Finite Group Databasebeta

← C2×#11754810 #14482717

Subgroups — C2×#11754810 #14482717

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×C5×#237C211yesmaximal, characteristic, complemented
2C22×#6782C211yesmaximal, characteristic, complemented
3C2×#91828C211yesmaximal, characteristic, complemented
4C2×C3×#4081C211yesmaximal, characteristic, complemented
5C2×#91575C211yesmaximal, characteristic, complemented
6C2×#67⋊Dic5C211yesmaximal, characteristic, complemented
7C2×#91558C211yesmaximal, characteristic, complemented
8C2×#91556C211yesmaximal, characteristic, complemented
9C2×#91555C211yesmaximal, characteristic, complemented
10C22×#6669C211yesmaximal, characteristic, complemented
11C2×#91542C211yesmaximal, characteristic, complemented
12#11754810C2116yesmaximal, direct product factor
13C2×#91424C211yesmaximal, characteristic, complemented
14C2×D3×#683C211yesmaximal, characteristic, complemented
15C2×#91351C211yesmaximal, characteristic, complemented
16C2×#91329C211yesmaximal, characteristic, complemented
17C2×#66158—31nomaximal, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C23×Dic15C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic
24C23×C5×Dic3C2211yescharacteristic
25C23×C5×Dic3C2211yescharacteristic
26C2×C5×#237—28no—
27C2×C5×#237C2218yescomplemented
28C22×C4×C5×D3C2211yescharacteristic
29C22×C5×Dic6C2211yescharacteristic
30C23×C3×Dic5C2211yescharacteristic
31C22×#1204C2211yescharacteristic
32C22×#1203C2211yescharacteristic
33C22×#1200C2211yescharacteristic
34C2×#6782—28no—
35C2×#6782C2218yescomplemented
36C22×D3×Dic5C2211yescharacteristic
37C22×D3×Dic5C2211yescharacteristic
38C2×#6719C2211yescharacteristic
39#91828C2218yescomplemented
40C2×#6714C2211yescharacteristic
41C2×#6712C2211yescharacteristic
42C2×C3×C22⋊Dic5C2211yescharacteristic
43C2×C3×C22⋊Dic5C2211yescharacteristic
44C2×C3×C22⋊Dic5C2211yescharacteristic
45C3×#4081C2218yescomplemented
46C2×C3×#683C2211yescharacteristic
47C2×C3×#683C2211yescharacteristic
48#91575C2218yescomplemented
49#67⋊Dic5C2218yescomplemented
50#91558C2218yescomplemented
51#91556C2218yescomplemented
52#91555C2218yescomplemented
53C2×Dic3⋊Dic5C2211yescharacteristic
54C2×#6669C2211yescharacteristic
55C2×#6669C2211yescharacteristic
56C2×#6669C2211yescharacteristic
57C2×#6669C2211yescharacteristic
58C2×#6669C2218yescomplemented
59#91542C2218yescomplemented
60C2×#6668C2211yescharacteristic
61C2×#6668C2211yescharacteristic
62C2×#6667C2211yescharacteristic
63C2×#6667C2211yescharacteristic
64C2×(C2×D3)⋊Dic5C2211yescharacteristic
65C2×Dic3×Dic5C2211yescharacteristic
66#91424C2218yescomplemented
67D3×#683C2218yescomplemented
68#91351C2218yescomplemented
69#91329C2218yescomplemented
70C2×#5655—51nomaximal, Hall
71C22×C5×#41—31no—
72C22×#711—31no—
73#66158—316no—
74C2×#4092—31no—
75C2×#4090—31no—
76C2×#4085—31no—
77C2×#4085—31no—
78C2×#4081—31no—
79C2×#4081D311yescharacteristic, complemented
80C2×D4×Dic5—31no—
81C2×#4075—31no—
82C2×#4075—31no—
83C2×C4×C22⋊D5—31no—
84C2×#4070—31no—
85C22×#683—31no—
86C22×#683—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C2×C3×C5×D4—24no—
92C2×C3×C5×D4C2314yes—
93C22×C3×C4×C5C2311yescharacteristic
94C2×#1220—24no—
95C2×#1220—24no—
96C2×#1220C2314yes—
97C2×#1220C2314yes—
98C22×Dic15—24no—
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2314yes—
102C22×Dic15C2311yescharacteristic
103C2×C5×#67—24no—
104C2×C5×#67D418yescomplemented
105C2×C5×#67C2314yes—
106C2×C5×#67C2314yes—
107C22×C5×Dic3—24no—
108C22×C5×Dic3—24no—
109C22×C5×Dic3C2311yescharacteristic
110C22×C5×Dic3C2311yescharacteristic
111C22×C5×Dic3C2314yes—
112C22×C5×Dic3C2314yes—
113C22×C5×Dic3C2311yescharacteristic
114C5×#237—232no—
115C2×C4×C5×D3—24no—
116C2×C4×C5×D3C2314yes—
117C2×C5×Dic6—24no—
118C2×C5×Dic6C2314yes—
119C22×C3×Dic5—24no—
120C22×C3×Dic5C2314yes—
121C22×C3×Dic5C2311yescharacteristic
122C22×C3×Dic5C2311yescharacteristic
123C22×C3×Dic5C2311yescharacteristic
124C22×C3×Dic5C2311yescharacteristic
125C2×#1204—24no—
126C2×#1204C2314yes—
127C2×#1203—24no—
128C2×#1203C2314yes—
129C2×#1200—24no—
130C2×#1200C2314yes—
131#6782—232no—
132C2×D3×Dic5—24no—
133C2×D3×Dic5—24no—
134C2×D3×Dic5C2314yes—
135C2×D3×Dic5C2314yes—
136#6719C2314yes—
137#6714C2314yes—
138#6712C2314yes—
139C3×C22⋊Dic5C2314yes—
140C3×C22⋊Dic5C2314yes—
141C3×C22⋊Dic5C2314yes—
142C3×#683C2314yes—
143C3×#683C2314yes—
144Dic3⋊Dic5C2314yes—
145#6669C2314yes—
146#6669C2314yes—
147#6669C2314yes—
148#6669C2314yes—
149#6668C2314yes—
150#6668C2314yes—
151#6667C2314yes—
152#6667C2314yes—
153(C2×D3)⋊Dic5C2314yes—
154Dic3×Dic5C2314yes—
155C22×#237D511yescharacteristic, complemented
156C22×#235—51no—
157C2×C3×#123—51no—
158C2×#939—51no—
159C22×Dic3⋊C4—51no—
160#5655—516no—
161C2×#896—51no—
162C2×#894—51no—
163C2×D3×C4⋊C4—51no—
164C2×#888—51no—
165C2×#886—51no—
166C2×#884—51no—
167C2×#883—51no—
168C2×#67⋊C4—51no—
169C2×#67⋊C4—51no—
170C2×#878—51no—
171C2×C5×#41—38no—
172C2×C5×#41—68no—
173C22×C5×Q8—31no—
174C22×C5×D4—31no—
175C22×C5×D4—31no—
176C22×C5×D4C2×D311yescharacteristic
177C23×C4×C5—31no—
178C23×C4×C5—31no—
179C23×C4×C5—31no—
180C22×C22⋊D5—31no—
181C22×C22⋊D5—31no—
182C22×C22⋊D5—31no—
183C23×Dic5—31no—
184C23×Dic5—31no—
185C23×Dic5—31no—
186C23×Dic5C2×D311yescharacteristic
187C2×#711—38no—
188C2×#711—68no—
189C22×C4×D5—31no—
190C22×Dic10—31no—
191C2×C22⋊Dic5—31no—
192C2×C22⋊Dic5—31no—
193C2×C22⋊Dic5C2×D311yescharacteristic
194C2×C22⋊Dic5C2×D311yescharacteristic
195C2×C22⋊Dic5C2×D311yescharacteristic
196#4092—38no—
197#4090—38no—
198#4085—38no—
199#4085—38no—
200#4081—38no—
201#4081C2×D318yescomplemented
202D4×Dic5—38no—
203#4075—38no—
204#4075—38no—
205C4×C22⋊D5—38no—
206C2×#685—31no—
207C2×#685—31no—
208C2×#685—31no—
209C2×C4⋊Dic5—31no—
210#4070—38no—
211C2×#683—31no—
212C2×#683—31no—
213C2×#683—31no—
214C2×#683—31no—
215C2×#683—31no—
216C2×#683—31no—
217C2×#683—38no—
218C2×#683—31no—
219C2×#683—38no—
220C2×#683C2×D311yescharacteristic
221C2×#683C2×D311yescharacteristic
222C2×C4×Dic5—31no—
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×D15—22no—
234C22×D15—22no—
235C22×D15—22no—
236C22×D15C2412yes—
237C22×C5×D3—22no—
238C22×C5×D3—22no—
239C22×C5×D3C2×D414yes—
240C22×C5×D3C2412yes—
241C3×C5×D4—28no—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5C2412yes—
244#1220—28no—
245#1220—28no—
246C2×Dic15—22no—
247C2×Dic15—22no—
248C2×Dic15—28no—
249C2×Dic15#4114yescomplemented
250C2×Dic15C2412yes—
251C2×Dic15C2412yes—
252C2×Dic15C2412yes—
253C5×#67—28no—
254C5×#67C2×D4116yescomplemented
255C2×C5×Dic3—22no—
256C2×C5×Dic3—22no—
257C2×C5×Dic3—28no—
258C2×C5×Dic3—28no—
259C2×C5×Dic3C2×D414yes—
260C2×C5×Dic3C2412yes—
261C2×C5×Dic3C2412yes—
262C2×C5×Dic3C2412yes—
263C4×C5×D3—28no—
264C5×Dic6—28no—
265C2×C3×Dic5—22no—
266C2×C3×Dic5—28no—
267C2×C3×Dic5—22no—
268C2×C3×Dic5—22no—
269C2×C3×Dic5—22no—
270C2×C3×Dic5C2412yes—
271C2×C3×Dic5C2412yes—
272C2×C3×Dic5C2412yes—
273C2×C3×Dic5C2412yes—
274#1204—28no—
275#1203—28no—
276#1200—28no—
277D3×Dic5—28no—
278D3×Dic5—28no—
279C22×C3×D4C2×D511yescharacteristic
280C23×C3×C4—51no—
281C22×#67—51no—
282C22×#67—51no—
283C22×#67C2×D511yescharacteristic
284C22×#67C2×D511yescharacteristic
285C23×Dic3—51no—
286C23×Dic3C2×D511yescharacteristic
287C23×Dic3C2×D511yescharacteristic
288C2×#237—28no—
289C2×#237C2×D518yescomplemented
290C2×#235—58no—
291C2×#235—108no—
292C22×D12—51no—
293C22×C4×D3—51no—
294C22×C4×D3—51no—
295C22×C4×D3—51no—
296C22×C4×D3C2×D511yescharacteristic
297C22×Dic6—51no—
298C22×Dic6C2×D511yescharacteristic
299C3×#123—58no—
300C2×C3×C4⋊C4—51no—
301C2×C3×C4⋊C4—51no—
302C2×C3×C22⋊C4—51no—
303C2×C3×C22⋊C4—51no—
304C2×C3×C22⋊C4—51no—
305C2×#217—51no—
306#939—58no—
307C2×(C2×D3)⋊C4—51no—
308C2×(C2×D3)⋊C4—51no—
309C2×(C2×D3)⋊C4—51no—
310C2×(C2×D3)⋊C4—51no—
311C2×C4⋊Dic3—51no—
312C2×C4⋊Dic3—51no—
313C2×Dic3⋊C4—51no—
314C2×Dic3⋊C4—58no—
315C2×Dic3⋊C4—51no—
316C2×Dic3⋊C4—51no—
317C2×Dic3⋊C4—51no—
318C2×Dic3⋊C4—51no—
319C2×Dic3⋊C4—51no—
320C2×C4×Dic3—51no—
321#896—58no—
322#894—58no—
323D3×C4⋊C4—58no—
324#888—58no—
325#886—58no—
326#884—58no—
327#883—58no—
328#67⋊C4—58no—
329#67⋊C4—58no—
330#878—58no—
331C24×C5—31no—
332C24×C5C22×D311yescharacteristic
333C24×C5C22×D311yescharacteristic
334C23×D5—31no—
335C5×#41—632no—
336C2×C5×Q8—34no—
337C2×C5×Q8—64no—
338C2×C5×D4—24no—
339C2×C5×D4—38no—
340C2×C5×D4—34no—
341C2×C5×D4—34no—
342C2×C5×D4—64no—
343C2×C5×D4C22×D314yes—
344C22×C4×C5—31no—
345C22×C4×C5—31no—
346C22×C4×C5—31no—
347C22×C4×C5—34no—
348C22×C4×C5—34no—
349C22×C4×C5—34no—
350C22×C4×C5—64no—
351C22×C4×C5—64no—
352C22×C4×C5—64no—
353C22×C4×C5C22×D311yescharacteristic
354C2×C22⋊D5—34no—
355C2×C22⋊D5—34no—
356C2×C22⋊D5—34no—
357C2×C22⋊D5—64no—
358C2×C22⋊D5—64no—
359C2×C22⋊D5—64no—
360C22×Dic5—24no—
361C22×Dic5—31no—
362C22×Dic5—31no—
363C22×Dic5—31no—
364C22×Dic5—34no—
365C22×Dic5—34no—
366C22×Dic5—34no—
367C22×Dic5—64no—
368C22×Dic5—64no—
369C22×Dic5—64no—
370C22×Dic5C22×D311yescharacteristic
371C22×Dic5C22×D311yescharacteristic
372C22×Dic5C22×D311yescharacteristic
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D314yes—
375#711—632no—
376C2×C4×D5—34no—
377C2×C4×D5—64no—
378C2×Dic10—34no—
379C2×Dic10—64no—
380C22⋊Dic5—34no—
381C22⋊Dic5—34no—
382C22⋊Dic5C22×D314yes—
383C22⋊Dic5C22×D314yes—
384C22⋊Dic5C22×D314yes—
385#685—34no—
386#685—34no—
387#685—34no—
388C4⋊Dic5—34no—
389#683—34no—
390#683—34no—
391#683—34no—
392#683—34no—
393#683—34no—
394#683—34no—
395#683—34no—
396#683C22×D314yes—
397#683C22×D314yes—
398C4×Dic5—34no—
399C22×#41—31no—
400C22×#41—151no—
401#547—1516no—
402C2×C4⋊Q8—151no—
403C2×#123—51no—
404C2×#123—151no—
405C2×#123—151no—
406C2×#123—151no—
407C2×C22⋊Q8—151no—
408C2×C22⋊Q8—151no—
409C2×#121—151no—
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×D15—22no—
428C2×D15—22no—
429C2×D15—22no—
430C2×D15—44no—
431C2×C5×D3—28no—
432C2×C5×D3—22no—
433C2×C5×D3—22no—
434C2×C5×D3C22×D414yes—
435C3×C4×C5—22no—
436Dic15—22no—
437Dic15—22no—
438Dic15C2×#4114yescomplemented
439C3×Dic5—22no—
440C3×Dic5—22no—
441C3×Dic5—22no—
442C3×Dic5—22no—
443C5×Dic3—22no—
444C5×Dic3—22no—
445C5×Dic3C22×D414yes—
446C24×C3C22×D511yescharacteristic
447C24×C3C22×D511yescharacteristic
448C23×D3—51no—
449C23×D3C22×D511yescharacteristic
450C2×C3×D4—24no—
451C2×C3×D4C22×D514yes—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4—51no—
455C22×C3×C4—54no—
456C22×C3×C4—51no—
457C22×C3×C4—104no—
458C22×C3×C4C22×D511yescharacteristic
459C2×#67—24no—
460C2×#67—54no—
461C2×#67—54no—
462C2×#67—104no—
463C2×#67—104no—
464C2×#67C22⋊D518yescomplemented
465C2×#67C22×D514yes—
466C2×#67C22×D514yes—
467C22×Dic3—24no—
468C22×Dic3—24no—
469C22×Dic3—51no—
470C22×Dic3—54no—
471C22×Dic3—51no—
472C22×Dic3—51no—
473C22×Dic3—104no—
474C22×Dic3C22×D514yes—
475C22×Dic3C22×D514yes—
476C22×Dic3C22×D511yescharacteristic
477C22×Dic3C22×D511yescharacteristic
478C22×Dic3C22×D511yescharacteristic
479#237—232no—
480#235—1032no—
481C2×D12—54no—
482C2×D12—104no—
483C2×C4×D3—24no—
484C2×C4×D3—54no—
485C2×C4×D3—54no—
486C2×C4×D3—54no—
487C2×C4×D3—104no—
488C2×C4×D3—104no—
489C2×C4×D3—104no—
490C2×C4×D3C22×D514yes—
491C2×Dic6—24no—
492C2×Dic6—54no—
493C2×Dic6—104no—
494C2×Dic6C22×D514yes—
495C3×C4⋊C4—54no—
496C3×C4⋊C4—54no—
497C3×C22⋊C4—54no—
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—
505C4⋊Dic3—54no—
506C4⋊Dic3—54no—
507Dic3⋊C4—54no—
508Dic3⋊C4—54no—
509Dic3⋊C4—54no—
510Dic3⋊C4—54no—
511Dic3⋊C4—54no—
512Dic3⋊C4—54no—
513C4×Dic3—54no—
514C23×C5—22no—
515C23×C5—22no—
516C23×C5—22no—
517C23×C5—22no—
518C23×C5—22no—
519C23×C5—34no—
520C23×C5—32no—
521C23×C5—62no—
522C23×C5—62no—
523C23×C5D3×D414yes—
524C23×C5C23×D312yes—
525C23×C5C23×D312yes—
526C23×C5C23×D311yescharacteristic
527C22×D5—32no—
528C22×D5—62no—
529C22×D5—62no—
530C22×D5—62no—
531C5×Q8—68no—
532C5×D4—28no—
533C5×D4—316no—
534C5×D4—68no—
535C2×C4×C5—22no—
536C2×C4×C5—34no—
537C2×C4×C5—32no—
538C2×C4×C5—32no—
539C2×C4×C5—32no—
540C2×C4×C5—68no—
541C2×C4×C5—68no—
542C2×C4×C5—62no—
543C2×C4×C5—62no—
544C2×C4×C5—68no—
545C2×C4×C5C23×D312yes—
546C22⋊D5—68no—
547C22⋊D5—68no—
548C22⋊D5—68no—
549C2×Dic5—22no—
550C2×Dic5—22no—
551C2×Dic5—28no—
552C2×Dic5—22no—
553C2×Dic5—22no—
554C2×Dic5—34no—
555C2×Dic5—32no—
556C2×Dic5—32no—
557C2×Dic5—32no—
558C2×Dic5—68no—
559C2×Dic5—68no—
560C2×Dic5—68no—
561C2×Dic5—62no—
562C2×Dic5—62no—
563C2×Dic5C23×D312yes—
564C2×Dic5C23×D312yes—
565C2×Dic5C23×D312yes—
566C2×Dic5C23×D312yes—
567C4×D5—68no—
568Dic10—68no—
569C2×#41—38no—
570C2×#41—68no—
571C2×#41—158no—
572C2×#41—308no—
573C22×Q8—31no—
574C22×Q8—151no—
575C22×D4—31no—
576C22×D4—31no—
577C22×D4—151no—
578C22×D4—151no—
579C22×D4—151no—
580C22×D4D3×D511yescharacteristic
581C23×C4—31no—
582C23×C4—31no—
583C23×C4—31no—
584C23×C4—51no—
585C23×C4—151no—
586C23×C4—151no—
587C23×C4—151no—
588C23×C4—151no—
589C4⋊Q8—158no—
590#123—58no—
591#123—158no—
592#123—158no—
593#123—158no—
594C22⋊Q8—158no—
595C22⋊Q8—158no—
596#121—158no—
597#121—158no—
598C4×D4—158no—
599C4×D4—158no—
600C2×C4⋊C4—51no—
601C2×C4⋊C4—51no—
602C2×C4⋊C4—158no—
603C2×C4⋊C4—151no—
604C2×C4⋊C4—151no—
605C2×C4⋊C4—151no—
606C2×C4⋊C4—151no—
607C2×C4⋊C4—151no—
608C2×C4⋊C4—158no—
609C2×C4⋊C4—151no—
610C2×C4⋊C4—151no—
611C2×C4⋊C4—151no—
612C2×C22⋊C4—51no—
613C2×C22⋊C4—51no—
614C2×C22⋊C4—51no—
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
627D15—42no—
628C5×D3—24no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3C2×C22⋊D514yes—
635C23×C3C23×D512yes—
636C23×C3C23×D512yes—
637C23×C3C23×D511yescharacteristic
638C22×D3—22no—
639C22×D3—22no—
640C22×D3—52no—
641C22×D3—102no—
642C22×D3—102no—
643C22×D3—102no—
644C22×D3C2×C22⋊D514yes—
645C22×D3C23×D512yes—
646C3×D4—28no—
647C2×C3×C4—22no—
648C2×C3×C4—52no—
649C2×C3×C4—52no—
650C2×C3×C4—52no—
651C2×C3×C4—52no—
652C2×C3×C4—102no—
653C2×C3×C4—102no—
654C2×C3×C4—102no—
655C2×C3×C4—102no—
656C2×C3×C4—108no—
657C2×C3×C4C23×D512yes—
658#67—28no—
659#67—108no—
660#67—108no—
661#67C2×C22⋊D5116yescomplemented
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—28no—
665C2×Dic3—28no—
666C2×Dic3—54no—
667C2×Dic3—52no—
668C2×Dic3—52no—
669C2×Dic3—52no—
670C2×Dic3—108no—
671C2×Dic3—102no—
672C2×Dic3—102no—
673C2×Dic3C2×C22⋊D514yes—
674C2×Dic3C23×D512yes—
675C2×Dic3C23×D512yes—
676C2×Dic3C23×D512yes—
677D12—108no—
678C4×D3—28no—
679C4×D3—108no—
680C4×D3—108no—
681C4×D3—108no—
682Dic6—28no—
683Dic6—108no—
684C22×C5—28no—
685C22×C5—22no—
686C22×C5—22no—
687C22×C5—22no—
688C22×C5—22no—
689C22×C5—22no—
690C22×C5—34no—
691C22×C5—44no—
692C22×C5—68no—
693C22×C5—62no—
694C22×C5—62no—
695C22×C5C2×D3×D414yes—
696C22×C5C2×D3×D412yes—
697C22×C5D3×#4112yes—
698C22×C5#101012yes—
699C22×C5C24×D311yescharacteristic
700C2×D5—62no—
701C2×D5—62no—
702C2×D5—62no—
703C2×D5—124no—
704C4×C5—22no—
705C4×C5—34no—
706C4×C5—62no—
707C4×C5—62no—
708Dic5—22no—
709Dic5—22no—
710Dic5—22no—
711Dic5—22no—
712Dic5—34no—
713Dic5—62no—
714Dic5—62no—
715C24—31no—
716C24—151no—
717C24C2×D3×D511yescharacteristic
718C24C2×D3×D511yescharacteristic
719#41—632no—
720#41—3032no—
721C2×Q8—34no—
722C2×Q8—64no—
723C2×Q8—154no—
724C2×Q8—304no—
725C2×D4—24no—
726C2×D4—38no—
727C2×D4—34no—
728C2×D4—34no—
729C2×D4—64no—
730C2×D4—154no—
731C2×D4—154no—
732C2×D4—154no—
733C2×D4—304no—
734C2×D4—304no—
735C2×D4—304no—
736C2×D4C2×D3×D514yes—
737C22×C4—31no—
738C22×C4—34no—
739C22×C4—34no—
740C22×C4—31no—
741C22×C4—31no—
742C22×C4—34no—
743C22×C4—54no—
744C22×C4—51no—
745C22×C4—51no—
746C22×C4—51no—
747C22×C4—51no—
748C22×C4—64no—
749C22×C4—64no—
750C22×C4—64no—
751C22×C4—104no—
752C22×C4—154no—
753C22×C4—154no—
754C22×C4—154no—
755C22×C4—151no—
756C22×C4—154no—
757C22×C4—151no—
758C22×C4—151no—
759C22×C4—304no—
760C22×C4—304no—
761C22×C4—304no—
762C22×C4—304no—
763C22×C4C2×D3×D511yescharacteristic
764C4⋊C4—54no—
765C4⋊C4—54no—
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—54no—
775C22⋊C4—54no—
776C22⋊C4—54no—
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×C3D5×#4112yes—
792C22×C3#415012yes—
793C22×C3C22×C22⋊D514yes—
794C22×C3C22×C22⋊D512yes—
795C22×C3C24×D511yescharacteristic
796C2×D3—28no—
797C2×D3—22no—
798C2×D3—22no—
799C2×D3—102no—
800C2×D3—102no—
801C2×D3—102no—
802C2×D3—204no—
803C2×D3C22×C22⋊D514yes—
804C3×C4—22no—
805C3×C4—102no—
806C3×C4—102no—
807C3×C4—102no—
808C3×C4—102no—
809Dic3—22no—
810Dic3—22no—
811Dic3—54no—
812Dic3—102no—
813Dic3—102no—
814Dic3C22×C22⋊D514yes—
815C2×C5—24no—
816C2×C5—42no—
817C2×C5—64no—
818C2×C5#565514yescomplemented
819C2×C5C22×D3×D411yescharacteristic
820C2×C5C2×D3×#4111yescharacteristic
821C2×C5C2×#101011yescharacteristic
822D5—122no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—34no—
829C23—32no—
830C23—62no—
831C23—62no—
832C23—152no—
833C23—302no—
834C23—302no—
835C23—302no—
836C23D3×C22⋊D514yes—
837C23C22×D3×D512yes—
838C23C22×D3×D512yes—
839C23C22×D3×D511yescharacteristic
840Q8—68no—
841Q8—308no—
842D4—28no—
843D4—316no—
844D4—68no—
845D4—308no—
846D4—308no—
847D4—308no—
848C2×C4—22no—
849C2×C4—34no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—52no—
854C2×C4—52no—
855C2×C4—52no—
856C2×C4—52no—
857C2×C4—68no—
858C2×C4—68no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—68no—
862C2×C4—102no—
863C2×C4—102no—
864C2×C4—102no—
865C2×C4—102no—
866C2×C4—108no—
867C2×C4—154no—
868C2×C4—152no—
869C2×C4—152no—
870C2×C4—152no—
871C2×C4—308no—
872C2×C4—308no—
873C2×C4—308no—
874C2×C4—308no—
875C2×C4—302no—
876C2×C4—302no—
877C2×C4C22×D3×D512yes—
878C2×C3—24no—
879C2×C3—42no—
880C2×C3#6615814yescomplemented
881C2×C3C2×D5×#4111yescharacteristic
882C2×C3C2×#415011yescharacteristic
883C2×C3C23×C22⋊D511yescharacteristic
884D3—24no—
885D3—202no—
886C5C2×#565511yescharacteristic, complemented, Sylow
887C22—28no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—34no—
894C22—44no—
895C22—68no—
896C22—62no—
897C22—62no—
898C22—302no—
899C22—302no—
900C22—302no—
901C22—604no—
902C22#9202012yes—
903C22#9202412yes—
904C22C2×D3×C22⋊D514yes—
905C22C2×D3×C22⋊D512yes—
906C22C23×D3×D511yescharacteristic
907C4—22no—
908C4—34no—
909C4—62no—
910C4—62no—
911C4—102no—
912C4—102no—
913C4—102no—
914C4—102no—
915C4—154no—
916C4—302no—
917C4—302no—
918C3C2×#6615811yescharacteristic, complemented, Sylow
919C2—24no—
920C2—42no—
921C2—64no—
922C2—602no—
923C2#1175481014yesdirect product factor
924C2C2×#9202011yescharacteristic
925C2C2×#9202411yescharacteristic
926C2C22×D3×C22⋊D511yescharacteristic
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×C5×#237C2semidirect
2. C22×#6782C2semidirect
3. C2×#91828C2semidirect
4. C2×C3×#4081C2semidirect
5. C2×#91575C2semidirect
6. C2×#67⋊Dic5C2semidirect
7. C2×#91558C2semidirect
8. C2×#91556C2semidirect
9. C2×#91555C2semidirect
10. C22×#6669C2semidirect
11. C2×#91542C2semidirect
12. #11754810C2direct (N × H)
13. C2×#91424C2semidirect
14. C2×D3×#683C2semidirect
15. C2×#91351C2semidirect
16. C2×#91329C2semidirect
27. C2×C5×#237C22semidirect
35. C2×#6782C22semidirect
39. #91828C22semidirect
45. C3×#4081C22semidirect
48. #91575C22semidirect
49. #67⋊Dic5C22semidirect
50. #91558C22semidirect
51. #91556C22semidirect
52. #91555C22semidirect
58. C2×#6669C22semidirect
59. #91542C22semidirect
66. #91424C22semidirect
67. D3×#683C22semidirect
68. #91351C22semidirect
69. #91329C22semidirect
79. C2×#4081D3semidirect
104. C2×C5×#67D4semidirect
155. C22×#237D5semidirect
201. #4081C2×D3semidirect
249. C2×Dic15#41semidirect
254. C5×#67C2×D4semidirect
289. C2×#237C2×D5semidirect
438. Dic15C2×#41semidirect
464. C2×#67C22⋊D5semidirect
623. C2×C3×C5#547semidirect
661. #67C2×C22⋊D5semidirect
783. C3×C5C2×#547semidirect
818. C2×C5#5655semidirect
880. C2×C3#66158semidirect
886. C5C2×#5655semidirect
918. C3C2×#66158semidirect
923. C2#11754810direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2372
C22×#67822
C2×#918282
C2×C3×#40812
C2×#915752
C2×#67⋊Dic52
C2×#915582
C2×#915562
C2×#915552
C22×#66692
C2×#915422
#117548102
C2×#914242
C2×D3×#6832
C2×#913512
C2×#913292
C2×#661583
C2×#56555