Finite Group Databasebeta

← C4×#91474 #14321390

Subgroups — C4×#91474 #14321390

Order 1920.

2448 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D3×D5C211yesmaximal, characteristic, complemented
2C2×C3×C4×D20C211yesmaximal, characteristic, complemented
3C2×#91474C211yesmaximal, characteristic
4C2×C4×#1202C211yesmaximal, characteristic, complemented
5C2×C4×#1201C211yesmaximal, characteristic, complemented
6C4×#6714C211yesmaximal, characteristic, complemented
7C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8#11748940C211yesmaximal, characteristic, complemented
9#11748911C211yesmaximal, characteristic, complemented
10#11748898C211yesmaximal, characteristic, complemented
11#11748897C211yesmaximal, characteristic, complemented
12#11748896C211yesmaximal, characteristic, complemented
13#11748890C211yesmaximal, characteristic, complemented
14C4×#6665C211yesmaximal, characteristic, complemented
15#11748700C211yesmaximal, characteristic, complemented
16C4×#4028—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic, complemented
23C22×#1202C2211yescharacteristic
24C22×#1201C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C22×D5×Dic3C2211yescharacteristic
28C2×C4×D3×D5—24no—
29C2×C4×D3×D5—24no—
30C2×C4×D3×D5—24no—
31C2×C3×C42×C5C2211yescharacteristic, complemented
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×C4×Dic15C2211yescharacteristic, complemented
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C4×C5×Dic3C2211yescharacteristic, complemented
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic, complemented
40C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
41C3×C4×D20—24no—
42C2×Dic3⋊Dic5C2211yescharacteristic, complemented
43C2×#6669C2211yescharacteristic, complemented
44C2×#6667C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×#6665C2211yescharacteristic, complemented
49C2×#6665C2211yescharacteristic, complemented
50#91474C418yesdirect product factor
51C4×#1202—24no—
52C4×#1201—24no—
53#91115C2211yescharacteristic, complemented
54#91115C2211yescharacteristic, complemented
55C5×C3⋊#95C2211yescharacteristic, complemented
56C5×C3⋊#95C2211yescharacteristic, complemented
57#90994C2211yescharacteristic, complemented
58#90994C2211yescharacteristic, complemented
59C4×#937—51nomaximal, Hall
60C23×C4×D5—31no—
61C2×C4×C22⋊D5—31no—
62C2×#4028—31no—
63C2×C4×D20—31no—
64C2×C4×D20D311yescharacteristic, complemented
65C4×C5×C22⋊C4—31no—
66#65247—31no—
67#65244—31no—
68#65239—31no—
69C4×#685—31no—
70C4×#685—31no—
71#64957—31no—
72#64957—31no—
73#64954—31no—
74#64954—31no—
75C23×D15C2311yescharacteristic
76C23×C5×D3C2311yescharacteristic
77C23×C3×D5C2311yescharacteristic
78C23×C3×D5C2311yescharacteristic
79C22×D3×D5—22no—
80C22×D3×D5—22no—
81C22×D3×D5—22no—
82C22×D3×D5—22no—
83C22×D3×D5—22no—
84C22×D3×D5—22no—
85C22×D3×D5C2×C414yescomplemented
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C2×C4×D15—22no—
93C2×C4×D15—22no—
94C2×C4×D15D414yescomplemented
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C2×C4×C5×D3—22no—
99C2×C4×C5×D3—22no—
100C2×C4×C5×D3D414yescomplemented
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C2×C3×D20—22no—
104C2×C3×D20—22no—
105C2×C3×D20C2×C414yescomplemented
106C2×C3×C4×D5—22no—
107C2×C3×C4×D5—22no—
108C2×C3×C4×D5—22no—
109C2×C3×C4×D5—22no—
110C2×C3×C4×D5—22no—
111C2×C3×C4×D5D414yescomplemented
112C2×#1202—22no—
113C2×#1202—22no—
114C2×#1202C2×C414yescomplemented
115C2×#1201—22no—
116C2×#1201—22no—
117C2×#1201C2×C414yescomplemented
118C2×#1200—22no—
119C2×#1200—22no—
120C2×#1200—22no—
121C2×D3×Dic5—22no—
122C2×D3×Dic5—22no—
123C2×D3×Dic5—22no—
124C2×D5×Dic3—22no—
125C2×D5×Dic3—22no—
126C2×D5×Dic3—22no—
127C4×D3×D5—232no—
128C3×C42×C5—22no—
129#6714—22no—
130#6714C2×C414yescomplemented
131C4×Dic15—22no—
132C5×(C2×D3)⋊C4—22no—
133C5×(C2×D3)⋊C4C2×C414yescomplemented
134C4×C5×Dic3—22no—
135C3×#685—22no—
136C3×#685—22no—
137C3×C4⋊Dic5—22no—
138Dic3⋊Dic5—22no—
139#6669—22no—
140#6667—22no—
141(C2×D3)⋊Dic5—22no—
142#6665—22no—
143#6665—22no—
144#6665—22no—
145#6665C2×C414yescomplemented
146C23×C4×D3—51no—
147C2×C3×C4×D4—51no—
148C2×#937—51no—
149C2×C4×#67—51no—
150C2×C4×#67—51no—
151#5220—51no—
152C4×#217—51no—
153#4989—51no—
154#4989—51no—
155#4956—51no—
156#4956—51no—
157#4955—51no—
158#4946—51no—
159C4×(C2×D3)⋊C4—51no—
160C4×(C2×D3)⋊C4D511yescharacteristic, complemented
161C24×D5—31no—
162C23×C4×C5—31no—
163C22×C22⋊D5—31no—
164C23×Dic5—31no—
165C22×D20—31no—
166C22×D20C2×D311yescharacteristic
167C22×C4×D5—31no—
168C22×C4×D5—31no—
169C22×C4×D5—31no—
170C22×C4×D5—64no—
171C22×C4×D5—64no—
172C22×C4×D5—64no—
173C22×C4×D5C2×D311yescharacteristic
174C22×C4×D5C2×D311yescharacteristic, complemented
175C2×C5×C22⋊C4—31no—
176C2×C5×C22⋊C4—31no—
177C2×C42×C5—31no—
178C2×C42×C5C2×D311yescharacteristic, complemented
179C2×C22⋊Dic5—31no—
180C4×C22⋊D5—64no—
181C2×#685—31no—
182C2×#685—31no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685C2×D311yescharacteristic
189C2×#685C2×D311yescharacteristic, complemented
190C2×C4⋊Dic5—31no—
191C2×C4⋊Dic5C2×D311yescharacteristic, complemented
192C2×#683—31no—
193C2×C4×Dic5—31no—
194#4028—38no—
195C4×D20—24no—
196C4×D20—64no—
197C5×#95—31no—
198C5×#95—31no—
199#3963—31no—
200#3963—31no—
201#3963—31no—
202#3963—31no—
203C4×#120—151noSylow
204C23×C3×C5C2411yescharacteristic
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—21no—
209C22×D15C22×C412yes—
210C22×D15C2×D412yes—
211C22×D15#4112yes—
212C22×C5×D3—21no—
213C22×C5×D3—21no—
214C22×C5×D3—21no—
215C22×C5×D3—21no—
216C22×C5×D3C22×C412yes—
217C22×C5×D3C2×D412yes—
218C22×C5×D3#4112yes—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5—21no—
222C22×C3×D5—21no—
223C22×C3×D5—21no—
224C22×C3×D5—21no—
225C22×C3×D5—21no—
226C22×C3×D5—21no—
227C22×C3×D5—21no—
228C22×C3×D5—21no—
229C22×C3×D5C22×C412yes—
230C22×C3×D5C22×C412yescomplemented
231C22×C3×D5C2×D412yes—
232C22×C3×D5#4112yes—
233C2×D3×D5—28no—
234C2×D3×D5—28no—
235C2×D3×D5—28no—
236C2×D3×D5—28no—
237C2×D3×D5—28no—
238C2×D3×D5—28no—
239C2×D3×D5—28no—
240C2×C3×C4×C5—21no—
241C2×C3×C4×C5—21no—
242C2×C3×C4×C5—21no—
243C2×C3×C4×C5—21no—
244C2×C3×C4×C5—21no—
245C2×C3×C4×C5C22×C412yescomplemented
246C2×C3×C4×C5C2×D412yes—
247C2×C3×C4×C5C2×D412yes—
248C2×C3×C4×C5C2×D412yes—
249C2×Dic15—21no—
250C2×Dic15—21no—
251C2×Dic15—21no—
252C2×Dic15—21no—
253C2×Dic15—21no—
254C2×Dic15—21no—
255C2×Dic15—21no—
256C2×Dic15C22×C412yescomplemented
257C2×Dic15C2×D412yes—
258C4×D15—28no—
259C2×C5×Dic3—21no—
260C2×C5×Dic3—21no—
261C2×C5×Dic3—21no—
262C2×C5×Dic3—21no—
263C2×C5×Dic3—21no—
264C2×C5×Dic3—21no—
265C2×C5×Dic3—21no—
266C2×C5×Dic3C22×C412yescomplemented
267C2×C5×Dic3C2×D412yes—
268C4×C5×D3—28no—
269C2×C3×Dic5—21no—
270C2×C3×Dic5—21no—
271C2×C3×Dic5—21no—
272C2×C3×Dic5—21no—
273C2×C3×Dic5—21no—
274C2×C3×Dic5C2×D412yes—
275C3×D20—28no—
276C3×C4×D5—28no—
277C3×C4×D5—44no—
278#1202—28no—
279#1201—28no—
280#1200—28no—
281D3×Dic5—28no—
282D5×Dic3—28no—
283C24×D3—51no—
284C22×C3×D4—51no—
285C23×C3×C4—51no—
286C23×C3×C4—51no—
287C22×#67—51no—
288C22×#67—51no—
289C23×Dic3—51no—
290C22×C4×D3—51no—
291C22×C4×D3—51no—
292C22×C4×D3—51no—
293C22×C4×D3—104no—
294C22×C4×D3—104no—
295C22×C4×D3—104no—
296C22×C4×D3C2×D511yescharacteristic
297C3×C4×D4—104no—
298C2×C3×C4⋊C4—51no—
299C2×C3×C22⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C42C2×D511yescharacteristic, complemented
302C2×#217—51no—
303C2×#217—51no—
304C2×#217—51no—
305C2×#217—51no—
306#937—58no—
307C4×#67—104no—
308C4×#67—104no—
309C2×(C2×D3)⋊C4—51no—
310C2×(C2×D3)⋊C4—51no—
311C2×(C2×D3)⋊C4—51no—
312C2×(C2×D3)⋊C4—51no—
313C2×(C2×D3)⋊C4C2×D511yescharacteristic
314C2×(C2×D3)⋊C4C2×D511yescharacteristic
315C2×Dic3⋊C4—51no—
316C2×Dic3⋊C4—51no—
317C2×C4×Dic3—51no—
318C2×C4×Dic3C2×D511yescharacteristic, complemented
319C3⋊#95—51no—
320C3⋊#95—51no—
321C3⋊#95—51no—
322C3⋊#95—51no—
323C3⋊#95C2×D511yescharacteristic, complemented
324C3⋊#95C2×D511yescharacteristic, complemented
325C24×C5—31no—
326C23×D5—31no—
327C23×D5—34no—
328C23×D5—62no—
329C23×D5—62no—
330C23×D5—62no—
331C23×D5—62no—
332C23×D5—62no—
333C23×D5—62no—
334C23×D5C22×D311yescharacteristic
335C23×D5C22×D311yescharacteristic
336C22×C4×C5—31no—
337C22×C4×C5—31no—
338C22×C4×C5—34no—
339C22×C4×C5—31no—
340C22×C4×C5—62no—
341C22×C4×C5—62no—
342C22×C4×C5C22×D311yescharacteristic
343C22×C4×C5C22×D311yescharacteristic
344C22×C4×C5C22×D311yescharacteristic
345C2×C22⋊D5—34no—
346C2×C22⋊D5—62no—
347C2×C22⋊D5—62no—
348C22×Dic5—31no—
349C22×Dic5—31no—
350C22×Dic5—31no—
351C22×Dic5—62no—
352C22×Dic5—62no—
353C22×Dic5—62no—
354C22×Dic5C22×D311yescharacteristic
355C22×Dic5C22×D311yescharacteristic
356C2×D20—22no—
357C2×D20—22no—
358C2×D20—34no—
359C2×D20—62no—
360C2×D20—62no—
361C2×D20C4×D314yescomplemented
362C2×C4×D5—22no—
363C2×C4×D5—22no—
364C2×C4×D5—22no—
365C2×C4×D5—22no—
366C2×C4×D5—22no—
367C2×C4×D5—34no—
368C2×C4×D5—632no—
369C2×C4×D5—62no—
370C2×C4×D5—62no—
371C2×C4×D5—62no—
372C2×C4×D5—62no—
373C2×C4×D5—62no—
374C2×C4×D5—62no—
375C2×C4×D5—62no—
376C2×C4×D5—62no—
377C2×C4×D5#6714yescomplemented
378C5×C22⋊C4—34no—
379C5×C22⋊C4—62no—
380C42×C5—22no—
381C42×C5—62no—
382C22⋊Dic5—62no—
383#685—22no—
384#685—22no—
385#685—34no—
386#685—34no—
387#685—62no—
388#685—62no—
389#685—62no—
390#685—62no—
391#685—62no—
392C4⋊Dic5—22no—
393C4⋊Dic5—62no—
394#683—62no—
395C4×Dic5—62no—
396C24×C4—151no—
397C2×#120—151no—
398C2×C4×D4—51no—
399C2×C4×D4—151no—
400C2×C4×D4—151no—
401#386—151no—
402#386—151no—
403#386—151no—
404#385—151no—
405#385—151no—
406#385—151no—
407#379—151no—
408C4×C22⋊C4—31no—
409C4×C22⋊C4—151no—
410C4×C22⋊C4—151no—
411C22×C3×C5C23×C411yescharacteristic
412C22×C3×C5C22×D411yescharacteristic
413C22×C3×C5C22×D411yescharacteristic
414C22×C3×C5C22×D411yescharacteristic
415C22×C3×C5C2×#4111yescharacteristic
416C22×C3×C5C2×#4111yescharacteristic
417C22×C3×C5C2×#4111yescharacteristic
418C2×D15—22no—
419C2×D15—22no—
420C2×D15—22no—
421C2×D15—22no—
422C2×D15—22no—
423C2×D15—22no—
424C2×D15C4×D414yescomplemented
425C2×C5×D3—22no—
426C2×C5×D3—22no—
427C2×C5×D3—22no—
428C2×C5×D3—22no—
429C2×C5×D3—22no—
430C2×C5×D3—22no—
431C2×C5×D3C4×D414yescomplemented
432C2×C3×D5—22no—
433C2×C3×D5—22no—
434C2×C3×D5—22no—
435C2×C3×D5—22no—
436C2×C3×D5—22no—
437C2×C3×D5—22no—
438C2×C3×D5—22no—
439C2×C3×D5—22no—
440C2×C3×D5—22no—
441C2×C3×D5—41no—
442C2×C3×D5—41no—
443C2×C3×D5—41no—
444C2×C3×D5—41no—
445C2×C3×D5C4×D414yescomplemented
446D3×D5—232no—
447C3×C4×C5—22no—
448C3×C4×C5—41no—
449C3×C4×C5#12014yescomplemented
450Dic15—22no—
451Dic15—22no—
452Dic15—41no—
453C3×Dic5—22no—
454C3×Dic5—41no—
455C5×Dic3—22no—
456C5×Dic3—22no—
457C5×Dic3—41no—
458C24×C3—51no—
459C24×C3—51no—
460C23×D3—51no—
461C23×D3—54no—
462C23×D3—102no—
463C23×D3—102no—
464C23×D3—102no—
465C23×D3—102no—
466C23×D3—102no—
467C23×D3—102no—
468C23×D3C22×D511yescharacteristic
469C2×C3×D4—54no—
470C2×C3×D4—102no—
471C2×C3×D4—102no—
472C22×C3×C4—51no—
473C22×C3×C4—54no—
474C22×C3×C4—51no—
475C22×C3×C4—102no—
476C22×C3×C4—102no—
477C22×C3×C4—102no—
478C22×C3×C4—102no—
479C22×C3×C4—102no—
480C22×C3×C4C22×D511yescharacteristic
481C22×C3×C4C22×D511yescharacteristic
482C22×C3×C4C22×D511yescharacteristic
483C2×#67—54no—
484C2×#67—54no—
485C2×#67—102no—
486C2×#67—102no—
487C2×#67—102no—
488C2×#67—102no—
489C22×Dic3—51no—
490C22×Dic3—51no—
491C22×Dic3—51no—
492C22×Dic3—102no—
493C22×Dic3—102no—
494C22×Dic3—102no—
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D511yescharacteristic
497C22×Dic3C22×D511yescharacteristic
498C2×C4×D3—22no—
499C2×C4×D3—22no—
500C2×C4×D3—54no—
501C2×C4×D3—1032no—
502C2×C4×D3—102no—
503C2×C4×D3—102no—
504C2×C4×D3—102no—
505C2×C4×D3—102no—
506C2×C4×D3—102no—
507C2×C4×D3—102no—
508C2×C4×D3—102no—
509C2×C4×D3—102no—
510C2×C4×D3D2014yescomplemented
511C3×C4⋊C4—102no—
512C3×C22⋊C4—102no—
513C3×C22⋊C4—102no—
514C3×C42—22no—
515#217—54no—
516#217—102no—
517#217—102no—
518#217—102no—
519(C2×D3)⋊C4—22no—
520(C2×D3)⋊C4—54no—
521(C2×D3)⋊C4—102no—
522(C2×D3)⋊C4—102no—
523(C2×D3)⋊C4—102no—
524(C2×D3)⋊C4C4×D514yescomplemented
525Dic3⋊C4—102no—
526Dic3⋊C4—102no—
527C4×Dic3—22no—
528C4×Dic3—102no—
529C23×C5—32no—
530C23×C5—32no—
531C23×C5—32no—
532C23×C5—61no—
533C23×C5—61no—
534C23×C5—61no—
535C23×C5—61no—
536C23×C5C23×D311yescharacteristic
537C22×D5—21no—
538C22×D5—21no—
539C22×D5—21no—
540C22×D5—21no—
541C22×D5—21no—
542C22×D5—21no—
543C22×D5—21no—
544C22×D5—21no—
545C22×D5—21no—
546C22×D5—21no—
547C22×D5—32no—
548C22×D5—32no—
549C22×D5—32no—
550C22×D5—68no—
551C22×D5—68no—
552C22×D5—68no—
553C22×D5—68no—
554C22×D5—68no—
555C22×D5—68no—
556C22×D5—61no—
557C22×D5—61no—
558C22×D5—61no—
559C22×D5—61no—
560C22×D5—68no—
561C22×D5C2×C4×D312yes—
562C22×D5C2×C4×D312yescomplemented
563C22×D5#23512yes—
564C22×D5C2×#6712yes—
565C2×C4×C5—21no—
566C2×C4×C5—21no—
567C2×C4×C5—21no—
568C2×C4×C5—21no—
569C2×C4×C5—21no—
570C2×C4×C5—32no—
571C2×C4×C5—32no—
572C2×C4×C5—61no—
573C2×C4×C5—61no—
574C2×C4×C5—61no—
575C2×C4×C5—61no—
576C2×C4×C5—68no—
577C2×C4×C5—61no—
578C2×C4×C5—61no—
579C2×C4×C5—61no—
580C2×C4×C5C2×C4×D312yescomplemented
581C2×C4×C5D3×D412yes—
582C2×C4×C5D3×D412yes—
583C2×C4×C5C2×#6712yes—
584C22⋊D5—68no—
585C2×Dic5—21no—
586C2×Dic5—21no—
587C2×Dic5—21no—
588C2×Dic5—21no—
589C2×Dic5—21no—
590C2×Dic5—32no—
591C2×Dic5—32no—
592C2×Dic5—68no—
593C2×Dic5—61no—
594C2×Dic5—61no—
595C2×Dic5—61no—
596C2×Dic5—61no—
597C2×Dic5—61no—
598C2×Dic5—61no—
599C2×Dic5—61no—
600C2×Dic5C2×#6712yes—
601D20—28no—
602D20—68no—
603C4×D5—28no—
604C4×D5—44no—
605C4×D5—68no—
606C4×D5—68no—
607C4×D5—68no—
608C25—151no—
609C22×D4—51no—
610C22×D4—151no—
611C22×D4—151no—
612C23×C4—31no—
613C23×C4—51no—
614C23×C4—51no—
615C23×C4—151no—
616C23×C4—151no—
617C23×C4—151no—
618C23×C4—151no—
619C23×C4—304no—
620C23×C4—304no—
621C23×C4—304no—
622#120—158no—
623C4×D4—104no—
624C4×D4—304no—
625C4×D4—304no—
626C2×C4⋊C4—51no—
627C2×C4⋊C4—151no—
628C2×C4⋊C4—151no—
629C2×C22⋊C4—31no—
630C2×C22⋊C4—31no—
631C2×C22⋊C4—51no—
632C2×C22⋊C4—51no—
633C2×C22⋊C4—151no—
634C2×C22⋊C4—151no—
635C2×C22⋊C4—151no—
636C2×C22⋊C4—151no—
637C2×C22⋊C4—151no—
638C2×C22⋊C4—151no—
639C2×C22⋊C4—151no—
640C2×C22⋊C4—151no—
641C2×C42—31no—
642C2×C42—151no—
643C2×C42D3×D511yescharacteristic, complemented
644#95—31no—
645#95—31no—
646#95—151no—
647#95—151no—
648#95—151no—
649#95—151no—
650C2×C3×C5C2×C4×D411yescharacteristic
651C2×C3×C5C2×C4×D411yescharacteristic
652C2×C3×C5C2×C4×D411yescharacteristic
653C2×C3×C5C2×#12011yescharacteristic
654C2×C3×C5#52511yescharacteristic
655C2×C3×C5#52511yescharacteristic
656C2×C3×C5#52511yescharacteristic
657D15—24no—
658C3×D5—24no—
659C3×D5—42no—
660C5×D3—24no—
661C23×C3—52no—
662C23×C3—52no—
663C23×C3—52no—
664C23×C3—52no—
665C23×C3—101no—
666C23×C3—101no—
667C23×C3—101no—
668C23×C3—101no—
669C23×C3—101no—
670C23×C3—101no—
671C23×C3—101no—
672C23×C3—101no—
673C23×C3—101no—
674C23×C3—101no—
675C23×C3C23×D511yescharacteristic
676C22×D3—21no—
677C22×D3—21no—
678C22×D3—21no—
679C22×D3—21no—
680C22×D3—52no—
681C22×D3—52no—
682C22×D3—52no—
683C22×D3—108no—
684C22×D3—108no—
685C22×D3—108no—
686C22×D3—108no—
687C22×D3—108no—
688C22×D3—108no—
689C22×D3—101no—
690C22×D3—101no—
691C22×D3—101no—
692C22×D3—101no—
693C22×D3—108no—
694C22×D3C2×C4×D512yes—
695C22×D3C2×D2012yes—
696C22×D3#70912yes—
697C3×D4—108no—
698C2×C3×C4—21no—
699C2×C3×C4—21no—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—21no—
703C2×C3×C4—52no—
704C2×C3×C4—101no—
705C2×C3×C4—101no—
706C2×C3×C4—108no—
707C2×C3×C4—101no—
708C2×C3×C4—101no—
709C2×C3×C4—101no—
710C2×C3×C4—204no—
711C2×C3×C4C2×C4×D512yescomplemented
712C2×C3×C4C2×D2012yes—
713C2×C3×C4D4×D512yes—
714C2×C3×C4D4×D512yes—
715#67—108no—
716#67—108no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—21no—
721C2×Dic3—21no—
722C2×Dic3—21no—
723C2×Dic3—21no—
724C2×Dic3—52no—
725C2×Dic3—52no—
726C2×Dic3—108no—
727C2×Dic3—101no—
728C2×Dic3—101no—
729C2×Dic3—101no—
730C2×Dic3—101no—
731C2×Dic3—101no—
732C2×Dic3—101no—
733C2×Dic3—101no—
734C2×Dic3C2×C4×D512yescomplemented
735C2×Dic3C2×D2012yes—
736C4×D3—28no—
737C4×D3—108no—
738C4×D3—108no—
739C4×D3—108no—
740C22×C5—34no—
741C22×C5—62no—
742C22×C5—62no—
743C22×C5—62no—
744C22×C5—62no—
745C22×C5—62no—
746C22×C5—62no—
747C22×C5C22×C4×D311yescharacteristic
748C22×C5C2×#23511yescharacteristic
749C22×C5C2×D3×D411yescharacteristic
750C22×C5C2×D3×D411yescharacteristic
751C22×C5D3×#4111yescharacteristic
752C22×C5D3×#4111yescharacteristic
753C22×C5C22×#6711yescharacteristic
754C2×D5—22no—
755C2×D5—22no—
756C2×D5—22no—
757C2×D5—22no—
758C2×D5—22no—
759C2×D5—22no—
760C2×D5—22no—
761C2×D5—22no—
762C2×D5—22no—
763C2×D5—34no—
764C2×D5—41no—
765C2×D5—41no—
766C2×D5—41no—
767C2×D5—41no—
768C2×D5—632no—
769C2×D5—62no—
770C2×D5—62no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—62no—
775C2×D5C4×#6714yescomplemented
776C4×C5—22no—
777C4×C5—41no—
778C4×C5—62no—
779C4×C5—62no—
780C4×C5—121no—
781C4×C5#93714yescomplemented
782Dic5—22no—
783Dic5—41no—
784Dic5—62no—
785Dic5—62no—
786Dic5—121no—
787C24—31no—
788C24—51no—
789C24—51no—
790C24—154no—
791C24—151no—
792C24—302no—
793C24—302no—
794C24—302no—
795C24—302no—
796C24—302no—
797C24—302no—
798C2×D4—54no—
799C2×D4—102no—
800C2×D4—102no—
801C2×D4—154no—
802C2×D4—154no—
803C2×D4—302no—
804C2×D4—302no—
805C2×D4—302no—
806C2×D4—302no—
807C22×C4—31no—
808C22×C4—31no—
809C22×C4—34no—
810C22×C4—31no—
811C22×C4—51no—
812C22×C4—54no—
813C22×C4—51no—
814C22×C4—62no—
815C22×C4—62no—
816C22×C4—102no—
817C22×C4—102no—
818C22×C4—102no—
819C22×C4—102no—
820C22×C4—102no—
821C22×C4—151no—
822C22×C4—151no—
823C22×C4—154no—
824C22×C4—151no—
825C22×C4—302no—
826C22×C4—302no—
827C22×C4—302no—
828C22×C4—302no—
829C22×C4—302no—
830C22×C4—3032no—
831C22×C4—302no—
832C22×C4—302no—
833C22×C4—302no—
834C22×C4—302no—
835C22×C4—302no—
836C22×C4—302no—
837C22×C4C2×D3×D511yescharacteristic
838C22×C4C2×D3×D511yescharacteristic
839C22×C4C2×D3×D511yescharacteristic
840C4⋊C4—102no—
841C4⋊C4—302no—
842C4⋊C4—302no—
843C22⋊C4—34no—
844C22⋊C4—62no—
845C22⋊C4—102no—
846C22⋊C4—102no—
847C22⋊C4—154no—
848C22⋊C4—154no—
849C22⋊C4—302no—
850C22⋊C4—302no—
851C22⋊C4—302no—
852C22⋊C4—302no—
853C22⋊C4—302no—
854C22⋊C4—302no—
855C42—22no—
856C42—62no—
857C42—302no—
858C3×C5C4×#12011yescharacteristic, complemented, Hall
859C22×C3—54no—
860C22×C3—102no—
861C22×C3—102no—
862C22×C3—102no—
863C22×C3—102no—
864C22×C3—102no—
865C22×C3—102no—
866C22×C3—102no—
867C22×C3—102no—
868C22×C3—102no—
869C22×C3—201no—
870C22×C3—201no—
871C22×C3—201no—
872C22×C3—201no—
873C22×C3C22×C4×D511yescharacteristic
874C22×C3C22×D2011yescharacteristic
875C22×C3C2×#70911yescharacteristic
876C22×C3C2×D4×D511yescharacteristic
877C22×C3C2×D4×D511yescharacteristic
878C22×C3D5×#4111yescharacteristic
879C22×C3D5×#4111yescharacteristic
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—22no—
886C2×D3—54no—
887C2×D3—1032no—
888C2×D3—102no—
889C2×D3—102no—
890C2×D3—102no—
891C2×D3—102no—
892C2×D3—102no—
893C2×D3—102no—
894C2×D3C4×D2014yescomplemented
895C3×C4—22no—
896C3×C4—41no—
897C3×C4—102no—
898C3×C4—201no—
899C3×C4#402814yescomplemented
900Dic3—22no—
901Dic3—22no—
902Dic3—41no—
903Dic3—102no—
904Dic3—102no—
905Dic3—201no—
906C2×C5—64no—
907C2×C5C4×D3×D411yescharacteristic
908C2×C5C4×D3×D411yescharacteristic
909C2×C5#554711yescharacteristic
910C2×C5#554711yescharacteristic
911C2×C5C2×C4×#6711yescharacteristic
912C2×C5C2×#93711yescharacteristic
913C2×C5#582811yescharacteristic
914D5—24no—
915D5—42no—
916D5—64no—
917C23—32no—
918C23—32no—
919C23—32no—
920C23—52no—
921C23—52no—
922C23—52no—
923C23—52no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—101no—
929C23—101no—
930C23—101no—
931C23—101no—
932C23—101no—
933C23—101no—
934C23—101no—
935C23—101no—
936C23—101no—
937C23—101no—
938C23—152no—
939C23—152no—
940C23—152no—
941C23—308no—
942C23—308no—
943C23—308no—
944C23—308no—
945C23—308no—
946C23—308no—
947C23—308no—
948C23—301no—
949C23—301no—
950C23—301no—
951C23—301no—
952C23C22×D3×D511yescharacteristic
953D4—108no—
954D4—308no—
955D4—308no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—32no—
962C2×C4—32no—
963C2×C4—52no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—68no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—101no—
973C2×C4—101no—
974C2×C4—108no—
975C2×C4—101no—
976C2×C4—101no—
977C2×C4—101no—
978C2×C4—152no—
979C2×C4—152no—
980C2×C4—204no—
981C2×C4—308no—
982C2×C4—308no—
983C2×C4—308no—
984C2×C4—301no—
985C2×C4—301no—
986C2×C4—301no—
987C2×C4—301no—
988C2×C4—308no—
989C2×C4—301no—
990C2×C4—301no—
991C2×C4—301no—
992C2×C4C4×D3×D512yescomplemented
993C2×C4D3×D2012yes—
994C2×C4#677712yes—
995C2×C4D5×#6712yes—
996C2×C3—104no—
997C2×C3—202no—
998C2×C3C2×C4×D2011yescharacteristic
999C2×C3C2×#402811yescharacteristic
1000C2×C3#6585811yescharacteristic
1001C2×C3C4×D4×D511yescharacteristic
1002C2×C3C4×D4×D511yescharacteristic
1003C2×C3#6588111yescharacteristic
1004C2×C3#6588111yescharacteristic
1005D3—24no—
1006D3—104no—
1007C5C4×#93711yescharacteristic, complemented, Sylow
1008C22—34no—
1009C22—54no—
1010C22—62no—
1011C22—62no—
1012C22—62no—
1013C22—62no—
1014C22—62no—
1015C22—62no—
1016C22—102no—
1017C22—102no—
1018C22—102no—
1019C22—102no—
1020C22—102no—
1021C22—102no—
1022C22—102no—
1023C22—102no—
1024C22—102no—
1025C22—154no—
1026C22—201no—
1027C22—201no—
1028C22—201no—
1029C22—201no—
1030C22—3032no—
1031C22—302no—
1032C22—302no—
1033C22—302no—
1034C22—302no—
1035C22—302no—
1036C22—302no—
1037C22C2×C4×D3×D511yescharacteristic
1038C22C2×D3×D2011yescharacteristic
1039C22C2×#677711yescharacteristic
1040C22D5×#23511yescharacteristic
1041C22D3×#70911yescharacteristic
1042C22#9201611yescharacteristic
1043C22C2×D5×#6711yescharacteristic
1044C4—22no—
1045C4—41no—
1046C4—62no—
1047C4—62no—
1048C4—102no—
1049C4—121no—
1050C4—201no—
1051C4—302no—
1052C4—302no—
1053C4—601no—
1054C4#9147414yesdirect product factor
1055C3C4×#402811yescharacteristic, complemented, Sylow
1056C2—64no—
1057C2—104no—
1058C2—202no—
1059C2—304no—
1060C2C4×D3×D2011yescharacteristic
1061C2C4×#677711yescharacteristic
1062C2#1175273911yescharacteristic
1063C2#1175274711yescharacteristic
1064C2C4×D5×#6711yescharacteristic
1065C2C2×#9147411yescharacteristic
1066C2#1175463111yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91474C2
hypercenterC2×C42D3×D5
hypocenterC3×C5C4×#120
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×C4×D3×D5C2semidirect
2. C2×C3×C4×D20C2semidirect
4. C2×C4×#1202C2semidirect
5. C2×C4×#1201C2semidirect
6. C4×#6714C2semidirect
7. C4×C5×(C2×D3)⋊C4C2semidirect
8. #11748940C2semidirect
9. #11748911C2semidirect
10. #11748898C2semidirect
11. #11748897C2semidirect
12. #11748896C2semidirect
13. #11748890C2semidirect
14. C4×#6665C2semidirect
15. #11748700C2semidirect
22. C22×C3×C4×D5C22semidirect
31. C2×C3×C42×C5C22semidirect
34. C2×C4×Dic15C22semidirect
37. C2×C4×C5×Dic3C22semidirect
39. C2×C3×#685C22semidirect
40. C2×C3×C4⋊Dic5C22semidirect
42. C2×Dic3⋊Dic5C22semidirect
43. C2×#6669C22semidirect
48. C2×#6665C22semidirect
49. C2×#6665C22semidirect
50. #91474C4direct (N × H)
53. #91115C22semidirect
54. #91115C22semidirect
55. C5×C3⋊#95C22semidirect
56. C5×C3⋊#95C22semidirect
57. #90994C22semidirect
58. #90994C22semidirect
64. C2×C4×D20D3semidirect
85. C22×D3×D5C2×C4semidirect
94. C2×C4×D15D4semidirect
100. C2×C4×C5×D3D4semidirect
105. C2×C3×D20C2×C4semidirect
111. C2×C3×C4×D5D4semidirect
114. C2×#1202C2×C4semidirect
117. C2×#1201C2×C4semidirect
130. #6714C2×C4semidirect
133. C5×(C2×D3)⋊C4C2×C4semidirect
145. #6665C2×C4semidirect
160. C4×(C2×D3)⋊C4D5semidirect
174. C22×C4×D5C2×D3semidirect
178. C2×C42×C5C2×D3semidirect
189. C2×#685C2×D3semidirect
191. C2×C4⋊Dic5C2×D3semidirect
230. C22×C3×D5C22×C4semidirect
245. C2×C3×C4×C5C22×C4semidirect
256. C2×Dic15C22×C4semidirect
266. C2×C5×Dic3C22×C4semidirect
301. C2×C3×C42C2×D5semidirect
318. C2×C4×Dic3C2×D5semidirect
323. C3⋊#95C2×D5semidirect
324. C3⋊#95C2×D5semidirect
361. C2×D20C4×D3semidirect
377. C2×C4×D5#67semidirect
424. C2×D15C4×D4semidirect
431. C2×C5×D3C4×D4semidirect
445. C2×C3×D5C4×D4semidirect
449. C3×C4×C5#120semidirect
510. C2×C4×D3D20semidirect
524. (C2×D3)⋊C4C4×D5semidirect
562. C22×D5C2×C4×D3semidirect
580. C2×C4×C5C2×C4×D3semidirect
643. C2×C42D3×D5semidirect
711. C2×C3×C4C2×C4×D5semidirect
734. C2×Dic3C2×C4×D5semidirect
775. C2×D5C4×#67semidirect
781. C4×C5#937semidirect
858. C3×C5C4×#120semidirect
894. C2×D3C4×D20semidirect
899. C3×C4#4028semidirect
992. C2×C4C4×D3×D5semidirect
1007. C5C4×#937semidirect
1054. C4#91474direct (N × H)
1055. C3C4×#4028semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D3×D52
C2×C3×C4×D202
C2×#914742
C2×C4×#12022
C2×C4×#12012
C4×#67142
C4×C5×(C2×D3)⋊C42
#117489402
#117489112
#117488982
#117488972
#117488962
#117488902
C4×#66652
#117487002
C4×#40283
C4×#9375