Finite Group Databasebeta

← C2×#11754792 #14482720

Subgroups — C2×#11754792 #14482720

Order 1920.

3264 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×C3×#711C211yesmaximal, characteristic, complemented
2C22×#6780C211yesmaximal, characteristic, complemented
3C2×#91824C211yesmaximal, characteristic, complemented
4C2×C5×#939C211yesmaximal, characteristic, complemented
5C2×#91574C211yesmaximal, characteristic, complemented
6C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
7C2×Dic5×#67C211yesmaximal, characteristic, complemented
8C2×#91549C211yesmaximal, characteristic, complemented
9C2×#91548C211yesmaximal, characteristic, complemented
10C22×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
11C2×#91539C211yesmaximal, characteristic, complemented
12#11754792C2116yesmaximal, direct product factor
13C2×#91447C211yesmaximal, characteristic, complemented
14C2×#91410C211yesmaximal, characteristic, complemented
15C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
16C2×#91327C211yesmaximal, characteristic, complemented
17C2×#65945—31nomaximal, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C23×C5×Dic3C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic
25C23×C3×Dic5C2211yescharacteristic
26C23×C3×Dic5C2211yescharacteristic
27C2×C3×#711—28no—
28C2×C3×#711C2218yescomplemented
29C22×C3×C4×D5C2211yescharacteristic
30C22×C3×Dic10C2211yescharacteristic
31C22×#1204C2211yescharacteristic
32C22×#1201C2211yescharacteristic
33C22×D3×Dic5C2211yescharacteristic
34C2×#6780—28no—
35C2×#6780C2218yescomplemented
36C22×D5×Dic3C2211yescharacteristic
37C22×D5×Dic3C2211yescharacteristic
38C2×#6719C2211yescharacteristic
39C2×#6719C2211yescharacteristic
40C2×#6719C2211yescharacteristic
41#91824C2218yescomplemented
42C2×#6712C2211yescharacteristic
43C2×#6712C2211yescharacteristic
44C2×C5×#217C2211yescharacteristic
45C5×#939C2218yescomplemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic
47C2×C5×Dic3⋊C4C2211yescharacteristic
48#91574C2218yescomplemented
49Dic3×C22⋊D5C2218yescomplemented
50Dic5×#67C2218yescomplemented
51#91549C2218yescomplemented
52#91548C2218yescomplemented
53C2×Dic3⋊Dic5C2211yescharacteristic
54C2×Dic3⋊Dic5C2211yescharacteristic
55C2×Dic3⋊Dic5C2211yescharacteristic
56C2×Dic3⋊Dic5C2211yescharacteristic
57C2×Dic3⋊Dic5C2218yescomplemented
58C2×#6669C2211yescharacteristic
59C2×#6669C2211yescharacteristic
60C2×#6668C2211yescharacteristic
61#91539C2218yescomplemented
62C2×(C2×D3)⋊Dic5C2211yescharacteristic
63C2×(C2×D3)⋊Dic5C2211yescharacteristic
64C2×#6665C2211yescharacteristic
65C2×Dic3×Dic5C2211yescharacteristic
66#91447C2218yescomplemented
67#91410C2218yescomplemented
68D5×Dic3⋊C4C2218yescomplemented
69#91327C2218yescomplemented
70C2×#5824—51nomaximal, Hall
71C22×#711—31no—
72C22×#711D311yescharacteristic, complemented
73C2×C5×#121—31no—
74C2×#4084—31no—
75C2×#4081—31no—
76C2×#4081—31no—
77C2×D4×Dic5—31no—
78C2×C4×C22⋊D5—31no—
79C22×C4⋊Dic5—31no—
80#65945—316no—
81C2×D5×C4⋊C4—31no—
82C2×#4034—31no—
83C2×#4029—31no—
84C2×#4029—31no—
85C2×#4024—31no—
86C2×#4024—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C2×C3×C5×D4—24no—
92C2×C3×C5×D4C2314yes—
93C22×C3×C4×C5C2311yescharacteristic
94C22×Dic15—24no—
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2314yes—
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C2×C5×#67—24no—
101C2×C5×#67—24no—
102C2×C5×#67C2314yes—
103C2×C5×#67C2314yes—
104C22×C5×Dic3—24no—
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2314yes—
108C22×C5×Dic3C2311yescharacteristic
109C2×C3×C22⋊D5—24no—
110C2×C3×C22⋊D5D418yescomplemented
111C2×C3×C22⋊D5C2314yes—
112C2×C3×C22⋊D5C2314yes—
113C22×C3×Dic5—24no—
114C22×C3×Dic5—24no—
115C22×C3×Dic5C2311yescharacteristic
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2314yes—
118C22×C3×Dic5C2314yes—
119C22×C3×Dic5C2311yescharacteristic
120C3×#711—232no—
121C2×C3×C4×D5—24no—
122C2×C3×C4×D5C2314yes—
123C2×C3×Dic10—24no—
124C2×C3×Dic10C2314yes—
125C2×#1204—24no—
126C2×#1204C2314yes—
127C2×#1201—24no—
128C2×#1201C2314yes—
129C2×D3×Dic5—24no—
130C2×D3×Dic5C2314yes—
131#6780—232no—
132C2×D5×Dic3—24no—
133C2×D5×Dic3—24no—
134C2×D5×Dic3C2314yes—
135C2×D5×Dic3C2314yes—
136#6719C2314yes—
137#6719C2314yes—
138#6719C2314yes—
139#6712C2314yes—
140#6712C2314yes—
141C5×#217C2314yes—
142C5×(C2×D3)⋊C4C2314yes—
143C5×Dic3⋊C4C2314yes—
144Dic3⋊Dic5C2314yes—
145Dic3⋊Dic5C2314yes—
146Dic3⋊Dic5C2314yes—
147Dic3⋊Dic5C2314yes—
148#6669C2314yes—
149#6669C2314yes—
150#6668C2314yes—
151(C2×D3)⋊Dic5C2314yes—
152(C2×D3)⋊Dic5C2314yes—
153#6665C2314yes—
154Dic3×Dic5C2314yes—
155C22×C3×#41—51no—
156C22×#237—51no—
157#5824—516no—
158C2×#946—51no—
159C2×#944—51no—
160C2×#939—51no—
161C2×#939D511yescharacteristic, complemented
162C2×#935—51no—
163C2×#935—51no—
164C2×D4×Dic3—51no—
165C2×#929—51no—
166C2×#929—51no—
167C2×C4×#67—51no—
168C2×#924—51no—
169C22×Dic3⋊C4—51no—
170C22×Dic3⋊C4—51no—
171C22×C5×D4—31no—
172C22×C5×D4—31no—
173C22×C5×D4C2×D311yescharacteristic
174C23×C4×C5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5C2×D311yescharacteristic
177C22×C22⋊D5C2×D311yescharacteristic
178C23×Dic5—31no—
179C23×Dic5—31no—
180C23×Dic5C2×D311yescharacteristic
181C23×Dic5C2×D311yescharacteristic
182C2×#711—28no—
183C2×#711—38no—
184C2×#711—68no—
185C2×#711C2×D318yescomplemented
186C22×C4×D5—31no—
187C22×C4×D5—31no—
188C22×C4×D5C2×D311yescharacteristic
189C22×Dic10—31no—
190C22×Dic10C2×D311yescharacteristic
191C5×#121—38no—
192C2×C5×C4⋊C4—31no—
193C2×C5×C22⋊C4—31no—
194C2×C5×C22⋊C4—31no—
195C2×C22⋊Dic5—31no—
196C2×C22⋊Dic5—31no—
197C2×C22⋊Dic5—31no—
198C2×C22⋊Dic5—31no—
199C2×C22⋊Dic5—31no—
200#4084—38no—
201#4081—38no—
202#4081—38no—
203D4×Dic5—38no—
204C4×C22⋊D5—38no—
205C2×#685—31no—
206C2×C4⋊Dic5—31no—
207C2×C4⋊Dic5—31no—
208C2×C4⋊Dic5—31no—
209C2×C4⋊Dic5—31no—
210C2×C4⋊Dic5—38no—
211C2×#683—31no—
212C2×#683—31no—
213C2×#683—31no—
214C2×#683—31no—
215C2×#683—31no—
216C2×C4×Dic5—31no—
217D5×C4⋊C4—38no—
218#4034—38no—
219#4029—38no—
220#4029—38no—
221#4024—38no—
222#4024—38no—
223C2×#547—151noSylow
224C23×C3×C5—22no—
225C23×C3×C5—22no—
226C23×C3×C5—22no—
227C23×C3×C5—22no—
228C23×C3×C5—22no—
229C23×C3×C5C2×D414yes—
230C23×C3×C5C2412yes—
231C23×C3×C5C2412yes—
232C23×C3×C5C2411yescharacteristic
233C22×C5×D3—22no—
234C22×C5×D3—22no—
235C22×C5×D3—22no—
236C22×C5×D3C2412yes—
237C22×C3×D5—22no—
238C22×C3×D5—22no—
239C22×C3×D5C2×D414yes—
240C22×C3×D5C2412yes—
241C3×C5×D4—28no—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5C2412yes—
244C2×Dic15—22no—
245C2×Dic15—28no—
246C2×Dic15—22no—
247C2×Dic15—22no—
248C2×Dic15—22no—
249C2×Dic15C2412yes—
250C2×Dic15C2412yes—
251C2×Dic15C2412yes—
252C2×Dic15C2412yes—
253C5×#67—28no—
254C5×#67—28no—
255C2×C5×Dic3—22no—
256C2×C5×Dic3—22no—
257C2×C5×Dic3—28no—
258C2×C5×Dic3#4114yescomplemented
259C2×C5×Dic3C2412yes—
260C2×C5×Dic3C2412yes—
261C2×C5×Dic3C2412yes—
262C3×C22⋊D5—28no—
263C3×C22⋊D5C2×D4116yescomplemented
264C2×C3×Dic5—22no—
265C2×C3×Dic5—22no—
266C2×C3×Dic5—28no—
267C2×C3×Dic5—28no—
268C2×C3×Dic5C2×D414yes—
269C2×C3×Dic5C2412yes—
270C2×C3×Dic5C2412yes—
271C2×C3×Dic5C2412yes—
272C3×C4×D5—28no—
273C3×Dic10—28no—
274#1204—28no—
275#1201—28no—
276D3×Dic5—28no—
277D5×Dic3—28no—
278D5×Dic3—28no—
279C2×C3×#41—58no—
280C2×C3×#41—108no—
281C22×C3×Q8—51no—
282C22×C3×D4—51no—
283C22×C3×D4—51no—
284C22×C3×D4C2×D511yescharacteristic
285C23×C3×C4—51no—
286C23×C3×C4—51no—
287C23×C3×C4—51no—
288C22×#67—51no—
289C22×#67C2×D511yescharacteristic
290C22×#67C2×D511yescharacteristic
291C23×Dic3—51no—
292C23×Dic3—51no—
293C23×Dic3—51no—
294C23×Dic3C2×D511yescharacteristic
295C2×#237—58no—
296C2×#237—108no—
297C22×C4×D3—51no—
298C22×Dic6—51no—
299C2×#217—51no—
300C2×#217—51no—
301C2×#217—51no—
302C2×#217—51no—
303C2×#217C2×D511yescharacteristic
304#946—58no—
305#944—58no—
306#939—58no—
307#939C2×D518yescomplemented
308#935—58no—
309#935—58no—
310D4×Dic3—58no—
311#929—58no—
312#929—58no—
313C4×#67—58no—
314C2×(C2×D3)⋊C4—51no—
315C2×(C2×D3)⋊C4—51no—
316C2×(C2×D3)⋊C4C2×D511yescharacteristic
317C2×C4⋊Dic3—51no—
318#924—58no—
319C2×Dic3⋊C4—51no—
320C2×Dic3⋊C4—51no—
321C2×Dic3⋊C4—51no—
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4—51no—
324C2×Dic3⋊C4—51no—
325C2×Dic3⋊C4—51no—
326C2×Dic3⋊C4—58no—
327C2×Dic3⋊C4—51no—
328C2×Dic3⋊C4—58no—
329C2×Dic3⋊C4C2×D511yescharacteristic
330C2×C4×Dic3—51no—
331C24×C5—31no—
332C24×C5C22×D311yescharacteristic
333C24×C5C22×D311yescharacteristic
334C23×D5C22×D311yescharacteristic
335C2×C5×D4—24no—
336C2×C5×D4—34no—
337C2×C5×D4—34no—
338C2×C5×D4—64no—
339C2×C5×D4—64no—
340C2×C5×D4C22×D314yes—
341C22×C4×C5—31no—
342C22×C4×C5—31no—
343C22×C4×C5—31no—
344C22×C4×C5—34no—
345C22×C4×C5—64no—
346C22×C4×C5C22×D311yescharacteristic
347C2×C22⋊D5—24no—
348C2×C22⋊D5—34no—
349C2×C22⋊D5—64no—
350C2×C22⋊D5#6718yescomplemented
351C2×C22⋊D5C22×D314yes—
352C2×C22⋊D5C22×D314yes—
353C22×Dic5—24no—
354C22×Dic5—24no—
355C22×Dic5—31no—
356C22×Dic5—31no—
357C22×Dic5—31no—
358C22×Dic5—31no—
359C22×Dic5—34no—
360C22×Dic5—34no—
361C22×Dic5—64no—
362C22×Dic5—64no—
363C22×Dic5C22×D311yescharacteristic
364C22×Dic5C22×D311yescharacteristic
365C22×Dic5C22×D314yes—
366C22×Dic5C22×D314yes—
367C22×Dic5C22×D311yescharacteristic
368#711—232no—
369#711—632no—
370C2×C4×D5—24no—
371C2×C4×D5—34no—
372C2×C4×D5—34no—
373C2×C4×D5—64no—
374C2×C4×D5—64no—
375C2×C4×D5C22×D314yes—
376C2×Dic10—24no—
377C2×Dic10—34no—
378C2×Dic10—64no—
379C2×Dic10C22×D314yes—
380C5×C4⋊C4—34no—
381C5×C22⋊C4—34no—
382C5×C22⋊C4—34no—
383C22⋊Dic5—34no—
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5—34no—
387C22⋊Dic5—34no—
388#685—34no—
389C4⋊Dic5—34no—
390C4⋊Dic5—34no—
391C4⋊Dic5—34no—
392C4⋊Dic5—34no—
393#683—34no—
394#683—34no—
395#683—34no—
396#683—34no—
397#683—34no—
398C4×Dic5—34no—
399C22×#41—51no—
400C22×#41—151no—
401#547—1516no—
402C2×C4⋊Q8—151no—
403C2×#123—151no—
404C2×#123—151no—
405C2×#123—151no—
406C2×#123—151no—
407C2×C22⋊Q8—151no—
408C2×C22⋊Q8—151no—
409C2×#121—31no—
410C2×#121—151no—
411C2×C4×D4—151no—
412C2×C4×D4—151no—
413C22×C4⋊C4—151no—
414C22×C4⋊C4—151no—
415C22×C3×C5—28no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—22no—
421C22×C3×C5—44no—
422C22×C3×C5C22×D414yes—
423C22×C3×C5C22×D412yes—
424C22×C3×C5C2×#4112yes—
425C22×C3×C52−1+412yes—
426C22×C3×C5C2511yescharacteristic
427C2×C5×D3—22no—
428C2×C5×D3—22no—
429C2×C5×D3—22no—
430C2×C5×D3—44no—
431C2×C3×D5—28no—
432C2×C3×D5—22no—
433C2×C3×D5—22no—
434C2×C3×D5C22×D414yes—
435C3×C4×C5—22no—
436Dic15—22no—
437Dic15—22no—
438Dic15—22no—
439Dic15—22no—
440C3×Dic5—22no—
441C3×Dic5—22no—
442C3×Dic5C22×D414yes—
443C5×Dic3—22no—
444C5×Dic3—22no—
445C5×Dic3C2×#4114yescomplemented
446C24×C3—51no—
447C24×C3C22×D511yescharacteristic
448C24×C3C22×D511yescharacteristic
449C23×D3C22×D511yescharacteristic
450C3×#41—1032no—
451C2×C3×Q8—54no—
452C2×C3×Q8—104no—
453C2×C3×D4—24no—
454C2×C3×D4—58no—
455C2×C3×D4—54no—
456C2×C3×D4—54no—
457C2×C3×D4—104no—
458C2×C3×D4C22×D514yes—
459C22×C3×C4—51no—
460C22×C3×C4—51no—
461C22×C3×C4—51no—
462C22×C3×C4—54no—
463C22×C3×C4—54no—
464C22×C3×C4—54no—
465C22×C3×C4—104no—
466C22×C3×C4—104no—
467C22×C3×C4—104no—
468C22×C3×C4C22×D511yescharacteristic
469C2×#67—24no—
470C2×#67—24no—
471C2×#67—54no—
472C2×#67—104no—
473C2×#67C22×D514yes—
474C2×#67C22×D514yes—
475C22×Dic3—24no—
476C22×Dic3—51no—
477C22×Dic3—51no—
478C22×Dic3—51no—
479C22×Dic3—51no—
480C22×Dic3—54no—
481C22×Dic3—54no—
482C22×Dic3—54no—
483C22×Dic3—104no—
484C22×Dic3—104no—
485C22×Dic3—104no—
486C22×Dic3C22×D511yescharacteristic
487C22×Dic3C22×D511yescharacteristic
488C22×Dic3C22×D514yes—
489C22×Dic3C22×D511yescharacteristic
490#237—1032no—
491C2×C4×D3—54no—
492C2×C4×D3—104no—
493C2×Dic6—54no—
494C2×Dic6—104no—
495#217—54no—
496#217—54no—
497#217—54no—
498#217—54no—
499#217C22×D514yes—
500(C2×D3)⋊C4—54no—
501(C2×D3)⋊C4—54no—
502(C2×D3)⋊C4C22×D514yes—
503C4⋊Dic3—54no—
504Dic3⋊C4—54no—
505Dic3⋊C4—54no—
506Dic3⋊C4—54no—
507Dic3⋊C4—54no—
508Dic3⋊C4—54no—
509Dic3⋊C4—54no—
510Dic3⋊C4—54no—
511Dic3⋊C4—54no—
512Dic3⋊C4C22×D514yes—
513C4×Dic3—54no—
514C23×C5—22no—
515C23×C5—22no—
516C23×C5—22no—
517C23×C5—22no—
518C23×C5—22no—
519C23×C5—32no—
520C23×C5—62no—
521C23×C5—62no—
522C23×C5—62no—
523C23×C5C2×#6714yes—
524C23×C5C23×D312yes—
525C23×C5C23×D312yes—
526C23×C5C23×D311yescharacteristic
527C22×D5—22no—
528C22×D5—22no—
529C22×D5C2×#6714yes—
530C22×D5C23×D312yes—
531C5×D4—28no—
532C5×D4—68no—
533C5×D4—68no—
534C2×C4×C5—22no—
535C2×C4×C5—34no—
536C2×C4×C5—32no—
537C2×C4×C5—32no—
538C2×C4×C5—32no—
539C2×C4×C5—68no—
540C2×C4×C5—62no—
541C2×C4×C5—62no—
542C2×C4×C5C23×D312yes—
543C22⋊D5—28no—
544C22⋊D5—68no—
545C22⋊D5C2×#67116yescomplemented
546C2×Dic5—22no—
547C2×Dic5—22no—
548C2×Dic5—28no—
549C2×Dic5—28no—
550C2×Dic5—32no—
551C2×Dic5—32no—
552C2×Dic5—32no—
553C2×Dic5—32no—
554C2×Dic5—62no—
555C2×Dic5—62no—
556C2×Dic5—62no—
557C2×Dic5—62no—
558C2×Dic5—68no—
559C2×Dic5—68no—
560C2×Dic5C2×#6714yes—
561C2×Dic5C23×D312yes—
562C2×Dic5C23×D312yes—
563C2×Dic5C23×D312yes—
564C4×D5—28no—
565C4×D5—68no—
566C4×D5—68no—
567Dic10—28no—
568Dic10—68no—
569C2×#41—58no—
570C2×#41—108no—
571C2×#41—158no—
572C2×#41—308no—
573C22×Q8—51no—
574C22×Q8—151no—
575C22×D4—31no—
576C22×D4—31no—
577C22×D4—51no—
578C22×D4—51no—
579C22×D4—151no—
580C22×D4D3×D511yescharacteristic
581C23×C4—31no—
582C23×C4—51no—
583C23×C4—51no—
584C23×C4—51no—
585C23×C4—151no—
586C23×C4—151no—
587C23×C4—151no—
588C23×C4—151no—
589C4⋊Q8—158no—
590#123—158no—
591#123—158no—
592#123—158no—
593#123—158no—
594C22⋊Q8—158no—
595C22⋊Q8—158no—
596#121—38no—
597#121—158no—
598C4×D4—158no—
599C4×D4—158no—
600C2×C4⋊C4—31no—
601C2×C4⋊C4—158no—
602C2×C4⋊C4—151no—
603C2×C4⋊C4—151no—
604C2×C4⋊C4—151no—
605C2×C4⋊C4—151no—
606C2×C4⋊C4—151no—
607C2×C4⋊C4—158no—
608C2×C4⋊C4—151no—
609C2×C4⋊C4—151no—
610C2×C4⋊C4—151no—
611C2×C4⋊C4—151no—
612C2×C22⋊C4—31no—
613C2×C22⋊C4—31no—
614C2×C22⋊C4—151no—
615C2×C22⋊C4—151no—
616C2×C22⋊C4—151no—
617C2×C22⋊C4—151no—
618C2×C22⋊C4—151no—
619C2×C22⋊C4—151no—
620C2×C42—151no—
621C2×C3×C5—24no—
622C2×C3×C5—42no—
623C2×C3×C5#54714yescomplemented
624C2×C3×C5C23×D411yescharacteristic
625C2×C3×C5C22×#4111yescharacteristic
626C2×C3×C5C2×2−1+411yescharacteristic
627C3×D5—24no—
628C5×D3—42no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—54no—
635C23×C3—52no—
636C23×C3—102no—
637C23×C3—102no—
638C23×C3D4×D514yes—
639C23×C3C23×D512yes—
640C23×C3C23×D512yes—
641C23×C3C23×D511yescharacteristic
642C22×D3—22no—
643C22×D3—22no—
644C22×D3—22no—
645C22×D3C23×D512yes—
646C3×Q8—108no—
647C3×D4—28no—
648C3×D4—516no—
649C3×D4—108no—
650C2×C3×C4—22no—
651C2×C3×C4—54no—
652C2×C3×C4—52no—
653C2×C3×C4—52no—
654C2×C3×C4—52no—
655C2×C3×C4—108no—
656C2×C3×C4—108no—
657C2×C3×C4—102no—
658C2×C3×C4—102no—
659C2×C3×C4—108no—
660C2×C3×C4C23×D512yes—
661#67—28no—
662#67—28no—
663#67—108no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—28no—
667C2×Dic3—52no—
668C2×Dic3—52no—
669C2×Dic3—52no—
670C2×Dic3—52no—
671C2×Dic3—108no—
672C2×Dic3—102no—
673C2×Dic3—102no—
674C2×Dic3—108no—
675C2×Dic3—102no—
676C2×Dic3—102no—
677C2×Dic3—108no—
678C2×Dic3#71114yescomplemented
679C2×Dic3C23×D512yes—
680C2×Dic3C23×D512yes—
681C2×Dic3C23×D512yes—
682C4×D3—108no—
683Dic6—108no—
684C22×C5—22no—
685C22×C5—22no—
686C22×C5—28no—
687C22×C5—22no—
688C22×C5—22no—
689C22×C5—22no—
690C22×C5—44no—
691C22×C5—62no—
692C22×C5—62no—
693C22×C5—62no—
694C22×C5—124no—
695C22×C5D3×#4112yes—
696C22×C5#101012yes—
697C22×C5C22×#6714yes—
698C22×C5C22×#6712yes—
699C22×C5C24×D311yescharacteristic
700C2×D5—22no—
701C2×D5—22no—
702C2×D5—28no—
703C2×D5C22×#6714yes—
704C4×C5—22no—
705C4×C5—34no—
706C4×C5—62no—
707C4×C5—62no—
708Dic5—22no—
709Dic5—22no—
710Dic5—62no—
711Dic5—62no—
712Dic5—62no—
713Dic5—62no—
714Dic5C22×#6714yes—
715C24—31no—
716C24—51no—
717C24C2×D3×D511yescharacteristic
718C24C2×D3×D511yescharacteristic
719#41—1032no—
720#41—3032no—
721C2×Q8—54no—
722C2×Q8—104no—
723C2×Q8—154no—
724C2×Q8—304no—
725C2×D4—24no—
726C2×D4—34no—
727C2×D4—34no—
728C2×D4—58no—
729C2×D4—54no—
730C2×D4—54no—
731C2×D4—64no—
732C2×D4—64no—
733C2×D4—104no—
734C2×D4—154no—
735C2×D4—304no—
736C2×D4C2×D3×D514yes—
737C22×C4—31no—
738C22×C4—34no—
739C22×C4—31no—
740C22×C4—31no—
741C22×C4—51no—
742C22×C4—54no—
743C22×C4—54no—
744C22×C4—51no—
745C22×C4—51no—
746C22×C4—54no—
747C22×C4—64no—
748C22×C4—104no—
749C22×C4—104no—
750C22×C4—104no—
751C22×C4—154no—
752C22×C4—154no—
753C22×C4—154no—
754C22×C4—154no—
755C22×C4—151no—
756C22×C4—151no—
757C22×C4—151no—
758C22×C4—151no—
759C22×C4—304no—
760C22×C4—304no—
761C22×C4—304no—
762C22×C4—304no—
763C22×C4C2×D3×D511yescharacteristic
764C4⋊C4—34no—
765C4⋊C4—154no—
766C4⋊C4—154no—
767C4⋊C4—154no—
768C4⋊C4—154no—
769C4⋊C4—154no—
770C4⋊C4—154no—
771C4⋊C4—154no—
772C4⋊C4—154no—
773C4⋊C4—154no—
774C22⋊C4—34no—
775C22⋊C4—34no—
776C22⋊C4—154no—
777C22⋊C4—154no—
778C22⋊C4—154no—
779C22⋊C4—154no—
780C22⋊C4—154no—
781C22⋊C4—154no—
782C42—154no—
783C3×C5C2×#54711yescharacteristic, complemented, Hall
784C22×C3—28no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—44no—
791C22×C3—54no—
792C22×C3—108no—
793C22×C3—102no—
794C22×C3—102no—
795C22×C3C2×D4×D514yes—
796C22×C3C2×D4×D512yes—
797C22×C3C2×#71112yes—
798C22×C3#415012yes—
799C22×C3C24×D511yescharacteristic
800C2×D3—22no—
801C2×D3—22no—
802C2×D3—22no—
803C2×D3—44no—
804C3×C4—22no—
805C3×C4—54no—
806C3×C4—102no—
807C3×C4—102no—
808Dic3—22no—
809Dic3—22no—
810Dic3—102no—
811Dic3—102no—
812Dic3—102no—
813Dic3—102no—
814Dic3C2×#71114yescomplemented
815C2×C5—24no—
816C2×C5—42no—
817C2×C5—122no—
818C2×C5#582414yescomplemented
819C2×C5C2×D3×#4111yescharacteristic
820C2×C5C2×#101011yescharacteristic
821C2×C5C23×#6711yescharacteristic
822D5—24no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—32no—
829C23—54no—
830C23—52no—
831C23—62no—
832C23—62no—
833C23—62no—
834C23—102no—
835C23—102no—
836C23D5×#6714yes—
837C23C22×D3×D512yes—
838C23C22×D3×D512yes—
839C23C22×D3×D511yescharacteristic
840Q8—108no—
841Q8—308no—
842D4—28no—
843D4—516no—
844D4—68no—
845D4—68no—
846D4—108no—
847D4—308no—
848C2×C4—22no—
849C2×C4—34no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—54no—
854C2×C4—52no—
855C2×C4—52no—
856C2×C4—52no—
857C2×C4—68no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—108no—
861C2×C4—108no—
862C2×C4—102no—
863C2×C4—102no—
864C2×C4—108no—
865C2×C4—152no—
866C2×C4—152no—
867C2×C4—152no—
868C2×C4—152no—
869C2×C4—308no—
870C2×C4—308no—
871C2×C4—308no—
872C2×C4—302no—
873C2×C4—302no—
874C2×C4—302no—
875C2×C4—302no—
876C2×C4—308no—
877C2×C4C22×D3×D512yes—
878C2×C3—24no—
879C2×C3—42no—
880C2×C3—104no—
881C2×C3#6594514yescomplemented
882C2×C3C22×D4×D511yescharacteristic
883C2×C3C22×#71111yescharacteristic
884C2×C3C2×#415011yescharacteristic
885D3—42no—
886C5C2×#582411yescharacteristic, complemented, Sylow
887C22—28no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—44no—
894C22—54no—
895C22—62no—
896C22—62no—
897C22—62no—
898C22—108no—
899C22—102no—
900C22—102no—
901C22—124no—
902C22#9202012yes—
903C22D3×#71112yes—
904C22C2×D5×#6714yes—
905C22C2×D5×#6712yes—
906C22C23×D3×D511yescharacteristic
907C4—22no—
908C4—34no—
909C4—54no—
910C4—62no—
911C4—62no—
912C4—102no—
913C4—102no—
914C4—302no—
915C4—302no—
916C4—302no—
917C4—302no—
918C3C2×#6594511yescharacteristic, complemented, Sylow
919C2—24no—
920C2—42no—
921C2—104no—
922C2—122no—
923C2#1175479214yesdirect product factor
924C2C2×#9202011yescharacteristic
925C2C2×D3×#71111yescharacteristic
926C2C22×D5×#6711yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#547
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×C3×#711C2semidirect
2. C22×#6780C2semidirect
3. C2×#91824C2semidirect
4. C2×C5×#939C2semidirect
5. C2×#91574C2semidirect
6. C2×Dic3×C22⋊D5C2semidirect
7. C2×Dic5×#67C2semidirect
8. C2×#91549C2semidirect
9. C2×#91548C2semidirect
10. C22×Dic3⋊Dic5C2semidirect
11. C2×#91539C2semidirect
12. #11754792C2direct (N × H)
13. C2×#91447C2semidirect
14. C2×#91410C2semidirect
15. C2×D5×Dic3⋊C4C2semidirect
16. C2×#91327C2semidirect
28. C2×C3×#711C22semidirect
35. C2×#6780C22semidirect
41. #91824C22semidirect
45. C5×#939C22semidirect
48. #91574C22semidirect
49. Dic3×C22⋊D5C22semidirect
50. Dic5×#67C22semidirect
51. #91549C22semidirect
52. #91548C22semidirect
57. C2×Dic3⋊Dic5C22semidirect
61. #91539C22semidirect
66. #91447C22semidirect
67. #91410C22semidirect
68. D5×Dic3⋊C4C22semidirect
69. #91327C22semidirect
72. C22×#711D3semidirect
110. C2×C3×C22⋊D5D4semidirect
161. C2×#939D5semidirect
185. C2×#711C2×D3semidirect
258. C2×C5×Dic3#41semidirect
263. C3×C22⋊D5C2×D4semidirect
307. #939C2×D5semidirect
350. C2×C22⋊D5#67semidirect
445. C5×Dic3C2×#41semidirect
545. C22⋊D5C2×#67semidirect
623. C2×C3×C5#547semidirect
678. C2×Dic3#711semidirect
783. C3×C5C2×#547semidirect
814. Dic3C2×#711semidirect
818. C2×C5#5824semidirect
881. C2×C3#65945semidirect
886. C5C2×#5824semidirect
918. C3C2×#65945semidirect
923. C2#11754792direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7112
C22×#67802
C2×#918242
C2×C5×#9392
C2×#915742
C2×Dic3×C22⋊D52
C2×Dic5×#672
C2×#915492
C2×#915482
C22×Dic3⋊Dic52
C2×#915392
#117547922
C2×#914472
C2×#914102
C2×D5×Dic3⋊C42
C2×#913272
C2×#659453
C2×#58245