#168—21no—
155C2×Q16—31no—
156C22×C8—51no—
157C22⋊Q8—301no—
158#117—301no—
159C2×C16—51no—
160C2×C16D3×D511yescharacteristic
161#107—31no—
162#107—151no—
163#107—151no—
164#106—301no—
165#103—301no—
166C2×C3×C5#48011yescharacteristic
167C2×C3×C5#50811yescharacteristic
168C2×C3×C5#51011yescharacteristic
169C3×D5—41no—
170C23×C3—51no—
171C2×C3×C4—51no—
172C2×C3×C4—101no—
173C2×C3×C4—101no—
174C2×C3×C4D4×D511yescharacteristic
175C2×Dic3—41no—
176C2×Dic3—41no—
177C2×Dic3—201no—
178C2×Dic3—201no—
179Dic6—41no—
180Dic6—41no—
181C3×C8—101no—
182C3×C8#70911yescharacteristic
183C3×C8#71111yescharacteristic
184C22×C5C2×D2411yescharacteristic
185C2×D5—21no—
186C2×D5—21no—
187C2×D5—21no—
188C4×C5—241no—
189C4×C5—241no—
190C4×C5#88611yescharacteristic
191C4×C5#90911yescharacteristic
192Dic5—21no—
193Dic5—241no—
194Dic5—241no—
195C2×Q8—61no—
196C22×C4—51no—
197Q16—61no—
198Q16—61no—
199C2×C8—51no—
200C2×C8—101no—
201C2×C8—101no—
202C2×C8C2×D3×D511yescharacteristic
203C4⋊C4—61no—
204C4⋊C4—301no—
205C4⋊C4—301no—
206C4⋊C4—601no—
207C22⋊C4—601no—
208C22⋊C4—601no—
209C42—601no—
210C16—21no—
211C16—101no—
212C3×C5#223711yescharacteristic, complemented, Hall
213C22×C3—101no—
214C22×C3—101no—
215C22×C3—101no—
216C22×C3D5×D811yescharacteristic
217C3×C4—101no—
218C3×C4#402911yescharacteristic
219C3×C4#406111yescharacteristic
220Dic3—81no—
221Dic3—81no—
222Dic3—401no—
223Dic3—401no—
224C2×C5#473611yescharacteristic
225C2×C5#490411yescharacteristic
226C2×C5#490911yescharacteristic
227D5—41no—
228C23—51no—
229Q8—121no—
230Q8—121no—
231C2×C4—51no—
232C2×C4—101no—
233C2×C4—101no—
234C2×C4—121no—
235C2×C4—121no—
236C2×C4—601no—
237C2×C4—601no—
238C2×C4D5×D1211yescharacteristic
239C8—101no—
240C8#676511yescharacteristic
241C8#678011yescharacteristic
242C2×C3—201no—
243C2×C3#6506311yescharacteristic
244C2×C3#6520411yescharacteristic
245C2×C3#6520811yescharacteristic
246C5#6910011yescharacteristic, complemented, Sylow
247C22—101no—
248C22—101no—
249C22—101no—
250C22D5×D2411yescharacteristic
251C4—101no—
252C4—241no—
253C4—241no—
254C4—1201no—
255C4—1201no—
256C4#9126011yescharacteristic
257C4#9141411yescharacteristic
258C3#1060000711yescharacteristic, complemented, Sylow
259C2—201no—
260C2#1174682811yescharacteristic
261C2#1174683411yescharacteristic
262C2#1174761711yescharacteristic
subgroupG/H
centerC22D5×D24
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×C16C22
socleC22×C3×C5C2×D8
prime radicalC22×C3×D5D8
hypercenterC2×C16D3×D5
hypocenterC3×C5#2237
LCSG ▷ C2×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
3. #11746325C2semidirect
4. C5×#4503C2semidirect
6. #11745942C2semidirect
7. #11745900C2semidirect
51. #4503D5semidirect
212. C3×C5#2237semidirect
246. C5#69100semidirect
258. C3#10600007semidirect

Maximal subgroups

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

subgroupindex
#117479422
#117476722
#117463252
C5×#45032
C3×#647272
#117459422
#117459002
#106000073
#691005