Finite Group Databasebeta

← C2×#11755287 #14481721

Subgroups — C2×#11755287 #14481721

Order 1920.

2592 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91835C211yesmaximal, characteristic, complemented
2C2×C5×#946C211yesmaximal, characteristic, complemented
3C2×C3×#4092C211yesmaximal, characteristic, complemented
4#11755287C2116yesmaximal, direct product factor
5C2×#91473C211yesmaximal, characteristic
6C2×D3×#685C211yesmaximal, characteristic
7C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
8C2×#91436C211yesmaximal, characteristic, complemented
9C2×#91430C211yesmaximal, characteristic, complemented
10C2×#91429C211yesmaximal, characteristic, complemented
11C2×#91422C211yesmaximal, characteristic, complemented
12C2×#91419C211yesmaximal, characteristic, complemented
13C2×#91417C211yesmaximal, characteristic, complemented
14C2×#91377C211yesmaximal, characteristic, complemented
15C2×#91352C211yesmaximal, characteristic, complemented
16C2×#91349C211yesmaximal, characteristic, complemented
17C2×#65968—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×C3×C5×Q8C2211yescharacteristic, complemented
20C22×C4×D15C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×#1204C2211yescharacteristic, complemented
24C22×#1204C2211yescharacteristic, complemented
25C22×#1204C2211yescharacteristic, complemented
26C22×#1200C2211yescharacteristic
27C22×D3×Dic5C2211yescharacteristic
28C22×D5×Dic3C2211yescharacteristic
29#91835C2218yescomplemented
30C2×#6714C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×C4⋊Dic15C2211yescharacteristic, complemented
33C2×#6712C2211yescharacteristic, complemented
34C2×#6712C2211yescharacteristic, complemented
35C5×#946C2218yescomplemented
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
39C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
40C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
41C3×#4092C2218yescomplemented
42C2×C3×#685C2211yescharacteristic
43C2×C3×#685C2211yescharacteristic
44C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
45C2×C3×#683C2211yescharacteristic, complemented
46C2×C3×#683C2211yescharacteristic, complemented
47C2×Dic3⋊Dic5C2211yescharacteristic, complemented
48C2×#6669C2211yescharacteristic, complemented
49C2×#6668C2211yescharacteristic, complemented
50C2×#6667C2211yescharacteristic
51C2×#6667C2211yescharacteristic
52C2×(C2×D3)⋊Dic5C2211yescharacteristic
53C2×(C2×D3)⋊Dic5C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55C2×#6665C2211yescharacteristic
56#91473C2218yes—
57D3×#685C2218yes—
58D5×(C2×D3)⋊C4C2218yes—
59#91436C2218yescomplemented
60#91430C2218yescomplemented
61#91429C2218yescomplemented
62#91422C2218yescomplemented
63#91419C2218yescomplemented
64#91417C2218yescomplemented
65#91377C2218yescomplemented
66#91352C2218yescomplemented
67#91349C2218yescomplemented
68C2×#5634—51nomaximal, Hall
69C2×C5×C22⋊Q8—31no—
70C2×#4092—31no—
71C2×#4092D311yescharacteristic, complemented
72C22×#685—31no—
73C2×#4070—31no—
74#65968—316no—
75C2×#4043—31no—
76C2×#4043—31no—
77C2×#4042—31no—
78C2×#4042—31no—
79C2×#4042—31no—
80C2×#4042—31no—
81C2×D5×C22⋊C4—31no—
82C2×D5×C22⋊C4—31no—
83C2×#4024—31no—
84C2×#4024—31no—
85C23×D15C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C3×D5C2311yescharacteristic
88C22×D3×D5—42no—
89C22×D3×D5—42no—
90C22×D3×D5Q818yescomplemented
91C22×D3×D5C2314yes—
92C2×C3×C5×Q8—42no—
93C2×C3×C5×Q8C2314yescomplemented
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C2×C4×D15—42no—
101C2×C4×D15C2314yes—
102C22×C5×Dic3C2311yescharacteristic
103C22×C5×Dic3C2311yescharacteristic
104C22×C5×Dic3C2311yescharacteristic
105C2×C4×C5×D3—42no—
106C2×C4×C5×D3C2314yes—
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C2×C3×C4×D5—42no—
111C2×C3×C4×D5C2314yes—
112C2×#1204—42no—
113C2×#1204—42no—
114C2×#1204—42no—
115C2×#1204C2314yescomplemented
116C2×#1204C2314yescomplemented
117C2×#1204C2314yescomplemented
118C2×#1200—42no—
119C2×#1200C2314yes—
120C2×D3×Dic5—42no—
121C2×D3×Dic5C2314yes—
122C2×D5×Dic3—42no—
123C2×D5×Dic3C2314yes—
124#6714C2314yes—
125#6714C2314yes—
126C4⋊Dic15C2314yescomplemented
127#6712C2314yescomplemented
128#6712C2314yescomplemented
129C5×(C2×D3)⋊C4C2314yes—
130C5×(C2×D3)⋊C4C2314yes—
131C5×C4⋊Dic3C2314yescomplemented
132C5×Dic3⋊C4C2314yescomplemented
133C5×Dic3⋊C4C2314yescomplemented
134C3×#685C2314yes—
135C3×#685C2314yes—
136C3×C4⋊Dic5C2314yescomplemented
137C3×#683C2314yescomplemented
138C3×#683C2314yescomplemented
139Dic3⋊Dic5C2314yescomplemented
140#6669C2314yescomplemented
141#6668C2314yescomplemented
142#6667C2314yes—
143#6667C2314yes—
144(C2×D3)⋊Dic5C2314yes—
145(C2×D3)⋊Dic5C2314yes—
146#6665C2314yes—
147#6665C2314yes—
148C2×C3×C22⋊Q8—51no—
149C2×#946—51no—
150C2×#946D511yescharacteristic, complemented
151C22×(C2×D3)⋊C4—51no—
152C2×#924—51no—
153#5634—516no—
154C2×#897—51no—
155C2×#897—51no—
156C2×#896—51no—
157C2×#896—51no—
158C2×#896—51no—
159C2×#896—51no—
160C2×D3×C22⋊C4—51no—
161C2×D3×C22⋊C4—51no—
162C2×#878—51no—
163C2×#878—51no—
164C24×D5—31no—
165C22×C5×Q8C2×D311yescharacteristic, complemented
166C23×C4×C5—31no—
167C23×Dic5—31no—
168C22×C4×D5—31no—
169C22×C4×D5—31no—
170C22×C4×D5—31no—
171C22×C4×D5C2×D311yescharacteristic
172C22×Dic10—31no—
173C22×Dic10—31no—
174C22×Dic10—31no—
175C5×C22⋊Q8—38no—
176C2×C5×C4⋊C4—31no—
177C2×C5×C4⋊C4—31no—
178C2×C5×C4⋊C4—31no—
179C2×C5×C22⋊C4—31no—
180C2×C5×C22⋊C4—31no—
181C2×C22⋊Dic5—31no—
182C2×C22⋊Dic5—31no—
183#4092—38no—
184#4092C2×D318yescomplemented
185C2×#685—31no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—38no—
192C2×#685C2×D311yescharacteristic
193C2×#685C2×D311yescharacteristic
194C2×C4⋊Dic5—31no—
195C2×C4⋊Dic5—31no—
196C2×C4⋊Dic5C2×D311yescharacteristic, complemented
197#4070—38no—
198C2×#683—31no—
199C2×#683—31no—
200C2×#683—31no—
201C2×#683—31no—
202C2×#683C2×D311yescharacteristic, complemented
203C2×#683C2×D311yescharacteristic, complemented
204#4043—38no—
205#4043—38no—
206#4042—38no—
207#4042—38no—
208#4042—38no—
209#4042—38no—
210D5×C22⋊C4—38no—
211D5×C22⋊C4—38no—
212#4024—38no—
213#4024—38no—
214C2×#543—151noSylow
215C23×C3×C5C2411yescharacteristic
216C22×D15—22no—
217C22×D15—22no—
218C22×D15C2×Q814yes—
219C22×D15C2412yes—
220C22×C5×D3—22no—
221C22×C5×D3—22no—
222C22×C5×D3C2×Q814yes—
223C22×C5×D3C2412yes—
224C22×C3×D5—22no—
225C22×C3×D5—22no—
226C22×C3×D5C2×Q814yes—
227C22×C3×D5C2412yes—
228C2×D3×D5—416no—
229C2×D3×D5—44no—
230C2×D3×D5—44no—
231C2×D3×D5C2×Q8116yescomplemented
232C3×C5×Q8—44no—
233C2×C3×C4×C5—22no—
234C2×C3×C4×C5—22no—
235C2×C3×C4×C5—22no—
236C2×C3×C4×C5C2412yes—
237C2×C3×C4×C5C2412yes—
238C2×C3×C4×C5C2412yes—
239C2×Dic15—22no—
240C2×Dic15—22no—
241C2×Dic15—22no—
242C2×Dic15C2412yes—
243C2×Dic15C2412yes—
244C2×Dic15C2412yes—
245C4×D15—44no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3—22no—
248C2×C5×Dic3—22no—
249C2×C5×Dic3C2412yes—
250C2×C5×Dic3C2412yes—
251C2×C5×Dic3C2412yes—
252C4×C5×D3—44no—
253C2×C3×Dic5—22no—
254C2×C3×Dic5—22no—
255C2×C3×Dic5—22no—
256C2×C3×Dic5C2412yes—
257C2×C3×Dic5C2412yes—
258C2×C3×Dic5C2412yes—
259C3×C4×D5—44no—
260#1204—44no—
261#1204—44no—
262#1204—44no—
263#1200—44no—
264D3×Dic5—44no—
265D5×Dic3—44no—
266C24×D3—51no—
267C22×C3×Q8C2×D511yescharacteristic, complemented
268C23×C3×C4—51no—
269C23×Dic3—51no—
270C22×C4×D3—51no—
271C22×C4×D3—51no—
272C22×C4×D3—51no—
273C22×C4×D3C2×D511yescharacteristic
274C22×Dic6—51no—
275C22×Dic6—51no—
276C22×Dic6—51no—
277C3×C22⋊Q8—58no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C4⋊C4—51no—
280C2×C3×C4⋊C4—51no—
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×#217—51no—
284C2×#217—51no—
285#946—58no—
286#946C2×D518yescomplemented
287C2×(C2×D3)⋊C4—51no—
288C2×(C2×D3)⋊C4—51no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—58no—
294C2×(C2×D3)⋊C4C2×D511yescharacteristic
295C2×(C2×D3)⋊C4C2×D511yescharacteristic
296C2×C4⋊Dic3—51no—
297C2×C4⋊Dic3—51no—
298C2×C4⋊Dic3C2×D511yescharacteristic, complemented
299#924—58no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4C2×D511yescharacteristic, complemented
305C2×Dic3⋊C4C2×D511yescharacteristic, complemented
306#897—58no—
307#897—58no—
308#896—58no—
309#896—58no—
310#896—58no—
311#896—58no—
312D3×C22⋊C4—58no—
313D3×C22⋊C4—58no—
314#878—58no—
315#878—58no—
316C24×C5—31no—
317C23×D5—31no—
318C23×D5—38no—
319C23×D5—34no—
320C23×D5—122no—
321C23×D5—122no—
322C23×D5C22×D311yescharacteristic
323C2×C5×Q8—42no—
324C2×C5×Q8C22×D314yescomplemented
325C22×C4×C5—31no—
326C22×C4×C5—31no—
327C22×C4×C5—31no—
328C22×C4×C5—34no—
329C22×C4×C5—122no—
330C22×C4×C5C22×D311yescharacteristic
331C22×C4×C5C22×D311yescharacteristic
332C22×C4×C5C22×D311yescharacteristic
333C22×Dic5—31no—
334C22×Dic5—31no—
335C22×Dic5—31no—
336C22×Dic5—34no—
337C22×Dic5—122no—
338C22×Dic5C22×D311yescharacteristic
339C22×Dic5C22×D311yescharacteristic
340C22×Dic5C22×D311yescharacteristic
341C2×C4×D5—34no—
342C2×C4×D5—34no—
343C2×C4×D5—34no—
344C2×C4×D5—42no—
345C2×C4×D5—122no—
346C2×C4×D5—122no—
347C2×C4×D5—122no—
348C2×C4×D5C22×D314yes—
349C2×Dic10—34no—
350C2×Dic10—34no—
351C2×Dic10—34no—
352C2×Dic10—122no—
353C2×Dic10—122no—
354C2×Dic10—122no—
355C5×C4⋊C4—34no—
356C5×C4⋊C4—34no—
357C5×C4⋊C4—34no—
358C5×C22⋊C4—34no—
359C5×C22⋊C4—34no—
360C22⋊Dic5—34no—
361C22⋊Dic5—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367#685—34no—
368#685C22×D314yes—
369#685C22×D314yes—
370C4⋊Dic5—34no—
371C4⋊Dic5—34no—
372C4⋊Dic5C22×D314yescomplemented
373#683—34no—
374#683—34no—
375#683—34no—
376#683—34no—
377#683C22×D314yescomplemented
378#683C22×D314yescomplemented
379#543—1516no—
380C2×C22⋊Q8—31no—
381C2×C22⋊Q8—51no—
382C2×C22⋊Q8—151no—
383C2×C22⋊Q8—151no—
384C2×C22⋊Q8—151no—
385C2×C22⋊Q8—151no—
386C2×C22⋊Q8—151no—
387C2×C22⋊Q8—151no—
388C2×C22⋊Q8—151no—
389C2×C22⋊Q8—151no—
390C2×C22⋊Q8—151no—
391C2×C22⋊Q8—151no—
392C22×C22⋊C4—151no—
393C22×C22⋊C4—151no—
394C22×C22⋊C4—151no—
395C22×C3×C5C22×Q812yes—
396C22×C3×C5H(5,𝔽2)12yes—
397C22×C3×C5H(5,𝔽2)12yes—
398C22×C3×C5C2511yescharacteristic
399C2×D15—28no—
400C2×D15—22no—
401C2×D15—22no—
402C2×D15C22×Q814yes—
403C2×C5×D3—28no—
404C2×C5×D3—22no—
405C2×C5×D3—22no—
406C2×C5×D3C22×Q814yes—
407C2×C3×D5—28no—
408C2×C3×D5—22no—
409C2×C3×D5—22no—
410C2×C3×D5C22×Q814yes—
411D3×D5—416no—
412C3×C4×C5—22no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415Dic15—22no—
416Dic15—22no—
417Dic15—22no—
418C3×Dic5—22no—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C5×Dic3—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C24×C3—51no—
425C23×D3—51no—
426C23×D3—58no—
427C23×D3—54no—
428C23×D3—202no—
429C23×D3—202no—
430C23×D3C22×D511yescharacteristic
431C2×C3×Q8—42no—
432C2×C3×Q8C22×D514yescomplemented
433C22×C3×C4—51no—
434C22×C3×C4—51no—
435C22×C3×C4—51no—
436C22×C3×C4—54no—
437C22×C3×C4—202no—
438C22×C3×C4C22×D511yescharacteristic
439C22×C3×C4C22×D511yescharacteristic
440C22×C3×C4C22×D511yescharacteristic
441C22×Dic3—51no—
442C22×Dic3—51no—
443C22×Dic3—51no—
444C22×Dic3—54no—
445C22×Dic3—202no—
446C22×Dic3C22×D511yescharacteristic
447C22×Dic3C22×D511yescharacteristic
448C22×Dic3C22×D511yescharacteristic
449C2×C4×D3—42no—
450C2×C4×D3—54no—
451C2×C4×D3—54no—
452C2×C4×D3—54no—
453C2×C4×D3—202no—
454C2×C4×D3—202no—
455C2×C4×D3—202no—
456C2×C4×D3C22×D514yes—
457C2×Dic6—54no—
458C2×Dic6—54no—
459C2×Dic6—54no—
460C2×Dic6—202no—
461C2×Dic6—202no—
462C2×Dic6—202no—
463C3×C4⋊C4—54no—
464C3×C4⋊C4—54no—
465C3×C4⋊C4—54no—
466C3×C22⋊C4—54no—
467C3×C22⋊C4—54no—
468#217—54no—
469#217—54no—
470(C2×D3)⋊C4—54no—
471(C2×D3)⋊C4—54no—
472(C2×D3)⋊C4—54no—
473(C2×D3)⋊C4—54no—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4—54no—
476(C2×D3)⋊C4C22×D514yes—
477(C2×D3)⋊C4C22×D514yes—
478C4⋊Dic3—54no—
479C4⋊Dic3—54no—
480C4⋊Dic3C22×D514yescomplemented
481Dic3⋊C4—54no—
482Dic3⋊C4—54no—
483Dic3⋊C4—54no—
484Dic3⋊C4—54no—
485Dic3⋊C4C22×D514yescomplemented
486Dic3⋊C4C22×D514yescomplemented
487C23×C5—34no—
488C23×C5—32no—
489C23×C5—62no—
490C23×C5—62no—
491C23×C5C23×D311yescharacteristic
492C22×D5—22no—
493C22×D5—22no—
494C22×D5—34no—
495C22×D5—32no—
496C22×D5—316no—
497C22×D5—62no—
498C22×D5—62no—
499C22×D5—1216no—
500C22×D5—124no—
501C22×D5—124no—
502C22×D5D3×Q814yes—
503C22×D5C23×D312yes—
504C5×Q8—44no—
505C2×C4×C5—22no—
506C2×C4×C5—22no—
507C2×C4×C5—22no—
508C2×C4×C5—32no—
509C2×C4×C5—32no—
510C2×C4×C5—32no—
511C2×C4×C5—62no—
512C2×C4×C5—62no—
513C2×C4×C5—62no—
514C2×C4×C5—124no—
515C2×C4×C5C23×D312yes—
516C2×C4×C5C23×D312yes—
517C2×C4×C5C23×D312yes—
518C2×Dic5—22no—
519C2×Dic5—22no—
520C2×Dic5—22no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—62no—
525C2×Dic5—62no—
526C2×Dic5—62no—
527C2×Dic5—124no—
528C2×Dic5C23×D312yes—
529C2×Dic5C23×D312yes—
530C2×Dic5C23×D312yes—
531C4×D5—44no—
532C4×D5—124no—
533C4×D5—124no—
534C4×D5—124no—
535Dic10—124no—
536Dic10—124no—
537Dic10—124no—
538C25—151no—
539C22×Q8—151no—
540C22×Q8—151no—
541C22×Q8—151no—
542C22×Q8D3×D511yescharacteristic, complemented
543C23×C4—31no—
544C23×C4—51no—
545C23×C4—151no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4—151no—
549C22⋊Q8—38no—
550C22⋊Q8—58no—
551C22⋊Q8—158no—
552C22⋊Q8—158no—
553C22⋊Q8—158no—
554C22⋊Q8—158no—
555C22⋊Q8—158no—
556C22⋊Q8—158no—
557C22⋊Q8—158no—
558C22⋊Q8—158no—
559C22⋊Q8—158no—
560C22⋊Q8—158no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—31no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—51no—
565C2×C4⋊C4—51no—
566C2×C4⋊C4—51no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C4⋊C4—151no—
570C2×C4⋊C4—151no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4—151no—
573C2×C22⋊C4—31no—
574C2×C22⋊C4—31no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—158no—
578C2×C22⋊C4—158no—
579C2×C22⋊C4—158no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4—151no—
587C2×C22⋊C4—151no—
588C2×C3×C5#54314yescomplemented
589C2×C3×C5C23×Q811yescharacteristic
590C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
591C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
592D15—24no—
593C3×D5—24no—
594C5×D3—24no—
595C23×C3—54no—
596C23×C3—52no—
597C23×C3—102no—
598C23×C3—102no—
599C23×C3C23×D511yescharacteristic
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—54no—
603C22×D3—52no—
604C22×D3—516no—
605C22×D3—102no—
606C22×D3—102no—
607C22×D3—2016no—
608C22×D3—204no—
609C22×D3—204no—
610C22×D3Q8×D514yes—
611C22×D3C23×D512yes—
612C3×Q8—44no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—52no—
617C2×C3×C4—52no—
618C2×C3×C4—52no—
619C2×C3×C4—102no—
620C2×C3×C4—102no—
621C2×C3×C4—102no—
622C2×C3×C4—204no—
623C2×C3×C4C23×D512yes—
624C2×C3×C4C23×D512yes—
625C2×C3×C4C23×D512yes—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—52no—
630C2×Dic3—52no—
631C2×Dic3—52no—
632C2×Dic3—102no—
633C2×Dic3—102no—
634C2×Dic3—102no—
635C2×Dic3—204no—
636C2×Dic3C23×D512yes—
637C2×Dic3C23×D512yes—
638C2×Dic3C23×D512yes—
639C4×D3—44no—
640C4×D3—204no—
641C4×D3—204no—
642C4×D3—204no—
643Dic6—204no—
644Dic6—204no—
645Dic6—204no—
646C22×C5—34no—
647C22×C5—68no—
648C22×C5—62no—
649C22×C5—62no—
650C22×C5#100412yes—
651C22×C5C2×D3×Q812yes—
652C22×C5#100912yes—
653C22×C5C24×D311yescharacteristic
654C2×D5—28no—
655C2×D5—22no—
656C2×D5—22no—
657C2×D5—34no—
658C2×D5—68no—
659C2×D5—62no—
660C2×D5—62no—
661C2×D5—1216no—
662C2×D5C2×D3×Q814yes—
663C4×C5—22no—
664C4×C5—22no—
665C4×C5—22no—
666C4×C5—62no—
667C4×C5—62no—
668C4×C5—62no—
669Dic5—22no—
670Dic5—22no—
671Dic5—22no—
672Dic5—62no—
673Dic5—62no—
674Dic5—62no—
675C24—31no—
676C24—51no—
677C24—154no—
678C24—158no—
679C24—151no—
680C24—602no—
681C24—602no—
682C2×Q8—42no—
683C2×Q8—154no—
684C2×Q8—154no—
685C2×Q8—154no—
686C2×Q8—602no—
687C2×Q8—602no—
688C2×Q8—602no—
689C2×Q8C2×D3×D514yescomplemented
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—34no—
694C22×C4—51no—
695C22×C4—51no—
696C22×C4—51no—
697C22×C4—54no—
698C22×C4—122no—
699C22×C4—154no—
700C22×C4—154no—
701C22×C4—154no—
702C22×C4—151no—
703C22×C4—151no—
704C22×C4—151no—
705C22×C4—154no—
706C22×C4—202no—
707C22×C4—602no—
708C22×C4—602no—
709C22×C4—602no—
710C22×C4—602no—
711C22×C4C2×D3×D511yescharacteristic
712C22×C4C2×D3×D511yescharacteristic
713C22×C4C2×D3×D511yescharacteristic
714C4⋊C4—34no—
715C4⋊C4—34no—
716C4⋊C4—34no—
717C4⋊C4—54no—
718C4⋊C4—54no—
719C4⋊C4—54no—
720C4⋊C4—154no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4—154no—
726C22⋊C4—34no—
727C22⋊C4—34no—
728C22⋊C4—54no—
729C22⋊C4—54no—
730C22⋊C4—154no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C22⋊C4—154no—
737C22⋊C4—154no—
738C3×C5C2×#54311yescharacteristic, complemented, Hall
739C22×C3—54no—
740C22×C3—108no—
741C22×C3—102no—
742C22×C3—102no—
743C22×C3#414412yes—
744C22×C3C2×Q8×D512yes—
745C22×C3#414912yes—
746C22×C3C24×D511yescharacteristic
747C2×D3—28no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—54no—
751C2×D3—108no—
752C2×D3—102no—
753C2×D3—102no—
754C2×D3—2016no—
755C2×D3C2×Q8×D514yes—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—102no—
760C3×C4—102no—
761C3×C4—102no—
762Dic3—22no—
763Dic3—22no—
764Dic3—22no—
765Dic3—102no—
766Dic3—102no—
767Dic3—102no—
768C2×C5—64no—
769C2×C5#563414yescomplemented
770C2×C5C2×#100411yescharacteristic
771C2×C5C22×D3×Q811yescharacteristic
772C2×C5C2×#100911yescharacteristic
773D5—24no—
774D5—64no—
775C23—34no—
776C23—32no—
777C23—54no—
778C23—52no—
779C23—62no—
780C23—62no—
781C23—102no—
782C23—102no—
783C23—1516no—
784C23—154no—
785C23—152no—
786C23—302no—
787C23—302no—
788C23—604no—
789C23—6016no—
790C23—604no—
791C23C22×D3×D511yescharacteristic
792Q8—44no—
793Q8—604no—
794Q8—604no—
795Q8—604no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—32no—
800C2×C4—32no—
801C2×C4—32no—
802C2×C4—52no—
803C2×C4—52no—
804C2×C4—52no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—102no—
809C2×C4—102no—
810C2×C4—102no—
811C2×C4—124no—
812C2×C4—152no—
813C2×C4—152no—
814C2×C4—152no—
815C2×C4—204no—
816C2×C4—302no—
817C2×C4—302no—
818C2×C4—302no—
819C2×C4—604no—
820C2×C4—604no—
821C2×C4—604no—
822C2×C4—604no—
823C2×C4C22×D3×D512yes—
824C2×C4C22×D3×D512yes—
825C2×C4C22×D3×D512yes—
826C2×C3—104no—
827C2×C3#6596814yescomplemented
828C2×C3C2×#414411yescharacteristic
829C2×C3C22×Q8×D511yescharacteristic
830C2×C3C2×#414911yescharacteristic
831D3—24no—
832D3—104no—
833C5C2×#563411yescharacteristic, complemented, Sylow
834C22—34no—
835C22—54no—
836C22—62no—
837C22—68no—
838C22—62no—
839C22—102no—
840C22—108no—
841C22—102no—
842C22—154no—
843C22—302no—
844C22—308no—
845C22—302no—
846C22—6016no—
847C22D3×Q8×D512yes—
848C22#9203512yes—
849C22#9204912yes—
850C22C23×D3×D511yescharacteristic
851C4—22no—
852C4—22no—
853C4—22no—
854C4—62no—
855C4—62no—
856C4—62no—
857C4—102no—
858C4—102no—
859C4—102no—
860C4—302no—
861C4—302no—
862C4—302no—
863C3C2×#6596811yescharacteristic, complemented, Sylow
864C2—64no—
865C2—104no—
866C2—304no—
867C2#1175528714yesdirect product factor
868C2C2×D3×Q8×D511yescharacteristic
869C2C2×#9203511yescharacteristic
870C2C2×#9204911yescharacteristic
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×C5C2×#543
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. C2×#91835C2semidirect
2. C2×C5×#946C2semidirect
3. C2×C3×#4092C2semidirect
4. #11755287C2direct (N × H)
8. C2×#91436C2semidirect
9. C2×#91430C2semidirect
10. C2×#91429C2semidirect
11. C2×#91422C2semidirect
12. C2×#91419C2semidirect
13. C2×#91417C2semidirect
14. C2×#91377C2semidirect
15. C2×#91352C2semidirect
16. C2×#91349C2semidirect
19. C22×C3×C5×Q8C22semidirect
23. C22×#1204C22semidirect
24. C22×#1204C22semidirect
25. C22×#1204C22semidirect
29. #91835C22semidirect
32. C2×C4⋊Dic15C22semidirect
33. C2×#6712C22semidirect
34. C2×#6712C22semidirect
35. C5×#946C22semidirect
38. C2×C5×C4⋊Dic3C22semidirect
39. C2×C5×Dic3⋊C4C22semidirect
40. C2×C5×Dic3⋊C4C22semidirect
41. C3×#4092C22semidirect
44. C2×C3×C4⋊Dic5C22semidirect
45. C2×C3×#683C22semidirect
46. C2×C3×#683C22semidirect
47. C2×Dic3⋊Dic5C22semidirect
48. C2×#6669C22semidirect
49. C2×#6668C22semidirect
59. #91436C22semidirect
60. #91430C22semidirect
61. #91429C22semidirect
62. #91422C22semidirect
63. #91419C22semidirect
64. #91417C22semidirect
65. #91377C22semidirect
66. #91352C22semidirect
67. #91349C22semidirect
71. C2×#4092D3semidirect
90. C22×D3×D5Q8semidirect
93. C2×C3×C5×Q8C23semidirect
115. C2×#1204C23semidirect
116. C2×#1204C23semidirect
117. C2×#1204C23semidirect
126. C4⋊Dic15C23semidirect
127. #6712C23semidirect
128. #6712C23semidirect
131. C5×C4⋊Dic3C23semidirect
132. C5×Dic3⋊C4C23semidirect
133. C5×Dic3⋊C4C23semidirect
136. C3×C4⋊Dic5C23semidirect
137. C3×#683C23semidirect
138. C3×#683C23semidirect
139. Dic3⋊Dic5C23semidirect
140. #6669C23semidirect
141. #6668C23semidirect
150. C2×#946D5semidirect
165. C22×C5×Q8C2×D3semidirect
184. #4092C2×D3semidirect
196. C2×C4⋊Dic5C2×D3semidirect
202. C2×#683C2×D3semidirect
203. C2×#683C2×D3semidirect
231. C2×D3×D5C2×Q8semidirect
267. C22×C3×Q8C2×D5semidirect
286. #946C2×D5semidirect
298. C2×C4⋊Dic3C2×D5semidirect
304. C2×Dic3⋊C4C2×D5semidirect
305. C2×Dic3⋊C4C2×D5semidirect
324. C2×C5×Q8C22×D3semidirect
372. C4⋊Dic5C22×D3semidirect
377. #683C22×D3semidirect
378. #683C22×D3semidirect
432. C2×C3×Q8C22×D5semidirect
480. C4⋊Dic3C22×D5semidirect
485. Dic3⋊C4C22×D5semidirect
486. Dic3⋊C4C22×D5semidirect
542. C22×Q8D3×D5semidirect
588. C2×C3×C5#543semidirect
689. C2×Q8C2×D3×D5semidirect
738. C3×C5C2×#543semidirect
769. C2×C5#5634semidirect
827. C2×C3#65968semidirect
833. C5C2×#5634semidirect
863. C3C2×#65968semidirect
867. C2#11755287direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918352
C2×C5×#9462
C2×C3×#40922
#117552872
C2×#914732
C2×D3×#6852
C2×D5×(C2×D3)⋊C42
C2×#914362
C2×#914302
C2×#914292
C2×#914222
C2×#914192
C2×#914172
C2×#913772
C2×#913522
C2×#913492
C2×#659683
C2×#56345