Finite Group Databasebeta

← #14328136

Subgroups — #14328136

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×D12C211yesmaximal, characteristic, complemented
2C2×#91475C211yesmaximal, characteristic
3C2×D3×#685C211yesmaximal, characteristic, complemented
4C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×#91441C211yesmaximal, characteristic, complemented
6#11751041C211yesmaximal, characteristic, complemented
7C3×C4×#685C211yesmaximal, characteristic, complemented
8#11748914C211yesmaximal, characteristic, complemented
9#11748908C211yesmaximal, characteristic, complemented
10#11748905C211yesmaximal, characteristic, complemented
11#11748901C211yesmaximal, characteristic, complemented
12#11748899C211yesmaximal, characteristic, complemented
13Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14#11748722C211yesmaximal, characteristic, complemented
15#11748685C211yesmaximal, characteristic, complemented
16#10614129—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C5×D12C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic, complemented
21C22×C3×C4×D5C2211yescharacteristic
22C22×#1203C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C22×D5×Dic3C2211yescharacteristic
26C2×C3×C42×C5C2211yescharacteristic, complemented
27C2×#6714C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6712C2211yescharacteristic, complemented
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
33C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
34C4×C5×D12—24no—
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic, complemented
38C2×#6668C2211yescharacteristic, complemented
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
44C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
45C2×#6665C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic, complemented
47#91475C418yescomplemented
48D3×#685—24no—
49D5×(C2×D3)⋊C4—24no—
50#91441—24no—
51#91115C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53C3×#3963C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55#90994C2211yescharacteristic, complemented
56#90994C2211yescharacteristic, complemented
57#73577—51nomaximal, Hall
58C2×C4×C5×D4—31no—
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×#685D311yescharacteristic, complemented
73C23×D15C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
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×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C2×C5×D12—22no—
93C2×C5×D12—22no—
94C2×C5×D12C2×C414yescomplemented
95C2×C4×C5×D3—22no—
96C2×C4×C5×D3—22no—
97C2×C4×C5×D3—22no—
98C2×C4×C5×D3—22no—
99C2×C4×C5×D3—41no—
100C2×C4×C5×D3—41no—
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C2×C3×C4×D5—22no—
105C2×C3×C4×D5—22no—
106C2×C3×C4×D5—41no—
107C2×#1203—41no—
108C2×#1203—41no—
109C2×#1203C2×C414yescomplemented
110C2×#1201—22no—
111C2×#1201—22no—
112C2×#1201C2×C414yescomplemented
113C2×D3×Dic5—22no—
114C2×D3×Dic5—22no—
115C2×D3×Dic5—41no—
116C2×D5×Dic3—22no—
117C2×D5×Dic3—22no—
118C2×D5×Dic3—41no—
119C3×C42×C5—22no—
120#6714—22no—
121#6714—22no—
122#6714C2×C414yescomplemented
123#6712—22no—
124C5×(C2×D3)⋊C4—22no—
125C5×(C2×D3)⋊C4D414yescomplemented
126C5×C4⋊Dic3—22no—
127C3×#685C2×C414yescomplemented
128C3×#685D414yescomplemented
129C3×C4×Dic5—41no—
130#6668—41no—
131#6667—22no—
132#6667—22no—
133(C2×D3)⋊Dic5—22no—
134(C2×D3)⋊Dic5—22no—
135(C2×D3)⋊Dic5—41no—
136(C2×D3)⋊Dic5C2×C414yescomplemented
137#6665—22no—
138Dic3×Dic5—22no—
139C22×(C2×D3)⋊C4—51no—
140C2×#882—51no—
141C2×#67⋊C4—51no—
142C2×D3×C22⋊C4—51no—
143C2×C4×D12D511yescharacteristic, complemented
144C3×C4×C22⋊C4—51no—
145#5213—51no—
146#4950—51no—
147#4940—51no—
148#4939—51no—
149C4×(C2×D3)⋊C4—51no—
150#4670—51no—
151#4668—51no—
152#4665—51no—
153#4665—51no—
154C24×D5—31no—
155C22×C5×D4—31no—
156C23×C4×C5—31no—
157C23×C4×C5—31no—
158C22×C22⋊D5—31no—
159C22×C22⋊D5—31no—
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×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—64no—
181C2×#685C2×D311yescharacteristic
182C2×#685C2×D311yescharacteristic
183C2×#683—31no—
184C2×#683—31no—
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#3963C2×D311yescharacteristic, complemented
193#3963C2×D311yescharacteristic, complemented
194#2358—151noSylow
195C23×C3×C5C2411yescharacteristic
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15—21no—
202C22×D15C22×C412yes—
203C22×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3—21no—
209C22×C5×D3—21no—
210C22×C5×D3—21no—
211C22×C5×D3—21no—
212C22×C5×D3—21no—
213C22×C5×D3C22×C412yes—
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—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5C22×C412yes—
238C2×C3×C4×C5C2×D412yes—
239C2×C3×C4×C5C2×D412yes—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—21no—
245C2×Dic15—21no—
246C2×Dic15—21no—
247C2×Dic15—21no—
248C2×Dic15C22×C412yes—
249C2×C5×Dic3—21no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3—21no—
254C2×C5×Dic3C2×D412yes—
255C5×D12—28no—
256C4×C5×D3—44no—
257C4×C5×D3—44no—
258C2×C3×Dic5—21no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5C22×C412yes—
266C2×C3×Dic5C2×D412yes—
267C3×C4×D5—44no—
268#1203—44no—
269#1201—28no—
270D3×Dic5—44no—
271D5×Dic3—44no—
272C24×D3—51no—
273C23×C3×C4—51no—
274C22×#67—51no—
275C23×Dic3—51no—
276C22×D12—51no—
277C22×D12C2×D511yescharacteristic
278C22×C4×D3—51no—
279C22×C4×D3C2×D511yescharacteristic
280C22×C4×D3C2×D511yescharacteristic, complemented
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×C3×C42—51no—
284C2×C3×C42C2×D511yescharacteristic, complemented
285C2×#217—51no—
286C2×(C2×D3)⋊C4—51no—
287C2×(C2×D3)⋊C4—51no—
288C2×(C2×D3)⋊C4—51no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4—104no—
296C2×(C2×D3)⋊C4C2×D511yescharacteristic
297C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
298C2×C4⋊Dic3—51no—
299C2×C4⋊Dic3C2×D511yescharacteristic, complemented
300C2×Dic3⋊C4—51no—
301C2×C4×Dic3—51no—
302#882—58no—
303#67⋊C4—104no—
304D3×C22⋊C4—104no—
305C4×D12—24no—
306C3×#95—51no—
307C3×#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95—51no—
312C24×C5—31no—
313C24×C5—31no—
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—31no—
327C22×C4×C5—31no—
328C22×C4×C5—62no—
329C22×C4×C5—62no—
330C22×C4×C5—62no—
331C22×C4×C5—62no—
332C22×C4×C5—121no—
333C22×C4×C5—121no—
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—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—22no—
362C22⋊Dic5—34no—
363C22⋊Dic5—62no—
364C22⋊Dic5—62no—
365C22⋊Dic5—121no—
366#685—34no—
367#685—62no—
368#685—62no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685C4×D314yescomplemented
373#685D1214yescomplemented
374#683—62no—
375#683—121no—
376C4×Dic5—41no—
377C4×Dic5—62no—
378C2×#120—151no—
379C2×C4×D4—31no—
380C2×C4×D4—151no—
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—51no—
392C4×C22⋊C4—151no—
393C22×C3×C5C23×C411yescharacteristic
394C22×C3×C5C22×D411yescharacteristic
395C22×C3×C5C22×D411yescharacteristic
396C22×C3×C5C2×#4111yescharacteristic
397C22×C3×C5C2×#4111yescharacteristic
398C22×C3×C5H(5,𝔽2)11yescharacteristic
399C22×C3×C5H(5,𝔽2)11yescharacteristic
400C2×D15—22no—
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—41no—
404C2×D15—41no—
405C2×D15—41no—
406C2×D15—41no—
407C2×C5×D3—22no—
408C2×C5×D3—22no—
409C2×C5×D3—22no—
410C2×C5×D3—22no—
411C2×C5×D3—22no—
412C2×C5×D3—22no—
413C2×C5×D3—22no—
414C2×C5×D3—22no—
415C2×C5×D3—22no—
416C2×C5×D3—41no—
417C2×C5×D3—41no—
418C2×C5×D3—41no—
419C2×C5×D3—41no—
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—
431C3×C4×C5—22no—
432Dic15—22no—
433Dic15—41no—
434Dic15—41no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C3×Dic5—41no—
438C5×Dic3—22no—
439C5×Dic3—41no—
440C24×C3—51no—
441C23×D3—51no—
442C23×D3—54no—
443C23×D3—102no—
444C23×D3—102no—
445C23×D3—102no—
446C23×D3—102no—
447C23×D3—201no—
448C23×D3—201no—
449C23×D3C22×D511yescharacteristic
450C23×D3C22×D511yescharacteristic
451C22×C3×C4—51no—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4—102no—
455C22×C3×C4—102no—
456C22×C3×C4—201no—
457C22×C3×C4C22×D511yescharacteristic
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C2×#67—54no—
461C2×#67—102no—
462C2×#67—102no—
463C22×Dic3—51no—
464C22×Dic3—51no—
465C22×Dic3—51no—
466C22×Dic3—102no—
467C22×Dic3—102no—
468C22×Dic3—201no—
469C22×Dic3C22×D511yescharacteristic
470C22×Dic3C22×D511yescharacteristic
471C2×D12—22no—
472C2×D12—22no—
473C2×D12—54no—
474C2×D12—201no—
475C2×D12—201no—
476C2×D12C4×D514yescomplemented
477C2×C4×D3—22no—
478C2×C4×D3—22no—
479C2×C4×D3—22no—
480C2×C4×D3—22no—
481C2×C4×D3—41no—
482C2×C4×D3—41no—
483C2×C4×D3—102no—
484C2×C4×D3—102no—
485C2×C4×D3—201no—
486C3×C22⋊C4—54no—
487C3×C22⋊C4—54no—
488C3×C42—22no—
489C3×C42—201no—
490#217—102no—
491(C2×D3)⋊C4—22no—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—102no—
495(C2×D3)⋊C4—102no—
496(C2×D3)⋊C4—102no—
497(C2×D3)⋊C4—102no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—102no—
500(C2×D3)⋊C4—201no—
501(C2×D3)⋊C4C22⋊D514yescomplemented
502C4⋊Dic3—22no—
503C4⋊Dic3—201no—
504Dic3⋊C4—102no—
505C4×Dic3—102no—
506C23×C5—32no—
507C23×C5—32no—
508C23×C5—32no—
509C23×C5—32no—
510C23×C5—61no—
511C23×C5—61no—
512C23×C5—61no—
513C23×C5—61no—
514C23×C5—61no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5—61no—
518C23×C5—61no—
519C23×C5—61no—
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×D5C2×D1212yes—
541C22×D5#23512yes—
542C5×D4—68no—
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—32no—
550C2×C4×C5—61no—
551C2×C4×C5—61no—
552C2×C4×C5—61no—
553C2×C4×C5—61no—
554C2×C4×C5—61no—
555C2×C4×C5—124no—
556C2×C4×C5—124no—
557C2×C4×C5C2×C4×D312yes—
558C2×C4×C5C2×D1212yes—
559C2×C4×C5D3×D412yes—
560C22⋊D5—68no—
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×D1212yes—
581C4×D5—44no—
582C4×D5—124no—
583C25—151no—
584C22×D4—31no—
585C22×D4—151no—
586C22×D4—151no—
587C23×C4—31no—
588C23×C4—31no—
589C23×C4—51no—
590C23×C4—151no—
591C23×C4—151no—
592#120—158no—
593C4×D4—64no—
594C4×D4—304no—
595C2×C4⋊C4—31no—
596C2×C4⋊C4—151no—
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—51no—
615C2×C42—151no—
616C2×C42D3×D511yescharacteristic, complemented
617#95—51no—
618#95—51no—
619#95—151no—
620#95—151no—
621#95—151no—
622#95—151no—
623C2×C3×C5C2×C4×D411yescharacteristic
624C2×C3×C5C2×C4×D411yescharacteristic
625C2×C3×C5#51811yescharacteristic
626C2×C3×C5D4211yescharacteristic
627C2×C3×C5#54611yescharacteristic
628C2×C3×C5#54611yescharacteristic
629C2×C3×C5#55111yescharacteristic
630D15—42no—
631C3×D5—24no—
632C5×D3—24no—
633C5×D3—42no—
634C23×C3—52no—
635C23×C3—52no—
636C23×C3—52no—
637C23×C3—101no—
638C23×C3—101no—
639C23×C3—101no—
640C23×C3—101no—
641C23×C3C23×D511yescharacteristic
642C22×D3—21no—
643C22×D3—21no—
644C22×D3—21no—
645C22×D3—21no—
646C22×D3—21no—
647C22×D3—21no—
648C22×D3—21no—
649C22×D3—21no—
650C22×D3—21no—
651C22×D3—21no—
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—108no—
661C22×D3—204no—
662C22×D3—204no—
663C22×D3—204no—
664C22×D3—204no—
665C22×D3—204no—
666C22×D3C2×C4×D512yes—
667C22×D3C2×C4×D512yes—
668C22×D3#70912yes—
669C22×D3C2×C22⋊D512yes—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
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×C4C2×C4×D512yes—
687C2×C3×C4D4×D512yes—
688C2×C3×C4C2×C22⋊D512yes—
689#67—108no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—52no—
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—204no—
705C2×Dic3C2×C22⋊D512yes—
706D12—28no—
707D12—204no—
708C4×D3—44no—
709C4×D3—44no—
710C4×D3—204no—
711C22×C5—34no—
712C22×C5—62no—
713C22×C5—62no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—62no—
717C22×C5—62no—
718C22×C5—62no—
719C22×C5—62no—
720C22×C5—62no—
721C22×C5—121no—
722C22×C5—121no—
723C22×C5—121no—
724C22×C5—121no—
725C22×C5C22×C4×D311yescharacteristic
726C22×C5C22×D1211yescharacteristic
727C22×C5C2×#23511yescharacteristic
728C22×C5C2×D3×D411yescharacteristic
729C22×C5#100411yescharacteristic
730C22×C5D3×#4111yescharacteristic
731C22×C5#100911yescharacteristic
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×D1214yescomplemented
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—22no—
750C4×C5—62no—
751C4×C5—121no—
752Dic5—22no—
753Dic5—22no—
754Dic5—41no—
755Dic5—62no—
756Dic5—121no—
757Dic5—121no—
758C24—31no—
759C24—31no—
760C24—51no—
761C24—154no—
762C24—151no—
763C24—302no—
764C24—302no—
765C24—302no—
766C24—302no—
767C24—601no—
768C24—601no—
769C2×D4—34no—
770C2×D4—62no—
771C2×D4—62no—
772C2×D4—154no—
773C2×D4—154no—
774C2×D4—302no—
775C2×D4—302no—
776C2×D4—601no—
777C2×D4—601no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—62no—
784C22×C4—62no—
785C22×C4—62no—
786C22×C4—62no—
787C22×C4—102no—
788C22×C4—102no—
789C22×C4—121no—
790C22×C4—121no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4—201no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4—302no—
799C22×C4—601no—
800C22×C4—601no—
801C22×C4C2×D3×D511yescharacteristic
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—62no—
805C4⋊C4—302no—
806C4⋊C4—601no—
807C22⋊C4—34no—
808C22⋊C4—54no—
809C22⋊C4—54no—
810C22⋊C4—62no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C22⋊C4—302no—
814C22⋊C4—302no—
815C22⋊C4—302no—
816C22⋊C4—302no—
817C22⋊C4—302no—
818C22⋊C4—302no—
819C22⋊C4—302no—
820C22⋊C4—601no—
821C42—22no—
822C42—201no—
823C42—302no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—54no—
826C22×C3—102no—
827C22×C3—102no—
828C22×C3—102no—
829C22×C3—102no—
830C22×C3—102no—
831C22×C3—102no—
832C22×C3C22×C4×D511yescharacteristic
833C22×C3C2×#70911yescharacteristic
834C22×C3C2×D4×D511yescharacteristic
835C22×C3#414411yescharacteristic
836C22×C3D5×#4111yescharacteristic
837C22×C3#414911yescharacteristic
838C22×C3C22×C22⋊D511yescharacteristic
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—41no—
849C2×D3—41no—
850C2×D3—41no—
851C2×D3—41no—
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—22no—
864C3×C4—102no—
865C3×C4—102no—
866C3×C4—201no—
867Dic3—22no—
868Dic3—41no—
869Dic3—102no—
870Dic3—201no—
871Dic3—201no—
872C2×C5—64no—
873C2×C5—122no—
874C2×C5C2×C4×D1211yescharacteristic
875C2×C5#549011yescharacteristic
876C2×C5#552711yescharacteristic
877C2×C5C4×D3×D411yescharacteristic
878C2×C5#554511yescharacteristic
879C2×C5D4×D1211yescharacteristic
880C2×C5#555411yescharacteristic
881D5—24no—
882D5—122no—
883C23—32no—
884C23—32no—
885C23—32no—
886C23—32no—
887C23—52no—
888C23—52no—
889C23—52no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—61no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23—101no—
904C23—152no—
905C23—308no—
906C23—308no—
907C23—301no—
908C23—301no—
909C23—301no—
910C23—301no—
911C23—301no—
912C23—301no—
913C23—604no—
914C23—604no—
915C23—604no—
916C23—604no—
917C23—604no—
918C23C22×D3×D511yescharacteristic
919D4—68no—
920D4—308no—
921D4—604no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—32no—
929C2×C4—52no—
930C2×C4—52no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—101no—
937C2×C4—101no—
938C2×C4—101no—
939C2×C4—101no—
940C2×C4—101no—
941C2×C4—101no—
942C2×C4—101no—
943C2×C4—124no—
944C2×C4—124no—
945C2×C4—152no—
946C2×C4—204no—
947C2×C4—301no—
948C2×C4—301no—
949C2×C4—301no—
950C2×C4—301no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—604no—
956C2×C4—604no—
957C2×C4C4×D3×D512yes—
958C2×C4D5×D1212yes—
959C2×C4D3×C22⋊D512yes—
960C2×C3—104no—
961C2×C3C4×D4×D511yescharacteristic
962C2×C3#6587911yescharacteristic
963C2×C3#6588411yescharacteristic
964C2×C3#6589011yescharacteristic
965C2×C3C2×C4×C22⋊D511yescharacteristic
966C2×C3D4×C22⋊D511yescharacteristic
967C2×C3#6616311yescharacteristic
968D3—24no—
969D3—42no—
970D3—202no—
971C5#7357711yescharacteristic, complemented, Sylow
972C22—34no—
973C22—54no—
974C22—62no—
975C22—62no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—62no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—102no—
984C22—102no—
985C22—102no—
986C22—102no—
987C22—102no—
988C22—102no—
989C22—121no—
990C22—121no—
991C22—121no—
992C22—121no—
993C22—302no—
994C22—302no—
995C22—302no—
996C22—6016no—
997C22—601no—
998C22—601no—
999C22—601no—
1000C22—601no—
1001C22C2×C4×D3×D511yescharacteristic
1002C22C2×D5×D1211yescharacteristic
1003C22D5×#23511yescharacteristic
1004C22D3×#70911yescharacteristic
1005C22#9201711yescharacteristic
1006C22#9201811yescharacteristic
1007C22C2×D3×C22⋊D511yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—22no—
1011C4—62no—
1012C4—102no—
1013C4—102no—
1014C4—121no—
1015C4—201no—
1016C4—302no—
1017C4—601no—
1018C4—601no—
1019C3#1061412911yescharacteristic, complemented, Sylow
1020C2—64no—
1021C2—104no—
1022C2—122no—
1023C2—602no—
1024C2C4×D5×D1211yescharacteristic
1025C2#1175272911yescharacteristic
1026C2#1175273611yescharacteristic
1027C2#1175275811yescharacteristic
1028C2C4×D3×C22⋊D511yescharacteristic
1029C2D12×C22⋊D511yescharacteristic
1030C2#1175465011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91475C2
hypercenterC2×C42D3×D5
hypocenterC3×C5#2358
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×D12C2semidirect
3. C2×D3×#685C2semidirect
4. C2×D5×(C2×D3)⋊C4C2semidirect
5. C2×#91441C2semidirect
6. #11751041C2semidirect
7. C3×C4×#685C2semidirect
8. #11748914C2semidirect
9. #11748908C2semidirect
10. #11748905C2semidirect
11. #11748901C2semidirect
12. #11748899C2semidirect
13. Dic5×(C2×D3)⋊C4C2semidirect
14. #11748722C2semidirect
15. #11748685C2semidirect
20. C22×C4×C5×D3C22semidirect
26. C2×C3×C42×C5C22semidirect
30. C2×#6712C22semidirect
32. C2×C5×(C2×D3)⋊C4C22semidirect
33. C2×C5×C4⋊Dic3C22semidirect
37. C2×C3×C4×Dic5C22semidirect
38. C2×#6668C22semidirect
43. C2×(C2×D3)⋊Dic5C22semidirect
44. C2×(C2×D3)⋊Dic5C22semidirect
46. C2×Dic3×Dic5C22semidirect
47. #91475C4semidirect
51. #91115C22semidirect
52. #91115C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
55. #90994C22semidirect
56. #90994C22semidirect
72. C4×#685D3semidirect
83. C22×D3×D5C2×C4semidirect
94. C2×C5×D12C2×C4semidirect
109. C2×#1203C2×C4semidirect
112. C2×#1201C2×C4semidirect
122. #6714C2×C4semidirect
125. C5×(C2×D3)⋊C4D4semidirect
127. C3×#685C2×C4semidirect
128. C3×#685D4semidirect
136. (C2×D3)⋊Dic5C2×C4semidirect
143. C2×C4×D12D5semidirect
167. C2×C42×C5C2×D3semidirect
186. C2×C4×Dic5C2×D3semidirect
192. #3963C2×D3semidirect
193. #3963C2×D3semidirect
280. C22×C4×D3C2×D5semidirect
284. C2×C3×C42C2×D5semidirect
297. C2×(C2×D3)⋊C4C2×D5semidirect
299. C2×C4⋊Dic3C2×D5semidirect
372. #685C4×D3semidirect
373. #685D12semidirect
420. C2×C5×D3C4×D4semidirect
427. C2×C3×D5C4×D4semidirect
476. C2×D12C4×D5semidirect
501. (C2×D3)⋊C4C22⋊D5semidirect
616. C2×C42D3×D5semidirect
746. C2×D5C4×D12semidirect
824. C3×C5#2358semidirect
860. C2×D3C4×C22⋊D5semidirect
971. C5#73577semidirect
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×D122
C2×#914752
C2×D3×#6852
C2×D5×(C2×D3)⋊C42
C2×#914412
#117510412
C3×C4×#6852
#117489142
#117489082
#117489052
#117489012
#117488992
Dic5×(C2×D3)⋊C42
#117487222
#117486852
#106141293
#735775