Finite Group Databasebeta

← #14307117

Subgroups — #14307117

Order 1920.

560 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 154 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
1C2×#91333C211yesmaximal, characteristic
2C2×#91233C211yesmaximal, characteristic
3C2×C3×#4002C211yesmaximal, characteristic
4#11746570C214yesmaximal
5#10604333—31nomaximal, Hall
6C22×Dic30C411yescharacteristic
7C22×C3⋊#170C2212yes—
8C22×C3×#170C2212yes—
9C2×C5×C4⋊Dic3C411yescharacteristic
10C2×C3×C4×Dic5C2211yescharacteristic
11C2×#6669C412yes—
12C2×Dic3×Dic5C2212yes—
13#91333—22no—
14#91333—22no—
15#91233—22no—
16C3×#4002—22no—
17#69838—51nomaximal, Hall
18C2×#4033—31no—
19C2×#4004—31no—
20C2×#4002D311yescharacteristic
21#64918—34no—
22C22×C3×C4×C5C2×C411yescharacteristic
23C22×Dic15C2×C412yes—
24C2×Dic30—22no—
25C2×Dic30—24no—
26C22×C5×Dic3C2×C412yes—
27C22×C3×Dic5C2×C411yescharacteristic
28C22×C3×Dic5C2311yescharacteristic
29C2×C3⋊#170—22no—
30C2×C3⋊#170—24no—
31C2×C3×#170—22no—
32C2×C3×#170—22no—
33C2×C3×#170Q814yescomplemented
34C5×C4⋊Dic3—22no—
35C3×C4×Dic5D412yes—
36C3×C4×Dic5D412yes—
37#6669—24no—
38Dic3×Dic5—22no—
39Dic3×Dic5—22no—
40C2×C4×Dic6—51no—
41C2×C3×#97—51no—
42C2×C4⋊(C3⋊C8)—51no—
43#4550—54no—
44C22×Dic10—31no—
45C22×#170—32no—
46C22×#170C2×D312yes—
47C2×C5×C4⋊C4—31no—
48C2×#683—32no—
49C2×C4×Dic5—32no—
50C2×C4×Dic5C2×D311yescharacteristic
51#4033—62no—
52#4033—62no—
53#4004—62no—
54#4002—22no—
55#1985—151noSylow
56C23×C3×C5C22×C411yescharacteristic
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C22⋊C412yes—
59C2×Dic15—22no—
60C2×Dic15—22no—
61C2×Dic15M1614yes—
62Dic30—28no—
63C2×C5×Dic3—22no—
64C2×C5×Dic3—24no—
65C2×C3×Dic5—22no—
66C2×C3×Dic5C22⋊C412yes—
67C2×C3×Dic5C2×D411yescharacteristic
68C2×C3×Dic5C2×D411yescharacteristic
69C2×C3×Dic5C2×Q812yes—
70C2×C3×Dic5#4112yes—
71C3⋊#170—42no—
72C3×#170—24no—
73C22×Dic6—51no—
74C22×C3×C8—52no—
75C2×C3×C42—51no—
76C2×C4⋊Dic3AGL(1,𝔽5)11yescharacteristic
77C2×Dic3⋊C4—52no—
78C2×C4×Dic3—52no—
79C22×C3⋊C8—52no—
80C4×Dic6—102no—
81C4×Dic6—102no—
82C3×#97—102no—
83C4⋊(C3⋊C8)—102no—
84C22×C4×C5—32no—
85C22×C4×C5C4×D311yescharacteristic
86C22×Dic5—32no—
87C22×Dic5C4×D311yescharacteristic
88C22×Dic5C22×D311yescharacteristic
89C2×Dic10—64no—
90C2×Dic10—62no—
91C2×#170—22no—
92C2×#170—22no—
93C2×#170—62no—
94C2×#170—64no—
95C2×#170Dic614yescomplemented
96C5×C4⋊C4—62no—
97#683—64no—
98C4×Dic5—62no—
99C4×Dic5—62no—
100C4×Dic5D1212yes—
101C4×Dic5#6712yes—
102C2×C4×Q8—151no—
103C2×C4⋊C8—151no—
104C2×#97—51no—
105#336—154no—
106C22×C3×C5C2×C22⋊C411yescharacteristic
107C22×C3×C5C4×Q812yes—
108C22×C3×C5C2×M1612yes—
109C22×C3×C5#13112yes—
110C3×C4×C5—22no—
111Dic15—24no—
112C3×Dic5—22no—
113C3×Dic5C22⋊Q812yes—
114C3×Dic5#12411yescharacteristic
115C3×Dic5C4⋊Q811yescharacteristic
116C5×Dic3—42no—
117C22×C3×C4—51no—
118C22×C3×C4—51no—
119C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
120C22×Dic3—52no—
121C22×Dic3C2×AGL(1,𝔽5)12yes—
122C2×Dic6—104no—
123C2×Dic6—102no—
124C2×C3×C8—54no—
125C2×C3×C8—102no—
126C2×C3×C8—102no—
127C3×C42—52no—
128C3×C42—52no—
129C4⋊Dic3—22no—
130Dic3⋊C4—104no—
131C4×Dic3—102no—
132C4×Dic3—102no—
133C2×C3⋊C8—102no—
134C2×C3⋊C8—104no—
135C23×C5C2×C4×D311yescharacteristic
136C2×C4×C5—22no—
137C2×C4×C5—64no—
138C2×C4×C5—62no—
139C2×C4×C5(C2×D3)⋊C412yes—
140C2×Dic5—22no—
141C2×Dic5—34no—
142C2×Dic5—62no—
143C2×Dic5—62no—
144C2×Dic5(C2×D3)⋊C412yes—
145C2×Dic5C2×Dic612yes—
146C2×Dic5C2×D1211yescharacteristic
147C2×Dic5#23512yes—
148C2×Dic5C2×#6711yescharacteristic
149Dic10—68no—
150#170—24no—
151#170—122no—
152C22×Q8—151no—
153C22×C8—52no—
154C22×C8—152no—
155C4×Q8—302no—
156C4×Q8—302no—
157C2×C4⋊C4—31no—
158C2×C4⋊C4—152no—
159C2×C42—51no—
160C2×C42—152no—
161C4⋊C8—302no—
162#97—102no—
163C2×C3×C5#39111yescharacteristic
164C2×C3×C5#40711yescharacteristic
165C2×C3×C5#40811yescharacteristic
166C2×C3×C5#44614yes—
167C23×C3C22×AGL(1,𝔽5)11yescharacteristic
168C2×C3×C4—22no—
169C2×C3×C4—52no—
170C2×C3×C4—52no—
171C2×C3×C4—51no—
172C2×C3×C4—51no—
173C2×C3×C4—52no—
174C2×C3×C4—102no—
175C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
176C2×Dic3—24no—
177C2×Dic3—22no—
178C2×Dic3—54no—
179C2×Dic3—102no—
180C2×Dic3—102no—
181Dic6—108no—
182C3×C8—104no—
183C3⋊C8—202no—
184C22×C5C4×Dic612yes—
185C22×C5D3×M1612yes—
186C22×C5#90712yes—
187C22×C5C2×(C2×D3)⋊C411yescharacteristic
188C4×C5—22no—
189C4×C5—122no—
190Dic5—22no—
191Dic5—64no—
192Dic5#86911yescharacteristic
193Dic5#87511yescharacteristic
194Dic5#92412yes—
195C2×Q8—304no—
196C2×Q8—302no—
197C22×C4—32no—
198C22×C4—51no—
199C22×C4—51no—
200C22×C4—152no—
201C22×C4D3×AGL(1,𝔽5)11yescharacteristic
202C2×C8—54no—
203C2×C8—102no—
204C2×C8—102no—
205C2×C8—302no—
206C2×C8—304no—
207C4⋊C4—62no—
208C4⋊C4—304no—
209C42—52no—
210C42—52no—
211C42—302no—
212C42—302no—
213C3×C5#198511yescharacteristic, complemented, Hall
214C22×C3D5⋊M1612yes—
215C22×C3#413112yes—
216C22×C3Q8×AGL(1,𝔽5)12yes—
217C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
218C3×C4—22no—
219C3×C4—52no—
220C3×C4—51no—
221C3×C4—51no—
222C3×C4—102no—
223Dic3—42no—
224Dic3—104no—
225C2×C5#470114yes—
226C2×C5#492911yescharacteristic
227C2×C5#512611yescharacteristic
228C2×C5#512911yescharacteristic
229C23C2×D3×AGL(1,𝔽5)11yescharacteristic
230Q8—308no—
231C2×C4—22no—
232C2×C4—52no—
233C2×C4—52no—
234C2×C4—51no—
235C2×C4—51no—
236C2×C4—52no—
237C2×C4—64no—
238C2×C4—62no—
239C2×C4—102no—
240C2×C4—154no—
241C2×C4—302no—
242C2×C4—302no—
243C2×C4(C2×D3)⋊AGL(1,𝔽5)12yes—
244C8—104no—
245C8—602no—
246C2×C3#6570714yes—
247C2×C3#6575511yescharacteristic
248C2×C3#6577611yescharacteristic
249C2×C3(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
250C5#6983811yescharacteristic, complemented, Sylow
251C22AGL(1,𝔽5)×Dic612yes—
252C22#9191312yes—
253C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
254C22#9193112yes—
255C4—22no—
256C4—52no—
257C4—51no—
258C4—51no—
259C4—102no—
260C4—122no—
261C4—304no—
262C3#1060433311yescharacteristic, complemented, Sylow
263C2#1175174911yescharacteristic
264C2#1175178414yes—
265C2#1175181111yescharacteristic
266C2#1175200311yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×AGL(1,𝔽5)
commutator, socle, prime radicalC23×C3×C5C22×C4
FittingC22×C3×C4×C5C2×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1985
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
33. C2×C3×#170Q8semidirect
95. C2×#170Dic6semidirect
213. C3×C5#1985semidirect
250. C5#69838semidirect
262. C3#10604333semidirect

Maximal subgroups

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

subgroupindex
C2×#913332
C2×#912332
C2×C3×#40022
#117465702
#106043333
#698385