Finite Group Databasebeta

← #14302960

Subgroups — #14302960

Order 1920.

628 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 156 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×#5812C211yesmaximal, characteristic, complemented
2C3×#66150C211yesmaximal, characteristic
3C2×#91120C211yesmaximal, characteristic, complemented
4#11748421C212yesmaximal
5#11745969C212yesmaximal, complemented
6#10602456—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C2×C3×#709C2211yescharacteristic
9C2×#6710C2212yes—
10C5×Q8×Dic3—24no—
11C5×#926—22no—
12C5×#926C2212yes—
13C3×#4093C412yescomplemented
14C3×#4092—22no—
15C3×#4090C412yescomplemented
16C3×#4075—22no—
17C3×#4072C2211yescharacteristic
18#91120—22no—
19#90977—24no—
20#71864—51nomaximal, Hall
21C5×#519—31no—
22#66150D311yescharacteristic
23C2×#3968—31no—
24#65294—32no—
25#64751—32no—
26C2×C3×C5×Q8—22no—
27C2×C3×C5×Q8—22no—
28C2×C3×C5×Q8C2×C412yes—
29C2×C3×C5×Q8D412yes—
30C22×C3×C4×C5D412yes—
31C22×C3×C4×C5C2311yescharacteristic
32C2×C3×C22⋊D5—21no—
33C3×#709—22no—
34C3×#709—22no—
35C2×C3×D20C2×C411yescharacteristic
36C2×C3×C4×D5—21no—
37C2×C3×Dic10C2×C411yescharacteristic
38#6710—22no—
39#6710—22no—
40C2×C3⋊#168—22no—
41C5×#217—22no—
42C5×C4⋊Dic3—24no—
43C5×C4⋊Dic3—22no—
44C4×C5×Dic3—24no—
45C4×C5×Dic3D414yes—
46C3×C22⋊Dic5—21no—
47C3×#685—24no—
48C3×C4⋊Dic5—21no—
49C3×#683—24no—
50C3×C4×Dic5C2×C412yes—
51C3×#536—51no—
52#5812D511yescharacteristic, complemented
53#5236—52no—
54C2×#836—51no—
55#4531—52no—
56C22×C5×Q8C2×D311yescharacteristic
57C2×#709C2×D311yescharacteristic
58C4×C5×Q8—64no—
59C5×#117—32no—
60C5×#117—62no—
61#4093Dic312yescomplemented
62#4092—22no—
63#4090Dic312yescomplemented
64#4075—22no—
65#4072C2×D311yescharacteristic
66C2×#681—32no—
67#3968—62no—
68#3937—64no—
69#1912—151noSylow
70C23×C3×C5C2×D411yescharacteristic
71C22×C3×D5—21no—
72C3×C5×Q8—24no—
73C3×C5×Q8—24no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5C22⋊C414yes—
77C2×C3×C4×C5C22×C411yescharacteristic
78C2×C3×C4×C5C2×D412yes—
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×C3×C4×C5#4112yes—
81C2×C5×Dic3—24no—
82C3×C22⋊D5—41no—
83C3×C22⋊D5—41no—
84C2×C3×Dic5—22no—
85C2×C3×Dic5—21no—
86C3×D20—22no—
87C3×C4×D5—42no—
88C3×Dic10—22no—
89C3⋊#168—42no—
90C2×C3×#41—51no—
91C22×C3×Q8C2×D511yescharacteristic
92C3×C4⋊Q8—52no—
93C3×#124—52no—
94C3×#123—102no—
95C3×C22⋊Q8—102no—
96C3×#117—51no—
97Q8×Dic3—24no—
98#926—22no—
99#926C2×D512yes—
100C2×#208—52no—
101#837—104no—
102#836—102no—
103C2×C5×Q8—22no—
104C2×C5×Q8—22no—
105C2×C5×Q8C2×Dic312yes—
106C2×C5×Q8#6712yes—
107C22×C4×C5#6712yes—
108C22×C4×C5C22×D311yescharacteristic
109C2×C22⋊D5—21no—
110#709—22no—
111#709—22no—
112C2×D20C2×Dic311yescharacteristic
113C2×C4×D5—21no—
114C2×Dic10C2×Dic311yescharacteristic
115C5×C4⋊C4—64no—
116C5×C4⋊C4—62no—
117C5×C22⋊C4—62no—
118C42×C5—34no—
119C42×C5—64no—
120C22⋊Dic5—21no—
121#685—24no—
122C4⋊Dic5—21no—
123#683—24no—
124C4×Dic5C2×Dic312yes—
125#681—62no—
126#681—62no—
127C2×#168—62no—
128#536—51no—
129#519—31no—
130#421—152no—
131C2×#101—151no—
132H(3,ℤ/4)—152no—
133C22×C3×C5—41no—
134C22×C3×C5C2×C22⋊C411yescharacteristic
135C22×C3×C5#12011yescharacteristic
136C22×C3×C5#12311yescharacteristic
137C2×C3×D5—42no—
138C2×C3×D5—41no—
139C3×C4×C5—24no—
140C3×C4×C5C4×D412yes—
141C3×C4×C5#12112yes—
142C3×Dic5—42no—
143C3×Dic5—41no—
144C5×Dic3—44no—
145C3×#41—102no—
146C3×#41—102no—
147C2×C3×Q8—22no—
148C2×C3×Q8—22no—
149C2×C3×Q8—51no—
150C2×C3×Q8C4×D512yes—
151C2×C3×Q8D2012yes—
152C2×C3×D4—51no—
153C2×C3×D4—101no—
154C22×C3×C4—101no—
155C22×C3×C4C22⋊D512yes—
156C22×C3×C4C22×D511yescharacteristic
157C3×C4⋊C4—104no—
158C3×C4⋊C4—101no—
159C3×C22⋊C4—101no—
160C3×C22⋊C4—104no—
161C3×C42—52no—
162#217—22no—
163C4⋊Dic3—24no—
164C4⋊Dic3—22no—
165C4×Dic3—24no—
166C4×Dic3C22⋊D514yes—
167#208—102no—
168#208—102no—
169C2×C3⋊C8—102no—
170C23×C5C2×#6711yescharacteristic
171C22×D5—21no—
172C5×Q8—24no—
173C5×Q8—24no—
174C2×C4×C5—22no—
175C2×C4×C5—22no—
176C2×C4×C5—64no—
177C2×C4×C5#21714yes—
178C2×C4×C5D3×D412yes—
179C2×C4×C5#23712yes—
180C2×C4×C5C22×Dic311yescharacteristic
181C2×C4×C5C2×#6711yescharacteristic
182C22⋊D5—41no—
183C22⋊D5—41no—
184C2×Dic5—22no—
185C2×Dic5—21no—
186D20—22no—
187C4×D5—42no—
188Dic10—22no—
189#168—122no—
190C2×#41—51no—
191C22×Q8D3×D511yescharacteristic
192C2×M16—152no—
193C4⋊Q8—52no—
194#124—52no—
195#123—102no—
196C22⋊Q8—102no—
197C4×Q8—64no—
198#117—32no—
199#117—51no—
200#117—62no—
201#104—304no—
202#101—302no—
203C2×C3×C5—21no—
204C2×C3×C5—21no—
205C2×C3×C5—21no—
206C2×C3×C5#38611yescharacteristic
207C3×D5—81no—
208C23×C3—101no—
209C23×C3C2×C22⋊D511yescharacteristic
210C3×Q8—24no—
211C3×Q8—24no—
212C3×Q8—102no—
213C3×D4—102no—
214C3×D4—201no—
215C3×D4—201no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—102no—
219C2×C3×C4—101no—
220C2×C3×C4—202no—
221C2×C3×C4#68514yes—
222C2×C3×C4C2×C4×D511yescharacteristic
223C2×C3×C4C2×D2011yescharacteristic
224C2×C3×C4#70912yes—
225C2×C3×C4C2×C22⋊D512yes—
226C2×Dic3—24no—
227C3⋊C8—202no—
228C22×C5—41no—
229C22×C5#93511yescharacteristic
230C22×C5#93711yescharacteristic
231C22×C5C2×#21711yescharacteristic
232C2×D5—42no—
233C2×D5—41no—
234C4×C5—24no—
235C4×C5—124no—
236C4×C5D4×Dic312yes—
237C4×C5#93912yes—
238Dic5—42no—
239Dic5—41no—
240#41—102no—
241#41—102no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—51no—
245C2×Q8D5×Dic312yes—
246C2×Q8#120212yes—
247C2×D4—51no—
248C2×D4—101no—
249C22×C4—101no—
250C22×C4#120112yes—
251C22×C4C2×D3×D511yescharacteristic
252M16—302no—
253M16—302no—
254C2×C8—302no—
255C4⋊C4—64no—
256C4⋊C4—62no—
257C4⋊C4—104no—
258C4⋊C4—101no—
259C22⋊C4—62no—
260C22⋊C4—101no—
261C22⋊C4—104no—
262C42—34no—
263C42—52no—
264C42—64no—
265C3×C5#191211yescharacteristic, complemented, Hall
266C22×C3—41no—
267C22×C3—202no—
268C22×C3—201no—
269C22×C3C2×#68511yescharacteristic
270C22×C3#407511yescharacteristic
271C22×C3#409911yescharacteristic
272C3×C4—24no—
273C3×C4—202no—
274C3×C4—201no—
275C3×C4C4×C22⋊D512yes—
276C3×C4#407612yes—
277Dic3—44no—
278C2×C5—21no—
279C2×C5—21no—
280C2×C5—21no—
281C2×C5#522011yescharacteristic
282D5—81no—
283C23—101no—
284C23C2×#120111yescharacteristic
285Q8—24no—
286Q8—24no—
287Q8—102no—
288D4—102no—
289D4—201no—
290D4—201no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—64no—
294C2×C4—102no—
295C2×C4—101no—
296C2×C4—202no—
297C2×C4#666514yes—
298C2×C4C2×D5×Dic311yescharacteristic
299C2×C4#677912yes—
300C2×C4C2×#120211yescharacteristic
301C2×C4D3×C22⋊D512yes—
302C8—602no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—401no—
307C2×C3#6550211yescharacteristic
308C5#7186411yescharacteristic, complemented, Sylow
309C22—41no—
310C22—202no—
311C22—201no—
312C22C2×#666511yescharacteristic
313C22#9153611yescharacteristic
314C22#9156811yescharacteristic
315C4—24no—
316C4—124no—
317C4—202no—
318C4—201no—
319C4Dic3×C22⋊D512yes—
320C4#9156912yes—
321C3#1060245611yescharacteristic, complemented, Sylow
322C2—21no—
323C2—21no—
324C2—21no—
325C2—401no—
326C2#1174949511yescharacteristic
subgroupG/H
centerC2#11749495
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC2×C3×C5#386
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5#1912
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5812C2semidirect
3. C2×#91120C2semidirect
5. #11745969C2semidirect
13. C3×#4093C4semidirect
15. C3×#4090C4semidirect
52. #5812D5semidirect
61. #4093Dic3semidirect
63. #4090Dic3semidirect
265. C3×C5#1912semidirect
308. C5#71864semidirect
321. C3#10602456semidirect

Maximal subgroups

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

subgroupindex
C5×#58122
C3×#661502
C2×#911202
#117484212
#117459692
#106024563
#718645