Finite Group Databasebeta

← C2×#11756413 #14482492

Subgroups — C2×#11756413 #14482492

Order 1920.

3800 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D15C211yesmaximal, characteristic, complemented
2C22×#6817C211yesmaximal, characteristic, complemented
3C2×C3×C5×#123C211yesmaximal, characteristic, complemented
4C2×#91828C211yesmaximal, characteristic, complemented
5C22×#6714C211yesmaximal, characteristic, complemented
6#11756413C2116yesmaximal, direct product factor
7C2×#91785C211yesmaximal, characteristic, complemented
8C2×#91784C211yesmaximal, characteristic, complemented
9C2×#91783C211yesmaximal, characteristic, complemented
10C2×#91782C211yesmaximal, characteristic, complemented
11C2×#91774C211yesmaximal, characteristic, complemented
12C2×#91773C211yesmaximal, characteristic, complemented
13C2×#91771C211yesmaximal, characteristic, complemented
14C2×#91771C211yesmaximal, characteristic, complemented
15C2×#91770C211yesmaximal, characteristic, complemented
16C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
17C2×#65988—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C24×D15C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic
21C23×C3×C4×C5C2211yescharacteristic, complemented
22C22×#1220C2211yescharacteristic
23C22×#1220C2211yescharacteristic
24C22×#1220C2211yescharacteristic, complemented
25C22×#1220C2211yescharacteristic, complemented
26C23×Dic15C2211yescharacteristic, complemented
27C2×D4×D15—28no—
28C2×D4×D15C2218yescomplemented
29C2×#6817—28no—
30C2×#6817C2218yescomplemented
31C22×D60C2211yescharacteristic
32C22×D60C2211yescharacteristic
33C22×D60C2211yescharacteristic, complemented
34C22×D60C2211yescharacteristic, complemented
35C22×C4×D15C2211yescharacteristic
36C22×C4×D15C2211yescharacteristic, complemented
37C22×C4×D15C2211yescharacteristic, complemented
38C22×C4×D15C2211yescharacteristic, complemented
39C22×Dic30C2211yescharacteristic, complemented
40C3×C5×#123C2218yescomplemented
41C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
42C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
43C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
44C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
45C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
46C2×#6719C2211yescharacteristic, complemented
47#91828C2218yescomplemented
48C2×#6714C2211yescharacteristic
49C2×#6714C2211yescharacteristic
50C2×#6714C2211yescharacteristic
51C2×#6714C2218yescomplemented
52C2×#6714C2211yescharacteristic, complemented
53C2×#6714C2211yescharacteristic, complemented
54C2×#6714C2211yescharacteristic, complemented
55C2×#6714C2211yescharacteristic, complemented
56C2×#6714C2211yescharacteristic, complemented
57C2×#6712C2211yescharacteristic, complemented
58C2×#6712C2211yescharacteristic, complemented
59C2×C4×Dic15C2211yescharacteristic, complemented
60#91785C2218yescomplemented
61#91784C2218yescomplemented
62#91783C2218yescomplemented
63#91782C2218yescomplemented
64#91774C2218yescomplemented
65#91773C2218yescomplemented
66#91771C2218yescomplemented
67#91771C2218yescomplemented
68#91770C2218yescomplemented
69C22⋊C4×D15C2218yescomplemented
70C2×#5654—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×#709—31no—
73C2×C5×#123D311yescharacteristic, complemented
74C2×#4085—31no—
75C22×#685—31no—
76#65988—316no—
77C2×#4042—31no—
78C2×#4041—31no—
79C2×#4040—31no—
80C2×#4039—31no—
81C2×#4031—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C2×#4027—31no—
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15—24no—
90C23×D15—24no—
91C23×D15—24no—
92C23×D15—24no—
93C23×D15—42no—
94C23×D15—42no—
95C23×D15C2311yescharacteristic
96C23×D15C2311yescharacteristic
97C23×D15C2314yes—
98C23×D15C2314yes—
99C23×D15C2311yescharacteristic
100C23×D15C2311yescharacteristic
101C2×C3×C5×D4—24no—
102C2×C3×C5×D4C2314yes—
103C22×C3×C4×C5—24no—
104C22×C3×C4×C5C2311yescharacteristic
105C22×C3×C4×C5C2311yescharacteristic
106C22×C3×C4×C5C2311yescharacteristic
107C22×C3×C4×C5C2311yescharacteristic
108C22×C3×C4×C5C2311yescharacteristic
109C22×C3×C4×C5C2314yescomplemented
110C2×#1220—24no—
111C2×#1220—24no—
112C2×#1220—42no—
113C2×#1220D418yescomplemented
114C2×#1220C2314yes—
115C2×#1220C2314yes—
116C2×#1220C2314yescomplemented
117C2×#1220C2314yescomplemented
118C22×Dic15—42no—
119C22×Dic15C2311yescharacteristic
120C22×Dic15C2311yescharacteristic
121C22×Dic15C2311yescharacteristic
122C22×Dic15C2311yescharacteristic
123C22×Dic15C2314yescomplemented
124D4×D15—232no—
125#6817—232no—
126C2×D60—24no—
127C2×D60—24no—
128C2×D60—24no—
129C2×D60—42no—
130C2×D60C2314yes—
131C2×D60C2314yes—
132C2×D60C2314yescomplemented
133C2×D60C2314yescomplemented
134C2×C4×D15—24no—
135C2×C4×D15—24no—
136C2×C4×D15—24no—
137C2×C4×D15—42no—
138C2×C4×D15C2314yes—
139C2×C4×D15C2314yescomplemented
140C2×C4×D15C2314yescomplemented
141C2×C4×D15C2314yescomplemented
142C2×Dic30—24no—
143C2×Dic30C2314yescomplemented
144C3×C5×C4⋊C4C2314yescomplemented
145C3×C5×C4⋊C4C2314yescomplemented
146C3×C5×C22⋊C4C2314yescomplemented
147C3×C5×C22⋊C4C2314yescomplemented
148C3×C5×C22⋊C4C2314yescomplemented
149#6719C2314yescomplemented
150#6714C2314yes—
151#6714C2314yes—
152#6714C2314yes—
153#6714C2314yescomplemented
154#6714C2314yescomplemented
155#6714C2314yescomplemented
156#6714C2314yescomplemented
157#6714C2314yescomplemented
158#6712C2314yescomplemented
159#6712C2314yescomplemented
160C4×Dic15C2314yescomplemented
161C22×D3×D4—51no—
162C22×#235—51no—
163C2×C3×#123D511yescharacteristic, complemented
164C2×#939—51no—
165C22×(C2×D3)⋊C4—51no—
166#5654—516no—
167C2×#896—51no—
168C2×#895—51no—
169C2×#894—51no—
170C2×#893—51no—
171C2×#885—51no—
172C2×#884—51no—
173C2×#882—51no—
174C2×#882—51no—
175C2×#67⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×D4C2×D311yescharacteristic
180C23×C4×C5C2×D311yescharacteristic, complemented
181C22×C22⋊D5—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C23×Dic5—31no—
186C2×D4×D5—38no—
187C2×D4×D5—68no—
188C2×#709—38no—
189C2×#709—68no—
190C22×D20—31no—
191C22×D20—31no—
192C22×D20—31no—
193C22×D20—31no—
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5—31no—
198C22×Dic10—31no—
199C5×#123C2×D318yescomplemented
200C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
201C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
202C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
203C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
204C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
205C2×C22⋊Dic5—31no—
206#4085—38no—
207C2×#685—31no—
208C2×#685—31no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—38no—
216C2×#683—31no—
217C2×#683—31no—
218C2×C4×Dic5—31no—
219#4042—38no—
220#4041—38no—
221#4040—38no—
222#4039—38no—
223#4031—38no—
224#4030—38no—
225#4028—38no—
226#4028—38no—
227#4027—38no—
228D5×C22⋊C4—38no—
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5C2×D414yes—
236C23×C3×C5C2412yes—
237C23×C3×C5C2412yes—
238C23×C3×C5C2411yescharacteristic
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15—22no—
243C22×D15—22no—
244C22×D15—22no—
245C22×D15—28no—
246C22×D15—22no—
247C22×D15—22no—
248C22×D15—22no—
249C22×D15—22no—
250C22×D15—28no—
251C22×D15—28no—
252C22×D15—28no—
253C22×D15—44no—
254C22×D15—44no—
255C22×D15—416no—
256C22×D15—416no—
257C22×D15C2×D414yes—
258C22×D15#4114yescomplemented
259C22×D15C2412yes—
260C22×D15C2412yes—
261C22×D15C2412yes—
262C22×D15C2412yes—
263C3×C5×D4—28no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5—22no—
266C2×C3×C4×C5—22no—
267C2×C3×C4×C5—28no—
268C2×C3×C4×C5—22no—
269C2×C3×C4×C5—22no—
270C2×C3×C4×C5C2412yes—
271C2×C3×C4×C5C2412yes—
272C2×C3×C4×C5C2412yes—
273C2×C3×C4×C5C2412yes—
274C2×C3×C4×C5C2412yes—
275#1220—28no—
276#1220—28no—
277#1220—44no—
278#1220C2×D4116yescomplemented
279C2×Dic15—22no—
280C2×Dic15—22no—
281C2×Dic15—22no—
282C2×Dic15—44no—
283C2×Dic15C2×D414yes—
284C2×Dic15C2412yes—
285C2×Dic15C2412yes—
286C2×Dic15C2412yes—
287C2×Dic15C2412yes—
288D60—28no—
289D60—28no—
290D60—28no—
291D60—44no—
292C4×D15—28no—
293C4×D15—28no—
294C4×D15—28no—
295C4×D15—44no—
296Dic30—28no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×D4C2×D511yescharacteristic
300C23×C3×C4C2×D511yescharacteristic, complemented
301C22×#67—51no—
302C22×#67—51no—
303C22×#67—51no—
304C22×#67—51no—
305C23×Dic3—51no—
306C2×D3×D4—58no—
307C2×D3×D4—108no—
308C2×#235—58no—
309C2×#235—108no—
310C22×D12—51no—
311C22×D12—51no—
312C22×D12—51no—
313C22×D12—51no—
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3—51no—
318C22×Dic6—51no—
319C3×#123C2×D518yescomplemented
320C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
321C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
322C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
323C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
324C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
325C2×#217—51no—
326#939—58no—
327C2×(C2×D3)⋊C4—51no—
328C2×(C2×D3)⋊C4—51no—
329C2×(C2×D3)⋊C4—51no—
330C2×(C2×D3)⋊C4—51no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4—51no—
334C2×(C2×D3)⋊C4—51no—
335C2×(C2×D3)⋊C4—58no—
336C2×Dic3⋊C4—51no—
337C2×Dic3⋊C4—51no—
338C2×C4×Dic3—51no—
339#896—58no—
340#895—58no—
341#894—58no—
342#893—58no—
343#885—58no—
344#884—58no—
345#882—58no—
346#882—58no—
347#67⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5C22×D311yescharacteristic
350C24×C5C22×D311yescharacteristic
351C23×D5—31no—
352C23×D5—31no—
353C23×D5—31no—
354C23×D5—31no—
355C23×D5—34no—
356C23×D5—34no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—64no—
360C23×D5—64no—
361C23×D5—122no—
362C23×D5—122no—
363C2×C5×D4—24no—
364C2×C5×D4C22×D314yes—
365C22×C4×C5—24no—
366C22×C4×C5C22×D311yescharacteristic
367C22×C4×C5C22×D311yescharacteristic
368C22×C4×C5C22×D311yescharacteristic
369C22×C4×C5C22×D311yescharacteristic
370C22×C4×C5C22×D311yescharacteristic
371C22×C4×C5C22×D314yescomplemented
372C2×C22⋊D5—38no—
373C2×C22⋊D5—34no—
374C2×C22⋊D5—34no—
375C2×C22⋊D5—34no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—64no—
378C2×C22⋊D5—64no—
379C2×C22⋊D5—122no—
380C22×Dic5—31no—
381C22×Dic5—31no—
382C22×Dic5—31no—
383C22×Dic5—31no—
384C22×Dic5—34no—
385C22×Dic5—122no—
386D4×D5—632no—
387#709—632no—
388C2×D20—34no—
389C2×D20—34no—
390C2×D20—34no—
391C2×D20—34no—
392C2×D20—64no—
393C2×D20—64no—
394C2×D20—64no—
395C2×D20—122no—
396C2×C4×D5—34no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—64no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5—122no—
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4C22×D314yescomplemented
407C5×C4⋊C4C22×D314yescomplemented
408C5×C22⋊C4C22×D314yescomplemented
409C5×C22⋊C4C22×D314yescomplemented
410C5×C22⋊C4C22×D314yescomplemented
411C22⋊Dic5—34no—
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418#685—34no—
419#685—34no—
420#683—34no—
421#683—34no—
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—151no—
428C2×#123D1511yescharacteristic, complemented
429C2×C22⋊Q8—151no—
430C2×#121—151no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—151no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
438C22×C22⋊C4—151no—
439C22×C3×C5—28no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—22no—
443C22×C3×C5—22no—
444C22×C3×C5—22no—
445C22×C3×C5—44no—
446C22×C3×C5C22×D414yes—
447C22×C3×C5C22×D412yes—
448C22×C3×C5C2×#4112yes—
449C22×C3×C5H(5,𝔽2)12yes—
450C22×C3×C5C2511yescharacteristic
451C2×D15—28no—
452C2×D15—28no—
453C2×D15—22no—
454C2×D15—22no—
455C2×D15—22no—
456C2×D15—22no—
457C2×D15—22no—
458C2×D15—22no—
459C2×D15—22no—
460C2×D15—22no—
461C2×D15—22no—
462C2×D15—22no—
463C2×D15—416no—
464C2×D15—416no—
465C2×D15—44no—
466C2×D15—44no—
467C2×D15C22×D414yes—
468C2×D15C2×#4114yescomplemented
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471C3×C4×C5—22no—
472C3×C4×C5—22no—
473C3×C4×C5—22no—
474Dic15—22no—
475Dic15—22no—
476Dic15—22no—
477Dic15C22×D414yes—
478C24×C3C22×D511yescharacteristic
479C24×C3C22×D511yescharacteristic
480C23×D3—51no—
481C23×D3—51no—
482C23×D3—51no—
483C23×D3—51no—
484C23×D3—54no—
485C23×D3—54no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—104no—
489C23×D3—104no—
490C23×D3—202no—
491C23×D3—202no—
492C2×C3×D4—24no—
493C2×C3×D4C22×D514yes—
494C22×C3×C4—24no—
495C22×C3×C4C22×D511yescharacteristic
496C22×C3×C4C22×D511yescharacteristic
497C22×C3×C4C22×D511yescharacteristic
498C22×C3×C4C22×D511yescharacteristic
499C22×C3×C4C22×D511yescharacteristic
500C22×C3×C4C22×D514yescomplemented
501C2×#67—58no—
502C2×#67—54no—
503C2×#67—54no—
504C2×#67—54no—
505C2×#67—54no—
506C2×#67—104no—
507C2×#67—104no—
508C2×#67—202no—
509C22×Dic3—51no—
510C22×Dic3—51no—
511C22×Dic3—51no—
512C22×Dic3—51no—
513C22×Dic3—54no—
514C22×Dic3—202no—
515D3×D4—1032no—
516#235—1032no—
517C2×D12—54no—
518C2×D12—54no—
519C2×D12—54no—
520C2×D12—54no—
521C2×D12—104no—
522C2×D12—104no—
523C2×D12—104no—
524C2×D12—202no—
525C2×C4×D3—54no—
526C2×C4×D3—54no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—104no—
530C2×C4×D3—104no—
531C2×C4×D3—104no—
532C2×C4×D3—202no—
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4C22×D514yescomplemented
536C3×C4⋊C4C22×D514yescomplemented
537C3×C22⋊C4C22×D514yescomplemented
538C3×C22⋊C4C22×D514yescomplemented
539C3×C22⋊C4C22×D514yescomplemented
540#217—54no—
541(C2×D3)⋊C4—54no—
542(C2×D3)⋊C4—54no—
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4—54no—
546(C2×D3)⋊C4—54no—
547(C2×D3)⋊C4—54no—
548(C2×D3)⋊C4—54no—
549Dic3⋊C4—54no—
550Dic3⋊C4—54no—
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—22no—
556C23×C5—22no—
557C23×C5D3×D414yes—
558C23×C5C23×D312yes—
559C23×C5C23×D312yes—
560C23×C5C23×D311yescharacteristic
561C22×D5—34no—
562C22×D5—34no—
563C22×D5—32no—
564C22×D5—32no—
565C22×D5—32no—
566C22×D5—32no—
567C22×D5—68no—
568C22×D5—68no—
569C22×D5—68no—
570C22×D5—62no—
571C22×D5—62no—
572C22×D5—62no—
573C22×D5—62no—
574C22×D5—62no—
575C22×D5—62no—
576C22×D5—68no—
577C22×D5—62no—
578C22×D5—62no—
579C22×D5—62no—
580C22×D5—62no—
581C22×D5—124no—
582C22×D5—124no—
583C22×D5—1216no—
584C22×D5—1216no—
585C5×D4—28no—
586C2×C4×C5—22no—
587C2×C4×C5—22no—
588C2×C4×C5—22no—
589C2×C4×C5—28no—
590C2×C4×C5—22no—
591C2×C4×C5—22no—
592C2×C4×C5C23×D312yes—
593C2×C4×C5C23×D312yes—
594C2×C4×C5C23×D312yes—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C22⋊D5—316no—
598C22⋊D5—68no—
599C22⋊D5—68no—
600C22⋊D5—124no—
601C2×Dic5—34no—
602C2×Dic5—32no—
603C2×Dic5—32no—
604C2×Dic5—32no—
605C2×Dic5—32no—
606C2×Dic5—62no—
607C2×Dic5—62no—
608C2×Dic5—62no—
609C2×Dic5—124no—
610D20—68no—
611D20—68no—
612D20—68no—
613D20—124no—
614C4×D5—68no—
615C4×D5—68no—
616C4×D5—68no—
617C4×D5—124no—
618Dic10—68no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—151no—
625C22×D4—151no—
626C22×D4—151no—
627C22×D4—151no—
628C22×D4—158no—
629C22×D4—151no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—308no—
634C22×D4C2×D1511yescharacteristic
635C23×C4—151no—
636C23×C4—151no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4C2×D1511yescharacteristic, complemented
641#124—158no—
642#123—158no—
643#123C2×D1518yescomplemented
644C22⋊Q8—158no—
645#121—158no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—151no—
653C2×C4⋊C4—151no—
654C2×C4⋊C4C2×D1511yescharacteristic, complemented
655C2×C4⋊C4C2×D1511yescharacteristic, complemented
656C2×C22⋊C4—151no—
657C2×C22⋊C4—151no—
658C2×C22⋊C4—151no—
659C2×C22⋊C4—151no—
660C2×C22⋊C4—151no—
661C2×C22⋊C4—151no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—158no—
666C2×C22⋊C4—158no—
667C2×C22⋊C4C2×D1511yescharacteristic, complemented
668C2×C22⋊C4C2×D1511yescharacteristic, complemented
669C2×C22⋊C4C2×D1511yescharacteristic, complemented
670C2×C42—151no—
671C2×C3×C5—24no—
672C2×C3×C5—42no—
673C2×C3×C5#54614yescomplemented
674C2×C3×C5C23×D411yescharacteristic
675C2×C3×C5C22×#4111yescharacteristic
676C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
677D15—24no—
678D15—24no—
679D15—42no—
680D15—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—22no—
685C23×C3—22no—
686C23×C3D4×D514yes—
687C23×C3C23×D512yes—
688C23×C3C23×D512yes—
689C23×C3C23×D511yescharacteristic
690C22×D3—54no—
691C22×D3—54no—
692C22×D3—52no—
693C22×D3—52no—
694C22×D3—52no—
695C22×D3—52no—
696C22×D3—108no—
697C22×D3—108no—
698C22×D3—108no—
699C22×D3—102no—
700C22×D3—102no—
701C22×D3—102no—
702C22×D3—102no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—108no—
706C22×D3—102no—
707C22×D3—102no—
708C22×D3—102no—
709C22×D3—102no—
710C22×D3—204no—
711C22×D3—204no—
712C22×D3—2016no—
713C22×D3—2016no—
714C3×D4—28no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—28no—
719C2×C3×C4—22no—
720C2×C3×C4—22no—
721C2×C3×C4C23×D512yes—
722C2×C3×C4C23×D512yes—
723C2×C3×C4C23×D512yes—
724C2×C3×C4C23×D512yes—
725C2×C3×C4C23×D512yes—
726#67—516no—
727#67—108no—
728#67—108no—
729#67—204no—
730C2×Dic3—54no—
731C2×Dic3—52no—
732C2×Dic3—52no—
733C2×Dic3—52no—
734C2×Dic3—52no—
735C2×Dic3—102no—
736C2×Dic3—102no—
737C2×Dic3—102no—
738C2×Dic3—204no—
739D12—108no—
740D12—108no—
741D12—108no—
742D12—204no—
743C4×D3—108no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—28no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—22no—
752C22×C5—22no—
753C22×C5—22no—
754C22×C5—44no—
755C22×C5C2×D3×D414yes—
756C22×C5C2×D3×D412yes—
757C22×C5D3×#4112yes—
758C22×C5#100912yes—
759C22×C5C24×D311yescharacteristic
760C2×D5—34no—
761C2×D5—34no—
762C2×D5—68no—
763C2×D5—68no—
764C2×D5—62no—
765C2×D5—62no—
766C2×D5—62no—
767C2×D5—62no—
768C2×D5—62no—
769C2×D5—62no—
770C2×D5—62no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—1216no—
775C2×D5—1216no—
776C2×D5—124no—
777C2×D5—124no—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—22no—
781C4×C5—22no—
782C4×C5—22no—
783Dic5—34no—
784Dic5—62no—
785Dic5—62no—
786Dic5—62no—
787C24—151no—
788C24—151no—
789C24—151no—
790C24—151no—
791C24—154no—
792C24—154no—
793C24—304no—
794C24—304no—
795C24—304no—
796C24—304no—
797C24—602no—
798C24—602no—
799C24C22×D1511yescharacteristic
800C24C22×D1511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—24no—
805C2×D4—158no—
806C2×D4—154no—
807C2×D4—154no—
808C2×D4—154no—
809C2×D4—154no—
810C2×D4—154no—
811C2×D4—154no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—304no—
815C2×D4—304no—
816C2×D4—304no—
817C2×D4—304no—
818C2×D4—3032no—
819C2×D4—304no—
820C2×D4—602no—
821C2×D4—602no—
822C2×D4C22×D1514yes—
823C22×C4—24no—
824C22×C4—151no—
825C22×C4—151no—
826C22×C4—151no—
827C22×C4—151no—
828C22×C4—154no—
829C22×C4—154no—
830C22×C4—154no—
831C22×C4—154no—
832C22×C4—154no—
833C22×C4—304no—
834C22×C4—304no—
835C22×C4—304no—
836C22×C4—602no—
837C22×C4—602no—
838C22×C4C22×D1511yescharacteristic
839C22×C4C22×D1511yescharacteristic
840C22×C4C22×D1511yescharacteristic
841C22×C4C22×D1511yescharacteristic
842C22×C4C22×D1511yescharacteristic
843C22×C4C22×D1514yescomplemented
844C4⋊C4—154no—
845C4⋊C4—154no—
846C4⋊C4C22×D1514yescomplemented
847C4⋊C4C22×D1514yescomplemented
848C22⋊C4—154no—
849C22⋊C4—154no—
850C22⋊C4—154no—
851C22⋊C4—154no—
852C22⋊C4—154no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4C22×D1514yescomplemented
858C22⋊C4C22×D1514yescomplemented
859C22⋊C4C22×D1514yescomplemented
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—28no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—44no—
869C22×C3C2×D4×D514yes—
870C22×C3C2×D4×D512yes—
871C22×C3D5×#4112yes—
872C22×C3#414912yes—
873C22×C3C24×D511yescharacteristic
874C2×D3—54no—
875C2×D3—54no—
876C2×D3—108no—
877C2×D3—108no—
878C2×D3—102no—
879C2×D3—102no—
880C2×D3—102no—
881C2×D3—102no—
882C2×D3—102no—
883C2×D3—102no—
884C2×D3—102no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—2016no—
889C2×D3—2016no—
890C2×D3—204no—
891C2×D3—204no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—22no—
896C3×C4—22no—
897Dic3—54no—
898Dic3—102no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—24no—
902C2×C5—42no—
903C2×C5#565414yescomplemented
904C2×C5C22×D3×D411yescharacteristic
905C2×C5C2×D3×#4111yescharacteristic
906C2×C5C2×#100911yescharacteristic
907D5—64no—
908D5—64no—
909D5—122no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—154no—
917C23—154no—
918C23—152no—
919C23—152no—
920C23—152no—
921C23—152no—
922C23—308no—
923C23—308no—
924C23—308no—
925C23—302no—
926C23—302no—
927C23—302no—
928C23—302no—
929C23—302no—
930C23—308no—
931C23—302no—
932C23—302no—
933C23—302no—
934C23—302no—
935C23—302no—
936C23—604no—
937C23—604no—
938C23—6016no—
939C23—6016no—
940C23D4×D1514yes—
941C23C23×D1512yes—
942C23C23×D1512yes—
943C23C23×D1511yescharacteristic
944Q8—308no—
945D4—28no—
946D4—1516no—
947D4—308no—
948D4—308no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—604no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—28no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—154no—
961C2×C4—152no—
962C2×C4—152no—
963C2×C4—152no—
964C2×C4—152no—
965C2×C4—308no—
966C2×C4—308no—
967C2×C4—308no—
968C2×C4—302no—
969C2×C4—302no—
970C2×C4—302no—
971C2×C4—604no—
972C2×C4—604no—
973C2×C4C23×D1512yes—
974C2×C4C23×D1512yes—
975C2×C4C23×D1512yes—
976C2×C4C23×D1512yes—
977C2×C4C23×D1512yes—
978C2×C3—24no—
979C2×C3—42no—
980C2×C3#6598814yescomplemented
981C2×C3C22×D4×D511yescharacteristic
982C2×C3C2×D5×#4111yescharacteristic
983C2×C3C2×#414911yescharacteristic
984D3—104no—
985D3—104no—
986D3—202no—
987D3—202no—
988C5C2×#565411yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—28no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—44no—
996C22—154no—
997C22—154no—
998C22—302no—
999C22—302no—
1000C22—302no—
1001C22—302no—
1002C22—308no—
1003C22—308no—
1004C22—302no—
1005C22—302no—
1006C22—302no—
1007C22—302no—
1008C22—302no—
1009C22—302no—
1010C22—6016no—
1011C22—6016no—
1012C22—604no—
1013C22—604no—
1014C22C2×D4×D1514yes—
1015C22C2×D4×D1512yes—
1016C22#41×D1512yes—
1017C22#9210012yes—
1018C22C24×D1511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—22no—
1023C4—22no—
1024C4—154no—
1025C4—302no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6598811yescharacteristic, complemented, Sylow
1029C2—24no—
1030C2—42no—
1031C2—304no—
1032C2—304no—
1033C2—602no—
1034C2—602no—
1035C2#1175641314yesdirect product factor
1036C2C22×D4×D1511yescharacteristic
1037C2C2×#41×D1511yescharacteristic
1038C2C2×#9210011yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#123C2
socleC23×C3×C5C24
hypercenterC2×#123D15
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×D4×D15C2semidirect
2. C22×#6817C2semidirect
3. C2×C3×C5×#123C2semidirect
4. C2×#91828C2semidirect
5. C22×#6714C2semidirect
6. #11756413C2direct (N × H)
7. C2×#91785C2semidirect
8. C2×#91784C2semidirect
9. C2×#91783C2semidirect
10. C2×#91782C2semidirect
11. C2×#91774C2semidirect
12. C2×#91773C2semidirect
13. C2×#91771C2semidirect
14. C2×#91771C2semidirect
15. C2×#91770C2semidirect
16. C2×C22⋊C4×D15C2semidirect
21. C23×C3×C4×C5C22semidirect
24. C22×#1220C22semidirect
25. C22×#1220C22semidirect
26. C23×Dic15C22semidirect
28. C2×D4×D15C22semidirect
30. C2×#6817C22semidirect
33. C22×D60C22semidirect
34. C22×D60C22semidirect
36. C22×C4×D15C22semidirect
37. C22×C4×D15C22semidirect
38. C22×C4×D15C22semidirect
39. C22×Dic30C22semidirect
40. C3×C5×#123C22semidirect
41. C2×C3×C5×C4⋊C4C22semidirect
42. C2×C3×C5×C4⋊C4C22semidirect
43. C2×C3×C5×C22⋊C4C22semidirect
44. C2×C3×C5×C22⋊C4C22semidirect
45. C2×C3×C5×C22⋊C4C22semidirect
46. C2×#6719C22semidirect
47. #91828C22semidirect
51. C2×#6714C22semidirect
52. C2×#6714C22semidirect
53. C2×#6714C22semidirect
54. C2×#6714C22semidirect
55. C2×#6714C22semidirect
56. C2×#6714C22semidirect
57. C2×#6712C22semidirect
58. C2×#6712C22semidirect
59. C2×C4×Dic15C22semidirect
60. #91785C22semidirect
61. #91784C22semidirect
62. #91783C22semidirect
63. #91782C22semidirect
64. #91774C22semidirect
65. #91773C22semidirect
66. #91771C22semidirect
67. #91771C22semidirect
68. #91770C22semidirect
69. C22⋊C4×D15C22semidirect
73. C2×C5×#123D3semidirect
109. C22×C3×C4×C5C23semidirect
113. C2×#1220D4semidirect
116. C2×#1220C23semidirect
117. C2×#1220C23semidirect
123. C22×Dic15C23semidirect
132. C2×D60C23semidirect
133. C2×D60C23semidirect
139. C2×C4×D15C23semidirect
140. C2×C4×D15C23semidirect
141. C2×C4×D15C23semidirect
143. C2×Dic30C23semidirect
144. C3×C5×C4⋊C4C23semidirect
145. C3×C5×C4⋊C4C23semidirect
146. C3×C5×C22⋊C4C23semidirect
147. C3×C5×C22⋊C4C23semidirect
148. C3×C5×C22⋊C4C23semidirect
149. #6719C23semidirect
153. #6714C23semidirect
154. #6714C23semidirect
155. #6714C23semidirect
156. #6714C23semidirect
157. #6714C23semidirect
158. #6712C23semidirect
159. #6712C23semidirect
160. C4×Dic15C23semidirect
163. C2×C3×#123D5semidirect
180. C23×C4×C5C2×D3semidirect
199. C5×#123C2×D3semidirect
200. C2×C5×C4⋊C4C2×D3semidirect
201. C2×C5×C4⋊C4C2×D3semidirect
202. C2×C5×C22⋊C4C2×D3semidirect
203. C2×C5×C22⋊C4C2×D3semidirect
204. C2×C5×C22⋊C4C2×D3semidirect
258. C22×D15#41semidirect
278. #1220C2×D4semidirect
300. C23×C3×C4C2×D5semidirect
319. C3×#123C2×D5semidirect
320. C2×C3×C4⋊C4C2×D5semidirect
321. C2×C3×C4⋊C4C2×D5semidirect
322. C2×C3×C22⋊C4C2×D5semidirect
323. C2×C3×C22⋊C4C2×D5semidirect
324. C2×C3×C22⋊C4C2×D5semidirect
371. C22×C4×C5C22×D3semidirect
406. C5×C4⋊C4C22×D3semidirect
407. C5×C4⋊C4C22×D3semidirect
408. C5×C22⋊C4C22×D3semidirect
409. C5×C22⋊C4C22×D3semidirect
410. C5×C22⋊C4C22×D3semidirect
428. C2×#123D15semidirect
468. C2×D15C2×#41semidirect
500. C22×C3×C4C22×D5semidirect
535. C3×C4⋊C4C22×D5semidirect
536. C3×C4⋊C4C22×D5semidirect
537. C3×C22⋊C4C22×D5semidirect
538. C3×C22⋊C4C22×D5semidirect
539. C3×C22⋊C4C22×D5semidirect
640. C23×C4C2×D15semidirect
643. #123C2×D15semidirect
654. C2×C4⋊C4C2×D15semidirect
655. C2×C4⋊C4C2×D15semidirect
667. C2×C22⋊C4C2×D15semidirect
668. C2×C22⋊C4C2×D15semidirect
669. C2×C22⋊C4C2×D15semidirect
673. C2×C3×C5#546semidirect
843. C22×C4C22×D15semidirect
846. C4⋊C4C22×D15semidirect
847. C4⋊C4C22×D15semidirect
857. C22⋊C4C22×D15semidirect
858. C22⋊C4C22×D15semidirect
859. C22⋊C4C22×D15semidirect
861. C3×C5C2×#546semidirect
903. C2×C5#5654semidirect
980. C2×C3#65988semidirect
988. C5C2×#5654semidirect
1028. C3C2×#65988semidirect
1035. C2#11756413direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D152
C22×#68172
C2×C3×C5×#1232
C2×#918282
C22×#67142
#117564132
C2×#917852
C2×#917842
C2×#917832
C2×#917822
C2×#917742
C2×#917732
C2×#917712
C2×#917702
C2×C22⋊C4×D152
C2×#659883
C2×#56545