Finite Group Databasebeta

← C3×#10598940 #14281363

Subgroups — C3×#10598940 #14281363

Order 1920.

540 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4042C211yesmaximal, characteristic
2C3×#65015C211yesmaximal, characteristic
3C3×D5×C22⋊C8C211yesmaximal, characteristic
4C3×C5×#324C211yesmaximal, characteristic, complemented
5C3×#64748C211yesmaximal, characteristic, complemented
6C3×#64689C211yesmaximal, characteristic, complemented
7C3×#64689C211yesmaximal, characteristic, complemented
8#10598940C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×C3×Dic10C411yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C3×#685C411yescharacteristic
13C2×C3×#685C411yescharacteristic
14C2×C3×#683C411yescharacteristic
15C2×C3×#683C2211yescharacteristic
16C2×C3×#676—21no—
17C2×C3×C8×D5—21no—
18C3×#4042—21no—
19C3×#4042—21no—
20C3×#4042—21no—
21C3×#4042—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23C3×C5×C22⋊C8C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3952—21no—
27C3×#3952—21no—
28C3×#1472—51nomaximal, Hall
29C2×#4042C2×C311yescharacteristic
30#65015C2×C311yescharacteristic
31D5×C22⋊C8C2×C311yescharacteristic
32C5×#324C2×C311yescharacteristic, complemented
33#64748C2×C311yescharacteristic, complemented
34#64689C2×C311yescharacteristic, complemented
35#64689C2×C311yescharacteristic, complemented
36C23×C3×D5C2×C411yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×C4×C5C2×C411yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C22×C3×Dic5C2×C411yescharacteristic
41C22×C3×Dic5C2×C411yescharacteristic
42C22×C3×Dic5C2×C411yescharacteristic
43C2×C3×C4×D5—42no—
44C2×C3×C4×D5D411yescharacteristic
45C2×C3×C4×D5D411yescharacteristic
46C2×C3×C4×D5D411yescharacteristic
47C2×C3×C4×D5D411yescharacteristic
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10—42no—
51C2×C3×C5×C8—21no—
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4—21no—
55C3×#685—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×#685—21no—
59C3×#683—21no—
60C3×#683—21no—
61C3×#683—21no—
62C3×#683—21no—
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65C3×#676—42no—
66C3×C8×D5—42no—
67C2×C3×C22⋊Q8—51no—
68C3×#407—51no—
69C2×C3×C22⋊C8—51no—
70C3×#324—51no—
71C3×#324—51no—
72C3×#324—51no—
73C3×#324D511yescharacteristic, complemented
74C22×C4×D5C22×C311yescharacteristic
75C22×Dic10C3×C411yescharacteristic
76C2×C5×C4⋊C4C22×C311yescharacteristic
77C2×#685C3×C411yescharacteristic
78C2×#685C3×C411yescharacteristic
79C2×#683C3×C411yescharacteristic
80C2×#683C22×C311yescharacteristic
81C2×#676—21no—
82C2×C8×D5—21no—
83#4042—21no—
84#4042—21no—
85#4042—21no—
86#4042—21no—
87C5×C22⋊C8C22×C311yescharacteristic
88C5×C22⋊C8C22×C311yescharacteristic
89C22⋊#168C22×C311yescharacteristic
90C22⋊#168C22×C311yescharacteristic
91#3952—21no—
92#3952—21no—
93#1472—51noSylow
94C23×C3×C5C22×C411yescharacteristic
95C22×C3×D5—21no—
96C22×C3×D5—21no—
97C22×C3×D5—22no—
98C22×C3×D5—41no—
99C22×C3×D5C22⋊C411yescharacteristic
100C22×C3×D5C22⋊C411yescharacteristic
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×Dic5—22no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5C22⋊C411yescharacteristic
116C2×C3×Dic5C22⋊C411yescharacteristic
117C3×C4×D5—22no—
118C3×C4×D5—22no—
119C3×C4×D5—41no—
120C3×C4×D5—41no—
121C3×Dic10—42no—
122C3×Dic10—42no—
123C3×C5×C8—41no—
124C3×C5×C8—41no—
125C3×#168—41no—
126C3×#168—41no—
127C22×C3×Q8—51no—
128C23×C3×C4—51no—
129C2×C3×M16—101no—
130C22×C3×C8—101no—
131C3×C22⋊Q8—101no—
132C3×C22⋊Q8—101no—
133C3×C22⋊Q8—101no—
134C3×C22⋊Q8—101no—
135C2×C3×C4⋊C4—51no—
136C2×C3×C4⋊C4—51no—
137C2×C3×C4⋊C4C2×D511yescharacteristic
138C2×C3×C22⋊C4—51no—
139C2×C3×C22⋊C4—51no—
140C3×C22⋊C8—51no—
141C3×C22⋊C8—51no—
142C3×C22⋊C8—101no—
143C3×C22⋊C8—101no—
144C3×C22⋊C8C2×D511yescharacteristic
145C3×C22⋊C8C2×D511yescharacteristic
146C23×D5C2×C3×C411yescharacteristic
147C22×C4×C5C2×C3×C411yescharacteristic
148C22×C4×C5C2×C3×C411yescharacteristic
149C22×C4×C5C23×C311yescharacteristic
150C22×Dic5C2×C3×C411yescharacteristic
151C22×Dic5C2×C3×C411yescharacteristic
152C22×Dic5C2×C3×C411yescharacteristic
153C2×C4×D5—42no—
154C2×C4×D5C3×D411yescharacteristic
155C2×C4×D5C3×D411yescharacteristic
156C2×C4×D5C3×D411yescharacteristic
157C2×C4×D5C3×D411yescharacteristic
158C2×Dic10—21no—
159C2×Dic10—21no—
160C2×Dic10—42no—
161C2×C5×C8—21no—
162C2×C5×C8—21no—
163C5×C4⋊C4—21no—
164C5×C4⋊C4—21no—
165#685—21no—
166#685—21no—
167#685—21no—
168#685—21no—
169#683—21no—
170#683—21no—
171#683—21no—
172#683—21no—
173C2×#168—21no—
174C2×#168—21no—
175#676—42no—
176C8×D5—42no—
177C2×C22⋊Q8—51no—
178#407—51no—
179C2×C22⋊C8—51no—
180#324—51no—
181#324—51no—
182#324—51no—
183#324C3×D511yescharacteristic, complemented
184C22×C3×C5—21no—
185C22×C3×C5—21no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5#13111yescharacteristic
188C22×C3×C5#13111yescharacteristic
189C2×C3×D5—21no—
190C2×C3×D5—21no—
191C2×C3×D5—21no—
192C2×C3×D5—21no—
193C2×C3×D5—21no—
194C2×C3×D5—42no—
195C2×C3×D5—42no—
196C2×C3×D5#10112yes—
197C3×C4×C5—21no—
198C3×C4×C5—21no—
199C3×C4×C5—41no—
200C3×C4×C5—41no—
201C3×Dic5—21no—
202C3×Dic5—41no—
203C3×Dic5—41no—
204C3×Dic5#9912yes—
205C24×C3—51no—
206C2×C3×Q8—101no—
207C2×C3×Q8—101no—
208C2×C3×Q8—202no—
209C22×C3×C4—51no—
210C22×C3×C4—51no—
211C22×C3×C4—51no—
212C22×C3×C4—51no—
213C22×C3×C4—51no—
214C22×C3×C4—51no—
215C22×C3×C4—51no—
216C22×C3×C4—202no—
217C22×C3×C4C4×D511yescharacteristic
218C22×C3×C4C4×D511yescharacteristic
219C22×C3×C4C22×D511yescharacteristic
220C3×M16—202no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—101no—
224C2×C3×C8—101no—
225C2×C3×C8—202no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—101no—
229C3×C4⋊C4—101no—
230C3×C4⋊C4—101no—
231C3×C4⋊C4—101no—
232C3×C22⋊C4—101no—
233C3×C22⋊C4—101no—
234C3×C22⋊C4—101no—
235C3×C22⋊C4—101no—
236C23×C5C22×C3×C411yescharacteristic
237C22×D5—21no—
238C22×D5—21no—
239C22×D5—22no—
240C22×D5—41no—
241C22×D5C3×C22⋊C411yescharacteristic
242C22×D5C3×C22⋊C411yescharacteristic
243C2×C4×C5—21no—
244C2×C4×C5—21no—
245C2×C4×C5—21no—
246C2×C4×C5—21no—
247C2×C4×C5—41no—
248C2×C4×C5—41no—
249C2×C4×C5C2×C3×D411yescharacteristic
250C2×C4×C5C2×C3×D411yescharacteristic
251C2×Dic5—22no—
252C2×Dic5—21no—
253C2×Dic5—21no—
254C2×Dic5—21no—
255C2×Dic5—21no—
256C2×Dic5—41no—
257C2×Dic5C3×C22⋊C411yescharacteristic
258C2×Dic5C3×C22⋊C411yescharacteristic
259C4×D5—22no—
260C4×D5—22no—
261C4×D5—41no—
262C4×D5—41no—
263Dic10—42no—
264Dic10—42no—
265C5×C8—41no—
266C5×C8—41no—
267#168—41no—
268#168—41no—
269C22×Q8—51no—
270C23×C4—51no—
271C2×M16—101no—
272C22×C8—101no—
273C22⋊Q8—101no—
274C22⋊Q8—101no—
275C22⋊Q8—101no—
276C22⋊Q8—101no—
277C2×C4⋊C4—51no—
278C2×C4⋊C4—51no—
279C2×C4⋊C4C2×C3×D511yescharacteristic
280C2×C22⋊C4—51no—
281C2×C22⋊C4—51no—
282C22⋊C8—51no—
283C22⋊C8—51no—
284C22⋊C8—101no—
285C22⋊C8—101no—
286C22⋊C8C2×C3×D511yescharacteristic
287C22⋊C8C2×C3×D511yescharacteristic
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#40811yescharacteristic
291C2×C3×C5C2×#9911yescharacteristic
292C2×C3×C5C2×#10111yescharacteristic
293C3×D5—22no—
294C3×D5—41no—
295C23×C3—51no—
296C23×C3—51no—
297C23×C3—102no—
298C23×C3—101no—
299C23×C3—101no—
300C23×C3—201no—
301C23×C3C2×C4×D511yescharacteristic
302C3×Q8—202no—
303C3×Q8—202no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—51no—
311C2×C3×C4—51no—
312C2×C3×C4—102no—
313C2×C3×C4—102no—
314C2×C3×C4—102no—
315C2×C3×C4—101no—
316C2×C3×C4—101no—
317C2×C3×C4—101no—
318C2×C3×C4—101no—
319C2×C3×C4—201no—
320C2×C3×C4—201no—
321C2×C3×C4—201no—
322C2×C3×C4D4×D511yescharacteristic
323C2×C3×C4D4×D511yescharacteristic
324C3×C8—41no—
325C3×C8—41no—
326C3×C8—201no—
327C3×C8—201no—
328C22×C5—21no—
329C22×C5—21no—
330C22×C5C2×C3×C22⋊C411yescharacteristic
331C22×C5C3×#13111yescharacteristic
332C22×C5C3×#13111yescharacteristic
333C2×D5—21no—
334C2×D5—21no—
335C2×D5—21no—
336C2×D5—21no—
337C2×D5—21no—
338C2×D5—42no—
339C2×D5—42no—
340C2×D5C3×#10112yes—
341C4×C5—21no—
342C4×C5—21no—
343C4×C5—41no—
344C4×C5—41no—
345Dic5—21no—
346Dic5—41no—
347Dic5—41no—
348Dic5C3×#9912yes—
349C24—51no—
350C2×Q8—101no—
351C2×Q8—101no—
352C2×Q8—202no—
353C22×C4—51no—
354C22×C4—51no—
355C22×C4—51no—
356C22×C4—51no—
357C22×C4—51no—
358C22×C4—51no—
359C22×C4—51no—
360C22×C4—202no—
361C22×C4C3×C4×D511yescharacteristic
362C22×C4C3×C4×D511yescharacteristic
363C22×C4C22×C3×D511yescharacteristic
364M16—202no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—101no—
368C2×C8—101no—
369C2×C8—202no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—101no—
373C4⋊C4—101no—
374C4⋊C4—101no—
375C4⋊C4—101no—
376C22⋊C4—101no—
377C22⋊C4—101no—
378C22⋊C4—101no—
379C22⋊C4—101no—
380C3×C5#147211yescharacteristic, complemented, Hall
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—52no—
384C22×C3—101no—
385C22×C3—101no—
386C22×C3—101no—
387C22×C3—101no—
388C22×C3—101no—
389C22×C3—202no—
390C22×C3—202no—
391C22×C3D5×C22⋊C411yescharacteristic
392C22×C3#404711yescharacteristic
393C22×C3#405311yescharacteristic
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—41no—
397C3×C4—41no—
398C3×C4—52no—
399C3×C4—101no—
400C3×C4—201no—
401C3×C4—201no—
402C2×C5—21no—
403C2×C5—21no—
404C2×C5C3×#40811yescharacteristic
405C2×C5C2×C3×#9911yescharacteristic
406C2×C5C2×C3×#10111yescharacteristic
407D5—22no—
408D5—41no—
409C23—51no—
410C23—51no—
411C23—102no—
412C23—101no—
413C23—101no—
414C23—201no—
415C23C2×C3×C4×D511yescharacteristic
416Q8—202no—
417Q8—202no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—51no—
425C2×C4—51no—
426C2×C4—102no—
427C2×C4—102no—
428C2×C4—102no—
429C2×C4—101no—
430C2×C4—101no—
431C2×C4—101no—
432C2×C4—101no—
433C2×C4—201no—
434C2×C4—201no—
435C2×C4—201no—
436C2×C4C3×D4×D511yescharacteristic
437C2×C4C3×D4×D511yescharacteristic
438C8—41no—
439C8—41no—
440C8—201no—
441C8—201no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—102no—
445C2×C3—201no—
446C2×C3#6501611yescharacteristic
447C2×C3D5×#9911yescharacteristic
448C2×C3D5×#10111yescharacteristic
449C5C3×#147211yescharacteristic, complemented, Sylow
450C22—21no—
451C22—21no—
452C22—52no—
453C22—101no—
454C22—101no—
455C22—101no—
456C22—101no—
457C22—101no—
458C22—202no—
459C22—202no—
460C22C3×D5×C22⋊C411yescharacteristic
461C22C3×#404711yescharacteristic
462C22C3×#405311yescharacteristic
463C4—21no—
464C4—21no—
465C4—41no—
466C4—41no—
467C4—52no—
468C4—101no—
469C4—201no—
470C4—201no—
471C3#1059894011yescharacteristic, direct product factor, Sylow
472C2—21no—
473C2—21no—
474C2—102no—
475C2—201no—
476C2C3×#6501611yescharacteristic
477C2C3×D5×#9911yescharacteristic
478C2C3×D5×#10111yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#324C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C4×C5C23×C3
hypercenterC3×#324D5
hypocenterC5C3×#1472
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#324

Complements

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

NH ≅ G/Ntype
4. C3×C5×#324C2semidirect
5. C3×#64748C2semidirect
6. C3×#64689C2semidirect
7. C3×#64689C2semidirect
8. #10598940C3direct (N × H)
32. C5×#324C2×C3semidirect
33. #64748C2×C3semidirect
34. #64689C2×C3semidirect
35. #64689C2×C3semidirect
73. C3×#324D5semidirect
183. #324C3×D5semidirect
380. C3×C5#1472semidirect
449. C5C3×#1472semidirect
471. C3#10598940direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40422
C3×#650152
C3×D5×C22⋊C82
C3×C5×#3242
C3×#647482
C3×#646892
#105989403
C3×#14725