Finite Group Databasebeta

← #14317136

Subgroups — #14317136

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
1C2×C5×#800C211yesmaximal, characteristic
2#11748018C211yesmaximal, characteristic, complemented
3Dic5×D24C211yesmaximal, characteristic
4C2×#90944C211yesmaximal, characteristic
5#11746324C211yesmaximal, characteristic, complemented
6C3×#64721C211yesmaximal, characteristic, complemented
7#11745900C211yesmaximal, characteristic, complemented
8#10602269—31nomaximal, Hall
9C2×Dic60C2211yescharacteristic
10C2×C5×Dic12C2211yescharacteristic
11C2×C5×D24C2211yescharacteristic
12Dic5×D12—21no—
13#91376—21no—
14C2×#6663—21no—
15C2×C3×C5×C16C2211yescharacteristic
16#91102C2211yescharacteristic
17C5×#800—22no—
18C3×C8×Dic5C2211yescharacteristic
19C2×C3×#672C2211yescharacteristic
20#90967—21no—
21#90944—22no—
22#69287—51nomaximal, Hall
23C2×C5×SD32—31no—
24#65470—31no—
25D8×Dic5—31no—
26C2×#3959—31no—
27#64784—31no—
28#64723—31no—
29#64721D311yescharacteristic, complemented
30C2×Dic30—21no—
31C2×C5×D12—21no—
32C2×C5×Dic6—21no—
33C2×D3×Dic5—41no—
34C2×C3×C5×C8C2311yescharacteristic
35C4⋊Dic15—21no—
36Dic60—21no—
37Dic60—21no—
38C5×Dic12—21no—
39C5×Dic12—21no—
40C5×D24—21no—
41C5×D24D412yes—
42C3×C4×Dic5D411yescharacteristic
43C2×C3×#168D411yescharacteristic
44#6668—41no—
45#6668—41no—
46(C2×D3)⋊Dic5—41no—
47#6663—42no—
48C3×C5×C16—21no—
49C3×#672—21no—
50C2×#800—51no—
51C2×#800D511yescharacteristic
52#4699—51no—
53C4×D24—51no—
54C3×C4⋊C16—51no—
55#4503—51no—
56#4503—51no—
57C2×C5×Q16—31no—
58C2×C5×D8—31no—
59#4090—61no—
60C2×#689—61no—
61D4×Dic5—61no—
62C2×Dic20—31no—
63C5×SD32—62no—
64C2×C5×C16C2×D311yescharacteristic
65#3964—61no—
66#3959—62no—
67#3950—31no—
68C8×Dic5C2×D311yescharacteristic
69C2×#672C2×D311yescharacteristic
70#2208—151noSylow
71C22×C5×D3—41no—
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×Dic15—41no—
74C2×Dic15—41no—
75Dic30—41no—
76Dic30—41no—
77C2×C5×Dic3—41no—
78C5×D12—22no—
79C5×D12—41no—
80C5×Dic6—41no—
81C5×Dic6—41no—
82C2×C3×Dic5D811yescharacteristic
83C2×C3×Dic5D811yescharacteristic
84D3×Dic5—82no—
85C3×C5×C8C2×D411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C3×#168—21no—
88C2×Dic12—51no—
89C2×Dic12—101no—
90C2×Dic12C2×D511yescharacteristic
91C2×D24C2×D511yescharacteristic
92C4×D12—101no—
93#869—101no—
94C2×C3×C16—51no—
95C2×C3×C16C2×D511yescharacteristic
96C3×C4×C8—51no—
97#821—101no—
98#818—51no—
99#800—22no—
100#800—102no—
101C2×C5×Q8—61no—
102C2×C5×D4—61no—
103C22×Dic5—121no—
104C2×Dic10—61no—
105C5×Q16—61no—
106C5×Q16—61no—
107C5×D8—32no—
108C5×D8—61no—
109C2×C5×C8C22×D311yescharacteristic
110C22⋊Dic5—121no—
111#689—122no—
112C4⋊Dic5—61no—
113#683—121no—
114#683—121no—
115C4×Dic5D1211yescharacteristic
116C2×#168D1211yescharacteristic
117Dic20—61no—
118Dic20—61no—
119C5×C16—21no—
120#672—21no—
121C2×SD32—31no—
122C2×SD32—151no—
123#494—151no—
124C4×D8—151no—
125C4⋊C16—51no—
126#358—151no—
127#358—151no—
128C22×C3×C5C2×D811yescharacteristic
129C2×C5×D3—42no—
130C2×C5×D3—81no—
131C2×C5×D3—81no—
132C3×C4×C5#12111yescharacteristic
133C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
134Dic15—81no—
135Dic15—81no—
136C3×Dic5—21no—
137C3×Dic5SD3212yescomplemented
138C5×Dic3—81no—
139C2×D12—21no—
140C2×C4×D3—201no—
141C2×Dic6—21no—
142C2×Dic6—101no—
143C2×C3×C8—51no—
144C2×C3×C8C22×D511yescharacteristic
145C3×C42—51no—
146(C2×D3)⋊C4—201no—
147C4⋊Dic3—101no—
148C4⋊Dic3—201no—
149C4⋊Dic3—201no—
150Dic12—21no—
151Dic12—21no—
152Dic12—101no—
153Dic12—101no—
154Dic12—202no—
155D24—21no—
156D24C22⋊D512yes—
157C3×C16—21no—
158C3×C16—101no—
159C23×C5—121no—
160C5×Q8—121no—
161C5×Q8—121no—
162C5×D4—62no—
163C5×D4—121no—
164C2×C4×C5—121no—
165C2×C4×C5C2×D1211yescharacteristic
166C2×Dic5—121no—
167C2×Dic5—121no—
168C2×Dic5—242no—
169C2×Dic5D2411yescharacteristic
170C2×Dic5D2411yescharacteristic
171Dic10—121no—
172Dic10—121no—
173C5×C8D3×D411yescharacteristic
174C5×C8#23911yescharacteristic
175#168—21no—
176C2×Q16—31no—
177C2×Q16—151no—
178C2×Q16—301no—
179C2×D8—31no—
180C4⋊Q8—301no—
181C4×D4—301no—
182SD32—62no—
183SD32—302no—
184C2×C16—51no—
185C2×C16D3×D511yescharacteristic
186#107—151no—
187#102—301no—
188C4×C8—51no—
189C2×C3×C5#45911yescharacteristic
190C2×C3×C5C2×SD3211yescharacteristic
191C2×C3×C5#51011yescharacteristic
192C5×D3—82no—
193C22×D3—41no—
194C2×C3×C4—51no—
195C2×C3×C4—51no—
196C2×C3×C4D4×D511yescharacteristic
197C2×Dic3—41no—
198C2×Dic3—201no—
199C2×Dic3—201no—
200D12—22no—
201D12—41no—
202C4×D3—402no—
203Dic6—41no—
204Dic6—41no—
205Dic6—201no—
206Dic6—201no—
207C3×C8—101no—
208C3×C8#71111yescharacteristic
209C3×C8C2×C22⋊D511yescharacteristic
210C22×C5—122no—
211C22×C5—241no—
212C22×C5—241no—
213C22×C5C2×D2411yescharacteristic
214C4×C5—241no—
215C4×C5#89511yescharacteristic
216C4×C5#90811yescharacteristic
217Dic5—21no—
218Dic5—241no—
219Dic5—241no—
220Dic5#80012yescomplemented
221C2×Q8—61no—
222C2×Q8—301no—
223C2×D4—61no—
224C22×C4—601no—
225Q16—61no—
226Q16—61no—
227Q16—301no—
228Q16—301no—
229Q16—602no—
230D8—32no—
231D8—61no—
232C2×C8—51no—
233C2×C8C2×D3×D511yescharacteristic
234C4⋊C4—301no—
235C4⋊C4—601no—
236C4⋊C4—601no—
237C22⋊C4—601no—
238C42—51no—
239C16—21no—
240C16—101no—
241C3×C5#220811yescharacteristic, complemented, Hall
242C22×C3D5×D811yescharacteristic
243C2×D3—42no—
244C2×D3—81no—
245C2×D3—81no—
246C3×C4—52no—
247C3×C4—101no—
248C3×C4#405711yescharacteristic
249C3×C4#408511yescharacteristic
250Dic3—81no—
251Dic3—401no—
252Dic3—401no—
253C2×C5—242no—
254C2×C5#484311yescharacteristic
255C2×C5C2×#80011yescharacteristic
256C2×C5#490911yescharacteristic
257C23—121no—
258Q8—121no—
259Q8—121no—
260Q8—601no—
261Q8—601no—
262D4—62no—
263D4—121no—
264C2×C4—51no—
265C2×C4—51no—
266C2×C4—121no—
267C2×C4—601no—
268C2×C4—601no—
269C2×C4—1202no—
270C2×C4D5×D1211yescharacteristic
271C8—101no—
272C8#676811yescharacteristic
273C8D3×C22⋊D511yescharacteristic
274C2×C3D5×SD3211yescharacteristic
275C2×C3#6520411yescharacteristic
276C2×C3#6543911yescharacteristic
277D3—82no—
278C5#6928711yescharacteristic, complemented, Sylow
279C22—122no—
280C22—241no—
281C22—241no—
282C22D5×D2411yescharacteristic
283C4—52no—
284C4—101no—
285C4—241no—
286C4—1201no—
287C4—1201no—
288C4#9125011yescharacteristic
289C4#9141611yescharacteristic
290C3#1060226911yescharacteristic, complemented, Sylow
291C2—242no—
292C2D5×#80011yescharacteristic
293C2#1174682811yescharacteristic
294C2#1174776411yescharacteristic
subgroupG/H
centerC22D5×D24
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×C16C22
socleC22×C3×C5C2×D8
prime radicalC2×C5×D24C22
hypercenterC2×C16D3×D5
hypocenterC3×C5#2208
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
2. #11748018C2semidirect
5. #11746324C2semidirect
6. C3×#64721C2semidirect
7. #11745900C2semidirect
29. #64721D3semidirect
137. C3×Dic5SD32semidirect
220. Dic5#800semidirect
241. C3×C5#2208semidirect
278. C5#69287semidirect
290. C3#10602269semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8002
#117480182
Dic5×D242
C2×#909442
#117463242
C3×#647212
#117459002
#106022693
#692875