Finite Group Databasebeta

← C2×#11755073 #14480321

Subgroups — C2×#11755073 #14480321

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×D4×D15C211yesmaximal, characteristic, complemented
2C22×#6790C211yesmaximal, characteristic, complemented
3C2×C5×#939C211yesmaximal, characteristic, complemented
4C2×C3×#4085C211yesmaximal, characteristic, complemented
5C2×#91577C211yesmaximal, characteristic, complemented
6C2×#91573C211yesmaximal, characteristic, complemented
7C2×#91572C211yesmaximal, characteristic, complemented
8C2×#91569C211yesmaximal, characteristic, complemented
9C2×#91566C211yesmaximal, characteristic, complemented
10C2×#91562C211yesmaximal, characteristic, complemented
11C22×#6667C211yesmaximal, characteristic, complemented
12#11755073C2116yesmaximal, direct product factor
13C2×#91476C211yesmaximal, characteristic, complemented
14C2×#91433C211yesmaximal, characteristic, complemented
15C2×#91355C211yesmaximal, characteristic, complemented
16C2×#91354C211yesmaximal, characteristic, complemented
17C2×#65939—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C24×D15C2211yescharacteristic, complemented
20C23×D3×D5C2211yescharacteristic, complemented
21C22×C3×C5×D4C2211yescharacteristic, complemented
22C22×#1220C2211yescharacteristic
23C22×#1220C2211yescharacteristic, complemented
24C2×D4×D15—28no—
25C2×D4×D15C2218yescomplemented
26C22×D60C2211yescharacteristic
27C22×C4×D15C2211yescharacteristic, complemented
28C22×C5×#67C2211yescharacteristic, complemented
29C22×C5×#67C2211yescharacteristic, complemented
30C23×C5×Dic3C2211yescharacteristic, complemented
31C22×C3×C22⋊D5C2211yescharacteristic, complemented
32C22×C3×C22⋊D5C2211yescharacteristic, complemented
33C23×C3×Dic5C2211yescharacteristic, complemented
34C2×#6790—28no—
35C2×#6790C2218yescomplemented
36C22×#1203C2211yescharacteristic
37C22×#1203C2211yescharacteristic, complemented
38C22×#1202C2211yescharacteristic
39C22×#1202C2211yescharacteristic, complemented
40C22×#1200C2211yescharacteristic, complemented
41C2×C5×#217C2211yescharacteristic, complemented
42C5×#939C2218yescomplemented
43C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
46C3×#4085C2218yescomplemented
47C2×C3×#685C2211yescharacteristic, complemented
48C2×C3×#683C2211yescharacteristic, complemented
49#91577C2218yescomplemented
50#91573C2218yescomplemented
51#91572C2218yescomplemented
52#91569C2218yescomplemented
53#91566C2218yescomplemented
54#91562C2218yescomplemented
55C2×Dic3⋊Dic5C2211yescharacteristic, complemented
56C2×#6668C2211yescharacteristic, complemented
57C2×#6667C2211yescharacteristic, complemented
58C2×#6667C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic, complemented
60C2×#6667C2211yescharacteristic, complemented
61C2×#6667C2211yescharacteristic, complemented
62C2×#6667C2211yescharacteristic, complemented
63C2×#6667C2218yescomplemented
64C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
65C2×#6665C2211yescharacteristic, complemented
66#91476C2218yescomplemented
67#91433C2218yescomplemented
68#91355C2218yescomplemented
69#91354C2218yescomplemented
70C2×#5605—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×D4×D5—31no—
73C2×C5×#121—31no—
74C2×#4085—31no—
75C2×#4085D311yescharacteristic, complemented
76C2×#4083—31no—
77C2×#4083—31no—
78C2×#4076—31no—
79C22×#685—31no—
80#65939—316no—
81C2×#4040—31no—
82C2×#4040—31no—
83C2×#4029—31no—
84C2×#4029—31no—
85C2×#4028—31no—
86C2×#4028—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15—24no—
90C23×D15—42no—
91C23×D15—42no—
92C23×D15—42no—
93C23×D15—42no—
94C23×D15D418yescomplemented
95C23×D15C2311yescharacteristic
96C23×D15C2311yescharacteristic
97C23×D15C2311yescharacteristic
98C23×D15C2314yes—
99C23×D15C2314yescomplemented
100C23×C5×D3C2311yescharacteristic
101C23×C3×D5C2311yescharacteristic
102C22×D3×D5—24no—
103C22×D3×D5—42no—
104C22×D3×D5—42no—
105C22×D3×D5C2314yescomplemented
106C2×C3×C5×D4—24no—
107C2×C3×C5×D4C2314yescomplemented
108C22×C3×C4×C5C2311yescharacteristic
109C2×#1220—24no—
110C2×#1220—24no—
111C2×#1220C2314yes—
112C2×#1220C2314yescomplemented
113C22×Dic15C2311yescharacteristic
114D4×D15—232no—
115C2×D60—24no—
116C2×D60C2314yes—
117C2×C4×D15—24no—
118C2×C4×D15C2314yescomplemented
119C2×C5×#67—24no—
120C2×C5×#67—42no—
121C2×C5×#67C2314yescomplemented
122C2×C5×#67C2314yescomplemented
123C22×C5×Dic3—42no—
124C22×C5×Dic3C2311yescharacteristic
125C22×C5×Dic3C2311yescharacteristic
126C22×C5×Dic3C2311yescharacteristic
127C22×C5×Dic3C2314yescomplemented
128C2×C3×C22⋊D5—24no—
129C2×C3×C22⋊D5—42no—
130C2×C3×C22⋊D5C2314yescomplemented
131C2×C3×C22⋊D5C2314yescomplemented
132C22×C3×Dic5—42no—
133C22×C3×Dic5C2311yescharacteristic
134C22×C3×Dic5C2311yescharacteristic
135C22×C3×Dic5C2311yescharacteristic
136C22×C3×Dic5C2314yescomplemented
137#6790—232no—
138C2×#1203—24no—
139C2×#1203—42no—
140C2×#1203C2314yes—
141C2×#1203C2314yescomplemented
142C2×#1202—24no—
143C2×#1202—42no—
144C2×#1202C2314yes—
145C2×#1202C2314yescomplemented
146C2×#1200—24no—
147C2×#1200C2314yescomplemented
148C5×#217C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yescomplemented
150C5×Dic3⋊C4C2314yescomplemented
151C3×C22⋊Dic5C2314yescomplemented
152C3×#685C2314yescomplemented
153C3×#683C2314yescomplemented
154Dic3⋊Dic5C2314yescomplemented
155#6668C2314yescomplemented
156#6667C2314yescomplemented
157#6667C2314yescomplemented
158#6667C2314yescomplemented
159#6667C2314yescomplemented
160#6667C2314yescomplemented
161#6667C2314yescomplemented
162(C2×D3)⋊Dic5C2314yescomplemented
163#6665C2314yescomplemented
164C22×D3×D4—51no—
165C22×D3×D4—51no—
166C2×C3×#121—51no—
167C2×#939—51no—
168C2×#939D511yescharacteristic, complemented
169C2×#937—51no—
170C2×#937—51no—
171C2×#930—51no—
172C22×(C2×D3)⋊C4—51no—
173#5605—516no—
174C2×#894—51no—
175C2×#894—51no—
176C2×#883—51no—
177C2×#883—51no—
178C2×#882—51no—
179C2×#882—51no—
180C24×D5—31no—
181C24×D5—31no—
182C24×D5—31no—
183C22×C5×D4—31no—
184C22×C5×D4—31no—
185C22×C5×D4C2×D311yescharacteristic, complemented
186C23×C4×C5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5—31no—
190C22×C22⋊D5—31no—
191C22×C22⋊D5C2×D311yescharacteristic, complemented
192C22×C22⋊D5C2×D311yescharacteristic, complemented
193C23×Dic5C2×D311yescharacteristic, complemented
194C2×D4×D5—38no—
195C2×D4×D5—38no—
196C2×D4×D5—68no—
197C2×D4×D5—68no—
198C22×D20—31no—
199C22×D20—31no—
200C22×D20—31no—
201C22×C4×D5—31no—
202C22×C4×D5—31no—
203C5×#121—38no—
204C2×C5×C4⋊C4—31no—
205C2×C5×C22⋊C4—31no—
206C2×C5×C22⋊C4—31no—
207C2×C22⋊Dic5—31no—
208C2×C22⋊Dic5C2×D311yescharacteristic, complemented
209#4085—38no—
210#4085C2×D318yescomplemented
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—31no—
220C2×#685—31no—
221C2×#685—38no—
222C2×#685C2×D311yescharacteristic, complemented
223C2×C4⋊Dic5—31no—
224C2×#683—31no—
225C2×#683C2×D311yescharacteristic, complemented
226#4040—38no—
227#4040—38no—
228#4029—38no—
229#4029—38no—
230#4028—38no—
231#4028—38no—
232C2×#534—151noSylow
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5—22no—
237C23×C3×C5—22no—
238C23×C3×C5C2×D414yes—
239C23×C3×C5C2412yes—
240C23×C3×C5C2412yes—
241C23×C3×C5C2411yescharacteristic
242C22×D15—22no—
243C22×D15—22no—
244C22×D15—22no—
245C22×D15—22no—
246C22×D15—22no—
247C22×D15—22no—
248C22×D15—22no—
249C22×D15—28no—
250C22×D15—416no—
251C22×D15—44no—
252C22×D15—44no—
253C22×D15—44no—
254C22×D15—44no—
255C22×D15—416no—
256C22×D15C2×D414yes—
257C22×D15C2×D414yes—
258C22×D15C2×D4116yescomplemented
259C22×D15C2412yes—
260C22×D15C2412yes—
261C22×D15C2412yes—
262C22×C5×D3—22no—
263C22×C5×D3—22no—
264C22×C5×D3—22no—
265C22×C5×D3C2412yes—
266C22×C3×D5—22no—
267C22×C3×D5—22no—
268C22×C3×D5—22no—
269C22×C3×D5C2412yes—
270C2×D3×D5—28no—
271C2×D3×D5—44no—
272C2×D3×D5—44no—
273C2×D3×D5—416no—
274C3×C5×D4—28no—
275C2×C3×C4×C5—22no—
276C2×C3×C4×C5C2412yes—
277#1220—28no—
278#1220—28no—
279C2×Dic15—22no—
280C2×Dic15C2412yes—
281D60—28no—
282C4×D15—28no—
283C5×#67—28no—
284C5×#67—44no—
285C2×C5×Dic3—22no—
286C2×C5×Dic3—22no—
287C2×C5×Dic3—22no—
288C2×C5×Dic3—44no—
289C2×C5×Dic3C2412yes—
290C2×C5×Dic3C2412yes—
291C2×C5×Dic3C2412yes—
292C3×C22⋊D5—28no—
293C3×C22⋊D5—44no—
294C2×C3×Dic5—22no—
295C2×C3×Dic5—22no—
296C2×C3×Dic5—22no—
297C2×C3×Dic5—44no—
298C2×C3×Dic5C2412yes—
299C2×C3×Dic5C2412yes—
300C2×C3×Dic5C2412yes—
301#1203—28no—
302#1203—44no—
303#1202—28no—
304#1202—44no—
305#1200—28no—
306C24×D3—51no—
307C24×D3—51no—
308C24×D3—51no—
309C22×C3×D4—51no—
310C22×C3×D4—51no—
311C22×C3×D4C2×D511yescharacteristic, complemented
312C23×C3×C4—51no—
313C22×#67—51no—
314C22×#67—51no—
315C22×#67—51no—
316C22×#67—51no—
317C22×#67C2×D511yescharacteristic, complemented
318C22×#67C2×D511yescharacteristic, complemented
319C23×Dic3C2×D511yescharacteristic, complemented
320C2×D3×D4—58no—
321C2×D3×D4—58no—
322C2×D3×D4—108no—
323C2×D3×D4—108no—
324C22×D12—51no—
325C22×D12—51no—
326C22×D12—51no—
327C22×C4×D3—51no—
328C22×C4×D3—51no—
329C3×#121—58no—
330C2×C3×C4⋊C4—51no—
331C2×C3×C22⋊C4—51no—
332C2×C3×C22⋊C4—51no—
333C2×#217—51no—
334C2×#217C2×D511yescharacteristic, complemented
335#939—58no—
336#939C2×D518yescomplemented
337#937—58no—
338#937—58no—
339#930—58no—
340C2×(C2×D3)⋊C4—51no—
341C2×(C2×D3)⋊C4—51no—
342C2×(C2×D3)⋊C4—51no—
343C2×(C2×D3)⋊C4—51no—
344C2×(C2×D3)⋊C4—51no—
345C2×(C2×D3)⋊C4—51no—
346C2×(C2×D3)⋊C4—51no—
347C2×(C2×D3)⋊C4—58no—
348C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
349C2×C4⋊Dic3—51no—
350C2×Dic3⋊C4—51no—
351C2×Dic3⋊C4C2×D511yescharacteristic, complemented
352#894—58no—
353#894—58no—
354#883—58no—
355#883—58no—
356#882—58no—
357#882—58no—
358C24×C5—31no—
359C24×C5C22×D311yescharacteristic
360C24×C5C22×D311yescharacteristic
361C23×D5—31no—
362C23×D5—31no—
363C23×D5—38no—
364C23×D5—34no—
365C23×D5—31no—
366C23×D5—34no—
367C23×D5—34no—
368C23×D5—64no—
369C23×D5—64no—
370C23×D5—122no—
371C23×D5—122no—
372C23×D5—122no—
373C23×D5—122no—
374C23×D5—122no—
375C23×D5—122no—
376C23×D5C22×D311yescharacteristic
377C2×C5×D4—24no—
378C2×C5×D4—34no—
379C2×C5×D4—34no—
380C2×C5×D4—64no—
381C2×C5×D4—122no—
382C2×C5×D4C22×D314yescomplemented
383C22×C4×C5—31no—
384C22×C4×C5—31no—
385C22×C4×C5—31no—
386C22×C4×C5—34no—
387C22×C4×C5—122no—
388C22×C4×C5C22×D311yescharacteristic
389C2×C22⋊D5—24no—
390C2×C22⋊D5—34no—
391C2×C22⋊D5—34no—
392C2×C22⋊D5—34no—
393C2×C22⋊D5—34no—
394C2×C22⋊D5—42no—
395C2×C22⋊D5—64no—
396C2×C22⋊D5—64no—
397C2×C22⋊D5—64no—
398C2×C22⋊D5—122no—
399C2×C22⋊D5C22×D314yescomplemented
400C2×C22⋊D5C22×D314yescomplemented
401C22×Dic5—31no—
402C22×Dic5—42no—
403C22×Dic5C22×D311yescharacteristic
404C22×Dic5C22×D311yescharacteristic
405C22×Dic5C22×D311yescharacteristic
406C22×Dic5C22×D314yescomplemented
407D4×D5—632no—
408D4×D5—632no—
409C2×D20—34no—
410C2×D20—34no—
411C2×D20—34no—
412C2×D20—64no—
413C2×D20—64no—
414C2×D20—122no—
415C2×C4×D5—34no—
416C2×C4×D5—34no—
417C2×C4×D5—64no—
418C2×C4×D5—64no—
419C5×C4⋊C4—34no—
420C5×C22⋊C4—34no—
421C5×C22⋊C4—34no—
422C22⋊Dic5—34no—
423C22⋊Dic5C22×D314yescomplemented
424#685—34no—
425#685—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685—34no—
430#685—34no—
431#685C22×D314yescomplemented
432C4⋊Dic5—34no—
433#683—34no—
434#683C22×D314yescomplemented
435C23×D4—151no—
436C23×D4—151no—
437#534—1516no—
438C2×#123—151no—
439C2×#123—151no—
440C2×#123—151no—
441C2×#123—151no—
442C2×#121—31no—
443C2×#121—51no—
444C2×#121—151no—
445C2×#121—151no—
446C2×#120—151no—
447C2×#120—151no—
448C2×#120—151no—
449C2×#120—151no—
450C22×C22⋊C4—151no—
451C22×C3×C5—28no—
452C22×C3×C5—22no—
453C22×C3×C5—22no—
454C22×C3×C5—22no—
455C22×C3×C5—22no—
456C22×C3×C5—22no—
457C22×C3×C5—44no—
458C22×C3×C5C22×D414yes—
459C22×C3×C5C22×D412yes—
460C22×C3×C5H(5,𝔽2)12yes—
461C22×C3×C5H(5,𝔽2)12yes—
462C22×C3×C5C2511yescharacteristic
463C2×D15—28no—
464C2×D15—28no—
465C2×D15—22no—
466C2×D15—22no—
467C2×D15—22no—
468C2×D15—22no—
469C2×D15—22no—
470C2×D15—22no—
471C2×D15—22no—
472C2×D15—416no—
473C2×D15—416no—
474C2×D15—44no—
475C2×D15C22×D414yes—
476C2×D15C22×D414yes—
477C2×C5×D3—22no—
478C2×C5×D3—22no—
479C2×C5×D3—22no—
480C2×C5×D3—44no—
481C2×C3×D5—22no—
482C2×C3×D5—22no—
483C2×C3×D5—22no—
484C2×C3×D5—44no—
485D3×D5—416no—
486C3×C4×C5—22no—
487Dic15—22no—
488C3×Dic5—22no—
489C3×Dic5—22no—
490C3×Dic5—22no—
491C5×Dic3—22no—
492C5×Dic3—22no—
493C5×Dic3—22no—
494C24×C3—51no—
495C24×C3C22×D511yescharacteristic
496C24×C3C22×D511yescharacteristic
497C23×D3—51no—
498C23×D3—51no—
499C23×D3—58no—
500C23×D3—54no—
501C23×D3—51no—
502C23×D3—54no—
503C23×D3—54no—
504C23×D3—104no—
505C23×D3—104no—
506C23×D3—202no—
507C23×D3—202no—
508C23×D3—202no—
509C23×D3—202no—
510C23×D3—202no—
511C23×D3—202no—
512C23×D3C22×D511yescharacteristic
513C2×C3×D4—24no—
514C2×C3×D4—54no—
515C2×C3×D4—54no—
516C2×C3×D4—104no—
517C2×C3×D4—202no—
518C2×C3×D4C22×D514yescomplemented
519C22×C3×C4—51no—
520C22×C3×C4—51no—
521C22×C3×C4—51no—
522C22×C3×C4—54no—
523C22×C3×C4—202no—
524C22×C3×C4C22×D511yescharacteristic
525C2×#67—24no—
526C2×#67—42no—
527C2×#67—54no—
528C2×#67—54no—
529C2×#67—54no—
530C2×#67—54no—
531C2×#67—104no—
532C2×#67—104no—
533C2×#67—104no—
534C2×#67—202no—
535C2×#67C22×D514yescomplemented
536C2×#67C22×D514yescomplemented
537C22×Dic3—42no—
538C22×Dic3—51no—
539C22×Dic3C22×D511yescharacteristic
540C22×Dic3C22×D511yescharacteristic
541C22×Dic3C22×D511yescharacteristic
542C22×Dic3C22×D514yescomplemented
543D3×D4—1032no—
544D3×D4—1032no—
545C2×D12—54no—
546C2×D12—54no—
547C2×D12—54no—
548C2×D12—104no—
549C2×D12—104no—
550C2×D12—202no—
551C2×C4×D3—54no—
552C2×C4×D3—54no—
553C2×C4×D3—104no—
554C2×C4×D3—104no—
555C3×C4⋊C4—54no—
556C3×C22⋊C4—54no—
557C3×C22⋊C4—54no—
558#217—54no—
559#217C22×D514yescomplemented
560(C2×D3)⋊C4—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
568C4⋊Dic3—54no—
569Dic3⋊C4—54no—
570Dic3⋊C4C22×D514yescomplemented
571C23×C5—22no—
572C23×C5—22no—
573C23×C5—22no—
574C23×C5—22no—
575C23×C5—22no—
576C23×C5—32no—
577C23×C5—62no—
578C23×C5—62no—
579C23×C5—62no—
580C23×C5D3×D414yes—
581C23×C5C23×D312yes—
582C23×C5C23×D312yes—
583C23×C5C23×D311yescharacteristic
584C22×D5—22no—
585C22×D5—22no—
586C22×D5—22no—
587C22×D5—34no—
588C22×D5—34no—
589C22×D5—32no—
590C22×D5—32no—
591C22×D5—316no—
592C22×D5—32no—
593C22×D5—68no—
594C22×D5—68no—
595C22×D5—62no—
596C22×D5—62no—
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—124no—
608C22×D5—124no—
609C22×D5—1216no—
610C22×D5—1216no—
611C22×D5C23×D312yes—
612C5×D4—28no—
613C5×D4—68no—
614C5×D4—124no—
615C2×C4×C5—22no—
616C2×C4×C5—32no—
617C2×C4×C5—32no—
618C2×C4×C5—32no—
619C2×C4×C5—62no—
620C2×C4×C5—62no—
621C2×C4×C5—62no—
622C2×C4×C5—124no—
623C2×C4×C5C23×D312yes—
624C22⋊D5—28no—
625C22⋊D5—44no—
626C22⋊D5—68no—
627C22⋊D5—68no—
628C22⋊D5—68no—
629C22⋊D5—124no—
630C2×Dic5—22no—
631C2×Dic5—22no—
632C2×Dic5—22no—
633C2×Dic5—32no—
634C2×Dic5—44no—
635C2×Dic5—62no—
636C2×Dic5C23×D312yes—
637C2×Dic5C23×D312yes—
638C2×Dic5C23×D312yes—
639D20—68no—
640D20—68no—
641D20—124no—
642C4×D5—68no—
643C4×D5—68no—
644C25—151no—
645C25—151no—
646C25—151no—
647C22×D4—31no—
648C22×D4—31no—
649C22×D4—51no—
650C22×D4—51no—
651C22×D4—151no—
652C22×D4—151no—
653C22×D4—151no—
654C22×D4—151no—
655C22×D4—158no—
656C22×D4—151no—
657C22×D4—151no—
658C22×D4—158no—
659C22×D4—151no—
660C22×D4—308no—
661C22×D4—308no—
662C22×D4D3×D511yescharacteristic, complemented
663C23×C4—31no—
664C23×C4—51no—
665C23×C4—151no—
666C23×C4—151no—
667#123—158no—
668#123—158no—
669#123—158no—
670#123—158no—
671#121—38no—
672#121—58no—
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⋊C4—151no—
683C2×C22⋊C4—31no—
684C2×C22⋊C4—31no—
685C2×C22⋊C4—51no—
686C2×C22⋊C4—51no—
687C2×C22⋊C4—151no—
688C2×C22⋊C4—151no—
689C2×C22⋊C4—151no—
690C2×C22⋊C4—151no—
691C2×C22⋊C4—158no—
692C2×C22⋊C4—151no—
693C2×C22⋊C4—151no—
694C2×C22⋊C4—151no—
695C2×C22⋊C4—151no—
696C2×C3×C5—24no—
697C2×C3×C5—42no—
698C2×C3×C5#53414yescomplemented
699C2×C3×C5C23×D411yescharacteristic
700C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
701C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
702D15—24no—
703D15—24no—
704D15—42no—
705C3×D5—42no—
706C5×D3—42no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—22no—
710C23×C3—22no—
711C23×C3—22no—
712C23×C3—52no—
713C23×C3—102no—
714C23×C3—102no—
715C23×C3—102no—
716C23×C3D4×D514yes—
717C23×C3C23×D512yes—
718C23×C3C23×D512yes—
719C23×C3C23×D511yescharacteristic
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—22no—
723C22×D3—54no—
724C22×D3—54no—
725C22×D3—52no—
726C22×D3—52no—
727C22×D3—516no—
728C22×D3—52no—
729C22×D3—108no—
730C22×D3—108no—
731C22×D3—102no—
732C22×D3—102no—
733C22×D3—102no—
734C22×D3—102no—
735C22×D3—102no—
736C22×D3—102no—
737C22×D3—102no—
738C22×D3—204no—
739C22×D3—204no—
740C22×D3—2016no—
741C22×D3—2016no—
742C22×D3—204no—
743C22×D3—204no—
744C22×D3—204no—
745C22×D3—204no—
746C22×D3—2016no—
747C22×D3C23×D512yes—
748C3×D4—28no—
749C3×D4—108no—
750C3×D4—204no—
751C2×C3×C4—22no—
752C2×C3×C4—52no—
753C2×C3×C4—52no—
754C2×C3×C4—52no—
755C2×C3×C4—102no—
756C2×C3×C4—102no—
757C2×C3×C4—102no—
758C2×C3×C4—204no—
759C2×C3×C4C23×D512yes—
760#67—28no—
761#67—44no—
762#67—108no—
763#67—108no—
764#67—108no—
765#67—204no—
766C2×Dic3—22no—
767C2×Dic3—22no—
768C2×Dic3—22no—
769C2×Dic3—44no—
770C2×Dic3—52no—
771C2×Dic3—102no—
772C2×Dic3C23×D512yes—
773C2×Dic3C23×D512yes—
774C2×Dic3C23×D512yes—
775D12—108no—
776D12—108no—
777D12—204no—
778C4×D3—108no—
779C4×D3—108no—
780C22×C5—22no—
781C22×C5—22no—
782C22×C5—28no—
783C22×C5—22no—
784C22×C5—22no—
785C22×C5—22no—
786C22×C5—44no—
787C22×C5—62no—
788C22×C5—62no—
789C22×C5—62no—
790C22×C5—124no—
791C22×C5C2×D3×D414yes—
792C22×C5C2×D3×D412yes—
793C22×C5#100412yes—
794C22×C5#100912yes—
795C22×C5C24×D311yescharacteristic
796C2×D5—22no—
797C2×D5—22no—
798C2×D5—22no—
799C2×D5—34no—
800C2×D5—34no—
801C2×D5—44no—
802C2×D5—62no—
803C2×D5—62no—
804C2×D5—62no—
805C2×D5—62no—
806C2×D5—68no—
807C2×D5—68no—
808C2×D5—62no—
809C2×D5—62no—
810C2×D5—62no—
811C2×D5—1216no—
812C2×D5—1216no—
813C2×D5—1216no—
814C2×D5—124no—
815C4×C5—22no—
816C4×C5—62no—
817C4×C5—62no—
818C4×C5—62no—
819Dic5—22no—
820Dic5—22no—
821Dic5—22no—
822Dic5—62no—
823C24—31no—
824C24—51no—
825C24—154no—
826C24—151no—
827C24—151no—
828C24—158no—
829C24—154no—
830C24—151no—
831C24—154no—
832C24—304no—
833C24—304no—
834C24—602no—
835C24—602no—
836C24—602no—
837C24—602no—
838C24—602no—
839C24—602no—
840C24C2×D3×D511yescharacteristic
841C24C2×D3×D511yescharacteristic
842C2×D4—24no—
843C2×D4—34no—
844C2×D4—34no—
845C2×D4—54no—
846C2×D4—54no—
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—202no—
858C2×D4—304no—
859C2×D4—304no—
860C2×D4—304no—
861C2×D4—3032no—
862C2×D4—3032no—
863C2×D4—304no—
864C2×D4—304no—
865C2×D4—602no—
866C2×D4—602no—
867C2×D4C2×D3×D514yescomplemented
868C22×C4—31no—
869C22×C4—31no—
870C22×C4—31no—
871C22×C4—34no—
872C22×C4—51no—
873C22×C4—51no—
874C22×C4—51no—
875C22×C4—54no—
876C22×C4—122no—
877C22×C4—154no—
878C22×C4—151no—
879C22×C4—154no—
880C22×C4—202no—
881C22×C4—304no—
882C22×C4—304no—
883C22×C4C2×D3×D511yescharacteristic
884C4⋊C4—34no—
885C4⋊C4—54no—
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⋊C4—154no—
900C3×C5C2×#53411yescharacteristic, complemented, Hall
901C22×C3—28no—
902C22×C3—22no—
903C22×C3—22no—
904C22×C3—22no—
905C22×C3—22no—
906C22×C3—22no—
907C22×C3—44no—
908C22×C3—102no—
909C22×C3—102no—
910C22×C3—102no—
911C22×C3—204no—
912C22×C3C2×D4×D514yes—
913C22×C3C2×D4×D512yes—
914C22×C3#414412yes—
915C22×C3#414912yes—
916C22×C3C24×D511yescharacteristic
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—44no—
921C2×D3—54no—
922C2×D3—54no—
923C2×D3—108no—
924C2×D3—108no—
925C2×D3—102no—
926C2×D3—102no—
927C2×D3—102no—
928C2×D3—102no—
929C2×D3—102no—
930C2×D3—102no—
931C2×D3—102no—
932C2×D3—2016no—
933C2×D3—2016no—
934C2×D3—2016no—
935C2×D3—204no—
936C3×C4—22no—
937C3×C4—102no—
938C3×C4—102no—
939C3×C4—102no—
940Dic3—22no—
941Dic3—22no—
942Dic3—22no—
943Dic3—102no—
944C2×C5—24no—
945C2×C5—42no—
946C2×C5—122no—
947C2×C5#560514yescomplemented
948C2×C5C22×D3×D411yescharacteristic
949C2×C5C2×#100411yescharacteristic
950C2×C5C2×#100911yescharacteristic
951D5—42no—
952D5—64no—
953D5—64no—
954D5—122no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—32no—
961C23—52no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—102no—
966C23—102no—
967C23—102no—
968C23—154no—
969C23—154no—
970C23—152no—
971C23—152no—
972C23—1516no—
973C23—152no—
974C23—308no—
975C23—308no—
976C23—302no—
977C23—302no—
978C23—302no—
979C23—302no—
980C23—302no—
981C23—302no—
982C23—302no—
983C23—6016no—
984C23—604no—
985C23—604no—
986C23—604no—
987C23—604no—
988C23—6016no—
989C23—604no—
990C23—604no—
991C23—6016no—
992C23#679014yes—
993C23C22×D3×D512yes—
994C23C22×D3×D512yes—
995C23C22×D3×D511yescharacteristic
996D4—28no—
997D4—68no—
998D4—108no—
999D4—124no—
1000D4—204no—
1001D4—308no—
1002D4—308no—
1003D4—308no—
1004D4—308no—
1005D4—308no—
1006D4—604no—
1007D4—604no—
1008C2×C4—22no—
1009C2×C4—32no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—52no—
1013C2×C4—52no—
1014C2×C4—52no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—102no—
1019C2×C4—102no—
1020C2×C4—102no—
1021C2×C4—124no—
1022C2×C4—152no—
1023C2×C4—204no—
1024C2×C4—308no—
1025C2×C4—308no—
1026C2×C4—302no—
1027C2×C4C22×D3×D512yes—
1028C2×C3—24no—
1029C2×C3—42no—
1030C2×C3—202no—
1031C2×C3#6593914yescomplemented
1032C2×C3C22×D4×D511yescharacteristic
1033C2×C3C2×#414411yescharacteristic
1034C2×C3C2×#414911yescharacteristic
1035D3—42no—
1036D3—104no—
1037D3—104no—
1038D3—202no—
1039C5C2×#560511yescharacteristic, complemented, Sylow
1040C22—28no—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—44no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—102no—
1051C22—102no—
1052C22—102no—
1053C22—124no—
1054C22—154no—
1055C22—154no—
1056C22—204no—
1057C22—308no—
1058C22—308no—
1059C22—302no—
1060C22—302no—
1061C22—302no—
1062C22—302no—
1063C22—302no—
1064C22—302no—
1065C22—302no—
1066C22—6016no—
1067C22—6016no—
1068C22—6016no—
1069C22—604no—
1070C22#9202612yes—
1071C22#9202712yes—
1072C22C2×#679014yes—
1073C22C2×#679012yes—
1074C22C23×D3×D511yescharacteristic
1075C4—22no—
1076C4—62no—
1077C4—62no—
1078C4—62no—
1079C4—102no—
1080C4—102no—
1081C4—102no—
1082C4—302no—
1083C3C2×#6593911yescharacteristic, complemented, Sylow
1084C2—24no—
1085C2—42no—
1086C2—122no—
1087C2—202no—
1088C2—304no—
1089C2—304no—
1090C2—602no—
1091C2#1175507314yesdirect product factor
1092C2C2×#9202611yescharacteristic
1093C2C2×#9202711yescharacteristic
1094C2C22×#679011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#534
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D4×D15C2semidirect
2. C22×#6790C2semidirect
3. C2×C5×#939C2semidirect
4. C2×C3×#4085C2semidirect
5. C2×#91577C2semidirect
6. C2×#91573C2semidirect
7. C2×#91572C2semidirect
8. C2×#91569C2semidirect
9. C2×#91566C2semidirect
10. C2×#91562C2semidirect
11. C22×#6667C2semidirect
12. #11755073C2direct (N × H)
13. C2×#91476C2semidirect
14. C2×#91433C2semidirect
15. C2×#91355C2semidirect
16. C2×#91354C2semidirect
19. C24×D15C22semidirect
20. C23×D3×D5C22semidirect
21. C22×C3×C5×D4C22semidirect
23. C22×#1220C22semidirect
25. C2×D4×D15C22semidirect
27. C22×C4×D15C22semidirect
28. C22×C5×#67C22semidirect
29. C22×C5×#67C22semidirect
30. C23×C5×Dic3C22semidirect
31. C22×C3×C22⋊D5C22semidirect
32. C22×C3×C22⋊D5C22semidirect
33. C23×C3×Dic5C22semidirect
35. C2×#6790C22semidirect
37. C22×#1203C22semidirect
39. C22×#1202C22semidirect
40. C22×#1200C22semidirect
41. C2×C5×#217C22semidirect
42. C5×#939C22semidirect
43. C2×C5×(C2×D3)⋊C4C22semidirect
44. C2×C5×Dic3⋊C4C22semidirect
45. C2×C3×C22⋊Dic5C22semidirect
46. C3×#4085C22semidirect
47. C2×C3×#685C22semidirect
48. C2×C3×#683C22semidirect
49. #91577C22semidirect
50. #91573C22semidirect
51. #91572C22semidirect
52. #91569C22semidirect
53. #91566C22semidirect
54. #91562C22semidirect
55. C2×Dic3⋊Dic5C22semidirect
56. C2×#6668C22semidirect
57. C2×#6667C22semidirect
58. C2×#6667C22semidirect
59. C2×#6667C22semidirect
60. C2×#6667C22semidirect
61. C2×#6667C22semidirect
62. C2×#6667C22semidirect
63. C2×#6667C22semidirect
64. C2×(C2×D3)⋊Dic5C22semidirect
65. C2×#6665C22semidirect
66. #91476C22semidirect
67. #91433C22semidirect
68. #91355C22semidirect
69. #91354C22semidirect
75. C2×#4085D3semidirect
94. C23×D15D4semidirect
99. C23×D15C23semidirect
105. C22×D3×D5C23semidirect
107. C2×C3×C5×D4C23semidirect
112. C2×#1220C23semidirect
118. C2×C4×D15C23semidirect
121. C2×C5×#67C23semidirect
122. C2×C5×#67C23semidirect
127. C22×C5×Dic3C23semidirect
130. C2×C3×C22⋊D5C23semidirect
131. C2×C3×C22⋊D5C23semidirect
136. C22×C3×Dic5C23semidirect
141. C2×#1203C23semidirect
145. C2×#1202C23semidirect
147. C2×#1200C23semidirect
148. C5×#217C23semidirect
149. C5×(C2×D3)⋊C4C23semidirect
150. C5×Dic3⋊C4C23semidirect
151. C3×C22⋊Dic5C23semidirect
152. C3×#685C23semidirect
153. C3×#683C23semidirect
154. Dic3⋊Dic5C23semidirect
155. #6668C23semidirect
156. #6667C23semidirect
157. #6667C23semidirect
158. #6667C23semidirect
159. #6667C23semidirect
160. #6667C23semidirect
161. #6667C23semidirect
162. (C2×D3)⋊Dic5C23semidirect
163. #6665C23semidirect
168. C2×#939D5semidirect
185. C22×C5×D4C2×D3semidirect
191. C22×C22⋊D5C2×D3semidirect
192. C22×C22⋊D5C2×D3semidirect
193. C23×Dic5C2×D3semidirect
208. C2×C22⋊Dic5C2×D3semidirect
210. #4085C2×D3semidirect
222. C2×#685C2×D3semidirect
225. C2×#683C2×D3semidirect
258. C22×D15C2×D4semidirect
311. C22×C3×D4C2×D5semidirect
317. C22×#67C2×D5semidirect
318. C22×#67C2×D5semidirect
319. C23×Dic3C2×D5semidirect
334. C2×#217C2×D5semidirect
336. #939C2×D5semidirect
348. C2×(C2×D3)⋊C4C2×D5semidirect
351. C2×Dic3⋊C4C2×D5semidirect
382. C2×C5×D4C22×D3semidirect
399. C2×C22⋊D5C22×D3semidirect
400. C2×C22⋊D5C22×D3semidirect
406. C22×Dic5C22×D3semidirect
423. C22⋊Dic5C22×D3semidirect
431. #685C22×D3semidirect
434. #683C22×D3semidirect
518. C2×C3×D4C22×D5semidirect
535. C2×#67C22×D5semidirect
536. C2×#67C22×D5semidirect
542. C22×Dic3C22×D5semidirect
559. #217C22×D5semidirect
567. (C2×D3)⋊C4C22×D5semidirect
570. Dic3⋊C4C22×D5semidirect
662. C22×D4D3×D5semidirect
698. C2×C3×C5#534semidirect
867. C2×D4C2×D3×D5semidirect
900. C3×C5C2×#534semidirect
947. C2×C5#5605semidirect
1031. C2×C3#65939semidirect
1039. C5C2×#5605semidirect
1083. C3C2×#65939semidirect
1091. C2#11755073direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D152
C22×#67902
C2×C5×#9392
C2×C3×#40852
C2×#915772
C2×#915732
C2×#915722
C2×#915692
C2×#915662
C2×#915622
C22×#66672
#117550732
C2×#914762
C2×#914332
C2×#913552
C2×#913542
C2×#659393
C2×#56055