Finite Group Databasebeta

← C3×#10602672 #14307987

Subgroups — C3×#10602672 #14307987

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#537C211yesmaximal, characteristic, complemented
2C2×C3×#4095C212yesmaximal, complemented
3C2×C3×#3969C212yesmaximal, complemented
4C3×#65277C211yesmaximal, characteristic, complemented
5C3×#64750C211yesmaximal, characteristic, complemented
6#10602672C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×#41C2212yes—
8C22×C3×D20C2211yescharacteristic
9C3×C5×C22⋊Q8—22no—
10C3×C5×#121—22no—
11C3×C5×#121—22no—
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C3×#4095—24no—
14C3×#4095—24no—
15C2×C3×#688—22no—
16C2×C3×#686—22no—
17C2×C3×#685—22no—
18C2×C3×C4×Dic5C2211yescharacteristic
19C2×C3×#681C2212yes—
20C3×#3969—24no—
21C3×#2006—51nomaximal, Hall
22C5×#537C2×C311yescharacteristic, complemented
23C2×#4095C2×C312yescomplemented
24C2×#3969C2×C312yescomplemented
25#65277C2×C311yescharacteristic, complemented
26#64750C2×C311yescharacteristic, complemented
27C23×C3×D5—21no—
28C3×C5×#41—22no—
29C3×C5×#41—22no—
30C3×C5×#41—22no—
31C3×C5×#41—22no—
32C2×C3×C5×Q8D412yes—
33C2×C3×C5×D4—22no—
34C2×C3×C5×D4—22no—
35C2×C3×C5×D4D412yes—
36C22×C3×C4×C5—22no—
37C22×C3×C4×C5D412yes—
38C22×C3×C4×C5C2311yescharacteristic
39C22×C3×Dic5—21no—
40C2×C3×D20—22no—
41C2×C3×D20—22no—
42C2×C3×D20—21no—
43C2×C3×D20D412yescomplemented
44C3×C5×C4⋊C4—22no—
45C3×C5×C4⋊C4—22no—
46C3×C5×C22⋊C4—24no—
47C3×#688—28no—
48C3×#686—28no—
49C3×#685—44no—
50C3×C4×Dic5—22no—
51C3×#681—22no—
52C3×#681D414yescomplemented
53C2×C3×#168—22no—
54C2×C3×AGL(1,ℤ/8)—52no—
55C3×#537D511yescharacteristic, complemented
56C2×C3×#104—52no—
57C3×#390—51no—
58C3×#343—51no—
59C2×C5×#41C22×C312yes—
60C22×D20C22×C311yescharacteristic
61C5×C22⋊Q8—22no—
62C5×#121—22no—
63C5×#121—22no—
64C2×C5×C4⋊C4C22×C311yescharacteristic
65#4095—24no—
66#4095—24no—
67C2×#688—22no—
68C2×#686—22no—
69C2×#685—22no—
70C2×C4×Dic5C22×C311yescharacteristic
71C2×#681C22×C312yes—
72#3969—24no—
73#2006—51noSylow
74C23×C3×C5—22no—
75C23×C3×C5C2×D411yescharacteristic
76C22×C3×D5—22no—
77C22×C3×D5—42no—
78C22×C3×D5—42no—
79C22×C3×D5—41no—
80C22×C3×D5—41no—
81C3×C5×Q8—22no—
82C3×C5×Q8—22no—
83C3×C5×D4—22no—
84C3×C5×D4—22no—
85C3×C5×D4—42no—
86C3×C5×D4—42no—
87C3×C5×D4—82no—
88C2×C3×C4×C5—22no—
89C2×C3×C4×C5—22no—
90C2×C3×C4×C5—42no—
91C2×C3×C4×C5—42no—
92C2×C3×C4×C5—42no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D412yes—
95C2×C3×C4×C5C2×D412yes—
96C2×C3×C4×C5#4111yescharacteristic
97C2×C3×Dic5—22no—
98C2×C3×Dic5—41no—
99C2×C3×Dic5—41no—
100C3×D20—24no—
101C3×D20—42no—
102C3×#168—24no—
103C2×C3×#41C2×D512yes—
104C22×C3×D4—51no—
105C3×AGL(1,ℤ/8)—104no—
106C3×AGL(1,ℤ/8)—104no—
107C2×C3×SD16—102no—
108C2×C3×D8—102no—
109C2×C3×M16—52no—
110C3×C22⋊Q8—22no—
111C3×#121—22no—
112C3×#121—22no—
113C2×C3×C4⋊C4C2×D511yescharacteristic
114C2×C3×C22⋊C4—102no—
115C2×C3×C42—51no—
116C3×#104—104no—
117C23×D5—21no—
118C5×#41—22no—
119C5×#41—22no—
120C5×#41—22no—
121C5×#41—22no—
122C2×C5×Q8C3×D412yes—
123C2×C5×D4—22no—
124C2×C5×D4—22no—
125C2×C5×D4C3×D412yes—
126C22×C4×C5—22no—
127C22×C4×C5C3×D412yes—
128C22×C4×C5C23×C311yescharacteristic
129C22×Dic5—21no—
130C2×D20—22no—
131C2×D20—22no—
132C2×D20—21no—
133C2×D20C3×D412yescomplemented
134C5×C4⋊C4—22no—
135C5×C4⋊C4—22no—
136C5×C22⋊C4—24no—
137#688—28no—
138#686—28no—
139#685—44no—
140C4×Dic5—22no—
141#681—22no—
142#681C3×D414yescomplemented
143C2×#168—22no—
144C2×AGL(1,ℤ/8)—52no—
145#537C3×D511yescharacteristic, complemented
146C2×#104—52no—
147#390—51no—
148#343—51no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—42no—
152C22×C3×C5—42no—
153C22×C3×C5—42no—
154C22×C3×C5#12011yescharacteristic
155C22×C3×C5#12111yescharacteristic
156C22×C3×C5#12711yescharacteristic
157C2×C3×D5—44no—
158C2×C3×D5—42no—
159C2×C3×D5—82no—
160C2×C3×D5—81no—
161C2×C3×D5—81no—
162C3×C4×C5—42no—
163C3×C4×C5—42no—
164C3×C4×C5#12012yes—
165C3×C4×C5#12112yes—
166C3×Dic5—42no—
167C24×C3—101no—
168C3×#41—22no—
169C3×#41—22no—
170C3×#41—22no—
171C3×#41—22no—
172C2×C3×Q8C22⋊D512yes—
173C2×C3×D4—22no—
174C2×C3×D4—22no—
175C2×C3×D4—52no—
176C2×C3×D4—102no—
177C2×C3×D4—101no—
178C2×C3×D4—102no—
179C2×C3×D4C22⋊D512yes—
180C22×C3×C4—22no—
181C22×C3×C4—101no—
182C22×C3×C4C22⋊D512yes—
183C22×C3×C4C22×D511yescharacteristic
184C3×SD16—108no—
185C3×D8—108no—
186C3×M16—54no—
187C3×M16—102no—
188C2×C3×C8—102no—
189C3×C4⋊C4—22no—
190C3×C4⋊C4—22no—
191C3×C22⋊C4—24no—
192C3×C22⋊C4—204no—
193C3×C42—102no—
194C23×C5—22no—
195C23×C5C2×C3×D411yescharacteristic
196C22×D5—22no—
197C22×D5—42no—
198C22×D5—42no—
199C22×D5—41no—
200C22×D5—41no—
201C5×Q8—22no—
202C5×Q8—22no—
203C5×D4—22no—
204C5×D4—22no—
205C5×D4—42no—
206C5×D4—42no—
207C5×D4—82no—
208C2×C4×C5—22no—
209C2×C4×C5—22no—
210C2×C4×C5—42no—
211C2×C4×C5—42no—
212C2×C4×C5—42no—
213C2×C4×C5C2×C3×D411yescharacteristic
214C2×C4×C5C2×C3×D412yes—
215C2×C4×C5C2×C3×D412yes—
216C2×C4×C5C3×#4111yescharacteristic
217C2×Dic5—22no—
218C2×Dic5—41no—
219C2×Dic5—41no—
220D20—24no—
221D20—42no—
222#168—24no—
223C2×#41C2×C3×D512yes—
224C22×D4—51no—
225AGL(1,ℤ/8)—104no—
226AGL(1,ℤ/8)—104no—
227C2×SD16—102no—
228C2×D8—102no—
229C2×M16—52no—
230C22⋊Q8—22no—
231#121—22no—
232#121—22no—
233C2×C4⋊C4C2×C3×D511yescharacteristic
234C2×C22⋊C4—102no—
235C2×C42—51no—
236#104—104no—
237C2×C3×C5—21no—
238C2×C3×C5—21no—
239C2×C3×C5—82no—
240C2×C3×C5#39211yescharacteristic
241C2×C3×C5#45311yescharacteristic
242C2×C3×C5#45411yescharacteristic
243C3×D5—82no—
244C23×C3—22no—
245C23×C3—102no—
246C23×C3—202no—
247C23×C3—202no—
248C23×C3—201no—
249C23×C3—201no—
250C23×C3C2×C22⋊D511yescharacteristic
251C3×Q8—22no—
252C3×Q8—22no—
253C3×D4—22no—
254C3×D4—22no—
255C3×D4—42no—
256C3×D4—42no—
257C3×D4—82no—
258C3×D4—104no—
259C3×D4—202no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—42no—
265C2×C3×C4—102no—
266C2×C3×C4—201no—
267C2×C3×C4—201no—
268C2×C3×C4D4×D511yescharacteristic
269C2×C3×C4D4×D512yes—
270C2×C3×C4#71111yescharacteristic
271C2×C3×C4C2×C22⋊D512yes—
272C3×C8—104no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—42no—
276C22×C5—42no—
277C22×C5—42no—
278C22×C5C3×#12011yescharacteristic
279C22×C5C3×#12111yescharacteristic
280C22×C5C3×#12711yescharacteristic
281C2×D5—44no—
282C2×D5—42no—
283C2×D5—82no—
284C2×D5—81no—
285C2×D5—81no—
286C4×C5—42no—
287C4×C5—42no—
288C4×C5C3×#12012yes—
289C4×C5C3×#12112yes—
290Dic5—42no—
291C24—101no—
292#41—22no—
293#41—22no—
294#41—22no—
295#41—22no—
296C2×Q8C3×C22⋊D512yes—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—52no—
300C2×D4—102no—
301C2×D4—101no—
302C2×D4—102no—
303C2×D4C3×C22⋊D512yes—
304C22×C4—22no—
305C22×C4—101no—
306C22×C4C3×C22⋊D512yes—
307C22×C4C22×C3×D511yescharacteristic
308SD16—108no—
309D8—108no—
310M16—54no—
311M16—102no—
312C2×C8—102no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C22⋊C4—24no—
316C22⋊C4—204no—
317C42—102no—
318C3×C5#200611yescharacteristic, complemented, Hall
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—42no—
322C22×C3—42no—
323C22×C3—42no—
324C22×C3—204no—
325C22×C3—202no—
326C22×C3—402no—
327C22×C3—401no—
328C22×C3—401no—
329C22×C3#408411yescharacteristic
330C22×C3#408611yescharacteristic
331C22×C3#409911yescharacteristic
332C3×C4—42no—
333C3×C4—42no—
334C3×C4—202no—
335C3×C4#408312yes—
336C3×C4#408512yes—
337C2×C5—21no—
338C2×C5—21no—
339C2×C5—82no—
340C2×C5C3×#39211yescharacteristic
341C2×C5C3×#45311yescharacteristic
342C2×C5C3×#45411yescharacteristic
343D5—82no—
344C23—22no—
345C23—102no—
346C23—202no—
347C23—202no—
348C23—201no—
349C23—201no—
350C23C2×C3×C22⋊D511yescharacteristic
351Q8—22no—
352Q8—22no—
353D4—22no—
354D4—22no—
355D4—42no—
356D4—42no—
357D4—82no—
358D4—104no—
359D4—202no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—102no—
366C2×C4—201no—
367C2×C4—201no—
368C2×C4C3×D4×D511yescharacteristic
369C2×C4C3×D4×D512yes—
370C2×C4C3×#71111yescharacteristic
371C2×C4C2×C3×C22⋊D512yes—
372C8—104no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—82no—
376C2×C3—402no—
377C2×C3#6551211yescharacteristic
378C2×C3#6553011yescharacteristic
379C2×C3#6553411yescharacteristic
380C5C3×#200611yescharacteristic, complemented, Sylow
381C22—21no—
382C22—21no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—204no—
387C22—202no—
388C22—402no—
389C22—401no—
390C22—401no—
391C22C3×#408411yescharacteristic
392C22C3×#408611yescharacteristic
393C22C3×#409911yescharacteristic
394C4—42no—
395C4—42no—
396C4—202no—
397C4C3×#408312yes—
398C4C3×#408512yes—
399C3#1060267211yescharacteristic, direct product factor, Sylow
400C2—21no—
401C2—21no—
402C2—82no—
403C2—402no—
404C2C3×#6551211yescharacteristic
405C2C3×#6553011yescharacteristic
406C2C3×#6553411yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#537C2
socleC22×C3×C5#120
hypercenterC3×#537D5
hypocenterC5C3×#2006
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#537

Complements

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

NH ≅ G/Ntype
1. C3×C5×#537C2semidirect
2. C2×C3×#4095C2semidirect
3. C2×C3×#3969C2semidirect
4. C3×#65277C2semidirect
5. C3×#64750C2semidirect
6. #10602672C3direct (N × H)
22. C5×#537C2×C3semidirect
23. C2×#4095C2×C3semidirect
24. C2×#3969C2×C3semidirect
25. #65277C2×C3semidirect
26. #64750C2×C3semidirect
43. C2×C3×D20D4semidirect
52. C3×#681D4semidirect
55. C3×#537D5semidirect
133. C2×D20C3×D4semidirect
142. #681C3×D4semidirect
145. #537C3×D5semidirect
318. C3×C5#2006semidirect
380. C5C3×#2006semidirect
399. C3#10602672direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5372
C2×C3×#40952
C2×C3×#39692
C3×#652772
C3×#647502
#106026723
C3×#20065