Finite Group Databasebeta

← C3×#10606404 #14327334

Subgroups — C3×#10606404 #14327334

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×D4×Dic5C211yesmaximal, characteristic
2C22×C3×#683C211yesmaximal, characteristic, complemented
3C2×C3×#4023C211yesmaximal, characteristic, complemented
4C3×C5×#386C211yesmaximal, characteristic
5C3×#65509C211yesmaximal, characteristic
6C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
7C3×#65234C211yesmaximal, characteristic, complemented
8C3×#65233C211yesmaximal, characteristic, complemented
9C3×#65231C211yesmaximal, characteristic, complemented
10C3×#65231C211yesmaximal, characteristic, complemented
11C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
12C3×#64943C211yesmaximal, characteristic, complemented
13C3×#64942C211yesmaximal, characteristic, complemented
14C3×#64939C211yesmaximal, characteristic, complemented
15C3×#64938C211yesmaximal, characteristic, complemented
16#10606404C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C2×C3×C22⋊Dic5C2211yescharacteristic
27C2×C3×C22⋊Dic5C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C3×D4×Dic5C418yescomplemented
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×#683—24no—
33C2×C3×#683C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic
36C2×C3×#683C2211yescharacteristic
37C2×C3×#683C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic
40C2×C3×C4×Dic5C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42C2×C3×C4×Dic5C2211yescharacteristic
43C2×C3×C4×Dic5C2211yescharacteristic
44C3×#4023—24no—
45C3×C5×#95C2211yescharacteristic
46C3×C5×#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#2352—51nomaximal, Hall
56C2×D4×Dic5C2×C311yescharacteristic
57C22×#683C2×C311yescharacteristic, complemented
58C2×#4023C2×C311yescharacteristic, complemented
59C5×#386C2×C311yescharacteristic
60#65509C2×C311yescharacteristic
61C4×C22⋊Dic5C2×C311yescharacteristic, complemented
62#65234C2×C311yescharacteristic, complemented
63#65233C2×C311yescharacteristic, complemented
64#65231C2×C311yescharacteristic, complemented
65#65231C2×C311yescharacteristic, complemented
66C22⋊C4×Dic5C2×C311yescharacteristic, complemented
67#64943C2×C311yescharacteristic, complemented
68#64942C2×C311yescharacteristic, complemented
69#64939C2×C311yescharacteristic, complemented
70#64938C2×C311yescharacteristic, complemented
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C2×C3×C5×D4—22no—
74C2×C3×C5×D4—22no—
75C2×C3×C5×D4C2×C414yes—
76C22×C3×C4×C5—22no—
77C22×C3×C4×C5—22no—
78C22×C3×C4×C5—41no—
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×Dic5—22no—
85C22×C3×Dic5—22no—
86C22×C3×Dic5—22no—
87C22×C3×Dic5—22no—
88C22×C3×Dic5—22no—
89C22×C3×Dic5—22no—
90C22×C3×Dic5—41no—
91C22×C3×Dic5C2×C414yes—
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
100C22×C3×Dic5C2311yescharacteristic
101C3×C5×C22⋊C4—22no—
102C3×C5×C22⋊C4—22no—
103C3×C5×C22⋊C4—41no—
104C3×C22⋊Dic5—22no—
105C3×C22⋊Dic5—22no—
106C3×C22⋊Dic5—41no—
107C3×C22⋊Dic5C2×C414yes—
108C3×C22⋊Dic5C2×C414yescomplemented
109C3×C4⋊Dic5C2×C414yescomplemented
110C3×#683—22no—
111C3×#683—22no—
112C3×#683—22no—
113C3×#683—22no—
114C3×#683—22no—
115C3×#683D414yescomplemented
116C3×C4×Dic5—22no—
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×#387—51no—
128C3×#386—51no—
129C3×#386D511yescharacteristic
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×C5×D4C22×C311yescharacteristic
137C23×C4×C5C22×C311yescharacteristic
138C23×Dic5C22×C311yescharacteristic
139C23×Dic5C22×C311yescharacteristic
140C23×Dic5C22×C311yescharacteristic
141C2×C5×C22⋊C4C22×C311yescharacteristic
142C2×C5×C22⋊C4C22×C311yescharacteristic
143C2×C5×C22⋊C4C22×C311yescharacteristic
144C2×C22⋊Dic5C22×C311yescharacteristic
145C2×C22⋊Dic5C22×C311yescharacteristic
146C2×C22⋊Dic5C22×C311yescharacteristic
147C2×C22⋊Dic5C22×C311yescharacteristic
148C2×C22⋊Dic5C22×C311yescharacteristic
149D4×Dic5C3×C418yescomplemented
150C2×C4⋊Dic5C22×C311yescharacteristic
151C2×#683—24no—
152C2×#683C22×C311yescharacteristic
153C2×#683C22×C311yescharacteristic
154C2×#683C22×C311yescharacteristic
155C2×#683C22×C311yescharacteristic
156C2×#683C22×C311yescharacteristic
157C2×#683C22×C311yescharacteristic
158C2×C4×Dic5C22×C311yescharacteristic
159C2×C4×Dic5C22×C311yescharacteristic
160C2×C4×Dic5C22×C311yescharacteristic
161C2×C4×Dic5C22×C311yescharacteristic
162C2×C4×Dic5C22×C311yescharacteristic
163#4023—24no—
164C5×#95C22×C311yescharacteristic
165C5×#95C22×C311yescharacteristic
166#3963C22×C311yescharacteristic
167#3963C22×C311yescharacteristic
168#3963C22×C311yescharacteristic
169#3963C22×C311yescharacteristic
170#3963C22×C311yescharacteristic
171#3963C22×C311yescharacteristic
172#3963C22×C311yescharacteristic
173#3963C22×C311yescharacteristic
174#2352—51noSylow
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5C22×C412yes—
186C23×C3×C5C22×C412yes—
187C23×C3×C5#4112yes—
188C23×C3×C5#4112yes—
189C23×C3×C5C2411yescharacteristic
190C3×C5×D4—28no—
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—44no—
205C2×C3×C4×C5C22×C412yes—
206C2×C3×C4×C5C2×D412yes—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—28no—
216C2×C3×Dic5—28no—
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×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—44no—
227C2×C3×Dic5C22×C412yes—
228C2×C3×Dic5C22×C412yes—
229C2×C3×Dic5C22×C412yes—
230C2×C3×Dic5C22×C412yes—
231C2×C3×Dic5C2×D412yes—
232C2×C3×Dic5C2×D412yes—
233C2×C3×Dic5#4112yes—
234C22×C3×D4C2×D511yescharacteristic
235C23×C3×C4—51no—
236C23×C3×C4—51no—
237C23×C3×C4—51no—
238C23×C3×C4C2×D511yescharacteristic
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—51no—
247C2×C3×C4⋊C4—51no—
248C2×C3×C4⋊C4—104no—
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⋊C4C2×D511yescharacteristic
255C2×C3×C22⋊C4C2×D511yescharacteristic
256C2×C3×C22⋊C4C2×D511yescharacteristic
257C2×C3×C42—51no—
258C2×C3×C42—51no—
259C2×C3×C42—51no—
260C2×C3×C42—51no—
261C2×C3×C42—51no—
262C3×#95—51no—
263C3×#95—51no—
264C3×#95—51no—
265C3×#95—51no—
266C3×#95—51no—
267C3×#95—51no—
268C3×#95—51no—
269C3×#95—51no—
270C3×#95C2×D511yescharacteristic
271C3×#95C2×D511yescharacteristic
272C24×C5C23×C311yescharacteristic
273C24×C5C23×C311yescharacteristic
274C2×C5×D4—22no—
275C2×C5×D4—22no—
276C2×C5×D4C2×C3×C414yes—
277C22×C4×C5—22no—
278C22×C4×C5—22no—
279C22×C4×C5—41no—
280C22×C4×C5C23×C311yescharacteristic
281C22×C4×C5C23×C311yescharacteristic
282C22×C4×C5C23×C311yescharacteristic
283C22×C4×C5C23×C311yescharacteristic
284C22×C4×C5C23×C311yescharacteristic
285C22×Dic5—22no—
286C22×Dic5—22no—
287C22×Dic5—22no—
288C22×Dic5—22no—
289C22×Dic5—22no—
290C22×Dic5—22no—
291C22×Dic5—41no—
292C22×Dic5C2×C3×C414yes—
293C22×Dic5C2×C3×C414yescomplemented
294C22×Dic5C23×C311yescharacteristic
295C22×Dic5C23×C311yescharacteristic
296C22×Dic5C23×C311yescharacteristic
297C22×Dic5C23×C311yescharacteristic
298C22×Dic5C23×C311yescharacteristic
299C22×Dic5C23×C311yescharacteristic
300C22×Dic5C23×C311yescharacteristic
301C22×Dic5C23×C311yescharacteristic
302C5×C22⋊C4—22no—
303C5×C22⋊C4—22no—
304C5×C22⋊C4—41no—
305C22⋊Dic5—22no—
306C22⋊Dic5—22no—
307C22⋊Dic5—41no—
308C22⋊Dic5C2×C3×C414yes—
309C22⋊Dic5C2×C3×C414yescomplemented
310C4⋊Dic5C2×C3×C414yescomplemented
311#683—22no—
312#683—22no—
313#683—22no—
314#683—22no—
315#683—22no—
316#683C3×D414yescomplemented
317C4×Dic5—22no—
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#387—51no—
329#386—51no—
330#386C3×D511yescharacteristic
331#382—51no—
332#380—51no—
333#380—51no—
334C4×C4⋊C4—51no—
335C4×C22⋊C4—51no—
336C4×C22⋊C4—51no—
337C22×C3×C5—22no—
338C22×C3×C5—22no—
339C22×C3×C5—22no—
340C22×C3×C5—22no—
341C22×C3×C5—22no—
342C22×C3×C5—22no—
343C22×C3×C5—22no—
344C22×C3×C5—22no—
345C22×C3×C5—22no—
346C22×C3×C5—41no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5#11714yescomplemented
351C22×C3×C5C23×C411yescharacteristic
352C22×C3×C5C22×D411yescharacteristic
353C22×C3×C5C2×#4111yescharacteristic
354C22×C3×C5C2×#4111yescharacteristic
355C22×C3×C5C2×#4111yescharacteristic
356C22×C3×C5H(5,𝔽2)11yescharacteristic
357C22×C3×C52−1+411yescharacteristic
358C3×C4×C5—22no—
359C3×C4×C5—22no—
360C3×C4×C5—41no—
361C3×C4×C5—41no—
362C3×C4×C5—41no—
363C3×Dic5—22no—
364C3×Dic5—22no—
365C3×Dic5—22no—
366C3×Dic5—22no—
367C3×Dic5—41no—
368C3×Dic5—41no—
369C3×Dic5—41no—
370C3×Dic5C4×D414yes—
371C24×C3C22×D511yescharacteristic
372C24×C3C22×D511yescharacteristic
373C2×C3×D4—22no—
374C2×C3×D4—22no—
375C2×C3×D4C4×D514yes—
376C22×C3×C4—22no—
377C22×C3×C4—22no—
378C22×C3×C4—41no—
379C22×C3×C4—51no—
380C22×C3×C4—54no—
381C22×C3×C4—54no—
382C22×C3×C4—51no—
383C22×C3×C4—51no—
384C22×C3×C4—51no—
385C22×C3×C4—51no—
386C22×C3×C4—51no—
387C22×C3×C4—51no—
388C22×C3×C4—51no—
389C22×C3×C4—102no—
390C22×C3×C4—102no—
391C22×C3×C4—102no—
392C22×C3×C4—102no—
393C22×C3×C4—102no—
394C22×C3×C4—102no—
395C22×C3×C4—201no—
396C22×C3×C4C22×D511yescharacteristic
397C22×C3×C4C22×D511yescharacteristic
398C22×C3×C4C22×D511yescharacteristic
399C22×C3×C4C22×D511yescharacteristic
400C22×C3×C4C22×D511yescharacteristic
401C3×C4⋊C4—54no—
402C3×C4⋊C4—54no—
403C3×C4⋊C4—102no—
404C3×C4⋊C4—102no—
405C3×C4⋊C4—102no—
406C3×C4⋊C4—102no—
407C3×C4⋊C4—102no—
408C3×C22⋊C4—22no—
409C3×C22⋊C4—22no—
410C3×C22⋊C4—41no—
411C3×C22⋊C4—54no—
412C3×C22⋊C4—54no—
413C3×C22⋊C4—102no—
414C3×C22⋊C4—102no—
415C3×C22⋊C4—201no—
416C3×C42—54no—
417C3×C42—102no—
418C3×C42—102no—
419C3×C42—201no—
420C3×C42—201no—
421C23×C5—21no—
422C23×C5—21no—
423C23×C5—21no—
424C23×C5—21no—
425C23×C5—21no—
426C23×C5—21no—
427C23×C5—21no—
428C23×C5—21no—
429C23×C5—21no—
430C23×C5—21no—
431C23×C5C22×C3×C412yes—
432C23×C5C22×C3×C412yes—
433C23×C5C3×#4112yes—
434C23×C5C3×#4112yes—
435C23×C5C24×C311yescharacteristic
436C5×D4—28no—
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—44no—
451C2×C4×C5C22×C3×C412yes—
452C2×C4×C5C2×C3×D412yes—
453C2×Dic5—21no—
454C2×Dic5—21no—
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—28no—
462C2×Dic5—28no—
463C2×Dic5—21no—
464C2×Dic5—21no—
465C2×Dic5—21no—
466C2×Dic5—21no—
467C2×Dic5—21no—
468C2×Dic5—21no—
469C2×Dic5—21no—
470C2×Dic5—21no—
471C2×Dic5—21no—
472C2×Dic5—44no—
473C2×Dic5C22×C3×C412yes—
474C2×Dic5C22×C3×C412yes—
475C2×Dic5C22×C3×C412yes—
476C2×Dic5C22×C3×C412yes—
477C2×Dic5C2×C3×D412yes—
478C2×Dic5C2×C3×D412yes—
479C2×Dic5C3×#4112yes—
480C22×D4C2×C3×D511yescharacteristic
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4C2×C3×D511yescharacteristic
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—51no—
493C2×C4⋊C4—51no—
494C2×C4⋊C4—104no—
495C2×C22⋊C4—51no—
496C2×C22⋊C4—51no—
497C2×C22⋊C4—51no—
498C2×C22⋊C4—51no—
499C2×C22⋊C4—51no—
500C2×C22⋊C4C2×C3×D511yescharacteristic
501C2×C22⋊C4C2×C3×D511yescharacteristic
502C2×C22⋊C4C2×C3×D511yescharacteristic
503C2×C42—51no—
504C2×C42—51no—
505C2×C42—51no—
506C2×C42—51no—
507C2×C42—51no—
508#95—51no—
509#95—51no—
510#95—51no—
511#95—51no—
512#95—51no—
513#95—51no—
514#95—51no—
515#95—51no—
516#95C2×C3×D511yescharacteristic
517#95C2×C3×D511yescharacteristic
518C2×C3×C5—24no—
519C2×C3×C5—42no—
520C2×C3×C5C2×#11711yescharacteristic
521C2×C3×C5C2×C4×D411yescharacteristic
522C2×C3×C5#52011yescharacteristic
523C2×C3×C5#54611yescharacteristic
524C2×C3×C5#54811yescharacteristic
525C2×C3×C5#55211yescharacteristic
526C2×C3×C5#55311yescharacteristic
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3C2×C4×D512yes—
538C23×C3C2×C4×D512yes—
539C23×C3#71112yes—
540C23×C3#71112yes—
541C23×C3C23×D511yescharacteristic
542C3×D4—28no—
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—44no—
557C2×C3×C4—52no—
558C2×C3×C4—52no—
559C2×C3×C4—52no—
560C2×C3×C4—52no—
561C2×C3×C4—52no—
562C2×C3×C4—52no—
563C2×C3×C4—52no—
564C2×C3×C4—108no—
565C2×C3×C4—108no—
566C2×C3×C4—101no—
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—101no—
581C2×C3×C4—101no—
582C2×C3×C4—101no—
583C2×C3×C4—204no—
584C2×C3×C4C2×C4×D512yes—
585C2×C3×C4D4×D512yes—
586C22×C5—22no—
587C22×C5—22no—
588C22×C5—22no—
589C22×C5—22no—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5—22no—
593C22×C5—22no—
594C22×C5—22no—
595C22×C5—41no—
596C22×C5—41no—
597C22×C5—41no—
598C22×C5—41no—
599C22×C5C3×#11714yescomplemented
600C22×C5C23×C3×C411yescharacteristic
601C22×C5C22×C3×D411yescharacteristic
602C22×C5C2×C3×#4111yescharacteristic
603C22×C5C2×C3×#4111yescharacteristic
604C22×C5C2×C3×#4111yescharacteristic
605C22×C5C3×H(5,𝔽2)11yescharacteristic
606C22×C5C3×2−1+411yescharacteristic
607C4×C5—22no—
608C4×C5—22no—
609C4×C5—41no—
610C4×C5—41no—
611C4×C5—41no—
612Dic5—22no—
613Dic5—22no—
614Dic5—22no—
615Dic5—22no—
616Dic5—41no—
617Dic5—41no—
618Dic5—41no—
619Dic5C3×C4×D414yes—
620C24C22×C3×D511yescharacteristic
621C24C22×C3×D511yescharacteristic
622C2×D4—22no—
623C2×D4—22no—
624C2×D4C3×C4×D514yes—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—41no—
628C22×C4—51no—
629C22×C4—54no—
630C22×C4—54no—
631C22×C4—51no—
632C22×C4—51no—
633C22×C4—51no—
634C22×C4—51no—
635C22×C4—51no—
636C22×C4—51no—
637C22×C4—51no—
638C22×C4—102no—
639C22×C4—102no—
640C22×C4—102no—
641C22×C4—102no—
642C22×C4—102no—
643C22×C4—102no—
644C22×C4—201no—
645C22×C4C22×C3×D511yescharacteristic
646C22×C4C22×C3×D511yescharacteristic
647C22×C4C22×C3×D511yescharacteristic
648C22×C4C22×C3×D511yescharacteristic
649C22×C4C22×C3×D511yescharacteristic
650C4⋊C4—54no—
651C4⋊C4—54no—
652C4⋊C4—102no—
653C4⋊C4—102no—
654C4⋊C4—102no—
655C4⋊C4—102no—
656C4⋊C4—102no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—41no—
660C22⋊C4—54no—
661C22⋊C4—54no—
662C22⋊C4—102no—
663C22⋊C4—102no—
664C22⋊C4—201no—
665C42—54no—
666C42—102no—
667C42—102no—
668C42—201no—
669C42—201no—
670C3×C5#235211yescharacteristic, complemented, Hall
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—22no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3#402314yescomplemented
685C22×C3C22×C4×D511yescharacteristic
686C22×C3C2×D4×D511yescharacteristic
687C22×C3C2×#71111yescharacteristic
688C22×C3C2×#71111yescharacteristic
689C22×C3#414411yescharacteristic
690C22×C3D5×#4111yescharacteristic
691C22×C3#415011yescharacteristic
692C3×C4—22no—
693C3×C4—22no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—54no—
698C3×C4—102no—
699C3×C4—102no—
700C3×C4—102no—
701C3×C4—102no—
702C3×C4—201no—
703C3×C4—201no—
704C3×C4—201no—
705C2×C5—24no—
706C2×C5—42no—
707C2×C5C2×C3×#11711yescharacteristic
708C2×C5C2×C3×C4×D411yescharacteristic
709C2×C5C3×#52011yescharacteristic
710C2×C5C3×#54611yescharacteristic
711C2×C5C3×#54811yescharacteristic
712C2×C5C3×#55211yescharacteristic
713C2×C5C3×#55311yescharacteristic
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23C2×C3×C4×D512yes—
725C23C2×C3×C4×D512yes—
726C23C3×#71112yes—
727C23C3×#71112yes—
728C23C23×C3×D511yescharacteristic
729D4—28no—
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—44no—
744C2×C4—52no—
745C2×C4—52no—
746C2×C4—52no—
747C2×C4—52no—
748C2×C4—52no—
749C2×C4—52no—
750C2×C4—52no—
751C2×C4—108no—
752C2×C4—108no—
753C2×C4—101no—
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—101no—
768C2×C4—101no—
769C2×C4—101no—
770C2×C4—204no—
771C2×C4C2×C3×C4×D512yes—
772C2×C4C3×D4×D512yes—
773C2×C3—24no—
774C2×C3—42no—
775C2×C3C2×#402311yescharacteristic
776C2×C3C4×D4×D511yescharacteristic
777C2×C3#6588011yescharacteristic
778C2×C3#6592511yescharacteristic
779C2×C3#6593211yescharacteristic
780C2×C3#6593511yescharacteristic
781C2×C3#6598411yescharacteristic
782C5C3×#235211yescharacteristic, complemented, Sylow
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22C3×#402314yescomplemented
797C22C22×C3×C4×D511yescharacteristic
798C22C2×C3×D4×D511yescharacteristic
799C22C2×C3×#71111yescharacteristic
800C22C2×C3×#71111yescharacteristic
801C22C3×#414411yescharacteristic
802C22C3×D5×#4111yescharacteristic
803C22C3×#415011yescharacteristic
804C4—22no—
805C4—22no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—54no—
810C4—102no—
811C4—102no—
812C4—102no—
813C4—102no—
814C4—201no—
815C4—201no—
816C4—201no—
817C3#1060640411yescharacteristic, direct product factor, Sylow
818C2—24no—
819C2—42no—
820C2C2×C3×#402311yescharacteristic
821C2C3×C4×D4×D511yescharacteristic
822C2C3×#6588011yescharacteristic
823C2C3×#6592511yescharacteristic
824C2C3×#6593211yescharacteristic
825C2C3×#6593511yescharacteristic
826C2C3×#6598411yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#386C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
cosocleC23×C5C24×C3
hypercenterC3×#386D5
hypocenterC5C3×#2352
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
2. C22×C3×#683C2semidirect
3. C2×C3×#4023C2semidirect
6. C3×C4×C22⋊Dic5C2semidirect
7. C3×#65234C2semidirect
8. C3×#65233C2semidirect
9. C3×#65231C2semidirect
10. C3×#65231C2semidirect
11. C3×C22⋊C4×Dic5C2semidirect
12. C3×#64943C2semidirect
13. C3×#64942C2semidirect
14. C3×#64939C2semidirect
15. C3×#64938C2semidirect
16. #10606404C3direct (N × H)
30. C3×D4×Dic5C4semidirect
57. C22×#683C2×C3semidirect
58. C2×#4023C2×C3semidirect
61. C4×C22⋊Dic5C2×C3semidirect
62. #65234C2×C3semidirect
63. #65233C2×C3semidirect
64. #65231C2×C3semidirect
65. #65231C2×C3semidirect
66. C22⋊C4×Dic5C2×C3semidirect
67. #64943C2×C3semidirect
68. #64942C2×C3semidirect
69. #64939C2×C3semidirect
70. #64938C2×C3semidirect
92. C22×C3×Dic5C2×C4semidirect
108. C3×C22⋊Dic5C2×C4semidirect
109. C3×C4⋊Dic5C2×C4semidirect
115. C3×#683D4semidirect
120. C3×C4×Dic5C2×C4semidirect
149. D4×Dic5C3×C4semidirect
293. C22×Dic5C2×C3×C4semidirect
309. C22⋊Dic5C2×C3×C4semidirect
310. C4⋊Dic5C2×C3×C4semidirect
316. #683C3×D4semidirect
321. C4×Dic5C2×C3×C4semidirect
350. C22×C3×C5#117semidirect
599. C22×C5C3×#117semidirect
670. C3×C5#2352semidirect
684. C22×C3#4023semidirect
782. C5C3×#2352semidirect
796. C22C3×#4023semidirect
817. C3#10606404direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic52
C22×C3×#6832
C2×C3×#40232
C3×C5×#3862
C3×#655092
C3×C4×C22⋊Dic52
C3×#652342
C3×#652332
C3×#652312
C3×C22⋊C4×Dic52
C3×#649432
C3×#649422
C3×#649392
C3×#649382
#106064043
C3×#23525