Finite Group Databasebeta

← #14320375

Subgroups — #14320375

Order 1920.

1424 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D15C211yesmaximal, characteristic
2C2×#91437C211yesmaximal, characteristic
3C2×C4×#1200C211yesmaximal, characteristic
4C5×#4980C211yesmaximal, characteristic, complemented
5C3×#65270C211yesmaximal, characteristic, complemented
6#11748888C211yesmaximal, characteristic
7#11748888C211yesmaximal, characteristic
8#11748888C211yesmaximal, characteristic
9#11748888C211yesmaximal, characteristic
10#11748847C211yesmaximal, characteristic, complemented
11#11748824C211yesmaximal, characteristic, complemented
12#11748689C211yesmaximal, characteristic, complemented
13#11748688C211yesmaximal, characteristic, complemented
14#11748687C211yesmaximal, characteristic, complemented
15#11748674C211yesmaximal, characteristic, complemented
16D5×#387—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C22×#1200C2211yescharacteristic
22C22×#1200C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C4⋊Dic15C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×#6712C2211yescharacteristic
28C4⋊C4×D15C418yescomplemented
29C2×C5×C4⋊Dic3C2211yescharacteristic
30C2×C4×C5×Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×#6669C2211yescharacteristic
35C2×Dic3×Dic5C2211yescharacteristic
36C2×Dic3×Dic5C2211yescharacteristic
37#91437—24no—
38C4×#1200—24no—
39C5×C3⋊#95C2211yescharacteristic
40C5×C3⋊#95C2211yescharacteristic
41C5×C3⋊#95C2211yescharacteristic
42C5×C3⋊#95C2211yescharacteristic
43C3×#3963C2211yescharacteristic
44C3×#3963C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55D3×#387—51nomaximal, Hall
56C2×D5×C4⋊C4—31no—
57C2×D5×C4⋊C4—31no—
58C2×C42×D5—31no—
59C5×#387—31no—
60#65270D311yescharacteristic, complemented
61#65267—31no—
62#65222—31no—
63D5×#95—31no—
64D5×#95—31no—
65D5×#95—31no—
66D5×#95—31no—
67#64944—31no—
68#64943—31no—
69#64942—31no—
70#64941—31no—
71C23×D15C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C2×C4×D15—22no—
79C2×C4×D15—22no—
80C2×C4×D15—22no—
81C2×C4×D15—22no—
82C2×C4×D15—22no—
83C2×C4×D15—22no—
84C2×C4×D15C2×C414yes—
85C2×C4×D15C2×C414yes—
86C2×C4×D15C2×C414yes—
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C2×#1200—22no—
96C2×#1200—22no—
97C2×#1200—22no—
98C2×#1200—22no—
99C2×#1200—22no—
100C2×#1200—22no—
101C2×#1200—22no—
102C2×#1200—22no—
103C2×#1200—22no—
104C2×#1200—22no—
105C2×#1200D414yes—
106C2×#1200Q814yes—
107C3×C5×C4⋊C4C2×C414yescomplemented
108C4⋊Dic15C2×C414yescomplemented
109#6712C2×C414yescomplemented
110#6712C2×C414yescomplemented
111C5×C4⋊Dic3—22no—
112C4×C5×Dic3—22no—
113C3×C4⋊Dic5—22no—
114C3×C4×Dic5—22no—
115#6669—22no—
116#6669—22no—
117Dic3×Dic5—22no—
118Dic3×Dic5—22no—
119C2×D3×C4⋊C4—51no—
120C2×D3×C4⋊C4—51no—
121C2×C42×D3—51no—
122C3×#387—51no—
123#4980D511yescharacteristic, complemented
124#4978—51no—
125#4933—51no—
126D3×#95—51no—
127D3×#95—51no—
128D3×#95—51no—
129D3×#95—51no—
130#4655—51no—
131#4654—51no—
132#4653—51no—
133#4652—51no—
134C22×C4×D5—31no—
135C22×C4×D5—31no—
136C22×C4×D5—31no—
137C22×C4×D5—31no—
138C22×C4×D5—31no—
139C22×C4×D5—31no—
140C22×C4×D5—31no—
141C2×C5×C4⋊C4—31no—
142C2×C5×C4⋊C4C2×D311yescharacteristic
143C2×C42×C5—31no—
144C2×C4⋊Dic5—31no—
145C2×C4⋊Dic5C2×D311yescharacteristic
146C2×#683—31no—
147C2×#683—31no—
148C2×#683—31no—
149C2×#683—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5—31no—
152C2×C4×Dic5C2×D311yescharacteristic
153D5×C4⋊C4—38no—
154D5×C4⋊C4—64no—
155C42×D5—64no—
156C5×#95—31no—
157C5×#95—31no—
158C5×#95—31no—
159C5×#95—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#3963C2×D311yescharacteristic
169#3963C2×D311yescharacteristic
170#3963C2×D311yescharacteristic
171#3963C2×D311yescharacteristic
172C2×#387—151noSylow
173C23×C3×C5C2411yescharacteristic
174C22×D15C22×C412yes—
175C22×D15C2×D412yes—
176C22×D15C2×Q812yes—
177C22×D15#4112yes—
178C22×D15#4112yes—
179C22×D15#4112yes—
180C22×D15#4112yes—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5C22×C412yes—
188C2×C3×C4×C5C22×C412yes—
189C2×C3×C4×C5C22×C412yes—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15C22×C412yes—
197C2×Dic15C22×C412yes—
198C2×Dic15C22×C412yes—
199C4×D15—28no—
200C4×D15—28no—
201C4×D15—28no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3C2×D412yes—
213C2×C5×Dic3C2×Q812yes—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5C2×D412yes—
225C2×C3×Dic5C2×Q812yes—
226#1200—28no—
227#1200—28no—
228#1200—44no—
229#1200—44no—
230C22×C4×D3—51no—
231C22×C4×D3—51no—
232C22×C4×D3—51no—
233C22×C4×D3—51no—
234C22×C4×D3—51no—
235C22×C4×D3—51no—
236C22×C4×D3—51no—
237C2×C3×C4⋊C4—51no—
238C2×C3×C4⋊C4C2×D511yescharacteristic
239C2×C3×C42—51no—
240C2×C4⋊Dic3—51no—
241C2×C4⋊Dic3C2×D511yescharacteristic
242C2×Dic3⋊C4—51no—
243C2×Dic3⋊C4—51no—
244C2×Dic3⋊C4—51no—
245C2×Dic3⋊C4—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3C2×D511yescharacteristic
249D3×C4⋊C4—58no—
250D3×C4⋊C4—104no—
251C42×D3—104no—
252C3×#95—51no—
253C3×#95—51no—
254C3×#95—51no—
255C3×#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95—51no—
260C3⋊#95—51no—
261C3⋊#95—51no—
262C3⋊#95—51no—
263C3⋊#95—51no—
264C3⋊#95C2×D511yescharacteristic
265C3⋊#95C2×D511yescharacteristic
266C3⋊#95C2×D511yescharacteristic
267C3⋊#95C2×D511yescharacteristic
268C23×D5—31no—
269C22×C4×C5—31no—
270C22×C4×C5—31no—
271C22×C4×C5—31no—
272C22×C4×C5—31no—
273C22×C4×C5C22×D311yescharacteristic
274C22×C4×C5C22×D311yescharacteristic
275C22×C4×C5C22×D311yescharacteristic
276C22×Dic5—31no—
277C22×Dic5—31no—
278C22×Dic5—31no—
279C22×Dic5C22×D311yescharacteristic
280C22×Dic5C22×D311yescharacteristic
281C22×Dic5C22×D311yescharacteristic
282C22×Dic5C22×D311yescharacteristic
283C2×C4×D5—34no—
284C2×C4×D5—34no—
285C2×C4×D5—34no—
286C2×C4×D5—34no—
287C2×C4×D5—34no—
288C2×C4×D5—62no—
289C2×C4×D5—62no—
290C2×C4×D5—62no—
291C2×C4×D5—62no—
292C2×C4×D5—62no—
293C2×C4×D5—62no—
294C2×C4×D5—62no—
295C2×C4×D5—62no—
296C2×C4×D5—62no—
297C2×C4×D5—62no—
298C2×C4×D5—62no—
299C2×C4×D5—62no—
300C2×C4×D5—62no—
301C2×C4×D5—62no—
302C2×C4×D5—62no—
303C2×C4×D5—62no—
304C5×C4⋊C4—62no—
305C5×C4⋊C4C4×D314yescomplemented
306C42×C5—62no—
307C4⋊Dic5—22no—
308C4⋊Dic5—34no—
309#683—34no—
310#683—34no—
311#683—62no—
312#683—62no—
313C4×Dic5—22no—
314C4×Dic5—62no—
315C4×Dic5—62no—
316C22×C4⋊C4—151no—
317C22×C4⋊C4—151no—
318C22×C42—151no—
319#387—31no—
320#387—51no—
321#387—151no—
322#387—151no—
323#387—151no—
324#387—151no—
325#387—151no—
326#387—151no—
327C2×#95—151no—
328C2×#95—151no—
329C2×#95—151no—
330C2×#95—151no—
331C22×C3×C5C23×C411yescharacteristic
332C22×C3×C5C22×D411yescharacteristic
333C22×C3×C5C22×Q811yescharacteristic
334C22×C3×C5C2×#4111yescharacteristic
335C22×C3×C5C2×#4111yescharacteristic
336C22×C3×C5C2×#4111yescharacteristic
337C22×C3×C5C2×#4111yescharacteristic
338C2×D15#11714yes—
339C2×D15C4×D414yes—
340C2×D15C4×Q814yes—
341C2×D15C22⋊Q814yes—
342C2×D15#12314yes—
343C2×D15#12514yes—
344C2×D15#12614yes—
345C3×C4×C5—22no—
346C3×C4×C5—22no—
347C3×C4×C5—22no—
348Dic15—22no—
349Dic15—22no—
350Dic15—22no—
351C3×Dic5—22no—
352C3×Dic5—22no—
353C3×Dic5—41no—
354C3×Dic5—41no—
355C5×Dic3—22no—
356C5×Dic3—22no—
357C5×Dic3—41no—
358C5×Dic3—41no—
359C23×D3—51no—
360C22×C3×C4—51no—
361C22×C3×C4—51no—
362C22×C3×C4—51no—
363C22×C3×C4—51no—
364C22×C3×C4C22×D511yescharacteristic
365C22×C3×C4C22×D511yescharacteristic
366C22×C3×C4C22×D511yescharacteristic
367C22×Dic3—51no—
368C22×Dic3—51no—
369C22×Dic3—51no—
370C22×Dic3C22×D511yescharacteristic
371C22×Dic3C22×D511yescharacteristic
372C22×Dic3C22×D511yescharacteristic
373C22×Dic3C22×D511yescharacteristic
374C2×C4×D3—54no—
375C2×C4×D3—54no—
376C2×C4×D3—54no—
377C2×C4×D3—54no—
378C2×C4×D3—54no—
379C2×C4×D3—102no—
380C2×C4×D3—102no—
381C2×C4×D3—102no—
382C2×C4×D3—102no—
383C2×C4×D3—102no—
384C2×C4×D3—102no—
385C2×C4×D3—102no—
386C2×C4×D3—102no—
387C2×C4×D3—102no—
388C2×C4×D3—102no—
389C2×C4×D3—102no—
390C2×C4×D3—102no—
391C2×C4×D3—102no—
392C2×C4×D3—102no—
393C2×C4×D3—102no—
394C2×C4×D3—102no—
395C3×C4⋊C4—102no—
396C3×C4⋊C4C4×D514yescomplemented
397C3×C42—102no—
398C4⋊Dic3—22no—
399C4⋊Dic3—54no—
400Dic3⋊C4—54no—
401Dic3⋊C4—54no—
402Dic3⋊C4—102no—
403Dic3⋊C4—102no—
404C4×Dic3—22no—
405C4×Dic3—102no—
406C4×Dic3—102no—
407C23×C5C23×D311yescharacteristic
408C22×D5—32no—
409C22×D5—32no—
410C22×D5—32no—
411C22×D5—32no—
412C22×D5—32no—
413C22×D5—32no—
414C22×D5—32no—
415C2×C4×C5—21no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—32no—
422C2×C4×C5—32no—
423C2×C4×C5—61no—
424C2×C4×C5—61no—
425C2×C4×C5—61no—
426C2×C4×C5—61no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5—61no—
433C2×C4×C5C2×C4×D312yes—
434C2×C4×C5C2×C4×D312yes—
435C2×C4×C5C2×C4×D312yes—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—21no—
446C2×Dic5—32no—
447C2×Dic5—32no—
448C2×Dic5—32no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5D3×D412yes—
456C2×Dic5D3×Q812yes—
457C4×D5—68no—
458C4×D5—68no—
459C4×D5—68no—
460C4×D5—68no—
461C4×D5—68no—
462C4×D5—124no—
463C4×D5—124no—
464C23×C4—151no—
465C23×C4—151no—
466C23×C4—151no—
467C23×C4—151no—
468C23×C4—151no—
469C23×C4—151no—
470C23×C4—151no—
471C2×C4⋊C4—31no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—151no—
474C2×C4⋊C4—151no—
475C2×C4⋊C4—151no—
476C2×C4⋊C4—158no—
477C2×C4⋊C4—151no—
478C2×C4⋊C4—151no—
479C2×C4⋊C4—304no—
480C2×C4⋊C4D3×D511yescharacteristic
481C2×C42—31no—
482C2×C42—51no—
483C2×C42—151no—
484C2×C42—151no—
485C2×C42—304no—
486#95—31no—
487#95—31no—
488#95—31no—
489#95—31no—
490#95—51no—
491#95—51no—
492#95—51no—
493#95—51no—
494#95—151no—
495#95—151no—
496#95—151no—
497#95—151no—
498#95—151no—
499#95—151no—
500#95—151no—
501#95—151no—
502C2×C3×C5C2×#11711yescharacteristic
503C2×C3×C5C2×C4×D411yescharacteristic
504C2×C3×C5C2×C4×Q811yescharacteristic
505C2×C3×C5C2×C22⋊Q811yescharacteristic
506C2×C3×C5C2×#12311yescharacteristic
507C2×C3×C5C2×#12511yescharacteristic
508C2×C3×C5C2×#12611yescharacteristic
509D15#38718yescomplemented
510C23×C3C23×D511yescharacteristic
511C22×D3—52no—
512C22×D3—52no—
513C22×D3—52no—
514C22×D3—52no—
515C22×D3—52no—
516C22×D3—52no—
517C22×D3—52no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—52no—
525C2×C3×C4—52no—
526C2×C3×C4—101no—
527C2×C3×C4—101no—
528C2×C3×C4—101no—
529C2×C3×C4—101no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4C2×C4×D512yes—
537C2×C3×C4C2×C4×D512yes—
538C2×C3×C4C2×C4×D512yes—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—52no—
550C2×Dic3—52no—
551C2×Dic3—52no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3D4×D512yes—
559C2×Dic3Q8×D512yes—
560C4×D3—108no—
561C4×D3—108no—
562C4×D3—108no—
563C4×D3—108no—
564C4×D3—108no—
565C4×D3—204no—
566C4×D3—204no—
567C22×C5C22×C4×D311yescharacteristic
568C22×C5C2×D3×D411yescharacteristic
569C22×C5C2×D3×Q811yescharacteristic
570C22×C5D3×#4111yescharacteristic
571C22×C5D3×#4111yescharacteristic
572C22×C5D3×#4111yescharacteristic
573C22×C5D3×#4111yescharacteristic
574C2×D5—34no—
575C2×D5—34no—
576C2×D5—34no—
577C2×D5—34no—
578C2×D5—34no—
579C2×D5—34no—
580C2×D5—34no—
581C4×C5—22no—
582C4×C5—22no—
583C4×C5—22no—
584C4×C5—62no—
585C4×C5—62no—
586C4×C5—121no—
587C4×C5—121no—
588Dic5—22no—
589Dic5—22no—
590Dic5—41no—
591Dic5—41no—
592Dic5—62no—
593Dic5—62no—
594Dic5—62no—
595C24—151no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—51no—
601C22×C4—51no—
602C22×C4—51no—
603C22×C4—51no—
604C22×C4—154no—
605C22×C4—154no—
606C22×C4—151no—
607C22×C4—151no—
608C22×C4—151no—
609C22×C4—154no—
610C22×C4—154no—
611C22×C4—154no—
612C22×C4—302no—
613C22×C4—302no—
614C22×C4—302no—
615C22×C4—302no—
616C22×C4—302no—
617C22×C4—302no—
618C22×C4—302no—
619C22×C4—302no—
620C22×C4—302no—
621C22×C4—302no—
622C22×C4—302no—
623C22×C4—302no—
624C22×C4—302no—
625C22×C4—302no—
626C22×C4—302no—
627C22×C4—302no—
628C22×C4C2×D3×D511yescharacteristic
629C22×C4C2×D3×D511yescharacteristic
630C22×C4C2×D3×D511yescharacteristic
631C4⋊C4—62no—
632C4⋊C4—102no—
633C4⋊C4—154no—
634C4⋊C4—154no—
635C4⋊C4—154no—
636C4⋊C4—302no—
637C4⋊C4—302no—
638C4⋊C4#120014yescomplemented
639C42—62no—
640C42—102no—
641C42—302no—
642C42—302no—
643C3×C5C2×#38711yescharacteristic, complemented, Hall
644C22×C3C22×C4×D511yescharacteristic
645C22×C3C2×D4×D511yescharacteristic
646C22×C3C2×Q8×D511yescharacteristic
647C22×C3D5×#4111yescharacteristic
648C22×C3D5×#4111yescharacteristic
649C22×C3D5×#4111yescharacteristic
650C22×C3D5×#4111yescharacteristic
651C2×D3—54no—
652C2×D3—54no—
653C2×D3—54no—
654C2×D3—54no—
655C2×D3—54no—
656C2×D3—54no—
657C2×D3—54no—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—102no—
662C3×C4—102no—
663C3×C4—201no—
664C3×C4—201no—
665Dic3—22no—
666Dic3—22no—
667Dic3—41no—
668Dic3—41no—
669Dic3—102no—
670Dic3—102no—
671Dic3—102no—
672C2×C5D3×#11711yescharacteristic
673C2×C5C4×D3×D411yescharacteristic
674C2×C5C4×D3×Q811yescharacteristic
675C2×C5D3×C22⋊Q811yescharacteristic
676C2×C5D3×#12311yescharacteristic
677C2×C5D3×#12511yescharacteristic
678C2×C5D3×#12611yescharacteristic
679D5—38no—
680C23—152no—
681C23—152no—
682C23—152no—
683C23—152no—
684C23—152no—
685C23—152no—
686C23—152no—
687C23C22×D3×D511yescharacteristic
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—32no—
695C2×C4—32no—
696C2×C4—52no—
697C2×C4—52no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—101no—
709C2×C4—101no—
710C2×C4—101no—
711C2×C4—101no—
712C2×C4—101no—
713C2×C4—101no—
714C2×C4—101no—
715C2×C4—101no—
716C2×C4—101no—
717C2×C4—101no—
718C2×C4—152no—
719C2×C4—152no—
720C2×C4—152no—
721C2×C4—308no—
722C2×C4—308no—
723C2×C4—308no—
724C2×C4—308no—
725C2×C4—308no—
726C2×C4—301no—
727C2×C4—301no—
728C2×C4—301no—
729C2×C4—301no—
730C2×C4—301no—
731C2×C4—301no—
732C2×C4—604no—
733C2×C4—604no—
734C2×C4C2×#120012yes—
735C2×C4C2×#120012yes—
736C2×C4C2×#120012yes—
737C2×C3D5×#11711yescharacteristic
738C2×C3C4×D4×D511yescharacteristic
739C2×C3C4×Q8×D511yescharacteristic
740C2×C3D5×C22⋊Q811yescharacteristic
741C2×C3D5×#12311yescharacteristic
742C2×C3D5×#12511yescharacteristic
743C2×C3D5×#12611yescharacteristic
744D3—58no—
745C5D3×#38711yescharacteristic, complemented, Sylow
746C22—154no—
747C22—154no—
748C22—154no—
749C22—154no—
750C22—154no—
751C22—154no—
752C22—154no—
753C22#9201611yescharacteristic
754C22#9201611yescharacteristic
755C22D3×D4×D511yescharacteristic
756C22#9202411yescharacteristic
757C22D3×Q8×D511yescharacteristic
758C22#9203411yescharacteristic
759C22C22×#120011yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—62no—
764C4—62no—
765C4—102no—
766C4—102no—
767C4—121no—
768C4—121no—
769C4—201no—
770C4—201no—
771C4—302no—
772C4—302no—
773C4—302no—
774C3D5×#38711yescharacteristic, complemented, Sylow
775C2—158no—
776C2#1175346811yescharacteristic
777C2#1175384411yescharacteristic
778C2#1175386711yescharacteristic
779C2#1175393111yescharacteristic
780C2#1175446111yescharacteristic
781C2D4×#120011yescharacteristic
782C2Q8×#120011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#387
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C5×#4980C2semidirect
5. C3×#65270C2semidirect
10. #11748847C2semidirect
11. #11748824C2semidirect
12. #11748689C2semidirect
13. #11748688C2semidirect
14. #11748687C2semidirect
15. #11748674C2semidirect
28. C4⋊C4×D15C4semidirect
60. #65270D3semidirect
107. C3×C5×C4⋊C4C2×C4semidirect
108. C4⋊Dic15C2×C4semidirect
109. #6712C2×C4semidirect
110. #6712C2×C4semidirect
123. #4980D5semidirect
305. C5×C4⋊C4C4×D3semidirect
396. C3×C4⋊C4C4×D5semidirect
509. D15#387semidirect
638. C4⋊C4#1200semidirect
643. C3×C5C2×#387semidirect
745. C5D3×#387semidirect
774. C3D5×#387semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D152
C2×#914372
C2×C4×#12002
C5×#49802
C3×#652702
#117488882
#117488472
#117488242
#117486892
#117486882
#117486872
#117486742
D5×#3873
D3×#3875