Finite Group Databasebeta

← C3×#10600769 #14282971

Subgroups — C3×#10600769 #14282971

Order 1920.

668 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
1C3×#66125C211yesmaximal, characteristic
2C3×C5×#407C211yesmaximal, characteristic, complemented
3C2×C3×#3963C211yesmaximal, characteristic, complemented
4C3×#64690C212yesmaximal, complemented
5C3×#64687C212yesmaximal, complemented
6#10600769C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C23×C3×Dic5—21no—
9C2×C3×#709C411yescharacteristic, complemented
10C2×C3×C5×M16—21no—
11C3×#4099—21no—
12C3×#4076C411yescharacteristic, complemented
13C3×#4076C2211yescharacteristic
14C3×#4075—21no—
15C3×C4×C22⋊D5—21no—
16C3×C4×C22⋊D5—21no—
17C3×#4072C411yescharacteristic, complemented
18C3×#4070C411yescharacteristic, complemented
19C3×#4070C2211yescharacteristic
20C3×C5×C22⋊C8—21no—
21C3×C5×C22⋊C8C2212yes—
22C3×#3963—21no—
23C3×#3963C2212yes—
24C3×#1504—51nomaximal, Hall
25#66125C2×C311yescharacteristic
26C5×#407C2×C311yescharacteristic, complemented
27C2×#3963C2×C311yescharacteristic, complemented
28#64690C2×C312yescomplemented
29#64687C2×C312yescomplemented
30C24×C3×C5D411yescharacteristic
31C22×C3×C4×C5—42no—
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C2×C3×C22⋊D5—21no—
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C22×C3×Dic5—24no—
42C22×C3×Dic5—22no—
43C22×C3×Dic5—42no—
44C22×C3×Dic5—42no—
45C3×#709—42no—
46C2×C3×D20C2×C411yescharacteristic, complemented
47C2×C3×C4×D5—21no—
48C2×C3×Dic10C2×C411yescharacteristic, complemented
49C3×C5×M16—42no—
50C2×C3×C5×C8—22no—
51C3×C22⋊Dic5—21no—
52C3×C22⋊Dic5—21no—
53C3×C22⋊Dic5—21no—
54C3×#685—21no—
55C3×#685—21no—
56C3×C4⋊Dic5C2×C411yescharacteristic, complemented
57C3×C4⋊Dic5C2×C411yescharacteristic, complemented
58C3×#683—21no—
59C3×#683—21no—
60C3×C4×Dic5—21no—
61C3×#525—51no—
62C3×#407D511yescharacteristic, complemented
63C2×C3×#95—51no—
64C3×#328—52no—
65C3×#327—52no—
66C23×C4×C5C22×C311yescharacteristic
67C23×Dic5—21no—
68C2×#709C3×C411yescharacteristic, complemented
69C2×C5×M16—21no—
70#4099—21no—
71#4076C3×C411yescharacteristic, complemented
72#4076C22×C311yescharacteristic
73#4075—21no—
74C4×C22⋊D5—21no—
75C4×C22⋊D5—21no—
76#4072C3×C411yescharacteristic, complemented
77#4070C3×C411yescharacteristic, complemented
78#4070C22×C311yescharacteristic
79C5×C22⋊C8—21no—
80C5×C22⋊C8C22×C312yes—
81#3963—21no—
82#3963C22×C312yes—
83#1504—51noSylow
84C23×C3×C5—22no—
85C23×C3×C5—22no—
86C23×C3×C5—21no—
87C23×C3×C5—21no—
88C23×C3×C5C22⋊C411yescharacteristic
89C23×C3×C5C22⋊C411yescharacteristic
90C23×C3×C5C2×D411yescharacteristic
91C22×C3×D5—21no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C22⋊C411yescharacteristic
99C2×C3×C4×C5C22⋊C411yescharacteristic
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C3×C22⋊D5—42no—
103C3×C22⋊D5—42no—
104C3×C22⋊D5—41no—
105C3×C22⋊D5—41no—
106C2×C3×Dic5—24no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—48no—
111C2×C3×Dic5—42no—
112C2×C3×Dic5—42no—
113C3×D20—41no—
114C3×C4×D5—42no—
115C3×Dic10—41no—
116C3×C5×C8—42no—
117C2×C3×#41—51no—
118C23×C3×C4—101no—
119C23×C3×C4C2×D511yescharacteristic
120C2×C3×M16—21no—
121C3×#123—101no—
122C3×C22⋊Q8—51no—
123C3×C22⋊Q8—51no—
124C3×#121—51no—
125C3×#121—51no—
126C3×#120—101no—
127C3×C4×D4—101no—
128C3×C4×D4—101no—
129C3×#117—51no—
130C3×C22⋊C8—21no—
131C3×C22⋊C8C2×D512yes—
132C3×#95—52no—
133C3×#95—101no—
134C24×C5C3×D411yescharacteristic
135C22×C4×C5—42no—
136C22×C4×C5C2×C3×C411yescharacteristic
137C22×C4×C5C2×C3×C411yescharacteristic
138C22×C4×C5C3×D411yescharacteristic
139C22×C4×C5C3×D411yescharacteristic
140C22×C4×C5C3×D411yescharacteristic
141C22×C4×C5C23×C311yescharacteristic
142C2×C22⋊D5—21no—
143C2×C22⋊D5—21no—
144C2×C22⋊D5—21no—
145C22×Dic5—24no—
146C22×Dic5—22no—
147C22×Dic5—42no—
148C22×Dic5—42no—
149#709—42no—
150C2×D20C2×C3×C411yescharacteristic, complemented
151C2×C4×D5—21no—
152C2×Dic10C2×C3×C411yescharacteristic, complemented
153C5×M16—42no—
154C2×C5×C8—22no—
155C22⋊Dic5—21no—
156C22⋊Dic5—21no—
157C22⋊Dic5—21no—
158#685—21no—
159#685—21no—
160C4⋊Dic5C2×C3×C411yescharacteristic, complemented
161C4⋊Dic5C2×C3×C411yescharacteristic, complemented
162#683—21no—
163#683—21no—
164C4×Dic5—21no—
165#525—51no—
166#407C3×D511yescharacteristic, complemented
167C2×#95—51no—
168#328—52no—
169#327—52no—
170C22×C3×C5—24no—
171C22×C3×C5—24no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—21no—
176C22×C3×C5—21no—
177C22×C3×C5—21no—
178C22×C3×C5#9912yes—
179C22×C3×C5#10412yes—
180C22×C3×C5C2×C22⋊C411yescharacteristic
181C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
182C22×C3×C5#13711yescharacteristic
183C2×C3×D5—41no—
184C2×C3×D5—41no—
185C2×C3×D5—41no—
186C3×C4×C5—21no—
187C3×C4×C5—21no—
188C3×C4×C5—21no—
189C3×C4×C5—21no—
190C3×Dic5—44no—
191C3×Dic5—41no—
192C3×Dic5—41no—
193C3×Dic5—41no—
194C24×C3D2011yescharacteristic
195C3×#41—202no—
196C2×C3×Q8—51no—
197C2×C3×D4—51no—
198C2×C3×D4—101no—
199C2×C3×D4—101no—
200C2×C3×D4—101no—
201C22×C3×C4—42no—
202C22×C3×C4—104no—
203C22×C3×C4—102no—
204C22×C3×C4—101no—
205C22×C3×C4—202no—
206C22×C3×C4—202no—
207C22×C3×C4C4×D511yescharacteristic
208C22×C3×C4C4×D511yescharacteristic
209C22×C3×C4D2011yescharacteristic
210C22×C3×C4C22⋊D511yescharacteristic
211C22×C3×C4C22⋊D511yescharacteristic
212C22×C3×C4C22×D511yescharacteristic
213C3×M16—42no—
214C2×C3×C8—22no—
215C3×C4⋊C4—51no—
216C3×C4⋊C4—51no—
217C3×C4⋊C4—101no—
218C3×C4⋊C4—101no—
219C3×C22⋊C4—101no—
220C3×C22⋊C4—101no—
221C3×C22⋊C4—101no—
222C3×C22⋊C4—101no—
223C3×C22⋊C4—101no—
224C3×C42—101no—
225C23×C5—22no—
226C23×C5—22no—
227C23×C5—21no—
228C23×C5—21no—
229C23×C5C3×C22⋊C411yescharacteristic
230C23×C5C3×C22⋊C411yescharacteristic
231C23×C5C2×C3×D411yescharacteristic
232C22×D5—21no—
233C2×C4×C5—22no—
234C2×C4×C5—22no—
235C2×C4×C5—41no—
236C2×C4×C5—41no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5C3×C22⋊C411yescharacteristic
240C2×C4×C5C3×C22⋊C411yescharacteristic
241C2×C4×C5C22×C3×C411yescharacteristic
242C2×C4×C5C2×C3×D411yescharacteristic
243C22⋊D5—42no—
244C22⋊D5—42no—
245C22⋊D5—41no—
246C22⋊D5—41no—
247C2×Dic5—24no—
248C2×Dic5—21no—
249C2×Dic5—21no—
250C2×Dic5—21no—
251C2×Dic5—48no—
252C2×Dic5—42no—
253C2×Dic5—42no—
254D20—41no—
255C4×D5—42no—
256Dic10—41no—
257C5×C8—42no—
258C2×#41—51no—
259C23×C4—101no—
260C23×C4C2×C3×D511yescharacteristic
261C2×M16—21no—
262#123—101no—
263C22⋊Q8—51no—
264C22⋊Q8—51no—
265#121—51no—
266#121—51no—
267#120—101no—
268C4×D4—101no—
269C4×D4—101no—
270#117—51no—
271C22⋊C8—21no—
272C22⋊C8C2×C3×D512yes—
273#95—52no—
274#95—101no—
275C2×C3×C5—21no—
276C2×C3×C5—22no—
277C2×C3×C5—22no—
278C2×C3×C5—21no—
279C2×C3×C5C2×#9911yescharacteristic
280C2×C3×C5#41711yescharacteristic
281C2×C3×C5C2×#10411yescharacteristic
282C3×D5—81no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—21no—
286C23×C3—21no—
287C23×C3—101no—
288C23×C3#68511yescharacteristic
289C23×C3#68511yescharacteristic
290C23×C3C2×D2011yescharacteristic
291C3×Q8—201no—
292C3×D4—201no—
293C3×D4—202no—
294C3×D4—202no—
295C3×D4—201no—
296C3×D4—201no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—104no—
304C2×C3×C4—101no—
305C2×C3×C4—101no—
306C2×C3×C4—101no—
307C2×C3×C4—202no—
308C2×C3×C4—208no—
309C2×C3×C4—202no—
310C2×C3×C4—202no—
311C2×C3×C4#68511yescharacteristic
312C2×C3×C4#68511yescharacteristic
313C2×C3×C4C2×C4×D511yescharacteristic
314C2×C3×C4C2×C22⋊D511yescharacteristic
315C3×C8—42no—
316C22×C5—24no—
317C22×C5—24no—
318C22×C5—21no—
319C22×C5—21no—
320C22×C5—21no—
321C22×C5—21no—
322C22×C5—21no—
323C22×C5—21no—
324C22×C5C3×#9912yes—
325C22×C5C3×#10412yes—
326C22×C5C2×C3×C22⋊C411yescharacteristic
327C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
328C22×C5C3×#13711yescharacteristic
329C2×D5—41no—
330C2×D5—41no—
331C2×D5—41no—
332C4×C5—21no—
333C4×C5—21no—
334C4×C5—21no—
335C4×C5—21no—
336Dic5—44no—
337Dic5—41no—
338Dic5—41no—
339Dic5—41no—
340C24C3×D2011yescharacteristic
341#41—202no—
342C2×Q8—51no—
343C2×D4—51no—
344C2×D4—101no—
345C2×D4—101no—
346C2×D4—101no—
347C22×C4—42no—
348C22×C4—104no—
349C22×C4—102no—
350C22×C4—101no—
351C22×C4—202no—
352C22×C4—202no—
353C22×C4C3×C4×D511yescharacteristic
354C22×C4C3×C4×D511yescharacteristic
355C22×C4C3×D2011yescharacteristic
356C22×C4C3×C22⋊D511yescharacteristic
357C22×C4C3×C22⋊D511yescharacteristic
358C22×C4C22×C3×D511yescharacteristic
359M16—42no—
360C2×C8—22no—
361C4⋊C4—51no—
362C4⋊C4—51no—
363C4⋊C4—101no—
364C4⋊C4—101no—
365C22⋊C4—101no—
366C22⋊C4—101no—
367C22⋊C4—101no—
368C22⋊C4—101no—
369C22⋊C4—101no—
370C42—101no—
371C3×C5#150411yescharacteristic, complemented, Hall
372C22×C3—24no—
373C22×C3—24no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—201no—
381C22×C3—201no—
382C22×C3—201no—
383C22×C3#393812yes—
384C22×C3#395712yes—
385C22×C3#405411yescharacteristic
386C22×C3#405511yescharacteristic
387C22×C3C2×#68511yescharacteristic
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—204no—
393C3×C4—201no—
394C3×C4—201no—
395C3×C4—201no—
396C2×C5—21no—
397C2×C5—22no—
398C2×C5—22no—
399C2×C5—21no—
400C2×C5C2×C3×#9911yescharacteristic
401C2×C5C3×#41711yescharacteristic
402C2×C5C2×C3×#10411yescharacteristic
403D5—81no—
404C23—22no—
405C23—22no—
406C23—21no—
407C23—21no—
408C23—101no—
409C23C3×#68511yescharacteristic
410C23C3×#68511yescharacteristic
411C23C2×C3×D2011yescharacteristic
412Q8—201no—
413D4—201no—
414D4—202no—
415D4—202no—
416D4—201no—
417D4—201no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—104no—
425C2×C4—101no—
426C2×C4—101no—
427C2×C4—101no—
428C2×C4—202no—
429C2×C4—208no—
430C2×C4—202no—
431C2×C4—202no—
432C2×C4C3×#68511yescharacteristic
433C2×C4C3×#68511yescharacteristic
434C2×C4C2×C3×C4×D511yescharacteristic
435C2×C4C2×C3×C22⋊D511yescharacteristic
436C8—42no—
437C2×C3—21no—
438C2×C3—22no—
439C2×C3—22no—
440C2×C3—21no—
441C2×C3—401no—
442C2×C3C2×#393811yescharacteristic
443C2×C3#6542211yescharacteristic
444C2×C3C2×#395711yescharacteristic
445C5C3×#150411yescharacteristic, complemented, Sylow
446C22—24no—
447C22—24no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—201no—
455C22—201no—
456C22—201no—
457C22C3×#393812yes—
458C22C3×#395712yes—
459C22C3×#405411yescharacteristic
460C22C3×#405511yescharacteristic
461C22C2×C3×#68511yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—204no—
467C4—201no—
468C4—201no—
469C4—201no—
470C3#1060076911yescharacteristic, direct product factor, Sylow
471C2—21no—
472C2—22no—
473C2—22no—
474C2—21no—
475C2—401no—
476C2C2×C3×#393811yescharacteristic
477C2C3×#6542211yescharacteristic
478C2C2×C3×#395711yescharacteristic
subgroupG/H
centerC22×C3C2×#685
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#407C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66125C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#407D5
hypocenterC5C3×#1504
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
2. C3×C5×#407C2semidirect
3. C2×C3×#3963C2semidirect
4. C3×#64690C2semidirect
5. C3×#64687C2semidirect
6. #10600769C3direct (N × H)
9. C2×C3×#709C4semidirect
12. C3×#4076C4semidirect
17. C3×#4072C4semidirect
18. C3×#4070C4semidirect
26. C5×#407C2×C3semidirect
27. C2×#3963C2×C3semidirect
28. #64690C2×C3semidirect
29. #64687C2×C3semidirect
46. C2×C3×D20C2×C4semidirect
48. C2×C3×Dic10C2×C4semidirect
56. C3×C4⋊Dic5C2×C4semidirect
57. C3×C4⋊Dic5C2×C4semidirect
62. C3×#407D5semidirect
68. C2×#709C3×C4semidirect
71. #4076C3×C4semidirect
76. #4072C3×C4semidirect
77. #4070C3×C4semidirect
150. C2×D20C2×C3×C4semidirect
152. C2×Dic10C2×C3×C4semidirect
160. C4⋊Dic5C2×C3×C4semidirect
161. C4⋊Dic5C2×C3×C4semidirect
166. #407C3×D5semidirect
371. C3×C5#1504semidirect
445. C5C3×#1504semidirect
470. C3#10600769direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661252
C3×C5×#4072
C2×C3×#39632
C3×#646902
C3×#646872
#106007693
C3×#15045