Finite Group Databasebeta

← C2×D5×#924 #14479436

Subgroups — C2×D5×#924 #14479436

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
1C23×C3×C4×D5C211yesmaximal, characteristic
2C22×D5×Dic6C211yesmaximal, characteristic, complemented
3C2×#91813C211yesmaximal, characteristic, complemented
4C2×C5×#924C211yesmaximal, characteristic, complemented
5C2×#91574C212yesmaximal, complemented
6C2×D5×#217C212yesmaximal
7C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
8D5×#924C2116yesmaximal, direct product factor
9C2×D5×Dic3⋊C4C212yesmaximal, complemented
10C2×#91360C211yesmaximal, characteristic, complemented
11C2×#91359C211yesmaximal, characteristic, complemented
12C2×#91349C212yesmaximal, complemented
13C2×D5×C22⋊Q8—31nomaximal, Hall
14C24×C3×D5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C22×Dic30C2211yescharacteristic, complemented
17C22×C5×Dic6C2211yescharacteristic, complemented
18C23×C3×Dic5C2211yescharacteristic
19C22×C3×C4×D5—28no—
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2218yes—
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×#1204C2212yescomplemented
26C22×D5×Dic3C2212yes—
27C22×D5×Dic3C2212yes—
28C2×D5×Dic6—28no—
29C2×D5×Dic6C2218yescomplemented
30C2×#6719C2212yes—
31C2×C4⋊Dic15C2211yescharacteristic, complemented
32#91813C2218yescomplemented
33C2×#6712C2212yescomplemented
34C2×C5×#217C2212yes—
35C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
36C5×#924C2218yescomplemented
37C2×C5×Dic3⋊C4C2212yescomplemented
38#91574C22116yescomplemented
39D5×#217C22116yes—
40C2×Dic3⋊Dic5C2212yescomplemented
41C2×#6669C2212yescomplemented
42C2×#6668C2212yescomplemented
43C2×#6665C2212yes—
44C2×#6665C2212yes—
45D5×C4⋊Dic3C2218yescomplemented
46D5×Dic3⋊C4C22116yescomplemented
47#91360C2218yescomplemented
48#91359C2218yescomplemented
49#91349C22116yescomplemented
50C22×#924—51nomaximal, Hall
51C22×Q8×D5—31no—
52C23×C4×D5D311yescharacteristic
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—
63C24×C3×C5C2311yescharacteristic
64C23×C3×D5—24no—
65C23×C3×D5—24no—
66C23×C3×D5Q818yescomplemented
67C23×C3×D5C2311yescharacteristic
68C23×C3×D5C2314yes—
69C23×C3×D5C2311yescharacteristic
70C22×C3×C4×C5—24no—
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2314yes—
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15C2312yes—
75C22×Dic15C2312yes—
76C2×Dic30—24no—
77C2×Dic30C2314yescomplemented
78C22×C5×Dic3C2312yes—
79C22×C5×Dic3C2312yes—
80C2×C5×Dic6—24no—
81C2×C5×Dic6C2314yescomplemented
82C22×C3×Dic5—24no—
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2314yes—
85C22×C3×Dic5C2311yescharacteristic
86C2×C3×C4×D5—24no—
87C2×C3×C4×D5—24no—
88C2×C3×C4×D5—24no—
89C2×C3×C4×D5—232no—
90C2×C3×C4×D5D418yes—
91C2×C3×C4×D5C2314yes—
92C2×C3×C4×D5C2314yes—
93C2×C3×C4×D5C2314yes—
94C2×C3×C4×D5C2314yes—
95C2×#1204—28no—
96C2×#1204C2318yescomplemented
97C2×D5×Dic3—28no—
98C2×D5×Dic3—28no—
99C2×D5×Dic3C2318yes—
100C2×D5×Dic3C2318yes—
101D5×Dic6—232no—
102#6719C2318yes—
103C4⋊Dic15C2314yescomplemented
104#6712C2318yescomplemented
105C5×#217C2318yes—
106C5×C4⋊Dic3C2314yescomplemented
107C5×Dic3⋊C4C2318yescomplemented
108Dic3⋊Dic5C2318yescomplemented
109#6669C2318yescomplemented
110#6668C2318yescomplemented
111#6665C2318yes—
112#6665C2318yes—
113C24×C3×C4—51no—
114C23×Dic6—51no—
115C22×#217—52no—
116C22×C4⋊Dic3—51no—
117C2×#924—51no—
118C2×#924—51no—
119C2×#924—52no—
120C2×#924—51no—
121C2×#924—516no—
122C2×#924—52no—
123C2×#924D511yescharacteristic, direct product factor
124C22×Dic3⋊C4—52no—
125C24×D5C2×D311yescharacteristic
126C22×C5×Q8—31no—
127C23×C4×C5C2×D311yescharacteristic
128C23×Dic5C2×D311yescharacteristic
129C2×Q8×D5—38no—
130C2×Q8×D5—68no—
131C22×C4×D5—28no—
132C22×C4×D5—32no—
133C22×C4×D5—32no—
134C22×C4×D5C2×D311yescharacteristic
135C22×C4×D5C2×D311yescharacteristic
136C22×C4×D5C2×D311yescharacteristic
137C22×C4×D5C2×D318yes—
138C22×C4×D5C2×D311yescharacteristic
139C22×Dic10—31no—
140C22×Dic10—32no—
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×C5—22no—
163C23×C3×C5—22no—
164C23×C3×C5C2×Q814yescomplemented
165C23×C3×C5C2412yes—
166C23×C3×C5C2411yescharacteristic
167C22×C3×D5—22no—
168C22×C3×D5—22no—
169C22×C3×D5—232no—
170C22×C3×D5—28no—
171C22×C3×D5—28no—
172C22×C3×D5C2×D414yes—
173C22×C3×D5C2×Q814yes—
174C22×C3×D5C2×Q8116yescomplemented
175C22×C3×D5C2×Q814yescomplemented
176C22×C3×D5#4114yes—
177C22×C3×D5C2412yes—
178C22×C3×D5C2412yes—
179C2×C3×C4×C5—22no—
180C2×C3×C4×C5—28no—
181C2×C3×C4×C5C2×D414yes—
182C2×C3×C4×C5C2412yes—
183C2×C3×C4×C5C2412yes—
184C2×Dic15—24no—
185C2×Dic15—24no—
186C2×Dic15C2414yes—
187C2×Dic15C2414yes—
188Dic30—28no—
189C2×C5×Dic3—24no—
190C2×C5×Dic3—24no—
191C2×C5×Dic3C2414yes—
192C2×C5×Dic3C2414yes—
193C5×Dic6—28no—
194C2×C3×Dic5—22no—
195C2×C3×Dic5—28no—
196C2×C3×Dic5C2×D414yes—
197C2×C3×Dic5C2412yes—
198C2×C3×Dic5C2412yes—
199C3×C4×D5—28no—
200C3×C4×D5—28no—
201C3×C4×D5—28no—
202C3×C4×D5C2×D4116yes—
203#1204—216no—
204D5×Dic3—216no—
205D5×Dic3—216no—
206C25×C3—51no—
207C23×C3×C4—51no—
208C23×C3×C4—51no—
209C23×C3×C4—51no—
210C23×C3×C4—51no—
211C23×C3×C4—58no—
212C23×C3×C4—51no—
213C23×C3×C4—108no—
214C23×C3×C4C2×D511yescharacteristic
215C23×Dic3—52no—
216C23×Dic3—52no—
217C22×Dic6—51no—
218C22×Dic6—52no—
219C22×Dic6—58no—
220C22×Dic6—108no—
221C22×Dic6C2×D511yescharacteristic, complemented
222C2×#217—52no—
223C2×#217—52no—
224C2×#217—52no—
225C2×#217—516no—
226C2×#217C2×D512yes—
227C2×C4⋊Dic3—51no—
228C2×C4⋊Dic3—52no—
229C2×C4⋊Dic3—58no—
230C2×C4⋊Dic3C2×D511yescharacteristic, complemented
231#924—58no—
232#924—58no—
233#924—516no—
234#924—58no—
235#924—516no—
236#924C2×D518yesdirect product factor
237C2×Dic3⋊C4—52no—
238C2×Dic3⋊C4—52no—
239C2×Dic3⋊C4—52no—
240C2×Dic3⋊C4—516no—
241C2×Dic3⋊C4C2×D512yescomplemented
242C24×C5C22×D311yescharacteristic
243C23×D5—24no—
244C23×D5—24no—
245C23×D5Dic618yescomplemented
246C23×D5C22×D314yes—
247C23×D5C22×D311yescharacteristic
248C23×D5C22×D311yescharacteristic
249C2×C5×Q8—34no—
250C2×C5×Q8—64no—
251C22×C4×C5—24no—
252C22×C4×C5—32no—
253C22×C4×C5—32no—
254C22×C4×C5C22×D311yescharacteristic
255C22×C4×C5C22×D314yes—
256C22×C4×C5C22×D311yescharacteristic
257C22×Dic5—24no—
258C22×Dic5—32no—
259C22×Dic5—32no—
260C22×Dic5C22×D314yes—
261C22×Dic5C22×D311yescharacteristic
262C22×Dic5C22×D311yescharacteristic
263Q8×D5—632no—
264C2×C4×D5—24no—
265C2×C4×D5—24no—
266C2×C4×D5—24no—
267C2×C4×D5—232no—
268C2×C4×D5—38no—
269C2×C4×D5—38no—
270C2×C4×D5—68no—
271C2×C4×D5—68no—
272C2×C4×D5#6718yes—
273C2×C4×D5C22×D314yes—
274C2×C4×D5C22×D314yes—
275C2×C4×D5C22×D314yes—
276C2×C4×D5C22×D314yes—
277C2×Dic10—34no—
278C2×Dic10—38no—
279C2×Dic10—64no—
280C2×Dic10—68no—
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—151no—
293C24×C4—51no—
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×C5—28no—
305C22×C3×C5—22no—
306C22×C3×C5—22no—
307C22×C3×C5C22×D412yes—
308C22×C3×C5C22×Q812yes—
309C22×C3×C5C22×Q814yescomplemented
310C22×C3×C5C2×#4112yes—
311C22×C3×C5C2511yescharacteristic
312C2×C3×D5—28no—
313C2×C3×D5—22no—
314C2×C3×D5—22no—
315C2×C3×D5—232no—
316C2×C3×D5C22⋊Q8116yescomplemented
317C2×C3×D5C22×D414yes—
318C2×C3×D5C22×Q814yes—
319C2×C3×D5C22×Q814yescomplemented
320C2×C3×D5C2×#4114yes—
321C3×C4×C5—22no—
322C3×C4×C5C22×D414yes—
323Dic15—24no—
324Dic15—24no—
325C3×Dic5—22no—
326C3×Dic5C22×D414yes—
327C5×Dic3—24no—
328C5×Dic3—24no—
329C24×C3—51no—
330C24×C3—58no—
331C24×C3—54no—
332C24×C3—51no—
333C24×C3—104no—
334C24×C3—104no—
335C24×C3C22×D511yescharacteristic
336C22×C3×C4—24no—
337C22×C3×C4—51no—
338C22×C3×C4—58no—
339C22×C3×C4—54no—
340C22×C3×C4—51no—
341C22×C3×C4—54no—
342C22×C3×C4—54no—
343C22×C3×C4—54no—
344C22×C3×C4—54no—
345C22×C3×C4—104no—
346C22×C3×C4—1032no—
347C22×C3×C4—104no—
348C22×C3×C4—104no—
349C22×C3×C4—104no—
350C22×C3×C4C22×D511yescharacteristic
351C22×C3×C4C22×D514yes—
352C22×C3×C4C22×D511yescharacteristic
353C22×Dic3—52no—
354C22×Dic3—52no—
355C22×Dic3—58no—
356C22×Dic3—58no—
357C22×Dic3—108no—
358C22×Dic3—108no—
359C22×Dic3C22×D512yes—
360C22×Dic3C22×D512yes—
361C2×Dic6—24no—
362C2×Dic6—54no—
363C2×Dic6—58no—
364C2×Dic6—1032no—
365C2×Dic6—108no—
366C2×Dic6—104no—
367C2×Dic6C22×D514yescomplemented
368#217—58no—
369#217—58no—
370#217—58no—
371#217C22×D518yes—
372C4⋊Dic3—54no—
373C4⋊Dic3—58no—
374C4⋊Dic3C22×D514yescomplemented
375Dic3⋊C4—58no—
376Dic3⋊C4—58no—
377Dic3⋊C4—58no—
378Dic3⋊C4C22×D518yescomplemented
379C23×C5—22no—
380C23×C5—22no—
381C23×C5C2×Dic614yescomplemented
382C23×C5C23×D312yes—
383C23×C5C23×D311yescharacteristic
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—232no—
387C22×D5—28no—
388C22×D5—28no—
389C22×D5C2×Dic614yes—
390C22×D5C2×Dic6116yescomplemented
391C22×D5C2×Dic614yescomplemented
392C22×D5#23514yes—
393C22×D5C2×#6714yes—
394C22×D5C23×D312yes—
395C22×D5C23×D312yes—
396C5×Q8—68no—
397C2×C4×C5—22no—
398C2×C4×C5—28no—
399C2×C4×C5—34no—
400C2×C4×C5—34no—
401C2×C4×C5—64no—
402C2×C4×C5—64no—
403C2×C4×C5C2×#6714yes—
404C2×C4×C5C23×D312yes—
405C2×C4×C5C23×D312yes—
406C2×Dic5—22no—
407C2×Dic5—28no—
408C2×Dic5—34no—
409C2×Dic5—34no—
410C2×Dic5—64no—
411C2×Dic5—64no—
412C2×Dic5C2×#6714yes—
413C2×Dic5C23×D312yes—
414C2×Dic5C23×D312yes—
415C4×D5—28no—
416C4×D5—28no—
417C4×D5—28no—
418C4×D5—616no—
419C4×D5—616no—
420C4×D5C2×#67116yes—
421Dic10—68no—
422Dic10—616no—
423C25—51no—
424C22×Q8—31no—
425C22×Q8—152no—
426C22×Q8—158no—
427C22×Q8—151no—
428C22×Q8—308no—
429C23×C4—51no—
430C23×C4—51no—
431C23×C4—51no—
432C23×C4—51no—
433C23×C4—58no—
434C23×C4—51no—
435C23×C4—108no—
436C23×C4—152no—
437C23×C4—152no—
438C23×C4D3×D511yescharacteristic
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×C5—24no—
460C2×C3×C5C2×C22⋊Q814yescomplemented
461C2×C3×C5C23×D411yescharacteristic
462C2×C3×C5C23×Q811yescharacteristic
463C2×C3×C5C22×#4111yescharacteristic
464C3×D5—24no—
465C3×D5C2×C22⋊Q818yescomplemented
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—54no—
469C23×C3—54no—
470C23×C3—54no—
471C23×C3—52no—
472C23×C3—54no—
473C23×C3—516no—
474C23×C3—52no—
475C23×C3—108no—
476C23×C3—1032no—
477C23×C3—108no—
478C23×C3—102no—
479C23×C3—102no—
480C23×C3Q8×D514yescomplemented
481C23×C3C23×D512yes—
482C23×C3C23×D511yescharacteristic
483C2×C3×C4—22no—
484C2×C3×C4—28no—
485C2×C3×C4—54no—
486C2×C3×C4—52no—
487C2×C3×C4—516no—
488C2×C3×C4—52no—
489C2×C3×C4—108no—
490C2×C3×C4—108no—
491C2×C3×C4—108no—
492C2×C3×C4—102no—
493C2×C3×C4—108no—
494C2×C3×C4D4×D514yes—
495C2×C3×C4C23×D512yes—
496C2×C3×C4C23×D512yes—
497C2×Dic3—24no—
498C2×Dic3—24no—
499C2×Dic3—54no—
500C2×Dic3—54no—
501C2×Dic3—1016no—
502C2×Dic3—1016no—
503C2×Dic3—104no—
504C2×Dic3—104no—
505C2×Dic3C23×D514yes—
506C2×Dic3C23×D514yes—
507Dic6—28no—
508Dic6—1016no—
509Dic6—108no—
510C22×C5—22no—
511C22×C5—22no—
512C22×C5—28no—
513C22×C5C22×Dic612yes—
514C22×C5C22×Dic614yescomplemented
515C22×C5C2×#23512yes—
516C22×C5C22×#6712yes—
517C22×C5C24×D311yescharacteristic
518C2×D5—22no—
519C2×D5—22no—
520C2×D5—28no—
521C2×D5—232no—
522C2×D5#924116yesdirect product factor
523C2×D5C22×Dic614yes—
524C2×D5C22×Dic614yescomplemented
525C2×D5C2×#23514yes—
526C2×D5C22×#6714yes—
527C4×C5—22no—
528C4×C5—64no—
529C4×C5—64no—
530C4×C5C22×#6714yes—
531Dic5—22no—
532Dic5—64no—
533Dic5—64no—
534Dic5C22×#6714yes—
535C24—51no—
536C24—58no—
537C24—54no—
538C24—51no—
539C24—104no—
540C24—104no—
541C24C2×D3×D511yescharacteristic
542C2×Q8—34no—
543C2×Q8—64no—
544C2×Q8—158no—
545C2×Q8—154no—
546C2×Q8—308no—
547C2×Q8—3032no—
548C2×Q8—304no—
549C22×C4—24no—
550C22×C4—32no—
551C22×C4—32no—
552C22×C4—51no—
553C22×C4—58no—
554C22×C4—54no—
555C22×C4—54no—
556C22×C4—51no—
557C22×C4—54no—
558C22×C4—54no—
559C22×C4—54no—
560C22×C4—104no—
561C22×C4—1032no—
562C22×C4—104no—
563C22×C4—104no—
564C22×C4—104no—
565C22×C4—158no—
566C22×C4—158no—
567C22×C4—152no—
568C22×C4—152no—
569C22×C4—308no—
570C22×C4—308no—
571C22×C4C2×D3×D514yes—
572C22×C4C2×D3×D511yescharacteristic
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—28no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—516no—
590C22×C3—54no—
591C22×C3—54no—
592C22×C3—54no—
593C22×C3—54no—
594C22×C3—1032no—
595C22×C3—108no—
596C22×C3—102no—
597C22×C3—102no—
598C22×C3C2×D4×D512yes—
599C22×C3C2×Q8×D512yes—
600C22×C3C2×Q8×D514yescomplemented
601C22×C3D5×#4112yes—
602C22×C3C24×D511yescharacteristic
603C3×C4—22no—
604C3×C4—54no—
605C3×C4—102no—
606C3×C4C2×D4×D514yes—
607Dic3—24no—
608Dic3—24no—
609Dic3—104no—
610Dic3—104no—
611C2×C5—24no—
612C2×C5C2×#92414yescomplemented
613C2×C5C23×Dic611yescharacteristic
614C2×C5C22×#23511yescharacteristic
615C2×C5C23×#6711yescharacteristic
616D5—24no—
617D5C2×#92418yesdirect product factor
618C23—22no—
619C23—22no—
620C23—54no—
621C23—54no—
622C23—54no—
623C23—52no—
624C23—54no—
625C23—516no—
626C23—52no—
627C23—108no—
628C23—1032no—
629C23—108no—
630C23—102no—
631C23—102no—
632C23D5×Dic614yescomplemented
633C23C22×D3×D512yes—
634C23C22×D3×D511yescharacteristic
635Q8—68no—
636Q8—3016no—
637Q8—308no—
638C2×C4—22no—
639C2×C4—28no—
640C2×C4—34no—
641C2×C4—34no—
642C2×C4—54no—
643C2×C4—52no—
644C2×C4—516no—
645C2×C4—52no—
646C2×C4—64no—
647C2×C4—64no—
648C2×C4—108no—
649C2×C4—108no—
650C2×C4—108no—
651C2×C4—102no—
652C2×C4—108no—
653C2×C4—154no—
654C2×C4—154no—
655C2×C4—3016no—
656C2×C4—3016no—
657C2×C4—304no—
658C2×C4—304no—
659C2×C4D5×#6714yes—
660C2×C4C22×D3×D512yes—
661C2×C4C22×D3×D512yes—
662C2×C3—24no—
663C2×C3—58no—
664C2×C3—104no—
665C2×C3D5×C22⋊Q814yescomplemented
666C2×C3C22×D4×D511yescharacteristic
667C2×C3C22×Q8×D511yescharacteristic
668C2×C3C2×D5×#4111yescharacteristic
669C5C22×#92411yescharacteristic, complemented, Sylow
670C22—22no—
671C22—28no—
672C22—22no—
673C22—54no—
674C22—516no—
675C22—54no—
676C22—54no—
677C22—54no—
678C22—1032no—
679C22—102no—
680C22—108no—
681C22—102no—
682C22C2×D5×Dic612yes—
683C22C2×D5×Dic614yescomplemented
684C22D5×#23512yes—
685C22C2×D5×#6712yes—
686C22C23×D3×D511yescharacteristic
687C4—22no—
688C4—54no—
689C4—64no—
690C4—64no—
691C4—102no—
692C4—304no—
693C4—304no—
694C4C2×D5×#6714yes—
695C3C2×D5×C22⋊Q811yescharacteristic, complemented, Sylow
696C2—24no—
697C2—58no—
698C2—104no—
699C2D5×#92414yesdirect product factor
700C2C22×D5×Dic611yescharacteristic
701C2C2×D5×#23511yescharacteristic
702C2C22×D5×#6711yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC24×C3×D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5C22×C22⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×D5×Dic6C2semidirect
3. C2×#91813C2semidirect
4. C2×C5×#924C2semidirect
5. C2×#91574C2semidirect
7. C2×D5×C4⋊Dic3C2semidirect
8. D5×#924C2direct (N × H)
9. C2×D5×Dic3⋊C4C2semidirect
10. C2×#91360C2semidirect
11. C2×#91359C2semidirect
12. C2×#91349C2semidirect
16. C22×Dic30C22semidirect
17. C22×C5×Dic6C22semidirect
25. C22×#1204C22semidirect
29. C2×D5×Dic6C22semidirect
31. C2×C4⋊Dic15C22semidirect
32. #91813C22semidirect
33. C2×#6712C22semidirect
35. C2×C5×C4⋊Dic3C22semidirect
36. C5×#924C22semidirect
37. C2×C5×Dic3⋊C4C22semidirect
38. #91574C22semidirect
40. C2×Dic3⋊Dic5C22semidirect
41. C2×#6669C22semidirect
42. C2×#6668C22semidirect
45. D5×C4⋊Dic3C22semidirect
46. D5×Dic3⋊C4C22semidirect
47. #91360C22semidirect
48. #91359C22semidirect
49. #91349C22semidirect
66. C23×C3×D5Q8semidirect
77. C2×Dic30C23semidirect
81. C2×C5×Dic6C23semidirect
96. C2×#1204C23semidirect
103. C4⋊Dic15C23semidirect
104. #6712C23semidirect
106. C5×C4⋊Dic3C23semidirect
107. C5×Dic3⋊C4C23semidirect
108. Dic3⋊Dic5C23semidirect
109. #6669C23semidirect
110. #6668C23semidirect
123. C2×#924D5direct (N × H)
164. C23×C3×C5C2×Q8semidirect
174. C22×C3×D5C2×Q8semidirect
175. C22×C3×D5C2×Q8semidirect
221. C22×Dic6C2×D5semidirect
230. C2×C4⋊Dic3C2×D5semidirect
236. #924C2×D5direct (N × H)
241. C2×Dic3⋊C4C2×D5semidirect
245. C23×D5Dic6semidirect
309. C22×C3×C5C22×Q8semidirect
316. C2×C3×D5C22⋊Q8semidirect
319. C2×C3×D5C22×Q8semidirect
367. C2×Dic6C22×D5semidirect
374. C4⋊Dic3C22×D5semidirect
378. Dic3⋊C4C22×D5semidirect
381. C23×C5C2×Dic6semidirect
390. C22×D5C2×Dic6semidirect
391. C22×D5C2×Dic6semidirect
460. C2×C3×C5C2×C22⋊Q8semidirect
465. C3×D5C2×C22⋊Q8semidirect
480. C23×C3Q8×D5semidirect
514. C22×C5C22×Dic6semidirect
522. C2×D5#924direct (N × H)
524. C2×D5C22×Dic6semidirect
585. C3×C5C22×C22⋊Q8semidirect
600. C22×C3C2×Q8×D5semidirect
612. C2×C5C2×#924semidirect
617. D5C2×#924direct (N × H)
632. C23D5×Dic6semidirect
665. C2×C3D5×C22⋊Q8semidirect
669. C5C22×#924semidirect
683. C22C2×D5×Dic6semidirect
695. C3C2×D5×C22⋊Q8semidirect
699. C2D5×#924direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×D52
C22×D5×Dic62
C2×#918132
C2×C5×#9242
C2×#915742
C2×D5×#2172
C2×D5×C4⋊Dic32
D5×#9242
C2×D5×Dic3⋊C42
C2×#913602
C2×#913592
C2×#913492
C2×D5×C22⋊Q83
C22×#9245