Finite Group Databasebeta

← C3×C4×#4085 #14321420

Subgroups — C3×C4×#4085 #14321420

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 932 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
4C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
5C22×C3×C4×Dic5C211yesmaximal, characteristic, complemented
6C3×#65509C211yesmaximal, characteristic, complemented
7C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
8C3×#65279C211yesmaximal, characteristic, complemented
9C3×#65261C211yesmaximal, characteristic, complemented
10C3×#65247C211yesmaximal, characteristic, complemented
11C3×#65246C211yesmaximal, characteristic, complemented
12C3×#65234C211yesmaximal, characteristic, complemented
13C3×#65231C211yesmaximal, characteristic, complemented
14C3×C4×#685C211yesmaximal, characteristic, complemented
15C3×C4×#683C211yesmaximal, characteristic, complemented
16C4×#4085C311yesmaximal, 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×#4085C418yesdirect product factor
35C3×C4×C22⋊D5—24no—
36C3×C4×C22⋊D5—24no—
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×#683C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic
45C2×C3×C4×Dic5—24no—
46C2×C3×C4×Dic5C2211yescharacteristic
47C2×C3×C4×Dic5C2211yescharacteristic
48C2×C3×C4×Dic5C2211yescharacteristic
49C2×C3×C4×Dic5C2211yescharacteristic
50C2×C3×C4×Dic5C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#3963C2211yescharacteristic
56C3×#3963C2211yescharacteristic
57C3×C4×#121—51nomaximal, Hall
58C2×C4×C5×D4C2×C311yescharacteristic, complemented
59C2×#4085C2×C311yescharacteristic
60C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
61C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
62C22×C4×Dic5C2×C311yescharacteristic, complemented
63#65509C2×C311yescharacteristic, complemented
64C4×C22⋊Dic5C2×C311yescharacteristic, complemented
65#65279C2×C311yescharacteristic, complemented
66#65261C2×C311yescharacteristic, complemented
67#65247C2×C311yescharacteristic, complemented
68#65246C2×C311yescharacteristic, complemented
69#65234C2×C311yescharacteristic, complemented
70#65231C2×C311yescharacteristic, complemented
71C4×#685C2×C311yescharacteristic, complemented
72C4×#683C2×C311yescharacteristic, complemented
73C24×C3×C5C2311yescharacteristic
74C24×C3×C5C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C2×C3×C5×D4—22no—
77C2×C3×C5×D4—22no—
78C2×C3×C5×D4C2×C414yescomplemented
79C22×C3×C4×C5—22no—
80C22×C3×C4×C5—22no—
81C22×C3×C4×C5—22no—
82C22×C3×C4×C5—22no—
83C22×C3×C4×C5—22no—
84C22×C3×C4×C5D414yescomplemented
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C2×C3×C22⋊D5—22no—
91C2×C3×C22⋊D5—22no—
92C2×C3×C22⋊D5—22no—
93C2×C3×C22⋊D5—22no—
94C2×C3×C22⋊D5C2×C414yescomplemented
95C2×C3×C22⋊D5C2×C414yescomplemented
96C22×C3×Dic5—22no—
97C22×C3×Dic5—22no—
98C22×C3×Dic5—22no—
99C22×C3×Dic5—22no—
100C22×C3×Dic5—22no—
101C22×C3×Dic5C2×C414yescomplemented
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C2×C3×C4×D5—22no—
110C2×C3×C4×D5—22no—
111C2×C3×C4×D5—22no—
112C3×C5×C4⋊C4—22no—
113C3×C5×C22⋊C4—22no—
114C3×C5×C22⋊C4—22no—
115C3×C42×C5—22no—
116C3×C22⋊Dic5—22no—
117C3×C22⋊Dic5—22no—
118C3×C22⋊Dic5—22no—
119C3×C22⋊Dic5C2×C414yescomplemented
120C3×#685—22no—
121C3×#685—22no—
122C3×#685—22no—
123C3×#685C2×C414yescomplemented
124C3×#683—22no—
125C3×#683—22no—
126C3×#683—22no—
127C3×#683C2×C414yescomplemented
128C3×C4×Dic5—22no—
129C3×C4×Dic5—22no—
130C3×C4×Dic5—22no—
131C3×C4×Dic5—22no—
132C3×C4×Dic5D414yescomplemented
133C2×C3×#121—51no—
134C2×C3×C4×D4—51no—
135C2×C3×C4×D4—51no—
136C2×C3×C4×D4D511yescharacteristic, complemented
137C22×C3×C42—51no—
138C3×#390—51no—
139C3×#389—51no—
140C3×#388—51no—
141C3×#388—51no—
142C3×#386—51no—
143C3×#386—51no—
144C3×#380—51no—
145C3×C4×C4⋊C4—51no—
146C3×C4×C22⋊C4—51no—
147C3×C4×C22⋊C4—51no—
148C22×C5×D4C22×C311yescharacteristic
149C23×C4×C5C22×C311yescharacteristic
150C23×C4×C5C22×C311yescharacteristic
151C22×C22⋊D5C22×C311yescharacteristic
152C22×C22⋊D5C22×C311yescharacteristic
153C23×Dic5C22×C311yescharacteristic
154C23×Dic5C22×C311yescharacteristic
155C22×C4×D5C22×C311yescharacteristic
156C4×C5×D4—24no—
157C2×C5×C4⋊C4C22×C311yescharacteristic
158C2×C5×C22⋊C4C22×C311yescharacteristic
159C2×C5×C22⋊C4C22×C311yescharacteristic
160C2×C42×C5C22×C311yescharacteristic
161C2×C22⋊Dic5C22×C311yescharacteristic
162C2×C22⋊Dic5C22×C311yescharacteristic
163C2×C22⋊Dic5C22×C311yescharacteristic
164C2×C22⋊Dic5C22×C311yescharacteristic
165#4085C3×C418yesdirect product factor
166C4×C22⋊D5—24no—
167C4×C22⋊D5—24no—
168C2×#685C22×C311yescharacteristic
169C2×#685C22×C311yescharacteristic
170C2×#685C22×C311yescharacteristic
171C2×#685C22×C311yescharacteristic
172C2×#683C22×C311yescharacteristic
173C2×#683C22×C311yescharacteristic
174C2×#683C22×C311yescharacteristic
175C2×#683C22×C311yescharacteristic
176C2×C4×Dic5—24no—
177C2×C4×Dic5C22×C311yescharacteristic
178C2×C4×Dic5C22×C311yescharacteristic
179C2×C4×Dic5C22×C311yescharacteristic
180C2×C4×Dic5C22×C311yescharacteristic
181C2×C4×Dic5C22×C311yescharacteristic
182#3963C22×C311yescharacteristic
183#3963C22×C311yescharacteristic
184#3963C22×C311yescharacteristic
185#3963C22×C311yescharacteristic
186#3963C22×C311yescharacteristic
187#3963C22×C311yescharacteristic
188C4×#121—51noSylow
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5C22×C412yes—
200C23×C3×C5C22×C412yes—
201C23×C3×C5C2×D412yes—
202C23×C3×C5#4112yes—
203C23×C3×C5C2411yescharacteristic
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5—21no—
210C22×C3×D5C22×C412yes—
211C3×C5×D4—28no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—28no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—44no—
224C2×C3×C4×C5C22×C412yes—
225C2×C3×C4×C5C2×D412yes—
226C2×C3×C4×C5C2×D412yes—
227C2×C3×C4×C5C2×D412yes—
228C2×C3×C4×C5#4112yes—
229C3×C22⋊D5—28no—
230C3×C22⋊D5—28no—
231C2×C3×Dic5—28no—
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—28no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5C22×C412yes—
248C2×C3×Dic5C22×C412yes—
249C2×C3×Dic5C22×C412yes—
250C2×C3×Dic5C2×D412yes—
251C2×C3×Dic5C2×D412yes—
252C2×C3×Dic5#4112yes—
253C2×C3×Dic5#4112yes—
254C3×C4×D5—44no—
255C22×C3×D4—51no—
256C22×C3×D4—51no—
257C22×C3×D4C2×D511yescharacteristic
258C23×C3×C4—51no—
259C23×C3×C4—51no—
260C23×C3×C4—51no—
261C23×C3×C4C2×D511yescharacteristic
262C23×C3×C4C2×D511yescharacteristic
263C3×#121—58no—
264C3×C4×D4—24no—
265C3×C4×D4—104no—
266C3×C4×D4—104no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C4⋊C4—51no—
270C2×C3×C4⋊C4—51no—
271C2×C3×C4⋊C4C2×D511yescharacteristic
272C2×C3×C22⋊C4—51no—
273C2×C3×C22⋊C4—51no—
274C2×C3×C22⋊C4—51no—
275C2×C3×C22⋊C4—51no—
276C2×C3×C22⋊C4—51no—
277C2×C3×C22⋊C4—51no—
278C2×C3×C22⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×C3×C22⋊C4C2×D511yescharacteristic
281C2×C3×C22⋊C4C2×D511yescharacteristic
282C2×C3×C42—51no—
283C2×C3×C42—51no—
284C2×C3×C42—51no—
285C2×C3×C42—51no—
286C2×C3×C42—51no—
287C2×C3×C42—104no—
288C2×C3×C42C2×D511yescharacteristic
289C3×#95—51no—
290C3×#95—51no—
291C3×#95—51no—
292C3×#95—51no—
293C3×#95—51no—
294C3×#95—51no—
295C24×C5C23×C311yescharacteristic
296C24×C5C23×C311yescharacteristic
297C23×D5C23×C311yescharacteristic
298C2×C5×D4—22no—
299C2×C5×D4—22no—
300C2×C5×D4C2×C3×C414yescomplemented
301C22×C4×C5—22no—
302C22×C4×C5—22no—
303C22×C4×C5—22no—
304C22×C4×C5—22no—
305C22×C4×C5—22no—
306C22×C4×C5C3×D414yescomplemented
307C22×C4×C5C23×C311yescharacteristic
308C22×C4×C5C23×C311yescharacteristic
309C22×C4×C5C23×C311yescharacteristic
310C22×C4×C5C23×C311yescharacteristic
311C22×C4×C5C23×C311yescharacteristic
312C2×C22⋊D5—22no—
313C2×C22⋊D5—22no—
314C2×C22⋊D5—22no—
315C2×C22⋊D5—22no—
316C2×C22⋊D5C2×C3×C414yescomplemented
317C2×C22⋊D5C2×C3×C414yescomplemented
318C22×Dic5—22no—
319C22×Dic5—22no—
320C22×Dic5—22no—
321C22×Dic5—22no—
322C22×Dic5—22no—
323C22×Dic5C2×C3×C414yescomplemented
324C22×Dic5C23×C311yescharacteristic
325C22×Dic5C23×C311yescharacteristic
326C22×Dic5C23×C311yescharacteristic
327C22×Dic5C23×C311yescharacteristic
328C22×Dic5C23×C311yescharacteristic
329C22×Dic5C23×C311yescharacteristic
330C22×Dic5C23×C311yescharacteristic
331C2×C4×D5—22no—
332C2×C4×D5—22no—
333C2×C4×D5—22no—
334C5×C4⋊C4—22no—
335C5×C22⋊C4—22no—
336C5×C22⋊C4—22no—
337C42×C5—22no—
338C22⋊Dic5—22no—
339C22⋊Dic5—22no—
340C22⋊Dic5—22no—
341C22⋊Dic5C2×C3×C414yescomplemented
342#685—22no—
343#685—22no—
344#685—22no—
345#685C2×C3×C414yescomplemented
346#683—22no—
347#683—22no—
348#683—22no—
349#683C2×C3×C414yescomplemented
350C4×Dic5—22no—
351C4×Dic5—22no—
352C4×Dic5—22no—
353C4×Dic5—22no—
354C4×Dic5C3×D414yescomplemented
355C2×#121—51no—
356C2×C4×D4—51no—
357C2×C4×D4—51no—
358C2×C4×D4C3×D511yescharacteristic, complemented
359C22×C42—51no—
360#390—51no—
361#389—51no—
362#388—51no—
363#388—51no—
364#386—51no—
365#386—51no—
366#380—51no—
367C4×C4⋊C4—51no—
368C4×C22⋊C4—51no—
369C4×C22⋊C4—51no—
370C22×C3×C5—22no—
371C22×C3×C5—22no—
372C22×C3×C5—22no—
373C22×C3×C5—22no—
374C22×C3×C5—22no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—22no—
378C22×C3×C5—22no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5C4×D414yescomplemented
384C22×C3×C5C23×C411yescharacteristic
385C22×C3×C5C22×D411yescharacteristic
386C22×C3×C5C22×D411yescharacteristic
387C22×C3×C5C2×#4111yescharacteristic
388C22×C3×C5C2×#4111yescharacteristic
389C22×C3×C5C2×#4111yescharacteristic
390C22×C3×C5C2×#4111yescharacteristic
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—41no—
401C3×C4×C5—41no—
402C3×C4×C5#12114yescomplemented
403C3×Dic5—22no—
404C3×Dic5—22no—
405C3×Dic5—22no—
406C3×Dic5—22no—
407C3×Dic5—41no—
408C3×Dic5—41no—
409C3×Dic5C4×D414yescomplemented
410C24×C3—51no—
411C24×C3C22×D511yescharacteristic
412C24×C3C22×D511yescharacteristic
413C2×C3×D4—22no—
414C2×C3×D4—22no—
415C2×C3×D4—54no—
416C2×C3×D4—54no—
417C2×C3×D4—102no—
418C2×C3×D4—102no—
419C2×C3×D4—102no—
420C2×C3×D4—102no—
421C2×C3×D4C4×D514yescomplemented
422C22×C3×C4—22no—
423C22×C3×C4—22no—
424C22×C3×C4—22no—
425C22×C3×C4—22no—
426C22×C3×C4—22no—
427C22×C3×C4—51no—
428C22×C3×C4—54no—
429C22×C3×C4—51no—
430C22×C3×C4—51no—
431C22×C3×C4—51no—
432C22×C3×C4—51no—
433C22×C3×C4—51no—
434C22×C3×C4—51no—
435C22×C3×C4—102no—
436C22×C3×C4—102no—
437C22×C3×C4—102no—
438C22×C3×C4—102no—
439C22×C3×C4—102no—
440C22×C3×C4—102no—
441C22×C3×C4—102no—
442C22×C3×C4—102no—
443C22×C3×C4C22⋊D514yescomplemented
444C22×C3×C4C22×D511yescharacteristic
445C22×C3×C4C22×D511yescharacteristic
446C22×C3×C4C22×D511yescharacteristic
447C22×C3×C4C22×D511yescharacteristic
448C22×C3×C4C22×D511yescharacteristic
449C3×C4⋊C4—22no—
450C3×C4⋊C4—54no—
451C3×C4⋊C4—102no—
452C3×C4⋊C4—102no—
453C3×C4⋊C4—102no—
454C3×C22⋊C4—22no—
455C3×C22⋊C4—22no—
456C3×C22⋊C4—54no—
457C3×C22⋊C4—54no—
458C3×C22⋊C4—102no—
459C3×C22⋊C4—102no—
460C3×C22⋊C4—102no—
461C3×C22⋊C4—102no—
462C3×C22⋊C4—102no—
463C3×C22⋊C4—102no—
464C3×C42—22no—
465C3×C42—54no—
466C3×C42—102no—
467C3×C42—102no—
468C3×C42—102no—
469C3×C42—102no—
470C23×C5—21no—
471C23×C5—21no—
472C23×C5—21no—
473C23×C5—21no—
474C23×C5—21no—
475C23×C5—21no—
476C23×C5—21no—
477C23×C5—21no—
478C23×C5—21no—
479C23×C5—21no—
480C23×C5C22×C3×C412yes—
481C23×C5C22×C3×C412yes—
482C23×C5C2×C3×D412yes—
483C23×C5C3×#4112yes—
484C23×C5C24×C311yescharacteristic
485C22×D5—21no—
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—21no—
489C22×D5—21no—
490C22×D5—21no—
491C22×D5C22×C3×C412yes—
492C5×D4—28no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—28no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—44no—
505C2×C4×C5C22×C3×C412yes—
506C2×C4×C5C2×C3×D412yes—
507C2×C4×C5C2×C3×D412yes—
508C2×C4×C5C2×C3×D412yes—
509C2×C4×C5C3×#4112yes—
510C22⋊D5—28no—
511C22⋊D5—28no—
512C2×Dic5—28no—
513C2×Dic5—21no—
514C2×Dic5—21no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5—21no—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—21no—
521C2×Dic5—28no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5C22×C3×C412yes—
529C2×Dic5C22×C3×C412yes—
530C2×Dic5C22×C3×C412yes—
531C2×Dic5C2×C3×D412yes—
532C2×Dic5C2×C3×D412yes—
533C2×Dic5C3×#4112yes—
534C2×Dic5C3×#4112yes—
535C4×D5—44no—
536C22×D4—51no—
537C22×D4—51no—
538C22×D4C2×C3×D511yescharacteristic
539C23×C4—51no—
540C23×C4—51no—
541C23×C4—51no—
542C23×C4C2×C3×D511yescharacteristic
543C23×C4C2×C3×D511yescharacteristic
544#121—58no—
545C4×D4—24no—
546C4×D4—104no—
547C4×D4—104no—
548C2×C4⋊C4—51no—
549C2×C4⋊C4—51no—
550C2×C4⋊C4—51no—
551C2×C4⋊C4—51no—
552C2×C4⋊C4C2×C3×D511yescharacteristic
553C2×C22⋊C4—51no—
554C2×C22⋊C4—51no—
555C2×C22⋊C4—51no—
556C2×C22⋊C4—51no—
557C2×C22⋊C4—51no—
558C2×C22⋊C4—51no—
559C2×C22⋊C4—51no—
560C2×C22⋊C4—51no—
561C2×C22⋊C4C2×C3×D511yescharacteristic
562C2×C22⋊C4C2×C3×D511yescharacteristic
563C2×C42—51no—
564C2×C42—51no—
565C2×C42—51no—
566C2×C42—51no—
567C2×C42—51no—
568C2×C42—104no—
569C2×C42C2×C3×D511yescharacteristic
570#95—51no—
571#95—51no—
572#95—51no—
573#95—51no—
574#95—51no—
575#95—51no—
576C2×C3×C5—24no—
577C2×C3×C5—42no—
578C2×C3×C5C2×C4×D411yescharacteristic
579C2×C3×C5C2×C4×D411yescharacteristic
580C2×C3×C5C4×#4111yescharacteristic
581C2×C3×C5C2×#12111yescharacteristic
582C2×C3×C5#52511yescharacteristic
583C2×C3×C5#52911yescharacteristic
584C2×C3×C5#53211yescharacteristic
585C3×D5—42no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—52no—
597C23×C3—101no—
598C23×C3—101no—
599C23×C3—101no—
600C23×C3—101no—
601C23×C3—101no—
602C23×C3—101no—
603C23×C3C2×C4×D512yes—
604C23×C3C2×C4×D512yes—
605C23×C3#70912yes—
606C23×C3C2×C22⋊D512yes—
607C23×C3C23×D511yescharacteristic
608C3×D4—28no—
609C3×D4—108no—
610C3×D4—108no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—28no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—44no—
623C2×C3×C4—52no—
624C2×C3×C4—52no—
625C2×C3×C4—52no—
626C2×C3×C4—52no—
627C2×C3×C4—52no—
628C2×C3×C4—52no—
629C2×C3×C4—52no—
630C2×C3×C4—108no—
631C2×C3×C4—108no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4—101no—
640C2×C3×C4—101no—
641C2×C3×C4—101no—
642C2×C3×C4—101no—
643C2×C3×C4—101no—
644C2×C3×C4—101no—
645C2×C3×C4—101no—
646C2×C3×C4—204no—
647C2×C3×C4C2×C4×D512yes—
648C2×C3×C4D4×D512yes—
649C2×C3×C4#71112yes—
650C2×C3×C4C2×C22⋊D512yes—
651C2×C3×C4C2×C22⋊D512yes—
652C22×C5—22no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—22no—
656C22×C5—22no—
657C22×C5—22no—
658C22×C5—22no—
659C22×C5—22no—
660C22×C5—22no—
661C22×C5—41no—
662C22×C5—41no—
663C22×C5—41no—
664C22×C5—41no—
665C22×C5C3×C4×D414yescomplemented
666C22×C5C23×C3×C411yescharacteristic
667C22×C5C22×C3×D411yescharacteristic
668C22×C5C22×C3×D411yescharacteristic
669C22×C5C2×C3×#4111yescharacteristic
670C22×C5C2×C3×#4111yescharacteristic
671C22×C5C2×C3×#4111yescharacteristic
672C22×C5C2×C3×#4111yescharacteristic
673C2×D5—22no—
674C2×D5—22no—
675C2×D5—22no—
676C2×D5—41no—
677C2×D5—41no—
678C2×D5—41no—
679C2×D5—41no—
680C4×C5—22no—
681C4×C5—22no—
682C4×C5—41no—
683C4×C5—41no—
684C4×C5C3×#12114yescomplemented
685Dic5—22no—
686Dic5—22no—
687Dic5—22no—
688Dic5—22no—
689Dic5—41no—
690Dic5—41no—
691Dic5C3×C4×D414yescomplemented
692C24—51no—
693C24C22×C3×D511yescharacteristic
694C24C22×C3×D511yescharacteristic
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—54no—
698C2×D4—54no—
699C2×D4—102no—
700C2×D4—102no—
701C2×D4—102no—
702C2×D4—102no—
703C2×D4C3×C4×D514yescomplemented
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—51no—
710C22×C4—54no—
711C22×C4—51no—
712C22×C4—51no—
713C22×C4—51no—
714C22×C4—51no—
715C22×C4—51no—
716C22×C4—51no—
717C22×C4—102no—
718C22×C4—102no—
719C22×C4—102no—
720C22×C4—102no—
721C22×C4—102no—
722C22×C4—102no—
723C22×C4—102no—
724C22×C4—102no—
725C22×C4C3×C22⋊D514yescomplemented
726C22×C4C22×C3×D511yescharacteristic
727C22×C4C22×C3×D511yescharacteristic
728C22×C4C22×C3×D511yescharacteristic
729C22×C4C22×C3×D511yescharacteristic
730C22×C4C22×C3×D511yescharacteristic
731C4⋊C4—22no—
732C4⋊C4—54no—
733C4⋊C4—102no—
734C4⋊C4—102no—
735C4⋊C4—102no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—54no—
739C22⋊C4—54no—
740C22⋊C4—102no—
741C22⋊C4—102no—
742C22⋊C4—102no—
743C22⋊C4—102no—
744C22⋊C4—102no—
745C22⋊C4—102no—
746C42—22no—
747C42—54no—
748C42—102no—
749C42—102no—
750C42—102no—
751C42—102no—
752C3×C5C4×#12111yescharacteristic, complemented, Hall
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—102no—
767C22×C3—102no—
768C22×C3—102no—
769C22×C3—201no—
770C22×C3—201no—
771C22×C3—201no—
772C22×C3—201no—
773C22×C3C4×C22⋊D514yescomplemented
774C22×C3C22×C4×D511yescharacteristic
775C22×C3C2×#70911yescharacteristic
776C22×C3C2×D4×D511yescharacteristic
777C22×C3C2×#71111yescharacteristic
778C22×C3D5×#4111yescharacteristic
779C22×C3D5×#4111yescharacteristic
780C22×C3C22×C22⋊D511yescharacteristic
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—41no—
784C3×C4—41no—
785C3×C4—54no—
786C3×C4—102no—
787C3×C4—102no—
788C3×C4—102no—
789C3×C4—102no—
790C3×C4—201no—
791C3×C4—201no—
792C3×C4#408514yesdirect product factor
793C2×C5—24no—
794C2×C5—42no—
795C2×C5C2×C3×C4×D411yescharacteristic
796C2×C5C2×C3×C4×D411yescharacteristic
797C2×C5C3×C4×#4111yescharacteristic
798C2×C5C2×C3×#12111yescharacteristic
799C2×C5C3×#52511yescharacteristic
800C2×C5C3×#52911yescharacteristic
801C2×C5C3×#53211yescharacteristic
802D5—42no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—52no—
814C23—101no—
815C23—101no—
816C23—101no—
817C23—101no—
818C23—101no—
819C23—101no—
820C23C2×C3×C4×D512yes—
821C23C2×C3×C4×D512yes—
822C23C3×#70912yes—
823C23C2×C3×C22⋊D512yes—
824C23C23×C3×D511yescharacteristic
825D4—28no—
826D4—108no—
827D4—108no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—28no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—44no—
840C2×C4—52no—
841C2×C4—52no—
842C2×C4—52no—
843C2×C4—52no—
844C2×C4—52no—
845C2×C4—52no—
846C2×C4—52no—
847C2×C4—108no—
848C2×C4—108no—
849C2×C4—101no—
850C2×C4—101no—
851C2×C4—101no—
852C2×C4—101no—
853C2×C4—101no—
854C2×C4—101no—
855C2×C4—101no—
856C2×C4—101no—
857C2×C4—101no—
858C2×C4—101no—
859C2×C4—101no—
860C2×C4—101no—
861C2×C4—101no—
862C2×C4—101no—
863C2×C4—204no—
864C2×C4C2×C3×C4×D512yes—
865C2×C4C3×D4×D512yes—
866C2×C4C3×#71112yes—
867C2×C4C2×C3×C22⋊D512yes—
868C2×C4C2×C3×C22⋊D512yes—
869C2×C3—24no—
870C2×C3—42no—
871C2×C3—202no—
872C2×C3C4×#71111yescharacteristic
873C2×C3#6587211yescharacteristic
874C2×C3C4×D4×D511yescharacteristic
875C2×C3#6588111yescharacteristic
876C2×C3C2×C4×C22⋊D511yescharacteristic
877C2×C3C2×#408511yescharacteristic
878C2×C3#6616611yescharacteristic
879C5C3×C4×#12111yescharacteristic, complemented, Sylow
880C22—22no—
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—102no—
894C22—102no—
895C22—102no—
896C22—201no—
897C22—201no—
898C22—201no—
899C22—201no—
900C22C3×C4×C22⋊D514yescomplemented
901C22C22×C3×C4×D511yescharacteristic
902C22C2×C3×#70911yescharacteristic
903C22C2×C3×D4×D511yescharacteristic
904C22C2×C3×#71111yescharacteristic
905C22C3×D5×#4111yescharacteristic
906C22C3×D5×#4111yescharacteristic
907C22C22×C3×C22⋊D511yescharacteristic
908C4—22no—
909C4—22no—
910C4—41no—
911C4—41no—
912C4—54no—
913C4—102no—
914C4—102no—
915C4—102no—
916C4—102no—
917C4—201no—
918C4—201no—
919C4C3×#408514yesdirect product factor
920C3C4×#408511yescharacteristic, direct product factor, Sylow
921C2—24no—
922C2—42no—
923C2—202no—
924C2C3×C4×#71111yescharacteristic
925C2C3×#6587211yescharacteristic
926C2C3×C4×D4×D511yescharacteristic
927C2C3×#6588111yescharacteristic
928C2C2×C3×C4×C22⋊D511yescharacteristic
929C2C2×C3×#408511yescharacteristic
930C2C3×#6616611yescharacteristic
subgroupG/H
centerC22×C3×C4C22×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×C4×#121
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ 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. C2×C3×C4×C22⋊D5C2semidirect
5. C22×C3×C4×Dic5C2semidirect
6. C3×#65509C2semidirect
7. C3×C4×C22⋊Dic5C2semidirect
8. C3×#65279C2semidirect
9. C3×#65261C2semidirect
10. C3×#65247C2semidirect
11. C3×#65246C2semidirect
12. C3×#65234C2semidirect
13. C3×#65231C2semidirect
14. C3×C4×#685C2semidirect
15. C3×C4×#683C2semidirect
16. C4×#4085C3direct (N × H)
34. C3×#4085C4direct (N × H)
58. C2×C4×C5×D4C2×C3semidirect
60. C2×C4×C22⋊D5C2×C3semidirect
61. C2×C4×C22⋊D5C2×C3semidirect
62. C22×C4×Dic5C2×C3semidirect
63. #65509C2×C3semidirect
64. C4×C22⋊Dic5C2×C3semidirect
65. #65279C2×C3semidirect
66. #65261C2×C3semidirect
67. #65247C2×C3semidirect
68. #65246C2×C3semidirect
69. #65234C2×C3semidirect
70. #65231C2×C3semidirect
71. C4×#685C2×C3semidirect
72. C4×#683C2×C3semidirect
78. C2×C3×C5×D4C2×C4semidirect
84. C22×C3×C4×C5D4semidirect
94. C2×C3×C22⋊D5C2×C4semidirect
95. C2×C3×C22⋊D5C2×C4semidirect
101. C22×C3×Dic5C2×C4semidirect
119. C3×C22⋊Dic5C2×C4semidirect
123. C3×#685C2×C4semidirect
127. C3×#683C2×C4semidirect
132. C3×C4×Dic5D4semidirect
136. C2×C3×C4×D4D5semidirect
165. #4085C3×C4direct (N × H)
300. C2×C5×D4C2×C3×C4semidirect
306. C22×C4×C5C3×D4semidirect
316. C2×C22⋊D5C2×C3×C4semidirect
317. C2×C22⋊D5C2×C3×C4semidirect
323. C22×Dic5C2×C3×C4semidirect
341. C22⋊Dic5C2×C3×C4semidirect
345. #685C2×C3×C4semidirect
349. #683C2×C3×C4semidirect
354. C4×Dic5C3×D4semidirect
358. C2×C4×D4C3×D5semidirect
383. C22×C3×C5C4×D4semidirect
402. C3×C4×C5#121semidirect
409. C3×Dic5C4×D4semidirect
421. C2×C3×D4C4×D5semidirect
443. C22×C3×C4C22⋊D5semidirect
665. C22×C5C3×C4×D4semidirect
684. C4×C5C3×#121semidirect
691. Dic5C3×C4×D4semidirect
703. C2×D4C3×C4×D5semidirect
725. C22×C4C3×C22⋊D5semidirect
752. C3×C5C4×#121semidirect
773. C22×C3C4×C22⋊D5semidirect
792. C3×C4#4085direct (N × H)
879. C5C3×C4×#121semidirect
900. C22C3×C4×C22⋊D5semidirect
919. C4C3×#4085direct (N × H)
920. C3C4×#4085direct (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
C22×C3×C4×Dic52
C3×#655092
C3×C4×C22⋊Dic52
C3×#652792
C3×#652612
C3×#652472
C3×#652462
C3×#652342
C3×#652312
C3×C4×#6852
C3×C4×#6832
C4×#40853
C3×C4×#1215