Finite Group Databasebeta

← #14307436

Subgroups — #14307436

Order 1920.

568 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 126 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#11752498C211yesmaximal, characteristic
2#11752341C211yesmaximal, characteristic
3C3×C42×AGL(1,𝔽5)C211yesmaximal, characteristic
4#11746526C214yesmaximal
5#10604587—31nomaximal, Hall
6C2×#6758C2212yes—
7C2×C3×C4×AGL(1,𝔽5)—22no—
8C2×C3×C4×AGL(1,𝔽5)C2212yes—
9#91759C411yescharacteristic, complemented
10C5×#870C411yescharacteristic, complemented
11C3×C42×D5C2211yescharacteristic
12#91468C412yescomplemented
13#91358C2212yes—
14#91349—22no—
15#91323—22no—
16#91233—22no—
17#69396—51nomaximal, Hall
18#66022—31no—
19C42×AGL(1,𝔽5)D311yescharacteristic
20#65682—31no—
21#64875—34no—
22C22×C3×AGL(1,𝔽5)—22no—
23C2×C3×C4×D5D412yes—
24C2×C3×C4×D5C2311yescharacteristic
25C2×#1204—22no—
26C2×C3⋊#170—22no—
27#6758—24no—
28C3×C4×AGL(1,𝔽5)—28no—
29C3×C4×AGL(1,𝔽5)—22no—
30C3×C4×AGL(1,𝔽5)Q814yescomplemented
31C3×C42×C5C2×C411yescharacteristic
32C4⋊Dic15C2×C412yes—
33#6712—22no—
34C5×C4⋊Dic3C2×C412yes—
35C5×Dic3⋊C4—22no—
36C3×C4×Dic5C2×C411yescharacteristic
37C3×C4×Dic5D412yes—
38#6668—22no—
39#6665—22no—
40Dic3×Dic5—22no—
41#5470—51no—
42C3×C43—51no—
43#4924—51no—
44#4523—54no—
45C2×C4×AGL(1,𝔽5)—22no—
46C2×C4×AGL(1,𝔽5)C2×D312yes—
47C2×#700—32no—
48C5×#125—31no—
49#4042—62no—
50#4038—32no—
51#4034—32no—
52#4033—62no—
53C42×D5C2×D311yescharacteristic
54#4016—31no—
55#4004—62no—
56#1994—151noSylow
57C22×C3×D5C2×D411yescharacteristic
58C2×C3×AGL(1,𝔽5)—28no—
59C2×C3×AGL(1,𝔽5)—24no—
60C2×C3×C4×C5C22⋊C412yes—
61C2×C3×C4×C5C22×C411yescharacteristic
62C2×Dic15—22no—
63C2×C5×Dic3—22no—
64C2×C3×Dic5C22⋊C412yes—
65C2×C3×Dic5C2×D411yescharacteristic
66C3×C4×D5—24no—
67C3×C4×D5C2×Q812yes—
68C3×C4×D5#4112yes—
69#1204—44no—
70C3⋊#170—42no—
71C2×C3×C42—51no—
72C2×C3×C42—52no—
73C2×C3×C42—102no—
74#926—52no—
75#924—102no—
76C2×#208—52no—
77#870—51no—
78#870AGL(1,𝔽5)11yescharacteristic, complemented
79#869—52no—
80C4×Dic6—102no—
81C4⋊(C3⋊C8)—102no—
82C22×AGL(1,𝔽5)—22no—
83C2×C4×D5#6712yes—
84C2×C4×D5C22×D311yescharacteristic
85C2×Dic10—62no—
86C2×#170—62no—
87C4×AGL(1,𝔽5)—28no—
88C4×AGL(1,𝔽5)—22no—
89C4×AGL(1,𝔽5)Dic614yescomplemented
90#700—64no—
91C5×C4⋊C4—32no—
92C5×C4⋊C4—62no—
93C42×C5C4×D311yescharacteristic
94#685—62no—
95C4⋊Dic5—32no—
96#683—62no—
97#683—62no—
98C4×Dic5—62no—
99C4×Dic5C4×D311yescharacteristic
100C4×Dic5D1212yes—
101#533—151no—
102#423—151no—
103C43—51no—
104#339—154no—
105C22×C3×C5C2×C22⋊C411yescharacteristic
106C2×C3×D5—22no—
107C2×C3×D5C22⋊Q812yes—
108C3×AGL(1,𝔽5)—28no—
109C3×C4×C5—22no—
110C3×C4×C5C4×Q812yes—
111Dic15—42no—
112C3×Dic5#10414yes—
113C3×Dic5#12411yescharacteristic
114C3×Dic5C4⋊Q811yescharacteristic
115C5×Dic3—42no—
116C22×C3×C4—51no—
117C22×C3×C4—52no—
118C22×C3×C4—102no—
119C2×Dic6—102no—
120C3×C42—52no—
121C3×C42—51no—
122C3×C42—54no—
123C3×C42—102no—
124C3×C42—108no—
125C3×C42C2×AGL(1,𝔽5)11yescharacteristic
126#217—102no—
127C4⋊Dic3—52no—
128C4⋊Dic3—102no—
129C4⋊Dic3C2×AGL(1,𝔽5)12yes—
130Dic3⋊C4—22no—
131Dic3⋊C4—102no—
132C4×Dic3—102no—
133#208—104no—
134C2×C3⋊C8—102no—
135C22×D5C2×#6711yescharacteristic
136C2×AGL(1,𝔽5)—28no—
137C2×AGL(1,𝔽5)—24no—
138C2×C4×C5—62no—
139C2×C4×C5(C2×D3)⋊C412yes—
140C2×C4×C5C2×C4×D311yescharacteristic
141C2×Dic5—62no—
142C2×Dic5(C2×D3)⋊C412yes—
143C2×Dic5C2×D1211yescharacteristic
144C4×D5—24no—
145C4×D5C2×Dic612yes—
146C4×D5#23512yes—
147Dic10—124no—
148#170—122no—
149C2×M16—152no—
150C4⋊Q8—152no—
151#125—31no—
152#125—151no—
153C22⋊Q8—302no—
154C4×Q8—302no—
155#117—152no—
156C2×C42—51no—
157C2×C42—52no—
158C2×C42—102no—
159C4⋊C8—302no—
160C2×C3×C5#39111yescharacteristic
161C2×C3×C5C2×#10412yes—
162C3×D5—22no—
163C23×C3—51no—
164C2×C3×C4—52no—
165C2×C3×C4—51no—
166C2×C3×C4—52no—
167C2×C3×C4—52no—
168C2×C3×C4—104no—
169C2×C3×C4—104no—
170C2×C3×C4—108no—
171C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
172C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
173C2×Dic3—22no—
174C2×Dic3—102no—
175Dic6—204no—
176C3⋊C8—202no—
177C22×C5C2×(C2×D3)⋊C411yescharacteristic
178C2×D5—22no—
179C2×D5#92412yes—
180AGL(1,𝔽5)—28no—
181C4×C5—22no—
182C4×C5—122no—
183C4×C5C4×Dic612yes—
184Dic5—122no—
185Dic5#80514yes—
186Dic5#86911yescharacteristic
187Dic5#87511yescharacteristic
188C2×Q8—302no—
189C22×C4—51no—
190C22×C4—52no—
191C22×C4—102no—
192M16—304no—
193C2×C8—302no—
194C4⋊C4—32no—
195C4⋊C4—62no—
196C4⋊C4—152no—
197C4⋊C4—302no—
198C4⋊C4—302no—
199C22⋊C4—302no—
200C42—52no—
201C42—51no—
202C42—54no—
203C42—102no—
204C42—108no—
205C42—302no—
206C42D3×AGL(1,𝔽5)11yescharacteristic
207C3×C5#199411yescharacteristic, complemented, Hall
208C22×C3—52no—
209C22×C3—102no—
210C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
211C3×C4—22no—
212C3×C4—54no—
213C3×C4—51no—
214C3×C4—51no—
215C3×C4—108no—
216C3×C4Q8×AGL(1,𝔽5)12yes—
217Dic3—42no—
218Dic3—202no—
219C2×C5C2×#80512yes—
220C2×C5#492911yescharacteristic
221D5—22no—
222C23—51no—
223Q8—604no—
224C2×C4—51no—
225C2×C4—52no—
226C2×C4—52no—
227C2×C4—52no—
228C2×C4—62no—
229C2×C4—104no—
230C2×C4—104no—
231C2×C4—108no—
232C2×C4—302no—
233C2×C4(C2×D3)⋊AGL(1,𝔽5)12yes—
234C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
235C8—602no—
236C2×C3—102no—
237C2×C3(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
238C2×C3D5⋊#10412yes—
239C5#6939611yescharacteristic, complemented, Sylow
240C22—52no—
241C22—102no—
242C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
243C4—22no—
244C4—54no—
245C4—51no—
246C4—51no—
247C4—108no—
248C4—122no—
249C4—602no—
250C4AGL(1,𝔽5)×Dic612yes—
251C3#1060458711yescharacteristic, complemented, Sylow
252C2—102no—
253C2D5⋊#80512yes—
254C2#1175174911yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1994
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
9. #91759C4semidirect
10. C5×#870C4semidirect
12. #91468C4semidirect
30. C3×C4×AGL(1,𝔽5)Q8semidirect
78. #870AGL(1,𝔽5)semidirect
89. C4×AGL(1,𝔽5)Dic6semidirect
207. C3×C5#1994semidirect
239. C5#69396semidirect
251. C3#10604587semidirect

Maximal subgroups

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

subgroupindex
#117524982
#117523412
C3×C42×AGL(1,𝔽5)2
#117465262
#106045873
#693965