Finite Group Databasebeta

← C3×#10614126 #14323349

Subgroups — C3×#10614126 #14323349

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
2C2×C3×#4083C211yesmaximal, characteristic
3C22×C3×#685C211yesmaximal, characteristic, complemented
4C3×#65509C211yesmaximal, characteristic, complemented
5C3×#65502C212yesmaximal, complemented
6C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
7C3×#65279C212yesmaximal, complemented
8C3×#65246C212yesmaximal, complemented
9C3×#65244C211yesmaximal, characteristic, complemented
10C3×#65235C211yesmaximal, characteristic, complemented
11C3×#65229C212yesmaximal, complemented
12#10614126C311yesmaximal, characteristic, direct product factor, Hall
13C24×C3×D5C2211yescharacteristic
14C22×C3×C5×D4C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×C4×C5C2211yescharacteristic, complemented
17C22×C3×C22⋊D5C2212yes—
18C23×C3×Dic5C2211yescharacteristic
19C3×C4×C5×D4—24no—
20C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
23C2×C3×C42×C5C2211yescharacteristic, complemented
24C2×C3×C22⋊Dic5C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C2×C3×C22⋊Dic5C2212yescomplemented
27C3×#4083C418yescomplemented
28C2×C3×#685—24no—
29C2×C3×#685C2212yes—
30C2×C3×#685C2212yes—
31C2×C3×#685C2212yes—
32C2×C3×#685C2212yes—
33C2×C3×#685C2212yes—
34C2×C3×#683C2212yescomplemented
35C2×C3×C4×Dic5C2212yescomplemented
36C3×#3963C2212yescomplemented
37C3×#3963C2212yescomplemented
38C3×#3963C2212yescomplemented
39C3×#2321—51nomaximal, Hall
40C2×C4×C5×D4C2×C311yescharacteristic, complemented
41C2×#4083C2×C311yescharacteristic
42C22×#685C2×C311yescharacteristic, complemented
43#65509C2×C311yescharacteristic, complemented
44#65502C2×C312yescomplemented
45C4×C22⋊Dic5C2×C311yescharacteristic, complemented
46#65279C2×C312yescomplemented
47#65246C2×C312yescomplemented
48#65244C2×C311yescharacteristic, complemented
49#65235C2×C311yescharacteristic, complemented
50#65229C2×C312yescomplemented
51C24×C3×C5C2311yescharacteristic
52C24×C3×C5C2311yescharacteristic
53C23×C3×D5—22no—
54C23×C3×D5—22no—
55C23×C3×D5—42no—
56C23×C3×D5—42no—
57C23×C3×D5C2×C414yescomplemented
58C23×C3×D5C2312yes—
59C2×C3×C5×D4—22no—
60C2×C3×C5×D4—22no—
61C2×C3×C5×D4C2×C414yes—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5—42no—
64C22×C3×C4×C5—42no—
65C22×C3×C4×C5D414yescomplemented
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2311yescharacteristic
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C2×C3×C22⋊D5—42no—
72C2×C3×C22⋊D5—42no—
73C2×C3×C22⋊D5C2×C418yescomplemented
74C22×C3×Dic5—22no—
75C22×C3×Dic5—42no—
76C22×C3×Dic5C2312yes—
77C22×C3×Dic5C2312yes—
78C22×C3×Dic5C2312yes—
79C3×C5×C4⋊C4—22no—
80C3×C5×C22⋊C4—22no—
81C3×C5×C22⋊C4—22no—
82C3×C42×C5—22no—
83C3×C22⋊Dic5—22no—
84C3×C22⋊Dic5—42no—
85C3×C22⋊Dic5C2×C414yescomplemented
86C3×#685—24no—
87C3×#685—24no—
88C3×#685—42no—
89C3×#685—42no—
90C3×#685C2×C418yescomplemented
91C3×#683—42no—
92C3×C4×Dic5—42no—
93C2×C3×#120—51no—
94C2×C3×C4×D4D511yescharacteristic, complemented
95C22×C3×C22⋊C4—51no—
96C3×#390—52no—
97C3×#388—52no—
98C3×#388—52no—
99C3×#386—51no—
100C3×#386—52no—
101C3×#385—51no—
102C3×#379—51no—
103C3×C4×C22⋊C4—51no—
104C24×D5C22×C311yescharacteristic
105C22×C5×D4C22×C311yescharacteristic
106C23×C4×C5C22×C311yescharacteristic
107C23×C4×C5C22×C311yescharacteristic, complemented
108C22×C22⋊D5C22×C312yes—
109C23×Dic5C22×C311yescharacteristic
110C4×C5×D4—24no—
111C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
112C2×C5×C22⋊C4C22×C311yescharacteristic
113C2×C5×C22⋊C4C22×C311yescharacteristic, complemented
114C2×C42×C5C22×C311yescharacteristic, complemented
115C2×C22⋊Dic5C22×C311yescharacteristic
116C2×C22⋊Dic5C22×C311yescharacteristic
117C2×C22⋊Dic5C22×C312yescomplemented
118#4083C3×C418yescomplemented
119C2×#685—24no—
120C2×#685C22×C312yes—
121C2×#685C22×C312yes—
122C2×#685C22×C312yes—
123C2×#685C22×C312yes—
124C2×#685C22×C312yes—
125C2×#683C22×C312yescomplemented
126C2×C4×Dic5C22×C312yescomplemented
127#3963C22×C312yescomplemented
128#3963C22×C312yescomplemented
129#3963C22×C312yescomplemented
130#2321—51noSylow
131C23×C3×C5—22no—
132C23×C3×C5—22no—
133C23×C3×C5—21no—
134C23×C3×C5—21no—
135C23×C3×C5—22no—
136C23×C3×C5—22no—
137C23×C3×C5C22×C412yes—
138C23×C3×C5C22×C412yes—
139C23×C3×C5C2×D412yes—
140C23×C3×C5#4112yes—
141C23×C3×C5C2411yescharacteristic
142C22×C3×D5—28no—
143C22×C3×D5—22no—
144C22×C3×D5—22no—
145C22×C3×D5—22no—
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5—22no—
149C22×C3×D5—48no—
150C22×C3×D5—44no—
151C22×C3×D5—44no—
152C22×C3×D5—48no—
153C22×C3×D5C22×C414yes—
154C3×C5×D4—28no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—44no—
164C2×C3×C4×C5—44no—
165C2×C3×C4×C5C22×C412yes—
166C2×C3×C4×C5C2×D412yes—
167C2×C3×C4×C5C2×D412yes—
168C3×C22⋊D5—48no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5—44no—
178C2×C3×Dic5C22×C414yes—
179C25×C3—51no—
180C22×C3×D4—52no—
181C22×C3×D4C2×D511yescharacteristic
182C23×C3×C4—51no—
183C23×C3×C4C2×D511yescharacteristic
184C23×C3×C4C2×D511yescharacteristic, complemented
185C3×#120—58no—
186C3×C4×D4—24no—
187C2×C3×C4⋊C4—52no—
188C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
189C2×C3×C22⋊C4—51no—
190C2×C3×C22⋊C4—52no—
191C2×C3×C22⋊C4—51no—
192C2×C3×C22⋊C4—52no—
193C2×C3×C22⋊C4—52no—
194C2×C3×C22⋊C4—52no—
195C2×C3×C22⋊C4—52no—
196C2×C3×C22⋊C4—52no—
197C2×C3×C22⋊C4—104no—
198C2×C3×C22⋊C4C2×D511yescharacteristic
199C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
200C2×C3×C42—52no—
201C2×C3×C42C2×D511yescharacteristic, complemented
202C3×#95—52no—
203C3×#95—52no—
204C3×#95—52no—
205C24×C5C23×C311yescharacteristic
206C24×C5C23×C311yescharacteristic
207C23×D5—22no—
208C23×D5—22no—
209C23×D5—42no—
210C23×D5—42no—
211C23×D5C2×C3×C414yescomplemented
212C23×D5C23×C312yes—
213C2×C5×D4—22no—
214C2×C5×D4—22no—
215C2×C5×D4C2×C3×C414yes—
216C22×C4×C5—22no—
217C22×C4×C5—42no—
218C22×C4×C5—42no—
219C22×C4×C5C3×D414yescomplemented
220C22×C4×C5C23×C311yescharacteristic
221C22×C4×C5C23×C311yescharacteristic
222C22×C4×C5C23×C311yescharacteristic
223C22×C4×C5C23×C311yescharacteristic
224C22×C4×C5C23×C311yescharacteristic
225C2×C22⋊D5—42no—
226C2×C22⋊D5—42no—
227C2×C22⋊D5C2×C3×C418yescomplemented
228C22×Dic5—22no—
229C22×Dic5—42no—
230C22×Dic5C23×C312yes—
231C22×Dic5C23×C312yes—
232C22×Dic5C23×C312yes—
233C5×C4⋊C4—22no—
234C5×C22⋊C4—22no—
235C5×C22⋊C4—22no—
236C42×C5—22no—
237C22⋊Dic5—22no—
238C22⋊Dic5—42no—
239C22⋊Dic5C2×C3×C414yescomplemented
240#685—24no—
241#685—24no—
242#685—42no—
243#685—42no—
244#685C2×C3×C418yescomplemented
245#683—42no—
246C4×Dic5—42no—
247C2×#120—51no—
248C2×C4×D4C3×D511yescharacteristic, complemented
249C22×C22⋊C4—51no—
250#390—52no—
251#388—52no—
252#388—52no—
253#386—51no—
254#386—52no—
255#385—51no—
256#379—51no—
257C4×C22⋊C4—51no—
258C22×C3×C5—24no—
259C22×C3×C5—22no—
260C22×C3×C5—22no—
261C22×C3×C5—24no—
262C22×C3×C5—22no—
263C22×C3×C5—24no—
264C22×C3×C5—41no—
265C22×C3×C5—41no—
266C22×C3×C5—42no—
267C22×C3×C5C4×D414yes—
268C22×C3×C5C23×C411yescharacteristic
269C22×C3×C5C22×D411yescharacteristic
270C22×C3×C5C2×#4111yescharacteristic
271C22×C3×C5H(5,𝔽2)12yes—
272C22×C3×C5H(5,𝔽2)12yes—
273C2×C3×D5—24no—
274C2×C3×D5—24no—
275C2×C3×D5—24no—
276C2×C3×D5—416no—
277C2×C3×D5—42no—
278C2×C3×D5—42no—
279C2×C3×D5—42no—
280C2×C3×D5—42no—
281C3×C4×C5—22no—
282C3×C4×C5—22no—
283C3×C4×C5—22no—
284C3×C4×C5—41no—
285C3×C4×C5—41no—
286C3×Dic5—24no—
287C3×Dic5—42no—
288C3×Dic5—42no—
289C24×C3—52no—
290C24×C3—54no—
291C24×C3—102no—
292C24×C3—102no—
293C24×C3—202no—
294C24×C3—202no—
295C24×C3C22×D511yescharacteristic
296C24×C3C22×D511yescharacteristic
297C2×C3×D4—22no—
298C2×C3×D4—22no—
299C2×C3×D4—58no—
300C2×C3×D4—202no—
301C2×C3×D4—202no—
302C2×C3×D4C4×D514yes—
303C22×C3×C4—22no—
304C22×C3×C4—42no—
305C22×C3×C4—42no—
306C22×C3×C4—52no—
307C22×C3×C4—52no—
308C22×C3×C4—52no—
309C22×C3×C4—102no—
310C22×C3×C4—202no—
311C22×C3×C4C22⋊D514yescomplemented
312C22×C3×C4C22×D511yescharacteristic
313C22×C3×C4C22×D511yescharacteristic
314C22×C3×C4C22×D511yescharacteristic
315C22×C3×C4C22×D511yescharacteristic
316C22×C3×C4C22×D511yescharacteristic
317C3×C4⋊C4—22no—
318C3×C4⋊C4—202no—
319C3×C22⋊C4—22no—
320C3×C22⋊C4—22no—
321C3×C22⋊C4—54no—
322C3×C22⋊C4—58no—
323C3×C22⋊C4—102no—
324C3×C22⋊C4—104no—
325C3×C22⋊C4—104no—
326C3×C22⋊C4—202no—
327C3×C22⋊C4—202no—
328C3×C22⋊C4—202no—
329C3×C42—22no—
330C3×C42—202no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—21no—
334C23×C5—21no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5C22×C3×C412yes—
338C23×C5C22×C3×C412yes—
339C23×C5C2×C3×D412yes—
340C23×C5C3×#4112yes—
341C23×C5C24×C311yescharacteristic
342C22×D5—28no—
343C22×D5—22no—
344C22×D5—22no—
345C22×D5—22no—
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—48no—
350C22×D5—44no—
351C22×D5—44no—
352C22×D5—48no—
353C22×D5C22×C3×C414yes—
354C5×D4—28no—
355C2×C4×C5—21no—
356C2×C4×C5—21no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—21no—
360C2×C4×C5—21no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—44no—
364C2×C4×C5—44no—
365C2×C4×C5C22×C3×C412yes—
366C2×C4×C5C2×C3×D412yes—
367C2×C4×C5C2×C3×D412yes—
368C22⋊D5—48no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—44no—
378C2×Dic5C22×C3×C414yes—
379C25—51no—
380C22×D4—52no—
381C22×D4C2×C3×D511yescharacteristic
382C23×C4—51no—
383C23×C4C2×C3×D511yescharacteristic
384C23×C4C2×C3×D511yescharacteristic, complemented
385#120—58no—
386C4×D4—24no—
387C2×C4⋊C4—52no—
388C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
389C2×C22⋊C4—51no—
390C2×C22⋊C4—52no—
391C2×C22⋊C4—51no—
392C2×C22⋊C4—52no—
393C2×C22⋊C4—52no—
394C2×C22⋊C4—52no—
395C2×C22⋊C4—52no—
396C2×C22⋊C4—52no—
397C2×C22⋊C4—104no—
398C2×C22⋊C4C2×C3×D511yescharacteristic
399C2×C22⋊C4C2×C3×D511yescharacteristic, complemented
400C2×C42—52no—
401C2×C42C2×C3×D511yescharacteristic, complemented
402#95—52no—
403#95—52no—
404#95—52no—
405C2×C3×C5—24no—
406C2×C3×C5—42no—
407C2×C3×C5C2×C4×D411yescharacteristic
408C2×C3×C5#51812yes—
409C2×C3×C5#53411yescharacteristic
410C2×C3×C5#53511yescharacteristic
411C2×C3×C5#53812yes—
412C3×D5—44no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—21no—
419C23×C3—54no—
420C23×C3—102no—
421C23×C3—102no—
422C23×C3—102no—
423C23×C3—102no—
424C23×C3—102no—
425C23×C3—102no—
426C23×C3—108no—
427C23×C3—208no—
428C23×C3—204no—
429C23×C3—208no—
430C23×C3—204no—
431C23×C3C2×C4×D512yes—
432C23×C3C2×C4×D512yes—
433C23×C3#70912yes—
434C23×C3C2×C22⋊D512yes—
435C23×C3C23×D511yescharacteristic
436C3×D4—28no—
437C3×D4—208no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—44no—
447C2×C3×C4—44no—
448C2×C3×C4—54no—
449C2×C3×C4—102no—
450C2×C3×C4—102no—
451C2×C3×C4—102no—
452C2×C3×C4—102no—
453C2×C3×C4—102no—
454C2×C3×C4—102no—
455C2×C3×C4—102no—
456C2×C3×C4—102no—
457C2×C3×C4—204no—
458C2×C3×C4C2×C4×D512yes—
459C2×C3×C4C2×C22⋊D512yes—
460C2×C3×C4C2×C22⋊D512yes—
461C22×C5—24no—
462C22×C5—22no—
463C22×C5—22no—
464C22×C5—24no—
465C22×C5—22no—
466C22×C5—24no—
467C22×C5—41no—
468C22×C5—41no—
469C22×C5—42no—
470C22×C5C3×C4×D414yes—
471C22×C5C23×C3×C411yescharacteristic
472C22×C5C22×C3×D411yescharacteristic
473C22×C5C2×C3×#4111yescharacteristic
474C22×C5C3×H(5,𝔽2)12yes—
475C22×C5C3×H(5,𝔽2)12yes—
476C2×D5—24no—
477C2×D5—24no—
478C2×D5—24no—
479C2×D5—416no—
480C2×D5—42no—
481C2×D5—42no—
482C2×D5—42no—
483C2×D5—42no—
484C4×C5—22no—
485C4×C5—22no—
486C4×C5—22no—
487C4×C5—41no—
488C4×C5—41no—
489Dic5—24no—
490Dic5—42no—
491Dic5—42no—
492C24—52no—
493C24—54no—
494C24—102no—
495C24—102no—
496C24—202no—
497C24—202no—
498C24C22×C3×D511yescharacteristic
499C24C22×C3×D511yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—58no—
503C2×D4—202no—
504C2×D4—202no—
505C2×D4C3×C4×D514yes—
506C22×C4—22no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—52no—
510C22×C4—52no—
511C22×C4—52no—
512C22×C4—102no—
513C22×C4—202no—
514C22×C4C3×C22⋊D514yescomplemented
515C22×C4C22×C3×D511yescharacteristic
516C22×C4C22×C3×D511yescharacteristic
517C22×C4C22×C3×D511yescharacteristic
518C22×C4C22×C3×D511yescharacteristic
519C22×C4C22×C3×D511yescharacteristic
520C4⋊C4—22no—
521C4⋊C4—202no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—54no—
525C22⋊C4—58no—
526C22⋊C4—102no—
527C22⋊C4—104no—
528C22⋊C4—104no—
529C22⋊C4—202no—
530C22⋊C4—202no—
531C22⋊C4—202no—
532C42—22no—
533C42—202no—
534C3×C5#232111yescharacteristic, complemented, Hall
535C22×C3—24no—
536C22×C3—22no—
537C22×C3—24no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—24no—
541C22×C3—41no—
542C22×C3—42no—
543C22×C3—41no—
544C22×C3—104no—
545C22×C3—104no—
546C22×C3—104no—
547C22×C3—2016no—
548C22×C3—202no—
549C22×C3—202no—
550C22×C3—202no—
551C22×C3—202no—
552C22×C3C4×C22⋊D514yes—
553C22×C3C22×C4×D511yescharacteristic
554C22×C3C2×#70911yescharacteristic
555C22×C3#414412yes—
556C22×C3#414912yes—
557C22×C3C22×C22⋊D511yescharacteristic
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—22no—
561C3×C4—41no—
562C3×C4—41no—
563C3×C4—104no—
564C3×C4—202no—
565C3×C4—202no—
566C2×C5—24no—
567C2×C5—42no—
568C2×C5C2×C3×C4×D411yescharacteristic
569C2×C5C3×#51812yes—
570C2×C5C3×#53411yescharacteristic
571C2×C5C3×#53511yescharacteristic
572C2×C5C3×#53812yes—
573D5—44no—
574C23—22no—
575C23—22no—
576C23—21no—
577C23—22no—
578C23—22no—
579C23—21no—
580C23—54no—
581C23—102no—
582C23—102no—
583C23—102no—
584C23—102no—
585C23—102no—
586C23—102no—
587C23—108no—
588C23—208no—
589C23—204no—
590C23—208no—
591C23—204no—
592C23C2×C3×C4×D512yes—
593C23C2×C3×C4×D512yes—
594C23C3×#70912yes—
595C23C2×C3×C22⋊D512yes—
596C23C23×C3×D511yescharacteristic
597D4—28no—
598D4—208no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—44no—
608C2×C4—44no—
609C2×C4—54no—
610C2×C4—102no—
611C2×C4—102no—
612C2×C4—102no—
613C2×C4—102no—
614C2×C4—102no—
615C2×C4—102no—
616C2×C4—102no—
617C2×C4—102no—
618C2×C4—204no—
619C2×C4C2×C3×C4×D512yes—
620C2×C4C2×C3×C22⋊D512yes—
621C2×C4C2×C3×C22⋊D512yes—
622C2×C3—24no—
623C2×C3—42no—
624C2×C3—204no—
625C2×C3#6587912yes—
626C2×C3#6589412yes—
627C2×C3C2×C4×C22⋊D511yescharacteristic
628C2×C3#6613811yescharacteristic
629C2×C3#6616411yescharacteristic
630C5C3×#232111yescharacteristic, complemented, Sylow
631C22—24no—
632C22—22no—
633C22—24no—
634C22—22no—
635C22—22no—
636C22—24no—
637C22—41no—
638C22—42no—
639C22—41no—
640C22—104no—
641C22—104no—
642C22—104no—
643C22—2016no—
644C22—202no—
645C22—202no—
646C22—202no—
647C22—202no—
648C22C3×C4×C22⋊D514yes—
649C22C22×C3×C4×D511yescharacteristic
650C22C2×C3×#70911yescharacteristic
651C22C3×#414412yes—
652C22C3×#414912yes—
653C22C22×C3×C22⋊D511yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—41no—
658C4—41no—
659C4—104no—
660C4—202no—
661C4—202no—
662C3#1061412611yescharacteristic, direct product factor, Sylow
663C2—24no—
664C2—42no—
665C2—204no—
666C2C3×#6587912yes—
667C2C3×#6589412yes—
668C2C2×C3×C4×C22⋊D511yescharacteristic
669C2C3×#6613811yescharacteristic
670C2C3×#6616411yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC2×C3×#4083C2
cosocleC23×C5C24×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×#2321
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×D4C2semidirect
3. C22×C3×#685C2semidirect
4. C3×#65509C2semidirect
5. C3×#65502C2semidirect
6. C3×C4×C22⋊Dic5C2semidirect
7. C3×#65279C2semidirect
8. C3×#65246C2semidirect
9. C3×#65244C2semidirect
10. C3×#65235C2semidirect
11. C3×#65229C2semidirect
12. #10614126C3direct (N × H)
16. C23×C3×C4×C5C22semidirect
20. C2×C3×C5×C4⋊C4C22semidirect
22. C2×C3×C5×C22⋊C4C22semidirect
23. C2×C3×C42×C5C22semidirect
26. C2×C3×C22⋊Dic5C22semidirect
27. C3×#4083C4semidirect
34. C2×C3×#683C22semidirect
35. C2×C3×C4×Dic5C22semidirect
36. C3×#3963C22semidirect
37. C3×#3963C22semidirect
38. C3×#3963C22semidirect
40. C2×C4×C5×D4C2×C3semidirect
42. C22×#685C2×C3semidirect
43. #65509C2×C3semidirect
44. #65502C2×C3semidirect
45. C4×C22⋊Dic5C2×C3semidirect
46. #65279C2×C3semidirect
47. #65246C2×C3semidirect
48. #65244C2×C3semidirect
49. #65235C2×C3semidirect
50. #65229C2×C3semidirect
57. C23×C3×D5C2×C4semidirect
65. C22×C3×C4×C5D4semidirect
73. C2×C3×C22⋊D5C2×C4semidirect
85. C3×C22⋊Dic5C2×C4semidirect
90. C3×#685C2×C4semidirect
94. C2×C3×C4×D4D5semidirect
107. C23×C4×C5C22×C3semidirect
111. C2×C5×C4⋊C4C22×C3semidirect
113. C2×C5×C22⋊C4C22×C3semidirect
114. C2×C42×C5C22×C3semidirect
117. C2×C22⋊Dic5C22×C3semidirect
118. #4083C3×C4semidirect
125. C2×#683C22×C3semidirect
126. C2×C4×Dic5C22×C3semidirect
127. #3963C22×C3semidirect
128. #3963C22×C3semidirect
129. #3963C22×C3semidirect
184. C23×C3×C4C2×D5semidirect
188. C2×C3×C4⋊C4C2×D5semidirect
199. C2×C3×C22⋊C4C2×D5semidirect
201. C2×C3×C42C2×D5semidirect
211. C23×D5C2×C3×C4semidirect
219. C22×C4×C5C3×D4semidirect
227. C2×C22⋊D5C2×C3×C4semidirect
239. C22⋊Dic5C2×C3×C4semidirect
244. #685C2×C3×C4semidirect
248. C2×C4×D4C3×D5semidirect
311. C22×C3×C4C22⋊D5semidirect
384. C23×C4C2×C3×D5semidirect
388. C2×C4⋊C4C2×C3×D5semidirect
399. C2×C22⋊C4C2×C3×D5semidirect
401. C2×C42C2×C3×D5semidirect
514. C22×C4C3×C22⋊D5semidirect
534. C3×C5#2321semidirect
630. C5C3×#2321semidirect
662. C3#10614126direct (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×C5×D42
C2×C3×#40832
C22×C3×#6852
C3×#655092
C3×#655022
C3×C4×C22⋊Dic52
C3×#652792
C3×#652462
C3×#652442
C3×#652352
C3×#652292
#106141263
C3×#23215