Finite Group Databasebeta

← #14323425

Subgroups — #14323425

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#937C211yesmaximal, characteristic
2C2×D3×C22⋊Dic5C211yesmaximal, characteristic, complemented
3C2×Dic5×#67C211yesmaximal, characteristic, complemented
4#11751322C211yesmaximal, characteristic, complemented
5C3×#65509C211yesmaximal, characteristic, complemented
6#11749519C211yesmaximal, characteristic, complemented
7#11749496C211yesmaximal, characteristic, complemented
8#11749492C211yesmaximal, characteristic, complemented
9#11749482C211yesmaximal, characteristic, complemented
10#11749478C211yesmaximal, characteristic, complemented
11#11749478C211yesmaximal, characteristic, complemented
12#11748903C211yesmaximal, characteristic, complemented
13#11748886C211yesmaximal, characteristic, complemented
14#11748794C211yesmaximal, characteristic, complemented
15#11748686C211yesmaximal, characteristic, complemented
16#10614309—31nomaximal, Hall
17C24×C5×D3C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic, complemented
22C22×D3×Dic5C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic, complemented
27C2×#6719C2211yescharacteristic, complemented
28C2×C4⋊Dic15C2211yescharacteristic, complemented
29C2×C4×Dic15C2211yescharacteristic, complemented
30C2×C5×#217C2211yescharacteristic
31C5×#937C418yescomplemented
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×C22⋊Dic5C2211yescharacteristic
36C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
37D3×C22⋊Dic5—24no—
38Dic5×#67—24no—
39C2×Dic3⋊Dic5C2211yescharacteristic, complemented
40C2×Dic3⋊Dic5C2211yescharacteristic, complemented
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×(C2×D3)⋊Dic5C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic, complemented
48C2×Dic3×Dic5C2211yescharacteristic, complemented
49C3×#3963C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#74876—51nomaximal, Hall
56C2×C5×#120—31no—
57C22×C22⋊Dic5—31no—
58C2×D4×Dic5—31no—
59#65536—31no—
60#65510—31no—
61#65510—31no—
62#65509—31no—
63#65509—31no—
64#65509D311yescharacteristic, complemented
65#65240—31no—
66#65240—31no—
67#65240—31no—
68#65240—31no—
69#65239—31no—
70C22⋊C4×Dic5—31no—
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×C5×D3—22no—
74C23×C5×D3—22no—
75C23×C5×D3—41no—
76C23×C5×D3—41no—
77C23×C5×D3—41no—
78C23×C5×D3—41no—
79C23×C5×D3C2×C414yescomplemented
80C23×C5×D3C2311yescharacteristic
81C23×C5×D3C2311yescharacteristic
82C2×C3×C5×D4—41no—
83C2×C3×C5×D4—41no—
84C2×C3×C5×D4C2×C414yescomplemented
85C22×C3×C4×C5C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C2×C5×#67—22no—
91C2×C5×#67—22no—
92C2×C5×#67—41no—
93C2×C5×#67—41no—
94C2×C5×#67C2×C414yes—
95C2×C5×#67C2×C414yescomplemented
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C22×C3×Dic5—22no—
99C22×C3×Dic5—41no—
100C22×C3×Dic5—41no—
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C2×D3×Dic5—22no—
106C2×D3×Dic5—41no—
107C2×D3×Dic5—41no—
108C2×D3×Dic5—41no—
109C2×D3×Dic5—41no—
110C2×D3×Dic5D414yescomplemented
111#6719—22no—
112#6719—22no—
113#6719—41no—
114#6719—41no—
115C4⋊Dic15—41no—
116C4×Dic15—41no—
117C5×#217C2×C414yescomplemented
118C5×(C2×D3)⋊C4C2×C414yescomplemented
119C5×(C2×D3)⋊C4C2×C414yescomplemented
120C3×C22⋊Dic5—22no—
121C3×C22⋊Dic5—41no—
122C3×C22⋊Dic5—41no—
123Dic3⋊Dic5—22no—
124Dic3⋊Dic5—41no—
125(C2×D3)⋊Dic5—22no—
126(C2×D3)⋊Dic5—22no—
127(C2×D3)⋊Dic5—22no—
128(C2×D3)⋊Dic5—22no—
129(C2×D3)⋊Dic5—41no—
130(C2×D3)⋊Dic5—41no—
131Dic3×Dic5—22no—
132Dic3×Dic5—41no—
133C2×#937D511yescharacteristic
134C2×C4×#67—51no—
135C2×D3×C22⋊C4—51no—
136C3×#386—51no—
137#5221—51no—
138#5213—51no—
139#4957—51no—
140#4956—51no—
141#4955—51no—
142#4944—51no—
143#4944—51no—
144#4670—51no—
145#4669—51no—
146#4668—51no—
147#4666—51no—
148C25×C5—31no—
149C22×C5×D4—31no—
150C22×C5×D4—31no—
151C22×C5×D4C2×D311yescharacteristic
152C23×Dic5—31no—
153C23×Dic5—31no—
154C23×Dic5C2×D311yescharacteristic, complemented
155C5×#120—38no—
156C2×C5×C22⋊C4—31no—
157C2×C5×C22⋊C4—31no—
158C2×C5×C22⋊C4—31no—
159C2×C22⋊Dic5—31no—
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163C2×C22⋊Dic5—31no—
164C2×C22⋊Dic5—31no—
165C2×C22⋊Dic5—31no—
166C2×C22⋊Dic5—31no—
167C2×C22⋊Dic5—31no—
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5—64no—
170C2×C22⋊Dic5C2×D311yescharacteristic
171C2×C22⋊Dic5C2×D311yescharacteristic
172C2×C22⋊Dic5C2×D311yescharacteristic, complemented
173D4×Dic5—64no—
174C2×C4⋊Dic5—31no—
175C2×C4⋊Dic5—31no—
176C2×C4⋊Dic5—31no—
177C2×C4×Dic5—31no—
178C2×C4×Dic5—31no—
179C2×C4×Dic5—31no—
180#3963—31no—
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963C2×D311yescharacteristic, complemented
185#3963C2×D311yescharacteristic, complemented
186#2321—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5C22×C412yes—
200C23×C3×C5C22×C412yes—
201C23×C3×C5C2411yescharacteristic
202C22×C5×D3—21no—
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—28no—
213C22×C5×D3—44no—
214C22×C5×D3—44no—
215C22×C5×D3—44no—
216C22×C5×D3—44no—
217C22×C5×D3—44no—
218C22×C5×D3—44no—
219C22×C5×D3C22×C412yes—
220C22×C5×D3C22×C412yes—
221C22×C5×D3C2×D412yes—
222C22×C5×D3#4112yes—
223C3×C5×D4—44no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5C22×C412yes—
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×Dic15C2×D412yes—
239C5×#67—28no—
240C5×#67—44no—
241C2×C5×Dic3—21no—
242C2×C5×Dic3—21no—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3C22×C412yes—
246C2×C5×Dic3C22×C412yes—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5—21no—
254C2×C3×Dic5—21no—
255C2×C3×Dic5—21no—
256C2×C3×Dic5—21no—
257C2×C3×Dic5—21no—
258C2×C3×Dic5—44no—
259C2×C3×Dic5C2×D412yes—
260D3×Dic5—44no—
261D3×Dic5—44no—
262C24×D3C2×D511yescharacteristic
263C22×C3×D4C2×D511yescharacteristic
264C23×C3×C4—51no—
265C22×#67C2×D511yescharacteristic
266C22×#67C2×D511yescharacteristic
267C22×C4×D3—51no—
268C22×C4×D3—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4—51no—
272C2×#217—51no—
273C2×#217—51no—
274C2×#217—51no—
275C2×#217—51no—
276C2×#217C2×D511yescharacteristic
277#937Dic518yescomplemented
278C4×#67—104no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×(C2×D3)⋊C4—51no—
284C2×(C2×D3)⋊C4—51no—
285C2×(C2×D3)⋊C4C2×D511yescharacteristic
286C2×(C2×D3)⋊C4C2×D511yescharacteristic
287C2×C4⋊Dic3—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4—51no—
290C2×C4×Dic3—51no—
291C2×C4×Dic3—51no—
292C2×C4×Dic3—51no—
293D3×C22⋊C4—104no—
294C3×#95—51no—
295C3×#95—51no—
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95—51no—
299C3⋊#95—51no—
300C24×C5—31no—
301C24×C5—31no—
302C24×C5—34no—
303C24×C5—62no—
304C24×C5—62no—
305C24×C5—121no—
306C24×C5—121no—
307C24×C5—121no—
308C24×C5—121no—
309C24×C5C22×D311yescharacteristic
310C24×C5C22×D311yescharacteristic
311C2×C5×D4—34no—
312C2×C5×D4—34no—
313C2×C5×D4—41no—
314C2×C5×D4—41no—
315C2×C5×D4—62no—
316C2×C5×D4—62no—
317C2×C5×D4—121no—
318C2×C5×D4—121no—
319C2×C5×D4C4×D314yescomplemented
320C22×C4×C5—31no—
321C22×C4×C5—31no—
322C22×C4×C5C22×D311yescharacteristic
323C22×Dic5—22no—
324C22×Dic5—31no—
325C22×Dic5—34no—
326C22×Dic5—31no—
327C22×Dic5—31no—
328C22×Dic5—31no—
329C22×Dic5—41no—
330C22×Dic5—41no—
331C22×Dic5—62no—
332C22×Dic5—121no—
333C22×Dic5—121no—
334C22×Dic5—121no—
335C22×Dic5—121no—
336C22×Dic5C22×D311yescharacteristic
337C22×Dic5C22×D311yescharacteristic
338C22×Dic5C22×D311yescharacteristic
339C22×Dic5C22×D311yescharacteristic
340C5×C22⋊C4—34no—
341C5×C22⋊C4—34no—
342C5×C22⋊C4—34no—
343C22⋊Dic5—22no—
344C22⋊Dic5—41no—
345C22⋊Dic5—41no—
346C22⋊Dic5—62no—
347C22⋊Dic5—62no—
348C22⋊Dic5—62no—
349C22⋊Dic5—62no—
350C22⋊Dic5—62no—
351C22⋊Dic5—62no—
352C22⋊Dic5—121no—
353C22⋊Dic5—121no—
354C22⋊Dic5—121no—
355C22⋊Dic5—121no—
356C4⋊Dic5—62no—
357C4⋊Dic5—121no—
358C4⋊Dic5—121no—
359C4×Dic5—62no—
360C4×Dic5—121no—
361C4×Dic5—121no—
362C2×#120—31no—
363C2×C4×D4—151no—
364C22×C22⋊C4—151no—
365#390—151no—
366#390—151no—
367#388—151no—
368#388—151no—
369#388—151no—
370#388—151no—
371#386—51no—
372#386—151no—
373#386—151no—
374#385—151no—
375#379—151no—
376C4×C22⋊C4—151no—
377C22×C3×C5—22no—
378C22×C3×C5—22no—
379C22×C3×C5—22no—
380C22×C3×C5—22no—
381C22×C3×C5—22no—
382C22×C3×C5—22no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5C23×C411yescharacteristic
392C22×C3×C5C22×D411yescharacteristic
393C22×C3×C5C2×#4111yescharacteristic
394C22×C3×C5H(5,𝔽2)11yescharacteristic
395C22×C3×C5H(5,𝔽2)11yescharacteristic
396C22×C3×C5H(5,𝔽2)11yescharacteristic
397C22×C3×C5H(5,𝔽2)11yescharacteristic
398C2×C5×D3—22no—
399C2×C5×D3—22no—
400C2×C5×D3—22no—
401C2×C5×D3—22no—
402C2×C5×D3—22no—
403C2×C5×D3—22no—
404C2×C5×D3—22no—
405C2×C5×D3—22no—
406C2×C5×D3—22no—
407C2×C5×D3—416no—
408C2×C5×D3—41no—
409C2×C5×D3—41no—
410C2×C5×D3—41no—
411C2×C5×D3—41no—
412C2×C5×D3C4×D414yes—
413C3×C4×C5—22no—
414Dic15—22no—
415Dic15—41no—
416Dic15—41no—
417Dic15—41no—
418C3×Dic5—22no—
419C3×Dic5—41no—
420C3×Dic5—41no—
421C3×Dic5—41no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C24×C3C22×D511yescharacteristic
425C24×C3C22×D511yescharacteristic
426C23×D3—22no—
427C23×D3—22no—
428C23×D3—41no—
429C23×D3—41no—
430C23×D3—41no—
431C23×D3—41no—
432C23×D3C2×Dic514yescomplemented
433C23×D3C22×D511yescharacteristic
434C23×D3C22×D511yescharacteristic
435C2×C3×D4—41no—
436C2×C3×D4—41no—
437C2×C3×D4C2×Dic514yescomplemented
438C22×C3×C4—51no—
439C22×C3×C4—51no—
440C22×C3×C4—51no—
441C22×C3×C4—51no—
442C22×C3×C4—102no—
443C22×C3×C4—201no—
444C22×C3×C4—201no—
445C22×C3×C4C22×D511yescharacteristic
446C2×#67—22no—
447C2×#67—22no—
448C2×#67—41no—
449C2×#67—41no—
450C2×#67C2×Dic514yes—
451C2×#67C2×Dic514yescomplemented
452C22×Dic3—51no—
453C22×Dic3—51no—
454C22×Dic3—51no—
455C22×Dic3—51no—
456C22×Dic3C22×D511yescharacteristic
457C22×Dic3C22×D511yescharacteristic
458C2×C4×D3—54no—
459C2×C4×D3—102no—
460C2×C4×D3—201no—
461C2×C4×D3—201no—
462C2×C4×D3—201no—
463C2×C4×D3—201no—
464C3×C22⋊C4—102no—
465C3×C22⋊C4—201no—
466C3×C22⋊C4—201no—
467#217—102no—
468#217—102no—
469#217—201no—
470#217—201no—
471#217C2×Dic514yescomplemented
472(C2×D3)⋊C4—102no—
473(C2×D3)⋊C4—102no—
474(C2×D3)⋊C4—102no—
475(C2×D3)⋊C4—102no—
476(C2×D3)⋊C4—201no—
477(C2×D3)⋊C4—201no—
478(C2×D3)⋊C4C2×Dic514yescomplemented
479(C2×D3)⋊C4C2×Dic514yescomplemented
480C4⋊Dic3—201no—
481Dic3⋊C4—102no—
482Dic3⋊C4—201no—
483C4×Dic3—102no—
484C4×Dic3—201no—
485C4×Dic3—201no—
486C23×C5—21no—
487C23×C5—21no—
488C23×C5—21no—
489C23×C5—21no—
490C23×C5—21no—
491C23×C5—21no—
492C23×C5—21no—
493C23×C5—21no—
494C23×C5—21no—
495C23×C5—21no—
496C23×C5—21no—
497C23×C5—21no—
498C23×C5—32no—
499C23×C5—32no—
500C23×C5—32no—
501C23×C5—32no—
502C23×C5—68no—
503C23×C5—61no—
504C23×C5—61no—
505C23×C5—61no—
506C23×C5—61no—
507C23×C5—61no—
508C23×C5—61no—
509C23×C5—61no—
510C23×C5—61no—
511C23×C5—61no—
512C23×C5—61no—
513C23×C5—124no—
514C23×C5—124no—
515C23×C5—124no—
516C23×C5—124no—
517C23×C5—124no—
518C23×C5—124no—
519C23×C5C2×C4×D312yes—
520C23×C5C2×C4×D312yes—
521C23×C5C23×D311yescharacteristic
522C5×D4—44no—
523C5×D4—68no—
524C5×D4—124no—
525C2×C4×C5—21no—
526C2×C4×C5—21no—
527C2×C4×C5—32no—
528C2×C4×C5—32no—
529C2×C4×C5—61no—
530C2×C4×C5—61no—
531C2×C4×C5—61no—
532C2×C4×C5—61no—
533C2×C4×C5C2×C4×D312yes—
534C2×Dic5—21no—
535C2×Dic5—21no—
536C2×Dic5—21no—
537C2×Dic5—21no—
538C2×Dic5—21no—
539C2×Dic5—21no—
540C2×Dic5—21no—
541C2×Dic5—21no—
542C2×Dic5—21no—
543C2×Dic5—21no—
544C2×Dic5—21no—
545C2×Dic5—32no—
546C2×Dic5—44no—
547C2×Dic5—61no—
548C2×Dic5—61no—
549C2×Dic5—61no—
550C2×Dic5—61no—
551C2×Dic5—61no—
552C2×Dic5—61no—
553C2×Dic5—61no—
554C2×Dic5—61no—
555C2×Dic5—61no—
556C2×Dic5—61no—
557C2×Dic5—61no—
558C2×Dic5—124no—
559C2×Dic5—124no—
560C2×Dic5D3×D412yes—
561C25—31no—
562C22×D4—31no—
563C22×D4—31no—
564C22×D4D3×D511yescharacteristic
565C23×C4—51no—
566C23×C4—151no—
567C23×C4—151no—
568#120—38no—
569C4×D4—304no—
570C2×C4⋊C4—151no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4—151no—
573C2×C22⋊C4—31no—
574C2×C22⋊C4—31no—
575C2×C22⋊C4—31no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—51no—
578C2×C22⋊C4—51no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4—151no—
587C2×C22⋊C4—151no—
588C2×C22⋊C4—151no—
589C2×C22⋊C4—304no—
590C2×C42—151no—
591C2×C42—151no—
592C2×C42—151no—
593#95—51no—
594#95—51no—
595#95—151no—
596#95—151no—
597#95—151no—
598#95—151no—
599C2×C3×C5—42no—
600C2×C3×C5—42no—
601C2×C3×C5C2×C4×D411yescharacteristic
602C2×C3×C5#51811yescharacteristic
603C2×C3×C5#51811yescharacteristic
604C2×C3×C5#53411yescharacteristic
605C2×C3×C5#53511yescharacteristic
606C2×C3×C5#53811yescharacteristic
607C2×C3×C5#53811yescharacteristic
608C5×D3—24no—
609C5×D3—42no—
610C23×C3—21no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—21no—
615C23×C3—21no—
616C23×C3—21no—
617C23×C3—21no—
618C23×C3—21no—
619C23×C3—21no—
620C23×C3—21no—
621C23×C3—21no—
622C23×C3C22×Dic512yes—
623C23×C3C22×Dic512yes—
624C23×C3C23×D511yescharacteristic
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—21no—
633C22×D3—21no—
634C22×D3—21no—
635C22×D3—28no—
636C22×D3—44no—
637C22×D3—44no—
638C22×D3—44no—
639C22×D3—44no—
640C22×D3—44no—
641C22×D3—44no—
642C22×D3D4×D512yes—
643C22×D3#71112yes—
644C22×D3C22×Dic512yes—
645C22×D3C22×Dic512yes—
646C3×D4—44no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—52no—
650C2×C3×C4—101no—
651C2×C3×C4—101no—
652C2×C3×C4—101no—
653C2×C3×C4—101no—
654C2×C3×C4—101no—
655C2×C3×C4—101no—
656C2×C3×C4—101no—
657C2×C3×C4—101no—
658C2×C3×C4—101no—
659C2×C3×C4—101no—
660C2×C3×C4—101no—
661C2×C3×C4—204no—
662C2×C3×C4C22×Dic512yes—
663#67—28no—
664#67—44no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—52no—
670C2×Dic3—101no—
671C2×Dic3—101no—
672C2×Dic3—101no—
673C2×Dic3—101no—
674C2×Dic3—101no—
675C2×Dic3—101no—
676C2×Dic3—101no—
677C2×Dic3—101no—
678C2×Dic3—101no—
679C2×Dic3—101no—
680C2×Dic3—101no—
681C2×Dic3C22×Dic512yes—
682C2×Dic3C22×Dic512yes—
683C4×D3—204no—
684C4×D3—204no—
685C22×C5—22no—
686C22×C5—22no—
687C22×C5—22no—
688C22×C5—22no—
689C22×C5—22no—
690C22×C5—22no—
691C22×C5—34no—
692C22×C5—41no—
693C22×C5—41no—
694C22×C5—41no—
695C22×C5—41no—
696C22×C5—41no—
697C22×C5—41no—
698C22×C5—41no—
699C22×C5—41no—
700C22×C5—62no—
701C22×C5—62no—
702C22×C5—62no—
703C22×C5—62no—
704C22×C5—62no—
705C22×C5—62no—
706C22×C5—62no—
707C22×C5—62no—
708C22×C5—62no—
709C22×C5—1216no—
710C22×C5—121no—
711C22×C5—121no—
712C22×C5—121no—
713C22×C5—121no—
714C22×C5C22×C4×D311yescharacteristic
715C22×C5C2×D3×D411yescharacteristic
716C22×C5#100411yescharacteristic
717C22×C5#100411yescharacteristic
718C22×C5#100411yescharacteristic
719C22×C5D3×#4111yescharacteristic
720C22×C5#100911yescharacteristic
721C4×C5—22no—
722C4×C5—62no—
723C4×C5—62no—
724Dic5—22no—
725Dic5—41no—
726Dic5—41no—
727Dic5—41no—
728Dic5—62no—
729Dic5—121no—
730Dic5—121no—
731Dic5—121no—
732C24—31no—
733C24—31no—
734C24—34no—
735C24—62no—
736C24—62no—
737C24—121no—
738C24—121no—
739C24—121no—
740C24—121no—
741C24C2×D3×D511yescharacteristic
742C24C2×D3×D511yescharacteristic
743C2×D4—34no—
744C2×D4—34no—
745C2×D4—41no—
746C2×D4—41no—
747C2×D4—62no—
748C2×D4—62no—
749C2×D4—121no—
750C2×D4—121no—
751C2×D4D3×Dic514yescomplemented
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—51no—
755C22×C4—51no—
756C22×C4—51no—
757C22×C4—51no—
758C22×C4—102no—
759C22×C4—154no—
760C22×C4—151no—
761C22×C4—151no—
762C22×C4—151no—
763C22×C4—151no—
764C22×C4—201no—
765C22×C4—201no—
766C22×C4—302no—
767C22×C4—601no—
768C22×C4—601no—
769C22×C4—601no—
770C22×C4—601no—
771C22×C4C2×D3×D511yescharacteristic
772C4⋊C4—302no—
773C4⋊C4—601no—
774C4⋊C4—601no—
775C22⋊C4—34no—
776C22⋊C4—34no—
777C22⋊C4—34no—
778C22⋊C4—102no—
779C22⋊C4—201no—
780C22⋊C4—201no—
781C22⋊C4—302no—
782C22⋊C4—302no—
783C22⋊C4—302no—
784C22⋊C4—302no—
785C22⋊C4—302no—
786C22⋊C4—302no—
787C22⋊C4—601no—
788C22⋊C4—601no—
789C22⋊C4—601no—
790C22⋊C4—601no—
791C42—302no—
792C42—601no—
793C42—601no—
794C3×C5#232111yescharacteristic, complemented, Hall
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—41no—
802C22×C3—41no—
803C22×C3—41no—
804C22×C3—41no—
805C22×C3—41no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3C2×D4×D511yescharacteristic
810C22×C3C2×#71111yescharacteristic
811C22×C3#414411yescharacteristic
812C22×C3#414411yescharacteristic
813C22×C3#414411yescharacteristic
814C22×C3#414411yescharacteristic
815C22×C3C23×Dic511yescharacteristic
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—22no—
819C2×D3—22no—
820C2×D3—22no—
821C2×D3—22no—
822C2×D3—22no—
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—416no—
826C2×D3—41no—
827C2×D3—41no—
828C2×D3—41no—
829C2×D3—41no—
830C2×D3D4×Dic514yes—
831C3×C4—22no—
832C3×C4—102no—
833C3×C4—201no—
834C3×C4—201no—
835C3×C4—201no—
836Dic3—22no—
837Dic3—22no—
838Dic3—102no—
839Dic3—201no—
840Dic3—201no—
841Dic3—201no—
842C2×C5—42no—
843C2×C5—42no—
844C2×C5—64no—
845C2×C5—122no—
846C2×C5#548611yescharacteristic
847C2×C5C4×D3×D411yescharacteristic
848C2×C5#554511yescharacteristic
849C2×C5#558911yescharacteristic
850C2×C5#560711yescharacteristic
851C2×C5#561311yescharacteristic
852C2×C5#565711yescharacteristic
853C23—21no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—32no—
866C23—32no—
867C23—32no—
868C23—32no—
869C23—68no—
870C23—61no—
871C23—61no—
872C23—61no—
873C23—61no—
874C23—61no—
875C23—61no—
876C23—61no—
877C23—61no—
878C23—61no—
879C23—61no—
880C23—124no—
881C23—124no—
882C23—124no—
883C23—124no—
884C23—124no—
885C23—124no—
886C23C2×D3×Dic512yes—
887C23C2×D3×Dic512yes—
888C23C22×D3×D511yescharacteristic
889D4—44no—
890D4—68no—
891D4—124no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—32no—
895C2×C4—32no—
896C2×C4—52no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—101no—
902C2×C4—101no—
903C2×C4—101no—
904C2×C4—101no—
905C2×C4—101no—
906C2×C4—101no—
907C2×C4—101no—
908C2×C4—101no—
909C2×C4—101no—
910C2×C4—101no—
911C2×C4—101no—
912C2×C4—152no—
913C2×C4—204no—
914C2×C4—301no—
915C2×C4—301no—
916C2×C4—301no—
917C2×C4—301no—
918C2×C4—301no—
919C2×C4—301no—
920C2×C4—301no—
921C2×C4—301no—
922C2×C4—301no—
923C2×C4—301no—
924C2×C4—301no—
925C2×C4—604no—
926C2×C4—604no—
927C2×C4C2×D3×Dic512yes—
928C2×C3—42no—
929C2×C3—42no—
930C2×C3#6592311yescharacteristic
931C2×C3#6592611yescharacteristic
932C2×C3#6592711yescharacteristic
933C2×C3#6592711yescharacteristic
934C2×C3C2×D4×Dic511yescharacteristic
935C2×C3#6613211yescharacteristic
936C2×C3#6613211yescharacteristic
937D3—24no—
938D3—42no—
939C5#7487611yescharacteristic, complemented, Sylow
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22—34no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—62no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—1216no—
965C22—121no—
966C22—121no—
967C22—121no—
968C22—121no—
969C22D3×D4×D511yescharacteristic
970C22D3×#71111yescharacteristic
971C22#9202511yescharacteristic
972C22#9202711yescharacteristic
973C22C22×D3×Dic511yescharacteristic
974C22#9204911yescharacteristic
975C22#9204911yescharacteristic
976C4—22no—
977C4—62no—
978C4—62no—
979C4—102no—
980C4—201no—
981C4—201no—
982C4—201no—
983C4—302no—
984C4—601no—
985C4—601no—
986C4—601no—
987C3#1061430911yescharacteristic, complemented, Sylow
988C2—42no—
989C2—42no—
990C2—64no—
991C2—122no—
992C2D3×D4×Dic511yescharacteristic
993C2#1175488611yescharacteristic
994C2#1175491411yescharacteristic
995C2#1175497111yescharacteristic
996C2#1175502211yescharacteristic
997C2#1175504611yescharacteristic
998C2#1175541011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C5×#937C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2321
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×D3×C22⋊Dic5C2semidirect
3. C2×Dic5×#67C2semidirect
4. #11751322C2semidirect
5. C3×#65509C2semidirect
6. #11749519C2semidirect
7. #11749496C2semidirect
8. #11749492C2semidirect
9. #11749482C2semidirect
10. #11749478C2semidirect
11. #11749478C2semidirect
12. #11748903C2semidirect
13. #11748886C2semidirect
14. #11748794C2semidirect
15. #11748686C2semidirect
21. C23×C3×Dic5C22semidirect
26. C2×#6719C22semidirect
27. C2×#6719C22semidirect
28. C2×C4⋊Dic15C22semidirect
29. C2×C4×Dic15C22semidirect
31. C5×#937C4semidirect
36. C2×C3×C22⋊Dic5C22semidirect
39. C2×Dic3⋊Dic5C22semidirect
40. C2×Dic3⋊Dic5C22semidirect
47. C2×Dic3×Dic5C22semidirect
48. C2×Dic3×Dic5C22semidirect
49. C3×#3963C22semidirect
50. C3×#3963C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
64. #65509D3semidirect
79. C23×C5×D3C2×C4semidirect
84. C2×C3×C5×D4C2×C4semidirect
95. C2×C5×#67C2×C4semidirect
110. C2×D3×Dic5D4semidirect
117. C5×#217C2×C4semidirect
118. C5×(C2×D3)⋊C4C2×C4semidirect
119. C5×(C2×D3)⋊C4C2×C4semidirect
154. C23×Dic5C2×D3semidirect
172. C2×C22⋊Dic5C2×D3semidirect
184. #3963C2×D3semidirect
185. #3963C2×D3semidirect
277. #937Dic5semidirect
319. C2×C5×D4C4×D3semidirect
432. C23×D3C2×Dic5semidirect
437. C2×C3×D4C2×Dic5semidirect
451. C2×#67C2×Dic5semidirect
471. #217C2×Dic5semidirect
478. (C2×D3)⋊C4C2×Dic5semidirect
479. (C2×D3)⋊C4C2×Dic5semidirect
751. C2×D4D3×Dic5semidirect
794. C3×C5#2321semidirect
939. C5#74876semidirect
987. C3#10614309semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9372
C2×D3×C22⋊Dic52
C2×Dic5×#672
#117513222
C3×#655092
#117495192
#117494962
#117494922
#117494822
#117494782
#117489032
#117488862
#117487942
#117486862
#106143093
#748765