Finite Group Databasebeta

← C2×#11753249 #14479637

Subgroups — C2×#11753249 #14479637

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
2C22×C4×D3×D5C211yesmaximal, characteristic, complemented
3C2×#91772C211yesmaximal, characteristic, complemented
4C2×C5×#884C211yesmaximal, characteristic, complemented
5C2×C3×#4027C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×Dic5×#67C211yesmaximal, characteristic, complemented
8C2×#91549C211yesmaximal, characteristic, complemented
9C2×#91475C211yesmaximal, characteristic, complemented
10C2×#91440C211yesmaximal, characteristic, complemented
11C2×#91422C211yesmaximal, characteristic, complemented
12C2×Dic5×D12C211yesmaximal, characteristic, complemented
13C2×#91402C211yesmaximal, characteristic, complemented
14C2×#91355C211yesmaximal, characteristic, complemented
15C2×#91352C211yesmaximal, characteristic, complemented
16#11753249C2116yesmaximal, direct product factor
17C2×#65940—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic, complemented
23C22×C5×D12C2211yescharacteristic
24C22×C4×C5×D3C2211yescharacteristic
25C22×C3×C22⋊D5C2211yescharacteristic
26C23×C3×Dic5C2211yescharacteristic, complemented
27C22×C3×C4×D5C2211yescharacteristic
28C22×#1204C2211yescharacteristic, complemented
29C22×#1203C2211yescharacteristic
30C22×#1201C2211yescharacteristic
31C22×#1200C2211yescharacteristic
32C2×#6782—28no—
33C2×#6782C2218yescomplemented
34C22×D3×Dic5C2211yescharacteristic
35C22×D3×Dic5C2211yescharacteristic, complemented
36C22×D5×Dic3C2211yescharacteristic
37C2×C4×D3×D5—28no—
38C2×C4×D3×D5C2218yescomplemented
39C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
40C2×#6719C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic
42C2×C4⋊Dic15C2211yescharacteristic, complemented
43C2×#6712C2211yescharacteristic, complemented
44#91772C2218yescomplemented
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
47C5×#884C2218yescomplemented
48C2×C3×#685C2211yescharacteristic
49C2×C3×#683C2211yescharacteristic, complemented
50C2×C3×C4×Dic5C2211yescharacteristic, complemented
51C3×#4027C2218yescomplemented
52#91577C2218yescomplemented
53Dic5×#67C2218yescomplemented
54#91549C2218yescomplemented
55C2×Dic3⋊Dic5C2211yescharacteristic, complemented
56C2×Dic3⋊Dic5C2211yescharacteristic, complemented
57C2×#6667C2211yescharacteristic
58C2×(C2×D3)⋊Dic5C2211yescharacteristic
59C2×(C2×D3)⋊Dic5C2211yescharacteristic
60C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
61C2×#6665C2211yescharacteristic
62C2×Dic3×Dic5C2211yescharacteristic, complemented
63#91475C2218yescomplemented
64#91440C2218yescomplemented
65#91422C2218yescomplemented
66Dic5×D12C2218yescomplemented
67#91402C2218yescomplemented
68#91355C2218yescomplemented
69#91352C2218yescomplemented
70C2×#5547—51nomaximal, Hall
71C22×#711—31no—
72C23×C4×D5—31no—
73C2×C5×#121—31no—
74C2×#4084—31no—
75C2×#4083—31no—
76C2×#4083—31no—
77C2×D4×Dic5—31no—
78C2×D4×Dic5—31no—
79C2×#4070—31no—
80#65940—316no—
81C2×#4043—31no—
82C2×#4038—31no—
83C2×#4029—31no—
84C2×#4029—31no—
85C2×#4027—31no—
86C2×#4027D311yescharacteristic, complemented
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
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
98C2×#1220—24no—
99C2×#1220C2314yes—
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2311yescharacteristic
103C2×C4×D15—24no—
104C2×C4×D15C2314yes—
105C2×C5×#67—24no—
106C2×C5×#67—24no—
107C2×C5×#67C2314yes—
108C2×C5×#67C2314yescomplemented
109C22×C5×Dic3C2311yescharacteristic
110C22×C5×Dic3C2311yescharacteristic
111C2×C5×D12—24no—
112C2×C5×D12C2314yes—
113C2×C4×C5×D3—24no—
114C2×C4×C5×D3C2314yes—
115C2×C3×C22⋊D5—24no—
116C2×C3×C22⋊D5C2314yes—
117C22×C3×Dic5—24no—
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2311yescharacteristic
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2314yescomplemented
122C2×C3×C4×D5—24no—
123C2×C3×C4×D5C2314yes—
124C2×#1204—24no—
125C2×#1204C2314yescomplemented
126C2×#1203—24no—
127C2×#1203C2314yes—
128C2×#1201—24no—
129C2×#1201C2314yes—
130C2×#1200D418yescomplemented
131C2×#1200C2314yes—
132#6782—232no—
133C2×D3×Dic5—24no—
134C2×D3×Dic5—24no—
135C2×D3×Dic5C2314yes—
136C2×D3×Dic5C2314yescomplemented
137C2×D5×Dic3—24no—
138C2×D5×Dic3C2314yes—
139C4×D3×D5—232no—
140C3×C5×C22⋊C4C2314yescomplemented
141#6719C2314yescomplemented
142#6714C2314yes—
143C4⋊Dic15C2314yescomplemented
144#6712C2314yescomplemented
145C5×(C2×D3)⋊C4C2314yescomplemented
146C5×Dic3⋊C4C2314yescomplemented
147C3×#685C2314yes—
148C3×#683C2314yescomplemented
149C3×C4×Dic5C2314yescomplemented
150Dic3⋊Dic5C2314yescomplemented
151Dic3⋊Dic5C2314yescomplemented
152#6667C2314yes—
153(C2×D3)⋊Dic5C2314yes—
154(C2×D3)⋊Dic5C2314yes—
155(C2×D3)⋊Dic5C2314yescomplemented
156#6665C2314yes—
157Dic3×Dic5C2314yescomplemented
158C22×#235—51no—
159C23×C4×D3—51no—
160C2×C3×C4×D4—51no—
161C2×#939—51no—
162C2×#937—51no—
163C2×C4×#67—51no—
164C2×C4×#67—51no—
165#5547—516no—
166C2×#896—51no—
167C2×#894—51no—
168C2×#884D511yescharacteristic, complemented
169C2×#883—51no—
170C2×#882—51no—
171C2×#878—51no—
172C2×C4×D12—51no—
173C2×#872—51no—
174C24×D5—31no—
175C22×C5×D4—31no—
176C22×C5×D4—31no—
177C22×C5×D4—31no—
178C23×C4×C5—31no—
179C22×C22⋊D5—31no—
180C22×C22⋊D5—31no—
181C22×C22⋊D5—31no—
182C22×C22⋊D5C2×D311yescharacteristic
183C23×Dic5—31no—
184C23×Dic5—31no—
185C23×Dic5C2×D311yescharacteristic, complemented
186C2×#711—38no—
187C2×#711—68no—
188C22×C4×D5—31no—
189C22×C4×D5—31no—
190C22×C4×D5—31no—
191C22×C4×D5—38no—
192C22×C4×D5—68no—
193C22×C4×D5C2×D311yescharacteristic
194C22×Dic10—31no—
195C5×#121—38no—
196C2×C5×C4⋊C4—31no—
197C2×C5×C22⋊C4—31no—
198C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
199C2×C22⋊Dic5—31no—
200C2×C22⋊Dic5—31no—
201C2×C22⋊Dic5—31no—
202C2×C22⋊Dic5—31no—
203#4084—38no—
204#4083—38no—
205#4083—38no—
206D4×Dic5—38no—
207D4×Dic5—38no—
208C2×#685—31no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685C2×D311yescharacteristic
212C2×C4⋊Dic5—31no—
213C2×C4⋊Dic5—31no—
214C2×C4⋊Dic5—31no—
215#4070—38no—
216C2×#683—31no—
217C2×#683C2×D311yescharacteristic, complemented
218C2×C4×Dic5—31no—
219C2×C4×Dic5C2×D311yescharacteristic, complemented
220#4043—38no—
221#4038—38no—
222#4029—38no—
223#4029—38no—
224#4027—38no—
225#4027C2×D318yescomplemented
226C2×#525—151noSylow
227C23×C3×C5—22no—
228C23×C3×C5—22no—
229C23×C3×C5—22no—
230C23×C3×C5C2412yes—
231C23×C3×C5C2411yescharacteristic
232C22×D15—22no—
233C22×D15—22no—
234C22×D15C2×D414yes—
235C22×D15C2412yes—
236C22×C5×D3—22no—
237C22×C5×D3—22no—
238C22×C5×D3—22no—
239C22×C5×D3—22no—
240C22×C5×D3—22no—
241C22×C5×D3#4114yescomplemented
242C22×C5×D3C2412yes—
243C22×C5×D3C2412yes—
244C22×C3×D5—22no—
245C22×C3×D5—22no—
246C22×C3×D5#4114yescomplemented
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×C5C2412yes—
255C2×C3×C4×C5C2412yes—
256#1220—28no—
257C2×Dic15—22no—
258C2×Dic15—22no—
259C2×Dic15—22no—
260C2×Dic15C2412yes—
261C2×Dic15C2412yes—
262C2×Dic15C2412yes—
263C4×D15—28no—
264C5×#67—28no—
265C5×#67—28no—
266C2×C5×Dic3—22no—
267C2×C5×Dic3C2×D414yes—
268C2×C5×Dic3C2412yes—
269C2×C5×Dic3C2412yes—
270C5×D12—28no—
271C4×C5×D3—28no—
272C3×C22⋊D5—28no—
273C2×C3×Dic5—22no—
274C2×C3×Dic5—22no—
275C2×C3×Dic5—28no—
276C2×C3×Dic5C2×D414yes—
277C2×C3×Dic5C2412yes—
278C2×C3×Dic5C2412yes—
279C2×C3×Dic5C2412yes—
280C3×C4×D5—28no—
281#1204—28no—
282#1203—28no—
283#1201—28no—
284#1200C2×D4116yescomplemented
285D3×Dic5—28no—
286D3×Dic5—28no—
287D5×Dic3—28no—
288C24×D3—51no—
289C22×C3×D4—51no—
290C23×C3×C4—51no—
291C23×C3×C4—51no—
292C22×#67—51no—
293C22×#67—51no—
294C22×#67C2×D511yescharacteristic
295C22×#67C2×D511yescharacteristic, complemented
296C23×Dic3—51no—
297C2×#235—58no—
298C2×#235—108no—
299C22×D12—51no—
300C22×D12C2×D511yescharacteristic
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×Dic6—51no—
309C3×C4×D4—58no—
310C2×C3×C4⋊C4—51no—
311C2×C3×C22⋊C4—51no—
312C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
313C2×C3×C42—51no—
314C2×#217—51no—
315C2×#217—51no—
316#939—58no—
317#937—58no—
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)⋊C4—51no—
325C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
326C2×C4⋊Dic3—51no—
327C2×Dic3⋊C4—51no—
328C2×Dic3⋊C4—51no—
329C2×Dic3⋊C4—51no—
330C2×Dic3⋊C4C2×D511yescharacteristic, complemented
331C2×C4×Dic3—51no—
332#896—58no—
333#894—58no—
334#884C2×D518yescomplemented
335#883—58no—
336#882—58no—
337#878—58no—
338C4×D12—58no—
339#872—58no—
340C24×C5—31no—
341C24×C5—31no—
342C24×C5C22×D311yescharacteristic
343C23×D5—31no—
344C23×D5—34no—
345C23×D5—64no—
346C23×D5—64no—
347C23×D5—64no—
348C23×D5C22×D311yescharacteristic
349C2×C5×D4—34no—
350C2×C5×D4—34no—
351C2×C5×D4—34no—
352C2×C5×D4—64no—
353C2×C5×D4—64no—
354C2×C5×D4—64no—
355C22×C4×C5—31no—
356C22×C4×C5—31no—
357C22×C4×C5—34no—
358C22×C4×C5—64no—
359C22×C4×C5C22×D311yescharacteristic
360C22×C4×C5C22×D311yescharacteristic
361C2×C22⋊D5—24no—
362C2×C22⋊D5—34no—
363C2×C22⋊D5—34no—
364C2×C22⋊D5—34no—
365C2×C22⋊D5—64no—
366C2×C22⋊D5—64no—
367C2×C22⋊D5—64no—
368C2×C22⋊D5C22×D314yes—
369C22×Dic5—24no—
370C22×Dic5—31no—
371C22×Dic5—31no—
372C22×Dic5—31no—
373C22×Dic5—34no—
374C22×Dic5—34no—
375C22×Dic5—64no—
376C22×Dic5—64no—
377C22×Dic5C22×D311yescharacteristic
378C22×Dic5C22×D311yescharacteristic
379C22×Dic5C22×D311yescharacteristic
380C22×Dic5C22×D314yescomplemented
381#711—632no—
382C2×C4×D5—24no—
383C2×C4×D5—38no—
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×D5C22×D314yes—
391C2×Dic10—34no—
392C2×Dic10—64no—
393C5×C4⋊C4—34no—
394C5×C22⋊C4—34no—
395C5×C22⋊C4C22×D314yescomplemented
396C22⋊Dic5—34no—
397C22⋊Dic5—34no—
398C22⋊Dic5—34no—
399C22⋊Dic5—34no—
400#685—34no—
401#685—34no—
402#685—34no—
403#685C22×D314yes—
404C4⋊Dic5—34no—
405C4⋊Dic5—34no—
406C4⋊Dic5—34no—
407#683—34no—
408#683C22×D314yescomplemented
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—31no—
419C2×#121—151no—
420C2×#120—151no—
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—22no—
428C22×C3×C5—22no—
429C22×C3×C5—22no—
430C22×C3×C5—44no—
431C22×C3×C5C22×D412yes—
432C22×C3×C5C2×#4112yes—
433C22×C3×C5C2×#4112yes—
434C22×C3×C5C2511yescharacteristic
435C2×D15—28no—
436C2×D15—22no—
437C2×D15—22no—
438C2×D15C22×D414yes—
439C2×C5×D3—28no—
440C2×C5×D3—22no—
441C2×C5×D3—22no—
442C2×C5×D3—22no—
443C2×C5×D3—22no—
444C2×C5×D3—22no—
445C2×C5×D3—44no—
446C2×C5×D3C2×#4114yescomplemented
447C2×C3×D5—28no—
448C2×C3×D5—22no—
449C2×C3×D5—22no—
450C2×C3×D5C2×#4114yescomplemented
451D3×D5—232no—
452C3×C4×C5—22no—
453C3×C4×C5—22no—
454Dic15—22no—
455Dic15—22no—
456Dic15—22no—
457C3×Dic5—22no—
458C3×Dic5—22no—
459C3×Dic5C22×D414yes—
460C5×Dic3—22no—
461C5×Dic3C22×D414yes—
462C24×C3—51no—
463C24×C3C22×D511yescharacteristic
464C23×D3—51no—
465C23×D3—54no—
466C23×D3—104no—
467C23×D3—104no—
468C23×D3—104no—
469C23×D3C22×D511yescharacteristic
470C23×D3C22×D511yescharacteristic
471C2×C3×D4—54no—
472C2×C3×D4—104no—
473C22×C3×C4—51no—
474C22×C3×C4—51no—
475C22×C3×C4—51no—
476C22×C3×C4—54no—
477C22×C3×C4—54no—
478C22×C3×C4—104no—
479C22×C3×C4—104no—
480C22×C3×C4C22×D511yescharacteristic
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×D514yescomplemented
490C22×Dic3—51no—
491C22×Dic3—51no—
492C22×Dic3—51no—
493C22×Dic3—54no—
494C22×Dic3—104no—
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D511yescharacteristic
497#235—1032no—
498C2×D12—24no—
499C2×D12—54no—
500C2×D12—104no—
501C2×D12C22×D514yes—
502C2×C4×D3—24no—
503C2×C4×D3—58no—
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×D3C22×D514yes—
513C2×Dic6—54no—
514C2×Dic6—104no—
515C3×C4⋊C4—54no—
516C3×C22⋊C4—54no—
517C3×C22⋊C4C22×D514yescomplemented
518C3×C42—54no—
519#217—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)⋊C4—54no—
526(C2×D3)⋊C4C22×D514yescomplemented
527C4⋊Dic3—54no—
528Dic3⋊C4—54no—
529Dic3⋊C4—54no—
530Dic3⋊C4—54no—
531Dic3⋊C4C22×D514yescomplemented
532C4×Dic3—54no—
533C23×C5—22no—
534C23×C5—22no—
535C23×C5—22no—
536C23×C5—34no—
537C23×C5—32no—
538C23×C5—32no—
539C23×C5—62no—
540C23×C5—62no—
541C23×C5—62no—
542C23×C5—62no—
543C23×C5—62no—
544C23×C5C23×D312yes—
545C23×C5C23×D311yescharacteristic
546C22×D5—22no—
547C22×D5—22no—
548C22×D5—34no—
549C22×D5—32no—
550C22×D5—68no—
551C22×D5—68no—
552C22×D5—632no—
553C22×D5—62no—
554C22×D5—62no—
555C22×D5—68no—
556C22×D5#23514yescomplemented
557C22×D5C23×D312yes—
558C5×D4—68no—
559C5×D4—68no—
560C5×D4—68no—
561C2×C4×C5—22no—
562C2×C4×C5—22no—
563C2×C4×C5—34no—
564C2×C4×C5—32no—
565C2×C4×C5—32no—
566C2×C4×C5—68no—
567C2×C4×C5—62no—
568C2×C4×C5C23×D312yes—
569C2×C4×C5C23×D312yes—
570C22⋊D5—28no—
571C22⋊D5—68no—
572C22⋊D5—68no—
573C22⋊D5—68no—
574C2×Dic5—22no—
575C2×Dic5—22no—
576C2×Dic5—28no—
577C2×Dic5—32no—
578C2×Dic5—32no—
579C2×Dic5—32no—
580C2×Dic5—62no—
581C2×Dic5—62no—
582C2×Dic5—62no—
583C2×Dic5—68no—
584C2×Dic5—68no—
585C2×Dic5D3×D414yes—
586C2×Dic5C23×D312yes—
587C2×Dic5C23×D312yes—
588C2×Dic5C23×D312yes—
589C4×D5—28no—
590C4×D5—316no—
591C4×D5—68no—
592C4×D5—68no—
593Dic10—68no—
594C25—151no—
595C2×#41—158no—
596C2×#41—308no—
597C22×Q8—151no—
598C22×D4—31no—
599C22×D4—31no—
600C22×D4—31no—
601C22×D4—51no—
602C22×D4—151no—
603C22×D4—151no—
604C22×D4—151no—
605C23×C4—31no—
606C23×C4—51no—
607C23×C4—51no—
608C23×C4—151no—
609C23×C4—158no—
610C23×C4—151no—
611C23×C4—151no—
612C23×C4—151no—
613C23×C4—151no—
614C23×C4—308no—
615#123—158no—
616#123—158no—
617C22⋊Q8—158no—
618C22⋊Q8—158no—
619#121—38no—
620#121—158no—
621#120—158no—
622#120—158no—
623C4×D4—58no—
624C4×D4—158no—
625C4×D4—158no—
626C4×D4—158no—
627#117—158no—
628C2×C4⋊C4—31no—
629C2×C4⋊C4—51no—
630C2×C4⋊C4—151no—
631C2×C4⋊C4—151no—
632C2×C4⋊C4—151no—
633C2×C4⋊C4—151no—
634C2×C22⋊C4—31no—
635C2×C22⋊C4—51no—
636C2×C22⋊C4—151no—
637C2×C22⋊C4—151no—
638C2×C22⋊C4—151no—
639C2×C22⋊C4—151no—
640C2×C22⋊C4—151no—
641C2×C22⋊C4—151no—
642C2×C22⋊C4—151no—
643C2×C22⋊C4D3×D511yescharacteristic, complemented
644C2×C42—51no—
645C2×C42—151no—
646C2×C3×C5—42no—
647C2×C3×C5#52514yescomplemented
648C2×C3×C5C23×D411yescharacteristic
649C2×C3×C5C22×#4111yescharacteristic
650C2×C3×C5C22×#4111yescharacteristic
651D15—24no—
652C3×D5—24no—
653C5×D3—24no—
654C5×D3—42no—
655C23×C3—22no—
656C23×C3—22no—
657C23×C3—22no—
658C23×C3—54no—
659C23×C3—52no—
660C23×C3—102no—
661C23×C3—102no—
662C23×C3C23×D512yes—
663C23×C3C23×D511yescharacteristic
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—22no—
668C22×D3—22no—
669C22×D3—54no—
670C22×D3—52no—
671C22×D3—108no—
672C22×D3—108no—
673C22×D3—1032no—
674C22×D3—102no—
675C22×D3—102no—
676C22×D3—108no—
677C22×D3#71114yescomplemented
678C22×D3C23×D512yes—
679C22×D3C23×D512yes—
680C3×D4—108no—
681C2×C3×C4—22no—
682C2×C3×C4—22no—
683C2×C3×C4—54no—
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×C4C23×D512yes—
692C2×C3×C4C23×D512yes—
693#67—28no—
694#67—28no—
695#67—108no—
696#67—108no—
697C2×Dic3—22no—
698C2×Dic3—52no—
699C2×Dic3—52no—
700C2×Dic3—52no—
701C2×Dic3—102no—
702C2×Dic3—102no—
703C2×Dic3—102no—
704C2×Dic3—108no—
705C2×Dic3D4×D514yes—
706C2×Dic3C23×D512yes—
707C2×Dic3C23×D512yes—
708D12—28no—
709D12—108no—
710C4×D3—28no—
711C4×D3—516no—
712C4×D3—108no—
713C4×D3—108no—
714C4×D3—108no—
715Dic6—108no—
716C22×C5—22no—
717C22×C5—22no—
718C22×C5—22no—
719C22×C5—34no—
720C22×C5—44no—
721C22×C5—62no—
722C22×C5—62no—
723C22×C5—68no—
724C22×C5—62no—
725C22×C5—62no—
726C22×C5—62no—
727C22×C5—124no—
728C22×C5C2×#23512yes—
729C22×C5C2×D3×D412yes—
730C22×C5D3×#4112yes—
731C22×C5C24×D311yescharacteristic
732C2×D5—22no—
733C2×D5—22no—
734C2×D5—28no—
735C2×D5—34no—
736C2×D5—632no—
737C2×D5—62no—
738C2×D5—62no—
739C2×D5—68no—
740C2×D5C2×#23514yescomplemented
741C4×C5—22no—
742C4×C5—22no—
743C4×C5—34no—
744C4×C5—62no—
745Dic5—22no—
746Dic5—22no—
747Dic5—62no—
748Dic5—62no—
749Dic5—62no—
750Dic5C2×D3×D414yes—
751C24—31no—
752C24—31no—
753C24—51no—
754C24—154no—
755C24—151no—
756C24—304no—
757C24—304no—
758C24—304no—
759C24C2×D3×D511yescharacteristic
760#41—3032no—
761C2×Q8—154no—
762C2×Q8—304no—
763C2×D4—34no—
764C2×D4—34no—
765C2×D4—34no—
766C2×D4—54no—
767C2×D4—64no—
768C2×D4—64no—
769C2×D4—64no—
770C2×D4—104no—
771C2×D4—154no—
772C2×D4—154no—
773C2×D4—154no—
774C2×D4—304no—
775C2×D4—304no—
776C2×D4—304no—
777C22×C4—31no—
778C22×C4—31no—
779C22×C4—34no—
780C22×C4—51no—
781C22×C4—54no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—54no—
785C22×C4—64no—
786C22×C4—104no—
787C22×C4—104no—
788C22×C4—154no—
789C22×C4—158no—
790C22×C4—154no—
791C22×C4—154no—
792C22×C4—154no—
793C22×C4—151no—
794C22×C4—151no—
795C22×C4—151no—
796C22×C4—154no—
797C22×C4—304no—
798C22×C4—304no—
799C22×C4—304no—
800C22×C4—304no—
801C22×C4—3032no—
802C22×C4C2×D3×D511yescharacteristic
803C22×C4C2×D3×D511yescharacteristic
804C4⋊C4—34no—
805C4⋊C4—54no—
806C4⋊C4—154no—
807C4⋊C4—154no—
808C4⋊C4—154no—
809C4⋊C4—154no—
810C22⋊C4—34no—
811C22⋊C4—54no—
812C22⋊C4—154no—
813C22⋊C4—154no—
814C22⋊C4—154no—
815C22⋊C4—154no—
816C22⋊C4—154no—
817C22⋊C4—154no—
818C22⋊C4—154no—
819C22⋊C4C2×D3×D514yescomplemented
820C42—54no—
821C42—154no—
822C3×C5C2×#52511yescharacteristic, complemented, Hall
823C22×C3—22no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—44no—
827C22×C3—54no—
828C22×C3—108no—
829C22×C3—102no—
830C22×C3—102no—
831C22×C3C2×D4×D512yes—
832C22×C3C2×#71112yes—
833C22×C3D5×#4112yes—
834C22×C3C24×D511yescharacteristic
835C2×D3—28no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—44no—
842C2×D3—54no—
843C2×D3—1032no—
844C2×D3—108no—
845C2×D3—102no—
846C2×D3—102no—
847C2×D3C2×#71114yescomplemented
848C3×C4—22no—
849C3×C4—22no—
850C3×C4—54no—
851C3×C4—102no—
852C3×C4—102no—
853Dic3—22no—
854Dic3—102no—
855Dic3—102no—
856Dic3—102no—
857Dic3C2×D4×D514yes—
858C2×C5—42no—
859C2×C5—64no—
860C2×C5—122no—
861C2×C5#554714yescomplemented
862C2×C5C22×#23511yescharacteristic
863C2×C5C22×D3×D411yescharacteristic
864C2×C5C2×D3×#4111yescharacteristic
865D5—24no—
866D5—64no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—34no—
871C23—32no—
872C23—32no—
873C23—54no—
874C23—52no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—102no—
881C23—102no—
882C23—154no—
883C23—152no—
884C23—308no—
885C23—308no—
886C23—308no—
887C23—3032no—
888C23—302no—
889C23—302no—
890C23C22×D3×D512yes—
891C23C22×D3×D511yescharacteristic
892Q8—308no—
893D4—68no—
894D4—68no—
895D4—68no—
896D4—108no—
897D4—308no—
898D4—308no—
899D4—308no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—34no—
903C2×C4—32no—
904C2×C4—32no—
905C2×C4—54no—
906C2×C4—52no—
907C2×C4—52no—
908C2×C4—52no—
909C2×C4—68no—
910C2×C4—62no—
911C2×C4—108no—
912C2×C4—108no—
913C2×C4—102no—
914C2×C4—102no—
915C2×C4—1516no—
916C2×C4—152no—
917C2×C4—152no—
918C2×C4—152no—
919C2×C4—308no—
920C2×C4—308no—
921C2×C4—308no—
922C2×C4—308no—
923C2×C4—302no—
924C2×C4—302no—
925C2×C4—302no—
926C2×C4C22×D3×D512yes—
927C2×C4C22×D3×D512yes—
928C2×C3—42no—
929C2×C3—104no—
930C2×C3#6594014yescomplemented
931C2×C3C22×D4×D511yescharacteristic
932C2×C3C22×#71111yescharacteristic
933C2×C3C2×D5×#4111yescharacteristic
934D3—24no—
935D3—42no—
936D3—104no—
937C5C2×#554711yescharacteristic, complemented, Sylow
938C22—22no—
939C22—22no—
940C22—22no—
941C22—34no—
942C22—44no—
943C22—54no—
944C22—68no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—108no—
951C22—102no—
952C22—102no—
953C22—124no—
954C22—154no—
955C22—3032no—
956C22—308no—
957C22—302no—
958C22—302no—
959C22D5×#23512yes—
960C22D3×D4×D512yes—
961C22D3×#71112yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—34no—
966C4—54no—
967C4—62no—
968C4—102no—
969C4—102no—
970C4—302no—
971C4—302no—
972C4—302no—
973C3C2×#6594011yescharacteristic, complemented, Sylow
974C2—42no—
975C2—64no—
976C2—104no—
977C2—122no—
978C2—304no—
979C2#1175324914yesdirect product factor
980C2C2×D5×#23511yescharacteristic
981C2C2×D3×D4×D511yescharacteristic
982C2C2×D3×#71111yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#525
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6782C2semidirect
2. C22×C4×D3×D5C2semidirect
3. C2×#91772C2semidirect
4. C2×C5×#884C2semidirect
5. C2×C3×#4027C2semidirect
6. C2×#91577C2semidirect
7. C2×Dic5×#67C2semidirect
8. C2×#91549C2semidirect
9. C2×#91475C2semidirect
10. C2×#91440C2semidirect
11. C2×#91422C2semidirect
12. C2×Dic5×D12C2semidirect
13. C2×#91402C2semidirect
14. C2×#91355C2semidirect
15. C2×#91352C2semidirect
16. #11753249C2direct (N × H)
22. C22×C5×#67C22semidirect
26. C23×C3×Dic5C22semidirect
28. C22×#1204C22semidirect
33. C2×#6782C22semidirect
35. C22×D3×Dic5C22semidirect
38. C2×C4×D3×D5C22semidirect
39. C2×C3×C5×C22⋊C4C22semidirect
40. C2×#6719C22semidirect
42. C2×C4⋊Dic15C22semidirect
43. C2×#6712C22semidirect
44. #91772C22semidirect
45. C2×C5×(C2×D3)⋊C4C22semidirect
46. C2×C5×Dic3⋊C4C22semidirect
47. C5×#884C22semidirect
49. C2×C3×#683C22semidirect
50. C2×C3×C4×Dic5C22semidirect
51. C3×#4027C22semidirect
52. #91577C22semidirect
53. Dic5×#67C22semidirect
54. #91549C22semidirect
55. C2×Dic3⋊Dic5C22semidirect
56. C2×Dic3⋊Dic5C22semidirect
60. C2×(C2×D3)⋊Dic5C22semidirect
62. C2×Dic3×Dic5C22semidirect
63. #91475C22semidirect
64. #91440C22semidirect
65. #91422C22semidirect
66. Dic5×D12C22semidirect
67. #91402C22semidirect
68. #91355C22semidirect
69. #91352C22semidirect
86. C2×#4027D3semidirect
108. C2×C5×#67C23semidirect
121. C22×C3×Dic5C23semidirect
125. C2×#1204C23semidirect
130. C2×#1200D4semidirect
136. C2×D3×Dic5C23semidirect
140. C3×C5×C22⋊C4C23semidirect
141. #6719C23semidirect
143. C4⋊Dic15C23semidirect
144. #6712C23semidirect
145. C5×(C2×D3)⋊C4C23semidirect
146. C5×Dic3⋊C4C23semidirect
148. C3×#683C23semidirect
149. C3×C4×Dic5C23semidirect
150. Dic3⋊Dic5C23semidirect
151. Dic3⋊Dic5C23semidirect
155. (C2×D3)⋊Dic5C23semidirect
157. Dic3×Dic5C23semidirect
168. C2×#884D5semidirect
185. C23×Dic5C2×D3semidirect
198. C2×C5×C22⋊C4C2×D3semidirect
217. C2×#683C2×D3semidirect
219. C2×C4×Dic5C2×D3semidirect
225. #4027C2×D3semidirect
241. C22×C5×D3#41semidirect
246. C22×C3×D5#41semidirect
284. #1200C2×D4semidirect
295. C22×#67C2×D5semidirect
312. C2×C3×C22⋊C4C2×D5semidirect
325. C2×(C2×D3)⋊C4C2×D5semidirect
330. C2×Dic3⋊C4C2×D5semidirect
334. #884C2×D5semidirect
380. C22×Dic5C22×D3semidirect
395. C5×C22⋊C4C22×D3semidirect
408. #683C22×D3semidirect
410. C4×Dic5C22×D3semidirect
446. C2×C5×D3C2×#41semidirect
450. C2×C3×D5C2×#41semidirect
489. C2×#67C22×D5semidirect
517. C3×C22⋊C4C22×D5semidirect
526. (C2×D3)⋊C4C22×D5semidirect
531. Dic3⋊C4C22×D5semidirect
556. C22×D5#235semidirect
643. C2×C22⋊C4D3×D5semidirect
647. C2×C3×C5#525semidirect
677. C22×D3#711semidirect
740. C2×D5C2×#235semidirect
819. C22⋊C4C2×D3×D5semidirect
822. C3×C5C2×#525semidirect
847. C2×D3C2×#711semidirect
861. C2×C5#5547semidirect
930. C2×C3#65940semidirect
937. C5C2×#5547semidirect
973. C3C2×#65940semidirect
979. C2#11753249direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67822
C22×C4×D3×D52
C2×#917722
C2×C5×#8842
C2×C3×#40272
C2×#915772
C2×Dic5×#672
C2×#915492
C2×#914752
C2×#914402
C2×#914222
C2×Dic5×D122
C2×#914022
C2×#913552
C2×#913522
#117532492
C2×#659403
C2×#55475