Finite Group Databasebeta

← #14293806

Subgroups — #14293806

Order 1920.

416 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C3×C5×#486C211yesmaximal, characteristic, complemented
2#11751189C211yesmaximal, characteristic, complemented
3#11751180C211yesmaximal, characteristic, complemented
4#11751174C211yesmaximal, characteristic
5#11751171C211yesmaximal, characteristic, complemented
6#11750794C211yesmaximal, characteristic, complemented
7#11746275C211yesmaximal, characteristic, complemented
8#10601979—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#127C2211yescharacteristic
11C2×#6715—22no—
12C2×#6706—22no—
13#91763C2211yescharacteristic
14#91758C2211yescharacteristic
15C3×C5×#102—22no—
16C3×C4×C5×C8C2211yescharacteristic
17#91119—22no—
18#91116—22no—
19#91093—22no—
20C4×C3⋊#168C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22#71186—51nomaximal, Hall
23C5×#486D311yescharacteristic, complemented
24#65377—31no—
25#65370—31no—
26#65362—31no—
27#65359—31no—
28#64982—31no—
29#64674—31no—
30C2×C3×C5×Q8—21no—
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×D60—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×Dic30—21no—
38C2×C3×C5×C8D412yes—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42#6715—44no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C2×C3⋊#168D412yes—
46C2×C3⋊#168D412yes—
47#6706—44no—
48C3×#486D511yescharacteristic, complemented
49#5088—51no—
50#5079—51no—
51#5073—51no—
52#5070—51no—
53#4693—51no—
54#4454—51no—
55C5×C4⋊Q8C2×D311yescharacteristic
56C5×#127C2×D311yescharacteristic
57C2×#686—62no—
58C2×#677—62no—
59#4020—31no—
60#4015—31no—
61C5×#102—22no—
62C4×C5×C8C2×D311yescharacteristic
63#3967—62no—
64#3964—62no—
65#3941—62no—
66C4×#168—31no—
67C4×#168—31no—
68#1717—151noSylow
69C23×C3×C5—41no—
70C22×D15—41no—
71C3×C5×Q8—42no—
72C3×C5×D4—42no—
73C3×C5×D4—42no—
74C3×C5×D4—42no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×Dic15—41no—
80D60—42no—
81D60—42no—
82D60—42no—
83Dic30—42no—
84C3×C5×C8—22no—
85C3⋊#168—22no—
86C3⋊#168—22no—
87C3×C4⋊Q8C2×D511yescharacteristic
88C3×#127C2×D511yescharacteristic
89C2×#213—102no—
90C2×#204—102no—
91#874—51no—
92#869—51no—
93C3×#102—22no—
94C3×C4×C8C2×D511yescharacteristic
95#835—102no—
96#832—102no—
97#809—102no—
98C4×C3⋊C8—51no—
99C4×C3⋊C8—51no—
100C2×C5×Q8—21no—
101C2×C5×D4—21no—
102C2×C5×D4—21no—
103C2×C5×D4—21no—
104C2×D20—61no—
105C2×D20—61no—
106C2×D20—61no—
107C2×Dic10—61no—
108C2×C5×C8#6712yes—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C42×C5C22×D311yescharacteristic
112#686—124no—
113C4⋊Dic5—61no—
114C4⋊Dic5—61no—
115C2×#168—32no—
116C2×#168—32no—
117#677—124no—
118#493—151no—
119#492—151no—
120#487—151no—
121#486—151no—
122#486—151no—
123#486D1511yescharacteristic, complemented
124#322—151no—
125C22×C3×C5—81no—
126C22×C3×C5—81no—
127C22×C3×C5—81no—
128C22×C3×C5#12711yescharacteristic
129C2×D15—81no—
130C2×D15—81no—
131C2×D15—81no—
132C3×C4×C5—81no—
133C3×C4×C5#13512yes—
134C3×C4×C5AGL(1,ℤ/8)12yes—
135C3×C4×C5AGL(1,ℤ/8)12yes—
136Dic15—81no—
137C2×C3×Q8—21no—
138C2×C3×D4—21no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×D12—101no—
142C2×D12—101no—
143C2×D12—101no—
144C2×Dic6—101no—
145C2×C3×C8C22⋊D512yes—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C42C22×D511yescharacteristic
149#213—204no—
150C4⋊Dic3—101no—
151C4⋊Dic3—101no—
152C2×C3⋊C8—52no—
153C2×C3⋊C8—52no—
154#204—204no—
155C23×C5—41no—
156C22×D5—121no—
157C5×Q8—42no—
158C5×D4—42no—
159C5×D4—42no—
160C5×D4—42no—
161C2×C4×C5—41no—
162C2×C4×C5D3×D411yescharacteristic
163C2×C4×C5D3×D411yescharacteristic
164C2×C4×C5C2×#6711yescharacteristic
165C2×Dic5—121no—
166D20—122no—
167D20—122no—
168D20—122no—
169Dic10—122no—
170C5×C8—22no—
171#168—62no—
172#168—62no—
173C2×SD16—302no—
174C2×D8—302no—
175C4⋊Q8—151no—
176C4⋊Q8C2×D1511yescharacteristic
177#127—151no—
178#127C2×D1511yescharacteristic
179#103—302no—
180#102—22no—
181#102—302no—
182#102—302no—
183C4×C8—151no—
184C4×C8—151no—
185C4×C8C2×D1511yescharacteristic
186C2×C3×C5—161no—
187C2×C3×C5#49511yescharacteristic
188C2×C3×C5#49611yescharacteristic
189C2×C3×C5#49611yescharacteristic
190D15—161no—
191C23×C3—41no—
192C22×D3—201no—
193C3×Q8—42no—
194C3×D4—42no—
195C3×D4—42no—
196C3×D4—42no—
197C2×C3×C4—41no—
198C2×C3×C4D4×D511yescharacteristic
199C2×C3×C4D4×D511yescharacteristic
200C2×C3×C4C2×C22⋊D511yescharacteristic
201C2×Dic3—201no—
202D12—202no—
203D12—202no—
204D12—202no—
205Dic6—202no—
206C3×C8—22no—
207C3⋊C8—102no—
208C3⋊C8—102no—
209C22×C5—81no—
210C22×C5—81no—
211C22×C5—81no—
212C22×C5#94011yescharacteristic
213C2×D5—241no—
214C2×D5—241no—
215C2×D5—241no—
216C4×C5—81no—
217C4×C5#91112yes—
218C4×C5#91612yes—
219C4×C5#94912yes—
220Dic5—241no—
221C2×Q8—21no—
222C2×Q8—301no—
223C2×D4—21no—
224C2×D4—21no—
225C2×D4—21no—
226C2×D4—301no—
227C2×D4—301no—
228C2×D4—301no—
229SD16—604no—
230D8—604no—
231C2×C8—152no—
232C2×C8—152no—
233C2×C8#122012yes—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—301no—
237C4⋊C4—301no—
238C42C22×D1511yescharacteristic
239C3×C5#171711yescharacteristic, complemented, Hall
240C22×C3—81no—
241C22×C3—81no—
242C22×C3—81no—
243C22×C3#408611yescharacteristic
244C2×D3—401no—
245C2×D3—401no—
246C2×D3—401no—
247C3×C4—81no—
248C3×C4#405712yes—
249C3×C4#406212yes—
250C3×C4#409512yes—
251Dic3—401no—
252C2×C5—161no—
253C2×C5#505811yescharacteristic
254C2×C5#515411yescharacteristic
255C2×C5#516811yescharacteristic
256D5—481no—
257C23—41no—
258C23—601no—
259Q8—42no—
260Q8—602no—
261D4—42no—
262D4—42no—
263D4—42no—
264D4—602no—
265D4—602no—
266D4—602no—
267C2×C4—41no—
268C2×C4—601no—
269C2×C4D4×D1511yescharacteristic
270C2×C4D4×D1511yescharacteristic
271C2×C4C2×#122011yescharacteristic
272C8—22no—
273C8—302no—
274C8—302no—
275C2×C3—161no—
276C2×C3#6534711yescharacteristic
277C2×C3#6544311yescharacteristic
278C2×C3#6545711yescharacteristic
279D3—801no—
280C5#7118611yescharacteristic, complemented, Sylow
281C22—81no—
282C22—81no—
283C22—81no—
284C22—1201no—
285C22—1201no—
286C22—1201no—
287C22#9182911yescharacteristic
288C4—81no—
289C4—1201no—
290C4#9180012yes—
291C4#9180512yes—
292C4#9183812yes—
293C3#1060197911yescharacteristic, complemented, Sylow
294C2—161no—
295C2—2401no—
296C2#1175115911yescharacteristic
297C2#1175125511yescharacteristic
298C2#1175126911yescharacteristic
subgroupG/H
centerC22#91829
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#486C2
socleC22×C3×C5#127
prime radical#11751174C2
hypercenter#486D15
hypocenterC3×C5#1717
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. C3×C5×#486C2semidirect
2. #11751189C2semidirect
3. #11751180C2semidirect
5. #11751171C2semidirect
6. #11750794C2semidirect
7. #11746275C2semidirect
23. C5×#486D3semidirect
48. C3×#486D5semidirect
123. #486D15semidirect
239. C3×C5#1717semidirect
280. C5#71186semidirect
293. C3#10601979semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4862
#117511892
#117511802
#117511742
#117511712
#117507942
#117462752
#106019793
#711865