Finite Group Databasebeta

← C3×#10599051 #14288855

Subgroups — C3×#10599051 #14288855

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65919C211yesmaximal, characteristic, complemented
2C3×#65316C211yesmaximal, characteristic, complemented
3C3×#65137C211yesmaximal, characteristic, complemented
4C3×#64984C211yesmaximal, characteristic
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7C3×#64676C211yesmaximal, characteristic, complemented
8#10599051C311yesmaximal, characteristic, direct product factor, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C3×#4093—21no—
11C2×C3×#688—21no—
12C2×C3×D40—22no—
13C2×C3×#677—21no—
14C3×#4040—22no—
15C3×#4039—21no—
16C3×#4021—21no—
17C3×#4020C2211yescharacteristic
18C3×#4020C2211yescharacteristic
19C3×C4×D20—21no—
20C3×C4×Dic10C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C4×C5×C8C2211yescharacteristic
23C3×#3953—21no—
24C3×#3941—21no—
25C3×C4⋊#168C2211yescharacteristic
26C3×#1620—51nomaximal, Hall
27#65919C2×C311yescharacteristic, complemented
28#65316C2×C311yescharacteristic, complemented
29#65137C2×C311yescharacteristic, complemented
30#64984C2×C311yescharacteristic
31C5×Q8⋊C8C2×C311yescharacteristic, complemented
32#64705C2×C311yescharacteristic, complemented
33#64676C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8D411yescharacteristic
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20D412yes—
41C2×C3×C4×D5—22no—
42C2×C3×Dic10D411yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C42×C5—21no—
48C3×C42×C5C2311yescharacteristic
49C3×#688—42no—
50C3×#685—22no—
51C3×#685—22no—
52C3×#685—22no—
53C3×C4⋊Dic5D411yescharacteristic
54C3×#683—21no—
55C3×C4×Dic5—21no—
56C2×C3×#168—21no—
57C3×D40—44no—
58C3×#677—42no—
59C3×#559—51no—
60C3×#493—51no—
61C3×#460—51no—
62C3×#460—51no—
63C3×#331—51no—
64C3×Q8⋊C8—51no—
65C3×Q8⋊C8D511yescharacteristic, complemented
66C4×C5×Q8C22×C311yescharacteristic
67#4093—21no—
68C2×#688—21no—
69C2×D40—22no—
70C2×#677—21no—
71#4040—22no—
72#4039—21no—
73#4021—21no—
74#4020C22×C311yescharacteristic
75#4020C22×C311yescharacteristic
76C4×D20—21no—
77C4×Dic10C22×C311yescharacteristic
78C5×C4⋊C8C22×C311yescharacteristic
79C4×C5×C8C22×C311yescharacteristic
80#3953—21no—
81#3941—21no—
82C4⋊#168C22×C311yescharacteristic
83#1620—51noSylow
84C22×C3×D5—22no—
85C22×C3×D5—41no—
86C3×C5×Q8—21no—
87C3×C5×Q8—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C3×D20—42no—
96C3×D20—42no—
97C3×D20—41no—
98C3×D20—41no—
99C3×D20—41no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105C3×C4×D5—82no—
106C3×Dic10—21no—
107C3×Dic10—21no—
108C3×C5×C8—22no—
109C3×C5×C8—41no—
110C3×#168—41no—
111C2×C3×SD16—101no—
112C2×C3×SD16—101no—
113C2×C3×D8—102no—
114C3×#127—51no—
115C3×#127—51no—
116C3×#124—101no—
117C3×#124—101no—
118C3×#123—102no—
119C3×C4×Q8—51no—
120C3×C4×Q8C2×D511yescharacteristic
121C3×C4×D4—101no—
122C3×C4×D4—101no—
123C3×C4⋊C8—51no—
124C3×C4⋊C8C2×D511yescharacteristic
125C3×#102—101no—
126C3×#102—101no—
127C3×C4×C8C2×D511yescharacteristic
128C2×C5×Q8C3×D411yescharacteristic
129C2×D20—21no—
130C2×D20—21no—
131C2×D20—21no—
132C2×D20—21no—
133C2×D20—21no—
134C2×D20C3×D412yes—
135C2×C4×D5—22no—
136C2×Dic10C3×D411yescharacteristic
137C2×C5×C8—21no—
138C2×C5×C8—21no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4C3×D411yescharacteristic
141C42×C5—21no—
142C42×C5C23×C311yescharacteristic
143#688—42no—
144#685—22no—
145#685—22no—
146#685—22no—
147C4⋊Dic5C3×D411yescharacteristic
148#683—21no—
149C4×Dic5—21no—
150C2×#168—21no—
151D40—44no—
152#677—42no—
153#559—51no—
154#493—51no—
155#460—51no—
156#460—51no—
157#331—51no—
158Q8⋊C8—51no—
159Q8⋊C8C3×D511yescharacteristic, complemented
160C22×C3×C5#12011yescharacteristic
161C2×C3×D5—42no—
162C2×C3×D5—42no—
163C2×C3×D5—42no—
164C2×C3×D5—81no—
165C2×C3×D5—81no—
166C2×C3×D5—81no—
167C3×C4×C5—21no—
168C3×C4×C5—41no—
169C3×C4×C5—41no—
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5#13511yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C3×Dic5—41no—
175C3×Dic5—41no—
176C2×C3×Q8—51no—
177C2×C3×Q8D2011yescharacteristic
178C2×C3×D4—52no—
179C2×C3×D4—101no—
180C2×C3×D4—101no—
181C2×C3×D4—101no—
182C2×C3×D4—101no—
183C2×C3×D4—101no—
184C22×C3×C4—102no—
185C3×SD16—202no—
186C3×SD16—202no—
187C3×D8—204no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—101no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—51no—
193C3×C4⋊C4—101no—
194C3×C4⋊C4D2011yescharacteristic
195C3×C22⋊C4—102no—
196C3×C22⋊C4—102no—
197C3×C22⋊C4—102no—
198C3×C42—21no—
199C3×C42—101no—
200C3×C42C22×D511yescharacteristic
201C22×D5—22no—
202C22×D5—41no—
203C5×Q8—21no—
204C5×Q8—21no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5C2×C3×D411yescharacteristic
208C2×C4×C5C2×C3×D411yescharacteristic
209C2×C4×C5C2×C3×D411yescharacteristic
210C2×Dic5—21no—
211C2×Dic5—21no—
212D20—42no—
213D20—42no—
214D20—41no—
215D20—41no—
216D20—41no—
217D20—41no—
218D20—41no—
219D20—41no—
220D20—41no—
221D20—41no—
222C4×D5—82no—
223Dic10—21no—
224Dic10—21no—
225C5×C8—22no—
226C5×C8—41no—
227#168—41no—
228C2×SD16—101no—
229C2×SD16—101no—
230C2×D8—102no—
231#127—51no—
232#127—51no—
233#124—101no—
234#124—101no—
235#123—102no—
236C4×Q8—51no—
237C4×Q8C2×C3×D511yescharacteristic
238C4×D4—101no—
239C4×D4—101no—
240C4⋊C8—51no—
241C4⋊C8C2×C3×D511yescharacteristic
242#102—101no—
243#102—101no—
244C4×C8C2×C3×D511yescharacteristic
245C2×C3×C5#44911yescharacteristic
246C2×C3×C5#44911yescharacteristic
247C2×C3×C5#45311yescharacteristic
248C3×D5—82no—
249C3×D5—161no—
250C23×C3—102no—
251C23×C3—201no—
252C3×Q8—21no—
253C3×Q8—21no—
254C3×Q8—101no—
255C3×Q8—101no—
256C3×D4—202no—
257C3×D4—202no—
258C3×D4—201no—
259C3×D4—201no—
260C3×D4—201no—
261C3×D4—201no—
262C3×D4—201no—
263C3×D4—201no—
264C3×D4—201no—
265C3×D4—201no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—101no—
269C2×C3×C4—101no—
270C2×C3×C4—402no—
271C2×C3×C4C2×D2011yescharacteristic
272C2×C3×C4D4×D511yescharacteristic
273C2×C3×C4D4×D511yescharacteristic
274C3×C8—22no—
275C3×C8—41no—
276C3×C8—201no—
277C22×C5C3×#12011yescharacteristic
278C2×D5—42no—
279C2×D5—42no—
280C2×D5—42no—
281C2×D5—81no—
282C2×D5—81no—
283C2×D5—81no—
284C4×C5—21no—
285C4×C5—41no—
286C4×C5—41no—
287C4×C5C3×#13511yescharacteristic
288C4×C5C3×#13511yescharacteristic
289C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
290C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
291Dic5—41no—
292Dic5—41no—
293C2×Q8—51no—
294C2×Q8C3×D2011yescharacteristic
295C2×D4—52no—
296C2×D4—101no—
297C2×D4—101no—
298C2×D4—101no—
299C2×D4—101no—
300C2×D4—101no—
301C22×C4—102no—
302SD16—202no—
303SD16—202no—
304D8—204no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—101no—
308C4⋊C4—21no—
309C4⋊C4—51no—
310C4⋊C4—101no—
311C4⋊C4C3×D2011yescharacteristic
312C22⋊C4—102no—
313C22⋊C4—102no—
314C22⋊C4—102no—
315C42—21no—
316C42—101no—
317C42C22×C3×D511yescharacteristic
318C3×C5#162011yescharacteristic, complemented, Hall
319C22×C3—202no—
320C22×C3—202no—
321C22×C3—202no—
322C22×C3—401no—
323C22×C3—401no—
324C22×C3—401no—
325C22×C3#402811yescharacteristic
326C3×C4—21no—
327C3×C4—41no—
328C3×C4—41no—
329C3×C4—201no—
330C3×C4—201no—
331C3×C4#405011yescharacteristic
332C3×C4#405411yescharacteristic
333C3×C4#406011yescharacteristic
334C3×C4#406511yescharacteristic
335C2×C5C3×#44911yescharacteristic
336C2×C5C3×#44911yescharacteristic
337C2×C5C3×#45311yescharacteristic
338D5—82no—
339D5—161no—
340C23—102no—
341C23—201no—
342Q8—21no—
343Q8—21no—
344Q8—101no—
345Q8—101no—
346D4—202no—
347D4—202no—
348D4—201no—
349D4—201no—
350D4—201no—
351D4—201no—
352D4—201no—
353D4—201no—
354D4—201no—
355D4—201no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—101no—
359C2×C4—101no—
360C2×C4—402no—
361C2×C4C2×C3×D2011yescharacteristic
362C2×C4C3×D4×D511yescharacteristic
363C2×C4C3×D4×D511yescharacteristic
364C8—22no—
365C8—41no—
366C8—201no—
367C2×C3—402no—
368C2×C3—801no—
369C2×C3#6502311yescharacteristic
370C2×C3#6510011yescharacteristic
371C2×C3#6511111yescharacteristic
372C5C3×#162011yescharacteristic, complemented, Sylow
373C22—202no—
374C22—202no—
375C22—202no—
376C22—401no—
377C22—401no—
378C22—401no—
379C22C3×#402811yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—201no—
384C4—201no—
385C4C3×#405011yescharacteristic
386C4C3×#405411yescharacteristic
387C4C3×#406011yescharacteristic
388C4C3×#406511yescharacteristic
389C3#1059905111yescharacteristic, direct product factor, Sylow
390C2—402no—
391C2—801no—
392C2C3×#6502311yescharacteristic
393C2C3×#6510011yescharacteristic
394C2C3×#6511111yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radicalC3×#64984C2
hypercenterC3×Q8⋊C8D5
hypocenterC5C3×#1620
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. C3×#65919C2semidirect
2. C3×#65316C2semidirect
3. C3×#65137C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
6. C3×#64705C2semidirect
7. C3×#64676C2semidirect
8. #10599051C3direct (N × H)
27. #65919C2×C3semidirect
28. #65316C2×C3semidirect
29. #65137C2×C3semidirect
31. C5×Q8⋊C8C2×C3semidirect
32. #64705C2×C3semidirect
33. #64676C2×C3semidirect
65. C3×Q8⋊C8D5semidirect
159. Q8⋊C8C3×D5semidirect
318. C3×C5#1620semidirect
372. C5C3×#1620semidirect
389. C3#10599051direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659192
C3×#653162
C3×#651372
C3×#649842
C3×C5×Q8⋊C82
C3×#647052
C3×#646762
#105990513
C3×#16205