Finite Group Databasebeta

← C3×#10599226 #14289287

Subgroups — C3×#10599226 #14289287

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×#65377C211yesmaximal, characteristic, complemented
3C3×#65137C211yesmaximal, characteristic, complemented
4C3×#65132C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic, complemented
6C3×#64704C211yesmaximal, characteristic, complemented
7C3×#64703C211yesmaximal, characteristic, complemented
8#10599226C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×#4093—21no—
11C3×Q8×Dic5—21no—
12C2×C3×D40—21no—
13C2×C3×#677—21no—
14C3×#4044—22no—
15C3×#4043—21no—
16C3×#4038—21no—
17C3×#4020C2211yescharacteristic
18C3×C4×D20C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×#3953—21no—
23C3×#3953—21no—
24C3×#3941—22no—
25C3×C4×#168C2211yescharacteristic
26C3×#1628—51nomaximal, Hall
27#66066C2×C311yescharacteristic, complemented
28#65377C2×C311yescharacteristic, complemented
29#65137C2×C311yescharacteristic, complemented
30#65132C2×C311yescharacteristic
31C5×#332C2×C311yescharacteristic, complemented
32#64704C2×C311yescharacteristic, complemented
33#64703C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×Dic10D411yescharacteristic
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D412yes—
45C3×C42×C5C2311yescharacteristic
46C3×#685—22no—
47C3×#685—22no—
48C3×#685—21no—
49C3×C4⋊Dic5—22no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×C4⋊Dic5D411yescharacteristic
52C3×#683—21no—
53C3×C4×Dic5—22no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56C3×D40—42no—
57C3×#677—42no—
58C3×#556—51no—
59C3×#486—51no—
60C3×#460—51no—
61C3×#459—51no—
62C3×#332D511yescharacteristic, complemented
63C3×Q8⋊C8—51no—
64C3×D4⋊C8—51no—
65C5×C4⋊Q8C22×C311yescharacteristic
66#4093—21no—
67Q8×Dic5—21no—
68C2×D40—21no—
69C2×#677—21no—
70#4044—22no—
71#4043—21no—
72#4038—21no—
73#4020C22×C311yescharacteristic
74C4×D20C22×C311yescharacteristic
75C4×Dic10C22×C311yescharacteristic
76C5×C4⋊C8C22×C311yescharacteristic
77C5×C4⋊C8C22×C311yescharacteristic
78#3953—21no—
79#3953—21no—
80#3941—22no—
81C4×#168C22×C311yescharacteristic
82#1628—51noSylow
83C22×C3×D5—21no—
84C22×C3×D5—41no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—21no—
94C3×D20—21no—
95C3×D20—21no—
96C3×D20—42no—
97C3×D20—41no—
98C3×D20—41no—
99C3×D20—41no—
100C3×D20—41no—
101C3×C4×D5—41no—
102C3×C4×D5—41no—
103C3×Dic10—21no—
104C3×Dic10—21no—
105C3×C5×C8—41no—
106C3×C5×C8—41no—
107C3×#168—41no—
108C2×C3×SD16—101no—
109C2×C3×D8—101no—
110C3×C4⋊Q8C2×D511yescharacteristic
111C3×#127—51no—
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⋊C8C2×D511yescharacteristic
120C3×C4⋊C8C2×D511yescharacteristic
121C3×#102—101no—
122C3×#102—101no—
123C3×#102—102no—
124C3×C4×C8—51no—
125C2×C5×Q8—21no—
126C2×D20—21no—
127C2×D20—21no—
128C2×D20—21no—
129C2×D20C3×D411yescharacteristic
130C2×C4×D5—21no—
131C2×Dic10C3×D411yescharacteristic
132C2×C5×C8—21no—
133C2×C5×C8—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4C3×D412yes—
136C42×C5C23×C311yescharacteristic
137#685—22no—
138#685—22no—
139#685—21no—
140C4⋊Dic5—22no—
141C4⋊Dic5C3×D411yescharacteristic
142C4⋊Dic5C3×D411yescharacteristic
143#683—21no—
144C4×Dic5—22no—
145C4×Dic5—21no—
146C2×#168—21no—
147D40—42no—
148#677—42no—
149#556—51no—
150#486—51no—
151#460—51no—
152#459—51no—
153#332C3×D511yescharacteristic, complemented
154Q8⋊C8—51no—
155D4⋊C8—51no—
156C22×C3×C5#12011yescharacteristic
157C2×C3×D5—41no—
158C2×C3×D5—41no—
159C2×C3×D5—41no—
160C2×C3×D5—81no—
161C2×C3×D5—81no—
162C2×C3×D5—81no—
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—51no—
175C2×C3×D4—101no—
176C2×C3×D4—101no—
177C2×C3×D4—101no—
178C22×C3×C4—101no—
179C3×SD16—202no—
180C3×D8—202no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
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⋊C4D2012yes—
190C3×C22⋊C4—102no—
191C3×C22⋊C4—102no—
192C3×C22⋊C4—101no—
193C3×C42—102no—
194C3×C42—101no—
195C3×C42C22×D511yescharacteristic
196C22×D5—21no—
197C22×D5—41no—
198C5×Q8—41no—
199C5×Q8—41no—
200C2×C4×C5—22no—
201C2×C4×C5C2×C3×D411yescharacteristic
202C2×C4×C5C2×C3×D411yescharacteristic
203C2×C4×C5C2×C3×D411yescharacteristic
204C2×Dic5—21no—
205C2×Dic5—21no—
206C2×Dic5—21no—
207D20—21no—
208D20—21no—
209D20—42no—
210D20—41no—
211D20—41no—
212D20—41no—
213D20—41no—
214C4×D5—41no—
215C4×D5—41no—
216Dic10—21no—
217Dic10—21no—
218C5×C8—41no—
219C5×C8—41no—
220#168—41no—
221C2×SD16—101no—
222C2×D8—101no—
223C4⋊Q8C2×C3×D511yescharacteristic
224#127—51no—
225#126—102no—
226#124—101no—
227C22⋊Q8—101no—
228C4×Q8—51no—
229C4×Q8—101no—
230C4×D4—51no—
231#117—101no—
232C4⋊C8C2×C3×D511yescharacteristic
233C4⋊C8C2×C3×D511yescharacteristic
234#102—101no—
235#102—101no—
236#102—102no—
237C4×C8—51no—
238C2×C3×C5#44911yescharacteristic
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#45411yescharacteristic
241C3×D5—81no—
242C3×D5—161no—
243C23×C3—101no—
244C23×C3—201no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×Q8—101no—
248C3×Q8—101no—
249C3×D4—101no—
250C3×D4—101no—
251C3×D4—202no—
252C3×D4—201no—
253C3×D4—201no—
254C3×D4—201no—
255C3×D4—201no—
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×C4C2×D2011yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C2×C3×C4D4×D511yescharacteristic
265C3×C8—41no—
266C3×C8—41no—
267C3×C8—201no—
268C22×C5C3×#12011yescharacteristic
269C2×D5—41no—
270C2×D5—41no—
271C2×D5—41no—
272C2×D5—81no—
273C2×D5—81no—
274C2×D5—81no—
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—51no—
287C2×D4—101no—
288C2×D4—101no—
289C2×D4—101no—
290C22×C4—101no—
291SD16—202no—
292D8—202no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—101no—
296C4⋊C4—21no—
297C4⋊C4—51no—
298C4⋊C4—51no—
299C4⋊C4—102no—
300C4⋊C4—101no—
301C4⋊C4C3×D2012yes—
302C22⋊C4—102no—
303C22⋊C4—102no—
304C22⋊C4—101no—
305C42—102no—
306C42—101no—
307C42C22×C3×D511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3—201no—
310C22×C3—201no—
311C22×C3—201no—
312C22×C3—401no—
313C22×C3—401no—
314C22×C3—401no—
315C22×C3#402811yescharacteristic
316C3×C4—21no—
317C3×C4—42no—
318C3×C4—201no—
319C3×C4—201no—
320C3×C4—201no—
321C3×C4#405711yescharacteristic
322C3×C4#406011yescharacteristic
323C3×C4#406211yescharacteristic
324C3×C4#406511yescharacteristic
325C2×C5C3×#44911yescharacteristic
326C2×C5C3×#44911yescharacteristic
327C2×C5C3×#45411yescharacteristic
328D5—81no—
329D5—161no—
330C23—101no—
331C23—201no—
332Q8—41no—
333Q8—41no—
334Q8—101no—
335Q8—101no—
336D4—101no—
337D4—101no—
338D4—202no—
339D4—201no—
340D4—201no—
341D4—201no—
342D4—201no—
343C2×C4—22no—
344C2×C4—101no—
345C2×C4—101no—
346C2×C4—101no—
347C2×C4—201no—
348C2×C4—201no—
349C2×C4C2×C3×D2011yescharacteristic
350C2×C4C3×D4×D511yescharacteristic
351C2×C4C3×D4×D511yescharacteristic
352C8—41no—
353C8—41no—
354C8—201no—
355C2×C3—401no—
356C2×C3—801no—
357C2×C3#6504211yescharacteristic
358C2×C3#6507011yescharacteristic
359C2×C3#6510011yescharacteristic
360C5C3×#162811yescharacteristic, complemented, Sylow
361C22—201no—
362C22—201no—
363C22—201no—
364C22—401no—
365C22—401no—
366C22—401no—
367C22C3×#402811yescharacteristic
368C4—21no—
369C4—42no—
370C4—201no—
371C4—201no—
372C4—201no—
373C4C3×#405711yescharacteristic
374C4C3×#406011yescharacteristic
375C4C3×#406211yescharacteristic
376C4C3×#406511yescharacteristic
377C3#1059922611yescharacteristic, direct product factor, Sylow
378C2—401no—
379C2—801no—
380C2C3×#6504211yescharacteristic
381C2C3×#6507011yescharacteristic
382C2C3×#6510011yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#332C2
socleC22×C3×C5#120
prime radicalC3×#65132C2
hypercenterC3×#332D5
hypocenterC5C3×#1628
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#332

Complements

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

NH ≅ G/Ntype
1. C3×#66066C2semidirect
2. C3×#65377C2semidirect
3. C3×#65137C2semidirect
5. C3×C5×#332C2semidirect
6. C3×#64704C2semidirect
7. C3×#64703C2semidirect
8. #10599226C3direct (N × H)
27. #66066C2×C3semidirect
28. #65377C2×C3semidirect
29. #65137C2×C3semidirect
31. C5×#332C2×C3semidirect
32. #64704C2×C3semidirect
33. #64703C2×C3semidirect
62. C3×#332D5semidirect
153. #332C3×D5semidirect
308. C3×C5#1628semidirect
360. C5C3×#1628semidirect
377. C3#10599226direct (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×#653772
C3×#651372
C3×#651322
C3×C5×#3322
C3×#647042
C3×#647032
#105992263
C3×#16285