Finite Group Databasebeta

← C3×#10605961 #14331128

Subgroups — C3×#10605961 #14331128

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4021C211yesmaximal, characteristic
2C3×C5×#382C211yesmaximal, characteristic, complemented
3C3×#65279C212yesmaximal, complemented
4C3×#65278C212yesmaximal, complemented
5C3×#65225C211yesmaximal, characteristic, complemented
6C3×#64959C212yesmaximal, complemented
7C3×#64957C212yesmaximal, complemented
8C3×#64954C212yesmaximal
9C3×#64935C212yesmaximal, complemented
10#10605961C311yesmaximal, characteristic, direct product factor, Hall
11C22×C3×D20C2211yescharacteristic
12C22×C3×C4×D5C2212yes—
13C22×C3×Dic10C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C3×C42×C5C2211yescharacteristic
17C2×C3×#685C2212yes—
18C2×C3×#685C2212yes—
19C2×C3×#685C2212yes—
20C2×C3×#685C2212yes—
21C2×C3×#685C2212yes—
22C2×C3×C4⋊Dic5C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×#683C2212yes—
25C2×C3×C4×Dic5C2212yes—
26C3×#4021C418yescomplemented
27C3×C5×#95C2212yes—
28C3×C5×#95C2212yes—
29C3×#3963C2212yes—
30C3×#3963C2212yes—
31C3×#3963C2212yes—
32C3×#3963C2212yes—
33C3×#2379—51nomaximal, Hall
34C2×#4021C2×C311yescharacteristic
35C5×#382C2×C311yescharacteristic, complemented
36#65279C2×C312yescomplemented
37#65278C2×C312yescomplemented
38#65225C2×C311yescharacteristic, complemented
39#64959C2×C312yescomplemented
40#64957C2×C312yescomplemented
41#64954C2×C312yes—
42#64935C2×C312yescomplemented
43C23×C3×D5C2312yes—
44C22×C3×C4×C5C2312yes—
45C22×C3×C4×C5C2312yes—
46C22×C3×C4×C5C2311yescharacteristic
47C22×C3×C4×C5C2311yescharacteristic
48C22×C3×C4×C5C2311yescharacteristic
49C22×C3×Dic5C2312yes—
50C22×C3×Dic5C2312yes—
51C22×C3×Dic5C2312yes—
52C2×C3×D20—41no—
53C2×C3×D20—41no—
54C2×C3×D20C2×C414yes—
55C2×C3×C4×D5—42no—
56C2×C3×C4×D5—42no—
57C2×C3×C4×D5—42no—
58C2×C3×Dic10—41no—
59C2×C3×Dic10—41no—
60C2×C3×Dic10C2×C414yescomplemented
61C3×C5×C4⋊C4—41no—
62C3×C5×C4⋊C4—41no—
63C3×C42×C5C2×C414yescomplemented
64C3×#685—42no—
65C3×#685—42no—
66C3×#685—42no—
67C3×#685C2×C418yescomplemented
68C3×#685C2×C418yescomplemented
69C3×C4⋊Dic5—41no—
70C3×C4⋊Dic5—41no—
71C3×#683—42no—
72C3×C4×Dic5—42no—
73C2×C3×#124—51no—
74C3×#391—52no—
75C3×#388—52no—
76C3×#388—52no—
77C3×#386—52no—
78C3×#385—52no—
79C3×#385—52no—
80C3×#382—51no—
81C3×#382D511yescharacteristic, complemented
82C22×D20C22×C311yescharacteristic
83C22×C4×D5C22×C312yes—
84C22×Dic10C22×C311yescharacteristic
85C2×C5×C4⋊C4C22×C311yescharacteristic
86C2×C5×C4⋊C4C22×C311yescharacteristic
87C2×C42×C5C22×C311yescharacteristic
88C2×#685C22×C312yes—
89C2×#685C22×C312yes—
90C2×#685C22×C312yes—
91C2×#685C22×C312yes—
92C2×#685C22×C312yes—
93C2×C4⋊Dic5C22×C311yescharacteristic
94C2×C4⋊Dic5C22×C311yescharacteristic
95C2×#683C22×C312yes—
96C2×C4×Dic5C22×C312yes—
97#4021C3×C418yescomplemented
98C5×#95C22×C312yes—
99C5×#95C22×C312yes—
100#3963C22×C312yes—
101#3963C22×C312yes—
102#3963C22×C312yes—
103#3963C22×C312yes—
104#2379—51noSylow
105C23×C3×C5C2411yescharacteristic
106C22×C3×D5—22no—
107C22×C3×D5—22no—
108C22×C3×D5—22no—
109C22×C3×D5—22no—
110C22×C3×D5—22no—
111C22×C3×D5—22no—
112C22×C3×D5C22×C414yes—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—21no—
116C2×C3×C4×C5—21no—
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—21no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5C22×C412yes—
126C2×C3×C4×C5C22×C412yes—
127C2×C3×C4×C5C22×C412yes—
128C2×C3×Dic5—22no—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—22no—
131C2×C3×Dic5—22no—
132C2×C3×Dic5—22no—
133C2×C3×Dic5—22no—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—22no—
136C2×C3×Dic5C22×C414yes—
137C3×D20—44no—
138C3×C4×D5—48no—
139C3×Dic10—44no—
140C22×C3×Q8—51no—
141C22×C3×D4—51no—
142C23×C3×C4—52no—
143C3×#124—58no—
144C2×C3×C4⋊C4—51no—
145C2×C3×C4⋊C4—51no—
146C2×C3×C4⋊C4—52no—
147C2×C3×C4⋊C4C2×D511yescharacteristic
148C2×C3×C4⋊C4C2×D511yescharacteristic
149C2×C3×C22⋊C4—52no—
150C2×C3×C22⋊C4—52no—
151C2×C3×C22⋊C4—52no—
152C2×C3×C22⋊C4—52no—
153C2×C3×C22⋊C4—52no—
154C2×C3×C42—52no—
155C2×C3×C42C2×D511yescharacteristic
156C3×#95—52no—
157C3×#95—52no—
158C3×#95—52no—
159C3×#95—52no—
160C3×#95C2×D512yes—
161C3×#95C2×D512yes—
162C23×D5C23×C312yes—
163C22×C4×C5C23×C312yes—
164C22×C4×C5C23×C312yes—
165C22×C4×C5C23×C311yescharacteristic
166C22×C4×C5C23×C311yescharacteristic
167C22×C4×C5C23×C311yescharacteristic
168C22×Dic5C23×C312yes—
169C22×Dic5C23×C312yes—
170C22×Dic5C23×C312yes—
171C2×D20—41no—
172C2×D20—41no—
173C2×D20C2×C3×C414yes—
174C2×C4×D5—42no—
175C2×C4×D5—42no—
176C2×C4×D5—42no—
177C2×Dic10—41no—
178C2×Dic10—41no—
179C2×Dic10C2×C3×C414yescomplemented
180C5×C4⋊C4—41no—
181C5×C4⋊C4—41no—
182C42×C5C2×C3×C414yescomplemented
183#685—42no—
184#685—42no—
185#685—42no—
186#685C2×C3×C418yescomplemented
187#685C2×C3×C418yescomplemented
188C4⋊Dic5—41no—
189C4⋊Dic5—41no—
190#683—42no—
191C4×Dic5—42no—
192C2×#124—51no—
193#391—52no—
194#388—52no—
195#388—52no—
196#386—52no—
197#385—52no—
198#385—52no—
199#382—51no—
200#382C3×D511yescharacteristic, complemented
201C22×C3×C5C23×C411yescharacteristic
202C22×C3×C5H(5,𝔽2)11yescharacteristic
203C22×C3×C5H(5,𝔽2)11yescharacteristic
204C22×C3×C5H(5,𝔽2)11yescharacteristic
205C22×C3×C5H(5,𝔽2)11yescharacteristic
206C22×C3×C52−1+411yescharacteristic
207C22×C3×C52−1+411yescharacteristic
208C2×C3×D5—24no—
209C2×C3×D5—24no—
210C2×C3×D5—24no—
211C2×C3×D5—42no—
212C2×C3×D5—42no—
213C2×C3×D5—42no—
214C2×C3×D5—42no—
215C3×C4×C5—22no—
216C3×C4×C5—22no—
217C3×C4×C5—22no—
218C3×C4×C5—42no—
219C3×C4×C5—42no—
220C3×Dic5—24no—
221C3×Dic5—42no—
222C3×Dic5—42no—
223C24×C3—52no—
224C2×C3×Q8—54no—
225C2×C3×Q8—201no—
226C2×C3×Q8—201no—
227C2×C3×D4—54no—
228C2×C3×D4—201no—
229C2×C3×D4—201no—
230C22×C3×C4—52no—
231C22×C3×C4—52no—
232C22×C3×C4—52no—
233C22×C3×C4—202no—
234C22×C3×C4—202no—
235C22×C3×C4—202no—
236C22×C3×C4C22×D512yes—
237C22×C3×C4C22×D512yes—
238C22×C3×C4C22×D511yescharacteristic
239C22×C3×C4C22×D511yescharacteristic
240C22×C3×C4C22×D511yescharacteristic
241C3×C4⋊C4—41no—
242C3×C4⋊C4—41no—
243C3×C4⋊C4—202no—
244C3×C4⋊C4—201no—
245C3×C4⋊C4—201no—
246C3×C22⋊C4—58no—
247C3×C22⋊C4—58no—
248C3×C22⋊C4—202no—
249C3×C22⋊C4—202no—
250C3×C22⋊C4—202no—
251C3×C42—202no—
252C3×C42C4×D514yescomplemented
253C23×C5C24×C311yescharacteristic
254C22×D5—22no—
255C22×D5—22no—
256C22×D5—22no—
257C22×D5—22no—
258C22×D5—22no—
259C22×D5—22no—
260C22×D5C22×C3×C414yes—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5C22×C3×C412yes—
274C2×C4×C5C22×C3×C412yes—
275C2×C4×C5C22×C3×C412yes—
276C2×Dic5—22no—
277C2×Dic5—22no—
278C2×Dic5—22no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—22no—
282C2×Dic5—22no—
283C2×Dic5—22no—
284C2×Dic5C22×C3×C414yes—
285D20—44no—
286C4×D5—48no—
287Dic10—44no—
288C22×Q8—51no—
289C22×D4—51no—
290C23×C4—52no—
291#124—58no—
292C2×C4⋊C4—51no—
293C2×C4⋊C4—51no—
294C2×C4⋊C4—52no—
295C2×C4⋊C4C2×C3×D511yescharacteristic
296C2×C4⋊C4C2×C3×D511yescharacteristic
297C2×C22⋊C4—52no—
298C2×C22⋊C4—52no—
299C2×C22⋊C4—52no—
300C2×C22⋊C4—52no—
301C2×C22⋊C4—52no—
302C2×C42—52no—
303C2×C42C2×C3×D511yescharacteristic
304#95—52no—
305#95—52no—
306#95—52no—
307#95—52no—
308#95C2×C3×D512yes—
309#95C2×C3×D512yes—
310C2×C3×C5#51811yescharacteristic
311C2×C3×C5#52011yescharacteristic
312C2×C3×C5#52011yescharacteristic
313C2×C3×C5H(3,𝔽4)11yescharacteristic
314C2×C3×C5#56211yescharacteristic
315C2×C3×C5#56211yescharacteristic
316C2×C3×C5#56311yescharacteristic
317C3×D5—44no—
318C23×C3—54no—
319C23×C3—102no—
320C23×C3—102no—
321C23×C3—102no—
322C23×C3—102no—
323C23×C3—102no—
324C23×C3—102no—
325C23×C3C23×D511yescharacteristic
326C3×Q8—204no—
327C3×D4—204no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—54no—
341C2×C3×C4—102no—
342C2×C3×C4—102no—
343C2×C3×C4—102no—
344C2×C3×C4—102no—
345C2×C3×C4—102no—
346C2×C3×C4—102no—
347C2×C3×C4—102no—
348C2×C3×C4—102no—
349C2×C3×C4—208no—
350C2×C3×C4C2×C4×D512yes—
351C2×C3×C4C2×C4×D512yes—
352C2×C3×C4C2×C4×D512yes—
353C22×C5C23×C3×C411yescharacteristic
354C22×C5C3×H(5,𝔽2)11yescharacteristic
355C22×C5C3×H(5,𝔽2)11yescharacteristic
356C22×C5C3×H(5,𝔽2)11yescharacteristic
357C22×C5C3×H(5,𝔽2)11yescharacteristic
358C22×C5C3×2−1+411yescharacteristic
359C22×C5C3×2−1+411yescharacteristic
360C2×D5—24no—
361C2×D5—24no—
362C2×D5—24no—
363C2×D5—42no—
364C2×D5—42no—
365C2×D5—42no—
366C2×D5—42no—
367C4×C5—22no—
368C4×C5—22no—
369C4×C5—22no—
370C4×C5—42no—
371C4×C5—42no—
372Dic5—24no—
373Dic5—42no—
374Dic5—42no—
375C24—52no—
376C2×Q8—54no—
377C2×Q8—201no—
378C2×Q8—201no—
379C2×D4—54no—
380C2×D4—201no—
381C2×D4—201no—
382C22×C4—52no—
383C22×C4—52no—
384C22×C4—52no—
385C22×C4—202no—
386C22×C4—202no—
387C22×C4—202no—
388C22×C4C22×C3×D512yes—
389C22×C4C22×C3×D512yes—
390C22×C4C22×C3×D511yescharacteristic
391C22×C4C22×C3×D511yescharacteristic
392C22×C4C22×C3×D511yescharacteristic
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—202no—
396C4⋊C4—201no—
397C4⋊C4—201no—
398C22⋊C4—58no—
399C22⋊C4—58no—
400C22⋊C4—202no—
401C22⋊C4—202no—
402C22⋊C4—202no—
403C42—202no—
404C42C3×C4×D514yescomplemented
405C3×C5#237911yescharacteristic, complemented, Hall
406C22×C3—104no—
407C22×C3—104no—
408C22×C3—104no—
409C22×C3—202no—
410C22×C3—202no—
411C22×C3—202no—
412C22×C3—202no—
413C22×C3C22×C4×D511yescharacteristic
414C22×C3#414411yescharacteristic
415C22×C3#414711yescharacteristic
416C22×C3#414911yescharacteristic
417C22×C3#414911yescharacteristic
418C22×C3#414911yescharacteristic
419C22×C3#415011yescharacteristic
420C3×C4—22no—
421C3×C4—22no—
422C3×C4—22no—
423C3×C4—42no—
424C3×C4—42no—
425C3×C4—104no—
426C3×C4—202no—
427C3×C4—202no—
428C2×C5C3×#51811yescharacteristic
429C2×C5C3×#52011yescharacteristic
430C2×C5C3×#52011yescharacteristic
431C2×C5C3×H(3,𝔽4)11yescharacteristic
432C2×C5C3×#56211yescharacteristic
433C2×C5C3×#56211yescharacteristic
434C2×C5C3×#56311yescharacteristic
435D5—44no—
436C23—54no—
437C23—102no—
438C23—102no—
439C23—102no—
440C23—102no—
441C23—102no—
442C23—102no—
443C23C23×C3×D511yescharacteristic
444Q8—204no—
445D4—204no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—54no—
459C2×C4—102no—
460C2×C4—102no—
461C2×C4—102no—
462C2×C4—102no—
463C2×C4—102no—
464C2×C4—102no—
465C2×C4—102no—
466C2×C4—102no—
467C2×C4—208no—
468C2×C4C2×C3×C4×D512yes—
469C2×C4C2×C3×C4×D512yes—
470C2×C4C2×C3×C4×D512yes—
471C2×C3—204no—
472C2×C3#6583811yescharacteristic
473C2×C3#6585511yescharacteristic
474C2×C3#6585711yescharacteristic
475C2×C3#6601711yescharacteristic
476C2×C3#6601811yescharacteristic
477C2×C3#6603311yescharacteristic
478C2×C3#6603411yescharacteristic
479C5C3×#237911yescharacteristic, complemented, Sylow
480C22—104no—
481C22—104no—
482C22—104no—
483C22—202no—
484C22—202no—
485C22—202no—
486C22—202no—
487C22C22×C3×C4×D511yescharacteristic
488C22C3×#414411yescharacteristic
489C22C3×#414711yescharacteristic
490C22C3×#414911yescharacteristic
491C22C3×#414911yescharacteristic
492C22C3×#414911yescharacteristic
493C22C3×#415011yescharacteristic
494C4—22no—
495C4—22no—
496C4—22no—
497C4—42no—
498C4—42no—
499C4—104no—
500C4—202no—
501C4—202no—
502C3#1060596111yescharacteristic, direct product factor, Sylow
503C2—204no—
504C2C3×#6583811yescharacteristic
505C2C3×#6585511yescharacteristic
506C2C3×#6585711yescharacteristic
507C2C3×#6601711yescharacteristic
508C2C3×#6601811yescharacteristic
509C2C3×#6603311yescharacteristic
510C2C3×#6603411yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#382C2
socleC23×C3×C5C24
prime radicalC22×C3×D20C22
cosocleC23×C5C24×C3
hypercenterC3×#382D5
hypocenterC5C3×#2379
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#382

Complements

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

NH ≅ G/Ntype
2. C3×C5×#382C2semidirect
3. C3×#65279C2semidirect
4. C3×#65278C2semidirect
5. C3×#65225C2semidirect
6. C3×#64959C2semidirect
7. C3×#64957C2semidirect
9. C3×#64935C2semidirect
10. #10605961C3direct (N × H)
26. C3×#4021C4semidirect
35. C5×#382C2×C3semidirect
36. #65279C2×C3semidirect
37. #65278C2×C3semidirect
38. #65225C2×C3semidirect
39. #64959C2×C3semidirect
40. #64957C2×C3semidirect
42. #64935C2×C3semidirect
60. C2×C3×Dic10C2×C4semidirect
63. C3×C42×C5C2×C4semidirect
67. C3×#685C2×C4semidirect
68. C3×#685C2×C4semidirect
81. C3×#382D5semidirect
97. #4021C3×C4semidirect
179. C2×Dic10C2×C3×C4semidirect
182. C42×C5C2×C3×C4semidirect
186. #685C2×C3×C4semidirect
187. #685C2×C3×C4semidirect
200. #382C3×D5semidirect
252. C3×C42C4×D5semidirect
404. C42C3×C4×D5semidirect
405. C3×C5#2379semidirect
479. C5C3×#2379semidirect
502. C3#10605961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40212
C3×C5×#3822
C3×#652792
C3×#652782
C3×#652252
C3×#649592
C3×#649572
C3×#649542
C3×#649352
#106059613
C3×#23795