Finite Group Databasebeta

← #14278014

Subgroups — #14278014

Order 1920.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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
1C3×#65157C211yesmaximal, characteristic
2#11746766C211yesmaximal, characteristic
3#11746762C211yesmaximal, characteristic
4#10598600—31nomaximal, Hall
5#91989—21no—
6C2×C3×Dic20C411yescharacteristic, complemented
7C2×C3×#676C2211yescharacteristic
8C3×#4043—21no—
9#91227—21no—
10C3×C5×#106C411yescharacteristic, complemented
11C3×#3942—21no—
12#67780—51nomaximal, Hall
13#65157D311yescharacteristic
14#64895—31no—
15#64891—31no—
16C2×C3×C4×D5D411yescharacteristic
17C2×C3×Dic10—21no—
18#6763—41no—
19C4⋊ΓL(1,𝔽16)—41no—
20C4×ΓL(1,𝔽16)—22no—
21C2×C3×C5×C8C2×C411yescharacteristic
22C3×C5×C4⋊C4—21no—
23C3×#685—41no—
24C3×C4⋊Dic5—41no—
25C2×C3×#168D411yescharacteristic
26C3×Dic20—41no—
27C3×#676—41no—
28C3⋊#674—41no—
29C3×#470—51no—
30#4557—51no—
31#4553—51no—
32#4130—61no—
33C2×Dic20Dic311yescharacteristic, complemented
34C2×#676C2×D311yescharacteristic
35#4043—21no—
36#3998—61no—
37C5×#106Dic311yescharacteristic, complemented
38#3942—21no—
39#1340—151noSylow
40C22×C3×D5D811yescharacteristic
41C2×ΓL(1,𝔽16)—42no—
42C2×C3×C4×C5—41no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×C3×Dic5—41no—
45C2×C3×Dic5SD1611yescharacteristic
46C3×C4×D5—21no—
47C3×C4×D5—21no—
48C3×Dic10—41no—
49C3×Dic10—41no—
50C3×C5×C8—21no—
51C3×#168—21no—
52C2×C3×Q16—51no—
53C2×C3×M16—51no—
54C3×C22⋊Q8—101no—
55#926—101no—
56C3×#106AGL(1,𝔽5)11yescharacteristic, complemented
57C3×#103—101no—
58#812—101no—
59C2×C4×D5#6711yescharacteristic
60C2×Dic10—21no—
61C22⋊AGL(1,𝔽5)—121no—
62C4⋊AGL(1,𝔽5)—121no—
63C4×AGL(1,𝔽5)—62no—
64C2×C5×C8C2×Dic311yescharacteristic
65C5×C4⋊C4—21no—
66#685—41no—
67C4⋊Dic5—41no—
68C2×#168#6711yescharacteristic
69Dic20—41no—
70#676—41no—
71#674—121no—
72#470—51no—
73#349—151no—
74H(3,ℤ/4)—151no—
75C22×C3×C5#10211yescharacteristic
76C2×C3×D5—21no—
77C2×C3×D5—41no—
78ΓL(1,𝔽16)—82no—
79C3×C4×C5—81no—
80C3×C4×C5#9911yescharacteristic
81C3×C4×C5#10411yescharacteristic
82C3×Dic5—21no—
83C3×Dic5—81no—
84C2×C3×Q8—101no—
85C22×C3×C4—51no—
86C3×Q16—201no—
87C3×M16—201no—
88C2×C3×C8—51no—
89C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
90C3×C4⋊C4—21no—
91C3×C4⋊C4—201no—
92C3×C22⋊C4—201no—
93#217—201no—
94C4⋊Dic3—201no—
95C4×Dic3—102no—
96C3⋊C16—201no—
97C22×D5#21311yescharacteristic
98C2×AGL(1,𝔽5)—122no—
99C2×C4×C5—41no—
100C2×C4×C5#21711yescharacteristic
101C2×Dic5—41no—
102C2×Dic5#21411yescharacteristic
103C4×D5—21no—
104C4×D5—21no—
105Dic10—41no—
106Dic10—41no—
107C5×C8—21no—
108#168—21no—
109C2×Q16—51no—
110C2×M16—51no—
111C22⋊Q8—101no—
112#117—301no—
113M32—301no—
114#106ΓL(1,𝔽16)11yescharacteristic, complemented
115#103—101no—
116C2×C3×C5—21no—
117C2×C3×C5#32711yescharacteristic
118C3×D5—41no—
119C23×C3—51no—
120C3×Q8—201no—
121C3×Q8—201no—
122C2×C3×C4—41no—
123C2×C3×C4—51no—
124C2×C3×C4—101no—
125C2×C3×C4—101no—
126C2×C3×C4—201no—
127C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
128C2×Dic3—202no—
129C3×C8—21no—
130C3×C8—101no—
131C22×C5#83211yescharacteristic
132C2×D5—21no—
133C2×D5—41no—
134AGL(1,𝔽5)—242no—
135C4×C5—81no—
136C4×C5#83411yescharacteristic
137C4×C5#83711yescharacteristic
138Dic5—21no—
139Dic5—81no—
140C2×Q8—101no—
141C22×C4—51no—
142Q16—201no—
143M16—201no—
144C2×C8—51no—
145C2×C8C2×ΓL(1,𝔽16)11yescharacteristic
146C4⋊C4—21no—
147C4⋊C4—201no—
148C4⋊C4—601no—
149C22⋊C4—201no—
150C22⋊C4—601no—
151C42—302no—
152C16—601no—
153C3×C5#134011yescharacteristic, complemented, Hall
154C22×C3—101no—
155C22×C3—201no—
156C22×C3#400711yescharacteristic
157C3×C4—81no—
158C3×C4—101no—
159C3×C4—401no—
160C3×C4#399911yescharacteristic
161C3×C4#401011yescharacteristic
162Dic3—402no—
163C2×C5—21no—
164C2×C5#453711yescharacteristic
165D5—41no—
166C23—51no—
167Q8—201no—
168Q8—201no—
169C2×C4—41no—
170C2×C4—51no—
171C2×C4—101no—
172C2×C4—101no—
173C2×C4—201no—
174C2×C4—602no—
175C2×C4#676311yescharacteristic
176C8—21no—
177C8—101no—
178C2×C3—21no—
179C2×C3—201no—
180C2×C3#6486811yescharacteristic
181C5#6778011yescharacteristic, complemented, Sylow
182C22—101no—
183C22—201no—
184C22#9123611yescharacteristic
185C4—81no—
186C4—101no—
187C4—401no—
188C4—1202no—
189C4#9122811yescharacteristic
190C4#9123911yescharacteristic
191C3#1059860011yescharacteristic, complemented, Sylow
192C2—21no—
193C2—201no—
194C2#1174673911yescharacteristic
subgroupG/H
centerC2#11746739
commutatorC2×C3×C5×C8C2×C4
FrattiniC2×C8C2×ΓL(1,𝔽16)
FittingC3×C5×#106C4
socleC2×C3×C5#327
prime radicalC22×C3×D5D8
cosocleC2×C3×#676C22
hypercenter#106ΓL(1,𝔽16)
hypocenterC3×C5#1340
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
6. C2×C3×Dic20C4semidirect
10. C3×C5×#106C4semidirect
33. C2×Dic20Dic3semidirect
37. C5×#106Dic3semidirect
56. C3×#106AGL(1,𝔽5)semidirect
114. #106ΓL(1,𝔽16)semidirect
153. C3×C5#1340semidirect
181. C5#67780semidirect
191. C3#10598600semidirect

Maximal subgroups

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

subgroupindex
C3×#651572
#117467662
#117467622
#105986003
#677805