Finite Group Databasebeta

← C2×#11754737 #14483314

Subgroups — C2×#11754737 #14483314

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×#91826C211yesmaximal, characteristic
2C2×C5×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#4081C211yesmaximal, characteristic, complemented
4C2×#91575C211yesmaximal, characteristic, complemented
5C2×#91562C211yesmaximal, characteristic, complemented
6C2×#91561C211yesmaximal, characteristic, complemented
7C2×#91556C211yesmaximal, characteristic, complemented
8C2×#91542C211yesmaximal, characteristic, complemented
9C22×#6667C211yesmaximal, characteristic, complemented
10C2×#91528C211yesmaximal, characteristic, complemented
11C2×#91526C211yesmaximal, characteristic, complemented
12#11754737C2116yesmaximal, direct product factor
13C2×#91419C211yesmaximal, characteristic, complemented
14C2×#91403C211yesmaximal, characteristic, complemented
15C2×#91380C211yesmaximal, characteristic, complemented
16C2×#91337C211yesmaximal, characteristic, complemented
17C2×#65890—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C23×C5×Dic3C2211yescharacteristic
23C23×C5×Dic3C2211yescharacteristic, complemented
24C23×C3×Dic5C2211yescharacteristic
25C22×#1204C2211yescharacteristic, complemented
26C22×#1200C2211yescharacteristic
27C22×#1200C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29#91826C2218yes—
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×C5×#217C2211yescharacteristic
33C2×C5×#217C2211yescharacteristic, complemented
34C5×D4×Dic3C2218yescomplemented
35C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
36C2×C4×C5×Dic3C2211yescharacteristic, complemented
37C2×C3×C22⋊Dic5C2211yescharacteristic
38C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
39C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
40C3×#4081C2218yescomplemented
41C2×C3×#683C2211yescharacteristic, complemented
42C2×C3×#683C2211yescharacteristic, complemented
43#91575C2218yescomplemented
44#91562C2218yescomplemented
45#91561C2218yescomplemented
46#91556C2218yescomplemented
47C2×Dic3⋊Dic5C2211yescharacteristic, complemented
48C2×#6669C2211yescharacteristic, complemented
49#91542C2218yescomplemented
50C2×#6668C2211yescharacteristic, complemented
51C2×#6668C2211yescharacteristic, complemented
52C2×#6668C2211yescharacteristic, complemented
53C2×#6667C2211yescharacteristic
54C2×#6667C2211yescharacteristic
55C2×#6667C2211yescharacteristic
56C2×#6667C2211yescharacteristic
57C2×#6667C2211yescharacteristic
58C2×#6667C2211yescharacteristic
59C2×#6667C2218yescomplemented
60#91528C2218yescomplemented
61C2×Dic3×Dic5C2211yescharacteristic, complemented
62C2×Dic3×Dic5C2211yescharacteristic, complemented
63#91526C2218yescomplemented
64#91419C2218yescomplemented
65#91403C2218yescomplemented
66#91380C2218yescomplemented
67#91337C2218yescomplemented
68C2×#5658—51nomaximal, Hall
69C2×C4×C5×D4—31no—
70C2×#4083—31no—
71C2×#4081D311yescharacteristic, complemented
72C2×#4075—31no—
73C2×C4×C22⋊D5—31no—
74C22×#685—31no—
75C2×#4070—31no—
76#65890—316no—
77C2×#4044—31no—
78C2×#4042—31no—
79C2×#4031—31no—
80C2×#4029—31no—
81C2×D5×C22⋊C4—31no—
82C2×#4023—31no—
83C2×#4022—31no—
84C2×#4018—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×D15—24no—
88C23×D15—24no—
89C23×D15—42no—
90C23×D15C2311yescharacteristic
91C23×D15C2314yes—
92C23×D15C2311yescharacteristic
93C2×C3×C5×D4—24no—
94C2×C3×C5×D4C2314yes—
95C22×C3×C4×C5C2311yescharacteristic
96C2×#1220—24no—
97C2×#1220—42no—
98C2×#1220C2314yes—
99C2×#1220C2314yes—
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C22×C5×Dic3—42no—
103C22×C5×Dic3—42no—
104C22×C5×Dic3C2311yescharacteristic
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2314yes—
109C22×C5×Dic3C2314yescomplemented
110C22×C3×Dic5—24no—
111C22×C3×Dic5C2314yes—
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C2×#1204—42no—
117C2×#1204C2314yescomplemented
118C2×#1200—24no—
119C2×#1200—42no—
120C2×#1200C2314yes—
121C2×#1200C2314yes—
122#6719C2314yes—
123#6714C2314yes—
124#6714C2314yes—
125C5×#217C2314yes—
126C5×#217C2314yescomplemented
127C5×C4⋊Dic3C2314yescomplemented
128C4×C5×Dic3C2314yescomplemented
129C3×C22⋊Dic5C2314yes—
130C3×C22⋊Dic5C2314yescomplemented
131C3×C22⋊Dic5C2314yescomplemented
132C3×#683C2314yescomplemented
133C3×#683C2314yescomplemented
134Dic3⋊Dic5C2314yescomplemented
135#6669C2314yescomplemented
136#6668C2314yescomplemented
137#6668C2314yescomplemented
138#6668C2314yescomplemented
139#6667C2314yes—
140#6667C2314yes—
141#6667C2314yes—
142#6667C2314yes—
143#6667C2314yes—
144#6667C2314yes—
145Dic3×Dic5C2314yescomplemented
146Dic3×Dic5C2314yescomplemented
147C2×C3×#123—51no—
148C2×#937—51no—
149C2×D4×Dic3D511yescharacteristic, complemented
150C22×(C2×D3)⋊C4—51no—
151C2×#926—51no—
152#5658—516no—
153C2×#898—51no—
154C2×#898—51no—
155C2×#897—51no—
156C2×#892—51no—
157C2×#886—51no—
158C2×#885—51no—
159C2×#883—51no—
160C2×#67⋊C4—51no—
161C2×D3×C22⋊C4—51no—
162C2×#878—51no—
163C24×D5—31no—
164C22×C5×D4C2×D311yescharacteristic
165C23×C4×C5—31no—
166C23×C4×C5—31no—
167C22×C22⋊D5—31no—
168C22×C22⋊D5—31no—
169C23×Dic5C2×D311yescharacteristic
170C22×C4×D5—31no—
171C22×C4×D5—31no—
172C22×Dic10—31no—
173C4×C5×D4—38no—
174C2×C5×C4⋊C4—31no—
175C2×C5×C22⋊C4—31no—
176C2×C5×C22⋊C4—31no—
177C2×C42×C5—31no—
178C2×C22⋊Dic5—31no—
179C2×C22⋊Dic5C2×D311yescharacteristic
180C2×C22⋊Dic5C2×D311yescharacteristic, complemented
181C2×C22⋊Dic5C2×D311yescharacteristic, complemented
182#4083—38no—
183#4081C2×D318yescomplemented
184#4075—38no—
185C4×C22⋊D5—38no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—38no—
195C2×C4⋊Dic5—31no—
196#4070—38no—
197C2×#683—31no—
198C2×#683—31no—
199C2×#683—31no—
200C2×#683—31no—
201C2×#683C2×D311yescharacteristic, complemented
202C2×#683C2×D311yescharacteristic, complemented
203C2×C4×Dic5—31no—
204C2×C4×Dic5—31no—
205#4044—38no—
206#4042—38no—
207#4031—38no—
208#4029—38no—
209D5×C22⋊C4—38no—
210#4023—38no—
211#4022—38no—
212#4018—38no—
213C2×#551—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5#4114yes—
220C23×C3×C5C2412yes—
221C23×C3×C5C2412yes—
222C23×C3×C5C2411yescharacteristic
223C22×D15—22no—
224C22×D15—22no—
225C22×D15—28no—
226C22×D15—22no—
227C22×D15—22no—
228C22×D15—22no—
229C22×D15—28no—
230C22×D15—44no—
231C22×D15—416no—
232C22×D15#4114yes—
233C22×D15C2412yes—
234C22×D15C2412yes—
235C3×C5×D4—28no—
236C2×C3×C4×C5—22no—
237C2×C3×C4×C5C2412yes—
238#1220—28no—
239#1220—44no—
240C2×Dic15—22no—
241C2×Dic15—22no—
242C2×Dic15C2412yes—
243C2×Dic15C2412yes—
244C2×C5×Dic3—22no—
245C2×C5×Dic3—22no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3—22no—
248C2×C5×Dic3—44no—
249C2×C5×Dic3—44no—
250C2×C5×Dic3C2412yes—
251C2×C5×Dic3C2412yes—
252C2×C5×Dic3C2412yes—
253C2×C5×Dic3C2412yes—
254C2×C3×Dic5—22no—
255C2×C3×Dic5—28no—
256C2×C3×Dic5—22no—
257C2×C3×Dic5—22no—
258C2×C3×Dic5—22no—
259C2×C3×Dic5C2412yes—
260C2×C3×Dic5C2412yes—
261C2×C3×Dic5C2412yes—
262C2×C3×Dic5C2412yes—
263#1204—44no—
264#1200—28no—
265#1200—44no—
266C24×D3—51no—
267C22×C3×D4C2×D511yescharacteristic
268C23×C3×C4—51no—
269C22×#67—51no—
270C22×#67—51no—
271C23×Dic3C2×D511yescharacteristic
272C23×Dic3C2×D511yescharacteristic, complemented
273C22×C4×D3—51no—
274C22×C4×D3—51no—
275C22×Dic6—51no—
276C3×#123—58no—
277C2×C3×C4⋊C4—51no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×C3×C22⋊C4—51no—
281C2×C3×C22⋊C4—51no—
282C2×#217—51no—
283C2×#217C2×D511yescharacteristic
284C2×#217C2×D511yescharacteristic, complemented
285#937—58no—
286D4×Dic3C2×D518yescomplemented
287C2×(C2×D3)⋊C4—51no—
288C2×(C2×D3)⋊C4—51no—
289C2×(C2×D3)⋊C4—58no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4—51no—
296#926—58no—
297C2×C4⋊Dic3—51no—
298C2×C4⋊Dic3—51no—
299C2×C4⋊Dic3—51no—
300C2×C4⋊Dic3C2×D511yescharacteristic, complemented
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3—51no—
305C2×C4×Dic3C2×D511yescharacteristic, complemented
306#898—58no—
307#898—58no—
308#897—58no—
309#892—58no—
310#886—58no—
311#885—58no—
312#883—58no—
313#67⋊C4—58no—
314D3×C22⋊C4—58no—
315#878—58no—
316C24×C5C22×D311yescharacteristic
317C24×C5C22×D311yescharacteristic
318C23×D5—31no—
319C23×D5—31no—
320C23×D5—34no—
321C23×D5—64no—
322C23×D5—64no—
323C23×D5—122no—
324C2×C5×D4—24no—
325C2×C5×D4C22×D314yes—
326C22×C4×C5—31no—
327C22×C4×C5—31no—
328C22×C4×C5—31no—
329C22×C4×C5—31no—
330C22×C4×C5—34no—
331C22×C4×C5—34no—
332C22×C4×C5—122no—
333C22×C4×C5—122no—
334C22×C4×C5C22×D311yescharacteristic
335C2×C22⋊D5—34no—
336C2×C22⋊D5—34no—
337C2×C22⋊D5—64no—
338C2×C22⋊D5—122no—
339C22×Dic5—24no—
340C22×Dic5—31no—
341C22×Dic5—31no—
342C22×Dic5C22×D311yescharacteristic
343C22×Dic5C22×D311yescharacteristic
344C22×Dic5C22×D311yescharacteristic
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D314yes—
347C2×C4×D5—34no—
348C2×C4×D5—34no—
349C2×C4×D5—64no—
350C2×C4×D5—122no—
351C2×Dic10—34no—
352C2×Dic10—122no—
353C5×C4⋊C4—34no—
354C5×C22⋊C4—34no—
355C5×C22⋊C4—34no—
356C42×C5—34no—
357C22⋊Dic5—34no—
358C22⋊Dic5C22×D314yes—
359C22⋊Dic5C22×D314yescomplemented
360C22⋊Dic5C22×D314yescomplemented
361#685—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367#685—34no—
368#685—34no—
369C4⋊Dic5—34no—
370#683—34no—
371#683—34no—
372#683—34no—
373#683—34no—
374#683C22×D314yescomplemented
375#683C22×D314yescomplemented
376C4×Dic5—34no—
377C4×Dic5—34no—
378#551—1516no—
379C2×#126—151no—
380C2×#126—151no—
381C2×#124—151no—
382C2×#123—51no—
383C2×#123—151no—
384C2×#123—151no—
385C2×C22⋊Q8—151no—
386C2×C22⋊Q8—151no—
387C2×#120—151no—
388C2×C4×D4—31no—
389C2×C4×D4—151no—
390C2×#117—151no—
391C2×#117—151no—
392C22×C22⋊C4—151no—
393C22×C22⋊C4—151no—
394C22×C3×C5—28no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5—22no—
400C22×C3×C5—44no—
401C22×C3×C5C2×#4114yes—
402C22×C3×C5C2×#4112yes—
403C22×C3×C5C2×#4112yes—
404C22×C3×C5H(5,𝔽2)12yes—
405C22×C3×C5C2511yescharacteristic
406C2×D15—28no—
407C2×D15—22no—
408C2×D15—22no—
409C2×D15—22no—
410C2×D15—22no—
411C2×D15—22no—
412C2×D15—416no—
413C2×D15—44no—
414C2×D15C2×#4114yes—
415C3×C4×C5—22no—
416Dic15—22no—
417Dic15—22no—
418C3×Dic5—22no—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C5×Dic3—22no—
425C5×Dic3—22no—
426C24×C3C22×D511yescharacteristic
427C24×C3C22×D511yescharacteristic
428C23×D3—51no—
429C23×D3—51no—
430C23×D3—54no—
431C23×D3—104no—
432C23×D3—104no—
433C23×D3—202no—
434C2×C3×D4—24no—
435C2×C3×D4C22×D514yes—
436C22×C3×C4—51no—
437C22×C3×C4—51no—
438C22×C3×C4—51no—
439C22×C3×C4—51no—
440C22×C3×C4—54no—
441C22×C3×C4—104no—
442C22×C3×C4C22×D511yescharacteristic
443C2×#67—54no—
444C2×#67—54no—
445C2×#67—104no—
446C2×#67—202no—
447C22×Dic3—42no—
448C22×Dic3—42no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3C22×D511yescharacteristic
452C22×Dic3C22×D511yescharacteristic
453C22×Dic3C22×D511yescharacteristic
454C22×Dic3C22×D511yescharacteristic
455C22×Dic3C22×D514yes—
456C22×Dic3C22×D514yescomplemented
457C2×C4×D3—54no—
458C2×C4×D3—54no—
459C2×C4×D3—104no—
460C2×C4×D3—202no—
461C2×Dic6—54no—
462C2×Dic6—202no—
463C3×C4⋊C4—54no—
464C3×C4⋊C4—54no—
465C3×C22⋊C4—54no—
466C3×C22⋊C4—54no—
467C3×C22⋊C4—54no—
468#217—54no—
469#217C22×D514yes—
470#217C22×D514yescomplemented
471(C2×D3)⋊C4—54no—
472(C2×D3)⋊C4—54no—
473(C2×D3)⋊C4—54no—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4—54no—
476(C2×D3)⋊C4—54no—
477(C2×D3)⋊C4—54no—
478(C2×D3)⋊C4—54no—
479C4⋊Dic3—54no—
480C4⋊Dic3—54no—
481C4⋊Dic3—54no—
482C4⋊Dic3C22×D514yescomplemented
483Dic3⋊C4—54no—
484Dic3⋊C4—54no—
485C4×Dic3—54no—
486C4×Dic3—54no—
487C4×Dic3C22×D514yescomplemented
488C23×C5—22no—
489C23×C5—22no—
490C23×C5—22no—
491C23×C5—22no—
492C23×C5—22no—
493C23×C5#23714yes—
494C23×C5C23×D312yes—
495C23×C5C23×D312yes—
496C23×C5C23×D311yescharacteristic
497C22×D5—34no—
498C22×D5—32no—
499C22×D5—32no—
500C22×D5—68no—
501C22×D5—62no—
502C22×D5—62no—
503C22×D5—68no—
504C22×D5—62no—
505C22×D5—62no—
506C22×D5—62no—
507C22×D5—124no—
508C22×D5—1216no—
509C5×D4—28no—
510C2×C4×C5—22no—
511C2×C4×C5—32no—
512C2×C4×C5—32no—
513C2×C4×C5—32no—
514C2×C4×C5—32no—
515C2×C4×C5—62no—
516C2×C4×C5—62no—
517C2×C4×C5—62no—
518C2×C4×C5—62no—
519C2×C4×C5—124no—
520C2×C4×C5—124no—
521C2×C4×C5C23×D312yes—
522C22⋊D5—68no—
523C22⋊D5—124no—
524C2×Dic5—28no—
525C2×Dic5—22no—
526C2×Dic5—22no—
527C2×Dic5—22no—
528C2×Dic5—22no—
529C2×Dic5—32no—
530C2×Dic5—32no—
531C2×Dic5—62no—
532C2×Dic5—62no—
533C2×Dic5C23×D312yes—
534C2×Dic5C23×D312yes—
535C2×Dic5C23×D312yes—
536C2×Dic5C23×D312yes—
537C4×D5—68no—
538C4×D5—124no—
539Dic10—124no—
540C25—151no—
541C22×Q8—151no—
542C22×D4—151no—
543C22×D4—151no—
544C22×D4D3×D511yescharacteristic
545C23×C4—31no—
546C23×C4—31no—
547C23×C4—51no—
548C23×C4—151no—
549C23×C4—151no—
550#126—158no—
551#126—158no—
552#124—158no—
553#123—58no—
554#123—158no—
555#123—158no—
556C22⋊Q8—158no—
557C22⋊Q8—158no—
558#120—158no—
559C4×D4—38no—
560C4×D4—158no—
561#117—158no—
562#117—158no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—51no—
565C2×C4⋊C4—51no—
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—31no—
573C2×C22⋊C4—51no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—158no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—158no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4—151no—
587C2×C42—31no—
588C2×C42—151no—
589C2×C42—151no—
590C2×C3×C5—24no—
591C2×C3×C5—42no—
592C2×C3×C5#55114yescomplemented
593C2×C3×C5C22×#4111yescharacteristic
594C2×C3×C5C22×#4111yescharacteristic
595C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
596D15—24no—
597D15—42no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3#70914yes—
604C23×C3C23×D512yes—
605C23×C3C23×D512yes—
606C23×C3C23×D511yescharacteristic
607C22×D3—54no—
608C22×D3—52no—
609C22×D3—52no—
610C22×D3—108no—
611C22×D3—102no—
612C22×D3—102no—
613C22×D3—108no—
614C22×D3—102no—
615C22×D3—102no—
616C22×D3—102no—
617C22×D3—204no—
618C22×D3—2016no—
619C3×D4—28no—
620C2×C3×C4—22no—
621C2×C3×C4—52no—
622C2×C3×C4—52no—
623C2×C3×C4—52no—
624C2×C3×C4—52no—
625C2×C3×C4—108no—
626C2×C3×C4—102no—
627C2×C3×C4—102no—
628C2×C3×C4—102no—
629C2×C3×C4—102no—
630C2×C3×C4C23×D512yes—
631#67—108no—
632#67—204no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—44no—
638C2×Dic3—44no—
639C2×Dic3—52no—
640C2×Dic3—52no—
641C2×Dic3—102no—
642C2×Dic3—102no—
643C2×Dic3C23×D512yes—
644C2×Dic3C23×D512yes—
645C2×Dic3C23×D512yes—
646C2×Dic3C23×D512yes—
647C4×D3—108no—
648C4×D3—204no—
649Dic6—204no—
650C22×C5—28no—
651C22×C5—22no—
652C22×C5—22no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—22no—
656C22×C5—44no—
657C22×C5C2×#23714yes—
658C22×C5C2×#23712yes—
659C22×C5D3×#4112yes—
660C22×C5#100912yes—
661C22×C5C24×D311yescharacteristic
662C2×D5—34no—
663C2×D5—68no—
664C2×D5—62no—
665C2×D5—62no—
666C2×D5—62no—
667C2×D5—62no—
668C2×D5—62no—
669C2×D5—1216no—
670C2×D5—124no—
671C4×C5—22no—
672C4×C5—62no—
673C4×C5—62no—
674C4×C5—62no—
675C4×C5—62no—
676Dic5—22no—
677Dic5—22no—
678Dic5—22no—
679Dic5—22no—
680Dic5—62no—
681Dic5—62no—
682C24—151no—
683C24—151no—
684C24—154no—
685C24—304no—
686C24—304no—
687C24—602no—
688C24C2×D3×D511yescharacteristic
689C24C2×D3×D511yescharacteristic
690C2×Q8—154no—
691C2×Q8—602no—
692C2×D4—24no—
693C2×D4—154no—
694C2×D4—154no—
695C2×D4—304no—
696C2×D4—602no—
697C2×D4C2×D3×D514yes—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—34no—
703C22×C4—34no—
704C22×C4—54no—
705C22×C4—51no—
706C22×C4—51no—
707C22×C4—51no—
708C22×C4—51no—
709C22×C4—104no—
710C22×C4—122no—
711C22×C4—122no—
712C22×C4—154no—
713C22×C4—154no—
714C22×C4—151no—
715C22×C4—151no—
716C22×C4—304no—
717C22×C4—602no—
718C22×C4C2×D3×D511yescharacteristic
719C4⋊C4—34no—
720C4⋊C4—54no—
721C4⋊C4—54no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4—154no—
726C4⋊C4—154no—
727C22⋊C4—34no—
728C22⋊C4—34no—
729C22⋊C4—54no—
730C22⋊C4—54no—
731C22⋊C4—54no—
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⋊C4—154no—
741C42—34no—
742C42—154no—
743C42—154no—
744C3×C5C2×#55111yescharacteristic, complemented, Hall
745C22×C3—28no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—44no—
752C22×C3C2×#70914yes—
753C22×C3C2×#70912yes—
754C22×C3#414412yes—
755C22×C3D5×#4112yes—
756C22×C3C24×D511yescharacteristic
757C2×D3—54no—
758C2×D3—108no—
759C2×D3—102no—
760C2×D3—102no—
761C2×D3—102no—
762C2×D3—102no—
763C2×D3—102no—
764C2×D3—2016no—
765C2×D3—204no—
766C3×C4—22no—
767C3×C4—102no—
768C3×C4—102no—
769C3×C4—102no—
770C3×C4—102no—
771Dic3—22no—
772Dic3—22no—
773Dic3—22no—
774Dic3—22no—
775Dic3—102no—
776Dic3—102no—
777C2×C5—24no—
778C2×C5—42no—
779C2×C5#565814yescomplemented
780C2×C5C22×#23711yescharacteristic
781C2×C5C2×D3×#4111yescharacteristic
782C2×C5C2×#100911yescharacteristic
783D5—64no—
784D5—122no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—154no—
791C23—152no—
792C23—152no—
793C23—308no—
794C23—302no—
795C23—302no—
796C23—302no—
797C23—302no—
798C23—308no—
799C23—302no—
800C23—604no—
801C23—6016no—
802C23#677914yes—
803C23C22×D3×D512yes—
804C23C22×D3×D512yes—
805C23C22×D3×D511yescharacteristic
806Q8—604no—
807D4—28no—
808D4—308no—
809D4—604no—
810C2×C4—22no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—52no—
816C2×C4—52no—
817C2×C4—52no—
818C2×C4—52no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—108no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—124no—
829C2×C4—124no—
830C2×C4—152no—
831C2×C4—152no—
832C2×C4—308no—
833C2×C4—302no—
834C2×C4—302no—
835C2×C4—604no—
836C2×C4C22×D3×D512yes—
837C2×C3—24no—
838C2×C3—42no—
839C2×C3#6589014yescomplemented
840C2×C3C22×#70911yescharacteristic
841C2×C3C2×#414411yescharacteristic
842C2×C3C2×D5×#4111yescharacteristic
843D3—104no—
844D3—202no—
845C5C2×#565811yescharacteristic, complemented, Sylow
846C22—22no—
847C22—22no—
848C22—28no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—154no—
854C22—302no—
855C22—302no—
856C22—308no—
857C22—302no—
858C22—302no—
859C22—302no—
860C22—6016no—
861C22—604no—
862C22#9202412yes—
863C22#9202712yes—
864C22C2×#677914yes—
865C22C2×#677912yes—
866C22C23×D3×D511yescharacteristic
867C4—22no—
868C4—62no—
869C4—62no—
870C4—62no—
871C4—62no—
872C4—102no—
873C4—102no—
874C4—102no—
875C4—102no—
876C4—302no—
877C4—302no—
878C3C2×#6589011yescharacteristic, complemented, Sylow
879C2—24no—
880C2—42no—
881C2—304no—
882C2—602no—
883C2#1175473714yesdirect product factor
884C2C2×#9202411yescharacteristic
885C2C2×#9202711yescharacteristic
886C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
prime radicalC2×#91826C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#551
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C5×D4×Dic3C2semidirect
3. C2×C3×#4081C2semidirect
4. C2×#91575C2semidirect
5. C2×#91562C2semidirect
6. C2×#91561C2semidirect
7. C2×#91556C2semidirect
8. C2×#91542C2semidirect
9. C22×#6667C2semidirect
10. C2×#91528C2semidirect
11. C2×#91526C2semidirect
12. #11754737C2direct (N × H)
13. C2×#91419C2semidirect
14. C2×#91403C2semidirect
15. C2×#91380C2semidirect
16. C2×#91337C2semidirect
23. C23×C5×Dic3C22semidirect
25. C22×#1204C22semidirect
33. C2×C5×#217C22semidirect
34. C5×D4×Dic3C22semidirect
35. C2×C5×C4⋊Dic3C22semidirect
36. C2×C4×C5×Dic3C22semidirect
38. C2×C3×C22⋊Dic5C22semidirect
39. C2×C3×C22⋊Dic5C22semidirect
40. C3×#4081C22semidirect
41. C2×C3×#683C22semidirect
42. C2×C3×#683C22semidirect
43. #91575C22semidirect
44. #91562C22semidirect
45. #91561C22semidirect
46. #91556C22semidirect
47. C2×Dic3⋊Dic5C22semidirect
48. C2×#6669C22semidirect
49. #91542C22semidirect
50. C2×#6668C22semidirect
51. C2×#6668C22semidirect
52. C2×#6668C22semidirect
59. C2×#6667C22semidirect
60. #91528C22semidirect
61. C2×Dic3×Dic5C22semidirect
62. C2×Dic3×Dic5C22semidirect
63. #91526C22semidirect
64. #91419C22semidirect
65. #91403C22semidirect
66. #91380C22semidirect
67. #91337C22semidirect
71. C2×#4081D3semidirect
109. C22×C5×Dic3C23semidirect
117. C2×#1204C23semidirect
126. C5×#217C23semidirect
127. C5×C4⋊Dic3C23semidirect
128. C4×C5×Dic3C23semidirect
130. C3×C22⋊Dic5C23semidirect
131. C3×C22⋊Dic5C23semidirect
132. C3×#683C23semidirect
133. C3×#683C23semidirect
134. Dic3⋊Dic5C23semidirect
135. #6669C23semidirect
136. #6668C23semidirect
137. #6668C23semidirect
138. #6668C23semidirect
145. Dic3×Dic5C23semidirect
146. Dic3×Dic5C23semidirect
149. C2×D4×Dic3D5semidirect
180. C2×C22⋊Dic5C2×D3semidirect
181. C2×C22⋊Dic5C2×D3semidirect
183. #4081C2×D3semidirect
201. C2×#683C2×D3semidirect
202. C2×#683C2×D3semidirect
272. C23×Dic3C2×D5semidirect
284. C2×#217C2×D5semidirect
286. D4×Dic3C2×D5semidirect
300. C2×C4⋊Dic3C2×D5semidirect
305. C2×C4×Dic3C2×D5semidirect
359. C22⋊Dic5C22×D3semidirect
360. C22⋊Dic5C22×D3semidirect
374. #683C22×D3semidirect
375. #683C22×D3semidirect
456. C22×Dic3C22×D5semidirect
470. #217C22×D5semidirect
482. C4⋊Dic3C22×D5semidirect
487. C4×Dic3C22×D5semidirect
592. C2×C3×C5#551semidirect
744. C3×C5C2×#551semidirect
779. C2×C5#5658semidirect
839. C2×C3#65890semidirect
845. C5C2×#5658semidirect
878. C3C2×#65890semidirect
883. C2#11754737direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918262
C2×C5×D4×Dic32
C2×C3×#40812
C2×#915752
C2×#915622
C2×#915612
C2×#915562
C2×#915422
C22×#66672
C2×#915282
C2×#915262
#117547372
C2×#914192
C2×#914032
C2×#913802
C2×#913372
C2×#658903
C2×#56585