Finite Group Databasebeta

← C3×#10606125 #14327107

Subgroups — C3×#10606125 #14327107

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2C2×C3×#4027C211yesmaximal, characteristic
3C2×C3×#4027C211yesmaximal, characteristic
4C3×C5×#385C211yesmaximal, characteristic, complemented
5C2×C3×#3963C211yesmaximal, characteristic, complemented
6C3×#65278C211yesmaximal, characteristic, complemented
7C3×#65276C211yesmaximal, characteristic, complemented
8C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
9C3×#65261C211yesmaximal, characteristic, complemented
10C3×#65239C211yesmaximal, characteristic, complemented
11C3×#65231C211yesmaximal, characteristic, complemented
12C3×#64957C211yesmaximal, characteristic, complemented
13C3×D5×#95C211yesmaximal, characteristic, complemented
14C3×#64939C211yesmaximal, characteristic, complemented
15C3×#64936C211yesmaximal, characteristic, complemented
16#10606125C311yesmaximal, characteristic, direct product factor, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C3×C4×C22⋊D5—24no—
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×C4⋊Dic5C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic
36C2×C3×#683C2211yescharacteristic
37C2×C3×#683C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×C4×Dic5C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42C2×C3×C4×Dic5C2211yescharacteristic
43C3×#4027—24no—
44C3×#4027C418yescomplemented
45C3×C5×#95C2211yescharacteristic
46C3×C5×#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#2349—51nomaximal, Hall
56C2×C4×C22⋊D5C2×C311yescharacteristic
57C2×#4027C2×C311yescharacteristic
58C2×#4027C2×C311yescharacteristic
59C5×#385C2×C311yescharacteristic, complemented
60C2×#3963C2×C311yescharacteristic, complemented
61#65278C2×C311yescharacteristic, complemented
62#65276C2×C311yescharacteristic, complemented
63C4⋊C4×Dic5C2×C311yescharacteristic, complemented
64#65261C2×C311yescharacteristic, complemented
65#65239C2×C311yescharacteristic, complemented
66#65231C2×C311yescharacteristic, complemented
67#64957C2×C311yescharacteristic, complemented
68D5×#95C2×C311yescharacteristic, complemented
69#64939C2×C311yescharacteristic, complemented
70#64936C2×C311yescharacteristic, complemented
71C24×C3×C5C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×C3×C4×C5—22no—
74C22×C3×C4×C5—22no—
75C22×C3×C4×C5—41no—
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×C3×C22⋊D5C2×C414yes—
83C2×C3×C22⋊D5D414yes—
84C2×C3×C22⋊D5Q814yes—
85C22×C3×Dic5—22no—
86C22×C3×Dic5—22no—
87C22×C3×Dic5—41no—
88C22×C3×Dic5—41no—
89C22×C3×Dic5—41no—
90C22×C3×Dic5C2×C414yescomplemented
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—22no—
101C2×C3×C4×D5—22no—
102C2×C3×C4×D5—41no—
103C2×C3×C4×D5—41no—
104C2×C3×C4×D5—41no—
105C2×C3×C4×D5—41no—
106C2×C3×C4×D5C2×C414yescomplemented
107C3×C5×C4⋊C4—22no—
108C3×C5×C4⋊C4—41no—
109C3×C5×C22⋊C4—22no—
110C3×C5×C22⋊C4C2×C414yescomplemented
111C3×C22⋊Dic5—22no—
112C3×#685—22no—
113C3×#685—22no—
114C3×#685C2×C414yescomplemented
115C3×C4⋊Dic5—22no—
116C3×C4⋊Dic5—41no—
117C3×#683—22no—
118C3×#683—22no—
119C3×#683—41no—
120C3×#683—41no—
121C3×#683C2×C414yescomplemented
122C3×C4×Dic5—22no—
123C3×C4×Dic5—22no—
124C3×C4×Dic5C2×C414yescomplemented
125C2×C3×C4×D4—51no—
126C2×C3×C4×D4—51no—
127C2×C3×C4×D4—51no—
128C3×#389—51no—
129C3×#389—51no—
130C3×#385—51no—
131C3×#385—51no—
132C3×#385—51no—
133C3×#385D511yescharacteristic, complemented
134C3×#382—51no—
135C3×#380—51no—
136C3×#380—51no—
137C3×C4×C4⋊C4—51no—
138C2×C3×#95—51no—
139C2×C3×#95—51no—
140C23×C4×C5C22×C311yescharacteristic
141C22×C22⋊D5C22×C311yescharacteristic
142C23×Dic5C22×C311yescharacteristic
143C23×Dic5C22×C311yescharacteristic
144C22×C4×D5C22×C311yescharacteristic
145C22×C4×D5C22×C311yescharacteristic
146C22×C4×D5C22×C311yescharacteristic
147C2×C5×C4⋊C4C22×C311yescharacteristic
148C2×C5×C4⋊C4C22×C311yescharacteristic
149C2×C5×C22⋊C4C22×C311yescharacteristic
150C2×C5×C22⋊C4C22×C311yescharacteristic
151C2×C22⋊Dic5C22×C311yescharacteristic
152C4×C22⋊D5—24no—
153C2×#685C22×C311yescharacteristic
154C2×#685C22×C311yescharacteristic
155C2×#685C22×C311yescharacteristic
156C2×C4⋊Dic5C22×C311yescharacteristic
157C2×C4⋊Dic5C22×C311yescharacteristic
158C2×#683C22×C311yescharacteristic
159C2×#683C22×C311yescharacteristic
160C2×#683C22×C311yescharacteristic
161C2×#683C22×C311yescharacteristic
162C2×#683C22×C311yescharacteristic
163C2×C4×Dic5C22×C311yescharacteristic
164C2×C4×Dic5C22×C311yescharacteristic
165C2×C4×Dic5C22×C311yescharacteristic
166#4027—24no—
167#4027C3×C418yescomplemented
168C5×#95C22×C311yescharacteristic
169C5×#95C22×C311yescharacteristic
170#3963C22×C311yescharacteristic
171#3963C22×C311yescharacteristic
172#3963C22×C311yescharacteristic
173#3963C22×C311yescharacteristic
174#3963C22×C311yescharacteristic
175#3963C22×C311yescharacteristic
176#3963C22×C311yescharacteristic
177#3963C22×C311yescharacteristic
178#2349—51noSylow
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5C22×C412yes—
184C23×C3×C5C2×D412yes—
185C23×C3×C5C2×Q812yes—
186C23×C3×C5C2411yescharacteristic
187C22×C3×D5—21no—
188C22×C3×D5—21no—
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5C22×C412yes—
192C22×C3×D5C2×D412yes—
193C22×C3×D5C2×Q812yes—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—44no—
210C2×C3×C4×C5C22×C412yes—
211C2×C3×C4×C5C22×C412yes—
212C2×C3×C4×C5#4112yes—
213C3×C22⋊D5C4⋊C4116yescomplemented
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—44no—
230C2×C3×Dic5—44no—
231C2×C3×Dic5C22×C412yes—
232C2×C3×Dic5C22×C412yes—
233C2×C3×Dic5C22×C412yes—
234C2×C3×Dic5C2×D412yes—
235C2×C3×Dic5C2×Q812yes—
236C2×C3×Dic5#4112yes—
237C3×C4×D5—44no—
238C3×C4×D5—44no—
239C3×C4×D5—44no—
240C22×C3×D4—51no—
241C23×C3×C4—51no—
242C23×C3×C4—51no—
243C23×C3×C4—51no—
244C23×C3×C4—51no—
245C23×C3×C4—51no—
246C23×C3×C4C2×D511yescharacteristic
247C3×C4×D4—58no—
248C3×C4×D4—104no—
249C3×C4×D4—104no—
250C2×C3×C4⋊C4—51no—
251C2×C3×C4⋊C4—51no—
252C2×C3×C4⋊C4—51no—
253C2×C3×C4⋊C4—51no—
254C2×C3×C4⋊C4—51no—
255C2×C3×C4⋊C4—51no—
256C2×C3×C4⋊C4—51no—
257C2×C3×C4⋊C4C2×D511yescharacteristic
258C2×C3×C4⋊C4C2×D511yescharacteristic
259C2×C3×C22⋊C4—51no—
260C2×C3×C22⋊C4—51no—
261C2×C3×C22⋊C4—51no—
262C2×C3×C22⋊C4—51no—
263C2×C3×C22⋊C4C2×D511yescharacteristic
264C2×C3×C22⋊C4C2×D511yescharacteristic
265C2×C3×C42—51no—
266C2×C3×C42—51no—
267C2×C3×C42—51no—
268C3×#95—51no—
269C3×#95—51no—
270C3×#95—51no—
271C3×#95—51no—
272C3×#95—51no—
273C3×#95—51no—
274C3×#95—51no—
275C3×#95—51no—
276C3×#95C2×D511yescharacteristic
277C3×#95C2×D511yescharacteristic
278C24×C5C23×C311yescharacteristic
279C23×D5C23×C311yescharacteristic
280C22×C4×C5—22no—
281C22×C4×C5—22no—
282C22×C4×C5—41no—
283C22×C4×C5C23×C311yescharacteristic
284C22×C4×C5C23×C311yescharacteristic
285C22×C4×C5C23×C311yescharacteristic
286C22×C4×C5C23×C311yescharacteristic
287C22×C4×C5C23×C311yescharacteristic
288C22×C4×C5C23×C311yescharacteristic
289C2×C22⋊D5C2×C3×C414yes—
290C2×C22⋊D5C3×D414yes—
291C2×C22⋊D5C3×Q814yes—
292C22×Dic5—22no—
293C22×Dic5—22no—
294C22×Dic5—41no—
295C22×Dic5—41no—
296C22×Dic5—41no—
297C22×Dic5C2×C3×C414yescomplemented
298C22×Dic5C23×C311yescharacteristic
299C22×Dic5C23×C311yescharacteristic
300C22×Dic5C23×C311yescharacteristic
301C22×Dic5C23×C311yescharacteristic
302C22×Dic5C23×C311yescharacteristic
303C22×Dic5C23×C311yescharacteristic
304C22×Dic5C23×C311yescharacteristic
305C2×C4×D5—22no—
306C2×C4×D5—22no—
307C2×C4×D5—22no—
308C2×C4×D5—22no—
309C2×C4×D5—41no—
310C2×C4×D5—41no—
311C2×C4×D5—41no—
312C2×C4×D5—41no—
313C2×C4×D5C2×C3×C414yescomplemented
314C5×C4⋊C4—22no—
315C5×C4⋊C4—41no—
316C5×C22⋊C4—22no—
317C5×C22⋊C4C2×C3×C414yescomplemented
318C22⋊Dic5—22no—
319#685—22no—
320#685—22no—
321#685C2×C3×C414yescomplemented
322C4⋊Dic5—22no—
323C4⋊Dic5—41no—
324#683—22no—
325#683—22no—
326#683—41no—
327#683—41no—
328#683C2×C3×C414yescomplemented
329C4×Dic5—22no—
330C4×Dic5—22no—
331C4×Dic5C2×C3×C414yescomplemented
332C2×C4×D4—51no—
333C2×C4×D4—51no—
334C2×C4×D4—51no—
335#389—51no—
336#389—51no—
337#385—51no—
338#385—51no—
339#385—51no—
340#385C3×D511yescharacteristic, complemented
341#382—51no—
342#380—51no—
343#380—51no—
344C4×C4⋊C4—51no—
345C2×#95—51no—
346C2×#95—51no—
347C22×C3×C5—22no—
348C22×C3×C5—22no—
349C22×C3×C5—22no—
350C22×C3×C5—22no—
351C22×C3×C5—22no—
352C22×C3×C5—22no—
353C22×C3×C5C2×C4⋊C414yes—
354C22×C3×C5C23×C411yescharacteristic
355C22×C3×C5C22×D411yescharacteristic
356C22×C3×C5C22×Q811yescharacteristic
357C22×C3×C5C2×#4111yescharacteristic
358C22×C3×C5C2×#4111yescharacteristic
359C22×C3×C5H(5,𝔽2)11yescharacteristic
360C22×C3×C5H(5,𝔽2)11yescharacteristic
361C2×C3×D5—22no—
362C2×C3×D5—22no—
363C2×C3×D5—22no—
364C2×C3×D5—22no—
365C2×C3×D5—22no—
366C2×C3×D5—22no—
367C2×C3×D5C2×C4⋊C414yes—
368C3×C4×C5—22no—
369C3×C4×C5—22no—
370C3×C4×C5—22no—
371C3×C4×C5—41no—
372C3×C4×C5—41no—
373C3×C4×C5—41no—
374C3×Dic5—22no—
375C3×Dic5—22no—
376C3×Dic5—22no—
377C3×Dic5—41no—
378C3×Dic5—41no—
379C3×Dic5—41no—
380C3×Dic5C2×C4⋊C414yes—
381C24×C3—51no—
382C24×C3C22×D511yescharacteristic
383C2×C3×D4—54no—
384C2×C3×D4—54no—
385C2×C3×D4—54no—
386C22×C3×C4—22no—
387C22×C3×C4—22no—
388C22×C3×C4—41no—
389C22×C3×C4—51no—
390C22×C3×C4—51no—
391C22×C3×C4—51no—
392C22×C3×C4—51no—
393C22×C3×C4—54no—
394C22×C3×C4—54no—
395C22×C3×C4—51no—
396C22×C3×C4—51no—
397C22×C3×C4—51no—
398C22×C3×C4—102no—
399C22×C3×C4—102no—
400C22×C3×C4—102no—
401C22×C3×C4—102no—
402C22×C3×C4—102no—
403C22×C3×C4—102no—
404C22×C3×C4—201no—
405C22×C3×C4—201no—
406C22×C3×C4—201no—
407C22×C3×C4—201no—
408C22×C3×C4—201no—
409C22×C3×C4—201no—
410C22×C3×C4—201no—
411C22×C3×C4C22×D511yescharacteristic
412C22×C3×C4C22×D511yescharacteristic
413C22×C3×C4C22×D511yescharacteristic
414C22×C3×C4C22×D511yescharacteristic
415C22×C3×C4C22×D511yescharacteristic
416C22×C3×C4C22×D511yescharacteristic
417C3×C4⋊C4—22no—
418C3×C4⋊C4—41no—
419C3×C4⋊C4—54no—
420C3×C4⋊C4—102no—
421C3×C4⋊C4—102no—
422C3×C4⋊C4—102no—
423C3×C4⋊C4—201no—
424C3×C4⋊C4—201no—
425C3×C4⋊C4—201no—
426C3×C22⋊C4—22no—
427C3×C22⋊C4—54no—
428C3×C22⋊C4—102no—
429C3×C22⋊C4—102no—
430C3×C22⋊C4—102no—
431C3×C22⋊C4C4×D514yescomplemented
432C3×C42—54no—
433C3×C42—102no—
434C3×C42—102no—
435C23×C5—21no—
436C23×C5—21no—
437C23×C5—21no—
438C23×C5—21no—
439C23×C5C22×C3×C412yes—
440C23×C5C2×C3×D412yes—
441C23×C5C2×C3×Q812yes—
442C23×C5C24×C311yescharacteristic
443C22×D5—21no—
444C22×D5—21no—
445C22×D5—21no—
446C22×D5—21no—
447C22×D5C22×C3×C412yes—
448C22×D5C2×C3×D412yes—
449C22×D5C2×C3×Q812yes—
450C2×C4×C5—21no—
451C2×C4×C5—21no—
452C2×C4×C5—21no—
453C2×C4×C5—21no—
454C2×C4×C5—21no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—21no—
459C2×C4×C5—21no—
460C2×C4×C5—21no—
461C2×C4×C5—21no—
462C2×C4×C5—21no—
463C2×C4×C5—21no—
464C2×C4×C5—21no—
465C2×C4×C5—44no—
466C2×C4×C5C22×C3×C412yes—
467C2×C4×C5C22×C3×C412yes—
468C2×C4×C5C3×#4112yes—
469C22⋊D5C3×C4⋊C4116yescomplemented
470C2×Dic5—21no—
471C2×Dic5—21no—
472C2×Dic5—21no—
473C2×Dic5—21no—
474C2×Dic5—21no—
475C2×Dic5—21no—
476C2×Dic5—21no—
477C2×Dic5—21no—
478C2×Dic5—21no—
479C2×Dic5—21no—
480C2×Dic5—21no—
481C2×Dic5—21no—
482C2×Dic5—21no—
483C2×Dic5—21no—
484C2×Dic5—21no—
485C2×Dic5—44no—
486C2×Dic5—44no—
487C2×Dic5C22×C3×C412yes—
488C2×Dic5C22×C3×C412yes—
489C2×Dic5C22×C3×C412yes—
490C2×Dic5C2×C3×D412yes—
491C2×Dic5C2×C3×Q812yes—
492C2×Dic5C3×#4112yes—
493C4×D5—44no—
494C4×D5—44no—
495C4×D5—44no—
496C22×D4—51no—
497C23×C4—51no—
498C23×C4—51no—
499C23×C4—51no—
500C23×C4—51no—
501C23×C4—51no—
502C23×C4C2×C3×D511yescharacteristic
503C4×D4—58no—
504C4×D4—104no—
505C4×D4—104no—
506C2×C4⋊C4—51no—
507C2×C4⋊C4—51no—
508C2×C4⋊C4—51no—
509C2×C4⋊C4—51no—
510C2×C4⋊C4—51no—
511C2×C4⋊C4—51no—
512C2×C4⋊C4—51no—
513C2×C4⋊C4C2×C3×D511yescharacteristic
514C2×C4⋊C4C2×C3×D511yescharacteristic
515C2×C22⋊C4—51no—
516C2×C22⋊C4—51no—
517C2×C22⋊C4—51no—
518C2×C22⋊C4—51no—
519C2×C22⋊C4C2×C3×D511yescharacteristic
520C2×C22⋊C4C2×C3×D511yescharacteristic
521C2×C42—51no—
522C2×C42—51no—
523C2×C42—51no—
524#95—51no—
525#95—51no—
526#95—51no—
527#95—51no—
528#95—51no—
529#95—51no—
530#95—51no—
531#95—51no—
532#95C2×C3×D511yescharacteristic
533#95C2×C3×D511yescharacteristic
534C2×C3×C5—24no—
535C2×C3×C5C22×C4⋊C411yescharacteristic
536C2×C3×C5C4×#4111yescharacteristic
537C2×C3×C5#51811yescharacteristic
538C2×C3×C5#54611yescharacteristic
539C2×C3×C5#54611yescharacteristic
540C2×C3×C5#55411yescharacteristic
541C2×C3×C5#55411yescharacteristic
542C3×D5—24no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—52no—
548C23×C3—52no—
549C23×C3—52no—
550C23×C3—101no—
551C23×C3—101no—
552C23×C3—101no—
553C23×C3—101no—
554C23×C3C2×C4×D512yes—
555C23×C3D4×D512yes—
556C23×C3Q8×D512yes—
557C23×C3C23×D511yescharacteristic
558C3×D4—516no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—44no—
575C2×C3×C4—52no—
576C2×C3×C4—52no—
577C2×C3×C4—52no—
578C2×C3×C4—52no—
579C2×C3×C4—52no—
580C2×C3×C4—52no—
581C2×C3×C4—101no—
582C2×C3×C4—101no—
583C2×C3×C4—101no—
584C2×C3×C4—101no—
585C2×C3×C4—101no—
586C2×C3×C4—101no—
587C2×C3×C4—101no—
588C2×C3×C4—101no—
589C2×C3×C4—101no—
590C2×C3×C4—101no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—204no—
597C2×C3×C4—204no—
598C2×C3×C4—204no—
599C2×C3×C4—204no—
600C2×C3×C4—204no—
601C2×C3×C4C2×C4×D512yes—
602C2×C3×C4C2×C4×D512yes—
603C2×C3×C4#71112yes—
604C22×C5—22no—
605C22×C5—22no—
606C22×C5—22no—
607C22×C5—22no—
608C22×C5—22no—
609C22×C5—22no—
610C22×C5C2×C3×C4⋊C414yes—
611C22×C5C23×C3×C411yescharacteristic
612C22×C5C22×C3×D411yescharacteristic
613C22×C5C22×C3×Q811yescharacteristic
614C22×C5C2×C3×#4111yescharacteristic
615C22×C5C2×C3×#4111yescharacteristic
616C22×C5C3×H(5,𝔽2)11yescharacteristic
617C22×C5C3×H(5,𝔽2)11yescharacteristic
618C2×D5—22no—
619C2×D5—22no—
620C2×D5—22no—
621C2×D5—22no—
622C2×D5—22no—
623C2×D5—22no—
624C2×D5C2×C3×C4⋊C414yes—
625C4×C5—22no—
626C4×C5—22no—
627C4×C5—22no—
628C4×C5—41no—
629C4×C5—41no—
630C4×C5—41no—
631Dic5—22no—
632Dic5—22no—
633Dic5—22no—
634Dic5—41no—
635Dic5—41no—
636Dic5—41no—
637Dic5C2×C3×C4⋊C414yes—
638C24—51no—
639C24C22×C3×D511yescharacteristic
640C2×D4—54no—
641C2×D4—54no—
642C2×D4—54no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—41no—
646C22×C4—51no—
647C22×C4—51no—
648C22×C4—51no—
649C22×C4—51no—
650C22×C4—54no—
651C22×C4—54no—
652C22×C4—51no—
653C22×C4—51no—
654C22×C4—51no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—102no—
659C22×C4—102no—
660C22×C4—102no—
661C22×C4—201no—
662C22×C4—201no—
663C22×C4—201no—
664C22×C4—201no—
665C22×C4—201no—
666C22×C4—201no—
667C22×C4—201no—
668C22×C4C22×C3×D511yescharacteristic
669C22×C4C22×C3×D511yescharacteristic
670C22×C4C22×C3×D511yescharacteristic
671C22×C4C22×C3×D511yescharacteristic
672C22×C4C22×C3×D511yescharacteristic
673C22×C4C22×C3×D511yescharacteristic
674C4⋊C4—22no—
675C4⋊C4—41no—
676C4⋊C4—54no—
677C4⋊C4—102no—
678C4⋊C4—102no—
679C4⋊C4—102no—
680C4⋊C4—201no—
681C4⋊C4—201no—
682C4⋊C4—201no—
683C22⋊C4—22no—
684C22⋊C4—54no—
685C22⋊C4—102no—
686C22⋊C4—102no—
687C22⋊C4—102no—
688C22⋊C4C3×C4×D514yescomplemented
689C42—54no—
690C42—102no—
691C42—102no—
692C3×C5#234911yescharacteristic, complemented, Hall
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—54no—
700C22×C3—102no—
701C22×C3—102no—
702C22×C3—102no—
703C22×C3—102no—
704C22×C3—102no—
705C22×C3—102no—
706C22×C3D5×C4⋊C414yes—
707C22×C3C22×C4×D511yescharacteristic
708C22×C3C2×D4×D511yescharacteristic
709C22×C3C2×#71111yescharacteristic
710C22×C3#414411yescharacteristic
711C22×C3C2×Q8×D511yescharacteristic
712C22×C3D5×#4111yescharacteristic
713C22×C3#414911yescharacteristic
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—54no—
721C3×C4—102no—
722C3×C4—102no—
723C3×C4—102no—
724C3×C4—201no—
725C3×C4—201no—
726C3×C4—201no—
727C2×C5—24no—
728C2×C5C22×C3×C4⋊C411yescharacteristic
729C2×C5C3×C4×#4111yescharacteristic
730C2×C5C3×#51811yescharacteristic
731C2×C5C3×#54611yescharacteristic
732C2×C5C3×#54611yescharacteristic
733C2×C5C3×#55411yescharacteristic
734C2×C5C3×#55411yescharacteristic
735D5—24no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—52no—
741C23—52no—
742C23—52no—
743C23—101no—
744C23—101no—
745C23—101no—
746C23—101no—
747C23C2×C3×C4×D512yes—
748C23C3×D4×D512yes—
749C23C3×Q8×D512yes—
750C23C23×C3×D511yescharacteristic
751D4—516no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—44no—
768C2×C4—52no—
769C2×C4—52no—
770C2×C4—52no—
771C2×C4—52no—
772C2×C4—52no—
773C2×C4—52no—
774C2×C4—101no—
775C2×C4—101no—
776C2×C4—101no—
777C2×C4—101no—
778C2×C4—101no—
779C2×C4—101no—
780C2×C4—101no—
781C2×C4—101no—
782C2×C4—101no—
783C2×C4—101no—
784C2×C4—101no—
785C2×C4—101no—
786C2×C4—101no—
787C2×C4—101no—
788C2×C4—101no—
789C2×C4—204no—
790C2×C4—204no—
791C2×C4—204no—
792C2×C4—204no—
793C2×C4—204no—
794C2×C4C2×C3×C4×D512yes—
795C2×C4C2×C3×C4×D512yes—
796C2×C4C3×#71112yes—
797C2×C3—24no—
798C2×C3—104no—
799C2×C3C2×D5×C4⋊C411yescharacteristic
800C2×C3C4×#71111yescharacteristic
801C2×C3#6587911yescharacteristic
802C2×C3#6592511yescharacteristic
803C2×C3#6596911yescharacteristic
804C2×C3#6597011yescharacteristic
805C2×C3#6598811yescharacteristic
806C5C3×#234911yescharacteristic, complemented, Sylow
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—54no—
814C22—102no—
815C22—102no—
816C22—102no—
817C22—102no—
818C22—102no—
819C22—102no—
820C22C3×D5×C4⋊C414yes—
821C22C22×C3×C4×D511yescharacteristic
822C22C2×C3×D4×D511yescharacteristic
823C22C2×C3×#71111yescharacteristic
824C22C3×#414411yescharacteristic
825C22C2×C3×Q8×D511yescharacteristic
826C22C3×D5×#4111yescharacteristic
827C22C3×#414911yescharacteristic
828C4—22no—
829C4—22no—
830C4—22no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—54no—
835C4—102no—
836C4—102no—
837C4—102no—
838C4—201no—
839C4—201no—
840C4—201no—
841C3#1060612511yescharacteristic, direct product factor, Sylow
842C2—24no—
843C2—104no—
844C2C2×C3×D5×C4⋊C411yescharacteristic
845C2C3×C4×#71111yescharacteristic
846C2C3×#6587911yescharacteristic
847C2C3×#6592511yescharacteristic
848C2C3×#6596911yescharacteristic
849C2C3×#6597011yescharacteristic
850C2C3×#6598811yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#385C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C5C24×C3
hypercenterC3×#385D5
hypocenterC5C3×#2349
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#385

Complements

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

NH ≅ G/Ntype
4. C3×C5×#385C2semidirect
5. C2×C3×#3963C2semidirect
6. C3×#65278C2semidirect
7. C3×#65276C2semidirect
8. C3×C4⋊C4×Dic5C2semidirect
9. C3×#65261C2semidirect
10. C3×#65239C2semidirect
11. C3×#65231C2semidirect
12. C3×#64957C2semidirect
13. C3×D5×#95C2semidirect
14. C3×#64939C2semidirect
15. C3×#64936C2semidirect
16. #10606125C3direct (N × H)
44. C3×#4027C4semidirect
59. C5×#385C2×C3semidirect
60. C2×#3963C2×C3semidirect
61. #65278C2×C3semidirect
62. #65276C2×C3semidirect
63. C4⋊C4×Dic5C2×C3semidirect
64. #65261C2×C3semidirect
65. #65239C2×C3semidirect
66. #65231C2×C3semidirect
67. #64957C2×C3semidirect
68. D5×#95C2×C3semidirect
69. #64939C2×C3semidirect
70. #64936C2×C3semidirect
90. C22×C3×Dic5C2×C4semidirect
106. C2×C3×C4×D5C2×C4semidirect
110. C3×C5×C22⋊C4C2×C4semidirect
114. C3×#685C2×C4semidirect
121. C3×#683C2×C4semidirect
124. C3×C4×Dic5C2×C4semidirect
133. C3×#385D5semidirect
167. #4027C3×C4semidirect
213. C3×C22⋊D5C4⋊C4semidirect
297. C22×Dic5C2×C3×C4semidirect
313. C2×C4×D5C2×C3×C4semidirect
317. C5×C22⋊C4C2×C3×C4semidirect
321. #685C2×C3×C4semidirect
328. #683C2×C3×C4semidirect
331. C4×Dic5C2×C3×C4semidirect
340. #385C3×D5semidirect
431. C3×C22⋊C4C4×D5semidirect
469. C22⋊D5C3×C4⋊C4semidirect
688. C22⋊C4C3×C4×D5semidirect
692. C3×C5#2349semidirect
806. C5C3×#2349semidirect
841. C3#10606125direct (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×#40272
C3×C5×#3852
C2×C3×#39632
C3×#652782
C3×#652762
C3×C4⋊C4×Dic52
C3×#652612
C3×#652392
C3×#652312
C3×#649572
C3×D5×#952
C3×#649392
C3×#649362
#106061253
C3×#23495