Finite Group Databasebeta

← C3×#10600817 #14302981

Subgroups — C3×#10600817 #14302981

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66138C211yesmaximal, characteristic
2C3×#66132C211yesmaximal, characteristic, complemented
3C2×C3×C5×#99C211yesmaximal, characteristic, complemented
4C2×C3×#3938C212yesmaximal, complemented
5C3×#64746C212yesmaximal, complemented
6#10600817C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C22×C3×C22⋊D5C2211yescharacteristic
9C2×C3×C5×C22⋊C4C2212yes—
10C3×#4099—21no—
11C2×C3×C22⋊Dic5—21no—
12C2×C3×C22⋊Dic5C2211yescharacteristic
13C2×C3×C22⋊Dic5C2212yes—
14C3×#4085—22no—
15C3×#4083C412yescomplemented
16C3×#4081C412yescomplemented
17C3×D4×Dic5—24no—
18C3×#4075—21no—
19C3×#4072—21no—
20C3×C5×#99—22no—
21C3×#3938—24no—
22C3×#1913—51nomaximal, Hall
23#66138C2×C311yescharacteristic
24#66132C2×C311yescharacteristic, complemented
25C2×C5×#99C2×C311yescharacteristic, complemented
26C2×#3938C2×C312yescomplemented
27#64746C2×C312yescomplemented
28C24×C3×C5D411yescharacteristic
29C24×C3×C5C2311yescharacteristic
30C23×C3×D5C2×C411yescharacteristic, complemented
31C2×C3×C5×D4—22no—
32C2×C3×C5×D4—22no—
33C2×C3×C5×D4C2×C412yes—
34C2×C3×C5×D4D412yes—
35C22×C3×C4×C5—22no—
36C22×C3×C4×C5D411yescharacteristic
37C2×C3×C22⋊D5—21no—
38C2×C3×C22⋊D5—21no—
39C2×C3×C22⋊D5—22no—
40C2×C3×C22⋊D5—22no—
41C2×C3×C22⋊D5—22no—
42C22×C3×Dic5—22no—
43C22×C3×Dic5—22no—
44C22×C3×Dic5—21no—
45C22×C3×Dic5C2×C411yescharacteristic, complemented
46C3×C5×C22⋊C4—22no—
47C3×C5×C22⋊C4—22no—
48C3×C22⋊Dic5—22no—
49C3×C22⋊Dic5—22no—
50C3×C22⋊Dic5—22no—
51C3×C22⋊Dic5—21no—
52C3×C22⋊Dic5C2×C412yescomplemented
53C3×C22⋊Dic5D414yescomplemented
54C3×#685—22no—
55C3×C4⋊Dic5—22no—
56C3×#683—22no—
57C3×C4×Dic5—22no—
58C3×#534—51no—
59C3×#518—51no—
60C2×C3×#99—52no—
61C2×C3×#99D511yescharacteristic, complemented
62C3×#342—52no—
63C22×C5×D4C22×C311yescharacteristic
64C22×C22⋊D5C22×C311yescharacteristic
65C2×C5×C22⋊C4C22×C312yes—
66#4099—21no—
67C2×C22⋊Dic5—21no—
68C2×C22⋊Dic5C22×C311yescharacteristic
69C2×C22⋊Dic5C22×C312yes—
70#4085—22no—
71#4083C3×C412yescomplemented
72#4081C3×C412yescomplemented
73D4×Dic5—24no—
74#4075—21no—
75#4072—21no—
76C5×#99—22no—
77#3938—24no—
78#1913—51noSylow
79C23×C3×C5—21no—
80C23×C3×C5—21no—
81C23×C3×C5—81no—
82C23×C3×C5—81no—
83C23×C3×C5C22⋊C412yes—
84C23×C3×C5C22×C411yescharacteristic
85C23×C3×C5C2×D411yescharacteristic
86C23×C3×C5C2×D411yescharacteristic
87C23×C3×C5C2×D412yes—
88C23×C3×C5#4112yes—
89C22×C3×D5—21no—
90C22×C3×D5—22no—
91C22×C3×D5—81no—
92C3×C5×D4—24no—
93C3×C5×D4—24no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—42no—
97C2×C3×C4×C5—82no—
98C2×C3×C4×C5C22⋊C412yes—
99C3×C22⋊D5—41no—
100C3×C22⋊D5—42no—
101C3×C22⋊D5—41no—
102C3×C22⋊D5—82no—
103C2×C3×Dic5—21no—
104C2×C3×Dic5—22no—
105C2×C3×Dic5—22no—
106C2×C3×Dic5—24no—
107C2×C3×Dic5—82no—
108C2×C3×Dic5—82no—
109C2×C3×Dic5—81no—
110C22×C3×D4—51no—
111C22×C3×D4C2×D511yescharacteristic
112C3×#123—52no—
113C3×#123—101no—
114C3×#121—102no—
115C3×#120—52no—
116C3×#120—101no—
117C3×C4×D4—104no—
118C3×#117—101no—
119C2×C3×C22⋊C4—52no—
120C2×C3×C22⋊C4—51no—
121C2×C3×C22⋊C4—101no—
122C2×C3×C22⋊C4C2×D512yes—
123C3×#99—22no—
124C3×#99—104no—
125C24×C5C3×D411yescharacteristic
126C24×C5C23×C311yescharacteristic
127C23×D5C2×C3×C411yescharacteristic, complemented
128C2×C5×D4—22no—
129C2×C5×D4—22no—
130C2×C5×D4C2×C3×C412yes—
131C2×C5×D4C3×D412yes—
132C22×C4×C5—22no—
133C22×C4×C5C3×D411yescharacteristic
134C2×C22⋊D5—21no—
135C2×C22⋊D5—22no—
136C2×C22⋊D5—21no—
137C2×C22⋊D5—22no—
138C2×C22⋊D5—22no—
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—21no—
142C22×Dic5C2×C3×C411yescharacteristic, complemented
143C5×C22⋊C4—22no—
144C5×C22⋊C4—22no—
145C22⋊Dic5—22no—
146C22⋊Dic5—22no—
147C22⋊Dic5—22no—
148C22⋊Dic5—21no—
149C22⋊Dic5C2×C3×C412yescomplemented
150C22⋊Dic5C3×D414yescomplemented
151#685—22no—
152C4⋊Dic5—22no—
153#683—22no—
154C4×Dic5—22no—
155#534—51no—
156#518—51no—
157C2×#99—52no—
158C2×#99C3×D511yescharacteristic, complemented
159#342—52no—
160C22×C3×C5—22no—
161C22×C3×C5—42no—
162C22×C3×C5—41no—
163C22×C3×C5—42no—
164C22×C3×C5—41no—
165C22×C3×C5—41no—
166C22×C3×C5—42no—
167C22×C3×C5—42no—
168C22×C3×C5—81no—
169C22×C3×C5C2×C22⋊C411yescharacteristic
170C22×C3×C5C4×D412yes—
171C22×C3×C5#12011yescharacteristic
172C22×C3×C5#12112yes—
173C22×C3×C5#12311yescharacteristic
174C2×C3×D5—42no—
175C2×C3×D5—41no—
176C2×C3×D5—82no—
177C3×C4×C5—22no—
178C3×C4×C5—82no—
179C3×Dic5—44no—
180C3×Dic5—42no—
181C3×Dic5—41no—
182C24×C3—51no—
183C24×C3D2011yescharacteristic
184C24×C3C22×D511yescharacteristic
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—101no—
188C2×C3×D4—102no—
189C2×C3×D4—102no—
190C2×C3×D4—101no—
191C2×C3×D4—102no—
192C2×C3×D4C4×D512yes—
193C2×C3×D4C22⋊D512yes—
194C22×C3×C4—22no—
195C22×C3×C4—51no—
196C22×C3×C4—102no—
197C22×C3×C4—102no—
198C22×C3×C4—101no—
199C22×C3×C4D2011yescharacteristic
200C3×C4⋊C4—102no—
201C3×C4⋊C4—102no—
202C3×C22⋊C4—22no—
203C3×C22⋊C4—22no—
204C3×C22⋊C4—52no—
205C3×C22⋊C4—54no—
206C3×C22⋊C4—102no—
207C3×C22⋊C4—102no—
208C3×C22⋊C4—102no—
209C3×C22⋊C4—101no—
210C3×C22⋊C4—102no—
211C3×C42—102no—
212C23×C5—21no—
213C23×C5—21no—
214C23×C5—81no—
215C23×C5—81no—
216C23×C5C3×C22⋊C412yes—
217C23×C5C22×C3×C411yescharacteristic
218C23×C5C2×C3×D411yescharacteristic
219C23×C5C2×C3×D412yes—
220C23×C5C2×C3×D411yescharacteristic
221C23×C5C3×#4112yes—
222C22×D5—21no—
223C22×D5—22no—
224C22×D5—81no—
225C5×D4—24no—
226C5×D4—24no—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5—42no—
230C2×C4×C5—82no—
231C2×C4×C5C3×C22⋊C412yes—
232C22⋊D5—41no—
233C22⋊D5—42no—
234C22⋊D5—41no—
235C22⋊D5—82no—
236C2×Dic5—21no—
237C2×Dic5—22no—
238C2×Dic5—22no—
239C2×Dic5—24no—
240C2×Dic5—82no—
241C2×Dic5—82no—
242C2×Dic5—81no—
243C22×D4—51no—
244C22×D4C2×C3×D511yescharacteristic
245#123—52no—
246#123—101no—
247#121—102no—
248#120—52no—
249#120—101no—
250C4×D4—104no—
251#117—101no—
252C2×C22⋊C4—52no—
253C2×C22⋊C4—51no—
254C2×C22⋊C4—101no—
255C2×C22⋊C4C2×C3×D512yes—
256#99—22no—
257#99—104no—
258C2×C3×C5—21no—
259C2×C3×C5—21no—
260C2×C3×C5—22no—
261C2×C3×C5—22no—
262C2×C3×C5—21no—
263C2×C3×C5—42no—
264C2×C3×C5#38611yescharacteristic
265C3×D5—81no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—81no—
269C23×C3—81no—
270C23×C3—101no—
271C23×C3—102no—
272C23×C3—401no—
273C23×C3#68512yes—
274C23×C3C2×C4×D511yescharacteristic
275C23×C3C2×D2011yescharacteristic
276C23×C3D4×D512yes—
277C23×C3#71112yes—
278C23×C3C2×C22⋊D511yescharacteristic
279C3×D4—24no—
280C3×D4—24no—
281C3×D4—201no—
282C3×D4—201no—
283C3×D4—202no—
284C3×D4—402no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—42no—
288C2×C3×C4—82no—
289C2×C3×C4—102no—
290C2×C3×C4—104no—
291C2×C3×C4—102no—
292C2×C3×C4—101no—
293C2×C3×C4—402no—
294C2×C3×C4—402no—
295C2×C3×C4—401no—
296C2×C3×C4#68512yes—
297C22×C5—22no—
298C22×C5—42no—
299C22×C5—41no—
300C22×C5—42no—
301C22×C5—41no—
302C22×C5—41no—
303C22×C5—42no—
304C22×C5—42no—
305C22×C5—81no—
306C22×C5C2×C3×C22⋊C411yescharacteristic
307C22×C5C3×C4×D412yes—
308C22×C5C3×#12011yescharacteristic
309C22×C5C3×#12112yes—
310C22×C5C3×#12311yescharacteristic
311C2×D5—42no—
312C2×D5—41no—
313C2×D5—82no—
314C4×C5—22no—
315C4×C5—82no—
316Dic5—44no—
317Dic5—42no—
318Dic5—41no—
319C24—51no—
320C24C3×D2011yescharacteristic
321C24C22×C3×D511yescharacteristic
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—101no—
325C2×D4—102no—
326C2×D4—102no—
327C2×D4—101no—
328C2×D4—102no—
329C2×D4C3×C4×D512yes—
330C2×D4C3×C22⋊D512yes—
331C22×C4—22no—
332C22×C4—51no—
333C22×C4—102no—
334C22×C4—102no—
335C22×C4—101no—
336C22×C4C3×D2011yescharacteristic
337C4⋊C4—102no—
338C4⋊C4—102no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—52no—
342C22⋊C4—54no—
343C22⋊C4—102no—
344C22⋊C4—102no—
345C22⋊C4—102no—
346C22⋊C4—101no—
347C22⋊C4—102no—
348C42—102no—
349C3×C5#191311yescharacteristic, complemented, Hall
350C22×C3—22no—
351C22×C3—42no—
352C22×C3—42no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—81no—
359C22×C3—202no—
360C22×C3—201no—
361C22×C3—402no—
362C22×C3#402712yes—
363C22×C3#402811yescharacteristic
364C22×C3#403211yescharacteristic
365C22×C3C2×#68511yescharacteristic
366C22×C3#408512yes—
367C3×C4—22no—
368C3×C4—82no—
369C3×C4—204no—
370C3×C4—202no—
371C3×C4—201no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5—22no—
375C2×C5—22no—
376C2×C5—21no—
377C2×C5—42no—
378C2×C5C3×#38611yescharacteristic
379D5—81no—
380C23—21no—
381C23—21no—
382C23—81no—
383C23—81no—
384C23—101no—
385C23—102no—
386C23—401no—
387C23C3×#68512yes—
388C23C2×C3×C4×D511yescharacteristic
389C23C2×C3×D2011yescharacteristic
390C23C3×D4×D512yes—
391C23C3×#71112yes—
392C23C2×C3×C22⋊D511yescharacteristic
393D4—24no—
394D4—24no—
395D4—202no—
396D4—201no—
397D4—201no—
398D4—402no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—42no—
402C2×C4—82no—
403C2×C4—102no—
404C2×C4—104no—
405C2×C4—102no—
406C2×C4—101no—
407C2×C4—402no—
408C2×C4—402no—
409C2×C4—401no—
410C2×C4C3×#68512yes—
411C2×C3—22no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—22no—
416C2×C3—42no—
417C2×C3—401no—
418C2×C3#6524711yescharacteristic
419C5C3×#191311yescharacteristic, complemented, Sylow
420C22—22no—
421C22—42no—
422C22—42no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—42no—
427C22—42no—
428C22—81no—
429C22—202no—
430C22—201no—
431C22—402no—
432C22C3×#402712yes—
433C22C3×#402811yescharacteristic
434C22C3×#403211yescharacteristic
435C22C2×C3×#68511yescharacteristic
436C22C3×#408512yes—
437C4—22no—
438C4—82no—
439C4—204no—
440C4—202no—
441C4—201no—
442C3#1060081711yescharacteristic, direct product factor, Sylow
443C2—22no—
444C2—21no—
445C2—21no—
446C2—21no—
447C2—22no—
448C2—42no—
449C2—401no—
450C2C3×#6524711yescharacteristic
subgroupG/H
centerC2×C3#65247
commutatorC23×C5C22×C3×C4
FrattiniC24C22×C3×D5
FittingC2×C3×C5×#99C2
socleC2×C3×C5#386
prime radicalC3×#66138C2
cosocleC24×C5C23×C3
hypercenterC2×C3×#99D5
hypocenterC5C3×#1913
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C24×C3 ◁ C2×C3×#99

Complements

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

NH ≅ G/Ntype
2. C3×#66132C2semidirect
3. C2×C3×C5×#99C2semidirect
4. C2×C3×#3938C2semidirect
5. C3×#64746C2semidirect
6. #10600817C3direct (N × H)
15. C3×#4083C4semidirect
16. C3×#4081C4semidirect
24. #66132C2×C3semidirect
25. C2×C5×#99C2×C3semidirect
26. C2×#3938C2×C3semidirect
27. #64746C2×C3semidirect
30. C23×C3×D5C2×C4semidirect
45. C22×C3×Dic5C2×C4semidirect
52. C3×C22⋊Dic5C2×C4semidirect
53. C3×C22⋊Dic5D4semidirect
61. C2×C3×#99D5semidirect
71. #4083C3×C4semidirect
72. #4081C3×C4semidirect
127. C23×D5C2×C3×C4semidirect
142. C22×Dic5C2×C3×C4semidirect
149. C22⋊Dic5C2×C3×C4semidirect
150. C22⋊Dic5C3×D4semidirect
158. C2×#99C3×D5semidirect
349. C3×C5#1913semidirect
419. C5C3×#1913semidirect
442. C3#10600817direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661382
C3×#661322
C2×C3×C5×#992
C2×C3×#39382
C3×#647462
#106008173
C3×#19135