Finite Group Databasebeta

← C2×#11753855 #14482654

Subgroups — C2×#11753855 #14482654

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×#6777C211yesmaximal, characteristic, complemented
2C22×#6772C211yesmaximal, characteristic, complemented
3C2×#91785C211yesmaximal, characteristic, complemented
4C2×C5×#895C211yesmaximal, characteristic, complemented
5C2×C3×#4040C211yesmaximal, characteristic, complemented
6C2×#91475C211yesmaximal, characteristic, complemented
7C2×#91475C211yesmaximal, characteristic, complemented
8C2×D3×#685C211yesmaximal, characteristic, complemented
9C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×#91462C211yesmaximal, characteristic, complemented
11C2×#91453C211yesmaximal, characteristic, complemented
12C2×#91441C211yesmaximal, characteristic, complemented
13C2×#91423C211yesmaximal, characteristic, complemented
14C2×#91408C211yesmaximal, characteristic, complemented
15C2×#91406C211yesmaximal, characteristic, complemented
16#11753855C2116yesmaximal, direct product factor
17C2×#65944—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×Dic30C2211yescharacteristic, complemented
22C22×C5×D12C2211yescharacteristic
23C22×C5×D12C2211yescharacteristic, complemented
24C22×C5×D12C2211yescharacteristic, complemented
25C22×C4×C5×D3C2211yescharacteristic, complemented
26C22×C3×D20C2211yescharacteristic
27C22×C3×C4×D5C2211yescharacteristic, complemented
28C22×#1203C2211yescharacteristic
29C22×#1201C2211yescharacteristic
30C22×#1201C2211yescharacteristic
31C22×#1201C2211yescharacteristic, complemented
32C22×#1201C2211yescharacteristic, complemented
33C22×D3×Dic5C2211yescharacteristic, complemented
34C22×D3×Dic5C2211yescharacteristic, complemented
35C22×D5×Dic3C2211yescharacteristic, complemented
36C2×#6777—28no—
37C2×#6777C2218yescomplemented
38C2×#6772—28no—
39C2×#6772C2218yescomplemented
40C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic
42C2×#6714C2211yescharacteristic
43C2×#6712C2211yescharacteristic, complemented
44C2×#6712C2211yescharacteristic, complemented
45#91785C2218yescomplemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C5×#895C2218yescomplemented
49C2×C3×#685C2211yescharacteristic, complemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×#685C2211yescharacteristic, complemented
52C2×C3×#683C2211yescharacteristic, complemented
53C3×#4040C2218yescomplemented
54C2×#6667C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
58C2×#6665C2211yescharacteristic, complemented
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91475C2218yescomplemented
61#91475C2218yescomplemented
62D3×#685C2218yescomplemented
63D5×(C2×D3)⋊C4C2218yescomplemented
64#91462C2218yescomplemented
65#91453C2218yescomplemented
66#91441C2218yescomplemented
67#91423C2218yescomplemented
68#91408C2218yescomplemented
69#91406C2218yescomplemented
70C2×#5654—51nomaximal, Hall
71C22×#711—31no—
72C22×D4×D5—31no—
73C2×C5×#121—31no—
74C2×#4085—31no—
75C2×#4083—31no—
76C2×#4083—31no—
77C2×#4081—31no—
78C2×C4×C22⋊D5—31no—
79C22×#685—31no—
80#65944—316no—
81C2×#4042—31no—
82C2×#4040D311yescharacteristic, complemented
83C2×#4031—31no—
84C2×#4030—31no—
85C2×#4027—31no—
86C2×D5×C22⋊C4—31no—
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C3×D5C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C22×D3×D5—24no—
94C22×D3×D5—24no—
95C22×D3×D5—24no—
96C22×D3×D5—24no—
97C22×D3×D5—42no—
98C22×D3×D5—42no—
99C22×D3×D5C2314yes—
100C22×D3×D5C2314yes—
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2311yescharacteristic
103C22×C3×C4×C5C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C2×C4×D15—24no—
108C2×C4×D15C2314yes—
109C2×Dic30—24no—
110C2×Dic30C2314yescomplemented
111C22×C5×Dic3C2311yescharacteristic
112C2×C5×D12—24no—
113C2×C5×D12—24no—
114C2×C5×D12—42no—
115C2×C5×D12C2314yes—
116C2×C5×D12C2314yescomplemented
117C2×C5×D12C2314yescomplemented
118C2×C4×C5×D3—42no—
119C2×C4×C5×D3C2314yescomplemented
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C2×C3×D20—24no—
123C2×C3×D20C2314yes—
124C2×C3×C4×D5—24no—
125C2×C3×C4×D5C2314yescomplemented
126C2×#1203—24no—
127C2×#1203C2314yes—
128C2×#1201—24no—
129C2×#1201—24no—
130C2×#1201—42no—
131C2×#1201D418yescomplemented
132C2×#1201C2314yes—
133C2×#1201C2314yes—
134C2×#1201C2314yescomplemented
135C2×#1201C2314yescomplemented
136C2×D3×Dic5—24no—
137C2×D3×Dic5—24no—
138C2×D3×Dic5C2314yescomplemented
139C2×D3×Dic5C2314yescomplemented
140C2×D5×Dic3—42no—
141C2×D5×Dic3C2314yescomplemented
142#6777—232no—
143#6772—232no—
144C3×C5×C4⋊C4C2314yescomplemented
145#6714C2314yes—
146#6714C2314yes—
147#6712C2314yescomplemented
148#6712C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yescomplemented
150C5×(C2×D3)⋊C4C2314yescomplemented
151C3×#685C2314yescomplemented
152C3×#685C2314yescomplemented
153C3×#685C2314yescomplemented
154C3×#683C2314yescomplemented
155#6667C2314yes—
156(C2×D3)⋊Dic5C2314yescomplemented
157(C2×D3)⋊Dic5C2314yescomplemented
158(C2×D3)⋊Dic5C2314yescomplemented
159#6665C2314yescomplemented
160Dic3×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×#895D511yescharacteristic, complemented
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—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4—31no—
182C23×C4×C5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C23×Dic5—31no—
189C23×Dic5—31no—
190C2×#711—38no—
191C2×#711—68no—
192C2×D4×D5—38no—
193C2×D4×D5—68no—
194C22×D20C2×D311yescharacteristic
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5C2×D311yescharacteristic, complemented
198C22×Dic10—31no—
199C5×#121—38no—
200C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4—31no—
203C2×C22⋊Dic5—31no—
204C2×C22⋊Dic5—31no—
205C2×C22⋊Dic5—31no—
206#4085—38no—
207#4083—38no—
208#4083—38no—
209#4081—38no—
210C4×C22⋊D5—38no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—38no—
216C2×#685C2×D311yescharacteristic, complemented
217C2×#685C2×D311yescharacteristic, complemented
218C2×#685C2×D311yescharacteristic, complemented
219C2×#683—31no—
220C2×#683—31no—
221C2×#683C2×D311yescharacteristic, complemented
222C2×C4×Dic5—31no—
223#4042—38no—
224#4040C2×D318yescomplemented
225#4031—38no—
226#4030—38no—
227#4027—38no—
228D5×C22⋊C4—38no—
229C2×#546—151noSylow
230C23×C3×C5C2411yescharacteristic
231C22×D15—22no—
232C22×D15—22no—
233C22×D15#4114yescomplemented
234C22×D15C2412yes—
235C22×C5×D3—22no—
236C22×C5×D3—22no—
237C22×C5×D3—22no—
238C22×C5×D3—22no—
239C22×C5×D3—22no—
240C22×C5×D3—22no—
241C22×C5×D3—22no—
242C22×C5×D3—22no—
243C22×C5×D3C2×D414yes—
244C22×C5×D3C2412yes—
245C22×C5×D3C2412yes—
246C22×C5×D3C2412yes—
247C22×C3×D5—22no—
248C22×C3×D5—22no—
249C22×C3×D5—22no—
250C22×C3×D5—22no—
251C22×C3×D5—22no—
252C22×C3×D5C2×D414yes—
253C22×C3×D5C2412yes—
254C22×C3×D5C2412yes—
255C2×D3×D5—28no—
256C2×D3×D5—28no—
257C2×D3×D5—28no—
258C2×D3×D5—28no—
259C2×D3×D5—44no—
260C2×D3×D5—44no—
261C2×D3×D5—416no—
262C2×D3×D5—416no—
263C2×C3×C4×C5—22no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5—22no—
266C2×C3×C4×C5C2412yes—
267C2×C3×C4×C5C2412yes—
268C2×C3×C4×C5C2412yes—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15C2×D414yes—
272C2×Dic15C2412yes—
273C2×Dic15C2412yes—
274C2×Dic15C2412yes—
275C4×D15—28no—
276Dic30—28no—
277C2×C5×Dic3—22no—
278C2×C5×Dic3C2412yes—
279C5×D12—28no—
280C5×D12—28no—
281C5×D12—44no—
282C4×C5×D3—44no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5C2412yes—
286C2×C3×Dic5C2412yes—
287C3×D20—28no—
288C3×C4×D5—28no—
289#1203—28no—
290#1201—28no—
291#1201—28no—
292#1201—44no—
293#1201C2×D4116yescomplemented
294D3×Dic5—28no—
295D3×Dic5—28no—
296D5×Dic3—44no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×D4—51no—
300C23×C3×C4—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67—51no—
304C22×#67—51no—
305C23×Dic3—51no—
306C2×D3×D4—58no—
307C2×D3×D4—108no—
308C2×#235—58no—
309C2×#235—108no—
310C22×D12—51no—
311C22×D12C2×D511yescharacteristic
312C22×D12C2×D511yescharacteristic, complemented
313C22×D12C2×D511yescharacteristic, complemented
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3C2×D511yescharacteristic, complemented
318C22×Dic6—51no—
319C3×#123—58no—
320C2×C3×C4⋊C4—51no—
321C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
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—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, complemented
335C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
336C2×Dic3⋊C4—51no—
337C2×Dic3⋊C4—51no—
338C2×C4×Dic3—51no—
339#896—58no—
340#895C2×D518yescomplemented
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—
352C23×D5—31no—
353C23×D5—34no—
354C23×D5—34no—
355C23×D5—64no—
356C23×D5—64no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—122no—
360C23×D5—122no—
361C23×D5C22×D311yescharacteristic
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×C5—34no—
371C22×C4×C5—122no—
372C22×C4×C5C22×D311yescharacteristic
373C22×C4×C5C22×D311yescharacteristic
374C22×C4×C5C22×D311yescharacteristic
375C2×C22⋊D5—38no—
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—
385C22×Dic5—31no—
386C22×Dic5—31no—
387C22×Dic5—31no—
388C22×Dic5—34no—
389C22×Dic5—34no—
390C22×Dic5—64no—
391C22×Dic5—64no—
392C22×Dic5C22×D311yescharacteristic
393C22×Dic5C22×D311yescharacteristic
394#711—632no—
395D4×D5—632no—
396C2×D20—24no—
397C2×D20C22×D314yes—
398C2×C4×D5—24no—
399C2×C4×D5—34no—
400C2×C4×D5—34no—
401C2×C4×D5—64no—
402C2×C4×D5—122no—
403C2×C4×D5C22×D314yescomplemented
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4C22×D314yescomplemented
407C5×C22⋊C4—34no—
408C5×C22⋊C4—34no—
409C22⋊Dic5—34no—
410C22⋊Dic5—34no—
411C22⋊Dic5—34no—
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685C22×D314yescomplemented
417#685C22×D314yescomplemented
418#685C22×D314yescomplemented
419#683—34no—
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—31no—
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×C5C22×D412yes—
440C22×C3×C5C2×#4112yes—
441C22×C3×C5H(5,𝔽2)12yes—
442C22×C3×C5C2511yescharacteristic
443C2×D15—28no—
444C2×D15—22no—
445C2×D15—22no—
446C2×D15C2×#4114yescomplemented
447C2×C5×D3—28no—
448C2×C5×D3—22no—
449C2×C5×D3—22no—
450C2×C5×D3—22no—
451C2×C5×D3—22no—
452C2×C5×D3—22no—
453C2×C5×D3—22no—
454C2×C5×D3—22no—
455C2×C5×D3—22no—
456C2×C5×D3—44no—
457C2×C5×D3—44no—
458C2×C5×D3C22×D414yes—
459C2×C3×D5—28no—
460C2×C3×D5—22no—
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—22no—
465C2×C3×D5—44no—
466C2×C3×D5C22×D414yes—
467D3×D5—416no—
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471C3×C4×C5—22no—
472Dic15—22no—
473Dic15—22no—
474Dic15C22×D414yes—
475C3×Dic5—22no—
476C3×Dic5—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3—51no—
480C23×D3—51no—
481C23×D3—54no—
482C23×D3—54no—
483C23×D3—104no—
484C23×D3—104no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—202no—
488C23×D3—202no—
489C23×D3C22×D511yescharacteristic
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—54no—
497C22×C3×C4—104no—
498C22×C3×C4C22×D511yescharacteristic
499C22×C3×C4C22×D511yescharacteristic
500C22×C3×C4C22×D511yescharacteristic
501C2×#67—58no—
502C2×#67—54no—
503C2×#67—54no—
504C2×#67—54no—
505C2×#67—54no—
506C2×#67—104no—
507C2×#67—104no—
508C2×#67—202no—
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—42no—
520C2×D12—54no—
521C2×D12—104no—
522C2×D12C22×D514yes—
523C2×D12C22×D514yescomplemented
524C2×D12C22×D514yescomplemented
525C2×C4×D3—42no—
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×D3C22×D514yescomplemented
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4—54no—
536C3×C4⋊C4C22×D514yescomplemented
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)⋊C4C22×D514yescomplemented
548(C2×D3)⋊C4C22×D514yescomplemented
549Dic3⋊C4—54no—
550Dic3⋊C4—54no—
551C4×Dic3—54no—
552C23×C5—34no—
553C23×C5—32no—
554C23×C5—32no—
555C23×C5—32no—
556C23×C5—62no—
557C23×C5—62no—
558C23×C5—62no—
559C23×C5—62no—
560C23×C5—62no—
561C23×C5—62no—
562C23×C5—62no—
563C23×C5—62no—
564C23×C5C23×D311yescharacteristic
565C22×D5—22no—
566C22×D5—22no—
567C22×D5—22no—
568C22×D5—22no—
569C22×D5—22no—
570C22×D5—34no—
571C22×D5—32no—
572C22×D5—68no—
573C22×D5—68no—
574C22×D5—68no—
575C22×D5—62no—
576C22×D5—62no—
577C22×D5—68no—
578C22×D5—124no—
579C22×D5—124no—
580C22×D5—1216no—
581C22×D5—1216no—
582C22×D5D3×D414yes—
583C22×D5C23×D312yes—
584C22×D5C23×D312yes—
585C5×D4—68no—
586C5×D4—68no—
587C5×D4—124no—
588C2×C4×C5—22no—
589C2×C4×C5—22no—
590C2×C4×C5—22no—
591C2×C4×C5—32no—
592C2×C4×C5—62no—
593C2×C4×C5—124no—
594C2×C4×C5C23×D312yes—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C22⋊D5—316no—
598C22⋊D5—68no—
599C22⋊D5—68no—
600C22⋊D5—68no—
601C22⋊D5—124no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—34no—
605C2×Dic5—32no—
606C2×Dic5—32no—
607C2×Dic5—32no—
608C2×Dic5—68no—
609C2×Dic5—68no—
610C2×Dic5—62no—
611C2×Dic5—62no—
612C2×Dic5C23×D312yes—
613C2×Dic5C23×D312yes—
614D20—28no—
615C4×D5—28no—
616C4×D5—68no—
617C4×D5—124no—
618Dic10—68no—
619C25—151no—
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—158no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4—308no—
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—38no—
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—151no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4D3×D511yescharacteristic, complemented
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—51no—
659C2×C22⋊C4—51no—
660C2×C22⋊C4—51no—
661C2×C22⋊C4—158no—
662C2×C22⋊C4—158no—
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⋊C4—151no—
670C2×C42—151no—
671C2×C3×C5#54614yescomplemented
672C2×C3×C5C23×D411yescharacteristic
673C2×C3×C5C22×#4111yescharacteristic
674C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
675D15—24no—
676C3×D5—24no—
677C3×D5—42no—
678C5×D3—24no—
679C5×D3—42no—
680C5×D3—42no—
681C23×C3—54no—
682C23×C3—52no—
683C23×C3—52no—
684C23×C3—102no—
685C23×C3—102no—
686C23×C3—102no—
687C23×C3—102no—
688C23×C3—102no—
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—22no—
698C22×D3—54no—
699C22×D3—52no—
700C22×D3—108no—
701C22×D3—108no—
702C22×D3—108no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—108no—
706C22×D3—204no—
707C22×D3—204no—
708C22×D3—2016no—
709C22×D3—2016no—
710C22×D3D4×D514yes—
711C22×D3C23×D512yes—
712C22×D3C23×D512yes—
713C22×D3C23×D512yes—
714C3×D4—108no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—52no—
719C2×C3×C4—52no—
720C2×C3×C4—108no—
721C2×C3×C4—102no—
722C2×C3×C4—102no—
723C2×C3×C4C23×D512yes—
724C2×C3×C4C23×D512yes—
725C2×C3×C4C23×D512yes—
726#67—516no—
727#67—108no—
728#67—108no—
729#67—204no—
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—44no—
742D12—108no—
743C4×D3—44no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—108no—
747Dic6—108no—
748C22×C5—34no—
749C22×C5—68no—
750C22×C5—62no—
751C22×C5—62no—
752C22×C5—62no—
753C22×C5—62no—
754C22×C5—62no—
755C22×C5—62no—
756C22×C5—62no—
757C22×C5—62no—
758C22×C5—124no—
759C22×C5—124no—
760C22×C5C2×D3×D412yes—
761C22×C5D3×#4112yes—
762C22×C5#100912yes—
763C22×C5C24×D311yescharacteristic
764C2×D5—28no—
765C2×D5—22no—
766C2×D5—22no—
767C2×D5—22no—
768C2×D5—22no—
769C2×D5—22no—
770C2×D5—34no—
771C2×D5—44no—
772C2×D5—68no—
773C2×D5—62no—
774C2×D5—62no—
775C2×D5—1216no—
776C2×D5—1216no—
777C2×D5C2×D3×D414yes—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—22no—
781C4×C5—62no—
782Dic5—22no—
783Dic5—22no—
784Dic5—34no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—31no—
789C24—31no—
790C24—51no—
791C24—51no—
792C24—154no—
793C24—154no—
794C24—151no—
795C24—304no—
796C24—304no—
797C24—304no—
798C24—304no—
799C24—602no—
800C24—602no—
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—158no—
815C2×D4—154no—
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—34no—
825C22×C4—51no—
826C22×C4—51no—
827C22×C4—54no—
828C22×C4—104no—
829C22×C4—122no—
830C22×C4—154no—
831C22×C4—154no—
832C22×C4—154no—
833C22×C4—151no—
834C22×C4—151no—
835C22×C4—151no—
836C22×C4—154no—
837C22×C4—304no—
838C22×C4—304no—
839C22×C4—304no—
840C22×C4—602no—
841C22×C4C2×D3×D511yescharacteristic
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—54no—
845C4⋊C4—154no—
846C4⋊C4—154no—
847C4⋊C4C2×D3×D514yescomplemented
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—54no—
851C22⋊C4—54no—
852C22⋊C4—54no—
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—54no—
863C22×C3—108no—
864C22×C3—102no—
865C22×C3—102no—
866C22×C3—102no—
867C22×C3—102no—
868C22×C3—102no—
869C22×C3—204no—
870C22×C3C2×D4×D512yes—
871C22×C3#414412yes—
872C22×C3D5×#4112yes—
873C22×C3C24×D511yescharacteristic
874C2×D3—28no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—44no—
884C2×D3—44no—
885C2×D3—54no—
886C2×D3—108no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—2016no—
890C2×D3—2016no—
891C2×D3C2×D4×D514yes—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—102no—
896C3×C4—102no—
897Dic3—22no—
898Dic3—54no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—64no—
902C2×C5—122no—
903C2×C5—122no—
904C2×C5#565414yescomplemented
905C2×C5C22×D3×D411yescharacteristic
906C2×C5C2×D3×#4111yescharacteristic
907C2×C5C2×#100911yescharacteristic
908D5—24no—
909D5—42no—
910D5—64no—
911C23—34no—
912C23—32no—
913C23—32no—
914C23—32no—
915C23—54no—
916C23—52no—
917C23—52no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—102no—
927C23—102no—
928C23—102no—
929C23—102no—
930C23—102no—
931C23—154no—
932C23—152no—
933C23—308no—
934C23—308no—
935C23—308no—
936C23—308no—
937C23—302no—
938C23—302no—
939C23—604no—
940C23—604no—
941C23—6016no—
942C23—6016no—
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—22no—
957C2×C4—32no—
958C2×C4—52no—
959C2×C4—52no—
960C2×C4—62no—
961C2×C4—108no—
962C2×C4—102no—
963C2×C4—102no—
964C2×C4—124no—
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×C4C22×D3×D512yes—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—104no—
979C2×C3—202no—
980C2×C3#6594414yescomplemented
981C2×C3C22×D4×D511yescharacteristic
982C2×C3C2×#414411yescharacteristic
983C2×C3C2×D5×#4111yescharacteristic
984D3—24no—
985D3—42no—
986D3—42no—
987D3—104no—
988C5C2×#565411yescharacteristic, complemented, Sylow
989C22—34no—
990C22—54no—
991C22—68no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—62no—
998C22—62no—
999C22—62no—
1000C22—108no—
1001C22—102no—
1002C22—102no—
1003C22—102no—
1004C22—102no—
1005C22—102no—
1006C22—124no—
1007C22—124no—
1008C22—154no—
1009C22—204no—
1010C22—308no—
1011C22—302no—
1012C22—302no—
1013C22—6016no—
1014C22—6016no—
1015C22#9201812yes—
1016C22D3×D4×D512yes—
1017C22#9203412yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—62no—
1023C4—102no—
1024C4—102no—
1025C4—154no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6594411yescharacteristic, complemented, Sylow
1029C2—64no—
1030C2—104no—
1031C2—122no—
1032C2—122no—
1033C2—202no—
1034C2—304no—
1035C2#1175385514yesdirect product factor
1036C2C2×#9201811yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#9203411yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6777C2semidirect
2. C22×#6772C2semidirect
3. C2×#91785C2semidirect
4. C2×C5×#895C2semidirect
5. C2×C3×#4040C2semidirect
6. C2×#91475C2semidirect
7. C2×#91475C2semidirect
8. C2×D3×#685C2semidirect
9. C2×D5×(C2×D3)⋊C4C2semidirect
10. C2×#91462C2semidirect
11. C2×#91453C2semidirect
12. C2×#91441C2semidirect
13. C2×#91423C2semidirect
14. C2×#91408C2semidirect
15. C2×#91406C2semidirect
16. #11753855C2direct (N × H)
21. C22×Dic30C22semidirect
23. C22×C5×D12C22semidirect
24. C22×C5×D12C22semidirect
25. C22×C4×C5×D3C22semidirect
27. C22×C3×C4×D5C22semidirect
31. C22×#1201C22semidirect
32. C22×#1201C22semidirect
33. C22×D3×Dic5C22semidirect
34. C22×D3×Dic5C22semidirect
35. C22×D5×Dic3C22semidirect
37. C2×#6777C22semidirect
39. C2×#6772C22semidirect
40. C2×C3×C5×C4⋊C4C22semidirect
43. C2×#6712C22semidirect
44. C2×#6712C22semidirect
45. #91785C22semidirect
46. C2×C5×(C2×D3)⋊C4C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C5×#895C22semidirect
49. C2×C3×#685C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×#685C22semidirect
52. C2×C3×#683C22semidirect
53. C3×#4040C22semidirect
55. C2×(C2×D3)⋊Dic5C22semidirect
56. C2×(C2×D3)⋊Dic5C22semidirect
57. C2×(C2×D3)⋊Dic5C22semidirect
58. C2×#6665C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91475C22semidirect
61. #91475C22semidirect
62. D3×#685C22semidirect
63. D5×(C2×D3)⋊C4C22semidirect
64. #91462C22semidirect
65. #91453C22semidirect
66. #91441C22semidirect
67. #91423C22semidirect
68. #91408C22semidirect
69. #91406C22semidirect
82. C2×#4040D3semidirect
110. C2×Dic30C23semidirect
116. C2×C5×D12C23semidirect
117. C2×C5×D12C23semidirect
119. C2×C4×C5×D3C23semidirect
125. C2×C3×C4×D5C23semidirect
131. C2×#1201D4semidirect
134. C2×#1201C23semidirect
135. C2×#1201C23semidirect
138. C2×D3×Dic5C23semidirect
139. C2×D3×Dic5C23semidirect
141. C2×D5×Dic3C23semidirect
144. C3×C5×C4⋊C4C23semidirect
147. #6712C23semidirect
148. #6712C23semidirect
149. C5×(C2×D3)⋊C4C23semidirect
150. C5×(C2×D3)⋊C4C23semidirect
151. C3×#685C23semidirect
152. C3×#685C23semidirect
153. C3×#685C23semidirect
154. C3×#683C23semidirect
156. (C2×D3)⋊Dic5C23semidirect
157. (C2×D3)⋊Dic5C23semidirect
158. (C2×D3)⋊Dic5C23semidirect
159. #6665C23semidirect
160. Dic3×Dic5C23semidirect
168. C2×#895D5semidirect
197. C22×C4×D5C2×D3semidirect
200. C2×C5×C4⋊C4C2×D3semidirect
216. C2×#685C2×D3semidirect
217. C2×#685C2×D3semidirect
218. C2×#685C2×D3semidirect
221. C2×#683C2×D3semidirect
224. #4040C2×D3semidirect
233. C22×D15#41semidirect
293. #1201C2×D4semidirect
312. C22×D12C2×D5semidirect
313. C22×D12C2×D5semidirect
317. C22×C4×D3C2×D5semidirect
321. C2×C3×C4⋊C4C2×D5semidirect
334. C2×(C2×D3)⋊C4C2×D5semidirect
335. C2×(C2×D3)⋊C4C2×D5semidirect
340. #895C2×D5semidirect
403. C2×C4×D5C22×D3semidirect
406. C5×C4⋊C4C22×D3semidirect
416. #685C22×D3semidirect
417. #685C22×D3semidirect
418. #685C22×D3semidirect
421. #683C22×D3semidirect
446. C2×D15C2×#41semidirect
523. C2×D12C22×D5semidirect
524. C2×D12C22×D5semidirect
532. C2×C4×D3C22×D5semidirect
536. C3×C4⋊C4C22×D5semidirect
547. (C2×D3)⋊C4C22×D5semidirect
548. (C2×D3)⋊C4C22×D5semidirect
655. C2×C4⋊C4D3×D5semidirect
671. C2×C3×C5#546semidirect
847. C4⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
904. C2×C5#5654semidirect
980. C2×C3#65944semidirect
988. C5C2×#5654semidirect
1028. C3C2×#65944semidirect
1035. C2#11753855direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67772
C22×#67722
C2×#917852
C2×C5×#8952
C2×C3×#40402
C2×#914752
C2×D3×#6852
C2×D5×(C2×D3)⋊C42
C2×#914622
C2×#914532
C2×#914412
C2×#914232
C2×#914082
C2×#914062
#117538552
C2×#659443
C2×#56545