Finite Group Databasebeta

← #14292200

Subgroups — #14292200

Order 1920.

332 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 86 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#11751189C211yesmaximal, characteristic
2C3×#65379C211yesmaximal, characteristic, complemented
3#11747064C211yesmaximal, characteristic
4#11746846C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6#11745868C211yesmaximal, characteristic, complemented
7#11745854C211yesmaximal, characteristic
8#10599263—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91763C2211yescharacteristic
11C2×C3×#689—21no—
12C3×C4×Dic10C2211yescharacteristic
13C2×#6658—21no—
14#91093—21no—
15#91093—21no—
16C4×C3⋊#168C2211yescharacteristic
17C5×C4⋊(C3⋊C8)C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×#3967—21no—
20C3×C4⋊#168C2211yescharacteristic
21#90982—21no—
22#90968—21no—
23Dic5×C3⋊C8—21no—
24#71055—51nomaximal, Hall
25#65379D311yescharacteristic, complemented
26#65377—31no—
27#65137—31no—
28#65119—31no—
29C5×#332—31no—
30#64705—31no—
31#64699—31no—
32C2×C3×C5×Q8—21no—
33C2×D60—21no—
34C2×D60—21no—
35C2×D60—21no—
36C2×C3×Dic10D411yescharacteristic
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—21no—
39C3×C42×C5C2311yescharacteristic
40C2×C3⋊#168D411yescharacteristic
41C2×C3⋊#168D411yescharacteristic
42C2×C5×C3⋊C8—21no—
43C2×C5×C3⋊C8—21no—
44C3×#689—42no—
45C3×C4⋊Dic5D411yescharacteristic
46C3×#683—21no—
47C3×C4×Dic5—21no—
48C2×C3×#168—21no—
49#6658—42no—
50C3×#462—51no—
51#5088—51no—
52#5027—51no—
53Q8×C3⋊C8—51no—
54#4547D511yescharacteristic, complemented
55#4485—51no—
56#4479—51no—
57C5×C4⋊Q8C2×D311yescharacteristic
58C2×#689—21no—
59C2×#677—61no—
60#4020—31no—
61C4×Dic10C2×D311yescharacteristic
62C5×C4⋊C8—31no—
63C5×C4⋊C8—31no—
64#3967—21no—
65#3953—61no—
66#3946—61no—
67C8×Dic5—61no—
68#3941—61no—
69#3941—61no—
70C4⋊#168C2×D311yescharacteristic
71C4×#168—31no—
72#1682—151noSylow
73C22×D15—41no—
74C3×C5×Q8—41no—
75C3×C5×Q8—41no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5#4111yescharacteristic
80D60—41no—
81D60—41no—
82D60—41no—
83D60—41no—
84D60—81no—
85C2×C3×Dic5—21no—
86C2×C3×Dic5—21no—
87C3×Dic10—21no—
88C3×Dic10D812yes—
89C3⋊#168—21no—
90C3⋊#168—21no—
91C3×#168—41no—
92C5×C3⋊C8—41no—
93C5×C3⋊C8—41no—
94C2×C3×Q16—101no—
95C3×C4⋊Q8C2×D511yescharacteristic
96C3×C4×Q8—51no—
97C2×#215—101no—
98#874—51no—
99C3×C4⋊C8—51no—
100C3×#103—101no—
101#809—101no—
102#809—101no—
103#809—101no—
104C4⋊(C3⋊C8)—101no—
105C4⋊(C3⋊C8)C2×D511yescharacteristic
106C4⋊(C3⋊C8)C2×D511yescharacteristic
107C4×C3⋊C8—51no—
108C4×C3⋊C8—101no—
109C2×C5×Q8—21no—
110C2×D20—61no—
111C2×D20—61no—
112C2×D20—61no—
113C2×Dic10#6711yescharacteristic
114C2×C5×C8—61no—
115C2×C5×C8—61no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—21no—
118C42×C5C22×D311yescharacteristic
119#689—42no—
120C4⋊Dic5#6711yescharacteristic
121#683—21no—
122C4×Dic5—21no—
123C2×#168—21no—
124C2×#168—31no—
125C2×#168—31no—
126#677—122no—
127#486—151no—
128#462—51no—
129#460—151no—
130C8×Q8—151no—
131#335—151no—
132#332—31no—
133#331—151no—
134C22×C3×C5#12111yescharacteristic
135C2×D15—81no—
136C2×D15—81no—
137C2×D15—81no—
138C3×C4×C5—21no—
139C3×C4×C5—81no—
140C3×C4×C5C2×D811yescharacteristic
141C3×C4×C5#13511yescharacteristic
142C3×C4×C5#13511yescharacteristic
143C3×C4×C5#13711yescharacteristic
144C3×Dic5—22no—
145C3×Dic5—41no—
146C2×C3×Q8—21no—
147C2×C3×Q8—51no—
148C2×D12—101no—
149C2×D12—101no—
150C2×D12—101no—
151C3×Q16—202no—
152C2×C3×C8—101no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—51no—
156C3×C4⋊C4—101no—
157C3×C42—101no—
158C3×C42C22×D511yescharacteristic
159#215—202no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—51no—
163C2×C3⋊C8—51no—
164C22×D5—121no—
165C5×Q8—41no—
166C5×Q8—41no—
167C2×C4×C5—41no—
168C2×C4×C5D3×D411yescharacteristic
169C2×C4×C5#23711yescharacteristic
170C2×C4×C5C2×#6711yescharacteristic
171C2×Dic5—21no—
172C2×Dic5—21no—
173D20—121no—
174D20—121no—
175D20—121no—
176D20—121no—
177D20—241no—
178Dic10—21no—
179Dic10#21312yes—
180C5×C8—121no—
181C5×C8—121no—
182#168—41no—
183#168—61no—
184#168—61no—
185C2×Q16—101no—
186C2×SD16—301no—
187C4⋊Q8D3×D511yescharacteristic
188#127—151no—
189C4×Q8—51no—
190C4⋊C8—31no—
191C4⋊C8—31no—
192C4⋊C8—51no—
193C4⋊C8—301no—
194#103—101no—
195#102—301no—
196#102—301no—
197#102—301no—
198C4×C8—151no—
199C4×C8—301no—
200C2×C3×C5#46411yescharacteristic
201C2×C3×C5#46611yescharacteristic
202C2×C3×C5#47111yescharacteristic
203D15—161no—
204C22×D3—201no—
205C3×Q8—41no—
206C3×Q8—41no—
207C3×Q8—52no—
208C3×Q8—101no—
209C2×C3×C4—41no—
210C2×C3×C4—101no—
211C2×C3×C4—101no—
212C2×C3×C4#70911yescharacteristic
213C2×C3×C4D4×D511yescharacteristic
214C2×C3×C4D4×D511yescharacteristic
215D12—201no—
216D12—201no—
217D12—201no—
218D12—201no—
219D12—401no—
220C3×C8—201no—
221C3⋊C8—41no—
222C3⋊C8—41no—
223C3⋊C8—101no—
224C3⋊C8—101no—
225C22×C5#93911yescharacteristic
226C2×D5—241no—
227C2×D5—241no—
228C2×D5—241no—
229C4×C5—21no—
230C4×C5—81no—
231C4×C5#91811yescharacteristic
232C4×C5#91911yescharacteristic
233C4×C5C2×#21311yescharacteristic
234C4×C5#95011yescharacteristic
235Dic5—22no—
236Dic5—41no—
237C2×Q8—21no—
238C2×Q8—51no—
239C2×D4—301no—
240C2×D4—301no—
241C2×D4—301no—
242Q16—202no—
243SD16—602no—
244C2×C8—61no—
245C2×C8—61no—
246C2×C8—101no—
247C2×C8—151no—
248C2×C8—151no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—51no—
252C4⋊C4—101no—
253C42—101no—
254C42C2×D3×D511yescharacteristic
255C3×C5#168211yescharacteristic, complemented, Hall
256C22×C3#403011yescharacteristic
257C2×D3—401no—
258C2×D3—401no—
259C2×D3—401no—
260C3×C4—21no—
261C3×C4—81no—
262C3×C4—102no—
263C3×C4—201no—
264C3×C4D5×D811yescharacteristic
265C3×C4#406211yescharacteristic
266C3×C4#406211yescharacteristic
267C3×C4#406411yescharacteristic
268C2×C5#503811yescharacteristic
269C2×C5#518511yescharacteristic
270C2×C5#520311yescharacteristic
271D5—481no—
272C23—601no—
273Q8—41no—
274Q8—41no—
275Q8—52no—
276Q8—101no—
277D4—601no—
278D4—601no—
279D4—601no—
280D4—601no—
281D4—1201no—
282C2×C4—41no—
283C2×C4—101no—
284C2×C4—101no—
285C2×C4#677911yescharacteristic
286C2×C4D5×#6711yescharacteristic
287C2×C4#679011yescharacteristic
288C8—121no—
289C8—121no—
290C8—201no—
291C8—301no—
292C8—301no—
293C2×C3#6504311yescharacteristic
294C2×C3#6506411yescharacteristic
295C2×C3#6508711yescharacteristic
296D3—801no—
297C5#7105511yescharacteristic, complemented, Sylow
298C22—1201no—
299C22—1201no—
300C22—1201no—
301C22#9155011yescharacteristic
302C4—21no—
303C4—81no—
304C4—102no—
305C4—201no—
306C4D5×#21311yescharacteristic
307C4#9149211yescharacteristic
308C4#9151211yescharacteristic
309C4#9152311yescharacteristic
310C3#1059926311yescharacteristic, complemented, Sylow
311C2—2401no—
312C2#1174902311yescharacteristic
313C2#1174925311yescharacteristic
314C2#1174937711yescharacteristic
subgroupG/H
centerC22#91550
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#121
prime radical#91763C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1682
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×#65379C2semidirect
4. #11746846C2semidirect
5. C5×#4547C2semidirect
6. #11745868C2semidirect
25. #65379D3semidirect
54. #4547D5semidirect
255. C3×C5#1682semidirect
297. C5#71055semidirect
310. C3#10599263semidirect

Maximal subgroups

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

subgroupindex
#117511892
C3×#653792
#117470642
#117468462
C5×#45472
#117458682
#117458542
#105992633
#710555