Finite Group Databasebeta

← C3×#10607564 #14326237

Subgroups — C3×#10607564 #14326237

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
1C2×C3×#4038C211yesmaximal, characteristic, complemented
2C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
3C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
4C3×C5×#388C211yesmaximal, characteristic, complemented
5C3×#65278C211yesmaximal, characteristic, complemented
6C3×#65244C211yesmaximal, characteristic
7C3×#65240C211yesmaximal, characteristic, complemented
8C3×#65234C211yesmaximal, characteristic, complemented
9C3×#65233C211yesmaximal, characteristic, complemented
10C3×C4×#685C211yesmaximal, characteristic, complemented
11C3×C4×#685C211yesmaximal, characteristic, complemented
12C3×#64957C211yesmaximal, characteristic, complemented
13C3×#64956C211yesmaximal, characteristic, complemented
14C3×#64955C211yesmaximal, characteristic, complemented
15C3×#64953C211yesmaximal, characteristic, complemented
16#10607564C311yesmaximal, characteristic, direct product factor, Hall
17C24×C3×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C42×C5C2211yescharacteristic, complemented
27C2×C3×C22⋊Dic5C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×C22⋊Dic5C2211yescharacteristic
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×C4⋊Dic5C2211yescharacteristic, complemented
39C2×C3×#683C2211yescharacteristic, complemented
40C2×C3×#683C2211yescharacteristic, complemented
41C2×C3×C4×Dic5C2211yescharacteristic, complemented
42C2×C3×C4×Dic5C2211yescharacteristic, complemented
43C2×C3×C4×Dic5C2211yescharacteristic, complemented
44C3×#4038—24no—
45C3×D5×C22⋊C4—24no—
46C3×D5×C22⋊C4C418yescomplemented
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
56C2×#4038C2×C311yescharacteristic, complemented
57C2×D5×C22⋊C4C2×C311yescharacteristic
58C2×D5×C22⋊C4C2×C311yescharacteristic
59C5×#388C2×C311yescharacteristic, complemented
60#65278C2×C311yescharacteristic, complemented
61#65244C2×C311yescharacteristic
62#65240C2×C311yescharacteristic, complemented
63#65234C2×C311yescharacteristic, complemented
64#65233C2×C311yescharacteristic, complemented
65C4×#685C2×C311yescharacteristic, complemented
66C4×#685C2×C311yescharacteristic, complemented
67#64957C2×C311yescharacteristic, complemented
68#64956C2×C311yescharacteristic, complemented
69#64955C2×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×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C2×C3×C4×D5—22no—
94C2×C3×C4×D5—22no—
95C2×C3×C4×D5—22no—
96C2×C3×C4×D5—22no—
97C2×C3×C4×D5—22no—
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—41no—
100C2×C3×C4×D5—41no—
101C2×C3×C4×D5—41no—
102C2×C3×C4×D5—41no—
103C2×C3×C4×D5C2×C414yescomplemented
104C2×C3×C4×D5C2×C414yescomplemented
105C3×C5×C4⋊C4—22no—
106C3×C5×C22⋊C4—22no—
107C3×C5×C22⋊C4—41no—
108C3×C5×C22⋊C4C2×C414yescomplemented
109C3×C42×C5—41no—
110C3×C22⋊Dic5—22no—
111C3×C22⋊Dic5—41no—
112C3×C22⋊Dic5C2×C414yescomplemented
113C3×#685—22no—
114C3×#685—22no—
115C3×#685—22no—
116C3×#685—22no—
117C3×#685—22no—
118C3×#685C2×C414yes—
119C3×#685C2×C414yes—
120C3×#685D414yes—
121C3×C4⋊Dic5—22no—
122C3×#683—41no—
123C3×#683—41no—
124C3×C4×Dic5—22no—
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×#388D511yescharacteristic, complemented
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⋊C4—51no—
142C24×D5C22×C311yescharacteristic
143C22×C4×D5C22×C311yescharacteristic
144C22×C4×D5C22×C311yescharacteristic
145C22×C4×D5C22×C311yescharacteristic
146C22×C4×D5C22×C311yescharacteristic
147C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
148C2×C5×C22⋊C4C22×C311yescharacteristic
149C2×C5×C22⋊C4C22×C311yescharacteristic
150C2×C5×C22⋊C4C22×C311yescharacteristic
151C2×C42×C5C22×C311yescharacteristic, complemented
152C2×C22⋊Dic5C22×C311yescharacteristic
153C2×C22⋊Dic5C22×C311yescharacteristic
154C2×C22⋊Dic5C22×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×C4⋊Dic5C22×C311yescharacteristic, complemented
164C2×#683C22×C311yescharacteristic, complemented
165C2×#683C22×C311yescharacteristic, complemented
166C2×C4×Dic5C22×C311yescharacteristic, complemented
167C2×C4×Dic5C22×C311yescharacteristic, complemented
168C2×C4×Dic5C22×C311yescharacteristic, complemented
169#4038—24no—
170D5×C22⋊C4—24no—
171D5×C22⋊C4C3×C418yescomplemented
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×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5C22×C412yes—
188C23×C3×C5C2411yescharacteristic
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—21no—
193C22×C3×D5—21no—
194C22×C3×D5—21no—
195C22×C3×D5—21no—
196C22×C3×D5—21no—
197C22×C3×D5—28no—
198C22×C3×D5—28no—
199C22×C3×D5—44no—
200C22×C3×D5—44no—
201C22×C3×D5—44no—
202C22×C3×D5—44no—
203C22×C3×D5—44no—
204C22×C3×D5C22×C412yes—
205C22×C3×D5C22×C412yes—
206C22×C3×D5C2×D412yes—
207C22×C3×D5#4112yes—
208C22×C3×D5#4112yes—
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×C5C22×C412yes—
226C2×C3×C4×C5C22×C412yes—
227C2×C3×C4×C5C2×D412yes—
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—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×Dic5C22×C412yes—
244C2×C3×Dic5C22×C412yes—
245C2×C3×Dic5C2×D412yes—
246C3×C4×D5—28no—
247C3×C4×D5—44no—
248C3×C4×D5—44no—
249C3×C4×D5—44no—
250C25×C3—51no—
251C23×C3×C4—51no—
252C23×C3×C4—51no—
253C23×C3×C4—51no—
254C23×C3×C4—51no—
255C3×#117—104no—
256C2×C3×C4⋊C4—51no—
257C2×C3×C4⋊C4—51no—
258C2×C3×C4⋊C4—51no—
259C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
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—104no—
273C2×C3×C22⋊C4C2×D511yescharacteristic
274C2×C3×C22⋊C4C2×D511yescharacteristic
275C2×C3×C22⋊C4C2×D511yescharacteristic
276C2×C3×C42—51no—
277C2×C3×C42—51no—
278C2×C3×C42—51no—
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×C5C23×C311yescharacteristic
299C22×C4×C5C23×C311yescharacteristic
300C22×C4×C5C23×C311yescharacteristic
301C22×C4×C5C23×C311yescharacteristic
302C22×C4×C5C23×C311yescharacteristic
303C22×C4×C5C23×C311yescharacteristic
304C22×Dic5C23×C311yescharacteristic
305C22×Dic5C23×C311yescharacteristic
306C22×Dic5C23×C311yescharacteristic
307C22×Dic5C23×C311yescharacteristic
308C22×Dic5C23×C311yescharacteristic
309C22×Dic5C23×C311yescharacteristic
310C2×C4×D5—22no—
311C2×C4×D5—22no—
312C2×C4×D5—22no—
313C2×C4×D5—22no—
314C2×C4×D5—22no—
315C2×C4×D5—22no—
316C2×C4×D5—41no—
317C2×C4×D5—41no—
318C2×C4×D5—41no—
319C2×C4×D5—41no—
320C2×C4×D5C2×C3×C414yescomplemented
321C2×C4×D5C2×C3×C414yescomplemented
322C5×C4⋊C4—22no—
323C5×C22⋊C4—22no—
324C5×C22⋊C4—41no—
325C5×C22⋊C4C2×C3×C414yescomplemented
326C42×C5—41no—
327C22⋊Dic5—22no—
328C22⋊Dic5—41no—
329C22⋊Dic5C2×C3×C414yescomplemented
330#685—22no—
331#685—22no—
332#685—22no—
333#685—22no—
334#685—22no—
335#685C2×C3×C414yes—
336#685C2×C3×C414yes—
337#685C3×D414yes—
338C4⋊Dic5—22no—
339#683—41no—
340#683—41no—
341C4×Dic5—22no—
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#388C3×D511yescharacteristic, complemented
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⋊C4—51no—
359C22×C3×C5—22no—
360C22×C3×C5—22no—
361C22×C3×C5—22no—
362C22×C3×C5—41no—
363C22×C3×C5—41no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
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—22no—
383C2×C3×D5—22no—
384C2×C3×D5—22no—
385C2×C3×D5—416no—
386C2×C3×D5#11714yescomplemented
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—51no—
411C22×C3×C4—51no—
412C22×C3×C4—51no—
413C22×C3×C4—54no—
414C22×C3×C4—54no—
415C22×C3×C4—51no—
416C22×C3×C4—51no—
417C22×C3×C4—51no—
418C22×C3×C4—102no—
419C22×C3×C4—102no—
420C22×C3×C4—102no—
421C22×C3×C4—102no—
422C22×C3×C4—102no—
423C22×C3×C4—102no—
424C22×C3×C4—201no—
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—22no—
435C3×C4⋊C4—102no—
436C3×C4⋊C4—201no—
437C3×C4⋊C4—201no—
438C3×C22⋊C4—22no—
439C3×C22⋊C4—41no—
440C3×C22⋊C4—54no—
441C3×C22⋊C4—54no—
442C3×C22⋊C4—54no—
443C3×C22⋊C4—54no—
444C3×C22⋊C4—102no—
445C3×C22⋊C4—102no—
446C3×C22⋊C4—102no—
447C3×C22⋊C4—102no—
448C3×C22⋊C4—102no—
449C3×C22⋊C4—102no—
450C3×C22⋊C4—201no—
451C3×C22⋊C4C4×D514yescomplemented
452C3×C42—41no—
453C3×C42—102no—
454C3×C42—102no—
455C3×C42—201no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—21no—
462C23×C5C22×C3×C412yes—
463C23×C5C24×C311yescharacteristic
464C22×D5—21no—
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—21no—
468C22×D5—21no—
469C22×D5—21no—
470C22×D5—21no—
471C22×D5—21no—
472C22×D5—28no—
473C22×D5—28no—
474C22×D5—44no—
475C22×D5—44no—
476C22×D5—44no—
477C22×D5—44no—
478C22×D5—44no—
479C22×D5C22×C3×C412yes—
480C22×D5C22×C3×C412yes—
481C22×D5C2×C3×D412yes—
482C22×D5C3×#4112yes—
483C22×D5C3×#4112yes—
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×C5C22×C3×C412yes—
501C2×C4×C5C22×C3×C412yes—
502C2×C4×C5C2×C3×D412yes—
503C2×Dic5—21no—
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×Dic5C22×C3×C412yes—
519C2×Dic5C22×C3×C412yes—
520C2×Dic5C2×C3×D412yes—
521C4×D5—28no—
522C4×D5—44no—
523C4×D5—44no—
524C4×D5—44no—
525C25—51no—
526C23×C4—51no—
527C23×C4—51no—
528C23×C4—51no—
529C23×C4—51no—
530#117—104no—
531C2×C4⋊C4—51no—
532C2×C4⋊C4—51no—
533C2×C4⋊C4—51no—
534C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
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—104no—
548C2×C22⋊C4C2×C3×D511yescharacteristic
549C2×C22⋊C4C2×C3×D511yescharacteristic
550C2×C22⋊C4C2×C3×D511yescharacteristic
551C2×C42—51no—
552C2×C42—51no—
553C2×C42—51no—
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—42no—
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—24no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—52no—
580C23×C3—52no—
581C23×C3—52no—
582C23×C3—52no—
583C23×C3—52no—
584C23×C3—52no—
585C23×C3—108no—
586C23×C3—108no—
587C23×C3—101no—
588C23×C3—101no—
589C23×C3—101no—
590C23×C3—101no—
591C23×C3—101no—
592C23×C3—101no—
593C23×C3—101no—
594C23×C3—101no—
595C23×C3—204no—
596C23×C3—204no—
597C23×C3—204no—
598C23×C3—204no—
599C23×C3—204no—
600C23×C3C2×C4×D512yes—
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—52no—
618C2×C3×C4—52no—
619C2×C3×C4—52no—
620C2×C3×C4—108no—
621C2×C3×C4—101no—
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—204no—
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—41no—
646C22×C5—41no—
647C22×C5—41no—
648C22×C5—41no—
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—22no—
666C2×D5—22no—
667C2×D5—22no—
668C2×D5—416no—
669C2×D5C3×#11714yescomplemented
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—51no—
694C22×C4—51no—
695C22×C4—51no—
696C22×C4—54no—
697C22×C4—54no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—51no—
701C22×C4—102no—
702C22×C4—102no—
703C22×C4—102no—
704C22×C4—102no—
705C22×C4—102no—
706C22×C4—102no—
707C22×C4—201no—
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—22no—
718C4⋊C4—102no—
719C4⋊C4—201no—
720C4⋊C4—201no—
721C22⋊C4—22no—
722C22⋊C4—41no—
723C22⋊C4—54no—
724C22⋊C4—54no—
725C22⋊C4—54no—
726C22⋊C4—54no—
727C22⋊C4—102no—
728C22⋊C4—102no—
729C22⋊C4—102no—
730C22⋊C4—102no—
731C22⋊C4—102no—
732C22⋊C4—102no—
733C22⋊C4—201no—
734C22⋊C4C3×C4×D514yescomplemented
735C42—41no—
736C42—102no—
737C42—102no—
738C42—201no—
739C3×C5#234211yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—54no—
748C22×C3—54no—
749C22×C3—102no—
750C22×C3—102no—
751C22×C3—102no—
752C22×C3—102no—
753C22×C3—102no—
754C22×C3—102no—
755C22×C3—102no—
756C22×C3—102no—
757C22×C3—102no—
758C22×C3—102no—
759C22×C3—102no—
760C22×C3—102no—
761C22×C3—2016no—
762C22×C3C22×C4×D511yescharacteristic
763C22×C3C2×D4×D511yescharacteristic
764C22×C3#414411yescharacteristic
765C22×C3D5×#4111yescharacteristic
766C22×C3D5×#4111yescharacteristic
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—42no—
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—24no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—52no—
798C23—52no—
799C23—52no—
800C23—52no—
801C23—52no—
802C23—52no—
803C23—108no—
804C23—108no—
805C23—101no—
806C23—101no—
807C23—101no—
808C23—101no—
809C23—101no—
810C23—101no—
811C23—101no—
812C23—101no—
813C23—204no—
814C23—204no—
815C23—204no—
816C23—204no—
817C23—204no—
818C23C2×C3×C4×D512yes—
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—52no—
836C2×C4—52no—
837C2×C4—52no—
838C2×C4—108no—
839C2×C4—101no—
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—204no—
855C2×C4—204no—
856C2×C4—204no—
857C2×C4C2×C3×C4×D512yes—
858C2×C4C2×C3×C4×D512yes—
859C2×C4C3×D4×D512yes—
860C2×C3—42no—
861C2×C3—104no—
862C2×C3—104no—
863C2×C3D5×#11711yescharacteristic
864C2×C3C4×D4×D511yescharacteristic
865C2×C3#6587911yescharacteristic
866C2×C3#6594411yescharacteristic
867C2×C3#6599311yescharacteristic
868C2×C3#6601011yescharacteristic
869C2×C3#6603911yescharacteristic
870C5C3×#234211yescharacteristic, complemented, Sylow
871C22—22no—
872C22—22no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—54no—
879C22—54no—
880C22—102no—
881C22—102no—
882C22—102no—
883C22—102no—
884C22—102no—
885C22—102no—
886C22—102no—
887C22—102no—
888C22—102no—
889C22—102no—
890C22—102no—
891C22—102no—
892C22—2016no—
893C22C22×C3×C4×D511yescharacteristic
894C22C2×C3×D4×D511yescharacteristic
895C22C3×#414411yescharacteristic
896C22C3×D5×#4111yescharacteristic
897C22C3×D5×#4111yescharacteristic
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#1060756411yescharacteristic, direct product factor, Sylow
913C2—42no—
914C2—104no—
915C2—104no—
916C2C3×D5×#11711yescharacteristic
917C2C3×C4×D4×D511yescharacteristic
918C2C3×#6587911yescharacteristic
919C2C3×#6594411yescharacteristic
920C2C3×#6599311yescharacteristic
921C2C3×#6601011yescharacteristic
922C2C3×#6603911yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#388C2
socleC23×C3×C5C24
prime radicalC24×C3×D5C22
cosocleC23×C5C24×C3
hypercenterC3×#388D5
hypocenterC5C3×#2342
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4038C2semidirect
4. C3×C5×#388C2semidirect
5. C3×#65278C2semidirect
7. C3×#65240C2semidirect
8. C3×#65234C2semidirect
9. C3×#65233C2semidirect
10. C3×C4×#685C2semidirect
11. C3×C4×#685C2semidirect
12. C3×#64957C2semidirect
13. C3×#64956C2semidirect
14. C3×#64955C2semidirect
15. C3×#64953C2semidirect
16. #10607564C3direct (N × H)
22. C2×C3×C5×C4⋊C4C22semidirect
26. C2×C3×C42×C5C22semidirect
38. C2×C3×C4⋊Dic5C22semidirect
39. C2×C3×#683C22semidirect
40. C2×C3×#683C22semidirect
41. C2×C3×C4×Dic5C22semidirect
42. C2×C3×C4×Dic5C22semidirect
43. C2×C3×C4×Dic5C22semidirect
46. 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
56. C2×#4038C2×C3semidirect
59. C5×#388C2×C3semidirect
60. #65278C2×C3semidirect
62. #65240C2×C3semidirect
63. #65234C2×C3semidirect
64. #65233C2×C3semidirect
65. C4×#685C2×C3semidirect
66. C4×#685C2×C3semidirect
67. #64957C2×C3semidirect
68. #64956C2×C3semidirect
69. #64955C2×C3semidirect
70. #64953C2×C3semidirect
103. C2×C3×C4×D5C2×C4semidirect
104. C2×C3×C4×D5C2×C4semidirect
108. C3×C5×C22⋊C4C2×C4semidirect
112. C3×C22⋊Dic5C2×C4semidirect
133. C3×#388D5semidirect
147. C2×C5×C4⋊C4C22×C3semidirect
151. C2×C42×C5C22×C3semidirect
163. C2×C4⋊Dic5C22×C3semidirect
164. C2×#683C22×C3semidirect
165. C2×#683C22×C3semidirect
166. C2×C4×Dic5C22×C3semidirect
167. C2×C4×Dic5C22×C3semidirect
168. C2×C4×Dic5C22×C3semidirect
171. 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
259. C2×C3×C4⋊C4C2×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
325. C5×C22⋊C4C2×C3×C4semidirect
329. C22⋊Dic5C2×C3×C4semidirect
350. #388C3×D5semidirect
386. C2×C3×D5#117semidirect
451. C3×C22⋊C4C4×D5semidirect
534. C2×C4⋊C4C2×C3×D5semidirect
554. C2×C42C2×C3×D5semidirect
561. #95C2×C3×D5semidirect
562. #95C2×C3×D5semidirect
669. C2×D5C3×#117semidirect
734. C22⋊C4C3×C4×D5semidirect
739. C3×C5#2342semidirect
870. C5C3×#2342semidirect
912. C3#10607564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40382
C2×C3×D5×C22⋊C42
C3×C5×#3882
C3×#652782
C3×#652442
C3×#652402
C3×#652342
C3×#652332
C3×C4×#6852
C3×#649572
C3×#649562
C3×#649552
C3×#649532
#106075643
C3×#23425