Finite Group Databasebeta

← #14292735

Subgroups — #14292735

Order 1920.

292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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×#65138C211yesmaximal, characteristic
2#11746948C211yesmaximal, characteristic
3#11746916C211yesmaximal, characteristic
4#11746861C211yesmaximal, characteristic
5#11746302C211yesmaximal, characteristic
6C5×#4479C211yesmaximal, characteristic
7#11745856C211yesmaximal, characteristic
8#10599386—31nomaximal, Hall
9#91758C2211yescharacteristic
10C2×C3×Dic20—21no—
11C3×#4015C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13C3×C5×C4⋊C8C2211yescharacteristic
14C4⋊(C3⋊#168)C2211yescharacteristic
15C5×C4⋊(C3⋊C8)C2211yescharacteristic
16C4×C5×C3⋊C8C2211yescharacteristic
17C3×#3948—21no—
18#90990—21no—
19#90987—21no—
20#90987—21no—
21#90982—21no—
22#90971—21no—
23#90952—21no—
24#71056—51nomaximal, Hall
25#65139—31no—
26#65138D311yescharacteristic
27#64969—31no—
28#64968—31no—
29C5×#335—31no—
30#64702—31no—
31#64701—31no—
32C2×Dic30—21no—
33C2×C3×Dic10—21no—
34C2×C3×Dic10D411yescharacteristic
35C2×C3×C5×C8—21no—
36C3×C42×C5C2311yescharacteristic
37C4⋊Dic15—21no—
38C4⋊Dic15—21no—
39C2×C3⋊#168—21no—
40C2×C5×C3⋊C8—21no—
41C2×C5×C3⋊C8D411yescharacteristic
42C2×C5×C3⋊C8D411yescharacteristic
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5D411yescharacteristic
46C3×#683—21no—
47C3×C4×Dic5—21no—
48C3×Dic20—42no—
49C3×#462—51no—
50#5080—51no—
51#5024—51no—
52#5021—51no—
53#4547—51no—
54#4481—51no—
55#4479D511yescharacteristic
56C2×Dic20—21no—
57#4015—31no—
58#4015C2×D311yescharacteristic
59C4×Dic10C2×D311yescharacteristic
60C5×C4⋊C8—31no—
61C5×C4⋊C8C2×D311yescharacteristic
62C4×C5×C8—31no—
63#3950—61no—
64#3949—61no—
65#3949—61no—
66#3948—21no—
67#3948—61no—
68#3947—61no—
69#3946—61no—
70C4⋊#168—31no—
71#1692—151noSylow
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5#4111yescharacteristic
75C2×Dic15—41no—
76Dic30—81no—
77C2×C3×Dic5—21no—
78C2×C3×Dic5—21no—
79C2×C3×Dic5—41no—
80C3×Dic10—21no—
81C3×Dic10—21no—
82C3×Dic10—41no—
83C3×Dic10—41no—
84C3×C5×C8—41no—
85C3⋊#168—41no—
86C5×C3⋊C8—21no—
87C5×C3⋊C8—41no—
88C5×C3⋊C8Q1612yescomplemented
89C2×C3×Q16—101no—
90C3×C4⋊Q8—51no—
91C3×C4×Q8—51no—
92#869—51no—
93C3×C4⋊C8C2×D511yescharacteristic
94C3×#103—101no—
95#835—101no—
96#808—101no—
97#808—101no—
98#807—101no—
99C4⋊(C3⋊C8)—51no—
100C4⋊(C3⋊C8)—101no—
101C4⋊(C3⋊C8)C2×D511yescharacteristic
102#803—101no—
103C4×C3⋊C8C2×D511yescharacteristic
104C2×Dic10—21no—
105C2×Dic10—61no—
106C2×Dic10#6711yescharacteristic
107C2×C5×C8—21no—
108C2×C5×C8—31no—
109C2×C5×C8—31no—
110C2×C5×C8—61no—
111C42×C5C22×D311yescharacteristic
112C4⋊Dic5—21no—
113C4⋊Dic5—21no—
114C4⋊Dic5—61no—
115C4⋊Dic5—61no—
116C4⋊Dic5#6711yescharacteristic
117#683—21no—
118C4×Dic5—21no—
119C2×#168—61no—
120Dic20—42no—
121#498—151no—
122#477—151no—
123#462—51no—
124#446—151no—
125#335—31no—
126#333—151no—
127#332—151no—
128C22×C3×C5#12111yescharacteristic
129C3×C4×C5—21no—
130C3×C4×C5C2×Q1611yescharacteristic
131C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
132C3×C4×C5#13711yescharacteristic
133C3×C4×C5#13711yescharacteristic
134Dic15—81no—
135C3×Dic5—41no—
136C3×Dic5—41no—
137C3×Dic5—81no—
138C2×C3×Q8—51no—
139C2×C3×Q8—101no—
140C2×Dic6—101no—
141C3×Q16—202no—
142C2×C3×C8—21no—
143C3×C4⋊C4—51no—
144C3×C4⋊C4—101no—
145C3×C4⋊C4—101no—
146C3×C4⋊C4—101no—
147C3×C42—101no—
148C3×C42C22×D511yescharacteristic
149C4⋊Dic3—101no—
150C4⋊Dic3—101no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—101no—
153C2×C3⋊C8D2011yescharacteristic
154C2×C3⋊C8D2011yescharacteristic
155C2×C4×C5D3×D411yescharacteristic
156C2×C4×C5#23711yescharacteristic
157C2×C4×C5C2×#6711yescharacteristic
158C2×Dic5—21no—
159C2×Dic5—21no—
160C2×Dic5—41no—
161C2×Dic5—121no—
162Dic10—21no—
163Dic10—21no—
164Dic10—41no—
165Dic10—41no—
166Dic10—241no—
167C5×C8—32no—
168C5×C8—41no—
169C5×C8—61no—
170C5×C8—121no—
171#168—121no—
172C2×Q16—101no—
173C4⋊Q8—51no—
174C4⋊Q8—151no—
175C4×Q8—51no—
176#107—301no—
177#106—301no—
178#106—301no—
179C4⋊C8—31no—
180C4⋊C8—151no—
181C4⋊C8—301no—
182C4⋊C8D3×D511yescharacteristic
183#103—101no—
184#103—301no—
185#97—301no—
186C4×C8—31no—
187C2×C3×C5#46211yescharacteristic
188C2×C3×C5#46811yescharacteristic
189C2×C3×C5#47111yescharacteristic
190C3×Q8—101no—
191C3×Q8—101no—
192C3×Q8—201no—
193C3×Q8—201no—
194C2×C3×C4—101no—
195C2×C3×C4—101no—
196C2×C3×C4—201no—
197C2×C3×C4C2×D2011yescharacteristic
198C2×C3×C4D4×D511yescharacteristic
199C2×C3×C4#71311yescharacteristic
200C2×Dic3—201no—
201Dic6—401no—
202C3×C8—41no—
203C3⋊C8—21no—
204C3⋊C8—41no—
205C3⋊C8—201no—
206C3⋊C8Dic2012yescomplemented
207C22×C5#93911yescharacteristic
208C4×C5—21no—
209C4×C5D3×Q1611yescharacteristic
210C4×C5#91811yescharacteristic
211C4×C5#93211yescharacteristic
212C4×C5#95111yescharacteristic
213Dic5—41no—
214Dic5—41no—
215Dic5—81no—
216Dic5—241no—
217C2×Q8—51no—
218C2×Q8—101no—
219C2×Q8—301no—
220Q16—202no—
221C2×C8—21no—
222C2×C8—31no—
223C2×C8—31no—
224C2×C8—61no—
225C2×C8—301no—
226C4⋊C4—51no—
227C4⋊C4—101no—
228C4⋊C4—101no—
229C4⋊C4—101no—
230C4⋊C4—301no—
231C4⋊C4—301no—
232C42—101no—
233C42C2×D3×D511yescharacteristic
234C3×C5#169211yescharacteristic, complemented, Hall
235C22×C3#404111yescharacteristic
236C3×C4—21no—
237C3×C4—201no—
238C3×C4—201no—
239C3×C4—401no—
240C3×C4C2×Dic2011yescharacteristic
241C3×C4#405511yescharacteristic
242C3×C4#405711yescharacteristic
243C3×C4#406411yescharacteristic
244Dic3—401no—
245C2×C5#504211yescharacteristic
246C2×C5#518211yescharacteristic
247C2×C5#520311yescharacteristic
248Q8—101no—
249Q8—101no—
250Q8—201no—
251Q8—201no—
252Q8—1201no—
253C2×C4—101no—
254C2×C4—101no—
255C2×C4—201no—
256C2×C4—601no—
257C2×C4#676611yescharacteristic
258C2×C4D3×D2011yescharacteristic
259C2×C4D5×#6711yescharacteristic
260C8—32no—
261C8—41no—
262C8—61no—
263C8—121no—
264C8—601no—
265C2×C3#6513811yescharacteristic
266C2×C3#6517511yescharacteristic
267C2×C3#6518711yescharacteristic
268C5#7105611yescharacteristic, complemented, Sylow
269C22#9140911yescharacteristic
270C4—21no—
271C4—201no—
272C4—201no—
273C4—401no—
274C4—1201no—
275C4D3×Dic2011yescharacteristic
276C4#9126311yescharacteristic
277C4#9148911yescharacteristic
278C4#9150811yescharacteristic
279C3#1059938611yescharacteristic, complemented, Sylow
280C2#1174746311yescharacteristic
281C2#1174784011yescharacteristic
282C2#1174818411yescharacteristic
subgroupG/H
centerC22#91409
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socle, prime radicalC22×C3×C5#121
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1692
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
88. C5×C3⋊C8Q16semidirect
206. C3⋊C8Dic20semidirect
234. C3×C5#1692semidirect
268. C5#71056semidirect
279. C3#10599386semidirect

Maximal subgroups

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

subgroupindex
C3×#651382
#117469482
#117469162
#117468612
#117463022
C5×#44792
#117458562
#105993863
#710565