Finite Group Databasebeta

← C3×#10601997 #14289149

Subgroups — C3×#10601997 #14289149

Order 1920.

420 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66055C211yesmaximal, characteristic, complemented
2C3×C5×#486C211yesmaximal, characteristic
3C3×#65364C211yesmaximal, characteristic
4C3×#65364C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×#64676C211yesmaximal, characteristic, complemented
7C3×#64676C211yesmaximal, characteristic, complemented
8#10601997C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#127C2211yescharacteristic
11C3×Q8×Dic5—21no—
12C3×#4090—21no—
13C2×C3×#687—21no—
14C2×C3×#687—21no—
15C3×#4036—21no—
16C3×#4035—22no—
17C3×#4033—21no—
18C3×C4×Dic10C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20C3×C5×#102—22no—
21C3×C4×C5×C8C2211yescharacteristic
22C3×#3964—21no—
23C3×#3964—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1626—51nomaximal, Hall
27#66055C2×C311yescharacteristic, complemented
28C5×#486C2×C311yescharacteristic
29#65364C2×C311yescharacteristic
30#65364C2×C311yescharacteristic
31#64767C2×C311yescharacteristic, complemented
32#64676C2×C311yescharacteristic, complemented
33#64676C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×Dic10D411yescharacteristic
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D412yes—
43C3×C42×C5C2311yescharacteristic
44C3×#687—42no—
45C3×#687—42no—
46C3×C4⋊Dic5—22no—
47C3×C4⋊Dic5D411yescharacteristic
48C3×C4⋊Dic5D411yescharacteristic
49C3×#683—22no—
50C3×#683—22no—
51C3×#683—21no—
52C3×#683—21no—
53C3×C4×Dic5—22no—
54C3×C4×Dic5—21no—
55C3×C4×Dic5—21no—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58C3×#557—51no—
59C3×#486D511yescharacteristic
60C3×#460—51no—
61C3×#460—51no—
62C3×#332—51no—
63C3×Q8⋊C8—51no—
64C3×Q8⋊C8—51no—
65C5×C4⋊Q8C22×C311yescharacteristic
66C5×#127C22×C311yescharacteristic
67Q8×Dic5—21no—
68#4090—21no—
69C2×#687—21no—
70C2×#687—21no—
71#4036—21no—
72#4035—22no—
73#4033—21no—
74C4×Dic10C22×C311yescharacteristic
75C4×Dic10C22×C311yescharacteristic
76C5×#102—22no—
77C4×C5×C8C22×C311yescharacteristic
78#3964—21no—
79#3964—21no—
80C4⋊#168C22×C311yescharacteristic
81C4⋊#168C22×C311yescharacteristic
82#1626—51noSylow
83C23×C3×C5—41no—
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C3×C5×D4—42no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×Dic5—21no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C3×Dic10—21no—
100C3×Dic10—21no—
101C3×Dic10—21no—
102C3×Dic10SD1612yescomplemented
103C3×C5×C8—41no—
104C3×#168—41no—
105C3×#168—41no—
106C2×C3×SD16—101no—
107C2×C3×SD16—101no—
108C3×C4⋊Q8—101no—
109C3×C4⋊Q8C2×D511yescharacteristic
110C3×#127C2×D511yescharacteristic
111C3×#125—101no—
112C3×#125—102no—
113C3×C4×Q8—51no—
114C3×C4×Q8—51no—
115C3×C4×Q8—101no—
116C3×C4×Q8—101no—
117C3×C4⋊C8—51no—
118C3×C4⋊C8—51no—
119C3×#102—22no—
120C3×#102—101no—
121C3×#102—101no—
122C3×C4×C8C2×D511yescharacteristic
123C2×C5×Q8—21no—
124C2×C5×D4—21no—
125C2×C5×D4—21no—
126C2×C5×D4—21no—
127C2×Dic10C3×D411yescharacteristic
128C2×Dic10C3×D411yescharacteristic
129C2×C5×C8—21no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4C3×D412yes—
132C42×C5C23×C311yescharacteristic
133#687—42no—
134#687—42no—
135C4⋊Dic5—22no—
136C4⋊Dic5C3×D411yescharacteristic
137C4⋊Dic5C3×D411yescharacteristic
138#683—22no—
139#683—22no—
140#683—21no—
141#683—21no—
142C4×Dic5—22no—
143C4×Dic5—21no—
144C4×Dic5—21no—
145C2×#168—21no—
146C2×#168—21no—
147#557—51no—
148#486C3×D511yescharacteristic
149#460—51no—
150#460—51no—
151#332—51no—
152Q8⋊C8—51no—
153Q8⋊C8—51no—
154C22×C3×C5—81no—
155C22×C3×C5—81no—
156C22×C3×C5—81no—
157C22×C3×C5#12011yescharacteristic
158C3×C4×C5—21no—
159C3×C4×C5—42no—
160C3×C4×C5C2×SD1611yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×Dic5—22no—
165C3×Dic5—41no—
166C3×Dic5—41no—
167C3×Dic5—41no—
168C2×C3×Q8—21no—
169C2×C3×Q8—51no—
170C2×C3×Q8—51no—
171C2×C3×D4—21no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C3×SD16—202no—
175C3×SD16—202no—
176C2×C3×C8—21no—
177C2×C3×C8—101no—
178C2×C3×C8—101no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—51no—
181C3×C4⋊C4—51no—
182C3×C4⋊C4—102no—
183C3×C4⋊C4—102no—
184C3×C4⋊C4—102no—
185C3×C4⋊C4—101no—
186C3×C4⋊C4—101no—
187C3×C4⋊C4C22⋊D512yes—
188C3×C42—102no—
189C3×C42—101no—
190C3×C42—101no—
191C3×C42C22×D511yescharacteristic
192C23×C5—41no—
193C5×Q8—41no—
194C5×Q8—41no—
195C5×D4—42no—
196C5×D4—41no—
197C5×D4—41no—
198C5×D4—41no—
199C5×D4—41no—
200C2×C4×C5—22no—
201C2×C4×C5C2×C3×D411yescharacteristic
202C2×C4×C5C2×C3×D411yescharacteristic
203C2×C4×C5C2×C3×D411yescharacteristic
204C2×Dic5—21no—
205C2×Dic5—21no—
206C2×Dic5—21no—
207C2×Dic5—21no—
208Dic10—21no—
209Dic10—21no—
210Dic10—21no—
211Dic10C3×SD1612yescomplemented
212C5×C8—41no—
213#168—41no—
214#168—41no—
215C2×SD16—101no—
216C2×SD16—101no—
217C4⋊Q8—101no—
218C4⋊Q8C2×C3×D511yescharacteristic
219#127C2×C3×D511yescharacteristic
220#125—101no—
221#125—102no—
222C4×Q8—51no—
223C4×Q8—51no—
224C4×Q8—101no—
225C4×Q8—101no—
226C4⋊C8—51no—
227C4⋊C8—51no—
228#102—22no—
229#102—101no—
230#102—101no—
231C4×C8C2×C3×D511yescharacteristic
232C2×C3×C5—161no—
233C2×C3×C5#44811yescharacteristic
234C2×C3×C5#44911yescharacteristic
235C2×C3×C5#45411yescharacteristic
236C23×C3—41no—
237C3×Q8—41no—
238C3×Q8—41no—
239C3×Q8—52no—
240C3×Q8—101no—
241C3×Q8—101no—
242C3×Q8—101no—
243C3×D4—42no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—41no—
248C2×C3×C4—22no—
249C2×C3×C4—101no—
250C2×C3×C4—101no—
251C2×C3×C4—101no—
252C2×C3×C4—101no—
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4C2×C22⋊D511yescharacteristic
256C3×C8—41no—
257C3×C8—201no—
258C3×C8—201no—
259C22×C5—81no—
260C22×C5—81no—
261C22×C5—81no—
262C22×C5C3×#12011yescharacteristic
263C4×C5—21no—
264C4×C5—42no—
265C4×C5C2×C3×SD1611yescharacteristic
266C4×C5C3×#13511yescharacteristic
267C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
268C4×C5C3×#13711yescharacteristic
269Dic5—22no—
270Dic5—41no—
271Dic5—41no—
272Dic5—41no—
273C2×Q8—21no—
274C2×Q8—51no—
275C2×Q8—51no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279SD16—202no—
280SD16—202no—
281C2×C8—21no—
282C2×C8—101no—
283C2×C8—101no—
284C4⋊C4—21no—
285C4⋊C4—51no—
286C4⋊C4—51no—
287C4⋊C4—102no—
288C4⋊C4—102no—
289C4⋊C4—102no—
290C4⋊C4—101no—
291C4⋊C4—101no—
292C4⋊C4C3×C22⋊D512yes—
293C42—102no—
294C42—101no—
295C42—101no—
296C42C22×C3×D511yescharacteristic
297C3×C5#162611yescharacteristic, complemented, Hall
298C22×C3—81no—
299C22×C3—81no—
300C22×C3—81no—
301C22×C3#408311yescharacteristic
302C3×C4—21no—
303C3×C4—42no—
304C3×C4—102no—
305C3×C4—201no—
306C3×C4—201no—
307C3×C4—201no—
308C3×C4#405711yescharacteristic
309C3×C4#405811yescharacteristic
310C3×C4D5×SD1611yescharacteristic
311C3×C4#406111yescharacteristic
312C2×C5—161no—
313C2×C5C3×#44811yescharacteristic
314C2×C5C3×#44911yescharacteristic
315C2×C5C3×#45411yescharacteristic
316C23—41no—
317Q8—41no—
318Q8—41no—
319Q8—52no—
320Q8—101no—
321Q8—101no—
322Q8—101no—
323D4—42no—
324D4—41no—
325D4—41no—
326D4—41no—
327D4—41no—
328C2×C4—22no—
329C2×C4—101no—
330C2×C4—101no—
331C2×C4—101no—
332C2×C4—101no—
333C2×C4C3×D4×D511yescharacteristic
334C2×C4C3×D4×D511yescharacteristic
335C2×C4C2×C3×C22⋊D511yescharacteristic
336C8—41no—
337C8—201no—
338C8—201no—
339C2×C3—161no—
340C2×C3#6535111yescharacteristic
341C2×C3#6544711yescharacteristic
342C2×C3#6545911yescharacteristic
343C5C3×#162611yescharacteristic, complemented, Sylow
344C22—81no—
345C22—81no—
346C22—81no—
347C22C3×#408311yescharacteristic
348C4—21no—
349C4—42no—
350C4—102no—
351C4—201no—
352C4—201no—
353C4—201no—
354C4C3×#405711yescharacteristic
355C4C3×#405811yescharacteristic
356C4C3×D5×SD1611yescharacteristic
357C4C3×#406111yescharacteristic
358C3#1060199711yescharacteristic, direct product factor, Sylow
359C2—161no—
360C2C3×#6535111yescharacteristic
361C2C3×#6544711yescharacteristic
362C2C3×#6545911yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#486C2
socleC22×C3×C5#120
prime radicalC3×C5×#127C22
hypercenterC3×#486D5
hypocenterC5C3×#1626
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#486

Complements

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

NH ≅ G/Ntype
1. C3×#66055C2semidirect
5. C3×#64767C2semidirect
6. C3×#64676C2semidirect
7. C3×#64676C2semidirect
8. #10601997C3direct (N × H)
27. #66055C2×C3semidirect
31. #64767C2×C3semidirect
32. #64676C2×C3semidirect
33. #64676C2×C3semidirect
102. C3×Dic10SD16semidirect
211. Dic10C3×SD16semidirect
297. C3×C5#1626semidirect
343. C5C3×#1626semidirect
358. C3#10601997direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660552
C3×C5×#4862
C3×#653642
C3×#647672
C3×#646762
#106019973
C3×#16265