Finite Group Databasebeta

← C2×#10617628 #13007730

Subgroups — C2×#10617628 #13007730

Order 1280.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#117C211yesmaximal, characteristic, complemented
2C2×#66125C211yesmaximal, characteristic
3C22×#4070C211yesmaximal, characteristic, complemented
4C2×#65867C212yesmaximal, complemented
5C2×#65863C212yesmaximal, complemented
6C2×#65868C212yesmaximal, complemented
7C2×#65857C211yesmaximal, characteristic, complemented
8#10617628C2132yesmaximal, direct product factor
9C2×#65865C214yesmaximal, complemented
10C2×#65853C211yesmaximal, characteristic, complemented
11C2×#65852C212yesmaximal, complemented
12C2×#65860C211yesmaximal, characteristic, complemented
13C2×#65850C211yesmaximal, characteristic, complemented
14C2×#65845C212yesmaximal, complemented
15C2×#65847C212yesmaximal, complemented
16C2×#65829C214yesmaximal, complemented
17C2×#65813C212yesmaximal, complemented
18C2×#65804C212yesmaximal, complemented
19C24×C4×C5C2211yescharacteristic
20C22×#709C2211yescharacteristic
21C23×Dic10C2211yescharacteristic
22C2×C5×#117C2211yescharacteristic
23C2×C5×#117C2211yescharacteristic
24C2×C5×#117C2212yes—
25C2×C5×#117C2212yes—
26C2×C5×#117C2211yescharacteristic
27C2×C5×#117C2211yescharacteristic
28C2×C5×#117C22116yescomplemented
29C22×C5×C4⋊C4C2211yescharacteristic
30C22×C5×C4⋊C4C2211yescharacteristic
31C22×C5×C22⋊C4C2212yes—
32C22×C42×C5C2212yes—
33C2×#4099C2212yes—
34C22×C22⋊Dic5C2212yes—
35#66125C22116yes—
36C2×#4076C2211yescharacteristic
37C2×#4076C2211yescharacteristic
38C2×#4075C2214yes—
39C2×#4075C2212yes—
40C2×C4×C22⋊D5C2212yes—
41C2×C4×C22⋊D5C2214yes—
42C2×C4×C22⋊D5C2212yes—
43C2×#4072C2214yes—
44C2×#4072C2211yescharacteristic
45C22×C4⋊Dic5C2211yescharacteristic
46C2×#4070C2212yes—
47C2×#4070C2214yes—
48C2×#4070C2211yescharacteristic
49C2×#4070C2212yes—
50C2×#4070C2212yes—
51C2×#4070C2211yescharacteristic
52C2×#4070C2212yes—
53C2×#4070C22116yescomplemented
54C22×#683C2212yes—
55#65868C22132yescomplemented
56#65867C22132yescomplemented
57#65865C22164yescomplemented
58#65863C22132yescomplemented
59#65860C22116yescomplemented
60#65857C22116yescomplemented
61#65853C22116yescomplemented
62#65852C22132yescomplemented
63#65850C22116yescomplemented
64#65847C22132yescomplemented
65C2×#4044C2214yescomplemented
66#65845C22132yescomplemented
67C2×#4043C2212yescomplemented
68C2×#4043C2212yescomplemented
69C2×#4042C2214yescomplemented
70C2×#4038C2212yescomplemented
71C2×D5×C4⋊C4C2212yescomplemented
72C2×#4036C2212yescomplemented
73C2×#4035C2214yescomplemented
74C2×#4035C2214yescomplemented
75C2×#4034C2212yescomplemented
76C2×#4033C2212yescomplemented
77C2×#4033C2212yescomplemented
78#65829C22164yescomplemented
79C2×#4032C2214yes—
80C2×#4031C2214yes—
81C2×#4029C2214yes—
82C2×#4027C2214yes—
83C2×#4025C2214yes—
84C2×#4025C2214yes—
85C2×#4024C2214yes—
86C2×#4023C2214yes—
87#65813C22132yescomplemented
88C2×#4022C2214yescomplemented
89C2×#4021C2212yescomplemented
90C2×C4×D20C2212yescomplemented
91C2×#4018C2214yescomplemented
92#65804C22132yescomplemented
93C2×#4016C2212yescomplemented
94C2×#4016C2214yescomplemented
95C2×#4015C2212yescomplemented
96C2×#4015C2212yescomplemented
97C2×C4×Dic10C2212yescomplemented
98C2×C4×Dic10C2212yescomplemented
99C2×C4×Dic10C2212yescomplemented
100C2×C4×Dic10C2214yescomplemented
101C2×#3495—51nomaximal, Sylow
102C25×C5C2311yescharacteristic
103C23×C4×C5—28no—
104C23×C4×C5C2311yescharacteristic
105C23×C4×C5C2311yescharacteristic
106C23×C4×C5C2311yescharacteristic
107C23×C4×C5C2311yescharacteristic
108C23×C4×C5C2311yescharacteristic
109C23×C4×C5C2318yes—
110C23×C4×C5C2312yes—
111C23×C4×C5C2312yes—
112C23×C4×C5C2311yescharacteristic
113C22×C22⋊D5C2312yes—
114C22×C22⋊D5C2312yes—
115C22×C22⋊D5C2312yes—
116C23×Dic5C2312yes—
117C23×Dic5C2312yes—
118C2×#709—28no—
119C2×#709C2318yes—
120C22×D20C2311yescharacteristic
121C22×C4×D5C2312yes—
122C22×C4×D5C2314yes—
123C22×Dic10—28no—
124C22×Dic10C2311yescharacteristic
125C22×Dic10C2312yes—
126C22×Dic10C2312yes—
127C22×Dic10C2318yes—
128C22×Dic10C2314yes—
129C5×#117C2318yes—
130C5×#117C23116yes—
131C5×#117C2318yes—
132C5×#117C2318yes—
133C5×#117C23116yes—
134C5×#117C2318yes—
135C2×C5×C4⋊C4C2311yescharacteristic
136C2×C5×C4⋊C4C2311yescharacteristic
137C2×C5×C4⋊C4C2311yescharacteristic
138C2×C5×C4⋊C4C2312yes—
139C2×C5×C4⋊C4C2312yes—
140C2×C5×C4⋊C4C2311yescharacteristic
141C2×C5×C4⋊C4C2318yes—
142C2×C5×C4⋊C4C2318yes—
143C2×C5×C22⋊C4C2312yes—
144C2×C5×C22⋊C4C2312yes—
145C2×C5×C22⋊C4C2312yes—
146C2×C5×C22⋊C4C2312yes—
147C2×C5×C22⋊C4C23116yes—
148C2×C42×C5C2312yes—
149C2×C42×C5C2312yes—
150C2×C42×C5C2312yes—
151C2×C42×C5C2312yes—
152C2×C42×C5C23116yes—
153#4099C23116yes—
154C2×C22⋊Dic5C2312yes—
155C2×C22⋊Dic5C2312yes—
156C2×C22⋊Dic5C2314yes—
157C2×C22⋊Dic5C23116yes—
158C2×C22⋊Dic5C2312yes—
159C2×C22⋊Dic5C2314yes—
160#4076C2318yes—
161#4076C2318yes—
162#4075C23132yes—
163#4075C23116yes—
164C4×C22⋊D5C23132yes—
165C4×C22⋊D5C23116yes—
166C4×C22⋊D5C23116yes—
167C2×#685C2312yes—
168C2×#685C2314yes—
169C2×#685C2314yes—
170C2×#685C2314yes—
171C2×#685C2312yes—
172#4072C23132yes—
173#4072C2318yes—
174C2×C4⋊Dic5C2311yescharacteristic
175C2×C4⋊Dic5C2311yescharacteristic
176C2×C4⋊Dic5C2312yes—
177C2×C4⋊Dic5C2314yes—
178C2×C4⋊Dic5C2314yes—
179C2×C4⋊Dic5C2314yes—
180C2×C4⋊Dic5C2312yes—
181C2×C4⋊Dic5C2318yes—
182#4070C2318yes—
183#4070C23116yes—
184#4070C23132yes—
185#4070C23116yes—
186#4070C2318yes—
187#4070C23116yes—
188#4070C23116yes—
189C2×#683C2312yes—
190C2×#683C2314yes—
191C2×#683C2314yes—
192C2×#683C2314yes—
193C2×#683C2314yes—
194C2×#683C2314yes—
195C2×#683C2314yes—
196C2×#683C2312yes—
197C2×#683C2314yes—
198C2×#683C23116yes—
199C2×C4×Dic5C2314yes—
200C2×C4×Dic5C2314yes—
201C2×C4×Dic5C2314yes—
202C2×C4×Dic5C2312yes—
203#4044C23132yescomplemented
204#4043C23116yescomplemented
205#4043C23116yescomplemented
206#4042C23132yescomplemented
207#4038C23116yescomplemented
208D5×C4⋊C4C23116yescomplemented
209#4036C23116yescomplemented
210#4035C23132yescomplemented
211#4035C23132yescomplemented
212#4034C23116yescomplemented
213#4033C23116yescomplemented
214#4033C23116yescomplemented
215#4032C23132yes—
216#4031C23132yes—
217#4029C23132yes—
218#4027C23132yes—
219#4025C23132yes—
220#4025C23132yes—
221#4024C23132yes—
222#4023C23132yes—
223#4022C23132yescomplemented
224#4021C23116yescomplemented
225C4×D20C23116yescomplemented
226#4018C23132yescomplemented
227#4016C23132yescomplemented
228#4016C23116yescomplemented
229#4015C23116yescomplemented
230#4015C23116yescomplemented
231C4×Dic10C23116yescomplemented
232C4×Dic10C23116yescomplemented
233C4×Dic10C23132yescomplemented
234C4×Dic10C23116yescomplemented
235#3495—532no—
236C2×#556—52no—
237C2×#554—52no—
238C2×#552—54no—
239C2×#552—52no—
240C2×#552—52no—
241C2×#551—54no—
242C2×#544—51no—
243C2×#542—52no—
244C2×#541—52no—
245C2×#536—51no—
246C2×#533—52no—
247C2×#529—52no—
248C2×#525—51no—
249C22×C22⋊Q8—51no—
250C2×#520—51no—
251C2×#519—51no—
252C22×#117D511yescharacteristic, complemented
253C24×C5—24no—
254C24×C5—24no—
255C24×C5—42no—
256C24×C5C2411yescharacteristic
257C24×C5C2414yes—
258C24×C5C2411yescharacteristic
259C24×C5C2411yescharacteristic
260C23×D5C2412yes—
261C22×C4×C5—24no—
262C22×C4×C5—28no—
263C22×C4×C5—24no—
264C22×C4×C5—24no—
265C22×C4×C5—24no—
266C22×C4×C5—24no—
267C22×C4×C5—232no—
268C22×C4×C5—44no—
269C22×C4×C5#4118yes—
270C22×C4×C5C2411yescharacteristic
271C22×C4×C5C2414yes—
272C22×C4×C5C2412yes—
273C22×C4×C5C2412yes—
274C22×C4×C5C2412yes—
275C22×C4×C5C2412yes—
276C22×C4×C5C2418yes—
277C22×C4×C5C2411yescharacteristic
278C22×C4×C5C2414yes—
279C22×C4×C5C2414yes—
280C22×C4×C5C2414yes—
281C22×C4×C5C2414yes—
282C22×C4×C5C2418yes—
283C22×C4×C5C2411yescharacteristic
284C22×C4×C5C2411yescharacteristic
285C22×C4×C5C2414yes—
286C2×C22⋊D5—28no—
287C2×C22⋊D5—28no—
288C2×C22⋊D5—44no—
289C2×C22⋊D5C2418yes—
290C2×C22⋊D5C2418yes—
291C2×C22⋊D5C2418yes—
292C22×Dic5—28no—
293C22×Dic5—44no—
294C22×Dic5C2418yes—
295C22×Dic5C2414yes—
296C22×Dic5C2412yes—
297C22×Dic5C2414yes—
298C22×Dic5C2412yes—
299C22×Dic5C2412yes—
300C22×Dic5C2418yes—
301#709—232no—
302C2×D20—24no—
303C2×D20C2414yes—
304C2×C4×D5—28no—
305C2×C4×D5—48no—
306C2×C4×D5C2418yes—
307C2×C4×D5C24116yes—
308C2×Dic10—28no—
309C2×Dic10—28no—
310C2×Dic10—232no—
311C2×Dic10—24no—
312C2×Dic10—48no—
313C2×Dic10C2418yes—
314C2×Dic10C2418yes—
315C2×Dic10C2414yes—
316C2×Dic10C24116yes—
317C5×C4⋊C4C2414yes—
318C5×C4⋊C4C2414yes—
319C5×C4⋊C4C2414yes—
320C5×C4⋊C4C2418yes—
321C5×C4⋊C4C2418yes—
322C5×C4⋊C4C2414yes—
323C5×C22⋊C4C2418yes—
324C5×C22⋊C4C2418yes—
325C5×C22⋊C4C2418yes—
326C5×C22⋊C4C2418yes—
327C42×C5C2418yes—
328C42×C5C2418yes—
329C42×C5C2418yes—
330C42×C5C2418yes—
331C22⋊Dic5C24116yes—
332C22⋊Dic5C24116yes—
333C22⋊Dic5C2418yes—
334C22⋊Dic5C2418yes—
335C22⋊Dic5C2418yes—
336#685C2418yes—
337#685C24116yes—
338#685C24116yes—
339#685C24116yes—
340#685C2418yes—
341C4⋊Dic5C2414yes—
342C4⋊Dic5C2414yes—
343C4⋊Dic5C2418yes—
344C4⋊Dic5C24116yes—
345C4⋊Dic5C24116yes—
346C4⋊Dic5C24116yes—
347C4⋊Dic5C2418yes—
348#683C2418yes—
349#683C24116yes—
350#683C24116yes—
351#683C24116yes—
352#683C24116yes—
353#683C24116yes—
354#683C24116yes—
355#683C2418yes—
356#683C24116yes—
357C4×Dic5C24116yes—
358C4×Dic5C24116yes—
359C4×Dic5C24116yes—
360C4×Dic5C2418yes—
361C22×#41—51no—
362C23×Q8—51no—
363C24×C4C2×D511yescharacteristic
364#556—532no—
365#554—532no—
366#552—532no—
367#552—564no—
368#552—532no—
369#551—564no—
370#544—516no—
371#542—532no—
372#541—532no—
373#536—516no—
374#533—532no—
375C2×C4⋊Q8—52no—
376C2×C4⋊Q8—52no—
377C2×C4⋊Q8—52no—
378#529—532no—
379C2×#126—54no—
380C2×#126—54no—
381C2×#126—54no—
382C2×#126—54no—
383C2×#125—54no—
384C2×#125—54no—
385C2×#125—52no—
386C2×#125—52no—
387C2×#125—54no—
388C2×#124—54no—
389C2×#124—52no—
390#525—516no—
391C2×#123—52no—
392C2×#123—54no—
393C2×#123—54no—
394C2×#123—54no—
395C2×C22⋊Q8—52no—
396C2×C22⋊Q8—52no—
397C2×C22⋊Q8—52no—
398C2×C22⋊Q8—52no—
399C2×C22⋊Q8—51no—
400C2×C22⋊Q8—51no—
401C2×C22⋊Q8—54no—
402C2×C22⋊Q8—516no—
403C2×C22⋊Q8—54no—
404C2×C22⋊Q8—52no—
405C2×C22⋊Q8—52no—
406C2×C22⋊Q8—54no—
407C2×#121—51no—
408C2×#121—51no—
409C2×#120—52no—
410#520—516no—
411#519—516no—
412C2×C4×Q8—52no—
413C2×C4×Q8—52no—
414C2×C4×Q8—52no—
415C2×C4×Q8—52no—
416C2×C4×Q8—52no—
417C2×C4×Q8—54no—
418C2×C4×D4—52no—
419C2×C4×D4—52no—
420C2×C4×D4—54no—
421C2×C4×D4—54no—
422C2×C4×D4—52no—
423C2×#117—51no—
424C2×#117—54no—
425C2×#117—52no—
426C2×#117—54no—
427C2×#117—54no—
428C2×#117C2×D511yescharacteristic
429C2×#117C2×D511yescharacteristic
430C2×#117C2×D512yes—
431C2×#117C2×D511yescharacteristic
432C2×#117C2×D512yes—
433C2×#117C2×D511yescharacteristic
434C2×#117C2×D5116yescomplemented
435C22×C4⋊C4—52no—
436C22×C4⋊C4—51no—
437C22×C4⋊C4—52no—
438C22×C4⋊C4C2×D511yescharacteristic
439C22×C4⋊C4C2×D511yescharacteristic
440C22×C22⋊C4—52no—
441C22×C22⋊C4C2×D512yes—
442C22×C42C2×D512yes—
443C23×C5—22no—
444C23×C5—22no—
445C23×C5—22no—
446C23×C5—22no—
447C23×C5—28no—
448C23×C5—22no—
449C23×C5—28no—
450C23×C5—22no—
451C23×C5—22no—
452C23×C5—44no—
453C23×C5—416no—
454C23×C5C2×#4114yes—
455C23×C52−1+414yes—
456C23×C5C2512yes—
457C23×C5C2512yes—
458C23×C5C2512yes—
459C23×C5C2511yescharacteristic
460C22×D5—24no—
461C22×D5—24no—
462C22×D5—24no—
463C22×D5C2514yes—
464C2×C4×C5—28no—
465C2×C4×C5—22no—
466C2×C4×C5—22no—
467C2×C4×C5—216no—
468C2×C4×C5—24no—
469C2×C4×C5—24no—
470C2×C4×C5—24no—
471C2×C4×C5—24no—
472C2×C4×C5—28no—
473C2×C4×C5—28no—
474C2×C4×C5—28no—
475C2×C4×C5—28no—
476C2×C4×C5—48no—
477C2×C4×C5C2×#4114yes—
478C2×C4×C5C2×#4114yes—
479C2×C4×C5C2×#41116yes—
480C2×C4×C5C2514yes—
481C2×C4×C5C2514yes—
482C2×C4×C5C2512yes—
483C2×C4×C5C2512yes—
484C2×C4×C5C2514yes—
485C2×C4×C5C2514yes—
486C2×C4×C5C2512yes—
487C2×C4×C5C2512yes—
488C22⋊D5—216no—
489C22⋊D5—216no—
490C22⋊D5—48no—
491C2×Dic5—216no—
492C2×Dic5—28no—
493C2×Dic5—24no—
494C2×Dic5—24no—
495C2×Dic5—24no—
496C2×Dic5—28no—
497C2×Dic5—48no—
498C2×Dic5C2514yes—
499C2×Dic5C2514yes—
500C2×Dic5C2514yes—
501C2×Dic5C2518yes—
502C2×Dic5C2518yes—
503D20—28no—
504C4×D5—216no—
505C4×D5—416no—
506Dic10—216no—
507Dic10—216no—
508Dic10—28no—
509Dic10—416no—
510C25C22×D511yescharacteristic
511C2×#41—58no—
512C2×#41—108no—
513C22×Q8—52no—
514C22×Q8—52no—
515C22×Q8—51no—
516C22×Q8—58no—
517C22×Q8—54no—
518C22×Q8—108no—
519C22×D4—52no—
520C22×D4—52no—
521C22×D4—52no—
522C22×D4—51no—
523C23×C4—28no—
524C23×C4—52no—
525C23×C4—52no—
526C23×C4—52no—
527C23×C4—54no—
528C23×C4C22×D512yes—
529C23×C4C22×D511yescharacteristic
530C23×C4C22×D511yescharacteristic
531C23×C4C22×D511yescharacteristic
532C23×C4C22×D511yescharacteristic
533C23×C4C22×D518yes—
534C23×C4C22×D511yescharacteristic
535C23×C4C22×D512yes—
536C23×C4C22×D511yescharacteristic
537C4⋊Q8—516no—
538C4⋊Q8—516no—
539C4⋊Q8—516no—
540#126—532no—
541#126—532no—
542#126—532no—
543#126—532no—
544#125—532no—
545#125—532no—
546#125—516no—
547#125—516no—
548#125—532no—
549#124—532no—
550#124—516no—
551#123—516no—
552#123—532no—
553#123—532no—
554#123—532no—
555C22⋊Q8—516no—
556C22⋊Q8—516no—
557C22⋊Q8—516no—
558C22⋊Q8—516no—
559C22⋊Q8—58no—
560C22⋊Q8—58no—
561C22⋊Q8—532no—
562C22⋊Q8—516no—
563C22⋊Q8—516no—
564C22⋊Q8—532no—
565C22⋊Q8—532no—
566#121—58no—
567#121—58no—
568#120—516no—
569C4×Q8—516no—
570C4×Q8—516no—
571C4×Q8—516no—
572C4×Q8—516no—
573C4×Q8—516no—
574C4×Q8—532no—
575C4×D4—516no—
576C4×D4—516no—
577C4×D4—532no—
578C4×D4—532no—
579C4×D4—516no—
580#117—58no—
581#117—532no—
582#117—516no—
583#117—532no—
584#117—532no—
585#117C22×D518yes—
586#117C22×D518yes—
587#117C22×D5116yes—
588#117C22×D518yes—
589#117C22×D5116yes—
590#117C22×D518yes—
591C2×C4⋊C4—52no—
592C2×C4⋊C4—54no—
593C2×C4⋊C4—52no—
594C2×C4⋊C4—54no—
595C2×C4⋊C4—58no—
596C2×C4⋊C4—54no—
597C2×C4⋊C4—516no—
598C2×C4⋊C4—51no—
599C2×C4⋊C4—51no—
600C2×C4⋊C4—54no—
601C2×C4⋊C4—54no—
602C2×C4⋊C4—54no—
603C2×C4⋊C4—54no—
604C2×C4⋊C4—54no—
605C2×C4⋊C4—52no—
606C2×C4⋊C4—52no—
607C2×C4⋊C4—54no—
608C2×C4⋊C4—54no—
609C2×C4⋊C4—516no—
610C2×C4⋊C4C22×D511yescharacteristic
611C2×C4⋊C4C22×D511yescharacteristic
612C2×C4⋊C4C22×D512yes—
613C2×C4⋊C4C22×D511yescharacteristic
614C2×C4⋊C4C22×D511yescharacteristic
615C2×C4⋊C4C22×D512yes—
616C2×C4⋊C4C22×D518yes—
617C2×C4⋊C4C22×D518yes—
618C2×C22⋊C4—54no—
619C2×C22⋊C4—54no—
620C2×C22⋊C4—516no—
621C2×C22⋊C4—52no—
622C2×C22⋊C4—52no—
623C2×C22⋊C4—52no—
624C2×C22⋊C4—52no—
625C2×C22⋊C4—54no—
626C2×C22⋊C4—54no—
627C2×C22⋊C4—52no—
628C2×C22⋊C4—54no—
629C2×C22⋊C4C22×D512yes—
630C2×C22⋊C4C22×D512yes—
631C2×C22⋊C4C22×D512yes—
632C2×C22⋊C4C22×D512yes—
633C2×C22⋊C4C22×D5116yes—
634C2×C42—54no—
635C2×C42—54no—
636C2×C42—54no—
637C2×C42—52no—
638C2×C42C22×D512yes—
639C2×C42C22×D512yes—
640C2×C42C22×D512yes—
641C2×C42C22×D512yes—
642C2×C42C22×D5116yes—
643C22×C5—22no—
644C22×C5—22no—
645C22×C5—22no—
646C22×C5—22no—
647C22×C5—28no—
648C22×C5—28no—
649C22×C5—22no—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—416no—
653C22×C5—44no—
654C22×C5C22×#4114yes—
655C22×C5C22×#4112yes—
656C22×C5C2×2−1+414yes—
657C22×C5C2×2−1+412yes—
658C22×C5#58512yes—
659C22×C5C2611yescharacteristic
660C2×D5—24no—
661C2×D5—24no—
662C2×D5—24no—
663C2×D5—48no—
664C4×C5—22no—
665C4×C5—22no—
666C4×C5—24no—
667C4×C5—24no—
668C4×C5—24no—
669C4×C5—24no—
670C4×C5C22×#4114yes—
671C4×C5C22×#4114yes—
672Dic5—28no—
673Dic5—24no—
674Dic5—24no—
675Dic5—24no—
676Dic5—28no—
677C24—24no—
678C24—24no—
679C24—42no—
680C24—52no—
681C24C23×D511yescharacteristic
682C24C23×D514yes—
683C24C23×D511yescharacteristic
684C24C23×D511yescharacteristic
685#41—1032no—
686C2×Q8—58no—
687C2×Q8—58no—
688C2×Q8—54no—
689C2×Q8—516no—
690C2×Q8—108no—
691C2×Q8—108no—
692C2×Q8—1032no—
693C2×Q8—104no—
694C2×Q8—208no—
695C2×D4—58no—
696C2×D4—58no—
697C2×D4—58no—
698C2×D4—54no—
699C2×D4—108no—
700C2×D4—108no—
701C2×D4—104no—
702C2×D4—204no—
703C22×C4—24no—
704C22×C4—28no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—232no—
710C22×C4—44no—
711C22×C4—58no—
712C22×C4—52no—
713C22×C4—52no—
714C22×C4—54no—
715C22×C4—52no—
716C22×C4—54no—
717C22×C4—58no—
718C22×C4—58no—
719C22×C4—516no—
720C22×C4—108no—
721C22×C4—108no—
722C22×C4—208no—
723C22×C4—204no—
724C22×C4#70918yes—
725C22×C4C23×D514yes—
726C22×C4C23×D518yes—
727C22×C4C23×D514yes—
728C22×C4C23×D514yes—
729C22×C4C23×D514yes—
730C22×C4C23×D514yes—
731C22×C4C23×D512yes—
732C22×C4C23×D512yes—
733C22×C4C23×D511yescharacteristic
734C22×C4C23×D512yes—
735C22×C4C23×D512yes—
736C22×C4C23×D511yescharacteristic
737C22×C4C23×D518yes—
738C22×C4C23×D514yes—
739C22×C4C23×D511yescharacteristic
740C22×C4C23×D511yescharacteristic
741C4⋊C4—58no—
742C4⋊C4—516no—
743C4⋊C4—58no—
744C4⋊C4—516no—
745C4⋊C4—516no—
746C4⋊C4—54no—
747C4⋊C4—54no—
748C4⋊C4—516no—
749C4⋊C4—516no—
750C4⋊C4—516no—
751C4⋊C4—516no—
752C4⋊C4—516no—
753C4⋊C4—58no—
754C4⋊C4—58no—
755C4⋊C4—516no—
756C4⋊C4—516no—
757C4⋊C4C23×D514yes—
758C4⋊C4C23×D514yes—
759C4⋊C4C23×D518yes—
760C4⋊C4C23×D514yes—
761C4⋊C4C23×D514yes—
762C4⋊C4C23×D518yes—
763C22⋊C4—516no—
764C22⋊C4—516no—
765C22⋊C4—58no—
766C22⋊C4—58no—
767C22⋊C4—58no—
768C22⋊C4—58no—
769C22⋊C4—516no—
770C22⋊C4—516no—
771C22⋊C4—58no—
772C22⋊C4—516no—
773C22⋊C4C23×D518yes—
774C22⋊C4C23×D518yes—
775C22⋊C4C23×D518yes—
776C22⋊C4C23×D518yes—
777C42—516no—
778C42—516no—
779C42—516no—
780C42—58no—
781C42C23×D518yes—
782C42C23×D518yes—
783C42C23×D518yes—
784C42C23×D518yes—
785C2×C5—24no—
786C2×C5—24no—
787C2×C5—42no—
788C2×C5#349514yescomplemented
789C2×C5C23×#4111yescharacteristic
790C2×C5C22×2−1+411yescharacteristic
791C2×C5C2×#58511yescharacteristic
792D5—44no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—28no—
798C23—22no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—44no—
803C23—416no—
804C23—54no—
805C23—104no—
806C23—104no—
807C23—104no—
808C23C2×#70914yes—
809C23#415014yes—
810C23C24×D512yes—
811C23C24×D512yes—
812C23C24×D512yes—
813C23C24×D511yescharacteristic
814Q8—1016no—
815Q8—1016no—
816Q8—108no—
817Q8—2016no—
818D4—1016no—
819D4—1016no—
820D4—108no—
821D4—208no—
822C2×C4—28no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—216no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—48no—
835C2×C4—54no—
836C2×C4—54no—
837C2×C4—58no—
838C2×C4—54no—
839C2×C4—58no—
840C2×C4—104no—
841C2×C4—1016no—
842C2×C4—108no—
843C2×C4—104no—
844C2×C4—108no—
845C2×C4—104no—
846C2×C4—1016no—
847C2×C4—2016no—
848C2×C4—208no—
849C2×C4C2×#70914yes—
850C2×C4C2×#70914yes—
851C2×C4C2×#709116yes—
852C2×C4C24×D514yes—
853C2×C4C24×D514yes—
854C2×C4C24×D512yes—
855C2×C4C24×D514yes—
856C2×C4C24×D514yes—
857C2×C4C24×D512yes—
858C2×C4C24×D512yes—
859C2×C4C24×D512yes—
860C5C2×#349511yescharacteristic, complemented, Sylow
861C22—28no—
862C22—28no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—416no—
871C22—44no—
872C22—104no—
873C22—104no—
874C22—104no—
875C22—208no—
876C22C22×#70914yes—
877C22C22×#70912yes—
878C22C2×#415014yes—
879C22C2×#415012yes—
880C22#6628312yes—
881C22C25×D511yescharacteristic
882C4—22no—
883C4—22no—
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—104no—
889C4—108no—
890C4—104no—
891C4—108no—
892C4—104no—
893C4C22×#70914yes—
894C4C22×#70914yes—
895C2—24no—
896C2—24no—
897C2—42no—
898C2—204no—
899C2#1061762814yesdirect product factor
900C2C23×#70911yescharacteristic
901C2C22×#415011yescharacteristic
902C2C2×#6628311yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC22×C5×#117C2
socleC23×C5C25
prime radicalC2×#66125C2
hypercenterC22×#117D5
hypocenterC5C2×#3495
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C22×C5×#117C2semidirect
3. C22×#4070C2semidirect
4. C2×#65867C2semidirect
5. C2×#65863C2semidirect
6. C2×#65868C2semidirect
7. C2×#65857C2semidirect
8. #10617628C2direct (N × H)
9. C2×#65865C2semidirect
10. C2×#65853C2semidirect
11. C2×#65852C2semidirect
12. C2×#65860C2semidirect
13. C2×#65850C2semidirect
14. C2×#65845C2semidirect
15. C2×#65847C2semidirect
16. C2×#65829C2semidirect
17. C2×#65813C2semidirect
18. C2×#65804C2semidirect
28. C2×C5×#117C22semidirect
53. C2×#4070C22semidirect
55. #65868C22semidirect
56. #65867C22semidirect
57. #65865C22semidirect
58. #65863C22semidirect
59. #65860C22semidirect
60. #65857C22semidirect
61. #65853C22semidirect
62. #65852C22semidirect
63. #65850C22semidirect
64. #65847C22semidirect
65. C2×#4044C22semidirect
66. #65845C22semidirect
67. C2×#4043C22semidirect
68. C2×#4043C22semidirect
69. C2×#4042C22semidirect
70. C2×#4038C22semidirect
71. C2×D5×C4⋊C4C22semidirect
72. C2×#4036C22semidirect
73. C2×#4035C22semidirect
74. C2×#4035C22semidirect
75. C2×#4034C22semidirect
76. C2×#4033C22semidirect
77. C2×#4033C22semidirect
78. #65829C22semidirect
87. #65813C22semidirect
88. C2×#4022C22semidirect
89. C2×#4021C22semidirect
90. C2×C4×D20C22semidirect
91. C2×#4018C22semidirect
92. #65804C22semidirect
93. C2×#4016C22semidirect
94. C2×#4016C22semidirect
95. C2×#4015C22semidirect
96. C2×#4015C22semidirect
97. C2×C4×Dic10C22semidirect
98. C2×C4×Dic10C22semidirect
99. C2×C4×Dic10C22semidirect
100. C2×C4×Dic10C22semidirect
203. #4044C23semidirect
204. #4043C23semidirect
205. #4043C23semidirect
206. #4042C23semidirect
207. #4038C23semidirect
208. D5×C4⋊C4C23semidirect
209. #4036C23semidirect
210. #4035C23semidirect
211. #4035C23semidirect
212. #4034C23semidirect
213. #4033C23semidirect
214. #4033C23semidirect
223. #4022C23semidirect
224. #4021C23semidirect
225. C4×D20C23semidirect
226. #4018C23semidirect
227. #4016C23semidirect
228. #4016C23semidirect
229. #4015C23semidirect
230. #4015C23semidirect
231. C4×Dic10C23semidirect
232. C4×Dic10C23semidirect
233. C4×Dic10C23semidirect
234. C4×Dic10C23semidirect
252. C22×#117D5semidirect
434. C2×#117C2×D5semidirect
788. C2×C5#3495semidirect
860. C5C2×#3495semidirect
899. C2#10617628direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1172
C2×#661252
C22×#40702
C2×#658672
C2×#658632
C2×#658682
C2×#658572
#106176282
C2×#658652
C2×#658532
C2×#658522
C2×#658602
C2×#658502
C2×#658452
C2×#658472
C2×#658292
C2×#658132
C2×#658042
C2×#34955