Finite Group Databasebeta

← #14315687

Subgroups — #14315687

Order 1920.

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

normal subgroups only

This group has 288 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
4#11746323C211yesmaximal, characteristic, complemented
5#11746318C212yesmaximal, complemented
6#10600151—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#69358—51nomaximal, Hall
18#65193—31no—
19#65184—32no—
20C5×#368D311yescharacteristic, complemented
21#64722—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
39#4502—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#2179—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⋊#168D812yes—
62#907—102no—
63#904—52no—
64C2×C3×C16C2×D511yescharacteristic
65C3×#108C2×D512yes—
66#825—102no—
67C8×Dic3—51no—
68C2×C3⋊C16—51no—
69Dic24—51no—
70#800—52no—
71D48—51no—
72#709—62no—
73C5×M16—22no—
74C2×C5×C8C22×D311yescharacteristic
75C4×Dic5—31no—
76C2×#168—31no—
77Dic20—32no—
78D40—32no—
79#677—62no—
80#676—122no—
81C8×D5—122no—
82C5×C16C4×D311yescharacteristic
83C5×C16C4×D311yescharacteristic
84#672—61no—
85#508—151no—
86#443—152no—
87#368D1511yescharacteristic, complemented
88#359—152no—
89#346—151no—
90C22×C3×C5#13511yescharacteristic
91C2×D15—42no—
92C3×C4×C5C4×D411yescharacteristic
93C3×C4×C5C2×D811yescharacteristic
94Dic15—41no—
95Dic15—42no—
96#235—102no—
97C3×M16—22no—
98C2×C3×C8C22×D511yescharacteristic
99C4×Dic3—51no—
100C2×C3⋊C8—51no—
101Dic12—52no—
102D24—52no—
103#204—102no—
104ΓL(1,𝔽25)—202no—
105D3×C8—202no—
106C3×C16C4×D511yescharacteristic
107C3×C16C4×D511yescharacteristic
108C3⋊C16—101no—
109C2×C4×C5D3×D411yescharacteristic
110C22⋊D5—122no—
111C2×Dic5—61no—
112D20—62no—
113C4×D5—122no—
114Dic10—62no—
115C5×C8—42no—
116C5×C8C2×C4×D311yescharacteristic
117C5×C8#23911yescharacteristic
118#168—32no—
119#135—152no—
120#131—302no—
121Q32—151no—
122SD32—152no—
123D16—151no—
124C2×C16—151no—
125C2×C16C2×D1511yescharacteristic
126#108C2×D1512yes—
127#104—302no—
128C4×C8—151no—
129C2×C3×C5—21no—
130C2×C3×C5C4×D811yescharacteristic
131D15—82no—
132C2×C3×C4D4×D511yescharacteristic
133#67—202no—
134C2×Dic3—101no—
135D12—102no—
136C4×D3—202no—
137Dic6—102no—
138C3×C8—42no—
139C3×C8C2×C4×D511yescharacteristic
140C3×C8#71311yescharacteristic
141C3⋊C8—52no—
142C22×C5#91911yescharacteristic
143C2×D5—122no—
144C4×C5#89311yescharacteristic
145C4×C5D3×D811yescharacteristic
146Dic5—121no—
147Dic5—122no—
148#41—302no—
149Q16—152no—
150SD16—302no—
151D8—152no—
152M16—22no—
153M16—602no—
154C2×C8—151no—
155C2×C8—602no—
156C2×C8C22×D1511yescharacteristic
157C42—151no—
158C16—301no—
159C16C4×D1511yescharacteristic
160C16C4×D1511yescharacteristic
161C3×C5#217911yescharacteristic, complemented, Hall
162C22×C3#406511yescharacteristic
163C2×D3—202no—
164C3×C4#403911yescharacteristic
165C3×C4D5×D811yescharacteristic
166Dic3—201no—
167Dic3—202no—
168C2×C5—21no—
169C2×C5#487211yescharacteristic
170D5—242no—
171Q8—302no—
172D4—302no—
173D4—602no—
174C2×C4—301no—
175C2×C4—602no—
176C2×C4D4×D1511yescharacteristic
177C8—42no—
178C8—152no—
179C8C2×C4×D1511yescharacteristic
180C8#682111yescharacteristic
181C2×C3—21no—
182C2×C3#6516111yescharacteristic
183D3—402no—
184C5#6935811yescharacteristic, complemented, Sylow
185C22—602no—
186C22#9180811yescharacteristic
187C4—601no—
188C4—602no—
189C4#9178211yescharacteristic
190C4D8×D1511yescharacteristic
191C3#1060015111yescharacteristic, complemented, Sylow
192C2—21no—
193C2—1202no—
194C2#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#2179
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. #11746323C2semidirect
5. #11746318C2semidirect
14. Dic120C4semidirect
15. #91084C4semidirect
16. D240C4semidirect
20. C5×#368D3semidirect
38. C3×#368D5semidirect
87. #368D15semidirect
161. C3×C5#2179semidirect
184. C5#69358semidirect
191. C3#10600151semidirect

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
#117463232
#117463182
#106001513
#693585