Finite Group Databasebeta

← #14278150

Subgroups — #14278150

Order 1920.

248 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 57 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×#65269C211yesmaximal, characteristic
2#11746790C211yesmaximal, characteristic
3#11746785C211yesmaximal, characteristic
4#10598718—31nomaximal, Hall
5C2×#6762—21no—
6C2×C3×C5×C4⋊C4C411yescharacteristic
7C2×C3×#683—21no—
8C2×C3×#683C2211yescharacteristic
9#91241—21no—
10C3×#3963—21no—
11C3×#3963C411yescharacteristic
12#67650—51nomaximal, Hall
13#65269D311yescharacteristic
14#64919—31no—
15#64914—31no—
16C22×C3×C4×C5—21no—
17C22×C3×C4×C5C2×C411yescharacteristic
18C22×C3×Dic5—21no—
19C22×C3×Dic5D411yescharacteristic
20C22×C3×Dic5D411yescharacteristic
21#6762—22no—
22#6762—41no—
23C2×C3⋊#170—41no—
24C2×C3⋊#170—41no—
25C3×C5×C4⋊C4—41no—
26C3×#683—41no—
27C3×#683—41no—
28C3×#683—41no—
29C3×#398—51no—
30#4530—51no—
31#4528—51no—
32C2×#704—61no—
33C2×C5×C4⋊C4Dic311yescharacteristic
34C2×#683—21no—
35C2×#683C2×D311yescharacteristic
36C22⋊#170—61no—
37#3963—21no—
38#3963Dic311yescharacteristic
39#1346—151noSylow
40C23×C3×C5C22⋊C411yescharacteristic
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—41no—
43C2×C3×C4×C5—41no—
44C2×C3×C4×C5—41no—
45C2×C3×C4×C5—41no—
46C2×C3×Dic5—21no—
47C2×C3×Dic5—21no—
48C2×C3×Dic5—22no—
49C2×C3×Dic5—21no—
50C2×C3×Dic5—41no—
51C2×C3×Dic5—41no—
52C2×C3×Dic5—41no—
53C2×C3×Dic5D811yescharacteristic
54C2×C3×Dic5SD1611yescharacteristic
55C3⋊#170—42no—
56C3⋊#170—81no—
57C2×C3×C4⋊C4—51no—
58C2×C3×C4⋊C4—101no—
59C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
60C2×#208—101no—
61C3×#95—51no—
62C3×#95—101no—
63#830—101no—
64C22×C4×C5—21no—
65C22×C4×C5C2×Dic311yescharacteristic
66C22×Dic5—21no—
67C22×Dic5#6711yescharacteristic
68C22×Dic5#6711yescharacteristic
69#704—62no—
70#704—121no—
71C2×#170—121no—
72C2×#170—121no—
73C5×C4⋊C4—41no—
74#683—41no—
75#683—41no—
76#683—41no—
77#398—51no—
78#343—151no—
79#324—151no—
80C22×C3×C5—21no—
81C22×C3×C5—21no—
82C22×C3×C5#9911yescharacteristic
83C22×C3×C5#10211yescharacteristic
84C22×C3×C5#10411yescharacteristic
85C3×C4×C5—41no—
86C3×C4×C5—81no—
87C3×Dic5—21no—
88C3×Dic5—21no—
89C3×Dic5—42no—
90C3×Dic5—41no—
91C22×C3×C4—21no—
92C22×C3×C4—51no—
93C22×C3×C4—51no—
94C22×C3×C4—101no—
95C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
96C3×C4⋊C4—41no—
97C3×C4⋊C4—201no—
98C3×C4⋊C4—201no—
99C3×C4⋊C4—201no—
100#208—102no—
101#208—201no—
102C2×C3⋊C8—201no—
103C2×C3⋊C8—201no—
104C23×C5#21711yescharacteristic
105C2×C4×C5—21no—
106C2×C4×C5—41no—
107C2×C4×C5—41no—
108C2×C4×C5—41no—
109C2×C4×C5—41no—
110C2×Dic5—21no—
111C2×Dic5—21no—
112C2×Dic5—22no—
113C2×Dic5—21no—
114C2×Dic5—41no—
115C2×Dic5—41no—
116C2×Dic5—41no—
117C2×Dic5#21311yescharacteristic
118C2×Dic5#21411yescharacteristic
119#170—122no—
120#170—241no—
121C2×M16—301no—
122C2×C4⋊C4—51no—
123C2×C4⋊C4—101no—
124C2×C4⋊C4ΓL(1,𝔽16)11yescharacteristic
125C22⋊C8—301no—
126#95—51no—
127#95—101no—
128C2×C3×C5—21no—
129C2×C3×C5—21no—
130C2×C3×C5#32711yescharacteristic
131C2×C3×C5#35211yescharacteristic
132C2×C3×C5#35611yescharacteristic
133C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
134C2×C3×C4—21no—
135C2×C3×C4—41no—
136C2×C3×C4—41no—
137C2×C3×C4—41no—
138C2×C3×C4—41no—
139C2×C3×C4—51no—
140C2×C3×C4—51no—
141C2×C3×C4—101no—
142C2×C3×C4—101no—
143C2×C3×C4—102no—
144C2×C3×C4—101no—
145C2×C3×C4—201no—
146C2×C3×C4—201no—
147C2×C3×C4—201no—
148C3⋊C8—202no—
149C3⋊C8—401no—
150C22×C5—21no—
151C22×C5—21no—
152C22×C5#83211yescharacteristic
153C22×C5#83411yescharacteristic
154C22×C5#83711yescharacteristic
155C4×C5—41no—
156C4×C5—81no—
157Dic5—21no—
158Dic5—21no—
159Dic5—42no—
160Dic5—41no—
161C22×C4—21no—
162C22×C4—51no—
163C22×C4—51no—
164C22×C4—101no—
165C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
166M16—302no—
167M16—601no—
168C2×C8—601no—
169C2×C8—601no—
170C4⋊C4—41no—
171C4⋊C4—201no—
172C4⋊C4—201no—
173C4⋊C4—201no—
174C3×C5#134611yescharacteristic, complemented, Hall
175C22×C3—21no—
176C22×C3—21no—
177C22×C3#400711yescharacteristic
178C22×C3#400811yescharacteristic
179C22×C3#401111yescharacteristic
180C3×C4—41no—
181C3×C4—81no—
182C3×C4—101no—
183C3×C4—101no—
184C3×C4—202no—
185C3×C4—201no—
186C2×C5—21no—
187C2×C5—21no—
188C2×C5#453711yescharacteristic
189C2×C5#453911yescharacteristic
190C2×C5#454811yescharacteristic
191C23#676311yescharacteristic
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—51no—
198C2×C4—51no—
199C2×C4—101no—
200C2×C4—101no—
201C2×C4—102no—
202C2×C4—101no—
203C2×C4—201no—
204C2×C4—201no—
205C2×C4—201no—
206C8—602no—
207C8—1201no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3#6491611yescharacteristic
211C2×C3#6492011yescharacteristic
212C2×C3#6492911yescharacteristic
213C5#6765011yescharacteristic, complemented, Sylow
214C22—21no—
215C22—21no—
216C22#9123611yescharacteristic
217C22#9123711yescharacteristic
218C22#9124011yescharacteristic
219C4—41no—
220C4—81no—
221C4—101no—
222C4—101no—
223C4—202no—
224C4—201no—
225C3#1059871811yescharacteristic, complemented, Sylow
226C2—21no—
227C2—21no—
228C2#1174678711yescharacteristic
229C2#1174679111yescharacteristic
230C2#1174680011yescharacteristic
subgroupG/H
centerC22#91240
commutatorC22×C3×C4×C5C2×C4
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5#99
prime radicalC23×C3×C5C22⋊C4
cosocleC2×C3×#683C22
hypercenterC2×C4⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1346
LCSG ▷ C22×C3×C4×C5 ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
174. C3×C5#1346semidirect
213. C5#67650semidirect
225. C3#10598718semidirect

Maximal subgroups

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

subgroupindex
C3×#652692
#117467902
#117467852
#105987183
#676505