Finite Group Databasebeta

← C2×#11753846 #14480358

Subgroups — C2×#11753846 #14480358

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D20C211yesmaximal, characteristic, complemented
2C22×D5×D12C211yesmaximal, characteristic, complemented
3C2×#91784C211yesmaximal, characteristic, complemented
4C2×C5×#894C211yesmaximal, characteristic, complemented
5C2×C3×#4040C211yesmaximal, characteristic, complemented
6C2×#91476C211yesmaximal, characteristic, complemented
7C2×#91476C211yesmaximal, characteristic, complemented
8C2×#91475C211yesmaximal, characteristic, complemented
9C2×#91474C211yesmaximal, characteristic, complemented
10C2×#91473C211yesmaximal, characteristic, complemented
11C2×#91461C211yesmaximal, characteristic, complemented
12C2×#91459C211yesmaximal, characteristic, complemented
13C2×#91420C211yesmaximal, characteristic, complemented
14C2×#91351C211yesmaximal, characteristic, complemented
15C2×#91348C211yesmaximal, characteristic, complemented
16#11753846C2116yesmaximal, direct product factor
17C2×#65987—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic, complemented
20C23×D3×D5C2211yescharacteristic, complemented
21C22×D60C2211yescharacteristic, complemented
22C22×D60C2211yescharacteristic, complemented
23C22×D60C2211yescharacteristic, complemented
24C22×C4×D15C2211yescharacteristic, complemented
25C22×C5×D12C2211yescharacteristic
26C22×C4×C5×D3C2211yescharacteristic, complemented
27C22×C3×D20C2211yescharacteristic
28C22×C3×C4×D5C2211yescharacteristic, complemented
29C22×#1203C2211yescharacteristic
30C22×#1203C2211yescharacteristic, complemented
31C22×#1203C2211yescharacteristic, complemented
32C22×#1202C2211yescharacteristic
33C22×#1202C2211yescharacteristic, complemented
34C22×#1202C2211yescharacteristic, complemented
35C22×#1201C2211yescharacteristic, complemented
36C22×#1200C2211yescharacteristic, complemented
37C2×D3×D20—28no—
38C2×D3×D20C2218yescomplemented
39C2×D5×D12—28no—
40C2×D5×D12C2218yescomplemented
41C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6714C2211yescharacteristic, complemented
44#91784C2218yescomplemented
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
49C5×#894C2218yescomplemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×#685C2211yescharacteristic, complemented
52C2×C3×#685C2211yescharacteristic, complemented
53C2×C3×#683C2211yescharacteristic, complemented
54C3×#4040C2218yescomplemented
55C2×#6669C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic, complemented
57C2×#6667C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
59C2×#6665C2211yescharacteristic, complemented
60#91476C2218yescomplemented
61#91476C2218yescomplemented
62#91475C2218yescomplemented
63#91474C2218yescomplemented
64#91473C2218yescomplemented
65#91461C2218yescomplemented
66#91459C2218yescomplemented
67#91420C2218yescomplemented
68#91351C2218yescomplemented
69#91348C2218yescomplemented
70C2×#5653—51nomaximal, Hall
71C22×D4×D5—31no—
72C23×D20—31no—
73C2×C5×#123—31no—
74C2×#4083—31no—
75C2×#4075—31no—
76#65987—316no—
77C2×#4041—31no—
78C2×#4041—31no—
79C2×#4040—31no—
80C2×#4040D311yescharacteristic, complemented
81C2×#4030—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C2×#4028—31no—
86C2×D5×C22⋊C4—31no—
87C23×D15C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C5×D3C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C23×C3×D5C2311yescharacteristic
94C22×D3×D5—24no—
95C22×D3×D5—24no—
96C22×D3×D5—42no—
97C22×D3×D5—42no—
98C22×D3×D5—42no—
99C22×D3×D5—42no—
100C22×D3×D5—42no—
101C22×D3×D5—42no—
102C22×D3×D5D418yescomplemented
103C22×D3×D5C2314yes—
104C22×D3×D5C2314yescomplemented
105C22×D3×D5C2314yescomplemented
106C22×C3×C4×C5C2311yescharacteristic
107C22×C3×C4×C5C2311yescharacteristic
108C22×C3×C4×C5C2311yescharacteristic
109C22×Dic15C2311yescharacteristic
110C2×D60—24no—
111C2×D60—24no—
112C2×D60—42no—
113C2×D60C2314yescomplemented
114C2×D60C2314yescomplemented
115C2×D60C2314yescomplemented
116C2×C4×D15—42no—
117C2×C4×D15C2314yescomplemented
118C22×C5×Dic3C2311yescharacteristic
119C22×C5×Dic3C2311yescharacteristic
120C2×C5×D12—24no—
121C2×C5×D12C2314yes—
122C2×C4×C5×D3—24no—
123C2×C4×C5×D3C2314yescomplemented
124C22×C3×Dic5C2311yescharacteristic
125C22×C3×Dic5C2311yescharacteristic
126C2×C3×D20—24no—
127C2×C3×D20C2314yes—
128C2×C3×C4×D5—24no—
129C2×C3×C4×D5C2314yescomplemented
130C2×#1203—24no—
131C2×#1203—24no—
132C2×#1203—42no—
133C2×#1203C2314yes—
134C2×#1203C2314yescomplemented
135C2×#1203C2314yescomplemented
136C2×#1202—24no—
137C2×#1202—24no—
138C2×#1202—42no—
139C2×#1202C2314yes—
140C2×#1202C2314yescomplemented
141C2×#1202C2314yescomplemented
142C2×#1201—42no—
143C2×#1201C2314yescomplemented
144C2×#1200—42no—
145C2×#1200C2314yescomplemented
146D3×D20—232no—
147D5×D12—232no—
148C3×C5×C4⋊C4C2314yescomplemented
149#6714C2314yescomplemented
150#6714C2314yescomplemented
151C5×(C2×D3)⋊C4C2314yescomplemented
152C5×(C2×D3)⋊C4C2314yescomplemented
153C5×(C2×D3)⋊C4C2314yescomplemented
154C5×Dic3⋊C4C2314yescomplemented
155C3×#685C2314yescomplemented
156C3×#685C2314yescomplemented
157C3×#685C2314yescomplemented
158C3×#683C2314yescomplemented
159#6669C2314yescomplemented
160#6667C2314yescomplemented
161#6667C2314yescomplemented
162(C2×D3)⋊Dic5C2314yescomplemented
163#6665C2314yescomplemented
164C22×D3×D4—51no—
165C23×D12—51no—
166C2×C3×#123—51no—
167C2×#937—51no—
168C2×#929—51no—
169#5653—516no—
170C2×#895—51no—
171C2×#895—51no—
172C2×#894—51no—
173C2×#894D511yescharacteristic, complemented
174C2×#884—51no—
175C2×#884—51no—
176C2×#882—51no—
177C2×#882—51no—
178C2×#882—51no—
179C2×D3×C22⋊C4—51no—
180C24×D5—31no—
181C24×D5—31no—
182C24×D5—31no—
183C22×C5×D4—31no—
184C23×C4×C5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C2×D4×D5—38no—
190C2×D4×D5—68no—
191C22×D20—31no—
192C22×D20—31no—
193C22×D20—31no—
194C22×D20—31no—
195C22×D20—31no—
196C22×D20—31no—
197C22×D20—38no—
198C22×D20—68no—
199C22×D20C2×D311yescharacteristic
200C22×C4×D5—31no—
201C22×C4×D5—31no—
202C22×C4×D5C2×D311yescharacteristic, complemented
203C5×#123—38no—
204C2×C5×C4⋊C4—31no—
205C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
206C2×C5×C22⋊C4—31no—
207C2×C5×C22⋊C4—31no—
208C2×C5×C22⋊C4—31no—
209C2×C22⋊Dic5—31no—
210#4083—38no—
211#4075—38no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685C2×D311yescharacteristic, complemented
218C2×#685C2×D311yescharacteristic, complemented
219C2×#685C2×D311yescharacteristic, complemented
220C2×#683—31no—
221C2×#683C2×D311yescharacteristic, complemented
222#4041—38no—
223#4041—38no—
224#4040—38no—
225#4040C2×D318yescomplemented
226#4030—38no—
227#4030—38no—
228#4028—38no—
229#4028—38no—
230#4028—38no—
231D5×C22⋊C4—38no—
232C2×#534—151noSylow
233C23×C3×C5C2411yescharacteristic
234C22×D15—22no—
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15—22no—
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15C2×D414yes—
243C22×D15C2412yes—
244C22×D15C2412yes—
245C22×D15C2412yes—
246C22×C5×D3—22no—
247C22×C5×D3—22no—
248C22×C5×D3—22no—
249C22×C5×D3—22no—
250C22×C5×D3—22no—
251C22×C5×D3C2×D414yes—
252C22×C5×D3C2412yes—
253C22×C5×D3C2412yes—
254C22×C3×D5—22no—
255C22×C3×D5—22no—
256C22×C3×D5—22no—
257C22×C3×D5—22no—
258C22×C3×D5—22no—
259C22×C3×D5C2×D414yes—
260C22×C3×D5C2412yes—
261C22×C3×D5C2412yes—
262C2×D3×D5—28no—
263C2×D3×D5—28no—
264C2×D3×D5—416no—
265C2×D3×D5—44no—
266C2×D3×D5—44no—
267C2×D3×D5—44no—
268C2×D3×D5—44no—
269C2×D3×D5—44no—
270C2×D3×D5—44no—
271C2×D3×D5—416no—
272C2×D3×D5—416no—
273C2×D3×D5C2×D4116yescomplemented
274C2×C3×C4×C5—22no—
275C2×C3×C4×C5—22no—
276C2×C3×C4×C5—22no—
277C2×C3×C4×C5C2412yes—
278C2×C3×C4×C5C2412yes—
279C2×C3×C4×C5C2412yes—
280C2×Dic15—22no—
281C2×Dic15C2412yes—
282D60—28no—
283D60—28no—
284D60—44no—
285C4×D15—44no—
286C2×C5×Dic3—22no—
287C2×C5×Dic3—22no—
288C2×C5×Dic3C2412yes—
289C2×C5×Dic3C2412yes—
290C5×D12—28no—
291C4×C5×D3—28no—
292C2×C3×Dic5—22no—
293C2×C3×Dic5—22no—
294C2×C3×Dic5C2412yes—
295C2×C3×Dic5C2412yes—
296C3×D20—28no—
297C3×C4×D5—28no—
298#1203—28no—
299#1203—28no—
300#1203—44no—
301#1202—28no—
302#1202—28no—
303#1202—44no—
304#1201—44no—
305#1200—44no—
306C24×D3—51no—
307C24×D3—51no—
308C24×D3—51no—
309C22×C3×D4—51no—
310C23×C3×C4—51no—
311C22×#67—51no—
312C22×#67—51no—
313C22×#67—51no—
314C22×#67—51no—
315C2×D3×D4—58no—
316C2×D3×D4—108no—
317C22×D12—51no—
318C22×D12—51no—
319C22×D12—51no—
320C22×D12—51no—
321C22×D12—51no—
322C22×D12—51no—
323C22×D12—58no—
324C22×D12—108no—
325C22×D12C2×D511yescharacteristic
326C22×C4×D3—51no—
327C22×C4×D3—51no—
328C22×C4×D3C2×D511yescharacteristic, complemented
329C3×#123—58no—
330C2×C3×C4⋊C4—51no—
331C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
332C2×C3×C22⋊C4—51no—
333C2×C3×C22⋊C4—51no—
334C2×C3×C22⋊C4—51no—
335C2×#217—51no—
336#937—58no—
337#929—58no—
338C2×(C2×D3)⋊C4—51no—
339C2×(C2×D3)⋊C4—51no—
340C2×(C2×D3)⋊C4—51no—
341C2×(C2×D3)⋊C4—51no—
342C2×(C2×D3)⋊C4—51no—
343C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
344C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
345C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
346C2×Dic3⋊C4—51no—
347C2×Dic3⋊C4C2×D511yescharacteristic, complemented
348#895—58no—
349#895—58no—
350#894—58no—
351#894C2×D518yescomplemented
352#884—58no—
353#884—58no—
354#882—58no—
355#882—58no—
356#882—58no—
357D3×C22⋊C4—58no—
358C24×C5—31no—
359C24×C5—31no—
360C23×D5—31no—
361C23×D5—38no—
362C23×D5—34no—
363C23×D5—31no—
364C23×D5—31no—
365C23×D5—34no—
366C23×D5—34no—
367C23×D5—64no—
368C23×D5—64no—
369C23×D5—122no—
370C23×D5—122no—
371C23×D5—122no—
372C23×D5—122no—
373C23×D5—122no—
374C23×D5—122no—
375C23×D5C22×D311yescharacteristic
376C23×D5C22×D311yescharacteristic
377C2×C5×D4—34no—
378C2×C5×D4—64no—
379C22×C4×C5—31no—
380C22×C4×C5—31no—
381C22×C4×C5—34no—
382C22×C4×C5—64no—
383C22×C4×C5C22×D311yescharacteristic
384C22×C4×C5C22×D311yescharacteristic
385C22×C4×C5C22×D311yescharacteristic
386C2×C22⋊D5—34no—
387C2×C22⋊D5—34no—
388C2×C22⋊D5—34no—
389C2×C22⋊D5—34no—
390C2×C22⋊D5—64no—
391C2×C22⋊D5—64no—
392C2×C22⋊D5—122no—
393C2×C22⋊D5—122no—
394C22×Dic5—31no—
395C22×Dic5C22×D311yescharacteristic
396C22×Dic5C22×D311yescharacteristic
397D4×D5—632no—
398C2×D20—24no—
399C2×D20—34no—
400C2×D20—34no—
401C2×D20—34no—
402C2×D20—34no—
403C2×D20—34no—
404C2×D20—34no—
405C2×D20—632no—
406C2×D20—64no—
407C2×D20—64no—
408C2×D20—64no—
409C2×D20—64no—
410C2×D20—122no—
411C2×D20—122no—
412C2×D20C22×D314yes—
413C2×C4×D5—24no—
414C2×C4×D5—34no—
415C2×C4×D5—34no—
416C2×C4×D5—122no—
417C2×C4×D5—122no—
418C2×C4×D5C22×D314yescomplemented
419C5×C4⋊C4—34no—
420C5×C4⋊C4C22×D314yescomplemented
421C5×C22⋊C4—34no—
422C5×C22⋊C4—34no—
423C5×C22⋊C4—34no—
424C22⋊Dic5—34no—
425#685—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685—34no—
430#685C22×D314yescomplemented
431#685C22×D314yescomplemented
432#685C22×D314yescomplemented
433#683—34no—
434#683C22×D314yescomplemented
435C23×D4—151no—
436C23×D4—151no—
437#534—1516no—
438C2×#123—31no—
439C2×#123—51no—
440C2×#123—151no—
441C2×#123—151no—
442C2×#121—151no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#121—151no—
446C2×#120—151no—
447C2×#120—151no—
448C2×#120—151no—
449C2×#120—151no—
450C22×C22⋊C4—151no—
451C22×C3×C5C22×D412yes—
452C22×C3×C5H(5,𝔽2)12yes—
453C22×C3×C5H(5,𝔽2)12yes—
454C22×C3×C5C2511yescharacteristic
455C2×D15—28no—
456C2×D15—22no—
457C2×D15—22no—
458C2×D15—22no—
459C2×D15—22no—
460C2×D15—22no—
461C2×D15—22no—
462C2×D15—22no—
463C2×D15—22no—
464C2×D15—44no—
465C2×D15—44no—
466C2×D15C22×D414yes—
467C2×C5×D3—28no—
468C2×C5×D3—22no—
469C2×C5×D3—22no—
470C2×C5×D3—22no—
471C2×C5×D3—22no—
472C2×C5×D3—22no—
473C2×C5×D3—44no—
474C2×C5×D3C22×D414yes—
475C2×C3×D5—28no—
476C2×C3×D5—22no—
477C2×C3×D5—22no—
478C2×C3×D5—22no—
479C2×C3×D5—22no—
480C2×C3×D5—22no—
481C2×C3×D5—44no—
482C2×C3×D5C22×D414yes—
483D3×D5—416no—
484D3×D5—416no—
485D3×D5—416no—
486C3×C4×C5—22no—
487C3×C4×C5—22no—
488C3×C4×C5—22no—
489Dic15—22no—
490C3×Dic5—22no—
491C3×Dic5—22no—
492C5×Dic3—22no—
493C5×Dic3—22no—
494C24×C3—51no—
495C24×C3—51no—
496C23×D3—51no—
497C23×D3—58no—
498C23×D3—54no—
499C23×D3—51no—
500C23×D3—51no—
501C23×D3—54no—
502C23×D3—54no—
503C23×D3—104no—
504C23×D3—104no—
505C23×D3—202no—
506C23×D3—202no—
507C23×D3—202no—
508C23×D3—202no—
509C23×D3—202no—
510C23×D3—202no—
511C23×D3C22×D511yescharacteristic
512C23×D3C22×D511yescharacteristic
513C2×C3×D4—54no—
514C2×C3×D4—104no—
515C22×C3×C4—51no—
516C22×C3×C4—51no—
517C22×C3×C4—54no—
518C22×C3×C4—104no—
519C22×C3×C4C22×D511yescharacteristic
520C22×C3×C4C22×D511yescharacteristic
521C22×C3×C4C22×D511yescharacteristic
522C2×#67—54no—
523C2×#67—54no—
524C2×#67—54no—
525C2×#67—54no—
526C2×#67—104no—
527C2×#67—104no—
528C2×#67—202no—
529C2×#67—202no—
530C22×Dic3—51no—
531C22×Dic3C22×D511yescharacteristic
532C22×Dic3C22×D511yescharacteristic
533D3×D4—1032no—
534C2×D12—24no—
535C2×D12—54no—
536C2×D12—54no—
537C2×D12—54no—
538C2×D12—54no—
539C2×D12—54no—
540C2×D12—54no—
541C2×D12—1032no—
542C2×D12—104no—
543C2×D12—104no—
544C2×D12—104no—
545C2×D12—104no—
546C2×D12—202no—
547C2×D12—202no—
548C2×D12C22×D514yes—
549C2×C4×D3—24no—
550C2×C4×D3—54no—
551C2×C4×D3—54no—
552C2×C4×D3—202no—
553C2×C4×D3—202no—
554C2×C4×D3C22×D514yescomplemented
555C3×C4⋊C4—54no—
556C3×C4⋊C4C22×D514yescomplemented
557C3×C22⋊C4—54no—
558C3×C22⋊C4—54no—
559C3×C22⋊C4—54no—
560#217—54no—
561(C2×D3)⋊C4—54no—
562(C2×D3)⋊C4—54no—
563(C2×D3)⋊C4—54no—
564(C2×D3)⋊C4—54no—
565(C2×D3)⋊C4—54no—
566(C2×D3)⋊C4C22×D514yescomplemented
567(C2×D3)⋊C4C22×D514yescomplemented
568(C2×D3)⋊C4C22×D514yescomplemented
569Dic3⋊C4—54no—
570Dic3⋊C4C22×D514yescomplemented
571C23×C5—34no—
572C23×C5—32no—
573C23×C5—32no—
574C23×C5—62no—
575C23×C5—62no—
576C23×C5—62no—
577C23×C5—62no—
578C23×C5—62no—
579C23×C5C23×D311yescharacteristic
580C22×D5—22no—
581C22×D5—22no—
582C22×D5—22no—
583C22×D5—22no—
584C22×D5—22no—
585C22×D5—34no—
586C22×D5—32no—
587C22×D5—316no—
588C22×D5—32no—
589C22×D5—32no—
590C22×D5—68no—
591C22×D5—62no—
592C22×D5—62no—
593C22×D5—62no—
594C22×D5—62no—
595C22×D5—62no—
596C22×D5—62no—
597C22×D5—62no—
598C22×D5—62no—
599C22×D5—68no—
600C22×D5—1216no—
601C22×D5—124no—
602C22×D5—124no—
603C22×D5—124no—
604C22×D5—124no—
605C22×D5—124no—
606C22×D5—124no—
607C22×D5—1216no—
608C22×D5—1216no—
609C22×D5D3×D414yes—
610C22×D5C23×D312yes—
611C22×D5C23×D312yes—
612C5×D4—68no—
613C2×C4×C5—22no—
614C2×C4×C5—22no—
615C2×C4×C5—22no—
616C2×C4×C5—32no—
617C2×C4×C5—32no—
618C2×C4×C5—68no—
619C2×C4×C5—62no—
620C2×C4×C5—62no—
621C2×C4×C5C23×D312yes—
622C2×C4×C5C23×D312yes—
623C2×C4×C5C23×D312yes—
624C22⋊D5—68no—
625C22⋊D5—68no—
626C22⋊D5—124no—
627C22⋊D5—124no—
628C2×Dic5—22no—
629C2×Dic5—22no—
630C2×Dic5—32no—
631C2×Dic5—62no—
632C2×Dic5C23×D312yes—
633C2×Dic5C23×D312yes—
634D20—28no—
635D20—68no—
636D20—68no—
637D20—68no—
638D20—68no—
639D20—124no—
640D20—124no—
641C4×D5—28no—
642C4×D5—124no—
643C4×D5—124no—
644C25—151no—
645C25—151no—
646C25—151no—
647C22×D4—31no—
648C22×D4—51no—
649C22×D4—158no—
650C22×D4—151no—
651C22×D4—151no—
652C22×D4—151no—
653C22×D4—158no—
654C22×D4—151no—
655C22×D4—151no—
656C22×D4—151no—
657C22×D4—151no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—151no—
661C22×D4—308no—
662C22×D4—308no—
663C23×C4—31no—
664C23×C4—51no—
665C23×C4—151no—
666C23×C4—151no—
667#123—38no—
668#123—58no—
669#123—158no—
670#123—158no—
671#121—158no—
672#121—158no—
673#121—158no—
674#121—158no—
675#120—158no—
676#120—158no—
677#120—158no—
678#120—158no—
679C2×C4⋊C4—31no—
680C2×C4⋊C4—51no—
681C2×C4⋊C4—151no—
682C2×C4⋊C4D3×D511yescharacteristic, complemented
683C2×C22⋊C4—31no—
684C2×C22⋊C4—31no—
685C2×C22⋊C4—31no—
686C2×C22⋊C4—51no—
687C2×C22⋊C4—51no—
688C2×C22⋊C4—51no—
689C2×C22⋊C4—158no—
690C2×C22⋊C4—151no—
691C2×C22⋊C4—151no—
692C2×C22⋊C4—151no—
693C2×C22⋊C4—151no—
694C2×C22⋊C4—151no—
695C2×C22⋊C4—151no—
696C2×C3×C5#53414yescomplemented
697C2×C3×C5C23×D411yescharacteristic
698C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
699C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
700D15—24no—
701D15—42no—
702D15—42no—
703C3×D5—24no—
704C3×D5—42no—
705C5×D3—24no—
706C5×D3—42no—
707C23×C3—54no—
708C23×C3—52no—
709C23×C3—52no—
710C23×C3—102no—
711C23×C3—102no—
712C23×C3—102no—
713C23×C3—102no—
714C23×C3—102no—
715C23×C3C23×D511yescharacteristic
716C22×D3—22no—
717C22×D3—22no—
718C22×D3—22no—
719C22×D3—22no—
720C22×D3—22no—
721C22×D3—54no—
722C22×D3—52no—
723C22×D3—516no—
724C22×D3—52no—
725C22×D3—52no—
726C22×D3—108no—
727C22×D3—102no—
728C22×D3—102no—
729C22×D3—102no—
730C22×D3—102no—
731C22×D3—102no—
732C22×D3—102no—
733C22×D3—102no—
734C22×D3—102no—
735C22×D3—108no—
736C22×D3—2016no—
737C22×D3—204no—
738C22×D3—204no—
739C22×D3—204no—
740C22×D3—204no—
741C22×D3—204no—
742C22×D3—204no—
743C22×D3—2016no—
744C22×D3—2016no—
745C22×D3D4×D514yes—
746C22×D3C23×D512yes—
747C22×D3C23×D512yes—
748C3×D4—108no—
749C2×C3×C4—22no—
750C2×C3×C4—22no—
751C2×C3×C4—22no—
752C2×C3×C4—52no—
753C2×C3×C4—52no—
754C2×C3×C4—108no—
755C2×C3×C4—102no—
756C2×C3×C4—102no—
757C2×C3×C4C23×D512yes—
758C2×C3×C4C23×D512yes—
759C2×C3×C4C23×D512yes—
760#67—108no—
761#67—108no—
762#67—204no—
763#67—204no—
764C2×Dic3—22no—
765C2×Dic3—22no—
766C2×Dic3—52no—
767C2×Dic3—102no—
768C2×Dic3C23×D512yes—
769C2×Dic3C23×D512yes—
770D12—28no—
771D12—108no—
772D12—108no—
773D12—108no—
774D12—108no—
775D12—204no—
776D12—204no—
777C4×D3—28no—
778C4×D3—204no—
779C4×D3—204no—
780C22×C5—34no—
781C22×C5—68no—
782C22×C5—62no—
783C22×C5—62no—
784C22×C5—62no—
785C22×C5—62no—
786C22×C5—62no—
787C22×C5—124no—
788C22×C5C2×D3×D412yes—
789C22×C5#100912yes—
790C22×C5#100912yes—
791C22×C5C24×D311yescharacteristic
792C2×D5—28no—
793C2×D5—22no—
794C2×D5—22no—
795C2×D5—22no—
796C2×D5—22no—
797C2×D5—22no—
798C2×D5—34no—
799C2×D5—44no—
800C2×D5—68no—
801C2×D5—62no—
802C2×D5—62no—
803C2×D5—62no—
804C2×D5—62no—
805C2×D5—62no—
806C2×D5—62no—
807C2×D5—62no—
808C2×D5—62no—
809C2×D5—1216no—
810C2×D5—1216no—
811C2×D5—1216no—
812C2×D5—124no—
813C2×D5—124no—
814C2×D5C2×D3×D414yes—
815C4×C5—22no—
816C4×C5—22no—
817C4×C5—22no—
818C4×C5—62no—
819C4×C5—62no—
820Dic5—22no—
821Dic5—22no—
822Dic5—62no—
823C24—31no—
824C24—31no—
825C24—51no—
826C24—51no—
827C24—154no—
828C24—158no—
829C24—154no—
830C24—154no—
831C24—151no—
832C24—151no—
833C24—151no—
834C24—304no—
835C24—304no—
836C24—602no—
837C24—602no—
838C24—602no—
839C24—602no—
840C24—602no—
841C24—602no—
842C2×D4—34no—
843C2×D4—54no—
844C2×D4—64no—
845C2×D4—104no—
846C2×D4—154no—
847C2×D4—154no—
848C2×D4—154no—
849C2×D4—154no—
850C2×D4—154no—
851C2×D4—154no—
852C2×D4—154no—
853C2×D4—154no—
854C2×D4—154no—
855C2×D4—154no—
856C2×D4—304no—
857C2×D4—304no—
858C2×D4—3032no—
859C2×D4—304no—
860C2×D4—304no—
861C2×D4—3032no—
862C2×D4—304no—
863C2×D4—304no—
864C2×D4—602no—
865C2×D4—602no—
866C2×D4—602no—
867C2×D4—602no—
868C22×C4—31no—
869C22×C4—31no—
870C22×C4—34no—
871C22×C4—51no—
872C22×C4—51no—
873C22×C4—54no—
874C22×C4—64no—
875C22×C4—104no—
876C22×C4—154no—
877C22×C4—151no—
878C22×C4—154no—
879C22×C4—602no—
880C22×C4—602no—
881C22×C4C2×D3×D511yescharacteristic
882C22×C4C2×D3×D511yescharacteristic
883C22×C4C2×D3×D511yescharacteristic
884C4⋊C4—34no—
885C4⋊C4—54no—
886C4⋊C4—154no—
887C4⋊C4C2×D3×D514yescomplemented
888C22⋊C4—34no—
889C22⋊C4—34no—
890C22⋊C4—34no—
891C22⋊C4—54no—
892C22⋊C4—54no—
893C22⋊C4—54no—
894C22⋊C4—154no—
895C22⋊C4—154no—
896C22⋊C4—154no—
897C22⋊C4—154no—
898C22⋊C4—154no—
899C22⋊C4—154no—
900C3×C5C2×#53411yescharacteristic, complemented, Hall
901C22×C3—54no—
902C22×C3—108no—
903C22×C3—102no—
904C22×C3—102no—
905C22×C3—102no—
906C22×C3—102no—
907C22×C3—102no—
908C22×C3—204no—
909C22×C3C2×D4×D512yes—
910C22×C3#414912yes—
911C22×C3#414912yes—
912C22×C3C24×D511yescharacteristic
913C2×D3—28no—
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—44no—
920C2×D3—54no—
921C2×D3—108no—
922C2×D3—102no—
923C2×D3—102no—
924C2×D3—102no—
925C2×D3—102no—
926C2×D3—102no—
927C2×D3—102no—
928C2×D3—102no—
929C2×D3—102no—
930C2×D3—2016no—
931C2×D3—2016no—
932C2×D3—2016no—
933C2×D3—204no—
934C2×D3—204no—
935C2×D3C2×D4×D514yes—
936C3×C4—22no—
937C3×C4—22no—
938C3×C4—22no—
939C3×C4—102no—
940C3×C4—102no—
941Dic3—22no—
942Dic3—22no—
943Dic3—102no—
944C2×C5—64no—
945C2×C5—122no—
946C2×C5#565314yescomplemented
947C2×C5C22×D3×D411yescharacteristic
948C2×C5C2×#100911yescharacteristic
949C2×C5C2×#100911yescharacteristic
950D5—24no—
951D5—42no—
952D5—64no—
953D5—122no—
954D5—122no—
955C23—34no—
956C23—32no—
957C23—32no—
958C23—54no—
959C23—52no—
960C23—52no—
961C23—62no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—102no—
967C23—102no—
968C23—102no—
969C23—102no—
970C23—102no—
971C23—1516no—
972C23—154no—
973C23—152no—
974C23—152no—
975C23—152no—
976C23—308no—
977C23—308no—
978C23—302no—
979C23—302no—
980C23—302no—
981C23—302no—
982C23—302no—
983C23—302no—
984C23—302no—
985C23—302no—
986C23—6016no—
987C23—604no—
988C23—604no—
989C23—604no—
990C23—604no—
991C23—604no—
992C23—604no—
993C23—6016no—
994C23—6016no—
995C23C22×D3×D511yescharacteristic
996D4—68no—
997D4—108no—
998D4—308no—
999D4—308no—
1000D4—308no—
1001D4—308no—
1002D4—308no—
1003D4—308no—
1004D4—604no—
1005D4—604no—
1006D4—604no—
1007D4—604no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—52no—
1014C2×C4—52no—
1015C2×C4—68no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—108no—
1019C2×C4—102no—
1020C2×C4—102no—
1021C2×C4—152no—
1022C2×C4—302no—
1023C2×C4—604no—
1024C2×C4—604no—
1025C2×C4C22×D3×D512yes—
1026C2×C4C22×D3×D512yes—
1027C2×C4C22×D3×D512yes—
1028C2×C3—104no—
1029C2×C3—202no—
1030C2×C3#6598714yescomplemented
1031C2×C3C22×D4×D511yescharacteristic
1032C2×C3C2×#414911yescharacteristic
1033C2×C3C2×#414911yescharacteristic
1034D3—24no—
1035D3—42no—
1036D3—104no—
1037D3—202no—
1038D3—202no—
1039C5C2×#565311yescharacteristic, complemented, Sylow
1040C22—34no—
1041C22—54no—
1042C22—68no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—108no—
1049C22—102no—
1050C22—102no—
1051C22—102no—
1052C22—102no—
1053C22—102no—
1054C22—124no—
1055C22—154no—
1056C22—204no—
1057C22—308no—
1058C22—302no—
1059C22—302no—
1060C22—302no—
1061C22—302no—
1062C22—302no—
1063C22—302no—
1064C22—302no—
1065C22—302no—
1066C22—6016no—
1067C22—6016no—
1068C22—6016no—
1069C22—604no—
1070C22—604no—
1071C22#9201912yes—
1072C22D3×D4×D512yes—
1073C22#9203512yes—
1074C22C23×D3×D511yescharacteristic
1075C4—22no—
1076C4—22no—
1077C4—22no—
1078C4—62no—
1079C4—62no—
1080C4—102no—
1081C4—102no—
1082C4—302no—
1083C3C2×#6598711yescharacteristic, complemented, Sylow
1084C2—64no—
1085C2—104no—
1086C2—122no—
1087C2—202no—
1088C2—304no—
1089C2—602no—
1090C2—602no—
1091C2#1175384614yesdirect product factor
1092C2C2×#9201911yescharacteristic
1093C2C2×D3×D4×D511yescharacteristic
1094C2C2×#9203511yescharacteristic
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×#534
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×D5×D12C2semidirect
3. C2×#91784C2semidirect
4. C2×C5×#894C2semidirect
5. C2×C3×#4040C2semidirect
6. C2×#91476C2semidirect
7. C2×#91476C2semidirect
8. C2×#91475C2semidirect
9. C2×#91474C2semidirect
10. C2×#91473C2semidirect
11. C2×#91461C2semidirect
12. C2×#91459C2semidirect
13. C2×#91420C2semidirect
14. C2×#91351C2semidirect
15. C2×#91348C2semidirect
16. #11753846C2direct (N × H)
19. C23×D3×D5C22semidirect
20. C23×D3×D5C22semidirect
21. C22×D60C22semidirect
22. C22×D60C22semidirect
23. C22×D60C22semidirect
24. C22×C4×D15C22semidirect
26. C22×C4×C5×D3C22semidirect
28. C22×C3×C4×D5C22semidirect
30. C22×#1203C22semidirect
31. C22×#1203C22semidirect
33. C22×#1202C22semidirect
34. C22×#1202C22semidirect
35. C22×#1201C22semidirect
36. C22×#1200C22semidirect
38. C2×D3×D20C22semidirect
40. C2×D5×D12C22semidirect
41. C2×C3×C5×C4⋊C4C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. #91784C22semidirect
45. C2×C5×(C2×D3)⋊C4C22semidirect
46. C2×C5×(C2×D3)⋊C4C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C5×Dic3⋊C4C22semidirect
49. C5×#894C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×#685C22semidirect
52. C2×C3×#685C22semidirect
53. C2×C3×#683C22semidirect
54. C3×#4040C22semidirect
55. C2×#6669C22semidirect
56. C2×#6667C22semidirect
57. C2×#6667C22semidirect
58. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×#6665C22semidirect
60. #91476C22semidirect
61. #91476C22semidirect
62. #91475C22semidirect
63. #91474C22semidirect
64. #91473C22semidirect
65. #91461C22semidirect
66. #91459C22semidirect
67. #91420C22semidirect
68. #91351C22semidirect
69. #91348C22semidirect
80. C2×#4040D3semidirect
102. C22×D3×D5D4semidirect
104. C22×D3×D5C23semidirect
105. C22×D3×D5C23semidirect
113. C2×D60C23semidirect
114. C2×D60C23semidirect
115. C2×D60C23semidirect
117. C2×C4×D15C23semidirect
123. C2×C4×C5×D3C23semidirect
129. C2×C3×C4×D5C23semidirect
134. C2×#1203C23semidirect
135. C2×#1203C23semidirect
140. C2×#1202C23semidirect
141. C2×#1202C23semidirect
143. C2×#1201C23semidirect
145. C2×#1200C23semidirect
148. C3×C5×C4⋊C4C23semidirect
149. #6714C23semidirect
150. #6714C23semidirect
151. C5×(C2×D3)⋊C4C23semidirect
152. C5×(C2×D3)⋊C4C23semidirect
153. C5×(C2×D3)⋊C4C23semidirect
154. C5×Dic3⋊C4C23semidirect
155. C3×#685C23semidirect
156. C3×#685C23semidirect
157. C3×#685C23semidirect
158. C3×#683C23semidirect
159. #6669C23semidirect
160. #6667C23semidirect
161. #6667C23semidirect
162. (C2×D3)⋊Dic5C23semidirect
163. #6665C23semidirect
173. C2×#894D5semidirect
202. C22×C4×D5C2×D3semidirect
205. C2×C5×C4⋊C4C2×D3semidirect
217. C2×#685C2×D3semidirect
218. C2×#685C2×D3semidirect
219. C2×#685C2×D3semidirect
221. C2×#683C2×D3semidirect
225. #4040C2×D3semidirect
273. C2×D3×D5C2×D4semidirect
328. C22×C4×D3C2×D5semidirect
331. C2×C3×C4⋊C4C2×D5semidirect
343. C2×(C2×D3)⋊C4C2×D5semidirect
344. C2×(C2×D3)⋊C4C2×D5semidirect
345. C2×(C2×D3)⋊C4C2×D5semidirect
347. C2×Dic3⋊C4C2×D5semidirect
351. #894C2×D5semidirect
418. C2×C4×D5C22×D3semidirect
420. C5×C4⋊C4C22×D3semidirect
430. #685C22×D3semidirect
431. #685C22×D3semidirect
432. #685C22×D3semidirect
434. #683C22×D3semidirect
554. C2×C4×D3C22×D5semidirect
556. C3×C4⋊C4C22×D5semidirect
566. (C2×D3)⋊C4C22×D5semidirect
567. (C2×D3)⋊C4C22×D5semidirect
568. (C2×D3)⋊C4C22×D5semidirect
570. Dic3⋊C4C22×D5semidirect
682. C2×C4⋊C4D3×D5semidirect
696. C2×C3×C5#534semidirect
887. C4⋊C4C2×D3×D5semidirect
900. C3×C5C2×#534semidirect
946. C2×C5#5653semidirect
1030. C2×C3#65987semidirect
1039. C5C2×#5653semidirect
1083. C3C2×#65987semidirect
1091. C2#11753846direct (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×D5×D122
C2×#917842
C2×C5×#8942
C2×C3×#40402
C2×#914762
C2×#914752
C2×#914742
C2×#914732
C2×#914612
C2×#914592
C2×#914202
C2×#913512
C2×#913482
#117538462
C2×#659873
C2×#56535