Finite Group Databasebeta

← C3×#10606395 #14323547

Subgroups — C3×#10606395 #14323547

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4081C211yesmaximal, characteristic
2C2×C3×D4×Dic5C211yesmaximal, characteristic
3C22×C3×#683C211yesmaximal, characteristic, complemented
4C3×C5×#386C211yesmaximal, characteristic
5C3×#65499C211yesmaximal, characteristic, complemented
6C3×#65235C212yesmaximal, complemented
7C3×#65233C212yesmaximal, complemented
8C3×#65232C211yesmaximal, characteristic, complemented
9C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
10C3×#64941C212yesmaximal, complemented
11C3×#64936C212yesmaximal, complemented
12#10606395C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C23×C3×Dic5C2211yescharacteristic
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2212yes—
20C2×C3×C22⋊Dic5C2211yescharacteristic
21C2×C3×C22⋊Dic5C2211yescharacteristic
22C2×C3×C22⋊Dic5C2211yescharacteristic
23C2×C3×C22⋊Dic5C2212yes—
24C3×#4081C418yescomplemented
25C3×D4×Dic5—24no—
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×C3×#683—24no—
28C2×C3×#683C2212yes—
29C2×C3×#683C2212yes—
30C2×C3×#683C2212yes—
31C2×C3×#683C2212yes—
32C2×C3×C4×Dic5C2211yescharacteristic
33C2×C3×C4×Dic5C2212yes—
34C3×C5×#95C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#2322—51nomaximal, Hall
40C2×#4081C2×C311yescharacteristic
41C2×D4×Dic5C2×C311yescharacteristic
42C22×#683C2×C311yescharacteristic, complemented
43C5×#386C2×C311yescharacteristic
44#65499C2×C311yescharacteristic, complemented
45#65235C2×C312yescomplemented
46#65233C2×C312yescomplemented
47#65232C2×C311yescharacteristic, complemented
48C22⋊C4×Dic5C2×C311yescharacteristic, complemented
49#64941C2×C312yescomplemented
50#64936C2×C312yescomplemented
51C24×C3×C5C2311yescharacteristic
52C24×C3×C5C2311yescharacteristic
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4C2×C414yes—
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—42no—
58C22×C3×C4×C5C2312yes—
59C22×C3×C4×C5C2312yes—
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×Dic5—22no—
62C22×C3×Dic5—22no—
63C22×C3×Dic5—22no—
64C22×C3×Dic5—42no—
65C22×C3×Dic5—42no—
66C22×C3×Dic5C2×C414yescomplemented
67C22×C3×Dic5D414yes—
68C22×C3×Dic5C2311yescharacteristic
69C22×C3×Dic5C2311yescharacteristic
70C22×C3×Dic5C2312yes—
71C22×C3×Dic5C2312yes—
72C22×C3×Dic5C2311yescharacteristic
73C22×C3×Dic5C2311yescharacteristic
74C3×C5×C22⋊C4—22no—
75C3×C5×C22⋊C4—42no—
76C3×C22⋊Dic5—22no—
77C3×C22⋊Dic5—22no—
78C3×C22⋊Dic5C2×C414yescomplemented
79C3×C22⋊Dic5C2×C418yescomplemented
80C3×C4⋊Dic5—22no—
81C3×#683—24no—
82C3×#683—24no—
83C3×#683—42no—
84C3×#683C2×C418yescomplemented
85C3×C4×Dic5—22no—
86C3×C4×Dic5—42no—
87C2×C3×#123—51no—
88C2×C3×C4×D4—51no—
89C22×C3×C4⋊C4—51no—
90C3×#389—52no—
91C3×#388—52no—
92C3×#387—52no—
93C3×#386D511yescharacteristic
94C3×#385—51no—
95C3×#385—52no—
96C3×#381—51no—
97C3×C4×C22⋊C4—51no—
98C22×C5×D4C22×C311yescharacteristic
99C23×C4×C5C22×C311yescharacteristic
100C23×Dic5C22×C311yescharacteristic
101C23×Dic5C22×C311yescharacteristic
102C23×Dic5C22×C311yescharacteristic
103C2×C5×C22⋊C4C22×C311yescharacteristic
104C2×C5×C22⋊C4C22×C312yes—
105C2×C22⋊Dic5C22×C311yescharacteristic
106C2×C22⋊Dic5C22×C311yescharacteristic
107C2×C22⋊Dic5C22×C311yescharacteristic
108C2×C22⋊Dic5C22×C312yes—
109#4081C3×C418yescomplemented
110D4×Dic5—24no—
111C2×C4⋊Dic5C22×C311yescharacteristic
112C2×#683—24no—
113C2×#683C22×C312yes—
114C2×#683C22×C312yes—
115C2×#683C22×C312yes—
116C2×#683C22×C312yes—
117C2×C4×Dic5C22×C311yescharacteristic
118C2×C4×Dic5C22×C312yes—
119C5×#95C22×C312yes—
120#3963C22×C312yes—
121#3963C22×C312yes—
122#3963C22×C312yes—
123#3963C22×C312yes—
124#2322—51noSylow
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—21no—
128C23×C3×C5—21no—
129C23×C3×C5—22no—
130C23×C3×C5—22no—
131C23×C3×C5C22×C412yes—
132C23×C3×C5C22×C412yes—
133C23×C3×C5C2×D412yes—
134C23×C3×C5#4112yes—
135C23×C3×C5C2411yescharacteristic
136C3×C5×D4—28no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—44no—
146C2×C3×C4×C5C22×C412yes—
147C2×C3×Dic5—28no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—44no—
159C2×C3×Dic5—44no—
160C2×C3×Dic5C22×C414yes—
161C2×C3×Dic5C22×C414yes—
162C2×C3×Dic5C2×D412yes—
163C2×C3×Dic5C2×D412yes—
164C22×C3×D4C2×D511yescharacteristic
165C23×C3×C4—51no—
166C23×C3×C4—51no—
167C23×C3×C4—51no—
168C23×C3×C4C2×D511yescharacteristic
169C3×#123—58no—
170C3×C4×D4—104no—
171C2×C3×C4⋊C4—52no—
172C2×C3×C4⋊C4—52no—
173C2×C3×C4⋊C4—52no—
174C2×C3×C4⋊C4—51no—
175C2×C3×C4⋊C4—52no—
176C2×C3×C4⋊C4—104no—
177C2×C3×C22⋊C4—51no—
178C2×C3×C22⋊C4—52no—
179C2×C3×C22⋊C4—51no—
180C2×C3×C22⋊C4—51no—
181C2×C3×C22⋊C4C2×D511yescharacteristic
182C2×C3×C22⋊C4C2×D512yes—
183C2×C3×C42—51no—
184C2×C3×C42—52no—
185C3×#95—52no—
186C3×#95—52no—
187C3×#95—52no—
188C3×#95—52no—
189C3×#95C2×D512yes—
190C24×C5C23×C311yescharacteristic
191C24×C5C23×C311yescharacteristic
192C2×C5×D4—22no—
193C2×C5×D4—22no—
194C2×C5×D4C2×C3×C414yes—
195C22×C4×C5—22no—
196C22×C4×C5—42no—
197C22×C4×C5C23×C312yes—
198C22×C4×C5C23×C312yes—
199C22×C4×C5C23×C311yescharacteristic
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—42no—
204C22×Dic5—42no—
205C22×Dic5C2×C3×C414yescomplemented
206C22×Dic5C3×D414yes—
207C22×Dic5C23×C311yescharacteristic
208C22×Dic5C23×C311yescharacteristic
209C22×Dic5C23×C312yes—
210C22×Dic5C23×C312yes—
211C22×Dic5C23×C311yescharacteristic
212C22×Dic5C23×C311yescharacteristic
213C5×C22⋊C4—22no—
214C5×C22⋊C4—42no—
215C22⋊Dic5—22no—
216C22⋊Dic5—22no—
217C22⋊Dic5C2×C3×C414yescomplemented
218C22⋊Dic5C2×C3×C418yescomplemented
219C4⋊Dic5—22no—
220#683—24no—
221#683—24no—
222#683—42no—
223#683C2×C3×C418yescomplemented
224C4×Dic5—22no—
225C4×Dic5—42no—
226C2×#123—51no—
227C2×C4×D4—51no—
228C22×C4⋊C4—51no—
229#389—52no—
230#388—52no—
231#387—52no—
232#386C3×D511yescharacteristic
233#385—51no—
234#385—52no—
235#381—51no—
236C4×C22⋊C4—51no—
237C22×C3×C5—24no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—24no—
241C22×C3×C5—22no—
242C22×C3×C5—24no—
243C22×C3×C5—41no—
244C22×C3×C5—41no—
245C22×C3×C5—42no—
246C22×C3×C5C4×D414yes—
247C22×C3×C5C23×C411yescharacteristic
248C22×C3×C5C22×D411yescharacteristic
249C22×C3×C5C2×#4111yescharacteristic
250C22×C3×C5H(5,𝔽2)12yes—
251C22×C3×C52−1+412yes—
252C3×C4×C5—22no—
253C3×C4×C5—42no—
254C3×C4×C5—42no—
255C3×Dic5—24no—
256C3×Dic5—24no—
257C3×Dic5—22no—
258C3×Dic5—22no—
259C3×Dic5—41no—
260C3×Dic5—41no—
261C24×C3C22×D511yescharacteristic
262C24×C3C22×D511yescharacteristic
263C2×C3×D4—22no—
264C2×C3×D4—22no—
265C2×C3×D4C4×D514yes—
266C22×C3×C4—22no—
267C22×C3×C4—42no—
268C22×C3×C4—54no—
269C22×C3×C4—52no—
270C22×C3×C4—51no—
271C22×C3×C4—52no—
272C22×C3×C4—51no—
273C22×C3×C4—54no—
274C22×C3×C4—51no—
275C22×C3×C4—51no—
276C22×C3×C4—102no—
277C22×C3×C4—102no—
278C22×C3×C4—102no—
279C22×C3×C4—202no—
280C22×C3×C4—202no—
281C22×C3×C4C22×D512yes—
282C22×C3×C4C22×D512yes—
283C22×C3×C4C22×D511yescharacteristic
284C3×C4⋊C4—58no—
285C3×C4⋊C4—104no—
286C3×C4⋊C4—104no—
287C3×C4⋊C4—102no—
288C3×C4⋊C4—202no—
289C3×C22⋊C4—22no—
290C3×C22⋊C4—42no—
291C3×C22⋊C4—54no—
292C3×C22⋊C4—58no—
293C3×C22⋊C4—102no—
294C3×C22⋊C4—102no—
295C3×C42—102no—
296C3×C42—202no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—22no—
302C23×C5—22no—
303C23×C5C22×C3×C412yes—
304C23×C5C22×C3×C412yes—
305C23×C5C2×C3×D412yes—
306C23×C5C3×#4112yes—
307C23×C5C24×C311yescharacteristic
308C5×D4—28no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—44no—
318C2×C4×C5C22×C3×C412yes—
319C2×Dic5—28no—
320C2×Dic5—22no—
321C2×Dic5—22no—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—22no—
325C2×Dic5—22no—
326C2×Dic5—21no—
327C2×Dic5—21no—
328C2×Dic5—22no—
329C2×Dic5—22no—
330C2×Dic5—44no—
331C2×Dic5—44no—
332C2×Dic5C22×C3×C414yes—
333C2×Dic5C22×C3×C414yes—
334C2×Dic5C2×C3×D412yes—
335C2×Dic5C2×C3×D412yes—
336C22×D4C2×C3×D511yescharacteristic
337C23×C4—51no—
338C23×C4—51no—
339C23×C4—51no—
340C23×C4C2×C3×D511yescharacteristic
341#123—58no—
342C4×D4—104no—
343C2×C4⋊C4—52no—
344C2×C4⋊C4—52no—
345C2×C4⋊C4—52no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4—52no—
348C2×C4⋊C4—104no—
349C2×C22⋊C4—51no—
350C2×C22⋊C4—52no—
351C2×C22⋊C4—51no—
352C2×C22⋊C4—51no—
353C2×C22⋊C4C2×C3×D511yescharacteristic
354C2×C22⋊C4C2×C3×D512yes—
355C2×C42—51no—
356C2×C42—52no—
357#95—52no—
358#95—52no—
359#95—52no—
360#95—52no—
361#95C2×C3×D512yes—
362C2×C3×C5—24no—
363C2×C3×C5—42no—
364C2×C3×C5C2×C4×D411yescharacteristic
365C2×C3×C5#52012yes—
366C2×C3×C5#53411yescharacteristic
367C2×C3×C5#53611yescharacteristic
368C2×C3×C5#53912yes—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3C2×C4×D512yes—
376C23×C3C2×C4×D512yes—
377C23×C3D4×D512yes—
378C23×C3#71112yes—
379C23×C3C23×D511yescharacteristic
380C3×D4—28no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—44no—
390C2×C3×C4—54no—
391C2×C3×C4—54no—
392C2×C3×C4—52no—
393C2×C3×C4—52no—
394C2×C3×C4—102no—
395C2×C3×C4—102no—
396C2×C3×C4—102no—
397C2×C3×C4—102no—
398C2×C3×C4—102no—
399C2×C3×C4—102no—
400C2×C3×C4—108no—
401C2×C3×C4—101no—
402C2×C3×C4—101no—
403C2×C3×C4—102no—
404C2×C3×C4—102no—
405C2×C3×C4—204no—
406C2×C3×C4—204no—
407C2×C3×C4C2×C4×D512yes—
408C22×C5—24no—
409C22×C5—22no—
410C22×C5—22no—
411C22×C5—24no—
412C22×C5—22no—
413C22×C5—24no—
414C22×C5—41no—
415C22×C5—41no—
416C22×C5—42no—
417C22×C5C3×C4×D414yes—
418C22×C5C23×C3×C411yescharacteristic
419C22×C5C22×C3×D411yescharacteristic
420C22×C5C2×C3×#4111yescharacteristic
421C22×C5C3×H(5,𝔽2)12yes—
422C22×C5C3×2−1+412yes—
423C4×C5—22no—
424C4×C5—42no—
425C4×C5—42no—
426Dic5—24no—
427Dic5—24no—
428Dic5—22no—
429Dic5—22no—
430Dic5—41no—
431Dic5—41no—
432C24C22×C3×D511yescharacteristic
433C24C22×C3×D511yescharacteristic
434C2×D4—22no—
435C2×D4—22no—
436C2×D4C3×C4×D514yes—
437C22×C4—22no—
438C22×C4—42no—
439C22×C4—54no—
440C22×C4—52no—
441C22×C4—51no—
442C22×C4—52no—
443C22×C4—51no—
444C22×C4—54no—
445C22×C4—51no—
446C22×C4—51no—
447C22×C4—102no—
448C22×C4—102no—
449C22×C4—102no—
450C22×C4—202no—
451C22×C4—202no—
452C22×C4C22×C3×D512yes—
453C22×C4C22×C3×D512yes—
454C22×C4C22×C3×D511yescharacteristic
455C4⋊C4—58no—
456C4⋊C4—104no—
457C4⋊C4—104no—
458C4⋊C4—102no—
459C4⋊C4—202no—
460C22⋊C4—22no—
461C22⋊C4—42no—
462C22⋊C4—54no—
463C22⋊C4—58no—
464C22⋊C4—102no—
465C22⋊C4—102no—
466C42—102no—
467C42—202no—
468C3×C5#232211yescharacteristic, complemented, Hall
469C22×C3—24no—
470C22×C3—22no—
471C22×C3—24no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—24no—
475C22×C3—41no—
476C22×C3—42no—
477C22×C3—41no—
478C22×C3#402714yes—
479C22×C3C22×C4×D511yescharacteristic
480C22×C3C2×D4×D511yescharacteristic
481C22×C3C2×#71111yescharacteristic
482C22×C3#414412yes—
483C22×C3#415012yes—
484C3×C4—22no—
485C3×C4—42no—
486C3×C4—42no—
487C3×C4—104no—
488C3×C4—104no—
489C3×C4—102no—
490C3×C4—102no—
491C3×C4—201no—
492C3×C4—201no—
493C2×C5—24no—
494C2×C5—42no—
495C2×C5C2×C3×C4×D411yescharacteristic
496C2×C5C3×#52012yes—
497C2×C5C3×#53411yescharacteristic
498C2×C5C3×#53611yescharacteristic
499C2×C5C3×#53912yes—
500C23—22no—
501C23—22no—
502C23—21no—
503C23—21no—
504C23—22no—
505C23—22no—
506C23C2×C3×C4×D512yes—
507C23C2×C3×C4×D512yes—
508C23C3×D4×D512yes—
509C23C3×#71112yes—
510C23C23×C3×D511yescharacteristic
511D4—28no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—44no—
521C2×C4—54no—
522C2×C4—54no—
523C2×C4—52no—
524C2×C4—52no—
525C2×C4—102no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—108no—
532C2×C4—101no—
533C2×C4—101no—
534C2×C4—102no—
535C2×C4—102no—
536C2×C4—204no—
537C2×C4—204no—
538C2×C4C2×C3×C4×D512yes—
539C2×C3—24no—
540C2×C3—42no—
541C2×C3C2×#402711yescharacteristic
542C2×C3#6588012yes—
543C2×C3#6592311yescharacteristic
544C2×C3#6593612yes—
545C2×C3#6598211yescharacteristic
546C5C3×#232211yescharacteristic, complemented, Sylow
547C22—24no—
548C22—22no—
549C22—24no—
550C22—22no—
551C22—24no—
552C22—22no—
553C22—41no—
554C22—42no—
555C22—41no—
556C22C3×#402714yes—
557C22C22×C3×C4×D511yescharacteristic
558C22C2×C3×D4×D511yescharacteristic
559C22C2×C3×#71111yescharacteristic
560C22C3×#414412yes—
561C22C3×#415012yes—
562C4—22no—
563C4—42no—
564C4—42no—
565C4—104no—
566C4—102no—
567C4—102no—
568C4—104no—
569C4—201no—
570C4—201no—
571C3#1060639511yescharacteristic, direct product factor, Sylow
572C2—24no—
573C2—42no—
574C2C2×C3×#402711yescharacteristic
575C2C3×#6588012yes—
576C2C3×#6592311yescharacteristic
577C2C3×#6593612yes—
578C2C3×#6598211yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#386C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
cosocleC23×C5C24×C3
hypercenterC3×#386D5
hypocenterC5C3×#2322
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
3. C22×C3×#683C2semidirect
5. C3×#65499C2semidirect
6. C3×#65235C2semidirect
7. C3×#65233C2semidirect
8. C3×#65232C2semidirect
9. C3×C22⋊C4×Dic5C2semidirect
10. C3×#64941C2semidirect
11. C3×#64936C2semidirect
12. #10606395C3direct (N × H)
24. C3×#4081C4semidirect
42. C22×#683C2×C3semidirect
44. #65499C2×C3semidirect
45. #65235C2×C3semidirect
46. #65233C2×C3semidirect
47. #65232C2×C3semidirect
48. C22⋊C4×Dic5C2×C3semidirect
49. #64941C2×C3semidirect
50. #64936C2×C3semidirect
66. C22×C3×Dic5C2×C4semidirect
78. C3×C22⋊Dic5C2×C4semidirect
79. C3×C22⋊Dic5C2×C4semidirect
84. C3×#683C2×C4semidirect
109. #4081C3×C4semidirect
205. C22×Dic5C2×C3×C4semidirect
217. C22⋊Dic5C2×C3×C4semidirect
218. C22⋊Dic5C2×C3×C4semidirect
223. #683C2×C3×C4semidirect
468. C3×C5#2322semidirect
546. C5C3×#2322semidirect
571. C3#10606395direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40812
C2×C3×D4×Dic52
C22×C3×#6832
C3×C5×#3862
C3×#654992
C3×#652352
C3×#652332
C3×#652322
C3×C22⋊C4×Dic52
C3×#649412
C3×#649362
#106063953
C3×#23225