Finite Group Databasebeta

← C2×D5×#946 #14479427

Subgroups — C2×D5×#946 #14479427

Order 1920.

3680 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Q8×D5C211yesmaximal, characteristic, complemented
2C22×C4×D3×D5C211yesmaximal, characteristic
3C2×#91835C211yesmaximal, characteristic, complemented
4C2×C5×#946C211yesmaximal, characteristic, complemented
5D5×#946C2116yesmaximal, direct product factor
6C2×D5×(C2×D3)⋊C4C212yesmaximal
7C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
8C2×#91411C212yesmaximal, complemented
9C2×#91410C212yesmaximal, complemented
10C2×D5×Dic3⋊C4C212yesmaximal, complemented
11C2×#91390C211yesmaximal, characteristic, complemented
12C2×#91369C211yesmaximal, characteristic, complemented
13C2×D5×C22⋊Q8—31nomaximal, Hall
14C23×D3×D5C2211yescharacteristic
15C22×C3×C5×Q8C2211yescharacteristic, complemented
16C22×C4×D15C2211yescharacteristic
17C22×C4×C5×D3C2211yescharacteristic
18C2×C3×Q8×D5—28no—
19C2×C3×Q8×D5C2218yescomplemented
20C22×C3×C4×D5C2212yes—
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×Dic10C2211yescharacteristic, complemented
23C22×C3×Dic10C2212yescomplemented
24C22×#1200C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C22×D5×Dic3C2211yescharacteristic
27C22×D5×Dic3C2212yes—
28C2×C4×D3×D5—28no—
29C2×C4×D3×D5C2218yes—
30#91835C2218yescomplemented
31C2×#6714C2212yes—
32C2×C4⋊Dic15C2211yescharacteristic, complemented
33C2×#6712C2212yescomplemented
34C5×#946C2218yescomplemented
35C2×C5×(C2×D3)⋊C4C2212yes—
36C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
37C2×C5×Dic3⋊C4C2212yescomplemented
38C2×Dic3⋊Dic5C2212yescomplemented
39C2×#6669C2212yescomplemented
40C2×#6668C2212yescomplemented
41C2×#6667C2212yes—
42C2×(C2×D3)⋊Dic5C2212yes—
43D5×(C2×D3)⋊C4C22116yes—
44D5×C4⋊Dic3C2218yescomplemented
45#91411C22116yescomplemented
46#91410C22116yescomplemented
47D5×Dic3⋊C4C22116yescomplemented
48#91390C2218yescomplemented
49#91369C2218yescomplemented
50C22×#946—51nomaximal, Hall
51C22×Q8×D5D311yescharacteristic, complemented
52C23×C4×D5—31no—
53C2×C5×C22⋊Q8—31no—
54C2×#4092—31no—
55C2×#4070—31no—
56D5×C22⋊Q8—316no—
57C2×#4043—31no—
58C2×#4042—32no—
59C2×D5×C4⋊C4—32no—
60C2×D5×C4⋊C4—31no—
61C2×D5×C22⋊C4—32no—
62C2×#4024—32no—
63C23×D15C2311yescharacteristic
64C23×C5×D3C2311yescharacteristic
65C23×C3×D5C2311yescharacteristic
66C22×D3×D5—24no—
67C22×D3×D5—24no—
68C22×D3×D5Q818yescomplemented
69C22×D3×D5C2314yes—
70C2×C3×C5×Q8—24no—
71C2×C3×C5×Q8C2314yescomplemented
72C22×C3×C4×C5C2312yes—
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2312yes—
76C2×C4×D15—24no—
77C2×C4×D15C2314yes—
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2312yes—
80C2×C4×C5×D3—24no—
81C2×C4×C5×D3C2314yes—
82C22×C3×Dic5C2312yes—
83C22×C3×Dic5C2311yescharacteristic
84C3×Q8×D5—232no—
85C2×C3×C4×D5—28no—
86C2×C3×C4×D5D418yes—
87C2×C3×C4×D5C2318yes—
88C2×C3×C4×D5C2314yes—
89C2×C3×Dic10—24no—
90C2×C3×Dic10—28no—
91C2×C3×Dic10C2318yescomplemented
92C2×C3×Dic10C2314yescomplemented
93C2×#1200—24no—
94C2×#1200C2314yes—
95C2×D3×Dic5—24no—
96C2×D3×Dic5C2314yes—
97C2×D5×Dic3—24no—
98C2×D5×Dic3—28no—
99C2×D5×Dic3C2314yes—
100C2×D5×Dic3C2318yes—
101C4×D3×D5—232no—
102#6714C2318yes—
103C4⋊Dic15C2314yescomplemented
104#6712C2318yescomplemented
105C5×(C2×D3)⋊C4C2318yes—
106C5×C4⋊Dic3C2314yescomplemented
107C5×Dic3⋊C4C2318yescomplemented
108Dic3⋊Dic5C2318yescomplemented
109#6669C2318yescomplemented
110#6668C2318yescomplemented
111#6667C2318yes—
112(C2×D3)⋊Dic5C2318yes—
113C23×C3×Q8—51no—
114C23×C4×D3—51no—
115C2×#946—51no—
116C2×#946—51no—
117C2×#946—516no—
118C2×#946—52no—
119C2×#946—51no—
120C2×#946—52no—
121C2×#946D511yescharacteristic, direct product factor
122C22×(C2×D3)⋊C4—52no—
123C22×C4⋊Dic3—51no—
124C22×Dic3⋊C4—52no—
125C24×D5—31no—
126C22×C5×Q8C2×D311yescharacteristic, complemented
127C23×C4×C5—31no—
128C23×Dic5—31no—
129C2×Q8×D5—28no—
130C2×Q8×D5C2×D318yescomplemented
131C22×C4×D5—32no—
132C22×C4×D5—31no—
133C22×C4×D5—31no—
134C22×C4×D5—31no—
135C22×C4×D5—38no—
136C22×C4×D5—68no—
137C22×C4×D5C2×D312yes—
138C22×C4×D5C2×D311yescharacteristic
139C22×Dic10C2×D312yescomplemented
140C22×Dic10C2×D311yescharacteristic, complemented
141C5×C22⋊Q8—38no—
142C2×C5×C4⋊C4—32no—
143C2×C5×C4⋊C4—31no—
144C2×C5×C22⋊C4—32no—
145C2×C22⋊Dic5—32no—
146#4092—38no—
147C2×#685—32no—
148C2×#685—32no—
149C2×C4⋊Dic5—31no—
150C2×C4⋊Dic5—32no—
151#4070—38no—
152C2×#683—32no—
153C2×#683—32no—
154C2×#683—32no—
155#4043—38no—
156#4042—316no—
157D5×C4⋊C4—316no—
158D5×C4⋊C4—38no—
159D5×C22⋊C4—316no—
160#4024—316no—
161C22×C22⋊Q8—151noSylow
162C23×C3×C5C2411yescharacteristic
163C22×D15—22no—
164C22×D15—22no—
165C22×D15C2×Q814yescomplemented
166C22×D15C2412yes—
167C22×C5×D3—22no—
168C22×C5×D3—22no—
169C22×C5×D3C2×Q814yescomplemented
170C22×C5×D3C2412yes—
171C22×C3×D5C2×D414yes—
172C22×C3×D5C2×Q814yes—
173C22×C3×D5#4114yes—
174C22×C3×D5C2412yes—
175C2×D3×D5—232no—
176C2×D3×D5—28no—
177C2×D3×D5—28no—
178C2×D3×D5C2×Q8116yescomplemented
179C3×C5×Q8—28no—
180C2×C3×C4×C5—24no—
181C2×C3×C4×C5C2×D414yes—
182C2×C3×C4×C5C2414yes—
183C2×C3×C4×C5C2412yes—
184C2×Dic15—22no—
185C2×Dic15—24no—
186C2×Dic15C2414yes—
187C2×Dic15C2412yes—
188C4×D15—28no—
189C2×C5×Dic3—22no—
190C2×C5×Dic3—24no—
191C2×C5×Dic3C2414yes—
192C2×C5×Dic3C2412yes—
193C4×C5×D3—28no—
194C2×C3×Dic5—24no—
195C2×C3×Dic5C2×D414yes—
196C2×C3×Dic5C2414yes—
197C2×C3×Dic5C2412yes—
198C3×C4×D5—216no—
199C3×C4×D5C2×D4116yes—
200C3×Dic10—28no—
201C3×Dic10—216no—
202#1200—28no—
203D3×Dic5—28no—
204D5×Dic3—28no—
205D5×Dic3—216no—
206C24×D3—51no—
207C22×C3×Q8—58no—
208C22×C3×Q8—52no—
209C22×C3×Q8—51no—
210C22×C3×Q8—108no—
211C22×C3×Q8C2×D511yescharacteristic, complemented
212C23×C3×C4—51no—
213C23×C3×C4—52no—
214C23×Dic3—51no—
215C23×Dic3—52no—
216C22×C4×D3—51no—
217C22×C4×D3—51no—
218C22×C4×D3—51no—
219C22×C4×D3—58no—
220C22×C4×D3—108no—
221C22×C4×D3C2×D511yescharacteristic
222#946—58no—
223#946—58no—
224#946—516no—
225#946—58no—
226#946—516no—
227#946C2×D518yesdirect product factor
228C2×(C2×D3)⋊C4—52no—
229C2×(C2×D3)⋊C4—52no—
230C2×(C2×D3)⋊C4—52no—
231C2×(C2×D3)⋊C4—516no—
232C2×(C2×D3)⋊C4C2×D512yes—
233C2×C4⋊Dic3—51no—
234C2×C4⋊Dic3—52no—
235C2×C4⋊Dic3—58no—
236C2×C4⋊Dic3C2×D511yescharacteristic, complemented
237C2×Dic3⋊C4—52no—
238C2×Dic3⋊C4—52no—
239C2×Dic3⋊C4—52no—
240C2×Dic3⋊C4—516no—
241C2×Dic3⋊C4C2×D512yescomplemented
242C24×C5—31no—
243C23×D5—31no—
244C23×D5—38no—
245C23×D5—34no—
246C23×D5—64no—
247C23×D5—64no—
248C23×D5C22×D311yescharacteristic
249C2×C5×Q8—24no—
250C2×C5×Q8C22×D314yescomplemented
251C22×C4×C5—32no—
252C22×C4×C5—31no—
253C22×C4×C5—34no—
254C22×C4×C5—64no—
255C22×C4×C5C22×D312yes—
256C22×C4×C5C22×D311yescharacteristic
257C22×Dic5—32no—
258C22×Dic5—31no—
259C22×Dic5—34no—
260C22×Dic5—64no—
261C22×Dic5C22×D312yes—
262C22×Dic5C22×D311yescharacteristic
263Q8×D5—232no—
264C2×C4×D5—28no—
265C2×C4×D5—34no—
266C2×C4×D5—38no—
267C2×C4×D5—34no—
268C2×C4×D5—34no—
269C2×C4×D5—68no—
270C2×C4×D5—64no—
271C2×C4×D5—64no—
272C2×C4×D5—64no—
273C2×C4×D5—632no—
274C2×C4×D5#6718yes—
275C2×C4×D5C22×D318yes—
276C2×C4×D5C22×D314yes—
277C2×Dic10—24no—
278C2×Dic10—28no—
279C2×Dic10C22×D318yescomplemented
280C2×Dic10C22×D314yescomplemented
281C5×C4⋊C4—38no—
282C5×C4⋊C4—34no—
283C5×C22⋊C4—38no—
284C22⋊Dic5—38no—
285#685—38no—
286#685—38no—
287C4⋊Dic5—34no—
288C4⋊Dic5—38no—
289#683—38no—
290#683—38no—
291#683—38no—
292C23×Q8—51no—
293C24×C4—151no—
294C2×C22⋊Q8—31no—
295C2×C22⋊Q8—152no—
296C2×C22⋊Q8—152no—
297C2×C22⋊Q8—151no—
298C2×C22⋊Q8—1516no—
299C2×C22⋊Q8—151no—
300C2×C22⋊Q8—151no—
301C22×C4⋊C4—152no—
302C22×C4⋊C4—151no—
303C22×C22⋊C4—152no—
304C22×C3×C5C22×D412yes—
305C22×C3×C5C22×Q812yes—
306C22×C3×C5C2×#4112yes—
307C22×C3×C5C2511yescharacteristic
308C2×D15—28no—
309C2×D15—22no—
310C2×D15—22no—
311C2×D15C22×Q814yescomplemented
312C2×C5×D3—28no—
313C2×C5×D3—22no—
314C2×C5×D3—22no—
315C2×C5×D3C22×Q814yescomplemented
316C2×C3×D5C22⋊Q8116yescomplemented
317C2×C3×D5C22×D414yes—
318C2×C3×D5C22×Q814yes—
319C2×C3×D5C2×#4114yes—
320D3×D5—232no—
321C3×C4×C5—24no—
322C3×C4×C5C22×D414yes—
323Dic15—22no—
324Dic15—24no—
325C3×Dic5—24no—
326C3×Dic5C22×D414yes—
327C5×Dic3—22no—
328C5×Dic3—24no—
329C24×C3—51no—
330C23×D3—51no—
331C23×D3—58no—
332C23×D3—54no—
333C23×D3—104no—
334C23×D3—104no—
335C23×D3C22×D511yescharacteristic
336C2×C3×Q8—24no—
337C2×C3×Q8—58no—
338C2×C3×Q8—54no—
339C2×C3×Q8—108no—
340C2×C3×Q8—1032no—
341C2×C3×Q8—104no—
342C2×C3×Q8C22×D514yescomplemented
343C22×C3×C4—51no—
344C22×C3×C4—58no—
345C22×C3×C4—54no—
346C22×C3×C4—52no—
347C22×C3×C4—58no—
348C22×C3×C4—108no—
349C22×C3×C4C22×D512yes—
350C22×C3×C4C22×D511yescharacteristic
351C22×Dic3—51no—
352C22×Dic3—52no—
353C22×Dic3—54no—
354C22×Dic3—58no—
355C22×Dic3—104no—
356C22×Dic3—108no—
357C22×Dic3C22×D511yescharacteristic
358C22×Dic3C22×D512yes—
359C2×C4×D3—24no—
360C2×C4×D3—54no—
361C2×C4×D3—54no—
362C2×C4×D3—54no—
363C2×C4×D3—1032no—
364C2×C4×D3—104no—
365C2×C4×D3—104no—
366C2×C4×D3—104no—
367C2×C4×D3C22×D514yes—
368(C2×D3)⋊C4—58no—
369(C2×D3)⋊C4—58no—
370(C2×D3)⋊C4—58no—
371(C2×D3)⋊C4C22×D518yes—
372C4⋊Dic3—54no—
373C4⋊Dic3—58no—
374C4⋊Dic3C22×D514yescomplemented
375Dic3⋊C4—58no—
376Dic3⋊C4—58no—
377Dic3⋊C4—58no—
378Dic3⋊C4C22×D518yescomplemented
379C23×C5—34no—
380C23×C5—32no—
381C23×C5—62no—
382C23×C5—62no—
383C23×C5C23×D311yescharacteristic
384C22×D5—34no—
385C22×D5—32no—
386C22×D5—316no—
387C22×D5—62no—
388C22×D5—62no—
389C22×D5—632no—
390C22×D5—68no—
391C22×D5—68no—
392C22×D5D3×Q814yes—
393C22×D5#23914yes—
394C22×D5C2×#6714yes—
395C22×D5C23×D312yes—
396C5×Q8—28no—
397C2×C4×C5—24no—
398C2×C4×C5—32no—
399C2×C4×C5—34no—
400C2×C4×C5—64no—
401C2×C4×C5—62no—
402C2×C4×C5—68no—
403C2×C4×C5C2×#6714yes—
404C2×C4×C5C23×D314yes—
405C2×C4×C5C23×D312yes—
406C2×Dic5—24no—
407C2×Dic5—34no—
408C2×Dic5—32no—
409C2×Dic5—64no—
410C2×Dic5—62no—
411C2×Dic5—68no—
412C2×Dic5C2×#6714yes—
413C2×Dic5C23×D314yes—
414C2×Dic5C23×D312yes—
415C4×D5—216no—
416C4×D5—616no—
417C4×D5—68no—
418C4×D5—68no—
419C4×D5—68no—
420C4×D5C2×#67116yes—
421Dic10—28no—
422Dic10—216no—
423C25—151no—
424C22×Q8—58no—
425C22×Q8—52no—
426C22×Q8—51no—
427C22×Q8—108no—
428C22×Q8D3×D511yescharacteristic, complemented
429C23×C4—31no—
430C23×C4—51no—
431C23×C4—52no—
432C23×C4—151no—
433C23×C4—158no—
434C23×C4—152no—
435C23×C4—151no—
436C23×C4—151no—
437C23×C4—151no—
438C23×C4—308no—
439C22⋊Q8—38no—
440C22⋊Q8—1516no—
441C22⋊Q8—1516no—
442C22⋊Q8—158no—
443C22⋊Q8—158no—
444C22⋊Q8—158no—
445C2×C4⋊C4—32no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—1516no—
448C2×C4⋊C4—158no—
449C2×C4⋊C4—152no—
450C2×C4⋊C4—152no—
451C2×C4⋊C4—152no—
452C2×C4⋊C4—152no—
453C2×C4⋊C4—151no—
454C2×C22⋊C4—32no—
455C2×C22⋊C4—1516no—
456C2×C22⋊C4—152no—
457C2×C22⋊C4—152no—
458C2×C22⋊C4—152no—
459C2×C3×C5C2×C22⋊Q814yescomplemented
460C2×C3×C5C23×D411yescharacteristic
461C2×C3×C5C23×Q811yescharacteristic
462C2×C3×C5C22×#4111yescharacteristic
463D15—24no—
464C3×D5C2×C22⋊Q818yescomplemented
465C5×D3—24no—
466C23×C3—54no—
467C23×C3—54no—
468C23×C3—54no—
469C23×C3—52no—
470C23×C3C23×D511yescharacteristic
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—54no—
474C22×D3—52no—
475C22×D3—516no—
476C22×D3—108no—
477C22×D3—1032no—
478C22×D3—108no—
479C22×D3—102no—
480C22×D3—102no—
481C22×D3Q8×D514yescomplemented
482C22×D3C23×D512yes—
483C3×Q8—28no—
484C3×Q8—1016no—
485C3×Q8—108no—
486C2×C3×C4—24no—
487C2×C3×C4—54no—
488C2×C3×C4—52no—
489C2×C3×C4—516no—
490C2×C3×C4—54no—
491C2×C3×C4—1016no—
492C2×C3×C4—104no—
493C2×C3×C4D4×D514yes—
494C2×C3×C4C23×D514yes—
495C2×C3×C4C23×D512yes—
496C2×Dic3—22no—
497C2×Dic3—24no—
498C2×Dic3—52no—
499C2×Dic3—54no—
500C2×Dic3—108no—
501C2×Dic3—1016no—
502C2×Dic3—102no—
503C2×Dic3—104no—
504C2×Dic3C23×D512yes—
505C2×Dic3C23×D514yes—
506C4×D3—28no—
507C4×D3—108no—
508C4×D3—108no—
509C4×D3—108no—
510C22×C5—34no—
511C22×C5—62no—
512C22×C5—62no—
513C22×C5—68no—
514C22×C5C2×D3×Q812yes—
515C22×C5C2×#23912yes—
516C22×C5C22×#6712yes—
517C22×C5C24×D311yescharacteristic
518C2×D5—34no—
519C2×D5—62no—
520C2×D5—62no—
521C2×D5—68no—
522C2×D5—632no—
523C2×D5#946116yesdirect product factor
524C2×D5C2×D3×Q814yes—
525C2×D5C2×#23914yes—
526C2×D5C22×#6714yes—
527C4×C5—24no—
528C4×C5—64no—
529C4×C5—62no—
530C4×C5C22×#6714yes—
531Dic5—24no—
532Dic5—64no—
533Dic5—62no—
534Dic5C22×#6714yes—
535C24—31no—
536C24—51no—
537C24—154no—
538C24—158no—
539C24—151no—
540C24—304no—
541C24—304no—
542C2×Q8—24no—
543C2×Q8—58no—
544C2×Q8—54no—
545C2×Q8—108no—
546C2×Q8—1032no—
547C2×Q8—104no—
548C2×Q8C2×D3×D514yescomplemented
549C22×C4—32no—
550C22×C4—31no—
551C22×C4—34no—
552C22×C4—51no—
553C22×C4—58no—
554C22×C4—54no—
555C22×C4—52no—
556C22×C4—58no—
557C22×C4—64no—
558C22×C4—108no—
559C22×C4—154no—
560C22×C4—158no—
561C22×C4—154no—
562C22×C4—154no—
563C22×C4—152no—
564C22×C4—151no—
565C22×C4—154no—
566C22×C4—304no—
567C22×C4—3032no—
568C22×C4—304no—
569C22×C4—304no—
570C22×C4—308no—
571C22×C4—304no—
572C22×C4C2×D3×D512yes—
573C22×C4C2×D3×D511yescharacteristic
574C4⋊C4—38no—
575C4⋊C4—34no—
576C4⋊C4—158no—
577C4⋊C4—158no—
578C4⋊C4—158no—
579C4⋊C4—158no—
580C4⋊C4—154no—
581C22⋊C4—38no—
582C22⋊C4—158no—
583C22⋊C4—158no—
584C22⋊C4—158no—
585C3×C5C22×C22⋊Q811yescharacteristic, complemented, Hall
586C22×C3—516no—
587C22×C3—54no—
588C22×C3—54no—
589C22×C3—54no—
590C22×C3C2×D4×D512yes—
591C22×C3C2×Q8×D512yes—
592C22×C3D5×#4112yes—
593C22×C3C24×D511yescharacteristic
594C2×D3—28no—
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—54no—
598C2×D3—1032no—
599C2×D3—108no—
600C2×D3—102no—
601C2×D3—102no—
602C2×D3C2×Q8×D514yescomplemented
603C3×C4—24no—
604C3×C4—54no—
605C3×C4—104no—
606C3×C4C2×D4×D514yes—
607Dic3—22no—
608Dic3—24no—
609Dic3—102no—
610Dic3—104no—
611C2×C5—64no—
612C2×C5C2×#94614yescomplemented
613C2×C5C22×D3×Q811yescharacteristic
614C2×C5C22×#23911yescharacteristic
615C2×C5C23×#6711yescharacteristic
616D5—64no—
617D5C2×#94618yesdirect product factor
618C23—34no—
619C23—32no—
620C23—54no—
621C23—54no—
622C23—54no—
623C23—52no—
624C23—62no—
625C23—62no—
626C23—1516no—
627C23—154no—
628C23—152no—
629C23—308no—
630C23—3032no—
631C23—308no—
632C23—302no—
633C23—302no—
634C23C22×D3×D511yescharacteristic
635Q8—28no—
636Q8—1016no—
637Q8—108no—
638C2×C4—24no—
639C2×C4—34no—
640C2×C4—32no—
641C2×C4—54no—
642C2×C4—52no—
643C2×C4—516no—
644C2×C4—54no—
645C2×C4—64no—
646C2×C4—62no—
647C2×C4—68no—
648C2×C4—1016no—
649C2×C4—104no—
650C2×C4—154no—
651C2×C4—152no—
652C2×C4—308no—
653C2×C4—308no—
654C2×C4—308no—
655C2×C4—3016no—
656C2×C4—304no—
657C2×C4—302no—
658C2×C4—308no—
659C2×C4D5×#6714yes—
660C2×C4C22×D3×D514yes—
661C2×C4C22×D3×D512yes—
662C2×C3—58no—
663C2×C3D5×C22⋊Q814yescomplemented
664C2×C3C22×D4×D511yescharacteristic
665C2×C3C22×Q8×D511yescharacteristic
666C2×C3C2×D5×#4111yescharacteristic
667D3—24no—
668D3—104no—
669C5C22×#94611yescharacteristic, complemented, Sylow
670C22—34no—
671C22—516no—
672C22—54no—
673C22—54no—
674C22—54no—
675C22—68no—
676C22—62no—
677C22—62no—
678C22—154no—
679C22—3032no—
680C22—308no—
681C22—302no—
682C22—302no—
683C22D3×Q8×D512yes—
684C22D5×#23912yes—
685C22C2×D5×#6712yes—
686C22C23×D3×D511yescharacteristic
687C4—24no—
688C4—54no—
689C4—62no—
690C4—64no—
691C4—104no—
692C4—302no—
693C4—304no—
694C4C2×D5×#6714yes—
695C3C2×D5×C22⋊Q811yescharacteristic, complemented, Sylow
696C2—58no—
697C2—64no—
698C2—304no—
699C2D5×#94614yesdirect product factor
700C2C2×D3×Q8×D511yescharacteristic
701C2C2×D5×#23911yescharacteristic
702C2C22×D5×#6711yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5C22×C22⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×Q8×D5C2semidirect
3. C2×#91835C2semidirect
4. C2×C5×#946C2semidirect
5. D5×#946C2direct (N × H)
7. C2×D5×C4⋊Dic3C2semidirect
8. C2×#91411C2semidirect
9. C2×#91410C2semidirect
10. C2×D5×Dic3⋊C4C2semidirect
11. C2×#91390C2semidirect
12. C2×#91369C2semidirect
15. C22×C3×C5×Q8C22semidirect
19. C2×C3×Q8×D5C22semidirect
22. C22×C3×Dic10C22semidirect
23. C22×C3×Dic10C22semidirect
30. #91835C22semidirect
32. C2×C4⋊Dic15C22semidirect
33. C2×#6712C22semidirect
34. C5×#946C22semidirect
36. C2×C5×C4⋊Dic3C22semidirect
37. C2×C5×Dic3⋊C4C22semidirect
38. C2×Dic3⋊Dic5C22semidirect
39. C2×#6669C22semidirect
40. C2×#6668C22semidirect
44. D5×C4⋊Dic3C22semidirect
45. #91411C22semidirect
46. #91410C22semidirect
47. D5×Dic3⋊C4C22semidirect
48. #91390C22semidirect
49. #91369C22semidirect
51. C22×Q8×D5D3semidirect
68. C22×D3×D5Q8semidirect
71. C2×C3×C5×Q8C23semidirect
91. C2×C3×Dic10C23semidirect
92. C2×C3×Dic10C23semidirect
103. C4⋊Dic15C23semidirect
104. #6712C23semidirect
106. C5×C4⋊Dic3C23semidirect
107. C5×Dic3⋊C4C23semidirect
108. Dic3⋊Dic5C23semidirect
109. #6669C23semidirect
110. #6668C23semidirect
121. C2×#946D5direct (N × H)
126. C22×C5×Q8C2×D3semidirect
130. C2×Q8×D5C2×D3semidirect
139. C22×Dic10C2×D3semidirect
140. C22×Dic10C2×D3semidirect
165. C22×D15C2×Q8semidirect
169. C22×C5×D3C2×Q8semidirect
178. C2×D3×D5C2×Q8semidirect
211. C22×C3×Q8C2×D5semidirect
227. #946C2×D5direct (N × H)
236. C2×C4⋊Dic3C2×D5semidirect
241. C2×Dic3⋊C4C2×D5semidirect
250. C2×C5×Q8C22×D3semidirect
279. C2×Dic10C22×D3semidirect
280. C2×Dic10C22×D3semidirect
311. C2×D15C22×Q8semidirect
315. C2×C5×D3C22×Q8semidirect
316. C2×C3×D5C22⋊Q8semidirect
342. C2×C3×Q8C22×D5semidirect
374. C4⋊Dic3C22×D5semidirect
378. Dic3⋊C4C22×D5semidirect
428. C22×Q8D3×D5semidirect
459. C2×C3×C5C2×C22⋊Q8semidirect
464. C3×D5C2×C22⋊Q8semidirect
481. C22×D3Q8×D5semidirect
523. C2×D5#946direct (N × H)
548. C2×Q8C2×D3×D5semidirect
585. C3×C5C22×C22⋊Q8semidirect
602. C2×D3C2×Q8×D5semidirect
612. C2×C5C2×#946semidirect
617. D5C2×#946direct (N × H)
663. C2×C3D5×C22⋊Q8semidirect
669. C5C22×#946semidirect
695. C3C2×D5×C22⋊Q8semidirect
699. C2D5×#946direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Q8×D52
C22×C4×D3×D52
C2×#918352
C2×C5×#9462
D5×#9462
C2×D5×(C2×D3)⋊C42
C2×D5×C4⋊Dic32
C2×#914112
C2×#914102
C2×D5×Dic3⋊C42
C2×#913902
C2×#913692
C2×D5×C22⋊Q83
C22×#9465