Finite Group Databasebeta

← C3×#10605305 #14326222

Subgroups — C3×#10605305 #14326222

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#685C211yesmaximal, characteristic
2C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
3C2×C3×#4018C211yesmaximal, characteristic, complemented
4C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#65499C211yesmaximal, characteristic, complemented
6C3×#65244C211yesmaximal, characteristic
7C3×#65235C211yesmaximal, characteristic, complemented
8C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
9C3×#65229C211yesmaximal, characteristic, complemented
10C3×#65229C211yesmaximal, characteristic, complemented
11C3×C4×#685C211yesmaximal, characteristic, complemented
12C3×#64958C211yesmaximal, characteristic, complemented
13C3×#64958C211yesmaximal, characteristic, complemented
14C3×#64956C211yesmaximal, characteristic, complemented
15C3×#64953C211yesmaximal, characteristic, complemented
16#10605305C311yesmaximal, characteristic, direct product factor, Hall
17C24×C3×D5C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C42×C5C2211yescharacteristic, complemented
25C2×C3×C42×C5C2211yescharacteristic, complemented
26C2×C3×C22⋊Dic5C2211yescharacteristic
27C2×C3×C22⋊Dic5C2211yescharacteristic
28C2×C3×#685—24no—
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic, complemented
40C2×C3×#683C2211yescharacteristic, complemented
41C2×C3×#683C2211yescharacteristic, complemented
42C2×C3×#683C2211yescharacteristic, complemented
43C2×C3×C4×Dic5C2211yescharacteristic, complemented
44C2×C3×C4×Dic5C2211yescharacteristic, complemented
45C3×D5×C22⋊C4C418yescomplemented
46C3×#4018—24no—
47C3×C5×#95C2211yescharacteristic, complemented
48C3×C5×#95C2211yescharacteristic, complemented
49C3×#3963C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53C3×#3963C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55C3×#2342—51nomaximal, Hall
56C22×#685C2×C311yescharacteristic
57C2×D5×C22⋊C4C2×C311yescharacteristic
58C2×#4018C2×C311yescharacteristic, complemented
59C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
60#65499C2×C311yescharacteristic, complemented
61#65244C2×C311yescharacteristic
62#65235C2×C311yescharacteristic, complemented
63C22⋊C4×Dic5C2×C311yescharacteristic, complemented
64#65229C2×C311yescharacteristic, complemented
65#65229C2×C311yescharacteristic, complemented
66C4×#685C2×C311yescharacteristic, complemented
67#64958C2×C311yescharacteristic, complemented
68#64958C2×C311yescharacteristic, complemented
69#64956C2×C311yescharacteristic, complemented
70#64953C2×C311yescharacteristic, complemented
71C24×C3×C5C2311yescharacteristic
72C23×C3×D5—22no—
73C23×C3×D5—22no—
74C23×C3×D5—22no—
75C23×C3×D5—22no—
76C23×C3×D5—41no—
77C23×C3×D5—41no—
78C23×C3×D5C2×C414yes—
79C23×C3×D5C2311yescharacteristic
80C23×C3×D5C2311yescharacteristic
81C22×C3×C4×C5—22no—
82C22×C3×C4×C5—22no—
83C22×C3×C4×C5—41no—
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×Dic5—22no—
91C22×C3×Dic5—22no—
92C22×C3×Dic5—41no—
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—22no—
101C2×C3×C4×D5—41no—
102C2×C3×C4×D5—41no—
103C2×C3×C4×D5C2×C414yescomplemented
104C2×C3×C4×D5C2×C414yescomplemented
105C3×C5×C22⋊C4—22no—
106C3×C5×C22⋊C4C2×C414yes—
107C3×C42×C5—22no—
108C3×C42×C5—41no—
109C3×C22⋊Dic5—22no—
110C3×C22⋊Dic5C2×C414yes—
111C3×#685—22no—
112C3×#685—22no—
113C3×#685—22no—
114C3×#685—22no—
115C3×#685—22no—
116C3×#685—41no—
117C3×#685—41no—
118C3×#685C2×C414yescomplemented
119C3×#685C2×C414yescomplemented
120C3×#685D414yes—
121C3×#683—22no—
122C3×#683—22no—
123C3×#683—41no—
124C3×#683—41no—
125C3×C4×Dic5—22no—
126C3×C4×Dic5—41no—
127C2×C3×#117—51no—
128C22×C3×C22⋊C4—51no—
129C22×C3×C22⋊C4—51no—
130C3×#388—51no—
131C3×#388—51no—
132C3×#388—51no—
133C3×#388—51no—
134C3×#385—51no—
135C3×#385—51no—
136C3×#381—51no—
137C3×#380—51no—
138C3×#379—51no—
139C3×C4×C22⋊C4—51no—
140C3×C4×C22⋊C4—51no—
141C3×C4×C22⋊C4D511yescharacteristic, complemented
142C24×D5C22×C311yescharacteristic
143C23×C4×C5C22×C311yescharacteristic
144C23×Dic5C22×C311yescharacteristic
145C22×C4×D5C22×C311yescharacteristic
146C22×C4×D5C22×C311yescharacteristic
147C2×C5×C22⋊C4C22×C311yescharacteristic
148C2×C5×C22⋊C4C22×C311yescharacteristic
149C2×C42×C5C22×C311yescharacteristic, complemented
150C2×C42×C5C22×C311yescharacteristic, complemented
151C2×C22⋊Dic5C22×C311yescharacteristic
152C2×C22⋊Dic5C22×C311yescharacteristic
153C2×#685—24no—
154C2×#685C22×C311yescharacteristic
155C2×#685C22×C311yescharacteristic
156C2×#685C22×C311yescharacteristic
157C2×#685C22×C311yescharacteristic
158C2×#685C22×C311yescharacteristic
159C2×#685C22×C311yescharacteristic
160C2×#685C22×C311yescharacteristic
161C2×#685C22×C311yescharacteristic
162C2×#685C22×C311yescharacteristic
163C2×#685C22×C311yescharacteristic
164C2×#683C22×C311yescharacteristic, complemented
165C2×#683C22×C311yescharacteristic, complemented
166C2×#683C22×C311yescharacteristic, complemented
167C2×#683C22×C311yescharacteristic, complemented
168C2×C4×Dic5C22×C311yescharacteristic, complemented
169C2×C4×Dic5C22×C311yescharacteristic, complemented
170D5×C22⋊C4C3×C418yescomplemented
171#4018—24no—
172C5×#95C22×C311yescharacteristic, complemented
173C5×#95C22×C311yescharacteristic, complemented
174#3963C22×C311yescharacteristic, complemented
175#3963C22×C311yescharacteristic, complemented
176#3963C22×C311yescharacteristic, complemented
177#3963C22×C311yescharacteristic, complemented
178#3963C22×C311yescharacteristic, complemented
179#3963C22×C311yescharacteristic, complemented
180#2342—51noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5C22×C412yes—
186C23×C3×C5#4112yes—
187C23×C3×C5#4112yes—
188C23×C3×C5C2411yescharacteristic
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—21no—
193C22×C3×D5—28no—
194C22×C3×D5—21no—
195C22×C3×D5—21no—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—28no—
201C22×C3×D5—44no—
202C22×C3×D5—44no—
203C22×C3×D5—44no—
204C22×C3×D5—44no—
205C22×C3×D5—44no—
206C22×C3×D5C22×C412yes—
207C22×C3×D5C22×C412yes—
208C22×C3×D5C2×D412yes—
209C22×C3×D5#4112yes—
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—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—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—44no—
226C2×C3×C4×C5C22×C412yes—
227C2×C3×C4×C5C22×C412yes—
228C2×C3×C4×C5C2×D412yes—
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—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—44no—
245C2×C3×Dic5C22×C412yes—
246C2×C3×Dic5C22×C412yes—
247C2×C3×Dic5C2×D412yes—
248C3×C4×D5—28no—
249C3×C4×D5—44no—
250C25×C3—51no—
251C23×C3×C4—51no—
252C23×C3×C4—51no—
253C23×C3×C4—51no—
254C23×C3×C4C2×D511yescharacteristic
255C3×#117—104no—
256C2×C3×C4⋊C4—51no—
257C2×C3×C4⋊C4—51no—
258C2×C3×C4⋊C4—51no—
259C2×C3×C4⋊C4—51no—
260C2×C3×C22⋊C4—51no—
261C2×C3×C22⋊C4—51no—
262C2×C3×C22⋊C4—51no—
263C2×C3×C22⋊C4—51no—
264C2×C3×C22⋊C4—58no—
265C2×C3×C22⋊C4—51no—
266C2×C3×C22⋊C4—51no—
267C2×C3×C22⋊C4—51no—
268C2×C3×C22⋊C4—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4—51no—
272C2×C3×C22⋊C4—51no—
273C2×C3×C22⋊C4—104no—
274C2×C3×C22⋊C4C2×D511yescharacteristic
275C2×C3×C22⋊C4C2×D511yescharacteristic
276C2×C3×C42—51no—
277C2×C3×C42—51no—
278C2×C3×C42C2×D511yescharacteristic, complemented
279C2×C3×C42C2×D511yescharacteristic, complemented
280C3×#95—51no—
281C3×#95—51no—
282C3×#95—51no—
283C3×#95—51no—
284C3×#95—51no—
285C3×#95—51no—
286C3×#95C2×D511yescharacteristic, complemented
287C3×#95C2×D511yescharacteristic, complemented
288C24×C5C23×C311yescharacteristic
289C23×D5—22no—
290C23×D5—22no—
291C23×D5—22no—
292C23×D5—22no—
293C23×D5—41no—
294C23×D5—41no—
295C23×D5C2×C3×C414yes—
296C23×D5C23×C311yescharacteristic
297C23×D5C23×C311yescharacteristic
298C22×C4×C5—22no—
299C22×C4×C5—22no—
300C22×C4×C5—41no—
301C22×C4×C5C23×C311yescharacteristic
302C22×C4×C5C23×C311yescharacteristic
303C22×C4×C5C23×C311yescharacteristic
304C22×C4×C5C23×C311yescharacteristic
305C22×C4×C5C23×C311yescharacteristic
306C22×C4×C5C23×C311yescharacteristic
307C22×Dic5—22no—
308C22×Dic5—22no—
309C22×Dic5—41no—
310C22×Dic5C23×C311yescharacteristic
311C22×Dic5C23×C311yescharacteristic
312C22×Dic5C23×C311yescharacteristic
313C22×Dic5C23×C311yescharacteristic
314C22×Dic5C23×C311yescharacteristic
315C22×Dic5C23×C311yescharacteristic
316C2×C4×D5—22no—
317C2×C4×D5—22no—
318C2×C4×D5—41no—
319C2×C4×D5—41no—
320C2×C4×D5C2×C3×C414yescomplemented
321C2×C4×D5C2×C3×C414yescomplemented
322C5×C22⋊C4—22no—
323C5×C22⋊C4C2×C3×C414yes—
324C42×C5—22no—
325C42×C5—41no—
326C22⋊Dic5—22no—
327C22⋊Dic5C2×C3×C414yes—
328#685—22no—
329#685—22no—
330#685—22no—
331#685—22no—
332#685—22no—
333#685—41no—
334#685—41no—
335#685C2×C3×C414yescomplemented
336#685C2×C3×C414yescomplemented
337#685C3×D414yes—
338#683—22no—
339#683—22no—
340#683—41no—
341#683—41no—
342C4×Dic5—22no—
343C4×Dic5—41no—
344C2×#117—51no—
345C22×C22⋊C4—51no—
346C22×C22⋊C4—51no—
347#388—51no—
348#388—51no—
349#388—51no—
350#388—51no—
351#385—51no—
352#385—51no—
353#381—51no—
354#380—51no—
355#379—51no—
356C4×C22⋊C4—51no—
357C4×C22⋊C4—51no—
358C4×C22⋊C4C3×D511yescharacteristic, complemented
359C22×C3×C5—22no—
360C22×C3×C5—22no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—22no—
365C22×C3×C5#11714yescomplemented
366C22×C3×C5C23×C411yescharacteristic
367C22×C3×C5C22×D411yescharacteristic
368C22×C3×C5C2×#4111yescharacteristic
369C22×C3×C5C2×#4111yescharacteristic
370C22×C3×C5C2×#4111yescharacteristic
371C22×C3×C5H(5,𝔽2)11yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C2×C3×D5—22no—
374C2×C3×D5—22no—
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×D5—22no—
382C2×C3×D5—416no—
383C2×C3×D5—41no—
384C2×C3×D5—41no—
385C2×C3×D5—41no—
386C2×C3×D5—41no—
387C2×C3×D5C4×D414yes—
388C3×C4×C5—22no—
389C3×C4×C5—22no—
390C3×C4×C5—22no—
391C3×C4×C5—41no—
392C3×C4×C5—41no—
393C3×C4×C5—41no—
394C3×Dic5—22no—
395C3×Dic5—22no—
396C3×Dic5—22no—
397C3×Dic5—41no—
398C3×Dic5—41no—
399C3×Dic5—41no—
400C24×C3—51no—
401C24×C3—51no—
402C24×C3—54no—
403C24×C3—102no—
404C24×C3—102no—
405C24×C3—102no—
406C24×C3—102no—
407C24×C3—201no—
408C24×C3—201no—
409C24×C3C22×D511yescharacteristic
410C22×C3×C4—22no—
411C22×C3×C4—22no—
412C22×C3×C4—41no—
413C22×C3×C4—51no—
414C22×C3×C4—51no—
415C22×C3×C4—51no—
416C22×C3×C4—54no—
417C22×C3×C4—54no—
418C22×C3×C4—51no—
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—102no—
422C22×C3×C4—102no—
423C22×C3×C4—102no—
424C22×C3×C4—102no—
425C22×C3×C4—201no—
426C22×C3×C4—201no—
427C22×C3×C4—201no—
428C22×C3×C4C22×D511yescharacteristic
429C22×C3×C4C22×D511yescharacteristic
430C22×C3×C4C22×D511yescharacteristic
431C22×C3×C4C22×D511yescharacteristic
432C22×C3×C4C22×D511yescharacteristic
433C22×C3×C4C22×D511yescharacteristic
434C3×C4⋊C4—102no—
435C3×C4⋊C4—102no—
436C3×C4⋊C4—201no—
437C3×C4⋊C4—201no—
438C3×C22⋊C4—22no—
439C3×C22⋊C4—54no—
440C3×C22⋊C4—54no—
441C3×C22⋊C4—54no—
442C3×C22⋊C4—54no—
443C3×C22⋊C4—102no—
444C3×C22⋊C4—102no—
445C3×C22⋊C4—102no—
446C3×C22⋊C4—102no—
447C3×C22⋊C4—102no—
448C3×C22⋊C4—102no—
449C3×C22⋊C4—201no—
450C3×C22⋊C4—201no—
451C3×C22⋊C4C4×D514yes—
452C3×C42—22no—
453C3×C42—41no—
454C3×C42—102no—
455C3×C42—201no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5C22×C3×C412yes—
461C23×C5C3×#4112yes—
462C23×C5C3×#4112yes—
463C23×C5C24×C311yescharacteristic
464C22×D5—21no—
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—21no—
468C22×D5—28no—
469C22×D5—21no—
470C22×D5—21no—
471C22×D5—21no—
472C22×D5—21no—
473C22×D5—21no—
474C22×D5—21no—
475C22×D5—28no—
476C22×D5—44no—
477C22×D5—44no—
478C22×D5—44no—
479C22×D5—44no—
480C22×D5—44no—
481C22×D5C22×C3×C412yes—
482C22×D5C22×C3×C412yes—
483C22×D5C2×C3×D412yes—
484C22×D5C3×#4112yes—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—21no—
490C2×C4×C5—21no—
491C2×C4×C5—21no—
492C2×C4×C5—21no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—44no—
501C2×C4×C5C22×C3×C412yes—
502C2×C4×C5C22×C3×C412yes—
503C2×C4×C5C2×C3×D412yes—
504C2×Dic5—21no—
505C2×Dic5—21no—
506C2×Dic5—21no—
507C2×Dic5—21no—
508C2×Dic5—21no—
509C2×Dic5—21no—
510C2×Dic5—21no—
511C2×Dic5—21no—
512C2×Dic5—21no—
513C2×Dic5—21no—
514C2×Dic5—21no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5—21no—
518C2×Dic5—21no—
519C2×Dic5—44no—
520C2×Dic5C22×C3×C412yes—
521C2×Dic5C22×C3×C412yes—
522C2×Dic5C2×C3×D412yes—
523C4×D5—28no—
524C4×D5—44no—
525C25—51no—
526C23×C4—51no—
527C23×C4—51no—
528C23×C4—51no—
529C23×C4C2×C3×D511yescharacteristic
530#117—104no—
531C2×C4⋊C4—51no—
532C2×C4⋊C4—51no—
533C2×C4⋊C4—51no—
534C2×C4⋊C4—51no—
535C2×C22⋊C4—51no—
536C2×C22⋊C4—51no—
537C2×C22⋊C4—51no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—58no—
540C2×C22⋊C4—51no—
541C2×C22⋊C4—51no—
542C2×C22⋊C4—51no—
543C2×C22⋊C4—51no—
544C2×C22⋊C4—51no—
545C2×C22⋊C4—51no—
546C2×C22⋊C4—51no—
547C2×C22⋊C4—51no—
548C2×C22⋊C4—104no—
549C2×C22⋊C4C2×C3×D511yescharacteristic
550C2×C22⋊C4C2×C3×D511yescharacteristic
551C2×C42—51no—
552C2×C42—51no—
553C2×C42C2×C3×D511yescharacteristic, complemented
554C2×C42C2×C3×D511yescharacteristic, complemented
555#95—51no—
556#95—51no—
557#95—51no—
558#95—51no—
559#95—51no—
560#95—51no—
561#95C2×C3×D511yescharacteristic, complemented
562#95C2×C3×D511yescharacteristic, complemented
563C2×C3×C5—24no—
564C2×C3×C5C2×#11711yescharacteristic
565C2×C3×C5C2×C4×D411yescharacteristic
566C2×C3×C5#51811yescharacteristic
567C2×C3×C5#54611yescharacteristic
568C2×C3×C5#54611yescharacteristic
569C2×C3×C5#55111yescharacteristic
570C2×C3×C5#55111yescharacteristic
571C3×D5—24no—
572C3×D5—42no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—52no—
578C23×C3—52no—
579C23×C3—52no—
580C23×C3—52no—
581C23×C3—108no—
582C23×C3—101no—
583C23×C3—101no—
584C23×C3—101no—
585C23×C3—101no—
586C23×C3—101no—
587C23×C3—101no—
588C23×C3—101no—
589C23×C3—101no—
590C23×C3—101no—
591C23×C3—101no—
592C23×C3—108no—
593C23×C3—204no—
594C23×C3—204no—
595C23×C3—204no—
596C23×C3—204no—
597C23×C3—204no—
598C23×C3C2×C4×D512yes—
599C23×C3#70912yes—
600C23×C3#70912yes—
601C23×C3C23×D511yescharacteristic
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—44no—
618C2×C3×C4—52no—
619C2×C3×C4—52no—
620C2×C3×C4—52no—
621C2×C3×C4—108no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4—101no—
625C2×C3×C4—101no—
626C2×C3×C4—101no—
627C2×C3×C4—101no—
628C2×C3×C4—101no—
629C2×C3×C4—101no—
630C2×C3×C4—101no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—204no—
638C2×C3×C4—204no—
639C2×C3×C4C2×C4×D512yes—
640C2×C3×C4C2×C4×D512yes—
641C2×C3×C4D4×D512yes—
642C22×C5—22no—
643C22×C5—22no—
644C22×C5—22no—
645C22×C5—22no—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5C3×#11714yescomplemented
649C22×C5C23×C3×C411yescharacteristic
650C22×C5C22×C3×D411yescharacteristic
651C22×C5C2×C3×#4111yescharacteristic
652C22×C5C2×C3×#4111yescharacteristic
653C22×C5C2×C3×#4111yescharacteristic
654C22×C5C3×H(5,𝔽2)11yescharacteristic
655C22×C5C3×H(5,𝔽2)11yescharacteristic
656C2×D5—22no—
657C2×D5—22no—
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—22no—
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—22no—
665C2×D5—416no—
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—41no—
670C2×D5C3×C4×D414yes—
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—22no—
674C4×C5—41no—
675C4×C5—41no—
676C4×C5—41no—
677Dic5—22no—
678Dic5—22no—
679Dic5—22no—
680Dic5—41no—
681Dic5—41no—
682Dic5—41no—
683C24—51no—
684C24—51no—
685C24—54no—
686C24—102no—
687C24—102no—
688C24—102no—
689C24—102no—
690C24—201no—
691C24—201no—
692C24C22×C3×D511yescharacteristic
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—41no—
696C22×C4—51no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—54no—
700C22×C4—54no—
701C22×C4—51no—
702C22×C4—51no—
703C22×C4—51no—
704C22×C4—102no—
705C22×C4—102no—
706C22×C4—102no—
707C22×C4—102no—
708C22×C4—201no—
709C22×C4—201no—
710C22×C4—201no—
711C22×C4C22×C3×D511yescharacteristic
712C22×C4C22×C3×D511yescharacteristic
713C22×C4C22×C3×D511yescharacteristic
714C22×C4C22×C3×D511yescharacteristic
715C22×C4C22×C3×D511yescharacteristic
716C22×C4C22×C3×D511yescharacteristic
717C4⋊C4—102no—
718C4⋊C4—102no—
719C4⋊C4—201no—
720C4⋊C4—201no—
721C22⋊C4—22no—
722C22⋊C4—54no—
723C22⋊C4—54no—
724C22⋊C4—54no—
725C22⋊C4—54no—
726C22⋊C4—102no—
727C22⋊C4—102no—
728C22⋊C4—102no—
729C22⋊C4—102no—
730C22⋊C4—102no—
731C22⋊C4—102no—
732C22⋊C4—201no—
733C22⋊C4—201no—
734C22⋊C4C3×C4×D514yes—
735C42—22no—
736C42—41no—
737C42—102no—
738C42—201no—
739C3×C5#234211yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—54no—
747C22×C3—102no—
748C22×C3—102no—
749C22×C3—102no—
750C22×C3—102no—
751C22×C3—102no—
752C22×C3—102no—
753C22×C3—102no—
754C22×C3—102no—
755C22×C3—102no—
756C22×C3—2016no—
757C22×C3—201no—
758C22×C3—201no—
759C22×C3—201no—
760C22×C3—201no—
761C22×C3#401814yescomplemented
762C22×C3C22×C4×D511yescharacteristic
763C22×C3C2×#70911yescharacteristic
764C22×C3C2×#70911yescharacteristic
765C22×C3C2×D4×D511yescharacteristic
766C22×C3#414411yescharacteristic
767C22×C3D5×#4111yescharacteristic
768C22×C3#414911yescharacteristic
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—22no—
772C3×C4—41no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—102no—
776C3×C4—102no—
777C3×C4—102no—
778C3×C4—201no—
779C3×C4—201no—
780C3×C4—201no—
781C2×C5—24no—
782C2×C5C2×C3×#11711yescharacteristic
783C2×C5C2×C3×C4×D411yescharacteristic
784C2×C5C3×#51811yescharacteristic
785C2×C5C3×#54611yescharacteristic
786C2×C5C3×#54611yescharacteristic
787C2×C5C3×#55111yescharacteristic
788C2×C5C3×#55111yescharacteristic
789D5—24no—
790D5—42no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—52no—
796C23—52no—
797C23—52no—
798C23—52no—
799C23—108no—
800C23—101no—
801C23—101no—
802C23—101no—
803C23—101no—
804C23—101no—
805C23—101no—
806C23—101no—
807C23—101no—
808C23—101no—
809C23—101no—
810C23—108no—
811C23—204no—
812C23—204no—
813C23—204no—
814C23—204no—
815C23—204no—
816C23C2×C3×C4×D512yes—
817C23C3×#70912yes—
818C23C3×#70912yes—
819C23C23×C3×D511yescharacteristic
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—44no—
836C2×C4—52no—
837C2×C4—52no—
838C2×C4—52no—
839C2×C4—108no—
840C2×C4—101no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—101no—
844C2×C4—101no—
845C2×C4—101no—
846C2×C4—101no—
847C2×C4—101no—
848C2×C4—101no—
849C2×C4—101no—
850C2×C4—101no—
851C2×C4—101no—
852C2×C4—101no—
853C2×C4—101no—
854C2×C4—101no—
855C2×C4—204no—
856C2×C4—204no—
857C2×C4C2×C3×C4×D512yes—
858C2×C4C2×C3×C4×D512yes—
859C2×C4C3×D4×D512yes—
860C2×C3—24no—
861C2×C3—104no—
862C2×C3—202no—
863C2×C3C2×#401811yescharacteristic
864C2×C3#6582411yescharacteristic
865C2×C3#6586111yescharacteristic
866C2×C3C4×D4×D511yescharacteristic
867C2×C3#6587911yescharacteristic
868C2×C3#6588411yescharacteristic
869C2×C3#6589011yescharacteristic
870C5C3×#234211yescharacteristic, complemented, Sylow
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—54no—
878C22—102no—
879C22—102no—
880C22—102no—
881C22—102no—
882C22—102no—
883C22—102no—
884C22—102no—
885C22—102no—
886C22—102no—
887C22—2016no—
888C22—201no—
889C22—201no—
890C22—201no—
891C22—201no—
892C22C3×#401814yescomplemented
893C22C22×C3×C4×D511yescharacteristic
894C22C2×C3×#70911yescharacteristic
895C22C2×C3×#70911yescharacteristic
896C22C2×C3×D4×D511yescharacteristic
897C22C3×#414411yescharacteristic
898C22C3×D5×#4111yescharacteristic
899C22C3×#414911yescharacteristic
900C4—22no—
901C4—22no—
902C4—22no—
903C4—41no—
904C4—41no—
905C4—41no—
906C4—102no—
907C4—102no—
908C4—102no—
909C4—201no—
910C4—201no—
911C4—201no—
912C3#1060530511yescharacteristic, direct product factor, Sylow
913C2—24no—
914C2—104no—
915C2—202no—
916C2C2×C3×#401811yescharacteristic
917C2C3×#6582411yescharacteristic
918C2C3×#6586111yescharacteristic
919C2C3×C4×D4×D511yescharacteristic
920C2C3×#6587911yescharacteristic
921C2C3×#6588411yescharacteristic
922C2C3×#6589011yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC24×C3×D5C22
cosocleC23×C5C24×C3
hypercenterC3×C4×C22⋊C4D5
hypocenterC5C3×#2342
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×#4018C2semidirect
4. C3×C4×C5×C22⋊C4C2semidirect
5. C3×#65499C2semidirect
7. C3×#65235C2semidirect
8. C3×C22⋊C4×Dic5C2semidirect
9. C3×#65229C2semidirect
10. C3×#65229C2semidirect
11. C3×C4×#685C2semidirect
12. C3×#64958C2semidirect
13. C3×#64958C2semidirect
14. C3×#64956C2semidirect
15. C3×#64953C2semidirect
16. #10605305C3direct (N × H)
24. C2×C3×C42×C5C22semidirect
25. C2×C3×C42×C5C22semidirect
39. C2×C3×#683C22semidirect
40. C2×C3×#683C22semidirect
41. C2×C3×#683C22semidirect
42. C2×C3×#683C22semidirect
43. C2×C3×C4×Dic5C22semidirect
44. C2×C3×C4×Dic5C22semidirect
45. C3×D5×C22⋊C4C4semidirect
47. C3×C5×#95C22semidirect
48. C3×C5×#95C22semidirect
49. C3×#3963C22semidirect
50. C3×#3963C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
58. C2×#4018C2×C3semidirect
59. C4×C5×C22⋊C4C2×C3semidirect
60. #65499C2×C3semidirect
62. #65235C2×C3semidirect
63. C22⋊C4×Dic5C2×C3semidirect
64. #65229C2×C3semidirect
65. #65229C2×C3semidirect
66. C4×#685C2×C3semidirect
67. #64958C2×C3semidirect
68. #64958C2×C3semidirect
69. #64956C2×C3semidirect
70. #64953C2×C3semidirect
103. C2×C3×C4×D5C2×C4semidirect
104. C2×C3×C4×D5C2×C4semidirect
118. C3×#685C2×C4semidirect
119. C3×#685C2×C4semidirect
141. C3×C4×C22⋊C4D5semidirect
149. C2×C42×C5C22×C3semidirect
150. C2×C42×C5C22×C3semidirect
164. C2×#683C22×C3semidirect
165. C2×#683C22×C3semidirect
166. C2×#683C22×C3semidirect
167. C2×#683C22×C3semidirect
168. C2×C4×Dic5C22×C3semidirect
169. C2×C4×Dic5C22×C3semidirect
170. D5×C22⋊C4C3×C4semidirect
172. C5×#95C22×C3semidirect
173. C5×#95C22×C3semidirect
174. #3963C22×C3semidirect
175. #3963C22×C3semidirect
176. #3963C22×C3semidirect
177. #3963C22×C3semidirect
178. #3963C22×C3semidirect
179. #3963C22×C3semidirect
278. C2×C3×C42C2×D5semidirect
279. C2×C3×C42C2×D5semidirect
286. C3×#95C2×D5semidirect
287. C3×#95C2×D5semidirect
320. C2×C4×D5C2×C3×C4semidirect
321. C2×C4×D5C2×C3×C4semidirect
335. #685C2×C3×C4semidirect
336. #685C2×C3×C4semidirect
358. C4×C22⋊C4C3×D5semidirect
365. C22×C3×C5#117semidirect
553. C2×C42C2×C3×D5semidirect
554. C2×C42C2×C3×D5semidirect
561. #95C2×C3×D5semidirect
562. #95C2×C3×D5semidirect
648. C22×C5C3×#117semidirect
739. C3×C5#2342semidirect
761. C22×C3#4018semidirect
870. C5C3×#2342semidirect
892. C22C3×#4018semidirect
912. C3#10605305direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6852
C2×C3×D5×C22⋊C42
C2×C3×#40182
C3×C4×C5×C22⋊C42
C3×#654992
C3×#652442
C3×#652352
C3×C22⋊C4×Dic52
C3×#652292
C3×C4×#6852
C3×#649582
C3×#649562
C3×#649532
#106053053
C3×#23425