Finite Group Databasebeta

← #14278116

Subgroups — #14278116

Order 1920.

292 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 54 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#11748761C211yesmaximal, characteristic
2#11746788C211yesmaximal, characteristic
3C3×#64915C211yesmaximal, characteristic
4#10598496—31nomaximal, Hall
5C2×#6763—21no—
6C2×C4⋊Dic15C411yescharacteristic, complemented
7C2×C3×#685C2211yescharacteristic
8C2×#6665—21no—
9C3×C22⋊#170—21no—
10C5×C3⋊#95C411yescharacteristic, complemented
11#90994—21no—
12#67450—51nomaximal, Hall
13#64963—31no—
14#64917—31no—
15#64915D311yescharacteristic
16C23×C3×D5D411yescharacteristic
17C22×ΓL(1,𝔽16)—41no—
18C22×C3×C4×C5C2×C411yescharacteristic
19C22×Dic15—21no—
20C22×C5×Dic3—21no—
21C22×C3×Dic5D411yescharacteristic
22#6763—22no—
23#6763—41no—
24C2×C3×#170—41no—
25C4⋊Dic15—41no—
26C3×#685—41no—
27#6665—41no—
28#6665—41no—
29#4953—51no—
30C3×#323—51no—
31#4526—51no—
32C2×C22⋊AGL(1,𝔽5)—61no—
33C2×#685—61no—
34C2×#685C2×D311yescharacteristic
35C2×C4⋊Dic5—31no—
36C22⋊#170—21no—
37C5×#95—31no—
38#3963—61no—
39#1344—151noSylow
40C23×C3×C5C22⋊C411yescharacteristic
41C22×C3×D5—21no—
42C22×C3×D5—21no—
43C22×C3×D5—41no—
44C22×C3×D5—41no—
45C22×C3×D5D811yescharacteristic
46C22×C3×D5SD1611yescharacteristic
47C2×ΓL(1,𝔽16)—42no—
48C2×ΓL(1,𝔽16)—81no—
49C2×ΓL(1,𝔽16)—81no—
50C2×C3×C4×C5—21no—
51C2×C3×C4×C5—41no—
52C2×Dic15—41no—
53C2×Dic15—41no—
54C2×Dic15—41no—
55C2×C5×Dic3—41no—
56C2×C5×Dic3—41no—
57C2×C5×Dic3—41no—
58C2×C3×Dic5—21no—
59C2×C3×Dic5—41no—
60C3×#170—81no—
61C2×C3×C22⋊C4—51no—
62C2×#217—101no—
63C2×#217—101no—
64C2×C4⋊Dic3—51no—
65C3×C22⋊C8—101no—
66C3⋊#95—101no—
67C3⋊#95AGL(1,𝔽5)11yescharacteristic, complemented
68C23×D5D1211yescharacteristic
69C22×AGL(1,𝔽5)—121no—
70C22×C4×C5—61no—
71C22×C4×C5C4×D311yescharacteristic
72C22×Dic5—61no—
73C22×Dic5#6711yescharacteristic
74C22⋊AGL(1,𝔽5)—62no—
75C22⋊AGL(1,𝔽5)—121no—
76C2×#170—41no—
77#685—41no—
78#685—121no—
79#685—121no—
80C4⋊Dic5—121no—
81#397—151no—
82#342—151no—
83#323—51no—
84C22×C3×C5—21no—
85C22×C3×C5—21no—
86C22×C3×C5#9911yescharacteristic
87C22×C3×C5#10211yescharacteristic
88C22×C3×C5#10411yescharacteristic
89C2×C3×D5—21no—
90C2×C3×D5—21no—
91C2×C3×D5—41no—
92C2×C3×D5—41no—
93C2×C3×D5—41no—
94C2×C3×D5—41no—
95C2×C3×D5—81no—
96ΓL(1,𝔽16)—82no—
97C3×C4×C5—41no—
98Dic15—81no—
99C3×Dic5—41no—
100C5×Dic3—81no—
101C24×C3—51no—
102C22×C3×C4—51no—
103C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
104C22×Dic3—21no—
105C22×Dic3—101no—
106C22×Dic3—201no—
107C2×C3×C8—201no—
108C3×C22⋊C4—201no—
109#217—102no—
110#217—201no—
111#217—201no—
112#217—201no—
113C4⋊Dic3—201no—
114C23×C5(C2×D3)⋊C411yescharacteristic
115C22×D5—21no—
116C22×D5—21no—
117C22×D5—41no—
118C22×D5—41no—
119C22×D5#20411yescharacteristic
120C22×D5D2411yescharacteristic
121C2×AGL(1,𝔽5)—122no—
122C2×AGL(1,𝔽5)—241no—
123C2×AGL(1,𝔽5)—241no—
124C2×C4×C5—21no—
125C2×C4×C5—41no—
126C2×C4×C5—121no—
127C2×C4×C5—121no—
128C2×C4×C5—121no—
129C2×Dic5—21no—
130C2×Dic5—41no—
131C2×Dic5—121no—
132C2×Dic5—121no—
133C2×Dic5—121no—
134#170—81no—
135C2×C4⋊C4—151no—
136C2×C22⋊C4—51no—
137C2×C22⋊C4—301no—
138C2×C22⋊C4—301no—
139C22⋊C8—101no—
140#95—31no—
141#95—301no—
142C2×C3×C5—21no—
143C2×C3×C5—21no—
144C2×C3×C5#32711yescharacteristic
145C2×C3×C5#35211yescharacteristic
146C2×C3×C5#35411yescharacteristic
147C3×D5—41no—
148C3×D5—41no—
149C23×C3—51no—
150C23×C3—51no—
151C23×C3—101no—
152C23×C3—101no—
153C23×C3—201no—
154C23×C3—201no—
155C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
156C2×C3×C4—21no—
157C2×C3×C4—41no—
158C2×C3×C4—101no—
159C2×C3×C4—201no—
160C2×Dic3—41no—
161C2×Dic3—41no—
162C2×Dic3—41no—
163C2×Dic3—202no—
164C2×Dic3—201no—
165C2×Dic3—201no—
166C2×Dic3—201no—
167C2×Dic3—401no—
168C2×Dic3—401no—
169C3×C8—401no—
170C22×C5—21no—
171C22×C5—21no—
172C22×C5#80611yescharacteristic
173C22×C5#82111yescharacteristic
174C22×C5#82511yescharacteristic
175C2×D5—21no—
176C2×D5—21no—
177C2×D5—41no—
178C2×D5—41no—
179C2×D5—41no—
180C2×D5—41no—
181C2×D5—81no—
182AGL(1,𝔽5)—242no—
183C4×C5—41no—
184C4×C5—241no—
185Dic5—41no—
186Dic5—241no—
187C24—51no—
188C22×C4—51no—
189C22×C4—61no—
190C22×C4—301no—
191C22×C4—601no—
192C22×C4D3×AGL(1,𝔽5)11yescharacteristic
193C2×C8—201no—
194C4⋊C4—601no—
195C22⋊C4—201no—
196C22⋊C4—302no—
197C22⋊C4—601no—
198C22⋊C4—601no—
199C22⋊C4—601no—
200C3×C5#134411yescharacteristic, complemented, Hall
201C22×C3—21no—
202C22×C3—21no—
203C22×C3—101no—
204C22×C3—101no—
205C22×C3—201no—
206C22×C3—201no—
207C22×C3—201no—
208C22×C3—201no—
209C22×C3—401no—
210C22×C3#399911yescharacteristic
211C22×C3#400711yescharacteristic
212C22×C3#401011yescharacteristic
213C3×C4—41no—
214C3×C4—201no—
215Dic3—81no—
216Dic3—402no—
217Dic3—401no—
218C2×C5—21no—
219C2×C5—21no—
220C2×C5#447011yescharacteristic
221C2×C5#447311yescharacteristic
222C2×C5#447611yescharacteristic
223D5—41no—
224D5—41no—
225C23—51no—
226C23—51no—
227C23—101no—
228C23—101no—
229C23—201no—
230C23—201no—
231C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—101no—
235C2×C4—121no—
236C2×C4—121no—
237C2×C4—121no—
238C2×C4—201no—
239C2×C4—602no—
240C2×C4—601no—
241C2×C4—601no—
242C2×C4—601no—
243C2×C4—1201no—
244C2×C4—1201no—
245C8—401no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—201no—
249C2×C3—201no—
250C2×C3#6485411yescharacteristic
251C2×C3#6486511yescharacteristic
252C2×C3#6486811yescharacteristic
253C5#6745011yescharacteristic, complemented, Sylow
254C22—21no—
255C22—21no—
256C22—101no—
257C22—101no—
258C22—201no—
259C22—201no—
260C22—201no—
261C22—201no—
262C22—401no—
263C22#9115211yescharacteristic
264C22#9115711yescharacteristic
265C22#9117311yescharacteristic
266C4—41no—
267C4—201no—
268C4—241no—
269C4—1202no—
270C4—1201no—
271C3#1059849611yescharacteristic, complemented, Sylow
272C2—21no—
273C2—21no—
274C2—201no—
275C2—201no—
276C2#1174649911yescharacteristic
277C2#1174655711yescharacteristic
278C2#1174658311yescharacteristic
subgroupG/H
centerC22#91173
commutator, FittingC22×C3×C4×C5C2×C4
Frattini, hypercenterC22×C4D3×AGL(1,𝔽5)
socleC22×C3×C5#99
prime radicalC23×C3×D5D4
cosocleC2×C3×#685C22
hypocenterC3×C5#1344
LCSG ▷ C22×C3×C4×C5 ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. C2×C4⋊Dic15C4semidirect
10. C5×C3⋊#95C4semidirect
67. C3⋊#95AGL(1,𝔽5)semidirect
200. C3×C5#1344semidirect
253. C5#67450semidirect
271. C3#10598496semidirect

Maximal subgroups

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

subgroupindex
#117487612
#117467882
C3×#649152
#105984963
#674505