Finite Group Databasebeta

← C2×#10618039 #13007012

Subgroups — C2×#10618039 #13007012

Order 1280.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#529C211yesmaximal, characteristic
2#10618039C2132yesmaximal, direct product factor
3C2×#66035C214yesmaximal, complemented
4C2×#66019C212yesmaximal, complemented
5C2×#66005C212yesmaximal, complemented
6C2×#65985C214yesmaximal, complemented
7C2×#65959C212yesmaximal, complemented
8C2×#65937C212yesmaximal
9C2×Q8×Dic10C211yesmaximal, characteristic, complemented
10C2×#65901C211yesmaximal, characteristic, complemented
11C2×#65876C212yesmaximal, complemented
12C2×#65876C211yesmaximal, characteristic, complemented
13C2×#65877C211yesmaximal, characteristic, complemented
14C2×#65875C212yesmaximal, complemented
15C2×#65853C212yesmaximal, complemented
16C2×#65852C212yesmaximal, complemented
17C2×#65804C211yesmaximal, characteristic, complemented
18C2×#65804C211yesmaximal, characteristic, complemented
19C5×#529C22116yes—
20C2×C5×#126C2212yes—
21C2×C5×#125C2211yescharacteristic
22C2×C5×#124C2211yescharacteristic
23C2×C5×#123C2212yes—
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C5×#121C2211yescharacteristic
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×D4C2212yes—
28C2×C4×C5×D4C2211yescharacteristic
29C2×C5×#117C2212yes—
30C22×C42×C5C2211yescharacteristic
31C2×Q8×Dic5C2212yes—
32C2×#4090C2212yes—
33C2×#4082C2214yes—
34C2×#4082C2212yes—
35C2×#4081C2214yes—
36C2×D4×Dic5C2212yes—
37C2×#4072C2212yes—
38C2×#4072C2212yes—
39C2×#4072C2212yes—
40C22×C4⋊Dic5C2212yes—
41C2×#4070C2212yes—
42C2×#4070C2212yes—
43C2×#4070C2212yes—
44C2×#4070C2212yes—
45C2×#4070C2212yes—
46C2×#4070C2211yescharacteristic
47C2×#4070C2211yescharacteristic
48#66035C22164yescomplemented
49#66019C22132yescomplemented
50#66005C22132yescomplemented
51#65985C22164yescomplemented
52#65959C22132yescomplemented
53#65937C22132yes—
54#65901C22116yescomplemented
55Q8×Dic10C22116yescomplemented
56#65877C22116yescomplemented
57#65876C22132yescomplemented
58#65876C22116yescomplemented
59#65875C22132yescomplemented
60#65853C22132yescomplemented
61#65852C22132yescomplemented
62C2×#4036C2214yes—
63C2×#4036C2212yes—
64C2×#4035C2214yes—
65C2×#4035C2214yes—
66C2×#4035C2214yes—
67C2×#4035C2214yes—
68C2×#4034C2214yes—
69C2×#4034C2214yes—
70C2×#4034C2212yes—
71C2×#4033C2212yes—
72C2×#4033C2214yes—
73C2×#4033C2212yes—
74C2×#4025C2214yes—
75C2×#4025C2214yes—
76C2×#4025C2214yes—
77C2×#4025C2214yes—
78C2×#4025C2214yes—
79C2×#4025C2214yes—
80C2×#4024C2214yes—
81C2×#4024C2214yes—
82C2×#4024C2214yes—
83C2×#4023C2214yes—
84#65804C22116yescomplemented
85#65804C22116yescomplemented
86C2×#4016C2212yes—
87C2×#4016C2212yes—
88C2×#4016C2212yes—
89C2×#4015C2211yescharacteristic
90C2×#4015C2211yescharacteristic
91C2×#4015C2212yes—
92C2×#4015C2211yescharacteristic
93C2×#4015C2211yescharacteristic
94C2×C4×Dic10C2212yes—
95C2×C4×Dic10C2212yes—
96C2×C4×Dic10C2211yescharacteristic
97C2×C4×Dic10C2211yescharacteristic
98C2×C4×Dic10C2212yes—
99C2×C4×Dic10C2212yes—
100C2×C4×Dic10C2212yes—
101C2×#3555—51nomaximal, Sylow
102C22×C5×Q8C2311yescharacteristic
103C22×C5×D4C2311yescharacteristic
104C22×C5×D4C2312yes—
105C23×C4×C5C2312yes—
106C23×C4×C5C2311yescharacteristic
107C23×C4×C5C2311yescharacteristic
108C23×C4×C5C2311yescharacteristic
109C23×Dic5C2314yes—
110C22×Dic10C2311yescharacteristic
111C22×Dic10C2311yescharacteristic
112C22×Dic10C2312yes—
113C22×Dic10C2312yes—
114C22×Dic10C2312yes—
115C22×Dic10C2314yes—
116C5×#126C23116yes—
117C5×#125C2318yes—
118C5×#124C2318yes—
119C5×#123C23116yes—
120C5×C22⋊Q8C2318yes—
121C5×#121C2318yes—
122C4×C5×Q8C2318yes—
123C4×C5×D4C23116yes—
124C4×C5×D4C2318yes—
125C5×#117C23116yes—
126C2×C5×C4⋊C4C2311yescharacteristic
127C2×C5×C4⋊C4C2312yes—
128C2×C5×C4⋊C4C2311yescharacteristic
129C2×C5×C4⋊C4C2312yes—
130C2×C5×C4⋊C4C2312yes—
131C2×C5×C4⋊C4C2312yes—
132C2×C5×C22⋊C4C2312yes—
133C2×C5×C22⋊C4C2312yes—
134C2×C5×C22⋊C4C2312yes—
135C2×C5×C22⋊C4C2312yes—
136C2×C5×C22⋊C4C2312yes—
137C2×C42×C5C2311yescharacteristic
138C2×C42×C5C2311yescharacteristic
139C2×C42×C5C2312yes—
140C2×C42×C5C2311yescharacteristic
141C2×C42×C5C2311yescharacteristic
142C2×C42×C5C2318yes—
143C2×C22⋊Dic5C2314yes—
144C2×C22⋊Dic5C2314yes—
145C2×C22⋊Dic5C2314yes—
146C2×C22⋊Dic5C2312yes—
147C2×C22⋊Dic5C2314yes—
148C2×C22⋊Dic5C2312yes—
149Q8×Dic5C23116yes—
150#4090C23116yes—
151#4082C23132yes—
152#4082C23116yes—
153#4081C23132yes—
154D4×Dic5C23116yes—
155#4072C23116yes—
156#4072C23116yes—
157#4072C23116yes—
158C2×C4⋊Dic5C2311yescharacteristic
159C2×C4⋊Dic5C2312yes—
160C2×C4⋊Dic5C2311yescharacteristic
161C2×C4⋊Dic5C2312yes—
162C2×C4⋊Dic5C2312yes—
163C2×C4⋊Dic5C2312yes—
164C2×C4⋊Dic5C2312yes—
165C2×C4⋊Dic5C2312yes—
166C2×C4⋊Dic5C2312yes—
167C2×C4⋊Dic5C2314yes—
168C2×C4⋊Dic5C2314yes—
169C2×C4⋊Dic5C23116yes—
170#4070C2318yes—
171#4070C2318yes—
172#4070C23116yes—
173#4070C23116yes—
174#4070C23116yes—
175#4070C23116yes—
176#4070C23116yes—
177C2×#683C2312yes—
178C2×#683C2312yes—
179C2×#683C2314yes—
180C2×#683C2314yes—
181C2×#683C2312yes—
182C2×#683C2312yes—
183C2×#683C2314yes—
184C2×#683C2314yes—
185C2×#683C2314yes—
186C2×#683C2314yes—
187C2×#683C2314yes—
188C2×#683C2314yes—
189C2×C4×Dic5C2314yes—
190C2×C4×Dic5C2312yes—
191C2×C4×Dic5C2312yes—
192C2×C4×Dic5C2314yes—
193C2×C4×Dic5C2314yes—
194C2×C4×Dic5C2314yes—
195#4036C23132yes—
196#4036C23116yes—
197#4035C23132yes—
198#4035C23132yes—
199#4035C23132yes—
200#4035C23132yes—
201#4034C23132yes—
202#4034C23116yes—
203#4034C23132yes—
204#4033C23116yes—
205#4033C23132yes—
206#4033C23116yes—
207#4025C23132yes—
208#4025C23132yes—
209#4025C23132yes—
210#4025C23132yes—
211#4025C23132yes—
212#4025C23132yes—
213#4024C23132yes—
214#4024C23132yes—
215#4024C23132yes—
216#4023C23132yes—
217#4016C23116yes—
218#4016C23116yes—
219#4016C23116yes—
220#4015C2318yes—
221#4015C2318yes—
222#4015C2318yes—
223#4015C2318yes—
224#4015C23116yes—
225C4×Dic10C2318yes—
226C4×Dic10C2318yes—
227C4×Dic10C23116yes—
228C4×Dic10C23116yes—
229C4×Dic10C23116yes—
230C4×Dic10C23116yes—
231C4×Dic10C23116yes—
232#3555—532no—
233C2×#563—54no—
234C2×Q82—51no—
235C2×#557—52no—
236C2×#557—51no—
237C2×#556—52no—
238C2×#556—52no—
239C2×#556—51no—
240C2×#554—51no—
241C2×#552—52no—
242C2×#544—52no—
243C2×#542—52no—
244C2×#541—54no—
245C2×#541—52no—
246C2×#541—52no—
247C2×#533—51no—
248C2×#533—51no—
249C2×#529D511yescharacteristic
250C24×C5C2411yescharacteristic
251C24×C5C2412yes—
252C2×C5×Q8—24no—
253C2×C5×Q8C2414yes—
254C2×C5×D4—24no—
255C2×C5×D4—44no—
256C2×C5×D4C2414yes—
257C2×C5×D4C2418yes—
258C22×C4×C5—28no—
259C22×C4×C5—24no—
260C22×C4×C5—24no—
261C22×C4×C5—42no—
262C22×C4×C5C2411yescharacteristic
263C22×C4×C5C2411yescharacteristic
264C22×C4×C5C2411yescharacteristic
265C22×C4×C5C2411yescharacteristic
266C22×C4×C5C2414yes—
267C22×C4×C5C2414yes—
268C22×C4×C5C2412yes—
269C22×C4×C5C2412yes—
270C22×C4×C5C2412yes—
271C22×C4×C5C2418yes—
272C22×C4×C5C2414yes—
273C22×C4×C5C2411yescharacteristic
274C22×C4×C5C2411yescharacteristic
275C22×Dic5—48no—
276C22×Dic5C2412yes—
277C22×Dic5C2412yes—
278C22×Dic5C2414yes—
279C22×Dic5C2412yes—
280C22×Dic5C2414yes—
281C22×Dic5C2412yes—
282C22×Dic5C24116yes—
283C2×Dic10—24no—
284C2×Dic10—24no—
285C2×Dic10—28no—
286C2×Dic10—48no—
287C2×Dic10—44no—
288C2×Dic10—44no—
289C2×Dic10C2414yes—
290C2×Dic10C2414yes—
291C2×Dic10C2418yes—
292C2×Dic10C2418yes—
293C2×Dic10C2418yes—
294C2×Dic10C24116yes—
295C5×C4⋊C4C2418yes—
296C5×C4⋊C4C2418yes—
297C5×C4⋊C4C2414yes—
298C5×C4⋊C4C2418yes—
299C5×C4⋊C4C2414yes—
300C5×C4⋊C4C2418yes—
301C5×C22⋊C4C2418yes—
302C5×C22⋊C4C2418yes—
303C5×C22⋊C4C2418yes—
304C5×C22⋊C4C2418yes—
305C5×C22⋊C4C2418yes—
306C42×C5C2414yes—
307C42×C5C2414yes—
308C42×C5C2414yes—
309C42×C5C2414yes—
310C42×C5C2418yes—
311C22⋊Dic5C24116yes—
312C22⋊Dic5C24116yes—
313C22⋊Dic5C24116yes—
314C22⋊Dic5C2418yes—
315C22⋊Dic5C24116yes—
316C22⋊Dic5C2418yes—
317C4⋊Dic5C2414yes—
318C4⋊Dic5C2418yes—
319C4⋊Dic5C2414yes—
320C4⋊Dic5C2418yes—
321C4⋊Dic5C2418yes—
322C4⋊Dic5C2418yes—
323C4⋊Dic5C2418yes—
324C4⋊Dic5C2418yes—
325C4⋊Dic5C2418yes—
326C4⋊Dic5C24116yes—
327C4⋊Dic5C24116yes—
328#683C2418yes—
329#683C2418yes—
330#683C24116yes—
331#683C24116yes—
332#683C2418yes—
333#683C2418yes—
334#683C24116yes—
335#683C24116yes—
336#683C24116yes—
337#683C24116yes—
338#683C24116yes—
339#683C24116yes—
340C4×Dic5C24116yes—
341C4×Dic5C2418yes—
342C4×Dic5C2418yes—
343C4×Dic5C24116yes—
344C4×Dic5C24116yes—
345C4×Dic5C24116yes—
346#563—564no—
347Q82—516no—
348#557—532no—
349#557—516no—
350#556—532no—
351#556—532no—
352#556—516no—
353#554—516no—
354#552—532no—
355#544—532no—
356#542—532no—
357#541—564no—
358#541—532no—
359#541—532no—
360#533—516no—
361#533—516no—
362C2×C4⋊Q8—52no—
363C2×C4⋊Q8—54no—
364C2×C4⋊Q8—52no—
365C2×C4⋊Q8—54no—
366C2×C4⋊Q8—51no—
367C2×C4⋊Q8—51no—
368C2×C4⋊Q8—51no—
369C2×C4⋊Q8—51no—
370C2×C4⋊Q8—52no—
371#529C2×D5116yes—
372C2×#126—54no—
373C2×#126—54no—
374C2×#126—54no—
375C2×#126—54no—
376C2×#126—54no—
377C2×#126—54no—
378C2×#126C2×D512yes—
379C2×#125—54no—
380C2×#125—54no—
381C2×#125—54no—
382C2×#125—54no—
383C2×#125—54no—
384C2×#125—52no—
385C2×#125—52no—
386C2×#125—52no—
387C2×#125—52no—
388C2×#125C2×D511yescharacteristic
389C2×#124—52no—
390C2×#124—54no—
391C2×#124C2×D511yescharacteristic
392C2×#123—54no—
393C2×#123C2×D512yes—
394C2×C22⋊Q8—52no—
395C2×C22⋊Q8—51no—
396C2×C22⋊Q8—51no—
397C2×C22⋊Q8—52no—
398C2×C22⋊Q8—52no—
399C2×C22⋊Q8—52no—
400C2×C22⋊Q8—52no—
401C2×C22⋊Q8—54no—
402C2×C22⋊Q8—54no—
403C2×C22⋊Q8—54no—
404C2×C22⋊Q8C2×D511yescharacteristic
405C2×#121C2×D511yescharacteristic
406C2×C4×Q8—52no—
407C2×C4×Q8—54no—
408C2×C4×Q8—52no—
409C2×C4×Q8—52no—
410C2×C4×Q8—52no—
411C2×C4×Q8—51no—
412C2×C4×Q8—52no—
413C2×C4×Q8—52no—
414C2×C4×Q8—51no—
415C2×C4×Q8—52no—
416C2×C4×Q8—52no—
417C2×C4×Q8C2×D511yescharacteristic
418C2×C4×D4—52no—
419C2×C4×D4C2×D512yes—
420C2×C4×D4C2×D511yescharacteristic
421C2×#117—52no—
422C2×#117—52no—
423C2×#117—52no—
424C2×#117—54no—
425C2×#117C2×D512yes—
426C22×C4⋊C4—52no—
427C22×C42C2×D511yescharacteristic
428C23×C5—22no—
429C23×C5—22no—
430C23×C5—24no—
431C23×C5—24no—
432C23×C5—24no—
433C23×C5—22no—
434C23×C5C2512yes—
435C23×C5C2514yes—
436C23×C5C2511yescharacteristic
437C5×Q8—28no—
438C5×D4—28no—
439C5×D4—48no—
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5—24no—
443C2×C4×C5—24no—
444C2×C4×C5—22no—
445C2×C4×C5—22no—
446C2×C4×C5—24no—
447C2×C4×C5—28no—
448C2×C4×C5—216no—
449C2×C4×C5—28no—
450C2×C4×C5—44no—
451C2×C4×C52−1+414yes—
452C2×C4×C52−1+414yes—
453C2×C4×C5C2512yes—
454C2×C4×C5C2514yes—
455C2×C4×C5C2514yes—
456C2×C4×C5C2514yes—
457C2×C4×C5C2512yes—
458C2×C4×C5C2512yes—
459C2×C4×C5C2512yes—
460C2×C4×C5C2512yes—
461C2×C4×C5C2512yes—
462C2×Dic5—24no—
463C2×Dic5—24no—
464C2×Dic5—28no—
465C2×Dic5—24no—
466C2×Dic5—28no—
467C2×Dic5—24no—
468C2×Dic5—416no—
469C2×Dic5C2518yes—
470C2×Dic5C2514yes—
471C2×Dic5C2514yes—
472C2×Dic5C2514yes—
473C2×Dic5C2518yes—
474C2×Dic5C2514yes—
475Dic10—28no—
476Dic10—28no—
477Dic10—216no—
478Dic10—416no—
479Dic10—48no—
480Dic10—48no—
481C22×Q8—51no—
482C22×Q8—51no—
483C22×Q8—52no—
484C22×Q8—52no—
485C22×Q8—52no—
486C22×Q8—54no—
487C22×Q8C22×D511yescharacteristic
488C22×D4C22×D511yescharacteristic
489C22×D4C22×D512yes—
490C23×C4—54no—
491C23×C4C22×D512yes—
492C23×C4C22×D511yescharacteristic
493C23×C4C22×D511yescharacteristic
494C23×C4C22×D511yescharacteristic
495C4⋊Q8—516no—
496C4⋊Q8—532no—
497C4⋊Q8—516no—
498C4⋊Q8—532no—
499C4⋊Q8—58no—
500C4⋊Q8—58no—
501C4⋊Q8—58no—
502C4⋊Q8—58no—
503C4⋊Q8—516no—
504#126—532no—
505#126—532no—
506#126—532no—
507#126—532no—
508#126—532no—
509#126—532no—
510#126C22×D5116yes—
511#125—532no—
512#125—532no—
513#125—532no—
514#125—516no—
515#125—532no—
516#125—532no—
517#125—516no—
518#125—516no—
519#125—516no—
520#125C22×D518yes—
521#124—516no—
522#124—532no—
523#124C22×D518yes—
524#123—532no—
525#123C22×D5116yes—
526C22⋊Q8—516no—
527C22⋊Q8—58no—
528C22⋊Q8—58no—
529C22⋊Q8—516no—
530C22⋊Q8—516no—
531C22⋊Q8—516no—
532C22⋊Q8—516no—
533C22⋊Q8—532no—
534C22⋊Q8—532no—
535C22⋊Q8—532no—
536C22⋊Q8C22×D518yes—
537#121C22×D518yes—
538C4×Q8—516no—
539C4×Q8—532no—
540C4×Q8—516no—
541C4×Q8—516no—
542C4×Q8—516no—
543C4×Q8—58no—
544C4×Q8—516no—
545C4×Q8—516no—
546C4×Q8—58no—
547C4×Q8—516no—
548C4×Q8—516no—
549C4×Q8C22×D518yes—
550C4×D4—516no—
551C4×D4C22×D5116yes—
552C4×D4C22×D518yes—
553#117—516no—
554#117—516no—
555#117—516no—
556#117—532no—
557#117C22×D5116yes—
558C2×C4⋊C4—51no—
559C2×C4⋊C4—52no—
560C2×C4⋊C4—54no—
561C2×C4⋊C4—516no—
562C2×C4⋊C4—52no—
563C2×C4⋊C4—52no—
564C2×C4⋊C4—51no—
565C2×C4⋊C4—52no—
566C2×C4⋊C4—54no—
567C2×C4⋊C4—52no—
568C2×C4⋊C4—52no—
569C2×C4⋊C4—52no—
570C2×C4⋊C4—52no—
571C2×C4⋊C4—54no—
572C2×C4⋊C4—54no—
573C2×C4⋊C4—54no—
574C2×C4⋊C4—54no—
575C2×C4⋊C4—54no—
576C2×C4⋊C4—52no—
577C2×C4⋊C4—52no—
578C2×C4⋊C4—52no—
579C2×C4⋊C4—54no—
580C2×C4⋊C4—54no—
581C2×C4⋊C4—54no—
582C2×C4⋊C4C22×D512yes—
583C2×C4⋊C4C22×D512yes—
584C2×C4⋊C4C22×D511yescharacteristic
585C2×C4⋊C4C22×D512yes—
586C2×C4⋊C4C22×D511yescharacteristic
587C2×C4⋊C4C22×D512yes—
588C2×C22⋊C4—52no—
589C2×C22⋊C4—54no—
590C2×C22⋊C4—52no—
591C2×C22⋊C4—54no—
592C2×C22⋊C4—54no—
593C2×C22⋊C4—54no—
594C2×C22⋊C4C22×D512yes—
595C2×C22⋊C4C22×D512yes—
596C2×C22⋊C4C22×D512yes—
597C2×C22⋊C4C22×D512yes—
598C2×C22⋊C4C22×D512yes—
599C2×C42—54no—
600C2×C42—52no—
601C2×C42—52no—
602C2×C42—54no—
603C2×C42—54no—
604C2×C42—54no—
605C2×C42C22×D511yescharacteristic
606C2×C42C22×D512yes—
607C2×C42C22×D511yescharacteristic
608C2×C42C22×D511yescharacteristic
609C2×C42C22×D511yescharacteristic
610C2×C42C22×D518yes—
611C22×C5—22no—
612C22×C5—22no—
613C22×C5—24no—
614C22×C5—24no—
615C22×C5—24no—
616C22×C5—22no—
617C22×C5—44no—
618C22×C5—48no—
619C22×C5C2×2−1+412yes—
620C22×C5C2×2−1+412yes—
621C22×C5#58512yes—
622C22×C5C2611yescharacteristic
623C4×C5—22no—
624C4×C5—24no—
625C4×C5—22no—
626C4×C5—24no—
627C4×C5—22no—
628C4×C5—22no—
629C4×C5—24no—
630C4×C5C2×2−1+414yes—
631C4×C5C2×2−1+414yes—
632Dic5—24no—
633Dic5—24no—
634Dic5—28no—
635Dic5—24no—
636Dic5—28no—
637Dic5—24no—
638C24C23×D511yescharacteristic
639C24C23×D512yes—
640C2×Q8—24no—
641C2×Q8—54no—
642C2×Q8—54no—
643C2×Q8—58no—
644C2×Q8—58no—
645C2×Q8—58no—
646C2×Q8—516no—
647C2×Q8—104no—
648C2×Q8—104no—
649C2×Q8—108no—
650C2×Q8—204no—
651C2×Q8—204no—
652C2×Q8—208no—
653C2×Q8C23×D514yes—
654C2×D4—24no—
655C2×D4—44no—
656C2×D4C23×D514yes—
657C2×D4C23×D518yes—
658C22×C4—28no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—42no—
662C22×C4—54no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—54no—
667C22×C4—52no—
668C22×C4—516no—
669C22×C4—208no—
670C22×C4C23×D514yes—
671C22×C4C23×D514yes—
672C22×C4C23×D518yes—
673C22×C4C23×D511yescharacteristic
674C22×C4C23×D512yes—
675C22×C4C23×D512yes—
676C22×C4C23×D512yes—
677C22×C4C23×D511yescharacteristic
678C22×C4C23×D511yescharacteristic
679C22×C4C23×D511yescharacteristic
680C22×C4C23×D514yes—
681C22×C4C23×D511yescharacteristic
682C22×C4C23×D511yescharacteristic
683C4⋊C4—54no—
684C4⋊C4—58no—
685C4⋊C4—516no—
686C4⋊C4—58no—
687C4⋊C4—58no—
688C4⋊C4—54no—
689C4⋊C4—58no—
690C4⋊C4—516no—
691C4⋊C4—58no—
692C4⋊C4—58no—
693C4⋊C4—58no—
694C4⋊C4—58no—
695C4⋊C4—516no—
696C4⋊C4—516no—
697C4⋊C4—516no—
698C4⋊C4—516no—
699C4⋊C4—516no—
700C4⋊C4—58no—
701C4⋊C4—58no—
702C4⋊C4—58no—
703C4⋊C4—516no—
704C4⋊C4—516no—
705C4⋊C4—516no—
706C4⋊C4C23×D518yes—
707C4⋊C4C23×D518yes—
708C4⋊C4C23×D514yes—
709C4⋊C4C23×D518yes—
710C4⋊C4C23×D514yes—
711C4⋊C4C23×D518yes—
712C22⋊C4—58no—
713C22⋊C4—516no—
714C22⋊C4—58no—
715C22⋊C4—516no—
716C22⋊C4—516no—
717C22⋊C4—516no—
718C22⋊C4C23×D518yes—
719C22⋊C4C23×D518yes—
720C22⋊C4C23×D518yes—
721C22⋊C4C23×D518yes—
722C22⋊C4C23×D518yes—
723C42—516no—
724C42—58no—
725C42—58no—
726C42—516no—
727C42—516no—
728C42—516no—
729C42C23×D514yes—
730C42C23×D514yes—
731C42C23×D514yes—
732C42C23×D514yes—
733C42C23×D518yes—
734C2×C5—42no—
735C2×C5—44no—
736C2×C5#355514yescomplemented
737C2×C5C22×2−1+411yescharacteristic
738C2×C5C22×2−1+411yescharacteristic
739C2×C5C2×#58511yescharacteristic
740C23—22no—
741C23—22no—
742C23—24no—
743C23—24no—
744C23—22no—
745C23—24no—
746C23C24×D512yes—
747C23C24×D514yes—
748C23C24×D511yescharacteristic
749Q8—28no—
750Q8—108no—
751Q8—108no—
752Q8—1016no—
753Q8—208no—
754Q8—208no—
755Q8—2016no—
756D4—28no—
757D4—48no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—28no—
766C2×C4—216no—
767C2×C4—28no—
768C2×C4—44no—
769C2×C4—58no—
770C2×C4—54no—
771C2×C4—54no—
772C2×C4—54no—
773C2×C4—58no—
774C2×C4—54no—
775C2×C4—104no—
776C2×C4—104no—
777C2×C4—108no—
778C2×C4—104no—
779C2×C4—108no—
780C2×C4—104no—
781C2×C4—2016no—
782C2×C4#415014yes—
783C2×C4#415014yes—
784C2×C4C24×D512yes—
785C2×C4C24×D514yes—
786C2×C4C24×D514yes—
787C2×C4C24×D514yes—
788C2×C4C24×D512yes—
789C2×C4C24×D512yes—
790C2×C4C24×D512yes—
791C2×C4C24×D512yes—
792C2×C4C24×D512yes—
793C5C2×#355511yescharacteristic, complemented, Sylow
794C22—22no—
795C22—22no—
796C22—24no—
797C22—24no—
798C22—22no—
799C22—24no—
800C22—44no—
801C22—48no—
802C22C2×#415012yes—
803C22C2×#415012yes—
804C22#6628312yes—
805C22C25×D511yescharacteristic
806C4—22no—
807C4—24no—
808C4—22no—
809C4—24no—
810C4—22no—
811C4—22no—
812C4—24no—
813C4—104no—
814C4—104no—
815C4—108no—
816C4—104no—
817C4—108no—
818C4—104no—
819C4C2×#415014yes—
820C4C2×#415014yes—
821C2—42no—
822C2—44no—
823C2#1061803914yesdirect product factor
824C2C22×#415011yescharacteristic
825C2C22×#415011yescharacteristic
826C2C2×#6628311yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#529C2
socleC23×C5C25
prime radicalC2×C5×#121C22
hypercenterC2×#529D5
hypocenterC5C2×#3555
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
2. #10618039C2direct (N × H)
3. C2×#66035C2semidirect
4. C2×#66019C2semidirect
5. C2×#66005C2semidirect
6. C2×#65985C2semidirect
7. C2×#65959C2semidirect
9. C2×Q8×Dic10C2semidirect
10. C2×#65901C2semidirect
11. C2×#65876C2semidirect
12. C2×#65876C2semidirect
13. C2×#65877C2semidirect
14. C2×#65875C2semidirect
15. C2×#65853C2semidirect
16. C2×#65852C2semidirect
17. C2×#65804C2semidirect
18. C2×#65804C2semidirect
48. #66035C22semidirect
49. #66019C22semidirect
50. #66005C22semidirect
51. #65985C22semidirect
52. #65959C22semidirect
54. #65901C22semidirect
55. Q8×Dic10C22semidirect
56. #65877C22semidirect
57. #65876C22semidirect
58. #65876C22semidirect
59. #65875C22semidirect
60. #65853C22semidirect
61. #65852C22semidirect
84. #65804C22semidirect
85. #65804C22semidirect
736. C2×C5#3555semidirect
793. C5C2×#3555semidirect
823. C2#10618039direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5292
#106180392
C2×#660352
C2×#660192
C2×#660052
C2×#659852
C2×#659592
C2×#659372
C2×Q8×Dic102
C2×#659012
C2×#658762
C2×#658772
C2×#658752
C2×#658532
C2×#658522
C2×#658042
C2×#35555