Finite Group Databasebeta

← C3×#10600246 #14300527

Subgroups — C3×#10600246 #14300527

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66125C211yesmaximal, characteristic
2C22×C3×#681C211yesmaximal, characteristic, complemented
3C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#3937C212yesmaximal, complemented
5C3×#64743C212yesmaximal, complemented
6#10600246C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C3×#709C2211yescharacteristic
9C2×C3×C5×C22⋊C4—21no—
10C2×C3×C42×C5C2212yes—
11C3×#4099—21no—
12C3×#4076C411yescharacteristic, complemented
13C3×#4076C411yescharacteristic, complemented
14C3×#4075—21no—
15C3×C4×C22⋊D5—21no—
16C3×C4×C22⋊D5—21no—
17C3×#4072C2211yescharacteristic
18C3×#4070C411yescharacteristic, complemented
19C3×#4070C411yescharacteristic, complemented
20C2×C3×#681—21no—
21C2×C3×#681—24no—
22C2×C3×#681C2212yes—
23C22×C3×#168—21no—
24C3×C5×#95—21no—
25C3×#3937—24no—
26C3×#1871—51nomaximal, Hall
27#66125C2×C311yescharacteristic
28C22×#681C2×C311yescharacteristic, complemented
29C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
30C2×#3937C2×C312yescomplemented
31#64743C2×C312yescomplemented
32C24×C3×C5D411yescharacteristic
33C22×C3×C4×C5—22no—
34C22×C3×C4×C5—22no—
35C22×C3×C4×C5—22no—
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5D411yescharacteristic
41C22×C3×C4×C5C2311yescharacteristic
42C2×C3×C22⋊D5—21no—
43C2×C3×C22⋊D5—21no—
44C2×C3×C22⋊D5—21no—
45C3×#709—22no—
46C3×#709—22no—
47C2×C3×D20C2×C411yescharacteristic
48C2×C3×C4×D5—21no—
49C2×C3×Dic10C2×C411yescharacteristic
50C3×C5×C22⋊C4—24no—
51C3×C42×C5—22no—
52C3×C42×C5—22no—
53C3×C22⋊Dic5—21no—
54C3×C22⋊Dic5—21no—
55C3×C22⋊Dic5—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×C4⋊Dic5C2×C411yescharacteristic
59C3×C4⋊Dic5C2×C411yescharacteristic
60C3×#683—21no—
61C3×#683—21no—
62C3×C4×Dic5—21no—
63C3×#681—24no—
64C3×#681—22no—
65C3×#681D414yescomplemented
66C2×C3×#168—24no—
67C2×C3×#168—22no—
68C22×C3×M16—51no—
69C3×#525—51no—
70C2×C3×#104—52no—
71C3×C4×C22⋊C4D511yescharacteristic, complemented
72C3×#339—52no—
73C23×C4×C5C22×C311yescharacteristic
74C2×#709C22×C311yescharacteristic
75C2×C5×C22⋊C4—21no—
76C2×C42×C5C22×C312yes—
77#4099—21no—
78#4076C3×C411yescharacteristic, complemented
79#4076C3×C411yescharacteristic, complemented
80#4075—21no—
81C4×C22⋊D5—21no—
82C4×C22⋊D5—21no—
83#4072C22×C311yescharacteristic
84#4070C3×C411yescharacteristic, complemented
85#4070C3×C411yescharacteristic, complemented
86C2×#681—21no—
87C2×#681—24no—
88C2×#681C22×C312yes—
89C22×#168—21no—
90C5×#95—21no—
91#3937—24no—
92#1871—51noSylow
93C23×C3×C5—22no—
94C23×C3×C5—22no—
95C23×C3×C5—41no—
96C23×C3×C5C22⋊C411yescharacteristic
97C23×C3×C5C22⋊C411yescharacteristic
98C23×C3×C5C2×D411yescharacteristic
99C22×C3×D5—21no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—22no—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—24no—
108C2×C3×C4×C5—42no—
109C2×C3×C4×C5—42no—
110C2×C3×C4×C5C22⋊C411yescharacteristic
111C2×C3×C4×C5C22⋊C411yescharacteristic
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×C3×C4×C5C2×D412yes—
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5#4112yes—
116C3×C22⋊D5—42no—
117C3×C22⋊D5—42no—
118C3×C22⋊D5—42no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5—21no—
121C2×C3×Dic5—21no—
122C3×D20—22no—
123C3×C4×D5—41no—
124C3×C4×D5—41no—
125C3×Dic10—22no—
126C3×#168—24no—
127C2×C3×#41—51no—
128C23×C3×C4C2×D511yescharacteristic
129C2×C3×M16—52no—
130C2×C3×M16—104no—
131C2×C3×M16—101no—
132C22×C3×C8—101no—
133C3×#123—101no—
134C3×C22⋊Q8—51no—
135C3×C22⋊Q8—51no—
136C3×#121—51no—
137C3×#121—51no—
138C3×#120—101no—
139C3×C4×D4—101no—
140C3×C4×D4—101no—
141C3×#117—51no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C42C2×D512yes—
144C3×#104—104no—
145C3×#95—21no—
146C24×C5C3×D411yescharacteristic
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5C2×C3×C411yescharacteristic
151C22×C4×C5C2×C3×C411yescharacteristic
152C22×C4×C5C3×D411yescharacteristic
153C22×C4×C5C3×D411yescharacteristic
154C22×C4×C5C3×D411yescharacteristic
155C22×C4×C5C23×C311yescharacteristic
156C2×C22⋊D5—21no—
157C2×C22⋊D5—21no—
158C2×C22⋊D5—21no—
159#709—22no—
160#709—22no—
161C2×D20C2×C3×C411yescharacteristic
162C2×C4×D5—21no—
163C2×Dic10C2×C3×C411yescharacteristic
164C5×C22⋊C4—24no—
165C42×C5—22no—
166C42×C5—22no—
167C22⋊Dic5—21no—
168C22⋊Dic5—21no—
169C22⋊Dic5—21no—
170#685—21no—
171#685—21no—
172C4⋊Dic5C2×C3×C411yescharacteristic
173C4⋊Dic5C2×C3×C411yescharacteristic
174#683—21no—
175#683—21no—
176C4×Dic5—21no—
177#681—24no—
178#681—22no—
179#681C3×D414yescomplemented
180C2×#168—24no—
181C2×#168—22no—
182C22×M16—51no—
183#525—51no—
184C2×#104—52no—
185C4×C22⋊C4C3×D511yescharacteristic, complemented
186#339—52no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—21no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5—44no—
195C22×C3×C5#10412yescomplemented
196C22×C3×C5C2×C22⋊C411yescharacteristic
197C22×C3×C5#12112yes—
198C2×C3×D5—41no—
199C2×C3×D5—41no—
200C2×C3×D5—41no—
201C3×C4×C5—21no—
202C3×C4×C5—21no—
203C3×C4×C5—44no—
204C3×C4×C5C4×D412yes—
205C3×C4×C5#12011yescharacteristic
206C3×C4×C5#12311yescharacteristic
207C3×Dic5—41no—
208C3×Dic5—41no—
209C3×Dic5—41no—
210C24×C3C22⋊D511yescharacteristic
211C3×#41—102no—
212C3×#41—102no—
213C2×C3×Q8—51no—
214C2×C3×D4—51no—
215C2×C3×D4—101no—
216C2×C3×D4—101no—
217C2×C3×D4—101no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—101no—
222C22×C3×C4C4×D511yescharacteristic
223C22×C3×C4C4×D511yescharacteristic
224C22×C3×C4D2011yescharacteristic
225C22×C3×C4D2011yescharacteristic
226C22×C3×C4C22⋊D511yescharacteristic
227C22×C3×C4C22×D511yescharacteristic
228C3×M16—54no—
229C3×M16—104no—
230C3×M16—102no—
231C2×C3×C8—104no—
232C2×C3×C8—102no—
233C3×C4⋊C4—51no—
234C3×C4⋊C4—51no—
235C3×C4⋊C4—101no—
236C3×C4⋊C4—101no—
237C3×C22⋊C4—24no—
238C3×C22⋊C4—101no—
239C3×C22⋊C4—101no—
240C3×C22⋊C4—101no—
241C3×C22⋊C4—101no—
242C3×C22⋊C4—101no—
243C3×C42—22no—
244C3×C42—22no—
245C3×C42—101no—
246C23×C5—22no—
247C23×C5—22no—
248C23×C5—41no—
249C23×C5C3×C22⋊C411yescharacteristic
250C23×C5C3×C22⋊C411yescharacteristic
251C23×C5C2×C3×D411yescharacteristic
252C22×D5—21no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—22no—
256C2×C4×C5—21no—
257C2×C4×C5—21no—
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5—24no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5C3×C22⋊C411yescharacteristic
264C2×C4×C5C3×C22⋊C411yescharacteristic
265C2×C4×C5C22×C3×C411yescharacteristic
266C2×C4×C5C2×C3×D411yescharacteristic
267C2×C4×C5C2×C3×D412yes—
268C2×C4×C5C3×#4112yes—
269C22⋊D5—42no—
270C22⋊D5—42no—
271C22⋊D5—42no—
272C2×Dic5—21no—
273C2×Dic5—21no—
274C2×Dic5—21no—
275D20—22no—
276C4×D5—41no—
277C4×D5—41no—
278Dic10—22no—
279#168—24no—
280C2×#41—51no—
281C23×C4C2×C3×D511yescharacteristic
282C2×M16—52no—
283C2×M16—104no—
284C2×M16—101no—
285C22×C8—101no—
286#123—101no—
287C22⋊Q8—51no—
288C22⋊Q8—51no—
289#121—51no—
290#121—51no—
291#120—101no—
292C4×D4—101no—
293C4×D4—101no—
294#117—51no—
295C2×C22⋊C4—21no—
296C2×C42C2×C3×D512yes—
297#104—104no—
298#95—21no—
299C2×C3×C5—22no—
300C2×C3×C5—22no—
301C2×C3×C5—41no—
302C2×C3×C5#38611yescharacteristic
303C2×C3×C5C2×#10411yescharacteristic
304C2×C3×C5#42111yescharacteristic
305C3×D5—81no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—41no—
309C23×C3—101no—
310C23×C3#68511yescharacteristic
311C23×C3#68511yescharacteristic
312C23×C3C2×C22⋊D511yescharacteristic
313C3×Q8—102no—
314C3×D4—102no—
315C3×D4—202no—
316C3×D4—202no—
317C3×D4—202no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—24no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—101no—
329C2×C3×C4—101no—
330C2×C3×C4—101no—
331C2×C3×C4—201no—
332C2×C3×C4—201no—
333C2×C3×C4#68511yescharacteristic
334C2×C3×C4#68511yescharacteristic
335C2×C3×C4C2×C4×D511yescharacteristic
336C2×C3×C4C2×D2011yescharacteristic
337C2×C3×C4D4×D512yes—
338C2×C3×C4#71112yes—
339C3×C8—104no—
340C22×C5—21no—
341C22×C5—21no—
342C22×C5—21no—
343C22×C5—21no—
344C22×C5—21no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—44no—
348C22×C5C3×#10412yescomplemented
349C22×C5C2×C3×C22⋊C411yescharacteristic
350C22×C5C3×#12112yes—
351C2×D5—41no—
352C2×D5—41no—
353C2×D5—41no—
354C4×C5—21no—
355C4×C5—21no—
356C4×C5—44no—
357C4×C5C3×C4×D412yes—
358C4×C5C3×#12011yescharacteristic
359C4×C5C3×#12311yescharacteristic
360Dic5—41no—
361Dic5—41no—
362Dic5—41no—
363C24C3×C22⋊D511yescharacteristic
364#41—102no—
365#41—102no—
366C2×Q8—51no—
367C2×D4—51no—
368C2×D4—101no—
369C2×D4—101no—
370C2×D4—101no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—101no—
375C22×C4C3×C4×D511yescharacteristic
376C22×C4C3×C4×D511yescharacteristic
377C22×C4C3×D2011yescharacteristic
378C22×C4C3×D2011yescharacteristic
379C22×C4C3×C22⋊D511yescharacteristic
380C22×C4C22×C3×D511yescharacteristic
381M16—54no—
382M16—104no—
383M16—102no—
384C2×C8—104no—
385C2×C8—102no—
386C4⋊C4—51no—
387C4⋊C4—51no—
388C4⋊C4—101no—
389C4⋊C4—101no—
390C22⋊C4—24no—
391C22⋊C4—101no—
392C22⋊C4—101no—
393C22⋊C4—101no—
394C22⋊C4—101no—
395C22⋊C4—101no—
396C42—22no—
397C42—22no—
398C42—101no—
399C3×C5#187111yescharacteristic, complemented, Hall
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—44no—
408C22×C3—201no—
409C22×C3—201no—
410C22×C3—201no—
411C22×C3#393712yescomplemented
412C22×C3C2×#68511yescharacteristic
413C22×C3#408512yes—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—44no—
417C3×C4—201no—
418C3×C4—201no—
419C3×C4—201no—
420C3×C4#402712yes—
421C3×C4#402811yescharacteristic
422C3×C4#403211yescharacteristic
423C2×C5—22no—
424C2×C5—22no—
425C2×C5—41no—
426C2×C5C3×#38611yescharacteristic
427C2×C5C2×C3×#10411yescharacteristic
428C2×C5C3×#42111yescharacteristic
429D5—81no—
430C23—22no—
431C23—22no—
432C23—41no—
433C23—101no—
434C23C3×#68511yescharacteristic
435C23C3×#68511yescharacteristic
436C23C2×C3×C22⋊D511yescharacteristic
437Q8—102no—
438D4—102no—
439D4—202no—
440D4—202no—
441D4—202no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—101no—
453C2×C4—101no—
454C2×C4—101no—
455C2×C4—201no—
456C2×C4—201no—
457C2×C4C3×#68511yescharacteristic
458C2×C4C3×#68511yescharacteristic
459C2×C4C2×C3×C4×D511yescharacteristic
460C2×C4C2×C3×D2011yescharacteristic
461C2×C4C3×D4×D512yes—
462C2×C4C3×#71112yes—
463C8—104no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—41no—
467C2×C3—401no—
468C2×C3C2×#393711yescharacteristic
469C2×C3#6524711yescharacteristic
470C2×C3#6529411yescharacteristic
471C5C3×#187111yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—44no—
480C22—201no—
481C22—201no—
482C22—201no—
483C22C3×#393712yescomplemented
484C22C2×C3×#68511yescharacteristic
485C22C3×#408512yes—
486C4—21no—
487C4—21no—
488C4—44no—
489C4—201no—
490C4—201no—
491C4—201no—
492C4C3×#402712yes—
493C4C3×#402811yescharacteristic
494C4C3×#403211yescharacteristic
495C3#1060024611yescharacteristic, direct product factor, Sylow
496C2—22no—
497C2—22no—
498C2—41no—
499C2—401no—
500C2C2×C3×#393711yescharacteristic
501C2C3×#6524711yescharacteristic
502C2C3×#6529411yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D20
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C4×C5×C22⋊C4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66125C2
cosocleC22×C4×C5C23×C3
hypercenterC3×C4×C22⋊C4D5
hypocenterC5C3×#1871
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#681C2semidirect
3. C3×C4×C5×C22⋊C4C2semidirect
4. C2×C3×#3937C2semidirect
5. C3×#64743C2semidirect
6. #10600246C3direct (N × H)
12. C3×#4076C4semidirect
13. C3×#4076C4semidirect
18. C3×#4070C4semidirect
19. C3×#4070C4semidirect
28. C22×#681C2×C3semidirect
29. C4×C5×C22⋊C4C2×C3semidirect
30. C2×#3937C2×C3semidirect
31. #64743C2×C3semidirect
65. C3×#681D4semidirect
71. C3×C4×C22⋊C4D5semidirect
78. #4076C3×C4semidirect
79. #4076C3×C4semidirect
84. #4070C3×C4semidirect
85. #4070C3×C4semidirect
179. #681C3×D4semidirect
185. C4×C22⋊C4C3×D5semidirect
195. C22×C3×C5#104semidirect
348. C22×C5C3×#104semidirect
399. C3×C5#1871semidirect
411. C22×C3#3937semidirect
471. C5C3×#1871semidirect
483. C22C3×#3937semidirect
495. C3#10600246direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661252
C22×C3×#6812
C3×C4×C5×C22⋊C42
C2×C3×#39372
C3×#647432
#106002463
C3×#18715