Finite Group Databasebeta

← C3×#10599095 #14282959

Subgroups — C3×#10599095 #14282959

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×#65940C211yesmaximal, characteristic
2C3×#65015C211yesmaximal, characteristic, complemented
3C3×D5×#95C211yesmaximal, characteristic, complemented
4C3×C5×#327C211yesmaximal, characteristic, complemented
5C3×#64757C211yesmaximal, characteristic, complemented
6C3×#64687C211yesmaximal, characteristic, complemented
7C3×#64672C211yesmaximal, characteristic, complemented
8#10599095C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#711C411yescharacteristic, complemented
10C22×C3×C4×D5—21no—
11C22×C3×C4×D5C2211yescharacteristic
12C3×C5×#121C2211yescharacteristic
13C3×#4084C411yescharacteristic, complemented
14C3×#4083—21no—
15C3×D4×Dic5—21no—
16C3×#4070C2211yescharacteristic
17C2×C3×#676—21no—
18C3×#4043C411yescharacteristic, complemented
19C3×#4038C411yescharacteristic, complemented
20C3×#4029—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#65940C2×C311yescharacteristic
30#65015C2×C311yescharacteristic, complemented
31D5×#95C2×C311yescharacteristic, complemented
32C5×#327C2×C311yescharacteristic, complemented
33#64757C2×C311yescharacteristic, complemented
34#64687C2×C311yescharacteristic, complemented
35#64672C2×C311yescharacteristic, complemented
36C23×C3×D5D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4C2×C411yescharacteristic, complemented
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5C2311yescharacteristic
41C2×C3×C22⋊D5—21no—
42C2×C3×C22⋊D5—21no—
43C22×C3×Dic5—21no—
44C22×C3×Dic5—21no—
45C22×C3×Dic5D411yescharacteristic
46C3×#711—42no—
47C2×C3×C4×D5—24no—
48C2×C3×C4×D5—42no—
49C2×C3×C4×D5—42no—
50C2×C3×C4×D5—42no—
51C2×C3×C4×D5C2×C411yescharacteristic
52C2×C3×C4×D5C2×C411yescharacteristic
53C2×C3×C4×D5D411yescharacteristic
54C2×C3×C4×D5D411yescharacteristic
55C2×C3×Dic10C2×C411yescharacteristic, complemented
56C2×C3×C5×C8—21no—
57C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
58C3×C5×C22⋊C4—21no—
59C3×C22⋊Dic5—21no—
60C3×C22⋊Dic5—21no—
61C3×#685—21no—
62C3×#685—21no—
63C3×C4⋊Dic5—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×#328—51no—
74C3×#327—51no—
75C3×#327D511yescharacteristic, complemented
76C2×#711C3×C411yescharacteristic, complemented
77C22×C4×D5—21no—
78C22×C4×D5C22×C311yescharacteristic
79C5×#121C22×C311yescharacteristic
80#4084C3×C411yescharacteristic, complemented
81#4083—21no—
82D4×Dic5—21no—
83#4070C22×C311yescharacteristic
84C2×#676—21no—
85#4043C3×C411yescharacteristic, complemented
86#4038C3×C411yescharacteristic, complemented
87#4029—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×C5—21no—
97C23×C3×C5C2×D411yescharacteristic
98C22×C3×D5—21no—
99C22×C3×D5—21no—
100C22×C3×D5—22no—
101C22×C3×D5—22no—
102C22×C3×D5C22⋊C411yescharacteristic
103C22×C3×D5C22⋊C411yescharacteristic
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C3×C5×D4—41no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C3×C22⋊D5—42no—
115C3×C22⋊D5—42no—
116C2×C3×Dic5—22no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5—42no—
121C2×C3×Dic5—41no—
122C2×C3×Dic5—41no—
123C2×C3×Dic5C22⋊C411yescharacteristic
124C2×C3×Dic5C22⋊C411yescharacteristic
125C3×C4×D5—22no—
126C3×C4×D5—22no—
127C3×C4×D5—41no—
128C3×C4×D5—41no—
129C3×C4×D5—48no—
130C3×Dic10—41no—
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⋊Q8—51no—
140C3×#121—51no—
141C3×#121C2×D511yescharacteristic
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×D4—21no—
154C2×C5×D4C2×C3×C411yescharacteristic, complemented
155C22×C4×C5—21no—
156C22×C4×C5C23×C311yescharacteristic
157C2×C22⋊D5—21no—
158C2×C22⋊D5—21no—
159C22×Dic5—21no—
160C22×Dic5—21no—
161C22×Dic5C3×D411yescharacteristic
162#711—42no—
163C2×C4×D5—24no—
164C2×C4×D5—42no—
165C2×C4×D5—42no—
166C2×C4×D5—42no—
167C2×C4×D5C2×C3×C411yescharacteristic
168C2×C4×D5C2×C3×C411yescharacteristic
169C2×C4×D5C3×D411yescharacteristic
170C2×C4×D5C3×D411yescharacteristic
171C2×Dic10C2×C3×C411yescharacteristic, complemented
172C2×C5×C8—21no—
173C5×C4⋊C4C2×C3×C411yescharacteristic, complemented
174C5×C22⋊C4—21no—
175C22⋊Dic5—21no—
176C22⋊Dic5—21no—
177#685—21no—
178#685—21no—
179C4⋊Dic5—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#328—51no—
190#327—51no—
191#327C3×D511yescharacteristic, complemented
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5—41no—
195C22×C3×C5—41no—
196C22×C3×C5—41no—
197C22×C3×C5C2×C22⋊C411yescharacteristic
198C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
199C22×C3×C5#13711yescharacteristic
200C2×C3×D5—24no—
201C2×C3×D5—24no—
202C2×C3×D5—21no—
203C2×C3×D5—21no—
204C2×C3×D5—21no—
205C2×C3×D5—21no—
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×Dic5—21no—
213C3×Dic5—21no—
214C3×Dic5—42no—
215C3×Dic5—41no—
216C3×Dic5—41no—
217C24×C3—51no—
218C3×#41—202no—
219C2×C3×Q8—51no—
220C2×C3×D4—21no—
221C2×C3×D4—101no—
222C2×C3×D4—101no—
223C2×C3×D4C4×D511yescharacteristic, complemented
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—104no—
231C22×C3×C4—101no—
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—51no—
241C3×C4⋊C4—101no—
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×C5—21no—
251C23×C5C2×C3×D411yescharacteristic
252C22×D5—21no—
253C22×D5—21no—
254C22×D5—22no—
255C22×D5—22no—
256C22×D5C3×C22⋊C411yescharacteristic
257C22×D5C3×C22⋊C411yescharacteristic
258C5×D4—41no—
259C5×D4—41no—
260C5×D4—41no—
261C2×C4×C5—22no—
262C2×C4×C5—21no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—41no—
266C2×C4×C5C22×C3×C411yescharacteristic
267C2×C4×C5C2×C3×D411yescharacteristic
268C22⋊D5—42no—
269C22⋊D5—42no—
270C2×Dic5—22no—
271C2×Dic5—21no—
272C2×Dic5—21no—
273C2×Dic5—41no—
274C2×Dic5—42no—
275C2×Dic5—41no—
276C2×Dic5—41no—
277C2×Dic5C3×C22⋊C411yescharacteristic
278C2×Dic5C3×C22⋊C411yescharacteristic
279C4×D5—22no—
280C4×D5—22no—
281C4×D5—41no—
282C4×D5—41no—
283C4×D5—48no—
284Dic10—41no—
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⋊Q8—51no—
294#121—51no—
295#121C2×C3×D511yescharacteristic
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×C5—81no—
309C2×C3×C5C2×#9911yescharacteristic
310C2×C3×C5#41711yescharacteristic
311C2×C3×C5C2×#10411yescharacteristic
312C3×D5—22no—
313C3×D5—22no—
314C23×C3—21no—
315C23×C3—51no—
316C23×C3—51no—
317C23×C3—102no—
318C23×C3—102no—
319C23×C3—101no—
320C23×C3—101no—
321C23×C3D4×D511yescharacteristic
322C3×Q8—201no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—41no—
326C3×D4—202no—
327C3×D4—202no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—51no—
334C2×C3×C4—51no—
335C2×C3×C4—102no—
336C2×C3×C4—102no—
337C2×C3×C4—102no—
338C2×C3×C4—101no—
339C2×C3×C4—101no—
340C2×C3×C4—201no—
341C2×C3×C4—201no—
342C2×C3×C4—208no—
343C2×C3×C4—201no—
344C2×C3×C4—202no—
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×C5—41no—
354C22×C5—41no—
355C22×C5—41no—
356C22×C5C2×C3×C22⋊C411yescharacteristic
357C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
358C22×C5C3×#13711yescharacteristic
359C2×D5—24no—
360C2×D5—24no—
361C2×D5—21no—
362C2×D5—21no—
363C2×D5—21no—
364C2×D5—21no—
365C2×D5C3×#9912yes—
366C2×D5C3×#10412yes—
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—42no—
370C4×C5—41no—
371Dic5—21no—
372Dic5—21no—
373Dic5—42no—
374Dic5—41no—
375Dic5—41no—
376C24—51no—
377#41—202no—
378C2×Q8—51no—
379C2×D4—21no—
380C2×D4—101no—
381C2×D4—101no—
382C2×D4C3×C4×D511yescharacteristic, complemented
383C22×C4—21no—
384C22×C4—51no—
385C22×C4—51no—
386C22×C4—51no—
387C22×C4—51no—
388C22×C4—51no—
389C22×C4—104no—
390C22×C4—101no—
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—51no—
400C4⋊C4—101no—
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—41no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—52no—
416C22×C3—52no—
417C22×C3—104no—
418C22×C3—104no—
419C22×C3—101no—
420C22×C3—101no—
421C22×C3—101no—
422C22×C3—101no—
423C22×C3D5×C22⋊C411yescharacteristic
424C22×C3#405711yescharacteristic
425C22×C3#406111yescharacteristic
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—42no—
429C3×C4—41no—
430C3×C4—101no—
431C3×C4—101no—
432C3×C4—202no—
433C3×C4—201no—
434C3×C4—201no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—81no—
438C2×C5C2×C3×#9911yescharacteristic
439C2×C5C3×#41711yescharacteristic
440C2×C5C2×C3×#10411yescharacteristic
441D5—22no—
442D5—22no—
443C23—21no—
444C23—51no—
445C23—51no—
446C23—102no—
447C23—102no—
448C23—101no—
449C23—101no—
450C23C3×D4×D511yescharacteristic
451Q8—201no—
452D4—41no—
453D4—41no—
454D4—41no—
455D4—202no—
456D4—202no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—51no—
463C2×C4—51no—
464C2×C4—102no—
465C2×C4—102no—
466C2×C4—102no—
467C2×C4—101no—
468C2×C4—101no—
469C2×C4—201no—
470C2×C4—201no—
471C2×C4—208no—
472C2×C4—201no—
473C2×C4—202no—
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—81no—
483C2×C3—102no—
484C2×C3—102no—
485C2×C3D5×#9911yescharacteristic
486C2×C3#6506011yescharacteristic
487C2×C3D5×#10411yescharacteristic
488C5C3×#150411yescharacteristic, complemented, Sylow
489C22—21no—
490C22—21no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—52no—
495C22—52no—
496C22—104no—
497C22—104no—
498C22—101no—
499C22—101no—
500C22—101no—
501C22—101no—
502C22C3×D5×C22⋊C411yescharacteristic
503C22C3×#405711yescharacteristic
504C22C3×#406111yescharacteristic
505C4—21no—
506C4—21no—
507C4—42no—
508C4—41no—
509C4—101no—
510C4—101no—
511C4—202no—
512C4—201no—
513C4—201no—
514C3#1059909511yescharacteristic, direct product factor, Sylow
515C2—21no—
516C2—21no—
517C2—81no—
518C2—102no—
519C2—102no—
520C2C3×D5×#9911yescharacteristic
521C2C3×#6506011yescharacteristic
522C2C3×D5×#10411yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#327C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#65940C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#327D5
hypocenterC5C3×#1504
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#327

Complements

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

NH ≅ G/Ntype
2. C3×#65015C2semidirect
3. C3×D5×#95C2semidirect
4. C3×C5×#327C2semidirect
5. C3×#64757C2semidirect
6. C3×#64687C2semidirect
7. C3×#64672C2semidirect
8. #10599095C3direct (N × H)
9. C2×C3×#711C4semidirect
13. C3×#4084C4semidirect
18. C3×#4043C4semidirect
19. C3×#4038C4semidirect
30. #65015C2×C3semidirect
31. D5×#95C2×C3semidirect
32. C5×#327C2×C3semidirect
33. #64757C2×C3semidirect
34. #64687C2×C3semidirect
35. #64672C2×C3semidirect
38. C2×C3×C5×D4C2×C4semidirect
55. C2×C3×Dic10C2×C4semidirect
57. C3×C5×C4⋊C4C2×C4semidirect
64. C3×C4⋊Dic5C2×C4semidirect
75. C3×#327D5semidirect
76. C2×#711C3×C4semidirect
80. #4084C3×C4semidirect
85. #4043C3×C4semidirect
86. #4038C3×C4semidirect
154. C2×C5×D4C2×C3×C4semidirect
171. C2×Dic10C2×C3×C4semidirect
173. C5×C4⋊C4C2×C3×C4semidirect
180. C4⋊Dic5C2×C3×C4semidirect
191. #327C3×D5semidirect
223. C2×C3×D4C4×D5semidirect
243. C3×C4⋊C4C4×D5semidirect
382. C2×D4C3×C4×D5semidirect
402. C4⋊C4C3×C4×D5semidirect
409. C3×C5#1504semidirect
488. C5C3×#1504semidirect
514. C3#10599095direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659402
C3×#650152
C3×D5×#952
C3×C5×#3272
C3×#647572
C3×#646872
C3×#646722
#105990953
C3×#15045