Finite Group Databasebeta

← #14281598

Subgroups — #14281598

Order 1920.

552 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#713C211yesmaximal, characteristic
2C4×D5×C3⋊C8C211yesmaximal, characteristic, complemented
3#11746869C211yesmaximal, characteristic, complemented
4#11746356C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745835C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10599022—31nomaximal, Hall
9C2×C3×#713C411yescharacteristic
10C3×C4×C5×Q8C2211yescharacteristic
11C3×Q8×Dic5C411yescharacteristic
12C3×#4039—21no—
13C3×#4039C411yescharacteristic
14C3×#4038—21no—
15C3×#4038C411yescharacteristic
16C3×C4×D20—21no—
17C3×C4×D20C2211yescharacteristic
18C3×C42×D5—21no—
19C3×C42×D5C2211yescharacteristic
20C2×D5×C3⋊C8—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C4×C5×C3⋊C8C2211yescharacteristic
25#90955—21no—
26Dic5×C3⋊C8—21no—
27Dic5×C3⋊C8—21no—
28#71638—51nomaximal, Hall
29C4×#713D311yescharacteristic
30#65122—31no—
31C4×C8×D5—31no—
32C5×Q8⋊C8—31no—
33Q8⋊#168—31no—
34#64703—31no—
35#64679—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C3×#713—22no—
38C3×#713C814yescomplemented
39C2×C3×D20—21no—
40C2×C3×D20C2×C411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5C2×C411yescharacteristic
45C2×C3×C4×D5D411yescharacteristic
46C2×C3×C4×D5D411yescharacteristic
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4C2×C411yescharacteristic
49C3×C42×C5—21no—
50C3×C42×C5C2311yescharacteristic
51C2×C3⋊#168—21no—
52C2×C3⋊#168—21no—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C3×#685—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×C4⋊Dic5—21no—
59C3×C4⋊Dic5C2×C411yescharacteristic
60C3×C4×Dic5—21no—
61C3×C4×Dic5—21no—
62C3×C4×Dic5C2×C411yescharacteristic
63C3×C4×Dic5D411yescharacteristic
64C3×C4×Dic5D411yescharacteristic
65D5×C3⋊C8—24no—
66C3×C4×#41—51no—
67#4925—51no—
68C2×C4×C3⋊C8—51no—
69#4535—51no—
70#4535D511yescharacteristic, complemented
71D4⋊(C3⋊C8)—51no—
72D4⋊(C3⋊C8)—51no—
73C2×#713Dic311yescharacteristic
74C4×C5×Q8C2×D311yescharacteristic
75Q8×Dic5Dic311yescharacteristic
76C2×C8×D5—61no—
77#4039—21no—
78#4039Dic311yescharacteristic
79#4038—21no—
80#4038Dic311yescharacteristic
81C4×D20—21no—
82C4×D20C2×D311yescharacteristic
83C42×D5—21no—
84C42×D5C2×D311yescharacteristic
85C5×C4⋊C8—31no—
86C4×C5×C8—31no—
87#3952—61no—
88C8×Dic5—61no—
89C8×Dic5—61no—
90C4⋊#168—31no—
91C4×#168—31no—
92#1476—151noSylow
93C22×C3×D5—21no—
94C22×C3×D5C22⋊C411yescharacteristic
95C3×C5×Q8—21no—
96C3×C5×Q8C2×C812yescomplemented
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×Dic5—21no—
103C2×C3×Dic5C22⋊C411yescharacteristic
104C2×C3×Dic5C22⋊C411yescharacteristic
105C2×C3×Dic5C22⋊C411yescharacteristic
106C3×D20—24no—
107C3×D20—21no—
108C3×D20C2×C812yescomplemented
109C3×C4×D5—21no—
110C3×C4×D5—21no—
111C3×C4×D5—24no—
112C3×C4×D5—22no—
113C3×C4×D5—41no—
114C3×C4×D5—41no—
115C3×C4×D5—42no—
116C3×C4×D5C2×C812yes—
117C3×C4×D5M1612yes—
118C3⋊#168—22no—
119C3⋊#168—41no—
120C5×C3⋊C8—22no—
121C5×C3⋊C8—41no—
122C2×C3×#41—51no—
123C3×C4×Q8—51no—
124C3×C4×Q8C2×D511yescharacteristic
125C3×C4×D4—51no—
126C3×C4×D4—51no—
127C3×C4×D4—101no—
128C3×C4×D4—101no—
129C3×#117—51no—
130C3×#117—101no—
131C2×C3×C42—51no—
132C2×C3×C42—101no—
133C22×C3⋊C8—101no—
134#830—101no—
135C4⋊(C3⋊C8)—51no—
136C4⋊(C3⋊C8)C2×D511yescharacteristic
137C4×C3⋊C8—51no—
138C4×C3⋊C8—101no—
139C4×C3⋊C8—101no—
140C4×C3⋊C8C2×D511yescharacteristic
141C2×C5×Q8C2×Dic311yescharacteristic
142#713—22no—
143#713C3⋊C814yescomplemented
144C2×D20—21no—
145C2×D20C2×Dic311yescharacteristic
146C2×C4×D5—21no—
147C2×C4×D5—21no—
148C2×C4×D5—21no—
149C2×C4×D5C2×Dic311yescharacteristic
150C2×C4×D5#6711yescharacteristic
151C2×C4×D5#6711yescharacteristic
152C2×C5×C8—61no—
153C2×C5×C8—61no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4C2×Dic311yescharacteristic
156C42×C5—21no—
157C42×C5C22×D311yescharacteristic
158#685—21no—
159#685—21no—
160#685—21no—
161C4⋊Dic5—21no—
162C4⋊Dic5C2×Dic311yescharacteristic
163C4×Dic5—21no—
164C4×Dic5—21no—
165C4×Dic5C2×Dic311yescharacteristic
166C4×Dic5#6711yescharacteristic
167C4×Dic5#6711yescharacteristic
168C2×#168—61no—
169C2×#168—61no—
170C8×D5—64no—
171C4×#41—51no—
172#431—151no—
173C2×C4×C8—151no—
174Q8⋊C8—31no—
175Q8⋊C8—151no—
176D4⋊C8—151no—
177D4⋊C8—151no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C2×C3×D5—21no—
180C2×C3×D5—21no—
181C2×C3×D5—22no—
182C2×C3×D5—41no—
183C2×C3×D5—41no—
184C2×C3×D5C22⋊C812yes—
185C3×C4×C5—22no—
186C3×C4×C5—21no—
187C3×C4×C5—41no—
188C3×C4×C5C22×C811yescharacteristic
189C3×C4×C5C2×M1611yescharacteristic
190C3×C4×C5#13511yescharacteristic
191C3×C4×C5#13511yescharacteristic
192C3×Dic5—21no—
193C3×Dic5—41no—
194C3×Dic5C22⋊C812yes—
195C3×Dic5#10412yes—
196C3×#41—54no—
197C3×#41—102no—
198C2×C3×Q8C4×D511yescharacteristic
199C2×C3×D4—51no—
200C2×C3×D4—101no—
201C22×C3×C4—51no—
202C22×C3×C4—51no—
203C22×C3×C4—51no—
204C22×C3×C4—101no—
205C22×C3×C4—101no—
206C22×C3×C4—101no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—51no—
209C3×C4⋊C4—101no—
210C3×C4⋊C4C4×D511yescharacteristic
211C3×C22⋊C4—101no—
212C3×C22⋊C4—101no—
213C3×C22⋊C4—101no—
214C3×C42—21no—
215C3×C42—51no—
216C3×C42—51no—
217C3×C42—51no—
218C3×C42—101no—
219C3×C42—101no—
220C3×C42C22×D511yescharacteristic
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—104no—
224C2×C3⋊C8—101no—
225C2×C3⋊C8—101no—
226C22×D5—21no—
227C22×D5#21711yescharacteristic
228C5×Q8—21no—
229C5×Q8C2×C3⋊C812yescomplemented
230C2×C4×C5—21no—
231C2×C4×C5—21no—
232C2×C4×C5C22×Dic311yescharacteristic
233C2×C4×C5C2×#6711yescharacteristic
234C2×C4×C5C2×#6711yescharacteristic
235C2×Dic5—21no—
236C2×Dic5#21711yescharacteristic
237C2×Dic5#21711yescharacteristic
238C2×Dic5#21711yescharacteristic
239D20—24no—
240D20—21no—
241D20C2×C3⋊C812yescomplemented
242C4×D5—21no—
243C4×D5—21no—
244C4×D5—24no—
245C4×D5—22no—
246C4×D5—41no—
247C4×D5—41no—
248C4×D5—42no—
249C4×D5C2×C3⋊C812yes—
250C4×D5#20812yes—
251C5×C8—62no—
252C5×C8—121no—
253#168—62no—
254#168—121no—
255C2×#41—51no—
256C22×C8—301no—
257C4×Q8—51no—
258C4×Q8D3×D511yescharacteristic
259C4×D4—51no—
260C4×D4—51no—
261C4×D4—101no—
262C4×D4—101no—
263#117—51no—
264#117—101no—
265C2×C42—51no—
266C2×C42—101no—
267C4⋊C8—31no—
268C4⋊C8—151no—
269C22⋊C8—301no—
270C4×C8—31no—
271C4×C8—151no—
272C4×C8—301no—
273C4×C8—301no—
274C2×C3×C5C2×C22⋊C811yescharacteristic
275C2×C3×C5#41611yescharacteristic
276C2×C3×C5C2×#10411yescharacteristic
277C3×D5—22no—
278C3×D5—42no—
279C23×C3—51no—
280C23×C3—101no—
281C3×Q8—21no—
282C3×Q8C8×D512yescomplemented
283C3×D4—52no—
284C3×D4—104no—
285C3×D4—101no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—51no—
289C2×C3×C4—51no—
290C2×C3×C4—52no—
291C2×C3×C4—52no—
292C2×C3×C4—51no—
293C2×C3×C4—102no—
294C2×C3×C4—104no—
295C2×C3×C4—101no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4—202no—
299C2×C3×C4—201no—
300C2×C3×C4—201no—
301C2×C3×C4C2×C4×D511yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C3⋊C8—22no—
305C3⋊C8—41no—
306C3⋊C8—102no—
307C3⋊C8—201no—
308C22×C5C2×#21711yescharacteristic
309C2×D5—21no—
310C2×D5—21no—
311C2×D5—22no—
312C2×D5—41no—
313C2×D5—41no—
314C2×D5#83012yes—
315C4×C5—22no—
316C4×C5—21no—
317C4×C5—41no—
318C4×C5C22×C3⋊C811yescharacteristic
319C4×C5C2×#20811yescharacteristic
320C4×C5#95011yescharacteristic
321C4×C5#95011yescharacteristic
322Dic5—21no—
323Dic5—41no—
324Dic5#83012yes—
325Dic5#83712yes—
326#41—54no—
327#41—102no—
328C2×Q8D5×Dic311yescharacteristic
329C2×D4—51no—
330C2×D4—101no—
331C22×C4—51no—
332C22×C4—51no—
333C22×C4—51no—
334C22×C4—101no—
335C22×C4—101no—
336C22×C4—101no—
337C2×C8—61no—
338C2×C8—61no—
339C2×C8—304no—
340C2×C8—301no—
341C2×C8—301no—
342C4⋊C4—21no—
343C4⋊C4—51no—
344C4⋊C4—101no—
345C4⋊C4D5×Dic311yescharacteristic
346C22⋊C4—101no—
347C22⋊C4—101no—
348C22⋊C4—101no—
349C42—21no—
350C42—51no—
351C42—51no—
352C42—51no—
353C42—101no—
354C42—101no—
355C42C2×D3×D511yescharacteristic
356C3×C5#147611yescharacteristic, complemented, Hall
357C22×C3—52no—
358C22×C3—101no—
359C22×C3—101no—
360C22×C3—102no—
361C22×C3—201no—
362C22×C3—201no—
363C22×C3D5×C22⋊C411yescharacteristic
364C3×C4—21no—
365C3×C4—22no—
366C3×C4—41no—
367C3×C4—52no—
368C3×C4—52no—
369C3×C4—101no—
370C3×C4—201no—
371C3×C4C2×C8×D511yescharacteristic
372C3×C4D5×M1611yescharacteristic
373C3×C4#406211yescharacteristic
374C3×C4#406511yescharacteristic
375C2×C5C2×#83011yescharacteristic
376C2×C5#523311yescharacteristic
377C2×C5C2×#83711yescharacteristic
378D5—22no—
379D5—42no—
380C23—51no—
381C23—101no—
382Q8—21no—
383Q8D5×C3⋊C812yescomplemented
384D4—52no—
385D4—104no—
386D4—101no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—51no—
390C2×C4—51no—
391C2×C4—52no—
392C2×C4—52no—
393C2×C4—51no—
394C2×C4—102no—
395C2×C4—104no—
396C2×C4—101no—
397C2×C4—101no—
398C2×C4—101no—
399C2×C4—202no—
400C2×C4—201no—
401C2×C4—201no—
402C2×C4C2×D5×Dic311yescharacteristic
403C2×C4D5×#6711yescharacteristic
404C2×C4D5×#6711yescharacteristic
405C8—62no—
406C8—121no—
407C8—302no—
408C8—601no—
409C2×C3—102no—
410C2×C3—202no—
411C2×C3D5×C22⋊C811yescharacteristic
412C2×C3#6509311yescharacteristic
413C2×C3D5×#10411yescharacteristic
414C5#7163811yescharacteristic, complemented, Sylow
415C22—52no—
416C22—101no—
417C22—101no—
418C22—102no—
419C22—201no—
420C22—201no—
421C22D5×#21711yescharacteristic
422C4—21no—
423C4—22no—
424C4—41no—
425C4—52no—
426C4—52no—
427C4—101no—
428C4—201no—
429C4C2×D5×C3⋊C811yescharacteristic
430C4D5×#20811yescharacteristic
431C4#9151411yescharacteristic
432C4#9151611yescharacteristic
433C3#1059902211yescharacteristic, complemented, Sylow
434C2—102no—
435C2—202no—
436C2D5×#83011yescharacteristic
437C2#1174920711yescharacteristic
438C2D5×#83711yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC3×C4×C5C22×C8
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#713C4
cosocleC3×C42×C5C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1476
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C4×D5×C3⋊C8C2semidirect
3. #11746869C2semidirect
4. #11746356C2semidirect
5. C5×#4535C2semidirect
6. #11745835C2semidirect
7. #11745834C2semidirect
38. C3×#713C8semidirect
70. #4535D5semidirect
96. C3×C5×Q8C2×C8semidirect
108. C3×D20C2×C8semidirect
143. #713C3⋊C8semidirect
229. C5×Q8C2×C3⋊C8semidirect
241. D20C2×C3⋊C8semidirect
282. C3×Q8C8×D5semidirect
356. C3×C5#1476semidirect
383. Q8D5×C3⋊C8semidirect
414. C5#71638semidirect
433. C3#10599022semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#7132
C4×D5×C3⋊C82
#117468692
#117463562
C5×#45352
#117458352
#117458342
#105990223
#716385