Finite Group Databasebeta

← C3×#10599113 #14288288

Subgroups — C3×#10599113 #14288288

Order 1920.

456 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65968C211yesmaximal, characteristic
2C3×#65332C211yesmaximal, characteristic, complemented
3C3×#65010C211yesmaximal, characteristic, complemented
4C3×#64963C211yesmaximal, characteristic
5C3×C5×#328C211yesmaximal, characteristic, complemented
6C3×#64688C211yesmaximal, characteristic
7C3×#64672C211yesmaximal, characteristic, complemented
8#10599113C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10C3×#4092—21no—
11C2×C3×#685—21no—
12C2×C3×#685C2211yescharacteristic
13C2×C3×C4⋊Dic5C2211yescharacteristic
14C3×#4070C2211yescharacteristic
15C3×#4043—21no—
16C3×#4042—21no—
17C3×#4042—21no—
18C3×D5×C22⋊C4—21no—
19C3×#4024—21no—
20C3×C5×C22⋊C8C2211yescharacteristic
21C3×C5×#95C2211yescharacteristic
22C3×#3967—21no—
23C3×#3963—21no—
24C3×C22⋊#168C2211yescharacteristic
25C3×#3949—21no—
26C3×#3948—21no—
27C3×#3940—21no—
28C3×#1608—51nomaximal, Hall
29#65968C2×C311yescharacteristic
30#65332C2×C311yescharacteristic, complemented
31#65010C2×C311yescharacteristic, complemented
32#64963C2×C311yescharacteristic
33C5×#328C2×C311yescharacteristic, complemented
34#64688C2×C311yescharacteristic
35#64672C2×C311yescharacteristic, complemented
36C23×C3×D5D411yescharacteristic
37C2×C3×C5×Q8D411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C22×C3×Dic5—21no—
41C22×C3×Dic5D411yescharacteristic
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5—21no—
44C2×C3×Dic10—21no—
45C2×C3×Dic10D411yescharacteristic
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C22⋊C4—21no—
50C3×C22⋊Dic5—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×#685—42no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5—21no—
59C3×C4⋊Dic5D411yescharacteristic
60C3×#683—21no—
61C3×#683—21no—
62C3×#683—21no—
63C2×C3×#168—21no—
64C3×#543—51no—
65C3×#483—51no—
66C3×#483—51no—
67C3×#397—51no—
68C3×#328—51no—
69C3×#328D511yescharacteristic, complemented
70C3×#323—51no—
71C5×C22⋊Q8C22×C311yescharacteristic
72#4092—21no—
73C2×#685—21no—
74C2×#685C22×C311yescharacteristic
75C2×C4⋊Dic5C22×C311yescharacteristic
76#4070C22×C311yescharacteristic
77#4043—21no—
78#4042—21no—
79#4042—21no—
80D5×C22⋊C4—21no—
81#4024—21no—
82C5×C22⋊C8C22×C311yescharacteristic
83C5×#95C22×C311yescharacteristic
84#3967—21no—
85#3963—21no—
86C22⋊#168C22×C311yescharacteristic
87#3949—21no—
88#3948—21no—
89#3940—21no—
90#1608—51noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×C3×D5—21no—
93C22×C3×D5—21no—
94C22×C3×D5—41no—
95C22×C3×D5—41no—
96C22×C3×D5SD1612yes—
97C3×C5×Q8—41no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×Dic5—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—41no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5—41no—
113C3×C4×D5—81no—
114C3×C4×D5—81no—
115C3×Dic10—41no—
116C3×Dic10—81no—
117C3×C5×C8—41no—
118C3×#168—41no—
119C3×C22⋊Q8—51no—
120C3×C22⋊Q8—101no—
121C3×C22⋊Q8—101no—
122C3×C22⋊Q8—101no—
123C3×C22⋊Q8—101no—
124C3×C22⋊Q8—101no—
125C3×C22⋊Q8C2×D511yescharacteristic
126C2×C3×C4⋊C4—51no—
127C2×C3×C22⋊C4—51no—
128C2×C3×C22⋊C4—101no—
129C2×C3×C22⋊C4—101no—
130C3×#106—101no—
131C3×#106—101no—
132C3×#103—101no—
133C3×#103—101no—
134C3×C22⋊C8—51no—
135C3×C22⋊C8C2×D511yescharacteristic
136C3×#95—101no—
137C3×#95C2×D511yescharacteristic
138C23×D5C3×D411yescharacteristic
139C2×C5×Q8C3×D411yescharacteristic
140C22×C4×C5—21no—
141C22×C4×C5C23×C311yescharacteristic
142C22×Dic5—21no—
143C22×Dic5C3×D411yescharacteristic
144C2×C4×D5—21no—
145C2×C4×D5—21no—
146C2×Dic10—21no—
147C2×Dic10C3×D411yescharacteristic
148C2×C5×C8—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4C3×D411yescharacteristic
151C5×C22⋊C4—21no—
152C22⋊Dic5—21no—
153#685—21no—
154#685—21no—
155#685—21no—
156#685—21no—
157#685—42no—
158C4⋊Dic5—21no—
159C4⋊Dic5—21no—
160C4⋊Dic5—21no—
161C4⋊Dic5C3×D411yescharacteristic
162#683—21no—
163#683—21no—
164#683—21no—
165C2×#168—21no—
166#543—51no—
167#483—51no—
168#483—51no—
169#397—51no—
170#328—51no—
171#328C3×D511yescharacteristic, complemented
172#323—51no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5#12011yescharacteristic
176C22×C3×C5C2×SD1611yescharacteristic
177C22×C3×C5#13711yescharacteristic
178C2×C3×D5—22no—
179C2×C3×D5—41no—
180C2×C3×D5—41no—
181C2×C3×D5—42no—
182C2×C3×D5—81no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—41no—
186C3×C4×C5—41no—
187C3×C4×C5—81no—
188C3×Dic5—41no—
189C3×Dic5—41no—
190C3×Dic5—41no—
191C3×Dic5—81no—
192C24×C3—51no—
193C2×C3×Q8—51no—
194C2×C3×Q8—101no—
195C2×C3×Q8D2011yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4—51no—
198C22×C3×C4—101no—
199C22×C3×C4—101no—
200C22×C3×C4—101no—
201C22×C3×C4C22×D511yescharacteristic
202C2×C3×C8—21no—
203C2×C3×C8—101no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—51no—
206C3×C4⋊C4—101no—
207C3×C4⋊C4—101no—
208C3×C4⋊C4—101no—
209C3×C4⋊C4—101no—
210C3×C4⋊C4—101no—
211C3×C4⋊C4—101no—
212C3×C4⋊C4D2011yescharacteristic
213C3×C22⋊C4—21no—
214C3×C22⋊C4—101no—
215C3×C22⋊C4—101no—
216C3×C22⋊C4—101no—
217C3×C22⋊C4—101no—
218C3×C22⋊C4—101no—
219C3×C22⋊C4—202no—
220C23×C5C2×C3×D411yescharacteristic
221C22×D5—21no—
222C22×D5—21no—
223C22×D5—41no—
224C22×D5—41no—
225C22×D5C3×SD1612yes—
226C5×Q8—41no—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C2×C4×C5C2×C3×D411yescharacteristic
234C2×C4×C5C2×C3×D411yescharacteristic
235C2×Dic5—21no—
236C2×Dic5—21no—
237C2×Dic5—21no—
238C2×Dic5—41no—
239C2×Dic5—41no—
240C2×Dic5—41no—
241C2×Dic5—41no—
242C4×D5—81no—
243C4×D5—81no—
244Dic10—41no—
245Dic10—81no—
246C5×C8—41no—
247#168—41no—
248C22⋊Q8—51no—
249C22⋊Q8—101no—
250C22⋊Q8—101no—
251C22⋊Q8—101no—
252C22⋊Q8—101no—
253C22⋊Q8—101no—
254C22⋊Q8C2×C3×D511yescharacteristic
255C2×C4⋊C4—51no—
256C2×C22⋊C4—51no—
257C2×C22⋊C4—101no—
258C2×C22⋊C4—101no—
259#106—101no—
260#106—101no—
261#103—101no—
262#103—101no—
263C22⋊C8—51no—
264C22⋊C8C2×C3×D511yescharacteristic
265#95—101no—
266#95C2×C3×D511yescharacteristic
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#44811yescharacteristic
270C2×C3×C5#45511yescharacteristic
271C2×C3×C5#45811yescharacteristic
272C3×D5—42no—
273C23×C3—52no—
274C23×C3—101no—
275C23×C3—101no—
276C23×C3—201no—
277C23×C3—201no—
278C23×C3D4×D511yescharacteristic
279C3×Q8—41no—
280C3×Q8—201no—
281C3×Q8—401no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—101no—
289C2×C3×C4—101no—
290C2×C3×C4—101no—
291C2×C3×C4—201no—
292C2×C3×C4—201no—
293C2×C3×C4—201no—
294C2×C3×C4—201no—
295C2×C3×C4—401no—
296C2×C3×C4—401no—
297C2×C3×C4C2×D2011yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299C3×C8—41no—
300C3×C8—201no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5C3×#12011yescharacteristic
304C22×C5C2×C3×SD1611yescharacteristic
305C22×C5C3×#13711yescharacteristic
306C2×D5—22no—
307C2×D5—41no—
308C2×D5—41no—
309C2×D5—42no—
310C2×D5—81no—
311C4×C5—21no—
312C4×C5—21no—
313C4×C5—41no—
314C4×C5—41no—
315C4×C5—81no—
316Dic5—41no—
317Dic5—41no—
318Dic5—41no—
319Dic5—81no—
320C24—51no—
321C2×Q8—51no—
322C2×Q8—101no—
323C2×Q8C3×D2011yescharacteristic
324C22×C4—21no—
325C22×C4—51no—
326C22×C4—101no—
327C22×C4—101no—
328C22×C4—101no—
329C22×C4C22×C3×D511yescharacteristic
330C2×C8—21no—
331C2×C8—101no—
332C4⋊C4—21no—
333C4⋊C4—51no—
334C4⋊C4—101no—
335C4⋊C4—101no—
336C4⋊C4—101no—
337C4⋊C4—101no—
338C4⋊C4—101no—
339C4⋊C4—101no—
340C4⋊C4C3×D2011yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—101no—
343C22⋊C4—101no—
344C22⋊C4—101no—
345C22⋊C4—101no—
346C22⋊C4—101no—
347C22⋊C4—202no—
348C3×C5#160811yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—102no—
352C22×C3—202no—
353C22×C3—201no—
354C22×C3—201no—
355C22×C3—401no—
356C22×C3#402811yescharacteristic
357C22×C3D5×SD1611yescharacteristic
358C22×C3#406411yescharacteristic
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—81no—
364C3×C4—201no—
365C3×C4—201no—
366C3×C4—201no—
367C3×C4—401no—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5C3×#44811yescharacteristic
371C2×C5C3×#45511yescharacteristic
372C2×C5C3×#45811yescharacteristic
373D5—42no—
374C23—52no—
375C23—101no—
376C23—101no—
377C23—201no—
378C23—201no—
379C23C3×D4×D511yescharacteristic
380Q8—41no—
381Q8—201no—
382Q8—401no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—101no—
390C2×C4—101no—
391C2×C4—101no—
392C2×C4—201no—
393C2×C4—201no—
394C2×C4—201no—
395C2×C4—201no—
396C2×C4—401no—
397C2×C4—401no—
398C2×C4C2×C3×D2011yescharacteristic
399C2×C4C3×D4×D511yescharacteristic
400C8—41no—
401C8—201no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—202no—
405C2×C3#6503111yescharacteristic
406C2×C3#6509511yescharacteristic
407C2×C3#6511411yescharacteristic
408C5C3×#160811yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—102no—
412C22—202no—
413C22—201no—
414C22—201no—
415C22—401no—
416C22C3×#402811yescharacteristic
417C22C3×D5×SD1611yescharacteristic
418C22C3×#406411yescharacteristic
419C4—21no—
420C4—21no—
421C4—41no—
422C4—41no—
423C4—81no—
424C4—201no—
425C4—201no—
426C4—201no—
427C4—401no—
428C3#1059911311yescharacteristic, direct product factor, Sylow
429C2—21no—
430C2—21no—
431C2—202no—
432C2C3×#6503111yescharacteristic
433C2C3×#6509511yescharacteristic
434C2C3×#6511411yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#328C2
socleC22×C3×C5#120
prime radicalC23×C3×D5D4
hypercenterC3×#328D5
hypocenterC5C3×#1608
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#328

Complements

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

NH ≅ G/Ntype
2. C3×#65332C2semidirect
3. C3×#65010C2semidirect
5. C3×C5×#328C2semidirect
7. C3×#64672C2semidirect
8. #10599113C3direct (N × H)
30. #65332C2×C3semidirect
31. #65010C2×C3semidirect
33. C5×#328C2×C3semidirect
35. #64672C2×C3semidirect
69. C3×#328D5semidirect
171. #328C3×D5semidirect
348. C3×C5#1608semidirect
408. C5C3×#1608semidirect
428. C3#10599113direct (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×#653322
C3×#650102
C3×#649632
C3×C5×#3282
C3×#646882
C3×#646722
#105991133
C3×#16085