Finite Group Databasebeta

← #14317140

Subgroups — #14317140

Order 1920.

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

normal subgroups only

This group has 332 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
1C3×#65161C211yesmaximal, characteristic
2#11748018C211yesmaximal, characteristic, complemented
3C2×#90942C211yesmaximal, characteristic
4C2×#90940C211yesmaximal, characteristic
5#11746313C211yesmaximal, characteristic, complemented
6C5×#4492C211yesmaximal, characteristic, complemented
7#11745927C211yesmaximal, characteristic, complemented
8#10600027—31nomaximal, Hall
9C2×Dic60C2211yescharacteristic
10C2×C5×Dic12C2211yescharacteristic
11C2×C3×D40C2211yescharacteristic
12C3×#4039—21no—
13#91376—21no—
14C2×#6663—21no—
15C3×C5×#107C2211yescharacteristic
16C2×C3⋊#672C2211yescharacteristic
17C2×C5×C3⋊C16C2211yescharacteristic
18C3×C8×Dic5C2211yescharacteristic
19C3×#3941—21no—
20#90942—22no—
21#90940—22no—
22#70892—51nomaximal, Hall
23#65470—31no—
24C2×#3960—31no—
25C2×#3932—31no—
26#65161D311yescharacteristic
27C5×#358—31no—
28#64721—31no—
29#64712—31no—
30C2×Dic30—21no—
31C2×C5×Dic6—21no—
32C2×C3×D20—21no—
33C2×C3×C4×D5—41no—
34C2×C3×C5×C8C2311yescharacteristic
35C3×C5×C4⋊C4—21no—
36Dic60—21no—
37Dic60—21no—
38C5×Dic12—21no—
39C5×Dic12—21no—
40C3×#685—41no—
41C3×C4×Dic5D411yescharacteristic
42C2×C3×#168D411yescharacteristic
43C3×D40—21no—
44C3×D40D412yes—
45#6668—41no—
46#6668—41no—
47#6663—42no—
48C3⋊#672—21no—
49C5×C3⋊C16—21no—
50C3×C4×D8—51no—
51C2×#827—51no—
52C2×#827—51no—
53#4699—51no—
54#4492—51no—
55#4492D511yescharacteristic, complemented
56C4⋊(C3⋊C16)—51no—
57C2×C5×Q16—31no—
58#4090—61no—
59C2×#689—61no—
60C2×Dic20—31no—
61C2×D40C2×D311yescharacteristic
62#4039—21no—
63C2×C5×C16—31no—
64C5×#107C2×D311yescharacteristic
65#3960—62no—
66C8×Dic5C2×D311yescharacteristic
67C2×#672—31no—
68#3941—21no—
69#3932—62no—
70#2208—151noSylow
71C22×C3×D5—41no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×Dic15—41no—
75Dic30—41no—
76Dic30—41no—
77C2×C5×Dic3—41no—
78C5×Dic6—41no—
79C5×Dic6—41no—
80C2×C3×Dic5D811yescharacteristic
81C2×C3×Dic5D811yescharacteristic
82C3×D20—22no—
83C3×D20—41no—
84C3×C4×D5—82no—
85C3×C5×C8C2×D411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C3×#168—21no—
88C2×C3×D8—51no—
89C3×C4×D4—101no—
90C2×Dic12—51no—
91C2×Dic12—101no—
92C2×Dic12C2×D511yescharacteristic
93#869—101no—
94C3×#107C2×D511yescharacteristic
95C3×#102—101no—
96C3×C4×C8—51no—
97#827—102no—
98#827—102no—
99C2×C3⋊C16—51no—
100C2×C3⋊C16C2×D511yescharacteristic
101C2×C5×Q8—61no—
102C2×D20—21no—
103C2×C4×D5—41no—
104C2×Dic10—61no—
105C5×Q16—61no—
106C5×Q16—61no—
107C2×C5×C8C22×D311yescharacteristic
108C5×C4⋊C4—21no—
109#689—122no—
110#685—41no—
111#683—121no—
112#683—121no—
113C4×Dic5#6711yescharacteristic
114C2×#168#6711yescharacteristic
115Dic20—61no—
116Dic20—61no—
117D40—21no—
118D40D1212yes—
119C5×C16—61no—
120#672—61no—
121C2×SD32—151no—
122C2×SD32—151no—
123#494—151no—
124C4×D8—51no—
125C4⋊C16—151no—
126#358—31no—
127#358—151no—
128C22×C3×C5C2×D811yescharacteristic
129C2×C3×D5—42no—
130C2×C3×D5—81no—
131C2×C3×D5—81no—
132C3×C4×C5—81no—
133C3×C4×C5#12111yescharacteristic
134C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
135Dic15—81no—
136C3×Dic5—21no—
137C3×Dic5SD3212yescomplemented
138C5×Dic3—81no—
139C2×C3×D4—101no—
140C22×C3×C4—201no—
141C2×Dic6—21no—
142C2×Dic6—101no—
143C3×D8—52no—
144C3×D8—101no—
145C2×C3×C8—51no—
146C2×C3×C8C22×D511yescharacteristic
147C3×C4⋊C4—21no—
148C3×C22⋊C4—201no—
149C3×C42—51no—
150C4⋊Dic3—201no—
151C4⋊Dic3—201no—
152Dic12—21no—
153Dic12—21no—
154Dic12—101no—
155Dic12—101no—
156Dic12—202no—
157C3⋊C16—21no—
158C3⋊C16—101no—
159C22×D5—41no—
160C5×Q8—121no—
161C5×Q8—121no—
162C2×C4×C5—41no—
163C2×C4×C5—121no—
164C2×C4×C5C2×#6711yescharacteristic
165C2×Dic5—121no—
166C2×Dic5#21311yescharacteristic
167C2×Dic5#21311yescharacteristic
168D20—22no—
169D20—41no—
170C4×D5—82no—
171Dic10—121no—
172Dic10—121no—
173C5×C8C2×D1211yescharacteristic
174C5×C8#23511yescharacteristic
175#168—21no—
176C2×Q16—31no—
177C2×Q16—151no—
178C2×Q16—301no—
179C2×D8—51no—
180C4⋊Q8—301no—
181C4×D4—101no—
182SD32—302no—
183SD32—302no—
184C2×C16—31no—
185C2×C16—151no—
186#107D3×D511yescharacteristic
187#102—101no—
188C4×C8—51no—
189C2×C3×C5#45911yescharacteristic
190C2×C3×C5C2×SD3211yescharacteristic
191C2×C3×C5#51011yescharacteristic
192C3×D5—82no—
193C23×C3—201no—
194C3×D4—102no—
195C3×D4—201no—
196C2×C3×C4—41no—
197C2×C3×C4—51no—
198C2×C3×C4—51no—
199C2×C3×C4—402no—
200C2×C3×C4D4×D511yescharacteristic
201C2×Dic3—41no—
202C2×Dic3—201no—
203Dic6—41no—
204Dic6—41no—
205Dic6—201no—
206Dic6—201no—
207C3×C8—101no—
208C3×C8#70911yescharacteristic
209C3×C8D4×D511yescharacteristic
210C22×C5C2×#21311yescharacteristic
211C2×D5—42no—
212C2×D5—81no—
213C2×D5—81no—
214C4×C5—81no—
215C4×C5—241no—
216C4×C5#93011yescharacteristic
217C4×C5#94911yescharacteristic
218Dic5—21no—
219Dic5—241no—
220Dic5#82712yescomplemented
221C2×Q8—61no—
222C2×Q8—301no—
223C2×D4—101no—
224C22×C4—201no—
225Q16—61no—
226Q16—61no—
227Q16—301no—
228Q16—301no—
229Q16—602no—
230D8—52no—
231D8—101no—
232C2×C8—51no—
233C2×C8C2×D3×D511yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—601no—
236C4⋊C4—601no—
237C22⋊C4—201no—
238C42—51no—
239C16—61no—
240C16—301no—
241C3×C5#220811yescharacteristic, complemented, Hall
242C22×C3—202no—
243C22×C3—401no—
244C22×C3—401no—
245C22×C3D5×D811yescharacteristic
246C3×C4—52no—
247C3×C4—81no—
248C3×C4—101no—
249C3×C4#403011yescharacteristic
250C3×C4#406011yescharacteristic
251Dic3—81no—
252Dic3—401no—
253C2×C5#501511yescharacteristic
254C2×C5C2×#82711yescharacteristic
255C2×C5#519511yescharacteristic
256D5—82no—
257C23—201no—
258Q8—121no—
259Q8—121no—
260Q8—601no—
261Q8—601no—
262D4—102no—
263D4—201no—
264C2×C4—41no—
265C2×C4—51no—
266C2×C4—51no—
267C2×C4—121no—
268C2×C4—402no—
269C2×C4—601no—
270C2×C4D5×#6711yescharacteristic
271C8—101no—
272C8#677111yescharacteristic
273C8D5×D1211yescharacteristic
274C2×C3—402no—
275C2×C3#6507511yescharacteristic
276C2×C3D5×SD3211yescharacteristic
277C2×C3#6520711yescharacteristic
278C5#7089211yescharacteristic, complemented, Sylow
279C22—202no—
280C22—401no—
281C22—401no—
282C22D5×#21311yescharacteristic
283C4—52no—
284C4—81no—
285C4—101no—
286C4—241no—
287C4—1201no—
288C4#9144811yescharacteristic
289C4#9150211yescharacteristic
290C3#1060002711yescharacteristic, complemented, Sylow
291C2—402no—
292C2#1174739911yescharacteristic
293C2D5×#82711yescharacteristic
294C2#1174829511yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
prime radicalC2×C3×D40C22
hypercenter#107D3×D5
hypocenterC3×C5#2208
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
2. #11748018C2semidirect
5. #11746313C2semidirect
6. C5×#4492C2semidirect
7. #11745927C2semidirect
55. #4492D5semidirect
137. C3×Dic5SD32semidirect
220. Dic5#827semidirect
241. C3×C5#2208semidirect
278. C5#70892semidirect
290. C3#10600027semidirect

Maximal subgroups

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

subgroupindex
C3×#651612
#117480182
C2×#909422
C2×#909402
#117463132
C5×#44922
#117459272
#106000273
#708925