Finite Group Databasebeta

← #14323426

Subgroups — #14323426

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×#91826C211yesmaximal, characteristic
2C2×#91561C211yesmaximal, characteristic, complemented
3C2×#91556C211yesmaximal, characteristic, complemented
4C5×#5220C211yesmaximal, characteristic, complemented
5C3×#65510C211yesmaximal, characteristic, complemented
6#11749520C211yesmaximal, characteristic, complemented
7#11749502C211yesmaximal, characteristic, complemented
8#11749498C211yesmaximal, characteristic, complemented
9#11749483C211yesmaximal, characteristic, complemented
10#11749480C211yesmaximal, characteristic, complemented
11#11749480C211yesmaximal, characteristic, complemented
12#11748898C211yesmaximal, characteristic, complemented
13#11748875C211yesmaximal, characteristic, complemented
14#11748829C211yesmaximal, characteristic, complemented
15#11748678C211yesmaximal, characteristic, complemented
16#10606607—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C23×C5×Dic3C2211yescharacteristic, complemented
22C22×#1200C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25#91826C418yescomplemented
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C2×C5×#217C2211yescharacteristic
30C2×C5×#217C2211yescharacteristic, complemented
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
34C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
35C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
36C2×C3×C4×Dic5C2211yescharacteristic, complemented
37#91561—24no—
38#91556—24no—
39C2×#6669C2211yescharacteristic, complemented
40C2×#6669C2211yescharacteristic, complemented
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×#6667C2211yescharacteristic
46C2×#6667C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic, complemented
48C2×Dic3×Dic5C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C5×C3⋊#95C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#76429—51nomaximal, Hall
56C2×#4083—31no—
57C2×C4×C22⋊D5—31no—
58C2×D5×C22⋊C4—31no—
59C5×#386—31no—
60#65510D311yescharacteristic, complemented
61#65502—31no—
62#65246—31no—
63#65245—31no—
64#65244—31no—
65#65233—31no—
66#65233—31no—
67#64959—31no—
68#64958—31no—
69#64957—31no—
70#64955—31no—
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×D15—22no—
74C23×D15—22no—
75C23×D15—41no—
76C23×D15—41no—
77C23×D15—41no—
78C23×D15—41no—
79C23×D15C2×C414yescomplemented
80C23×D15C2311yescharacteristic
81C23×D15C2311yescharacteristic
82C2×C3×C5×D4—41no—
83C2×C3×C5×D4—41no—
84C2×C3×C5×D4C2×C414yescomplemented
85C22×C3×C4×C5C2311yescharacteristic
86C2×#1220—22no—
87C2×#1220—22no—
88C2×#1220—41no—
89C2×#1220—41no—
90C2×#1220C2×C414yes—
91C2×#1220C2×C414yescomplemented
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×C5×Dic3—22no—
95C22×C5×Dic3—41no—
96C22×C5×Dic3—41no—
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C2×#1200—22no—
106C2×#1200—41no—
107C2×#1200—41no—
108C2×#1200—41no—
109C2×#1200—41no—
110C2×#1200D414yescomplemented
111#6719C2×C414yescomplemented
112#6714C2×C414yescomplemented
113#6714C2×C414yescomplemented
114C5×#217—22no—
115C5×#217—41no—
116C5×#217—41no—
117C3×C22⋊Dic5—22no—
118C3×C22⋊Dic5—22no—
119C3×C22⋊Dic5—41no—
120C3×C22⋊Dic5—41no—
121C3×C4⋊Dic5—41no—
122C3×C4×Dic5—41no—
123#6669—22no—
124#6669—41no—
125#6667—22no—
126#6667—22no—
127#6667—22no—
128#6667—22no—
129#6667—41no—
130#6667—41no—
131Dic3×Dic5—22no—
132Dic3×Dic5—41no—
133C2×#937—51no—
134C2×#67⋊C4—51no—
135C2×D3×C22⋊C4—51no—
136C3×#390—51no—
137#5220D511yescharacteristic, complemented
138#4990—51no—
139#4989—51no—
140#4958—51no—
141#4957—51no—
142#4956—51no—
143#4955—51no—
144#4945—51no—
145#4945—51no—
146#4940—51no—
147C4×(C2×D3)⋊C4—51no—
148C24×D5—31no—
149C22×C5×D4C2×D311yescharacteristic
150C23×C4×C5—31no—
151C22×C22⋊D5—31no—
152C22×C22⋊D5—31no—
153C22×C4×D5—31no—
154C22×C4×D5—31no—
155C2×C5×C22⋊C4—31no—
156C2×C5×C22⋊C4—31no—
157C2×C5×C22⋊C4—31no—
158C2×C22⋊Dic5—31no—
159C2×C22⋊Dic5C2×D311yescharacteristic
160C2×C22⋊Dic5C2×D311yescharacteristic
161C2×C22⋊Dic5C2×D311yescharacteristic, complemented
162C2×C22⋊Dic5C2×D311yescharacteristic, complemented
163#4083—38no—
164C4×C22⋊D5—64no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#685—31no—
173C2×C4⋊Dic5C2×D311yescharacteristic, complemented
174C2×#683—31no—
175C2×#683—31no—
176C2×C4×Dic5—31no—
177C2×C4×Dic5—31no—
178C2×C4×Dic5C2×D311yescharacteristic, complemented
179D5×C22⋊C4—64no—
180C5×#95—31no—
181C5×#95—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
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×D15—21no—
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—21no—
209C22×D15—21no—
210C22×D15—21no—
211C22×D15—21no—
212C22×D15—28no—
213C22×D15—44no—
214C22×D15—44no—
215C22×D15—44no—
216C22×D15—44no—
217C22×D15—44no—
218C22×D15—44no—
219C22×D15C22×C412yes—
220C22×D15C22×C412yes—
221C22×D15C2×D412yes—
222C22×D15#4112yes—
223C3×C5×D4—44no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5C22×C412yes—
227#1220—28no—
228#1220—44no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15C22×C412yes—
234C2×Dic15C22×C412yes—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3—21no—
240C2×C5×Dic3—21no—
241C2×C5×Dic3—21no—
242C2×C5×Dic3—21no—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3—44no—
247C2×C5×Dic3C2×D412yes—
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—21no—
259C2×C3×Dic5C2×D412yes—
260#1200—44no—
261#1200—44no—
262C24×D3—51no—
263C22×C3×D4C2×D511yescharacteristic
264C22×#67—51no—
265C22×#67—51no—
266C23×Dic3C2×D511yescharacteristic, complemented
267C22×C4×D3—51no—
268C22×C4×D3—51no—
269C2×C3×C4⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4—51no—
272C2×C3×C22⋊C4—51no—
273C2×C3×C22⋊C4—51no—
274C2×C3×C42—51no—
275C2×#217—51no—
276C2×#217C2×D511yescharacteristic
277C2×#217C2×D511yescharacteristic
278C2×#217C2×D511yescharacteristic, complemented
279#937—58no—
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)⋊C4—51no—
286C2×(C2×D3)⋊C4—51no—
287C2×(C2×D3)⋊C4—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4—51no—
290C2×C4×Dic3—51no—
291C2×C4×Dic3—51no—
292#67⋊C4—104no—
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×C5C22×D311yescharacteristic
301C24×C5C22×D311yescharacteristic
302C23×D5—31no—
303C23×D5—31no—
304C23×D5—34no—
305C23×D5—62no—
306C23×D5—62no—
307C23×D5—121no—
308C23×D5—121no—
309C23×D5—121no—
310C23×D5—121no—
311C2×C5×D4—41no—
312C2×C5×D4—41no—
313C2×C5×D4C4×D314yescomplemented
314C22×C4×C5—31no—
315C22×C4×C5—31no—
316C22×C4×C5—31no—
317C22×C4×C5—31no—
318C22×C4×C5—62no—
319C22×C4×C5—121no—
320C22×C4×C5—121no—
321C22×C4×C5C22×D311yescharacteristic
322C2×C22⋊D5—34no—
323C2×C22⋊D5—34no—
324C2×C22⋊D5—62no—
325C2×C22⋊D5—62no—
326C2×C22⋊D5—121no—
327C2×C22⋊D5—121no—
328C22×Dic5—31no—
329C22×Dic5—31no—
330C22×Dic5C22×D311yescharacteristic
331C22×Dic5C22×D311yescharacteristic
332C22×Dic5C22×D311yescharacteristic
333C22×Dic5C22×D311yescharacteristic
334C2×C4×D5—34no—
335C2×C4×D5—62no—
336C2×C4×D5—121no—
337C2×C4×D5—121no—
338C2×C4×D5—121no—
339C2×C4×D5—121no—
340C5×C22⋊C4—62no—
341C5×C22⋊C4—121no—
342C5×C22⋊C4—121no—
343C22⋊Dic5—22no—
344C22⋊Dic5—22no—
345C22⋊Dic5—34no—
346C22⋊Dic5—41no—
347C22⋊Dic5—41no—
348#685—34no—
349#685—34no—
350#685—62no—
351#685—62no—
352#685—62no—
353#685—62no—
354#685—121no—
355#685—121no—
356C4⋊Dic5—41no—
357#683—62no—
358#683—121no—
359C4×Dic5—41no—
360C4×Dic5—62no—
361C4×Dic5—121no—
362C2×#120—151no—
363C2×C4×D4—151no—
364C22×C22⋊C4—151no—
365#390—51no—
366#390—151no—
367#388—151no—
368#388—151no—
369#388—151no—
370#388—151no—
371#386—31no—
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×D15—22no—
399C2×D15—22no—
400C2×D15—22no—
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—22no—
405C2×D15—22no—
406C2×D15—22no—
407C2×D15—416no—
408C2×D15—41no—
409C2×D15—41no—
410C2×D15—41no—
411C2×D15—41no—
412C2×D15C4×D414yes—
413C3×C4×C5—22no—
414Dic15—22no—
415Dic15—22no—
416C3×Dic5—22no—
417C3×Dic5—41no—
418C3×Dic5—41no—
419C3×Dic5—41no—
420C5×Dic3—22no—
421C5×Dic3—41no—
422C5×Dic3—41no—
423C5×Dic3—41no—
424C24×C3C22×D511yescharacteristic
425C24×C3C22×D511yescharacteristic
426C23×D3—51no—
427C23×D3—51no—
428C23×D3—54no—
429C23×D3—102no—
430C23×D3—102no—
431C23×D3—201no—
432C23×D3—201no—
433C23×D3—201no—
434C23×D3—201no—
435C2×C3×D4—41no—
436C2×C3×D4—41no—
437C2×C3×D4C4×D514yescomplemented
438C22×C3×C4—51no—
439C22×C3×C4—51no—
440C22×C3×C4—51no—
441C22×C3×C4—51no—
442C22×C3×C4C22×D511yescharacteristic
443C2×#67—54no—
444C2×#67—54no—
445C2×#67—102no—
446C2×#67—102no—
447C2×#67—201no—
448C2×#67—201no—
449C22×Dic3—22no—
450C22×Dic3—41no—
451C22×Dic3—41no—
452C22×Dic3—51no—
453C22×Dic3—51no—
454C22×Dic3C22×D511yescharacteristic
455C22×Dic3C22×D511yescharacteristic
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×C4⋊C4—201no—
465C3×C22⋊C4—102no—
466C3×C22⋊C4—102no—
467C3×C22⋊C4—201no—
468C3×C22⋊C4—201no—
469C3×C42—201no—
470#217—22no—
471#217—41no—
472#217—41no—
473#217—54no—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4—54no—
476(C2×D3)⋊C4—102no—
477(C2×D3)⋊C4—102no—
478(C2×D3)⋊C4—102no—
479(C2×D3)⋊C4—102no—
480(C2×D3)⋊C4—201no—
481(C2×D3)⋊C4—201no—
482Dic3⋊C4—102no—
483Dic3⋊C4—201no—
484C4×Dic3—102no—
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×C5C2×C4×D312yes—
499C23×C5C2×C4×D312yes—
500C23×C5C23×D311yescharacteristic
501C22×D5—32no—
502C22×D5—32no—
503C22×D5—32no—
504C22×D5—32no—
505C22×D5—68no—
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—61no—
516C22×D5—124no—
517C22×D5—124no—
518C22×D5—124no—
519C22×D5—124no—
520C22×D5—124no—
521C22×D5—124no—
522C5×D4—44no—
523C2×C4×C5—21no—
524C2×C4×C5—21no—
525C2×C4×C5—32no—
526C2×C4×C5—61no—
527C2×C4×C5—61no—
528C2×C4×C5—61no—
529C2×C4×C5—61no—
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—124no—
538C2×C4×C5C2×C4×D312yes—
539C22⋊D5—68no—
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—21no—
550C2×Dic5—21no—
551C2×Dic5—21no—
552C2×Dic5—32no—
553C2×Dic5—32no—
554C2×Dic5—61no—
555C2×Dic5—61no—
556C2×Dic5—61no—
557C2×Dic5—61no—
558C2×Dic5D3×D412yes—
559C4×D5—124no—
560C4×D5—124no—
561C25—151no—
562C22×D4—151no—
563C22×D4—151no—
564C22×D4D3×D511yescharacteristic
565C23×C4—31no—
566C23×C4—151no—
567C23×C4—151no—
568#120—158no—
569C4×D4—304no—
570C2×C4⋊C4—51no—
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—51no—
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—51no—
591C2×C42—151no—
592C2×C42—151no—
593#95—31no—
594#95—31no—
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
608D15—24no—
609D15—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×C3C2×C4×D512yes—
623C23×C3C2×C4×D512yes—
624C23×C3C23×D511yescharacteristic
625C22×D3—52no—
626C22×D3—52no—
627C22×D3—52no—
628C22×D3—52no—
629C22×D3—108no—
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—101no—
640C22×D3—204no—
641C22×D3—204no—
642C22×D3—204no—
643C22×D3—204no—
644C22×D3—204no—
645C22×D3—204no—
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×C4C2×C4×D512yes—
662#67—108no—
663#67—204no—
664C2×Dic3—21no—
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—21no—
674C2×Dic3—21no—
675C2×Dic3—44no—
676C2×Dic3—52no—
677C2×Dic3—52no—
678C2×Dic3—101no—
679C2×Dic3—101no—
680C2×Dic3—101no—
681C2×Dic3—101no—
682C2×Dic3D4×D512yes—
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—41no—
692C22×C5—41no—
693C22×C5—41no—
694C22×C5—41no—
695C22×C5—41no—
696C22×C5—41no—
697C22×C5—41no—
698C22×C5—41no—
699C22×C5C22×C4×D311yescharacteristic
700C22×C5C2×D3×D411yescharacteristic
701C22×C5#100411yescharacteristic
702C22×C5#100411yescharacteristic
703C22×C5#100411yescharacteristic
704C22×C5D3×#4111yescharacteristic
705C22×C5#100911yescharacteristic
706C2×D5—34no—
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—62no—
723C4×C5—121no—
724C4×C5—121no—
725C4×C5—121no—
726Dic5—22no—
727Dic5—41no—
728Dic5—41no—
729Dic5—41no—
730Dic5—62no—
731Dic5—62no—
732C24—151no—
733C24—151no—
734C24—154no—
735C24—302no—
736C24—302no—
737C24—601no—
738C24—601no—
739C24—601no—
740C24—601no—
741C24C2×D3×D511yescharacteristic
742C24C2×D3×D511yescharacteristic
743C2×D4—41no—
744C2×D4—41no—
745C2×D4—154no—
746C2×D4—154no—
747C2×D4—302no—
748C2×D4—302no—
749C2×D4—601no—
750C2×D4—601no—
751C2×D4#120014yescomplemented
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—51no—
757C22×C4—51no—
758C22×C4—51no—
759C22×C4—51no—
760C22×C4—62no—
761C22×C4—121no—
762C22×C4—121no—
763C22×C4—154no—
764C22×C4—151no—
765C22×C4—151no—
766C22×C4—302no—
767C22×C4—601no—
768C22×C4—601no—
769C22×C4—601no—
770C22×C4—601no—
771C22×C4C2×D3×D511yescharacteristic
772C4⋊C4—201no—
773C4⋊C4—302no—
774C4⋊C4—601no—
775C22⋊C4—62no—
776C22⋊C4—102no—
777C22⋊C4—102no—
778C22⋊C4—121no—
779C22⋊C4—121no—
780C22⋊C4—154no—
781C22⋊C4—154no—
782C22⋊C4—154no—
783C22⋊C4—201no—
784C22⋊C4—201no—
785C22⋊C4—302no—
786C22⋊C4—302no—
787C22⋊C4—302no—
788C22⋊C4—302no—
789C22⋊C4—601no—
790C22⋊C4—601no—
791C42—201no—
792C42—302no—
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×C3C22×C4×D511yescharacteristic
810C22×C3C2×D4×D511yescharacteristic
811C22×C3#414411yescharacteristic
812C22×C3#414411yescharacteristic
813C22×C3#414411yescharacteristic
814C22×C3D5×#4111yescharacteristic
815C22×C3#414911yescharacteristic
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—102no—
833C3×C4—201no—
834C3×C4—201no—
835C3×C4—201no—
836Dic3—22no—
837Dic3—41no—
838Dic3—41no—
839Dic3—41no—
840Dic3—102no—
841Dic3—102no—
842C2×C5—42no—
843C2×C5—42no—
844C2×C5#548611yescharacteristic
845C2×C5C4×D3×D411yescharacteristic
846C2×C5#554511yescharacteristic
847C2×C5#560511yescharacteristic
848C2×C5#561311yescharacteristic
849C2×C5#567811yescharacteristic
850C2×C5#571511yescharacteristic
851D5—64no—
852D5—122no—
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—152no—
866C23—152no—
867C23—152no—
868C23—152no—
869C23—308no—
870C23—301no—
871C23—301no—
872C23—301no—
873C23—301no—
874C23—301no—
875C23—301no—
876C23—301no—
877C23—301no—
878C23—301no—
879C23—301no—
880C23—604no—
881C23—604no—
882C23—604no—
883C23—604no—
884C23—604no—
885C23—604no—
886C23C2×#120012yes—
887C23C2×#120012yes—
888C23C22×D3×D511yescharacteristic
889D4—44no—
890D4—308no—
891D4—604no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—32no—
895C2×C4—52no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—101no—
908C2×C4—101no—
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—101no—
918C2×C4—124no—
919C2×C4—152no—
920C2×C4—152no—
921C2×C4—301no—
922C2×C4—301no—
923C2×C4—301no—
924C2×C4—301no—
925C2×C4—604no—
926C2×C4—604no—
927C2×C4C2×#120012yes—
928C2×C3—42no—
929C2×C3—42no—
930C2×C3#6582011yescharacteristic
931C2×C3C4×D4×D511yescharacteristic
932C2×C3#6587911yescharacteristic
933C2×C3#6592311yescharacteristic
934C2×C3#6594111yescharacteristic
935C2×C3#6594711yescharacteristic
936C2×C3#6599111yescharacteristic
937D3—104no—
938D3—202no—
939C5#7642911yescharacteristic, complemented, Sylow
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—154no—
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—
969C22D3×D4×D511yescharacteristic
970C22#9202411yescharacteristic
971C22#9202611yescharacteristic
972C22#9202711yescharacteristic
973C22C22×#120011yescharacteristic
974C22#9204911yescharacteristic
975C22#9204911yescharacteristic
976C4—22no—
977C4—62no—
978C4—102no—
979C4—121no—
980C4—121no—
981C4—121no—
982C4—201no—
983C4—201no—
984C4—201no—
985C4—302no—
986C4—302no—
987C3#1060660711yescharacteristic, complemented, Sylow
988C2—42no—
989C2—42no—
990C2—304no—
991C2—602no—
992C2D4×#120011yescharacteristic
993C2#1175490011yescharacteristic
994C2#1175492211yescharacteristic
995C2#1175498111yescharacteristic
996C2#1175502511yescharacteristic
997C2#1175505111yescharacteristic
998C2#1175541311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91826C2
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×#91561C2semidirect
3. C2×#91556C2semidirect
4. C5×#5220C2semidirect
5. C3×#65510C2semidirect
6. #11749520C2semidirect
7. #11749502C2semidirect
8. #11749498C2semidirect
9. #11749483C2semidirect
10. #11749480C2semidirect
11. #11749480C2semidirect
12. #11748898C2semidirect
13. #11748875C2semidirect
14. #11748829C2semidirect
15. #11748678C2semidirect
21. C23×C5×Dic3C22semidirect
25. #91826C4semidirect
30. C2×C5×#217C22semidirect
33. C2×C3×C22⋊Dic5C22semidirect
34. C2×C3×C22⋊Dic5C22semidirect
35. C2×C3×C4⋊Dic5C22semidirect
36. C2×C3×C4×Dic5C22semidirect
39. C2×#6669C22semidirect
40. C2×#6669C22semidirect
47. C2×Dic3×Dic5C22semidirect
48. C2×Dic3×Dic5C22semidirect
49. C5×C3⋊#95C22semidirect
50. C5×C3⋊#95C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
60. #65510D3semidirect
79. C23×D15C2×C4semidirect
84. C2×C3×C5×D4C2×C4semidirect
91. C2×#1220C2×C4semidirect
110. C2×#1200D4semidirect
111. #6719C2×C4semidirect
112. #6714C2×C4semidirect
113. #6714C2×C4semidirect
137. #5220D5semidirect
161. C2×C22⋊Dic5C2×D3semidirect
162. C2×C22⋊Dic5C2×D3semidirect
173. C2×C4⋊Dic5C2×D3semidirect
178. C2×C4×Dic5C2×D3semidirect
266. C23×Dic3C2×D5semidirect
278. C2×#217C2×D5semidirect
298. C3⋊#95C2×D5semidirect
299. C3⋊#95C2×D5semidirect
313. C2×C5×D4C4×D3semidirect
437. C2×C3×D4C4×D5semidirect
751. C2×D4#1200semidirect
794. C3×C5#2321semidirect
939. C5#76429semidirect
987. C3#10606607semidirect

Maximal subgroups

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

subgroupindex
C2×#918262
C2×#915612
C2×#915562
C5×#52202
C3×#655102
#117495202
#117495022
#117494982
#117494832
#117494802
#117488982
#117488752
#117488292
#117486782
#106066073
#764295