Finite Group Databasebeta

← #14315236

Subgroups — #14315236

Order 1920.

292 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 86 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#11751740C212yesmaximal, complemented
2#11748064C211yesmaximal, characteristic
3#11746760C211yesmaximal, characteristic, complemented
4C3×#64885C211yesmaximal, characteristic, complemented
5#11746553C212yesmaximal, complemented
6#10604083—31nomaximal, Hall
7#91793C411yescharacteristic
8#91290C2212yes—
9#91227C2212yes—
10C2×C3×#674C2211yescharacteristic
11C2×C3×#674C2211yescharacteristic
12#91166—22no—
13#91164—22no—
14C5×#819C411yescharacteristic
15C3×C8×Dic5C2211yescharacteristic
16#90981C412yes—
17#69056—51nomaximal, Hall
18#65725—32no—
19#65184—31no—
20#64898—32no—
21#64889—31no—
22#64885D311yescharacteristic, complemented
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—22no—
34C3×#674—21no—
35C3×#674D411yescharacteristic
36C3×#674D411yescharacteristic
37#4901—52no—
38#4700—51no—
39C3×C4×C16—51no—
40#4508—52no—
41#4463—51no—
42#4053—32no—
43#4050—31no—
44#3998—32no—
45C2×#674C2×D311yescharacteristic
46C2×#674C2×D311yescharacteristic
47#3990—62no—
48D5⋊C16—62no—
49C5×#108—31no—
50#3957—32no—
51C8×Dic5C2×D311yescharacteristic
52#2170—151noSylow
53C2×C3×C4×C5C22×C411yescharacteristic
54#1220—22no—
55D60C2×C812yes—
56C4×D15—22no—
57Dic30C2×C812yes—
58C2×C3×Dic5—21no—
59C3×C5×C8C2×C811yescharacteristic
60C3×C5×C8C2×C811yescharacteristic
61C3×#168C2×D411yescharacteristic
62C3×#168#4111yescharacteristic
63C5×C3⋊C8—22no—
64#904—51no—
65#901—52no—
66C2×C3×C16—51no—
67C2×C3×C16—51no—
68C3×C4×C8—51no—
69#819AGL(1,𝔽5)11yescharacteristic
70#812—52no—
71#805—52no—
72#798—102no—
73D3×C16—102no—
74#709—32no—
75C5×M16—32no—
76C2×C5×C8C4×D311yescharacteristic
77C4×Dic5C4×D311yescharacteristic
78C2×#168C22×D311yescharacteristic
79Dic20—31no—
80D40—31no—
81#677—32no—
82#676—62no—
83C8×D5—62no—
84#674—21no—
85#674—62no—
86#674D1211yescharacteristic
87#674D1211yescharacteristic
88#504—152no—
89#443—151no—
90#364—151no—
91#350—152no—
92C4×C16—51no—
93C22×C3×C5#13111yescharacteristic
94C2×D15—22no—
95C3×C4×C5C4×D411yescharacteristic
96C3×C4×C5C22×C811yescharacteristic
97Dic15—22no—
98C3×Dic5—22no—
99#235—52no—
100C2×C3×C8—51no—
101C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
102C3×C42—51no—
103#208C2×AGL(1,𝔽5)12yes—
104Dic12—51no—
105D24—51no—
106#204—52no—
107ΓL(1,𝔽25)—102no—
108D3×C8—102no—
109C3×C16—51no—
110C3×C16—51no—
111C3×C16—101no—
112C3⋊C16—102no—
113C2×C4×C5C2×C4×D311yescharacteristic
114C22⋊D5—62no—
115C2×Dic5—21no—
116D20—32no—
117C4×D5—62no—
118Dic10—32no—
119C5×C8—62no—
120C5×C8D3×C811yescharacteristic
121C5×C8D3×C811yescharacteristic
122#168C2×D1211yescharacteristic
123#168#23511yescharacteristic
124#135—151no—
125#131—152no—
126M32—152no—
127M32—302no—
128C2×C16—51no—
129C2×C16—51no—
130C2×C16—302no—
131#108—31no—
132#104—152no—
133C4×C8—51no—
134C2×C3×C5—21no—
135C2×C3×C5C8×D411yescharacteristic
136D15—42no—
137C2×C3×C4—101no—
138C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
139#67—102no—
140D12—52no—
141C4×D3—102no—
142Dic6—52no—
143C3×C8—51no—
144C3×C8—51no—
145C3×C8D5⋊C811yescharacteristic
146C3×C8D5⋊C811yescharacteristic
147C3⋊C8—22no—
148C22×C5#90111yescharacteristic
149C2×D5—62no—
150C4×C5C4×D1211yescharacteristic
151C4×C5C2×D3×C811yescharacteristic
152Dic5—22no—
153Dic5—62no—
154#41—152no—
155Q16—151no—
156SD16—152no—
157D8—151no—
158M16—32no—
159M16—302no—
160C2×C8—51no—
161C2×C8—302no—
162C2×C8D3×AGL(1,𝔽5)11yescharacteristic
163C42—51no—
164C16—51no—
165C16—51no—
166C16—101no—
167C16—302no—
168C3×C5#217011yescharacteristic, complemented, Hall
169C22×C3#413311yescharacteristic
170C2×D3—102no—
171C3×C4—102no—
172C3×C4C2×D5⋊C811yescharacteristic
173C3×C4D4×AGL(1,𝔽5)11yescharacteristic
174Dic3—102no—
175C2×C5—21no—
176C2×C5C8×D1211yescharacteristic
177D5—122no—
178Q8—152no—
179D4—152no—
180D4—302no—
181C2×C4—101no—
182C2×C4—302no—
183C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
184C8—51no—
185C8—51no—
186C8—62no—
187C8#673811yescharacteristic
188C8#673811yescharacteristic
189C2×C3—21no—
190C2×C3#6570211yescharacteristic
191D3—202no—
192C5#6905611yescharacteristic, complemented, Sylow
193C22—302no—
194C22#9191411yescharacteristic
195C4—102no—
196C4—302no—
197C4AGL(1,𝔽5)×D1211yescharacteristic
198C4C2×#673811yescharacteristic
199C3#1060408311yescharacteristic, complemented, Sylow
200C2—21no—
201C2—602no—
202C2#1175189311yescharacteristic
subgroupG/H
centerC4AGL(1,𝔽5)×D12
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#2170
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. #11751740C2semidirect
3. #11746760C2semidirect
4. C3×#64885C2semidirect
5. #11746553C2semidirect
22. #64885D3semidirect
168. C3×C5#2170semidirect
192. C5#69056semidirect
199. C3#10604083semidirect

Maximal subgroups

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

subgroupindex
#117517402
#117480642
#117467602
C3×#648852
#117465532
#106040833
#690565