Finite Group Databasebeta

← #14285749

Subgroups — #14285749

Order 1920.

336 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 110 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#11752342C211yesmaximal, characteristic
2C3×#65683C211yesmaximal, characteristic
3C4×D5×C3⋊C8C211yesmaximal, characteristic
4#11746514C212yesmaximal, complemented
5#11746512C212yesmaximal, complemented
6#10603820—31nomaximal, Hall
7C3×C42×D5C2211yescharacteristic
8C2×D5×C3⋊C8C411yescharacteristic
9C2×D5×C3⋊C8C411yescharacteristic
10#91232—21no—
11#91231—21no—
12C4⋊(C3⋊#170)C2212yes—
13C3×#4003—21no—
14C3×#4002—21no—
15C3×C4⋊#170C2212yes—
16C4×C3⋊#168C411yescharacteristic
17C4×C5×C3⋊C8C411yescharacteristic
18Dic5×C3⋊C8C2211yescharacteristic
19Dic5×C3⋊C8C2211yescharacteristic
20#70794—51nomaximal, Hall
21#65683—31no—
22#65683D311yescharacteristic
23C4×C8×D5—31no—
24#64882—32no—
25#64881—32no—
26C2×C3×C4×D5C2×C411yescharacteristic
27C2×C3×C4×D5D411yescharacteristic
28C2×C3×C4×D5Q811yescharacteristic
29C2×C3⋊#170—22no—
30C2×C3×#170—22no—
31C3×C42×C5C2×C411yescharacteristic
32C2×C3⋊#168C2×C411yescharacteristic
33C2×C3⋊#168C2×C411yescharacteristic
34C2×C5×C3⋊C8C2×C411yescharacteristic
35C2×C5×C3⋊C8C2×C411yescharacteristic
36C3×C4×Dic5D411yescharacteristic
37C3×C4×Dic5Q811yescharacteristic
38C3×C4×Dic5C2311yescharacteristic
39D5×C3⋊C8—22no—
40D5×C3⋊C8—22no—
41C3×#432—51no—
42#4926—51no—
43C2×C4×C3⋊C8—51no—
44#4480—52no—
45#4479—52no—
46C2×C8×D5—31no—
47C2×C8×D5—31no—
48C42×D5C2×D311yescharacteristic
49#4003—21no—
50#4003—61no—
51#4002—21no—
52#4002—61no—
53C4⋊#170—32no—
54C4⋊#170C2×D312yes—
55C4×C5×C8—31no—
56C8×Dic5—31no—
57C8×Dic5—31no—
58C4×#168—31no—
59#1568—151noSylow
60C22×C3×D5C4⋊C411yescharacteristic
61C2×C3×C4×C5C4⋊C411yescharacteristic
62C2×C3×C4×C5C4⋊C411yescharacteristic
63C2×C3×C4×C5C22×C411yescharacteristic
64C2×C3×Dic5C4⋊C411yescharacteristic
65C2×C3×Dic5C2×D411yescharacteristic
66C2×C3×Dic5C2×Q811yescharacteristic
67C3×C4×D5—22no—
68C3×C4×D5—21no—
69C3×C4×D5—21no—
70C3×C4×D5—22no—
71C3⋊#170—42no—
72C3×#170—42no—
73C3⋊#168—21no—
74C3⋊#168—21no—
75C5×C3⋊C8M1612yes—
76C5×C3⋊C8M1612yes—
77C2×C3×C42—51no—
78C22×C3⋊C8—51no—
79C22×C3⋊C8—51no—
80C3×C4⋊C8—52no—
81C3×C22⋊C8—101no—
82C3×#97—101no—
83#830—101no—
84C4⋊(C3⋊C8)—52no—
85#803—101no—
86C4×C3⋊C8—51no—
87C4×C3⋊C8—51no—
88C4×C3⋊C8—51no—
89C4×C3⋊C8AGL(1,𝔽5)11yescharacteristic
90C2×C4×D5Dic611yescharacteristic
91C2×C4×D5C4×D311yescharacteristic
92C2×C4×D5#6711yescharacteristic
93C2×#170—22no—
94C2×#170—62no—
95C2×C5×C8—31no—
96C2×C5×C8—31no—
97C42×C5C4×D311yescharacteristic
98C4×Dic5Dic611yescharacteristic
99C4×Dic5#6711yescharacteristic
100C4×Dic5C22×D311yescharacteristic
101C2×#168—31no—
102C2×#168—31no—
103C8×D5—62no—
104C8×D5—62no—
105#432—51no—
106#432—151no—
107C2×C4×C8—151no—
108#335—152no—
109#334—152no—
110C22×C3×C5C2×C4⋊C411yescharacteristic
111C2×C3×D5—21no—
112C2×C3×D5—21no—
113C2×C3×D5#10812yes—
114C3×C4×C5—21no—
115C3×C4×C5—21no—
116C3×C4×C5C2×M1611yescharacteristic
117C3×C4×C5C2×M1611yescharacteristic
118C3×Dic5—21no—
119C3×Dic5—21no—
120C3×Dic5#13512yes—
121C22×C3×C4—51no—
122C22×C3×C4—51no—
123C22×C3×C4—51no—
124C2×C3×C8—102no—
125C3×C42—51no—
126C3×C42—51no—
127C3×C42—51no—
128C3×C42C2×AGL(1,𝔽5)11yescharacteristic
129C2×C3⋊C8—51no—
130C2×C3⋊C8—51no—
131C2×C3⋊C8—102no—
132C2×C3⋊C8—102no—
133C2×C3⋊C8—102no—
134C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
135C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
136C22×D5Dic3⋊C411yescharacteristic
137C2×C4×C5Dic3⋊C411yescharacteristic
138C2×C4×C5Dic3⋊C411yescharacteristic
139C2×C4×C5C2×C4×D311yescharacteristic
140C2×Dic5Dic3⋊C411yescharacteristic
141C2×Dic5C2×Dic611yescharacteristic
142C2×Dic5C2×#6711yescharacteristic
143C4×D5—22no—
144C4×D5—21no—
145C4×D5—21no—
146C4×D5—22no—
147#170—42no—
148#170—122no—
149C5×C8—32no—
150C5×C8—32no—
151#168—61no—
152#168—61no—
153C22×C8—151no—
154C22×C8—151no—
155C2×C42—51no—
156C4⋊C8—52no—
157C4⋊C8—152no—
158C22⋊C8—101no—
159C22⋊C8—301no—
160#97—101no—
161#97—301no—
162C4×C8—31no—
163C4×C8—151no—
164C4×C8—151no—
165C4×C8—151no—
166C2×C3×C5#42311yescharacteristic
167C2×C3×C5#42711yescharacteristic
168C2×C3×C5C2×#10811yescharacteristic
169C3×D5—22no—
170C23×C3—51no—
171C2×C3×C4—51no—
172C2×C3×C4—51no—
173C2×C3×C4—51no—
174C2×C3×C4—102no—
175C2×C3×C4—102no—
176C2×C3×C4—101no—
177C2×C3×C4—101no—
178C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
179C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
180C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
181C3×C8—202no—
182C3⋊C8—101no—
183C3⋊C8—101no—
184C3⋊C8—202no—
185C3⋊C8#70012yes—
186C3⋊C8#70012yes—
187C22×C5C2×Dic3⋊C411yescharacteristic
188C2×D5—21no—
189C2×D5—21no—
190C2×D5#82212yes—
191C4×C5—21no—
192C4×C5—21no—
193C4×C5D3×M1611yescharacteristic
194C4×C5D3×M1611yescharacteristic
195Dic5—21no—
196Dic5—21no—
197Dic5#95012yes—
198C22×C4—51no—
199C22×C4—51no—
200C22×C4—51no—
201C2×C8—31no—
202C2×C8—31no—
203C2×C8—102no—
204C2×C8—151no—
205C2×C8—151no—
206C2×C8—302no—
207C2×C8—302no—
208C2×C8—302no—
209C42—51no—
210C42—51no—
211C42—51no—
212C42D3×AGL(1,𝔽5)11yescharacteristic
213C3×C5#156811yescharacteristic, complemented, Hall
214C22×C3—52no—
215C22×C3—101no—
216C22×C3—101no—
217C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
218C3×C4—21no—
219C3×C4—21no—
220C3×C4—52no—
221C3×C4—101no—
222C3×C4—101no—
223C3×C4C2×#70011yescharacteristic
224C3×C4C2×#70011yescharacteristic
225C2×C5#499811yescharacteristic
226C2×C5#511811yescharacteristic
227C2×C5C2×#82211yescharacteristic
228D5—22no—
229C23—51no—
230C2×C4—51no—
231C2×C4—51no—
232C2×C4—51no—
233C2×C4—102no—
234C2×C4—102no—
235C2×C4—101no—
236C2×C4—101no—
237C2×C4Dic3⋊AGL(1,𝔽5)11yescharacteristic
238C2×C4Dic3⋊AGL(1,𝔽5)11yescharacteristic
239C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
240C8—32no—
241C8—32no—
242C8—202no—
243C8—301no—
244C8—301no—
245C8—602no—
246C2×C3—102no—
247C2×C3#6568111yescharacteristic
248C2×C3#6572111yescharacteristic
249C2×C3D5⋊#10811yescharacteristic
250C5#7079411yescharacteristic, complemented, Sylow
251C22—52no—
252C22—101no—
253C22—101no—
254C22C2×Dic3⋊AGL(1,𝔽5)11yescharacteristic
255C4—21no—
256C4—21no—
257C4—52no—
258C4—101no—
259C4—101no—
260C4D3×#70011yescharacteristic
261C4D3×#70011yescharacteristic
262C3#1060382011yescharacteristic, complemented, Sylow
263C2—102no—
264C2#1175172611yescharacteristic
265C2D5⋊#82211yescharacteristic
266C2#1175182411yescharacteristic
subgroupG/H
centerC22C2×Dic3⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC22×C3×D5C4⋊C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1568
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
4. #11746514C2semidirect
5. #11746512C2semidirect
213. C3×C5#1568semidirect
250. C5#70794semidirect
262. C3#10603820semidirect

Maximal subgroups

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

subgroupindex
#117523422
C3×#656832
C4×D5×C3⋊C82
#117465142
#117465122
#106038203
#707945