Finite Group Databasebeta

← C3×#10600759 #14301985

Subgroups — C3×#10600759 #14301985

Order 1920.

716 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×#66125C211yesmaximal, characteristic
2C2×C3×#4072C211yesmaximal, characteristic, complemented
3C3×C5×#407C211yesmaximal, characteristic, complemented
4C2×C3×#3957C212yesmaximal, complemented
5C3×#64775C212yesmaximal, complemented
6#10600759C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C3×#709C2211yescharacteristic
9C2×C3×C5×M16C2212yes—
10C3×#4099—21no—
11C2×C3×C22⋊Dic5—21no—
12C3×#4076C412yescomplemented
13C3×#4075—21no—
14C3×C4×C22⋊D5—22no—
15C3×#4072—24no—
16C3×#4072C2211yescharacteristic
17C2×C3×C4⋊Dic5—21no—
18C3×#4070C412yescomplemented
19C2×C3×C4×Dic5C2212yes—
20C3×C5×C22⋊C8—22no—
21C3×#3957—24no—
22C3×#1897—51nomaximal, Hall
23#66125C2×C311yescharacteristic
24C2×#4072C2×C311yescharacteristic, complemented
25C5×#407C2×C311yescharacteristic, complemented
26C2×#3957C2×C312yescomplemented
27#64775C2×C312yescomplemented
28C24×C3×C5D411yescharacteristic
29C22×C3×C4×C5—22no—
30C22×C3×C4×C5—22no—
31C22×C3×C4×C5C2×C412yes—
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D412yes—
34C22×C3×C4×C5C2311yescharacteristic
35C2×C3×C22⋊D5—22no—
36C2×C3×C22⋊D5—21no—
37C22×C3×Dic5—22no—
38C3×#709—22no—
39C3×#709—22no—
40C2×C3×D20C2×C411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×C3×Dic10C2×C411yescharacteristic
43C3×C5×M16—22no—
44C3×C5×M16—22no—
45C2×C3×C5×C8—22no—
46C3×C22⋊Dic5—24no—
47C3×C22⋊Dic5—22no—
48C3×C22⋊Dic5—21no—
49C3×#685—22no—
50C3×C4⋊Dic5—24no—
51C3×C4⋊Dic5C2×C412yes—
52C3×#683—22no—
53C3×C4×Dic5—22no—
54C3×C4×Dic5—21no—
55C3×C4×Dic5D414yescomplemented
56C3×#525—51no—
57C2×C3×#117—51no—
58C2×C3×#104—52no—
59C3×#407D511yescharacteristic, complemented
60C3×#339—52no—
61C23×C4×C5C22×C311yescharacteristic
62C2×#709C22×C311yescharacteristic
63C2×C5×M16C22×C312yes—
64#4099—21no—
65C2×C22⋊Dic5—21no—
66#4076C3×C412yescomplemented
67#4075—21no—
68C4×C22⋊D5—22no—
69#4072—24no—
70#4072C22×C311yescharacteristic
71C2×C4⋊Dic5—21no—
72#4070C3×C412yescomplemented
73C2×C4×Dic5C22×C312yes—
74C5×C22⋊C8—22no—
75#3957—24no—
76#1897—51noSylow
77C23×C3×C5—21no—
78C23×C3×C5—21no—
79C23×C3×C5—42no—
80C23×C3×C5C22⋊C412yes—
81C23×C3×C5C2×D411yescharacteristic
82C22×C3×D5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—24no—
86C2×C3×C4×C5—24no—
87C2×C3×C4×C5C22⋊C412yes—
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D412yes—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5#4112yes—
92C3×C22⋊D5—44no—
93C3×C22⋊D5—41no—
94C3×C22⋊D5—41no—
95C2×C3×Dic5—22no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—24no—
98C2×C3×Dic5—44no—
99C3×D20—22no—
100C3×C4×D5—42no—
101C3×Dic10—22no—
102C3×C5×C8—42no—
103C2×C3×#41—51no—
104C23×C3×C4C2×D511yescharacteristic
105C2×C3×M16C2×D512yes—
106C3×#123—101no—
107C3×C22⋊Q8—52no—
108C3×#121—52no—
109C3×#120—101no—
110C3×C4×D4—102no—
111C3×#117—51no—
112C3×#117—104no—
113C2×C3×C4⋊C4—101no—
114C2×C3×C22⋊C4—101no—
115C2×C3×C42—52no—
116C3×#104—104no—
117C3×C22⋊C8—22no—
118C24×C5C3×D411yescharacteristic
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5C2×C3×C412yes—
122C22×C4×C5C3×D411yescharacteristic
123C22×C4×C5C3×D412yes—
124C22×C4×C5C23×C311yescharacteristic
125C2×C22⋊D5—22no—
126C2×C22⋊D5—21no—
127C22×Dic5—22no—
128#709—22no—
129#709—22no—
130C2×D20C2×C3×C411yescharacteristic
131C2×C4×D5—21no—
132C2×Dic10C2×C3×C411yescharacteristic
133C5×M16—22no—
134C5×M16—22no—
135C2×C5×C8—22no—
136C22⋊Dic5—24no—
137C22⋊Dic5—22no—
138C22⋊Dic5—21no—
139#685—22no—
140C4⋊Dic5—24no—
141C4⋊Dic5C2×C3×C412yes—
142#683—22no—
143C4×Dic5—22no—
144C4×Dic5—21no—
145C4×Dic5C3×D414yescomplemented
146#525—51no—
147C2×#117—51no—
148C2×#104—52no—
149#407C3×D511yescharacteristic, complemented
150#339—52no—
151C22×C3×C5—22no—
152C22×C3×C5—22no—
153C22×C3×C5—22no—
154C22×C3×C5—22no—
155C22×C3×C5—42no—
156C22×C3×C5—42no—
157C22×C3×C5C2×C22⋊C411yescharacteristic
158C22×C3×C5#12011yescharacteristic
159C22×C3×C5#12311yescharacteristic
160C2×C3×D5—41no—
161C2×C3×D5—42no—
162C3×C4×C5—22no—
163C3×C4×C5C4×D412yes—
164C3×C4×C5#12112yes—
165C3×Dic5—44no—
166C3×Dic5—41no—
167C3×Dic5—42no—
168C24×C3D2011yescharacteristic
169C3×#41—102no—
170C3×#41—102no—
171C2×C3×Q8—51no—
172C2×C3×D4—51no—
173C2×C3×D4—102no—
174C2×C3×D4—101no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—102no—
178C22×C3×C4—101no—
179C22×C3×C4C4×D512yes—
180C22×C3×C4D2011yescharacteristic
181C22×C3×C4C22⋊D512yes—
182C22×C3×C4C22×D511yescharacteristic
183C3×M16—22no—
184C3×M16—22no—
185C2×C3×C8—22no—
186C3×C4⋊C4—52no—
187C3×C4⋊C4—104no—
188C3×C4⋊C4—102no—
189C3×C22⋊C4—104no—
190C3×C22⋊C4—102no—
191C3×C22⋊C4—101no—
192C3×C22⋊C4—102no—
193C3×C42—54no—
194C3×C42—102no—
195C3×C42—101no—
196C23×C5—21no—
197C23×C5—21no—
198C23×C5—42no—
199C23×C5C3×C22⋊C412yes—
200C23×C5C2×C3×D411yescharacteristic
201C22×D5—21no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—24no—
205C2×C4×C5—24no—
206C2×C4×C5C3×C22⋊C412yes—
207C2×C4×C5C22×C3×C411yescharacteristic
208C2×C4×C5C2×C3×D412yes—
209C2×C4×C5C2×C3×D411yescharacteristic
210C2×C4×C5C3×#4112yes—
211C22⋊D5—44no—
212C22⋊D5—41no—
213C22⋊D5—41no—
214C2×Dic5—22no—
215C2×Dic5—21no—
216C2×Dic5—24no—
217C2×Dic5—44no—
218D20—22no—
219C4×D5—42no—
220Dic10—22no—
221C5×C8—42no—
222C2×#41—51no—
223C23×C4C2×C3×D511yescharacteristic
224C2×M16C2×C3×D512yes—
225#123—101no—
226C22⋊Q8—52no—
227#121—52no—
228#120—101no—
229C4×D4—102no—
230#117—51no—
231#117—104no—
232C2×C4⋊C4—101no—
233C2×C22⋊C4—101no—
234C2×C42—52no—
235#104—104no—
236C22⋊C8—22no—
237C2×C3×C5—21no—
238C2×C3×C5—21no—
239C2×C3×C5—42no—
240C2×C3×C5#38611yescharacteristic
241C2×C3×C5#42112yes—
242C3×D5—81no—
243C23×C3—21no—
244C23×C3—21no—
245C23×C3—42no—
246C23×C3—101no—
247C23×C3#68512yes—
248C23×C3C2×D2011yescharacteristic
249C3×Q8—102no—
250C3×D4—102no—
251C3×D4—204no—
252C3×D4—201no—
253C3×D4—201no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—24no—
257C2×C3×C4—24no—
258C2×C3×C4—104no—
259C2×C3×C4—102no—
260C2×C3×C4—101no—
261C2×C3×C4—204no—
262C2×C3×C4—202no—
263C2×C3×C4#68512yes—
264C2×C3×C4C2×C4×D511yescharacteristic
265C2×C3×C4D4×D512yes—
266C2×C3×C4#71112yes—
267C2×C3×C4C2×C22⋊D511yescharacteristic
268C3×C8—42no—
269C22×C5—22no—
270C22×C5—22no—
271C22×C5—22no—
272C22×C5—22no—
273C22×C5—42no—
274C22×C5—42no—
275C22×C5C2×C3×C22⋊C411yescharacteristic
276C22×C5C3×#12011yescharacteristic
277C22×C5C3×#12311yescharacteristic
278C2×D5—41no—
279C2×D5—42no—
280C4×C5—22no—
281C4×C5C3×C4×D412yes—
282C4×C5C3×#12112yes—
283Dic5—44no—
284Dic5—41no—
285Dic5—42no—
286C24C3×D2011yescharacteristic
287#41—102no—
288#41—102no—
289C2×Q8—51no—
290C2×D4—51no—
291C2×D4—102no—
292C2×D4—101no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—102no—
296C22×C4—101no—
297C22×C4C3×C4×D512yes—
298C22×C4C3×D2011yescharacteristic
299C22×C4C3×C22⋊D512yes—
300C22×C4C22×C3×D511yescharacteristic
301M16—22no—
302M16—22no—
303C2×C8—22no—
304C4⋊C4—52no—
305C4⋊C4—104no—
306C4⋊C4—102no—
307C22⋊C4—104no—
308C22⋊C4—102no—
309C22⋊C4—101no—
310C22⋊C4—102no—
311C42—54no—
312C42—102no—
313C42—101no—
314C3×C5#189711yescharacteristic, complemented, Hall
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—202no—
322C22×C3—201no—
323C22×C3#402811yescharacteristic
324C22×C3#403211yescharacteristic
325C22×C3C2×#68511yescharacteristic
326C3×C4—22no—
327C3×C4—204no—
328C3×C4—202no—
329C3×C4—201no—
330C3×C4#402712yes—
331C3×C4#408512yes—
332C2×C5—21no—
333C2×C5—21no—
334C2×C5—42no—
335C2×C5C3×#38611yescharacteristic
336C2×C5C3×#42112yes—
337D5—81no—
338C23—21no—
339C23—21no—
340C23—42no—
341C23—101no—
342C23C3×#68512yes—
343C23C2×C3×D2011yescharacteristic
344Q8—102no—
345D4—102no—
346D4—204no—
347D4—201no—
348D4—201no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—104no—
354C2×C4—102no—
355C2×C4—101no—
356C2×C4—204no—
357C2×C4—202no—
358C2×C4C3×#68512yes—
359C2×C4C2×C3×C4×D511yescharacteristic
360C2×C4C3×D4×D512yes—
361C2×C4C3×#71112yes—
362C2×C4C2×C3×C22⋊D511yescharacteristic
363C8—42no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—42no—
367C2×C3—401no—
368C2×C3#6524711yescharacteristic
369C2×C3#6542812yes—
370C5C3×#189711yescharacteristic, complemented, Sylow
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—42no—
376C22—42no—
377C22—202no—
378C22—201no—
379C22C3×#402811yescharacteristic
380C22C3×#403211yescharacteristic
381C22C2×C3×#68511yescharacteristic
382C4—22no—
383C4—204no—
384C4—202no—
385C4—201no—
386C4C3×#402712yes—
387C4C3×#408512yes—
388C3#1060075911yescharacteristic, direct product factor, Sylow
389C2—21no—
390C2—21no—
391C2—42no—
392C2—401no—
393C2C3×#6524711yescharacteristic
394C2C3×#6542812yes—
subgroupG/H
centerC2×C3×C4C2×C22⋊D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#407C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66125C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#407D5
hypocenterC5C3×#1897
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4072C2semidirect
3. C3×C5×#407C2semidirect
4. C2×C3×#3957C2semidirect
5. C3×#64775C2semidirect
6. #10600759C3direct (N × H)
12. C3×#4076C4semidirect
18. C3×#4070C4semidirect
24. C2×#4072C2×C3semidirect
25. C5×#407C2×C3semidirect
26. C2×#3957C2×C3semidirect
27. #64775C2×C3semidirect
55. C3×C4×Dic5D4semidirect
59. C3×#407D5semidirect
66. #4076C3×C4semidirect
72. #4070C3×C4semidirect
145. C4×Dic5C3×D4semidirect
149. #407C3×D5semidirect
314. C3×C5#1897semidirect
370. C5C3×#1897semidirect
388. C3#10600759direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661252
C2×C3×#40722
C3×C5×#4072
C2×C3×#39572
C3×#647752
#106007593
C3×#18975