Finite Group Databasebeta

← C2×#11753859 #14482649

Subgroups — C2×#11753859 #14482649

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×D20C211yesmaximal, characteristic, complemented
2C22×#6773C211yesmaximal, characteristic, complemented
3C2×#91784C211yesmaximal, characteristic, complemented
4C2×C5×#896C211yesmaximal, characteristic, complemented
5C2×C3×#4040C211yesmaximal, characteristic, complemented
6C2×#91476C211yesmaximal, characteristic, complemented
7C2×#91476C211yesmaximal, characteristic, complemented
8C2×#91473C211yesmaximal, characteristic, complemented
9C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×#91459C211yesmaximal, characteristic, complemented
11C2×#91455C211yesmaximal, characteristic, complemented
12C2×#91446C211yesmaximal, characteristic, complemented
13C2×#91433C211yesmaximal, characteristic, complemented
14C2×#91409C211yesmaximal, characteristic, complemented
15C2×#91396C211yesmaximal, characteristic, complemented
16#11753859C2116yesmaximal, direct product factor
17C2×#65964—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×D60C2211yescharacteristic, complemented
22C22×D60C2211yescharacteristic, complemented
23C22×C4×D15C2211yescharacteristic, complemented
24C22×C4×C5×D3C2211yescharacteristic
25C22×C5×Dic6C2211yescharacteristic, complemented
26C22×C3×D20C2211yescharacteristic
27C22×C3×C4×D5C2211yescharacteristic, complemented
28C22×#1203C2211yescharacteristic
29C22×#1202C2211yescharacteristic
30C22×#1202C2211yescharacteristic
31C22×#1202C2211yescharacteristic, complemented
32C22×#1202C2211yescharacteristic, complemented
33C22×#1200C2211yescharacteristic, complemented
34C22×#1200C2211yescharacteristic, complemented
35C22×D5×Dic3C2211yescharacteristic, complemented
36C2×D3×D20—28no—
37C2×D3×D20C2218yescomplemented
38C2×#6773—28no—
39C2×#6773C2218yescomplemented
40C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43#91784C2218yescomplemented
44C2×C5×(C2×D3)⋊C4C2211yescharacteristic
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic
46C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
47C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
48C5×#896C2218yescomplemented
49C2×C3×#685C2211yescharacteristic, complemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×#685C2211yescharacteristic, complemented
52C2×C3×#683C2211yescharacteristic, complemented
53C3×#4040C2218yescomplemented
54C2×#6667C2211yescharacteristic, complemented
55C2×#6667C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×#6665C2211yescharacteristic, complemented
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91476C2218yescomplemented
61#91476C2218yescomplemented
62#91473C2218yescomplemented
63D5×(C2×D3)⋊C4C2218yescomplemented
64#91459C2218yescomplemented
65#91455C2218yescomplemented
66#91446C2218yescomplemented
67#91433C2218yescomplemented
68#91409C2218yescomplemented
69#91396C2218yescomplemented
70C2×#5654—51nomaximal, Hall
71C22×#713—31no—
72C23×D20—31no—
73C2×C5×C22⋊Q8—31no—
74C2×#4093—31no—
75C2×C4×C22⋊D5—31no—
76#65964—316no—
77C2×#4041—31no—
78C2×#4041—31no—
79C2×#4041—31no—
80C2×#4040—31no—
81C2×#4040D311yescharacteristic, complemented
82C2×#4039—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C2×D5×C22⋊C4—31no—
86C2×D5×C22⋊C4—31no—
87C23×D15C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
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
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
115C22×C5×Dic3C2311yescharacteristic
116C2×C4×C5×D3—24no—
117C2×C4×C5×D3C2314yes—
118C2×C5×Dic6—24no—
119C2×C5×Dic6C2314yescomplemented
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×#1202—24no—
129C2×#1202—24no—
130C2×#1202—42no—
131C2×#1202D418yescomplemented
132C2×#1202C2314yes—
133C2×#1202C2314yes—
134C2×#1202C2314yescomplemented
135C2×#1202C2314yescomplemented
136C2×#1200—24no—
137C2×#1200—24no—
138C2×#1200C2314yescomplemented
139C2×#1200C2314yescomplemented
140C2×D5×Dic3—42no—
141C2×D5×Dic3C2314yescomplemented
142D3×D20—232no—
143#6773—232no—
144C3×C5×C4⋊C4C2314yescomplemented
145#6714C2314yescomplemented
146#6714C2314yescomplemented
147C5×(C2×D3)⋊C4C2314yes—
148C5×(C2×D3)⋊C4C2314yes—
149C5×Dic3⋊C4C2314yescomplemented
150C5×Dic3⋊C4C2314yescomplemented
151C3×#685C2314yescomplemented
152C3×#685C2314yescomplemented
153C3×#685C2314yescomplemented
154C3×#683C2314yescomplemented
155#6667C2314yescomplemented
156#6667C2314yescomplemented
157#6667C2314yescomplemented
158(C2×D3)⋊Dic5C2314yes—
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×#896D511yescharacteristic, complemented
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—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×Q8—31no—
180C23×C4×C5—31no—
181C22×C22⋊D5—31no—
182C2×#713—38no—
183C2×#713—68no—
184C22×D20—31no—
185C22×D20—31no—
186C22×D20—31no—
187C22×D20—31no—
188C22×D20—31no—
189C22×D20—31no—
190C22×D20—31no—
191C22×D20—38no—
192C22×D20—68no—
193C22×D20C2×D311yescharacteristic
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5—31no—
198C22×C4×D5C2×D311yescharacteristic, complemented
199C5×C22⋊Q8—38no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C4⋊C4—31no—
202C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
203C2×C5×C22⋊C4—31no—
204C2×C5×C22⋊C4—31no—
205C2×C22⋊Dic5—31no—
206#4093—38no—
207C4×C22⋊D5—38no—
208C2×#685—31no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685C2×D311yescharacteristic, complemented
215C2×#685C2×D311yescharacteristic, complemented
216C2×#685C2×D311yescharacteristic, complemented
217C2×#683C2×D311yescharacteristic, complemented
218C2×C4×Dic5—31no—
219#4041—38no—
220#4041—38no—
221#4041—38no—
222#4040—38no—
223#4040C2×D318yescomplemented
224#4039—38no—
225#4028—38no—
226#4028—38no—
227D5×C22⋊C4—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#4114yescomplemented
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×Dic15C2412yes—
271D60—28no—
272D60—28no—
273D60—44no—
274C4×D15—44no—
275C2×C5×Dic3—22no—
276C2×C5×Dic3—22no—
277C2×C5×Dic3C2×D414yes—
278C2×C5×Dic3C2412yes—
279C2×C5×Dic3C2412yes—
280C2×C5×Dic3C2412yes—
281C4×C5×D3—28no—
282C5×Dic6—28no—
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#1202—28no—
291#1202—28no—
292#1202—44no—
293#1202C2×D4116yescomplemented
294#1200—28no—
295#1200—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×D12—51no—
312C22×D12—51no—
313C22×D12—51no—
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3C2×D511yescharacteristic
318C22×Dic6C2×D511yescharacteristic, complemented
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
335C2×(C2×D3)⋊C4C2×D511yescharacteristic
336C2×Dic3⋊C4C2×D511yescharacteristic, complemented
337C2×Dic3⋊C4C2×D511yescharacteristic, complemented
338C2×C4×Dic3—51no—
339#896C2×D518yescomplemented
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—
350C23×D5—31no—
351C23×D5—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×Q8—34no—
364C2×C5×Q8—64no—
365C22×C4×C5—31no—
366C22×C4×C5—31no—
367C22×C4×C5—31no—
368C22×C4×C5—34no—
369C22×C4×C5—64no—
370C22×C4×C5C22×D311yescharacteristic
371C22×C4×C5C22×D311yescharacteristic
372C22×C4×C5C22×D311yescharacteristic
373C2×C22⋊D5—34no—
374C2×C22⋊D5—64no—
375C22×Dic5—31no—
376C22×Dic5C22×D311yescharacteristic
377C22×Dic5C22×D311yescharacteristic
378#713—632no—
379C2×D20—24no—
380C2×D20—38no—
381C2×D20—34no—
382C2×D20—34no—
383C2×D20—34no—
384C2×D20—34no—
385C2×D20—34no—
386C2×D20—34no—
387C2×D20—34no—
388C2×D20—632no—
389C2×D20—64no—
390C2×D20—64no—
391C2×D20—64no—
392C2×D20—64no—
393C2×D20—122no—
394C2×D20—122no—
395C2×D20C22×D314yes—
396C2×C4×D5—24no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—34no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5—122no—
404C2×C4×D5—122no—
405C2×C4×D5C22×D314yescomplemented
406C5×C4⋊C4—34no—
407C5×C4⋊C4—34no—
408C5×C4⋊C4C22×D314yescomplemented
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×D314yescomplemented
419#685C22×D314yescomplemented
420#685C22×D314yescomplemented
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—31no—
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×D3C2×#4114yescomplemented
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—
473C3×Dic5—22no—
474C3×Dic5—22no—
475C5×Dic3—22no—
476C5×Dic3—22no—
477C5×Dic3C22×D414yes—
478C24×C3—51no—
479C24×C3—51no—
480C23×D3—51no—
481C23×D3—51no—
482C23×D3—51no—
483C23×D3—54no—
484C23×D3—54no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—104no—
489C23×D3—202no—
490C23×D3—202no—
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—54no—
511C22×Dic3—202no—
512C22×Dic3C22×D511yescharacteristic
513C22×Dic3C22×D511yescharacteristic
514C22×Dic3C22×D511yescharacteristic
515D3×D4—1032no—
516#235—1032no—
517C2×D12—54no—
518C2×D12—54no—
519C2×D12—54no—
520C2×D12—54no—
521C2×D12—104no—
522C2×D12—104no—
523C2×D12—104no—
524C2×D12—202no—
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—24no—
534C2×Dic6C22×D514yescomplemented
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×D514yes—
548(C2×D3)⋊C4C22×D514yes—
549Dic3⋊C4C22×D514yescomplemented
550Dic3⋊C4C22×D514yescomplemented
551C4×Dic3—54no—
552C23×C5—34no—
553C23×C5—32no—
554C23×C5—62no—
555C23×C5—62no—
556C23×C5C23×D311yescharacteristic
557C22×D5—22no—
558C22×D5—22no—
559C22×D5—22no—
560C22×D5—22no—
561C22×D5—22no—
562C22×D5—34no—
563C22×D5—32no—
564C22×D5—32no—
565C22×D5—32no—
566C22×D5—68no—
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—124no—
579C22×D5—124no—
580C22×D5—1216no—
581C22×D5—1216no—
582C22×D5D3×D414yes—
583C22×D5C23×D312yes—
584C22×D5C23×D312yes—
585C5×Q8—68no—
586C2×C4×C5—22no—
587C2×C4×C5—22no—
588C2×C4×C5—22no—
589C2×C4×C5—34no—
590C2×C4×C5—32no—
591C2×C4×C5—32no—
592C2×C4×C5—32no—
593C2×C4×C5—68no—
594C2×C4×C5—62no—
595C2×C4×C5—62no—
596C2×C4×C5C23×D312yes—
597C2×C4×C5C23×D312yes—
598C2×C4×C5C23×D312yes—
599C22⋊D5—68no—
600C2×Dic5—22no—
601C2×Dic5—22no—
602C2×Dic5—32no—
603C2×Dic5—62no—
604C2×Dic5C23×D312yes—
605C2×Dic5C23×D312yes—
606D20—28no—
607D20—316no—
608D20—68no—
609D20—68no—
610D20—68no—
611D20—68no—
612D20—124no—
613D20—124no—
614C4×D5—28no—
615C4×D5—68no—
616C4×D5—68no—
617C4×D5—124no—
618C4×D5—124no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—31no—
624C22×D4—51no—
625C22×D4—158no—
626C22×D4—151no—
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—58no—
643#123—158no—
644C22⋊Q8—38no—
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—31no—
654C2×C4⋊C4—51no—
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—
676D15—42no—
677D15—42no—
678C3×D5—24no—
679C3×D5—42no—
680C5×D3—24no—
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—54no—
693C22×D3—52no—
694C22×D3—52no—
695C22×D3—52no—
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—108no—
708C22×D3—204no—
709C22×D3—204no—
710C22×D3—2016no—
711C22×D3—2016no—
712C22×D3#71314yescomplemented
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—22no—
732C2×Dic3—52no—
733C2×Dic3—102no—
734C2×Dic3—204no—
735C2×Dic3D4×D514yes—
736C2×Dic3C23×D512yes—
737C2×Dic3C23×D512yes—
738C2×Dic3C23×D512yes—
739D12—108no—
740D12—108no—
741D12—108no—
742D12—204no—
743C4×D3—28no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—28no—
748C22×C5—34no—
749C22×C5—68no—
750C22×C5—62no—
751C22×C5—62no—
752C22×C5C2×D3×D412yes—
753C22×C5D3×#4112yes—
754C22×C5#100912yes—
755C22×C5C24×D311yescharacteristic
756C2×D5—28no—
757C2×D5—22no—
758C2×D5—22no—
759C2×D5—22no—
760C2×D5—22no—
761C2×D5—22no—
762C2×D5—34no—
763C2×D5—44no—
764C2×D5—68no—
765C2×D5—62no—
766C2×D5—62no—
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×D3×D414yes—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—22no—
781C4×C5—34no—
782C4×C5—62no—
783C4×C5—62no—
784Dic5—22no—
785Dic5—22no—
786Dic5—62no—
787C24—31no—
788C24—51no—
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—34no—
803C2×Q8—64no—
804C2×D4—54no—
805C2×D4—104no—
806C2×D4—154no—
807C2×D4—158no—
808C2×D4—154no—
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—3032no—
819C2×D4—304no—
820C2×D4—304no—
821C2×D4—602no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—34no—
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—34no—
846C4⋊C4—54no—
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×C3C2×#71312yes—
872C22×C3#414912yes—
873C22×C3C24×D511yescharacteristic
874C2×D3—28no—
875C2×D3—22no—
876C2×D3—22no—
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×#71314yescomplemented
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—102no—
896C3×C4—102no—
897Dic3—22no—
898Dic3—22no—
899Dic3—102no—
900Dic3C2×D4×D514yes—
901C2×C5—64no—
902C2×C5#565414yescomplemented
903C2×C5C22×D3×D411yescharacteristic
904C2×C5C2×D3×#4111yescharacteristic
905C2×C5C2×#100911yescharacteristic
906D5—24no—
907D5—42no—
908D5—64no—
909D5—122no—
910D5—122no—
911C23—34no—
912C23—32no—
913C23—54no—
914C23—52no—
915C23—52no—
916C23—62no—
917C23—62no—
918C23—102no—
919C23—102no—
920C23—102no—
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—68no—
945D4—108no—
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—34no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—32no—
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—202no—
980C2×C3#6596414yescomplemented
981C2×C3C22×D4×D511yescharacteristic
982C2×C3C22×#71311yescharacteristic
983C2×C3C2×#414911yescharacteristic
984D3—24no—
985D3—104no—
986D3—202no—
987D3—202no—
988C5C2×#565411yescharacteristic, complemented, Sylow
989C22—34no—
990C22—54no—
991C22—68no—
992C22—62no—
993C22—62no—
994C22—108no—
995C22—102no—
996C22—102no—
997C22—102no—
998C22—102no—
999C22—102no—
1000C22—154no—
1001C22—204no—
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—
1017C22D3×#71312yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—34no—
1023C4—62no—
1024C4—62no—
1025C4—102no—
1026C4—102no—
1027C4—302no—
1028C3C2×#6596411yescharacteristic, complemented, Sylow
1029C2—64no—
1030C2—104no—
1031C2—202no—
1032C2—304no—
1033C2—602no—
1034C2—602no—
1035C2#1175385914yesdirect product factor
1036C2C2×#9201911yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×D3×#71311yescharacteristic
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×D3×D20C2semidirect
2. C22×#6773C2semidirect
3. C2×#91784C2semidirect
4. C2×C5×#896C2semidirect
5. C2×C3×#4040C2semidirect
6. C2×#91476C2semidirect
7. C2×#91476C2semidirect
8. C2×#91473C2semidirect
9. C2×D5×(C2×D3)⋊C4C2semidirect
10. C2×#91459C2semidirect
11. C2×#91455C2semidirect
12. C2×#91446C2semidirect
13. C2×#91433C2semidirect
14. C2×#91409C2semidirect
15. C2×#91396C2semidirect
16. #11753859C2direct (N × H)
21. C22×D60C22semidirect
22. C22×D60C22semidirect
23. C22×C4×D15C22semidirect
25. C22×C5×Dic6C22semidirect
27. C22×C3×C4×D5C22semidirect
31. C22×#1202C22semidirect
32. C22×#1202C22semidirect
33. C22×#1200C22semidirect
34. C22×#1200C22semidirect
35. C22×D5×Dic3C22semidirect
37. C2×D3×D20C22semidirect
39. C2×#6773C22semidirect
40. C2×C3×C5×C4⋊C4C22semidirect
41. C2×#6714C22semidirect
42. C2×#6714C22semidirect
43. #91784C22semidirect
46. C2×C5×Dic3⋊C4C22semidirect
47. C2×C5×Dic3⋊C4C22semidirect
48. C5×#896C22semidirect
49. C2×C3×#685C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×#685C22semidirect
52. C2×C3×#683C22semidirect
53. C3×#4040C22semidirect
54. C2×#6667C22semidirect
55. C2×#6667C22semidirect
56. C2×#6667C22semidirect
58. C2×#6665C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91476C22semidirect
61. #91476C22semidirect
62. #91473C22semidirect
63. D5×(C2×D3)⋊C4C22semidirect
64. #91459C22semidirect
65. #91455C22semidirect
66. #91446C22semidirect
67. #91433C22semidirect
68. #91409C22semidirect
69. #91396C22semidirect
81. C2×#4040D3semidirect
109. C2×D60C23semidirect
110. C2×D60C23semidirect
112. C2×C4×D15C23semidirect
119. C2×C5×Dic6C23semidirect
125. C2×C3×C4×D5C23semidirect
131. C2×#1202D4semidirect
134. C2×#1202C23semidirect
135. C2×#1202C23semidirect
138. C2×#1200C23semidirect
139. C2×#1200C23semidirect
141. C2×D5×Dic3C23semidirect
144. C3×C5×C4⋊C4C23semidirect
145. #6714C23semidirect
146. #6714C23semidirect
149. C5×Dic3⋊C4C23semidirect
150. C5×Dic3⋊C4C23semidirect
151. C3×#685C23semidirect
152. C3×#685C23semidirect
153. C3×#685C23semidirect
154. C3×#683C23semidirect
155. #6667C23semidirect
156. #6667C23semidirect
157. #6667C23semidirect
159. #6665C23semidirect
160. Dic3×Dic5C23semidirect
167. C2×#896D5semidirect
198. C22×C4×D5C2×D3semidirect
202. C2×C5×C4⋊C4C2×D3semidirect
214. C2×#685C2×D3semidirect
215. C2×#685C2×D3semidirect
216. C2×#685C2×D3semidirect
217. C2×#683C2×D3semidirect
223. #4040C2×D3semidirect
245. C22×C5×D3#41semidirect
293. #1202C2×D4semidirect
318. C22×Dic6C2×D5semidirect
321. C2×C3×C4⋊C4C2×D5semidirect
336. C2×Dic3⋊C4C2×D5semidirect
337. C2×Dic3⋊C4C2×D5semidirect
339. #896C2×D5semidirect
405. C2×C4×D5C22×D3semidirect
408. C5×C4⋊C4C22×D3semidirect
418. #685C22×D3semidirect
419. #685C22×D3semidirect
420. #685C22×D3semidirect
421. #683C22×D3semidirect
458. C2×C5×D3C2×#41semidirect
534. C2×Dic6C22×D5semidirect
536. C3×C4⋊C4C22×D5semidirect
549. Dic3⋊C4C22×D5semidirect
550. Dic3⋊C4C22×D5semidirect
655. C2×C4⋊C4D3×D5semidirect
671. C2×C3×C5#546semidirect
712. C22×D3#713semidirect
847. C4⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
891. C2×D3C2×#713semidirect
902. C2×C5#5654semidirect
980. C2×C3#65964semidirect
988. C5C2×#5654semidirect
1028. C3C2×#65964semidirect
1035. C2#11753859direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D202
C22×#67732
C2×#917842
C2×C5×#8962
C2×C3×#40402
C2×#914762
C2×#914732
C2×D5×(C2×D3)⋊C42
C2×#914592
C2×#914552
C2×#914462
C2×#914332
C2×#914092
C2×#913962
#117538592
C2×#659643
C2×#56545