Finite Group Databasebeta

← C3×#10600457 #14307984

Subgroups — C3×#10600457 #14307984

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×#4078C212yesmaximal, complemented
2C3×#65844C211yesmaximal, characteristic, complemented
3C3×C5×#390C211yesmaximal, characteristic, complemented
4C2×C3×#3937C212yesmaximal, complemented
5C3×#64750C211yesmaximal, characteristic, complemented
6#10600457C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×C3×#709C2212yes—
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×C3×C5×C22⋊C4—22no—
11C2×C3×C42×C5C2211yescharacteristic
12C2×C3×#687—22no—
13C3×#4078—24no—
14C3×#4078—24no—
15C2×C3×#686—22no—
16C3×#4076—22no—
17C2×C3×#681C2212yes—
18C3×#4043—22no—
19C3×#4041—22no—
20C3×#3937—24no—
21C3×#2006—51nomaximal, Hall
22C2×#4078C2×C312yescomplemented
23#65844C2×C311yescharacteristic, complemented
24C5×#390C2×C311yescharacteristic, complemented
25C2×#3937C2×C312yescomplemented
26#64750C2×C311yescharacteristic, complemented
27C24×C3×C5—21no—
28C2×C3×C5×D4—22no—
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—21no—
31C2×C3×C5×D4D412yescomplemented
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5D412yes—
34C22×C3×C4×C5C2311yescharacteristic
35C2×C3×C22⋊D5—22no—
36C3×#709—22no—
37C3×#709—22no—
38C3×#709—22no—
39C3×#709—22no—
40C2×C3×D20—22no—
41C2×C3×D20D412yes—
42C2×C3×C4×D5—22no—
43C2×C3×Dic10D412yes—
44C3×C5×C4⋊C4—22no—
45C3×C5×C22⋊C4—44no—
46C3×C42×C5—22no—
47C3×#687—28no—
48C3×#686—28no—
49C3×#685—24no—
50C3×C4⋊Dic5—22no—
51C3×#681—22no—
52C3×#681D414yescomplemented
53C2×C3×#168—22no—
54C2×C3×AGL(1,ℤ/8)—52no—
55C3×#537—51no—
56C2×C3×#104—52no—
57C3×#390D511yescharacteristic, complemented
58C3×#343—51no—
59C22×C5×D4C22×C311yescharacteristic
60C2×#709C22×C312yes—
61C2×C5×C4⋊C4C22×C311yescharacteristic
62C2×C5×C22⋊C4—22no—
63C2×C42×C5C22×C311yescharacteristic
64C2×#687—22no—
65#4078—24no—
66#4078—24no—
67C2×#686—22no—
68#4076—22no—
69C2×#681C22×C312yes—
70#4043—22no—
71#4041—22no—
72#3937—24no—
73#2006—51noSylow
74C23×C3×C5—22no—
75C23×C3×C5—42no—
76C23×C3×C5—42no—
77C23×C3×C5—41no—
78C23×C3×C5—41no—
79C23×C3×C5C2×D411yescharacteristic
80C22×C3×D5—22no—
81C3×C5×D4—24no—
82C3×C5×D4—42no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—42no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D412yes—
90C2×C3×C4×C5C2×D412yes—
91C2×C3×C4×C5#4111yescharacteristic
92C3×C22⋊D5—42no—
93C3×C22⋊D5—42no—
94C2×C3×Dic5—22no—
95C3×D20—22no—
96C3×D20—22no—
97C3×D20—82no—
98C3×C4×D5—42no—
99C3×C4×D5—42no—
100C3×Dic10—22no—
101C3×Dic10—22no—
102C3×#168—24no—
103C2×C3×#41—52no—
104C22×C3×D4C2×D511yescharacteristic
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—102no—
111C3×#121—102no—
112C3×#121—102no—
113C2×C3×C4⋊C4C2×D511yescharacteristic
114C2×C3×C22⋊C4—22no—
115C2×C3×C42C2×D511yescharacteristic
116C3×#104—104no—
117C24×C5—21no—
118C2×C5×D4—22no—
119C2×C5×D4—22no—
120C2×C5×D4—21no—
121C2×C5×D4C3×D412yescomplemented
122C22×C4×C5—21no—
123C22×C4×C5C3×D412yes—
124C22×C4×C5C23×C311yescharacteristic
125C2×C22⋊D5—22no—
126#709—22no—
127#709—22no—
128#709—22no—
129#709—22no—
130C2×D20—22no—
131C2×D20C3×D412yes—
132C2×C4×D5—22no—
133C2×Dic10C3×D412yes—
134C5×C4⋊C4—22no—
135C5×C22⋊C4—44no—
136C42×C5—22no—
137#687—28no—
138#686—28no—
139#685—24no—
140C4⋊Dic5—22no—
141#681—22no—
142#681C3×D414yescomplemented
143C2×#168—22no—
144C2×AGL(1,ℤ/8)—52no—
145#537—51no—
146C2×#104—52no—
147#390C3×D511yescharacteristic, complemented
148#343—51no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—44no—
152C22×C3×C5—42no—
153C22×C3×C5—82no—
154C22×C3×C5—81no—
155C22×C3×C5—81no—
156C22×C3×C5#12011yescharacteristic
157C22×C3×C5#12111yescharacteristic
158C22×C3×C5#12711yescharacteristic
159C2×C3×D5—42no—
160C2×C3×D5—42no—
161C2×C3×D5—42no—
162C3×C4×C5—42no—
163C3×C4×C5—42no—
164C3×C4×C5#12012yes—
165C3×C4×C5#12112yes—
166C3×Dic5—42no—
167C24×C3—21no—
168C3×#41—102no—
169C3×#41—102no—
170C3×#41—102no—
171C3×#41—102no—
172C2×C3×Q8—52no—
173C2×C3×D4—21no—
174C2×C3×D4—22no—
175C2×C3×D4—22no—
176C2×C3×D4—52no—
177C2×C3×D4—102no—
178C2×C3×D4—102no—
179C2×C3×D4D2012yescomplemented
180C22×C3×C4—21no—
181C22×C3×C4—102no—
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—102no—
191C3×C22⋊C4—44no—
192C3×C22⋊C4—104no—
193C3×C42—22no—
194C23×C5—22no—
195C23×C5—42no—
196C23×C5—42no—
197C23×C5—41no—
198C23×C5—41no—
199C23×C5C2×C3×D411yescharacteristic
200C22×D5—22no—
201C5×D4—24no—
202C5×D4—42no—
203C2×C4×C5—22no—
204C2×C4×C5—22no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—42no—
208C2×C4×C5C2×C3×D411yescharacteristic
209C2×C4×C5C2×C3×D412yes—
210C2×C4×C5C2×C3×D412yes—
211C2×C4×C5C3×#4111yescharacteristic
212C22⋊D5—42no—
213C22⋊D5—42no—
214C2×Dic5—22no—
215D20—22no—
216D20—22no—
217D20—82no—
218C4×D5—42no—
219C4×D5—42no—
220Dic10—22no—
221Dic10—22no—
222#168—24no—
223C2×#41—52no—
224C22×D4C2×C3×D511yescharacteristic
225AGL(1,ℤ/8)—104no—
226AGL(1,ℤ/8)—104no—
227C2×SD16—102no—
228C2×D8—102no—
229C2×M16—52no—
230C22⋊Q8—102no—
231#121—102no—
232#121—102no—
233C2×C4⋊C4C2×C3×D511yescharacteristic
234C2×C22⋊C4—22no—
235C2×C42C2×C3×D511yescharacteristic
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—42no—
246C23×C3—42no—
247C23×C3—41no—
248C23×C3—41no—
249C23×C3—102no—
250C23×C3C2×C22⋊D511yescharacteristic
251C3×Q8—102no—
252C3×Q8—102no—
253C3×D4—24no—
254C3×D4—42no—
255C3×D4—102no—
256C3×D4—102no—
257C3×D4—202no—
258C3×D4—202no—
259C3×D4—402no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—42no—
265C2×C3×C4—102no—
266C2×C3×C4—202no—
267C2×C3×C4—202no—
268C2×C3×C4C2×D2011yescharacteristic
269C2×C3×C4#70911yescharacteristic
270C2×C3×C4D4×D512yes—
271C2×C3×C4D4×D512yes—
272C3×C8—104no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—44no—
276C22×C5—42no—
277C22×C5—82no—
278C22×C5—81no—
279C22×C5—81no—
280C22×C5C3×#12011yescharacteristic
281C22×C5C3×#12111yescharacteristic
282C22×C5C3×#12711yescharacteristic
283C2×D5—42no—
284C2×D5—42no—
285C2×D5—42no—
286C4×C5—42no—
287C4×C5—42no—
288C4×C5C3×#12012yes—
289C4×C5C3×#12112yes—
290Dic5—42no—
291C24—21no—
292#41—102no—
293#41—102no—
294#41—102no—
295#41—102no—
296C2×Q8—52no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—52no—
301C2×D4—102no—
302C2×D4—102no—
303C2×D4C3×D2012yescomplemented
304C22×C4—21no—
305C22×C4—102no—
306C22×C4C3×C22⋊D512yes—
307C22×C4C22×C3×D511yescharacteristic
308SD16—108no—
309D8—108no—
310M16—54no—
311M16—102no—
312C2×C8—102no—
313C4⋊C4—22no—
314C4⋊C4—102no—
315C22⋊C4—44no—
316C22⋊C4—104no—
317C42—22no—
318C3×C5#200611yescharacteristic, complemented, Hall
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—44no—
322C22×C3—42no—
323C22×C3—82no—
324C22×C3—81no—
325C22×C3—81no—
326C22×C3—202no—
327C22×C3—202no—
328C22×C3—202no—
329C22×C3#407611yescharacteristic
330C22×C3#408311yescharacteristic
331C22×C3#408611yescharacteristic
332C3×C4—42no—
333C3×C4—42no—
334C3×C4—202no—
335C3×C4#402812yes—
336C3×C4#403012yes—
337C2×C5—21no—
338C2×C5—21no—
339C2×C5—82no—
340C2×C5C3×#39211yescharacteristic
341C2×C5C3×#45311yescharacteristic
342C2×C5C3×#45411yescharacteristic
343D5—82no—
344C23—22no—
345C23—42no—
346C23—42no—
347C23—41no—
348C23—41no—
349C23—102no—
350C23C2×C3×C22⋊D511yescharacteristic
351Q8—102no—
352Q8—102no—
353D4—24no—
354D4—42no—
355D4—102no—
356D4—102no—
357D4—202no—
358D4—202no—
359D4—402no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—102no—
366C2×C4—202no—
367C2×C4—202no—
368C2×C4C2×C3×D2011yescharacteristic
369C2×C4C3×#70911yescharacteristic
370C2×C4C3×D4×D512yes—
371C2×C4C3×D4×D512yes—
372C8—104no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—82no—
376C2×C3—402no—
377C2×C3#6524911yescharacteristic
378C2×C3#6535111yescharacteristic
379C2×C3#6536611yescharacteristic
380C5C3×#200611yescharacteristic, complemented, Sylow
381C22—21no—
382C22—21no—
383C22—44no—
384C22—42no—
385C22—82no—
386C22—81no—
387C22—81no—
388C22—202no—
389C22—202no—
390C22—202no—
391C22C3×#407611yescharacteristic
392C22C3×#408311yescharacteristic
393C22C3×#408611yescharacteristic
394C4—42no—
395C4—42no—
396C4—202no—
397C4C3×#402812yes—
398C4C3×#403012yes—
399C3#1060045711yescharacteristic, direct product factor, Sylow
400C2—21no—
401C2—21no—
402C2—82no—
403C2—402no—
404C2C3×#6524911yescharacteristic
405C2C3×#6535111yescharacteristic
406C2C3×#6536611yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#390C2
socleC22×C3×C5#120
hypercenterC3×#390D5
hypocenterC5C3×#2006
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4078C2semidirect
2. C3×#65844C2semidirect
3. C3×C5×#390C2semidirect
4. C2×C3×#3937C2semidirect
5. C3×#64750C2semidirect
6. #10600457C3direct (N × H)
22. C2×#4078C2×C3semidirect
23. #65844C2×C3semidirect
24. C5×#390C2×C3semidirect
25. C2×#3937C2×C3semidirect
26. #64750C2×C3semidirect
31. C2×C3×C5×D4D4semidirect
52. C3×#681D4semidirect
57. C3×#390D5semidirect
121. C2×C5×D4C3×D4semidirect
142. #681C3×D4semidirect
147. #390C3×D5semidirect
179. C2×C3×D4D20semidirect
303. C2×D4C3×D20semidirect
318. C3×C5#2006semidirect
380. C5C3×#2006semidirect
399. C3#10600457direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40782
C3×#658442
C3×C5×#3902
C2×C3×#39372
C3×#647502
#106004573
C3×#20065