Finite Group Databasebeta

← #14293820

Subgroups — #14293820

Order 1920.

416 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C5×#4694C211yesmaximal, characteristic, complemented
2C3×#64983C211yesmaximal, characteristic, complemented
3#11747079C211yesmaximal, characteristic, complemented
4#11747039C211yesmaximal, characteristic
5#11746924C211yesmaximal, characteristic, complemented
6#11746901C211yesmaximal, characteristic, complemented
7#11746276C211yesmaximal, characteristic, complemented
8#10601981—31nomaximal, Hall
9C5×#874C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4020C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C2×#6655—22no—
14C2×#6652—22no—
15C3×C4×C5×C8C2211yescharacteristic
16C4×C3⋊#168C2211yescharacteristic
17C4×C3⋊#168C2211yescharacteristic
18C5×#821—22no—
19C3×#3953—22no—
20#90970—22no—
21#90966—22no—
22#71187—51nomaximal, Hall
23C5×#486—31no—
24#65382—31no—
25#65374—31no—
26#65362—31no—
27#65359—31no—
28#64983D311yescharacteristic, complemented
29#64675—31no—
30C2×C5×D12—21no—
31C2×C5×D12—21no—
32C2×C5×D12—21no—
33C2×C5×Dic6—21no—
34C2×C3×D20—21no—
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×Dic10—21no—
38C2×C3×C5×C8D412yes—
39C3×C42×C5C2311yescharacteristic
40C2×C3⋊#168D412yes—
41C2×C3⋊#168D412yes—
42C5×C4⋊Dic3—21no—
43C5×C4⋊Dic3—21no—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5—21no—
46#6655—44no—
47#6652—44no—
48C3×#486—51no—
49#5088—51no—
50#5079—51no—
51#5076—51no—
52#5073—51no—
53#4694D511yescharacteristic, complemented
54#4455—51no—
55C5×C4⋊Q8—31no—
56C5×#127—31no—
57C2×#688—62no—
58C2×#686—62no—
59#4020C2×D311yescharacteristic
60#4015C2×D311yescharacteristic
61C5×#102—62no—
62C4×C5×C8C2×D311yescharacteristic
63#3964—62no—
64#3953—22no—
65#3942—62no—
66C4×#168—31no—
67C4×#168—31no—
68#1717—151noSylow
69C22×C5×D3—41no—
70C22×C3×D5—41no—
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C5×Dic3—41no—
75C5×D12—42no—
76C5×D12—42no—
77C5×D12—42no—
78C5×Dic6—42no—
79C2×C3×Dic5—41no—
80C3×D20—42no—
81C3×D20—42no—
82C3×D20—42no—
83C3×Dic10—42no—
84C3×C5×C8—22no—
85C3⋊#168—22no—
86C3⋊#168—22no—
87C3×C4⋊Q8—51no—
88C3×#127—51no—
89C2×#214—102no—
90C2×#213—102no—
91#874C2×D511yescharacteristic
92#869C2×D511yescharacteristic
93C3×#102—102no—
94C3×C4×C8C2×D511yescharacteristic
95#835—102no—
96#821—22no—
97#809—102no—
98C4×C3⋊C8—51no—
99C4×C3⋊C8—51no—
100C2×C5×Q8—61no—
101C2×C5×D4—61no—
102C2×C5×D4—61no—
103C2×C5×D4—61no—
104C2×D20—21no—
105C2×D20—21no—
106C2×D20—21no—
107C2×Dic10—21no—
108C2×C5×C8#6712yes—
109C5×C4⋊C4—61no—
110C5×C4⋊C4—61no—
111C42×C5C22×D311yescharacteristic
112#688—124no—
113#686—124no—
114C4⋊Dic5—21no—
115C4⋊Dic5—21no—
116C2×#168—32no—
117C2×#168—32no—
118#493—151no—
119#492—151no—
120#487—151no—
121#486—31no—
122#486—51no—
123#486—151no—
124#322—151no—
125C22×C3×C5#12711yescharacteristic
126C2×C5×D3—81no—
127C2×C5×D3—81no—
128C2×C5×D3—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—
135C3×Dic5—81no—
136C5×Dic3—81no—
137C2×C3×Q8—101no—
138C2×C3×D4—101no—
139C2×C3×D4—101no—
140C2×C3×D4—101no—
141C2×D12—21no—
142C2×D12—21no—
143C2×D12—21no—
144C2×Dic6—21no—
145C2×C3×C8C22⋊D512yes—
146C3×C4⋊C4—101no—
147C3×C4⋊C4—101no—
148C3×C42C22×D511yescharacteristic
149#214—204no—
150#213—204no—
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153C2×C3⋊C8—52no—
154C2×C3⋊C8—52no—
155C23×C5—121no—
156C22×D5—41no—
157C5×Q8—122no—
158C5×D4—122no—
159C5×D4—122no—
160C5×D4—122no—
161C2×C4×C5—121no—
162C2×C4×C5D3×D411yescharacteristic
163C2×C4×C5D3×D411yescharacteristic
164C2×C4×C5C2×#6711yescharacteristic
165C2×Dic5—41no—
166D20—42no—
167D20—42no—
168D20—42no—
169Dic10—42no—
170C5×C8—22no—
171#168—62no—
172#168—62no—
173C2×SD16—302no—
174C2×D8—302no—
175C4⋊Q8—31no—
176C4⋊Q8—51no—
177#127—31no—
178#127—51no—
179#103—302no—
180#102—62no—
181#102—102no—
182#102—302no—
183C4×C8—151no—
184C4×C8—151no—
185C4×C8D3×D511yescharacteristic
186C2×C3×C5#49511yescharacteristic
187C2×C3×C5#49611yescharacteristic
188C2×C3×C5#49611yescharacteristic
189C3×D5—161no—
190C5×D3—161no—
191C23×C3—201no—
192C22×D3—41no—
193C3×Q8—202no—
194C3×D4—202no—
195C3×D4—202no—
196C3×D4—202no—
197C2×C3×C4—201no—
198C2×C3×C4D4×D511yescharacteristic
199C2×C3×C4D4×D511yescharacteristic
200C2×C3×C4C2×C22⋊D511yescharacteristic
201C2×Dic3—41no—
202D12—42no—
203D12—42no—
204D12—42no—
205Dic6—42no—
206C3×C8—22no—
207C3⋊C8—102no—
208C3⋊C8—102no—
209C22×C5—241no—
210C22×C5—241no—
211C22×C5—241no—
212C22×C5#94011yescharacteristic
213C2×D5—81no—
214C2×D5—81no—
215C2×D5—81no—
216C4×C5—241no—
217C4×C5#91112yes—
218C4×C5#91412yes—
219C4×C5#95012yes—
220Dic5—81no—
221C2×Q8—61no—
222C2×Q8—101no—
223C2×D4—61no—
224C2×D4—61no—
225C2×D4—61no—
226C2×D4—101no—
227C2×D4—101no—
228C2×D4—101no—
229SD16—604no—
230D8—604no—
231C2×C8—152no—
232C2×C8—152no—
233C2×C8#120112yes—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—101no—
237C4⋊C4—101no—
238C42C2×D3×D511yescharacteristic
239C3×C5#171711yescharacteristic, complemented, Hall
240C22×C3—401no—
241C22×C3—401no—
242C22×C3—401no—
243C22×C3#408611yescharacteristic
244C2×D3—81no—
245C2×D3—81no—
246C2×D3—81no—
247C3×C4—401no—
248C3×C4#405712yes—
249C3×C4#406012yes—
250C3×C4#409612yes—
251Dic3—81no—
252C2×C5—481no—
253C2×C5#505911yescharacteristic
254C2×C5#515411yescharacteristic
255C2×C5#517611yescharacteristic
256D5—161no—
257C23—121no—
258C23—201no—
259Q8—122no—
260Q8—202no—
261D4—122no—
262D4—122no—
263D4—122no—
264D4—202no—
265D4—202no—
266D4—202no—
267C2×C4—121no—
268C2×C4—201no—
269C2×C4#677711yescharacteristic
270C2×C4#677711yescharacteristic
271C2×C4C2×#120111yescharacteristic
272C8—22no—
273C8—302no—
274C8—302no—
275C2×C3—801no—
276C2×C3#6534811yescharacteristic
277C2×C3#6544311yescharacteristic
278C2×C3#6546511yescharacteristic
279D3—161no—
280C5#7118711yescharacteristic, complemented, Sylow
281C22—241no—
282C22—241no—
283C22—241no—
284C22—401no—
285C22—401no—
286C22—401no—
287C22#9146311yescharacteristic
288C4—241no—
289C4—401no—
290C4#9125712yes—
291C4#9125812yes—
292C4#9129712yes—
293C3#1060198111yescharacteristic, complemented, Sylow
294C2—481no—
295C2—801no—
296C2#1174704011yescharacteristic
297C2#1174801311yescharacteristic
298C2#1174801511yescharacteristic
subgroupG/H
centerC22#91463
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#127
prime radical#11747039C2
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. C5×#4694C2semidirect
2. C3×#64983C2semidirect
3. #11747079C2semidirect
5. #11746924C2semidirect
6. #11746901C2semidirect
7. #11746276C2semidirect
28. #64983D3semidirect
53. #4694D5semidirect
239. C3×C5#1717semidirect
280. C5#71187semidirect
293. C3#10601981semidirect

Maximal subgroups

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

subgroupindex
C5×#46942
C3×#649832
#117470792
#117470392
#117469242
#117469012
#117462762
#106019813
#711875