Finite Group Databasebeta

← C3×#10602021 #14289620

Subgroups — C3×#10602021 #14289620

Order 1920.

468 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×#66060C211yesmaximal, characteristic
2C3×C5×#487C211yesmaximal, characteristic, complemented
3C3×#65373C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic, complemented
7C3×#64679C211yesmaximal, characteristic, complemented
8#10602021C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#713—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×#4092—21no—
13C3×#4041—21no—
14C3×#4040—22no—
15C3×D5×C4⋊C4—21no—
16C3×C4×D20C2211yescharacteristic
17C3×C4×D20C2211yescharacteristic
18C3×C5×#103—22no—
19C3×C4×C5×C8C2211yescharacteristic
20C3×#3941—21no—
21C3×#3941—21no—
22C3×#3940—21no—
23C3×#3940—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1635—51nomaximal, Hall
27#66060C2×C311yescharacteristic
28C5×#487C2×C311yescharacteristic, complemented
29#65373C2×C311yescharacteristic, complemented
30#65373C2×C311yescharacteristic, complemented
31#64767C2×C311yescharacteristic, complemented
32#64679C2×C311yescharacteristic, complemented
33#64679C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C3×#713—42no—
37C3×#713—42no—
38C2×C3×D20—22no—
39C2×C3×D20D411yescharacteristic
40C2×C3×D20D411yescharacteristic
41C2×C3×C4×D5—22no—
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D412yes—
49C3×C42×C5C2311yescharacteristic
50C3×#685—22no—
51C3×#685—21no—
52C3×#685—21no—
53C3×C4⋊Dic5D411yescharacteristic
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—22no—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58C3×#547—51no—
59C3×#487D511yescharacteristic, complemented
60C3×#476—51no—
61C3×#476—51no—
62C3×#332—51no—
63C3×D4⋊C8—51no—
64C3×D4⋊C8—51no—
65C2×#713—21no—
66C5×C4⋊Q8C22×C311yescharacteristic
67C5×C4⋊Q8C22×C311yescharacteristic
68#4092—21no—
69#4041—21no—
70#4040—22no—
71D5×C4⋊C4—21no—
72C4×D20C22×C311yescharacteristic
73C4×D20C22×C311yescharacteristic
74C5×#103—22no—
75C4×C5×C8C22×C311yescharacteristic
76#3941—21no—
77#3941—21no—
78#3940—21no—
79#3940—21no—
80C4⋊#168C22×C311yescharacteristic
81C4⋊#168C22×C311yescharacteristic
82#1635—51noSylow
83C22×C3×D5—21no—
84C22×C3×D5—21no—
85C3×C5×Q8—42no—
86C3×C5×Q8—41no—
87C3×C5×Q8—41no—
88C2×C3×C4×C5—22no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C3×D20—21no—
96C3×D20—21no—
97C3×D20—21no—
98C3×D20—44no—
99C3×D20SD1612yes—
100C3×C4×D5—44no—
101C3×C4×D5—41no—
102C3×C4×D5—41no—
103C3×C4×D5—41no—
104C3×C4×D5—41no—
105C3×C5×C8—41no—
106C3×#168—41no—
107C3×#168—41no—
108C2×C3×#41—101no—
109C3×C4⋊Q8C2×D511yescharacteristic
110C3×C4⋊Q8C2×D511yescharacteristic
111C3×#123—102no—
112C3×C22⋊Q8—101no—
113C3×#121—101no—
114C3×C4×D4—51no—
115C3×C4×D4—51no—
116C2×C3×C4⋊C4—101no—
117C3×#106—101no—
118C3×#106—101no—
119C3×C4⋊C8—51no—
120C3×C4⋊C8—51no—
121C3×#103—22no—
122C3×#102—101no—
123C3×#102—101no—
124C3×C4×C8C2×D511yescharacteristic
125C2×C5×Q8—21no—
126C2×C5×Q8—21no—
127#713—42no—
128#713—42no—
129C2×D20—22no—
130C2×D20C3×D411yescharacteristic
131C2×D20C3×D411yescharacteristic
132C2×C4×D5—22no—
133C2×C4×D5—21no—
134C2×C4×D5—21no—
135C2×C5×C8—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4C3×D412yes—
140C42×C5C23×C311yescharacteristic
141#685—22no—
142#685—21no—
143#685—21no—
144C4⋊Dic5C3×D411yescharacteristic
145C4⋊Dic5C3×D411yescharacteristic
146#683—22no—
147C2×#168—21no—
148C2×#168—21no—
149#547—51no—
150#487C3×D511yescharacteristic, complemented
151#476—51no—
152#476—51no—
153#332—51no—
154D4⋊C8—51no—
155D4⋊C8—51no—
156C22×C3×C5#12011yescharacteristic
157C2×C3×D5—22no—
158C2×C3×D5—41no—
159C2×C3×D5—41no—
160C2×C3×D5—41no—
161C2×C3×D5—41no—
162C2×C3×D5—41no—
163C3×C4×C5—21no—
164C3×C4×C5—42no—
165C3×C4×C5—81no—
166C3×C4×C5C2×SD1611yescharacteristic
167C3×C4×C5#13511yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×C4×C5#13711yescharacteristic
170C3×Dic5—41no—
171C3×Dic5—41no—
172C3×#41—202no—
173C3×#41—202no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×D4—51no—
177C2×C3×D4—51no—
178C2×C3×D4—102no—
179C22×C3×C4—102no—
180C22×C3×C4—101no—
181C22×C3×C4—101no—
182C2×C3×C8—21no—
183C2×C3×C8—101no—
184C2×C3×C8—101no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—51no—
189C3×C4⋊C4—51no—
190C3×C4⋊C4—102no—
191C3×C4⋊C4C22⋊D512yes—
192C3×C22⋊C4—102no—
193C3×C22⋊C4—101no—
194C3×C22⋊C4—101no—
195C3×C42C22×D511yescharacteristic
196C22×D5—21no—
197C22×D5—21no—
198C5×Q8—42no—
199C5×Q8—41no—
200C5×Q8—41no—
201C2×C4×C5—22no—
202C2×C4×C5—41no—
203C2×C4×C5C2×C3×D411yescharacteristic
204C2×C4×C5C2×C3×D411yescharacteristic
205C2×C4×C5C2×C3×D411yescharacteristic
206C2×Dic5—21no—
207C2×Dic5—21no—
208D20—21no—
209D20—21no—
210D20—21no—
211D20—44no—
212D20C3×SD1612yes—
213C4×D5—44no—
214C4×D5—41no—
215C4×D5—41no—
216C4×D5—41no—
217C4×D5—41no—
218C5×C8—41no—
219#168—41no—
220#168—41no—
221C2×#41—101no—
222C4⋊Q8C2×C3×D511yescharacteristic
223C4⋊Q8C2×C3×D511yescharacteristic
224#123—102no—
225C22⋊Q8—101no—
226#121—101no—
227C4×D4—51no—
228C4×D4—51no—
229C2×C4⋊C4—101no—
230#106—101no—
231#106—101no—
232C4⋊C8—51no—
233C4⋊C8—51no—
234#103—22no—
235#102—101no—
236#102—101no—
237C4×C8C2×C3×D511yescharacteristic
238C2×C3×C5#45011yescharacteristic
239C2×C3×C5#45211yescharacteristic
240C2×C3×C5#45411yescharacteristic
241C3×D5—42no—
242C3×D5—81no—
243C23×C3—101no—
244C23×C3—101no—
245C3×Q8—42no—
246C3×Q8—41no—
247C3×Q8—41no—
248C3×D4—52no—
249C3×D4—101no—
250C3×D4—101no—
251C3×D4—101no—
252C3×D4—204no—
253C2×C3×C4—22no—
254C2×C3×C4—41no—
255C2×C3×C4—101no—
256C2×C3×C4—101no—
257C2×C3×C4—204no—
258C2×C3×C4—201no—
259C2×C3×C4—201no—
260C2×C3×C4—201no—
261C2×C3×C4—201no—
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C2×C3×C4C2×C22⋊D511yescharacteristic
265C3×C8—41no—
266C3×C8—201no—
267C3×C8—201no—
268C22×C5C3×#12011yescharacteristic
269C2×D5—22no—
270C2×D5—41no—
271C2×D5—41no—
272C2×D5—41no—
273C2×D5—41no—
274C2×D5—41no—
275C4×C5—21no—
276C4×C5—42no—
277C4×C5—81no—
278C4×C5C2×C3×SD1611yescharacteristic
279C4×C5C3×#13511yescharacteristic
280C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
281C4×C5C3×#13711yescharacteristic
282Dic5—41no—
283Dic5—41no—
284#41—202no—
285#41—202no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×D4—51no—
289C2×D4—51no—
290C2×D4—102no—
291C22×C4—102no—
292C22×C4—101no—
293C22×C4—101no—
294C2×C8—21no—
295C2×C8—101no—
296C2×C8—101no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—51no—
301C4⋊C4—51no—
302C4⋊C4—102no—
303C4⋊C4C3×C22⋊D512yes—
304C22⋊C4—102no—
305C22⋊C4—101no—
306C22⋊C4—101no—
307C42C22×C3×D511yescharacteristic
308C3×C5#163511yescharacteristic, complemented, Hall
309C22×C3—102no—
310C22×C3—201no—
311C22×C3—201no—
312C22×C3—201no—
313C22×C3—201no—
314C22×C3—201no—
315C22×C3#408311yescharacteristic
316C3×C4—21no—
317C3×C4—42no—
318C3×C4—81no—
319C3×C4—201no—
320C3×C4—201no—
321C3×C4D5×SD1611yescharacteristic
322C3×C4#406011yescharacteristic
323C3×C4#406411yescharacteristic
324C3×C4#406511yescharacteristic
325C2×C5C3×#45011yescharacteristic
326C2×C5C3×#45211yescharacteristic
327C2×C5C3×#45411yescharacteristic
328D5—42no—
329D5—81no—
330C23—101no—
331C23—101no—
332Q8—42no—
333Q8—41no—
334Q8—41no—
335D4—52no—
336D4—101no—
337D4—101no—
338D4—101no—
339D4—204no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—101no—
343C2×C4—101no—
344C2×C4—204no—
345C2×C4—201no—
346C2×C4—201no—
347C2×C4—201no—
348C2×C4—201no—
349C2×C4C3×D4×D511yescharacteristic
350C2×C4C3×D4×D511yescharacteristic
351C2×C4C2×C3×C22⋊D511yescharacteristic
352C8—41no—
353C8—201no—
354C8—201no—
355C2×C3—202no—
356C2×C3—401no—
357C2×C3#6535111yescharacteristic
358C2×C3#6545811yescharacteristic
359C2×C3#6547611yescharacteristic
360C5C3×#163511yescharacteristic, complemented, Sylow
361C22—102no—
362C22—201no—
363C22—201no—
364C22—201no—
365C22—201no—
366C22—201no—
367C22C3×#408311yescharacteristic
368C4—21no—
369C4—42no—
370C4—81no—
371C4—201no—
372C4—201no—
373C4C3×D5×SD1611yescharacteristic
374C4C3×#406011yescharacteristic
375C4C3×#406411yescharacteristic
376C4C3×#406511yescharacteristic
377C3#1060202111yescharacteristic, direct product factor, Sylow
378C2—202no—
379C2—401no—
380C2C3×#6535111yescharacteristic
381C2C3×#6545811yescharacteristic
382C2C3×#6547611yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#487C2
socleC22×C3×C5#120
prime radicalC3×#66060C2
hypercenterC3×#487D5
hypocenterC5C3×#1635
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#487

Complements

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

NH ≅ G/Ntype
2. C3×C5×#487C2semidirect
3. C3×#65373C2semidirect
4. C3×#65373C2semidirect
5. C3×#64767C2semidirect
6. C3×#64679C2semidirect
7. C3×#64679C2semidirect
8. #10602021C3direct (N × H)
28. C5×#487C2×C3semidirect
29. #65373C2×C3semidirect
30. #65373C2×C3semidirect
31. #64767C2×C3semidirect
32. #64679C2×C3semidirect
33. #64679C2×C3semidirect
59. C3×#487D5semidirect
150. #487C3×D5semidirect
308. C3×C5#1635semidirect
360. C5C3×#1635semidirect
377. C3#10602021direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660602
C3×C5×#4872
C3×#653732
C3×#647672
C3×#646792
#106020213
C3×#16355