Finite Group Databasebeta

← #14317199

Subgroups — #14317199

Order 1920.

340 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 83 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×C5×SD32C211yesmaximal, characteristic, complemented
2#11751292C211yesmaximal, characteristic, complemented
3D8×Dic15C211yesmaximal, characteristic, complemented
4C2×#91110C211yesmaximal, characteristic
5#11746385C211yesmaximal, characteristic, complemented
6#11746330C211yesmaximal, characteristic, complemented
7#11746322C211yesmaximal, characteristic, complemented
8#10602270—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10C2×C3×C5×D8C2211yescharacteristic
11#91836—21no—
12C2×#6717—21no—
13D4×Dic15—21no—
14C2×D120C2211yescharacteristic
15C3×C5×SD32—22no—
16C2×C3×C5×C16C2211yescharacteristic
17#91116—21no—
18#91110—22no—
19#91102C2211yescharacteristic
20C8×Dic15C2211yescharacteristic
21C2×C3⋊#672C2211yescharacteristic
22#71477—51nomaximal, Hall
23C2×C5×SD32D311yescharacteristic, complemented
24#65480—31no—
25D8×Dic5—31no—
26C2×#3958—31no—
27#64784—31no—
28#64729—31no—
29#64721—31no—
30C2×C3×C5×Q8—21no—
31C2×C3×C5×D4—21no—
32C22×Dic15—41no—
33C2×D60—21no—
34C3×C5×Q16—21no—
35C3×C5×Q16—21no—
36C3×C5×D8—21no—
37C3×C5×D8D412yes—
38C2×C3×C5×C8C2311yescharacteristic
39#6719—41no—
40#6717—42no—
41#6714—41no—
42#6714—41no—
43C4⋊Dic15—21no—
44C4×Dic15D411yescharacteristic
45C2×C3⋊#168D411yescharacteristic
46D120—21no—
47D120—21no—
48C3×C5×C16—21no—
49C3⋊#672—21no—
50C2×C3×SD32D511yescharacteristic, complemented
51#5191—51no—
52Dic3×D8—51no—
53C2×#826—51no—
54#4564—51no—
55#4509—51no—
56Dic3⋊C16—51no—
57C2×C5×Q16C2×D311yescharacteristic
58C2×C5×D8C2×D311yescharacteristic
59#4093—61no—
60C2×#688—61no—
61D4×Dic5—61no—
62C2×D40—31no—
63C5×SD32—22no—
64C2×C5×C16C2×D311yescharacteristic
65#3964—61no—
66#3958—62no—
67#3950—31no—
68C8×Dic5—31no—
69C2×#672—31no—
70#2210—151noSylow
71C23×C3×C5—41no—
72C22×D15—41no—
73C3×C5×Q8—41no—
74C3×C5×Q8—41no—
75C3×C5×D4—22no—
76C3×C5×D4—41no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×Dic15—41no—
80C2×Dic15—82no—
81C2×Dic15D811yescharacteristic
82C2×Dic15D811yescharacteristic
83D60—41no—
84D60—41no—
85C3×C5×C8C2×D411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C3⋊#168—21no—
88C2×C3×Q16C2×D511yescharacteristic
89C2×C3×D8C2×D511yescharacteristic
90#947—101no—
91C2×#215—101no—
92D4×Dic3—101no—
93C2×D24—51no—
94C3×SD32—22no—
95C2×C3×C16C2×D511yescharacteristic
96#832—101no—
97#826—102no—
98#818—51no—
99C8×Dic3—51no—
100C2×C3⋊C16—51no—
101C2×C5×Q8—21no—
102C2×C5×D4—21no—
103C22×Dic5—121no—
104C2×D20—61no—
105C5×Q16—21no—
106C5×Q16—21no—
107C5×D8—21no—
108C5×D8#6712yes—
109C2×C5×C8C22×D311yescharacteristic
110C22⋊Dic5—121no—
111#688—122no—
112#685—121no—
113#685—121no—
114C4⋊Dic5—61no—
115C4×Dic5—31no—
116C2×#168—31no—
117D40—61no—
118D40—61no—
119C5×C16—21no—
120#672—61no—
121C2×SD32D1511yescharacteristic, complemented
122C2×D16—151no—
123#495—151no—
124C4×D8—151no—
125C4⋊C16—151no—
126#358—151no—
127#357—151no—
128C22×C3×C5—42no—
129C22×C3×C5—81no—
130C22×C3×C5—81no—
131C22×C3×C5C2×D811yescharacteristic
132C2×D15—81no—
133C2×D15—81no—
134C2×D15—81no—
135C3×C4×C5—81no—
136C3×C4×C5#12111yescharacteristic
137C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
138Dic15—21no—
139Dic15—21no—
140Dic15—81no—
141C2×C3×Q8—21no—
142C2×C3×D4—21no—
143C22×Dic3—201no—
144C2×D12—101no—
145C3×Q16—21no—
146C3×Q16—21no—
147C3×D8—21no—
148C3×D8C22⋊D512yes—
149C2×C3×C8C22×D511yescharacteristic
150#217—201no—
151#215—202no—
152(C2×D3)⋊C4—201no—
153(C2×D3)⋊C4—201no—
154C4⋊Dic3—101no—
155C4×Dic3—51no—
156C2×C3⋊C8—51no—
157D24—101no—
158D24—101no—
159C3×C16—21no—
160C3⋊C16—101no—
161C23×C5—41no—
162C22×D5—121no—
163C5×Q8—41no—
164C5×Q8—41no—
165C5×D4—22no—
166C5×D4—41no—
167C2×C4×C5—41no—
168C2×C4×C5D3×D411yescharacteristic
169C2×Dic5—31no—
170C2×Dic5—31no—
171C2×Dic5—121no—
172C2×Dic5—242no—
173D20—121no—
174D20—121no—
175C5×C8#23711yescharacteristic
176C5×C8C2×#6711yescharacteristic
177#168—61no—
178C2×Q16C2×D1511yescharacteristic
179C2×SD16—301no—
180C2×D8—151no—
181C2×D8C2×D1511yescharacteristic
182#124—301no—
183C4×D4—301no—
184SD32—22no—
185D16—302no—
186C2×C16—151no—
187C2×C16C2×D1511yescharacteristic
188#107—151no—
189#102—301no—
190C4×C8—151no—
191C2×C3×C5—82no—
192C2×C3×C5#45911yescharacteristic
193C2×C3×C5#50811yescharacteristic
194C2×C3×C5#50911yescharacteristic
195D15—161no—
196C23×C3—41no—
197C22×D3—201no—
198C3×Q8—41no—
199C3×Q8—41no—
200C3×D4—22no—
201C3×D4—41no—
202C2×C3×C4—41no—
203C2×C3×C4D4×D511yescharacteristic
204C2×Dic3—51no—
205C2×Dic3—51no—
206C2×Dic3—201no—
207C2×Dic3—402no—
208D12—201no—
209D12—201no—
210C3×C8#71111yescharacteristic
211C3×C8C2×C22⋊D511yescharacteristic
212C3⋊C8—101no—
213C22×C5—42no—
214C22×C5—81no—
215C22×C5—81no—
216C22×C5D3×D811yescharacteristic
217C2×D5—241no—
218C2×D5—241no—
219C2×D5—241no—
220C4×C5—81no—
221C4×C5#91111yescharacteristic
222C4×C5#93911yescharacteristic
223Dic5—61no—
224Dic5—61no—
225Dic5—241no—
226C2×Q8—21no—
227C2×D4—21no—
228C2×D4—301no—
229C22×C4—601no—
230Q16—21no—
231Q16—21no—
232SD16—602no—
233D8—21no—
234D8—301no—
235D8—301no—
236D8#122012yes—
237C2×C8—151no—
238C2×C8C22×D1511yescharacteristic
239C4⋊C4—301no—
240C22⋊C4—601no—
241C22⋊C4—601no—
242C22⋊C4—601no—
243C42—151no—
244C16—21no—
245C16—301no—
246C3×C5#221011yescharacteristic, complemented, Hall
247C22×C3—42no—
248C22×C3—81no—
249C22×C3—81no—
250C22×C3D5×D811yescharacteristic
251C2×D3—401no—
252C2×D3—401no—
253C2×D3—401no—
254C3×C4—81no—
255C3×C4#405711yescharacteristic
256C3×C4#408511yescharacteristic
257Dic3—101no—
258Dic3—101no—
259Dic3—401no—
260C2×C5—82no—
261C2×C5#491411yescharacteristic
262C2×C5#491611yescharacteristic
263C2×C5#515011yescharacteristic
264D5—481no—
265C23—41no—
266C23—601no—
267Q8—41no—
268Q8—41no—
269D4—22no—
270D4—41no—
271D4—601no—
272D4—601no—
273C2×C4—41no—
274C2×C4—151no—
275C2×C4—151no—
276C2×C4—601no—
277C2×C4—1202no—
278C2×C4D4×D1511yescharacteristic
279C8—301no—
280C8#681911yescharacteristic
281C8C2×#122011yescharacteristic
282C2×C3—82no—
283C2×C3#6520311yescharacteristic
284C2×C3#6520511yescharacteristic
285C2×C3#6543911yescharacteristic
286D3—801no—
287C5#7147711yescharacteristic, complemented, Sylow
288C22—42no—
289C22—81no—
290C22—81no—
291C22—1201no—
292C22—1201no—
293C22—1201no—
294C22D8×D1511yescharacteristic
295C4—81no—
296C4—301no—
297C4—301no—
298C4—1201no—
299C4#9180011yescharacteristic
300C4#9182811yescharacteristic
301C3#1060227011yescharacteristic, complemented, Sylow
302C2—82no—
303C2—2401no—
304C2#1175101511yescharacteristic
305C2#1175101711yescharacteristic
306C2#1175125111yescharacteristic
subgroupG/H
centerC22D8×D15
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC2×C3×C5×SD32C2
socleC22×C3×C5C2×D8
prime radicalC2×#91110C2
hypercenterC2×SD32D15
hypocenterC3×C5#2210
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×SD32C2semidirect
2. #11751292C2semidirect
3. D8×Dic15C2semidirect
5. #11746385C2semidirect
6. #11746330C2semidirect
7. #11746322C2semidirect
23. C2×C5×SD32D3semidirect
50. C2×C3×SD32D5semidirect
121. C2×SD32D15semidirect
246. C3×C5#2210semidirect
287. C5#71477semidirect
301. C3#10602270semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×SD322
#117512922
D8×Dic152
C2×#911102
#117463852
#117463302
#117463222
#106022703
#714775