Finite Group Databasebeta

← #14317020

Subgroups — #14317020

Order 1920.

448 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 68 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×#5722C211yesmaximal, characteristic, complemented
2#11751196C211yesmaximal, characteristic
3#11749396C212yesmaximal
4C3×#64768C211yesmaximal, characteristic, complemented
5#11746016C212yesmaximal, complemented
6#10602735—31nomaximal, Hall
7#92098C2211yescharacteristic
8C3×C5×C4⋊Q8C2211yescharacteristic
9#91831—21no—
10C5×#944—21no—
11C5×#944C2212yes—
12C5×#888—22no—
13C5×#887—22no—
14C4×C5×Dic6—21no—
15#91321—22no—
16#91120C2211yescharacteristic
17#91089—21no—
18C3×#3968C2212yes—
19#90980—22no—
20#69169—51nomaximal, Hall
21C5×Q82—31no—
22#65384—32no—
23#65384—31no—
24#64768—32no—
25#64768D311yescharacteristic, complemented
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×Q8C2311yescharacteristic
28#6821—41no—
29Q8×D15—41no—
30#6817—22no—
31#6817—21no—
32C2×C5×Dic6—21no—
33C2×C5×Dic6—21no—
34C2×C5×Dic6D412yes—
35C3×C5×C4⋊C4—22no—
36C3×C42×C5D411yescharacteristic
37#6718—41no—
38#6717—41no—
39#6710—21no—
40C5×C4⋊Dic3—21no—
41C5×Dic3⋊C4—22no—
42C5×Dic3⋊C4—22no—
43C5×Dic3⋊C4—22no—
44C4×C5×Dic3—22no—
45C4×C5×Dic3—21no—
46C4×C5×Dic3D412yes—
47C3×#681—22no—
48#6663—42no—
49#6660—42no—
50#5722D511yescharacteristic, complemented
51#5095—51no—
52#4752—52no—
53C3×#356—51no—
54#4478—52no—
55#4147—31no—
56C5×C4⋊Q8—32no—
57C5×C4⋊Q8—62no—
58C5×C4⋊Q8—61no—
59C5×C4⋊Q8C2×D311yescharacteristic
60C4×C5×Q8—62no—
61C4×C5×Q8—61no—
62#4088—62no—
63#4088—61no—
64#3968—31no—
65#3968C2×D312yes—
66#3937—62no—
67#3937—61no—
68#2205—151noSylow
69C3×C5×Q8—41no—
70C3×C5×Q8—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75#1220—41no—
76D60—22no—
77D60—21no—
78C4×D15—42no—
79C4×D15—41no—
80Dic30—22no—
81Dic30—21no—
82C2×C5×Dic3—22no—
83C2×C5×Dic3—22no—
84C5×Dic6—24no—
85C5×Dic6—42no—
86C5×Dic6—81no—
87C3⋊#168—41no—
88C3×#168—42no—
89#1007—51no—
90C3×C4⋊Q8C2×D511yescharacteristic
91#944—21no—
92#944C2×D512yes—
93#942—101no—
94#909—102no—
95#888—22no—
96#887—22no—
97C4×Dic6—21no—
98C3×#101—52no—
99#836—51no—
100#825—102no—
101#805—101no—
102C2×C5×Q8—32no—
103C2×C5×Q8—61no—
104C2×C5×Q8—61no—
105C2×C5×Q8D1211yescharacteristic
106C2×C5×Q8C22×D311yescharacteristic
107#713—121no—
108Q8×D5—121no—
109#709—61no—
110#709—62no—
111C5×C4⋊C4—22no—
112C5×C4⋊C4—62no—
113C5×C4⋊C4—61no—
114C5×C4⋊C4—62no—
115C5×C4⋊C4—62no—
116C42×C5—32no—
117C42×C5—62no—
118C42×C5—61no—
119C42×C5D1211yescharacteristic
120#689—122no—
121#689—121no—
122#688—122no—
123#688—121no—
124#681—22no—
125#681—61no—
126Q82—31no—
127#456—152no—
128#456—151no—
129#356—51no—
130#356—152no—
131C22×C3×C5#12011yescharacteristic
132C2×D15—41no—
133C3×C4×C5—22no—
134C3×C4×C5—22no—
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137Dic15—41no—
138C5×Dic3—24no—
139C5×Dic3—42no—
140C2×C3×Q8C22⋊D511yescharacteristic
141C2×C3×Q8C22×D511yescharacteristic
142#239—201no—
143D3×Q8—201no—
144#235—101no—
145#235—102no—
146C2×Dic6—21no—
147C2×Dic6—21no—
148C2×Dic6C22⋊D512yes—
149C3×M16—102no—
150C3×C4⋊C4—22no—
151C3×C42C22⋊D511yescharacteristic
152#216—201no—
153#215—201no—
154C4⋊Dic3—21no—
155Dic3⋊C4—22no—
156Dic3⋊C4—22no—
157Dic3⋊C4—22no—
158C4×Dic3—22no—
159C4×Dic3—21no—
160C4×Dic3C22⋊D512yes—
161#208—101no—
162Dic12—202no—
163#204—202no—
164C5×Q8—41no—
165C5×Q8—41no—
166C5×Q8—64no—
167C5×Q8—122no—
168C5×Q8—241no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5—62no—
172C2×C4×C5—62no—
173C2×C4×C5C2×D1211yescharacteristic
174C2×C4×C5D3×D412yes—
175C22⋊D5—121no—
176D20—62no—
177D20—61no—
178C4×D5—122no—
179C4×D5—121no—
180Dic10—62no—
181Dic10—61no—
182#168—42no—
183#168—121no—
1842−1+4—151no—
185#137—302no—
186#137—301no—
187C4⋊Q8—32no—
188C4⋊Q8—62no—
189C4⋊Q8—61no—
190C4⋊Q8D3×D511yescharacteristic
191C4×Q8—62no—
192C4×Q8—61no—
193#104—302no—
194#104—301no—
195#101—52no—
196#101—151no—
197C2×C3×C5—21no—
198C2×C3×C5B(4,𝔽2)11yescharacteristic
199D15—81no—
200C3×Q8—41no—
201C3×Q8—41no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4C2×C22⋊D511yescharacteristic
205C2×C3×C4C2×C22⋊D512yes—
206#67—201no—
207C2×Dic3—22no—
208C2×Dic3—22no—
209D12—102no—
210D12—101no—
211C4×D3—201no—
212C4×D3—202no—
213Dic6—24no—
214Dic6—42no—
215Dic6—81no—
216Dic6—102no—
217Dic6—101no—
218C3×C8—202no—
219C3⋊C8—201no—
220C22×C5#88211yescharacteristic
221C2×D5—121no—
222C4×C5—22no—
223C4×C5—22no—
224C4×C5—21no—
225C4×C5—41no—
226C4×C5—64no—
227C4×C5—122no—
228Dic5—121no—
229#41—301no—
230#41—302no—
231#41—601no—
232C2×Q8—32no—
233C2×Q8—61no—
234C2×Q8—61no—
235C2×Q8—601no—
236C2×Q8#120311yescharacteristic
237C2×Q8C2×D3×D511yescharacteristic
238Q16—602no—
239Q16—601no—
240SD16—602no—
241SD16—601no—
242M16—102no—
243M16—301no—
244C4⋊C4—22no—
245C4⋊C4—62no—
246C4⋊C4—61no—
247C4⋊C4—62no—
248C4⋊C4—62no—
249C42—32no—
250C42—62no—
251C42—61no—
252C42#120311yescharacteristic
253C3×C5#220511yescharacteristic, complemented, Hall
254C22×C3#409911yescharacteristic
255C2×D3—201no—
256C3×C4—22no—
257C3×C4—21no—
258C3×C4—22no—
259C3×C4—41no—
260Dic3—24no—
261Dic3—42no—
262Dic3—201no—
263C2×C5—21no—
264C2×C5#474111yescharacteristic
265D5—241no—
266Q8—41no—
267Q8—41no—
268Q8—64no—
269Q8—122no—
270Q8—241no—
271Q8—302no—
272Q8—301no—
273D4—302no—
274D4—301no—
275D4—601no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—62no—
279C2×C4—62no—
280C2×C4—602no—
281C2×C4—601no—
282C2×C4C2×#120311yescharacteristic
283C2×C4D3×C22⋊D512yes—
284C8—202no—
285C8—601no—
286C2×C3—21no—
287C2×C3#6553311yescharacteristic
288D3—401no—
289C5#6916911yescharacteristic, complemented, Sylow
290C22—601no—
291C22#9157011yescharacteristic
292C4—22no—
293C4—22no—
294C4—21no—
295C4—41no—
296C4—64no—
297C4—122no—
298C4—601no—
299C3#1060273511yescharacteristic, complemented, Sylow
300C2—21no—
301C2—1201no—
302C2#1174917811yescharacteristic
subgroupG/H
centerC2#11749178
commutator, cosocleC2×C3×C5×Q8C23
FrattiniC2×Q8C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC2×C3×C5B(4,𝔽2)
prime radical#92098C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#2205
LCSG ▷ C2×C3×C5×Q8 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5722C2semidirect
4. C3×#64768C2semidirect
5. #11746016C2semidirect
25. #64768D3semidirect
50. #5722D5semidirect
253. C3×C5#2205semidirect
289. C5#69169semidirect
299. C3#10602735semidirect

Maximal subgroups

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

subgroupindex
C5×#57222
#117511962
#117493962
C3×#647682
#117460162
#106027353
#691695