Finite Group Databasebeta

← C3×#10615847 #14425378

Subgroups — C3×#10615847 #14425378

Order 1920.

1396 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×2−1+4C211yesmaximal, characteristic, complemented
2C3×#66156C212yesmaximal, complemented
3C3×#66150C211yesmaximal, characteristic, complemented
4C3×#65535C214yesmaximal, complemented
5C3×#65534C214yesmaximal, complemented
6C3×#65525C212yesmaximal, complemented
7C2×C3×#3968C211yesmaximal, characteristic, complemented
8#10615847C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×2−1+4—24no—
10C3×C5×2−1+4—22no—
11C3×C5×2−1+4C2214yes—
12C2×C3×C5×#41—22no—
13C2×C3×C5×#41—22no—
14C2×C3×C5×#41C2212yes—
15C22×C3×C5×Q8—22no—
16C22×C3×C5×Q8C2211yescharacteristic
17C2×C3×#709C2211yescharacteristic
18C3×#4097C2214yescomplemented
19C3×#4096—24no—
20C3×#4095C2214yescomplemented
21C3×#4093C2212yescomplemented
22C3×#4092—22no—
23C3×#4090C2212yescomplemented
24C3×#4088—22no—
25C3×#4078—22no—
26C3×#4075—22no—
27C3×#4072C2211yescharacteristic
28C2×C3×#681C2212yes—
29C3×#3969C2218yescomplemented
30C3×#3968C2214yescomplemented
31C3×#3020—51nomaximal, Hall
32C2×C5×2−1+4C2×C311yescharacteristic, complemented
33#66156C2×C312yescomplemented
34#66150C2×C311yescharacteristic, complemented
35#65535C2×C314yescomplemented
36#65534C2×C314yescomplemented
37#65525C2×C312yescomplemented
38C2×#3968C2×C311yescharacteristic, complemented
39C3×C5×#41—28no—
40C3×C5×#41—28no—
41C3×C5×#41—28no—
42C3×C5×#41—28no—
43C3×C5×#41—22no—
44C3×C5×#41—22no—
45C3×C5×#41D414yes—
46C3×C5×#41C2314yes—
47C2×C3×C5×Q8—22no—
48C2×C3×C5×Q8—28no—
49C2×C3×C5×Q8—28no—
50C2×C3×C5×Q8—22no—
51C2×C3×C5×Q8—22no—
52C2×C3×C5×Q8D412yes—
53C2×C3×C5×Q8D412yes—
54C2×C3×C5×Q8C2312yes—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4D412yes—
58C22×C3×C4×C5—24no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5D412yes—
61C22×C3×C4×C5C2311yescharacteristic
62C2×C3×C22⋊D5—21no—
63C3×#709—22no—
64C3×#709—22no—
65C2×C3×D20C2311yescharacteristic
66C2×C3×C4×D5—21no—
67C2×C3×Dic10C2311yescharacteristic
68C3×C22⋊Dic5—21no—
69C3×#689—24no—
70C3×#688—24no—
71C3×#687—24no—
72C3×#686—24no—
73C3×#685—24no—
74C3×C4⋊Dic5—21no—
75C3×#683—24no—
76C3×C4×Dic5C2312yes—
77C3×#681—22no—
78C3×#681C2314yes—
79C2×C3×#168—22no—
80C2×C3×2−1+4D511yescharacteristic, complemented
81C3×#575—52no—
82C3×#536—51no—
83C3×#456—54no—
84C3×#454—54no—
85C3×#421—52no—
86C2×C3×#101—51no—
87C5×2−1+4—24no—
88C5×2−1+4—22no—
89C5×2−1+4C22×C314yes—
90C2×C5×#41—22no—
91C2×C5×#41—22no—
92C2×C5×#41C22×C312yes—
93C22×C5×Q8—22no—
94C22×C5×Q8C22×C311yescharacteristic
95C2×#709C22×C311yescharacteristic
96#4097C22×C314yescomplemented
97#4096—24no—
98#4095C22×C314yescomplemented
99#4093C22×C312yescomplemented
100#4092—22no—
101#4090C22×C312yescomplemented
102#4088—22no—
103#4078—22no—
104#4075—22no—
105#4072C22×C311yescharacteristic
106C2×#681C22×C312yes—
107#3969C22×C318yescomplemented
108#3968C22×C314yescomplemented
109#3020—51noSylow
110C23×C3×C5—22no—
111C23×C3×C5C2×D411yescharacteristic
112C22×C3×D5—21no—
113C3×C5×Q8—28no—
114C3×C5×Q8—22no—
115C3×C5×Q8—24no—
116C3×C5×Q8—24no—
117C3×C5×Q8C2×D414yes—
118C3×C5×D4—28no—
119C3×C5×D4—24no—
120C3×C5×D4—24no—
121C3×C5×D4—22no—
122C3×C5×D4C2×D414yes—
123C2×C3×C4×C5—216no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—24no—
128C2×C3×C4×C5—24no—
129C2×C3×C4×C5C2×D414yes—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D412yes—
132C2×C3×C4×C5C2×D412yes—
133C2×C3×C4×C5C2411yescharacteristic
134C3×C22⋊D5—41no—
135C3×C22⋊D5—41no—
136C2×C3×Dic5—22no—
137C2×C3×Dic5—21no—
138C3×D20—22no—
139C3×C4×D5—42no—
140C3×Dic10—22no—
141C3×#168—24no—
142C3×2−1+4—24no—
143C3×2−1+4—22no—
144C3×2−1+4C2×D514yes—
145C2×C3×#41—22no—
146C2×C3×#41—22no—
147C2×C3×#41—51no—
148C2×C3×#41C2×D512yes—
149C22×C3×Q8—22no—
150C22×C3×Q8C2×D511yescharacteristic
151C3×#137—54no—
152C3×#137—102no—
153C3×AGL(1,ℤ/8)—54no—
154C3×AGL(1,ℤ/8)—102no—
155C3×#135—104no—
156C2×C3×M16—52no—
157C3×C4⋊Q8—52no—
158C3×#124—52no—
159C3×#123—102no—
160C3×C22⋊Q8—102no—
161C3×#117—51no—
162C3×#104—58no—
163C3×#101—54no—
164C5×#41—28no—
165C5×#41—28no—
166C5×#41—28no—
167C5×#41—28no—
168C5×#41—22no—
169C5×#41—22no—
170C5×#41C3×D414yes—
171C5×#41C23×C314yes—
172C2×C5×Q8—22no—
173C2×C5×Q8—28no—
174C2×C5×Q8—28no—
175C2×C5×Q8—22no—
176C2×C5×Q8—22no—
177C2×C5×Q8C3×D412yes—
178C2×C5×Q8C3×D412yes—
179C2×C5×Q8C23×C312yes—
180C2×C5×D4—22no—
181C2×C5×D4—22no—
182C2×C5×D4C3×D412yes—
183C22×C4×C5—24no—
184C22×C4×C5—22no—
185C22×C4×C5C3×D412yes—
186C22×C4×C5C23×C311yescharacteristic
187C2×C22⋊D5—21no—
188#709—22no—
189#709—22no—
190C2×D20C23×C311yescharacteristic
191C2×C4×D5—21no—
192C2×Dic10C23×C311yescharacteristic
193C22⋊Dic5—21no—
194#689—24no—
195#688—24no—
196#687—24no—
197#686—24no—
198#685—24no—
199C4⋊Dic5—21no—
200#683—24no—
201C4×Dic5C23×C312yes—
202#681—22no—
203#681C23×C314yes—
204C2×#168—22no—
205C2×2−1+4C3×D511yescharacteristic, complemented
206#575—52no—
207#536—51no—
208#456—54no—
209#454—54no—
210#421—52no—
211C2×#101—51no—
212C22×C3×C5—24no—
213C22×C3×C5—41no—
214C22×C3×C5—44no—
215C22×C3×C5#12011yescharacteristic
216C22×C3×C5#12011yescharacteristic
217C22×C3×C5C22×D411yescharacteristic
218C2×C3×D5—42no—
219C2×C3×D5—41no—
220C3×C4×C5—24no—
221C3×C4×C5—24no—
222C3×C4×C5#12012yes—
223C3×C4×C5C22×D412yes—
224C3×Dic5—42no—
225C3×Dic5—41no—
226C3×#41—28no—
227C3×#41—28no—
228C3×#41—28no—
229C3×#41—28no—
230C3×#41—22no—
231C3×#41—22no—
232C3×#41—102no—
233C3×#41—102no—
234C3×#41C22⋊D514yes—
235C3×#41C22×D514yes—
236C2×C3×Q8—22no—
237C2×C3×Q8—28no—
238C2×C3×Q8—28no—
239C2×C3×Q8—22no—
240C2×C3×Q8—22no—
241C2×C3×Q8—51no—
242C2×C3×Q8C22⋊D512yes—
243C2×C3×Q8C22⋊D512yes—
244C2×C3×Q8C22×D512yes—
245C2×C3×D4—22no—
246C2×C3×D4—22no—
247C2×C3×D4—51no—
248C2×C3×D4—101no—
249C2×C3×D4C22⋊D512yes—
250C22×C3×C4—24no—
251C22×C3×C4—22no—
252C22×C3×C4—101no—
253C22×C3×C4C22⋊D512yes—
254C22×C3×C4C22×D511yescharacteristic
255C3×Q16—104no—
256C3×SD16—104no—
257C3×SD16—104no—
258C3×D8—104no—
259C3×M16—54no—
260C3×M16—102no—
261C2×C3×C8—102no—
262C3×C4⋊C4—104no—
263C3×C4⋊C4—101no—
264C3×C22⋊C4—101no—
265C3×C22⋊C4—104no—
266C3×C42—52no—
267C23×C5—22no—
268C23×C5C2×C3×D411yescharacteristic
269C22×D5—21no—
270C5×Q8—28no—
271C5×Q8—22no—
272C5×Q8—24no—
273C5×Q8—24no—
274C5×Q8C2×C3×D414yes—
275C5×D4—28no—
276C5×D4—24no—
277C5×D4—24no—
278C5×D4—22no—
279C5×D4C2×C3×D414yes—
280C2×C4×C5—216no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—24no—
285C2×C4×C5—24no—
286C2×C4×C5C2×C3×D414yes—
287C2×C4×C5C2×C3×D411yescharacteristic
288C2×C4×C5C2×C3×D412yes—
289C2×C4×C5C2×C3×D412yes—
290C2×C4×C5C24×C311yescharacteristic
291C22⋊D5—41no—
292C22⋊D5—41no—
293C2×Dic5—22no—
294C2×Dic5—21no—
295D20—22no—
296C4×D5—42no—
297Dic10—22no—
298#168—24no—
2992−1+4—24no—
3002−1+4—22no—
3012−1+4C2×C3×D514yes—
302C2×#41—22no—
303C2×#41—22no—
304C2×#41—51no—
305C2×#41C2×C3×D512yes—
306C22×Q8—22no—
307C22×Q8C2×C3×D511yescharacteristic
308#137—54no—
309#137—102no—
310AGL(1,ℤ/8)—54no—
311AGL(1,ℤ/8)—102no—
312#135—104no—
313C2×M16—52no—
314C4⋊Q8—52no—
315#124—52no—
316#123—102no—
317C22⋊Q8—102no—
318#117—51no—
319#104—58no—
320#101—54no—
321C2×C3×C5—21no—
322C2×C3×C5—21no—
323C2×C3×C5—21no—
324C2×C3×C5—44no—
325C2×C3×C5C2×#12011yescharacteristic
326C3×D5—81no—
327C23×C3—22no—
328C23×C3—101no—
329C23×C3C2×C22⋊D511yescharacteristic
330C3×Q8—28no—
331C3×Q8—22no—
332C3×Q8—24no—
333C3×Q8—24no—
334C3×Q8—102no—
335C3×Q8C2×C22⋊D514yes—
336C3×D4—28no—
337C3×D4—24no—
338C3×D4—24no—
339C3×D4—22no—
340C3×D4—102no—
341C3×D4—201no—
342C3×D4—201no—
343C3×D4C2×C22⋊D514yes—
344C2×C3×C4—216no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—102no—
351C2×C3×C4—101no—
352C2×C3×C4—202no—
353C2×C3×C4C2×C22⋊D514yes—
354C2×C3×C4C2×C22⋊D511yescharacteristic
355C2×C3×C4C2×C22⋊D512yes—
356C2×C3×C4C2×C22⋊D512yes—
357C2×C3×C4C23×D511yescharacteristic
358C3×C8—104no—
359C22×C5—24no—
360C22×C5—41no—
361C22×C5—44no—
362C22×C5C3×#12011yescharacteristic
363C22×C5C3×#12011yescharacteristic
364C22×C5C22×C3×D411yescharacteristic
365C2×D5—42no—
366C2×D5—41no—
367C4×C5—24no—
368C4×C5—24no—
369C4×C5C3×#12012yes—
370C4×C5C22×C3×D412yes—
371Dic5—42no—
372Dic5—41no—
373#41—28no—
374#41—28no—
375#41—28no—
376#41—28no—
377#41—22no—
378#41—22no—
379#41—102no—
380#41—102no—
381#41C3×C22⋊D514yes—
382#41C22×C3×D514yes—
383C2×Q8—22no—
384C2×Q8—28no—
385C2×Q8—28no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—51no—
389C2×Q8C3×C22⋊D512yes—
390C2×Q8C3×C22⋊D512yes—
391C2×Q8C22×C3×D512yes—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—51no—
395C2×D4—101no—
396C2×D4C3×C22⋊D512yes—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—101no—
400C22×C4C3×C22⋊D512yes—
401C22×C4C22×C3×D511yescharacteristic
402Q16—104no—
403SD16—104no—
404SD16—104no—
405D8—104no—
406M16—54no—
407M16—102no—
408C2×C8—102no—
409C4⋊C4—101no—
410C4⋊C4—104no—
411C22⋊C4—101no—
412C22⋊C4—104no—
413C42—52no—
414C3×C5#302011yescharacteristic, complemented, Hall
415C22×C3—24no—
416C22×C3—41no—
417C22×C3—44no—
418C22×C3—202no—
419C22×C3—201no—
420C22×C3#409911yescharacteristic
421C22×C3#409911yescharacteristic
422C22×C3C22×C22⋊D511yescharacteristic
423C3×C4—24no—
424C3×C4—24no—
425C3×C4—202no—
426C3×C4—201no—
427C3×C4#409912yes—
428C3×C4C22×C22⋊D512yes—
429C2×C5—21no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—44no—
433C2×C5C2×C3×#12011yescharacteristic
434D5—81no—
435C23—22no—
436C23—101no—
437C23C2×C3×C22⋊D511yescharacteristic
438Q8—28no—
439Q8—22no—
440Q8—24no—
441Q8—24no—
442Q8—102no—
443Q8C2×C3×C22⋊D514yes—
444D4—28no—
445D4—24no—
446D4—24no—
447D4—22no—
448D4—102no—
449D4—201no—
450D4—201no—
451D4C2×C3×C22⋊D514yes—
452C2×C4—216no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—102no—
459C2×C4—101no—
460C2×C4—202no—
461C2×C4C2×C3×C22⋊D514yes—
462C2×C4C2×C3×C22⋊D511yescharacteristic
463C2×C4C2×C3×C22⋊D512yes—
464C2×C4C2×C3×C22⋊D512yes—
465C2×C4C23×C3×D511yescharacteristic
466C8—104no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—44no—
471C2×C3—401no—
472C2×C3C2×#409911yescharacteristic
473C5C3×#302011yescharacteristic, complemented, Sylow
474C22—24no—
475C22—41no—
476C22—44no—
477C22—202no—
478C22—201no—
479C22C3×#409911yescharacteristic
480C22C3×#409911yescharacteristic
481C22C22×C3×C22⋊D511yescharacteristic
482C4—24no—
483C4—24no—
484C4—202no—
485C4—201no—
486C4C3×#409912yes—
487C4C22×C3×C22⋊D512yes—
488C3#1061584711yescharacteristic, direct product factor, Sylow
489C2—21no—
490C2—21no—
491C2—21no—
492C2—44no—
493C2—401no—
494C2C2×C3×#409911yescharacteristic
subgroupG/H
centerC2×C3C2×#4099
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×2−1+4C2
socleC2×C3×C5C2×#120
hypercenterC2×C3×2−1+4D5
hypocenterC5C3×#3020
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×2−1+4C2semidirect
2. C3×#66156C2semidirect
3. C3×#66150C2semidirect
4. C3×#65535C2semidirect
5. C3×#65534C2semidirect
6. C3×#65525C2semidirect
7. C2×C3×#3968C2semidirect
8. #10615847C3direct (N × H)
18. C3×#4097C22semidirect
20. C3×#4095C22semidirect
21. C3×#4093C22semidirect
23. C3×#4090C22semidirect
29. C3×#3969C22semidirect
30. C3×#3968C22semidirect
32. C2×C5×2−1+4C2×C3semidirect
33. #66156C2×C3semidirect
34. #66150C2×C3semidirect
35. #65535C2×C3semidirect
36. #65534C2×C3semidirect
37. #65525C2×C3semidirect
38. C2×#3968C2×C3semidirect
80. C2×C3×2−1+4D5semidirect
96. #4097C22×C3semidirect
98. #4095C22×C3semidirect
99. #4093C22×C3semidirect
101. #4090C22×C3semidirect
107. #3969C22×C3semidirect
108. #3968C22×C3semidirect
205. C2×2−1+4C3×D5semidirect
414. C3×C5#3020semidirect
473. C5C3×#3020semidirect
488. C3#10615847direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×2−1+42
C3×#661562
C3×#661502
C3×#655352
C3×#655342
C3×#655252
C2×C3×#39682
#106158473
C3×#30205