Finite Group Databasebeta

← C2×#11753861 #14482650

Subgroups — C2×#11753861 #14482650

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×D3×D20C211yesmaximal, characteristic, complemented
2C22×#6766C211yesmaximal, characteristic, complemented
3C2×#91783C211yesmaximal, characteristic, complemented
4C2×C5×#896C211yesmaximal, characteristic, complemented
5C2×C3×#4041C211yesmaximal, characteristic, complemented
6C2×#91474C211yesmaximal, characteristic, complemented
7C2×#91474C211yesmaximal, characteristic, complemented
8C2×#91473C211yesmaximal, characteristic, complemented
9C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×#91459C211yesmaximal, characteristic, complemented
11C2×#91455C211yesmaximal, characteristic, complemented
12C2×#91444C211yesmaximal, characteristic, complemented
13C2×#91441C211yesmaximal, characteristic, complemented
14C2×#91409C211yesmaximal, characteristic, complemented
15C2×#91407C211yesmaximal, characteristic, complemented
16#11753861C2116yesmaximal, direct product factor
17C2×#65964—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C4×C5×D3C2211yescharacteristic
23C22×C5×Dic6C2211yescharacteristic, complemented
24C22×C3×D20C2211yescharacteristic
25C22×C3×D20C2211yescharacteristic, complemented
26C22×C3×D20C2211yescharacteristic, complemented
27C22×C3×C4×D5C2211yescharacteristic, complemented
28C22×#1202C2211yescharacteristic
29C22×#1202C2211yescharacteristic
30C22×#1202C2211yescharacteristic, complemented
31C22×#1202C2211yescharacteristic, complemented
32C22×#1201C2211yescharacteristic
33C22×#1200C2211yescharacteristic, complemented
34C22×D5×Dic3C2211yescharacteristic, complemented
35C22×D5×Dic3C2211yescharacteristic, complemented
36C2×D3×D20—28no—
37C2×D3×D20C2218yescomplemented
38C2×#6766—28no—
39C2×#6766C2218yescomplemented
40C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6714C2211yescharacteristic, complemented
44C2×#6712C2211yescharacteristic, complemented
45#91783C2218yescomplemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic
48C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
50C5×#896C2218yescomplemented
51C2×C3×#685C2211yescharacteristic, complemented
52C2×C3×#685C2211yescharacteristic, complemented
53C3×#4041C2218yescomplemented
54C2×#6667C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×#6665C2211yescharacteristic, complemented
57C2×#6665C2211yescharacteristic, complemented
58C2×#6665C2211yescharacteristic, complemented
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91474C2218yescomplemented
61#91474C2218yescomplemented
62#91473C2218yescomplemented
63D5×(C2×D3)⋊C4C2218yescomplemented
64#91459C2218yescomplemented
65#91455C2218yescomplemented
66#91444C2218yescomplemented
67#91441C2218yescomplemented
68#91409C2218yescomplemented
69#91407C2218yescomplemented
70C2×#5610—51nomaximal, Hall
71C22×#713—31no—
72C23×D20—31no—
73C2×C5×C22⋊Q8—31no—
74C2×#4093—31no—
75C2×C4×C22⋊D5—31no—
76#65964—316no—
77C2×#4041—31no—
78C2×#4041—31no—
79C2×#4041D311yescharacteristic, complemented
80C2×#4040—31no—
81C2×#4040—31no—
82C2×#4039—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C2×D5×C22⋊C4—31no—
86C2×D5×C22⋊C4—31no—
87C23×D15C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C23×C3×D5C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C22×D3×D5—24no—
94C22×D3×D5—24no—
95C22×D3×D5—24no—
96C22×D3×D5—24no—
97C22×D3×D5—42no—
98C22×D3×D5—42no—
99C22×D3×D5C2314yes—
100C22×D3×D5C2314yes—
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2311yescharacteristic
103C22×C3×C4×C5C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C2×D60—24no—
107C2×D60C2314yes—
108C2×C4×D15—24no—
109C2×C4×D15C2314yescomplemented
110C22×C5×Dic3C2311yescharacteristic
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C2×C4×C5×D3—24no—
114C2×C4×C5×D3C2314yes—
115C2×C5×Dic6—24no—
116C2×C5×Dic6C2314yescomplemented
117C22×C3×Dic5C2311yescharacteristic
118C2×C3×D20—24no—
119C2×C3×D20—24no—
120C2×C3×D20—42no—
121C2×C3×D20C2314yes—
122C2×C3×D20C2314yescomplemented
123C2×C3×D20C2314yescomplemented
124C2×C3×C4×D5—42no—
125C2×C3×C4×D5C2314yescomplemented
126C2×#1202—24no—
127C2×#1202—24no—
128C2×#1202—42no—
129C2×#1202D418yescomplemented
130C2×#1202C2314yes—
131C2×#1202C2314yes—
132C2×#1202C2314yescomplemented
133C2×#1202C2314yescomplemented
134C2×#1201—24no—
135C2×#1201C2314yes—
136C2×#1200—42no—
137C2×#1200C2314yescomplemented
138C2×D5×Dic3—24no—
139C2×D5×Dic3—24no—
140C2×D5×Dic3C2314yescomplemented
141C2×D5×Dic3C2314yescomplemented
142D3×D20—232no—
143#6766—232no—
144C3×C5×C4⋊C4C2314yescomplemented
145#6714C2314yescomplemented
146#6714C2314yescomplemented
147#6714C2314yescomplemented
148#6712C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yes—
150C5×(C2×D3)⋊C4C2314yes—
151C5×Dic3⋊C4C2314yescomplemented
152C5×Dic3⋊C4C2314yescomplemented
153C3×#685C2314yescomplemented
154C3×#685C2314yescomplemented
155#6667C2314yescomplemented
156(C2×D3)⋊Dic5C2314yes—
157#6665C2314yescomplemented
158#6665C2314yescomplemented
159#6665C2314yescomplemented
160Dic3×Dic5C2314yescomplemented
161C22×#237—51no—
162C22×D3×D4—51no—
163C2×C3×#121—51no—
164C2×#939—51no—
165C2×#937—51no—
166C2×#937—51no—
167C2×#935—51no—
168C2×C4×#67—51no—
169C22×(C2×D3)⋊C4—51no—
170#5610—516no—
171C2×#896D511yescharacteristic, complemented
172C2×#894—51no—
173C2×#885—51no—
174C2×#884—51no—
175C2×#67⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×Q8—31no—
180C23×C4×C5—31no—
181C22×C22⋊D5—31no—
182C2×#713—38no—
183C2×#713—68no—
184C22×D20—31no—
185C22×D20—31no—
186C22×D20—31no—
187C22×D20—31no—
188C22×D20—31no—
189C22×D20—38no—
190C22×D20—68no—
191C22×D20C2×D311yescharacteristic
192C22×D20C2×D311yescharacteristic, complemented
193C22×D20C2×D311yescharacteristic, complemented
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5—31no—
198C22×C4×D5C2×D311yescharacteristic, complemented
199C5×C22⋊Q8—38no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C4⋊C4—31no—
202C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
203C2×C5×C22⋊C4—31no—
204C2×C5×C22⋊C4—31no—
205C2×C22⋊Dic5—31no—
206#4093—38no—
207C4×C22⋊D5—38no—
208C2×#685—31no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685C2×D311yescharacteristic, complemented
216C2×#685C2×D311yescharacteristic, complemented
217C2×#683—31no—
218C2×C4×Dic5—31no—
219#4041—38no—
220#4041—38no—
221#4041C2×D318yescomplemented
222#4040—38no—
223#4040—38no—
224#4039—38no—
225#4028—38no—
226#4028—38no—
227D5×C22⋊C4—38no—
228D5×C22⋊C4—38no—
229C2×#546—151noSylow
230C23×C3×C5C2411yescharacteristic
231C22×D15—22no—
232C22×D15—22no—
233C22×D15—22no—
234C22×D15—22no—
235C22×D15—22no—
236C22×D15C2×D414yes—
237C22×D15C2412yes—
238C22×D15C2412yes—
239C22×C5×D3—22no—
240C22×C5×D3—22no—
241C22×C5×D3#4114yescomplemented
242C22×C5×D3C2412yes—
243C22×C3×D5—22no—
244C22×C3×D5—22no—
245C22×C3×D5—22no—
246C22×C3×D5—22no—
247C22×C3×D5—22no—
248C22×C3×D5—22no—
249C22×C3×D5—22no—
250C22×C3×D5—22no—
251C22×C3×D5C2×D414yes—
252C22×C3×D5C2412yes—
253C22×C3×D5C2412yes—
254C22×C3×D5C2412yes—
255C2×D3×D5—28no—
256C2×D3×D5—28no—
257C2×D3×D5—28no—
258C2×D3×D5—28no—
259C2×D3×D5—44no—
260C2×D3×D5—44no—
261C2×D3×D5—416no—
262C2×D3×D5—416no—
263C2×C3×C4×C5—22no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5—22no—
266C2×C3×C4×C5C2412yes—
267C2×C3×C4×C5C2412yes—
268C2×C3×C4×C5C2412yes—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273D60—28no—
274C4×D15—28no—
275C2×C5×Dic3—22no—
276C2×C5×Dic3—22no—
277C2×C5×Dic3C2×D414yes—
278C2×C5×Dic3C2412yes—
279C2×C5×Dic3C2412yes—
280C2×C5×Dic3C2412yes—
281C4×C5×D3—28no—
282C5×Dic6—28no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5C2412yes—
285C3×D20—28no—
286C3×D20—28no—
287C3×D20—44no—
288C3×C4×D5—44no—
289#1202—28no—
290#1202—28no—
291#1202—44no—
292#1202C2×D4116yescomplemented
293#1201—28no—
294#1200—44no—
295D5×Dic3—28no—
296D5×Dic3—28no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×D4—51no—
300C22×C3×D4—51no—
301C22×C3×D4—51no—
302C23×C3×C4—51no—
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—51no—
306C22×#67—51no—
307C22×#67—51no—
308C23×Dic3—51no—
309C23×Dic3—51no—
310C2×#237—58no—
311C2×#237—108no—
312C2×D3×D4—58no—
313C2×D3×D4—108no—
314C22×D12—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3C2×D511yescharacteristic
318C22×Dic6C2×D511yescharacteristic, complemented
319C3×#121—58no—
320C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4—51no—
323C2×#217—51no—
324C2×#217—51no—
325C2×#217—51no—
326#939—58no—
327#937—58no—
328#937—58no—
329#935—58no—
330C4×#67—58no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4—51no—
334C2×(C2×D3)⋊C4—51no—
335C2×(C2×D3)⋊C4—51no—
336C2×(C2×D3)⋊C4—58no—
337C2×(C2×D3)⋊C4C2×D511yescharacteristic
338C2×(C2×D3)⋊C4C2×D511yescharacteristic
339C2×Dic3⋊C4—51no—
340C2×Dic3⋊C4C2×D511yescharacteristic, complemented
341C2×Dic3⋊C4C2×D511yescharacteristic, complemented
342C2×C4×Dic3—51no—
343#896C2×D518yescomplemented
344#894—58no—
345#885—58no—
346#884—58no—
347#67⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C23×D5—31no—
351C23×D5—31no—
352C23×D5—34no—
353C23×D5—34no—
354C23×D5—64no—
355C23×D5—64no—
356C23×D5—64no—
357C23×D5—64no—
358C23×D5—122no—
359C23×D5—122no—
360C23×D5C22×D311yescharacteristic
361C23×D5C22×D311yescharacteristic
362C23×D5C22×D311yescharacteristic
363C2×C5×Q8—34no—
364C2×C5×Q8—64no—
365C22×C4×C5—31no—
366C22×C4×C5—31no—
367C22×C4×C5—31no—
368C22×C4×C5—34no—
369C22×C4×C5—64no—
370C22×C4×C5C22×D311yescharacteristic
371C22×C4×C5C22×D311yescharacteristic
372C22×C4×C5C22×D311yescharacteristic
373C2×C22⋊D5—34no—
374C2×C22⋊D5—64no—
375C22×Dic5—31no—
376C22×Dic5—31no—
377C22×Dic5C22×D311yescharacteristic
378#713—632no—
379C2×D20—24no—
380C2×D20—24no—
381C2×D20—38no—
382C2×D20—34no—
383C2×D20—34no—
384C2×D20—34no—
385C2×D20—34no—
386C2×D20—34no—
387C2×D20—42no—
388C2×D20—632no—
389C2×D20—64no—
390C2×D20—64no—
391C2×D20—64no—
392C2×D20—122no—
393C2×D20C22×D314yes—
394C2×D20C22×D314yescomplemented
395C2×D20C22×D314yescomplemented
396C2×C4×D5—34no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—42no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5—64no—
404C2×C4×D5—122no—
405C2×C4×D5C22×D314yescomplemented
406C5×C4⋊C4—34no—
407C5×C4⋊C4—34no—
408C5×C4⋊C4C22×D314yescomplemented
409C5×C22⋊C4—34no—
410C5×C22⋊C4—34no—
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#685C22×D314yescomplemented
420#685C22×D314yescomplemented
421#683—34no—
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—151no—
428C2×#123—151no—
429C2×C22⋊Q8—31no—
430C2×#121—51no—
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×C5C22×D412yes—
440C22×C3×C5C2×#4112yes—
441C22×C3×C5H(5,𝔽2)12yes—
442C22×C3×C5C2511yescharacteristic
443C2×D15—28no—
444C2×D15—22no—
445C2×D15—22no—
446C2×D15—22no—
447C2×D15—22no—
448C2×D15—22no—
449C2×D15—44no—
450C2×D15C22×D414yes—
451C2×C5×D3—28no—
452C2×C5×D3—22no—
453C2×C5×D3—22no—
454C2×C5×D3C2×#4114yescomplemented
455C2×C3×D5—28no—
456C2×C3×D5—22no—
457C2×C3×D5—22no—
458C2×C3×D5—22no—
459C2×C3×D5—22no—
460C2×C3×D5—22no—
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—44no—
465C2×C3×D5—44no—
466C2×C3×D5C22×D414yes—
467D3×D5—416no—
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471C3×C4×C5—22no—
472Dic15—22no—
473Dic15—22no—
474C3×Dic5—22no—
475C5×Dic3—22no—
476C5×Dic3—22no—
477C5×Dic3C22×D414yes—
478C24×C3—51no—
479C24×C3—51no—
480C24×C3—51no—
481C23×D3—51no—
482C23×D3—51no—
483C23×D3—54no—
484C23×D3—54no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—104no—
489C23×D3—202no—
490C23×D3—202no—
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—54no—
493C2×C3×D4—54no—
494C2×C3×D4—54no—
495C2×C3×D4—104no—
496C2×C3×D4—104no—
497C2×C3×D4—202no—
498C22×C3×C4—51no—
499C22×C3×C4—54no—
500C22×C3×C4—202no—
501C22×C3×C4C22×D511yescharacteristic
502C22×C3×C4C22×D511yescharacteristic
503C22×C3×C4C22×D511yescharacteristic
504C2×#67—54no—
505C2×#67—58no—
506C2×#67—54no—
507C2×#67—54no—
508C2×#67—54no—
509C2×#67—54no—
510C2×#67—104no—
511C2×#67—104no—
512C2×#67—104no—
513C2×#67—202no—
514C22×Dic3—51no—
515C22×Dic3—51no—
516C22×Dic3—54no—
517C22×Dic3—54no—
518C22×Dic3—104no—
519C22×Dic3—104no—
520C22×Dic3C22×D511yescharacteristic
521C22×Dic3C22×D511yescharacteristic
522C22×Dic3C22×D511yescharacteristic
523#237—1032no—
524D3×D4—1032no—
525C2×D12—54no—
526C2×D12—104no—
527C2×C4×D3—24no—
528C2×C4×D3—54no—
529C2×C4×D3—54no—
530C2×C4×D3—104no—
531C2×C4×D3—202no—
532C2×C4×D3C22×D514yes—
533C2×Dic6—24no—
534C2×Dic6C22×D514yescomplemented
535C3×C4⋊C4C22×D514yescomplemented
536C3×C22⋊C4—54no—
537C3×C22⋊C4—54no—
538#217—54no—
539#217—54no—
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)⋊C4C22×D514yes—
547(C2×D3)⋊C4C22×D514yes—
548Dic3⋊C4—54no—
549Dic3⋊C4C22×D514yescomplemented
550Dic3⋊C4C22×D514yescomplemented
551C4×Dic3—54no—
552C23×C5—34no—
553C23×C5—32no—
554C23×C5—62no—
555C23×C5—62no—
556C23×C5C23×D311yescharacteristic
557C22×D5—22no—
558C22×D5—22no—
559C22×D5—22no—
560C22×D5—22no—
561C22×D5—22no—
562C22×D5—22no—
563C22×D5—22no—
564C22×D5—22no—
565C22×D5—34no—
566C22×D5—32no—
567C22×D5—32no—
568C22×D5—68no—
569C22×D5—68no—
570C22×D5—68no—
571C22×D5—62no—
572C22×D5—62no—
573C22×D5—62no—
574C22×D5—62no—
575C22×D5—62no—
576C22×D5—68no—
577C22×D5—124no—
578C22×D5—124no—
579C22×D5—1216no—
580C22×D5—1216no—
581C22×D5D3×D414yes—
582C22×D5C23×D312yes—
583C22×D5C23×D312yes—
584C22×D5C23×D312yes—
585C5×Q8—68no—
586C2×C4×C5—22no—
587C2×C4×C5—22no—
588C2×C4×C5—22no—
589C2×C4×C5—34no—
590C2×C4×C5—32no—
591C2×C4×C5—32no—
592C2×C4×C5—32no—
593C2×C4×C5—68no—
594C2×C4×C5—62no—
595C2×C4×C5—62no—
596C2×C4×C5C23×D312yes—
597C2×C4×C5C23×D312yes—
598C2×C4×C5C23×D312yes—
599C22⋊D5—68no—
600C2×Dic5—22no—
601C2×Dic5—32no—
602C2×Dic5—32no—
603C2×Dic5—62no—
604C2×Dic5—62no—
605C2×Dic5C23×D312yes—
606D20—28no—
607D20—28no—
608D20—316no—
609D20—44no—
610D20—68no—
611D20—68no—
612D20—68no—
613D20—124no—
614C4×D5—44no—
615C4×D5—68no—
616C4×D5—68no—
617C4×D5—68no—
618C4×D5—124no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—31no—
624C22×D4—51no—
625C22×D4—51no—
626C22×D4—51no—
627C22×D4—158no—
628C22×D4—151no—
629C22×D4—151no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4—308no—
635C23×C4—31no—
636C23×C4—51no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—158no—
642#123—158no—
643#123—158no—
644C22⋊Q8—38no—
645#121—58no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—31no—
653C2×C4⋊C4—31no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4D3×D511yescharacteristic, complemented
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—51no—
659C2×C22⋊C4—51no—
660C2×C22⋊C4—158no—
661C2×C22⋊C4—158no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—151no—
668C2×C22⋊C4—151no—
669C2×C22⋊C4—151no—
670C2×C42—151no—
671C2×C3×C5#54614yescomplemented
672C2×C3×C5C23×D411yescharacteristic
673C2×C3×C5C22×#4111yescharacteristic
674C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
675D15—24no—
676D15—42no—
677C3×D5—24no—
678C3×D5—42no—
679C3×D5—42no—
680C5×D3—24no—
681C23×C3—54no—
682C23×C3—52no—
683C23×C3—52no—
684C23×C3—52no—
685C23×C3—102no—
686C23×C3—102no—
687C23×C3—102no—
688C23×C3—102no—
689C23×C3—102no—
690C23×C3—102no—
691C23×C3—102no—
692C23×C3—102no—
693C23×C3C23×D511yescharacteristic
694C22×D3—22no—
695C22×D3—22no—
696C22×D3—54no—
697C22×D3—52no—
698C22×D3—52no—
699C22×D3—108no—
700C22×D3—108no—
701C22×D3—102no—
702C22×D3—102no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—108no—
707C22×D3—108no—
708C22×D3—204no—
709C22×D3—204no—
710C22×D3—2016no—
711C22×D3—2016no—
712C22×D3#71314yescomplemented
713C22×D3C23×D512yes—
714C3×D4—108no—
715C3×D4—108no—
716C3×D4—204no—
717C2×C3×C4—22no—
718C2×C3×C4—22no—
719C2×C3×C4—22no—
720C2×C3×C4—52no—
721C2×C3×C4—102no—
722C2×C3×C4—204no—
723C2×C3×C4C23×D512yes—
724C2×C3×C4C23×D512yes—
725C2×C3×C4C23×D512yes—
726#67—516no—
727#67—108no—
728#67—108no—
729#67—108no—
730#67—204no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—52no—
734C2×Dic3—52no—
735C2×Dic3—108no—
736C2×Dic3—102no—
737C2×Dic3—102no—
738C2×Dic3—108no—
739C2×Dic3D4×D514yes—
740C2×Dic3C23×D512yes—
741C2×Dic3C23×D512yes—
742C2×Dic3C23×D512yes—
743D12—108no—
744C4×D3—28no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—28no—
748C22×C5—34no—
749C22×C5—62no—
750C22×C5—62no—
751C22×C5—68no—
752C22×C5C2×D3×D412yes—
753C22×C5#100412yes—
754C22×C5D3×#4112yes—
755C22×C5C24×D311yescharacteristic
756C2×D5—22no—
757C2×D5—22no—
758C2×D5—28no—
759C2×D5—22no—
760C2×D5—22no—
761C2×D5—22no—
762C2×D5—22no—
763C2×D5—22no—
764C2×D5—22no—
765C2×D5—34no—
766C2×D5—44no—
767C2×D5—44no—
768C2×D5—62no—
769C2×D5—62no—
770C2×D5—68no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—1216no—
775C2×D5—1216no—
776C2×D5—124no—
777C2×D5C2×D3×D414yes—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—22no—
781C4×C5—34no—
782C4×C5—62no—
783C4×C5—62no—
784Dic5—22no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—51no—
789C24—51no—
790C24—51no—
791C24—154no—
792C24—154no—
793C24—151no—
794C24—151no—
795C24—304no—
796C24—304no—
797C24—304no—
798C24—304no—
799C24—602no—
800C24—602no—
801#41—3032no—
802C2×Q8—34no—
803C2×Q8—64no—
804C2×D4—54no—
805C2×D4—54no—
806C2×D4—54no—
807C2×D4—104no—
808C2×D4—104no—
809C2×D4—154no—
810C2×D4—158no—
811C2×D4—154no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—154no—
816C2×D4—202no—
817C2×D4—304no—
818C2×D4—304no—
819C2×D4—3032no—
820C2×D4—304no—
821C2×D4—304no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—34no—
827C22×C4—51no—
828C22×C4—54no—
829C22×C4—64no—
830C22×C4—154no—
831C22×C4—154no—
832C22×C4—154no—
833C22×C4—151no—
834C22×C4—151no—
835C22×C4—154no—
836C22×C4—202no—
837C22×C4—304no—
838C22×C4—304no—
839C22×C4—304no—
840C22×C4—602no—
841C22×C4C2×D3×D511yescharacteristic
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—34no—
845C4⋊C4—34no—
846C4⋊C4—154no—
847C4⋊C4C2×D3×D514yescomplemented
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—54no—
851C22⋊C4—54no—
852C22⋊C4—154no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4—154no—
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—54no—
863C22×C3—108no—
864C22×C3—102no—
865C22×C3—102no—
866C22×C3—102no—
867C22×C3—102no—
868C22×C3—102no—
869C22×C3—102no—
870C22×C3—102no—
871C22×C3—102no—
872C22×C3—204no—
873C22×C3—204no—
874C22×C3C2×D4×D512yes—
875C22×C3C2×#71312yes—
876C22×C3#414912yes—
877C22×C3C24×D511yescharacteristic
878C2×D3—28no—
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—54no—
882C2×D3—108no—
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×D3C2×#71314yescomplemented
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—102no—
896Dic3—22no—
897Dic3—22no—
898Dic3—102no—
899Dic3—102no—
900Dic3C2×D4×D514yes—
901C2×C5—64no—
902C2×C5#561014yescomplemented
903C2×C5C22×D3×D411yescharacteristic
904C2×C5C2×#100411yescharacteristic
905C2×C5C2×D3×#4111yescharacteristic
906D5—24no—
907D5—42no—
908D5—42no—
909D5—64no—
910D5—122no—
911C23—34no—
912C23—32no—
913C23—54no—
914C23—52no—
915C23—52no—
916C23—52no—
917C23—62no—
918C23—62no—
919C23—102no—
920C23—102no—
921C23—102no—
922C23—102no—
923C23—102no—
924C23—102no—
925C23—102no—
926C23—102no—
927C23—154no—
928C23—152no—
929C23—152no—
930C23—308no—
931C23—308no—
932C23—308no—
933C23—308no—
934C23—302no—
935C23—302no—
936C23—302no—
937C23—302no—
938C23—302no—
939C23—604no—
940C23—604no—
941C23—6016no—
942C23—6016no—
943C23C22×D3×D511yescharacteristic
944Q8—68no—
945D4—108no—
946D4—108no—
947D4—1516no—
948D4—204no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—34no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—32no—
961C2×C4—52no—
962C2×C4—68no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—102no—
966C2×C4—152no—
967C2×C4—152no—
968C2×C4—204no—
969C2×C4—308no—
970C2×C4—308no—
971C2×C4—308no—
972C2×C4—302no—
973C2×C4—302no—
974C2×C4—604no—
975C2×C4C22×D3×D512yes—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—104no—
979C2×C3—202no—
980C2×C3—202no—
981C2×C3#6596414yescomplemented
982C2×C3C22×D4×D511yescharacteristic
983C2×C3C22×#71311yescharacteristic
984C2×C3C2×#414911yescharacteristic
985D3—24no—
986D3—104no—
987D3—202no—
988C5C2×#561011yescharacteristic, complemented, Sylow
989C22—34no—
990C22—54no—
991C22—68no—
992C22—62no—
993C22—62no—
994C22—108no—
995C22—102no—
996C22—102no—
997C22—102no—
998C22—102no—
999C22—102no—
1000C22—102no—
1001C22—102no—
1002C22—102no—
1003C22—154no—
1004C22—204no—
1005C22—204no—
1006C22—308no—
1007C22—302no—
1008C22—302no—
1009C22—302no—
1010C22—302no—
1011C22—302no—
1012C22—6016no—
1013C22—6016no—
1014C22—604no—
1015C22#9201712yes—
1016C22D3×D4×D512yes—
1017C22D3×#71312yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—34no—
1023C4—62no—
1024C4—62no—
1025C4—102no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6596411yescharacteristic, complemented, Sylow
1029C2—64no—
1030C2—104no—
1031C2—202no—
1032C2—202no—
1033C2—304no—
1034C2—602no—
1035C2#1175386114yesdirect product factor
1036C2C2×#9201711yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×D3×#71311yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×D20C2semidirect
2. C22×#6766C2semidirect
3. C2×#91783C2semidirect
4. C2×C5×#896C2semidirect
5. C2×C3×#4041C2semidirect
6. C2×#91474C2semidirect
7. C2×#91474C2semidirect
8. C2×#91473C2semidirect
9. C2×D5×(C2×D3)⋊C4C2semidirect
10. C2×#91459C2semidirect
11. C2×#91455C2semidirect
12. C2×#91444C2semidirect
13. C2×#91441C2semidirect
14. C2×#91409C2semidirect
15. C2×#91407C2semidirect
16. #11753861C2direct (N × H)
21. C22×C4×D15C22semidirect
23. C22×C5×Dic6C22semidirect
25. C22×C3×D20C22semidirect
26. C22×C3×D20C22semidirect
27. C22×C3×C4×D5C22semidirect
30. C22×#1202C22semidirect
31. C22×#1202C22semidirect
33. C22×#1200C22semidirect
34. C22×D5×Dic3C22semidirect
35. C22×D5×Dic3C22semidirect
37. C2×D3×D20C22semidirect
39. C2×#6766C22semidirect
40. C2×C3×C5×C4⋊C4C22semidirect
41. C2×#6714C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. C2×#6712C22semidirect
45. #91783C22semidirect
48. C2×C5×Dic3⋊C4C22semidirect
49. C2×C5×Dic3⋊C4C22semidirect
50. C5×#896C22semidirect
51. C2×C3×#685C22semidirect
52. C2×C3×#685C22semidirect
53. C3×#4041C22semidirect
54. C2×#6667C22semidirect
56. C2×#6665C22semidirect
57. C2×#6665C22semidirect
58. C2×#6665C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91474C22semidirect
61. #91474C22semidirect
62. #91473C22semidirect
63. D5×(C2×D3)⋊C4C22semidirect
64. #91459C22semidirect
65. #91455C22semidirect
66. #91444C22semidirect
67. #91441C22semidirect
68. #91409C22semidirect
69. #91407C22semidirect
79. C2×#4041D3semidirect
109. C2×C4×D15C23semidirect
116. C2×C5×Dic6C23semidirect
122. C2×C3×D20C23semidirect
123. C2×C3×D20C23semidirect
125. C2×C3×C4×D5C23semidirect
129. C2×#1202D4semidirect
132. C2×#1202C23semidirect
133. C2×#1202C23semidirect
137. C2×#1200C23semidirect
140. C2×D5×Dic3C23semidirect
141. C2×D5×Dic3C23semidirect
144. C3×C5×C4⋊C4C23semidirect
145. #6714C23semidirect
146. #6714C23semidirect
147. #6714C23semidirect
148. #6712C23semidirect
151. C5×Dic3⋊C4C23semidirect
152. C5×Dic3⋊C4C23semidirect
153. C3×#685C23semidirect
154. C3×#685C23semidirect
155. #6667C23semidirect
157. #6665C23semidirect
158. #6665C23semidirect
159. #6665C23semidirect
160. Dic3×Dic5C23semidirect
171. C2×#896D5semidirect
192. C22×D20C2×D3semidirect
193. C22×D20C2×D3semidirect
198. C22×C4×D5C2×D3semidirect
202. C2×C5×C4⋊C4C2×D3semidirect
215. C2×#685C2×D3semidirect
216. C2×#685C2×D3semidirect
221. #4041C2×D3semidirect
241. C22×C5×D3#41semidirect
292. #1202C2×D4semidirect
318. C22×Dic6C2×D5semidirect
320. C2×C3×C4⋊C4C2×D5semidirect
340. C2×Dic3⋊C4C2×D5semidirect
341. C2×Dic3⋊C4C2×D5semidirect
343. #896C2×D5semidirect
394. C2×D20C22×D3semidirect
395. C2×D20C22×D3semidirect
405. C2×C4×D5C22×D3semidirect
408. C5×C4⋊C4C22×D3semidirect
419. #685C22×D3semidirect
420. #685C22×D3semidirect
454. C2×C5×D3C2×#41semidirect
534. C2×Dic6C22×D5semidirect
535. C3×C4⋊C4C22×D5semidirect
549. Dic3⋊C4C22×D5semidirect
550. Dic3⋊C4C22×D5semidirect
655. C2×C4⋊C4D3×D5semidirect
671. C2×C3×C5#546semidirect
712. C22×D3#713semidirect
847. C4⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
891. C2×D3C2×#713semidirect
902. C2×C5#5610semidirect
981. C2×C3#65964semidirect
988. C5C2×#5610semidirect
1028. C3C2×#65964semidirect
1035. C2#11753861direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D202
C22×#67662
C2×#917832
C2×C5×#8962
C2×C3×#40412
C2×#914742
C2×#914732
C2×D5×(C2×D3)⋊C42
C2×#914592
C2×#914552
C2×#914442
C2×#914412
C2×#914092
C2×#914072
#117538612
C2×#659643
C2×#56105