Finite Group Databasebeta

← C2×#11752800 #14483316

Subgroups — C2×#11752800 #14483316

Order 1920.

2656 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91770C211yesmaximal, characteristic, complemented
2C2×C5×#877C211yesmaximal, characteristic, complemented
3C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#91576C211yesmaximal, characteristic, complemented
5C2×#91564C211yesmaximal, characteristic
6C2×#91542C211yesmaximal, characteristic, complemented
7C22×#6665C211yesmaximal, characteristic, complemented
8C2×C4×#1202C211yesmaximal, characteristic, complemented
9C2×#91366C211yesmaximal, characteristic, complemented
10C2×#91363C211yesmaximal, characteristic, complemented
11C2×#91357C211yesmaximal, characteristic, complemented
12C2×#91354C211yesmaximal, characteristic, complemented
13C2×#91353C211yesmaximal, characteristic, complemented
14C2×#91349C211yesmaximal, characteristic, complemented
15C2×#91348C211yesmaximal, characteristic, complemented
16#11752800C2116yesmaximal, direct product factor
17C2×#65861—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C23×Dic15C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic, complemented
22C23×C5×Dic3C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×#1204C2211yescharacteristic, complemented
26C22×#1202C2211yescharacteristic
27C22×#1202C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×#6714C2211yescharacteristic, complemented
30C2×#6712C2211yescharacteristic, complemented
31C2×C4×Dic15C2211yescharacteristic, complemented
32#91770C2218yescomplemented
33C2×C5×#217C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
35C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C4×C5×Dic3C2211yescharacteristic, complemented
37C2×C4×C5×Dic3C2211yescharacteristic, complemented
38C5×#877C2218yescomplemented
39C2×C3×C22⋊Dic5C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C3×D5×C22⋊C4C2218yescomplemented
43#91576C2218yescomplemented
44#91564C2218yes—
45C2×Dic3⋊Dic5C2211yescharacteristic, complemented
46C2×#6669C2211yescharacteristic, complemented
47#91542C2218yescomplemented
48C2×#6668C2211yescharacteristic, complemented
49C2×#6668C2211yescharacteristic, complemented
50C2×#6668C2211yescharacteristic, complemented
51C2×#6667C2211yescharacteristic, complemented
52C2×#6667C2211yescharacteristic, complemented
53C2×#6665C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55C2×#6665C2211yescharacteristic
56C2×#6665C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59C2×#6665C2218yescomplemented
60C4×#1202C2218yescomplemented
61#91366C2218yescomplemented
62#91363C2218yescomplemented
63#91357C2218yescomplemented
64#91354C2218yescomplemented
65#91353C2218yescomplemented
66#91349C2218yescomplemented
67#91348C2218yescomplemented
68C2×#5495—51nomaximal, Hall
69C2×C5×#117—31no—
70C2×#4075—31no—
71C22×#685—31no—
72#65861—316no—
73C2×#4044—31no—
74C2×#4042—31no—
75C2×#4040—31no—
76C2×#4040—31no—
77C2×#4028—31no—
78C2×#4027—31no—
79C2×D5×C22⋊C4D311yescharacteristic, complemented
80C2×#4024—31no—
81C2×#4022—31no—
82C2×#4021—31no—
83C2×C4×D20—31no—
84C2×#4018—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C3×D5—24no—
88C23×C3×D5—24no—
89C23×C3×D5—42no—
90C23×C3×D5C2311yescharacteristic
91C23×C3×D5C2314yes—
92C23×C3×D5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C2×#1220—24no—
96C2×#1220C2314yes—
97C22×Dic15—42no—
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2314yes—
102C2×C4×D15—42no—
103C2×C4×D15C2314yescomplemented
104C22×C5×Dic3—24no—
105C22×C5×Dic3C2314yes—
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C2×C3×C4×D5—24no—
113C2×C3×C4×D5—42no—
114C2×C3×C4×D5C2314yes—
115C2×C3×C4×D5C2314yes—
116C2×#1204—42no—
117C2×#1204C2314yescomplemented
118C2×#1202—24no—
119C2×#1202—42no—
120C2×#1202C2314yes—
121C2×#1202C2314yes—
122C3×C5×C22⋊C4C2314yes—
123#6714C2314yescomplemented
124#6712C2314yescomplemented
125C4×Dic15C2314yescomplemented
126C5×#217C2314yes—
127C5×Dic3⋊C4C2314yescomplemented
128C5×Dic3⋊C4C2314yescomplemented
129C4×C5×Dic3C2314yescomplemented
130C4×C5×Dic3C2314yescomplemented
131C3×C22⋊Dic5C2314yes—
132C3×#685C2314yes—
133C3×#685C2314yes—
134Dic3⋊Dic5C2314yescomplemented
135#6669C2314yescomplemented
136#6668C2314yescomplemented
137#6668C2314yescomplemented
138#6668C2314yescomplemented
139#6667C2314yescomplemented
140#6667C2314yescomplemented
141#6665C2314yes—
142#6665C2314yes—
143#6665C2314yes—
144#6665C2314yes—
145#6665C2314yes—
146#6665C2314yes—
147C22×C3×C22⋊C4—51no—
148C2×#953—51no—
149C22×#217—51no—
150C2×#929—51no—
151C2×C4×#67—51no—
152C2×#926—51no—
153C2×#924—51no—
154#5495—516no—
155C2×#886—51no—
156C2×#885—51no—
157C2×#883—51no—
158C2×#67⋊C4—51no—
159C2×#879—51no—
160C2×#879—51no—
161C2×#878—51no—
162C2×#877D511yescharacteristic, complemented
163C24×D5C2×D311yescharacteristic
164C23×C4×C5—31no—
165C22×C22⋊D5—31no—
166C23×Dic5—31no—
167C22×D20—31no—
168C22×D20—31no—
169C22×C4×D5—31no—
170C22×C4×D5C2×D311yescharacteristic
171C22×C4×D5C2×D311yescharacteristic
172C22×Dic10—31no—
173C5×#117—38no—
174C2×C5×C4⋊C4—31no—
175C2×C5×C4⋊C4—31no—
176C2×C5×C22⋊C4—31no—
177C2×C5×C22⋊C4C2×D311yescharacteristic
178C2×C42×C5—31no—
179C2×C42×C5—31no—
180C2×C22⋊Dic5C2×D311yescharacteristic
181#4075—38no—
182C2×#685—31no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685—38no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685C2×D311yescharacteristic
193C2×#685C2×D311yescharacteristic
194C2×C4⋊Dic5—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×#683—31no—
198C2×#683—31no—
199C2×#683—31no—
200C2×C4×Dic5—31no—
201#4044—38no—
202#4042—38no—
203#4040—38no—
204#4040—38no—
205#4028—38no—
206#4027—38no—
207D5×C22⋊C4C2×D318yescomplemented
208#4024—38no—
209#4022—38no—
210#4021—38no—
211C4×D20—38no—
212#4018—38no—
213C2×#551—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5#4114yes—
217C23×C3×C5C2412yes—
218C23×C3×C5C2411yescharacteristic
219C22×D15—22no—
220C22×D15—22no—
221C22×D15—22no—
222C22×D15C2412yes—
223C22×C3×D5—22no—
224C22×C3×D5—22no—
225C22×C3×D5—28no—
226C22×C3×D5—22no—
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5—28no—
230C22×C3×D5—44no—
231C22×C3×D5—416no—
232C22×C3×D5#4114yes—
233C22×C3×D5C2412yes—
234C22×C3×D5C2412yes—
235C2×C3×C4×C5—22no—
236C2×C3×C4×C5—22no—
237C2×C3×C4×C5C2412yes—
238C2×C3×C4×C5C2412yes—
239#1220—28no—
240C2×Dic15—22no—
241C2×Dic15—22no—
242C2×Dic15—22no—
243C2×Dic15—44no—
244C2×Dic15C2412yes—
245C2×Dic15C2412yes—
246C2×Dic15C2412yes—
247C4×D15—44no—
248C2×C5×Dic3—22no—
249C2×C5×Dic3—28no—
250C2×C5×Dic3—22no—
251C2×C5×Dic3—22no—
252C2×C5×Dic3—22no—
253C2×C5×Dic3C2412yes—
254C2×C5×Dic3C2412yes—
255C2×C5×Dic3C2412yes—
256C2×C5×Dic3C2412yes—
257C2×C3×Dic5—22no—
258C2×C3×Dic5—22no—
259C2×C3×Dic5C2412yes—
260C2×C3×Dic5C2412yes—
261C3×C4×D5—28no—
262C3×C4×D5—44no—
263#1204—44no—
264#1202—28no—
265#1202—44no—
266C25×C3—51no—
267C23×C3×C4—51no—
268C23×C3×C4—51no—
269C22×#67—51no—
270C22×#67—51no—
271C22×#67—51no—
272C23×Dic3—51no—
273C23×Dic3C2×D511yescharacteristic
274C22×C4×D3—51no—
275C22×Dic6—51no—
276C2×C3×C22⋊C4—51no—
277C2×C3×C22⋊C4—51no—
278C2×C3×C22⋊C4—51no—
279C2×C3×C22⋊C4—58no—
280C2×C3×C22⋊C4C2×D511yescharacteristic
281#953—58no—
282C2×#217—51no—
283C2×#217—51no—
284C2×#217—51no—
285C2×#217—58no—
286C2×#217—51no—
287C2×#217—51no—
288C2×#217—51no—
289C2×#217C2×D511yescharacteristic
290#929—58no—
291C4×#67—58no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295#926—58no—
296C2×C4⋊Dic3—51no—
297C2×C4⋊Dic3—51no—
298C2×C4⋊Dic3—51no—
299#924—58no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4C2×D511yescharacteristic, complemented
304C2×Dic3⋊C4C2×D511yescharacteristic, complemented
305C2×C4×Dic3—51no—
306C2×C4×Dic3C2×D511yescharacteristic, complemented
307C2×C4×Dic3C2×D511yescharacteristic, complemented
308#886—58no—
309#885—58no—
310#883—58no—
311#67⋊C4—58no—
312#879—58no—
313#879—58no—
314#878—58no—
315#877C2×D518yescomplemented
316C24×C5C22×D311yescharacteristic
317C23×D5—24no—
318C23×D5—24no—
319C23×D5—31no—
320C23×D5—42no—
321C23×D5C22×D311yescharacteristic
322C23×D5C22×D314yes—
323C23×D5C22×D311yescharacteristic
324C22×C4×C5—31no—
325C22×C4×C5—31no—
326C22×C4×C5—31no—
327C22×C4×C5—31no—
328C22×C4×C5—34no—
329C22×C4×C5—64no—
330C22×C4×C5C22×D311yescharacteristic
331C22×C4×C5C22×D311yescharacteristic
332C2×C22⋊D5—34no—
333C2×C22⋊D5—64no—
334C22×Dic5—31no—
335C22×Dic5—31no—
336C22×Dic5—31no—
337C22×Dic5—34no—
338C22×Dic5—122no—
339C22×Dic5C22×D311yescharacteristic
340C22×Dic5C22×D311yescharacteristic
341C2×D20—34no—
342C2×D20—34no—
343C2×D20—64no—
344C2×D20—122no—
345C2×C4×D5—24no—
346C2×C4×D5—34no—
347C2×C4×D5—42no—
348C2×C4×D5—122no—
349C2×C4×D5C22×D314yes—
350C2×C4×D5C22×D314yes—
351C2×Dic10—34no—
352C2×Dic10—122no—
353C5×C4⋊C4—34no—
354C5×C4⋊C4—34no—
355C5×C22⋊C4—34no—
356C5×C22⋊C4C22×D314yes—
357C42×C5—34no—
358C42×C5—34no—
359C22⋊Dic5C22×D314yes—
360#685—34no—
361#685—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367#685—34no—
368#685—34no—
369#685C22×D314yes—
370#685C22×D314yes—
371C4⋊Dic5—34no—
372#683—34no—
373#683—34no—
374#683—34no—
375#683—34no—
376#683—34no—
377C4×Dic5—34no—
378#551—1516no—
379C2×#126—151no—
380C2×#126—151no—
381C2×#124—151no—
382C2×#123—151no—
383C2×#123—151no—
384C2×#123—151no—
385C2×C22⋊Q8—151no—
386C2×C22⋊Q8—151no—
387C2×#120—151no—
388C2×C4×D4—151no—
389C2×C4×D4—151no—
390C2×#117—31no—
391C2×#117—151no—
392C22×C22⋊C4—51no—
393C22×C22⋊C4—151no—
394C22×C3×C5—28no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5C2×#4114yes—
398C22×C3×C5C2×#4112yes—
399C22×C3×C5C2×#4112yes—
400C22×C3×C5H(5,𝔽2)12yes—
401C22×C3×C5C2511yescharacteristic
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—22no—
405C2×D15—44no—
406C2×C3×D5—28no—
407C2×C3×D5—22no—
408C2×C3×D5—22no—
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—22no—
412C2×C3×D5—416no—
413C2×C3×D5—44no—
414C2×C3×D5C2×#4114yes—
415C3×C4×C5—22no—
416C3×C4×C5—22no—
417Dic15—22no—
418Dic15—22no—
419Dic15—22no—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C5×Dic3—22no—
425C5×Dic3—22no—
426C24×C3—51no—
427C24×C3—51no—
428C24×C3—54no—
429C24×C3—104no—
430C24×C3—104no—
431C24×C3—202no—
432C24×C3C22×D511yescharacteristic
433C23×D3—51no—
434C22×C3×C4—51no—
435C22×C3×C4—51no—
436C22×C3×C4—54no—
437C22×C3×C4—54no—
438C22×C3×C4—104no—
439C22×C3×C4—202no—
440C22×C3×C4C22×D511yescharacteristic
441C22×C3×C4C22×D511yescharacteristic
442C2×#67—54no—
443C2×#67—54no—
444C2×#67—54no—
445C2×#67—104no—
446C2×#67—104no—
447C2×#67—202no—
448C22×Dic3—24no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—51no—
452C22×Dic3—54no—
453C22×Dic3—202no—
454C22×Dic3C22×D514yes—
455C22×Dic3C22×D511yescharacteristic
456C22×Dic3C22×D511yescharacteristic
457C22×Dic3C22×D511yescharacteristic
458C22×Dic3C22×D511yescharacteristic
459C2×C4×D3—54no—
460C2×C4×D3—202no—
461C2×Dic6—54no—
462C2×Dic6—202no—
463C3×C22⋊C4—54no—
464C3×C22⋊C4—54no—
465C3×C22⋊C4—54no—
466C3×C22⋊C4C22×D514yes—
467#217—54no—
468#217—54no—
469#217—54no—
470#217—54no—
471#217—54no—
472#217—54no—
473#217C22×D514yes—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4—54no—
476(C2×D3)⋊C4—54no—
477C4⋊Dic3—54no—
478C4⋊Dic3—54no—
479C4⋊Dic3—54no—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4—54no—
483Dic3⋊C4C22×D514yescomplemented
484Dic3⋊C4C22×D514yescomplemented
485C4×Dic3—54no—
486C4×Dic3C22×D514yescomplemented
487C4×Dic3C22×D514yescomplemented
488C23×C5—22no—
489C23×C5—22no—
490C23×C5#23514yes—
491C23×C5C23×D312yes—
492C23×C5C23×D311yescharacteristic
493C22×D5—22no—
494C22×D5—22no—
495C22×D5—28no—
496C22×D5—22no—
497C22×D5—22no—
498C22×D5—22no—
499C22×D5—28no—
500C22×D5—32no—
501C22×D5—44no—
502C22×D5—416no—
503C22×D5—62no—
504C22×D5—62no—
505C22×D5—62no—
506C22×D5#23714yes—
507C22×D5C23×D312yes—
508C22×D5C23×D312yes—
509C2×C4×C5—22no—
510C2×C4×C5—22no—
511C2×C4×C5—32no—
512C2×C4×C5—32no—
513C2×C4×C5—32no—
514C2×C4×C5—32no—
515C2×C4×C5—68no—
516C2×C4×C5—62no—
517C2×C4×C5—62no—
518C2×C4×C5—62no—
519C2×C4×C5—62no—
520C2×C4×C5C23×D312yes—
521C2×C4×C5C23×D312yes—
522C22⋊D5—68no—
523C2×Dic5—22no—
524C2×Dic5—22no—
525C2×Dic5—32no—
526C2×Dic5—32no—
527C2×Dic5—32no—
528C2×Dic5—62no—
529C2×Dic5—62no—
530C2×Dic5—62no—
531C2×Dic5—124no—
532C2×Dic5C23×D312yes—
533C2×Dic5C23×D312yes—
534D20—68no—
535D20—124no—
536C4×D5—28no—
537C4×D5—44no—
538C4×D5—124no—
539Dic10—124no—
540C25—51no—
541C22×Q8—151no—
542C22×D4—151no—
543C22×D4—151no—
544C22×D4—151no—
545C23×C4—31no—
546C23×C4—51no—
547C23×C4—51no—
548C23×C4—151no—
549C23×C4—151no—
550#126—158no—
551#126—158no—
552#124—158no—
553#123—158no—
554#123—158no—
555#123—158no—
556C22⋊Q8—158no—
557C22⋊Q8—158no—
558#120—158no—
559C4×D4—158no—
560C4×D4—158no—
561#117—38no—
562#117—158no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—151no—
566C2×C4⋊C4—151no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C4⋊C4—151no—
570C2×C4⋊C4—151no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—51no—
573C2×C22⋊C4—51no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—58no—
576C2×C22⋊C4—151no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—158no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4D3×D511yescharacteristic
587C2×C42—31no—
588C2×C42—31no—
589C2×C42—151no—
590C2×C3×C5—24no—
591C2×C3×C5#55114yescomplemented
592C2×C3×C5C22×#4111yescharacteristic
593C2×C3×C5C22×#4111yescharacteristic
594C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
595D15—42no—
596C3×D5—24no—
597C3×D5—42no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—54no—
601C23×C3—52no—
602C23×C3—52no—
603C23×C3—108no—
604C23×C3—102no—
605C23×C3—102no—
606C23×C3—108no—
607C23×C3—102no—
608C23×C3—102no—
609C23×C3—102no—
610C23×C3—204no—
611C23×C3—2016no—
612C23×C3#70914yes—
613C23×C3C23×D512yes—
614C23×C3C23×D511yescharacteristic
615C22×D3—52no—
616C22×D3—102no—
617C22×D3—102no—
618C22×D3—102no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—52no—
622C2×C3×C4—52no—
623C2×C3×C4—108no—
624C2×C3×C4—102no—
625C2×C3×C4—102no—
626C2×C3×C4—204no—
627C2×C3×C4C23×D512yes—
628C2×C3×C4C23×D512yes—
629#67—108no—
630#67—108no—
631#67—204no—
632C2×Dic3—28no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—52no—
638C2×Dic3—52no—
639C2×Dic3—52no—
640C2×Dic3—102no—
641C2×Dic3—102no—
642C2×Dic3—102no—
643C2×Dic3—204no—
644C2×Dic3C23×D512yes—
645C2×Dic3C23×D512yes—
646C2×Dic3C23×D512yes—
647C2×Dic3C23×D512yes—
648C4×D3—204no—
649Dic6—204no—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—28no—
653C22×C5C2×#23514yes—
654C22×C5C2×#23512yes—
655C22×C5C2×#23712yes—
656C22×C5#100412yes—
657C22×C5C24×D311yescharacteristic
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—28no—
661C2×D5—22no—
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—416no—
665C2×D5—44no—
666C2×D5—62no—
667C2×D5—62no—
668C2×D5—62no—
669C2×D5—124no—
670C2×D5C2×#23714yes—
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—62no—
674C4×C5—62no—
675C4×C5—62no—
676C4×C5—62no—
677Dic5—22no—
678Dic5—22no—
679Dic5—62no—
680Dic5—62no—
681Dic5—62no—
682C24—51no—
683C24—51no—
684C24—54no—
685C24—104no—
686C24—104no—
687C24—151no—
688C24—202no—
689C24C2×D3×D511yescharacteristic
690C2×Q8—154no—
691C2×Q8—602no—
692C2×D4—154no—
693C2×D4—154no—
694C2×D4—154no—
695C2×D4—304no—
696C2×D4—304no—
697C2×D4—602no—
698C22×C4—34no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—51no—
704C22×C4—51no—
705C22×C4—54no—
706C22×C4—54no—
707C22×C4—64no—
708C22×C4—104no—
709C22×C4—151no—
710C22×C4—151no—
711C22×C4—151no—
712C22×C4—154no—
713C22×C4—154no—
714C22×C4—202no—
715C22×C4—602no—
716C22×C4—602no—
717C22×C4C2×D3×D511yescharacteristic
718C22×C4C2×D3×D511yescharacteristic
719C4⋊C4—34no—
720C4⋊C4—34no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4—154no—
726C4⋊C4—154no—
727C22⋊C4—34no—
728C22⋊C4—54no—
729C22⋊C4—54no—
730C22⋊C4—54no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C22⋊C4—154no—
737C22⋊C4—154no—
738C22⋊C4—154no—
739C22⋊C4—154no—
740C22⋊C4C2×D3×D514yes—
741C42—34no—
742C42—34no—
743C42—154no—
744C3×C5C2×#55111yescharacteristic, complemented, Hall
745C22×C3—28no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—54no—
749C22×C3—108no—
750C22×C3—102no—
751C22×C3—102no—
752C22×C3—102no—
753C22×C3—102no—
754C22×C3—102no—
755C22×C3—2016no—
756C22×C3—204no—
757C22×C3C2×#70914yes—
758C22×C3C2×#70912yes—
759C22×C3D5×#4112yes—
760C22×C3#414912yes—
761C22×C3C24×D511yescharacteristic
762C2×D3—102no—
763C2×D3—102no—
764C2×D3—102no—
765C2×D3—204no—
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—102no—
769C3×C4—102no—
770Dic3—22no—
771Dic3—22no—
772Dic3—22no—
773Dic3—22no—
774Dic3—102no—
775Dic3—102no—
776Dic3—102no—
777C2×C5—24no—
778C2×C5#549514yescomplemented
779C2×C5C22×#23511yescharacteristic
780C2×C5C22×#23711yescharacteristic
781C2×C5C2×#100411yescharacteristic
782D5—24no—
783D5—42no—
784D5—122no—
785C23—22no—
786C23—22no—
787C23—54no—
788C23—52no—
789C23—52no—
790C23—108no—
791C23—102no—
792C23—102no—
793C23—108no—
794C23—102no—
795C23—102no—
796C23—102no—
797C23—152no—
798C23—204no—
799C23—2016no—
800C23—302no—
801C23—302no—
802C23—302no—
803C23#677114yes—
804C23C22×D3×D512yes—
805C23C22×D3×D511yescharacteristic
806Q8—604no—
807D4—308no—
808D4—308no—
809D4—604no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—52no—
817C2×C4—52no—
818C2×C4—68no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—108no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—152no—
827C2×C4—152no—
828C2×C4—152no—
829C2×C4—204no—
830C2×C4—302no—
831C2×C4—302no—
832C2×C4—302no—
833C2×C4—604no—
834C2×C4—604no—
835C2×C4C22×D3×D512yes—
836C2×C4C22×D3×D512yes—
837C2×C3—24no—
838C2×C3—104no—
839C2×C3—202no—
840C2×C3#6586114yescomplemented
841C2×C3C22×#70911yescharacteristic
842C2×C3C2×D5×#4111yescharacteristic
843C2×C3C2×#414911yescharacteristic
844D3—202no—
845C5C2×#549511yescharacteristic, complemented, Sylow
846C22—28no—
847C22—22no—
848C22—22no—
849C22—54no—
850C22—108no—
851C22—102no—
852C22—102no—
853C22—102no—
854C22—102no—
855C22—102no—
856C22—2016no—
857C22—204no—
858C22—302no—
859C22—302no—
860C22—302no—
861C22—604no—
862C22C2×#677114yes—
863C22C2×#677112yes—
864C22D5×#23712yes—
865C22#9202612yes—
866C22C23×D3×D511yescharacteristic
867C4—22no—
868C4—22no—
869C4—62no—
870C4—62no—
871C4—62no—
872C4—62no—
873C4—102no—
874C4—102no—
875C4—302no—
876C4—302no—
877C4—302no—
878C3C2×#6586111yescharacteristic, complemented, Sylow
879C2—24no—
880C2—104no—
881C2—202no—
882C2—602no—
883C2#1175280014yesdirect product factor
884C2C22×#677111yescharacteristic
885C2C2×D5×#23711yescharacteristic
886C2C2×#9202611yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
prime radicalC2×#91564C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#551
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×#91770C2semidirect
2. C2×C5×#877C2semidirect
3. C2×C3×D5×C22⋊C4C2semidirect
4. C2×#91576C2semidirect
6. C2×#91542C2semidirect
7. C22×#6665C2semidirect
8. C2×C4×#1202C2semidirect
9. C2×#91366C2semidirect
10. C2×#91363C2semidirect
11. C2×#91357C2semidirect
12. C2×#91354C2semidirect
13. C2×#91353C2semidirect
14. C2×#91349C2semidirect
15. C2×#91348C2semidirect
16. #11752800C2direct (N × H)
21. C22×C4×D15C22semidirect
25. C22×#1204C22semidirect
29. C2×#6714C22semidirect
30. C2×#6712C22semidirect
31. C2×C4×Dic15C22semidirect
32. #91770C22semidirect
34. C2×C5×Dic3⋊C4C22semidirect
35. C2×C5×Dic3⋊C4C22semidirect
36. C2×C4×C5×Dic3C22semidirect
37. C2×C4×C5×Dic3C22semidirect
38. C5×#877C22semidirect
42. C3×D5×C22⋊C4C22semidirect
43. #91576C22semidirect
45. C2×Dic3⋊Dic5C22semidirect
46. C2×#6669C22semidirect
47. #91542C22semidirect
48. C2×#6668C22semidirect
49. C2×#6668C22semidirect
50. C2×#6668C22semidirect
51. C2×#6667C22semidirect
52. C2×#6667C22semidirect
59. C2×#6665C22semidirect
60. C4×#1202C22semidirect
61. #91366C22semidirect
62. #91363C22semidirect
63. #91357C22semidirect
64. #91354C22semidirect
65. #91353C22semidirect
66. #91349C22semidirect
67. #91348C22semidirect
79. C2×D5×C22⋊C4D3semidirect
103. C2×C4×D15C23semidirect
117. C2×#1204C23semidirect
123. #6714C23semidirect
124. #6712C23semidirect
125. C4×Dic15C23semidirect
127. C5×Dic3⋊C4C23semidirect
128. C5×Dic3⋊C4C23semidirect
129. C4×C5×Dic3C23semidirect
130. C4×C5×Dic3C23semidirect
134. Dic3⋊Dic5C23semidirect
135. #6669C23semidirect
136. #6668C23semidirect
137. #6668C23semidirect
138. #6668C23semidirect
139. #6667C23semidirect
140. #6667C23semidirect
162. C2×#877D5semidirect
207. D5×C22⋊C4C2×D3semidirect
303. C2×Dic3⋊C4C2×D5semidirect
304. C2×Dic3⋊C4C2×D5semidirect
306. C2×C4×Dic3C2×D5semidirect
307. C2×C4×Dic3C2×D5semidirect
315. #877C2×D5semidirect
483. Dic3⋊C4C22×D5semidirect
484. Dic3⋊C4C22×D5semidirect
486. C4×Dic3C22×D5semidirect
487. C4×Dic3C22×D5semidirect
591. C2×C3×C5#551semidirect
744. C3×C5C2×#551semidirect
778. C2×C5#5495semidirect
840. C2×C3#65861semidirect
845. C5C2×#5495semidirect
878. C3C2×#65861semidirect
883. C2#11752800direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917702
C2×C5×#8772
C2×C3×D5×C22⋊C42
C2×#915762
C2×#915642
C2×#915422
C22×#66652
C2×C4×#12022
C2×#913662
C2×#913632
C2×#913572
C2×#913542
C2×#913532
C2×#913492
C2×#913482
#117528002
C2×#658613
C2×#54955