Finite Group Databasebeta

← C3×#10599936 #14313198

Subgroups — C3×#10599936 #14313198

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65987C211yesmaximal, characteristic
2C3×D5×#100C211yesmaximal, characteristic, complemented
3C3×D5×#99C211yesmaximal, characteristic, complemented
4C3×C5×#352C211yesmaximal, characteristic, complemented
5C3×#64759C211yesmaximal, characteristic, complemented
6C3×#64695C211yesmaximal, characteristic, complemented
7C3×#64691C211yesmaximal, characteristic, complemented
8#10599936C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×D4×D5C2211yescharacteristic
10C22×C3×D20C411yescharacteristic, complemented
11C3×C5×#123C2211yescharacteristic
12C3×#4083C2211yescharacteristic
13C3×#4075C411yescharacteristic, complemented
14C3×D5×M16—21no—
15C3×#4041—21no—
16C3×#4040—21no—
17C3×#4030—21no—
18C3×#4028—21no—
19C3×#4028C411yescharacteristic, complemented
20C3×D5×C22⋊C4—21no—
21C3×D5×C22⋊C4C411yescharacteristic, complemented
22C3×C5×#100C2211yescharacteristic
23C3×C5×#99C2211yescharacteristic
24C3×#3966C2211yescharacteristic
25C3×#3965C2211yescharacteristic
26C3×#3955—21no—
27C3×#3938—21no—
28C3×#2121—51nomaximal, Hall
29#65987C2×C311yescharacteristic
30D5×#100C2×C311yescharacteristic, complemented
31D5×#99C2×C311yescharacteristic, complemented
32C5×#352C2×C311yescharacteristic, complemented
33#64759C2×C311yescharacteristic, complemented
34#64695C2×C311yescharacteristic, complemented
35#64691C2×C311yescharacteristic, complemented
36C23×C3×D5C2×C411yescharacteristic
37C23×C3×D5C2×C411yescharacteristic, complemented
38C23×C3×D5D411yescharacteristic
39C2×C3×C5×D4C2311yescharacteristic
40C22×C3×C4×C5C2×C411yescharacteristic, complemented
41C2×C3×C22⋊D5—21no—
42C2×C3×C22⋊D5C2×C411yescharacteristic
43C2×C3×C22⋊D5D411yescharacteristic
44C3×D4×D5—41no—
45C3×D4×D5—41no—
46C2×C3×D20—21no—
47C2×C3×D20—21no—
48C2×C3×D20—21no—
49C2×C3×D20—41no—
50C2×C3×D20—41no—
51C2×C3×D20D411yescharacteristic
52C2×C3×C4×D5—21no—
53C2×C3×C4×D5—41no—
54C2×C3×C4×D5D411yescharacteristic
55C3×C5×M16—21no—
56C3×C5×C4⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
60C3×C22⋊Dic5—21no—
61C3×C22⋊Dic5C2×C411yescharacteristic, complemented
62C3×#685—21no—
63C3×#685—21no—
64C3×#685—21no—
65C3×#685—21no—
66C3×#685—41no—
67C3×#683—21no—
68C3×#681—21no—
69C3×#676—41no—
70C3×C8×D5—41no—
71C3×#534—51no—
72C2×C3×#100—51no—
73C2×C3×#99—51no—
74C3×#352—51no—
75C3×#352D511yescharacteristic, complemented
76C3×AΣL(1,𝔽16)—51no—
77C3×AΣL(1,𝔽16)—51no—
78C2×D4×D5C22×C311yescharacteristic
79C22×D20C3×C411yescharacteristic, complemented
80C5×#123C22×C311yescharacteristic
81#4083C22×C311yescharacteristic
82#4075C3×C411yescharacteristic, complemented
83D5×M16—21no—
84#4041—21no—
85#4040—21no—
86#4030—21no—
87#4028—21no—
88#4028C3×C411yescharacteristic, complemented
89D5×C22⋊C4—21no—
90D5×C22⋊C4C3×C411yescharacteristic, complemented
91C5×#100C22×C311yescharacteristic
92C5×#99C22×C311yescharacteristic
93#3966C22×C311yescharacteristic
94#3965C22×C311yescharacteristic
95#3955—21no—
96#3938—21no—
97#2121—51noSylow
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×C3×D5—21no—
101C22×C3×D5—21no—
102C22×C3×D5—21no—
103C22×C3×D5—21no—
104C22×C3×D5—21no—
105C22×C3×D5—41no—
106C22×C3×D5—81no—
107C22×C3×D5—81no—
108C22×C3×D5—81no—
109C22×C3×D5C22⋊C411yescharacteristic
110C22×C3×D5C22⋊C411yescharacteristic
111C22×C3×D5C22⋊C411yescharacteristic
112C3×C5×D4—41no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5C2×D411yescharacteristic
118C3×C22⋊D5—41no—
119C3×C22⋊D5—41no—
120C3×C22⋊D5—81no—
121C2×C3×Dic5—21no—
122C2×C3×Dic5—41no—
123C2×C3×Dic5C22⋊C411yescharacteristic
124C3×D20—41no—
125C3×D20—42no—
126C3×D20—41no—
127C3×D20—41no—
128C3×D20—81no—
129C3×C4×D5—21no—
130C3×C4×D5—21no—
131C3×C4×D5—81no—
132C3×C4×D5—82no—
133C3×C5×C8—41no—
134C3×#168—41no—
135C22×C3×D4—51no—
136C22×C3×D4—51no—
137C2×C3×M16—101no—
138C3×#123—51no—
139C3×#123—101no—
140C3×#123C2×D511yescharacteristic
141C3×#121—101no—
142C3×#121—101no—
143C3×#120—51no—
144C3×#120—51no—
145C3×#120—101no—
146C2×C3×C22⋊C4—51no—
147C2×C3×C22⋊C4—101no—
148C3×#100—51no—
149C3×#100—101no—
150C3×#100C2×D511yescharacteristic
151C3×#99—51no—
152C3×#99—101no—
153C3×#99C2×D511yescharacteristic
154C23×D5C2×C3×C411yescharacteristic
155C23×D5C2×C3×C411yescharacteristic, complemented
156C23×D5C3×D411yescharacteristic
157C2×C5×D4C23×C311yescharacteristic
158C22×C4×C5C2×C3×C411yescharacteristic, complemented
159C2×C22⋊D5—21no—
160C2×C22⋊D5C2×C3×C411yescharacteristic
161C2×C22⋊D5C3×D411yescharacteristic
162D4×D5—41no—
163D4×D5—41no—
164C2×D20—21no—
165C2×D20—21no—
166C2×D20—21no—
167C2×D20—41no—
168C2×D20—41no—
169C2×D20C3×D411yescharacteristic
170C2×C4×D5—21no—
171C2×C4×D5—41no—
172C2×C4×D5C3×D411yescharacteristic
173C5×M16—21no—
174C5×C4⋊C4—21no—
175C5×C22⋊C4—21no—
176C5×C22⋊C4—21no—
177C5×C22⋊C4C2×C3×C411yescharacteristic, complemented
178C22⋊Dic5—21no—
179C22⋊Dic5C2×C3×C411yescharacteristic, complemented
180#685—21no—
181#685—21no—
182#685—21no—
183#685—21no—
184#685—41no—
185#683—21no—
186#681—21no—
187#676—41no—
188C8×D5—41no—
189#534—51no—
190C2×#100—51no—
191C2×#99—51no—
192#352—51no—
193#352C3×D511yescharacteristic, complemented
194AΣL(1,𝔽16)—51no—
195AΣL(1,𝔽16)—51no—
196C22×C3×C5—21no—
197C22×C3×C5—21no—
198C22×C3×C5—41no—
199C22×C3×C5—41no—
200C22×C3×C5C2×C22⋊C411yescharacteristic
201C2×C3×D5—21no—
202C2×C3×D5—21no—
203C2×C3×D5—41no—
204C2×C3×D5—42no—
205C2×C3×D5—41no—
206C2×C3×D5—41no—
207C2×C3×D5—41no—
208C2×C3×D5—41no—
209C2×C3×D5—41no—
210C2×C3×D5—81no—
211C2×C3×D5—81no—
212C2×C3×D5—81no—
213C2×C3×D5—82no—
214C2×C3×D5#9911yescharacteristic
215C2×C3×D5#9911yescharacteristic
216C3×C4×C5—21no—
217C3×C4×C5—41no—
218C3×C4×C5—41no—
219C3×C4×C5—81no—
220C3×Dic5—21no—
221C3×Dic5—41no—
222C3×Dic5—81no—
223C24×C3—51no—
224C24×C3—51no—
225C24×C3—51no—
226C2×C3×D4—51no—
227C2×C3×D4—51no—
228C2×C3×D4—51no—
229C2×C3×D4—101no—
230C2×C3×D4—101no—
231C2×C3×D4—101no—
232C2×C3×D4—101no—
233C2×C3×D4—201no—
234C2×C3×D4—201no—
235C2×C3×D4—201no—
236C2×C3×D4—201no—
237C2×C3×D4C22×D511yescharacteristic
238C22×C3×C4—51no—
239C22×C3×C4—101no—
240C22×C3×C4—201no—
241C22×C3×C4C4×D511yescharacteristic, complemented
242C3×M16—21no—
243C3×M16—101no—
244C3×M16—201no—
245C2×C3×C8—201no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—101no—
248C3×C22⋊C4—21no—
249C3×C22⋊C4—21no—
250C3×C22⋊C4—51no—
251C3×C22⋊C4—101no—
252C3×C22⋊C4—101no—
253C3×C22⋊C4—101no—
254C3×C22⋊C4—101no—
255C3×C22⋊C4—101no—
256C3×C22⋊C4—201no—
257C3×C22⋊C4C4×D511yescharacteristic, complemented
258C23×C5C22×C3×C411yescharacteristic
259C23×C5C2×C3×D411yescharacteristic
260C22×D5—21no—
261C22×D5—21no—
262C22×D5—21no—
263C22×D5—21no—
264C22×D5—21no—
265C22×D5—41no—
266C22×D5—81no—
267C22×D5—81no—
268C22×D5—81no—
269C22×D5C3×C22⋊C411yescharacteristic
270C22×D5C3×C22⋊C411yescharacteristic
271C22×D5C3×C22⋊C411yescharacteristic
272C5×D4—41no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5C2×C3×D411yescharacteristic
278C22⋊D5—41no—
279C22⋊D5—41no—
280C22⋊D5—81no—
281C2×Dic5—21no—
282C2×Dic5—41no—
283C2×Dic5C3×C22⋊C411yescharacteristic
284D20—41no—
285D20—42no—
286D20—41no—
287D20—41no—
288D20—81no—
289C4×D5—21no—
290C4×D5—21no—
291C4×D5—81no—
292C4×D5—82no—
293C5×C8—41no—
294#168—41no—
295C22×D4—51no—
296C22×D4—51no—
297C2×M16—101no—
298#123—51no—
299#123—101no—
300#123C2×C3×D511yescharacteristic
301#121—101no—
302#121—101no—
303#120—51no—
304#120—51no—
305#120—101no—
306C2×C22⋊C4—51no—
307C2×C22⋊C4—101no—
308#100—51no—
309#100—101no—
310#100C2×C3×D511yescharacteristic
311#99—51no—
312#99—101no—
313#99C2×C3×D511yescharacteristic
314C2×C3×C5—21no—
315C2×C3×C5—41no—
316C2×C3×C5—41no—
317C2×C3×C5C2×#9911yescharacteristic
318C3×D5—21no—
319C3×D5—21no—
320C3×D5—41no—
321C3×D5—41no—
322C3×D5—81no—
323C23×C3—51no—
324C23×C3—51no—
325C23×C3—51no—
326C23×C3—101no—
327C23×C3—101no—
328C23×C3—101no—
329C23×C3—101no—
330C23×C3—101no—
331C23×C3—201no—
332C23×C3—401no—
333C23×C3—401no—
334C23×C3—401no—
335C23×C3C2×C4×D511yescharacteristic
336C23×C3D4×D511yescharacteristic
337C3×D4—41no—
338C3×D4—201no—
339C3×D4—201no—
340C3×D4—201no—
341C3×D4—202no—
342C3×D4—201no—
343C3×D4—201no—
344C3×D4—401no—
345C3×D4—401no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—51no—
351C2×C3×C4—101no—
352C2×C3×C4—101no—
353C2×C3×C4—101no—
354C2×C3×C4—201no—
355C2×C3×C4—401no—
356C2×C3×C4—402no—
357C2×C3×C4D4×D511yescharacteristic
358C3×C8—41no—
359C3×C8—201no—
360C22×C5—21no—
361C22×C5—21no—
362C22×C5—41no—
363C22×C5—41no—
364C22×C5C2×C3×C22⋊C411yescharacteristic
365C2×D5—21no—
366C2×D5—21no—
367C2×D5—41no—
368C2×D5—42no—
369C2×D5—41no—
370C2×D5—41no—
371C2×D5—41no—
372C2×D5—41no—
373C2×D5—41no—
374C2×D5—81no—
375C2×D5—81no—
376C2×D5—81no—
377C2×D5—82no—
378C2×D5C3×#9911yescharacteristic
379C2×D5C3×#9911yescharacteristic
380C4×C5—21no—
381C4×C5—41no—
382C4×C5—41no—
383C4×C5—81no—
384Dic5—21no—
385Dic5—41no—
386Dic5—81no—
387C24—51no—
388C24—51no—
389C24—51no—
390C2×D4—51no—
391C2×D4—51no—
392C2×D4—51no—
393C2×D4—101no—
394C2×D4—101no—
395C2×D4—101no—
396C2×D4—101no—
397C2×D4—201no—
398C2×D4—201no—
399C2×D4—201no—
400C2×D4—201no—
401C2×D4C22×C3×D511yescharacteristic
402C22×C4—51no—
403C22×C4—101no—
404C22×C4—201no—
405C22×C4C3×C4×D511yescharacteristic, complemented
406M16—21no—
407M16—101no—
408M16—201no—
409C2×C8—201no—
410C4⋊C4—21no—
411C4⋊C4—101no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—51no—
415C22⋊C4—101no—
416C22⋊C4—101no—
417C22⋊C4—101no—
418C22⋊C4—101no—
419C22⋊C4—101no—
420C22⋊C4—201no—
421C22⋊C4C3×C4×D511yescharacteristic, complemented
422C3×C5#212111yescharacteristic, complemented, Hall
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—51no—
428C22×C3—51no—
429C22×C3—101no—
430C22×C3—101no—
431C22×C3—201no—
432C22×C3—201no—
433C22×C3—201no—
434C22×C3—201no—
435C22×C3—201no—
436C22×C3—202no—
437C22×C3—201no—
438C22×C3—401no—
439C22×C3—401no—
440C22×C3—401no—
441C22×C3—402no—
442C22×C3D5×C22⋊C411yescharacteristic
443C3×C4—21no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—81no—
447C3×C4—101no—
448C3×C4—201no—
449C3×C4—401no—
450C2×C5—21no—
451C2×C5—41no—
452C2×C5—41no—
453C2×C5C2×C3×#9911yescharacteristic
454D5—21no—
455D5—21no—
456D5—41no—
457D5—41no—
458D5—81no—
459C23—51no—
460C23—51no—
461C23—51no—
462C23—101no—
463C23—101no—
464C23—101no—
465C23—101no—
466C23—101no—
467C23—201no—
468C23—401no—
469C23—401no—
470C23—401no—
471C23C2×C3×C4×D511yescharacteristic
472C23C3×D4×D511yescharacteristic
473D4—41no—
474D4—201no—
475D4—201no—
476D4—201no—
477D4—202no—
478D4—201no—
479D4—201no—
480D4—401no—
481D4—401no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—51no—
487C2×C4—101no—
488C2×C4—101no—
489C2×C4—101no—
490C2×C4—201no—
491C2×C4—401no—
492C2×C4—402no—
493C2×C4C3×D4×D511yescharacteristic
494C8—41no—
495C8—201no—
496C2×C3—21no—
497C2×C3—41no—
498C2×C3—41no—
499C2×C3—101no—
500C2×C3—101no—
501C2×C3—201no—
502C2×C3—201no—
503C2×C3—401no—
504C2×C3D5×#9911yescharacteristic
505C5C3×#212111yescharacteristic, complemented, Sylow
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—51no—
511C22—51no—
512C22—101no—
513C22—101no—
514C22—201no—
515C22—201no—
516C22—201no—
517C22—201no—
518C22—201no—
519C22—202no—
520C22—201no—
521C22—401no—
522C22—401no—
523C22—401no—
524C22—402no—
525C22C3×D5×C22⋊C411yescharacteristic
526C4—21no—
527C4—41no—
528C4—41no—
529C4—81no—
530C4—101no—
531C4—201no—
532C4—401no—
533C3#1059993611yescharacteristic, direct product factor, Sylow
534C2—21no—
535C2—41no—
536C2—41no—
537C2—101no—
538C2—101no—
539C2—201no—
540C2—201no—
541C2—401no—
542C2C3×D5×#9911yescharacteristic
subgroupG/H
centerC2×C3D5×#99
commutatorC23×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#352C2
socleC2×C3×C5C2×#99
prime radicalC3×#65987C2
cosocleC2×C5×D4C23×C3
hypercenterC3×#352D5
hypocenterC5C3×#2121
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#352

Complements

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

NH ≅ G/Ntype
2. C3×D5×#100C2semidirect
3. C3×D5×#99C2semidirect
4. C3×C5×#352C2semidirect
5. C3×#64759C2semidirect
6. C3×#64695C2semidirect
7. C3×#64691C2semidirect
8. #10599936C3direct (N × H)
10. C22×C3×D20C4semidirect
13. C3×#4075C4semidirect
19. C3×#4028C4semidirect
21. C3×D5×C22⋊C4C4semidirect
30. D5×#100C2×C3semidirect
31. D5×#99C2×C3semidirect
32. C5×#352C2×C3semidirect
33. #64759C2×C3semidirect
34. #64695C2×C3semidirect
35. #64691C2×C3semidirect
37. C23×C3×D5C2×C4semidirect
40. C22×C3×C4×C5C2×C4semidirect
59. C3×C5×C22⋊C4C2×C4semidirect
61. C3×C22⋊Dic5C2×C4semidirect
75. C3×#352D5semidirect
79. C22×D20C3×C4semidirect
82. #4075C3×C4semidirect
88. #4028C3×C4semidirect
90. D5×C22⋊C4C3×C4semidirect
155. C23×D5C2×C3×C4semidirect
158. C22×C4×C5C2×C3×C4semidirect
177. C5×C22⋊C4C2×C3×C4semidirect
179. C22⋊Dic5C2×C3×C4semidirect
193. #352C3×D5semidirect
241. C22×C3×C4C4×D5semidirect
257. C3×C22⋊C4C4×D5semidirect
405. C22×C4C3×C4×D5semidirect
421. C22⋊C4C3×C4×D5semidirect
422. C3×C5#2121semidirect
505. C5C3×#2121semidirect
533. C3#10599936direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659872
C3×D5×#1002
C3×D5×#992
C3×C5×#3522
C3×#647592
C3×#646952
C3×#646912
#105999363
C3×#21215