Finite Group Databasebeta

← C2×#11756414 #14482672

Subgroups — C2×#11756414 #14482672

Order 1920.

3264 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6819C211yesmaximal, characteristic, complemented
2C22×#6817C211yesmaximal, characteristic, complemented
3C2×C3×C5×#123C211yesmaximal, characteristic, complemented
4C2×#91828C211yesmaximal, characteristic, complemented
5C22×#6712C211yesmaximal, characteristic, complemented
6#11756414C2116yesmaximal, direct product factor
7C2×#91785C211yesmaximal, characteristic, complemented
8C2×#91783C211yesmaximal, characteristic, complemented
9C2×C4⋊C4×D15C211yesmaximal, characteristic, complemented
10C2×#91777C211yesmaximal, characteristic, complemented
11C2×#91775C211yesmaximal, characteristic, complemented
12C2×#91773C211yesmaximal, characteristic, complemented
13C2×#91772C211yesmaximal, characteristic, complemented
14C2×#91770C211yesmaximal, characteristic, complemented
15C2×#91770C211yesmaximal, characteristic, complemented
16C2×#91767C211yesmaximal, characteristic, complemented
17C2×#65989—31nomaximal, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic
23C22×#1220C2211yescharacteristic
24C23×Dic15C2211yescharacteristic
25C23×Dic15C2211yescharacteristic
26C23×Dic15C2211yescharacteristic
27C2×#6819—28no—
28C2×#6819C2218yescomplemented
29C2×#6817—28no—
30C2×#6817C2218yescomplemented
31C22×D60C2211yescharacteristic
32C22×C4×D15C2211yescharacteristic
33C22×C4×D15C2211yescharacteristic
34C22×C4×D15C2211yescharacteristic
35C22×C4×D15C2211yescharacteristic
36C22×Dic30C2211yescharacteristic
37C22×Dic30C2211yescharacteristic
38C3×C5×#123C2218yescomplemented
39C2×C3×C5×C4⋊C4C2211yescharacteristic
40C2×C3×C5×C4⋊C4C2211yescharacteristic
41C2×C3×C5×C22⋊C4C2211yescharacteristic
42C2×C3×C5×C22⋊C4C2211yescharacteristic
43C2×C3×C5×C22⋊C4C2211yescharacteristic
44C2×#6719C2211yescharacteristic
45#91828C2218yescomplemented
46C2×#6714C2211yescharacteristic
47C2×#6714C2211yescharacteristic
48C2×#6714C2211yescharacteristic
49C2×#6714C2211yescharacteristic
50C2×C4⋊Dic15C2211yescharacteristic
51C2×C4⋊Dic15C2211yescharacteristic
52C2×#6712C2211yescharacteristic
53C2×#6712C2211yescharacteristic
54C2×#6712C2211yescharacteristic
55C2×#6712C2211yescharacteristic
56C2×#6712C2211yescharacteristic
57C2×#6712C2211yescharacteristic
58C2×#6712C2218yescomplemented
59C2×C4×Dic15C2211yescharacteristic
60#91785C2218yescomplemented
61#91783C2218yescomplemented
62C4⋊C4×D15C2218yescomplemented
63#91777C2218yescomplemented
64#91775C2218yescomplemented
65#91773C2218yescomplemented
66#91772C2218yescomplemented
67#91770C2218yescomplemented
68#91770C2218yescomplemented
69#91767C2218yescomplemented
70C2×#5655—51nomaximal, Hall
71C22×#711—31no—
72C22×#709—31no—
73C2×C5×#123D311yescharacteristic, complemented
74C2×#4085—31no—
75C22×#683—31no—
76#65989—316no—
77C2×#4042—31no—
78C2×#4040—31no—
79C2×D5×C4⋊C4—31no—
80C2×#4034—31no—
81C2×#4032—31no—
82C2×#4030—31no—
83C2×#4029—31no—
84C2×#4027—31no—
85C2×#4027—31no—
86C2×#4024—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×D15C2311yescharacteristic
91C2×C3×C5×D4—24no—
92C2×C3×C5×D4C2314yes—
93C22×C3×C4×C5—24no—
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C22×C3×C4×C5C2314yes—
100C2×#1220—24no—
101C2×#1220—24no—
102C2×#1220—24no—
103C2×#1220D418yescomplemented
104C2×#1220C2314yes—
105C2×#1220C2314yes—
106C2×#1220C2314yes—
107C2×#1220C2314yes—
108C22×Dic15—24no—
109C22×Dic15—24no—
110C22×Dic15—24no—
111C22×Dic15C2314yes—
112C22×Dic15C2314yes—
113C22×Dic15C2314yes—
114C22×Dic15C2311yescharacteristic
115C22×Dic15C2311yescharacteristic
116C22×Dic15C2311yescharacteristic
117C22×Dic15C2311yescharacteristic
118C22×Dic15C2311yescharacteristic
119C22×Dic15C2311yescharacteristic
120#6819—232no—
121#6817—232no—
122C2×D60—24no—
123C2×D60C2314yes—
124C2×C4×D15—24no—
125C2×C4×D15—24no—
126C2×C4×D15—24no—
127C2×C4×D15—24no—
128C2×C4×D15C2314yes—
129C2×C4×D15C2314yes—
130C2×C4×D15C2314yes—
131C2×C4×D15C2314yes—
132C2×Dic30—24no—
133C2×Dic30—24no—
134C2×Dic30C2314yes—
135C2×Dic30C2314yes—
136C3×C5×C4⋊C4C2314yes—
137C3×C5×C4⋊C4C2314yes—
138C3×C5×C22⋊C4C2314yes—
139C3×C5×C22⋊C4C2314yes—
140C3×C5×C22⋊C4C2314yes—
141#6719C2314yes—
142#6714C2314yes—
143#6714C2314yes—
144#6714C2314yes—
145#6714C2314yes—
146C4⋊Dic15C2314yes—
147C4⋊Dic15C2314yes—
148#6712C2314yes—
149#6712C2314yes—
150#6712C2314yes—
151#6712C2314yes—
152#6712C2314yes—
153#6712C2314yes—
154C4×Dic15C2314yes—
155C22×#237—51no—
156C22×#235—51no—
157C2×C3×#123D511yescharacteristic, complemented
158C2×#939—51no—
159C22×Dic3⋊C4—51no—
160#5655—516no—
161C2×#896—51no—
162C2×#894—51no—
163C2×D3×C4⋊C4—51no—
164C2×#888—51no—
165C2×#886—51no—
166C2×#884—51no—
167C2×#883—51no—
168C2×#67⋊C4—51no—
169C2×#67⋊C4—51no—
170C2×#878—51no—
171C22×C5×D4C2×D311yescharacteristic
172C23×C4×C5C2×D311yescharacteristic
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C23×Dic5—31no—
178C23×Dic5—31no—
179C23×Dic5—31no—
180C2×#711—38no—
181C2×#711—68no—
182C2×#709—38no—
183C2×#709—68no—
184C22×D20—31no—
185C22×C4×D5—31no—
186C22×C4×D5—31no—
187C22×C4×D5—31no—
188C22×C4×D5—31no—
189C22×Dic10—31no—
190C22×Dic10—31no—
191C5×#123C2×D318yescomplemented
192C2×C5×C4⋊C4C2×D311yescharacteristic
193C2×C5×C4⋊C4C2×D311yescharacteristic
194C2×C5×C22⋊C4C2×D311yescharacteristic
195C2×C5×C22⋊C4C2×D311yescharacteristic
196C2×C5×C22⋊C4C2×D311yescharacteristic
197C2×C22⋊Dic5—31no—
198#4085—38no—
199C2×#685—31no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×C4⋊Dic5—31no—
204C2×C4⋊Dic5—31no—
205C2×#683—31no—
206C2×#683—31no—
207C2×#683—31no—
208C2×#683—31no—
209C2×#683—31no—
210C2×#683—31no—
211C2×#683—38no—
212C2×C4×Dic5—31no—
213#4042—38no—
214#4040—38no—
215D5×C4⋊C4—38no—
216#4034—38no—
217#4032—38no—
218#4030—38no—
219#4029—38no—
220#4027—38no—
221#4027—38no—
222#4024—38no—
223C2×#547—151noSylow
224C23×C3×C5—22no—
225C23×C3×C5—22no—
226C23×C3×C5—22no—
227C23×C3×C5—22no—
228C23×C3×C5—22no—
229C23×C3×C5C2×D414yes—
230C23×C3×C5C2412yes—
231C23×C3×C5C2412yes—
232C23×C3×C5C2411yescharacteristic
233C22×D15—22no—
234C22×D15—22no—
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15C2×D414yes—
239C22×D15C2412yes—
240C22×D15C2412yes—
241C3×C5×D4—28no—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5—22no—
245C2×C3×C4×C5—28no—
246C2×C3×C4×C5—22no—
247C2×C3×C4×C5—22no—
248C2×C3×C4×C5C2412yes—
249C2×C3×C4×C5C2412yes—
250C2×C3×C4×C5C2412yes—
251C2×C3×C4×C5C2412yes—
252C2×C3×C4×C5C2412yes—
253#1220—28no—
254#1220—28no—
255#1220—28no—
256#1220C2×D4116yescomplemented
257C2×Dic15—22no—
258C2×Dic15—22no—
259C2×Dic15—22no—
260C2×Dic15—28no—
261C2×Dic15—22no—
262C2×Dic15—28no—
263C2×Dic15—28no—
264C2×Dic15C2×D414yes—
265C2×Dic15#4114yescomplemented
266C2×Dic15C2412yes—
267C2×Dic15C2412yes—
268C2×Dic15C2412yes—
269C2×Dic15C2412yes—
270C2×Dic15C2412yes—
271C2×Dic15C2412yes—
272D60—28no—
273C4×D15—28no—
274C4×D15—28no—
275C4×D15—28no—
276C4×D15—28no—
277Dic30—28no—
278Dic30—28no—
279C22×C3×D4C2×D511yescharacteristic
280C23×C3×C4C2×D511yescharacteristic
281C22×#67—51no—
282C22×#67—51no—
283C22×#67—51no—
284C22×#67—51no—
285C23×Dic3—51no—
286C23×Dic3—51no—
287C23×Dic3—51no—
288C2×#237—58no—
289C2×#237—108no—
290C2×#235—58no—
291C2×#235—108no—
292C22×D12—51no—
293C22×C4×D3—51no—
294C22×C4×D3—51no—
295C22×C4×D3—51no—
296C22×C4×D3—51no—
297C22×Dic6—51no—
298C22×Dic6—51no—
299C3×#123C2×D518yescomplemented
300C2×C3×C4⋊C4C2×D511yescharacteristic
301C2×C3×C4⋊C4C2×D511yescharacteristic
302C2×C3×C22⋊C4C2×D511yescharacteristic
303C2×C3×C22⋊C4C2×D511yescharacteristic
304C2×C3×C22⋊C4C2×D511yescharacteristic
305C2×#217—51no—
306#939—58no—
307C2×(C2×D3)⋊C4—51no—
308C2×(C2×D3)⋊C4—51no—
309C2×(C2×D3)⋊C4—51no—
310C2×(C2×D3)⋊C4—51no—
311C2×C4⋊Dic3—51no—
312C2×C4⋊Dic3—51no—
313C2×Dic3⋊C4—58no—
314C2×Dic3⋊C4—51no—
315C2×Dic3⋊C4—51no—
316C2×Dic3⋊C4—51no—
317C2×Dic3⋊C4—51no—
318C2×Dic3⋊C4—51no—
319C2×Dic3⋊C4—51no—
320C2×C4×Dic3—51no—
321#896—58no—
322#894—58no—
323D3×C4⋊C4—58no—
324#888—58no—
325#886—58no—
326#884—58no—
327#883—58no—
328#67⋊C4—58no—
329#67⋊C4—58no—
330#878—58no—
331C24×C5C22×D311yescharacteristic
332C24×C5C22×D311yescharacteristic
333C23×D5—31no—
334C23×D5—31no—
335C2×C5×D4—24no—
336C2×C5×D4C22×D314yes—
337C22×C4×C5—24no—
338C22×C4×C5C22×D311yescharacteristic
339C22×C4×C5C22×D311yescharacteristic
340C22×C4×C5C22×D311yescharacteristic
341C22×C4×C5C22×D311yescharacteristic
342C22×C4×C5C22×D311yescharacteristic
343C22×C4×C5C22×D314yes—
344C2×C22⋊D5—38no—
345C2×C22⋊D5—34no—
346C2×C22⋊D5—34no—
347C2×C22⋊D5—34no—
348C2×C22⋊D5—34no—
349C2×C22⋊D5—64no—
350C2×C22⋊D5—64no—
351C2×C22⋊D5—64no—
352C22×Dic5—31no—
353C22×Dic5—31no—
354C22×Dic5—31no—
355C22×Dic5—31no—
356C22×Dic5—31no—
357C22×Dic5—31no—
358C22×Dic5—34no—
359C22×Dic5—34no—
360C22×Dic5—34no—
361C22×Dic5—64no—
362C22×Dic5—64no—
363C22×Dic5—64no—
364#711—632no—
365#709—632no—
366C2×D20—34no—
367C2×D20—64no—
368C2×C4×D5—34no—
369C2×C4×D5—34no—
370C2×C4×D5—34no—
371C2×C4×D5—34no—
372C2×C4×D5—64no—
373C2×C4×D5—64no—
374C2×C4×D5—64no—
375C2×C4×D5—64no—
376C2×Dic10—34no—
377C2×Dic10—34no—
378C2×Dic10—64no—
379C2×Dic10—64no—
380C5×C4⋊C4C22×D314yes—
381C5×C4⋊C4C22×D314yes—
382C5×C22⋊C4C22×D314yes—
383C5×C22⋊C4C22×D314yes—
384C5×C22⋊C4C22×D314yes—
385C22⋊Dic5—34no—
386#685—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390C4⋊Dic5—34no—
391C4⋊Dic5—34no—
392#683—34no—
393#683—34no—
394#683—34no—
395#683—34no—
396#683—34no—
397#683—34no—
398C4×Dic5—34no—
399C22×#41—151no—
400C22×#41—151no—
401#547—1516no—
402C2×C4⋊Q8—151no—
403C2×#123—151no—
404C2×#123—151no—
405C2×#123—151no—
406C2×#123D1511yescharacteristic, complemented
407C2×C22⋊Q8—151no—
408C2×C22⋊Q8—151no—
409C2×#121—151no—
410C2×#121—151no—
411C2×C4×D4—151no—
412C2×C4×D4—151no—
413C22×C4⋊C4—151no—
414C22×C4⋊C4—151no—
415C22×C3×C5—28no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—22no—
421C22×C3×C5—44no—
422C22×C3×C5C22×D414yes—
423C22×C3×C5C22×D412yes—
424C22×C3×C5C2×#4112yes—
425C22×C3×C52−1+412yes—
426C22×C3×C5C2511yescharacteristic
427C2×D15—28no—
428C2×D15—22no—
429C2×D15—22no—
430C2×D15—22no—
431C2×D15—22no—
432C2×D15—22no—
433C2×D15—44no—
434C2×D15C22×D414yes—
435C3×C4×C5—22no—
436C3×C4×C5—22no—
437C3×C4×C5—22no—
438C3×C4×C5—22no—
439C3×C4×C5—22no—
440Dic15—22no—
441Dic15—22no—
442Dic15—22no—
443Dic15—22no—
444Dic15C22×D414yes—
445Dic15C2×#4114yescomplemented
446C24×C3C22×D511yescharacteristic
447C24×C3C22×D511yescharacteristic
448C23×D3—51no—
449C23×D3—51no—
450C2×C3×D4—24no—
451C2×C3×D4C22×D514yes—
452C22×C3×C4—24no—
453C22×C3×C4C22×D511yescharacteristic
454C22×C3×C4C22×D511yescharacteristic
455C22×C3×C4C22×D511yescharacteristic
456C22×C3×C4C22×D514yes—
457C22×C3×C4C22×D511yescharacteristic
458C22×C3×C4C22×D511yescharacteristic
459C2×#67—58no—
460C2×#67—54no—
461C2×#67—54no—
462C2×#67—54no—
463C2×#67—54no—
464C2×#67—104no—
465C2×#67—104no—
466C2×#67—104no—
467C22×Dic3—51no—
468C22×Dic3—51no—
469C22×Dic3—54no—
470C22×Dic3—54no—
471C22×Dic3—54no—
472C22×Dic3—51no—
473C22×Dic3—51no—
474C22×Dic3—51no—
475C22×Dic3—51no—
476C22×Dic3—104no—
477C22×Dic3—104no—
478C22×Dic3—104no—
479#237—1032no—
480#235—1032no—
481C2×D12—54no—
482C2×D12—104no—
483C2×C4×D3—54no—
484C2×C4×D3—54no—
485C2×C4×D3—54no—
486C2×C4×D3—54no—
487C2×C4×D3—104no—
488C2×C4×D3—104no—
489C2×C4×D3—104no—
490C2×C4×D3—104no—
491C2×Dic6—54no—
492C2×Dic6—54no—
493C2×Dic6—104no—
494C2×Dic6—104no—
495C3×C4⋊C4C22×D514yes—
496C3×C4⋊C4C22×D514yes—
497C3×C22⋊C4C22×D514yes—
498C3×C22⋊C4C22×D514yes—
499C3×C22⋊C4C22×D514yes—
500#217—54no—
501(C2×D3)⋊C4—54no—
502(C2×D3)⋊C4—54no—
503(C2×D3)⋊C4—54no—
504(C2×D3)⋊C4—54no—
505C4⋊Dic3—54no—
506C4⋊Dic3—54no—
507Dic3⋊C4—54no—
508Dic3⋊C4—54no—
509Dic3⋊C4—54no—
510Dic3⋊C4—54no—
511Dic3⋊C4—54no—
512Dic3⋊C4—54no—
513C4×Dic3—54no—
514C23×C5—22no—
515C23×C5—22no—
516C23×C5—22no—
517C23×C5—22no—
518C23×C5—22no—
519C23×C5D3×D414yes—
520C23×C5C23×D312yes—
521C23×C5C23×D312yes—
522C23×C5C23×D311yescharacteristic
523C22×D5—34no—
524C22×D5—32no—
525C22×D5—32no—
526C22×D5—62no—
527C22×D5—62no—
528C22×D5—62no—
529C22×D5—62no—
530C22×D5—62no—
531C5×D4—28no—
532C2×C4×C5—22no—
533C2×C4×C5—22no—
534C2×C4×C5—22no—
535C2×C4×C5—28no—
536C2×C4×C5—22no—
537C2×C4×C5—22no—
538C2×C4×C5C23×D312yes—
539C2×C4×C5C23×D312yes—
540C2×C4×C5C23×D312yes—
541C2×C4×C5C23×D312yes—
542C2×C4×C5C23×D312yes—
543C22⋊D5—316no—
544C22⋊D5—68no—
545C22⋊D5—68no—
546C22⋊D5—68no—
547C2×Dic5—34no—
548C2×Dic5—34no—
549C2×Dic5—32no—
550C2×Dic5—32no—
551C2×Dic5—32no—
552C2×Dic5—32no—
553C2×Dic5—32no—
554C2×Dic5—32no—
555C2×Dic5—68no—
556C2×Dic5—68no—
557C2×Dic5—62no—
558C2×Dic5—62no—
559C2×Dic5—62no—
560C2×Dic5—68no—
561C2×Dic5—62no—
562D20—68no—
563C4×D5—68no—
564C4×D5—68no—
565C4×D5—68no—
566C4×D5—68no—
567Dic10—68no—
568Dic10—68no—
569C2×#41—158no—
570C2×#41—158no—
571C2×#41—308no—
572C2×#41—308no—
573C22×Q8—151no—
574C22×Q8—151no—
575C22×D4—151no—
576C22×D4—151no—
577C22×D4—151no—
578C22×D4—151no—
579C22×D4—151no—
580C22×D4C2×D1511yescharacteristic
581C23×C4—151no—
582C23×C4—151no—
583C23×C4—151no—
584C23×C4—151no—
585C23×C4—151no—
586C23×C4—151no—
587C23×C4—151no—
588C23×C4C2×D1511yescharacteristic
589C4⋊Q8—158no—
590#123—158no—
591#123—158no—
592#123—158no—
593#123C2×D1518yescomplemented
594C22⋊Q8—158no—
595C22⋊Q8—158no—
596#121—158no—
597#121—158no—
598C4×D4—158no—
599C4×D4—158no—
600C2×C4⋊C4—151no—
601C2×C4⋊C4—151no—
602C2×C4⋊C4—151no—
603C2×C4⋊C4—151no—
604C2×C4⋊C4—151no—
605C2×C4⋊C4—151no—
606C2×C4⋊C4—158no—
607C2×C4⋊C4—151no—
608C2×C4⋊C4—151no—
609C2×C4⋊C4—158no—
610C2×C4⋊C4C2×D1511yescharacteristic
611C2×C4⋊C4C2×D1511yescharacteristic
612C2×C22⋊C4—151no—
613C2×C22⋊C4—151no—
614C2×C22⋊C4—151no—
615C2×C22⋊C4—151no—
616C2×C22⋊C4—151no—
617C2×C22⋊C4C2×D1511yescharacteristic
618C2×C22⋊C4C2×D1511yescharacteristic
619C2×C22⋊C4C2×D1511yescharacteristic
620C2×C42—151no—
621C2×C3×C5—24no—
622C2×C3×C5—42no—
623C2×C3×C5#54714yescomplemented
624C2×C3×C5C23×D411yescharacteristic
625C2×C3×C5C22×#4111yescharacteristic
626C2×C3×C5C2×2−1+411yescharacteristic
627D15—24no—
628D15—42no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3D4×D514yes—
635C23×C3C23×D512yes—
636C23×C3C23×D512yes—
637C23×C3C23×D511yescharacteristic
638C22×D3—54no—
639C22×D3—52no—
640C22×D3—52no—
641C22×D3—102no—
642C22×D3—102no—
643C22×D3—102no—
644C22×D3—102no—
645C22×D3—102no—
646C3×D4—28no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—28no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4C23×D512yes—
654C2×C3×C4C23×D512yes—
655C2×C3×C4C23×D512yes—
656C2×C3×C4C23×D512yes—
657C2×C3×C4C23×D512yes—
658#67—516no—
659#67—108no—
660#67—108no—
661#67—108no—
662C2×Dic3—54no—
663C2×Dic3—54no—
664C2×Dic3—52no—
665C2×Dic3—52no—
666C2×Dic3—52no—
667C2×Dic3—52no—
668C2×Dic3—52no—
669C2×Dic3—52no—
670C2×Dic3—108no—
671C2×Dic3—108no—
672C2×Dic3—102no—
673C2×Dic3—102no—
674C2×Dic3—102no—
675C2×Dic3—108no—
676C2×Dic3—102no—
677D12—108no—
678C4×D3—108no—
679C4×D3—108no—
680C4×D3—108no—
681C4×D3—108no—
682Dic6—108no—
683Dic6—108no—
684C22×C5—28no—
685C22×C5—22no—
686C22×C5—22no—
687C22×C5—22no—
688C22×C5—22no—
689C22×C5—22no—
690C22×C5—44no—
691C22×C5C2×D3×D414yes—
692C22×C5C2×D3×D412yes—
693C22×C5D3×#4112yes—
694C22×C5#101012yes—
695C22×C5C24×D311yescharacteristic
696C2×D5—34no—
697C2×D5—68no—
698C2×D5—62no—
699C2×D5—62no—
700C2×D5—62no—
701C2×D5—62no—
702C2×D5—62no—
703C2×D5—124no—
704C4×C5—22no—
705C4×C5—22no—
706C4×C5—22no—
707C4×C5—22no—
708C4×C5—22no—
709Dic5—34no—
710Dic5—34no—
711Dic5—62no—
712Dic5—62no—
713Dic5—62no—
714Dic5—62no—
715C24—151no—
716C24—151no—
717C24C22×D1511yescharacteristic
718C24C22×D1511yescharacteristic
719#41—3032no—
720#41—3032no—
721C2×Q8—154no—
722C2×Q8—154no—
723C2×Q8—304no—
724C2×Q8—304no—
725C2×D4—24no—
726C2×D4—158no—
727C2×D4—154no—
728C2×D4—154no—
729C2×D4—154no—
730C2×D4—154no—
731C2×D4—154no—
732C2×D4—304no—
733C2×D4—304no—
734C2×D4—304no—
735C2×D4—304no—
736C2×D4C22×D1514yes—
737C22×C4—24no—
738C22×C4—151no—
739C22×C4—151no—
740C22×C4—154no—
741C22×C4—154no—
742C22×C4—154no—
743C22×C4—151no—
744C22×C4—151no—
745C22×C4—151no—
746C22×C4—151no—
747C22×C4—154no—
748C22×C4—154no—
749C22×C4—154no—
750C22×C4—154no—
751C22×C4—304no—
752C22×C4—304no—
753C22×C4—304no—
754C22×C4—304no—
755C22×C4—304no—
756C22×C4—304no—
757C22×C4—304no—
758C22×C4C22×D1514yes—
759C22×C4C22×D1511yescharacteristic
760C22×C4C22×D1511yescharacteristic
761C22×C4C22×D1511yescharacteristic
762C22×C4C22×D1511yescharacteristic
763C22×C4C22×D1511yescharacteristic
764C4⋊C4—154no—
765C4⋊C4—154no—
766C4⋊C4—154no—
767C4⋊C4—154no—
768C4⋊C4—154no—
769C4⋊C4—154no—
770C4⋊C4—154no—
771C4⋊C4—154no—
772C4⋊C4C22×D1514yes—
773C4⋊C4C22×D1514yes—
774C22⋊C4—154no—
775C22⋊C4—154no—
776C22⋊C4—154no—
777C22⋊C4—154no—
778C22⋊C4—154no—
779C22⋊C4C22×D1514yes—
780C22⋊C4C22×D1514yes—
781C22⋊C4C22×D1514yes—
782C42—154no—
783C3×C5C2×#54711yescharacteristic, complemented, Hall
784C22×C3—28no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—44no—
791C22×C3C2×D4×D514yes—
792C22×C3C2×D4×D512yes—
793C22×C3D5×#4112yes—
794C22×C3#415012yes—
795C22×C3C24×D511yescharacteristic
796C2×D3—54no—
797C2×D3—108no—
798C2×D3—102no—
799C2×D3—102no—
800C2×D3—102no—
801C2×D3—102no—
802C2×D3—102no—
803C2×D3—204no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809Dic3—54no—
810Dic3—54no—
811Dic3—102no—
812Dic3—102no—
813Dic3—102no—
814Dic3—102no—
815C2×C5—24no—
816C2×C5—42no—
817C2×C5#565514yescomplemented
818C2×C5C22×D3×D411yescharacteristic
819C2×C5C2×D3×#4111yescharacteristic
820C2×C5C2×#101011yescharacteristic
821D5—64no—
822D5—122no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—154no—
829C23—152no—
830C23—152no—
831C23—302no—
832C23—302no—
833C23—302no—
834C23—302no—
835C23—302no—
836C23D4×D1514yes—
837C23C23×D1512yes—
838C23C23×D1512yes—
839C23C23×D1511yescharacteristic
840Q8—308no—
841Q8—308no—
842D4—28no—
843D4—1516no—
844D4—308no—
845D4—308no—
846D4—308no—
847D4—308no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—28no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—154no—
855C2×C4—154no—
856C2×C4—152no—
857C2×C4—152no—
858C2×C4—152no—
859C2×C4—152no—
860C2×C4—152no—
861C2×C4—152no—
862C2×C4—308no—
863C2×C4—308no—
864C2×C4—308no—
865C2×C4—308no—
866C2×C4—308no—
867C2×C4—308no—
868C2×C4—302no—
869C2×C4—302no—
870C2×C4—302no—
871C2×C4—308no—
872C2×C4—302no—
873C2×C4C23×D1512yes—
874C2×C4C23×D1512yes—
875C2×C4C23×D1512yes—
876C2×C4C23×D1512yes—
877C2×C4C23×D1512yes—
878C2×C3—24no—
879C2×C3—42no—
880C2×C3#6598914yescomplemented
881C2×C3C22×D4×D511yescharacteristic
882C2×C3C2×D5×#4111yescharacteristic
883C2×C3C2×#415011yescharacteristic
884D3—104no—
885D3—202no—
886C5C2×#565511yescharacteristic, complemented, Sylow
887C22—22no—
888C22—22no—
889C22—28no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—44no—
894C22—154no—
895C22—302no—
896C22—302no—
897C22—308no—
898C22—302no—
899C22—302no—
900C22—302no—
901C22—604no—
902C22C2×D4×D1514yes—
903C22C2×D4×D1512yes—
904C22#41×D1512yes—
905C22#9210112yes—
906C22C24×D1511yescharacteristic
907C4—22no—
908C4—22no—
909C4—22no—
910C4—22no—
911C4—22no—
912C4—154no—
913C4—154no—
914C4—302no—
915C4—302no—
916C4—302no—
917C4—302no—
918C3C2×#6598911yescharacteristic, complemented, Sylow
919C2—24no—
920C2—42no—
921C2—304no—
922C2—602no—
923C2#1175641414yesdirect product factor
924C2C22×D4×D1511yescharacteristic
925C2C2×#41×D1511yescharacteristic
926C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#123C2
socleC23×C3×C5C24
hypercenterC2×#123D15
hypocenterC3×C5C2×#547
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×#6819C2semidirect
2. C22×#6817C2semidirect
3. C2×C3×C5×#123C2semidirect
4. C2×#91828C2semidirect
5. C22×#6712C2semidirect
6. #11756414C2direct (N × H)
7. C2×#91785C2semidirect
8. C2×#91783C2semidirect
9. C2×C4⋊C4×D15C2semidirect
10. C2×#91777C2semidirect
11. C2×#91775C2semidirect
12. C2×#91773C2semidirect
13. C2×#91772C2semidirect
14. C2×#91770C2semidirect
15. C2×#91770C2semidirect
16. C2×#91767C2semidirect
28. C2×#6819C22semidirect
30. C2×#6817C22semidirect
38. C3×C5×#123C22semidirect
45. #91828C22semidirect
58. C2×#6712C22semidirect
60. #91785C22semidirect
61. #91783C22semidirect
62. C4⋊C4×D15C22semidirect
63. #91777C22semidirect
64. #91775C22semidirect
65. #91773C22semidirect
66. #91772C22semidirect
67. #91770C22semidirect
68. #91770C22semidirect
69. #91767C22semidirect
73. C2×C5×#123D3semidirect
103. C2×#1220D4semidirect
157. C2×C3×#123D5semidirect
191. C5×#123C2×D3semidirect
256. #1220C2×D4semidirect
265. C2×Dic15#41semidirect
299. C3×#123C2×D5semidirect
406. C2×#123D15semidirect
445. Dic15C2×#41semidirect
593. #123C2×D15semidirect
623. C2×C3×C5#547semidirect
783. C3×C5C2×#547semidirect
817. C2×C5#5655semidirect
880. C2×C3#65989semidirect
886. C5C2×#5655semidirect
918. C3C2×#65989semidirect
923. C2#11756414direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68192
C22×#68172
C2×C3×C5×#1232
C2×#918282
C22×#67122
#117564142
C2×#917852
C2×#917832
C2×C4⋊C4×D152
C2×#917772
C2×#917752
C2×#917732
C2×#917722
C2×#917702
C2×#917672
C2×#659893
C2×#56555