Finite Group Databasebeta

← C3×#10599157 #14284124

Subgroups — C3×#10599157 #14284124

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66025C211yesmaximal, characteristic
2C3×#64996C211yesmaximal, characteristic, complemented
3C3×#64994C211yesmaximal, characteristic, complemented
4C3×C5×#330C211yesmaximal, characteristic, complemented
5C3×#64763C211yesmaximal, characteristic, complemented
6C3×#64684C211yesmaximal, characteristic, complemented
7C3×#64684C211yesmaximal, characteristic, complemented
8#10599157C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×#125C2211yescharacteristic
10C2×C3×#676—21no—
11C3×#4044—21no—
12C3×#4043C411yescharacteristic
13C3×#4041C411yescharacteristic
14C3×#4040—21no—
15C3×#4039—21no—
16C3×#4039C411yescharacteristic
17C3×#4038—21no—
18C3×#4033C411yescharacteristic
19C3×#4021C2211yescharacteristic
20C3×C42×D5C2211yescharacteristic
21C3×C5×#97C2211yescharacteristic
22C3×C5×#97C2211yescharacteristic
23C3×#3952—21no—
24C3×#3946—21no—
25C3×C8×Dic5—21no—
26C3×#3935C2211yescharacteristic
27C3×#3935C2211yescharacteristic
28C3×#1529—51nomaximal, Hall
29#66025C2×C311yescharacteristic
30#64996C2×C311yescharacteristic, complemented
31#64994C2×C311yescharacteristic, complemented
32C5×#330C2×C311yescharacteristic, complemented
33#64763C2×C311yescharacteristic, complemented
34#64684C2×C311yescharacteristic, complemented
35#64684C2×C311yescharacteristic, complemented
36C2×C3×D20—21no—
37C2×C3×D20C2×C411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5C2×C411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×C3×Dic10C2×C411yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4C2×C411yescharacteristic
48C3×C5×C4⋊C4C2×C411yescharacteristic
49C3×C42×C5C2311yescharacteristic
50C3×#685—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×C4⋊Dic5—21no—
56C3×#683—21no—
57C3×C4×Dic5—21no—
58C3×C4×Dic5C2×C411yescharacteristic
59C3×C4×Dic5D411yescharacteristic
60C3×C4×Dic5D411yescharacteristic
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C3×#676—24no—
64C3×#529—51no—
65C3×#432—51no—
66C3×C4×M16—51no—
67C3×#330—51no—
68C3×#330D511yescharacteristic, complemented
69C3×#329—51no—
70C3×#329—51no—
71C5×#125C22×C311yescharacteristic
72C2×#676—21no—
73#4044—21no—
74#4043C3×C411yescharacteristic
75#4041C3×C411yescharacteristic
76#4040—21no—
77#4039—21no—
78#4039C3×C411yescharacteristic
79#4038—21no—
80#4033C3×C411yescharacteristic
81#4021C22×C311yescharacteristic
82C42×D5C22×C311yescharacteristic
83C5×#97C22×C311yescharacteristic
84C5×#97C22×C311yescharacteristic
85#3952—21no—
86#3946—21no—
87C8×Dic5—21no—
88#3935C22×C311yescharacteristic
89#3935C22×C311yescharacteristic
90#1529—51noSylow
91C22×C3×D5—21no—
92C22×C3×D5C22⋊C411yescharacteristic
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×Dic5—21no—
99C2×C3×Dic5C22⋊C411yescharacteristic
100C2×C3×Dic5C22⋊C411yescharacteristic
101C2×C3×Dic5C22⋊C411yescharacteristic
102C3×D20—41no—
103C3×D20—42no—
104C3×C4×D5—22no—
105C3×C4×D5—41no—
106C3×C4×D5—41no—
107C3×C4×D5—42no—
108C3×Dic10—41no—
109C3×C5×C8—22no—
110C3×C5×C8—41no—
111C3×#168—22no—
112C3×#168—41no—
113C2×C3×M16—101no—
114C3×#126—101no—
115C3×#125C2×D511yescharacteristic
116C3×#124—51no—
117C3×#123—101no—
118C3×C22⋊Q8—51no—
119C3×#121—51no—
120C3×C4×Q8—51no—
121C3×C4×D4—51no—
122C3×C4×D4—101no—
123C3×#117—101no—
124C2×C3×C42—51no—
125C3×C4⋊C8—101no—
126C3×C22⋊C8—101no—
127C3×#97—51no—
128C3×#97—51no—
129C3×#97C2×D511yescharacteristic
130C3×#97C2×D511yescharacteristic
131C3×C4×C8—101no—
132C2×D20—21no—
133C2×D20C2×C3×C411yescharacteristic
134C2×C4×D5—21no—
135C2×C4×D5C2×C3×C411yescharacteristic
136C2×C4×D5C3×D411yescharacteristic
137C2×C4×D5C3×D411yescharacteristic
138C2×Dic10C2×C3×C411yescharacteristic
139C2×C5×C8—21no—
140C2×C5×C8—21no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4C2×C3×C411yescharacteristic
144C5×C4⋊C4C2×C3×C411yescharacteristic
145C42×C5C23×C311yescharacteristic
146#685—21no—
147#685—21no—
148#685—21no—
149#685—21no—
150#685—21no—
151C4⋊Dic5—21no—
152#683—21no—
153C4×Dic5—21no—
154C4×Dic5C2×C3×C411yescharacteristic
155C4×Dic5C3×D411yescharacteristic
156C4×Dic5C3×D411yescharacteristic
157C2×#168—21no—
158C2×#168—21no—
159#676—24no—
160#529—51no—
161#432—51no—
162C4×M16—51no—
163#330—51no—
164#330C3×D511yescharacteristic, complemented
165#329—51no—
166#329—51no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C2×C3×D5—21no—
169C2×C3×D5—21no—
170C2×C3×D5—21no—
171C2×C3×D5—41no—
172C2×C3×D5—41no—
173C2×C3×D5—41no—
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176C3×C4×C5—21no—
177C3×C4×C5—41no—
178C3×C4×C5—41no—
179C3×Dic5—21no—
180C3×Dic5—21no—
181C3×Dic5—41no—
182C3×Dic5#10412yes—
183C2×C3×Q8—51no—
184C2×C3×D4—51no—
185C2×C3×D4—101no—
186C22×C3×C4—51no—
187C22×C3×C4—51no—
188C22×C3×C4—51no—
189C22×C3×C4—101no—
190C3×M16—104no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—101no—
194C2×C3×C8—101no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—101no—
198C3×C4⋊C4—101no—
199C3×C4⋊C4C4×D511yescharacteristic
200C3×C4⋊C4C4×D511yescharacteristic
201C3×C22⋊C4—101no—
202C3×C22⋊C4—101no—
203C3×C22⋊C4—101no—
204C3×C22⋊C4—101no—
205C3×C22⋊C4—101no—
206C3×C42—51no—
207C3×C42—51no—
208C3×C42—51no—
209C3×C42—101no—
210C3×C42C22×D511yescharacteristic
211C22×D5—21no—
212C22×D5C3×C22⋊C411yescharacteristic
213C2×C4×C5—21no—
214C2×C4×C5—21no—
215C2×C4×C5C22×C3×C411yescharacteristic
216C2×C4×C5C2×C3×D411yescharacteristic
217C2×C4×C5C2×C3×D411yescharacteristic
218C2×Dic5—21no—
219C2×Dic5C3×C22⋊C411yescharacteristic
220C2×Dic5C3×C22⋊C411yescharacteristic
221C2×Dic5C3×C22⋊C411yescharacteristic
222D20—41no—
223D20—42no—
224C4×D5—22no—
225C4×D5—41no—
226C4×D5—41no—
227C4×D5—42no—
228Dic10—41no—
229C5×C8—22no—
230C5×C8—41no—
231#168—22no—
232#168—41no—
233C2×M16—101no—
234#126—101no—
235#125C2×C3×D511yescharacteristic
236#124—51no—
237#123—101no—
238C22⋊Q8—51no—
239#121—51no—
240C4×Q8—51no—
241C4×D4—51no—
242C4×D4—101no—
243#117—101no—
244C2×C42—51no—
245C4⋊C8—101no—
246C22⋊C8—101no—
247#97—51no—
248#97—51no—
249#97C2×C3×D511yescharacteristic
250#97C2×C3×D511yescharacteristic
251C4×C8—101no—
252C2×C3×C5#41311yescharacteristic
253C2×C3×C5C2×#10411yescharacteristic
254C2×C3×C5#42111yescharacteristic
255C3×D5—41no—
256C3×D5—81no—
257C23×C3—51no—
258C23×C3—101no—
259C3×Q8—201no—
260C3×D4—201no—
261C3×D4—202no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—51no—
265C2×C3×C4—51no—
266C2×C3×C4—51no—
267C2×C3×C4—102no—
268C2×C3×C4—101no—
269C2×C3×C4—201no—
270C2×C3×C4—201no—
271C2×C3×C4—202no—
272C2×C3×C4C2×C4×D511yescharacteristic
273C2×C3×C4D4×D511yescharacteristic
274C2×C3×C4D4×D511yescharacteristic
275C3×C8—22no—
276C3×C8—41no—
277C3×C8—102no—
278C3×C8—201no—
279C22×C5C2×C3×C22⋊C411yescharacteristic
280C2×D5—21no—
281C2×D5—21no—
282C2×D5—21no—
283C2×D5—41no—
284C2×D5—41no—
285C2×D5—41no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—41no—
290C4×C5—41no—
291Dic5—21no—
292Dic5—21no—
293Dic5—41no—
294Dic5C3×#10412yes—
295C2×Q8—51no—
296C2×D4—51no—
297C2×D4—101no—
298C22×C4—51no—
299C22×C4—51no—
300C22×C4—51no—
301C22×C4—101no—
302M16—104no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—101no—
306C2×C8—101no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—101no—
310C4⋊C4—101no—
311C4⋊C4C3×C4×D511yescharacteristic
312C4⋊C4C3×C4×D511yescharacteristic
313C22⋊C4—101no—
314C22⋊C4—101no—
315C22⋊C4—101no—
316C22⋊C4—101no—
317C22⋊C4—101no—
318C42—51no—
319C42—51no—
320C42—51no—
321C42—101no—
322C42C22×C3×D511yescharacteristic
323C3×C5#152911yescharacteristic, complemented, Hall
324C22×C3—101no—
325C22×C3—101no—
326C22×C3—101no—
327C22×C3—201no—
328C22×C3—201no—
329C22×C3—201no—
330C22×C3D5×C22⋊C411yescharacteristic
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—41no—
335C3×C4—41no—
336C3×C4—52no—
337C3×C4—101no—
338C3×C4—101no—
339C3×C4—201no—
340C2×C5C3×#41311yescharacteristic
341C2×C5C2×C3×#10411yescharacteristic
342C2×C5C3×#42111yescharacteristic
343D5—41no—
344D5—81no—
345C23—51no—
346C23—101no—
347Q8—201no—
348D4—201no—
349D4—202no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—51no—
353C2×C4—51no—
354C2×C4—51no—
355C2×C4—102no—
356C2×C4—101no—
357C2×C4—201no—
358C2×C4—201no—
359C2×C4—202no—
360C2×C4C2×C3×C4×D511yescharacteristic
361C2×C4C3×D4×D511yescharacteristic
362C2×C4C3×D4×D511yescharacteristic
363C8—22no—
364C8—41no—
365C8—102no—
366C8—201no—
367C2×C3—201no—
368C2×C3—401no—
369C2×C3#6504011yescharacteristic
370C2×C3D5×#10411yescharacteristic
371C2×C3#6511011yescharacteristic
372C5C3×#152911yescharacteristic, complemented, Sylow
373C22—101no—
374C22—101no—
375C22—101no—
376C22—201no—
377C22—201no—
378C22—201no—
379C22C3×D5×C22⋊C411yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—41no—
384C4—41no—
385C4—52no—
386C4—101no—
387C4—101no—
388C4—201no—
389C3#1059915711yescharacteristic, direct product factor, Sylow
390C2—201no—
391C2—401no—
392C2C3×#6504011yescharacteristic
393C2C3×D5×#10411yescharacteristic
394C2C3×#6511011yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#330C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4041C4
cosocleC42×C5C23×C3
hypercenterC3×#330D5
hypocenterC5C3×#1529
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#330

Complements

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

NH ≅ G/Ntype
2. C3×#64996C2semidirect
3. C3×#64994C2semidirect
4. C3×C5×#330C2semidirect
5. C3×#64763C2semidirect
6. C3×#64684C2semidirect
7. C3×#64684C2semidirect
8. #10599157C3direct (N × H)
30. #64996C2×C3semidirect
31. #64994C2×C3semidirect
32. C5×#330C2×C3semidirect
33. #64763C2×C3semidirect
34. #64684C2×C3semidirect
35. #64684C2×C3semidirect
68. C3×#330D5semidirect
164. #330C3×D5semidirect
323. C3×C5#1529semidirect
372. C5C3×#1529semidirect
389. C3#10599157direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660252
C3×#649962
C3×#649942
C3×C5×#3302
C3×#647632
C3×#646842
#105991573
C3×#15295