Finite Group Databasebeta

← C3×#10610448 #14425462

Subgroups — C3×#10610448 #14425462

Order 1920.

1472 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66283C211yesmaximal, characteristic, complemented
2C3×#66164C211yesmaximal, characteristic, complemented
3C2×C3×#4054C212yesmaximal, complemented
4C3×C5×#413C211yesmaximal, characteristic, complemented
5C3×#65428C212yesmaximal, complemented
6C3×#65042C214yesmaximal, complemented
7C3×#65036C214yesmaximal, complemented
8#10610448C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C3×#4150—22no—
11C3×#4149—22no—
12C3×D5×#41—24no—
13C3×#4147C2212yescomplemented
14C3×#4144—22no—
15C3×#4144C2212yescomplemented
16C2×C3×#709—22no—
17C2×C3×#709C2212yes—
18C22×C3×D20C2211yescharacteristic, complemented
19C2×C3×C5×M16C2212yescomplemented
20C3×#4093C2212yescomplemented
21C3×#4086C2212yescomplemented
22C3×#4083—22no—
23C3×#4076—22no—
24C3×#4072C2211yescharacteristic, complemented
25C3×#4054—24no—
26C3×#4054C2218yescomplemented
27C2×C3×D40—22no—
28C2×C3×#677—22no—
29C3×C5×#101C2212yescomplemented
30C3×C5×#100C2212yescomplemented
31C3×#3957C2218yescomplemented
32C3×#3021—51nomaximal, Hall
33#66283C2×C311yescharacteristic, complemented
34#66164C2×C311yescharacteristic, complemented
35C2×#4054C2×C312yescomplemented
36C5×#413C2×C311yescharacteristic, complemented
37#65428C2×C312yescomplemented
38#65042C2×C314yescomplemented
39#65036C2×C314yescomplemented
40C23×C3×D5—21no—
41C3×C5×#41—22no—
42C3×C5×#41—22no—
43C2×C3×C5×Q8C2311yescharacteristic
44C2×C3×C5×D4D412yes—
45C2×C3×C5×D4C2311yescharacteristic
46C22×C3×C4×C5D412yes—
47C22×C3×C4×C5C2311yescharacteristic
48C2×C3×C22⋊D5—24no—
49C2×C3×C22⋊D5—22no—
50C2×C3×C22⋊D5—24no—
51C3×#713—24no—
52C3×Q8×D5—24no—
53C3×#711—28no—
54C3×#711—24no—
55C3×D4×D5—28no—
56C3×D4×D5—24no—
57C3×#709—24no—
58C3×#709—24no—
59C3×#709—22no—
60C3×#709—24no—
61C3×#709—22no—
62C3×#709D414yescomplemented
63C3×#709C2314yes—
64C2×C3×D20—22no—
65C2×C3×D20—22no—
66C2×C3×D20—22no—
67C2×C3×D20—21no—
68C2×C3×D20D412yescomplemented
69C2×C3×D20C2312yes—
70C2×C3×C4×D5—24no—
71C2×C3×C4×D5—22no—
72C2×C3×Dic10—22no—
73C2×C3×Dic10D412yescomplemented
74C3×C5×M16—22no—
75C3×C5×M16C2314yes—
76C2×C3×C5×C8—22no—
77C3×C22⋊Dic5—21no—
78C3×#685—24no—
79C3×C4⋊Dic5—21no—
80C3×C4×Dic5C2312yes—
81C3×D40—28no—
82C3×#677—28no—
83C3×#585—51no—
84C2×C3×AGL(1,ℤ/8)—52no—
85C3×#535—51no—
86C3×#454—54no—
87C3×#453—54no—
88C3×#421—52no—
89C3×#413D511yescharacteristic, complemented
90C2×C5×#41C22×C311yescharacteristic
91#4150—22no—
92#4149—22no—
93D5×#41—24no—
94#4147C22×C312yescomplemented
95#4144—22no—
96#4144C22×C312yescomplemented
97C2×#709—22no—
98C2×#709C22×C312yes—
99C22×D20C22×C311yescharacteristic, complemented
100C2×C5×M16C22×C312yescomplemented
101#4093C22×C312yescomplemented
102#4086C22×C312yescomplemented
103#4083—22no—
104#4076—22no—
105#4072C22×C311yescharacteristic, complemented
106#4054—24no—
107#4054C22×C318yescomplemented
108C2×D40—22no—
109C2×#677—22no—
110C5×#101C22×C312yescomplemented
111C5×#100C22×C312yescomplemented
112#3957C22×C318yescomplemented
113#3021—51noSylow
114C23×C3×C5C2×D412yes—
115C23×C3×C5C2×D411yescharacteristic
116C22×C3×D5—24no—
117C22×C3×D5—22no—
118C22×C3×D5—22no—
119C22×C3×D5—42no—
120C22×C3×D5—82no—
121C3×C5×Q8—22no—
122C3×C5×D4—24no—
123C3×C5×D4—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5C2×D412yes—
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D412yes—
129C2×C3×C4×C5C2×D412yes—
130C2×C3×C4×C5C2411yescharacteristic
131C3×C22⋊D5—28no—
132C3×C22⋊D5—24no—
133C3×C22⋊D5—24no—
134C3×C22⋊D5—84no—
135C2×C3×Dic5—24no—
136C2×C3×Dic5—22no—
137C2×C3×Dic5—22no—
138C3×D20—24no—
139C3×D20—22no—
140C3×D20—24no—
141C3×D20—41no—
142C3×D20—41no—
143C3×D20C2×D414yes—
144C3×C4×D5—28no—
145C3×C4×D5—24no—
146C3×C4×D5—24no—
147C3×Dic10—24no—
148C3×Dic10—22no—
149C3×Dic10C2×D414yes—
150C3×C5×C8—24no—
151C3×2−1+4—52no—
152C3×2−1+4—102no—
153C3×H(5,𝔽2)—52no—
154C3×H(5,𝔽2)—102no—
155C3×H(5,𝔽2)—102no—
156C2×C3×#41—52no—
157C2×C3×#41—104no—
158C2×C3×#41—102no—
159C2×C3×#41C2×D511yescharacteristic
160C22×C3×D4—51no—
161C3×AGL(1,ℤ/8)—58no—
162C3×AGL(1,ℤ/8)—104no—
163C2×C3×SD16—102no—
164C2×C3×D8—102no—
165C2×C3×M16C2×D512yescomplemented
166C3×#127—52no—
167C3×#124—52no—
168C3×#121—102no—
169C3×#120—102no—
170C3×#117—51no—
171C3×#104—58no—
172C3×#101C2×D512yescomplemented
173C3×#100C2×D512yescomplemented
174C23×D5—21no—
175C5×#41—22no—
176C5×#41—22no—
177C2×C5×Q8C23×C311yescharacteristic
178C2×C5×D4C3×D412yes—
179C2×C5×D4C23×C311yescharacteristic
180C22×C4×C5C3×D412yes—
181C22×C4×C5C23×C311yescharacteristic
182C2×C22⋊D5—24no—
183C2×C22⋊D5—22no—
184C2×C22⋊D5—24no—
185#713—24no—
186Q8×D5—24no—
187#711—28no—
188#711—24no—
189D4×D5—28no—
190D4×D5—24no—
191#709—24no—
192#709—24no—
193#709—22no—
194#709—24no—
195#709—22no—
196#709C3×D414yescomplemented
197#709C23×C314yes—
198C2×D20—22no—
199C2×D20—22no—
200C2×D20—22no—
201C2×D20—21no—
202C2×D20C3×D412yescomplemented
203C2×D20C23×C312yes—
204C2×C4×D5—24no—
205C2×C4×D5—22no—
206C2×Dic10—22no—
207C2×Dic10C3×D412yescomplemented
208C5×M16—22no—
209C5×M16C23×C314yes—
210C2×C5×C8—22no—
211C22⋊Dic5—21no—
212#685—24no—
213C4⋊Dic5—21no—
214C4×Dic5C23×C312yes—
215D40—28no—
216#677—28no—
217#585—51no—
218C2×AGL(1,ℤ/8)—52no—
219#535—51no—
220#454—54no—
221#453—54no—
222#421—52no—
223#413C3×D511yescharacteristic, complemented
224C22×C3×C5—22no—
225C22×C3×C5—41no—
226C22×C3×C5—42no—
227C22×C3×C5#12012yes—
228C22×C3×C5C22×D411yescharacteristic
229C2×C3×D5—24no—
230C2×C3×D5—44no—
231C2×C3×D5—42no—
232C2×C3×D5—82no—
233C2×C3×D5—84no—
234C2×C3×D5—84no—
235C3×C4×C5—22no—
236C3×C4×C5#12011yescharacteristic
237C3×C4×C5#12011yescharacteristic
238C3×C4×C5C22×D412yes—
239C3×Dic5—24no—
240C3×Dic5—42no—
241C24×C3—101no—
242C3×#41—22no—
243C3×#41—22no—
244C3×#41—54no—
245C3×#41—54no—
246C3×#41—104no—
247C3×#41—104no—
248C3×#41—104no—
249C3×#41—108no—
250C3×#41—104no—
251C3×#41—102no—
252C3×#41—104no—
253C3×#41—102no—
254C2×C3×Q8—52no—
255C2×C3×Q8—102no—
256C2×C3×Q8—104no—
257C2×C3×Q8C22×D511yescharacteristic
258C2×C3×D4—52no—
259C2×C3×D4—52no—
260C2×C3×D4—102no—
261C2×C3×D4—104no—
262C2×C3×D4—108no—
263C2×C3×D4—102no—
264C2×C3×D4—104no—
265C2×C3×D4—104no—
266C2×C3×D4—101no—
267C2×C3×D4—102no—
268C2×C3×D4—102no—
269C2×C3×D4D2012yes—
270C2×C3×D4C22×D511yescharacteristic
271C22×C3×C4—104no—
272C22×C3×C4—102no—
273C22×C3×C4D2012yes—
274C22×C3×C4C22×D511yescharacteristic
275C3×SD16—108no—
276C3×D8—108no—
277C3×M16—22no—
278C3×M16C22×D514yes—
279C2×C3×C8—22no—
280C3×C4⋊C4—101no—
281C3×C22⋊C4—101no—
282C3×C22⋊C4—104no—
283C3×C42—52no—
284C23×C5C2×C3×D412yes—
285C23×C5C2×C3×D411yescharacteristic
286C22×D5—24no—
287C22×D5—22no—
288C22×D5—22no—
289C22×D5—42no—
290C22×D5—82no—
291C5×Q8—22no—
292C5×D4—24no—
293C5×D4—22no—
294C2×C4×C5—22no—
295C2×C4×C5—22no—
296C2×C4×C5C2×C3×D412yes—
297C2×C4×C5C2×C3×D411yescharacteristic
298C2×C4×C5C2×C3×D412yes—
299C2×C4×C5C2×C3×D412yes—
300C2×C4×C5C24×C311yescharacteristic
301C22⋊D5—28no—
302C22⋊D5—24no—
303C22⋊D5—24no—
304C22⋊D5—84no—
305C2×Dic5—24no—
306C2×Dic5—22no—
307C2×Dic5—22no—
308D20—24no—
309D20—22no—
310D20—24no—
311D20—41no—
312D20—41no—
313D20C2×C3×D414yes—
314C4×D5—28no—
315C4×D5—24no—
316C4×D5—24no—
317Dic10—24no—
318Dic10—22no—
319Dic10C2×C3×D414yes—
320C5×C8—24no—
3212−1+4—52no—
3222−1+4—102no—
323H(5,𝔽2)—52no—
324H(5,𝔽2)—102no—
325H(5,𝔽2)—102no—
326C2×#41—52no—
327C2×#41—104no—
328C2×#41—102no—
329C2×#41C2×C3×D511yescharacteristic
330C22×D4—51no—
331AGL(1,ℤ/8)—58no—
332AGL(1,ℤ/8)—104no—
333C2×SD16—102no—
334C2×D8—102no—
335C2×M16C2×C3×D512yescomplemented
336#127—52no—
337#124—52no—
338#121—102no—
339#120—102no—
340#117—51no—
341#104—58no—
342#101C2×C3×D512yescomplemented
343#100C2×C3×D512yescomplemented
344C2×C3×C5—21no—
345C2×C3×C5—22no—
346C2×C3×C5—42no—
347C2×C3×C5C2×#12011yescharacteristic
348C3×D5—44no—
349C3×D5—82no—
350C23×C3—104no—
351C23×C3—102no—
352C23×C3—102no—
353C23×C3—202no—
354C23×C3—402no—
355C23×C3C2×D2012yes—
356C23×C3C2×D2011yescharacteristic
357C3×Q8—22no—
358C3×Q8—54no—
359C3×Q8—104no—
360C3×Q8—102no—
361C3×D4—24no—
362C3×D4—22no—
363C3×D4—54no—
364C3×D4—104no—
365C3×D4—108no—
366C3×D4—104no—
367C3×D4—104no—
368C3×D4—104no—
369C3×D4—102no—
370C3×D4—201no—
371C3×D4—201no—
372C3×D4—404no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—108no—
376C2×C3×C4—104no—
377C2×C3×C4—102no—
378C2×C3×C4—104no—
379C2×C3×C4—104no—
380C2×C3×C4—102no—
381C2×C3×C4C2×D2012yes—
382C2×C3×C4C2×D2011yescharacteristic
383C2×C3×C4D4×D512yes—
384C2×C3×C4D4×D512yes—
385C2×C3×C4C23×D511yescharacteristic
386C3×C8—24no—
387C22×C5—22no—
388C22×C5—41no—
389C22×C5—42no—
390C22×C5C3×#12012yes—
391C22×C5C22×C3×D411yescharacteristic
392C2×D5—24no—
393C2×D5—44no—
394C2×D5—42no—
395C2×D5—82no—
396C2×D5—84no—
397C2×D5—84no—
398C4×C5—22no—
399C4×C5C3×#12011yescharacteristic
400C4×C5C3×#12011yescharacteristic
401C4×C5C22×C3×D412yes—
402Dic5—24no—
403Dic5—42no—
404C24—101no—
405#41—22no—
406#41—22no—
407#41—54no—
408#41—54no—
409#41—104no—
410#41—104no—
411#41—104no—
412#41—108no—
413#41—104no—
414#41—102no—
415#41—104no—
416#41—102no—
417C2×Q8—52no—
418C2×Q8—102no—
419C2×Q8—104no—
420C2×Q8C22×C3×D511yescharacteristic
421C2×D4—52no—
422C2×D4—52no—
423C2×D4—102no—
424C2×D4—104no—
425C2×D4—108no—
426C2×D4—102no—
427C2×D4—104no—
428C2×D4—104no—
429C2×D4—101no—
430C2×D4—102no—
431C2×D4—102no—
432C2×D4C3×D2012yes—
433C2×D4C22×C3×D511yescharacteristic
434C22×C4—104no—
435C22×C4—102no—
436C22×C4C3×D2012yes—
437C22×C4C22×C3×D511yescharacteristic
438SD16—108no—
439D8—108no—
440M16—22no—
441M16C22×C3×D514yes—
442C2×C8—22no—
443C4⋊C4—101no—
444C22⋊C4—101no—
445C22⋊C4—104no—
446C42—52no—
447C3×C5#302111yescharacteristic, complemented, Hall
448C22×C3—22no—
449C22×C3—41no—
450C22×C3—42no—
451C22×C3—104no—
452C22×C3—204no—
453C22×C3—202no—
454C22×C3—402no—
455C22×C3—404no—
456C22×C3—404no—
457C22×C3#402812yes—
458C22×C3C22×D2011yescharacteristic
459C3×C4—22no—
460C3×C4—104no—
461C3×C4—202no—
462C3×C4#402811yescharacteristic
463C3×C4#402811yescharacteristic
464C3×C4C2×D4×D512yes—
465C2×C5—21no—
466C2×C5—22no—
467C2×C5—42no—
468C2×C5C2×C3×#12011yescharacteristic
469D5—44no—
470D5—82no—
471C23—104no—
472C23—102no—
473C23—102no—
474C23—202no—
475C23—402no—
476C23C2×C3×D2012yes—
477C23C2×C3×D2011yescharacteristic
478Q8—22no—
479Q8—54no—
480Q8—104no—
481Q8—102no—
482D4—24no—
483D4—22no—
484D4—54no—
485D4—104no—
486D4—108no—
487D4—104no—
488D4—104no—
489D4—104no—
490D4—102no—
491D4—201no—
492D4—201no—
493D4—404no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—108no—
497C2×C4—104no—
498C2×C4—102no—
499C2×C4—104no—
500C2×C4—104no—
501C2×C4—102no—
502C2×C4C2×C3×D2012yes—
503C2×C4C2×C3×D2011yescharacteristic
504C2×C4C3×D4×D512yes—
505C2×C4C3×D4×D512yes—
506C2×C4C23×C3×D511yescharacteristic
507C8—24no—
508C2×C3—21no—
509C2×C3—22no—
510C2×C3—42no—
511C2×C3—204no—
512C2×C3—402no—
513C2×C3C2×#402811yescharacteristic
514C5C3×#302111yescharacteristic, complemented, Sylow
515C22—22no—
516C22—41no—
517C22—42no—
518C22—104no—
519C22—204no—
520C22—202no—
521C22—402no—
522C22—404no—
523C22—404no—
524C22C3×#402812yes—
525C22C22×C3×D2011yescharacteristic
526C4—22no—
527C4—104no—
528C4—202no—
529C4C3×#402811yescharacteristic
530C4C3×#402811yescharacteristic
531C4C2×C3×D4×D512yes—
532C3#1061044811yescharacteristic, direct product factor, Sylow
533C2—21no—
534C2—22no—
535C2—42no—
536C2—204no—
537C2—402no—
538C2C2×C3×#402811yescharacteristic
subgroupG/H
centerC2×C3C2×#4028
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#413C2
socleC2×C3×C5C2×#120
hypercenterC3×#413D5
hypocenterC5C3×#3021
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#413

Complements

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

NH ≅ G/Ntype
1. C3×#66283C2semidirect
2. C3×#66164C2semidirect
3. C2×C3×#4054C2semidirect
4. C3×C5×#413C2semidirect
5. C3×#65428C2semidirect
6. C3×#65042C2semidirect
7. C3×#65036C2semidirect
8. #10610448C3direct (N × H)
13. C3×#4147C22semidirect
15. C3×#4144C22semidirect
18. C22×C3×D20C22semidirect
19. C2×C3×C5×M16C22semidirect
20. C3×#4093C22semidirect
21. C3×#4086C22semidirect
24. C3×#4072C22semidirect
26. C3×#4054C22semidirect
29. C3×C5×#101C22semidirect
30. C3×C5×#100C22semidirect
31. C3×#3957C22semidirect
33. #66283C2×C3semidirect
34. #66164C2×C3semidirect
35. C2×#4054C2×C3semidirect
36. C5×#413C2×C3semidirect
37. #65428C2×C3semidirect
38. #65042C2×C3semidirect
39. #65036C2×C3semidirect
62. C3×#709D4semidirect
68. C2×C3×D20D4semidirect
73. C2×C3×Dic10D4semidirect
89. C3×#413D5semidirect
94. #4147C22×C3semidirect
96. #4144C22×C3semidirect
99. C22×D20C22×C3semidirect
100. C2×C5×M16C22×C3semidirect
101. #4093C22×C3semidirect
102. #4086C22×C3semidirect
105. #4072C22×C3semidirect
107. #4054C22×C3semidirect
110. C5×#101C22×C3semidirect
111. C5×#100C22×C3semidirect
112. #3957C22×C3semidirect
165. C2×C3×M16C2×D5semidirect
172. C3×#101C2×D5semidirect
173. C3×#100C2×D5semidirect
196. #709C3×D4semidirect
202. C2×D20C3×D4semidirect
207. C2×Dic10C3×D4semidirect
223. #413C3×D5semidirect
335. C2×M16C2×C3×D5semidirect
342. #101C2×C3×D5semidirect
343. #100C2×C3×D5semidirect
447. C3×C5#3021semidirect
514. C5C3×#3021semidirect
532. C3#10610448direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#662832
C3×#661642
C2×C3×#40542
C3×C5×#4132
C3×#654282
C3×#650422
C3×#650362
#106104483
C3×#30215