Finite Group Databasebeta

← C2×#11753871 #14482653

Subgroups — C2×#11753871 #14482653

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×D5×D12C211yesmaximal, characteristic, complemented
2C22×#6768C211yesmaximal, characteristic, complemented
3C2×#91783C211yesmaximal, characteristic, complemented
4C2×C5×#895C211yesmaximal, characteristic, complemented
5C2×C3×#4042C211yesmaximal, characteristic, complemented
6C2×#91475C211yesmaximal, characteristic, complemented
7C2×#91475C211yesmaximal, characteristic, complemented
8C2×#91473C211yesmaximal, characteristic, complemented
9C2×D3×#685C211yesmaximal, characteristic, complemented
10C2×#91446C211yesmaximal, characteristic, complemented
11C2×#91440C211yesmaximal, characteristic, complemented
12C2×#91423C211yesmaximal, characteristic, complemented
13C2×#91420C211yesmaximal, characteristic, complemented
14C2×#91416C211yesmaximal, characteristic, complemented
15C2×#91326C211yesmaximal, characteristic, complemented
16#11753871C2116yesmaximal, direct product factor
17C2×#65944—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C5×D12C2211yescharacteristic
23C22×C5×D12C2211yescharacteristic, complemented
24C22×C5×D12C2211yescharacteristic, complemented
25C22×C4×C5×D3C2211yescharacteristic, complemented
26C22×C3×C4×D5C2211yescharacteristic
27C22×C3×Dic10C2211yescharacteristic, complemented
28C22×#1203C2211yescharacteristic
29C22×#1203C2211yescharacteristic
30C22×#1203C2211yescharacteristic, complemented
31C22×#1203C2211yescharacteristic, complemented
32C22×#1201C2211yescharacteristic
33C22×#1200C2211yescharacteristic, complemented
34C22×D3×Dic5C2211yescharacteristic, complemented
35C22×D3×Dic5C2211yescharacteristic, complemented
36C2×D5×D12—28no—
37C2×D5×D12C2218yescomplemented
38C2×#6768—28no—
39C2×#6768C2218yescomplemented
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, complemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C5×#895C2218yescomplemented
49C2×C3×#685C2211yescharacteristic
50C2×C3×#685C2211yescharacteristic
51C2×C3×#683C2211yescharacteristic, complemented
52C2×C3×#683C2211yescharacteristic, complemented
53C3×#4042C2218yescomplemented
54C2×#6667C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
58C2×#6665C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91475C2218yescomplemented
61#91475C2218yescomplemented
62#91473C2218yescomplemented
63D3×#685C2218yescomplemented
64#91446C2218yescomplemented
65#91440C2218yescomplemented
66#91423C2218yescomplemented
67#91420C2218yescomplemented
68#91416C2218yescomplemented
69#91326C2218yescomplemented
70C2×#5630—51nomaximal, Hall
71C22×#711—31no—
72C22×D4×D5—31no—
73C2×C5×#121—31no—
74C2×#4085—31no—
75C2×#4083—31no—
76C2×#4083—31no—
77C2×#4081—31no—
78C2×C4×C22⋊D5—31no—
79C22×#685—31no—
80#65944—316no—
81C2×#4042D311yescharacteristic, complemented
82C2×#4040—31no—
83C2×#4031—31no—
84C2×#4030—31no—
85C2×#4027—31no—
86C2×D5×C22⋊C4—31no—
87C23×D15C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C5×D3C2311yescharacteristic
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
111C2×C5×D12—24no—
112C2×C5×D12—24no—
113C2×C5×D12—42no—
114C2×C5×D12C2314yes—
115C2×C5×D12C2314yescomplemented
116C2×C5×D12C2314yescomplemented
117C2×C4×C5×D3—42no—
118C2×C4×C5×D3C2314yescomplemented
119C22×C3×Dic5C2311yescharacteristic
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C2×C3×C4×D5—24no—
123C2×C3×C4×D5C2314yes—
124C2×C3×Dic10—24no—
125C2×C3×Dic10C2314yescomplemented
126C2×#1203—24no—
127C2×#1203—24no—
128C2×#1203—42no—
129C2×#1203D418yescomplemented
130C2×#1203C2314yes—
131C2×#1203C2314yes—
132C2×#1203C2314yescomplemented
133C2×#1203C2314yescomplemented
134C2×#1201—24no—
135C2×#1201C2314yes—
136C2×#1200—42no—
137C2×#1200C2314yescomplemented
138C2×D3×Dic5—24no—
139C2×D3×Dic5—24no—
140C2×D3×Dic5C2314yescomplemented
141C2×D3×Dic5C2314yescomplemented
142D5×D12—232no—
143#6768—232no—
144C3×C5×C4⋊C4C2314yescomplemented
145#6714C2314yescomplemented
146#6714C2314yescomplemented
147#6714C2314yescomplemented
148#6712C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yescomplemented
150C5×(C2×D3)⋊C4C2314yescomplemented
151C3×#685C2314yes—
152C3×#685C2314yes—
153C3×#683C2314yescomplemented
154C3×#683C2314yescomplemented
155#6667C2314yescomplemented
156(C2×D3)⋊Dic5C2314yescomplemented
157(C2×D3)⋊Dic5C2314yescomplemented
158(C2×D3)⋊Dic5C2314yescomplemented
159#6665C2314yes—
160Dic3×Dic5C2314yescomplemented
161C22×#239—51no—
162C23×D12—51no—
163C2×C3×C22⋊Q8—51no—
164C2×#947—51no—
165C2×C4×#67—51no—
166#5630—516no—
167C2×#895—51no—
168C2×#895—51no—
169C2×#895D511yescharacteristic, complemented
170C2×#894—51no—
171C2×#894—51no—
172C2×#893—51no—
173C2×#882—51no—
174C2×#882—51no—
175C2×D3×C22⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4—31no—
182C23×C4×C5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C23×Dic5—31no—
189C23×Dic5—31no—
190C2×#711—38no—
191C2×#711—68no—
192C2×D4×D5—38no—
193C2×D4×D5—68no—
194C22×D20—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5C2×D311yescharacteristic
198C22×Dic10C2×D311yescharacteristic, complemented
199C5×#121—38no—
200C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4—31no—
203C2×C22⋊Dic5—31no—
204C2×C22⋊Dic5—31no—
205C2×C22⋊Dic5—31no—
206#4085—38no—
207#4083—38no—
208#4083—38no—
209#4081—38no—
210C4×C22⋊D5—38no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—38no—
217C2×#685C2×D311yescharacteristic
218C2×#685C2×D311yescharacteristic
219C2×#683—31no—
220C2×#683C2×D311yescharacteristic, complemented
221C2×#683C2×D311yescharacteristic, complemented
222C2×C4×Dic5—31no—
223#4042C2×D318yescomplemented
224#4040—38no—
225#4031—38no—
226#4030—38no—
227#4027—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—22no—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—22no—
247C22×C5×D3C2×D414yes—
248C22×C5×D3C2412yes—
249C22×C5×D3C2412yes—
250C22×C5×D3C2412yes—
251C22×C3×D5—22no—
252C22×C3×D5—22no—
253C22×C3×D5#4114yescomplemented
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×Dic3C2412yes—
277C5×D12—28no—
278C5×D12—28no—
279C5×D12—44no—
280C4×C5×D3—44no—
281C2×C3×Dic5—22no—
282C2×C3×Dic5—22no—
283C2×C3×Dic5C2×D414yes—
284C2×C3×Dic5C2412yes—
285C2×C3×Dic5C2412yes—
286C2×C3×Dic5C2412yes—
287C3×C4×D5—28no—
288C3×Dic10—28no—
289#1203—28no—
290#1203—28no—
291#1203—44no—
292#1203C2×D4116yescomplemented
293#1201—28no—
294#1200—44no—
295D3×Dic5—28no—
296D3×Dic5—28no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×Q8—51no—
300C23×C3×C4—51no—
301C22×#67—51no—
302C2×#239—58no—
303C2×#239—108no—
304C22×D12—51no—
305C22×D12—51no—
306C22×D12—51no—
307C22×D12—51no—
308C22×D12—51no—
309C22×D12—58no—
310C22×D12—108no—
311C22×D12C2×D511yescharacteristic
312C22×D12C2×D511yescharacteristic, complemented
313C22×D12C2×D511yescharacteristic, complemented
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3—51no—
318C22×C4×D3C2×D511yescharacteristic, complemented
319C3×C22⋊Q8—58no—
320C2×C3×C4⋊C4—51no—
321C2×C3×C4⋊C4—51no—
322C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
323C2×C3×C22⋊C4—51no—
324C2×C3×C22⋊C4—51no—
325C2×#217—51no—
326#947—58no—
327C4×#67—58no—
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)⋊C4C2×D511yescharacteristic, complemented
336C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
337C2×Dic3⋊C4—51no—
338C2×C4×Dic3—51no—
339#895—58no—
340#895—58no—
341#895C2×D518yescomplemented
342#894—58no—
343#894—58no—
344#893—58no—
345#882—58no—
346#882—58no—
347D3×C22⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5—31no—
351C24×C5—31no—
352C23×D5—31no—
353C23×D5—31no—
354C23×D5—34no—
355C23×D5—34no—
356C23×D5—64no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—64no—
360C23×D5—122no—
361C23×D5—122no—
362C23×D5C22×D311yescharacteristic
363C2×C5×D4—34no—
364C2×C5×D4—34no—
365C2×C5×D4—34no—
366C2×C5×D4—64no—
367C2×C5×D4—64no—
368C2×C5×D4—122no—
369C22×C4×C5—31no—
370C22×C4×C5—34no—
371C22×C4×C5—122no—
372C22×C4×C5C22×D311yescharacteristic
373C22×C4×C5C22×D311yescharacteristic
374C22×C4×C5C22×D311yescharacteristic
375C2×C22⋊D5—34no—
376C2×C22⋊D5—38no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—34no—
380C2×C22⋊D5—34no—
381C2×C22⋊D5—64no—
382C2×C22⋊D5—64no—
383C2×C22⋊D5—64no—
384C2×C22⋊D5—122no—
385C22×Dic5—31no—
386C22×Dic5—31no—
387C22×Dic5—34no—
388C22×Dic5—34no—
389C22×Dic5—64no—
390C22×Dic5—64no—
391C22×Dic5C22×D311yescharacteristic
392C22×Dic5C22×D311yescharacteristic
393C22×Dic5C22×D311yescharacteristic
394#711—632no—
395D4×D5—632no—
396C2×D20—34no—
397C2×D20—64no—
398C2×C4×D5—24no—
399C2×C4×D5—34no—
400C2×C4×D5—34no—
401C2×C4×D5—64no—
402C2×C4×D5—122no—
403C2×C4×D5C22×D314yes—
404C2×Dic10—24no—
405C2×Dic10C22×D314yescomplemented
406C5×C4⋊C4C22×D314yescomplemented
407C5×C22⋊C4—34no—
408C5×C22⋊C4—34no—
409C22⋊Dic5—34no—
410C22⋊Dic5—34no—
411C22⋊Dic5—34no—
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685C22×D314yes—
418#685C22×D314yes—
419#683—34no—
420#683C22×D314yescomplemented
421#683C22×D314yescomplemented
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—151no—
428C2×#123—151no—
429C2×C22⋊Q8—51no—
430C2×#121—31no—
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×D3—22no—
455C2×C5×D3—22no—
456C2×C5×D3—22no—
457C2×C5×D3—22no—
458C2×C5×D3—22no—
459C2×C5×D3—22no—
460C2×C5×D3—44no—
461C2×C5×D3—44no—
462C2×C5×D3C22×D414yes—
463C2×C3×D5—28no—
464C2×C3×D5—22no—
465C2×C3×D5—22no—
466C2×C3×D5C2×#4114yescomplemented
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—
475C3×Dic5—22no—
476C3×Dic5C22×D414yes—
477C5×Dic3—22no—
478C24×C3—51no—
479C23×D3—51no—
480C23×D3—51no—
481C23×D3—54no—
482C23×D3—54no—
483C23×D3—104no—
484C23×D3—104no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—202no—
488C23×D3—202no—
489C23×D3C22×D511yescharacteristic
490C23×D3C22×D511yescharacteristic
491C23×D3C22×D511yescharacteristic
492C2×C3×Q8—54no—
493C2×C3×Q8—104no—
494C22×C3×C4—51no—
495C22×C3×C4—51no—
496C22×C3×C4—51no—
497C22×C3×C4—54no—
498C22×C3×C4—104no—
499C22×C3×C4C22×D511yescharacteristic
500C22×C3×C4C22×D511yescharacteristic
501C22×C3×C4C22×D511yescharacteristic
502C2×#67—54no—
503C2×#67—104no—
504C22×Dic3—51no—
505C22×Dic3—51no—
506C22×Dic3C22×D511yescharacteristic
507#239—1032no—
508C2×D12—24no—
509C2×D12—24no—
510C2×D12—42no—
511C2×D12—58no—
512C2×D12—54no—
513C2×D12—54no—
514C2×D12—54no—
515C2×D12—54no—
516C2×D12—54no—
517C2×D12—1032no—
518C2×D12—104no—
519C2×D12—104no—
520C2×D12—104no—
521C2×D12—202no—
522C2×D12C22×D514yes—
523C2×D12C22×D514yescomplemented
524C2×D12C22×D514yescomplemented
525C2×C4×D3—42no—
526C2×C4×D3—54no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—54no—
530C2×C4×D3—104no—
531C2×C4×D3—104no—
532C2×C4×D3—104no—
533C2×C4×D3—202no—
534C2×C4×D3C22×D514yescomplemented
535C3×C4⋊C4—54no—
536C3×C4⋊C4—54no—
537C3×C4⋊C4C22×D514yescomplemented
538C3×C22⋊C4—54no—
539C3×C22⋊C4—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)⋊C4—54no—
547(C2×D3)⋊C4—54no—
548(C2×D3)⋊C4C22×D514yescomplemented
549(C2×D3)⋊C4C22×D514yescomplemented
550Dic3⋊C4—54no—
551C4×Dic3—54no—
552C23×C5—34no—
553C23×C5—32no—
554C23×C5—32no—
555C23×C5—32no—
556C23×C5—62no—
557C23×C5—62no—
558C23×C5—62no—
559C23×C5—62no—
560C23×C5—62no—
561C23×C5—62no—
562C23×C5—62no—
563C23×C5—62no—
564C23×C5C23×D311yescharacteristic
565C22×D5—22no—
566C22×D5—22no—
567C22×D5—34no—
568C22×D5—32no—
569C22×D5—32no—
570C22×D5—68no—
571C22×D5—68no—
572C22×D5—62no—
573C22×D5—62no—
574C22×D5—62no—
575C22×D5—62no—
576C22×D5—62no—
577C22×D5—68no—
578C22×D5—68no—
579C22×D5—124no—
580C22×D5—124no—
581C22×D5—1216no—
582C22×D5—1216no—
583C22×D5#23914yescomplemented
584C22×D5C23×D312yes—
585C5×D4—68no—
586C5×D4—68no—
587C5×D4—124no—
588C2×C4×C5—22no—
589C2×C4×C5—22no—
590C2×C4×C5—22no—
591C2×C4×C5—32no—
592C2×C4×C5—62no—
593C2×C4×C5—124no—
594C2×C4×C5C23×D312yes—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C22⋊D5—316no—
598C22⋊D5—68no—
599C22⋊D5—68no—
600C22⋊D5—68no—
601C22⋊D5—124no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—32no—
605C2×Dic5—32no—
606C2×Dic5—68no—
607C2×Dic5—62no—
608C2×Dic5—62no—
609C2×Dic5—68no—
610C2×Dic5D3×D414yes—
611C2×Dic5C23×D312yes—
612C2×Dic5C23×D312yes—
613C2×Dic5C23×D312yes—
614D20—68no—
615C4×D5—28no—
616C4×D5—68no—
617C4×D5—124no—
618Dic10—28no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—51no—
624C22×D4—31no—
625C22×D4—31no—
626C22×D4—31no—
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—58no—
645#121—38no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—51no—
653C2×C4⋊C4—51no—
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—
678C5×D3—24no—
679C5×D3—42no—
680C5×D3—42no—
681C23×C3—54no—
682C23×C3—52no—
683C23×C3—102no—
684C23×C3—102no—
685C23×C3C23×D511yescharacteristic
686C22×D3—22no—
687C22×D3—22no—
688C22×D3—22no—
689C22×D3—22no—
690C22×D3—22no—
691C22×D3—22no—
692C22×D3—22no—
693C22×D3—22no—
694C22×D3—54no—
695C22×D3—52no—
696C22×D3—52no—
697C22×D3—108no—
698C22×D3—108no—
699C22×D3—108no—
700C22×D3—102no—
701C22×D3—102no—
702C22×D3—102no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—108no—
706C22×D3—204no—
707C22×D3—204no—
708C22×D3—2016no—
709C22×D3—2016no—
710C22×D3D4×D514yes—
711C22×D3C23×D512yes—
712C22×D3C23×D512yes—
713C22×D3C23×D512yes—
714C3×Q8—108no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—54no—
719C2×C3×C4—52no—
720C2×C3×C4—52no—
721C2×C3×C4—52no—
722C2×C3×C4—108no—
723C2×C3×C4—102no—
724C2×C3×C4—102no—
725C2×C3×C4C23×D512yes—
726C2×C3×C4C23×D512yes—
727C2×C3×C4C23×D512yes—
728#67—108no—
729C2×Dic3—22no—
730C2×Dic3—52no—
731C2×Dic3—52no—
732C2×Dic3—102no—
733C2×Dic3—102no—
734C2×Dic3C23×D512yes—
735D12—28no—
736D12—28no—
737D12—44no—
738D12—516no—
739D12—108no—
740D12—108no—
741D12—108no—
742D12—204no—
743C4×D3—44no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—108no—
747C4×D3—204no—
748C22×C5—34no—
749C22×C5—62no—
750C22×C5—62no—
751C22×C5—68no—
752C22×C5—62no—
753C22×C5—62no—
754C22×C5—62no—
755C22×C5—62no—
756C22×C5—62no—
757C22×C5—62no—
758C22×C5—124no—
759C22×C5—124no—
760C22×C5C2×D3×D412yes—
761C22×C5C2×#23912yes—
762C22×C5#100912yes—
763C22×C5C24×D311yescharacteristic
764C2×D5—22no—
765C2×D5—22no—
766C2×D5—28no—
767C2×D5—34no—
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×#23914yescomplemented
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—22no—
781C4×C5—62no—
782Dic5—22no—
783Dic5—22no—
784Dic5—62no—
785Dic5—62no—
786Dic5C2×D3×D414yes—
787C24—31no—
788C24—31no—
789C24—31no—
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—54no—
803C2×Q8—104no—
804C2×D4—34no—
805C2×D4—34no—
806C2×D4—34no—
807C2×D4—64no—
808C2×D4—64no—
809C2×D4—122no—
810C2×D4—154no—
811C2×D4—158no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—154no—
816C2×D4—154no—
817C2×D4—304no—
818C2×D4—304no—
819C2×D4—3032no—
820C2×D4—304no—
821C2×D4—304no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—34no—
825C22×C4—51no—
826C22×C4—51no—
827C22×C4—51no—
828C22×C4—54no—
829C22×C4—104no—
830C22×C4—122no—
831C22×C4—154no—
832C22×C4—154no—
833C22×C4—154no—
834C22×C4—151no—
835C22×C4—151no—
836C22×C4—154no—
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—54no—
845C4⋊C4—54no—
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×C3C2×D4×D512yes—
867C22×C3#414412yes—
868C22×C3D5×#4112yes—
869C22×C3C24×D511yescharacteristic
870C2×D3—28no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—44no—
880C2×D3—44no—
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×D4×D514yes—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—54no—
896C3×C4—102no—
897C3×C4—102no—
898Dic3—22no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—64no—
902C2×C5—122no—
903C2×C5—122no—
904C2×C5#563014yescomplemented
905C2×C5C22×D3×D411yescharacteristic
906C2×C5C22×#23911yescharacteristic
907C2×C5C2×#100911yescharacteristic
908D5—24no—
909D5—64no—
910D5—122no—
911C23—34no—
912C23—32no—
913C23—32no—
914C23—32no—
915C23—54no—
916C23—52no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
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—108no—
945D4—68no—
946D4—68no—
947D4—124no—
948D4—1516no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—32no—
958C2×C4—54no—
959C2×C4—52no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—62no—
963C2×C4—108no—
964C2×C4—102no—
965C2×C4—102no—
966C2×C4—124no—
967C2×C4—152no—
968C2×C4—152no—
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#6594414yescomplemented
980C2×C3C22×D4×D511yescharacteristic
981C2×C3C2×#414411yescharacteristic
982C2×C3C2×D5×#4111yescharacteristic
983D3—24no—
984D3—42no—
985D3—42no—
986D3—104no—
987D3—202no—
988C5C2×#563011yescharacteristic, complemented, Sylow
989C22—34no—
990C22—54no—
991C22—68no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—62no—
998C22—62no—
999C22—62no—
1000C22—108no—
1001C22—102no—
1002C22—102no—
1003C22—124no—
1004C22—124no—
1005C22—154no—
1006C22—308no—
1007C22—302no—
1008C22—302no—
1009C22—302no—
1010C22—302no—
1011C22—302no—
1012C22—6016no—
1013C22—6016no—
1014C22—604no—
1015C22#9201812yes—
1016C22D3×D4×D512yes—
1017C22D5×#23912yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—54no—
1023C4—62no—
1024C4—102no—
1025C4—102no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6594411yescharacteristic, complemented, Sylow
1029C2—64no—
1030C2—104no—
1031C2—122no—
1032C2—122no—
1033C2—304no—
1034C2—602no—
1035C2#1175387114yesdirect product factor
1036C2C2×#9201811yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×D5×#23911yescharacteristic
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×D5×D12C2semidirect
2. C22×#6768C2semidirect
3. C2×#91783C2semidirect
4. C2×C5×#895C2semidirect
5. C2×C3×#4042C2semidirect
6. C2×#91475C2semidirect
7. C2×#91475C2semidirect
8. C2×#91473C2semidirect
9. C2×D3×#685C2semidirect
10. C2×#91446C2semidirect
11. C2×#91440C2semidirect
12. C2×#91423C2semidirect
13. C2×#91420C2semidirect
14. C2×#91416C2semidirect
15. C2×#91326C2semidirect
16. #11753871C2direct (N × H)
21. C22×C4×D15C22semidirect
23. C22×C5×D12C22semidirect
24. C22×C5×D12C22semidirect
25. C22×C4×C5×D3C22semidirect
27. C22×C3×Dic10C22semidirect
30. C22×#1203C22semidirect
31. C22×#1203C22semidirect
33. C22×#1200C22semidirect
34. C22×D3×Dic5C22semidirect
35. C22×D3×Dic5C22semidirect
37. C2×D5×D12C22semidirect
39. C2×#6768C22semidirect
40. C2×C3×C5×C4⋊C4C22semidirect
41. C2×#6714C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. C2×#6712C22semidirect
45. #91783C22semidirect
46. C2×C5×(C2×D3)⋊C4C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C5×#895C22semidirect
51. C2×C3×#683C22semidirect
52. C2×C3×#683C22semidirect
53. C3×#4042C22semidirect
54. C2×#6667C22semidirect
55. C2×(C2×D3)⋊Dic5C22semidirect
56. C2×(C2×D3)⋊Dic5C22semidirect
57. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91475C22semidirect
61. #91475C22semidirect
62. #91473C22semidirect
63. D3×#685C22semidirect
64. #91446C22semidirect
65. #91440C22semidirect
66. #91423C22semidirect
67. #91420C22semidirect
68. #91416C22semidirect
69. #91326C22semidirect
81. C2×#4042D3semidirect
109. C2×C4×D15C23semidirect
115. C2×C5×D12C23semidirect
116. C2×C5×D12C23semidirect
118. C2×C4×C5×D3C23semidirect
125. C2×C3×Dic10C23semidirect
129. C2×#1203D4semidirect
132. C2×#1203C23semidirect
133. C2×#1203C23semidirect
137. C2×#1200C23semidirect
140. C2×D3×Dic5C23semidirect
141. C2×D3×Dic5C23semidirect
144. C3×C5×C4⋊C4C23semidirect
145. #6714C23semidirect
146. #6714C23semidirect
147. #6714C23semidirect
148. #6712C23semidirect
149. C5×(C2×D3)⋊C4C23semidirect
150. C5×(C2×D3)⋊C4C23semidirect
153. C3×#683C23semidirect
154. C3×#683C23semidirect
155. #6667C23semidirect
156. (C2×D3)⋊Dic5C23semidirect
157. (C2×D3)⋊Dic5C23semidirect
158. (C2×D3)⋊Dic5C23semidirect
160. Dic3×Dic5C23semidirect
169. C2×#895D5semidirect
198. C22×Dic10C2×D3semidirect
200. C2×C5×C4⋊C4C2×D3semidirect
220. C2×#683C2×D3semidirect
221. C2×#683C2×D3semidirect
223. #4042C2×D3semidirect
253. C22×C3×D5#41semidirect
292. #1203C2×D4semidirect
312. C22×D12C2×D5semidirect
313. C22×D12C2×D5semidirect
318. C22×C4×D3C2×D5semidirect
322. C2×C3×C4⋊C4C2×D5semidirect
335. C2×(C2×D3)⋊C4C2×D5semidirect
336. C2×(C2×D3)⋊C4C2×D5semidirect
341. #895C2×D5semidirect
405. C2×Dic10C22×D3semidirect
406. C5×C4⋊C4C22×D3semidirect
420. #683C22×D3semidirect
421. #683C22×D3semidirect
466. C2×C3×D5C2×#41semidirect
523. C2×D12C22×D5semidirect
524. C2×D12C22×D5semidirect
534. C2×C4×D3C22×D5semidirect
537. C3×C4⋊C4C22×D5semidirect
548. (C2×D3)⋊C4C22×D5semidirect
549. (C2×D3)⋊C4C22×D5semidirect
583. C22×D5#239semidirect
655. C2×C4⋊C4D3×D5semidirect
671. C2×C3×C5#546semidirect
777. C2×D5C2×#239semidirect
847. C4⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
904. C2×C5#5630semidirect
979. C2×C3#65944semidirect
988. C5C2×#5630semidirect
1028. C3C2×#65944semidirect
1035. C2#11753871direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×D122
C22×#67682
C2×#917832
C2×C5×#8952
C2×C3×#40422
C2×#914752
C2×#914732
C2×D3×#6852
C2×#914462
C2×#914402
C2×#914232
C2×#914202
C2×#914162
C2×#913262
#117538712
C2×#659443
C2×#56305