Finite Group Databasebeta

← C3×#10599129 #14283300

Subgroups — C3×#10599129 #14283300

Order 1920.

548 conjugacy classes of subgroups.

The subgroup lattice has 492 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×#64953C211yesmaximal, characteristic
4C3×C5×#328C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6C3×#64687C211yesmaximal, characteristic, complemented
7C3×#64672C211yesmaximal, characteristic, complemented
8#10599129C311yesmaximal, 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×#676—21no—
16C3×#4043C411yescharacteristic, complemented
17C3×#4042—21no—
18C3×D5×C4⋊C4—21no—
19C3×D5×C4⋊C4C411yescharacteristic, complemented
20C3×D5×C22⋊C4—21no—
21C3×#4024—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23C3×C5×#95C2211yescharacteristic
24C3×#3963—21no—
25C3×#3963C2211yescharacteristic
26C3×C22⋊#168C2211yescharacteristic
27C3×#3952—21no—
28C3×#1511—51nomaximal, Hall
29D5×C22⋊Q8C2×C311yescharacteristic
30#65015C2×C311yescharacteristic
31#64953C2×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—21no—
58C3×#685—21no—
59C3×#685—42no—
60C3×C4⋊Dic5—21no—
61C3×C4⋊Dic5C2×C411yescharacteristic
62C3×#683—21no—
63C3×#683—21no—
64C3×#683—21no—
65C2×C3×#168—21no—
66C3×#676—42no—
67C2×C3×C22⋊Q8—51no—
68C3×#407—51no—
69C3×#381—51no—
70C3×#328—51no—
71C3×#328—51no—
72C3×#328—51no—
73C3×#328D511yescharacteristic, complemented
74C2×Q8×D5C3×C411yescharacteristic, complemented
75C22×C4×D5C22×C311yescharacteristic
76C5×C22⋊Q8C22×C311yescharacteristic
77#4092C3×C411yescharacteristic, complemented
78C2×#685—21no—
79#4070C22×C311yescharacteristic
80C2×#676—21no—
81#4043C3×C411yescharacteristic, complemented
82#4042—21no—
83D5×C4⋊C4—21no—
84D5×C4⋊C4C3×C411yescharacteristic, complemented
85D5×C22⋊C4—21no—
86#4024—21no—
87C5×C22⋊C8C22×C311yescharacteristic
88C5×#95C22×C311yescharacteristic
89#3963—21no—
90#3963C22×C311yescharacteristic
91C22⋊#168C22×C311yescharacteristic
92#3952—21no—
93#1511—51noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—21no—
96C22×C3×D5—21no—
97C22×C3×D5—22no—
98C22×C3×D5—41no—
99C22×C3×D5C22⋊C411yescharacteristic
100C22×C3×D5C22⋊C411yescharacteristic
101C3×C5×Q8—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—41no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5C22⋊C411yescharacteristic
117C2×C3×Dic5C22⋊C411yescharacteristic
118C3×C4×D5—22no—
119C3×C4×D5—22no—
120C3×C4×D5—41no—
121C3×C4×D5—41no—
122C3×C4×D5—42no—
123C3×C4×D5—42no—
124C3×Dic10—42no—
125C3×Dic10—41no—
126C3×C5×C8—41no—
127C3×#168—41no—
128C22×C3×Q8—51no—
129C23×C3×C4—51no—
130C2×C3×M16—101no—
131C3×C22⋊Q8—51no—
132C3×C22⋊Q8—51no—
133C3×C22⋊Q8—51no—
134C3×C22⋊Q8—101no—
135C3×C22⋊Q8—101no—
136C3×C22⋊Q8C2×D511yescharacteristic
137C2×C3×C4⋊C4—51no—
138C2×C3×C4⋊C4—101no—
139C2×C3×C22⋊C4—101no—
140C2×C3×C22⋊C4—101no—
141C3×C22⋊C8—51no—
142C3×C22⋊C8—101no—
143C3×C22⋊C8C2×D511yescharacteristic
144C3×#95—51no—
145C3×#95—101no—
146C3×#95C2×D511yescharacteristic
147C23×D5C3×D411yescharacteristic
148C2×C5×Q8C2×C3×C411yescharacteristic
149C22×C4×C5—21no—
150C22×C4×C5C23×C311yescharacteristic
151C22×Dic5—21no—
152C22×Dic5C3×D411yescharacteristic
153Q8×D5—42no—
154C2×C4×D5—21no—
155C2×C4×D5—21no—
156C2×C4×D5—42no—
157C2×C4×D5C2×C3×C411yescharacteristic
158C2×C4×D5C2×C3×C411yescharacteristic
159C2×C4×D5C3×D411yescharacteristic
160C2×C4×D5C3×D411yescharacteristic
161C2×Dic10—21no—
162C2×Dic10C2×C3×C411yescharacteristic
163C2×C5×C8—21no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4C2×C3×C411yescharacteristic
166C5×C22⋊C4—21no—
167C22⋊Dic5—21no—
168#685—21no—
169#685—21no—
170#685—42no—
171C4⋊Dic5—21no—
172C4⋊Dic5C2×C3×C411yescharacteristic
173#683—21no—
174#683—21no—
175#683—21no—
176C2×#168—21no—
177#676—42no—
178C2×C22⋊Q8—51no—
179#407—51no—
180#381—51no—
181#328—51no—
182#328—51no—
183#328—51no—
184#328C3×D511yescharacteristic, complemented
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5C2×C22⋊C411yescharacteristic
188C22×C3×C5#13711yescharacteristic
189C22×C3×C5#13711yescharacteristic
190C2×C3×D5—21no—
191C2×C3×D5—21no—
192C2×C3×D5—21no—
193C2×C3×D5—21no—
194C2×C3×D5—21no—
195C2×C3×D5—42no—
196C2×C3×D5—42no—
197C2×C3×D5#9912yes—
198C3×C4×C5—21no—
199C3×C4×C5—21no—
200C3×C4×C5—41no—
201C3×C4×C5—41no—
202C3×C4×C5—81no—
203C3×Dic5—21no—
204C3×Dic5—21no—
205C3×Dic5—41no—
206C3×Dic5—41no—
207C3×Dic5—81no—
208C24×C3—51no—
209C2×C3×Q8—51no—
210C2×C3×Q8—101no—
211C2×C3×Q8—202no—
212C2×C3×Q8C4×D511yescharacteristic
213C22×C3×C4—21no—
214C22×C3×C4—51no—
215C22×C3×C4—51no—
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—202no—
223C22×C3×C4C22×D511yescharacteristic
224C3×M16—202no—
225C2×C3×C8—21no—
226C2×C3×C8—101no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—51no—
229C3×C4⋊C4—101no—
230C3×C4⋊C4—101no—
231C3×C4⋊C4—101no—
232C3×C4⋊C4—101no—
233C3×C4⋊C4C4×D511yescharacteristic
234C3×C22⋊C4—21no—
235C3×C22⋊C4—101no—
236C3×C22⋊C4—101no—
237C3×C22⋊C4—101no—
238C3×C22⋊C4—202no—
239C23×C5C2×C3×D411yescharacteristic
240C22×D5—21no—
241C22×D5—21no—
242C22×D5—22no—
243C22×D5—41no—
244C22×D5C3×C22⋊C411yescharacteristic
245C22×D5C3×C22⋊C411yescharacteristic
246C5×Q8—41no—
247C2×C4×C5—21no—
248C2×C4×C5—21no—
249C2×C4×C5—41no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5C22×C3×C411yescharacteristic
254C2×C4×C5C2×C3×D411yescharacteristic
255C2×Dic5—21no—
256C2×Dic5—21no—
257C2×Dic5—41no—
258C2×Dic5—41no—
259C2×Dic5—41no—
260C2×Dic5—41no—
261C2×Dic5C3×C22⋊C411yescharacteristic
262C2×Dic5C3×C22⋊C411yescharacteristic
263C4×D5—22no—
264C4×D5—22no—
265C4×D5—41no—
266C4×D5—41no—
267C4×D5—42no—
268C4×D5—42no—
269Dic10—42no—
270Dic10—41no—
271C5×C8—41no—
272#168—41no—
273C22×Q8—51no—
274C23×C4—51no—
275C2×M16—101no—
276C22⋊Q8—51no—
277C22⋊Q8—51no—
278C22⋊Q8—51no—
279C22⋊Q8—101no—
280C22⋊Q8—101no—
281C22⋊Q8C2×C3×D511yescharacteristic
282C2×C4⋊C4—51no—
283C2×C4⋊C4—101no—
284C2×C22⋊C4—101no—
285C2×C22⋊C4—101no—
286C22⋊C8—51no—
287C22⋊C8—101no—
288C22⋊C8C2×C3×D511yescharacteristic
289#95—51no—
290#95—101no—
291#95C2×C3×D511yescharacteristic
292C2×C3×C5—21no—
293C2×C3×C5—21no—
294C2×C3×C5C2×#9911yescharacteristic
295C2×C3×C5#41911yescharacteristic
296C2×C3×C5#42111yescharacteristic
297C3×D5—22no—
298C3×D5—41no—
299C23×C3—51no—
300C23×C3—51no—
301C23×C3—102no—
302C23×C3—101no—
303C23×C3—101no—
304C23×C3—201no—
305C23×C3D4×D511yescharacteristic
306C3×Q8—41no—
307C3×Q8—201no—
308C3×Q8—202no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—51no—
316C2×C3×C4—51no—
317C2×C3×C4—102no—
318C2×C3×C4—102no—
319C2×C3×C4—101no—
320C2×C3×C4—101no—
321C2×C3×C4—201no—
322C2×C3×C4—201no—
323C2×C3×C4—202no—
324C2×C3×C4—202no—
325C2×C3×C4—201no—
326C2×C3×C4—201no—
327C2×C3×C4—201no—
328C2×C3×C4—201no—
329C2×C3×C4C2×C4×D511yescharacteristic
330C2×C3×C4D4×D511yescharacteristic
331C3×C8—41no—
332C3×C8—201no—
333C22×C5—21no—
334C22×C5—21no—
335C22×C5C2×C3×C22⋊C411yescharacteristic
336C22×C5C3×#13711yescharacteristic
337C22×C5C3×#13711yescharacteristic
338C2×D5—21no—
339C2×D5—21no—
340C2×D5—21no—
341C2×D5—21no—
342C2×D5—21no—
343C2×D5—42no—
344C2×D5—42no—
345C2×D5C3×#9912yes—
346C4×C5—21no—
347C4×C5—21no—
348C4×C5—41no—
349C4×C5—41no—
350C4×C5—81no—
351Dic5—21no—
352Dic5—21no—
353Dic5—41no—
354Dic5—41no—
355Dic5—81no—
356C24—51no—
357C2×Q8—51no—
358C2×Q8—101no—
359C2×Q8—202no—
360C2×Q8C3×C4×D511yescharacteristic
361C22×C4—21no—
362C22×C4—51no—
363C22×C4—51no—
364C22×C4—51no—
365C22×C4—51no—
366C22×C4—51no—
367C22×C4—101no—
368C22×C4—101no—
369C22×C4—101no—
370C22×C4—202no—
371C22×C4C22×C3×D511yescharacteristic
372M16—202no—
373C2×C8—21no—
374C2×C8—101no—
375C4⋊C4—21no—
376C4⋊C4—51no—
377C4⋊C4—101no—
378C4⋊C4—101no—
379C4⋊C4—101no—
380C4⋊C4—101no—
381C4⋊C4C3×C4×D511yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—101no—
384C22⋊C4—101no—
385C22⋊C4—101no—
386C22⋊C4—202no—
387C3×C5#151111yescharacteristic, complemented, Hall
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—52no—
391C22×C3—101no—
392C22×C3—101no—
393C22×C3—101no—
394C22×C3—101no—
395C22×C3—101no—
396C22×C3—202no—
397C22×C3—202no—
398C22×C3D5×C22⋊C411yescharacteristic
399C22×C3#406111yescharacteristic
400C22×C3#406411yescharacteristic
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—41no—
404C3×C4—41no—
405C3×C4—81no—
406C3×C4—101no—
407C3×C4—101no—
408C3×C4—201no—
409C3×C4—201no—
410C3×C4—401no—
411C2×C5—21no—
412C2×C5—21no—
413C2×C5C2×C3×#9911yescharacteristic
414C2×C5C3×#41911yescharacteristic
415C2×C5C3×#42111yescharacteristic
416D5—22no—
417D5—41no—
418C23—51no—
419C23—51no—
420C23—102no—
421C23—101no—
422C23—101no—
423C23—201no—
424C23C3×D4×D511yescharacteristic
425Q8—41no—
426Q8—201no—
427Q8—202no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—51no—
435C2×C4—51no—
436C2×C4—102no—
437C2×C4—102no—
438C2×C4—101no—
439C2×C4—101no—
440C2×C4—201no—
441C2×C4—201no—
442C2×C4—202no—
443C2×C4—202no—
444C2×C4—201no—
445C2×C4—201no—
446C2×C4—201no—
447C2×C4—201no—
448C2×C4C2×C3×C4×D511yescharacteristic
449C2×C4C3×D4×D511yescharacteristic
450C8—41no—
451C8—201no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—102no—
455C2×C3—201no—
456C2×C3D5×#9911yescharacteristic
457C2×C3#6509111yescharacteristic
458C2×C3#6511011yescharacteristic
459C5C3×#151111yescharacteristic, complemented, Sylow
460C22—21no—
461C22—21no—
462C22—52no—
463C22—101no—
464C22—101no—
465C22—101no—
466C22—101no—
467C22—101no—
468C22—202no—
469C22—202no—
470C22C3×D5×C22⋊C411yescharacteristic
471C22C3×#406111yescharacteristic
472C22C3×#406411yescharacteristic
473C4—21no—
474C4—21no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—101no—
479C4—101no—
480C4—201no—
481C4—201no—
482C4—401no—
483C3#1059912911yescharacteristic, direct product factor, Sylow
484C2—21no—
485C2—21no—
486C2—102no—
487C2—201no—
488C2C3×D5×#9911yescharacteristic
489C2C3×#6509111yescharacteristic
490C2C3×#6511011yescharacteristic
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×#1511
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. #10599129C3direct (N × H)
9. C2×C3×Q8×D5C4semidirect
12. C3×#4092C4semidirect
16. C3×#4043C4semidirect
19. C3×D5×C4⋊C4C4semidirect
32. C5×#328C2×C3semidirect
33. #64758C2×C3semidirect
34. #64687C2×C3semidirect
35. #64672C2×C3semidirect
73. C3×#328D5semidirect
74. C2×Q8×D5C3×C4semidirect
77. #4092C3×C4semidirect
81. #4043C3×C4semidirect
84. D5×C4⋊C4C3×C4semidirect
184. #328C3×D5semidirect
387. C3×C5#1511semidirect
459. C5C3×#1511semidirect
483. C3#10599129direct (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×#649532
C3×C5×#3282
C3×#647582
C3×#646872
C3×#646722
#105991293
C3×#15115