Finite Group Databasebeta

← #14315676

Subgroups — #14315676

Order 1920.

292 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 70 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#11751683C212yesmaximal, complemented
2#11746834C211yesmaximal, characteristic
3#11746722C211yesmaximal, characteristic, complemented
4C3×C16×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
5#11746463C212yesmaximal, complemented
6#10604136—31nomaximal, Hall
7#91914—22no—
8#91271C2212yes—
9#91225C2212yes—
10C3×C8×AGL(1,𝔽5)C2211yescharacteristic
11C3×D5⋊C16C2211yescharacteristic
12#91158—22no—
13D240C411yescharacteristic, complemented
14C5×Dic24C411yescharacteristic, complemented
15C3×D5×C16C2211yescharacteristic
16#90945C412yescomplemented
17#69067—51nomaximal, Hall
18#65740—32no—
19#65208—31no—
20#64909—32no—
21#64851—31no—
22C16×AGL(1,𝔽5)D311yescharacteristic, complemented
23#6773—22no—
24#6758—22no—
25C3×C4×AGL(1,𝔽5)D411yescharacteristic
26C3×D5⋊C8D411yescharacteristic
27#6740—42no—
28#6738—42no—
29D120C2×C412yes—
30C5×Dic12C2×C412yes—
31C3×C8×D5C2311yescharacteristic
32#6660—22no—
33C3×#674—21no—
34C3×C5×C16C2×C411yescharacteristic
35C3×#672C2×C411yescharacteristic
36#4904—51no—
37#4700—52no—
38C3×C4×C16—51no—
39#4510—52no—
40#4506—51no—
41#4133—62no—
42#4065—32no—
43#4010—62no—
44#3996—32no—
45C8×AGL(1,𝔽5)C2×D311yescharacteristic
46D5⋊C16C2×D311yescharacteristic
47C5×Q32—31no—
48#3960—32no—
49D80—31no—
50D5×C16C2×D311yescharacteristic
51#2178—151noSylow
52C2×C3×AGL(1,𝔽5)—21no—
53D60—22no—
54C5×Dic6—22no—
55C3×C4×D5C2×D411yescharacteristic
56#1202—42no—
57#1200—42no—
58C3⋊#170—42no—
59C3×#170D811yescharacteristic
60C3×#170D811yescharacteristic
61C3×C5×C8C22×C411yescharacteristic
62C3×#168#4111yescharacteristic
63#904—52no—
64#901—102no—
65C2×C3×C16—51no—
66C2×C3×C16—51no—
67C3×C4×C8—51no—
68#819—52no—
69#805—102no—
70Dic24AGL(1,𝔽5)11yescharacteristic, complemented
71#800—52no—
72D48—51no—
73#713—62no—
74C4×AGL(1,𝔽5)D1211yescharacteristic
75#700—62no—
76#700—122no—
77D5⋊C8—122no—
78D5⋊C8D1211yescharacteristic
79C5×Q16—32no—
80#688—62no—
81D40—32no—
82C8×D5C22×D311yescharacteristic
83#674—21no—
84C5×C16C4×D311yescharacteristic
85#672C4×D311yescharacteristic
86#508—151no—
87#443—152no—
88#368—151no—
89#359—152no—
90C4×C16—51no—
91C2×D15—42no—
92C2×C3×D5#13511yescharacteristic
93C3×AGL(1,𝔽5)—22no—
94C3×C4×C5C4×D411yescharacteristic
95C3×Dic5C2×D811yescharacteristic
96C5×Dic3—42no—
97#235—102no—
98C2×C3×C8—51no—
99C2×C3×C8—51no—
100C3×C42—51no—
101#208—102no—
102Dic12C2×AGL(1,𝔽5)12yes—
103D24—52no—
104#204—102no—
105ΓL(1,𝔽25)—202no—
106D3×C8—202no—
107C3×C16—51no—
108C3×C16—101no—
109C3×C16C2×AGL(1,𝔽5)11yescharacteristic
110C2×AGL(1,𝔽5)—21no—
111C5×Q8—62no—
112D20—62no—
113D20—122no—
114C4×D5—122no—
115C4×D5C2×D1211yescharacteristic
116#170—122no—
117#170D2411yescharacteristic
118#170D2411yescharacteristic
119C5×C8C2×C4×D311yescharacteristic
120#168#23511yescharacteristic
121#135—152no—
122#131—302no—
123Q32—31no—
124SD32—152no—
125D16—151no—
126C2×C16—51no—
127C2×C16—51no—
128#108—152no—
129#104—302no—
130C4×C8—51no—
131C2×C3×C5C4×D811yescharacteristic
132D15—82no—
133C3×D5—21no—
134C2×C3×C4—51no—
135C2×C3×C4—101no—
136#67—202no—
137D12—102no—
138C4×D3—202no—
139Dic6—22no—
140C3×C8—51no—
141C3×C8—51no—
142C3×C8—51no—
143C3×C8C22×AGL(1,𝔽5)11yescharacteristic
144C3⋊C8—202no—
145C2×D5—122no—
146C2×D5#90411yescharacteristic
147AGL(1,𝔽5)—22no—
148C4×C5—122no—
149C4×C5C4×D1211yescharacteristic
150Dic5C2×D2411yescharacteristic
151#41—302no—
152Q16—32no—
153SD16—302no—
154D8—152no—
155M16—302no—
156M16—602no—
157C2×C8—51no—
158C2×C8—51no—
159C2×C8—602no—
160C42—51no—
161C16—51no—
162C16—101no—
163C16D3×AGL(1,𝔽5)11yescharacteristic
164C3×C5#217811yescharacteristic, complemented, Hall
165C22×C3—51no—
166C2×D3—202no—
167C3×C4—51no—
168C3×C4—102no—
169C3×C4D4×AGL(1,𝔽5)11yescharacteristic
170Dic3—42no—
171C2×C5C4×D2411yescharacteristic
172D5—21no—
173D5—242no—
174Q8—62no—
175D4—302no—
176D4—602no—
177C2×C4—51no—
178C2×C4—101no—
179C2×C4—602no—
180C8—51no—
181C8—51no—
182C8—51no—
183C8—602no—
184C8C2×D3×AGL(1,𝔽5)11yescharacteristic
185C2×C3—101no—
186C2×C3D8×AGL(1,𝔽5)11yescharacteristic
187D3—402no—
188C5#6906711yescharacteristic, complemented, Sylow
189C22—51no—
190C22—602no—
191C4—51no—
192C4—102no—
193C4—122no—
194C4AGL(1,𝔽5)×D1211yescharacteristic
195C3#1060413611yescharacteristic, complemented, Sylow
196C2—101no—
197C2—1202no—
198C2AGL(1,𝔽5)×D2411yescharacteristic
subgroupG/H
centerC2AGL(1,𝔽5)×D24
commutatorC3×C5×C8C22×C4
FrattiniC8C2×D3×AGL(1,𝔽5)
FittingC3×C5×C16C2×C4
socleC2×C3×C5C4×D8
prime radical#11746834C2
cosocleC3×C8×D5C23
hypercenterC16D3×AGL(1,𝔽5)
hypocenterC3×C5#2178
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16

Complements

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

NH ≅ G/Ntype
1. #11751683C2semidirect
3. #11746722C2semidirect
4. C3×C16×AGL(1,𝔽5)C2semidirect
5. #11746463C2semidirect
13. D240C4semidirect
14. C5×Dic24C4semidirect
16. #90945C4semidirect
22. C16×AGL(1,𝔽5)D3semidirect
70. Dic24AGL(1,𝔽5)semidirect
164. C3×C5#2178semidirect
188. C5#69067semidirect
195. C3#10604136semidirect

Maximal subgroups

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

subgroupindex
#117516832
#117468342
#117467222
C3×C16×AGL(1,𝔽5)2
#117464632
#106041363
#690675