Finite Group Databasebeta

← C3×#10598963 #14281916

Subgroups — C3×#10598963 #14281916

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65891C211yesmaximal, characteristic
2C3×D5×C4⋊C8C211yesmaximal, characteristic, complemented
3C3×C4×#676C211yesmaximal, characteristic, complemented
4C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6C3×#64704C211yesmaximal, characteristic, complemented
7C3×#64676C211yesmaximal, characteristic, complemented
8#10598963C311yesmaximal, characteristic, direct product factor, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C3×#4084C411yescharacteristic
11C3×#4082C411yescharacteristic
12C3×C4×C22⋊D5—21no—
13C3×#4072—21no—
14C2×C3×#676—21no—
15C2×C3×C8×D5—21no—
16C3×#4043C411yescharacteristic
17C3×#4036C411yescharacteristic
18C3×#4029—21no—
19C3×#4025—21no—
20C3×C42×D5C2211yescharacteristic
21C3×C4×Dic10C2211yescharacteristic
22C3×C5×C4⋊C8C2211yescharacteristic
23C3×C4×C5×C8C2211yescharacteristic
24C3×#3947—21no—
25C3×#3946—21no—
26C3×C4⋊#168C2211yescharacteristic
27C3×C4×#168C2211yescharacteristic
28C3×#1483—51nomaximal, Hall
29#65891C2×C311yescharacteristic
30D5×C4⋊C8C2×C311yescharacteristic, complemented
31C4×#676C2×C311yescharacteristic, complemented
32C5×D4⋊C8C2×C311yescharacteristic, complemented
33D4⋊#168C2×C311yescharacteristic, complemented
34#64704C2×C311yescharacteristic, complemented
35#64676C2×C311yescharacteristic, complemented
36C2×C3×C5×D4C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×C3×C22⋊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⋊C4C2×C411yescharacteristic
46C3×C5×C22⋊C4—21no—
47C3×C42×C5C2311yescharacteristic
48C3×C22⋊Dic5—21no—
49C3×C22⋊Dic5—21no—
50C3×C22⋊Dic5—21no—
51C3×#685—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—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×C8×D5—42no—
65C3×#529—51no—
66C2×C3×C4⋊C8—51no—
67C3×C4×M16—51no—
68C3×Q8⋊C8—51no—
69C3×Q8⋊C8—51no—
70C3×D4⋊C8—51no—
71C3×D4⋊C8D511yescharacteristic, complemented
72C4×C5×D4C22×C311yescharacteristic
73#4084C3×C411yescharacteristic
74#4082C3×C411yescharacteristic
75C4×C22⋊D5—21no—
76#4072—21no—
77C2×#676—21no—
78C2×C8×D5—21no—
79#4043C3×C411yescharacteristic
80#4036C3×C411yescharacteristic
81#4029—21no—
82#4025—21no—
83C42×D5C22×C311yescharacteristic
84C4×Dic10C22×C311yescharacteristic
85C5×C4⋊C8C22×C311yescharacteristic
86C4×C5×C8C22×C311yescharacteristic
87#3947—21no—
88#3946—21no—
89C4⋊#168C22×C311yescharacteristic
90C4×#168C22×C311yescharacteristic
91#1483—51noSylow
92C23×C3×C5—21no—
93C22×C3×D5C22⋊C411yescharacteristic
94C3×C5×D4—21no—
95C3×C5×D4—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C3×C22⋊D5—42no—
103C2×C3×Dic5—21no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5C22⋊C411yescharacteristic
106C2×C3×Dic5C22⋊C411yescharacteristic
107C2×C3×Dic5C22⋊C411yescharacteristic
108C3×C4×D5—22no—
109C3×C4×D5—21no—
110C3×C4×D5—21no—
111C3×C4×D5—21no—
112C3×C4×D5—21no—
113C3×Dic10—21no—
114C3×Dic10—21no—
115C3×C5×C8—22no—
116C3×C5×C8—41no—
117C3×#168—22no—
118C3×#168—41no—
119C2×C3×M16—101no—
120C22×C3×C8—101no—
121C3×#126—101no—
122C3×#125—51no—
123C3×#124—51no—
124C3×#123—101no—
125C3×C22⋊Q8—51no—
126C3×#121—51no—
127C3×C4×Q8—51no—
128C3×C4×D4—101no—
129C3×C4×D4C2×D511yescharacteristic
130C3×#117—101no—
131C2×C3×C42—51no—
132C3×C4⋊C8—51no—
133C3×C4⋊C8—101no—
134C3×C4⋊C8C2×D511yescharacteristic
135C3×#97—101no—
136C3×C4×C8—51no—
137C3×C4×C8C2×D511yescharacteristic
138C2×C5×D4C2×C3×C411yescharacteristic
139C22×C4×C5—21no—
140C2×C22⋊D5—21no—
141C2×C4×D5C2×C3×C411yescharacteristic
142C2×C4×D5C3×D411yescharacteristic
143C2×C4×D5C3×D411yescharacteristic
144C2×Dic10C2×C3×C411yescharacteristic
145C2×C5×C8—21no—
146C2×C5×C8—21no—
147C5×C4⋊C4C2×C3×C411yescharacteristic
148C5×C22⋊C4—21no—
149C42×C5C23×C311yescharacteristic
150C22⋊Dic5—21no—
151C22⋊Dic5—21no—
152C22⋊Dic5—21no—
153#685—21no—
154C4⋊Dic5—21no—
155C4⋊Dic5—21no—
156C4⋊Dic5C2×C3×C411yescharacteristic
157#683—21no—
158#683—21no—
159C4×Dic5—21no—
160C4×Dic5C2×C3×C411yescharacteristic
161C4×Dic5C3×D411yescharacteristic
162C4×Dic5C3×D411yescharacteristic
163C2×#168—21no—
164C2×#168—21no—
165#676—24no—
166C8×D5—42no—
167#529—51no—
168C2×C4⋊C8—51no—
169C4×M16—51no—
170Q8⋊C8—51no—
171Q8⋊C8—51no—
172D4⋊C8—51no—
173D4⋊C8C3×D511yescharacteristic, complemented
174C22×C3×C5—41no—
175C22×C3×C5—41no—
176C22×C3×C5—41no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C2×C3×D5—21no—
179C2×C3×D5—21no—
180C2×C3×D5#10412yes—
181C3×C4×C5—21no—
182C3×C4×C5—41no—
183C3×C4×C5#13111yescharacteristic
184C3×C4×C5#13111yescharacteristic
185C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
186C3×C4×C5#13711yescharacteristic
187C3×Dic5—21no—
188C3×Dic5—21no—
189C3×Dic5—21no—
190C3×Dic5—41no—
191C3×Dic5—41no—
192C2×C3×Q8—51no—
193C2×C3×D4—101no—
194C2×C3×D4C4×D511yescharacteristic
195C22×C3×C4—21no—
196C22×C3×C4—51no—
197C22×C3×C4—51no—
198C22×C3×C4—51no—
199C3×M16—104no—
200C2×C3×C8—21no—
201C2×C3×C8—21no—
202C2×C3×C8—101no—
203C2×C3×C8—101no—
204C2×C3×C8—202no—
205C3×C4⋊C4—51no—
206C3×C4⋊C4—101no—
207C3×C4⋊C4—101no—
208C3×C4⋊C4—101no—
209C3×C4⋊C4—101no—
210C3×C4⋊C4C4×D511yescharacteristic
211C3×C22⋊C4—21no—
212C3×C22⋊C4—101no—
213C3×C22⋊C4—101no—
214C3×C22⋊C4—101no—
215C3×C22⋊C4—101no—
216C3×C42—51no—
217C3×C42—51no—
218C3×C42—51no—
219C3×C42—101no—
220C3×C42C22×D511yescharacteristic
221C23×C5—21no—
222C22×D5C3×C22⋊C411yescharacteristic
223C5×D4—21no—
224C5×D4—21no—
225C2×C4×C5—21no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5C22×C3×C411yescharacteristic
229C2×C4×C5C2×C3×D411yescharacteristic
230C2×C4×C5C2×C3×D411yescharacteristic
231C22⋊D5—42no—
232C2×Dic5—21no—
233C2×Dic5—21no—
234C2×Dic5C3×C22⋊C411yescharacteristic
235C2×Dic5C3×C22⋊C411yescharacteristic
236C2×Dic5C3×C22⋊C411yescharacteristic
237C4×D5—22no—
238C4×D5—21no—
239C4×D5—21no—
240C4×D5—21no—
241C4×D5—21no—
242Dic10—21no—
243Dic10—21no—
244C5×C8—22no—
245C5×C8—41no—
246#168—22no—
247#168—41no—
248C2×M16—101no—
249C22×C8—101no—
250#126—101no—
251#125—51no—
252#124—51no—
253#123—101no—
254C22⋊Q8—51no—
255#121—51no—
256C4×Q8—51no—
257C4×D4—101no—
258C4×D4C2×C3×D511yescharacteristic
259#117—101no—
260C2×C42—51no—
261C4⋊C8—51no—
262C4⋊C8—101no—
263C4⋊C8C2×C3×D511yescharacteristic
264#97—101no—
265C4×C8—51no—
266C4×C8C2×C3×D511yescharacteristic
267C2×C3×C5—81no—
268C2×C3×C5#40811yescharacteristic
269C2×C3×C5#41711yescharacteristic
270C2×C3×C5C2×#10411yescharacteristic
271C3×D5—22no—
272C23×C3—21no—
273C23×C3—51no—
274C3×Q8—101no—
275C3×Q8—101no—
276C3×D4—21no—
277C3×D4—21no—
278C3×D4—202no—
279C2×C3×C4—21no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—51no—
283C2×C3×C4—51no—
284C2×C3×C4—51no—
285C2×C3×C4—102no—
286C2×C3×C4—101no—
287C2×C3×C4—101no—
288C2×C3×C4—101no—
289C2×C3×C4—101no—
290C2×C3×C4—101no—
291C2×C3×C4—101no—
292C2×C3×C4C2×C4×D511yescharacteristic
293C2×C3×C4D4×D511yescharacteristic
294C2×C3×C4D4×D511yescharacteristic
295C3×C8—22no—
296C3×C8—41no—
297C3×C8—102no—
298C3×C8—201no—
299C22×C5—41no—
300C22×C5—41no—
301C22×C5—41no—
302C22×C5C2×C3×C22⋊C411yescharacteristic
303C2×D5—21no—
304C2×D5—21no—
305C2×D5C3×#10412yes—
306C4×C5—21no—
307C4×C5—41no—
308C4×C5C3×#13111yescharacteristic
309C4×C5C3×#13111yescharacteristic
310C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
311C4×C5C3×#13711yescharacteristic
312Dic5—21no—
313Dic5—21no—
314Dic5—21no—
315Dic5—41no—
316Dic5—41no—
317C2×Q8—51no—
318C2×D4—101no—
319C2×D4C3×C4×D511yescharacteristic
320C22×C4—21no—
321C22×C4—51no—
322C22×C4—51no—
323C22×C4—51no—
324M16—104no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—101no—
328C2×C8—101no—
329C2×C8—202no—
330C4⋊C4—51no—
331C4⋊C4—101no—
332C4⋊C4—101no—
333C4⋊C4—101no—
334C4⋊C4—101no—
335C4⋊C4C3×C4×D511yescharacteristic
336C22⋊C4—21no—
337C22⋊C4—101no—
338C22⋊C4—101no—
339C22⋊C4—101no—
340C22⋊C4—101no—
341C42—51no—
342C42—51no—
343C42—51no—
344C42—101no—
345C42C22×C3×D511yescharacteristic
346C3×C5#148311yescharacteristic, complemented, Hall
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—52no—
351C22×C3—101no—
352C22×C3—101no—
353C22×C3D5×C22⋊C411yescharacteristic
354C3×C4—21no—
355C3×C4—41no—
356C3×C4—101no—
357C3×C4—101no—
358C3×C4—101no—
359C3×C4—201no—
360C3×C4—201no—
361C3×C4#404711yescharacteristic
362C3×C4#405311yescharacteristic
363C3×C4#405711yescharacteristic
364C3×C4#406111yescharacteristic
365C2×C5—81no—
366C2×C5C3×#40811yescharacteristic
367C2×C5C3×#41711yescharacteristic
368C2×C5C2×C3×#10411yescharacteristic
369D5—22no—
370C23—21no—
371C23—51no—
372Q8—101no—
373Q8—101no—
374D4—21no—
375D4—21no—
376D4—202no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—51no—
381C2×C4—51no—
382C2×C4—51no—
383C2×C4—102no—
384C2×C4—101no—
385C2×C4—101no—
386C2×C4—101no—
387C2×C4—101no—
388C2×C4—101no—
389C2×C4—101no—
390C2×C4C2×C3×C4×D511yescharacteristic
391C2×C4C3×D4×D511yescharacteristic
392C2×C4C3×D4×D511yescharacteristic
393C8—22no—
394C8—41no—
395C8—102no—
396C8—201no—
397C2×C3—81no—
398C2×C3—102no—
399C2×C3#6501611yescharacteristic
400C2×C3#6506011yescharacteristic
401C2×C3D5×#10411yescharacteristic
402C5C3×#148311yescharacteristic, complemented, Sylow
403C22—41no—
404C22—41no—
405C22—41no—
406C22—52no—
407C22—101no—
408C22—101no—
409C22C3×D5×C22⋊C411yescharacteristic
410C4—21no—
411C4—41no—
412C4—101no—
413C4—101no—
414C4—101no—
415C4—201no—
416C4—201no—
417C4C3×#404711yescharacteristic
418C4C3×#405311yescharacteristic
419C4C3×#405711yescharacteristic
420C4C3×#406111yescharacteristic
421C3#1059896311yescharacteristic, direct product factor, Sylow
422C2—81no—
423C2—102no—
424C2C3×#6501611yescharacteristic
425C2C3×#6506011yescharacteristic
426C2C3×D5×#10411yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4084C4
cosocleC42×C5C23×C3
hypercenterC3×D4⋊C8D5
hypocenterC5C3×#1483
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×D5×C4⋊C8C2semidirect
3. C3×C4×#676C2semidirect
4. C3×C5×D4⋊C8C2semidirect
5. C3×D4⋊#168C2semidirect
6. C3×#64704C2semidirect
7. C3×#64676C2semidirect
8. #10598963C3direct (N × H)
30. D5×C4⋊C8C2×C3semidirect
31. C4×#676C2×C3semidirect
32. C5×D4⋊C8C2×C3semidirect
33. D4⋊#168C2×C3semidirect
34. #64704C2×C3semidirect
35. #64676C2×C3semidirect
71. C3×D4⋊C8D5semidirect
173. D4⋊C8C3×D5semidirect
346. C3×C5#1483semidirect
402. C5C3×#1483semidirect
421. C3#10598963direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658912
C3×D5×C4⋊C82
C3×C4×#6762
C3×C5×D4⋊C82
C3×D4⋊#1682
C3×#647042
C3×#646762
#105989633
C3×#14835