Finite Group Databasebeta

← #14317151

Subgroups — #14317151

Order 1920.

308 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 79 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#11751284C211yesmaximal, characteristic
2C2×#91113C211yesmaximal, characteristic
3C2×Dic120C211yesmaximal, characteristic
4#11750974C211yesmaximal, characteristic
5C3×C5×#358C211yesmaximal, characteristic
6#11746322C211yesmaximal, characteristic
7#11746313C211yesmaximal, characteristic
8#10600029—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10#91833—21no—
11C2×#6718—21no—
12C2×Dic60C2211yescharacteristic
13C2×Dic60C2211yescharacteristic
14#91776—21no—
15C2×C3×C5×C16C2211yescharacteristic
16C3×C5×#107C2211yescharacteristic
17#91113—22no—
18C8×Dic15C2211yescharacteristic
19C2×C3⋊#672C2211yescharacteristic
20#91094—21no—
21Dic120—22no—
22#69236—51nomaximal, Hall
23#65470—31no—
24C2×#3961—31no—
25C2×Dic40—31no—
26#65162—31no—
27C5×#358D311yescharacteristic
28#64721—31no—
29#64712—31no—
30C2×C3×C5×Q8—21no—
31C2×Dic30—21no—
32C2×Dic30—21no—
33C3×C5×Q16—21no—
34C3×C5×Q16—21no—
35C2×C3×C5×C8C2311yescharacteristic
36C3×C5×C4⋊C4—21no—
37#6718—42no—
38#6712—41no—
39#6712—41no—
40#6712—41no—
41C4×Dic15—41no—
42C4×Dic15D411yescharacteristic
43C2×C3⋊#168D411yescharacteristic
44Dic60—21no—
45Dic60—21no—
46Dic60—21no—
47Dic60D412yes—
48C3×C5×C16—21no—
49C3⋊#672—21no—
50#5183—51no—
51C2×#829—51no—
52C2×Dic24—51no—
53#4873—51no—
54C3×#358D511yescharacteristic
55Dic3⋊C16—51no—
56#4492—51no—
57C2×C5×Q16C2×D311yescharacteristic
58#4090—61no—
59C2×#689—61no—
60C2×Dic20—31no—
61C2×Dic20—31no—
62#4033—61no—
63C2×C5×C16C2×D311yescharacteristic
64C5×#107C2×D311yescharacteristic
65#3961—62no—
66C8×Dic5—31no—
67C2×#672—31no—
68#3942—61no—
69Dic40—62no—
70#2209—151noSylow
71C3×C5×Q8—41no—
72C3×C5×Q8—41no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×Dic15—41no—
77C2×Dic15—41no—
78C2×Dic15D811yescharacteristic
79C2×Dic15D811yescharacteristic
80Dic30—22no—
81Dic30—41no—
82Dic30—41no—
83Dic30—41no—
84C3×C5×C8C2×D411yescharacteristic
85C3×C5×C8#4111yescharacteristic
86C3⋊#168—21no—
87C2×C3×Q16C2×D511yescharacteristic
88#944—101no—
89C2×#216—101no—
90C2×Dic12—51no—
91C2×Dic12—51no—
92#887—101no—
93C2×C3×C16C2×D511yescharacteristic
94C3×#107C2×D511yescharacteristic
95#829—102no—
96C8×Dic3—51no—
97C2×C3⋊C16—51no—
98#810—101no—
99Dic24—102no—
100C2×C5×Q8—21no—
101C2×Dic10—61no—
102C2×Dic10—61no—
103C5×Q16—21no—
104C5×Q16—21no—
105C2×C5×C8C22×D311yescharacteristic
106C5×C4⋊C4—21no—
107#689—122no—
108#683—121no—
109#683—121no—
110#683—121no—
111C4×Dic5—31no—
112C4×Dic5—121no—
113C2×#168—31no—
114Dic20—32no—
115Dic20—61no—
116Dic20—61no—
117Dic20—61no—
118C5×C16—21no—
119#672—61no—
120C2×Q32—151no—
121C2×Q32—151no—
122#494—151no—
123C4×Q16—151no—
124C4⋊C16—151no—
125#358—151no—
126#358D1511yescharacteristic
127C22×C3×C5C2×D811yescharacteristic
128C3×C4×C5—81no—
129C3×C4×C5—81no—
130C3×C4×C5#12111yescharacteristic
131C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
132Dic15—21no—
133Dic15—42no—
134Dic15—81no—
135Dic15Q3212yescomplemented
136C2×C3×Q8—21no—
137C2×Dic6—101no—
138C2×Dic6—101no—
139C3×Q16—21no—
140C3×Q16—21no—
141C2×C3×C8C22×D511yescharacteristic
142C3×C4⋊C4—21no—
143#216—202no—
144Dic3⋊C4—201no—
145Dic3⋊C4—201no—
146Dic3⋊C4—201no—
147C4×Dic3—51no—
148C4×Dic3—201no—
149C2×C3⋊C8—51no—
150Dic12—52no—
151Dic12—101no—
152Dic12—101no—
153Dic12—101no—
154C3×C16—21no—
155C3⋊C16—101no—
156C5×Q8—41no—
157C5×Q8—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5D3×D411yescharacteristic
161C2×Dic5—31no—
162C2×Dic5—31no—
163C2×Dic5—121no—
164C2×Dic5—121no—
165Dic10—62no—
166Dic10—121no—
167Dic10—121no—
168Dic10—121no—
169C5×C8#23511yescharacteristic
170C5×C8D3×D411yescharacteristic
171#168—61no—
172C2×Q16—151no—
173C2×Q16—151no—
174C2×Q16—301no—
175C2×Q16C2×D1511yescharacteristic
176C4⋊Q8—301no—
177C4×Q8—301no—
178Q32—302no—
179Q32—302no—
180C2×C16—151no—
181C2×C16C2×D1511yescharacteristic
182#107C2×D1511yescharacteristic
183#103—301no—
184C4×C8—151no—
185C2×C3×C5#45911yescharacteristic
186C2×C3×C5C2×Q3211yescharacteristic
187C2×C3×C5#51011yescharacteristic
188C3×Q8—41no—
189C3×Q8—41no—
190C2×C3×C4—41no—
191C2×C3×C4—41no—
192C2×C3×C4D4×D511yescharacteristic
193C2×Dic3—51no—
194C2×Dic3—51no—
195C2×Dic3—201no—
196C2×Dic3—201no—
197Dic6—102no—
198Dic6—201no—
199Dic6—201no—
200Dic6—201no—
201C3×C8#70911yescharacteristic
202C3×C8D4×D511yescharacteristic
203C3⋊C8—101no—
204C22×C5D3×D811yescharacteristic
205C4×C5—81no—
206C4×C5—81no—
207C4×C5#88411yescharacteristic
208C4×C5#91411yescharacteristic
209Dic5—32no—
210Dic5—61no—
211Dic5—122no—
212Dic5—241no—
213C2×Q8—21no—
214C2×Q8—301no—
215C2×Q8—301no—
216Q16—21no—
217Q16—21no—
218Q16—152no—
219Q16—301no—
220Q16—301no—
221Q16—301no—
222Q16—602no—
223C2×C8—151no—
224C2×C8C22×D1511yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—601no—
227C4⋊C4—601no—
228C4⋊C4—601no—
229C42—151no—
230C42—601no—
231C16—21no—
232C16—301no—
233C3×C5#220911yescharacteristic, complemented, Hall
234C22×C3D5×D811yescharacteristic
235C3×C4—81no—
236C3×C4—81no—
237C3×C4#403011yescharacteristic
238C3×C4#406011yescharacteristic
239Dic3—52no—
240Dic3—101no—
241Dic3—202no—
242Dic3—401no—
243C2×C5#478611yescharacteristic
244C2×C5#491511yescharacteristic
245C2×C5D3×Q3211yescharacteristic
246Q8—41no—
247Q8—41no—
248Q8—302no—
249Q8—601no—
250Q8—601no—
251Q8—601no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—151no—
255C2×C4—151no—
256C2×C4—601no—
257C2×C4—601no—
258C2×C4D4×D1511yescharacteristic
259C8—301no—
260C8#681711yescharacteristic
261C8D4×D1511yescharacteristic
262C2×C3#6507511yescharacteristic
263C2×C3#6520411yescharacteristic
264C2×C3D5×Q3211yescharacteristic
265C5#6923611yescharacteristic, complemented, Sylow
266C22D8×D1511yescharacteristic
267C4—81no—
268C4—81no—
269C4—152no—
270C4—301no—
271C4—602no—
272C4—1201no—
273C4#9177311yescharacteristic
274C4#9180311yescharacteristic
275C3#1060002911yescharacteristic, complemented, Sylow
276C2#1175088711yescharacteristic
277C2#1175101611yescharacteristic
278C2D15×Q3211yescharacteristic
subgroupG/H
centerC22D8×D15
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#358C2
socle, prime radicalC22×C3×C5C2×D8
hypercenter#358D15
hypocenterC3×C5#2209
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
135. Dic15Q32semidirect
233. C3×C5#2209semidirect
265. C5#69236semidirect
275. C3#10600029semidirect

Maximal subgroups

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

subgroupindex
#117512842
C2×#911132
C2×Dic1202
#117509742
C3×C5×#3582
#117463222
#117463132
#106000293
#692365