Finite Group Databasebeta

← C3×#10607036 #14327325

Subgroups — C3×#10607036 #14327325

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4039C211yesmaximal, characteristic
2C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#4018C211yesmaximal, characteristic, complemented
4C3×C5×#387C211yesmaximal, characteristic, complemented
5C3×#65279C211yesmaximal, characteristic, complemented
6C3×#65270C211yesmaximal, characteristic, complemented
7C3×C4×#685C211yesmaximal, characteristic, complemented
8C3×#64959C211yesmaximal, characteristic, complemented
9C3×#64956C211yesmaximal, characteristic, complemented
10C3×#64956C211yesmaximal, characteristic, complemented
11C3×#64955C211yesmaximal, characteristic, complemented
12C3×#64954C211yesmaximal, characteristic
13C3×#64954C211yesmaximal, characteristic
14C3×#64939C211yesmaximal, characteristic, complemented
15C3×#64938C211yesmaximal, characteristic, complemented
16#10607036C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×D20C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C42×C5C2211yescharacteristic
25C2×C3×#685C2211yescharacteristic
26C2×C3×#685C2211yescharacteristic
27C2×C3×#685C2211yescharacteristic
28C2×C3×#685C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic
36C2×C3×#683C2211yescharacteristic
37C2×C3×#683C2211yescharacteristic
38C2×C3×C4×Dic5C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic
40C2×C3×C4×Dic5C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42C3×#4039C418yescomplemented
43C3×D5×C4⋊C4—24no—
44C3×#4018—24no—
45C3×C5×#95C2211yescharacteristic
46C3×C5×#95C2211yescharacteristic
47C3×C5×#95C2211yescharacteristic
48C3×C5×#95C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#2352—51nomaximal, Hall
56C2×#4039C2×C311yescharacteristic
57C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
58C2×#4018C2×C311yescharacteristic, complemented
59C5×#387C2×C311yescharacteristic, complemented
60#65279C2×C311yescharacteristic, complemented
61#65270C2×C311yescharacteristic, complemented
62C4×#685C2×C311yescharacteristic, complemented
63#64959C2×C311yescharacteristic, complemented
64#64956C2×C311yescharacteristic, complemented
65#64956C2×C311yescharacteristic, complemented
66#64955C2×C311yescharacteristic, complemented
67#64954C2×C311yescharacteristic
68#64954C2×C311yescharacteristic
69#64939C2×C311yescharacteristic, complemented
70#64938C2×C311yescharacteristic, complemented
71C23×C3×D5C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C2×C3×D20—22no—
87C2×C3×D20—22no—
88C2×C3×D20C2×C414yes—
89C2×C3×C4×D5—22no—
90C2×C3×C4×D5—22no—
91C2×C3×C4×D5—22no—
92C2×C3×C4×D5—22no—
93C2×C3×C4×D5—22no—
94C2×C3×C4×D5—22no—
95C2×C3×C4×D5—22no—
96C2×C3×C4×D5—22no—
97C2×C3×C4×D5—41no—
98C2×C3×C4×D5—41no—
99C2×C3×C4×D5C2×C414yes—
100C2×C3×C4×D5C2×C414yescomplemented
101C3×C5×C4⋊C4—22no—
102C3×C5×C4⋊C4C2×C414yescomplemented
103C3×C42×C5—22no—
104C3×#685—22no—
105C3×#685—22no—
106C3×#685—22no—
107C3×#685—22no—
108C3×#685—41no—
109C3×#685—41no—
110C3×#685C2×C414yes—
111C3×#685C2×C414yescomplemented
112C3×C4⋊Dic5—22no—
113C3×#683—22no—
114C3×#683—22no—
115C3×#683—22no—
116C3×#683D414yescomplemented
117C3×C4×Dic5—22no—
118C3×C4×Dic5—41no—
119C3×C4×Dic5—41no—
120C3×C4×Dic5C2×C414yescomplemented
121C2×C3×C4×D4—51no—
122C2×C3×#117—51no—
123C22×C3×C4⋊C4—51no—
124C3×#388—51no—
125C3×#388—51no—
126C3×#387—51no—
127C3×#387D511yescharacteristic, complemented
128C3×#386—51no—
129C3×#386—51no—
130C3×#382—51no—
131C3×#380—51no—
132C3×#380—51no—
133C3×C4×C4⋊C4—51no—
134C3×C4×C22⋊C4—51no—
135C3×C4×C22⋊C4—51no—
136C22×D20C22×C311yescharacteristic
137C22×C4×D5C22×C311yescharacteristic
138C22×C4×D5C22×C311yescharacteristic
139C22×C4×D5C22×C311yescharacteristic
140C22×C4×D5C22×C311yescharacteristic
141C2×C5×C4⋊C4C22×C311yescharacteristic
142C2×C5×C4⋊C4C22×C311yescharacteristic
143C2×C42×C5C22×C311yescharacteristic
144C2×#685C22×C311yescharacteristic
145C2×#685C22×C311yescharacteristic
146C2×#685C22×C311yescharacteristic
147C2×#685C22×C311yescharacteristic
148C2×#685C22×C311yescharacteristic
149C2×#685C22×C311yescharacteristic
150C2×#685C22×C311yescharacteristic
151C2×#685C22×C311yescharacteristic
152C2×C4⋊Dic5C22×C311yescharacteristic
153C2×#683C22×C311yescharacteristic
154C2×#683C22×C311yescharacteristic
155C2×#683C22×C311yescharacteristic
156C2×#683C22×C311yescharacteristic
157C2×C4×Dic5C22×C311yescharacteristic
158C2×C4×Dic5C22×C311yescharacteristic
159C2×C4×Dic5C22×C311yescharacteristic
160C2×C4×Dic5C22×C311yescharacteristic
161#4039C3×C418yescomplemented
162D5×C4⋊C4—24no—
163#4018—24no—
164C5×#95C22×C311yescharacteristic
165C5×#95C22×C311yescharacteristic
166C5×#95C22×C311yescharacteristic
167C5×#95C22×C311yescharacteristic
168#3963C22×C311yescharacteristic
169#3963C22×C311yescharacteristic
170#3963C22×C311yescharacteristic
171#3963C22×C311yescharacteristic
172#3963C22×C311yescharacteristic
173#3963C22×C311yescharacteristic
174#2352—51noSylow
175C23×C3×C5C2411yescharacteristic
176C22×C3×D5—21no—
177C22×C3×D5—21no—
178C22×C3×D5—21no—
179C22×C3×D5—21no—
180C22×C3×D5—21no—
181C22×C3×D5—21no—
182C22×C3×D5—21no—
183C22×C3×D5—21no—
184C22×C3×D5—21no—
185C22×C3×D5—21no—
186C22×C3×D5C22×C412yes—
187C22×C3×D5C22×C412yes—
188C22×C3×D5#4112yes—
189C22×C3×D5#4112yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
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×C5C22×C412yes—
208C2×C3×C4×C5C22×C412yes—
209C2×C3×C4×C5C22×C412yes—
210C2×C3×C4×C5C2×D412yes—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5C22×C412yes—
225C2×C3×Dic5C22×C412yes—
226C2×C3×Dic5C2×D412yes—
227C2×C3×Dic5C2×D412yes—
228C2×C3×Dic5#4112yes—
229C3×D20—28no—
230C3×C4×D5—28no—
231C3×C4×D5—28no—
232C3×C4×D5—44no—
233C3×C4×D5—44no—
234C22×C3×D4—51no—
235C23×C3×C4—51no—
236C23×C3×C4—51no—
237C23×C3×C4—51no—
238C23×C3×C4—51no—
239C3×C4×D4—58no—
240C3×#117—104no—
241C2×C3×C4⋊C4—51no—
242C2×C3×C4⋊C4—51no—
243C2×C3×C4⋊C4—51no—
244C2×C3×C4⋊C4—51no—
245C2×C3×C4⋊C4—51no—
246C2×C3×C4⋊C4—104no—
247C2×C3×C4⋊C4C2×D511yescharacteristic
248C2×C3×C4⋊C4C2×D511yescharacteristic
249C2×C3×C22⋊C4—51no—
250C2×C3×C22⋊C4—51no—
251C2×C3×C22⋊C4—51no—
252C2×C3×C22⋊C4—51no—
253C2×C3×C22⋊C4—51no—
254C2×C3×C22⋊C4—51no—
255C2×C3×C22⋊C4—51no—
256C2×C3×C22⋊C4—51no—
257C2×C3×C42—51no—
258C2×C3×C42—51no—
259C2×C3×C42—51no—
260C2×C3×C42—51no—
261C2×C3×C42C2×D511yescharacteristic
262C3×#95—51no—
263C3×#95—51no—
264C3×#95—51no—
265C3×#95—51no—
266C3×#95—51no—
267C3×#95—51no—
268C3×#95C2×D511yescharacteristic
269C3×#95C2×D511yescharacteristic
270C3×#95C2×D511yescharacteristic
271C3×#95C2×D511yescharacteristic
272C23×D5C23×C311yescharacteristic
273C23×D5C23×C311yescharacteristic
274C22×C4×C5C23×C311yescharacteristic
275C22×C4×C5C23×C311yescharacteristic
276C22×C4×C5C23×C311yescharacteristic
277C22×C4×C5C23×C311yescharacteristic
278C22×C4×C5C23×C311yescharacteristic
279C22×C4×C5C23×C311yescharacteristic
280C22×C4×C5C23×C311yescharacteristic
281C22×Dic5C23×C311yescharacteristic
282C22×Dic5C23×C311yescharacteristic
283C22×Dic5C23×C311yescharacteristic
284C22×Dic5C23×C311yescharacteristic
285C22×Dic5C23×C311yescharacteristic
286C22×Dic5C23×C311yescharacteristic
287C2×D20—22no—
288C2×D20—22no—
289C2×D20C2×C3×C414yes—
290C2×C4×D5—22no—
291C2×C4×D5—22no—
292C2×C4×D5—22no—
293C2×C4×D5—22no—
294C2×C4×D5—22no—
295C2×C4×D5—22no—
296C2×C4×D5—22no—
297C2×C4×D5—22no—
298C2×C4×D5—41no—
299C2×C4×D5—41no—
300C2×C4×D5C2×C3×C414yes—
301C2×C4×D5C2×C3×C414yescomplemented
302C5×C4⋊C4—22no—
303C5×C4⋊C4C2×C3×C414yescomplemented
304C42×C5—22no—
305#685—22no—
306#685—22no—
307#685—22no—
308#685—22no—
309#685—41no—
310#685—41no—
311#685C2×C3×C414yes—
312#685C2×C3×C414yescomplemented
313C4⋊Dic5—22no—
314#683—22no—
315#683—22no—
316#683—22no—
317#683C3×D414yescomplemented
318C4×Dic5—22no—
319C4×Dic5—41no—
320C4×Dic5—41no—
321C4×Dic5C2×C3×C414yescomplemented
322C2×C4×D4—51no—
323C2×#117—51no—
324C22×C4⋊C4—51no—
325#388—51no—
326#388—51no—
327#387—51no—
328#387C3×D511yescharacteristic, complemented
329#386—51no—
330#386—51no—
331#382—51no—
332#380—51no—
333#380—51no—
334C4×C4⋊C4—51no—
335C4×C22⋊C4—51no—
336C4×C22⋊C4—51no—
337C22×C3×C5C23×C411yescharacteristic
338C22×C3×C5C22×D411yescharacteristic
339C22×C3×C5C2×#4111yescharacteristic
340C22×C3×C5C2×#4111yescharacteristic
341C22×C3×C5C2×#4111yescharacteristic
342C22×C3×C5H(5,𝔽2)11yescharacteristic
343C22×C3×C52−1+411yescharacteristic
344C2×C3×D5—22no—
345C2×C3×D5—22no—
346C2×C3×D5—22no—
347C2×C3×D5—22no—
348C2×C3×D5—22no—
349C2×C3×D5—22no—
350C2×C3×D5—22no—
351C2×C3×D5—22no—
352C2×C3×D5—22no—
353C2×C3×D5—41no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C2×C3×D5#11714yescomplemented
358C3×C4×C5—22no—
359C3×C4×C5—22no—
360C3×C4×C5—22no—
361C3×C4×C5—22no—
362C3×C4×C5—41no—
363C3×C4×C5—41no—
364C3×C4×C5—41no—
365C3×Dic5—22no—
366C3×Dic5—22no—
367C3×Dic5—41no—
368C3×Dic5—41no—
369C3×Dic5—41no—
370C3×Dic5C4×D414yes—
371C24×C3—51no—
372C24×C3—51no—
373C2×C3×D4—54no—
374C2×C3×D4—102no—
375C2×C3×D4—102no—
376C22×C3×C4—51no—
377C22×C3×C4—51no—
378C22×C3×C4—51no—
379C22×C3×C4—54no—
380C22×C3×C4—54no—
381C22×C3×C4—51no—
382C22×C3×C4—51no—
383C22×C3×C4—51no—
384C22×C3×C4—102no—
385C22×C3×C4—102no—
386C22×C3×C4—102no—
387C22×C3×C4—102no—
388C22×C3×C4—102no—
389C22×C3×C4—102no—
390C22×C3×C4—102no—
391C22×C3×C4—102no—
392C22×C3×C4—201no—
393C22×C3×C4—201no—
394C22×C3×C4C22×D511yescharacteristic
395C22×C3×C4C22×D511yescharacteristic
396C22×C3×C4C22×D511yescharacteristic
397C22×C3×C4C22×D511yescharacteristic
398C22×C3×C4C22×D511yescharacteristic
399C22×C3×C4C22×D511yescharacteristic
400C22×C3×C4C22×D511yescharacteristic
401C3×C4⋊C4—22no—
402C3×C4⋊C4—54no—
403C3×C4⋊C4—102no—
404C3×C4⋊C4—102no—
405C3×C4⋊C4—102no—
406C3×C4⋊C4—102no—
407C3×C4⋊C4C4×D514yescomplemented
408C3×C22⋊C4—54no—
409C3×C22⋊C4—54no—
410C3×C22⋊C4—102no—
411C3×C22⋊C4—102no—
412C3×C22⋊C4—102no—
413C3×C22⋊C4—102no—
414C3×C22⋊C4—201no—
415C3×C22⋊C4—201no—
416C3×C42—22no—
417C3×C42—54no—
418C3×C42—102no—
419C3×C42—201no—
420C3×C42—201no—
421C23×C5C24×C311yescharacteristic
422C22×D5—21no—
423C22×D5—21no—
424C22×D5—21no—
425C22×D5—21no—
426C22×D5—21no—
427C22×D5—21no—
428C22×D5—21no—
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—21no—
432C22×D5C22×C3×C412yes—
433C22×D5C22×C3×C412yes—
434C22×D5C3×#4112yes—
435C22×D5C3×#4112yes—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—21no—
444C2×C4×C5—21no—
445C2×C4×C5—21no—
446C2×C4×C5—21no—
447C2×C4×C5—21no—
448C2×C4×C5—21no—
449C2×C4×C5—21no—
450C2×C4×C5—21no—
451C2×C4×C5—21no—
452C2×C4×C5—21no—
453C2×C4×C5C22×C3×C412yes—
454C2×C4×C5C22×C3×C412yes—
455C2×C4×C5C22×C3×C412yes—
456C2×C4×C5C2×C3×D412yes—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—21no—
462C2×Dic5—21no—
463C2×Dic5—21no—
464C2×Dic5—21no—
465C2×Dic5—21no—
466C2×Dic5—21no—
467C2×Dic5—21no—
468C2×Dic5—21no—
469C2×Dic5—21no—
470C2×Dic5C22×C3×C412yes—
471C2×Dic5C22×C3×C412yes—
472C2×Dic5C2×C3×D412yes—
473C2×Dic5C2×C3×D412yes—
474C2×Dic5C3×#4112yes—
475D20—28no—
476C4×D5—28no—
477C4×D5—28no—
478C4×D5—44no—
479C4×D5—44no—
480C22×D4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—51no—
485C4×D4—58no—
486#117—104no—
487C2×C4⋊C4—51no—
488C2×C4⋊C4—51no—
489C2×C4⋊C4—51no—
490C2×C4⋊C4—51no—
491C2×C4⋊C4—51no—
492C2×C4⋊C4—104no—
493C2×C4⋊C4C2×C3×D511yescharacteristic
494C2×C4⋊C4C2×C3×D511yescharacteristic
495C2×C22⋊C4—51no—
496C2×C22⋊C4—51no—
497C2×C22⋊C4—51no—
498C2×C22⋊C4—51no—
499C2×C22⋊C4—51no—
500C2×C22⋊C4—51no—
501C2×C22⋊C4—51no—
502C2×C22⋊C4—51no—
503C2×C42—51no—
504C2×C42—51no—
505C2×C42—51no—
506C2×C42—51no—
507C2×C42C2×C3×D511yescharacteristic
508#95—51no—
509#95—51no—
510#95—51no—
511#95—51no—
512#95—51no—
513#95—51no—
514#95C2×C3×D511yescharacteristic
515#95C2×C3×D511yescharacteristic
516#95C2×C3×D511yescharacteristic
517#95C2×C3×D511yescharacteristic
518C2×C3×C5C2×#11711yescharacteristic
519C2×C3×C5C2×C4×D411yescharacteristic
520C2×C3×C5#52011yescharacteristic
521C2×C3×C5#54611yescharacteristic
522C2×C3×C5#54811yescharacteristic
523C2×C3×C5#55211yescharacteristic
524C2×C3×C5#55311yescharacteristic
525C3×D5—24no—
526C3×D5—42no—
527C23×C3—52no—
528C23×C3—52no—
529C23×C3—52no—
530C23×C3—52no—
531C23×C3—101no—
532C23×C3—101no—
533C23×C3—101no—
534C23×C3—101no—
535C23×C3—101no—
536C23×C3—101no—
537C23×C3—101no—
538C23×C3—101no—
539C23×C3—101no—
540C23×C3—101no—
541C23×C3C23×D511yescharacteristic
542C3×D4—108no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—52no—
561C2×C3×C4—52no—
562C2×C3×C4—52no—
563C2×C3×C4—52no—
564C2×C3×C4—52no—
565C2×C3×C4—108no—
566C2×C3×C4—108no—
567C2×C3×C4—101no—
568C2×C3×C4—101no—
569C2×C3×C4—101no—
570C2×C3×C4—101no—
571C2×C3×C4—101no—
572C2×C3×C4—101no—
573C2×C3×C4—101no—
574C2×C3×C4—101no—
575C2×C3×C4—101no—
576C2×C3×C4—101no—
577C2×C3×C4—101no—
578C2×C3×C4—101no—
579C2×C3×C4—101no—
580C2×C3×C4—204no—
581C2×C3×C4—204no—
582C2×C3×C4C2×C4×D512yes—
583C2×C3×C4C2×C4×D512yes—
584C2×C3×C4C2×C4×D512yes—
585C2×C3×C4D4×D512yes—
586C22×C5C23×C3×C411yescharacteristic
587C22×C5C22×C3×D411yescharacteristic
588C22×C5C2×C3×#4111yescharacteristic
589C22×C5C2×C3×#4111yescharacteristic
590C22×C5C2×C3×#4111yescharacteristic
591C22×C5C3×H(5,𝔽2)11yescharacteristic
592C22×C5C3×2−1+411yescharacteristic
593C2×D5—22no—
594C2×D5—22no—
595C2×D5—22no—
596C2×D5—22no—
597C2×D5—22no—
598C2×D5—22no—
599C2×D5—22no—
600C2×D5—22no—
601C2×D5—22no—
602C2×D5—41no—
603C2×D5—41no—
604C2×D5—41no—
605C2×D5—41no—
606C2×D5C3×#11714yescomplemented
607C4×C5—22no—
608C4×C5—22no—
609C4×C5—22no—
610C4×C5—22no—
611C4×C5—41no—
612C4×C5—41no—
613C4×C5—41no—
614Dic5—22no—
615Dic5—22no—
616Dic5—41no—
617Dic5—41no—
618Dic5—41no—
619Dic5C3×C4×D414yes—
620C24—51no—
621C24—51no—
622C2×D4—54no—
623C2×D4—102no—
624C2×D4—102no—
625C22×C4—51no—
626C22×C4—51no—
627C22×C4—51no—
628C22×C4—54no—
629C22×C4—54no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—51no—
633C22×C4—102no—
634C22×C4—102no—
635C22×C4—102no—
636C22×C4—102no—
637C22×C4—102no—
638C22×C4—102no—
639C22×C4—102no—
640C22×C4—102no—
641C22×C4—201no—
642C22×C4—201no—
643C22×C4C22×C3×D511yescharacteristic
644C22×C4C22×C3×D511yescharacteristic
645C22×C4C22×C3×D511yescharacteristic
646C22×C4C22×C3×D511yescharacteristic
647C22×C4C22×C3×D511yescharacteristic
648C22×C4C22×C3×D511yescharacteristic
649C22×C4C22×C3×D511yescharacteristic
650C4⋊C4—22no—
651C4⋊C4—54no—
652C4⋊C4—102no—
653C4⋊C4—102no—
654C4⋊C4—102no—
655C4⋊C4—102no—
656C4⋊C4C3×C4×D514yescomplemented
657C22⋊C4—54no—
658C22⋊C4—54no—
659C22⋊C4—102no—
660C22⋊C4—102no—
661C22⋊C4—102no—
662C22⋊C4—102no—
663C22⋊C4—201no—
664C22⋊C4—201no—
665C42—22no—
666C42—54no—
667C42—102no—
668C42—201no—
669C42—201no—
670C3×C5#235211yescharacteristic, complemented, Hall
671C22×C3—54no—
672C22×C3—102no—
673C22×C3—102no—
674C22×C3—102no—
675C22×C3—102no—
676C22×C3—102no—
677C22×C3—102no—
678C22×C3—102no—
679C22×C3—102no—
680C22×C3—102no—
681C22×C3—201no—
682C22×C3—201no—
683C22×C3—201no—
684C22×C3—201no—
685C22×C3C22×C4×D511yescharacteristic
686C22×C3C2×D4×D511yescharacteristic
687C22×C3#414711yescharacteristic
688C22×C3D5×#4111yescharacteristic
689C22×C3D5×#4111yescharacteristic
690C22×C3D5×#4111yescharacteristic
691C22×C3#414911yescharacteristic
692C3×C4—22no—
693C3×C4—22no—
694C3×C4—22no—
695C3×C4—22no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—54no—
700C3×C4—102no—
701C3×C4—102no—
702C3×C4—201no—
703C3×C4—201no—
704C3×C4—201no—
705C2×C5C2×C3×#11711yescharacteristic
706C2×C5C2×C3×C4×D411yescharacteristic
707C2×C5C3×#52011yescharacteristic
708C2×C5C3×#54611yescharacteristic
709C2×C5C3×#54811yescharacteristic
710C2×C5C3×#55211yescharacteristic
711C2×C5C3×#55311yescharacteristic
712D5—24no—
713D5—42no—
714C23—52no—
715C23—52no—
716C23—52no—
717C23—52no—
718C23—101no—
719C23—101no—
720C23—101no—
721C23—101no—
722C23—101no—
723C23—101no—
724C23—101no—
725C23—101no—
726C23—101no—
727C23—101no—
728C23C23×C3×D511yescharacteristic
729D4—108no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—52no—
748C2×C4—52no—
749C2×C4—52no—
750C2×C4—52no—
751C2×C4—52no—
752C2×C4—108no—
753C2×C4—108no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—101no—
758C2×C4—101no—
759C2×C4—101no—
760C2×C4—101no—
761C2×C4—101no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—101no—
766C2×C4—101no—
767C2×C4—204no—
768C2×C4—204no—
769C2×C4C2×C3×C4×D512yes—
770C2×C4C2×C3×C4×D512yes—
771C2×C4C2×C3×C4×D512yes—
772C2×C4C3×D4×D512yes—
773C2×C3—104no—
774C2×C3—202no—
775C2×C3D5×#11711yescharacteristic
776C2×C3C4×D4×D511yescharacteristic
777C2×C3#6590811yescharacteristic
778C2×C3#6596711yescharacteristic
779C2×C3#6598811yescharacteristic
780C2×C3#6602711yescharacteristic
781C2×C3#6604311yescharacteristic
782C5C3×#235211yescharacteristic, complemented, Sylow
783C22—54no—
784C22—102no—
785C22—102no—
786C22—102no—
787C22—102no—
788C22—102no—
789C22—102no—
790C22—102no—
791C22—102no—
792C22—102no—
793C22—201no—
794C22—201no—
795C22—201no—
796C22—201no—
797C22C22×C3×C4×D511yescharacteristic
798C22C2×C3×D4×D511yescharacteristic
799C22C3×#414711yescharacteristic
800C22C3×D5×#4111yescharacteristic
801C22C3×D5×#4111yescharacteristic
802C22C3×D5×#4111yescharacteristic
803C22C3×#414911yescharacteristic
804C4—22no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—54no—
812C4—102no—
813C4—102no—
814C4—201no—
815C4—201no—
816C4—201no—
817C3#1060703611yescharacteristic, direct product factor, Sylow
818C2—104no—
819C2—202no—
820C2C3×D5×#11711yescharacteristic
821C2C3×C4×D4×D511yescharacteristic
822C2C3×#6590811yescharacteristic
823C2C3×#6596711yescharacteristic
824C2C3×#6598811yescharacteristic
825C2C3×#6602711yescharacteristic
826C2C3×#6604311yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#387C2
socleC23×C3×C5C24
prime radicalC22×C3×D20C22
cosocleC23×C5C24×C3
hypercenterC3×#387D5
hypocenterC5C3×#2352
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#387

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5×C4⋊C4C2semidirect
3. C2×C3×#4018C2semidirect
4. C3×C5×#387C2semidirect
5. C3×#65279C2semidirect
6. C3×#65270C2semidirect
7. C3×C4×#685C2semidirect
8. C3×#64959C2semidirect
9. C3×#64956C2semidirect
10. C3×#64956C2semidirect
11. C3×#64955C2semidirect
14. C3×#64939C2semidirect
15. C3×#64938C2semidirect
16. #10607036C3direct (N × H)
42. C3×#4039C4semidirect
57. C2×D5×C4⋊C4C2×C3semidirect
58. C2×#4018C2×C3semidirect
59. C5×#387C2×C3semidirect
60. #65279C2×C3semidirect
61. #65270C2×C3semidirect
62. C4×#685C2×C3semidirect
63. #64959C2×C3semidirect
64. #64956C2×C3semidirect
65. #64956C2×C3semidirect
66. #64955C2×C3semidirect
69. #64939C2×C3semidirect
70. #64938C2×C3semidirect
100. C2×C3×C4×D5C2×C4semidirect
102. C3×C5×C4⋊C4C2×C4semidirect
111. C3×#685C2×C4semidirect
116. C3×#683D4semidirect
120. C3×C4×Dic5C2×C4semidirect
127. C3×#387D5semidirect
161. #4039C3×C4semidirect
301. C2×C4×D5C2×C3×C4semidirect
303. C5×C4⋊C4C2×C3×C4semidirect
312. #685C2×C3×C4semidirect
317. #683C3×D4semidirect
321. C4×Dic5C2×C3×C4semidirect
328. #387C3×D5semidirect
357. C2×C3×D5#117semidirect
407. C3×C4⋊C4C4×D5semidirect
606. C2×D5C3×#117semidirect
656. C4⋊C4C3×C4×D5semidirect
670. C3×C5#2352semidirect
782. C5C3×#2352semidirect
817. C3#10607036direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40392
C2×C3×D5×C4⋊C42
C2×C3×#40182
C3×C5×#3872
C3×#652792
C3×#652702
C3×C4×#6852
C3×#649592
C3×#649562
C3×#649552
C3×#649542
C3×#649392
C3×#649382
#106070363
C3×#23525