Finite Group Databasebeta

← C2×#11755023 #14480326

Subgroups — C2×#11755023 #14480326

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×#6790C211yesmaximal, characteristic, complemented
2C22×D5×#67C211yesmaximal, characteristic, complemented
3C2×#91826C211yesmaximal, characteristic, complemented
4C2×C5×#938C211yesmaximal, characteristic, complemented
5C2×C3×#4083C211yesmaximal, characteristic, complemented
6C2×#91572C211yesmaximal, characteristic, complemented
7C2×#91565C211yesmaximal, characteristic, complemented
8C2×#91564C211yesmaximal, characteristic, complemented
9C2×#91562C211yesmaximal, characteristic, complemented
10C2×#91558C211yesmaximal, characteristic, complemented
11C2×#91548C211yesmaximal, characteristic, complemented
12#11755023C2116yesmaximal, direct product factor
13C2×D3×#685C211yesmaximal, characteristic, complemented
14C2×#91454C211yesmaximal, characteristic, complemented
15C2×#91413C211yesmaximal, characteristic, complemented
16C2×#91356C211yesmaximal, characteristic, complemented
17C2×#65939—31nomaximal, Hall
18C24×D15C2211yescharacteristic, complemented
19C24×C3×D5C2211yescharacteristic, complemented
20C23×D3×D5C2211yescharacteristic
21C22×C3×C5×D4C2211yescharacteristic, complemented
22C22×#1220C2211yescharacteristic
23C22×#1220C2211yescharacteristic, complemented
24C22×C5×#67C2211yescharacteristic, complemented
25C22×C5×#67C2211yescharacteristic, complemented
26C22×C4×C5×D3C2211yescharacteristic, complemented
27C22×C3×C22⋊D5C2211yescharacteristic
28C22×C3×C22⋊D5C2211yescharacteristic, complemented
29C2×#6790—28no—
30C2×#6790C2218yescomplemented
31C2×D5×#67—28no—
32C2×D5×#67C2218yescomplemented
33C22×#1203C2211yescharacteristic, complemented
34C22×#1202C2211yescharacteristic
35C22×#1202C2211yescharacteristic
36C22×#1202C2211yescharacteristic, complemented
37C22×#1201C2211yescharacteristic, complemented
38C22×#1200C2211yescharacteristic, complemented
39C22×D3×Dic5C2211yescharacteristic, complemented
40C22×D5×Dic3C2211yescharacteristic, complemented
41C2×#6719C2211yescharacteristic, complemented
42#91826C2218yescomplemented
43C2×#6714C2211yescharacteristic, complemented
44C2×#6714C2211yescharacteristic, complemented
45C2×C5×#217C2211yescharacteristic, complemented
46C2×C5×#217C2211yescharacteristic, complemented
47C5×#938C2218yescomplemented
48C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
49C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
50C3×#4083C2218yescomplemented
51C2×C3×#685C2211yescharacteristic, complemented
52C2×C3×#685C2211yescharacteristic, complemented
53#91572C2218yescomplemented
54#91565C2218yescomplemented
55#91564C2218yescomplemented
56#91562C2218yescomplemented
57#91558C2218yescomplemented
58#91548C2218yescomplemented
59C2×Dic3⋊Dic5C2211yescharacteristic, complemented
60C2×#6669C2211yescharacteristic, complemented
61C2×#6668C2211yescharacteristic, complemented
62C2×#6667C2211yescharacteristic, complemented
63C2×#6667C2211yescharacteristic, complemented
64C2×#6665C2211yescharacteristic, complemented
65C2×#6665C2211yescharacteristic, complemented
66D3×#685C2218yescomplemented
67#91454C2218yescomplemented
68#91413C2218yescomplemented
69#91356C2218yescomplemented
70C2×#5589—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×D4×D5—31no—
73C2×C5×#121—31no—
74C2×#4085—31no—
75C2×#4085—31no—
76C2×#4083—31no—
77C2×#4083D311yescharacteristic, complemented
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×D15C2311yescharacteristic
93C23×D15C2311yescharacteristic
94C23×D15C2314yescomplemented
95C23×C5×D3C2311yescharacteristic
96C23×C3×D5—24no—
97C23×C3×D5—42no—
98C23×C3×D5—42no—
99C23×C3×D5C2311yescharacteristic
100C23×C3×D5C2311yescharacteristic
101C23×C3×D5C2314yescomplemented
102C22×D3×D5—42no—
103C22×D3×D5—42no—
104C22×D3×D5D418yescomplemented
105C22×D3×D5C2314yes—
106C2×C3×C5×D4—42no—
107C2×C3×C5×D4C2314yescomplemented
108C22×C3×C4×C5C2311yescharacteristic
109C2×#1220—24no—
110C2×#1220—42no—
111C2×#1220C2314yes—
112C2×#1220C2314yescomplemented
113C22×Dic15C2311yescharacteristic
114C22×Dic15C2311yescharacteristic
115C2×C5×#67—24no—
116C2×C5×#67—24no—
117C2×C5×#67C2314yescomplemented
118C2×C5×#67C2314yescomplemented
119C22×C5×Dic3C2311yescharacteristic
120C22×C5×Dic3C2311yescharacteristic
121C22×C5×Dic3C2311yescharacteristic
122C2×C4×C5×D3—42no—
123C2×C4×C5×D3C2314yescomplemented
124C2×C3×C22⋊D5—24no—
125C2×C3×C22⋊D5—42no—
126C2×C3×C22⋊D5C2314yes—
127C2×C3×C22⋊D5C2314yescomplemented
128C22×C3×Dic5C2311yescharacteristic
129C22×C3×Dic5C2311yescharacteristic
130#6790—232no—
131D5×#67—232no—
132C2×#1203—24no—
133C2×#1203C2314yescomplemented
134C2×#1202—24no—
135C2×#1202—24no—
136C2×#1202—42no—
137C2×#1202C2314yes—
138C2×#1202C2314yes—
139C2×#1202C2314yescomplemented
140C2×#1201—24no—
141C2×#1201C2314yescomplemented
142C2×#1200—24no—
143C2×#1200C2314yescomplemented
144C2×D3×Dic5—42no—
145C2×D3×Dic5C2314yescomplemented
146C2×D5×Dic3—24no—
147C2×D5×Dic3C2314yescomplemented
148#6719C2314yescomplemented
149#6714C2314yescomplemented
150#6714C2314yescomplemented
151C5×#217C2314yescomplemented
152C5×#217C2314yescomplemented
153C5×C4⋊Dic3C2314yescomplemented
154C3×C22⋊Dic5C2314yescomplemented
155C3×#685C2314yescomplemented
156C3×#685C2314yescomplemented
157Dic3⋊Dic5C2314yescomplemented
158#6669C2314yescomplemented
159#6668C2314yescomplemented
160#6667C2314yescomplemented
161#6667C2314yescomplemented
162#6665C2314yescomplemented
163#6665C2314yescomplemented
164C23×#67—51no—
165C22×D3×D4—51no—
166C2×C3×#120—51no—
167C2×#953—51no—
168C2×#938—51no—
169C2×#938D511yescharacteristic, complemented
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×#883—51no—
179C2×D3×C22⋊C4—51no—
180C24×D5—31no—
181C24×D5—31no—
182C24×D5C2×D311yescharacteristic, complemented
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
192C22×C22⋊D5C2×D311yescharacteristic, complemented
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×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#4085—38no—
211#4083—38no—
212#4083C2×D318yescomplemented
213#4076—38no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685—31no—
218C2×#685—31no—
219C2×#685—31no—
220C2×#685—38no—
221C2×#685C2×D311yescharacteristic, complemented
222C2×#685C2×D311yescharacteristic, complemented
223C2×C4⋊Dic5—31no—
224C2×#683—31no—
225C2×#683—31no—
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×C5—22no—
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—28no—
248C22×D15—44no—
249C22×D15—44no—
250C22×D15—416no—
251C22×D15C2×D414yes—
252C22×D15C2412yes—
253C22×D15C2412yes—
254C22×C5×D3—22no—
255C22×C5×D3—22no—
256C22×C5×D3C2×D414yes—
257C22×C5×D3C2412yes—
258C22×C3×D5—22no—
259C22×C3×D5—22no—
260C22×C3×D5—22no—
261C22×C3×D5—22no—
262C22×C3×D5—22no—
263C22×C3×D5—28no—
264C22×C3×D5—44no—
265C22×C3×D5—44no—
266C22×C3×D5—416no—
267C22×C3×D5C2×D414yes—
268C22×C3×D5C2412yes—
269C22×C3×D5C2412yes—
270C2×D3×D5—416no—
271C2×D3×D5—44no—
272C2×D3×D5—44no—
273C2×D3×D5C2×D4116yescomplemented
274C3×C5×D4—44no—
275C2×C3×C4×C5—22no—
276C2×C3×C4×C5C2412yes—
277#1220—28no—
278#1220—44no—
279C2×Dic15—22no—
280C2×Dic15—22no—
281C2×Dic15C2412yes—
282C2×Dic15C2412yes—
283C5×#67—28no—
284C5×#67—28no—
285C2×C5×Dic3—22no—
286C2×C5×Dic3—22no—
287C2×C5×Dic3—22no—
288C2×C5×Dic3C2412yes—
289C2×C5×Dic3C2412yes—
290C2×C5×Dic3C2412yes—
291C4×C5×D3—44no—
292C3×C22⋊D5—28no—
293C3×C22⋊D5—44no—
294C2×C3×Dic5—22no—
295C2×C3×Dic5—22no—
296C2×C3×Dic5C2412yes—
297C2×C3×Dic5C2412yes—
298#1203—28no—
299#1202—28no—
300#1202—28no—
301#1202—44no—
302#1201—28no—
303#1200—28no—
304D3×Dic5—44no—
305D5×Dic3—28no—
306C25×C3—51no—
307C24×D3—51no—
308C24×D3—51no—
309C22×C3×D4—51no—
310C22×C3×D4—51no—
311C22×C3×D4C2×D511yescharacteristic, complemented
312C22×#67—51no—
313C22×#67—51no—
314C22×#67—51no—
315C22×#67—58no—
316C22×#67—51no—
317C22×#67—51no—
318C22×#67—51no—
319C22×#67—108no—
320C22×#67C2×D511yescharacteristic, complemented
321C22×#67C2×D511yescharacteristic, complemented
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⋊C4—51no—
333#953—58no—
334C2×#217—51no—
335C2×#217—51no—
336C2×#217—51no—
337C2×#217C2×D511yescharacteristic, complemented
338C2×#217C2×D511yescharacteristic, complemented
339#938—58no—
340#938C2×D518yescomplemented
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)⋊C4—51no—
348C2×C4⋊Dic3—51no—
349C2×C4⋊Dic3C2×D511yescharacteristic, complemented
350C2×Dic3⋊C4—51no—
351C2×Dic3⋊C4—51no—
352#886—58no—
353#884—58no—
354#884—58no—
355#883—58no—
356#883—58no—
357D3×C22⋊C4—58no—
358C24×C5—31no—
359C24×C5C22×D311yescharacteristic
360C24×C5C22×D311yescharacteristic
361C23×D5—24no—
362C23×D5—31no—
363C23×D5—38no—
364C23×D5—34no—
365C23×D5—31no—
366C23×D5—34no—
367C23×D5—42no—
368C23×D5—42no—
369C23×D5—64no—
370C23×D5—122no—
371C23×D5—122no—
372C23×D5—122no—
373C23×D5—122no—
374C23×D5C22×D311yescharacteristic
375C23×D5C22×D311yescharacteristic
376C23×D5C22×D314yescomplemented
377C2×C5×D4—34no—
378C2×C5×D4—34no—
379C2×C5×D4—42no—
380C2×C5×D4—64no—
381C2×C5×D4—64no—
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×D314yes—
400C2×C22⋊D5C22×D314yescomplemented
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—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#685C22×D314yescomplemented
431#685C22×D314yescomplemented
432C4⋊Dic5—34no—
433#683—34no—
434#683—34no—
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—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—22no—
455C22×C3×C5—22no—
456C22×C3×C5—22no—
457C22×C3×C5—44no—
458C22×C3×C5—44no—
459C22×C3×C5C22×D412yes—
460C22×C3×C5H(5,𝔽2)12yes—
461C22×C3×C5H(5,𝔽2)12yes—
462C22×C3×C5C2511yescharacteristic
463C2×D15—28no—
464C2×D15—22no—
465C2×D15—22no—
466C2×D15—22no—
467C2×D15—22no—
468C2×D15—22no—
469C2×D15—416no—
470C2×D15—44no—
471C2×D15C22×D414yes—
472C2×C5×D3—28no—
473C2×C5×D3—22no—
474C2×C5×D3—22no—
475C2×C5×D3C22×D414yes—
476C2×C3×D5—28no—
477C2×C3×D5—22no—
478C2×C3×D5—22no—
479C2×C3×D5—22no—
480C2×C3×D5—22no—
481C2×C3×D5—22no—
482C2×C3×D5—416no—
483C2×C3×D5—44no—
484C2×C3×D5C22×D414yes—
485D3×D5—416no—
486C3×C4×C5—22no—
487Dic15—22no—
488Dic15—22no—
489C3×Dic5—22no—
490C3×Dic5—22no—
491C5×Dic3—22no—
492C5×Dic3—22no—
493C5×Dic3—22no—
494C24×C3—51no—
495C24×C3—51no—
496C24×C3—54no—
497C24×C3—104no—
498C24×C3—202no—
499C24×C3—202no—
500C24×C3C22×D511yescharacteristic
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—42no—
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×C4C22×D511yescharacteristic
522C2×#67—24no—
523C2×#67—24no—
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—1032no—
533C2×#67—104no—
534C2×#67—104no—
535C2×#67—202no—
536C2×#67—202no—
537C2×#67C22×D514yescomplemented
538C2×#67C22×D514yescomplemented
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—42no—
550C2×C4×D3—54no—
551C2×C4×D3—54no—
552C2×C4×D3—104no—
553C2×C4×D3—202no—
554C2×C4×D3C22×D514yescomplemented
555C3×C22⋊C4—54no—
556C3×C22⋊C4—54no—
557C3×C22⋊C4—54no—
558#217—54no—
559#217—54no—
560#217—54no—
561#217C22×D514yescomplemented
562#217C22×D514yescomplemented
563(C2×D3)⋊C4—54no—
564(C2×D3)⋊C4—54no—
565(C2×D3)⋊C4—54no—
566(C2×D3)⋊C4—54no—
567C4⋊Dic3—54no—
568C4⋊Dic3C22×D514yescomplemented
569Dic3⋊C4—54no—
570Dic3⋊C4—54no—
571C23×C5—22no—
572C23×C5—22no—
573C23×C5—22no—
574C23×C5—22no—
575C23×C5—22no—
576C23×C5—22no—
577C23×C5—34no—
578C23×C5—32no—
579C23×C5—62no—
580C23×C5—62no—
581C23×C5C23×D312yes—
582C23×C5C23×D312yes—
583C23×C5C23×D311yescharacteristic
584C22×D5—22no—
585C22×D5—22no—
586C22×D5—22no—
587C22×D5—22no—
588C22×D5—22no—
589C22×D5—28no—
590C22×D5—34no—
591C22×D5—32no—
592C22×D5—316no—
593C22×D5—32no—
594C22×D5—44no—
595C22×D5—44no—
596C22×D5—416no—
597C22×D5—68no—
598C22×D5—62no—
599C22×D5—62no—
600C22×D5—62no—
601C22×D5—62no—
602C22×D5—62no—
603C22×D5—124no—
604C22×D5—124no—
605C22×D5—1216no—
606C22×D5—124no—
607C22×D5—124no—
608C22×D5—1216no—
609C22×D5D3×D414yes—
610C22×D5C23×D312yes—
611C22×D5C23×D312yes—
612C5×D4—44no—
613C5×D4—68no—
614C5×D4—68no—
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—32no—
633C2×Dic5—32no—
634C2×Dic5—62no—
635C2×Dic5—62no—
636C2×Dic5—124no—
637C2×Dic5C23×D312yes—
638C2×Dic5C23×D312yes—
639D20—68no—
640D20—68no—
641D20—124no—
642C4×D5—68no—
643C4×D5—68no—
644C25—51no—
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—158no—
657C22×D4—151no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—308no—
661C22×D4—308no—
662C22×D4D3×D511yescharacteristic, complemented
663C23×C4—31no—
664C23×C4—151no—
665C23×C4—151no—
666C23×C4—151no—
667#123—158no—
668#123—158no—
669#123—158no—
670#123—158no—
671#121—38no—
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—151no—
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—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—42no—
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—42no—
704C3×D5—24no—
705C3×D5—42no—
706C5×D3—24no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—22no—
710C23×C3—22no—
711C23×C3—22no—
712C23×C3—22no—
713C23×C3—54no—
714C23×C3—52no—
715C23×C3—52no—
716C23×C3—108no—
717C23×C3—102no—
718C23×C3—102no—
719C23×C3—102no—
720C23×C3—102no—
721C23×C3—102no—
722C23×C3—204no—
723C23×C3—204no—
724C23×C3—2016no—
725C23×C3C23×D512yes—
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—108no—
735C22×D3—102no—
736C22×D3—102no—
737C22×D3—102no—
738C22×D3—102no—
739C22×D3—102no—
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—44no—
749C3×D4—108no—
750C3×D4—204no—
751C2×C3×C4—22no—
752C2×C3×C4—52no—
753C2×C3×C4—52no—
754C2×C3×C4—102no—
755C2×C3×C4—102no—
756C2×C3×C4C23×D512yes—
757#67—28no—
758#67—28no—
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—44no—
778C4×D3—108no—
779C4×D3—204no—
780C22×C5—22no—
781C22×C5—22no—
782C22×C5—22no—
783C22×C5—22no—
784C22×C5—22no—
785C22×C5—22no—
786C22×C5—34no—
787C22×C5—44no—
788C22×C5—44no—
789C22×C5—62no—
790C22×C5—62no—
791C22×C5—68no—
792C22×C5C2×D3×D412yes—
793C22×C5#100412yes—
794C22×C5#100412yes—
795C22×C5C24×D311yescharacteristic
796C2×D5—22no—
797C2×D5—22no—
798C2×D5—28no—
799C2×D5—22no—
800C2×D5—22no—
801C2×D5—22no—
802C2×D5—34no—
803C2×D5—416no—
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—62no—
817C4×C5—62no—
818C4×C5—62no—
819Dic5—22no—
820Dic5—22no—
821Dic5—62no—
822Dic5—62no—
823C24—31no—
824C24—51no—
825C24—51no—
826C24—54no—
827C24—104no—
828C24—154no—
829C24—158no—
830C24—151no—
831C24—151no—
832C24—154no—
833C24—202no—
834C24—202no—
835C24—304no—
836C24—602no—
837C24—602no—
838C24—602no—
839C24—602no—
840C24C2×D3×D511yescharacteristic
841C24C2×D3×D511yescharacteristic
842C2×D4—34no—
843C2×D4—34no—
844C2×D4—42no—
845C2×D4—54no—
846C2×D4—54no—
847C2×D4—64no—
848C2×D4—64no—
849C2×D4—104no—
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—122no—
875C22×C4—154no—
876C22×C4—154no—
877C22×C4—154no—
878C22×C4—151no—
879C22×C4—151no—
880C22×C4—304no—
881C22×C4—304no—
882C22×C4—602no—
883C22×C4C2×D3×D511yescharacteristic
884C4⋊C4—34no—
885C4⋊C4—154no—
886C4⋊C4—154no—
887C4⋊C4—154no—
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—22no—
902C22×C3—22no—
903C22×C3—22no—
904C22×C3—22no—
905C22×C3—22no—
906C22×C3—22no—
907C22×C3—44no—
908C22×C3—44no—
909C22×C3—54no—
910C22×C3—108no—
911C22×C3—102no—
912C22×C3—102no—
913C22×C3—102no—
914C22×C3—102no—
915C22×C3—102no—
916C22×C3—2016no—
917C22×C3—204no—
918C22×C3C2×D4×D512yes—
919C22×C3#414412yes—
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—102no—
938C3×C4—102no—
939Dic3—22no—
940Dic3—22no—
941Dic3—22no—
942Dic3—102no—
943Dic3—102no—
944C2×C5—42no—
945C2×C5—42no—
946C2×C5—64no—
947C2×C5#558914yescomplemented
948C2×C5C22×D3×D411yescharacteristic
949C2×C5C2×#100411yescharacteristic
950C2×C5C2×#100411yescharacteristic
951D5—24no—
952D5—42no—
953D5—64no—
954D5—122no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—34no—
962C23—32no—
963C23—54no—
964C23—52no—
965C23—52no—
966C23—62no—
967C23—62no—
968C23—108no—
969C23—102no—
970C23—102no—
971C23—102no—
972C23—102no—
973C23—102no—
974C23—1516no—
975C23—154no—
976C23—152no—
977C23—152no—
978C23—204no—
979C23—204no—
980C23—2016no—
981C23—308no—
982C23—302no—
983C23—302no—
984C23—302no—
985C23—302no—
986C23—302no—
987C23—604no—
988C23—604no—
989C23—6016no—
990C23—6016no—
991C23—604no—
992C23—604no—
993C23C22×D3×D512yes—
994C23C22×D3×D512yes—
995C23C22×D3×D511yescharacteristic
996D4—44no—
997D4—68no—
998D4—68no—
999D4—108no—
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—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—102no—
1018C2×C4—102no—
1019C2×C4—124no—
1020C2×C4—152no—
1021C2×C4—152no—
1022C2×C4—308no—
1023C2×C4—308no—
1024C2×C4—302no—
1025C2×C4—302no—
1026C2×C4—604no—
1027C2×C4C22×D3×D512yes—
1028C2×C3—42no—
1029C2×C3—42no—
1030C2×C3—104no—
1031C2×C3—202no—
1032C2×C3#6593914yescomplemented
1033C2×C3C22×D4×D511yescharacteristic
1034C2×C3C2×#414411yescharacteristic
1035C2×C3C2×#414911yescharacteristic
1036D3—24no—
1037D3—104no—
1038D3—202no—
1039C5C2×#558911yescharacteristic, complemented, Sylow
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—34no—
1047C22—44no—
1048C22—44no—
1049C22—54no—
1050C22—68no—
1051C22—62no—
1052C22—62no—
1053C22—108no—
1054C22—102no—
1055C22—102no—
1056C22—102no—
1057C22—102no—
1058C22—102no—
1059C22—154no—
1060C22—2016no—
1061C22—204no—
1062C22—308no—
1063C22—302no—
1064C22—302no—
1065C22—302no—
1066C22—302no—
1067C22—302no—
1068C22—6016no—
1069C22—6016no—
1070C22—604no—
1071C22D3×D4×D512yes—
1072C22#9202612yes—
1073C22#9204912yes—
1074C22C23×D3×D511yescharacteristic
1075C4—22no—
1076C4—62no—
1077C4—62no—
1078C4—62no—
1079C4—102no—
1080C4—102no—
1081C4—302no—
1082C4—302no—
1083C3C2×#6593911yescharacteristic, complemented, Sylow
1084C2—42no—
1085C2—42no—
1086C2—64no—
1087C2—104no—
1088C2—202no—
1089C2—304no—
1090C2—602no—
1091C2#1175502314yesdirect product factor
1092C2C2×D3×D4×D511yescharacteristic
1093C2C2×#9202611yescharacteristic
1094C2C2×#9204911yescharacteristic
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×#6790C2semidirect
2. C22×D5×#67C2semidirect
3. C2×#91826C2semidirect
4. C2×C5×#938C2semidirect
5. C2×C3×#4083C2semidirect
6. C2×#91572C2semidirect
7. C2×#91565C2semidirect
8. C2×#91564C2semidirect
9. C2×#91562C2semidirect
10. C2×#91558C2semidirect
11. C2×#91548C2semidirect
12. #11755023C2direct (N × H)
13. C2×D3×#685C2semidirect
14. C2×#91454C2semidirect
15. C2×#91413C2semidirect
16. C2×#91356C2semidirect
18. C24×D15C22semidirect
19. C24×C3×D5C22semidirect
21. C22×C3×C5×D4C22semidirect
23. C22×#1220C22semidirect
24. C22×C5×#67C22semidirect
25. C22×C5×#67C22semidirect
26. C22×C4×C5×D3C22semidirect
28. C22×C3×C22⋊D5C22semidirect
30. C2×#6790C22semidirect
32. C2×D5×#67C22semidirect
33. C22×#1203C22semidirect
36. C22×#1202C22semidirect
37. C22×#1201C22semidirect
38. C22×#1200C22semidirect
39. C22×D3×Dic5C22semidirect
40. C22×D5×Dic3C22semidirect
41. C2×#6719C22semidirect
42. #91826C22semidirect
43. C2×#6714C22semidirect
44. C2×#6714C22semidirect
45. C2×C5×#217C22semidirect
46. C2×C5×#217C22semidirect
47. C5×#938C22semidirect
48. C2×C5×C4⋊Dic3C22semidirect
49. C2×C3×C22⋊Dic5C22semidirect
50. C3×#4083C22semidirect
51. C2×C3×#685C22semidirect
52. C2×C3×#685C22semidirect
53. #91572C22semidirect
54. #91565C22semidirect
55. #91564C22semidirect
56. #91562C22semidirect
57. #91558C22semidirect
58. #91548C22semidirect
59. C2×Dic3⋊Dic5C22semidirect
60. C2×#6669C22semidirect
61. C2×#6668C22semidirect
62. C2×#6667C22semidirect
63. C2×#6667C22semidirect
64. C2×#6665C22semidirect
65. C2×#6665C22semidirect
66. D3×#685C22semidirect
67. #91454C22semidirect
68. #91413C22semidirect
69. #91356C22semidirect
77. C2×#4083D3semidirect
94. C23×D15C23semidirect
101. C23×C3×D5C23semidirect
104. C22×D3×D5D4semidirect
107. C2×C3×C5×D4C23semidirect
112. C2×#1220C23semidirect
117. C2×C5×#67C23semidirect
118. C2×C5×#67C23semidirect
123. C2×C4×C5×D3C23semidirect
127. C2×C3×C22⋊D5C23semidirect
133. C2×#1203C23semidirect
139. C2×#1202C23semidirect
141. C2×#1201C23semidirect
143. C2×#1200C23semidirect
145. C2×D3×Dic5C23semidirect
147. C2×D5×Dic3C23semidirect
148. #6719C23semidirect
149. #6714C23semidirect
150. #6714C23semidirect
151. C5×#217C23semidirect
152. C5×#217C23semidirect
153. C5×C4⋊Dic3C23semidirect
154. C3×C22⋊Dic5C23semidirect
155. C3×#685C23semidirect
156. C3×#685C23semidirect
157. Dic3⋊Dic5C23semidirect
158. #6669C23semidirect
159. #6668C23semidirect
160. #6667C23semidirect
161. #6667C23semidirect
162. #6665C23semidirect
163. #6665C23semidirect
169. C2×#938D5semidirect
182. C24×D5C2×D3semidirect
185. C22×C5×D4C2×D3semidirect
192. C22×C22⋊D5C2×D3semidirect
208. C2×C22⋊Dic5C2×D3semidirect
212. #4083C2×D3semidirect
221. C2×#685C2×D3semidirect
222. C2×#685C2×D3semidirect
273. C2×D3×D5C2×D4semidirect
311. C22×C3×D4C2×D5semidirect
320. C22×#67C2×D5semidirect
321. C22×#67C2×D5semidirect
328. C22×C4×D3C2×D5semidirect
337. C2×#217C2×D5semidirect
338. C2×#217C2×D5semidirect
340. #938C2×D5semidirect
349. C2×C4⋊Dic3C2×D5semidirect
376. C23×D5C22×D3semidirect
382. C2×C5×D4C22×D3semidirect
400. C2×C22⋊D5C22×D3semidirect
423. C22⋊Dic5C22×D3semidirect
430. #685C22×D3semidirect
431. #685C22×D3semidirect
518. C2×C3×D4C22×D5semidirect
537. C2×#67C22×D5semidirect
538. C2×#67C22×D5semidirect
554. C2×C4×D3C22×D5semidirect
561. #217C22×D5semidirect
562. #217C22×D5semidirect
568. C4⋊Dic3C22×D5semidirect
662. C22×D4D3×D5semidirect
698. C2×C3×C5#534semidirect
867. C2×D4C2×D3×D5semidirect
900. C3×C5C2×#534semidirect
947. C2×C5#5589semidirect
1032. C2×C3#65939semidirect
1039. C5C2×#5589semidirect
1083. C3C2×#65939semidirect
1091. C2#11755023direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67902
C22×D5×#672
C2×#918262
C2×C5×#9382
C2×C3×#40832
C2×#915722
C2×#915652
C2×#915642
C2×#915622
C2×#915582
C2×#915482
#117550232
C2×D3×#6852
C2×#914542
C2×#914132
C2×#913562
C2×#659393
C2×#55895