Finite Group Databasebeta

← C2×#11753847 #14480356

Subgroups — C2×#11753847 #14480356

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×#6777C211yesmaximal, characteristic, complemented
2C22×D5×D12C211yesmaximal, characteristic, complemented
3C2×#91783C211yesmaximal, characteristic, complemented
4C2×C5×#895C211yesmaximal, characteristic, complemented
5C2×C3×#4040C211yesmaximal, characteristic, complemented
6C2×#91476C211yesmaximal, characteristic, complemented
7C2×#91475C211yesmaximal, characteristic, complemented
8C2×#91475C211yesmaximal, characteristic, complemented
9C2×#91474C211yesmaximal, characteristic, complemented
10C2×D3×#685C211yesmaximal, characteristic, complemented
11C2×#91454C211yesmaximal, characteristic, complemented
12C2×#91453C211yesmaximal, characteristic, complemented
13C2×#91447C211yesmaximal, characteristic, complemented
14C2×#91416C211yesmaximal, characteristic, complemented
15C2×#91355C211yesmaximal, characteristic, complemented
16#11753847C2116yesmaximal, direct product factor
17C2×#65939—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic, complemented
20C23×D3×D5C2211yescharacteristic, complemented
21C22×D60C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic, complemented
23C22×C5×D12C2211yescharacteristic, complemented
24C22×C5×D12C2211yescharacteristic, complemented
25C22×C5×D12C2211yescharacteristic, complemented
26C22×C4×C5×D3C2211yescharacteristic, complemented
27C22×C3×D20C2211yescharacteristic
28C22×C3×C4×D5C2211yescharacteristic, complemented
29C22×#1203C2211yescharacteristic
30C22×#1203C2211yescharacteristic, complemented
31C22×#1203C2211yescharacteristic, complemented
32C22×#1202C2211yescharacteristic, complemented
33C22×#1201C2211yescharacteristic
34C22×#1201C2211yescharacteristic, complemented
35C22×#1201C2211yescharacteristic, complemented
36C22×D3×Dic5C2211yescharacteristic, complemented
37C2×#6777—28no—
38C2×#6777C2218yescomplemented
39C2×D5×D12—28no—
40C2×D5×D12C2218yescomplemented
41C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6714C2211yescharacteristic, complemented
44C2×#6714C2211yescharacteristic, complemented
45C2×#6712C2211yescharacteristic, complemented
46#91783C2218yescomplemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C5×#895C2218yescomplemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×#685C2211yescharacteristic, complemented
52C2×C3×#685C2211yescharacteristic, complemented
53C2×C3×#683C2211yescharacteristic, complemented
54C3×#4040C2218yescomplemented
55C2×Dic3⋊Dic5C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
59C2×#6665C2211yescharacteristic, complemented
60#91476C2218yescomplemented
61#91475C2218yescomplemented
62#91475C2218yescomplemented
63#91474C2218yescomplemented
64D3×#685C2218yescomplemented
65#91454C2218yescomplemented
66#91453C2218yescomplemented
67#91447C2218yescomplemented
68#91416C2218yescomplemented
69#91355C2218yescomplemented
70C2×#5653—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×D4×D5—31no—
73C2×C5×#121—31no—
74C2×#4085—31no—
75C2×#4085—31no—
76C2×#4083—31no—
77C2×#4083—31no—
78C2×#4076—31no—
79C22×#685—31no—
80#65939—316no—
81C2×#4040—31no—
82C2×#4040D311yescharacteristic, complemented
83C2×#4029—31no—
84C2×#4029—31no—
85C2×#4028—31no—
86C2×#4028—31no—
87C23×D15C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
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
110C22×Dic15C2311yescharacteristic
111C2×D60—24no—
112C2×D60C2314yes—
113C2×C4×D15—24no—
114C2×C4×D15C2314yescomplemented
115C22×C5×Dic3C2311yescharacteristic
116C2×C5×D12—24no—
117C2×C5×D12—24no—
118C2×C5×D12—42no—
119C2×C5×D12C2314yescomplemented
120C2×C5×D12C2314yescomplemented
121C2×C5×D12C2314yescomplemented
122C2×C4×C5×D3—42no—
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—42no—
137C2×#1202C2314yescomplemented
138C2×#1201—24no—
139C2×#1201—24no—
140C2×#1201—42no—
141C2×#1201C2314yes—
142C2×#1201C2314yescomplemented
143C2×#1201C2314yescomplemented
144C2×D3×Dic5—42no—
145C2×D3×Dic5C2314yescomplemented
146#6777—232no—
147D5×D12—232no—
148C3×C5×C4⋊C4C2314yescomplemented
149#6714C2314yescomplemented
150#6714C2314yescomplemented
151#6714C2314yescomplemented
152#6712C2314yescomplemented
153C5×(C2×D3)⋊C4C2314yescomplemented
154C5×(C2×D3)⋊C4C2314yescomplemented
155C3×#685C2314yescomplemented
156C3×#685C2314yescomplemented
157C3×#685C2314yescomplemented
158C3×#683C2314yescomplemented
159Dic3⋊Dic5C2314yescomplemented
160#6667C2314yescomplemented
161(C2×D3)⋊Dic5C2314yescomplemented
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×#895D511yescharacteristic, complemented
172C2×#894—51no—
173C2×#894—51no—
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—
184C22×C5×D4—31no—
185C22×C5×D4—31no—
186C23×C4×C5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5—31no—
190C22×C22⋊D5—31no—
191C22×C22⋊D5—31no—
192C22×C22⋊D5—31no—
193C23×Dic5—31no—
194C2×D4×D5—38no—
195C2×D4×D5—38no—
196C2×D4×D5—68no—
197C2×D4×D5—68no—
198C22×D20—31no—
199C22×D20—31no—
200C22×D20C2×D311yescharacteristic
201C22×C4×D5—31no—
202C22×C4×D5C2×D311yescharacteristic, complemented
203C5×#121—38no—
204C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
205C2×C5×C22⋊C4—31no—
206C2×C5×C22⋊C4—31no—
207C2×C22⋊Dic5—31no—
208C2×C22⋊Dic5—31no—
209#4085—38no—
210#4085—38no—
211#4083—38no—
212#4083—38no—
213#4076—38no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685—31no—
218C2×#685—31no—
219C2×#685—38no—
220C2×#685C2×D311yescharacteristic, complemented
221C2×#685C2×D311yescharacteristic, complemented
222C2×#685C2×D311yescharacteristic, complemented
223C2×C4⋊Dic5—31no—
224C2×#683—31no—
225C2×#683C2×D311yescharacteristic, complemented
226#4040—38no—
227#4040C2×D318yescomplemented
228#4029—38no—
229#4029—38no—
230#4028—38no—
231#4028—38no—
232C2×#534—151noSylow
233C23×C3×C5C2411yescharacteristic
234C22×D15—22no—
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15—22no—
239C22×D15C2×D414yes—
240C22×D15C2412yes—
241C22×D15C2412yes—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—22no—
247C22×C5×D3—22no—
248C22×C5×D3—22no—
249C22×C5×D3—22no—
250C22×C5×D3C2×D414yes—
251C22×C5×D3C2412yes—
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×Dic15—22no—
282C2×Dic15C2412yes—
283C2×Dic15C2412yes—
284D60—28no—
285C4×D15—28no—
286C2×C5×Dic3—22no—
287C2×C5×Dic3C2412yes—
288C5×D12—28no—
289C5×D12—28no—
290C5×D12—44no—
291C4×C5×D3—44no—
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—44no—
302#1201—28no—
303#1201—28no—
304#1201—44no—
305D3×Dic5—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—58no—
322C22×D12—108no—
323C22×D12C2×D511yescharacteristic, complemented
324C22×D12C2×D511yescharacteristic, complemented
325C22×D12C2×D511yescharacteristic, complemented
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)⋊C4—51no—
344C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
345C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
346C2×Dic3⋊C4—51no—
347C2×Dic3⋊C4—51no—
348#895—58no—
349#895C2×D518yescomplemented
350#894—58no—
351#894—58no—
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—
360C24×C5—31no—
361C23×D5—31no—
362C23×D5—38no—
363C23×D5—34no—
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—34no—
379C2×C5×D4—34no—
380C2×C5×D4—64no—
381C2×C5×D4—64no—
382C2×C5×D4—122no—
383C22×C4×C5—31no—
384C22×C4×C5—34no—
385C22×C4×C5—122no—
386C22×C4×C5C22×D311yescharacteristic
387C22×C4×C5C22×D311yescharacteristic
388C22×C4×C5C22×D311yescharacteristic
389C2×C22⋊D5—34no—
390C2×C22⋊D5—34no—
391C2×C22⋊D5—34no—
392C2×C22⋊D5—34no—
393C2×C22⋊D5—34no—
394C2×C22⋊D5—34no—
395C2×C22⋊D5—64no—
396C2×C22⋊D5—64no—
397C2×C22⋊D5—64no—
398C2×C22⋊D5—64no—
399C2×C22⋊D5—122no—
400C2×C22⋊D5—122no—
401C22×Dic5—31no—
402C22×Dic5—31no—
403C22×Dic5—34no—
404C22×Dic5—122no—
405C22×Dic5C22×D311yescharacteristic
406C22×Dic5C22×D311yescharacteristic
407D4×D5—632no—
408D4×D5—632no—
409C2×D20—24no—
410C2×D20—34no—
411C2×D20—34no—
412C2×D20—64no—
413C2×D20—122no—
414C2×D20C22×D314yes—
415C2×C4×D5—24no—
416C2×C4×D5—34no—
417C2×C4×D5—64no—
418C2×C4×D5C22×D314yescomplemented
419C5×C4⋊C4C22×D314yescomplemented
420C5×C22⋊C4—34no—
421C5×C22⋊C4—34no—
422C22⋊Dic5—34no—
423C22⋊Dic5—34no—
424#685—34no—
425#685—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685C22×D314yescomplemented
430#685C22×D314yescomplemented
431#685C22×D314yescomplemented
432C4⋊Dic5—34no—
433#683—34no—
434#683C22×D314yescomplemented
435C23×D4—151no—
436C23×D4—151no—
437#534—1516no—
438C2×#123—51no—
439C2×#123—151no—
440C2×#123—151no—
441C2×#123—151no—
442C2×#121—31no—
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—44no—
462C2×D15C22×D414yes—
463C2×C5×D3—28no—
464C2×C5×D3—22no—
465C2×C5×D3—22no—
466C2×C5×D3—22no—
467C2×C5×D3—22no—
468C2×C5×D3—22no—
469C2×C5×D3—22no—
470C2×C5×D3—22no—
471C2×C5×D3—22no—
472C2×C5×D3—44no—
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—
490Dic15—22no—
491C3×Dic5—22no—
492C3×Dic5—22no—
493C5×Dic3—22no—
494C24×C3—51no—
495C24×C3—51no—
496C23×D3—51no—
497C23×D3—58no—
498C23×D3—54no—
499C23×D3—51no—
500C23×D3—54no—
501C23×D3—54no—
502C23×D3—104no—
503C23×D3—104no—
504C23×D3—202no—
505C23×D3—202no—
506C23×D3—202no—
507C23×D3—202no—
508C23×D3—202no—
509C23×D3—202no—
510C23×D3C22×D511yescharacteristic
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×Dic3—51no—
532C22×Dic3C22×D511yescharacteristic
533D3×D4—1032no—
534C2×D12—24no—
535C2×D12—24no—
536C2×D12—42no—
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—202no—
546C2×D12C22×D514yescomplemented
547C2×D12C22×D514yescomplemented
548C2×D12C22×D514yescomplemented
549C2×C4×D3—42no—
550C2×C4×D3—54no—
551C2×C4×D3—54no—
552C2×C4×D3—104no—
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)⋊C4—54no—
567(C2×D3)⋊C4C22×D514yescomplemented
568(C2×D3)⋊C4C22×D514yescomplemented
569Dic3⋊C4—54no—
570Dic3⋊C4—54no—
571C23×C5—34no—
572C23×C5—32no—
573C23×C5—32no—
574C23×C5—32no—
575C23×C5—62no—
576C23×C5—62no—
577C23×C5—62no—
578C23×C5—62no—
579C23×C5—62no—
580C23×C5—62no—
581C23×C5—62no—
582C23×C5—62no—
583C23×C5C23×D311yescharacteristic
584C22×D5—22no—
585C22×D5—22no—
586C22×D5—22no—
587C22×D5—22no—
588C22×D5—22no—
589C22×D5—34no—
590C22×D5—32no—
591C22×D5—316no—
592C22×D5—32no—
593C22×D5—68no—
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—
613C5×D4—68no—
614C5×D4—124no—
615C2×C4×C5—22no—
616C2×C4×C5—22no—
617C2×C4×C5—22no—
618C2×C4×C5—32no—
619C2×C4×C5—62no—
620C2×C4×C5—124no—
621C2×C4×C5C23×D312yes—
622C2×C4×C5C23×D312yes—
623C2×C4×C5C23×D312yes—
624C22⋊D5—68no—
625C22⋊D5—68no—
626C22⋊D5—68no—
627C22⋊D5—68no—
628C22⋊D5—124no—
629C22⋊D5—124no—
630C2×Dic5—22no—
631C2×Dic5—22no—
632C2×Dic5—32no—
633C2×Dic5—32no—
634C2×Dic5—62no—
635C2×Dic5—62no—
636C2×Dic5—124no—
637C2×Dic5C23×D312yes—
638C2×Dic5C23×D312yes—
639D20—28no—
640D20—68no—
641D20—124no—
642C4×D5—28no—
643C4×D5—68no—
644C25—151no—
645C25—151no—
646C25—151no—
647C22×D4—31no—
648C22×D4—31no—
649C22×D4—31no—
650C22×D4—51no—
651C22×D4—151no—
652C22×D4—158no—
653C22×D4—151no—
654C22×D4—151no—
655C22×D4—151no—
656C22×D4—158no—
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—58no—
668#123—158no—
669#123—158no—
670#123—158no—
671#121—38no—
672#121—158no—
673#121—158no—
674#121—158no—
675#120—158no—
676#120—158no—
677#120—158no—
678#120—158no—
679C2×C4⋊C4—51no—
680C2×C4⋊C4—151no—
681C2×C4⋊C4—151no—
682C2×C4⋊C4D3×D511yescharacteristic, complemented
683C2×C22⋊C4—31no—
684C2×C22⋊C4—31no—
685C2×C22⋊C4—51no—
686C2×C22⋊C4—51no—
687C2×C22⋊C4—51no—
688C2×C22⋊C4—158no—
689C2×C22⋊C4—151no—
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—
702C3×D5—24no—
703C3×D5—42no—
704C5×D3—24no—
705C5×D3—42no—
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—22no—
722C22×D3—22no—
723C22×D3—22no—
724C22×D3—54no—
725C22×D3—52no—
726C22×D3—516no—
727C22×D3—52no—
728C22×D3—108no—
729C22×D3—108no—
730C22×D3—102no—
731C22×D3—102no—
732C22×D3—102no—
733C22×D3—102no—
734C22×D3—102no—
735C22×D3—2016no—
736C22×D3—204no—
737C22×D3—204no—
738C22×D3—204no—
739C22×D3—204no—
740C22×D3—204no—
741C22×D3—204no—
742C22×D3—2016no—
743C22×D3—2016no—
744C22×D3D4×D514yes—
745C22×D3C23×D512yes—
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—52no—
766C2×Dic3—52no—
767C2×Dic3—102no—
768C2×Dic3—102no—
769C2×Dic3C23×D512yes—
770D12—28no—
771D12—28no—
772D12—44no—
773D12—108no—
774D12—108no—
775D12—108no—
776D12—204no—
777C4×D3—44no—
778C4×D3—108no—
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—62no—
788C22×C5—62no—
789C22×C5—62no—
790C22×C5—124no—
791C22×C5—124no—
792C22×C5C2×D3×D412yes—
793C22×C5#100912yes—
794C22×C5#100912yes—
795C22×C5C24×D311yescharacteristic
796C2×D5—28no—
797C2×D5—22no—
798C2×D5—22no—
799C2×D5—22no—
800C2×D5—22no—
801C2×D5—22no—
802C2×D5—34no—
803C2×D5—44no—
804C2×D5—68no—
805C2×D5—62no—
806C2×D5—62no—
807C2×D5—62no—
808C2×D5—62no—
809C2×D5—62no—
810C2×D5—1216no—
811C2×D5—1216no—
812C2×D5—1216no—
813C2×D5—124no—
814C2×D5C2×D3×D414yes—
815C4×C5—22no—
816C4×C5—22no—
817C4×C5—22no—
818C4×C5—62no—
819Dic5—22no—
820Dic5—22no—
821Dic5—62no—
822Dic5—62no—
823C24—31no—
824C24—31no—
825C24—31no—
826C24—51no—
827C24—51no—
828C24—154no—
829C24—158no—
830C24—154no—
831C24—154no—
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—34no—
844C2×D4—34no—
845C2×D4—54no—
846C2×D4—64no—
847C2×D4—64no—
848C2×D4—104no—
849C2×D4—122no—
850C2×D4—154no—
851C2×D4—154no—
852C2×D4—154no—
853C2×D4—154no—
854C2×D4—154no—
855C2×D4—154no—
856C2×D4—154no—
857C2×D4—154no—
858C2×D4—304no—
859C2×D4—3032no—
860C2×D4—304no—
861C2×D4—304no—
862C2×D4—3032no—
863C2×D4—304no—
864C2×D4—304no—
865C2×D4—602no—
866C2×D4—602no—
867C2×D4—602no—
868C22×C4—31no—
869C22×C4—34no—
870C22×C4—51no—
871C22×C4—51no—
872C22×C4—54no—
873C22×C4—104no—
874C22×C4—122no—
875C22×C4—154no—
876C22×C4—151no—
877C22×C4—151no—
878C22×C4—154no—
879C22×C4—304no—
880C22×C4—602no—
881C22×C4C2×D3×D511yescharacteristic
882C22×C4C2×D3×D511yescharacteristic
883C22×C4C2×D3×D511yescharacteristic
884C4⋊C4—54no—
885C4⋊C4—154no—
886C4⋊C4—154no—
887C4⋊C4C2×D3×D514yescomplemented
888C22⋊C4—34no—
889C22⋊C4—34no—
890C22⋊C4—54no—
891C22⋊C4—54no—
892C22⋊C4—54no—
893C22⋊C4—154no—
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#414412yes—
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—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—44no—
923C2×D3—44no—
924C2×D3—54no—
925C2×D3—108no—
926C2×D3—102no—
927C2×D3—102no—
928C2×D3—102no—
929C2×D3—102no—
930C2×D3—102no—
931C2×D3—2016no—
932C2×D3—2016no—
933C2×D3—2016no—
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—102no—
943Dic3—102no—
944C2×C5—64no—
945C2×C5—122no—
946C2×C5—122no—
947C2×C5#565314yescomplemented
948C2×C5C22×D3×D411yescharacteristic
949C2×C5C2×#100911yescharacteristic
950C2×C5C2×#100911yescharacteristic
951D5—24no—
952D5—42no—
953D5—64no—
954D5—122no—
955C23—34no—
956C23—32no—
957C23—32no—
958C23—32no—
959C23—54no—
960C23—52no—
961C23—52no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—102no—
971C23—102no—
972C23—102no—
973C23—102no—
974C23—102no—
975C23—1516no—
976C23—154no—
977C23—152no—
978C23—152no—
979C23—308no—
980C23—308no—
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—68no—
998D4—108no—
999D4—124no—
1000D4—308no—
1001D4—308no—
1002D4—308no—
1003D4—308no—
1004D4—308no—
1005D4—604no—
1006D4—604no—
1007D4—604no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—32no—
1012C2×C4—52no—
1013C2×C4—52no—
1014C2×C4—62no—
1015C2×C4—108no—
1016C2×C4—102no—
1017C2×C4—102no—
1018C2×C4—124no—
1019C2×C4—152no—
1020C2×C4—152no—
1021C2×C4—308no—
1022C2×C4—302no—
1023C2×C4—302no—
1024C2×C4—604no—
1025C2×C4C22×D3×D512yes—
1026C2×C4C22×D3×D512yes—
1027C2×C4C22×D3×D512yes—
1028C2×C3—104no—
1029C2×C3—202no—
1030C2×C3#6593914yescomplemented
1031C2×C3C22×D4×D511yescharacteristic
1032C2×C3C2×#414411yescharacteristic
1033C2×C3C2×#414911yescharacteristic
1034D3—24no—
1035D3—42no—
1036D3—42no—
1037D3—104no—
1038D3—202no—
1039C5C2×#565311yescharacteristic, complemented, Sylow
1040C22—34no—
1041C22—54no—
1042C22—68no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—108no—
1052C22—102no—
1053C22—102no—
1054C22—102no—
1055C22—102no—
1056C22—102no—
1057C22—124no—
1058C22—124no—
1059C22—154no—
1060C22—204no—
1061C22—308no—
1062C22—302no—
1063C22—302no—
1064C22—302no—
1065C22—302no—
1066C22—302no—
1067C22—6016no—
1068C22—6016no—
1069C22—6016no—
1070C22—604no—
1071C22#9201812yes—
1072C22D3×D4×D512yes—
1073C22#9203512yes—
1074C22C23×D3×D511yescharacteristic
1075C4—22no—
1076C4—22no—
1077C4—22no—
1078C4—62no—
1079C4—102no—
1080C4—102no—
1081C4—302no—
1082C4—302no—
1083C3C2×#6593911yescharacteristic, complemented, Sylow
1084C2—64no—
1085C2—104no—
1086C2—122no—
1087C2—122no—
1088C2—202no—
1089C2—304no—
1090C2—602no—
1091C2#1175384714yesdirect product factor
1092C2C2×#9201811yescharacteristic
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×#6777C2semidirect
2. C22×D5×D12C2semidirect
3. C2×#91783C2semidirect
4. C2×C5×#895C2semidirect
5. C2×C3×#4040C2semidirect
6. C2×#91476C2semidirect
7. C2×#91475C2semidirect
8. C2×#91475C2semidirect
9. C2×#91474C2semidirect
10. C2×D3×#685C2semidirect
11. C2×#91454C2semidirect
12. C2×#91453C2semidirect
13. C2×#91447C2semidirect
14. C2×#91416C2semidirect
15. C2×#91355C2semidirect
16. #11753847C2direct (N × H)
19. C23×D3×D5C22semidirect
20. C23×D3×D5C22semidirect
22. C22×C4×D15C22semidirect
23. C22×C5×D12C22semidirect
24. C22×C5×D12C22semidirect
25. C22×C5×D12C22semidirect
26. C22×C4×C5×D3C22semidirect
28. C22×C3×C4×D5C22semidirect
30. C22×#1203C22semidirect
31. C22×#1203C22semidirect
32. C22×#1202C22semidirect
34. C22×#1201C22semidirect
35. C22×#1201C22semidirect
36. C22×D3×Dic5C22semidirect
38. C2×#6777C22semidirect
40. C2×D5×D12C22semidirect
41. C2×C3×C5×C4⋊C4C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. C2×#6714C22semidirect
45. C2×#6712C22semidirect
46. #91783C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C5×(C2×D3)⋊C4C22semidirect
49. C5×#895C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×#685C22semidirect
52. C2×C3×#685C22semidirect
53. C2×C3×#683C22semidirect
54. C3×#4040C22semidirect
55. C2×Dic3⋊Dic5C22semidirect
56. C2×#6667C22semidirect
57. C2×(C2×D3)⋊Dic5C22semidirect
58. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×#6665C22semidirect
60. #91476C22semidirect
61. #91475C22semidirect
62. #91475C22semidirect
63. #91474C22semidirect
64. D3×#685C22semidirect
65. #91454C22semidirect
66. #91453C22semidirect
67. #91447C22semidirect
68. #91416C22semidirect
69. #91355C22semidirect
82. C2×#4040D3semidirect
102. C22×D3×D5D4semidirect
104. C22×D3×D5C23semidirect
105. C22×D3×D5C23semidirect
114. C2×C4×D15C23semidirect
119. C2×C5×D12C23semidirect
120. C2×C5×D12C23semidirect
121. C2×C5×D12C23semidirect
123. C2×C4×C5×D3C23semidirect
129. C2×C3×C4×D5C23semidirect
134. C2×#1203C23semidirect
135. C2×#1203C23semidirect
137. C2×#1202C23semidirect
142. C2×#1201C23semidirect
143. C2×#1201C23semidirect
145. C2×D3×Dic5C23semidirect
148. C3×C5×C4⋊C4C23semidirect
149. #6714C23semidirect
150. #6714C23semidirect
151. #6714C23semidirect
152. #6712C23semidirect
153. C5×(C2×D3)⋊C4C23semidirect
154. C5×(C2×D3)⋊C4C23semidirect
155. C3×#685C23semidirect
156. C3×#685C23semidirect
157. C3×#685C23semidirect
158. C3×#683C23semidirect
159. Dic3⋊Dic5C23semidirect
160. #6667C23semidirect
161. (C2×D3)⋊Dic5C23semidirect
162. (C2×D3)⋊Dic5C23semidirect
163. #6665C23semidirect
171. C2×#895D5semidirect
202. C22×C4×D5C2×D3semidirect
204. C2×C5×C4⋊C4C2×D3semidirect
220. C2×#685C2×D3semidirect
221. C2×#685C2×D3semidirect
222. C2×#685C2×D3semidirect
225. C2×#683C2×D3semidirect
227. #4040C2×D3semidirect
273. C2×D3×D5C2×D4semidirect
323. C22×D12C2×D5semidirect
324. C22×D12C2×D5semidirect
325. C22×D12C2×D5semidirect
328. C22×C4×D3C2×D5semidirect
331. C2×C3×C4⋊C4C2×D5semidirect
344. C2×(C2×D3)⋊C4C2×D5semidirect
345. C2×(C2×D3)⋊C4C2×D5semidirect
349. #895C2×D5semidirect
418. C2×C4×D5C22×D3semidirect
419. C5×C4⋊C4C22×D3semidirect
429. #685C22×D3semidirect
430. #685C22×D3semidirect
431. #685C22×D3semidirect
434. #683C22×D3semidirect
546. C2×D12C22×D5semidirect
547. C2×D12C22×D5semidirect
548. C2×D12C22×D5semidirect
554. C2×C4×D3C22×D5semidirect
556. C3×C4⋊C4C22×D5semidirect
567. (C2×D3)⋊C4C22×D5semidirect
568. (C2×D3)⋊C4C22×D5semidirect
682. C2×C4⋊C4D3×D5semidirect
696. C2×C3×C5#534semidirect
887. C4⋊C4C2×D3×D5semidirect
900. C3×C5C2×#534semidirect
947. C2×C5#5653semidirect
1030. C2×C3#65939semidirect
1039. C5C2×#5653semidirect
1083. C3C2×#65939semidirect
1091. C2#11753847direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67772
C22×D5×D122
C2×#917832
C2×C5×#8952
C2×C3×#40402
C2×#914762
C2×#914752
C2×#914742
C2×D3×#6852
C2×#914542
C2×#914532
C2×#914472
C2×#914162
C2×#913552
#117538472
C2×#659393
C2×#56535