Finite Group Databasebeta

← C3×#10599801 #14307993

Subgroups — C3×#10599801 #14307993

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
1C2×C3×#4054C212yesmaximal, complemented
2C3×#65844C211yesmaximal, characteristic, complemented
3C2×C3×#3957C212yesmaximal, complemented
4C3×#65277C211yesmaximal, characteristic, complemented
5C3×C5×#343C211yesmaximal, characteristic, complemented
6#10599801C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#709C2212yes—
8C22×C3×D20C2211yescharacteristic
9C2×C3×C5×M16C2212yes—
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C3×#4076—22no—
12C2×C3×#685—22no—
13C2×C3×C4×Dic5C2211yescharacteristic
14C3×#4054—24no—
15C3×#4054—24no—
16C2×C3×D40—22no—
17C2×C3×#677—22no—
18C3×#4043—22no—
19C3×#4041—22no—
20C3×#3957—24no—
21C3×#2006—51nomaximal, Hall
22C2×#4054C2×C312yescomplemented
23#65844C2×C311yescharacteristic, complemented
24C2×#3957C2×C312yescomplemented
25#65277C2×C311yescharacteristic, complemented
26C5×#343C2×C311yescharacteristic, complemented
27C23×C3×D5—21no—
28C22×C3×C4×C5D412yes—
29C22×C3×C4×C5C2311yescharacteristic
30C2×C3×C22⋊D5—22no—
31C22×C3×Dic5—21no—
32C3×#709—22no—
33C3×#709—22no—
34C3×#709—22no—
35C3×#709—22no—
36C2×C3×D20—22no—
37C2×C3×D20—22no—
38C2×C3×D20—21no—
39C2×C3×D20—22no—
40C2×C3×D20D412yes—
41C2×C3×D20D412yescomplemented
42C2×C3×C4×D5—22no—
43C2×C3×Dic10D412yes—
44C3×C5×M16—22no—
45C3×C5×M16D414yescomplemented
46C2×C3×C5×C8—22no—
47C3×C5×C4⋊C4—22no—
48C3×#685—24no—
49C3×#685—44no—
50C3×C4⋊Dic5—22no—
51C3×C4×Dic5—22no—
52C3×D40—28no—
53C3×#677—28no—
54C2×C3×AGL(1,ℤ/8)—52no—
55C3×#537—51no—
56C2×C3×#104—52no—
57C3×#390—51no—
58C3×#343D511yescharacteristic, complemented
59C2×#709C22×C312yes—
60C22×D20C22×C311yescharacteristic
61C2×C5×M16C22×C312yes—
62C2×C5×C4⋊C4C22×C311yescharacteristic
63#4076—22no—
64C2×#685—22no—
65C2×C4×Dic5C22×C311yescharacteristic
66#4054—24no—
67#4054—24no—
68C2×D40—22no—
69C2×#677—22no—
70#4043—22no—
71#4041—22no—
72#3957—24no—
73#2006—51noSylow
74C23×C3×C5C2×D411yescharacteristic
75C22×C3×D5—22no—
76C22×C3×D5—22no—
77C22×C3×D5—42no—
78C22×C3×D5—42no—
79C22×C3×D5—41no—
80C22×C3×D5—41no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—42no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D412yes—
85C2×C3×C4×C5C2×D412yes—
86C2×C3×C4×C5#4111yescharacteristic
87C3×C22⋊D5—42no—
88C3×C22⋊D5—42no—
89C2×C3×Dic5—22no—
90C2×C3×Dic5—22no—
91C2×C3×Dic5—41no—
92C2×C3×Dic5—41no—
93C3×D20—24no—
94C3×D20—22no—
95C3×D20—22no—
96C3×D20—42no—
97C3×D20—82no—
98C3×C4×D5—42no—
99C3×C4×D5—42no—
100C3×Dic10—22no—
101C3×Dic10—22no—
102C3×C5×C8—24no—
103C2×C3×#41—52no—
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×M16C2×D512yes—
110C3×C22⋊Q8—102no—
111C3×#121—102no—
112C3×#121—102no—
113C2×C3×C4⋊C4C2×D511yescharacteristic
114C2×C3×C22⋊C4—102no—
115C2×C3×C42—51no—
116C3×#104—104no—
117C23×D5—21no—
118C22×C4×C5C3×D412yes—
119C22×C4×C5C23×C311yescharacteristic
120C2×C22⋊D5—22no—
121C22×Dic5—21no—
122#709—22no—
123#709—22no—
124#709—22no—
125#709—22no—
126C2×D20—22no—
127C2×D20—22no—
128C2×D20—21no—
129C2×D20—22no—
130C2×D20C3×D412yes—
131C2×D20C3×D412yescomplemented
132C2×C4×D5—22no—
133C2×Dic10C3×D412yes—
134C5×M16—22no—
135C5×M16C3×D414yescomplemented
136C2×C5×C8—22no—
137C5×C4⋊C4—22no—
138#685—24no—
139#685—44no—
140C4⋊Dic5—22no—
141C4×Dic5—22no—
142D40—28no—
143#677—28no—
144C2×AGL(1,ℤ/8)—52no—
145#537—51no—
146C2×#104—52no—
147#390—51no—
148#343C3×D511yescharacteristic, complemented
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5#12011yescharacteristic
152C22×C3×C5#12111yescharacteristic
153C22×C3×C5#12711yescharacteristic
154C2×C3×D5—44no—
155C2×C3×D5—42no—
156C2×C3×D5—42no—
157C2×C3×D5—42no—
158C2×C3×D5—42no—
159C2×C3×D5—82no—
160C2×C3×D5—81no—
161C2×C3×D5—81no—
162C3×C4×C5—42no—
163C3×C4×C5#12012yes—
164C3×C4×C5#12112yes—
165C3×Dic5—42no—
166C3×Dic5—42no—
167C24×C3—101no—
168C3×#41—102no—
169C3×#41—102no—
170C3×#41—102no—
171C3×#41—102no—
172C2×C3×Q8—52no—
173C2×C3×D4—52no—
174C2×C3×D4—52no—
175C2×C3×D4—102no—
176C2×C3×D4—102no—
177C2×C3×D4—102no—
178C2×C3×D4—102no—
179C2×C3×D4—101no—
180C22×C3×C4—101no—
181C22×C3×C4—102no—
182C22×C3×C4D2012yes—
183C22×C3×C4C22×D511yescharacteristic
184C3×SD16—108no—
185C3×D8—108no—
186C3×M16—22no—
187C3×M16D2014yescomplemented
188C2×C3×C8—22no—
189C3×C4⋊C4—22no—
190C3×C4⋊C4—102no—
191C3×C22⋊C4—104no—
192C3×C22⋊C4—204no—
193C3×C42—102no—
194C23×C5C2×C3×D411yescharacteristic
195C22×D5—22no—
196C22×D5—22no—
197C22×D5—42no—
198C22×D5—42no—
199C22×D5—41no—
200C22×D5—41no—
201C2×C4×C5—22no—
202C2×C4×C5—42no—
203C2×C4×C5C2×C3×D412yes—
204C2×C4×C5C2×C3×D411yescharacteristic
205C2×C4×C5C2×C3×D412yes—
206C2×C4×C5C3×#4111yescharacteristic
207C22⋊D5—42no—
208C22⋊D5—42no—
209C2×Dic5—22no—
210C2×Dic5—22no—
211C2×Dic5—41no—
212C2×Dic5—41no—
213D20—24no—
214D20—22no—
215D20—22no—
216D20—42no—
217D20—82no—
218C4×D5—42no—
219C4×D5—42no—
220Dic10—22no—
221Dic10—22no—
222C5×C8—24no—
223C2×#41—52no—
224C22×D4—51no—
225AGL(1,ℤ/8)—104no—
226AGL(1,ℤ/8)—104no—
227C2×SD16—102no—
228C2×D8—102no—
229C2×M16C2×C3×D512yes—
230C22⋊Q8—102no—
231#121—102no—
232#121—102no—
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#39211yescharacteristic
240C2×C3×C5#45311yescharacteristic
241C2×C3×C5#45411yescharacteristic
242C3×D5—82no—
243C3×D5—82no—
244C23×C3—102no—
245C23×C3—102no—
246C23×C3—202no—
247C23×C3—202no—
248C23×C3—201no—
249C23×C3—201no—
250C23×C3C2×D2011yescharacteristic
251C3×Q8—102no—
252C3×Q8—102no—
253C3×D4—102no—
254C3×D4—104no—
255C3×D4—102no—
256C3×D4—202no—
257C3×D4—202no—
258C3×D4—202no—
259C3×D4—402no—
260C2×C3×C4—22no—
261C2×C3×C4—42no—
262C2×C3×C4—102no—
263C2×C3×C4—102no—
264C2×C3×C4—201no—
265C2×C3×C4—201no—
266C2×C3×C4—202no—
267C2×C3×C4—202no—
268C2×C3×C4C2×D2012yes—
269C2×C3×C4D4×D511yescharacteristic
270C2×C3×C4D4×D512yes—
271C2×C3×C4#71311yescharacteristic
272C3×C8—24no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5C3×#12011yescharacteristic
276C22×C5C3×#12111yescharacteristic
277C22×C5C3×#12711yescharacteristic
278C2×D5—44no—
279C2×D5—42no—
280C2×D5—42no—
281C2×D5—42no—
282C2×D5—42no—
283C2×D5—82no—
284C2×D5—81no—
285C2×D5—81no—
286C4×C5—42no—
287C4×C5C3×#12012yes—
288C4×C5C3×#12112yes—
289Dic5—42no—
290Dic5—42no—
291C24—101no—
292#41—102no—
293#41—102no—
294#41—102no—
295#41—102no—
296C2×Q8—52no—
297C2×D4—52no—
298C2×D4—52no—
299C2×D4—102no—
300C2×D4—102no—
301C2×D4—102no—
302C2×D4—102no—
303C2×D4—101no—
304C22×C4—101no—
305C22×C4—102no—
306C22×C4C3×D2012yes—
307C22×C4C22×C3×D511yescharacteristic
308SD16—108no—
309D8—108no—
310M16—22no—
311M16C3×D2014yescomplemented
312C2×C8—22no—
313C4⋊C4—22no—
314C4⋊C4—102no—
315C22⋊C4—104no—
316C22⋊C4—204no—
317C42—102no—
318C3×C5#200611yescharacteristic, complemented, Hall
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—204no—
322C22×C3—202no—
323C22×C3—202no—
324C22×C3—202no—
325C22×C3—202no—
326C22×C3—402no—
327C22×C3—401no—
328C22×C3—401no—
329C22×C3#402011yescharacteristic
330C22×C3#402811yescharacteristic
331C22×C3#404111yescharacteristic
332C3×C4—42no—
333C3×C4—202no—
334C3×C4—202no—
335C3×C4#402812yes—
336C3×C4#404112yes—
337C2×C5—21no—
338C2×C5—21no—
339C2×C5C3×#39211yescharacteristic
340C2×C5C3×#45311yescharacteristic
341C2×C5C3×#45411yescharacteristic
342D5—82no—
343D5—82no—
344C23—102no—
345C23—102no—
346C23—202no—
347C23—202no—
348C23—201no—
349C23—201no—
350C23C2×C3×D2011yescharacteristic
351Q8—102no—
352Q8—102no—
353D4—102no—
354D4—104no—
355D4—102no—
356D4—202no—
357D4—202no—
358D4—202no—
359D4—402no—
360C2×C4—22no—
361C2×C4—42no—
362C2×C4—102no—
363C2×C4—102no—
364C2×C4—201no—
365C2×C4—201no—
366C2×C4—202no—
367C2×C4—202no—
368C2×C4C2×C3×D2012yes—
369C2×C4C3×D4×D511yescharacteristic
370C2×C4C3×D4×D512yes—
371C2×C4C3×#71311yescharacteristic
372C8—24no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—402no—
376C2×C3—402no—
377C2×C3#6496011yescharacteristic
378C2×C3#6503611yescharacteristic
379C2×C3#6504211yescharacteristic
380C5C3×#200611yescharacteristic, complemented, Sylow
381C22—21no—
382C22—21no—
383C22—204no—
384C22—202no—
385C22—202no—
386C22—202no—
387C22—202no—
388C22—402no—
389C22—401no—
390C22—401no—
391C22C3×#402011yescharacteristic
392C22C3×#402811yescharacteristic
393C22C3×#404111yescharacteristic
394C4—42no—
395C4—202no—
396C4—202no—
397C4C3×#402812yes—
398C4C3×#404112yes—
399C3#1059980111yescharacteristic, direct product factor, Sylow
400C2—21no—
401C2—21no—
402C2—402no—
403C2—402no—
404C2C3×#6496011yescharacteristic
405C2C3×#6503611yescharacteristic
406C2C3×#6504211yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#343C2
socleC22×C3×C5#120
hypercenterC3×#343D5
hypocenterC5C3×#2006
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4054C2semidirect
2. C3×#65844C2semidirect
3. C2×C3×#3957C2semidirect
4. C3×#65277C2semidirect
5. C3×C5×#343C2semidirect
6. #10599801C3direct (N × H)
22. C2×#4054C2×C3semidirect
23. #65844C2×C3semidirect
24. C2×#3957C2×C3semidirect
25. #65277C2×C3semidirect
26. C5×#343C2×C3semidirect
41. C2×C3×D20D4semidirect
45. C3×C5×M16D4semidirect
58. C3×#343D5semidirect
131. C2×D20C3×D4semidirect
135. C5×M16C3×D4semidirect
148. #343C3×D5semidirect
187. C3×M16D20semidirect
311. M16C3×D20semidirect
318. C3×C5#2006semidirect
380. C5C3×#2006semidirect
399. C3#10599801direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40542
C3×#658442
C2×C3×#39572
C3×#652772
C3×C5×#3432
#105998013
C3×#20065