Finite Group Databasebeta

← C3×#10599094 #14282810

Subgroups — C3×#10599094 #14282810

Order 1920.

608 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65940C211yesmaximal, characteristic
2C3×D5×C22⋊C8C211yesmaximal, characteristic, complemented
3C3×#64955C211yesmaximal, characteristic, complemented
4C3×C5×#327C211yesmaximal, characteristic, complemented
5C3×#64757C211yesmaximal, characteristic, complemented
6C3×#64687C211yesmaximal, characteristic, complemented
7C3×#64672C211yesmaximal, characteristic, complemented
8#10599094C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#711C411yescharacteristic, complemented
10C22×C3×C4×D5C2211yescharacteristic
11C3×C5×#121C2211yescharacteristic
12C3×#4084C411yescharacteristic, complemented
13C3×#4083—21no—
14C3×D4×Dic5—21no—
15C2×C3×#685—21no—
16C3×#4070C2211yescharacteristic
17C2×C3×C4×Dic5—21no—
18C2×C3×C8×D5—21no—
19C3×#4043C411yescharacteristic, complemented
20C3×#4038C411yescharacteristic, complemented
21C3×#4029—21no—
22C3×#4027—21no—
23C3×C5×C22⋊C8C2211yescharacteristic
24C3×C5×#95C2211yescharacteristic
25C3×#3963C2211yescharacteristic
26C3×C22⋊#168C2211yescharacteristic
27C3×#3952—21no—
28C3×#1501—51nomaximal, Hall
29#65940C2×C311yescharacteristic
30D5×C22⋊C8C2×C311yescharacteristic, complemented
31#64955C2×C311yescharacteristic, complemented
32C5×#327C2×C311yescharacteristic, complemented
33#64757C2×C311yescharacteristic, complemented
34#64687C2×C311yescharacteristic, complemented
35#64672C2×C311yescharacteristic, complemented
36C23×C3×D5D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4C2×C411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5C2311yescharacteristic
41C2×C3×C22⋊D5—21no—
42C2×C3×C22⋊D5—21no—
43C22×C3×Dic5—21no—
44C22×C3×Dic5—21no—
45C22×C3×Dic5D411yescharacteristic
46C3×#711—42no—
47C2×C3×C4×D5—42no—
48C2×C3×C4×D5C2×C411yescharacteristic
49C2×C3×C4×D5C2×C411yescharacteristic
50C2×C3×C4×D5D411yescharacteristic
51C2×C3×C4×D5D411yescharacteristic
52C2×C3×Dic10C2×C411yescharacteristic
53C2×C3×C5×C8—21no—
54C3×C5×C4⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4—21no—
56C3×C22⋊Dic5—21no—
57C3×C22⋊Dic5—21no—
58C3×#685—24no—
59C3×#685—21no—
60C3×#685—21no—
61C3×C4⋊Dic5—21no—
62C3×C4⋊Dic5C2×C411yescharacteristic
63C3×#683—21no—
64C3×C4×Dic5—21no—
65C3×C4×Dic5—42no—
66C2×C3×#168—21no—
67C3×C8×D5—42no—
68C3×#525—51no—
69C2×C3×C22⋊C8—51no—
70C3×C4×C22⋊C4—51no—
71C3×#328—51no—
72C3×#328—51no—
73C3×#327—51no—
74C3×#327D511yescharacteristic, complemented
75C2×#711C3×C411yescharacteristic, complemented
76C22×C4×D5C22×C311yescharacteristic
77C5×#121C22×C311yescharacteristic
78#4084C3×C411yescharacteristic, complemented
79#4083—21no—
80D4×Dic5—21no—
81C2×#685—21no—
82#4070C22×C311yescharacteristic
83C2×C4×Dic5—21no—
84C2×C8×D5—21no—
85#4043C3×C411yescharacteristic, complemented
86#4038C3×C411yescharacteristic, complemented
87#4029—21no—
88#4027—21no—
89C5×C22⋊C8C22×C311yescharacteristic
90C5×#95C22×C311yescharacteristic
91#3963C22×C311yescharacteristic
92C22⋊#168C22×C311yescharacteristic
93#3952—21no—
94#1501—51noSylow
95C23×C3×C5—21no—
96C23×C3×C5C2×D411yescharacteristic
97C22×C3×D5—21no—
98C22×C3×D5—21no—
99C22×C3×D5—22no—
100C22×C3×D5—41no—
101C22×C3×D5C22⋊C411yescharacteristic
102C22×C3×D5C22⋊C411yescharacteristic
103C3×C5×D4—41no—
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C2×C3×C4×C5—22no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C3×C22⋊D5—42no—
114C3×C22⋊D5—42no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—22no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5—42no—
122C2×C3×Dic5C22⋊C411yescharacteristic
123C2×C3×Dic5C22⋊C411yescharacteristic
124C3×C4×D5—22no—
125C3×C4×D5—22no—
126C3×C4×D5—41no—
127C3×C4×D5—41no—
128C3×Dic10—41no—
129C3×C5×C8—41no—
130C3×#168—41no—
131C2×C3×#41—51no—
132C23×C3×C4—51no—
133C22×C3×C8—101no—
134C3×#123—101no—
135C3×C22⋊Q8—51no—
136C3×C22⋊Q8—51no—
137C3×#121—51no—
138C3×#121C2×D511yescharacteristic
139C3×#120—101no—
140C3×C4×D4—101no—
141C3×C4×D4—101no—
142C3×#117—51no—
143C2×C3×C22⋊C4—101no—
144C2×C3×C42—101no—
145C3×C22⋊C8—51no—
146C3×C22⋊C8—101no—
147C3×C22⋊C8C2×D511yescharacteristic
148C3×#95—51no—
149C3×#95C2×D511yescharacteristic
150C23×D5C3×D411yescharacteristic
151C2×C5×D4—21no—
152C2×C5×D4C2×C3×C411yescharacteristic
153C22×C4×C5—21no—
154C22×C4×C5C23×C311yescharacteristic
155C2×C22⋊D5—21no—
156C2×C22⋊D5—21no—
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5C3×D411yescharacteristic
160#711—42no—
161C2×C4×D5—42no—
162C2×C4×D5C2×C3×C411yescharacteristic
163C2×C4×D5C2×C3×C411yescharacteristic
164C2×C4×D5C3×D411yescharacteristic
165C2×C4×D5C3×D411yescharacteristic
166C2×Dic10C2×C3×C411yescharacteristic
167C2×C5×C8—21no—
168C5×C4⋊C4C2×C3×C411yescharacteristic
169C5×C22⋊C4—21no—
170C22⋊Dic5—21no—
171C22⋊Dic5—21no—
172#685—24no—
173#685—21no—
174#685—21no—
175C4⋊Dic5—21no—
176C4⋊Dic5C2×C3×C411yescharacteristic
177#683—21no—
178C4×Dic5—21no—
179C4×Dic5—42no—
180C2×#168—21no—
181C8×D5—42no—
182#525—51no—
183C2×C22⋊C8—51no—
184C4×C22⋊C4—51no—
185#328—51no—
186#328—51no—
187#327—51no—
188#327C3×D511yescharacteristic, complemented
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5—41no—
194C22×C3×C5C2×C22⋊C411yescharacteristic
195C22×C3×C5#13511yescharacteristic
196C22×C3×C5#13511yescharacteristic
197C2×C3×D5—21no—
198C2×C3×D5—21no—
199C2×C3×D5—21no—
200C2×C3×D5—21no—
201C2×C3×D5—21no—
202C2×C3×D5—42no—
203C2×C3×D5—42no—
204C2×C3×D5#10412yes—
205C3×C4×C5—21no—
206C3×C4×C5—21no—
207C3×C4×C5—42no—
208C3×C4×C5—41no—
209C3×Dic5—21no—
210C3×Dic5—42no—
211C3×Dic5—41no—
212C3×Dic5—41no—
213C3×Dic5#9912yes—
214C24×C3—51no—
215C3×#41—202no—
216C2×C3×Q8—51no—
217C2×C3×D4—21no—
218C2×C3×D4—101no—
219C2×C3×D4—101no—
220C2×C3×D4C4×D511yescharacteristic
221C22×C3×C4—21no—
222C22×C3×C4—51no—
223C22×C3×C4—51no—
224C22×C3×C4—51no—
225C22×C3×C4—51no—
226C22×C3×C4—51no—
227C22×C3×C4—101no—
228C22×C3×C4—101no—
229C22×C3×C4—202no—
230C22×C3×C4C22×D511yescharacteristic
231C2×C3×C8—21no—
232C2×C3×C8—101no—
233C2×C3×C8—202no—
234C3×C4⋊C4—51no—
235C3×C4⋊C4—101no—
236C3×C4⋊C4—101no—
237C3×C4⋊C4C4×D511yescharacteristic
238C3×C22⋊C4—21no—
239C3×C22⋊C4—101no—
240C3×C22⋊C4—101no—
241C3×C22⋊C4—104no—
242C3×C22⋊C4—101no—
243C3×C22⋊C4—101no—
244C3×C42—101no—
245C3×C42—202no—
246C23×C5—21no—
247C23×C5C2×C3×D411yescharacteristic
248C22×D5—21no—
249C22×D5—21no—
250C22×D5—22no—
251C22×D5—41no—
252C22×D5C3×C22⋊C411yescharacteristic
253C22×D5C3×C22⋊C411yescharacteristic
254C5×D4—41no—
255C5×D4—41no—
256C5×D4—41no—
257C2×C4×C5—22no—
258C2×C4×C5—21no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
262C2×C4×C5C22×C3×C411yescharacteristic
263C2×C4×C5C2×C3×D411yescharacteristic
264C22⋊D5—42no—
265C22⋊D5—42no—
266C2×Dic5—22no—
267C2×Dic5—22no—
268C2×Dic5—21no—
269C2×Dic5—21no—
270C2×Dic5—41no—
271C2×Dic5—41no—
272C2×Dic5—42no—
273C2×Dic5C3×C22⋊C411yescharacteristic
274C2×Dic5C3×C22⋊C411yescharacteristic
275C4×D5—22no—
276C4×D5—22no—
277C4×D5—41no—
278C4×D5—41no—
279Dic10—41no—
280C5×C8—41no—
281#168—41no—
282C2×#41—51no—
283C23×C4—51no—
284C22×C8—101no—
285#123—101no—
286C22⋊Q8—51no—
287C22⋊Q8—51no—
288#121—51no—
289#121C2×C3×D511yescharacteristic
290#120—101no—
291C4×D4—101no—
292C4×D4—101no—
293#117—51no—
294C2×C22⋊C4—101no—
295C2×C42—101no—
296C22⋊C8—51no—
297C22⋊C8—101no—
298C22⋊C8C2×C3×D511yescharacteristic
299#95—51no—
300#95C2×C3×D511yescharacteristic
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5—81no—
304C2×C3×C5C2×#9911yescharacteristic
305C2×C3×C5#41611yescharacteristic
306C2×C3×C5C2×#10411yescharacteristic
307C3×D5—22no—
308C3×D5—41no—
309C23×C3—21no—
310C23×C3—51no—
311C23×C3—51no—
312C23×C3—102no—
313C23×C3—101no—
314C23×C3—101no—
315C23×C3—201no—
316C23×C3D4×D511yescharacteristic
317C3×Q8—201no—
318C3×D4—41no—
319C3×D4—41no—
320C3×D4—41no—
321C3×D4—202no—
322C3×D4—202no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—51no—
329C2×C3×C4—51no—
330C2×C3×C4—102no—
331C2×C3×C4—102no—
332C2×C3×C4—102no—
333C2×C3×C4—102no—
334C2×C3×C4—101no—
335C2×C3×C4—101no—
336C2×C3×C4—201no—
337C2×C3×C4—201no—
338C2×C3×C4—202no—
339C2×C3×C4—201no—
340C2×C3×C4—201no—
341C2×C3×C4C2×C4×D511yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C3×C8—41no—
344C3×C8—201no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—41no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5C2×C3×C22⋊C411yescharacteristic
351C22×C5C3×#13511yescharacteristic
352C22×C5C3×#13511yescharacteristic
353C2×D5—21no—
354C2×D5—21no—
355C2×D5—21no—
356C2×D5—21no—
357C2×D5—21no—
358C2×D5—42no—
359C2×D5—42no—
360C2×D5C3×#10412yes—
361C4×C5—21no—
362C4×C5—21no—
363C4×C5—42no—
364C4×C5—41no—
365Dic5—21no—
366Dic5—42no—
367Dic5—41no—
368Dic5—41no—
369Dic5C3×#9912yes—
370C24—51no—
371#41—202no—
372C2×Q8—51no—
373C2×D4—21no—
374C2×D4—101no—
375C2×D4—101no—
376C2×D4C3×C4×D511yescharacteristic
377C22×C4—21no—
378C22×C4—51no—
379C22×C4—51no—
380C22×C4—51no—
381C22×C4—51no—
382C22×C4—51no—
383C22×C4—101no—
384C22×C4—101no—
385C22×C4—202no—
386C22×C4C22×C3×D511yescharacteristic
387C2×C8—21no—
388C2×C8—101no—
389C2×C8—202no—
390C4⋊C4—51no—
391C4⋊C4—101no—
392C4⋊C4—101no—
393C4⋊C4C3×C4×D511yescharacteristic
394C22⋊C4—21no—
395C22⋊C4—101no—
396C22⋊C4—101no—
397C22⋊C4—104no—
398C22⋊C4—101no—
399C22⋊C4—101no—
400C42—101no—
401C42—202no—
402C3×C5#150111yescharacteristic, complemented, Hall
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—52no—
409C22×C3—101no—
410C22×C3—101no—
411C22×C3—101no—
412C22×C3—101no—
413C22×C3—101no—
414C22×C3—202no—
415C22×C3—202no—
416C22×C3D5×C22⋊C411yescharacteristic
417C22×C3#405811yescharacteristic
418C22×C3#406211yescharacteristic
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—42no—
422C3×C4—41no—
423C3×C4—52no—
424C3×C4—101no—
425C3×C4—202no—
426C3×C4—201no—
427C3×C4—201no—
428C2×C5—21no—
429C2×C5—21no—
430C2×C5—81no—
431C2×C5C2×C3×#9911yescharacteristic
432C2×C5C3×#41611yescharacteristic
433C2×C5C2×C3×#10411yescharacteristic
434D5—22no—
435D5—41no—
436C23—21no—
437C23—51no—
438C23—51no—
439C23—102no—
440C23—101no—
441C23—101no—
442C23—201no—
443C23C3×D4×D511yescharacteristic
444Q8—201no—
445D4—41no—
446D4—41no—
447D4—41no—
448D4—202no—
449D4—202no—
450C2×C4—22no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—51no—
456C2×C4—51no—
457C2×C4—102no—
458C2×C4—102no—
459C2×C4—102no—
460C2×C4—102no—
461C2×C4—101no—
462C2×C4—101no—
463C2×C4—201no—
464C2×C4—201no—
465C2×C4—202no—
466C2×C4—201no—
467C2×C4—201no—
468C2×C4C2×C3×C4×D511yescharacteristic
469C2×C4C3×D4×D511yescharacteristic
470C8—41no—
471C8—201no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—81no—
475C2×C3—102no—
476C2×C3—201no—
477C2×C3D5×#9911yescharacteristic
478C2×C3#6506111yescharacteristic
479C2×C3D5×#10411yescharacteristic
480C5C3×#150111yescharacteristic, complemented, Sylow
481C22—21no—
482C22—21no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—52no—
487C22—101no—
488C22—101no—
489C22—101no—
490C22—101no—
491C22—101no—
492C22—202no—
493C22—202no—
494C22C3×D5×C22⋊C411yescharacteristic
495C22C3×#405811yescharacteristic
496C22C3×#406211yescharacteristic
497C4—21no—
498C4—21no—
499C4—42no—
500C4—41no—
501C4—52no—
502C4—101no—
503C4—202no—
504C4—201no—
505C4—201no—
506C3#1059909411yescharacteristic, direct product factor, Sylow
507C2—21no—
508C2—21no—
509C2—81no—
510C2—102no—
511C2—201no—
512C2C3×D5×#9911yescharacteristic
513C2C3×#6506111yescharacteristic
514C2C3×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×#65940C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#327D5
hypocenterC5C3×#1501
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×D5×C22⋊C8C2semidirect
3. C3×#64955C2semidirect
4. C3×C5×#327C2semidirect
5. C3×#64757C2semidirect
6. C3×#64687C2semidirect
7. C3×#64672C2semidirect
8. #10599094C3direct (N × H)
9. C2×C3×#711C4semidirect
12. C3×#4084C4semidirect
19. C3×#4043C4semidirect
20. C3×#4038C4semidirect
30. D5×C22⋊C8C2×C3semidirect
31. #64955C2×C3semidirect
32. C5×#327C2×C3semidirect
33. #64757C2×C3semidirect
34. #64687C2×C3semidirect
35. #64672C2×C3semidirect
74. C3×#327D5semidirect
75. C2×#711C3×C4semidirect
78. #4084C3×C4semidirect
85. #4043C3×C4semidirect
86. #4038C3×C4semidirect
188. #327C3×D5semidirect
402. C3×C5#1501semidirect
480. C5C3×#1501semidirect
506. C3#10599094direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659402
C3×D5×C22⋊C82
C3×#649552
C3×C5×#3272
C3×#647572
C3×#646872
C3×#646722
#105990943
C3×#15015