Finite Group Databasebeta

← C2×#11753103 #14483298

Subgroups — C2×#11753103 #14483298

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×#91767C211yesmaximal, characteristic, complemented
2C2×C5×#886C211yesmaximal, characteristic, complemented
3C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#91563C211yesmaximal, characteristic
5C2×#67⋊Dic5C211yesmaximal, characteristic, complemented
6C22×#6665C211yesmaximal, characteristic, complemented
7C2×#91529C211yesmaximal, characteristic, complemented
8C2×#91462C211yesmaximal, characteristic, complemented
9C2×#91457C211yesmaximal, characteristic, complemented
10C2×#91447C211yesmaximal, characteristic, complemented
11C2×#91440C211yesmaximal, characteristic, complemented
12C2×#91361C211yesmaximal, characteristic, complemented
13C2×#91361C211yesmaximal, characteristic, complemented
14C2×#91360C211yesmaximal, characteristic, complemented
15C2×#91358C211yesmaximal, characteristic, complemented
16#11753103C2116yesmaximal, direct product factor
17C2×#65992—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×Dic30C2211yescharacteristic, complemented
21C22×C5×#67C2211yescharacteristic
22C23×C5×Dic3C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C22×#1201C2211yescharacteristic
27C22×D3×Dic5C2211yescharacteristic, complemented
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30C2×C4⋊Dic15C2211yescharacteristic, complemented
31C2×#6712C2211yescharacteristic, complemented
32C2×#6712C2211yescharacteristic, complemented
33#91767C2218yescomplemented
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
37C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
38C5×#886C2218yescomplemented
39C2×C3×C22⋊Dic5C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C3×D5×C22⋊C4C2218yescomplemented
43#91563C2218yes—
44#67⋊Dic5C2218yescomplemented
45C2×Dic3⋊Dic5C2211yescharacteristic, complemented
46C2×Dic3⋊Dic5C2211yescharacteristic, complemented
47C2×Dic3⋊Dic5C2211yescharacteristic, complemented
48C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
49C2×#6665C2211yescharacteristic
50C2×#6665C2211yescharacteristic
51C2×#6665C2211yescharacteristic
52C2×#6665C2211yescharacteristic
53C2×#6665C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55C2×#6665C2218yescomplemented
56#91529C2218yescomplemented
57C2×Dic3×Dic5C2211yescharacteristic, complemented
58C2×Dic3×Dic5C2211yescharacteristic, complemented
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91462C2218yescomplemented
61#91457C2218yescomplemented
62#91447C2218yescomplemented
63#91440C2218yescomplemented
64#91361C2218yescomplemented
65#91361C2218yescomplemented
66#91360C2218yescomplemented
67#91358C2218yescomplemented
68C2×#5495—51nomaximal, Hall
69C2×C5×#123—31no—
70C2×#4083—31no—
71C2×D4×Dic5—31no—
72C22×#685—31no—
73C2×#4072—31no—
74#65992—316no—
75C2×#4044—31no—
76C2×#4044—31no—
77C2×#4043—31no—
78C2×#4038—31no—
79C2×#4032—31no—
80C2×#4031—31no—
81C2×#4029—31no—
82C2×#4027—31no—
83C2×D5×C22⋊C4D311yescharacteristic, complemented
84C2×#4024—31no—
85C24×C3×C5C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
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
95C22×Dic15—42no—
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2314yes—
101C2×Dic30—42no—
102C2×Dic30C2314yescomplemented
103C2×C5×#67—24no—
104C2×C5×#67C2314yes—
105C22×C5×Dic3—24no—
106C22×C5×Dic3C2314yes—
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×#1201—24no—
117C2×#1201—42no—
118C2×#1201C2314yes—
119C2×#1201C2314yes—
120C2×D3×Dic5—42no—
121C2×D3×Dic5C2314yescomplemented
122C3×C5×C22⋊C4C2314yes—
123#6719C2314yes—
124C4⋊Dic15C2314yescomplemented
125#6712C2314yescomplemented
126#6712C2314yescomplemented
127C5×(C2×D3)⋊C4C2314yescomplemented
128C5×(C2×D3)⋊C4C2314yescomplemented
129C5×C4⋊Dic3C2314yescomplemented
130C5×C4⋊Dic3C2314yescomplemented
131C3×C22⋊Dic5C2314yes—
132C3×#685C2314yes—
133C3×#685C2314yes—
134Dic3⋊Dic5C2314yescomplemented
135Dic3⋊Dic5C2314yescomplemented
136Dic3⋊Dic5C2314yescomplemented
137(C2×D3)⋊Dic5C2314yescomplemented
138#6665C2314yes—
139#6665C2314yes—
140#6665C2314yes—
141#6665C2314yes—
142#6665C2314yes—
143#6665C2314yes—
144Dic3×Dic5C2314yescomplemented
145Dic3×Dic5C2314yescomplemented
146Dic3×Dic5C2314yescomplemented
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×#886D511yescharacteristic, complemented
156C2×#885—51no—
157C2×#883—51no—
158C2×#67⋊C4—51no—
159C2×#879—51no—
160C2×#879—51no—
161C2×#878—51no—
162C2×#877—51no—
163C24×D5C2×D311yescharacteristic
164C22×C5×D4—31no—
165C23×C4×C5—31no—
166C22×C22⋊D5—31no—
167C22×C22⋊D5—31no—
168C23×Dic5—31no—
169C23×Dic5—31no—
170C22×C4×D5C2×D311yescharacteristic
171C22×C4×D5C2×D311yescharacteristic
172C22×Dic10—31no—
173C5×#123—38no—
174C2×C5×C4⋊C4—31no—
175C2×C5×C4⋊C4—31no—
176C2×C5×C22⋊C4—31no—
177C2×C5×C22⋊C4—31no—
178C2×C5×C22⋊C4C2×D311yescharacteristic
179C2×C22⋊Dic5—31no—
180C2×C22⋊Dic5—31no—
181C2×C22⋊Dic5C2×D311yescharacteristic
182#4083—38no—
183D4×Dic5—38no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—38no—
191C2×#685C2×D311yescharacteristic
192C2×#685C2×D311yescharacteristic
193#4072—38no—
194C2×C4⋊Dic5—31no—
195C2×C4⋊Dic5—31no—
196C2×C4⋊Dic5—31no—
197C2×C4⋊Dic5—31no—
198C2×#683—31no—
199C2×#683—31no—
200C2×C4×Dic5—31no—
201C2×C4×Dic5—31no—
202C2×C4×Dic5—31no—
203#4044—38no—
204#4044—38no—
205#4043—38no—
206#4038—38no—
207#4032—38no—
208#4031—38no—
209#4029—38no—
210#4027—38no—
211D5×C22⋊C4C2×D318yescomplemented
212#4024—38no—
213C2×#551—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5#4114yes—
217C23×C3×C5C2412yes—
218C23×C3×C5C2411yescharacteristic
219C22×C5×D3—22no—
220C22×C5×D3—22no—
221C22×C5×D3—22no—
222C22×C5×D3C2412yes—
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—
239C2×Dic15—22no—
240C2×Dic15—22no—
241C2×Dic15—22no—
242C2×Dic15—22no—
243C2×Dic15—44no—
244C2×Dic15C2412yes—
245C2×Dic15C2412yes—
246C2×Dic15C2412yes—
247C2×Dic15C2412yes—
248Dic30—44no—
249C5×#67—28no—
250C2×C5×Dic3—28no—
251C2×C5×Dic3—22no—
252C2×C5×Dic3—22no—
253C2×C5×Dic3—22no—
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#1201—28no—
264#1201—44no—
265D3×Dic5—44no—
266C25×C3—51no—
267C23×C3×C4—51no—
268C23×C3×C4—51no—
269C22×#67—51no—
270C22×#67—51no—
271C22×#67C2×D511yescharacteristic
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—51no—
286C2×#217—58no—
287C2×#217—51no—
288C2×#217—51no—
289C2×#217—51no—
290#929—58no—
291C4×#67—58no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
294C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
295#926—58no—
296C2×C4⋊Dic3—51no—
297C2×C4⋊Dic3C2×D511yescharacteristic, complemented
298C2×C4⋊Dic3C2×D511yescharacteristic, complemented
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#886C2×D518yescomplemented
309#885—58no—
310#883—58no—
311#67⋊C4—58no—
312#879—58no—
313#879—58no—
314#878—58no—
315#877—58no—
316C24×C5—31no—
317C24×C5C22×D311yescharacteristic
318C23×D5—24no—
319C23×D5—24no—
320C23×D5—42no—
321C23×D5C22×D311yescharacteristic
322C23×D5C22×D314yes—
323C23×D5C22×D311yescharacteristic
324C2×C5×D4—34no—
325C2×C5×D4—64no—
326C22×C4×C5—31no—
327C22×C4×C5—31no—
328C22×C4×C5—31no—
329C22×C4×C5—34no—
330C22×C4×C5—64no—
331C22×C4×C5C22×D311yescharacteristic
332C22×C4×C5C22×D311yescharacteristic
333C2×C22⋊D5—34no—
334C2×C22⋊D5—34no—
335C2×C22⋊D5—64no—
336C2×C22⋊D5—122no—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—31no—
341C22×Dic5—34no—
342C22×Dic5—34no—
343C22×Dic5—122no—
344C22×Dic5—122no—
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D311yescharacteristic
347C2×C4×D5—24no—
348C2×C4×D5—42no—
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⋊C4—34no—
357C5×C22⋊C4C22×D314yes—
358C22⋊Dic5—34no—
359C22⋊Dic5—34no—
360C22⋊Dic5C22×D314yes—
361#685—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367#685C22×D314yes—
368#685C22×D314yes—
369C4⋊Dic5—34no—
370C4⋊Dic5—34no—
371C4⋊Dic5—34no—
372C4⋊Dic5—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—31no—
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—151no—
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×C5×D3—22no—
403C2×C5×D3—22no—
404C2×C5×D3—22no—
405C2×C5×D3—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—
420Dic15—22no—
421C3×Dic5—22no—
422C3×Dic5—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×D3C22×D511yescharacteristic
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—24no—
443C2×#67—54no—
444C2×#67—54no—
445C2×#67—104no—
446C2×#67—202no—
447C2×#67C22×D514yes—
448C22×Dic3—24no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—51no—
452C22×Dic3—51no—
453C22×Dic3—54no—
454C22×Dic3—202no—
455C22×Dic3C22×D514yes—
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#217—54no—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4C22×D514yescomplemented
476(C2×D3)⋊C4C22×D514yescomplemented
477C4⋊Dic3—54no—
478C4⋊Dic3C22×D514yescomplemented
479C4⋊Dic3C22×D514yescomplemented
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—32no—
491C23×C5—62no—
492C23×C5—62no—
493C23×C5—62no—
494C23×C5#23514yes—
495C23×C5C23×D312yes—
496C23×C5C23×D311yescharacteristic
497C22×D5—22no—
498C22×D5—22no—
499C22×D5—28no—
500C22×D5—22no—
501C22×D5—22no—
502C22×D5—22no—
503C22×D5—28no—
504C22×D5—44no—
505C22×D5—416no—
506C22×D5#23714yes—
507C22×D5C23×D312yes—
508C22×D5C23×D312yes—
509C5×D4—68no—
510C2×C4×C5—22no—
511C2×C4×C5—22no—
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×C5C23×D312yes—
520C2×C4×C5C23×D312yes—
521C22⋊D5—68no—
522C22⋊D5—124no—
523C2×Dic5—22no—
524C2×Dic5—22no—
525C2×Dic5—32no—
526C2×Dic5—32no—
527C2×Dic5—32no—
528C2×Dic5—32no—
529C2×Dic5—62no—
530C2×Dic5—62no—
531C2×Dic5—62no—
532C2×Dic5—62no—
533C2×Dic5—124no—
534C2×Dic5—124no—
535C2×Dic5C23×D312yes—
536C2×Dic5C23×D312yes—
537C4×D5—28no—
538C4×D5—44no—
539Dic10—124no—
540C25—51no—
541C22×Q8—151no—
542C22×D4—31no—
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—38no—
554#123—158no—
555#123—158no—
556C22⋊Q8—158no—
557C22⋊Q8—158no—
558#120—158no—
559C4×D4—158no—
560C4×D4—158no—
561#117—158no—
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—31no—
573C2×C22⋊C4—51no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—58no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—158no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4D3×D511yescharacteristic
587C2×C42—151no—
588C2×C42—151no—
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
595C3×D5—24no—
596C3×D5—42no—
597C5×D3—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#71114yes—
613C23×C3C23×D512yes—
614C23×C3C23×D511yescharacteristic
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3C23×D512yes—
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—28no—
630#67—108no—
631#67—204no—
632C2×Dic3—28no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—52no—
637C2×Dic3—52no—
638C2×Dic3—52no—
639C2×Dic3—52no—
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—28no—
653C22×C5—62no—
654C22×C5—62no—
655C22×C5—62no—
656C22×C5—124no—
657C22×C5C2×#23514yes—
658C22×C5C2×#23512yes—
659C22×C5C2×#23712yes—
660C22×C5#100412yes—
661C22×C5C24×D311yescharacteristic
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—28no—
665C2×D5—22no—
666C2×D5—22no—
667C2×D5—22no—
668C2×D5—416no—
669C2×D5—44no—
670C2×D5C2×#23714yes—
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—62no—
674C4×C5—62no—
675C4×C5—62no—
676Dic5—22no—
677Dic5—22no—
678Dic5—62no—
679Dic5—62no—
680Dic5—62no—
681Dic5—62no—
682C24—31no—
683C24—51no—
684C24—51no—
685C24—54no—
686C24—104no—
687C24—104no—
688C24—202no—
689C24C2×D3×D511yescharacteristic
690C2×Q8—154no—
691C2×Q8—602no—
692C2×D4—34no—
693C2×D4—64no—
694C2×D4—154no—
695C2×D4—154no—
696C2×D4—304no—
697C2×D4—602no—
698C22×C4—34no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—51no—
703C22×C4—51no—
704C22×C4—54no—
705C22×C4—54no—
706C22×C4—64no—
707C22×C4—104no—
708C22×C4—154no—
709C22×C4—151no—
710C22×C4—151no—
711C22×C4—151no—
712C22×C4—151no—
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—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⋊C4C2×D3×D514yes—
741C42—154no—
742C42—154no—
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×#71114yes—
758C22×C3C2×#71112yes—
759C22×C3D5×#4112yes—
760C22×C3#414912yes—
761C22×C3C24×D511yescharacteristic
762C2×D3—22no—
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—44no—
766C3×C4—22no—
767C3×C4—22no—
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—122no—
779C2×C5#549514yescomplemented
780C2×C5C22×#23511yescharacteristic
781C2×C5C22×#23711yescharacteristic
782C2×C5C2×#100411yescharacteristic
783D5—24no—
784D5—42no—
785C23—22no—
786C23—22no—
787C23—32no—
788C23—54no—
789C23—52no—
790C23—52no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—108no—
795C23—102no—
796C23—102no—
797C23—108no—
798C23—102no—
799C23—102no—
800C23—102no—
801C23—204no—
802C23—2016no—
803C23#677214yes—
804C23C22×D3×D512yes—
805C23C22×D3×D511yescharacteristic
806Q8—604no—
807D4—68no—
808D4—308no—
809D4—604no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—52no—
816C2×C4—52no—
817C2×C4—68no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—108no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—152no—
825C2×C4—152no—
826C2×C4—152no—
827C2×C4—152no—
828C2×C4—204no—
829C2×C4—302no—
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#6599214yescomplemented
841C2×C3C22×#71111yescharacteristic
842C2×C3C2×D5×#4111yescharacteristic
843C2×C3C2×#414911yescharacteristic
844D3—42no—
845C5C2×#549511yescharacteristic, complemented, Sylow
846C22—28no—
847C22—22no—
848C22—22no—
849C22—54no—
850C22—62no—
851C22—62no—
852C22—62no—
853C22—108no—
854C22—102no—
855C22—102no—
856C22—102no—
857C22—102no—
858C22—102no—
859C22—124no—
860C22—2016no—
861C22—204no—
862C22C2×#677214yes—
863C22C2×#677212yes—
864C22D5×#23712yes—
865C22#9202612yes—
866C22C23×D3×D511yescharacteristic
867C4—22no—
868C4—22no—
869C4—62no—
870C4—62no—
871C4—62no—
872C4—102no—
873C4—102no—
874C4—302no—
875C4—302no—
876C4—302no—
877C4—302no—
878C3C2×#6599211yescharacteristic, complemented, Sylow
879C2—24no—
880C2—104no—
881C2—122no—
882C2—202no—
883C2#1175310314yesdirect product factor
884C2C22×#677211yescharacteristic
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×#91563C2
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×#91767C2semidirect
2. C2×C5×#886C2semidirect
3. C2×C3×D5×C22⋊C4C2semidirect
5. C2×#67⋊Dic5C2semidirect
6. C22×#6665C2semidirect
7. C2×#91529C2semidirect
8. C2×#91462C2semidirect
9. C2×#91457C2semidirect
10. C2×#91447C2semidirect
11. C2×#91440C2semidirect
12. C2×#91361C2semidirect
13. C2×#91361C2semidirect
14. C2×#91360C2semidirect
15. C2×#91358C2semidirect
16. #11753103C2direct (N × H)
20. C22×Dic30C22semidirect
27. C22×D3×Dic5C22semidirect
30. C2×C4⋊Dic15C22semidirect
31. C2×#6712C22semidirect
32. C2×#6712C22semidirect
33. #91767C22semidirect
34. C2×C5×(C2×D3)⋊C4C22semidirect
35. C2×C5×(C2×D3)⋊C4C22semidirect
36. C2×C5×C4⋊Dic3C22semidirect
37. C2×C5×C4⋊Dic3C22semidirect
38. C5×#886C22semidirect
42. C3×D5×C22⋊C4C22semidirect
44. #67⋊Dic5C22semidirect
45. C2×Dic3⋊Dic5C22semidirect
46. C2×Dic3⋊Dic5C22semidirect
47. C2×Dic3⋊Dic5C22semidirect
48. C2×(C2×D3)⋊Dic5C22semidirect
55. C2×#6665C22semidirect
56. #91529C22semidirect
57. C2×Dic3×Dic5C22semidirect
58. C2×Dic3×Dic5C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91462C22semidirect
61. #91457C22semidirect
62. #91447C22semidirect
63. #91440C22semidirect
64. #91361C22semidirect
65. #91361C22semidirect
66. #91360C22semidirect
67. #91358C22semidirect
83. C2×D5×C22⋊C4D3semidirect
102. C2×Dic30C23semidirect
121. C2×D3×Dic5C23semidirect
124. C4⋊Dic15C23semidirect
125. #6712C23semidirect
126. #6712C23semidirect
127. C5×(C2×D3)⋊C4C23semidirect
128. C5×(C2×D3)⋊C4C23semidirect
129. C5×C4⋊Dic3C23semidirect
130. C5×C4⋊Dic3C23semidirect
134. Dic3⋊Dic5C23semidirect
135. Dic3⋊Dic5C23semidirect
136. Dic3⋊Dic5C23semidirect
137. (C2×D3)⋊Dic5C23semidirect
144. Dic3×Dic5C23semidirect
145. Dic3×Dic5C23semidirect
146. Dic3×Dic5C23semidirect
155. C2×#886D5semidirect
211. D5×C22⋊C4C2×D3semidirect
293. C2×(C2×D3)⋊C4C2×D5semidirect
294. C2×(C2×D3)⋊C4C2×D5semidirect
297. C2×C4⋊Dic3C2×D5semidirect
298. C2×C4⋊Dic3C2×D5semidirect
308. #886C2×D5semidirect
475. (C2×D3)⋊C4C22×D5semidirect
476. (C2×D3)⋊C4C22×D5semidirect
478. C4⋊Dic3C22×D5semidirect
479. C4⋊Dic3C22×D5semidirect
591. C2×C3×C5#551semidirect
744. C3×C5C2×#551semidirect
779. C2×C5#5495semidirect
840. C2×C3#65992semidirect
845. C5C2×#5495semidirect
878. C3C2×#65992semidirect
883. C2#11753103direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917672
C2×C5×#8862
C2×C3×D5×C22⋊C42
C2×#915632
C2×#67⋊Dic52
C22×#66652
C2×#915292
C2×#914622
C2×#914572
C2×#914472
C2×#914402
C2×#913612
C2×#913602
C2×#913582
#117531032
C2×#659923
C2×#54955