Finite Group Databasebeta

← #14322561

Subgroups — #14322561

Order 1920.

1760 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6766C211yesmaximal, characteristic
2C2×#91393C211yesmaximal, characteristic, complemented
3C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
4#11750768C211yesmaximal, characteristic, complemented
5C5×#4646C211yesmaximal, characteristic, complemented
6C3×#64954C211yesmaximal, characteristic, complemented
7#11748913C211yesmaximal, characteristic, complemented
8#11748912C211yesmaximal, characteristic, complemented
9#11748907C211yesmaximal, characteristic, complemented
10#11748896C211yesmaximal, characteristic, complemented
11#11748885C211yesmaximal, characteristic, complemented
12#11748885C211yesmaximal, characteristic, complemented
13#11748872C211yesmaximal, characteristic, complemented
14#11748863C211yesmaximal, characteristic, complemented
15#11748692C211yesmaximal, characteristic, complemented
16#10608213—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×C5×Dic6C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×#1202C2211yescharacteristic
22C22×#1202C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C22×D5×Dic3C2211yescharacteristic
25C22×D5×Dic3C2211yescharacteristic
26C2×#6766—24no—
27C2×#6766—24no—
28C2×#6766C418yescomplemented
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×C5×Dic3⋊C4C2211yescharacteristic
34C2×C4×C5×Dic3C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×Dic3⋊Dic5C2211yescharacteristic
39C2×#6669C2211yescharacteristic
40C2×#6669C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47#91393—24no—
48D5×Dic3⋊C4—24no—
49C3×C5×#95C2211yescharacteristic
50#91115C2211yescharacteristic
51C5×C3⋊#95C2211yescharacteristic
52C5×C3⋊#95C2211yescharacteristic
53C5×C3⋊#95C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#74662—51nomaximal, Hall
58C22×#713—31no—
59C2×D5×C4⋊C4—31no—
60C2×#4018—31no—
61C5×#391—31no—
62#65519—31no—
63#65277—31no—
64#65228—31no—
65#64956—31no—
66#64956—31no—
67#64956—31no—
68#64956—31no—
69#64954—31no—
70#64954—31no—
71#64954—31no—
72#64954D311yescharacteristic, complemented
73C23×D15C2311yescharacteristic
74C23×C3×D5C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C2×C4×D15—22no—
83C2×C4×D15—22no—
84C2×C4×D15C2×C414yescomplemented
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C2×C5×Dic6—22no—
90C2×C5×Dic6—22no—
91C2×C5×Dic6C2×C414yescomplemented
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C2×C3×D20—22no—
95C2×C3×D20—22no—
96C2×C3×D20C2×C414yes—
97C2×C3×C4×D5—22no—
98C2×C3×C4×D5—41no—
99C2×C3×C4×D5—41no—
100C2×#1202—22no—
101C2×#1202—22no—
102C2×#1202—22no—
103C2×#1202—22no—
104C2×#1202C2×C414yes—
105C2×#1202C2×C414yescomplemented
106C2×D5×Dic3—22no—
107C2×D5×Dic3—22no—
108C2×D5×Dic3—22no—
109C2×D5×Dic3—41no—
110C2×D5×Dic3—41no—
111C2×D5×Dic3C2×C414yes—
112C2×D5×Dic3C2×C414yescomplemented
113C2×D5×Dic3D414yes—
114C2×D5×Dic3D414yes—
115#6766—232no—
116#6714—41no—
117#6714—41no—
118#6712—22no—
119#6712—22no—
120C5×Dic3⋊C4—22no—
121C4×C5×Dic3—22no—
122C3×#685—22no—
123C3×#685—41no—
124C3×#685—41no—
125Dic3⋊Dic5—22no—
126#6669—22no—
127#6669—22no—
128#6667—41no—
129#6667—41no—
130#6665—22no—
131#6665—41no—
132#6665—41no—
133Dic3×Dic5—22no—
134C22×#237—51no—
135C22×Dic3⋊C4—51no—
136C2×#877—51no—
137C3×#386—51no—
138#5220—51no—
139#5213—51no—
140#4958—51no—
141#4957—51no—
142#4957—51no—
143#4942—51no—
144#4942—51no—
145#4667—51no—
146#4667—51no—
147#4646—51no—
148#4646D511yescharacteristic, complemented
149C22×C5×Q8—31no—
150C2×#713—38no—
151C2×#713—64no—
152C2×#713—64no—
153C22×D20—31no—
154C22×D20—31no—
155C22×D20C2×D311yescharacteristic
156C22×C4×D5—31no—
157C22×C4×D5—31no—
158C22×C4×D5—31no—
159C22×C4×D5—31no—
160C22×C4×D5C2×D311yescharacteristic
161C2×C5×C4⋊C4—31no—
162C2×C42×C5—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×#683—31no—
176C2×#683—31no—
177C2×#683—31no—
178C2×C4×Dic5—31no—
179D5×C4⋊C4—64no—
180#4018—64no—
181C5×#95—31no—
182C5×#95—31no—
183C5×#95—31no—
184C5×#95C2×D311yescharacteristic
185#3963—31no—
186#3963—31no—
187#3963—31no—
188#3963C2×D311yescharacteristic
189#2311—151noSylow
190C23×C3×C5C2411yescharacteristic
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15—21no—
195C22×D15—21no—
196C22×D15—21no—
197C22×D15C22×C412yes—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5C22×C412yes—
209C22×C3×D5C22×C412yes—
210C22×C3×D5C2×D412yes—
211C22×C3×D5C2×D412yes—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5C22×C412yes—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15C22×C412yes—
228C2×Dic15C2×D412yes—
229C2×Dic15C2×D412yes—
230C4×D15—28no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3C22×C412yes—
240C2×C5×Dic3C22×C412yes—
241C2×C5×Dic3C2×D412yes—
242C2×C5×Dic3C2×D412yes—
243C5×Dic6—28no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C3×D20—28no—
251C3×C4×D5—44no—
252#1202—28no—
253#1202—28no—
254D5×Dic3—28no—
255D5×Dic3—44no—
256D5×Dic3C22⋊C4116yescomplemented
257C22×C3×D4—51no—
258C23×C3×C4—51no—
259C22×#67—51no—
260C22×#67—51no—
261C23×Dic3—51no—
262C23×Dic3—51no—
263C23×Dic3—51no—
264C2×#237—58no—
265C2×#237—104no—
266C2×#237—104no—
267C22×C4×D3—51no—
268C22×Dic6C2×D511yescharacteristic
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×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×Dic3⋊C4—51no—
280C2×Dic3⋊C4—51no—
281C2×Dic3⋊C4—51no—
282C2×Dic3⋊C4—51no—
283C2×Dic3⋊C4—51no—
284C2×Dic3⋊C4—104no—
285C2×Dic3⋊C4C2×D511yescharacteristic
286C2×C4×Dic3—51no—
287C2×C4×Dic3C2×D511yescharacteristic
288#877—104no—
289C3×#95—51no—
290C3×#95C2×D511yescharacteristic
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95C2×D511yescharacteristic
295C3⋊#95C2×D511yescharacteristic
296C3⋊#95C2×D511yescharacteristic
297C23×D5—31no—
298C23×D5C22×D311yescharacteristic
299C23×D5C22×D311yescharacteristic
300C2×C5×Q8—34no—
301C2×C5×Q8—62no—
302C2×C5×Q8—62no—
303C22×C4×C5—31no—
304C22×C4×C5—31no—
305C22×C4×C5—31no—
306C22×C4×C5—31no—
307C22×C4×C5C22×D311yescharacteristic
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C22×Dic5—31no—
311C22×Dic5—31no—
312C22×Dic5—31no—
313C22×Dic5C22×D311yescharacteristic
314C22×Dic5C22×D311yescharacteristic
315#713—632no—
316C2×D20—22no—
317C2×D20—22no—
318C2×D20—34no—
319C2×D20—34no—
320C2×D20—62no—
321C2×D20—62no—
322C2×D20—62no—
323C2×D20—62no—
324C2×D20C4×D314yes—
325C2×C4×D5—22no—
326C2×C4×D5—34no—
327C2×C4×D5—34no—
328C2×C4×D5—34no—
329C2×C4×D5—34no—
330C2×C4×D5—34no—
331C2×C4×D5—41no—
332C2×C4×D5—41no—
333C2×C4×D5—62no—
334C2×C4×D5—62no—
335C2×C4×D5—62no—
336C2×C4×D5—62no—
337C2×C4×D5—62no—
338C2×C4×D5—121no—
339C2×C4×D5—121no—
340C5×C4⋊C4—62no—
341C42×C5—62no—
342#685—22no—
343#685—41no—
344#685—41no—
345#685—62no—
346#685—121no—
347#685—121no—
348#685—121no—
349#685—121no—
350#685—121no—
351#685—121no—
352C4⋊Dic5—62no—
353#683—62no—
354#683—62no—
355#683—62no—
356#683—62no—
357C4×Dic5—62no—
358C22×#41—151no—
359C2×#117—151no—
360C22×C4⋊C4—151no—
361#391—31no—
362#391—151no—
363#390—151no—
364#390—151no—
365#386—51no—
366#386—151no—
367#386—151no—
368#386—151no—
369#380—151no—
370#380—151no—
371#380—151no—
372#380—151no—
373C22×C3×C5C23×C411yescharacteristic
374C22×C3×C5C22×D411yescharacteristic
375C22×C3×C5C22×D411yescharacteristic
376C22×C3×C5H(5,𝔽2)11yescharacteristic
377C22×C3×C5H(5,𝔽2)11yescharacteristic
378C22×C3×C52−1+411yescharacteristic
379C22×C3×C52−1+411yescharacteristic
380C2×D15—22no—
381C2×D15—22no—
382C2×D15—22no—
383C2×D15—41no—
384C2×D15—41no—
385C2×D15—41no—
386C2×D15—41no—
387C2×C3×D5—22no—
388C2×C3×D5—22no—
389C2×C3×D5—22no—
390C2×C3×D5—22no—
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5—22no—
395C2×C3×D5—22no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399C2×C3×D5—41no—
400C2×C3×D5C2×C22⋊C414yes—
401C3×C4×C5—22no—
402C3×C4×C5—41no—
403C3×C4×C5—41no—
404Dic15—41no—
405Dic15—41no—
406Dic15C2×C22⋊C414yes—
407C3×Dic5—41no—
408C3×Dic5—41no—
409C5×Dic3—22no—
410C5×Dic3—41no—
411C5×Dic3—41no—
412C5×Dic3C2×C22⋊C414yes—
413C24×C3—51no—
414C24×C3—51no—
415C23×D3—51no—
416C2×C3×D4—54no—
417C2×C3×D4—102no—
418C2×C3×D4—102no—
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—102no—
422C22×C3×C4—201no—
423C22×C3×C4—201no—
424C22×C3×C4C22×D511yescharacteristic
425C22×C3×C4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C2×#67—54no—
428C2×#67—54no—
429C2×#67—102no—
430C2×#67—102no—
431C2×#67—102no—
432C2×#67—102no—
433C22×Dic3—51no—
434C22×Dic3—54no—
435C22×Dic3—54no—
436C22×Dic3—54no—
437C22×Dic3—54no—
438C22×Dic3—51no—
439C22×Dic3—51no—
440C22×Dic3—102no—
441C22×Dic3—102no—
442C22×Dic3—102no—
443C22×Dic3—201no—
444C22×Dic3—201no—
445C22×Dic3C22×D511yescharacteristic
446C22×Dic3C22×D511yescharacteristic
447C22×Dic3C22×D511yescharacteristic
448C22×Dic3C22×D511yescharacteristic
449#237—1032no—
450C2×C4×D3—54no—
451C2×C4×D3—102no—
452C2×C4×D3—102no—
453C2×Dic6—22no—
454C2×Dic6—22no—
455C2×Dic6C4×D514yescomplemented
456C3×C22⋊C4—102no—
457C3×C22⋊C4—201no—
458C3×C22⋊C4—201no—
459#217—102no—
460#217—201no—
461#217—201no—
462(C2×D3)⋊C4—201no—
463(C2×D3)⋊C4—201no—
464(C2×D3)⋊C4—201no—
465(C2×D3)⋊C4—201no—
466Dic3⋊C4—22no—
467Dic3⋊C4—102no—
468Dic3⋊C4—102no—
469Dic3⋊C4—102no—
470Dic3⋊C4—102no—
471Dic3⋊C4—102no—
472C4×Dic3—22no—
473C4×Dic3—102no—
474C23×C5C23×D311yescharacteristic
475C22×D5—21no—
476C22×D5—21no—
477C22×D5—21no—
478C22×D5—21no—
479C22×D5—21no—
480C22×D5—21no—
481C22×D5—21no—
482C22×D5—21no—
483C22×D5—21no—
484C22×D5—21no—
485C22×D5—32no—
486C22×D5—61no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5—61no—
492C22×D5C2×C4×D312yes—
493C22×D5C2×C4×D312yes—
494C22×D5D3×D412yes—
495C22×D5D3×D412yes—
496C5×Q8—68no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—32no—
506C2×C4×C5—32no—
507C2×C4×C5—32no—
508C2×C4×C5—32no—
509C2×C4×C5—61no—
510C2×C4×C5—61no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—61no—
517C2×C4×C5C2×C4×D312yes—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—32no—
525C2×Dic5—32no—
526C2×Dic5—32no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533D20—28no—
534D20—68no—
535D20—68no—
536C4×D5—316no—
537C4×D5—44no—
538C4×D5—68no—
539C4×D5—68no—
540C4×D5—124no—
541C2×#41—158no—
542C2×#41—304no—
543C2×#41—304no—
544C22×Q8—31no—
545C22×D4—51no—
546C22×D4—151no—
547C22×D4—151no—
548C23×C4—51no—
549C23×C4—151no—
550C23×C4—151no—
551C23×C4—151no—
552C23×C4—151no—
553#117—304no—
554C2×C4⋊C4—31no—
555C2×C4⋊C4—151no—
556C2×C4⋊C4—151no—
557C2×C4⋊C4—151no—
558C2×C4⋊C4—151no—
559C2×C4⋊C4—151no—
560C2×C4⋊C4—304no—
561C2×C22⋊C4—51no—
562C2×C22⋊C4—51no—
563C2×C22⋊C4—51no—
564C2×C22⋊C4—151no—
565C2×C22⋊C4—151no—
566C2×C22⋊C4—151no—
567C2×C22⋊C4—151no—
568C2×C22⋊C4—151no—
569C2×C22⋊C4—151no—
570C2×C22⋊C4—151no—
571C2×C42—31no—
572C2×C42—151no—
573#95—31no—
574#95—31no—
575#95—31no—
576#95—51no—
577#95—151no—
578#95—151no—
579#95—151no—
580#95D3×D511yescharacteristic
581C2×C3×C5C22×C22⋊C411yescharacteristic
582C2×C3×C5#52011yescharacteristic
583C2×C3×C5#52011yescharacteristic
584C2×C3×C5#53511yescharacteristic
585C2×C3×C5#53611yescharacteristic
586C2×C3×C5#53711yescharacteristic
587C2×C3×C5#53711yescharacteristic
588D15—42no—
589C3×D5—24no—
590C3×D5—42no—
591C23×C3—52no—
592C23×C3—52no—
593C23×C3—52no—
594C23×C3—52no—
595C23×C3—101no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3—101no—
599C23×C3—101no—
600C23×C3—101no—
601C23×C3—101no—
602C23×C3—101no—
603C23×C3—101no—
604C23×C3—101no—
605C23×C3C23×D511yescharacteristic
606C22×D3—52no—
607C22×D3—101no—
608C22×D3—101no—
609C22×D3—101no—
610C22×D3—101no—
611C22×D3—101no—
612C22×D3—101no—
613C3×D4—108no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4—101no—
625C2×C3×C4—101no—
626C2×C3×C4—101no—
627C2×C3×C4—101no—
628C2×C3×C4—204no—
629C2×C3×C4C2×C4×D512yes—
630#67—108no—
631#67—108no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—52no—
641C2×Dic3—52no—
642C2×Dic3—52no—
643C2×Dic3—516no—
644C2×Dic3—108no—
645C2×Dic3—101no—
646C2×Dic3—101no—
647C2×Dic3—101no—
648C2×Dic3—101no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—204no—
652C2×Dic3C2×C4×D512yes—
653C2×Dic3C2×C4×D512yes—
654C2×Dic3D4×D512yes—
655C2×Dic3D4×D512yes—
656C4×D3—108no—
657Dic6—28no—
658C22×C5C22×C4×D311yescharacteristic
659C22×C5C2×D3×D411yescharacteristic
660C22×C5C2×D3×D411yescharacteristic
661C22×C5#100411yescharacteristic
662C22×C5#100411yescharacteristic
663C22×C5#101011yescharacteristic
664C22×C5#101011yescharacteristic
665C2×D5—22no—
666C2×D5—22no—
667C2×D5—22no—
668C2×D5—22no—
669C2×D5—22no—
670C2×D5—22no—
671C2×D5—22no—
672C2×D5—22no—
673C2×D5—22no—
674C2×D5—41no—
675C2×D5—41no—
676C2×D5—41no—
677C2×D5—41no—
678C2×D5—62no—
679C2×D5—62no—
680C2×D5—62no—
681C2×D5—121no—
682C2×D5—121no—
683C2×D5—121no—
684C2×D5—121no—
685C2×D5D3×C22⋊C414yes—
686C4×C5—22no—
687C4×C5—34no—
688C4×C5—41no—
689C4×C5—41no—
690C4×C5—62no—
691C4×C5—121no—
692C4×C5—121no—
693Dic5—34no—
694Dic5—41no—
695Dic5—41no—
696Dic5—121no—
697Dic5—121no—
698C24—51no—
699C24—51no—
700C24—151no—
701#41—3032no—
702C2×Q8—34no—
703C2×Q8—62no—
704C2×Q8—62no—
705C2×D4—54no—
706C2×D4—102no—
707C2×D4—102no—
708C2×D4—154no—
709C2×D4—154no—
710C2×D4—302no—
711C2×D4—302no—
712C2×D4—302no—
713C2×D4—302no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—51no—
719C22×C4—51no—
720C22×C4—102no—
721C22×C4—154no—
722C22×C4—154no—
723C22×C4—154no—
724C22×C4—154no—
725C22×C4—151no—
726C22×C4—154no—
727C22×C4—151no—
728C22×C4—151no—
729C22×C4—201no—
730C22×C4—201no—
731C22×C4—302no—
732C22×C4—302no—
733C22×C4—302no—
734C22×C4—302no—
735C22×C4—302no—
736C22×C4—601no—
737C22×C4—601no—
738C22×C4C2×D3×D511yescharacteristic
739C22×C4C2×D3×D511yescharacteristic
740C22×C4C2×D3×D511yescharacteristic
741C4⋊C4—62no—
742C4⋊C4—302no—
743C4⋊C4—302no—
744C4⋊C4—302no—
745C4⋊C4—302no—
746C4⋊C4—302no—
747C22⋊C4—102no—
748C22⋊C4—201no—
749C22⋊C4—201no—
750C22⋊C4—302no—
751C22⋊C4—601no—
752C22⋊C4—601no—
753C22⋊C4—601no—
754C22⋊C4—601no—
755C22⋊C4—601no—
756C22⋊C4—601no—
757C42—62no—
758C42—302no—
759C3×C5#231111yescharacteristic, complemented, Hall
760C22×C3—54no—
761C22×C3—102no—
762C22×C3—102no—
763C22×C3—102no—
764C22×C3—102no—
765C22×C3—102no—
766C22×C3—102no—
767C22×C3—102no—
768C22×C3—102no—
769C22×C3—102no—
770C22×C3—201no—
771C22×C3—201no—
772C22×C3—201no—
773C22×C3—201no—
774C22×C3C22×C4×D511yescharacteristic
775C22×C3C2×D4×D511yescharacteristic
776C22×C3C2×D4×D511yescharacteristic
777C22×C3#414711yescharacteristic
778C22×C3#414711yescharacteristic
779C22×C3#414911yescharacteristic
780C22×C3#414911yescharacteristic
781C2×D3—102no—
782C2×D3—102no—
783C2×D3—102no—
784C2×D3—201no—
785C2×D3—201no—
786C2×D3—201no—
787C2×D3—201no—
788C3×C4—22no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—201no—
792C3×C4—201no—
793Dic3—22no—
794Dic3—41no—
795Dic3—41no—
796Dic3—54no—
797Dic3—201no—
798Dic3—201no—
799Dic3D5×C22⋊C414yes—
800C2×C5C2×D3×C22⋊C411yescharacteristic
801C2×C5#554611yescharacteristic
802C2×C5#554611yescharacteristic
803C2×C5#559211yescharacteristic
804C2×C5#559711yescharacteristic
805C2×C5#559711yescharacteristic
806C2×C5#564811yescharacteristic
807D5—24no—
808D5—42no—
809D5—122no—
810C23—52no—
811C23—52no—
812C23—52no—
813C23—52no—
814C23—101no—
815C23—101no—
816C23—101no—
817C23—101no—
818C23—101no—
819C23—101no—
820C23—101no—
821C23—101no—
822C23—101no—
823C23—101no—
824C23—152no—
825C23—301no—
826C23—301no—
827C23—301no—
828C23—301no—
829C23—301no—
830C23—301no—
831C23C22×D3×D511yescharacteristic
832Q8—68no—
833D4—108no—
834D4—308no—
835D4—308no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—32no—
845C2×C4—32no—
846C2×C4—32no—
847C2×C4—32no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—101no—
857C2×C4—101no—
858C2×C4—101no—
859C2×C4—101no—
860C2×C4—101no—
861C2×C4—101no—
862C2×C4—1516no—
863C2×C4—152no—
864C2×C4—152no—
865C2×C4—152no—
866C2×C4—204no—
867C2×C4—308no—
868C2×C4—308no—
869C2×C4—301no—
870C2×C4—301no—
871C2×C4—301no—
872C2×C4—301no—
873C2×C4—301no—
874C2×C4—301no—
875C2×C4—604no—
876C2×C4C4×D3×D512yes—
877C2×C3—104no—
878C2×C3—202no—
879C2×C3C2×D5×C22⋊C411yescharacteristic
880C2×C3#6590811yescharacteristic
881C2×C3#6590811yescharacteristic
882C2×C3#6596311yescharacteristic
883C2×C3#6596311yescharacteristic
884C2×C3#6600811yescharacteristic
885C2×C3#6605811yescharacteristic
886D3—202no—
887C5#7466211yescharacteristic, complemented, Sylow
888C22—54no—
889C22—102no—
890C22—102no—
891C22—102no—
892C22—102no—
893C22—102no—
894C22—102no—
895C22—102no—
896C22—102no—
897C22—102no—
898C22—201no—
899C22—201no—
900C22—201no—
901C22—201no—
902C22—302no—
903C22—302no—
904C22—302no—
905C22—601no—
906C22—601no—
907C22—601no—
908C22—601no—
909C22#9200011yescharacteristic
910C22C2×C4×D3×D511yescharacteristic
911C22#9201711yescharacteristic
912C22D3×D4×D511yescharacteristic
913C22D3×D4×D511yescharacteristic
914C22#9202611yescharacteristic
915C22#9202811yescharacteristic
916C4—22no—
917C4—34no—
918C4—41no—
919C4—41no—
920C4—62no—
921C4—121no—
922C4—121no—
923C4—154no—
924C4—201no—
925C4—201no—
926C4—601no—
927C4—601no—
928C3#1060821311yescharacteristic, complemented, Sylow
929C2—104no—
930C2—202no—
931C2—602no—
932C2#1175252011yescharacteristic
933C2#1175283211yescharacteristic
934C2D3×D5×C22⋊C411yescharacteristic
935C2#1175322411yescharacteristic
936C2#1175340111yescharacteristic
937C2#1175341211yescharacteristic
938C2#1175341411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6766C2
hypercenter#95D3×D5
hypocenterC3×C5#2311
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#91393C2semidirect
3. C2×D5×Dic3⋊C4C2semidirect
4. #11750768C2semidirect
5. C5×#4646C2semidirect
6. C3×#64954C2semidirect
7. #11748913C2semidirect
8. #11748912C2semidirect
9. #11748907C2semidirect
10. #11748896C2semidirect
11. #11748885C2semidirect
12. #11748885C2semidirect
13. #11748872C2semidirect
14. #11748863C2semidirect
15. #11748692C2semidirect
28. C2×#6766C4semidirect
72. #64954D3semidirect
84. C2×C4×D15C2×C4semidirect
91. C2×C5×Dic6C2×C4semidirect
105. C2×#1202C2×C4semidirect
112. C2×D5×Dic3C2×C4semidirect
148. #4646D5semidirect
256. D5×Dic3C22⋊C4semidirect
455. C2×Dic6C4×D5semidirect
759. C3×C5#2311semidirect
887. C5#74662semidirect
928. C3#10608213semidirect

Maximal subgroups

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

subgroupindex
C22×#67662
C2×#913932
C2×D5×Dic3⋊C42
#117507682
C5×#46462
C3×#649542
#117489132
#117489122
#117489072
#117488962
#117488852
#117488722
#117488632
#117486922
#106082133
#746625