Finite Group Databasebeta

← C2×#11753231 #14482595

Subgroups — C2×#11753231 #14482595

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×D3×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×#6772C211yesmaximal, characteristic, complemented
3C2×#91774C211yesmaximal, characteristic, complemented
4C2×C5×#882C211yesmaximal, characteristic, complemented
5C2×C3×#4029C211yesmaximal, characteristic, complemented
6C2×#91558C211yesmaximal, characteristic, complemented
7C2×D3×C22⋊Dic5C211yesmaximal, characteristic, complemented
8C2×#91549C211yesmaximal, characteristic, complemented
9C2×#91475C211yesmaximal, characteristic, complemented
10C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#91442C211yesmaximal, characteristic, complemented
12C2×#91435C211yesmaximal, characteristic, complemented
13C2×#91432C211yesmaximal, characteristic, complemented
14C2×#91427C211yesmaximal, characteristic, complemented
15C2×#91416C211yesmaximal, characteristic, complemented
16#11753231C2116yesmaximal, direct product factor
17C2×#65925—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×Dic30C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic, complemented
23C22×C5×D12C2211yescharacteristic
24C22×C5×D12C2211yescharacteristic, complemented
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×C4×D5C2211yescharacteristic, complemented
27C2×D3×C22⋊D5—28no—
28C2×D3×C22⋊D5C2218yescomplemented
29C22×#1203C2211yescharacteristic
30C22×#1203C2211yescharacteristic, complemented
31C22×#1201C2211yescharacteristic
32C22×#1201C2211yescharacteristic, complemented
33C22×D3×Dic5C2211yescharacteristic
34C22×D3×Dic5C2211yescharacteristic, complemented
35C22×D3×Dic5C2211yescharacteristic, complemented
36C22×D3×Dic5C2211yescharacteristic, complemented
37C22×D5×Dic3C2211yescharacteristic, complemented
38C2×#6772—28no—
39C2×#6772C2218yescomplemented
40C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C2×#6719C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6714C2211yescharacteristic, complemented
44C2×C4×Dic15C2211yescharacteristic, complemented
45#91774C2218yescomplemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C5×#882C2218yescomplemented
49C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
52C2×C3×#683C2211yescharacteristic, complemented
53C3×#4029C2218yescomplemented
54#91558C2218yescomplemented
55D3×C22⋊Dic5C2218yescomplemented
56#91549C2218yescomplemented
57C2×Dic3⋊Dic5C2211yescharacteristic, complemented
58C2×#6669C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic5C2211yescharacteristic
61C2×(C2×D3)⋊Dic5C2211yescharacteristic
62C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
63#91475C2218yescomplemented
64D5×(C2×D3)⋊C4C2218yescomplemented
65#91442C2218yescomplemented
66#91435C2218yescomplemented
67#91432C2218yescomplemented
68#91427C2218yescomplemented
69#91416C2218yescomplemented
70C2×#5654—51nomaximal, Hall
71C23×C22⋊D5—31no—
72C22×#711—31no—
73C2×C5×#120—31no—
74C22×C22⋊Dic5—31no—
75C2×#4085—31no—
76C2×#4085—31no—
77C2×#4084—31no—
78C2×#4083—31no—
79C2×D4×Dic5—31no—
80#65925—316no—
81C2×#4032—31no—
82C2×#4031—31no—
83C2×#4029D311yescharacteristic, complemented
84C2×#4027—31no—
85C2×D5×C22⋊C4—31no—
86C2×#4024—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3—24no—
90C23×C5×D3—24no—
91C23×C5×D3—42no—
92C23×C5×D3C2311yescharacteristic
93C23×C5×D3C2314yes—
94C23×C5×D3C2311yescharacteristic
95C23×C5×D3C2311yescharacteristic
96C23×C3×D5C2311yescharacteristic
97C22×D3×D5—24no—
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5C2314yes—
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2311yescharacteristic
103C2×#1220—24no—
104C2×#1220C2314yes—
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C2×Dic30—24no—
109C2×Dic30C2314yescomplemented
110C2×C5×#67—42no—
111C2×C5×#67C2314yescomplemented
112C22×C5×Dic3C2311yescharacteristic
113C2×C5×D12—24no—
114C2×C5×D12—24no—
115C2×C5×D12C2314yes—
116C2×C5×D12C2314yescomplemented
117C2×C3×C22⋊D5—24no—
118C2×C3×C22⋊D5C2314yes—
119C22×C3×Dic5C2311yescharacteristic
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C2×C3×C4×D5—24no—
123C2×C3×C4×D5C2314yescomplemented
124D3×C22⋊D5—232no—
125C2×#1203—24no—
126C2×#1203—42no—
127C2×#1203C2314yes—
128C2×#1203C2314yescomplemented
129C2×#1201—24no—
130C2×#1201D418yescomplemented
131C2×#1201C2314yes—
132C2×#1201C2314yescomplemented
133C2×D3×Dic5—24no—
134C2×D3×Dic5—24no—
135C2×D3×Dic5—24no—
136C2×D3×Dic5—42no—
137C2×D3×Dic5C2314yes—
138C2×D3×Dic5C2314yescomplemented
139C2×D3×Dic5C2314yescomplemented
140C2×D3×Dic5C2314yescomplemented
141C2×D5×Dic3—42no—
142C2×D5×Dic3C2314yescomplemented
143#6772—232no—
144C3×C5×C22⋊C4C2314yescomplemented
145#6719C2314yescomplemented
146#6714C2314yescomplemented
147#6714C2314yescomplemented
148C4×Dic15C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yes—
150C5×(C2×D3)⋊C4C2314yescomplemented
151C3×C22⋊Dic5C2314yescomplemented
152C3×#685C2314yescomplemented
153C3×C4⋊Dic5C2314yescomplemented
154C3×#683C2314yescomplemented
155Dic3⋊Dic5C2314yescomplemented
156#6669C2314yescomplemented
157#6667C2314yescomplemented
158(C2×D3)⋊Dic5C2314yes—
159(C2×D3)⋊Dic5C2314yes—
160(C2×D3)⋊Dic5C2314yescomplemented
161C22×D3×D4—51no—
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×#882D511yescharacteristic, complemented
175C2×#67⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C25×C5—31no—
178C24×D5—31no—
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—38no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—68no—
189C22×C22⋊D5C2×D311yescharacteristic
190C23×Dic5—31no—
191C23×Dic5—31no—
192C23×Dic5—31no—
193C23×Dic5—31no—
194C2×#711—38no—
195C2×#711—68no—
196C22×C4×D5—31no—
197C22×C4×D5C2×D311yescharacteristic, complemented
198C22×Dic10—31no—
199C5×#120—38no—
200C2×C5×C22⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
203C2×C22⋊Dic5—31no—
204C2×C22⋊Dic5—31no—
205C2×C22⋊Dic5—31no—
206C2×C22⋊Dic5—31no—
207C2×C22⋊Dic5—38no—
208C2×C22⋊Dic5C2×D311yescharacteristic, complemented
209#4085—38no—
210#4085—38no—
211#4084—38no—
212#4083—38no—
213D4×Dic5—38no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685C2×D311yescharacteristic, complemented
218C2×C4⋊Dic5—31no—
219C2×C4⋊Dic5C2×D311yescharacteristic, complemented
220C2×#683—31no—
221C2×#683C2×D311yescharacteristic, complemented
222C2×C4×Dic5—31no—
223#4032—38no—
224#4031—38no—
225#4029C2×D318yescomplemented
226#4027—38no—
227D5×C22⋊C4—38no—
228#4024—38no—
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5C2412yes—
234C23×C3×C5C2411yescharacteristic
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15C2412yes—
239C22×C5×D3—22no—
240C22×C5×D3—22no—
241C22×C5×D3—22no—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—28no—
247C22×C5×D3—28no—
248C22×C5×D3—44no—
249C22×C5×D3—416no—
250C22×C5×D3C2×D414yes—
251C22×C5×D3#4114yescomplemented
252C22×C5×D3C2412yes—
253C22×C5×D3C2412yes—
254C22×C5×D3C2412yes—
255C22×C3×D5—22no—
256C22×C3×D5—22no—
257C22×C3×D5C2×D414yes—
258C22×C3×D5C2412yes—
259C2×D3×D5—28no—
260C2×D3×D5—28no—
261C2×D3×D5—44no—
262C2×D3×D5—416no—
263C2×C3×C4×C5—22no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266C2×C3×C4×C5C2412yes—
267#1220—28no—
268C2×Dic15—22no—
269C2×Dic15—22no—
270C2×Dic15C2×D414yes—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273C2×Dic15C2412yes—
274Dic30—28no—
275C5×#67—44no—
276C2×C5×Dic3—22no—
277C2×C5×Dic3C2412yes—
278C5×D12—28no—
279C5×D12—28no—
280C3×C22⋊D5—28no—
281C2×C3×Dic5—22no—
282C2×C3×Dic5—22no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5C2412yes—
285C2×C3×Dic5C2412yes—
286C2×C3×Dic5C2412yes—
287C3×C4×D5—28no—
288#1203—28no—
289#1203—44no—
290#1201—28no—
291#1201C2×D4116yescomplemented
292D3×Dic5—28no—
293D3×Dic5—28no—
294D3×Dic5—28no—
295D3×Dic5—44no—
296D5×Dic3—44no—
297C24×D3—51no—
298C24×D3C2×D511yescharacteristic
299C22×C3×D4—51no—
300C23×C3×C4—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67—51no—
304C22×#67C2×D511yescharacteristic, complemented
305C23×Dic3—51no—
306C2×D3×D4—58no—
307C2×D3×D4—108no—
308C2×#235—58no—
309C2×#235—108no—
310C22×D12—51no—
311C22×D12—51no—
312C22×D12C2×D511yescharacteristic
313C22×D12C2×D511yescharacteristic, complemented
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3—51no—
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⋊C4C2×D511yescharacteristic, complemented
325C2×#217—51no—
326#939—58no—
327C2×(C2×D3)⋊C4—51no—
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—58no—
334C2×(C2×D3)⋊C4C2×D511yescharacteristic
335C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
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#882C2×D518yescomplemented
347#67⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5—31no—
351C24×C5—31no—
352C24×C5—34no—
353C24×C5—64no—
354C24×C5—64no—
355C24×C5—122no—
356C24×C5C22×D311yescharacteristic
357C23×D5—31no—
358C23×D5—34no—
359C23×D5—64no—
360C23×D5—64no—
361C23×D5—122no—
362C23×D5C22×D311yescharacteristic
363C2×C5×D4—34no—
364C2×C5×D4—34no—
365C2×C5×D4—34no—
366C2×C5×D4—64no—
367C2×C5×D4—64no—
368C2×C5×D4—122no—
369C22×C4×C5—31no—
370C22×C4×C5C22×D311yescharacteristic
371C22×C4×C5C22×D311yescharacteristic
372C2×C22⋊D5—24no—
373C2×C22⋊D5—38no—
374C2×C22⋊D5—34no—
375C2×C22⋊D5—34no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—64no—
380C2×C22⋊D5—64no—
381C2×C22⋊D5—632no—
382C2×C22⋊D5—64no—
383C2×C22⋊D5—122no—
384C2×C22⋊D5C22×D314yes—
385C22×Dic5—31no—
386C22×Dic5—31no—
387C22×Dic5—31no—
388C22×Dic5—34no—
389C22×Dic5—34no—
390C22×Dic5—34no—
391C22×Dic5—34no—
392C22×Dic5—64no—
393C22×Dic5—64no—
394C22×Dic5—64no—
395C22×Dic5—122no—
396C22×Dic5C22×D311yescharacteristic
397C22×Dic5C22×D311yescharacteristic
398C22×Dic5C22×D311yescharacteristic
399#711—632no—
400C2×C4×D5—24no—
401C2×C4×D5—34no—
402C2×C4×D5—122no—
403C2×C4×D5C22×D314yescomplemented
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C22⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4C22×D314yescomplemented
409C22⋊Dic5—34no—
410C22⋊Dic5—34no—
411C22⋊Dic5—34no—
412C22⋊Dic5—34no—
413C22⋊Dic5C22×D314yescomplemented
414#685—34no—
415#685—34no—
416#685—34no—
417#685C22×D314yescomplemented
418C4⋊Dic5—34no—
419C4⋊Dic5C22×D314yescomplemented
420#683—34no—
421#683C22×D314yescomplemented
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
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—31no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
438C22×C22⋊C4—151no—
439C22×C3×C5—22no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—44no—
443C22×C3×C5C22×D412yes—
444C22×C3×C5C2×#4112yes—
445C22×C3×C5H(5,𝔽2)12yes—
446C22×C3×C5C2511yescharacteristic
447C2×D15—22no—
448C2×D15—22no—
449C2×D15—22no—
450C2×D15—44no—
451C2×C5×D3—28no—
452C2×C5×D3—28no—
453C2×C5×D3—22no—
454C2×C5×D3—22no—
455C2×C5×D3—22no—
456C2×C5×D3—22no—
457C2×C5×D3—22no—
458C2×C5×D3—22no—
459C2×C5×D3—22no—
460C2×C5×D3—416no—
461C2×C5×D3—44no—
462C2×C5×D3C22×D414yes—
463C2×C5×D3C2×#4114yescomplemented
464C2×C3×D5—28no—
465C2×C3×D5—22no—
466C2×C3×D5—22no—
467C2×C3×D5C22×D414yes—
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471Dic15—22no—
472Dic15—22no—
473Dic15C22×D414yes—
474C3×Dic5—22no—
475C3×Dic5—22no—
476C3×Dic5—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3C22×D511yescharacteristic
480C23×D3—24no—
481C23×D3—24no—
482C23×D3—42no—
483C23×D3—51no—
484C23×D3—54no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—202no—
488C23×D3C22×D511yescharacteristic
489C23×D3C22×D514yes—
490C23×D3C22×D511yescharacteristic
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—54no—
493C2×C3×D4—104no—
494C22×C3×C4—51no—
495C22×C3×C4—51no—
496C22×C3×C4—51no—
497C22×C3×C4—54no—
498C22×C3×C4—104no—
499C22×C3×C4C22×D511yescharacteristic
500C22×C3×C4C22×D511yescharacteristic
501C2×#67—42no—
502C2×#67—58no—
503C2×#67—54no—
504C2×#67—54no—
505C2×#67—54no—
506C2×#67—104no—
507C2×#67—104no—
508C2×#67C22×D514yescomplemented
509C22×Dic3—51no—
510C22×Dic3—51no—
511C22×Dic3—51no—
512C22×Dic3—54no—
513C22×Dic3—202no—
514C22×Dic3C22×D511yescharacteristic
515D3×D4—1032no—
516#235—1032no—
517C2×D12—24no—
518C2×D12—24no—
519C2×D12—54no—
520C2×D12—54no—
521C2×D12—104no—
522C2×D12—202no—
523C2×D12C22×D514yes—
524C2×D12C22×D514yescomplemented
525C2×C4×D3—54no—
526C2×C4×D3—54no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—104no—
530C2×C4×D3—104no—
531C2×C4×D3—104no—
532C2×C4×D3—202no—
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4—54no—
536C3×C4⋊C4—54no—
537C3×C22⋊C4—54no—
538C3×C22⋊C4—54no—
539C3×C22⋊C4C22×D514yescomplemented
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)⋊C4C22×D514yes—
548(C2×D3)⋊C4C22×D514yescomplemented
549Dic3⋊C4—54no—
550Dic3⋊C4—54no—
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—34no—
556C23×C5—34no—
557C23×C5—32no—
558C23×C5—32no—
559C23×C5—32no—
560C23×C5—68no—
561C23×C5—68no—
562C23×C5—62no—
563C23×C5—62no—
564C23×C5—62no—
565C23×C5—62no—
566C23×C5—62no—
567C23×C5—62no—
568C23×C5—62no—
569C23×C5—124no—
570C23×C5—1216no—
571C23×C5C23×D312yes—
572C23×C5C23×D311yescharacteristic
573C22×D5—22no—
574C22×D5—22no—
575C22×D5—32no—
576C22×D5—68no—
577C22×D5—62no—
578C22×D5—62no—
579C22×D5—62no—
580C22×D5—68no—
581C22×D5—124no—
582C22×D5—1216no—
583C22×D5D3×D414yes—
584C22×D5C23×D312yes—
585C5×D4—68no—
586C5×D4—68no—
587C5×D4—124no—
588C2×C4×C5—22no—
589C2×C4×C5—22no—
590C2×C4×C5—32no—
591C2×C4×C5—62no—
592C2×C4×C5C23×D312yes—
593C2×C4×C5C23×D312yes—
594C22⋊D5—28no—
595C22⋊D5—316no—
596C22⋊D5—68no—
597C22⋊D5—68no—
598C22⋊D5—68no—
599C22⋊D5—124no—
600C2×Dic5—22no—
601C2×Dic5—22no—
602C2×Dic5—22no—
603C2×Dic5—34no—
604C2×Dic5—32no—
605C2×Dic5—32no—
606C2×Dic5—32no—
607C2×Dic5—68no—
608C2×Dic5—68no—
609C2×Dic5—68no—
610C2×Dic5—62no—
611C2×Dic5—62no—
612C2×Dic5—124no—
613C2×Dic5C23×D312yes—
614C2×Dic5C23×D312yes—
615C2×Dic5C23×D312yes—
616C4×D5—28no—
617C4×D5—124no—
618Dic10—68no—
619C25—31no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—31no—
626C22×D4—31no—
627C22×D4—51no—
628C22×D4—151no—
629C22×D4—151no—
630C22×D4—158no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4—308no—
635C23×C4—51no—
636C23×C4—151no—
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—38no—
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—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—51no—
659C2×C22⋊C4—51no—
660C2×C22⋊C4—158no—
661C2×C22⋊C4—158no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—151no—
668C2×C22⋊C4—151no—
669C2×C22⋊C4D3×D511yescharacteristic, complemented
670C2×C42—151no—
671C2×C3×C5—42no—
672C2×C3×C5#54614yescomplemented
673C2×C3×C5C23×D411yescharacteristic
674C2×C3×C5C22×#4111yescharacteristic
675C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
676D15—42no—
677C3×D5—24no—
678C5×D3—24no—
679C5×D3—24no—
680C5×D3—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—54no—
685C23×C3—52no—
686C23×C3—102no—
687C23×C3—102no—
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—44no—
700C22×D3—416no—
701C22×D3—52no—
702C22×D3—108no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—108no—
707C22×D3—204no—
708C22×D3—2016no—
709C22×D3D4×D514yes—
710C22×D3#71114yescomplemented
711C22×D3C23×D512yes—
712C22×D3C23×D512yes—
713C22×D3C23×D512yes—
714C3×D4—108no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—52no—
718C2×C3×C4—52no—
719C2×C3×C4—52no—
720C2×C3×C4—108no—
721C2×C3×C4—102no—
722C2×C3×C4—102no—
723C2×C3×C4—102no—
724C2×C3×C4C23×D512yes—
725C2×C3×C4C23×D512yes—
726#67—44no—
727#67—516no—
728#67—108no—
729#67—108no—
730C2×Dic3—22no—
731C2×Dic3—54no—
732C2×Dic3—52no—
733C2×Dic3—52no—
734C2×Dic3—52no—
735C2×Dic3—102no—
736C2×Dic3—102no—
737C2×Dic3—204no—
738C2×Dic3C23×D512yes—
739D12—28no—
740D12—28no—
741D12—108no—
742D12—204no—
743C4×D3—108no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—34no—
752C22×C5—34no—
753C22×C5—44no—
754C22×C5—68no—
755C22×C5—68no—
756C22×C5—62no—
757C22×C5—62no—
758C22×C5—62no—
759C22×C5—62no—
760C22×C5—62no—
761C22×C5—62no—
762C22×C5—62no—
763C22×C5—1216no—
764C22×C5—124no—
765C22×C5C2×D3×D412yes—
766C22×C5D3×#4112yes—
767C22×C5#100912yes—
768C22×C5C24×D311yescharacteristic
769C2×D5—28no—
770C2×D5—22no—
771C2×D5—22no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—62no—
775C2×D5—1216no—
776C2×D5—124no—
777C2×D5C2×D3×D414yes—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—62no—
781Dic5—22no—
782Dic5—22no—
783Dic5—22no—
784Dic5—34no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—31no—
789C24—31no—
790C24—34no—
791C24—51no—
792C24—64no—
793C24—64no—
794C24—122no—
795C24—154no—
796C24—151no—
797C24—304no—
798C24—304no—
799C24—602no—
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—34no—
805C2×D4—34no—
806C2×D4—34no—
807C2×D4—54no—
808C2×D4—64no—
809C2×D4—64no—
810C2×D4—104no—
811C2×D4—122no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—158no—
816C2×D4—154no—
817C2×D4—154no—
818C2×D4—304no—
819C2×D4—304no—
820C2×D4—3032no—
821C2×D4—304no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—51no—
825C22×C4—51no—
826C22×C4—51no—
827C22×C4—54no—
828C22×C4—104no—
829C22×C4—154no—
830C22×C4—154no—
831C22×C4—154no—
832C22×C4—154no—
833C22×C4—154no—
834C22×C4—151no—
835C22×C4—151no—
836C22×C4—151no—
837C22×C4—304no—
838C22×C4—304no—
839C22×C4—304no—
840C22×C4—602no—
841C22×C4—602no—
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—54no—
845C4⋊C4—54no—
846C4⋊C4—154no—
847C4⋊C4—154no—
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—54no—
851C22⋊C4—54no—
852C22⋊C4—154no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4C2×D3×D514yescomplemented
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—44no—
866C22×C3—54no—
867C22×C3—108no—
868C22×C3—102no—
869C22×C3—102no—
870C22×C3C2×D4×D512yes—
871C22×C3C2×#71112yes—
872C22×C3#414412yes—
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—44no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—2016no—
889C2×D3—204no—
890C2×D3C2×D4×D514yes—
891C2×D3C2×#71114yescomplemented
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—102no—
895C3×C4—102no—
896C3×C4—102no—
897Dic3—22no—
898Dic3—54no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—42no—
902C2×C5—64no—
903C2×C5—64no—
904C2×C5—122no—
905C2×C5#565414yescomplemented
906C2×C5C22×D3×D411yescharacteristic
907C2×C5C2×D3×#4111yescharacteristic
908C2×C5C2×#100911yescharacteristic
909D5—24no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—34no—
915C23—34no—
916C23—32no—
917C23—32no—
918C23—32no—
919C23—54no—
920C23—52no—
921C23—68no—
922C23—68no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—102no—
931C23—102no—
932C23—124no—
933C23—1216no—
934C23—152no—
935C23—308no—
936C23—308no—
937C23—302no—
938C23—302no—
939C23—302no—
940C23—604no—
941C23—6016no—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—68no—
946D4—68no—
947D4—108no—
948D4—124no—
949D4—1516no—
950D4—308no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—32no—
957C2×C4—52no—
958C2×C4—52no—
959C2×C4—52no—
960C2×C4—62no—
961C2×C4—108no—
962C2×C4—102no—
963C2×C4—102no—
964C2×C4—102no—
965C2×C4—154no—
966C2×C4—152no—
967C2×C4—152no—
968C2×C4—152no—
969C2×C4—308no—
970C2×C4—308no—
971C2×C4—308no—
972C2×C4—302no—
973C2×C4—302no—
974C2×C4—604no—
975C2×C4—604no—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—104no—
980C2×C3#6592514yescomplemented
981C2×C3C22×D4×D511yescharacteristic
982C2×C3C22×#71111yescharacteristic
983C2×C3C2×#414411yescharacteristic
984D3—24no—
985D3—24no—
986D3—42no—
987D3—202no—
988C5C2×#565411yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—34no—
993C22—34no—
994C22—44no—
995C22—54no—
996C22—68no—
997C22—68no—
998C22—62no—
999C22—62no—
1000C22—62no—
1001C22—62no—
1002C22—62no—
1003C22—62no—
1004C22—62no—
1005C22—108no—
1006C22—102no—
1007C22—102no—
1008C22—1216no—
1009C22—124no—
1010C22—302no—
1011C22—302no—
1012C22—302no—
1013C22—6016no—
1014C22—604no—
1015C22#9201812yes—
1016C22D3×D4×D512yes—
1017C22D3×#71112yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—62no—
1022C4—102no—
1023C4—102no—
1024C4—102no—
1025C4—154no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6592511yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—64no—
1031C2—64no—
1032C2—104no—
1033C2—122no—
1034C2—602no—
1035C2#1175323114yesdirect product factor
1036C2C2×#9201811yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×D3×#71111yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×C22⋊D5C2semidirect
2. C22×#6772C2semidirect
3. C2×#91774C2semidirect
4. C2×C5×#882C2semidirect
5. C2×C3×#4029C2semidirect
6. C2×#91558C2semidirect
7. C2×D3×C22⋊Dic5C2semidirect
8. C2×#91549C2semidirect
9. C2×#91475C2semidirect
10. C2×D5×(C2×D3)⋊C4C2semidirect
11. C2×#91442C2semidirect
12. C2×#91435C2semidirect
13. C2×#91432C2semidirect
14. C2×#91427C2semidirect
15. C2×#91416C2semidirect
16. #11753231C2direct (N × H)
21. C22×Dic30C22semidirect
22. C22×C5×#67C22semidirect
24. C22×C5×D12C22semidirect
26. C22×C3×C4×D5C22semidirect
28. C2×D3×C22⋊D5C22semidirect
30. C22×#1203C22semidirect
32. C22×#1201C22semidirect
34. C22×D3×Dic5C22semidirect
35. C22×D3×Dic5C22semidirect
36. C22×D3×Dic5C22semidirect
37. C22×D5×Dic3C22semidirect
39. C2×#6772C22semidirect
40. C2×C3×C5×C22⋊C4C22semidirect
41. C2×#6719C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. C2×C4×Dic15C22semidirect
45. #91774C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C5×#882C22semidirect
49. C2×C3×C22⋊Dic5C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×C4⋊Dic5C22semidirect
52. C2×C3×#683C22semidirect
53. C3×#4029C22semidirect
54. #91558C22semidirect
55. D3×C22⋊Dic5C22semidirect
56. #91549C22semidirect
57. C2×Dic3⋊Dic5C22semidirect
58. C2×#6669C22semidirect
59. C2×#6667C22semidirect
62. C2×(C2×D3)⋊Dic5C22semidirect
63. #91475C22semidirect
64. D5×(C2×D3)⋊C4C22semidirect
65. #91442C22semidirect
66. #91435C22semidirect
67. #91432C22semidirect
68. #91427C22semidirect
69. #91416C22semidirect
83. C2×#4029D3semidirect
109. C2×Dic30C23semidirect
111. C2×C5×#67C23semidirect
116. C2×C5×D12C23semidirect
123. C2×C3×C4×D5C23semidirect
128. C2×#1203C23semidirect
130. C2×#1201D4semidirect
132. C2×#1201C23semidirect
138. C2×D3×Dic5C23semidirect
139. C2×D3×Dic5C23semidirect
140. C2×D3×Dic5C23semidirect
142. C2×D5×Dic3C23semidirect
144. C3×C5×C22⋊C4C23semidirect
145. #6719C23semidirect
146. #6714C23semidirect
147. #6714C23semidirect
148. C4×Dic15C23semidirect
150. C5×(C2×D3)⋊C4C23semidirect
151. C3×C22⋊Dic5C23semidirect
152. C3×#685C23semidirect
153. C3×C4⋊Dic5C23semidirect
154. C3×#683C23semidirect
155. Dic3⋊Dic5C23semidirect
156. #6669C23semidirect
157. #6667C23semidirect
160. (C2×D3)⋊Dic5C23semidirect
174. C2×#882D5semidirect
197. C22×C4×D5C2×D3semidirect
202. C2×C5×C22⋊C4C2×D3semidirect
208. C2×C22⋊Dic5C2×D3semidirect
217. C2×#685C2×D3semidirect
219. C2×C4⋊Dic5C2×D3semidirect
221. C2×#683C2×D3semidirect
225. #4029C2×D3semidirect
251. C22×C5×D3#41semidirect
291. #1201C2×D4semidirect
304. C22×#67C2×D5semidirect
313. C22×D12C2×D5semidirect
324. C2×C3×C22⋊C4C2×D5semidirect
335. C2×(C2×D3)⋊C4C2×D5semidirect
346. #882C2×D5semidirect
403. C2×C4×D5C22×D3semidirect
408. C5×C22⋊C4C22×D3semidirect
413. C22⋊Dic5C22×D3semidirect
417. #685C22×D3semidirect
419. C4⋊Dic5C22×D3semidirect
421. #683C22×D3semidirect
463. C2×C5×D3C2×#41semidirect
508. C2×#67C22×D5semidirect
524. C2×D12C22×D5semidirect
539. C3×C22⋊C4C22×D5semidirect
548. (C2×D3)⋊C4C22×D5semidirect
669. C2×C22⋊C4D3×D5semidirect
672. C2×C3×C5#546semidirect
710. C22×D3#711semidirect
859. C22⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
891. C2×D3C2×#711semidirect
905. C2×C5#5654semidirect
980. C2×C3#65925semidirect
988. C5C2×#5654semidirect
1028. C3C2×#65925semidirect
1035. C2#11753231direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊D52
C22×#67722
C2×#917742
C2×C5×#8822
C2×C3×#40292
C2×#915582
C2×D3×C22⋊Dic52
C2×#915492
C2×#914752
C2×D5×(C2×D3)⋊C42
C2×#914422
C2×#914352
C2×#914322
C2×#914272
C2×#914162
#117532312
C2×#659253
C2×#56545