Finite Group Databasebeta

← C3×#10599128 #14283151

Subgroups — C3×#10599128 #14283151

Order 1920.

588 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×C22⋊Q8C211yesmaximal, characteristic
2C3×#65015C211yesmaximal, characteristic
3C3×#64955C211yesmaximal, characteristic
4C3×C5×#328C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6C3×#64687C211yesmaximal, characteristic, complemented
7C3×#64672C211yesmaximal, characteristic, complemented
8#10599128C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×Q8×D5C411yescharacteristic, complemented
10C22×C3×C4×D5C2211yescharacteristic
11C3×C5×C22⋊Q8C2211yescharacteristic
12C3×#4092C411yescharacteristic, complemented
13C2×C3×#685—21no—
14C3×#4070C2211yescharacteristic
15C2×C3×C4×Dic5—21no—
16C2×C3×#676—21no—
17C3×#4043C411yescharacteristic, complemented
18C3×#4042—21no—
19C3×D5×C4⋊C4—21no—
20C3×D5×C4⋊C4C411yescharacteristic, complemented
21C3×D5×C22⋊C4—21no—
22C3×#4024—21no—
23C3×C5×C22⋊C8C2211yescharacteristic
24C3×C5×#95C2211yescharacteristic
25C3×#3963C2211yescharacteristic
26C3×C22⋊#168C2211yescharacteristic
27C3×#3952—21no—
28C3×#1508—51nomaximal, Hall
29D5×C22⋊Q8C2×C311yescharacteristic
30#65015C2×C311yescharacteristic
31#64955C2×C311yescharacteristic
32C5×#328C2×C311yescharacteristic, complemented
33#64758C2×C311yescharacteristic, complemented
34#64687C2×C311yescharacteristic, complemented
35#64672C2×C311yescharacteristic, complemented
36C23×C3×D5D411yescharacteristic
37C2×C3×C5×Q8C2×C411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C22×C3×Dic5—21no—
41C22×C3×Dic5D411yescharacteristic
42C3×Q8×D5—42no—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—42no—
46C2×C3×C4×D5C2×C411yescharacteristic
47C2×C3×C4×D5C2×C411yescharacteristic
48C2×C3×C4×D5D411yescharacteristic
49C2×C3×C4×D5D411yescharacteristic
50C2×C3×Dic10—21no—
51C2×C3×Dic10C2×C411yescharacteristic
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4—21no—
56C3×C22⋊Dic5—21no—
57C3×#685—24no—
58C3×#685—21no—
59C3×#685—21no—
60C3×C4⋊Dic5—21no—
61C3×C4⋊Dic5C2×C411yescharacteristic
62C3×#683—21no—
63C3×#683—21no—
64C3×#683—21no—
65C3×C4×Dic5—42no—
66C2×C3×#168—21no—
67C3×#676—42no—
68C2×C3×C22⋊Q8—51no—
69C3×#407—51no—
70C3×C4×C22⋊C4—51no—
71C3×#328—51no—
72C3×#328—51no—
73C3×#328—51no—
74C3×#328D511yescharacteristic, complemented
75C2×Q8×D5C3×C411yescharacteristic, complemented
76C22×C4×D5C22×C311yescharacteristic
77C5×C22⋊Q8C22×C311yescharacteristic
78#4092C3×C411yescharacteristic, complemented
79C2×#685—21no—
80#4070C22×C311yescharacteristic
81C2×C4×Dic5—21no—
82C2×#676—21no—
83#4043C3×C411yescharacteristic, complemented
84#4042—21no—
85D5×C4⋊C4—21no—
86D5×C4⋊C4C3×C411yescharacteristic, complemented
87D5×C22⋊C4—21no—
88#4024—21no—
89C5×C22⋊C8C22×C311yescharacteristic
90C5×#95C22×C311yescharacteristic
91#3963C22×C311yescharacteristic
92C22⋊#168C22×C311yescharacteristic
93#3952—21no—
94#1508—51noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×C3×D5—21no—
97C22×C3×D5—21no—
98C22×C3×D5—22no—
99C22×C3×D5—41no—
100C22×C3×D5C22⋊C411yescharacteristic
101C22×C3×D5C22⋊C411yescharacteristic
102C3×C5×Q8—41no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×Dic5—22no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5C22⋊C411yescharacteristic
118C2×C3×Dic5C22⋊C411yescharacteristic
119C3×C4×D5—22no—
120C3×C4×D5—22no—
121C3×C4×D5—41no—
122C3×C4×D5—41no—
123C3×C4×D5—42no—
124C3×C4×D5—42no—
125C3×Dic10—42no—
126C3×Dic10—41no—
127C3×C5×C8—41no—
128C3×#168—41no—
129C22×C3×Q8—51no—
130C23×C3×C4—51no—
131C2×C3×M16—101no—
132C3×C22⋊Q8—51no—
133C3×C22⋊Q8—51no—
134C3×C22⋊Q8—51no—
135C3×C22⋊Q8—101no—
136C3×C22⋊Q8—101no—
137C3×C22⋊Q8C2×D511yescharacteristic
138C2×C3×C4⋊C4—51no—
139C2×C3×C4⋊C4—101no—
140C2×C3×C22⋊C4—101no—
141C2×C3×C22⋊C4—101no—
142C2×C3×C42—101no—
143C3×C22⋊C8—51no—
144C3×C22⋊C8—101no—
145C3×C22⋊C8C2×D511yescharacteristic
146C3×#95—51no—
147C3×#95C2×D511yescharacteristic
148C23×D5C3×D411yescharacteristic
149C2×C5×Q8C2×C3×C411yescharacteristic
150C22×C4×C5—21no—
151C22×C4×C5C23×C311yescharacteristic
152C22×Dic5—21no—
153C22×Dic5C3×D411yescharacteristic
154Q8×D5—42no—
155C2×C4×D5—21no—
156C2×C4×D5—21no—
157C2×C4×D5—42no—
158C2×C4×D5C2×C3×C411yescharacteristic
159C2×C4×D5C2×C3×C411yescharacteristic
160C2×C4×D5C3×D411yescharacteristic
161C2×C4×D5C3×D411yescharacteristic
162C2×Dic10—21no—
163C2×Dic10C2×C3×C411yescharacteristic
164C2×C5×C8—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4C2×C3×C411yescharacteristic
167C5×C22⋊C4—21no—
168C22⋊Dic5—21no—
169#685—24no—
170#685—21no—
171#685—21no—
172C4⋊Dic5—21no—
173C4⋊Dic5C2×C3×C411yescharacteristic
174#683—21no—
175#683—21no—
176#683—21no—
177C4×Dic5—42no—
178C2×#168—21no—
179#676—42no—
180C2×C22⋊Q8—51no—
181#407—51no—
182C4×C22⋊C4—51no—
183#328—51no—
184#328—51no—
185#328—51no—
186#328C3×D511yescharacteristic, complemented
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5C2×C22⋊C411yescharacteristic
190C22×C3×C5#13711yescharacteristic
191C22×C3×C5#13711yescharacteristic
192C2×C3×D5—21no—
193C2×C3×D5—21no—
194C2×C3×D5—21no—
195C2×C3×D5—21no—
196C2×C3×D5—21no—
197C2×C3×D5—42no—
198C2×C3×D5—42no—
199C2×C3×D5#10412yes—
200C3×C4×C5—21no—
201C3×C4×C5—21no—
202C3×C4×C5—42no—
203C3×C4×C5—41no—
204C3×C4×C5—41no—
205C3×Dic5—21no—
206C3×Dic5—42no—
207C3×Dic5—41no—
208C3×Dic5—41no—
209C3×Dic5#9912yes—
210C24×C3—51no—
211C2×C3×Q8—51no—
212C2×C3×Q8—101no—
213C2×C3×Q8—202no—
214C2×C3×Q8C4×D511yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—51no—
217C22×C3×C4—51no—
218C22×C3×C4—51no—
219C22×C3×C4—51no—
220C22×C3×C4—51no—
221C22×C3×C4—101no—
222C22×C3×C4—101no—
223C22×C3×C4—101no—
224C22×C3×C4—202no—
225C22×C3×C4C22×D511yescharacteristic
226C3×M16—202no—
227C2×C3×C8—21no—
228C2×C3×C8—101no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—51no—
231C3×C4⋊C4—101no—
232C3×C4⋊C4—101no—
233C3×C4⋊C4—101no—
234C3×C4⋊C4—101no—
235C3×C4⋊C4C4×D511yescharacteristic
236C3×C22⋊C4—21no—
237C3×C22⋊C4—101no—
238C3×C22⋊C4—101no—
239C3×C22⋊C4—104no—
240C3×C22⋊C4—101no—
241C3×C42—202no—
242C23×C5C2×C3×D411yescharacteristic
243C22×D5—21no—
244C22×D5—21no—
245C22×D5—22no—
246C22×D5—41no—
247C22×D5C3×C22⋊C411yescharacteristic
248C22×D5C3×C22⋊C411yescharacteristic
249C5×Q8—41no—
250C2×C4×C5—22no—
251C2×C4×C5—21no—
252C2×C4×C5—21no—
253C2×C4×C5—41no—
254C2×C4×C5—41no—
255C2×C4×C5—41no—
256C2×C4×C5C22×C3×C411yescharacteristic
257C2×C4×C5C2×C3×D411yescharacteristic
258C2×Dic5—22no—
259C2×Dic5—22no—
260C2×Dic5—21no—
261C2×Dic5—21no—
262C2×Dic5—41no—
263C2×Dic5—41no—
264C2×Dic5C3×C22⋊C411yescharacteristic
265C2×Dic5C3×C22⋊C411yescharacteristic
266C4×D5—22no—
267C4×D5—22no—
268C4×D5—41no—
269C4×D5—41no—
270C4×D5—42no—
271C4×D5—42no—
272Dic10—42no—
273Dic10—41no—
274C5×C8—41no—
275#168—41no—
276C22×Q8—51no—
277C23×C4—51no—
278C2×M16—101no—
279C22⋊Q8—51no—
280C22⋊Q8—51no—
281C22⋊Q8—51no—
282C22⋊Q8—101no—
283C22⋊Q8—101no—
284C22⋊Q8C2×C3×D511yescharacteristic
285C2×C4⋊C4—51no—
286C2×C4⋊C4—101no—
287C2×C22⋊C4—101no—
288C2×C22⋊C4—101no—
289C2×C42—101no—
290C22⋊C8—51no—
291C22⋊C8—101no—
292C22⋊C8C2×C3×D511yescharacteristic
293#95—51no—
294#95C2×C3×D511yescharacteristic
295C2×C3×C5—21no—
296C2×C3×C5—21no—
297C2×C3×C5C2×#9911yescharacteristic
298C2×C3×C5#41911yescharacteristic
299C2×C3×C5C2×#10411yescharacteristic
300C3×D5—22no—
301C3×D5—41no—
302C23×C3—51no—
303C23×C3—51no—
304C23×C3—102no—
305C23×C3—101no—
306C23×C3—101no—
307C23×C3—201no—
308C23×C3D4×D511yescharacteristic
309C3×Q8—41no—
310C3×Q8—201no—
311C3×Q8—202no—
312C2×C3×C4—22no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—51no—
319C2×C3×C4—51no—
320C2×C3×C4—102no—
321C2×C3×C4—102no—
322C2×C3×C4—102no—
323C2×C3×C4—102no—
324C2×C3×C4—101no—
325C2×C3×C4—101no—
326C2×C3×C4—201no—
327C2×C3×C4—201no—
328C2×C3×C4—202no—
329C2×C3×C4—202no—
330C2×C3×C4—201no—
331C2×C3×C4—201no—
332C2×C3×C4C2×C4×D511yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C3×C8—41no—
335C3×C8—201no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5C2×C3×C22⋊C411yescharacteristic
339C22×C5C3×#13711yescharacteristic
340C22×C5C3×#13711yescharacteristic
341C2×D5—21no—
342C2×D5—21no—
343C2×D5—21no—
344C2×D5—21no—
345C2×D5—21no—
346C2×D5—42no—
347C2×D5—42no—
348C2×D5C3×#10412yes—
349C4×C5—21no—
350C4×C5—21no—
351C4×C5—42no—
352C4×C5—41no—
353C4×C5—41no—
354Dic5—21no—
355Dic5—42no—
356Dic5—41no—
357Dic5—41no—
358Dic5C3×#9912yes—
359C24—51no—
360C2×Q8—51no—
361C2×Q8—101no—
362C2×Q8—202no—
363C2×Q8C3×C4×D511yescharacteristic
364C22×C4—21no—
365C22×C4—51no—
366C22×C4—51no—
367C22×C4—51no—
368C22×C4—51no—
369C22×C4—51no—
370C22×C4—101no—
371C22×C4—101no—
372C22×C4—101no—
373C22×C4—202no—
374C22×C4C22×C3×D511yescharacteristic
375M16—202no—
376C2×C8—21no—
377C2×C8—101no—
378C4⋊C4—21no—
379C4⋊C4—51no—
380C4⋊C4—101no—
381C4⋊C4—101no—
382C4⋊C4—101no—
383C4⋊C4—101no—
384C4⋊C4C3×C4×D511yescharacteristic
385C22⋊C4—21no—
386C22⋊C4—101no—
387C22⋊C4—101no—
388C22⋊C4—104no—
389C22⋊C4—101no—
390C42—202no—
391C3×C5#150811yescharacteristic, complemented, Hall
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—52no—
395C22×C3—101no—
396C22×C3—101no—
397C22×C3—101no—
398C22×C3—101no—
399C22×C3—101no—
400C22×C3—202no—
401C22×C3—202no—
402C22×C3D5×C22⋊C411yescharacteristic
403C22×C3#406111yescharacteristic
404C22×C3#406411yescharacteristic
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—42no—
408C3×C4—41no—
409C3×C4—41no—
410C3×C4—52no—
411C3×C4—101no—
412C3×C4—202no—
413C3×C4—201no—
414C3×C4—201no—
415C2×C5—21no—
416C2×C5—21no—
417C2×C5C2×C3×#9911yescharacteristic
418C2×C5C3×#41911yescharacteristic
419C2×C5C2×C3×#10411yescharacteristic
420D5—22no—
421D5—41no—
422C23—51no—
423C23—51no—
424C23—102no—
425C23—101no—
426C23—101no—
427C23—201no—
428C23C3×D4×D511yescharacteristic
429Q8—41no—
430Q8—201no—
431Q8—202no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—51no—
439C2×C4—51no—
440C2×C4—102no—
441C2×C4—102no—
442C2×C4—102no—
443C2×C4—102no—
444C2×C4—101no—
445C2×C4—101no—
446C2×C4—201no—
447C2×C4—201no—
448C2×C4—202no—
449C2×C4—202no—
450C2×C4—201no—
451C2×C4—201no—
452C2×C4C2×C3×C4×D511yescharacteristic
453C2×C4C3×D4×D511yescharacteristic
454C8—41no—
455C8—201no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—102no—
459C2×C3—201no—
460C2×C3D5×#9911yescharacteristic
461C2×C3#6509111yescharacteristic
462C2×C3D5×#10411yescharacteristic
463C5C3×#150811yescharacteristic, complemented, Sylow
464C22—21no—
465C22—21no—
466C22—52no—
467C22—101no—
468C22—101no—
469C22—101no—
470C22—101no—
471C22—101no—
472C22—202no—
473C22—202no—
474C22C3×D5×C22⋊C411yescharacteristic
475C22C3×#406111yescharacteristic
476C22C3×#406411yescharacteristic
477C4—21no—
478C4—21no—
479C4—42no—
480C4—41no—
481C4—41no—
482C4—52no—
483C4—101no—
484C4—202no—
485C4—201no—
486C4—201no—
487C3#1059912811yescharacteristic, direct product factor, Sylow
488C2—21no—
489C2—21no—
490C2—102no—
491C2—201no—
492C2C3×D5×#9911yescharacteristic
493C2C3×#6509111yescharacteristic
494C2C3×D5×#10411yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#328C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5D4
cosocleC22×C4×C5C23×C3
hypercenterC3×#328D5
hypocenterC5C3×#1508
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#328

Complements

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

NH ≅ G/Ntype
4. C3×C5×#328C2semidirect
5. C3×#64758C2semidirect
6. C3×#64687C2semidirect
7. C3×#64672C2semidirect
8. #10599128C3direct (N × H)
9. C2×C3×Q8×D5C4semidirect
12. C3×#4092C4semidirect
17. C3×#4043C4semidirect
20. C3×D5×C4⋊C4C4semidirect
32. C5×#328C2×C3semidirect
33. #64758C2×C3semidirect
34. #64687C2×C3semidirect
35. #64672C2×C3semidirect
74. C3×#328D5semidirect
75. C2×Q8×D5C3×C4semidirect
78. #4092C3×C4semidirect
83. #4043C3×C4semidirect
86. D5×C4⋊C4C3×C4semidirect
186. #328C3×D5semidirect
391. C3×C5#1508semidirect
463. C5C3×#1508semidirect
487. C3#10599128direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×C22⋊Q82
C3×#650152
C3×#649552
C3×C5×#3282
C3×#647582
C3×#646872
C3×#646722
#105991283
C3×#15085