Finite Group Databasebeta

← #28293150

Subgroups — #28293150

Order 13568.

7106 conjugacy classes of subgroups.

The subgroup lattice has 1532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288783C214yesmaximal, complemented
2#20288771C214yesmaximal, complemented
3#20288764C214yesmaximal, complemented
4#20288754C214yesmaximal, complemented
5#20288693C214yesmaximal, complemented
6#20288683C214yesmaximal, complemented
7#20288655C214yesmaximal, complemented
8#20288643C214yesmaximal, complemented
9#20288573C212yesmaximal, complemented
10#20288545C214yesmaximal, complemented
11#20288513C211yesmaximal, characteristic, complemented
12#20288474C211yesmaximal, characteristic, complemented
13#20288418C212yesmaximal, complemented
14#20288408C214yesmaximal, complemented
15#20288360C211yesmaximal, characteristic, complemented
16#20288355C211yesmaximal, characteristic, complemented
17#20288142C212yesmaximal, complemented
18#20288124C214yesmaximal, complemented
19#20288100C212yesmaximal, complemented
20C2×#16811215C214yesmaximal, complemented
21C4×#13133262C211yesmaximal, characteristic, complemented
22C2×#16811102C211yesmaximal, characteristic, complemented
23C4×H(5,𝔽2)×C53C211yesmaximal, characteristic, complemented
24C2×#13133262C2211yescharacteristic
25C22×#11719947C2211yescharacteristic
26#16811356C2214yescomplemented
27#16811351C2214yescomplemented
28#16811345C2214yescomplemented
29#16811343C2214yescomplemented
30#16811341C2214yescomplemented
31#16811333C2214yescomplemented
32#16811332C2214yescomplemented
33#16811332C2214yescomplemented
34#16811330C2214yescomplemented
35#16811328C2214yescomplemented
36#16811328C2214yescomplemented
37#16811323C2214yescomplemented
38#16811322C2218yescomplemented
39#16811322C2218yescomplemented
40#16811319C2218yescomplemented
41#16811317C2214yescomplemented
42#16811314C2214yescomplemented
43#16811313C2218yescomplemented
44#16811313C2218yescomplemented
45#16811312C2214yescomplemented
46#16811312C2214yescomplemented
47#16811308C2214yescomplemented
48#16811306C2218yescomplemented
49#16811306C2218yescomplemented
50#16811306C2218yescomplemented
51#16811302C2218yescomplemented
52#16811302C2218yescomplemented
53#16811299C2218yescomplemented
54#16811299C2218yescomplemented
55#16811299C2218yescomplemented
56#16811297C2218yescomplemented
57D4×Dic106C2214yescomplemented
58#16811282C2218yescomplemented
59#16811278C2214yescomplemented
60#16811277C2214yescomplemented
61#16811277C2214yescomplemented
62#16811274C2214yescomplemented
63#16811272C2214yescomplemented
64#16811272C2214yescomplemented
65#16811272C2214yescomplemented
66#16811268C2214yescomplemented
67#16811268C2214yescomplemented
68#16811267C2214yescomplemented
69#16811267C2214yescomplemented
70#16811267C2214yescomplemented
71#16811263C2218yescomplemented
72#16811261C2214yescomplemented
73D4×C22⋊D53C2214yescomplemented
74#16811251C2212yescomplemented
75#16811249C2214yescomplemented
76#16811245C2212yescomplemented
77#16811245C2212yescomplemented
78#16811244C2214yescomplemented
79#16811238C2212yescomplemented
80#16811238C2212yescomplemented
81#16811238C2214yescomplemented
82#16811235C2214yescomplemented
83#16811231C2214yescomplemented
84#16811231C2212yescomplemented
85#16811231C2212yescomplemented
86#16811224C2212yescomplemented
87#16811224C2212yescomplemented
88#16811220C2218yescomplemented
89#16811215C2218yescomplemented
90#16811215C2218yescomplemented
91#16811215C2218yescomplemented
92#16811215C2214yescomplemented
93#16811215C2218yescomplemented
94#16811215C2218yescomplemented
95#16811215C2218yescomplemented
96#16811215C2218yescomplemented
97#16811215C2214yescomplemented
98#16811215C2218yescomplemented
99#16811211C2218yescomplemented
100#16811206C2218yescomplemented
101#16811206C2214yescomplemented
102#16811206C2214yescomplemented
103#16811201C2212yes—
104#16811199C2212yescomplemented
105#16811194C2212yescomplemented
106#16811185C2214yescomplemented
107#16811182C2214yes—
108#16811182C2214yescomplemented
109#16811180C2214yescomplemented
110#16811177C2214yescomplemented
111#16811176C2212yescomplemented
112#16811169C2212yes—
113#16811157C2214yescomplemented
114#16811157C2218yescomplemented
115#16811157C2214yescomplemented
116#16811157C2214yescomplemented
117#16811155C2214yescomplemented
118#16811153C2218yescomplemented
119#16811153C2218yescomplemented
120#16811153C2218yescomplemented
121#16811151C2214yescomplemented
122#16811151C2214yescomplemented
123C2×#13133211C2214yescomplemented
124C2×#13133210C2214yescomplemented
125C2×#13133209C2214yescomplemented
126C2×#13133207C2214yescomplemented
127#16811135C2212yescomplemented
128#16811134C2218yescomplemented
129#16811132C2218yescomplemented
130#16811132C2218yescomplemented
131#16811130C2212yescomplemented
132C2×#13133201C2214yescomplemented
133C2×#13133200C2214yescomplemented
134C2×#13133199C2214yescomplemented
135C2×#13133198C2214yescomplemented
136C2×#13133196C2214yescomplemented
137C2×#13133195C2214yescomplemented
138C2×#13133194C2214yescomplemented
139C2×#13133189C2214yes—
140#16811104C2212yescomplemented
141#16811102C2214yescomplemented
142#16811102C2214yescomplemented
143#16811102C2214yescomplemented
144#16811102C2214yescomplemented
145#16811102C2214yescomplemented
146#16811098C2211yescharacteristic
147#16811096C2214yescomplemented
148#16811095C2214yescomplemented
149C4×#11719945C2212yescomplemented
150C4×#11719947C2214yescomplemented
151C2×C4×Dic106C2211yescharacteristic, complemented
152C2×#13133182C2211yescharacteristic, complemented
153C2×D4×Dic53C2211yescharacteristic
154C2×C4×C22⋊D53C2214yescomplemented
155C2×C4×C22⋊D53C2212yescomplemented
156C2×#13133177C2212yescomplemented
157C4×D4×D53C2214yescomplemented
158C2×#13133174C2211yescharacteristic, complemented
159C2×#13133173C2212yescomplemented
160C22×#11719919C2212yescomplemented
161C2×C4⋊C4×D53C2211yescharacteristic, complemented
162C2×H(5,𝔽2)×C53C2211yescharacteristic
163C53×#520C2212yescomplemented
164C53×#520C2214yescomplemented
165C53×#518C2211yescharacteristic
166C53×#518C2214yescomplemented
167C53×#518C2214yescomplemented
168C4×#41×C53C2214yescomplemented
169C4×#41×C53C2212yescomplemented
170C2×C4×D4×C53C2211yescharacteristic
171C2×C4×D4×C53C2214yescomplemented
172C2×C4×D4×C53C2214yescomplemented
173#13133262—28no—
174C2×#11719945C2312yes—
175C2×#11719945C2318yes—
176C2×#11719947—28no—
177C2×#11719947C2314yes—
178C2×#11719947C2314yes—
179C2×#11719947C2314yes—
180C22×Dic106C2311yescharacteristic
181C22×Dic106C2314yes—
182C22×C22⋊D53C2312yes—
183C22×C22⋊D53C2314yes—
184C22×C22⋊D53C2314yes—
185C2×D4×D53C2314yes—
186C23×Dic53C2312yes—
187C23×Dic53C2312yes—
188C22×C4×D53C2311yescharacteristic
189C22×C4×D53C2312yes—
190C22×C4×D53C2314yes—
191#13133217C2314yes—
192#13133217C2314yes—
193#13133216C2314yes—
194#13133216C2312yes—
195#13133216C2312yes—
196#13133215C2314yes—
197#13133215C2312yes—
198#13133213C2312yes—
199#13133212C2318yes—
200#13133212C2318yes—
201#13133212C2314yes—
202#13133212C2314yes—
203#13133211C2318yes—
204#13133211C2314yes—
205#13133211C2318yes—
206#13133211C2314yes—
207#13133211C2314yes—
208#13133211C2318yes—
209#13133211C2314yes—
210#13133210C2314yes—
211#13133210C2318yes—
212#13133210C2318yes—
213#13133210C2318yes—
214#13133210C2318yes—
215#13133210C2314yes—
216#13133210C2318yes—
217#13133209C2314yes—
218#13133209C2318yes—
219#13133209C2318yes—
220#13133209C2314yes—
221#13133209C2314yes—
222#13133209C2318yes—
223#13133208C2312yes—
224#13133208C2312yes—
225#13133208C2314yes—
226#13133207C2314yes—
227#13133207C2318yes—
228#13133207C2318yes—
229#13133207C2318yes—
230#13133207C2318yes—
231#13133207C2314yes—
232#13133207C2318yes—
233#13133206C2312yes—
234#13133205C2314yes—
235#13133205C2314yes—
236#13133205C2314yes—
237#13133204C2312yes—
238#13133204C2314yes—
239#13133203C2314yes—
240#13133203C2318yes—
241#13133203C2318yes—
242#13133203C2314yes—
243#13133202C2318yes—
244#13133202C2314yes—
245#13133202C2314yes—
246#13133201C2318yes—
247#13133201C2318yes—
248#13133201C2318yes—
249#13133201C2314yes—
250#13133201C2318yes—
251#13133200C2318yes—
252#13133200C2318yes—
253#13133200C2318yes—
254#13133200C2314yes—
255#13133200C2314yes—
256#13133200C2318yes—
257#13133200C2314yes—
258#13133200C2318yes—
259#13133200C2314yes—
260#13133199C2318yes—
261#13133199C2318yes—
262#13133199C2314yes—
263#13133199C2318yes—
264#13133199C2314yes—
265#13133199C2318yes—
266#13133198C2318yes—
267#13133198C2318yes—
268#13133198C2318yes—
269#13133198C2314yes—
270#13133198C2318yes—
271#13133197C2314yes—
272#13133197C2314yes—
273#13133197C2312yes—
274#13133197C2312yes—
275#13133196C2314yes—
276#13133196C2314yes—
277#13133196C2314yes—
278#13133196C2318yes—
279#13133196C2318yes—
280#13133196C2318yes—
281#13133196C2314yes—
282#13133196C2318yes—
283#13133196C2314yes—
284#13133196C2318yes—
285#13133195C2318yes—
286#13133195C2318yes—
287#13133195C2318yes—
288#13133195C2314yes—
289#13133195C2314yes—
290#13133195C2318yes—
291#13133194C2318yes—
292#13133194C2318yes—
293#13133194C2318yes—
294#13133194C2318yes—
295#13133194C2314yes—
296#13133194C2318yes—
297#13133194C2314yes—
298#13133193C2312yes—
299#13133193C2312yes—
300#13133193C2314yes—
301#13133192C2312yes—
302#13133192C2312yes—
303#13133191C2318yes—
304#13133191C2318yes—
305#13133191C2314yes—
306#13133191C2314yes—
307#13133191C2314yes—
308#13133190C2318yes—
309#13133190C2314yes—
310#13133190C2314yes—
311#13133189C2318yes—
312#13133189C2318yes—
313#13133189C2318yes—
314#13133189C2318yes—
315#13133189C2314yes—
316#13133189C2318yes—
317#13133189C2314yes—
318#13133188C2312yes—
319#13133188C2312yes—
320#13133188C2314yes—
321#13133187C2318yes—
322#13133187C2314yes—
323#13133186C2318yes—
324#13133186C2318yes—
325#13133185C2318yes—
326#13133185C2314yes—
327C4×Dic106C2318yes—
328C4×Dic106C2314yes—
329C4×Dic106C2318yes—
330C4×Dic106C2314yes—
331C4×Dic106C2314yes—
332C4×Dic106C2314yes—
333C4×Dic106C2312yes—
334C4×Dic106C2312yes—
335#13133182C2314yes—
336#13133182C2314yes—
337#13133182C2314yes—
338C4×D212C2314yes—
339C4×D212C2314yes—
340C4×D212C2318yes—
341C4×D212C2312yes—
342C4×D212C2312yes—
343D4×Dic53C2314yes—
344D4×Dic53C2314yes—
345D4×Dic53C2314yes—
346D4×Dic53C2314yes—
347#13133179C2314yes—
348C4×C22⋊D53C2314yes—
349C4×C22⋊D53C2314yes—
350C4×C22⋊D53C2314yes—
351C4×C22⋊D53C2314yes—
352C4×C22⋊D53C2318yes—
353C4×C22⋊D53C2318yes—
354C4×C22⋊D53C2318yes—
355C4×C22⋊D53C2318yes—
356C4×C22⋊D53C2314yes—
357C4×C22⋊D53C2318yes—
358C4×C22⋊D53C2318yes—
359C4×C22⋊D53C2318yes—
360C4×C22⋊D53C2318yes—
361C4×C22⋊D53C2314yes—
362#13133177C2318yes—
363#13133177C2318yes—
364#13133177C2318yes—
365#13133177C2318yes—
366#13133176C2318yes—
367#13133176C2318yes—
368#13133176C2312yes—
369#13133175C2314yes—
370#13133174C2318yes—
371#13133174C2318yes—
372#13133174C2318yes—
373#13133174C2312yes—
374#13133174C2312yes—
375#13133174C2312yes—
376#13133174C2312yes—
377#13133174C2314yes—
378#13133173C2318yes—
379#13133173C2318yes—
380#13133173C2318yes—
381C2×C4⋊Dic53C2314yes—
382C2×C4⋊Dic53C2314yes—
383C2×C4⋊Dic53C2314yes—
384C2×C4⋊Dic53C2311yescharacteristic
385C2×#11719919C2314yes—
386C2×#11719919C2314yes—
387C2×#11719919C2314yes—
388C2×#11719919C2314yes—
389C2×#11719919C2314yes—
390C2×#11719919C2312yes—
391C2×#11719919C2311yescharacteristic
392C2×#11719919C2312yes—
393C2×#11719919C2312yes—
394C2×#11719919C2314yes—
395C2×#11719919C2314yes—
396C2×#11719919C2314yes—
397C2×#11719919C2314yes—
398C2×#11719919C2311yescharacteristic
399C2×#11719919C2314yes—
400C4⋊C4×D53C2314yes—
401C4⋊C4×D53C2314yes—
402C4⋊C4×D53C2314yes—
403C2×C22⋊Dic53C2314yes—
404C2×C22⋊Dic53C2314yes—
405C2×C22⋊Dic53C2314yes—
406C2×C22⋊Dic53C2312yes—
407C2×C22⋊Dic53C2314yes—
408C2×#11719921C2314yes—
409C2×#11719921C2314yes—
410C2×#11719921C2314yes—
411C2×#11719921C2311yescharacteristic
412C2×#11719921C2311yescharacteristic
413C2×#11719921C2314yes—
414C22⋊C4×D53C2318yes—
415C2×C4×Dic53C2312yes—
416C2×C4×Dic53C2312yes—
417C2×C4×Dic53C2311yescharacteristic
418C2×C4×Dic53C2314yes—
419C42×D53C2314yes—
420H(5,𝔽2)×C53—28no—
421C2×#41×C53C2314yes—
422C2×#41×C53C2312yes—
423C22×D4×C53C2314yes—
424C22×D4×C53C2314yes—
425C22×D4×C53C2311yescharacteristic
426C23×C4×C53C2312yes—
427C23×C4×C53C2314yes—
428C4×Q8×C53C2312yes—
429C4×Q8×C53C2314yes—
430C4×Q8×C53C2312yes—
431C4×D4×C53C2314yes—
432C4×D4×C53C2314yes—
433C4×D4×C53C2314yes—
434C4×D4×C53C2318yes—
435C4×D4×C53C2314yes—
436C4×D4×C53C2314yes—
437C4×D4×C53C2314yes—
438C4×D4×C53C2318yes—
439C4×D4×C53C2312yes—
440C4×D4×C53C2318yes—
441C4×D4×C53C2318yes—
442C4×D4×C53C2318yes—
443C4×D4×C53C2314yes—
444C4×D4×C53C2312yes—
445#117×C53C2312yes—
446#117×C53C2318yes—
447#117×C53C2314yes—
448#117×C53C2314yes—
449C2×C4⋊C4×C53C2314yes—
450C2×C4⋊C4×C53C2311yescharacteristic
451C2×C4⋊C4×C53C2314yes—
452C2×C22⋊C4×C53C2312yes—
453C2×C22⋊C4×C53C2314yes—
454C2×C22⋊C4×C53C2318yes—
455C2×C22⋊C4×C53C2314yes—
456C2×C42×C53C2311yescharacteristic
457C2×C42×C53C2314yes—
458C2×C42×C53C2314yes—
459C24×C53C2414yes—
460C24×C53C2412yes—
461C23×D53C2414yes—
462C23×D53C2411yescharacteristic
463#41×C53—216no—
464#41×C53—28no—
465C2×Q8×C53C2412yes—
466C2×D4×C53—216no—
467C2×D4×C53—216no—
468C2×D4×C53#4118yescomplemented
469C2×D4×C53C2418yes—
470C2×D4×C53C2414yes—
471C2×D4×C53C2412yes—
472C2×D4×C53C2414yes—
473C22×C4×C53—84no—
474C22×C4×C53—82no—
475C22×C4×C53C2414yes—
476C22×C4×C53C2414yes—
477C22×C4×C53C2411yescharacteristic
478C22×C4×C53C2414yes—
479C22×C4×C53C2414yes—
480C22×C4×C53C2411yescharacteristic
481C22×C4×C53C2414yes—
482C22×C4×C53C2414yes—
483C22×C4×C53C2412yes—
484C22×C4×C53C2414yes—
485C22×C4×C53C2414yes—
486C22×C4×C53C2418yes—
487C22×C4×C53C2411yescharacteristic
488C2×C22⋊D53—28no—
489C2×C22⋊D53—216no—
490C2×C22⋊D53—84no—
491C2×C22⋊D53C2418yes—
492C2×C22⋊D53C2418yes—
493C2×C22⋊D53C2414yes—
494C2×C22⋊D53C2414yes—
495C2×C22⋊D53C2414yes—
496C2×C22⋊D53C2414yes—
497C2×C22⋊D53C2418yes—
498C2×C22⋊D53C2414yes—
499C22×Dic53—28no—
500C22×Dic53—82no—
501C22×Dic53C2412yes—
502C22×Dic53C2414yes—
503C22×Dic53C2414yes—
504C22×Dic53C2414yes—
505C22×Dic53C2411yescharacteristic
506C22×Dic53C2411yescharacteristic
507C22×Dic53C2414yes—
508C22×Dic53C2411yescharacteristic
509C22×Dic53C2412yes—
510C22×Dic53C2414yes—
511C22×Dic53C2414yes—
512C22×Dic53C2414yes—
513#11719947—216no—
514#11719947—216no—
515#11719947—216no—
516D4×D53—216no—
517#11719945—28no—
518#11719945—88no—
519C2×D212C2412yes—
520C2×D212C2414yes—
521C2×D212C2414yes—
522C2×C4×D53—24no—
523C2×C4×D53—84no—
524C2×C4×D53—82no—
525C2×C4×D53C2414yes—
526C2×C4×D53C2412yes—
527C2×C4×D53C2412yes—
528C2×C4×D53C2414yes—
529C2×C4×D53C2414yes—
530C2×C4×D53C2418yes—
531C2×C4×D53C2418yes—
532C2×Dic106—24no—
533C2×Dic106—84no—
534C2×Dic106C2414yes—
535C2×Dic106C2412yes—
536C2×Dic106C2414yes—
537C2×Dic106C2414yes—
538C2×Dic106C2418yes—
539C4⋊C4×C53C2414yes—
540C4⋊C4×C53C2412yes—
541C4⋊C4×C53C2418yes—
542C4⋊C4×C53C2414yes—
543C4⋊C4×C53C2412yes—
544C4⋊C4×C53C2414yes—
545C22⋊C4×C53C2418yes—
546C22⋊C4×C53C2414yes—
547C22⋊C4×C53C2418yes—
548C22⋊C4×C53C2418yes—
549C22⋊C4×C53C2414yes—
550C22⋊C4×C53C2414yes—
551C42×C53C2412yes—
552C42×C53C2414yes—
553C42×C53C2412yes—
554C42×C53C2418yes—
555C42×C53C2414yes—
556C42×C53C2414yes—
557C22⋊Dic53C2418yes—
558C22⋊Dic53C2414yes—
559C22⋊Dic53C2414yes—
560C22⋊Dic53C2414yes—
561C22⋊Dic53C2414yes—
562C22⋊Dic53C2418yes—
563C22⋊Dic53C2418yes—
564C22⋊Dic53C2418yes—
565C22⋊Dic53C2418yes—
566C22⋊Dic53C2414yes—
567#11719921C2414yes—
568#11719921C2418yes—
569#11719921C2414yes—
570#11719921C2414yes—
571#11719921C2414yes—
572#11719921C2414yes—
573#11719921C2412yes—
574#11719921C2412yes—
575#11719921C2412yes—
576#11719921C2412yes—
577#11719921C2418yes—
578#11719921C2418yes—
579#11719921C2418yes—
580#11719921C2414yes—
581#11719921C2414yes—
582#11719921C2414yes—
583#11719921C2414yes—
584#11719921C2414yes—
585C4⋊Dic53C2414yes—
586C4⋊Dic53C2412yes—
587C4⋊Dic53C2414yes—
588C4⋊Dic53C2414yes—
589C4⋊Dic53C2414yes—
590C4⋊Dic53C2418yes—
591C4⋊Dic53C2418yes—
592C4⋊Dic53C2418yes—
593C4⋊Dic53C2412yes—
594C4⋊Dic53C2414yes—
595#11719919C2414yes—
596#11719919C2414yes—
597#11719919C2418yes—
598#11719919C2411yescharacteristic
599#11719919C2411yescharacteristic
600#11719919C2411yescharacteristic
601#11719919C2411yescharacteristic
602#11719919C2414yes—
603#11719919C2414yes—
604#11719919C2414yes—
605#11719919C2414yes—
606#11719919C2414yes—
607#11719919C2414yes—
608#11719919C2414yes—
609#11719919C2414yes—
610#11719919C2414yes—
611#11719919C2414yes—
612#11719919C2412yes—
613#11719919C2412yes—
614#11719919C2418yes—
615#11719919C2418yes—
616#11719919C2418yes—
617#11719919C2418yes—
618#11719919C2418yes—
619#11719919C2414yes—
620#11719919C2414yes—
621#11719919C2414yes—
622#11719919C2414yes—
623C4×Dic53C2414yes—
624C4×Dic53C2414yes—
625C4×Dic53C2414yes—
626C4×Dic53C2418yes—
627C4×Dic53C2418yes—
628C4×Dic53C2418yes—
629C4×Dic53C2412yes—
630C4×Dic53C2412yes—
631C23×C53—28no—
632C23×C53—42no—
633C23×C53—42no—
634C23×C53—44no—
635C23×C53—44no—
636C23×C53C2×#4118yes—
637C23×C53C2514yes—
638C23×C53C2514yes—
639C23×C53C2511yescharacteristic
640C22×D53—22no—
641C22×D53—28no—
642C22×D53—41no—
643C22×D53—41no—
644C22×D53—44no—
645C22×D53—44no—
646C22×D53C2512yes—
647C22×D53C2514yes—
648Q8×C53—24no—
649D4×C53—216no—
650D4×C53—28no—
651D4×C53—24no—
652D4×C53C2×#41116yes—
653C2×C4×C53—28no—
654C2×C4×C53—28no—
655C2×C4×C53—44no—
656C2×C4×C53—44no—
657C2×C4×C53—42no—
658C2×C4×C53—48no—
659C2×C4×C53—44no—
660C2×C4×C53—41no—
661C2×C4×C53—44no—
662C2×C4×C53—44no—
663C2×C4×C53—44no—
664C2×C4×C53—41no—
665C2×C4×C53C2×#4114yes—
666C2×C4×C53C2514yes—
667C2×C4×C53C2514yes—
668C2×C4×C53C2511yescharacteristic
669C2×C4×C53C2514yes—
670C2×C4×C53C2512yes—
671C2×C4×C53C2511yescharacteristic
672C2×C4×C53C2514yes—
673C2×C4×C53C2512yes—
674C22⋊D53—28no—
675C22⋊D53—216no—
676C22⋊D53—216no—
677C22⋊D53—44no—
678C22⋊D53—48no—
679C22⋊D53—44no—
680C22⋊D53—44no—
681C22⋊D53—44no—
682C2×Dic53—24no—
683C2×Dic53—22no—
684C2×Dic53—28no—
685C2×Dic53—28no—
686C2×Dic53—28no—
687C2×Dic53—44no—
688C2×Dic53—44no—
689C2×Dic53—42no—
690C2×Dic53—41no—
691C2×Dic53—44no—
692C2×Dic53—41no—
693C2×Dic53—44no—
694C2×Dic53C2511yescharacteristic
695C2×Dic53C2514yes—
696C2×Dic53C2514yes—
697C2×Dic53C2514yes—
698C2×Dic53C2512yes—
699C2×Dic53C2514yes—
700C2×Dic53C2514yes—
701C2×Dic53C2511yescharacteristic
702C2×Dic53C2511yescharacteristic
703C2×Dic53C2511yescharacteristic
704D212—24no—
705D212—44no—
706D212—44no—
707C4×D53—24no—
708C4×D53—24no—
709C4×D53—28no—
710C4×D53—44no—
711C4×D53—48no—
712C4×D53—48no—
713C4×D53—44no—
714Dic106—28no—
715Dic106—24no—
716Dic106—44no—
717Dic106—48no—
718Dic106—44no—
719#62847—531nomaximal, Sylow
720C22×C53—21no—
721C22×C53—24no—
722C22×C53—21no—
723C22×C53—24no—
724C22×C53—24no—
725C22×C53—24no—
726C22×C53—24no—
727C22×C53—48no—
728C22×C53—88no—
729C22×C53C22×#4118yes—
730C22×C53C22×#4112yes—
731C22×C53C2611yescharacteristic
732C2×D53—22no—
733C2×D53—24no—
734C2×D53—22no—
735C2×D53—24no—
736C2×D53—24no—
737C2×D53—22no—
738C2×D53—44no—
739C2×D53—88no—
740C4×C53—24no—
741C4×C53—24no—
742C4×C53—21no—
743C4×C53—24no—
744C4×C53—21no—
745C4×C53—24no—
746C4×C53—22no—
747C4×C53C22×#4114yes—
748Dic53—24no—
749Dic53—24no—
750Dic53—21no—
751Dic53—21no—
752Dic53—21no—
753Dic53—24no—
754Dic53—24no—
755Dic53—21no—
756Dic53—22no—
757Dic53—24no—
758#3521—534no—
759#3521—534no—
760#3520—534no—
761#3520—534no—
762#3515—534no—
763#3515—534no—
764#3513—534no—
765#3513—534no—
766#3507—532no—
767#3505—534no—
768#3501—531no—
769#3496—531no—
770#3492—532no—
771#3491—534no—
772#3485—531no—
773#3485—531no—
774#3461—532no—
775#3459—534no—
776#3455—532no—
777C2×#539—534no—
778C4×H(5,𝔽2)—531no—
779C4×H(5,𝔽2)D5311yescharacteristic, complemented
780C2×#520—531no—
781C2×C53—22no—
782C2×C53—28no—
783C2×C53—44no—
784C2×C53C23×#4111yescharacteristic
785C2×C53H(7,𝔽2)11yescharacteristic
786C2×C532−1+611yescharacteristic
787D53—42no—
788D53—44no—
789C2×H(5,𝔽2)—531no—
790C2×H(5,𝔽2)C2×D5311yescharacteristic
791C22×#41—531no—
792#559—534no—
793#557—534no—
794#556—534no—
795#556—534no—
796#556—534no—
797#554—534no—
798#554—534no—
799#554—534no—
800#554—534no—
801#554—534no—
802#554—534no—
803#553—538no—
804#553—538no—
805#553—538no—
806#553—534no—
807#553—534no—
808#552—534no—
809#552—538no—
810#552—538no—
811#552—538no—
812#552—538no—
813#552—538no—
814#552—534no—
815#552—534no—
816#552—534no—
817#551—538no—
818#551—538no—
819#551—538no—
820#551—538no—
821#551—538no—
822#551—538no—
823D4×Q8—534no—
824#548—538no—
825#547—534no—
826#547—534no—
827#547—534no—
828#547—534no—
829#547—534no—
830#547—534no—
831#547—534no—
832#546—534no—
833#546—534no—
834#546—534no—
835#546—534no—
836#546—534no—
837#546—534no—
838#546—538no—
839D42—534no—
840#544—532no—
841#543—534no—
842#542—532no—
843#542—532no—
844#542—532no—
845#542—532no—
846#542—534no—
847#542—534no—
848#541—532no—
849#541—532no—
850#541—534no—
851#541—534no—
852#540—532no—
853#540—532no—
854#539—534no—
855#539—538no—
856#539—538no—
857#539—538no—
858#539—538no—
859#539—538no—
860#539—538no—
861#539—538no—
862#539—534no—
863#539—538no—
864#539—538no—
865#538—534no—
866#538—534no—
867#538—538no—
868#538—538no—
869#537—532no—
870#536—532no—
871#536—532no—
872#534—534no—
873#534—534no—
874#534—534no—
875#533—534no—
876#533—532no—
877#533—534no—
878#532—532no—
879#529—538no—
880#529—538no—
881#529—538no—
882#529—534no—
883#529—534no—
884#529—534no—
885#529—534no—
886#529—534no—
887#529—538no—
888#529—534no—
889C2×#126—534no—
890C2×#126—534no—
891C2×#125—534no—
892C2×#125—534no—
893#525—532no—
894#525—538no—
895#525—538no—
896#525—538no—
897#525—532no—
898C2×#123—534no—
899C2×#123—534no—
900C2×#123—534no—
901C2×#123—534no—
902C2×C22⋊Q8—534no—
903C2×C22⋊Q8—534no—
904C2×C22⋊Q8—534no—
905C2×#121—534no—
906#520—534no—
907#520—534no—
908#520—534no—
909#520—534no—
910#520—534no—
911#520—532no—
912#520C2×D5312yescomplemented
913#520C2×D5314yescomplemented
914#518—531no—
915#518—534no—
916#518—534no—
917#518C2×D5311yescharacteristic
918#518C2×D5314yescomplemented
919#518C2×D5314yescomplemented
920C4×#41—534no—
921C4×#41—532no—
922C4×#41C2×D5312yescomplemented
923C4×#41C2×D5314yescomplemented
924C2×C4×Q8—531no—
925C2×C4×Q8—531no—
926C2×C4×D4—531no—
927C2×C4×D4—532no—
928C2×C4×D4—534no—
929C2×C4×D4—534no—
930C2×C4×D4—532no—
931C2×C4×D4C2×D5311yescharacteristic
932C2×C4×D4C2×D5314yescomplemented
933C2×C4×D4C2×D5314yescomplemented
934C2×#117—532no—
935C2×#117—531no—
936C22×C4⋊C4—532no—
937C22×C4⋊C4—531no—
938C53#6284711yescharacteristic, complemented, Sylow
939H(5,𝔽2)—28no—
940H(5,𝔽2)—1068no—
941C2×#41—534no—
942C2×#41—534no—
943C2×#41—534no—
944C2×#41—532no—
945C2×#41—538no—
946C2×#41—1068no—
947C2×#41C22×D5312yes—
948C2×#41C22×D5314yes—
949C22×Q8—531no—
950C22×Q8—534no—
951C22×D4—532no—
952C22×D4—534no—
953C22×D4—534no—
954C22×D4—534no—
955C22×D4C22×D5314yes—
956C22×D4C22×D5314yes—
957C22×D4C22×D5311yescharacteristic
958C23×C4—532no—
959C23×C4—532no—
960C23×C4—531no—
961C23×C4—532no—
962C23×C4—534no—
963C23×C4C22×D5312yes—
964C23×C4C22×D5314yes—
965C4⋊Q8—532no—
966C4⋊Q8—534no—
967C4⋊Q8—532no—
968C4⋊Q8—532no—
969C4⋊Q8—534no—
970C4⋊Q8—534no—
971C4⋊Q8—534no—
972#127—532no—
973#126—534no—
974#126—538no—
975#126—534no—
976#126—538no—
977#126—534no—
978#126—538no—
979#126—538no—
980#126—538no—
981#126—538no—
982#126—534no—
983#126—538no—
984#126—534no—
985#126—538no—
986#126—538no—
987#126—538no—
988#126—534no—
989#126—534no—
990#126—534no—
991#125—534no—
992#125—538no—
993#125—538no—
994#125—538no—
995#125—538no—
996#125—534no—
997#125—538no—
998#125—534no—
999#125—532no—
1000#125—532no—
1001#125—534no—
1002#125—538no—
1003#125—538no—
1004#125—538no—
1005#125—534no—
1006#125—534no—
1007#124—532no—
1008#124—534no—
1009#124—532no—
1010#124—534no—
1011#124—538no—
1012#124—534no—
1013#124—538no—
1014#124—534no—
1015#124—534no—
1016#124—534no—
1017#123—534no—
1018#123—538no—
1019#123—538no—
1020#123—538no—
1021#123—538no—
1022#123—534no—
1023#123—538no—
1024#123—538no—
1025#123—538no—
1026#123—534no—
1027#123—538no—
1028#123—538no—
1029#123—534no—
1030#123—534no—
1031#123—534no—
1032#123—538no—
1033#123—534no—
1034#123—534no—
1035#123—534no—
1036#123—538no—
1037#123—538no—
1038#123—538no—
1039#123—538no—
1040#123—538no—
1041#123—538no—
1042#123—538no—
1043#123—538no—
1044#123—534no—
1045C22⋊Q8—532no—
1046C22⋊Q8—532no—
1047C22⋊Q8—534no—
1048C22⋊Q8—534no—
1049C22⋊Q8—538no—
1050C22⋊Q8—538no—
1051C22⋊Q8—538no—
1052C22⋊Q8—538no—
1053C22⋊Q8—534no—
1054C22⋊Q8—538no—
1055C22⋊Q8—534no—
1056C22⋊Q8—534no—
1057C22⋊Q8—534no—
1058C22⋊Q8—534no—
1059C22⋊Q8—538no—
1060C22⋊Q8—538no—
1061C22⋊Q8—538no—
1062C22⋊Q8—538no—
1063C22⋊Q8—532no—
1064C22⋊Q8—532no—
1065C22⋊Q8—534no—
1066C22⋊Q8—534no—
1067C22⋊Q8—534no—
1068C22⋊Q8—534no—
1069C22⋊Q8—538no—
1070C22⋊Q8—538no—
1071C22⋊Q8—538no—
1072C22⋊Q8—538no—
1073C22⋊Q8—534no—
1074C22⋊Q8—538no—
1075#121—534no—
1076#121—538no—
1077#121—538no—
1078#121—538no—
1079#121—538no—
1080#121—532no—
1081#121—532no—
1082#121—534no—
1083#121—538no—
1084#121—534no—
1085#121—534no—
1086#121—538no—
1087#121—538no—
1088#121—534no—
1089#121—534no—
1090#121—532no—
1091#121—532no—
1092#121—534no—
1093#121—538no—
1094#121—534no—
1095#120—538no—
1096#120—538no—
1097#120—534no—
1098#120—538no—
1099#120—534no—
1100#120—538no—
1101C4×Q8—534no—
1102C4×Q8—534no—
1103C4×Q8—534no—
1104C4×Q8—534no—
1105C4×Q8—534no—
1106C4×Q8—532no—
1107C4×Q8—532no—
1108C4×Q8—538no—
1109C4×Q8—534no—
1110C4×Q8—534no—
1111C4×Q8—538no—
1112C4×Q8C22×D5312yes—
1113C4×Q8C22×D5312yes—
1114C4×Q8C22×D5314yes—
1115C4×D4—534no—
1116C4×D4—534no—
1117C4×D4—534no—
1118C4×D4—534no—
1119C4×D4—538no—
1120C4×D4—534no—
1121C4×D4—538no—
1122C4×D4—538no—
1123C4×D4—538no—
1124C4×D4—538no—
1125C4×D4—534no—
1126C4×D4—538no—
1127C4×D4—538no—
1128C4×D4—534no—
1129C4×D4—534no—
1130C4×D4—538no—
1131C4×D4—534no—
1132C4×D4—534no—
1133C4×D4—534no—
1134C4×D4—538no—
1135C4×D4—538no—
1136C4×D4—538no—
1137C4×D4—538no—
1138C4×D4—532no—
1139C4×D4—532no—
1140C4×D4—538no—
1141C4×D4—534no—
1142C4×D4—534no—
1143C4×D4C22×D5314yes—
1144C4×D4C22×D5314yes—
1145C4×D4C22×D5314yes—
1146C4×D4C22×D5318yes—
1147C4×D4C22×D5312yes—
1148C4×D4C22×D5314yes—
1149C4×D4C22×D5318yes—
1150C4×D4C22×D5318yes—
1151C4×D4C22×D5314yes—
1152C4×D4C22×D5318yes—
1153C4×D4C22×D5314yes—
1154C4×D4C22×D5314yes—
1155C4×D4C22×D5312yes—
1156C4×D4C22×D5318yes—
1157#117—532no—
1158#117—538no—
1159#117—538no—
1160#117—534no—
1161#117—538no—
1162#117—538no—
1163#117—538no—
1164#117—532no—
1165#117—532no—
1166#117—532no—
1167#117—532no—
1168#117—534no—
1169#117—538no—
1170#117—538no—
1171#117—538no—
1172#117C22×D5312yes—
1173#117C22×D5314yes—
1174#117C22×D5318yes—
1175#117C22×D5314yes—
1176C2×C4⋊C4—531no—
1177C2×C4⋊C4—532no—
1178C2×C4⋊C4—531no—
1179C2×C4⋊C4—532no—
1180C2×C4⋊C4—532no—
1181C2×C4⋊C4—534no—
1182C2×C4⋊C4—534no—
1183C2×C4⋊C4—534no—
1184C2×C4⋊C4—534no—
1185C2×C4⋊C4—531no—
1186C2×C4⋊C4—534no—
1187C2×C4⋊C4—534no—
1188C2×C4⋊C4—534no—
1189C2×C4⋊C4—534no—
1190C2×C4⋊C4—534no—
1191C2×C4⋊C4—534no—
1192C2×C4⋊C4—534no—
1193C2×C4⋊C4—534no—
1194C2×C4⋊C4—534no—
1195C2×C4⋊C4—534no—
1196C2×C4⋊C4—534no—
1197C2×C4⋊C4—534no—
1198C2×C4⋊C4C22×D5311yescharacteristic
1199C2×C4⋊C4C22×D5314yes—
1200C2×C4⋊C4C22×D5314yes—
1201C2×C22⋊C4—532no—
1202C2×C22⋊C4—534no—
1203C2×C22⋊C4—534no—
1204C2×C22⋊C4—534no—
1205C2×C22⋊C4—534no—
1206C2×C22⋊C4—531no—
1207C2×C22⋊C4—531no—
1208C2×C22⋊C4—534no—
1209C2×C22⋊C4—534no—
1210C2×C22⋊C4—534no—
1211C2×C22⋊C4—534no—
1212C2×C22⋊C4—538no—
1213C2×C22⋊C4C22×D5312yes—
1214C2×C22⋊C4C22×D5314yes—
1215C2×C22⋊C4C22×D5314yes—
1216C2×C22⋊C4C22×D5318yes—
1217C2×C42—532no—
1218C2×C42—532no—
1219C2×C42—531no—
1220C2×C42—534no—
1221C2×C42—534no—
1222C2×C42C22×D5311yescharacteristic
1223C2×C42C22×D5314yes—
1224C2×C42C22×D5314yes—
1225C24—534no—
1226C24—531no—
1227C24C23×D5314yes—
1228C24C23×D5312yes—
1229#41—216no—
1230#41—28no—
1231#41—10616no—
1232#41—10616no—
1233#41—10616no—
1234#41—1068no—
1235#41—4248no—
1236C2×Q8—534no—
1237C2×Q8—532no—
1238C2×Q8—534no—
1239C2×Q8—534no—
1240C2×Q8—538no—
1241C2×Q8—1064no—
1242C2×Q8—4244no—
1243C2×Q8C23×D5312yes—
1244C2×D4—216no—
1245C2×D4—216no—
1246C2×D4—538no—
1247C2×D4—538no—
1248C2×D4—534no—
1249C2×D4—534no—
1250C2×D4—534no—
1251C2×D4—534no—
1252C2×D4—538no—
1253C2×D4—534no—
1254C2×D4—532no—
1255C2×D4—534no—
1256C2×D4—534no—
1257C2×D4—1068no—
1258C2×D4—10616no—
1259C2×D4—10616no—
1260C2×D4—4244no—
1261C2×D4#1171994518yescomplemented
1262C2×D4C23×D5314yes—
1263C2×D4C23×D5318yes—
1264C2×D4C23×D5312yes—
1265C2×D4C23×D5314yes—
1266C22×C4—82no—
1267C22×C4—84no—
1268C22×C4—532no—
1269C22×C4—534no—
1270C22×C4—534no—
1271C22×C4—534no—
1272C22×C4—531no—
1273C22×C4—531no—
1274C22×C4—534no—
1275C22×C4—531no—
1276C22×C4—532no—
1277C22×C4—534no—
1278C22×C4—534no—
1279C22×C4—534no—
1280C22×C4—534no—
1281C22×C4—532no—
1282C22×C4—532no—
1283C22×C4—534no—
1284C22×C4—534no—
1285C22×C4—538no—
1286C22×C4—538no—
1287C22×C4—1068no—
1288C22×C4—1064no—
1289C22×C4—4244no—
1290C22×C4—4242no—
1291C22×C4—4242no—
1292C22×C4C23×D5314yes—
1293C22×C4C23×D5314yes—
1294C22×C4C23×D5311yescharacteristic
1295C22×C4C23×D5312yes—
1296C22×C4C23×D5314yes—
1297C22×C4C23×D5314yes—
1298C22×C4C23×D5311yescharacteristic
1299C22×C4C23×D5314yes—
1300C22×C4C23×D5314yes—
1301C22×C4C23×D5314yes—
1302C22×C4C23×D5314yes—
1303C22×C4C23×D5318yes—
1304C22×C4C23×D5311yescharacteristic
1305C4⋊C4—531no—
1306C4⋊C4—531no—
1307C4⋊C4—534no—
1308C4⋊C4—534no—
1309C4⋊C4—531no—
1310C4⋊C4—531no—
1311C4⋊C4—534no—
1312C4⋊C4—534no—
1313C4⋊C4—534no—
1314C4⋊C4—534no—
1315C4⋊C4—534no—
1316C4⋊C4—532no—
1317C4⋊C4—538no—
1318C4⋊C4—534no—
1319C4⋊C4—534no—
1320C4⋊C4—534no—
1321C4⋊C4—534no—
1322C4⋊C4—534no—
1323C4⋊C4—534no—
1324C4⋊C4—534no—
1325C4⋊C4—534no—
1326C4⋊C4—534no—
1327C4⋊C4—532no—
1328C4⋊C4—532no—
1329C4⋊C4—538no—
1330C4⋊C4—538no—
1331C4⋊C4—538no—
1332C4⋊C4—538no—
1333C4⋊C4—538no—
1334C4⋊C4—538no—
1335C4⋊C4—538no—
1336C4⋊C4—538no—
1337C4⋊C4—532no—
1338C4⋊C4—534no—
1339C4⋊C4—534no—
1340C4⋊C4—534no—
1341C4⋊C4—534no—
1342C4⋊C4—534no—
1343C4⋊C4C23×D5314yes—
1344C4⋊C4C23×D5312yes—
1345C4⋊C4C23×D5314yes—
1346C4⋊C4C23×D5318yes—
1347C4⋊C4C23×D5312yes—
1348C4⋊C4C23×D5314yes—
1349C22⋊C4—534no—
1350C22⋊C4—538no—
1351C22⋊C4—534no—
1352C22⋊C4—534no—
1353C22⋊C4—534no—
1354C22⋊C4—538no—
1355C22⋊C4—538no—
1356C22⋊C4—538no—
1357C22⋊C4—538no—
1358C22⋊C4—534no—
1359C22⋊C4—538no—
1360C22⋊C4—534no—
1361C22⋊C4—534no—
1362C22⋊C4—534no—
1363C22⋊C4—534no—
1364C22⋊C4—534no—
1365C22⋊C4—532no—
1366C22⋊C4—532no—
1367C22⋊C4—532no—
1368C22⋊C4—532no—
1369C22⋊C4—538no—
1370C22⋊C4—538no—
1371C22⋊C4—538no—
1372C22⋊C4—534no—
1373C22⋊C4—534no—
1374C22⋊C4—534no—
1375C22⋊C4—534no—
1376C22⋊C4—534no—
1377C22⋊C4C23×D5318yes—
1378C22⋊C4C23×D5314yes—
1379C22⋊C4C23×D5318yes—
1380C22⋊C4C23×D5314yes—
1381C22⋊C4C23×D5318yes—
1382C22⋊C4C23×D5314yes—
1383C42—534no—
1384C42—538no—
1385C42—538no—
1386C42—538no—
1387C42—534no—
1388C42—534no—
1389C42—532no—
1390C42—532no—
1391C42C23×D5312yes—
1392C42C23×D5312yes—
1393C42C23×D5314yes—
1394C42C23×D5318yes—
1395C42C23×D5314yes—
1396C42C23×D5314yes—
1397C23—28no—
1398C23—42no—
1399C23—42no—
1400C23—44no—
1401C23—44no—
1402C23—534no—
1403C23—532no—
1404C23—1068no—
1405C23—1062no—
1406C23—2124no—
1407C23—2124no—
1408C23—2121no—
1409C23—2121no—
1410C23C2×#1171994518yes—
1411C23C24×D5314yes—
1412C23C24×D5314yes—
1413C23C24×D5311yescharacteristic
1414Q8—24no—
1415Q8—1068no—
1416Q8—1064no—
1417Q8—2124no—
1418Q8—2124no—
1419Q8—2128no—
1420D4—216no—
1421D4—28no—
1422D4—24no—
1423D4—10616no—
1424D4—1068no—
1425D4—10616no—
1426D4—1064no—
1427D4—2124no—
1428D4—2124no—
1429D4—2124no—
1430D4—2124no—
1431D4—2124no—
1432D4—2128no—
1433D4—2124no—
1434D4C2×#11719945116yes—
1435C2×C4—28no—
1436C2×C4—28no—
1437C2×C4—41no—
1438C2×C4—44no—
1439C2×C4—44no—
1440C2×C4—44no—
1441C2×C4—42no—
1442C2×C4—44no—
1443C2×C4—48no—
1444C2×C4—41no—
1445C2×C4—44no—
1446C2×C4—44no—
1447C2×C4—532no—
1448C2×C4—534no—
1449C2×C4—534no—
1450C2×C4—534no—
1451C2×C4—531no—
1452C2×C4—534no—
1453C2×C4—534no—
1454C2×C4—531no—
1455C2×C4—531no—
1456C2×C4—531no—
1457C2×C4—1062no—
1458C2×C4—1064no—
1459C2×C4—1068no—
1460C2×C4—1068no—
1461C2×C4—1068no—
1462C2×C4—1064no—
1463C2×C4—1064no—
1464C2×C4—1068no—
1465C2×C4—2124no—
1466C2×C4—2124no—
1467C2×C4—2128no—
1468C2×C4—2128no—
1469C2×C4—2124no—
1470C2×C4—2121no—
1471C2×C4—2121no—
1472C2×C4—2122no—
1473C2×C4—2124no—
1474C2×C4—2124no—
1475C2×C4—2124no—
1476C2×C4C2×#1171994514yes—
1477C2×C4C24×D5312yes—
1478C2×C4C24×D5311yescharacteristic
1479C2×C4C24×D5314yes—
1480C2×C4C24×D5311yescharacteristic
1481C2×C4C24×D5314yes—
1482C2×C4C24×D5314yes—
1483C2×C4C24×D5314yes—
1484C2×C4C24×D5312yes—
1485C22—21no—
1486C22—24no—
1487C22—21no—
1488C22—24no—
1489C22—24no—
1490C22—24no—
1491C22—24no—
1492C22—48no—
1493C22—88no—
1494C22—1062no—
1495C22—1064no—
1496C22—1062no—
1497C22—1064no—
1498C22—1064no—
1499C22—1062no—
1500C22—4248no—
1501C22—2124no—
1502C22C22×#1171994518yes—
1503C22C22×#1171994512yes—
1504C22C25×D5311yescharacteristic
1505C4—24no—
1506C4—21no—
1507C4—21no—
1508C4—24no—
1509C4—24no—
1510C4—22no—
1511C4—24no—
1512C4—1061no—
1513C4—1061no—
1514C4—1064no—
1515C4—1064no—
1516C4—1061no—
1517C4—1064no—
1518C4—1064no—
1519C4—1061no—
1520C4—1064no—
1521C4—1062no—
1522C4C22×#1171994514yes—
1523C2—22no—
1524C2—28no—
1525C2—44no—
1526C2—2124no—
1527C2—2122no—
1528C2C23×#1171994511yescharacteristic
1529C2#2028952511yescharacteristic
1530C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC4×H(5,𝔽2)×C53C2
hypercenterC4×H(5,𝔽2)D53
hypocenterC53#62847
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #20288783C2semidirect
2. #20288771C2semidirect
3. #20288764C2semidirect
4. #20288754C2semidirect
5. #20288693C2semidirect
6. #20288683C2semidirect
7. #20288655C2semidirect
8. #20288643C2semidirect
9. #20288573C2semidirect
10. #20288545C2semidirect
11. #20288513C2semidirect
12. #20288474C2semidirect
13. #20288418C2semidirect
14. #20288408C2semidirect
15. #20288360C2semidirect
16. #20288355C2semidirect
17. #20288142C2semidirect
18. #20288124C2semidirect
19. #20288100C2semidirect
20. C2×#16811215C2semidirect
21. C4×#13133262C2semidirect
22. C2×#16811102C2semidirect
23. C4×H(5,𝔽2)×C53C2semidirect
26. #16811356C22semidirect
27. #16811351C22semidirect
28. #16811345C22semidirect
29. #16811343C22semidirect
30. #16811341C22semidirect
31. #16811333C22semidirect
32. #16811332C22semidirect
33. #16811332C22semidirect
34. #16811330C22semidirect
35. #16811328C22semidirect
36. #16811328C22semidirect
37. #16811323C22semidirect
38. #16811322C22semidirect
39. #16811322C22semidirect
40. #16811319C22semidirect
41. #16811317C22semidirect
42. #16811314C22semidirect
43. #16811313C22semidirect
44. #16811313C22semidirect
45. #16811312C22semidirect
46. #16811312C22semidirect
47. #16811308C22semidirect
48. #16811306C22semidirect
49. #16811306C22semidirect
50. #16811306C22semidirect
51. #16811302C22semidirect
52. #16811302C22semidirect
53. #16811299C22semidirect
54. #16811299C22semidirect
55. #16811299C22semidirect
56. #16811297C22semidirect
57. D4×Dic106C22semidirect
58. #16811282C22semidirect
59. #16811278C22semidirect
60. #16811277C22semidirect
61. #16811277C22semidirect
62. #16811274C22semidirect
63. #16811272C22semidirect
64. #16811272C22semidirect
65. #16811272C22semidirect
66. #16811268C22semidirect
67. #16811268C22semidirect
68. #16811267C22semidirect
69. #16811267C22semidirect
70. #16811267C22semidirect
71. #16811263C22semidirect
72. #16811261C22semidirect
73. D4×C22⋊D53C22semidirect
74. #16811251C22semidirect
75. #16811249C22semidirect
76. #16811245C22semidirect
77. #16811245C22semidirect
78. #16811244C22semidirect
79. #16811238C22semidirect
80. #16811238C22semidirect
81. #16811238C22semidirect
82. #16811235C22semidirect
83. #16811231C22semidirect
84. #16811231C22semidirect
85. #16811231C22semidirect
86. #16811224C22semidirect
87. #16811224C22semidirect
88. #16811220C22semidirect
89. #16811215C22semidirect
90. #16811215C22semidirect
91. #16811215C22semidirect
92. #16811215C22semidirect
93. #16811215C22semidirect
94. #16811215C22semidirect
95. #16811215C22semidirect
96. #16811215C22semidirect
97. #16811215C22semidirect
98. #16811215C22semidirect
99. #16811211C22semidirect
100. #16811206C22semidirect
101. #16811206C22semidirect
102. #16811206C22semidirect
104. #16811199C22semidirect
105. #16811194C22semidirect
106. #16811185C22semidirect
108. #16811182C22semidirect
109. #16811180C22semidirect
110. #16811177C22semidirect
111. #16811176C22semidirect
113. #16811157C22semidirect
114. #16811157C22semidirect
115. #16811157C22semidirect
116. #16811157C22semidirect
117. #16811155C22semidirect
118. #16811153C22semidirect
119. #16811153C22semidirect
120. #16811153C22semidirect
121. #16811151C22semidirect
122. #16811151C22semidirect
123. C2×#13133211C22semidirect
124. C2×#13133210C22semidirect
125. C2×#13133209C22semidirect
126. C2×#13133207C22semidirect
127. #16811135C22semidirect
128. #16811134C22semidirect
129. #16811132C22semidirect
130. #16811132C22semidirect
131. #16811130C22semidirect
132. C2×#13133201C22semidirect
133. C2×#13133200C22semidirect
134. C2×#13133199C22semidirect
135. C2×#13133198C22semidirect
136. C2×#13133196C22semidirect
137. C2×#13133195C22semidirect
138. C2×#13133194C22semidirect
140. #16811104C22semidirect
141. #16811102C22semidirect
142. #16811102C22semidirect
143. #16811102C22semidirect
144. #16811102C22semidirect
145. #16811102C22semidirect
147. #16811096C22semidirect
148. #16811095C22semidirect
149. C4×#11719945C22semidirect
150. C4×#11719947C22semidirect
151. C2×C4×Dic106C22semidirect
152. C2×#13133182C22semidirect
154. C2×C4×C22⋊D53C22semidirect
155. C2×C4×C22⋊D53C22semidirect
156. C2×#13133177C22semidirect
157. C4×D4×D53C22semidirect
158. C2×#13133174C22semidirect
159. C2×#13133173C22semidirect
160. C22×#11719919C22semidirect
161. C2×C4⋊C4×D53C22semidirect
163. C53×#520C22semidirect
164. C53×#520C22semidirect
166. C53×#518C22semidirect
167. C53×#518C22semidirect
168. C4×#41×C53C22semidirect
169. C4×#41×C53C22semidirect
171. C2×C4×D4×C53C22semidirect
172. C2×C4×D4×C53C22semidirect
468. C2×D4×C53#41semidirect
779. C4×H(5,𝔽2)D53semidirect
912. #520C2×D53semidirect
913. #520C2×D53semidirect
918. #518C2×D53semidirect
919. #518C2×D53semidirect
922. C4×#41C2×D53semidirect
923. C4×#41C2×D53semidirect
932. C2×C4×D4C2×D53semidirect
933. C2×C4×D4C2×D53semidirect
938. C53#62847semidirect
1261. C2×D4#11719945semidirect

Maximal subgroups

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

subgroupindex
#202887832
#202887712
#202887642
#202887542
#202886932
#202886832
#202886552
#202886432
#202885732
#202885452
#202885132
#202884742
#202884182
#202884082
#202883602
#202883552
#202881422
#202881242
#202881002
C2×#168112152
C4×#131332622
C2×#168111022
C4×H(5,𝔽2)×C532
#6284753