Finite Group Databasebeta

← #14284331

Subgroups — #14284331

Order 1920.

496 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 89 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
1D15×#124C211yesmaximal, characteristic
2#11750806C212yesmaximal, complemented
3C3×C5×#329C211yesmaximal, characteristic, complemented
4#11746361C211yesmaximal, characteristic, complemented
5#11746285C212yesmaximal, complemented
6#10599140—31nomaximal, Hall
7C2×Q8×D15C411yescharacteristic
8C2×D4×D15C411yescharacteristic
9C3×C5×#124C2211yescharacteristic
10#91836C411yescharacteristic
11#91825C411yescharacteristic
12#91774—22no—
13C22⋊C4×D15—22no—
14#91764C2211yescharacteristic
15C42×D15C2211yescharacteristic
16C3×C5×#97C2212yescomplemented
17#91104—22no—
18#91098—22no—
19#91087C2212yescomplemented
20#68347—51nomaximal, Hall
21D5×#124—31no—
22#64994—32no—
23C5×#329D311yescharacteristic, complemented
24#64760—31no—
25#64684—32no—
26C23×D15—21no—
27C2×C3×C5×Q8C2×C411yescharacteristic
28C2×C3×C5×D4C2×C411yescharacteristic
29C2×#1220—21no—
30Q8×D15—42no—
31D4×D15—42no—
32C2×D60C2×C411yescharacteristic
33C2×C4×D15—21no—
34C2×C4×D15C2×C411yescharacteristic
35C2×C4×D15D412yes—
36C2×Dic30—21no—
37C2×Dic30C2×C411yescharacteristic
38C2×C3×C5×C8—22no—
39C3×C5×C22⋊C4—22no—
40C3×C42×C5C2311yescharacteristic
41#6719—22no—
42#6714—22no—
43#6714—22no—
44C4×Dic15C2×C411yescharacteristic
45C4×Dic15D412yes—
46C2×C3⋊#168—22no—
47D3×#124—51no—
48#4705—52no—
49C3×#329D511yescharacteristic, complemented
50#4540—51no—
51#4464—52no—
52C2×Q8×D5—31no—
53C2×D4×D5—31no—
54C5×#124C2×D311yescharacteristic
55#4093—31no—
56#4082—31no—
57#4031—62no—
58D5×C22⋊C4—62no—
59#4021—31no—
60C42×D5—31no—
61C5×#97C2×D312yescomplemented
62#3952—62no—
63#3946—62no—
64#3935—32no—
65#1533—151noSylow
66C23×C3×C5—21no—
67C22×D15—21no—
68C22×D15—44no—
69C22×D15—42no—
70C22×D15C22⋊C411yescharacteristic
71C3×C5×Q8—41no—
72C3×C5×D4—41no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5C22×C411yescharacteristic
75C2×C3×C4×C5C2×D412yes—
76#1220—42no—
77C2×Dic15—21no—
78C2×Dic15C22⋊C412yes—
79C2×Dic15C22⋊C411yescharacteristic
80D60—41no—
81C4×D15—22no—
82C4×D15—42no—
83C4×D15—42no—
84Dic30—42no—
85Dic30—41no—
86C3×C5×C8—42no—
87C3⋊#168—42no—
88C2×D3×Q8—51no—
89C2×D3×D4—51no—
90C3×#124C2×D511yescharacteristic
91#947—51no—
92#936—51no—
93#885—102no—
94D3×C22⋊C4—102no—
95#875—51no—
96C42×D3—51no—
97C3×#97C2×D512yescomplemented
98(C2×D3)⋊C8—102no—
99Dic3⋊C8—102no—
100#803—52no—
101C23×D5—61no—
102C2×C5×Q8C4×D311yescharacteristic
103C2×C5×D4C4×D311yescharacteristic
104C2×C22⋊D5—61no—
105Q8×D5—122no—
106D4×D5—122no—
107C2×D20—31no—
108C2×C4×D5—31no—
109C2×C4×D5—32no—
110C2×C4×D5—61no—
111C2×Dic10—31no—
112C2×Dic10—61no—
113C2×C5×C8—22no—
114C5×C22⋊C4—22no—
115C42×C5C22×D311yescharacteristic
116C22⋊Dic5—62no—
117#685—62no—
118#685—62no—
119C4×Dic5—31no—
120C4×Dic5—32no—
121C2×#168—62no—
122C2×#124—151no—
123#432—152no—
124#329—151no—
125#329—152no—
126#329D1511yescharacteristic, complemented
127C22×C3×C5—41no—
128C22×C3×C5—42no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C2×D15—22no—
131C2×D15—41no—
132C2×D15—42no—
133C2×D15—84no—
134C2×D15#10012yes—
135C3×C4×C5—21no—
136C3×C4×C5—22no—
137C3×C4×C5—41no—
138Dic15—21no—
139Dic15—22no—
140Dic15—41no—
141C23×D3—101no—
142C2×C3×Q8C4×D511yescharacteristic
143C2×C3×D4C4×D511yescharacteristic
144C2×#67—101no—
145D3×Q8—202no—
146D3×D4—202no—
147C2×D12—51no—
148C2×C4×D3—51no—
149C2×C4×D3—52no—
150C2×C4×D3—101no—
151C2×Dic6—51no—
152C2×Dic6—101no—
153C2×C3×C8—22no—
154C3×C22⋊C4—22no—
155C3×C42C22×D511yescharacteristic
156#217—102no—
157(C2×D3)⋊C4—102no—
158(C2×D3)⋊C4—102no—
159C4×Dic3—51no—
160C4×Dic3—52no—
161C2×C3⋊C8—102no—
162C23×C5—21no—
163C22×D5—31no—
164C22×D5—61no—
165C22×D5—122no—
166C22×D5—124no—
167C5×Q8—41no—
168C5×D4—41no—
169C2×C4×C5—21no—
170C2×C4×C5C2×C4×D311yescharacteristic
171C2×C4×C5D3×D412yes—
172C22⋊D5—122no—
173C2×Dic5—32no—
174C2×Dic5—31no—
175C2×Dic5—61no—
176D20—121no—
177C4×D5—62no—
178C4×D5—122no—
179C4×D5—122no—
180Dic10—122no—
181Dic10—121no—
182C5×C8—42no—
183#168—122no—
184C22×Q8—151no—
185C22×D4—151no—
186#124—151no—
187#124—151no—
188#124—151no—
189#124—302no—
190#124C2×D1511yescharacteristic
191C2×C22⋊C4—302no—
192C2×C42—151no—
193C4⋊C8—302no—
194C22⋊C8—302no—
195#97—152no—
196#97C2×D1512yescomplemented
197C2×C3×C5—81no—
198C2×C3×C5C2×#10011yescharacteristic
199C2×C3×C5#42112yes—
200D15—22no—
201D15—81no—
202C23×C3—21no—
203C22×D3—51no—
204C22×D3—101no—
205C22×D3—202no—
206C22×D3—204no—
207C3×Q8—41no—
208C3×D4—41no—
209C2×C3×C4—21no—
210C2×C3×C4C2×C4×D511yescharacteristic
211C2×C3×C4D4×D512yes—
212#67—202no—
213C2×Dic3—52no—
214C2×Dic3—51no—
215C2×Dic3—101no—
216D12—201no—
217C4×D3—102no—
218C4×D3—202no—
219C4×D3—202no—
220Dic6—202no—
221Dic6—201no—
222C3×C8—42no—
223C3⋊C8—202no—
224C22×C5—41no—
225C22×C5—42no—
226C22×C5D3×C22⋊C411yescharacteristic
227C2×D5—32no—
228C2×D5—62no—
229C2×D5—121no—
230C2×D5—122no—
231C2×D5—244no—
232C4×C5—21no—
233C4×C5—22no—
234C4×C5—41no—
235Dic5—61no—
236Dic5—62no—
237Dic5—121no—
238C24—301no—
239C2×Q8—151no—
240C2×Q8—301no—
241C2×Q8—602no—
242C2×Q8C4×D1511yescharacteristic
243C2×D4—151no—
244C2×D4—301no—
245C2×D4—602no—
246C2×D4C4×D1511yescharacteristic
247C22×C4—151no—
248C22×C4—152no—
249C22×C4—301no—
250C2×C8—22no—
251C2×C8—302no—
252C22⋊C4—22no—
253C22⋊C4—302no—
254C22⋊C4—302no—
255C22⋊C4—302no—
256C42—151no—
257C42—152no—
258C42C22×D1511yescharacteristic
259C3×C5#153311yescharacteristic, complemented, Hall
260C22×C3—41no—
261C22×C3—42no—
262C22×C3D5×C22⋊C411yescharacteristic
263C2×D3—52no—
264C2×D3—102no—
265C2×D3—201no—
266C2×D3—202no—
267C2×D3—404no—
268C3×C4—21no—
269C3×C4—22no—
270C3×C4—41no—
271Dic3—101no—
272Dic3—102no—
273Dic3—201no—
274C2×C5—81no—
275C2×C5D3×#10011yescharacteristic
276C2×C5#482112yes—
277D5—62no—
278D5—241no—
279C23—21no—
280C23—151no—
281C23—301no—
282C23—602no—
283C23—604no—
284Q8—41no—
285Q8—601no—
286Q8—602no—
287D4—41no—
288D4—601no—
289D4—602no—
290C2×C4—21no—
291C2×C4—152no—
292C2×C4—151no—
293C2×C4—302no—
294C2×C4—301no—
295C2×C4—602no—
296C2×C4—602no—
297C2×C4C2×C4×D1511yescharacteristic
298C2×C4D4×D1512yes—
299C8—42no—
300C8—602no—
301C2×C3—81no—
302C2×C3D5×#10011yescharacteristic
303C2×C3#6511012yes—
304D3—102no—
305D3—401no—
306C5#6834711yescharacteristic, complemented, Sylow
307C22—42no—
308C22—41no—
309C22—152no—
310C22—302no—
311C22—602no—
312C22—601no—
313C22—1204no—
314C22C22⋊C4×D1511yescharacteristic
315C4—22no—
316C4—21no—
317C4—41no—
318C4—302no—
319C4—301no—
320C4—601no—
321C3#1059914011yescharacteristic, complemented, Sylow
322C2—81no—
323C2—302no—
324C2—1201no—
325C2D15×#10011yescharacteristic
326C2#1175092212yes—
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#329C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×D4×D15C4
cosocleC3×C42×C5C23
hypercenter#329D15
hypocenterC3×C5#1533
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #11750806C2semidirect
3. C3×C5×#329C2semidirect
4. #11746361C2semidirect
5. #11746285C2semidirect
16. C3×C5×#97C22semidirect
19. #91087C22semidirect
23. C5×#329D3semidirect
49. C3×#329D5semidirect
61. C5×#97C2×D3semidirect
97. C3×#97C2×D5semidirect
126. #329D15semidirect
196. #97C2×D15semidirect
259. C3×C5#1533semidirect
306. C5#68347semidirect
321. C3#10599140semidirect

Maximal subgroups

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

subgroupindex
D15×#1242
#117508062
C3×C5×#3292
#117463612
#117462852
#105991403
#683475