Finite Group Databasebeta

← C3×#10601773 #14287997

Subgroups — C3×#10601773 #14287997

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65968C211yesmaximal, characteristic
2C3×C5×#451C211yesmaximal, characteristic, complemented
3C3×#65520C211yesmaximal, characteristic
4C3×#65517C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6C3×#64688C211yesmaximal, characteristic
7C3×#64687C211yesmaximal, characteristic, complemented
8#10601773C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×C3×C5×Q16—21no—
11C3×C5×C22⋊Q8C2211yescharacteristic
12C3×#4092—21no—
13C2×C3×#689—21no—
14C2×C3×#685—21no—
15C2×C3×#685C2211yescharacteristic
16C3×#4070C2211yescharacteristic
17C3×#4043—21no—
18C3×#4042—21no—
19C3×#4042—21no—
20C3×D5×C22⋊C4—21no—
21C3×#4024—21no—
22C3×C5×#103—21no—
23C3×C5×C22⋊C8C2211yescharacteristic
24C3×#3967—21no—
25C3×#3963—21no—
26C3×#3963C2211yescharacteristic
27C3×C22⋊#168C2211yescharacteristic
28C3×#1602—51nomaximal, Hall
29#65968C2×C311yescharacteristic
30C5×#451C2×C311yescharacteristic, complemented
31#65520C2×C311yescharacteristic
32#65517C2×C311yescharacteristic, complemented
33#64758C2×C311yescharacteristic, complemented
34#64688C2×C311yescharacteristic
35#64687C2×C311yescharacteristic, complemented
36C23×C3×D5D411yescharacteristic
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8—42no—
40C2×C3×C5×Q8D411yescharacteristic
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C22×C3×Dic5—21no—
44C22×C3×Dic5D411yescharacteristic
45C2×C3×C4×D5—21no—
46C2×C3×C4×D5—21no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10D411yescharacteristic
49C3×C5×Q16—42no—
50C2×C3×C5×C8—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C22⋊C4—21no—
54C3×C22⋊Dic5—21no—
55C3×#689—42no—
56C3×#685—21no—
57C3×#685—21no—
58C3×#685—21no—
59C3×#685—21no—
60C3×#685—42no—
61C3×C4⋊Dic5—21no—
62C3×C4⋊Dic5D411yescharacteristic
63C3×#683—21no—
64C3×#683—21no—
65C3×#683—21no—
66C2×C3×#168—21no—
67C3×#543—51no—
68C3×#451—51no—
69C3×#451D511yescharacteristic, complemented
70C3×#393—51no—
71C3×#328—51no—
72C3×#328—51no—
73C3×#323—51no—
74C22×C5×Q8C22×C311yescharacteristic
75C2×C5×Q16—21no—
76C5×C22⋊Q8C22×C311yescharacteristic
77#4092—21no—
78C2×#689—21no—
79C2×#685—21no—
80C2×#685C22×C311yescharacteristic
81#4070C22×C311yescharacteristic
82#4043—21no—
83#4042—21no—
84#4042—21no—
85D5×C22⋊C4—21no—
86#4024—21no—
87C5×#103—21no—
88C5×C22⋊C8C22×C311yescharacteristic
89#3967—21no—
90#3963—21no—
91#3963C22×C311yescharacteristic
92C22⋊#168C22×C311yescharacteristic
93#1602—51noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—21no—
96C22×C3×D5—21no—
97C22×C3×D5—41no—
98C22×C3×D5—41no—
99C22×C3×D5Q1612yescomplemented
100C3×C5×Q8—22no—
101C3×C5×Q8—22no—
102C3×C5×Q8—41no—
103C3×C5×Q8—41no—
104C3×C5×Q8—41no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5—41no—
120C3×C4×D5—81no—
121C3×C4×D5—81no—
122C3×Dic10—41no—
123C3×Dic10—81no—
124C3×C5×C8—41no—
125C3×#168—41no—
126C22×C3×Q8C2×D511yescharacteristic
127C2×C3×Q16—21no—
128C2×C3×Q16—101no—
129C3×C22⋊Q8—51no—
130C3×C22⋊Q8—101no—
131C3×C22⋊Q8—101no—
132C3×C22⋊Q8—101no—
133C3×C22⋊Q8—101no—
134C3×C22⋊Q8—101no—
135C3×C22⋊Q8C2×D511yescharacteristic
136C2×C3×C22⋊C4—51no—
137C2×C3×C22⋊C4—101no—
138C2×C3×C22⋊C4—101no—
139C3×#103—21no—
140C3×#103—101no—
141C3×C22⋊C8—51no—
142C3×C22⋊C8C2×D511yescharacteristic
143C3×#95—51no—
144C3×#95—101no—
145C23×D5C3×D411yescharacteristic
146C2×C5×Q8—21no—
147C2×C5×Q8—21no—
148C2×C5×Q8—42no—
149C2×C5×Q8C3×D411yescharacteristic
150C22×C4×C5—21no—
151C22×C4×C5C23×C311yescharacteristic
152C22×Dic5—21no—
153C22×Dic5C3×D411yescharacteristic
154C2×C4×D5—21no—
155C2×C4×D5—21no—
156C2×Dic10—21no—
157C2×Dic10C3×D411yescharacteristic
158C5×Q16—42no—
159C2×C5×C8—21no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4C3×D411yescharacteristic
162C5×C22⋊C4—21no—
163C22⋊Dic5—21no—
164#689—42no—
165#685—21no—
166#685—21no—
167#685—21no—
168#685—21no—
169#685—42no—
170C4⋊Dic5—21no—
171C4⋊Dic5C3×D411yescharacteristic
172#683—21no—
173#683—21no—
174#683—21no—
175C2×#168—21no—
176#543—51no—
177#451—51no—
178#451C3×D511yescharacteristic, complemented
179#393—51no—
180#328—51no—
181#328—51no—
182#323—51no—
183C22×C3×C5—21no—
184C22×C3×C5—21no—
185C22×C3×C5#12011yescharacteristic
186C22×C3×C5C2×Q1611yescharacteristic
187C22×C3×C5#13711yescharacteristic
188C2×C3×D5—22no—
189C2×C3×D5—41no—
190C2×C3×D5—41no—
191C2×C3×D5—42no—
192C2×C3×D5—81no—
193C3×C4×C5—21no—
194C3×C4×C5—21no—
195C3×C4×C5—41no—
196C3×C4×C5—41no—
197C3×C4×C5—42no—
198C3×Dic5—41no—
199C3×Dic5—41no—
200C3×Dic5—41no—
201C3×Dic5—81no—
202C24×C3—51no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—42no—
206C2×C3×Q8—51no—
207C2×C3×Q8—101no—
208C2×C3×Q8C22⋊D511yescharacteristic
209C22×C3×C4—21no—
210C22×C3×C4—51no—
211C22×C3×C4—101no—
212C22×C3×C4—101no—
213C22×C3×C4—101no—
214C22×C3×C4C22×D511yescharacteristic
215C3×Q16—42no—
216C3×Q16—202no—
217C2×C3×C8—21no—
218C2×C3×C8—101no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—51no—
221C3×C4⋊C4—101no—
222C3×C4⋊C4—101no—
223C3×C4⋊C4—101no—
224C3×C4⋊C4—101no—
225C3×C4⋊C4C22⋊D511yescharacteristic
226C3×C22⋊C4—21no—
227C3×C22⋊C4—101no—
228C3×C22⋊C4—101no—
229C3×C22⋊C4—101no—
230C3×C22⋊C4—101no—
231C3×C22⋊C4—101no—
232C3×C22⋊C4—202no—
233C23×C5C2×C3×D411yescharacteristic
234C22×D5—21no—
235C22×D5—21no—
236C22×D5—41no—
237C22×D5—41no—
238C22×D5C3×Q1612yescomplemented
239C5×Q8—22no—
240C5×Q8—22no—
241C5×Q8—41no—
242C5×Q8—41no—
243C5×Q8—41no—
244C2×C4×C5—22no—
245C2×C4×C5—21no—
246C2×C4×C5—21no—
247C2×C4×C5—41no—
248C2×C4×C5—41no—
249C2×C4×C5—41no—
250C2×C4×C5C2×C3×D411yescharacteristic
251C2×C4×C5C2×C3×D411yescharacteristic
252C2×Dic5—21no—
253C2×Dic5—21no—
254C2×Dic5—21no—
255C2×Dic5—41no—
256C2×Dic5—41no—
257C2×Dic5—41no—
258C2×Dic5—41no—
259C4×D5—81no—
260C4×D5—81no—
261Dic10—41no—
262Dic10—81no—
263C5×C8—41no—
264#168—41no—
265C22×Q8C2×C3×D511yescharacteristic
266C2×Q16—21no—
267C2×Q16—101no—
268C22⋊Q8—51no—
269C22⋊Q8—101no—
270C22⋊Q8—101no—
271C22⋊Q8—101no—
272C22⋊Q8—101no—
273C22⋊Q8—101no—
274C22⋊Q8C2×C3×D511yescharacteristic
275C2×C22⋊C4—51no—
276C2×C22⋊C4—101no—
277C2×C22⋊C4—101no—
278#103—21no—
279#103—101no—
280C22⋊C8—51no—
281C22⋊C8C2×C3×D511yescharacteristic
282#95—51no—
283#95—101no—
284C2×C3×C5—21no—
285C2×C3×C5—21no—
286C2×C3×C5#45111yescharacteristic
287C2×C3×C5#45511yescharacteristic
288C2×C3×C5B(4,𝔽2)11yescharacteristic
289C3×D5—42no—
290C23×C3—52no—
291C23×C3—101no—
292C23×C3—101no—
293C23×C3—201no—
294C23×C3—201no—
295C23×C3D4×D511yescharacteristic
296C3×Q8—22no—
297C3×Q8—22no—
298C3×Q8—41no—
299C3×Q8—41no—
300C3×Q8—41no—
301C3×Q8—201no—
302C3×Q8—401no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—101no—
310C2×C3×C4—101no—
311C2×C3×C4—101no—
312C2×C3×C4—201no—
313C2×C3×C4—201no—
314C2×C3×C4—201no—
315C2×C3×C4—201no—
316C2×C3×C4—401no—
317C2×C3×C4—401no—
318C2×C3×C4D4×D511yescharacteristic
319C2×C3×C4C2×C22⋊D511yescharacteristic
320C3×C8—41no—
321C3×C8—201no—
322C22×C5—21no—
323C22×C5—21no—
324C22×C5C3×#12011yescharacteristic
325C22×C5C2×C3×Q1611yescharacteristic
326C22×C5C3×#13711yescharacteristic
327C2×D5—22no—
328C2×D5—41no—
329C2×D5—41no—
330C2×D5—42no—
331C2×D5—81no—
332C4×C5—21no—
333C4×C5—21no—
334C4×C5—41no—
335C4×C5—41no—
336C4×C5—42no—
337Dic5—41no—
338Dic5—41no—
339Dic5—41no—
340Dic5—81no—
341C24—51no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—42no—
345C2×Q8—51no—
346C2×Q8—101no—
347C2×Q8C3×C22⋊D511yescharacteristic
348C22×C4—21no—
349C22×C4—51no—
350C22×C4—101no—
351C22×C4—101no—
352C22×C4—101no—
353C22×C4C22×C3×D511yescharacteristic
354Q16—42no—
355Q16—202no—
356C2×C8—21no—
357C2×C8—101no—
358C4⋊C4—21no—
359C4⋊C4—51no—
360C4⋊C4—101no—
361C4⋊C4—101no—
362C4⋊C4—101no—
363C4⋊C4—101no—
364C4⋊C4C3×C22⋊D511yescharacteristic
365C22⋊C4—21no—
366C22⋊C4—101no—
367C22⋊C4—101no—
368C22⋊C4—101no—
369C22⋊C4—101no—
370C22⋊C4—101no—
371C22⋊C4—202no—
372C3×C5#160211yescharacteristic, complemented, Hall
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—102no—
376C22×C3—202no—
377C22×C3—201no—
378C22×C3—201no—
379C22×C3—401no—
380C22×C3D5×Q1611yescharacteristic
381C22×C3#406411yescharacteristic
382C22×C3#408311yescharacteristic
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—42no—
386C3×C4—41no—
387C3×C4—41no—
388C3×C4—201no—
389C3×C4—201no—
390C3×C4—201no—
391C3×C4—401no—
392C2×C5—21no—
393C2×C5—21no—
394C2×C5C3×#45111yescharacteristic
395C2×C5C3×#45511yescharacteristic
396C2×C5C3×B(4,𝔽2)11yescharacteristic
397D5—42no—
398C23—52no—
399C23—101no—
400C23—101no—
401C23—201no—
402C23—201no—
403C23C3×D4×D511yescharacteristic
404Q8—22no—
405Q8—22no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—201no—
410Q8—401no—
411C2×C4—22no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—101no—
418C2×C4—101no—
419C2×C4—101no—
420C2×C4—201no—
421C2×C4—201no—
422C2×C4—201no—
423C2×C4—201no—
424C2×C4—401no—
425C2×C4—401no—
426C2×C4C3×D4×D511yescharacteristic
427C2×C4C2×C3×C22⋊D511yescharacteristic
428C8—41no—
429C8—201no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—202no—
433C2×C3#6532111yescharacteristic
434C2×C3#6547511yescharacteristic
435C2×C3#6549111yescharacteristic
436C5C3×#160211yescharacteristic, complemented, Sylow
437C22—21no—
438C22—21no—
439C22—102no—
440C22—202no—
441C22—201no—
442C22—201no—
443C22—401no—
444C22C3×D5×Q1611yescharacteristic
445C22C3×#406411yescharacteristic
446C22C3×#408311yescharacteristic
447C4—21no—
448C4—21no—
449C4—42no—
450C4—41no—
451C4—41no—
452C4—201no—
453C4—201no—
454C4—201no—
455C4—401no—
456C3#1060177311yescharacteristic, direct product factor, Sylow
457C2—21no—
458C2—21no—
459C2—202no—
460C2C3×#6532111yescharacteristic
461C2C3×#6547511yescharacteristic
462C2C3×#6549111yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#451C2
socleC22×C3×C5#120
prime radicalC23×C3×D5D4
hypercenterC3×#451D5
hypocenterC5C3×#1602
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#451

Complements

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

NH ≅ G/Ntype
2. C3×C5×#451C2semidirect
4. C3×#65517C2semidirect
5. C3×#64758C2semidirect
7. C3×#64687C2semidirect
8. #10601773C3direct (N × H)
30. C5×#451C2×C3semidirect
32. #65517C2×C3semidirect
33. #64758C2×C3semidirect
35. #64687C2×C3semidirect
69. C3×#451D5semidirect
99. C22×C3×D5Q16semidirect
178. #451C3×D5semidirect
238. C22×D5C3×Q16semidirect
372. C3×C5#1602semidirect
436. C5C3×#1602semidirect
456. C3#10601773direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659682
C3×C5×#4512
C3×#655202
C3×#655172
C3×#647582
C3×#646882
C3×#646872
#106017733
C3×#16025