Finite Group Databasebeta

← C3×#10599570 #14301373

Subgroups — C3×#10599570 #14301373

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×#66079C211yesmaximal, characteristic, complemented
2C3×#65811C211yesmaximal, characteristic
3C3×#65428C211yesmaximal, characteristic, complemented
4C3×#65295C211yesmaximal, characteristic, complemented
5C3×#65294C211yesmaximal, characteristic, complemented
6C3×C5×#339C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10599570C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C2×C3×C42×C5C2211yescharacteristic
14C3×#4076—22no—
15C3×#4072C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17C3×#4053—22no—
18C3×D5×M16—22no—
19C3×#4047—22no—
20C3×#4021C411yescharacteristic, complemented
21C3×#4021C411yescharacteristic, complemented
22C3×#4020C411yescharacteristic, complemented
23C3×C4×D20—22no—
24C3×#4015C411yescharacteristic, complemented
25C3×#3957—22no—
26C3×#3938—22no—
27C3×#3937—22no—
28C3×#1884—51nomaximal, Hall
29#66079C2×C311yescharacteristic, complemented
30#65811C2×C311yescharacteristic
31#65428C2×C311yescharacteristic, complemented
32#65295C2×C311yescharacteristic, complemented
33#65294C2×C311yescharacteristic, complemented
34C5×#339C2×C311yescharacteristic, complemented
35#64743C2×C311yescharacteristic, complemented
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×C3×C22⋊D5—21no—
39C2×C3×C22⋊D5D412yes—
40C3×#709—21no—
41C3×#709—21no—
42C3×#709—21no—
43C3×#709—21no—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C3×#709—21no—
48C2×C3×D20—22no—
49C2×C3×D20C2×C411yescharacteristic
50C2×C3×D20C2×C411yescharacteristic
51C2×C3×C4×D5—21no—
52C2×C3×C4×D5D412yes—
53C2×C3×Dic10C2×C411yescharacteristic
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×C42×C5—21no—
62C3×C42×C5C2×C411yescharacteristic
63C3×C42×C5C2×C411yescharacteristic
64C3×C22⋊Dic5—21no—
65C3×#685—22no—
66C3×#685—22no—
67C3×C4⋊Dic5—22no—
68C3×C4⋊Dic5—21no—
69C3×C4×Dic5—21no—
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×#421—51no—
79C3×#410—51no—
80C3×#339—51no—
81C3×#339D511yescharacteristic, complemented
82C2×#709C22×C311yescharacteristic
83C2×#709C22×C311yescharacteristic
84C2×C5×M16C22×C311yescharacteristic
85C5×#117C22×C311yescharacteristic
86C2×C42×C5C22×C311yescharacteristic
87#4076—22no—
88#4072C22×C311yescharacteristic
89C2×#681C22×C311yescharacteristic
90#4053—22no—
91D5×M16—22no—
92#4047—22no—
93#4021C3×C411yescharacteristic, complemented
94#4021C3×C411yescharacteristic, complemented
95#4020C3×C411yescharacteristic, complemented
96C4×D20—22no—
97#4015C3×C411yescharacteristic, complemented
98#3957—22no—
99#3938—22no—
100#3937—22no—
101#1884—51noSylow
102C23×C3×C5C2×D411yescharacteristic
103C22×C3×D5—21no—
104C22×C3×D5C22⋊C412yes—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—42no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C3×C22⋊D5—22no—
116C3×C22⋊D5—22no—
117C3×C22⋊D5—41no—
118C3×C22⋊D5—41no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5C22⋊C412yes—
122C3×D20—21no—
123C3×D20—21no—
124C3×D20—21no—
125C3×D20—21no—
126C3×D20—44no—
127C3×C4×D5—22no—
128C3×C4×D5—22no—
129C3×C4×D5—41no—
130C3×C4×D5—41no—
131C3×Dic10—21no—
132C3×Dic10—21no—
133C3×Dic10—21no—
134C3×Dic10—21no—
135C3×C5×C8—22no—
136C3×#168—22no—
137C2×C3×#41—51no—
138C2×C3×#41—51no—
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×C42C2×D511yescharacteristic
153C3×#104—102no—
154C3×#104—102no—
155C3×#99—102no—
156C22×C4×C5—21no—
157C22×C4×C5C23×C311yescharacteristic
158C2×C22⋊D5—21no—
159C2×C22⋊D5C3×D412yes—
160#709—21no—
161#709—21no—
162#709—21no—
163#709—21no—
164#709—21no—
165#709—21no—
166#709—21no—
167#709—21no—
168C2×D20—22no—
169C2×D20C2×C3×C411yescharacteristic
170C2×D20C2×C3×C411yescharacteristic
171C2×C4×D5—21no—
172C2×C4×D5C3×D412yes—
173C2×Dic10C2×C3×C411yescharacteristic
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—
181C42×C5—21no—
182C42×C5C2×C3×C411yescharacteristic
183C42×C5C2×C3×C411yescharacteristic
184C22⋊Dic5—21no—
185#685—22no—
186#685—22no—
187C4⋊Dic5—22no—
188C4⋊Dic5—21no—
189C4×Dic5—21no—
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#421—51no—
199#410—51no—
200#339—51no—
201#339C3×D511yescharacteristic, complemented
202C22×C3×C5—41no—
203C22×C3×C5C2×C22⋊C411yescharacteristic
204C22×C3×C5#12111yescharacteristic
205C22×C3×C5#12111yescharacteristic
206C2×C3×D5—22no—
207C2×C3×D5—42no—
208C2×C3×D5—42no—
209C2×C3×D5—41no—
210C3×C4×C5—22no—
211C3×C4×C5—41no—
212C3×C4×C5—81no—
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5C4×D411yescharacteristic
215C3×C4×C5#12011yescharacteristic
216C3×C4×C5#12311yescharacteristic
217C3×Dic5—22no—
218C3×Dic5—41no—
219C3×Dic5—81no—
220C3×#41—101no—
221C3×#41—101no—
222C3×#41—101no—
223C3×#41—101no—
224C3×#41—101no—
225C3×#41—101no—
226C3×#41—101no—
227C3×#41—101no—
228C2×C3×Q8—51no—
229C2×C3×Q8—51no—
230C2×C3×D4—52no—
231C2×C3×D4—51no—
232C2×C3×D4—51no—
233C2×C3×D4—102no—
234C2×C3×D4—101no—
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×M16D2012yescomplemented
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—21no—
256C3×C42—101no—
257C3×C42C4×D511yescharacteristic
258C3×C42C4×D511yescharacteristic
259C23×C5C2×C3×D411yescharacteristic
260C22×D5—21no—
261C22×D5C3×C22⋊C412yes—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—42no—
265C2×C4×C5—41no—
266C2×C4×C5C22×C3×C411yescharacteristic
267C2×C4×C5C2×C3×D411yescharacteristic
268C2×C4×C5C2×C3×D411yescharacteristic
269C2×C4×C5C2×C3×D411yescharacteristic
270C2×C4×C5C3×#4111yescharacteristic
271C2×C4×C5C3×#4111yescharacteristic
272C22⋊D5—22no—
273C22⋊D5—22no—
274C22⋊D5—41no—
275C22⋊D5—41no—
276C2×Dic5—21no—
277C2×Dic5—41no—
278C2×Dic5C3×C22⋊C412yes—
279D20—21no—
280D20—21no—
281D20—21no—
282D20—21no—
283D20—44no—
284C4×D5—22no—
285C4×D5—22no—
286C4×D5—41no—
287C4×D5—41no—
288Dic10—21no—
289Dic10—21no—
290Dic10—21no—
291Dic10—21no—
292C5×C8—22no—
293#168—22no—
294C2×#41—51no—
295C2×#41—51no—
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×C42C2×C3×D511yescharacteristic
310#104—102no—
311#104—102no—
312#99—102no—
313C2×C3×C5—21no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5#38611yescharacteristic
317C3×D5—42no—
318C3×D5—81no—
319C23×C3—52no—
320C23×C3—101no—
321C23×C3D4×D511yescharacteristic
322C3×Q8—101no—
323C3×Q8—101no—
324C3×Q8—101no—
325C3×Q8—101no—
326C3×D4—102no—
327C3×D4—102no—
328C3×D4—101no—
329C3×D4—101no—
330C3×D4—101no—
331C3×D4—101no—
332C3×D4—204no—
333C3×D4—201no—
334C3×D4—201no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—42no—
338C2×C3×C4—41no—
339C2×C3×C4—52no—
340C2×C3×C4—102no—
341C2×C3×C4—102no—
342C2×C3×C4—101no—
343C2×C3×C4—201no—
344C2×C3×C4—201no—
345C2×C3×C4—201no—
346C2×C3×C4C2×C4×D511yescharacteristic
347C2×C3×C4C2×D2011yescharacteristic
348C2×C3×C4#70911yescharacteristic
349C2×C3×C4D4×D511yescharacteristic
350C2×C3×C4D4×D511yescharacteristic
351C2×C3×C4#71311yescharacteristic
352C3×C8—22no—
353C3×C8—102no—
354C22×C5—41no—
355C22×C5C2×C3×C22⋊C411yescharacteristic
356C22×C5C3×#12111yescharacteristic
357C22×C5C3×#12111yescharacteristic
358C2×D5—22no—
359C2×D5—42no—
360C2×D5—42no—
361C2×D5—41no—
362C4×C5—22no—
363C4×C5—41no—
364C4×C5—81no—
365C4×C5C3×C4×D411yescharacteristic
366C4×C5C3×C4×D411yescharacteristic
367C4×C5C3×#12011yescharacteristic
368C4×C5C3×#12311yescharacteristic
369Dic5—22no—
370Dic5—41no—
371Dic5—81no—
372#41—101no—
373#41—101no—
374#41—101no—
375#41—101no—
376#41—101no—
377#41—101no—
378#41—101no—
379#41—101no—
380C2×Q8—51no—
381C2×Q8—51no—
382C2×D4—52no—
383C2×D4—51no—
384C2×D4—51no—
385C2×D4—102no—
386C2×D4—101no—
387C22×C4—21no—
388C22×C4—52no—
389C22×C4—101no—
390C22×C4C22×C3×D511yescharacteristic
391M16—21no—
392M16—52no—
393M16—104no—
394M16—101no—
395M16C3×D2012yescomplemented
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—21no—
408C42—101no—
409C42C3×C4×D511yescharacteristic
410C42C3×C4×D511yescharacteristic
411C3×C5#188411yescharacteristic, complemented, Hall
412C22×C3—41no—
413C22×C3—102no—
414C22×C3—202no—
415C22×C3—202no—
416C22×C3—201no—
417C22×C3D5×C22⋊C411yescharacteristic
418C22×C3#403011yescharacteristic
419C22×C3#404111yescharacteristic
420C3×C4—22no—
421C3×C4—41no—
422C3×C4—81no—
423C3×C4—102no—
424C3×C4—201no—
425C3×C4—401no—
426C3×C4C4×D2011yescharacteristic
427C3×C4#402811yescharacteristic
428C3×C4#403911yescharacteristic
429C3×C4#404011yescharacteristic
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—21no—
433C2×C5C3×#38611yescharacteristic
434D5—42no—
435D5—81no—
436C23—52no—
437C23—101no—
438C23C3×D4×D511yescharacteristic
439Q8—101no—
440Q8—101no—
441Q8—101no—
442Q8—101no—
443D4—102no—
444D4—102no—
445D4—101no—
446D4—101no—
447D4—101no—
448D4—101no—
449D4—204no—
450D4—201no—
451D4—201no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—52no—
457C2×C4—102no—
458C2×C4—102no—
459C2×C4—101no—
460C2×C4—201no—
461C2×C4—201no—
462C2×C4—201no—
463C2×C4C2×C3×C4×D511yescharacteristic
464C2×C4C2×C3×D2011yescharacteristic
465C2×C4C3×#70911yescharacteristic
466C2×C4C3×D4×D511yescharacteristic
467C2×C4C3×D4×D511yescharacteristic
468C2×C4C3×#71311yescharacteristic
469C8—22no—
470C8—102no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—202no—
475C2×C3—401no—
476C2×C3#6495411yescharacteristic
477C5C3×#188411yescharacteristic, complemented, Sylow
478C22—41no—
479C22—102no—
480C22—202no—
481C22—202no—
482C22—201no—
483C22C3×D5×C22⋊C411yescharacteristic
484C22C3×#403011yescharacteristic
485C22C3×#404111yescharacteristic
486C4—22no—
487C4—41no—
488C4—81no—
489C4—102no—
490C4—201no—
491C4—401no—
492C4C3×C4×D2011yescharacteristic
493C4C3×#402811yescharacteristic
494C4C3×#403911yescharacteristic
495C4C3×#404011yescharacteristic
496C3#1059957011yescharacteristic, direct product factor, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—202no—
501C2—401no—
502C2C3×#6495411yescharacteristic
subgroupG/H
centerC3×C4#4028
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#339C2
socleC2×C3×C5#386
prime radicalC3×#65811C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#339D5
hypocenterC5C3×#1884
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#339

Complements

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

NH ≅ G/Ntype
1. C3×#66079C2semidirect
3. C3×#65428C2semidirect
4. C3×#65295C2semidirect
5. C3×#65294C2semidirect
6. C3×C5×#339C2semidirect
7. C3×#64743C2semidirect
8. #10599570C3direct (N × H)
20. C3×#4021C4semidirect
21. C3×#4021C4semidirect
22. C3×#4020C4semidirect
24. C3×#4015C4semidirect
29. #66079C2×C3semidirect
31. #65428C2×C3semidirect
32. #65295C2×C3semidirect
33. #65294C2×C3semidirect
34. C5×#339C2×C3semidirect
35. #64743C2×C3semidirect
56. C3×C5×M16D4semidirect
71. C3×#681D4semidirect
81. C3×#339D5semidirect
93. #4021C3×C4semidirect
94. #4021C3×C4semidirect
95. #4020C3×C4semidirect
97. #4015C3×C4semidirect
176. C5×M16C3×D4semidirect
191. #681C3×D4semidirect
201. #339C3×D5semidirect
243. C3×M16D20semidirect
395. M16C3×D20semidirect
411. C3×C5#1884semidirect
477. C5C3×#1884semidirect
496. C3#10599570direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660792
C3×#658112
C3×#654282
C3×#652952
C3×#652942
C3×C5×#3392
C3×#647432
#105995703
C3×#18845