Finite Group Databasebeta

← C2×#11753290 #14480902

Subgroups — C2×#11753290 #14480902

Order 1920.

2672 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91775C211yesmaximal, characteristic, complemented
2C2×C5×#884C211yesmaximal, characteristic, complemented
3C2×C3×#4031C211yesmaximal, characteristic, complemented
4C2×#91577C211yesmaximal, characteristic, complemented
5C2×#91571C211yesmaximal, characteristic, complemented
6C2×#67⋊Dic5C211yesmaximal, characteristic, complemented
7C2×#91558C211yesmaximal, characteristic, complemented
8C2×#91475C211yesmaximal, characteristic, complemented
9C2×D3×#685C211yesmaximal, characteristic, complemented
10C2×#91457C211yesmaximal, characteristic, complemented
11C2×Dic5×D12C211yesmaximal, characteristic, complemented
12C2×#91387C211yesmaximal, characteristic, complemented
13C2×#91369C211yesmaximal, characteristic, complemented
14C2×#91362C211yesmaximal, characteristic, complemented
15C2×#91326C211yesmaximal, characteristic, complemented
16#11753290C2116yesmaximal, direct product factor
17C2×#65951—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C23×Dic15C2211yescharacteristic, complemented
21C22×C5×#67C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic, complemented
23C22×C5×D12C2211yescharacteristic
24C22×C4×C5×D3C2211yescharacteristic
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×Dic10C2211yescharacteristic, complemented
27C22×#1203C2211yescharacteristic
28C22×#1201C2211yescharacteristic
29C22×D3×Dic5C2211yescharacteristic
30C22×D3×Dic5C2211yescharacteristic, complemented
31C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×C4⋊Dic15C2211yescharacteristic, complemented
35C2×C4⋊Dic15C2211yescharacteristic, complemented
36#91775C2218yescomplemented
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
39C5×#884C2218yescomplemented
40C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C2×C3×C4×Dic5C2211yescharacteristic, complemented
44C3×#4031C2218yescomplemented
45#91577C2218yescomplemented
46#91571C2218yescomplemented
47#67⋊Dic5C2218yescomplemented
48#91558C2218yescomplemented
49C2×Dic3⋊Dic5C2211yescharacteristic, complemented
50C2×#6669C2211yescharacteristic, complemented
51C2×#6669C2211yescharacteristic, complemented
52C2×#6667C2211yescharacteristic
53C2×#6667C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91475C2218yescomplemented
61D3×#685C2218yescomplemented
62#91457C2218yescomplemented
63Dic5×D12C2218yescomplemented
64#91387C2218yescomplemented
65#91369C2218yescomplemented
66#91362C2218yescomplemented
67#91326C2218yescomplemented
68C2×#5678—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4085—31no—
71C2×#4085—31no—
72C2×#4083—31no—
73C2×#4083—31no—
74C2×D4×Dic5—31no—
75C2×D4×Dic5—31no—
76C22×#685—31no—
77C2×#4070—31no—
78#65951—316no—
79C2×#4044—31no—
80C2×#4044—31no—
81C2×#4032—31no—
82C2×#4032—31no—
83C2×#4031—31no—
84C2×#4031D311yescharacteristic, complemented
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C3×D5C2311yescharacteristic
90C22×D3×D5—24no—
91C22×D3×D5—42no—
92C22×D3×D5—42no—
93C22×D3×D5C2314yes—
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C2×#1220—42no—
97C2×#1220C2314yes—
98C22×Dic15—42no—
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2314yescomplemented
103C2×C5×#67—24no—
104C2×C5×#67—42no—
105C2×C5×#67C2314yes—
106C2×C5×#67C2314yescomplemented
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2311yescharacteristic
109C2×C5×D12—24no—
110C2×C5×D12C2314yes—
111C2×C4×C5×D3—42no—
112C2×C4×C5×D3C2314yes—
113C2×C3×C22⋊D5—42no—
114C2×C3×C22⋊D5C2314yes—
115C22×C3×Dic5C2311yescharacteristic
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2311yescharacteristic
118C2×C3×Dic10—42no—
119C2×C3×Dic10C2314yescomplemented
120C2×#1203—42no—
121C2×#1203C2314yes—
122C2×#1201—42no—
123C2×#1201C2314yes—
124C2×D3×Dic5—42no—
125C2×D3×Dic5—42no—
126C2×D3×Dic5C2314yes—
127C2×D3×Dic5C2314yescomplemented
128C3×C5×C22⋊C4C2314yescomplemented
129#6714C2314yes—
130#6714C2314yes—
131C4⋊Dic15C2314yescomplemented
132C4⋊Dic15C2314yescomplemented
133C5×(C2×D3)⋊C4C2314yescomplemented
134C5×Dic3⋊C4C2314yescomplemented
135C3×C22⋊Dic5C2314yescomplemented
136C3×#685C2314yes—
137C3×#685C2314yes—
138C3×C4×Dic5C2314yescomplemented
139Dic3⋊Dic5C2314yescomplemented
140#6669C2314yescomplemented
141#6669C2314yescomplemented
142#6667C2314yes—
143#6667C2314yes—
144(C2×D3)⋊Dic5C2314yes—
145(C2×D3)⋊Dic5C2314yes—
146(C2×D3)⋊Dic5C2314yescomplemented
147#6665C2314yes—
148#6665C2314yes—
149Dic3×Dic5C2314yescomplemented
150C2×C3×#124—51no—
151C2×#947—51no—
152C2×#946—51no—
153C2×#939—51no—
154C2×#937—51no—
155#5678—516no—
156C2×#886—51no—
157C2×#884—51no—
158C2×#884D511yescharacteristic, complemented
159C2×#883—51no—
160C2×#882—51no—
161C2×#67⋊C4—51no—
162C2×D3×C22⋊C4—51no—
163C2×#879—51no—
164C2×#876—51no—
165C2×C4×D12—51no—
166C24×D5—31no—
167C22×C5×D4—31no—
168C22×C5×D4—31no—
169C22×C5×D4—31no—
170C23×C4×C5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5—31no—
174C22×C22⋊D5C2×D311yescharacteristic
175C23×Dic5—31no—
176C23×Dic5—31no—
177C23×Dic5—31no—
178C22×Dic10C2×D311yescharacteristic, complemented
179C5×#121—38no—
180C2×C5×C4⋊C4—31no—
181C2×C5×C22⋊C4—31no—
182C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
183C2×C22⋊Dic5—31no—
184C2×C22⋊Dic5—31no—
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5C2×D311yescharacteristic, complemented
187#4085—38no—
188#4085—38no—
189#4083—38no—
190#4083—38no—
191D4×Dic5—38no—
192D4×Dic5—38no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×#685—38no—
200C2×#685C2×D311yescharacteristic
201C2×#685C2×D311yescharacteristic
202C2×C4⋊Dic5—31no—
203C2×C4⋊Dic5—31no—
204C2×C4⋊Dic5—31no—
205#4070—38no—
206C2×#683—31no—
207C2×#683—31no—
208C2×C4×Dic5—31no—
209C2×C4×Dic5C2×D311yescharacteristic, complemented
210#4044—38no—
211#4044—38no—
212#4032—38no—
213#4032—38no—
214#4031—38no—
215#4031C2×D318yescomplemented
216C2×#538—151noSylow
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5—22no—
220C23×C3×C5C2412yes—
221C23×C3×C5C2411yescharacteristic
222C22×D15—22no—
223C22×D15—22no—
224C22×D15—22no—
225C22×D15C2412yes—
226C22×C5×D3—22no—
227C22×C5×D3—22no—
228C22×C5×D3—22no—
229C22×C5×D3—22no—
230C22×C5×D3—22no—
231C22×C5×D3#4114yes—
232C22×C5×D3C2412yes—
233C22×C5×D3C2412yes—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5—22no—
237C22×C3×D5C2412yes—
238C2×D3×D5—28no—
239C2×D3×D5—44no—
240C2×D3×D5—44no—
241C2×D3×D5—416no—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5C2412yes—
245C2×C3×C4×C5C2412yes—
246#1220—44no—
247C2×Dic15—22no—
248C2×Dic15—22no—
249C2×Dic15—22no—
250C2×Dic15—44no—
251C2×Dic15C2412yes—
252C2×Dic15C2412yes—
253C2×Dic15C2412yes—
254C5×#67—28no—
255C5×#67—44no—
256C2×C5×Dic3—22no—
257C2×C5×Dic3—22no—
258C2×C5×Dic3C2412yes—
259C2×C5×Dic3C2412yes—
260C5×D12—28no—
261C4×C5×D3—44no—
262C3×C22⋊D5—44no—
263C2×C3×Dic5—22no—
264C2×C3×Dic5—22no—
265C2×C3×Dic5—22no—
266C2×C3×Dic5C2412yes—
267C2×C3×Dic5C2412yes—
268C2×C3×Dic5C2412yes—
269C3×Dic10—44no—
270#1203—44no—
271#1201—44no—
272D3×Dic5—44no—
273D3×Dic5—44no—
274C24×D3—51no—
275C22×C3×Q8—51no—
276C22×C3×D4—51no—
277C22×#67—51no—
278C22×#67—51no—
279C22×#67C2×D511yescharacteristic
280C22×#67C2×D511yescharacteristic, complemented
281C23×Dic3—51no—
282C22×D12—51no—
283C22×D12C2×D511yescharacteristic
284C22×C4×D3—51no—
285C22×C4×D3—51no—
286C22×C4×D3C2×D511yescharacteristic
287C3×#124—58no—
288C2×C3×C22⋊C4—51no—
289C2×C3×C22⋊C4—51no—
290C2×C3×C22⋊C4—51no—
291C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
292C2×C3×C42—51no—
293C2×#217—51no—
294C2×#217—51no—
295#947—58no—
296#946—58no—
297#939—58no—
298#937—58no—
299C2×(C2×D3)⋊C4—51no—
300C2×(C2×D3)⋊C4—51no—
301C2×(C2×D3)⋊C4—51no—
302C2×(C2×D3)⋊C4—51no—
303C2×(C2×D3)⋊C4—51no—
304C2×(C2×D3)⋊C4—51no—
305C2×(C2×D3)⋊C4—51no—
306C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
307C2×C4⋊Dic3—51no—
308C2×C4⋊Dic3—51no—
309C2×Dic3⋊C4—51no—
310C2×Dic3⋊C4—51no—
311C2×Dic3⋊C4—51no—
312C2×Dic3⋊C4C2×D511yescharacteristic, complemented
313C2×C4×Dic3—51no—
314#886—58no—
315#884—58no—
316#884C2×D518yescomplemented
317#883—58no—
318#882—58no—
319#67⋊C4—58no—
320D3×C22⋊C4—58no—
321#879—58no—
322#876—58no—
323C4×D12—58no—
324C24×C5—31no—
325C24×C5—31no—
326C24×C5C22×D311yescharacteristic
327C23×D5—31no—
328C23×D5—34no—
329C23×D5—64no—
330C23×D5—122no—
331C23×D5—122no—
332C23×D5C22×D311yescharacteristic
333C2×C5×D4—34no—
334C2×C5×D4—34no—
335C2×C5×D4—34no—
336C2×C5×D4—64no—
337C2×C5×D4—64no—
338C2×C5×D4—122no—
339C22×C4×C5—31no—
340C22×C4×C5—31no—
341C22×C4×C5—34no—
342C22×C4×C5—122no—
343C22×C4×C5C22×D311yescharacteristic
344C22×C4×C5C22×D311yescharacteristic
345C2×C22⋊D5—34no—
346C2×C22⋊D5—34no—
347C2×C22⋊D5—34no—
348C2×C22⋊D5—42no—
349C2×C22⋊D5—122no—
350C2×C22⋊D5—122no—
351C2×C22⋊D5—122no—
352C2×C22⋊D5C22×D314yes—
353C22×Dic5—31no—
354C22×Dic5—31no—
355C22×Dic5—31no—
356C22×Dic5—34no—
357C22×Dic5—34no—
358C22×Dic5—34no—
359C22×Dic5—122no—
360C22×Dic5—122no—
361C22×Dic5—122no—
362C22×Dic5C22×D311yescharacteristic
363C22×Dic5C22×D311yescharacteristic
364C22×Dic5C22×D311yescharacteristic
365C2×Dic10—42no—
366C2×Dic10C22×D314yescomplemented
367C5×C4⋊C4—34no—
368C5×C22⋊C4—34no—
369C5×C22⋊C4C22×D314yescomplemented
370C22⋊Dic5—34no—
371C22⋊Dic5—34no—
372C22⋊Dic5—34no—
373C22⋊Dic5C22×D314yescomplemented
374#685—34no—
375#685—34no—
376#685—34no—
377#685—34no—
378#685—34no—
379#685—34no—
380#685C22×D314yes—
381#685C22×D314yes—
382C4⋊Dic5—34no—
383C4⋊Dic5—34no—
384C4⋊Dic5—34no—
385#683—34no—
386#683—34no—
387C4×Dic5—34no—
388C4×Dic5C22×D314yescomplemented
389#538—1516no—
390C2×#126—151no—
391C2×#126—151no—
392C2×#124—51no—
393C2×#124—151no—
394C2×#123—151no—
395C2×#123—151no—
396C2×C22⋊Q8—151no—
397C2×#121—31no—
398C2×#121—151no—
399C2×#121—151no—
400C2×#120—151no—
401C2×#120—151no—
402C2×C4×D4—151no—
403C2×C4×D4—151no—
404C22×C22⋊C4—151no—
405C22×C3×C5—22no—
406C22×C3×C5—22no—
407C22×C3×C5—22no—
408C22×C3×C5—44no—
409C22×C3×C5C2×#4112yes—
410C22×C3×C5H(5,𝔽2)12yes—
411C22×C3×C5H(5,𝔽2)12yes—
412C22×C3×C5C2511yescharacteristic
413C2×D15—22no—
414C2×D15—22no—
415C2×D15—22no—
416C2×D15—44no—
417C2×C5×D3—28no—
418C2×C5×D3—22no—
419C2×C5×D3—22no—
420C2×C5×D3—22no—
421C2×C5×D3—22no—
422C2×C5×D3—22no—
423C2×C5×D3—44no—
424C2×C5×D3C2×#4114yes—
425C2×C3×D5—22no—
426C2×C3×D5—22no—
427C2×C3×D5—22no—
428C2×C3×D5—44no—
429D3×D5—416no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432Dic15—22no—
433Dic15—22no—
434Dic15—22no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C3×Dic5—22no—
438C5×Dic3—22no—
439C5×Dic3—22no—
440C24×C3—51no—
441C24×C3C22×D511yescharacteristic
442C23×D3—51no—
443C23×D3—54no—
444C23×D3—104no—
445C23×D3—202no—
446C23×D3—202no—
447C23×D3C22×D511yescharacteristic
448C23×D3C22×D511yescharacteristic
449C2×C3×Q8—54no—
450C2×C3×Q8—202no—
451C2×C3×D4—54no—
452C2×C3×D4—202no—
453C22×C3×C4—51no—
454C22×C3×C4—51no—
455C22×C3×C4—51no—
456C22×C3×C4C22×D511yescharacteristic
457C22×C3×C4C22×D511yescharacteristic
458C2×#67—24no—
459C2×#67—42no—
460C2×#67—54no—
461C2×#67—54no—
462C2×#67—202no—
463C2×#67—202no—
464C2×#67C22×D514yes—
465C2×#67C22×D514yescomplemented
466C22×Dic3—51no—
467C22×Dic3—51no—
468C22×Dic3—51no—
469C22×Dic3—54no—
470C22×Dic3—202no—
471C22×Dic3C22×D511yescharacteristic
472C22×Dic3C22×D511yescharacteristic
473C2×D12—24no—
474C2×D12—54no—
475C2×D12—202no—
476C2×D12C22×D514yes—
477C2×C4×D3—42no—
478C2×C4×D3—54no—
479C2×C4×D3—54no—
480C2×C4×D3—202no—
481C2×C4×D3—202no—
482C2×C4×D3C22×D514yes—
483C3×C22⋊C4—54no—
484C3×C22⋊C4—54no—
485C3×C22⋊C4—54no—
486C3×C22⋊C4C22×D514yescomplemented
487C3×C42—54no—
488#217—54no—
489#217—54no—
490(C2×D3)⋊C4—54no—
491(C2×D3)⋊C4—54no—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4—54no—
496(C2×D3)⋊C4—54no—
497(C2×D3)⋊C4C22×D514yescomplemented
498C4⋊Dic3—54no—
499C4⋊Dic3—54no—
500Dic3⋊C4—54no—
501Dic3⋊C4—54no—
502Dic3⋊C4—54no—
503Dic3⋊C4C22×D514yescomplemented
504C4×Dic3—54no—
505C23×C5—22no—
506C23×C5—22no—
507C23×C5—22no—
508C23×C5—34no—
509C23×C5—32no—
510C23×C5—32no—
511C23×C5—62no—
512C23×C5—62no—
513C23×C5—62no—
514C23×C5—62no—
515C23×C5—62no—
516C23×C5C23×D312yes—
517C23×C5C23×D311yescharacteristic
518C22×D5—22no—
519C22×D5—22no—
520C22×D5—22no—
521C22×D5—32no—
522C22×D5—68no—
523C22×D5—62no—
524C22×D5—62no—
525C22×D5—62no—
526C22×D5—124no—
527C22×D5—124no—
528C22×D5—1216no—
529C22×D5C23×D312yes—
530C5×D4—68no—
531C5×D4—68no—
532C5×D4—124no—
533C2×C4×C5—22no—
534C2×C4×C5—22no—
535C2×C4×C5—32no—
536C2×C4×C5—32no—
537C2×C4×C5—62no—
538C2×C4×C5—62no—
539C2×C4×C5—124no—
540C2×C4×C5C23×D312yes—
541C2×C4×C5C23×D312yes—
542C22⋊D5—44no—
543C22⋊D5—124no—
544C22⋊D5—124no—
545C22⋊D5—124no—
546C2×Dic5—22no—
547C2×Dic5—22no—
548C2×Dic5—22no—
549C2×Dic5—32no—
550C2×Dic5—32no—
551C2×Dic5—32no—
552C2×Dic5—62no—
553C2×Dic5—62no—
554C2×Dic5—62no—
555C2×Dic5—124no—
556C2×Dic5—124no—
557C2×Dic5—124no—
558C2×Dic5C23×D312yes—
559C2×Dic5C23×D312yes—
560C2×Dic5C23×D312yes—
561Dic10—44no—
562C25—151no—
563C22×Q8—51no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—31no—
567C22×D4—51no—
568C22×D4—151no—
569C22×D4—151no—
570C22×D4—151no—
571C23×C4—31no—
572C23×C4—151no—
573C23×C4—151no—
574C23×C4—151no—
575#126—158no—
576#126—158no—
577#124—58no—
578#124—158no—
579#123—158no—
580#123—158no—
581C22⋊Q8—158no—
582#121—38no—
583#121—158no—
584#121—158no—
585#120—158no—
586#120—158no—
587C4×D4—158no—
588C4×D4—158no—
589C2×C4⋊C4—31no—
590C2×C4⋊C4—151no—
591C2×C4⋊C4—151no—
592C2×C4⋊C4—151no—
593C2×C4⋊C4—151no—
594C2×C4⋊C4—151no—
595C2×C22⋊C4—31no—
596C2×C22⋊C4—51no—
597C2×C22⋊C4—51no—
598C2×C22⋊C4—51no—
599C2×C22⋊C4—158no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4—151no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4D3×D511yescharacteristic, complemented
610C2×C42—51no—
611C2×C42—151no—
612C2×C3×C5—42no—
613C2×C3×C5#53814yescomplemented
614C2×C3×C5C22×#4111yescharacteristic
615C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
616C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
617D15—42no—
618C3×D5—42no—
619C5×D3—24no—
620C5×D3—42no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3—52no—
625C23×C3—102no—
626C23×C3—102no—
627C23×C3—102no—
628C23×C3C23×D512yes—
629C23×C3C23×D511yescharacteristic
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—22no—
635C22×D3—52no—
636C22×D3—102no—
637C22×D3—102no—
638C22×D3—102no—
639C22×D3—108no—
640C22×D3—204no—
641C22×D3—204no—
642C22×D3—2016no—
643C22×D3#71114yes—
644C22×D3C23×D512yes—
645C22×D3C23×D512yes—
646C3×Q8—204no—
647C3×D4—204no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—52no—
651C2×C3×C4—52no—
652C2×C3×C4—52no—
653C2×C3×C4—102no—
654C2×C3×C4—102no—
655C2×C3×C4—102no—
656C2×C3×C4C23×D512yes—
657C2×C3×C4C23×D512yes—
658#67—28no—
659#67—44no—
660#67—204no—
661#67—204no—
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—52no—
665C2×Dic3—52no—
666C2×Dic3—52no—
667C2×Dic3—102no—
668C2×Dic3—102no—
669C2×Dic3—102no—
670C2×Dic3—204no—
671C2×Dic3C23×D512yes—
672C2×Dic3C23×D512yes—
673D12—28no—
674D12—204no—
675C4×D3—44no—
676C4×D3—204no—
677C4×D3—204no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—22no—
681C22×C5—34no—
682C22×C5—44no—
683C22×C5—68no—
684C22×C5—62no—
685C22×C5—62no—
686C22×C5—62no—
687C22×C5—62no—
688C22×C5—62no—
689C22×C5—124no—
690C22×C5#100412yes—
691C22×C5D3×#4112yes—
692C22×C5#100912yes—
693C22×C5C24×D311yescharacteristic
694C2×D5—22no—
695C2×D5—22no—
696C2×D5—22no—
697C2×D5—44no—
698C2×D5—62no—
699C2×D5—62no—
700C2×D5—62no—
701C2×D5—1216no—
702C2×D5—124no—
703C4×C5—22no—
704C4×C5—22no—
705C4×C5—62no—
706C4×C5—62no—
707Dic5—22no—
708Dic5—22no—
709Dic5—22no—
710Dic5—62no—
711Dic5—62no—
712Dic5—62no—
713C24—31no—
714C24—31no—
715C24—51no—
716C24—154no—
717C24—151no—
718C24—304no—
719C24—602no—
720C24—602no—
721C24C2×D3×D511yescharacteristic
722C2×Q8—54no—
723C2×Q8—202no—
724C2×D4—34no—
725C2×D4—34no—
726C2×D4—34no—
727C2×D4—54no—
728C2×D4—64no—
729C2×D4—64no—
730C2×D4—122no—
731C2×D4—154no—
732C2×D4—154no—
733C2×D4—154no—
734C2×D4—202no—
735C2×D4—602no—
736C2×D4—602no—
737C2×D4—602no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—34no—
741C22×C4—51no—
742C22×C4—51no—
743C22×C4—51no—
744C22×C4—122no—
745C22×C4—154no—
746C22×C4—154no—
747C22×C4—151no—
748C22×C4—151no—
749C22×C4—151no—
750C22×C4—154no—
751C22×C4—602no—
752C22×C4—602no—
753C22×C4—602no—
754C22×C4C2×D3×D511yescharacteristic
755C22×C4C2×D3×D511yescharacteristic
756C4⋊C4—34no—
757C4⋊C4—154no—
758C4⋊C4—154no—
759C4⋊C4—154no—
760C4⋊C4—154no—
761C4⋊C4—154no—
762C22⋊C4—34no—
763C22⋊C4—54no—
764C22⋊C4—54no—
765C22⋊C4—54no—
766C22⋊C4—154no—
767C22⋊C4—154no—
768C22⋊C4—154no—
769C22⋊C4—154no—
770C22⋊C4—154no—
771C22⋊C4—154no—
772C22⋊C4—154no—
773C22⋊C4—154no—
774C22⋊C4—154no—
775C22⋊C4C2×D3×D514yescomplemented
776C42—54no—
777C42—154no—
778C3×C5C2×#53811yescharacteristic, complemented, Hall
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—44no—
783C22×C3—102no—
784C22×C3—102no—
785C22×C3—102no—
786C22×C3—204no—
787C22×C3C2×#71112yes—
788C22×C3#414412yes—
789C22×C3#414912yes—
790C22×C3C24×D511yescharacteristic
791C2×D3—28no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—44no—
798C2×D3—102no—
799C2×D3—102no—
800C2×D3—102no—
801C2×D3—2016no—
802C2×D3—204no—
803C2×D3C2×#71114yes—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—102no—
807C3×C4—102no—
808C3×C4—102no—
809Dic3—22no—
810Dic3—22no—
811Dic3—102no—
812Dic3—102no—
813Dic3—102no—
814C2×C5—42no—
815C2×C5—64no—
816C2×C5—122no—
817C2×C5#567814yescomplemented
818C2×C5C2×#100411yescharacteristic
819C2×C5C2×D3×#4111yescharacteristic
820C2×C5C2×#100911yescharacteristic
821D5—42no—
822D5—122no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—34no—
827C23—32no—
828C23—32no—
829C23—52no—
830C23—62no—
831C23—62no—
832C23—62no—
833C23—62no—
834C23—62no—
835C23—102no—
836C23—102no—
837C23—102no—
838C23—152no—
839C23—308no—
840C23—302no—
841C23—302no—
842C23—302no—
843C23—604no—
844C23—604no—
845C23—6016no—
846C23C22×D3×D512yes—
847C23C22×D3×D511yescharacteristic
848Q8—204no—
849D4—68no—
850D4—68no—
851D4—124no—
852D4—204no—
853D4—604no—
854D4—604no—
855D4—604no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—52no—
861C2×C4—52no—
862C2×C4—52no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—102no—
866C2×C4—102no—
867C2×C4—102no—
868C2×C4—124no—
869C2×C4—152no—
870C2×C4—152no—
871C2×C4—152no—
872C2×C4—302no—
873C2×C4—302no—
874C2×C4—302no—
875C2×C4—604no—
876C2×C4—604no—
877C2×C4—604no—
878C2×C4C22×D3×D512yes—
879C2×C4C22×D3×D512yes—
880C2×C3—42no—
881C2×C3—202no—
882C2×C3#6595114yescomplemented
883C2×C3C22×#71111yescharacteristic
884C2×C3C2×#414411yescharacteristic
885C2×C3C2×#414911yescharacteristic
886D3—24no—
887D3—42no—
888D3—202no—
889C5C2×#567811yescharacteristic, complemented, Sylow
890C22—22no—
891C22—22no—
892C22—22no—
893C22—34no—
894C22—44no—
895C22—68no—
896C22—62no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—102no—
902C22—102no—
903C22—102no—
904C22—124no—
905C22—204no—
906C22—302no—
907C22—302no—
908C22—302no—
909C22—6016no—
910C22—604no—
911C22#9201912yes—
912C22D3×#71112yes—
913C22#9202512yes—
914C22C23×D3×D511yescharacteristic
915C4—22no—
916C4—22no—
917C4—62no—
918C4—62no—
919C4—102no—
920C4—102no—
921C4—102no—
922C4—302no—
923C4—302no—
924C4—302no—
925C3C2×#6595111yescharacteristic, complemented, Sylow
926C2—42no—
927C2—64no—
928C2—122no—
929C2—202no—
930C2—602no—
931C2#1175329014yesdirect product factor
932C2C2×#9201911yescharacteristic
933C2C2×D3×#71111yescharacteristic
934C2C2×#9202511yescharacteristic
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×#538
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. C2×#91775C2semidirect
2. C2×C5×#884C2semidirect
3. C2×C3×#4031C2semidirect
4. C2×#91577C2semidirect
5. C2×#91571C2semidirect
6. C2×#67⋊Dic5C2semidirect
7. C2×#91558C2semidirect
8. C2×#91475C2semidirect
9. C2×D3×#685C2semidirect
10. C2×#91457C2semidirect
11. C2×Dic5×D12C2semidirect
12. C2×#91387C2semidirect
13. C2×#91369C2semidirect
14. C2×#91362C2semidirect
15. C2×#91326C2semidirect
16. #11753290C2direct (N × H)
20. C23×Dic15C22semidirect
22. C22×C5×#67C22semidirect
26. C22×C3×Dic10C22semidirect
30. C22×D3×Dic5C22semidirect
31. C2×C3×C5×C22⋊C4C22semidirect
34. C2×C4⋊Dic15C22semidirect
35. C2×C4⋊Dic15C22semidirect
36. #91775C22semidirect
37. C2×C5×(C2×D3)⋊C4C22semidirect
38. C2×C5×Dic3⋊C4C22semidirect
39. C5×#884C22semidirect
40. C2×C3×C22⋊Dic5C22semidirect
43. C2×C3×C4×Dic5C22semidirect
44. C3×#4031C22semidirect
45. #91577C22semidirect
46. #91571C22semidirect
47. #67⋊Dic5C22semidirect
48. #91558C22semidirect
49. C2×Dic3⋊Dic5C22semidirect
50. C2×#6669C22semidirect
51. C2×#6669C22semidirect
56. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91475C22semidirect
61. D3×#685C22semidirect
62. #91457C22semidirect
63. Dic5×D12C22semidirect
64. #91387C22semidirect
65. #91369C22semidirect
66. #91362C22semidirect
67. #91326C22semidirect
84. C2×#4031D3semidirect
102. C22×Dic15C23semidirect
106. C2×C5×#67C23semidirect
119. C2×C3×Dic10C23semidirect
127. C2×D3×Dic5C23semidirect
128. C3×C5×C22⋊C4C23semidirect
131. C4⋊Dic15C23semidirect
132. C4⋊Dic15C23semidirect
133. C5×(C2×D3)⋊C4C23semidirect
134. C5×Dic3⋊C4C23semidirect
135. C3×C22⋊Dic5C23semidirect
138. C3×C4×Dic5C23semidirect
139. Dic3⋊Dic5C23semidirect
140. #6669C23semidirect
141. #6669C23semidirect
146. (C2×D3)⋊Dic5C23semidirect
149. Dic3×Dic5C23semidirect
158. C2×#884D5semidirect
178. C22×Dic10C2×D3semidirect
182. C2×C5×C22⋊C4C2×D3semidirect
186. C2×C22⋊Dic5C2×D3semidirect
209. C2×C4×Dic5C2×D3semidirect
215. #4031C2×D3semidirect
280. C22×#67C2×D5semidirect
291. C2×C3×C22⋊C4C2×D5semidirect
306. C2×(C2×D3)⋊C4C2×D5semidirect
312. C2×Dic3⋊C4C2×D5semidirect
316. #884C2×D5semidirect
366. C2×Dic10C22×D3semidirect
369. C5×C22⋊C4C22×D3semidirect
373. C22⋊Dic5C22×D3semidirect
388. C4×Dic5C22×D3semidirect
465. C2×#67C22×D5semidirect
486. C3×C22⋊C4C22×D5semidirect
497. (C2×D3)⋊C4C22×D5semidirect
503. Dic3⋊C4C22×D5semidirect
609. C2×C22⋊C4D3×D5semidirect
613. C2×C3×C5#538semidirect
775. C22⋊C4C2×D3×D5semidirect
778. C3×C5C2×#538semidirect
817. C2×C5#5678semidirect
882. C2×C3#65951semidirect
889. C5C2×#5678semidirect
925. C3C2×#65951semidirect
931. C2#11753290direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917752
C2×C5×#8842
C2×C3×#40312
C2×#915772
C2×#915712
C2×#67⋊Dic52
C2×#915582
C2×#914752
C2×D3×#6852
C2×#914572
C2×Dic5×D122
C2×#913872
C2×#913692
C2×#913622
C2×#913262
#117532902
C2×#659513
C2×#56785