Finite Group Databasebeta

← #14298416

Subgroups — #14298416

Order 1920.

544 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 140 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×C3×#4038C211yesmaximal, characteristic
2#11748341C212yesmaximal
3#11746351C211yesmaximal, characteristic, complemented
4C5×#4530C211yesmaximal, characteristic, complemented
5#11745985C212yesmaximal, complemented
6#10599784—31nomaximal, Hall
7C22×C3×C4×D5C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×#6710C2212yes—
10C2×C5×#208C2212yes—
11C2×C3×#685C412yes—
12C2×C3×C4⋊Dic5C2211yescharacteristic
13C2×C3×C4×Dic5C412yes—
14C3×#4038—24no—
15#90955—24no—
16#71589—51nomaximal, Hall
17C2×#4038D311yescharacteristic
18#65415—32no—
19C5×#343—31no—
20#64774—32no—
21#64750—31no—
22C23×C3×D5C2×C411yescharacteristic
23C22×C3×C4×C5C2×C412yes—
24C22×C3×C4×C5C2311yescharacteristic
25C22×C3×Dic5C2×C411yescharacteristic
26C22×C3×Dic5C2×C412yes—
27C2×C3×C4×D5—22no—
28C2×C3×C4×D5—21no—
29C2×C3×C4×D5—21no—
30C2×C3×C4×D5D414yes—
31C3×C5×C4⋊C4—22no—
32#6710—22no—
33#6710—22no—
34C2×C3⋊#168—22no—
35C5×#208—22no—
36C5×#208—22no—
37C2×C5×C3⋊C8—22no—
38C3×#685—24no—
39C3×C4⋊Dic5—22no—
40C3×C4×Dic5—24no—
41C2×C3×#117—51no—
42#5207—52no—
43#4530—51no—
44#4530—52no—
45#4530D511yescharacteristic, complemented
46C22×C4×D5C2×D311yescharacteristic
47C2×C5×M16—32no—
48C2×C5×C4⋊C4C2×D311yescharacteristic
49C2×#685Dic312yes—
50C2×C4⋊Dic5C2×D311yescharacteristic
51C2×C4×Dic5Dic312yes—
52C2×#681—32no—
53#4038—24no—
54#3952—64no—
55#1822—151noSylow
56C23×C3×C5C22×C411yescharacteristic
57C22×C3×D5—21no—
58C22×C3×D5—21no—
59C22×C3×D5—41no—
60C22×C3×D5—41no—
61C22×C3×D5C22⋊C412yes—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×C3×C4×C5C2×D412yes—
65C2×C3×C4×C5#4112yes—
66C2×C3×C4×C5#4111yescharacteristic
67C2×C3×C4×C5#4111yescharacteristic
68C2×C3×Dic5—21no—
69C2×C3×Dic5—21no—
70C2×C3×Dic5—22no—
71C2×C3×Dic5—42no—
72C2×C3×Dic5C22⋊C412yes—
73C3×C4×D5—24no—
74C3×C4×D5—24no—
75C3⋊#168—42no—
76C5×C3⋊C8—42no—
77C23×C3×C4—51no—
78C3×#117—104no—
79C2×C3×C4⋊C4—51no—
80C2×C3×C4⋊C4C2×D511yescharacteristic
81C2×C3×C22⋊C4—52no—
82C2×C3×C42—52no—
83C2×#208—52no—
84C2×#208C2×D512yes—
85#830—104no—
86C23×D5C2×Dic311yescharacteristic
87C22×C4×C5C2×Dic312yes—
88C22×C4×C5C22×D311yescharacteristic
89C22×Dic5C2×Dic311yescharacteristic
90C22×Dic5C2×Dic312yes—
91C2×C4×D5—22no—
92C2×C4×D5—21no—
93C2×C4×D5—21no—
94C2×C4×D5#6714yes—
95C5×M16—62no—
96C5×M16—62no—
97C2×C5×C8—62no—
98C5×C4⋊C4—22no—
99#685—24no—
100C4⋊Dic5—22no—
101C4×Dic5—24no—
102#681—62no—
103#681—62no—
104C2×#168—62no—
105C2×#117—51no—
106#407—152no—
107#343—31no—
108#343—152no—
109#343—151no—
110C22×C3×C5—21no—
111C22×C3×C5—21no—
112C22×C3×C5C2×C22⋊C411yescharacteristic
113C22×C3×C5#11711yescharacteristic
114C22×C3×C5#11711yescharacteristic
115C2×C3×D5—22no—
116C2×C3×D5—22no—
117C2×C3×D5—22no—
118C2×C3×D5—42no—
119C2×C3×D5—42no—
120C3×C4×C5—42no—
121C3×C4×C5#12312yes—
122C3×C4×C5#12312yes—
123C3×Dic5—22no—
124C3×Dic5—42no—
125C24×C3—51no—
126C22×C3×C4—51no—
127C22×C3×C4—54no—
128C22×C3×C4—52no—
129C22×C3×C4—102no—
130C22×C3×C4—101no—
131C22×C3×C4—101no—
132C22×C3×C4C4×D512yes—
133C22×C3×C4C22×D511yescharacteristic
134C3×C4⋊C4—22no—
135C3×C4⋊C4—102no—
136C3×C22⋊C4—104no—
137C3×C42—104no—
138#208—22no—
139#208—22no—
140#208—102no—
141#208—102no—
142C2×C3⋊C8—22no—
143C2×C3⋊C8—102no—
144C23×C5C22×Dic311yescharacteristic
145C22×D5—21no—
146C22×D5—21no—
147C22×D5—41no—
148C22×D5—41no—
149C22×D5#21712yes—
150C2×C4×C5—22no—
151C2×C4×C5—42no—
152C2×C4×C5#23512yes—
153C2×C4×C5#23511yescharacteristic
154C2×C4×C5#23511yescharacteristic
155C2×C4×C5C2×#6712yes—
156C2×Dic5—21no—
157C2×Dic5—21no—
158C2×Dic5—22no—
159C2×Dic5—42no—
160C2×Dic5#21712yes—
161C4×D5—24no—
162C4×D5—24no—
163C5×C8—122no—
164#168—122no—
165C23×C4—51no—
166C2×M16—32no—
167C2×M16—152no—
168#117—104no—
169C2×C4⋊C4—51no—
170C2×C4⋊C4D3×D511yescharacteristic
171C2×C22⋊C4—52no—
172C2×C42—52no—
173C22⋊C8—304no—
174C2×C3×C5—21no—
175C2×C3×C5—21no—
176C2×C3×C5#38111yescharacteristic
177C2×C3×C5#41311yescharacteristic
178C2×C3×C5#41311yescharacteristic
179C3×D5—42no—
180C23×C3—52no—
181C23×C3—101no—
182C23×C3—101no—
183C23×C3—201no—
184C23×C3—201no—
185C23×C3C2×C4×D511yescharacteristic
186C2×C3×C4—22no—
187C2×C3×C4—42no—
188C2×C3×C4—52no—
189C2×C3×C4—101no—
190C2×C3×C4—101no—
191C2×C3×C4—104no—
192C2×C3×C4—104no—
193C2×C3×C4—102no—
194C2×C3×C4—202no—
195C2×C3×C4#70912yes—
196C2×C3×C4D4×D512yes—
197C2×C3×C4#71111yescharacteristic
198C2×C3×C4#71311yescharacteristic
199C3⋊C8—42no—
200C3⋊C8—202no—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5#92611yescharacteristic
204C22×C5#92611yescharacteristic
205C22×C5C2×#21711yescharacteristic
206C2×D5—22no—
207C2×D5—22no—
208C2×D5—22no—
209C2×D5—42no—
210C2×D5—42no—
211C4×C5—42no—
212C4×C5#92912yes—
213C4×C5#92912yes—
214Dic5—22no—
215Dic5—42no—
216C24—51no—
217C22×C4—51no—
218C22×C4—54no—
219C22×C4—52no—
220C22×C4—102no—
221C22×C4—101no—
222C22×C4—101no—
223C22×C4D5×Dic312yes—
224C22×C4C2×D3×D511yescharacteristic
225M16—62no—
226M16—62no—
227M16—302no—
228M16—302no—
229C2×C8—62no—
230C2×C8—302no—
231C4⋊C4—22no—
232C4⋊C4—102no—
233C22⋊C4—104no—
234C42—104no—
235C3×C5#182211yescharacteristic, complemented, Hall
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—102no—
239C22×C3—102no—
240C22×C3—102no—
241C22×C3—202no—
242C22×C3—202no—
243C22×C3#401811yescharacteristic
244C22×C3D5×C22⋊C411yescharacteristic
245C22×C3#403811yescharacteristic
246C3×C4—42no—
247C3×C4—102no—
248C3×C4—202no—
249C3×C4#402912yes—
250C3×C4#404012yes—
251C2×C5—21no—
252C2×C5—21no—
253C2×C5#521111yescharacteristic
254C2×C5#523711yescharacteristic
255C2×C5#523711yescharacteristic
256D5—42no—
257C23—52no—
258C23—101no—
259C23—101no—
260C23—201no—
261C23—201no—
262C23C2×D5×Dic311yescharacteristic
263C2×C4—22no—
264C2×C4—42no—
265C2×C4—52no—
266C2×C4—101no—
267C2×C4—101no—
268C2×C4—104no—
269C2×C4—104no—
270C2×C4—102no—
271C2×C4—202no—
272C2×C4#677112yes—
273C2×C4#677211yescharacteristic
274C2×C4#677311yescharacteristic
275C2×C4D5×#6712yes—
276C8—122no—
277C8—602no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—202no—
281C2×C3#6495311yescharacteristic
282C2×C3#6503411yescharacteristic
283C2×C3#6504011yescharacteristic
284C5#7158911yescharacteristic, complemented, Sylow
285C22—21no—
286C22—21no—
287C22—102no—
288C22—102no—
289C22—102no—
290C22—202no—
291C22—202no—
292C22#9135711yescharacteristic
293C22#9135811yescharacteristic
294C22D5×#21711yescharacteristic
295C4—42no—
296C4—102no—
297C4—202no—
298C4#9134812yes—
299C4#9144712yes—
300C3#1059978411yescharacteristic, complemented, Sylow
301C2—21no—
302C2—21no—
303C2—202no—
304C2#1174873711yescharacteristic
305C2#1174912311yescharacteristic
306C2#1174936911yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1822
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #11746351C2semidirect
4. C5×#4530C2semidirect
5. #11745985C2semidirect
45. #4530D5semidirect
235. C3×C5#1822semidirect
284. C5#71589semidirect
300. C3#10599784semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40382
#117483412
#117463512
C5×#45302
#117459852
#105997843
#715895