Finite Group Databasebeta

← C3×#10602135 #14290628

Subgroups — C3×#10602135 #14290628

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66061C211yesmaximal, characteristic
2C3×C5×#498C211yesmaximal, characteristic, complemented
3C3×#65383C211yesmaximal, characteristic, complemented
4C3×#65372C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic
7C3×#64676C211yesmaximal, characteristic, complemented
8#10602135C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×Q8×D5—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×#4092—21no—
13C2×C3×#688—21no—
14C3×#4042—22no—
15C3×#4039—21no—
16C3×#4034—21no—
17C3×C4×D20C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C3×C5×#106—22no—
20C3×C4×C5×C8C2211yescharacteristic
21C3×#3967—21no—
22C3×#3942—21no—
23C3×#3940—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1651—51nomaximal, Hall
27#66061C2×C311yescharacteristic
28C5×#498C2×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—
36C3×Q8×D5—42no—
37C3×Q8×D5—42no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—22no—
40C2×C3×C4×D5—21no—
41C2×C3×Dic10—22no—
42C2×C3×Dic10D411yescharacteristic
43C2×C3×C5×C8—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D412yes—
48C3×C42×C5C2311yescharacteristic
49C3×#688—42no—
50C3×#685—22no—
51C3×#685—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×C4⋊Dic5D411yescharacteristic
54C3×#683—22no—
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59C3×D4×Q8—51no—
60C3×#498D511yescharacteristic, complemented
61C3×#475—51no—
62C3×#461—51no—
63C3×#332—51no—
64C3×Q8⋊C8—51no—
65C3×D4⋊C8—51no—
66C2×Q8×D5—21no—
67C5×C4⋊Q8C22×C311yescharacteristic
68C5×C4⋊Q8C22×C311yescharacteristic
69#4092—21no—
70C2×#688—21no—
71#4042—22no—
72#4039—21no—
73#4034—21no—
74C4×D20C22×C311yescharacteristic
75C4×Dic10C22×C311yescharacteristic
76C5×#106—22no—
77C4×C5×C8C22×C311yescharacteristic
78#3967—21no—
79#3942—21no—
80#3940—21no—
81C4⋊#168C22×C311yescharacteristic
82C4⋊#168C22×C311yescharacteristic
83#1651—51noSylow
84C22×C3×D5—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C3×C5×Q8—41no—
88C3×C5×Q8—41no—
89C2×C3×C4×C5—22no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×Dic5—21no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—21no—
97C3×D20—21no—
98C3×D20SD1612yes—
99C3×C4×D5—44no—
100C3×C4×D5—41no—
101C3×C4×D5—41no—
102C3×Dic10—21no—
103C3×Dic10—44no—
104C3×Dic10SD1612yescomplemented
105C3×C5×C8—22no—
106C3×#168—41no—
107C3×#168—41no—
108C22×C3×Q8—101no—
109C2×C3×SD16—101no—
110C3×C4⋊Q8—101no—
111C3×C4⋊Q8C2×D511yescharacteristic
112C3×C4⋊Q8C2×D511yescharacteristic
113C3×C22⋊Q8—101no—
114C3×C22⋊Q8—102no—
115C3×C4×Q8—51no—
116C3×C4×D4—51no—
117C3×C4×D4—101no—
118C3×#106—22no—
119C3×#106—101no—
120C3×C4⋊C8—51no—
121C3×C4⋊C8—51no—
122C3×#103—101no—
123C3×#103—101no—
124C3×C4×C8C2×D511yescharacteristic
125C2×C5×Q8—21no—
126C2×C5×Q8—21no—
127Q8×D5—42no—
128Q8×D5—42no—
129C2×D20C3×D411yescharacteristic
130C2×C4×D5—22no—
131C2×C4×D5—21no—
132C2×Dic10—22no—
133C2×Dic10C3×D411yescharacteristic
134C2×C5×C8—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4C3×D412yes—
139C42×C5C23×C311yescharacteristic
140#688—42no—
141#685—22no—
142#685—21no—
143C4⋊Dic5C3×D411yescharacteristic
144C4⋊Dic5C3×D411yescharacteristic
145#683—22no—
146#683—21no—
147C4×Dic5—21no—
148C2×#168—21no—
149C2×#168—21no—
150D4×Q8—51no—
151#498C3×D511yescharacteristic, complemented
152#475—51no—
153#461—51no—
154#332—51no—
155Q8⋊C8—51no—
156D4⋊C8—51no—
157C22×C3×C5#12011yescharacteristic
158C2×C3×D5—22no—
159C2×C3×D5—41no—
160C2×C3×D5—41no—
161C3×C4×C5—21no—
162C3×C4×C5—42no—
163C3×C4×C5—81no—
164C3×C4×C5C2×SD1611yescharacteristic
165C3×C4×C5C2×SD1611yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5#13711yescharacteristic
168C3×Dic5—22no—
169C3×Dic5—41no—
170C3×Dic5—41no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—51no—
174C2×C3×Q8—102no—
175C2×C3×Q8—202no—
176C2×C3×Q8—202no—
177C2×C3×D4—51no—
178C22×C3×C4—102no—
179C22×C3×C4—101no—
180C3×SD16—202no—
181C2×C3×C8—21no—
182C2×C3×C8—101no—
183C2×C3×C8—101no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—51no—
188C3×C4⋊C4—51no—
189C3×C4⋊C4—102no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4C22⋊D512yes—
192C3×C22⋊C4—102no—
193C3×C22⋊C4—101no—
194C3×C42—101no—
195C3×C42C22×D511yescharacteristic
196C22×D5—21no—
197C5×Q8—41no—
198C5×Q8—41no—
199C5×Q8—41no—
200C5×Q8—41no—
201C2×C4×C5—22no—
202C2×C4×C5—41no—
203C2×C4×C5C2×C3×D411yescharacteristic
204C2×C4×C5C2×C3×D411yescharacteristic
205C2×C4×C5C2×C3×D411yescharacteristic
206C2×Dic5—21no—
207C2×Dic5—21no—
208C2×Dic5—21no—
209D20—21no—
210D20C3×SD1612yes—
211C4×D5—44no—
212C4×D5—41no—
213C4×D5—41no—
214Dic10—21no—
215Dic10—44no—
216Dic10C3×SD1612yescomplemented
217C5×C8—22no—
218#168—41no—
219#168—41no—
220C22×Q8—101no—
221C2×SD16—101no—
222C4⋊Q8—101no—
223C4⋊Q8C2×C3×D511yescharacteristic
224C4⋊Q8C2×C3×D511yescharacteristic
225C22⋊Q8—101no—
226C22⋊Q8—102no—
227C4×Q8—51no—
228C4×D4—51no—
229C4×D4—101no—
230#106—22no—
231#106—101no—
232C4⋊C8—51no—
233C4⋊C8—51no—
234#103—101no—
235#103—101no—
236C4×C8C2×C3×D511yescharacteristic
237C2×C3×C5#44811yescharacteristic
238C2×C3×C5#45011yescharacteristic
239C2×C3×C5#45611yescharacteristic
240C3×D5—42no—
241C23×C3—101no—
242C3×Q8—41no—
243C3×Q8—41no—
244C3×Q8—41no—
245C3×Q8—41no—
246C3×Q8—52no—
247C3×Q8—101no—
248C3×Q8—204no—
249C3×D4—52no—
250C3×D4—101no—
251C2×C3×C4—22no—
252C2×C3×C4—41no—
253C2×C3×C4—101no—
254C2×C3×C4—101no—
255C2×C3×C4—101no—
256C2×C3×C4—204no—
257C2×C3×C4—201no—
258C2×C3×C4—201no—
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4C2×C22⋊D511yescharacteristic
262C3×C8—22no—
263C3×C8—201no—
264C3×C8—201no—
265C22×C5C3×#12011yescharacteristic
266C2×D5—22no—
267C2×D5—41no—
268C2×D5—41no—
269C4×C5—21no—
270C4×C5—42no—
271C4×C5—81no—
272C4×C5C2×C3×SD1611yescharacteristic
273C4×C5C2×C3×SD1611yescharacteristic
274C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
275C4×C5C3×#13711yescharacteristic
276Dic5—22no—
277Dic5—41no—
278Dic5—41no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—51no—
282C2×Q8—102no—
283C2×Q8—202no—
284C2×Q8—202no—
285C2×D4—51no—
286C22×C4—102no—
287C22×C4—101no—
288SD16—202no—
289C2×C8—21no—
290C2×C8—101no—
291C2×C8—101no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—51no—
296C4⋊C4—51no—
297C4⋊C4—102no—
298C4⋊C4—101no—
299C4⋊C4C3×C22⋊D512yes—
300C22⋊C4—102no—
301C22⋊C4—101no—
302C42—101no—
303C42C22×C3×D511yescharacteristic
304C3×C5#165111yescharacteristic, complemented, Hall
305C22×C3—102no—
306C22×C3—201no—
307C22×C3—201no—
308C22×C3#408311yescharacteristic
309C3×C4—21no—
310C3×C4—42no—
311C3×C4—81no—
312C3×C4—102no—
313C3×C4—201no—
314C3×C4—201no—
315C3×C4D5×SD1611yescharacteristic
316C3×C4D5×SD1611yescharacteristic
317C3×C4#406011yescharacteristic
318C3×C4#406111yescharacteristic
319C2×C5C3×#44811yescharacteristic
320C2×C5C3×#45011yescharacteristic
321C2×C5C3×#45611yescharacteristic
322D5—42no—
323C23—101no—
324Q8—41no—
325Q8—41no—
326Q8—41no—
327Q8—41no—
328Q8—52no—
329Q8—101no—
330Q8—204no—
331D4—52no—
332D4—101no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—101no—
336C2×C4—101no—
337C2×C4—101no—
338C2×C4—204no—
339C2×C4—201no—
340C2×C4—201no—
341C2×C4C3×D4×D511yescharacteristic
342C2×C4C3×D4×D511yescharacteristic
343C2×C4C2×C3×C22⋊D511yescharacteristic
344C8—22no—
345C8—201no—
346C8—201no—
347C2×C3—202no—
348C2×C3#6538411yescharacteristic
349C2×C3#6545811yescharacteristic
350C2×C3#6545911yescharacteristic
351C5C3×#165111yescharacteristic, complemented, Sylow
352C22—102no—
353C22—201no—
354C22—201no—
355C22C3×#408311yescharacteristic
356C4—21no—
357C4—42no—
358C4—81no—
359C4—102no—
360C4—201no—
361C4—201no—
362C4C3×D5×SD1611yescharacteristic
363C4C3×D5×SD1611yescharacteristic
364C4C3×#406011yescharacteristic
365C4C3×#406111yescharacteristic
366C3#1060213511yescharacteristic, direct product factor, Sylow
367C2—202no—
368C2C3×#6538411yescharacteristic
369C2C3×#6545811yescharacteristic
370C2C3×#6545911yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#498C2
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC3×#498D5
hypocenterC5C3×#1651
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#498

Complements

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

NH ≅ G/Ntype
2. C3×C5×#498C2semidirect
3. C3×#65383C2semidirect
5. C3×#64767C2semidirect
7. C3×#64676C2semidirect
8. #10602135C3direct (N × H)
28. C5×#498C2×C3semidirect
29. #65383C2×C3semidirect
31. #64767C2×C3semidirect
33. #64676C2×C3semidirect
60. C3×#498D5semidirect
104. C3×Dic10SD16semidirect
151. #498C3×D5semidirect
216. Dic10C3×SD16semidirect
304. C3×C5#1651semidirect
351. C5C3×#1651semidirect
366. C3#10602135direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660612
C3×C5×#4982
C3×#653832
C3×#653722
C3×#647672
C3×#646792
C3×#646762
#106021353
C3×#16515