Finite Group Databasebeta

← C3×#10614072 #14329025

Subgroups — C3×#10614072 #14329025

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 648 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×#4084C211yesmaximal, characteristic
3C2×C3×#4038C211yesmaximal, characteristic, complemented
4C3×#65510C211yesmaximal, characteristic, complemented
5C3×#65502C212yesmaximal, complemented
6C3×C4×C22⋊Dic5C212yesmaximal, complemented
7C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
8C3×#65246C212yesmaximal, complemented
9C3×#65233C212yesmaximal, complemented
10C3×C4×#685C211yesmaximal, characteristic, complemented
11C3×#65217C211yesmaximal, characteristic, complemented
12#10614072C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2212yes—
15C22×C3×C22⋊D5C2212yes—
16C22×C3×C4×D5C2211yescharacteristic
17C3×C4×C5×D4—24no—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2212yes—
20C2×C3×C42×C5C2211yescharacteristic
21C2×C3×C22⋊Dic5C2212yes—
22C2×C3×C22⋊Dic5C2212yes—
23C2×C3×C22⋊Dic5C2212yes—
24C3×#4084C418yescomplemented
25C2×C3×#685C2211yescharacteristic
26C2×C3×#685C2211yescharacteristic
27C2×C3×#685C2212yes—
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2212yes—
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×C3×C4×Dic5C2212yes—
33C2×C3×C4×Dic5C2212yes—
34C3×#4038—24no—
35C3×#3963C2212yes—
36C3×#3963C2211yescharacteristic
37C3×#3963C2211yescharacteristic
38C3×#3963C2212yes—
39C3×#2363—51nomaximal, Hall
40C2×C4×C5×D4C2×C311yescharacteristic, complemented
41C2×#4084C2×C311yescharacteristic
42C2×#4038C2×C311yescharacteristic, complemented
43#65510C2×C311yescharacteristic, complemented
44#65502C2×C312yescomplemented
45C4×C22⋊Dic5C2×C312yescomplemented
46C4⋊C4×Dic5C2×C311yescharacteristic, complemented
47#65246C2×C312yescomplemented
48#65233C2×C312yescomplemented
49C4×#685C2×C311yescharacteristic, complemented
50#65217C2×C311yescharacteristic, complemented
51C24×C3×C5C2312yes—
52C23×C3×D5C2311yescharacteristic
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4C2×C414yes—
56C22×C3×C4×C5—24no—
57C22×C3×C4×C5—24no—
58C22×C3×C4×C5—42no—
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×C4×C5C2312yes—
61C22×C3×C4×C5C2311yescharacteristic
62C22×C3×C4×C5C2311yescharacteristic
63C2×C3×C22⋊D5—42no—
64C2×C3×C22⋊D5—42no—
65C2×C3×C22⋊D5C2×C418yescomplemented
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2312yes—
68C22×C3×Dic5C2311yescharacteristic
69C22×C3×Dic5C2312yes—
70C22×C3×Dic5C2311yescharacteristic
71C2×C3×C4×D5—22no—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5C2×C414yescomplemented
74C3×C5×C4⋊C4D414yescomplemented
75C3×C5×C22⋊C4—24no—
76C3×C42×C5—22no—
77C3×C22⋊Dic5—24no—
78C3×C22⋊Dic5—42no—
79C3×C22⋊Dic5C2×C418yescomplemented
80C3×#685—24no—
81C3×#685—22no—
82C3×#685—22no—
83C3×C4⋊Dic5—22no—
84C3×C4⋊Dic5C2×C414yescomplemented
85C3×#683—42no—
86C3×C4×Dic5—24no—
87C3×C4×Dic5—22no—
88C3×C4×Dic5—42no—
89C2×C3×#121—51no—
90C2×C3×C4×D4D511yescharacteristic, complemented
91C2×C3×#117—51no—
92C3×#390—51no—
93C3×#390—52no—
94C3×#389—51no—
95C3×#388—52no—
96C3×#386—52no—
97C3×C4×C4⋊C4—51no—
98C3×C4×C22⋊C4—52no—
99C3×C4×C22⋊C4—51no—
100C22×C5×D4C22×C311yescharacteristic
101C23×C4×C5C22×C312yes—
102C22×C22⋊D5C22×C312yes—
103C22×C4×D5C22×C311yescharacteristic
104C4×C5×D4—24no—
105C2×C5×C4⋊C4C22×C311yescharacteristic
106C2×C5×C22⋊C4C22×C312yes—
107C2×C42×C5C22×C311yescharacteristic
108C2×C22⋊Dic5C22×C312yes—
109C2×C22⋊Dic5C22×C312yes—
110C2×C22⋊Dic5C22×C312yes—
111#4084C3×C418yescomplemented
112C2×#685C22×C312yes—
113C2×#685C22×C311yescharacteristic
114C2×#685C22×C311yescharacteristic
115C2×C4⋊Dic5C22×C311yescharacteristic
116C2×C4⋊Dic5C22×C311yescharacteristic
117C2×#683C22×C312yes—
118C2×C4×Dic5C22×C312yes—
119C2×C4×Dic5C22×C311yescharacteristic
120C2×C4×Dic5C22×C312yes—
121#4038—24no—
122#3963C22×C312yes—
123#3963C22×C311yescharacteristic
124#3963C22×C311yescharacteristic
125#3963C22×C312yes—
126#2363—51noSylow
127C23×C3×C5—22no—
128C23×C3×C5—22no—
129C23×C3×C5—22no—
130C23×C3×C5—22no—
131C23×C3×C5—22no—
132C23×C3×C5—22no—
133C23×C3×C5C22×C414yes—
134C23×C3×C5C2411yescharacteristic
135C22×C3×D5—21no—
136C22×C3×D5—21no—
137C22×C3×D5—21no—
138C22×C3×D5—21no—
139C22×C3×D5—21no—
140C22×C3×D5—21no—
141C22×C3×D5C22×C412yes—
142C3×C5×D4—28no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—48no—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C2×D414yes—
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5#4112yes—
155C2×C3×C4×C5#4112yes—
156C3×C22⋊D5—48no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—21no—
160C2×C3×Dic5—21no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—21no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—21no—
169C2×C3×Dic5C22×C414yes—
170C2×C3×Dic5C22×C412yes—
171C2×C3×Dic5#4112yes—
172C3×C4×D5—28no—
173C22×C3×D4—52no—
174C22×C3×D4C2×D511yescharacteristic
175C23×C3×C4—51no—
176C23×C3×C4C2×D512yes—
177C3×#121—58no—
178C3×C4×D4—24no—
179C3×#117—104no—
180C2×C3×C4⋊C4—51no—
181C2×C3×C4⋊C4—51no—
182C2×C3×C4⋊C4—52no—
183C2×C3×C4⋊C4C2×D511yescharacteristic
184C2×C3×C22⋊C4—52no—
185C2×C3×C22⋊C4—52no—
186C2×C3×C22⋊C4—51no—
187C2×C3×C22⋊C4—51no—
188C2×C3×C22⋊C4—52no—
189C2×C3×C22⋊C4—52no—
190C2×C3×C22⋊C4C2×D512yes—
191C2×C3×C42—51no—
192C2×C3×C42—52no—
193C2×C3×C42—52no—
194C2×C3×C42C2×D511yescharacteristic
195C3×#95—51no—
196C3×#95—52no—
197C3×#95—51no—
198C3×#95—52no—
199C24×C5C23×C312yes—
200C23×D5C23×C311yescharacteristic
201C2×C5×D4—22no—
202C2×C5×D4—22no—
203C2×C5×D4C2×C3×C414yes—
204C22×C4×C5—24no—
205C22×C4×C5—24no—
206C22×C4×C5—42no—
207C22×C4×C5C23×C311yescharacteristic
208C22×C4×C5C23×C312yes—
209C22×C4×C5C23×C311yescharacteristic
210C22×C4×C5C23×C311yescharacteristic
211C2×C22⋊D5—42no—
212C2×C22⋊D5—42no—
213C2×C22⋊D5C2×C3×C418yescomplemented
214C22×Dic5C23×C311yescharacteristic
215C22×Dic5C23×C312yes—
216C22×Dic5C23×C311yescharacteristic
217C22×Dic5C23×C312yes—
218C22×Dic5C23×C311yescharacteristic
219C2×C4×D5—22no—
220C2×C4×D5—22no—
221C2×C4×D5C2×C3×C414yescomplemented
222C5×C4⋊C4C3×D414yescomplemented
223C5×C22⋊C4—24no—
224C42×C5—22no—
225C22⋊Dic5—24no—
226C22⋊Dic5—42no—
227C22⋊Dic5C2×C3×C418yescomplemented
228#685—24no—
229#685—22no—
230#685—22no—
231C4⋊Dic5—22no—
232C4⋊Dic5C2×C3×C414yescomplemented
233#683—42no—
234C4×Dic5—24no—
235C4×Dic5—22no—
236C4×Dic5—42no—
237C2×#121—51no—
238C2×C4×D4C3×D511yescharacteristic, complemented
239C2×#117—51no—
240#390—51no—
241#390—52no—
242#389—51no—
243#388—52no—
244#386—52no—
245C4×C4⋊C4—51no—
246C4×C22⋊C4—52no—
247C4×C22⋊C4—51no—
248C22×C3×C5—24no—
249C22×C3×C5—24no—
250C22×C3×C5—24no—
251C22×C3×C5—42no—
252C22×C3×C5—42no—
253C22×C3×C5—42no—
254C22×C3×C5—42no—
255C22×C3×C5C23×C411yescharacteristic
256C22×C3×C5C22×D411yescharacteristic
257C22×C3×C5C2×#4111yescharacteristic
258C22×C3×C5C2×#4111yescharacteristic
259C22×C3×C5C2×#4111yescharacteristic
260C22×C3×C5H(5,𝔽2)11yescharacteristic
261C22×C3×C5H(5,𝔽2)11yescharacteristic
262C2×C3×D5—22no—
263C2×C3×D5—22no—
264C2×C3×D5—22no—
265C2×C3×D5—41no—
266C2×C3×D5—41no—
267C2×C3×D5—41no—
268C2×C3×D5—41no—
269C3×C4×C5—22no—
270C3×C4×C5—24no—
271C3×C4×C5—41no—
272C3×C4×C5C4×D414yes—
273C3×Dic5—22no—
274C3×Dic5—24no—
275C3×Dic5—22no—
276C3×Dic5—42no—
277C3×Dic5—41no—
278C24×C3—51no—
279C24×C3C22×D512yes—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—58no—
283C2×C3×D4—202no—
284C2×C3×D4—202no—
285C2×C3×D4C4×D514yes—
286C22×C3×C4—24no—
287C22×C3×C4—24no—
288C22×C3×C4—42no—
289C22×C3×C4—51no—
290C22×C3×C4—52no—
291C22×C3×C4—51no—
292C22×C3×C4—54no—
293C22×C3×C4—51no—
294C22×C3×C4—52no—
295C22×C3×C4—102no—
296C22×C3×C4—102no—
297C22×C3×C4C22×D511yescharacteristic
298C22×C3×C4C22×D511yescharacteristic
299C22×C3×C4C22×D512yes—
300C22×C3×C4C22×D511yescharacteristic
301C3×C4⋊C4—54no—
302C3×C4⋊C4—102no—
303C3×C4⋊C4—202no—
304C3×C4⋊C4C22⋊D514yescomplemented
305C3×C22⋊C4—24no—
306C3×C22⋊C4—58no—
307C3×C22⋊C4—102no—
308C3×C22⋊C4—104no—
309C3×C22⋊C4—102no—
310C3×C22⋊C4—104no—
311C3×C22⋊C4—202no—
312C3×C42—22no—
313C3×C42—102no—
314C3×C42—104no—
315C3×C42—202no—
316C23×C5—22no—
317C23×C5—22no—
318C23×C5—22no—
319C23×C5—22no—
320C23×C5—22no—
321C23×C5—22no—
322C23×C5C22×C3×C414yes—
323C23×C5C24×C311yescharacteristic
324C22×D5—21no—
325C22×D5—21no—
326C22×D5—21no—
327C22×D5—21no—
328C22×D5—21no—
329C22×D5—21no—
330C22×D5C22×C3×C412yes—
331C5×D4—28no—
332C2×C4×C5—21no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—48no—
340C2×C4×C5C22×C3×C412yes—
341C2×C4×C5C2×C3×D414yes—
342C2×C4×C5C2×C3×D412yes—
343C2×C4×C5C3×#4112yes—
344C2×C4×C5C3×#4112yes—
345C22⋊D5—48no—
346C2×Dic5—21no—
347C2×Dic5—21no—
348C2×Dic5—21no—
349C2×Dic5—21no—
350C2×Dic5—22no—
351C2×Dic5—22no—
352C2×Dic5—22no—
353C2×Dic5—21no—
354C2×Dic5—21no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—21no—
358C2×Dic5C22×C3×C414yes—
359C2×Dic5C22×C3×C412yes—
360C2×Dic5C3×#4112yes—
361C4×D5—28no—
362C22×D4—52no—
363C22×D4C2×C3×D511yescharacteristic
364C23×C4—51no—
365C23×C4C2×C3×D512yes—
366#121—58no—
367C4×D4—24no—
368#117—104no—
369C2×C4⋊C4—51no—
370C2×C4⋊C4—51no—
371C2×C4⋊C4—52no—
372C2×C4⋊C4C2×C3×D511yescharacteristic
373C2×C22⋊C4—52no—
374C2×C22⋊C4—52no—
375C2×C22⋊C4—52no—
376C2×C22⋊C4—51no—
377C2×C22⋊C4—51no—
378C2×C22⋊C4—52no—
379C2×C22⋊C4C2×C3×D512yes—
380C2×C42—52no—
381C2×C42—51no—
382C2×C42—52no—
383C2×C42C2×C3×D511yescharacteristic
384#95—51no—
385#95—52no—
386#95—51no—
387#95—52no—
388C2×C3×C5—44no—
389C2×C3×C5C2×C4×D411yescharacteristic
390C2×C3×C5C4×#4111yescharacteristic
391C2×C3×C5#51811yescharacteristic
392C2×C3×C5#54611yescharacteristic
393C2×C3×C5#55011yescharacteristic
394C2×C3×C5#55311yescharacteristic
395C2×C3×C5#55511yescharacteristic
396C3×D5—42no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—52no—
404C23×C3—101no—
405C23×C3—101no—
406C23×C3—101no—
407C23×C3—101no—
408C23×C3—101no—
409C23×C3—101no—
410C23×C3C2×C4×D514yes—
411C23×C3C23×D511yescharacteristic
412C3×D4—28no—
413C3×D4—208no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—48no—
422C2×C3×C4—52no—
423C2×C3×C4—54no—
424C2×C3×C4—52no—
425C2×C3×C4—101no—
426C2×C3×C4—101no—
427C2×C3×C4—101no—
428C2×C3×C4—102no—
429C2×C3×C4—102no—
430C2×C3×C4—101no—
431C2×C3×C4—108no—
432C2×C3×C4—101no—
433C2×C3×C4—101no—
434C2×C3×C4—102no—
435C2×C3×C4—101no—
436C2×C3×C4—102no—
437C2×C3×C4—102no—
438C2×C3×C4C2×C4×D512yes—
439C2×C3×C4#70912yes—
440C2×C3×C4#71112yes—
441C2×C3×C4C2×C22⋊D514yes—
442C2×C3×C4C2×C22⋊D512yes—
443C22×C5—24no—
444C22×C5—24no—
445C22×C5—24no—
446C22×C5—42no—
447C22×C5—42no—
448C22×C5—42no—
449C22×C5—42no—
450C22×C5C23×C3×C411yescharacteristic
451C22×C5C22×C3×D411yescharacteristic
452C22×C5C2×C3×#4111yescharacteristic
453C22×C5C2×C3×#4111yescharacteristic
454C22×C5C2×C3×#4111yescharacteristic
455C22×C5C3×H(5,𝔽2)11yescharacteristic
456C22×C5C3×H(5,𝔽2)11yescharacteristic
457C2×D5—22no—
458C2×D5—22no—
459C2×D5—22no—
460C2×D5—41no—
461C2×D5—41no—
462C2×D5—41no—
463C2×D5—41no—
464C4×C5—22no—
465C4×C5—24no—
466C4×C5—41no—
467C4×C5C3×C4×D414yes—
468Dic5—22no—
469Dic5—24no—
470Dic5—22no—
471Dic5—42no—
472Dic5—41no—
473C24—51no—
474C24C22×C3×D512yes—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—58no—
478C2×D4—202no—
479C2×D4—202no—
480C2×D4C3×C4×D514yes—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—42no—
484C22×C4—51no—
485C22×C4—52no—
486C22×C4—51no—
487C22×C4—54no—
488C22×C4—51no—
489C22×C4—52no—
490C22×C4—102no—
491C22×C4—102no—
492C22×C4C22×C3×D511yescharacteristic
493C22×C4C22×C3×D511yescharacteristic
494C22×C4C22×C3×D512yes—
495C22×C4C22×C3×D511yescharacteristic
496C4⋊C4—54no—
497C4⋊C4—102no—
498C4⋊C4—202no—
499C4⋊C4C3×C22⋊D514yescomplemented
500C22⋊C4—24no—
501C22⋊C4—58no—
502C22⋊C4—102no—
503C22⋊C4—104no—
504C22⋊C4—102no—
505C22⋊C4—104no—
506C22⋊C4—202no—
507C42—22no—
508C42—102no—
509C42—104no—
510C42—202no—
511C3×C5#236311yescharacteristic, complemented, Hall
512C22×C3—24no—
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—102no—
520C22×C3—102no—
521C22×C3—102no—
522C22×C3—201no—
523C22×C3—201no—
524C22×C3—201no—
525C22×C3—201no—
526C22×C3C22×C4×D511yescharacteristic
527C22×C3C2×#70911yescharacteristic
528C22×C3C2×#71111yescharacteristic
529C22×C3#414411yescharacteristic
530C22×C3D5×#4111yescharacteristic
531C22×C3#414911yescharacteristic
532C22×C3C22×C22⋊D511yescharacteristic
533C3×C4—22no—
534C3×C4—24no—
535C3×C4—41no—
536C3×C4—102no—
537C3×C4—104no—
538C3×C4—102no—
539C3×C4—201no—
540C3×C4—202no—
541C3×C4C4×C22⋊D514yes—
542C2×C5—44no—
543C2×C5C2×C3×C4×D411yescharacteristic
544C2×C5C3×C4×#4111yescharacteristic
545C2×C5C3×#51811yescharacteristic
546C2×C5C3×#54611yescharacteristic
547C2×C5C3×#55011yescharacteristic
548C2×C5C3×#55311yescharacteristic
549C2×C5C3×#55511yescharacteristic
550D5—42no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—52no—
558C23—101no—
559C23—101no—
560C23—101no—
561C23—101no—
562C23—101no—
563C23—101no—
564C23C2×C3×C4×D514yes—
565C23C23×C3×D511yescharacteristic
566D4—28no—
567D4—208no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—48no—
576C2×C4—52no—
577C2×C4—54no—
578C2×C4—52no—
579C2×C4—101no—
580C2×C4—101no—
581C2×C4—101no—
582C2×C4—102no—
583C2×C4—102no—
584C2×C4—101no—
585C2×C4—108no—
586C2×C4—101no—
587C2×C4—101no—
588C2×C4—102no—
589C2×C4—101no—
590C2×C4—102no—
591C2×C4—102no—
592C2×C4C2×C3×C4×D512yes—
593C2×C4C3×#70912yes—
594C2×C4C3×#71112yes—
595C2×C4C2×C3×C22⋊D514yes—
596C2×C4C2×C3×C22⋊D512yes—
597C2×C3—44no—
598C2×C3—202no—
599C2×C3C4×#71111yescharacteristic
600C2×C3#6587911yescharacteristic
601C2×C3#6589211yescharacteristic
602C2×C3#6589711yescharacteristic
603C2×C3C2×C4×C22⋊D511yescharacteristic
604C2×C3#6614011yescharacteristic
605C2×C3#6616811yescharacteristic
606C5C3×#236311yescharacteristic, complemented, Sylow
607C22—24no—
608C22—24no—
609C22—24no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—102no—
615C22—102no—
616C22—102no—
617C22—201no—
618C22—201no—
619C22—201no—
620C22—201no—
621C22C22×C3×C4×D511yescharacteristic
622C22C2×C3×#70911yescharacteristic
623C22C2×C3×#71111yescharacteristic
624C22C3×#414411yescharacteristic
625C22C3×D5×#4111yescharacteristic
626C22C3×#414911yescharacteristic
627C22C22×C3×C22⋊D511yescharacteristic
628C4—22no—
629C4—24no—
630C4—41no—
631C4—102no—
632C4—104no—
633C4—102no—
634C4—201no—
635C4—202no—
636C4C3×C4×C22⋊D514yes—
637C3#1061407211yescharacteristic, direct product factor, Sylow
638C2—44no—
639C2—202no—
640C2C3×C4×#71111yescharacteristic
641C2C3×#6587911yescharacteristic
642C2C3×#6589211yescharacteristic
643C2C3×#6589711yescharacteristic
644C2C2×C3×C4×C22⋊D511yescharacteristic
645C2C3×#6614011yescharacteristic
646C2C3×#6616811yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC2×C3×#4084C2
cosocleC23×C5C24×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×#2363
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. C2×C3×#4038C2semidirect
4. C3×#65510C2semidirect
5. C3×#65502C2semidirect
6. C3×C4×C22⋊Dic5C2semidirect
7. C3×C4⋊C4×Dic5C2semidirect
8. C3×#65246C2semidirect
9. C3×#65233C2semidirect
10. C3×C4×#685C2semidirect
11. C3×#65217C2semidirect
12. #10614072C3direct (N × H)
24. C3×#4084C4semidirect
40. C2×C4×C5×D4C2×C3semidirect
42. C2×#4038C2×C3semidirect
43. #65510C2×C3semidirect
44. #65502C2×C3semidirect
45. C4×C22⋊Dic5C2×C3semidirect
46. C4⋊C4×Dic5C2×C3semidirect
47. #65246C2×C3semidirect
48. #65233C2×C3semidirect
49. C4×#685C2×C3semidirect
50. #65217C2×C3semidirect
65. C2×C3×C22⋊D5C2×C4semidirect
73. C2×C3×C4×D5C2×C4semidirect
74. C3×C5×C4⋊C4D4semidirect
79. C3×C22⋊Dic5C2×C4semidirect
84. C3×C4⋊Dic5C2×C4semidirect
90. C2×C3×C4×D4D5semidirect
111. #4084C3×C4semidirect
213. C2×C22⋊D5C2×C3×C4semidirect
221. C2×C4×D5C2×C3×C4semidirect
222. C5×C4⋊C4C3×D4semidirect
227. C22⋊Dic5C2×C3×C4semidirect
232. C4⋊Dic5C2×C3×C4semidirect
238. C2×C4×D4C3×D5semidirect
304. C3×C4⋊C4C22⋊D5semidirect
499. C4⋊C4C3×C22⋊D5semidirect
511. C3×C5#2363semidirect
606. C5C3×#2363semidirect
637. C3#10614072direct (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×#40842
C2×C3×#40382
C3×#655102
C3×#655022
C3×C4×C22⋊Dic52
C3×C4⋊C4×Dic52
C3×#652462
C3×#652332
C3×C4×#6852
C3×#652172
#106140723
C3×#23635