Finite Group Databasebeta

← C2×#10618184 #13007736

Subgroups — C2×#10618184 #13007736

Order 1280.

7022 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#533C211yesmaximal, characteristic, complemented
2#10618184C2132yesmaximal, direct product factor
3C2×D5×C4⋊Q8C211yesmaximal, characteristic, complemented
4C2×#66062C211yesmaximal, characteristic, complemented
5C2×#66062C211yesmaximal, characteristic, complemented
6C2×#66062C211yesmaximal, characteristic, complemented
7C2×#66028C212yesmaximal, complemented
8C2×#66019C212yesmaximal, complemented
9C2×#65973C212yesmaximal, complemented
10C2×#65962C212yesmaximal
11C2×#65975C212yesmaximal, complemented
12C2×#65959C212yesmaximal, complemented
13C2×#65915C212yesmaximal, complemented
14C2×#65917C212yesmaximal, complemented
15C2×#65906C212yesmaximal, complemented
16C2×#65903C212yesmaximal, complemented
17C2×#65867C212yesmaximal, complemented
18C2×#65863C212yesmaximal, complemented
19C2×#65804C211yesmaximal, characteristic, complemented
20C2×C4×#709C211yesmaximal, characteristic
21C22×Q8×D5C2212yes—
22C22×#709C2211yescharacteristic
23C5×#533C22116yescomplemented
24C2×C5×C4⋊Q8C2211yescharacteristic
25C2×C5×C4⋊Q8C2211yescharacteristic
26C2×C5×#125C2212yes—
27C2×C5×C22⋊Q8C2212yes—
28C2×C5×C22⋊Q8C2212yes—
29C2×C4×C5×Q8C2212yes—
30C2×C4×C5×Q8C2212yes—
31C2×C5×#117C2212yes—
32C22×C42×C5C2211yescharacteristic
33C2×#4092C2212yes—
34C2×#4092C2212yes—
35C2×#4092C2212yes—
36C2×Q8×Dic5C2212yes—
37C2×Q8×Dic5C2212yes—
38C2×Q8×Dic5C2212yes—
39C2×#4090C2212yes—
40C2×C4×C22⋊D5C2211yescharacteristic
41C2×C4×C22⋊D5C2211yescharacteristic
42C2×C4×C22⋊D5C2211yescharacteristic
43C2×C4×C22⋊D5C2211yescharacteristic
44C2×#4072C2211yescharacteristic
45C2×#4072C2212yes—
46C2×#4070C2212yes—
47C2×#4070C2212yes—
48#66062C22116yescomplemented
49#66062C22116yescomplemented
50#66062C22116yescomplemented
51D5×C4⋊Q8C22116yescomplemented
52#66028C22132yescomplemented
53#66019C22132yescomplemented
54#65975C22132yescomplemented
55#65973C22132yescomplemented
56#65962C22132yes—
57#65959C22132yescomplemented
58#65917C22132yescomplemented
59#65915C22132yescomplemented
60#65906C22132yescomplemented
61#65903C22132yescomplemented
62#65867C22132yescomplemented
63#65863C22132yescomplemented
64C2×#4044C2214yes—
65C2×#4043C2212yes—
66C2×#4043C2212yes—
67C2×#4043C2212yes—
68C2×#4040C2214yes—
69C2×#4038C2212yes—
70C2×#4038C2212yes—
71C2×#4038C2214yes—
72C2×#4038C2212yes—
73C2×D5×C4⋊C4C2212yes—
74C2×D5×C4⋊C4C2212yes—
75C2×#4036C2214yes—
76C2×#4036C2212yes—
77C2×#4036C2212yes—
78C2×#4036C2212yes—
79C2×#4035C2214yes—
80C2×#4035C2214yes—
81C2×#4034C2212yes—
82C2×#4034C2214yes—
83C2×#4034C2212yes—
84C2×#4033C2212yes—
85C2×#4033C2214yes—
86C2×#4033C2212yes—
87C2×#4033C2212yes—
88C2×#4031C2214yes—
89C2×#4029C2214yes—
90C2×#4025C2214yes—
91C2×#4025C2214yes—
92C2×#4022C2214yes—
93C4×#709C22116yes—
94C2×C4×D20C2211yescharacteristic
95C2×C4×D20C2211yescharacteristic
96C2×#4018C2214yes—
97C2×#4018C2211yescharacteristic
98C2×#4018C2211yescharacteristic
99C2×C42×D5C2211yescharacteristic
100C2×C42×D5C2211yescharacteristic
101#65804C22116yescomplemented
102C2×#4016C2214yes—
103C2×#4016C2212yes—
104C2×#4015C2211yescharacteristic
105C2×#4015C2211yescharacteristic
106C2×C4×Dic10C2214yes—
107C2×C4×Dic10C2211yescharacteristic
108C2×C4×Dic10C2212yes—
109C2×C4×Dic10C2211yescharacteristic
110C2×C4×Dic10C2212yes—
111C2×#3509—51nomaximal, Sylow
112C22×C5×Q8C2312yes—
113C22×C5×Q8C2312yes—
114C23×C4×C5C2311yescharacteristic
115C23×C4×C5C2311yescharacteristic
116C23×C4×C5C2311yescharacteristic
117C22×C22⋊D5C2311yescharacteristic
118C22×C22⋊D5C2311yescharacteristic
119C2×Q8×D5—216no—
120C2×Q8×D5C23116yes—
121C2×#709—28no—
122C2×#709C2318yes—
123C22×D20C2311yescharacteristic
124C22×C4×D5C2311yescharacteristic
125C22×C4×D5C2311yescharacteristic
126C22×C4×D5C2311yescharacteristic
127C22×C4×D5C2311yescharacteristic
128C22×C4×D5C2311yescharacteristic
129C22×C4×D5C2314yes—
130C22×C4×D5C2311yescharacteristic
131C22×Dic10C2311yescharacteristic
132C22×Dic10C2312yes—
133C22×Dic10C2312yes—
134C22×Dic10C2314yes—
135C5×C4⋊Q8C2318yes—
136C5×C4⋊Q8C2318yes—
137C5×#125C23116yes—
138C5×C22⋊Q8C23116yes—
139C5×C22⋊Q8C23116yes—
140C4×C5×Q8C23116yes—
141C4×C5×Q8C23116yes—
142C5×#117C23116yes—
143C2×C5×C4⋊C4C2312yes—
144C2×C5×C4⋊C4C2314yes—
145C2×C5×C4⋊C4C2312yes—
146C2×C5×C4⋊C4C2312yes—
147C2×C5×C4⋊C4C2314yes—
148C2×C5×C4⋊C4C2312yes—
149C2×C5×C22⋊C4C2314yes—
150C2×C42×C5C2311yescharacteristic
151C2×C42×C5C2311yescharacteristic
152C2×C42×C5C2311yescharacteristic
153C2×C42×C5C2314yes—
154C2×C42×C5C2311yescharacteristic
155C2×C42×C5C2318yes—
156C2×C22⋊Dic5C2311yescharacteristic
157C2×C22⋊Dic5C2311yescharacteristic
158C2×C22⋊Dic5C2314yes—
159#4092C23116yes—
160#4092C23116yes—
161#4092C23116yes—
162Q8×Dic5C23116yes—
163Q8×Dic5C23116yes—
164Q8×Dic5C23116yes—
165#4090C23116yes—
166C4×C22⋊D5C2318yes—
167C4×C22⋊D5C2318yes—
168C4×C22⋊D5C2318yes—
169C4×C22⋊D5C2318yes—
170C2×#685C2311yescharacteristic
171C2×#685C2311yescharacteristic
172C2×#685C2311yescharacteristic
173C2×#685C2311yescharacteristic
174C2×#685C2314yes—
175C2×#685C2314yes—
176C2×#685C2314yes—
177#4072C23116yes—
178#4072C2318yes—
179C2×C4⋊Dic5C2312yes—
180C2×C4⋊Dic5C2312yes—
181C2×C4⋊Dic5C2311yescharacteristic
182C2×C4⋊Dic5C2311yescharacteristic
183C2×C4⋊Dic5C2314yes—
184C2×C4⋊Dic5C2312yes—
185C2×C4⋊Dic5C2312yes—
186C2×C4⋊Dic5C2314yes—
187C2×C4⋊Dic5C2314yes—
188#4070C23116yes—
189#4070C23116yes—
190C2×#683C2311yescharacteristic
191C2×#683C2314yes—
192C2×#683C2311yescharacteristic
193C2×#683C2314yes—
194C2×#683C2311yescharacteristic
195C2×#683C2311yescharacteristic
196C2×#683C2314yes—
197C2×#683C2314yes—
198C2×#683C2314yes—
199C2×#683C2314yes—
200C2×#683C2314yes—
201C2×C4×Dic5C2314yes—
202C2×C4×Dic5C2311yescharacteristic
203C2×C4×Dic5C2311yescharacteristic
204C2×C4×Dic5C2311yescharacteristic
205C2×C4×Dic5C2311yescharacteristic
206C2×C4×Dic5C2314yes—
207C2×C4×Dic5C2314yes—
208C2×C4×Dic5C2311yescharacteristic
209C2×C4×Dic5C2311yescharacteristic
210C2×C4×Dic5C2314yes—
211#4044C23132yes—
212#4043C23116yes—
213#4043C23116yes—
214#4043C23116yes—
215#4040C23132yes—
216#4038C23116yes—
217#4038C23116yes—
218#4038C23116yes—
219#4038C23132yes—
220D5×C4⋊C4C23116yes—
221D5×C4⋊C4C23116yes—
222#4036C23116yes—
223#4036C23116yes—
224#4036C23116yes—
225#4036C23132yes—
226#4035C23132yes—
227#4035C23132yes—
228#4034C23116yes—
229#4034C23116yes—
230#4034C23132yes—
231#4033C23116yes—
232#4033C23116yes—
233#4033C23116yes—
234#4033C23132yes—
235#4031C23132yes—
236#4029C23132yes—
237#4025C23132yes—
238#4025C23132yes—
239#4022C23132yes—
240C4×D20C2318yes—
241C4×D20C2318yes—
242#4018C2318yes—
243#4018C2318yes—
244#4018C23132yes—
245C42×D5C2318yes—
246C42×D5C2318yes—
247#4016C23116yes—
248#4016C23132yes—
249#4015C2318yes—
250#4015C2318yes—
251C4×Dic10C23116yes—
252C4×Dic10C23116yes—
253C4×Dic10C2318yes—
254C4×Dic10C2318yes—
255C4×Dic10C23132yes—
256#3509—532no—
257C2×#557—52no—
258C2×#557—52no—
259C2×#556—52no—
260C2×#556—52no—
261C2×#552—52no—
262C2×#552—52no—
263C2×#552—52no—
264C2×#552—52no—
265C2×#541—52no—
266C2×#541—52no—
267C2×#536—52no—
268C2×#533—51no—
269C2×#533—51no—
270C2×#533—51no—
271C2×#533—51no—
272C2×#533D511yescharacteristic, complemented
273C22×C4⋊Q8—51no—
274C2×#519—52no—
275C2×C4×#41—51no—
276C24×C5C2411yescharacteristic
277C23×D5C2411yescharacteristic
278C23×D5C2411yescharacteristic
279C2×C5×Q8—28no—
280C2×C5×Q8—28no—
281C2×C5×Q8C2418yes—
282C2×C5×Q8C2418yes—
283C22×C4×C5—24no—
284C22×C4×C5—24no—
285C22×C4×C5—24no—
286C22×C4×C5C2411yescharacteristic
287C22×C4×C5C2411yescharacteristic
288C22×C4×C5C2411yescharacteristic
289C22×C4×C5C2414yes—
290C22×C4×C5C2414yes—
291C22×C4×C5C2414yes—
292C22×C4×C5C2414yes—
293C22×C4×C5C2414yes—
294C22×C4×C5C2411yescharacteristic
295C22×C4×C5C2411yescharacteristic
296C22×C4×C5C2411yescharacteristic
297C2×C22⋊D5—24no—
298C2×C22⋊D5—24no—
299C2×C22⋊D5C2414yes—
300C2×C22⋊D5C2414yes—
301C22×Dic5C2414yes—
302C22×Dic5C2414yes—
303C22×Dic5C2411yescharacteristic
304C22×Dic5C2411yescharacteristic
305C22×Dic5C2411yescharacteristic
306C22×Dic5C2411yescharacteristic
307C22×Dic5C2411yescharacteristic
308C22×Dic5C2411yescharacteristic
309Q8×D5—264no—
310#709—232no—
311C2×D20—24no—
312C2×D20C2414yes—
313C2×C4×D5—216no—
314C2×C4×D5—24no—
315C2×C4×D5—24no—
316C2×C4×D5—24no—
317C2×C4×D5—24no—
318C2×C4×D5—24no—
319C2×C4×D5#4118yes—
320C2×C4×D5C2414yes—
321C2×C4×D5C24116yes—
322C2×C4×D5C2414yes—
323C2×C4×D5C2414yes—
324C2×C4×D5C2414yes—
325C2×C4×D5C2414yes—
326C2×C4×D5C2414yes—
327C2×Dic10—28no—
328C2×Dic10—28no—
329C2×Dic10—24no—
330C2×Dic10—216no—
331C2×Dic10C2414yes—
332C2×Dic10C2418yes—
333C2×Dic10C24116yes—
334C2×Dic10C2418yes—
335C5×C4⋊C4C2418yes—
336C5×C4⋊C4C2418yes—
337C5×C4⋊C4C24116yes—
338C5×C4⋊C4C24116yes—
339C5×C4⋊C4C2418yes—
340C5×C4⋊C4C2418yes—
341C5×C22⋊C4C24116yes—
342C42×C5C2414yes—
343C42×C5C2414yes—
344C42×C5C2414yes—
345C42×C5C2414yes—
346C42×C5C24116yes—
347C22⋊Dic5C2414yes—
348C22⋊Dic5C2414yes—
349C22⋊Dic5C24116yes—
350#685C2414yes—
351#685C2414yes—
352#685C2414yes—
353#685C2414yes—
354#685C24116yes—
355#685C24116yes—
356#685C24116yes—
357C4⋊Dic5C2418yes—
358C4⋊Dic5C2418yes—
359C4⋊Dic5C2414yes—
360C4⋊Dic5C2414yes—
361C4⋊Dic5C24116yes—
362C4⋊Dic5C2418yes—
363C4⋊Dic5C2418yes—
364C4⋊Dic5C24116yes—
365C4⋊Dic5C24116yes—
366#683C2414yes—
367#683C24116yes—
368#683C2414yes—
369#683C24116yes—
370#683C2414yes—
371#683C2414yes—
372#683C24116yes—
373#683C24116yes—
374#683C24116yes—
375#683C24116yes—
376#683C24116yes—
377C4×Dic5C24116yes—
378C4×Dic5C2414yes—
379C4×Dic5C2414yes—
380C4×Dic5C2414yes—
381C4×Dic5C2414yes—
382C4×Dic5C24116yes—
383C4×Dic5C24116yes—
384C4×Dic5C2414yes—
385C4×Dic5C2414yes—
386C4×Dic5C24116yes—
387C22×#41—51no—
388C23×Q8—52no—
389#557—532no—
390#557—532no—
391#556—532no—
392#556—532no—
393#552—532no—
394#552—532no—
395#552—532no—
396#552—532no—
397#541—532no—
398#541—532no—
399#536—532no—
400#533—516no—
401#533—516no—
402#533—516no—
403#533—516no—
404#533C2×D5116yescomplemented
405C2×C4⋊Q8—52no—
406C2×C4⋊Q8—516no—
407C2×C4⋊Q8—52no—
408C2×C4⋊Q8—52no—
409C2×C4⋊Q8—54no—
410C2×C4⋊Q8—51no—
411C2×C4⋊Q8—51no—
412C2×C4⋊Q8C2×D511yescharacteristic
413C2×C4⋊Q8C2×D511yescharacteristic
414C2×#126—54no—
415C2×#126—54no—
416C2×#126—54no—
417C2×#126—54no—
418C2×#125—54no—
419C2×#125—54no—
420C2×#125—52no—
421C2×#125—52no—
422C2×#125—52no—
423C2×#125—54no—
424C2×#125—52no—
425C2×#125—54no—
426C2×#125C2×D512yes—
427C2×#124—54no—
428C2×#123—54no—
429C2×#123—54no—
430C2×C22⋊Q8—52no—
431C2×C22⋊Q8—52no—
432C2×C22⋊Q8—52no—
433C2×C22⋊Q8—52no—
434C2×C22⋊Q8—52no—
435C2×C22⋊Q8—52no—
436C2×C22⋊Q8—52no—
437C2×C22⋊Q8—52no—
438C2×C22⋊Q8C2×D512yes—
439C2×C22⋊Q8C2×D512yes—
440#519—532no—
441C4×#41—516no—
442C2×C4×Q8—52no—
443C2×C4×Q8—52no—
444C2×C4×Q8—52no—
445C2×C4×Q8—52no—
446C2×C4×Q8—54no—
447C2×C4×Q8—52no—
448C2×C4×Q8—52no—
449C2×C4×Q8—51no—
450C2×C4×Q8—51no—
451C2×C4×Q8—52no—
452C2×C4×Q8—54no—
453C2×C4×Q8—52no—
454C2×C4×Q8C2×D512yes—
455C2×C4×Q8C2×D512yes—
456C2×C4×D4—51no—
457C2×C4×D4—51no—
458C2×C4×D4—51no—
459C2×C4×D4—51no—
460C2×C4×D4—51no—
461C2×C4×D4—51no—
462C2×#117—51no—
463C2×#117—52no—
464C2×#117—52no—
465C2×#117—54no—
466C2×#117—52no—
467C2×#117—52no—
468C2×#117—51no—
469C2×#117—51no—
470C2×#117—54no—
471C2×#117C2×D512yes—
472C22×C4⋊C4—52no—
473C22×C4⋊C4—52no—
474C22×C42—51no—
475C22×C42—51no—
476C22×C42C2×D511yescharacteristic
477C23×C5—22no—
478C23×C5—22no—
479C23×C5—22no—
480C23×C5C2512yes—
481C23×C5C2511yescharacteristic
482C22×D5—22no—
483C22×D5—22no—
484C22×D5—22no—
485C22×D5—22no—
486C22×D5—22no—
487C22×D5C2×#4114yes—
488C22×D5C2512yes—
489C22×D5C2512yes—
490C5×Q8—216no—
491C5×Q8—216no—
492C2×C4×C5—28no—
493C2×C4×C5—22no—
494C2×C4×C5—22no—
495C2×C4×C5—22no—
496C2×C4×C5—28no—
497C2×C4×C5—28no—
498C2×C4×C5—28no—
499C2×C4×C5—28no—
500C2×C4×C5C2×#4114yes—
501C2×C4×C52−1+414yes—
502C2×C4×C52−1+414yes—
503C2×C4×C5C2512yes—
504C2×C4×C5C2518yes—
505C2×C4×C5C2518yes—
506C2×C4×C5C2512yes—
507C2×C4×C5C2512yes—
508C2×C4×C5C2512yes—
509C2×C4×C5C2512yes—
510C2×C4×C5C2512yes—
511C22⋊D5—28no—
512C22⋊D5—28no—
513C2×Dic5—28no—
514C2×Dic5—22no—
515C2×Dic5—28no—
516C2×Dic5—22no—
517C2×Dic5—22no—
518C2×Dic5—22no—
519C2×Dic5—22no—
520C2×Dic5C2×#4114yes—
521C2×Dic5C2512yes—
522C2×Dic5C2512yes—
523C2×Dic5C2518yes—
524C2×Dic5C2512yes—
525C2×Dic5C2512yes—
526C2×Dic5C2512yes—
527C2×Dic5C2518yes—
528C2×Dic5C2512yes—
529D20—28no—
530C4×D5—232no—
531C4×D5—28no—
532C4×D5—28no—
533C4×D5—28no—
534C4×D5—28no—
535C4×D5—28no—
536C4×D5C2×#41116yes—
537Dic10—216no—
538Dic10—216no—
539Dic10—28no—
540Dic10—232no—
541C2×#41—58no—
542C2×#41—108no—
543C22×Q8—516no—
544C22×Q8—52no—
545C22×Q8—52no—
546C22×Q8—54no—
547C22×Q8—51no—
548C22×Q8—1016no—
549C22×Q8C22×D512yes—
550C22×Q8C22×D512yes—
551C22×D4—51no—
552C22×D4—51no—
553C22×D4—51no—
554C23×C4—51no—
555C23×C4—54no—
556C23×C4—51no—
557C23×C4—51no—
558C23×C4—51no—
559C23×C4—51no—
560C23×C4—51no—
561C23×C4C22×D511yescharacteristic
562C23×C4C22×D511yescharacteristic
563C23×C4C22×D511yescharacteristic
564C4⋊Q8—516no—
565C4⋊Q8—516no—
566C4⋊Q8—516no—
567C4⋊Q8—532no—
568C4⋊Q8—58no—
569C4⋊Q8—58no—
570C4⋊Q8C22×D518yes—
571C4⋊Q8C22×D518yes—
572#126—532no—
573#126—532no—
574#126—532no—
575#126—532no—
576#125—516no—
577#125—516no—
578#125—516no—
579#125—532no—
580#125—532no—
581#125—532no—
582#125—516no—
583#125—532no—
584#125C22×D5116yes—
585#124—532no—
586#123—532no—
587#123—532no—
588C22⋊Q8—516no—
589C22⋊Q8—516no—
590C22⋊Q8—516no—
591C22⋊Q8—516no—
592C22⋊Q8—516no—
593C22⋊Q8—516no—
594C22⋊Q8—516no—
595C22⋊Q8—516no—
596C22⋊Q8C22×D5116yes—
597C22⋊Q8C22×D5116yes—
598C4×Q8—516no—
599C4×Q8—516no—
600C4×Q8—516no—
601C4×Q8—516no—
602C4×Q8—532no—
603C4×Q8—516no—
604C4×Q8—516no—
605C4×Q8—58no—
606C4×Q8—58no—
607C4×Q8—516no—
608C4×Q8—532no—
609C4×Q8—516no—
610C4×Q8C22×D5116yes—
611C4×Q8C22×D5116yes—
612C4×D4—58no—
613C4×D4—58no—
614C4×D4—58no—
615C4×D4—58no—
616C4×D4—58no—
617C4×D4—58no—
618#117—58no—
619#117—516no—
620#117—516no—
621#117—532no—
622#117—516no—
623#117—516no—
624#117—58no—
625#117—58no—
626#117—532no—
627#117C22×D5116yes—
628C2×C4⋊C4—52no—
629C2×C4⋊C4—52no—
630C2×C4⋊C4—54no—
631C2×C4⋊C4—54no—
632C2×C4⋊C4—52no—
633C2×C4⋊C4—51no—
634C2×C4⋊C4—51no—
635C2×C4⋊C4—51no—
636C2×C4⋊C4—51no—
637C2×C4⋊C4—51no—
638C2×C4⋊C4—51no—
639C2×C4⋊C4—52no—
640C2×C4⋊C4—54no—
641C2×C4⋊C4—54no—
642C2×C4⋊C4—54no—
643C2×C4⋊C4—54no—
644C2×C4⋊C4—54no—
645C2×C4⋊C4—54no—
646C2×C4⋊C4—54no—
647C2×C4⋊C4—54no—
648C2×C4⋊C4—516no—
649C2×C4⋊C4—516no—
650C2×C4⋊C4C22×D512yes—
651C2×C4⋊C4C22×D512yes—
652C2×C4⋊C4C22×D512yes—
653C2×C4⋊C4C22×D512yes—
654C2×C4⋊C4C22×D514yes—
655C2×C4⋊C4C22×D514yes—
656C2×C22⋊C4—51no—
657C2×C22⋊C4—51no—
658C2×C22⋊C4—54no—
659C2×C22⋊C4—51no—
660C2×C22⋊C4—51no—
661C2×C22⋊C4—54no—
662C2×C22⋊C4—51no—
663C2×C22⋊C4—51no—
664C2×C22⋊C4—54no—
665C2×C22⋊C4—54no—
666C2×C22⋊C4C22×D514yes—
667C2×C42—51no—
668C2×C42—54no—
669C2×C42—54no—
670C2×C42—54no—
671C2×C42—51no—
672C2×C42—54no—
673C2×C42—51no—
674C2×C42—51no—
675C2×C42—51no—
676C2×C42—51no—
677C2×C42—58no—
678C2×C42—58no—
679C2×C42C22×D511yescharacteristic
680C2×C42C22×D514yes—
681C2×C42C22×D511yescharacteristic
682C2×C42C22×D511yescharacteristic
683C2×C42C22×D518yes—
684C2×C42C22×D511yescharacteristic
685C22×C5—22no—
686C22×C5—22no—
687C22×C5—22no—
688C22×C5—44no—
689C22×C5C22×#4112yes—
690C22×C5C2×2−1+412yes—
691C22×C5C2×2−1+412yes—
692C22×C5C2611yescharacteristic
693C2×D5—22no—
694C2×D5—22no—
695C2×D5—28no—
696C2×D5—22no—
697C2×D5—22no—
698C2×D5—22no—
699C2×D5—44no—
700C2×D5C22×#4114yes—
701C4×C5—28no—
702C4×C5—22no—
703C4×C5—22no—
704C4×C5—22no—
705C4×C5—28no—
706C4×C5C22×#4114yes—
707C4×C5C2×2−1+414yes—
708C4×C5C2×2−1+414yes—
709Dic5—28no—
710Dic5—22no—
711Dic5—28no—
712Dic5—22no—
713Dic5—22no—
714Dic5—22no—
715Dic5—22no—
716Dic5C22×#4114yes—
717C24—51no—
718C24—51no—
719C24C23×D511yescharacteristic
720#41—1032no—
721C2×Q8—28no—
722C2×Q8—28no—
723C2×Q8—58no—
724C2×Q8—58no—
725C2×Q8—516no—
726C2×Q8—54no—
727C2×Q8—1016no—
728C2×Q8—104no—
729C2×Q8—1064no—
730C2×Q8—108no—
731C2×Q8—108no—
732C2×Q8C23×D518yes—
733C2×Q8C23×D518yes—
734C2×D4—54no—
735C2×D4—54no—
736C2×D4—54no—
737C2×D4—104no—
738C2×D4—104no—
739C2×D4—104no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—51no—
744C22×C4—58no—
745C22×C4—54no—
746C22×C4—51no—
747C22×C4—51no—
748C22×C4—54no—
749C22×C4—51no—
750C22×C4—51no—
751C22×C4—54no—
752C22×C4—51no—
753C22×C4—54no—
754C22×C4—54no—
755C22×C4—54no—
756C22×C4—54no—
757C22×C4—54no—
758C22×C4—516no—
759C22×C4—1016no—
760C22×C4—104no—
761C22×C4—104no—
762C22×C4—104no—
763C22×C4—104no—
764C22×C4—104no—
765C22×C4C23×D514yes—
766C22×C4C23×D514yes—
767C22×C4C23×D514yes—
768C22×C4C23×D511yescharacteristic
769C22×C4C23×D514yes—
770C22×C4C23×D514yes—
771C22×C4C23×D511yescharacteristic
772C22×C4C23×D511yescharacteristic
773C22×C4C23×D511yescharacteristic
774C22×C4C23×D511yescharacteristic
775C22×C4C23×D511yescharacteristic
776C4⋊C4—58no—
777C4⋊C4—58no—
778C4⋊C4—516no—
779C4⋊C4—516no—
780C4⋊C4—58no—
781C4⋊C4—54no—
782C4⋊C4—54no—
783C4⋊C4—54no—
784C4⋊C4—54no—
785C4⋊C4—54no—
786C4⋊C4—54no—
787C4⋊C4—58no—
788C4⋊C4—516no—
789C4⋊C4—516no—
790C4⋊C4—516no—
791C4⋊C4—516no—
792C4⋊C4—516no—
793C4⋊C4—516no—
794C4⋊C4—516no—
795C4⋊C4—516no—
796C4⋊C4C23×D518yes—
797C4⋊C4C23×D518yes—
798C4⋊C4C23×D518yes—
799C4⋊C4C23×D518yes—
800C4⋊C4C23×D5116yes—
801C4⋊C4C23×D5116yes—
802C22⋊C4—54no—
803C22⋊C4—54no—
804C22⋊C4—516no—
805C22⋊C4—54no—
806C22⋊C4—54no—
807C22⋊C4—516no—
808C22⋊C4—54no—
809C22⋊C4—54no—
810C22⋊C4—516no—
811C22⋊C4—516no—
812C22⋊C4C23×D5116yes—
813C42—54no—
814C42—54no—
815C42—54no—
816C42—54no—
817C42—54no—
818C42—54no—
819C42—516no—
820C42—516no—
821C42—516no—
822C42—516no—
823C42C23×D514yes—
824C42C23×D514yes—
825C42C23×D514yes—
826C42C23×D514yes—
827C42C23×D5116yes—
828C2×C5—42no—
829C2×C5#350914yescomplemented
830C2×C5C23×#4111yescharacteristic
831C2×C5C22×2−1+411yescharacteristic
832C2×C5C22×2−1+411yescharacteristic
833D5—24no—
834D5—42no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—54no—
839C23—52no—
840C23—52no—
841C23—102no—
842C23—102no—
843C23—102no—
844C23—102no—
845C23—102no—
846C23C24×D512yes—
847C23C24×D511yescharacteristic
848Q8—216no—
849Q8—216no—
850Q8—1032no—
851Q8—108no—
852Q8—1016no—
853Q8—1016no—
854D4—108no—
855D4—108no—
856D4—108no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—28no—
860C2×C4—22no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—54no—
866C2×C4—52no—
867C2×C4—516no—
868C2×C4—52no—
869C2×C4—52no—
870C2×C4—58no—
871C2×C4—52no—
872C2×C4—52no—
873C2×C4—58no—
874C2×C4—52no—
875C2×C4—1032no—
876C2×C4—102no—
877C2×C4—102no—
878C2×C4—108no—
879C2×C4—102no—
880C2×C4—108no—
881C2×C4—102no—
882C2×C4—102no—
883C2×C4—108no—
884C2×C4—108no—
885C2×C4—108no—
886C2×C4—108no—
887C2×C4—108no—
888C2×C4#414714yes—
889C2×C4D5×#4114yes—
890C2×C4#415014yes—
891C2×C4C24×D512yes—
892C2×C4C24×D518yes—
893C2×C4C24×D518yes—
894C2×C4C24×D512yes—
895C2×C4C24×D512yes—
896C2×C4C24×D512yes—
897C2×C4C24×D512yes—
898C2×C4C24×D512yes—
899C5C2×#350911yescharacteristic, complemented, Sylow
900C22—22no—
901C22—22no—
902C22—22no—
903C22—44no—
904C22—54no—
905C22—102no—
906C22—102no—
907C22—108no—
908C22—102no—
909C22—102no—
910C22—102no—
911C22—204no—
912C22C2×#414712yes—
913C22C2×D5×#4112yes—
914C22C2×#415012yes—
915C22C25×D511yescharacteristic
916C4—22no—
917C4—22no—
918C4—28no—
919C4—22no—
920C4—28no—
921C4—54no—
922C4—102no—
923C4—102no—
924C4—108no—
925C4—102no—
926C4—102no—
927C4—102no—
928C4—108no—
929C4C2×#414714yes—
930C4C2×D5×#4114yes—
931C4C2×#415014yes—
932C2—42no—
933C2—104no—
934C2—202no—
935C2#1061818414yesdirect product factor
936C2C22×#414711yescharacteristic
937C2C22×#415011yescharacteristic
938C2C22×D5×#4111yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#533C2
socleC23×C5C25
prime radicalC22×#709C22
hypercenterC2×#533D5
hypocenterC5C2×#3509
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C5×#533C2semidirect
2. #10618184C2direct (N × H)
3. C2×D5×C4⋊Q8C2semidirect
4. C2×#66062C2semidirect
5. C2×#66062C2semidirect
6. C2×#66062C2semidirect
7. C2×#66028C2semidirect
8. C2×#66019C2semidirect
9. C2×#65973C2semidirect
11. C2×#65975C2semidirect
12. C2×#65959C2semidirect
13. C2×#65915C2semidirect
14. C2×#65917C2semidirect
15. C2×#65906C2semidirect
16. C2×#65903C2semidirect
17. C2×#65867C2semidirect
18. C2×#65863C2semidirect
19. C2×#65804C2semidirect
23. C5×#533C22semidirect
48. #66062C22semidirect
49. #66062C22semidirect
50. #66062C22semidirect
51. D5×C4⋊Q8C22semidirect
52. #66028C22semidirect
53. #66019C22semidirect
54. #65975C22semidirect
55. #65973C22semidirect
57. #65959C22semidirect
58. #65917C22semidirect
59. #65915C22semidirect
60. #65906C22semidirect
61. #65903C22semidirect
62. #65867C22semidirect
63. #65863C22semidirect
101. #65804C22semidirect
272. C2×#533D5semidirect
404. #533C2×D5semidirect
829. C2×C5#3509semidirect
899. C5C2×#3509semidirect
935. C2#10618184direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5332
#106181842
C2×D5×C4⋊Q82
C2×#660622
C2×#660282
C2×#660192
C2×#659732
C2×#659622
C2×#659752
C2×#659592
C2×#659152
C2×#659172
C2×#659062
C2×#659032
C2×#658672
C2×#658632
C2×#658042
C2×C4×#7092
C2×#35095