Finite Group Databasebeta

← #14316198

Subgroups — #14316198

Order 1920.

432 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 87 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×Q16×D15C211yesmaximal, characteristic
2C2×C3×C5×Q32C211yesmaximal, characteristic, complemented
3#11751289C211yesmaximal, characteristic
4C2×#91113C211yesmaximal, characteristic, complemented
5#11746385C211yesmaximal, characteristic, complemented
6#11746328C211yesmaximal, characteristic
7#11746324C211yesmaximal, characteristic, complemented
8#10602295—31nomaximal, Hall
9C2×Q8×D15—21no—
10C2×C3×C5×Q16C2211yescharacteristic
11C2×C3×C5×Q16C2211yescharacteristic
12#91835—21no—
13C2×#6718—21no—
14Q16×D15—22no—
15Q16×D15—22no—
16C2×Dic60C2211yescharacteristic
17C2×C8×D15C2211yescharacteristic
18C3×C5×Q32—22no—
19C2×C3×C5×C16C2211yescharacteristic
20#91119—21no—
21#91113—22no—
22#91102C2211yescharacteristic
23C2×C3⋊#672C2211yescharacteristic
24#71502—51nomaximal, Hall
25C2×D5×Q16—31no—
26C2×C5×Q32D311yescharacteristic, complemented
27#65477—31no—
28C2×#3961—31no—
29#64784—31no—
30#64727—31no—
31#64723—31no—
32C2×C3×C5×Q8—21no—
33C2×C3×C5×Q8—21no—
34Q8×D15—24no—
35Q8×D15—42no—
36C2×C4×D15—41no—
37C2×C4×D15D411yescharacteristic
38C2×Dic30—21no—
39C2×Dic30—41no—
40C3×C5×Q16—21no—
41C3×C5×Q16—21no—
42C3×C5×Q16—21no—
43C3×C5×Q16D412yes—
44C2×C3×C5×C8C2311yescharacteristic
45#6718—24no—
46#6714—41no—
47C4⋊Dic15—21no—
48#6712—41no—
49C2×C3⋊#168D411yescharacteristic
50Dic60—21no—
51Dic60D412yes—
52C8×D15—21no—
53C8×D15—21no—
54C3×C5×C16—21no—
55C3⋊#672—21no—
56C2×D3×Q16—51no—
57C2×C3×Q32D511yescharacteristic, complemented
58#5188—51no—
59C2×#829—51no—
60#4564—51no—
61(C2×D3)⋊C16—51no—
62#4503—51no—
63C2×Q8×D5—61no—
64C2×C5×Q16C2×D311yescharacteristic
65C2×C5×Q16C2×D311yescharacteristic
66#4092—61no—
67C2×#689—61no—
68D5×Q16—62no—
69D5×Q16—62no—
70C2×Dic20—31no—
71C2×C8×D5—31no—
72C5×Q32—22no—
73C2×C5×C16C2×D311yescharacteristic
74#3967—61no—
75#3961—62no—
76#3950—31no—
77C2×#672—31no—
78#2188—151noSylow
79C22×D15D811yescharacteristic
80C3×C5×Q8—22no—
81C3×C5×Q8—41no—
82C3×C5×Q8—41no—
83C3×C5×Q8—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—41no—
88C2×Dic15—41no—
89C2×Dic15D811yescharacteristic
90C4×D15—21no—
91C4×D15—21no—
92C4×D15—44no—
93Dic30—22no—
94Dic30—44no—
95Dic30—41no—
96C3×C5×C8C2×D411yescharacteristic
97C3×C5×C8C2×D411yescharacteristic
98C3⋊#168—21no—
99C2×D3×Q8—101no—
100C2×C3×Q16C2×D511yescharacteristic
101C2×C3×Q16C2×D511yescharacteristic
102#946—101no—
103C2×#216—101no—
104D3×Q16—102no—
105D3×Q16—102no—
106C2×Dic12—51no—
107C2×D3×C8—51no—
108C3×Q32—22no—
109C2×C3×C16C2×D511yescharacteristic
110#835—101no—
111#829—102no—
112#818—51no—
113C2×C3⋊C16—51no—
114C2×C5×Q8—21no—
115C2×C5×Q8—21no—
116Q8×D5—64no—
117Q8×D5—122no—
118C2×C4×D5—31no—
119C2×C4×D5—121no—
120C2×Dic10—61no—
121C2×Dic10—121no—
122C5×Q16—21no—
123C5×Q16—21no—
124C5×Q16—21no—
125C5×Q16#6712yes—
126C2×C5×C8C22×D311yescharacteristic
127#689—64no—
128#685—121no—
129C4⋊Dic5—61no—
130#683—121no—
131C2×#168—31no—
132Dic20—32no—
133Dic20—61no—
134C8×D5—61no—
135C8×D5—61no—
136C5×C16—21no—
137#672—61no—
138C22×Q16—151no—
139C2×Q32—151no—
140C2×Q32D1511yescharacteristic, complemented
141#467—151no—
142#358—151no—
143#358—151no—
144C22⋊C16—151no—
145C22×C3×C5C2×D811yescharacteristic
146C2×D15—21no—
147C2×D15—21no—
148C2×D15Q3212yescomplemented
149C3×C4×C5—42no—
150C3×C4×C5—81no—
151C3×C4×C5#12011yescharacteristic
152C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
153Dic15—21no—
154Dic15—42no—
155Dic15—81no—
156C2×C3×Q8—21no—
157C2×C3×Q8—21no—
158D3×Q8—104no—
159D3×Q8—202no—
160C2×C4×D3—51no—
161C2×C4×D3—201no—
162C2×Dic6—101no—
163C2×Dic6—201no—
164C3×Q16—21no—
165C3×Q16—21no—
166C3×Q16—21no—
167C3×Q16C22⋊D512yes—
168C2×C3×C8C22×D511yescharacteristic
169#216—104no—
170(C2×D3)⋊C4—201no—
171C4⋊Dic3—101no—
172Dic3⋊C4—201no—
173C2×C3⋊C8—51no—
174Dic12—52no—
175Dic12—101no—
176D3×C8—101no—
177D3×C8—101no—
178C3×C16—21no—
179C3⋊C16—101no—
180C22×D5—31no—
181C5×Q8—22no—
182C5×Q8—41no—
183C5×Q8—41no—
184C5×Q8—41no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5D3×D411yescharacteristic
188C2×Dic5—31no—
189C2×Dic5—121no—
190C2×Dic5—121no—
191C4×D5—61no—
192C4×D5—61no—
193C4×D5—124no—
194Dic10—62no—
195Dic10—124no—
196Dic10—121no—
197C5×C8D3×D411yescharacteristic
198C5×C8C2×#6711yescharacteristic
199#168—61no—
200C22×Q8—301no—
201C2×Q16—151no—
202C2×Q16—301no—
203C2×Q16—302no—
204C2×Q16—302no—
205C2×Q16C2×D1511yescharacteristic
206C2×Q16C2×D1511yescharacteristic
207C22×C8—151no—
208C22⋊Q8—301no—
209Q32—22no—
210Q32—302no—
211C2×C16—151no—
212C2×C16C2×D1511yescharacteristic
213#107—151no—
214#103—301no—
215C2×C3×C5#44711yescharacteristic
216C2×C3×C5C2×Q3211yescharacteristic
217C2×C3×C5#51011yescharacteristic
218D15—22no—
219C22×D3—51no—
220C3×Q8—22no—
221C3×Q8—41no—
222C3×Q8—41no—
223C3×Q8—41no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4D4×D511yescharacteristic
227C2×Dic3—51no—
228C2×Dic3—201no—
229C2×Dic3—201no—
230C4×D3—101no—
231C4×D3—101no—
232C4×D3—204no—
233Dic6—102no—
234Dic6—204no—
235Dic6—201no—
236C3×C8D4×D511yescharacteristic
237C3×C8C2×C22⋊D511yescharacteristic
238C3⋊C8—101no—
239C22×C5D3×D811yescharacteristic
240C2×D5—32no—
241C2×D5—61no—
242C2×D5—61no—
243C4×C5—42no—
244C4×C5—81no—
245C4×C5#91111yescharacteristic
246C4×C5#93711yescharacteristic
247Dic5—61no—
248Dic5—122no—
249Dic5—241no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—304no—
253C2×Q8—301no—
254C2×Q8—601no—
255C2×Q8—602no—
256C22×C4—151no—
257C22×C4—601no—
258Q16—21no—
259Q16—21no—
260Q16—21no—
261Q16—152no—
262Q16—304no—
263Q16—301no—
264Q16#122012yes—
265C2×C8—151no—
266C2×C8—301no—
267C2×C8—301no—
268C2×C8C22×D1511yescharacteristic
269C4⋊C4—301no—
270C4⋊C4—601no—
271C22⋊C4—601no—
272C16—21no—
273C16—301no—
274C3×C5#218811yescharacteristic, complemented, Hall
275C22×C3D5×D811yescharacteristic
276C2×D3—52no—
277C2×D3—101no—
278C2×D3—101no—
279C3×C4—42no—
280C3×C4—81no—
281C3×C4#405711yescharacteristic
282C3×C4#408311yescharacteristic
283Dic3—101no—
284Dic3—202no—
285Dic3—401no—
286C2×C5D3×Q3211yescharacteristic
287C2×C5#491811yescharacteristic
288C2×C5#515611yescharacteristic
289D5—62no—
290C23—151no—
291Q8—22no—
292Q8—41no—
293Q8—41no—
294Q8—41no—
295Q8—302no—
296Q8—604no—
297Q8—601no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—151no—
301C2×C4—301no—
302C2×C4—301no—
303C2×C4—604no—
304C2×C4—601no—
305C2×C4—601no—
306C2×C4D4×D1511yescharacteristic
307C8—301no—
308C8D4×D1511yescharacteristic
309C8C2×#122011yescharacteristic
310C2×C3D5×Q3211yescharacteristic
311C2×C3#6520711yescharacteristic
312C2×C3#6544511yescharacteristic
313D3—102no—
314C5#7150211yescharacteristic, complemented, Sylow
315C22—152no—
316C22—301no—
317C22—301no—
318C22D8×D1511yescharacteristic
319C4—42no—
320C4—81no—
321C4—301no—
322C4—602no—
323C4—1201no—
324C4#9180011yescharacteristic
325C4#9182611yescharacteristic
326C3#1060229511yescharacteristic, complemented, Sylow
327C2—302no—
328C2D15×Q3211yescharacteristic
329C2#1175101911yescharacteristic
330C2#1175125711yescharacteristic
subgroupG/H
centerC22D8×D15
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC2×C3×C5×Q32C2
socleC22×C3×C5C2×D8
prime radicalC22×D15D8
hypercenterC2×Q32D15
hypocenterC3×C5#2188
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×Q32C2semidirect
4. C2×#91113C2semidirect
5. #11746385C2semidirect
7. #11746324C2semidirect
26. C2×C5×Q32D3semidirect
57. C2×C3×Q32D5semidirect
140. C2×Q32D15semidirect
148. C2×D15Q32semidirect
274. C3×C5#2188semidirect
314. C5#71502semidirect
326. C3#10602295semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D152
C2×C3×C5×Q322
#117512892
C2×#911132
#117463852
#117463282
#117463242
#106022953
#715025