Finite Group Databasebeta

← C3×#10598968 #14282277

Subgroups — C3×#10598968 #14282277

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D4×D5C211yesmaximal, characteristic
2C3×#65124C211yesmaximal, characteristic, complemented
3C3×C4×#676C211yesmaximal, characteristic, complemented
4C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic, complemented
7C3×#64679C211yesmaximal, characteristic, complemented
8#10598968C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×D4×D5C411yescharacteristic
10C22×C3×C4×D5—21no—
11C3×C4×C5×D4C2211yescharacteristic
12C3×D4×Dic5C411yescharacteristic
13C3×C4×C22⋊D5—21no—
14C2×C3×#676—21no—
15C3×#4039C411yescharacteristic
16C3×D5×C4⋊C4C411yescharacteristic
17C3×#4027—21no—
18C3×D5×C22⋊C4—21no—
19C3×C4×D20C2211yescharacteristic
20C3×C42×D5C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic, complemented
22C3×C4×C5×C8C2211yescharacteristic, complemented
23C3×#3952—21no—
24C3×#3947—21no—
25C3×#3947—21no—
26C3×C4⋊#168C2211yescharacteristic, complemented
27C3×C4×#168C2211yescharacteristic, complemented
28C3×#1490—51nomaximal, Hall
29C4×D4×D5C2×C311yescharacteristic
30#65124C2×C311yescharacteristic, complemented
31C4×#676C2×C311yescharacteristic, complemented
32C5×D4⋊C8C2×C311yescharacteristic, complemented
33D4⋊#168C2×C311yescharacteristic, complemented
34#64703C2×C311yescharacteristic, complemented
35#64679C2×C311yescharacteristic, complemented
36C23×C3×D5—21no—
37C2×C3×C5×D4C2×C411yescharacteristic
38C22×C3×C4×C5—21no—
39C2×C3×C22⋊D5—21no—
40C22×C3×Dic5—21no—
41C3×D4×D5—22no—
42C3×D4×D5—22no—
43C2×C3×D20C2×C411yescharacteristic
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—21no—
46C2×C3×C4×D5—21no—
47C2×C3×C4×D5—42no—
48C2×C3×C4×D5—42no—
49C2×C3×C4×D5C2×C411yescharacteristic
50C2×C3×C4×D5D411yescharacteristic
51C2×C3×C4×D5D411yescharacteristic
52C2×C3×C5×C8—21no—
53C2×C3×C5×C8—21no—
54C3×C5×C4⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4—21no—
56C3×C42×C5C2311yescharacteristic
57C3×C22⋊Dic5—21no—
58C3×#685—21no—
59C3×#685—21no—
60C3×C4⋊Dic5C2×C411yescharacteristic
61C3×#683—21no—
62C3×C4×Dic5C2×C411yescharacteristic
63C3×C4×Dic5D411yescharacteristic
64C3×C4×Dic5D411yescharacteristic
65C2×C3×#168—21no—
66C2×C3×#168—21no—
67C3×#676—24no—
68C2×C3×C4×D4—51no—
69C3×#432—51no—
70C3×C4×M16—51no—
71C3×D4⋊C8—51no—
72C3×D4⋊C8—51no—
73C3×D4⋊C8—51no—
74C3×D4⋊C8D511yescharacteristic, complemented
75C2×D4×D5C3×C411yescharacteristic
76C22×C4×D5—21no—
77C4×C5×D4C22×C311yescharacteristic
78D4×Dic5C3×C411yescharacteristic
79C4×C22⋊D5—21no—
80C2×#676—21no—
81#4039C3×C411yescharacteristic
82D5×C4⋊C4C3×C411yescharacteristic
83#4027—21no—
84D5×C22⋊C4—21no—
85C4×D20C22×C311yescharacteristic
86C42×D5C22×C311yescharacteristic
87C5×C4⋊C8C22×C311yescharacteristic, complemented
88C4×C5×C8C22×C311yescharacteristic, complemented
89#3952—21no—
90#3947—21no—
91#3947—21no—
92C4⋊#168C22×C311yescharacteristic, complemented
93C4×#168C22×C311yescharacteristic, complemented
94#1490—51noSylow
95C23×C3×C5—21no—
96C22×C3×D5—24no—
97C22×C3×D5—21no—
98C22×C3×D5—42no—
99C22×C3×D5—42no—
100C22×C3×D5C22⋊C411yescharacteristic
101C3×C5×D4—21no—
102C3×C5×D4M1612yescomplemented
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C3×C22⋊D5—24no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—42no—
112C2×C3×Dic5C22⋊C411yescharacteristic
113C2×C3×Dic5C22⋊C411yescharacteristic
114C2×C3×Dic5C22⋊C411yescharacteristic
115C3×D20—21no—
116C3×D20M1612yescomplemented
117C3×C4×D5—22no—
118C3×C4×D5—21no—
119C3×C4×D5—21no—
120C3×C4×D5—21no—
121C3×C4×D5—21no—
122C3×C4×D5—42no—
123C3×C4×D5—42no—
124C3×C4×D5—41no—
125C3×C4×D5—41no—
126C3×C5×C8—22no—
127C3×C5×C8—41no—
128C3×#168—22no—
129C3×#168—41no—
130C22×C3×D4—51no—
131C23×C3×C4—101no—
132C2×C3×M16—101no—
133C3×C4×D4—51no—
134C3×C4×D4—51no—
135C3×C4×D4—51no—
136C3×C4×D4—101no—
137C3×C4×D4—101no—
138C3×C4×D4C2×D511yescharacteristic
139C2×C3×C4⋊C4—51no—
140C2×C3×C22⋊C4—101no—
141C2×C3×C42—51no—
142C3×C4⋊C8—51no—
143C3×C4⋊C8C2×D511yescharacteristic, complemented
144C3×C22⋊C8—101no—
145C3×#97—101no—
146C3×#97—101no—
147C3×C4×C8—51no—
148C3×C4×C8C2×D511yescharacteristic, complemented
149C23×D5—21no—
150C2×C5×D4C2×C3×C411yescharacteristic
151C22×C4×C5—21no—
152C2×C22⋊D5—21no—
153C22×Dic5—21no—
154D4×D5—22no—
155D4×D5—22no—
156C2×D20C2×C3×C411yescharacteristic
157C2×C4×D5—21no—
158C2×C4×D5—21no—
159C2×C4×D5—21no—
160C2×C4×D5—42no—
161C2×C4×D5—42no—
162C2×C4×D5C2×C3×C411yescharacteristic
163C2×C4×D5C3×D411yescharacteristic
164C2×C4×D5C3×D411yescharacteristic
165C2×C5×C8—21no—
166C2×C5×C8—21no—
167C5×C4⋊C4C2×C3×C411yescharacteristic
168C5×C22⋊C4—21no—
169C42×C5C23×C311yescharacteristic
170C22⋊Dic5—21no—
171#685—21no—
172#685—21no—
173C4⋊Dic5C2×C3×C411yescharacteristic
174#683—21no—
175C4×Dic5C2×C3×C411yescharacteristic
176C4×Dic5C3×D411yescharacteristic
177C4×Dic5C3×D411yescharacteristic
178C2×#168—21no—
179C2×#168—21no—
180#676—24no—
181C2×C4×D4—51no—
182#432—51no—
183C4×M16—51no—
184D4⋊C8—51no—
185D4⋊C8—51no—
186D4⋊C8—51no—
187D4⋊C8C3×D511yescharacteristic, complemented
188C22×C3×C5—22no—
189C22×C3×C5—41no—
190C22×C3×C5—41no—
191C22×C3×C5C2×C22⋊C411yescharacteristic
192C2×C3×D5—21no—
193C2×C3×D5—21no—
194C2×C3×D5—22no—
195C2×C3×D5—48no—
196C2×C3×D5—41no—
197C2×C3×D5—41no—
198C2×C3×D5#10412yes—
199C3×C4×C5—21no—
200C3×C4×C5—41no—
201C3×C4×C5C2×M1611yescharacteristic
202C3×C4×C5C2×M1611yescharacteristic
203C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
204C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
205C3×Dic5—21no—
206C3×Dic5—21no—
207C3×Dic5—21no—
208C3×Dic5—41no—
209C24×C3—101no—
210C2×C3×D4—51no—
211C2×C3×D4—101no—
212C2×C3×D4—102no—
213C2×C3×D4—102no—
214C2×C3×D4C4×D511yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—51no—
217C22×C3×C4—51no—
218C22×C3×C4—51no—
219C22×C3×C4—101no—
220C22×C3×C4—101no—
221C22×C3×C4—101no—
222C22×C3×C4—101no—
223C22×C3×C4—202no—
224C22×C3×C4—202no—
225C3×M16—104no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—101no—
229C2×C3×C8—101no—
230C3×C4⋊C4—51no—
231C3×C4⋊C4—101no—
232C3×C4⋊C4C4×D511yescharacteristic
233C3×C22⋊C4—21no—
234C3×C22⋊C4—101no—
235C3×C22⋊C4—101no—
236C3×C22⋊C4—101no—
237C3×C42—51no—
238C3×C42—51no—
239C3×C42—51no—
240C3×C42C22×D511yescharacteristic
241C23×C5—21no—
242C22×D5—24no—
243C22×D5—21no—
244C22×D5—42no—
245C22×D5—42no—
246C22×D5C3×C22⋊C411yescharacteristic
247C5×D4—21no—
248C5×D4C3×M1612yescomplemented
249C2×C4×C5—21no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
252C2×C4×C5C22×C3×C411yescharacteristic
253C2×C4×C5C2×C3×D411yescharacteristic
254C2×C4×C5C2×C3×D411yescharacteristic
255C22⋊D5—24no—
256C2×Dic5—21no—
257C2×Dic5—42no—
258C2×Dic5C3×C22⋊C411yescharacteristic
259C2×Dic5C3×C22⋊C411yescharacteristic
260C2×Dic5C3×C22⋊C411yescharacteristic
261D20—21no—
262D20C3×M1612yescomplemented
263C4×D5—22no—
264C4×D5—21no—
265C4×D5—21no—
266C4×D5—21no—
267C4×D5—21no—
268C4×D5—42no—
269C4×D5—42no—
270C4×D5—41no—
271C4×D5—41no—
272C5×C8—22no—
273C5×C8—41no—
274#168—22no—
275#168—41no—
276C22×D4—51no—
277C23×C4—101no—
278C2×M16—101no—
279C4×D4—51no—
280C4×D4—51no—
281C4×D4—51no—
282C4×D4—101no—
283C4×D4—101no—
284C4×D4C2×C3×D511yescharacteristic
285C2×C4⋊C4—51no—
286C2×C22⋊C4—101no—
287C2×C42—51no—
288C4⋊C8—51no—
289C4⋊C8C2×C3×D511yescharacteristic, complemented
290C22⋊C8—101no—
291#97—101no—
292#97—101no—
293C4×C8—51no—
294C4×C8C2×C3×D511yescharacteristic, complemented
295C2×C3×C5—42no—
296C2×C3×C5#40711yescharacteristic
297C2×C3×C5#41811yescharacteristic
298C2×C3×C5C2×#10411yescharacteristic
299C3×D5—22no—
300C3×D5—42no—
301C23×C3—21no—
302C23×C3—51no—
303C23×C3—104no—
304C23×C3—101no—
305C23×C3—202no—
306C23×C3—202no—
307C3×D4—21no—
308C3×D4—52no—
309C3×D4—104no—
310C3×D4—101no—
311C3×D4#67612yescomplemented
312C2×C3×C4—21no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—51no—
316C2×C3×C4—51no—
317C2×C3×C4—51no—
318C2×C3×C4—102no—
319C2×C3×C4—101no—
320C2×C3×C4—101no—
321C2×C3×C4—101no—
322C2×C3×C4—101no—
323C2×C3×C4—101no—
324C2×C3×C4—202no—
325C2×C3×C4—202no—
326C2×C3×C4—202no—
327C2×C3×C4—201no—
328C2×C3×C4—201no—
329C2×C3×C4C2×C4×D511yescharacteristic
330C2×C3×C4D4×D511yescharacteristic
331C2×C3×C4D4×D511yescharacteristic
332C3×C8—22no—
333C3×C8—41no—
334C3×C8—102no—
335C3×C8—201no—
336C22×C5—22no—
337C22×C5—41no—
338C22×C5—41no—
339C22×C5C2×C3×C22⋊C411yescharacteristic
340C2×D5—21no—
341C2×D5—21no—
342C2×D5—22no—
343C2×D5—48no—
344C2×D5—41no—
345C2×D5—41no—
346C2×D5C3×#10412yes—
347C4×C5—21no—
348C4×C5—41no—
349C4×C5C2×C3×M1611yescharacteristic
350C4×C5C2×C3×M1611yescharacteristic
351C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
352C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
353Dic5—21no—
354Dic5—21no—
355Dic5—21no—
356Dic5—41no—
357C24—101no—
358C2×D4—51no—
359C2×D4—101no—
360C2×D4—102no—
361C2×D4—102no—
362C2×D4C3×C4×D511yescharacteristic
363C22×C4—21no—
364C22×C4—51no—
365C22×C4—51no—
366C22×C4—51no—
367C22×C4—101no—
368C22×C4—101no—
369C22×C4—101no—
370C22×C4—101no—
371C22×C4—202no—
372C22×C4—202no—
373M16—104no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—101no—
377C2×C8—101no—
378C4⋊C4—51no—
379C4⋊C4—101no—
380C4⋊C4C3×C4×D511yescharacteristic
381C22⋊C4—21no—
382C22⋊C4—101no—
383C22⋊C4—101no—
384C22⋊C4—101no—
385C42—51no—
386C42—51no—
387C42—51no—
388C42C22×C3×D511yescharacteristic
389C3×C5#149011yescharacteristic, complemented, Hall
390C22×C3—22no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—52no—
394C22×C3—101no—
395C22×C3—101no—
396C22×C3—102no—
397C22×C3—208no—
398C22×C3—201no—
399C22×C3—201no—
400C22×C3D5×C22⋊C411yescharacteristic
401C3×C4—21no—
402C3×C4—41no—
403C3×C4—101no—
404C3×C4—101no—
405C3×C4—101no—
406C3×C4—201no—
407C3×C4C2×#67611yescharacteristic
408C3×C4D5×M1611yescharacteristic
409C3×C4#405711yescharacteristic
410C3×C4#406011yescharacteristic
411C2×C5—42no—
412C2×C5C3×#40711yescharacteristic
413C2×C5C3×#41811yescharacteristic
414C2×C5C2×C3×#10411yescharacteristic
415D5—22no—
416D5—42no—
417C23—21no—
418C23—51no—
419C23—104no—
420C23—101no—
421C23—202no—
422C23—202no—
423D4—21no—
424D4—52no—
425D4—104no—
426D4—101no—
427D4C3×#67612yescomplemented
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—51no—
432C2×C4—51no—
433C2×C4—51no—
434C2×C4—102no—
435C2×C4—101no—
436C2×C4—101no—
437C2×C4—101no—
438C2×C4—101no—
439C2×C4—101no—
440C2×C4—202no—
441C2×C4—202no—
442C2×C4—202no—
443C2×C4—201no—
444C2×C4—201no—
445C2×C4C2×C3×C4×D511yescharacteristic
446C2×C4C3×D4×D511yescharacteristic
447C2×C4C3×D4×D511yescharacteristic
448C8—22no—
449C8—41no—
450C8—102no—
451C8—201no—
452C2×C3—42no—
453C2×C3—102no—
454C2×C3—202no—
455C2×C3#6501511yescharacteristic
456C2×C3#6505911yescharacteristic
457C2×C3D5×#10411yescharacteristic
458C5C3×#149011yescharacteristic, complemented, Sylow
459C22—22no—
460C22—41no—
461C22—41no—
462C22—52no—
463C22—101no—
464C22—101no—
465C22—102no—
466C22—208no—
467C22—201no—
468C22—201no—
469C22C3×D5×C22⋊C411yescharacteristic
470C4—21no—
471C4—41no—
472C4—101no—
473C4—101no—
474C4—101no—
475C4—201no—
476C4C2×C3×#67611yescharacteristic
477C4C3×D5×M1611yescharacteristic
478C4C3×#405711yescharacteristic
479C4C3×#406011yescharacteristic
480C3#1059896811yescharacteristic, direct product factor, Sylow
481C2—42no—
482C2—102no—
483C2—202no—
484C2C3×#6501511yescharacteristic
485C2C3×#6505911yescharacteristic
486C2C3×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×D4×D5C4
cosocleC42×C5C23×C3
hypercenterC3×D4⋊C8D5
hypocenterC5C3×#1490
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×#65124C2semidirect
3. C3×C4×#676C2semidirect
4. C3×C5×D4⋊C8C2semidirect
5. C3×D4⋊#168C2semidirect
6. C3×#64703C2semidirect
7. C3×#64679C2semidirect
8. #10598968C3direct (N × H)
21. C3×C5×C4⋊C8C22semidirect
22. C3×C4×C5×C8C22semidirect
26. C3×C4⋊#168C22semidirect
27. C3×C4×#168C22semidirect
30. #65124C2×C3semidirect
31. C4×#676C2×C3semidirect
32. C5×D4⋊C8C2×C3semidirect
33. D4⋊#168C2×C3semidirect
34. #64703C2×C3semidirect
35. #64679C2×C3semidirect
74. C3×D4⋊C8D5semidirect
87. C5×C4⋊C8C22×C3semidirect
88. C4×C5×C8C22×C3semidirect
92. C4⋊#168C22×C3semidirect
93. C4×#168C22×C3semidirect
102. C3×C5×D4M16semidirect
116. C3×D20M16semidirect
143. C3×C4⋊C8C2×D5semidirect
148. C3×C4×C8C2×D5semidirect
187. D4⋊C8C3×D5semidirect
248. C5×D4C3×M16semidirect
262. D20C3×M16semidirect
289. C4⋊C8C2×C3×D5semidirect
294. C4×C8C2×C3×D5semidirect
311. C3×D4#676semidirect
389. C3×C5#1490semidirect
427. D4C3×#676semidirect
458. C5C3×#1490semidirect
480. C3#10598968direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×D4×D52
C3×#651242
C3×C4×#6762
C3×C5×D4⋊C82
C3×D4⋊#1682
C3×#647032
C3×#646792
#105989683
C3×#14905