Finite Group Databasebeta

← C2×#11753215 #14480330

Subgroups — C2×#11753215 #14480330

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×D12C211yesmaximal, characteristic, complemented
3C2×#91771C211yesmaximal, characteristic, complemented
4C2×C5×#884C211yesmaximal, characteristic, complemented
5C2×C3×#4029C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×#91573C211yesmaximal, characteristic, complemented
8C2×#91558C211yesmaximal, characteristic, complemented
9C2×#91476C211yesmaximal, characteristic, complemented
10C2×D3×#685C211yesmaximal, characteristic, complemented
11C2×#91460C211yesmaximal, characteristic, complemented
12C2×#91438C211yesmaximal, characteristic, complemented
13C2×#91433C211yesmaximal, characteristic, complemented
14C2×#91416C211yesmaximal, characteristic, complemented
15C2×#91348C211yesmaximal, characteristic, complemented
16#11753215C2116yesmaximal, direct product factor
17C2×#65939—31nomaximal, Hall
18C24×D15C2211yescharacteristic, complemented
19C23×D3×D5C2211yescharacteristic
20C23×D3×D5C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic, complemented
22C22×D60C2211yescharacteristic
23C22×D60C2211yescharacteristic, complemented
24C22×C5×#67C2211yescharacteristic, complemented
25C22×C5×#67C2211yescharacteristic, complemented
26C22×C5×D12C2211yescharacteristic, complemented
27C22×C4×C5×D3C2211yescharacteristic, complemented
28C22×C3×C22⋊D5C2211yescharacteristic
29C22×C3×C4×D5C2211yescharacteristic, complemented
30C2×#6790—28no—
31C2×#6790C2218yescomplemented
32C22×#1203C2211yescharacteristic
33C22×#1203C2211yescharacteristic, complemented
34C22×#1203C2211yescharacteristic, complemented
35C22×#1203C2211yescharacteristic, complemented
36C22×#1202C2211yescharacteristic
37C22×#1200C2211yescharacteristic, complemented
38C22×D3×Dic5C2211yescharacteristic, complemented
39C2×D5×D12—28no—
40C2×D5×D12C2218yescomplemented
41C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6714C2211yescharacteristic, complemented
44#91771C2218yescomplemented
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
47C5×#884C2218yescomplemented
48C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
49C2×C3×#685C2211yescharacteristic, complemented
50C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
51C2×C3×#683C2211yescharacteristic, complemented
52C3×#4029C2218yescomplemented
53#91577C2218yescomplemented
54#91573C2218yescomplemented
55#91558C2218yescomplemented
56C2×#6669C2211yescharacteristic, complemented
57C2×#6667C2211yescharacteristic, complemented
58C2×#6667C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic, complemented
60C2×#6667C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
62C2×#6665C2211yescharacteristic, complemented
63#91476C2218yescomplemented
64D3×#685C2218yescomplemented
65#91460C2218yescomplemented
66#91438C2218yescomplemented
67#91433C2218yescomplemented
68#91416C2218yescomplemented
69#91348C2218yescomplemented
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×#4040—31no—
83C2×#4029—31no—
84C2×#4029D311yescharacteristic, complemented
85C2×#4028—31no—
86C2×#4028—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15—24no—
89C23×D15—42no—
90C23×D15—42no—
91C23×D15C2311yescharacteristic
92C23×D15C2311yescharacteristic
93C23×D15C2311yescharacteristic
94C23×D15C2314yescomplemented
95C23×C5×D3C2311yescharacteristic
96C23×C5×D3C2311yescharacteristic
97C23×C3×D5C2311yescharacteristic
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—42no—
109C2×#1220C2314yescomplemented
110C22×Dic15C2311yescharacteristic
111C2×D60—24no—
112C2×D60—42no—
113C2×D60C2314yes—
114C2×D60C2314yescomplemented
115C2×C5×#67—24no—
116C2×C5×#67—42no—
117C2×C5×#67C2314yescomplemented
118C2×C5×#67C2314yescomplemented
119C22×C5×Dic3C2311yescharacteristic
120C22×C5×Dic3C2311yescharacteristic
121C2×C5×D12—24no—
122C2×C5×D12C2314yescomplemented
123C2×C4×C5×D3—42no—
124C2×C4×C5×D3C2314yescomplemented
125C2×C3×C22⋊D5—24no—
126C2×C3×C22⋊D5C2314yes—
127C22×C3×Dic5C2311yescharacteristic
128C22×C3×Dic5C2311yescharacteristic
129C22×C3×Dic5C2311yescharacteristic
130C2×C3×C4×D5—24no—
131C2×C3×C4×D5C2314yescomplemented
132#6790—232no—
133C2×#1203—24no—
134C2×#1203—24no—
135C2×#1203—24no—
136C2×#1203—42no—
137C2×#1203C2314yes—
138C2×#1203C2314yescomplemented
139C2×#1203C2314yescomplemented
140C2×#1203C2314yescomplemented
141C2×#1202—24no—
142C2×#1202C2314yes—
143C2×#1200—24no—
144C2×#1200C2314yescomplemented
145C2×D3×Dic5—42no—
146C2×D3×Dic5C2314yescomplemented
147D5×D12—232no—
148C3×C5×C22⋊C4C2314yescomplemented
149#6714C2314yescomplemented
150#6714C2314yescomplemented
151C5×(C2×D3)⋊C4C2314yescomplemented
152C5×Dic3⋊C4C2314yescomplemented
153C3×C22⋊Dic5C2314yescomplemented
154C3×#685C2314yescomplemented
155C3×C4⋊Dic5C2314yescomplemented
156C3×#683C2314yescomplemented
157#6669C2314yescomplemented
158#6667C2314yescomplemented
159#6667C2314yescomplemented
160#6667C2314yescomplemented
161#6667C2314yescomplemented
162(C2×D3)⋊Dic5C2314yescomplemented
163#6665C2314yescomplemented
164C22×D3×D4—51no—
165C23×D12—51no—
166C2×C3×#123—51no—
167C2×#937—51no—
168C2×#929—51no—
169#5653—516no—
170C2×#895—51no—
171C2×#895—51no—
172C2×#894—51no—
173C2×#894—51no—
174C2×#884—51no—
175C2×#884D511yescharacteristic, complemented
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⋊D5C2×D311yescharacteristic
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×D5C2×D311yescharacteristic, complemented
203C5×#121—38no—
204C2×C5×C4⋊C4—31no—
205C2×C5×C22⋊C4—31no—
206C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
207C2×C22⋊Dic5—31no—
208C2×C22⋊Dic5C2×D311yescharacteristic, complemented
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—31no—
220C2×#685—31no—
221C2×#685—38no—
222C2×#685C2×D311yescharacteristic, complemented
223C2×C4⋊Dic5C2×D311yescharacteristic, complemented
224C2×#683—31no—
225C2×#683C2×D311yescharacteristic, complemented
226#4040—38no—
227#4040—38no—
228#4029—38no—
229#4029C2×D318yescomplemented
230#4028—38no—
231#4028—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×D15—22no—
244C22×D15—22no—
245C22×D15—22no—
246C22×D15—28no—
247C22×D15—44no—
248C22×D15—44no—
249C22×D15—416no—
250C22×D15C2×D414yes—
251C22×D15C2412yes—
252C22×D15C2412yes—
253C22×D15C2412yes—
254C22×C5×D3—22no—
255C22×C5×D3—22no—
256C22×C5×D3—22no—
257C22×C5×D3—22no—
258C22×C5×D3—22no—
259C22×C5×D3C2×D414yes—
260C22×C5×D3C2412yes—
261C22×C5×D3C2412yes—
262C22×C3×D5—22no—
263C22×C3×D5—22no—
264C22×C3×D5C2×D414yes—
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—44no—
279C2×Dic15—22no—
280C2×Dic15C2412yes—
281D60—28no—
282D60—44no—
283C5×#67—28no—
284C5×#67—44no—
285C2×C5×Dic3—22no—
286C2×C5×Dic3—22no—
287C2×C5×Dic3C2412yes—
288C2×C5×Dic3C2412yes—
289C5×D12—28no—
290C4×C5×D3—44no—
291C3×C22⋊D5—28no—
292C2×C3×Dic5—22no—
293C2×C3×Dic5—22no—
294C2×C3×Dic5—22no—
295C2×C3×Dic5C2412yes—
296C2×C3×Dic5C2412yes—
297C2×C3×Dic5C2412yes—
298C3×C4×D5—28no—
299#1203—28no—
300#1203—28no—
301#1203—28no—
302#1203—44no—
303#1202—28no—
304#1200—28no—
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×#67C2×D511yescharacteristic, complemented
314C22×#67C2×D511yescharacteristic, complemented
315C2×D3×D4—58no—
316C2×D3×D4—108no—
317C22×D12—51no—
318C22×D12—51no—
319C22×D12—51no—
320C22×D12—51no—
321C22×D12—51no—
322C22×D12—51no—
323C22×D12—58no—
324C22×D12—108no—
325C22×D12C2×D511yescharacteristic, 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⋊C4—51no—
332C2×C3×C22⋊C4—51no—
333C2×C3×C22⋊C4—51no—
334C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
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)⋊C4—51no—
345C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
346C2×Dic3⋊C4—51no—
347C2×Dic3⋊C4C2×D511yescharacteristic, complemented
348#895—58no—
349#895—58no—
350#894—58no—
351#894—58no—
352#884—58no—
353#884C2×D518yescomplemented
354#882—58no—
355#882—58no—
356#882—58no—
357D3×C22⋊C4—58no—
358C24×C5—31no—
359C24×C5—31no—
360C24×C5C22×D311yescharacteristic
361C23×D5—31no—
362C23×D5—38no—
363C23×D5—34no—
364C23×D5—31no—
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—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—31no—
385C22×C4×C5—34no—
386C22×C4×C5—122no—
387C22×C4×C5C22×D311yescharacteristic
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—34no—
395C2×C22⋊D5—64no—
396C2×C22⋊D5—64no—
397C2×C22⋊D5—64no—
398C2×C22⋊D5—122no—
399C2×C22⋊D5—122no—
400C2×C22⋊D5C22×D314yes—
401C22×Dic5—31no—
402C22×Dic5—34no—
403C22×Dic5—122no—
404C22×Dic5C22×D311yescharacteristic
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—24no—
416C2×C4×D5—34no—
417C2×C4×D5—64no—
418C2×C4×D5C22×D314yescomplemented
419C5×C4⋊C4—34no—
420C5×C22⋊C4—34no—
421C5×C22⋊C4C22×D314yescomplemented
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⋊Dic5C22×D314yescomplemented
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×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—22no—
466C2×D15—22no—
467C2×D15—22no—
468C2×D15—416no—
469C2×D15—44no—
470C2×D15—44no—
471C2×D15C22×D414yes—
472C2×C5×D3—28no—
473C2×C5×D3—22no—
474C2×C5×D3—22no—
475C2×C5×D3—22no—
476C2×C5×D3—22no—
477C2×C5×D3—22no—
478C2×C5×D3—44no—
479C2×C5×D3C22×D414yes—
480C2×C3×D5—28no—
481C2×C3×D5—22no—
482C2×C3×D5—22no—
483C2×C3×D5C22×D414yes—
484D3×D5—416no—
485D3×D5—416no—
486C3×C4×C5—22no—
487C3×C4×C5—22no—
488Dic15—22no—
489C3×Dic5—22no—
490C3×Dic5—22no—
491C3×Dic5—22no—
492C5×Dic3—22no—
493C5×Dic3—22no—
494C24×C3—51no—
495C24×C3C22×D511yescharacteristic
496C23×D3—51no—
497C23×D3—58no—
498C23×D3—54no—
499C23×D3—51no—
500C23×D3—51no—
501C23×D3—54no—
502C23×D3—54no—
503C23×D3—104no—
504C23×D3—104no—
505C23×D3—202no—
506C23×D3—202no—
507C23×D3—202no—
508C23×D3—202no—
509C23×D3—202no—
510C23×D3—202no—
511C23×D3C22×D511yescharacteristic
512C23×D3C22×D511yescharacteristic
513C2×C3×D4—54no—
514C2×C3×D4—104no—
515C22×C3×C4—51no—
516C22×C3×C4—51no—
517C22×C3×C4—51no—
518C22×C3×C4—54no—
519C22×C3×C4—104no—
520C22×C3×C4C22×D511yescharacteristic
521C22×C3×C4C22×D511yescharacteristic
522C2×#67—24no—
523C2×#67—42no—
524C2×#67—54no—
525C2×#67—54no—
526C2×#67—104no—
527C2×#67—202no—
528C2×#67C22×D514yescomplemented
529C2×#67C22×D514yescomplemented
530C22×Dic3—51no—
531C22×Dic3C22×D511yescharacteristic
532C22×Dic3C22×D511yescharacteristic
533D3×D4—1032no—
534C2×D12—24no—
535C2×D12—54no—
536C2×D12—54no—
537C2×D12—54no—
538C2×D12—54no—
539C2×D12—54no—
540C2×D12—54no—
541C2×D12—1032no—
542C2×D12—104no—
543C2×D12—104no—
544C2×D12—104no—
545C2×D12—104no—
546C2×D12—202no—
547C2×D12—202no—
548C2×D12C22×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⋊C4—54no—
557C3×C22⋊C4—54no—
558C3×C22⋊C4—54no—
559C3×C22⋊C4C22×D514yescomplemented
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)⋊C4—54no—
568(C2×D3)⋊C4C22×D514yescomplemented
569Dic3⋊C4—54no—
570Dic3⋊C4C22×D514yescomplemented
571C23×C5—22no—
572C23×C5—22no—
573C23×C5—22no—
574C23×C5—34no—
575C23×C5—32no—
576C23×C5—32no—
577C23×C5—62no—
578C23×C5—62no—
579C23×C5—62no—
580C23×C5—62no—
581C23×C5—62no—
582C23×C5C23×D312yes—
583C23×C5C23×D311yescharacteristic
584C22×D5—22no—
585C22×D5—22no—
586C22×D5—34no—
587C22×D5—32no—
588C22×D5—316no—
589C22×D5—32no—
590C22×D5—32no—
591C22×D5—68no—
592C22×D5—62no—
593C22×D5—62no—
594C22×D5—62no—
595C22×D5—62no—
596C22×D5—62no—
597C22×D5—62no—
598C22×D5—62no—
599C22×D5—62no—
600C22×D5—68no—
601C22×D5—1216no—
602C22×D5—124no—
603C22×D5—124no—
604C22×D5—124no—
605C22×D5—124no—
606C22×D5—1216no—
607C22×D5—124no—
608C22×D5—124no—
609C22×D5—1216no—
610C22×D5D3×D414yes—
611C22×D5C23×D312yes—
612C5×D4—68no—
613C5×D4—68no—
614C5×D4—124no—
615C2×C4×C5—22no—
616C2×C4×C5—22no—
617C2×C4×C5—32no—
618C2×C4×C5—32no—
619C2×C4×C5—62no—
620C2×C4×C5—62no—
621C2×C4×C5—124no—
622C2×C4×C5C23×D312yes—
623C2×C4×C5C23×D312yes—
624C22⋊D5—28no—
625C22⋊D5—68no—
626C22⋊D5—68no—
627C22⋊D5—68no—
628C22⋊D5—124no—
629C22⋊D5—124no—
630C2×Dic5—22no—
631C2×Dic5—22no—
632C2×Dic5—22no—
633C2×Dic5—32no—
634C2×Dic5—62no—
635C2×Dic5—124no—
636C2×Dic5C23×D312yes—
637C2×Dic5C23×D312yes—
638C2×Dic5C23×D312yes—
639D20—68no—
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—151no—
657C22×D4—158no—
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—31no—
680C2×C4⋊C4—51no—
681C2×C4⋊C4—51no—
682C2×C4⋊C4—151no—
683C2×C22⋊C4—31no—
684C2×C22⋊C4—51no—
685C2×C22⋊C4—51no—
686C2×C22⋊C4—158no—
687C2×C22⋊C4—151no—
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—
703D15—42no—
704C3×D5—24no—
705C5×D3—24no—
706C5×D3—42no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—22no—
710C23×C3—54no—
711C23×C3—52no—
712C23×C3—102no—
713C23×C3—102no—
714C23×C3C23×D512yes—
715C23×C3C23×D511yescharacteristic
716C22×D3—22no—
717C22×D3—22no—
718C22×D3—22no—
719C22×D3—22no—
720C22×D3—22no—
721C22×D3—54no—
722C22×D3—52no—
723C22×D3—516no—
724C22×D3—52no—
725C22×D3—52no—
726C22×D3—108no—
727C22×D3—108no—
728C22×D3—102no—
729C22×D3—102no—
730C22×D3—102no—
731C22×D3—102no—
732C22×D3—102no—
733C22×D3—102no—
734C22×D3—102no—
735C22×D3—102no—
736C22×D3—2016no—
737C22×D3—204no—
738C22×D3—204no—
739C22×D3—204no—
740C22×D3—204no—
741C22×D3—2016no—
742C22×D3—204no—
743C22×D3—204no—
744C22×D3—2016no—
745C22×D3D4×D514yes—
746C22×D3C23×D512yes—
747C22×D3C23×D512yes—
748C3×D4—108no—
749C2×C3×C4—22no—
750C2×C3×C4—22no—
751C2×C3×C4—52no—
752C2×C3×C4—52no—
753C2×C3×C4—52no—
754C2×C3×C4—108no—
755C2×C3×C4—102no—
756C2×C3×C4—102no—
757C2×C3×C4—102no—
758C2×C3×C4C23×D512yes—
759C2×C3×C4C23×D512yes—
760#67—28no—
761#67—44no—
762#67—108no—
763#67—204no—
764C2×Dic3—22no—
765C2×Dic3—22no—
766C2×Dic3—52no—
767C2×Dic3—102no—
768C2×Dic3C23×D512yes—
769C2×Dic3C23×D512yes—
770D12—28no—
771D12—108no—
772D12—108no—
773D12—108no—
774D12—108no—
775D12—204no—
776D12—204no—
777C4×D3—44no—
778C4×D3—108no—
779C4×D3—204no—
780C22×C5—22no—
781C22×C5—22no—
782C22×C5—22no—
783C22×C5—34no—
784C22×C5—44no—
785C22×C5—68no—
786C22×C5—62no—
787C22×C5—62no—
788C22×C5—62no—
789C22×C5—62no—
790C22×C5—62no—
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—34no—
800C2×D5—68no—
801C2×D5—62no—
802C2×D5—62no—
803C2×D5—62no—
804C2×D5—62no—
805C2×D5—62no—
806C2×D5—62no—
807C2×D5—62no—
808C2×D5—62no—
809C2×D5—1216no—
810C2×D5—1216no—
811C2×D5—1216no—
812C2×D5—124no—
813C2×D5—124no—
814C2×D5C2×D3×D414yes—
815C4×C5—22no—
816C4×C5—22no—
817C4×C5—62no—
818C4×C5—62no—
819Dic5—22no—
820Dic5—22no—
821Dic5—22no—
822Dic5—62no—
823C24—31no—
824C24—31no—
825C24—51no—
826C24—154no—
827C24—158no—
828C24—154no—
829C24—151no—
830C24—151no—
831C24—151no—
832C24—154no—
833C24—304no—
834C24—304no—
835C24—602no—
836C24—602no—
837C24—602no—
838C24—602no—
839C24—602no—
840C24—602no—
841C24C2×D3×D511yescharacteristic
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—304no—
860C2×D4—3032no—
861C2×D4—304no—
862C2×D4—304no—
863C2×D4—304no—
864C2×D4—3032no—
865C2×D4—602no—
866C2×D4—602no—
867C2×D4—602no—
868C22×C4—31no—
869C22×C4—31no—
870C22×C4—34no—
871C22×C4—51no—
872C22×C4—51no—
873C22×C4—51no—
874C22×C4—54no—
875C22×C4—104no—
876C22×C4—122no—
877C22×C4—154no—
878C22×C4—154no—
879C22×C4—151no—
880C22×C4—304no—
881C22×C4—602no—
882C22×C4C2×D3×D511yescharacteristic
883C22×C4C2×D3×D511yescharacteristic
884C4⋊C4—34no—
885C4⋊C4—54no—
886C4⋊C4—54no—
887C4⋊C4—154no—
888C22⋊C4—34no—
889C22⋊C4—54no—
890C22⋊C4—54no—
891C22⋊C4—154no—
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×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—44no—
920C2×D3—54no—
921C2×D3—108no—
922C2×D3—102no—
923C2×D3—102no—
924C2×D3—102no—
925C2×D3—102no—
926C2×D3—102no—
927C2×D3—102no—
928C2×D3—102no—
929C2×D3—102no—
930C2×D3—2016no—
931C2×D3—2016no—
932C2×D3—2016no—
933C2×D3—204no—
934C2×D3—204no—
935C2×D3C2×D4×D514yes—
936C3×C4—22no—
937C3×C4—22no—
938C3×C4—102no—
939C3×C4—102no—
940C3×C4—102no—
941Dic3—22no—
942Dic3—22no—
943Dic3—102no—
944C2×C5—42no—
945C2×C5—64no—
946C2×C5—122no—
947C2×C5#565314yescomplemented
948C2×C5C22×D3×D411yescharacteristic
949C2×C5C2×#100911yescharacteristic
950C2×C5C2×#100911yescharacteristic
951D5—24no—
952D5—64no—
953D5—122no—
954D5—122no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—34no—
959C23—32no—
960C23—32no—
961C23—54no—
962C23—52no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—62no—
968C23—102no—
969C23—102no—
970C23—1516no—
971C23—154no—
972C23—152no—
973C23—152no—
974C23—152no—
975C23—308no—
976C23—308no—
977C23—302no—
978C23—302no—
979C23—302no—
980C23—302no—
981C23—302no—
982C23—302no—
983C23—302no—
984C23—302no—
985C23—604no—
986C23—604no—
987C23—6016no—
988C23—604no—
989C23—604no—
990C23—6016no—
991C23—604no—
992C23—604no—
993C23—6016no—
994C23C22×D3×D512yes—
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—32no—
1011C2×C4—32no—
1012C2×C4—52no—
1013C2×C4—52no—
1014C2×C4—52no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—108no—
1018C2×C4—102no—
1019C2×C4—102no—
1020C2×C4—102no—
1021C2×C4—124no—
1022C2×C4—152no—
1023C2×C4—308no—
1024C2×C4—302no—
1025C2×C4—604no—
1026C2×C4C22×D3×D512yes—
1027C2×C4C22×D3×D512yes—
1028C2×C3—42no—
1029C2×C3—104no—
1030C2×C3#6593914yescomplemented
1031C2×C3C22×D4×D511yescharacteristic
1032C2×C3C2×#414411yescharacteristic
1033C2×C3C2×#414911yescharacteristic
1034D3—24no—
1035D3—42no—
1036D3—104no—
1037D3—202no—
1038D3—202no—
1039C5C2×#565311yescharacteristic, complemented, Sylow
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—34no—
1044C22—44no—
1045C22—54no—
1046C22—62no—
1047C22—62no—
1048C22—68no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—102no—
1053C22—102no—
1054C22—108no—
1055C22—124no—
1056C22—154no—
1057C22—302no—
1058C22—302no—
1059C22—308no—
1060C22—302no—
1061C22—302no—
1062C22—302no—
1063C22—302no—
1064C22—302no—
1065C22—302no—
1066C22—6016no—
1067C22—6016no—
1068C22—6016no—
1069C22—604no—
1070C22—604no—
1071C22#9201912yes—
1072C22D3×D4×D512yes—
1073C22#9202712yes—
1074C22C23×D3×D511yescharacteristic
1075C4—22no—
1076C4—22no—
1077C4—62no—
1078C4—62no—
1079C4—102no—
1080C4—102no—
1081C4—102no—
1082C4—302no—
1083C3C2×#6593911yescharacteristic, complemented, Sylow
1084C2—42no—
1085C2—64no—
1086C2—104no—
1087C2—122no—
1088C2—304no—
1089C2—602no—
1090C2—602no—
1091C2#1175321514yesdirect product factor
1092C2C2×#9201911yescharacteristic
1093C2C2×D3×D4×D511yescharacteristic
1094C2C2×#9202711yescharacteristic
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×#6790C2semidirect
2. C22×D5×D12C2semidirect
3. C2×#91771C2semidirect
4. C2×C5×#884C2semidirect
5. C2×C3×#4029C2semidirect
6. C2×#91577C2semidirect
7. C2×#91573C2semidirect
8. C2×#91558C2semidirect
9. C2×#91476C2semidirect
10. C2×D3×#685C2semidirect
11. C2×#91460C2semidirect
12. C2×#91438C2semidirect
13. C2×#91433C2semidirect
14. C2×#91416C2semidirect
15. C2×#91348C2semidirect
16. #11753215C2direct (N × H)
18. C24×D15C22semidirect
20. C23×D3×D5C22semidirect
21. C22×#1220C22semidirect
23. C22×D60C22semidirect
24. C22×C5×#67C22semidirect
25. C22×C5×#67C22semidirect
26. C22×C5×D12C22semidirect
27. C22×C4×C5×D3C22semidirect
29. C22×C3×C4×D5C22semidirect
31. C2×#6790C22semidirect
33. C22×#1203C22semidirect
34. C22×#1203C22semidirect
35. C22×#1203C22semidirect
37. C22×#1200C22semidirect
38. C22×D3×Dic5C22semidirect
40. C2×D5×D12C22semidirect
41. C2×C3×C5×C22⋊C4C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. #91771C22semidirect
45. C2×C5×(C2×D3)⋊C4C22semidirect
46. C2×C5×Dic3⋊C4C22semidirect
47. C5×#884C22semidirect
48. C2×C3×C22⋊Dic5C22semidirect
49. C2×C3×#685C22semidirect
50. C2×C3×C4⋊Dic5C22semidirect
51. C2×C3×#683C22semidirect
52. C3×#4029C22semidirect
53. #91577C22semidirect
54. #91573C22semidirect
55. #91558C22semidirect
56. C2×#6669C22semidirect
57. C2×#6667C22semidirect
58. C2×#6667C22semidirect
59. C2×#6667C22semidirect
60. C2×#6667C22semidirect
61. C2×(C2×D3)⋊Dic5C22semidirect
62. C2×#6665C22semidirect
63. #91476C22semidirect
64. D3×#685C22semidirect
65. #91460C22semidirect
66. #91438C22semidirect
67. #91433C22semidirect
68. #91416C22semidirect
69. #91348C22semidirect
84. C2×#4029D3semidirect
94. C23×D15C23semidirect
103. C22×D3×D5D4semidirect
105. C22×D3×D5C23semidirect
109. C2×#1220C23semidirect
114. C2×D60C23semidirect
117. C2×C5×#67C23semidirect
118. C2×C5×#67C23semidirect
122. C2×C5×D12C23semidirect
124. C2×C4×C5×D3C23semidirect
131. C2×C3×C4×D5C23semidirect
138. C2×#1203C23semidirect
139. C2×#1203C23semidirect
140. C2×#1203C23semidirect
144. C2×#1200C23semidirect
146. C2×D3×Dic5C23semidirect
148. C3×C5×C22⋊C4C23semidirect
149. #6714C23semidirect
150. #6714C23semidirect
151. C5×(C2×D3)⋊C4C23semidirect
152. C5×Dic3⋊C4C23semidirect
153. C3×C22⋊Dic5C23semidirect
154. C3×#685C23semidirect
155. C3×C4⋊Dic5C23semidirect
156. C3×#683C23semidirect
157. #6669C23semidirect
158. #6667C23semidirect
159. #6667C23semidirect
160. #6667C23semidirect
161. #6667C23semidirect
162. (C2×D3)⋊Dic5C23semidirect
163. #6665C23semidirect
175. C2×#884D5semidirect
202. C22×C4×D5C2×D3semidirect
206. C2×C5×C22⋊C4C2×D3semidirect
208. C2×C22⋊Dic5C2×D3semidirect
222. C2×#685C2×D3semidirect
223. C2×C4⋊Dic5C2×D3semidirect
225. C2×#683C2×D3semidirect
229. #4029C2×D3semidirect
273. C2×D3×D5C2×D4semidirect
313. C22×#67C2×D5semidirect
314. C22×#67C2×D5semidirect
325. C22×D12C2×D5semidirect
328. C22×C4×D3C2×D5semidirect
334. C2×C3×C22⋊C4C2×D5semidirect
345. C2×(C2×D3)⋊C4C2×D5semidirect
347. C2×Dic3⋊C4C2×D5semidirect
353. #884C2×D5semidirect
418. C2×C4×D5C22×D3semidirect
421. C5×C22⋊C4C22×D3semidirect
423. C22⋊Dic5C22×D3semidirect
431. #685C22×D3semidirect
432. C4⋊Dic5C22×D3semidirect
434. #683C22×D3semidirect
528. C2×#67C22×D5semidirect
529. C2×#67C22×D5semidirect
548. C2×D12C22×D5semidirect
554. C2×C4×D3C22×D5semidirect
559. C3×C22⋊C4C22×D5semidirect
568. (C2×D3)⋊C4C22×D5semidirect
570. Dic3⋊C4C22×D5semidirect
695. C2×C22⋊C4D3×D5semidirect
697. C2×C3×C5#534semidirect
899. C22⋊C4C2×D3×D5semidirect
900. C3×C5C2×#534semidirect
947. C2×C5#5653semidirect
1030. C2×C3#65939semidirect
1039. C5C2×#5653semidirect
1083. C3C2×#65939semidirect
1091. C2#11753215direct (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×D122
C2×#917712
C2×C5×#8842
C2×C3×#40292
C2×#915772
C2×#915732
C2×#915582
C2×#914762
C2×D3×#6852
C2×#914602
C2×#914382
C2×#914332
C2×#914162
C2×#913482
#117532152
C2×#659393
C2×#56535