Finite Group Databasebeta

← C3×#10606124 #14326999

Subgroups — C3×#10606124 #14326999

Order 1920.

1552 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2C22×C3×#683C211yesmaximal, characteristic, complemented
3C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#4027C211yesmaximal, characteristic
5C2×C3×#4027C211yesmaximal, characteristic
6C3×C5×#385C211yesmaximal, characteristic, complemented
7C3×#65278C211yesmaximal, characteristic, complemented
8C3×#65265C211yesmaximal, characteristic, complemented
9C3×#65261C211yesmaximal, characteristic, complemented
10C3×#65239C211yesmaximal, characteristic, complemented
11C3×#65231C211yesmaximal, characteristic, complemented
12C3×#64957C211yesmaximal, characteristic, complemented
13C3×#64956C211yesmaximal, characteristic, complemented
14C3×#64938C211yesmaximal, characteristic, complemented
15C3×#64936C211yesmaximal, characteristic, complemented
16#10606124C311yesmaximal, characteristic, direct product factor, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C3×C4×C22⋊D5—24no—
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×C4⋊Dic5C2211yescharacteristic
35C2×C3×#683—24no—
36C2×C3×#683C2211yescharacteristic
37C2×C3×#683C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×#683C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic
45C2×C3×C4×Dic5C2211yescharacteristic
46C2×C3×C4×Dic5C2211yescharacteristic
47C2×C3×C4×Dic5C2211yescharacteristic
48C3×D5×C4⋊C4—24no—
49C3×#4027—24no—
50C3×#4027C418yescomplemented
51C3×C5×#95C2211yescharacteristic
52C3×C5×#95C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#3963C2211yescharacteristic
56C3×#3963C2211yescharacteristic
57C3×D4×C4⋊C4—51nomaximal, Hall
58C2×C4×C22⋊D5C2×C311yescharacteristic
59C22×#683C2×C311yescharacteristic, complemented
60C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
61C2×#4027C2×C311yescharacteristic
62C2×#4027C2×C311yescharacteristic
63C5×#385C2×C311yescharacteristic, complemented
64#65278C2×C311yescharacteristic, complemented
65#65265C2×C311yescharacteristic, complemented
66#65261C2×C311yescharacteristic, complemented
67#65239C2×C311yescharacteristic, complemented
68#65231C2×C311yescharacteristic, complemented
69#64957C2×C311yescharacteristic, complemented
70#64956C2×C311yescharacteristic, complemented
71#64938C2×C311yescharacteristic, complemented
72#64936C2×C311yescharacteristic, complemented
73C24×C3×C5C2311yescharacteristic
74C23×C3×D5C2311yescharacteristic
75C22×C3×C4×C5—22no—
76C22×C3×C4×C5—22no—
77C22×C3×C4×C5—41no—
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C2×C3×C22⋊D5C2×C414yes—
85C2×C3×C22⋊D5D414yes—
86C2×C3×C22⋊D5Q814yes—
87C22×C3×Dic5—22no—
88C22×C3×Dic5—22no—
89C22×C3×Dic5—22no—
90C22×C3×Dic5—22no—
91C22×C3×Dic5—41no—
92C22×C3×Dic5C2×C414yescomplemented
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C2×C3×C4×D5—22no—
101C2×C3×C4×D5—22no—
102C2×C3×C4×D5—22no—
103C2×C3×C4×D5—22no—
104C2×C3×C4×D5—22no—
105C2×C3×C4×D5—22no—
106C2×C3×C4×D5—41no—
107C2×C3×C4×D5—41no—
108C2×C3×C4×D5C2×C414yescomplemented
109C3×C5×C4⋊C4—22no—
110C3×C5×C4⋊C4—41no—
111C3×C5×C22⋊C4—22no—
112C3×C5×C22⋊C4C2×C414yescomplemented
113C3×C22⋊Dic5—22no—
114C3×#685—22no—
115C3×#685—22no—
116C3×#685C2×C414yescomplemented
117C3×C4⋊Dic5—22no—
118C3×C4⋊Dic5—41no—
119C3×#683—22no—
120C3×#683—22no—
121C3×#683—22no—
122C3×#683—22no—
123C3×#683—22no—
124C3×#683—22no—
125C3×#683—22no—
126C3×#683C2×C414yescomplemented
127C3×#683D414yescomplemented
128C3×C4×Dic5—22no—
129C3×C4×Dic5—22no—
130C3×C4×Dic5C2×C414yescomplemented
131C2×C3×C4×D4—51no—
132C2×C3×C4×D4—51no—
133C2×C3×C4×D4—51no—
134C22×C3×C4⋊C4—51no—
135C22×C3×C4⋊C4—51no—
136C3×#389—51no—
137C3×#389—51no—
138C3×#385—51no—
139C3×#385—51no—
140C3×#385—51no—
141C3×#385D511yescharacteristic, complemented
142C3×#384—51no—
143C3×#380—51no—
144C3×#380—51no—
145C3×C4×C4⋊C4—51no—
146C23×C4×C5C22×C311yescharacteristic
147C22×C22⋊D5C22×C311yescharacteristic
148C23×Dic5C22×C311yescharacteristic
149C23×Dic5C22×C311yescharacteristic
150C22×C4×D5C22×C311yescharacteristic
151C22×C4×D5C22×C311yescharacteristic
152C22×C4×D5C22×C311yescharacteristic
153C2×C5×C4⋊C4C22×C311yescharacteristic
154C2×C5×C4⋊C4C22×C311yescharacteristic
155C2×C5×C22⋊C4C22×C311yescharacteristic
156C2×C5×C22⋊C4C22×C311yescharacteristic
157C2×C22⋊Dic5C22×C311yescharacteristic
158C4×C22⋊D5—24no—
159C2×#685C22×C311yescharacteristic
160C2×#685C22×C311yescharacteristic
161C2×#685C22×C311yescharacteristic
162C2×C4⋊Dic5C22×C311yescharacteristic
163C2×C4⋊Dic5C22×C311yescharacteristic
164C2×#683—24no—
165C2×#683C22×C311yescharacteristic
166C2×#683C22×C311yescharacteristic
167C2×#683C22×C311yescharacteristic
168C2×#683C22×C311yescharacteristic
169C2×#683C22×C311yescharacteristic
170C2×#683C22×C311yescharacteristic
171C2×#683C22×C311yescharacteristic
172C2×#683C22×C311yescharacteristic
173C2×#683C22×C311yescharacteristic
174C2×C4×Dic5C22×C311yescharacteristic
175C2×C4×Dic5C22×C311yescharacteristic
176C2×C4×Dic5C22×C311yescharacteristic
177D5×C4⋊C4—24no—
178#4027—24no—
179#4027C3×C418yescomplemented
180C5×#95C22×C311yescharacteristic
181C5×#95C22×C311yescharacteristic
182#3963C22×C311yescharacteristic
183#3963C22×C311yescharacteristic
184#3963C22×C311yescharacteristic
185#3963C22×C311yescharacteristic
186D4×C4⋊C4—51noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5C22×C412yes—
192C23×C3×C5C2×D412yes—
193C23×C3×C5C2×Q812yes—
194C23×C3×C5C2411yescharacteristic
195C22×C3×D5—21no—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5C22×C412yes—
200C22×C3×D5C2×D412yes—
201C22×C3×D5C2×Q812yes—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
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—21no—
217C2×C3×C4×C5—44no—
218C2×C3×C4×C5C22×C412yes—
219C2×C3×C4×C5C22×C412yes—
220C2×C3×C4×C5C2×D412yes—
221C3×C22⋊D5C4⋊C4116yescomplemented
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—28no—
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—44no—
237C2×C3×Dic5C22×C412yes—
238C2×C3×Dic5C22×C412yes—
239C2×C3×Dic5C22×C412yes—
240C2×C3×Dic5C2×D412yes—
241C2×C3×Dic5C2×D412yes—
242C2×C3×Dic5C2×D412yes—
243C2×C3×Dic5C2×Q812yes—
244C2×C3×Dic5#4112yes—
245C3×C4×D5—28no—
246C3×C4×D5—44no—
247C3×C4×D5—44no—
248C22×C3×D4—51no—
249C23×C3×C4—51no—
250C23×C3×C4—51no—
251C23×C3×C4—51no—
252C23×C3×C4—51no—
253C23×C3×C4—51no—
254C23×C3×C4C2×D511yescharacteristic
255C3×C4×D4—58no—
256C3×C4×D4—104no—
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⋊C4—51no—
263C2×C3×C4⋊C4—51no—
264C2×C3×C4⋊C4—51no—
265C2×C3×C4⋊C4—51no—
266C2×C3×C4⋊C4—51no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C4⋊C4—104no—
270C2×C3×C4⋊C4—104no—
271C2×C3×C4⋊C4C2×D511yescharacteristic
272C2×C3×C4⋊C4C2×D511yescharacteristic
273C2×C3×C22⋊C4—51no—
274C2×C3×C22⋊C4—51no—
275C2×C3×C22⋊C4—51no—
276C2×C3×C22⋊C4—51no—
277C2×C3×C22⋊C4C2×D511yescharacteristic
278C2×C3×C22⋊C4C2×D511yescharacteristic
279C2×C3×C42—51no—
280C2×C3×C42—51no—
281C2×C3×C42—51no—
282C3×#95—51no—
283C3×#95—51no—
284C3×#95—51no—
285C3×#95—51no—
286C3×#95C2×D511yescharacteristic
287C3×#95C2×D511yescharacteristic
288C24×C5C23×C311yescharacteristic
289C23×D5C23×C311yescharacteristic
290C22×C4×C5—22no—
291C22×C4×C5—22no—
292C22×C4×C5—41no—
293C22×C4×C5C23×C311yescharacteristic
294C22×C4×C5C23×C311yescharacteristic
295C22×C4×C5C23×C311yescharacteristic
296C22×C4×C5C23×C311yescharacteristic
297C22×C4×C5C23×C311yescharacteristic
298C22×C4×C5C23×C311yescharacteristic
299C2×C22⋊D5C2×C3×C414yes—
300C2×C22⋊D5C3×D414yes—
301C2×C22⋊D5C3×Q814yes—
302C22×Dic5—22no—
303C22×Dic5—22no—
304C22×Dic5—22no—
305C22×Dic5—22no—
306C22×Dic5—41no—
307C22×Dic5C2×C3×C414yescomplemented
308C22×Dic5C23×C311yescharacteristic
309C22×Dic5C23×C311yescharacteristic
310C22×Dic5C23×C311yescharacteristic
311C22×Dic5C23×C311yescharacteristic
312C22×Dic5C23×C311yescharacteristic
313C22×Dic5C23×C311yescharacteristic
314C22×Dic5C23×C311yescharacteristic
315C2×C4×D5—22no—
316C2×C4×D5—22no—
317C2×C4×D5—22no—
318C2×C4×D5—22no—
319C2×C4×D5—22no—
320C2×C4×D5—22no—
321C2×C4×D5—41no—
322C2×C4×D5—41no—
323C2×C4×D5C2×C3×C414yescomplemented
324C5×C4⋊C4—22no—
325C5×C4⋊C4—41no—
326C5×C22⋊C4—22no—
327C5×C22⋊C4C2×C3×C414yescomplemented
328C22⋊Dic5—22no—
329#685—22no—
330#685—22no—
331#685C2×C3×C414yescomplemented
332C4⋊Dic5—22no—
333C4⋊Dic5—41no—
334#683—22no—
335#683—22no—
336#683—22no—
337#683—22no—
338#683—22no—
339#683—22no—
340#683—22no—
341#683C2×C3×C414yescomplemented
342#683C3×D414yescomplemented
343C4×Dic5—22no—
344C4×Dic5—22no—
345C4×Dic5C2×C3×C414yescomplemented
346C2×C4×D4—51no—
347C2×C4×D4—51no—
348C2×C4×D4—51no—
349C22×C4⋊C4—51no—
350C22×C4⋊C4—51no—
351#389—51no—
352#389—51no—
353#385—51no—
354#385—51no—
355#385—51no—
356#385C3×D511yescharacteristic, complemented
357#384—51no—
358#380—51no—
359#380—51no—
360C4×C4⋊C4—51no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—22no—
365C22×C3×C5—22no—
366C22×C3×C5—22no—
367C22×C3×C5C2×C4⋊C414yescomplemented
368C22×C3×C5C23×C411yescharacteristic
369C22×C3×C5C22×D411yescharacteristic
370C22×C3×C5C22×D411yescharacteristic
371C22×C3×C5C22×Q811yescharacteristic
372C22×C3×C5C2×#4111yescharacteristic
373C22×C3×C5H(5,𝔽2)11yescharacteristic
374C22×C3×C52−1+411yescharacteristic
375C2×C3×D5—22no—
376C2×C3×D5—22no—
377C2×C3×D5—22no—
378C2×C3×D5—22no—
379C2×C3×D5—22no—
380C2×C3×D5—22no—
381C2×C3×D5C2×C4⋊C414yescomplemented
382C3×C4×C5—22no—
383C3×C4×C5—22no—
384C3×C4×C5—22no—
385C3×C4×C5—41no—
386C3×C4×C5—41no—
387C3×C4×C5—41no—
388C3×Dic5—22no—
389C3×Dic5—22no—
390C3×Dic5—41no—
391C3×Dic5—41no—
392C3×Dic5—41no—
393C3×Dic5C2×C4⋊C414yescomplemented
394C3×Dic5C4×D414yescomplemented
395C24×C3—51no—
396C24×C3C22×D511yescharacteristic
397C2×C3×D4—54no—
398C2×C3×D4—54no—
399C2×C3×D4—54no—
400C22×C3×C4—22no—
401C22×C3×C4—22no—
402C22×C3×C4—41no—
403C22×C3×C4—51no—
404C22×C3×C4—51no—
405C22×C3×C4—54no—
406C22×C3×C4—51no—
407C22×C3×C4—51no—
408C22×C3×C4—54no—
409C22×C3×C4—51no—
410C22×C3×C4—51no—
411C22×C3×C4—51no—
412C22×C3×C4—102no—
413C22×C3×C4—102no—
414C22×C3×C4—102no—
415C22×C3×C4—102no—
416C22×C3×C4—102no—
417C22×C3×C4—102no—
418C22×C3×C4—102no—
419C22×C3×C4—102no—
420C22×C3×C4—102no—
421C22×C3×C4—102no—
422C22×C3×C4—201no—
423C22×C3×C4—201no—
424C22×C3×C4—201no—
425C22×C3×C4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C22×C3×C4C22×D511yescharacteristic
428C22×C3×C4C22×D511yescharacteristic
429C22×C3×C4C22×D511yescharacteristic
430C22×C3×C4C22×D511yescharacteristic
431C3×C4⋊C4—22no—
432C3×C4⋊C4—41no—
433C3×C4⋊C4—54no—
434C3×C4⋊C4—54no—
435C3×C4⋊C4—102no—
436C3×C4⋊C4—102no—
437C3×C4⋊C4—102no—
438C3×C4⋊C4—102no—
439C3×C4⋊C4—102no—
440C3×C4⋊C4—102no—
441C3×C4⋊C4—102no—
442C3×C4⋊C4—102no—
443C3×C4⋊C4—201no—
444C3×C22⋊C4—22no—
445C3×C22⋊C4—54no—
446C3×C22⋊C4—102no—
447C3×C22⋊C4—102no—
448C3×C22⋊C4—102no—
449C3×C22⋊C4C4×D514yescomplemented
450C3×C42—54no—
451C3×C42—102no—
452C3×C42—102no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5—21no—
457C23×C5C22×C3×C412yes—
458C23×C5C2×C3×D412yes—
459C23×C5C2×C3×Q812yes—
460C23×C5C24×C311yescharacteristic
461C22×D5—21no—
462C22×D5—21no—
463C22×D5—21no—
464C22×D5—21no—
465C22×D5C22×C3×C412yes—
466C22×D5C2×C3×D412yes—
467C22×D5C2×C3×Q812yes—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—21no—
471C2×C4×C5—21no—
472C2×C4×C5—21no—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
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—44no—
484C2×C4×C5C22×C3×C412yes—
485C2×C4×C5C22×C3×C412yes—
486C2×C4×C5C2×C3×D412yes—
487C22⋊D5C3×C4⋊C4116yescomplemented
488C2×Dic5—21no—
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—28no—
493C2×Dic5—21no—
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—44no—
503C2×Dic5C22×C3×C412yes—
504C2×Dic5C22×C3×C412yes—
505C2×Dic5C22×C3×C412yes—
506C2×Dic5C2×C3×D412yes—
507C2×Dic5C2×C3×D412yes—
508C2×Dic5C2×C3×D412yes—
509C2×Dic5C2×C3×Q812yes—
510C2×Dic5C3×#4112yes—
511C4×D5—28no—
512C4×D5—44no—
513C4×D5—44no—
514C22×D4—51no—
515C23×C4—51no—
516C23×C4—51no—
517C23×C4—51no—
518C23×C4—51no—
519C23×C4—51no—
520C23×C4C2×C3×D511yescharacteristic
521C4×D4—58no—
522C4×D4—104no—
523C4×D4—104no—
524C2×C4⋊C4—51no—
525C2×C4⋊C4—51no—
526C2×C4⋊C4—51no—
527C2×C4⋊C4—51no—
528C2×C4⋊C4—51no—
529C2×C4⋊C4—51no—
530C2×C4⋊C4—51no—
531C2×C4⋊C4—51no—
532C2×C4⋊C4—51no—
533C2×C4⋊C4—51no—
534C2×C4⋊C4—51no—
535C2×C4⋊C4—104no—
536C2×C4⋊C4—104no—
537C2×C4⋊C4C2×C3×D511yescharacteristic
538C2×C4⋊C4C2×C3×D511yescharacteristic
539C2×C22⋊C4—51no—
540C2×C22⋊C4—51no—
541C2×C22⋊C4—51no—
542C2×C22⋊C4—51no—
543C2×C22⋊C4C2×C3×D511yescharacteristic
544C2×C22⋊C4C2×C3×D511yescharacteristic
545C2×C42—51no—
546C2×C42—51no—
547C2×C42—51no—
548#95—51no—
549#95—51no—
550#95—51no—
551#95—51no—
552#95C2×C3×D511yescharacteristic
553#95C2×C3×D511yescharacteristic
554C2×C3×C5—24no—
555C2×C3×C5C22×C4⋊C411yescharacteristic
556C2×C3×C5C2×C4×D411yescharacteristic
557C2×C3×C5#52011yescharacteristic
558C2×C3×C5D4211yescharacteristic
559C2×C3×C5#54711yescharacteristic
560C2×C3×C5D4×Q811yescharacteristic
561C2×C3×C5#55411yescharacteristic
562C3×D5—24no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—52no—
568C23×C3—52no—
569C23×C3—52no—
570C23×C3—101no—
571C23×C3—101no—
572C23×C3—101no—
573C23×C3—101no—
574C23×C3C2×C4×D512yes—
575C23×C3D4×D512yes—
576C23×C3Q8×D512yes—
577C23×C3C23×D511yescharacteristic
578C3×D4—516no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—44no—
595C2×C3×C4—52no—
596C2×C3×C4—52no—
597C2×C3×C4—52no—
598C2×C3×C4—52no—
599C2×C3×C4—52no—
600C2×C3×C4—52no—
601C2×C3×C4—52no—
602C2×C3×C4—52no—
603C2×C3×C4—108no—
604C2×C3×C4—108no—
605C2×C3×C4—101no—
606C2×C3×C4—101no—
607C2×C3×C4—101no—
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—204no—
619C2×C3×C4—204no—
620C2×C3×C4—204no—
621C2×C3×C4C2×C4×D512yes—
622C2×C3×C4C2×C4×D512yes—
623C2×C3×C4D4×D512yes—
624C22×C5—22no—
625C22×C5—22no—
626C22×C5—22no—
627C22×C5—22no—
628C22×C5—22no—
629C22×C5—22no—
630C22×C5C2×C3×C4⋊C414yescomplemented
631C22×C5C23×C3×C411yescharacteristic
632C22×C5C22×C3×D411yescharacteristic
633C22×C5C22×C3×D411yescharacteristic
634C22×C5C22×C3×Q811yescharacteristic
635C22×C5C2×C3×#4111yescharacteristic
636C22×C5C3×H(5,𝔽2)11yescharacteristic
637C22×C5C3×2−1+411yescharacteristic
638C2×D5—22no—
639C2×D5—22no—
640C2×D5—22no—
641C2×D5—22no—
642C2×D5—22no—
643C2×D5—22no—
644C2×D5C2×C3×C4⋊C414yescomplemented
645C4×C5—22no—
646C4×C5—22no—
647C4×C5—22no—
648C4×C5—41no—
649C4×C5—41no—
650C4×C5—41no—
651Dic5—22no—
652Dic5—22no—
653Dic5—41no—
654Dic5—41no—
655Dic5—41no—
656Dic5C2×C3×C4⋊C414yescomplemented
657Dic5C3×C4×D414yescomplemented
658C24—51no—
659C24C22×C3×D511yescharacteristic
660C2×D4—54no—
661C2×D4—54no—
662C2×D4—54no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—41no—
666C22×C4—51no—
667C22×C4—51no—
668C22×C4—54no—
669C22×C4—51no—
670C22×C4—51no—
671C22×C4—54no—
672C22×C4—51no—
673C22×C4—51no—
674C22×C4—51no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—201no—
686C22×C4—201no—
687C22×C4—201no—
688C22×C4C22×C3×D511yescharacteristic
689C22×C4C22×C3×D511yescharacteristic
690C22×C4C22×C3×D511yescharacteristic
691C22×C4C22×C3×D511yescharacteristic
692C22×C4C22×C3×D511yescharacteristic
693C22×C4C22×C3×D511yescharacteristic
694C4⋊C4—22no—
695C4⋊C4—41no—
696C4⋊C4—54no—
697C4⋊C4—54no—
698C4⋊C4—102no—
699C4⋊C4—102no—
700C4⋊C4—102no—
701C4⋊C4—102no—
702C4⋊C4—102no—
703C4⋊C4—102no—
704C4⋊C4—102no—
705C4⋊C4—102no—
706C4⋊C4—201no—
707C22⋊C4—22no—
708C22⋊C4—54no—
709C22⋊C4—102no—
710C22⋊C4—102no—
711C22⋊C4—102no—
712C22⋊C4C3×C4×D514yescomplemented
713C42—54no—
714C42—102no—
715C42—102no—
716C3×C5D4×C4⋊C411yescharacteristic, complemented, Hall
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—54no—
724C22×C3—102no—
725C22×C3—102no—
726C22×C3—102no—
727C22×C3—102no—
728C22×C3—102no—
729C22×C3—102no—
730C22×C3D5×C4⋊C414yescomplemented
731C22×C3C22×C4×D511yescharacteristic
732C22×C3C2×D4×D511yescharacteristic
733C22×C3C2×D4×D511yescharacteristic
734C22×C3#414411yescharacteristic
735C22×C3C2×Q8×D511yescharacteristic
736C22×C3D5×#4111yescharacteristic
737C22×C3#415011yescharacteristic
738C3×C4—22no—
739C3×C4—22no—
740C3×C4—22no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—54no—
745C3×C4—54no—
746C3×C4—102no—
747C3×C4—102no—
748C3×C4—201no—
749C3×C4—201no—
750C3×C4—201no—
751C2×C5—24no—
752C2×C5C22×C3×C4⋊C411yescharacteristic
753C2×C5C2×C3×C4×D411yescharacteristic
754C2×C5C3×#52011yescharacteristic
755C2×C5C3×D4211yescharacteristic
756C2×C5C3×#54711yescharacteristic
757C2×C5C3×D4×Q811yescharacteristic
758C2×C5C3×#55411yescharacteristic
759D5—24no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—52no—
765C23—52no—
766C23—52no—
767C23—101no—
768C23—101no—
769C23—101no—
770C23—101no—
771C23C2×C3×C4×D512yes—
772C23C3×D4×D512yes—
773C23C3×Q8×D512yes—
774C23C23×C3×D511yescharacteristic
775D4—516no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—44no—
792C2×C4—52no—
793C2×C4—52no—
794C2×C4—52no—
795C2×C4—52no—
796C2×C4—52no—
797C2×C4—52no—
798C2×C4—52no—
799C2×C4—52no—
800C2×C4—108no—
801C2×C4—108no—
802C2×C4—101no—
803C2×C4—101no—
804C2×C4—101no—
805C2×C4—101no—
806C2×C4—101no—
807C2×C4—101no—
808C2×C4—101no—
809C2×C4—101no—
810C2×C4—101no—
811C2×C4—101no—
812C2×C4—101no—
813C2×C4—101no—
814C2×C4—101no—
815C2×C4—204no—
816C2×C4—204no—
817C2×C4—204no—
818C2×C4C2×C3×C4×D512yes—
819C2×C4C2×C3×C4×D512yes—
820C2×C4C3×D4×D512yes—
821C2×C3—24no—
822C2×C3—104no—
823C2×C3C2×D5×C4⋊C411yescharacteristic
824C2×C3C4×D4×D511yescharacteristic
825C2×C3#6588011yescharacteristic
826C2×C3#6592411yescharacteristic
827C2×C3#6596611yescharacteristic
828C2×C3#6597011yescharacteristic
829C2×C3#6598911yescharacteristic
830C5C3×D4×C4⋊C411yescharacteristic, complemented, Sylow
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—54no—
838C22—102no—
839C22—102no—
840C22—102no—
841C22—102no—
842C22—102no—
843C22—102no—
844C22C3×D5×C4⋊C414yescomplemented
845C22C22×C3×C4×D511yescharacteristic
846C22C2×C3×D4×D511yescharacteristic
847C22C2×C3×D4×D511yescharacteristic
848C22C3×#414411yescharacteristic
849C22C2×C3×Q8×D511yescharacteristic
850C22C3×D5×#4111yescharacteristic
851C22C3×#415011yescharacteristic
852C4—22no—
853C4—22no—
854C4—22no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—54no—
859C4—54no—
860C4—102no—
861C4—102no—
862C4—201no—
863C4—201no—
864C4—201no—
865C3#1060612411yescharacteristic, direct product factor, Sylow
866C2—24no—
867C2—104no—
868C2C2×C3×D5×C4⋊C411yescharacteristic
869C2C3×C4×D4×D511yescharacteristic
870C2C3×#6588011yescharacteristic
871C2C3×#6592411yescharacteristic
872C2C3×#6596611yescharacteristic
873C2C3×#6597011yescharacteristic
874C2C3×#6598911yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#385C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C5C24×C3
hypercenterC3×#385D5
hypocenterC5C3×D4×C4⋊C4
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#385

Complements

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

NH ≅ G/Ntype
2. C22×C3×#683C2semidirect
3. C2×C3×D5×C4⋊C4C2semidirect
6. C3×C5×#385C2semidirect
7. C3×#65278C2semidirect
8. C3×#65265C2semidirect
9. C3×#65261C2semidirect
10. C3×#65239C2semidirect
11. C3×#65231C2semidirect
12. C3×#64957C2semidirect
13. C3×#64956C2semidirect
14. C3×#64938C2semidirect
15. C3×#64936C2semidirect
16. #10606124C3direct (N × H)
50. C3×#4027C4semidirect
59. C22×#683C2×C3semidirect
60. C2×D5×C4⋊C4C2×C3semidirect
63. C5×#385C2×C3semidirect
64. #65278C2×C3semidirect
65. #65265C2×C3semidirect
66. #65261C2×C3semidirect
67. #65239C2×C3semidirect
68. #65231C2×C3semidirect
69. #64957C2×C3semidirect
70. #64956C2×C3semidirect
71. #64938C2×C3semidirect
72. #64936C2×C3semidirect
92. C22×C3×Dic5C2×C4semidirect
108. C2×C3×C4×D5C2×C4semidirect
112. C3×C5×C22⋊C4C2×C4semidirect
116. C3×#685C2×C4semidirect
126. C3×#683C2×C4semidirect
127. C3×#683D4semidirect
130. C3×C4×Dic5C2×C4semidirect
141. C3×#385D5semidirect
179. #4027C3×C4semidirect
221. C3×C22⋊D5C4⋊C4semidirect
307. C22×Dic5C2×C3×C4semidirect
323. C2×C4×D5C2×C3×C4semidirect
327. C5×C22⋊C4C2×C3×C4semidirect
331. #685C2×C3×C4semidirect
341. #683C2×C3×C4semidirect
342. #683C3×D4semidirect
345. C4×Dic5C2×C3×C4semidirect
356. #385C3×D5semidirect
367. C22×C3×C5C2×C4⋊C4semidirect
381. C2×C3×D5C2×C4⋊C4semidirect
393. C3×Dic5C2×C4⋊C4semidirect
394. C3×Dic5C4×D4semidirect
449. C3×C22⋊C4C4×D5semidirect
487. C22⋊D5C3×C4⋊C4semidirect
630. C22×C5C2×C3×C4⋊C4semidirect
644. C2×D5C2×C3×C4⋊C4semidirect
656. Dic5C2×C3×C4⋊C4semidirect
657. Dic5C3×C4×D4semidirect
712. C22⋊C4C3×C4×D5semidirect
716. C3×C5D4×C4⋊C4semidirect
730. C22×C3D5×C4⋊C4semidirect
830. C5C3×D4×C4⋊C4semidirect
844. C22C3×D5×C4⋊C4semidirect
865. C3#10606124direct (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×C22⋊D52
C22×C3×#6832
C2×C3×D5×C4⋊C42
C2×C3×#40272
C3×C5×#3852
C3×#652782
C3×#652652
C3×#652612
C3×#652392
C3×#652312
C3×#649572
C3×#649562
C3×#649382
C3×#649362
#106061243
C3×D4×C4⋊C45