Finite Group Databasebeta

← C2×#11753853 #14479645

Subgroups — C2×#11753853 #14479645

Order 1920.

3760 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D3×D5C211yesmaximal, characteristic, complemented
2C22×#6766C211yesmaximal, characteristic, complemented
3C2×#91782C211yesmaximal, characteristic, complemented
4C2×C5×#896C211yesmaximal, characteristic, complemented
5C2×C3×#4040C211yesmaximal, characteristic, complemented
6C2×#91476C211yesmaximal, characteristic, complemented
7C2×#91474C211yesmaximal, characteristic, complemented
8C2×#91459C211yesmaximal, characteristic, complemented
9C2×#91454C211yesmaximal, characteristic, complemented
10C2×#91442C211yesmaximal, characteristic, complemented
11C2×#91424C211yesmaximal, characteristic, complemented
12C2×#91406C211yesmaximal, characteristic, complemented
13C2×#91396C211yesmaximal, characteristic, complemented
14C2×#91394C211yesmaximal, characteristic, complemented
15C2×#91348C211yesmaximal, characteristic, complemented
16#11753853C2116yesmaximal, direct product factor
17C2×#65961—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C4×C5×D3C2211yescharacteristic
23C22×C5×Dic6C2211yescharacteristic, complemented
24C22×C3×D20C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic
26C22×#1203C2211yescharacteristic
27C22×#1202C2211yescharacteristic
28C22×#1202C2211yescharacteristic
29C22×#1202C2211yescharacteristic, complemented
30C22×#1201C2211yescharacteristic
31C22×#1200C2211yescharacteristic
32C22×D3×Dic5C2211yescharacteristic
33C22×D5×Dic3C2211yescharacteristic
34C22×D5×Dic3C2211yescharacteristic, complemented
35C2×C4×D3×D5—28no—
36C2×C4×D3×D5C2218yescomplemented
37C2×#6766—28no—
38C2×#6766C2218yescomplemented
39C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
40C2×#6714C2211yescharacteristic
41C2×#6714C2211yescharacteristic, complemented
42C2×C4×Dic15C2211yescharacteristic, complemented
43#91782C2218yescomplemented
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
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×#685C2211yescharacteristic, complemented
52C2×C3×#683C2211yescharacteristic, complemented
53C3×#4040C2218yescomplemented
54C2×Dic3⋊Dic5C2211yescharacteristic, complemented
55C2×#6669C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic
57C2×#6667C2211yescharacteristic, complemented
58C2×#6665C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91476C2218yescomplemented
61#91474C2218yescomplemented
62#91459C2218yescomplemented
63#91454C2218yescomplemented
64#91442C2218yescomplemented
65#91424C2218yescomplemented
66#91406C2218yescomplemented
67#91396C2218yescomplemented
68#91394C2218yescomplemented
69#91348C2218yescomplemented
70C2×#5656—51nomaximal, Hall
71C22×#713—31no—
72C23×C4×D5—31no—
73C2×C5×C22⋊Q8—31no—
74C2×#4092—31no—
75C2×#4076—31no—
76#65961—316no—
77C2×#4041—31no—
78C2×#4040—31no—
79C2×#4040D311yescharacteristic, complemented
80C2×#4039—31no—
81C2×#4039—31no—
82C2×#4038—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C2×#4027—31no—
86C2×#4027—31no—
87C23×D15C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C23×C3×D5C2311yescharacteristic
92C22×D3×D5—24no—
93C22×D3×D5—24no—
94C22×D3×D5—24no—
95C22×D3×D5C2314yes—
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C2×D60—24no—
102C2×D60C2314yes—
103C2×C4×D15—24no—
104C2×C4×D15—24no—
105C2×C4×D15C2314yes—
106C2×C4×D15C2314yescomplemented
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C2×C4×C5×D3—24no—
111C2×C4×C5×D3C2314yes—
112C2×C5×Dic6—24no—
113C2×C5×Dic6C2314yescomplemented
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C2×C3×D20—24no—
117C2×C3×D20C2314yes—
118C2×C3×C4×D5—24no—
119C2×C3×C4×D5C2314yes—
120C2×#1203—24no—
121C2×#1203C2314yes—
122C2×#1202—24no—
123C2×#1202—24no—
124C2×#1202—24no—
125C2×#1202C2314yes—
126C2×#1202C2314yes—
127C2×#1202C2314yescomplemented
128C2×#1201—24no—
129C2×#1201C2314yes—
130C2×#1200—24no—
131C2×#1200C2314yes—
132C2×D3×Dic5—24no—
133C2×D3×Dic5C2314yes—
134C2×D5×Dic3—24no—
135C2×D5×Dic3D418yescomplemented
136C2×D5×Dic3C2314yes—
137C2×D5×Dic3C2314yescomplemented
138C4×D3×D5—232no—
139#6766—232no—
140C3×C5×C4⋊C4C2314yescomplemented
141#6714C2314yes—
142#6714C2314yescomplemented
143C4×Dic15C2314yescomplemented
144C5×(C2×D3)⋊C4C2314yes—
145C5×(C2×D3)⋊C4C2314yes—
146C5×Dic3⋊C4C2314yescomplemented
147C5×Dic3⋊C4C2314yescomplemented
148C3×#685C2314yes—
149C3×#685C2314yescomplemented
150C3×#685C2314yescomplemented
151C3×#683C2314yescomplemented
152Dic3⋊Dic5C2314yescomplemented
153#6669C2314yescomplemented
154#6667C2314yes—
155#6667C2314yescomplemented
156#6665C2314yes—
157Dic3×Dic5C2314yescomplemented
158C22×#237—51no—
159C23×C4×D3—51no—
160C2×C3×#123—51no—
161C2×#937—51no—
162C2×#929—51no—
163#5656—516no—
164C2×#896—51no—
165C2×#896D511yescharacteristic, complemented
166C2×#893—51no—
167C2×#893—51no—
168C2×#884—51no—
169C2×#884—51no—
170C2×#882—51no—
171C2×#67⋊C4—51no—
172C2×#67⋊C4—51no—
173C2×#877—51no—
174C24×D5—31no—
175C22×C5×Q8—31no—
176C23×C4×C5—31no—
177C22×C22⋊D5—31no—
178C22×C22⋊D5—31no—
179C23×Dic5—31no—
180C2×#713—38no—
181C2×#713—68no—
182C22×D20—31no—
183C22×D20—31no—
184C22×D20—31no—
185C22×D20—31no—
186C22×D20C2×D311yescharacteristic
187C22×C4×D5—31no—
188C22×C4×D5—31no—
189C22×C4×D5—31no—
190C22×C4×D5—31no—
191C22×C4×D5—31no—
192C22×C4×D5—38no—
193C22×C4×D5—68no—
194C22×C4×D5C2×D311yescharacteristic
195C5×C22⋊Q8—38no—
196C2×C5×C4⋊C4—31no—
197C2×C5×C4⋊C4—31no—
198C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
199C2×C5×C22⋊C4—31no—
200C2×C5×C22⋊C4—31no—
201#4092—38no—
202#4076—38no—
203C2×#685—31no—
204C2×#685—31no—
205C2×#685—31no—
206C2×#685—31no—
207C2×#685—31no—
208C2×#685C2×D311yescharacteristic
209C2×#685C2×D311yescharacteristic, complemented
210C2×#685C2×D311yescharacteristic, complemented
211C2×C4⋊Dic5—31no—
212C2×#683—31no—
213C2×#683C2×D311yescharacteristic, complemented
214C2×C4×Dic5—31no—
215C2×C4×Dic5—31no—
216#4041—38no—
217#4040—38no—
218#4040C2×D318yescomplemented
219#4039—38no—
220#4039—38no—
221#4038—38no—
222#4028—38no—
223#4028—38no—
224#4027—38no—
225#4027—38no—
226C2×#525—151noSylow
227C23×C3×C5C2411yescharacteristic
228C22×D15—22no—
229C22×D15—22no—
230C22×D15—22no—
231C22×D15—22no—
232C22×D15—22no—
233C22×D15#4114yescomplemented
234C22×D15C2412yes—
235C22×D15C2412yes—
236C22×C5×D3—22no—
237C22×C5×D3—22no—
238C22×C5×D3#4114yescomplemented
239C22×C5×D3C2412yes—
240C22×C3×D5—22no—
241C22×C3×D5—22no—
242C22×C3×D5—22no—
243C22×C3×D5—22no—
244C22×C3×D5—22no—
245C22×C3×D5C2×D414yes—
246C22×C3×D5C2412yes—
247C22×C3×D5C2412yes—
248C2×D3×D5—232no—
249C2×D3×D5—28no—
250C2×D3×D5—28no—
251C2×D3×D5—28no—
252C2×C3×C4×C5—22no—
253C2×C3×C4×C5—22no—
254C2×C3×C4×C5—22no—
255C2×C3×C4×C5C2412yes—
256C2×C3×C4×C5C2412yes—
257C2×C3×C4×C5C2412yes—
258C2×Dic15—22no—
259C2×Dic15C2×D414yes—
260C2×Dic15C2412yes—
261C2×Dic15C2412yes—
262D60—28no—
263C4×D15—28no—
264C4×D15—28no—
265C2×C5×Dic3—22no—
266C2×C5×Dic3—22no—
267C2×C5×Dic3C2×D414yes—
268C2×C5×Dic3C2412yes—
269C2×C5×Dic3C2412yes—
270C2×C5×Dic3C2412yes—
271C4×C5×D3—28no—
272C5×Dic6—28no—
273C2×C3×Dic5—22no—
274C2×C3×Dic5—22no—
275C2×C3×Dic5C2412yes—
276C2×C3×Dic5C2412yes—
277C3×D20—28no—
278C3×C4×D5—28no—
279#1203—28no—
280#1202—28no—
281#1202—28no—
282#1202—28no—
283#1201—28no—
284#1200—28no—
285D3×Dic5—28no—
286D5×Dic3—28no—
287D5×Dic3C2×D4116yescomplemented
288C24×D3—51no—
289C22×C3×D4—51no—
290C23×C3×C4—51no—
291C22×#67—51no—
292C22×#67—51no—
293C22×#67—51no—
294C22×#67—51no—
295C23×Dic3—51no—
296C23×Dic3—51no—
297C2×#237—58no—
298C2×#237—108no—
299C22×D12—51no—
300C22×D12—51no—
301C22×C4×D3—51no—
302C22×C4×D3—51no—
303C22×C4×D3—51no—
304C22×C4×D3—51no—
305C22×C4×D3—58no—
306C22×C4×D3—108no—
307C22×C4×D3C2×D511yescharacteristic
308C22×Dic6C2×D511yescharacteristic, complemented
309C3×#123—58no—
310C2×C3×C4⋊C4—51no—
311C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
312C2×C3×C22⋊C4—51no—
313C2×C3×C22⋊C4—51no—
314C2×C3×C22⋊C4—51no—
315C2×#217—51no—
316#937—58no—
317#929—58no—
318C2×(C2×D3)⋊C4—51no—
319C2×(C2×D3)⋊C4—51no—
320C2×(C2×D3)⋊C4—51no—
321C2×(C2×D3)⋊C4—51no—
322C2×(C2×D3)⋊C4C2×D511yescharacteristic
323C2×(C2×D3)⋊C4C2×D511yescharacteristic
324C2×Dic3⋊C4—51no—
325C2×Dic3⋊C4—51no—
326C2×Dic3⋊C4C2×D511yescharacteristic, complemented
327C2×Dic3⋊C4C2×D511yescharacteristic, complemented
328C2×C4×Dic3—51no—
329C2×C4×Dic3—51no—
330#896—58no—
331#896C2×D518yescomplemented
332#893—58no—
333#893—58no—
334#884—58no—
335#884—58no—
336#882—58no—
337#67⋊C4—58no—
338#67⋊C4—58no—
339#877—58no—
340C24×C5—31no—
341C23×D5—31no—
342C23×D5—31no—
343C23×D5—34no—
344C23×D5—64no—
345C23×D5—64no—
346C23×D5—64no—
347C23×D5C22×D311yescharacteristic
348C23×D5C22×D311yescharacteristic
349C2×C5×Q8—34no—
350C2×C5×Q8—64no—
351C22×C4×C5—31no—
352C22×C4×C5—31no—
353C22×C4×C5—31no—
354C22×C4×C5—34no—
355C22×C4×C5—64no—
356C22×C4×C5C22×D311yescharacteristic
357C22×C4×C5C22×D311yescharacteristic
358C22×C4×C5C22×D311yescharacteristic
359C2×C22⋊D5—34no—
360C2×C22⋊D5—34no—
361C2×C22⋊D5—64no—
362C2×C22⋊D5—64no—
363C22×Dic5—31no—
364C22×Dic5—31no—
365C22×Dic5—34no—
366C22×Dic5—64no—
367C22×Dic5C22×D311yescharacteristic
368C22×Dic5C22×D311yescharacteristic
369#713—632no—
370C2×D20—24no—
371C2×D20—34no—
372C2×D20—34no—
373C2×D20—34no—
374C2×D20—34no—
375C2×D20—64no—
376C2×D20—64no—
377C2×D20—64no—
378C2×D20—64no—
379C2×D20C22×D314yes—
380C2×C4×D5—24no—
381C2×C4×D5—38no—
382C2×C4×D5—34no—
383C2×C4×D5—34no—
384C2×C4×D5—34no—
385C2×C4×D5—34no—
386C2×C4×D5—34no—
387C2×C4×D5—632no—
388C2×C4×D5—64no—
389C2×C4×D5—64no—
390C2×C4×D5—64no—
391C2×C4×D5—64no—
392C2×C4×D5C22×D314yes—
393C5×C4⋊C4—34no—
394C5×C4⋊C4—34no—
395C5×C4⋊C4C22×D314yescomplemented
396C5×C22⋊C4—34no—
397C5×C22⋊C4—34no—
398#685—34no—
399#685—34no—
400#685—34no—
401#685—34no—
402#685—34no—
403#685C22×D314yes—
404#685C22×D314yescomplemented
405#685C22×D314yescomplemented
406C4⋊Dic5—34no—
407#683—34no—
408#683C22×D314yescomplemented
409C4×Dic5—34no—
410C4×Dic5—34no—
411C22×#41—151no—
412C24×C4—151no—
413#525—1516no—
414C2×#123—51no—
415C2×#123—151no—
416C2×C22⋊Q8—31no—
417C2×C22⋊Q8—151no—
418C2×#121—151no—
419C2×#121—151no—
420C2×#120—151no—
421C2×#120—151no—
422C2×C4×D4—151no—
423C2×C4×D4—151no—
424C2×C4×D4—151no—
425C2×C4×D4—151no—
426C2×#117—151no—
427C22×C3×C5C22×D412yes—
428C22×C3×C5C2×#4112yes—
429C22×C3×C5C2×#4112yes—
430C22×C3×C5C2511yescharacteristic
431C2×D15—28no—
432C2×D15—22no—
433C2×D15—22no—
434C2×D15—22no—
435C2×D15—22no—
436C2×D15—22no—
437C2×D15—44no—
438C2×D15C2×#4114yescomplemented
439C2×C5×D3—28no—
440C2×C5×D3—22no—
441C2×C5×D3—22no—
442C2×C5×D3C2×#4114yescomplemented
443C2×C3×D5—28no—
444C2×C3×D5—22no—
445C2×C3×D5—22no—
446C2×C3×D5—22no—
447C2×C3×D5—22no—
448C2×C3×D5—22no—
449C2×C3×D5—44no—
450C2×C3×D5C22×D414yes—
451D3×D5—232no—
452C3×C4×C5—22no—
453C3×C4×C5—22no—
454C3×C4×C5—22no—
455Dic15—22no—
456Dic15C22×D414yes—
457C3×Dic5—22no—
458C3×Dic5—22no—
459C5×Dic3—22no—
460C5×Dic3—22no—
461C5×Dic3C22×D414yes—
462C24×C3—51no—
463C24×C3—51no—
464C23×D3—51no—
465C23×D3—51no—
466C23×D3—54no—
467C23×D3—104no—
468C23×D3—104no—
469C23×D3—104no—
470C23×D3C22×D511yescharacteristic
471C2×C3×D4—54no—
472C2×C3×D4—104no—
473C22×C3×C4—51no—
474C22×C3×C4—51no—
475C22×C3×C4—54no—
476C22×C3×C4—104no—
477C22×C3×C4C22×D511yescharacteristic
478C22×C3×C4C22×D511yescharacteristic
479C22×C3×C4C22×D511yescharacteristic
480C2×#67—54no—
481C2×#67—54no—
482C2×#67—54no—
483C2×#67—54no—
484C2×#67—104no—
485C2×#67—104no—
486C2×#67—104no—
487C2×#67—104no—
488C22×Dic3—51no—
489C22×Dic3—58no—
490C22×Dic3—54no—
491C22×Dic3—51no—
492C22×Dic3—54no—
493C22×Dic3—104no—
494C22×Dic3C22×D511yescharacteristic
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D511yescharacteristic
497#237—1032no—
498C2×D12—54no—
499C2×D12—54no—
500C2×D12—104no—
501C2×D12—104no—
502C2×C4×D3—24no—
503C2×C4×D3—54no—
504C2×C4×D3—54no—
505C2×C4×D3—54no—
506C2×C4×D3—54no—
507C2×C4×D3—1032no—
508C2×C4×D3—104no—
509C2×C4×D3—104no—
510C2×C4×D3—104no—
511C2×C4×D3—104no—
512C2×C4×D3C22×D514yes—
513C2×Dic6—24no—
514C2×Dic6C22×D514yescomplemented
515C3×C4⋊C4—54no—
516C3×C4⋊C4C22×D514yescomplemented
517C3×C22⋊C4—54no—
518C3×C22⋊C4—54no—
519C3×C22⋊C4—54no—
520#217—54no—
521(C2×D3)⋊C4—54no—
522(C2×D3)⋊C4—54no—
523(C2×D3)⋊C4—54no—
524(C2×D3)⋊C4—54no—
525(C2×D3)⋊C4C22×D514yes—
526(C2×D3)⋊C4C22×D514yes—
527Dic3⋊C4—54no—
528Dic3⋊C4—54no—
529Dic3⋊C4C22×D514yescomplemented
530Dic3⋊C4C22×D514yescomplemented
531C4×Dic3—54no—
532C4×Dic3—54no—
533C23×C5—34no—
534C23×C5—32no—
535C23×C5—62no—
536C23×C5—62no—
537C23×C5C23×D311yescharacteristic
538C22×D5—22no—
539C22×D5—22no—
540C22×D5—22no—
541C22×D5—22no—
542C22×D5—22no—
543C22×D5—34no—
544C22×D5—32no—
545C22×D5—32no—
546C22×D5—68no—
547C22×D5—68no—
548C22×D5—632no—
549C22×D5—62no—
550C22×D5—62no—
551C22×D5—68no—
552C22×D5—62no—
553C22×D5—62no—
554C22×D5—62no—
555C22×D5D3×D414yes—
556C22×D5C23×D312yes—
557C22×D5C23×D312yes—
558C5×Q8—68no—
559C2×C4×C5—22no—
560C2×C4×C5—22no—
561C2×C4×C5—22no—
562C2×C4×C5—34no—
563C2×C4×C5—32no—
564C2×C4×C5—32no—
565C2×C4×C5—32no—
566C2×C4×C5—68no—
567C2×C4×C5—62no—
568C2×C4×C5—62no—
569C2×C4×C5C23×D312yes—
570C2×C4×C5C23×D312yes—
571C2×C4×C5C23×D312yes—
572C22⋊D5—68no—
573C22⋊D5—68no—
574C2×Dic5—22no—
575C2×Dic5—22no—
576C2×Dic5—34no—
577C2×Dic5—32no—
578C2×Dic5—32no—
579C2×Dic5—68no—
580C2×Dic5—62no—
581C2×Dic5C23×D312yes—
582C2×Dic5C23×D312yes—
583D20—28no—
584D20—68no—
585D20—68no—
586D20—68no—
587D20—68no—
588C4×D5—28no—
589C4×D5—316no—
590C4×D5—68no—
591C4×D5—68no—
592C4×D5—68no—
593C4×D5—68no—
594C25—151no—
595C2×#41—158no—
596C2×#41—308no—
597C22×Q8—31no—
598C22×D4—51no—
599C22×D4—151no—
600C22×D4—151no—
601C22×D4—151no—
602C22×D4—151no—
603C22×D4—151no—
604C22×D4—151no—
605C23×C4—31no—
606C23×C4—51no—
607C23×C4—151no—
608C23×C4—158no—
609C23×C4—151no—
610C23×C4—151no—
611C23×C4—151no—
612C23×C4—151no—
613C23×C4—151no—
614C23×C4—308no—
615#123—58no—
616#123—158no—
617C22⋊Q8—38no—
618C22⋊Q8—158no—
619#121—158no—
620#121—158no—
621#120—158no—
622#120—158no—
623C4×D4—158no—
624C4×D4—158no—
625C4×D4—158no—
626C4×D4—158no—
627#117—158no—
628C2×C4⋊C4—31no—
629C2×C4⋊C4—31no—
630C2×C4⋊C4—51no—
631C2×C4⋊C4—151no—
632C2×C4⋊C4—151no—
633C2×C4⋊C4D3×D511yescharacteristic, complemented
634C2×C22⋊C4—31no—
635C2×C22⋊C4—31no—
636C2×C22⋊C4—51no—
637C2×C22⋊C4—51no—
638C2×C22⋊C4—51no—
639C2×C22⋊C4—151no—
640C2×C22⋊C4—151no—
641C2×C22⋊C4—151no—
642C2×C22⋊C4—151no—
643C2×C22⋊C4—151no—
644C2×C42—151no—
645C2×C42—151no—
646C2×C3×C5#52514yescomplemented
647C2×C3×C5C23×D411yescharacteristic
648C2×C3×C5C22×#4111yescharacteristic
649C2×C3×C5C22×#4111yescharacteristic
650D15—24no—
651D15—42no—
652C3×D5—24no—
653C3×D5—42no—
654C5×D3—24no—
655C23×C3—54no—
656C23×C3—52no—
657C23×C3—52no—
658C23×C3—102no—
659C23×C3—102no—
660C23×C3—102no—
661C23×C3—102no—
662C23×C3—102no—
663C23×C3C23×D511yescharacteristic
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—54no—
667C22×D3—52no—
668C22×D3—52no—
669C22×D3—108no—
670C22×D3—108no—
671C22×D3—1032no—
672C22×D3—102no—
673C22×D3—102no—
674C22×D3—108no—
675C22×D3—102no—
676C22×D3—102no—
677C22×D3—102no—
678C22×D3#71314yescomplemented
679C22×D3C23×D512yes—
680C3×D4—108no—
681C2×C3×C4—22no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—52no—
685C2×C3×C4—52no—
686C2×C3×C4—108no—
687C2×C3×C4—102no—
688C2×C3×C4—102no—
689C2×C3×C4C23×D512yes—
690C2×C3×C4C23×D512yes—
691C2×C3×C4C23×D512yes—
692#67—108no—
693#67—108no—
694#67—108no—
695#67—108no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—54no—
699C2×Dic3—52no—
700C2×Dic3—516no—
701C2×Dic3—52no—
702C2×Dic3—108no—
703C2×Dic3—102no—
704C2×Dic3D4×D514yes—
705C2×Dic3C23×D512yes—
706C2×Dic3C23×D512yes—
707C2×Dic3C23×D512yes—
708D12—108no—
709D12—108no—
710C4×D3—28no—
711C4×D3—108no—
712C4×D3—108no—
713C4×D3—108no—
714C4×D3—108no—
715Dic6—28no—
716C22×C5—34no—
717C22×C5—68no—
718C22×C5—62no—
719C22×C5—62no—
720C22×C5C2×D3×D412yes—
721C22×C5D3×#4112yes—
722C22×C5D3×#4112yes—
723C22×C5C24×D311yescharacteristic
724C2×D5—28no—
725C2×D5—22no—
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—34no—
731C2×D5—44no—
732C2×D5—632no—
733C2×D5—68no—
734C2×D5—62no—
735C2×D5—62no—
736C2×D5—62no—
737C2×D5—62no—
738C2×D5—62no—
739C2×D5—124no—
740C2×D5C2×D3×D414yes—
741C4×C5—22no—
742C4×C5—22no—
743C4×C5—22no—
744C4×C5—34no—
745C4×C5—62no—
746C4×C5—62no—
747Dic5—22no—
748Dic5—22no—
749Dic5—34no—
750Dic5—62no—
751C24—31no—
752C24—51no—
753C24—51no—
754C24—154no—
755C24—151no—
756C24—151no—
757C24—304no—
758C24—304no—
759C24—304no—
760#41—3032no—
761C2×Q8—34no—
762C2×Q8—64no—
763C2×D4—54no—
764C2×D4—104no—
765C2×D4—154no—
766C2×D4—154no—
767C2×D4—154no—
768C2×D4—154no—
769C2×D4—154no—
770C2×D4—154no—
771C2×D4—304no—
772C2×D4—304no—
773C2×D4—304no—
774C2×D4—304no—
775C2×D4—304no—
776C2×D4—304no—
777C22×C4—31no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—34no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—54no—
784C22×C4—64no—
785C22×C4—104no—
786C22×C4—154no—
787C22×C4—154no—
788C22×C4—158no—
789C22×C4—154no—
790C22×C4—154no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—154no—
794C22×C4—154no—
795C22×C4—304no—
796C22×C4—304no—
797C22×C4—304no—
798C22×C4—3032no—
799C22×C4—304no—
800C22×C4—304no—
801C22×C4C2×D3×D511yescharacteristic
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—34no—
805C4⋊C4—34no—
806C4⋊C4—54no—
807C4⋊C4—154no—
808C4⋊C4—154no—
809C4⋊C4C2×D3×D514yescomplemented
810C22⋊C4—34no—
811C22⋊C4—34no—
812C22⋊C4—54no—
813C22⋊C4—54no—
814C22⋊C4—54no—
815C22⋊C4—154no—
816C22⋊C4—154no—
817C22⋊C4—154no—
818C22⋊C4—154no—
819C22⋊C4—154no—
820C42—154no—
821C42—154no—
822C3×C5C2×#52511yescharacteristic, complemented, Hall
823C22×C3—54no—
824C22×C3—108no—
825C22×C3—102no—
826C22×C3—102no—
827C22×C3—102no—
828C22×C3—102no—
829C22×C3—102no—
830C22×C3—204no—
831C22×C3C2×D4×D512yes—
832C22×C3C2×#71312yes—
833C22×C3D5×#4112yes—
834C22×C3C24×D511yescharacteristic
835C2×D3—28no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—54no—
839C2×D3—1032no—
840C2×D3—108no—
841C2×D3—102no—
842C2×D3—102no—
843C2×D3—102no—
844C2×D3—102no—
845C2×D3—102no—
846C2×D3—204no—
847C2×D3C2×#71314yescomplemented
848C3×C4—22no—
849C3×C4—22no—
850C3×C4—22no—
851C3×C4—102no—
852C3×C4—102no—
853Dic3—22no—
854Dic3—22no—
855Dic3—54no—
856Dic3—102no—
857Dic3C2×D4×D514yes—
858C2×C5—64no—
859C2×C5#565614yescomplemented
860C2×C5C22×D3×D411yescharacteristic
861C2×C5C2×D3×#4111yescharacteristic
862C2×C5C2×D3×#4111yescharacteristic
863D5—24no—
864D5—42no—
865D5—64no—
866D5—122no—
867C23—34no—
868C23—32no—
869C23—54no—
870C23—52no—
871C23—52no—
872C23—62no—
873C23—62no—
874C23—102no—
875C23—102no—
876C23—102no—
877C23—102no—
878C23—102no—
879C23—154no—
880C23—152no—
881C23—152no—
882C23—308no—
883C23—308no—
884C23—308no—
885C23—3032no—
886C23—302no—
887C23—302no—
888C23—302no—
889C23—302no—
890C23—302no—
891C23C22×D3×D511yescharacteristic
892Q8—68no—
893D4—108no—
894D4—308no—
895D4—308no—
896D4—308no—
897D4—308no—
898D4—308no—
899D4—308no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—34no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—52no—
908C2×C4—52no—
909C2×C4—68no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—108no—
913C2×C4—102no—
914C2×C4—102no—
915C2×C4—1516no—
916C2×C4—154no—
917C2×C4—152no—
918C2×C4—152no—
919C2×C4—308no—
920C2×C4—308no—
921C2×C4—308no—
922C2×C4—308no—
923C2×C4—308no—
924C2×C4—302no—
925C2×C4C22×D3×D512yes—
926C2×C4C22×D3×D512yes—
927C2×C4C22×D3×D512yes—
928C2×C3—104no—
929C2×C3—202no—
930C2×C3#6596114yescomplemented
931C2×C3C22×D4×D511yescharacteristic
932C2×C3C22×#71311yescharacteristic
933C2×C3C2×D5×#4111yescharacteristic
934D3—24no—
935D3—104no—
936D3—202no—
937C5C2×#565611yescharacteristic, complemented, Sylow
938C22—34no—
939C22—54no—
940C22—68no—
941C22—62no—
942C22—62no—
943C22—108no—
944C22—102no—
945C22—102no—
946C22—102no—
947C22—102no—
948C22—102no—
949C22—154no—
950C22—204no—
951C22—3032no—
952C22—308no—
953C22—302no—
954C22—302no—
955C22—302no—
956C22—302no—
957C22—302no—
958C22—604no—
959C22#9201612yes—
960C22D3×D4×D512yes—
961C22D3×#71312yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—22no—
966C4—34no—
967C4—62no—
968C4—62no—
969C4—102no—
970C4—102no—
971C4—154no—
972C4—302no—
973C3C2×#6596111yescharacteristic, complemented, Sylow
974C2—64no—
975C2—104no—
976C2—202no—
977C2—304no—
978C2—602no—
979C2#1175385314yesdirect product factor
980C2C2×#9201611yescharacteristic
981C2C2×D3×D4×D511yescharacteristic
982C2C2×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×#525
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×C4×D3×D5C2semidirect
2. C22×#6766C2semidirect
3. C2×#91782C2semidirect
4. C2×C5×#896C2semidirect
5. C2×C3×#4040C2semidirect
6. C2×#91476C2semidirect
7. C2×#91474C2semidirect
8. C2×#91459C2semidirect
9. C2×#91454C2semidirect
10. C2×#91442C2semidirect
11. C2×#91424C2semidirect
12. C2×#91406C2semidirect
13. C2×#91396C2semidirect
14. C2×#91394C2semidirect
15. C2×#91348C2semidirect
16. #11753853C2direct (N × H)
21. C22×C4×D15C22semidirect
23. C22×C5×Dic6C22semidirect
29. C22×#1202C22semidirect
34. C22×D5×Dic3C22semidirect
36. C2×C4×D3×D5C22semidirect
38. C2×#6766C22semidirect
39. C2×C3×C5×C4⋊C4C22semidirect
41. C2×#6714C22semidirect
42. C2×C4×Dic15C22semidirect
43. #91782C22semidirect
46. C2×C5×Dic3⋊C4C22semidirect
47. C2×C5×Dic3⋊C4C22semidirect
48. C5×#896C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×#685C22semidirect
52. C2×C3×#683C22semidirect
53. C3×#4040C22semidirect
54. C2×Dic3⋊Dic5C22semidirect
55. C2×#6669C22semidirect
57. C2×#6667C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91476C22semidirect
61. #91474C22semidirect
62. #91459C22semidirect
63. #91454C22semidirect
64. #91442C22semidirect
65. #91424C22semidirect
66. #91406C22semidirect
67. #91396C22semidirect
68. #91394C22semidirect
69. #91348C22semidirect
79. C2×#4040D3semidirect
106. C2×C4×D15C23semidirect
113. C2×C5×Dic6C23semidirect
127. C2×#1202C23semidirect
135. C2×D5×Dic3D4semidirect
137. C2×D5×Dic3C23semidirect
140. C3×C5×C4⋊C4C23semidirect
142. #6714C23semidirect
143. C4×Dic15C23semidirect
146. C5×Dic3⋊C4C23semidirect
147. C5×Dic3⋊C4C23semidirect
149. C3×#685C23semidirect
150. C3×#685C23semidirect
151. C3×#683C23semidirect
152. Dic3⋊Dic5C23semidirect
153. #6669C23semidirect
155. #6667C23semidirect
157. Dic3×Dic5C23semidirect
165. C2×#896D5semidirect
198. C2×C5×C4⋊C4C2×D3semidirect
209. C2×#685C2×D3semidirect
210. C2×#685C2×D3semidirect
213. C2×#683C2×D3semidirect
218. #4040C2×D3semidirect
233. C22×D15#41semidirect
238. C22×C5×D3#41semidirect
287. D5×Dic3C2×D4semidirect
308. C22×Dic6C2×D5semidirect
311. C2×C3×C4⋊C4C2×D5semidirect
326. C2×Dic3⋊C4C2×D5semidirect
327. C2×Dic3⋊C4C2×D5semidirect
331. #896C2×D5semidirect
395. C5×C4⋊C4C22×D3semidirect
404. #685C22×D3semidirect
405. #685C22×D3semidirect
408. #683C22×D3semidirect
438. C2×D15C2×#41semidirect
442. C2×C5×D3C2×#41semidirect
514. C2×Dic6C22×D5semidirect
516. C3×C4⋊C4C22×D5semidirect
529. Dic3⋊C4C22×D5semidirect
530. Dic3⋊C4C22×D5semidirect
633. C2×C4⋊C4D3×D5semidirect
646. C2×C3×C5#525semidirect
678. C22×D3#713semidirect
809. C4⋊C4C2×D3×D5semidirect
822. C3×C5C2×#525semidirect
847. C2×D3C2×#713semidirect
859. C2×C5#5656semidirect
930. C2×C3#65961semidirect
937. C5C2×#5656semidirect
973. C3C2×#65961semidirect
979. C2#11753853direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D3×D52
C22×#67662
C2×#917822
C2×C5×#8962
C2×C3×#40402
C2×#914762
C2×#914742
C2×#914592
C2×#914542
C2×#914422
C2×#914242
C2×#914062
C2×#913962
C2×#913942
C2×#913482
#117538532
C2×#659613
C2×#56565