Finite Group Databasebeta

← #14278265

Subgroups — #14278265

Order 1920.

324 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C3×#64962C211yesmaximal, characteristic
2#11746788C211yesmaximal, characteristic
3#11746786C211yesmaximal, characteristic
4#10598497—31nomaximal, Hall
5C22×C3×Dic10C411yescharacteristic, complemented
6C2×#6763—21no—
7C2×C3×#685—21no—
8C2×C3×#685C2211yescharacteristic
9#91241—21no—
10C3×C5×#95C411yescharacteristic, complemented
11C3×#3963—21no—
12#67646—51nomaximal, Hall
13#64962D311yescharacteristic
14#64917—31no—
15#64915—31no—
16C23×C3×D5D411yescharacteristic
17C22×ΓL(1,𝔽16)—41no—
18C22×C3×C4×C5—21no—
19C22×C3×C4×C5C2×C411yescharacteristic
20C22×C3×Dic5—21no—
21C22×C3×Dic5D411yescharacteristic
22C2×C3×Dic10—41no—
23C2×C3×Dic10—42no—
24#6763—22no—
25#6763—41no—
26C2×C3⋊#170—41no—
27C3×#685—41no—
28C3×#685—42no—
29C3×#393—51no—
30#4526—51no—
31#4525—51no—
32C22×Dic10Dic311yescharacteristic, complemented
33C2×C22⋊AGL(1,𝔽5)—61no—
34C2×#685—21no—
35C2×#685C2×D311yescharacteristic
36C22⋊#170—61no—
37C5×#95Dic311yescharacteristic, complemented
38#3963—21no—
39#1351—151noSylow
40C23×C3×C5C22⋊C411yescharacteristic
41C22×C3×D5—21no—
42C22×C3×D5—21no—
43C22×C3×D5—41no—
44C22×C3×D5—41no—
45C22×C3×D5SD1611yescharacteristic
46C22×C3×D5Q1611yescharacteristic
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×C3×C4×C5—41no—
53C2×C3×C4×C5—41no—
54C2×C3×C4×C5—41no—
55C2×C3×Dic5—22no—
56C2×C3×Dic5—21no—
57C2×C3×Dic5—41no—
58C2×C3×Dic5—41no—
59C2×C3×Dic5—41no—
60C3×Dic10—42no—
61C3×Dic10—42no—
62C3⋊#170—81no—
63C22×C3×Q8—51no—
64C2×C3×C22⋊C4—51no—
65C2×C3×C22⋊C4—101no—
66C2×#217—101no—
67C3×#95—101no—
68C3×#95AGL(1,𝔽5)11yescharacteristic, complemented
69#830—101no—
70C23×D5#6711yescharacteristic
71C22×AGL(1,𝔽5)—121no—
72C22×C4×C5—21no—
73C22×C4×C5C2×Dic311yescharacteristic
74C22×Dic5—21no—
75C22×Dic5#6711yescharacteristic
76C2×Dic10—41no—
77C2×Dic10—42no—
78C22⋊AGL(1,𝔽5)—62no—
79C22⋊AGL(1,𝔽5)—121no—
80C2×#170—121no—
81#685—41no—
82#685—42no—
83#393—51no—
84#342—151no—
85#323—151no—
86C22×C3×C5—21no—
87C22×C3×C5—21no—
88C22×C3×C5#9911yescharacteristic
89C22×C3×C5#10311yescharacteristic
90C22×C3×C5#10411yescharacteristic
91C2×C3×D5—21no—
92C2×C3×D5—21no—
93C2×C3×D5—41no—
94C2×C3×D5—41no—
95C2×C3×D5—41no—
96C2×C3×D5—41no—
97C2×C3×D5—81no—
98ΓL(1,𝔽16)—82no—
99C3×C4×C5—41no—
100C3×C4×C5—81no—
101C3×Dic5—42no—
102C3×Dic5—41no—
103C24×C3—51no—
104C2×C3×Q8—201no—
105C2×C3×Q8—202no—
106C22×C3×C4—21no—
107C22×C3×C4—51no—
108C22×C3×C4—101no—
109C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
110C22×Dic3—201no—
111C3×C22⋊C4—201no—
112C3×C22⋊C4—202no—
113#217—102no—
114#217—201no—
115C2×C3⋊C8—201no—
116C23×C5#21711yescharacteristic
117C22×D5—21no—
118C22×D5—21no—
119C22×D5—41no—
120C22×D5—41no—
121C22×D5#21511yescharacteristic
122C22×D5#21611yescharacteristic
123C2×AGL(1,𝔽5)—122no—
124C2×AGL(1,𝔽5)—241no—
125C2×AGL(1,𝔽5)—241no—
126C2×C4×C5—21no—
127C2×C4×C5—41no—
128C2×C4×C5—41no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×Dic5—22no—
132C2×Dic5—21no—
133C2×Dic5—41no—
134C2×Dic5—41no—
135C2×Dic5—41no—
136Dic10—42no—
137Dic10—42no—
138#170—241no—
139C22×Q8—51no—
140C2×C22⋊C4—51no—
141C2×C22⋊C4—101no—
142C2×C22⋊C4—301no—
143C22⋊C8—301no—
144#95—101no—
145#95ΓL(1,𝔽16)11yescharacteristic, complemented
146C2×C3×C5—21no—
147C2×C3×C5—21no—
148C2×C3×C5#32811yescharacteristic
149C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
150C2×C3×C5#35411yescharacteristic
151C3×D5—41no—
152C3×D5—41no—
153C23×C3—51no—
154C23×C3—51no—
155C23×C3—101no—
156C23×C3—101no—
157C23×C3—201no—
158C23×C3—201no—
159C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
160C3×Q8—202no—
161C3×Q8—202no—
162C2×C3×C4—21no—
163C2×C3×C4—41no—
164C2×C3×C4—41no—
165C2×C3×C4—41no—
166C2×C3×C4—41no—
167C2×C3×C4—102no—
168C2×C3×C4—101no—
169C2×C3×C4—201no—
170C2×C3×C4—201no—
171C2×C3×C4—201no—
172C2×Dic3—202no—
173C2×Dic3—401no—
174C2×Dic3—401no—
175C3⋊C8—401no—
176C22×C5—21no—
177C22×C5—21no—
178C22×C5#83411yescharacteristic
179C22×C5#83511yescharacteristic
180C22×C5#83711yescharacteristic
181C2×D5—21no—
182C2×D5—21no—
183C2×D5—41no—
184C2×D5—41no—
185C2×D5—41no—
186C2×D5—41no—
187C2×D5—81no—
188AGL(1,𝔽5)—242no—
189C4×C5—41no—
190C4×C5—81no—
191Dic5—42no—
192Dic5—41no—
193C24—51no—
194C2×Q8—201no—
195C2×Q8—202no—
196C22×C4—21no—
197C22×C4—51no—
198C22×C4—101no—
199C22×C4—601no—
200C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
201C2×C8—601no—
202C22⋊C4—201no—
203C22⋊C4—202no—
204C22⋊C4—302no—
205C22⋊C4—601no—
206C3×C5#135111yescharacteristic, complemented, Hall
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—101no—
210C22×C3—101no—
211C22×C3—201no—
212C22×C3—201no—
213C22×C3—201no—
214C22×C3—201no—
215C22×C3—401no—
216C22×C3#399911yescharacteristic
217C22×C3#400811yescharacteristic
218C22×C3#400911yescharacteristic
219C3×C4—41no—
220C3×C4—81no—
221C3×C4—201no—
222C3×C4—202no—
223Dic3—402no—
224C2×C5—21no—
225C2×C5—21no—
226C2×C5#453611yescharacteristic
227C2×C5#453811yescharacteristic
228C2×C5#454111yescharacteristic
229D5—41no—
230D5—41no—
231C23—51no—
232C23—51no—
233C23—101no—
234C23—101no—
235C23—201no—
236C23—201no—
237C23#676311yescharacteristic
238Q8—202no—
239Q8—202no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—102no—
246C2×C4—101no—
247C2×C4—201no—
248C2×C4—201no—
249C2×C4—201no—
250C2×C4—602no—
251C2×C4—1201no—
252C2×C4—1201no—
253C8—1201no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—201no—
257C2×C3—201no—
258C2×C3#6485411yescharacteristic
259C2×C3#6486411yescharacteristic
260C2×C3#6486911yescharacteristic
261C5#6764611yescharacteristic, complemented, Sylow
262C22—21no—
263C22—21no—
264C22—101no—
265C22—101no—
266C22—201no—
267C22—201no—
268C22—201no—
269C22—201no—
270C22—401no—
271C22#9122811yescharacteristic
272C22#9123711yescharacteristic
273C22#9123811yescharacteristic
274C4—41no—
275C4—81no—
276C4—201no—
277C4—202no—
278C4—1202no—
279C3#1059849711yescharacteristic, complemented, Sylow
280C2—21no—
281C2—21no—
282C2—201no—
283C2—201no—
284C2#1174672511yescharacteristic
285C2#1174673511yescharacteristic
286C2#1174674011yescharacteristic
subgroupG/H
centerC22#91228
commutatorC22×C3×C4×C5C2×C4
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC3×C5×#95C4
socleC22×C3×C5#99
prime radicalC23×C3×D5D4
cosocleC2×C3×#685C22
hypercenter#95ΓL(1,𝔽16)
hypocenterC3×C5#1351
LCSG ▷ C22×C3×C4×C5 ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
5. C22×C3×Dic10C4semidirect
10. C3×C5×#95C4semidirect
32. C22×Dic10Dic3semidirect
37. C5×#95Dic3semidirect
68. C3×#95AGL(1,𝔽5)semidirect
145. #95ΓL(1,𝔽16)semidirect
206. C3×C5#1351semidirect
261. C5#67646semidirect
279. C3#10598497semidirect

Maximal subgroups

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

subgroupindex
C3×#649622
#117467882
#117467862
#105984973
#676465