Finite Group Databasebeta

← C3×#10602163 #14290565

Subgroups — C3×#10602163 #14290565

Order 1920.

400 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66066C211yesmaximal, characteristic
2C3×C5×#500C211yesmaximal, characteristic, complemented
3C3×#65383C211yesmaximal, characteristic, complemented
4C3×#65372C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic
7C3×#64676C211yesmaximal, characteristic, complemented
8#10602163C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×#4093—21no—
12C3×Q8×Dic5—21no—
13C2×C3×#688—21no—
14C3×#4044—22no—
15C3×#4043—21no—
16C3×#4038—21no—
17C3×C4×D20C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C3×C5×#107—22no—
20C3×C4×C5×C8C2211yescharacteristic
21C3×#3967—21no—
22C3×#3942—21no—
23C3×#3940—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1650—51nomaximal, Hall
27#66066C2×C311yescharacteristic
28C5×#500C2×C311yescharacteristic, complemented
29#65383C2×C311yescharacteristic, complemented
30#65372C2×C311yescharacteristic
31#64767C2×C311yescharacteristic, complemented
32#64679C2×C311yescharacteristic
33#64676C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×C5×C8—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D412yes—
44C3×C42×C5C2311yescharacteristic
45C3×#688—42no—
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—
56C2×C3×#168—21no—
57C3×#556—51no—
58C3×#500D511yescharacteristic, complemented
59C3×#475—51no—
60C3×#461—51no—
61C3×#332—51no—
62C3×Q8⋊C8—51no—
63C3×D4⋊C8—51no—
64C5×C4⋊Q8C22×C311yescharacteristic
65C5×C4⋊Q8C22×C311yescharacteristic
66#4093—21no—
67Q8×Dic5—21no—
68C2×#688—21no—
69#4044—22no—
70#4043—21no—
71#4038—21no—
72C4×D20C22×C311yescharacteristic
73C4×Dic10C22×C311yescharacteristic
74C5×#107—22no—
75C4×C5×C8C22×C311yescharacteristic
76#3967—21no—
77#3942—21no—
78#3940—21no—
79C4⋊#168C22×C311yescharacteristic
80C4⋊#168C22×C311yescharacteristic
81#1650—51noSylow
82C22×C3×D5—21no—
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×Dic5—21no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C3×D20—21no—
96C3×D20—21no—
97C3×C4×D5—41no—
98C3×C4×D5—41no—
99C3×Dic10—21no—
100C3×Dic10—21no—
101C3×C5×C8—22no—
102C3×#168—41no—
103C3×#168—41no—
104C2×C3×SD16—101no—
105C3×C4⋊Q8C2×D511yescharacteristic
106C3×C4⋊Q8C2×D511yescharacteristic
107C3×#126—102no—
108C3×#124—101no—
109C3×C22⋊Q8—101no—
110C3×C4×Q8—51no—
111C3×C4×Q8—101no—
112C3×C4×D4—51no—
113C3×#117—101no—
114C3×#107—22no—
115C3×#106—101no—
116C3×C4⋊C8—51no—
117C3×C4⋊C8—51no—
118C3×#103—101no—
119C3×#103—101no—
120C3×C4×C8C2×D511yescharacteristic
121C2×C5×Q8—21no—
122C2×C5×Q8—21no—
123C2×D20C3×D411yescharacteristic
124C2×C4×D5—21no—
125C2×Dic10C3×D411yescharacteristic
126C2×C5×C8—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4C3×D412yes—
131C42×C5C23×C311yescharacteristic
132#688—42no—
133#685—22no—
134#685—22no—
135#685—21no—
136C4⋊Dic5—22no—
137C4⋊Dic5C3×D411yescharacteristic
138C4⋊Dic5C3×D411yescharacteristic
139#683—21no—
140C4×Dic5—22no—
141C4×Dic5—21no—
142C2×#168—21no—
143C2×#168—21no—
144#556—51no—
145#500C3×D511yescharacteristic, complemented
146#475—51no—
147#461—51no—
148#332—51no—
149Q8⋊C8—51no—
150D4⋊C8—51no—
151C22×C3×C5#12011yescharacteristic
152C2×C3×D5—41no—
153C2×C3×D5—41no—
154C2×C3×D5—41no—
155C3×C4×C5—21no—
156C3×C4×C5—42no—
157C3×C4×C5—81no—
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×Dic5—41no—
163C3×Dic5—41no—
164C3×Dic5—41no—
165C2×C3×Q8—21no—
166C2×C3×Q8—21no—
167C2×C3×Q8—51no—
168C2×C3×D4—51no—
169C22×C3×C4—101no—
170C3×SD16—202no—
171C2×C3×C8—21no—
172C2×C3×C8—101no—
173C2×C3×C8—101no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—51no—
178C3×C4⋊C4—51no—
179C3×C4⋊C4—102no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4C22⋊D512yes—
182C3×C22⋊C4—102no—
183C3×C22⋊C4—102no—
184C3×C22⋊C4—101no—
185C3×C42—102no—
186C3×C42—101no—
187C3×C42C22×D511yescharacteristic
188C22×D5—21no—
189C5×Q8—41no—
190C5×Q8—41no—
191C5×Q8—41no—
192C5×Q8—41no—
193C2×C4×C5—22no—
194C2×C4×C5—41no—
195C2×C4×C5C2×C3×D411yescharacteristic
196C2×C4×C5C2×C3×D411yescharacteristic
197C2×C4×C5C2×C3×D411yescharacteristic
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5—21no—
201D20—21no—
202D20—21no—
203C4×D5—41no—
204C4×D5—41no—
205Dic10—21no—
206Dic10—21no—
207C5×C8—22no—
208#168—41no—
209#168—41no—
210C2×SD16—101no—
211C4⋊Q8C2×C3×D511yescharacteristic
212C4⋊Q8C2×C3×D511yescharacteristic
213#126—102no—
214#124—101no—
215C22⋊Q8—101no—
216C4×Q8—51no—
217C4×Q8—101no—
218C4×D4—51no—
219#117—101no—
220#107—22no—
221#106—101no—
222C4⋊C8—51no—
223C4⋊C8—51no—
224#103—101no—
225#103—101no—
226C4×C8C2×C3×D511yescharacteristic
227C2×C3×C5#44911yescharacteristic
228C2×C3×C5#45211yescharacteristic
229C2×C3×C5#45611yescharacteristic
230C3×D5—81no—
231C23×C3—101no—
232C3×Q8—41no—
233C3×Q8—41no—
234C3×Q8—41no—
235C3×Q8—41no—
236C3×Q8—101no—
237C3×Q8—101no—
238C3×D4—101no—
239C3×D4—101no—
240C2×C3×C4—22no—
241C2×C3×C4—41no—
242C2×C3×C4—101no—
243C2×C3×C4—101no—
244C2×C3×C4—101no—
245C2×C3×C4—201no—
246C2×C3×C4—201no—
247C2×C3×C4D4×D511yescharacteristic
248C2×C3×C4D4×D511yescharacteristic
249C2×C3×C4C2×C22⋊D511yescharacteristic
250C3×C8—22no—
251C3×C8—201no—
252C3×C8—201no—
253C22×C5C3×#12011yescharacteristic
254C2×D5—41no—
255C2×D5—41no—
256C2×D5—41no—
257C4×C5—21no—
258C4×C5—42no—
259C4×C5—81no—
260C4×C5C3×#13511yescharacteristic
261C4×C5C3×#13511yescharacteristic
262C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
263C4×C5C3×#13711yescharacteristic
264Dic5—41no—
265Dic5—41no—
266Dic5—41no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—51no—
270C2×D4—51no—
271C22×C4—101no—
272SD16—202no—
273C2×C8—21no—
274C2×C8—101no—
275C2×C8—101no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—51no—
280C4⋊C4—51no—
281C4⋊C4—102no—
282C4⋊C4—101no—
283C4⋊C4C3×C22⋊D512yes—
284C22⋊C4—102no—
285C22⋊C4—102no—
286C22⋊C4—101no—
287C42—102no—
288C42—101no—
289C42C22×C3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3—201no—
292C22×C3—201no—
293C22×C3—201no—
294C22×C3#408311yescharacteristic
295C3×C4—21no—
296C3×C4—42no—
297C3×C4—81no—
298C3×C4—201no—
299C3×C4—201no—
300C3×C4—201no—
301C3×C4#405711yescharacteristic
302C3×C4#405811yescharacteristic
303C3×C4#406411yescharacteristic
304C3×C4#406511yescharacteristic
305C2×C5C3×#44911yescharacteristic
306C2×C5C3×#45211yescharacteristic
307C2×C5C3×#45611yescharacteristic
308D5—81no—
309C23—101no—
310Q8—41no—
311Q8—41no—
312Q8—41no—
313Q8—41no—
314Q8—101no—
315Q8—101no—
316D4—101no—
317D4—101no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—101no—
321C2×C4—101no—
322C2×C4—101no—
323C2×C4—201no—
324C2×C4—201no—
325C2×C4C3×D4×D511yescharacteristic
326C2×C4C3×D4×D511yescharacteristic
327C2×C4C2×C3×C22⋊D511yescharacteristic
328C8—22no—
329C8—201no—
330C8—201no—
331C2×C3—401no—
332C2×C3#6538411yescharacteristic
333C2×C3#6544711yescharacteristic
334C2×C3#6547611yescharacteristic
335C5C3×#165011yescharacteristic, complemented, Sylow
336C22—201no—
337C22—201no—
338C22—201no—
339C22C3×#408311yescharacteristic
340C4—21no—
341C4—42no—
342C4—81no—
343C4—201no—
344C4—201no—
345C4—201no—
346C4C3×#405711yescharacteristic
347C4C3×#405811yescharacteristic
348C4C3×#406411yescharacteristic
349C4C3×#406511yescharacteristic
350C3#1060216311yescharacteristic, direct product factor, Sylow
351C2—401no—
352C2C3×#6538411yescharacteristic
353C2C3×#6544711yescharacteristic
354C2C3×#6547611yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#500C2
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC3×#500D5
hypocenterC5C3×#1650
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#500

Complements

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

NH ≅ G/Ntype
2. C3×C5×#500C2semidirect
3. C3×#65383C2semidirect
5. C3×#64767C2semidirect
7. C3×#64676C2semidirect
8. #10602163C3direct (N × H)
28. C5×#500C2×C3semidirect
29. #65383C2×C3semidirect
31. #64767C2×C3semidirect
33. #64676C2×C3semidirect
58. C3×#500D5semidirect
145. #500C3×D5semidirect
290. C3×C5#1650semidirect
335. C5C3×#1650semidirect
350. C3#10602163direct (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×#5002
C3×#653832
C3×#653722
C3×#647672
C3×#646792
C3×#646762
#106021633
C3×#16505