Finite Group Databasebeta

← #14327058

Subgroups — #14327058

Order 1920.

1552 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91770C211yesmaximal, characteristic
2C2×#91556C211yesmaximal, characteristic
3C2×#91552C211yesmaximal, characteristic
4C22×#6669C211yesmaximal, characteristic, complemented
5C2×#91437C211yesmaximal, characteristic, complemented
6C5×#4950C211yesmaximal, characteristic, complemented
7C3×#65239C211yesmaximal, characteristic, complemented
8#11749516C211yesmaximal, characteristic, complemented
9#11748902C211yesmaximal, characteristic, complemented
10#11748898C211yesmaximal, characteristic, complemented
11#11748866C211yesmaximal, characteristic, complemented
12#11748863C211yesmaximal, characteristic, complemented
13#11748695C211yesmaximal, characteristic, complemented
14#11748676C211yesmaximal, characteristic, complemented
15#11748663C211yesmaximal, characteristic, complemented
16#10606124—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C23×C5×Dic3C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C22×#1200C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×C4×Dic15C2211yescharacteristic
28#91770C418yescomplemented
29C2×C5×#217C2211yescharacteristic
30C2×C5×C4⋊Dic3C2211yescharacteristic
31C2×C5×C4⋊Dic3C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×C4⋊Dic5C2211yescharacteristic
35#91556—24no—
36#91552—24no—
37C2×#6669—24no—
38C2×#6669C2211yescharacteristic
39C2×#6669C2211yescharacteristic
40C2×#6669C2211yescharacteristic
41C2×#6669C2211yescharacteristic
42C2×#6669C2211yescharacteristic
43C2×#6669C2211yescharacteristic
44C2×#6669C2211yescharacteristic
45C2×#6669C2211yescharacteristic
46C2×#6667C2211yescharacteristic
47C2×#6667C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50#91437—24no—
51C5×C3⋊#95C2211yescharacteristic
52C5×C3⋊#95C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#74393—51nomaximal, Hall
58C2×C4×C22⋊D5—31no—
59C22×#683—31no—
60C2×D5×C4⋊C4—31no—
61C2×#4027—31no—
62C2×#4027—31no—
63C5×#385—31no—
64#65278—31no—
65#65265—31no—
66#65261—31no—
67#65239D311yescharacteristic, complemented
68#65231—31no—
69#64957—31no—
70#64956—31no—
71#64938—31no—
72#64936—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C2×#1220C2×C414yes—
78C2×#1220D414yes—
79C2×#1220Q814yes—
80C22×Dic15—22no—
81C22×Dic15—22no—
82C22×Dic15C2×C414yescomplemented
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C2×C4×D15—22no—
87C2×C4×D15—22no—
88C2×C4×D15C2×C414yescomplemented
89C22×C5×Dic3—22no—
90C22×C5×Dic3—22no—
91C22×C5×Dic3—41no—
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C3×Dic5—22no—
97C22×C3×Dic5—22no—
98C22×C3×Dic5—41no—
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C2×#1200—22no—
104C2×#1200—22no—
105C2×#1200—22no—
106C2×#1200—22no—
107C2×#1200—41no—
108C2×#1200—41no—
109C3×C5×C22⋊C4C2×C414yescomplemented
110#6714C2×C414yescomplemented
111#6712C2×C414yescomplemented
112C4×Dic15C2×C414yescomplemented
113C5×#217—22no—
114C5×C4⋊Dic3—22no—
115C5×C4⋊Dic3—41no—
116C3×C22⋊Dic5—22no—
117C3×C4⋊Dic5—22no—
118C3×C4⋊Dic5—41no—
119#6669—22no—
120#6669—22no—
121#6669—22no—
122#6669—22no—
123#6669—22no—
124#6669—22no—
125#6669—22no—
126#6669D414yescomplemented
127#6667—22no—
128#6667—22no—
129Dic3×Dic5—22no—
130Dic3×Dic5—22no—
131C2×C4×#67—51no—
132C22×Dic3⋊C4—51no—
133C2×D3×C4⋊C4—51no—
134C2×#67⋊C4—51no—
135C2×#67⋊C4—51no—
136C3×#385—51no—
137#4989—51no—
138#4976—51no—
139#4975—51no—
140#4950D511yescharacteristic, complemented
141#4942—51no—
142#4668—51no—
143#4667—51no—
144#4649—51no—
145#4647—51no—
146C23×C4×C5—31no—
147C22×C22⋊D5—31no—
148C23×Dic5—31no—
149C23×Dic5C2×D311yescharacteristic
150C22×C4×D5—31no—
151C22×C4×D5—31no—
152C22×C4×D5—31no—
153C2×C5×C4⋊C4—31no—
154C2×C5×C4⋊C4—31no—
155C2×C5×C22⋊C4—31no—
156C2×C5×C22⋊C4C2×D311yescharacteristic
157C2×C22⋊Dic5C2×D311yescharacteristic
158C4×C22⋊D5—64no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×C4⋊Dic5C2×D311yescharacteristic
163C2×C4⋊Dic5C2×D311yescharacteristic
164C2×#683—31no—
165C2×#683—31no—
166C2×#683—31no—
167C2×#683—31no—
168C2×#683—31no—
169C2×#683—31no—
170C2×#683—31no—
171C2×#683—31no—
172C2×#683—31no—
173C2×#683—64no—
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177D5×C4⋊C4—64no—
178#4027—38no—
179#4027—64no—
180C5×#95—31no—
181C5×#95—31no—
182#3963—31no—
183#3963—31no—
184#3963C2×D311yescharacteristic
185#3963C2×D311yescharacteristic
186D4×C4⋊C4—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5C22×C412yes—
192C23×C3×C5C2×D412yes—
193C23×C3×C5C2×Q812yes—
194C23×C3×C5C2411yescharacteristic
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15C22×C412yes—
200C22×D15C2×D412yes—
201C22×D15C2×Q812yes—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5C22×C412yes—
207C2×C3×C4×C5C22×C412yes—
208#1220C4⋊C4116yescomplemented
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—28no—
212C2×Dic15C22×C412yes—
213C2×Dic15C22×C412yes—
214C2×Dic15C22×C412yes—
215C2×Dic15C2×D412yes—
216C2×Dic15C2×D412yes—
217C2×Dic15C2×Q812yes—
218C2×Dic15#4112yes—
219C4×D15—28no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—21no—
227C2×C5×Dic3—21no—
228C2×C5×Dic3—21no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—44no—
232C2×C5×Dic3C2×D412yes—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—44no—
245C2×C3×Dic5C2×D412yes—
246#1200—44no—
247#1200—44no—
248C23×C3×C4—51no—
249C22×#67—51no—
250C23×Dic3—51no—
251C23×Dic3C2×D511yescharacteristic
252C22×C4×D3—51no—
253C22×C4×D3—51no—
254C22×C4×D3—51no—
255C2×C3×C4⋊C4—51no—
256C2×C3×C4⋊C4—51no—
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4C2×D511yescharacteristic
259C2×#217C2×D511yescharacteristic
260C4×#67—104no—
261C2×(C2×D3)⋊C4—51no—
262C2×(C2×D3)⋊C4—51no—
263C2×(C2×D3)⋊C4—51no—
264C2×C4⋊Dic3C2×D511yescharacteristic
265C2×C4⋊Dic3C2×D511yescharacteristic
266C2×Dic3⋊C4—51no—
267C2×Dic3⋊C4—51no—
268C2×Dic3⋊C4—51no—
269C2×Dic3⋊C4—51no—
270C2×Dic3⋊C4—51no—
271C2×Dic3⋊C4—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×Dic3⋊C4—51no—
275C2×Dic3⋊C4—104no—
276C2×C4×Dic3—51no—
277C2×C4×Dic3—51no—
278C2×C4×Dic3—51no—
279D3×C4⋊C4—104no—
280#67⋊C4—58no—
281#67⋊C4—104no—
282C3×#95—51no—
283C3×#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95C2×D511yescharacteristic
287C3⋊#95C2×D511yescharacteristic
288C24×C5C22×D311yescharacteristic
289C23×D5—31no—
290C22×C4×C5—31no—
291C22×C4×C5—31no—
292C22×C4×C5—31no—
293C22×C4×C5—31no—
294C22×C4×C5—62no—
295C22×C4×C5—62no—
296C22×C4×C5—121no—
297C22×C4×C5C22×D311yescharacteristic
298C22×C4×C5C22×D311yescharacteristic
299C2×C22⋊D5—34no—
300C2×C22⋊D5—34no—
301C2×C22⋊D5—34no—
302C22×Dic5—22no—
303C22×Dic5—22no—
304C22×Dic5—31no—
305C22×Dic5—31no—
306C22×Dic5—34no—
307C22×Dic5—31no—
308C22×Dic5—41no—
309C22×Dic5—62no—
310C22×Dic5—62no—
311C22×Dic5C22×D311yescharacteristic
312C22×Dic5C22×D311yescharacteristic
313C22×Dic5C22×D311yescharacteristic
314C22×Dic5C22×D311yescharacteristic
315C2×C4×D5—34no—
316C2×C4×D5—62no—
317C2×C4×D5—62no—
318C2×C4×D5—62no—
319C2×C4×D5—62no—
320C2×C4×D5—62no—
321C2×C4×D5—62no—
322C2×C4×D5—121no—
323C2×C4×D5—121no—
324C5×C4⋊C4—62no—
325C5×C4⋊C4—121no—
326C5×C22⋊C4—62no—
327C5×C22⋊C4C4×D314yescomplemented
328C22⋊Dic5—22no—
329#685—34no—
330#685—62no—
331#685—62no—
332C4⋊Dic5—22no—
333C4⋊Dic5—41no—
334#683—34no—
335#683—34no—
336#683—62no—
337#683—62no—
338#683—62no—
339#683—62no—
340#683—62no—
341#683—62no—
342#683—62no—
343C4×Dic5—34no—
344C4×Dic5—62no—
345C4×Dic5—62no—
346C2×C4×D4—151no—
347C2×C4×D4—151no—
348C2×C4×D4—151no—
349C22×C4⋊C4—151no—
350C22×C4⋊C4—151no—
351#389—151no—
352#389—151no—
353#385—31no—
354#385—51no—
355#385—151no—
356#385—151no—
357#384—151no—
358#380—151no—
359#380—151no—
360C4×C4⋊C4—151no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—22no—
365C22×C3×C5—22no—
366C22×C3×C5—22no—
367C22×C3×C5C2×C4⋊C414yescomplemented
368C22×C3×C5C23×C411yescharacteristic
369C22×C3×C5C22×D411yescharacteristic
370C22×C3×C5C22×D411yescharacteristic
371C22×C3×C5C22×Q811yescharacteristic
372C22×C3×C5C2×#4111yescharacteristic
373C22×C3×C5H(5,𝔽2)11yescharacteristic
374C22×C3×C52−1+411yescharacteristic
375C2×D15—22no—
376C2×D15—22no—
377C2×D15—22no—
378C2×D15—22no—
379C2×D15—22no—
380C2×D15—22no—
381C2×D15C2×C4⋊C414yescomplemented
382C3×C4×C5—22no—
383C3×C4×C5—22no—
384Dic15—22no—
385Dic15C2×C4⋊C414yescomplemented
386Dic15C4×D414yescomplemented
387C3×Dic5—22no—
388C3×Dic5—41no—
389C3×Dic5—41no—
390C3×Dic5—41no—
391C5×Dic3—22no—
392C5×Dic3—41no—
393C5×Dic3—41no—
394C5×Dic3—41no—
395C24×C3C22×D511yescharacteristic
396C23×D3—51no—
397C22×C3×C4—51no—
398C22×C3×C4—51no—
399C22×C3×C4—51no—
400C22×C3×C4—51no—
401C22×C3×C4—102no—
402C22×C3×C4—102no—
403C22×C3×C4—201no—
404C22×C3×C4C22×D511yescharacteristic
405C22×C3×C4C22×D511yescharacteristic
406C2×#67—54no—
407C2×#67—54no—
408C2×#67—54no—
409C22×Dic3—22no—
410C22×Dic3—22no—
411C22×Dic3—41no—
412C22×Dic3—51no—
413C22×Dic3—51no—
414C22×Dic3—54no—
415C22×Dic3—51no—
416C22×Dic3—102no—
417C22×Dic3—102no—
418C22×Dic3C22×D511yescharacteristic
419C22×Dic3C22×D511yescharacteristic
420C22×Dic3C22×D511yescharacteristic
421C22×Dic3C22×D511yescharacteristic
422C2×C4×D3—54no—
423C2×C4×D3—102no—
424C2×C4×D3—102no—
425C2×C4×D3—102no—
426C2×C4×D3—102no—
427C2×C4×D3—102no—
428C2×C4×D3—102no—
429C2×C4×D3—201no—
430C2×C4×D3—201no—
431C3×C4⋊C4—102no—
432C3×C4⋊C4—201no—
433C3×C22⋊C4—102no—
434C3×C22⋊C4C4×D514yescomplemented
435#217—22no—
436(C2×D3)⋊C4—54no—
437(C2×D3)⋊C4—102no—
438(C2×D3)⋊C4—102no—
439C4⋊Dic3—22no—
440C4⋊Dic3—41no—
441Dic3⋊C4—54no—
442Dic3⋊C4—54no—
443Dic3⋊C4—102no—
444Dic3⋊C4—102no—
445Dic3⋊C4—102no—
446Dic3⋊C4—102no—
447Dic3⋊C4—102no—
448Dic3⋊C4—102no—
449Dic3⋊C4—102no—
450C4×Dic3—54no—
451C4×Dic3—102no—
452C4×Dic3—102no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5—21no—
457C23×C5C2×C4×D312yes—
458C23×C5D3×D412yes—
459C23×C5D3×Q812yes—
460C23×C5C23×D311yescharacteristic
461C22×D5—32no—
462C22×D5—32no—
463C22×D5—32no—
464C22×D5—61no—
465C22×D5—61no—
466C22×D5—61no—
467C22×D5—61no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—21no—
471C2×C4×C5—21no—
472C2×C4×C5—32no—
473C2×C4×C5—61no—
474C2×C4×C5—61no—
475C2×C4×C5—61no—
476C2×C4×C5—61no—
477C2×C4×C5—61no—
478C2×C4×C5—61no—
479C2×C4×C5—61no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—61no—
483C2×C4×C5—61no—
484C2×C4×C5—124no—
485C2×C4×C5C2×C4×D312yes—
486C2×C4×C5C2×C4×D312yes—
487C22⋊D5—316no—
488C2×Dic5—21no—
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494C2×Dic5—21no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—21no—
498C2×Dic5—21no—
499C2×Dic5—32no—
500C2×Dic5—32no—
501C2×Dic5—32no—
502C2×Dic5—32no—
503C2×Dic5—32no—
504C2×Dic5—32no—
505C2×Dic5—32no—
506C2×Dic5—44no—
507C2×Dic5—68no—
508C2×Dic5—61no—
509C2×Dic5—61no—
510C2×Dic5D3×D412yes—
511C4×D5—68no—
512C4×D5—124no—
513C4×D5—124no—
514C22×D4—151no—
515C23×C4—31no—
516C23×C4—51no—
517C23×C4—151no—
518C23×C4—151no—
519C23×C4—151no—
520C23×C4—151no—
521C4×D4—158no—
522C4×D4—304no—
523C4×D4—304no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—31no—
526C2×C4⋊C4—51no—
527C2×C4⋊C4—51no—
528C2×C4⋊C4—151no—
529C2×C4⋊C4—151no—
530C2×C4⋊C4—151no—
531C2×C4⋊C4—151no—
532C2×C4⋊C4—151no—
533C2×C4⋊C4—151no—
534C2×C4⋊C4—151no—
535C2×C4⋊C4—151no—
536C2×C4⋊C4—151no—
537C2×C4⋊C4—304no—
538C2×C4⋊C4—304no—
539C2×C22⋊C4—31no—
540C2×C22⋊C4—51no—
541C2×C22⋊C4—151no—
542C2×C22⋊C4—151no—
543C2×C22⋊C4—151no—
544C2×C22⋊C4D3×D511yescharacteristic
545C2×C42—151no—
546C2×C42—151no—
547C2×C42—151no—
548#95—31no—
549#95—31no—
550#95—51no—
551#95—51no—
552#95—151no—
553#95—151no—
554C2×C3×C5—24no—
555C2×C3×C5C22×C4⋊C411yescharacteristic
556C2×C3×C5C2×C4×D411yescharacteristic
557C2×C3×C5#52011yescharacteristic
558C2×C3×C5D4211yescharacteristic
559C2×C3×C5#54711yescharacteristic
560C2×C3×C5D4×Q811yescharacteristic
561C2×C3×C5#55411yescharacteristic
562D15—24no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3C2×C4×D512yes—
568C23×C3D4×D512yes—
569C23×C3Q8×D512yes—
570C23×C3C23×D511yescharacteristic
571C22×D3—52no—
572C22×D3—52no—
573C22×D3—52no—
574C22×D3—101no—
575C22×D3—101no—
576C22×D3—101no—
577C22×D3—101no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—52no—
583C2×C3×C4—101no—
584C2×C3×C4—101no—
585C2×C3×C4—101no—
586C2×C3×C4—101no—
587C2×C3×C4—101no—
588C2×C3×C4—101no—
589C2×C3×C4—101no—
590C2×C3×C4—101no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—204no—
595C2×C3×C4C2×C4×D512yes—
596C2×C3×C4C2×C4×D512yes—
597#67—516no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—44no—
610C2×Dic3—52no—
611C2×Dic3—52no—
612C2×Dic3—52no—
613C2×Dic3—52no—
614C2×Dic3—52no—
615C2×Dic3—52no—
616C2×Dic3—52no—
617C2×Dic3—108no—
618C2×Dic3—101no—
619C2×Dic3—101no—
620C2×Dic3D4×D512yes—
621C4×D3—108no—
622C4×D3—204no—
623C4×D3—204no—
624C22×C5—22no—
625C22×C5—22no—
626C22×C5—22no—
627C22×C5—22no—
628C22×C5—22no—
629C22×C5—22no—
630C22×C5D3×C4⋊C414yescomplemented
631C22×C5C22×C4×D311yescharacteristic
632C22×C5C2×D3×D411yescharacteristic
633C22×C5C2×D3×D411yescharacteristic
634C22×C5#100411yescharacteristic
635C22×C5C2×D3×Q811yescharacteristic
636C22×C5D3×#4111yescharacteristic
637C22×C5#101011yescharacteristic
638C2×D5—34no—
639C2×D5—62no—
640C2×D5—62no—
641C2×D5—62no—
642C2×D5—62no—
643C2×D5—62no—
644C2×D5—62no—
645C4×C5—22no—
646C4×C5—22no—
647C4×C5—62no—
648C4×C5—121no—
649C4×C5—121no—
650C4×C5—121no—
651Dic5—22no—
652Dic5—34no—
653Dic5—34no—
654Dic5—41no—
655Dic5—41no—
656Dic5—41no—
657Dic5—62no—
658C24—151no—
659C24C2×D3×D511yescharacteristic
660C2×D4—154no—
661C2×D4—154no—
662C2×D4—154no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—51no—
668C22×C4—51no—
669C22×C4—51no—
670C22×C4—51no—
671C22×C4—62no—
672C22×C4—62no—
673C22×C4—102no—
674C22×C4—102no—
675C22×C4—121no—
676C22×C4—151no—
677C22×C4—151no—
678C22×C4—154no—
679C22×C4—151no—
680C22×C4—154no—
681C22×C4—201no—
682C22×C4—302no—
683C22×C4—302no—
684C22×C4—302no—
685C22×C4—302no—
686C22×C4—302no—
687C22×C4—302no—
688C22×C4—302no—
689C22×C4—302no—
690C22×C4—601no—
691C22×C4—601no—
692C22×C4C2×D3×D511yescharacteristic
693C22×C4C2×D3×D511yescharacteristic
694C4⋊C4—62no—
695C4⋊C4—102no—
696C4⋊C4—121no—
697C4⋊C4—154no—
698C4⋊C4—154no—
699C4⋊C4—201no—
700C4⋊C4—302no—
701C4⋊C4—302no—
702C4⋊C4—302no—
703C4⋊C4—302no—
704C4⋊C4—302no—
705C4⋊C4—302no—
706C4⋊C4—302no—
707C22⋊C4—62no—
708C22⋊C4—102no—
709C22⋊C4—154no—
710C22⋊C4—302no—
711C22⋊C4—302no—
712C22⋊C4#120014yescomplemented
713C42—154no—
714C42—302no—
715C42—302no—
716C3×C5D4×C4⋊C411yescharacteristic, complemented, Hall
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3D5×C4⋊C414yescomplemented
724C22×C3C22×C4×D511yescharacteristic
725C22×C3C2×D4×D511yescharacteristic
726C22×C3C2×D4×D511yescharacteristic
727C22×C3#414411yescharacteristic
728C22×C3C2×Q8×D511yescharacteristic
729C22×C3D5×#4111yescharacteristic
730C22×C3#415011yescharacteristic
731C2×D3—54no—
732C2×D3—102no—
733C2×D3—102no—
734C2×D3—102no—
735C2×D3—102no—
736C2×D3—102no—
737C2×D3—102no—
738C3×C4—22no—
739C3×C4—22no—
740C3×C4—102no—
741C3×C4—201no—
742C3×C4—201no—
743C3×C4—201no—
744Dic3—22no—
745Dic3—41no—
746Dic3—41no—
747Dic3—41no—
748Dic3—54no—
749Dic3—54no—
750Dic3—102no—
751C2×C5—24no—
752C2×C5C2×D3×C4⋊C411yescharacteristic
753C2×C5C4×D3×D411yescharacteristic
754C2×C5#554611yescharacteristic
755C2×C5#559011yescharacteristic
756C2×C5#563211yescharacteristic
757C2×C5#563611yescharacteristic
758C2×C5#565511yescharacteristic
759D5—64no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—152no—
765C23—152no—
766C23—152no—
767C23—301no—
768C23—301no—
769C23—301no—
770C23—301no—
771C23D15⋊Q812yes—
772C23#677712yes—
773C23C2×#120012yes—
774C23C22×D3×D511yescharacteristic
775D4—1516no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—32no—
781C2×C4—52no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—101no—
794C2×C4—101no—
795C2×C4—101no—
796C2×C4—101no—
797C2×C4—101no—
798C2×C4—101no—
799C2×C4—101no—
800C2×C4—101no—
801C2×C4—101no—
802C2×C4—101no—
803C2×C4—101no—
804C2×C4—124no—
805C2×C4—152no—
806C2×C4—152no—
807C2×C4—152no—
808C2×C4—152no—
809C2×C4—152no—
810C2×C4—152no—
811C2×C4—152no—
812C2×C4—204no—
813C2×C4—308no—
814C2×C4—308no—
815C2×C4—301no—
816C2×C4—301no—
817C2×C4—604no—
818C2×C4—604no—
819C2×C4C2×#120012yes—
820C2×C4C2×#120012yes—
821C2×C3—24no—
822C2×C3C2×D5×C4⋊C411yescharacteristic
823C2×C3C4×D4×D511yescharacteristic
824C2×C3#6588011yescharacteristic
825C2×C3#6592411yescharacteristic
826C2×C3#6596611yescharacteristic
827C2×C3#6597011yescharacteristic
828C2×C3#6598911yescharacteristic
829D3—104no—
830C5#7439311yescharacteristic, complemented, Sylow
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—154no—
838C22—302no—
839C22—302no—
840C22—302no—
841C22—302no—
842C22—302no—
843C22—302no—
844C22#9143714yescomplemented
845C22C2×D15⋊Q811yescharacteristic
846C22C2×#677711yescharacteristic
847C22#9202011yescharacteristic
848C22D3×D4×D511yescharacteristic
849C22#9202411yescharacteristic
850C22#9202511yescharacteristic
851C22C22×#120011yescharacteristic
852C4—22no—
853C4—22no—
854C4—62no—
855C4—102no—
856C4—121no—
857C4—121no—
858C4—121no—
859C4—154no—
860C4—154no—
861C4—201no—
862C4—201no—
863C4—201no—
864C4—302no—
865C3#1060612411yescharacteristic, complemented, Sylow
866C2—24no—
867C2—304no—
868C2#1175286211yescharacteristic
869C2#1175288111yescharacteristic
870C2#1175304211yescharacteristic
871C2#1175322511yescharacteristic
872C2C2×#9143711yescharacteristic
873C2D4×#120011yescharacteristic
874C2#1175491611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5D4×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C22×#6669C2semidirect
5. C2×#91437C2semidirect
6. C5×#4950C2semidirect
7. C3×#65239C2semidirect
8. #11749516C2semidirect
9. #11748902C2semidirect
10. #11748898C2semidirect
11. #11748866C2semidirect
12. #11748863C2semidirect
13. #11748695C2semidirect
14. #11748676C2semidirect
15. #11748663C2semidirect
28. #91770C4semidirect
67. #65239D3semidirect
82. C22×Dic15C2×C4semidirect
88. C2×C4×D15C2×C4semidirect
109. C3×C5×C22⋊C4C2×C4semidirect
110. #6714C2×C4semidirect
111. #6712C2×C4semidirect
112. C4×Dic15C2×C4semidirect
126. #6669D4semidirect
140. #4950D5semidirect
208. #1220C4⋊C4semidirect
327. C5×C22⋊C4C4×D3semidirect
367. C22×C3×C5C2×C4⋊C4semidirect
381. C2×D15C2×C4⋊C4semidirect
385. Dic15C2×C4⋊C4semidirect
386. Dic15C4×D4semidirect
434. C3×C22⋊C4C4×D5semidirect
630. C22×C5D3×C4⋊C4semidirect
712. C22⋊C4#1200semidirect
716. C3×C5D4×C4⋊C4semidirect
723. C22×C3D5×C4⋊C4semidirect
830. C5#74393semidirect
844. C22#91437semidirect
865. C3#10606124semidirect

Maximal subgroups

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

subgroupindex
C2×#917702
C2×#915562
C2×#915522
C22×#66692
C2×#914372
C5×#49502
C3×#652392
#117495162
#117489022
#117488982
#117488662
#117488632
#117486952
#117486762
#117486632
#106061243
#743935