Finite Group Databasebeta

← #14317112

Subgroups — #14317112

Order 1920.

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

normal subgroups only

This group has 332 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, complemented
2C2×#91112C211yesmaximal, characteristic
3C2×#91084C211yesmaximal, characteristic
4#11750973C211yesmaximal, characteristic
5C3×C5×#358C211yesmaximal, characteristic, complemented
6#11746322C211yesmaximal, characteristic, complemented
7#11746313C211yesmaximal, characteristic, complemented
8#10600027—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10#91833—21no—
11C2×#6718—21no—
12C2×Dic60C2211yescharacteristic
13C2×D120C2211yescharacteristic
14#91782—21no—
15C2×C3×C5×C16C2211yescharacteristic
16C3×C5×#107C2211yescharacteristic
17#91112—22no—
18C8×Dic15C2211yescharacteristic
19C2×C3⋊#672C2211yescharacteristic
20#91093—21no—
21#91084—22no—
22#69234—51nomaximal, Hall
23#65470—31no—
24C2×#3960—31no—
25C2×#3932—31no—
26#65161—31no—
27C5×#358D311yescharacteristic, complemented
28#64721—31no—
29#64712—31no—
30C2×C3×C5×Q8—21no—
31C2×D60—21no—
32C2×C4×D15—41no—
33C2×Dic30—21no—
34C3×C5×Q16—21no—
35C3×C5×Q16—21no—
36C2×C3×C5×C8C2311yescharacteristic
37C3×C5×C4⋊C4—21no—
38#6718—42no—
39#6714—41no—
40#6712—41no—
41#6712—41no—
42C4×Dic15D411yescharacteristic
43C2×C3⋊#168D411yescharacteristic
44Dic60—21no—
45Dic60—21no—
46D120—21no—
47D120D412yes—
48C3×C5×C16—21no—
49C3⋊#672—21no—
50#5183—51no—
51C2×#828—51no—
52C2×#800—51no—
53#4872—51no—
54C3×#358D511yescharacteristic, complemented
55Dic3⋊C16—51no—
56#4492—51no—
57C2×C5×Q16C2×D311yescharacteristic
58#4090—61no—
59C2×#689—61no—
60C2×Dic20—31no—
61C2×D40—31no—
62#4039—61no—
63C2×C5×C16C2×D311yescharacteristic
64C5×#107C2×D311yescharacteristic
65#3960—62no—
66C8×Dic5—31no—
67C2×#672—31no—
68#3941—61no—
69#3932—62no—
70#2208—151noSylow
71C22×D15—41no—
72C3×C5×Q8—41no—
73C3×C5×Q8—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×Dic15—41no—
78C2×Dic15D811yescharacteristic
79C2×Dic15D811yescharacteristic
80D60—22no—
81D60—41no—
82C4×D15—82no—
83Dic30—41no—
84Dic30—41no—
85C3×C5×C8C2×D411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C3⋊#168—21no—
88C2×C3×Q16C2×D511yescharacteristic
89#944—101no—
90C2×#216—101no—
91C2×Dic12—51no—
92C2×D24—51no—
93#893—101no—
94C2×C3×C16C2×D511yescharacteristic
95C3×#107C2×D511yescharacteristic
96#828—102no—
97C8×Dic3—51no—
98C2×C3⋊C16—51no—
99#809—101no—
100#800—102no—
101C2×C5×Q8—21no—
102C2×D20—61no—
103C2×C4×D5—121no—
104C2×Dic10—61no—
105C5×Q16—21no—
106C5×Q16—21no—
107C2×C5×C8C22×D311yescharacteristic
108C5×C4⋊C4—21no—
109#689—122no—
110#685—121no—
111#683—121no—
112#683—121no—
113C4×Dic5—31no—
114C2×#168—31no—
115Dic20—61no—
116Dic20—61no—
117D40—32no—
118D40—61no—
119C5×C16—21no—
120#672—61no—
121C2×SD32—151no—
122C2×SD32—151no—
123#494—151no—
124C4×D8—151no—
125C4⋊C16—151no—
126#358—151no—
127#358D1511yescharacteristic, complemented
128C22×C3×C5C2×D811yescharacteristic
129C2×D15—42no—
130C2×D15—81no—
131C2×D15—81no—
132C3×C4×C5—81no—
133C3×C4×C5—81no—
134C3×C4×C5#12111yescharacteristic
135C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
136Dic15—21no—
137Dic15—81no—
138Dic15SD3212yescomplemented
139C2×C3×Q8—21no—
140C2×D12—101no—
141C2×C4×D3—201no—
142C2×Dic6—101no—
143C3×Q16—21no—
144C3×Q16—21no—
145C2×C3×C8C22×D511yescharacteristic
146C3×C4⋊C4—21no—
147#216—202no—
148(C2×D3)⋊C4—201no—
149Dic3⋊C4—201no—
150Dic3⋊C4—201no—
151C4×Dic3—51no—
152C2×C3⋊C8—51no—
153Dic12—101no—
154Dic12—101no—
155D24—52no—
156D24—101no—
157C3×C16—21no—
158C3⋊C16—101no—
159C22×D5—121no—
160C5×Q8—41no—
161C5×Q8—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5D3×D411yescharacteristic
165C2×Dic5—31no—
166C2×Dic5—31no—
167C2×Dic5—121no—
168D20—62no—
169D20—121no—
170C4×D5—242no—
171Dic10—121no—
172Dic10—121no—
173C5×C8#23511yescharacteristic
174C5×C8D3×D411yescharacteristic
175#168—61no—
176C2×Q16—151no—
177C2×Q16—301no—
178C2×Q16C2×D1511yescharacteristic
179C2×D8—151no—
180C4⋊Q8—301no—
181C4×D4—301no—
182SD32—302no—
183SD32—302no—
184C2×C16—151no—
185C2×C16C2×D1511yescharacteristic
186#107C2×D1511yescharacteristic
187#102—301no—
188C4×C8—151no—
189C2×C3×C5#45911yescharacteristic
190C2×C3×C5C2×SD3211yescharacteristic
191C2×C3×C5#51011yescharacteristic
192D15—82no—
193C22×D3—201no—
194C3×Q8—41no—
195C3×Q8—41no—
196C2×C3×C4—41no—
197C2×C3×C4—41no—
198C2×C3×C4D4×D511yescharacteristic
199C2×Dic3—51no—
200C2×Dic3—51no—
201C2×Dic3—201no—
202D12—102no—
203D12—201no—
204C4×D3—402no—
205Dic6—201no—
206Dic6—201no—
207C3×C8#70911yescharacteristic
208C3×C8D4×D511yescharacteristic
209C3⋊C8—101no—
210C22×C5D3×D811yescharacteristic
211C2×D5—122no—
212C2×D5—241no—
213C2×D5—241no—
214C4×C5—81no—
215C4×C5—81no—
216C4×C5#88411yescharacteristic
217C4×C5#91411yescharacteristic
218Dic5—32no—
219Dic5—61no—
220Dic5—241no—
221C2×Q8—21no—
222C2×Q8—301no—
223C2×D4—301no—
224C22×C4—601no—
225Q16—21no—
226Q16—21no—
227Q16—301no—
228Q16—301no—
229Q16—602no—
230D8—152no—
231D8—301no—
232C2×C8—151no—
233C2×C8C22×D1511yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—601no—
236C4⋊C4—601no—
237C22⋊C4—601no—
238C42—151no—
239C16—21no—
240C16—301no—
241C3×C5#220811yescharacteristic, complemented, Hall
242C22×C3D5×D811yescharacteristic
243C2×D3—202no—
244C2×D3—401no—
245C2×D3—401no—
246C3×C4—81no—
247C3×C4—81no—
248C3×C4#403011yescharacteristic
249C3×C4#406011yescharacteristic
250Dic3—52no—
251Dic3—101no—
252Dic3—401no—
253C2×C5#478611yescharacteristic
254C2×C5D3×SD3211yescharacteristic
255C2×C5#491811yescharacteristic
256D5—242no—
257C23—601no—
258Q8—41no—
259Q8—41no—
260Q8—601no—
261Q8—601no—
262D4—302no—
263D4—601no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—151no—
267C2×C4—151no—
268C2×C4—601no—
269C2×C4—1202no—
270C2×C4D4×D1511yescharacteristic
271C8—301no—
272C8#681711yescharacteristic
273C8D4×D1511yescharacteristic
274C2×C3#6507511yescharacteristic
275C2×C3D5×SD3211yescharacteristic
276C2×C3#6520711yescharacteristic
277D3—402no—
278C5#6923411yescharacteristic, complemented, Sylow
279C22—602no—
280C22—1201no—
281C22—1201no—
282C22D8×D1511yescharacteristic
283C4—81no—
284C4—81no—
285C4—152no—
286C4—301no—
287C4—1201no—
288C4#9177311yescharacteristic
289C4#9180311yescharacteristic
290C3#1060002711yescharacteristic, complemented, Sylow
291C2—1202no—
292C2#1175088711yescharacteristic
293C2D15×SD3211yescharacteristic
294C2#1175101911yescharacteristic
subgroupG/H
centerC22D8×D15
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#358C2
socleC22×C3×C5C2×D8
prime radicalC2×D120C22
hypercenter#358D15
hypocenterC3×C5#2208
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
1. #11751284C2semidirect
5. C3×C5×#358C2semidirect
6. #11746322C2semidirect
7. #11746313C2semidirect
27. C5×#358D3semidirect
54. C3×#358D5semidirect
127. #358D15semidirect
138. Dic15SD32semidirect
241. C3×C5#2208semidirect
278. C5#69234semidirect
290. C3#10600027semidirect

Maximal subgroups

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

subgroupindex
#117512842
C2×#911122
C2×#910842
#117509732
C3×C5×#3582
#117463222
#117463132
#106000273
#692345