Finite Group Databasebeta

← #14315297

Subgroups — #14315297

Order 1920.

288 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 84 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#11751742C212yesmaximal, complemented
2#11748064C211yesmaximal, characteristic
3#11746757C211yesmaximal, characteristic, complemented
4C3×#64889C211yesmaximal, characteristic, complemented
5#11746552C212yesmaximal, complemented
6#10604084—31nomaximal, Hall
7#91793C411yescharacteristic
8#91290C2212yes—
9C2×C3⋊#674C2211yescharacteristic
10C2×C3⋊#674C2211yescharacteristic
11C3×#3998C2212yes—
12#91166—22no—
13#91164—22no—
14C5×#819C411yescharacteristic
15C3×C8×Dic5C2211yescharacteristic
16#90981C412yes—
17#69301—51nomaximal, Hall
18#65725—32no—
19#65184—31no—
20#64898—32no—
21#64889D311yescharacteristic, complemented
22#64886—31no—
23#6817C2×C412yes—
24C2×C3×C5×C8C2×C411yescharacteristic
25Dic60C811yescharacteristic
26D120C811yescharacteristic
27#6706C812yes—
28C5×#208C2×C412yes—
29C3×C4×Dic5C2×C411yescharacteristic
30C2×C3×#168C2311yescharacteristic
31#6651—22no—
32#6648—22no—
33C3⋊#674—21no—
34C3⋊#674D412yes—
35C3×#674—22no—
36#4907—52no—
37#4700—51no—
38C3×#364—51no—
39#4515—52no—
40#4461—51no—
41#4053—32no—
42#4050—31no—
43#3998C2×D312yes—
44C2×#674—31no—
45C2×#674—31no—
46#3990—62no—
47D5⋊C16—62no—
48C5×#108—31no—
49#3957—32no—
50C8×Dic5C2×D311yescharacteristic
51#2171—151noSylow
52C2×C3×C4×C5C22×C411yescharacteristic
53#1220—22no—
54D60C2×C812yes—
55C4×D15—22no—
56Dic30C2×C812yes—
57C2×C3×Dic5—21no—
58C3×C5×C8C2×C811yescharacteristic
59C3×C5×C8C2×C811yescharacteristic
60C3×#168C2×D411yescharacteristic
61C3×#168#4111yescharacteristic
62C5×C3⋊C8—22no—
63#904—51no—
64#901—52no—
65C3×M32—52no—
66C3×C4×C8—51no—
67#819AGL(1,𝔽5)11yescharacteristic
68C2×C3⋊C16—51no—
69C2×C3⋊C16—51no—
70#805—52no—
71#798—102no—
72D3×C16—102no—
73#709—32no—
74C5×M16—32no—
75C2×C5×C8C4×D311yescharacteristic
76C4×Dic5C4×D311yescharacteristic
77C2×#168C22×D311yescharacteristic
78Dic20—31no—
79D40—31no—
80#677—32no—
81#676—62no—
82C8×D5—62no—
83#674—22no—
84#674—32no—
85#674—61no—
86#504—152no—
87#443—151no—
88#364—51no—
89#350—152no—
90#346—151no—
91C22×C3×C5#13111yescharacteristic
92C2×D15—22no—
93C3×C4×C5C4×D411yescharacteristic
94C3×C4×C5C22×C811yescharacteristic
95Dic15—22no—
96C3×Dic5—41no—
97#235—52no—
98C2×C3×C8—51no—
99C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
100C3×C42—51no—
101#208C2×AGL(1,𝔽5)12yes—
102Dic12—51no—
103D24—51no—
104#204—52no—
105ΓL(1,𝔽25)—102no—
106D3×C8—102no—
107C3×C16—102no—
108C3⋊C16—52no—
109C3⋊C16—101no—
110C2×C4×C5C2×C4×D311yescharacteristic
111C22⋊D5—62no—
112C2×Dic5—21no—
113D20—32no—
114C4×D5—62no—
115Dic10—32no—
116C5×C8—62no—
117C5×C8D3×C811yescharacteristic
118C5×C8D3×C811yescharacteristic
119#168D3×D411yescharacteristic
120#168#23911yescharacteristic
121#135—151no—
122#131—152no—
123M32—52no—
124M32—302no—
125C2×C16—151no—
126C2×C16—151no—
127C2×C16—302no—
128#108—31no—
129#104—152no—
130C4×C8—51no—
131C2×C3×C5—21no—
132C2×C3×C5C8×D411yescharacteristic
133D15—42no—
134C2×C3×C4—101no—
135C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
136#67—102no—
137D12—52no—
138C4×D3—102no—
139Dic6—52no—
140C3×C8—51no—
141C3×C8—51no—
142C3×C8D5⋊C811yescharacteristic
143C3×C8D5⋊C811yescharacteristic
144C3⋊C8—22no—
145C22×C5#90711yescharacteristic
146C2×D5—62no—
147C4×C5#89311yescharacteristic
148C4×C5C2×D3×C811yescharacteristic
149Dic5—41no—
150Dic5—62no—
151#41—152no—
152Q16—151no—
153SD16—152no—
154D8—151no—
155M16—32no—
156M16—302no—
157C2×C8—51no—
158C2×C8—302no—
159C2×C8D3×AGL(1,𝔽5)11yescharacteristic
160C42—51no—
161C16—102no—
162C16—152no—
163C16—301no—
164C3×C5#217111yescharacteristic, complemented, Hall
165C22×C3#413311yescharacteristic
166C2×D3—102no—
167C3×C4—201no—
168C3×C4C2×D5⋊C811yescharacteristic
169C3×C4D4×AGL(1,𝔽5)11yescharacteristic
170Dic3—102no—
171C2×C5—21no—
172C2×C5#483411yescharacteristic
173D5—122no—
174Q8—152no—
175D4—152no—
176D4—302no—
177C2×C4—101no—
178C2×C4—302no—
179C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
180C8—51no—
181C8—51no—
182C8—62no—
183C8#673811yescharacteristic
184C8#673811yescharacteristic
185C2×C3—21no—
186C2×C3#6570211yescharacteristic
187D3—202no—
188C5#6930111yescharacteristic, complemented, Sylow
189C22—302no—
190C22#9191611yescharacteristic
191C4—201no—
192C4—302no—
193C4#9192111yescharacteristic
194C4C2×#673811yescharacteristic
195C3#1060408411yescharacteristic, complemented, Sylow
196C2—21no—
197C2—602no—
198C2#1175190411yescharacteristic
subgroupG/H
centerC4#91921
commutatorC3×C4×C5C22×C8
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC2×C3×C5C8×D4
prime radical#91793C4
cosocleC2×C3×#168C23
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5#2171
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. #11751742C2semidirect
3. #11746757C2semidirect
4. C3×#64889C2semidirect
5. #11746552C2semidirect
21. #64889D3semidirect
164. C3×C5#2171semidirect
188. C5#69301semidirect
195. C3#10604084semidirect

Maximal subgroups

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

subgroupindex
#117517422
#117480642
#117467572
C3×#648892
#117465522
#106040843
#693015