Finite Group Databasebeta

← #14316039

Subgroups — #14316039

Order 1920.

532 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 92 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×C3×D5×D8C211yesmaximal, characteristic, complemented
2C2×#91110C211yesmaximal, characteristic, complemented
3#11747899C211yesmaximal, characteristic, complemented
4C2×#90938C211yesmaximal, characteristic, complemented
5C5×#4562C211yesmaximal, characteristic, complemented
6#11745891C211yesmaximal, characteristic, complemented
7#11745879C211yesmaximal, characteristic, complemented
8#10599984—31nomaximal, Hall
9C2×C3×D4×D5—21no—
10C2×C3×C5×D8C2211yescharacteristic
11C2×D120C2211yescharacteristic, complemented
12C2×C3×#686—21no—
13C3×D5×D8—22no—
14C3×D5×D8—22no—
15C2×C3×D40C2211yescharacteristic
16C2×C3×C8×D5C2211yescharacteristic
17#91450—21no—
18#91110—22no—
19C2×C3⋊#672C2211yescharacteristic, complemented
20C5×#818C2211yescharacteristic, complemented
21C2×C5×C3⋊C16C2211yescharacteristic, complemented
22#90969—21no—
23#90938—22no—
24#72035—51nomaximal, Hall
25C2×D5×D8D311yescharacteristic, complemented
26C2×#3958—31no—
27C2×D80—31no—
28#65172—31no—
29C5×#357—31no—
30#64727—31no—
31#64711—31no—
32C23×C3×D5—41no—
33C2×C3×C5×D4—21no—
34C2×D60—21no—
35C2×C3×C22⋊D5—41no—
36C3×D4×D5—24no—
37C3×D4×D5—42no—
38C2×C3×D20—21no—
39C2×C3×C4×D5D411yescharacteristic
40C2×#1202—41no—
41C3×C5×D8—21no—
42C3×C5×D8D412yescomplemented
43C2×C3×C5×C8C2311yescharacteristic
44D120—21no—
45D120—21no—
46C5×C4⋊Dic3—21no—
47C3×#686—24no—
48C2×C3×#168D411yescharacteristic
49C3×D40—21no—
50C3×D40D412yescomplemented
51C3×C8×D5—21no—
52C3×C8×D5—21no—
53#6667—41no—
54C3⋊#672—21no—
55C5×C3⋊C16—21no—
56C22×C3×D8—51no—
57C2×#826—51no—
58C2×#826—51no—
59#5115—51no—
60#4562—51no—
61#4562D511yescharacteristic, complemented
62#4549—51no—
63C2×D4×D5—21no—
64C2×C5×D8C2×D311yescharacteristic
65C2×#686—21no—
66D5×D8—22no—
67D5×D8—22no—
68C2×D40—31no—
69C2×D40C2×D311yescharacteristic
70C2×C8×D5C2×D311yescharacteristic
71#4041—61no—
72C2×C5×C16—31no—
73C5×#107—31no—
74#3958—62no—
75C2×#672—31no—
76#3941—61no—
77D80—62no—
78#2184—151noSylow
79C23×C3×C5—41no—
80C22×D15—41no—
81C22×C3×D5—44no—
82C22×C3×D5—41no—
83C22×C3×D5—82no—
84C22×C3×D5—82no—
85C22×C3×D5D811yescharacteristic
86C3×C5×D4—22no—
87C3×C5×D4—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89D60—41no—
90D60—41no—
91C2×C5×Dic3—41no—
92C3×C22⋊D5—44no—
93C2×C3×Dic5D811yescharacteristic
94C3×D20—22no—
95C3×D20—41no—
96C3×C4×D5—21no—
97C3×C4×D5—21no—
98#1202—82no—
99C3×C5×C8C2×D411yescharacteristic
100C3×C5×C8C2×D411yescharacteristic
101C3×#168—21no—
102C22×C3×D4—101no—
103C2×C3×D8—51no—
104C2×C3×D8—101no—
105C2×C3×D8—102no—
106C2×C3×D8—102no—
107C2×C3×D8C2×D511yescharacteristic
108C22×C3×C8—51no—
109#930—101no—
110C2×D24—51no—
111#826—102no—
112#826—102no—
113#821—101no—
114#818C2×D511yescharacteristic, complemented
115C2×C3⋊C16—51no—
116C2×C3⋊C16C2×D511yescharacteristic, complemented
117C23×D5—41no—
118C2×C5×D4—21no—
119C2×C22⋊D5—41no—
120D4×D5—24no—
121D4×D5—42no—
122C2×D20—21no—
123C2×D20—61no—
124C2×D20—121no—
125C2×C4×D5#6711yescharacteristic
126C5×D8—21no—
127C5×D8#6712yescomplemented
128C2×C5×C8C22×D311yescharacteristic
129C5×C4⋊C4—61no—
130#686—24no—
131#685—121no—
132C2×#168#6711yescharacteristic
133D40—21no—
134D40—61no—
135D40—61no—
136D40#6712yescomplemented
137C8×D5—21no—
138C8×D5—21no—
139C5×C16—61no—
140#672—61no—
141C22×D8—51no—
142C2×D16—151no—
143C2×D16—151no—
144#466—151no—
145#357—31no—
146#357—151no—
147C22⋊C16—151no—
148C22×C3×C5—42no—
149C22×C3×C5—81no—
150C22×C3×C5—81no—
151C22×C3×C5C2×D811yescharacteristic
152C2×D15—81no—
153C2×D15—81no—
154C2×D15—81no—
155C2×C3×D5—21no—
156C2×C3×D5—21no—
157C2×C3×D5—42no—
158C2×C3×D5—88no—
159C2×C3×D5—81no—
160C2×C3×D5—81no—
161C2×C3×D5D1612yescomplemented
162C3×C4×C5#12011yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×Dic5—21no—
165C5×Dic3—81no—
166C24×C3—201no—
167C2×C3×D4—21no—
168C2×C3×D4—104no—
169C2×C3×D4—101no—
170C2×C3×D4—201no—
171C2×C3×D4—202no—
172C22×C3×C4—51no—
173C2×#67—201no—
174C2×D12—101no—
175C3×D8—21no—
176C3×D8—52no—
177C3×D8—104no—
178C3×D8—101no—
179C3×D8D2012yescomplemented
180C2×C3×C8—51no—
181C2×C3×C8—101no—
182C2×C3×C8—101no—
183C2×C3×C8C22×D511yescharacteristic
184(C2×D3)⋊C4—201no—
185C4⋊Dic3—21no—
186D24—101no—
187D24—101no—
188C3⋊C16—21no—
189C3⋊C16—101no—
190C23×C5—41no—
191C22×D5—44no—
192C22×D5—41no—
193C22×D5—82no—
194C22×D5—82no—
195C22×D5—121no—
196C22×D5#21311yescharacteristic
197C5×D4—22no—
198C5×D4—41no—
199C2×C4×C5—121no—
200C2×C4×C5C2×#6711yescharacteristic
201C22⋊D5—44no—
202C2×Dic5#21311yescharacteristic
203D20—22no—
204D20—41no—
205D20—121no—
206D20—121no—
207D20—242no—
208C4×D5—21no—
209C4×D5—21no—
210C5×C8C2×#6711yescharacteristic
211C5×C8C2×#6711yescharacteristic
212#168—21no—
213C22×D4—101no—
214C2×D8—51no—
215C2×D8—101no—
216C2×D8—102no—
217C2×D8—102no—
218C2×D8—151no—
219C2×D8D3×D511yescharacteristic
220C22×C8—51no—
221#121—301no—
222D16—302no—
223D16—302no—
224C2×C16—31no—
225C2×C16—151no—
226#107—31no—
227#102—301no—
228C2×C3×C5—82no—
229C2×C3×C5#44711yescharacteristic
230C2×C3×C5C2×D1611yescharacteristic
231C2×C3×C5#50911yescharacteristic
232D15—161no—
233C3×D5—22no—
234C3×D5—82no—
235C23×C3—41no—
236C23×C3—51no—
237C23×C3—204no—
238C23×C3—201no—
239C23×C3—402no—
240C23×C3—402no—
241C22×D3—201no—
242C3×D4—22no—
243C3×D4—41no—
244C3×D4—102no—
245C3×D4—204no—
246C3×D4—201no—
247C2×C3×C4—51no—
248C2×C3×C4—101no—
249C2×C3×C4—101no—
250C2×C3×C4D4×D511yescharacteristic
251#67—402no—
252C2×Dic3—41no—
253D12—201no—
254D12—201no—
255C3×C8—101no—
256C3×C8C2×D2011yescharacteristic
257C3×C8D4×D511yescharacteristic
258C22×C5—42no—
259C22×C5—81no—
260C22×C5—81no—
261C22×C5C2×#21311yescharacteristic
262C2×D5—21no—
263C2×D5—21no—
264C2×D5—42no—
265C2×D5—88no—
266C2×D5—81no—
267C2×D5—81no—
268C2×D5—241no—
269C2×D5—241no—
270C2×D5—241no—
271C2×D5#82612yescomplemented
272C4×C5—241no—
273C4×C5#93211yescharacteristic
274C4×C5#95311yescharacteristic
275Dic5—21no—
276C24—201no—
277C2×D4—21no—
278C2×D4—104no—
279C2×D4—101no—
280C2×D4—201no—
281C2×D4—202no—
282C2×D4—301no—
283C2×D4—601no—
284C22×C4—51no—
285D8—21no—
286D8—52no—
287D8—104no—
288D8—101no—
289D8—301no—
290D8—301no—
291D8#120212yescomplemented
292C2×C8—51no—
293C2×C8—101no—
294C2×C8—101no—
295C2×C8C2×D3×D511yescharacteristic
296C4⋊C4—61no—
297C22⋊C4—601no—
298C16—61no—
299C16—301no—
300C3×C5#218411yescharacteristic, complemented, Hall
301C22×C3—42no—
302C22×C3—52no—
303C22×C3—81no—
304C22×C3—81no—
305C22×C3—101no—
306C22×C3—101no—
307C22×C3—202no—
308C22×C3—408no—
309C22×C3—401no—
310C22×C3—401no—
311C22×C3D5×D811yescharacteristic
312C2×D3—401no—
313C2×D3—401no—
314C2×D3—401no—
315C3×C4—101no—
316C3×C4#402811yescharacteristic
317C3×C4#406011yescharacteristic
318Dic3—81no—
319C2×C5—82no—
320C2×C5C2×#82611yescharacteristic
321C2×C5#514711yescharacteristic
322C2×C5#521711yescharacteristic
323D5—22no—
324D5—82no—
325D5—481no—
326C23—41no—
327C23—51no—
328C23—204no—
329C23—201no—
330C23—402no—
331C23—402no—
332C23—601no—
333D4—22no—
334D4—41no—
335D4—102no—
336D4—204no—
337D4—201no—
338D4—601no—
339D4—601no—
340D4—1202no—
341C2×C4—51no—
342C2×C4—101no—
343C2×C4—101no—
344C2×C4—121no—
345C2×C4D5×#6711yescharacteristic
346C8—101no—
347C8C2×#120211yescharacteristic
348C8D5×#6711yescharacteristic
349C2×C3—82no—
350C2×C3—102no—
351C2×C3—402no—
352C2×C3#6506211yescharacteristic
353C2×C3D5×D1611yescharacteristic
354C2×C3#6520311yescharacteristic
355D3—801no—
356C5#7203511yescharacteristic, complemented, Sylow
357C22—42no—
358C22—52no—
359C22—81no—
360C22—81no—
361C22—101no—
362C22—101no—
363C22—202no—
364C22—408no—
365C22—401no—
366C22—401no—
367C22—1201no—
368C22—1201no—
369C22—1201no—
370C22D5×#21311yescharacteristic
371C4—101no—
372C4—241no—
373C4#9149111yescharacteristic
374C4#9156411yescharacteristic
375C3#1059998411yescharacteristic, complemented, Sylow
376C2—82no—
377C2—102no—
378C2—402no—
379C2—2401no—
380C2D5×#82611yescharacteristic
381C2#1174827811yescharacteristic
382C2#1174902211yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C2×D8
hypercenterC2×D8D3×D5
hypocenterC3×C5#2184
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×D8C2semidirect
2. C2×#91110C2semidirect
3. #11747899C2semidirect
4. C2×#90938C2semidirect
5. C5×#4562C2semidirect
6. #11745891C2semidirect
7. #11745879C2semidirect
11. C2×D120C22semidirect
19. C2×C3⋊#672C22semidirect
20. C5×#818C22semidirect
21. C2×C5×C3⋊C16C22semidirect
25. C2×D5×D8D3semidirect
42. C3×C5×D8D4semidirect
50. C3×D40D4semidirect
61. #4562D5semidirect
114. #818C2×D5semidirect
116. C2×C3⋊C16C2×D5semidirect
127. C5×D8#67semidirect
136. D40#67semidirect
161. C2×C3×D5D16semidirect
179. C3×D8D20semidirect
271. C2×D5#826semidirect
291. D8#1202semidirect
300. C3×C5#2184semidirect
356. C5#72035semidirect
375. C3#10599984semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×D82
C2×#911102
#117478992
C2×#909382
C5×#45622
#117458912
#117458792
#105999843
#720355