Finite Group Databasebeta

← C2×#10618487 #13007630

Subgroups — C2×#10618487 #13007630

Order 1280.

7478 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#544C211yesmaximal, characteristic, complemented
2#10618487C2132yesmaximal, direct product factor
3C2×#66061C212yesmaximal, complemented
4C2×#66063C212yesmaximal, complemented
5C2×D5×C4⋊Q8C212yesmaximal, complemented
6C2×#66056C212yesmaximal, complemented
7C2×#66023C212yesmaximal, complemented
8C2×#66019C212yesmaximal, complemented
9C2×#66024C212yesmaximal, complemented
10C2×#66022C212yesmaximal, complemented
11C2×#65970C214yesmaximal, complemented
12C2×#65966C214yesmaximal, complemented
13C2×#65857C211yesmaximal, characteristic
14C2×#65853C211yesmaximal, characteristic, complemented
15C2×#65851C211yesmaximal, characteristic, complemented
16C2×#65856C211yesmaximal, characteristic
17C2×#65838C211yesmaximal, characteristic
18C22×#4034C211yesmaximal, characteristic, complemented
19C22×Q8×D5C2214yes—
20C22×#709C2211yescharacteristic
21C23×Dic10C2212yes—
22C5×#544C22116yescomplemented
23C2×C5×C4⋊Q8C2212yes—
24C2×C5×C4⋊Q8C2212yes—
25C2×C5×#125C2212yes—
26C2×C5×#125C2212yes—
27C2×C5×C22⋊Q8C2214yes—
28C2×C5×#117C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C22×C5×C4⋊C4C2211yescharacteristic
31C2×#4092C2214yes—
32C2×#4090C2214yes—
33C2×#4090C2214yes—
34C2×C4×C22⋊D5C2214yes—
35C2×#4072C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×#683C2212yes—
38C22×C4×Dic5C2211yescharacteristic
39#66063C22132yescomplemented
40#66061C22132yescomplemented
41D5×C4⋊Q8C22132yescomplemented
42#66056C22132yescomplemented
43#66024C22132yescomplemented
44#66023C22132yescomplemented
45#66022C22132yescomplemented
46#66019C22132yescomplemented
47#65970C22164yescomplemented
48#65966C22164yescomplemented
49#65857C22116yes—
50#65856C22116yes—
51#65853C22116yescomplemented
52#65851C22116yescomplemented
53C2×#4043C2214yes—
54C2×#4042C2214yes—
55C2×#4042C2214yes—
56C2×#4042C2214yes—
57C2×#4042C2214yes—
58#65838C22116yes—
59C2×#4039C2211yescharacteristic
60C2×#4039C2212yes—
61C2×#4039C2211yescharacteristic
62C2×#4038C2212yes—
63C2×#4038C2212yes—
64C2×D5×C4⋊C4C2212yes—
65C2×D5×C4⋊C4C2214yes—
66C2×D5×C4⋊C4C2212yes—
67C2×#4036C2211yescharacteristic
68C2×#4036C2211yescharacteristic
69C2×#4036C2212yes—
70C2×#4035C2214yes—
71C2×#4035C2214yes—
72C2×#4034C2212yes—
73C2×#4034C2212yes—
74C2×#4034C2212yes—
75C2×#4034C2212yes—
76C2×#4034C2212yes—
77C2×#4034C2214yes—
78C2×#4034C2214yes—
79C2×#4034C2211yescharacteristic
80C2×#4034C2211yescharacteristic
81C2×#4034C22116yescomplemented
82C2×#4033C2212yes—
83C2×#4033C2214yes—
84C2×#4033C2214yes—
85C2×#4033C2211yescharacteristic
86C2×#4033C2211yescharacteristic
87C2×#4027C2212yes—
88C2×#4027C2214yes—
89C2×#4027C2212yes—
90C2×#4024C2212yes—
91C2×#4024C2214yes—
92C2×#4024C2212yes—
93C2×C4×D20C2212yes—
94C2×#4018C2212yes—
95C2×C42×D5C2212yes—
96C2×#4016C2212yes—
97C2×#4015C2212yes—
98C2×C4×Dic10C2212yes—
99C2×C4×Dic10C2212yes—
100C2×C4×Dic10C2212yes—
101C2×#3503—51nomaximal, Sylow
102C22×C5×Q8C2314yes—
103C23×C4×C5C2312yes—
104C23×C4×C5C2311yescharacteristic
105C22×C22⋊D5C2312yes—
106C23×Dic5C2311yescharacteristic
107C23×Dic5C2311yescharacteristic
108C23×Dic5C2312yes—
109C2×Q8×D5—416no—
110C2×Q8×D5C23132yes—
111C2×#709Q8116yescomplemented
112C2×#709C2318yes—
113C22×D20C2311yescharacteristic
114C22×C4×D5C2312yes—
115C22×C4×D5C2312yes—
116C22×C4×D5C2314yes—
117C22×C4×D5C2314yes—
118C22×C4×D5C2312yes—
119C22×Dic10—48no—
120C22×Dic10C2312yes—
121C22×Dic10C2312yes—
122C22×Dic10C2314yes—
123C22×Dic10C2314yes—
124C22×Dic10C2314yes—
125C22×Dic10C23116yes—
126C22×Dic10C2311yescharacteristic
127C5×C4⋊Q8C23116yes—
128C5×C4⋊Q8C23116yes—
129C5×#125C23116yes—
130C5×#125C23116yes—
131C5×C22⋊Q8C23132yes—
132C5×#117C2318yes—
133C5×#117C2318yes—
134C2×C5×C4⋊C4C2312yes—
135C2×C5×C4⋊C4C2311yescharacteristic
136C2×C5×C4⋊C4C2314yes—
137C2×C5×C4⋊C4C2314yes—
138C2×C5×C4⋊C4C2311yescharacteristic
139C2×C5×C4⋊C4C2312yes—
140C2×C5×C4⋊C4C2314yes—
141C2×C5×C4⋊C4C2311yescharacteristic
142C2×C5×C4⋊C4C2311yescharacteristic
143C2×C5×C4⋊C4C2318yes—
144C2×C5×C22⋊C4C2312yes—
145C2×C5×C22⋊C4C2312yes—
146C2×C42×C5C2312yes—
147C2×C42×C5C2312yes—
148C2×C22⋊Dic5C2312yes—
149#4092C23132yes—
150#4090C23132yes—
151#4090C23132yes—
152C4×C22⋊D5C23132yes—
153C2×#685C2312yes—
154C2×#685C2312yes—
155C2×#685C2314yes—
156C2×#685C2314yes—
157#4072C2318yes—
158C2×C4⋊Dic5C2312yes—
159C2×C4⋊Dic5C2312yes—
160C2×C4⋊Dic5C2312yes—
161C2×C4⋊Dic5C2311yescharacteristic
162C2×C4⋊Dic5C2312yes—
163C2×C4⋊Dic5C2314yes—
164C2×C4⋊Dic5C2311yescharacteristic
165C2×C4⋊Dic5C2318yes—
166C2×#683C2312yes—
167C2×#683C2312yes—
168C2×#683C2312yes—
169C2×#683C2312yes—
170C2×#683C2314yes—
171C2×#683C2314yes—
172C2×#683C2314yes—
173C2×#683C2312yes—
174C2×#683C2312yes—
175C2×#683C2314yes—
176C2×#683C2314yes—
177C2×#683C2314yes—
178C2×#683C23116yes—
179C2×C4×Dic5C2311yescharacteristic
180C2×C4×Dic5C2311yescharacteristic
181C2×C4×Dic5C2312yes—
182C2×C4×Dic5C2314yes—
183C2×C4×Dic5C2311yescharacteristic
184C2×C4×Dic5C2312yes—
185C2×C4×Dic5C2312yes—
186C2×C4×Dic5C2311yescharacteristic
187C2×C4×Dic5C2314yes—
188C2×C4×Dic5C2318yes—
189#4043C23132yes—
190#4042C23132yes—
191#4042C23132yes—
192#4042C23132yes—
193#4042C23132yes—
194#4039C2318yes—
195#4039C23116yes—
196#4039C2318yes—
197#4038C23116yes—
198#4038C23116yes—
199D5×C4⋊C4C23116yes—
200D5×C4⋊C4C23116yes—
201D5×C4⋊C4C23132yes—
202#4036C2318yes—
203#4036C2318yes—
204#4036C23116yes—
205#4035C23132yes—
206#4035C23132yes—
207#4034C23116yes—
208#4034C23116yes—
209#4034C23132yes—
210#4034C2318yes—
211#4034C23116yes—
212#4034C23132yes—
213#4034C23116yes—
214#4034C23116yes—
215#4034C2318yes—
216#4033C2318yes—
217#4033C23116yes—
218#4033C23132yes—
219#4033C2318yes—
220#4033C23132yes—
221#4027C23116yes—
222#4027C23116yes—
223#4027C23132yes—
224#4024C23116yes—
225#4024C23116yes—
226#4024C23132yes—
227C4×D20C23116yes—
228#4018C23116yes—
229C42×D5C23116yes—
230#4016C23116yes—
231#4015C23116yes—
232C4×Dic10C23116yes—
233C4×Dic10C23116yes—
234C4×Dic10C23116yes—
235#3503—532no—
236C2×Q82—52no—
237C2×#557—52no—
238C2×#554—52no—
239C2×#554—54no—
240C2×D4×Q8—52no—
241C2×D4×Q8—54no—
242C2×#544—52no—
243C2×#544—52no—
244C2×#544—51no—
245C2×#544D511yescharacteristic, complemented
246C2×#533—52no—
247C2×#533—51no—
248C22×C4⋊Q8—52no—
249C22×C4⋊Q8—51no—
250C2×#520—51no—
251C2×#520—51no—
252C2×C4×#41—51no—
253C24×C5C2411yescharacteristic
254C23×D5C2412yes—
255C2×C5×Q8—48no—
256C2×C5×Q8C24116yes—
257C22×C4×C5—44no—
258C22×C4×C5C2×Q818yescomplemented
259C22×C4×C5C2412yes—
260C22×C4×C5C2412yes—
261C22×C4×C5C2412yes—
262C22×C4×C5C2412yes—
263C22×C4×C5C2414yes—
264C22×C4×C5C2418yes—
265C22×C4×C5C2411yescharacteristic
266C22×C4×C5C2411yescharacteristic
267C22×C4×C5C2414yes—
268C2×C22⋊D5C2×Q8116yescomplemented
269C2×C22⋊D5C2418yes—
270C22×Dic5—24no—
271C22×Dic5—24no—
272C22×Dic5—44no—
273C22×Dic5C2412yes—
274C22×Dic5C2412yes—
275C22×Dic5C2414yes—
276C22×Dic5C2411yescharacteristic
277C22×Dic5C2414yes—
278C22×Dic5C2414yes—
279C22×Dic5C2411yescharacteristic
280C22×Dic5C2418yes—
281C22×Dic5C2412yes—
282C22×Dic5C2411yescharacteristic
283C22×Dic5C2411yescharacteristic
284Q8×D5—464no—
285#709C2×Q8164yescomplemented
286C2×D20C2×Q818yescomplemented
287C2×D20C2414yes—
288C2×C4×D5—28no—
289C2×C4×D5—28no—
290C2×C4×D5—48no—
291C2×C4×D5—48no—
292C2×C4×D5C2×Q8116yescomplemented
293C2×C4×D5C2418yes—
294C2×C4×D5C2418yes—
295C2×C4×D5C24116yes—
296C2×C4×D5C24116yes—
297C2×C4×D5C2418yes—
298C2×Dic10—216no—
299C2×Dic10—28no—
300C2×Dic10—28no—
301C2×Dic10—432no—
302C2×Dic10—48no—
303C2×Dic10—48no—
304C2×Dic10C2×Q818yescomplemented
305C2×Dic10C24116yes—
306C2×Dic10C2418yes—
307C2×Dic10C2418yes—
308C2×Dic10C24116yes—
309C2×Dic10C24116yes—
310C2×Dic10C2414yes—
311C5×C4⋊C4C2418yes—
312C5×C4⋊C4C2418yes—
313C5×C4⋊C4C2414yes—
314C5×C4⋊C4C2414yes—
315C5×C4⋊C4C2414yes—
316C5×C4⋊C4C2414yes—
317C5×C4⋊C4C24116yes—
318C5×C4⋊C4C24116yes—
319C5×C4⋊C4C24116yes—
320C5×C22⋊C4C2418yes—
321C5×C22⋊C4C2418yes—
322C42×C5C2418yes—
323C42×C5C2418yes—
324C22⋊Dic5C2418yes—
325#685C2418yes—
326#685C2418yes—
327#685C24116yes—
328#685C24116yes—
329C4⋊Dic5C2418yes—
330C4⋊Dic5C2418yes—
331C4⋊Dic5C2418yes—
332C4⋊Dic5C2414yes—
333C4⋊Dic5C2418yes—
334C4⋊Dic5C24116yes—
335C4⋊Dic5C2414yes—
336#683C2418yes—
337#683C2418yes—
338#683C2418yes—
339#683C2418yes—
340#683C24116yes—
341#683C24116yes—
342#683C24116yes—
343#683C2418yes—
344#683C2418yes—
345#683C24116yes—
346#683C24116yes—
347#683C24116yes—
348C4×Dic5C2414yes—
349C4×Dic5C2414yes—
350C4×Dic5C2418yes—
351C4×Dic5C24116yes—
352C4×Dic5C2414yes—
353C4×Dic5C2418yes—
354C4×Dic5C2418yes—
355C4×Dic5C2414yes—
356C4×Dic5C24116yes—
357C22×#41—51no—
358C23×Q8—54no—
359C23×Q8—52no—
360Q82—532no—
361#557—532no—
362#554—532no—
363#554—564no—
364D4×Q8—532no—
365D4×Q8—564no—
366#544—532no—
367#544—532no—
368#544—516no—
369#544C2×D5116yescomplemented
370#533—532no—
371#533—516no—
372C2×C4⋊Q8—54no—
373C2×C4⋊Q8—54no—
374C2×C4⋊Q8—532no—
375C2×C4⋊Q8—51no—
376C2×C4⋊Q8—52no—
377C2×C4⋊Q8—52no—
378C2×C4⋊Q8—54no—
379C2×C4⋊Q8—52no—
380C2×C4⋊Q8—52no—
381C2×C4⋊Q8—51no—
382C2×C4⋊Q8—54no—
383C2×C4⋊Q8—52no—
384C2×C4⋊Q8—516no—
385C2×C4⋊Q8—52no—
386C2×C4⋊Q8C2×D512yes—
387C2×C4⋊Q8C2×D512yes—
388C2×#125—54no—
389C2×#125—54no—
390C2×#125—51no—
391C2×#125—51no—
392C2×#125—52no—
393C2×#125—52no—
394C2×#125C2×D512yes—
395C2×#125C2×D512yes—
396C2×C22⋊Q8—54no—
397C2×C22⋊Q8—54no—
398C2×C22⋊Q8—54no—
399C2×C22⋊Q8—54no—
400C2×C22⋊Q8—54no—
401C2×C22⋊Q8—54no—
402C2×C22⋊Q8—52no—
403C2×C22⋊Q8—52no—
404C2×C22⋊Q8—54no—
405C2×C22⋊Q8C2×D514yes—
406#520—516no—
407#520—516no—
408C4×#41—516no—
409C2×C4×Q8—51no—
410C2×C4×Q8—51no—
411C2×C4×Q8—52no—
412C2×C4×Q8—54no—
413C2×C4×Q8—54no—
414C2×C4×Q8—52no—
415C2×C4×Q8—52no—
416C2×C4×Q8—52no—
417C2×C4×D4—54no—
418C2×C4×D4—51no—
419C2×C4×D4—51no—
420C2×C4×D4—52no—
421C2×C4×D4—52no—
422C2×C4×D4—52no—
423C2×C4×D4—54no—
424C2×C4×D4—52no—
425C2×#117—51no—
426C2×#117—52no—
427C2×#117—52no—
428C2×#117—52no—
429C2×#117C2×D511yescharacteristic
430C2×#117C2×D511yescharacteristic
431C22×C4⋊C4—52no—
432C22×C4⋊C4—51no—
433C22×C4⋊C4—52no—
434C22×C4⋊C4—52no—
435C22×C4⋊C4—54no—
436C22×C4⋊C4C2×D511yescharacteristic
437C22×C42—51no—
438C22×C42—52no—
439C23×C5—22no—
440C23×C5—22no—
441C23×C5C22×Q814yes—
442C23×C5C2512yes—
443C23×C5C2511yescharacteristic
444C22×D5—24no—
445C22×D5—24no—
446C22×D5C22×Q818yes—
447C22×D5C2514yes—
448C5×Q8—416no—
449C2×C4×C5—28no—
450C2×C4×C5—24no—
451C2×C4×C5—24no—
452C2×C4×C5—24no—
453C2×C4×C5—24no—
454C2×C4×C5—48no—
455C2×C4×C5C22×Q814yes—
456C2×C4×C5C22×Q814yes—
457C2×C4×C5C22×Q8116yescomplemented
458C2×C4×C5C2514yes—
459C2×C4×C5C2514yes—
460C2×C4×C5C2514yes—
461C2×C4×C5C2518yes—
462C2×C4×C5C2514yes—
463C2×C4×C5C2512yes—
464C2×C4×C5C2512yes—
465C22⋊D5C22×Q8132yescomplemented
466C2×Dic5—24no—
467C2×Dic5—28no—
468C2×Dic5—22no—
469C2×Dic5—24no—
470C2×Dic5—22no—
471C2×Dic5—28no—
472C2×Dic5—28no—
473C2×Dic5—48no—
474C2×Dic5C22×Q818yes—
475C2×Dic5H(5,𝔽2)14yes—
476C2×Dic52−1+414yes—
477C2×Dic5C2514yes—
478C2×Dic5C2512yes—
479C2×Dic5C2512yes—
480C2×Dic5C2518yes—
481C2×Dic5C2514yes—
482C2×Dic5C2514yes—
483C2×Dic5C2512yes—
484C2×Dic5C2512yes—
485D20C22×Q8116yescomplemented
486C4×D5—216no—
487C4×D5—216no—
488C4×D5—416no—
489C4×D5—416no—
490C4×D5C22×Q8132yescomplemented
491Dic10—232no—
492Dic10—216no—
493Dic10—216no—
494Dic10—416no—
495Dic10—416no—
496Dic10C22×Q8116yescomplemented
497C2×#41—516no—
498C2×#41—58no—
499C22×Q8—532no—
500C22×Q8—51no—
501C22×Q8—52no—
502C22×Q8—54no—
503C22×Q8—52no—
504C22×Q8—54no—
505C22×Q8—54no—
506C22×Q8—516no—
507C22×Q8—208no—
508C22×Q8—2016no—
509C22×Q8C22×D514yes—
510C22×D4—52no—
511C22×D4—51no—
512C23×C4—52no—
513C23×C4—51no—
514C23×C4—51no—
515C23×C4—52no—
516C23×C4—52no—
517C23×C4—52no—
518C23×C4—54no—
519C23×C4—54no—
520C23×C4C22×D512yes—
521C23×C4C22×D511yescharacteristic
522C4⋊Q8—532no—
523C4⋊Q8—532no—
524C4⋊Q8—58no—
525C4⋊Q8—516no—
526C4⋊Q8—516no—
527C4⋊Q8—532no—
528C4⋊Q8—516no—
529C4⋊Q8—516no—
530C4⋊Q8—58no—
531C4⋊Q8—532no—
532C4⋊Q8—516no—
533C4⋊Q8—516no—
534C4⋊Q8C22×D5116yes—
535C4⋊Q8C22×D5116yes—
536#125—58no—
537#125—58no—
538#125—532no—
539#125—532no—
540#125—516no—
541#125—516no—
542#125C22×D5116yes—
543#125C22×D5116yes—
544C22⋊Q8—532no—
545C22⋊Q8—532no—
546C22⋊Q8—532no—
547C22⋊Q8—532no—
548C22⋊Q8—532no—
549C22⋊Q8—532no—
550C22⋊Q8—516no—
551C22⋊Q8—516no—
552C22⋊Q8—532no—
553C22⋊Q8C22×D5132yes—
554C4×Q8—58no—
555C4×Q8—58no—
556C4×Q8—516no—
557C4×Q8—532no—
558C4×Q8—532no—
559C4×Q8—516no—
560C4×Q8—516no—
561C4×Q8—516no—
562C4×D4—532no—
563C4×D4—58no—
564C4×D4—58no—
565C4×D4—516no—
566C4×D4—516no—
567C4×D4—516no—
568C4×D4—532no—
569C4×D4—516no—
570#117—58no—
571#117—516no—
572#117—516no—
573#117—516no—
574#117C22×D518yes—
575#117C22×D518yes—
576C2×C4⋊C4—52no—
577C2×C4⋊C4—51no—
578C2×C4⋊C4—54no—
579C2×C4⋊C4—52no—
580C2×C4⋊C4—54no—
581C2×C4⋊C4—54no—
582C2×C4⋊C4—52no—
583C2×C4⋊C4—58no—
584C2×C4⋊C4—54no—
585C2×C4⋊C4—54no—
586C2×C4⋊C4—516no—
587C2×C4⋊C4—51no—
588C2×C4⋊C4—52no—
589C2×C4⋊C4—52no—
590C2×C4⋊C4—52no—
591C2×C4⋊C4—54no—
592C2×C4⋊C4—52no—
593C2×C4⋊C4—52no—
594C2×C4⋊C4—52no—
595C2×C4⋊C4—54no—
596C2×C4⋊C4—52no—
597C2×C4⋊C4—516no—
598C2×C4⋊C4—516no—
599C2×C4⋊C4—532no—
600C2×C4⋊C4C22×D511yescharacteristic
601C2×C4⋊C4C22×D512yes—
602C2×C4⋊C4C22×D514yes—
603C2×C4⋊C4C22×D512yes—
604C2×C4⋊C4C22×D518yes—
605C2×C4⋊C4C22×D511yescharacteristic
606C2×C4⋊C4C22×D511yescharacteristic
607C2×C4⋊C4C22×D511yescharacteristic
608C2×C4⋊C4C22×D514yes—
609C2×C4⋊C4C22×D514yes—
610C2×C22⋊C4—52no—
611C2×C22⋊C4—54no—
612C2×C22⋊C4—52no—
613C2×C22⋊C4—52no—
614C2×C22⋊C4—54no—
615C2×C22⋊C4C22×D512yes—
616C2×C22⋊C4C22×D512yes—
617C2×C42—51no—
618C2×C42—54no—
619C2×C42—54no—
620C2×C42—52no—
621C2×C42—52no—
622C2×C42—52no—
623C2×C42—51no—
624C2×C42—51no—
625C2×C42—58no—
626C2×C42—51no—
627C2×C42—516no—
628C2×C42C22×D512yes—
629C2×C42C22×D512yes—
630C22×C5—22no—
631C22×C5—22no—
632C22×C5—28no—
633C22×C5C23×Q814yes—
634C22×C5C23×Q812yes—
635C22×C5C2×H(5,𝔽2)12yes—
636C22×C5C2×2−1+412yes—
637C22×C5C2611yescharacteristic
638C2×D5—24no—
639C2×D5—24no—
640C2×D5—216no—
641C2×D5C23×Q818yes—
642C4×C5—28no—
643C4×C5—24no—
644C4×C5—24no—
645C4×C5—24no—
646C4×C5—24no—
647C4×C5C23×Q814yes—
648C4×C5C23×Q814yes—
649Dic5—24no—
650Dic5—28no—
651Dic5—22no—
652Dic5—24no—
653Dic5—22no—
654Dic5C23×Q818yes—
655Dic5C2×H(5,𝔽2)14yes—
656Dic5C2×2−1+414yes—
657C24—52no—
658C24C23×D511yescharacteristic
659#41—564no—
660C2×Q8—48no—
661C2×Q8—58no—
662C2×Q8—54no—
663C2×Q8—58no—
664C2×Q8—516no—
665C2×Q8—58no—
666C2×Q8—516no—
667C2×Q8—516no—
668C2×Q8—1016no—
669C2×Q8—108no—
670C2×Q8—108no—
671C2×Q8—208no—
672C2×Q8—208no—
673C2×Q8—2032no—
674C2×Q8—2064no—
675C2×Q8C23×D5116yes—
676C2×D4—516no—
677C2×D4—58no—
678C2×D4—58no—
679C2×D4—54no—
680C22×C4—44no—
681C22×C4—52no—
682C22×C4—51no—
683C22×C4—51no—
684C22×C4—516no—
685C22×C4—58no—
686C22×C4—54no—
687C22×C4—54no—
688C22×C4—52no—
689C22×C4—51no—
690C22×C4—51no—
691C22×C4—52no—
692C22×C4—54no—
693C22×C4—58no—
694C22×C4—58no—
695C22×C4—58no—
696C22×C4—516no—
697C22×C4—516no—
698C22×C4—108no—
699C22×C4—108no—
700C22×C4—104no—
701C22×C4—104no—
702C22×C4—208no—
703C22×C4—208no—
704C22×C4—204no—
705C22×C4Q8×D518yescomplemented
706C22×C4C23×D512yes—
707C22×C4C23×D512yes—
708C22×C4C23×D512yes—
709C22×C4C23×D514yes—
710C22×C4C23×D512yes—
711C22×C4C23×D518yes—
712C22×C4C23×D511yescharacteristic
713C22×C4C23×D511yescharacteristic
714C22×C4C23×D514yes—
715C4⋊C4—58no—
716C4⋊C4—54no—
717C4⋊C4—516no—
718C4⋊C4—58no—
719C4⋊C4—516no—
720C4⋊C4—516no—
721C4⋊C4—58no—
722C4⋊C4—516no—
723C4⋊C4—516no—
724C4⋊C4—54no—
725C4⋊C4—58no—
726C4⋊C4—58no—
727C4⋊C4—58no—
728C4⋊C4—516no—
729C4⋊C4—58no—
730C4⋊C4—58no—
731C4⋊C4—58no—
732C4⋊C4—516no—
733C4⋊C4—58no—
734C4⋊C4C23×D514yes—
735C4⋊C4C23×D518yes—
736C4⋊C4C23×D5116yes—
737C4⋊C4C23×D518yes—
738C4⋊C4C23×D514yes—
739C4⋊C4C23×D514yes—
740C4⋊C4C23×D514yes—
741C4⋊C4C23×D5116yes—
742C4⋊C4C23×D5116yes—
743C22⋊C4—58no—
744C22⋊C4—516no—
745C22⋊C4—58no—
746C22⋊C4—58no—
747C22⋊C4—516no—
748C22⋊C4C23×D518yes—
749C22⋊C4C23×D518yes—
750C42—54no—
751C42—54no—
752C42—58no—
753C42—58no—
754C42—54no—
755C42—54no—
756C42—516no—
757C42—516no—
758C42—58no—
759C42C23×D518yes—
760C42C23×D518yes—
761C2×C5—24no—
762C2×C5#350314yescomplemented
763C2×C5C24×Q811yescharacteristic
764C2×C5C22×H(5,𝔽2)11yescharacteristic
765C2×C5C22×2−1+411yescharacteristic
766D5—28no—
767C23—22no—
768C23—22no—
769C23—58no—
770C23—54no—
771C23—104no—
772C23—104no—
773C23C2×Q8×D514yes—
774C23C24×D512yes—
775C23C24×D511yescharacteristic
776Q8—416no—
777Q8—516no—
778Q8—1032no—
779Q8—1016no—
780Q8—1016no—
781Q8—2016no—
782Q8—2016no—
783D4—532no—
784D4—516no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—48no—
791C2×C4—58no—
792C2×C4—54no—
793C2×C4—54no—
794C2×C4—54no—
795C2×C4—52no—
796C2×C4—52no—
797C2×C4—532no—
798C2×C4—54no—
799C2×C4—52no—
800C2×C4—52no—
801C2×C4—54no—
802C2×C4—58no—
803C2×C4—1016no—
804C2×C4—1016no—
805C2×C4—108no—
806C2×C4—108no—
807C2×C4—102no—
808C2×C4—104no—
809C2×C4—108no—
810C2×C4—102no—
811C2×C4—104no—
812C2×C4—2016no—
813C2×C4—2016no—
814C2×C4—208no—
815C2×C4C2×Q8×D514yes—
816C2×C4C2×Q8×D514yes—
817C2×C4C2×Q8×D5116yescomplemented
818C2×C4C24×D514yes—
819C2×C4C24×D514yes—
820C2×C4C24×D514yes—
821C2×C4C24×D518yes—
822C2×C4C24×D514yes—
823C2×C4C24×D512yes—
824C2×C4C24×D512yes—
825C5C2×#350311yescharacteristic, complemented, Sylow
826C22—22no—
827C22—22no—
828C22—28no—
829C22—58no—
830C22—104no—
831C22—104no—
832C22—1016no—
833C22C22×Q8×D514yes—
834C22C22×Q8×D512yes—
835C22D5×H(5,𝔽2)12yes—
836C22D5×2−1+412yes—
837C22C25×D511yescharacteristic
838C4—28no—
839C4—24no—
840C4—24no—
841C4—24no—
842C4—24no—
843C4—58no—
844C4—54no—
845C4—54no—
846C4—102no—
847C4—104no—
848C4—108no—
849C4—102no—
850C4—104no—
851C4C22×Q8×D514yes—
852C4C22×Q8×D514yes—
853C2—24no—
854C2—108no—
855C2#1061848714yesdirect product factor
856C2C23×Q8×D511yescharacteristic
857C2C2×D5×H(5,𝔽2)11yescharacteristic
858C2C2×D5×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#544C2
socleC23×C5C25
prime radicalC22×#709C22
hypercenterC2×#544D5
hypocenterC5C2×#3503
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×C5×#544C2semidirect
2. #10618487C2direct (N × H)
3. C2×#66061C2semidirect
4. C2×#66063C2semidirect
5. C2×D5×C4⋊Q8C2semidirect
6. C2×#66056C2semidirect
7. C2×#66023C2semidirect
8. C2×#66019C2semidirect
9. C2×#66024C2semidirect
10. C2×#66022C2semidirect
11. C2×#65970C2semidirect
12. C2×#65966C2semidirect
14. C2×#65853C2semidirect
15. C2×#65851C2semidirect
18. C22×#4034C2semidirect
22. C5×#544C22semidirect
39. #66063C22semidirect
40. #66061C22semidirect
41. D5×C4⋊Q8C22semidirect
42. #66056C22semidirect
43. #66024C22semidirect
44. #66023C22semidirect
45. #66022C22semidirect
46. #66019C22semidirect
47. #65970C22semidirect
48. #65966C22semidirect
51. #65853C22semidirect
52. #65851C22semidirect
81. C2×#4034C22semidirect
111. C2×#709Q8semidirect
245. C2×#544D5semidirect
258. C22×C4×C5C2×Q8semidirect
268. C2×C22⋊D5C2×Q8semidirect
285. #709C2×Q8semidirect
286. C2×D20C2×Q8semidirect
292. C2×C4×D5C2×Q8semidirect
304. C2×Dic10C2×Q8semidirect
369. #544C2×D5semidirect
457. C2×C4×C5C22×Q8semidirect
465. C22⋊D5C22×Q8semidirect
485. D20C22×Q8semidirect
490. C4×D5C22×Q8semidirect
496. Dic10C22×Q8semidirect
705. C22×C4Q8×D5semidirect
762. C2×C5#3503semidirect
817. C2×C4C2×Q8×D5semidirect
825. C5C2×#3503semidirect
855. C2#10618487direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5442
#106184872
C2×#660612
C2×#660632
C2×D5×C4⋊Q82
C2×#660562
C2×#660232
C2×#660192
C2×#660242
C2×#660222
C2×#659702
C2×#659662
C2×#658572
C2×#658532
C2×#658512
C2×#658562
C2×#658382
C22×#40342
C2×#35035