Finite Group Databasebeta

← #14316173

Subgroups — #14316173

Order 1920.

512 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 82 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×#91256C211yesmaximal, characteristic
2#11751289C211yesmaximal, characteristic, complemented
3C2×C5×#828C211yesmaximal, characteristic, complemented
4C2×C3×#3960C211yesmaximal, characteristic, complemented
5#11745894C211yesmaximal, characteristic, complemented
6#11745892C211yesmaximal, characteristic, complemented
7#11745881C211yesmaximal, characteristic, complemented
8#10602278—31nomaximal, Hall
9C2×#6777—21no—
10C2×C3×C5×Q16C2211yescharacteristic, complemented
11#91835—21no—
12C2×C8×D15C2211yescharacteristic
13C2×C5×D24C2211yescharacteristic
14C2×C3×D40C2211yescharacteristic
15C2×#6652—21no—
16#91256—22no—
17#91256—22no—
18#91119—21no—
19#91102C2211yescharacteristic, complemented
20C5×#828—22no—
21C2×C5×C3⋊C16C2211yescharacteristic, complemented
22C3×#3960—22no—
23C2×C3×#672C2211yescharacteristic, complemented
24#71485—51nomaximal, Hall
25C2×D5×D8—31no—
26C2×C5×SD32—31no—
27#65477—31no—
28C2×#3960D311yescharacteristic, complemented
29#64782—31no—
30#64729—31no—
31#64727—31no—
32C22×D3×D5—41no—
33C2×C3×C5×Q8—21no—
34C2×C4×D15D411yescharacteristic
35C2×C5×D12—21no—
36C2×C3×D20—21no—
37C2×#1201—41no—
38#6777—24no—
39#6777—42no—
40C3×C5×Q16—21no—
41C3×C5×Q16—21no—
42C2×C3×C5×C8C2311yescharacteristic
43#6714—41no—
44C4⋊Dic15—21no—
45#6712—41no—
46C2×C3⋊#168D411yescharacteristic
47C8×D15—21no—
48C8×D15—21no—
49C5×D24—21no—
50C5×D24D412yes—
51C3×D40—21no—
52C3×D40D412yes—
53#6652—24no—
54C3×#672—21no—
55C5×C3⋊C16—21no—
56C2×D3×D8—51no—
57C2×C3×SD32—51no—
58#5188—51no—
59C2×#828D511yescharacteristic, complemented
60#4562—51no—
61#4509—51no—
62(C2×D3)⋊C16—51no—
63C2×D4×D5—61no—
64C2×C5×Q16C2×D311yescharacteristic, complemented
65C2×C5×D8—31no—
66#4092—61no—
67C2×#686—61no—
68D5×D8—62no—
69D5×D8—62no—
70C2×D40C2×D311yescharacteristic
71C2×C8×D5—31no—
72C5×SD32—62no—
73C2×C5×C16—31no—
74#3967—61no—
75#3960—22no—
76#3950—31no—
77C2×#672C2×D311yescharacteristic, complemented
78#2187—151noSylow
79C22×D15D811yescharacteristic
80C22×C5×D3—41no—
81C22×C3×D5—41no—
82C2×D3×D5—44no—
83C2×D3×D5—82no—
84C2×D3×D5—82no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—41no—
90C2×Dic15D811yescharacteristic
91C4×D15—21no—
92C4×D15—21no—
93C5×D12—22no—
94C5×D12—41no—
95C3×D20—22no—
96C3×D20—41no—
97#1201—44no—
98C3×C5×C8C2×D411yescharacteristic
99C3×C5×C8C2×D411yescharacteristic
100C3⋊#168—21no—
101C2×D3×D4—101no—
102C2×C3×Q16C2×D511yescharacteristic, complemented
103C2×C3×D8—51no—
104#946—101no—
105C2×#213—101no—
106D3×D8—102no—
107D3×D8—102no—
108C2×D24C2×D511yescharacteristic
109C2×D3×C8—51no—
110C3×SD32—102no—
111C2×C3×C16—51no—
112#835—101no—
113#828—22no—
114#818—51no—
115C2×C3⋊C16C2×D511yescharacteristic, complemented
116C23×D5—121no—
117C2×C5×Q8—21no—
118C2×C5×D4—61no—
119C2×C22⋊D5—121no—
120D4×D5—64no—
121D4×D5—122no—
122C2×D20—21no—
123C2×C4×D5—31no—
124C5×Q16—21no—
125C5×Q16—21no—
126C5×D8—32no—
127C5×D8—61no—
128C2×C5×C8C22×D311yescharacteristic
129#686—64no—
130#685—121no—
131C4⋊Dic5—61no—
132#683—121no—
133C2×#168—31no—
134D40—21no—
135D40#6712yes—
136C8×D5—61no—
137C8×D5—61no—
138C5×C16—61no—
139#672—21no—
140C22×D8—151no—
141C2×SD32—31no—
142C2×SD32—51no—
143#467—151no—
144#357—151no—
145#357—151no—
146C22⋊C16—151no—
147C22×C3×C5C2×D811yescharacteristic
148C2×D15—21no—
149C2×D15—21no—
150C2×D15SD3212yescomplemented
151C2×C5×D3—42no—
152C2×C5×D3—81no—
153C2×C5×D3—81no—
154C2×C3×D5—42no—
155C2×C3×D5—81no—
156C2×C3×D5—81no—
157D3×D5—88no—
158C3×C4×C5—81no—
159C3×C4×C5#12011yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161Dic15—21no—
162Dic15—81no—
163C23×D3—201no—
164C2×C3×Q8—21no—
165C2×C3×D4—101no—
166C2×#67—201no—
167D3×D4—104no—
168D3×D4—202no—
169C2×D12—21no—
170C2×C4×D3—51no—
171C3×Q16—21no—
172C3×Q16—21no—
173C3×D8—52no—
174C3×D8—101no—
175C2×C3×C8C22×D511yescharacteristic
176#213—104no—
177(C2×D3)⋊C4—201no—
178C4⋊Dic3—101no—
179Dic3⋊C4—201no—
180C2×C3⋊C8—51no—
181D24—21no—
182D24C22⋊D512yes—
183D3×C8—101no—
184D3×C8—101no—
185C3×C16—101no—
186C3⋊C16—21no—
187C23×C5—121no—
188C22×D5—31no—
189C22×D5—41no—
190C22×D5—124no—
191C22×D5—242no—
192C22×D5—242no—
193C5×Q8—41no—
194C5×Q8—41no—
195C5×D4—62no—
196C5×D4—121no—
197C2×C4×C5—41no—
198C2×C4×C5D3×D411yescharacteristic
199C22⋊D5—124no—
200C2×Dic5—31no—
201C2×Dic5—121no—
202D20—22no—
203D20—41no—
204C4×D5—61no—
205C4×D5—61no—
206C5×C8D3×D411yescharacteristic
207C5×C8C2×#6711yescharacteristic
208#168—61no—
209C22×D4—301no—
210C2×Q16D3×D511yescharacteristic, complemented
211C2×D8—31no—
212C2×D8—51no—
213C2×D8—301no—
214C2×D8—302no—
215C2×D8—302no—
216C22×C8—151no—
217C22⋊Q8—301no—
218SD32—62no—
219SD32—102no—
220C2×C16—31no—
221C2×C16—51no—
222#107—151no—
223#103—301no—
224C2×C3×C5#44711yescharacteristic
225C2×C3×C5C2×SD3211yescharacteristic
226C2×C3×C5#50911yescharacteristic
227D15—22no—
228C3×D5—82no—
229C5×D3—82no—
230C23×C3—201no—
231C22×D3—41no—
232C22×D3—51no—
233C22×D3—204no—
234C22×D3—402no—
235C22×D3—402no—
236C3×Q8—41no—
237C3×Q8—41no—
238C3×D4—102no—
239C3×D4—201no—
240C2×C3×C4—41no—
241C2×C3×C4D4×D511yescharacteristic
242#67—204no—
243C2×Dic3—51no—
244C2×Dic3—201no—
245D12—22no—
246D12—41no—
247C4×D3—101no—
248C4×D3—101no—
249C3×C8D4×D511yescharacteristic
250C3×C8C2×C22⋊D511yescharacteristic
251C3⋊C8—101no—
252C22×C5—122no—
253C22×C5—241no—
254C22×C5—241no—
255C22×C5D3×D811yescharacteristic
256C2×D5—32no—
257C2×D5—42no—
258C2×D5—61no—
259C2×D5—61no—
260C2×D5—81no—
261C2×D5—81no—
262C2×D5—248no—
263C4×C5—81no—
264C4×C5#91111yescharacteristic
265C4×C5#93711yescharacteristic
266Dic5—61no—
267Dic5—241no—
268C24—601no—
269C2×Q8—21no—
270C2×D4—61no—
271C2×D4—101no—
272C2×D4—304no—
273C2×D4—601no—
274C2×D4—602no—
275C22×C4—151no—
276Q16—21no—
277Q16—21no—
278D8—32no—
279D8—52no—
280D8—61no—
281D8—101no—
282D8—304no—
283C2×C8—151no—
284C2×C8—301no—
285C2×C8—301no—
286C2×C8C2×D3×D511yescharacteristic
287C4⋊C4—301no—
288C4⋊C4—601no—
289C22⋊C4—601no—
290C16—61no—
291C16—101no—
292C3×C5#218711yescharacteristic, complemented, Hall
293C22×C3—202no—
294C22×C3—401no—
295C22×C3—401no—
296C22×C3D5×D811yescharacteristic
297C2×D3—42no—
298C2×D3—52no—
299C2×D3—81no—
300C2×D3—81no—
301C2×D3—101no—
302C2×D3—101no—
303C2×D3—408no—
304C3×C4—81no—
305C3×C4#405711yescharacteristic
306C3×C4#408311yescharacteristic
307Dic3—101no—
308Dic3—401no—
309C2×C5—242no—
310C2×C5D3×SD3211yescharacteristic
311C2×C5#491411yescharacteristic
312C2×C5#515611yescharacteristic
313D5—62no—
314D5—82no—
315C23—121no—
316C23—151no—
317C23—201no—
318C23—604no—
319C23—1202no—
320C23—1202no—
321Q8—41no—
322Q8—41no—
323D4—62no—
324D4—102no—
325D4—121no—
326D4—201no—
327D4—604no—
328C2×C4—41no—
329C2×C4—151no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—601no—
333C2×C4#679011yescharacteristic
334C8—301no—
335C8D5×#6711yescharacteristic
336C8D3×C22⋊D511yescharacteristic
337C2×C3—402no—
338C2×C3D5×SD3211yescharacteristic
339C2×C3#6520311yescharacteristic
340C2×C3#6544511yescharacteristic
341D3—82no—
342D3—102no—
343C5#7148511yescharacteristic, complemented, Sylow
344C22—122no—
345C22—152no—
346C22—202no—
347C22—241no—
348C22—241no—
349C22—301no—
350C22—301no—
351C22—401no—
352C22—401no—
353C22—1208no—
354C22#9148111yescharacteristic
355C4—81no—
356C4—301no—
357C4—1201no—
358C4#9148211yescharacteristic
359C4#9157711yescharacteristic
360C3#1060227811yescharacteristic, complemented, Sylow
361C2—242no—
362C2—302no—
363C2—402no—
364C2#1174829211yescharacteristic
365C2#1174829311yescharacteristic
366C2#1174915311yescharacteristic
subgroupG/H
centerC22#91481
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C2×D8
prime radicalC2×#91256C2
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2187
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #11751289C2semidirect
3. C2×C5×#828C2semidirect
4. C2×C3×#3960C2semidirect
5. #11745894C2semidirect
6. #11745892C2semidirect
7. #11745881C2semidirect
10. C2×C3×C5×Q16C22semidirect
19. #91102C22semidirect
21. C2×C5×C3⋊C16C22semidirect
23. C2×C3×#672C22semidirect
28. C2×#3960D3semidirect
59. C2×#828D5semidirect
64. C2×C5×Q16C2×D3semidirect
77. C2×#672C2×D3semidirect
102. C2×C3×Q16C2×D5semidirect
115. C2×C3⋊C16C2×D5semidirect
150. C2×D15SD32semidirect
210. C2×Q16D3×D5semidirect
292. C3×C5#2187semidirect
343. C5#71485semidirect
360. C3#10602278semidirect

Maximal subgroups

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

subgroupindex
C2×#912562
#117512892
C2×C5×#8282
C2×C3×#39602
#117458942
#117458922
#117458812
#106022783
#714855