Finite Group Databasebeta

← #14328097

Subgroups — #14328097

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
2C2×#91826C211yesmaximal, characteristic
3C2×C4×#1220C211yesmaximal, characteristic, complemented
4C22×#6714C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
6#11751321C211yesmaximal, characteristic, complemented
7#11751314C211yesmaximal, characteristic, complemented
8#11751311C211yesmaximal, characteristic, complemented
9#11751091C211yesmaximal, characteristic, complemented
10#11751090C211yesmaximal, characteristic, complemented
11#11751058C211yesmaximal, characteristic, complemented
12#11751057C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
14#11751041C211yesmaximal, characteristic, complemented
15C4×#6714C211yesmaximal, characteristic, complemented
16#10614129—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C23×C3×C4×C5C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic
23C23×Dic15C2211yescharacteristic
24C22×C4×D15C2211yescharacteristic
25C22×C4×D15C2211yescharacteristic
26C3×C4×C5×D4—24no—
27C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
30C2×C3×C42×C5C2211yescharacteristic, complemented
31C2×#6719C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×#6719C2211yescharacteristic, complemented
34C2×#6719C2211yescharacteristic, complemented
35#91826C418yescomplemented
36C4×#1220—24no—
37C2×#6714—24no—
38C2×#6714C2211yescharacteristic
39C2×#6714C2211yescharacteristic
40C2×#6714C2211yescharacteristic
41C2×#6714C2211yescharacteristic
42C2×#6714C2211yescharacteristic
43C2×#6714C2211yescharacteristic
44C2×#6714C2211yescharacteristic
45C2×#6714C2211yescharacteristic
46C2×#6712C2211yescharacteristic, complemented
47C2×#6712C2211yescharacteristic, complemented
48C2×C4×Dic15C2211yescharacteristic, complemented
49C2×C4×Dic15C2211yescharacteristic, complemented
50C22⋊C4×D15—24no—
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53#91115C2211yescharacteristic, complemented
54#91115C2211yescharacteristic, complemented
55#91115C2211yescharacteristic, complemented
56#91115C2211yescharacteristic, complemented
57#82398—51nomaximal, Hall
58C2×C4×C5×D4D311yescharacteristic, complemented
59C2×#4083—31no—
60C2×C4×C22⋊D5—31no—
61C22×#685—31no—
62C2×D5×C22⋊C4—31no—
63#65509—31no—
64#65502—31no—
65#65499—31no—
66#65279—31no—
67#65278—31no—
68#65246—31no—
69#65245—31no—
70C22⋊C4×Dic5—31no—
71#65229—31no—
72C4×#685—31no—
73C24×C3×C5C2311yescharacteristic
74C24×C3×C5C2311yescharacteristic
75C23×D15—22no—
76C23×D15—22no—
77C23×D15—22no—
78C23×D15—22no—
79C23×D15—41no—
80C23×D15—41no—
81C23×D15C2×C414yescomplemented
82C23×D15C2311yescharacteristic
83C23×D15C2311yescharacteristic
84C2×C3×C5×D4—22no—
85C2×C3×C5×D4—22no—
86C2×C3×C5×D4C2×C414yescomplemented
87C22×C3×C4×C5—22no—
88C22×C3×C4×C5—22no—
89C22×C3×C4×C5—22no—
90C22×C3×C4×C5—22no—
91C22×C3×C4×C5—41no—
92C22×C3×C4×C5—41no—
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C2×#1220—22no—
99C2×#1220—22no—
100C2×#1220—41no—
101C2×#1220—41no—
102C2×#1220C2×C414yescomplemented
103C2×#1220C2×C414yescomplemented
104C22×Dic15—22no—
105C22×Dic15—22no—
106C22×Dic15—41no—
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109C22×Dic15C2311yescharacteristic
110C22×Dic15C2311yescharacteristic
111C22×Dic15C2311yescharacteristic
112C22×Dic15C2311yescharacteristic
113C2×C4×D15—22no—
114C2×C4×D15—22no—
115C2×C4×D15—22no—
116C2×C4×D15—22no—
117C2×C4×D15—41no—
118C2×C4×D15—41no—
119C3×C5×C4⋊C4—22no—
120C3×C5×C22⋊C4—22no—
121C3×C5×C22⋊C4D414yescomplemented
122C3×C42×C5—22no—
123#6719—22no—
124#6719—22no—
125#6719—41no—
126#6719C2×C414yescomplemented
127#6714—22no—
128#6714—22no—
129#6714—22no—
130#6714—22no—
131#6714—22no—
132#6714C2×C414yescomplemented
133#6714C2×C414yescomplemented
134#6714D414yescomplemented
135#6712—22no—
136#6712—41no—
137C4×Dic15—22no—
138C4×Dic15—41no—
139C2×C3×C4×D4D511yescharacteristic, complemented
140C2×#937—51no—
141C2×C4×#67—51no—
142C22×(C2×D3)⋊C4—51no—
143C2×D3×C22⋊C4—51no—
144#5220—51no—
145#5213—51no—
146#5210—51no—
147#4990—51no—
148#4989—51no—
149#4957—51no—
150#4956—51no—
151Dic3×C22⋊C4—51no—
152#4940—51no—
153C4×(C2×D3)⋊C4—51no—
154C24×D5—31no—
155C22×C5×D4C2×D311yescharacteristic
156C23×C4×C5C2×D311yescharacteristic
157C23×C4×C5C2×D311yescharacteristic, complemented
158C22×C22⋊D5—31no—
159C22×C22⋊D5—31no—
160C23×Dic5—31no—
161C22×C4×D5—31no—
162C22×C4×D5—31no—
163C4×C5×D4—24no—
164C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
165C2×C5×C22⋊C4C2×D311yescharacteristic
166C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
167C2×C42×C5C2×D311yescharacteristic, complemented
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5—31no—
170C2×C22⋊Dic5—31no—
171C2×C22⋊Dic5—31no—
172#4083—38no—
173C4×C22⋊D5—64no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—31no—
181C2×#685—31no—
182C2×#685—64no—
183C2×#683—31no—
184C2×#683—31no—
185C2×C4×Dic5—31no—
186C2×C4×Dic5—31no—
187D5×C22⋊C4—64no—
188#3963—31no—
189#3963—31no—
190#3963—31no—
191#3963—31no—
192#3963—31no—
193#3963—31no—
194#2358—151noSylow
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5—21no—
200C23×C3×C5—21no—
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—21no—
205C23×C3×C5C22×C412yes—
206C23×C3×C5C22×C412yes—
207C23×C3×C5C2×D412yes—
208C23×C3×C5#4112yes—
209C23×C3×C5C2411yescharacteristic
210C22×D15—21no—
211C22×D15—21no—
212C22×D15—21no—
213C22×D15—21no—
214C22×D15—28no—
215C22×D15—21no—
216C22×D15—21no—
217C22×D15—21no—
218C22×D15—21no—
219C22×D15—21no—
220C22×D15—21no—
221C22×D15—28no—
222C22×D15—44no—
223C22×D15—44no—
224C22×D15—44no—
225C22×D15—44no—
226C22×D15—44no—
227C22×D15C22×C412yes—
228C22×D15C22×C412yes—
229C22×D15C2×D412yes—
230C22×D15#4112yes—
231C3×C5×D4—28no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5—21no—
239C2×C3×C4×C5—21no—
240C2×C3×C4×C5—21no—
241C2×C3×C4×C5—21no—
242C2×C3×C4×C5—21no—
243C2×C3×C4×C5—44no—
244C2×C3×C4×C5—44no—
245C2×C3×C4×C5C22×C412yes—
246C2×C3×C4×C5C2×D412yes—
247C2×C3×C4×C5C2×D412yes—
248C2×C3×C4×C5C2×D412yes—
249#1220—28no—
250#1220—44no—
251C2×Dic15—21no—
252C2×Dic15—21no—
253C2×Dic15—21no—
254C2×Dic15—21no—
255C2×Dic15—21no—
256C2×Dic15—21no—
257C2×Dic15—21no—
258C2×Dic15—21no—
259C2×Dic15—21no—
260C2×Dic15—21no—
261C2×Dic15—21no—
262C2×Dic15—21no—
263C2×Dic15—21no—
264C2×Dic15—21no—
265C2×Dic15—21no—
266C2×Dic15—44no—
267C2×Dic15C22×C412yes—
268C2×Dic15C22×C412yes—
269C2×Dic15C2×D412yes—
270C4×D15—44no—
271C4×D15—44no—
272C24×D3—51no—
273C22×C3×D4C2×D511yescharacteristic
274C23×C3×C4C2×D511yescharacteristic
275C23×C3×C4C2×D511yescharacteristic, complemented
276C22×#67—51no—
277C22×#67—51no—
278C23×Dic3—51no—
279C22×C4×D3—51no—
280C22×C4×D3—51no—
281C3×C4×D4—24no—
282C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
283C2×C3×C22⋊C4C2×D511yescharacteristic
284C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
285C2×C3×C42C2×D511yescharacteristic, complemented
286C2×#217—51no—
287C2×#217—51no—
288C2×#217—51no—
289C2×#217—51no—
290#937—58no—
291C4×#67—104no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4—51no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4—51no—
299C2×(C2×D3)⋊C4—51no—
300C2×(C2×D3)⋊C4—104no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3—51no—
305D3×C22⋊C4—104no—
306C3⋊#95—51no—
307C3⋊#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95—51no—
312C24×C5C22×D311yescharacteristic
313C24×C5C22×D311yescharacteristic
314C23×D5—31no—
315C23×D5—31no—
316C23×D5—34no—
317C23×D5—62no—
318C23×D5—62no—
319C23×D5—62no—
320C23×D5—62no—
321C23×D5—121no—
322C23×D5—121no—
323C2×C5×D4—22no—
324C2×C5×D4—22no—
325C2×C5×D4C4×D314yescomplemented
326C22×C4×C5—22no—
327C22×C4×C5—22no—
328C22×C4×C5—22no—
329C22×C4×C5—22no—
330C22×C4×C5—41no—
331C22×C4×C5—41no—
332C22×C4×C5C22×D311yescharacteristic
333C22×C4×C5C22×D311yescharacteristic
334C22×C4×C5C22×D311yescharacteristic
335C22×C4×C5C22×D311yescharacteristic
336C22×C4×C5C22×D311yescharacteristic
337C2×C22⋊D5—34no—
338C2×C22⋊D5—34no—
339C2×C22⋊D5—62no—
340C2×C22⋊D5—62no—
341C2×C22⋊D5—121no—
342C2×C22⋊D5—121no—
343C22×Dic5—31no—
344C22×Dic5—31no—
345C22×Dic5—31no—
346C22×Dic5—31no—
347C22×Dic5—31no—
348C22×Dic5—31no—
349C22×Dic5—62no—
350C22×Dic5—62no—
351C22×Dic5—121no—
352C2×C4×D5—62no—
353C2×C4×D5—62no—
354C2×C4×D5—62no—
355C2×C4×D5—62no—
356C2×C4×D5—121no—
357C2×C4×D5—121no—
358C5×C4⋊C4—22no—
359C5×C22⋊C4—22no—
360C5×C22⋊C4#6714yescomplemented
361C42×C5—22no—
362C22⋊Dic5—34no—
363C22⋊Dic5—62no—
364C22⋊Dic5—62no—
365C22⋊Dic5—121no—
366#685—34no—
367#685—34no—
368#685—34no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—62no—
374#683—62no—
375#683—121no—
376C4×Dic5—62no—
377C4×Dic5—121no—
378C2×#120—151no—
379C2×C4×D4—151no—
380C2×C4×D4D1511yescharacteristic, complemented
381C22×C22⋊C4—151no—
382C22×C22⋊C4—151no—
383#390—151no—
384#388—151no—
385#388—151no—
386#386—151no—
387#386—151no—
388#386—151no—
389#385—151no—
390#385—151no—
391C4×C22⋊C4—151no—
392C4×C22⋊C4—151no—
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5—22no—
400C22×C3×C5—22no—
401C22×C3×C5—22no—
402C22×C3×C5—41no—
403C22×C3×C5—41no—
404C22×C3×C5—41no—
405C22×C3×C5—41no—
406C22×C3×C5C4×D414yescomplemented
407C22×C3×C5C23×C411yescharacteristic
408C22×C3×C5C22×D411yescharacteristic
409C22×C3×C5C22×D411yescharacteristic
410C22×C3×C5C2×#4111yescharacteristic
411C22×C3×C5C2×#4111yescharacteristic
412C22×C3×C5H(5,𝔽2)11yescharacteristic
413C22×C3×C5H(5,𝔽2)11yescharacteristic
414C2×D15—22no—
415C2×D15—22no—
416C2×D15—22no—
417C2×D15—22no—
418C2×D15—22no—
419C2×D15—22no—
420C2×D15—22no—
421C2×D15—22no—
422C2×D15—22no—
423C2×D15—416no—
424C2×D15—41no—
425C2×D15—41no—
426C2×D15—41no—
427C2×D15—41no—
428C2×D15C4×D414yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432C3×C4×C5—22no—
433C3×C4×C5—41no—
434Dic15—22no—
435Dic15—22no—
436Dic15—22no—
437Dic15—41no—
438Dic15—41no—
439Dic15—41no—
440C24×C3C22×D511yescharacteristic
441C24×C3C22×D511yescharacteristic
442C23×D3—51no—
443C23×D3—51no—
444C23×D3—54no—
445C23×D3—102no—
446C23×D3—102no—
447C23×D3—102no—
448C23×D3—102no—
449C23×D3—201no—
450C23×D3—201no—
451C2×C3×D4—22no—
452C2×C3×D4—22no—
453C2×C3×D4C4×D514yescomplemented
454C22×C3×C4—22no—
455C22×C3×C4—22no—
456C22×C3×C4—22no—
457C22×C3×C4—22no—
458C22×C3×C4—41no—
459C22×C3×C4—41no—
460C22×C3×C4C22×D511yescharacteristic
461C22×C3×C4C22×D511yescharacteristic
462C22×C3×C4C22×D511yescharacteristic
463C22×C3×C4C22×D511yescharacteristic
464C22×C3×C4C22×D511yescharacteristic
465C2×#67—54no—
466C2×#67—54no—
467C2×#67—102no—
468C2×#67—102no—
469C2×#67—201no—
470C2×#67—201no—
471C22×Dic3—51no—
472C22×Dic3—51no—
473C22×Dic3—51no—
474C22×Dic3—51no—
475C22×Dic3—51no—
476C22×Dic3—51no—
477C22×Dic3—102no—
478C22×Dic3—102no—
479C22×Dic3—201no—
480C2×C4×D3—102no—
481C2×C4×D3—102no—
482C2×C4×D3—102no—
483C2×C4×D3—102no—
484C2×C4×D3—201no—
485C2×C4×D3—201no—
486C3×C4⋊C4—22no—
487C3×C22⋊C4—22no—
488C3×C22⋊C4C22⋊D514yescomplemented
489C3×C42—22no—
490#217—54no—
491#217—102no—
492#217—102no—
493#217—201no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4—54no—
496(C2×D3)⋊C4—54no—
497(C2×D3)⋊C4—102no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—102no—
500(C2×D3)⋊C4—102no—
501(C2×D3)⋊C4—102no—
502Dic3⋊C4—102no—
503Dic3⋊C4—201no—
504C4×Dic3—102no—
505C4×Dic3—201no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—21no—
511C23×C5—21no—
512C23×C5—21no—
513C23×C5—21no—
514C23×C5—21no—
515C23×C5—21no—
516C23×C5C2×C4×D312yes—
517C23×C5C2×C4×D312yes—
518C23×C5#23512yes—
519C23×C5C2×#6712yes—
520C23×C5C23×D311yescharacteristic
521C22×D5—32no—
522C22×D5—32no—
523C22×D5—32no—
524C22×D5—32no—
525C22×D5—68no—
526C22×D5—61no—
527C22×D5—61no—
528C22×D5—61no—
529C22×D5—61no—
530C22×D5—68no—
531C22×D5—61no—
532C22×D5—61no—
533C22×D5—61no—
534C22×D5—61no—
535C22×D5—61no—
536C22×D5—61no—
537C22×D5—124no—
538C22×D5—124no—
539C22×D5—124no—
540C22×D5—124no—
541C22×D5—124no—
542C5×D4—28no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—21no—
548C2×C4×C5—21no—
549C2×C4×C5—21no—
550C2×C4×C5—21no—
551C2×C4×C5—21no—
552C2×C4×C5—21no—
553C2×C4×C5—21no—
554C2×C4×C5—44no—
555C2×C4×C5—44no—
556C2×C4×C5C2×C4×D312yes—
557C2×C4×C5D3×D412yes—
558C2×C4×C5C2×#6712yes—
559C2×C4×C5C2×#6712yes—
560C22⋊D5—68no—
561C22⋊D5—124no—
562C2×Dic5—32no—
563C2×Dic5—32no—
564C2×Dic5—32no—
565C2×Dic5—61no—
566C2×Dic5—61no—
567C2×Dic5—61no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5—61no—
575C2×Dic5—61no—
576C2×Dic5—61no—
577C2×Dic5—61no—
578C2×Dic5—61no—
579C2×Dic5—61no—
580C2×Dic5—124no—
581C4×D5—124no—
582C4×D5—124no—
583C25—151no—
584C22×D4—151no—
585C22×D4—151no—
586C22×D4C2×D1511yescharacteristic
587C23×C4—151no—
588C23×C4—151no—
589C23×C4—151no—
590C23×C4C2×D1511yescharacteristic
591C23×C4C2×D1511yescharacteristic, complemented
592#120—158no—
593C4×D4—24no—
594C4×D4—304no—
595C2×C4⋊C4—151no—
596C2×C4⋊C4—151no—
597C2×C4⋊C4C2×D1511yescharacteristic, complemented
598C2×C22⋊C4—151no—
599C2×C22⋊C4—151no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4—151no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4—151no—
610C2×C22⋊C4—304no—
611C2×C22⋊C4—304no—
612C2×C22⋊C4C2×D1511yescharacteristic
613C2×C22⋊C4C2×D1511yescharacteristic, complemented
614C2×C42—151no—
615C2×C42—151no—
616C2×C42C2×D1511yescharacteristic, complemented
617#95—151no—
618#95—151no—
619#95—151no—
620#95—151no—
621#95—151no—
622#95—151no—
623C2×C3×C5—24no—
624C2×C3×C5—42no—
625C2×C3×C5C2×C4×D411yescharacteristic
626C2×C3×C5C2×C4×D411yescharacteristic
627C2×C3×C5#51811yescharacteristic
628C2×C3×C5D4211yescharacteristic
629C2×C3×C5#54611yescharacteristic
630C2×C3×C5#54611yescharacteristic
631C2×C3×C5#55111yescharacteristic
632D15—24no—
633D15—42no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—21no—
639C23×C3—21no—
640C23×C3—21no—
641C23×C3—21no—
642C23×C3—21no—
643C23×C3—21no—
644C23×C3C2×C4×D512yes—
645C23×C3C2×C4×D512yes—
646C23×C3#70912yes—
647C23×C3C2×C22⋊D512yes—
648C23×C3C23×D511yescharacteristic
649C22×D3—52no—
650C22×D3—52no—
651C22×D3—52no—
652C22×D3—52no—
653C22×D3—108no—
654C22×D3—101no—
655C22×D3—101no—
656C22×D3—101no—
657C22×D3—101no—
658C22×D3—101no—
659C22×D3—101no—
660C22×D3—101no—
661C22×D3—101no—
662C22×D3—101no—
663C22×D3—101no—
664C22×D3—108no—
665C22×D3—204no—
666C22×D3—204no—
667C22×D3—204no—
668C22×D3—204no—
669C22×D3—204no—
670C3×D4—28no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—44no—
683C2×C3×C4—44no—
684C2×C3×C4C2×C4×D512yes—
685C2×C3×C4D4×D512yes—
686C2×C3×C4C2×C22⋊D512yes—
687C2×C3×C4C2×C22⋊D512yes—
688#67—108no—
689#67—204no—
690C2×Dic3—52no—
691C2×Dic3—52no—
692C2×Dic3—52no—
693C2×Dic3—101no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3—101no—
697C2×Dic3—101no—
698C2×Dic3—101no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3—101no—
703C2×Dic3—101no—
704C2×Dic3—101no—
705C2×Dic3—101no—
706C2×Dic3—101no—
707C2×Dic3—101no—
708C2×Dic3—204no—
709C4×D3—204no—
710C4×D3—204no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—22no—
716C22×C5—22no—
717C22×C5—22no—
718C22×C5—22no—
719C22×C5—22no—
720C22×C5—41no—
721C22×C5—41no—
722C22×C5—41no—
723C22×C5—41no—
724C22×C5C4×#6714yescomplemented
725C22×C5C22×C4×D311yescharacteristic
726C22×C5C2×#23511yescharacteristic
727C22×C5C2×D3×D411yescharacteristic
728C22×C5#100411yescharacteristic
729C22×C5D3×#4111yescharacteristic
730C22×C5#100911yescharacteristic
731C22×C5C22×#6711yescharacteristic
732C2×D5—34no—
733C2×D5—62no—
734C2×D5—62no—
735C2×D5—62no—
736C2×D5—62no—
737C2×D5—62no—
738C2×D5—62no—
739C2×D5—62no—
740C2×D5—62no—
741C2×D5—62no—
742C2×D5—1216no—
743C2×D5—121no—
744C2×D5—121no—
745C2×D5—121no—
746C2×D5—121no—
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—22no—
750C4×C5—22no—
751C4×C5—41no—
752Dic5—62no—
753Dic5—62no—
754Dic5—62no—
755Dic5—121no—
756Dic5—121no—
757Dic5—121no—
758C24—151no—
759C24—151no—
760C24—154no—
761C24—302no—
762C24—302no—
763C24—302no—
764C24—302no—
765C24—601no—
766C24—601no—
767C24C22×D1511yescharacteristic
768C24C22×D1511yescharacteristic
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—154no—
772C2×D4—154no—
773C2×D4—302no—
774C2×D4—302no—
775C2×D4—601no—
776C2×D4—601no—
777C2×D4C4×D1514yescomplemented
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—151no—
785C22×C4—151no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—151no—
789C22×C4—151no—
790C22×C4—302no—
791C22×C4—302no—
792C22×C4—302no—
793C22×C4—302no—
794C22×C4—302no—
795C22×C4—302no—
796C22×C4—601no—
797C22×C4—601no—
798C22×C4—601no—
799C22×C4C22×D1511yescharacteristic
800C22×C4C22×D1511yescharacteristic
801C22×C4C22×D1511yescharacteristic
802C22×C4C22×D1511yescharacteristic
803C22×C4C22×D1511yescharacteristic
804C4⋊C4—22no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—22no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C22⋊C4—154no—
812C22⋊C4—302no—
813C22⋊C4—302no—
814C22⋊C4—302no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—601no—
820C22⋊C4#122014yescomplemented
821C42—22no—
822C42—302no—
823C42—601no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3C4×C22⋊D514yescomplemented
839C22×C3C22×C4×D511yescharacteristic
840C22×C3C2×#70911yescharacteristic
841C22×C3C2×D4×D511yescharacteristic
842C22×C3#414411yescharacteristic
843C22×C3D5×#4111yescharacteristic
844C22×C3#414911yescharacteristic
845C22×C3C22×C22⋊D511yescharacteristic
846C2×D3—54no—
847C2×D3—102no—
848C2×D3—102no—
849C2×D3—102no—
850C2×D3—102no—
851C2×D3—102no—
852C2×D3—102no—
853C2×D3—102no—
854C2×D3—102no—
855C2×D3—102no—
856C2×D3—2016no—
857C2×D3—201no—
858C2×D3—201no—
859C2×D3—201no—
860C2×D3—201no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—41no—
866Dic3—102no—
867Dic3—102no—
868Dic3—102no—
869Dic3—201no—
870Dic3—201no—
871Dic3—201no—
872C2×C5—24no—
873C2×C5—42no—
874C2×C5C4×D3×D411yescharacteristic
875C2×C5#554511yescharacteristic
876C2×C5#555011yescharacteristic
877C2×C5#555611yescharacteristic
878C2×C5C2×C4×#6711yescharacteristic
879C2×C5D4×#6711yescharacteristic
880C2×C5#582911yescharacteristic
881D5—64no—
882D5—122no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—152no—
894C23—152no—
895C23—152no—
896C23—152no—
897C23—308no—
898C23—301no—
899C23—301no—
900C23—301no—
901C23—301no—
902C23—308no—
903C23—301no—
904C23—301no—
905C23—301no—
906C23—301no—
907C23—301no—
908C23—301no—
909C23—604no—
910C23—604no—
911C23—604no—
912C23—604no—
913C23—604no—
914C23C2×C4×D1512yes—
915C23C2×C4×D1512yes—
916C23#681712yes—
917C23C2×#122012yes—
918C23C23×D1511yescharacteristic
919D4—28no—
920D4—308no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—44no—
934C2×C4—44no—
935C2×C4—152no—
936C2×C4—152no—
937C2×C4—152no—
938C2×C4—301no—
939C2×C4—301no—
940C2×C4—301no—
941C2×C4—301no—
942C2×C4—301no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4—301no—
947C2×C4—301no—
948C2×C4—301no—
949C2×C4—301no—
950C2×C4—301no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—604no—
954C2×C4—604no—
955C2×C4—604no—
956C2×C4C2×C4×D1512yes—
957C2×C4D4×D1512yes—
958C2×C4C2×#122012yes—
959C2×C4C2×#122012yes—
960C2×C3—24no—
961C2×C3—42no—
962C2×C3C4×D4×D511yescharacteristic
963C2×C3#6587911yescharacteristic
964C2×C3#6588411yescharacteristic
965C2×C3#6589011yescharacteristic
966C2×C3C2×C4×C22⋊D511yescharacteristic
967C2×C3D4×C22⋊D511yescharacteristic
968C2×C3#6616311yescharacteristic
969D3—104no—
970D3—202no—
971C5#8239811yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—41no—
985C22—154no—
986C22—302no—
987C22—302no—
988C22—302no—
989C22—302no—
990C22—302no—
991C22—302no—
992C22—302no—
993C22—302no—
994C22—302no—
995C22—6016no—
996C22—601no—
997C22—601no—
998C22—601no—
999C22—601no—
1000C22C4×#122014yescomplemented
1001C22C22×C4×D1511yescharacteristic
1002C22C2×#681711yescharacteristic
1003C22C2×D4×D1511yescharacteristic
1004C22#9209511yescharacteristic
1005C22#41×D1511yescharacteristic
1006C22#9210011yescharacteristic
1007C22C22×#122011yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—22no—
1011C4—22no—
1012C4—41no—
1013C4—302no—
1014C4—302no—
1015C4—302no—
1016C4—601no—
1017C4—601no—
1018C4—601no—
1019C3#1061412911yescharacteristic, complemented, Sylow
1020C2—24no—
1021C2—42no—
1022C2—304no—
1023C2—602no—
1024C2C4×D4×D1511yescharacteristic
1025C2#1175630411yescharacteristic
1026C2#1175630911yescharacteristic
1027C2#1175631511yescharacteristic
1028C2C2×C4×#122011yescharacteristic
1029C2D4×#122011yescharacteristic
1030C2#1175658811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC2×C3×C4×C5×D4C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91826C2
hypercenterC2×C4×D4D15
hypocenterC3×C5#2358
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. C22×#6714C2semidirect
5. C2×C22⋊C4×D15C2semidirect
6. #11751321C2semidirect
7. #11751314C2semidirect
8. #11751311C2semidirect
9. #11751091C2semidirect
10. #11751090C2semidirect
11. #11751058C2semidirect
12. #11751057C2semidirect
13. C22⋊C4×Dic15C2semidirect
14. #11751041C2semidirect
15. C4×#6714C2semidirect
20. C23×C3×C4×C5C22semidirect
27. C2×C3×C5×C4⋊C4C22semidirect
29. C2×C3×C5×C22⋊C4C22semidirect
30. C2×C3×C42×C5C22semidirect
33. C2×#6719C22semidirect
34. C2×#6719C22semidirect
35. #91826C4semidirect
46. C2×#6712C22semidirect
47. C2×#6712C22semidirect
48. C2×C4×Dic15C22semidirect
49. C2×C4×Dic15C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. #91115C22semidirect
54. #91115C22semidirect
55. #91115C22semidirect
56. #91115C22semidirect
58. C2×C4×C5×D4D3semidirect
81. C23×D15C2×C4semidirect
86. C2×C3×C5×D4C2×C4semidirect
102. C2×#1220C2×C4semidirect
103. C2×#1220C2×C4semidirect
121. C3×C5×C22⋊C4D4semidirect
126. #6719C2×C4semidirect
132. #6714C2×C4semidirect
133. #6714C2×C4semidirect
134. #6714D4semidirect
139. C2×C3×C4×D4D5semidirect
157. C23×C4×C5C2×D3semidirect
164. C2×C5×C4⋊C4C2×D3semidirect
166. C2×C5×C22⋊C4C2×D3semidirect
167. C2×C42×C5C2×D3semidirect
275. C23×C3×C4C2×D5semidirect
282. C2×C3×C4⋊C4C2×D5semidirect
284. C2×C3×C22⋊C4C2×D5semidirect
285. C2×C3×C42C2×D5semidirect
325. C2×C5×D4C4×D3semidirect
360. C5×C22⋊C4#67semidirect
380. C2×C4×D4D15semidirect
406. C22×C3×C5C4×D4semidirect
428. C2×D15C4×D4semidirect
453. C2×C3×D4C4×D5semidirect
488. C3×C22⋊C4C22⋊D5semidirect
591. C23×C4C2×D15semidirect
597. C2×C4⋊C4C2×D15semidirect
613. C2×C22⋊C4C2×D15semidirect
616. C2×C42C2×D15semidirect
724. C22×C5C4×#67semidirect
777. C2×D4C4×D15semidirect
820. C22⋊C4#1220semidirect
824. C3×C5#2358semidirect
838. C22×C3C4×C22⋊D5semidirect
971. C5#82398semidirect
1000. C22C4×#1220semidirect
1019. C3#10614129semidirect

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×#918262
C2×C4×#12202
C22×#67142
C2×C22⋊C4×D152
#117513212
#117513142
#117513112
#117510912
#117510902
#117510582
#117510572
C22⋊C4×Dic152
#117510412
C4×#67142
#106141293
#823985