Finite Group Databasebeta

← #14318201

Subgroups — #14318201

Order 1920.

240 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 69 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#11750959C211yesmaximal, characteristic, complemented
3C3×C5×#365C211yesmaximal, characteristic, complemented
4#11746339C211yesmaximal, characteristic
5#11746332C211yesmaximal, characteristic, complemented
6#11746315C211yesmaximal, characteristic, complemented
7#11746309C211yesmaximal, characteristic
8#10600109—31nomaximal, Hall
9#91796—21no—
10#91793C2211yescharacteristic
11#91779—21no—
12C3×C5×M32C2211yescharacteristic
13C3×C5×#108C2211yescharacteristic
14C3×C5×#106C2211yescharacteristic
15#91109—21no—
16#91101C2211yescharacteristic
17C8×Dic15C2211yescharacteristic
18#91096C2211yescharacteristic
19#91091—21no—
20#69316—51nomaximal, Hall
21#65184—31no—
22#65147—31no—
23C5×#365D311yescharacteristic, complemented
24#64738—31no—
25#64731—31no—
26#64714—31no—
27#64708—31no—
28#6817—21no—
29C3×C5×M16—21no—
30C2×C3×C5×C8C2311yescharacteristic
31C3×C5×C4⋊C4—21no—
32C4⋊Dic15—21no—
33C4⋊Dic15—41no—
34#6712—41no—
35C4×Dic15D411yescharacteristic
36C2×C3⋊#168D411yescharacteristic
37Dic60Q811yescharacteristic
38D120Q811yescharacteristic
39#6706—21no—
40#6705—41no—
41C8×D15—41no—
42C3×C5×C16—21no—
43C3⋊#672—21no—
44#4895—51no—
45#4858—51no—
46C3×#365D511yescharacteristic, complemented
47#4518—51no—
48#4511—51no—
49#4494—51no—
50#4488—51no—
51#4053—61no—
52#4050—31no—
53#4036—61no—
54C5×M32C2×D311yescharacteristic
55C5×#108C2×D311yescharacteristic
56C5×#106C2×D311yescharacteristic
57#3957—61no—
58#3949—31no—
59C8×Dic5—31no—
60#3944—31no—
61#3939—61no—
62#2231—151noSylow
63C2×C3×C4×C5—41no—
64C2×C3×C4×C5C2×D411yescharacteristic
65#1220—41no—
66C2×Dic15—21no—
67C2×Dic15—41no—
68D60—21no—
69C4×D15—41no—
70Dic30—21no—
71C3×C5×C8—41no—
72C3×C5×C8C2×Q811yescharacteristic
73C3×C5×C8#4111yescharacteristic
74C3⋊#168SD1611yescharacteristic
75C3⋊#168SD1611yescharacteristic
76#907—101no—
77#904—51no—
78#890—101no—
79C3×M32C2×D511yescharacteristic
80C3×#108C2×D511yescharacteristic
81C3×#106C2×D511yescharacteristic
82#825—101no—
83#817—51no—
84C8×Dic3—51no—
85#812—51no—
86#807—101no—
87#709—61no—
88C5×M16—21no—
89C2×C5×C8C22×D311yescharacteristic
90C5×C4⋊C4—21no—
91C4⋊Dic5—61no—
92C4⋊Dic5—121no—
93#683—121no—
94C4×Dic5—31no—
95C2×#168—31no—
96Dic20—31no—
97D40—31no—
98#677—61no—
99#676—121no—
100C8×D5—121no—
101C5×C16—21no—
102#672—61no—
103#499—151no—
104#443—151no—
105#365—151no—
106#365D1511yescharacteristic, complemented
107#364—151no—
108#360—151no—
109#360—151no—
110C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
111C2×D15—41no—
112C3×C4×C5—81no—
113C3×C4×C5C22⋊Q811yescharacteristic
114C3×C4×C5C2×SD1611yescharacteristic
115Dic15—41no—
116Dic15—41no—
117Dic15—81no—
118#235—101no—
119C3×M16—21no—
120C2×C3×C8C22×D511yescharacteristic
121C3×C4⋊C4—21no—
122C4⋊Dic3—101no—
123C4⋊Dic3—201no—
124Dic3⋊C4—201no—
125C4×Dic3—51no—
126C2×C3⋊C8—51no—
127Dic12—51no—
128D24—51no—
129#204—101no—
130ΓL(1,𝔽25)—201no—
131D3×C8—201no—
132C3×C16—21no—
133C3⋊C16—101no—
134C2×C4×C5—41no—
135C2×C4×C5D3×D411yescharacteristic
136C22⋊D5—121no—
137C2×Dic5—61no—
138C2×Dic5—121no—
139D20—61no—
140C4×D5—121no—
141Dic10—61no—
142C5×C8—41no—
143C5×C8#23511yescharacteristic
144C5×C8D3×Q811yescharacteristic
145#168—31no—
146#168—31no—
147#135—151no—
148#131—301no—
149#125—301no—
150M32—151no—
151M32C2×D1511yescharacteristic
152#108C2×D1511yescharacteristic
153#107—301no—
154#106—151no—
155#106C2×D1511yescharacteristic
156#104—301no—
157C4×C8—151no—
158C2×C3×C5—21no—
159C2×C3×C5#47611yescharacteristic
160D15—81no—
161C2×C3×C4—41no—
162C2×C3×C4D4×D511yescharacteristic
163#67—201no—
164C2×Dic3—101no—
165C2×Dic3—201no—
166D12—101no—
167C4×D3—201no—
168Dic6—101no—
169C3×C8—41no—
170C3×C8#70911yescharacteristic
171C3×C8Q8×D511yescharacteristic
172C3⋊C8—51no—
173C3⋊C8—51no—
174C22×C5#91411yescharacteristic
175C2×D5—121no—
176C4×C5—81no—
177C4×C5#89611yescharacteristic
178C4×C5D3×SD1611yescharacteristic
179Dic5—121no—
180Dic5—121no—
181Dic5—241no—
182#41—301no—
183Q16—151no—
184SD16—301no—
185D8—151no—
186M16—21no—
187M16—601no—
188C2×C8—151no—
189C2×C8—601no—
190C2×C8C22×D1511yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—301no—
193C4⋊C4—601no—
194C4⋊C4—601no—
195C42—151no—
196C16—21no—
197C16—301no—
198C3×C5#223111yescharacteristic, complemented, Hall
199C22×C3#406011yescharacteristic
200C2×D3—201no—
201C3×C4—81no—
202C3×C4#404211yescharacteristic
203C3×C4D5×SD1611yescharacteristic
204Dic3—201no—
205Dic3—201no—
206Dic3—401no—
207C2×C5—21no—
208C2×C5#487011yescharacteristic
209D5—241no—
210Q8—301no—
211D4—301no—
212D4—601no—
213C2×C4—41no—
214C2×C4—301no—
215C2×C4—601no—
216C2×C4—601no—
217C2×C4D4×D1511yescharacteristic
218C8—41no—
219C8—151no—
220C8—151no—
221C8#681711yescharacteristic
222C8Q8×D1511yescharacteristic
223C2×C3—21no—
224C2×C3#6515911yescharacteristic
225D3—401no—
226C5#6931611yescharacteristic, complemented, Sylow
227C22—601no—
228C22#9180311yescharacteristic
229C4—81no—
230C4—601no—
231C4—601no—
232C4—1201no—
233C4#9178511yescharacteristic
234C4SD16×D1511yescharacteristic
235C3#1060010911yescharacteristic, complemented, Sylow
236C2—21no—
237C2—1201no—
238C2#1175097111yescharacteristic
subgroupG/H
centerC2#11750971
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#365C2
socleC2×C3×C5#476
prime radical#91793C22
hypercenter#365D15
hypocenterC3×C5#2231
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
2. #11750959C2semidirect
3. C3×C5×#365C2semidirect
5. #11746332C2semidirect
6. #11746315C2semidirect
23. C5×#365D3semidirect
46. C3×#365D5semidirect
106. #365D15semidirect
198. C3×C5#2231semidirect
226. C5#69316semidirect
235. C3#10600109semidirect

Maximal subgroups

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

subgroupindex
#117509962
#117509592
C3×C5×#3652
#117463392
#117463322
#117463152
#117463092
#106001093
#693165