Finite Group Databasebeta

← C3×#10599127 #14282965

Subgroups — C3×#10599127 #14282965

Order 1920.

668 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65961C211yesmaximal, characteristic
2C3×#65015C211yesmaximal, characteristic, complemented
3C3×D5×#95C211yesmaximal, characteristic, complemented
4C3×C5×#328C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6C3×#64690C211yesmaximal, characteristic, complemented
7C3×#64671C211yesmaximal, characteristic, complemented
8#10599127C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#713C411yescharacteristic, complemented
10C22×C3×C4×D5—21no—
11C22×C3×C4×D5C2211yescharacteristic
12C3×C5×C22⋊Q8C2211yescharacteristic
13C3×#4092C411yescharacteristic, complemented
14C3×#4076C2211yescharacteristic
15C2×C3×#676—21no—
16C3×#4041C411yescharacteristic, complemented
17C3×#4040—21no—
18C3×#4039—21no—
19C3×#4038C411yescharacteristic, complemented
20C3×#4028—21no—
21C3×#4027—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23C3×C5×#95C2211yescharacteristic
24C3×#3963—21no—
25C3×#3963C2211yescharacteristic
26C3×C22⋊#168C2211yescharacteristic
27C3×#3952—21no—
28C3×#1504—51nomaximal, Hall
29#65961C2×C311yescharacteristic
30#65015C2×C311yescharacteristic, complemented
31D5×#95C2×C311yescharacteristic, complemented
32C5×#328C2×C311yescharacteristic, complemented
33#64758C2×C311yescharacteristic, complemented
34#64690C2×C311yescharacteristic, complemented
35#64671C2×C311yescharacteristic, complemented
36C23×C3×D5D411yescharacteristic
37C2×C3×C5×Q8C2×C411yescharacteristic, complemented
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×C3×C22⋊D5—21no—
41C22×C3×Dic5—21no—
42C22×C3×Dic5D411yescharacteristic
43C3×#713—42no—
44C2×C3×D20—21no—
45C2×C3×D20—21no—
46C2×C3×D20C2×C411yescharacteristic, complemented
47C2×C3×C4×D5—24no—
48C2×C3×C4×D5—21no—
49C2×C3×C4×D5—42no—
50C2×C3×C4×D5—42no—
51C2×C3×C4×D5—42no—
52C2×C3×C4×D5C2×C411yescharacteristic
53C2×C3×C4×D5C2×C411yescharacteristic
54C2×C3×C4×D5D411yescharacteristic
55C2×C3×C4×D5D411yescharacteristic
56C2×C3×C5×C8—21no—
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
59C3×C5×C22⋊C4—21no—
60C3×#685—21no—
61C3×#685—21no—
62C3×#685—21no—
63C3×#685—21no—
64C3×C4⋊Dic5C2×C411yescharacteristic, complemented
65C3×#683—21no—
66C3×C4×Dic5—21no—
67C2×C3×#168—21no—
68C3×#676—42no—
69C3×#525—51no—
70C3×#407—51no—
71C2×C3×#95—51no—
72C3×#328—51no—
73C3×#328D511yescharacteristic, complemented
74C3×#327—51no—
75C3×#327—51no—
76C2×#713C3×C411yescharacteristic, complemented
77C22×C4×D5—21no—
78C22×C4×D5C22×C311yescharacteristic
79C5×C22⋊Q8C22×C311yescharacteristic
80#4092C3×C411yescharacteristic, complemented
81#4076C22×C311yescharacteristic
82C2×#676—21no—
83#4041C3×C411yescharacteristic, complemented
84#4040—21no—
85#4039—21no—
86#4038C3×C411yescharacteristic, complemented
87#4028—21no—
88#4027—21no—
89C5×C22⋊C8C22×C311yescharacteristic
90C5×#95C22×C311yescharacteristic
91#3963—21no—
92#3963C22×C311yescharacteristic
93C22⋊#168C22×C311yescharacteristic
94#3952—21no—
95#1504—51noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×C3×D5—21no—
98C22×C3×D5—21no—
99C22×C3×D5—22no—
100C22×C3×D5—22no—
101C22×C3×D5—21no—
102C22×C3×D5C22⋊C411yescharacteristic
103C22×C3×D5C22⋊C411yescharacteristic
104C3×C5×Q8—41no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C3×C22⋊D5—41no—
114C3×C22⋊D5—41no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5C22⋊C411yescharacteristic
121C2×C3×Dic5C22⋊C411yescharacteristic
122C3×D20—41no—
123C3×D20—42no—
124C3×D20—42no—
125C3×C4×D5—22no—
126C3×C4×D5—22no—
127C3×C4×D5—41no—
128C3×C4×D5—41no—
129C3×C4×D5—42no—
130C3×C4×D5—48no—
131C3×C5×C8—41no—
132C3×#168—41no—
133C2×C3×#41—51no—
134C23×C3×C4—51no—
135C23×C3×C4—101no—
136C2×C3×M16—101no—
137C3×#123—101no—
138C3×C22⋊Q8—51no—
139C3×C22⋊Q8C2×D511yescharacteristic
140C3×#121—51no—
141C3×#121—51no—
142C3×#120—101no—
143C3×C4×D4—101no—
144C3×C4×D4—101no—
145C3×#117—51no—
146C3×C22⋊C8—51no—
147C3×C22⋊C8—101no—
148C3×C22⋊C8C2×D511yescharacteristic
149C3×#95—51no—
150C3×#95—101no—
151C3×#95C2×D511yescharacteristic
152C23×D5C3×D411yescharacteristic
153C2×C5×Q8C2×C3×C411yescharacteristic, complemented
154C22×C4×C5—21no—
155C22×C4×C5C23×C311yescharacteristic
156C2×C22⋊D5—21no—
157C22×Dic5—21no—
158C22×Dic5C3×D411yescharacteristic
159#713—42no—
160C2×D20—21no—
161C2×D20—21no—
162C2×D20C2×C3×C411yescharacteristic, complemented
163C2×C4×D5—24no—
164C2×C4×D5—21no—
165C2×C4×D5—42no—
166C2×C4×D5—42no—
167C2×C4×D5—42no—
168C2×C4×D5C2×C3×C411yescharacteristic
169C2×C4×D5C2×C3×C411yescharacteristic
170C2×C4×D5C3×D411yescharacteristic
171C2×C4×D5C3×D411yescharacteristic
172C2×C5×C8—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4C2×C3×C411yescharacteristic, complemented
175C5×C22⋊C4—21no—
176#685—21no—
177#685—21no—
178#685—21no—
179#685—21no—
180C4⋊Dic5C2×C3×C411yescharacteristic, complemented
181#683—21no—
182C4×Dic5—21no—
183C2×#168—21no—
184#676—42no—
185#525—51no—
186#407—51no—
187C2×#95—51no—
188#328—51no—
189#328C3×D511yescharacteristic, complemented
190#327—51no—
191#327—51no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5C2×C22⋊C411yescharacteristic
195C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
196C22×C3×C5#13711yescharacteristic
197C2×C3×D5—24no—
198C2×C3×D5—24no—
199C2×C3×D5—21no—
200C2×C3×D5—21no—
201C2×C3×D5—21no—
202C2×C3×D5—21no—
203C2×C3×D5—41no—
204C2×C3×D5—41no—
205C2×C3×D5—41no—
206C2×C3×D5#9912yes—
207C2×C3×D5#10412yes—
208C3×C4×C5—21no—
209C3×C4×C5—21no—
210C3×C4×C5—42no—
211C3×C4×C5—41no—
212C3×C4×C5—41no—
213C3×Dic5—21no—
214C3×Dic5—21no—
215C3×Dic5—42no—
216C3×Dic5—41no—
217C24×C3—51no—
218C3×#41—202no—
219C2×C3×Q8C4×D511yescharacteristic, complemented
220C2×C3×D4—51no—
221C2×C3×D4—101no—
222C2×C3×D4—101no—
223C2×C3×D4—101no—
224C22×C3×C4—21no—
225C22×C3×C4—51no—
226C22×C3×C4—51no—
227C22×C3×C4—51no—
228C22×C3×C4—51no—
229C22×C3×C4—51no—
230C22×C3×C4—101no—
231C22×C3×C4—104no—
232C22×C3×C4—101no—
233C22×C3×C4—202no—
234C22×C3×C4—202no—
235C22×C3×C4—202no—
236C22×C3×C4C22×D511yescharacteristic
237C3×M16—202no—
238C2×C3×C8—21no—
239C2×C3×C8—101no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—51no—
242C3×C4⋊C4—101no—
243C3×C4⋊C4C4×D511yescharacteristic, complemented
244C3×C22⋊C4—21no—
245C3×C22⋊C4—101no—
246C3×C22⋊C4—101no—
247C3×C22⋊C4—101no—
248C3×C22⋊C4—101no—
249C3×C42—101no—
250C23×C5C2×C3×D411yescharacteristic
251C22×D5—21no—
252C22×D5—21no—
253C22×D5—22no—
254C22×D5—22no—
255C22×D5—21no—
256C22×D5C3×C22⋊C411yescharacteristic
257C22×D5C3×C22⋊C411yescharacteristic
258C5×Q8—41no—
259C2×C4×C5—22no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5C22×C3×C411yescharacteristic
266C2×C4×C5C2×C3×D411yescharacteristic
267C22⋊D5—41no—
268C22⋊D5—41no—
269C2×Dic5—22no—
270C2×Dic5—21no—
271C2×Dic5—41no—
272C2×Dic5—41no—
273C2×Dic5—41no—
274C2×Dic5C3×C22⋊C411yescharacteristic
275C2×Dic5C3×C22⋊C411yescharacteristic
276D20—41no—
277D20—42no—
278D20—42no—
279C4×D5—22no—
280C4×D5—22no—
281C4×D5—41no—
282C4×D5—41no—
283C4×D5—42no—
284C4×D5—48no—
285C5×C8—41no—
286#168—41no—
287C2×#41—51no—
288C23×C4—51no—
289C23×C4—101no—
290C2×M16—101no—
291#123—101no—
292C22⋊Q8—51no—
293C22⋊Q8C2×C3×D511yescharacteristic
294#121—51no—
295#121—51no—
296#120—101no—
297C4×D4—101no—
298C4×D4—101no—
299#117—51no—
300C22⋊C8—51no—
301C22⋊C8—101no—
302C22⋊C8C2×C3×D511yescharacteristic
303#95—51no—
304#95—101no—
305#95C2×C3×D511yescharacteristic
306C2×C3×C5—21no—
307C2×C3×C5—21no—
308C2×C3×C5C2×#9911yescharacteristic
309C2×C3×C5#41711yescharacteristic
310C2×C3×C5C2×#10411yescharacteristic
311C3×D5—22no—
312C3×D5—22no—
313C3×D5—81no—
314C23×C3—51no—
315C23×C3—51no—
316C23×C3—102no—
317C23×C3—102no—
318C23×C3—101no—
319C23×C3—101no—
320C23×C3—101no—
321C23×C3D4×D511yescharacteristic
322C3×Q8—41no—
323C3×D4—201no—
324C3×D4—202no—
325C3×D4—202no—
326C3×D4—201no—
327C3×D4—201no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—51no—
335C2×C3×C4—51no—
336C2×C3×C4—102no—
337C2×C3×C4—102no—
338C2×C3×C4—102no—
339C2×C3×C4—101no—
340C2×C3×C4—201no—
341C2×C3×C4—201no—
342C2×C3×C4—202no—
343C2×C3×C4—208no—
344C2×C3×C4—201no—
345C2×C3×C4—201no—
346C2×C3×C4—201no—
347C2×C3×C4C2×C4×D511yescharacteristic
348C2×C3×C4D4×D511yescharacteristic
349C3×C8—41no—
350C3×C8—201no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5C2×C3×C22⋊C411yescharacteristic
354C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
355C22×C5C3×#13711yescharacteristic
356C2×D5—24no—
357C2×D5—24no—
358C2×D5—21no—
359C2×D5—21no—
360C2×D5—21no—
361C2×D5—21no—
362C2×D5—41no—
363C2×D5—41no—
364C2×D5—41no—
365C2×D5C3×#9912yes—
366C2×D5C3×#10412yes—
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—42no—
370C4×C5—41no—
371C4×C5—41no—
372Dic5—21no—
373Dic5—21no—
374Dic5—42no—
375Dic5—41no—
376C24—51no—
377#41—202no—
378C2×Q8C3×C4×D511yescharacteristic, complemented
379C2×D4—51no—
380C2×D4—101no—
381C2×D4—101no—
382C2×D4—101no—
383C22×C4—21no—
384C22×C4—51no—
385C22×C4—51no—
386C22×C4—51no—
387C22×C4—51no—
388C22×C4—51no—
389C22×C4—101no—
390C22×C4—104no—
391C22×C4—101no—
392C22×C4—202no—
393C22×C4—202no—
394C22×C4—202no—
395C22×C4C22×C3×D511yescharacteristic
396M16—202no—
397C2×C8—21no—
398C2×C8—101no—
399C4⋊C4—21no—
400C4⋊C4—51no—
401C4⋊C4—101no—
402C4⋊C4C3×C4×D511yescharacteristic, complemented
403C22⋊C4—21no—
404C22⋊C4—101no—
405C22⋊C4—101no—
406C22⋊C4—101no—
407C22⋊C4—101no—
408C42—101no—
409C3×C5#150411yescharacteristic, complemented, Hall
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—52no—
413C22×C3—52no—
414C22×C3—104no—
415C22×C3—104no—
416C22×C3—101no—
417C22×C3—101no—
418C22×C3—101no—
419C22×C3—101no—
420C22×C3—201no—
421C22×C3—201no—
422C22×C3—201no—
423C22×C3D5×C22⋊C411yescharacteristic
424C22×C3#406011yescharacteristic
425C22×C3#406411yescharacteristic
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—42no—
429C3×C4—41no—
430C3×C4—41no—
431C3×C4—101no—
432C3×C4—101no—
433C3×C4—202no—
434C3×C4—201no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5C2×C3×#9911yescharacteristic
438C2×C5C3×#41711yescharacteristic
439C2×C5C2×C3×#10411yescharacteristic
440D5—22no—
441D5—22no—
442D5—81no—
443C23—51no—
444C23—51no—
445C23—102no—
446C23—102no—
447C23—101no—
448C23—101no—
449C23—101no—
450C23C3×D4×D511yescharacteristic
451Q8—41no—
452D4—201no—
453D4—202no—
454D4—202no—
455D4—201no—
456D4—201no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—51no—
464C2×C4—51no—
465C2×C4—102no—
466C2×C4—102no—
467C2×C4—102no—
468C2×C4—101no—
469C2×C4—201no—
470C2×C4—201no—
471C2×C4—202no—
472C2×C4—208no—
473C2×C4—201no—
474C2×C4—201no—
475C2×C4—201no—
476C2×C4C2×C3×C4×D511yescharacteristic
477C2×C4C3×D4×D511yescharacteristic
478C8—41no—
479C8—201no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—102no—
483C2×C3—102no—
484C2×C3—401no—
485C2×C3D5×#9911yescharacteristic
486C2×C3#6509211yescharacteristic
487C2×C3D5×#10411yescharacteristic
488C5C3×#150411yescharacteristic, complemented, Sylow
489C22—21no—
490C22—21no—
491C22—52no—
492C22—52no—
493C22—104no—
494C22—104no—
495C22—101no—
496C22—101no—
497C22—101no—
498C22—101no—
499C22—201no—
500C22—201no—
501C22—201no—
502C22C3×D5×C22⋊C411yescharacteristic
503C22C3×#406011yescharacteristic
504C22C3×#406411yescharacteristic
505C4—21no—
506C4—21no—
507C4—42no—
508C4—41no—
509C4—41no—
510C4—101no—
511C4—101no—
512C4—202no—
513C4—201no—
514C3#1059912711yescharacteristic, direct product factor, Sylow
515C2—21no—
516C2—21no—
517C2—102no—
518C2—102no—
519C2—401no—
520C2C3×D5×#9911yescharacteristic
521C2C3×#6509211yescharacteristic
522C2C3×D5×#10411yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#328C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#65961C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#328D5
hypocenterC5C3×#1504
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#328

Complements

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

NH ≅ G/Ntype
2. C3×#65015C2semidirect
3. C3×D5×#95C2semidirect
4. C3×C5×#328C2semidirect
5. C3×#64758C2semidirect
6. C3×#64690C2semidirect
7. C3×#64671C2semidirect
8. #10599127C3direct (N × H)
9. C2×C3×#713C4semidirect
13. C3×#4092C4semidirect
16. C3×#4041C4semidirect
19. C3×#4038C4semidirect
30. #65015C2×C3semidirect
31. D5×#95C2×C3semidirect
32. C5×#328C2×C3semidirect
33. #64758C2×C3semidirect
34. #64690C2×C3semidirect
35. #64671C2×C3semidirect
37. C2×C3×C5×Q8C2×C4semidirect
46. C2×C3×D20C2×C4semidirect
58. C3×C5×C4⋊C4C2×C4semidirect
64. C3×C4⋊Dic5C2×C4semidirect
73. C3×#328D5semidirect
76. C2×#713C3×C4semidirect
80. #4092C3×C4semidirect
83. #4041C3×C4semidirect
86. #4038C3×C4semidirect
153. C2×C5×Q8C2×C3×C4semidirect
162. C2×D20C2×C3×C4semidirect
174. C5×C4⋊C4C2×C3×C4semidirect
180. C4⋊Dic5C2×C3×C4semidirect
189. #328C3×D5semidirect
219. C2×C3×Q8C4×D5semidirect
243. C3×C4⋊C4C4×D5semidirect
378. C2×Q8C3×C4×D5semidirect
402. C4⋊C4C3×C4×D5semidirect
409. C3×C5#1504semidirect
488. C5C3×#1504semidirect
514. C3#10599127direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659612
C3×#650152
C3×D5×#952
C3×C5×#3282
C3×#647582
C3×#646902
C3×#646712
#105991273
C3×#15045