Finite Group Databasebeta

← #14292752

Subgroups — #14292752

Order 1920.

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

normal subgroups only

This group has 292 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
1C3×#65139C211yesmaximal, characteristic
2#11747094C211yesmaximal, characteristic
3#11746947C211yesmaximal, characteristic
4#11746862C211yesmaximal, characteristic
5#11746300C211yesmaximal, characteristic
6C5×#4482C211yesmaximal, characteristic
7#11745861C211yesmaximal, characteristic
8#10599267—31nomaximal, Hall
9C5×#869C2211yescharacteristic
10C3×#4015C2211yescharacteristic
11C3×C4×Dic10C2211yescharacteristic
12C2×#6661—21no—
13C3×C5×C4⋊C8C2211yescharacteristic
14C4⋊(C3⋊#168)C2211yescharacteristic
15C4×C3⋊#168C2211yescharacteristic
16C5×C4⋊(C3⋊C8)C2211yescharacteristic
17C3×#3950—21no—
18C3×#3948—21no—
19#90986—21no—
20#90986—21no—
21#90982—21no—
22#90972—21no—
23#90952—21no—
24#71152—51nomaximal, Hall
25#65379—31no—
26#65368—31no—
27#65139D311yescharacteristic
28#65120—31no—
29C5×#332—31no—
30#64701—31no—
31#64699—31no—
32C2×C5×Dic6—21no—
33C2×C3×Dic10—21no—
34C2×C3×Dic10D411yescharacteristic
35C2×C3×C5×C8—21no—
36C3×C42×C5C2311yescharacteristic
37C2×C3⋊#168—21no—
38C2×C3⋊#168D411yescharacteristic
39C2×C3⋊#168D411yescharacteristic
40C5×C4⋊Dic3—21no—
41C5×C4⋊Dic3—21no—
42C2×C5×C3⋊C8—21no—
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5D411yescharacteristic
46C3×#683—21no—
47C3×C4×Dic5—21no—
48#6661—42no—
49C3×#477—51no—
50#5080—51no—
51#5031—51no—
52#5024—51no—
53#4546—51no—
54#4482D511yescharacteristic
55#4479—51no—
56C5×C4⋊Q8—31no—
57C2×#689—61no—
58#4015C2×D311yescharacteristic
59C4×Dic10C2×D311yescharacteristic
60C5×C4⋊C8—31no—
61C5×C4⋊C8C2×D311yescharacteristic
62#3967—61no—
63#3950—21no—
64#3948—21no—
65#3947—61no—
66#3946—61no—
67#3940—61no—
68#3940—61no—
69C4⋊#168—31no—
70C4×#168—31no—
71#1692—151noSylow
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5#4111yescharacteristic
75C2×C5×Dic3—41no—
76C5×Dic6—41no—
77C5×Dic6—41no—
78C2×C3×Dic5—21no—
79C2×C3×Dic5—21no—
80C2×C3×Dic5—41no—
81C3×Dic10—21no—
82C3×Dic10—21no—
83C3×Dic10—81no—
84C3×C5×C8—41no—
85C3⋊#168—21no—
86C3⋊#168—41no—
87C3⋊#168Q1612yescomplemented
88C5×C3⋊C8—41no—
89C3×C4⋊Q8—51no—
90C3×C4×Q8—51no—
91C2×#216—101no—
92#869C2×D511yescharacteristic
93C3×#107—101no—
94C3×C4⋊C8C2×D511yescharacteristic
95C3×#103—101no—
96#810—101no—
97#808—101no—
98#808—101no—
99C4⋊(C3⋊C8)—51no—
100C4⋊(C3⋊C8)—101no—
101C4⋊(C3⋊C8)C2×D511yescharacteristic
102#803—101no—
103C4×C3⋊C8—51no—
104C2×C5×Q8—61no—
105C2×Dic10—21no—
106C2×Dic10#6711yescharacteristic
107C2×C5×C8—21no—
108C2×C5×C8—61no—
109C5×C4⋊C4—61no—
110C5×C4⋊C4—61no—
111C42×C5C22×D311yescharacteristic
112#689—122no—
113C4⋊Dic5—21no—
114C4⋊Dic5—21no—
115C4⋊Dic5#6711yescharacteristic
116#683—21no—
117C4×Dic5—21no—
118C2×#168—31no—
119C2×#168—31no—
120C2×#168—61no—
121#498—151no—
122#477—51no—
123#462—151no—
124#446—151no—
125#335—151no—
126#333—151no—
127#332—31no—
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
134C3×Dic5—41no—
135C3×Dic5—41no—
136C3×Dic5—81no—
137C5×Dic3—81no—
138C2×C3×Q8—51no—
139C2×C3×Q8—101no—
140C2×Dic6—21no—
141C2×C3×C8—21no—
142C3×C4⋊C4—51no—
143C3×C4⋊C4—101no—
144C3×C4⋊C4—101no—
145C3×C4⋊C4—101no—
146C3×C42—101no—
147C3×C42C22×D511yescharacteristic
148#216—202no—
149C4⋊Dic3—21no—
150C4⋊Dic3—21no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—51no—
153C2×C3⋊C8—51no—
154C2×C3⋊C8—101no—
155C5×Q8—121no—
156C5×Q8—121no—
157C2×C4×C5—121no—
158C2×C4×C5D3×D411yescharacteristic
159C2×C4×C5#23711yescharacteristic
160C2×C4×C5C2×#6711yescharacteristic
161C2×Dic5—21no—
162C2×Dic5—21no—
163C2×Dic5—41no—
164Dic10—21no—
165Dic10—21no—
166Dic10—81no—
167C5×C8—41no—
168C5×C8—121no—
169#168—32no—
170#168—61no—
171#168—121no—
172C2×Q16—301no—
173C4⋊Q8—31no—
174C4⋊Q8—51no—
175C4×Q8—51no—
176#107—101no—
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—151no—
187C2×C3×C5#46211yescharacteristic
188C2×C3×C5#46811yescharacteristic
189C2×C3×C5#47111yescharacteristic
190C3×Q8—101no—
191C3×Q8—101no—
192C3×Q8—401no—
193C2×C3×C4—101no—
194C2×C3×C4—101no—
195C2×C3×C4—201no—
196C2×C3×C4#70911yescharacteristic
197C2×C3×C4D4×D511yescharacteristic
198C2×C3×C4D4×D511yescharacteristic
199C2×Dic3—41no—
200Dic6—41no—
201Dic6—41no—
202C3×C8—41no—
203C3⋊C8—41no—
204C3⋊C8—52no—
205C3⋊C8—101no—
206C3⋊C8—201no—
207C22×C5#93911yescharacteristic
208C4×C5—21no—
209C4×C5—241no—
210C4×C5D3×Q1611yescharacteristic
211C4×C5#91811yescharacteristic
212C4×C5#94211yescharacteristic
213C4×C5#94911yescharacteristic
214Dic5—41no—
215Dic5—41no—
216Dic5—81no—
217C2×Q8—51no—
218C2×Q8—61no—
219C2×Q8—101no—
220Q16—602no—
221C2×C8—21no—
222C2×C8—61no—
223C2×C8—151no—
224C2×C8—151no—
225C2×C8—301no—
226C4⋊C4—51no—
227C4⋊C4—61no—
228C4⋊C4—61no—
229C4⋊C4—101no—
230C4⋊C4—101no—
231C4⋊C4—101no—
232C42—101no—
233C42C2×D3×D511yescharacteristic
234C3×C5#169211yescharacteristic, complemented, Hall
235C22×C3#403011yescharacteristic
236C3×C4—21no—
237C3×C4—201no—
238C3×C4—201no—
239C3×C4—401no—
240C3×C4#405711yescharacteristic
241C3×C4#406111yescharacteristic
242C3×C4#406111yescharacteristic
243C3×C4D5×Q1611yescharacteristic
244Dic3—81no—
245C2×C5#504911yescharacteristic
246C2×C5#518211yescharacteristic
247C2×C5#520011yescharacteristic
248Q8—101no—
249Q8—101no—
250Q8—121no—
251Q8—121no—
252Q8—401no—
253C2×C4—101no—
254C2×C4—101no—
255C2×C4—121no—
256C2×C4—201no—
257C2×C4#676511yescharacteristic
258C2×C4#677711yescharacteristic
259C2×C4D5×#6711yescharacteristic
260C8—41no—
261C8—121no—
262C8—152no—
263C8—301no—
264C8—601no—
265C2×C3#6504311yescharacteristic
266C2×C3#6506911yescharacteristic
267C2×C3#6508211yescharacteristic
268C5#7115211yescharacteristic, complemented, Sylow
269C22#9140811yescharacteristic
270C4—21no—
271C4—201no—
272C4—201no—
273C4—241no—
274C4—401no—
275C4#9126411yescharacteristic
276C4#9128011yescharacteristic
277C4#9147811yescharacteristic
278C4#9151311yescharacteristic
279C3#1059926711yescharacteristic, complemented, Sylow
280C2#1174731111yescharacteristic
281C2#1174783811yescharacteristic
282C2#1174817911yescharacteristic
subgroupG/H
centerC22#91408
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
87. C3⋊#168Q16semidirect
234. C3×C5#1692semidirect
268. C5#71152semidirect
279. C3#10599267semidirect

Maximal subgroups

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

subgroupindex
C3×#651392
#117470942
#117469472
#117468622
#117463002
C5×#44822
#117458612
#105992673
#711525