Finite Group Databasebeta

← C3×#10598915 #14281171

Subgroups — C3×#10598915 #14281171

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
1C2×C3×#4029C211yesmaximal, characteristic
2C3×#65015C211yesmaximal, characteristic, complemented
3C3×D5×C22⋊C8C211yesmaximal, characteristic, complemented
4C3×C5×#323C211yesmaximal, characteristic, complemented
5C3×#64745C211yesmaximal, characteristic, complemented
6C3×#64689C211yesmaximal, characteristic, complemented
7C3×#64689C211yesmaximal, characteristic, complemented
8#10598915C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C22⋊D5C411yescharacteristic
10C22×C3×C4×D5C2211yescharacteristic
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×C3×C22⋊Dic5C411yescharacteristic
13C2×C3×#685C411yescharacteristic
14C2×C3×C4⋊Dic5C411yescharacteristic
15C2×C3×#683C2211yescharacteristic
16C2×C3×#676—21no—
17C2×C3×C8×D5—21no—
18C3×#4029—21no—
19C3×#4029—21no—
20C3×#4029—21no—
21C3×#4029—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23C3×C5×C22⋊C8C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3952—21no—
27C3×#3952—21no—
28C3×#1468—51nomaximal, Hall
29C2×#4029C2×C311yescharacteristic
30#65015C2×C311yescharacteristic, complemented
31D5×C22⋊C8C2×C311yescharacteristic, complemented
32C5×#323C2×C311yescharacteristic, complemented
33#64745C2×C311yescharacteristic, complemented
34#64689C2×C311yescharacteristic, complemented
35#64689C2×C311yescharacteristic, complemented
36C24×C3×C5C2×C411yescharacteristic
37C23×C3×D5C2×C411yescharacteristic
38C22×C3×C4×C5C2×C411yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—21no—
42C2×C3×C22⋊D5—42no—
43C22×C3×Dic5C2×C411yescharacteristic
44C22×C3×Dic5C2×C411yescharacteristic
45C22×C3×Dic5C2×C411yescharacteristic
46C2×C3×C4×D5—42no—
47C2×C3×C4×D5D411yescharacteristic
48C2×C3×C4×D5D411yescharacteristic
49C2×C3×C4×D5D411yescharacteristic
50C2×C3×C4×D5D411yescharacteristic
51C2×C3×C5×C8—21no—
52C2×C3×C5×C8—21no—
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C22⋊Dic5—21no—
56C3×C22⋊Dic5—21no—
57C3×#685—21no—
58C3×#685—21no—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C3×#683—21no—
62C3×#683—21no—
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65C3×#676—42no—
66C3×C8×D5—42no—
67C2×C3×#123—51no—
68C3×#407—51no—
69C2×C3×C22⋊C8—51no—
70C3×#324—51no—
71C3×#324—51no—
72C3×#323—51no—
73C3×#323D511yescharacteristic, complemented
74C22×C22⋊D5C3×C411yescharacteristic
75C22×C4×D5C22×C311yescharacteristic
76C2×C5×C22⋊C4C22×C311yescharacteristic
77C2×C22⋊Dic5C3×C411yescharacteristic
78C2×#685C3×C411yescharacteristic
79C2×C4⋊Dic5C3×C411yescharacteristic
80C2×#683C22×C311yescharacteristic
81C2×#676—21no—
82C2×C8×D5—21no—
83#4029—21no—
84#4029—21no—
85#4029—21no—
86#4029—21no—
87C5×C22⋊C8C22×C311yescharacteristic
88C5×C22⋊C8C22×C311yescharacteristic
89C22⋊#168C22×C311yescharacteristic
90C22⋊#168C22×C311yescharacteristic
91#3952—21no—
92#3952—21no—
93#1468—51noSylow
94C23×C3×C5—21no—
95C23×C3×C5—21no—
96C23×C3×C5—21no—
97C23×C3×C5—41no—
98C23×C3×C5—41no—
99C23×C3×C5C22×C411yescharacteristic
100C22×C3×D5—21no—
101C22×C3×D5—21no—
102C22×C3×D5—22no—
103C22×C3×D5—41no—
104C22×C3×D5C22⋊C411yescharacteristic
105C22×C3×D5C22⋊C411yescharacteristic
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C3×C22⋊D5—42no—
112C3×C22⋊D5—42no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5C22⋊C411yescharacteristic
120C2×C3×Dic5C22⋊C411yescharacteristic
121C3×C4×D5—22no—
122C3×C4×D5—22no—
123C3×C4×D5—41no—
124C3×C4×D5—41no—
125C3×C5×C8—41no—
126C3×C5×C8—41no—
127C3×#168—41no—
128C3×#168—41no—
129C22×C3×D4—51no—
130C23×C3×C4—51no—
131C2×C3×M16—101no—
132C22×C3×C8—101no—
133C3×#123—101no—
134C3×#123—101no—
135C3×#123—101no—
136C3×#123—101no—
137C2×C3×C4⋊C4—51no—
138C2×C3×C4⋊C4—51no—
139C2×C3×C22⋊C4—51no—
140C2×C3×C22⋊C4—51no—
141C2×C3×C22⋊C4C2×D511yescharacteristic
142C3×C22⋊C8—51no—
143C3×C22⋊C8—51no—
144C3×C22⋊C8—101no—
145C3×C22⋊C8—101no—
146C3×C22⋊C8C2×D511yescharacteristic
147C3×C22⋊C8C2×D511yescharacteristic
148C24×C5C2×C3×C411yescharacteristic
149C23×D5C2×C3×C411yescharacteristic
150C22×C4×C5C2×C3×C411yescharacteristic
151C22×C4×C5C23×C311yescharacteristic
152C2×C22⋊D5—21no—
153C2×C22⋊D5—21no—
154C2×C22⋊D5—42no—
155C22×Dic5C2×C3×C411yescharacteristic
156C22×Dic5C2×C3×C411yescharacteristic
157C22×Dic5C2×C3×C411yescharacteristic
158C2×C4×D5—42no—
159C2×C4×D5C3×D411yescharacteristic
160C2×C4×D5C3×D411yescharacteristic
161C2×C4×D5C3×D411yescharacteristic
162C2×C4×D5C3×D411yescharacteristic
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C5×C22⋊C4—21no—
166C5×C22⋊C4—21no—
167C22⋊Dic5—21no—
168C22⋊Dic5—21no—
169#685—21no—
170#685—21no—
171C4⋊Dic5—21no—
172C4⋊Dic5—21no—
173#683—21no—
174#683—21no—
175C2×#168—21no—
176C2×#168—21no—
177#676—42no—
178C8×D5—42no—
179C2×#123—51no—
180#407—51no—
181C2×C22⋊C8—51no—
182#324—51no—
183#324—51no—
184#323—51no—
185#323C3×D511yescharacteristic, complemented
186C22×C3×C5—21no—
187C22×C3×C5—21no—
188C22×C3×C5—41no—
189C22×C3×C5—41no—
190C22×C3×C5—41no—
191C22×C3×C5—81no—
192C22×C3×C5—81no—
193C22×C3×C5C2×C22⋊C411yescharacteristic
194C22×C3×C5#13111yescharacteristic
195C22×C3×C5#13111yescharacteristic
196C2×C3×D5—21no—
197C2×C3×D5—21no—
198C2×C3×D5—21no—
199C2×C3×D5—21no—
200C2×C3×D5—21no—
201C2×C3×D5—42no—
202C2×C3×D5—42no—
203C2×C3×D5#9912yes—
204C3×C4×C5—21no—
205C3×C4×C5—21no—
206C3×C4×C5—41no—
207C3×Dic5—21no—
208C3×Dic5—21no—
209C3×Dic5—41no—
210C3×Dic5—41no—
211C24×C3—51no—
212C24×C3C4×D511yescharacteristic
213C2×C3×D4—101no—
214C2×C3×D4—101no—
215C2×C3×D4—202no—
216C22×C3×C4—51no—
217C22×C3×C4—51no—
218C22×C3×C4—51no—
219C22×C3×C4—51no—
220C22×C3×C4—51no—
221C22×C3×C4—51no—
222C22×C3×C4—51no—
223C22×C3×C4—202no—
224C22×C3×C4C4×D511yescharacteristic
225C22×C3×C4C22×D511yescharacteristic
226C3×M16—202no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—101no—
230C2×C3×C8—101no—
231C2×C3×C8—202no—
232C3×C4⋊C4—101no—
233C3×C4⋊C4—101no—
234C3×C4⋊C4—101no—
235C3×C4⋊C4—101no—
236C3×C22⋊C4—21no—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—101no—
239C3×C22⋊C4—101no—
240C3×C22⋊C4—101no—
241C3×C22⋊C4—101no—
242C23×C5—21no—
243C23×C5—21no—
244C23×C5—21no—
245C23×C5—41no—
246C23×C5—41no—
247C23×C5C22×C3×C411yescharacteristic
248C22×D5—21no—
249C22×D5—21no—
250C22×D5—22no—
251C22×D5—41no—
252C22×D5C3×C22⋊C411yescharacteristic
253C22×D5C3×C22⋊C411yescharacteristic
254C2×C4×C5—21no—
255C2×C4×C5—41no—
256C2×C4×C5—41no—
257C2×C4×C5C2×C3×D411yescharacteristic
258C2×C4×C5C2×C3×D411yescharacteristic
259C22⋊D5—42no—
260C22⋊D5—42no—
261C2×Dic5—21no—
262C2×Dic5—21no—
263C2×Dic5—21no—
264C2×Dic5—21no—
265C2×Dic5—41no—
266C2×Dic5—41no—
267C2×Dic5C3×C22⋊C411yescharacteristic
268C2×Dic5C3×C22⋊C411yescharacteristic
269C4×D5—22no—
270C4×D5—22no—
271C4×D5—41no—
272C4×D5—41no—
273C5×C8—41no—
274C5×C8—41no—
275#168—41no—
276#168—41no—
277C22×D4—51no—
278C23×C4—51no—
279C2×M16—101no—
280C22×C8—101no—
281#123—101no—
282#123—101no—
283#123—101no—
284#123—101no—
285C2×C4⋊C4—51no—
286C2×C4⋊C4—51no—
287C2×C22⋊C4—51no—
288C2×C22⋊C4—51no—
289C2×C22⋊C4C2×C3×D511yescharacteristic
290C22⋊C8—51no—
291C22⋊C8—51no—
292C22⋊C8—101no—
293C22⋊C8—101no—
294C22⋊C8C2×C3×D511yescharacteristic
295C22⋊C8C2×C3×D511yescharacteristic
296C2×C3×C5—21no—
297C2×C3×C5—21no—
298C2×C3×C5—81no—
299C2×C3×C5#40811yescharacteristic
300C2×C3×C5C2×#9911yescharacteristic
301C2×C3×C5#41311yescharacteristic
302C3×D5—22no—
303C3×D5—41no—
304C23×C3—21no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—51no—
310C23×C3—51no—
311C23×C3—102no—
312C23×C3—101no—
313C23×C3—101no—
314C23×C3—201no—
315C23×C3C2×C4×D511yescharacteristic
316C3×D4—202no—
317C3×D4—202no—
318C2×C3×C4—21no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—51no—
322C2×C3×C4—51no—
323C2×C3×C4—102no—
324C2×C3×C4—102no—
325C2×C3×C4—101no—
326C2×C3×C4—101no—
327C2×C3×C4—101no—
328C2×C3×C4—101no—
329C2×C3×C4—201no—
330C2×C3×C4—201no—
331C2×C3×C4—201no—
332C2×C3×C4—201no—
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C3×C8—41no—
336C3×C8—41no—
337C3×C8—201no—
338C3×C8—201no—
339C22×C5—21no—
340C22×C5—21no—
341C22×C5—41no—
342C22×C5—41no—
343C22×C5—41no—
344C22×C5—81no—
345C22×C5—81no—
346C22×C5C2×C3×C22⋊C411yescharacteristic
347C22×C5C3×#13111yescharacteristic
348C22×C5C3×#13111yescharacteristic
349C2×D5—21no—
350C2×D5—21no—
351C2×D5—21no—
352C2×D5—21no—
353C2×D5—21no—
354C2×D5—42no—
355C2×D5—42no—
356C2×D5C3×#9912yes—
357C4×C5—21no—
358C4×C5—21no—
359C4×C5—41no—
360Dic5—21no—
361Dic5—21no—
362Dic5—41no—
363Dic5—41no—
364C24—51no—
365C24C3×C4×D511yescharacteristic
366C2×D4—101no—
367C2×D4—101no—
368C2×D4—202no—
369C22×C4—51no—
370C22×C4—51no—
371C22×C4—51no—
372C22×C4—51no—
373C22×C4—51no—
374C22×C4—51no—
375C22×C4—51no—
376C22×C4—202no—
377C22×C4C3×C4×D511yescharacteristic
378C22×C4C22×C3×D511yescharacteristic
379M16—202no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—101no—
383C2×C8—101no—
384C2×C8—202no—
385C4⋊C4—101no—
386C4⋊C4—101no—
387C4⋊C4—101no—
388C4⋊C4—101no—
389C22⋊C4—21no—
390C22⋊C4—21no—
391C22⋊C4—101no—
392C22⋊C4—101no—
393C22⋊C4—101no—
394C22⋊C4—101no—
395C3×C5#146811yescharacteristic, complemented, Hall
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—52no—
402C22×C3—81no—
403C22×C3—81no—
404C22×C3—101no—
405C22×C3—101no—
406C22×C3—101no—
407C22×C3—101no—
408C22×C3—101no—
409C22×C3—202no—
410C22×C3—202no—
411C22×C3D5×C22⋊C411yescharacteristic
412C22×C3#404711yescharacteristic
413C22×C3#405311yescharacteristic
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—41no—
417C3×C4—101no—
418C3×C4—101no—
419C3×C4—201no—
420C3×C4—201no—
421C2×C5—21no—
422C2×C5—21no—
423C2×C5—81no—
424C2×C5C3×#40811yescharacteristic
425C2×C5C2×C3×#9911yescharacteristic
426C2×C5C3×#41311yescharacteristic
427D5—22no—
428D5—41no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—41no—
433C23—41no—
434C23—51no—
435C23—51no—
436C23—102no—
437C23—101no—
438C23—101no—
439C23—201no—
440C23C2×C3×C4×D511yescharacteristic
441D4—202no—
442D4—202no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—51no—
447C2×C4—51no—
448C2×C4—102no—
449C2×C4—102no—
450C2×C4—101no—
451C2×C4—101no—
452C2×C4—101no—
453C2×C4—101no—
454C2×C4—201no—
455C2×C4—201no—
456C2×C4—201no—
457C2×C4—201no—
458C2×C4C3×D4×D511yescharacteristic
459C2×C4C3×D4×D511yescharacteristic
460C8—41no—
461C8—41no—
462C8—201no—
463C8—201no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—81no—
467C2×C3—102no—
468C2×C3—201no—
469C2×C3#6501611yescharacteristic
470C2×C3D5×#9911yescharacteristic
471C2×C3#6503411yescharacteristic
472C5C3×#146811yescharacteristic, complemented, Sylow
473C22—21no—
474C22—21no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—52no—
479C22—81no—
480C22—81no—
481C22—101no—
482C22—101no—
483C22—101no—
484C22—101no—
485C22—101no—
486C22—202no—
487C22—202no—
488C22C3×D5×C22⋊C411yescharacteristic
489C22C3×#404711yescharacteristic
490C22C3×#405311yescharacteristic
491C4—21no—
492C4—21no—
493C4—41no—
494C4—101no—
495C4—101no—
496C4—201no—
497C4—201no—
498C3#1059891511yescharacteristic, direct product factor, Sylow
499C2—21no—
500C2—21no—
501C2—81no—
502C2—102no—
503C2—201no—
504C2C3×#6501611yescharacteristic
505C2C3×D5×#9911yescharacteristic
506C2C3×#6503411yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#323C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C22⋊D5C4
cosocleC22×C4×C5C23×C3
hypercenterC3×#323D5
hypocenterC5C3×#1468
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#323

Complements

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

NH ≅ G/Ntype
2. C3×#65015C2semidirect
3. C3×D5×C22⋊C8C2semidirect
4. C3×C5×#323C2semidirect
5. C3×#64745C2semidirect
6. C3×#64689C2semidirect
7. C3×#64689C2semidirect
8. #10598915C3direct (N × H)
30. #65015C2×C3semidirect
31. D5×C22⋊C8C2×C3semidirect
32. C5×#323C2×C3semidirect
33. #64745C2×C3semidirect
34. #64689C2×C3semidirect
35. #64689C2×C3semidirect
73. C3×#323D5semidirect
185. #323C3×D5semidirect
395. C3×C5#1468semidirect
472. C5C3×#1468semidirect
498. C3#10598915direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40292
C3×#650152
C3×D5×C22⋊C82
C3×C5×#3232
C3×#647452
C3×#646892
#105989153
C3×#14685