Finite Group Databasebeta

← D5×#5605 #14480305

Subgroups — D5×#5605 #14480305

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 1508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×D4×D5C212yesmaximal, complemented
2#11756364C211yesmaximal, characteristic, complemented
3C5×#5605C211yesmaximal, characteristic, complemented
4C3×D5×#121C211yesmaximal, characteristic, complemented
5#11755073C212yesmaximal, complemented
6#11755067C212yesmaximal, complemented
7D5×#939C212yesmaximal, complemented
8#11755025C212yesmaximal, complemented
9D5×#937C212yesmaximal, complemented
10#11754674C211yesmaximal, characteristic, complemented
11#11754660C211yesmaximal, characteristic, complemented
12D5×#930C211yesmaximal, characteristic, complemented
13C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14#11753849C212yesmaximal, complemented
15D5×#894C212yesmaximal, complemented
16#11753218C212yesmaximal, complemented
17#11753217C212yesmaximal, complemented
18D5×#883C212yesmaximal, complemented
19D5×#882C212yesmaximal, complemented
20D5×#534—31nomaximal, Hall
21C23×D3×D5C2211yescharacteristic
22C23×D3×D5C2212yescomplemented
23C2×D4×D15C2212yescomplemented
24C2×C5×D3×D4C2212yescomplemented
25C2×C3×D4×D5C2212yescomplemented
26C2×C3×D4×D5C2211yescharacteristic, complemented
27C22×C3×C4×D5C2211yescharacteristic, complemented
28C2×#6790C2212yescomplemented
29C2×#6790C2212yescomplemented
30C2×D3×C22⋊D5C2212yescomplemented
31C2×D3×C22⋊D5C2212yescomplemented
32C2×D5×#67C2212yes—
33C2×D5×#67C2212yescomplemented
34C2×D5×#67C2212yescomplemented
35C22×D5×Dic3C2211yescharacteristic, complemented
36D3×D4×D5—216no—
37C2×#6777C2212yescomplemented
38C2×D3×D20C2212yescomplemented
39C2×D5×D12C2212yes—
40C2×D5×D12C2211yescharacteristic, complemented
41C2×C4×D3×D5C2212yescomplemented
42C3×C5×#121C2211yescharacteristic, complemented
43#91828C2212yescomplemented
44#91826C2212yescomplemented
45#91819C2211yescharacteristic, complemented
46C2×#6714C2211yescharacteristic, complemented
47#91783C2212yescomplemented
48#91772C2212yescomplemented
49#91771C2212yescomplemented
50C5×#939C2212yescomplemented
51C5×#937C2212yescomplemented
52C5×#930C2211yescharacteristic, complemented
53C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
54C5×#894C2212yescomplemented
55C5×#883C2212yescomplemented
56C5×#882C2212yescomplemented
57C3×#4085C2212yescomplemented
58C3×#4084C2211yescharacteristic, complemented
59C3×#4076C2211yescharacteristic, complemented
60C3×#4041C2211yescharacteristic, complemented
61C3×D5×C4⋊C4C2211yescharacteristic, complemented
62C3×#4030C2212yescomplemented
63C3×D5×C22⋊C4C2212yescomplemented
64#91577C2212yescomplemented
65#91577C2212yescomplemented
66#91573C2212yescomplemented
67#91572C2212yescomplemented
68#91571C2212yescomplemented
69#91570C2212yescomplemented
70#91569C2212yescomplemented
71#91568C2212yescomplemented
72#91566C2212yescomplemented
73#91562C2212yescomplemented
74#91555C2212yescomplemented
75#91550C2212yescomplemented
76#91549C2212yescomplemented
77D5×#217C2212yescomplemented
78C2×#6667C2211yescharacteristic, complemented
79C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
80#91476C2212yescomplemented
81#91476C2212yescomplemented
82#91475C2212yescomplemented
83#91475C2212yescomplemented
84#91474C2212yescomplemented
85#91474C2212yescomplemented
86D5×(C2×D3)⋊C4C2212yescomplemented
87D5×(C2×D3)⋊C4C2212yescomplemented
88D5×(C2×D3)⋊C4C2212yescomplemented
89D5×(C2×D3)⋊C4C2212yescomplemented
90D5×(C2×D3)⋊C4C2212yescomplemented
91D5×(C2×D3)⋊C4C2212yescomplemented
92#91457C2212yescomplemented
93#91452C2212yescomplemented
94#91450C2211yescharacteristic, complemented
95#91449C2211yescharacteristic, complemented
96#91448C2212yescomplemented
97#91438C2212yescomplemented
98#91433C2212yescomplemented
99#91427C2212yescomplemented
100#91423C2212yescomplemented
101D5×C4⋊Dic3C2211yescharacteristic, complemented
102#91409C2212yescomplemented
103#91408C2212yescomplemented
104D5×Dic3⋊C4C2212yescomplemented
105#91356C2212yescomplemented
106#91355C2212yescomplemented
107#91354C2212yescomplemented
108#91351C2212yescomplemented
109C2×#5605—51nomaximal, Hall
110C22×D4×D5—32no—
111C5×#534—31no—
112#66138—32no—
113#65987—32no—
114#65987—32no—
115D5×#123—32no—
116D5×#123—32no—
117#65939—32no—
118#65939—31no—
119#65939—31no—
120D5×#121—32no—
121D5×#121—31no—
122D5×#121D311yescharacteristic, complemented
123#65923—32no—
124#65923—32no—
125D5×#120—32no—
126D5×#120—32no—
127#65827—31no—
128C2×D5×C22⋊C4—31no—
129C23×D15C2311yescharacteristic
130C23×D15C2312yescomplemented
131C23×C5×D3C2311yescharacteristic
132C23×C5×D3C2312yescomplemented
133C23×C3×D5C2312yes—
134C23×C3×D5C2311yescharacteristic
135C22×D3×D5—28no—
136C22×D3×D5—42no—
137C22×D3×D5—42no—
138C22×D3×D5—44no—
139C22×D3×D5—44no—
140C22×D3×D5D418yescomplemented
141C22×D3×D5C2312yes—
142C22×D3×D5C2312yes—
143C22×D3×D5C2312yes—
144C22×D3×D5C2312yescomplemented
145C22×D3×D5C2312yescomplemented
146C2×C3×C5×D4C2312yescomplemented
147C2×C3×C5×D4C2311yescharacteristic, complemented
148C22×C3×C4×C5C2311yescharacteristic, complemented
149C2×#1220C2312yes—
150C2×#1220C2312yescomplemented
151C2×#1220C2312yescomplemented
152C22×Dic15C2311yescharacteristic, complemented
153D4×D15—28no—
154C2×D60C2312yes—
155C2×D60C2311yescharacteristic, complemented
156C2×C4×D15C2312yescomplemented
157C2×C5×#67C2312yes—
158C2×C5×#67C2312yescomplemented
159C2×C5×#67C2312yescomplemented
160C22×C5×Dic3C2311yescharacteristic, complemented
161C5×D3×D4—28no—
162C2×C5×D12C2312yes—
163C2×C5×D12C2311yescharacteristic, complemented
164C2×C4×C5×D3C2312yescomplemented
165C2×C3×C22⋊D5C2312yescomplemented
166C2×C3×C22⋊D5C2312yescomplemented
167C2×C3×C22⋊D5C2312yescomplemented
168C22×C3×Dic5C2311yescharacteristic, complemented
169C3×D4×D5—28no—
170C3×D4×D5—42no—
171C2×C3×D20C2312yescomplemented
172C2×C3×D20C2311yescharacteristic, complemented
173C2×C3×C4×D5—42no—
174C2×C3×C4×D5C2312yes—
175C2×C3×C4×D5C2311yescharacteristic
176C2×C3×C4×D5C2311yescharacteristic
177C2×C3×C4×D5C2311yescharacteristic, complemented
178C2×C3×C4×D5C2311yescharacteristic, complemented
179#6790—28no—
180#6790—28no—
181D3×C22⋊D5—28no—
182D3×C22⋊D5—28no—
183D5×#67—28no—
184D5×#67—28no—
185D5×#67—44no—
186C2×#1203C2312yes—
187C2×#1203C2312yes—
188C2×#1203C2312yescomplemented
189C2×#1202C2312yes—
190C2×#1202C2312yescomplemented
191C2×#1202C2312yescomplemented
192C2×#1201C2312yes—
193C2×#1201C2312yescomplemented
194C2×#1201C2312yescomplemented
195C2×#1200C2312yescomplemented
196C2×D3×Dic5C2312yescomplemented
197C2×D5×Dic3—42no—
198C2×D5×Dic3C2312yes—
199C2×D5×Dic3C2312yes—
200C2×D5×Dic3C2312yescomplemented
201#6777—28no—
202D3×D20—28no—
203D5×D12—28no—
204D5×D12—42no—
205C4×D3×D5—28no—
206C3×C5×C4⋊C4C2311yescharacteristic, complemented
207C3×C5×C22⋊C4C2312yescomplemented
208#6719C2312yescomplemented
209#6714C2312yescomplemented
210#6714C2312yescomplemented
211#6714C2312yescomplemented
212#6714C2312yescomplemented
213C4⋊Dic15C2311yescharacteristic, complemented
214#6712C2312yescomplemented
215C5×#217C2312yescomplemented
216C5×(C2×D3)⋊C4C2312yescomplemented
217C5×(C2×D3)⋊C4C2312yescomplemented
218C5×(C2×D3)⋊C4C2312yescomplemented
219C5×(C2×D3)⋊C4C2312yescomplemented
220C5×C4⋊Dic3C2311yescharacteristic, complemented
221C5×Dic3⋊C4C2312yescomplemented
222C3×C22⋊Dic5C2312yescomplemented
223C3×#685C2312yescomplemented
224C3×#685C2312yescomplemented
225C3×C4⋊Dic5C2311yescharacteristic, complemented
226C3×#683C2312yescomplemented
227Dic3⋊Dic5C2312yescomplemented
228#6669C2312yescomplemented
229#6668C2312yescomplemented
230#6667C2312yescomplemented
231#6667C2312yescomplemented
232#6667C2312yescomplemented
233#6667C2312yescomplemented
234(C2×D3)⋊Dic5C2312yescomplemented
235(C2×D3)⋊Dic5C2312yescomplemented
236(C2×D3)⋊Dic5C2312yescomplemented
237(C2×D3)⋊Dic5C2312yescomplemented
238#6665C2312yescomplemented
239#6665C2312yescomplemented
240C22×D3×D4—52no—
241C2×C3×#121—51no—
242C2×#939—52no—
243C2×#937—52no—
244C2×#930—51no—
245C22×(C2×D3)⋊C4—51no—
246#5605—52no—
247#5605—51no—
248#5605—52no—
249#5605—52no—
250#5605—51no—
251#5605—51no—
252#5605—52no—
253#5605—52no—
254#5605—52no—
255#5605D511yescharacteristic, direct product factor
256C2×#894—52no—
257C2×#883—52no—
258C2×#882—52no—
259C24×D5—31no—
260C24×D5—32no—
261C22×C5×D4—32no—
262C22×C22⋊D5—32no—
263C22×C22⋊D5—32no—
264C2×D4×D5—32no—
265C2×D4×D5—32no—
266C2×D4×D5—32no—
267C2×D4×D5—32no—
268C2×D4×D5—32no—
269C2×D4×D5—32no—
270C2×D4×D5—32no—
271C2×D4×D5—32no—
272C2×D4×D5—31no—
273C2×D4×D5—616no—
274C2×D4×D5C2×D312yescomplemented
275C2×D4×D5C2×D311yescharacteristic, complemented
276C22×D20—32no—
277C22×C4×D5—31no—
278C22×C4×D5—32no—
279C22×C4×D5C2×D311yescharacteristic, complemented
280C5×#123—32no—
281C5×#123—32no—
282C5×#121—32no—
283C5×#121—31no—
284C5×#121C2×D311yescharacteristic, complemented
285C5×#120—32no—
286C5×#120—32no—
287C2×C5×C22⋊C4—31no—
288#4099—32no—
289#4099—32no—
290C2×C22⋊Dic5—31no—
291#4085—32no—
292#4085—32no—
293#4085—32no—
294#4085C2×D312yescomplemented
295#4084—32no—
296#4084—31no—
297#4084C2×D311yescharacteristic, complemented
298#4083—32no—
299#4083—32no—
300#4083—32no—
301#4083—32no—
302#4083—32no—
303#4083—32no—
304#4081—32no—
305#4081—32no—
306#4076—31no—
307#4076—32no—
308#4076C2×D311yescharacteristic, complemented
309#4075—32no—
310#4075—32no—
311C2×#685—31no—
312C2×#685—31no—
313#4041—32no—
314#4041—31no—
315#4041C2×D311yescharacteristic, complemented
316#4040—32no—
317#4040—32no—
318#4040—32no—
319#4040—32no—
320D5×C4⋊C4—32no—
321D5×C4⋊C4—31no—
322D5×C4⋊C4C2×D311yescharacteristic, complemented
323#4032—32no—
324#4032—32no—
325#4030—32no—
326#4030—32no—
327#4030—32no—
328#4030C2×D312yescomplemented
329#4029—32no—
330#4029—32no—
331#4029—32no—
332#4029—32no—
333#4028—32no—
334#4028—32no—
335#4028—32no—
336#4028—32no—
337#4028—32no—
338#4028—32no—
339D5×C22⋊C4—32no—
340D5×C22⋊C4—32no—
341D5×C22⋊C4—32no—
342D5×C22⋊C4—32no—
343D5×C22⋊C4—32no—
344D5×C22⋊C4—32no—
345D5×C22⋊C4—32no—
346D5×C22⋊C4C2×D312yescomplemented
347C2×#534—151noSylow
348C23×C3×C5C2412yes—
349C23×C3×C5C2411yescharacteristic
350C22×D15—24no—
351C22×D15—41no—
352C22×D15—41no—
353C22×D15—42no—
354C22×D15—42no—
355C22×D15C2×D414yescomplemented
356C22×D15C2412yes—
357C22×D15C2412yes—
358C22×C5×D3—24no—
359C22×C5×D3—41no—
360C22×C5×D3—41no—
361C22×C5×D3—42no—
362C22×C5×D3—42no—
363C22×C5×D3C2×D414yescomplemented
364C22×C5×D3C2412yes—
365C22×C5×D3C2412yes—
366C22×C3×D5—22no—
367C22×C3×D5—22no—
368C22×C3×D5—24no—
369C22×C3×D5—24no—
370C22×C3×D5—24no—
371C22×C3×D5C2×D414yes—
372C22×C3×D5C2412yes—
373C22×C3×D5C2411yescharacteristic
374C22×C3×D5C2411yescharacteristic
375C2×D3×D5—24no—
376C2×D3×D5—24no—
377C2×D3×D5—24no—
378C2×D3×D5—24no—
379C2×D3×D5—24no—
380C2×D3×D5—24no—
381C2×D3×D5—24no—
382C2×D3×D5—416no—
383C2×D3×D5—432no—
384C2×D3×D5—42no—
385C2×D3×D5—42no—
386C2×D3×D5—42no—
387C2×D3×D5—42no—
388C2×D3×D5—42no—
389C2×D3×D5—42no—
390C2×D3×D5C2×D418yes—
391C2×D3×D5C2×D418yescomplemented
392C3×C5×D4—24no—
393C3×C5×D4—41no—
394C2×C3×C4×C5—41no—
395C2×C3×C4×C5C2412yes—
396C2×C3×C4×C5C2411yescharacteristic
397C2×C3×C4×C5C2411yescharacteristic
398#1220—24no—
399#1220—24no—
400#1220—42no—
401C2×Dic15—41no—
402C2×Dic15C2412yes—
403C2×Dic15C2412yes—
404D60—24no—
405D60—41no—
406C4×D15—24no—
407C5×#67—24no—
408C5×#67—24no—
409C5×#67—42no—
410C2×C5×Dic3—41no—
411C2×C5×Dic3C2412yes—
412C2×C5×Dic3C2412yes—
413C5×D12—24no—
414C5×D12—41no—
415C4×C5×D3—24no—
416C3×C22⋊D5—24no—
417C3×C22⋊D5—24no—
418C3×C22⋊D5—42no—
419C2×C3×Dic5—41no—
420C2×C3×Dic5C2411yescharacteristic
421C2×C3×Dic5C2411yescharacteristic
422C2×C3×Dic5C2412yes—
423C3×D20—24no—
424C3×D20—41no—
425C3×C4×D5—24no—
426C3×C4×D5—22no—
427C3×C4×D5—22no—
428C3×C4×D5—41no—
429C3×C4×D5—41no—
430#1203—24no—
431#1203—24no—
432#1203—42no—
433#1202—24no—
434#1202—24no—
435#1202—42no—
436#1201—24no—
437#1201—24no—
438#1201—42no—
439#1200—24no—
440D3×Dic5—24no—
441D5×Dic3—24no—
442D5×Dic3—24no—
443D5×Dic3—42no—
444C24×D3—51no—
445C24×D3—52no—
446C22×C3×D4—52no—
447C22×C3×D4—51no—
448C23×C3×C4—51no—
449C22×#67—52no—
450C22×#67—52no—
451C22×#67—52no—
452C23×Dic3—51no—
453C2×D3×D4—52no—
454C2×D3×D4—52no—
455C2×D3×D4—52no—
456C2×D3×D4—52no—
457C2×D3×D4—52no—
458C2×D3×D4—52no—
459C2×D3×D4—52no—
460C2×D3×D4—1016no—
461C2×D3×D4C2×D512yescomplemented
462C22×D12—52no—
463C22×D12—51no—
464C22×C4×D3—52no—
465C3×#121—51no—
466C3×#121—52no—
467C3×#121—51no—
468C3×#121—51no—
469C3×#121—52no—
470C3×#121C2×D511yescharacteristic, complemented
471C2×C3×C4⋊C4—51no—
472C2×C3×C22⋊C4—52no—
473C2×#217—52no—
474#939—52no—
475#939—52no—
476#939—52no—
477#939—52no—
478#939—52no—
479#939—52no—
480#939—52no—
481#939C2×D512yescomplemented
482#937—52no—
483#937—52no—
484#937—52no—
485#937—52no—
486#937—52no—
487#937—52no—
488#937—52no—
489#937C2×D512yescomplemented
490#930—51no—
491#930—52no—
492#930—51no—
493#930—52no—
494#930—51no—
495#930C2×D511yescharacteristic, complemented
496C2×(C2×D3)⋊C4—51no—
497C2×(C2×D3)⋊C4—51no—
498C2×(C2×D3)⋊C4—51no—
499C2×(C2×D3)⋊C4—52no—
500C2×(C2×D3)⋊C4—52no—
501C2×(C2×D3)⋊C4—52no—
502C2×(C2×D3)⋊C4—52no—
503C2×(C2×D3)⋊C4—52no—
504C2×(C2×D3)⋊C4—52no—
505C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
506C2×C4⋊Dic3—51no—
507C2×Dic3⋊C4—52no—
508#894—52no—
509#894—52no—
510#894—52no—
511#894—52no—
512#894—52no—
513#894—52no—
514#894—52no—
515#894C2×D512yescomplemented
516#883—52no—
517#883—52no—
518#883—52no—
519#883—52no—
520#883—52no—
521#883—52no—
522#883—52no—
523#883C2×D512yescomplemented
524#882—52no—
525#882—52no—
526#882—52no—
527#882—52no—
528#882—52no—
529#882—52no—
530#882—52no—
531#882C2×D512yescomplemented
532C24×C5—31no—
533C24×C5—32no—
534C23×D5—31no—
535C23×D5—32no—
536C23×D5—38no—
537C23×D5—32no—
538C23×D5—32no—
539C23×D5—32no—
540C23×D5—32no—
541C23×D5—32no—
542C23×D5—68no—
543C23×D5—122no—
544C23×D5—122no—
545C23×D5—124no—
546C23×D5—124no—
547C23×D5C22×D312yes—
548C23×D5C22×D311yescharacteristic
549C2×C5×D4—32no—
550C2×C5×D4—32no—
551C2×C5×D4—32no—
552C2×C5×D4—32no—
553C2×C5×D4—31no—
554C2×C5×D4—68no—
555C2×C5×D4C22×D312yescomplemented
556C2×C5×D4C22×D311yescharacteristic, complemented
557C22×C4×C5—31no—
558C22×C4×C5—32no—
559C22×C4×C5C22×D311yescharacteristic, complemented
560C2×C22⋊D5—32no—
561C2×C22⋊D5—32no—
562C2×C22⋊D5—32no—
563C2×C22⋊D5—32no—
564C2×C22⋊D5—32no—
565C2×C22⋊D5—32no—
566C2×C22⋊D5—32no—
567C2×C22⋊D5—32no—
568C2×C22⋊D5—32no—
569C2×C22⋊D5—68no—
570C2×C22⋊D5—68no—
571C2×C22⋊D5C22×D312yescomplemented
572C2×C22⋊D5C22×D312yescomplemented
573C2×C22⋊D5C22×D312yescomplemented
574C22×Dic5—31no—
575C22×Dic5—32no—
576C22×Dic5C22×D311yescharacteristic, complemented
577D4×D5—28no—
578D4×D5—42no—
579D4×D5—68no—
580D4×D5—68no—
581D4×D5—68no—
582D4×D5—68no—
583D4×D5—68no—
584D4×D5—68no—
585D4×D5—68no—
586D4×D5—122no—
587D4×D5—124no—
588C2×D20—32no—
589C2×D20—32no—
590C2×D20—32no—
591C2×D20—32no—
592C2×D20—31no—
593C2×D20—68no—
594C2×D20C22×D312yescomplemented
595C2×D20C22×D311yescharacteristic, complemented
596C2×C4×D5—32no—
597C2×C4×D5—32no—
598C2×C4×D5—32no—
599C2×C4×D5—32no—
600C2×C4×D5—32no—
601C2×C4×D5—42no—
602C2×C4×D5—68no—
603C2×C4×D5—122no—
604C2×C4×D5C22×D312yes—
605C2×C4×D5C22×D311yescharacteristic
606C2×C4×D5C22×D311yescharacteristic
607C2×C4×D5C22×D311yescharacteristic, complemented
608C2×C4×D5C22×D311yescharacteristic, complemented
609C5×C4⋊C4—32no—
610C5×C4⋊C4—31no—
611C5×C4⋊C4C22×D311yescharacteristic, complemented
612C5×C22⋊C4—32no—
613C5×C22⋊C4—32no—
614C5×C22⋊C4—32no—
615C5×C22⋊C4—32no—
616C5×C22⋊C4—32no—
617C5×C22⋊C4C22×D312yescomplemented
618C22⋊Dic5—32no—
619C22⋊Dic5—32no—
620C22⋊Dic5—32no—
621C22⋊Dic5—32no—
622C22⋊Dic5—32no—
623C22⋊Dic5C22×D312yescomplemented
624#685—32no—
625#685—32no—
626#685—32no—
627#685—32no—
628#685—32no—
629#685—32no—
630#685—32no—
631#685—32no—
632#685—32no—
633#685—32no—
634#685C22×D312yescomplemented
635#685C22×D312yescomplemented
636C4⋊Dic5—31no—
637C4⋊Dic5—32no—
638C4⋊Dic5C22×D311yescharacteristic, complemented
639#683—32no—
640#683—32no—
641#683—32no—
642#683C22×D312yescomplemented
643C23×D4—152no—
644#534—31no—
645#534—151no—
646#534—152no—
647#534—152no—
648#534—152no—
649#534—151no—
650#534—152no—
651#534—152no—
652#534—152no—
653#534—151no—
654C2×#123—152no—
655C2×#123—152no—
656C2×#121—51no—
657C2×#121—151no—
658C2×#121—152no—
659C2×#120—152no—
660C2×#120—152no—
661C22×C22⋊C4—151no—
662C22×C3×C5—21no—
663C22×C3×C5—21no—
664C22×C3×C5—22no—
665C22×C3×C5—22no—
666C22×C3×C5—22no—
667C22×C3×C5C22×D412yes—
668C22×C3×C5C2511yescharacteristic
669C2×D15—22no—
670C2×D15—22no—
671C2×D15—22no—
672C2×D15—22no—
673C2×D15—22no—
674C2×D15—44no—
675C2×D15—48no—
676C2×D15C22×D414yes—
677C2×C5×D3—22no—
678C2×C5×D3—22no—
679C2×C5×D3—22no—
680C2×C5×D3—22no—
681C2×C5×D3—22no—
682C2×C5×D3—44no—
683C2×C5×D3—48no—
684C2×C5×D3C22×D414yes—
685C2×C3×D5—21no—
686C2×C3×D5—21no—
687C2×C3×D5—28no—
688C2×C3×D5—22no—
689C2×C3×D5—22no—
690C2×C3×D5—22no—
691C2×C3×D5—48no—
692C2×C3×D5C22×D412yes—
693C2×C3×D5C22×D412yes—
694C2×C3×D5H(5,𝔽2)12yes—
695C2×C3×D5H(5,𝔽2)12yes—
696D3×D5—216no—
697D3×D5—48no—
698D3×D5—48no—
699D3×D5—48no—
700D3×D5—48no—
701C3×C4×C5—22no—
702C3×C4×C5—21no—
703C3×C4×C5—21no—
704Dic15—22no—
705Dic15—22no—
706C3×Dic5—22no—
707C3×Dic5—21no—
708C3×Dic5—21no—
709C5×Dic3—22no—
710C5×Dic3—22no—
711C24×C3—51no—
712C24×C3—52no—
713C23×D3—51no—
714C23×D3—52no—
715C23×D3—58no—
716C23×D3—52no—
717C23×D3—52no—
718C23×D3—52no—
719C23×D3—52no—
720C23×D3—52no—
721C23×D3—108no—
722C23×D3—202no—
723C23×D3—202no—
724C23×D3—204no—
725C23×D3—204no—
726C23×D3C22×D511yescharacteristic
727C23×D3C22×D512yescomplemented
728C2×C3×D4—52no—
729C2×C3×D4—52no—
730C2×C3×D4—52no—
731C2×C3×D4—52no—
732C2×C3×D4—51no—
733C2×C3×D4—108no—
734C2×C3×D4—202no—
735C2×C3×D4C22×D512yescomplemented
736C2×C3×D4C22×D511yescharacteristic, complemented
737C22×C3×C4—51no—
738C22×C3×C4—52no—
739C22×C3×C4—51no—
740C22×C3×C4—51no—
741C22×C3×C4—51no—
742C22×C3×C4—51no—
743C22×C3×C4—202no—
744C22×C3×C4C22×D511yescharacteristic, complemented
745C2×#67—52no—
746C2×#67—52no—
747C2×#67—52no—
748C2×#67—52no—
749C2×#67—52no—
750C2×#67—52no—
751C2×#67—52no—
752C2×#67—52no—
753C2×#67—52no—
754C2×#67—108no—
755C2×#67—108no—
756C2×#67—204no—
757C2×#67C22×D512yes—
758C2×#67C22×D512yescomplemented
759C2×#67C22×D512yescomplemented
760C22×Dic3—51no—
761C22×Dic3—52no—
762C22×Dic3—52no—
763C22×Dic3—52no—
764C22×Dic3—202no—
765C22×Dic3C22×D511yescharacteristic, complemented
766D3×D4—28no—
767D3×D4—108no—
768D3×D4—108no—
769D3×D4—108no—
770D3×D4—108no—
771D3×D4—108no—
772D3×D4—108no—
773D3×D4—108no—
774C2×D12—52no—
775C2×D12—52no—
776C2×D12—52no—
777C2×D12—52no—
778C2×D12—51no—
779C2×D12—108no—
780C2×D12—202no—
781C2×D12C22×D512yes—
782C2×D12C22×D511yescharacteristic, complemented
783C2×C4×D3—52no—
784C2×C4×D3—52no—
785C2×C4×D3—52no—
786C2×C4×D3—108no—
787C2×C4×D3C22×D512yescomplemented
788C3×C4⋊C4—52no—
789C3×C4⋊C4—51no—
790C3×C4⋊C4C22×D511yescharacteristic, complemented
791C3×C22⋊C4—52no—
792C3×C22⋊C4—52no—
793C3×C22⋊C4—52no—
794C3×C22⋊C4C22×D512yescomplemented
795#217—52no—
796#217—52no—
797#217—52no—
798#217C22×D512yescomplemented
799(C2×D3)⋊C4—52no—
800(C2×D3)⋊C4—52no—
801(C2×D3)⋊C4—52no—
802(C2×D3)⋊C4—52no—
803(C2×D3)⋊C4—52no—
804(C2×D3)⋊C4—52no—
805(C2×D3)⋊C4—52no—
806(C2×D3)⋊C4—52no—
807(C2×D3)⋊C4—52no—
808(C2×D3)⋊C4—52no—
809(C2×D3)⋊C4—52no—
810(C2×D3)⋊C4—52no—
811(C2×D3)⋊C4C22×D512yescomplemented
812(C2×D3)⋊C4C22×D512yescomplemented
813(C2×D3)⋊C4C22×D512yescomplemented
814(C2×D3)⋊C4C22×D512yescomplemented
815C4⋊Dic3—51no—
816C4⋊Dic3—52no—
817C4⋊Dic3C22×D511yescharacteristic, complemented
818Dic3⋊C4—52no—
819Dic3⋊C4—52no—
820Dic3⋊C4—52no—
821Dic3⋊C4C22×D512yescomplemented
822C23×C5—32no—
823C23×C5—34no—
824C23×C5—32no—
825C23×C5—64no—
826C23×C5—121no—
827C23×C5—121no—
828C23×C5—122no—
829C23×C5—122no—
830C23×C5C23×D312yes—
831C23×C5C23×D311yescharacteristic
832C22×D5—22no—
833C22×D5—22no—
834C22×D5—24no—
835C22×D5—24no—
836C22×D5—24no—
837C22×D5—32no—
838C22×D5—34no—
839C22×D5—38no—
840C22×D5—38no—
841C22×D5—32no—
842C22×D5—64no—
843C22×D5—64no—
844C22×D5—64no—
845C22×D5—64no—
846C22×D5—64no—
847C22×D5—64no—
848C22×D5—64no—
849C22×D5—64no—
850C22×D5—1216no—
851C22×D5—122no—
852C22×D5—122no—
853C22×D5—122no—
854C22×D5—122no—
855C22×D5—122no—
856C22×D5—122no—
857C22×D5—1232no—
858C22×D5—121no—
859C22×D5—122no—
860C22×D5—121no—
861C22×D5—122no—
862C22×D5D3×D414yes—
863C22×D5C23×D312yes—
864C22×D5C23×D311yescharacteristic
865C22×D5C23×D311yescharacteristic
866C5×D4—24no—
867C5×D4—41no—
868C5×D4—64no—
869C5×D4—64no—
870C5×D4—64no—
871C5×D4—121no—
872C5×D4—122no—
873C2×C4×C5—32no—
874C2×C4×C5—32no—
875C2×C4×C5—41no—
876C2×C4×C5—64no—
877C2×C4×C5—121no—
878C2×C4×C5C23×D312yes—
879C2×C4×C5C23×D311yescharacteristic
880C2×C4×C5C23×D311yescharacteristic
881C22⋊D5—24no—
882C22⋊D5—24no—
883C22⋊D5—42no—
884C22⋊D5—64no—
885C22⋊D5—64no—
886C22⋊D5—64no—
887C22⋊D5—64no—
888C22⋊D5—64no—
889C22⋊D5—64no—
890C22⋊D5—122no—
891C22⋊D5—122no—
892C22⋊D5—122no—
893C2×Dic5—32no—
894C2×Dic5—32no—
895C2×Dic5—41no—
896C2×Dic5—64no—
897C2×Dic5—121no—
898C2×Dic5C23×D311yescharacteristic
899C2×Dic5C23×D312yes—
900C2×Dic5C23×D311yescharacteristic
901D20—24no—
902D20—41no—
903D20—64no—
904D20—64no—
905D20—64no—
906D20—121no—
907D20—122no—
908C4×D5—24no—
909C4×D5—22no—
910C4×D5—22no—
911C4×D5—41no—
912C4×D5—41no—
913C4×D5—64no—
914C4×D5—64no—
915C4×D5—64no—
916C4×D5—64no—
917C4×D5—122no—
918C25—151no—
919C25—152no—
920C22×D4—32no—
921C22×D4—52no—
922C22×D4—51no—
923C22×D4—152no—
924C22×D4—152no—
925C22×D4—151no—
926C22×D4—152no—
927C22×D4—152no—
928C22×D4—152no—
929C22×D4—152no—
930C22×D4—152no—
931C22×D4—152no—
932C22×D4—152no—
933C22×D4—152no—
934C22×D4—152no—
935C22×D4—3016no—
936C23×C4—51no—
937C23×C4—152no—
938C23×C4—151no—
939#123—32no—
940#123—32no—
941#123—152no—
942#123—152no—
943#123—152no—
944#123—152no—
945#123—152no—
946#123—152no—
947#123—152no—
948#123—152no—
949#123—152no—
950#123—152no—
951#123—152no—
952#123—152no—
953#123—152no—
954#123—152no—
955#121—32no—
956#121—31no—
957#121—51no—
958#121—52no—
959#121—51no—
960#121—51no—
961#121—52no—
962#121—152no—
963#121—152no—
964#121—152no—
965#121—151no—
966#121—152no—
967#121—152no—
968#121—151no—
969#121—152no—
970#121—152no—
971#121—152no—
972#121—152no—
973#121—151no—
974#121D3×D511yescharacteristic, complemented
975#120—32no—
976#120—32no—
977#120—152no—
978#120—152no—
979#120—152no—
980#120—152no—
981#120—152no—
982#120—152no—
983#120—152no—
984#120—152no—
985#120—152no—
986#120—152no—
987#120—152no—
988#120—152no—
989#120—152no—
990#120—152no—
991C2×C4⋊C4—51no—
992C2×C4⋊C4—152no—
993C2×C4⋊C4—151no—
994C2×C22⋊C4—31no—
995C2×C22⋊C4—52no—
996C2×C22⋊C4—152no—
997C2×C22⋊C4—152no—
998C2×C22⋊C4—152no—
999C2×C22⋊C4—152no—
1000C2×C22⋊C4—152no—
1001C2×C22⋊C4—152no—
1002C2×C22⋊C4—152no—
1003C2×C22⋊C4—151no—
1004C2×C22⋊C4—151no—
1005C2×C22⋊C4—151no—
1006C2×C3×C5—22no—
1007C2×C3×C5—42no—
1008C2×C3×C5C23×D411yescharacteristic
1009C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
1010C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
1011D15—24no—
1012D15—42no—
1013C3×D5—22no—
1014C3×D5—42no—
1015C3×D5#53414yescomplemented
1016C5×D3—24no—
1017C5×D3—42no—
1018C23×C3—51no—
1019C23×C3—54no—
1020C23×C3—51no—
1021C23×C3—52no—
1022C23×C3—102no—
1023C23×C3—102no—
1024C23×C3—104no—
1025C23×C3—104no—
1026C23×C3—104no—
1027C23×C3C23×D512yes—
1028C23×C3C23×D511yescharacteristic
1029C22×D3—24no—
1030C22×D3—41no—
1031C22×D3—41no—
1032C22×D3—42no—
1033C22×D3—42no—
1034C22×D3—52no—
1035C22×D3—54no—
1036C22×D3—58no—
1037C22×D3—58no—
1038C22×D3—52no—
1039C22×D3—104no—
1040C22×D3—104no—
1041C22×D3—104no—
1042C22×D3—104no—
1043C22×D3—104no—
1044C22×D3—104no—
1045C22×D3—104no—
1046C22×D3—104no—
1047C22×D3—202no—
1048C22×D3—202no—
1049C22×D3—202no—
1050C22×D3—202no—
1051C22×D3—202no—
1052C22×D3—202no—
1053C22×D3—2016no—
1054C22×D3—2032no—
1055C22×D3—201no—
1056C22×D3—201no—
1057C22×D3—202no—
1058C22×D3—202no—
1059C22×D3D4×D514yescomplemented
1060C22×D3C23×D512yes—
1061C22×D3C23×D512yes—
1062C3×D4—24no—
1063C3×D4—41no—
1064C3×D4—104no—
1065C3×D4—104no—
1066C3×D4—104no—
1067C3×D4—201no—
1068C3×D4—202no—
1069C2×C3×C4—41no—
1070C2×C3×C4—52no—
1071C2×C3×C4—51no—
1072C2×C3×C4—51no—
1073C2×C3×C4—104no—
1074C2×C3×C4—102no—
1075C2×C3×C4—102no—
1076C2×C3×C4—201no—
1077C2×C3×C4—201no—
1078C2×C3×C4—201no—
1079C2×C3×C4C23×D512yes—
1080C2×C3×C4C23×D511yescharacteristic
1081C2×C3×C4C23×D511yescharacteristic
1082#67—24no—
1083#67—24no—
1084#67—42no—
1085#67—104no—
1086#67—104no—
1087#67—104no—
1088#67—104no—
1089#67—104no—
1090#67—104no—
1091#67—202no—
1092#67—202no—
1093#67—202no—
1094C2×Dic3—41no—
1095C2×Dic3—52no—
1096C2×Dic3—52no—
1097C2×Dic3—104no—
1098C2×Dic3—104no—
1099C2×Dic3—202no—
1100C2×Dic3—201no—
1101C2×Dic3C23×D512yes—
1102C2×Dic3C23×D512yes—
1103D12—24no—
1104D12—41no—
1105D12—104no—
1106D12—104no—
1107D12—104no—
1108D12—201no—
1109D12—202no—
1110C4×D3—24no—
1111C4×D3—104no—
1112C4×D3—104no—
1113C4×D3—104no—
1114C22×C5—21no—
1115C22×C5—21no—
1116C22×C5—22no—
1117C22×C5—22no—
1118C22×C5—22no—
1119C22×C5—34no—
1120C22×C5—62no—
1121C22×C5—62no—
1122C22×C5—62no—
1123C22×C5—62no—
1124C22×C5—62no—
1125C22×C5—124no—
1126C22×C5—128no—
1127C22×C5C2×D3×D412yes—
1128C22×C5C24×D311yescharacteristic
1129C2×D5—21no—
1130C2×D5—21no—
1131C2×D5—28no—
1132C2×D5—22no—
1133C2×D5—22no—
1134C2×D5—22no—
1135C2×D5—34no—
1136C2×D5—48no—
1137C2×D5—62no—
1138C2×D5—62no—
1139C2×D5—616no—
1140C2×D5—62no—
1141C2×D5—62no—
1142C2×D5—62no—
1143C2×D5—128no—
1144C2×D5—128no—
1145C2×D5—128no—
1146C2×D5—124no—
1147C2×D5—128no—
1148C2×D5—128no—
1149C2×D5C2×D3×D412yes—
1150C2×D5C2×D3×D412yes—
1151C2×D5#100412yes—
1152C2×D5#100912yes—
1153C4×C5—22no—
1154C4×C5—21no—
1155C4×C5—21no—
1156C4×C5—62no—
1157C4×C5—62no—
1158Dic5—22no—
1159Dic5—21no—
1160Dic5—21no—
1161Dic5—62no—
1162Dic5—62no—
1163C24—31no—
1164C24—32no—
1165C24—51no—
1166C24—52no—
1167C24—152no—
1168C24—152no—
1169C24—158no—
1170C24—152no—
1171C24—152no—
1172C24—152no—
1173C24—151no—
1174C24—152no—
1175C24—308no—
1176C24—602no—
1177C24—602no—
1178C24—604no—
1179C24—604no—
1180C2×D4—32no—
1181C2×D4—32no—
1182C2×D4—32no—
1183C2×D4—32no—
1184C2×D4—31no—
1185C2×D4—52no—
1186C2×D4—52no—
1187C2×D4—52no—
1188C2×D4—52no—
1189C2×D4—51no—
1190C2×D4—68no—
1191C2×D4—108no—
1192C2×D4—152no—
1193C2×D4—152no—
1194C2×D4—152no—
1195C2×D4—152no—
1196C2×D4—152no—
1197C2×D4—152no—
1198C2×D4—152no—
1199C2×D4—152no—
1200C2×D4—152no—
1201C2×D4—152no—
1202C2×D4—152no—
1203C2×D4—152no—
1204C2×D4—152no—
1205C2×D4—151no—
1206C2×D4—202no—
1207C2×D4—308no—
1208C2×D4—308no—
1209C2×D4—308no—
1210C2×D4—308no—
1211C2×D4—308no—
1212C2×D4—308no—
1213C2×D4—308no—
1214C2×D4—308no—
1215C2×D4—308no—
1216C2×D4—308no—
1217C2×D4—602no—
1218C2×D4—604no—
1219C2×D4C2×D3×D512yescomplemented
1220C2×D4C2×D3×D511yescharacteristic, complemented
1221C22×C4—31no—
1222C22×C4—32no—
1223C22×C4—51no—
1224C22×C4—51no—
1225C22×C4—52no—
1226C22×C4—51no—
1227C22×C4—51no—
1228C22×C4—51no—
1229C22×C4—152no—
1230C22×C4—152no—
1231C22×C4—152no—
1232C22×C4—152no—
1233C22×C4—152no—
1234C22×C4—151no—
1235C22×C4—152no—
1236C22×C4—202no—
1237C22×C4—308no—
1238C22×C4—602no—
1239C22×C4C2×D3×D511yescharacteristic, complemented
1240C4⋊C4—32no—
1241C4⋊C4—31no—
1242C4⋊C4—52no—
1243C4⋊C4—51no—
1244C4⋊C4—152no—
1245C4⋊C4—152no—
1246C4⋊C4—152no—
1247C4⋊C4—152no—
1248C4⋊C4—151no—
1249C4⋊C4C2×D3×D511yescharacteristic, complemented
1250C22⋊C4—32no—
1251C22⋊C4—32no—
1252C22⋊C4—32no—
1253C22⋊C4—32no—
1254C22⋊C4—32no—
1255C22⋊C4—52no—
1256C22⋊C4—52no—
1257C22⋊C4—52no—
1258C22⋊C4—152no—
1259C22⋊C4—152no—
1260C22⋊C4—152no—
1261C22⋊C4—152no—
1262C22⋊C4—152no—
1263C22⋊C4—152no—
1264C22⋊C4—152no—
1265C22⋊C4—152no—
1266C22⋊C4—152no—
1267C22⋊C4—152no—
1268C22⋊C4—152no—
1269C22⋊C4—152no—
1270C22⋊C4—152no—
1271C22⋊C4—152no—
1272C22⋊C4—152no—
1273C22⋊C4C2×D3×D512yescomplemented
1274C3×C5C2×#53411yescharacteristic, complemented, Hall
1275C22×C3—21no—
1276C22×C3—21no—
1277C22×C3—22no—
1278C22×C3—22no—
1279C22×C3—22no—
1280C22×C3—52no—
1281C22×C3—52no—
1282C22×C3—52no—
1283C22×C3—52no—
1284C22×C3—108no—
1285C22×C3—101no—
1286C22×C3—101no—
1287C22×C3—102no—
1288C22×C3—102no—
1289C22×C3—102no—
1290C22×C3—208no—
1291C22×C3C2×D4×D512yes—
1292C22×C3C24×D511yescharacteristic
1293C2×D3—22no—
1294C2×D3—22no—
1295C2×D3—22no—
1296C2×D3—22no—
1297C2×D3—22no—
1298C2×D3—44no—
1299C2×D3—48no—
1300C2×D3—54no—
1301C2×D3—1016no—
1302C2×D3—102no—
1303C2×D3—102no—
1304C2×D3—102no—
1305C2×D3—102no—
1306C2×D3—102no—
1307C2×D3—208no—
1308C2×D3—208no—
1309C2×D3—208no—
1310C2×D3—208no—
1311C2×D3—204no—
1312C2×D3—208no—
1313C2×D3C2×D4×D514yes—
1314C3×C4—22no—
1315C3×C4—21no—
1316C3×C4—21no—
1317C3×C4—102no—
1318C3×C4—101no—
1319C3×C4—101no—
1320Dic3—22no—
1321Dic3—22no—
1322Dic3—102no—
1323Dic3—102no—
1324C2×C5—22no—
1325C2×C5—42no—
1326C2×C5—64no—
1327C2×C5—122no—
1328C2×C5C22×D3×D411yescharacteristic
1329C2×C5C2×#100411yescharacteristic
1330C2×C5C2×#100911yescharacteristic
1331D5—22no—
1332D5—42no—
1333D5—64no—
1334D5—122no—
1335D5#560514yesdirect product factor
1336C23—32no—
1337C23—34no—
1338C23—32no—
1339C23—51no—
1340C23—54no—
1341C23—51no—
1342C23—52no—
1343C23—64no—
1344C23—102no—
1345C23—102no—
1346C23—104no—
1347C23—104no—
1348C23—104no—
1349C23—121no—
1350C23—121no—
1351C23—122no—
1352C23—122no—
1353C23—158no—
1354C23—158no—
1355C23—152no—
1356C23—154no—
1357C23—152no—
1358C23—304no—
1359C23—304no—
1360C23—304no—
1361C23—304no—
1362C23—304no—
1363C23—304no—
1364C23—304no—
1365C23—304no—
1366C23—601no—
1367C23—601no—
1368C23—602no—
1369C23—602no—
1370C23—602no—
1371C23—602no—
1372C23—602no—
1373C23—602no—
1374C23—602no—
1375C23—602no—
1376C23—6016no—
1377C23—6032no—
1378C23C22×D3×D512yes—
1379C23C22×D3×D511yescharacteristic
1380D4—24no—
1381D4—41no—
1382D4—64no—
1383D4—64no—
1384D4—64no—
1385D4—104no—
1386D4—104no—
1387D4—104no—
1388D4—121no—
1389D4—122no—
1390D4—201no—
1391D4—202no—
1392D4—304no—
1393D4—304no—
1394D4—304no—
1395D4—304no—
1396D4—304no—
1397D4—304no—
1398D4—304no—
1399D4—304no—
1400D4—304no—
1401D4—601no—
1402D4—602no—
1403D4—602no—
1404D4—602no—
1405D4—602no—
1406C2×C4—32no—
1407C2×C4—32no—
1408C2×C4—41no—
1409C2×C4—51no—
1410C2×C4—52no—
1411C2×C4—51no—
1412C2×C4—64no—
1413C2×C4—102no—
1414C2×C4—102no—
1415C2×C4—104no—
1416C2×C4—121no—
1417C2×C4—152no—
1418C2×C4—152no—
1419C2×C4—201no—
1420C2×C4—201no—
1421C2×C4—201no—
1422C2×C4—304no—
1423C2×C4—304no—
1424C2×C4—304no—
1425C2×C4—304no—
1426C2×C4—304no—
1427C2×C4—602no—
1428C2×C4—601no—
1429C2×C4C22×D3×D511yescharacteristic
1430C2×C4C22×D3×D511yescharacteristic
1431C2×C4C22×D3×D512yes—
1432C2×C3—22no—
1433C2×C3—42no—
1434C2×C3—54no—
1435C2×C3—102no—
1436C2×C3—202no—
1437C2×C3C22×D4×D511yescharacteristic
1438C2×C3D5×H(5,𝔽2)11yescharacteristic
1439C2×C3D5×H(5,𝔽2)11yescharacteristic
1440D3—24no—
1441D3—42no—
1442D3—104no—
1443D3—202no—
1444C5C2×#560511yescharacteristic, complemented, Sylow
1445C22—21no—
1446C22—21no—
1447C22—22no—
1448C22—22no—
1449C22—22no—
1450C22—34no—
1451C22—52no—
1452C22—52no—
1453C22—52no—
1454C22—52no—
1455C22—62no—
1456C22—62no—
1457C22—62no—
1458C22—62no—
1459C22—62no—
1460C22—108no—
1461C22—101no—
1462C22—101no—
1463C22—102no—
1464C22—102no—
1465C22—102no—
1466C22—124no—
1467C22—128no—
1468C22—154no—
1469C22—208no—
1470C22—3016no—
1471C22—302no—
1472C22—302no—
1473C22—302no—
1474C22—302no—
1475C22—302no—
1476C22—604no—
1477C22—608no—
1478C22—608no—
1479C22—608no—
1480C22—608no—
1481C22—608no—
1482C22D3×D4×D512yes—
1483C22C23×D3×D511yescharacteristic
1484C4—22no—
1485C4—21no—
1486C4—21no—
1487C4—62no—
1488C4—62no—
1489C4—102no—
1490C4—101no—
1491C4—101no—
1492C4—302no—
1493C4—302no—
1494C3D5×#53411yescharacteristic, complemented, Sylow
1495C2—22no—
1496C2—42no—
1497C2—54no—
1498C2—64no—
1499C2—102no—
1500C2—122no—
1501C2—202no—
1502C2—304no—
1503C2—602no—
1504C2C2×D3×D4×D511yescharacteristic
1505C2D5×#100411yescharacteristic
1506C2D5×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#121C22
hypercenter#121D3×D5
hypocenterC3×C5C2×#534
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D3×D4×D5C2semidirect
2. #11756364C2semidirect
3. C5×#5605C2semidirect
4. C3×D5×#121C2semidirect
5. #11755073C2semidirect
6. #11755067C2semidirect
7. D5×#939C2semidirect
8. #11755025C2semidirect
9. D5×#937C2semidirect
10. #11754674C2semidirect
11. #11754660C2semidirect
12. D5×#930C2semidirect
13. C2×D5×(C2×D3)⋊C4C2semidirect
14. #11753849C2semidirect
15. D5×#894C2semidirect
16. #11753218C2semidirect
17. #11753217C2semidirect
18. D5×#883C2semidirect
19. D5×#882C2semidirect
22. C23×D3×D5C22semidirect
23. C2×D4×D15C22semidirect
24. C2×C5×D3×D4C22semidirect
25. C2×C3×D4×D5C22semidirect
26. C2×C3×D4×D5C22semidirect
27. C22×C3×C4×D5C22semidirect
28. C2×#6790C22semidirect
29. C2×#6790C22semidirect
30. C2×D3×C22⋊D5C22semidirect
31. C2×D3×C22⋊D5C22semidirect
33. C2×D5×#67C22semidirect
34. C2×D5×#67C22semidirect
35. C22×D5×Dic3C22semidirect
37. C2×#6777C22semidirect
38. C2×D3×D20C22semidirect
40. C2×D5×D12C22semidirect
41. C2×C4×D3×D5C22semidirect
42. C3×C5×#121C22semidirect
43. #91828C22semidirect
44. #91826C22semidirect
45. #91819C22semidirect
46. C2×#6714C22semidirect
47. #91783C22semidirect
48. #91772C22semidirect
49. #91771C22semidirect
50. C5×#939C22semidirect
51. C5×#937C22semidirect
52. C5×#930C22semidirect
53. C2×C5×(C2×D3)⋊C4C22semidirect
54. C5×#894C22semidirect
55. C5×#883C22semidirect
56. C5×#882C22semidirect
57. C3×#4085C22semidirect
58. C3×#4084C22semidirect
59. C3×#4076C22semidirect
60. C3×#4041C22semidirect
61. C3×D5×C4⋊C4C22semidirect
62. C3×#4030C22semidirect
63. C3×D5×C22⋊C4C22semidirect
64. #91577C22semidirect
65. #91577C22semidirect
66. #91573C22semidirect
67. #91572C22semidirect
68. #91571C22semidirect
69. #91570C22semidirect
70. #91569C22semidirect
71. #91568C22semidirect
72. #91566C22semidirect
73. #91562C22semidirect
74. #91555C22semidirect
75. #91550C22semidirect
76. #91549C22semidirect
77. D5×#217C22semidirect
78. C2×#6667C22semidirect
79. C2×(C2×D3)⋊Dic5C22semidirect
80. #91476C22semidirect
81. #91476C22semidirect
82. #91475C22semidirect
83. #91475C22semidirect
84. #91474C22semidirect
85. #91474C22semidirect
86. D5×(C2×D3)⋊C4C22semidirect
87. D5×(C2×D3)⋊C4C22semidirect
88. D5×(C2×D3)⋊C4C22semidirect
89. D5×(C2×D3)⋊C4C22semidirect
90. D5×(C2×D3)⋊C4C22semidirect
91. D5×(C2×D3)⋊C4C22semidirect
92. #91457C22semidirect
93. #91452C22semidirect
94. #91450C22semidirect
95. #91449C22semidirect
96. #91448C22semidirect
97. #91438C22semidirect
98. #91433C22semidirect
99. #91427C22semidirect
100. #91423C22semidirect
101. D5×C4⋊Dic3C22semidirect
102. #91409C22semidirect
103. #91408C22semidirect
104. D5×Dic3⋊C4C22semidirect
105. #91356C22semidirect
106. #91355C22semidirect
107. #91354C22semidirect
108. #91351C22semidirect
122. D5×#121D3semidirect
130. C23×D15C23semidirect
132. C23×C5×D3C23semidirect
140. C22×D3×D5D4semidirect
144. C22×D3×D5C23semidirect
145. C22×D3×D5C23semidirect
146. C2×C3×C5×D4C23semidirect
147. C2×C3×C5×D4C23semidirect
148. C22×C3×C4×C5C23semidirect
150. C2×#1220C23semidirect
151. C2×#1220C23semidirect
152. C22×Dic15C23semidirect
155. C2×D60C23semidirect
156. C2×C4×D15C23semidirect
158. C2×C5×#67C23semidirect
159. C2×C5×#67C23semidirect
160. C22×C5×Dic3C23semidirect
163. C2×C5×D12C23semidirect
164. C2×C4×C5×D3C23semidirect
165. C2×C3×C22⋊D5C23semidirect
166. C2×C3×C22⋊D5C23semidirect
167. C2×C3×C22⋊D5C23semidirect
168. C22×C3×Dic5C23semidirect
171. C2×C3×D20C23semidirect
172. C2×C3×D20C23semidirect
177. C2×C3×C4×D5C23semidirect
178. C2×C3×C4×D5C23semidirect
188. C2×#1203C23semidirect
190. C2×#1202C23semidirect
191. C2×#1202C23semidirect
193. C2×#1201C23semidirect
194. C2×#1201C23semidirect
195. C2×#1200C23semidirect
196. C2×D3×Dic5C23semidirect
200. C2×D5×Dic3C23semidirect
206. C3×C5×C4⋊C4C23semidirect
207. C3×C5×C22⋊C4C23semidirect
208. #6719C23semidirect
209. #6714C23semidirect
210. #6714C23semidirect
211. #6714C23semidirect
212. #6714C23semidirect
213. C4⋊Dic15C23semidirect
214. #6712C23semidirect
215. C5×#217C23semidirect
216. C5×(C2×D3)⋊C4C23semidirect
217. C5×(C2×D3)⋊C4C23semidirect
218. C5×(C2×D3)⋊C4C23semidirect
219. C5×(C2×D3)⋊C4C23semidirect
220. C5×C4⋊Dic3C23semidirect
221. C5×Dic3⋊C4C23semidirect
222. C3×C22⋊Dic5C23semidirect
223. C3×#685C23semidirect
224. C3×#685C23semidirect
225. C3×C4⋊Dic5C23semidirect
226. C3×#683C23semidirect
227. Dic3⋊Dic5C23semidirect
228. #6669C23semidirect
229. #6668C23semidirect
230. #6667C23semidirect
231. #6667C23semidirect
232. #6667C23semidirect
233. #6667C23semidirect
234. (C2×D3)⋊Dic5C23semidirect
235. (C2×D3)⋊Dic5C23semidirect
236. (C2×D3)⋊Dic5C23semidirect
237. (C2×D3)⋊Dic5C23semidirect
238. #6665C23semidirect
239. #6665C23semidirect
255. #5605D5direct (N × H)
274. C2×D4×D5C2×D3semidirect
275. C2×D4×D5C2×D3semidirect
279. C22×C4×D5C2×D3semidirect
284. C5×#121C2×D3semidirect
294. #4085C2×D3semidirect
297. #4084C2×D3semidirect
308. #4076C2×D3semidirect
315. #4041C2×D3semidirect
322. D5×C4⋊C4C2×D3semidirect
328. #4030C2×D3semidirect
346. D5×C22⋊C4C2×D3semidirect
355. C22×D15C2×D4semidirect
363. C22×C5×D3C2×D4semidirect
391. C2×D3×D5C2×D4semidirect
461. C2×D3×D4C2×D5semidirect
470. C3×#121C2×D5semidirect
481. #939C2×D5semidirect
489. #937C2×D5semidirect
495. #930C2×D5semidirect
505. C2×(C2×D3)⋊C4C2×D5semidirect
515. #894C2×D5semidirect
523. #883C2×D5semidirect
531. #882C2×D5semidirect
555. C2×C5×D4C22×D3semidirect
556. C2×C5×D4C22×D3semidirect
559. C22×C4×C5C22×D3semidirect
571. C2×C22⋊D5C22×D3semidirect
572. C2×C22⋊D5C22×D3semidirect
573. C2×C22⋊D5C22×D3semidirect
576. C22×Dic5C22×D3semidirect
594. C2×D20C22×D3semidirect
595. C2×D20C22×D3semidirect
607. C2×C4×D5C22×D3semidirect
608. C2×C4×D5C22×D3semidirect
611. C5×C4⋊C4C22×D3semidirect
617. C5×C22⋊C4C22×D3semidirect
623. C22⋊Dic5C22×D3semidirect
634. #685C22×D3semidirect
635. #685C22×D3semidirect
638. C4⋊Dic5C22×D3semidirect
642. #683C22×D3semidirect
727. C23×D3C22×D5semidirect
735. C2×C3×D4C22×D5semidirect
736. C2×C3×D4C22×D5semidirect
744. C22×C3×C4C22×D5semidirect
758. C2×#67C22×D5semidirect
759. C2×#67C22×D5semidirect
765. C22×Dic3C22×D5semidirect
782. C2×D12C22×D5semidirect
787. C2×C4×D3C22×D5semidirect
790. C3×C4⋊C4C22×D5semidirect
794. C3×C22⋊C4C22×D5semidirect
798. #217C22×D5semidirect
811. (C2×D3)⋊C4C22×D5semidirect
812. (C2×D3)⋊C4C22×D5semidirect
813. (C2×D3)⋊C4C22×D5semidirect
814. (C2×D3)⋊C4C22×D5semidirect
817. C4⋊Dic3C22×D5semidirect
821. Dic3⋊C4C22×D5semidirect
974. #121D3×D5semidirect
1015. C3×D5#534semidirect
1059. C22×D3D4×D5semidirect
1219. C2×D4C2×D3×D5semidirect
1220. C2×D4C2×D3×D5semidirect
1239. C22×C4C2×D3×D5semidirect
1249. C4⋊C4C2×D3×D5semidirect
1273. C22⋊C4C2×D3×D5semidirect
1274. C3×C5C2×#534semidirect
1335. D5#5605direct (N × H)
1444. C5C2×#5605semidirect
1494. C3D5×#534semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D4×D52
#117563642
C5×#56052
C3×D5×#1212
#117550732
#117550672
D5×#9392
#117550252
D5×#9372
#117546742
#117546602
D5×#9302
C2×D5×(C2×D3)⋊C42
#117538492
D5×#8942
#117532182
#117532172
D5×#8832
D5×#8822
D5×#5343
C2×#56055