Finite Group Databasebeta

← C3×#10614058 #14324033

Subgroups — C3×#10614058 #14324033

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 908 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×#4085C211yesmaximal, characteristic
3C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C3×#65509C211yesmaximal, characteristic, complemented
5C3×#65502C211yesmaximal, characteristic, complemented
6C3×#65499C211yesmaximal, characteristic, complemented
7C2×C3×#3963C211yesmaximal, characteristic, complemented
8C3×#65278C211yesmaximal, characteristic, complemented
9C3×#65267C211yesmaximal, characteristic, complemented
10C3×#65247C211yesmaximal, characteristic, complemented
11C3×#65245C211yesmaximal, characteristic, complemented
12C3×#65233C211yesmaximal, characteristic, complemented
13C3×#65231C211yesmaximal, characteristic, complemented
14C3×#65229C211yesmaximal, characteristic, complemented
15C3×#65222C211yesmaximal, characteristic, complemented
16#10614058C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C3×C4×C5×D4—24no—
26C2×C3×C5×C4⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C42×C5C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C3×#4085C418yescomplemented
35C3×C4×C22⋊D5—24no—
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×#683C2211yescharacteristic
44C2×C3×C4×Dic5C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#2325—51nomaximal, Hall
56C2×C4×C5×D4C2×C311yescharacteristic, complemented
57C2×#4085C2×C311yescharacteristic
58C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
59#65509C2×C311yescharacteristic, complemented
60#65502C2×C311yescharacteristic, complemented
61#65499C2×C311yescharacteristic, complemented
62C2×#3963C2×C311yescharacteristic, complemented
63#65278C2×C311yescharacteristic, complemented
64#65267C2×C311yescharacteristic, complemented
65#65247C2×C311yescharacteristic, complemented
66#65245C2×C311yescharacteristic, complemented
67#65233C2×C311yescharacteristic, complemented
68#65231C2×C311yescharacteristic, complemented
69#65229C2×C311yescharacteristic, complemented
70#65222C2×C311yescharacteristic, complemented
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C2×C3×C5×D4—22no—
75C2×C3×C5×D4—22no—
76C2×C3×C5×D4C2×C414yescomplemented
77C22×C3×C4×C5—22no—
78C22×C3×C4×C5—41no—
79C22×C3×C4×C5—41no—
80C22×C3×C4×C5—41no—
81C22×C3×C4×C5—41no—
82C22×C3×C4×C5D414yescomplemented
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C2×C3×C22⋊D5—22no—
89C2×C3×C22⋊D5—22no—
90C2×C3×C22⋊D5—41no—
91C2×C3×C22⋊D5—41no—
92C2×C3×C22⋊D5C2×C414yescomplemented
93C2×C3×C22⋊D5C2×C414yescomplemented
94C22×C3×Dic5—22no—
95C22×C3×Dic5—41no—
96C22×C3×Dic5—41no—
97C22×C3×Dic5—41no—
98C22×C3×Dic5—41no—
99C22×C3×Dic5C2×C414yescomplemented
100C22×C3×Dic5C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C2×C3×C4×D5—22no—
108C2×C3×C4×D5—41no—
109C2×C3×C4×D5—41no—
110C3×C5×C4⋊C4—22no—
111C3×C5×C22⋊C4—22no—
112C3×C5×C22⋊C4—22no—
113C3×C42×C5—22no—
114C3×C22⋊Dic5—22no—
115C3×C22⋊Dic5—41no—
116C3×C22⋊Dic5—41no—
117C3×C22⋊Dic5C2×C414yescomplemented
118C3×#685—22no—
119C3×#685—41no—
120C3×#685—41no—
121C3×#685C2×C414yescomplemented
122C3×#683—22no—
123C3×#683—41no—
124C3×#683—41no—
125C3×#683C2×C414yescomplemented
126C3×C4×Dic5—22no—
127C2×C3×#121—51no—
128C2×C3×C4×D4—51no—
129C2×C3×C4×D4D511yescharacteristic, complemented
130C3×#388—51no—
131C3×#388—51no—
132C3×#387—51no—
133C3×#387—51no—
134C3×#386—51no—
135C3×#386—51no—
136C3×#386—51no—
137C3×#386—51no—
138C3×#385—51no—
139C3×#385—51no—
140C3×#380—51no—
141C2×C3×#95—51no—
142C22×C5×D4C22×C311yescharacteristic
143C23×C4×C5C22×C311yescharacteristic
144C23×C4×C5C22×C311yescharacteristic
145C22×C22⋊D5C22×C311yescharacteristic
146C22×C22⋊D5C22×C311yescharacteristic
147C23×Dic5C22×C311yescharacteristic
148C23×Dic5C22×C311yescharacteristic
149C22×C4×D5C22×C311yescharacteristic
150C4×C5×D4—24no—
151C2×C5×C4⋊C4C22×C311yescharacteristic
152C2×C5×C22⋊C4C22×C311yescharacteristic
153C2×C5×C22⋊C4C22×C311yescharacteristic
154C2×C42×C5C22×C311yescharacteristic
155C2×C22⋊Dic5C22×C311yescharacteristic
156C2×C22⋊Dic5C22×C311yescharacteristic
157C2×C22⋊Dic5C22×C311yescharacteristic
158C2×C22⋊Dic5C22×C311yescharacteristic
159#4085C3×C418yescomplemented
160C4×C22⋊D5—24no—
161C2×#685C22×C311yescharacteristic
162C2×#685C22×C311yescharacteristic
163C2×#685C22×C311yescharacteristic
164C2×#685C22×C311yescharacteristic
165C2×#683C22×C311yescharacteristic
166C2×#683C22×C311yescharacteristic
167C2×#683C22×C311yescharacteristic
168C2×#683C22×C311yescharacteristic
169C2×C4×Dic5C22×C311yescharacteristic
170#3963C22×C311yescharacteristic
171#3963C22×C311yescharacteristic
172#3963C22×C311yescharacteristic
173#3963C22×C311yescharacteristic
174#3963C22×C311yescharacteristic
175#3963C22×C311yescharacteristic
176#3963C22×C311yescharacteristic
177#3963C22×C311yescharacteristic
178#3963C22×C311yescharacteristic
179#3963C22×C311yescharacteristic
180#2325—51noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5C22×C412yes—
192C23×C3×C5C22×C412yes—
193C23×C3×C5C2×D412yes—
194C23×C3×C5#4112yes—
195C23×C3×C5C2411yescharacteristic
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5C22×C412yes—
203C3×C5×D4—28no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—44no—
217C2×C3×C4×C5—44no—
218C2×C3×C4×C5C22×C412yes—
219C2×C3×C4×C5C2×D412yes—
220C2×C3×C4×C5C2×D412yes—
221C3×C22⋊D5—28no—
222C3×C22⋊D5—44no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—44no—
242C2×C3×Dic5—44no—
243C2×C3×Dic5C22×C412yes—
244C2×C3×Dic5C22×C412yes—
245C2×C3×Dic5C22×C412yes—
246C3×C4×D5—44no—
247C22×C3×D4—51no—
248C22×C3×D4—51no—
249C22×C3×D4C2×D511yescharacteristic
250C23×C3×C4—51no—
251C23×C3×C4—51no—
252C23×C3×C4—51no—
253C23×C3×C4C2×D511yescharacteristic
254C23×C3×C4C2×D511yescharacteristic
255C3×#121—58no—
256C3×C4×D4—24no—
257C3×C4×D4—104no—
258C2×C3×C4⋊C4—51no—
259C2×C3×C4⋊C4—51no—
260C2×C3×C4⋊C4—51no—
261C2×C3×C4⋊C4—51no—
262C2×C3×C4⋊C4C2×D511yescharacteristic
263C2×C3×C22⋊C4—51no—
264C2×C3×C22⋊C4—51no—
265C2×C3×C22⋊C4—51no—
266C2×C3×C22⋊C4—51no—
267C2×C3×C22⋊C4—51no—
268C2×C3×C22⋊C4—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4C2×D511yescharacteristic
272C2×C3×C22⋊C4C2×D511yescharacteristic
273C2×C3×C42—51no—
274C2×C3×C42C2×D511yescharacteristic
275C3×#95—51no—
276C3×#95—51no—
277C3×#95—51no—
278C3×#95—51no—
279C3×#95—51no—
280C3×#95—51no—
281C3×#95—51no—
282C3×#95—51no—
283C3×#95—51no—
284C3×#95—51no—
285C24×C5C23×C311yescharacteristic
286C24×C5C23×C311yescharacteristic
287C23×D5C23×C311yescharacteristic
288C2×C5×D4—22no—
289C2×C5×D4—22no—
290C2×C5×D4C2×C3×C414yescomplemented
291C22×C4×C5—22no—
292C22×C4×C5—41no—
293C22×C4×C5—41no—
294C22×C4×C5—41no—
295C22×C4×C5—41no—
296C22×C4×C5C3×D414yescomplemented
297C22×C4×C5C23×C311yescharacteristic
298C22×C4×C5C23×C311yescharacteristic
299C22×C4×C5C23×C311yescharacteristic
300C22×C4×C5C23×C311yescharacteristic
301C22×C4×C5C23×C311yescharacteristic
302C2×C22⋊D5—22no—
303C2×C22⋊D5—22no—
304C2×C22⋊D5—41no—
305C2×C22⋊D5—41no—
306C2×C22⋊D5C2×C3×C414yescomplemented
307C2×C22⋊D5C2×C3×C414yescomplemented
308C22×Dic5—22no—
309C22×Dic5—41no—
310C22×Dic5—41no—
311C22×Dic5—41no—
312C22×Dic5—41no—
313C22×Dic5C2×C3×C414yescomplemented
314C22×Dic5C23×C311yescharacteristic
315C22×Dic5C23×C311yescharacteristic
316C22×Dic5C23×C311yescharacteristic
317C22×Dic5C23×C311yescharacteristic
318C22×Dic5C23×C311yescharacteristic
319C22×Dic5C23×C311yescharacteristic
320C22×Dic5C23×C311yescharacteristic
321C2×C4×D5—22no—
322C2×C4×D5—41no—
323C2×C4×D5—41no—
324C5×C4⋊C4—22no—
325C5×C22⋊C4—22no—
326C5×C22⋊C4—22no—
327C42×C5—22no—
328C22⋊Dic5—22no—
329C22⋊Dic5—41no—
330C22⋊Dic5—41no—
331C22⋊Dic5C2×C3×C414yescomplemented
332#685—22no—
333#685—41no—
334#685—41no—
335#685C2×C3×C414yescomplemented
336#683—22no—
337#683—41no—
338#683—41no—
339#683C2×C3×C414yescomplemented
340C4×Dic5—22no—
341C2×#121—51no—
342C2×C4×D4—51no—
343C2×C4×D4C3×D511yescharacteristic, complemented
344#388—51no—
345#388—51no—
346#387—51no—
347#387—51no—
348#386—51no—
349#386—51no—
350#386—51no—
351#386—51no—
352#385—51no—
353#385—51no—
354#380—51no—
355C2×#95—51no—
356C22×C3×C5—22no—
357C22×C3×C5—22no—
358C22×C3×C5—22no—
359C22×C3×C5—22no—
360C22×C3×C5—22no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—22no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5—41no—
368C22×C3×C5—41no—
369C22×C3×C5C4×D414yes—
370C22×C3×C5C23×C411yescharacteristic
371C22×C3×C5C22×D411yescharacteristic
372C22×C3×C5C2×#4111yescharacteristic
373C22×C3×C5H(5,𝔽2)11yescharacteristic
374C22×C3×C5H(5,𝔽2)11yescharacteristic
375C22×C3×C5H(5,𝔽2)11yescharacteristic
376C22×C3×C52−1+411yescharacteristic
377C2×C3×D5—22no—
378C2×C3×D5—22no—
379C2×C3×D5—22no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C2×C3×D5—41no—
383C2×C3×D5—41no—
384C3×C4×C5—22no—
385C3×C4×C5—22no—
386C3×C4×C5—22no—
387C3×C4×C5—41no—
388C3×C4×C5—41no—
389C3×Dic5—22no—
390C3×Dic5—22no—
391C3×Dic5—22no—
392C3×Dic5—41no—
393C3×Dic5—41no—
394C3×Dic5—41no—
395C3×Dic5—41no—
396C24×C3—51no—
397C24×C3C22×D511yescharacteristic
398C24×C3C22×D511yescharacteristic
399C2×C3×D4—22no—
400C2×C3×D4—22no—
401C2×C3×D4—54no—
402C2×C3×D4—54no—
403C2×C3×D4—102no—
404C2×C3×D4—102no—
405C2×C3×D4—201no—
406C2×C3×D4—201no—
407C2×C3×D4C4×D514yescomplemented
408C22×C3×C4—22no—
409C22×C3×C4—41no—
410C22×C3×C4—41no—
411C22×C3×C4—41no—
412C22×C3×C4—41no—
413C22×C3×C4—51no—
414C22×C3×C4—51no—
415C22×C3×C4—51no—
416C22×C3×C4—54no—
417C22×C3×C4—51no—
418C22×C3×C4—51no—
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—102no—
422C22×C3×C4—102no—
423C22×C3×C4—201no—
424C22×C3×C4—201no—
425C22×C3×C4—201no—
426C22×C3×C4—201no—
427C22×C3×C4—201no—
428C22×C3×C4—201no—
429C22×C3×C4C22⋊D514yescomplemented
430C22×C3×C4C22×D511yescharacteristic
431C22×C3×C4C22×D511yescharacteristic
432C22×C3×C4C22×D511yescharacteristic
433C22×C3×C4C22×D511yescharacteristic
434C22×C3×C4C22×D511yescharacteristic
435C3×C4⋊C4—22no—
436C3×C4⋊C4—54no—
437C3×C4⋊C4—102no—
438C3×C4⋊C4—201no—
439C3×C4⋊C4—201no—
440C3×C22⋊C4—22no—
441C3×C22⋊C4—22no—
442C3×C22⋊C4—54no—
443C3×C22⋊C4—54no—
444C3×C22⋊C4—102no—
445C3×C22⋊C4—102no—
446C3×C22⋊C4—201no—
447C3×C22⋊C4—201no—
448C3×C22⋊C4—201no—
449C3×C22⋊C4—201no—
450C3×C42—22no—
451C3×C42—102no—
452C23×C5—21no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—21no—
462C23×C5C22×C3×C412yes—
463C23×C5C22×C3×C412yes—
464C23×C5C2×C3×D412yes—
465C23×C5C3×#4112yes—
466C23×C5C24×C311yescharacteristic
467C22×D5—21no—
468C22×D5—21no—
469C22×D5—21no—
470C22×D5—21no—
471C22×D5—21no—
472C22×D5—21no—
473C22×D5C22×C3×C412yes—
474C5×D4—28no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—21no—
484C2×C4×C5—21no—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—44no—
488C2×C4×C5—44no—
489C2×C4×C5C22×C3×C412yes—
490C2×C4×C5C2×C3×D412yes—
491C2×C4×C5C2×C3×D412yes—
492C22⋊D5—28no—
493C22⋊D5—44no—
494C2×Dic5—21no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—21no—
498C2×Dic5—21no—
499C2×Dic5—21no—
500C2×Dic5—21no—
501C2×Dic5—21no—
502C2×Dic5—21no—
503C2×Dic5—21no—
504C2×Dic5—21no—
505C2×Dic5—21no—
506C2×Dic5—21no—
507C2×Dic5—21no—
508C2×Dic5—21no—
509C2×Dic5—21no—
510C2×Dic5—21no—
511C2×Dic5—21no—
512C2×Dic5—44no—
513C2×Dic5—44no—
514C2×Dic5C22×C3×C412yes—
515C2×Dic5C22×C3×C412yes—
516C2×Dic5C22×C3×C412yes—
517C4×D5—44no—
518C22×D4—51no—
519C22×D4—51no—
520C22×D4C2×C3×D511yescharacteristic
521C23×C4—51no—
522C23×C4—51no—
523C23×C4—51no—
524C23×C4C2×C3×D511yescharacteristic
525C23×C4C2×C3×D511yescharacteristic
526#121—58no—
527C4×D4—24no—
528C4×D4—104no—
529C2×C4⋊C4—51no—
530C2×C4⋊C4—51no—
531C2×C4⋊C4—51no—
532C2×C4⋊C4—51no—
533C2×C4⋊C4C2×C3×D511yescharacteristic
534C2×C22⋊C4—51no—
535C2×C22⋊C4—51no—
536C2×C22⋊C4—51no—
537C2×C22⋊C4—51no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—51no—
540C2×C22⋊C4—51no—
541C2×C22⋊C4—51no—
542C2×C22⋊C4C2×C3×D511yescharacteristic
543C2×C22⋊C4C2×C3×D511yescharacteristic
544C2×C42—51no—
545C2×C42C2×C3×D511yescharacteristic
546#95—51no—
547#95—51no—
548#95—51no—
549#95—51no—
550#95—51no—
551#95—51no—
552#95—51no—
553#95—51no—
554#95—51no—
555#95—51no—
556C2×C3×C5—24no—
557C2×C3×C5—42no—
558C2×C3×C5C2×C4×D411yescharacteristic
559C2×C3×C5#51811yescharacteristic
560C2×C3×C5#52011yescharacteristic
561C2×C3×C5#53411yescharacteristic
562C2×C3×C5#53711yescharacteristic
563C2×C3×C5#53811yescharacteristic
564C2×C3×C5#53911yescharacteristic
565C3×D5—42no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—52no—
577C23×C3—101no—
578C23×C3—101no—
579C23×C3—101no—
580C23×C3—101no—
581C23×C3—101no—
582C23×C3—101no—
583C23×C3C2×C4×D512yes—
584C23×C3C2×C4×D512yes—
585C23×C3#70912yes—
586C23×C3C2×C22⋊D512yes—
587C23×C3C23×D511yescharacteristic
588C3×D4—28no—
589C3×D4—108no—
590C3×D4—204no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—44no—
604C2×C3×C4—44no—
605C2×C3×C4—52no—
606C2×C3×C4—52no—
607C2×C3×C4—52no—
608C2×C3×C4—101no—
609C2×C3×C4—101no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
614C2×C3×C4—101no—
615C2×C3×C4—101no—
616C2×C3×C4—101no—
617C2×C3×C4—101no—
618C2×C3×C4—101no—
619C2×C3×C4—101no—
620C2×C3×C4—101no—
621C2×C3×C4—101no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4—101no—
625C2×C3×C4—101no—
626C2×C3×C4—204no—
627C2×C3×C4—204no—
628C2×C3×C4—204no—
629C2×C3×C4C2×C4×D512yes—
630C2×C3×C4C2×C22⋊D512yes—
631C2×C3×C4C2×C22⋊D512yes—
632C22×C5—22no—
633C22×C5—22no—
634C22×C5—22no—
635C22×C5—22no—
636C22×C5—22no—
637C22×C5—22no—
638C22×C5—22no—
639C22×C5—22no—
640C22×C5—22no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5—41no—
644C22×C5—41no—
645C22×C5C3×C4×D414yes—
646C22×C5C23×C3×C411yescharacteristic
647C22×C5C22×C3×D411yescharacteristic
648C22×C5C2×C3×#4111yescharacteristic
649C22×C5C3×H(5,𝔽2)11yescharacteristic
650C22×C5C3×H(5,𝔽2)11yescharacteristic
651C22×C5C3×H(5,𝔽2)11yescharacteristic
652C22×C5C3×2−1+411yescharacteristic
653C2×D5—22no—
654C2×D5—22no—
655C2×D5—22no—
656C2×D5—41no—
657C2×D5—41no—
658C2×D5—41no—
659C2×D5—41no—
660C4×C5—22no—
661C4×C5—22no—
662C4×C5—22no—
663C4×C5—41no—
664C4×C5—41no—
665Dic5—22no—
666Dic5—22no—
667Dic5—22no—
668Dic5—41no—
669Dic5—41no—
670Dic5—41no—
671Dic5—41no—
672C24—51no—
673C24C22×C3×D511yescharacteristic
674C24C22×C3×D511yescharacteristic
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—54no—
678C2×D4—54no—
679C2×D4—102no—
680C2×D4—102no—
681C2×D4—201no—
682C2×D4—201no—
683C2×D4C3×C4×D514yescomplemented
684C22×C4—22no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—51no—
690C22×C4—51no—
691C22×C4—51no—
692C22×C4—54no—
693C22×C4—51no—
694C22×C4—51no—
695C22×C4—51no—
696C22×C4—51no—
697C22×C4—102no—
698C22×C4—102no—
699C22×C4—201no—
700C22×C4—201no—
701C22×C4—201no—
702C22×C4—201no—
703C22×C4—201no—
704C22×C4—201no—
705C22×C4C3×C22⋊D514yescomplemented
706C22×C4C22×C3×D511yescharacteristic
707C22×C4C22×C3×D511yescharacteristic
708C22×C4C22×C3×D511yescharacteristic
709C22×C4C22×C3×D511yescharacteristic
710C22×C4C22×C3×D511yescharacteristic
711C4⋊C4—22no—
712C4⋊C4—54no—
713C4⋊C4—102no—
714C4⋊C4—201no—
715C4⋊C4—201no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—54no—
719C22⋊C4—54no—
720C22⋊C4—102no—
721C22⋊C4—102no—
722C22⋊C4—201no—
723C22⋊C4—201no—
724C22⋊C4—201no—
725C22⋊C4—201no—
726C42—22no—
727C42—102no—
728C3×C5#232511yescharacteristic, complemented, Hall
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—102no—
743C22×C3—102no—
744C22×C3—102no—
745C22×C3—201no—
746C22×C3—201no—
747C22×C3—201no—
748C22×C3—201no—
749C22×C3C4×C22⋊D514yes—
750C22×C3C22×C4×D511yescharacteristic
751C22×C3C2×#70911yescharacteristic
752C22×C3#414411yescharacteristic
753C22×C3#414411yescharacteristic
754C22×C3#414911yescharacteristic
755C22×C3#415011yescharacteristic
756C22×C3C22×C22⋊D511yescharacteristic
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—102no—
763C3×C4—102no—
764C3×C4—102no—
765C3×C4—201no—
766C3×C4—201no—
767C3×C4—201no—
768C3×C4—201no—
769C2×C5—24no—
770C2×C5—42no—
771C2×C5C2×C3×C4×D411yescharacteristic
772C2×C5C3×#51811yescharacteristic
773C2×C5C3×#52011yescharacteristic
774C2×C5C3×#53411yescharacteristic
775C2×C5C3×#53711yescharacteristic
776C2×C5C3×#53811yescharacteristic
777C2×C5C3×#53911yescharacteristic
778D5—42no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—52no—
790C23—101no—
791C23—101no—
792C23—101no—
793C23—101no—
794C23—101no—
795C23—101no—
796C23C2×C3×C4×D512yes—
797C23C2×C3×C4×D512yes—
798C23C3×#70912yes—
799C23C2×C3×C22⋊D512yes—
800C23C23×C3×D511yescharacteristic
801D4—28no—
802D4—108no—
803D4—204no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—52no—
819C2×C4—52no—
820C2×C4—52no—
821C2×C4—101no—
822C2×C4—101no—
823C2×C4—101no—
824C2×C4—101no—
825C2×C4—101no—
826C2×C4—101no—
827C2×C4—101no—
828C2×C4—101no—
829C2×C4—101no—
830C2×C4—101no—
831C2×C4—101no—
832C2×C4—101no—
833C2×C4—101no—
834C2×C4—101no—
835C2×C4—101no—
836C2×C4—101no—
837C2×C4—101no—
838C2×C4—101no—
839C2×C4—204no—
840C2×C4—204no—
841C2×C4—204no—
842C2×C4C2×C3×C4×D512yes—
843C2×C4C2×C3×C22⋊D512yes—
844C2×C4C2×C3×C22⋊D512yes—
845C2×C3—24no—
846C2×C3—42no—
847C2×C3—202no—
848C2×C3#6587911yescharacteristic
849C2×C3#6588011yescharacteristic
850C2×C3#6589411yescharacteristic
851C2×C3#6589811yescharacteristic
852C2×C3C2×C4×C22⋊D511yescharacteristic
853C2×C3#6613811yescharacteristic
854C2×C3#6616711yescharacteristic
855C5C3×#232511yescharacteristic, complemented, Sylow
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—102no—
870C22—102no—
871C22—102no—
872C22—201no—
873C22—201no—
874C22—201no—
875C22—201no—
876C22C3×C4×C22⋊D514yes—
877C22C22×C3×C4×D511yescharacteristic
878C22C2×C3×#70911yescharacteristic
879C22C3×#414411yescharacteristic
880C22C3×#414411yescharacteristic
881C22C3×#414911yescharacteristic
882C22C3×#415011yescharacteristic
883C22C22×C3×C22⋊D511yescharacteristic
884C4—22no—
885C4—22no—
886C4—22no—
887C4—41no—
888C4—41no—
889C4—102no—
890C4—102no—
891C4—102no—
892C4—201no—
893C4—201no—
894C4—201no—
895C4—201no—
896C3#1061405811yescharacteristic, direct product factor, Sylow
897C2—24no—
898C2—42no—
899C2—202no—
900C2C3×#6587911yescharacteristic
901C2C3×#6588011yescharacteristic
902C2C3×#6589411yescharacteristic
903C2C3×#6589811yescharacteristic
904C2C2×C3×C4×C22⋊D511yescharacteristic
905C2C3×#6613811yescharacteristic
906C2C3×#6616711yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC2×C3×#4085C2
cosocleC23×C5C24×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×#2325
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×C4×C22⋊D5C2semidirect
4. C3×#65509C2semidirect
5. C3×#65502C2semidirect
6. C3×#65499C2semidirect
7. C2×C3×#3963C2semidirect
8. C3×#65278C2semidirect
9. C3×#65267C2semidirect
10. C3×#65247C2semidirect
11. C3×#65245C2semidirect
12. C3×#65233C2semidirect
13. C3×#65231C2semidirect
14. C3×#65229C2semidirect
15. C3×#65222C2semidirect
16. #10614058C3direct (N × H)
34. C3×#4085C4semidirect
56. C2×C4×C5×D4C2×C3semidirect
58. C2×C4×C22⋊D5C2×C3semidirect
59. #65509C2×C3semidirect
60. #65502C2×C3semidirect
61. #65499C2×C3semidirect
62. C2×#3963C2×C3semidirect
63. #65278C2×C3semidirect
64. #65267C2×C3semidirect
65. #65247C2×C3semidirect
66. #65245C2×C3semidirect
67. #65233C2×C3semidirect
68. #65231C2×C3semidirect
69. #65229C2×C3semidirect
70. #65222C2×C3semidirect
76. C2×C3×C5×D4C2×C4semidirect
82. C22×C3×C4×C5D4semidirect
92. C2×C3×C22⋊D5C2×C4semidirect
93. C2×C3×C22⋊D5C2×C4semidirect
99. C22×C3×Dic5C2×C4semidirect
117. C3×C22⋊Dic5C2×C4semidirect
121. C3×#685C2×C4semidirect
125. C3×#683C2×C4semidirect
129. C2×C3×C4×D4D5semidirect
159. #4085C3×C4semidirect
290. C2×C5×D4C2×C3×C4semidirect
296. C22×C4×C5C3×D4semidirect
306. C2×C22⋊D5C2×C3×C4semidirect
307. C2×C22⋊D5C2×C3×C4semidirect
313. C22×Dic5C2×C3×C4semidirect
331. C22⋊Dic5C2×C3×C4semidirect
335. #685C2×C3×C4semidirect
339. #683C2×C3×C4semidirect
343. C2×C4×D4C3×D5semidirect
407. C2×C3×D4C4×D5semidirect
429. C22×C3×C4C22⋊D5semidirect
683. C2×D4C3×C4×D5semidirect
705. C22×C4C3×C22⋊D5semidirect
728. C3×C5#2325semidirect
855. C5C3×#2325semidirect
896. C3#10614058direct (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×#40852
C2×C3×C4×C22⋊D52
C3×#655092
C3×#655022
C3×#654992
C2×C3×#39632
C3×#652782
C3×#652672
C3×#652472
C3×#652452
C3×#652332
C3×#652312
C3×#652292
C3×#652222
#106140583
C3×#23255