Finite Group Databasebeta

← #14278142

Subgroups — #14278142

Order 1920.

248 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 65 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#11751082C211yesmaximal, characteristic
2C3×C5×#343C211yesmaximal, characteristic
3#11746349C211yesmaximal, characteristic
4#10597986—31nomaximal, Hall
5C2×C3×C5×M16—21no—
6C2×C3×C5×C4⋊C4C2211yescharacteristic
7C2×C4⋊Dic15C411yescharacteristic
8C2×#6712—21no—
9#91115—21no—
10#91115C411yescharacteristic
11#91114—21no—
12#67495—51nomaximal, Hall
13#65272—31no—
14C5×#343D311yescharacteristic
15#64748—31no—
16C22×C3×C4×C5C2×C411yescharacteristic
17C22×C3×C4×C5D411yescharacteristic
18C22×C3×C4×C5D411yescharacteristic
19C22×Dic15—21no—
20C22×Dic15—21no—
21C3×C5×M16—22no—
22C3×C5×M16—41no—
23C2×C3×C5×C8—41no—
24C3×C5×C4⋊C4—41no—
25C4⋊Dic15—41no—
26#6712—41no—
27#6712—41no—
28C2×C3⋊#168—41no—
29#4981—51no—
30C3×#343D511yescharacteristic
31#4528—51no—
32C2×C5×M16—21no—
33C2×C5×C4⋊C4C2×D311yescharacteristic
34C2×C4⋊Dic5—31no—
35C2×#683—61no—
36#3963—31no—
37#3963—61no—
38C22⋊#168—61no—
39#1346—151noSylow
40C23×C3×C5C22⋊C411yescharacteristic
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5—21no—
45C2×C3×C4×C5—41no—
46C2×C3×C4×C5—41no—
47C2×C3×C4×C5D811yescharacteristic
48C2×C3×C4×C5SD1611yescharacteristic
49C2×Dic15—22no—
50C2×Dic15—41no—
51C2×Dic15—41no—
52C2×Dic15—41no—
53C2×Dic15—41no—
54C2×Dic15—41no—
55C3×C5×C8—42no—
56C3⋊#168—81no—
57C2×C3×M16—21no—
58C2×C3×C4⋊C4C2×D511yescharacteristic
59C2×C4⋊Dic3—51no—
60C2×Dic3⋊C4—101no—
61C3⋊#95—51no—
62C3⋊#95—101no—
63#830—101no—
64C22×C4×C5C4×D311yescharacteristic
65C22×C4×C5D1211yescharacteristic
66C22×C4×C5#6711yescharacteristic
67C22×Dic5—61no—
68C22×Dic5—61no—
69C5×M16—22no—
70C5×M16—41no—
71C2×C5×C8—41no—
72C5×C4⋊C4—41no—
73C4⋊Dic5—121no—
74#683—121no—
75#683—121no—
76C2×#168—121no—
77#398—151no—
78#343D1511yescharacteristic
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—21no—
86C3×C4×C5—21no—
87C3×C4×C5—41no—
88C3×C4×C5—41no—
89Dic15—42no—
90Dic15—81no—
91C22×C3×C4C4×D511yescharacteristic
92C22×C3×C4D2011yescharacteristic
93C22×C3×C4C22⋊D511yescharacteristic
94C22×Dic3—101no—
95C22×Dic3—101no—
96C3×M16—22no—
97C3×M16—41no—
98C2×C3×C8—41no—
99C3×C4⋊C4—41no—
100C4⋊Dic3—201no—
101Dic3⋊C4—201no—
102Dic3⋊C4—201no—
103C2×C3⋊C8—201no—
104C23×C5(C2×D3)⋊C411yescharacteristic
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—41no—
110C2×C4×C5—41no—
111C2×C4×C5#21311yescharacteristic
112C2×C4×C5#21511yescharacteristic
113C2×Dic5—62no—
114C2×Dic5—121no—
115C2×Dic5—121no—
116C2×Dic5—121no—
117C2×Dic5—121no—
118C2×Dic5—121no—
119C5×C8—42no—
120#168—241no—
121C2×M16—21no—
122C2×C4⋊C4—151no—
123C2×C4⋊C4—301no—
124C2×C4⋊C4C2×D1511yescharacteristic
125C22⋊C8—301no—
126#95—151no—
127#95—301no—
128C2×C3×C5—21no—
129C2×C3×C5—21no—
130C2×C3×C5#32711yescharacteristic
131C2×C3×C5#35211yescharacteristic
132C2×C3×C5#35611yescharacteristic
133C23×C3#68511yescharacteristic
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—41no—
139C2×C3×C4—41no—
140C2×C3×C4#68611yescharacteristic
141C2×C3×C4#68811yescharacteristic
142C2×Dic3—102no—
143C2×Dic3—201no—
144C2×Dic3—201no—
145C2×Dic3—201no—
146C2×Dic3—201no—
147C2×Dic3—201no—
148C3×C8—42no—
149C3⋊C8—401no—
150C22×C5—21no—
151C22×C5—21no—
152C22×C5#80511yescharacteristic
153C22×C5#80611yescharacteristic
154C22×C5#80911yescharacteristic
155C4×C5—21no—
156C4×C5—21no—
157C4×C5—41no—
158C4×C5—41no—
159Dic5—122no—
160Dic5—241no—
161C22×C4—301no—
162C22×C4—301no—
163C22×C4C4×D1511yescharacteristic
164C22×C4D6011yescharacteristic
165C22×C4#122011yescharacteristic
166M16—22no—
167M16—41no—
168C2×C8—41no—
169C2×C8—601no—
170C4⋊C4—41no—
171C4⋊C4—601no—
172C4⋊C4—601no—
173C4⋊C4—601no—
174C3×C5#134611yescharacteristic, complemented, Hall
175C22×C3—21no—
176C22×C3—21no—
177C22×C3#393711yescharacteristic
178C22×C3#393811yescharacteristic
179C22×C3#394111yescharacteristic
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—41no—
183C3×C4—41no—
184Dic3—202no—
185Dic3—401no—
186C2×C5—21no—
187C2×C5—21no—
188C2×C5#445111yescharacteristic
189C2×C5#447611yescharacteristic
190C2×C5#447811yescharacteristic
191C23#671411yescharacteristic
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—302no—
199C2×C4—601no—
200C2×C4—601no—
201C2×C4—601no—
202C2×C4—601no—
203C2×C4—601no—
204C2×C4#671511yescharacteristic
205C2×C4#671711yescharacteristic
206C8—42no—
207C8—1201no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3#6467111yescharacteristic
211C2×C3#6469611yescharacteristic
212C2×C3#6469811yescharacteristic
213C5#6749511yescharacteristic, complemented, Sylow
214C22—21no—
215C22—21no—
216C22#9108911yescharacteristic
217C22#9109011yescharacteristic
218C22#9109311yescharacteristic
219C4—21no—
220C4—21no—
221C4—41no—
222C4—41no—
223C4—602no—
224C4—1201no—
225C3#1059798611yescharacteristic, complemented, Sylow
226C2—21no—
227C2—21no—
228C2#1174627211yescharacteristic
229C2#1174629711yescharacteristic
230C2#1174629911yescharacteristic
subgroupG/H
centerC22#91090
commutatorC22×C3×C4×C5C2×C4
FrattiniC2×C4⋊C4C2×D15
FittingC3×C5×#343C2
socleC22×C3×C5#99
prime radicalC23×C3×C5C22⋊C4
cosocleC2×C3×C5×C4⋊C4C22
hypercenter#343D15
hypocenterC3×C5#1346
LCSG ▷ C22×C3×C4×C5 ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
174. C3×C5#1346semidirect
213. C5#67495semidirect
225. C3#10597986semidirect

Maximal subgroups

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

subgroupindex
#117510822
C3×C5×#3432
#117463492
#105979863
#674955