Finite Group Databasebeta

← C3×#10605189 #14326687

Subgroups — C3×#10605189 #14326687

Order 1920.

1096 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
1C22×C3×#683C211yesmaximal, characteristic
2C3×C4×C5×C22⋊C4C211yesmaximal, characteristic
3C3×#65501C211yesmaximal, characteristic
4C3×#65231C211yesmaximal, characteristic
5C3×#65231C211yesmaximal, characteristic
6C3×C22⋊C4×Dic5C211yesmaximal, characteristic
7C3×C22⋊C4×Dic5C211yesmaximal, characteristic
8C3×#65222C212yesmaximal, complemented
9C3×C4×#683C212yesmaximal, complemented
10C3×#64944C212yesmaximal, complemented
11C3×#64936C212yesmaximal, complemented
12#10605189C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C3×Dic5C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C2×C3×C5×C22⋊C4C2211yescharacteristic
17C2×C3×C5×C22⋊C4C2211yescharacteristic
18C2×C3×C42×C5C2212yes—
19C2×C3×C22⋊Dic5C2211yescharacteristic
20C2×C3×C22⋊Dic5C2211yescharacteristic
21C2×C3×C4⋊Dic5C2212yes—
22C2×C3×#683C418yescomplemented
23C2×C3×#683C2212yes—
24C2×C3×#683C2212yes—
25C2×C3×#683C2211yescharacteristic
26C2×C3×#683C2211yescharacteristic
27C2×C3×#683C2211yescharacteristic
28C2×C3×#683C2211yescharacteristic
29C2×C3×C4×Dic5C2212yes—
30C2×C3×C4×Dic5C2212yes—
31C3×C5×#95C2212yes—
32C3×#3963C2212yes—
33C3×#3963C2212yes—
34C3×#3963C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2212yes—
37C3×#2345—51nomaximal, Hall
38C22×#683C2×C311yescharacteristic
39C4×C5×C22⋊C4C2×C311yescharacteristic
40#65501C2×C311yescharacteristic
41#65231C2×C311yescharacteristic
42#65231C2×C311yescharacteristic
43C22⋊C4×Dic5C2×C311yescharacteristic
44C22⋊C4×Dic5C2×C311yescharacteristic
45#65222C2×C312yescomplemented
46C4×#683C2×C312yescomplemented
47#64944C2×C312yescomplemented
48#64936C2×C312yescomplemented
49C24×C3×C5C2311yescharacteristic
50C22×C3×C4×C5—42no—
51C22×C3×C4×C5C2×C414yes—
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2312yes—
56C22×C3×Dic5—24no—
57C22×C3×Dic5—42no—
58C22×C3×Dic5C2×C414yes—
59C22×C3×Dic5C2×C414yes—
60C22×C3×Dic5C2312yes—
61C22×C3×Dic5C2312yes—
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2311yescharacteristic
65C22×C3×Dic5C2311yescharacteristic
66C3×C5×C22⋊C4—22no—
67C3×C5×C22⋊C4Q814yes—
68C3×C42×C5—42no—
69C3×C22⋊Dic5—22no—
70C3×C22⋊Dic5—22no—
71C3×C4⋊Dic5—42no—
72C3×#683—24no—
73C3×#683—42no—
74C3×#683C2×C414yes—
75C3×#683C2×C414yes—
76C3×#683C2×C414yes—
77C3×#683C2×C414yes—
78C3×C4×Dic5—24no—
79C3×C4×Dic5—42no—
80C22×C3×C4⋊C4—51no—
81C3×#389—52no—
82C3×#387—52no—
83C3×#387—52no—
84C3×#380—51no—
85C3×#380—51no—
86C3×#380—51no—
87C3×C4×C4⋊C4—52no—
88C3×C4×C22⋊C4—51no—
89C3×C4×C22⋊C4—51no—
90C3×C4×C22⋊C4D511yescharacteristic
91C23×C4×C5C22×C311yescharacteristic
92C23×Dic5C22×C311yescharacteristic
93C23×Dic5C22×C311yescharacteristic
94C2×C5×C22⋊C4C22×C311yescharacteristic
95C2×C5×C22⋊C4C22×C311yescharacteristic
96C2×C42×C5C22×C312yes—
97C2×C22⋊Dic5C22×C311yescharacteristic
98C2×C22⋊Dic5C22×C311yescharacteristic
99C2×C4⋊Dic5C22×C312yes—
100C2×#683C3×C418yescomplemented
101C2×#683C22×C312yes—
102C2×#683C22×C312yes—
103C2×#683C22×C311yescharacteristic
104C2×#683C22×C311yescharacteristic
105C2×#683C22×C311yescharacteristic
106C2×#683C22×C311yescharacteristic
107C2×C4×Dic5C22×C312yes—
108C2×C4×Dic5C22×C312yes—
109C5×#95C22×C312yes—
110#3963C22×C312yes—
111#3963C22×C312yes—
112#3963C22×C312yes—
113#3963C22×C312yes—
114#3963C22×C312yes—
115#2345—51noSylow
116C23×C3×C5—22no—
117C23×C3×C5—22no—
118C23×C3×C5C22×C412yes—
119C23×C3×C5C2×Q812yes—
120C23×C3×C5#4112yes—
121C23×C3×C5C2411yescharacteristic
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—44no—
130C2×C3×C4×C5C22×C412yes—
131C2×C3×C4×C5C22×C412yes—
132C2×C3×C4×C5C2×Q814yes—
133C2×C3×Dic5—22no—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—22no—
136C2×C3×Dic5—28no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5—22no—
139C2×C3×Dic5—22no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—44no—
144C2×C3×Dic5C22×C412yes—
145C2×C3×Dic5C22×C412yes—
146C2×C3×Dic5C22×C412yes—
147C2×C3×Dic5C22×C412yes—
148C2×C3×Dic5#4114yes—
149C23×C3×C4—51no—
150C23×C3×C4—51no—
151C23×C3×C4C2×D511yescharacteristic
152C2×C3×C4⋊C4—58no—
153C2×C3×C4⋊C4—51no—
154C2×C3×C4⋊C4—51no—
155C2×C3×C4⋊C4—51no—
156C2×C3×C4⋊C4—51no—
157C2×C3×C4⋊C4—52no—
158C2×C3×C4⋊C4—52no—
159C2×C3×C4⋊C4—52no—
160C2×C3×C22⋊C4—51no—
161C2×C3×C22⋊C4—51no—
162C2×C3×C22⋊C4C2×D511yescharacteristic
163C2×C3×C22⋊C4C2×D511yescharacteristic
164C2×C3×C42—52no—
165C2×C3×C42—52no—
166C2×C3×C42C2×D512yes—
167C3×#95—52no—
168C3×#95—52no—
169C3×#95—52no—
170C3×#95—52no—
171C3×#95—52no—
172C3×#95C2×D512yes—
173C24×C5C23×C311yescharacteristic
174C22×C4×C5—42no—
175C22×C4×C5C2×C3×C414yes—
176C22×C4×C5C23×C312yes—
177C22×C4×C5C23×C311yescharacteristic
178C22×C4×C5C23×C311yescharacteristic
179C22×C4×C5C23×C312yes—
180C22×Dic5—24no—
181C22×Dic5—42no—
182C22×Dic5C2×C3×C414yes—
183C22×Dic5C2×C3×C414yes—
184C22×Dic5C23×C312yes—
185C22×Dic5C23×C312yes—
186C22×Dic5C23×C311yescharacteristic
187C22×Dic5C23×C311yescharacteristic
188C22×Dic5C23×C311yescharacteristic
189C22×Dic5C23×C311yescharacteristic
190C5×C22⋊C4—22no—
191C5×C22⋊C4C3×Q814yes—
192C42×C5—42no—
193C22⋊Dic5—22no—
194C22⋊Dic5—22no—
195C4⋊Dic5—42no—
196#683—24no—
197#683—42no—
198#683C2×C3×C414yes—
199#683C2×C3×C414yes—
200#683C2×C3×C414yes—
201#683C2×C3×C414yes—
202C4×Dic5—24no—
203C4×Dic5—42no—
204C22×C4⋊C4—51no—
205#389—52no—
206#387—52no—
207#387—52no—
208#380—51no—
209#380—51no—
210#380—51no—
211C4×C4⋊C4—52no—
212C4×C22⋊C4—51no—
213C4×C22⋊C4—51no—
214C4×C22⋊C4C3×D511yescharacteristic
215C22×C3×C5—22no—
216C22×C3×C5—22no—
217C22×C3×C5—24no—
218C22×C3×C5—24no—
219C22×C3×C5C4×Q814yes—
220C22×C3×C5C23×C411yescharacteristic
221C22×C3×C5C22×Q811yescharacteristic
222C22×C3×C5C2×#4111yescharacteristic
223C22×C3×C5C2×#4112yes—
224C22×C3×C5H(5,𝔽2)12yes—
225C3×C4×C5—22no—
226C3×C4×C5—22no—
227C3×C4×C5—24no—
228C3×C4×C5—42no—
229C3×Dic5—22no—
230C3×Dic5—22no—
231C3×Dic5—22no—
232C3×Dic5—42no—
233C3×Dic5—42no—
234C3×Dic5#11714yes—
235C24×C3C22×D511yescharacteristic
236C22×C3×C4—42no—
237C22×C3×C4—51no—
238C22×C3×C4—54no—
239C22×C3×C4—51no—
240C22×C3×C4—51no—
241C22×C3×C4—51no—
242C22×C3×C4—54no—
243C22×C3×C4—52no—
244C22×C3×C4—52no—
245C22×C3×C4—104no—
246C22×C3×C4—202no—
247C22×C3×C4C4×D514yes—
248C22×C3×C4C22×D512yes—
249C22×C3×C4C22×D512yes—
250C22×C3×C4C22×D511yescharacteristic
251C22×C3×C4C22×D511yescharacteristic
252C3×C4⋊C4—54no—
253C3×C4⋊C4—54no—
254C3×C4⋊C4—54no—
255C3×C4⋊C4—54no—
256C3×C4⋊C4—104no—
257C3×C4⋊C4—202no—
258C3×C4⋊C4—202no—
259C3×C22⋊C4—22no—
260C3×C22⋊C4—102no—
261C3×C22⋊C4—102no—
262C3×C22⋊C4Dic1014yes—
263C3×C42—42no—
264C3×C42—104no—
265C3×C42—202no—
266C23×C5—22no—
267C23×C5—22no—
268C23×C5C22×C3×C412yes—
269C23×C5C2×C3×Q812yes—
270C23×C5C3×#4112yes—
271C23×C5C24×C311yescharacteristic
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5—22no—
279C2×C4×C5—44no—
280C2×C4×C5C22×C3×C412yes—
281C2×C4×C5C22×C3×C412yes—
282C2×C4×C5C2×C3×Q814yes—
283C2×Dic5—22no—
284C2×Dic5—22no—
285C2×Dic5—22no—
286C2×Dic5—28no—
287C2×Dic5—22no—
288C2×Dic5—22no—
289C2×Dic5—22no—
290C2×Dic5—22no—
291C2×Dic5—22no—
292C2×Dic5—22no—
293C2×Dic5—44no—
294C2×Dic5C22×C3×C412yes—
295C2×Dic5C22×C3×C412yes—
296C2×Dic5C22×C3×C412yes—
297C2×Dic5C22×C3×C412yes—
298C2×Dic5C3×#4114yes—
299C23×C4—51no—
300C23×C4—51no—
301C23×C4C2×C3×D511yescharacteristic
302C2×C4⋊C4—58no—
303C2×C4⋊C4—51no—
304C2×C4⋊C4—51no—
305C2×C4⋊C4—51no—
306C2×C4⋊C4—51no—
307C2×C4⋊C4—52no—
308C2×C4⋊C4—52no—
309C2×C4⋊C4—52no—
310C2×C22⋊C4—51no—
311C2×C22⋊C4—51no—
312C2×C22⋊C4C2×C3×D511yescharacteristic
313C2×C22⋊C4C2×C3×D511yescharacteristic
314C2×C42—52no—
315C2×C42—52no—
316C2×C42C2×C3×D512yes—
317#95—52no—
318#95—52no—
319#95—52no—
320#95—52no—
321#95—52no—
322#95C2×C3×D512yes—
323C2×C3×C5—24no—
324C2×C3×C5C2×#11711yescharacteristic
325C2×C3×C5C2×C4×Q811yescharacteristic
326C2×C3×C5#51811yescharacteristic
327C2×C3×C5#55312yes—
328C2×C3×C5#55412yes—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3C2×Dic1012yes—
332C23×C3C2×C4×D512yes—
333C23×C3#70912yes—
334C23×C3C23×D511yescharacteristic
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—44no—
343C2×C3×C4—52no—
344C2×C3×C4—54no—
345C2×C3×C4—52no—
346C2×C3×C4—52no—
347C2×C3×C4—52no—
348C2×C3×C4—108no—
349C2×C3×C4—102no—
350C2×C3×C4—102no—
351C2×C3×C4—102no—
352C2×C3×C4—102no—
353C2×C3×C4—102no—
354C2×C3×C4—102no—
355C2×C3×C4—102no—
356C2×C3×C4—102no—
357C2×C3×C4—102no—
358C2×C3×C4—204no—
359C2×C3×C4C2×Dic1014yes—
360C2×C3×C4C2×C4×D512yes—
361C2×C3×C4C2×C4×D512yes—
362C22×C5—22no—
363C22×C5—22no—
364C22×C5—24no—
365C22×C5—24no—
366C22×C5C3×C4×Q814yes—
367C22×C5C23×C3×C411yescharacteristic
368C22×C5C22×C3×Q811yescharacteristic
369C22×C5C2×C3×#4111yescharacteristic
370C22×C5C2×C3×#4112yes—
371C22×C5C3×H(5,𝔽2)12yes—
372C4×C5—22no—
373C4×C5—22no—
374C4×C5—24no—
375C4×C5—42no—
376Dic5—22no—
377Dic5—22no—
378Dic5—22no—
379Dic5—42no—
380Dic5—42no—
381Dic5C3×#11714yes—
382C24C22×C3×D511yescharacteristic
383C22×C4—42no—
384C22×C4—51no—
385C22×C4—54no—
386C22×C4—51no—
387C22×C4—51no—
388C22×C4—51no—
389C22×C4—54no—
390C22×C4—52no—
391C22×C4—52no—
392C22×C4—104no—
393C22×C4—202no—
394C22×C4C3×C4×D514yes—
395C22×C4C22×C3×D512yes—
396C22×C4C22×C3×D512yes—
397C22×C4C22×C3×D511yescharacteristic
398C22×C4C22×C3×D511yescharacteristic
399C4⋊C4—54no—
400C4⋊C4—54no—
401C4⋊C4—54no—
402C4⋊C4—54no—
403C4⋊C4—104no—
404C4⋊C4—202no—
405C4⋊C4—202no—
406C22⋊C4—22no—
407C22⋊C4—102no—
408C22⋊C4—102no—
409C22⋊C4C3×Dic1014yes—
410C42—42no—
411C42—104no—
412C42—202no—
413C3×C5#234511yescharacteristic, complemented, Hall
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—24no—
417C22×C3—24no—
418C22×C3C4×Dic1014yes—
419C22×C3C22×Dic1011yescharacteristic
420C22×C3C22×C4×D511yescharacteristic
421C22×C3C2×#70911yescharacteristic
422C22×C3#414412yes—
423C22×C3D5×#4112yes—
424C3×C4—22no—
425C3×C4—22no—
426C3×C4—24no—
427C3×C4—42no—
428C3×C4—54no—
429C3×C4—102no—
430C3×C4—102no—
431C3×C4—102no—
432C3×C4—202no—
433C3×C4—202no—
434C2×C5—24no—
435C2×C5C2×C3×#11711yescharacteristic
436C2×C5C2×C3×C4×Q811yescharacteristic
437C2×C5C3×#51811yescharacteristic
438C2×C5C3×#55312yes—
439C2×C5C3×#55412yes—
440C23—22no—
441C23—22no—
442C23C2×C3×Dic1012yes—
443C23C2×C3×C4×D512yes—
444C23C3×#70912yes—
445C23C23×C3×D511yescharacteristic
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—44no—
454C2×C4—52no—
455C2×C4—54no—
456C2×C4—52no—
457C2×C4—52no—
458C2×C4—52no—
459C2×C4—108no—
460C2×C4—102no—
461C2×C4—102no—
462C2×C4—102no—
463C2×C4—102no—
464C2×C4—102no—
465C2×C4—102no—
466C2×C4—102no—
467C2×C4—102no—
468C2×C4—102no—
469C2×C4—204no—
470C2×C4C2×C3×Dic1014yes—
471C2×C4C2×C3×C4×D512yes—
472C2×C4C2×C3×C4×D512yes—
473C2×C3—24no—
474C2×C3C2×C4×Dic1011yescharacteristic
475C2×C3#6582011yescharacteristic
476C2×C3D5×#11711yescharacteristic
477C2×C3#6587312yes—
478C2×C3#6587412yes—
479C5C3×#234511yescharacteristic, complemented, Sylow
480C22—22no—
481C22—24no—
482C22—24no—
483C22—22no—
484C22C3×C4×Dic1014yes—
485C22C22×C3×Dic1011yescharacteristic
486C22C22×C3×C4×D511yescharacteristic
487C22C2×C3×#70911yescharacteristic
488C22C3×#414412yes—
489C22C3×D5×#4112yes—
490C4—24no—
491C4—22no—
492C4—22no—
493C4—42no—
494C4—54no—
495C4—102no—
496C4—102no—
497C4—102no—
498C4—202no—
499C4—202no—
500C3#1060518911yescharacteristic, direct product factor, Sylow
501C2—24no—
502C2C2×C3×C4×Dic1011yescharacteristic
503C2C3×#6582011yescharacteristic
504C2C3×D5×#11711yescharacteristic
505C2C3×#6587312yes—
506C2C3×#6587412yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C5C24×C3
hypercenterC3×C4×C22⋊C4D5
hypocenterC5C3×#2345
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C3×#65222C2semidirect
9. C3×C4×#683C2semidirect
10. C3×#64944C2semidirect
11. C3×#64936C2semidirect
12. #10605189C3direct (N × H)
22. C2×C3×#683C4semidirect
45. #65222C2×C3semidirect
46. C4×#683C2×C3semidirect
47. #64944C2×C3semidirect
48. #64936C2×C3semidirect
100. C2×#683C3×C4semidirect
413. C3×C5#2345semidirect
479. C5C3×#2345semidirect
500. C3#10605189direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6832
C3×C4×C5×C22⋊C42
C3×#655012
C3×#652312
C3×C22⋊C4×Dic52
C3×#652222
C3×C4×#6832
C3×#649442
C3×#649362
#106051893
C3×#23455