Finite Group Databasebeta

← C3×#10598967 #14282214

Subgroups — C3×#10598967 #14282214

Order 1920.

532 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#711C211yesmaximal, characteristic
2C3×#65126C211yesmaximal, 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#10598967C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#711C411yescharacteristic
10C3×C4×C5×D4C2211yescharacteristic
11C3×D4×Dic5C411yescharacteristic
12C3×C4×C22⋊D5—21no—
13C2×C3×C4×Dic5—21no—
14C2×C3×#676—21no—
15C2×C3×#676—21no—
16C3×#4038C411yescharacteristic
17C3×#4033C411yescharacteristic
18C3×#4027—21no—
19C3×#4023—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×#1489—51nomaximal, Hall
29C4×#711C2×C311yescharacteristic
30#65126C2×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—
39C22×C3×Dic5—21no—
40C22×C3×Dic5—21no—
41C3×#711—22no—
42C3×#711—22no—
43C2×C3×C4×D5C2×C411yescharacteristic
44C2×C3×C4×D5D411yescharacteristic
45C2×C3×C4×D5D411yescharacteristic
46C2×C3×Dic10C2×C411yescharacteristic
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8—21no—
49C3×C5×C4⋊C4C2×C411yescharacteristic
50C3×C5×C22⋊C4—21no—
51C3×C42×C5C2311yescharacteristic
52C3×C22⋊Dic5—21no—
53C3×#685—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56C3×#683—21no—
57C3×C4×Dic5—21no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5—21no—
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65C3×#676—24no—
66C3×#676—42no—
67C3×C4×#41—51no—
68C3×#423—51no—
69C3×C4×M16—51no—
70C3×Q8⋊C8—51no—
71C3×Q8⋊C8—51no—
72C3×D4⋊C8—51no—
73C3×D4⋊C8D511yescharacteristic, complemented
74C2×#711C3×C411yescharacteristic
75C4×C5×D4C22×C311yescharacteristic
76D4×Dic5C3×C411yescharacteristic
77C4×C22⋊D5—21no—
78C2×C4×Dic5—21no—
79C2×#676—21no—
80C2×#676—21no—
81#4038C3×C411yescharacteristic
82#4033C3×C411yescharacteristic
83#4027—21no—
84#4023—21no—
85C42×D5C22×C311yescharacteristic
86C4×Dic10C22×C311yescharacteristic
87C5×C4⋊C8C22×C311yescharacteristic
88C4×C5×C8C22×C311yescharacteristic
89#3947—21no—
90#3946—21no—
91C4⋊#168C22×C311yescharacteristic
92C4×#168C22×C311yescharacteristic
93#1489—51noSylow
94C23×C3×C5—21no—
95C22×C3×D5C22⋊C411yescharacteristic
96C3×C5×D4—21no—
97C3×C5×D4M1612yescomplemented
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C3×C22⋊D5—24no—
105C2×C3×Dic5—24no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—42no—
109C2×C3×Dic5C22⋊C411yescharacteristic
110C2×C3×Dic5C22⋊C411yescharacteristic
111C2×C3×Dic5C22⋊C411yescharacteristic
112C3×C4×D5—21no—
113C3×C4×D5—21no—
114C3×C4×D5—21no—
115C3×C4×D5—21no—
116C3×C4×D5—22no—
117C3×Dic10—21no—
118C3×Dic10M1612yescomplemented
119C3×C5×C8—22no—
120C3×C5×C8—41no—
121C3×#168—22no—
122C3×#168—41no—
123C2×C3×#41—51no—
124C2×C3×M16—101no—
125C2×C3×M16—101no—
126C3×C4×Q8—51no—
127C3×C4×Q8—51no—
128C3×C4×D4—51no—
129C3×C4×D4—101no—
130C3×C4×D4—101no—
131C3×C4×D4C2×D511yescharacteristic
132C3×#117—51no—
133C3×#117—101no—
134C2×C3×C42—51no—
135C2×C3×C42—101no—
136C3×C4⋊C8—51no—
137C3×C4⋊C8—101no—
138C3×C4⋊C8C2×D511yescharacteristic
139C3×#97—101no—
140C3×C4×C8—51no—
141C3×C4×C8C2×D511yescharacteristic
142C2×C5×D4C2×C3×C411yescharacteristic
143C22×C4×C5—21no—
144C2×C22⋊D5—21no—
145C22×Dic5—21no—
146C22×Dic5—21no—
147#711—22no—
148#711—22no—
149C2×C4×D5C2×C3×C411yescharacteristic
150C2×C4×D5C3×D411yescharacteristic
151C2×C4×D5C3×D411yescharacteristic
152C2×Dic10C2×C3×C411yescharacteristic
153C2×C5×C8—21no—
154C2×C5×C8—21no—
155C5×C4⋊C4C2×C3×C411yescharacteristic
156C5×C22⋊C4—21no—
157C42×C5C23×C311yescharacteristic
158C22⋊Dic5—21no—
159#685—21no—
160C4⋊Dic5C2×C3×C411yescharacteristic
161#683—21no—
162#683—21no—
163C4×Dic5—21no—
164C4×Dic5—21no—
165C4×Dic5—21no—
166C4×Dic5C2×C3×C411yescharacteristic
167C4×Dic5C3×D411yescharacteristic
168C4×Dic5C3×D411yescharacteristic
169C2×#168—21no—
170C2×#168—21no—
171#676—24no—
172#676—42no—
173C4×#41—51no—
174#423—51no—
175C4×M16—51no—
176Q8⋊C8—51no—
177Q8⋊C8—51no—
178D4⋊C8—51no—
179D4⋊C8C3×D511yescharacteristic, complemented
180C22×C3×C5—22no—
181C22×C3×C5—41no—
182C22×C3×C5—41no—
183C22×C3×C5C2×C22⋊C411yescharacteristic
184C2×C3×D5—21no—
185C2×C3×D5—21no—
186C2×C3×D5—21no—
187C3×C4×C5—21no—
188C3×C4×C5—41no—
189C3×C4×C5C2×M1611yescharacteristic
190C3×C4×C5C2×M1611yescharacteristic
191C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
192C3×C4×C5#13711yescharacteristic
193C3×Dic5—22no—
194C3×Dic5—21no—
195C3×Dic5—21no—
196C3×Dic5—41no—
197C3×Dic5#10412yes—
198C3×#41—102no—
199C3×#41—102no—
200C2×C3×Q8—51no—
201C2×C3×D4—101no—
202C2×C3×D4C4×D511yescharacteristic
203C22×C3×C4—21no—
204C22×C3×C4—51no—
205C22×C3×C4—51no—
206C22×C3×C4—51no—
207C22×C3×C4—101no—
208C22×C3×C4—101no—
209C3×M16—104no—
210C3×M16—202no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—101no—
214C2×C3×C8—101no—
215C3×C4⋊C4—51no—
216C3×C4⋊C4—101no—
217C3×C4⋊C4—101no—
218C3×C4⋊C4C4×D511yescharacteristic
219C3×C22⋊C4—21no—
220C3×C22⋊C4—101no—
221C3×C22⋊C4—101no—
222C3×C42—51no—
223C3×C42—51no—
224C3×C42—51no—
225C3×C42—101no—
226C3×C42—101no—
227C3×C42—101no—
228C3×C42C22×D511yescharacteristic
229C23×C5—21no—
230C22×D5C3×C22⋊C411yescharacteristic
231C5×D4—21no—
232C5×D4C3×M1612yescomplemented
233C2×C4×C5—21no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5C22×C3×C411yescharacteristic
237C2×C4×C5C2×C3×D411yescharacteristic
238C2×C4×C5C2×C3×D411yescharacteristic
239C22⋊D5—24no—
240C2×Dic5—24no—
241C2×Dic5—21no—
242C2×Dic5—21no—
243C2×Dic5—42no—
244C2×Dic5C3×C22⋊C411yescharacteristic
245C2×Dic5C3×C22⋊C411yescharacteristic
246C2×Dic5C3×C22⋊C411yescharacteristic
247C4×D5—21no—
248C4×D5—21no—
249C4×D5—21no—
250C4×D5—21no—
251C4×D5—22no—
252Dic10—21no—
253Dic10C3×M1612yescomplemented
254C5×C8—22no—
255C5×C8—41no—
256#168—22no—
257#168—41no—
258C2×#41—51no—
259C2×M16—101no—
260C2×M16—101no—
261C4×Q8—51no—
262C4×Q8—51no—
263C4×D4—51no—
264C4×D4—101no—
265C4×D4—101no—
266C4×D4C2×C3×D511yescharacteristic
267#117—51no—
268#117—101no—
269C2×C42—51no—
270C2×C42—101no—
271C4⋊C8—51no—
272C4⋊C8—101no—
273C4⋊C8C2×C3×D511yescharacteristic
274#97—101no—
275C4×C8—51no—
276C4×C8C2×C3×D511yescharacteristic
277C2×C3×C5—42no—
278C2×C3×C5#40711yescharacteristic
279C2×C3×C5#41711yescharacteristic
280C2×C3×C5C2×#10411yescharacteristic
281C3×D5—41no—
282C23×C3—21no—
283C23×C3—51no—
284C3×Q8—52no—
285C3×Q8—101no—
286C3×D4—21no—
287C3×D4—104no—
288C3×D4#67612yescomplemented
289C2×C3×C4—21no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—51no—
293C2×C3×C4—51no—
294C2×C3×C4—51no—
295C2×C3×C4—102no—
296C2×C3×C4—104no—
297C2×C3×C4—101no—
298C2×C3×C4—101no—
299C2×C3×C4—101no—
300C2×C3×C4—101no—
301C2×C3×C4—101no—
302C2×C3×C4—101no—
303C2×C3×C4—202no—
304C2×C3×C4C2×C4×D511yescharacteristic
305C2×C3×C4D4×D511yescharacteristic
306C2×C3×C4D4×D511yescharacteristic
307C3×C8—22no—
308C3×C8—41no—
309C3×C8—102no—
310C3×C8—201no—
311C22×C5—22no—
312C22×C5—41no—
313C22×C5—41no—
314C22×C5C2×C3×C22⋊C411yescharacteristic
315C2×D5—21no—
316C2×D5—21no—
317C2×D5—21no—
318C4×C5—21no—
319C4×C5—41no—
320C4×C5C2×C3×M1611yescharacteristic
321C4×C5C2×C3×M1611yescharacteristic
322C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
323C4×C5C3×#13711yescharacteristic
324Dic5—22no—
325Dic5—21no—
326Dic5—21no—
327Dic5—41no—
328Dic5C3×#10412yes—
329#41—102no—
330#41—102no—
331C2×Q8—51no—
332C2×D4—101no—
333C2×D4C3×C4×D511yescharacteristic
334C22×C4—21no—
335C22×C4—51no—
336C22×C4—51no—
337C22×C4—51no—
338C22×C4—101no—
339C22×C4—101no—
340M16—104no—
341M16—202no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—101no—
345C2×C8—101no—
346C4⋊C4—51no—
347C4⋊C4—101no—
348C4⋊C4—101no—
349C4⋊C4C3×C4×D511yescharacteristic
350C22⋊C4—21no—
351C22⋊C4—101no—
352C22⋊C4—101no—
353C42—51no—
354C42—51no—
355C42—51no—
356C42—101no—
357C42—101no—
358C42—101no—
359C42C22×C3×D511yescharacteristic
360C3×C5#148911yescharacteristic, complemented, Hall
361C22×C3—22no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—101no—
365C22×C3—101no—
366C22×C3—101no—
367C22×C3D5×C22⋊C411yescharacteristic
368C3×C4—21no—
369C3×C4—41no—
370C3×C4—52no—
371C3×C4—101no—
372C3×C4—101no—
373C3×C4—102no—
374C3×C4—201no—
375C3×C4C2×#67611yescharacteristic
376C3×C4D5×M1611yescharacteristic
377C3×C4#405711yescharacteristic
378C3×C4#406111yescharacteristic
379C2×C5—42no—
380C2×C5C3×#40711yescharacteristic
381C2×C5C3×#41711yescharacteristic
382C2×C5C2×C3×#10411yescharacteristic
383D5—41no—
384C23—21no—
385C23—51no—
386Q8—52no—
387Q8—101no—
388D4—21no—
389D4—104no—
390D4C3×#67612yescomplemented
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—51no—
395C2×C4—51no—
396C2×C4—51no—
397C2×C4—102no—
398C2×C4—104no—
399C2×C4—101no—
400C2×C4—101no—
401C2×C4—101no—
402C2×C4—101no—
403C2×C4—101no—
404C2×C4—101no—
405C2×C4—202no—
406C2×C4C2×C3×C4×D511yescharacteristic
407C2×C4C3×D4×D511yescharacteristic
408C2×C4C3×D4×D511yescharacteristic
409C8—22no—
410C8—41no—
411C8—102no—
412C8—201no—
413C2×C3—42no—
414C2×C3—201no—
415C2×C3#6501511yescharacteristic
416C2×C3#6506011yescharacteristic
417C2×C3D5×#10411yescharacteristic
418C5C3×#148911yescharacteristic, complemented, Sylow
419C22—22no—
420C22—41no—
421C22—41no—
422C22—101no—
423C22—101no—
424C22—101no—
425C22C3×D5×C22⋊C411yescharacteristic
426C4—21no—
427C4—41no—
428C4—52no—
429C4—101no—
430C4—101no—
431C4—102no—
432C4—201no—
433C4C2×C3×#67611yescharacteristic
434C4C3×D5×M1611yescharacteristic
435C4C3×#405711yescharacteristic
436C4C3×#406111yescharacteristic
437C3#1059896711yescharacteristic, direct product factor, Sylow
438C2—42no—
439C2—201no—
440C2C3×#6501511yescharacteristic
441C2C3×#6506011yescharacteristic
442C2C3×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 radicalC2×C3×#711C4
cosocleC42×C5C23×C3
hypercenterC3×D4⋊C8D5
hypocenterC5C3×#1489
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×#65126C2semidirect
3. C3×C4×#676C2semidirect
4. C3×C5×D4⋊C8C2semidirect
5. C3×D4⋊#168C2semidirect
6. C3×#64704C2semidirect
7. C3×#64676C2semidirect
8. #10598967C3direct (N × H)
30. #65126C2×C3semidirect
31. C4×#676C2×C3semidirect
32. C5×D4⋊C8C2×C3semidirect
33. D4⋊#168C2×C3semidirect
34. #64704C2×C3semidirect
35. #64676C2×C3semidirect
73. C3×D4⋊C8D5semidirect
97. C3×C5×D4M16semidirect
118. C3×Dic10M16semidirect
179. D4⋊C8C3×D5semidirect
232. C5×D4C3×M16semidirect
253. Dic10C3×M16semidirect
288. C3×D4#676semidirect
360. C3×C5#1489semidirect
390. D4C3×#676semidirect
418. C5C3×#1489semidirect
437. C3#10598967direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×#7112
C3×#651262
C3×C4×#6762
C3×C5×D4⋊C82
C3×D4⋊#1682
C3×#647042
C3×#646762
#105989673
C3×#14895