Finite Group Databasebeta

← C3×#10604464 #14303043

Subgroups — C3×#10604464 #14303043

Order 1920.

680 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66256C211yesmaximal, characteristic, complemented
2C3×#65926C211yesmaximal, characteristic
3C2×C3×#4013C212yesmaximal, complemented
4C3×#65777C211yesmaximal, characteristic, complemented
5C3×#64867C212yesmaximal, complemented
6#10604464C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C22⋊D5C2211yescharacteristic
8C2×C3×#711C2211yescharacteristic
9C2×C3×#704—21no—
10C2×C3×#704C2212yes—
11C2×C3×#704C2212yes—
12C3×#4131—24no—
13C3×D5⋊M16—21no—
14C3×C5×#120C411yescharacteristic
15C3×#4099C411yescharacteristic
16C3×#4086—21no—
17C3×#4085—21no—
18C3×#4083C411yescharacteristic
19C3×#4031—21no—
20C3×#4030—21no—
21C3×#4028C411yescharacteristic
22C3×#4023C2211yescharacteristic
23C3×#4013—21no—
24C3×#4013—24no—
25C3×#4005—21no—
26C3×#1914—51nomaximal, Hall
27#66256C2×C311yescharacteristic, complemented
28#65926C2×C311yescharacteristic
29C2×#4013C2×C312yescomplemented
30#65777C2×C311yescharacteristic, complemented
31#64867C2×C312yescomplemented
32C24×C3×C5C2×C411yescharacteristic
33C23×C3×D5C2×C411yescharacteristic
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4C2×C411yescharacteristic
36C2×C3×C22⋊D5—21no—
37C2×C3×C22⋊D5—21no—
38C2×C3×C22⋊D5—21no—
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—22no—
41C2×C3×C22⋊D5—22no—
42C2×C3×C22⋊D5C2×C411yescharacteristic
43C2×C3×C22⋊D5D411yescharacteristic
44C22×C3×Dic5D411yescharacteristic
45C22×C3×Dic5C2311yescharacteristic
46C3×#711—22no—
47C3×#711—22no—
48C2×C3×D20—21no—
49C2×C3×C4×D5D411yescharacteristic
50C2×C3×Dic10D411yescharacteristic
51C3×#704—22no—
52C3×#704—22no—
53C3×#704—22no—
54C3×#704—22no—
55C3×#704D414yescomplemented
56C2×C3×#170—22no—
57C2×C3×#170—22no—
58C2×C3×#170—22no—
59C3×#700—22no—
60C3×D5⋊C8—22no—
61C3×C5×C22⋊C4—21no—
62C3×C5×C22⋊C4C2×C411yescharacteristic
63C3×C22⋊Dic5—21no—
64C3×C22⋊Dic5C2×C411yescharacteristic
65C3×#685—21no—
66C3×#685—21no—
67C3×#683—21no—
68C3×C4×Dic5—21no—
69C3×#568—51no—
70C3×#535—51no—
71C3×#413—51no—
72C2×C3×#100—52no—
73C3×#344—52no—
74C22×C22⋊D5C22×C311yescharacteristic
75C2×#711C22×C311yescharacteristic
76C2×#704—21no—
77C2×#704C22×C312yes—
78C2×#704C22×C312yes—
79#4131—24no—
80D5⋊M16—21no—
81C5×#120C3×C411yescharacteristic
82#4099C3×C411yescharacteristic
83#4086—21no—
84#4085—21no—
85#4083C3×C411yescharacteristic
86#4031—21no—
87#4030—21no—
88#4028C3×C411yescharacteristic
89#4023C22×C311yescharacteristic
90#4013—21no—
91#4013—24no—
92#4005—21no—
93#1914—51noSylow
94C23×C3×C5—21no—
95C23×C3×C5—22no—
96C23×C3×C5—81no—
97C23×C3×C5C22⋊C411yescharacteristic
98C23×C3×C5C22×C411yescharacteristic
99C22×C3×D5—21no—
100C22×C3×D5—22no—
101C22×C3×D5—81no—
102C22×C3×D5C22⋊C411yescharacteristic
103C3×C5×D4—22no—
104C3×C5×D4—81no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5C22⋊C411yescharacteristic
107C3×C22⋊D5—22no—
108C3×C22⋊D5—22no—
109C3×C22⋊D5—41no—
110C3×C22⋊D5—42no—
111C3×C22⋊D5—41no—
112C3×C22⋊D5—81no—
113C3×C22⋊D5—81no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5C22⋊C411yescharacteristic
118C2×C3×Dic5C2×D412yes—
119C2×C3×Dic5C2×D411yescharacteristic
120C2×C3×Dic5C2×D411yescharacteristic
121C2×C3×Dic5#4112yes—
122C3×D20—81no—
123C3×C4×D5—21no—
124C3×C4×D5—21no—
125C3×Dic10—22no—
126C3×#170—24no—
127C3×#170—42no—
128C2×C3×#41—51no—
129C22×C3×D4—51no—
130C3×#131—104no—
131C2×C3×M16—52no—
132C2×C3×M16—52no—
133C2×C3×M16—101no—
134C2×C3×M16—101no—
135C3×#127—101no—
136C3×#124—101no—
137C3×#121—101no—
138C3×#121—101no—
139C3×#120—51no—
140C3×#120—51no—
141C3×#120—51no—
142C3×#120AGL(1,𝔽5)11yescharacteristic
143C3×#117—51no—
144C3×#101—101no—
145C3×#100—104no—
146C3×#100—101no—
147C24×C5C2×C3×C411yescharacteristic
148C23×D5C2×C3×C411yescharacteristic
149C2×C5×D4—21no—
150C2×C5×D4C2×C3×C411yescharacteristic
151C2×C22⋊D5—21no—
152C2×C22⋊D5—21no—
153C2×C22⋊D5—22no—
154C2×C22⋊D5—21no—
155C2×C22⋊D5—21no—
156C2×C22⋊D5—22no—
157C2×C22⋊D5C2×C3×C411yescharacteristic
158C2×C22⋊D5C3×D411yescharacteristic
159C22×Dic5C3×D411yescharacteristic
160C22×Dic5C23×C311yescharacteristic
161#711—22no—
162#711—22no—
163C2×D20—21no—
164C2×C4×D5C3×D411yescharacteristic
165C2×Dic10C3×D411yescharacteristic
166#704—22no—
167#704—22no—
168#704—22no—
169#704—22no—
170#704C3×D414yescomplemented
171C2×#170—22no—
172C2×#170—22no—
173C2×#170—22no—
174#700—22no—
175D5⋊C8—22no—
176C5×C22⋊C4—21no—
177C5×C22⋊C4C2×C3×C411yescharacteristic
178C22⋊Dic5—21no—
179C22⋊Dic5C2×C3×C411yescharacteristic
180#685—21no—
181#685—21no—
182#683—21no—
183C4×Dic5—21no—
184#568—51no—
185#535—51no—
186#413—51no—
187C2×#100—52no—
188#344—52no—
189C22×C3×C5—21no—
190C22×C3×C5—41no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5—41no—
194C22×C3×C5—41no—
195C22×C3×C5—82no—
196C22×C3×C5C2×C22⋊C411yescharacteristic
197C22×C3×C5C4×D412yes—
198C2×C3×D5—21no—
199C2×C3×D5—41no—
200C2×C3×D5—41no—
201C2×C3×D5—41no—
202C2×C3×D5—41no—
203C2×C3×D5—82no—
204C3×C4×C5—21no—
205C3×C4×C5—41no—
206C3×Dic5—21no—
207C3×Dic5—41no—
208C3×Dic5#12011yescharacteristic
209C3×Dic5#12112yes—
210C3×Dic5#12311yescharacteristic
211C24×C3—51no—
212C24×C3C2×AGL(1,𝔽5)11yescharacteristic
213C3×#41—102no—
214C3×#41—102no—
215C2×C3×Q8—51no—
216C2×C3×D4—21no—
217C2×C3×D4—51no—
218C2×C3×D4—51no—
219C2×C3×D4—101no—
220C2×C3×D4—102no—
221C2×C3×D4—101no—
222C2×C3×D4—101no—
223C2×C3×D4—102no—
224C2×C3×D4—101no—
225C2×C3×D4—101no—
226C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
227C22×C3×C4—51no—
228C22×C3×C4—51no—
229C22×C3×C4—51no—
230C3×M16—54no—
231C3×M16—102no—
232C3×M16—102no—
233C3×M16—102no—
234C3×M16—102no—
235C3×M16—102no—
236C2×C3×C8—102no—
237C2×C3×C8—102no—
238C2×C3×C8—102no—
239C2×C3×C8—102no—
240C3×C4⋊C4—101no—
241C3×C22⋊C4—21no—
242C3×C22⋊C4—51no—
243C3×C22⋊C4—101no—
244C3×C22⋊C4—101no—
245C3×C22⋊C4—101no—
246C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
247C3×C42—101no—
248C23×C5—21no—
249C23×C5—22no—
250C23×C5—81no—
251C23×C5C3×C22⋊C411yescharacteristic
252C23×C5C22×C3×C411yescharacteristic
253C22×D5—21no—
254C22×D5—22no—
255C22×D5—81no—
256C22×D5C3×C22⋊C411yescharacteristic
257C5×D4—22no—
258C5×D4—81no—
259C2×C4×C5—21no—
260C2×C4×C5C3×C22⋊C411yescharacteristic
261C22⋊D5—22no—
262C22⋊D5—22no—
263C22⋊D5—41no—
264C22⋊D5—42no—
265C22⋊D5—41no—
266C22⋊D5—81no—
267C22⋊D5—81no—
268C2×Dic5—21no—
269C2×Dic5—21no—
270C2×Dic5—21no—
271C2×Dic5C3×C22⋊C411yescharacteristic
272C2×Dic5C2×C3×D412yes—
273C2×Dic5C2×C3×D411yescharacteristic
274C2×Dic5C2×C3×D411yescharacteristic
275C2×Dic5C3×#4112yes—
276D20—81no—
277C4×D5—21no—
278C4×D5—21no—
279Dic10—22no—
280#170—24no—
281#170—42no—
282C2×#41—51no—
283C22×D4—51no—
284#131—104no—
285C2×M16—52no—
286C2×M16—52no—
287C2×M16—101no—
288C2×M16—101no—
289#127—101no—
290#124—101no—
291#121—101no—
292#121—101no—
293#120—51no—
294#120—51no—
295#120—51no—
296#120C3×AGL(1,𝔽5)11yescharacteristic
297#117—51no—
298#101—101no—
299#100—104no—
300#100—101no—
301C2×C3×C5—21no—
302C2×C3×C5—22no—
303C2×C3×C5—41no—
304C2×C3×C5—81no—
305C2×C3×C5#38611yescharacteristic
306C3×D5—41no—
307C3×D5—81no—
308C23×C3—21no—
309C23×C3—22no—
310C23×C3—51no—
311C23×C3—81no—
312C23×C3—101no—
313C23×C3—102no—
314C23×C3—401no—
315C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
316C23×C3C22×AGL(1,𝔽5)11yescharacteristic
317C3×Q8—102no—
318C3×D4—22no—
319C3×D4—81no—
320C3×D4—102no—
321C3×D4—102no—
322C3×D4—201no—
323C3×D4—202no—
324C3×D4—201no—
325C3×D4—401no—
326C3×D4—401no—
327C3×D4—401no—
328C2×C3×C4—21no—
329C2×C3×C4—52no—
330C2×C3×C4—52no—
331C2×C3×C4—51no—
332C2×C3×C4—51no—
333C2×C3×C4—51no—
334C2×C3×C4—101no—
335C2×C3×C4—101no—
336C2×C3×C4—101no—
337C2×C3×C4—101no—
338C2×C3×C4—101no—
339C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
340C3×C8—104no—
341C3×C8—202no—
342C22×C5—21no—
343C22×C5—41no—
344C22×C5—41no—
345C22×C5—41no—
346C22×C5—41no—
347C22×C5—41no—
348C22×C5—82no—
349C22×C5C2×C3×C22⋊C411yescharacteristic
350C22×C5C3×C4×D412yes—
351C2×D5—21no—
352C2×D5—41no—
353C2×D5—41no—
354C2×D5—41no—
355C2×D5—41no—
356C2×D5—82no—
357C4×C5—21no—
358C4×C5—41no—
359Dic5—21no—
360Dic5—41no—
361Dic5C3×#12011yescharacteristic
362Dic5C3×#12112yes—
363Dic5C3×#12311yescharacteristic
364C24—51no—
365C24C2×C3×AGL(1,𝔽5)11yescharacteristic
366#41—102no—
367#41—102no—
368C2×Q8—51no—
369C2×D4—21no—
370C2×D4—51no—
371C2×D4—51no—
372C2×D4—101no—
373C2×D4—102no—
374C2×D4—101no—
375C2×D4—101no—
376C2×D4—102no—
377C2×D4—101no—
378C2×D4—101no—
379C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
380C22×C4—51no—
381C22×C4—51no—
382C22×C4—51no—
383M16—54no—
384M16—102no—
385M16—102no—
386M16—102no—
387M16—102no—
388M16—102no—
389C2×C8—102no—
390C2×C8—102no—
391C2×C8—102no—
392C2×C8—102no—
393C4⋊C4—101no—
394C22⋊C4—21no—
395C22⋊C4—51no—
396C22⋊C4—101no—
397C22⋊C4—101no—
398C22⋊C4—101no—
399C22⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
400C42—101no—
401C3×C5#191411yescharacteristic, complemented, Hall
402C22×C3—21no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—82no—
409C22×C3—101no—
410C22×C3—201no—
411C22×C3—201no—
412C22×C3—201no—
413C22×C3—201no—
414C22×C3—402no—
415C22×C3D4×AGL(1,𝔽5)12yes—
416C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
417C3×C4—21no—
418C3×C4—41no—
419C3×C4—51no—
420C3×C4—52no—
421C3×C4—51no—
422C3×C4—101no—
423C3×C4—201no—
424C2×C5—21no—
425C2×C5—22no—
426C2×C5—41no—
427C2×C5—81no—
428C2×C5C3×#38611yescharacteristic
429D5—41no—
430D5—81no—
431C23—21no—
432C23—22no—
433C23—51no—
434C23—81no—
435C23—101no—
436C23—102no—
437C23—401no—
438C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
439C23C22×C3×AGL(1,𝔽5)11yescharacteristic
440Q8—102no—
441D4—22no—
442D4—81no—
443D4—102no—
444D4—102no—
445D4—201no—
446D4—202no—
447D4—201no—
448D4—401no—
449D4—401no—
450D4—401no—
451C2×C4—21no—
452C2×C4—52no—
453C2×C4—52no—
454C2×C4—51no—
455C2×C4—51no—
456C2×C4—51no—
457C2×C4—101no—
458C2×C4—101no—
459C2×C4—101no—
460C2×C4—101no—
461C2×C4—101no—
462C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
463C8—104no—
464C8—202no—
465C2×C3—21no—
466C2×C3—22no—
467C2×C3—41no—
468C2×C3—81no—
469C2×C3—201no—
470C2×C3—401no—
471C2×C3#6577911yescharacteristic
472C5C3×#191411yescharacteristic, complemented, Sylow
473C22—21no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—82no—
480C22—101no—
481C22—201no—
482C22—201no—
483C22—201no—
484C22—201no—
485C22—402no—
486C22C3×D4×AGL(1,𝔽5)12yes—
487C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
488C4—21no—
489C4—41no—
490C4—51no—
491C4—52no—
492C4—51no—
493C4—101no—
494C4—201no—
495C3#1060446411yescharacteristic, direct product factor, Sylow
496C2—21no—
497C2—22no—
498C2—41no—
499C2—81no—
500C2—201no—
501C2—401no—
502C2C3×#6577911yescharacteristic
subgroupG/H
centerC2×C3#65779
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC3×C5×#120C4
socleC2×C3×C5#386
prime radicalC3×#65926C2
cosocleC22×Dic5C23×C3
hypercenterC3×#120AGL(1,𝔽5)
hypocenterC5C3×#1914
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C3×#120

Complements

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

NH ≅ G/Ntype
1. C3×#66256C2semidirect
3. C2×C3×#4013C2semidirect
4. C3×#65777C2semidirect
5. C3×#64867C2semidirect
6. #10604464C3direct (N × H)
27. #66256C2×C3semidirect
29. C2×#4013C2×C3semidirect
30. #65777C2×C3semidirect
31. #64867C2×C3semidirect
55. C3×#704D4semidirect
170. #704C3×D4semidirect
401. C3×C5#1914semidirect
472. C5C3×#1914semidirect
495. C3#10604464direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#662562
C3×#659262
C2×C3×#40132
C3×#657772
C3×#648672
#106044643
C3×#19145