Finite Group Databasebeta

← C3×#10601810 #14289050

Subgroups — C3×#10601810 #14289050

Order 1920.

480 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×#65897C211yesmaximal, characteristic, complemented
2C3×C5×#459C211yesmaximal, characteristic, complemented
3C3×#65365C211yesmaximal, characteristic, complemented
4C3×#65361C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic, complemented
7C3×#64701C211yesmaximal, characteristic, complemented
8#10601810C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×D8—21no—
10C3×C5×#127C2211yescharacteristic
11C3×C4×C5×D4C2211yescharacteristic
12C3×#4084—21no—
13C2×C3×#687—22no—
14C2×C3×#686—21no—
15C3×#4076—21no—
16C3×#4072—21no—
17C3×#4038—21no—
18C3×#4031—22no—
19C3×C4×D20C2211yescharacteristic
20C3×#4015C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×#102—21no—
23C3×#3964—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1624—51nomaximal, Hall
27#65897C2×C311yescharacteristic, complemented
28C5×#459C2×C311yescharacteristic, complemented
29#65365C2×C311yescharacteristic, complemented
30#65361C2×C311yescharacteristic, complemented
31D4⋊#168C2×C311yescharacteristic, complemented
32#64703C2×C311yescharacteristic, complemented
33#64701C2×C311yescharacteristic, complemented
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4D411yescharacteristic
38C22×C3×C4×C5—21no—
39C2×C3×C22⋊D5—22no—
40C2×C3×D20D411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×C3×Dic10D412yes—
43C3×C5×D8—42no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C5×C22⋊C4—21no—
47C3×C42×C5C2311yescharacteristic
48C3×C22⋊Dic5—22no—
49C3×#687—44no—
50C3×#686—42no—
51C3×#685—22no—
52C3×#685—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5D411yescharacteristic
56C3×C4×Dic5—22no—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59C3×#555—51no—
60C3×#492—51no—
61C3×#459—51no—
62C3×#459D511yescharacteristic, complemented
63C3×#333—51no—
64C3×D4⋊C8—51no—
65C3×D4⋊C8—51no—
66C2×C5×D8—21no—
67C5×#127C22×C311yescharacteristic
68C4×C5×D4C22×C311yescharacteristic
69#4084—21no—
70C2×#687—22no—
71C2×#686—21no—
72#4076—21no—
73#4072—21no—
74#4038—21no—
75#4031—22no—
76C4×D20C22×C311yescharacteristic
77#4015C22×C311yescharacteristic
78C5×C4⋊C8C22×C311yescharacteristic
79C5×#102—21no—
80#3964—21no—
81C4⋊#168C22×C311yescharacteristic
82C4×#168C22×C311yescharacteristic
83#1624—51noSylow
84C23×C3×C5—21no—
85C23×C3×C5—41no—
86C22×C3×D5—21no—
87C3×C5×D4—21no—
88C3×C5×D4—21no—
89C3×C5×D4—42no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C3×C22⋊D5—82no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—22no—
103C3×D20—21no—
104C3×D20—21no—
105C3×C4×D5—41no—
106C3×C4×D5—41no—
107C3×Dic10—42no—
108C3×C5×C8—41no—
109C3×#168—22no—
110C3×#168—41no—
111C2×C3×SD16—102no—
112C2×C3×D8—21no—
113C2×C3×D8—101no—
114C3×C4⋊Q8—51no—
115C3×#127C2×D511yescharacteristic
116C3×#124—102no—
117C3×#121—101no—
118C3×#121—101no—
119C3×C4×D4—51no—
120C3×C4×D4C2×D511yescharacteristic
121C3×#117—101no—
122C3×#117—101no—
123C3×C4⋊C8—51no—
124C3×C4⋊C8C2×D511yescharacteristic
125C3×#102—21no—
126C3×#102—101no—
127C3×C4×C8—51no—
128C2×C5×D4—21no—
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4C3×D411yescharacteristic
132C22×C4×C5—21no—
133C2×C22⋊D5—22no—
134C2×D20C3×D411yescharacteristic
135C2×C4×D5—21no—
136C2×Dic10C3×D412yes—
137C5×D8—42no—
138C2×C5×C8—21no—
139C5×C4⋊C4C3×D411yescharacteristic
140C5×C22⋊C4—21no—
141C42×C5C23×C311yescharacteristic
142C22⋊Dic5—22no—
143#687—44no—
144#686—42no—
145#685—22no—
146#685—21no—
147C4⋊Dic5—21no—
148C4⋊Dic5—21no—
149C4⋊Dic5C3×D411yescharacteristic
150C4×Dic5—22no—
151C2×#168—21no—
152C2×#168—21no—
153#555—51no—
154#492—51no—
155#459—51no—
156#459C3×D511yescharacteristic, complemented
157#333—51no—
158D4⋊C8—51no—
159D4⋊C8—51no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5—81no—
164C22×C3×C5—81no—
165C22×C3×C5—81no—
166C22×C3×C5#12011yescharacteristic
167C2×C3×D5—41no—
168C2×C3×D5—41no—
169C2×C3×D5—41no—
170C3×C4×C5—21no—
171C3×C4×C5—41no—
172C3×C4×C5#13511yescharacteristic
173C3×C4×C5#13511yescharacteristic
174C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
175C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
176C3×Dic5—41no—
177C3×Dic5—42no—
178C2×C3×Q8—52no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—51no—
183C2×C3×D4—102no—
184C2×C3×D4C22⋊D511yescharacteristic
185C22×C3×C4—21no—
186C22×C3×C4—101no—
187C3×SD16—204no—
188C3×D8—42no—
189C3×D8—202no—
190C2×C3×C8—21no—
191C2×C3×C8—101no—
192C2×C3×C8—101no—
193C3×C4⋊C4—51no—
194C3×C4⋊C4—101no—
195C3×C4⋊C4—101no—
196C3×C4⋊C4C22⋊D511yescharacteristic
197C3×C22⋊C4—21no—
198C3×C22⋊C4—102no—
199C3×C22⋊C4—102no—
200C3×C22⋊C4—101no—
201C3×C42—102no—
202C3×C42C22×D511yescharacteristic
203C23×C5—21no—
204C23×C5—41no—
205C22×D5—21no—
206C5×D4—21no—
207C5×D4—21no—
208C5×D4—42no—
209C5×D4—41no—
210C5×D4—41no—
211C5×D4—41no—
212C5×D4—41no—
213C2×C4×C5—21no—
214C2×C4×C5—41no—
215C2×C4×C5—41no—
216C2×C4×C5C2×C3×D411yescharacteristic
217C2×C4×C5C2×C3×D411yescharacteristic
218C2×C4×C5C2×C3×D411yescharacteristic
219C22⋊D5—82no—
220C2×Dic5—21no—
221C2×Dic5—22no—
222D20—21no—
223D20—21no—
224C4×D5—41no—
225C4×D5—41no—
226Dic10—42no—
227C5×C8—41no—
228#168—22no—
229#168—41no—
230C2×SD16—102no—
231C2×D8—21no—
232C2×D8—101no—
233C4⋊Q8—51no—
234#127C2×C3×D511yescharacteristic
235#124—102no—
236#121—101no—
237#121—101no—
238C4×D4—51no—
239C4×D4C2×C3×D511yescharacteristic
240#117—101no—
241#117—101no—
242C4⋊C8—51no—
243C4⋊C8C2×C3×D511yescharacteristic
244#102—21no—
245#102—101no—
246C4×C8—51no—
247C2×C3×C5—81no—
248C2×C3×C5—161no—
249C2×C3×C5#44911yescharacteristic
250C2×C3×C5#44911yescharacteristic
251C2×C3×C5#45311yescharacteristic
252C3×D5—81no—
253C23×C3—21no—
254C23×C3—41no—
255C23×C3—101no—
256C3×Q8—202no—
257C3×D4—21no—
258C3×D4—21no—
259C3×D4—42no—
260C3×D4—41no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—41no—
264C3×D4—101no—
265C3×D4—101no—
266C3×D4—402no—
267C2×C3×C4—21no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—101no—
271C2×C3×C4—102no—
272C2×C3×C4—201no—
273C2×C3×C4—201no—
274C2×C3×C4D4×D511yescharacteristic
275C2×C3×C4D4×D511yescharacteristic
276C2×C3×C4C2×C22⋊D511yescharacteristic
277C3×C8—41no—
278C3×C8—102no—
279C3×C8—201no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5—81no—
284C22×C5—81no—
285C22×C5—81no—
286C22×C5C3×#12011yescharacteristic
287C2×D5—41no—
288C2×D5—41no—
289C2×D5—41no—
290C4×C5—21no—
291C4×C5—41no—
292C4×C5C3×#13511yescharacteristic
293C4×C5C3×#13511yescharacteristic
294C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
295C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
296Dic5—41no—
297Dic5—42no—
298C2×Q8—52no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—51no—
303C2×D4—102no—
304C2×D4C3×C22⋊D511yescharacteristic
305C22×C4—21no—
306C22×C4—101no—
307SD16—204no—
308D8—42no—
309D8—202no—
310C2×C8—21no—
311C2×C8—101no—
312C2×C8—101no—
313C4⋊C4—51no—
314C4⋊C4—101no—
315C4⋊C4—101no—
316C4⋊C4C3×C22⋊D511yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—102no—
319C22⋊C4—102no—
320C22⋊C4—101no—
321C42—102no—
322C42C22×C3×D511yescharacteristic
323C3×C5#162411yescharacteristic, complemented, Hall
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—81no—
328C22×C3—81no—
329C22×C3—81no—
330C22×C3—201no—
331C22×C3—201no—
332C22×C3—201no—
333C22×C3#408311yescharacteristic
334C3×C4—21no—
335C3×C4—41no—
336C3×C4—201no—
337C3×C4—202no—
338C3×C4#405711yescharacteristic
339C3×C4#405811yescharacteristic
340C3×C4#407811yescharacteristic
341C3×C4#409611yescharacteristic
342C2×C5—81no—
343C2×C5—161no—
344C2×C5C3×#44911yescharacteristic
345C2×C5C3×#44911yescharacteristic
346C2×C5C3×#45311yescharacteristic
347D5—81no—
348C23—21no—
349C23—41no—
350C23—101no—
351Q8—202no—
352D4—21no—
353D4—21no—
354D4—42no—
355D4—41no—
356D4—41no—
357D4—41no—
358D4—41no—
359D4—101no—
360D4—101no—
361D4—402no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—101no—
366C2×C4—102no—
367C2×C4—201no—
368C2×C4—201no—
369C2×C4C3×D4×D511yescharacteristic
370C2×C4C3×D4×D511yescharacteristic
371C2×C4C2×C3×C22⋊D511yescharacteristic
372C8—41no—
373C8—102no—
374C8—201no—
375C2×C3—81no—
376C2×C3—161no—
377C2×C3—401no—
378C2×C3#6532611yescharacteristic
379C2×C3#6544711yescharacteristic
380C2×C3#6548711yescharacteristic
381C5C3×#162411yescharacteristic, complemented, Sylow
382C22—41no—
383C22—41no—
384C22—41no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—201no—
389C22—201no—
390C22—201no—
391C22C3×#408311yescharacteristic
392C4—21no—
393C4—41no—
394C4—201no—
395C4—202no—
396C4C3×#405711yescharacteristic
397C4C3×#405811yescharacteristic
398C4C3×#407811yescharacteristic
399C4C3×#409611yescharacteristic
400C3#1060181011yescharacteristic, direct product factor, Sylow
401C2—81no—
402C2—161no—
403C2—401no—
404C2C3×#6532611yescharacteristic
405C2C3×#6544711yescharacteristic
406C2C3×#6548711yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#459C2
socleC22×C3×C5#120
hypercenterC3×#459D5
hypocenterC5C3×#1624
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
1. C3×#65897C2semidirect
2. C3×C5×#459C2semidirect
3. C3×#65365C2semidirect
4. C3×#65361C2semidirect
5. C3×D4⋊#168C2semidirect
6. C3×#64703C2semidirect
7. C3×#64701C2semidirect
8. #10601810C3direct (N × H)
27. #65897C2×C3semidirect
28. C5×#459C2×C3semidirect
29. #65365C2×C3semidirect
30. #65361C2×C3semidirect
31. D4⋊#168C2×C3semidirect
32. #64703C2×C3semidirect
33. #64701C2×C3semidirect
62. C3×#459D5semidirect
156. #459C3×D5semidirect
323. C3×C5#1624semidirect
381. C5C3×#1624semidirect
400. C3#10601810direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658972
C3×C5×#4592
C3×#653652
C3×#653612
C3×D4⋊#1682
C3×#647032
C3×#647012
#106018103
C3×#16245