Finite Group Databasebeta

← C2×#11753688 #14482890

Subgroups — C2×#11753688 #14482890

Order 1920.

3240 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6771C211yesmaximal, characteristic, complemented
2C22×D3×Dic10C211yesmaximal, characteristic, complemented
3C2×#91785C211yesmaximal, characteristic, complemented
4C2×C5×#893C211yesmaximal, characteristic, complemented
5C2×C3×#4042C211yesmaximal, characteristic, complemented
6C2×#91462C211yesmaximal, characteristic, complemented
7C2×#91454C211yesmaximal, characteristic, complemented
8C2×#91453C211yesmaximal, characteristic, complemented
9C2×#91440C211yesmaximal, characteristic, complemented
10C2×#91416C211yesmaximal, characteristic, complemented
11C2×#91406C211yesmaximal, characteristic, complemented
12C2×#91353C211yesmaximal, characteristic, complemented
13C2×#91352C211yesmaximal, characteristic, complemented
14C2×#91326C211yesmaximal, characteristic, complemented
15C2×#91324C211yesmaximal, characteristic, complemented
16#11753688C2116yesmaximal, direct product factor
17C2×#65886—31nomaximal, Hall
18C22×C4×D15C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C22×C5×D12C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×C4×C5×D3C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×Dic10C2211yescharacteristic
25C22×#1204C2211yescharacteristic
26C22×#1204C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1203C2211yescharacteristic
29C22×#1202C2211yescharacteristic
30C22×#1201C2211yescharacteristic
31C22×#1201C2211yescharacteristic
32C22×D3×Dic5C2211yescharacteristic
33C22×D3×Dic5C2211yescharacteristic
34C2×#6771—28no—
35C2×#6771C2218yescomplemented
36C2×D3×Dic10—28no—
37C2×D3×Dic10C2218yescomplemented
38C2×C3×C5×C4⋊C4C2211yescharacteristic
39C2×#6714C2211yescharacteristic
40C2×#6714C2211yescharacteristic
41C2×#6712C2211yescharacteristic
42C2×#6712C2211yescharacteristic
43#91785C2218yescomplemented
44C2×C5×(C2×D3)⋊C4C2211yescharacteristic
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic
46C2×C4×C5×Dic3C2211yescharacteristic
47C5×#893C2218yescomplemented
48C2×C3×#685C2211yescharacteristic
49C2×C3×#685C2211yescharacteristic
50C2×C3×#683C2211yescharacteristic
51C2×C3×#683C2211yescharacteristic
52C3×#4042C2218yescomplemented
53C2×Dic3⋊Dic5C2211yescharacteristic
54C2×#6667C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic
60#91462C2218yescomplemented
61#91454C2218yescomplemented
62#91453C2218yescomplemented
63#91440C2218yescomplemented
64#91416C2218yescomplemented
65#91406C2218yescomplemented
66#91353C2218yescomplemented
67#91352C2218yescomplemented
68#91326C2218yescomplemented
69#91324C2218yescomplemented
70C2×#5633—51nomaximal, Hall
71C22×#709—31no—
72C23×Dic10—31no—
73C2×C4×C5×D4—31no—
74C2×#4085—31no—
75C2×#4085—31no—
76C2×#4076—31no—
77C2×#4070—31no—
78#65886—316no—
79C2×#4042—31no—
80C2×#4042D311yescharacteristic, complemented
81C2×#4031—31no—
82C2×#4031—31no—
83C2×#4027—31no—
84C2×#4027—31no—
85C2×#4021—31no—
86C2×C4×Dic10—31no—
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C2×C4×D15—24no—
98C2×C4×D15C2314yes—
99C2×Dic30—24no—
100C2×Dic30C2314yes—
101C22×C5×Dic3C2311yescharacteristic
102C22×C5×Dic3C2311yescharacteristic
103C2×C5×D12—24no—
104C2×C5×D12C2314yes—
105C2×C4×C5×D3—24no—
106C2×C4×C5×D3—24no—
107C2×C4×C5×D3C2314yes—
108C2×C4×C5×D3C2314yes—
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C2×C3×C4×D5—24no—
113C2×C3×C4×D5C2314yes—
114C2×C3×Dic10—24no—
115C2×C3×Dic10C2314yes—
116C2×#1204—24no—
117C2×#1204D418yescomplemented
118C2×#1204C2314yes—
119C2×#1204C2314yes—
120C2×#1203—24no—
121C2×#1203—24no—
122C2×#1203C2314yes—
123C2×#1203C2314yes—
124C2×#1202—24no—
125C2×#1202C2314yes—
126C2×#1201—24no—
127C2×#1201—24no—
128C2×#1201C2314yes—
129C2×#1201C2314yes—
130C2×D3×Dic5—24no—
131C2×D3×Dic5—24no—
132C2×D3×Dic5C2314yes—
133C2×D3×Dic5C2314yes—
134#6771—232no—
135D3×Dic10—232no—
136C3×C5×C4⋊C4C2314yes—
137#6714C2314yes—
138#6714C2314yes—
139#6712C2314yes—
140#6712C2314yes—
141C5×(C2×D3)⋊C4C2314yes—
142C5×(C2×D3)⋊C4C2314yes—
143C4×C5×Dic3C2314yes—
144C3×#685C2314yes—
145C3×#685C2314yes—
146C3×#683C2314yes—
147C3×#683C2314yes—
148Dic3⋊Dic5C2314yes—
149#6667C2314yes—
150(C2×D3)⋊Dic5C2314yes—
151(C2×D3)⋊Dic5C2314yes—
152#6665C2314yes—
153Dic3×Dic5C2314yes—
154Dic3×Dic5C2314yes—
155C22×D3×Q8—51no—
156C22×#235—51no—
157C2×C3×C22⋊Q8—51no—
158C2×#947—51no—
159C2×C4×#67—51no—
160#5633—516no—
161C2×#896—51no—
162C2×#896—51no—
163C2×#895—51no—
164C2×#893—51no—
165C2×#893D511yescharacteristic, complemented
166C2×#887—51no—
167C2×#885—51no—
168C2×#885—51no—
169C2×#884—51no—
170C2×#884—51no—
171C22×C5×D4—31no—
172C23×C4×C5—31no—
173C23×C4×C5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C22×C22⋊D5—31no—
178C23×Dic5—31no—
179C23×Dic5—31no—
180C2×#709—38no—
181C2×#709—68no—
182C22×D20—31no—
183C22×C4×D5—31no—
184C22×C4×D5C2×D311yescharacteristic
185C22×Dic10—31no—
186C22×Dic10—31no—
187C22×Dic10—31no—
188C22×Dic10—38no—
189C22×Dic10—68no—
190C22×Dic10C2×D311yescharacteristic
191C4×C5×D4—38no—
192C2×C5×C4⋊C4C2×D311yescharacteristic
193C2×C5×C22⋊C4—31no—
194C2×C5×C22⋊C4—31no—
195C2×C42×C5—31no—
196C2×C22⋊Dic5—31no—
197C2×C22⋊Dic5—31no—
198#4085—38no—
199#4085—38no—
200#4076—38no—
201C2×#685—31no—
202C2×#685—31no—
203C2×#685—31no—
204C2×#685—31no—
205C2×#685C2×D311yescharacteristic
206C2×#685C2×D311yescharacteristic
207C2×C4⋊Dic5—31no—
208#4070—38no—
209C2×#683—31no—
210C2×#683—31no—
211C2×#683C2×D311yescharacteristic
212C2×#683C2×D311yescharacteristic
213C2×C4×Dic5—31no—
214C2×C4×Dic5—31no—
215#4042—38no—
216#4042C2×D318yescomplemented
217#4031—38no—
218#4031—38no—
219#4027—38no—
220#4027—38no—
221#4021—38no—
222C4×Dic10—38no—
223C2×#548—151noSylow
224C23×C3×C5C2411yescharacteristic
225C22×D15—22no—
226C22×D15—22no—
227C22×D15—22no—
228C22×D15C2412yes—
229C22×C5×D3—22no—
230C22×C5×D3—22no—
231C22×C5×D3—22no—
232C22×C5×D3—22no—
233C22×C5×D3—22no—
234C22×C5×D3#4114yescomplemented
235C22×C5×D3C2412yes—
236C22×C5×D3C2412yes—
237C22×C3×D5—22no—
238C22×C3×D5—22no—
239C22×C3×D5—22no—
240C22×C3×D5C2412yes—
241C2×C3×C4×C5—22no—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5C2412yes—
245C2×C3×C4×C5C2412yes—
246C2×C3×C4×C5C2412yes—
247C2×Dic15—22no—
248C2×Dic15—22no—
249C2×Dic15C2×D414yes—
250C2×Dic15C2412yes—
251C2×Dic15C2412yes—
252C2×Dic15C2412yes—
253C4×D15—28no—
254Dic30—28no—
255C2×C5×Dic3—22no—
256C2×C5×Dic3C2×D414yes—
257C2×C5×Dic3C2412yes—
258C2×C5×Dic3C2412yes—
259C5×D12—28no—
260C4×C5×D3—28no—
261C4×C5×D3—28no—
262C2×C3×Dic5—22no—
263C2×C3×Dic5—22no—
264C2×C3×Dic5C2×D414yes—
265C2×C3×Dic5C2412yes—
266C2×C3×Dic5C2412yes—
267C2×C3×Dic5C2412yes—
268C3×C4×D5—28no—
269C3×Dic10—28no—
270#1204—28no—
271#1204C2×D4116yescomplemented
272#1203—28no—
273#1203—28no—
274#1202—28no—
275#1201—28no—
276#1201—28no—
277D3×Dic5—28no—
278D3×Dic5—28no—
279C22×C3×Q8—51no—
280C23×C3×C4—51no—
281C22×#67—51no—
282C22×#67—51no—
283C22×#67—51no—
284C2×D3×Q8—58no—
285C2×D3×Q8—108no—
286C2×#235—58no—
287C2×#235—108no—
288C22×D12—51no—
289C22×D12—51no—
290C22×D12C2×D511yescharacteristic
291C22×C4×D3—51no—
292C22×C4×D3—51no—
293C22×C4×D3—51no—
294C22×C4×D3C2×D511yescharacteristic
295C22×C4×D3C2×D511yescharacteristic
296C22×Dic6—51no—
297C22×Dic6—51no—
298C22×Dic6—51no—
299C3×C22⋊Q8—58no—
300C2×C3×C4⋊C4—51no—
301C2×C3×C4⋊C4—51no—
302C2×C3×C4⋊C4C2×D511yescharacteristic
303C2×C3×C22⋊C4—51no—
304C2×C3×C22⋊C4—51no—
305C2×#217—51no—
306#947—58no—
307C4×#67—58no—
308C2×(C2×D3)⋊C4—51no—
309C2×(C2×D3)⋊C4—51no—
310C2×(C2×D3)⋊C4—51no—
311C2×(C2×D3)⋊C4—51no—
312C2×(C2×D3)⋊C4—51no—
313C2×(C2×D3)⋊C4C2×D511yescharacteristic
314C2×(C2×D3)⋊C4C2×D511yescharacteristic
315C2×Dic3⋊C4—51no—
316C2×Dic3⋊C4—51no—
317C2×Dic3⋊C4—51no—
318C2×C4×Dic3—51no—
319C2×C4×Dic3—51no—
320C2×C4×Dic3C2×D511yescharacteristic
321#896—58no—
322#896—58no—
323#895—58no—
324#893—58no—
325#893C2×D518yescomplemented
326#887—58no—
327#885—58no—
328#885—58no—
329#884—58no—
330#884—58no—
331C24×C5—31no—
332C24×C5—31no—
333C23×D5—31no—
334C23×D5C22×D311yescharacteristic
335C2×C5×D4—34no—
336C2×C5×D4—64no—
337C22×C4×C5—31no—
338C22×C4×C5—31no—
339C22×C4×C5—34no—
340C22×C4×C5—34no—
341C22×C4×C5—64no—
342C22×C4×C5—64no—
343C22×C4×C5C22×D311yescharacteristic
344C22×C4×C5C22×D311yescharacteristic
345C22×C4×C5C22×D311yescharacteristic
346C2×C22⋊D5—34no—
347C2×C22⋊D5—34no—
348C2×C22⋊D5—34no—
349C2×C22⋊D5—34no—
350C2×C22⋊D5—64no—
351C2×C22⋊D5—64no—
352C2×C22⋊D5—64no—
353C2×C22⋊D5—64no—
354C22×Dic5—31no—
355C22×Dic5—31no—
356C22×Dic5—31no—
357C22×Dic5—34no—
358C22×Dic5—34no—
359C22×Dic5—64no—
360C22×Dic5—64no—
361C22×Dic5C22×D311yescharacteristic
362C22×Dic5C22×D311yescharacteristic
363C22×Dic5C22×D311yescharacteristic
364#709—632no—
365C2×D20—34no—
366C2×D20—64no—
367C2×C4×D5—24no—
368C2×C4×D5—34no—
369C2×C4×D5—64no—
370C2×C4×D5C22×D314yes—
371C2×Dic10—24no—
372C2×Dic10—38no—
373C2×Dic10—34no—
374C2×Dic10—34no—
375C2×Dic10—34no—
376C2×Dic10—632no—
377C2×Dic10—64no—
378C2×Dic10—64no—
379C2×Dic10C22×D314yes—
380C5×C4⋊C4C22×D314yes—
381C5×C22⋊C4—34no—
382C5×C22⋊C4—34no—
383C42×C5—34no—
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386#685—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390#685C22×D314yes—
391#685C22×D314yes—
392C4⋊Dic5—34no—
393#683—34no—
394#683—34no—
395#683C22×D314yes—
396#683C22×D314yes—
397C4×Dic5—34no—
398C4×Dic5—34no—
399C22×#41—151no—
400C23×Q8—151no—
401#548—1516no—
402C2×#124—151no—
403C2×#124—151no—
404C2×#124—151no—
405C2×C22⋊Q8—51no—
406C2×C22⋊Q8—151no—
407C2×C22⋊Q8—151no—
408C2×#121—151no—
409C2×#121—151no—
410C2×#121—151no—
411C2×C4×Q8—151no—
412C2×C4×D4—31no—
413C2×C4×D4—151no—
414C2×C4×D4—151no—
415C22×C3×C5C22×D412yes—
416C22×C3×C5C2×#4112yes—
417C22×C3×C52−1+412yes—
418C22×C3×C5C2511yescharacteristic
419C2×D15—22no—
420C2×D15—22no—
421C2×D15—22no—
422C2×D15—44no—
423C2×C5×D3—28no—
424C2×C5×D3—22no—
425C2×C5×D3—22no—
426C2×C5×D3—22no—
427C2×C5×D3—22no—
428C2×C5×D3—22no—
429C2×C5×D3—44no—
430C2×C5×D3C2×#4114yescomplemented
431C2×C3×D5—22no—
432C2×C3×D5—22no—
433C2×C3×D5—22no—
434C2×C3×D5—44no—
435C3×C4×C5—22no—
436C3×C4×C5—22no—
437C3×C4×C5—22no—
438Dic15—22no—
439Dic15—22no—
440Dic15C22×D414yes—
441C3×Dic5—22no—
442C3×Dic5—22no—
443C3×Dic5C22×D414yes—
444C5×Dic3—22no—
445C5×Dic3C22×D414yes—
446C24×C3—51no—
447C23×D3—51no—
448C23×D3C22×D511yescharacteristic
449C23×D3C22×D511yescharacteristic
450C2×C3×Q8—54no—
451C2×C3×Q8—104no—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4—51no—
455C22×C3×C4—54no—
456C22×C3×C4—104no—
457C22×C3×C4C22×D511yescharacteristic
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C2×#67—54no—
461C2×#67—54no—
462C2×#67—54no—
463C2×#67—104no—
464C2×#67—104no—
465C2×#67—104no—
466C22×Dic3—51no—
467C22×Dic3—51no—
468C22×Dic3—51no—
469C22×Dic3C22×D511yescharacteristic
470C22×Dic3C22×D511yescharacteristic
471D3×Q8—1032no—
472#235—1032no—
473C2×D12—24no—
474C2×D12—54no—
475C2×D12—54no—
476C2×D12—104no—
477C2×D12—104no—
478C2×D12C22×D514yes—
479C2×C4×D3—24no—
480C2×C4×D3—24no—
481C2×C4×D3—54no—
482C2×C4×D3—54no—
483C2×C4×D3—54no—
484C2×C4×D3—104no—
485C2×C4×D3—104no—
486C2×C4×D3—104no—
487C2×C4×D3C22×D514yes—
488C2×C4×D3C22×D514yes—
489C2×Dic6—58no—
490C2×Dic6—54no—
491C2×Dic6—54no—
492C2×Dic6—54no—
493C2×Dic6—104no—
494C2×Dic6—104no—
495C3×C4⋊C4—54no—
496C3×C4⋊C4—54no—
497C3×C4⋊C4C22×D514yes—
498C3×C22⋊C4—54no—
499C3×C22⋊C4—54no—
500#217—54no—
501(C2×D3)⋊C4—54no—
502(C2×D3)⋊C4—54no—
503(C2×D3)⋊C4—54no—
504(C2×D3)⋊C4—54no—
505(C2×D3)⋊C4—54no—
506(C2×D3)⋊C4C22×D514yes—
507(C2×D3)⋊C4C22×D514yes—
508Dic3⋊C4—54no—
509Dic3⋊C4—54no—
510Dic3⋊C4—54no—
511C4×Dic3—54no—
512C4×Dic3—54no—
513C4×Dic3C22×D514yes—
514C23×C5—34no—
515C23×C5—32no—
516C23×C5—32no—
517C23×C5—62no—
518C23×C5—62no—
519C23×C5—62no—
520C23×C5—62no—
521C23×C5—62no—
522C23×C5C23×D311yescharacteristic
523C22×D5—22no—
524C22×D5—22no—
525C22×D5—22no—
526C22×D5—32no—
527C22×D5—62no—
528C22×D5—62no—
529C22×D5—62no—
530C22×D5C23×D312yes—
531C5×D4—68no—
532C2×C4×C5—22no—
533C2×C4×C5—22no—
534C2×C4×C5—22no—
535C2×C4×C5—34no—
536C2×C4×C5—32no—
537C2×C4×C5—32no—
538C2×C4×C5—68no—
539C2×C4×C5—68no—
540C2×C4×C5—62no—
541C2×C4×C5C23×D312yes—
542C2×C4×C5C23×D312yes—
543C2×C4×C5C23×D312yes—
544C22⋊D5—68no—
545C22⋊D5—68no—
546C22⋊D5—68no—
547C22⋊D5—68no—
548C2×Dic5—22no—
549C2×Dic5—22no—
550C2×Dic5—34no—
551C2×Dic5—32no—
552C2×Dic5—32no—
553C2×Dic5—32no—
554C2×Dic5—68no—
555C2×Dic5—62no—
556C2×Dic5—62no—
557C2×Dic5—68no—
558C2×Dic5D3×D414yes—
559C2×Dic5C23×D312yes—
560C2×Dic5C23×D312yes—
561C2×Dic5C23×D312yes—
562D20—68no—
563C4×D5—28no—
564C4×D5—68no—
565Dic10—28no—
566Dic10—316no—
567Dic10—68no—
568Dic10—68no—
569C2×#41—158no—
570C2×#41—308no—
571C22×Q8—51no—
572C22×Q8—151no—
573C22×Q8—151no—
574C22×Q8—158no—
575C22×Q8—151no—
576C22×Q8—308no—
577C22×D4—31no—
578C22×D4—151no—
579C22×D4—151no—
580C22×D4—151no—
581C22×D4—151no—
582C22×D4—151no—
583C23×C4—31no—
584C23×C4—31no—
585C23×C4—51no—
586C23×C4—151no—
587C23×C4—151no—
588C23×C4—151no—
589#124—158no—
590#124—158no—
591#124—158no—
592C22⋊Q8—58no—
593C22⋊Q8—158no—
594C22⋊Q8—158no—
595#121—158no—
596#121—158no—
597#121—158no—
598C4×Q8—158no—
599C4×D4—38no—
600C4×D4—158no—
601C4×D4—158no—
602C2×C4⋊C4—51no—
603C2×C4⋊C4—51no—
604C2×C4⋊C4—151no—
605C2×C4⋊C4—151no—
606C2×C4⋊C4—151no—
607C2×C4⋊C4D3×D511yescharacteristic
608C2×C22⋊C4—31no—
609C2×C22⋊C4—31no—
610C2×C22⋊C4—51no—
611C2×C22⋊C4—51no—
612C2×C22⋊C4—151no—
613C2×C22⋊C4—151no—
614C2×C22⋊C4—151no—
615C2×C22⋊C4—151no—
616C2×C22⋊C4—151no—
617C2×C22⋊C4—151no—
618C2×C42—31no—
619C2×C42—151no—
620C2×C42—151no—
621C2×C3×C5#54814yescomplemented
622C2×C3×C5C23×D411yescharacteristic
623C2×C3×C5C22×#4111yescharacteristic
624C2×C3×C5C2×2−1+411yescharacteristic
625D15—42no—
626C3×D5—42no—
627C5×D3—24no—
628C5×D3—42no—
629C23×C3—52no—
630C23×C3—102no—
631C23×C3—102no—
632C23×C3—102no—
633C23×C3C23×D511yescharacteristic
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—22no—
637C22×D3—22no—
638C22×D3—22no—
639C22×D3—52no—
640C22×D3—102no—
641C22×D3—102no—
642C22×D3—102no—
643C22×D3#70914yescomplemented
644C22×D3C23×D512yes—
645C22×D3C23×D512yes—
646C3×Q8—108no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—54no—
651C2×C3×C4—52no—
652C2×C3×C4—52no—
653C2×C3×C4—52no—
654C2×C3×C4—108no—
655C2×C3×C4—102no—
656C2×C3×C4—102no—
657C2×C3×C4C23×D512yes—
658C2×C3×C4C23×D512yes—
659C2×C3×C4C23×D512yes—
660#67—108no—
661#67—108no—
662#67—108no—
663C2×Dic3—22no—
664C2×Dic3—54no—
665C2×Dic3—52no—
666C2×Dic3—52no—
667C2×Dic3—52no—
668C2×Dic3—102no—
669C2×Dic3—102no—
670C2×Dic3D4×D514yes—
671C2×Dic3C23×D512yes—
672C2×Dic3C23×D512yes—
673D12—28no—
674D12—108no—
675D12—108no—
676C4×D3—28no—
677C4×D3—28no—
678C4×D3—108no—
679C4×D3—108no—
680C4×D3—108no—
681Dic6—516no—
682Dic6—108no—
683Dic6—108no—
684C22×C5—34no—
685C22×C5—68no—
686C22×C5—62no—
687C22×C5—62no—
688C22×C5—62no—
689C22×C5—62no—
690C22×C5—62no—
691C22×C5—124no—
692C22×C5C2×D3×D412yes—
693C22×C5#100712yes—
694C22×C5D3×#4112yes—
695C22×C5C24×D311yescharacteristic
696C2×D5—22no—
697C2×D5—22no—
698C2×D5—22no—
699C2×D5—44no—
700C2×D5—62no—
701C2×D5—62no—
702C2×D5—62no—
703C2×D5—124no—
704C4×C5—22no—
705C4×C5—22no—
706C4×C5—22no—
707C4×C5—34no—
708C4×C5—62no—
709Dic5—22no—
710Dic5—22no—
711Dic5—34no—
712Dic5—62no—
713Dic5—62no—
714Dic5C2×D3×D414yes—
715C24—31no—
716C24—31no—
717C24—51no—
718C24—151no—
719#41—3032no—
720C2×Q8—54no—
721C2×Q8—104no—
722C2×Q8—154no—
723C2×Q8—158no—
724C2×Q8—154no—
725C2×Q8—154no—
726C2×Q8—304no—
727C2×Q8—304no—
728C2×Q8—3032no—
729C2×D4—34no—
730C2×D4—64no—
731C2×D4—154no—
732C2×D4—154no—
733C2×D4—154no—
734C2×D4—154no—
735C2×D4—154no—
736C2×D4—304no—
737C2×D4—304no—
738C2×D4—304no—
739C2×D4—304no—
740C2×D4—304no—
741C22×C4—31no—
742C22×C4—31no—
743C22×C4—34no—
744C22×C4—34no—
745C22×C4—51no—
746C22×C4—51no—
747C22×C4—51no—
748C22×C4—54no—
749C22×C4—64no—
750C22×C4—64no—
751C22×C4—104no—
752C22×C4—154no—
753C22×C4—154no—
754C22×C4—151no—
755C22×C4—151no—
756C22×C4—151no—
757C22×C4—154no—
758C22×C4—304no—
759C22×C4—304no—
760C22×C4—304no—
761C22×C4C2×D3×D511yescharacteristic
762C22×C4C2×D3×D511yescharacteristic
763C22×C4C2×D3×D511yescharacteristic
764C4⋊C4—54no—
765C4⋊C4—54no—
766C4⋊C4—154no—
767C4⋊C4—154no—
768C4⋊C4—154no—
769C4⋊C4C2×D3×D514yes—
770C22⋊C4—34no—
771C22⋊C4—34no—
772C22⋊C4—54no—
773C22⋊C4—54no—
774C22⋊C4—154no—
775C22⋊C4—154no—
776C22⋊C4—154no—
777C22⋊C4—154no—
778C22⋊C4—154no—
779C22⋊C4—154no—
780C42—34no—
781C42—154no—
782C42—154no—
783C3×C5C2×#54811yescharacteristic, complemented, Hall
784C22×C3—102no—
785C22×C3—102no—
786C22×C3—102no—
787C22×C3—204no—
788C22×C3C2×#70912yes—
789C22×C3C2×D4×D512yes—
790C22×C3#415012yes—
791C22×C3C24×D511yescharacteristic
792C2×D3—28no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—44no—
799C2×D3—102no—
800C2×D3—102no—
801C2×D3—102no—
802C2×D3—204no—
803C2×D3C2×#70914yescomplemented
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—54no—
808C3×C4—102no—
809C3×C4—102no—
810Dic3—22no—
811Dic3—54no—
812Dic3—102no—
813Dic3—102no—
814Dic3C2×D4×D514yes—
815C2×C5—64no—
816C2×C5—122no—
817C2×C5#563314yescomplemented
818C2×C5C22×D3×D411yescharacteristic
819C2×C5C2×#100711yescharacteristic
820C2×C5C2×D3×#4111yescharacteristic
821D5—42no—
822D5—122no—
823C23—34no—
824C23—32no—
825C23—32no—
826C23—52no—
827C23—62no—
828C23—62no—
829C23—62no—
830C23—62no—
831C23—62no—
832C23—102no—
833C23—102no—
834C23—102no—
835C23—152no—
836C23—302no—
837C23—302no—
838C23—302no—
839C23C22×D3×D511yescharacteristic
840Q8—108no—
841Q8—1516no—
842Q8—308no—
843Q8—308no—
844D4—68no—
845D4—308no—
846D4—308no—
847D4—308no—
848D4—308no—
849D4—308no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—34no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—54no—
857C2×C4—52no—
858C2×C4—52no—
859C2×C4—52no—
860C2×C4—68no—
861C2×C4—68no—
862C2×C4—62no—
863C2×C4—108no—
864C2×C4—102no—
865C2×C4—102no—
866C2×C4—154no—
867C2×C4—152no—
868C2×C4—152no—
869C2×C4—152no—
870C2×C4—308no—
871C2×C4—308no—
872C2×C4—308no—
873C2×C4—302no—
874C2×C4—302no—
875C2×C4C22×D3×D512yes—
876C2×C4C22×D3×D512yes—
877C2×C4C22×D3×D512yes—
878C2×C3—202no—
879C2×C3#6588614yescomplemented
880C2×C3C22×#70911yescharacteristic
881C2×C3C22×D4×D511yescharacteristic
882C2×C3C2×#415011yescharacteristic
883D3—24no—
884D3—42no—
885D3—202no—
886C5C2×#563311yescharacteristic, complemented, Sylow
887C22—34no—
888C22—68no—
889C22—62no—
890C22—62no—
891C22—62no—
892C22—62no—
893C22—62no—
894C22—102no—
895C22—102no—
896C22—102no—
897C22—124no—
898C22—204no—
899C22—302no—
900C22—302no—
901C22—302no—
902C22—604no—
903C22D3×#70912yes—
904C22D3×D4×D512yes—
905C22#9203012yes—
906C22C23×D3×D511yescharacteristic
907C4—22no—
908C4—22no—
909C4—22no—
910C4—34no—
911C4—54no—
912C4—62no—
913C4—102no—
914C4—102no—
915C4—154no—
916C4—302no—
917C4—302no—
918C3C2×#6588611yescharacteristic, complemented, Sylow
919C2—64no—
920C2—122no—
921C2—202no—
922C2—602no—
923C2#1175368814yesdirect product factor
924C2C2×D3×#70911yescharacteristic
925C2C2×D3×D4×D511yescharacteristic
926C2C2×#9203011yescharacteristic
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×#548
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×#6771C2semidirect
2. C22×D3×Dic10C2semidirect
3. C2×#91785C2semidirect
4. C2×C5×#893C2semidirect
5. C2×C3×#4042C2semidirect
6. C2×#91462C2semidirect
7. C2×#91454C2semidirect
8. C2×#91453C2semidirect
9. C2×#91440C2semidirect
10. C2×#91416C2semidirect
11. C2×#91406C2semidirect
12. C2×#91353C2semidirect
13. C2×#91352C2semidirect
14. C2×#91326C2semidirect
15. C2×#91324C2semidirect
16. #11753688C2direct (N × H)
35. C2×#6771C22semidirect
37. C2×D3×Dic10C22semidirect
43. #91785C22semidirect
47. C5×#893C22semidirect
52. C3×#4042C22semidirect
60. #91462C22semidirect
61. #91454C22semidirect
62. #91453C22semidirect
63. #91440C22semidirect
64. #91416C22semidirect
65. #91406C22semidirect
66. #91353C22semidirect
67. #91352C22semidirect
68. #91326C22semidirect
69. #91324C22semidirect
80. C2×#4042D3semidirect
117. C2×#1204D4semidirect
165. C2×#893D5semidirect
216. #4042C2×D3semidirect
234. C22×C5×D3#41semidirect
271. #1204C2×D4semidirect
325. #893C2×D5semidirect
430. C2×C5×D3C2×#41semidirect
621. C2×C3×C5#548semidirect
643. C22×D3#709semidirect
783. C3×C5C2×#548semidirect
803. C2×D3C2×#709semidirect
817. C2×C5#5633semidirect
879. C2×C3#65886semidirect
886. C5C2×#5633semidirect
918. C3C2×#65886semidirect
923. C2#11753688direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67712
C22×D3×Dic102
C2×#917852
C2×C5×#8932
C2×C3×#40422
C2×#914622
C2×#914542
C2×#914532
C2×#914402
C2×#914162
C2×#914062
C2×#913532
C2×#913522
C2×#913262
C2×#913242
#117536882
C2×#658863
C2×#56335