Finite Group Databasebeta

← C3×#10605192 #14327322

Subgroups — C3×#10605192 #14327322

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#683C211yesmaximal, characteristic, complemented
2C2×C3×#4027C211yesmaximal, characteristic
3C2×C3×#4018C211yesmaximal, characteristic, complemented
4C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#65502C211yesmaximal, characteristic
6C3×#65247C211yesmaximal, characteristic
7C3×#65231C211yesmaximal, characteristic, complemented
8C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
9C3×#65229C211yesmaximal, characteristic, complemented
10C3×#65222C211yesmaximal, characteristic, complemented
11C3×C4×#683C211yesmaximal, characteristic, complemented
12C3×#64958C211yesmaximal, characteristic, complemented
13C3×#64956C211yesmaximal, characteristic, complemented
14C3×#64941C211yesmaximal, characteristic, complemented
15C3×#64939C211yesmaximal, characteristic, complemented
16#10605192C311yesmaximal, characteristic, direct product factor, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C42×C5C2211yescharacteristic
25C2×C3×C42×C5C2211yescharacteristic
26C2×C3×C22⋊Dic5C2211yescharacteristic
27C2×C3×#685C2211yescharacteristic
28C2×C3×#685C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#683—24no—
33C2×C3×#683C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
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×#4027C418yescomplemented
44C3×#4018—24no—
45C3×C5×#95C2211yescharacteristic
46C3×C5×#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#2352—51nomaximal, Hall
56C22×#683C2×C311yescharacteristic, complemented
57C2×#4027C2×C311yescharacteristic
58C2×#4018C2×C311yescharacteristic, complemented
59C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
60#65502C2×C311yescharacteristic
61#65247C2×C311yescharacteristic
62#65231C2×C311yescharacteristic, complemented
63C22⋊C4×Dic5C2×C311yescharacteristic, complemented
64#65229C2×C311yescharacteristic, complemented
65#65222C2×C311yescharacteristic, complemented
66C4×#683C2×C311yescharacteristic, complemented
67#64958C2×C311yescharacteristic, complemented
68#64956C2×C311yescharacteristic, complemented
69#64941C2×C311yescharacteristic, complemented
70#64939C2×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⋊D5—22no—
83C2×C3×C22⋊D5—22no—
84C2×C3×C22⋊D5C2×C414yes—
85C22×C3×Dic5—22no—
86C22×C3×Dic5—22no—
87C22×C3×Dic5—22no—
88C22×C3×Dic5—22no—
89C22×C3×Dic5—41no—
90C22×C3×Dic5C2×C414yes—
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×D5C2×C414yescomplemented
101C3×C5×C22⋊C4—22no—
102C3×C5×C22⋊C4C2×C414yes—
103C3×C42×C5—22no—
104C3×C42×C5—41no—
105C3×C22⋊Dic5—22no—
106C3×#685—22no—
107C3×#685—22no—
108C3×#685—41no—
109C3×#685—41no—
110C3×#685C2×C414yescomplemented
111C3×#683—22no—
112C3×#683—22no—
113C3×#683—22no—
114C3×#683—22no—
115C3×#683—22no—
116C3×#683C2×C414yescomplemented
117C3×#683D414yescomplemented
118C3×C4×Dic5—22no—
119C3×C4×Dic5—41no—
120C3×C4×Dic5C2×C414yescomplemented
121C2×C3×C4×D4—51no—
122C2×C3×#117—51no—
123C22×C3×C4⋊C4—51no—
124C3×#388—51no—
125C3×#388—51no—
126C3×#387—51no—
127C3×#387—51no—
128C3×#386—51no—
129C3×#386—51no—
130C3×#382—51no—
131C3×#380—51no—
132C3×#380—51no—
133C3×C4×C4⋊C4—51no—
134C3×C4×C22⋊C4—51no—
135C3×C4×C22⋊C4D511yescharacteristic, complemented
136C23×C4×C5C22×C311yescharacteristic
137C22×C22⋊D5C22×C311yescharacteristic
138C23×Dic5C22×C311yescharacteristic
139C23×Dic5C22×C311yescharacteristic
140C22×C4×D5C22×C311yescharacteristic
141C2×C5×C22⋊C4C22×C311yescharacteristic
142C2×C5×C22⋊C4C22×C311yescharacteristic
143C2×C42×C5C22×C311yescharacteristic
144C2×C42×C5C22×C311yescharacteristic
145C2×C22⋊Dic5C22×C311yescharacteristic
146C2×#685C22×C311yescharacteristic
147C2×#685C22×C311yescharacteristic
148C2×#685C22×C311yescharacteristic
149C2×#685C22×C311yescharacteristic
150C2×#685C22×C311yescharacteristic
151C2×#683—24no—
152C2×#683C22×C311yescharacteristic
153C2×#683C22×C311yescharacteristic
154C2×#683C22×C311yescharacteristic
155C2×#683C22×C311yescharacteristic
156C2×#683C22×C311yescharacteristic
157C2×#683C22×C311yescharacteristic
158C2×#683C22×C311yescharacteristic
159C2×C4×Dic5C22×C311yescharacteristic
160C2×C4×Dic5C22×C311yescharacteristic
161C2×C4×Dic5C22×C311yescharacteristic
162#4027C3×C418yescomplemented
163#4018—24no—
164C5×#95C22×C311yescharacteristic
165C5×#95C22×C311yescharacteristic
166#3963C22×C311yescharacteristic
167#3963C22×C311yescharacteristic
168#3963C22×C311yescharacteristic
169#3963C22×C311yescharacteristic
170#3963C22×C311yescharacteristic
171#3963C22×C311yescharacteristic
172#3963C22×C311yescharacteristic
173#3963C22×C311yescharacteristic
174#2352—51noSylow
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5C22×C412yes—
180C23×C3×C5#4112yes—
181C23×C3×C5#4112yes—
182C23×C3×C5C2411yescharacteristic
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×D5C22×C412yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
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—44no—
206C2×C3×C4×C5C22×C412yes—
207C2×C3×C4×C5C22×C412yes—
208C2×C3×C4×C5C2×D412yes—
209C3×C22⋊D5—28no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—28no—
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—44no—
227C2×C3×Dic5C22×C412yes—
228C2×C3×Dic5C22×C412yes—
229C2×C3×Dic5C22×C412yes—
230C2×C3×Dic5C2×D412yes—
231C2×C3×Dic5C2×D412yes—
232C2×C3×Dic5#4112yes—
233C3×C4×D5—28no—
234C22×C3×D4—51no—
235C23×C3×C4—51no—
236C23×C3×C4—51no—
237C23×C3×C4—51no—
238C23×C3×C4C2×D511yescharacteristic
239C3×C4×D4—58no—
240C3×#117—104no—
241C2×C3×C4⋊C4—51no—
242C2×C3×C4⋊C4—51no—
243C2×C3×C4⋊C4—51no—
244C2×C3×C4⋊C4—51no—
245C2×C3×C4⋊C4—51no—
246C2×C3×C4⋊C4—51no—
247C2×C3×C4⋊C4—51no—
248C2×C3×C4⋊C4—104no—
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⋊C4C2×D511yescharacteristic
256C2×C3×C22⋊C4C2×D511yescharacteristic
257C2×C3×C42—51no—
258C2×C3×C42—51no—
259C2×C3×C42—51no—
260C2×C3×C42C2×D511yescharacteristic
261C2×C3×C42C2×D511yescharacteristic
262C3×#95—51no—
263C3×#95—51no—
264C3×#95—51no—
265C3×#95—51no—
266C3×#95—51no—
267C3×#95—51no—
268C3×#95—51no—
269C3×#95—51no—
270C3×#95C2×D511yescharacteristic
271C3×#95C2×D511yescharacteristic
272C24×C5C23×C311yescharacteristic
273C23×D5C23×C311yescharacteristic
274C22×C4×C5—22no—
275C22×C4×C5—22no—
276C22×C4×C5—41no—
277C22×C4×C5C23×C311yescharacteristic
278C22×C4×C5C23×C311yescharacteristic
279C22×C4×C5C23×C311yescharacteristic
280C22×C4×C5C23×C311yescharacteristic
281C22×C4×C5C23×C311yescharacteristic
282C22×C4×C5C23×C311yescharacteristic
283C2×C22⋊D5—22no—
284C2×C22⋊D5—22no—
285C2×C22⋊D5C2×C3×C414yes—
286C22×Dic5—22no—
287C22×Dic5—22no—
288C22×Dic5—22no—
289C22×Dic5—22no—
290C22×Dic5—41no—
291C22×Dic5C2×C3×C414yes—
292C22×Dic5C23×C311yescharacteristic
293C22×Dic5C23×C311yescharacteristic
294C22×Dic5C23×C311yescharacteristic
295C22×Dic5C23×C311yescharacteristic
296C22×Dic5C23×C311yescharacteristic
297C22×Dic5C23×C311yescharacteristic
298C22×Dic5C23×C311yescharacteristic
299C2×C4×D5—22no—
300C2×C4×D5—22no—
301C2×C4×D5C2×C3×C414yescomplemented
302C5×C22⋊C4—22no—
303C5×C22⋊C4C2×C3×C414yes—
304C42×C5—22no—
305C42×C5—41no—
306C22⋊Dic5—22no—
307#685—22no—
308#685—22no—
309#685—41no—
310#685—41no—
311#685C2×C3×C414yescomplemented
312#683—22no—
313#683—22no—
314#683—22no—
315#683—22no—
316#683—22no—
317#683C2×C3×C414yescomplemented
318#683C3×D414yescomplemented
319C4×Dic5—22no—
320C4×Dic5—41no—
321C4×Dic5C2×C3×C414yescomplemented
322C2×C4×D4—51no—
323C2×#117—51no—
324C22×C4⋊C4—51no—
325#388—51no—
326#388—51no—
327#387—51no—
328#387—51no—
329#386—51no—
330#386—51no—
331#382—51no—
332#380—51no—
333#380—51no—
334C4×C4⋊C4—51no—
335C4×C22⋊C4—51no—
336C4×C22⋊C4C3×D511yescharacteristic, complemented
337C22×C3×C5—22no—
338C22×C3×C5—22no—
339C22×C3×C5—22no—
340C22×C3×C5—22no—
341C22×C3×C5—22no—
342C22×C3×C5—22no—
343C22×C3×C5#11714yescomplemented
344C22×C3×C5C23×C411yescharacteristic
345C22×C3×C5C22×D411yescharacteristic
346C22×C3×C5C2×#4111yescharacteristic
347C22×C3×C5C2×#4111yescharacteristic
348C22×C3×C5C2×#4111yescharacteristic
349C22×C3×C5H(5,𝔽2)11yescharacteristic
350C22×C3×C52−1+411yescharacteristic
351C2×C3×D5—22no—
352C2×C3×D5—22no—
353C2×C3×D5—22no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C2×C3×D5—41no—
358C3×C4×C5—22no—
359C3×C4×C5—22no—
360C3×C4×C5—22no—
361C3×C4×C5—41no—
362C3×C4×C5—41no—
363C3×C4×C5—41no—
364C3×Dic5—22no—
365C3×Dic5—22no—
366C3×Dic5—22no—
367C3×Dic5—41no—
368C3×Dic5—41no—
369C3×Dic5—41no—
370C3×Dic5C4×D414yes—
371C24×C3—51no—
372C24×C3C22×D511yescharacteristic
373C2×C3×D4—54no—
374C2×C3×D4—102no—
375C2×C3×D4—102no—
376C22×C3×C4—22no—
377C22×C3×C4—22no—
378C22×C3×C4—41no—
379C22×C3×C4—51no—
380C22×C3×C4—54no—
381C22×C3×C4—51no—
382C22×C3×C4—51no—
383C22×C3×C4—51no—
384C22×C3×C4—54no—
385C22×C3×C4—51no—
386C22×C3×C4—51no—
387C22×C3×C4—51no—
388C22×C3×C4—102no—
389C22×C3×C4—102no—
390C22×C3×C4—102no—
391C22×C3×C4—102no—
392C22×C3×C4—102no—
393C22×C3×C4—102no—
394C22×C3×C4—201no—
395C22×C3×C4C22×D511yescharacteristic
396C22×C3×C4C22×D511yescharacteristic
397C22×C3×C4C22×D511yescharacteristic
398C22×C3×C4C22×D511yescharacteristic
399C22×C3×C4C22×D511yescharacteristic
400C22×C3×C4C22×D511yescharacteristic
401C3×C4⋊C4—54no—
402C3×C4⋊C4—54no—
403C3×C4⋊C4—102no—
404C3×C4⋊C4—102no—
405C3×C4⋊C4—102no—
406C3×C4⋊C4—102no—
407C3×C4⋊C4—102no—
408C3×C22⋊C4—22no—
409C3×C22⋊C4—54no—
410C3×C22⋊C4—102no—
411C3×C22⋊C4—102no—
412C3×C22⋊C4—102no—
413C3×C22⋊C4—201no—
414C3×C22⋊C4—201no—
415C3×C22⋊C4C4×D514yes—
416C3×C42—22no—
417C3×C42—41no—
418C3×C42—54no—
419C3×C42—102no—
420C3×C42—201no—
421C23×C5—21no—
422C23×C5—21no—
423C23×C5—21no—
424C23×C5—21no—
425C23×C5C22×C3×C412yes—
426C23×C5C3×#4112yes—
427C23×C5C3×#4112yes—
428C23×C5C24×C311yescharacteristic
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—21no—
432C22×D5—21no—
433C22×D5—21no—
434C22×D5—21no—
435C22×D5C22×C3×C412yes—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—21no—
444C2×C4×C5—21no—
445C2×C4×C5—21no—
446C2×C4×C5—21no—
447C2×C4×C5—21no—
448C2×C4×C5—21no—
449C2×C4×C5—21no—
450C2×C4×C5—21no—
451C2×C4×C5—44no—
452C2×C4×C5C22×C3×C412yes—
453C2×C4×C5C22×C3×C412yes—
454C2×C4×C5C2×C3×D412yes—
455C22⋊D5—28no—
456C2×Dic5—21no—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—21no—
462C2×Dic5—28no—
463C2×Dic5—21no—
464C2×Dic5—21no—
465C2×Dic5—21no—
466C2×Dic5—21no—
467C2×Dic5—21no—
468C2×Dic5—21no—
469C2×Dic5—21no—
470C2×Dic5—21no—
471C2×Dic5—21no—
472C2×Dic5—44no—
473C2×Dic5C22×C3×C412yes—
474C2×Dic5C22×C3×C412yes—
475C2×Dic5C22×C3×C412yes—
476C2×Dic5C2×C3×D412yes—
477C2×Dic5C2×C3×D412yes—
478C2×Dic5C3×#4112yes—
479C4×D5—28no—
480C22×D4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4C2×C3×D511yescharacteristic
485C4×D4—58no—
486#117—104no—
487C2×C4⋊C4—51no—
488C2×C4⋊C4—51no—
489C2×C4⋊C4—51no—
490C2×C4⋊C4—51no—
491C2×C4⋊C4—51no—
492C2×C4⋊C4—51no—
493C2×C4⋊C4—51no—
494C2×C4⋊C4—104no—
495C2×C22⋊C4—51no—
496C2×C22⋊C4—51no—
497C2×C22⋊C4—51no—
498C2×C22⋊C4—51no—
499C2×C22⋊C4—51no—
500C2×C22⋊C4—51no—
501C2×C22⋊C4C2×C3×D511yescharacteristic
502C2×C22⋊C4C2×C3×D511yescharacteristic
503C2×C42—51no—
504C2×C42—51no—
505C2×C42—51no—
506C2×C42C2×C3×D511yescharacteristic
507C2×C42C2×C3×D511yescharacteristic
508#95—51no—
509#95—51no—
510#95—51no—
511#95—51no—
512#95—51no—
513#95—51no—
514#95—51no—
515#95—51no—
516#95C2×C3×D511yescharacteristic
517#95C2×C3×D511yescharacteristic
518C2×C3×C5—24no—
519C2×C3×C5C2×#11711yescharacteristic
520C2×C3×C5C2×C4×D411yescharacteristic
521C2×C3×C5#52011yescharacteristic
522C2×C3×C5#54611yescharacteristic
523C2×C3×C5#54811yescharacteristic
524C2×C3×C5#55211yescharacteristic
525C2×C3×C5#55311yescharacteristic
526C3×D5—42no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—52no—
532C23×C3—101no—
533C23×C3—101no—
534C23×C3—101no—
535C23×C3—101no—
536C23×C3—101no—
537C23×C3—101no—
538C23×C3C2×C4×D512yes—
539C23×C3#70912yes—
540C23×C3#70912yes—
541C23×C3C23×D511yescharacteristic
542C3×D4—108no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—44no—
559C2×C3×C4—52no—
560C2×C3×C4—52no—
561C2×C3×C4—52no—
562C2×C3×C4—52no—
563C2×C3×C4—52no—
564C2×C3×C4—52no—
565C2×C3×C4—108no—
566C2×C3×C4—108no—
567C2×C3×C4—101no—
568C2×C3×C4—101no—
569C2×C3×C4—101no—
570C2×C3×C4—101no—
571C2×C3×C4—101no—
572C2×C3×C4—101no—
573C2×C3×C4—101no—
574C2×C3×C4—101no—
575C2×C3×C4—101no—
576C2×C3×C4—101no—
577C2×C3×C4—101no—
578C2×C3×C4—101no—
579C2×C3×C4—101no—
580C2×C3×C4—101no—
581C2×C3×C4—101no—
582C2×C3×C4—204no—
583C2×C3×C4C2×C4×D512yes—
584C2×C3×C4C2×C4×D512yes—
585C2×C3×C4D4×D512yes—
586C22×C5—22no—
587C22×C5—22no—
588C22×C5—22no—
589C22×C5—22no—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5C3×#11714yescomplemented
593C22×C5C23×C3×C411yescharacteristic
594C22×C5C22×C3×D411yescharacteristic
595C22×C5C2×C3×#4111yescharacteristic
596C22×C5C2×C3×#4111yescharacteristic
597C22×C5C2×C3×#4111yescharacteristic
598C22×C5C3×H(5,𝔽2)11yescharacteristic
599C22×C5C3×2−1+411yescharacteristic
600C2×D5—22no—
601C2×D5—22no—
602C2×D5—22no—
603C2×D5—41no—
604C2×D5—41no—
605C2×D5—41no—
606C2×D5—41no—
607C4×C5—22no—
608C4×C5—22no—
609C4×C5—22no—
610C4×C5—41no—
611C4×C5—41no—
612C4×C5—41no—
613Dic5—22no—
614Dic5—22no—
615Dic5—22no—
616Dic5—41no—
617Dic5—41no—
618Dic5—41no—
619Dic5C3×C4×D414yes—
620C24—51no—
621C24C22×C3×D511yescharacteristic
622C2×D4—54no—
623C2×D4—102no—
624C2×D4—102no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—41no—
628C22×C4—51no—
629C22×C4—54no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—51no—
633C22×C4—54no—
634C22×C4—51no—
635C22×C4—51no—
636C22×C4—51no—
637C22×C4—102no—
638C22×C4—102no—
639C22×C4—102no—
640C22×C4—102no—
641C22×C4—102no—
642C22×C4—102no—
643C22×C4—201no—
644C22×C4C22×C3×D511yescharacteristic
645C22×C4C22×C3×D511yescharacteristic
646C22×C4C22×C3×D511yescharacteristic
647C22×C4C22×C3×D511yescharacteristic
648C22×C4C22×C3×D511yescharacteristic
649C22×C4C22×C3×D511yescharacteristic
650C4⋊C4—54no—
651C4⋊C4—54no—
652C4⋊C4—102no—
653C4⋊C4—102no—
654C4⋊C4—102no—
655C4⋊C4—102no—
656C4⋊C4—102no—
657C22⋊C4—22no—
658C22⋊C4—54no—
659C22⋊C4—102no—
660C22⋊C4—102no—
661C22⋊C4—102no—
662C22⋊C4—201no—
663C22⋊C4—201no—
664C22⋊C4C3×C4×D514yes—
665C42—22no—
666C42—41no—
667C42—54no—
668C42—102no—
669C42—201no—
670C3×C5#235211yescharacteristic, complemented, Hall
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—102no—
678C22×C3—102no—
679C22×C3—102no—
680C22×C3—201no—
681C22×C3—201no—
682C22×C3—201no—
683C22×C3—201no—
684C22×C3#401814yescomplemented
685C22×C3C22×C4×D511yescharacteristic
686C22×C3C2×#70911yescharacteristic
687C22×C3C2×#70911yescharacteristic
688C22×C3C2×D4×D511yescharacteristic
689C22×C3#414411yescharacteristic
690C22×C3D5×#4111yescharacteristic
691C22×C3#415011yescharacteristic
692C3×C4—22no—
693C3×C4—22no—
694C3×C4—22no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—54no—
699C3×C4—102no—
700C3×C4—102no—
701C3×C4—102no—
702C3×C4—201no—
703C3×C4—201no—
704C3×C4—201no—
705C2×C5—24no—
706C2×C5C2×C3×#11711yescharacteristic
707C2×C5C2×C3×C4×D411yescharacteristic
708C2×C5C3×#52011yescharacteristic
709C2×C5C3×#54611yescharacteristic
710C2×C5C3×#54811yescharacteristic
711C2×C5C3×#55211yescharacteristic
712C2×C5C3×#55311yescharacteristic
713D5—42no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—52no—
719C23—101no—
720C23—101no—
721C23—101no—
722C23—101no—
723C23—101no—
724C23—101no—
725C23C2×C3×C4×D512yes—
726C23C3×#70912yes—
727C23C3×#70912yes—
728C23C23×C3×D511yescharacteristic
729D4—108no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—44no—
746C2×C4—52no—
747C2×C4—52no—
748C2×C4—52no—
749C2×C4—52no—
750C2×C4—52no—
751C2×C4—52no—
752C2×C4—108no—
753C2×C4—108no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—101no—
758C2×C4—101no—
759C2×C4—101no—
760C2×C4—101no—
761C2×C4—101no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—101no—
766C2×C4—101no—
767C2×C4—101no—
768C2×C4—101no—
769C2×C4—204no—
770C2×C4C2×C3×C4×D512yes—
771C2×C4C2×C3×C4×D512yes—
772C2×C4C3×D4×D512yes—
773C2×C3—24no—
774C2×C3—202no—
775C2×C3C2×#401811yescharacteristic
776C2×C3#6582411yescharacteristic
777C2×C3#6586511yescharacteristic
778C2×C3#6587411yescharacteristic
779C2×C3C4×D4×D511yescharacteristic
780C2×C3#6588011yescharacteristic
781C2×C3#6588611yescharacteristic
782C5C3×#235211yescharacteristic, complemented, Sylow
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—102no—
790C22—102no—
791C22—102no—
792C22—201no—
793C22—201no—
794C22—201no—
795C22—201no—
796C22C3×#401814yescomplemented
797C22C22×C3×C4×D511yescharacteristic
798C22C2×C3×#70911yescharacteristic
799C22C2×C3×#70911yescharacteristic
800C22C2×C3×D4×D511yescharacteristic
801C22C3×#414411yescharacteristic
802C22C3×D5×#4111yescharacteristic
803C22C3×#415011yescharacteristic
804C4—22no—
805C4—22no—
806C4—22no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—54no—
811C4—102no—
812C4—102no—
813C4—102no—
814C4—201no—
815C4—201no—
816C4—201no—
817C3#1060519211yescharacteristic, direct product factor, Sylow
818C2—24no—
819C2—202no—
820C2C2×C3×#401811yescharacteristic
821C2C3×#6582411yescharacteristic
822C2C3×#6586511yescharacteristic
823C2C3×#6587411yescharacteristic
824C2C3×C4×D4×D511yescharacteristic
825C2C3×#6588011yescharacteristic
826C2C3×#6588611yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C5C24×C3
hypercenterC3×C4×C22⋊C4D5
hypocenterC5C3×#2352
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#683C2semidirect
3. C2×C3×#4018C2semidirect
4. C3×C4×C5×C22⋊C4C2semidirect
7. C3×#65231C2semidirect
8. C3×C22⋊C4×Dic5C2semidirect
9. C3×#65229C2semidirect
10. C3×#65222C2semidirect
11. C3×C4×#683C2semidirect
12. C3×#64958C2semidirect
13. C3×#64956C2semidirect
14. C3×#64941C2semidirect
15. C3×#64939C2semidirect
16. #10605192C3direct (N × H)
43. C3×#4027C4semidirect
56. C22×#683C2×C3semidirect
58. C2×#4018C2×C3semidirect
59. C4×C5×C22⋊C4C2×C3semidirect
62. #65231C2×C3semidirect
63. C22⋊C4×Dic5C2×C3semidirect
64. #65229C2×C3semidirect
65. #65222C2×C3semidirect
66. C4×#683C2×C3semidirect
67. #64958C2×C3semidirect
68. #64956C2×C3semidirect
69. #64941C2×C3semidirect
70. #64939C2×C3semidirect
100. C2×C3×C4×D5C2×C4semidirect
110. C3×#685C2×C4semidirect
116. C3×#683C2×C4semidirect
117. C3×#683D4semidirect
120. C3×C4×Dic5C2×C4semidirect
135. C3×C4×C22⋊C4D5semidirect
162. #4027C3×C4semidirect
301. C2×C4×D5C2×C3×C4semidirect
311. #685C2×C3×C4semidirect
317. #683C2×C3×C4semidirect
318. #683C3×D4semidirect
321. C4×Dic5C2×C3×C4semidirect
336. C4×C22⋊C4C3×D5semidirect
343. C22×C3×C5#117semidirect
592. C22×C5C3×#117semidirect
670. C3×C5#2352semidirect
684. C22×C3#4018semidirect
782. C5C3×#2352semidirect
796. C22C3×#4018semidirect
817. C3#10605192direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6832
C2×C3×#40272
C2×C3×#40182
C3×C4×C5×C22⋊C42
C3×#655022
C3×#652472
C3×#652312
C3×C22⋊C4×Dic52
C3×#652292
C3×#652222
C3×C4×#6832
C3×#649582
C3×#649562
C3×#649412
C3×#649392
#106051923
C3×#23525