Finite Group Databasebeta

← C2×#11753870 #14482651

Subgroups — C2×#11753870 #14482651

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×D5×D12C211yesmaximal, characteristic, complemented
2C22×#6769C211yesmaximal, characteristic, complemented
3C2×#91784C211yesmaximal, characteristic, complemented
4C2×C5×#894C211yesmaximal, characteristic, complemented
5C2×C3×#4042C211yesmaximal, characteristic, complemented
6C2×#91476C211yesmaximal, characteristic, complemented
7C2×#91476C211yesmaximal, characteristic, complemented
8C2×#91473C211yesmaximal, characteristic, complemented
9C2×D3×#685C211yesmaximal, characteristic, complemented
10C2×#91444C211yesmaximal, characteristic, complemented
11C2×#91433C211yesmaximal, characteristic, complemented
12C2×#91420C211yesmaximal, characteristic, complemented
13C2×#91416C211yesmaximal, characteristic, complemented
14C2×#91406C211yesmaximal, characteristic, complemented
15C2×#91326C211yesmaximal, characteristic, complemented
16#11753870C2116yesmaximal, direct product factor
17C2×#65988—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×D60C2211yescharacteristic, complemented
22C22×D60C2211yescharacteristic, complemented
23C22×C4×D15C2211yescharacteristic, complemented
24C22×C5×D12C2211yescharacteristic
25C22×C4×C5×D3C2211yescharacteristic, complemented
26C22×C3×C4×D5C2211yescharacteristic
27C22×C3×Dic10C2211yescharacteristic, complemented
28C22×#1203C2211yescharacteristic
29C22×#1203C2211yescharacteristic
30C22×#1203C2211yescharacteristic, complemented
31C22×#1203C2211yescharacteristic, complemented
32C22×#1202C2211yescharacteristic
33C22×#1200C2211yescharacteristic, complemented
34C22×#1200C2211yescharacteristic, complemented
35C22×D3×Dic5C2211yescharacteristic, complemented
36C2×D5×D12—28no—
37C2×D5×D12C2218yescomplemented
38C2×#6769—28no—
39C2×#6769C2218yescomplemented
40C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43#91784C2218yescomplemented
44C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
48C5×#894C2218yescomplemented
49C2×C3×#685C2211yescharacteristic
50C2×C3×#685C2211yescharacteristic
51C2×C3×#683C2211yescharacteristic, complemented
52C2×C3×#683C2211yescharacteristic, complemented
53C3×#4042C2218yescomplemented
54C2×#6667C2211yescharacteristic, complemented
55C2×#6667C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
58C2×#6665C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91476C2218yescomplemented
61#91476C2218yescomplemented
62#91473C2218yescomplemented
63D3×#685C2218yescomplemented
64#91444C2218yescomplemented
65#91433C2218yescomplemented
66#91420C2218yescomplemented
67#91416C2218yescomplemented
68#91406C2218yescomplemented
69#91326C2218yescomplemented
70C2×#5630—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×#709—31no—
73C2×C5×#123—31no—
74C2×#4085—31no—
75C22×#685—31no—
76#65988—316no—
77C2×#4042D311yescharacteristic, complemented
78C2×#4041—31no—
79C2×#4040—31no—
80C2×#4039—31no—
81C2×#4031—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C2×#4027—31no—
86C2×D5×C22⋊C4—31no—
87C23×D15C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C5×D3C2311yescharacteristic
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
105C2×D60—24no—
106C2×D60—24no—
107C2×D60—42no—
108C2×D60C2314yes—
109C2×D60C2314yescomplemented
110C2×D60C2314yescomplemented
111C2×C4×D15—42no—
112C2×C4×D15C2314yescomplemented
113C22×C5×Dic3C2311yescharacteristic
114C22×C5×Dic3C2311yescharacteristic
115C2×C5×D12—24no—
116C2×C5×D12C2314yes—
117C2×C4×C5×D3—24no—
118C2×C4×C5×D3C2314yescomplemented
119C22×C3×Dic5C2311yescharacteristic
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C2×C3×C4×D5—24no—
123C2×C3×C4×D5C2314yes—
124C2×C3×Dic10—24no—
125C2×C3×Dic10C2314yescomplemented
126C2×#1203—24no—
127C2×#1203—24no—
128C2×#1203—42no—
129C2×#1203D418yescomplemented
130C2×#1203C2314yes—
131C2×#1203C2314yes—
132C2×#1203C2314yescomplemented
133C2×#1203C2314yescomplemented
134C2×#1202—24no—
135C2×#1202C2314yes—
136C2×#1200—24no—
137C2×#1200—24no—
138C2×#1200C2314yescomplemented
139C2×#1200C2314yescomplemented
140C2×D3×Dic5—42no—
141C2×D3×Dic5C2314yescomplemented
142D5×D12—232no—
143#6769—232no—
144C3×C5×C4⋊C4C2314yescomplemented
145#6714C2314yescomplemented
146#6714C2314yescomplemented
147C5×(C2×D3)⋊C4C2314yescomplemented
148C5×(C2×D3)⋊C4C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yescomplemented
150C5×Dic3⋊C4C2314yescomplemented
151C3×#685C2314yes—
152C3×#685C2314yes—
153C3×#683C2314yescomplemented
154C3×#683C2314yescomplemented
155#6667C2314yescomplemented
156#6667C2314yescomplemented
157#6667C2314yescomplemented
158(C2×D3)⋊Dic5C2314yescomplemented
159#6665C2314yes—
160Dic3×Dic5C2314yescomplemented
161C22×#239—51no—
162C23×D12—51no—
163C2×C3×C22⋊Q8—51no—
164C2×#947—51no—
165C2×C4×#67—51no—
166#5630—516no—
167C2×#895—51no—
168C2×#895—51no—
169C2×#895—51no—
170C2×#894—51no—
171C2×#894D511yescharacteristic, complemented
172C2×#893—51no—
173C2×#882—51no—
174C2×#882—51no—
175C2×D3×C22⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×D4—31no—
180C23×C4×C5—31no—
181C22×C22⋊D5—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C23×Dic5—31no—
186C2×D4×D5—38no—
187C2×D4×D5—68no—
188C2×#709—38no—
189C2×#709—68no—
190C22×D20—31no—
191C22×D20—31no—
192C22×D20—31no—
193C22×D20—31no—
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5C2×D311yescharacteristic
198C22×Dic10C2×D311yescharacteristic, complemented
199C5×#123—38no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
202C2×C5×C22⋊C4—31no—
203C2×C5×C22⋊C4—31no—
204C2×C5×C22⋊C4—31no—
205C2×C22⋊Dic5—31no—
206#4085—38no—
207C2×#685—31no—
208C2×#685—31no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—38no—
214C2×#685C2×D311yescharacteristic
215C2×#685C2×D311yescharacteristic
216C2×#683C2×D311yescharacteristic, complemented
217C2×#683C2×D311yescharacteristic, complemented
218C2×C4×Dic5—31no—
219#4042C2×D318yescomplemented
220#4041—38no—
221#4040—38no—
222#4039—38no—
223#4031—38no—
224#4030—38no—
225#4028—38no—
226#4028—38no—
227#4027—38no—
228D5×C22⋊C4—38no—
229C2×#546—151noSylow
230C23×C3×C5C2411yescharacteristic
231C22×D15—22no—
232C22×D15—22no—
233C22×D15—22no—
234C22×D15—22no—
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15—22no—
239C22×D15C2×D414yes—
240C22×D15C2412yes—
241C22×D15C2412yes—
242C22×D15C2412yes—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—22no—
247C22×C5×D3—22no—
248C22×C5×D3C2×D414yes—
249C22×C5×D3C2412yes—
250C22×C5×D3C2412yes—
251C22×C3×D5—22no—
252C22×C3×D5—22no—
253C22×C3×D5#4114yescomplemented
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×Dic15C2412yes—
271D60—28no—
272D60—28no—
273D60—44no—
274C4×D15—44no—
275C2×C5×Dic3—22no—
276C2×C5×Dic3—22no—
277C2×C5×Dic3C2412yes—
278C2×C5×Dic3C2412yes—
279C5×D12—28no—
280C4×C5×D3—28no—
281C2×C3×Dic5—22no—
282C2×C3×Dic5—22no—
283C2×C3×Dic5C2×D414yes—
284C2×C3×Dic5C2412yes—
285C2×C3×Dic5C2412yes—
286C2×C3×Dic5C2412yes—
287C3×C4×D5—28no—
288C3×Dic10—28no—
289#1203—28no—
290#1203—28no—
291#1203—44no—
292#1203C2×D4116yescomplemented
293#1202—28no—
294#1200—28no—
295#1200—28no—
296D3×Dic5—44no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×Q8—51no—
300C23×C3×C4—51no—
301C22×#67—51no—
302C2×#239—58no—
303C2×#239—108no—
304C22×D12—51no—
305C22×D12—51no—
306C22×D12—51no—
307C22×D12—51no—
308C22×D12—51no—
309C22×D12—51no—
310C22×D12—51no—
311C22×D12—58no—
312C22×D12—108no—
313C22×D12C2×D511yescharacteristic
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3—51no—
318C22×C4×D3C2×D511yescharacteristic, complemented
319C3×C22⋊Q8—58no—
320C2×C3×C4⋊C4—51no—
321C2×C3×C4⋊C4—51no—
322C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
323C2×C3×C22⋊C4—51no—
324C2×C3×C22⋊C4—51no—
325C2×#217—51no—
326#947—58no—
327C4×#67—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)⋊C4C2×D511yescharacteristic, complemented
335C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
336C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
337C2×Dic3⋊C4C2×D511yescharacteristic, complemented
338C2×C4×Dic3—51no—
339#895—58no—
340#895—58no—
341#895—58no—
342#894—58no—
343#894C2×D518yescomplemented
344#893—58no—
345#882—58no—
346#882—58no—
347D3×C22⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5—31no—
351C23×D5—31no—
352C23×D5—31no—
353C23×D5—31no—
354C23×D5—34no—
355C23×D5—34no—
356C23×D5—64no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—64no—
360C23×D5—122no—
361C23×D5—122no—
362C23×D5C22×D311yescharacteristic
363C2×C5×D4—34no—
364C2×C5×D4—64no—
365C22×C4×C5—31no—
366C22×C4×C5—31no—
367C22×C4×C5—34no—
368C22×C4×C5—64no—
369C22×C4×C5C22×D311yescharacteristic
370C22×C4×C5C22×D311yescharacteristic
371C22×C4×C5C22×D311yescharacteristic
372C2×C22⋊D5—38no—
373C2×C22⋊D5—34no—
374C2×C22⋊D5—34no—
375C2×C22⋊D5—34no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—64no—
378C2×C22⋊D5—64no—
379C2×C22⋊D5—122no—
380C22×Dic5—31no—
381C22×Dic5—34no—
382C22×Dic5—122no—
383C22×Dic5C22×D311yescharacteristic
384C22×Dic5C22×D311yescharacteristic
385C22×Dic5C22×D311yescharacteristic
386D4×D5—632no—
387#709—632no—
388C2×D20—34no—
389C2×D20—34no—
390C2×D20—34no—
391C2×D20—34no—
392C2×D20—64no—
393C2×D20—64no—
394C2×D20—64no—
395C2×D20—122no—
396C2×C4×D5—24no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—64no—
401C2×C4×D5—64no—
402C2×C4×D5—122no—
403C2×C4×D5C22×D314yes—
404C2×Dic10—24no—
405C2×Dic10C22×D314yescomplemented
406C5×C4⋊C4—34no—
407C5×C4⋊C4C22×D314yescomplemented
408C5×C22⋊C4—34no—
409C5×C22⋊C4—34no—
410C5×C22⋊C4—34no—
411C22⋊Dic5—34no—
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418#685C22×D314yes—
419#685C22×D314yes—
420#683C22×D314yescomplemented
421#683C22×D314yescomplemented
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—31no—
428C2×#123—151no—
429C2×C22⋊Q8—51no—
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×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×D15—22no—
447C2×D15—22no—
448C2×D15—22no—
449C2×D15—22no—
450C2×D15—22no—
451C2×D15—22no—
452C2×D15—44no—
453C2×D15—44no—
454C2×D15C22×D414yes—
455C2×C5×D3—28no—
456C2×C5×D3—22no—
457C2×C5×D3—22no—
458C2×C5×D3—22no—
459C2×C5×D3—22no—
460C2×C5×D3—22no—
461C2×C5×D3—44no—
462C2×C5×D3C22×D414yes—
463C2×C3×D5—28no—
464C2×C3×D5—22no—
465C2×C3×D5—22no—
466C2×C3×D5C2×#4114yescomplemented
467D3×D5—416no—
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471C3×C4×C5—22no—
472Dic15—22no—
473C3×Dic5—22no—
474C3×Dic5—22no—
475C3×Dic5C22×D414yes—
476C5×Dic3—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C23×D3—51no—
480C23×D3—51no—
481C23×D3—51no—
482C23×D3—54no—
483C23×D3—54no—
484C23×D3—104no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—202no—
489C23×D3—202no—
490C23×D3C22×D511yescharacteristic
491C23×D3C22×D511yescharacteristic
492C2×C3×Q8—54no—
493C2×C3×Q8—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
501C22×C3×C4C22×D511yescharacteristic
502C2×#67—54no—
503C2×#67—104no—
504C22×Dic3—51no—
505C22×Dic3C22×D511yescharacteristic
506C22×Dic3C22×D511yescharacteristic
507#239—1032no—
508C2×D12—24no—
509C2×D12—58no—
510C2×D12—54no—
511C2×D12—54no—
512C2×D12—54no—
513C2×D12—54no—
514C2×D12—54no—
515C2×D12—54no—
516C2×D12—54no—
517C2×D12—1032no—
518C2×D12—104no—
519C2×D12—104no—
520C2×D12—104no—
521C2×D12—104no—
522C2×D12—202no—
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—54no—
530C2×C4×D3—104no—
531C2×C4×D3—104no—
532C2×C4×D3—202no—
533C2×C4×D3—202no—
534C2×C4×D3C22×D514yescomplemented
535C3×C4⋊C4—54no—
536C3×C4⋊C4—54no—
537C3×C4⋊C4C22×D514yescomplemented
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
549(C2×D3)⋊C4C22×D514yescomplemented
550Dic3⋊C4C22×D514yescomplemented
551C4×Dic3—54no—
552C23×C5—34no—
553C23×C5—32no—
554C23×C5—32no—
555C23×C5—62no—
556C23×C5—62no—
557C23×C5—62no—
558C23×C5—62no—
559C23×C5—62no—
560C23×C5C23×D311yescharacteristic
561C22×D5—22no—
562C22×D5—22no—
563C22×D5—34no—
564C22×D5—32no—
565C22×D5—32no—
566C22×D5—32no—
567C22×D5—68no—
568C22×D5—68no—
569C22×D5—62no—
570C22×D5—62no—
571C22×D5—62no—
572C22×D5—62no—
573C22×D5—62no—
574C22×D5—62no—
575C22×D5—62no—
576C22×D5—62no—
577C22×D5—68no—
578C22×D5—68no—
579C22×D5—124no—
580C22×D5—124no—
581C22×D5—1216no—
582C22×D5—1216no—
583C22×D5#23914yescomplemented
584C22×D5C23×D312yes—
585C5×D4—68no—
586C2×C4×C5—22no—
587C2×C4×C5—22no—
588C2×C4×C5—22no—
589C2×C4×C5—32no—
590C2×C4×C5—32no—
591C2×C4×C5—68no—
592C2×C4×C5—62no—
593C2×C4×C5—62no—
594C2×C4×C5C23×D312yes—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C22⋊D5—316no—
598C22⋊D5—68no—
599C22⋊D5—68no—
600C22⋊D5—124no—
601C2×Dic5—22no—
602C2×Dic5—22no—
603C2×Dic5—32no—
604C2×Dic5—62no—
605C2×Dic5—124no—
606C2×Dic5D3×D414yes—
607C2×Dic5C23×D312yes—
608C2×Dic5C23×D312yes—
609C2×Dic5C23×D312yes—
610D20—68no—
611D20—68no—
612D20—68no—
613D20—124no—
614C4×D5—28no—
615C4×D5—68no—
616C4×D5—68no—
617C4×D5—124no—
618Dic10—28no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—51no—
624C22×D4—31no—
625C22×D4—151no—
626C22×D4—158no—
627C22×D4—151no—
628C22×D4—151no—
629C22×D4—151no—
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—38no—
643#123—158no—
644C22⋊Q8—58no—
645#121—158no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—31no—
653C2×C4⋊C4—51no—
654C2×C4⋊C4—51no—
655C2×C4⋊C4D3×D511yescharacteristic, complemented
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—31no—
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—
676D15—42no—
677D15—42no—
678C3×D5—24no—
679C5×D3—24no—
680C5×D3—42no—
681C23×C3—54no—
682C23×C3—52no—
683C23×C3—102no—
684C23×C3—102no—
685C23×C3C23×D511yescharacteristic
686C22×D3—22no—
687C22×D3—22no—
688C22×D3—22no—
689C22×D3—22no—
690C22×D3—22no—
691C22×D3—54no—
692C22×D3—52no—
693C22×D3—52no—
694C22×D3—52no—
695C22×D3—108no—
696C22×D3—108no—
697C22×D3—108no—
698C22×D3—102no—
699C22×D3—102no—
700C22×D3—102no—
701C22×D3—102no—
702C22×D3—102no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—108no—
707C22×D3—204no—
708C22×D3—204no—
709C22×D3—2016no—
710C22×D3—2016no—
711C22×D3D4×D514yes—
712C22×D3C23×D512yes—
713C22×D3C23×D512yes—
714C3×Q8—108no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—54no—
719C2×C3×C4—52no—
720C2×C3×C4—52no—
721C2×C3×C4—52no—
722C2×C3×C4—108no—
723C2×C3×C4—102no—
724C2×C3×C4—102no—
725C2×C3×C4C23×D512yes—
726C2×C3×C4C23×D512yes—
727C2×C3×C4C23×D512yes—
728#67—108no—
729C2×Dic3—22no—
730C2×Dic3—22no—
731C2×Dic3—52no—
732C2×Dic3—102no—
733C2×Dic3C23×D512yes—
734C2×Dic3C23×D512yes—
735D12—28no—
736D12—516no—
737D12—108no—
738D12—108no—
739D12—108no—
740D12—108no—
741D12—204no—
742D12—204no—
743C4×D3—28no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747C4×D3—204no—
748C22×C5—34no—
749C22×C5—62no—
750C22×C5—62no—
751C22×C5—68no—
752C22×C5—62no—
753C22×C5—62no—
754C22×C5—62no—
755C22×C5—124no—
756C22×C5C2×D3×D412yes—
757C22×C5C2×#23912yes—
758C22×C5#100912yes—
759C22×C5C24×D311yescharacteristic
760C2×D5—22no—
761C2×D5—22no—
762C2×D5—28no—
763C2×D5—34no—
764C2×D5—62no—
765C2×D5—62no—
766C2×D5—68no—
767C2×D5—62no—
768C2×D5—62no—
769C2×D5—62no—
770C2×D5—62no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—1216no—
774C2×D5—1216no—
775C2×D5—124no—
776C2×D5—124no—
777C2×D5C2×#23914yescomplemented
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—22no—
781C4×C5—62no—
782C4×C5—62no—
783Dic5—22no—
784Dic5—22no—
785Dic5—62no—
786Dic5C2×D3×D414yes—
787C24—31no—
788C24—31no—
789C24—51no—
790C24—154no—
791C24—154no—
792C24—151no—
793C24—151no—
794C24—151no—
795C24—304no—
796C24—304no—
797C24—304no—
798C24—304no—
799C24—602no—
800C24—602no—
801#41—3032no—
802C2×Q8—54no—
803C2×Q8—104no—
804C2×D4—34no—
805C2×D4—64no—
806C2×D4—154no—
807C2×D4—154no—
808C2×D4—158no—
809C2×D4—154no—
810C2×D4—154no—
811C2×D4—154no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—304no—
816C2×D4—304no—
817C2×D4—304no—
818C2×D4—304no—
819C2×D4—3032no—
820C2×D4—304no—
821C2×D4—602no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—34no—
826C22×C4—51no—
827C22×C4—51no—
828C22×C4—51no—
829C22×C4—54no—
830C22×C4—64no—
831C22×C4—104no—
832C22×C4—154no—
833C22×C4—154no—
834C22×C4—154no—
835C22×C4—151no—
836C22×C4—154no—
837C22×C4—304no—
838C22×C4—304no—
839C22×C4—602no—
840C22×C4—602no—
841C22×C4C2×D3×D511yescharacteristic
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—34no—
845C4⋊C4—54no—
846C4⋊C4—54no—
847C4⋊C4C2×D3×D514yescomplemented
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—34no—
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×C3C2×D4×D512yes—
867C22×C3D5×#4112yes—
868C22×C3#414912yes—
869C22×C3C24×D511yescharacteristic
870C2×D3—28no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—44no—
877C2×D3—54no—
878C2×D3—108no—
879C2×D3—102no—
880C2×D3—102no—
881C2×D3—102no—
882C2×D3—102no—
883C2×D3—102no—
884C2×D3—102no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—2016no—
888C2×D3—2016no—
889C2×D3—204no—
890C2×D3—204no—
891C2×D3C2×D4×D514yes—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—54no—
896C3×C4—102no—
897C3×C4—102no—
898Dic3—22no—
899Dic3—22no—
900Dic3—102no—
901C2×C5—64no—
902C2×C5—122no—
903C2×C5#563014yescomplemented
904C2×C5C22×D3×D411yescharacteristic
905C2×C5C22×#23911yescharacteristic
906C2×C5C2×#100911yescharacteristic
907D5—24no—
908D5—64no—
909D5—122no—
910D5—122no—
911C23—34no—
912C23—32no—
913C23—32no—
914C23—54no—
915C23—52no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—102no—
922C23—102no—
923C23—154no—
924C23—152no—
925C23—152no—
926C23—152no—
927C23—308no—
928C23—308no—
929C23—308no—
930C23—308no—
931C23—302no—
932C23—302no—
933C23—302no—
934C23—302no—
935C23—302no—
936C23—302no—
937C23—302no—
938C23—302no—
939C23—604no—
940C23—604no—
941C23—6016no—
942C23—6016no—
943C23C22×D3×D511yescharacteristic
944Q8—108no—
945D4—68no—
946D4—1516no—
947D4—308no—
948D4—308no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—604no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—54no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—52no—
963C2×C4—68no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—108no—
967C2×C4—102no—
968C2×C4—102no—
969C2×C4—152no—
970C2×C4—308no—
971C2×C4—308no—
972C2×C4—302no—
973C2×C4—604no—
974C2×C4—604no—
975C2×C4C22×D3×D512yes—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—104no—
979C2×C3#6598814yescomplemented
980C2×C3C22×D4×D511yescharacteristic
981C2×C3C2×D5×#4111yescharacteristic
982C2×C3C2×#414911yescharacteristic
983D3—24no—
984D3—42no—
985D3—104no—
986D3—202no—
987D3—202no—
988C5C2×#563011yescharacteristic, complemented, Sylow
989C22—34no—
990C22—54no—
991C22—68no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—108no—
998C22—102no—
999C22—102no—
1000C22—124no—
1001C22—154no—
1002C22—308no—
1003C22—302no—
1004C22—302no—
1005C22—302no—
1006C22—302no—
1007C22—302no—
1008C22—302no—
1009C22—302no—
1010C22—302no—
1011C22—6016no—
1012C22—6016no—
1013C22—604no—
1014C22—604no—
1015C22#9201912yes—
1016C22D3×D4×D512yes—
1017C22D5×#23912yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—54no—
1023C4—62no—
1024C4—62no—
1025C4—102no—
1026C4—102no—
1027C4—302no—
1028C3C2×#6598811yescharacteristic, complemented, Sylow
1029C2—64no—
1030C2—104no—
1031C2—122no—
1032C2—304no—
1033C2—602no—
1034C2—602no—
1035C2#1175387014yesdirect product factor
1036C2C2×#9201911yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×D5×#23911yescharacteristic
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×D5×D12C2semidirect
2. C22×#6769C2semidirect
3. C2×#91784C2semidirect
4. C2×C5×#894C2semidirect
5. C2×C3×#4042C2semidirect
6. C2×#91476C2semidirect
7. C2×#91476C2semidirect
8. C2×#91473C2semidirect
9. C2×D3×#685C2semidirect
10. C2×#91444C2semidirect
11. C2×#91433C2semidirect
12. C2×#91420C2semidirect
13. C2×#91416C2semidirect
14. C2×#91406C2semidirect
15. C2×#91326C2semidirect
16. #11753870C2direct (N × H)
21. C22×D60C22semidirect
22. C22×D60C22semidirect
23. C22×C4×D15C22semidirect
25. C22×C4×C5×D3C22semidirect
27. C22×C3×Dic10C22semidirect
30. C22×#1203C22semidirect
31. C22×#1203C22semidirect
33. C22×#1200C22semidirect
34. C22×#1200C22semidirect
35. C22×D3×Dic5C22semidirect
37. C2×D5×D12C22semidirect
39. C2×#6769C22semidirect
40. C2×C3×C5×C4⋊C4C22semidirect
41. C2×#6714C22semidirect
42. C2×#6714C22semidirect
43. #91784C22semidirect
44. C2×C5×(C2×D3)⋊C4C22semidirect
45. C2×C5×(C2×D3)⋊C4C22semidirect
46. C2×C5×(C2×D3)⋊C4C22semidirect
47. C2×C5×Dic3⋊C4C22semidirect
48. C5×#894C22semidirect
51. C2×C3×#683C22semidirect
52. C2×C3×#683C22semidirect
53. C3×#4042C22semidirect
54. C2×#6667C22semidirect
55. C2×#6667C22semidirect
56. C2×#6667C22semidirect
57. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91476C22semidirect
61. #91476C22semidirect
62. #91473C22semidirect
63. D3×#685C22semidirect
64. #91444C22semidirect
65. #91433C22semidirect
66. #91420C22semidirect
67. #91416C22semidirect
68. #91406C22semidirect
69. #91326C22semidirect
77. C2×#4042D3semidirect
109. C2×D60C23semidirect
110. C2×D60C23semidirect
112. C2×C4×D15C23semidirect
118. C2×C4×C5×D3C23semidirect
125. C2×C3×Dic10C23semidirect
129. C2×#1203D4semidirect
132. C2×#1203C23semidirect
133. C2×#1203C23semidirect
138. C2×#1200C23semidirect
139. C2×#1200C23semidirect
141. C2×D3×Dic5C23semidirect
144. C3×C5×C4⋊C4C23semidirect
145. #6714C23semidirect
146. #6714C23semidirect
147. C5×(C2×D3)⋊C4C23semidirect
148. C5×(C2×D3)⋊C4C23semidirect
149. C5×(C2×D3)⋊C4C23semidirect
150. C5×Dic3⋊C4C23semidirect
153. C3×#683C23semidirect
154. C3×#683C23semidirect
155. #6667C23semidirect
156. #6667C23semidirect
157. #6667C23semidirect
158. (C2×D3)⋊Dic5C23semidirect
160. Dic3×Dic5C23semidirect
171. C2×#894D5semidirect
198. C22×Dic10C2×D3semidirect
201. C2×C5×C4⋊C4C2×D3semidirect
216. C2×#683C2×D3semidirect
217. C2×#683C2×D3semidirect
219. #4042C2×D3semidirect
253. C22×C3×D5#41semidirect
292. #1203C2×D4semidirect
318. C22×C4×D3C2×D5semidirect
322. C2×C3×C4⋊C4C2×D5semidirect
334. C2×(C2×D3)⋊C4C2×D5semidirect
335. C2×(C2×D3)⋊C4C2×D5semidirect
336. C2×(C2×D3)⋊C4C2×D5semidirect
337. C2×Dic3⋊C4C2×D5semidirect
343. #894C2×D5semidirect
405. C2×Dic10C22×D3semidirect
407. C5×C4⋊C4C22×D3semidirect
420. #683C22×D3semidirect
421. #683C22×D3semidirect
466. C2×C3×D5C2×#41semidirect
534. C2×C4×D3C22×D5semidirect
537. C3×C4⋊C4C22×D5semidirect
547. (C2×D3)⋊C4C22×D5semidirect
548. (C2×D3)⋊C4C22×D5semidirect
549. (C2×D3)⋊C4C22×D5semidirect
550. Dic3⋊C4C22×D5semidirect
583. C22×D5#239semidirect
655. C2×C4⋊C4D3×D5semidirect
671. C2×C3×C5#546semidirect
777. C2×D5C2×#239semidirect
847. C4⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
903. C2×C5#5630semidirect
979. C2×C3#65988semidirect
988. C5C2×#5630semidirect
1028. C3C2×#65988semidirect
1035. C2#11753870direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×D122
C22×#67692
C2×#917842
C2×C5×#8942
C2×C3×#40422
C2×#914762
C2×#914732
C2×D3×#6852
C2×#914442
C2×#914332
C2×#914202
C2×#914162
C2×#914062
C2×#913262
#117538702
C2×#659883
C2×#56305