Finite Group Databasebeta

← C3×#10599745 #14295361

Subgroups — C3×#10599745 #14295361

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4027C211yesmaximal, characteristic
2C2×C3×#3938C212yesmaximal
3C3×C22⋊C4×Dic5C212yesmaximal, complemented
4C3×C5×#342C211yesmaximal, characteristic, complemented
5C3×#64746C211yesmaximal, characteristic, complemented
6#10599745C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C22⋊D5C2211yescharacteristic
8C23×C3×Dic5C2211yescharacteristic
9C22×C3×C4×D5C411yescharacteristic, complemented
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×C3×C5×C22⋊C4C2212yes—
12C2×C3×C22⋊Dic5C2212yes—
13C2×C3×#685C411yescharacteristic, complemented
14C2×C3×#683C411yescharacteristic, complemented
15C2×C3×C4×Dic5—22no—
16C2×C3×C4×Dic5C411yescharacteristic, complemented
17C3×#4027—22no—
18C3×#4027—22no—
19C3×#3963—22no—
20C3×#3938C418yescomplemented
21C3×C4×#99—51nomaximal, Hall
22C2×#4027C2×C311yescharacteristic
23C2×#3938C2×C312yes—
24C22⋊C4×Dic5C2×C312yescomplemented
25C5×#342C2×C311yescharacteristic, complemented
26#64746C2×C311yescharacteristic, complemented
27C24×C3×C5C2311yescharacteristic
28C23×C3×D5C2×C411yescharacteristic
29C22×C3×C4×C5—22no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5C2×C411yescharacteristic
32C2×C3×C22⋊D5—22no—
33C2×C3×C22⋊D5—21no—
34C2×C3×C22⋊D5—21no—
35C2×C3×C22⋊D5C2×C414yes—
36C22×C3×Dic5—22no—
37C22×C3×Dic5—42no—
38C22×C3×Dic5C2×C411yescharacteristic
39C22×C3×Dic5C2×C411yescharacteristic
40C22×C3×Dic5C2×C411yescharacteristic
41C22×C3×Dic5D412yes—
42C22×C3×Dic5D412yes—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—42no—
46C3×C5×C22⋊C4—22no—
47C3×C5×C22⋊C4—22no—
48C3×C5×C22⋊C4C2×C414yescomplemented
49C3×C22⋊Dic5—22no—
50C3×C22⋊Dic5C2×C414yescomplemented
51C3×#685—22no—
52C3×#683—22no—
53C3×C4×Dic5—21no—
54C3×C4×Dic5—21no—
55C3×C4×Dic5—44no—
56C2×C3×C4×D4—51no—
57C2×C3×#99—52no—
58C3×C4×C22⋊C4—52no—
59C3×#342—51no—
60C3×#342D511yescharacteristic, complemented
61C22×C22⋊D5C22×C311yescharacteristic
62C23×Dic5C22×C311yescharacteristic
63C22×C4×D5C3×C411yescharacteristic, complemented
64C2×C5×C22⋊C4C22×C311yescharacteristic
65C2×C5×C22⋊C4C22×C312yes—
66C2×C22⋊Dic5C22×C312yes—
67C2×#685C3×C411yescharacteristic, complemented
68C2×#683C3×C411yescharacteristic, complemented
69C2×C4×Dic5—22no—
70C2×C4×Dic5C3×C411yescharacteristic, complemented
71#4027—22no—
72#4027—22no—
73#3963—22no—
74#3938C3×C418yescomplemented
75C4×#99—51noSylow
76C23×C3×C5—41no—
77C23×C3×C5—41no—
78C23×C3×C5C22×C411yescharacteristic
79C23×C3×C5C22×C412yes—
80C23×C3×C5C2×D412yes—
81C23×C3×C5#4111yescharacteristic
82C23×C3×C5#4111yescharacteristic
83C22×C3×D5—21no—
84C22×C3×D5—21no—
85C22×C3×D5—41no—
86C22×C3×D5—41no—
87C22×C3×D5C4212yescomplemented
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—24no—
91C2×C3×C4×C5—42no—
92C2×C3×C4×C5—42no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95C3×C22⋊D5—24no—
96C3×C22⋊D5—24no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5—24no—
100C2×C3×Dic5—22no—
101C2×C3×Dic5—24no—
102C2×C3×Dic5—41no—
103C2×C3×Dic5—42no—
104C2×C3×Dic5—42no—
105C2×C3×Dic5—42no—
106C2×C3×Dic5C4212yescomplemented
107C2×C3×Dic5C22⋊C411yescharacteristic
108C2×C3×Dic5C22⋊C412yes—
109C2×C3×Dic5C22⋊C411yescharacteristic
110C3×C4×D5—42no—
111C3×C4×D5—42no—
112C22×C3×D4—51no—
113C23×C3×C4—51no—
114C23×C3×C4—51no—
115C3×C4×D4—102no—
116C3×C4×D4—102no—
117C2×C3×C4⋊C4—51no—
118C2×C3×C22⋊C4—52no—
119C2×C3×C22⋊C4—51no—
120C2×C3×C22⋊C4C2×D511yescharacteristic
121C2×C3×C22⋊C4C2×D512yes—
122C2×C3×C42—51no—
123C2×C3×C42—102no—
124C3×#99—58no—
125C3×#95—102no—
126C24×C5C23×C311yescharacteristic
127C23×D5C2×C3×C411yescharacteristic
128C22×C4×C5—22no—
129C22×C4×C5C2×C3×C411yescharacteristic
130C22×C4×C5C2×C3×C411yescharacteristic
131C2×C22⋊D5—22no—
132C2×C22⋊D5—21no—
133C2×C22⋊D5—21no—
134C2×C22⋊D5C2×C3×C414yes—
135C22×Dic5—22no—
136C22×Dic5—42no—
137C22×Dic5C2×C3×C411yescharacteristic
138C22×Dic5C2×C3×C411yescharacteristic
139C22×Dic5C2×C3×C411yescharacteristic
140C22×Dic5C3×D412yes—
141C22×Dic5C3×D412yes—
142C2×C4×D5—21no—
143C2×C4×D5—21no—
144C2×C4×D5—42no—
145C5×C22⋊C4—22no—
146C5×C22⋊C4—22no—
147C5×C22⋊C4C2×C3×C414yescomplemented
148C22⋊Dic5—22no—
149C22⋊Dic5C2×C3×C414yescomplemented
150#685—22no—
151#683—22no—
152C4×Dic5—21no—
153C4×Dic5—21no—
154C4×Dic5—44no—
155C2×C4×D4—51no—
156C2×#99—52no—
157C4×C22⋊C4—52no—
158#342—51no—
159#342C3×D511yescharacteristic, complemented
160C22×C3×C5—22no—
161C22×C3×C5—21no—
162C22×C3×C5—22no—
163C22×C3×C5—21no—
164C22×C3×C5—42no—
165C22×C3×C5—41no—
166C22×C3×C5—41no—
167C22×C3×C5C2×C4211yescharacteristic
168C22×C3×C5C2×C22⋊C411yescharacteristic
169C22×C3×C5#11711yescharacteristic
170C22×C3×C5C4×D412yes—
171C22×C3×C5C4×D412yes—
172C2×C3×D5—22no—
173C2×C3×D5—42no—
174C2×C3×D5—41no—
175C2×C3×D5—41no—
176C2×C3×D5—42no—
177C3×C4×C5—44no—
178C3×C4×C5—41no—
179C3×C4×C5—41no—
180C3×Dic5—22no—
181C3×Dic5—21no—
182C3×Dic5—22no—
183C3×Dic5—44no—
184C3×Dic5#9912yescomplemented
185C24×C3—51no—
186C24×C3C22×D511yescharacteristic
187C2×C3×D4—54no—
188C2×C3×D4—102no—
189C2×C3×D4—101no—
190C2×C3×D4—101no—
191C22×C3×C4—22no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4—52no—
195C22×C3×C4—51no—
196C22×C3×C4—52no—
197C22×C3×C4—101no—
198C22×C3×C4—101no—
199C22×C3×C4—102no—
200C22×C3×C4—202no—
201C22×C3×C4—202no—
202C22×C3×C4C4×D511yescharacteristic
203C22×C3×C4C4×D511yescharacteristic
204C3×C4⋊C4—102no—
205C3×C22⋊C4—22no—
206C3×C22⋊C4—22no—
207C3×C22⋊C4—54no—
208C3×C22⋊C4—102no—
209C3×C22⋊C4—102no—
210C3×C22⋊C4C4×D514yescomplemented
211C3×C42—101no—
212C3×C42—101no—
213C3×C42—204no—
214C23×C5—41no—
215C23×C5—41no—
216C23×C5C22×C3×C411yescharacteristic
217C23×C5C22×C3×C412yes—
218C23×C5C2×C3×D412yes—
219C23×C5C3×#4111yescharacteristic
220C23×C5C3×#4111yescharacteristic
221C22×D5—21no—
222C22×D5—21no—
223C22×D5—41no—
224C22×D5—41no—
225C22×D5C3×C4212yescomplemented
226C2×C4×C5—21no—
227C2×C4×C5—21no—
228C2×C4×C5—24no—
229C2×C4×C5—42no—
230C2×C4×C5—42no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C22⋊D5—24no—
234C22⋊D5—24no—
235C2×Dic5—21no—
236C2×Dic5—21no—
237C2×Dic5—24no—
238C2×Dic5—22no—
239C2×Dic5—24no—
240C2×Dic5—41no—
241C2×Dic5—42no—
242C2×Dic5—42no—
243C2×Dic5—42no—
244C2×Dic5C3×C4212yescomplemented
245C2×Dic5C3×C22⋊C411yescharacteristic
246C2×Dic5C3×C22⋊C412yes—
247C2×Dic5C3×C22⋊C411yescharacteristic
248C4×D5—42no—
249C4×D5—42no—
250C22×D4—51no—
251C23×C4—51no—
252C23×C4—51no—
253C4×D4—102no—
254C4×D4—102no—
255C2×C4⋊C4—51no—
256C2×C22⋊C4—52no—
257C2×C22⋊C4—51no—
258C2×C22⋊C4C2×C3×D511yescharacteristic
259C2×C22⋊C4C2×C3×D512yes—
260C2×C42—51no—
261C2×C42—102no—
262#99—58no—
263#95—102no—
264C2×C3×C5—22no—
265C2×C3×C5—22no—
266C2×C3×C5—21no—
267C2×C3×C5—21no—
268C2×C3×C5C4×C22⋊C411yescharacteristic
269C2×C3×C5C2×#9911yescharacteristic
270C2×C3×C5#41011yescharacteristic
271C3×D5—42no—
272C23×C3—41no—
273C23×C3—41no—
274C23×C3—52no—
275C23×C3—101no—
276C23×C3—101no—
277C23×C3—201no—
278C23×C3—201no—
279C23×C3C2×C4×D511yescharacteristic
280C23×C3C2×C4×D512yes—
281C23×C3D4×D512yes—
282C23×C3#71111yescharacteristic
283C23×C3#71311yescharacteristic
284C3×D4—104no—
285C3×D4—104no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—24no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—51no—
294C2×C3×C4—52no—
295C2×C3×C4—51no—
296C2×C3×C4—52no—
297C2×C3×C4—104no—
298C2×C3×C4—102no—
299C2×C3×C4—101no—
300C2×C3×C4—101no—
301C2×C3×C4—104no—
302C2×C3×C4—202no—
303C2×C3×C4—202no—
304C2×C3×C4—201no—
305C2×C3×C4—202no—
306C2×C3×C4—202no—
307C2×C3×C4—202no—
308C22×C5—22no—
309C22×C5—21no—
310C22×C5—22no—
311C22×C5—21no—
312C22×C5—42no—
313C22×C5—41no—
314C22×C5—41no—
315C22×C5C2×C3×C4211yescharacteristic
316C22×C5C2×C3×C22⋊C411yescharacteristic
317C22×C5C3×#11711yescharacteristic
318C22×C5C3×C4×D412yes—
319C22×C5C3×C4×D412yes—
320C2×D5—22no—
321C2×D5—42no—
322C2×D5—41no—
323C2×D5—41no—
324C2×D5—42no—
325C4×C5—44no—
326C4×C5—41no—
327C4×C5—41no—
328Dic5—22no—
329Dic5—21no—
330Dic5—22no—
331Dic5—44no—
332Dic5C3×#9912yescomplemented
333C24—51no—
334C24C22×C3×D511yescharacteristic
335C2×D4—54no—
336C2×D4—102no—
337C2×D4—101no—
338C2×D4—101no—
339C22×C4—22no—
340C22×C4—51no—
341C22×C4—51no—
342C22×C4—52no—
343C22×C4—51no—
344C22×C4—52no—
345C22×C4—101no—
346C22×C4—101no—
347C22×C4—102no—
348C22×C4—202no—
349C22×C4—202no—
350C22×C4C3×C4×D511yescharacteristic
351C22×C4C3×C4×D511yescharacteristic
352C4⋊C4—102no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—54no—
356C22⋊C4—102no—
357C22⋊C4—102no—
358C22⋊C4C3×C4×D514yescomplemented
359C42—101no—
360C42—101no—
361C42—204no—
362C3×C5C4×#9911yescharacteristic, complemented, Hall
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—22no—
366C22×C3—21no—
367C22×C3—42no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—102no—
371C22×C3—202no—
372C22×C3—202no—
373C22×C3—201no—
374C22×C3—201no—
375C22×C3C42×D511yescharacteristic
376C22×C3D5×C22⋊C411yescharacteristic
377C22×C3#402712yes—
378C22×C3#403811yescharacteristic
379C22×C3#403912yes—
380C3×C4—44no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—52no—
384C3×C4—102no—
385C3×C4—101no—
386C3×C4—102no—
387C3×C4—204no—
388C2×C5—22no—
389C2×C5—22no—
390C2×C5—21no—
391C2×C5—21no—
392C2×C5C3×C4×C22⋊C411yescharacteristic
393C2×C5C2×C3×#9911yescharacteristic
394C2×C5C3×#41011yescharacteristic
395D5—42no—
396C23—41no—
397C23—41no—
398C23—52no—
399C23—101no—
400C23—101no—
401C23—201no—
402C23—201no—
403C23C2×C3×C4×D511yescharacteristic
404C23C2×C3×C4×D512yes—
405C23C3×D4×D512yes—
406C23C3×#71111yescharacteristic
407C23C3×#71311yescharacteristic
408D4—104no—
409D4—104no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—24no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—51no—
418C2×C4—52no—
419C2×C4—51no—
420C2×C4—52no—
421C2×C4—104no—
422C2×C4—102no—
423C2×C4—101no—
424C2×C4—101no—
425C2×C4—104no—
426C2×C4—202no—
427C2×C4—202no—
428C2×C4—202no—
429C2×C4—201no—
430C2×C4—202no—
431C2×C4—202no—
432C2×C3—22no—
433C2×C3—22no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—202no—
437C2×C3#6495511yescharacteristic
438C2×C3#6502911yescharacteristic
439C2×C3D5×#9911yescharacteristic
440C5C3×C4×#9911yescharacteristic, complemented, Sylow
441C22—22no—
442C22—21no—
443C22—22no—
444C22—21no—
445C22—42no—
446C22—41no—
447C22—41no—
448C22—102no—
449C22—202no—
450C22—202no—
451C22—201no—
452C22—201no—
453C22C3×C42×D511yescharacteristic
454C22C3×D5×C22⋊C411yescharacteristic
455C22C3×#402712yes—
456C22C3×#403811yescharacteristic
457C22C3×#403912yes—
458C4—44no—
459C4—41no—
460C4—41no—
461C4—52no—
462C4—101no—
463C4—102no—
464C4—102no—
465C4—204no—
466C3#1059974511yescharacteristic, direct product factor, Sylow
467C2—22no—
468C2—22no—
469C2—21no—
470C2—21no—
471C2—202no—
472C2C3×#6495511yescharacteristic
473C2C3×#6502911yescharacteristic
474C2C3×D5×#9911yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC22×C5C2×C3×C42
FrattiniC24C22×C3×D5
FittingC3×C5×#342C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C22⋊D5C22
cosocleC24×C5C23×C3
hypercenterC3×#342D5
hypocenterC5C3×C4×#99
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C3×#342

Complements

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

NH ≅ G/Ntype
3. C3×C22⋊C4×Dic5C2semidirect
4. C3×C5×#342C2semidirect
5. C3×#64746C2semidirect
6. #10599745C3direct (N × H)
9. C22×C3×C4×D5C4semidirect
13. C2×C3×#685C4semidirect
14. C2×C3×#683C4semidirect
16. C2×C3×C4×Dic5C4semidirect
20. C3×#3938C4semidirect
24. C22⋊C4×Dic5C2×C3semidirect
25. C5×#342C2×C3semidirect
26. #64746C2×C3semidirect
48. C3×C5×C22⋊C4C2×C4semidirect
50. C3×C22⋊Dic5C2×C4semidirect
60. C3×#342D5semidirect
63. C22×C4×D5C3×C4semidirect
67. C2×#685C3×C4semidirect
68. C2×#683C3×C4semidirect
70. C2×C4×Dic5C3×C4semidirect
74. #3938C3×C4semidirect
87. C22×C3×D5C42semidirect
106. C2×C3×Dic5C42semidirect
147. C5×C22⋊C4C2×C3×C4semidirect
149. C22⋊Dic5C2×C3×C4semidirect
159. #342C3×D5semidirect
184. C3×Dic5#99semidirect
210. C3×C22⋊C4C4×D5semidirect
225. C22×D5C3×C42semidirect
244. C2×Dic5C3×C42semidirect
332. Dic5C3×#99semidirect
358. C22⋊C4C3×C4×D5semidirect
362. C3×C5C4×#99semidirect
440. C5C3×C4×#99semidirect
466. C3#10599745direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40272
C2×C3×#39382
C3×C22⋊C4×Dic52
C3×C5×#3422
C3×#647462
#105997453
C3×C4×#995