Finite Group Databasebeta

← C3×#10607221 #14330838

Subgroups — C3×#10607221 #14330838

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4030C211yesmaximal, characteristic
2C3×C5×#388C211yesmaximal, characteristic, complemented
3C3×#65278C211yesmaximal, characteristic, complemented
4C3×#65276C211yesmaximal, characteristic, complemented
5C3×#65247C211yesmaximal, characteristic, complemented
6C3×#65247C211yesmaximal, characteristic, complemented
7C3×#65246C211yesmaximal, characteristic, complemented
8C3×#65245C211yesmaximal, characteristic, complemented
9C3×#65239C211yesmaximal, characteristic, complemented
10C3×#65228C211yesmaximal, characteristic, complemented
11C3×#65222C211yesmaximal, characteristic, complemented
12C3×#64959C211yesmaximal, characteristic, complemented
13C3×#64954C211yesmaximal, characteristic, complemented
14C3×#64953C211yesmaximal, characteristic, complemented
15C3×#64944C211yesmaximal, characteristic, complemented
16#10607221C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C22⋊D5C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C42×C5C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
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×C4⋊Dic5C2211yescharacteristic
38C2×C3×C4⋊Dic5C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42C3×#4030C418yescomplemented
43C3×C5×#95C2211yescharacteristic
44C3×C5×#95C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#2377—51nomaximal, Hall
54C2×#4030C2×C311yescharacteristic
55C5×#388C2×C311yescharacteristic, complemented
56#65278C2×C311yescharacteristic, complemented
57#65276C2×C311yescharacteristic, complemented
58#65247C2×C311yescharacteristic, complemented
59#65247C2×C311yescharacteristic, complemented
60#65246C2×C311yescharacteristic, complemented
61#65245C2×C311yescharacteristic, complemented
62#65239C2×C311yescharacteristic, complemented
63#65228C2×C311yescharacteristic, complemented
64#65222C2×C311yescharacteristic, complemented
65#64959C2×C311yescharacteristic, complemented
66#64954C2×C311yescharacteristic, complemented
67#64953C2×C311yescharacteristic, complemented
68#64944C2×C311yescharacteristic, complemented
69C24×C3×C5C2311yescharacteristic
70C23×C3×D5C2311yescharacteristic
71C23×C3×D5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C2×C3×C22⋊D5—41no—
79C2×C3×C22⋊D5—41no—
80C2×C3×C22⋊D5—41no—
81C2×C3×C22⋊D5—41no—
82C2×C3×C22⋊D5C2×C414yes—
83C2×C3×C22⋊D5C2×C414yescomplemented
84C22×C3×Dic5—41no—
85C22×C3×Dic5—41no—
86C22×C3×Dic5—41no—
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C2×C3×D20—41no—
94C2×C3×D20—41no—
95C2×C3×D20C2×C414yescomplemented
96C2×C3×C4×D5—41no—
97C2×C3×C4×D5—41no—
98C2×C3×C4×D5—41no—
99C2×C3×C4×D5—41no—
100C2×C3×C4×D5—41no—
101C2×C3×C4×D5C2×C414yescomplemented
102C3×C5×C4⋊C4—41no—
103C3×C5×C22⋊C4—41no—
104C3×C5×C22⋊C4—41no—
105C3×C5×C22⋊C4C2×C414yescomplemented
106C3×C42×C5—41no—
107C3×C22⋊Dic5—41no—
108C3×#685—41no—
109C3×#685—41no—
110C3×#685—41no—
111C3×#685—41no—
112C3×#685—41no—
113C3×#685—41no—
114C3×#685—41no—
115C3×#685C2×C414yescomplemented
116C3×C4⋊Dic5—41no—
117C3×C4⋊Dic5—41no—
118C3×#683—41no—
119C3×#683C2×C414yescomplemented
120C3×C4×Dic5—41no—
121C2×C3×#121—51no—
122C3×#390—51no—
123C3×#390—51no—
124C3×#388—51no—
125C3×#388D511yescharacteristic, complemented
126C3×#387—51no—
127C3×#387—51no—
128C3×#386—51no—
129C3×#386—51no—
130C3×#386—51no—
131C3×#386—51no—
132C3×#385—51no—
133C3×#385—51no—
134C3×#381—51no—
135C3×#380—51no—
136C22×C22⋊D5C22×C311yescharacteristic
137C22×C22⋊D5C22×C311yescharacteristic
138C23×Dic5C22×C311yescharacteristic
139C22×D20C22×C311yescharacteristic
140C22×C4×D5C22×C311yescharacteristic
141C22×C4×D5C22×C311yescharacteristic
142C2×C5×C4⋊C4C22×C311yescharacteristic
143C2×C5×C22⋊C4C22×C311yescharacteristic
144C2×C5×C22⋊C4C22×C311yescharacteristic
145C2×C5×C22⋊C4C22×C311yescharacteristic
146C2×C42×C5C22×C311yescharacteristic
147C2×C22⋊Dic5C22×C311yescharacteristic
148C2×#685C22×C311yescharacteristic
149C2×#685C22×C311yescharacteristic
150C2×#685C22×C311yescharacteristic
151C2×#685C22×C311yescharacteristic
152C2×#685C22×C311yescharacteristic
153C2×#685C22×C311yescharacteristic
154C2×#685C22×C311yescharacteristic
155C2×#685C22×C311yescharacteristic
156C2×C4⋊Dic5C22×C311yescharacteristic
157C2×C4⋊Dic5C22×C311yescharacteristic
158C2×#683C22×C311yescharacteristic
159C2×#683C22×C311yescharacteristic
160C2×C4×Dic5C22×C311yescharacteristic
161#4030C3×C418yescomplemented
162C5×#95C22×C311yescharacteristic
163C5×#95C22×C311yescharacteristic
164#3963C22×C311yescharacteristic
165#3963C22×C311yescharacteristic
166#3963C22×C311yescharacteristic
167#3963C22×C311yescharacteristic
168#3963C22×C311yescharacteristic
169#3963C22×C311yescharacteristic
170#3963C22×C311yescharacteristic
171#3963C22×C311yescharacteristic
172#2377—51noSylow
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5C22×C412yes—
180C23×C3×C5C2411yescharacteristic
181C22×C3×D5—21no—
182C22×C3×D5—21no—
183C22×C3×D5—21no—
184C22×C3×D5—21no—
185C22×C3×D5—21no—
186C22×C3×D5—21no—
187C22×C3×D5—21no—
188C22×C3×D5—21no—
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—21no—
193C22×C3×D5C22×C412yes—
194C22×C3×D5C22×C412yes—
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—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5C22×C412yes—
212C2×C3×C4×C5C22×C412yes—
213C3×C22⋊D5—44no—
214C3×C22⋊D5—44no—
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—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—44no—
232C2×C3×Dic5C22×C412yes—
233C2×C3×Dic5C22×C412yes—
234C3×D20—44no—
235C3×C4×D5—44no—
236C3×C4×D5—44no—
237C22×C3×D4—51no—
238C22×C3×D4—51no—
239C22×C3×D4—51no—
240C23×C3×C4—51no—
241C23×C3×C4—51no—
242C23×C3×C4—51no—
243C3×#121—58no—
244C2×C3×C4⋊C4—51no—
245C2×C3×C4⋊C4—51no—
246C2×C3×C4⋊C4—51no—
247C2×C3×C4⋊C4—51no—
248C2×C3×C4⋊C4C2×D511yescharacteristic
249C2×C3×C22⋊C4—51no—
250C2×C3×C22⋊C4—51no—
251C2×C3×C22⋊C4—51no—
252C2×C3×C22⋊C4—51no—
253C2×C3×C22⋊C4—51no—
254C2×C3×C22⋊C4—51no—
255C2×C3×C22⋊C4—51no—
256C2×C3×C22⋊C4—51no—
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4C2×D511yescharacteristic
259C2×C3×C22⋊C4C2×D511yescharacteristic
260C2×C3×C22⋊C4C2×D511yescharacteristic
261C2×C3×C42—51no—
262C2×C3×C42C2×D511yescharacteristic
263C3×#95—51no—
264C3×#95—51no—
265C3×#95—51no—
266C3×#95—51no—
267C3×#95—51no—
268C3×#95—51no—
269C3×#95—51no—
270C3×#95—51no—
271C3×#95C2×D511yescharacteristic
272C3×#95C2×D511yescharacteristic
273C24×C5C23×C311yescharacteristic
274C23×D5C23×C311yescharacteristic
275C23×D5C23×C311yescharacteristic
276C22×C4×C5C23×C311yescharacteristic
277C22×C4×C5C23×C311yescharacteristic
278C22×C4×C5C23×C311yescharacteristic
279C22×C4×C5C23×C311yescharacteristic
280C22×C4×C5C23×C311yescharacteristic
281C22×C4×C5C23×C311yescharacteristic
282C2×C22⋊D5—41no—
283C2×C22⋊D5—41no—
284C2×C22⋊D5—41no—
285C2×C22⋊D5—41no—
286C2×C22⋊D5C2×C3×C414yes—
287C2×C22⋊D5C2×C3×C414yescomplemented
288C22×Dic5—41no—
289C22×Dic5—41no—
290C22×Dic5—41no—
291C22×Dic5C23×C311yescharacteristic
292C22×Dic5C23×C311yescharacteristic
293C22×Dic5C23×C311yescharacteristic
294C22×Dic5C23×C311yescharacteristic
295C22×Dic5C23×C311yescharacteristic
296C22×Dic5C23×C311yescharacteristic
297C2×D20—41no—
298C2×D20—41no—
299C2×D20C2×C3×C414yescomplemented
300C2×C4×D5—41no—
301C2×C4×D5—41no—
302C2×C4×D5—41no—
303C2×C4×D5—41no—
304C2×C4×D5—41no—
305C2×C4×D5C2×C3×C414yescomplemented
306C5×C4⋊C4—41no—
307C5×C22⋊C4—41no—
308C5×C22⋊C4—41no—
309C5×C22⋊C4C2×C3×C414yescomplemented
310C42×C5—41no—
311C22⋊Dic5—41no—
312#685—41no—
313#685—41no—
314#685—41no—
315#685—41no—
316#685—41no—
317#685—41no—
318#685—41no—
319#685C2×C3×C414yescomplemented
320C4⋊Dic5—41no—
321C4⋊Dic5—41no—
322#683—41no—
323#683C2×C3×C414yescomplemented
324C4×Dic5—41no—
325C2×#121—51no—
326#390—51no—
327#390—51no—
328#388—51no—
329#388C3×D511yescharacteristic, complemented
330#387—51no—
331#387—51no—
332#386—51no—
333#386—51no—
334#386—51no—
335#386—51no—
336#385—51no—
337#385—51no—
338#381—51no—
339#380—51no—
340C22×C3×C5—22no—
341C22×C3×C5—22no—
342C22×C3×C5—22no—
343C22×C3×C5—41no—
344C22×C3×C5—41no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C23×C411yescharacteristic
348C22×C3×C5H(5,𝔽2)11yescharacteristic
349C22×C3×C5H(5,𝔽2)11yescharacteristic
350C22×C3×C5H(5,𝔽2)11yescharacteristic
351C22×C3×C5H(5,𝔽2)11yescharacteristic
352C22×C3×C5H(5,𝔽2)11yescharacteristic
353C22×C3×C52−1+411yescharacteristic
354C2×C3×D5—22no—
355C2×C3×D5—22no—
356C2×C3×D5—22no—
357C2×C3×D5—22no—
358C2×C3×D5—22no—
359C2×C3×D5—22no—
360C2×C3×D5—41no—
361C2×C3×D5—41no—
362C2×C3×D5—41no—
363C2×C3×D5—41no—
364C2×C3×D5—41no—
365C2×C3×D5—41no—
366C2×C3×D5—41no—
367C2×C3×D5—41no—
368C3×C4×C5—22no—
369C3×C4×C5—22no—
370C3×C4×C5—41no—
371C3×C4×C5—41no—
372C3×C4×C5—41no—
373C3×C4×C5—41no—
374C3×Dic5—22no—
375C3×Dic5—22no—
376C3×Dic5—41no—
377C3×Dic5—41no—
378C3×Dic5—41no—
379C3×Dic5—41no—
380C24×C3—51no—
381C24×C3—51no—
382C24×C3C22×D511yescharacteristic
383C2×C3×D4—54no—
384C2×C3×D4—54no—
385C2×C3×D4—54no—
386C2×C3×D4—201no—
387C2×C3×D4—201no—
388C2×C3×D4—201no—
389C2×C3×D4—201no—
390C2×C3×D4—201no—
391C2×C3×D4—201no—
392C22×C3×C4—51no—
393C22×C3×C4—51no—
394C22×C3×C4—54no—
395C22×C3×C4—51no—
396C22×C3×C4—51no—
397C22×C3×C4—51no—
398C22×C3×C4—51no—
399C22×C3×C4—201no—
400C22×C3×C4—201no—
401C22×C3×C4—201no—
402C22×C3×C4—201no—
403C22×C3×C4—201no—
404C22×C3×C4—201no—
405C22×C3×C4—201no—
406C22×C3×C4—201no—
407C22×C3×C4C22×D511yescharacteristic
408C22×C3×C4C22×D511yescharacteristic
409C22×C3×C4C22×D511yescharacteristic
410C22×C3×C4C22×D511yescharacteristic
411C22×C3×C4C22×D511yescharacteristic
412C22×C3×C4C22×D511yescharacteristic
413C3×C4⋊C4—41no—
414C3×C4⋊C4—54no—
415C3×C4⋊C4—201no—
416C3×C4⋊C4—201no—
417C3×C4⋊C4—201no—
418C3×C22⋊C4—41no—
419C3×C22⋊C4—41no—
420C3×C22⋊C4—54no—
421C3×C22⋊C4—201no—
422C3×C22⋊C4—201no—
423C3×C22⋊C4—201no—
424C3×C22⋊C4—201no—
425C3×C22⋊C4—201no—
426C3×C22⋊C4—201no—
427C3×C22⋊C4—201no—
428C3×C22⋊C4—201no—
429C3×C22⋊C4C4×D514yescomplemented
430C3×C42—41no—
431C3×C42—201no—
432C23×C5—21no—
433C23×C5—21no—
434C23×C5—21no—
435C23×C5—21no—
436C23×C5—21no—
437C23×C5—21no—
438C23×C5C22×C3×C412yes—
439C23×C5C24×C311yescharacteristic
440C22×D5—21no—
441C22×D5—21no—
442C22×D5—21no—
443C22×D5—21no—
444C22×D5—21no—
445C22×D5—21no—
446C22×D5—21no—
447C22×D5—21no—
448C22×D5—21no—
449C22×D5—21no—
450C22×D5—21no—
451C22×D5—21no—
452C22×D5C22×C3×C412yes—
453C22×D5C22×C3×C412yes—
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—21no—
466C2×C4×C5—21no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5C22×C3×C412yes—
471C2×C4×C5C22×C3×C412yes—
472C22⋊D5—44no—
473C22⋊D5—44no—
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—21no—
486C2×Dic5—21no—
487C2×Dic5—21no—
488C2×Dic5—21no—
489C2×Dic5—21no—
490C2×Dic5—44no—
491C2×Dic5C22×C3×C412yes—
492C2×Dic5C22×C3×C412yes—
493D20—44no—
494C4×D5—44no—
495C4×D5—44no—
496C22×D4—51no—
497C22×D4—51no—
498C22×D4—51no—
499C23×C4—51no—
500C23×C4—51no—
501C23×C4—51no—
502#121—58no—
503C2×C4⋊C4—51no—
504C2×C4⋊C4—51no—
505C2×C4⋊C4—51no—
506C2×C4⋊C4—51no—
507C2×C4⋊C4C2×C3×D511yescharacteristic
508C2×C22⋊C4—51no—
509C2×C22⋊C4—51no—
510C2×C22⋊C4—51no—
511C2×C22⋊C4—51no—
512C2×C22⋊C4—51no—
513C2×C22⋊C4—51no—
514C2×C22⋊C4—51no—
515C2×C22⋊C4—51no—
516C2×C22⋊C4—51no—
517C2×C22⋊C4C2×C3×D511yescharacteristic
518C2×C22⋊C4C2×C3×D511yescharacteristic
519C2×C22⋊C4C2×C3×D511yescharacteristic
520C2×C42—51no—
521C2×C42C2×C3×D511yescharacteristic
522#95—51no—
523#95—51no—
524#95—51no—
525#95—51no—
526#95—51no—
527#95—51no—
528#95—51no—
529#95—51no—
530#95C2×C3×D511yescharacteristic
531#95C2×C3×D511yescharacteristic
532C2×C3×C5—42no—
533C2×C3×C5#51811yescharacteristic
534C2×C3×C5#51811yescharacteristic
535C2×C3×C5#52011yescharacteristic
536C2×C3×C5#56011yescharacteristic
537C2×C3×C5#56011yescharacteristic
538C2×C3×C5#56211yescharacteristic
539C2×C3×C5#56211yescharacteristic
540C3×D5—42no—
541C3×D5—42no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—52no—
549C23×C3—52no—
550C23×C3—101no—
551C23×C3—101no—
552C23×C3—101no—
553C23×C3—101no—
554C23×C3—101no—
555C23×C3—101no—
556C23×C3—101no—
557C23×C3—101no—
558C23×C3—101no—
559C23×C3—101no—
560C23×C3—101no—
561C23×C3—101no—
562C23×C3C2×C4×D512yes—
563C23×C3C23×D511yescharacteristic
564C3×D4—204no—
565C3×D4—204no—
566C3×D4—204no—
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—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—52no—
584C2×C3×C4—52no—
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—101no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4—101no—
600C2×C3×C4—101no—
601C2×C3×C4—204no—
602C2×C3×C4—204no—
603C2×C3×C4—204no—
604C2×C3×C4C2×C4×D512yes—
605C2×C3×C4C2×C4×D512yes—
606C22×C5—22no—
607C22×C5—22no—
608C22×C5—22no—
609C22×C5—41no—
610C22×C5—41no—
611C22×C5—41no—
612C22×C5—41no—
613C22×C5C23×C3×C411yescharacteristic
614C22×C5C3×H(5,𝔽2)11yescharacteristic
615C22×C5C3×H(5,𝔽2)11yescharacteristic
616C22×C5C3×H(5,𝔽2)11yescharacteristic
617C22×C5C3×H(5,𝔽2)11yescharacteristic
618C22×C5C3×H(5,𝔽2)11yescharacteristic
619C22×C5C3×2−1+411yescharacteristic
620C2×D5—22no—
621C2×D5—22no—
622C2×D5—22no—
623C2×D5—22no—
624C2×D5—22no—
625C2×D5—22no—
626C2×D5—41no—
627C2×D5—41no—
628C2×D5—41no—
629C2×D5—41no—
630C2×D5—41no—
631C2×D5—41no—
632C2×D5—41no—
633C2×D5—41no—
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—41no—
637C4×C5—41no—
638C4×C5—41no—
639C4×C5—41no—
640Dic5—22no—
641Dic5—22no—
642Dic5—41no—
643Dic5—41no—
644Dic5—41no—
645Dic5—41no—
646C24—51no—
647C24—51no—
648C24C22×C3×D511yescharacteristic
649C2×D4—54no—
650C2×D4—54no—
651C2×D4—54no—
652C2×D4—201no—
653C2×D4—201no—
654C2×D4—201no—
655C2×D4—201no—
656C2×D4—201no—
657C2×D4—201no—
658C22×C4—51no—
659C22×C4—51no—
660C22×C4—54no—
661C22×C4—51no—
662C22×C4—51no—
663C22×C4—51no—
664C22×C4—51no—
665C22×C4—201no—
666C22×C4—201no—
667C22×C4—201no—
668C22×C4—201no—
669C22×C4—201no—
670C22×C4—201no—
671C22×C4—201no—
672C22×C4—201no—
673C22×C4C22×C3×D511yescharacteristic
674C22×C4C22×C3×D511yescharacteristic
675C22×C4C22×C3×D511yescharacteristic
676C22×C4C22×C3×D511yescharacteristic
677C22×C4C22×C3×D511yescharacteristic
678C22×C4C22×C3×D511yescharacteristic
679C4⋊C4—41no—
680C4⋊C4—54no—
681C4⋊C4—201no—
682C4⋊C4—201no—
683C4⋊C4—201no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—54no—
687C22⋊C4—201no—
688C22⋊C4—201no—
689C22⋊C4—201no—
690C22⋊C4—201no—
691C22⋊C4—201no—
692C22⋊C4—201no—
693C22⋊C4—201no—
694C22⋊C4—201no—
695C22⋊C4C3×C4×D514yescomplemented
696C42—41no—
697C42—201no—
698C3×C5#237711yescharacteristic, complemented, Hall
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—102no—
707C22×C3—102no—
708C22×C3—102no—
709C22×C3—102no—
710C22×C3—102no—
711C22×C3—102no—
712C22×C3—201no—
713C22×C3—201no—
714C22×C3—201no—
715C22×C3—201no—
716C22×C3—201no—
717C22×C3—201no—
718C22×C3—201no—
719C22×C3—201no—
720C22×C3C22×C4×D511yescharacteristic
721C22×C3#414411yescharacteristic
722C22×C3#414411yescharacteristic
723C22×C3#414911yescharacteristic
724C22×C3#414911yescharacteristic
725C22×C3#414911yescharacteristic
726C22×C3#415011yescharacteristic
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—102no—
734C3×C4—102no—
735C3×C4—201no—
736C3×C4—201no—
737C3×C4—201no—
738C3×C4—201no—
739C2×C5—42no—
740C2×C5C3×#51811yescharacteristic
741C2×C5C3×#51811yescharacteristic
742C2×C5C3×#52011yescharacteristic
743C2×C5C3×#56011yescharacteristic
744C2×C5C3×#56011yescharacteristic
745C2×C5C3×#56211yescharacteristic
746C2×C5C3×#56211yescharacteristic
747D5—42no—
748D5—42no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—52no—
756C23—52no—
757C23—101no—
758C23—101no—
759C23—101no—
760C23—101no—
761C23—101no—
762C23—101no—
763C23—101no—
764C23—101no—
765C23—101no—
766C23—101no—
767C23—101no—
768C23—101no—
769C23C2×C3×C4×D512yes—
770C23C23×C3×D511yescharacteristic
771D4—204no—
772D4—204no—
773D4—204no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—52no—
791C2×C4—52no—
792C2×C4—101no—
793C2×C4—101no—
794C2×C4—101no—
795C2×C4—101no—
796C2×C4—101no—
797C2×C4—101no—
798C2×C4—101no—
799C2×C4—101no—
800C2×C4—101no—
801C2×C4—101no—
802C2×C4—101no—
803C2×C4—101no—
804C2×C4—101no—
805C2×C4—101no—
806C2×C4—101no—
807C2×C4—101no—
808C2×C4—204no—
809C2×C4—204no—
810C2×C4—204no—
811C2×C4C2×C3×C4×D512yes—
812C2×C4C2×C3×C4×D512yes—
813C2×C3—42no—
814C2×C3—202no—
815C2×C3—202no—
816C2×C3#6585711yescharacteristic
817C2×C3#6587911yescharacteristic
818C2×C3#6587911yescharacteristic
819C2×C3#6595411yescharacteristic
820C2×C3#6600111yescharacteristic
821C2×C3#6601811yescharacteristic
822C2×C3#6604511yescharacteristic
823C5C3×#237711yescharacteristic, complemented, Sylow
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—102no—
832C22—102no—
833C22—102no—
834C22—102no—
835C22—102no—
836C22—102no—
837C22—201no—
838C22—201no—
839C22—201no—
840C22—201no—
841C22—201no—
842C22—201no—
843C22—201no—
844C22—201no—
845C22C22×C3×C4×D511yescharacteristic
846C22C3×#414411yescharacteristic
847C22C3×#414411yescharacteristic
848C22C3×#414911yescharacteristic
849C22C3×#414911yescharacteristic
850C22C3×#414911yescharacteristic
851C22C3×#415011yescharacteristic
852C4—22no—
853C4—22no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—102no—
859C4—102no—
860C4—201no—
861C4—201no—
862C4—201no—
863C4—201no—
864C3#1060722111yescharacteristic, direct product factor, Sylow
865C2—42no—
866C2—202no—
867C2—202no—
868C2C3×#6585711yescharacteristic
869C2C3×#6587911yescharacteristic
870C2C3×#6587911yescharacteristic
871C2C3×#6595411yescharacteristic
872C2C3×#6600111yescharacteristic
873C2C3×#6601811yescharacteristic
874C2C3×#6604511yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#388C2
socleC23×C3×C5C24
prime radicalC2×C3×#4030C2
cosocleC23×C5C24×C3
hypercenterC3×#388D5
hypocenterC5C3×#2377
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
2. C3×C5×#388C2semidirect
3. C3×#65278C2semidirect
4. C3×#65276C2semidirect
5. C3×#65247C2semidirect
6. C3×#65247C2semidirect
7. C3×#65246C2semidirect
8. C3×#65245C2semidirect
9. C3×#65239C2semidirect
10. C3×#65228C2semidirect
11. C3×#65222C2semidirect
12. C3×#64959C2semidirect
13. C3×#64954C2semidirect
14. C3×#64953C2semidirect
15. C3×#64944C2semidirect
16. #10607221C3direct (N × H)
42. C3×#4030C4semidirect
55. C5×#388C2×C3semidirect
56. #65278C2×C3semidirect
57. #65276C2×C3semidirect
58. #65247C2×C3semidirect
59. #65247C2×C3semidirect
60. #65246C2×C3semidirect
61. #65245C2×C3semidirect
62. #65239C2×C3semidirect
63. #65228C2×C3semidirect
64. #65222C2×C3semidirect
65. #64959C2×C3semidirect
66. #64954C2×C3semidirect
67. #64953C2×C3semidirect
68. #64944C2×C3semidirect
83. C2×C3×C22⋊D5C2×C4semidirect
95. C2×C3×D20C2×C4semidirect
101. C2×C3×C4×D5C2×C4semidirect
105. C3×C5×C22⋊C4C2×C4semidirect
115. C3×#685C2×C4semidirect
119. C3×#683C2×C4semidirect
125. C3×#388D5semidirect
161. #4030C3×C4semidirect
287. C2×C22⋊D5C2×C3×C4semidirect
299. C2×D20C2×C3×C4semidirect
305. C2×C4×D5C2×C3×C4semidirect
309. C5×C22⋊C4C2×C3×C4semidirect
319. #685C2×C3×C4semidirect
323. #683C2×C3×C4semidirect
329. #388C3×D5semidirect
429. C3×C22⋊C4C4×D5semidirect
695. C22⋊C4C3×C4×D5semidirect
698. C3×C5#2377semidirect
823. C5C3×#2377semidirect
864. C3#10607221direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40302
C3×C5×#3882
C3×#652782
C3×#652762
C3×#652472
C3×#652462
C3×#652452
C3×#652392
C3×#652282
C3×#652222
C3×#649592
C3×#649542
C3×#649532
C3×#649442
#106072213
C3×#23775