Finite Group Databasebeta

← C3×#10601990 #14289275

Subgroups — C3×#10601990 #14289275

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66066C211yesmaximal, characteristic, complemented
2C3×C5×#486C211yesmaximal, characteristic, complemented
3C3×#65364C211yesmaximal, characteristic, complemented
4C3×#65361C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic, complemented
7C3×#64676C211yesmaximal, characteristic, complemented
8#10601990C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#127C2211yescharacteristic
11C3×#4093—21no—
12C3×Q8×Dic5—21no—
13C2×C3×#687—21no—
14C2×C3×#686—21no—
15C3×#4044—22no—
16C3×#4043—21no—
17C3×#4038—21no—
18C3×C4×D20C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20C3×C5×#102—22no—
21C3×C4×C5×C8C2211yescharacteristic
22C3×#3964—21no—
23C3×#3964—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1628—51nomaximal, Hall
27#66066C2×C311yescharacteristic, complemented
28C5×#486C2×C311yescharacteristic, complemented
29#65364C2×C311yescharacteristic, complemented
30#65361C2×C311yescharacteristic
31#64767C2×C311yescharacteristic, complemented
32#64679C2×C311yescharacteristic, complemented
33#64676C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×Dic10D411yescharacteristic
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D412yes—
44C3×C42×C5C2311yescharacteristic
45C3×#687—42no—
46C3×#686—42no—
47C3×#685—22no—
48C3×#685—22no—
49C3×#685—21no—
50C3×C4⋊Dic5—22no—
51C3×C4⋊Dic5D411yescharacteristic
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—22no—
55C3×C4×Dic5—21no—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58C3×#556—51no—
59C3×#486D511yescharacteristic, complemented
60C3×#460—51no—
61C3×#459—51no—
62C3×#332—51no—
63C3×Q8⋊C8—51no—
64C3×D4⋊C8—51no—
65C5×C4⋊Q8C22×C311yescharacteristic
66C5×#127C22×C311yescharacteristic
67#4093—21no—
68Q8×Dic5—21no—
69C2×#687—21no—
70C2×#686—21no—
71#4044—22no—
72#4043—21no—
73#4038—21no—
74C4×D20C22×C311yescharacteristic
75C4×Dic10C22×C311yescharacteristic
76C5×#102—22no—
77C4×C5×C8C22×C311yescharacteristic
78#3964—21no—
79#3964—21no—
80C4⋊#168C22×C311yescharacteristic
81C4⋊#168C22×C311yescharacteristic
82#1628—51noSylow
83C23×C3×C5—41no—
84C22×C3×D5—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C3×C5×D4—42no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×Dic5—21no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C3×D20—21no—
100C3×D20—21no—
101C3×C4×D5—41no—
102C3×C4×D5—41no—
103C3×Dic10—21no—
104C3×Dic10—21no—
105C3×C5×C8—41no—
106C3×#168—41no—
107C3×#168—41no—
108C2×C3×SD16—101no—
109C2×C3×D8—101no—
110C3×C4⋊Q8C2×D511yescharacteristic
111C3×#127C2×D511yescharacteristic
112C3×#126—102no—
113C3×#124—101no—
114C3×C22⋊Q8—101no—
115C3×C4×Q8—51no—
116C3×C4×Q8—101no—
117C3×C4×D4—51no—
118C3×#117—101no—
119C3×C4⋊C8—51no—
120C3×C4⋊C8—51no—
121C3×#102—22no—
122C3×#102—101no—
123C3×#102—101no—
124C3×C4×C8C2×D511yescharacteristic
125C2×C5×Q8—21no—
126C2×C5×D4—21no—
127C2×C5×D4—21no—
128C2×C5×D4—21no—
129C2×D20C3×D411yescharacteristic
130C2×C4×D5—21no—
131C2×Dic10C3×D411yescharacteristic
132C2×C5×C8—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4C3×D412yes—
135C42×C5C23×C311yescharacteristic
136#687—42no—
137#686—42no—
138#685—22no—
139#685—22no—
140#685—21no—
141C4⋊Dic5—22no—
142C4⋊Dic5C3×D411yescharacteristic
143C4⋊Dic5C3×D411yescharacteristic
144#683—21no—
145C4×Dic5—22no—
146C4×Dic5—21no—
147C2×#168—21no—
148C2×#168—21no—
149#556—51no—
150#486C3×D511yescharacteristic, complemented
151#460—51no—
152#459—51no—
153#332—51no—
154Q8⋊C8—51no—
155D4⋊C8—51no—
156C22×C3×C5—81no—
157C22×C3×C5—81no—
158C22×C3×C5—81no—
159C22×C3×C5#12011yescharacteristic
160C2×C3×D5—41no—
161C2×C3×D5—41no—
162C2×C3×D5—41no—
163C3×C4×C5—21no—
164C3×C4×C5—42no—
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×Dic5—41no—
170C3×Dic5—41no—
171C3×Dic5—41no—
172C2×C3×Q8—21no—
173C2×C3×Q8—51no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—51no—
178C22×C3×C4—101no—
179C3×SD16—202no—
180C3×D8—202no—
181C2×C3×C8—21no—
182C2×C3×C8—101no—
183C2×C3×C8—101no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—51no—
186C3×C4⋊C4—51no—
187C3×C4⋊C4—102no—
188C3×C4⋊C4—101no—
189C3×C4⋊C4C22⋊D512yes—
190C3×C22⋊C4—102no—
191C3×C22⋊C4—102no—
192C3×C22⋊C4—101no—
193C3×C42—102no—
194C3×C42—101no—
195C3×C42C22×D511yescharacteristic
196C23×C5—41no—
197C22×D5—21no—
198C5×Q8—41no—
199C5×Q8—41no—
200C5×D4—42no—
201C5×D4—41no—
202C5×D4—41no—
203C5×D4—41no—
204C5×D4—41no—
205C2×C4×C5—22no—
206C2×C4×C5C2×C3×D411yescharacteristic
207C2×C4×C5C2×C3×D411yescharacteristic
208C2×C4×C5C2×C3×D411yescharacteristic
209C2×Dic5—21no—
210C2×Dic5—21no—
211C2×Dic5—21no—
212D20—21no—
213D20—21no—
214C4×D5—41no—
215C4×D5—41no—
216Dic10—21no—
217Dic10—21no—
218C5×C8—41no—
219#168—41no—
220#168—41no—
221C2×SD16—101no—
222C2×D8—101no—
223C4⋊Q8C2×C3×D511yescharacteristic
224#127C2×C3×D511yescharacteristic
225#126—102no—
226#124—101no—
227C22⋊Q8—101no—
228C4×Q8—51no—
229C4×Q8—101no—
230C4×D4—51no—
231#117—101no—
232C4⋊C8—51no—
233C4⋊C8—51no—
234#102—22no—
235#102—101no—
236#102—101no—
237C4×C8C2×C3×D511yescharacteristic
238C2×C3×C5—161no—
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#44911yescharacteristic
241C2×C3×C5#45411yescharacteristic
242C3×D5—81no—
243C23×C3—41no—
244C23×C3—101no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×Q8—101no—
248C3×Q8—101no—
249C3×D4—42no—
250C3×D4—41no—
251C3×D4—41no—
252C3×D4—41no—
253C3×D4—41no—
254C3×D4—101no—
255C3×D4—101no—
256C2×C3×C4—22no—
257C2×C3×C4—101no—
258C2×C3×C4—101no—
259C2×C3×C4—101no—
260C2×C3×C4—201no—
261C2×C3×C4—201no—
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C2×C3×C4C2×C22⋊D511yescharacteristic
265C3×C8—41no—
266C3×C8—201no—
267C3×C8—201no—
268C22×C5—81no—
269C22×C5—81no—
270C22×C5—81no—
271C22×C5C3×#12011yescharacteristic
272C2×D5—41no—
273C2×D5—41no—
274C2×D5—41no—
275C4×C5—21no—
276C4×C5—42no—
277C4×C5C3×#13511yescharacteristic
278C4×C5C3×#13511yescharacteristic
279C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
280C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
281Dic5—41no—
282Dic5—41no—
283Dic5—41no—
284C2×Q8—21no—
285C2×Q8—51no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—51no—
290C22×C4—101no—
291SD16—202no—
292D8—202no—
293C2×C8—21no—
294C2×C8—101no—
295C2×C8—101no—
296C4⋊C4—21no—
297C4⋊C4—51no—
298C4⋊C4—51no—
299C4⋊C4—102no—
300C4⋊C4—101no—
301C4⋊C4C3×C22⋊D512yes—
302C22⋊C4—102no—
303C22⋊C4—102no—
304C22⋊C4—101no—
305C42—102no—
306C42—101no—
307C42C22×C3×D511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3—81no—
310C22×C3—81no—
311C22×C3—81no—
312C22×C3—201no—
313C22×C3—201no—
314C22×C3—201no—
315C22×C3#408311yescharacteristic
316C3×C4—21no—
317C3×C4—42no—
318C3×C4—201no—
319C3×C4—201no—
320C3×C4—201no—
321C3×C4#405711yescharacteristic
322C3×C4#405811yescharacteristic
323C3×C4#406011yescharacteristic
324C3×C4#406211yescharacteristic
325C2×C5—161no—
326C2×C5C3×#44911yescharacteristic
327C2×C5C3×#44911yescharacteristic
328C2×C5C3×#45411yescharacteristic
329D5—81no—
330C23—41no—
331C23—101no—
332Q8—41no—
333Q8—41no—
334Q8—101no—
335Q8—101no—
336D4—42no—
337D4—41no—
338D4—41no—
339D4—41no—
340D4—41no—
341D4—101no—
342D4—101no—
343C2×C4—22no—
344C2×C4—101no—
345C2×C4—101no—
346C2×C4—101no—
347C2×C4—201no—
348C2×C4—201no—
349C2×C4C3×D4×D511yescharacteristic
350C2×C4C3×D4×D511yescharacteristic
351C2×C4C2×C3×C22⋊D511yescharacteristic
352C8—41no—
353C8—201no—
354C8—201no—
355C2×C3—161no—
356C2×C3—401no—
357C2×C3#6535111yescharacteristic
358C2×C3#6544711yescharacteristic
359C2×C3#6546111yescharacteristic
360C5C3×#162811yescharacteristic, complemented, Sylow
361C22—81no—
362C22—81no—
363C22—81no—
364C22—201no—
365C22—201no—
366C22—201no—
367C22C3×#408311yescharacteristic
368C4—21no—
369C4—42no—
370C4—201no—
371C4—201no—
372C4—201no—
373C4C3×#405711yescharacteristic
374C4C3×#405811yescharacteristic
375C4C3×#406011yescharacteristic
376C4C3×#406211yescharacteristic
377C3#1060199011yescharacteristic, direct product factor, Sylow
378C2—161no—
379C2—401no—
380C2C3×#6535111yescharacteristic
381C2C3×#6544711yescharacteristic
382C2C3×#6546111yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#486C2
socleC22×C3×C5#120
prime radicalC3×#65361C2
hypercenterC3×#486D5
hypocenterC5C3×#1628
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#486

Complements

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

NH ≅ G/Ntype
1. C3×#66066C2semidirect
2. C3×C5×#486C2semidirect
3. C3×#65364C2semidirect
5. C3×#64767C2semidirect
6. C3×#64679C2semidirect
7. C3×#64676C2semidirect
8. #10601990C3direct (N × H)
27. #66066C2×C3semidirect
28. C5×#486C2×C3semidirect
29. #65364C2×C3semidirect
31. #64767C2×C3semidirect
32. #64679C2×C3semidirect
33. #64676C2×C3semidirect
59. C3×#486D5semidirect
150. #486C3×D5semidirect
308. C3×C5#1628semidirect
360. C5C3×#1628semidirect
377. C3#10601990direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660662
C3×C5×#4862
C3×#653642
C3×#653612
C3×#647672
C3×#646792
C3×#646762
#106019903
C3×#16285