Finite Group Databasebeta

← #14316027

Subgroups — #14316027

Order 1920.

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

normal subgroups only

This group has 532 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×D8×D15C211yesmaximal, characteristic, complemented
2C2×#91110C211yesmaximal, characteristic, complemented
3C2×D240C211yesmaximal, characteristic, complemented
4#11750984C211yesmaximal, characteristic, complemented
5C3×C5×#357C211yesmaximal, characteristic, complemented
6#11746328C211yesmaximal, characteristic, complemented
7#11746312C211yesmaximal, characteristic, complemented
8#10599984—31nomaximal, Hall
9C2×D4×D15—21no—
10C2×C3×C5×D8C2211yescharacteristic
11C2×#6715—21no—
12D8×D15—22no—
13D8×D15—22no—
14C2×D120C2211yescharacteristic
15C2×D120C2211yescharacteristic, complemented
16C2×C8×D15C2211yescharacteristic
17#91784—21no—
18C2×C3×C5×C16C2211yescharacteristic, complemented
19C3×C5×#107C2211yescharacteristic, complemented
20#91110—22no—
21C2×C3⋊#672C2211yescharacteristic, complemented
22#91093—21no—
23D240—22no—
24#69191—51nomaximal, Hall
25C2×D5×D8—31no—
26C2×#3958—31no—
27C2×D80—31no—
28#65172—31no—
29C5×#357D311yescharacteristic, complemented
30#64727—31no—
31#64711—31no—
32C23×D15—41no—
33C2×C3×C5×D4—21no—
34C2×#1220—41no—
35D4×D15—24no—
36D4×D15—42no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—41no—
40C2×C4×D15D411yescharacteristic
41C3×C5×D8—21no—
42C3×C5×D8D412yescomplemented
43C2×C3×C5×C8C2311yescharacteristic
44C3×C5×C4⋊C4—21no—
45#6715—24no—
46#6714—41no—
47C2×C3⋊#168D411yescharacteristic
48D120—21no—
49D120—21no—
50D120—21no—
51D120D412yescomplemented
52C8×D15—21no—
53C8×D15—21no—
54C3×C5×C16—21no—
55C3⋊#672—21no—
56C2×D3×D8—51no—
57C2×#826—51no—
58C2×D48—51no—
59#4883—51no—
60C3×#357D511yescharacteristic, complemented
61(C2×D3)⋊C16—51no—
62#4491—51no—
63C2×D4×D5—61no—
64C2×C5×D8C2×D311yescharacteristic
65C2×#686—61no—
66D5×D8—62no—
67D5×D8—62no—
68C2×D40—31no—
69C2×D40—31no—
70C2×C8×D5—31no—
71#4041—61no—
72C2×C5×C16C2×D311yescharacteristic, complemented
73C5×#107C2×D311yescharacteristic, complemented
74#3958—62no—
75C2×#672—31no—
76#3941—61no—
77D80—62no—
78#2184—151noSylow
79C23×C3×C5—41no—
80C22×D15—44no—
81C22×D15—41no—
82C22×D15—41no—
83C22×D15—82no—
84C22×D15—82no—
85C22×D15D811yescharacteristic
86C3×C5×D4—22no—
87C3×C5×D4—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90#1220—44no—
91C2×Dic15D811yescharacteristic
92D60—22no—
93D60—41no—
94D60—41no—
95D60—41no—
96D60—82no—
97C4×D15—21no—
98C4×D15—21no—
99C3×C5×C8C2×D411yescharacteristic
100C3×C5×C8C2×D411yescharacteristic
101C3⋊#168—21no—
102C2×D3×D4—101no—
103C2×C3×D8C2×D511yescharacteristic
104C2×#213—101no—
105D3×D8—102no—
106D3×D8—102no—
107C2×D24—51no—
108C2×D24—51no—
109C2×D3×C8—51no—
110#895—101no—
111C2×C3×C16C2×D511yescharacteristic, complemented
112C3×#107C2×D511yescharacteristic, complemented
113#826—102no—
114C2×C3⋊C16—51no—
115#809—101no—
116D48—102no—
117C23×D5—121no—
118C2×C5×D4—21no—
119C2×C22⋊D5—121no—
120D4×D5—64no—
121D4×D5—122no—
122C2×D20—61no—
123C2×D20—61no—
124C2×D20—121no—
125C2×C4×D5—31no—
126C5×D8—21no—
127C5×D8D1212yescomplemented
128C2×C5×C8C22×D311yescharacteristic
129C5×C4⋊C4—21no—
130#686—64no—
131#685—121no—
132C2×#168—31no—
133D40—32no—
134D40—61no—
135D40—61no—
136D40—61no—
137C8×D5—61no—
138C8×D5—61no—
139C5×C16—21no—
140#672—61no—
141C22×D8—151no—
142C2×D16—151no—
143C2×D16—151no—
144#466—151no—
145#357—151no—
146#357D1511yescharacteristic, complemented
147C22⋊C16—151no—
148C22×C3×C5—42no—
149C22×C3×C5—81no—
150C22×C3×C5—81no—
151C22×C3×C5C2×D811yescharacteristic
152C2×D15—21no—
153C2×D15—21no—
154C2×D15—42no—
155C2×D15—88no—
156C2×D15—81no—
157C2×D15—81no—
158C2×D15—81no—
159C2×D15—81no—
160C2×D15—81no—
161C2×D15D1612yescomplemented
162C3×C4×C5—81no—
163C3×C4×C5#12011yescharacteristic
164C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
165Dic15—21no—
166C23×D3—201no—
167C2×C3×D4—21no—
168C2×#67—201no—
169D3×D4—104no—
170D3×D4—202no—
171C2×D12—101no—
172C2×D12—101no—
173C2×D12—201no—
174C2×C4×D3—51no—
175C3×D8—21no—
176C3×D8D2012yescomplemented
177C2×C3×C8C22×D511yescharacteristic
178C3×C4⋊C4—21no—
179#213—104no—
180(C2×D3)⋊C4—201no—
181C2×C3⋊C8—51no—
182D24—52no—
183D24—101no—
184D24—101no—
185D24—101no—
186D3×C8—101no—
187D3×C8—101no—
188C3×C16—21no—
189C3⋊C16—101no—
190C23×C5—41no—
191C22×D5—31no—
192C22×D5—124no—
193C22×D5—121no—
194C22×D5—121no—
195C22×D5—242no—
196C22×D5—242no—
197C5×D4—22no—
198C5×D4—41no—
199C2×C4×C5—41no—
200C2×C4×C5D3×D411yescharacteristic
201C22⋊D5—124no—
202C2×Dic5—31no—
203D20—62no—
204D20—121no—
205D20—121no—
206D20—121no—
207D20—242no—
208C4×D5—61no—
209C4×D5—61no—
210C5×C8C2×D1211yescharacteristic
211C5×C8D3×D411yescharacteristic
212#168—61no—
213C22×D4—301no—
214C2×D8—151no—
215C2×D8—151no—
216C2×D8—301no—
217C2×D8—302no—
218C2×D8—302no—
219C2×D8C2×D1511yescharacteristic
220C22×C8—151no—
221#121—301no—
222D16—302no—
223D16—302no—
224C2×C16—151no—
225C2×C16C2×D1511yescharacteristic, complemented
226#107C2×D1511yescharacteristic, complemented
227#102—301no—
228C2×C3×C5—82no—
229C2×C3×C5#44711yescharacteristic
230C2×C3×C5C2×D1611yescharacteristic
231C2×C3×C5#50911yescharacteristic
232D15—22no—
233D15—82no—
234D15—161no—
235C23×C3—41no—
236C22×D3—51no—
237C22×D3—204no—
238C22×D3—201no—
239C22×D3—201no—
240C22×D3—402no—
241C22×D3—402no—
242C3×D4—22no—
243C3×D4—41no—
244C2×C3×C4—41no—
245C2×C3×C4D4×D511yescharacteristic
246#67—204no—
247C2×Dic3—51no—
248D12—102no—
249D12—201no—
250D12—201no—
251D12—201no—
252D12—402no—
253C4×D3—101no—
254C4×D3—101no—
255C3×C8C2×D2011yescharacteristic
256C3×C8D4×D511yescharacteristic
257C3⋊C8—101no—
258C22×C5—42no—
259C22×C5—81no—
260C22×C5—81no—
261C22×C5D3×D811yescharacteristic
262C2×D5—32no—
263C2×D5—61no—
264C2×D5—61no—
265C2×D5—122no—
266C2×D5—248no—
267C2×D5—241no—
268C2×D5—241no—
269C2×D5—241no—
270C2×D5—241no—
271C2×D5—241no—
272C4×C5—81no—
273C4×C5#88211yescharacteristic
274C4×C5#91411yescharacteristic
275Dic5—61no—
276C24—601no—
277C2×D4—21no—
278C2×D4—304no—
279C2×D4—301no—
280C2×D4—301no—
281C2×D4—601no—
282C2×D4—601no—
283C2×D4—602no—
284C22×C4—151no—
285D8—21no—
286D8—152no—
287D8—304no—
288D8—301no—
289D8—301no—
290D8—301no—
291D8D6012yescomplemented
292C2×C8—151no—
293C2×C8—301no—
294C2×C8—301no—
295C2×C8C22×D1511yescharacteristic
296C4⋊C4—21no—
297C22⋊C4—601no—
298C16—21no—
299C16—301no—
300C3×C5#218411yescharacteristic, complemented, Hall
301C22×C3—42no—
302C22×C3—81no—
303C22×C3—81no—
304C22×C3D5×D811yescharacteristic
305C2×D3—52no—
306C2×D3—101no—
307C2×D3—101no—
308C2×D3—202no—
309C2×D3—408no—
310C2×D3—401no—
311C2×D3—401no—
312C2×D3—401no—
313C2×D3—401no—
314C2×D3—401no—
315C3×C4—81no—
316C3×C4#402811yescharacteristic
317C3×C4#406011yescharacteristic
318Dic3—101no—
319C2×C5—82no—
320C2×C5#477311yescharacteristic
321C2×C5D3×D1611yescharacteristic
322C2×C5#491411yescharacteristic
323D5—62no—
324D5—242no—
325D5—481no—
326C23—41no—
327C23—151no—
328C23—604no—
329C23—601no—
330C23—601no—
331C23—1202no—
332C23—1202no—
333D4—22no—
334D4—41no—
335D4—302no—
336D4—604no—
337D4—601no—
338D4—601no—
339D4—601no—
340D4—1202no—
341C2×C4—41no—
342C2×C4—151no—
343C2×C4—301no—
344C2×C4—301no—
345C2×C4D4×D1511yescharacteristic
346C8—301no—
347C8C2×D6011yescharacteristic
348C8D4×D1511yescharacteristic
349C2×C3—82no—
350C2×C3#6506211yescharacteristic
351C2×C3D5×D1611yescharacteristic
352C2×C3#6520311yescharacteristic
353D3—102no—
354D3—402no—
355D3—801no—
356C5#6919111yescharacteristic, complemented, Sylow
357C22—42no—
358C22—81no—
359C22—81no—
360C22—152no—
361C22—301no—
362C22—301no—
363C22—602no—
364C22—1208no—
365C22—1201no—
366C22—1201no—
367C22—1201no—
368C22—1201no—
369C22—1201no—
370C22D8×D1511yescharacteristic
371C4—81no—
372C4—301no—
373C4#9177111yescharacteristic
374C4#9180311yescharacteristic
375C3#1059998411yescharacteristic, complemented, Sylow
376C2—82no—
377C2—302no—
378C2—1202no—
379C2—2401no—
380C2#1175087411yescharacteristic
381C2D15×D1611yescharacteristic
382C2#1175101511yescharacteristic
subgroupG/H
centerC22D8×D15
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#357C2
socleC22×C3×C5C2×D8
hypercenter#357D15
hypocenterC3×C5#2184
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
1. C2×D8×D15C2semidirect
2. C2×#91110C2semidirect
3. C2×D240C2semidirect
4. #11750984C2semidirect
5. C3×C5×#357C2semidirect
6. #11746328C2semidirect
7. #11746312C2semidirect
15. C2×D120C22semidirect
18. C2×C3×C5×C16C22semidirect
19. C3×C5×#107C22semidirect
21. C2×C3⋊#672C22semidirect
29. C5×#357D3semidirect
42. C3×C5×D8D4semidirect
51. D120D4semidirect
60. C3×#357D5semidirect
72. C2×C5×C16C2×D3semidirect
73. C5×#107C2×D3semidirect
111. C2×C3×C16C2×D5semidirect
112. C3×#107C2×D5semidirect
127. C5×D8D12semidirect
146. #357D15semidirect
161. C2×D15D16semidirect
176. C3×D8D20semidirect
225. C2×C16C2×D15semidirect
226. #107C2×D15semidirect
291. D8D60semidirect
300. C3×C5#2184semidirect
356. C5#69191semidirect
375. C3#10599984semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D152
C2×#911102
C2×D2402
#117509842
C3×C5×#3572
#117463282
#117463122
#105999843
#691915