Finite Group Databasebeta

← #14292734

Subgroups — #14292734

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
1#11751181C211yesmaximal, characteristic
2C3×#65380C211yesmaximal, characteristic
3#11747095C211yesmaximal, characteristic
4#11746862C211yesmaximal, characteristic
5C5×#4546C211yesmaximal, characteristic
6#11745868C211yesmaximal, characteristic
7#11745860C211yesmaximal, characteristic
8#10599305—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×C4×Dic10C2211yescharacteristic
12C2×#6662—21no—
13#91092—21no—
14#91092—21no—
15C4×C3⋊#168C2211yescharacteristic
16C5×C4⋊(C3⋊C8)C2211yescharacteristic
17C5×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×#3942—21no—
19C3×#3939—21no—
20C3×C4⋊#168C2211yescharacteristic
21#90982—21no—
22#90974—21no—
23#90952—21no—
24#71152—51nomaximal, Hall
25#65380D311yescharacteristic
26#65368—31no—
27#65138—31no—
28#65120—31no—
29C5×#333—31no—
30#64706—31no—
31#64699—31no—
32C2×C3×C5×Q8—21no—
33C2×Dic30—21no—
34C2×C3×Dic10D411yescharacteristic
35C3×C5×C4⋊C4—21no—
36C3×C5×C4⋊C4—21no—
37C3×C42×C5C2311yescharacteristic
38C4⋊Dic15—21no—
39C4⋊Dic15—21no—
40C2×C3⋊#168D411yescharacteristic
41C2×C3⋊#168D411yescharacteristic
42C2×C5×C3⋊C8—21no—
43C2×C5×C3⋊C8—21no—
44C3×C4⋊Dic5D411yescharacteristic
45C3×#683—21no—
46C3×C4×Dic5—21no—
47C2×C3×#168—21no—
48#6662—42no—
49C3×#477—51no—
50#5080—51no—
51#5031—51no—
52#5024—51no—
53#4546D511yescharacteristic
54#4482—51no—
55#4479—51no—
56C5×C4⋊Q8C2×D311yescharacteristic
57C2×Dic20—61no—
58#4015—31no—
59C4×Dic10C2×D311yescharacteristic
60C5×C4⋊C8—31no—
61C5×C4⋊C8—31no—
62#3948—61no—
63#3947—61no—
64#3946—61no—
65#3942—21no—
66#3940—61no—
67#3940—61no—
68#3939—21no—
69C4⋊#168C2×D311yescharacteristic
70C4×#168—31no—
71#1692—151noSylow
72C3×C5×Q8—81no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4111yescharacteristic
77C2×Dic15—41no—
78Dic30—41no—
79Dic30—41no—
80C2×C3×Dic5—21no—
81C2×C3×Dic5—21no—
82C3×Dic10—21no—
83C3×Dic10—21no—
84C3⋊#168—21no—
85C3⋊#168Q1612yescomplemented
86C3×#168—41no—
87C5×C3⋊C8—41no—
88C5×C3⋊C8—41no—
89C3×C4⋊Q8C2×D511yescharacteristic
90C3×C4×Q8—51no—
91C2×#216—101no—
92#869—51no—
93C3×#107—101no—
94C3×C4⋊C8—51no—
95C3×#103—101no—
96#810—101no—
97#808—101no—
98#808—101no—
99C4⋊(C3⋊C8)—101no—
100C4⋊(C3⋊C8)C2×D511yescharacteristic
101C4⋊(C3⋊C8)C2×D511yescharacteristic
102#803—101no—
103C4×C3⋊C8—51no—
104C2×C5×Q8—21no—
105C2×Dic10—61no—
106C2×Dic10#6711yescharacteristic
107C2×C5×C8—61no—
108C2×C5×C8—61no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C42×C5C22×D311yescharacteristic
112C4⋊Dic5—61no—
113C4⋊Dic5—61no—
114C4⋊Dic5#6711yescharacteristic
115#683—21no—
116C4×Dic5—21no—
117C2×#168—21no—
118C2×#168—31no—
119C2×#168—31no—
120Dic20—122no—
121#498—151no—
122#477—51no—
123#462—151no—
124#446—151no—
125#335—151no—
126#333—31no—
127#332—151no—
128C22×C3×C5#12111yescharacteristic
129C3×C4×C5—21no—
130C3×C4×C5—81no—
131C3×C4×C5C2×Q1611yescharacteristic
132C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
133C3×C4×C5#13711yescharacteristic
134C3×C4×C5#13711yescharacteristic
135Dic15—81no—
136C3×Dic5—41no—
137C3×Dic5—41no—
138C2×C3×Q8—21no—
139C2×C3×Q8—51no—
140C2×Dic6—101no—
141C2×C3×C8—101no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—51no—
145C3×C4⋊C4—101no—
146C3×C42—101no—
147C3×C42C22×D511yescharacteristic
148#216—202no—
149C4⋊Dic3—101no—
150C4⋊Dic3—101no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—51no—
154C2×C3⋊C8—51no—
155C5×Q8—81no—
156C2×C4×C5—41no—
157C2×C4×C5D3×D411yescharacteristic
158C2×C4×C5#23711yescharacteristic
159C2×C4×C5C2×#6711yescharacteristic
160C2×Dic5—21no—
161C2×Dic5—21no—
162C2×Dic5—121no—
163Dic10—21no—
164Dic10—21no—
165Dic10—121no—
166Dic10—121no—
167C5×C8—121no—
168C5×C8—121no—
169#168—32no—
170#168—41no—
171#168—61no—
172C2×Q16—301no—
173C4⋊Q8—151no—
174C4⋊Q8D3×D511yescharacteristic
175C4×Q8—51no—
176#107—101no—
177#106—301no—
178#106—301no—
179C4⋊C8—31no—
180C4⋊C8—31no—
181C4⋊C8—51no—
182C4⋊C8—301no—
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—81no—
191C3×Q8—101no—
192C3×Q8—101no—
193C2×C3×C4—41no—
194C2×C3×C4—101no—
195C2×C3×C4—101no—
196C2×C3×C4#70911yescharacteristic
197C2×C3×C4D4×D511yescharacteristic
198C2×C3×C4D4×D511yescharacteristic
199C2×Dic3—201no—
200Dic6—201no—
201Dic6—201no—
202C3×C8—201no—
203C3⋊C8—41no—
204C3⋊C8—41no—
205C3⋊C8—52no—
206C3⋊C8—101no—
207C22×C5#93911yescharacteristic
208C4×C5—21no—
209C4×C5—81no—
210C4×C5D3×Q1611yescharacteristic
211C4×C5#91811yescharacteristic
212C4×C5#94211yescharacteristic
213C4×C5#94911yescharacteristic
214Dic5—41no—
215Dic5—41no—
216Dic5—241no—
217C2×Q8—21no—
218C2×Q8—51no—
219C2×Q8—301no—
220Q16—602no—
221C2×C8—61no—
222C2×C8—61no—
223C2×C8—101no—
224C2×C8—151no—
225C2×C8—151no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—51no—
229C4⋊C4—101no—
230C4⋊C4—301no—
231C4⋊C4—301no—
232C42—101no—
233C42C2×D3×D511yescharacteristic
234C3×C5#169211yescharacteristic, complemented, Hall
235C22×C3#403011yescharacteristic
236C3×C4—21no—
237C3×C4—81no—
238C3×C4—201no—
239C3×C4—201no—
240C3×C4#406011yescharacteristic
241C3×C4#406111yescharacteristic
242C3×C4D5×Q1611yescharacteristic
243C3×C4#406411yescharacteristic
244Dic3—401no—
245C2×C5#504911yescharacteristic
246C2×C5#518211yescharacteristic
247C2×C5#520011yescharacteristic
248Q8—81no—
249Q8—101no—
250Q8—101no—
251Q8—601no—
252Q8—601no—
253C2×C4—41no—
254C2×C4—101no—
255C2×C4—101no—
256C2×C4—601no—
257C2×C4#677911yescharacteristic
258C2×C4D5×#6711yescharacteristic
259C2×C4#679011yescharacteristic
260C8—121no—
261C8—121no—
262C8—152no—
263C8—201no—
264C8—301no—
265C2×C3#6503711yescharacteristic
266C2×C3#6508211yescharacteristic
267C2×C3#6510111yescharacteristic
268C5#7115211yescharacteristic, complemented, Sylow
269C22#9155011yescharacteristic
270C4—21no—
271C4—81no—
272C4—201no—
273C4—201no—
274C4—1201no—
275C4#9150211yescharacteristic
276C4#9151111yescharacteristic
277C4#9151511yescharacteristic
278C4#9152411yescharacteristic
279C3#1059930511yescharacteristic, complemented, Sylow
280C2#1174913111yescharacteristic
281C2#1174925411yescharacteristic
282C2#1174927311yescharacteristic
subgroupG/H
centerC22#91550
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socle, prime radicalC22×C3×C5#121
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1692
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
85. C3⋊#168Q16semidirect
234. C3×C5#1692semidirect
268. C5#71152semidirect
279. C3#10599305semidirect

Maximal subgroups

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

subgroupindex
#117511812
C3×#653802
#117470952
#117468622
C5×#45462
#117458682
#117458602
#105993053
#711525