Finite Group Databasebeta

← #14315628

Subgroups — #14315628

Order 1920.

292 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 83 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#11751005C211yesmaximal, characteristic
2#11750996C212yesmaximal, complemented
3C3×C5×#368C211yesmaximal, characteristic, complemented
4C16×Dic15C211yesmaximal, characteristic, complemented
5#11746318C212yesmaximal, complemented
6#10600150—31nomaximal, Hall
7#91796—22no—
8#91793C2212yes—
9C2×C3×C5×C16C2211yescharacteristic
10C3×C5×#108C2212yes—
11#91109—22no—
12C8×Dic15C2211yescharacteristic
13C2×C3⋊#672C2211yescharacteristic
14Dic120C411yescharacteristic, complemented
15#91084C412yescomplemented
16D240C411yescharacteristic, complemented
17#69357—51nomaximal, Hall
18#65193—31no—
19#65184—32no—
20C5×#368D311yescharacteristic, complemented
21C16×Dic5—31no—
22#64717—32no—
23#6817—22no—
24C3×C5×M16—22no—
25C2×C3×C5×C8C2311yescharacteristic
26C4×Dic15D411yescharacteristic
27C2×C3⋊#168D411yescharacteristic
28Dic60C2×C412yes—
29D120C2×C412yes—
30#6706—22no—
31#6705—42no—
32C8×D15—42no—
33C3×C5×C16C2×C411yescharacteristic
34C3×C5×C16C2×C411yescharacteristic
35C3⋊#672—21no—
36#4904—51no—
37#4895—52no—
38C3×#368D511yescharacteristic, complemented
39Dic3×C16—51no—
40#4497—52no—
41#4053—62no—
42#4050—32no—
43C2×C5×C16C2×D311yescharacteristic
44C5×#108C2×D312yes—
45#3957—62no—
46C8×Dic5—31no—
47C2×#672—31no—
48Dic40—31no—
49#3932—32no—
50D80—31no—
51#2178—151noSylow
52C2×C3×C4×C5C2×D411yescharacteristic
53#1220—42no—
54C2×Dic15—21no—
55D60—22no—
56C4×D15—42no—
57Dic30—22no—
58C3×C5×C8—42no—
59C3×C5×C8C22×C411yescharacteristic
60C3×C5×C8#4111yescharacteristic
61C3⋊#168D811yescharacteristic
62C3⋊#168D811yescharacteristic
63#907—102no—
64#904—52no—
65C2×C3×C16C2×D511yescharacteristic
66C3×#108C2×D512yes—
67#825—102no—
68C8×Dic3—51no—
69C2×C3⋊C16—51no—
70Dic24—51no—
71#800—52no—
72D48—51no—
73#709—62no—
74C5×M16—22no—
75C2×C5×C8C22×D311yescharacteristic
76C4×Dic5—31no—
77C2×#168—31no—
78Dic20—32no—
79D40—32no—
80#677—62no—
81#676—122no—
82C8×D5—122no—
83C5×C16C4×D311yescharacteristic
84C5×C16C4×D311yescharacteristic
85#672—61no—
86#508—151no—
87#443—152no—
88#368D1511yescharacteristic, complemented
89#359—152no—
90C4×C16—151no—
91C22×C3×C5#13511yescharacteristic
92C2×D15—42no—
93C3×C4×C5C4×D411yescharacteristic
94C3×C4×C5C2×D811yescharacteristic
95Dic15—22no—
96Dic15—42no—
97#235—102no—
98C3×M16—22no—
99C2×C3×C8C22×D511yescharacteristic
100C4×Dic3—51no—
101C2×C3⋊C8—51no—
102Dic12—52no—
103D24—52no—
104#204—102no—
105ΓL(1,𝔽25)—202no—
106D3×C8—202no—
107C3×C16C4×D511yescharacteristic
108C3×C16C4×D511yescharacteristic
109C3⋊C16—101no—
110C2×C4×C5D3×D411yescharacteristic
111C22⋊D5—122no—
112C2×Dic5—61no—
113D20—62no—
114C4×D5—122no—
115Dic10—62no—
116C5×C8—42no—
117C5×C8C2×C4×D311yescharacteristic
118C5×C8#23911yescharacteristic
119#168—31no—
120#168—31no—
121#135—152no—
122#131—302no—
123Q32—151no—
124SD32—152no—
125D16—151no—
126C2×C16—151no—
127C2×C16C2×D1511yescharacteristic
128#108C2×D1512yes—
129#104—302no—
130C4×C8—151no—
131C2×C3×C5—21no—
132C2×C3×C5C4×D811yescharacteristic
133D15—82no—
134C2×C3×C4D4×D511yescharacteristic
135#67—202no—
136C2×Dic3—101no—
137D12—102no—
138C4×D3—202no—
139Dic6—102no—
140C3×C8—42no—
141C3×C8C2×C4×D511yescharacteristic
142C3×C8#71311yescharacteristic
143C3⋊C8—51no—
144C3⋊C8—51no—
145C22×C5#91911yescharacteristic
146C2×D5—122no—
147C4×C5#89311yescharacteristic
148C4×C5D3×D811yescharacteristic
149Dic5—62no—
150Dic5—122no—
151#41—302no—
152Q16—152no—
153SD16—302no—
154D8—152no—
155M16—22no—
156M16—602no—
157C2×C8—151no—
158C2×C8—602no—
159C2×C8C22×D1511yescharacteristic
160C42—151no—
161C16—301no—
162C16C4×D1511yescharacteristic
163C16C4×D1511yescharacteristic
164C3×C5#217811yescharacteristic, complemented, Hall
165C22×C3#406511yescharacteristic
166C2×D3—202no—
167C3×C4#403911yescharacteristic
168C3×C4D5×D811yescharacteristic
169Dic3—102no—
170Dic3—202no—
171C2×C5—21no—
172C2×C5#487211yescharacteristic
173D5—242no—
174Q8—302no—
175D4—302no—
176D4—602no—
177C2×C4—301no—
178C2×C4—602no—
179C2×C4D4×D1511yescharacteristic
180C8—42no—
181C8—151no—
182C8—151no—
183C8C2×C4×D1511yescharacteristic
184C8#682111yescharacteristic
185C2×C3—21no—
186C2×C3#6516111yescharacteristic
187D3—402no—
188C5#6935711yescharacteristic, complemented, Sylow
189C22—602no—
190C22#9180811yescharacteristic
191C4—302no—
192C4—602no—
193C4#9178211yescharacteristic
194C4D8×D1511yescharacteristic
195C3#1060015011yescharacteristic, complemented, Sylow
196C2—21no—
197C2—1202no—
198C2#1175097311yescharacteristic
subgroupG/H
centerC4D8×D15
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C22×D15
FittingC3×C5×#368C2
socleC2×C3×C5C4×D8
prime radical#11751005C2
cosocleC2×C3×C5×C8C23
hypercenter#368D15
hypocenterC3×C5#2178
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #368

Complements

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

NH ≅ G/Ntype
2. #11750996C2semidirect
3. C3×C5×#368C2semidirect
4. C16×Dic15C2semidirect
5. #11746318C2semidirect
14. Dic120C4semidirect
15. #91084C4semidirect
16. D240C4semidirect
20. C5×#368D3semidirect
38. C3×#368D5semidirect
88. #368D15semidirect
164. C3×C5#2178semidirect
188. C5#69357semidirect
195. C3#10600150semidirect

Maximal subgroups

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

subgroupindex
#117510052
#117509962
C3×C5×#3682
C16×Dic152
#117463182
#106001503
#693575