Finite Group Databasebeta

← C2×D5×#897 #14479430

Subgroups — C2×D5×#897 #14479430

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×C4×D3×D5C211yesmaximal, characteristic
2C22×D5×Dic6C211yesmaximal, characteristic, complemented
3C2×#91786C211yesmaximal, characteristic, complemented
4C2×C5×#897C211yesmaximal, characteristic, complemented
5C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×D5×(C2×D3)⋊C4C212yesmaximal
7C2×#91419C212yesmaximal, complemented
8C2×#91417C212yesmaximal, complemented
9C2×D5×C4⋊Dic3C212yesmaximal, complemented
10C2×#91383C211yesmaximal, characteristic, complemented
11C2×#91365C211yesmaximal, characteristic, complemented
12D5×#897C2116yesmaximal, direct product factor
13C2×D5×C22⋊Q8—31nomaximal, Hall
14C23×D3×D5C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C22×Dic30C2211yescharacteristic, complemented
17C22×C4×C5×D3C2211yescharacteristic
18C22×C5×Dic6C2211yescharacteristic, complemented
19C22×C3×C4×D5C2212yes—
20C22×C3×C4×D5C2211yescharacteristic
21C22×#1204C2212yescomplemented
22C22×#1200C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C22×D5×Dic3C2211yescharacteristic
25C22×D5×Dic3C2212yes—
26C2×C4×D3×D5—28no—
27C2×C4×D3×D5C2218yes—
28C2×D5×Dic6—28no—
29C2×D5×Dic6C2218yescomplemented
30C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
31C2×#6714C2212yes—
32C2×C4⋊Dic15C2212yescomplemented
33#91786C2218yescomplemented
34C2×C5×(C2×D3)⋊C4C2212yes—
35C2×C5×C4⋊Dic3C2212yescomplemented
36C5×#897C2218yescomplemented
37C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
38C2×C3×#683C2212yescomplemented
39C3×D5×C4⋊C4C2218yescomplemented
40C2×#6668C2212yescomplemented
41C2×#6668C2212yescomplemented
42C2×#6667C2212yes—
43C2×(C2×D3)⋊Dic5C2212yes—
44D5×(C2×D3)⋊C4C22116yes—
45#91419C22116yescomplemented
46#91417C22116yescomplemented
47D5×C4⋊Dic3C22116yescomplemented
48#91383C2218yescomplemented
49#91365C2218yescomplemented
50C22×#897—51nomaximal, Hall
51C22×Q8×D5—31no—
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⋊C4D311yescharacteristic, complemented
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—
70C22×C3×C4×C5C2312yes—
71C22×C3×C4×C5C2311yescharacteristic
72C22×Dic15C2311yescharacteristic
73C22×Dic15C2312yes—
74C2×C4×D15—24no—
75C2×C4×D15C2314yes—
76C2×Dic30—24no—
77C2×Dic30C2314yescomplemented
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2312yes—
80C2×C4×C5×D3—24no—
81C2×C4×C5×D3C2314yes—
82C2×C5×Dic6—24no—
83C2×C5×Dic6C2314yescomplemented
84C22×C3×Dic5C2312yes—
85C22×C3×Dic5C2311yescharacteristic
86C2×C3×C4×D5—28no—
87C2×C3×C4×D5D418yes—
88C2×C3×C4×D5C2318yes—
89C2×C3×C4×D5C2314yes—
90C2×#1204—28no—
91C2×#1204C2318yescomplemented
92C2×#1200—24no—
93C2×#1200C2314yes—
94C2×D3×Dic5—24no—
95C2×D3×Dic5C2314yes—
96C2×D5×Dic3—28no—
97C2×D5×Dic3—24no—
98C2×D5×Dic3C2314yes—
99C2×D5×Dic3C2318yes—
100C4×D3×D5—232no—
101D5×Dic6—232no—
102C3×C5×C4⋊C4C2314yescomplemented
103#6714C2318yes—
104C4⋊Dic15C2318yescomplemented
105C5×(C2×D3)⋊C4C2318yes—
106C5×C4⋊Dic3C2318yescomplemented
107C3×C4⋊Dic5C2314yescomplemented
108C3×#683C2318yescomplemented
109#6668C2318yescomplemented
110#6668C2318yescomplemented
111#6667C2318yes—
112(C2×D3)⋊Dic5C2318yes—
113C23×C4×D3—51no—
114C23×Dic6—51no—
115C22×C3×C4⋊C4—51no—
116C22×(C2×D3)⋊C4—52no—
117C22×C4⋊Dic3—52no—
118C2×#897—51no—
119C2×#897—51no—
120C2×#897—51no—
121C2×#897—52no—
122C2×#897—52no—
123C2×#897—516no—
124C2×#897D511yescharacteristic, direct product factor
125C24×D5—31no—
126C22×C5×Q8—31no—
127C23×C4×C5—31no—
128C23×Dic5—31no—
129C2×Q8×D5—38no—
130C2×Q8×D5—68no—
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×Dic10—31no—
140C22×Dic10—32no—
141C5×C22⋊Q8—38no—
142C2×C5×C4⋊C4—32no—
143C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
144C2×C5×C22⋊C4—32no—
145C2×C22⋊Dic5—32no—
146#4092—38no—
147C2×#685—32no—
148C2×#685—32no—
149C2×C4⋊Dic5—32no—
150C2×C4⋊Dic5C2×D311yescharacteristic, complemented
151#4070—38no—
152C2×#683—32no—
153C2×#683—32no—
154C2×#683C2×D312yescomplemented
155#4043—38no—
156#4042—316no—
157D5×C4⋊C4—316no—
158D5×C4⋊C4C2×D318yescomplemented
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
179C2×C3×C4×C5—24no—
180C2×C3×C4×C5C2×D414yes—
181C2×C3×C4×C5C2414yes—
182C2×C3×C4×C5C2412yes—
183C2×Dic15—22no—
184C2×Dic15—24no—
185C2×Dic15C2414yes—
186C2×Dic15C2412yes—
187C4×D15—28no—
188Dic30—28no—
189C2×C5×Dic3—22no—
190C2×C5×Dic3—24no—
191C2×C5×Dic3C2414yes—
192C2×C5×Dic3C2412yes—
193C4×C5×D3—28no—
194C5×Dic6—28no—
195C2×C3×Dic5—24no—
196C2×C3×Dic5C2×D414yes—
197C2×C3×Dic5C2414yes—
198C2×C3×Dic5C2412yes—
199C3×C4×D5—216no—
200C3×C4×D5C2×D4116yes—
201#1204—216no—
202#1200—28no—
203D3×Dic5—28no—
204D5×Dic3—216no—
205D5×Dic3—28no—
206C24×D3—51no—
207C23×C3×C4—51no—
208C23×C3×C4—52no—
209C23×Dic3—52no—
210C23×Dic3—51no—
211C22×C4×D3—51no—
212C22×C4×D3—51no—
213C22×C4×D3—51no—
214C22×C4×D3—58no—
215C22×C4×D3—108no—
216C22×C4×D3C2×D511yescharacteristic
217C22×Dic6—51no—
218C22×Dic6—52no—
219C22×Dic6—58no—
220C22×Dic6—108no—
221C22×Dic6C2×D511yescharacteristic, complemented
222C2×C3×C4⋊C4—52no—
223C2×C3×C4⋊C4—51no—
224C2×C3×C4⋊C4—58no—
225C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
226C2×(C2×D3)⋊C4—52no—
227C2×(C2×D3)⋊C4—52no—
228C2×(C2×D3)⋊C4—52no—
229C2×(C2×D3)⋊C4—516no—
230C2×(C2×D3)⋊C4C2×D512yes—
231C2×C4⋊Dic3—52no—
232C2×C4⋊Dic3—52no—
233C2×C4⋊Dic3—52no—
234C2×C4⋊Dic3—516no—
235C2×C4⋊Dic3C2×D512yescomplemented
236#897—58no—
237#897—58no—
238#897—58no—
239#897—516no—
240#897—516no—
241#897C2×D518yesdirect product factor
242C24×C5—31no—
243C23×D5—31no—
244C23×D5—38no—
245C23×D5—34no—
246C23×D5—64no—
247C23×D5—64no—
248C23×D5C22×D311yescharacteristic
249C2×C5×Q8—34no—
250C2×C5×Q8—64no—
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—632no—
264C2×C4×D5—28no—
265C2×C4×D5—34no—
266C2×C4×D5—38no—
267C2×C4×D5—34no—
268C2×C4×D5—34no—
269C2×C4×D5—64no—
270C2×C4×D5—68no—
271C2×C4×D5—64no—
272C2×C4×D5—64no—
273C2×C4×D5—632no—
274C2×C4×D5D1218yes—
275C2×C4×D5C22×D318yes—
276C2×C4×D5C22×D314yes—
277C2×Dic10—34no—
278C2×Dic10—38no—
279C2×Dic10—64no—
280C2×Dic10—68no—
281C5×C4⋊C4—38no—
282C5×C4⋊C4C22×D314yescomplemented
283C5×C22⋊C4—38no—
284C22⋊Dic5—38no—
285#685—38no—
286#685—38no—
287C4⋊Dic5—38no—
288C4⋊Dic5C22×D314yescomplemented
289#683—38no—
290#683—38no—
291#683C22×D318yescomplemented
292C23×Q8—151no—
293C24×C4—151no—
294C2×C22⋊Q8—31no—
295C2×C22⋊Q8—152no—
296C2×C22⋊Q8—152no—
297C2×C22⋊Q8—1516no—
298C2×C22⋊Q8—151no—
299C2×C22⋊Q8—151no—
300C2×C22⋊Q8—151no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—152no—
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
336C22×C3×C4—51no—
337C22×C3×C4—58no—
338C22×C3×C4—54no—
339C22×C3×C4—52no—
340C22×C3×C4—58no—
341C22×C3×C4—108no—
342C22×C3×C4C22×D512yes—
343C22×C3×C4C22×D511yescharacteristic
344C22×Dic3—51no—
345C22×Dic3—52no—
346C22×Dic3—54no—
347C22×Dic3—58no—
348C22×Dic3—108no—
349C22×Dic3—104no—
350C22×Dic3C22×D511yescharacteristic
351C22×Dic3C22×D512yes—
352C2×C4×D3—24no—
353C2×C4×D3—54no—
354C2×C4×D3—54no—
355C2×C4×D3—54no—
356C2×C4×D3—1032no—
357C2×C4×D3—104no—
358C2×C4×D3—104no—
359C2×C4×D3—104no—
360C2×C4×D3C22×D514yes—
361C2×Dic6—24no—
362C2×Dic6—54no—
363C2×Dic6—58no—
364C2×Dic6—1032no—
365C2×Dic6—108no—
366C2×Dic6—104no—
367C2×Dic6C22×D514yescomplemented
368C3×C4⋊C4—58no—
369C3×C4⋊C4—54no—
370C3×C4⋊C4C22×D514yescomplemented
371(C2×D3)⋊C4—58no—
372(C2×D3)⋊C4—58no—
373(C2×D3)⋊C4—58no—
374(C2×D3)⋊C4C22×D518yes—
375C4⋊Dic3—58no—
376C4⋊Dic3—58no—
377C4⋊Dic3—58no—
378C4⋊Dic3C22×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×D5C2×D1214yes—
393C22×D5#23714yes—
394C22×D5D3×Q814yes—
395C22×D5C23×D312yes—
396C5×Q8—68no—
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×D1214yes—
404C2×C4×C5C23×D314yes—
405C2×C4×C5C23×D312yes—
406C2×Dic5—24no—
407C2×Dic5—32no—
408C2×Dic5—34no—
409C2×Dic5—64no—
410C2×Dic5—62no—
411C2×Dic5—68no—
412C2×Dic5C2×D1214yes—
413C2×Dic5C23×D314yes—
414C2×Dic5C23×D312yes—
415C4×D5—216no—
416C4×D5—68no—
417C4×D5—616no—
418C4×D5—68no—
419C4×D5—68no—
420C4×D5C2×D12116yes—
421Dic10—68no—
422Dic10—616no—
423C25—151no—
424C22×Q8—31no—
425C22×Q8—152no—
426C22×Q8—158no—
427C22×Q8—151no—
428C22×Q8—308no—
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—52no—
447C2×C4⋊C4—51no—
448C2×C4⋊C4—58no—
449C2×C4⋊C4—1516no—
450C2×C4⋊C4—152no—
451C2×C4⋊C4—152no—
452C2×C4⋊C4—152no—
453C2×C4⋊C4D3×D511yescharacteristic, complemented
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—
483C2×C3×C4—24no—
484C2×C3×C4—54no—
485C2×C3×C4—52no—
486C2×C3×C4—516no—
487C2×C3×C4—54no—
488C2×C3×C4—1016no—
489C2×C3×C4—104no—
490C2×C3×C4D4×D514yes—
491C2×C3×C4C23×D514yes—
492C2×C3×C4C23×D512yes—
493C2×Dic3—24no—
494C2×Dic3—22no—
495C2×Dic3—52no—
496C2×Dic3—54no—
497C2×Dic3—1016no—
498C2×Dic3—108no—
499C2×Dic3—104no—
500C2×Dic3—102no—
501C2×Dic3C23×D512yes—
502C2×Dic3C23×D514yes—
503C4×D3—28no—
504C4×D3—108no—
505C4×D3—108no—
506C4×D3—108no—
507Dic6—28no—
508Dic6—1016no—
509Dic6—108no—
510C22×C5—34no—
511C22×C5—62no—
512C22×C5—62no—
513C22×C5—68no—
514C22×C5C22×D1212yes—
515C22×C5C2×#23712yes—
516C22×C5C2×D3×Q812yes—
517C22×C5C24×D311yescharacteristic
518C2×D5—34no—
519C2×D5—62no—
520C2×D5—62no—
521C2×D5—68no—
522C2×D5—632no—
523C2×D5#897116yesdirect product factor
524C2×D5C22×D1214yes—
525C2×D5C2×#23714yes—
526C2×D5C2×D3×Q814yes—
527C4×C5—24no—
528C4×C5—64no—
529C4×C5—62no—
530C4×C5C22×D1214yes—
531Dic5—24no—
532Dic5—64no—
533Dic5—62no—
534Dic5C22×D1214yes—
535C24—31no—
536C24—51no—
537C24—154no—
538C24—158no—
539C24—151no—
540C24—304no—
541C24—304no—
542C2×Q8—34no—
543C2×Q8—64no—
544C2×Q8—158no—
545C2×Q8—154no—
546C2×Q8—308no—
547C2×Q8—3032no—
548C2×Q8—304no—
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—58no—
576C4⋊C4—54no—
577C4⋊C4—158no—
578C4⋊C4—158no—
579C4⋊C4—158no—
580C4⋊C4C2×D3×D514yescomplemented
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—24no—
608Dic3—22no—
609Dic3—104no—
610Dic3—102no—
611C2×C5—64no—
612C2×C5C2×#89714yescomplemented
613C2×C5C23×D1211yescharacteristic
614C2×C5C22×#23711yescharacteristic
615C2×C5C22×D3×Q811yescharacteristic
616D5—64no—
617D5C2×#89718yesdirect 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—68no—
636Q8—3016no—
637Q8—308no—
638C2×C4—24no—
639C2×C4—34no—
640C2×C4—32no—
641C2×C4—54no—
642C2×C4—52no—
643C2×C4—516no—
644C2×C4—54no—
645C2×C4—62no—
646C2×C4—64no—
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—302no—
657C2×C4—304no—
658C2×C4—308no—
659C2×C4D5×D1214yes—
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×#89711yescharacteristic, 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—
683C22C2×D5×D1212yes—
684C22D5×#23712yes—
685C22D3×Q8×D512yes—
686C22C23×D3×D511yescharacteristic
687C4—24no—
688C4—54no—
689C4—62no—
690C4—64no—
691C4—104no—
692C4—302no—
693C4—304no—
694C4C2×D5×D1214yes—
695C3C2×D5×C22⋊Q811yescharacteristic, complemented, Sylow
696C2—58no—
697C2—64no—
698C2—304no—
699C2D5×#89714yesdirect product factor
700C2C22×D5×D1211yescharacteristic
701C2C2×D5×#23711yescharacteristic
702C2C2×D3×Q8×D511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C22×C22⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×D5×Dic6C2semidirect
3. C2×#91786C2semidirect
4. C2×C5×#897C2semidirect
5. C2×C3×D5×C4⋊C4C2semidirect
7. C2×#91419C2semidirect
8. C2×#91417C2semidirect
9. C2×D5×C4⋊Dic3C2semidirect
10. C2×#91383C2semidirect
11. C2×#91365C2semidirect
12. D5×#897C2direct (N × H)
16. C22×Dic30C22semidirect
18. C22×C5×Dic6C22semidirect
21. C22×#1204C22semidirect
29. C2×D5×Dic6C22semidirect
30. C2×C3×C5×C4⋊C4C22semidirect
32. C2×C4⋊Dic15C22semidirect
33. #91786C22semidirect
35. C2×C5×C4⋊Dic3C22semidirect
36. C5×#897C22semidirect
37. C2×C3×C4⋊Dic5C22semidirect
38. C2×C3×#683C22semidirect
39. C3×D5×C4⋊C4C22semidirect
40. C2×#6668C22semidirect
41. C2×#6668C22semidirect
45. #91419C22semidirect
46. #91417C22semidirect
47. D5×C4⋊Dic3C22semidirect
48. #91383C22semidirect
49. #91365C22semidirect
60. C2×D5×C4⋊C4D3semidirect
68. C22×D3×D5Q8semidirect
77. C2×Dic30C23semidirect
83. C2×C5×Dic6C23semidirect
91. C2×#1204C23semidirect
102. C3×C5×C4⋊C4C23semidirect
104. C4⋊Dic15C23semidirect
106. C5×C4⋊Dic3C23semidirect
107. C3×C4⋊Dic5C23semidirect
108. C3×#683C23semidirect
109. #6668C23semidirect
110. #6668C23semidirect
124. C2×#897D5direct (N × H)
143. C2×C5×C4⋊C4C2×D3semidirect
150. C2×C4⋊Dic5C2×D3semidirect
154. C2×#683C2×D3semidirect
158. D5×C4⋊C4C2×D3semidirect
165. C22×D15C2×Q8semidirect
169. C22×C5×D3C2×Q8semidirect
178. C2×D3×D5C2×Q8semidirect
221. C22×Dic6C2×D5semidirect
225. C2×C3×C4⋊C4C2×D5semidirect
235. C2×C4⋊Dic3C2×D5semidirect
241. #897C2×D5direct (N × H)
282. C5×C4⋊C4C22×D3semidirect
288. C4⋊Dic5C22×D3semidirect
291. #683C22×D3semidirect
311. C2×D15C22×Q8semidirect
315. C2×C5×D3C22×Q8semidirect
316. C2×C3×D5C22⋊Q8semidirect
367. C2×Dic6C22×D5semidirect
370. C3×C4⋊C4C22×D5semidirect
378. C4⋊Dic3C22×D5semidirect
453. C2×C4⋊C4D3×D5semidirect
459. C2×C3×C5C2×C22⋊Q8semidirect
464. C3×D5C2×C22⋊Q8semidirect
481. C22×D3Q8×D5semidirect
523. C2×D5#897direct (N × H)
580. C4⋊C4C2×D3×D5semidirect
585. C3×C5C22×C22⋊Q8semidirect
602. C2×D3C2×Q8×D5semidirect
612. C2×C5C2×#897semidirect
617. D5C2×#897direct (N × H)
663. C2×C3D5×C22⋊Q8semidirect
669. C5C22×#897semidirect
695. C3C2×D5×C22⋊Q8semidirect
699. C2D5×#897direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D3×D52
C22×D5×Dic62
C2×#917862
C2×C5×#8972
C2×C3×D5×C4⋊C42
C2×D5×(C2×D3)⋊C42
C2×#914192
C2×#914172
C2×D5×C4⋊Dic32
C2×#913832
C2×#913652
D5×#8972
C2×D5×C22⋊Q83
C22×#8975