Finite Group Databasebeta

← C3×C4×#4076 #14321432

Subgroups — C3×C4×#4076 #14321432

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C42×C5C211yesmaximal, characteristic, complemented
2C2×C3×#4076C211yesmaximal, characteristic
3C2×C3×C4×C22⋊D5C212yesmaximal, complemented
4C2×C3×C4×D20C211yesmaximal, characteristic, complemented
5C3×#65502C212yesmaximal, complemented
6C3×#65501C211yesmaximal, characteristic, complemented
7C3×#65229C212yesmaximal, complemented
8C3×#65228C211yesmaximal, characteristic, complemented
9C3×C4×#685C212yesmaximal, complemented
10C3×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
11C3×#65217C211yesmaximal, characteristic, complemented
12C4×#4076C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C22×C3×C22⋊D5C2212yes—
17C22×C3×D20C2211yescharacteristic
18C22×C3×C4×D5C2212yes—
19C2×C3×C42×C5—24no—
20C2×C3×C42×C5C2211yescharacteristic
21C2×C3×C42×C5C2211yescharacteristic
22C2×C3×C42×C5C2211yescharacteristic
23C2×C3×C42×C5C2211yescharacteristic
24C2×C3×C22⋊Dic5C2212yes—
25C3×#4076C418yesdirect product factor
26C3×C4×C22⋊D5—28no—
27C2×C3×#685C2212yes—
28C2×C3×#685C2212yes—
29C2×C3×#685C2212yes—
30C2×C3×#685C2212yes—
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×#683C2212yes—
35C2×C3×C4×Dic5C2212yes—
36C3×C4×D20—24no—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#3963C2212yes—
40C3×C4×#121—51nomaximal, Hall
41C22×C42×C5C2×C311yescharacteristic, complemented
42C2×#4076C2×C311yescharacteristic
43C2×C4×C22⋊D5C2×C312yescomplemented
44C2×C4×D20C2×C311yescharacteristic, complemented
45#65502C2×C312yescomplemented
46#65501C2×C311yescharacteristic, complemented
47#65229C2×C312yescomplemented
48#65228C2×C311yescharacteristic, complemented
49C4×#685C2×C312yescomplemented
50C4×C4⋊Dic5C2×C311yescharacteristic, complemented
51#65217C2×C311yescharacteristic, complemented
52C24×C3×C5C2311yescharacteristic
53C23×C3×D5C2312yes—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5—22no—
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5C2×C414yescomplemented
62C22×C3×C4×C5D414yescomplemented
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2311yescharacteristic
68C22×C3×C4×C5C2311yescharacteristic
69C2×C3×C22⋊D5—24no—
70C2×C3×C22⋊D5—24no—
71C2×C3×C22⋊D5C2×C418yescomplemented
72C22×C3×Dic5C2312yes—
73C22×C3×Dic5C2312yes—
74C22×C3×Dic5C2312yes—
75C2×C3×D20—22no—
76C2×C3×D20—22no—
77C2×C3×D20C2×C414yescomplemented
78C2×C3×C4×D5—24no—
79C2×C3×C4×D5—24no—
80C2×C3×C4×D5—24no—
81C3×C42×C5—22no—
82C3×C42×C5—22no—
83C3×C42×C5—22no—
84C3×C42×C5D414yescomplemented
85C3×C22⋊Dic5—24no—
86C3×#685—24no—
87C3×#685—24no—
88C3×#685—24no—
89C3×#685C2×C418yescomplemented
90C3×C4⋊Dic5—22no—
91C3×C4⋊Dic5—22no—
92C3×C4⋊Dic5C2×C414yescomplemented
93C3×#683—24no—
94C3×C4×Dic5—24no—
95C2×C3×#121—51no—
96C2×C3×C4×D4—52no—
97C2×C3×C4×D4—51no—
98C22×C3×C42D511yescharacteristic, complemented
99C3×#390—51no—
100C3×#389—51no—
101C3×#388—52no—
102C3×#386—52no—
103C3×#380—51no—
104C3×C4×C4⋊C4—51no—
105C3×C4×C22⋊C4—52no—
106C23×C4×C5C22×C311yescharacteristic
107C23×C4×C5C22×C311yescharacteristic
108C23×C4×C5C22×C311yescharacteristic
109C22×C22⋊D5C22×C312yes—
110C22×D20C22×C311yescharacteristic
111C22×C4×D5C22×C312yes—
112C2×C42×C5—24no—
113C2×C42×C5C22×C311yescharacteristic
114C2×C42×C5C22×C311yescharacteristic
115C2×C42×C5C22×C311yescharacteristic
116C2×C42×C5C22×C311yescharacteristic
117C2×C22⋊Dic5C22×C312yes—
118#4076C3×C418yesdirect product factor
119C4×C22⋊D5—28no—
120C2×#685C22×C312yes—
121C2×#685C22×C312yes—
122C2×#685C22×C312yes—
123C2×#685C22×C312yes—
124C2×C4⋊Dic5C22×C311yescharacteristic
125C2×C4⋊Dic5C22×C311yescharacteristic
126C2×C4⋊Dic5C22×C311yescharacteristic
127C2×#683C22×C312yes—
128C2×C4×Dic5C22×C312yes—
129C4×D20—24no—
130#3963C22×C312yes—
131#3963C22×C312yes—
132#3963C22×C312yes—
133C4×#121—51noSylow
134C23×C3×C5—21no—
135C23×C3×C5—21no—
136C23×C3×C5—21no—
137C23×C3×C5—21no—
138C23×C3×C5C22×C412yes—
139C23×C3×C5C2×D412yes—
140C23×C3×C5#4112yes—
141C23×C3×C5C2411yescharacteristic
142C22×C3×D5—22no—
143C22×C3×D5—22no—
144C22×C3×D5—22no—
145C22×C3×D5—22no—
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5C22×C414yes—
149C2×C3×C4×C5—28no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—21no—
158C2×C3×C4×C5—28no—
159C2×C3×C4×C5—28no—
160C2×C3×C4×C5C22×C412yes—
161C2×C3×C4×C5C22×C412yes—
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2×D412yes—
164C2×C3×C4×C5C2×D412yes—
165C2×C3×C4×C5C2×D412yes—
166C2×C3×C4×C5C2×D412yes—
167C2×C3×C4×C5#4112yes—
168C2×C3×C4×C5#4112yes—
169C2×C3×C4×C5#4112yes—
170C3×C22⋊D5—216no—
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—22no—
178C2×C3×Dic5—22no—
179C2×C3×Dic5C22×C414yes—
180C3×D20—28no—
181C3×C4×D5—48no—
182C22×C3×D4—52no—
183C22×C3×D4—51no—
184C23×C3×C4—52no—
185C23×C3×C4C2×D511yescharacteristic
186C23×C3×C4C2×D511yescharacteristic
187C23×C3×C4C2×D511yescharacteristic
188C3×#121—58no—
189C3×C4×D4—108no—
190C3×C4×D4—104no—
191C2×C3×C4⋊C4—51no—
192C2×C3×C4⋊C4—51no—
193C2×C3×C4⋊C4—51no—
194C2×C3×C4⋊C4—52no—
195C2×C3×C22⋊C4—52no—
196C2×C3×C22⋊C4—52no—
197C2×C3×C22⋊C4—52no—
198C2×C3×C22⋊C4—52no—
199C2×C3×C22⋊C4—52no—
200C2×C3×C42—24no—
201C2×C3×C42—52no—
202C2×C3×C42C2×D511yescharacteristic
203C2×C3×C42C2×D511yescharacteristic
204C2×C3×C42C2×D511yescharacteristic
205C2×C3×C42C2×D511yescharacteristic
206C3×#95—52no—
207C3×#95—52no—
208C3×#95—52no—
209C24×C5C23×C311yescharacteristic
210C23×D5C23×C312yes—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5C2×C3×C414yescomplemented
219C22×C4×C5C3×D414yescomplemented
220C22×C4×C5C23×C311yescharacteristic
221C22×C4×C5C23×C311yescharacteristic
222C22×C4×C5C23×C311yescharacteristic
223C22×C4×C5C23×C311yescharacteristic
224C22×C4×C5C23×C311yescharacteristic
225C22×C4×C5C23×C311yescharacteristic
226C2×C22⋊D5—24no—
227C2×C22⋊D5—24no—
228C2×C22⋊D5C2×C3×C418yescomplemented
229C22×Dic5C23×C312yes—
230C22×Dic5C23×C312yes—
231C22×Dic5C23×C312yes—
232C2×D20—22no—
233C2×D20—22no—
234C2×D20C2×C3×C414yescomplemented
235C2×C4×D5—24no—
236C2×C4×D5—24no—
237C2×C4×D5—24no—
238C42×C5—22no—
239C42×C5—22no—
240C42×C5—22no—
241C42×C5C3×D414yescomplemented
242C22⋊Dic5—24no—
243#685—24no—
244#685—24no—
245#685—24no—
246#685C2×C3×C418yescomplemented
247C4⋊Dic5—22no—
248C4⋊Dic5—22no—
249C4⋊Dic5C2×C3×C414yescomplemented
250#683—24no—
251C4×Dic5—24no—
252C2×#121—51no—
253C2×C4×D4—52no—
254C2×C4×D4—51no—
255C22×C42C3×D511yescharacteristic, complemented
256#390—51no—
257#389—51no—
258#388—52no—
259#386—52no—
260#380—51no—
261C4×C4⋊C4—51no—
262C4×C22⋊C4—52no—
263C22×C3×C5—22no—
264C22×C3×C5—22no—
265C22×C3×C5—22no—
266C22×C3×C5—22no—
267C22×C3×C5—22no—
268C22×C3×C5—22no—
269C22×C3×C5C4×D414yescomplemented
270C22×C3×C5C23×C411yescharacteristic
271C22×C3×C5C22×D411yescharacteristic
272C22×C3×C5C22×D411yescharacteristic
273C22×C3×C5C2×#4111yescharacteristic
274C22×C3×C5C2×#4111yescharacteristic
275C22×C3×C5C2×#4111yescharacteristic
276C22×C3×C5C2×#4111yescharacteristic
277C2×C3×D5—24no—
278C2×C3×D5—24no—
279C2×C3×D5—24no—
280C2×C3×D5—42no—
281C2×C3×D5—42no—
282C2×C3×D5—42no—
283C2×C3×D5—42no—
284C3×C4×C5—22no—
285C3×C4×C5—22no—
286C3×C4×C5—22no—
287C3×C4×C5—22no—
288C3×C4×C5C4×D414yescomplemented
289C3×C4×C5#12114yescomplemented
290C3×Dic5—24no—
291C3×Dic5—42no—
292C3×Dic5—42no—
293C24×C3—52no—
294C24×C3C22×D511yescharacteristic
295C2×C3×D4—58no—
296C2×C3×D4—54no—
297C2×C3×D4—104no—
298C2×C3×D4—104no—
299C2×C3×D4—102no—
300C2×C3×D4—102no—
301C22×C3×C4—22no—
302C22×C3×C4—22no—
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
308C22×C3×C4—52no—
309C22×C3×C4—52no—
310C22×C3×C4—52no—
311C22×C3×C4—104no—
312C22×C3×C4—104no—
313C22×C3×C4—104no—
314C22×C3×C4C4×D514yescomplemented
315C22×C3×C4D2014yescomplemented
316C22×C3×C4C22×D511yescharacteristic
317C22×C3×C4C22×D511yescharacteristic
318C22×C3×C4C22×D511yescharacteristic
319C22×C3×C4C22×D511yescharacteristic
320C22×C3×C4C22×D511yescharacteristic
321C22×C3×C4C22×D511yescharacteristic
322C3×C4⋊C4—54no—
323C3×C4⋊C4—104no—
324C3×C4⋊C4—102no—
325C3×C4⋊C4—102no—
326C3×C22⋊C4—58no—
327C3×C22⋊C4—104no—
328C3×C22⋊C4—104no—
329C3×C22⋊C4—104no—
330C3×C22⋊C4—104no—
331C3×C42—22no—
332C3×C42—22no—
333C3×C42—22no—
334C3×C42—104no—
335C3×C42C22⋊D514yescomplemented
336C23×C5—21no—
337C23×C5—21no—
338C23×C5—21no—
339C23×C5—21no—
340C23×C5C22×C3×C412yes—
341C23×C5C2×C3×D412yes—
342C23×C5C3×#4112yes—
343C23×C5C24×C311yescharacteristic
344C22×D5—22no—
345C22×D5—22no—
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5C22×C3×C414yes—
351C2×C4×C5—28no—
352C2×C4×C5—21no—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5—21no—
356C2×C4×C5—21no—
357C2×C4×C5—21no—
358C2×C4×C5—21no—
359C2×C4×C5—21no—
360C2×C4×C5—28no—
361C2×C4×C5—28no—
362C2×C4×C5C22×C3×C412yes—
363C2×C4×C5C22×C3×C412yes—
364C2×C4×C5C2×C3×D412yes—
365C2×C4×C5C2×C3×D412yes—
366C2×C4×C5C2×C3×D412yes—
367C2×C4×C5C2×C3×D412yes—
368C2×C4×C5C2×C3×D412yes—
369C2×C4×C5C3×#4112yes—
370C2×C4×C5C3×#4112yes—
371C2×C4×C5C3×#4112yes—
372C22⋊D5—216no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5C22×C3×C414yes—
382D20—28no—
383C4×D5—48no—
384C22×D4—52no—
385C22×D4—51no—
386C23×C4—52no—
387C23×C4C2×C3×D511yescharacteristic
388C23×C4C2×C3×D511yescharacteristic
389C23×C4C2×C3×D511yescharacteristic
390#121—58no—
391C4×D4—108no—
392C4×D4—104no—
393C2×C4⋊C4—51no—
394C2×C4⋊C4—51no—
395C2×C4⋊C4—52no—
396C2×C4⋊C4—51no—
397C2×C22⋊C4—52no—
398C2×C22⋊C4—52no—
399C2×C22⋊C4—52no—
400C2×C22⋊C4—52no—
401C2×C22⋊C4—52no—
402C2×C42—24no—
403C2×C42—52no—
404C2×C42C2×C3×D511yescharacteristic
405C2×C42C2×C3×D511yescharacteristic
406C2×C42C2×C3×D511yescharacteristic
407C2×C42C2×C3×D511yescharacteristic
408#95—52no—
409#95—52no—
410#95—52no—
411C2×C3×C5—24no—
412C2×C3×C5C2×C4×D411yescharacteristic
413C2×C3×C5C2×C4×D411yescharacteristic
414C2×C3×C5C4×#4111yescharacteristic
415C2×C3×C5C2×#12111yescharacteristic
416C2×C3×C5#52511yescharacteristic
417C2×C3×C5#52911yescharacteristic
418C2×C3×C5#53211yescharacteristic
419C3×D5—44no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—54no—
425C23×C3—102no—
426C23×C3—102no—
427C23×C3—102no—
428C23×C3—102no—
429C23×C3—102no—
430C23×C3—102no—
431C23×C3C2×C4×D512yes—
432C23×C3C2×D2012yes—
433C23×C3#70912yes—
434C23×C3C23×D511yescharacteristic
435C3×D4—1016no—
436C3×D4—108no—
437C2×C3×C4—28no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—28no—
447C2×C3×C4—28no—
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—208no—
458C2×C3×C4C2×C4×D512yes—
459C2×C3×C4C2×C4×D512yes—
460C2×C3×C4C2×D2012yes—
461C2×C3×C4C2×D2012yes—
462C2×C3×C4#70912yes—
463C2×C3×C4#70912yes—
464C2×C3×C4#70912yes—
465C2×C3×C4C2×C22⋊D512yes—
466C2×C3×C4C2×C22⋊D512yes—
467C2×C3×C4C2×C22⋊D512yes—
468C22×C5—22no—
469C22×C5—22no—
470C22×C5—22no—
471C22×C5—22no—
472C22×C5—22no—
473C22×C5—22no—
474C22×C5C3×C4×D414yescomplemented
475C22×C5C23×C3×C411yescharacteristic
476C22×C5C22×C3×D411yescharacteristic
477C22×C5C22×C3×D411yescharacteristic
478C22×C5C2×C3×#4111yescharacteristic
479C22×C5C2×C3×#4111yescharacteristic
480C22×C5C2×C3×#4111yescharacteristic
481C22×C5C2×C3×#4111yescharacteristic
482C2×D5—24no—
483C2×D5—24no—
484C2×D5—24no—
485C2×D5—42no—
486C2×D5—42no—
487C2×D5—42no—
488C2×D5—42no—
489C4×C5—22no—
490C4×C5—22no—
491C4×C5—22no—
492C4×C5—22no—
493C4×C5C3×C4×D414yescomplemented
494C4×C5C3×#12114yescomplemented
495Dic5—24no—
496Dic5—42no—
497Dic5—42no—
498C24—52no—
499C24C22×C3×D511yescharacteristic
500C2×D4—58no—
501C2×D4—54no—
502C2×D4—104no—
503C2×D4—104no—
504C2×D4—102no—
505C2×D4—102no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—52no—
514C22×C4—52no—
515C22×C4—52no—
516C22×C4—104no—
517C22×C4—104no—
518C22×C4—104no—
519C22×C4C3×C4×D514yescomplemented
520C22×C4C3×D2014yescomplemented
521C22×C4C22×C3×D511yescharacteristic
522C22×C4C22×C3×D511yescharacteristic
523C22×C4C22×C3×D511yescharacteristic
524C22×C4C22×C3×D511yescharacteristic
525C22×C4C22×C3×D511yescharacteristic
526C22×C4C22×C3×D511yescharacteristic
527C4⋊C4—54no—
528C4⋊C4—104no—
529C4⋊C4—102no—
530C4⋊C4—102no—
531C22⋊C4—58no—
532C22⋊C4—104no—
533C22⋊C4—104no—
534C22⋊C4—104no—
535C22⋊C4—104no—
536C42—22no—
537C42—22no—
538C42—22no—
539C42—104no—
540C42C3×C22⋊D514yescomplemented
541C3×C5C4×#12111yescharacteristic, complemented, Hall
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—104no—
549C22×C3—104no—
550C22×C3—104no—
551C22×C3—202no—
552C22×C3—202no—
553C22×C3—202no—
554C22×C3—202no—
555C22×C3C4×D2014yescomplemented
556C22×C3C22×C4×D511yescharacteristic
557C22×C3C22×D2011yescharacteristic
558C22×C3C2×#70911yescharacteristic
559C22×C3C2×#70911yescharacteristic
560C22×C3C2×#70911yescharacteristic
561C22×C3C2×#70911yescharacteristic
562C22×C3C22×C22⋊D511yescharacteristic
563C3×C4—22no—
564C3×C4—22no—
565C3×C4—22no—
566C3×C4—22no—
567C3×C4—104no—
568C3×C4—202no—
569C3×C4—202no—
570C3×C4C4×C22⋊D514yescomplemented
571C3×C4#407614yesdirect product factor
572C2×C5—24no—
573C2×C5C2×C3×C4×D411yescharacteristic
574C2×C5C2×C3×C4×D411yescharacteristic
575C2×C5C3×C4×#4111yescharacteristic
576C2×C5C2×C3×#12111yescharacteristic
577C2×C5C3×#52511yescharacteristic
578C2×C5C3×#52911yescharacteristic
579C2×C5C3×#53211yescharacteristic
580D5—44no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—54no—
586C23—102no—
587C23—102no—
588C23—102no—
589C23—102no—
590C23—102no—
591C23—102no—
592C23C2×C3×C4×D512yes—
593C23C2×C3×D2012yes—
594C23C3×#70912yes—
595C23C23×C3×D511yescharacteristic
596D4—1016no—
597D4—108no—
598C2×C4—28no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—28no—
608C2×C4—28no—
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—208no—
619C2×C4C2×C3×C4×D512yes—
620C2×C4C2×C3×C4×D512yes—
621C2×C4C2×C3×D2012yes—
622C2×C4C2×C3×D2012yes—
623C2×C4C3×#70912yes—
624C2×C4C3×#70912yes—
625C2×C4C3×#70912yes—
626C2×C4C2×C3×C22⋊D512yes—
627C2×C4C2×C3×C22⋊D512yes—
628C2×C4C2×C3×C22⋊D512yes—
629C2×C3—24no—
630C2×C3—204no—
631C2×C3C2×C4×D2011yescharacteristic
632C2×C3C4×#70911yescharacteristic
633C2×C3#6581111yescharacteristic
634C2×C3#6581311yescharacteristic
635C2×C3C2×C4×C22⋊D511yescharacteristic
636C2×C3C2×#407611yescharacteristic
637C2×C3#6612511yescharacteristic
638C5C3×C4×#12111yescharacteristic, complemented, Sylow
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—104no—
646C22—104no—
647C22—104no—
648C22—202no—
649C22—202no—
650C22—202no—
651C22—202no—
652C22C3×C4×D2014yescomplemented
653C22C22×C3×C4×D511yescharacteristic
654C22C22×C3×D2011yescharacteristic
655C22C2×C3×#70911yescharacteristic
656C22C2×C3×#70911yescharacteristic
657C22C2×C3×#70911yescharacteristic
658C22C2×C3×#70911yescharacteristic
659C22C22×C3×C22⋊D511yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—104no—
665C4—202no—
666C4—202no—
667C4C3×C4×C22⋊D514yescomplemented
668C4C3×#407614yesdirect product factor
669C3C4×#407611yescharacteristic, direct product factor, Sylow
670C2—24no—
671C2—204no—
672C2C2×C3×C4×D2011yescharacteristic
673C2C3×C4×#70911yescharacteristic
674C2C3×#6581111yescharacteristic
675C2C3×#6581311yescharacteristic
676C2C2×C3×C4×C22⋊D511yescharacteristic
677C2C2×C3×#407611yescharacteristic
678C2C3×#6612511yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC22×C3×C42×C5C2
socleC23×C3×C5C24
prime radicalC2×C3×#4076C2
cosocleC23×C5C24×C3
hypercenterC22×C3×C42D5
hypocenterC5C3×C4×#121
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C22×C3×C42

Complements

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

NH ≅ G/Ntype
1. C22×C3×C42×C5C2semidirect
3. C2×C3×C4×C22⋊D5C2semidirect
4. C2×C3×C4×D20C2semidirect
5. C3×#65502C2semidirect
6. C3×#65501C2semidirect
7. C3×#65229C2semidirect
8. C3×#65228C2semidirect
9. C3×C4×#685C2semidirect
10. C3×C4×C4⋊Dic5C2semidirect
11. C3×#65217C2semidirect
12. C4×#4076C3direct (N × H)
25. C3×#4076C4direct (N × H)
41. C22×C42×C5C2×C3semidirect
43. C2×C4×C22⋊D5C2×C3semidirect
44. C2×C4×D20C2×C3semidirect
45. #65502C2×C3semidirect
46. #65501C2×C3semidirect
47. #65229C2×C3semidirect
48. #65228C2×C3semidirect
49. C4×#685C2×C3semidirect
50. C4×C4⋊Dic5C2×C3semidirect
51. #65217C2×C3semidirect
61. C22×C3×C4×C5C2×C4semidirect
62. C22×C3×C4×C5D4semidirect
71. C2×C3×C22⋊D5C2×C4semidirect
77. C2×C3×D20C2×C4semidirect
84. C3×C42×C5D4semidirect
89. C3×#685C2×C4semidirect
92. C3×C4⋊Dic5C2×C4semidirect
98. C22×C3×C42D5semidirect
118. #4076C3×C4direct (N × H)
218. C22×C4×C5C2×C3×C4semidirect
219. C22×C4×C5C3×D4semidirect
228. C2×C22⋊D5C2×C3×C4semidirect
234. C2×D20C2×C3×C4semidirect
241. C42×C5C3×D4semidirect
246. #685C2×C3×C4semidirect
249. C4⋊Dic5C2×C3×C4semidirect
255. C22×C42C3×D5semidirect
269. C22×C3×C5C4×D4semidirect
288. C3×C4×C5C4×D4semidirect
289. C3×C4×C5#121semidirect
314. C22×C3×C4C4×D5semidirect
315. C22×C3×C4D20semidirect
335. C3×C42C22⋊D5semidirect
474. C22×C5C3×C4×D4semidirect
493. C4×C5C3×C4×D4semidirect
494. C4×C5C3×#121semidirect
519. C22×C4C3×C4×D5semidirect
520. C22×C4C3×D20semidirect
540. C42C3×C22⋊D5semidirect
541. C3×C5C4×#121semidirect
555. C22×C3C4×D20semidirect
570. C3×C4C4×C22⋊D5semidirect
571. C3×C4#4076direct (N × H)
638. C5C3×C4×#121semidirect
652. C22C3×C4×D20semidirect
667. C4C3×C4×C22⋊D5semidirect
668. C4C3×#4076direct (N × H)
669. C3C4×#4076direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C42×C52
C2×C3×#40762
C2×C3×C4×C22⋊D52
C2×C3×C4×D202
C3×#655022
C3×#655012
C3×#652292
C3×#652282
C3×C4×#6852
C3×C4×C4⋊Dic52
C3×#652172
C4×#40763
C3×C4×#1215