Finite Group Databasebeta

← #41×#1203 #14483155

Subgroups — #41×#1203 #14483155

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D15C211yesmaximal, characteristic, complemented
2C2×C5×D3×#41C211yesmaximal, characteristic, complemented
3C3×#41×Dic5C211yesmaximal, characteristic, complemented
4#11755245C211yesmaximal, characteristic, complemented
5Q8×#1203C211yesmaximal, characteristic, complemented
6#11755134C211yesmaximal, characteristic, complemented
7#11755131C211yesmaximal, characteristic, complemented
8#11754982C213yesmaximal, complemented
9#11754975C213yesmaximal, complemented
10#11754965C213yesmaximal, complemented
11D4×#1203C213yesmaximal, complemented
12#11754592C213yesmaximal, complemented
13#11754584C213yesmaximal, complemented
14#11754572C213yesmaximal, complemented
15C2×C4×#1203C213yesmaximal, complemented
16#41×C22⋊D5—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18#41×D15—28no—
19C2×#6821C2211yescharacteristic, complemented
20C2×Q8×D15C2211yescharacteristic, complemented
21C2×#6819C2213yescomplemented
22C2×D4×D15C2213yescomplemented
23C2×#6817C2213yescomplemented
24C22×C4×D15C2213yescomplemented
25C5×D3×#41—28no—
26C2×C5×#239C2211yescharacteristic, complemented
27C2×C5×D3×Q8C2211yescharacteristic, complemented
28C2×C5×#237C2213yescomplemented
29C2×C5×D3×D4C2213yescomplemented
30C2×C5×#235C2213yescomplemented
31C22×C4×C5×D3C2213yescomplemented
32C22×#1203C2213yes—
33C3×Q8×Dic5C2211yescharacteristic, complemented
34C3×Q8×Dic5C2211yescharacteristic, complemented
35C3×D4×Dic5C2213yescomplemented
36C3×D4×Dic5C2213yescomplemented
37C3×#4072C2213yescomplemented
38C2×C3×C4×Dic5C2213yescomplemented
39#91573C2216yescomplemented
40#91570C2216yescomplemented
41#91566C2216yescomplemented
42#91566C2216yescomplemented
43#91543C2216yescomplemented
44#91542C2216yescomplemented
45C2×#6668C2213yescomplemented
46C2×#6667C2213yescomplemented
47C2×(C2×D3)⋊Dic5C2213yescomplemented
48#91466C2213yescomplemented
49#91466C2213yescomplemented
50#91460C2213yescomplemented
51#91460C2213yescomplemented
52#91451C2213yescomplemented
53C4×#1203C2211yescharacteristic
54C4×#1203C2213yes—
55C4×#1203C2213yescomplemented
56C4×#1203C2213yescomplemented
57C4×#1203C2213yescomplemented
58C4×#1203C2213yescomplemented
59C4×#1203C2213yescomplemented
60C4×#1203C2213yescomplemented
61C4×#1203C2216yescomplemented
62#91383C2213yescomplemented
63#91383C2213yescomplemented
64#91376C2213yescomplemented
65#91375C2213yescomplemented
66#91373C2213yescomplemented
67#91365C2213yescomplemented
68#91365C2213yescomplemented
69#41×D12—51nomaximal, Hall
70C22×C5×#41—31no—
71C2×D5×#41—31no—
72#66168—31no—
73#66166—33no—
74#66165—31no—
75#66163—33no—
76#66162—33no—
77#41×Dic5D311yescharacteristic, complemented
78#66158—33no—
79#66151—31no—
80Q8×C22⋊D5—31no—
81#66140—33no—
82D4×C22⋊D5—33no—
83#66125—33no—
84C2×C4×C22⋊D5—33no—
85C23×D15C2313yes—
86C23×C5×D3C2313yes—
87C3×C5×#41D418yescomplemented
88C2×C3×C5×Q8C2311yescharacteristic
89C2×C3×C5×D4C2313yes—
90C22×C3×C4×C5C2313yes—
91C2×#1220C2316yes—
92C22×Dic15C2313yes—
93#6821—24no—
94Q8×D15—24no—
95#6819—212no—
96D4×D15—212no—
97#6817—212no—
98C2×D60C2313yes—
99C2×C4×D15—212no—
100C2×C4×D15C2311yescharacteristic
101C2×C4×D15C2313yes—
102C2×C4×D15C2313yes—
103C2×C4×D15C2313yes—
104C2×Dic30C2313yes—
105C2×C5×#67C2316yes—
106C22×C5×Dic3C2313yes—
107C5×#239—24no—
108C5×D3×Q8—24no—
109C5×#237—212no—
110C5×D3×D4—212no—
111C5×#235—212no—
112C2×C5×D12C2313yes—
113C2×C4×C5×D3—212no—
114C2×C4×C5×D3C2311yescharacteristic
115C2×C4×C5×D3C2313yes—
116C2×C4×C5×D3C2313yes—
117C2×C4×C5×D3C2313yes—
118C2×C5×Dic6C2313yes—
119C22×C3×Dic5C2313yes—
120C22×C3×Dic5C2313yes—
121C2×#1203—212no—
122C2×#1203C2313yes—
123C2×#1203C2313yes—
124C2×#1203C2313yes—
125C2×#1203C2316yes—
126C2×#1203C2311yescharacteristic
127C3×C22⋊Dic5C2316yes—
128C3×C4⋊Dic5C2313yes—
129C3×C4⋊Dic5C2313yes—
130C3×C4×Dic5C2313yes—
131C3×C4×Dic5C2313yes—
132C3×C4×Dic5C2311yescharacteristic
133C3×C4×Dic5C2313yes—
134#6668C2311yescharacteristic
135#6668C2313yes—
136#6668C2313yes—
137#6668C2313yes—
138#6668C2316yes—
139#6667C2311yescharacteristic
140#6667C2313yes—
141#6667C2313yes—
142#6667C2313yes—
143#6667C2316yes—
144(C2×D3)⋊Dic5C2311yescharacteristic
145(C2×D3)⋊Dic5C2313yes—
146(C2×D3)⋊Dic5C2313yes—
147(C2×D3)⋊Dic5C2313yes—
148(C2×D3)⋊Dic5C2316yes—
149C2×D3×#41—51no—
150C2×D3×#41D511yescharacteristic, complemented
151C3×C4×#41—51no—
152#5577—51no—
153#5576—51no—
154#5576—51no—
155Q8×D12—51no—
156#5555—53no—
157#5554—53no—
158#5554—53no—
159D4×D12—53no—
160#5524—53no—
161#5524—53no—
162#5477—53no—
163C2×C4×D12—53no—
164C2×C5×#41—31no—
165C2×C5×#41—33no—
166C2×C5×#41—33no—
167C2×C5×#41—68no—
168C2×C5×#41C2×D311yescharacteristic
169C22×C5×Q8—31no—
170C22×C5×D4—33no—
171C23×C4×C5—33no—
172C22×C22⋊D5—33no—
173D5×#41—68no—
174C2×#713—31no—
175C2×Q8×D5—31no—
176C2×#711—33no—
177C2×D4×D5—33no—
178C2×#709—33no—
179C22×C4×D5—33no—
180#4099—36no—
181C2×C22⋊Dic5—33no—
182#4093—33no—
183#4092—33no—
184#4092—33no—
185Q8×Dic5C2×D311yescharacteristic, complemented
186Q8×Dic5C2×D311yescharacteristic, complemented
187#4090—33no—
188#4086—33no—
189#4085—36no—
190#4085—36no—
191#4084—33no—
192#4084—33no—
193#4083—36no—
194#4082—33no—
195#4081—36no—
196D4×Dic5C2×D313yescomplemented
197D4×Dic5C2×D313yescomplemented
198#4076—33no—
199#4076—33no—
200#4075—36no—
201C4×C22⋊D5—31no—
202C4×C22⋊D5—33no—
203C4×C22⋊D5—33no—
204C4×C22⋊D5—33no—
205C4×C22⋊D5—33no—
206C4×C22⋊D5—33no—
207C4×C22⋊D5—33no—
208C4×C22⋊D5—33no—
209C4×C22⋊D5—36no—
210C2×#685—33no—
211#4072C2×D313yescomplemented
212#4070—33no—
213#4070—33no—
214C2×#683—33no—
215C2×C4×Dic5C2×D313yescomplemented
216D4×#41—151noSylow
217C23×C3×C5C2413yes—
218C22×D15—26no—
219C22×D15—26no—
220C22×D15—43no—
221C22×D15C2413yes—
222C22×D15C2411yescharacteristic
223C22×C5×D3—26no—
224C22×C5×D3—26no—
225C22×C5×D3—43no—
226C22×C5×D3C2413yes—
227C22×C5×D3C2411yescharacteristic
228C3×C5×Q8C2×D414yescomplemented
229C3×C5×D4C2×D4112yescomplemented
230C2×C3×C4×C5C2×D4112yescomplemented
231C2×C3×C4×C5C2411yescharacteristic
232C2×C3×C4×C5C2413yes—
233#1220—212no—
234C2×Dic15—26no—
235C2×Dic15C2413yes—
236C2×Dic15C2411yescharacteristic
237D60—26no—
238C4×D15—22no—
239C4×D15—26no—
240C4×D15—26no—
241C4×D15—26no—
242Dic30—26no—
243C5×#67—212no—
244C2×C5×Dic3—26no—
245C2×C5×Dic3C2413yes—
246C2×C5×Dic3C2411yescharacteristic
247C5×D12—26no—
248C4×C5×D3—22no—
249C4×C5×D3—26no—
250C4×C5×D3—26no—
251C4×C5×D3—26no—
252C5×Dic6—26no—
253C2×C3×Dic5—26no—
254C2×C3×Dic5—43no—
255C2×C3×Dic5C2411yescharacteristic
256C2×C3×Dic5C2413yes—
257C2×C3×Dic5C2413yes—
258C2×C3×Dic5C2411yescharacteristic
259#1203—26no—
260#1203—26no—
261#1203—26no—
262#1203—46no—
263#1203#4114yesdirect product factor
264C2×C3×#41C2×D511yescharacteristic
265D3×#41—28no—
266D3×#41—108no—
267C2×#239—51no—
268C2×#239C2×D511yescharacteristic, complemented
269C2×D3×Q8—51no—
270C2×D3×Q8C2×D511yescharacteristic, complemented
271C2×#237—53no—
272C2×#237C2×D513yescomplemented
273C2×D3×D4—53no—
274C2×D3×D4C2×D513yescomplemented
275C2×#235—53no—
276C2×#235C2×D513yescomplemented
277C22×D12—53no—
278C22×C4×D3—53no—
279C22×C4×D3C2×D513yescomplemented
280C3×C4×Q8—51no—
281C3×C4×Q8—51no—
282C3×C4×D4—53no—
283C3×C4×D4—53no—
284C3×#117—53no—
285C2×C3×C42—53no—
286#930—56no—
287#930—56no—
288C2×(C2×D3)⋊C4—53no—
289C2×(C2×D3)⋊C4—53no—
290C2×C4⋊Dic3—53no—
291#897—53no—
292#897—53no—
293#897—53no—
294#897—53no—
295#895—53no—
296#895—53no—
297#895—53no—
298#895—53no—
299#886—56no—
300#886—56no—
301#882—56no—
302#882—56no—
303#875—53no—
304#875—53no—
305#874—53no—
306C4×D12—51no—
307C4×D12—53no—
308C4×D12—53no—
309C4×D12—53no—
310C4×D12—53no—
311C4×D12—53no—
312C4×D12—53no—
313C4×D12—53no—
314C4×D12—56no—
315#869—53no—
316C24×C5—33no—
317C23×D5—33no—
318C5×#41—64no—
319C5×#41—612no—
320C5×#41—612no—
321C5×#41D1218yescomplemented
322C2×C5×Q8—33no—
323C2×C5×Q8—64no—
324C2×C5×Q8C22×D311yescharacteristic
325C2×C5×D4—36no—
326C2×C5×D4—33no—
327C2×C5×D4—612no—
328C2×C5×D4C22×D313yes—
329C22×C4×C5—33no—
330C22×C4×C5—31no—
331C22×C4×C5—33no—
332C22×C4×C5—33no—
333C22×C4×C5—33no—
334C22×C4×C5—612no—
335C22×C4×C5C22×D313yes—
336C2×C22⋊D5—36no—
337C2×C22⋊D5—31no—
338C2×C22⋊D5—33no—
339C2×C22⋊D5—33no—
340C2×C22⋊D5—33no—
341C2×C22⋊D5—36no—
342C2×C22⋊D5—612no—
343C22×Dic5—33no—
344C22×Dic5C22×D313yes—
345C22×Dic5C22×D313yes—
346#713—64no—
347Q8×D5—64no—
348#711—612no—
349D4×D5—612no—
350#709—612no—
351C2×D20—33no—
352C2×C4×D5—31no—
353C2×C4×D5—33no—
354C2×C4×D5—33no—
355C2×C4×D5—33no—
356C2×C4×D5—612no—
357C2×Dic10—33no—
358C22⋊Dic5—31no—
359C22⋊Dic5—33no—
360C22⋊Dic5—33no—
361C22⋊Dic5—33no—
362C22⋊Dic5—36no—
363C22⋊Dic5C22×D316yes—
364#685—31no—
365#685—33no—
366#685—33no—
367#685—33no—
368#685—36no—
369C4⋊Dic5C22×D313yes—
370C4⋊Dic5C22×D313yes—
371#683—31no—
372#683—33no—
373#683—33no—
374#683—33no—
375#683—36no—
376C4×Dic5C22×D311yescharacteristic
377C4×Dic5C22×D313yes—
378C4×Dic5C22×D313yes—
379C4×Dic5C22×D313yes—
380C22×#41—31no—
381C22×#41—151no—
382#550—151no—
383D4×Q8—151no—
384#548—151no—
385#548—151no—
386#547—153no—
387#546—153no—
388#546—153no—
389D42—153no—
390#532—153no—
391#525—153no—
392#525—153no—
393C4×#41—51no—
394C2×C4×D4—153no—
395C22×C3×C5—23no—
396C22×C3×C5—23no—
397C22×C3×C5C22×D416yes—
398C22×C3×C5C2511yescharacteristic
399C2×D15—21no—
400C2×D15—21no—
401C2×D15—23no—
402C2×D15—23no—
403C2×D15—23no—
404C2×D15—412no—
405C2×D15C2×#4112yescomplemented
406C2×C5×D3—21no—
407C2×C5×D3—21no—
408C2×C5×D3—23no—
409C2×C5×D3—23no—
410C2×C5×D3—23no—
411C2×C5×D3—412no—
412C2×C5×D3C2×#4112yescomplemented
413C3×C4×C5C22×D416yes—
414C3×C4×C5C22×D412yes—
415Dic15—23no—
416Dic15—21no—
417C3×Dic5—23no—
418C3×Dic5—23no—
419C3×Dic5—21no—
420C3×Dic5C2×#4112yescomplemented
421C5×Dic3—23no—
422C5×Dic3—21no—
423C23×D3—53no—
424C23×D3C22×D513yes—
425C3×#41C22⋊D518yescomplemented
426C2×C3×Q8C22×D511yescharacteristic
427C2×C3×D4C22×D513yes—
428C22×C3×C4—53no—
429C22×C3×C4—53no—
430C22×C3×C4C22×D513yes—
431C2×#67—56no—
432C2×#67C22×D516yes—
433C22×Dic3—53no—
434C22×Dic3C22×D513yes—
435#239—24no—
436#239—104no—
437D3×Q8—24no—
438D3×Q8—104no—
439#237—212no—
440#237—1012no—
441D3×D4—212no—
442D3×D4—1012no—
443#235—212no—
444#235—1012no—
445C2×D12—51no—
446C2×D12—53no—
447C2×D12—53no—
448C2×D12—53no—
449C2×D12—53no—
450C2×D12—56no—
451C2×D12—1012no—
452C2×D12C22×D513yes—
453C2×C4×D3—212no—
454C2×C4×D3—51no—
455C2×C4×D3—53no—
456C2×C4×D3—53no—
457C2×C4×D3—53no—
458C2×C4×D3—1012no—
459C2×C4×D3C22×D511yescharacteristic
460C2×C4×D3C22×D513yes—
461C2×C4×D3C22×D513yes—
462C2×C4×D3C22×D513yes—
463C2×Dic6—53no—
464C2×Dic6C22×D513yes—
465C3×C4⋊C4—53no—
466C3×C4⋊C4—53no—
467C3×C22⋊C4—56no—
468C3×C42—53no—
469C3×C42—51no—
470C3×C42—53no—
471C3×C42—53no—
472(C2×D3)⋊C4—51no—
473(C2×D3)⋊C4—53no—
474(C2×D3)⋊C4—53no—
475(C2×D3)⋊C4—53no—
476(C2×D3)⋊C4—56no—
477(C2×D3)⋊C4—51no—
478(C2×D3)⋊C4—53no—
479(C2×D3)⋊C4—53no—
480(C2×D3)⋊C4—53no—
481(C2×D3)⋊C4—56no—
482C4⋊Dic3—53no—
483C4⋊Dic3—56no—
484C4⋊Dic3—51no—
485C4⋊Dic3—53no—
486C4⋊Dic3—53no—
487C23×C5—31no—
488C23×C5—33no—
489C23×C5—66no—
490C23×C5—66no—
491C23×C5—123no—
492C23×C5C23×D313yes—
493C22×D5—31no—
494C22×D5—33no—
495C22×D5—66no—
496C22×D5—66no—
497C22×D5—123no—
498C5×Q8—66no—
499C5×Q8C2×D1214yescomplemented
500C5×D4—612no—
501C5×D4—66no—
502C5×D4C2×D12112yescomplemented
503C2×C4×C5—31no—
504C2×C4×C5—33no—
505C2×C4×C5—66no—
506C2×C4×C5—62no—
507C2×C4×C5—66no—
508C2×C4×C5—66no—
509C2×C4×C5—66no—
510C2×C4×C5C2×D12112yescomplemented
511C2×C4×C5C23×D313yes—
512C2×C4×C5C23×D311yescharacteristic
513C22⋊D5—34no—
514C22⋊D5—66no—
515C22⋊D5—66no—
516C22⋊D5—612no—
517C22⋊D5—66no—
518C22⋊D5—126no—
519C2×Dic5—26no—
520C2×Dic5—33no—
521C2×Dic5—31no—
522C2×Dic5—43no—
523C2×Dic5—66no—
524C2×Dic5C23×D311yescharacteristic
525C2×Dic5C23×D313yes—
526C2×Dic5C23×D313yes—
527C2×Dic5C23×D311yescharacteristic
528D20—66no—
529C4×D5—62no—
530C4×D5—66no—
531C4×D5—66no—
532C4×D5—66no—
533Dic10—66no—
534C2×#41—31no—
535C2×#41—33no—
536C2×#41—33no—
537C2×#41—68no—
538C2×#41—151no—
539C2×#41—153no—
540C2×#41—153no—
541C2×#41—308no—
542C2×#41D3×D511yescharacteristic
543C22×Q8—31no—
544C22×Q8—151no—
545C22×D4—33no—
546C22×D4—153no—
547C22×D4—153no—
548C23×C4—33no—
549C23×C4—153no—
550C4⋊Q8—153no—
551#127—153no—
552#124—153no—
553#124—153no—
554#123—156no—
555#123—156no—
556C22⋊Q8—153no—
557C22⋊Q8—153no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—153no—
561#121—153no—
562#121—153no—
563#121—153no—
564#121—156no—
565#121—156no—
566#120—156no—
567#120—156no—
568C4×Q8—51no—
569C4×Q8—51no—
570C4×D4—53no—
571C4×D4—53no—
572C4×D4—151no—
573C4×D4—153no—
574C4×D4—153no—
575C4×D4—153no—
576C4×D4—153no—
577C4×D4—153no—
578C4×D4—153no—
579C4×D4—153no—
580C4×D4—156no—
581#117—53no—
582C2×C4⋊C4—153no—
583C2×C22⋊C4—153no—
584C2×C22⋊C4—153no—
585C2×C42—53no—
586C2×C3×C5—26no—
587C2×C3×C5C23×D411yescharacteristic
588C2×C3×C5C22×#4111yescharacteristic
589C2×C3×C5#58511yescharacteristic
590D15—22no—
591D15—43no—
592C5×D3—22no—
593C5×D3—43no—
594C23×C3C23×D513yes—
595C22×D3—26no—
596C22×D3—26no—
597C22×D3—43no—
598C22×D3—51no—
599C22×D3—53no—
600C22×D3—106no—
601C22×D3—106no—
602C22×D3—203no—
603C22×D3C23×D513yes—
604C22×D3C23×D511yescharacteristic
605C3×Q8C2×C22⋊D514yescomplemented
606C3×D4C2×C22⋊D5112yescomplemented
607C2×C3×C4—51no—
608C2×C3×C4—53no—
609C2×C3×C4—53no—
610C2×C3×C4—51no—
611C2×C3×C4—106no—
612C2×C3×C4—203no—
613C2×C3×C4C2×C22⋊D5112yescomplemented
614C2×C3×C4C23×D513yes—
615C2×C3×C4C23×D511yescharacteristic
616#67—212no—
617#67—1012no—
618C2×Dic3—26no—
619C2×Dic3—53no—
620C2×Dic3—51no—
621C2×Dic3—106no—
622C2×Dic3C23×D513yes—
623C2×Dic3C23×D511yescharacteristic
624D12—26no—
625D12—54no—
626D12—106no—
627D12—106no—
628D12—106no—
629D12—106no—
630D12—206no—
631C4×D3—22no—
632C4×D3—26no—
633C4×D3—26no—
634C4×D3—26no—
635C4×D3—102no—
636C4×D3—106no—
637C4×D3—106no—
638C4×D3—106no—
639Dic6—26no—
640Dic6—106no—
641C22×C5—23no—
642C22×C5—23no—
643C22×C5—32no—
644C22×C5—61no—
645C22×C5—61no—
646C22×C5—63no—
647C22×C5—63no—
648C22×C5—63no—
649C22×C5—1212no—
650C22×C5C22×D1216yes—
651C22×C5C24×D311yescharacteristic
652C2×D5—32no—
653C2×D5—61no—
654C2×D5—61no—
655C2×D5—63no—
656C2×D5—63no—
657C2×D5—63no—
658C2×D5—1212no—
659C4×C5—61no—
660C4×C5—63no—
661C4×C5C22×D1216yes—
662C4×C5C22×D1212yes—
663Dic5—23no—
664Dic5—21no—
665Dic5—23no—
666Dic5—63no—
667Dic5—61no—
668Dic5D3×#4112yescomplemented
669C24—33no—
670C24—153no—
671#41—64no—
672#41—612no—
673#41—612no—
674#41—304no—
675#41—3012no—
676#41—3012no—
677#41#120318yesdirect product factor
678C2×Q8—33no—
679C2×Q8—64no—
680C2×Q8—153no—
681C2×Q8—304no—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—36no—
684C2×D4—33no—
685C2×D4—612no—
686C2×D4—151no—
687C2×D4—153no—
688C2×D4—153no—
689C2×D4—153no—
690C2×D4—156no—
691C2×D4—156no—
692C2×D4—153no—
693C2×D4—3012no—
694C2×D4—3012no—
695C2×D4C2×D3×D513yes—
696C22×C4—33no—
697C22×C4—33no—
698C22×C4—33no—
699C22×C4—31no—
700C22×C4—33no—
701C22×C4—53no—
702C22×C4—53no—
703C22×C4—612no—
704C22×C4—153no—
705C22×C4—153no—
706C22×C4—153no—
707C22×C4—151no—
708C22×C4—153no—
709C22×C4—3012no—
710C22×C4C2×D3×D513yes—
711C4⋊C4—53no—
712C4⋊C4—53no—
713C4⋊C4—151no—
714C4⋊C4—153no—
715C4⋊C4—153no—
716C4⋊C4—153no—
717C4⋊C4—156no—
718C22⋊C4—56no—
719C22⋊C4—151no—
720C22⋊C4—153no—
721C22⋊C4—153no—
722C22⋊C4—153no—
723C22⋊C4—156no—
724C22⋊C4—151no—
725C22⋊C4—153no—
726C22⋊C4—153no—
727C22⋊C4—153no—
728C22⋊C4—156no—
729C42—53no—
730C42—53no—
731C42—51no—
732C42—53no—
733C3×C5D4×#4111yescharacteristic, complemented, Hall
734C22×C3—23no—
735C22×C3—23no—
736C22×C3C22×C22⋊D516yes—
737C22×C3C24×D511yescharacteristic
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—23no—
741C2×D3—23no—
742C2×D3—23no—
743C2×D3—412no—
744C2×D3—52no—
745C2×D3—101no—
746C2×D3—101no—
747C2×D3—103no—
748C2×D3—103no—
749C2×D3—103no—
750C2×D3—2012no—
751C2×D3D5×#4112yescomplemented
752C3×C4—52no—
753C3×C4—103no—
754C3×C4—103no—
755C3×C4—101no—
756C3×C4C22×C22⋊D516yes—
757C3×C4C22×C22⋊D512yes—
758Dic3—23no—
759Dic3—21no—
760Dic3—103no—
761Dic3—101no—
762C2×C5—26no—
763C2×C5—62no—
764C2×C5—123no—
765C2×C5C23×D1211yescharacteristic
766C2×C5C2×D3×#4111yescharacteristic
767C2×C5#596411yescharacteristic
768D5—62no—
769D5—123no—
770C23—31no—
771C23—33no—
772C23—66no—
773C23—66no—
774C23—123no—
775C23—151no—
776C23—153no—
777C23—306no—
778C23—306no—
779C23—603no—
780C23C22×D3×D513yes—
781Q8—66no—
782Q8—306no—
783Q8C2×#120314yescomplemented
784D4—612no—
785D4—66no—
786D4—154no—
787D4—306no—
788D4—306no—
789D4—306no—
790D4—3012no—
791D4—306no—
792D4—606no—
793D4C2×#1203112yescomplemented
794C2×C4—31no—
795C2×C4—33no—
796C2×C4—51no—
797C2×C4—51no—
798C2×C4—53no—
799C2×C4—53no—
800C2×C4—66no—
801C2×C4—62no—
802C2×C4—66no—
803C2×C4—66no—
804C2×C4—66no—
805C2×C4—106no—
806C2×C4—151no—
807C2×C4—153no—
808C2×C4—203no—
809C2×C4—306no—
810C2×C4—302no—
811C2×C4—306no—
812C2×C4—306no—
813C2×C4—306no—
814C2×C4C2×#1203112yescomplemented
815C2×C4C22×D3×D513yes—
816C2×C4C22×D3×D511yescharacteristic
817C2×C3—26no—
818C2×C3C2×D5×#4111yescharacteristic
819C2×C3#6628311yescharacteristic
820C2×C3C23×C22⋊D511yescharacteristic
821D3—22no—
822D3—43no—
823D3—102no—
824D3—203no—
825C5#41×D1211yescharacteristic, complemented, Sylow
826C22—23no—
827C22—23no—
828C22—32no—
829C22—61no—
830C22—61no—
831C22—63no—
832C22—63no—
833C22—63no—
834C22—1212no—
835C22—152no—
836C22—301no—
837C22—301no—
838C22—303no—
839C22—303no—
840C22—303no—
841C22—6012no—
842C22C22×#120316yes—
843C22C23×D3×D511yescharacteristic
844C4—52no—
845C4—61no—
846C4—63no—
847C4—101no—
848C4—103no—
849C4—103no—
850C4—301no—
851C4—303no—
852C4C22×#120312yes—
853C4C22×#120316yes—
854C3#41×C22⋊D511yescharacteristic, complemented, Sylow
855C2—26no—
856C2—62no—
857C2—123no—
858C2—302no—
859C2—603no—
860C2D3×D5×#4111yescharacteristic
861C2#1175705811yescharacteristic
862C2C23×#120311yescharacteristic
subgroupG/H
centerC2×C4C22×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×#41C22
hypercenterC2×#41D3×D5
hypocenterC3×C5D4×#41
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×D15C2semidirect
2. C2×C5×D3×#41C2semidirect
3. C3×#41×Dic5C2semidirect
4. #11755245C2semidirect
5. Q8×#1203C2semidirect
6. #11755134C2semidirect
7. #11755131C2semidirect
8. #11754982C2semidirect
9. #11754975C2semidirect
10. #11754965C2semidirect
11. D4×#1203C2semidirect
12. #11754592C2semidirect
13. #11754584C2semidirect
14. #11754572C2semidirect
15. C2×C4×#1203C2semidirect
19. C2×#6821C22semidirect
20. C2×Q8×D15C22semidirect
21. C2×#6819C22semidirect
22. C2×D4×D15C22semidirect
23. C2×#6817C22semidirect
24. C22×C4×D15C22semidirect
26. C2×C5×#239C22semidirect
27. C2×C5×D3×Q8C22semidirect
28. C2×C5×#237C22semidirect
29. C2×C5×D3×D4C22semidirect
30. C2×C5×#235C22semidirect
31. C22×C4×C5×D3C22semidirect
33. C3×Q8×Dic5C22semidirect
34. C3×Q8×Dic5C22semidirect
35. C3×D4×Dic5C22semidirect
36. C3×D4×Dic5C22semidirect
37. C3×#4072C22semidirect
38. C2×C3×C4×Dic5C22semidirect
39. #91573C22semidirect
40. #91570C22semidirect
41. #91566C22semidirect
42. #91566C22semidirect
43. #91543C22semidirect
44. #91542C22semidirect
45. C2×#6668C22semidirect
46. C2×#6667C22semidirect
47. C2×(C2×D3)⋊Dic5C22semidirect
48. #91466C22semidirect
49. #91466C22semidirect
50. #91460C22semidirect
51. #91460C22semidirect
52. #91451C22semidirect
55. C4×#1203C22semidirect
56. C4×#1203C22semidirect
57. C4×#1203C22semidirect
58. C4×#1203C22semidirect
59. C4×#1203C22semidirect
60. C4×#1203C22semidirect
61. C4×#1203C22semidirect
62. #91383C22semidirect
63. #91383C22semidirect
64. #91376C22semidirect
65. #91375C22semidirect
66. #91373C22semidirect
67. #91365C22semidirect
68. #91365C22semidirect
77. #41×Dic5D3semidirect
87. C3×C5×#41D4semidirect
150. C2×D3×#41D5semidirect
185. Q8×Dic5C2×D3semidirect
186. Q8×Dic5C2×D3semidirect
196. D4×Dic5C2×D3semidirect
197. D4×Dic5C2×D3semidirect
211. #4072C2×D3semidirect
215. C2×C4×Dic5C2×D3semidirect
228. C3×C5×Q8C2×D4semidirect
229. C3×C5×D4C2×D4semidirect
230. C2×C3×C4×C5C2×D4semidirect
263. #1203#41direct (N × H)
268. C2×#239C2×D5semidirect
270. C2×D3×Q8C2×D5semidirect
272. C2×#237C2×D5semidirect
274. C2×D3×D4C2×D5semidirect
276. C2×#235C2×D5semidirect
279. C22×C4×D3C2×D5semidirect
321. C5×#41D12semidirect
405. C2×D15C2×#41semidirect
412. C2×C5×D3C2×#41semidirect
420. C3×Dic5C2×#41semidirect
425. C3×#41C22⋊D5semidirect
499. C5×Q8C2×D12semidirect
502. C5×D4C2×D12semidirect
510. C2×C4×C5C2×D12semidirect
605. C3×Q8C2×C22⋊D5semidirect
606. C3×D4C2×C22⋊D5semidirect
613. C2×C3×C4C2×C22⋊D5semidirect
668. Dic5D3×#41semidirect
677. #41#1203direct (N × H)
733. C3×C5D4×#41semidirect
751. C2×D3D5×#41semidirect
783. Q8C2×#1203semidirect
793. D4C2×#1203semidirect
814. C2×C4C2×#1203semidirect
825. C5#41×D12semidirect
854. C3#41×C22⋊D5semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D152
C2×C5×D3×#412
C3×#41×Dic52
#117552452
Q8×#12032
#117551342
#117551312
#117549822
#117549752
#117549652
D4×#12032
#117545922
#117545842
#117545722
C2×C4×#12032
#41×C22⋊D53
#41×D125