Finite Group Databasebeta

← #14317096

Subgroups — #14317096

Order 1920.

348 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 82 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×#91084C211yesmaximal, characteristic, complemented
2#11748005C211yesmaximal, characteristic
3#11747873C211yesmaximal, characteristic, complemented
4C2×#90942C211yesmaximal, characteristic, complemented
5C5×Dic3⋊C16C211yesmaximal, characteristic, complemented
6C3×#64729C211yesmaximal, characteristic, complemented
7#11745895C211yesmaximal, characteristic, complemented
8#10600085—31nomaximal, Hall
9C2×Dic60C2211yescharacteristic
10C2×D120C2211yescharacteristic
11C2×C3×D40C2211yescharacteristic
12#91458—21no—
13#91340—21no—
14C2×#6653—21no—
15C2×C3×C5×C16C2211yescharacteristic
16#91084—22no—
17C5×C8×Dic3C2211yescharacteristic
18C2×C5×C3⋊C16C2211yescharacteristic
19C3×#3950C2211yescharacteristic
20#90974—21no—
21#90942—22no—
22#69204—51nomaximal, Hall
23C2×#3932—31no—
24C2×#3932—31no—
25C4×Dic20—31no—
26#64984—31no—
27C5×C4⋊C16—31no—
28#64729—31no—
29#64729D311yescharacteristic, complemented
30C2×D60—21no—
31C2×Dic30—21no—
32C2×C3×D20—21no—
33C2×#1202—41no—
34C2×#1202—41no—
35C2×C3×C5×C8C2311yescharacteristic
36Dic60—21no—
37Dic60D412yescomplemented
38D120—21no—
39D120—21no—
40C4×C5×Dic3D411yescharacteristic
41C2×C5×C3⋊C8D411yescharacteristic
42C3×C4⋊Dic5—21no—
43C3×D40—21no—
44C3×D40—21no—
45#6669—41no—
46Dic3×Dic5—41no—
47#6653—42no—
48C3×C5×C16—21no—
49C5×C3⋊C16—21no—
50#5151—51no—
51C2×#827—51no—
52C2×#800—51no—
53#4873—51no—
54C3×#357—51no—
55Dic3⋊C16D511yescharacteristic, complemented
56#4491—51no—
57C2×Dic20—31no—
58C2×D40—31no—
59C2×D40—61no—
60C2×D40C2×D311yescharacteristic
61#4020—61no—
62C4×Dic10—61no—
63C2×C5×C16—31no—
64C2×C5×C16C2×D311yescharacteristic
65C4×C5×C8—31no—
66#3950C2×D311yescharacteristic
67#3948—61no—
68#3932—62no—
69#3932—62no—
70#2207—151noSylow
71C22×D15—41no—
72C22×C3×D5—41no—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×Dic15—41no—
75D60—41no—
76D60—41no—
77Dic30—22no—
78Dic30—41no—
79C2×C5×Dic3D811yescharacteristic
80C2×C5×Dic3D811yescharacteristic
81C2×C3×Dic5—41no—
82C3×D20—41no—
83C3×D20—41no—
84#1202—82no—
85#1202—82no—
86C3×C5×C8C2×D411yescharacteristic
87C3×C5×C8#4111yescharacteristic
88C5×C3⋊C8—21no—
89C2×C3×D8—51no—
90#940—101no—
91C2×#213—101no—
92C2×Dic12—51no—
93C2×D24—51no—
94#887—101no—
95C2×C3×C16C2×D511yescharacteristic
96C3×#107—51no—
97#827—102no—
98C8×Dic3C2×D511yescharacteristic
99C2×C3⋊C16C2×D511yescharacteristic
100#810—101no—
101#800—102no—
102C2×D20—21no—
103C2×D20—61no—
104C2×D20—121no—
105C2×D20—121no—
106C2×Dic10—61no—
107C2×C5×C8—31no—
108C2×C5×C8C22×D311yescharacteristic
109C42×C5—31no—
110C4⋊Dic5—21no—
111#683—121no—
112C4×Dic5—121no—
113Dic20—32no—
114Dic20—61no—
115D40—21no—
116D40—21no—
117D40—61no—
118D40—61no—
119D40—122no—
120C5×C16—21no—
121C5×C16—61no—
122C2×SD32—151no—
123C2×SD32—151no—
124#493—151no—
125C4×Q16—151no—
126C4⋊C16—31no—
127#357—51no—
128#357—151no—
129C22×C3×C5C2×D811yescharacteristic
130C2×D15—81no—
131C2×D15—81no—
132C2×D15—81no—
133C2×C3×D5—81no—
134C2×C3×D5—81no—
135C2×C3×D5—81no—
136C3×C4×C5#12111yescharacteristic
137C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
138Dic15—42no—
139C3×Dic5—81no—
140C5×Dic3—21no—
141C5×Dic3SD3212yescomplemented
142C2×C3×D4—101no—
143C2×#67—201no—
144C2×#67—201no—
145C2×D12—101no—
146C2×Dic6—101no—
147C3×D8—101no—
148C3×D8—101no—
149C2×C3×C8C22×D511yescharacteristic
150C3×C4⋊C4—101no—
151#213—202no—
152Dic3⋊C4—201no—
153C4×Dic3—201no—
154C4×Dic3D2011yescharacteristic
155C2×C3⋊C8D2011yescharacteristic
156Dic12—52no—
157Dic12—101no—
158D24—101no—
159D24—101no—
160C3×C16—21no—
161C3⋊C16—21no—
162C22×D5—41no—
163C22×D5—121no—
164C2×C4×C5—31no—
165C2×C4×C5—31no—
166C2×C4×C5D3×D411yescharacteristic
167C2×Dic5—41no—
168C2×Dic5—121no—
169D20—41no—
170D20—41no—
171D20—121no—
172D20—121no—
173D20—242no—
174D20—242no—
175Dic10—62no—
176Dic10—121no—
177C5×C8—61no—
178C5×C8#23511yescharacteristic
179C5×C8D3×D411yescharacteristic
180C2×Q16—151no—
181C2×D8—51no—
182C2×D8—151no—
183C2×D8—301no—
184#127—301no—
185C4×Q8—301no—
186SD32—302no—
187SD32—302no—
188C2×C16—31no—
189C2×C16D3×D511yescharacteristic
190#107—51no—
191#103—301no—
192C4×C8—31no—
193C2×C3×C5#45911yescharacteristic
194C2×C3×C5C2×SD3211yescharacteristic
195C2×C3×C5#50911yescharacteristic
196D15—161no—
197C3×D5—161no—
198C23×C3—201no—
199C22×D3—201no—
200C3×D4—201no—
201C3×D4—201no—
202C2×C3×C4—201no—
203C2×C3×C4C2×D2011yescharacteristic
204#67—402no—
205#67—402no—
206C2×Dic3—201no—
207C2×Dic3D4011yescharacteristic
208C2×Dic3D4011yescharacteristic
209D12—201no—
210D12—201no—
211Dic6—102no—
212Dic6—201no—
213C3×C8D4×D511yescharacteristic
214C3×C8#71311yescharacteristic
215C3⋊C8—21no—
216C22×C5D3×D811yescharacteristic
217C2×D5—81no—
218C2×D5—81no—
219C2×D5—81no—
220C2×D5—241no—
221C2×D5—241no—
222C2×D5—241no—
223C4×C5—32no—
224C4×C5—61no—
225C4×C5#88411yescharacteristic
226C4×C5#91411yescharacteristic
227Dic5—81no—
228Dic5—122no—
229C2×Q8—301no—
230C2×D4—101no—
231C2×D4—301no—
232C2×D4—601no—
233C2×D4—601no—
234Q16—152no—
235Q16—301no—
236D8—101no—
237D8—101no—
238D8—301no—
239D8—301no—
240D8—602no—
241C2×C8—31no—
242C2×C8C2×D3×D511yescharacteristic
243C4⋊C4—101no—
244C4⋊C4—601no—
245C42—31no—
246C42—601no—
247C16—21no—
248C16—61no—
249C3×C5#220711yescharacteristic, complemented, Hall
250C22×C3—401no—
251C22×C3—401no—
252C22×C3—401no—
253C22×C3C2×D4011yescharacteristic
254C2×D3—401no—
255C2×D3—401no—
256C2×D3—401no—
257C3×C4—401no—
258C3×C4#404111yescharacteristic
259C3×C4#405411yescharacteristic
260Dic3—21no—
261Dic3—202no—
262Dic3#393212yescomplemented
263C2×C5#478611yescharacteristic
264C2×C5#491111yescharacteristic
265C2×C5D3×SD3211yescharacteristic
266D5—161no—
267D5—481no—
268C23—201no—
269C23—601no—
270Q8—302no—
271Q8—601no—
272D4—201no—
273D4—201no—
274D4—601no—
275D4—601no—
276D4—1202no—
277D4—1202no—
278C2×C4—31no—
279C2×C4—31no—
280C2×C4—201no—
281C2×C4—601no—
282C2×C4D3×D2011yescharacteristic
283C8—61no—
284C8#677311yescharacteristic
285C8#679011yescharacteristic
286C2×C3—801no—
287C2×C3#6513211yescharacteristic
288C2×C3C2×#393211yescharacteristic
289C2×C3#6519711yescharacteristic
290D3—801no—
291C5#6920411yescharacteristic, complemented, Sylow
292C22—401no—
293C22—401no—
294C22—401no—
295C22—1201no—
296C22—1201no—
297C22—1201no—
298C22D3×D4011yescharacteristic
299C4—32no—
300C4—61no—
301C4—401no—
302C4—602no—
303C4#9125311yescharacteristic
304C4#9145911yescharacteristic
305C3#1060008511yescharacteristic, complemented, Sylow
306C2—801no—
307C2—2401no—
308C2D3×#393211yescharacteristic
309C2#1174682011yescharacteristic
310C2#1174800611yescharacteristic
subgroupG/H
centerC22D3×D40
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×C16C22
socleC22×C3×C5C2×D8
prime radical#11748005C2
hypercenterC2×C16D3×D5
hypocenterC3×C5#2207
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C2×#91084C2semidirect
3. #11747873C2semidirect
4. C2×#90942C2semidirect
5. C5×Dic3⋊C16C2semidirect
6. C3×#64729C2semidirect
7. #11745895C2semidirect
29. #64729D3semidirect
37. Dic60D4semidirect
55. Dic3⋊C16D5semidirect
141. C5×Dic3SD32semidirect
249. C3×C5#2207semidirect
262. Dic3#3932semidirect
291. C5#69204semidirect
305. C3#10600085semidirect

Maximal subgroups

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

subgroupindex
C2×#910842
#117480052
#117478732
C2×#909422
C5×Dic3⋊C162
C3×#647292
#117458952
#106000853
#692045