Finite Group Databasebeta

← C2×#11754767 #14479584

Subgroups — C2×#11754767 #14479584

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×#6782C211yesmaximal, characteristic, complemented
2C23×D3×Dic5C211yesmaximal, characteristic, complemented
3C2×#91828C211yesmaximal, characteristic, complemented
4C2×C5×#937C211yesmaximal, characteristic, complemented
5C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
6C2×#91576C211yesmaximal, characteristic, complemented
7C2×#91570C211yesmaximal, characteristic, complemented
8C2×#91558C211yesmaximal, characteristic, complemented
9C2×#91555C211yesmaximal, characteristic, complemented
10C2×#91552C211yesmaximal, characteristic, complemented
11C2×Dic5×#67C211yesmaximal, characteristic, complemented
12#11754767C2116yesmaximal, direct product factor
13C2×#91436C211yesmaximal, characteristic, complemented
14C2×#91427C211yesmaximal, characteristic, complemented
15C2×#91405C211yesmaximal, characteristic, complemented
16C2×#91398C211yesmaximal, characteristic, complemented
17C2×#65920—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic, complemented
22C23×Dic15C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic
24C22×C5×#67C2211yescharacteristic
25C23×C3×Dic5C2211yescharacteristic
26C23×C3×Dic5C2211yescharacteristic, complemented
27C22×#1204C2211yescharacteristic, complemented
28C22×#1203C2211yescharacteristic
29C22×#1203C2211yescharacteristic
30C22×#1200C2211yescharacteristic, complemented
31C2×#6782—28no—
32C2×#6782C2218yescomplemented
33C22×D3×Dic5—28no—
34C22×D3×Dic5C2211yescharacteristic
35C22×D3×Dic5C2211yescharacteristic
36C22×D3×Dic5C2211yescharacteristic
37C22×D3×Dic5C2211yescharacteristic
38C22×D3×Dic5C2218yescomplemented
39C2×#6719C2211yescharacteristic, complemented
40#91828C2218yescomplemented
41C2×#6714C2211yescharacteristic, complemented
42C2×#6712C2211yescharacteristic, complemented
43C2×C5×#217C2211yescharacteristic
44C5×#937C2218yescomplemented
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×C22⋊Dic5C2211yescharacteristic
48C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
49C3×D4×Dic5C2218yescomplemented
50C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
51C2×C3×C4×Dic5C2211yescharacteristic, complemented
52#91576C2218yescomplemented
53#91570C2218yescomplemented
54#91558C2218yescomplemented
55#91555C2218yescomplemented
56#91552C2218yescomplemented
57Dic5×#67C2218yescomplemented
58C2×Dic3⋊Dic5C2211yescharacteristic, complemented
59C2×#6669C2211yescharacteristic, complemented
60C2×#6669C2211yescharacteristic, complemented
61C2×#6668C2211yescharacteristic, complemented
62C2×#6667C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic5C2211yescharacteristic
64C2×(C2×D3)⋊Dic5C2211yescharacteristic
65C2×Dic3×Dic5C2211yescharacteristic, complemented
66#91436C2218yescomplemented
67#91427C2218yescomplemented
68#91405C2218yescomplemented
69#91398C2218yescomplemented
70C2×#5547—51nomaximal, Hall
71C24×Dic5—31no—
72C22×#711—31no—
73C2×C5×#120—31no—
74C2×#4099—31no—
75C2×#4085—31no—
76C2×#4085—31no—
77C2×#4081—31no—
78C2×D4×Dic5—31no—
79C2×D4×Dic5D311yescharacteristic, complemented
80#65920—316no—
81C2×#4032—31no—
82C2×#4027—31no—
83C2×#4027—31no—
84C2×#4024—31no—
85C2×#4024—31no—
86C2×#4023—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3—24no—
91C23×C5×D3—24no—
92C23×C5×D3—24no—
93C23×C5×D3C2314yes—
94C23×C5×D3C2311yescharacteristic
95C23×C5×D3C2311yescharacteristic
96C2×C3×C5×D4—24no—
97C2×C3×C5×D4C2314yes—
98C22×C3×C4×C5C2311yescharacteristic
99C2×#1220—24no—
100C2×#1220—24no—
101C2×#1220C2314yes—
102C2×#1220C2314yescomplemented
103C22×Dic15—24no—
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2314yes—
107C22×Dic15C2311yescharacteristic
108C2×C5×#67—24no—
109C2×C5×#67—24no—
110C2×C5×#67C2314yes—
111C2×C5×#67C2314yes—
112C22×C5×Dic3C2311yescharacteristic
113C22×C5×Dic3C2311yescharacteristic
114C22×C3×Dic5—24no—
115C22×C3×Dic5—24no—
116C22×C3×Dic5C2314yes—
117C22×C3×Dic5C2311yescharacteristic
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2311yescharacteristic
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2314yescomplemented
122C2×#1204—24no—
123C2×#1204C2314yescomplemented
124C2×#1203—24no—
125C2×#1203—24no—
126C2×#1203C2314yes—
127C2×#1203C2314yes—
128C2×#1200—24no—
129C2×#1200C2314yescomplemented
130#6782—232no—
131C2×D3×Dic5—24no—
132C2×D3×Dic5—24no—
133C2×D3×Dic5—24no—
134C2×D3×Dic5—232no—
135C2×D3×Dic5D418yescomplemented
136C2×D3×Dic5C2314yes—
137C2×D3×Dic5C2314yes—
138C2×D3×Dic5C2314yes—
139C2×D3×Dic5C2314yes—
140#6719C2314yescomplemented
141#6714C2314yescomplemented
142#6712C2314yescomplemented
143C5×#217C2314yes—
144C5×(C2×D3)⋊C4C2314yes—
145C5×(C2×D3)⋊C4C2314yes—
146C3×C22⋊Dic5C2314yes—
147C3×C22⋊Dic5C2314yescomplemented
148C3×C4⋊Dic5C2314yescomplemented
149C3×C4×Dic5C2314yescomplemented
150Dic3⋊Dic5C2314yescomplemented
151#6669C2314yescomplemented
152#6669C2314yescomplemented
153#6668C2314yescomplemented
154#6667C2314yescomplemented
155(C2×D3)⋊Dic5C2314yes—
156(C2×D3)⋊Dic5C2314yes—
157Dic3×Dic5C2314yescomplemented
158C22×#235—51no—
159C23×C4×D3—51no—
160C2×C3×C4×D4—51no—
161C2×#939—51no—
162C2×#937D511yescharacteristic, complemented
163C2×C4×#67—51no—
164C2×C4×#67—51no—
165#5547—516no—
166C2×#896—51no—
167C2×#894—51no—
168C2×#884—51no—
169C2×#883—51no—
170C2×#882—51no—
171C2×#878—51no—
172C2×C4×D12—51no—
173C2×#872—51no—
174C25×C5—31no—
175C22×C5×D4—31no—
176C22×C5×D4—31no—
177C22×C5×D4C2×D311yescharacteristic
178C22×C22⋊D5—31no—
179C22×C22⋊D5—31no—
180C22×C22⋊D5—31no—
181C22×C22⋊D5—31no—
182C23×Dic5—31no—
183C23×Dic5—31no—
184C23×Dic5—31no—
185C23×Dic5—31no—
186C23×Dic5—31no—
187C23×Dic5—38no—
188C23×Dic5—68no—
189C23×Dic5C2×D311yescharacteristic
190C23×Dic5C2×D311yescharacteristic, complemented
191C2×#711—38no—
192C2×#711—68no—
193C22×C4×D5—31no—
194C22×Dic10—31no—
195C5×#120—38no—
196C2×C5×C22⋊C4—31no—
197C2×C5×C22⋊C4—31no—
198C2×C5×C22⋊C4—31no—
199#4099—38no—
200C2×C22⋊Dic5—31no—
201C2×C22⋊Dic5—31no—
202C2×C22⋊Dic5—31no—
203C2×C22⋊Dic5C2×D311yescharacteristic
204C2×C22⋊Dic5C2×D311yescharacteristic, complemented
205#4085—38no—
206#4085—38no—
207#4081—38no—
208D4×Dic5—38no—
209D4×Dic5C2×D318yescomplemented
210C2×#685—31no—
211C2×#685—31no—
212C2×C4⋊Dic5—31no—
213C2×C4⋊Dic5C2×D311yescharacteristic, complemented
214C2×#683—31no—
215C2×#683—31no—
216C2×#683—31no—
217C2×#683—31no—
218C2×C4×Dic5—31no—
219C2×C4×Dic5C2×D311yescharacteristic, complemented
220#4032—38no—
221#4027—38no—
222#4027—38no—
223#4024—38no—
224#4024—38no—
225#4023—38no—
226C2×#525—151noSylow
227C23×C3×C5—22no—
228C23×C3×C5—22no—
229C23×C3×C5—22no—
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5#4114yescomplemented
233C23×C3×C5C2412yes—
234C23×C3×C5C2412yes—
235C23×C3×C5C2411yescharacteristic
236C22×D15—22no—
237C22×D15—22no—
238C22×D15—22no—
239C22×D15C2412yes—
240C22×C5×D3—232no—
241C22×C5×D3—22no—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—28no—
246C22×C5×D3—28no—
247C22×C5×D3—28no—
248C22×C5×D3C2×D414yes—
249C22×C5×D3#4114yescomplemented
250C22×C5×D3C2412yes—
251C22×C5×D3C2412yes—
252C3×C5×D4—28no—
253C2×C3×C4×C5—22no—
254C2×C3×C4×C5C2412yes—
255#1220—28no—
256#1220—28no—
257C2×Dic15—22no—
258C2×Dic15—22no—
259C2×Dic15—28no—
260C2×Dic15C2×D414yes—
261C2×Dic15C2412yes—
262C2×Dic15C2412yes—
263C2×Dic15C2412yes—
264C5×#67—28no—
265C5×#67—28no—
266C2×C5×Dic3—22no—
267C2×C5×Dic3—22no—
268C2×C5×Dic3C2412yes—
269C2×C5×Dic3C2412yes—
270C2×C3×Dic5—22no—
271C2×C3×Dic5—22no—
272C2×C3×Dic5—22no—
273C2×C3×Dic5—28no—
274C2×C3×Dic5—28no—
275C2×C3×Dic5C2×D414yes—
276C2×C3×Dic5C2412yes—
277C2×C3×Dic5C2412yes—
278C2×C3×Dic5C2412yes—
279C2×C3×Dic5C2412yes—
280#1204—28no—
281#1203—28no—
282#1203—28no—
283#1200—28no—
284D3×Dic5—28no—
285D3×Dic5—28no—
286D3×Dic5—28no—
287D3×Dic5C2×D4116yescomplemented
288C24×D3C2×D511yescharacteristic
289C22×C3×D4C2×D511yescharacteristic
290C23×C3×C4—51no—
291C23×C3×C4—51no—
292C22×#67—51no—
293C22×#67—51no—
294C22×#67C2×D511yescharacteristic
295C22×#67C2×D511yescharacteristic
296C23×Dic3—51no—
297C2×#235—58no—
298C2×#235—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—51no—
307C22×C4×D3—108no—
308C22×Dic6—51no—
309C3×C4×D4—58no—
310C2×C3×C4⋊C4—51no—
311C2×C3×C22⋊C4—51no—
312C2×C3×C22⋊C4—51no—
313C2×C3×C42—51no—
314C2×#217—51no—
315C2×#217C2×D511yescharacteristic
316#939—58no—
317#937C2×D518yescomplemented
318C4×#67—58no—
319C4×#67—58no—
320C2×(C2×D3)⋊C4—51no—
321C2×(C2×D3)⋊C4—51no—
322C2×(C2×D3)⋊C4—51no—
323C2×(C2×D3)⋊C4—51no—
324C2×(C2×D3)⋊C4C2×D511yescharacteristic
325C2×(C2×D3)⋊C4C2×D511yescharacteristic
326C2×C4⋊Dic3—51no—
327C2×Dic3⋊C4—51no—
328C2×Dic3⋊C4—51no—
329C2×Dic3⋊C4—51no—
330C2×Dic3⋊C4—51no—
331C2×C4×Dic3—51no—
332#896—58no—
333#894—58no—
334#884—58no—
335#883—58no—
336#882—58no—
337#878—58no—
338C4×D12—58no—
339#872—58no—
340C24×C5—31no—
341C24×C5—31no—
342C24×C5—34no—
343C24×C5—64no—
344C24×C5—64no—
345C24×C5—64no—
346C24×C5C22×D311yescharacteristic
347C24×C5C22×D311yescharacteristic
348C23×D5—31no—
349C2×C5×D4—24no—
350C2×C5×D4—34no—
351C2×C5×D4—34no—
352C2×C5×D4—64no—
353C2×C5×D4—64no—
354C2×C5×D4C22×D314yes—
355C22×C4×C5—31no—
356C22×C4×C5—31no—
357C22×C4×C5C22×D311yescharacteristic
358C2×C22⋊D5—34no—
359C2×C22⋊D5—34no—
360C2×C22⋊D5—34no—
361C2×C22⋊D5—34no—
362C2×C22⋊D5—64no—
363C2×C22⋊D5—64no—
364C2×C22⋊D5—64no—
365C2×C22⋊D5—64no—
366C22×Dic5—24no—
367C22×Dic5—24no—
368C22×Dic5—31no—
369C22×Dic5—38no—
370C22×Dic5—34no—
371C22×Dic5—31no—
372C22×Dic5—31no—
373C22×Dic5—34no—
374C22×Dic5—34no—
375C22×Dic5—34no—
376C22×Dic5—34no—
377C22×Dic5—64no—
378C22×Dic5—632no—
379C22×Dic5—64no—
380C22×Dic5—64no—
381C22×Dic5—64no—
382C22×Dic5C22×D311yescharacteristic
383C22×Dic5C22×D311yescharacteristic
384C22×Dic5C22×D311yescharacteristic
385C22×Dic5C22×D314yes—
386C22×Dic5C22×D311yescharacteristic
387C22×Dic5C22×D314yescomplemented
388#711—632no—
389C2×C4×D5—34no—
390C2×C4×D5—64no—
391C2×Dic10—34no—
392C2×Dic10—64no—
393C5×C22⋊C4—34no—
394C5×C22⋊C4—34no—
395C5×C22⋊C4—34no—
396C22⋊Dic5—34no—
397C22⋊Dic5—34no—
398C22⋊Dic5—34no—
399C22⋊Dic5C22×D314yes—
400C22⋊Dic5C22×D314yescomplemented
401#685—34no—
402#685—34no—
403C4⋊Dic5—34no—
404C4⋊Dic5C22×D314yescomplemented
405#683—34no—
406#683—34no—
407#683—34no—
408#683—34no—
409C4×Dic5—34no—
410C4×Dic5C22×D314yescomplemented
411C22×#41—151no—
412C24×C4—151no—
413#525—1516no—
414C2×#123—151no—
415C2×#123—151no—
416C2×C22⋊Q8—151no—
417C2×C22⋊Q8—151no—
418C2×#121—151no—
419C2×#121—151no—
420C2×#120—31no—
421C2×#120—151no—
422C2×C4×D4—51no—
423C2×C4×D4—151no—
424C2×C4×D4—151no—
425C2×C4×D4—151no—
426C2×#117—151no—
427C22×C3×C5—28no—
428C22×C3×C5—22no—
429C22×C3×C5—22no—
430C22×C3×C5—22no—
431C22×C3×C5—22no—
432C22×C3×C5—22no—
433C22×C3×C5—44no—
434C22×C3×C5C22×D412yes—
435C22×C3×C5C2×#4112yes—
436C22×C3×C5C2×#4112yes—
437C22×C3×C5C2×#4114yescomplemented
438C22×C3×C5C2511yescharacteristic
439C2×D15—22no—
440C2×D15—22no—
441C2×D15—22no—
442C2×D15—44no—
443C2×C5×D3—232no—
444C2×C5×D3—28no—
445C2×C5×D3—28no—
446C2×C5×D3—22no—
447C2×C5×D3—22no—
448C2×C5×D3—22no—
449C2×C5×D3—22no—
450C2×C5×D3C22×D414yes—
451C2×C5×D3C2×#4114yescomplemented
452C3×C4×C5—22no—
453Dic15—22no—
454Dic15—22no—
455Dic15C22×D414yes—
456C3×Dic5—22no—
457C3×Dic5—22no—
458C3×Dic5—22no—
459C3×Dic5C22×D414yes—
460C5×Dic3—22no—
461C5×Dic3—22no—
462C24×C3C22×D511yescharacteristic
463C24×C3C22×D511yescharacteristic
464C23×D3—24no—
465C23×D3—24no—
466C23×D3—24no—
467C23×D3—51no—
468C23×D3C22×D514yes—
469C23×D3C22×D511yescharacteristic
470C23×D3C22×D511yescharacteristic
471C2×C3×D4—24no—
472C2×C3×D4C22×D514yes—
473C22×C3×C4—51no—
474C22×C3×C4—51no—
475C22×C3×C4—51no—
476C22×C3×C4—51no—
477C22×C3×C4—54no—
478C22×C3×C4—54no—
479C22×C3×C4—104no—
480C22×C3×C4—104no—
481C22×C3×C4C22×D511yescharacteristic
482C2×#67—24no—
483C2×#67—24no—
484C2×#67—54no—
485C2×#67—54no—
486C2×#67—104no—
487C2×#67—104no—
488C2×#67C22×D514yes—
489C2×#67C22×D514yes—
490C22×Dic3—51no—
491C22×Dic3—54no—
492C22×Dic3—51no—
493C22×Dic3—51no—
494C22×Dic3—104no—
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D511yescharacteristic
497#235—1032no—
498C2×D12—54no—
499C2×D12—54no—
500C2×D12—104no—
501C2×D12—104no—
502C2×C4×D3—58no—
503C2×C4×D3—54no—
504C2×C4×D3—54no—
505C2×C4×D3—54no—
506C2×C4×D3—54no—
507C2×C4×D3—54no—
508C2×C4×D3—1032no—
509C2×C4×D3—104no—
510C2×C4×D3—104no—
511C2×C4×D3—104no—
512C2×C4×D3—104no—
513C2×Dic6—54no—
514C2×Dic6—104no—
515C3×C4⋊C4—54no—
516C3×C22⋊C4—54no—
517C3×C22⋊C4—54no—
518C3×C42—54no—
519#217—54no—
520#217C22×D514yes—
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—
527C4⋊Dic3—54no—
528Dic3⋊C4—54no—
529Dic3⋊C4—54no—
530Dic3⋊C4—54no—
531Dic3⋊C4—54no—
532C4×Dic3—54no—
533C23×C5—22no—
534C23×C5—22no—
535C23×C5—22no—
536C23×C5—22no—
537C23×C5—22no—
538C23×C5—34no—
539C23×C5—34no—
540C23×C5—32no—
541C23×C5—32no—
542C23×C5—68no—
543C23×C5—68no—
544C23×C5—632no—
545C23×C5—62no—
546C23×C5—62no—
547C23×C5—68no—
548C23×C5—62no—
549C23×C5—62no—
550C23×C5#23514yescomplemented
551C23×C5C23×D312yes—
552C23×C5C23×D312yes—
553C23×C5C23×D311yescharacteristic
554C22×D5—32no—
555C22×D5—62no—
556C22×D5—62no—
557C22×D5—62no—
558C5×D4—28no—
559C5×D4—68no—
560C5×D4—68no—
561C2×C4×C5—22no—
562C2×C4×C5—32no—
563C2×C4×C5—32no—
564C2×C4×C5—62no—
565C2×C4×C5—62no—
566C2×C4×C5C23×D312yes—
567C22⋊D5—68no—
568C22⋊D5—68no—
569C22⋊D5—68no—
570C22⋊D5—68no—
571C2×Dic5—22no—
572C2×Dic5—22no—
573C2×Dic5—22no—
574C2×Dic5—28no—
575C2×Dic5—28no—
576C2×Dic5—34no—
577C2×Dic5—32no—
578C2×Dic5—316no—
579C2×Dic5—32no—
580C2×Dic5—32no—
581C2×Dic5—68no—
582C2×Dic5—68no—
583C2×Dic5—68no—
584C2×Dic5—62no—
585C2×Dic5—62no—
586C2×Dic5—68no—
587C2×Dic5D3×D414yes—
588C2×Dic5C23×D312yes—
589C2×Dic5C23×D312yes—
590C2×Dic5C23×D312yes—
591C2×Dic5C23×D312yes—
592C4×D5—68no—
593Dic10—68no—
594C25—31no—
595C2×#41—158no—
596C2×#41—308no—
597C22×Q8—151no—
598C22×D4—31no—
599C22×D4—31no—
600C22×D4—151no—
601C22×D4—151no—
602C22×D4—151no—
603C22×D4—151no—
604C22×D4D3×D511yescharacteristic
605C23×C4—51no—
606C23×C4—51no—
607C23×C4—151no—
608C23×C4—151no—
609C23×C4—151no—
610C23×C4—151no—
611C23×C4—151no—
612C23×C4—158no—
613C23×C4—151no—
614C23×C4—308no—
615#123—158no—
616#123—158no—
617C22⋊Q8—158no—
618C22⋊Q8—158no—
619#121—158no—
620#121—158no—
621#120—38no—
622#120—158no—
623C4×D4—58no—
624C4×D4—158no—
625C4×D4—158no—
626C4×D4—158no—
627#117—158no—
628C2×C4⋊C4—51no—
629C2×C4⋊C4—151no—
630C2×C4⋊C4—151no—
631C2×C4⋊C4—151no—
632C2×C4⋊C4—151no—
633C2×C4⋊C4—151no—
634C2×C22⋊C4—31no—
635C2×C22⋊C4—31no—
636C2×C22⋊C4—31no—
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—51no—
645C2×C42—151no—
646C2×C3×C5—24no—
647C2×C3×C5—42no—
648C2×C3×C5#52514yescomplemented
649C2×C3×C5C23×D411yescharacteristic
650C2×C3×C5C22×#4111yescharacteristic
651C2×C3×C5C22×#4111yescharacteristic
652D15—42no—
653C5×D3—24no—
654C5×D3—24no—
655C23×C3—22no—
656C23×C3—22no—
657C23×C3—22no—
658C23×C3—22no—
659C23×C3—22no—
660C23×C3#71114yescomplemented
661C23×C3C23×D512yes—
662C23×C3C23×D512yes—
663C23×C3C23×D511yescharacteristic
664C22×D3—232no—
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—22no—
668C22×D3—22no—
669C22×D3—28no—
670C22×D3—28no—
671C22×D3—28no—
672C22×D3—52no—
673C22×D3—102no—
674C22×D3—102no—
675C22×D3—102no—
676C22×D3D4×D514yes—
677C22×D3#71114yescomplemented
678C22×D3C23×D512yes—
679C22×D3C23×D512yes—
680C3×D4—28no—
681C2×C3×C4—22no—
682C2×C3×C4—54no—
683C2×C3×C4—52no—
684C2×C3×C4—52no—
685C2×C3×C4—52no—
686C2×C3×C4—52no—
687C2×C3×C4—108no—
688C2×C3×C4—108no—
689C2×C3×C4—102no—
690C2×C3×C4—102no—
691C2×C3×C4—102no—
692C2×C3×C4C23×D512yes—
693#67—28no—
694#67—28no—
695#67—108no—
696#67—108no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—54no—
700C2×Dic3—52no—
701C2×Dic3—52no—
702C2×Dic3—52no—
703C2×Dic3—108no—
704C2×Dic3—102no—
705C2×Dic3—102no—
706C2×Dic3C23×D512yes—
707C2×Dic3C23×D512yes—
708D12—108no—
709D12—108no—
710C4×D3—516no—
711C4×D3—108no—
712C4×D3—108no—
713C4×D3—108no—
714C4×D3—108no—
715Dic6—108no—
716C22×C5—22no—
717C22×C5—22no—
718C22×C5—28no—
719C22×C5—22no—
720C22×C5—22no—
721C22×C5—22no—
722C22×C5—34no—
723C22×C5—34no—
724C22×C5—44no—
725C22×C5—632no—
726C22×C5—62no—
727C22×C5—62no—
728C22×C5—62no—
729C22×C5—62no—
730C22×C5—68no—
731C22×C5—68no—
732C22×C5C2×#23512yes—
733C22×C5C2×#23514yescomplemented
734C22×C5C2×D3×D412yes—
735C22×C5D3×#4112yes—
736C22×C5C24×D311yescharacteristic
737C2×D5—62no—
738C2×D5—62no—
739C2×D5—62no—
740C2×D5—124no—
741C4×C5—22no—
742C4×C5—62no—
743C4×C5—62no—
744Dic5—22no—
745Dic5—22no—
746Dic5—22no—
747Dic5—34no—
748Dic5—62no—
749Dic5—62no—
750Dic5C2×D3×D414yes—
751C24—31no—
752C24—31no—
753C24—34no—
754C24—64no—
755C24—64no—
756C24—64no—
757C24—151no—
758C24C2×D3×D511yescharacteristic
759C24C2×D3×D511yescharacteristic
760#41—3032no—
761C2×Q8—154no—
762C2×Q8—304no—
763C2×D4—24no—
764C2×D4—34no—
765C2×D4—34no—
766C2×D4—64no—
767C2×D4—64no—
768C2×D4—154no—
769C2×D4—154no—
770C2×D4—154no—
771C2×D4—154no—
772C2×D4—304no—
773C2×D4—304no—
774C2×D4—304no—
775C2×D4—304no—
776C2×D4C2×D3×D514yes—
777C22×C4—31no—
778C22×C4—31no—
779C22×C4—51no—
780C22×C4—54no—
781C22×C4—54no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—51no—
785C22×C4—104no—
786C22×C4—104no—
787C22×C4—154no—
788C22×C4—154no—
789C22×C4—158no—
790C22×C4—154no—
791C22×C4—154no—
792C22×C4—154no—
793C22×C4—151no—
794C22×C4—154no—
795C22×C4—151no—
796C22×C4—151no—
797C22×C4—304no—
798C22×C4—304no—
799C22×C4—3032no—
800C22×C4—304no—
801C22×C4—304no—
802C22×C4—304no—
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—54no—
805C4⋊C4—154no—
806C4⋊C4—154no—
807C4⋊C4—154no—
808C4⋊C4—154no—
809C4⋊C4—154no—
810C22⋊C4—34no—
811C22⋊C4—34no—
812C22⋊C4—34no—
813C22⋊C4—54no—
814C22⋊C4—54no—
815C22⋊C4—154no—
816C22⋊C4—154no—
817C22⋊C4—154no—
818C22⋊C4—154no—
819C22⋊C4—154no—
820C42—54no—
821C42—154no—
822C3×C5C2×#52511yescharacteristic, complemented, Hall
823C22×C3—28no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—44no—
830C22×C3C2×D4×D512yes—
831C22×C3C2×#71112yes—
832C22×C3C2×#71112yes—
833C22×C3C2×#71114yescomplemented
834C22×C3C24×D511yescharacteristic
835C2×D3—232no—
836C2×D3—28no—
837C2×D3—28no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—102no—
843C2×D3—102no—
844C2×D3—102no—
845C2×D3—204no—
846C2×D3C2×D4×D514yes—
847C2×D3C2×#71114yescomplemented
848C3×C4—22no—
849C3×C4—54no—
850C3×C4—102no—
851C3×C4—102no—
852C3×C4—102no—
853Dic3—22no—
854Dic3—22no—
855Dic3—54no—
856Dic3—102no—
857Dic3—102no—
858C2×C5—24no—
859C2×C5—42no—
860C2×C5—64no—
861C2×C5—64no—
862C2×C5#554714yescomplemented
863C2×C5C22×#23511yescharacteristic
864C2×C5C22×D3×D411yescharacteristic
865C2×C5C2×D3×#4111yescharacteristic
866D5—122no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—34no—
873C23—34no—
874C23—32no—
875C23—32no—
876C23—68no—
877C23—68no—
878C23—632no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—68no—
884C23—152no—
885C23—302no—
886C23—302no—
887C23—302no—
888C23#678214yescomplemented
889C23C22×D3×D512yes—
890C23C22×D3×D512yes—
891C23C22×D3×D511yescharacteristic
892Q8—308no—
893D4—28no—
894D4—68no—
895D4—68no—
896D4—308no—
897D4—308no—
898D4—308no—
899D4—308no—
900C2×C4—22no—
901C2×C4—32no—
902C2×C4—32no—
903C2×C4—54no—
904C2×C4—52no—
905C2×C4—52no—
906C2×C4—52no—
907C2×C4—52no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—108no—
911C2×C4—108no—
912C2×C4—102no—
913C2×C4—102no—
914C2×C4—102no—
915C2×C4—1516no—
916C2×C4—154no—
917C2×C4—152no—
918C2×C4—152no—
919C2×C4—152no—
920C2×C4—308no—
921C2×C4—308no—
922C2×C4—308no—
923C2×C4—308no—
924C2×C4—308no—
925C2×C4—302no—
926C2×C4—302no—
927C2×C4C22×D3×D512yes—
928C2×C3—24no—
929C2×C3—42no—
930C2×C3#6592014yescomplemented
931C2×C3C22×D4×D511yescharacteristic
932C2×C3C22×#71111yescharacteristic
933C2×C3C22×#71111yescharacteristic
934D3—24no—
935D3—24no—
936D3—202no—
937C5C2×#554711yescharacteristic, complemented, Sylow
938C22—28no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—34no—
945C22—34no—
946C22—44no—
947C22—632no—
948C22—62no—
949C22—62no—
950C22—68no—
951C22—68no—
952C22—62no—
953C22—62no—
954C22—302no—
955C22—302no—
956C22—302no—
957C22—604no—
958C22D3×D4×D512yes—
959C22D3×#71112yes—
960C22C2×#678212yes—
961C22C2×#678214yescomplemented
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—54no—
965C4—62no—
966C4—62no—
967C4—102no—
968C4—102no—
969C4—102no—
970C4—154no—
971C4—302no—
972C4—302no—
973C3C2×#6592011yescharacteristic, complemented, Sylow
974C2—24no—
975C2—42no—
976C2—64no—
977C2—64no—
978C2—602no—
979C2#1175476714yesdirect product factor
980C2C2×D3×D4×D511yescharacteristic
981C2C2×D3×#71111yescharacteristic
982C2C22×#678211yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#525
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6782C2semidirect
2. C23×D3×Dic5C2semidirect
3. C2×#91828C2semidirect
4. C2×C5×#937C2semidirect
5. C2×C3×D4×Dic5C2semidirect
6. C2×#91576C2semidirect
7. C2×#91570C2semidirect
8. C2×#91558C2semidirect
9. C2×#91555C2semidirect
10. C2×#91552C2semidirect
11. C2×Dic5×#67C2semidirect
12. #11754767C2direct (N × H)
13. C2×#91436C2semidirect
14. C2×#91427C2semidirect
15. C2×#91405C2semidirect
16. C2×#91398C2semidirect
21. C22×#1220C22semidirect
26. C23×C3×Dic5C22semidirect
27. C22×#1204C22semidirect
30. C22×#1200C22semidirect
32. C2×#6782C22semidirect
38. C22×D3×Dic5C22semidirect
39. C2×#6719C22semidirect
40. #91828C22semidirect
41. C2×#6714C22semidirect
42. C2×#6712C22semidirect
44. C5×#937C22semidirect
48. C2×C3×C22⋊Dic5C22semidirect
49. C3×D4×Dic5C22semidirect
50. C2×C3×C4⋊Dic5C22semidirect
51. C2×C3×C4×Dic5C22semidirect
52. #91576C22semidirect
53. #91570C22semidirect
54. #91558C22semidirect
55. #91555C22semidirect
56. #91552C22semidirect
57. Dic5×#67C22semidirect
58. C2×Dic3⋊Dic5C22semidirect
59. C2×#6669C22semidirect
60. C2×#6669C22semidirect
61. C2×#6668C22semidirect
62. C2×#6667C22semidirect
65. C2×Dic3×Dic5C22semidirect
66. #91436C22semidirect
67. #91427C22semidirect
68. #91405C22semidirect
69. #91398C22semidirect
79. C2×D4×Dic5D3semidirect
102. C2×#1220C23semidirect
121. C22×C3×Dic5C23semidirect
123. C2×#1204C23semidirect
129. C2×#1200C23semidirect
135. C2×D3×Dic5D4semidirect
140. #6719C23semidirect
141. #6714C23semidirect
142. #6712C23semidirect
147. C3×C22⋊Dic5C23semidirect
148. C3×C4⋊Dic5C23semidirect
149. C3×C4×Dic5C23semidirect
150. Dic3⋊Dic5C23semidirect
151. #6669C23semidirect
152. #6669C23semidirect
153. #6668C23semidirect
154. #6667C23semidirect
157. Dic3×Dic5C23semidirect
162. C2×#937D5semidirect
190. C23×Dic5C2×D3semidirect
204. C2×C22⋊Dic5C2×D3semidirect
209. D4×Dic5C2×D3semidirect
213. C2×C4⋊Dic5C2×D3semidirect
219. C2×C4×Dic5C2×D3semidirect
232. C23×C3×C5#41semidirect
249. C22×C5×D3#41semidirect
287. D3×Dic5C2×D4semidirect
317. #937C2×D5semidirect
387. C22×Dic5C22×D3semidirect
400. C22⋊Dic5C22×D3semidirect
404. C4⋊Dic5C22×D3semidirect
410. C4×Dic5C22×D3semidirect
437. C22×C3×C5C2×#41semidirect
451. C2×C5×D3C2×#41semidirect
550. C23×C5#235semidirect
648. C2×C3×C5#525semidirect
660. C23×C3#711semidirect
677. C22×D3#711semidirect
733. C22×C5C2×#235semidirect
822. C3×C5C2×#525semidirect
833. C22×C3C2×#711semidirect
847. C2×D3C2×#711semidirect
862. C2×C5#5547semidirect
888. C23#6782semidirect
930. C2×C3#65920semidirect
937. C5C2×#5547semidirect
961. C22C2×#6782semidirect
973. C3C2×#65920semidirect
979. C2#11754767direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67822
C23×D3×Dic52
C2×#918282
C2×C5×#9372
C2×C3×D4×Dic52
C2×#915762
C2×#915702
C2×#915582
C2×#915552
C2×#915522
C2×Dic5×#672
#117547672
C2×#914362
C2×#914272
C2×#914052
C2×#913982
C2×#659203
C2×#55475