Finite Group Databasebeta

← #14292013

Subgroups — #14292013

Order 1920.

332 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 84 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#11750947C211yesmaximal, characteristic
2#11747085C211yesmaximal, characteristic
3#11746994C211yesmaximal, characteristic
4#11746921C211yesmaximal, characteristic, complemented
5C5×#4480C211yesmaximal, characteristic, complemented
6C3×#64702C211yesmaximal, characteristic, complemented
7#11745860C211yesmaximal, characteristic, complemented
8#10599332—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C2×#6658—21no—
13C2×#6648—21no—
14C3×C5×C4⋊C8C2211yescharacteristic
15#91105—21no—
16#91102—21no—
17C5×C4⋊(C3⋊C8)C2211yescharacteristic
18C4×C5×C3⋊C8C2211yescharacteristic
19C3×C4⋊#168C2211yescharacteristic
20#90974—21no—
21#90974—21no—
22#90971—21no—
23#90957—21no—
24#68445—51nomaximal, Hall
25#65135—31no—
26#65130—31no—
27C8×D20—31no—
28#64970—31no—
29C5×#334—31no—
30#64706—31no—
31#64702D311yescharacteristic, complemented
32C2×D60D411yescharacteristic
33C2×C4×D15—21no—
34C2×Dic30—21no—
35C2×C3×Dic10—21no—
36C2×C3×C5×C8—21no—
37C3×C42×C5C2311yescharacteristic
38#6714—21no—
39C4⋊Dic15—21no—
40C4⋊Dic15—21no—
41C4⋊Dic15D411yescharacteristic
42C2×C5×C3⋊C8—21no—
43C2×C5×C3⋊C8D411yescharacteristic
44C2×C5×C3⋊C8D411yescharacteristic
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C2×C3×#168—21no—
48#6658—42no—
49#6648—42no—
50#5093—51no—
51#5083—51no—
52#4846—51no—
53#4834—51no—
54C3×#332—51no—
55#4482—51no—
56#4480D511yescharacteristic, complemented
57C2×#677—61no—
58C2×C8×D5—61no—
59C4×D20—31no—
60#4015—31no—
61#4015C2×D311yescharacteristic
62C5×C4⋊C8—31no—
63C5×C4⋊C8C2×D311yescharacteristic
64C4×C5×C8—31no—
65#3953—61no—
66#3952—61no—
67#3950—61no—
68#3948—61no—
69#3948—61no—
70#3948—61no—
71C4⋊#168C2×D311yescharacteristic
72#1679—151noSylow
73C22×D15—21no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4111yescharacteristic
77C2×Dic15—21no—
78C2×Dic15—41no—
79D60—21no—
80D60SD1612yes—
81C4×D15—41no—
82C4×D15—41no—
83Dic30—41no—
84Dic30—41no—
85C2×C3×Dic5—41no—
86C3×Dic10—41no—
87C3×Dic10—41no—
88C3×C5×C8—41no—
89C3×#168—41no—
90C5×C3⋊C8—21no—
91C5×C3⋊C8—21no—
92C5×C3⋊C8—41no—
93C3×C4⋊Q8—51no—
94C2×#215—101no—
95C2×D3×C8—101no—
96C4×D12—51no—
97#869—51no—
98C3×C4⋊C8—51no—
99C3×C4⋊C8C2×D511yescharacteristic
100#835—101no—
101#821—101no—
102(C2×D3)⋊C8—101no—
103#818—101no—
104#810—101no—
105#810—101no—
106C4⋊(C3⋊C8)C2×D511yescharacteristic
107C4×C3⋊C8C2×D511yescharacteristic
108C2×D20—31no—
109C2×C4×D5—61no—
110C2×Dic10—21no—
111C2×Dic10—61no—
112C2×C5×C8—21no—
113C2×C5×C8—31no—
114C2×C5×C8—31no—
115C2×C5×C8—61no—
116C42×C5C22×D311yescharacteristic
117#685—61no—
118C4⋊Dic5—21no—
119C4⋊Dic5—21no—
120C4⋊Dic5—31no—
121C4⋊Dic5—61no—
122C4⋊Dic5—61no—
123C2×#168—21no—
124#677—122no—
125C8×D5—122no—
126#487—151no—
127#474—151no—
128#461—151no—
129C8×D4—151no—
130#334—31no—
131#332—51no—
132#332—151no—
133C22×C3×C5#12111yescharacteristic
134C2×D15—22no—
135C2×D15—41no—
136C2×D15—41no—
137C3×C4×C5—21no—
138C3×C4×C5C2×SD1611yescharacteristic
139C3×C4×C5#13511yescharacteristic
140C3×C4×C5#13511yescharacteristic
141C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
142Dic15—41no—
143Dic15—81no—
144C3×Dic5—81no—
145C2×C3×Q8—101no—
146C2×D12—51no—
147C2×C4×D3—101no—
148C2×Dic6—101no—
149C2×C3×C8—21no—
150C2×C3×C8—101no—
151C3×C4⋊C4—101no—
152C3×C4⋊C4—101no—
153C3×C42C22×D511yescharacteristic
154#215—202no—
155(C2×D3)⋊C4—101no—
156C4⋊Dic3—51no—
157C4⋊Dic3—101no—
158C4⋊Dic3—101no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8D2011yescharacteristic
161C2×C3⋊C8D2011yescharacteristic
162D3×C8—202no—
163C22×D5—61no—
164C2×C4×C5#23511yescharacteristic
165C2×C4×C5D3×D411yescharacteristic
166C2×C4×C5D3×D411yescharacteristic
167C2×Dic5—41no—
168C2×Dic5—61no—
169C2×Dic5—121no—
170D20—32no—
171D20—61no—
172C4×D5—121no—
173C4×D5—121no—
174Dic10—41no—
175Dic10—41no—
176Dic10—121no—
177Dic10—121no—
178C5×C8—41no—
179C5×C8—61no—
180C5×C8—61no—
181C5×C8—121no—
182#168—41no—
183C2×SD16—301no—
184C22×C8—301no—
185C4⋊Q8—51no—
186C4⋊Q8—151no—
187C4×D4—151no—
188#107—301no—
189C4⋊C8—31no—
190C4⋊C8—51no—
191C4⋊C8D3×D511yescharacteristic
192#103—301no—
193#103—301no—
194#103—301no—
195#102—301no—
196C22⋊C8—301no—
197C4×C8—31no—
198C2×C3×C5#46311yescharacteristic
199C2×C3×C5#46511yescharacteristic
200C2×C3×C5#47311yescharacteristic
201D15—42no—
202C22×D3—101no—
203C3×Q8—201no—
204C3×Q8—201no—
205C2×C3×C4—201no—
206C2×C3×C4C2×D2011yescharacteristic
207C2×C3×C4D4×D511yescharacteristic
208C2×C3×C4#71311yescharacteristic
209C2×Dic3—101no—
210C2×Dic3—201no—
211D12—52no—
212D12—101no—
213C4×D3—201no—
214C4×D3—201no—
215Dic6—201no—
216Dic6—201no—
217C3×C8—41no—
218C3×C8—201no—
219C3⋊C8—21no—
220C3⋊C8—21no—
221C3⋊C8—41no—
222C22×C5#88411yescharacteristic
223C2×D5—62no—
224C2×D5—121no—
225C2×D5—121no—
226C4×C5—21no—
227C4×C5#91211yescharacteristic
228C4×C5D3×SD1611yescharacteristic
229C4×C5#91411yescharacteristic
230C4×C5#91911yescharacteristic
231Dic5—81no—
232Dic5—121no—
233Dic5—241no—
234C2×Q8—101no—
235C2×Q8—301no—
236C2×D4—151no—
237C22×C4—301no—
238SD16—602no—
239C2×C8—21no—
240C2×C8—31no—
241C2×C8—31no—
242C2×C8—61no—
243C2×C8—101no—
244C2×C8—602no—
245C4⋊C4—101no—
246C4⋊C4—101no—
247C4⋊C4—151no—
248C4⋊C4—301no—
249C4⋊C4—301no—
250C22⋊C4—301no—
251C42C2×D3×D511yescharacteristic
252C3×C5#167911yescharacteristic, complemented, Hall
253C22×C3#404111yescharacteristic
254C2×D3—102no—
255C2×D3—201no—
256C2×D3—201no—
257C3×C4—21no—
258C3×C4—401no—
259C3×C4#405011yescharacteristic
260C3×C4#405411yescharacteristic
261C3×C4D5×SD1611yescharacteristic
262C3×C4#406211yescharacteristic
263Dic3—201no—
264Dic3—401no—
265C2×C5#475511yescharacteristic
266C2×C5#477811yescharacteristic
267C2×C5#481911yescharacteristic
268D5—122no—
269C23—301no—
270Q8—201no—
271Q8—201no—
272Q8—601no—
273Q8—601no—
274D4—152no—
275D4—301no—
276C2×C4—201no—
277C2×C4—301no—
278C2×C4—601no—
279C2×C4—601no—
280C2×C4—601no—
281C2×C4#677311yescharacteristic
282C2×C4D3×D2011yescharacteristic
283C2×C4#679011yescharacteristic
284C8—41no—
285C8—61no—
286C8—61no—
287C8—121no—
288C8—201no—
289C2×C3#6513311yescharacteristic
290C2×C3#6515311yescharacteristic
291C2×C3#6518511yescharacteristic
292D3—202no—
293C5#6844511yescharacteristic, complemented, Sylow
294C22—302no—
295C22—601no—
296C22—601no—
297C22#9145911yescharacteristic
298C4—21no—
299C4—401no—
300C4—601no—
301C4—1201no—
302C4#9125311yescharacteristic
303C4#9127511yescharacteristic
304C4#9149711yescharacteristic
305C4#9150511yescharacteristic
306C3#1059933211yescharacteristic, complemented, Sylow
307C2—602no—
308C2#1174732711yescharacteristic
309C2#1174779811yescharacteristic
310C2#1174820011yescharacteristic
subgroupG/H
centerC22#91459
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radicalC2×D60D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1679
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
4. #11746921C2semidirect
5. C5×#4480C2semidirect
6. C3×#64702C2semidirect
7. #11745860C2semidirect
31. #64702D3semidirect
56. #4480D5semidirect
252. C3×C5#1679semidirect
293. C5#68445semidirect
306. C3#10599332semidirect

Maximal subgroups

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

subgroupindex
#117509472
#117470852
#117469942
#117469212
C5×#44802
C3×#647022
#117458602
#105993323
#684455