Finite Group Databasebeta

← C3×#10599221 #14285246

Subgroups — C3×#10599221 #14285246

Order 1920.

456 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×D5×C4⋊Q8C211yesmaximal, characteristic
2C3×#65124C211yesmaximal, characteristic
3C3×#65124C211yesmaximal, characteristic
4C3×C5×#332C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×#64706C211yesmaximal, characteristic, complemented
7C3×#64702C211yesmaximal, characteristic, complemented
8#10599221C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×Q8×D5—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×#4090—21no—
12C3×D5×C4⋊C4—21no—
13C3×D5×C4⋊C4C412yes—
14C3×#4034—21no—
15C3×#4034C412yes—
16C3×C42×D5C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×#3952—21no—
21C3×#3952—21no—
22C3×#3947—21no—
23C3×#3947—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1556—51nomaximal, Hall
27D5×C4⋊Q8C2×C311yescharacteristic
28#65124C2×C311yescharacteristic
29#65124C2×C311yescharacteristic
30C5×#332C2×C311yescharacteristic, complemented
31#64767C2×C311yescharacteristic, complemented
32#64706C2×C311yescharacteristic, complemented
33#64702C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C3×Q8×D5—42no—
36C3×Q8×D5—42no—
37C2×C3×C4×D5—22no—
38C2×C3×C4×D5C2×C411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×Dic10—21no—
42C2×C3×Dic10—22no—
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4C2×C412yes—
47C3×C42×C5C2311yescharacteristic
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5C2×C412yes—
50C3×#683—22no—
51C3×#683—22no—
52C3×C4×Dic5C2×C411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57C2×C3×C4⋊Q8—51no—
58C3×#432—51no—
59C3×#432—51no—
60C3×#332—51no—
61C3×#332—51no—
62C3×#332—51no—
63C3×#332D511yescharacteristic, complemented
64C2×Q8×D5—21no—
65C5×C4⋊Q8C22×C311yescharacteristic
66#4090—21no—
67D5×C4⋊C4—21no—
68D5×C4⋊C4C3×C412yes—
69#4034—21no—
70#4034C3×C412yes—
71C42×D5C22×C311yescharacteristic
72#4015C22×C311yescharacteristic
73C5×C4⋊C8C22×C311yescharacteristic
74C5×C4⋊C8C22×C311yescharacteristic
75#3952—21no—
76#3952—21no—
77#3947—21no—
78#3947—21no—
79C4⋊#168C22×C311yescharacteristic
80C4⋊#168C22×C311yescharacteristic
81#1556—51noSylow
82C22×C3×D5C22⋊C411yescharacteristic
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×Dic5—22no—
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C22⋊C411yescharacteristic
93C3×C4×D5—22no—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×C4×D5—21no—
97C3×C4×D5—21no—
98C3×C4×D5—44no—
99C3×Dic10—44no—
100C3×Dic10—41no—
101C3×Dic10—41no—
102C3×C5×C8—41no—
103C3×C5×C8—41no—
104C3×#168—41no—
105C3×#168—41no—
106C22×C3×Q8—101no—
107C3×C4⋊Q8—52no—
108C3×C4⋊Q8—51no—
109C3×C4⋊Q8—101no—
110C3×C4⋊Q8—101no—
111C3×C4⋊Q8C2×D511yescharacteristic
112C2×C3×C4⋊C4—52no—
113C2×C3×C4⋊C4—101no—
114C2×C3×C42—51no—
115C3×C4⋊C8—51no—
116C3×C4⋊C8—51no—
117C3×C4⋊C8C2×D511yescharacteristic
118C3×C4⋊C8C2×D511yescharacteristic
119C3×C22⋊C8—101no—
120C3×C22⋊C8—101no—
121C3×#97—101no—
122C3×#97—101no—
123C2×C5×Q8—21no—
124Q8×D5—42no—
125Q8×D5—42no—
126C2×C4×D5—22no—
127C2×C4×D5C2×C3×C411yescharacteristic
128C2×C4×D5C3×D411yescharacteristic
129C2×C4×D5C3×D411yescharacteristic
130C2×Dic10—21no—
131C2×Dic10—22no—
132C2×C5×C8—21no—
133C2×C5×C8—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4C2×C3×C412yes—
136C42×C5C23×C311yescharacteristic
137C4⋊Dic5—21no—
138C4⋊Dic5C2×C3×C412yes—
139#683—22no—
140#683—22no—
141C4×Dic5C2×C3×C411yescharacteristic
142C4×Dic5C3×D411yescharacteristic
143C4×Dic5C3×D411yescharacteristic
144C2×#168—21no—
145C2×#168—21no—
146C2×C4⋊Q8—51no—
147#432—51no—
148#432—51no—
149#332—51no—
150#332—51no—
151#332—51no—
152#332C3×D511yescharacteristic, complemented
153C22×C3×C5C2×C22⋊C411yescharacteristic
154C2×C3×D5—21no—
155C2×C3×D5—21no—
156C2×C3×D5#10112yes—
157C3×C4×C5—21no—
158C3×C4×C5—42no—
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162C3×C4×C5#13711yescharacteristic
163C3×Dic5—21no—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C3×Dic5—42no—
167C2×C3×Q8—21no—
168C2×C3×Q8—102no—
169C2×C3×Q8—101no—
170C2×C3×Q8—202no—
171C2×C3×Q8—202no—
172C22×C3×C4—51no—
173C22×C3×C4—51no—
174C22×C3×C4—51no—
175C22×C3×C4—102no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—101no—
179C2×C3×C8—101no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—52no—
182C3×C4⋊C4—102no—
183C3×C4⋊C4—102no—
184C3×C4⋊C4—101no—
185C3×C4⋊C4C4×D512yes—
186C3×C42—51no—
187C3×C42—51no—
188C3×C42—51no—
189C3×C42C22×D511yescharacteristic
190C22×D5C3×C22⋊C411yescharacteristic
191C5×Q8—41no—
192C5×Q8—41no—
193C2×C4×C5—22no—
194C2×C4×C5C22×C3×C411yescharacteristic
195C2×C4×C5C2×C3×D411yescharacteristic
196C2×C4×C5C2×C3×D411yescharacteristic
197C2×Dic5—22no—
198C2×Dic5C3×C22⋊C411yescharacteristic
199C2×Dic5C3×C22⋊C411yescharacteristic
200C2×Dic5C3×C22⋊C411yescharacteristic
201C4×D5—22no—
202C4×D5—21no—
203C4×D5—21no—
204C4×D5—21no—
205C4×D5—21no—
206C4×D5—44no—
207Dic10—44no—
208Dic10—41no—
209Dic10—41no—
210C5×C8—41no—
211C5×C8—41no—
212#168—41no—
213#168—41no—
214C22×Q8—101no—
215C4⋊Q8—52no—
216C4⋊Q8—51no—
217C4⋊Q8—101no—
218C4⋊Q8—101no—
219C4⋊Q8C2×C3×D511yescharacteristic
220C2×C4⋊C4—52no—
221C2×C4⋊C4—101no—
222C2×C42—51no—
223C4⋊C8—51no—
224C4⋊C8—51no—
225C4⋊C8C2×C3×D511yescharacteristic
226C4⋊C8C2×C3×D511yescharacteristic
227C22⋊C8—101no—
228C22⋊C8—101no—
229#97—101no—
230#97—101no—
231C2×C3×C5C2×#10111yescharacteristic
232C2×C3×C5#41811yescharacteristic
233C2×C3×C5#41911yescharacteristic
234C3×D5—22no—
235C23×C3—51no—
236C3×Q8—41no—
237C3×Q8—41no—
238C3×Q8—204no—
239C3×Q8—201no—
240C3×Q8—201no—
241C2×C3×C4—22no—
242C2×C3×C4—51no—
243C2×C3×C4—51no—
244C2×C3×C4—51no—
245C2×C3×C4—102no—
246C2×C3×C4—101no—
247C2×C3×C4—101no—
248C2×C3×C4—101no—
249C2×C3×C4—101no—
250C2×C3×C4—102no—
251C2×C3×C4—204no—
252C2×C3×C4C2×C4×D511yescharacteristic
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C3×C8—41no—
256C3×C8—41no—
257C3×C8—201no—
258C3×C8—201no—
259C22×C5C2×C3×C22⋊C411yescharacteristic
260C2×D5—21no—
261C2×D5—21no—
262C2×D5C3×#10112yes—
263C4×C5—21no—
264C4×C5—42no—
265C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
266C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
267C4×C5C3×#13711yescharacteristic
268C4×C5C3×#13711yescharacteristic
269Dic5—21no—
270Dic5—21no—
271Dic5—21no—
272Dic5—42no—
273C2×Q8—21no—
274C2×Q8—102no—
275C2×Q8—101no—
276C2×Q8—202no—
277C2×Q8—202no—
278C22×C4—51no—
279C22×C4—51no—
280C22×C4—51no—
281C22×C4—102no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—101no—
285C2×C8—101no—
286C4⋊C4—21no—
287C4⋊C4—52no—
288C4⋊C4—102no—
289C4⋊C4—102no—
290C4⋊C4—101no—
291C4⋊C4C3×C4×D512yes—
292C42—51no—
293C42—51no—
294C42—51no—
295C42C22×C3×D511yescharacteristic
296C3×C5#155611yescharacteristic, complemented, Hall
297C22×C3—52no—
298C22×C3—101no—
299C22×C3—101no—
300C22×C3D5×C22⋊C411yescharacteristic
301C3×C4—21no—
302C3×C4—42no—
303C3×C4—101no—
304C3×C4—101no—
305C3×C4—101no—
306C3×C4—202no—
307C3×C4#405711yescharacteristic
308C3×C4#406011yescharacteristic
309C3×C4#406111yescharacteristic
310C3×C4#406411yescharacteristic
311C2×C5C2×C3×#10111yescharacteristic
312C2×C5C3×#41811yescharacteristic
313C2×C5C3×#41911yescharacteristic
314D5—22no—
315C23—51no—
316Q8—41no—
317Q8—41no—
318Q8—204no—
319Q8—201no—
320Q8—201no—
321C2×C4—22no—
322C2×C4—51no—
323C2×C4—51no—
324C2×C4—51no—
325C2×C4—102no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—101no—
329C2×C4—101no—
330C2×C4—102no—
331C2×C4—204no—
332C2×C4C2×C3×C4×D511yescharacteristic
333C2×C4C3×D4×D511yescharacteristic
334C2×C4C3×D4×D511yescharacteristic
335C8—41no—
336C8—41no—
337C8—201no—
338C8—201no—
339C2×C3—102no—
340C2×C3D5×#10111yescharacteristic
341C2×C3#6505911yescharacteristic
342C2×C3#6509111yescharacteristic
343C5C3×#155611yescharacteristic, complemented, Sylow
344C22—52no—
345C22—101no—
346C22—101no—
347C22C3×D5×C22⋊C411yescharacteristic
348C4—21no—
349C4—42no—
350C4—101no—
351C4—101no—
352C4—101no—
353C4—202no—
354C4C3×#405711yescharacteristic
355C4C3×#406011yescharacteristic
356C4C3×#406111yescharacteristic
357C4C3×#406411yescharacteristic
358C3#1059922111yescharacteristic, direct product factor, Sylow
359C2—102no—
360C2C3×D5×#10111yescharacteristic
361C2C3×#6505911yescharacteristic
362C2C3×#6509111yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#332C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC42×C5C23×C3
hypercenterC3×#332D5
hypocenterC5C3×#1556
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#332

Complements

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

NH ≅ G/Ntype
4. C3×C5×#332C2semidirect
5. C3×#64767C2semidirect
6. C3×#64706C2semidirect
7. C3×#64702C2semidirect
8. #10599221C3direct (N × H)
30. C5×#332C2×C3semidirect
31. #64767C2×C3semidirect
32. #64706C2×C3semidirect
33. #64702C2×C3semidirect
63. C3×#332D5semidirect
152. #332C3×D5semidirect
296. C3×C5#1556semidirect
343. C5C3×#1556semidirect
358. C3#10599221direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
C3×#651242
C3×C5×#3322
C3×#647672
C3×#647062
C3×#647022
#105992213
C3×#15565