Finite Group Databasebeta

← #14317181

Subgroups — #14317181

Order 1920.

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

normal subgroups only

This group has 308 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
1C5×#4873C211yesmaximal, characteristic
2#11748033C211yesmaximal, characteristic
3C2×#90948C211yesmaximal, characteristic
4C2×#90946C211yesmaximal, characteristic
5#11746313C211yesmaximal, characteristic
6C3×#64712C211yesmaximal, characteristic
7Dic3⋊#672C211yesmaximal, characteristic
8#10601709—31nomaximal, Hall
9C2×Dic60C2211yescharacteristic
10C2×C5×Dic12C2211yescharacteristic
11C5×#887—21no—
12C2×C3×Dic20C2211yescharacteristic
13#91389—21no—
14C2×#6662—21no—
15C3×C5×#107C2211yescharacteristic
16C2×C3⋊#672C2211yescharacteristic
17C5×C8×Dic3C2211yescharacteristic
18C5×#810—21no—
19C2×C3×#672C2211yescharacteristic
20#90948—22no—
21#90946—22no—
22#69236—51nomaximal, Hall
23C4×C5×Q16—31no—
24C2×#3961—31no—
25C2×#3961—31no—
26#64988—31no—
27#64712—31no—
28#64712D311yescharacteristic
29C4⋊#672—31no—
30C2×Dic30—21no—
31C2×C5×Dic6—21no—
32C2×C3×Dic10—21no—
33C2×C3×C5×C8C2311yescharacteristic
34C3×C5×C4⋊C4—21no—
35Dic60—21no—
36Dic60—21no—
37C5×Dic3⋊C4—41no—
38C4×C5×Dic3—41no—
39C4×C5×Dic3D411yescharacteristic
40C2×C5×C3⋊C8D411yescharacteristic
41C5×Dic12—21no—
42C5×Dic12D412yes—
43C3×Dic20—21no—
44C3×Dic20—21no—
45Dic3⋊Dic5—41no—
46Dic3⋊Dic5—41no—
47#6662—42no—
48C3⋊#672—21no—
49C3×#672—21no—
50#5183—51no—
51C2×#829—51no—
52C2×Dic24—51no—
53#4873D511yescharacteristic
54C3×#358—51no—
55Dic3⋊C16—51no—
56#4492—51no—
57C2×C5×Q16—31no—
58C4×C5×Q8—61no—
59C2×Dic20—31no—
60C2×Dic20—61no—
61C2×Dic20C2×D311yescharacteristic
62#4015—61no—
63C5×#107C2×D311yescharacteristic
64C5×#103—61no—
65C4×C5×C8—31no—
66#3961—62no—
67#3961—62no—
68C2×#672—31no—
69C2×#672C2×D311yescharacteristic
70#2209—151noSylow
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×Dic15—41no—
74Dic30—41no—
75Dic30—41no—
76C2×C5×Dic3—41no—
77C2×C5×Dic3D811yescharacteristic
78C2×C5×Dic3D811yescharacteristic
79C5×Dic6—22no—
80C5×Dic6—41no—
81C2×C3×Dic5—41no—
82C3×Dic10—41no—
83C3×Dic10—41no—
84C3×C5×C8C2×D411yescharacteristic
85C3×C5×C8#4111yescharacteristic
86C5×C3⋊C8—21no—
87C2×C3×Q16—51no—
88#944—101no—
89C2×#216—101no—
90C2×Dic12—51no—
91C2×Dic12C2×D511yescharacteristic
92#887—21no—
93C2×C3×C16—51no—
94C3×#107C2×D511yescharacteristic
95#829—102no—
96C8×Dic3C2×D511yescharacteristic
97C2×C3⋊C16—51no—
98#810—21no—
99Dic24—102no—
100C2×C5×Q8—61no—
101C2×Dic10—21no—
102C2×Dic10—61no—
103C5×Q16—32no—
104C5×Q16—61no—
105C2×C5×C8—31no—
106C2×C5×C8C22×D311yescharacteristic
107C5×C4⋊C4—21no—
108C5×C4⋊C4—121no—
109C42×C5—31no—
110C42×C5—121no—
111C4⋊Dic5—121no—
112C4⋊Dic5—121no—
113Dic20—21no—
114Dic20—21no—
115Dic20—61no—
116Dic20—61no—
117Dic20—122no—
118#672—21no—
119#672—61no—
120C2×Q32—151no—
121C2×Q32—151no—
122#494—151no—
123C4×Q16—31no—
124C4⋊C16—151no—
125#358—51no—
126#358—151no—
127C22×C3×C5C2×D811yescharacteristic
128C3×C4×C5—81no—
129C3×C4×C5#12111yescharacteristic
130C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
131Dic15—81no—
132C3×Dic5—81no—
133C5×Dic3—21no—
134C5×Dic3—42no—
135C5×Dic3Q3212yescomplemented
136C2×C3×Q8—101no—
137C2×Dic6—21no—
138C2×Dic6—101no—
139C3×Q16—101no—
140C3×Q16—101no—
141C2×C3×C8C22×D511yescharacteristic
142C3×C4⋊C4—21no—
143#216—202no—
144Dic3⋊C4—41no—
145Dic3⋊C4—201no—
146Dic3⋊C4—201no—
147C4×Dic3—41no—
148C4×Dic3C22⋊D511yescharacteristic
149C2×C3⋊C8C22⋊D511yescharacteristic
150Dic12—21no—
151Dic12—101no—
152Dic12—101no—
153Dic12D2012yes—
154C3×C16—101no—
155C3⋊C16—101no—
156C5×Q8—62no—
157C5×Q8—121no—
158C2×C4×C5—31no—
159C2×C4×C5—31no—
160C2×C4×C5—41no—
161C2×C4×C5—121no—
162C2×C4×C5D3×D411yescharacteristic
163C2×Dic5—41no—
164C2×Dic5—121no—
165Dic10—41no—
166Dic10—41no—
167Dic10—121no—
168Dic10—121no—
169C5×C8—61no—
170C5×C8#23511yescharacteristic
171C5×C8D3×D411yescharacteristic
172C2×Q16—31no—
173C2×Q16—51no—
174C2×Q16—151no—
175C2×Q16—301no—
176C4⋊Q8—301no—
177C4×Q8—61no—
178Q32—302no—
179Q32—302no—
180C2×C16—51no—
181C2×C16—151no—
182#107D3×D511yescharacteristic
183#103—61no—
184C4×C8—31no—
185C2×C3×C5#45911yescharacteristic
186C2×C3×C5C2×Q3211yescharacteristic
187C2×C3×C5#51011yescharacteristic
188C3×Q8—201no—
189C3×Q8—201no—
190C2×C3×C4—41no—
191C2×C3×C4—201no—
192C2×C3×C4C2×C22⋊D511yescharacteristic
193C2×Dic3—41no—
194C2×Dic3—201no—
195C2×Dic3#68611yescharacteristic
196C2×Dic3#68611yescharacteristic
197Dic6—22no—
198Dic6—41no—
199Dic6—201no—
200Dic6—201no—
201C3×C8C2×D2011yescharacteristic
202C3×C8#70911yescharacteristic
203C3⋊C8—21no—
204C22×C5D3×D811yescharacteristic
205C4×C5—32no—
206C4×C5—61no—
207C4×C5—81no—
208C4×C5—122no—
209C4×C5#88411yescharacteristic
210C4×C5#91411yescharacteristic
211Dic5—81no—
212Dic5—241no—
213C2×Q8—61no—
214C2×Q8—101no—
215C2×Q8—301no—
216Q16—32no—
217Q16—61no—
218Q16—101no—
219Q16—101no—
220Q16—301no—
221Q16—301no—
222Q16—602no—
223C2×C8—31no—
224C2×C8C2×D3×D511yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—121no—
227C4⋊C4—601no—
228C4⋊C4—601no—
229C42—31no—
230C42—121no—
231C16—101no—
232C16—301no—
233C3×C5#220911yescharacteristic, complemented, Hall
234C22×C3C2×#68611yescharacteristic
235C3×C4—81no—
236C3×C4—401no—
237C3×C4#407611yescharacteristic
238C3×C4#409511yescharacteristic
239Dic3—21no—
240Dic3—42no—
241Dic3—401no—
242Dic3#396112yescomplemented
243C2×C5#478611yescharacteristic
244C2×C5#491511yescharacteristic
245C2×C5D3×Q3211yescharacteristic
246Q8—62no—
247Q8—121no—
248Q8—201no—
249Q8—201no—
250Q8—601no—
251Q8—601no—
252C2×C4—31no—
253C2×C4—31no—
254C2×C4—41no—
255C2×C4—121no—
256C2×C4—201no—
257C2×C4—601no—
258C2×C4D3×C22⋊D511yescharacteristic
259C8—61no—
260C8#677111yescharacteristic
261C8D3×D2011yescharacteristic
262C2×C3#6530411yescharacteristic
263C2×C3C2×#396111yescharacteristic
264C2×C3#6548411yescharacteristic
265C5#6923611yescharacteristic, complemented, Sylow
266C22D3×#68611yescharacteristic
267C4—32no—
268C4—61no—
269C4—81no—
270C4—122no—
271C4—401no—
272C4—1201no—
273C4#9145411yescharacteristic
274C4#9150411yescharacteristic
275C3#1060170911yescharacteristic, complemented, Sylow
276C2#1174740211yescharacteristic
277C2#1174827311yescharacteristic
278C2D3×#396111yescharacteristic
subgroupG/H
centerC22D3×#686
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socle, prime radicalC22×C3×C5C2×D8
hypercenter#107D3×D5
hypocenterC3×C5#2209
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
135. C5×Dic3Q32semidirect
233. C3×C5#2209semidirect
242. Dic3#3961semidirect
265. C5#69236semidirect
275. C3#10601709semidirect

Maximal subgroups

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

subgroupindex
C5×#48732
#117480332
C2×#909482
C2×#909462
#117463132
C3×#647122
Dic3⋊#6722
#106017093
#692365