Finite Group Databasebeta

← C3×#10599071 #14283022

Subgroups — C3×#10599071 #14283022

Order 1920.

544 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×#65930C211yesmaximal, characteristic
2C3×#65008C211yesmaximal, characteristic, complemented
3C3×#64937C211yesmaximal, characteristic, complemented
4C3×C5×#327C211yesmaximal, characteristic, complemented
5C3×#64757C211yesmaximal, characteristic, complemented
6C3×#64690C211yesmaximal, characteristic, complemented
7C3×#64671C211yesmaximal, characteristic, complemented
8#10599071C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#711—21no—
10C3×C5×#121C2211yescharacteristic
11C3×#4086C411yescharacteristic, complemented
12C3×#4085—21no—
13C3×D4×Dic5C411yescharacteristic, complemented
14C3×#4076C2211yescharacteristic
15C2×C3×C4×Dic5—21no—
16C2×C3×C4×Dic5C2211yescharacteristic
17C3×#4039C411yescharacteristic, complemented
18C3×#4034C411yescharacteristic, complemented
19C3×#4031—21no—
20C3×#4027—21no—
21C3×C5×C22⋊C8C2211yescharacteristic
22C3×C5×#95C2211yescharacteristic
23C3×#3963—21no—
24C3×#3963C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3947—21no—
27C3×#3946—21no—
28C3×#1505—51nomaximal, Hall
29#65930C2×C311yescharacteristic
30#65008C2×C311yescharacteristic, complemented
31#64937C2×C311yescharacteristic, complemented
32C5×#327C2×C311yescharacteristic, complemented
33#64757C2×C311yescharacteristic, complemented
34#64690C2×C311yescharacteristic, complemented
35#64671C2×C311yescharacteristic, complemented
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—21no—
42C2×C3×C22⋊D5—21no—
43C22×C3×Dic5—21no—
44C22×C3×Dic5—21no—
45C22×C3×Dic5D411yescharacteristic
46C22×C3×Dic5D411yescharacteristic
47C3×#711—42no—
48C3×#711—42no—
49C2×C3×D20C2×C411yescharacteristic
50C2×C3×C4×D5—21no—
51C2×C3×Dic10—21no—
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4C2×C411yescharacteristic
54C3×C5×C22⋊C4—21no—
55C3×C22⋊Dic5—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×C4⋊Dic5C2×C411yescharacteristic
59C3×#683—21no—
60C3×C4×Dic5—24no—
61C3×C4×Dic5C2×C411yescharacteristic
62C3×C4×Dic5C2×C411yescharacteristic
63C3×C4×Dic5D411yescharacteristic
64C3×C4×Dic5D411yescharacteristic
65C2×C3×#168—21no—
66C3×#532—51no—
67C3×#432—51no—
68C3×#376—51no—
69C3×#327—51no—
70C3×#327—51no—
71C3×#327—51no—
72C3×#327D511yescharacteristic, complemented
73C2×#711—21no—
74C5×#121C22×C311yescharacteristic
75#4086C3×C411yescharacteristic, complemented
76#4085—21no—
77D4×Dic5C3×C411yescharacteristic, complemented
78#4076C22×C311yescharacteristic
79C2×C4×Dic5—21no—
80C2×C4×Dic5C22×C311yescharacteristic
81#4039C3×C411yescharacteristic, complemented
82#4034C3×C411yescharacteristic, complemented
83#4031—21no—
84#4027—21no—
85C5×C22⋊C8C22×C311yescharacteristic
86C5×#95C22×C311yescharacteristic
87#3963—21no—
88#3963C22×C311yescharacteristic
89C22⋊#168C22×C311yescharacteristic
90#3947—21no—
91#3946—21no—
92#1505—51noSylow
93C23×C3×C5—21no—
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—21no—
96C3×C5×D4—41no—
97C3×C5×D4—41no—
98C3×C5×D4—41no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C22×C411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C3×C22⋊D5—42no—
107C3×C22⋊D5—41no—
108C3×C22⋊D5—41no—
109C3×C22⋊D5—42no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5—22no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—42no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5C22⋊C411yescharacteristic
119C2×C3×Dic5C22⋊C411yescharacteristic
120C2×C3×Dic5C22⋊C411yescharacteristic
121C2×C3×Dic5C22⋊C411yescharacteristic
122C3×D20—41no—
123C3×C4×D5—42no—
124C3×Dic10—42no—
125C3×C5×C8—41no—
126C3×#168—41no—
127C2×C3×#41—101no—
128C3×C4⋊Q8—51no—
129C3×#127—51no—
130C3×#124—101no—
131C3×#121—51no—
132C3×#121—101no—
133C3×#121C2×D511yescharacteristic
134C3×C4×D4—51no—
135C3×C4×D4—51no—
136C3×C4×D4—101no—
137C2×C3×C42—51no—
138C2×C3×C42—101no—
139C3×C4⋊C8—101no—
140C3×C22⋊C8—51no—
141C3×C22⋊C8C2×D511yescharacteristic
142C3×#97—101no—
143C3×#95—51no—
144C3×#95—101no—
145C3×#95C2×D511yescharacteristic
146C2×C5×D4—21no—
147C2×C5×D4C2×C3×C411yescharacteristic
148C22×C4×C5—21no—
149C22×C4×C5C23×C311yescharacteristic
150C2×C22⋊D5—21no—
151C2×C22⋊D5—21no—
152C2×C22⋊D5—21no—
153C22×Dic5—21no—
154C22×Dic5—21no—
155C22×Dic5C3×D411yescharacteristic
156C22×Dic5C3×D411yescharacteristic
157#711—42no—
158#711—42no—
159C2×D20C2×C3×C411yescharacteristic
160C2×C4×D5—21no—
161C2×Dic10—21no—
162C2×C5×C8—21no—
163C5×C4⋊C4C2×C3×C411yescharacteristic
164C5×C22⋊C4—21no—
165C22⋊Dic5—21no—
166#685—21no—
167#685—21no—
168C4⋊Dic5C2×C3×C411yescharacteristic
169#683—21no—
170C4×Dic5—24no—
171C4×Dic5C2×C3×C411yescharacteristic
172C4×Dic5C2×C3×C411yescharacteristic
173C4×Dic5C3×D411yescharacteristic
174C4×Dic5C3×D411yescharacteristic
175C2×#168—21no—
176#532—51no—
177#432—51no—
178#376—51no—
179#327—51no—
180#327—51no—
181#327—51no—
182#327C3×D511yescharacteristic, complemented
183C22×C3×C5—21no—
184C22×C3×C5—21no—
185C22×C3×C5—41no—
186C22×C3×C5—41no—
187C22×C3×C5—41no—
188C22×C3×C5C2×C22⋊C411yescharacteristic
189C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
190C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
191C2×C3×D5—41no—
192C2×C3×D5—41no—
193C2×C3×D5—41no—
194C3×C4×C5—21no—
195C3×C4×C5—21no—
196C3×C4×C5—42no—
197C3×C4×C5—41no—
198C3×Dic5—21no—
199C3×Dic5—21no—
200C3×Dic5—21no—
201C3×Dic5—42no—
202C3×Dic5—41no—
203C3×Dic5#10412yes—
204C3×#41—202no—
205C3×#41—202no—
206C2×C3×Q8—101no—
207C2×C3×D4—21no—
208C2×C3×D4—51no—
209C2×C3×D4—101no—
210C2×C3×D4—101no—
211C2×C3×D4—101no—
212C2×C3×D4C4×D511yescharacteristic
213C22×C3×C4—21no—
214C22×C3×C4—51no—
215C22×C3×C4—51no—
216C22×C3×C4—101no—
217C22×C3×C4—101no—
218C22×C3×C4—101no—
219C22×C3×C4C22×D511yescharacteristic
220C2×C3×C8—21no—
221C2×C3×C8—101no—
222C3×C4⋊C4—51no—
223C3×C4⋊C4—101no—
224C3×C4⋊C4C4×D511yescharacteristic
225C3×C22⋊C4—21no—
226C3×C22⋊C4—101no—
227C3×C22⋊C4—101no—
228C3×C22⋊C4—101no—
229C3×C42—51no—
230C3×C42—51no—
231C3×C42—51no—
232C3×C42—51no—
233C3×C42—104no—
234C23×C5—21no—
235C23×C5C2×C3×D411yescharacteristic
236C22×D5—21no—
237C5×D4—41no—
238C5×D4—41no—
239C5×D4—41no—
240C2×C4×C5—22no—
241C2×C4×C5—21no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5C22×C3×C411yescharacteristic
246C2×C4×C5C2×C3×D411yescharacteristic
247C22⋊D5—42no—
248C22⋊D5—41no—
249C22⋊D5—41no—
250C22⋊D5—42no—
251C2×Dic5—21no—
252C2×Dic5—21no—
253C2×Dic5—22no—
254C2×Dic5—22no—
255C2×Dic5—21no—
256C2×Dic5—42no—
257C2×Dic5—41no—
258C2×Dic5—41no—
259C2×Dic5C3×C22⋊C411yescharacteristic
260C2×Dic5C3×C22⋊C411yescharacteristic
261C2×Dic5C3×C22⋊C411yescharacteristic
262C2×Dic5C3×C22⋊C411yescharacteristic
263D20—41no—
264C4×D5—42no—
265Dic10—42no—
266C5×C8—41no—
267#168—41no—
268C2×#41—101no—
269C4⋊Q8—51no—
270#127—51no—
271#124—101no—
272#121—51no—
273#121—101no—
274#121C2×C3×D511yescharacteristic
275C4×D4—51no—
276C4×D4—51no—
277C4×D4—101no—
278C2×C42—51no—
279C2×C42—101no—
280C4⋊C8—101no—
281C22⋊C8—51no—
282C22⋊C8C2×C3×D511yescharacteristic
283#97—101no—
284#95—51no—
285#95—101no—
286#95C2×C3×D511yescharacteristic
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—81no—
290C2×C3×C5#41011yescharacteristic
291C2×C3×C5#41811yescharacteristic
292C2×C3×C5C2×#10411yescharacteristic
293C3×D5—81no—
294C23×C3—21no—
295C23×C3—101no—
296C23×C3D4×D511yescharacteristic
297C3×Q8—202no—
298C3×D4—41no—
299C3×D4—41no—
300C3×D4—41no—
301C3×D4—201no—
302C3×D4—202no—
303C3×D4—202no—
304C3×D4—201no—
305C3×D4—201no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—51no—
312C2×C3×C4—51no—
313C2×C3×C4—51no—
314C2×C3×C4—51no—
315C2×C3×C4—102no—
316C2×C3×C4—101no—
317C2×C3×C4—101no—
318C2×C3×C4—102no—
319C2×C3×C4—101no—
320C2×C3×C4—202no—
321C2×C3×C4—202no—
322C2×C3×C4—201no—
323C2×C3×C4—201no—
324C2×C3×C4C2×C4×D511yescharacteristic
325C2×C3×C4D4×D511yescharacteristic
326C3×C8—41no—
327C3×C8—201no—
328C22×C5—21no—
329C22×C5—21no—
330C22×C5—41no—
331C22×C5—41no—
332C22×C5—41no—
333C22×C5C2×C3×C22⋊C411yescharacteristic
334C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
335C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
336C2×D5—41no—
337C2×D5—41no—
338C2×D5—41no—
339C4×C5—21no—
340C4×C5—21no—
341C4×C5—42no—
342C4×C5—41no—
343Dic5—21no—
344Dic5—21no—
345Dic5—21no—
346Dic5—42no—
347Dic5—41no—
348Dic5C3×#10412yes—
349#41—202no—
350#41—202no—
351C2×Q8—101no—
352C2×D4—21no—
353C2×D4—51no—
354C2×D4—101no—
355C2×D4—101no—
356C2×D4—101no—
357C2×D4C3×C4×D511yescharacteristic
358C22×C4—21no—
359C22×C4—51no—
360C22×C4—51no—
361C22×C4—101no—
362C22×C4—101no—
363C22×C4—101no—
364C22×C4C22×C3×D511yescharacteristic
365C2×C8—21no—
366C2×C8—101no—
367C4⋊C4—51no—
368C4⋊C4—101no—
369C4⋊C4C3×C4×D511yescharacteristic
370C22⋊C4—21no—
371C22⋊C4—101no—
372C22⋊C4—101no—
373C22⋊C4—101no—
374C42—51no—
375C42—51no—
376C42—51no—
377C42—51no—
378C42—104no—
379C3×C5#150511yescharacteristic, complemented, Hall
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—41no—
385C22×C3—201no—
386C22×C3—201no—
387C22×C3—201no—
388C22×C3D5×C22⋊C411yescharacteristic
389C22×C3#405711yescharacteristic
390C22×C3#406011yescharacteristic
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—42no—
394C3×C4—41no—
395C3×C4—52no—
396C3×C4—101no—
397C3×C4—101no—
398C3×C4—101no—
399C3×C4—202no—
400C3×C4—201no—
401C2×C5—21no—
402C2×C5—21no—
403C2×C5—81no—
404C2×C5C3×#41011yescharacteristic
405C2×C5C3×#41811yescharacteristic
406C2×C5C2×C3×#10411yescharacteristic
407D5—81no—
408C23—21no—
409C23—101no—
410C23C3×D4×D511yescharacteristic
411Q8—202no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—201no—
416D4—202no—
417D4—202no—
418D4—201no—
419D4—201no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—51no—
426C2×C4—51no—
427C2×C4—51no—
428C2×C4—51no—
429C2×C4—102no—
430C2×C4—101no—
431C2×C4—101no—
432C2×C4—102no—
433C2×C4—101no—
434C2×C4—202no—
435C2×C4—202no—
436C2×C4—201no—
437C2×C4—201no—
438C2×C4C2×C3×C4×D511yescharacteristic
439C2×C4C3×D4×D511yescharacteristic
440C8—41no—
441C8—201no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—81no—
445C2×C3—401no—
446C2×C3#6502911yescharacteristic
447C2×C3#6505911yescharacteristic
448C2×C3D5×#10411yescharacteristic
449C5C3×#150511yescharacteristic, complemented, Sylow
450C22—21no—
451C22—21no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—201no—
456C22—201no—
457C22—201no—
458C22C3×D5×C22⋊C411yescharacteristic
459C22C3×#405711yescharacteristic
460C22C3×#406011yescharacteristic
461C4—21no—
462C4—21no—
463C4—42no—
464C4—41no—
465C4—52no—
466C4—101no—
467C4—101no—
468C4—101no—
469C4—202no—
470C4—201no—
471C3#1059907111yescharacteristic, direct product factor, Sylow
472C2—21no—
473C2—21no—
474C2—81no—
475C2—401no—
476C2C3×#6502911yescharacteristic
477C2C3×#6505911yescharacteristic
478C2C3×D5×#10411yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#327C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#65930C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#327D5
hypocenterC5C3×#1505
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#327

Complements

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

NH ≅ G/Ntype
2. C3×#65008C2semidirect
3. C3×#64937C2semidirect
4. C3×C5×#327C2semidirect
5. C3×#64757C2semidirect
6. C3×#64690C2semidirect
7. C3×#64671C2semidirect
8. #10599071C3direct (N × H)
11. C3×#4086C4semidirect
13. C3×D4×Dic5C4semidirect
17. C3×#4039C4semidirect
18. C3×#4034C4semidirect
30. #65008C2×C3semidirect
31. #64937C2×C3semidirect
32. C5×#327C2×C3semidirect
33. #64757C2×C3semidirect
34. #64690C2×C3semidirect
35. #64671C2×C3semidirect
72. C3×#327D5semidirect
75. #4086C3×C4semidirect
77. D4×Dic5C3×C4semidirect
81. #4039C3×C4semidirect
82. #4034C3×C4semidirect
182. #327C3×D5semidirect
379. C3×C5#1505semidirect
449. C5C3×#1505semidirect
471. C3#10599071direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659302
C3×#650082
C3×#649372
C3×C5×#3272
C3×#647572
C3×#646902
C3×#646712
#105990713
C3×#15055