Finite Group Databasebeta

← C2×#11754809 #14482591

Subgroups — C2×#11754809 #14482591

Order 1920.

3800 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×D3×D4C211yesmaximal, characteristic, complemented
2C22×#6782C211yesmaximal, characteristic, complemented
3C2×#91828C211yesmaximal, characteristic, complemented
4C2×C3×#4081C211yesmaximal, characteristic, complemented
5C2×#91570C211yesmaximal, characteristic, complemented
6C2×#91570C211yesmaximal, characteristic, complemented
7C2×#67⋊Dic5C211yesmaximal, characteristic, complemented
8C2×#91557C211yesmaximal, characteristic, complemented
9C2×D3×C22⋊Dic5C211yesmaximal, characteristic, complemented
10C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
11C2×#91525C211yesmaximal, characteristic, complemented
12#11754809C2116yesmaximal, direct product factor
13C2×#91446C211yesmaximal, characteristic, complemented
14C2×#91423C211yesmaximal, characteristic, complemented
15C2×#91416C211yesmaximal, characteristic, complemented
16C2×#91352C211yesmaximal, characteristic, complemented
17C2×#66140—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C24×C5×D3C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic
21C22×#1220C2211yescharacteristic, complemented
22C22×#1220C2211yescharacteristic, complemented
23C23×Dic15C2211yescharacteristic, complemented
24C22×C5×#67C2211yescharacteristic
25C22×C5×#67C2211yescharacteristic
26C2×C5×D3×D4—28no—
27C2×C5×D3×D4C2218yescomplemented
28C22×C5×D12C2211yescharacteristic
29C22×C4×C5×D3C2211yescharacteristic
30C23×C3×Dic5C2211yescharacteristic, complemented
31C22×#1204C2211yescharacteristic, complemented
32C22×#1203C2211yescharacteristic
33C22×#1203C2211yescharacteristic, complemented
34C22×#1203C2211yescharacteristic, complemented
35C22×#1200C2211yescharacteristic, complemented
36C2×#6782—28no—
37C2×#6782C2218yescomplemented
38C22×D3×Dic5C2211yescharacteristic, complemented
39C22×D3×Dic5C2211yescharacteristic, complemented
40C2×#6719C2211yescharacteristic, complemented
41#91828C2218yescomplemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6712C2211yescharacteristic, complemented
44C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
45C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
46C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
47C3×#4081C2218yescomplemented
48C2×C3×#683C2211yescharacteristic, complemented
49C2×C3×#683C2211yescharacteristic, complemented
50#91570C2218yescomplemented
51#91570C2218yescomplemented
52#67⋊Dic5C2218yescomplemented
53#91557C2218yescomplemented
54D3×C22⋊Dic5C2218yescomplemented
55C2×Dic3⋊Dic5C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×(C2×D3)⋊Dic5C2211yescharacteristic
59C2×(C2×D3)⋊Dic5C2218yescomplemented
60C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
64C2×Dic3×Dic5C2211yescharacteristic, complemented
65#91525C2218yescomplemented
66#91446C2218yescomplemented
67#91423C2218yescomplemented
68#91416C2218yescomplemented
69#91352C2218yescomplemented
70C2×#5654—51nomaximal, Hall
71C23×C5×D4—31no—
72C22×#711—31no—
73C2×#4099—31no—
74C2×#4099—31no—
75C22×C22⋊Dic5—31no—
76C22×C22⋊Dic5—31no—
77#66140—316no—
78C2×#4085—31no—
79C2×#4085—31no—
80C2×#4084—31no—
81C2×#4082—31no—
82C2×#4081—31no—
83C2×#4081D311yescharacteristic, complemented
84C2×D4×Dic5—31no—
85C2×C4×C22⋊D5—31no—
86C2×#4070—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3—24no—
91C23×C5×D3—24no—
92C23×C5×D3—24no—
93C23×C5×D3—24no—
94C23×C5×D3—42no—
95C23×C5×D3—42no—
96C23×C5×D3C2311yescharacteristic
97C23×C5×D3C2314yes—
98C23×C5×D3C2314yes—
99C23×C5×D3C2311yescharacteristic
100C23×C5×D3C2311yescharacteristic
101C2×C3×C5×D4—24no—
102C2×C3×C5×D4C2314yes—
103C22×C3×C4×C5C2311yescharacteristic
104C2×#1220—24no—
105C2×#1220—42no—
106C2×#1220C2314yescomplemented
107C2×#1220C2314yescomplemented
108C22×Dic15—42no—
109C22×Dic15C2311yescharacteristic
110C22×Dic15C2311yescharacteristic
111C22×Dic15C2311yescharacteristic
112C22×Dic15C2314yescomplemented
113C2×C5×#67—24no—
114C2×C5×#67D418yescomplemented
115C2×C5×#67C2314yes—
116C2×C5×#67C2314yes—
117C22×C5×Dic3C2311yescharacteristic
118C5×D3×D4—232no—
119C2×C5×D12—24no—
120C2×C5×D12C2314yes—
121C2×C4×C5×D3—24no—
122C2×C4×C5×D3C2314yes—
123C22×C3×Dic5—24no—
124C22×C3×Dic5C2311yescharacteristic
125C22×C3×Dic5C2311yescharacteristic
126C22×C3×Dic5C2311yescharacteristic
127C22×C3×Dic5C2311yescharacteristic
128C22×C3×Dic5C2314yescomplemented
129C2×#1204—24no—
130C2×#1204C2314yescomplemented
131C2×#1203—24no—
132C2×#1203—24no—
133C2×#1203—42no—
134C2×#1203C2314yes—
135C2×#1203C2314yescomplemented
136C2×#1203C2314yescomplemented
137C2×#1200—24no—
138C2×#1200C2314yescomplemented
139#6782—232no—
140C2×D3×Dic5—24no—
141C2×D3×Dic5—42no—
142C2×D3×Dic5C2314yescomplemented
143C2×D3×Dic5C2314yescomplemented
144#6719C2314yescomplemented
145#6714C2314yescomplemented
146#6712C2314yescomplemented
147C3×C22⋊Dic5C2314yescomplemented
148C3×C22⋊Dic5C2314yescomplemented
149C3×C22⋊Dic5C2314yescomplemented
150C3×#683C2314yescomplemented
151C3×#683C2314yescomplemented
152Dic3⋊Dic5C2314yescomplemented
153(C2×D3)⋊Dic5C2314yes—
154(C2×D3)⋊Dic5C2314yes—
155(C2×D3)⋊Dic5C2314yes—
156(C2×D3)⋊Dic5C2314yescomplemented
157(C2×D3)⋊Dic5C2314yescomplemented
158(C2×D3)⋊Dic5C2314yescomplemented
159(C2×D3)⋊Dic5C2314yescomplemented
160Dic3×Dic5C2314yescomplemented
161C22×D3×D4D511yescharacteristic, complemented
162C22×#235—51no—
163C2×C3×#123—51no—
164C2×#939—51no—
165C22×(C2×D3)⋊C4—51no—
166#5654—516no—
167C2×#896—51no—
168C2×#895—51no—
169C2×#894—51no—
170C2×#893—51no—
171C2×#885—51no—
172C2×#884—51no—
173C2×#882—51no—
174C2×#882—51no—
175C2×#67⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C25×C5—31no—
178C25×C5—31no—
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4—38no—
182C22×C5×D4—31no—
183C22×C5×D4—68no—
184C22×C5×D4C2×D311yescharacteristic
185C23×C4×C5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5—31no—
190C22×C22⋊D5—31no—
191C23×Dic5—31no—
192C23×Dic5—31no—
193C23×Dic5—31no—
194C23×Dic5C2×D311yescharacteristic, complemented
195C2×#711—38no—
196C2×#711—68no—
197C22×C4×D5—31no—
198C22×Dic10—31no—
199#4099—38no—
200#4099—38no—
201C2×C22⋊Dic5—31no—
202C2×C22⋊Dic5—31no—
203C2×C22⋊Dic5—31no—
204C2×C22⋊Dic5—31no—
205C2×C22⋊Dic5—31no—
206C2×C22⋊Dic5—31no—
207C2×C22⋊Dic5—31no—
208C2×C22⋊Dic5—31no—
209C2×C22⋊Dic5—38no—
210C2×C22⋊Dic5—38no—
211C2×C22⋊Dic5C2×D311yescharacteristic, complemented
212C2×C22⋊Dic5C2×D311yescharacteristic, complemented
213C2×C22⋊Dic5C2×D311yescharacteristic, complemented
214#4085—38no—
215#4085—38no—
216#4084—38no—
217#4082—38no—
218#4081—38no—
219#4081C2×D318yescomplemented
220D4×Dic5—38no—
221C4×C22⋊D5—38no—
222C2×#685—31no—
223C2×C4⋊Dic5—31no—
224#4070—38no—
225C2×#683—31no—
226C2×#683C2×D311yescharacteristic, complemented
227C2×#683C2×D311yescharacteristic, complemented
228C2×C4×Dic5—31no—
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5C2×D414yes—
236C23×C3×C5C2412yes—
237C23×C3×C5C2412yes—
238C23×C3×C5C2411yescharacteristic
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15C2412yes—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—22no—
247C22×C5×D3—22no—
248C22×C5×D3—28no—
249C22×C5×D3—22no—
250C22×C5×D3—22no—
251C22×C5×D3—28no—
252C22×C5×D3—28no—
253C22×C5×D3—28no—
254C22×C5×D3—44no—
255C22×C5×D3—44no—
256C22×C5×D3—416no—
257C22×C5×D3—416no—
258C22×C5×D3C2×D414yes—
259C22×C5×D3#4114yescomplemented
260C22×C5×D3C2412yes—
261C22×C5×D3C2412yes—
262C22×C5×D3C2412yes—
263C3×C5×D4—28no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266#1220—28no—
267#1220—44no—
268C2×Dic15—22no—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15—44no—
272C2×Dic15C2412yes—
273C2×Dic15C2412yes—
274C2×Dic15C2412yes—
275C5×#67—28no—
276C5×#67C2×D4116yescomplemented
277C2×C5×Dic3C2×D414yes—
278C2×C5×Dic3C2412yes—
279C5×D12—28no—
280C4×C5×D3—28no—
281C2×C3×Dic5—22no—
282C2×C3×Dic5—28no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5—22no—
286C2×C3×Dic5C2412yes—
287C2×C3×Dic5C2412yes—
288C2×C3×Dic5C2412yes—
289C2×C3×Dic5C2412yes—
290#1204—28no—
291#1203—28no—
292#1203—28no—
293#1203—44no—
294#1200—28no—
295D3×Dic5—28no—
296D3×Dic5—44no—
297C24×D3C2×D511yescharacteristic
298C24×D3C2×D511yescharacteristic
299C22×C3×D4C2×D511yescharacteristic
300C23×C3×C4—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67C2×D511yescharacteristic
304C22×#67C2×D511yescharacteristic
305C23×Dic3—51no—
306C2×D3×D4—28no—
307C2×D3×D4C2×D518yescomplemented
308C2×#235—58no—
309C2×#235—108no—
310C22×D12—51no—
311C22×D12—51no—
312C22×D12—51no—
313C22×D12C2×D511yescharacteristic
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3C2×D511yescharacteristic
318C22×Dic6—51no—
319C3×#123—58no—
320C2×C3×C4⋊C4—51no—
321C2×C3×C4⋊C4—51no—
322C2×C3×C22⋊C4—51no—
323C2×C3×C22⋊C4—51no—
324C2×C3×C22⋊C4—51no—
325C2×#217—51no—
326#939—58no—
327C2×(C2×D3)⋊C4—58no—
328C2×(C2×D3)⋊C4—51no—
329C2×(C2×D3)⋊C4—51no—
330C2×(C2×D3)⋊C4—51no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4—51no—
334C2×(C2×D3)⋊C4—51no—
335C2×(C2×D3)⋊C4—51no—
336C2×Dic3⋊C4—51no—
337C2×Dic3⋊C4—51no—
338C2×C4×Dic3—51no—
339#896—58no—
340#895—58no—
341#894—58no—
342#893—58no—
343#885—58no—
344#884—58no—
345#882—58no—
346#882—58no—
347#67⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5—31no—
351C24×C5—31no—
352C24×C5—34no—
353C24×C5—34no—
354C24×C5—64no—
355C24×C5—64no—
356C24×C5—64no—
357C24×C5—64no—
358C24×C5—122no—
359C24×C5—122no—
360C24×C5C22×D311yescharacteristic
361C24×C5C22×D311yescharacteristic
362C23×D5—31no—
363C2×C5×D4—24no—
364C2×C5×D4—38no—
365C2×C5×D4—34no—
366C2×C5×D4—34no—
367C2×C5×D4—34no—
368C2×C5×D4—64no—
369C2×C5×D4—64no—
370C2×C5×D4—632no—
371C2×C5×D4C22×D314yes—
372C22×C4×C5—31no—
373C22×C4×C5—34no—
374C22×C4×C5—64no—
375C22×C4×C5C22×D311yescharacteristic
376C2×C22⋊D5—34no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—34no—
380C2×C22⋊D5—34no—
381C2×C22⋊D5—64no—
382C2×C22⋊D5—64no—
383C2×C22⋊D5—64no—
384C2×C22⋊D5—122no—
385C2×C22⋊D5—122no—
386C22×Dic5—24no—
387C22×Dic5—31no—
388C22×Dic5—31no—
389C22×Dic5—31no—
390C22×Dic5—34no—
391C22×Dic5—34no—
392C22×Dic5—34no—
393C22×Dic5—64no—
394C22×Dic5—122no—
395C22×Dic5—122no—
396C22×Dic5C22×D311yescharacteristic
397C22×Dic5C22×D311yescharacteristic
398C22×Dic5C22×D311yescharacteristic
399C22×Dic5C22×D311yescharacteristic
400C22×Dic5C22×D314yescomplemented
401#711—632no—
402C2×C4×D5—34no—
403C2×C4×D5—64no—
404C2×Dic10—34no—
405C2×Dic10—64no—
406C22⋊Dic5—34no—
407C22⋊Dic5—34no—
408C22⋊Dic5—34no—
409C22⋊Dic5—34no—
410C22⋊Dic5—34no—
411C22⋊Dic5—34no—
412C22⋊Dic5—34no—
413C22⋊Dic5—34no—
414C22⋊Dic5C22×D314yescomplemented
415C22⋊Dic5C22×D314yescomplemented
416C22⋊Dic5C22×D314yescomplemented
417#685—34no—
418C4⋊Dic5—34no—
419#683—34no—
420#683C22×D314yescomplemented
421#683C22×D314yescomplemented
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—31no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—51no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—151no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—151no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
438C22×C22⋊C4—151no—
439C22×C3×C5—28no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—22no—
443C22×C3×C5—22no—
444C22×C3×C5—22no—
445C22×C3×C5—44no—
446C22×C3×C5C22×D414yes—
447C22×C3×C5C22×D412yes—
448C22×C3×C5C2×#4112yes—
449C22×C3×C5H(5,𝔽2)12yes—
450C22×C3×C5C2511yescharacteristic
451C2×D15—22no—
452C2×D15—22no—
453C2×D15—22no—
454C2×D15—44no—
455C2×C5×D3—28no—
456C2×C5×D3—28no—
457C2×C5×D3—22no—
458C2×C5×D3—22no—
459C2×C5×D3—22no—
460C2×C5×D3—22no—
461C2×C5×D3—22no—
462C2×C5×D3—22no—
463C2×C5×D3—22no—
464C2×C5×D3—416no—
465C2×C5×D3—416no—
466C2×C5×D3—44no—
467C2×C5×D3C22×D414yes—
468C2×C5×D3C2×#4114yescomplemented
469C3×C4×C5—22no—
470Dic15—22no—
471Dic15—22no—
472Dic15—22no—
473C3×Dic5—22no—
474C3×Dic5—22no—
475C3×Dic5—22no—
476C3×Dic5—22no—
477C5×Dic3C22×D414yes—
478C24×C3C22×D511yescharacteristic
479C24×C3C22×D511yescharacteristic
480C23×D3—24no—
481C23×D3—24no—
482C23×D3—24no—
483C23×D3—24no—
484C23×D3—42no—
485C23×D3—42no—
486C23×D3—51no—
487C23×D3C22×D511yescharacteristic
488C23×D3C22×D514yes—
489C23×D3C22×D514yes—
490C23×D3C22×D511yescharacteristic
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—24no—
493C2×C3×D4C22×D514yes—
494C22×C3×C4—51no—
495C22×C3×C4—51no—
496C22×C3×C4—51no—
497C22×C3×C4—51no—
498C22×C3×C4—54no—
499C22×C3×C4—104no—
500C22×C3×C4C22×D511yescharacteristic
501C2×#67—24no—
502C2×#67—54no—
503C2×#67—54no—
504C2×#67—104no—
505C2×#67—202no—
506C2×#67C22⋊D518yescomplemented
507C2×#67C22×D514yes—
508C2×#67C22×D514yes—
509C22×Dic3—51no—
510C22×Dic3—51no—
511C22×Dic3—51no—
512C22×Dic3—54no—
513C22×Dic3—202no—
514C22×Dic3C22×D511yescharacteristic
515D3×D4—232no—
516#235—1032no—
517C2×D12—24no—
518C2×D12—54no—
519C2×D12—54no—
520C2×D12—54no—
521C2×D12—104no—
522C2×D12—104no—
523C2×D12—202no—
524C2×D12C22×D514yes—
525C2×C4×D3—24no—
526C2×C4×D3—54no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—104no—
530C2×C4×D3—104no—
531C2×C4×D3—202no—
532C2×C4×D3C22×D514yes—
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4—54no—
536C3×C4⋊C4—54no—
537C3×C22⋊C4—54no—
538C3×C22⋊C4—54no—
539C3×C22⋊C4—54no—
540#217—54no—
541(C2×D3)⋊C4—54no—
542(C2×D3)⋊C4—54no—
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4—54no—
546(C2×D3)⋊C4—54no—
547(C2×D3)⋊C4—54no—
548(C2×D3)⋊C4—54no—
549Dic3⋊C4—54no—
550Dic3⋊C4—54no—
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—22no—
556C23×C5—22no—
557C23×C5—34no—
558C23×C5—34no—
559C23×C5—32no—
560C23×C5—32no—
561C23×C5—32no—
562C23×C5—68no—
563C23×C5—68no—
564C23×C5—68no—
565C23×C5—62no—
566C23×C5—62no—
567C23×C5—62no—
568C23×C5—62no—
569C23×C5—68no—
570C23×C5—62no—
571C23×C5—62no—
572C23×C5—62no—
573C23×C5—124no—
574C23×C5—124no—
575C23×C5—1216no—
576C23×C5—1216no—
577C23×C5D3×D414yes—
578C23×C5C23×D312yes—
579C23×C5C23×D312yes—
580C23×C5C23×D311yescharacteristic
581C22×D5—32no—
582C22×D5—62no—
583C22×D5—62no—
584C22×D5—62no—
585C5×D4—28no—
586C5×D4—316no—
587C5×D4—68no—
588C5×D4—68no—
589C2×C4×C5—22no—
590C2×C4×C5—34no—
591C2×C4×C5—32no—
592C2×C4×C5—68no—
593C2×C4×C5C23×D312yes—
594C22⋊D5—68no—
595C22⋊D5—68no—
596C22⋊D5—68no—
597C22⋊D5—124no—
598C22⋊D5—124no—
599C2×Dic5—22no—
600C2×Dic5—22no—
601C2×Dic5—28no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—32no—
605C2×Dic5—32no—
606C2×Dic5—32no—
607C2×Dic5—68no—
608C2×Dic5—62no—
609C2×Dic5—62no—
610C2×Dic5—62no—
611C2×Dic5—124no—
612C2×Dic5—124no—
613C2×Dic5C23×D312yes—
614C2×Dic5C23×D312yes—
615C2×Dic5C23×D312yes—
616C2×Dic5C23×D312yes—
617C4×D5—68no—
618Dic10—68no—
619C25—31no—
620C25—31no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—31no—
626C22×D4—38no—
627C22×D4—31no—
628C22×D4—68no—
629C22×D4—151no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4D3×D511yescharacteristic
635C23×C4—31no—
636C23×C4—51no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—158no—
642#123—58no—
643#123—158no—
644C22⋊Q8—158no—
645#121—158no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—51no—
653C2×C4⋊C4—51no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—51no—
657C2×C22⋊C4—51no—
658C2×C22⋊C4—51no—
659C2×C22⋊C4—158no—
660C2×C22⋊C4—151no—
661C2×C22⋊C4—151no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—158no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—151no—
668C2×C22⋊C4—151no—
669C2×C22⋊C4—151no—
670C2×C42—151no—
671C2×C3×C5—24no—
672C2×C3×C5—42no—
673C2×C3×C5#54614yescomplemented
674C2×C3×C5C23×D411yescharacteristic
675C2×C3×C5C22×#4111yescharacteristic
676C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
677D15—42no—
678C5×D3—24no—
679C5×D3—24no—
680C5×D3—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—22no—
685C23×C3—22no—
686C23×C3C2×C22⋊D514yes—
687C23×C3C23×D512yes—
688C23×C3C23×D512yes—
689C23×C3C23×D511yescharacteristic
690C22×D3—22no—
691C22×D3—22no—
692C22×D3—22no—
693C22×D3—22no—
694C22×D3—22no—
695C22×D3—22no—
696C22×D3—22no—
697C22×D3—28no—
698C22×D3—28no—
699C22×D3—28no—
700C22×D3—28no—
701C22×D3—44no—
702C22×D3—44no—
703C22×D3—416no—
704C22×D3—416no—
705C22×D3—52no—
706C22×D3—102no—
707C22×D3—102no—
708C22×D3—102no—
709C22×D3#71114yescomplemented
710C22×D3C2×C22⋊D514yes—
711C22×D3C23×D512yes—
712C22×D3C23×D512yes—
713C22×D3C23×D512yes—
714C3×D4—28no—
715C2×C3×C4—22no—
716C2×C3×C4—52no—
717C2×C3×C4—52no—
718C2×C3×C4—52no—
719C2×C3×C4—52no—
720C2×C3×C4—102no—
721C2×C3×C4—102no—
722C2×C3×C4—102no—
723C2×C3×C4—102no—
724C2×C3×C4—108no—
725C2×C3×C4C23×D512yes—
726#67—28no—
727#67—108no—
728#67—204no—
729#67C2×C22⋊D5116yescomplemented
730C2×Dic3—52no—
731C2×Dic3—52no—
732C2×Dic3—52no—
733C2×Dic3—102no—
734C2×Dic3—102no—
735C2×Dic3—102no—
736C2×Dic3—204no—
737C2×Dic3C2×C22⋊D514yes—
738C2×Dic3C23×D512yes—
739D12—28no—
740D12—108no—
741D12—108no—
742D12—204no—
743C4×D3—28no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—28no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—22no—
752C22×C5—22no—
753C22×C5—22no—
754C22×C5—34no—
755C22×C5—34no—
756C22×C5—44no—
757C22×C5—68no—
758C22×C5—68no—
759C22×C5—62no—
760C22×C5—62no—
761C22×C5—62no—
762C22×C5—62no—
763C22×C5—62no—
764C22×C5—62no—
765C22×C5—62no—
766C22×C5—1216no—
767C22×C5—1216no—
768C22×C5—124no—
769C22×C5C2×D3×D414yes—
770C22×C5C2×D3×D412yes—
771C22×C5D3×#4112yes—
772C22×C5#100912yes—
773C22×C5C24×D311yescharacteristic
774C2×D5—62no—
775C2×D5—62no—
776C2×D5—62no—
777C2×D5—124no—
778C4×C5—22no—
779C4×C5—34no—
780Dic5—22no—
781Dic5—22no—
782Dic5—22no—
783Dic5—22no—
784Dic5—62no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—31no—
789C24—31no—
790C24—34no—
791C24—34no—
792C24—64no—
793C24—64no—
794C24—64no—
795C24—64no—
796C24—122no—
797C24—122no—
798C24—151no—
799C24C2×D3×D511yescharacteristic
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—24no—
805C2×D4—38no—
806C2×D4—34no—
807C2×D4—34no—
808C2×D4—34no—
809C2×D4—64no—
810C2×D4—64no—
811C2×D4—632no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—154no—
816C2×D4—154no—
817C2×D4—304no—
818C2×D4—304no—
819C2×D4—304no—
820C2×D4—602no—
821C2×D4—602no—
822C2×D4C2×D3×D514yes—
823C22×C4—31no—
824C22×C4—34no—
825C22×C4—54no—
826C22×C4—51no—
827C22×C4—51no—
828C22×C4—51no—
829C22×C4—51no—
830C22×C4—64no—
831C22×C4—104no—
832C22×C4—154no—
833C22×C4—154no—
834C22×C4—154no—
835C22×C4—151no—
836C22×C4—151no—
837C22×C4—151no—
838C22×C4—154no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—602no—
842C22×C4—602no—
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—54no—
845C4⋊C4—54no—
846C4⋊C4—154no—
847C4⋊C4—154no—
848C22⋊C4—54no—
849C22⋊C4—54no—
850C22⋊C4—54no—
851C22⋊C4—154no—
852C22⋊C4—154no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4—154no—
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—28no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—44no—
869C22×C3C2×#71112yes—
870C22×C3#414412yes—
871C22×C3C22×C22⋊D514yes—
872C22×C3C22×C22⋊D512yes—
873C22×C3C24×D511yescharacteristic
874C2×D3—28no—
875C2×D3—28no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—416no—
884C2×D3—416no—
885C2×D3—44no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—204no—
890C2×D3C2×#71114yescomplemented
891C2×D3C22×C22⋊D514yes—
892C3×C4—22no—
893C3×C4—102no—
894C3×C4—102no—
895C3×C4—102no—
896C3×C4—102no—
897Dic3—102no—
898Dic3—102no—
899Dic3—102no—
900Dic3C22×C22⋊D514yes—
901C2×C5—24no—
902C2×C5—42no—
903C2×C5—64no—
904C2×C5—64no—
905C2×C5—122no—
906C2×C5#565414yescomplemented
907C2×C5C22×D3×D411yescharacteristic
908C2×C5C2×D3×#4111yescharacteristic
909C2×C5C2×#100911yescharacteristic
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—34no—
917C23—34no—
918C23—32no—
919C23—32no—
920C23—32no—
921C23—68no—
922C23—68no—
923C23—68no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—68no—
931C23—62no—
932C23—124no—
933C23—124no—
934C23—1216no—
935C23—1216no—
936C23—152no—
937C23—302no—
938C23—302no—
939C23—302no—
940C23D3×C22⋊D514yes—
941C23C22×D3×D512yes—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—28no—
946D4—316no—
947D4—68no—
948D4—68no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—604no—
953D4—604no—
954C2×C4—22no—
955C2×C4—34no—
956C2×C4—32no—
957C2×C4—52no—
958C2×C4—52no—
959C2×C4—52no—
960C2×C4—52no—
961C2×C4—68no—
962C2×C4—102no—
963C2×C4—102no—
964C2×C4—102no—
965C2×C4—102no—
966C2×C4—108no—
967C2×C4—152no—
968C2×C4—152no—
969C2×C4—152no—
970C2×C4—308no—
971C2×C4—308no—
972C2×C4—302no—
973C2×C4—302no—
974C2×C4—302no—
975C2×C4—604no—
976C2×C4—604no—
977C2×C4C22×D3×D512yes—
978C2×C3—24no—
979C2×C3—42no—
980C2×C3#6614014yescomplemented
981C2×C3C22×#71111yescharacteristic
982C2×C3C2×#414411yescharacteristic
983C2×C3C23×C22⋊D511yescharacteristic
984D3—24no—
985D3—24no—
986D3—42no—
987D3—202no—
988C5C2×#565411yescharacteristic, complemented, Sylow
989C22—28no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—34no—
996C22—34no—
997C22—44no—
998C22—62no—
999C22—68no—
1000C22—68no—
1001C22—62no—
1002C22—62no—
1003C22—62no—
1004C22—62no—
1005C22—62no—
1006C22—62no—
1007C22—1216no—
1008C22—1216no—
1009C22—124no—
1010C22—302no—
1011C22—302no—
1012C22—302no—
1013C22—604no—
1014C22D3×#71112yes—
1015C22#9202712yes—
1016C22C2×D3×C22⋊D514yes—
1017C22C2×D3×C22⋊D512yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—34no—
1021C4—102no—
1022C4—102no—
1023C4—102no—
1024C4—102no—
1025C4—302no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6614011yescharacteristic, complemented, Sylow
1029C2—24no—
1030C2—42no—
1031C2—64no—
1032C2—64no—
1033C2—122no—
1034C2—602no—
1035C2#1175480914yesdirect product factor
1036C2C2×D3×#71111yescharacteristic
1037C2C2×#9202711yescharacteristic
1038C2C22×D3×C22⋊D511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C5×D3×D4C2semidirect
2. C22×#6782C2semidirect
3. C2×#91828C2semidirect
4. C2×C3×#4081C2semidirect
5. C2×#91570C2semidirect
6. C2×#91570C2semidirect
7. C2×#67⋊Dic5C2semidirect
8. C2×#91557C2semidirect
9. C2×D3×C22⋊Dic5C2semidirect
10. C22×(C2×D3)⋊Dic5C2semidirect
11. C2×#91525C2semidirect
12. #11754809C2direct (N × H)
13. C2×#91446C2semidirect
14. C2×#91423C2semidirect
15. C2×#91416C2semidirect
16. C2×#91352C2semidirect
21. C22×#1220C22semidirect
22. C22×#1220C22semidirect
23. C23×Dic15C22semidirect
27. C2×C5×D3×D4C22semidirect
30. C23×C3×Dic5C22semidirect
31. C22×#1204C22semidirect
33. C22×#1203C22semidirect
34. C22×#1203C22semidirect
35. C22×#1200C22semidirect
37. C2×#6782C22semidirect
38. C22×D3×Dic5C22semidirect
39. C22×D3×Dic5C22semidirect
40. C2×#6719C22semidirect
41. #91828C22semidirect
42. C2×#6714C22semidirect
43. C2×#6712C22semidirect
44. C2×C3×C22⋊Dic5C22semidirect
45. C2×C3×C22⋊Dic5C22semidirect
46. C2×C3×C22⋊Dic5C22semidirect
47. C3×#4081C22semidirect
48. C2×C3×#683C22semidirect
49. C2×C3×#683C22semidirect
50. #91570C22semidirect
51. #91570C22semidirect
52. #67⋊Dic5C22semidirect
53. #91557C22semidirect
54. D3×C22⋊Dic5C22semidirect
55. C2×Dic3⋊Dic5C22semidirect
59. C2×(C2×D3)⋊Dic5C22semidirect
60. C2×(C2×D3)⋊Dic5C22semidirect
61. C2×(C2×D3)⋊Dic5C22semidirect
62. C2×(C2×D3)⋊Dic5C22semidirect
63. C2×(C2×D3)⋊Dic5C22semidirect
64. C2×Dic3×Dic5C22semidirect
65. #91525C22semidirect
66. #91446C22semidirect
67. #91423C22semidirect
68. #91416C22semidirect
69. #91352C22semidirect
83. C2×#4081D3semidirect
106. C2×#1220C23semidirect
107. C2×#1220C23semidirect
112. C22×Dic15C23semidirect
114. C2×C5×#67D4semidirect
128. C22×C3×Dic5C23semidirect
130. C2×#1204C23semidirect
135. C2×#1203C23semidirect
136. C2×#1203C23semidirect
138. C2×#1200C23semidirect
142. C2×D3×Dic5C23semidirect
143. C2×D3×Dic5C23semidirect
144. #6719C23semidirect
145. #6714C23semidirect
146. #6712C23semidirect
147. C3×C22⋊Dic5C23semidirect
148. C3×C22⋊Dic5C23semidirect
149. C3×C22⋊Dic5C23semidirect
150. C3×#683C23semidirect
151. C3×#683C23semidirect
152. Dic3⋊Dic5C23semidirect
156. (C2×D3)⋊Dic5C23semidirect
157. (C2×D3)⋊Dic5C23semidirect
158. (C2×D3)⋊Dic5C23semidirect
159. (C2×D3)⋊Dic5C23semidirect
160. Dic3×Dic5C23semidirect
161. C22×D3×D4D5semidirect
194. C23×Dic5C2×D3semidirect
211. C2×C22⋊Dic5C2×D3semidirect
212. C2×C22⋊Dic5C2×D3semidirect
213. C2×C22⋊Dic5C2×D3semidirect
219. #4081C2×D3semidirect
226. C2×#683C2×D3semidirect
227. C2×#683C2×D3semidirect
259. C22×C5×D3#41semidirect
276. C5×#67C2×D4semidirect
307. C2×D3×D4C2×D5semidirect
400. C22×Dic5C22×D3semidirect
414. C22⋊Dic5C22×D3semidirect
415. C22⋊Dic5C22×D3semidirect
416. C22⋊Dic5C22×D3semidirect
420. #683C22×D3semidirect
421. #683C22×D3semidirect
468. C2×C5×D3C2×#41semidirect
506. C2×#67C22⋊D5semidirect
673. C2×C3×C5#546semidirect
709. C22×D3#711semidirect
729. #67C2×C22⋊D5semidirect
861. C3×C5C2×#546semidirect
890. C2×D3C2×#711semidirect
906. C2×C5#5654semidirect
980. C2×C3#66140semidirect
988. C5C2×#5654semidirect
1028. C3C2×#66140semidirect
1035. C2#11754809direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×D3×D42
C22×#67822
C2×#918282
C2×C3×#40812
C2×#915702
C2×#67⋊Dic52
C2×#915572
C2×D3×C22⋊Dic52
C22×(C2×D3)⋊Dic52
C2×#915252
#117548092
C2×#914462
C2×#914232
C2×#914162
C2×#913522
C2×#661403
C2×#56545