Finite Group Databasebeta

← C3×#10598958 #14281555

Subgroups — C3×#10598958 #14281555

Order 1920.

552 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#711C211yesmaximal, characteristic
2C3×#65122C211yesmaximal, characteristic, complemented
3C3×C4×C8×D5C211yesmaximal, characteristic, complemented
4C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6C3×#64704C211yesmaximal, characteristic, complemented
7C3×#64676C211yesmaximal, characteristic, complemented
8#10598958C311yesmaximal, 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×C8×D5—21no—
15C3×#4038C411yescharacteristic
16C3×#4033C411yescharacteristic
17C3×#4027—21no—
18C3×#4023—21no—
19C3×C42×D5C2211yescharacteristic
20C3×C4×Dic10C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C4×C5×C8C2211yescharacteristic
23C3×#3952—21no—
24C3×C8×Dic5—21no—
25C3×C8×Dic5—21no—
26C3×C4⋊#168C2211yescharacteristic
27C3×C4×#168C2211yescharacteristic
28C3×#1476—51nomaximal, Hall
29C4×#711C2×C311yescharacteristic
30#65122C2×C311yescharacteristic, complemented
31C4×C8×D5C2×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×#711C814yescomplemented
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×C8×D5—24no—
66C3×C4×#41—51no—
67C3×#431—51no—
68C2×C3×C4×C8—51no—
69C3×Q8⋊C8—51no—
70C3×Q8⋊C8—51no—
71C3×D4⋊C8—51no—
72C3×D4⋊C8D511yescharacteristic, complemented
73C2×#711C3×C411yescharacteristic
74C4×C5×D4C22×C311yescharacteristic
75D4×Dic5C3×C411yescharacteristic
76C4×C22⋊D5—21no—
77C2×C4×Dic5—21no—
78C2×C8×D5—21no—
79#4038C3×C411yescharacteristic
80#4033C3×C411yescharacteristic
81#4027—21no—
82#4023—21no—
83C42×D5C22×C311yescharacteristic
84C4×Dic10C22×C311yescharacteristic
85C5×C4⋊C8C22×C311yescharacteristic
86C4×C5×C8C22×C311yescharacteristic
87#3952—21no—
88C8×Dic5—21no—
89C8×Dic5—21no—
90C4⋊#168C22×C311yescharacteristic
91C4×#168C22×C311yescharacteristic
92#1476—51noSylow
93C23×C3×C5—21no—
94C22×C3×D5C22⋊C411yescharacteristic
95C3×C5×D4—21no—
96C3×C5×D4C2×C812yescomplemented
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C3×C22⋊D5—24no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5—24no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—42no—
108C2×C3×Dic5C22⋊C411yescharacteristic
109C2×C3×Dic5C22⋊C411yescharacteristic
110C2×C3×Dic5C22⋊C411yescharacteristic
111C3×C4×D5—21no—
112C3×C4×D5—21no—
113C3×C4×D5—22no—
114C3×C4×D5C2×C812yes—
115C3×C4×D5M1612yes—
116C3×Dic10—21no—
117C3×Dic10C2×C812yescomplemented
118C3×C5×C8—22no—
119C3×C5×C8—41no—
120C3×#168—22no—
121C3×#168—41no—
122C2×C3×#41—51no—
123C22×C3×C8—101no—
124C3×C4×Q8—51no—
125C3×C4×Q8—51no—
126C3×C4×D4—51no—
127C3×C4×D4—101no—
128C3×C4×D4—101no—
129C3×C4×D4C2×D511yescharacteristic
130C3×#117—51no—
131C3×#117—101no—
132C2×C3×C42—51no—
133C2×C3×C42—101no—
134C3×C4⋊C8—51no—
135C3×C4⋊C8C2×D511yescharacteristic
136C3×C22⋊C8—101no—
137C3×C4×C8—51no—
138C3×C4×C8—101no—
139C3×C4×C8—101no—
140C3×C4×C8C2×D511yescharacteristic
141C2×C5×D4C2×C3×C411yescharacteristic
142C22×C4×C5—21no—
143C2×C22⋊D5—21no—
144C22×Dic5—21no—
145C22×Dic5—21no—
146#711—22no—
147#711C3×C814yescomplemented
148C2×C4×D5C2×C3×C411yescharacteristic
149C2×C4×D5C3×D411yescharacteristic
150C2×C4×D5C3×D411yescharacteristic
151C2×Dic10C2×C3×C411yescharacteristic
152C2×C5×C8—21no—
153C2×C5×C8—21no—
154C5×C4⋊C4C2×C3×C411yescharacteristic
155C5×C22⋊C4—21no—
156C42×C5C23×C311yescharacteristic
157C22⋊Dic5—21no—
158#685—21no—
159C4⋊Dic5C2×C3×C411yescharacteristic
160#683—21no—
161#683—21no—
162C4×Dic5—21no—
163C4×Dic5—21no—
164C4×Dic5—21no—
165C4×Dic5C2×C3×C411yescharacteristic
166C4×Dic5C3×D411yescharacteristic
167C4×Dic5C3×D411yescharacteristic
168C2×#168—21no—
169C2×#168—21no—
170C8×D5—24no—
171C4×#41—51no—
172#431—51no—
173C2×C4×C8—51no—
174Q8⋊C8—51no—
175Q8⋊C8—51no—
176D4⋊C8—51no—
177D4⋊C8C3×D511yescharacteristic, complemented
178C22×C3×C5—22no—
179C22×C3×C5—41no—
180C22×C3×C5—41no—
181C22×C3×C5C2×C22⋊C411yescharacteristic
182C2×C3×D5—21no—
183C2×C3×D5—21no—
184C2×C3×D5C22⋊C812yes—
185C3×C4×C5—21no—
186C3×C4×C5—41no—
187C3×C4×C5C22×C811yescharacteristic
188C3×C4×C5C2×M1611yescharacteristic
189C3×C4×C5#13511yescharacteristic
190C3×C4×C5#13511yescharacteristic
191C3×Dic5—22no—
192C3×Dic5—21no—
193C3×Dic5—41no—
194C3×Dic5C22⋊C812yes—
195C3×Dic5#10412yes—
196C3×#41—54no—
197C3×#41—102no—
198C2×C3×Q8—51no—
199C2×C3×D4—101no—
200C2×C3×D4C4×D511yescharacteristic
201C22×C3×C4—21no—
202C22×C3×C4—51no—
203C22×C3×C4—51no—
204C22×C3×C4—51no—
205C22×C3×C4—101no—
206C22×C3×C4—101no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—104no—
210C2×C3×C8—101no—
211C2×C3×C8—101no—
212C3×C4⋊C4—51no—
213C3×C4⋊C4—101no—
214C3×C4⋊C4—101no—
215C3×C4⋊C4C4×D511yescharacteristic
216C3×C22⋊C4—21no—
217C3×C22⋊C4—101no—
218C3×C22⋊C4—101no—
219C3×C42—51no—
220C3×C42—51no—
221C3×C42—51no—
222C3×C42—101no—
223C3×C42—101no—
224C3×C42—101no—
225C3×C42C22×D511yescharacteristic
226C23×C5—21no—
227C22×D5C3×C22⋊C411yescharacteristic
228C5×D4—21no—
229C5×D4C2×C3×C812yescomplemented
230C2×C4×C5—21no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C2×C4×C5C22×C3×C411yescharacteristic
234C2×C4×C5C2×C3×D411yescharacteristic
235C2×C4×C5C2×C3×D411yescharacteristic
236C22⋊D5—24no—
237C2×Dic5—21no—
238C2×Dic5—24no—
239C2×Dic5—21no—
240C2×Dic5—42no—
241C2×Dic5C3×C22⋊C411yescharacteristic
242C2×Dic5C3×C22⋊C411yescharacteristic
243C2×Dic5C3×C22⋊C411yescharacteristic
244C4×D5—21no—
245C4×D5—21no—
246C4×D5—22no—
247C4×D5C2×C3×C812yes—
248C4×D5C3×M1612yes—
249Dic10—21no—
250Dic10C2×C3×C812yescomplemented
251C5×C8—22no—
252C5×C8—41no—
253#168—22no—
254#168—41no—
255C2×#41—51no—
256C22×C8—101no—
257C4×Q8—51no—
258C4×Q8—51no—
259C4×D4—51no—
260C4×D4—101no—
261C4×D4—101no—
262C4×D4C2×C3×D511yescharacteristic
263#117—51no—
264#117—101no—
265C2×C42—51no—
266C2×C42—101no—
267C4⋊C8—51no—
268C4⋊C8C2×C3×D511yescharacteristic
269C22⋊C8—101no—
270C4×C8—51no—
271C4×C8—101no—
272C4×C8—101no—
273C4×C8C2×C3×D511yescharacteristic
274C2×C3×C5—42no—
275C2×C3×C5C2×C22⋊C811yescharacteristic
276C2×C3×C5#41611yescharacteristic
277C2×C3×C5C2×#10411yescharacteristic
278C3×D5—22no—
279C23×C3—21no—
280C23×C3—51no—
281C3×Q8—52no—
282C3×Q8—101no—
283C3×D4—21no—
284C3×D4—104no—
285C3×D4C8×D512yescomplemented
286C2×C3×C4—21no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—51no—
290C2×C3×C4—51no—
291C2×C3×C4—52no—
292C2×C3×C4—52no—
293C2×C3×C4—51no—
294C2×C3×C4—102no—
295C2×C3×C4—104no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4—101no—
299C2×C3×C4—101no—
300C2×C3×C4—202no—
301C2×C3×C4C2×C4×D511yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C3×C8—22no—
305C3×C8—41no—
306C3×C8—102no—
307C3×C8—201no—
308C22×C5—22no—
309C22×C5—41no—
310C22×C5—41no—
311C22×C5C2×C3×C22⋊C411yescharacteristic
312C2×D5—21no—
313C2×D5—21no—
314C2×D5C3×C22⋊C812yes—
315C4×C5—21no—
316C4×C5—41no—
317C4×C5C22×C3×C811yescharacteristic
318C4×C5C2×C3×M1611yescharacteristic
319C4×C5C3×#13511yescharacteristic
320C4×C5C3×#13511yescharacteristic
321Dic5—22no—
322Dic5—21no—
323Dic5—41no—
324Dic5C3×C22⋊C812yes—
325Dic5C3×#10412yes—
326#41—54no—
327#41—102no—
328C2×Q8—51no—
329C2×D4—101no—
330C2×D4C3×C4×D511yescharacteristic
331C22×C4—21no—
332C22×C4—51no—
333C22×C4—51no—
334C22×C4—51no—
335C22×C4—101no—
336C22×C4—101no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—104no—
340C2×C8—101no—
341C2×C8—101no—
342C4⋊C4—51no—
343C4⋊C4—101no—
344C4⋊C4—101no—
345C4⋊C4C3×C4×D511yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—101no—
348C22⋊C4—101no—
349C42—51no—
350C42—51no—
351C42—51no—
352C42—101no—
353C42—101no—
354C42—101no—
355C42C22×C3×D511yescharacteristic
356C3×C5#147611yescharacteristic, complemented, Hall
357C22×C3—22no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—52no—
361C22×C3—101no—
362C22×C3—101no—
363C22×C3D5×C22⋊C411yescharacteristic
364C3×C4—21no—
365C3×C4—41no—
366C3×C4—52no—
367C3×C4—52no—
368C3×C4—101no—
369C3×C4—102no—
370C3×C4—201no—
371C3×C4C2×C8×D511yescharacteristic
372C3×C4D5×M1611yescharacteristic
373C3×C4#405811yescharacteristic
374C3×C4#406211yescharacteristic
375C2×C5—42no—
376C2×C5C2×C3×C22⋊C811yescharacteristic
377C2×C5C3×#41611yescharacteristic
378C2×C5C2×C3×#10411yescharacteristic
379D5—22no—
380C23—21no—
381C23—51no—
382Q8—52no—
383Q8—101no—
384D4—21no—
385D4—104no—
386D4C3×C8×D512yescomplemented
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—51no—
391C2×C4—51no—
392C2×C4—52no—
393C2×C4—52no—
394C2×C4—51no—
395C2×C4—102no—
396C2×C4—104no—
397C2×C4—101no—
398C2×C4—101no—
399C2×C4—101no—
400C2×C4—101no—
401C2×C4—202no—
402C2×C4C2×C3×C4×D511yescharacteristic
403C2×C4C3×D4×D511yescharacteristic
404C2×C4C3×D4×D511yescharacteristic
405C8—22no—
406C8—41no—
407C8—102no—
408C8—201no—
409C2×C3—42no—
410C2×C3—102no—
411C2×C3D5×C22⋊C811yescharacteristic
412C2×C3#6506111yescharacteristic
413C2×C3D5×#10411yescharacteristic
414C5C3×#147611yescharacteristic, complemented, Sylow
415C22—22no—
416C22—41no—
417C22—41no—
418C22—52no—
419C22—101no—
420C22—101no—
421C22C3×D5×C22⋊C411yescharacteristic
422C4—21no—
423C4—41no—
424C4—52no—
425C4—52no—
426C4—101no—
427C4—102no—
428C4—201no—
429C4C2×C3×C8×D511yescharacteristic
430C4C3×D5×M1611yescharacteristic
431C4C3×#405811yescharacteristic
432C4C3×#406211yescharacteristic
433C3#1059895811yescharacteristic, direct product factor, Sylow
434C2—42no—
435C2—102no—
436C2C3×D5×C22⋊C811yescharacteristic
437C2C3×#6506111yescharacteristic
438C2C3×D5×#10411yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC4×C5C22×C3×C8
FrattiniC42C22×C3×D5
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#711C4
cosocleC42×C5C23×C3
hypercenterC3×D4⋊C8D5
hypocenterC5C3×#1476
LCSG ▷ 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×#65122C2semidirect
3. C3×C4×C8×D5C2semidirect
4. C3×C5×D4⋊C8C2semidirect
5. C3×D4⋊#168C2semidirect
6. C3×#64704C2semidirect
7. C3×#64676C2semidirect
8. #10598958C3direct (N × H)
30. #65122C2×C3semidirect
31. C4×C8×D5C2×C3semidirect
32. C5×D4⋊C8C2×C3semidirect
33. D4⋊#168C2×C3semidirect
34. #64704C2×C3semidirect
35. #64676C2×C3semidirect
42. C3×#711C8semidirect
72. C3×D4⋊C8D5semidirect
96. C3×C5×D4C2×C8semidirect
117. C3×Dic10C2×C8semidirect
147. #711C3×C8semidirect
177. D4⋊C8C3×D5semidirect
229. C5×D4C2×C3×C8semidirect
250. Dic10C2×C3×C8semidirect
285. C3×D4C8×D5semidirect
356. C3×C5#1476semidirect
386. D4C3×C8×D5semidirect
414. C5C3×#1476semidirect
433. C3#10598958direct (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×#651222
C3×C4×C8×D52
C3×C5×D4⋊C82
C3×D4⋊#1682
C3×#647042
C3×#646762
#105989583
C3×#14765