Finite Group Databasebeta

← #14323381

Subgroups — #14323381

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×#91782C211yesmaximal, characteristic, complemented
2C2×#91476C211yesmaximal, characteristic
3C2×#91473C211yesmaximal, characteristic, complemented
4C5×#4990C211yesmaximal, characteristic, complemented
5C3×#65279C211yesmaximal, characteristic, complemented
6#11748940C211yesmaximal, characteristic, complemented
7#11748918C211yesmaximal, characteristic, complemented
8#11748917C211yesmaximal, characteristic, complemented
9#11748912C211yesmaximal, characteristic, complemented
10#11748908C211yesmaximal, characteristic, complemented
11#11748904C211yesmaximal, characteristic, complemented
12#11748895C211yesmaximal, characteristic, complemented
13#11748794C211yesmaximal, characteristic, complemented
14#11748791C211yesmaximal, characteristic, complemented
15C4×#6667C211yesmaximal, characteristic, complemented
16#10607557—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic, complemented
21C22×#1203C2211yescharacteristic
22C22×#1202C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic, complemented
27C2×C4×Dic15C2211yescharacteristic, complemented
28#91782—24no—
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C4×C5×Dic3C2211yescharacteristic, complemented
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×C4×Dic5C2211yescharacteristic, complemented
37C2×Dic3⋊Dic5C2211yescharacteristic, complemented
38C2×#6668C2211yescharacteristic, complemented
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic, complemented
42C2×#6667C2211yescharacteristic, complemented
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47#91476C418yescomplemented
48#91473—24no—
49C5×C3⋊#95C2211yescharacteristic, complemented
50C5×C3⋊#95C2211yescharacteristic, complemented
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#75826—51nomaximal, Hall
56C2×#4039—31no—
57C2×#4028—31no—
58C2×D5×C22⋊C4—31no—
59C5×#388—31no—
60#65279D311yescharacteristic, complemented
61#65246—31no—
62#65245—31no—
63#65244—31no—
64#65240—31no—
65#65228—31no—
66C4×#685—31no—
67#64958—31no—
68#64957—31no—
69#64954—31no—
70#64954—31no—
71C23×D15C2311yescharacteristic
72C23×D15C2311yescharacteristic
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
87C2×D60—22no—
88C2×D60—22no—
89C2×D60C2×C414yes—
90C2×C4×D15—22no—
91C2×C4×D15—41no—
92C2×C4×D15—41no—
93C2×C4×D15—41no—
94C2×C4×D15—41no—
95C2×C4×D15D414yescomplemented
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C2×#1203—41no—
103C2×#1203—41no—
104C2×#1203C2×C414yescomplemented
105C2×#1202—41no—
106C2×#1202—41no—
107C2×#1202C2×C414yescomplemented
108C2×#1200—22no—
109C2×#1200—41no—
110C2×#1200—41no—
111C3×C5×C4⋊C4—22no—
112#6714—22no—
113#6714—22no—
114C4×Dic15—22no—
115C5×(C2×D3)⋊C4—22no—
116C5×(C2×D3)⋊C4—41no—
117C5×(C2×D3)⋊C4C2×C414yescomplemented
118C4×C5×Dic3—41no—
119C3×#685—22no—
120C3×#685—41no—
121C3×#685C2×C414yescomplemented
122C3×C4×Dic5—41no—
123Dic3⋊Dic5—41no—
124#6668—41no—
125#6667—22no—
126#6667—41no—
127#6667—41no—
128#6667C2×C414yescomplemented
129(C2×D3)⋊Dic5—22no—
130(C2×D3)⋊Dic5—41no—
131#6665—22no—
132#6665—41no—
133C2×#893—51no—
134C2×#882—51no—
135C2×D3×C22⋊C4—51no—
136C3×#388—51no—
137#4990D511yescharacteristic, complemented
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×C22⋊D5—31no—
150C22×D20—31no—
151C22×D20—31no—
152C22×C4×D5—31no—
153C22×C4×D5—31no—
154C22×C4×D5—31no—
155C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
156C2×C5×C22⋊C4—31no—
157C2×C5×C22⋊C4—31no—
158C2×C5×C22⋊C4—31no—
159C2×C42×C5—31no—
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685C2×D311yescharacteristic
171C2×#685C2×D311yescharacteristic
172C2×#685C2×D311yescharacteristic
173C2×C4⋊Dic5—31no—
174C2×#683—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5C2×D311yescharacteristic, complemented
177#4039—64no—
178#4028—38no—
179D5×C22⋊C4—64no—
180C5×#95—31no—
181C5×#95—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×D15—21no—
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—21no—
198C22×D15C22×C412yes—
199C22×D15C22×C412yes—
200C22×D15C2×D412yes—
201C22×D15#4112yes—
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×D3C22×C412yes—
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×Dic15C2×D412yes—
238D60—28no—
239C4×D15—44no—
240C4×D15—44no—
241C2×C5×Dic3—21no—
242C2×C5×Dic3—21no—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3—21no—
247C2×C5×Dic3—21no—
248C2×C5×Dic3—21no—
249C2×C5×Dic3C22×C412yes—
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#1202—44no—
261#1200—44no—
262C24×D3—51no—
263C22×#67—51no—
264C22×D12—51no—
265C22×D12—51no—
266C22×C4×D3—51no—
267C22×C4×D3—51no—
268C22×C4×D3—51no—
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)⋊C4C2×D511yescharacteristic
285C2×(C2×D3)⋊C4C2×D511yescharacteristic
286C2×(C2×D3)⋊C4C2×D511yescharacteristic
287C2×C4⋊Dic3—51no—
288C2×Dic3⋊C4—51no—
289C2×C4×Dic3—51no—
290C2×C4×Dic3C2×D511yescharacteristic, complemented
291#893—104no—
292#882—58no—
293D3×C22⋊C4—104no—
294C3×#95—51no—
295C3×#95—51no—
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95C2×D511yescharacteristic, complemented
299C3⋊#95C2×D511yescharacteristic, complemented
300C24×C5—31no—
301C23×D5—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
311C22×C4×C5—31no—
312C22×C4×C5—31no—
313C22×C4×C5—31no—
314C22×C4×C5C22×D311yescharacteristic
315C22×C4×C5C22×D311yescharacteristic
316C22×C4×C5C22×D311yescharacteristic
317C2×C22⋊D5—34no—
318C2×C22⋊D5—121no—
319C2×C22⋊D5—121no—
320C22×Dic5—31no—
321C22×Dic5—31no—
322C22×Dic5C22×D311yescharacteristic
323C22×Dic5C22×D311yescharacteristic
324C22×Dic5C22×D311yescharacteristic
325C2×D20—34no—
326C2×D20—34no—
327C2×D20—62no—
328C2×D20—62no—
329C2×D20—121no—
330C2×D20—121no—
331C2×C4×D5—34no—
332C2×C4×D5—62no—
333C2×C4×D5—62no—
334C2×C4×D5—121no—
335C2×C4×D5—121no—
336C2×C4×D5—121no—
337C2×C4×D5—121no—
338C2×C4×D5—121no—
339C2×C4×D5—121no—
340C5×C4⋊C4—22no—
341C5×C22⋊C4—34no—
342C5×C22⋊C4—62no—
343C5×C22⋊C4—121no—
344C42×C5—121no—
345C22⋊Dic5—62no—
346C22⋊Dic5—121no—
347#685—22no—
348#685—34no—
349#685—41no—
350#685—62no—
351#685—62no—
352#685—62no—
353#685—62no—
354#685—121no—
355#685—121no—
356#685—121no—
357#685C4×D314yescomplemented
358C4⋊Dic5—121no—
359#683—121no—
360C4×Dic5—41no—
361C4×Dic5—62no—
362C2×#120—151no—
363C2×C4×D4—151no—
364C22×C22⋊C4—151no—
365#390—151no—
366#390—151no—
367#388—31no—
368#388—51no—
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—22no—
388C2×D15—22no—
389C2×D15—22no—
390C2×D15—22no—
391C2×D15—22no—
392C2×D15—22no—
393C2×D15—41no—
394C2×D15—41no—
395C2×D15—41no—
396C2×D15—41no—
397C2×D15C4×D414yes—
398C2×C5×D3—22no—
399C2×C5×D3—22no—
400C2×C5×D3—22no—
401C2×C5×D3—41no—
402C2×C5×D3—41no—
403C2×C5×D3—41no—
404C2×C5×D3—41no—
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—
418C3×Dic5—22no—
419C3×Dic5—41no—
420C3×Dic5—41no—
421C5×Dic3—22no—
422C5×Dic3—41no—
423C5×Dic3—41no—
424C24×C3—51no—
425C23×D3—51no—
426C23×D3—51no—
427C23×D3—54no—
428C23×D3—102no—
429C23×D3—102no—
430C23×D3—201no—
431C23×D3—201no—
432C23×D3—201no—
433C23×D3—201no—
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×Dic3C22×D511yescharacteristic
447C22×Dic3C22×D511yescharacteristic
448C22×Dic3C22×D511yescharacteristic
449C2×D12—54no—
450C2×D12—54no—
451C2×D12—102no—
452C2×D12—102no—
453C2×D12—201no—
454C2×D12—201no—
455C2×C4×D3—54no—
456C2×C4×D3—102no—
457C2×C4×D3—102no—
458C2×C4×D3—201no—
459C2×C4×D3—201no—
460C2×C4×D3—201no—
461C2×C4×D3—201no—
462C2×C4×D3—201no—
463C2×C4×D3—201no—
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—41no—
473(C2×D3)⋊C4—54no—
474(C2×D3)⋊C4—102no—
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)⋊C4C4×D514yescomplemented
482C4⋊Dic3—201no—
483Dic3⋊C4—201no—
484C4×Dic3—41no—
485C4×Dic3—102no—
486C23×C5—32no—
487C23×C5—61no—
488C23×C5—61no—
489C23×C5—61no—
490C23×C5—61no—
491C23×C5—61no—
492C23×C5—61no—
493C23×C5C23×D311yescharacteristic
494C22×D5—21no—
495C22×D5—21no—
496C22×D5—21no—
497C22×D5—21no—
498C22×D5—21no—
499C22×D5—21no—
500C22×D5—32no—
501C22×D5—32no—
502C22×D5—32no—
503C22×D5—32no—
504C22×D5—68no—
505C22×D5—61no—
506C22×D5—61no—
507C22×D5—61no—
508C22×D5—61no—
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—
522C2×C4×C5—21no—
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—32no—
530C2×C4×C5—61no—
531C2×C4×C5—61no—
532C2×C4×C5—61no—
533C2×C4×C5—61no—
534C2×C4×C5—61no—
535C2×C4×C5—61no—
536C2×C4×C5—61no—
537C2×C4×C5—61no—
538C2×C4×C5C2×C4×D312yes—
539C2×C4×C5D3×D412yes—
540C22⋊D5—124no—
541C2×Dic5—21no—
542C2×Dic5—21no—
543C2×Dic5—21no—
544C2×Dic5—21no—
545C2×Dic5—21no—
546C2×Dic5—21no—
547C2×Dic5—21no—
548C2×Dic5—21no—
549C2×Dic5—32no—
550C2×Dic5—61no—
551C2×Dic5—61no—
552C2×Dic5—61no—
553C2×Dic5—61no—
554C2×Dic5—61no—
555C2×Dic5C2×C4×D312yes—
556D20—68no—
557D20—124no—
558C4×D5—124no—
559C4×D5—124no—
560C4×D5—124no—
561C25—151no—
562C22×D4—151no—
563C22×D4—151no—
564C22×D4—151no—
565C23×C4—151no—
566C23×C4—151no—
567C23×C4—151no—
568#120—158no—
569C4×D4—304no—
570C2×C4⋊C4—151no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4D3×D511yescharacteristic, complemented
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—31no—
591C2×C42—51no—
592C2×C42—151no—
593#95—31no—
594#95—31no—
595#95—51no—
596#95—51no—
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—24no—
607D15—42no—
608C3×D5—42no—
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—52no—
625C22×D3—52no—
626C22×D3—52no—
627C22×D3—52no—
628C22×D3—108no—
629C22×D3—101no—
630C22×D3—101no—
631C22×D3—101no—
632C22×D3—101no—
633C22×D3—101no—
634C22×D3—101no—
635C22×D3—101no—
636C22×D3—101no—
637C22×D3—101no—
638C22×D3—101no—
639C22×D3—204no—
640C22×D3—204no—
641C22×D3—204no—
642C22×D3—204no—
643C22×D3—204no—
644C22×D3—204no—
645C22×D3C2×C4×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×C4D4×D512yes—
664#67—204no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—52no—
674C2×Dic3—101no—
675C2×Dic3—101no—
676C2×Dic3—101no—
677C2×Dic3—101no—
678C2×Dic3—101no—
679C2×Dic3C2×C4×D512yes—
680D12—108no—
681D12—204no—
682C4×D3—204no—
683C4×D3—204no—
684C4×D3—204no—
685C22×C5—62no—
686C22×C5—62no—
687C22×C5—62no—
688C22×C5—121no—
689C22×C5—121no—
690C22×C5—121no—
691C22×C5—121no—
692C22×C5C22×C4×D311yescharacteristic
693C22×C5C2×D3×D411yescharacteristic
694C22×C5#100411yescharacteristic
695C22×C5D3×#4111yescharacteristic
696C22×C5#100911yescharacteristic
697C22×C5#100911yescharacteristic
698C22×C5#100911yescharacteristic
699C2×D5—22no—
700C2×D5—22no—
701C2×D5—22no—
702C2×D5—34no—
703C2×D5—41no—
704C2×D5—41no—
705C2×D5—41no—
706C2×D5—41no—
707C2×D5—62no—
708C2×D5—62no—
709C2×D5—62no—
710C2×D5—62no—
711C2×D5—62no—
712C2×D5—62no—
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—
726C4×C5—121no—
727Dic5—22no—
728Dic5—41no—
729Dic5—41no—
730Dic5—62no—
731Dic5—121no—
732C24—31no—
733C24—51no—
734C24—154no—
735C24—151no—
736C24—151no—
737C24—302no—
738C24—302no—
739C24—601no—
740C24—601no—
741C24—601no—
742C24—601no—
743C2×D4—154no—
744C2×D4—154no—
745C2×D4—154no—
746C2×D4—302no—
747C2×D4—302no—
748C2×D4—601no—
749C2×D4—601no—
750C2×D4—601no—
751C2×D4—601no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—51no—
756C22×C4—51no—
757C22×C4—51no—
758C22×C4—151no—
759C22×C4—154no—
760C22×C4—151no—
761C22×C4—302no—
762C22×C4—302no—
763C22×C4—601no—
764C22×C4—601no—
765C22×C4—601no—
766C22×C4—601no—
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—34no—
776C22⋊C4—54no—
777C22⋊C4—62no—
778C22⋊C4—102no—
779C22⋊C4—121no—
780C22⋊C4—154no—
781C22⋊C4—201no—
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—121no—
792C42—201no—
793C42—302no—
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×D4×D511yescharacteristic
804C22×C3#414411yescharacteristic
805C22×C3D5×#4111yescharacteristic
806C22×C3#414911yescharacteristic
807C22×C3#414911yescharacteristic
808C22×C3#414911yescharacteristic
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—54no—
817C2×D3—102no—
818C2×D3—102no—
819C2×D3—102no—
820C2×D3—102no—
821C2×D3—102no—
822C2×D3—102no—
823C2×D3—102no—
824C2×D3—102no—
825C2×D3—102no—
826C2×D3—2016no—
827C2×D3—201no—
828C2×D3—201no—
829C2×D3—201no—
830C2×D3—201no—
831C3×C4—22no—
832C3×C4—22no—
833C3×C4—41no—
834C3×C4—102no—
835C3×C4—201no—
836C3×C4—201no—
837Dic3—22no—
838Dic3—41no—
839Dic3—41no—
840Dic3—102no—
841Dic3—201no—
842C2×C5—122no—
843C2×C5#552111yescharacteristic
844C2×C5C4×D3×D411yescharacteristic
845C2×C5#554511yescharacteristic
846C2×C5#560511yescharacteristic
847C2×C5#565711yescharacteristic
848C2×C5#567411yescharacteristic
849C2×C5#570411yescharacteristic
850D5—42no—
851D5—64no—
852D5—122no—
853C23—32no—
854C23—52no—
855C23—61no—
856C23—61no—
857C23—61no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—101no—
862C23—101no—
863C23—101no—
864C23—101no—
865C23—101no—
866C23—101no—
867C23—152no—
868C23—152no—
869C23—152no—
870C23—152no—
871C23—308no—
872C23—301no—
873C23—301no—
874C23—301no—
875C23—301no—
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—308no—
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—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—101no—
910C2×C4—101no—
911C2×C4—101no—
912C2×C4—101no—
913C2×C4—101no—
914C2×C4—101no—
915C2×C4—101no—
916C2×C4—101no—
917C2×C4—152no—
918C2×C4—301no—
919C2×C4—301no—
920C2×C4—301no—
921C2×C4—301no—
922C2×C4—301no—
923C2×C4—604no—
924C2×C4—604no—
925C2×C4—604no—
926C2×C4C4×D3×D512yes—
927C2×C4#679012yes—
928C2×C3—202no—
929C2×C3#6585511yescharacteristic
930C2×C3C4×D4×D511yescharacteristic
931C2×C3#6587911yescharacteristic
932C2×C3#6593911yescharacteristic
933C2×C3#6599111yescharacteristic
934C2×C3#6600811yescharacteristic
935C2×C3#6603811yescharacteristic
936D3—42no—
937D3—104no—
938D3—202no—
939C5#7582611yescharacteristic, complemented, Sylow
940C22—62no—
941C22—62no—
942C22—62no—
943C22—102no—
944C22—102no—
945C22—102no—
946C22—121no—
947C22—121no—
948C22—121no—
949C22—121no—
950C22—154no—
951C22—201no—
952C22—201no—
953C22—201no—
954C22—201no—
955C22—302no—
956C22—302no—
957C22—302no—
958C22—302no—
959C22—302no—
960C22—302no—
961C22—302no—
962C22—302no—
963C22—302no—
964C22—6016no—
965C22—601no—
966C22—601no—
967C22—601no—
968C22—601no—
969C22C2×C4×D3×D511yescharacteristic
970C22#9201611yescharacteristic
971C22#9202611yescharacteristic
972C22#9202711yescharacteristic
973C22#9203511yescharacteristic
974C22#9203511yescharacteristic
975C22C2×#679011yescharacteristic
976C4—22no—
977C4—22no—
978C4—41no—
979C4—62no—
980C4—102no—
981C4—121no—
982C4—121no—
983C4—201no—
984C4—201no—
985C4—302no—
986C4—601no—
987C3#1060755711yescharacteristic, complemented, Sylow
988C2—122no—
989C2—202no—
990C2—304no—
991C2—602no—
992C2#1175383711yescharacteristic
993C2#1175383911yescharacteristic
994C2#1175393211yescharacteristic
995C2#1175393311yescharacteristic
996C2C4×#679011yescharacteristic
997C2#1175507311yescharacteristic
998C2#1175528611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91476C2
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×#91782C2semidirect
3. C2×#91473C2semidirect
4. C5×#4990C2semidirect
5. C3×#65279C2semidirect
6. #11748940C2semidirect
7. #11748918C2semidirect
8. #11748917C2semidirect
9. #11748912C2semidirect
10. #11748908C2semidirect
11. #11748904C2semidirect
12. #11748895C2semidirect
13. #11748794C2semidirect
14. #11748791C2semidirect
15. C4×#6667C2semidirect
20. C22×C4×D15C22semidirect
24. C2×C3×C5×C4⋊C4C22semidirect
26. C2×#6714C22semidirect
27. C2×C4×Dic15C22semidirect
32. C2×C4×C5×Dic3C22semidirect
36. C2×C3×C4×Dic5C22semidirect
37. C2×Dic3⋊Dic5C22semidirect
38. C2×#6668C22semidirect
41. C2×#6667C22semidirect
42. C2×#6667C22semidirect
47. #91476C4semidirect
49. C5×C3⋊#95C22semidirect
50. C5×C3⋊#95C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
60. #65279D3semidirect
81. C22×D3×D5C2×C4semidirect
95. C2×C4×D15D4semidirect
104. C2×#1203C2×C4semidirect
107. C2×#1202C2×C4semidirect
117. C5×(C2×D3)⋊C4C2×C4semidirect
121. C3×#685C2×C4semidirect
128. #6667C2×C4semidirect
137. #4990D5semidirect
155. C2×C5×C4⋊C4C2×D3semidirect
176. C2×C4×Dic5C2×D3semidirect
184. #3963C2×D3semidirect
185. #3963C2×D3semidirect
269. C2×C3×C4⋊C4C2×D5semidirect
290. C2×C4×Dic3C2×D5semidirect
298. C3⋊#95C2×D5semidirect
299. C3⋊#95C2×D5semidirect
357. #685C4×D3semidirect
481. (C2×D3)⋊C4C4×D5semidirect
572. C2×C4⋊C4D3×D5semidirect
794. C3×C5#2321semidirect
939. C5#75826semidirect
987. C3#10607557semidirect

Maximal subgroups

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

subgroupindex
C2×#917822
C2×#914762
C2×#914732
C5×#49902
C3×#652792
#117489402
#117489182
#117489172
#117489122
#117489082
#117489042
#117488952
#117487942
#117487912
C4×#66672
#106075573
#758265