Finite Group Databasebeta

← #14293814

Subgroups — #14293814

Order 1920.

416 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 94 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
1#11751177C211yesmaximal, characteristic, complemented
2C5×#5073C211yesmaximal, characteristic
3C3×#65359C211yesmaximal, characteristic, complemented
4#11746920C211yesmaximal, characteristic, complemented
5#11746906C211yesmaximal, characteristic, complemented
6#11746901C211yesmaximal, characteristic, complemented
7#11745831C211yesmaximal, characteristic, complemented
8#10602071—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10C2×#6716—22no—
11#91758C2211yescharacteristic
12C2×C5×#213—22no—
13C5×#874C2211yescharacteristic
14C3×#4015C2211yescharacteristic
15C4×C3⋊#168C2211yescharacteristic
16C4×C5×C3⋊C8C2211yescharacteristic
17C3×#3964—22no—
18C3×C4×#168C2211yescharacteristic
19#90971—22no—
20#90967—22no—
21#90966—22no—
22#71187—51nomaximal, Hall
23C5×#493—31no—
24#65365—31no—
25#65359—31no—
26#65359—31no—
27#65359D311yescharacteristic, complemented
28#64970—31no—
29#64674—31no—
30C2×C3×C5×D4—21no—
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4—21no—
33C2×Dic30—21no—
34C2×C5×D12—21no—
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C3×Dic10—21no—
38C3×C42×C5C2311yescharacteristic
39#6716—44no—
40C4⋊Dic15—21no—
41C4⋊Dic15—21no—
42C2×C3⋊#168D412yes—
43C5×#213—44no—
44C2×C5×C3⋊C8D412yes—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C2×C3×#168D412yes—
48C3×#486—51no—
49#5088—51no—
50#5079—51no—
51#5076—51no—
52#5073D511yescharacteristic
53#4694—51no—
54#4455—51no—
55C2×C5×D8—62no—
56C5×#127—31no—
57C5×#127C2×D311yescharacteristic
58C2×#687—62no—
59#4015—31no—
60#4015C2×D311yescharacteristic
61C4×C5×C8—31no—
62#3964—22no—
63#3964—62no—
64#3964—62no—
65#3948—62no—
66C4×#168—31no—
67C4×#168C2×D311yescharacteristic
68#1717—151noSylow
69C23×C3×C5—41no—
70C22×C5×D3—41no—
71C3×C5×D4—42no—
72C3×C5×D4—42no—
73C3×C5×D4—42no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×Dic15—41no—
78Dic30—42no—
79C5×D12—42no—
80C5×D12—42no—
81C5×D12—42no—
82C2×C3×Dic5—41no—
83C3×Dic10—42no—
84C3⋊#168—22no—
85C3×#168—22no—
86C5×C3⋊C8—22no—
87C3×C4⋊Q8—51no—
88C3×#127C2×D511yescharacteristic
89C2×#214—102no—
90C2×#213—22no—
91#874C2×D511yescharacteristic
92#869—51no—
93C3×#102—102no—
94C3×C4×C8—51no—
95#835—102no—
96#821—102no—
97#809—102no—
98C4×C3⋊C8—51no—
99C4×C3⋊C8C2×D511yescharacteristic
100C2×C5×D4—21no—
101C2×C5×D4—21no—
102C2×C5×D4—21no—
103C2×C5×D4—61no—
104C2×C5×D4—61no—
105C2×C5×D4—61no—
106C2×Dic10—21no—
107C2×Dic10—61no—
108C5×D8—124no—
109C2×C5×C8—32no—
110C42×C5C22×D311yescharacteristic
111#687—124no—
112C4⋊Dic5—21no—
113C4⋊Dic5—21no—
114C4⋊Dic5—61no—
115C4⋊Dic5—61no—
116C2×#168—32no—
117C2×#168#6712yes—
118#493—31no—
119#492—151no—
120#487—151no—
121#486—51no—
122#486—151no—
123#486—151no—
124#322—151no—
125C22×C3×C5—81no—
126C22×C3×C5—81no—
127C22×C3×C5—81no—
128C22×C3×C5#12711yescharacteristic
129C2×C5×D3—81no—
130C2×C5×D3—81no—
131C2×C5×D3—81no—
132C3×C4×C5#13512yes—
133C3×C4×C5AGL(1,ℤ/8)12yes—
134C3×C4×C5AGL(1,ℤ/8)12yes—
135Dic15—81no—
136C3×Dic5—81no—
137C2×C3×Q8—101no—
138C2×C3×D4—21no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×D12—21no—
142C2×D12—21no—
143C2×D12—21no—
144C2×Dic6—101no—
145C2×C3×C8—52no—
146C3×C4⋊C4—101no—
147C3×C4⋊C4—101no—
148C3×C42C22×D511yescharacteristic
149#214—204no—
150#213—44no—
151C4⋊Dic3—101no—
152C4⋊Dic3—101no—
153C2×C3⋊C8—52no—
154C2×C3⋊C8C22⋊D512yes—
155C23×C5—41no—
156C23×C5—121no—
157C5×D4—42no—
158C5×D4—42no—
159C5×D4—42no—
160C5×D4—122no—
161C5×D4—122no—
162C5×D4—122no—
163C2×C4×C5D3×D411yescharacteristic
164C2×C4×C5D3×D411yescharacteristic
165C2×C4×C5C2×#6711yescharacteristic
166C2×Dic5—41no—
167C2×Dic5—121no—
168Dic10—42no—
169Dic10—122no—
170C5×C8—62no—
171#168—22no—
172#168—62no—
173C2×SD16—302no—
174C2×D8—62no—
175C4⋊Q8—51no—
176C4⋊Q8—151no—
177#127—31no—
178#127D3×D511yescharacteristic
179#103—302no—
180#102—102no—
181#102—302no—
182#102—302no—
183C4×C8—31no—
184C4×C8—51no—
185C4×C8—151no—
186C2×C3×C5—161no—
187C2×C3×C5#49511yescharacteristic
188C2×C3×C5#49611yescharacteristic
189C2×C3×C5#49611yescharacteristic
190C5×D3—161no—
191C23×C3—41no—
192C22×D3—41no—
193C3×Q8—202no—
194C3×D4—42no—
195C3×D4—42no—
196C3×D4—42no—
197C2×C3×C4—201no—
198C2×C3×C4D4×D511yescharacteristic
199C2×C3×C4D4×D511yescharacteristic
200C2×C3×C4C2×C22⋊D511yescharacteristic
201C2×Dic3—201no—
202D12—42no—
203D12—42no—
204D12—42no—
205Dic6—202no—
206C3×C8—102no—
207C3⋊C8—22no—
208C3⋊C8—102no—
209C22×C5—81no—
210C22×C5—81no—
211C22×C5—81no—
212C22×C5—241no—
213C22×C5—241no—
214C22×C5—241no—
215C22×C5#94011yescharacteristic
216C4×C5#91112yes—
217C4×C5#91412yes—
218C4×C5#95012yes—
219Dic5—81no—
220Dic5—241no—
221C2×Q8—101no—
222C2×Q8—301no—
223C2×D4—21no—
224C2×D4—21no—
225C2×D4—21no—
226C2×D4—61no—
227C2×D4—61no—
228C2×D4—61no—
229SD16—604no—
230D8—124no—
231C2×C8—32no—
232C2×C8—52no—
233C2×C8—152no—
234C4⋊C4—101no—
235C4⋊C4—101no—
236C4⋊C4—301no—
237C4⋊C4—301no—
238C42C2×D3×D511yescharacteristic
239C3×C5#171711yescharacteristic, complemented, Hall
240C22×C3—81no—
241C22×C3—81no—
242C22×C3—81no—
243C22×C3#408611yescharacteristic
244C2×D3—81no—
245C2×D3—81no—
246C2×D3—81no—
247C3×C4—401no—
248C3×C4#405712yes—
249C3×C4#405812yes—
250C3×C4#407812yes—
251Dic3—401no—
252C2×C5—161no—
253C2×C5—481no—
254C2×C5#505911yescharacteristic
255C2×C5#515411yescharacteristic
256C2×C5#517611yescharacteristic
257C23—41no—
258C23—121no—
259Q8—202no—
260Q8—602no—
261D4—42no—
262D4—42no—
263D4—42no—
264D4—122no—
265D4—122no—
266D4—122no—
267C2×C4—201no—
268C2×C4—601no—
269C2×C4D5×#6711yescharacteristic
270C2×C4D3×C22⋊D511yescharacteristic
271C2×C4#679011yescharacteristic
272C8—62no—
273C8—102no—
274C8—302no—
275C2×C3—161no—
276C2×C3#6536311yescharacteristic
277C2×C3#6544311yescharacteristic
278C2×C3#6544411yescharacteristic
279D3—161no—
280C5#7118711yescharacteristic, complemented, Sylow
281C22—81no—
282C22—81no—
283C22—81no—
284C22—241no—
285C22—241no—
286C22—241no—
287C22#9156711yescharacteristic
288C4—401no—
289C4—1201no—
290C4#9149012yes—
291C4#9149412yes—
292C4#9150012yes—
293C3#1060207111yescharacteristic, complemented, Sylow
294C2—161no—
295C2—481no—
296C2#1174906711yescharacteristic
297C2#1174907111yescharacteristic
298C2#1174907711yescharacteristic
subgroupG/H
centerC22#91567
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#127
prime radicalC5×#5073C2
hypercenter#127D3×D5
hypocenterC3×C5#1717
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11751177C2semidirect
3. C3×#65359C2semidirect
4. #11746920C2semidirect
5. #11746906C2semidirect
6. #11746901C2semidirect
7. #11745831C2semidirect
27. #65359D3semidirect
239. C3×C5#1717semidirect
280. C5#71187semidirect
293. C3#10602071semidirect

Maximal subgroups

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

subgroupindex
#117511772
C5×#50732
C3×#653592
#117469202
#117469062
#117469012
#117458312
#106020713
#711875