Finite Group Databasebeta

← C3×#10599104 #14283200

Subgroups — C3×#10599104 #14283200

Order 1920.

484 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65958C211yesmaximal, characteristic
2C3×#65008C211yesmaximal, characteristic, complemented
3C3×#64938C211yesmaximal, characteristic, complemented
4C3×C5×#328C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6C3×#64690C211yesmaximal, characteristic
7C3×#64671C211yesmaximal, characteristic
8#10599104C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10C3×#4093C411yescharacteristic, complemented
11C3×Q8×Dic5C411yescharacteristic, complemented
12C3×#4076C2211yescharacteristic
13C2×C3×#683—21no—
14C2×C3×C4×Dic5—21no—
15C2×C3×C4×Dic5C2211yescharacteristic
16C3×#4044—21no—
17C3×#4039C411yescharacteristic, complemented
18C3×#4038—21no—
19C3×#4036C411yescharacteristic, complemented
20C3×#4032—21no—
21C3×#4027—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23C3×C5×#95C2211yescharacteristic
24C3×#3963C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3947—21no—
27C3×#3946—21no—
28C3×#1509—51nomaximal, Hall
29#65958C2×C311yescharacteristic
30#65008C2×C311yescharacteristic, complemented
31#64938C2×C311yescharacteristic, complemented
32C5×#328C2×C311yescharacteristic, complemented
33#64758C2×C311yescharacteristic, complemented
34#64690C2×C311yescharacteristic
35#64671C2×C311yescharacteristic
36C2×C3×C5×Q8C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×C3×C22⋊D5—21no—
40C22×C3×Dic5—21no—
41C22×C3×Dic5D411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C2×C3×D20C2×C411yescharacteristic
44C2×C3×C4×D5—21no—
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4C2×C411yescharacteristic
48C3×C5×C22⋊C4—21no—
49C3×#685—21no—
50C3×#685—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5C2×C411yescharacteristic
56C3×#683—24no—
57C3×#683—21no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5—42no—
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5C2×C411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63C3×C4×Dic5D411yescharacteristic
64C2×C3×#168—21no—
65C3×#529—51no—
66C3×#432—51no—
67C3×C4×C4⋊C4—51no—
68C3×#328—51no—
69C3×#328D511yescharacteristic, complemented
70C3×#327—51no—
71C3×#327—51no—
72C5×C22⋊Q8C22×C311yescharacteristic
73#4093C3×C411yescharacteristic, complemented
74Q8×Dic5C3×C411yescharacteristic, complemented
75#4076C22×C311yescharacteristic
76C2×#683—21no—
77C2×C4×Dic5—21no—
78C2×C4×Dic5C22×C311yescharacteristic
79#4044—21no—
80#4039C3×C411yescharacteristic, complemented
81#4038—21no—
82#4036C3×C411yescharacteristic, complemented
83#4032—21no—
84#4027—21no—
85C5×C22⋊C8C22×C311yescharacteristic
86C5×#95C22×C311yescharacteristic
87#3963C22×C311yescharacteristic
88C22⋊#168C22×C311yescharacteristic
89#3947—21no—
90#3946—21no—
91#1509—51noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×C3×D5—21no—
94C3×C5×Q8—41no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C3×C22⋊D5—41no—
104C3×C22⋊D5—41no—
105C2×C3×Dic5—21no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5C22⋊C411yescharacteristic
113C2×C3×Dic5C22⋊C411yescharacteristic
114C2×C3×Dic5C22⋊C411yescharacteristic
115C2×C3×Dic5C22⋊C411yescharacteristic
116C3×D20—41no—
117C3×C4×D5—42no—
118C3×C5×C8—41no—
119C3×#168—41no—
120C3×#126—101no—
121C3×#125—51no—
122C3×#124—51no—
123C3×#123—101no—
124C3×C22⋊Q8C2×D511yescharacteristic
125C3×#121—51no—
126C3×C4×Q8—51no—
127C3×C4×D4—51no—
128C3×C4×D4—101no—
129C3×#117—101no—
130C2×C3×C4⋊C4—101no—
131C2×C3×C42—51no—
132C2×C3×C42—101no—
133C3×C4⋊C8—101no—
134C3×C22⋊C8—51no—
135C3×C22⋊C8C2×D511yescharacteristic
136C3×#97—101no—
137C3×#95—51no—
138C3×#95C2×D511yescharacteristic
139C2×C5×Q8C2×C3×C411yescharacteristic
140C22×C4×C5—21no—
141C22×C4×C5C23×C311yescharacteristic
142C2×C22⋊D5—21no—
143C22×Dic5—21no—
144C22×Dic5C3×D411yescharacteristic
145C22×Dic5C3×D411yescharacteristic
146C2×D20C2×C3×C411yescharacteristic
147C2×C4×D5—21no—
148C2×C5×C8—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4C2×C3×C411yescharacteristic
151C5×C22⋊C4—21no—
152#685—21no—
153#685—21no—
154#685—21no—
155#685—21no—
156C4⋊Dic5—21no—
157C4⋊Dic5—21no—
158C4⋊Dic5C2×C3×C411yescharacteristic
159#683—24no—
160#683—21no—
161C4×Dic5—21no—
162C4×Dic5—42no—
163C4×Dic5C2×C3×C411yescharacteristic
164C4×Dic5C2×C3×C411yescharacteristic
165C4×Dic5C3×D411yescharacteristic
166C4×Dic5C3×D411yescharacteristic
167C2×#168—21no—
168#529—51no—
169#432—51no—
170C4×C4⋊C4—51no—
171#328—51no—
172#328C3×D511yescharacteristic, complemented
173#327—51no—
174#327—51no—
175C22×C3×C5—21no—
176C22×C3×C5—21no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C2×C3×D5—41no—
181C2×C3×D5—41no—
182C2×C3×D5—41no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—42no—
186C3×C4×C5—41no—
187C3×C4×C5—41no—
188C3×Dic5—21no—
189C3×Dic5—21no—
190C3×Dic5—21no—
191C3×Dic5—42no—
192C3×Dic5—41no—
193C3×Dic5#10412yes—
194C2×C3×Q8C4×D511yescharacteristic
195C2×C3×D4—51no—
196C2×C3×D4—101no—
197C22×C3×C4—21no—
198C22×C3×C4—51no—
199C22×C3×C4—51no—
200C22×C3×C4—101no—
201C22×C3×C4—101no—
202C22×C3×C4C22×D511yescharacteristic
203C2×C3×C8—21no—
204C2×C3×C8—101no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—51no—
207C3×C4⋊C4—101no—
208C3×C4⋊C4—101no—
209C3×C4⋊C4—101no—
210C3×C4⋊C4—104no—
211C3×C4⋊C4C4×D511yescharacteristic
212C3×C22⋊C4—21no—
213C3×C22⋊C4—101no—
214C3×C22⋊C4—101no—
215C3×C22⋊C4—101no—
216C3×C22⋊C4—101no—
217C3×C42—51no—
218C3×C42—51no—
219C3×C42—51no—
220C3×C42—51no—
221C3×C42—101no—
222C3×C42—202no—
223C23×C5C2×C3×D411yescharacteristic
224C22×D5—21no—
225C5×Q8—41no—
226C2×C4×C5—22no—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5—41no—
232C2×C4×C5C22×C3×C411yescharacteristic
233C2×C4×C5C2×C3×D411yescharacteristic
234C22⋊D5—41no—
235C22⋊D5—41no—
236C2×Dic5—21no—
237C2×Dic5—21no—
238C2×Dic5—22no—
239C2×Dic5—22no—
240C2×Dic5—21no—
241C2×Dic5—41no—
242C2×Dic5—41no—
243C2×Dic5C3×C22⋊C411yescharacteristic
244C2×Dic5C3×C22⋊C411yescharacteristic
245C2×Dic5C3×C22⋊C411yescharacteristic
246C2×Dic5C3×C22⋊C411yescharacteristic
247D20—41no—
248C4×D5—42no—
249C5×C8—41no—
250#168—41no—
251#126—101no—
252#125—51no—
253#124—51no—
254#123—101no—
255C22⋊Q8C2×C3×D511yescharacteristic
256#121—51no—
257C4×Q8—51no—
258C4×D4—51no—
259C4×D4—101no—
260#117—101no—
261C2×C4⋊C4—101no—
262C2×C42—51no—
263C2×C42—101no—
264C4⋊C8—101no—
265C22⋊C8—51no—
266C22⋊C8C2×C3×D511yescharacteristic
267#97—101no—
268#95—51no—
269#95C2×C3×D511yescharacteristic
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5#41011yescharacteristic
273C2×C3×C5#41711yescharacteristic
274C2×C3×C5C2×#10411yescharacteristic
275C3×D5—81no—
276C23×C3—101no—
277C23×C3D4×D511yescharacteristic
278C3×Q8—41no—
279C3×D4—201no—
280C3×D4—201no—
281C3×D4—201no—
282C2×C3×C4—22no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—51no—
289C2×C3×C4—51no—
290C2×C3×C4—51no—
291C2×C3×C4—51no—
292C2×C3×C4—102no—
293C2×C3×C4—101no—
294C2×C3×C4—101no—
295C2×C3×C4—102no—
296C2×C3×C4—101no—
297C2×C3×C4—202no—
298C2×C3×C4—201no—
299C2×C3×C4—201no—
300C2×C3×C4C2×C4×D511yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C3×C8—41no—
303C3×C8—201no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5C2×C3×C22⋊C411yescharacteristic
307C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
308C22×C5C3×#13711yescharacteristic
309C2×D5—41no—
310C2×D5—41no—
311C2×D5—41no—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—42no—
315C4×C5—41no—
316C4×C5—41no—
317Dic5—21no—
318Dic5—21no—
319Dic5—21no—
320Dic5—42no—
321Dic5—41no—
322Dic5C3×#10412yes—
323C2×Q8C3×C4×D511yescharacteristic
324C2×D4—51no—
325C2×D4—101no—
326C22×C4—21no—
327C22×C4—51no—
328C22×C4—51no—
329C22×C4—101no—
330C22×C4—101no—
331C22×C4C22×C3×D511yescharacteristic
332C2×C8—21no—
333C2×C8—101no—
334C4⋊C4—21no—
335C4⋊C4—51no—
336C4⋊C4—101no—
337C4⋊C4—101no—
338C4⋊C4—101no—
339C4⋊C4—104no—
340C4⋊C4C3×C4×D511yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—101no—
343C22⋊C4—101no—
344C22⋊C4—101no—
345C22⋊C4—101no—
346C42—51no—
347C42—51no—
348C42—51no—
349C42—51no—
350C42—101no—
351C42—202no—
352C3×C5#150911yescharacteristic, complemented, Hall
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—201no—
356C22×C3—201no—
357C22×C3—201no—
358C22×C3D5×C22⋊C411yescharacteristic
359C22×C3#406011yescharacteristic
360C22×C3#406411yescharacteristic
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—42no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—52no—
367C3×C4—101no—
368C3×C4—101no—
369C3×C4—101no—
370C3×C4—202no—
371C3×C4—201no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5C3×#41011yescharacteristic
375C2×C5C3×#41711yescharacteristic
376C2×C5C2×C3×#10411yescharacteristic
377D5—81no—
378C23—101no—
379C23C3×D4×D511yescharacteristic
380Q8—41no—
381D4—201no—
382D4—201no—
383D4—201no—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—51no—
391C2×C4—51no—
392C2×C4—51no—
393C2×C4—51no—
394C2×C4—102no—
395C2×C4—101no—
396C2×C4—101no—
397C2×C4—102no—
398C2×C4—101no—
399C2×C4—202no—
400C2×C4—201no—
401C2×C4—201no—
402C2×C4C2×C3×C4×D511yescharacteristic
403C2×C4C3×D4×D511yescharacteristic
404C8—41no—
405C8—201no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—401no—
409C2×C3#6502911yescharacteristic
410C2×C3#6509211yescharacteristic
411C2×C3D5×#10411yescharacteristic
412C5C3×#150911yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—201no—
416C22—201no—
417C22—201no—
418C22C3×D5×C22⋊C411yescharacteristic
419C22C3×#406011yescharacteristic
420C22C3×#406411yescharacteristic
421C4—21no—
422C4—21no—
423C4—42no—
424C4—41no—
425C4—41no—
426C4—52no—
427C4—101no—
428C4—101no—
429C4—101no—
430C4—202no—
431C4—201no—
432C3#1059910411yescharacteristic, direct product factor, Sylow
433C2—21no—
434C2—21no—
435C2—401no—
436C2C3×#6502911yescharacteristic
437C2C3×#6509211yescharacteristic
438C2C3×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 radicalC3×#4076C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#328D5
hypocenterC5C3×#1509
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
2. C3×#65008C2semidirect
3. C3×#64938C2semidirect
4. C3×C5×#328C2semidirect
5. C3×#64758C2semidirect
8. #10599104C3direct (N × H)
10. C3×#4093C4semidirect
11. C3×Q8×Dic5C4semidirect
17. C3×#4039C4semidirect
19. C3×#4036C4semidirect
30. #65008C2×C3semidirect
31. #64938C2×C3semidirect
32. C5×#328C2×C3semidirect
33. #64758C2×C3semidirect
69. C3×#328D5semidirect
73. #4093C3×C4semidirect
74. Q8×Dic5C3×C4semidirect
80. #4039C3×C4semidirect
82. #4036C3×C4semidirect
172. #328C3×D5semidirect
352. C3×C5#1509semidirect
412. C5C3×#1509semidirect
432. C3#10599104direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659582
C3×#650082
C3×#649382
C3×C5×#3282
C3×#647582
C3×#646902
C3×#646712
#105991043
C3×#15095