Finite Group Databasebeta

← C3×#10601210 #14301367

Subgroups — C3×#10601210 #14301367

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66166C211yesmaximal, characteristic
2C3×#66079C211yesmaximal, characteristic, complemented
3C3×C5×#421C211yesmaximal, characteristic, complemented
4C3×#65525C211yesmaximal, characteristic, complemented
5C3×#65295C211yesmaximal, characteristic, complemented
6C3×#64775C211yesmaximal, characteristic, complemented
7C3×#64752C211yesmaximal, characteristic, complemented
8#10601210C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C3×#4093C411yescharacteristic, complemented
14C3×#4090C411yescharacteristic, complemented
15C3×#4086C411yescharacteristic, complemented
16C3×#4085—22no—
17C3×#4082C411yescharacteristic, complemented
18C3×C4×C22⋊D5—22no—
19C3×#4072C2211yescharacteristic
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×C3×#681C2211yescharacteristic
22C3×#4053—22no—
23C3×D5×M16—22no—
24C3×#4047—22no—
25C3×C5×#104—22no—
26C3×#3969—22no—
27C3×#3938—22no—
28C3×#1884—51nomaximal, Hall
29#66166C2×C311yescharacteristic
30#66079C2×C311yescharacteristic, complemented
31C5×#421C2×C311yescharacteristic, complemented
32#65525C2×C311yescharacteristic, complemented
33#65295C2×C311yescharacteristic, complemented
34#64775C2×C311yescharacteristic, complemented
35#64752C2×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×C5C2311yescharacteristic
45C2×C3×C22⋊D5—22no—
46C2×C3×C22⋊D5D412yes—
47C22×C3×Dic5—21no—
48C3×#709—21no—
49C3×#709—21no—
50C3×#709—21no—
51C3×#709—21no—
52C2×C3×D20C2×C411yescharacteristic
53C2×C3×C4×D5D412yes—
54C2×C3×Dic10C2×C411yescharacteristic
55C3×C5×M16—21no—
56C3×C5×M16D412yescomplemented
57C2×C3×C5×C8—21no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C42×C5—21no—
61C3×C22⋊Dic5—22no—
62C3×C22⋊Dic5—21no—
63C3×#685—22no—
64C3×C4⋊Dic5—21no—
65C3×#683—22no—
66C3×C4×Dic5—21no—
67C3×C4×Dic5—21no—
68C3×C4×Dic5C2×C411yescharacteristic
69C3×C4×Dic5C2×C411yescharacteristic
70C3×#681—21no—
71C3×#681D412yescomplemented
72C2×C3×#168—21no—
73C3×#676—24no—
74C3×C8×D5—24no—
75C3×#568—51no—
76C3×#532—51no—
77C3×#421—51no—
78C3×#421D511yescharacteristic, complemented
79C3×#410—51no—
80C3×#339—51no—
81C3×#339—51no—
82C2×C5×#41C22×C311yescharacteristic
83C2×#709C22×C311yescharacteristic
84C2×C5×M16C22×C311yescharacteristic
85C5×#117C22×C311yescharacteristic
86#4093C3×C411yescharacteristic, complemented
87#4090C3×C411yescharacteristic, complemented
88#4086C3×C411yescharacteristic, complemented
89#4085—22no—
90#4082C3×C411yescharacteristic, complemented
91C4×C22⋊D5—22no—
92#4072C22×C311yescharacteristic
93C2×C4×Dic5C22×C311yescharacteristic
94C2×#681C22×C311yescharacteristic
95#4053—22no—
96D5×M16—22no—
97#4047—22no—
98C5×#104—22no—
99#3969—22no—
100#3938—22no—
101#1884—51noSylow
102C23×C3×C5—21no—
103C23×C3×C5C2×D411yescharacteristic
104C22×C3×D5C22⋊C412yes—
105C3×C5×Q8—21no—
106C3×C5×Q8—21no—
107C3×C5×D4—21no—
108C3×C5×D4—21no—
109C3×C5×D4—41no—
110C3×C5×D4—41no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—41no—
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—22no—
122C3×C22⋊D5—22no—
123C3×C22⋊D5—44no—
124C2×C3×Dic5—21no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—42no—
127C2×C3×Dic5—41no—
128C2×C3×Dic5C22⋊C412yes—
129C3×D20—21no—
130C3×D20—21no—
131C3×C4×D5—22no—
132C3×C4×D5—22no—
133C3×Dic10—21no—
134C3×Dic10—21no—
135C3×C5×C8—22no—
136C3×#168—22no—
137C2×C3×#41—51no—
138C2×C3×#41C2×D511yescharacteristic
139C3×#131—102no—
140C3×#131—102no—
141C2×C3×M16—51no—
142C2×C3×M16—102no—
143C2×C3×M16C2×D511yescharacteristic
144C3×C4⋊Q8—51no—
145C3×#127—51no—
146C3×#124—51no—
147C3×#124—51no—
148C3×#121—102no—
149C3×C4×D4—102no—
150C3×#117—51no—
151C3×#117C2×D511yescharacteristic
152C2×C3×C42—51no—
153C3×#104—22no—
154C3×#104—102no—
155C3×#99—102no—
156C5×#41—21no—
157C5×#41—21no—
158C5×#41—21no—
159C5×#41—21no—
160C2×C5×Q8C2×C3×C411yescharacteristic
161C2×C5×D4—21no—
162C2×C5×D4C2×C3×C411yescharacteristic
163C22×C4×C5—21no—
164C22×C4×C5C23×C311yescharacteristic
165C2×C22⋊D5—22no—
166C2×C22⋊D5C3×D412yes—
167C22×Dic5—21no—
168#709—21no—
169#709—21no—
170#709—21no—
171#709—21no—
172C2×D20C2×C3×C411yescharacteristic
173C2×C4×D5C3×D412yes—
174C2×Dic10C2×C3×C411yescharacteristic
175C5×M16—21no—
176C5×M16C3×D412yescomplemented
177C2×C5×C8—21no—
178C5×C4⋊C4—21no—
179C5×C22⋊C4—21no—
180C42×C5—21no—
181C22⋊Dic5—22no—
182C22⋊Dic5—21no—
183#685—22no—
184C4⋊Dic5—21no—
185#683—22no—
186C4×Dic5—21no—
187C4×Dic5—21no—
188C4×Dic5C2×C3×C411yescharacteristic
189C4×Dic5C2×C3×C411yescharacteristic
190#681—21no—
191#681C3×D412yescomplemented
192C2×#168—21no—
193#676—24no—
194C8×D5—24no—
195#568—51no—
196#532—51no—
197#421—51no—
198#421C3×D511yescharacteristic, complemented
199#410—51no—
200#339—51no—
201#339—51no—
202C22×C3×C5—41no—
203C22×C3×C5—42no—
204C22×C3×C5—41no—
205C22×C3×C5C2×C22⋊C411yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C22×C3×C5#12111yescharacteristic
208C2×C3×D5—22no—
209C2×C3×D5—42no—
210C3×C4×C5—41no—
211C3×C4×C5—81no—
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12011yescharacteristic
215C3×C4×C5#12311yescharacteristic
216C3×Dic5—22no—
217C3×Dic5—22no—
218C3×Dic5—41no—
219C3×Dic5—81no—
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—52no—
232C2×C3×D4—51no—
233C2×C3×D4—102no—
234C2×C3×D4C4×D511yescharacteristic
235C22×C3×C4—21no—
236C22×C3×C4—52no—
237C22×C3×C4—101no—
238C22×C3×C4C22×D511yescharacteristic
239C3×M16—21no—
240C3×M16—52no—
241C3×M16—104no—
242C3×M16—101no—
243C3×M16C22⋊D512yescomplemented
244C2×C3×C8—21no—
245C2×C3×C8—104no—
246C2×C3×C8—101no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—102no—
249C3×C4⋊C4—101no—
250C3×C22⋊C4—21no—
251C3×C22⋊C4—102no—
252C3×C22⋊C4—102no—
253C3×C22⋊C4—101no—
254C3×C42—21no—
255C3×C42—51no—
256C3×C42—51no—
257C3×C42—101no—
258C3×C42—101no—
259C23×C5—21no—
260C23×C5C2×C3×D411yescharacteristic
261C22×D5C3×C22⋊C412yes—
262C5×Q8—21no—
263C5×Q8—21no—
264C5×D4—21no—
265C5×D4—21no—
266C5×D4—41no—
267C5×D4—41no—
268C2×C4×C5—21no—
269C2×C4×C5—41no—
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—22no—
279C22⋊D5—22no—
280C22⋊D5—44no—
281C2×Dic5—21no—
282C2×Dic5—21no—
283C2×Dic5—42no—
284C2×Dic5—41no—
285C2×Dic5C3×C22⋊C412yes—
286D20—21no—
287D20—21no—
288C4×D5—22no—
289C4×D5—22no—
290Dic10—21no—
291Dic10—21no—
292C5×C8—22no—
293#168—22no—
294C2×#41—51no—
295C2×#41C2×C3×D511yescharacteristic
296#131—102no—
297#131—102no—
298C2×M16—51no—
299C2×M16—102no—
300C2×M16C2×C3×D511yescharacteristic
301C4⋊Q8—51no—
302#127—51no—
303#124—51no—
304#124—51no—
305#121—102no—
306C4×D4—102no—
307#117—51no—
308#117C2×C3×D511yescharacteristic
309C2×C42—51no—
310#104—22no—
311#104—102no—
312#99—102no—
313C2×C3×C5—21no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5—81no—
317C2×C3×C5#38611yescharacteristic
318C3×D5—42no—
319C23×C3—21no—
320C23×C3—52no—
321C23×C3D4×D511yescharacteristic
322C3×Q8—21no—
323C3×Q8—21no—
324C3×Q8—101no—
325C3×Q8—101no—
326C3×D4—21no—
327C3×D4—21no—
328C3×D4—41no—
329C3×D4—41no—
330C3×D4—102no—
331C3×D4—102no—
332C3×D4—101no—
333C3×D4—101no—
334C3×D4—204no—
335C2×C3×C4—21no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—52no—
340C2×C3×C4—101no—
341C2×C3×C4—102no—
342C2×C3×C4—102no—
343C2×C3×C4—101no—
344C2×C3×C4—202no—
345C2×C3×C4—201no—
346C2×C3×C4C2×C4×D511yescharacteristic
347C2×C3×C4#70911yescharacteristic
348C2×C3×C4D4×D511yescharacteristic
349C2×C3×C4D4×D511yescharacteristic
350C2×C3×C4#71111yescharacteristic
351C2×C3×C4C2×C22⋊D511yescharacteristic
352C3×C8—22no—
353C3×C8—102no—
354C22×C5—41no—
355C22×C5—42no—
356C22×C5—41no—
357C22×C5C2×C3×C22⋊C411yescharacteristic
358C22×C5C3×#12111yescharacteristic
359C22×C5C3×#12111yescharacteristic
360C2×D5—22no—
361C2×D5—42no—
362C4×C5—41no—
363C4×C5—81no—
364C4×C5C3×C4×D411yescharacteristic
365C4×C5C3×C4×D411yescharacteristic
366C4×C5C3×#12011yescharacteristic
367C4×C5C3×#12311yescharacteristic
368Dic5—22no—
369Dic5—22no—
370Dic5—41no—
371Dic5—81no—
372#41—21no—
373#41—21no—
374#41—21no—
375#41—21no—
376#41—101no—
377#41—101no—
378#41—101no—
379#41—101no—
380C2×Q8—51no—
381C2×Q8C3×C4×D511yescharacteristic
382C2×D4—21no—
383C2×D4—52no—
384C2×D4—51no—
385C2×D4—102no—
386C2×D4C3×C4×D511yescharacteristic
387C22×C4—21no—
388C22×C4—52no—
389C22×C4—101no—
390C22×C4C22×C3×D511yescharacteristic
391M16—21no—
392M16—52no—
393M16—104no—
394M16—101no—
395M16C3×C22⋊D512yescomplemented
396C2×C8—21no—
397C2×C8—104no—
398C2×C8—101no—
399C4⋊C4—21no—
400C4⋊C4—102no—
401C4⋊C4—101no—
402C22⋊C4—21no—
403C22⋊C4—102no—
404C22⋊C4—102no—
405C22⋊C4—101no—
406C42—21no—
407C42—51no—
408C42—51no—
409C42—101no—
410C42—101no—
411C3×C5#188411yescharacteristic, complemented, Hall
412C22×C3—41no—
413C22×C3—42no—
414C22×C3—41no—
415C22×C3—102no—
416C22×C3—202no—
417C22×C3D5×C22⋊C411yescharacteristic
418C22×C3#403011yescharacteristic
419C22×C3#408411yescharacteristic
420C3×C4—41no—
421C3×C4—81no—
422C3×C4—102no—
423C3×C4—102no—
424C3×C4—201no—
425C3×C4—401no—
426C3×C4#402711yescharacteristic
427C3×C4#402911yescharacteristic
428C3×C4C4×C22⋊D511yescharacteristic
429C3×C4#408311yescharacteristic
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—21no—
433C2×C5—81no—
434C2×C5C3×#38611yescharacteristic
435D5—42no—
436C23—21no—
437C23—52no—
438C23C3×D4×D511yescharacteristic
439Q8—21no—
440Q8—21no—
441Q8—101no—
442Q8—101no—
443D4—21no—
444D4—21no—
445D4—41no—
446D4—41no—
447D4—102no—
448D4—102no—
449D4—101no—
450D4—101no—
451D4—204no—
452C2×C4—21no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—52no—
457C2×C4—101no—
458C2×C4—102no—
459C2×C4—102no—
460C2×C4—101no—
461C2×C4—202no—
462C2×C4—201no—
463C2×C4C2×C3×C4×D511yescharacteristic
464C2×C4C3×#70911yescharacteristic
465C2×C4C3×D4×D511yescharacteristic
466C2×C4C3×D4×D511yescharacteristic
467C2×C4C3×#71111yescharacteristic
468C2×C4C2×C3×C22⋊D511yescharacteristic
469C8—22no—
470C8—102no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—81no—
475C2×C3—202no—
476C2×C3#6524511yescharacteristic
477C5C3×#188411yescharacteristic, complemented, Sylow
478C22—41no—
479C22—42no—
480C22—41no—
481C22—102no—
482C22—202no—
483C22C3×D5×C22⋊C411yescharacteristic
484C22C3×#403011yescharacteristic
485C22C3×#408411yescharacteristic
486C4—41no—
487C4—81no—
488C4—102no—
489C4—102no—
490C4—201no—
491C4—401no—
492C4C3×#402711yescharacteristic
493C4C3×#402911yescharacteristic
494C4C3×C4×C22⋊D511yescharacteristic
495C4C3×#408311yescharacteristic
496C3#1060121011yescharacteristic, direct product factor, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—81no—
501C2—202no—
502C2C3×#6524511yescharacteristic
subgroupG/H
centerC3×C4#4083
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#421C2
socleC2×C3×C5#386
prime radicalC3×#66166C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#421D5
hypocenterC5C3×#1884
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#421

Complements

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

NH ≅ G/Ntype
2. C3×#66079C2semidirect
3. C3×C5×#421C2semidirect
4. C3×#65525C2semidirect
5. C3×#65295C2semidirect
6. C3×#64775C2semidirect
7. C3×#64752C2semidirect
8. #10601210C3direct (N × H)
13. C3×#4093C4semidirect
14. C3×#4090C4semidirect
15. C3×#4086C4semidirect
17. C3×#4082C4semidirect
30. #66079C2×C3semidirect
31. C5×#421C2×C3semidirect
32. #65525C2×C3semidirect
33. #65295C2×C3semidirect
34. #64775C2×C3semidirect
35. #64752C2×C3semidirect
56. C3×C5×M16D4semidirect
71. C3×#681D4semidirect
78. C3×#421D5semidirect
86. #4093C3×C4semidirect
87. #4090C3×C4semidirect
88. #4086C3×C4semidirect
90. #4082C3×C4semidirect
176. C5×M16C3×D4semidirect
191. #681C3×D4semidirect
198. #421C3×D5semidirect
243. C3×M16C22⋊D5semidirect
395. M16C3×C22⋊D5semidirect
411. C3×C5#1884semidirect
477. C5C3×#1884semidirect
496. C3#10601210direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661662
C3×#660792
C3×C5×#4212
C3×#655252
C3×#652952
C3×#647752
C3×#647522
#106012103
C3×#18845