Finite Group Databasebeta

← #14323382

Subgroups — #14323382

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×#893C211yesmaximal, characteristic, complemented
2C2×#91475C211yesmaximal, characteristic
3C2×D3×#685C211yesmaximal, characteristic, complemented
4#11751091C211yesmaximal, characteristic, complemented
5C3×#65279C211yesmaximal, characteristic, complemented
6#11748940C211yesmaximal, characteristic, complemented
7#11748915C211yesmaximal, characteristic, complemented
8#11748914C211yesmaximal, characteristic, complemented
9#11748910C211yesmaximal, characteristic, complemented
10#11748908C211yesmaximal, characteristic, complemented
11#11748901C211yesmaximal, characteristic, complemented
12#11748893C211yesmaximal, characteristic, complemented
13#11748854C211yesmaximal, characteristic, complemented
14#11748770C211yesmaximal, characteristic, complemented
15C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
16#10614126—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C5×D12C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic, complemented
21C22×#1203C2211yescharacteristic
22C22×#1201C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×C4×Dic15C2211yescharacteristic, complemented
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
31C2×C4×C5×Dic3C2211yescharacteristic, complemented
32C5×#893—24no—
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×C4×Dic5C2211yescharacteristic, complemented
37C2×#6669C2211yescharacteristic, 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×#6665C2211yescharacteristic
47#91475C418yescomplemented
48D3×#685—24no—
49#91115C2211yescharacteristic, complemented
50#91115C2211yescharacteristic, complemented
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#75826—51nomaximal, Hall
56C2×C4×C5×D4—31no—
57C2×#4083—31no—
58C22×#685—31no—
59#65509—31no—
60#65502—31no—
61#65502—31no—
62C4×C22⋊Dic5—31no—
63#65279—31no—
64#65279D311yescharacteristic, complemented
65#65246—31no—
66#65246—31no—
67#65244—31no—
68#65235—31no—
69#65229—31no—
70#65229—31no—
71C23×D15C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C23×C5×D3C2311yescharacteristic
74C23×C3×D5C2311yescharacteristic
75C22×D3×D5—22no—
76C22×D3×D5—22no—
77C22×D3×D5—41no—
78C22×D3×D5—41no—
79C22×D3×D5—41no—
80C22×D3×D5—41no—
81C22×D3×D5C2×C414yescomplemented
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C2×C5×D12—22no—
91C2×C5×D12—22no—
92C2×C5×D12C2×C414yes—
93C2×C4×C5×D3—22no—
94C2×C4×C5×D3—41no—
95C2×C4×C5×D3—41no—
96C2×C4×C5×D3—41no—
97C2×C4×C5×D3—41no—
98C2×C4×C5×D3D414yescomplemented
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C2×#1203—41no—
103C2×#1203—41no—
104C2×#1203C2×C414yescomplemented
105C2×#1201—41no—
106C2×#1201—41no—
107C2×#1201C2×C414yescomplemented
108C2×D3×Dic5—22no—
109C2×D3×Dic5—41no—
110C2×D3×Dic5—41no—
111C3×C5×C4⋊C4—22no—
112#6714—22no—
113#6714—41no—
114#6714C2×C414yescomplemented
115C4×Dic15—41no—
116C5×(C2×D3)⋊C4—22no—
117C5×(C2×D3)⋊C4—22no—
118C4×C5×Dic3—22no—
119C3×#685—22no—
120C3×#685—41no—
121C3×#685C2×C414yescomplemented
122C3×C4×Dic5—41no—
123#6669—41no—
124#6668—41no—
125#6667—22no—
126#6667—41no—
127(C2×D3)⋊Dic5—22no—
128(C2×D3)⋊Dic5—41no—
129(C2×D3)⋊Dic5—41no—
130(C2×D3)⋊Dic5C2×C414yescomplemented
131#6665—22no—
132#6665—41no—
133C2×#893D511yescharacteristic, complemented
134C2×#882—51no—
135C2×D3×C22⋊C4—51no—
136C3×#388—51no—
137#4990—51no—
138#4957—51no—
139#4956—51no—
140#4955—51no—
141#4951—51no—
142#4939—51no—
143C4×(C2×D3)⋊C4—51no—
144#4669—51no—
145#4668—51no—
146#4665—51no—
147#4665—51no—
148C24×D5—31no—
149C22×C5×D4—31no—
150C23×C4×C5—31no—
151C23×C4×C5—31no—
152C22×C22⋊D5—31no—
153C22×C22⋊D5—31no—
154C23×Dic5—31no—
155C4×C5×D4—64no—
156C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
157C2×C5×C22⋊C4—31no—
158C2×C5×C22⋊C4—31no—
159C2×C42×C5—31no—
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163C2×C22⋊Dic5—31no—
164#4083—38no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#685—64no—
173C2×#685C2×D311yescharacteristic
174C2×#685C2×D311yescharacteristic
175C2×#685C2×D311yescharacteristic
176C2×#683—31no—
177C2×#683—31no—
178C2×C4×Dic5—31no—
179C2×C4×Dic5C2×D311yescharacteristic, complemented
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×C5C2411yescharacteristic
188C22×D15—21no—
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15C22×C412yes—
195C22×C5×D3—21no—
196C22×C5×D3—21no—
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3—21no—
200C22×C5×D3—21no—
201C22×C5×D3—21no—
202C22×C5×D3—21no—
203C22×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C5×D3C22×C412yes—
206C22×C5×D3C22×C412yes—
207C22×C5×D3C2×D412yes—
208C22×C5×D3#4112yes—
209C22×C3×D5—21no—
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—21no—
213C22×C3×D5—21no—
214C22×C3×D5—21no—
215C22×C3×D5C22×C412yes—
216C2×D3×D5—28no—
217C2×D3×D5—44no—
218C2×D3×D5—44no—
219C2×D3×D5—44no—
220C2×D3×D5—44no—
221C2×D3×D5—44no—
222C2×D3×D5—44no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5C22×C412yes—
231C2×C3×C4×C5C2×D412yes—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15C22×C412yes—
241C2×C5×Dic3—21no—
242C2×C5×Dic3—21no—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3C2×D412yes—
247C5×D12—28no—
248C4×C5×D3—44no—
249C4×C5×D3—44no—
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×Dic5C22×C412yes—
259#1203—44no—
260#1201—44no—
261D3×Dic5—44no—
262C24×D3—51no—
263C22×#67—51no—
264C22×D12—51no—
265C22×D12C2×D511yescharacteristic
266C22×C4×D3—51no—
267C22×C4×D3C2×D511yescharacteristic
268C22×C4×D3C2×D511yescharacteristic, complemented
269C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4—51no—
272C2×C3×C22⋊C4—51no—
273C2×C3×C42—51no—
274C2×#217—51no—
275C2×#217—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
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, complemented
287C2×C4⋊Dic3—51no—
288C2×Dic3⋊C4—51no—
289C2×C4×Dic3—51no—
290C2×C4×Dic3C2×D511yescharacteristic, complemented
291#893—24no—
292#882—58no—
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—
302C23×D5—31no—
303C23×D5—34no—
304C23×D5—62no—
305C23×D5—62no—
306C23×D5—121no—
307C23×D5—121no—
308C23×D5—121no—
309C23×D5—121no—
310C23×D5C22×D311yescharacteristic
311C2×C5×D4—34no—
312C2×C5×D4—62no—
313C2×C5×D4—62no—
314C22×C4×C5—31no—
315C22×C4×C5—34no—
316C22×C4×C5—31no—
317C22×C4×C5—62no—
318C22×C4×C5—121no—
319C22×C4×C5—121no—
320C22×C4×C5—121no—
321C22×C4×C5—121no—
322C22×C4×C5C22×D311yescharacteristic
323C22×C4×C5C22×D311yescharacteristic
324C22×C4×C5C22×D311yescharacteristic
325C2×C22⋊D5—34no—
326C2×C22⋊D5—34no—
327C2×C22⋊D5—121no—
328C2×C22⋊D5—121no—
329C2×C22⋊D5—121no—
330C2×C22⋊D5—121no—
331C22×Dic5—31no—
332C22×Dic5—31no—
333C22×Dic5—31no—
334C22×Dic5—62no—
335C22×Dic5—121no—
336C22×Dic5—121no—
337C22×Dic5C22×D311yescharacteristic
338C22×Dic5C22×D311yescharacteristic
339C22×Dic5C22×D311yescharacteristic
340C5×C4⋊C4—22no—
341C5×C22⋊C4—62no—
342C5×C22⋊C4—62no—
343C42×C5—62no—
344C22⋊Dic5—34no—
345C22⋊Dic5—62no—
346C22⋊Dic5—121no—
347C22⋊Dic5—121no—
348#685—22no—
349#685—34no—
350#685—41no—
351#685—62no—
352#685—62no—
353#685—62no—
354#685—121no—
355#685—121no—
356#685—121no—
357#685C4×D314yescomplemented
358#683—121no—
359#683—121no—
360C4×Dic5—41no—
361C4×Dic5—121no—
362C2×#120—151no—
363C2×C4×D4—31no—
364C22×C22⋊C4—151no—
365#390—151no—
366#390—151no—
367#388—51no—
368#388—151no—
369#388—151no—
370#388—151no—
371#386—151no—
372#386—151no—
373#386—151no—
374#385—151no—
375#379—151no—
376C4×C22⋊C4—151no—
377C22×C3×C5C23×C411yescharacteristic
378C22×C3×C5C22×D411yescharacteristic
379C22×C3×C5C2×#4111yescharacteristic
380C22×C3×C5H(5,𝔽2)11yescharacteristic
381C22×C3×C5H(5,𝔽2)11yescharacteristic
382C22×C3×C5H(5,𝔽2)11yescharacteristic
383C22×C3×C5H(5,𝔽2)11yescharacteristic
384C2×D15—22no—
385C2×D15—22no—
386C2×D15—22no—
387C2×D15—41no—
388C2×D15—41no—
389C2×D15—41no—
390C2×D15—41no—
391C2×C5×D3—22no—
392C2×C5×D3—22no—
393C2×C5×D3—22no—
394C2×C5×D3—22no—
395C2×C5×D3—22no—
396C2×C5×D3—22no—
397C2×C5×D3—22no—
398C2×C5×D3—22no—
399C2×C5×D3—22no—
400C2×C5×D3—41no—
401C2×C5×D3—41no—
402C2×C5×D3—41no—
403C2×C5×D3—41no—
404C2×C5×D3C4×D414yes—
405C2×C3×D5—22no—
406C2×C3×D5—22no—
407C2×C3×D5—22no—
408C2×C3×D5—41no—
409C2×C3×D5—41no—
410C2×C3×D5—41no—
411C2×C3×D5—41no—
412D3×D5—416no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—41no—
416Dic15—22no—
417Dic15—41no—
418Dic15—41no—
419C3×Dic5—22no—
420C3×Dic5—41no—
421C3×Dic5—41no—
422C5×Dic3—22no—
423C5×Dic3—41no—
424C24×C3—51no—
425C23×D3—51no—
426C23×D3—54no—
427C23×D3—102no—
428C23×D3—102no—
429C23×D3—201no—
430C23×D3—201no—
431C23×D3—201no—
432C23×D3—201no—
433C23×D3C22×D511yescharacteristic
434C23×D3C22×D511yescharacteristic
435C22×C3×C4—51no—
436C22×C3×C4—51no—
437C22×C3×C4—51no—
438C22×C3×C4C22×D511yescharacteristic
439C22×C3×C4C22×D511yescharacteristic
440C22×C3×C4C22×D511yescharacteristic
441C2×#67—54no—
442C2×#67—201no—
443C2×#67—201no—
444C22×Dic3—51no—
445C22×Dic3—51no—
446C22×Dic3—51no—
447C22×Dic3C22×D511yescharacteristic
448C22×Dic3C22×D511yescharacteristic
449C2×D12—22no—
450C2×D12—22no—
451C2×D12—54no—
452C2×D12—201no—
453C2×D12—201no—
454C2×D12C4×D514yes—
455C2×C4×D3—22no—
456C2×C4×D3—41no—
457C2×C4×D3—41no—
458C2×C4×D3—41no—
459C2×C4×D3—41no—
460C2×C4×D3—102no—
461C2×C4×D3—201no—
462C2×C4×D3—201no—
463C2×C4×D3C22⋊D514yescomplemented
464C3×C4⋊C4—22no—
465C3×C22⋊C4—54no—
466C3×C22⋊C4—102no—
467C3×C22⋊C4—201no—
468C3×C42—201no—
469#217—102no—
470#217—201no—
471(C2×D3)⋊C4—22no—
472(C2×D3)⋊C4—22no—
473(C2×D3)⋊C4—54no—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4—102no—
476(C2×D3)⋊C4—102no—
477(C2×D3)⋊C4—102no—
478(C2×D3)⋊C4—201no—
479(C2×D3)⋊C4—201no—
480(C2×D3)⋊C4—201no—
481(C2×D3)⋊C4—201no—
482C4⋊Dic3—201no—
483Dic3⋊C4—201no—
484C4×Dic3—22no—
485C4×Dic3—201no—
486C23×C5—32no—
487C23×C5—32no—
488C23×C5—32no—
489C23×C5—32no—
490C23×C5—61no—
491C23×C5—61no—
492C23×C5—61no—
493C23×C5—61no—
494C23×C5—61no—
495C23×C5—61no—
496C23×C5—61no—
497C23×C5—61no—
498C23×C5—61no—
499C23×C5—61no—
500C23×C5C23×D311yescharacteristic
501C22×D5—21no—
502C22×D5—21no—
503C22×D5—21no—
504C22×D5—21no—
505C22×D5—21no—
506C22×D5—21no—
507C22×D5—32no—
508C22×D5—68no—
509C22×D5—61no—
510C22×D5—61no—
511C22×D5—61no—
512C22×D5—61no—
513C22×D5—61no—
514C22×D5—61no—
515C22×D5—124no—
516C22×D5—124no—
517C22×D5—124no—
518C22×D5—124no—
519C22×D5—124no—
520C22×D5—124no—
521C22×D5C2×C4×D312yes—
522C5×D4—68no—
523C2×C4×C5—21no—
524C2×C4×C5—21no—
525C2×C4×C5—21no—
526C2×C4×C5—21no—
527C2×C4×C5—21no—
528C2×C4×C5—21no—
529C2×C4×C5—21no—
530C2×C4×C5—32no—
531C2×C4×C5—61no—
532C2×C4×C5—61no—
533C2×C4×C5—61no—
534C2×C4×C5—61no—
535C2×C4×C5—61no—
536C2×C4×C5—124no—
537C2×C4×C5—124no—
538C2×C4×C5C2×C4×D312yes—
539C2×C4×C5D3×D412yes—
540C22⋊D5—124no—
541C22⋊D5—124no—
542C2×Dic5—21no—
543C2×Dic5—21no—
544C2×Dic5—21no—
545C2×Dic5—21no—
546C2×Dic5—21no—
547C2×Dic5—21no—
548C2×Dic5—21no—
549C2×Dic5—21no—
550C2×Dic5—32no—
551C2×Dic5—61no—
552C2×Dic5—61no—
553C2×Dic5—61no—
554C2×Dic5—61no—
555C2×Dic5—61no—
556C2×Dic5—61no—
557C2×Dic5—61no—
558C2×Dic5—61no—
559C2×Dic5—124no—
560C2×Dic5C2×C4×D312yes—
561C25—151no—
562C22×D4—31no—
563C22×D4—151no—
564C22×D4—151no—
565C23×C4—31no—
566C23×C4—31no—
567C23×C4—151no—
568#120—158no—
569C4×D4—64no—
570C2×C4⋊C4—151no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4D3×D511yescharacteristic, complemented
573C2×C22⋊C4—31no—
574C2×C22⋊C4—31no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—51no—
578C2×C22⋊C4—151no—
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—31no—
591C2×C42—51no—
592C2×C42—151no—
593#95—51no—
594#95—51no—
595#95—151no—
596#95—151no—
597#95—151no—
598#95—151no—
599C2×C3×C5C2×C4×D411yescharacteristic
600C2×C3×C5#51811yescharacteristic
601C2×C3×C5#51811yescharacteristic
602C2×C3×C5#53411yescharacteristic
603C2×C3×C5#53511yescharacteristic
604C2×C3×C5#53811yescharacteristic
605C2×C3×C5#53811yescharacteristic
606D15—42no—
607C3×D5—42no—
608C5×D3—24no—
609C5×D3—42no—
610C23×C3—52no—
611C23×C3—101no—
612C23×C3—101no—
613C23×C3—101no—
614C23×C3—101no—
615C23×C3—101no—
616C23×C3—101no—
617C23×C3C23×D511yescharacteristic
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—52no—
629C22×D3—101no—
630C22×D3—101no—
631C22×D3—101no—
632C22×D3—101no—
633C22×D3—101no—
634C22×D3—101no—
635C22×D3—108no—
636C22×D3—204no—
637C22×D3—204no—
638C22×D3—204no—
639C22×D3—204no—
640C22×D3—204no—
641C22×D3—204no—
642C22×D3C2×C4×D512yes—
643C22×D3C2×C4×D512yes—
644C22×D3#70912yes—
645C22×D3C2×C22⋊D512yes—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—52no—
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—101no—
662C2×C3×C4C2×C4×D512yes—
663C2×C3×C4C2×C22⋊D512yes—
664#67—204no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—52no—
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×Dic3C2×C22⋊D512yes—
680D12—28no—
681D12—204no—
682C4×D3—44no—
683C4×D3—44no—
684C4×D3—204no—
685C22×C5—34no—
686C22×C5—62no—
687C22×C5—62no—
688C22×C5—62no—
689C22×C5—62no—
690C22×C5—62no—
691C22×C5—62no—
692C22×C5—62no—
693C22×C5—62no—
694C22×C5—62no—
695C22×C5—121no—
696C22×C5—121no—
697C22×C5—121no—
698C22×C5—121no—
699C22×C5C22×C4×D311yescharacteristic
700C22×C5C2×D3×D411yescharacteristic
701C22×C5#100411yescharacteristic
702C22×C5D3×#4111yescharacteristic
703C22×C5#100911yescharacteristic
704C22×C5#100911yescharacteristic
705C22×C5#100911yescharacteristic
706C2×D5—22no—
707C2×D5—22no—
708C2×D5—22no—
709C2×D5—41no—
710C2×D5—41no—
711C2×D5—41no—
712C2×D5—41no—
713C2×D5—62no—
714C2×D5—62no—
715C2×D5—62no—
716C2×D5—1216no—
717C2×D5—121no—
718C2×D5—121no—
719C2×D5—121no—
720C2×D5—121no—
721C4×C5—22no—
722C4×C5—22no—
723C4×C5—41no—
724C4×C5—62no—
725C4×C5—121no—
726Dic5—22no—
727Dic5—41no—
728Dic5—41no—
729Dic5—62no—
730Dic5—121no—
731Dic5—121no—
732C24—31no—
733C24—31no—
734C24—51no—
735C24—154no—
736C24—151no—
737C24—302no—
738C24—302no—
739C24—601no—
740C24—601no—
741C24—601no—
742C24—601no—
743C2×D4—34no—
744C2×D4—62no—
745C2×D4—62no—
746C2×D4—154no—
747C2×D4—154no—
748C2×D4—601no—
749C2×D4—601no—
750C2×D4—601no—
751C2×D4—601no—
752C22×C4—31no—
753C22×C4—34no—
754C22×C4—31no—
755C22×C4—51no—
756C22×C4—51no—
757C22×C4—51no—
758C22×C4—62no—
759C22×C4—121no—
760C22×C4—121no—
761C22×C4—121no—
762C22×C4—121no—
763C22×C4—151no—
764C22×C4—151no—
765C22×C4—151no—
766C22×C4—302no—
767C22×C4—601no—
768C22×C4—601no—
769C22×C4C2×D3×D511yescharacteristic
770C22×C4C2×D3×D511yescharacteristic
771C22×C4C2×D3×D511yescharacteristic
772C4⋊C4—22no—
773C4⋊C4—601no—
774C4⋊C4—601no—
775C22⋊C4—54no—
776C22⋊C4—62no—
777C22⋊C4—62no—
778C22⋊C4—102no—
779C22⋊C4—154no—
780C22⋊C4—154no—
781C22⋊C4—201no—
782C22⋊C4—302no—
783C22⋊C4—302no—
784C22⋊C4—302no—
785C22⋊C4—302no—
786C22⋊C4—601no—
787C22⋊C4—601no—
788C22⋊C4—601no—
789C22⋊C4—601no—
790C22⋊C4—601no—
791C42—62no—
792C42—201no—
793C42—601no—
794C3×C5#232111yescharacteristic, complemented, Hall
795C22×C3—102no—
796C22×C3—102no—
797C22×C3—102no—
798C22×C3—201no—
799C22×C3—201no—
800C22×C3—201no—
801C22×C3—201no—
802C22×C3C22×C4×D511yescharacteristic
803C22×C3C2×#70911yescharacteristic
804C22×C3#414411yescharacteristic
805C22×C3#414411yescharacteristic
806C22×C3#414911yescharacteristic
807C22×C3#414911yescharacteristic
808C22×C3C22×C22⋊D511yescharacteristic
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—41no—
819C2×D3—41no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—102no—
823C2×D3—102no—
824C2×D3—102no—
825C2×D3—2016no—
826C2×D3—201no—
827C2×D3—201no—
828C2×D3—201no—
829C2×D3—201no—
830C2×D3C4×C22⋊D514yes—
831C3×C4—22no—
832C3×C4—22no—
833C3×C4—41no—
834C3×C4—102no—
835C3×C4—201no—
836C3×C4—201no—
837Dic3—22no—
838Dic3—41no—
839Dic3—102no—
840Dic3—201no—
841Dic3—201no—
842C2×C5—64no—
843C2×C5—122no—
844C2×C5#552111yescharacteristic
845C2×C5C4×D3×D411yescharacteristic
846C2×C5#554511yescharacteristic
847C2×C5#560511yescharacteristic
848C2×C5#565711yescharacteristic
849C2×C5#567411yescharacteristic
850C2×C5#570411yescharacteristic
851D5—42no—
852D5—122no—
853C23—32no—
854C23—32no—
855C23—32no—
856C23—32no—
857C23—52no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—61no—
865C23—61no—
866C23—61no—
867C23—61no—
868C23—101no—
869C23—101no—
870C23—101no—
871C23—101no—
872C23—101no—
873C23—101no—
874C23—152no—
875C23—308no—
876C23—301no—
877C23—301no—
878C23—301no—
879C23—301no—
880C23—301no—
881C23—301no—
882C23—604no—
883C23—604no—
884C23—604no—
885C23—604no—
886C23—604no—
887C23—604no—
888C23C22×D3×D511yescharacteristic
889D4—68no—
890D4—604no—
891D4—604no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—32no—
900C2×C4—52no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—101no—
907C2×C4—101no—
908C2×C4—101no—
909C2×C4—101no—
910C2×C4—101no—
911C2×C4—101no—
912C2×C4—101no—
913C2×C4—101no—
914C2×C4—124no—
915C2×C4—124no—
916C2×C4—152no—
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×C4C4×D3×D512yes—
927C2×C4D3×C22⋊D512yes—
928C2×C3—202no—
929C2×C3#6587911yescharacteristic
930C2×C3#6587911yescharacteristic
931C2×C3#6589411yescharacteristic
932C2×C3#6589411yescharacteristic
933C2×C3C2×C4×C22⋊D511yescharacteristic
934C2×C3#6613811yescharacteristic
935C2×C3#6616411yescharacteristic
936D3—24no—
937D3—42no—
938D3—202no—
939C5#7582611yescharacteristic, complemented, Sylow
940C22—34no—
941C22—62no—
942C22—62no—
943C22—62no—
944C22—62no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—102no—
951C22—102no—
952C22—102no—
953C22—121no—
954C22—121no—
955C22—121no—
956C22—121no—
957C22—201no—
958C22—201no—
959C22—201no—
960C22—201no—
961C22—302no—
962C22—302no—
963C22—302no—
964C22—6016no—
965C22—601no—
966C22—601no—
967C22—601no—
968C22—601no—
969C22C2×C4×D3×D511yescharacteristic
970C22D3×#70911yescharacteristic
971C22#9202511yescharacteristic
972C22#9202711yescharacteristic
973C22#9203511yescharacteristic
974C22#9203511yescharacteristic
975C22C2×D3×C22⋊D511yescharacteristic
976C4—22no—
977C4—22no—
978C4—41no—
979C4—62no—
980C4—102no—
981C4—121no—
982C4—201no—
983C4—201no—
984C4—302no—
985C4—601no—
986C4—601no—
987C3#1061412611yescharacteristic, complemented, Sylow
988C2—64no—
989C2—122no—
990C2—202no—
991C2—602no—
992C2#1175383711yescharacteristic
993C2#1175384111yescharacteristic
994C2#1175391711yescharacteristic
995C2#1175391811yescharacteristic
996C2C4×D3×C22⋊D511yescharacteristic
997C2#1175506711yescharacteristic
998C2#1175527911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91475C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2321
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#893C2semidirect
3. C2×D3×#685C2semidirect
4. #11751091C2semidirect
5. C3×#65279C2semidirect
6. #11748940C2semidirect
7. #11748915C2semidirect
8. #11748914C2semidirect
9. #11748910C2semidirect
10. #11748908C2semidirect
11. #11748901C2semidirect
12. #11748893C2semidirect
13. #11748854C2semidirect
14. #11748770C2semidirect
15. C4×(C2×D3)⋊Dic5C2semidirect
20. C22×C4×C5×D3C22semidirect
24. C2×C3×C5×C4⋊C4C22semidirect
28. C2×C4×Dic15C22semidirect
30. C2×C5×(C2×D3)⋊C4C22semidirect
31. C2×C4×C5×Dic3C22semidirect
36. C2×C3×C4×Dic5C22semidirect
37. C2×#6669C22semidirect
38. C2×#6668C22semidirect
43. C2×(C2×D3)⋊Dic5C22semidirect
44. C2×(C2×D3)⋊Dic5C22semidirect
47. #91475C4semidirect
49. #91115C22semidirect
50. #91115C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
64. #65279D3semidirect
81. C22×D3×D5C2×C4semidirect
98. C2×C4×C5×D3D4semidirect
104. C2×#1203C2×C4semidirect
107. C2×#1201C2×C4semidirect
114. #6714C2×C4semidirect
121. C3×#685C2×C4semidirect
130. (C2×D3)⋊Dic5C2×C4semidirect
133. C2×#893D5semidirect
156. C2×C5×C4⋊C4C2×D3semidirect
179. C2×C4×Dic5C2×D3semidirect
184. #3963C2×D3semidirect
185. #3963C2×D3semidirect
268. C22×C4×D3C2×D5semidirect
269. C2×C3×C4⋊C4C2×D5semidirect
286. C2×(C2×D3)⋊C4C2×D5semidirect
290. C2×C4×Dic3C2×D5semidirect
357. #685C4×D3semidirect
463. C2×C4×D3C22⋊D5semidirect
572. C2×C4⋊C4D3×D5semidirect
794. C3×C5#2321semidirect
939. C5#75826semidirect
987. C3#10614126semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8932
C2×#914752
C2×D3×#6852
#117510912
C3×#652792
#117489402
#117489152
#117489142
#117489102
#117489082
#117489012
#117488932
#117488542
#117487702
C4×(C2×D3)⋊Dic52
#106141263
#758265