Finite Group Databasebeta

← #14300380

Subgroups — #14300380

Order 1920.

520 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 148 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
1C5×#5819C211yesmaximal, characteristic
2#11751341C211yesmaximal, characteristic
3C3×#65523C211yesmaximal, characteristic
4#11748435C212yesmaximal, complemented
5#11745990C212yesmaximal, complemented
6#10602819—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8#91815C2212yes—
9C5×#948—24no—
10C2×C5×#208—22no—
11C2×C5×#208C2212yes—
12C2×C3×#681C2211yescharacteristic
13C22×C3×#168C2211yescharacteristic
14#91118C414yes—
15C3×C22⋊#168—22no—
16#90983—24no—
17#70002—51nomaximal, Hall
18C5×#568—31no—
19#65529—31no—
20#65523D311yescharacteristic
21#65408—32no—
22#64776—32no—
23C3×C5×#41—22no—
24C3×C5×#41—22no—
25C2×C3×C5×Q8Q811yescharacteristic
26C2×C3×C5×D4C2×C412yes—
27C2×C3×C5×D4Q811yescharacteristic
28C22×C3×C4×C5D412yes—
29C22×C3×C4×C5C2311yescharacteristic
30#6719C2×C414yes—
31C4⋊Dic15—22no—
32C4×Dic15—22no—
33C5×#208—24no—
34C5×#208—22no—
35C5×#208—22no—
36C2×C5×C3⋊C8—24no—
37C2×C5×C3⋊C8D414yes—
38C3×#681—22no—
39C2×C3×#168—22no—
40C2×C3×#168—21no—
41C2×C3×#168—21no—
42#5819D511yescharacteristic
43C3×#408—51no—
44#5240—51no—
45#5102—52no—
46#4559—52no—
47C2×C5×#41C2×D311yescharacteristic
48C5×#131—64no—
49C2×C5×M16—32no—
50C2×C5×M16—62no—
51#4072—32no—
52C2×#681C2×D311yescharacteristic
53C22×#168C2×D311yescharacteristic
54#3966—34no—
55C22⋊#168—22no—
56#3946—64no—
57#1868—151noSylow
58C23×C3×C5C4⋊C412yes—
59C23×C3×C5C22×C411yescharacteristic
60C3×C5×Q8—22no—
61C3×C5×D4—24no—
62C3×C5×D4—22no—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5—22no—
65C2×C3×C4×C5C4⋊C412yes—
66C2×C3×C4×C5C2×D412yes—
67C2×C3×C4×C5C2×D411yescharacteristic
68C2×C3×C4×C5C2×Q811yescharacteristic
69C2×C3×C4×C5#4112yes—
70C2×Dic15—24no—
71C3×#168—41no—
72C3×#168—41no—
73C5×C3⋊C8—24no—
74C2×C3×#41C2×D511yescharacteristic
75C2×C3×M16—51no—
76C22×C3×C8—51no—
77#948—24no—
78#926—52no—
79C2×#208—22no—
80C2×#208C2×D512yes—
81C3×C22⋊C8—102no—
82#834—54no—
83Dic3⋊C8—104no—
84C5×#41—22no—
85C5×#41—22no—
86C2×C5×Q8Dic611yescharacteristic
87C2×C5×D4Dic611yescharacteristic
88C2×C5×D4C4×D312yes—
89C22×C4×C5#6712yes—
90C22×C4×C5C22×D311yescharacteristic
91C5×M16—64no—
92C5×M16—62no—
93C5×M16—62no—
94C2×C5×C8—34no—
95C2×C5×C8—64no—
96C22⋊Dic5—34no—
97C4⋊Dic5—62no—
98C4×Dic5—62no—
99#681—22no—
100C2×#168—22no—
101C2×#168—21no—
102C2×#168—21no—
103#568—31no—
104#424—152no—
105#410—151no—
106#408—51no—
107#344—152no—
108C22×C3×C5—22no—
109C22×C3×C5—41no—
110C22×C3×C5—42no—
111C22×C3×C5C2×C4⋊C411yescharacteristic
112C22×C3×C5C4×D412yes—
113C3×C4×C5—22no—
114C3×C4×C5#12011yescharacteristic
115C3×C4×C5C22⋊Q812yes—
116C3×C4×C5#12311yescharacteristic
117Dic15—44no—
118C3×#41—22no—
119C3×#41—22no—
120C2×C3×Q8Dic1011yescharacteristic
121C2×C3×D4Dic1011yescharacteristic
122C2×C3×D4C4×D512yes—
123C22×C3×C4C22⋊D512yes—
124C22×C3×C4C22×D511yescharacteristic
125C3×M16—102no—
126C2×C3×C8—102no—
127C2×C3×C8—101no—
128C2×C3×C8—101no—
129#217—54no—
130C4⋊Dic3—102no—
131C4×Dic3—102no—
132#208—24no—
133#208—22no—
134#208—22no—
135C2×C3⋊C8—24no—
136C2×C3⋊C8C22⋊D514yes—
137C23×C5Dic3⋊C412yes—
138C23×C5C2×C4×D311yescharacteristic
139C5×Q8—22no—
140C5×D4—24no—
141C5×D4—22no—
142C2×C4×C5—22no—
143C2×C4×C5—22no—
144C2×C4×C5Dic3⋊C412yes—
145C2×C4×C5C2×Dic611yescharacteristic
146C2×C4×C5D3×D412yes—
147C2×C4×C5#23712yes—
148C2×C4×C5C2×#6711yescharacteristic
149C2×Dic5—64no—
150C5×C8—64no—
151#168—41no—
152#168—41no—
153C2×#41D3×D511yescharacteristic
154#131—64no—
155C2×M16—32no—
156C2×M16—51no—
157C2×M16—62no—
158C22×C8—51no—
159#117—152no—
160C4⋊C8—304no—
161#99—154no—
162C22⋊C8—102no—
163C2×C3×C5—22no—
164C2×C3×C5—21no—
165C2×C3×C5—42no—
166C2×C3×C5#38511yescharacteristic
167C23×C3#68312yes—
168C23×C3C2×C4×D511yescharacteristic
169C3×Q8—22no—
170C3×D4—24no—
171C3×D4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4#68312yes—
175C2×C3×C4C2×Dic1011yescharacteristic
176C2×C3×C4#70912yes—
177C2×C3×C4C2×C22⋊D511yescharacteristic
178C2×C3×C4C2×C22⋊D512yes—
179C2×Dic3—104no—
180C3×C8—201no—
181C3×C8—201no—
182C3⋊C8—24no—
183C22×C5—22no—
184C22×C5—41no—
185C22×C5—42no—
186C22×C5#67⋊C412yes—
187C22×C5C2×Dic3⋊C411yescharacteristic
188C4×C5—22no—
189C4×C5#87812yes—
190C4×C5#93511yescharacteristic
191C4×C5#93711yescharacteristic
192Dic5—124no—
193#41—22no—
194#41—22no—
195C2×Q8#120411yescharacteristic
196C2×D4#120012yes—
197C2×D4#120411yescharacteristic
198C22×C4#120112yes—
199C22×C4C2×D3×D511yescharacteristic
200M16—64no—
201M16—62no—
202M16—62no—
203M16—102no—
204C2×C8—34no—
205C2×C8—64no—
206C2×C8—101no—
207C2×C8—101no—
208C2×C8—102no—
209C4⋊C4—302no—
210C22⋊C4—154no—
211C42—302no—
212C3×C5#186811yescharacteristic, complemented, Hall
213C22×C3—22no—
214C22×C3—41no—
215C22×C3—42no—
216C22×C3C2×#68311yescharacteristic
217C22×C3C4×C22⋊D512yes—
218C3×C4—22no—
219C3×C4#407012yes—
220C3×C4#407511yescharacteristic
221C3×C4#409911yescharacteristic
222Dic3—204no—
223C2×C5—22no—
224C2×C5—21no—
225C2×C5—42no—
226C2×C5#494611yescharacteristic
227C23#666912yes—
228C23C2×#120011yescharacteristic
229Q8—22no—
230D4—24no—
231D4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—304no—
235C2×C4#666912yes—
236C2×C4#677912yes—
237C2×C4C2×#120111yescharacteristic
238C2×C4C2×#120411yescharacteristic
239C2×C4D3×C22⋊D512yes—
240C8—64no—
241C8—201no—
242C8—201no—
243C2×C3—22no—
244C2×C3—21no—
245C2×C3—42no—
246C2×C3#6549911yescharacteristic
247C5#7000211yescharacteristic, complemented, Sylow
248C22—22no—
249C22—41no—
250C22—42no—
251C22C2×#666911yescharacteristic
252C22#9155612yes—
253C4—22no—
254C4—604no—
255C4#9153611yescharacteristic
256C4#9156811yescharacteristic
257C4#9157512yes—
258C3#1060281911yescharacteristic, complemented, Sylow
259C2—22no—
260C2—21no—
261C2—42no—
262C2#1174951211yescharacteristic
subgroupG/H
centerC4#91568
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC2×C3×C5#385
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1868
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #11748435C2semidirect
5. #11745990C2semidirect
212. C3×C5#1868semidirect
247. C5#70002semidirect
258. C3#10602819semidirect

Maximal subgroups

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

subgroupindex
C5×#58192
#117513412
C3×#655232
#117484352
#117459902
#106028193
#700025