Finite Group Databasebeta

← C3×#10606325 #14324030

Subgroups — C3×#10606325 #14324030

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
2C2×C3×#4039C211yesmaximal, characteristic, complemented
3C2×C3×#4030C211yesmaximal, characteristic
4C3×C5×#385C211yesmaximal, characteristic, complemented
5C3×#65502C211yesmaximal, characteristic, complemented
6C3×#65278C211yesmaximal, characteristic, complemented
7C3×#65276C211yesmaximal, characteristic, complemented
8C3×#65267C211yesmaximal, characteristic, complemented
9C3×#65245C211yesmaximal, characteristic, complemented
10C3×#65245C211yesmaximal, characteristic, complemented
11C3×#65240C211yesmaximal, characteristic, complemented
12C3×#64959C211yesmaximal, characteristic, complemented
13C3×#64954C211yesmaximal, characteristic, complemented
14C3×D5×#95C211yesmaximal, characteristic, complemented
15C3×#64941C211yesmaximal, characteristic, complemented
16#10606325C311yesmaximal, characteristic, direct product factor, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C4⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C3×C4×C22⋊D5—24no—
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×C4⋊Dic5C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42C2×C3×C4×Dic5C2211yescharacteristic
43C3×#4039—24no—
44C3×#4030C418yescomplemented
45C3×C5×#95C2211yescharacteristic
46C3×C5×#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#2325—51nomaximal, Hall
56C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
57C2×#4039C2×C311yescharacteristic, complemented
58C2×#4030C2×C311yescharacteristic
59C5×#385C2×C311yescharacteristic, complemented
60#65502C2×C311yescharacteristic, complemented
61#65278C2×C311yescharacteristic, complemented
62#65276C2×C311yescharacteristic, complemented
63#65267C2×C311yescharacteristic, complemented
64#65245C2×C311yescharacteristic, complemented
65#65245C2×C311yescharacteristic, complemented
66#65240C2×C311yescharacteristic, complemented
67#64959C2×C311yescharacteristic, complemented
68#64954C2×C311yescharacteristic, complemented
69D5×#95C2×C311yescharacteristic, complemented
70#64941C2×C311yescharacteristic, complemented
71C24×C3×C5C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C22×C3×C4×C5—22no—
75C22×C3×C4×C5—41no—
76C22×C3×C4×C5—41no—
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C2×C3×C22⋊D5—22no—
84C2×C3×C22⋊D5—22no—
85C2×C3×C22⋊D5—41no—
86C2×C3×C22⋊D5—41no—
87C2×C3×C22⋊D5C2×C414yescomplemented
88C2×C3×C22⋊D5C2×C414yescomplemented
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C2×C3×D20—22no—
96C2×C3×D20—22no—
97C2×C3×D20C2×C414yescomplemented
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—41no—
101C2×C3×C4×D5—41no—
102C2×C3×C4×D5—41no—
103C2×C3×C4×D5—41no—
104C2×C3×C4×D5—41no—
105C2×C3×C4×D5—41no—
106C2×C3×C4×D5—41no—
107C2×C3×C4×D5—41no—
108C2×C3×C4×D5C2×C414yescomplemented
109C2×C3×C4×D5D414yescomplemented
110C3×C5×C4⋊C4—22no—
111C3×C5×C4⋊C4—41no—
112C3×C5×C22⋊C4—41no—
113C3×C5×C22⋊C4C2×C414yescomplemented
114C3×C22⋊Dic5—22no—
115C3×C22⋊Dic5—41no—
116C3×#685—22no—
117C3×#685—22no—
118C3×#685—22no—
119C3×#685—41no—
120C3×#685—41no—
121C3×#685C2×C414yescomplemented
122C3×C4⋊Dic5—41no—
123C3×#683—22no—
124C3×#683C2×C414yescomplemented
125C3×C4×Dic5—22no—
126C3×C4×Dic5—22no—
127C2×C3×#121—51no—
128C2×C3×C4×D4—51no—
129C2×C3×C4×D4—51no—
130C3×#388—51no—
131C3×#388—51no—
132C3×#387—51no—
133C3×#387—51no—
134C3×#386—51no—
135C3×#386—51no—
136C3×#386—51no—
137C3×#386—51no—
138C3×#385—51no—
139C3×#385D511yescharacteristic, complemented
140C3×#380—51no—
141C2×C3×#95—51no—
142C23×C4×C5C22×C311yescharacteristic
143C22×C22⋊D5C22×C311yescharacteristic
144C22×C22⋊D5C22×C311yescharacteristic
145C22×D20C22×C311yescharacteristic
146C22×C4×D5C22×C311yescharacteristic
147C22×C4×D5C22×C311yescharacteristic
148C22×C4×D5C22×C311yescharacteristic
149C22×C4×D5C22×C311yescharacteristic
150C2×C5×C4⋊C4C22×C311yescharacteristic
151C2×C5×C4⋊C4C22×C311yescharacteristic
152C2×C5×C22⋊C4C22×C311yescharacteristic
153C2×C5×C22⋊C4C22×C311yescharacteristic
154C2×C22⋊Dic5C22×C311yescharacteristic
155C2×C22⋊Dic5C22×C311yescharacteristic
156C4×C22⋊D5—24no—
157C2×#685C22×C311yescharacteristic
158C2×#685C22×C311yescharacteristic
159C2×#685C22×C311yescharacteristic
160C2×#685C22×C311yescharacteristic
161C2×#685C22×C311yescharacteristic
162C2×#685C22×C311yescharacteristic
163C2×C4⋊Dic5C22×C311yescharacteristic
164C2×#683C22×C311yescharacteristic
165C2×#683C22×C311yescharacteristic
166C2×C4×Dic5C22×C311yescharacteristic
167C2×C4×Dic5C22×C311yescharacteristic
168#4039—24no—
169#4030C3×C418yescomplemented
170C5×#95C22×C311yescharacteristic
171C5×#95C22×C311yescharacteristic
172#3963C22×C311yescharacteristic
173#3963C22×C311yescharacteristic
174#3963C22×C311yescharacteristic
175#3963C22×C311yescharacteristic
176#3963C22×C311yescharacteristic
177#3963C22×C311yescharacteristic
178#3963C22×C311yescharacteristic
179#3963C22×C311yescharacteristic
180#2325—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—21no—
198C22×C3×D5—21no—
199C22×C3×D5C22×C412yes—
200C22×C3×D5C22×C412yes—
201C22×C3×D5C2×D412yes—
202C22×C3×D5#4112yes—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—44no—
219C2×C3×C4×C5C22×C412yes—
220C2×C3×C4×C5C22×C412yes—
221C2×C3×C4×C5C2×D412yes—
222C3×C22⋊D5—28no—
223C3×C22⋊D5—44no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5C22×C412yes—
240C2×C3×Dic5C22×C412yes—
241C2×C3×Dic5C2×D412yes—
242C3×D20—28no—
243C3×C4×D5—44no—
244C3×C4×D5—44no—
245C3×C4×D5—44no—
246C3×C4×D5—44no—
247C22×C3×D4—51no—
248C22×C3×D4—51no—
249C22×C3×D4—51no—
250C23×C3×C4—51no—
251C23×C3×C4—51no—
252C23×C3×C4—51no—
253C23×C3×C4—51no—
254C23×C3×C4C2×D511yescharacteristic
255C3×#121—58no—
256C3×C4×D4—104no—
257C3×C4×D4—104no—
258C2×C3×C4⋊C4—51no—
259C2×C3×C4⋊C4—51no—
260C2×C3×C4⋊C4—51no—
261C2×C3×C4⋊C4C2×D511yescharacteristic
262C2×C3×C4⋊C4C2×D511yescharacteristic
263C2×C3×C22⋊C4—51no—
264C2×C3×C22⋊C4—51no—
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⋊C4C2×D511yescharacteristic
272C2×C3×C22⋊C4C2×D511yescharacteristic
273C2×C3×C42—51no—
274C2×C3×C42—51no—
275C3×#95—51no—
276C3×#95—51no—
277C3×#95—51no—
278C3×#95—51no—
279C3×#95—51no—
280C3×#95—51no—
281C3×#95—51no—
282C3×#95—51no—
283C3×#95C2×D511yescharacteristic
284C3×#95C2×D511yescharacteristic
285C24×C5C23×C311yescharacteristic
286C23×D5C23×C311yescharacteristic
287C23×D5C23×C311yescharacteristic
288C22×C4×C5—22no—
289C22×C4×C5—41no—
290C22×C4×C5—41no—
291C22×C4×C5C23×C311yescharacteristic
292C22×C4×C5C23×C311yescharacteristic
293C22×C4×C5C23×C311yescharacteristic
294C22×C4×C5C23×C311yescharacteristic
295C22×C4×C5C23×C311yescharacteristic
296C22×C4×C5C23×C311yescharacteristic
297C2×C22⋊D5—22no—
298C2×C22⋊D5—22no—
299C2×C22⋊D5—41no—
300C2×C22⋊D5—41no—
301C2×C22⋊D5C2×C3×C414yescomplemented
302C2×C22⋊D5C2×C3×C414yescomplemented
303C22×Dic5C23×C311yescharacteristic
304C22×Dic5C23×C311yescharacteristic
305C22×Dic5C23×C311yescharacteristic
306C22×Dic5C23×C311yescharacteristic
307C22×Dic5C23×C311yescharacteristic
308C22×Dic5C23×C311yescharacteristic
309C2×D20—22no—
310C2×D20—22no—
311C2×D20C2×C3×C414yescomplemented
312C2×C4×D5—22no—
313C2×C4×D5—22no—
314C2×C4×D5—41no—
315C2×C4×D5—41no—
316C2×C4×D5—41no—
317C2×C4×D5—41no—
318C2×C4×D5—41no—
319C2×C4×D5—41no—
320C2×C4×D5—41no—
321C2×C4×D5—41no—
322C2×C4×D5C2×C3×C414yescomplemented
323C2×C4×D5C3×D414yescomplemented
324C5×C4⋊C4—22no—
325C5×C4⋊C4—41no—
326C5×C22⋊C4—41no—
327C5×C22⋊C4C2×C3×C414yescomplemented
328C22⋊Dic5—22no—
329C22⋊Dic5—41no—
330#685—22no—
331#685—22no—
332#685—22no—
333#685—41no—
334#685—41no—
335#685C2×C3×C414yescomplemented
336C4⋊Dic5—41no—
337#683—22no—
338#683C2×C3×C414yescomplemented
339C4×Dic5—22no—
340C4×Dic5—22no—
341C2×#121—51no—
342C2×C4×D4—51no—
343C2×C4×D4—51no—
344#388—51no—
345#388—51no—
346#387—51no—
347#387—51no—
348#386—51no—
349#386—51no—
350#386—51no—
351#386—51no—
352#385—51no—
353#385C3×D511yescharacteristic, complemented
354#380—51no—
355C2×#95—51no—
356C22×C3×C5—22no—
357C22×C3×C5—22no—
358C22×C3×C5—22no—
359C22×C3×C5—41no—
360C22×C3×C5—41no—
361C22×C3×C5—41no—
362C22×C3×C5—41no—
363C22×C3×C5C23×C411yescharacteristic
364C22×C3×C5C22×D411yescharacteristic
365C22×C3×C5C2×#4111yescharacteristic
366C22×C3×C5H(5,𝔽2)11yescharacteristic
367C22×C3×C5H(5,𝔽2)11yescharacteristic
368C22×C3×C5H(5,𝔽2)11yescharacteristic
369C22×C3×C52−1+411yescharacteristic
370C2×C3×D5—22no—
371C2×C3×D5—22no—
372C2×C3×D5—22no—
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—41no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C2×C3×D5—41no—
383C2×C3×D5C4×D414yes—
384C3×C4×C5—22no—
385C3×C4×C5—22no—
386C3×C4×C5—22no—
387C3×C4×C5—41no—
388C3×C4×C5—41no—
389C3×C4×C5—41no—
390C3×Dic5—22no—
391C3×Dic5—22no—
392C3×Dic5—22no—
393C3×Dic5—41no—
394C3×Dic5—41no—
395C3×Dic5—41no—
396C24×C3—51no—
397C24×C3—51no—
398C24×C3C22×D511yescharacteristic
399C2×C3×D4—54no—
400C2×C3×D4—54no—
401C2×C3×D4—54no—
402C2×C3×D4—102no—
403C2×C3×D4—102no—
404C2×C3×D4—102no—
405C2×C3×D4—102no—
406C2×C3×D4—201no—
407C2×C3×D4—201no—
408C22×C3×C4—22no—
409C22×C3×C4—41no—
410C22×C3×C4—41no—
411C22×C3×C4—51no—
412C22×C3×C4—51no—
413C22×C3×C4—51no—
414C22×C3×C4—54no—
415C22×C3×C4—54no—
416C22×C3×C4—51no—
417C22×C3×C4—51no—
418C22×C3×C4—51no—
419C22×C3×C4—102no—
420C22×C3×C4—102no—
421C22×C3×C4—201no—
422C22×C3×C4—201no—
423C22×C3×C4—201no—
424C22×C3×C4—201no—
425C22×C3×C4—201no—
426C22×C3×C4—201no—
427C22×C3×C4—201no—
428C22×C3×C4—201no—
429C22×C3×C4C22×D511yescharacteristic
430C22×C3×C4C22×D511yescharacteristic
431C22×C3×C4C22×D511yescharacteristic
432C22×C3×C4C22×D511yescharacteristic
433C22×C3×C4C22×D511yescharacteristic
434C22×C3×C4C22×D511yescharacteristic
435C3×C4⋊C4—22no—
436C3×C4⋊C4—41no—
437C3×C4⋊C4—54no—
438C3×C4⋊C4—102no—
439C3×C4⋊C4—201no—
440C3×C22⋊C4—41no—
441C3×C22⋊C4—54no—
442C3×C22⋊C4—102no—
443C3×C22⋊C4—102no—
444C3×C22⋊C4—102no—
445C3×C22⋊C4—102no—
446C3×C22⋊C4—201no—
447C3×C22⋊C4—201no—
448C3×C22⋊C4—201no—
449C3×C22⋊C4C4×D514yescomplemented
450C3×C42—102no—
451C3×C42—102no—
452C23×C5—21no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5C22×C3×C412yes—
459C23×C5C24×C311yescharacteristic
460C22×D5—21no—
461C22×D5—21no—
462C22×D5—21no—
463C22×D5—21no—
464C22×D5—21no—
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—21no—
468C22×D5—21no—
469C22×D5—21no—
470C22×D5C22×C3×C412yes—
471C22×D5C22×C3×C412yes—
472C22×D5C2×C3×D412yes—
473C22×D5C3×#4112yes—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—21no—
484C2×C4×C5—21no—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—44no—
490C2×C4×C5C22×C3×C412yes—
491C2×C4×C5C22×C3×C412yes—
492C2×C4×C5C2×C3×D412yes—
493C22⋊D5—28no—
494C22⋊D5—44no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—21no—
498C2×Dic5—21no—
499C2×Dic5—21no—
500C2×Dic5—21no—
501C2×Dic5—21no—
502C2×Dic5—21no—
503C2×Dic5—21no—
504C2×Dic5—21no—
505C2×Dic5—21no—
506C2×Dic5—21no—
507C2×Dic5—21no—
508C2×Dic5—21no—
509C2×Dic5—21no—
510C2×Dic5C22×C3×C412yes—
511C2×Dic5C22×C3×C412yes—
512C2×Dic5C2×C3×D412yes—
513D20—28no—
514C4×D5—44no—
515C4×D5—44no—
516C4×D5—44no—
517C4×D5—44no—
518C22×D4—51no—
519C22×D4—51no—
520C22×D4—51no—
521C23×C4—51no—
522C23×C4—51no—
523C23×C4—51no—
524C23×C4—51no—
525C23×C4C2×C3×D511yescharacteristic
526#121—58no—
527C4×D4—104no—
528C4×D4—104no—
529C2×C4⋊C4—51no—
530C2×C4⋊C4—51no—
531C2×C4⋊C4—51no—
532C2×C4⋊C4C2×C3×D511yescharacteristic
533C2×C4⋊C4C2×C3×D511yescharacteristic
534C2×C22⋊C4—51no—
535C2×C22⋊C4—51no—
536C2×C22⋊C4—51no—
537C2×C22⋊C4—51no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—51no—
540C2×C22⋊C4—51no—
541C2×C22⋊C4—51no—
542C2×C22⋊C4C2×C3×D511yescharacteristic
543C2×C22⋊C4C2×C3×D511yescharacteristic
544C2×C42—51no—
545C2×C42—51no—
546#95—51no—
547#95—51no—
548#95—51no—
549#95—51no—
550#95—51no—
551#95—51no—
552#95—51no—
553#95—51no—
554#95C2×C3×D511yescharacteristic
555#95C2×C3×D511yescharacteristic
556C2×C3×C5—42no—
557C2×C3×C5C2×C4×D411yescharacteristic
558C2×C3×C5#51811yescharacteristic
559C2×C3×C5#52011yescharacteristic
560C2×C3×C5#53411yescharacteristic
561C2×C3×C5#53711yescharacteristic
562C2×C3×C5#53811yescharacteristic
563C2×C3×C5#53911yescharacteristic
564C3×D5—24no—
565C3×D5—42no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—52no—
573C23×C3—52no—
574C23×C3—52no—
575C23×C3—52no—
576C23×C3—101no—
577C23×C3—101no—
578C23×C3—101no—
579C23×C3—101no—
580C23×C3—101no—
581C23×C3—101no—
582C23×C3—101no—
583C23×C3—101no—
584C23×C3—101no—
585C23×C3—101no—
586C23×C3C2×C4×D512yes—
587C23×C3C23×D511yescharacteristic
588C3×D4—108no—
589C3×D4—108no—
590C3×D4—204no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—44no—
607C2×C3×C4—52no—
608C2×C3×C4—52no—
609C2×C3×C4—52no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
614C2×C3×C4—101no—
615C2×C3×C4—101no—
616C2×C3×C4—101no—
617C2×C3×C4—101no—
618C2×C3×C4—101no—
619C2×C3×C4—101no—
620C2×C3×C4—101no—
621C2×C3×C4—101no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4—101no—
625C2×C3×C4—204no—
626C2×C3×C4—204no—
627C2×C3×C4—204no—
628C2×C3×C4—204no—
629C2×C3×C4C2×C4×D512yes—
630C2×C3×C4C2×C4×D512yes—
631C2×C3×C4D4×D512yes—
632C22×C5—22no—
633C22×C5—22no—
634C22×C5—22no—
635C22×C5—41no—
636C22×C5—41no—
637C22×C5—41no—
638C22×C5—41no—
639C22×C5C23×C3×C411yescharacteristic
640C22×C5C22×C3×D411yescharacteristic
641C22×C5C2×C3×#4111yescharacteristic
642C22×C5C3×H(5,𝔽2)11yescharacteristic
643C22×C5C3×H(5,𝔽2)11yescharacteristic
644C22×C5C3×H(5,𝔽2)11yescharacteristic
645C22×C5C3×2−1+411yescharacteristic
646C2×D5—22no—
647C2×D5—22no—
648C2×D5—22no—
649C2×D5—22no—
650C2×D5—22no—
651C2×D5—22no—
652C2×D5—22no—
653C2×D5—22no—
654C2×D5—22no—
655C2×D5—41no—
656C2×D5—41no—
657C2×D5—41no—
658C2×D5—41no—
659C2×D5C3×C4×D414yes—
660C4×C5—22no—
661C4×C5—22no—
662C4×C5—22no—
663C4×C5—41no—
664C4×C5—41no—
665C4×C5—41no—
666Dic5—22no—
667Dic5—22no—
668Dic5—22no—
669Dic5—41no—
670Dic5—41no—
671Dic5—41no—
672C24—51no—
673C24—51no—
674C24C22×C3×D511yescharacteristic
675C2×D4—54no—
676C2×D4—54no—
677C2×D4—54no—
678C2×D4—102no—
679C2×D4—102no—
680C2×D4—102no—
681C2×D4—102no—
682C2×D4—201no—
683C2×D4—201no—
684C22×C4—22no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—51no—
688C22×C4—51no—
689C22×C4—51no—
690C22×C4—54no—
691C22×C4—54no—
692C22×C4—51no—
693C22×C4—51no—
694C22×C4—51no—
695C22×C4—102no—
696C22×C4—102no—
697C22×C4—201no—
698C22×C4—201no—
699C22×C4—201no—
700C22×C4—201no—
701C22×C4—201no—
702C22×C4—201no—
703C22×C4—201no—
704C22×C4—201no—
705C22×C4C22×C3×D511yescharacteristic
706C22×C4C22×C3×D511yescharacteristic
707C22×C4C22×C3×D511yescharacteristic
708C22×C4C22×C3×D511yescharacteristic
709C22×C4C22×C3×D511yescharacteristic
710C22×C4C22×C3×D511yescharacteristic
711C4⋊C4—22no—
712C4⋊C4—41no—
713C4⋊C4—54no—
714C4⋊C4—102no—
715C4⋊C4—201no—
716C22⋊C4—41no—
717C22⋊C4—54no—
718C22⋊C4—102no—
719C22⋊C4—102no—
720C22⋊C4—102no—
721C22⋊C4—102no—
722C22⋊C4—201no—
723C22⋊C4—201no—
724C22⋊C4—201no—
725C22⋊C4C3×C4×D514yescomplemented
726C42—102no—
727C42—102no—
728C3×C5#232511yescharacteristic, complemented, Hall
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—54no—
737C22×C3—102no—
738C22×C3—102no—
739C22×C3—102no—
740C22×C3—102no—
741C22×C3—102no—
742C22×C3—102no—
743C22×C3—102no—
744C22×C3—102no—
745C22×C3—102no—
746C22×C3—201no—
747C22×C3—201no—
748C22×C3—201no—
749C22×C3—201no—
750C22×C3C22×C4×D511yescharacteristic
751C22×C3C2×D4×D511yescharacteristic
752C22×C3#414411yescharacteristic
753C22×C3#414411yescharacteristic
754C22×C3#414711yescharacteristic
755C22×C3D5×#4111yescharacteristic
756C22×C3#414911yescharacteristic
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—41no—
763C3×C4—102no—
764C3×C4—102no—
765C3×C4—102no—
766C3×C4—201no—
767C3×C4—201no—
768C3×C4—201no—
769C2×C5—42no—
770C2×C5C2×C3×C4×D411yescharacteristic
771C2×C5C3×#51811yescharacteristic
772C2×C5C3×#52011yescharacteristic
773C2×C5C3×#53411yescharacteristic
774C2×C5C3×#53711yescharacteristic
775C2×C5C3×#53811yescharacteristic
776C2×C5C3×#53911yescharacteristic
777D5—24no—
778D5—42no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—52no—
786C23—52no—
787C23—52no—
788C23—52no—
789C23—101no—
790C23—101no—
791C23—101no—
792C23—101no—
793C23—101no—
794C23—101no—
795C23—101no—
796C23—101no—
797C23—101no—
798C23—101no—
799C23C2×C3×C4×D512yes—
800C23C23×C3×D511yescharacteristic
801D4—108no—
802D4—108no—
803D4—204no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—44no—
820C2×C4—52no—
821C2×C4—52no—
822C2×C4—52no—
823C2×C4—101no—
824C2×C4—101no—
825C2×C4—101no—
826C2×C4—101no—
827C2×C4—101no—
828C2×C4—101no—
829C2×C4—101no—
830C2×C4—101no—
831C2×C4—101no—
832C2×C4—101no—
833C2×C4—101no—
834C2×C4—101no—
835C2×C4—101no—
836C2×C4—101no—
837C2×C4—101no—
838C2×C4—204no—
839C2×C4—204no—
840C2×C4—204no—
841C2×C4—204no—
842C2×C4C2×C3×C4×D512yes—
843C2×C4C2×C3×C4×D512yes—
844C2×C4C3×D4×D512yes—
845C2×C3—42no—
846C2×C3—104no—
847C2×C3—202no—
848C2×C3#6583811yescharacteristic
849C2×C3C4×D4×D511yescharacteristic
850C2×C3#6587911yescharacteristic
851C2×C3#6592311yescharacteristic
852C2×C3#6596311yescharacteristic
853C2×C3#6597211yescharacteristic
854C2×C3#6599111yescharacteristic
855C5C3×#232511yescharacteristic, complemented, Sylow
856C22—22no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—54no—
864C22—102no—
865C22—102no—
866C22—102no—
867C22—102no—
868C22—102no—
869C22—102no—
870C22—102no—
871C22—102no—
872C22—102no—
873C22—201no—
874C22—201no—
875C22—201no—
876C22—201no—
877C22C22×C3×C4×D511yescharacteristic
878C22C2×C3×D4×D511yescharacteristic
879C22C3×#414411yescharacteristic
880C22C3×#414411yescharacteristic
881C22C3×#414711yescharacteristic
882C22C3×D5×#4111yescharacteristic
883C22C3×#414911yescharacteristic
884C4—22no—
885C4—22no—
886C4—22no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—102no—
891C4—102no—
892C4—102no—
893C4—201no—
894C4—201no—
895C4—201no—
896C3#1060632511yescharacteristic, direct product factor, Sylow
897C2—42no—
898C2—104no—
899C2—202no—
900C2C3×#6583811yescharacteristic
901C2C3×C4×D4×D511yescharacteristic
902C2C3×#6587911yescharacteristic
903C2C3×#6592311yescharacteristic
904C2C3×#6596311yescharacteristic
905C2C3×#6597211yescharacteristic
906C2C3×#6599111yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#385C2
socleC23×C3×C5C24
prime radicalC2×C3×#4030C2
cosocleC23×C5C24×C3
hypercenterC3×#385D5
hypocenterC5C3×#2325
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#385

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C22⋊D5C2semidirect
2. C2×C3×#4039C2semidirect
4. C3×C5×#385C2semidirect
5. C3×#65502C2semidirect
6. C3×#65278C2semidirect
7. C3×#65276C2semidirect
8. C3×#65267C2semidirect
9. C3×#65245C2semidirect
10. C3×#65245C2semidirect
11. C3×#65240C2semidirect
12. C3×#64959C2semidirect
13. C3×#64954C2semidirect
14. C3×D5×#95C2semidirect
15. C3×#64941C2semidirect
16. #10606325C3direct (N × H)
44. C3×#4030C4semidirect
56. C2×C4×C22⋊D5C2×C3semidirect
57. C2×#4039C2×C3semidirect
59. C5×#385C2×C3semidirect
60. #65502C2×C3semidirect
61. #65278C2×C3semidirect
62. #65276C2×C3semidirect
63. #65267C2×C3semidirect
64. #65245C2×C3semidirect
65. #65245C2×C3semidirect
66. #65240C2×C3semidirect
67. #64959C2×C3semidirect
68. #64954C2×C3semidirect
69. D5×#95C2×C3semidirect
70. #64941C2×C3semidirect
87. C2×C3×C22⋊D5C2×C4semidirect
88. C2×C3×C22⋊D5C2×C4semidirect
97. C2×C3×D20C2×C4semidirect
108. C2×C3×C4×D5C2×C4semidirect
109. C2×C3×C4×D5D4semidirect
113. C3×C5×C22⋊C4C2×C4semidirect
121. C3×#685C2×C4semidirect
124. C3×#683C2×C4semidirect
139. C3×#385D5semidirect
169. #4030C3×C4semidirect
301. C2×C22⋊D5C2×C3×C4semidirect
302. C2×C22⋊D5C2×C3×C4semidirect
311. C2×D20C2×C3×C4semidirect
322. C2×C4×D5C2×C3×C4semidirect
323. C2×C4×D5C3×D4semidirect
327. C5×C22⋊C4C2×C3×C4semidirect
335. #685C2×C3×C4semidirect
338. #683C2×C3×C4semidirect
353. #385C3×D5semidirect
449. C3×C22⋊C4C4×D5semidirect
725. C22⋊C4C3×C4×D5semidirect
728. C3×C5#2325semidirect
855. C5C3×#2325semidirect
896. C3#10606325direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
C2×C3×#40392
C2×C3×#40302
C3×C5×#3852
C3×#655022
C3×#652782
C3×#652762
C3×#652672
C3×#652452
C3×#652402
C3×#649592
C3×#649542
C3×D5×#952
C3×#649412
#106063253
C3×#23255