Finite Group Databasebeta

← #14328133

Subgroups — #14328133

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×C4×C5×#67C211yesmaximal, characteristic, complemented
2C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×#91577C211yesmaximal, characteristic
4C2×D3×#685C211yesmaximal, characteristic, complemented
5C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6#11751314C211yesmaximal, characteristic, complemented
7#11749519C211yesmaximal, characteristic, complemented
8#11749518C211yesmaximal, characteristic, complemented
9#11749483C211yesmaximal, characteristic, complemented
10Dic3×#685C211yesmaximal, characteristic, complemented
11Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#11748728C211yesmaximal, characteristic, complemented
13#11748727C211yesmaximal, characteristic, complemented
14#11748716C211yesmaximal, characteristic, complemented
15#11748703C211yesmaximal, characteristic, complemented
16#10614129—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic, complemented
19C22×#1220C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C22×D5×Dic3C2211yescharacteristic
26C2×#6719C2211yescharacteristic, complemented
27C2×#6714C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×C5×#217C2211yescharacteristic, complemented
30C4×C5×#67—24no—
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
33C2×C4×C5×Dic3C2211yescharacteristic, complemented
34C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
35C3×C4×C22⋊D5—24no—
36C2×C3×#685C2211yescharacteristic
37C2×C3×#683C2211yescharacteristic, complemented
38C2×C3×C4×Dic5C2211yescharacteristic, complemented
39#91577C418yescomplemented
40C2×#6669C2211yescharacteristic, complemented
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic, complemented
49D3×#685—24no—
50D5×(C2×D3)⋊C4—24no—
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#82398—51nomaximal, Hall
58C2×C4×C5×D4—31no—
59C2×#4083—31no—
60C2×C4×C22⋊D5D311yescharacteristic, complemented
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
74C23×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C23×C3×D5C2311yescharacteristic
77C22×D3×D5—22no—
78C22×D3×D5—22no—
79C22×D3×D5—22no—
80C22×D3×D5—22no—
81C22×D3×D5—41no—
82C22×D3×D5—41no—
83C22×D3×D5C2×C414yescomplemented
84C22×C3×C4×C5—22no—
85C22×C3×C4×C5—22no—
86C22×C3×C4×C5—41no—
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C2×#1220—41no—
90C2×#1220—41no—
91C2×#1220C2×C414yescomplemented
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C2×C5×#67—22no—
96C2×C5×#67—22no—
97C2×C5×#67C2×C414yescomplemented
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C2×C4×C5×D3—22no—
102C2×C4×C5×D3—22no—
103C2×C4×C5×D3—41no—
104C2×C3×C22⋊D5—22no—
105C2×C3×C22⋊D5—22no—
106C2×C3×C22⋊D5C2×C414yescomplemented
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C2×C3×C4×D5—22no—
111C2×C3×C4×D5—22no—
112C2×C3×C4×D5—41no—
113C2×D3×Dic5—22no—
114C2×D3×Dic5—22no—
115C2×D3×Dic5—41no—
116C2×D5×Dic3—22no—
117C2×D5×Dic3—22no—
118C2×D5×Dic3—41no—
119#6719—41no—
120#6714—22no—
121#6714—22no—
122C5×#217—22no—
123C5×(C2×D3)⋊C4D414yescomplemented
124C5×Dic3⋊C4—22no—
125C4×C5×Dic3—22no—
126C3×C22⋊Dic5—22no—
127C3×#685D414yescomplemented
128C3×#683—22no—
129C3×C4×Dic5—22no—
130#6669—41no—
131#6667—22no—
132#6667—22no—
133#6667C2×C414yescomplemented
134(C2×D3)⋊Dic5—22no—
135(C2×D3)⋊Dic5C2×C414yescomplemented
136#6665—22no—
137#6665C2×C414yescomplemented
138Dic3×Dic5—41no—
139C2×C3×C4×D4—51no—
140C2×#937—51no—
141C2×C4×#67D511yescharacteristic, complemented
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×D4—31no—
156C23×C4×C5—31no—
157C23×C4×C5C2×D311yescharacteristic, complemented
158C22×C22⋊D5—31no—
159C22×C22⋊D5C2×D311yescharacteristic
160C23×Dic5—31no—
161C22×C4×D5—31no—
162C22×C4×D5C2×D311yescharacteristic
163C4×C5×D4—64no—
164C2×C5×C4⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4—31no—
167C2×C42×C5—31no—
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5—31no—
170C2×C22⋊Dic5—31no—
171C2×C22⋊Dic5C2×D311yescharacteristic, complemented
172#4083—38no—
173C4×C22⋊D5—24no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—31no—
181C2×#685—64no—
182C2×#685C2×D311yescharacteristic
183C2×#683—31no—
184C2×#683C2×D311yescharacteristic, complemented
185C2×C4×Dic5—31no—
186C2×C4×Dic5C2×D311yescharacteristic, complemented
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×C5C22×C412yes—
202C23×C3×C5C2411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—21no—
209C22×D15C22×C412yes—
210C22×C5×D3—21no—
211C22×C5×D3—21no—
212C22×C5×D3—21no—
213C22×C5×D3—21no—
214C22×C5×D3C22×C412yes—
215C22×C5×D3C2×D412yes—
216C22×C5×D3#4112yes—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5C22×C412yes—
222C22×C3×D5C2×D412yes—
223C22×C3×D5#4112yes—
224C2×D3×D5—28no—
225C2×D3×D5—28no—
226C2×D3×D5—44no—
227C2×D3×D5—44no—
228C2×D3×D5—44no—
229C2×D3×D5—44no—
230C2×D3×D5—44no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—44no—
236C2×C3×C4×C5C2×D412yes—
237C2×C3×C4×C5C2×D412yes—
238#1220—44no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—21no—
245C2×Dic15—21no—
246C2×Dic15—21no—
247C2×Dic15C22×C412yes—
248C5×#67—28no—
249C2×C5×Dic3—21no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3—21no—
254C2×C5×Dic3—21no—
255C2×C5×Dic3—21no—
256C2×C5×Dic3C22×C412yes—
257C2×C5×Dic3C2×D412yes—
258C4×C5×D3—44no—
259C3×C22⋊D5—28no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5—21no—
266C2×C3×Dic5—21no—
267C2×C3×Dic5C22×C412yes—
268C2×C3×Dic5C2×D412yes—
269C3×C4×D5—44no—
270D3×Dic5—44no—
271D5×Dic3—44no—
272C24×D3—51no—
273C22×C3×D4—51no—
274C23×C3×C4—51no—
275C23×C3×C4C2×D511yescharacteristic, complemented
276C22×#67—51no—
277C22×#67C2×D511yescharacteristic
278C23×Dic3—51no—
279C22×C4×D3—51no—
280C22×C4×D3C2×D511yescharacteristic
281C3×C4×D4—104no—
282C2×C3×C4⋊C4—51no—
283C2×C3×C22⋊C4—51no—
284C2×C3×C22⋊C4—51no—
285C2×C3×C42—51no—
286C2×#217—51no—
287C2×#217—51no—
288C2×#217—51no—
289C2×#217C2×D511yescharacteristic, complemented
290#937—58no—
291C4×#67—24no—
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—104no—
300C2×(C2×D3)⋊C4C2×D511yescharacteristic
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4C2×D511yescharacteristic, complemented
303C2×C4×Dic3—51no—
304C2×C4×Dic3C2×D511yescharacteristic, complemented
305D3×C22⋊C4—104no—
306C3⋊#95—51no—
307C3⋊#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95—51no—
312C24×C5—31no—
313C24×C5C22×D311yescharacteristic
314C23×D5—31no—
315C23×D5—34no—
316C23×D5—62no—
317C23×D5—62no—
318C23×D5—62no—
319C23×D5—62no—
320C23×D5—121no—
321C23×D5—121no—
322C23×D5C22×D311yescharacteristic
323C2×C5×D4—34no—
324C2×C5×D4—62no—
325C2×C5×D4—62no—
326C22×C4×C5—22no—
327C22×C4×C5—22no—
328C22×C4×C5—31no—
329C22×C4×C5—31no—
330C22×C4×C5—31no—
331C22×C4×C5—41no—
332C22×C4×C5—62no—
333C22×C4×C5—62no—
334C22×C4×C5—121no—
335C22×C4×C5C22×D311yescharacteristic
336C22×C4×C5C22×D311yescharacteristic
337C2×C22⋊D5—22no—
338C2×C22⋊D5—22no—
339C2×C22⋊D5—34no—
340C2×C22⋊D5—121no—
341C2×C22⋊D5—121no—
342C2×C22⋊D5C4×D314yescomplemented
343C22×Dic5—31no—
344C22×Dic5—31no—
345C22×Dic5—31no—
346C22×Dic5—62no—
347C22×Dic5—62no—
348C22×Dic5—121no—
349C22×Dic5C22×D311yescharacteristic
350C22×Dic5C22×D311yescharacteristic
351C22×Dic5C22×D311yescharacteristic
352C2×C4×D5—22no—
353C2×C4×D5—22no—
354C2×C4×D5—41no—
355C2×C4×D5—62no—
356C2×C4×D5—62no—
357C2×C4×D5—121no—
358C5×C4⋊C4—62no—
359C5×C22⋊C4—34no—
360C5×C22⋊C4—62no—
361C42×C5—62no—
362C22⋊Dic5—22no—
363C22⋊Dic5—34no—
364C22⋊Dic5—62no—
365C22⋊Dic5—121no—
366#685—34no—
367#685—34no—
368#685—62no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685#6714yescomplemented
374#683—22no—
375#683—121no—
376C4×Dic5—22no—
377C4×Dic5—121no—
378C2×#120—151no—
379C2×C4×D4—31no—
380C2×C4×D4—51no—
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—41no—
397C22×C3×C5—41no—
398C22×C3×C5—41no—
399C22×C3×C5—41no—
400C22×C3×C5C23×C411yescharacteristic
401C22×C3×C5C22×D411yescharacteristic
402C22×C3×C5C22×D411yescharacteristic
403C22×C3×C5C2×#4111yescharacteristic
404C22×C3×C5C2×#4111yescharacteristic
405C22×C3×C5H(5,𝔽2)11yescharacteristic
406C22×C3×C5H(5,𝔽2)11yescharacteristic
407C2×D15—22no—
408C2×D15—22no—
409C2×D15—22no—
410C2×D15—41no—
411C2×D15—41no—
412C2×D15—41no—
413C2×D15—41no—
414C2×C5×D3—22no—
415C2×C5×D3—22no—
416C2×C5×D3—22no—
417C2×C5×D3—22no—
418C2×C5×D3—22no—
419C2×C5×D3—22no—
420C2×C5×D3C4×D414yescomplemented
421C2×C3×D5—22no—
422C2×C3×D5—22no—
423C2×C3×D5—22no—
424C2×C3×D5—22no—
425C2×C3×D5—22no—
426C2×C3×D5—22no—
427C2×C3×D5C4×D414yescomplemented
428D3×D5—416no—
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431Dic15—22no—
432Dic15—41no—
433Dic15—41no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C3×Dic5—41no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—41no—
440C24×C3—51no—
441C24×C3C22×D511yescharacteristic
442C23×D3—51no—
443C23×D3—54no—
444C23×D3—102no—
445C23×D3—102no—
446C23×D3—102no—
447C23×D3—102no—
448C23×D3—201no—
449C23×D3—201no—
450C23×D3C22×D511yescharacteristic
451C2×C3×D4—54no—
452C2×C3×D4—102no—
453C2×C3×D4—102no—
454C22×C3×C4—22no—
455C22×C3×C4—22no—
456C22×C3×C4—41no—
457C22×C3×C4—51no—
458C22×C3×C4—51no—
459C22×C3×C4—51no—
460C22×C3×C4—102no—
461C22×C3×C4—102no—
462C22×C3×C4—201no—
463C22×C3×C4C22×D511yescharacteristic
464C22×C3×C4C22×D511yescharacteristic
465C2×#67—22no—
466C2×#67—22no—
467C2×#67—54no—
468C2×#67—201no—
469C2×#67—201no—
470C2×#67C4×D514yescomplemented
471C22×Dic3—51no—
472C22×Dic3—51no—
473C22×Dic3—51no—
474C22×Dic3—102no—
475C22×Dic3—102no—
476C22×Dic3—201no—
477C22×Dic3C22×D511yescharacteristic
478C22×Dic3C22×D511yescharacteristic
479C22×Dic3C22×D511yescharacteristic
480C2×C4×D3—22no—
481C2×C4×D3—22no—
482C2×C4×D3—41no—
483C2×C4×D3—102no—
484C2×C4×D3—102no—
485C2×C4×D3—201no—
486C3×C4⋊C4—102no—
487C3×C22⋊C4—54no—
488C3×C22⋊C4—102no—
489C3×C42—102no—
490#217—22no—
491#217—54no—
492#217—102no—
493#217—201no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4—54no—
496(C2×D3)⋊C4—102no—
497(C2×D3)⋊C4—102no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—102no—
500(C2×D3)⋊C4—102no—
501(C2×D3)⋊C4C22⋊D514yescomplemented
502Dic3⋊C4—22no—
503Dic3⋊C4—201no—
504C4×Dic3—22no—
505C4×Dic3—201no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—21no—
511C23×C5—21no—
512C23×C5—32no—
513C23×C5—32no—
514C23×C5—32no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5—61no—
518C23×C5—61no—
519C23×C5C2×C4×D312yes—
520C23×C5C23×D311yescharacteristic
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—32no—
526C22×D5—68no—
527C22×D5—61no—
528C22×D5—61no—
529C22×D5—61no—
530C22×D5—61no—
531C22×D5—61no—
532C22×D5—61no—
533C22×D5—68no—
534C22×D5—124no—
535C22×D5—124no—
536C22×D5—124no—
537C22×D5—124no—
538C22×D5—124no—
539C22×D5C2×C4×D312yes—
540C22×D5#23512yes—
541C22×D5C2×#6712yes—
542C5×D4—68no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—32no—
548C2×C4×C5—32no—
549C2×C4×C5—44no—
550C2×C4×C5—61no—
551C2×C4×C5—61no—
552C2×C4×C5—61no—
553C2×C4×C5—61no—
554C2×C4×C5—61no—
555C2×C4×C5—61no—
556C2×C4×C5—61no—
557C2×C4×C5—124no—
558C2×C4×C5D3×D412yes—
559C2×C4×C5C2×#6712yes—
560C22⋊D5—28no—
561C22⋊D5—124no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
567C2×Dic5—21no—
568C2×Dic5—21no—
569C2×Dic5—32no—
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—124no—
579C2×Dic5C2×C4×D312yes—
580C2×Dic5C2×#6712yes—
581C4×D5—44no—
582C4×D5—124no—
583C25—151no—
584C22×D4—31no—
585C22×D4—51no—
586C22×D4—151no—
587C23×C4—31no—
588C23×C4—51no—
589C23×C4—151no—
590C23×C4—151no—
591C23×C4D3×D511yescharacteristic, complemented
592#120—158no—
593C4×D4—64no—
594C4×D4—104no—
595C2×C4⋊C4—31no—
596C2×C4⋊C4—51no—
597C2×C4⋊C4—151no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—31no—
600C2×C22⋊C4—51no—
601C2×C22⋊C4—51no—
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—151no—
611C2×C22⋊C4—151no—
612C2×C22⋊C4—304no—
613C2×C22⋊C4—304no—
614C2×C42—31no—
615C2×C42—51no—
616C2×C42—151no—
617#95—151no—
618#95—151no—
619#95—151no—
620#95—151no—
621#95—151no—
622#95—151no—
623C2×C3×C5—42no—
624C2×C3×C5C2×C4×D411yescharacteristic
625C2×C3×C5C2×C4×D411yescharacteristic
626C2×C3×C5#51811yescharacteristic
627C2×C3×C5D4211yescharacteristic
628C2×C3×C5#54611yescharacteristic
629C2×C3×C5#54611yescharacteristic
630C2×C3×C5#55111yescharacteristic
631D15—42no—
632C3×D5—24no—
633C5×D3—24no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—21no—
639C23×C3—21no—
640C23×C3—52no—
641C23×C3—52no—
642C23×C3—52no—
643C23×C3—101no—
644C23×C3—101no—
645C23×C3—101no—
646C23×C3—101no—
647C23×C3C2×C4×D512yes—
648C23×C3C23×D511yescharacteristic
649C22×D3—21no—
650C22×D3—21no—
651C22×D3—21no—
652C22×D3—21no—
653C22×D3—52no—
654C22×D3—108no—
655C22×D3—101no—
656C22×D3—101no—
657C22×D3—101no—
658C22×D3—101no—
659C22×D3—101no—
660C22×D3—101no—
661C22×D3—108no—
662C22×D3—204no—
663C22×D3—204no—
664C22×D3—204no—
665C22×D3—204no—
666C22×D3—204no—
667C22×D3C2×C4×D512yes—
668C22×D3#70912yes—
669C22×D3C2×C22⋊D512yes—
670C3×D4—108no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—44no—
676C2×C3×C4—52no—
677C2×C3×C4—52no—
678C2×C3×C4—101no—
679C2×C3×C4—101no—
680C2×C3×C4—101no—
681C2×C3×C4—101no—
682C2×C3×C4—101no—
683C2×C3×C4—101no—
684C2×C3×C4—101no—
685C2×C3×C4—204no—
686C2×C3×C4D4×D512yes—
687C2×C3×C4C2×C22⋊D512yes—
688#67—28no—
689#67—204no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—52no—
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—204no—
707C2×Dic3C2×C4×D512yes—
708C2×Dic3C2×C22⋊D512yes—
709C4×D3—44no—
710C4×D3—204no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—34no—
715C22×C5—41no—
716C22×C5—41no—
717C22×C5—41no—
718C22×C5—41no—
719C22×C5—62no—
720C22×C5—62no—
721C22×C5—62no—
722C22×C5—62no—
723C22×C5—62no—
724C22×C5—62no—
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—22no—
733C2×D5—22no—
734C2×D5—22no—
735C2×D5—22no—
736C2×D5—22no—
737C2×D5—22no—
738C2×D5—62no—
739C2×D5—62no—
740C2×D5—62no—
741C2×D5—1216no—
742C2×D5—121no—
743C2×D5—121no—
744C2×D5—121no—
745C2×D5—121no—
746C2×D5C4×#6714yescomplemented
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—62no—
750C4×C5—62no—
751C4×C5—121no—
752Dic5—22no—
753Dic5—22no—
754Dic5—41no—
755Dic5—62no—
756Dic5—121no—
757Dic5—121no—
758C24—31no—
759C24—51no—
760C24—154no—
761C24—151no—
762C24—302no—
763C24—302no—
764C24—302no—
765C24—302no—
766C24—601no—
767C24—601no—
768C24C2×D3×D511yescharacteristic
769C2×D4—34no—
770C2×D4—54no—
771C2×D4—62no—
772C2×D4—62no—
773C2×D4—102no—
774C2×D4—102no—
775C2×D4—154no—
776C2×D4—601no—
777C2×D4—601no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—31no—
783C22×C4—41no—
784C22×C4—51no—
785C22×C4—51no—
786C22×C4—51no—
787C22×C4—62no—
788C22×C4—62no—
789C22×C4—102no—
790C22×C4—102no—
791C22×C4—121no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4—151no—
795C22×C4—201no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4—302no—
799C22×C4—302no—
800C22×C4—601no—
801C22×C4—601no—
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—62no—
805C4⋊C4—102no—
806C4⋊C4—601no—
807C22⋊C4—34no—
808C22⋊C4—54no—
809C22⋊C4—62no—
810C22⋊C4—102no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C22⋊C4—154no—
814C22⋊C4—302no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—302no—
820C22⋊C4—601no—
821C42—62no—
822C42—102no—
823C42—601no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—54no—
833C22×C3—102no—
834C22×C3—102no—
835C22×C3—102no—
836C22×C3—102no—
837C22×C3—102no—
838C22×C3—102no—
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—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—102no—
853C2×D3—102no—
854C2×D3—102no—
855C2×D3—2016no—
856C2×D3—201no—
857C2×D3—201no—
858C2×D3—201no—
859C2×D3—201no—
860C2×D3C4×C22⋊D514yescomplemented
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—102no—
864C3×C4—102no—
865C3×C4—201no—
866Dic3—22no—
867Dic3—22no—
868Dic3—41no—
869Dic3—102no—
870Dic3—201no—
871Dic3—201no—
872C2×C5—42no—
873C2×C5—64no—
874C2×C5C4×D3×D411yescharacteristic
875C2×C5#554511yescharacteristic
876C2×C5#555011yescharacteristic
877C2×C5#555611yescharacteristic
878C2×C5C2×C4×#6711yescharacteristic
879C2×C5D4×#6711yescharacteristic
880C2×C5#582911yescharacteristic
881D5—24no—
882D5—122no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—32no—
890C23—32no—
891C23—32no—
892C23—52no—
893C23—52no—
894C23—52no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—101no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23—152no—
904C23—308no—
905C23—308no—
906C23—301no—
907C23—301no—
908C23—301no—
909C23—301no—
910C23—301no—
911C23—301no—
912C23—604no—
913C23—604no—
914C23—604no—
915C23—604no—
916C23—604no—
917C23C4×D3×D512yes—
918C23C22×D3×D511yescharacteristic
919D4—68no—
920D4—108no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—32no—
927C2×C4—32no—
928C2×C4—44no—
929C2×C4—52no—
930C2×C4—52no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—101no—
939C2×C4—101no—
940C2×C4—101no—
941C2×C4—101no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—101no—
945C2×C4—124no—
946C2×C4—152no—
947C2×C4—204no—
948C2×C4—301no—
949C2×C4—301no—
950C2×C4—301no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—301no—
956C2×C4—604no—
957C2×C4—604no—
958C2×C4D5×#6712yes—
959C2×C4D3×C22⋊D512yes—
960C2×C3—42no—
961C2×C3—104no—
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—24no—
970D3—202no—
971C5#8239811yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—34no—
976C22—41no—
977C22—41no—
978C22—41no—
979C22—41no—
980C22—54no—
981C22—62no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—62no—
987C22—102no—
988C22—102no—
989C22—102no—
990C22—102no—
991C22—102no—
992C22—102no—
993C22—302no—
994C22—302no—
995C22—302no—
996C22—6016no—
997C22—601no—
998C22—601no—
999C22—601no—
1000C22—601no—
1001C22C2×C4×D3×D511yescharacteristic
1002C22D5×#23511yescharacteristic
1003C22D3×#70911yescharacteristic
1004C22#9201911yescharacteristic
1005C22C2×D5×#6711yescharacteristic
1006C22C2×D3×C22⋊D511yescharacteristic
1007C22#9204911yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—62no—
1011C4—62no—
1012C4—102no—
1013C4—102no—
1014C4—121no—
1015C4—201no—
1016C4—302no—
1017C4—601no—
1018C4—601no—
1019C3#1061412911yescharacteristic, complemented, Sylow
1020C2—42no—
1021C2—64no—
1022C2—104no—
1023C2—602no—
1024C2C4×D5×#6711yescharacteristic
1025C2C4×D3×C22⋊D511yescharacteristic
1026C2#1175462911yescharacteristic
1027C2#1175463811yescharacteristic
1028C2#1175465111yescharacteristic
1029C2#1175467711yescharacteristic
1030C2#67×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91577C2
hypercenterC23×C4D3×D5
hypocenterC3×C5#2358
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×#67C2semidirect
2. C2×C3×C4×C22⋊D5C2semidirect
4. C2×D3×#685C2semidirect
5. C2×D5×(C2×D3)⋊C4C2semidirect
6. #11751314C2semidirect
7. #11749519C2semidirect
8. #11749518C2semidirect
9. #11749483C2semidirect
10. Dic3×#685C2semidirect
11. Dic5×(C2×D3)⋊C4C2semidirect
12. #11748728C2semidirect
13. #11748727C2semidirect
14. #11748716C2semidirect
15. #11748703C2semidirect
18. C23×C3×C4×C5C22semidirect
26. C2×#6719C22semidirect
29. C2×C5×#217C22semidirect
32. C2×C5×Dic3⋊C4C22semidirect
33. C2×C4×C5×Dic3C22semidirect
34. C2×C3×C22⋊Dic5C22semidirect
37. C2×C3×#683C22semidirect
38. C2×C3×C4×Dic5C22semidirect
39. #91577C4semidirect
40. C2×#6669C22semidirect
48. C2×Dic3×Dic5C22semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
60. C2×C4×C22⋊D5D3semidirect
83. C22×D3×D5C2×C4semidirect
91. C2×#1220C2×C4semidirect
97. C2×C5×#67C2×C4semidirect
106. C2×C3×C22⋊D5C2×C4semidirect
123. C5×(C2×D3)⋊C4D4semidirect
127. C3×#685D4semidirect
133. #6667C2×C4semidirect
135. (C2×D3)⋊Dic5C2×C4semidirect
137. #6665C2×C4semidirect
141. C2×C4×#67D5semidirect
157. C23×C4×C5C2×D3semidirect
171. C2×C22⋊Dic5C2×D3semidirect
184. C2×#683C2×D3semidirect
186. C2×C4×Dic5C2×D3semidirect
275. C23×C3×C4C2×D5semidirect
289. C2×#217C2×D5semidirect
302. C2×Dic3⋊C4C2×D5semidirect
304. C2×C4×Dic3C2×D5semidirect
342. C2×C22⋊D5C4×D3semidirect
373. #685#67semidirect
420. C2×C5×D3C4×D4semidirect
427. C2×C3×D5C4×D4semidirect
470. C2×#67C4×D5semidirect
501. (C2×D3)⋊C4C22⋊D5semidirect
591. C23×C4D3×D5semidirect
746. C2×D5C4×#67semidirect
824. C3×C5#2358semidirect
860. C2×D3C4×C22⋊D5semidirect
971. C5#82398semidirect
1019. C3#10614129semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×#672
C2×C3×C4×C22⋊D52
C2×#915772
C2×D3×#6852
C2×D5×(C2×D3)⋊C42
#117513142
#117495192
#117495182
#117494832
Dic3×#6852
Dic5×(C2×D3)⋊C42
#117487282
#117487272
#117487162
#117487032
#106141293
#823985