Finite Group Databasebeta

← #14293819

Subgroups — #14293819

Order 1920.

416 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 100 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#11750795C211yesmaximal, characteristic, complemented
2C3×#64983C211yesmaximal, characteristic, complemented
3#11747075C211yesmaximal, characteristic, complemented
4#11747035C211yesmaximal, characteristic
5#11746921C211yesmaximal, characteristic, complemented
6#11746890C211yesmaximal, characteristic, complemented
7C5×#4455C211yesmaximal, characteristic, complemented
8#10598885—31nomaximal, Hall
9#91763C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×#4020C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C2×#6658—22no—
14C2×#6653—22no—
15C3×C4×C5×C8C2211yescharacteristic
16#91105—22no—
17C4×C5×C3⋊C8C2211yescharacteristic
18C4×C5×C3⋊C8C2211yescharacteristic
19C3×#3953—22no—
20#90974—22no—
21#90965—22no—
22#71188—51nomaximal, Hall
23#64984—31no—
24#64983—31no—
25#64983—31no—
26#64983D311yescharacteristic, complemented
27#64982—31no—
28#64970—31no—
29C5×#322—31no—
30C2×D60—21no—
31C2×D60—21no—
32C2×D60—21no—
33C2×Dic30—21no—
34C2×C3×D20—21no—
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×Dic10—21no—
38C2×C3×C5×C8D412yes—
39C3×C42×C5C2311yescharacteristic
40C4⋊Dic15—21no—
41C4⋊Dic15—21no—
42C2×C5×C3⋊C8D412yes—
43C2×C5×C3⋊C8D412yes—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5—21no—
46#6658—44no—
47#6653—44no—
48C3×#486—51no—
49#5093—51no—
50#5085—51no—
51#5073—51no—
52#5070—51no—
53#4694—51no—
54#4455D511yescharacteristic, complemented
55C2×D40—62no—
56C2×#677—62no—
57#4020—31no—
58#4020C2×D311yescharacteristic
59#4015—31no—
60#4015C2×D311yescharacteristic
61C4×C5×C8—31no—
62C4×C5×C8—31no—
63C4×C5×C8C2×D311yescharacteristic
64#3953—22no—
65#3953—62no—
66#3953—62no—
67#3948—62no—
68#1717—151noSylow
69C22×D15—41no—
70C22×C3×D5—41no—
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×Dic15—41no—
75D60—42no—
76D60—42no—
77D60—42no—
78Dic30—42no—
79C2×C3×Dic5—41no—
80C3×D20—42no—
81C3×D20—42no—
82C3×D20—42no—
83C3×Dic10—42no—
84C3×C5×C8—22no—
85C5×C3⋊C8—22no—
86C5×C3⋊C8—22no—
87C3×C4⋊Q8—51no—
88C3×#127—51no—
89C2×#215—102no—
90C2×#213—102no—
91#874—51no—
92#869—51no—
93C3×#102—102no—
94C3×C4×C8C2×D511yescharacteristic
95#832—102no—
96#821—102no—
97#810—102no—
98C4×C3⋊C8C2×D511yescharacteristic
99C4×C3⋊C8C2×D511yescharacteristic
100C2×D20—21no—
101C2×D20—21no—
102C2×D20—21no—
103C2×D20—61no—
104C2×D20—61no—
105C2×D20—61no—
106C2×Dic10—21no—
107C2×Dic10—61no—
108C2×C5×C8—32no—
109C2×C5×C8—32no—
110C2×C5×C8#6712yes—
111C42×C5C22×D311yescharacteristic
112C4⋊Dic5—21no—
113C4⋊Dic5—21no—
114C4⋊Dic5—61no—
115C4⋊Dic5—61no—
116D40—124no—
117#677—124no—
118#493—151no—
119#492—151no—
120#487—151no—
121#486—51no—
122#486—151no—
123#486—151no—
124#322—31no—
125C22×C3×C5#12711yescharacteristic
126C2×D15—81no—
127C2×D15—81no—
128C2×D15—81no—
129C2×C3×D5—81no—
130C2×C3×D5—81no—
131C2×C3×D5—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—101no—
139C2×C3×D4—101no—
140C2×C3×D4—101no—
141C2×D12—101no—
142C2×D12—101no—
143C2×D12—101no—
144C2×Dic6—101no—
145C2×C3×C8D2012yes—
146C3×C4⋊C4—101no—
147C3×C4⋊C4—101no—
148C3×C42C22×D511yescharacteristic
149#215—204no—
150#213—204no—
151C4⋊Dic3—101no—
152C4⋊Dic3—101no—
153C2×C3⋊C8D2012yes—
154C2×C3⋊C8D2012yes—
155C22×D5—41no—
156C22×D5—121no—
157C2×C4×C5D3×D411yescharacteristic
158C2×C4×C5D3×D411yescharacteristic
159C2×C4×C5C2×#6711yescharacteristic
160C2×Dic5—41no—
161C2×Dic5—121no—
162D20—42no—
163D20—42no—
164D20—42no—
165D20—122no—
166D20—122no—
167D20—122no—
168Dic10—42no—
169Dic10—122no—
170C5×C8—22no—
171C5×C8—62no—
172C5×C8—62no—
173C2×SD16—302no—
174C2×D8—302no—
175C4⋊Q8—51no—
176C4⋊Q8—151no—
177#127—51no—
178#127—151no—
179#103—302no—
180#102—102no—
181#102—302no—
182#102—302no—
183C4×C8—31no—
184C4×C8—31no—
185C4×C8D3×D511yescharacteristic
186C2×C3×C5#49511yescharacteristic
187C2×C3×C5#49611yescharacteristic
188C2×C3×C5#49611yescharacteristic
189D15—161no—
190C3×D5—161no—
191C23×C3—201no—
192C22×D3—201no—
193C3×Q8—202no—
194C3×D4—202no—
195C3×D4—202no—
196C3×D4—202no—
197C2×C3×C4—201no—
198C2×C3×C4C2×D2011yescharacteristic
199C2×C3×C4C2×D2011yescharacteristic
200C2×C3×C4C2×D2011yescharacteristic
201C2×Dic3—201no—
202D12—202no—
203D12—202no—
204D12—202no—
205Dic6—202no—
206C3×C8—22no—
207C3⋊C8—22no—
208C3⋊C8—22no—
209C22×C5#94011yescharacteristic
210C2×D5—81no—
211C2×D5—81no—
212C2×D5—81no—
213C2×D5—241no—
214C2×D5—241no—
215C2×D5—241no—
216C4×C5#91112yes—
217C4×C5#91412yes—
218C4×C5#95012yes—
219Dic5—81no—
220Dic5—241no—
221C2×Q8—101no—
222C2×Q8—301no—
223C2×D4—101no—
224C2×D4—101no—
225C2×D4—101no—
226C2×D4—301no—
227C2×D4—301no—
228C2×D4—301no—
229SD16—604no—
230D8—604no—
231C2×C8—32no—
232C2×C8—32no—
233C2×C8#120212yes—
234C4⋊C4—101no—
235C4⋊C4—101no—
236C4⋊C4—301no—
237C4⋊C4—301no—
238C42C2×D3×D511yescharacteristic
239C3×C5#171711yescharacteristic, complemented, Hall
240C22×C3—401no—
241C22×C3—401no—
242C22×C3—401no—
243C22×C3#402011yescharacteristic
244C2×D3—401no—
245C2×D3—401no—
246C2×D3—401no—
247C3×C4—401no—
248C3×C4#405012yes—
249C3×C4#405412yes—
250C3×C4#405412yes—
251Dic3—401no—
252C2×C5#505911yescharacteristic
253C2×C5#515411yescharacteristic
254C2×C5#517611yescharacteristic
255D5—161no—
256D5—481no—
257C23—201no—
258C23—601no—
259Q8—202no—
260Q8—602no—
261D4—202no—
262D4—202no—
263D4—202no—
264D4—602no—
265D4—602no—
266D4—602no—
267C2×C4—201no—
268C2×C4—601no—
269C2×C4D3×D2011yescharacteristic
270C2×C4D3×D2011yescharacteristic
271C2×C4C2×#120211yescharacteristic
272C8—22no—
273C8—62no—
274C8—62no—
275C2×C3—801no—
276C2×C3#6498511yescharacteristic
277C2×C3#6500111yescharacteristic
278C2×C3#6500111yescharacteristic
279D3—801no—
280C5#7118811yescharacteristic, complemented, Sylow
281C22—401no—
282C22—401no—
283C22—401no—
284C22—1201no—
285C22—1201no—
286C22—1201no—
287C22#9145811yescharacteristic
288C4—401no—
289C4—1201no—
290C4#9125312yes—
291C4#9125412yes—
292C4#9131112yes—
293C3#1059888511yescharacteristic, complemented, Sylow
294C2—801no—
295C2—2401no—
296C2#1174707211yescharacteristic
297C2#1174800711yescharacteristic
298C2#1174800911yescharacteristic
subgroupG/H
centerC22#91458
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#127
prime radical#11747035C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#1717
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #11750795C2semidirect
2. C3×#64983C2semidirect
3. #11747075C2semidirect
5. #11746921C2semidirect
6. #11746890C2semidirect
7. C5×#4455C2semidirect
26. #64983D3semidirect
54. #4455D5semidirect
239. C3×C5#1717semidirect
280. C5#71188semidirect
293. C3#10598885semidirect

Maximal subgroups

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

subgroupindex
#117507952
C3×#649832
#117470752
#117470352
#117469212
#117468902
C5×#44552
#105988853
#711885