Finite Group Databasebeta

← #14318191

Subgroups — #14318191

Order 1920.

252 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 66 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#11750996C211yesmaximal, characteristic
2#11748035C211yesmaximal, characteristic, complemented
3C5×#4494C211yesmaximal, characteristic, complemented
4C3×#64714C211yesmaximal, characteristic, complemented
5#11745931C211yesmaximal, characteristic, complemented
6#11745914C211yesmaximal, characteristic
7#11745913C211yesmaximal, characteristic
8#10600108—31nomaximal, Hall
9#91796—21no—
10#91793C2211yescharacteristic
11#91470—21no—
12C3×C5×#108C2211yescharacteristic
13#91109—21no—
14C8×Dic15C2211yescharacteristic
15C5×#817C2211yescharacteristic
16C5×#812C2211yescharacteristic
17C3×#3949C2211yescharacteristic
18C3×#3944C2211yescharacteristic
19#90986—21no—
20#69315—51nomaximal, Hall
21#65184—31no—
22#65144—31no—
23C5×#365—31no—
24#64738—31no—
25#64731—31no—
26#64714D311yescharacteristic, complemented
27#64708—31no—
28#6817—21no—
29C2×#1204—41no—
30C3×C5×M16—21no—
31C2×C3×C5×C8C2311yescharacteristic
32C4×Dic15D411yescharacteristic
33C2×C3⋊#168D411yescharacteristic
34Dic60Q811yescharacteristic, complemented
35D120Q811yescharacteristic, complemented
36#6706—21no—
37#6705—41no—
38C8×D15—41no—
39C5×C4⋊Dic3—21no—
40C3×C4⋊Dic5—21no—
41#6669—41no—
42C3×#672—21no—
43C5×C3⋊C16—21no—
44#4895—51no—
45#4855—51no—
46C3×#365—51no—
47#4518—51no—
48#4511—51no—
49#4494D511yescharacteristic, complemented
50#4488—51no—
51#4053—61no—
52#4050—31no—
53#4034—61no—
54C5×M32—31no—
55C5×#108C2×D311yescharacteristic
56C5×#106—31no—
57#3957—61no—
58#3949C2×D311yescharacteristic
59C8×Dic5—31no—
60#3944C2×D311yescharacteristic
61#3940—61no—
62#2230—151noSylow
63C2×C3×C4×C5C2×D411yescharacteristic
64#1220—41no—
65C2×Dic15—21no—
66D60—21no—
67C4×D15—41no—
68Dic30—21no—
69C2×C5×Dic3—41no—
70C2×C3×Dic5—41no—
71#1204—82no—
72C3×C5×C8—41no—
73C3×C5×C8C2×Q811yescharacteristic
74C3×C5×C8#4111yescharacteristic
75C3⋊#168SD1611yescharacteristic
76C3⋊#168SD1611yescharacteristic
77#907—101no—
78#904—51no—
79#888—101no—
80C3×M32—51no—
81C3×#108C2×D511yescharacteristic
82C3×#106—51no—
83#825—101no—
84#817C2×D511yescharacteristic
85C8×Dic3—51no—
86#812C2×D511yescharacteristic
87#808—101no—
88#709—61no—
89C2×Dic10—121no—
90C5×M16—21no—
91C2×C5×C8C22×D311yescharacteristic
92C5×C4⋊C4—61no—
93C4⋊Dic5—21no—
94#683—121no—
95C4×Dic5—31no—
96C2×#168—31no—
97Dic20—31no—
98D40—31no—
99#677—61no—
100#676—121no—
101C8×D5—121no—
102C5×C16—61no—
103#672—21no—
104#498—151no—
105#443—151no—
106#365—31no—
107#365—51no—
108#364—151no—
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—22no—
116Dic15—41no—
117C3×Dic5—81no—
118C5×Dic3—81no—
119#235—101no—
120C2×Dic6—201no—
121C3×M16—21no—
122C2×C3×C8C22×D511yescharacteristic
123C3×C4⋊C4—101no—
124C4⋊Dic3—21no—
125Dic3⋊C4—201no—
126C4×Dic3—51no—
127C2×C3⋊C8—51no—
128Dic12—51no—
129D24—51no—
130#204—101no—
131ΓL(1,𝔽25)—201no—
132D3×C8—201no—
133C3×C16—101no—
134C3⋊C16—21no—
135C2×C4×C5—121no—
136C2×C4×C5D3×D411yescharacteristic
137C22⋊D5—121no—
138C2×Dic5—41no—
139C2×Dic5—61no—
140D20—61no—
141C4×D5—121no—
142Dic10—61no—
143Dic10—242no—
144C5×C8—41no—
145C5×C8#23511yescharacteristic
146C5×C8D3×Q811yescharacteristic
147#168—31no—
148#168—31no—
149#135—151no—
150#131—301no—
151C4⋊Q8—301no—
152M32—31no—
153M32—51no—
154#108D3×D511yescharacteristic
155#106—31no—
156#106—51no—
157#106—301no—
158#104—301no—
159C4×C8—151no—
160C2×C3×C5—21no—
161C2×C3×C5#47611yescharacteristic
162D15—81no—
163C2×C3×C4—201no—
164C2×C3×C4D4×D511yescharacteristic
165#67—201no—
166C2×Dic3—41no—
167C2×Dic3—101no—
168D12—101no—
169C4×D3—201no—
170Dic6—101no—
171Dic6—402no—
172C3×C8—41no—
173C3×C8#70911yescharacteristic
174C3×C8Q8×D511yescharacteristic
175C3⋊C8—51no—
176C3⋊C8—51no—
177C22×C5#91411yescharacteristic
178C2×D5—121no—
179C4×C5—241no—
180C4×C5#89611yescharacteristic
181C4×C5D3×SD1611yescharacteristic
182Dic5—62no—
183Dic5—81no—
184Dic5—121no—
185#41—301no—
186C2×Q8—601no—
187Q16—151no—
188SD16—301no—
189D8—151no—
190M16—21no—
191M16—601no—
192C2×C8—151no—
193C2×C8—601no—
194C2×C8C2×D3×D511yescharacteristic
195C4⋊C4—61no—
196C4⋊C4—101no—
197C4⋊C4—601no—
198C42—151no—
199C16—61no—
200C16—101no—
201C3×C5#223011yescharacteristic, complemented, Hall
202C22×C3#406011yescharacteristic
203C2×D3—201no—
204C3×C4—401no—
205C3×C4#404211yescharacteristic
206C3×C4D5×SD1611yescharacteristic
207Dic3—81no—
208Dic3—102no—
209Dic3—201no—
210C2×C5—21no—
211C2×C5#487011yescharacteristic
212D5—241no—
213Q8—301no—
214Q8—1202no—
215D4—301no—
216D4—601no—
217C2×C4—121no—
218C2×C4—201no—
219C2×C4—301no—
220C2×C4—601no—
221C2×C4#679011yescharacteristic
222C8—41no—
223C8—151no—
224C8—151no—
225C8D15⋊Q811yescharacteristic
226C8#677111yescharacteristic
227C2×C3—21no—
228C2×C3#6515911yescharacteristic
229D3—401no—
230C5#6931511yescharacteristic, complemented, Sylow
231C22—601no—
232C22#9150611yescharacteristic
233C4—241no—
234C4—302no—
235C4—401no—
236C4—601no—
237C4#9137711yescharacteristic
238C4#9148711yescharacteristic
239C3#1060010811yescharacteristic, complemented, Sylow
240C2—21no—
241C2—1201no—
242C2#1174718311yescharacteristic
subgroupG/H
centerC2#11747183
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#108C22
socleC2×C3×C5#476
prime radical#91793C22
hypercenter#108D3×D5
hypocenterC3×C5#2230
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
2. #11748035C2semidirect
3. C5×#4494C2semidirect
4. C3×#64714C2semidirect
5. #11745931C2semidirect
26. #64714D3semidirect
34. Dic60Q8semidirect
35. D120Q8semidirect
49. #4494D5semidirect
201. C3×C5#2230semidirect
230. C5#69315semidirect
239. C3#10600108semidirect

Maximal subgroups

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

subgroupindex
#117509962
#117480352
C5×#44942
C3×#647142
#117459312
#117459142
#117459132
#106001083
#693155