Finite Group Databasebeta

← C3×#10600805 #14301164

Subgroups — C3×#10600805 #14301164

Order 1920.

620 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66156C211yesmaximal, characteristic
2C3×#66079C211yesmaximal, characteristic, complemented
3C3×C5×#408C211yesmaximal, characteristic, complemented
4C3×#65525C211yesmaximal, characteristic, complemented
5C3×#65402C211yesmaximal, characteristic, complemented
6C3×#64776C211yesmaximal, characteristic, complemented
7C3×#64772C211yesmaximal, characteristic, complemented
8#10600805C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C22×C3×C5×C8C2211yescharacteristic
13C3×#4097—21no—
14C3×#4096—22no—
15C3×#4095—21no—
16C3×#4088C412yescomplemented
17C3×#4078C412yescomplemented
18C3×#4072C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21C3×#4053—22no—
22C3×D5×M16—22no—
23C3×#4047—22no—
24C3×C5×C22⋊C8—22no—
25C3×#3969—22no—
26C3×#3953—21no—
27C3×#3948—21no—
28C3×#1881—51nomaximal, Hall
29#66156C2×C311yescharacteristic
30#66079C2×C311yescharacteristic, complemented
31C5×#408C2×C311yescharacteristic, complemented
32#65525C2×C311yescharacteristic, complemented
33#65402C2×C311yescharacteristic, complemented
34#64776C2×C311yescharacteristic, complemented
35#64772C2×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—21no—
46C3×#709—21no—
47C3×#709—21no—
48C3×#709C2×C412yes—
49C3×#709D412yes—
50C2×C3×D20D411yescharacteristic
51C2×C3×C4×D5—21no—
52C2×C3×Dic10D411yescharacteristic
53C3×C5×M16—21no—
54C3×C5×M16—21no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8—21no—
57C2×C3×C5×C8—21no—
58C2×C3×C5×C8D412yes—
59C3×C22⋊Dic5—21no—
60C3×#689—22no—
61C3×#688—22no—
62C3×#687—22no—
63C3×#686—22no—
64C3×C4⋊Dic5—21no—
65C3×C4×Dic5—21no—
66C3×#681—21no—
67C3×#681—21no—
68C3×#681C2×C412yes—
69C3×#681D412yes—
70C2×C3×#168—21no—
71C2×C3×#168—21no—
72C3×#676—24no—
73C3×C8×D5—24no—
74C3×#575—51no—
75C3×#568—51no—
76C3×#421—51no—
77C3×#416—51no—
78C3×#408D511yescharacteristic, complemented
79C3×#344—51no—
80C3×#341—51no—
81C2×C5×#41C22×C311yescharacteristic
82C2×#709C22×C311yescharacteristic
83C2×C5×M16C22×C311yescharacteristic
84C22×C5×C8C22×C311yescharacteristic
85#4097—21no—
86#4096—22no—
87#4095—21no—
88#4088C3×C412yescomplemented
89#4078C3×C412yescomplemented
90#4072C22×C311yescharacteristic
91C2×#681C22×C311yescharacteristic
92C2×#681C22×C311yescharacteristic
93#4053—22no—
94D5×M16—22no—
95#4047—22no—
96C5×C22⋊C8—22no—
97#3969—22no—
98#3953—21no—
99#3948—21no—
100#1881—51noSylow
101C23×C3×C5—21no—
102C23×C3×C5#4111yescharacteristic
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—21no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5C22×C411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C3×C22⋊D5—22no—
120C3×C22⋊D5—22no—
121C2×C3×Dic5—21no—
122C2×C3×Dic5—41no—
123C3×D20—21no—
124C3×D20C22⋊C412yes—
125C3×C4×D5—22no—
126C3×C4×D5—22no—
127C3×Dic10—21no—
128C3×Dic10C22⋊C412yes—
129C3×C5×C8—22no—
130C3×C5×C8—41no—
131C3×#168—22no—
132C3×#168—22no—
133C2×C3×#41—51no—
134C2×C3×#41C2×D511yescharacteristic
135C3×#137—52no—
136C3×#137—101no—
137C3×AGL(1,ℤ/8)—52no—
138C3×AGL(1,ℤ/8)—101no—
139C3×#135—102no—
140C3×#131—102no—
141C3×#131—102no—
142C2×C3×M16—51no—
143C2×C3×M16—51no—
144C2×C3×M16—102no—
145C2×C3×M16C2×D511yescharacteristic
146C22×C3×C8C2×D511yescharacteristic
147C3×#117—51no—
148C3×#104—102no—
149C3×#103—101no—
150C3×#102—101no—
151C3×C22⋊C8—22no—
152C5×#41—21no—
153C5×#41—21no—
154C5×#41—21no—
155C5×#41—21no—
156C2×C5×Q8C2×C3×C411yescharacteristic
157C2×C5×D4—21no—
158C2×C5×D4C2×C3×C411yescharacteristic
159C22×C4×C5—21no—
160C22×C4×C5C23×C311yescharacteristic
161C2×C22⋊D5—21no—
162#709—21no—
163#709—21no—
164#709C2×C3×C412yes—
165#709C3×D412yes—
166C2×D20C3×D411yescharacteristic
167C2×C4×D5—21no—
168C2×Dic10C3×D411yescharacteristic
169C5×M16—21no—
170C5×M16—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8C3×D412yes—
175C22⋊Dic5—21no—
176#689—22no—
177#688—22no—
178#687—22no—
179#686—22no—
180C4⋊Dic5—21no—
181C4×Dic5—21no—
182#681—21no—
183#681—21no—
184#681C2×C3×C412yes—
185#681C3×D412yes—
186C2×#168—21no—
187C2×#168—21no—
188#676—24no—
189C8×D5—24no—
190#575—51no—
191#568—51no—
192#421—51no—
193#416—51no—
194#408C3×D511yescharacteristic, complemented
195#344—51no—
196#341—51no—
197C22×C3×C5—41no—
198C22×C3×C5—42no—
199C22×C3×C5—41no—
200C22×C3×C5C4×D411yescharacteristic
201C22×C3×C5#12111yescharacteristic
202C22×C3×C5#12311yescharacteristic
203C2×C3×D5—22no—
204C2×C3×D5—81no—
205C3×C4×C5—41no—
206C3×C4×C5C2×C22⋊C411yescharacteristic
207C3×C4×C5C4×D411yescharacteristic
208C3×C4×C5#12011yescharacteristic
209C3×C4×C5#12111yescharacteristic
210C3×Dic5—22no—
211C3×Dic5—81no—
212C3×#41—21no—
213C3×#41—21no—
214C3×#41—21no—
215C3×#41—21no—
216C3×#41—52no—
217C3×#41—52no—
218C3×#41—101no—
219C3×#41—101no—
220C2×C3×Q8—51no—
221C2×C3×Q8C4×D511yescharacteristic
222C2×C3×D4—21no—
223C2×C3×D4—51no—
224C2×C3×D4—101no—
225C2×C3×D4C4×D511yescharacteristic
226C22×C3×C4—21no—
227C22×C3×C4—101no—
228C22×C3×C4C22×D511yescharacteristic
229C3×Q16—102no—
230C3×SD16—102no—
231C3×SD16—102no—
232C3×D8—102no—
233C3×M16—21no—
234C3×M16—21no—
235C3×M16—52no—
236C3×M16—52no—
237C3×M16—104no—
238C3×M16—101no—
239C3×M16—101no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—104no—
244C2×C3×C8—101no—
245C2×C3×C8—101no—
246C2×C3×C8C22⋊D512yes—
247C3×C4⋊C4—101no—
248C3×C22⋊C4—101no—
249C3×C42—101no—
250C23×C5—21no—
251C23×C5C3×#4111yescharacteristic
252C22×D5—21no—
253C5×Q8—21no—
254C5×Q8—21no—
255C5×D4—21no—
256C5×D4—21no—
257C5×D4—41no—
258C5×D4—41no—
259C2×C4×C5—21no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
262C2×C4×C5C22×C3×C411yescharacteristic
263C2×C4×C5C2×C3×D411yescharacteristic
264C2×C4×C5C2×C3×D411yescharacteristic
265C2×C4×C5C2×C3×D411yescharacteristic
266C2×C4×C5C2×C3×D411yescharacteristic
267C2×C4×C5C3×#4111yescharacteristic
268C22⋊D5—22no—
269C22⋊D5—22no—
270C2×Dic5—21no—
271C2×Dic5—41no—
272D20—21no—
273D20C3×C22⋊C412yes—
274C4×D5—22no—
275C4×D5—22no—
276Dic10—21no—
277Dic10C3×C22⋊C412yes—
278C5×C8—22no—
279C5×C8—41no—
280#168—22no—
281#168—22no—
282C2×#41—51no—
283C2×#41C2×C3×D511yescharacteristic
284#137—52no—
285#137—101no—
286AGL(1,ℤ/8)—52no—
287AGL(1,ℤ/8)—101no—
288#135—102no—
289#131—102no—
290#131—102no—
291C2×M16—51no—
292C2×M16—51no—
293C2×M16—102no—
294C2×M16C2×C3×D511yescharacteristic
295C22×C8C2×C3×D511yescharacteristic
296#117—51no—
297#104—102no—
298#103—101no—
299#102—101no—
300C22⋊C8—22no—
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5—21no—
304C2×C3×C5—81no—
305C2×C3×C5#38611yescharacteristic
306C3×D5—42no—
307C23×C3—21no—
308C23×C3—101no—
309C23×C3#70911yescharacteristic
310C3×Q8—21no—
311C3×Q8—21no—
312C3×Q8—52no—
313C3×Q8—101no—
314C3×D4—21no—
315C3×D4—21no—
316C3×D4—41no—
317C3×D4—41no—
318C3×D4—52no—
319C3×D4—102no—
320C3×D4—102no—
321C3×D4—101no—
322C2×C3×C4—21no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—101no—
326C2×C3×C4—102no—
327C2×C3×C4—102no—
328C2×C3×C4—201no—
329C2×C3×C4C2×C4×D511yescharacteristic
330C2×C3×C4D4×D511yescharacteristic
331C2×C3×C4D4×D511yescharacteristic
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4#71111yescharacteristic
334C2×C3×C4C2×C22⋊D511yescharacteristic
335C3×C8—22no—
336C3×C8—41no—
337C3×C8—102no—
338C3×C8—102no—
339C22×C5—41no—
340C22×C5—42no—
341C22×C5—41no—
342C22×C5C3×C4×D411yescharacteristic
343C22×C5C3×#12111yescharacteristic
344C22×C5C3×#12311yescharacteristic
345C2×D5—22no—
346C2×D5—81no—
347C4×C5—41no—
348C4×C5C2×C3×C22⋊C411yescharacteristic
349C4×C5C3×C4×D411yescharacteristic
350C4×C5C3×#12011yescharacteristic
351C4×C5C3×#12111yescharacteristic
352Dic5—22no—
353Dic5—81no—
354#41—21no—
355#41—21no—
356#41—21no—
357#41—21no—
358#41—52no—
359#41—52no—
360#41—101no—
361#41—101no—
362C2×Q8—51no—
363C2×Q8C3×C4×D511yescharacteristic
364C2×D4—21no—
365C2×D4—51no—
366C2×D4—101no—
367C2×D4C3×C4×D511yescharacteristic
368C22×C4—21no—
369C22×C4—101no—
370C22×C4C22×C3×D511yescharacteristic
371Q16—102no—
372SD16—102no—
373SD16—102no—
374D8—102no—
375M16—21no—
376M16—21no—
377M16—52no—
378M16—52no—
379M16—104no—
380M16—101no—
381M16—101no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—104no—
386C2×C8—101no—
387C2×C8—101no—
388C2×C8C3×C22⋊D512yes—
389C4⋊C4—101no—
390C22⋊C4—101no—
391C42—101no—
392C3×C5#188111yescharacteristic, complemented, Hall
393C22×C3—41no—
394C22×C3—42no—
395C22×C3—41no—
396C22×C3—102no—
397C22×C3—401no—
398C22×C3#402911yescharacteristic
399C22×C3#403011yescharacteristic
400C22×C3C4×C22⋊D511yescharacteristic
401C3×C4—41no—
402C3×C4—102no—
403C3×C4—401no—
404C3×C4D5×C22⋊C411yescharacteristic
405C3×C4#402711yescharacteristic
406C3×C4#408311yescharacteristic
407C3×C4#408411yescharacteristic
408C2×C5—21no—
409C2×C5—21no—
410C2×C5—21no—
411C2×C5—81no—
412C2×C5C3×#38611yescharacteristic
413D5—42no—
414C23—21no—
415C23—101no—
416C23C3×#70911yescharacteristic
417Q8—21no—
418Q8—21no—
419Q8—52no—
420Q8—101no—
421D4—21no—
422D4—21no—
423D4—41no—
424D4—41no—
425D4—52no—
426D4—102no—
427D4—102no—
428D4—101no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—101no—
433C2×C4—102no—
434C2×C4—102no—
435C2×C4—201no—
436C2×C4C2×C3×C4×D511yescharacteristic
437C2×C4C3×D4×D511yescharacteristic
438C2×C4C3×D4×D511yescharacteristic
439C2×C4C3×D4×D511yescharacteristic
440C2×C4C3×#71111yescharacteristic
441C2×C4C2×C3×C22⋊D511yescharacteristic
442C8—22no—
443C8—41no—
444C8—102no—
445C8—102no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—81no—
450C2×C3—202no—
451C2×C3#6524511yescharacteristic
452C5C3×#188111yescharacteristic, complemented, Sylow
453C22—41no—
454C22—42no—
455C22—41no—
456C22—102no—
457C22—401no—
458C22C3×#402911yescharacteristic
459C22C3×#403011yescharacteristic
460C22C3×C4×C22⋊D511yescharacteristic
461C4—41no—
462C4—102no—
463C4—401no—
464C4C3×D5×C22⋊C411yescharacteristic
465C4C3×#402711yescharacteristic
466C4C3×#408311yescharacteristic
467C4C3×#408411yescharacteristic
468C3#1060080511yescharacteristic, direct product factor, Sylow
469C2—21no—
470C2—21no—
471C2—21no—
472C2—81no—
473C2—202no—
474C2C3×#6524511yescharacteristic
subgroupG/H
centerC3×C4#4083
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#408C2
socleC2×C3×C5#386
prime radicalC3×#66156C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#408D5
hypocenterC5C3×#1881
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#408

Complements

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

NH ≅ G/Ntype
2. C3×#66079C2semidirect
3. C3×C5×#408C2semidirect
4. C3×#65525C2semidirect
5. C3×#65402C2semidirect
6. C3×#64776C2semidirect
7. C3×#64772C2semidirect
8. #10600805C3direct (N × H)
16. C3×#4088C4semidirect
17. C3×#4078C4semidirect
30. #66079C2×C3semidirect
31. C5×#408C2×C3semidirect
32. #65525C2×C3semidirect
33. #65402C2×C3semidirect
34. #64776C2×C3semidirect
35. #64772C2×C3semidirect
78. C3×#408D5semidirect
88. #4088C3×C4semidirect
89. #4078C3×C4semidirect
194. #408C3×D5semidirect
392. C3×C5#1881semidirect
452. C5C3×#1881semidirect
468. C3#10600805direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661562
C3×#660792
C3×C5×#4082
C3×#655252
C3×#654022
C3×#647762
C3×#647722
#106008053
C3×#18815