Finite Group Databasebeta

← #14278194

Subgroups — #14278194

Order 1920.

232 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 73 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#11751217C211yesmaximal, characteristic
2C3×C5×C22⋊C16C211yesmaximal, characteristic
3#11746372C211yesmaximal, characteristic
4#10598019—31nomaximal, Hall
5C22×C3×C5×C8C2211yescharacteristic
6C2×C4⋊Dic15—21no—
7#91813—21no—
8C2×Dic60C411yescharacteristic, complemented
9C2×C3×C5×C16—21no—
10#91102C411yescharacteristic, complemented
11#91100—21no—
12#67528—51nomaximal, Hall
13#65405—31no—
14C5×C22⋊C16D311yescharacteristic
15#64771—31no—
16C22×C3×C4×C5D411yescharacteristic
17C22×Dic15—41no—
18C2×Dic30—21no—
19C2×C3×C5×C8—41no—
20C2×C3×C5×C8C2×C411yescharacteristic
21C2×C3×C5×C8D411yescharacteristic
22#6719—41no—
23C4⋊Dic15—22no—
24C4⋊Dic15—21no—
25C4⋊Dic15—41no—
26#6712—41no—
27Dic60—41no—
28C3×C5×C16—41no—
29#5116—51no—
30C3×C22⋊C16D511yescharacteristic
31#4551—51no—
32C22×C5×C8C2×D311yescharacteristic
33C2×C4⋊Dic5—61no—
34#4070—61no—
35C2×Dic20—31no—
36C2×C5×C16—21no—
37#3950—31no—
38#3948—61no—
39#1348—151noSylow
40C23×C3×C5D811yescharacteristic
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×C3×C4×C5SD1611yescharacteristic
45C2×Dic15—42no—
46C2×Dic15—41no—
47C2×Dic15—41no—
48C2×Dic15—81no—
49C2×Dic15—81no—
50Dic30—41no—
51Dic30—41no—
52C3×C5×C8—21no—
53C3×C5×C8—21no—
54C22×C3×C8C2×D511yescharacteristic
55C2×C4⋊Dic3—101no—
56#924—101no—
57C2×Dic12—51no—
58C2×C3×C16—21no—
59#818—51no—
60#816—101no—
61C22×C4×C5D1211yescharacteristic
62C22×Dic5—121no—
63C2×Dic10—61no—
64C2×C5×C8—41no—
65C2×C5×C8C4×D311yescharacteristic
66C2×C5×C8#6711yescharacteristic
67C22⋊Dic5—121no—
68C4⋊Dic5—62no—
69C4⋊Dic5—61no—
70C4⋊Dic5—121no—
71#683—121no—
72Dic20—121no—
73C5×C16—41no—
74#467—151no—
75C22⋊C16D1511yescharacteristic
76#340—151no—
77C22×C3×C5—21no—
78C22×C3×C5—21no—
79C22×C3×C5#10211yescharacteristic
80C22×C3×C5SD3211yescharacteristic
81C22×C3×C5Q3211yescharacteristic
82C3×C4×C5—21no—
83C3×C4×C5#9911yescharacteristic
84C3×C4×C5#10411yescharacteristic
85Dic15—82no—
86Dic15—81no—
87Dic15—81no—
88C22×C3×C4D2011yescharacteristic
89C22×Dic3—201no—
90C2×Dic6—101no—
91C2×C3×C8—41no—
92C2×C3×C8C4×D511yescharacteristic
93C2×C3×C8C22⋊D511yescharacteristic
94#217—201no—
95C4⋊Dic3—102no—
96C4⋊Dic3—101no—
97C4⋊Dic3—201no—
98Dic3⋊C4—201no—
99Dic12—201no—
100C3×C16—41no—
101C23×C5D2411yescharacteristic
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5#20411yescharacteristic
105C2×C4×C5(C2×D3)⋊C411yescharacteristic
106C2×Dic5—122no—
107C2×Dic5—121no—
108C2×Dic5—121no—
109C2×Dic5—241no—
110C2×Dic5—241no—
111Dic10—121no—
112Dic10—121no—
113C5×C8—21no—
114C5×C8—21no—
115C2×Q16—151no—
116C22×C8C2×D1511yescharacteristic
117C22⋊Q8—301no—
118C2×C4⋊C4—301no—
119C2×C16—21no—
120#107—151no—
121#103—301no—
122C2×C3×C5—21no—
123C2×C3×C5—21no—
124C2×C3×C5#32711yescharacteristic
125C2×C3×C5#35811yescharacteristic
126C2×C3×C5#36011yescharacteristic
127C23×C3D4011yescharacteristic
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4#67711yescharacteristic
131C2×C3×C4#68511yescharacteristic
132C2×Dic3—202no—
133C2×Dic3—201no—
134C2×Dic3—201no—
135C2×Dic3—401no—
136C2×Dic3—401no—
137Dic6—201no—
138Dic6—201no—
139C3×C8—21no—
140C3×C8—21no—
141C22×C5—21no—
142C22×C5—21no—
143C22×C5#80011yescharacteristic
144C22×C5Dic2411yescharacteristic
145C22×C5#82111yescharacteristic
146C4×C5—21no—
147C4×C5#80611yescharacteristic
148C4×C5#82511yescharacteristic
149Dic5—242no—
150Dic5—241no—
151Dic5—241no—
152C2×Q8—301no—
153C22×C4—601no—
154C22×C4D6011yescharacteristic
155Q16—601no—
156C2×C8—41no—
157C2×C8C4×D1511yescharacteristic
158C2×C8#122011yescharacteristic
159C4⋊C4—302no—
160C4⋊C4—301no—
161C4⋊C4—601no—
162C4⋊C4—601no—
163C22⋊C4—601no—
164C16—41no—
165C3×C5#134811yescharacteristic, complemented, Hall
166C22×C3—21no—
167C22×C3—21no—
168C22×C3#393211yescharacteristic
169C22×C3Dic4011yescharacteristic
170C22×C3#395311yescharacteristic
171C3×C4—21no—
172C3×C4#393811yescharacteristic
173C3×C4#395711yescharacteristic
174Dic3—402no—
175Dic3—401no—
176Dic3—401no—
177C2×C5—21no—
178C2×C5—21no—
179C2×C5#447011yescharacteristic
180C2×C5#450311yescharacteristic
181C2×C5#451811yescharacteristic
182C23D12011yescharacteristic
183Q8—601no—
184Q8—601no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—602no—
188C2×C4—601no—
189C2×C4—601no—
190C2×C4—1201no—
191C2×C4—1201no—
192C2×C4#670611yescharacteristic
193C2×C4#671411yescharacteristic
194C8—21no—
195C8—21no—
196C2×C3—21no—
197C2×C3—21no—
198C2×C3#6469011yescharacteristic
199C2×C3#6472311yescharacteristic
200C2×C3#6473811yescharacteristic
201C5#6752811yescharacteristic, complemented, Sylow
202C22—21no—
203C22—21no—
204C22#9108411yescharacteristic
205C22Dic12011yescharacteristic
206C22#9110511yescharacteristic
207C4—21no—
208C4—1202no—
209C4—1201no—
210C4—1201no—
211C4#9109011yescharacteristic
212C4#9110911yescharacteristic
213C3#1059801911yescharacteristic, complemented, Sylow
214C2—21no—
215C2—21no—
216C2#1174629111yescharacteristic
217C2#1174632411yescharacteristic
218C2#1174633911yescharacteristic
subgroupG/H
centerC22#91105
commutatorC2×C3×C5×C8C2×C4
FrattiniC22×C8C2×D15
FittingC3×C5×C22⋊C16C2
socleC22×C3×C5#102
prime radicalC23×C3×C5D8
cosocleC22×C3×C5×C8C22
hypercenterC22⋊C16D15
hypocenterC3×C5#1348
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
8. C2×Dic60C4semidirect
10. #91102C4semidirect
165. C3×C5#1348semidirect
201. C5#67528semidirect
213. C3#10598019semidirect

Maximal subgroups

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

subgroupindex
#117512172
C3×C5×C22⋊C162
#117463722
#105980193
#675285