Finite Group Databasebeta

← C2×#10618827 #13007629

Subgroups — C2×#10618827 #13007629

Order 1280.

7478 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#554C211yesmaximal, characteristic, complemented
2#10618827C2132yesmaximal, direct product factor
3C2×D5×C4⋊Q8C211yesmaximal, characteristic, complemented
4C2×#66056C211yesmaximal, characteristic, complemented
5C2×#66023C212yesmaximal, complemented
6C2×#66019C212yesmaximal, complemented
7C2×#65969C212yesmaximal, complemented
8C2×#65966C214yesmaximal, complemented
9C2×#65957C214yesmaximal, complemented
10C2×#65956C212yesmaximal, complemented
11C2×#65912C211yesmaximal, characteristic, complemented
12C2×Q8×Dic10C211yesmaximal, characteristic, complemented
13C2×#65877C211yesmaximal, characteristic, complemented
14C2×D4×Dic10C212yesmaximal, complemented
15C2×#65880C212yesmaximal
16C2×C4×#711C211yesmaximal, characteristic
17C2×#65845C212yesmaximal, complemented
18C22×#4034C212yesmaximal, complemented
19C22×Q8×D5C2212yes—
20C22×#711C2211yescharacteristic
21C23×Dic10C2214yes—
22C5×#554C22116yescomplemented
23C2×C5×C4⋊Q8C2211yescharacteristic
24C2×C5×#125C2212yes—
25C2×C5×C22⋊Q8C2212yes—
26C2×C5×C22⋊Q8C2214yes—
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C4×C5×D4C2212yes—
30C22×C5×C4⋊C4C2212yes—
31C2×#4092C2211yescharacteristic
32C2×Q8×Dic5C2212yes—
33C2×#4090C2211yescharacteristic
34C2×#4090C2212yes—
35C2×#4090C2214yes—
36C2×D4×Dic5C2211yescharacteristic
37C2×D4×Dic5C2212yes—
38C2×C4×C22⋊D5C2214yes—
39C2×C4×C22⋊D5C2212yes—
40C22×C4⋊Dic5C2212yes—
41C2×#4070C2212yes—
42C2×#4070C2214yes—
43C22×#683C2214yes—
44C22×C4×Dic5C2212yes—
45D5×C4⋊Q8C22116yescomplemented
46#66056C22116yescomplemented
47#66023C22132yescomplemented
48#66019C22132yescomplemented
49#65969C22132yescomplemented
50#65966C22164yescomplemented
51#65957C22164yescomplemented
52#65956C22132yescomplemented
53#65912C22116yescomplemented
54Q8×Dic10C22116yescomplemented
55#65880C22132yes—
56#65877C22116yescomplemented
57D4×Dic10C22132yescomplemented
58C4×#711C22116yes—
59#65845C22132yescomplemented
60C2×#4043C2211yescharacteristic
61C2×#4043C2214yes—
62C2×#4042C2214yes—
63C2×#4042C2212yes—
64C2×#4038C2211yescharacteristic
65C2×D5×C4⋊C4C2212yes—
66C2×D5×C4⋊C4C2212yes—
67C2×#4036C2212yes—
68C2×#4035C2214yes—
69C2×#4035C2214yes—
70C2×#4035C2212yes—
71C2×#4035C2214yes—
72C2×#4034C2212yes—
73C2×#4034C2211yescharacteristic
74C2×#4034C2212yes—
75C2×#4034C2214yes—
76C2×#4034C2214yes—
77C2×#4034C2212yes—
78C2×#4034C2214yes—
79C2×#4034C2212yes—
80C2×#4034C2212yes—
81C2×#4034C22132yescomplemented
82C2×#4033C2212yes—
83C2×#4033C2214yes—
84C2×#4033C2211yescharacteristic
85C2×#4033C2212yes—
86C2×#4027C2212yes—
87C2×#4027C2214yes—
88C2×#4024C2214yes—
89C2×#4024C2214yes—
90C2×#4024C2214yes—
91C2×#4023C2214yes—
92C2×#4023C2212yes—
93C2×#4018C2212yes—
94C2×C42×D5C2211yescharacteristic
95C2×#4015C2212yes—
96C2×#4015C2211yescharacteristic
97C2×C4×Dic10C2211yescharacteristic
98C2×C4×Dic10C2212yes—
99C2×C4×Dic10C2212yes—
100C2×C4×Dic10C2211yescharacteristic
101C2×#3503—51nomaximal, Sylow
102C22×C5×Q8C2311yescharacteristic
103C22×C5×Q8C2312yes—
104C22×C5×D4C2311yescharacteristic
105C23×C4×C5C2312yes—
106C23×C4×C5C2314yes—
107C22×C22⋊D5C2312yes—
108C23×Dic5C2312yes—
109C23×Dic5C2314yes—
110C23×Dic5C2312yes—
111C2×Q8×D5—48no—
112C2×Q8×D5C23116yes—
113C2×#711Q8116yescomplemented
114C2×#711C2318yes—
115C22×C4×D5C2311yescharacteristic
116C22×C4×D5C2311yescharacteristic
117C22×C4×D5C2314yes—
118C22×C4×D5C2311yescharacteristic
119C22×Dic10—416no—
120C22×Dic10C2311yescharacteristic
121C22×Dic10C2312yes—
122C22×Dic10C2314yes—
123C22×Dic10C2312yes—
124C22×Dic10C2314yes—
125C22×Dic10C2314yes—
126C22×Dic10C23132yes—
127C22×Dic10C2311yescharacteristic
128C5×C4⋊Q8C2318yes—
129C5×#125C23116yes—
130C5×C22⋊Q8C23116yes—
131C5×C22⋊Q8C23132yes—
132C4×C5×Q8C2318yes—
133C4×C5×D4C2318yes—
134C4×C5×D4C23116yes—
135C2×C5×C4⋊C4C2312yes—
136C2×C5×C4⋊C4C2312yes—
137C2×C5×C4⋊C4C2314yes—
138C2×C5×C4⋊C4C2311yescharacteristic
139C2×C5×C4⋊C4C2311yescharacteristic
140C2×C5×C4⋊C4C2314yes—
141C2×C5×C4⋊C4C2312yes—
142C2×C5×C4⋊C4C23116yes—
143C2×C5×C22⋊C4C2314yes—
144C2×C5×C22⋊C4C2312yes—
145C2×C42×C5C2311yescharacteristic
146C2×C42×C5C2312yes—
147C2×C22⋊Dic5C2314yes—
148C2×C22⋊Dic5C2312yes—
149#4092C2318yes—
150Q8×Dic5C23116yes—
151#4090C23132yes—
152#4090C23116yes—
153#4090C2318yes—
154D4×Dic5C2318yes—
155D4×Dic5C23116yes—
156C4×C22⋊D5C23116yes—
157C4×C22⋊D5C23132yes—
158C2×#685C2312yes—
159C2×#685C2312yes—
160C2×#685C2312yes—
161C2×C4⋊Dic5C2311yescharacteristic
162C2×C4⋊Dic5C2312yes—
163C2×C4⋊Dic5C2311yescharacteristic
164C2×C4⋊Dic5C2312yes—
165C2×C4⋊Dic5C2314yes—
166C2×C4⋊Dic5C2312yes—
167C2×C4⋊Dic5C2314yes—
168C2×C4⋊Dic5C23116yes—
169#4070C23132yes—
170#4070C23116yes—
171C2×#683C2312yes—
172C2×#683C2312yes—
173C2×#683C2312yes—
174C2×#683C2312yes—
175C2×#683C2314yes—
176C2×#683C2312yes—
177C2×#683C2312yes—
178C2×#683C2312yes—
179C2×#683C2314yes—
180C2×#683C2314yes—
181C2×#683C2314yes—
182C2×#683C2314yes—
183C2×#683C2314yes—
184C2×#683C23132yes—
185C2×C4×Dic5C2311yescharacteristic
186C2×C4×Dic5C2312yes—
187C2×C4×Dic5C2314yes—
188C2×C4×Dic5C2312yes—
189C2×C4×Dic5C2311yescharacteristic
190C2×C4×Dic5C2311yescharacteristic
191C2×C4×Dic5C2314yes—
192C2×C4×Dic5C2312yes—
193C2×C4×Dic5C2312yes—
194C2×C4×Dic5C23116yes—
195#4043C2318yes—
196#4043C23132yes—
197#4042C23132yes—
198#4042C23116yes—
199#4038C2318yes—
200D5×C4⋊C4C23116yes—
201D5×C4⋊C4C23116yes—
202#4036C23116yes—
203#4035C23132yes—
204#4035C23116yes—
205#4035C23132yes—
206#4035C23132yes—
207#4034C23116yes—
208#4034C23116yes—
209#4034C23116yes—
210#4034C23116yes—
211#4034C2318yes—
212#4034C23116yes—
213#4034C23132yes—
214#4034C23132yes—
215#4034C23132yes—
216#4033C23116yes—
217#4033C23116yes—
218#4033C2318yes—
219#4033C23132yes—
220#4027C23116yes—
221#4027C23132yes—
222#4024C23132yes—
223#4024C23132yes—
224#4024C23132yes—
225#4023C23116yes—
226#4023C23132yes—
227#4018C23116yes—
228C42×D5C2318yes—
229#4015C2318yes—
230#4015C23116yes—
231C4×Dic10C2318yes—
232C4×Dic10C2318yes—
233C4×Dic10C23116yes—
234C4×Dic10C23116yes—
235#3503—532no—
236C2×Q82—51no—
237C2×Q82—51no—
238C2×#557—52no—
239C2×#554—52no—
240C2×#554—51no—
241C2×#554—52no—
242C2×#554D511yescharacteristic, complemented
243C2×D4×Q8—54no—
244C2×D4×Q8—52no—
245C2×#544—52no—
246C2×#544—54no—
247C2×#533—52no—
248C2×#533—51no—
249C22×C4⋊Q8—51no—
250C22×C4⋊Q8—52no—
251C2×#520—52no—
252C2×C4×#41—51no—
253C24×C5C2412yes—
254C23×D5C2411yescharacteristic
255C2×C5×Q8—24no—
256C2×C5×Q8—44no—
257C2×C5×Q8C2414yes—
258C2×C5×Q8C2418yes—
259C2×C5×D4C2×Q818yescomplemented
260C2×C5×D4C2414yes—
261C22×C4×C5—28no—
262C22×C4×C5—48no—
263C22×C4×C5C2412yes—
264C22×C4×C5C2411yescharacteristic
265C22×C4×C5C2412yes—
266C22×C4×C5C2412yes—
267C22×C4×C5C2414yes—
268C22×C4×C5C2418yes—
269C22×C4×C5C24116yes—
270C22×C4×C5C2411yescharacteristic
271C22×C4×C5C2411yescharacteristic
272C2×C22⋊D5C2×Q8116yescomplemented
273C2×C22⋊D5C2418yes—
274C22×Dic5—28no—
275C22×Dic5—48no—
276C22×Dic5C2×Q8116yescomplemented
277C22×Dic5C2412yes—
278C22×Dic5C2411yescharacteristic
279C22×Dic5C2412yes—
280C22×Dic5C2414yes—
281C22×Dic5C2418yes—
282C22×Dic5C2412yes—
283C22×Dic5C24116yes—
284C22×Dic5C2412yes—
285C22×Dic5C2411yescharacteristic
286C22×Dic5C2418yes—
287C22×Dic5C2411yescharacteristic
288Q8×D5—432no—
289#711C2×Q8164yescomplemented
290C2×C4×D5—24no—
291C2×C4×D5—24no—
292C2×C4×D5—48no—
293C2×C4×D5C2×Q818yescomplemented
294C2×C4×D5C2414yes—
295C2×C4×D5C2414yes—
296C2×C4×D5C24116yes—
297C2×C4×D5C2414yes—
298C2×Dic10—24no—
299C2×Dic10—28no—
300C2×Dic10—216no—
301C2×Dic10—464no—
302C2×Dic10—48no—
303C2×Dic10—48no—
304C2×Dic10—44no—
305C2×Dic10C2×Q818yescomplemented
306C2×Dic10C2418yes—
307C2×Dic10C24116yes—
308C2×Dic10C2414yes—
309C2×Dic10C24116yes—
310C2×Dic10C24116yes—
311C2×Dic10C2418yes—
312C2×Dic10C2414yes—
313C5×C4⋊C4C2414yes—
314C5×C4⋊C4C24116yes—
315C5×C4⋊C4C2418yes—
316C5×C4⋊C4C2414yes—
317C5×C4⋊C4C2418yes—
318C5×C4⋊C4C2418yes—
319C5×C4⋊C4C24116yes—
320C5×C22⋊C4C24116yes—
321C5×C22⋊C4C2418yes—
322C42×C5C2418yes—
323C42×C5C2414yes—
324C22⋊Dic5C24116yes—
325C22⋊Dic5C2418yes—
326#685C2418yes—
327#685C2418yes—
328#685C2418yes—
329C4⋊Dic5C2414yes—
330C4⋊Dic5C2418yes—
331C4⋊Dic5C2414yes—
332C4⋊Dic5C2418yes—
333C4⋊Dic5C24116yes—
334C4⋊Dic5C2418yes—
335C4⋊Dic5C24116yes—
336#683C2418yes—
337#683C2418yes—
338#683C2418yes—
339#683C2418yes—
340#683C24116yes—
341#683C2418yes—
342#683C2418yes—
343#683C2418yes—
344#683C24116yes—
345#683C24116yes—
346#683C24116yes—
347#683C24116yes—
348#683C24116yes—
349C4×Dic5C2414yes—
350C4×Dic5C2418yes—
351C4×Dic5C24116yes—
352C4×Dic5C2418yes—
353C4×Dic5C2414yes—
354C4×Dic5C2414yes—
355C4×Dic5C24116yes—
356C4×Dic5C2418yes—
357C4×Dic5C2418yes—
358C22×#41—51no—
359C23×Q8—52no—
360C23×Q8—54no—
361Q82—516no—
362Q82—516no—
363#557—532no—
364#554—532no—
365#554—516no—
366#554—532no—
367#554C2×D5116yescomplemented
368D4×Q8—564no—
369D4×Q8—532no—
370#544—532no—
371#544—564no—
372#533—532no—
373#533—516no—
374C2×C4⋊Q8—52no—
375C2×C4⋊Q8—51no—
376C2×C4⋊Q8—54no—
377C2×C4⋊Q8—516no—
378C2×C4⋊Q8—52no—
379C2×C4⋊Q8—51no—
380C2×C4⋊Q8—54no—
381C2×C4⋊Q8—54no—
382C2×C4⋊Q8—52no—
383C2×C4⋊Q8—52no—
384C2×C4⋊Q8—52no—
385C2×C4⋊Q8—54no—
386C2×C4⋊Q8—52no—
387C2×C4⋊Q8—532no—
388C2×C4⋊Q8—51no—
389C2×C4⋊Q8—52no—
390C2×C4⋊Q8C2×D511yescharacteristic
391C2×#125—52no—
392C2×#125—54no—
393C2×#125—54no—
394C2×#125—54no—
395C2×#125—52no—
396C2×#125C2×D512yes—
397C2×C22⋊Q8—51no—
398C2×C22⋊Q8—52no—
399C2×C22⋊Q8—54no—
400C2×C22⋊Q8—52no—
401C2×C22⋊Q8—54no—
402C2×C22⋊Q8—51no—
403C2×C22⋊Q8—54no—
404C2×C22⋊Q8—54no—
405C2×C22⋊Q8—54no—
406C2×C22⋊Q8—54no—
407C2×C22⋊Q8C2×D512yes—
408C2×C22⋊Q8C2×D514yes—
409#520—532no—
410C4×#41—516no—
411C2×C4×Q8—52no—
412C2×C4×Q8—51no—
413C2×C4×Q8—52no—
414C2×C4×Q8—54no—
415C2×C4×Q8—52no—
416C2×C4×Q8—51no—
417C2×C4×Q8—52no—
418C2×C4×Q8—52no—
419C2×C4×Q8—51no—
420C2×C4×Q8C2×D511yescharacteristic
421C2×C4×D4—51no—
422C2×C4×D4—52no—
423C2×C4×D4—52no—
424C2×C4×D4—54no—
425C2×C4×D4—52no—
426C2×C4×D4—54no—
427C2×C4×D4C2×D511yescharacteristic
428C2×C4×D4C2×D512yes—
429C2×#117—51no—
430C2×#117—52no—
431C2×#117—54no—
432C2×#117—52no—
433C22×C4⋊C4—54no—
434C22×C4⋊C4—52no—
435C22×C4⋊C4—52no—
436C22×C4⋊C4—52no—
437C22×C4⋊C4C2×D512yes—
438C22×C42—52no—
439C22×C42—51no—
440C23×C5—24no—
441C23×C5—24no—
442C23×C5C22×Q818yes—
443C23×C5C2514yes—
444C23×C5C2511yescharacteristic
445C22×D5—22no—
446C22×D5—22no—
447C22×D5C22×Q814yes—
448C22×D5C2512yes—
449C5×Q8—28no—
450C5×Q8—48no—
451C5×D4C22×Q8116yescomplemented
452C2×C4×C5—24no—
453C2×C4×C5—28no—
454C2×C4×C5—22no—
455C2×C4×C5—24no—
456C2×C4×C5—24no—
457C2×C4×C5—216no—
458C2×C4×C5—416no—
459C2×C4×C5C22×Q814yes—
460C2×C4×C52−1+414yes—
461C2×C4×C5C2514yes—
462C2×C4×C5C2514yes—
463C2×C4×C5C2512yes—
464C2×C4×C5C2518yes—
465C2×C4×C5C2514yes—
466C2×C4×C5C2512yes—
467C2×C4×C5C2512yes—
468C22⋊D5C22×Q8132yescomplemented
469C2×Dic5—28no—
470C2×Dic5—24no—
471C2×Dic5—24no—
472C2×Dic5—24no—
473C2×Dic5—22no—
474C2×Dic5—216no—
475C2×Dic5—416no—
476C2×Dic5C22×Q818yes—
477C2×Dic5C22×Q814yes—
478C2×Dic5C22×Q8132yescomplemented
479C2×Dic5H(5,𝔽2)14yes—
480C2×Dic5C2514yes—
481C2×Dic5C2512yes—
482C2×Dic5C2514yes—
483C2×Dic5C2514yes—
484C2×Dic5C2518yes—
485C2×Dic5C2514yes—
486C2×Dic5C2512yes—
487C2×Dic5C2512yes—
488C4×D5—28no—
489C4×D5—28no—
490C4×D5—416no—
491C4×D5C22×Q8116yescomplemented
492Dic10—28no—
493Dic10—216no—
494Dic10—232no—
495Dic10—416no—
496Dic10—416no—
497Dic10—48no—
498Dic10C22×Q8116yescomplemented
499C2×#41—516no—
500C2×#41—58no—
501C22×Q8—516no—
502C22×Q8—51no—
503C22×Q8—51no—
504C22×Q8—54no—
505C22×Q8—52no—
506C22×Q8—54no—
507C22×Q8—54no—
508C22×Q8—52no—
509C22×Q8—532no—
510C22×Q8—2016no—
511C22×Q8—208no—
512C22×Q8C22×D511yescharacteristic
513C22×Q8C22×D512yes—
514C22×D4—52no—
515C22×D4C22×D511yescharacteristic
516C23×C4—52no—
517C23×C4—51no—
518C23×C4—52no—
519C23×C4—54no—
520C23×C4—51no—
521C23×C4—51no—
522C23×C4—54no—
523C23×C4C22×D512yes—
524C23×C4C22×D514yes—
525C4⋊Q8—516no—
526C4⋊Q8—58no—
527C4⋊Q8—532no—
528C4⋊Q8—516no—
529C4⋊Q8—58no—
530C4⋊Q8—532no—
531C4⋊Q8—532no—
532C4⋊Q8—516no—
533C4⋊Q8—516no—
534C4⋊Q8—516no—
535C4⋊Q8—532no—
536C4⋊Q8—516no—
537C4⋊Q8—58no—
538C4⋊Q8—516no—
539C4⋊Q8C22×D518yes—
540#125—516no—
541#125—532no—
542#125—532no—
543#125—532no—
544#125—516no—
545#125C22×D5116yes—
546C22⋊Q8—58no—
547C22⋊Q8—516no—
548C22⋊Q8—532no—
549C22⋊Q8—516no—
550C22⋊Q8—58no—
551C22⋊Q8—532no—
552C22⋊Q8—532no—
553C22⋊Q8—532no—
554C22⋊Q8—532no—
555C22⋊Q8—532no—
556C22⋊Q8C22×D5116yes—
557C22⋊Q8C22×D5132yes—
558C4×Q8—516no—
559C4×Q8—58no—
560C4×Q8—516no—
561C4×Q8—532no—
562C4×Q8—516no—
563C4×Q8—58no—
564C4×Q8—516no—
565C4×Q8—516no—
566C4×Q8—58no—
567C4×Q8C22×D518yes—
568C4×D4—58no—
569C4×D4—516no—
570C4×D4—516no—
571C4×D4—532no—
572C4×D4—516no—
573C4×D4—532no—
574C4×D4C22×D518yes—
575C4×D4C22×D5116yes—
576#117—58no—
577#117—516no—
578#117—532no—
579#117—516no—
580C2×C4⋊C4—54no—
581C2×C4⋊C4—52no—
582C2×C4⋊C4—51no—
583C2×C4⋊C4—52no—
584C2×C4⋊C4—54no—
585C2×C4⋊C4—54no—
586C2×C4⋊C4—52no—
587C2×C4⋊C4—532no—
588C2×C4⋊C4—54no—
589C2×C4⋊C4—54no—
590C2×C4⋊C4—516no—
591C2×C4⋊C4—52no—
592C2×C4⋊C4—52no—
593C2×C4⋊C4—52no—
594C2×C4⋊C4—51no—
595C2×C4⋊C4—52no—
596C2×C4⋊C4—54no—
597C2×C4⋊C4—52no—
598C2×C4⋊C4—52no—
599C2×C4⋊C4—54no—
600C2×C4⋊C4—52no—
601C2×C4⋊C4—54no—
602C2×C4⋊C4—516no—
603C2×C4⋊C4—516no—
604C2×C4⋊C4C22×D512yes—
605C2×C4⋊C4C22×D512yes—
606C2×C4⋊C4C22×D511yescharacteristic
607C2×C4⋊C4C22×D514yes—
608C2×C4⋊C4C22×D5116yes—
609C2×C4⋊C4C22×D511yescharacteristic
610C2×C4⋊C4C22×D514yes—
611C2×C4⋊C4C22×D512yes—
612C2×C22⋊C4—54no—
613C2×C22⋊C4—52no—
614C2×C22⋊C4—52no—
615C2×C22⋊C4—52no—
616C2×C22⋊C4—52no—
617C2×C22⋊C4C22×D514yes—
618C2×C22⋊C4C22×D512yes—
619C2×C42—51no—
620C2×C42—52no—
621C2×C42—54no—
622C2×C42—54no—
623C2×C42—52no—
624C2×C42—52no—
625C2×C42—52no—
626C2×C42—51no—
627C2×C42—516no—
628C2×C42—51no—
629C2×C42—58no—
630C2×C42C22×D512yes—
631C2×C42C22×D511yescharacteristic
632C22×C5—24no—
633C22×C5—24no—
634C22×C5—216no—
635C22×C5C23×Q818yes—
636C22×C5C23×Q812yes—
637C22×C5C2×H(5,𝔽2)12yes—
638C22×C5C2×2−1+412yes—
639C22×C5C2611yescharacteristic
640C2×D5—22no—
641C2×D5—22no—
642C2×D5—28no—
643C2×D5C23×Q814yes—
644C4×C5—24no—
645C4×C5—28no—
646C4×C5—22no—
647C4×C5—24no—
648C4×C5—24no—
649C4×C5C23×Q814yes—
650C4×C5C2×2−1+414yes—
651Dic5—28no—
652Dic5—24no—
653Dic5—24no—
654Dic5—24no—
655Dic5—22no—
656Dic5C23×Q818yes—
657Dic5C23×Q814yes—
658Dic5C2×H(5,𝔽2)14yes—
659C24—51no—
660C24C23×D512yes—
661#41—564no—
662C2×Q8—24no—
663C2×Q8—44no—
664C2×Q8—58no—
665C2×Q8—54no—
666C2×Q8—54no—
667C2×Q8—516no—
668C2×Q8—58no—
669C2×Q8—516no—
670C2×Q8—516no—
671C2×Q8—58no—
672C2×Q8—108no—
673C2×Q8—1016no—
674C2×Q8—104no—
675C2×Q8—208no—
676C2×Q8—208no—
677C2×Q8—204no—
678C2×Q8—2064no—
679C2×Q8—2032no—
680C2×Q8C23×D514yes—
681C2×Q8C23×D518yes—
682C2×D4—516no—
683C2×D4—58no—
684C2×D4Q8×D518yescomplemented
685C2×D4C23×D514yes—
686C22×C4—28no—
687C22×C4—48no—
688C22×C4—516no—
689C22×C4—58no—
690C22×C4—52no—
691C22×C4—51no—
692C22×C4—51no—
693C22×C4—58no—
694C22×C4—54no—
695C22×C4—58no—
696C22×C4—52no—
697C22×C4—51no—
698C22×C4—52no—
699C22×C4—54no—
700C22×C4—52no—
701C22×C4—516no—
702C22×C4—54no—
703C22×C4—54no—
704C22×C4—516no—
705C22×C4—104no—
706C22×C4—108no—
707C22×C4—104no—
708C22×C4—208no—
709C22×C4—208no—
710C22×C4C23×D518yes—
711C22×C4C23×D512yes—
712C22×C4C23×D512yes—
713C22×C4C23×D511yescharacteristic
714C22×C4C23×D514yes—
715C22×C4C23×D512yes—
716C22×C4C23×D5116yes—
717C22×C4C23×D511yescharacteristic
718C22×C4C23×D511yescharacteristic
719C4⋊C4—516no—
720C4⋊C4—58no—
721C4⋊C4—54no—
722C4⋊C4—58no—
723C4⋊C4—516no—
724C4⋊C4—516no—
725C4⋊C4—58no—
726C4⋊C4—516no—
727C4⋊C4—516no—
728C4⋊C4—58no—
729C4⋊C4—58no—
730C4⋊C4—58no—
731C4⋊C4—54no—
732C4⋊C4—58no—
733C4⋊C4—516no—
734C4⋊C4—58no—
735C4⋊C4—58no—
736C4⋊C4—516no—
737C4⋊C4—58no—
738C4⋊C4—516no—
739C4⋊C4C23×D518yes—
740C4⋊C4C23×D518yes—
741C4⋊C4C23×D514yes—
742C4⋊C4C23×D5116yes—
743C4⋊C4C23×D514yes—
744C4⋊C4C23×D5116yes—
745C4⋊C4C23×D518yes—
746C22⋊C4—516no—
747C22⋊C4—58no—
748C22⋊C4—58no—
749C22⋊C4—58no—
750C22⋊C4—58no—
751C22⋊C4C23×D5116yes—
752C22⋊C4C23×D518yes—
753C42—54no—
754C42—54no—
755C42—58no—
756C42—58no—
757C42—58no—
758C42—54no—
759C42—516no—
760C42—516no—
761C42—58no—
762C42C23×D514yes—
763C42C23×D518yes—
764C2×C5—28no—
765C2×C5#350314yescomplemented
766C2×C5C24×Q811yescharacteristic
767C2×C5C22×H(5,𝔽2)11yescharacteristic
768C2×C5C22×2−1+411yescharacteristic
769D5—24no—
770C23—24no—
771C23—24no—
772C23—54no—
773C23—52no—
774C23—102no—
775C23—102no—
776C23C2×Q8×D518yes—
777C23C24×D514yes—
778C23C24×D511yescharacteristic
779Q8—28no—
780Q8—48no—
781Q8—516no—
782Q8—1016no—
783Q8—1032no—
784Q8—108no—
785Q8—2016no—
786Q8—2016no—
787Q8—208no—
788D4—532no—
789D4C2×Q8×D5116yescomplemented
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—22no—
795C2×C4—216no—
796C2×C4—416no—
797C2×C4—54no—
798C2×C4—58no—
799C2×C4—532no—
800C2×C4—54no—
801C2×C4—54no—
802C2×C4—52no—
803C2×C4—52no—
804C2×C4—516no—
805C2×C4—54no—
806C2×C4—52no—
807C2×C4—54no—
808C2×C4—58no—
809C2×C4—54no—
810C2×C4—108no—
811C2×C4—1016no—
812C2×C4—102no—
813C2×C4—104no—
814C2×C4—104no—
815C2×C4—108no—
816C2×C4—104no—
817C2×C4—108no—
818C2×C4—2016no—
819C2×C4—2016no—
820C2×C4C2×Q8×D514yes—
821C2×C4#415014yes—
822C2×C4C24×D514yes—
823C2×C4C24×D514yes—
824C2×C4C24×D512yes—
825C2×C4C24×D518yes—
826C2×C4C24×D514yes—
827C2×C4C24×D512yes—
828C2×C4C24×D512yes—
829C5C2×#350311yescharacteristic, complemented, Sylow
830C22—24no—
831C22—24no—
832C22—216no—
833C22—54no—
834C22—102no—
835C22—102no—
836C22—108no—
837C22C22×Q8×D518yes—
838C22C22×Q8×D512yes—
839C22C2×#415012yes—
840C22D5×H(5,𝔽2)12yes—
841C22C25×D511yescharacteristic
842C4—24no—
843C4—24no—
844C4—24no—
845C4—28no—
846C4—22no—
847C4—54no—
848C4—58no—
849C4—54no—
850C4—102no—
851C4—104no—
852C4—104no—
853C4—108no—
854C4—104no—
855C4C22×Q8×D514yes—
856C4C2×#415014yes—
857C2—28no—
858C2—104no—
859C2#1061882714yesdirect product factor
860C2C23×Q8×D511yescharacteristic
861C2C22×#415011yescharacteristic
862C2C2×D5×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#554C2
socleC23×C5C25
prime radicalC22×#711C22
hypercenterC2×#554D5
hypocenterC5C2×#3503
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×C5×#554C2semidirect
2. #10618827C2direct (N × H)
3. C2×D5×C4⋊Q8C2semidirect
4. C2×#66056C2semidirect
5. C2×#66023C2semidirect
6. C2×#66019C2semidirect
7. C2×#65969C2semidirect
8. C2×#65966C2semidirect
9. C2×#65957C2semidirect
10. C2×#65956C2semidirect
11. C2×#65912C2semidirect
12. C2×Q8×Dic10C2semidirect
13. C2×#65877C2semidirect
14. C2×D4×Dic10C2semidirect
17. C2×#65845C2semidirect
18. C22×#4034C2semidirect
22. C5×#554C22semidirect
45. D5×C4⋊Q8C22semidirect
46. #66056C22semidirect
47. #66023C22semidirect
48. #66019C22semidirect
49. #65969C22semidirect
50. #65966C22semidirect
51. #65957C22semidirect
52. #65956C22semidirect
53. #65912C22semidirect
54. Q8×Dic10C22semidirect
56. #65877C22semidirect
57. D4×Dic10C22semidirect
59. #65845C22semidirect
81. C2×#4034C22semidirect
113. C2×#711Q8semidirect
242. C2×#554D5semidirect
259. C2×C5×D4C2×Q8semidirect
272. C2×C22⋊D5C2×Q8semidirect
276. C22×Dic5C2×Q8semidirect
289. #711C2×Q8semidirect
293. C2×C4×D5C2×Q8semidirect
305. C2×Dic10C2×Q8semidirect
367. #554C2×D5semidirect
451. C5×D4C22×Q8semidirect
468. C22⋊D5C22×Q8semidirect
478. C2×Dic5C22×Q8semidirect
491. C4×D5C22×Q8semidirect
498. Dic10C22×Q8semidirect
684. C2×D4Q8×D5semidirect
765. C2×C5#3503semidirect
789. D4C2×Q8×D5semidirect
829. C5C2×#3503semidirect
859. C2#10618827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5542
#106188272
C2×D5×C4⋊Q82
C2×#660562
C2×#660232
C2×#660192
C2×#659692
C2×#659662
C2×#659572
C2×#659562
C2×#659122
C2×Q8×Dic102
C2×#658772
C2×D4×Dic102
C2×#658802
C2×C4×#7112
C2×#658452
C22×#40342
C2×#35035