Finite Group Databasebeta

← C3×#10601149 #14305985

Subgroups — C3×#10601149 #14305985

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66166C211yesmaximal, characteristic
2C2×C3×C5×#104C211yesmaximal, characteristic, complemented
3C2×C3×#3969C211yesmaximal, characteristic, complemented
4C2×C3×#3957C211yesmaximal, characteristic, complemented
5C3×#65407C211yesmaximal, characteristic, complemented
6C3×C42×Dic5C211yesmaximal, characteristic, complemented
7C2×C3×#3937C211yesmaximal, characteristic, complemented
8#10601149C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C3×#4093C411yescharacteristic, complemented
14C3×#4090C411yescharacteristic, complemented
15C3×#4086C411yescharacteristic, complemented
16C3×#4085—22no—
17C3×#4082C411yescharacteristic, complemented
18C3×C4×C22⋊D5—22no—
19C2×C3×C4×Dic5—22no—
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×C3×C4×Dic5C2211yescharacteristic
22C2×C3×#681C2211yescharacteristic
23C3×C5×#104—22no—
24C3×#3969—22no—
25C3×#3957—22no—
26C3×#3946—22no—
27C3×#3937—22no—
28C3×#1962—51nomaximal, Hall
29#66166C2×C311yescharacteristic
30C2×C5×#104C2×C311yescharacteristic, complemented
31C2×#3969C2×C311yescharacteristic, complemented
32C2×#3957C2×C311yescharacteristic, complemented
33#65407C2×C311yescharacteristic, complemented
34C42×Dic5C2×C311yescharacteristic, complemented
35C2×#3937C2×C311yescharacteristic, complemented
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C2×C3×C5×Q8C2×C411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4C2×C411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C2×C3×C22⋊D5—21no—
47C2×C3×C22⋊D5—22no—
48C22×C3×Dic5—21no—
49C22×C3×Dic5D412yes—
50C3×#709—21no—
51C3×#709—21no—
52C3×#709—21no—
53C3×#709—21no—
54C2×C3×D20C2×C411yescharacteristic
55C2×C3×C4×D5—21no—
56C2×C3×Dic10C2×C411yescharacteristic
57C3×C5×M16—21no—
58C3×C5×M16—21no—
59C2×C3×C5×C8—21no—
60C3×C42×C5—21no—
61C3×C42×C5D412yescomplemented
62C3×C22⋊Dic5—22no—
63C3×#685—22no—
64C3×#683—22no—
65C3×C4×Dic5—28no—
66C3×C4×Dic5—21no—
67C3×C4×Dic5C2×C411yescharacteristic
68C3×C4×Dic5C2×C411yescharacteristic
69C3×C4×Dic5D412yes—
70C3×C4×Dic5D412yescomplemented
71C3×#681—21no—
72C3×#681—21no—
73C2×C3×#168—21no—
74C3×#532—51no—
75C3×#423—51no—
76C2×C3×#104—51no—
77C2×C3×#104—51no—
78C2×C3×#104—51no—
79C2×C3×#104D511yescharacteristic, complemented
80C3×C43—51no—
81C2×C5×#41C22×C311yescharacteristic
82C2×#709C22×C311yescharacteristic
83C2×C5×M16C22×C311yescharacteristic
84C2×C42×C5C22×C311yescharacteristic
85#4093C3×C411yescharacteristic, complemented
86#4090C3×C411yescharacteristic, complemented
87#4086C3×C411yescharacteristic, complemented
88#4085—22no—
89#4082C3×C411yescharacteristic, complemented
90C4×C22⋊D5—22no—
91C2×C4×Dic5—22no—
92C2×C4×Dic5C22×C311yescharacteristic
93C2×C4×Dic5C22×C311yescharacteristic
94C2×#681C22×C311yescharacteristic
95C5×#104—22no—
96#3969—22no—
97#3957—22no—
98#3946—22no—
99#3937—22no—
100#1962—51noSylow
101C23×C3×C5—21no—
102C23×C3×C5C2×D411yescharacteristic
103C22×C3×D5—21no—
104C3×C5×Q8—21no—
105C3×C5×Q8—21no—
106C3×C5×D4—21no—
107C3×C5×D4—21no—
108C3×C5×D4—41no—
109C3×C5×D4—41no—
110C2×C3×C4×C5—24no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5C22×C411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C2×C3×C4×C5#4111yescharacteristic
121C3×C22⋊D5—41no—
122C3×C22⋊D5—41no—
123C3×C22⋊D5—44no—
124C2×C3×Dic5—24no—
125C2×C3×Dic5—22no—
126C2×C3×Dic5—24no—
127C2×C3×Dic5—21no—
128C2×C3×Dic5C22⋊C412yes—
129C2×C3×Dic5C22⋊C412yes—
130C3×D20—21no—
131C3×D20—21no—
132C3×C4×D5—41no—
133C3×C4×D5—41no—
134C3×Dic10—21no—
135C3×Dic10—21no—
136C3×C5×C8—41no—
137C3×#168—41no—
138C2×C3×#41—51no—
139C2×C3×#41C2×D511yescharacteristic
140C2×C3×M16—51no—
141C2×C3×M16C2×D511yescharacteristic
142C3×C4⋊Q8—51no—
143C3×#127—51no—
144C3×#124—51no—
145C3×#124—51no—
146C3×#121—102no—
147C3×C4×D4—102no—
148C2×C3×C42—51no—
149C2×C3×C42—51no—
150C2×C3×C42—102no—
151C2×C3×C42C2×D511yescharacteristic
152C3×C4⋊C8—102no—
153C3×#104—22no—
154C3×#104—102no—
155C3×#104—102no—
156C3×#104—102no—
157C5×#41—21no—
158C5×#41—21no—
159C5×#41—21no—
160C5×#41—21no—
161C2×C5×Q8C2×C3×C411yescharacteristic
162C2×C5×D4—21no—
163C2×C5×D4C2×C3×C411yescharacteristic
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5C23×C311yescharacteristic
167C2×C22⋊D5—21no—
168C2×C22⋊D5—22no—
169C22×Dic5—21no—
170C22×Dic5C3×D412yes—
171#709—21no—
172#709—21no—
173#709—21no—
174#709—21no—
175C2×D20C2×C3×C411yescharacteristic
176C2×C4×D5—21no—
177C2×Dic10C2×C3×C411yescharacteristic
178C5×M16—21no—
179C5×M16—21no—
180C2×C5×C8—21no—
181C42×C5—21no—
182C42×C5C3×D412yescomplemented
183C22⋊Dic5—22no—
184#685—22no—
185#683—22no—
186C4×Dic5—28no—
187C4×Dic5—21no—
188C4×Dic5C2×C3×C411yescharacteristic
189C4×Dic5C2×C3×C411yescharacteristic
190C4×Dic5C3×D412yes—
191C4×Dic5C3×D412yescomplemented
192#681—21no—
193#681—21no—
194C2×#168—21no—
195#532—51no—
196#423—51no—
197C2×#104—51no—
198C2×#104—51no—
199C2×#104—51no—
200C2×#104C3×D511yescharacteristic, complemented
201C43—51no—
202C22×C3×C5—22no—
203C22×C3×C5—41no—
204C22×C3×C5—42no—
205C22×C3×C5C2×C22⋊C411yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C22×C3×C5#12111yescharacteristic
208C2×C3×D5—41no—
209C2×C3×D5—42no—
210C3×C4×C5—24no—
211C3×C4×C5—41no—
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12411yescharacteristic
215C3×C4×C5#12711yescharacteristic
216C3×Dic5—24no—
217C3×Dic5—22no—
218C3×Dic5—41no—
219C3×Dic5#10414yescomplemented
220C3×#41—21no—
221C3×#41—21no—
222C3×#41—21no—
223C3×#41—21no—
224C3×#41—101no—
225C3×#41—101no—
226C3×#41—101no—
227C3×#41—101no—
228C2×C3×Q8—51no—
229C2×C3×Q8C4×D511yescharacteristic
230C2×C3×D4—21no—
231C2×C3×D4—51no—
232C2×C3×D4—102no—
233C2×C3×D4—101no—
234C2×C3×D4C4×D511yescharacteristic
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—52no—
238C22×C3×C4—101no—
239C22×C3×C4—101no—
240C22×C3×C4C22×D511yescharacteristic
241C3×M16—21no—
242C3×M16—21no—
243C3×M16—101no—
244C3×M16—101no—
245C2×C3×C8—21no—
246C2×C3×C8—101no—
247C3×C4⋊C4—102no—
248C3×C22⋊C4—102no—
249C3×C22⋊C4—102no—
250C3×C42—21no—
251C3×C42—51no—
252C3×C42—51no—
253C3×C42—52no—
254C3×C42—52no—
255C3×C42—108no—
256C3×C42—101no—
257C3×C42C22⋊D512yescomplemented
258C23×C5—21no—
259C23×C5C2×C3×D411yescharacteristic
260C22×D5—21no—
261C5×Q8—21no—
262C5×Q8—21no—
263C5×D4—21no—
264C5×D4—21no—
265C5×D4—41no—
266C5×D4—41no—
267C2×C4×C5—24no—
268C2×C4×C5—22no—
269C2×C4×C5—21no—
270C2×C4×C5—41no—
271C2×C4×C5—41no—
272C2×C4×C5C22×C3×C411yescharacteristic
273C2×C4×C5C2×C3×D411yescharacteristic
274C2×C4×C5C2×C3×D411yescharacteristic
275C2×C4×C5C2×C3×D411yescharacteristic
276C2×C4×C5C3×#4111yescharacteristic
277C2×C4×C5C3×#4111yescharacteristic
278C22⋊D5—41no—
279C22⋊D5—41no—
280C22⋊D5—44no—
281C2×Dic5—24no—
282C2×Dic5—22no—
283C2×Dic5—24no—
284C2×Dic5—21no—
285C2×Dic5C3×C22⋊C412yes—
286C2×Dic5C3×C22⋊C412yes—
287D20—21no—
288D20—21no—
289C4×D5—41no—
290C4×D5—41no—
291Dic10—21no—
292Dic10—21no—
293C5×C8—41no—
294#168—41no—
295C2×#41—51no—
296C2×#41C2×C3×D511yescharacteristic
297C2×M16—51no—
298C2×M16C2×C3×D511yescharacteristic
299C4⋊Q8—51no—
300#127—51no—
301#124—51no—
302#124—51no—
303#121—102no—
304C4×D4—102no—
305C2×C42—51no—
306C2×C42—51no—
307C2×C42—102no—
308C2×C42C2×C3×D511yescharacteristic
309C4⋊C8—102no—
310#104—22no—
311#104—102no—
312#104—102no—
313#104—102no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5—81no—
317C2×C3×C5#39011yescharacteristic
318C2×C3×C5C2×#10412yes—
319C3×D5—81no—
320C23×C3—21no—
321C23×C3—101no—
322C23×C3D4×D511yescharacteristic
323C3×Q8—21no—
324C3×Q8—21no—
325C3×Q8—101no—
326C3×Q8—101no—
327C3×D4—21no—
328C3×D4—21no—
329C3×D4—41no—
330C3×D4—41no—
331C3×D4—101no—
332C3×D4—101no—
333C3×D4—204no—
334C3×D4—201no—
335C3×D4—201no—
336C2×C3×C4—24no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—52no—
342C2×C3×C4—52no—
343C2×C3×C4—104no—
344C2×C3×C4—104no—
345C2×C3×C4—102no—
346C2×C3×C4—101no—
347C2×C3×C4—201no—
348C2×C3×C4—201no—
349C2×C3×C4C2×C4×D511yescharacteristic
350C2×C3×C4#70911yescharacteristic
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4#71111yescharacteristic
354C2×C3×C4C2×C22⋊D511yescharacteristic
355C3×C8—41no—
356C3×C8—201no—
357C22×C5—22no—
358C22×C5—41no—
359C22×C5—42no—
360C22×C5C2×C3×C22⋊C411yescharacteristic
361C22×C5C3×#12111yescharacteristic
362C22×C5C3×#12111yescharacteristic
363C2×D5—41no—
364C2×D5—42no—
365C4×C5—24no—
366C4×C5—41no—
367C4×C5C3×C4×D411yescharacteristic
368C4×C5C3×C4×D411yescharacteristic
369C4×C5C3×#12411yescharacteristic
370C4×C5C3×#12711yescharacteristic
371Dic5—24no—
372Dic5—22no—
373Dic5—41no—
374Dic5C3×#10414yescomplemented
375#41—21no—
376#41—21no—
377#41—21no—
378#41—21no—
379#41—101no—
380#41—101no—
381#41—101no—
382#41—101no—
383C2×Q8—51no—
384C2×Q8C3×C4×D511yescharacteristic
385C2×D4—21no—
386C2×D4—51no—
387C2×D4—102no—
388C2×D4—101no—
389C2×D4C3×C4×D511yescharacteristic
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—52no—
393C22×C4—101no—
394C22×C4—101no—
395C22×C4C22×C3×D511yescharacteristic
396M16—21no—
397M16—21no—
398M16—101no—
399M16—101no—
400C2×C8—21no—
401C2×C8—101no—
402C4⋊C4—102no—
403C22⋊C4—102no—
404C22⋊C4—102no—
405C42—21no—
406C42—51no—
407C42—51no—
408C42—52no—
409C42—52no—
410C42—108no—
411C42—101no—
412C42C3×C22⋊D512yescomplemented
413C3×C5#196211yescharacteristic, complemented, Hall
414C22×C3—22no—
415C22×C3—42no—
416C22×C3—41no—
417C22×C3—202no—
418C22×C3—201no—
419C22×C3D5×C22⋊C411yescharacteristic
420C22×C3#403011yescharacteristic
421C22×C3#408511yescharacteristic
422C3×C4—24no—
423C3×C4—41no—
424C3×C4—54no—
425C3×C4—104no—
426C3×C4—102no—
427C3×C4—201no—
428C3×C4#402711yescharacteristic
429C3×C4#403111yescharacteristic
430C3×C4C4×C22⋊D511yescharacteristic
431C3×C4#408611yescharacteristic
432C2×C5—21no—
433C2×C5—21no—
434C2×C5—81no—
435C2×C5C3×#39011yescharacteristic
436C2×C5C2×C3×#10412yes—
437D5—81no—
438C23—21no—
439C23—101no—
440C23C3×D4×D511yescharacteristic
441Q8—21no—
442Q8—21no—
443Q8—101no—
444Q8—101no—
445D4—21no—
446D4—21no—
447D4—41no—
448D4—41no—
449D4—101no—
450D4—101no—
451D4—204no—
452D4—201no—
453D4—201no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—21no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—52no—
460C2×C4—52no—
461C2×C4—104no—
462C2×C4—104no—
463C2×C4—102no—
464C2×C4—101no—
465C2×C4—201no—
466C2×C4—201no—
467C2×C4C2×C3×C4×D511yescharacteristic
468C2×C4C3×#70911yescharacteristic
469C2×C4C3×D4×D511yescharacteristic
470C2×C4C3×D4×D511yescharacteristic
471C2×C4C3×#71111yescharacteristic
472C2×C4C2×C3×C22⋊D511yescharacteristic
473C8—41no—
474C8—201no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—81no—
478C2×C3—401no—
479C2×C3D5×#10412yes—
480C2×C3#6524611yescharacteristic
481C5C3×#196211yescharacteristic, complemented, Sylow
482C22—22no—
483C22—42no—
484C22—41no—
485C22—202no—
486C22—201no—
487C22C3×D5×C22⋊C411yescharacteristic
488C22C3×#403011yescharacteristic
489C22C3×#408511yescharacteristic
490C4—24no—
491C4—41no—
492C4—54no—
493C4—104no—
494C4—102no—
495C4—201no—
496C4C3×#402711yescharacteristic
497C4C3×#403111yescharacteristic
498C4C3×C4×C22⋊D511yescharacteristic
499C4C3×#408611yescharacteristic
500C3#1060114911yescharacteristic, direct product factor, Sylow
501C2—21no—
502C2—21no—
503C2—81no—
504C2—401no—
505C2C3×D5×#10412yes—
506C2C3×#6524611yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#104C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66166C2
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#104D5
hypocenterC5C3×#1962
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#104C2semidirect
3. C2×C3×#3969C2semidirect
4. C2×C3×#3957C2semidirect
5. C3×#65407C2semidirect
6. C3×C42×Dic5C2semidirect
7. C2×C3×#3937C2semidirect
8. #10601149C3direct (N × H)
13. C3×#4093C4semidirect
14. C3×#4090C4semidirect
15. C3×#4086C4semidirect
17. C3×#4082C4semidirect
30. C2×C5×#104C2×C3semidirect
31. C2×#3969C2×C3semidirect
32. C2×#3957C2×C3semidirect
33. #65407C2×C3semidirect
34. C42×Dic5C2×C3semidirect
35. C2×#3937C2×C3semidirect
61. C3×C42×C5D4semidirect
70. C3×C4×Dic5D4semidirect
79. C2×C3×#104D5semidirect
85. #4093C3×C4semidirect
86. #4090C3×C4semidirect
87. #4086C3×C4semidirect
89. #4082C3×C4semidirect
182. C42×C5C3×D4semidirect
191. C4×Dic5C3×D4semidirect
200. C2×#104C3×D5semidirect
219. C3×Dic5#104semidirect
257. C3×C42C22⋊D5semidirect
374. Dic5C3×#104semidirect
412. C42C3×C22⋊D5semidirect
413. C3×C5#1962semidirect
481. C5C3×#1962semidirect
500. C3#10601149direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661662
C2×C3×C5×#1042
C2×C3×#39692
C2×C3×#39572
C3×#654072
C3×C42×Dic52
C2×C3×#39372
#106011493
C3×#19625