Finite Group Databasebeta

← C2×#11755412 #14483336

Subgroups — C2×#11755412 #14483336

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
1C22×#6719C211yesmaximal, characteristic, complemented
2C2×C5×#953C211yesmaximal, characteristic
3C22×C3×C22⋊Dic5C211yesmaximal, characteristic, complemented
4C2×#91576C211yesmaximal, characteristic, complemented
5C2×#91574C211yesmaximal, characteristic, complemented
6#11755412C2116yesmaximal, direct product factor
7C2×#67⋊Dic5C211yesmaximal, characteristic, complemented
8C2×#91555C211yesmaximal, characteristic, complemented
9C2×Dic5×#67C211yesmaximal, characteristic, complemented
10C2×#91543C211yesmaximal, characteristic, complemented
11C2×#91539C211yesmaximal, characteristic, complemented
12C2×#91532C211yesmaximal, characteristic, complemented
13C2×#91531C211yesmaximal, characteristic, complemented
14C2×#91530C211yesmaximal, characteristic, complemented
15C2×#91528C211yesmaximal, characteristic, complemented
16C2×#91525C211yesmaximal, characteristic, complemented
17C2×#65921—31nomaximal, Hall
18C25×C3×C5C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C23×Dic15C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic
24C23×C3×Dic5C2211yescharacteristic
25C23×C3×Dic5C2211yescharacteristic
26C22×#1204C2211yescharacteristic, complemented
27C22×D3×Dic5C2211yescharacteristic, complemented
28C2×#6719C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C2×#6719C2211yescharacteristic
32C2×#6719C2218yescomplemented
33C5×#953C2218yes—
34C2×C5×#217C2211yescharacteristic
35C2×C5×#217C2211yescharacteristic
36C2×C5×#217C2211yescharacteristic
37C2×C3×C22⋊Dic5C2211yescharacteristic
38C2×C3×C22⋊Dic5C2211yescharacteristic
39C2×C3×C22⋊Dic5C2211yescharacteristic
40C2×C3×C22⋊Dic5C2211yescharacteristic
41C2×C3×C22⋊Dic5C2218yescomplemented
42#91576C2218yescomplemented
43#91574C2218yescomplemented
44#67⋊Dic5C2218yescomplemented
45#91555C2218yescomplemented
46Dic5×#67C2218yescomplemented
47C2×Dic3⋊Dic5C2211yescharacteristic, complemented
48C2×Dic3⋊Dic5C2211yescharacteristic, complemented
49C2×#6669C2211yescharacteristic, complemented
50C2×#6669C2211yescharacteristic, complemented
51C2×#6669C2211yescharacteristic, complemented
52#91543C2218yescomplemented
53C2×#6668C2211yescharacteristic, complemented
54C2×#6668C2211yescharacteristic, complemented
55C2×#6668C2211yescharacteristic, complemented
56#91539C2218yescomplemented
57C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
60#91532C2218yescomplemented
61#91531C2218yescomplemented
62#91530C2218yescomplemented
63#91528C2218yescomplemented
64C2×Dic3×Dic5C2211yescharacteristic, complemented
65C2×Dic3×Dic5C2211yescharacteristic, complemented
66C2×Dic3×Dic5C2211yescharacteristic, complemented
67#91525C2218yescomplemented
68C2×#5495—51nomaximal, Hall
69C2×C5×#120—31no—
70C22×C22⋊Dic5—31no—
71C22×C22⋊Dic5D311yescharacteristic, complemented
72C2×#4082—31no—
73C2×#4081—31no—
74C2×#4081—31no—
75C2×#4081—31no—
76C2×D4×Dic5—31no—
77C2×D4×Dic5—31no—
78#65921—316no—
79C2×#4025—31no—
80C2×#4025—31no—
81C2×#4024—31no—
82C2×#4024—31no—
83C2×#4023—31no—
84C2×#4023—31no—
85C24×C3×C5—24no—
86C24×C3×C5—24no—
87C24×C3×C5—42no—
88C24×C3×C5C2311yescharacteristic
89C24×C3×C5C2314yes—
90C24×C3×C5C2311yescharacteristic
91C24×C3×C5C2311yescharacteristic
92C23×C5×D3C2311yescharacteristic
93C22×Dic15—24no—
94C22×Dic15—42no—
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2314yes—
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2314yes—
101C2×C5×#67—24no—
102C2×C5×#67—24no—
103C2×C5×#67—42no—
104C2×C5×#67C2314yes—
105C2×C5×#67C2314yes—
106C2×C5×#67C2314yes—
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C22×C3×Dic5—24no—
111C22×C3×Dic5—42no—
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C22×C3×Dic5C2314yes—
117C22×C3×Dic5C2314yes—
118C2×#1204—42no—
119C2×#1204C2314yescomplemented
120C2×D3×Dic5—42no—
121C2×D3×Dic5C2314yescomplemented
122#6719C2314yes—
123#6719C2314yes—
124#6719C2314yes—
125#6719C2314yes—
126C5×#217C2314yes—
127C5×#217C2314yes—
128C5×#217C2314yes—
129C3×C22⋊Dic5C2314yes—
130C3×C22⋊Dic5C2314yes—
131C3×C22⋊Dic5C2314yes—
132C3×C22⋊Dic5C2314yes—
133Dic3⋊Dic5C2314yescomplemented
134Dic3⋊Dic5C2314yescomplemented
135#6669C2314yescomplemented
136#6669C2314yescomplemented
137#6669C2314yescomplemented
138#6668C2314yescomplemented
139#6668C2314yescomplemented
140#6668C2314yescomplemented
141(C2×D3)⋊Dic5C2314yescomplemented
142(C2×D3)⋊Dic5C2314yescomplemented
143(C2×D3)⋊Dic5C2314yescomplemented
144Dic3×Dic5C2314yescomplemented
145Dic3×Dic5C2314yescomplemented
146Dic3×Dic5C2314yescomplemented
147C22×C3×C22⋊C4—51no—
148C2×#953D511yescharacteristic
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×#877—51no—
163C25×C5C2×D311yescharacteristic
164C22×C5×D4—31no—
165C22×C5×D4—31no—
166C22×C5×D4—31no—
167C23×Dic5—31no—
168C23×Dic5—31no—
169C23×Dic5—31no—
170C23×Dic5C2×D311yescharacteristic
171C23×Dic5C2×D311yescharacteristic
172C22×Dic10—31no—
173C5×#120—38no—
174C2×C5×C22⋊C4—31no—
175C2×C5×C22⋊C4—31no—
176C2×C5×C22⋊C4—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5—31no—
179C2×C22⋊Dic5—31no—
180C2×C22⋊Dic5—31no—
181C2×C22⋊Dic5—38no—
182C2×C22⋊Dic5—31no—
183C2×C22⋊Dic5—31no—
184C2×C22⋊Dic5—31no—
185C2×C22⋊Dic5C2×D311yescharacteristic
186C2×C22⋊Dic5C2×D311yescharacteristic
187C2×C22⋊Dic5C2×D311yescharacteristic
188C2×C22⋊Dic5C2×D311yescharacteristic
189C2×C22⋊Dic5C2×D318yescomplemented
190#4082—38no—
191#4081—38no—
192#4081—38no—
193#4081—38no—
194D4×Dic5—38no—
195D4×Dic5—38no—
196C2×C4⋊Dic5—31no—
197C2×C4⋊Dic5—31no—
198C2×#683—31no—
199C2×#683—31no—
200C2×#683—31no—
201C2×#683—31no—
202C2×#683—31no—
203C2×#683—31no—
204C2×C4×Dic5—31no—
205C2×C4×Dic5—31no—
206C2×C4×Dic5—31no—
207#4025—38no—
208#4025—38no—
209#4024—38no—
210#4024—38no—
211#4023—38no—
212#4023—38no—
213C2×#551—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5—22no—
218C23×C3×C5—28no—
219C23×C3×C5—28no—
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5—44no—
224C23×C3×C5—416no—
225C23×C3×C5#4114yes—
226C23×C3×C5#4114yes—
227C23×C3×C5C2412yes—
228C23×C3×C5C2412yes—
229C23×C3×C5C2412yes—
230C23×C3×C5C2411yescharacteristic
231C22×C5×D3—22no—
232C22×C5×D3—22no—
233C22×C5×D3—22no—
234C22×C5×D3C2412yes—
235C2×Dic15—28no—
236C2×Dic15—22no—
237C2×Dic15—22no—
238C2×Dic15—22no—
239C2×Dic15—22no—
240C2×Dic15—44no—
241C2×Dic15C2412yes—
242C2×Dic15C2412yes—
243C2×Dic15C2412yes—
244C2×Dic15C2412yes—
245C5×#67—28no—
246C5×#67—28no—
247C5×#67—44no—
248C2×C5×Dic3—22no—
249C2×C5×Dic3—22no—
250C2×C5×Dic3—22no—
251C2×C5×Dic3C2412yes—
252C2×C5×Dic3C2412yes—
253C2×C5×Dic3C2412yes—
254C2×C3×Dic5—28no—
255C2×C3×Dic5—22no—
256C2×C3×Dic5—22no—
257C2×C3×Dic5—22no—
258C2×C3×Dic5—22no—
259C2×C3×Dic5—44no—
260C2×C3×Dic5C2412yes—
261C2×C3×Dic5C2412yes—
262C2×C3×Dic5C2412yes—
263C2×C3×Dic5C2412yes—
264#1204—44no—
265D3×Dic5—44no—
266C25×C3C2×D511yescharacteristic
267C23×C3×C4—51no—
268C23×C3×C4—51no—
269C22×#67C2×D511yescharacteristic
270C22×#67C2×D511yescharacteristic
271C22×#67C2×D511yescharacteristic
272C23×Dic3—51no—
273C23×Dic3—51no—
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—51no—
280C2×C3×C22⋊C4—58no—
281#953C2×D518yes—
282C2×#217—51no—
283C2×#217—51no—
284C2×#217—58no—
285C2×#217—51no—
286C2×#217—51no—
287C2×#217C2×D511yescharacteristic
288C2×#217C2×D511yescharacteristic
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⋊C4—51no—
304C2×Dic3⋊C4—51no—
305C2×C4×Dic3—51no—
306C2×C4×Dic3—51no—
307C2×C4×Dic3—51no—
308#886—58no—
309#885—58no—
310#883—58no—
311#67⋊C4—58no—
312#879—58no—
313#879—58no—
314#878—58no—
315#877—58no—
316C24×C5—24no—
317C24×C5—24no—
318C24×C5—31no—
319C24×C5—42no—
320C24×C5C22×D311yescharacteristic
321C24×C5C22×D314yes—
322C24×C5C22×D311yescharacteristic
323C24×C5C22×D311yescharacteristic
324C2×C5×D4—34no—
325C2×C5×D4—34no—
326C2×C5×D4—34no—
327C2×C5×D4—64no—
328C2×C5×D4—64no—
329C2×C5×D4—122no—
330C22×C4×C5—31no—
331C22×C4×C5—31no—
332C22×C4×C5—31no—
333C22×Dic5—24no—
334C22×Dic5—31no—
335C22×Dic5—31no—
336C22×Dic5—31no—
337C22×Dic5—31no—
338C22×Dic5—34no—
339C22×Dic5—34no—
340C22×Dic5—34no—
341C22×Dic5—42no—
342C22×Dic5—64no—
343C22×Dic5—122no—
344C22×Dic5—122no—
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D311yescharacteristic
348C22×Dic5C22×D311yescharacteristic
349C22×Dic5C22×D314yes—
350C22×Dic5C22×D314yes—
351C2×Dic10—34no—
352C2×Dic10—122no—
353C5×C22⋊C4—34no—
354C5×C22⋊C4—34no—
355C5×C22⋊C4—34no—
356C22⋊Dic5—34no—
357C22⋊Dic5—34no—
358C22⋊Dic5—34no—
359C22⋊Dic5—34no—
360C22⋊Dic5—34no—
361C22⋊Dic5—34no—
362C22⋊Dic5—34no—
363C22⋊Dic5C22×D314yes—
364C22⋊Dic5C22×D314yes—
365C22⋊Dic5C22×D314yes—
366C22⋊Dic5C22×D314yes—
367C4⋊Dic5—34no—
368C4⋊Dic5—34no—
369#683—34no—
370#683—34no—
371#683—34no—
372#683—34no—
373#683—34no—
374#683—34no—
375C4×Dic5—34no—
376C4×Dic5—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—31no—
388C2×C4×D4—151no—
389C2×C4×D4—151no—
390C2×#117—151no—
391C2×#117—151no—
392C22×C22⋊C4—51no—
393C22×C22⋊C4—151no—
394C22×C3×C5—28no—
395C22×C3×C5—28no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5—22no—
400C22×C3×C5—22no—
401C22×C3×C5—22no—
402C22×C3×C5—22no—
403C22×C3×C5—416no—
404C22×C3×C5—44no—
405C22×C3×C5C2×#4114yes—
406C22×C3×C5C2×#4112yes—
407C22×C3×C5C2×#4114yes—
408C22×C3×C5C2×#4112yes—
409C22×C3×C5H(5,𝔽2)12yes—
410C22×C3×C5C2511yescharacteristic
411C2×C5×D3—22no—
412C2×C5×D3—22no—
413C2×C5×D3—22no—
414C2×C5×D3—44no—
415Dic15—22no—
416Dic15—22no—
417Dic15—22no—
418Dic15—22no—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C3×Dic5—22no—
423C5×Dic3—22no—
424C5×Dic3—22no—
425C5×Dic3—22no—
426C24×C3—24no—
427C24×C3—24no—
428C24×C3—42no—
429C24×C3C22×D511yescharacteristic
430C24×C3C22×D514yes—
431C24×C3C22×D511yescharacteristic
432C24×C3C22×D511yescharacteristic
433C23×D3C22×D511yescharacteristic
434C22×C3×C4—51no—
435C22×C3×C4—51no—
436C22×C3×C4—51no—
437C22×C3×C4—51no—
438C22×C3×C4—54no—
439C22×C3×C4—54no—
440C22×C3×C4—104no—
441C22×C3×C4—202no—
442C2×#67—24no—
443C2×#67—24no—
444C2×#67—42no—
445C2×#67C22×D514yes—
446C2×#67C22×D514yes—
447C2×#67C22×D514yes—
448C22×Dic3—54no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—51no—
452C22×Dic3—51no—
453C22×Dic3—54no—
454C22×Dic3—104no—
455C22×Dic3—202no—
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⋊C4—54no—
467#217—54no—
468#217—54no—
469#217—54no—
470#217—54no—
471#217C22×D514yes—
472#217C22×D514yes—
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⋊C4—54no—
484Dic3⋊C4—54no—
485C4×Dic3—54no—
486C4×Dic3—54no—
487C4×Dic3—54no—
488C23×C5—22no—
489C23×C5—22no—
490C23×C5—22no—
491C23×C5—22no—
492C23×C5—28no—
493C23×C5—22no—
494C23×C5—28no—
495C23×C5—22no—
496C23×C5—22no—
497C23×C5—32no—
498C23×C5—44no—
499C23×C5—416no—
500C23×C5—62no—
501C23×C5—62no—
502C23×C5—62no—
503C23×C5#23514yes—
504C23×C5#23714yes—
505C23×C5C23×D312yes—
506C23×C5C23×D312yes—
507C23×C5C23×D312yes—
508C23×C5C23×D311yescharacteristic
509C5×D4—68no—
510C5×D4—68no—
511C5×D4—124no—
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×Dic5—28no—
519C2×Dic5—22no—
520C2×Dic5—22no—
521C2×Dic5—22no—
522C2×Dic5—22no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—32no—
526C2×Dic5—32no—
527C2×Dic5—44no—
528C2×Dic5—68no—
529C2×Dic5—62no—
530C2×Dic5—62no—
531C2×Dic5—62no—
532C2×Dic5—62no—
533C2×Dic5—124no—
534C2×Dic5—124no—
535C2×Dic5C23×D312yes—
536C2×Dic5C23×D312yes—
537C2×Dic5C23×D312yes—
538C2×Dic5C23×D312yes—
539Dic10—124no—
540C25D3×D511yescharacteristic
541C22×Q8—151no—
542C22×D4—31no—
543C22×D4—31no—
544C22×D4—31no—
545C23×C4—51no—
546C23×C4—51no—
547C23×C4—151no—
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—38no—
559C4×D4—158no—
560C4×D4—158no—
561#117—158no—
562#117—158no—
563C2×C4⋊C4—151no—
564C2×C4⋊C4—151no—
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—31no—
573C2×C22⋊C4—31no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—51no—
578C2×C22⋊C4—58no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4—158no—
587C2×C42—151no—
588C2×C42—151no—
589C2×C42—151no—
590C2×C3×C5—24no—
591C2×C3×C5—24no—
592C2×C3×C5—42no—
593C2×C3×C5#55114yescomplemented
594C2×C3×C5C22×#4111yescharacteristic
595C2×C3×C5C22×#4111yescharacteristic
596C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
597C5×D3—42no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—28no—
603C23×C3—22no—
604C23×C3—28no—
605C23×C3—22no—
606C23×C3—22no—
607C23×C3—44no—
608C23×C3—416no—
609C23×C3#71114yes—
610C23×C3#71114yes—
611C23×C3C23×D512yes—
612C23×C3C23×D512yes—
613C23×C3C23×D512yes—
614C23×C3C23×D511yescharacteristic
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3C23×D512yes—
619C2×C3×C4—52no—
620C2×C3×C4—52no—
621C2×C3×C4—52no—
622C2×C3×C4—52no—
623C2×C3×C4—108no—
624C2×C3×C4—102no—
625C2×C3×C4—102no—
626C2×C3×C4—102no—
627C2×C3×C4—102no—
628C2×C3×C4—204no—
629#67—28no—
630#67—28no—
631#67—44no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—52no—
636C2×Dic3—52no—
637C2×Dic3—52no—
638C2×Dic3—52no—
639C2×Dic3—108no—
640C2×Dic3—102no—
641C2×Dic3—102no—
642C2×Dic3—102no—
643C2×Dic3—102no—
644C2×Dic3—204no—
645C2×Dic3C23×D512yes—
646C2×Dic3C23×D512yes—
647C2×Dic3C23×D512yes—
648C4×D3—204no—
649Dic6—204no—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—22no—
653C22×C5—22no—
654C22×C5—28no—
655C22×C5—28no—
656C22×C5—22no—
657C22×C5—22no—
658C22×C5—22no—
659C22×C5—416no—
660C22×C5—44no—
661C22×C5—62no—
662C22×C5—62no—
663C22×C5—62no—
664C22×C5—124no—
665C22×C5C2×#23514yes—
666C22×C5C2×#23512yes—
667C22×C5C2×#23714yes—
668C22×C5C2×#23712yes—
669C22×C5#100412yes—
670C22×C5C24×D311yescharacteristic
671C4×C5—62no—
672C4×C5—62no—
673C4×C5—62no—
674Dic5—22no—
675Dic5—22no—
676Dic5—22no—
677Dic5—22no—
678Dic5—62no—
679Dic5—62no—
680Dic5—62no—
681Dic5—62no—
682C24—24no—
683C24—24no—
684C24—31no—
685C24—42no—
686C24C2×D3×D511yescharacteristic
687C24C2×D3×D514yes—
688C24C2×D3×D511yescharacteristic
689C24C2×D3×D511yescharacteristic
690C2×Q8—154no—
691C2×Q8—602no—
692C2×D4—34no—
693C2×D4—34no—
694C2×D4—34no—
695C2×D4—64no—
696C2×D4—64no—
697C2×D4—122no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—54no—
702C22×C4—51no—
703C22×C4—51no—
704C22×C4—51no—
705C22×C4—51no—
706C22×C4—54no—
707C22×C4—104no—
708C22×C4—154no—
709C22×C4—154no—
710C22×C4—151no—
711C22×C4—151no—
712C22×C4—151no—
713C22×C4—151no—
714C22×C4—154no—
715C22×C4—202no—
716C22×C4—304no—
717C22×C4—602no—
718C22×C4—602no—
719C4⋊C4—154no—
720C4⋊C4—154no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4—154no—
726C4⋊C4—154no—
727C22⋊C4—34no—
728C22⋊C4—34no—
729C22⋊C4—34no—
730C22⋊C4—54no—
731C22⋊C4—54no—
732C22⋊C4—54no—
733C22⋊C4—54no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C22⋊C4—154no—
737C22⋊C4—154no—
738C22⋊C4—154no—
739C22⋊C4—154no—
740C22⋊C4—154no—
741C42—154no—
742C42—154no—
743C42—154no—
744C3×C5C2×#55111yescharacteristic, complemented, Hall
745C22×C3—28no—
746C22×C3—28no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—416no—
755C22×C3—44no—
756C22×C3C2×#71114yes—
757C22×C3C2×#71112yes—
758C22×C3C2×#71114yes—
759C22×C3C2×#71112yes—
760C22×C3#414412yes—
761C22×C3C24×D511yescharacteristic
762C2×D3—22no—
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—44no—
766C3×C4—102no—
767C3×C4—102no—
768C3×C4—102no—
769C3×C4—102no—
770Dic3—22no—
771Dic3—22no—
772Dic3—22no—
773Dic3—102no—
774Dic3—102no—
775Dic3—102no—
776Dic3—102no—
777C2×C5—24no—
778C2×C5—24no—
779C2×C5—42no—
780C2×C5—122no—
781C2×C5#549514yescomplemented
782C2×C5C22×#23511yescharacteristic
783C2×C5C22×#23711yescharacteristic
784C2×C5C2×#100411yescharacteristic
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—28no—
790C23—22no—
791C23—28no—
792C23—22no—
793C23—22no—
794C23—32no—
795C23—44no—
796C23—416no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23#678014yes—
801C23#678214yes—
802C23C22×D3×D512yes—
803C23C22×D3×D512yes—
804C23C22×D3×D512yes—
805C23C22×D3×D511yescharacteristic
806Q8—604no—
807D4—68no—
808D4—68no—
809D4—124no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—52no—
814C2×C4—52no—
815C2×C4—52no—
816C2×C4—52no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—108no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—152no—
826C2×C4—152no—
827C2×C4—152no—
828C2×C4—152no—
829C2×C4—204no—
830C2×C4—308no—
831C2×C4—302no—
832C2×C4—302no—
833C2×C4—302no—
834C2×C4—302no—
835C2×C4—604no—
836C2×C4—604no—
837C2×C3—24no—
838C2×C3—24no—
839C2×C3—42no—
840C2×C3#6592114yescomplemented
841C2×C3C22×#71111yescharacteristic
842C2×C3C22×#71111yescharacteristic
843C2×C3C2×#414411yescharacteristic
844D3—42no—
845C5C2×#549511yescharacteristic, complemented, Sylow
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—28no—
851C22—28no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—416no—
856C22—44no—
857C22—62no—
858C22—62no—
859C22—62no—
860C22—124no—
861C22C2×#678014yes—
862C22C2×#678012yes—
863C22C2×#678214yes—
864C22C2×#678212yes—
865C22#9204912yes—
866C22C23×D3×D511yescharacteristic
867C4—62no—
868C4—62no—
869C4—62no—
870C4—102no—
871C4—102no—
872C4—102no—
873C4—102no—
874C4—302no—
875C4—302no—
876C4—302no—
877C4—302no—
878C3C2×#6592111yescharacteristic, complemented, Sylow
879C2—24no—
880C2—24no—
881C2—42no—
882C2—122no—
883C2#1175541214yesdirect product factor
884C2C22×#678011yescharacteristic
885C2C22×#678211yescharacteristic
886C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC25×C3×C5C22
socleC23×C3×C5C24
prime radicalC2×C5×#953C2
hypercenterC25D3×D5
hypocenterC3×C5C2×#551
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C22×#6719C2semidirect
3. C22×C3×C22⋊Dic5C2semidirect
4. C2×#91576C2semidirect
5. C2×#91574C2semidirect
6. #11755412C2direct (N × H)
7. C2×#67⋊Dic5C2semidirect
8. C2×#91555C2semidirect
9. C2×Dic5×#67C2semidirect
10. C2×#91543C2semidirect
11. C2×#91539C2semidirect
12. C2×#91532C2semidirect
13. C2×#91531C2semidirect
14. C2×#91530C2semidirect
15. C2×#91528C2semidirect
16. C2×#91525C2semidirect
26. C22×#1204C22semidirect
27. C22×D3×Dic5C22semidirect
32. C2×#6719C22semidirect
41. C2×C3×C22⋊Dic5C22semidirect
42. #91576C22semidirect
43. #91574C22semidirect
44. #67⋊Dic5C22semidirect
45. #91555C22semidirect
46. Dic5×#67C22semidirect
47. C2×Dic3⋊Dic5C22semidirect
48. C2×Dic3⋊Dic5C22semidirect
49. C2×#6669C22semidirect
50. C2×#6669C22semidirect
51. C2×#6669C22semidirect
52. #91543C22semidirect
53. C2×#6668C22semidirect
54. C2×#6668C22semidirect
55. C2×#6668C22semidirect
56. #91539C22semidirect
57. C2×(C2×D3)⋊Dic5C22semidirect
58. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×(C2×D3)⋊Dic5C22semidirect
60. #91532C22semidirect
61. #91531C22semidirect
62. #91530C22semidirect
63. #91528C22semidirect
64. C2×Dic3×Dic5C22semidirect
65. C2×Dic3×Dic5C22semidirect
66. C2×Dic3×Dic5C22semidirect
67. #91525C22semidirect
71. C22×C22⋊Dic5D3semidirect
119. C2×#1204C23semidirect
121. C2×D3×Dic5C23semidirect
133. Dic3⋊Dic5C23semidirect
134. Dic3⋊Dic5C23semidirect
135. #6669C23semidirect
136. #6669C23semidirect
137. #6669C23semidirect
138. #6668C23semidirect
139. #6668C23semidirect
140. #6668C23semidirect
141. (C2×D3)⋊Dic5C23semidirect
142. (C2×D3)⋊Dic5C23semidirect
143. (C2×D3)⋊Dic5C23semidirect
144. Dic3×Dic5C23semidirect
145. Dic3×Dic5C23semidirect
146. Dic3×Dic5C23semidirect
189. C2×C22⋊Dic5C2×D3semidirect
593. C2×C3×C5#551semidirect
744. C3×C5C2×#551semidirect
781. C2×C5#5495semidirect
840. C2×C3#65921semidirect
845. C5C2×#5495semidirect
878. C3C2×#65921semidirect
883. C2#11755412direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67192
C2×C5×#9532
C22×C3×C22⋊Dic52
C2×#915762
C2×#915742
#117554122
C2×#67⋊Dic52
C2×#915552
C2×Dic5×#672
C2×#915432
C2×#915392
C2×#915322
C2×#915312
C2×#915302
C2×#915282
C2×#915252
C2×#659213
C2×#54955