Finite Group Databasebeta

← C2×#11753212 #14480334

Subgroups — C2×#11753212 #14480334

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×D5×#67C211yesmaximal, characteristic, complemented
2C22×D3×D20C211yesmaximal, characteristic, complemented
3C2×#91773C211yesmaximal, characteristic, complemented
4C2×C5×#883C211yesmaximal, characteristic, complemented
5C2×C3×#4028C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×#91564C211yesmaximal, characteristic, complemented
8C2×#91533C211yesmaximal, characteristic, complemented
9C2×#91474C211yesmaximal, characteristic, complemented
10C2×#91473C211yesmaximal, characteristic, complemented
11C2×#91465C211yesmaximal, characteristic, complemented
12C2×#91459C211yesmaximal, characteristic, complemented
13C2×#91452C211yesmaximal, characteristic, complemented
14C2×#91413C211yesmaximal, characteristic, complemented
15C2×#91407C211yesmaximal, characteristic, complemented
16#11753212C2116yesmaximal, direct product factor
17C2×#65987—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic, complemented
19C23×D3×D5C2211yescharacteristic
20C23×D3×D5C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic, complemented
22C22×#1220C2211yescharacteristic, complemented
23C22×D60C2211yescharacteristic, complemented
24C22×C4×D15C2211yescharacteristic, complemented
25C22×C5×#67C2211yescharacteristic
26C22×C4×C5×D3C2211yescharacteristic, complemented
27C22×C3×C22⋊D5C2211yescharacteristic, complemented
28C22×C3×D20C2211yescharacteristic
29C22×C3×D20C2211yescharacteristic, complemented
30C2×D5×#67—28no—
31C2×D5×#67C2218yescomplemented
32C22×#1202C2211yescharacteristic
33C22×#1202C2211yescharacteristic, complemented
34C22×#1202C2211yescharacteristic, complemented
35C22×#1202C2211yescharacteristic, complemented
36C22×#1201C2211yescharacteristic
37C22×#1200C2211yescharacteristic, complemented
38C22×D5×Dic3C2211yescharacteristic, complemented
39C2×D3×D20—28no—
40C2×D3×D20C2218yescomplemented
41C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6712C2211yescharacteristic, complemented
44#91773C2218yescomplemented
45C2×C5×#217C2211yescharacteristic, complemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
48C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
49C5×#883C2218yescomplemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×#685C2211yescharacteristic, complemented
52C3×#4028C2218yescomplemented
53#91577C2218yescomplemented
54#91564C2218yescomplemented
55C2×#6668C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
58C2×#6665C2211yescharacteristic, complemented
59C2×#6665C2211yescharacteristic, complemented
60C2×#6665C2211yescharacteristic, complemented
61C2×#6665C2211yescharacteristic, complemented
62#91533C2218yescomplemented
63#91474C2218yescomplemented
64#91473C2218yescomplemented
65#91465C2218yescomplemented
66#91459C2218yescomplemented
67#91452C2218yescomplemented
68#91413C2218yescomplemented
69#91407C2218yescomplemented
70C2×#5589—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×#4040—31no—
81C2×#4030—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C2×#4028D311yescharacteristic, complemented
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C3×D5—24no—
92C23×C3×D5—42no—
93C23×C3×D5—42no—
94C23×C3×D5C2311yescharacteristic
95C23×C3×D5C2311yescharacteristic
96C23×C3×D5C2311yescharacteristic
97C23×C3×D5C2314yescomplemented
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5—42no—
101C22×D3×D5—42no—
102C22×D3×D5—42no—
103C22×D3×D5D418yescomplemented
104C22×D3×D5C2314yes—
105C22×D3×D5C2314yescomplemented
106C22×C3×C4×C5C2311yescharacteristic
107C22×C3×C4×C5C2311yescharacteristic
108C2×#1220—24no—
109C2×#1220—42no—
110C2×#1220C2314yescomplemented
111C2×#1220C2314yescomplemented
112C22×Dic15C2311yescharacteristic
113C22×Dic15C2311yescharacteristic
114C2×D60—24no—
115C2×D60C2314yescomplemented
116C2×C4×D15—42no—
117C2×C4×D15C2314yescomplemented
118C2×C5×#67—24no—
119C2×C5×#67C2314yes—
120C22×C5×Dic3C2311yescharacteristic
121C22×C5×Dic3C2311yescharacteristic
122C22×C5×Dic3C2311yescharacteristic
123C2×C4×C5×D3—24no—
124C2×C4×C5×D3C2314yescomplemented
125C2×C3×C22⋊D5—42no—
126C2×C3×C22⋊D5C2314yescomplemented
127C22×C3×Dic5C2311yescharacteristic
128C2×C3×D20—24no—
129C2×C3×D20—42no—
130C2×C3×D20C2314yes—
131C2×C3×D20C2314yescomplemented
132D5×#67—232no—
133C2×#1202—24no—
134C2×#1202—24no—
135C2×#1202—24no—
136C2×#1202—42no—
137C2×#1202C2314yes—
138C2×#1202C2314yescomplemented
139C2×#1202C2314yescomplemented
140C2×#1202C2314yescomplemented
141C2×#1201—24no—
142C2×#1201C2314yes—
143C2×#1200—42no—
144C2×#1200C2314yescomplemented
145C2×D5×Dic3—24no—
146C2×D5×Dic3C2314yescomplemented
147D3×D20—232no—
148C3×C5×C22⋊C4C2314yescomplemented
149#6714C2314yescomplemented
150#6712C2314yescomplemented
151C5×#217C2314yescomplemented
152C5×(C2×D3)⋊C4C2314yescomplemented
153C5×C4⋊Dic3C2314yescomplemented
154C5×Dic3⋊C4C2314yescomplemented
155C3×#685C2314yescomplemented
156C3×#685C2314yescomplemented
157#6668C2314yescomplemented
158#6667C2314yescomplemented
159(C2×D3)⋊Dic5C2314yescomplemented
160#6665C2314yescomplemented
161#6665C2314yescomplemented
162#6665C2314yescomplemented
163#6665C2314yescomplemented
164C23×#67—51no—
165C22×D3×D4—51no—
166C2×C3×#120—51no—
167C2×#953—51no—
168C2×#938—51no—
169C2×#938—51no—
170C2×#937—51no—
171C2×#937—51no—
172C2×#935—51no—
173#5589—516no—
174C2×#886—51no—
175C2×#884—51no—
176C2×#884—51no—
177C2×#883—51no—
178C2×#883D511yescharacteristic, complemented
179C2×D3×C22⋊C4—51no—
180C24×D5—31no—
181C24×D5—31no—
182C24×D5C2×D311yescharacteristic, complemented
183C22×C5×D4—31no—
184C23×C4×C5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5C2×D311yescharacteristic, complemented
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—38no—
197C22×D20—68no—
198C22×D20C2×D311yescharacteristic
199C22×D20C2×D311yescharacteristic, complemented
200C22×C4×D5—31no—
201C22×C4×D5—31no—
202C22×C4×D5—31no—
203C5×#123—38no—
204C2×C5×C4⋊C4—31no—
205C2×C5×C4⋊C4—31no—
206C2×C5×C22⋊C4—31no—
207C2×C5×C22⋊C4—31no—
208C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
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×#685—31no—
218C2×#685C2×D311yescharacteristic, complemented
219C2×#685C2×D311yescharacteristic, complemented
220C2×#683—31no—
221C2×#683—31no—
222#4041—38no—
223#4041—38no—
224#4040—38no—
225#4040—38no—
226#4030—38no—
227#4030—38no—
228#4028—38no—
229#4028—38no—
230#4028C2×D318yescomplemented
231D5×C22⋊C4—38no—
232C2×#534—151noSylow
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5C2412yes—
237C23×C3×C5C2411yescharacteristic
238C22×D15—22no—
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15—22no—
243C22×D15C2×D414yes—
244C22×D15C2412yes—
245C22×D15C2412yes—
246C22×C5×D3—22no—
247C22×C5×D3—22no—
248C22×C5×D3C2×D414yes—
249C22×C5×D3C2412yes—
250C22×C3×D5—22no—
251C22×C3×D5—22no—
252C22×C3×D5—22no—
253C22×C3×D5—22no—
254C22×C3×D5—22no—
255C22×C3×D5—22no—
256C22×C3×D5—22no—
257C22×C3×D5—22no—
258C22×C3×D5—28no—
259C22×C3×D5—44no—
260C22×C3×D5—44no—
261C22×C3×D5—416no—
262C22×C3×D5C2×D414yes—
263C22×C3×D5C2412yes—
264C22×C3×D5C2412yes—
265C22×C3×D5C2412yes—
266C2×D3×D5—28no—
267C2×D3×D5—416no—
268C2×D3×D5—44no—
269C2×D3×D5—44no—
270C2×D3×D5—44no—
271C2×D3×D5—44no—
272C2×D3×D5—416no—
273C2×D3×D5C2×D4116yescomplemented
274C2×C3×C4×C5—22no—
275C2×C3×C4×C5—22no—
276C2×C3×C4×C5C2412yes—
277C2×C3×C4×C5C2412yes—
278#1220—28no—
279#1220—44no—
280C2×Dic15—22no—
281C2×Dic15—22no—
282C2×Dic15C2412yes—
283C2×Dic15C2412yes—
284D60—28no—
285C4×D15—44no—
286C5×#67—28no—
287C2×C5×Dic3—22no—
288C2×C5×Dic3—22no—
289C2×C5×Dic3—22no—
290C2×C5×Dic3C2412yes—
291C2×C5×Dic3C2412yes—
292C2×C5×Dic3C2412yes—
293C4×C5×D3—28no—
294C3×C22⋊D5—44no—
295C2×C3×Dic5—22no—
296C2×C3×Dic5C2412yes—
297C3×D20—28no—
298C3×D20—44no—
299#1202—28no—
300#1202—28no—
301#1202—28no—
302#1202—44no—
303#1201—28no—
304#1200—44no—
305D5×Dic3—28no—
306C25×C3—51no—
307C24×D3—51no—
308C24×D3—51no—
309C22×C3×D4—51no—
310C22×C3×D4—51no—
311C22×C3×D4—51no—
312C22×#67—51no—
313C22×#67—51no—
314C22×#67—51no—
315C22×#67—58no—
316C22×#67—51no—
317C22×#67—51no—
318C22×#67—51no—
319C22×#67—51no—
320C22×#67—108no—
321C22×#67C2×D511yescharacteristic
322C23×Dic3—51no—
323C2×D3×D4—58no—
324C2×D3×D4—108no—
325C22×D12—51no—
326C22×C4×D3—51no—
327C22×C4×D3—51no—
328C22×C4×D3C2×D511yescharacteristic, complemented
329C3×#120—58no—
330C2×C3×C22⋊C4—51no—
331C2×C3×C22⋊C4—51no—
332C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
333#953—58no—
334C2×#217—51no—
335C2×#217—51no—
336C2×#217—51no—
337C2×#217—51no—
338C2×#217C2×D511yescharacteristic, complemented
339#938—58no—
340#938—58no—
341#937—58no—
342#937—58no—
343#935—58no—
344C2×(C2×D3)⋊C4—51no—
345C2×(C2×D3)⋊C4—51no—
346C2×(C2×D3)⋊C4—51no—
347C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
348C2×C4⋊Dic3—51no—
349C2×C4⋊Dic3C2×D511yescharacteristic, complemented
350C2×Dic3⋊C4—51no—
351C2×Dic3⋊C4C2×D511yescharacteristic, complemented
352#886—58no—
353#884—58no—
354#884—58no—
355#883—58no—
356#883C2×D518yescomplemented
357D3×C22⋊C4—58no—
358C24×C5—31no—
359C24×C5C22×D311yescharacteristic
360C23×D5—24no—
361C23×D5—31no—
362C23×D5—38no—
363C23×D5—34no—
364C23×D5—31no—
365C23×D5—34no—
366C23×D5—42no—
367C23×D5—42no—
368C23×D5—64no—
369C23×D5—122no—
370C23×D5—122no—
371C23×D5—122no—
372C23×D5—122no—
373C23×D5C22×D311yescharacteristic
374C23×D5C22×D311yescharacteristic
375C23×D5C22×D311yescharacteristic
376C23×D5C22×D314yescomplemented
377C2×C5×D4—34no—
378C2×C5×D4—64no—
379C22×C4×C5—31no—
380C22×C4×C5—31no—
381C22×C4×C5—31no—
382C22×C4×C5—34no—
383C22×C4×C5—64no—
384C22×C4×C5C22×D311yescharacteristic
385C22×C4×C5C22×D311yescharacteristic
386C2×C22⋊D5—34no—
387C2×C22⋊D5—34no—
388C2×C22⋊D5—34no—
389C2×C22⋊D5—42no—
390C2×C22⋊D5—64no—
391C2×C22⋊D5—64no—
392C2×C22⋊D5—122no—
393C2×C22⋊D5C22×D314yescomplemented
394C22×Dic5—31no—
395C22×Dic5—31no—
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—42no—
405C2×D20—632no—
406C2×D20—64no—
407C2×D20—64no—
408C2×D20—64no—
409C2×D20—64no—
410C2×D20—122no—
411C2×D20C22×D314yes—
412C2×D20C22×D314yescomplemented
413C2×C4×D5—34no—
414C2×C4×D5—34no—
415C2×C4×D5—34no—
416C2×C4×D5—64no—
417C2×C4×D5—122no—
418C2×C4×D5—122no—
419C5×C4⋊C4—34no—
420C5×C4⋊C4—34no—
421C5×C22⋊C4—34no—
422C5×C22⋊C4—34no—
423C5×C22⋊C4C22×D314yescomplemented
424C22⋊Dic5—34no—
425#685—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685—34no—
430#685—34no—
431#685C22×D314yescomplemented
432#685C22×D314yescomplemented
433#683—34no—
434#683—34no—
435C23×D4—151no—
436C23×D4—151no—
437#534—1516no—
438C2×#123—31no—
439C2×#123—151no—
440C2×#123—151no—
441C2×#123—151no—
442C2×#121—151no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#121—151no—
446C2×#120—51no—
447C2×#120—151no—
448C2×#120—151no—
449C2×#120—151no—
450C22×C22⋊C4—151no—
451C22×C3×C5—22no—
452C22×C3×C5—22no—
453C22×C3×C5—22no—
454C22×C3×C5—44no—
455C22×C3×C5C22×D412yes—
456C22×C3×C5H(5,𝔽2)12yes—
457C22×C3×C5H(5,𝔽2)12yes—
458C22×C3×C5C2511yescharacteristic
459C2×D15—28no—
460C2×D15—22no—
461C2×D15—22no—
462C2×D15—22no—
463C2×D15—22no—
464C2×D15—22no—
465C2×D15—44no—
466C2×D15C22×D414yes—
467C2×C5×D3—28no—
468C2×C5×D3—22no—
469C2×C5×D3—22no—
470C2×C5×D3C22×D414yes—
471C2×C3×D5—28no—
472C2×C3×D5—22no—
473C2×C3×D5—22no—
474C2×C3×D5—22no—
475C2×C3×D5—22no—
476C2×C3×D5—22no—
477C2×C3×D5—22no—
478C2×C3×D5—22no—
479C2×C3×D5—22no—
480C2×C3×D5—416no—
481C2×C3×D5—44no—
482C2×C3×D5—44no—
483C2×C3×D5C22×D414yes—
484D3×D5—416no—
485D3×D5—416no—
486C3×C4×C5—22no—
487C3×C4×C5—22no—
488Dic15—22no—
489Dic15—22no—
490C3×Dic5—22no—
491C5×Dic3—22no—
492C5×Dic3—22no—
493C5×Dic3—22no—
494C24×C3—51no—
495C24×C3—51no—
496C24×C3—51no—
497C24×C3—54no—
498C24×C3—104no—
499C24×C3—202no—
500C24×C3—202no—
501C24×C3C22×D511yescharacteristic
502C23×D3—51no—
503C23×D3—58no—
504C23×D3—54no—
505C23×D3—51no—
506C23×D3—54no—
507C23×D3—104no—
508C23×D3—202no—
509C23×D3—202no—
510C23×D3—202no—
511C23×D3—202no—
512C23×D3C22×D511yescharacteristic
513C2×C3×D4—54no—
514C2×C3×D4—54no—
515C2×C3×D4—54no—
516C2×C3×D4—104no—
517C2×C3×D4—202no—
518C2×C3×D4—202no—
519C22×C3×C4—51no—
520C22×C3×C4C22×D511yescharacteristic
521C22×C3×C4C22×D511yescharacteristic
522C2×#67—24no—
523C2×#67—54no—
524C2×#67—54no—
525C2×#67—54no—
526C2×#67—54no—
527C2×#67—54no—
528C2×#67—54no—
529C2×#67—54no—
530C2×#67—104no—
531C2×#67—104no—
532C2×#67—104no—
533C2×#67—1032no—
534C2×#67—104no—
535C2×#67—104no—
536C2×#67—202no—
537C2×#67—202no—
538C2×#67C22×D514yes—
539C22×Dic3—51no—
540C22×Dic3—51no—
541C22×Dic3—54no—
542C22×Dic3—104no—
543C22×Dic3C22×D511yescharacteristic
544C22×Dic3C22×D511yescharacteristic
545C22×Dic3C22×D511yescharacteristic
546D3×D4—1032no—
547C2×D12—54no—
548C2×D12—104no—
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×C22⋊C4—54no—
556C3×C22⋊C4—54no—
557C3×C22⋊C4C22×D514yescomplemented
558#217—54no—
559#217—54no—
560#217—54no—
561#217—54no—
562#217C22×D514yescomplemented
563(C2×D3)⋊C4—54no—
564(C2×D3)⋊C4—54no—
565(C2×D3)⋊C4—54no—
566(C2×D3)⋊C4C22×D514yescomplemented
567C4⋊Dic3—54no—
568C4⋊Dic3C22×D514yescomplemented
569Dic3⋊C4—54no—
570Dic3⋊C4C22×D514yescomplemented
571C23×C5—22no—
572C23×C5—22no—
573C23×C5—22no—
574C23×C5—34no—
575C23×C5—32no—
576C23×C5—62no—
577C23×C5—62no—
578C23×C5C23×D312yes—
579C23×C5C23×D311yescharacteristic
580C22×D5—22no—
581C22×D5—22no—
582C22×D5—22no—
583C22×D5—22no—
584C22×D5—22no—
585C22×D5—22no—
586C22×D5—22no—
587C22×D5—22no—
588C22×D5—28no—
589C22×D5—34no—
590C22×D5—32no—
591C22×D5—316no—
592C22×D5—32no—
593C22×D5—44no—
594C22×D5—44no—
595C22×D5—416no—
596C22×D5—68no—
597C22×D5—62no—
598C22×D5—62no—
599C22×D5—62no—
600C22×D5—62no—
601C22×D5—62no—
602C22×D5—124no—
603C22×D5—124no—
604C22×D5—1216no—
605C22×D5—124no—
606C22×D5—124no—
607C22×D5—1216no—
608C22×D5D3×D414yes—
609C22×D5C23×D312yes—
610C22×D5C23×D312yes—
611C22×D5C23×D312yes—
612C5×D4—68no—
613C2×C4×C5—22no—
614C2×C4×C5—22no—
615C2×C4×C5—32no—
616C2×C4×C5—32no—
617C2×C4×C5—32no—
618C2×C4×C5—68no—
619C2×C4×C5—62no—
620C2×C4×C5—62no—
621C2×C4×C5—62no—
622C2×C4×C5C23×D312yes—
623C2×C4×C5C23×D312yes—
624C22⋊D5—44no—
625C22⋊D5—68no—
626C22⋊D5—68no—
627C22⋊D5—124no—
628C2×Dic5—22no—
629C2×Dic5—32no—
630C2×Dic5—32no—
631C2×Dic5—62no—
632C2×Dic5—62no—
633C2×Dic5C23×D312yes—
634D20—28no—
635D20—44no—
636D20—68no—
637D20—68no—
638D20—68no—
639D20—68no—
640D20—124no—
641C4×D5—68no—
642C4×D5—124no—
643C4×D5—124no—
644C25—51no—
645C25—151no—
646C25—151no—
647C22×D4—31no—
648C22×D4—51no—
649C22×D4—51no—
650C22×D4—51no—
651C22×D4—158no—
652C22×D4—151no—
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—151no—
665C23×C4—151no—
666C23×C4—151no—
667#123—38no—
668#123—158no—
669#123—158no—
670#123—158no—
671#121—158no—
672#121—158no—
673#121—158no—
674#121—158no—
675#120—58no—
676#120—158no—
677#120—158no—
678#120—158no—
679C2×C4⋊C4—31no—
680C2×C4⋊C4—31no—
681C2×C4⋊C4—151no—
682C2×C4⋊C4—151no—
683C2×C22⋊C4—31no—
684C2×C22⋊C4—31no—
685C2×C22⋊C4—51no—
686C2×C22⋊C4—51no—
687C2×C22⋊C4—158no—
688C2×C22⋊C4—151no—
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⋊C4D3×D511yescharacteristic, complemented
696C2×C3×C5—42no—
697C2×C3×C5#53414yescomplemented
698C2×C3×C5C23×D411yescharacteristic
699C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
700C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
701D15—24no—
702D15—42no—
703C3×D5—24no—
704C3×D5—42no—
705C3×D5—42no—
706C5×D3—24no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—22no—
710C23×C3—54no—
711C23×C3—52no—
712C23×C3—52no—
713C23×C3—52no—
714C23×C3—108no—
715C23×C3—102no—
716C23×C3—102no—
717C23×C3—102no—
718C23×C3—102no—
719C23×C3—102no—
720C23×C3—102no—
721C23×C3—102no—
722C23×C3—102no—
723C23×C3—204no—
724C23×C3—204no—
725C23×C3—2016no—
726C23×C3C23×D512yes—
727C23×C3C23×D511yescharacteristic
728C22×D3—22no—
729C22×D3—22no—
730C22×D3—54no—
731C22×D3—52no—
732C22×D3—516no—
733C22×D3—52no—
734C22×D3—102no—
735C22×D3—102no—
736C22×D3—102no—
737C22×D3—102no—
738C22×D3—102no—
739C22×D3—108no—
740C22×D3—2016no—
741C22×D3—204no—
742C22×D3—204no—
743C22×D3—204no—
744C22×D3—204no—
745C22×D3—2016no—
746C22×D3D4×D514yes—
747C22×D3C23×D512yes—
748C3×D4—108no—
749C3×D4—204no—
750C3×D4—204no—
751C2×C3×C4—22no—
752C2×C3×C4—22no—
753C2×C3×C4—52no—
754C2×C3×C4—102no—
755C2×C3×C4C23×D512yes—
756C2×C3×C4C23×D512yes—
757#67—28no—
758#67—108no—
759#67—108no—
760#67—108no—
761#67—108no—
762#67—108no—
763#67—204no—
764#67—204no—
765C2×Dic3—22no—
766C2×Dic3—22no—
767C2×Dic3—22no—
768C2×Dic3—52no—
769C2×Dic3—52no—
770C2×Dic3—108no—
771C2×Dic3—102no—
772C2×Dic3—102no—
773C2×Dic3C23×D512yes—
774C2×Dic3C23×D512yes—
775C2×Dic3C23×D512yes—
776D12—108no—
777C4×D3—28no—
778C4×D3—204no—
779C4×D3—204no—
780C22×C5—22no—
781C22×C5—22no—
782C22×C5—22no—
783C22×C5—34no—
784C22×C5—44no—
785C22×C5—62no—
786C22×C5—62no—
787C22×C5—68no—
788C22×C5C2×D3×D412yes—
789C22×C5#100412yes—
790C22×C5#100412yes—
791C22×C5C24×D311yescharacteristic
792C2×D5—22no—
793C2×D5—22no—
794C2×D5—28no—
795C2×D5—22no—
796C2×D5—22no—
797C2×D5—22no—
798C2×D5—22no—
799C2×D5—22no—
800C2×D5—22no—
801C2×D5—34no—
802C2×D5—416no—
803C2×D5—44no—
804C2×D5—44no—
805C2×D5—62no—
806C2×D5—62no—
807C2×D5—68no—
808C2×D5—62no—
809C2×D5—62no—
810C2×D5—62no—
811C2×D5—1216no—
812C2×D5—1216no—
813C2×D5—124no—
814C2×D5C2×D3×D414yes—
815C4×C5—22no—
816C4×C5—22no—
817C4×C5—62no—
818C4×C5—62no—
819C4×C5—62no—
820Dic5—22no—
821Dic5—62no—
822Dic5—62no—
823C24—31no—
824C24—51no—
825C24—51no—
826C24—51no—
827C24—54no—
828C24—104no—
829C24—154no—
830C24—158no—
831C24—154no—
832C24—151no—
833C24—151no—
834C24—202no—
835C24—202no—
836C24—304no—
837C24—602no—
838C24—602no—
839C24—602no—
840C24—602no—
841C24C2×D3×D511yescharacteristic
842C2×D4—34no—
843C2×D4—54no—
844C2×D4—54no—
845C2×D4—54no—
846C2×D4—64no—
847C2×D4—104no—
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—202no—
857C2×D4—202no—
858C2×D4—304no—
859C2×D4—3032no—
860C2×D4—304no—
861C2×D4—304no—
862C2×D4—304no—
863C2×D4—3032no—
864C2×D4—304no—
865C2×D4—304no—
866C2×D4—602no—
867C2×D4—602no—
868C22×C4—31no—
869C22×C4—31no—
870C22×C4—31no—
871C22×C4—34no—
872C22×C4—51no—
873C22×C4—64no—
874C22×C4—154no—
875C22×C4—154no—
876C22×C4—151no—
877C22×C4—151no—
878C22×C4—154no—
879C22×C4—304no—
880C22×C4—602no—
881C22×C4—602no—
882C22×C4C2×D3×D511yescharacteristic
883C22×C4C2×D3×D511yescharacteristic
884C4⋊C4—34no—
885C4⋊C4—34no—
886C4⋊C4—154no—
887C4⋊C4—154no—
888C22⋊C4—34no—
889C22⋊C4—34no—
890C22⋊C4—54no—
891C22⋊C4—54no—
892C22⋊C4—154no—
893C22⋊C4—154no—
894C22⋊C4—154no—
895C22⋊C4—154no—
896C22⋊C4—154no—
897C22⋊C4—154no—
898C22⋊C4—154no—
899C22⋊C4C2×D3×D514yescomplemented
900C3×C5C2×#53411yescharacteristic, complemented, Hall
901C22×C3—22no—
902C22×C3—22no—
903C22×C3—22no—
904C22×C3—44no—
905C22×C3—54no—
906C22×C3—108no—
907C22×C3—102no—
908C22×C3—102no—
909C22×C3—102no—
910C22×C3—102no—
911C22×C3—102no—
912C22×C3—102no—
913C22×C3—102no—
914C22×C3—102no—
915C22×C3—2016no—
916C22×C3—204no—
917C22×C3—204no—
918C22×C3C2×D4×D512yes—
919C22×C3#414912yes—
920C22×C3#414912yes—
921C22×C3C24×D511yescharacteristic
922C2×D3—28no—
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—54no—
926C2×D3—108no—
927C2×D3—102no—
928C2×D3—102no—
929C2×D3—102no—
930C2×D3—102no—
931C2×D3—102no—
932C2×D3—2016no—
933C2×D3—2016no—
934C2×D3—204no—
935C2×D3C2×D4×D514yes—
936C3×C4—22no—
937C3×C4—22no—
938C3×C4—102no—
939Dic3—22no—
940Dic3—22no—
941Dic3—22no—
942Dic3—102no—
943Dic3—102no—
944C2×C5—42no—
945C2×C5—64no—
946C2×C5#558914yescomplemented
947C2×C5C22×D3×D411yescharacteristic
948C2×C5C2×#100411yescharacteristic
949C2×C5C2×#100411yescharacteristic
950D5—24no—
951D5—42no—
952D5—42no—
953D5—64no—
954D5—122no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—34no—
959C23—32no—
960C23—54no—
961C23—52no—
962C23—52no—
963C23—52no—
964C23—62no—
965C23—62no—
966C23—108no—
967C23—102no—
968C23—102no—
969C23—102no—
970C23—102no—
971C23—102no—
972C23—102no—
973C23—102no—
974C23—102no—
975C23—1516no—
976C23—154no—
977C23—152no—
978C23—152no—
979C23—204no—
980C23—204no—
981C23—2016no—
982C23—308no—
983C23—302no—
984C23—302no—
985C23—302no—
986C23—302no—
987C23—302no—
988C23—604no—
989C23—604no—
990C23—604no—
991C23—604no—
992C23—6016no—
993C23—6016no—
994C23C22×D3×D512yes—
995C23C22×D3×D511yescharacteristic
996D4—68no—
997D4—108no—
998D4—204no—
999D4—204no—
1000D4—308no—
1001D4—308no—
1002D4—308no—
1003D4—308no—
1004D4—308no—
1005D4—308no—
1006D4—604no—
1007D4—604no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—52no—
1014C2×C4—68no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—102no—
1019C2×C4—152no—
1020C2×C4—152no—
1021C2×C4—308no—
1022C2×C4—302no—
1023C2×C4—302no—
1024C2×C4—604no—
1025C2×C4—604no—
1026C2×C4C22×D3×D512yes—
1027C2×C4C22×D3×D512yes—
1028C2×C3—42no—
1029C2×C3—104no—
1030C2×C3—202no—
1031C2×C3—202no—
1032C2×C3#6598714yescomplemented
1033C2×C3C22×D4×D511yescharacteristic
1034C2×C3C2×#414911yescharacteristic
1035C2×C3C2×#414911yescharacteristic
1036D3—24no—
1037D3—104no—
1038D3—202no—
1039C5C2×#558911yescharacteristic, complemented, Sylow
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—34no—
1044C22—44no—
1045C22—54no—
1046C22—62no—
1047C22—62no—
1048C22—68no—
1049C22—102no—
1050C22—102no—
1051C22—108no—
1052C22—102no—
1053C22—102no—
1054C22—102no—
1055C22—102no—
1056C22—102no—
1057C22—102no—
1058C22—154no—
1059C22—2016no—
1060C22—204no—
1061C22—204no—
1062C22—302no—
1063C22—302no—
1064C22—308no—
1065C22—302no—
1066C22—302no—
1067C22—302no—
1068C22—6016no—
1069C22—6016no—
1070C22—604no—
1071C22#9201712yes—
1072C22D3×D4×D512yes—
1073C22#9202612yes—
1074C22C23×D3×D511yescharacteristic
1075C4—22no—
1076C4—22no—
1077C4—62no—
1078C4—62no—
1079C4—62no—
1080C4—102no—
1081C4—302no—
1082C4—302no—
1083C3C2×#6598711yescharacteristic, complemented, Sylow
1084C2—42no—
1085C2—64no—
1086C2—104no—
1087C2—202no—
1088C2—202no—
1089C2—304no—
1090C2—602no—
1091C2#1175321214yesdirect product factor
1092C2C2×#9201711yescharacteristic
1093C2C2×D3×D4×D511yescharacteristic
1094C2C2×#9202611yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#534
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D5×#67C2semidirect
2. C22×D3×D20C2semidirect
3. C2×#91773C2semidirect
4. C2×C5×#883C2semidirect
5. C2×C3×#4028C2semidirect
6. C2×#91577C2semidirect
7. C2×#91564C2semidirect
8. C2×#91533C2semidirect
9. C2×#91474C2semidirect
10. C2×#91473C2semidirect
11. C2×#91465C2semidirect
12. C2×#91459C2semidirect
13. C2×#91452C2semidirect
14. C2×#91413C2semidirect
15. C2×#91407C2semidirect
16. #11753212C2direct (N × H)
18. C24×C3×D5C22semidirect
20. C23×D3×D5C22semidirect
21. C22×#1220C22semidirect
22. C22×#1220C22semidirect
23. C22×D60C22semidirect
24. C22×C4×D15C22semidirect
26. C22×C4×C5×D3C22semidirect
27. C22×C3×C22⋊D5C22semidirect
29. C22×C3×D20C22semidirect
31. C2×D5×#67C22semidirect
33. C22×#1202C22semidirect
34. C22×#1202C22semidirect
35. C22×#1202C22semidirect
37. C22×#1200C22semidirect
38. C22×D5×Dic3C22semidirect
40. C2×D3×D20C22semidirect
41. C2×C3×C5×C22⋊C4C22semidirect
42. C2×#6714C22semidirect
43. C2×#6712C22semidirect
44. #91773C22semidirect
45. C2×C5×#217C22semidirect
46. C2×C5×(C2×D3)⋊C4C22semidirect
47. C2×C5×C4⋊Dic3C22semidirect
48. C2×C5×Dic3⋊C4C22semidirect
49. C5×#883C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×#685C22semidirect
52. C3×#4028C22semidirect
53. #91577C22semidirect
54. #91564C22semidirect
55. C2×#6668C22semidirect
56. C2×#6667C22semidirect
57. C2×(C2×D3)⋊Dic5C22semidirect
58. C2×#6665C22semidirect
59. C2×#6665C22semidirect
60. C2×#6665C22semidirect
61. C2×#6665C22semidirect
62. #91533C22semidirect
63. #91474C22semidirect
64. #91473C22semidirect
65. #91465C22semidirect
66. #91459C22semidirect
67. #91452C22semidirect
68. #91413C22semidirect
69. #91407C22semidirect
85. C2×#4028D3semidirect
97. C23×C3×D5C23semidirect
103. C22×D3×D5D4semidirect
105. C22×D3×D5C23semidirect
110. C2×#1220C23semidirect
111. C2×#1220C23semidirect
115. C2×D60C23semidirect
117. C2×C4×D15C23semidirect
124. C2×C4×C5×D3C23semidirect
126. C2×C3×C22⋊D5C23semidirect
131. C2×C3×D20C23semidirect
138. C2×#1202C23semidirect
139. C2×#1202C23semidirect
140. C2×#1202C23semidirect
144. C2×#1200C23semidirect
146. C2×D5×Dic3C23semidirect
148. C3×C5×C22⋊C4C23semidirect
149. #6714C23semidirect
150. #6712C23semidirect
151. C5×#217C23semidirect
152. C5×(C2×D3)⋊C4C23semidirect
153. C5×C4⋊Dic3C23semidirect
154. C5×Dic3⋊C4C23semidirect
155. C3×#685C23semidirect
156. C3×#685C23semidirect
157. #6668C23semidirect
158. #6667C23semidirect
159. (C2×D3)⋊Dic5C23semidirect
160. #6665C23semidirect
161. #6665C23semidirect
162. #6665C23semidirect
163. #6665C23semidirect
178. C2×#883D5semidirect
182. C24×D5C2×D3semidirect
188. C22×C22⋊D5C2×D3semidirect
199. C22×D20C2×D3semidirect
208. C2×C5×C22⋊C4C2×D3semidirect
218. C2×#685C2×D3semidirect
219. C2×#685C2×D3semidirect
230. #4028C2×D3semidirect
273. C2×D3×D5C2×D4semidirect
328. C22×C4×D3C2×D5semidirect
332. C2×C3×C22⋊C4C2×D5semidirect
338. C2×#217C2×D5semidirect
347. C2×(C2×D3)⋊C4C2×D5semidirect
349. C2×C4⋊Dic3C2×D5semidirect
351. C2×Dic3⋊C4C2×D5semidirect
356. #883C2×D5semidirect
376. C23×D5C22×D3semidirect
393. C2×C22⋊D5C22×D3semidirect
412. C2×D20C22×D3semidirect
423. C5×C22⋊C4C22×D3semidirect
431. #685C22×D3semidirect
432. #685C22×D3semidirect
554. C2×C4×D3C22×D5semidirect
557. C3×C22⋊C4C22×D5semidirect
562. #217C22×D5semidirect
566. (C2×D3)⋊C4C22×D5semidirect
568. C4⋊Dic3C22×D5semidirect
570. Dic3⋊C4C22×D5semidirect
695. C2×C22⋊C4D3×D5semidirect
697. C2×C3×C5#534semidirect
899. C22⋊C4C2×D3×D5semidirect
900. C3×C5C2×#534semidirect
946. C2×C5#5589semidirect
1032. C2×C3#65987semidirect
1039. C5C2×#5589semidirect
1083. C3C2×#65987semidirect
1091. C2#11753212direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×#672
C22×D3×D202
C2×#917732
C2×C5×#8832
C2×C3×#40282
C2×#915772
C2×#915642
C2×#915332
C2×#914742
C2×#914732
C2×#914652
C2×#914592
C2×#914522
C2×#914132
C2×#914072
#117532122
C2×#659873
C2×#55895