Finite Group Databasebeta

← C3×#10599278 #14285022

Subgroups — C3×#10599278 #14285022

Order 1920.

504 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66059C211yesmaximal, characteristic
2C3×#65124C211yesmaximal, characteristic, complemented
3C3×D5×C4⋊C8C211yesmaximal, characteristic, complemented
4C3×C5×#333C211yesmaximal, characteristic, complemented
5C3×#64766C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7C3×#64705C211yesmaximal, characteristic, complemented
8#10599278C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#713C412yes—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×#4093C412yes—
12C2×C3×C8×D5—21no—
13C3×#4041—21no—
14C3×#4041—21no—
15C3×#4039—21no—
16C3×#4039—21no—
17C3×#4020C2211yescharacteristic
18C3×C42×D5C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×#3952—21no—
22C3×#3947—21no—
23C3×#3946—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1551—51nomaximal, Hall
27#66059C2×C311yescharacteristic
28#65124C2×C311yescharacteristic, complemented
29D5×C4⋊C8C2×C311yescharacteristic, complemented
30C5×#333C2×C311yescharacteristic, complemented
31#64766C2×C311yescharacteristic, complemented
32#64705C2×C311yescharacteristic, complemented
33#64705C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8C2×C412yes—
35C3×#713—44no—
36C2×C3×D20—22no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20C2×C412yes—
40C2×C3×C4×D5—22no—
41C2×C3×C4×D5C2×C411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×C4×D5D411yescharacteristic
44C2×C3×C5×C8—21no—
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C42×C5C2311yescharacteristic
49C3×#685—22no—
50C3×#685—22no—
51C3×C4×Dic5C2×C411yescharacteristic
52C3×C4×Dic5D411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56C3×C8×D5—42no—
57C3×#532—51no—
58C3×#432—51no—
59C2×C3×C4⋊C8—51no—
60C3×#333—51no—
61C3×#333D511yescharacteristic, complemented
62C3×#331—51no—
63C3×#331—51no—
64C2×#713C3×C412yes—
65C5×C4⋊Q8C22×C311yescharacteristic
66#4093C3×C412yes—
67C2×C8×D5—21no—
68#4041—21no—
69#4041—21no—
70#4039—21no—
71#4039—21no—
72#4020C22×C311yescharacteristic
73C42×D5C22×C311yescharacteristic
74C5×C4⋊C8C22×C311yescharacteristic
75C5×C4⋊C8C22×C311yescharacteristic
76#3952—21no—
77#3947—21no—
78#3946—21no—
79C4⋊#168C22×C311yescharacteristic
80C4⋊#168C22×C311yescharacteristic
81#1551—51noSylow
82C22×C3×D5—22no—
83C22×C3×D5C22⋊C411yescharacteristic
84C3×C5×Q8—42no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×Dic5C22⋊C411yescharacteristic
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C3×D20—42no—
93C3×D20—44no—
94C3×D20—41no—
95C3×D20—41no—
96C3×D20—41no—
97C3×D20—41no—
98C3×C4×D5—22no—
99C3×C4×D5—21no—
100C3×C4×D5—21no—
101C3×C4×D5—21no—
102C3×C4×D5—21no—
103C3×C4×D5—44no—
104C3×C5×C8—41no—
105C3×C5×C8—41no—
106C3×#168—41no—
107C3×#168—41no—
108C2×C3×#41—52no—
109C22×C3×C8—101no—
110C3×C4⋊Q8C2×D511yescharacteristic
111C3×#127—51no—
112C3×#124—52no—
113C3×#121—101no—
114C3×#121—101no—
115C3×C4×D4—101no—
116C3×C4×D4—101no—
117C2×C3×C42—51no—
118C3×C4⋊C8—51no—
119C3×C4⋊C8—51no—
120C3×C4⋊C8—101no—
121C3×C4⋊C8C2×D511yescharacteristic
122C3×C4⋊C8C2×D511yescharacteristic
123C3×C22⋊C8—101no—
124C3×#97—101no—
125C2×C5×Q8C2×C3×C412yes—
126#713—44no—
127C2×D20—22no—
128C2×D20—21no—
129C2×D20—21no—
130C2×D20C2×C3×C412yes—
131C2×C4×D5—22no—
132C2×C4×D5C2×C3×C411yescharacteristic
133C2×C4×D5C3×D411yescharacteristic
134C2×C4×D5C3×D411yescharacteristic
135C2×C5×C8—21no—
136C2×C5×C8—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C42×C5C23×C311yescharacteristic
140#685—22no—
141#685—22no—
142C4×Dic5C2×C3×C411yescharacteristic
143C4×Dic5C3×D411yescharacteristic
144C4×Dic5C3×D411yescharacteristic
145C2×#168—21no—
146C2×#168—21no—
147C8×D5—42no—
148#532—51no—
149#432—51no—
150C2×C4⋊C8—51no—
151#333—51no—
152#333C3×D511yescharacteristic, complemented
153#331—51no—
154#331—51no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—42no—
159C2×C3×D5—42no—
160C2×C3×D5—42no—
161C2×C3×D5#10012yes—
162C3×C4×C5—21no—
163C3×C4×C5—42no—
164C3×C4×C5#13511yescharacteristic
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5#13711yescharacteristic
168C3×Dic5—21no—
169C3×Dic5—21no—
170C3×Dic5—21no—
171C3×#41—204no—
172C2×C3×Q8C4×D512yes—
173C2×C3×D4—52no—
174C2×C3×D4—102no—
175C2×C3×D4—101no—
176C2×C3×D4—101no—
177C22×C3×C4—51no—
178C22×C3×C4—51no—
179C22×C3×C4—51no—
180C22×C3×C4—102no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—101no—
184C2×C3×C8—101no—
185C2×C3×C8—202no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C22⋊C4—102no—
189C3×C22⋊C4—102no—
190C3×C42—51no—
191C3×C42—51no—
192C3×C42—51no—
193C3×C42C22×D511yescharacteristic
194C22×D5—22no—
195C22×D5C3×C22⋊C411yescharacteristic
196C5×Q8—42no—
197C2×C4×C5—22no—
198C2×C4×C5C22×C3×C411yescharacteristic
199C2×C4×C5C2×C3×D411yescharacteristic
200C2×C4×C5C2×C3×D411yescharacteristic
201C2×Dic5C3×C22⋊C411yescharacteristic
202C2×Dic5C3×C22⋊C411yescharacteristic
203C2×Dic5C3×C22⋊C411yescharacteristic
204D20—42no—
205D20—44no—
206D20—41no—
207D20—41no—
208D20—41no—
209D20—41no—
210C4×D5—22no—
211C4×D5—21no—
212C4×D5—21no—
213C4×D5—21no—
214C4×D5—21no—
215C4×D5—44no—
216C5×C8—41no—
217C5×C8—41no—
218#168—41no—
219#168—41no—
220C2×#41—52no—
221C22×C8—101no—
222C4⋊Q8C2×C3×D511yescharacteristic
223#127—51no—
224#124—52no—
225#121—101no—
226#121—101no—
227C4×D4—101no—
228C4×D4—101no—
229C2×C42—51no—
230C4⋊C8—51no—
231C4⋊C8—51no—
232C4⋊C8—101no—
233C4⋊C8C2×C3×D511yescharacteristic
234C4⋊C8C2×C3×D511yescharacteristic
235C22⋊C8—101no—
236#97—101no—
237C2×C3×C5C2×#10011yescharacteristic
238C2×C3×C5#41611yescharacteristic
239C2×C3×C5#41711yescharacteristic
240C3×D5—22no—
241C3×D5—82no—
242C23×C3—51no—
243C23×C3—102no—
244C3×Q8—42no—
245C3×D4—202no—
246C3×D4—204no—
247C3×D4—201no—
248C3×D4—201no—
249C3×D4—201no—
250C3×D4—201no—
251C2×C3×C4—22no—
252C2×C3×C4—51no—
253C2×C3×C4—51no—
254C2×C3×C4—51no—
255C2×C3×C4—102no—
256C2×C3×C4—101no—
257C2×C3×C4—101no—
258C2×C3×C4—101no—
259C2×C3×C4—101no—
260C2×C3×C4—204no—
261C2×C3×C4C2×C4×D511yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C3×C8—41no—
265C3×C8—41no—
266C3×C8—201no—
267C3×C8—201no—
268C22×C5C2×C3×C22⋊C411yescharacteristic
269C2×D5—21no—
270C2×D5—21no—
271C2×D5—42no—
272C2×D5—42no—
273C2×D5—42no—
274C2×D5C3×#10012yes—
275C4×C5—21no—
276C4×C5—42no—
277C4×C5C3×#13511yescharacteristic
278C4×C5C3×#13511yescharacteristic
279C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
280C4×C5C3×#13711yescharacteristic
281Dic5—21no—
282Dic5—21no—
283Dic5—21no—
284#41—204no—
285C2×Q8C3×C4×D512yes—
286C2×D4—52no—
287C2×D4—102no—
288C2×D4—101no—
289C2×D4—101no—
290C22×C4—51no—
291C22×C4—51no—
292C22×C4—51no—
293C22×C4—102no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—101no—
297C2×C8—101no—
298C2×C8—202no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C22⋊C4—102no—
302C22⋊C4—102no—
303C42—51no—
304C42—51no—
305C42—51no—
306C42C22×C3×D511yescharacteristic
307C3×C5#155111yescharacteristic, complemented, Hall
308C22×C3—52no—
309C22×C3—101no—
310C22×C3—101no—
311C22×C3—202no—
312C22×C3—202no—
313C22×C3—202no—
314C22×C3D5×C22⋊C411yescharacteristic
315C3×C4—21no—
316C3×C4—42no—
317C3×C4—101no—
318C3×C4—101no—
319C3×C4—101no—
320C3×C4#406011yescharacteristic
321C3×C4#406211yescharacteristic
322C3×C4#406411yescharacteristic
323C3×C4#406511yescharacteristic
324C2×C5C2×C3×#10011yescharacteristic
325C2×C5C3×#41611yescharacteristic
326C2×C5C3×#41711yescharacteristic
327D5—22no—
328D5—82no—
329C23—51no—
330C23—102no—
331Q8—42no—
332D4—202no—
333D4—204no—
334D4—201no—
335D4—201no—
336D4—201no—
337D4—201no—
338C2×C4—22no—
339C2×C4—51no—
340C2×C4—51no—
341C2×C4—51no—
342C2×C4—102no—
343C2×C4—101no—
344C2×C4—101no—
345C2×C4—101no—
346C2×C4—101no—
347C2×C4—204no—
348C2×C4C2×C3×C4×D511yescharacteristic
349C2×C4C3×D4×D511yescharacteristic
350C2×C4C3×D4×D511yescharacteristic
351C8—41no—
352C8—41no—
353C8—201no—
354C8—201no—
355C2×C3—102no—
356C2×C3—402no—
357C2×C3D5×#10011yescharacteristic
358C2×C3#6509211yescharacteristic
359C2×C3#6509311yescharacteristic
360C5C3×#155111yescharacteristic, complemented, Sylow
361C22—52no—
362C22—101no—
363C22—101no—
364C22—202no—
365C22—202no—
366C22—202no—
367C22C3×D5×C22⋊C411yescharacteristic
368C4—21no—
369C4—42no—
370C4—101no—
371C4—101no—
372C4—101no—
373C4C3×#406011yescharacteristic
374C4C3×#406211yescharacteristic
375C4C3×#406411yescharacteristic
376C4C3×#406511yescharacteristic
377C3#1059927811yescharacteristic, direct product factor, Sylow
378C2—102no—
379C2—402no—
380C2C3×D5×#10011yescharacteristic
381C2C3×#6509211yescharacteristic
382C2C3×#6509311yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#333C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66059C2
cosocleC42×C5C23×C3
hypercenterC3×#333D5
hypocenterC5C3×#1551
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#333

Complements

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

NH ≅ G/Ntype
2. C3×#65124C2semidirect
3. C3×D5×C4⋊C8C2semidirect
4. C3×C5×#333C2semidirect
5. C3×#64766C2semidirect
6. C3×#64705C2semidirect
7. C3×#64705C2semidirect
8. #10599278C3direct (N × H)
28. #65124C2×C3semidirect
29. D5×C4⋊C8C2×C3semidirect
30. C5×#333C2×C3semidirect
31. #64766C2×C3semidirect
32. #64705C2×C3semidirect
33. #64705C2×C3semidirect
61. C3×#333D5semidirect
152. #333C3×D5semidirect
307. C3×C5#1551semidirect
360. C5C3×#1551semidirect
377. C3#10599278direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660592
C3×#651242
C3×D5×C4⋊C82
C3×C5×#3332
C3×#647662
C3×#647052
#105992783
C3×#15515