Finite Group Databasebeta

← #14318185

Subgroups — #14318185

Order 1920.

252 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 70 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#11748068C211yesmaximal, characteristic
2#11748027C211yesmaximal, characteristic, complemented
3#11746339C211yesmaximal, characteristic
4C5×#4511C211yesmaximal, characteristic, complemented
5C3×#64733C211yesmaximal, characteristic, complemented
6#11745938C211yesmaximal, characteristic, complemented
7#11745913C211yesmaximal, characteristic
8#10600100—31nomaximal, Hall
9#91793C2211yescharacteristic
10#91469—21no—
11#91291—21no—
12C3×C5×M32C2211yescharacteristic
13#91101C2211yescharacteristic
14C5×C8×Dic3C2211yescharacteristic
15C5×#812C2211yescharacteristic
16C3×#3951C2211yescharacteristic
17C3×#3949C2211yescharacteristic
18#90987—21no—
19#90980—21no—
20#69315—51nomaximal, Hall
21#64989—31no—
22#64969—31no—
23C5×#364—31no—
24#64738—31no—
25#64738—31no—
26#64733—31no—
27#64733D311yescharacteristic, complemented
28#6817—21no—
29C2×#1204—41no—
30C2×C3×C5×C8C2311yescharacteristic
31C4⋊Dic15—21no—
32Dic60Q811yescharacteristic, complemented
33D120Q811yescharacteristic, complemented
34#6706—21no—
35C4×C5×Dic3D411yescharacteristic
36C2×C5×C3⋊C8D411yescharacteristic
37C3×C4⋊Dic5—21no—
38C3×#681—21no—
39Dic3⋊Dic5—41no—
40#6651—41no—
41#6648—41no—
42C3×C5×C16—21no—
43C5×C3⋊C16—21no—
44#4895—51no—
45#4855—51no—
46C3×#365—51no—
47#4518—51no—
48#4511D511yescharacteristic, complemented
49#4494—51no—
50#4488—51no—
51#4050—31no—
52#4047—61no—
53#4015—61no—
54C5×M32—31no—
55C5×M32C2×D311yescharacteristic
56C4×C5×C8—31no—
57#3951C2×D311yescharacteristic
58#3949—31no—
59#3949—61no—
60#3949C2×D311yescharacteristic
61#3937—61no—
62#2230—151noSylow
63C2×C3×C4×C5C2×D411yescharacteristic
64#1220—41no—
65C2×Dic15—41no—
66D60—21no—
67C4×D15—41no—
68Dic30—21no—
69C2×C5×Dic3—21no—
70C2×C3×Dic5—41no—
71#1204—82no—
72C3×C5×C8C2×Q811yescharacteristic
73C3×C5×C8#4111yescharacteristic
74C3×#168—41no—
75C5×C3⋊C8SD1611yescharacteristic
76C5×C3⋊C8SD1611yescharacteristic
77#907—101no—
78#904—51no—
79#888—101no—
80C3×M32C2×D511yescharacteristic
81C3×#108—51no—
82C3×#106—51no—
83#825—101no—
84#817—51no—
85C8×Dic3C2×D511yescharacteristic
86#812C2×D511yescharacteristic
87#808—101no—
88#709—61no—
89C2×Dic10—121no—
90C2×C5×C8—31no—
91C2×C5×C8C22×D311yescharacteristic
92C42×C5—31no—
93C4⋊Dic5—21no—
94C4⋊Dic5—61no—
95C4⋊Dic5—121no—
96#681—21no—
97Dic20—31no—
98D40—31no—
99#677—61no—
100#676—121no—
101C8×D5—121no—
102C5×C16—21no—
103C5×C16—61no—
104#498—151no—
105#443—151no—
106#365—51no—
107#365—151no—
108#364—31no—
109#360—151no—
110#360—151no—
111C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
112C2×D15—41no—
113C3×C4×C5C22⋊Q811yescharacteristic
114C3×C4×C5C2×SD1611yescharacteristic
115Dic15—41no—
116Dic15—81no—
117C3×Dic5—81no—
118C5×Dic3—22no—
119#235—101no—
120C2×Dic6—201no—
121C3×M16—101no—
122C2×C3×C8C22×D511yescharacteristic
123C3×C4⋊C4—101no—
124C4⋊Dic3—101no—
125Dic3⋊C4—201no—
126C4×Dic3D2011yescharacteristic
127C2×C3⋊C8D2011yescharacteristic
128Dic12—51no—
129D24—51no—
130#204—101no—
131ΓL(1,𝔽25)—201no—
132D3×C8—201no—
133C3×C16—21no—
134C3⋊C16—21no—
135C2×C4×C5—61no—
136C2×C4×C5D3×D411yescharacteristic
137C22⋊D5—121no—
138C2×Dic5—41no—
139C2×Dic5—121no—
140D20—61no—
141C4×D5—121no—
142Dic10—61no—
143Dic10—242no—
144C5×C8—31no—
145C5×C8—31no—
146C5×C8#23511yescharacteristic
147C5×C8D3×Q811yescharacteristic
148#168—41no—
149#135—151no—
150#131—301no—
151C4⋊Q8—301no—
152M32—31no—
153M32D3×D511yescharacteristic
154#108—51no—
155#106—51no—
156#106—151no—
157#106—301no—
158#104—301no—
159C4×C8—31no—
160C2×C3×C5—21no—
161C2×C3×C5#47611yescharacteristic
162D15—81no—
163C2×C3×C4—201no—
164C2×C3×C4C2×D2011yescharacteristic
165#67—201no—
166C2×Dic3—21no—
167C2×Dic3—201no—
168D12—101no—
169C4×D3—201no—
170Dic6—101no—
171Dic6—402no—
172C3×C8—201no—
173C3×C8#71111yescharacteristic
174C3×C8Q8×D511yescharacteristic
175C3⋊C8#67711yescharacteristic
176C3⋊C8#67711yescharacteristic
177C22×C5#91411yescharacteristic
178C2×D5—121no—
179C4×C5—62no—
180C4×C5#89611yescharacteristic
181C4×C5D3×SD1611yescharacteristic
182Dic5—81no—
183Dic5—121no—
184Dic5—241no—
185#41—301no—
186C2×Q8—601no—
187Q16—151no—
188SD16—301no—
189D8—151no—
190M16—101no—
191M16—601no—
192C2×C8—31no—
193C2×C8—601no—
194C2×C8C2×D3×D511yescharacteristic
195C4⋊C4—101no—
196C4⋊C4—301no—
197C4⋊C4—601no—
198C42—31no—
199C16—21no—
200C16—61no—
201C3×C5#223011yescharacteristic, complemented, Hall
202C22×C3#405411yescharacteristic
203C2×D3—201no—
204C3×C4—401no—
205C3×C4#404311yescharacteristic
206C3×C4C2×#67711yescharacteristic
207Dic3—22no—
208Dic3—201no—
209Dic3—401no—
210C2×C5—21no—
211C2×C5#487011yescharacteristic
212D5—241no—
213Q8—301no—
214Q8—1202no—
215D4—301no—
216D4—601no—
217C2×C4—61no—
218C2×C4—201no—
219C2×C4—601no—
220C2×C4—601no—
221C2×C4D3×D2011yescharacteristic
222C8—31no—
223C8—31no—
224C8—201no—
225C8D15⋊Q811yescharacteristic
226C8#678211yescharacteristic
227C2×C3—21no—
228C2×C3#6513111yescharacteristic
229D3—401no—
230C5#6931511yescharacteristic, complemented, Sylow
231C22—601no—
232C22#9125311yescharacteristic
233C4—62no—
234C4—401no—
235C4—601no—
236C4—1201no—
237C4D3×#67711yescharacteristic
238C4#9142911yescharacteristic
239C3#1060010011yescharacteristic, complemented, Sylow
240C2—21no—
241C2—1201no—
242C2#1174779011yescharacteristic
subgroupG/H
centerC2#11747790
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×M32C22
socleC2×C3×C5#476
prime radical#91793C22
hypercenterM32D3×D5
hypocenterC3×C5#2230
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
2. #11748027C2semidirect
4. C5×#4511C2semidirect
5. C3×#64733C2semidirect
6. #11745938C2semidirect
27. #64733D3semidirect
32. Dic60Q8semidirect
33. D120Q8semidirect
48. #4511D5semidirect
201. C3×C5#2230semidirect
230. C5#69315semidirect
239. C3#10600100semidirect

Maximal subgroups

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

subgroupindex
#117480682
#117480272
#117463392
C5×#45112
C3×#647332
#117459382
#117459132
#106001003
#693155