Finite Group Databasebeta

← #14324034

Subgroups — #14324034

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
2C2×#91828C211yesmaximal, characteristic
3C2×C4×#1220C211yesmaximal, characteristic, complemented
4#11751321C211yesmaximal, characteristic, complemented
5#11751314C211yesmaximal, characteristic, complemented
6#11751311C211yesmaximal, characteristic, complemented
7C2×#91115C211yesmaximal, characteristic, complemented
8#11751090C211yesmaximal, characteristic, complemented
9#11751079C211yesmaximal, characteristic, complemented
10#11751059C211yesmaximal, characteristic, complemented
11#11751057C211yesmaximal, characteristic, complemented
12#11751045C211yesmaximal, characteristic, complemented
13#11751043C211yesmaximal, characteristic, complemented
14#11751041C211yesmaximal, characteristic, complemented
15#11751034C211yesmaximal, characteristic, complemented
16#10614058—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C23×Dic15C2211yescharacteristic
23C23×Dic15C2211yescharacteristic
24C22×C4×D15C2211yescharacteristic
25C3×C4×C5×D4—24no—
26C2×C3×C5×C4⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C42×C5C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C2×#6719C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×#6719C2211yescharacteristic
34#91828C418yescomplemented
35C4×#1220—24no—
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×#6714C2211yescharacteristic
39C2×#6714C2211yescharacteristic
40C2×#6712C2211yescharacteristic
41C2×#6712C2211yescharacteristic
42C2×#6712C2211yescharacteristic
43C2×#6712C2211yescharacteristic
44C2×C4×Dic15C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#91115C2211yescharacteristic
54#91115C2211yescharacteristic
55#82327—51nomaximal, Hall
56C2×C4×C5×D4D311yescharacteristic, complemented
57C2×#4085—31no—
58C2×C4×C22⋊D5—31no—
59#65509—31no—
60#65502—31no—
61#65499—31no—
62C2×#3963—31no—
63#65278—31no—
64#65267—31no—
65#65247—31no—
66#65245—31no—
67#65233—31no—
68#65231—31no—
69#65229—31no—
70#65222—31no—
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×D15C2311yescharacteristic
74C2×C3×C5×D4—22no—
75C2×C3×C5×D4—22no—
76C2×C3×C5×D4C2×C414yescomplemented
77C22×C3×C4×C5—22no—
78C22×C3×C4×C5—41no—
79C22×C3×C4×C5—41no—
80C22×C3×C4×C5—41no—
81C22×C3×C4×C5—41no—
82C22×C3×C4×C5D414yescomplemented
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C2×#1220—22no—
89C2×#1220—22no—
90C2×#1220—41no—
91C2×#1220—41no—
92C2×#1220C2×C414yescomplemented
93C2×#1220C2×C414yescomplemented
94C22×Dic15—22no—
95C22×Dic15—41no—
96C22×Dic15—41no—
97C22×Dic15—41no—
98C22×Dic15—41no—
99C22×Dic15C2×C414yescomplemented
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C2×C4×D15—22no—
108C2×C4×D15—41no—
109C2×C4×D15—41no—
110C3×C5×C4⋊C4—22no—
111C3×C5×C22⋊C4—22no—
112C3×C5×C22⋊C4—22no—
113C3×C42×C5—22no—
114#6719—22no—
115#6719—41no—
116#6719—41no—
117#6719C2×C414yescomplemented
118#6714—22no—
119#6714—41no—
120#6714—41no—
121#6714C2×C414yescomplemented
122#6712—22no—
123#6712—41no—
124#6712—41no—
125#6712C2×C414yescomplemented
126C4×Dic15—22no—
127C2×C3×C4×D4D511yescharacteristic, complemented
128C2×#939—51no—
129C2×C4×#67—51no—
130#5220—51no—
131#5213—51no—
132#5210—51no—
133C2×C3⋊#95—51no—
134#4989—51no—
135#4978—51no—
136#4958—51no—
137#4956—51no—
138#4944—51no—
139#4942—51no—
140#4940—51no—
141#4933—51no—
142C22×C5×D4C2×D311yescharacteristic
143C23×C4×C5C2×D311yescharacteristic
144C23×C4×C5C2×D311yescharacteristic
145C22×C22⋊D5—31no—
146C22×C22⋊D5—31no—
147C23×Dic5—31no—
148C23×Dic5—31no—
149C22×C4×D5—31no—
150C4×C5×D4—24no—
151C2×C5×C4⋊C4C2×D311yescharacteristic
152C2×C5×C22⋊C4C2×D311yescharacteristic
153C2×C5×C22⋊C4C2×D311yescharacteristic
154C2×C42×C5C2×D311yescharacteristic
155C2×C22⋊Dic5—31no—
156C2×C22⋊Dic5—31no—
157C2×C22⋊Dic5—31no—
158C2×C22⋊Dic5—31no—
159#4085—38no—
160C4×C22⋊D5—64no—
161C2×#685—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#683—31no—
166C2×#683—31no—
167C2×#683—31no—
168C2×#683—31no—
169C2×C4×Dic5—31no—
170#3963—31no—
171#3963—31no—
172#3963—31no—
173#3963—31no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963—31no—
179#3963—31no—
180#2325—151noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5C22×C412yes—
192C23×C3×C5C22×C412yes—
193C23×C3×C5C2×D412yes—
194C23×C3×C5#4112yes—
195C23×C3×C5C2411yescharacteristic
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15—21no—
202C22×D15C22×C412yes—
203C3×C5×D4—28no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—44no—
217C2×C3×C4×C5—44no—
218C2×C3×C4×C5C22×C412yes—
219C2×C3×C4×C5C2×D412yes—
220C2×C3×C4×C5C2×D412yes—
221#1220—28no—
222#1220—44no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—44no—
242C2×Dic15—44no—
243C2×Dic15C22×C412yes—
244C2×Dic15C22×C412yes—
245C2×Dic15C22×C412yes—
246C4×D15—44no—
247C22×C3×D4C2×D511yescharacteristic
248C23×C3×C4C2×D511yescharacteristic
249C23×C3×C4C2×D511yescharacteristic
250C22×#67—51no—
251C22×#67—51no—
252C23×Dic3—51no—
253C23×Dic3—51no—
254C22×C4×D3—51no—
255C3×C4×D4—24no—
256C2×C3×C4⋊C4C2×D511yescharacteristic
257C2×C3×C22⋊C4C2×D511yescharacteristic
258C2×C3×C22⋊C4C2×D511yescharacteristic
259C2×C3×C42C2×D511yescharacteristic
260C2×#217—51no—
261C2×#217—51no—
262C2×#217—51no—
263C2×#217—51no—
264#939—58no—
265C4×#67—104no—
266C2×(C2×D3)⋊C4—51no—
267C2×(C2×D3)⋊C4—51no—
268C2×(C2×D3)⋊C4—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×Dic3⋊C4—51no—
271C2×Dic3⋊C4—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×C4×Dic3—51no—
275C3⋊#95—51no—
276C3⋊#95—51no—
277C3⋊#95—51no—
278C3⋊#95—51no—
279C3⋊#95—51no—
280C3⋊#95—51no—
281C3⋊#95—51no—
282C3⋊#95—51no—
283C3⋊#95—51no—
284C3⋊#95—51no—
285C24×C5C22×D311yescharacteristic
286C24×C5C22×D311yescharacteristic
287C23×D5—31no—
288C2×C5×D4—22no—
289C2×C5×D4—22no—
290C2×C5×D4C4×D314yescomplemented
291C22×C4×C5—22no—
292C22×C4×C5—41no—
293C22×C4×C5—41no—
294C22×C4×C5—41no—
295C22×C4×C5—41no—
296C22×C4×C5#6714yescomplemented
297C22×C4×C5C22×D311yescharacteristic
298C22×C4×C5C22×D311yescharacteristic
299C22×C4×C5C22×D311yescharacteristic
300C22×C4×C5C22×D311yescharacteristic
301C22×C4×C5C22×D311yescharacteristic
302C2×C22⋊D5—34no—
303C2×C22⋊D5—34no—
304C2×C22⋊D5—62no—
305C2×C22⋊D5—62no—
306C2×C22⋊D5—121no—
307C2×C22⋊D5—121no—
308C22×Dic5—31no—
309C22×Dic5—31no—
310C22×Dic5—31no—
311C22×Dic5—34no—
312C22×Dic5—31no—
313C22×Dic5—31no—
314C22×Dic5—31no—
315C22×Dic5—31no—
316C22×Dic5—62no—
317C22×Dic5—121no—
318C22×Dic5—121no—
319C22×Dic5—121no—
320C22×Dic5—121no—
321C2×C4×D5—62no—
322C2×C4×D5—121no—
323C2×C4×D5—121no—
324C5×C4⋊C4—22no—
325C5×C22⋊C4—22no—
326C5×C22⋊C4—22no—
327C42×C5—22no—
328C22⋊Dic5—34no—
329C22⋊Dic5—62no—
330C22⋊Dic5—121no—
331C22⋊Dic5—121no—
332#685—34no—
333#685—62no—
334#685—121no—
335#685—121no—
336#683—34no—
337#683—62no—
338#683—121no—
339#683—121no—
340C4×Dic5—62no—
341C2×#121—151no—
342C2×C4×D4—151no—
343C2×C4×D4D1511yescharacteristic, complemented
344#388—151no—
345#388—151no—
346#387—151no—
347#387—151no—
348#386—151no—
349#386—151no—
350#386—151no—
351#386—151no—
352#385—151no—
353#385—151no—
354#380—151no—
355C2×#95—151no—
356C22×C3×C5—22no—
357C22×C3×C5—22no—
358C22×C3×C5—22no—
359C22×C3×C5—22no—
360C22×C3×C5—22no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—22no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5—41no—
368C22×C3×C5—41no—
369C22×C3×C5C4×D414yes—
370C22×C3×C5C23×C411yescharacteristic
371C22×C3×C5C22×D411yescharacteristic
372C22×C3×C5C2×#4111yescharacteristic
373C22×C3×C5H(5,𝔽2)11yescharacteristic
374C22×C3×C5H(5,𝔽2)11yescharacteristic
375C22×C3×C5H(5,𝔽2)11yescharacteristic
376C22×C3×C52−1+411yescharacteristic
377C2×D15—22no—
378C2×D15—22no—
379C2×D15—22no—
380C2×D15—41no—
381C2×D15—41no—
382C2×D15—41no—
383C2×D15—41no—
384C3×C4×C5—22no—
385C3×C4×C5—22no—
386C3×C4×C5—22no—
387C3×C4×C5—41no—
388C3×C4×C5—41no—
389Dic15—22no—
390Dic15—22no—
391Dic15—22no—
392Dic15—41no—
393Dic15—41no—
394Dic15—41no—
395Dic15—41no—
396C24×C3C22×D511yescharacteristic
397C24×C3C22×D511yescharacteristic
398C23×D3—51no—
399C2×C3×D4—22no—
400C2×C3×D4—22no—
401C2×C3×D4C4×D514yescomplemented
402C22×C3×C4—22no—
403C22×C3×C4—41no—
404C22×C3×C4—41no—
405C22×C3×C4—41no—
406C22×C3×C4—41no—
407C22×C3×C4C22⋊D514yescomplemented
408C22×C3×C4C22×D511yescharacteristic
409C22×C3×C4C22×D511yescharacteristic
410C22×C3×C4C22×D511yescharacteristic
411C22×C3×C4C22×D511yescharacteristic
412C22×C3×C4C22×D511yescharacteristic
413C2×#67—54no—
414C2×#67—54no—
415C2×#67—102no—
416C2×#67—102no—
417C2×#67—201no—
418C2×#67—201no—
419C22×Dic3—51no—
420C22×Dic3—51no—
421C22×Dic3—51no—
422C22×Dic3—54no—
423C22×Dic3—51no—
424C22×Dic3—51no—
425C22×Dic3—51no—
426C22×Dic3—51no—
427C22×Dic3—102no—
428C22×Dic3—201no—
429C22×Dic3—201no—
430C22×Dic3—201no—
431C22×Dic3—201no—
432C2×C4×D3—102no—
433C2×C4×D3—201no—
434C2×C4×D3—201no—
435C3×C4⋊C4—22no—
436C3×C22⋊C4—22no—
437C3×C22⋊C4—22no—
438C3×C42—22no—
439#217—54no—
440#217—102no—
441#217—201no—
442#217—201no—
443(C2×D3)⋊C4—54no—
444(C2×D3)⋊C4—102no—
445(C2×D3)⋊C4—201no—
446(C2×D3)⋊C4—201no—
447Dic3⋊C4—54no—
448Dic3⋊C4—102no—
449Dic3⋊C4—201no—
450Dic3⋊C4—201no—
451C4×Dic3—102no—
452C23×C5—21no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—21no—
462C23×C5C2×C4×D312yes—
463C23×C5C2×C4×D312yes—
464C23×C5#23512yes—
465C23×C5C2×#6712yes—
466C23×C5C23×D311yescharacteristic
467C22×D5—32no—
468C22×D5—61no—
469C22×D5—61no—
470C22×D5—61no—
471C22×D5—61no—
472C22×D5—61no—
473C22×D5—61no—
474C5×D4—28no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—21no—
484C2×C4×C5—21no—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—44no—
488C2×C4×C5—44no—
489C2×C4×C5C2×C4×D312yes—
490C2×C4×C5C2×#6712yes—
491C2×C4×C5C2×#6712yes—
492C22⋊D5—68no—
493C22⋊D5—124no—
494C2×Dic5—32no—
495C2×Dic5—32no—
496C2×Dic5—32no—
497C2×Dic5—61no—
498C2×Dic5—61no—
499C2×Dic5—61no—
500C2×Dic5—61no—
501C2×Dic5—61no—
502C2×Dic5—61no—
503C2×Dic5—61no—
504C2×Dic5—61no—
505C2×Dic5—61no—
506C2×Dic5—61no—
507C2×Dic5—61no—
508C2×Dic5—61no—
509C2×Dic5—61no—
510C2×Dic5—61no—
511C2×Dic5—61no—
512C2×Dic5—61no—
513C2×Dic5—61no—
514C2×Dic5—61no—
515C2×Dic5—124no—
516C2×Dic5—124no—
517C4×D5—124no—
518C22×D4—151no—
519C22×D4—151no—
520C22×D4C2×D1511yescharacteristic
521C23×C4—151no—
522C23×C4—151no—
523C23×C4—151no—
524C23×C4C2×D1511yescharacteristic
525C23×C4C2×D1511yescharacteristic
526#121—158no—
527C4×D4—24no—
528C4×D4—304no—
529C2×C4⋊C4—151no—
530C2×C4⋊C4—151no—
531C2×C4⋊C4—151no—
532C2×C4⋊C4—151no—
533C2×C4⋊C4C2×D1511yescharacteristic
534C2×C22⋊C4—151no—
535C2×C22⋊C4—151no—
536C2×C22⋊C4—151no—
537C2×C22⋊C4—151no—
538C2×C22⋊C4—151no—
539C2×C22⋊C4—151no—
540C2×C22⋊C4—151no—
541C2×C22⋊C4—151no—
542C2×C22⋊C4C2×D1511yescharacteristic
543C2×C22⋊C4C2×D1511yescharacteristic
544C2×C42—151no—
545C2×C42C2×D1511yescharacteristic
546#95—151no—
547#95—151no—
548#95—151no—
549#95—151no—
550#95—151no—
551#95—151no—
552#95—151no—
553#95—151no—
554#95—151no—
555#95—151no—
556C2×C3×C5—24no—
557C2×C3×C5—42no—
558C2×C3×C5C2×C4×D411yescharacteristic
559C2×C3×C5#51811yescharacteristic
560C2×C3×C5#52011yescharacteristic
561C2×C3×C5#53411yescharacteristic
562C2×C3×C5#53711yescharacteristic
563C2×C3×C5#53811yescharacteristic
564C2×C3×C5#53911yescharacteristic
565D15—42no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3C2×C4×D512yes—
577C23×C3C2×C4×D512yes—
578C23×C3#70912yes—
579C23×C3C2×C22⋊D512yes—
580C23×C3C23×D511yescharacteristic
581C22×D3—52no—
582C22×D3—101no—
583C22×D3—101no—
584C22×D3—101no—
585C22×D3—101no—
586C22×D3—101no—
587C22×D3—101no—
588C3×D4—28no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—44no—
602C2×C3×C4—44no—
603C2×C3×C4C2×C4×D512yes—
604C2×C3×C4C2×C22⋊D512yes—
605C2×C3×C4C2×C22⋊D512yes—
606#67—108no—
607#67—204no—
608C2×Dic3—52no—
609C2×Dic3—52no—
610C2×Dic3—52no—
611C2×Dic3—101no—
612C2×Dic3—101no—
613C2×Dic3—101no—
614C2×Dic3—101no—
615C2×Dic3—101no—
616C2×Dic3—101no—
617C2×Dic3—101no—
618C2×Dic3—101no—
619C2×Dic3—101no—
620C2×Dic3—101no—
621C2×Dic3—101no—
622C2×Dic3—101no—
623C2×Dic3—101no—
624C2×Dic3—101no—
625C2×Dic3—101no—
626C2×Dic3—101no—
627C2×Dic3—101no—
628C2×Dic3—101no—
629C2×Dic3—204no—
630C2×Dic3—204no—
631C4×D3—204no—
632C22×C5—22no—
633C22×C5—22no—
634C22×C5—22no—
635C22×C5—22no—
636C22×C5—22no—
637C22×C5—22no—
638C22×C5—22no—
639C22×C5—22no—
640C22×C5—22no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5—41no—
644C22×C5—41no—
645C22×C5C4×#6714yes—
646C22×C5C22×C4×D311yescharacteristic
647C22×C5C2×#23511yescharacteristic
648C22×C5#100411yescharacteristic
649C22×C5#100411yescharacteristic
650C22×C5#100911yescharacteristic
651C22×C5#101011yescharacteristic
652C22×C5C22×#6711yescharacteristic
653C2×D5—62no—
654C2×D5—62no—
655C2×D5—62no—
656C2×D5—121no—
657C2×D5—121no—
658C2×D5—121no—
659C2×D5—121no—
660C4×C5—22no—
661C4×C5—22no—
662C4×C5—22no—
663C4×C5—41no—
664C4×C5—41no—
665Dic5—62no—
666Dic5—62no—
667Dic5—62no—
668Dic5—121no—
669Dic5—121no—
670Dic5—121no—
671Dic5—121no—
672C24—151no—
673C24C22×D1511yescharacteristic
674C24C22×D1511yescharacteristic
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—154no—
678C2×D4—154no—
679C2×D4—302no—
680C2×D4—302no—
681C2×D4—601no—
682C2×D4—601no—
683C2×D4C4×D1514yescomplemented
684C22×C4—22no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—151no—
690C22×C4—151no—
691C22×C4—151no—
692C22×C4—154no—
693C22×C4—151no—
694C22×C4—151no—
695C22×C4—151no—
696C22×C4—151no—
697C22×C4—302no—
698C22×C4—302no—
699C22×C4—601no—
700C22×C4—601no—
701C22×C4—601no—
702C22×C4—601no—
703C22×C4—601no—
704C22×C4—601no—
705C22×C4#122014yescomplemented
706C22×C4C22×D1511yescharacteristic
707C22×C4C22×D1511yescharacteristic
708C22×C4C22×D1511yescharacteristic
709C22×C4C22×D1511yescharacteristic
710C22×C4C22×D1511yescharacteristic
711C4⋊C4—22no—
712C4⋊C4—154no—
713C4⋊C4—302no—
714C4⋊C4—601no—
715C4⋊C4—601no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—154no—
719C22⋊C4—154no—
720C22⋊C4—302no—
721C22⋊C4—302no—
722C22⋊C4—601no—
723C22⋊C4—601no—
724C22⋊C4—601no—
725C22⋊C4—601no—
726C42—22no—
727C42—302no—
728C3×C5#232511yescharacteristic, complemented, Hall
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3C4×C22⋊D514yes—
743C22×C3C22×C4×D511yescharacteristic
744C22×C3C2×#70911yescharacteristic
745C22×C3#414411yescharacteristic
746C22×C3#414411yescharacteristic
747C22×C3#414911yescharacteristic
748C22×C3#415011yescharacteristic
749C22×C3C22×C22⋊D511yescharacteristic
750C2×D3—102no—
751C2×D3—102no—
752C2×D3—102no—
753C2×D3—201no—
754C2×D3—201no—
755C2×D3—201no—
756C2×D3—201no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—41no—
761C3×C4—41no—
762Dic3—102no—
763Dic3—102no—
764Dic3—102no—
765Dic3—201no—
766Dic3—201no—
767Dic3—201no—
768Dic3—201no—
769C2×C5—24no—
770C2×C5—42no—
771C2×C5#554511yescharacteristic
772C2×C5#554611yescharacteristic
773C2×C5#556011yescharacteristic
774C2×C5#556411yescharacteristic
775C2×C5C2×C4×#6711yescharacteristic
776C2×C5#580411yescharacteristic
777C2×C5#583311yescharacteristic
778D5—122no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—152no—
790C23—301no—
791C23—301no—
792C23—301no—
793C23—301no—
794C23—301no—
795C23—301no—
796C23C2×C4×D1512yes—
797C23C2×C4×D1512yes—
798C23#681712yes—
799C23C2×#122012yes—
800C23C23×D1511yescharacteristic
801D4—28no—
802D4—308no—
803D4—604no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—152no—
819C2×C4—152no—
820C2×C4—152no—
821C2×C4—301no—
822C2×C4—301no—
823C2×C4—301no—
824C2×C4—301no—
825C2×C4—301no—
826C2×C4—301no—
827C2×C4—301no—
828C2×C4—301no—
829C2×C4—301no—
830C2×C4—301no—
831C2×C4—301no—
832C2×C4—301no—
833C2×C4—301no—
834C2×C4—301no—
835C2×C4—301no—
836C2×C4—301no—
837C2×C4—301no—
838C2×C4—301no—
839C2×C4—604no—
840C2×C4—604no—
841C2×C4—604no—
842C2×C4C2×C4×D1512yes—
843C2×C4C2×#122012yes—
844C2×C4C2×#122012yes—
845C2×C3—24no—
846C2×C3—42no—
847C2×C3#6587911yescharacteristic
848C2×C3#6588011yescharacteristic
849C2×C3#6589411yescharacteristic
850C2×C3#6589811yescharacteristic
851C2×C3C2×C4×C22⋊D511yescharacteristic
852C2×C3#6613811yescharacteristic
853C2×C3#6616711yescharacteristic
854D3—202no—
855C5#8232711yescharacteristic, complemented, Sylow
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—302no—
870C22—302no—
871C22—302no—
872C22—601no—
873C22—601no—
874C22—601no—
875C22—601no—
876C22C4×#122014yes—
877C22C22×C4×D1511yescharacteristic
878C22C2×#681711yescharacteristic
879C22#9209511yescharacteristic
880C22#9209511yescharacteristic
881C22#9210011yescharacteristic
882C22#9210111yescharacteristic
883C22C22×#122011yescharacteristic
884C4—22no—
885C4—22no—
886C4—22no—
887C4—41no—
888C4—41no—
889C4—302no—
890C4—302no—
891C4—302no—
892C4—601no—
893C4—601no—
894C4—601no—
895C4—601no—
896C3#1061405811yescharacteristic, complemented, Sylow
897C2—24no—
898C2—42no—
899C2—602no—
900C2#1175630411yescharacteristic
901C2#1175630511yescharacteristic
902C2#1175631911yescharacteristic
903C2#1175632311yescharacteristic
904C2C2×C4×#122011yescharacteristic
905C2#1175656311yescharacteristic
906C2#1175659211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC2×C3×C4×C5×D4C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91828C2
hypercenterC2×C4×D4D15
hypocenterC3×C5#2325
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×D4C2semidirect
3. C2×C4×#1220C2semidirect
4. #11751321C2semidirect
5. #11751314C2semidirect
6. #11751311C2semidirect
7. C2×#91115C2semidirect
8. #11751090C2semidirect
9. #11751079C2semidirect
10. #11751059C2semidirect
11. #11751057C2semidirect
12. #11751045C2semidirect
13. #11751043C2semidirect
14. #11751041C2semidirect
15. #11751034C2semidirect
34. #91828C4semidirect
56. C2×C4×C5×D4D3semidirect
76. C2×C3×C5×D4C2×C4semidirect
82. C22×C3×C4×C5D4semidirect
92. C2×#1220C2×C4semidirect
93. C2×#1220C2×C4semidirect
99. C22×Dic15C2×C4semidirect
117. #6719C2×C4semidirect
121. #6714C2×C4semidirect
125. #6712C2×C4semidirect
127. C2×C3×C4×D4D5semidirect
290. C2×C5×D4C4×D3semidirect
296. C22×C4×C5#67semidirect
343. C2×C4×D4D15semidirect
401. C2×C3×D4C4×D5semidirect
407. C22×C3×C4C22⋊D5semidirect
683. C2×D4C4×D15semidirect
705. C22×C4#1220semidirect
728. C3×C5#2325semidirect
855. C5#82327semidirect
896. C3#10614058semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×#918282
C2×C4×#12202
#117513212
#117513142
#117513112
C2×#911152
#117510902
#117510792
#117510592
#117510572
#117510452
#117510432
#117510412
#117510342
#106140583
#823275