Finite Group Databasebeta

← C3×#10602640 #14313201

Subgroups — C3×#10602640 #14313201

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#534C211yesmaximal, characteristic
2C2×C3×#3966C211yesmaximal, characteristic, complemented
3C2×C3×#3965C211yesmaximal, characteristic, complemented
4C3×#64759C212yesmaximal, complemented
5C3×#64756C212yesmaximal, complemented
6#10602640C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4C411yescharacteristic, complemented
8C22×C3×C5×D4C2211yescharacteristic
9C3×C5×#123—21no—
10C3×C5×#123C411yescharacteristic, complemented
11C3×C5×#123C2211yescharacteristic
12C3×C5×#121—21no—
13C3×C5×#121—21no—
14C3×C5×#120—21no—
15C3×C5×#120C411yescharacteristic, complemented
16C3×C5×#120C2211yescharacteristic
17C2×C3×C5×C22⋊C4C411yescharacteristic, complemented
18C2×C3×C22⋊Dic5—21no—
19C2×C3×#681—21no—
20C3×#3966—21no—
21C3×#3966C2212yes—
22C3×#3965—21no—
23C3×#3965C2212yes—
24C3×#2121—51nomaximal, Hall
25C5×#534C2×C311yescharacteristic
26C2×#3966C2×C311yescharacteristic, complemented
27C2×#3965C2×C311yescharacteristic, complemented
28#64759C2×C312yescomplemented
29#64756C2×C312yescomplemented
30C24×C3×C5C2×C411yescharacteristic
31C24×C3×C5C2×C411yescharacteristic, complemented
32C24×C3×C5D411yescharacteristic
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—41no—
38C2×C3×C5×D4—41no—
39C2×C3×C5×D4—41no—
40C2×C3×C5×D4—41no—
41C2×C3×C5×D4C2×C411yescharacteristic
42C2×C3×C5×D4D411yescharacteristic
43C2×C3×C5×D4D411yescharacteristic
44C2×C3×C5×D4C2311yescharacteristic
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5C2×C411yescharacteristic, complemented
47C22×C3×C4×C5D411yescharacteristic
48C22×C3×Dic5—41no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C22⋊C4—21no—
52C3×C5×C22⋊C4—21no—
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
57C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
58C3×C22⋊Dic5—22no—
59C3×C22⋊Dic5—41no—
60C3×#681—22no—
61C3×#681—41no—
62C2×C3×#168—41no—
63C3×#534D511yescharacteristic
64C2×C3×#100—51no—
65C2×C3×#99—51no—
66C3×#352—52no—
67C3×AΣL(1,𝔽16)—52no—
68C22×C5×D4C3×C411yescharacteristic, complemented
69C22×C5×D4C22×C311yescharacteristic
70C5×#123—21no—
71C5×#123C3×C411yescharacteristic, complemented
72C5×#123C22×C311yescharacteristic
73C5×#121—21no—
74C5×#121—21no—
75C5×#120—21no—
76C5×#120C3×C411yescharacteristic, complemented
77C5×#120C22×C311yescharacteristic
78C2×C5×C22⋊C4C3×C411yescharacteristic, complemented
79C2×C22⋊Dic5—21no—
80C2×#681—21no—
81#3966—21no—
82#3966C22×C312yes—
83#3965—21no—
84#3965C22×C312yes—
85#2121—51noSylow
86C23×C3×C5—21no—
87C23×C3×C5—21no—
88C23×C3×C5—21no—
89C23×C3×C5—21no—
90C23×C3×C5—21no—
91C23×C3×C5—41no—
92C23×C3×C5—81no—
93C23×C3×C5—81no—
94C23×C3×C5—81no—
95C23×C3×C5C22⋊C411yescharacteristic
96C23×C3×C5C22⋊C411yescharacteristic
97C23×C3×C5C22⋊C411yescharacteristic
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C3×C5×D4—41no—
103C3×C5×D4—41no—
104C3×C5×D4—42no—
105C3×C5×D4—41no—
106C3×C5×D4—41no—
107C3×C5×D4—81no—
108C3×C5×D4—81no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—81no—
116C2×C3×C4×C5C22⋊C411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×Dic5—42no—
119C2×C3×Dic5—82no—
120C3×#168—42no—
121C22×C3×D4Dic511yescharacteristic, complemented
122C22×C3×D4C2×D511yescharacteristic
123C2×C3×M16—101no—
124C3×#123—21no—
125C3×#123Dic511yescharacteristic, complemented
126C3×#123C2×D511yescharacteristic
127C3×#121—21no—
128C3×#121—21no—
129C3×#120—21no—
130C3×#120Dic511yescharacteristic, complemented
131C3×#120C2×D511yescharacteristic
132C2×C3×C22⋊C4—101no—
133C2×C3×C22⋊C4Dic511yescharacteristic, complemented
134C3×#100—52no—
135C3×#100—101no—
136C3×#99—52no—
137C3×#99—101no—
138C24×C5C2×C3×C411yescharacteristic
139C24×C5C2×C3×C411yescharacteristic, complemented
140C24×C5C3×D411yescharacteristic
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—41no—
146C2×C5×D4—41no—
147C2×C5×D4—41no—
148C2×C5×D4—41no—
149C2×C5×D4C2×C3×C411yescharacteristic
150C2×C5×D4C3×D411yescharacteristic
151C2×C5×D4C3×D411yescharacteristic
152C2×C5×D4C23×C311yescharacteristic
153C22×C4×C5—21no—
154C22×C4×C5C2×C3×C411yescharacteristic, complemented
155C22×C4×C5C3×D411yescharacteristic
156C22×Dic5—41no—
157C5×C4⋊C4—21no—
158C5×C4⋊C4—21no—
159C5×C22⋊C4—21no—
160C5×C22⋊C4—21no—
161C5×C22⋊C4—21no—
162C5×C22⋊C4—21no—
163C5×C22⋊C4—21no—
164C5×C22⋊C4C2×C3×C411yescharacteristic, complemented
165C5×C22⋊C4C2×C3×C411yescharacteristic, complemented
166C22⋊Dic5—22no—
167C22⋊Dic5—41no—
168#681—22no—
169#681—41no—
170C2×#168—41no—
171#534C3×D511yescharacteristic
172C2×#100—51no—
173C2×#99—51no—
174#352—52no—
175AΣL(1,𝔽16)—52no—
176C22×C3×C5—21no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5—21no—
180C22×C3×C5—41no—
181C22×C3×C5—41no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—42no—
186C22×C3×C5—41no—
187C22×C3×C5—41no—
188C22×C3×C5—41no—
189C22×C3×C5—81no—
190C22×C3×C5—81no—
191C22×C3×C5—81no—
192C22×C3×C5—82no—
193C22×C3×C5#9911yescharacteristic
194C22×C3×C5#9911yescharacteristic
195C22×C3×C5C2×C22⋊C411yescharacteristic
196C3×C4×C5—21no—
197C3×C4×C5—21no—
198C3×C4×C5—41no—
199C3×C4×C5—41no—
200C3×C4×C5—41no—
201C3×Dic5—82no—
202C24×C3C2×Dic511yescharacteristic
203C24×C3C2×Dic511yescharacteristic, complemented
204C24×C3C22⋊D511yescharacteristic
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—41no—
210C2×C3×D4—41no—
211C2×C3×D4—41no—
212C2×C3×D4—41no—
213C2×C3×D4C2×Dic511yescharacteristic
214C2×C3×D4C22⋊D511yescharacteristic
215C2×C3×D4C22⋊D511yescharacteristic
216C2×C3×D4C22×D511yescharacteristic
217C22×C3×C4—21no—
218C22×C3×C4—201no—
219C22×C3×C4C2×Dic511yescharacteristic, complemented
220C22×C3×C4C22⋊D511yescharacteristic
221C3×M16—102no—
222C3×M16—201no—
223C2×C3×C8—201no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C22⋊C4—21no—
227C3×C22⋊C4—21no—
228C3×C22⋊C4—21no—
229C3×C22⋊C4—21no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—102no—
232C3×C22⋊C4—201no—
233C3×C22⋊C4C2×Dic511yescharacteristic, complemented
234C3×C22⋊C4C2×Dic511yescharacteristic, complemented
235C23×C5—21no—
236C23×C5—21no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—21no—
240C23×C5—41no—
241C23×C5—81no—
242C23×C5—81no—
243C23×C5—81no—
244C23×C5C3×C22⋊C411yescharacteristic
245C23×C5C3×C22⋊C411yescharacteristic
246C23×C5C3×C22⋊C411yescharacteristic
247C23×C5C22×C3×C411yescharacteristic
248C23×C5C2×C3×D411yescharacteristic
249C5×D4—41no—
250C5×D4—41no—
251C5×D4—41no—
252C5×D4—41no—
253C5×D4—42no—
254C5×D4—41no—
255C5×D4—41no—
256C5×D4—81no—
257C5×D4—81no—
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—41no—
264C2×C4×C5—81no—
265C2×C4×C5C3×C22⋊C411yescharacteristic
266C2×C4×C5C2×C3×D411yescharacteristic
267C2×Dic5—42no—
268C2×Dic5—82no—
269#168—42no—
270C22×D4C3×Dic511yescharacteristic, complemented
271C22×D4C2×C3×D511yescharacteristic
272C2×M16—101no—
273#123—21no—
274#123C3×Dic511yescharacteristic, complemented
275#123C2×C3×D511yescharacteristic
276#121—21no—
277#121—21no—
278#120—21no—
279#120C3×Dic511yescharacteristic, complemented
280#120C2×C3×D511yescharacteristic
281C2×C22⋊C4—101no—
282C2×C22⋊C4C3×Dic511yescharacteristic, complemented
283#100—52no—
284#100—101no—
285#99—52no—
286#99—101no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5—41no—
291C2×C3×C5—41no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5—81no—
295C2×C3×C5C2×#9911yescharacteristic
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—41no—
302C23×C3—81no—
303C23×C3—81no—
304C23×C3—81no—
305C23×C3C22⋊Dic511yescharacteristic
306C23×C3C22⋊Dic511yescharacteristic
307C23×C3C22⋊Dic511yescharacteristic
308C23×C3C22×Dic511yescharacteristic
309C23×C3C2×C22⋊D511yescharacteristic
310C3×D4—41no—
311C3×D4—41no—
312C3×D4—41no—
313C3×D4—41no—
314C3×D4—42no—
315C3×D4—41no—
316C3×D4—41no—
317C3×D4—81no—
318C3×D4—81no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—41no—
325C2×C3×C4—81no—
326C2×C3×C4—202no—
327C2×C3×C4—402no—
328C2×C3×C4C22⋊Dic511yescharacteristic
329C2×C3×C4C2×C22⋊D511yescharacteristic
330C3×C8—202no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—21no—
334C22×C5—21no—
335C22×C5—41no—
336C22×C5—41no—
337C22×C5—41no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—42no—
341C22×C5—41no—
342C22×C5—41no—
343C22×C5—41no—
344C22×C5—81no—
345C22×C5—81no—
346C22×C5—81no—
347C22×C5—82no—
348C22×C5C3×#9911yescharacteristic
349C22×C5C3×#9911yescharacteristic
350C22×C5C2×C3×C22⋊C411yescharacteristic
351C4×C5—21no—
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—41no—
355C4×C5—41no—
356Dic5—82no—
357C24C2×C3×Dic511yescharacteristic
358C24C2×C3×Dic511yescharacteristic, complemented
359C24C3×C22⋊D511yescharacteristic
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4C2×C3×Dic511yescharacteristic
369C2×D4C3×C22⋊D511yescharacteristic
370C2×D4C3×C22⋊D511yescharacteristic
371C2×D4C22×C3×D511yescharacteristic
372C22×C4—21no—
373C22×C4—201no—
374C22×C4C2×C3×Dic511yescharacteristic, complemented
375C22×C4C3×C22⋊D511yescharacteristic
376M16—102no—
377M16—201no—
378C2×C8—201no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C22⋊C4—21no—
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—102no—
387C22⋊C4—201no—
388C22⋊C4C2×C3×Dic511yescharacteristic, complemented
389C22⋊C4C2×C3×Dic511yescharacteristic, complemented
390C3×C5#212111yescharacteristic, complemented, Hall
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—42no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—81no—
405C22×C3—81no—
406C22×C3—81no—
407C22×C3—82no—
408C22×C3#396611yescharacteristic
409C22×C3#396611yescharacteristic
410C22×C3C2×C22⋊Dic511yescharacteristic
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—41no—
414C3×C4—41no—
415C3×C4—41no—
416C3×C4—402no—
417C2×C5—21no—
418C2×C5—21no—
419C2×C5—21no—
420C2×C5—41no—
421C2×C5—41no—
422C2×C5—41no—
423C2×C5—41no—
424C2×C5—81no—
425C2×C5C2×C3×#9911yescharacteristic
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—41no—
432C23—81no—
433C23—81no—
434C23—81no—
435C23C3×C22⋊Dic511yescharacteristic
436C23C3×C22⋊Dic511yescharacteristic
437C23C3×C22⋊Dic511yescharacteristic
438C23C22×C3×Dic511yescharacteristic
439C23C2×C3×C22⋊D511yescharacteristic
440D4—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444D4—42no—
445D4—41no—
446D4—41no—
447D4—81no—
448D4—81no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—81no—
456C2×C4—202no—
457C2×C4—402no—
458C2×C4C3×C22⋊Dic511yescharacteristic
459C2×C4C2×C3×C22⋊D511yescharacteristic
460C8—202no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—41no—
465C2×C3—41no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3—81no—
469C2×C3C2×#396611yescharacteristic
470C5C3×#212111yescharacteristic, complemented, Sylow
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—42no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—82no—
488C22C3×#396611yescharacteristic
489C22C3×#396611yescharacteristic
490C22C2×C3×C22⋊Dic511yescharacteristic
491C4—21no—
492C4—21no—
493C4—41no—
494C4—41no—
495C4—41no—
496C4—402no—
497C3#1060264011yescharacteristic, direct product factor, Sylow
498C2—21no—
499C2—21no—
500C2—21no—
501C2—41no—
502C2—41no—
503C2—41no—
504C2—41no—
505C2—81no—
506C2C2×C3×#396611yescharacteristic
subgroupG/H
centerC2×C3C2×#3966
commutatorC23×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
Fitting, prime radicalC3×C5×#534C2
socleC2×C3×C5C2×#99
cosocleC2×C5×D4C23×C3
hypercenterC3×#534D5
hypocenterC5C3×#2121
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C22×C3×D4 ◁ C3×#534

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3966C2semidirect
3. C2×C3×#3965C2semidirect
4. C3×#64759C2semidirect
5. C3×#64756C2semidirect
6. #10602640C3direct (N × H)
7. C22×C3×C5×D4C4semidirect
10. C3×C5×#123C4semidirect
15. C3×C5×#120C4semidirect
17. C2×C3×C5×C22⋊C4C4semidirect
26. C2×#3966C2×C3semidirect
27. C2×#3965C2×C3semidirect
28. #64759C2×C3semidirect
29. #64756C2×C3semidirect
31. C24×C3×C5C2×C4semidirect
46. C22×C3×C4×C5C2×C4semidirect
56. C3×C5×C22⋊C4C2×C4semidirect
57. C3×C5×C22⋊C4C2×C4semidirect
68. C22×C5×D4C3×C4semidirect
71. C5×#123C3×C4semidirect
76. C5×#120C3×C4semidirect
78. C2×C5×C22⋊C4C3×C4semidirect
121. C22×C3×D4Dic5semidirect
125. C3×#123Dic5semidirect
130. C3×#120Dic5semidirect
133. C2×C3×C22⋊C4Dic5semidirect
139. C24×C5C2×C3×C4semidirect
154. C22×C4×C5C2×C3×C4semidirect
164. C5×C22⋊C4C2×C3×C4semidirect
165. C5×C22⋊C4C2×C3×C4semidirect
203. C24×C3C2×Dic5semidirect
219. C22×C3×C4C2×Dic5semidirect
233. C3×C22⋊C4C2×Dic5semidirect
234. C3×C22⋊C4C2×Dic5semidirect
270. C22×D4C3×Dic5semidirect
274. #123C3×Dic5semidirect
279. #120C3×Dic5semidirect
282. C2×C22⋊C4C3×Dic5semidirect
358. C24C2×C3×Dic5semidirect
374. C22×C4C2×C3×Dic5semidirect
388. C22⋊C4C2×C3×Dic5semidirect
389. C22⋊C4C2×C3×Dic5semidirect
390. C3×C5#2121semidirect
470. C5C3×#2121semidirect
497. C3#10602640direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5342
C2×C3×#39662
C2×C3×#39652
C3×#647592
C3×#647562
#106026403
C3×#21215