Finite Group Databasebeta

← C3×#10605742 #14327101

Subgroups — C3×#10605742 #14327101

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2C2×C3×#4027C212yesmaximal
3C3×C5×#380C211yesmaximal, characteristic, complemented
4C2×C3×#3963C211yesmaximal, characteristic, complemented
5C3×#65278C212yesmaximal, complemented
6C3×#65261C212yesmaximal, complemented
7C3×#65235C212yesmaximal, complemented
8C3×#64956C211yesmaximal, characteristic, complemented
9C3×D5×#95C211yesmaximal, characteristic, complemented
10C3×#64939C211yesmaximal, characteristic, complemented
11C3×#64938C211yesmaximal, characteristic, complemented
12#10605742C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C23×C3×Dic5C2212yes—
16C22×C3×C4×D5C2212yes—
17C22×C3×C4×D5C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2212yes—
19C2×C3×C5×C22⋊C4C2212yes—
20C2×C3×C22⋊Dic5C2211yescharacteristic
21C3×C4×C22⋊D5C418yescomplemented
22C2×C3×#685C2212yes—
23C2×C3×#685C2211yescharacteristic
24C2×C3×#683C2212yes—
25C2×C3×#683C2212yes—
26C2×C3×#683C2212yes—
27C2×C3×#683C2211yescharacteristic
28C2×C3×C4×Dic5C2212yes—
29C2×C3×C4×Dic5C2211yescharacteristic
30C3×#4027—28no—
31C3×C5×#95C2211yescharacteristic
32C3×C5×#95C2211yescharacteristic
33C3×#3963C2211yescharacteristic
34C3×#3963C2211yescharacteristic
35C3×#3963C2212yes—
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38C3×#2349—51nomaximal, Hall
39C2×C4×C22⋊D5C2×C311yescharacteristic
40C2×#4027C2×C312yes—
41C5×#380C2×C311yescharacteristic, complemented
42C2×#3963C2×C311yescharacteristic, complemented
43#65278C2×C312yescomplemented
44#65261C2×C312yescomplemented
45#65235C2×C312yescomplemented
46#64956C2×C311yescharacteristic, complemented
47D5×#95C2×C311yescharacteristic, complemented
48#64939C2×C311yescharacteristic, complemented
49#64938C2×C311yescharacteristic, complemented
50C24×C3×C5C2311yescharacteristic
51C23×C3×D5C2311yescharacteristic
52C22×C3×C4×C5—42no—
53C22×C3×C4×C5C2×C414yescomplemented
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2312yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C2×C3×C22⋊D5C2×C414yes—
59C2×C3×C22⋊D5D414yes—
60C2×C3×C22⋊D5Q814yes—
61C22×C3×Dic5—24no—
62C22×C3×Dic5—24no—
63C22×C3×Dic5—42no—
64C22×C3×Dic5C2312yes—
65C22×C3×Dic5C2311yescharacteristic
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2312yes—
68C22×C3×Dic5C2311yescharacteristic
69C2×C3×C4×D5—24no—
70C2×C3×C4×D5—24no—
71C2×C3×C4×D5—42no—
72C2×C3×C4×D5—42no—
73C2×C3×C4×D5C2×C414yescomplemented
74C3×C5×C4⋊C4—42no—
75C3×C5×C22⋊C4—24no—
76C3×C22⋊Dic5C2×C414yescomplemented
77C3×#685—24no—
78C3×#685C2×C414yescomplemented
79C3×#683—24no—
80C3×#683—24no—
81C3×#683—42no—
82C3×#683C2×C414yescomplemented
83C3×C4×Dic5—24no—
84C3×C4×Dic5C2×C414yescomplemented
85C2×C3×C4×D4—51no—
86C2×C3×C4×D4—52no—
87C3×#389—52no—
88C3×#385—52no—
89C3×#385—52no—
90C3×#382—51no—
91C3×#380—51no—
92C3×#380D511yescharacteristic, complemented
93C3×C4×C4⋊C4—51no—
94C2×C3×#95—51no—
95C2×C3×#95—51no—
96C23×C4×C5C22×C311yescharacteristic
97C22×C22⋊D5C22×C311yescharacteristic
98C23×Dic5C22×C312yes—
99C22×C4×D5C22×C312yes—
100C22×C4×D5C22×C311yescharacteristic
101C2×C5×C4⋊C4C22×C312yes—
102C2×C5×C22⋊C4C22×C312yes—
103C2×C22⋊Dic5C22×C311yescharacteristic
104C4×C22⋊D5C3×C418yescomplemented
105C2×#685C22×C312yes—
106C2×#685C22×C311yescharacteristic
107C2×#683C22×C312yes—
108C2×#683C22×C312yes—
109C2×#683C22×C312yes—
110C2×#683C22×C311yescharacteristic
111C2×C4×Dic5C22×C312yes—
112C2×C4×Dic5C22×C311yescharacteristic
113#4027—28no—
114C5×#95C22×C311yescharacteristic
115C5×#95C22×C311yescharacteristic
116#3963C22×C311yescharacteristic
117#3963C22×C311yescharacteristic
118#3963C22×C312yes—
119#3963C22×C312yes—
120#3963C22×C312yes—
121#2349—51noSylow
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5C22×C412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5C2×Q812yes—
127C23×C3×C5C2411yescharacteristic
128C22×C3×D5—22no—
129C22×C3×D5—22no—
130C22×C3×D5C22×C412yes—
131C22×C3×D5C2×D412yes—
132C22×C3×D5C2×Q812yes—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—44no—
142C2×C3×C4×C5C22×C412yes—
143C2×C3×C4×C5C22×C412yes—
144C3×C22⋊D5C4⋊C4116yescomplemented
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—48no—
153C2×C3×Dic5C22×C412yes—
154C2×C3×Dic5C22×C412yes—
155C2×C3×Dic5C22×C412yes—
156C2×C3×Dic5C2×D412yes—
157C2×C3×Dic5C2×Q812yes—
158C2×C3×Dic5#4114yes—
159C3×C4×D5—44no—
160C3×C4×D5—48no—
161C22×C3×D4—51no—
162C23×C3×C4—51no—
163C23×C3×C4—52no—
164C23×C3×C4—52no—
165C23×C3×C4C2×D511yescharacteristic
166C3×C4×D4—58no—
167C3×C4×D4—108no—
168C2×C3×C4⋊C4—51no—
169C2×C3×C4⋊C4—52no—
170C2×C3×C4⋊C4—52no—
171C2×C3×C4⋊C4—52no—
172C2×C3×C4⋊C4C2×D512yes—
173C2×C3×C22⋊C4—51no—
174C2×C3×C22⋊C4—51no—
175C2×C3×C22⋊C4—52no—
176C2×C3×C22⋊C4C2×D512yes—
177C2×C3×C42—51no—
178C2×C3×C42—52no—
179C3×#95—51no—
180C3×#95—51no—
181C3×#95—52no—
182C3×#95—52no—
183C3×#95—52no—
184C3×#95C2×D511yescharacteristic
185C3×#95C2×D511yescharacteristic
186C24×C5C23×C311yescharacteristic
187C23×D5C23×C311yescharacteristic
188C22×C4×C5—42no—
189C22×C4×C5C2×C3×C414yescomplemented
190C22×C4×C5C23×C312yes—
191C22×C4×C5C23×C312yes—
192C22×C4×C5C23×C311yescharacteristic
193C22×C4×C5C23×C311yescharacteristic
194C2×C22⋊D5C2×C3×C414yes—
195C2×C22⋊D5C3×D414yes—
196C2×C22⋊D5C3×Q814yes—
197C22×Dic5—24no—
198C22×Dic5—24no—
199C22×Dic5—42no—
200C22×Dic5C23×C312yes—
201C22×Dic5C23×C311yescharacteristic
202C22×Dic5C23×C311yescharacteristic
203C22×Dic5C23×C312yes—
204C22×Dic5C23×C311yescharacteristic
205C2×C4×D5—24no—
206C2×C4×D5—24no—
207C2×C4×D5—42no—
208C2×C4×D5—42no—
209C2×C4×D5C2×C3×C414yescomplemented
210C5×C4⋊C4—42no—
211C5×C22⋊C4—24no—
212C22⋊Dic5C2×C3×C414yescomplemented
213#685—24no—
214#685C2×C3×C414yescomplemented
215#683—24no—
216#683—24no—
217#683—42no—
218#683C2×C3×C414yescomplemented
219C4×Dic5—24no—
220C4×Dic5C2×C3×C414yescomplemented
221C2×C4×D4—51no—
222C2×C4×D4—52no—
223#389—52no—
224#385—52no—
225#385—52no—
226#382—51no—
227#380—51no—
228#380C3×D511yescharacteristic, complemented
229C4×C4⋊C4—51no—
230C2×#95—51no—
231C2×#95—51no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5—24no—
235C22×C3×C5—24no—
236C22×C3×C5C2×C4⋊C414yes—
237C22×C3×C5C23×C411yescharacteristic
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C22×Q811yescharacteristic
240C22×C3×C5C2×#4112yes—
241C22×C3×C5H(5,𝔽2)12yes—
242C2×C3×D5—22no—
243C2×C3×D5—22no—
244C2×C3×D5—24no—
245C2×C3×D5—24no—
246C2×C3×D5C2×C4⋊C414yes—
247C3×C4×C5—22no—
248C3×C4×C5—22no—
249C3×C4×C5—42no—
250C3×C4×C5—42no—
251C3×Dic5—22no—
252C3×Dic5—22no—
253C3×Dic5—24no—
254C3×Dic5—42no—
255C3×Dic5C2×C4⋊C414yes—
256C24×C3—51no—
257C24×C3C22×D511yescharacteristic
258C2×C3×D4—54no—
259C2×C3×D4—54no—
260C2×C3×D4—54no—
261C22×C3×C4—42no—
262C22×C3×C4—51no—
263C22×C3×C4—52no—
264C22×C3×C4—51no—
265C22×C3×C4—51no—
266C22×C3×C4—54no—
267C22×C3×C4—52no—
268C22×C3×C4—104no—
269C22×C3×C4—104no—
270C22×C3×C4—104no—
271C22×C3×C4—104no—
272C22×C3×C4—202no—
273C22×C3×C4—202no—
274C22×C3×C4—202no—
275C22×C3×C4C4×D514yescomplemented
276C22×C3×C4C22×D512yes—
277C22×C3×C4C22×D512yes—
278C22×C3×C4C22×D511yescharacteristic
279C22×C3×C4C22×D511yescharacteristic
280C3×C4⋊C4—42no—
281C3×C4⋊C4—54no—
282C3×C4⋊C4—104no—
283C3×C4⋊C4—104no—
284C3×C4⋊C4—202no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—54no—
287C3×C22⋊C4—54no—
288C3×C22⋊C4—104no—
289C3×C42—54no—
290C3×C42—104no—
291C23×C5—22no—
292C23×C5—22no—
293C23×C5C22×C3×C412yes—
294C23×C5C2×C3×D412yes—
295C23×C5C2×C3×Q812yes—
296C23×C5C24×C311yescharacteristic
297C22×D5—22no—
298C22×D5—22no—
299C22×D5C22×C3×C412yes—
300C22×D5C2×C3×D412yes—
301C22×D5C2×C3×Q812yes—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—44no—
311C2×C4×C5C22×C3×C412yes—
312C2×C4×C5C22×C3×C412yes—
313C22⋊D5C3×C4⋊C4116yescomplemented
314C2×Dic5—22no—
315C2×Dic5—22no—
316C2×Dic5—22no—
317C2×Dic5—22no—
318C2×Dic5—22no—
319C2×Dic5—22no—
320C2×Dic5—22no—
321C2×Dic5—48no—
322C2×Dic5C22×C3×C412yes—
323C2×Dic5C22×C3×C412yes—
324C2×Dic5C22×C3×C412yes—
325C2×Dic5C2×C3×D412yes—
326C2×Dic5C2×C3×Q812yes—
327C2×Dic5C3×#4114yes—
328C4×D5—44no—
329C4×D5—48no—
330C22×D4—51no—
331C23×C4—51no—
332C23×C4—52no—
333C23×C4—52no—
334C23×C4C2×C3×D511yescharacteristic
335C4×D4—58no—
336C4×D4—108no—
337C2×C4⋊C4—51no—
338C2×C4⋊C4—52no—
339C2×C4⋊C4—52no—
340C2×C4⋊C4—52no—
341C2×C4⋊C4C2×C3×D512yes—
342C2×C22⋊C4—51no—
343C2×C22⋊C4—51no—
344C2×C22⋊C4—52no—
345C2×C22⋊C4C2×C3×D512yes—
346C2×C42—51no—
347C2×C42—52no—
348#95—51no—
349#95—51no—
350#95—52no—
351#95—52no—
352#95—52no—
353#95C2×C3×D511yescharacteristic
354#95C2×C3×D511yescharacteristic
355C2×C3×C5—24no—
356C2×C3×C5C22×C4⋊C411yescharacteristic
357C2×C3×C5C4×#4111yescharacteristic
358C2×C3×C5#51811yescharacteristic
359C2×C3×C5#54612yes—
360C2×C3×C5#55412yes—
361C3×D5—24no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—52no—
365C23×C3—52no—
366C23×C3—52no—
367C23×C3—102no—
368C23×C3—102no—
369C23×C3C2×C4×D512yes—
370C23×C3D4×D512yes—
371C23×C3Q8×D512yes—
372C23×C3C23×D511yescharacteristic
373C3×D4—516no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—44no—
383C2×C3×C4—52no—
384C2×C3×C4—52no—
385C2×C3×C4—52no—
386C2×C3×C4—52no—
387C2×C3×C4—52no—
388C2×C3×C4—54no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4—102no—
392C2×C3×C4—102no—
393C2×C3×C4—102no—
394C2×C3×C4—102no—
395C2×C3×C4—102no—
396C2×C3×C4—204no—
397C2×C3×C4—208no—
398C2×C3×C4—208no—
399C2×C3×C4C2×C4×D512yes—
400C2×C3×C4C2×C4×D512yes—
401C22×C5—22no—
402C22×C5—22no—
403C22×C5—24no—
404C22×C5—24no—
405C22×C5C2×C3×C4⋊C414yes—
406C22×C5C23×C3×C411yescharacteristic
407C22×C5C22×C3×D411yescharacteristic
408C22×C5C22×C3×Q811yescharacteristic
409C22×C5C2×C3×#4112yes—
410C22×C5C3×H(5,𝔽2)12yes—
411C2×D5—22no—
412C2×D5—22no—
413C2×D5—24no—
414C2×D5—24no—
415C2×D5C2×C3×C4⋊C414yes—
416C4×C5—22no—
417C4×C5—22no—
418C4×C5—42no—
419C4×C5—42no—
420Dic5—22no—
421Dic5—22no—
422Dic5—24no—
423Dic5—42no—
424Dic5C2×C3×C4⋊C414yes—
425C24—51no—
426C24C22×C3×D511yescharacteristic
427C2×D4—54no—
428C2×D4—54no—
429C2×D4—54no—
430C22×C4—42no—
431C22×C4—51no—
432C22×C4—52no—
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—54no—
436C22×C4—52no—
437C22×C4—104no—
438C22×C4—104no—
439C22×C4—104no—
440C22×C4—104no—
441C22×C4—202no—
442C22×C4—202no—
443C22×C4—202no—
444C22×C4C3×C4×D514yescomplemented
445C22×C4C22×C3×D512yes—
446C22×C4C22×C3×D512yes—
447C22×C4C22×C3×D511yescharacteristic
448C22×C4C22×C3×D511yescharacteristic
449C4⋊C4—42no—
450C4⋊C4—54no—
451C4⋊C4—104no—
452C4⋊C4—104no—
453C4⋊C4—202no—
454C22⋊C4—24no—
455C22⋊C4—54no—
456C22⋊C4—54no—
457C22⋊C4—104no—
458C42—54no—
459C42—104no—
460C3×C5#234911yescharacteristic, complemented, Hall
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—24no—
464C22×C3—24no—
465C22×C3—54no—
466C22×C3—102no—
467C22×C3—102no—
468C22×C3—104no—
469C22×C3—104no—
470C22×C3D5×C4⋊C414yes—
471C22×C3C22×C4×D511yescharacteristic
472C22×C3C2×D4×D511yescharacteristic
473C22×C3#414412yes—
474C22×C3C2×Q8×D511yescharacteristic
475C22×C3D5×#4112yes—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—42no—
479C3×C4—42no—
480C3×C4—54no—
481C3×C4—102no—
482C3×C4—102no—
483C3×C4—104no—
484C3×C4—202no—
485C2×C5—24no—
486C2×C5C22×C3×C4⋊C411yescharacteristic
487C2×C5C3×C4×#4111yescharacteristic
488C2×C5C3×#51811yescharacteristic
489C2×C5C3×#54612yes—
490C2×C5C3×#55412yes—
491D5—24no—
492C23—22no—
493C23—22no—
494C23—52no—
495C23—52no—
496C23—52no—
497C23—102no—
498C23—102no—
499C23C2×C3×C4×D512yes—
500C23C3×D4×D512yes—
501C23C3×Q8×D512yes—
502C23C23×C3×D511yescharacteristic
503D4—516no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—44no—
513C2×C4—52no—
514C2×C4—52no—
515C2×C4—52no—
516C2×C4—52no—
517C2×C4—52no—
518C2×C4—54no—
519C2×C4—102no—
520C2×C4—102no—
521C2×C4—102no—
522C2×C4—102no—
523C2×C4—102no—
524C2×C4—102no—
525C2×C4—102no—
526C2×C4—204no—
527C2×C4—208no—
528C2×C4—208no—
529C2×C4C2×C3×C4×D512yes—
530C2×C4C2×C3×C4×D512yes—
531C2×C3—24no—
532C2×C3—104no—
533C2×C3#6582011yescharacteristic
534C2×C3C2×D5×C4⋊C411yescharacteristic
535C2×C3#6585611yescharacteristic
536C2×C3#6594412yes—
537C2×C3#6597012yes—
538C5C3×#234911yescharacteristic, complemented, Sylow
539C22—22no—
540C22—24no—
541C22—24no—
542C22—22no—
543C22—54no—
544C22—102no—
545C22—104no—
546C22—104no—
547C22—102no—
548C22C3×D5×C4⋊C414yes—
549C22C22×C3×C4×D511yescharacteristic
550C22C2×C3×D4×D511yescharacteristic
551C22C3×#414412yes—
552C22C2×C3×Q8×D511yescharacteristic
553C22C3×D5×#4112yes—
554C4—22no—
555C4—22no—
556C4—42no—
557C4—42no—
558C4—54no—
559C4—102no—
560C4—104no—
561C4—102no—
562C4—202no—
563C3#1060574211yescharacteristic, direct product factor, Sylow
564C2—24no—
565C2—104no—
566C2C3×#6582011yescharacteristic
567C2C2×C3×D5×C4⋊C411yescharacteristic
568C2C3×#6585611yescharacteristic
569C2C3×#6594412yes—
570C2C3×#6597012yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#380C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C5C24×C3
hypercenterC3×#380D5
hypocenterC5C3×#2349
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
3. C3×C5×#380C2semidirect
4. C2×C3×#3963C2semidirect
5. C3×#65278C2semidirect
6. C3×#65261C2semidirect
7. C3×#65235C2semidirect
8. C3×#64956C2semidirect
9. C3×D5×#95C2semidirect
10. C3×#64939C2semidirect
11. C3×#64938C2semidirect
12. #10605742C3direct (N × H)
21. C3×C4×C22⋊D5C4semidirect
41. C5×#380C2×C3semidirect
42. C2×#3963C2×C3semidirect
43. #65278C2×C3semidirect
44. #65261C2×C3semidirect
45. #65235C2×C3semidirect
46. #64956C2×C3semidirect
47. D5×#95C2×C3semidirect
48. #64939C2×C3semidirect
49. #64938C2×C3semidirect
53. C22×C3×C4×C5C2×C4semidirect
73. C2×C3×C4×D5C2×C4semidirect
76. C3×C22⋊Dic5C2×C4semidirect
78. C3×#685C2×C4semidirect
82. C3×#683C2×C4semidirect
84. C3×C4×Dic5C2×C4semidirect
92. C3×#380D5semidirect
104. C4×C22⋊D5C3×C4semidirect
144. C3×C22⋊D5C4⋊C4semidirect
189. C22×C4×C5C2×C3×C4semidirect
209. C2×C4×D5C2×C3×C4semidirect
212. C22⋊Dic5C2×C3×C4semidirect
214. #685C2×C3×C4semidirect
218. #683C2×C3×C4semidirect
220. C4×Dic5C2×C3×C4semidirect
228. #380C3×D5semidirect
275. C22×C3×C4C4×D5semidirect
313. C22⋊D5C3×C4⋊C4semidirect
444. C22×C4C3×C4×D5semidirect
460. C3×C5#2349semidirect
538. C5C3×#2349semidirect
563. C3#10605742direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
C2×C3×#40272
C3×C5×#3802
C2×C3×#39632
C3×#652782
C3×#652612
C3×#652352
C3×#649562
C3×D5×#952
C3×#649392
C3×#649382
#106057423
C3×#23495