Finite Group Databasebeta

← C2×#11754874 #14483313

Subgroups — C2×#11754874 #14483313

Order 1920.

2656 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91824C211yesmaximal, characteristic, complemented
2C2×C5×#937C211yesmaximal, characteristic
3C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
4C2×#91574C211yesmaximal, characteristic, complemented
5C2×#91555C211yesmaximal, characteristic, complemented
6C2×D3×C22⋊Dic5C211yesmaximal, characteristic, complemented
7C2×Dic5×#67C211yesmaximal, characteristic, complemented
8C2×#91539C211yesmaximal, characteristic, complemented
9C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
10C2×#91532C211yesmaximal, characteristic, complemented
11C2×#91525C211yesmaximal, characteristic, complemented
12#11754874C2116yesmaximal, direct product factor
13C2×#91436C211yesmaximal, characteristic, complemented
14C2×#91398C211yesmaximal, characteristic, complemented
15C2×#91372C211yesmaximal, characteristic, complemented
16C2×#91341C211yesmaximal, characteristic, complemented
17C2×#65921—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C23×Dic15C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C23×C3×Dic5C2211yescharacteristic, complemented
25C22×#1204C2211yescharacteristic, complemented
26C22×D3×Dic5C2211yescharacteristic
27C22×D3×Dic5C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6719C2211yescharacteristic, complemented
30C2×#6719C2211yescharacteristic, complemented
31#91824C2218yescomplemented
32C2×#6712C2211yescharacteristic, complemented
33C2×#6712C2211yescharacteristic, complemented
34C2×C5×#217C2211yescharacteristic
35C5×#937C2218yes—
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×C22⋊Dic5C2211yescharacteristic
39C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
40C3×D4×Dic5C2218yescomplemented
41C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
42C2×C3×C4×Dic5C2211yescharacteristic, complemented
43#91574C2218yescomplemented
44#91555C2218yescomplemented
45D3×C22⋊Dic5C2218yescomplemented
46Dic5×#67C2218yescomplemented
47C2×Dic3⋊Dic5C2211yescharacteristic, complemented
48C2×#6669C2211yescharacteristic, complemented
49C2×#6669C2211yescharacteristic, complemented
50C2×#6669C2211yescharacteristic, complemented
51C2×#6668C2211yescharacteristic, complemented
52#91539C2218yescomplemented
53C2×(C2×D3)⋊Dic5C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×(C2×D3)⋊Dic5C2211yescharacteristic
59C2×(C2×D3)⋊Dic5C2218yescomplemented
60#91532C2218yescomplemented
61C2×Dic3×Dic5C2211yescharacteristic, complemented
62C2×Dic3×Dic5C2211yescharacteristic, complemented
63#91525C2218yescomplemented
64#91436C2218yescomplemented
65#91398C2218yescomplemented
66#91372C2218yescomplemented
67#91341C2218yescomplemented
68C2×#5556—51nomaximal, Hall
69C2×C5×#120—31no—
70C22×C22⋊Dic5—31no—
71C22×C22⋊Dic5—31no—
72C2×#4082—31no—
73C2×#4081—31no—
74C2×#4081—31no—
75C2×#4081—31no—
76C2×D4×Dic5—31no—
77C2×D4×Dic5D311yescharacteristic, complemented
78#65921—316no—
79C2×#4025—31no—
80C2×#4025—31no—
81C2×#4024—31no—
82C2×#4024—31no—
83C2×#4023—31no—
84C2×#4023—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×C5×D3—24no—
88C23×C5×D3—24no—
89C23×C5×D3—42no—
90C23×C5×D3C2311yescharacteristic
91C23×C5×D3C2314yes—
92C23×C5×D3C2311yescharacteristic
93C2×C3×C5×D4—24no—
94C2×C3×C5×D4C2314yes—
95C22×C3×C4×C5C2311yescharacteristic
96C22×Dic15—24no—
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2314yes—
101C22×Dic15C2311yescharacteristic
102C2×C5×#67—24no—
103C2×C5×#67—42no—
104C2×C5×#67C2314yes—
105C2×C5×#67C2314yes—
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C22×C3×Dic5—42no—
109C22×C3×Dic5—42no—
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2314yes—
115C22×C3×Dic5C2314yescomplemented
116C2×#1204—42no—
117C2×#1204C2314yescomplemented
118C2×D3×Dic5—24no—
119C2×D3×Dic5—42no—
120C2×D3×Dic5C2314yes—
121C2×D3×Dic5C2314yes—
122#6719C2314yes—
123#6719C2314yescomplemented
124#6719C2314yescomplemented
125#6712C2314yescomplemented
126#6712C2314yescomplemented
127C5×#217C2314yes—
128C5×(C2×D3)⋊C4C2314yes—
129C5×(C2×D3)⋊C4C2314yes—
130C3×C22⋊Dic5C2314yes—
131C3×C22⋊Dic5C2314yescomplemented
132C3×C4⋊Dic5C2314yescomplemented
133C3×C4×Dic5C2314yescomplemented
134Dic3⋊Dic5C2314yescomplemented
135#6669C2314yescomplemented
136#6669C2314yescomplemented
137#6669C2314yescomplemented
138#6668C2314yescomplemented
139(C2×D3)⋊Dic5C2314yes—
140(C2×D3)⋊Dic5C2314yes—
141(C2×D3)⋊Dic5C2314yes—
142(C2×D3)⋊Dic5C2314yes—
143(C2×D3)⋊Dic5C2314yes—
144(C2×D3)⋊Dic5C2314yes—
145Dic3×Dic5C2314yescomplemented
146Dic3×Dic5C2314yescomplemented
147C2×C3×C4×D4—51no—
148C2×#937D511yescharacteristic
149C2×#935—51no—
150C2×#929—51no—
151C2×C4×#67—51no—
152C22×(C2×D3)⋊C4—51no—
153C2×#924—51no—
154#5556—516no—
155C2×#898—51no—
156C2×#896—51no—
157C2×#885—51no—
158C2×#883—51no—
159C2×D3×C22⋊C4—51no—
160C2×#877—51no—
161C2×#876—51no—
162C2×#872—51no—
163C25×C5—31no—
164C22×C5×D4—31no—
165C22×C5×D4—31no—
166C22×C5×D4C2×D311yescharacteristic
167C23×Dic5—31no—
168C23×Dic5—31no—
169C23×Dic5—31no—
170C23×Dic5C2×D311yescharacteristic
171C23×Dic5C2×D311yescharacteristic, complemented
172C22×Dic10—31no—
173C5×#120—38no—
174C2×C5×C22⋊C4—31no—
175C2×C5×C22⋊C4—31no—
176C2×C5×C22⋊C4—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5—31no—
179C2×C22⋊Dic5—31no—
180C2×C22⋊Dic5—31no—
181C2×C22⋊Dic5—31no—
182C2×C22⋊Dic5—31no—
183C2×C22⋊Dic5—31no—
184C2×C22⋊Dic5—31no—
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5—38no—
187C2×C22⋊Dic5—38no—
188C2×C22⋊Dic5C2×D311yescharacteristic
189C2×C22⋊Dic5C2×D311yescharacteristic, complemented
190#4082—38no—
191#4081—38no—
192#4081—38no—
193#4081—38no—
194D4×Dic5—38no—
195D4×Dic5C2×D318yescomplemented
196C2×C4⋊Dic5—31no—
197C2×C4⋊Dic5C2×D311yescharacteristic, complemented
198C2×#683—31no—
199C2×#683—31no—
200C2×#683—31no—
201C2×#683—31no—
202C2×#683—31no—
203C2×#683—31no—
204C2×C4×Dic5—31no—
205C2×C4×Dic5—31no—
206C2×C4×Dic5C2×D311yescharacteristic, complemented
207#4025—38no—
208#4025—38no—
209#4024—38no—
210#4024—38no—
211#4023—38no—
212#4023—38no—
213C2×#551—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5#4114yes—
220C23×C3×C5C2412yes—
221C23×C3×C5C2412yes—
222C23×C3×C5C2411yescharacteristic
223C22×C5×D3—22no—
224C22×C5×D3—22no—
225C22×C5×D3—28no—
226C22×C5×D3—22no—
227C22×C5×D3—22no—
228C22×C5×D3—22no—
229C22×C5×D3—28no—
230C22×C5×D3—44no—
231C22×C5×D3—416no—
232C22×C5×D3#4114yes—
233C22×C5×D3C2412yes—
234C22×C5×D3C2412yes—
235C3×C5×D4—28no—
236C2×C3×C4×C5—22no—
237C2×C3×C4×C5C2412yes—
238C2×Dic15—22no—
239C2×Dic15—28no—
240C2×Dic15—22no—
241C2×Dic15—22no—
242C2×Dic15—22no—
243C2×Dic15C2412yes—
244C2×Dic15C2412yes—
245C2×Dic15C2412yes—
246C2×Dic15C2412yes—
247C5×#67—28no—
248C5×#67—44no—
249C2×C5×Dic3—22no—
250C2×C5×Dic3—22no—
251C2×C5×Dic3C2412yes—
252C2×C5×Dic3C2412yes—
253C2×C3×Dic5—22no—
254C2×C3×Dic5—22no—
255C2×C3×Dic5—22no—
256C2×C3×Dic5—22no—
257C2×C3×Dic5—44no—
258C2×C3×Dic5—44no—
259C2×C3×Dic5C2412yes—
260C2×C3×Dic5C2412yes—
261C2×C3×Dic5C2412yes—
262C2×C3×Dic5C2412yes—
263#1204—44no—
264D3×Dic5—28no—
265D3×Dic5—44no—
266C24×D3C2×D511yescharacteristic
267C22×C3×D4C2×D511yescharacteristic
268C23×C3×C4—51no—
269C23×C3×C4—51no—
270C22×#67C2×D511yescharacteristic
271C22×#67C2×D511yescharacteristic
272C23×Dic3—51no—
273C22×C4×D3—51no—
274C22×C4×D3—51no—
275C22×Dic6—51no—
276C3×C4×D4—58no—
277C2×C3×C4⋊C4—51no—
278C2×C3×C22⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×C3×C42—51no—
281C2×#217—51no—
282C2×#217—51no—
283C2×#217—51no—
284C2×#217C2×D511yescharacteristic
285#937C2×D518yes—
286#935—58no—
287#929—58no—
288C4×#67—58no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4—58no—
296C2×(C2×D3)⋊C4C2×D511yescharacteristic
297C2×(C2×D3)⋊C4C2×D511yescharacteristic
298C2×C4⋊Dic3—51no—
299#924—58no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4—51no—
305C2×Dic3⋊C4—51no—
306C2×C4×Dic3—51no—
307C2×C4×Dic3—51no—
308#898—58no—
309#896—58no—
310#885—58no—
311#883—58no—
312D3×C22⋊C4—58no—
313#877—58no—
314#876—58no—
315#872—58no—
316C24×C5—31no—
317C24×C5—31no—
318C24×C5—34no—
319C24×C5—64no—
320C24×C5—64no—
321C24×C5—122no—
322C24×C5C22×D311yescharacteristic
323C24×C5C22×D311yescharacteristic
324C2×C5×D4—24no—
325C2×C5×D4—34no—
326C2×C5×D4—34no—
327C2×C5×D4—64no—
328C2×C5×D4—122no—
329C2×C5×D4C22×D314yes—
330C22×C4×C5—31no—
331C22×C4×C5—31no—
332C22×C4×C5C22×D311yescharacteristic
333C22×Dic5—31no—
334C22×Dic5—31no—
335C22×Dic5—31no—
336C22×Dic5—31no—
337C22×Dic5—34no—
338C22×Dic5—34no—
339C22×Dic5—34no—
340C22×Dic5—42no—
341C22×Dic5—42no—
342C22×Dic5—64no—
343C22×Dic5—64no—
344C22×Dic5—122no—
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D311yescharacteristic
348C22×Dic5C22×D311yescharacteristic
349C22×Dic5C22×D314yes—
350C22×Dic5C22×D314yescomplemented
351C2×Dic10—34no—
352C2×Dic10—122no—
353C5×C22⋊C4—34no—
354C5×C22⋊C4—34no—
355C5×C22⋊C4—34no—
356C22⋊Dic5—34no—
357C22⋊Dic5—34no—
358C22⋊Dic5—34no—
359C22⋊Dic5—34no—
360C22⋊Dic5—34no—
361C22⋊Dic5—34no—
362C22⋊Dic5—34no—
363C22⋊Dic5—34no—
364C22⋊Dic5—34no—
365C22⋊Dic5C22×D314yes—
366C22⋊Dic5C22×D314yescomplemented
367C4⋊Dic5—34no—
368C4⋊Dic5C22×D314yescomplemented
369#683—34no—
370#683—34no—
371#683—34no—
372#683—34no—
373#683—34no—
374#683—34no—
375C4×Dic5—34no—
376C4×Dic5—34no—
377C4×Dic5C22×D314yescomplemented
378#551—1516no—
379C2×#126—151no—
380C2×#126—151no—
381C2×#124—151no—
382C2×#123—151no—
383C2×#123—151no—
384C2×#123—151no—
385C2×C22⋊Q8—151no—
386C2×C22⋊Q8—151no—
387C2×#120—31no—
388C2×C4×D4—51no—
389C2×C4×D4—151no—
390C2×#117—151no—
391C2×#117—151no—
392C22×C22⋊C4—151no—
393C22×C22⋊C4—151no—
394C22×C3×C5—28no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5—22no—
400C22×C3×C5—44no—
401C22×C3×C5C2×#4114yes—
402C22×C3×C5C2×#4112yes—
403C22×C3×C5C2×#4112yes—
404C22×C3×C5H(5,𝔽2)12yes—
405C22×C3×C5C2511yescharacteristic
406C2×C5×D3—28no—
407C2×C5×D3—22no—
408C2×C5×D3—22no—
409C2×C5×D3—22no—
410C2×C5×D3—22no—
411C2×C5×D3—22no—
412C2×C5×D3—416no—
413C2×C5×D3—44no—
414C2×C5×D3C2×#4114yes—
415C3×C4×C5—22no—
416Dic15—22no—
417Dic15—22no—
418Dic15—22no—
419Dic15—22no—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C3×Dic5—22no—
423C3×Dic5—22no—
424C5×Dic3—22no—
425C5×Dic3—22no—
426C24×C3C22×D511yescharacteristic
427C24×C3C22×D511yescharacteristic
428C23×D3—24no—
429C23×D3—24no—
430C23×D3—42no—
431C23×D3C22×D511yescharacteristic
432C23×D3C22×D514yes—
433C23×D3C22×D511yescharacteristic
434C2×C3×D4—24no—
435C2×C3×D4C22×D514yes—
436C22×C3×C4—51no—
437C22×C3×C4—51no—
438C22×C3×C4—51no—
439C22×C3×C4—51no—
440C22×C3×C4—54no—
441C22×C3×C4—54no—
442C22×C3×C4—202no—
443C22×C3×C4—202no—
444C22×C3×C4C22×D511yescharacteristic
445C2×#67—24no—
446C2×#67—42no—
447C2×#67C22×D514yes—
448C2×#67C22×D514yes—
449C22×Dic3—54no—
450C22×Dic3—51no—
451C22×Dic3—51no—
452C22×Dic3—51no—
453C22×Dic3—51no—
454C22×Dic3—104no—
455C22×Dic3C22×D511yescharacteristic
456C22×Dic3C22×D511yescharacteristic
457C2×C4×D3—54no—
458C2×C4×D3—54no—
459C2×C4×D3—104no—
460C2×C4×D3—202no—
461C2×Dic6—54no—
462C2×Dic6—202no—
463C3×C4⋊C4—54no—
464C3×C22⋊C4—54no—
465C3×C22⋊C4—54no—
466C3×C42—54no—
467#217—54no—
468#217—54no—
469#217—54no—
470#217C22×D514yes—
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)⋊C4—54no—
477(C2×D3)⋊C4C22×D514yes—
478(C2×D3)⋊C4C22×D514yes—
479C4⋊Dic3—54no—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4—54no—
483Dic3⋊C4—54no—
484Dic3⋊C4—54no—
485Dic3⋊C4—54no—
486C4×Dic3—54no—
487C4×Dic3—54no—
488C23×C5—22no—
489C23×C5—22no—
490C23×C5—22no—
491C23×C5—22no—
492C23×C5—22no—
493C23×C5—34no—
494C23×C5—32no—
495C23×C5—32no—
496C23×C5—68no—
497C23×C5—62no—
498C23×C5—62no—
499C23×C5—68no—
500C23×C5—62no—
501C23×C5—62no—
502C23×C5—62no—
503C23×C5—124no—
504C23×C5—1216no—
505C23×C5#23514yes—
506C23×C5C23×D312yes—
507C23×C5C23×D312yes—
508C23×C5C23×D311yescharacteristic
509C5×D4—28no—
510C5×D4—68no—
511C5×D4—124no—
512C2×C4×C5—22no—
513C2×C4×C5—32no—
514C2×C4×C5—32no—
515C2×C4×C5—62no—
516C2×C4×C5—62no—
517C2×C4×C5C23×D312yes—
518C2×Dic5—22no—
519C2×Dic5—22no—
520C2×Dic5—22no—
521C2×Dic5—22no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—32no—
526C2×Dic5—44no—
527C2×Dic5—44no—
528C2×Dic5—68no—
529C2×Dic5—68no—
530C2×Dic5—62no—
531C2×Dic5—62no—
532C2×Dic5—62no—
533C2×Dic5—62no—
534C2×Dic5—124no—
535C2×Dic5C23×D312yes—
536C2×Dic5C23×D312yes—
537C2×Dic5C23×D312yes—
538C2×Dic5C23×D312yes—
539Dic10—124no—
540C25—31no—
541C22×Q8—151no—
542C22×D4—31no—
543C22×D4—31no—
544C22×D4D3×D511yescharacteristic
545C23×C4—51no—
546C23×C4—51no—
547C23×C4—151no—
548C23×C4—151no—
549C23×C4—151no—
550#126—158no—
551#126—158no—
552#124—158no—
553#123—158no—
554#123—158no—
555#123—158no—
556C22⋊Q8—158no—
557C22⋊Q8—158no—
558#120—38no—
559C4×D4—58no—
560C4×D4—158no—
561#117—158no—
562#117—158no—
563C2×C4⋊C4—51no—
564C2×C4⋊C4—151no—
565C2×C4⋊C4—151no—
566C2×C4⋊C4—151no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C4⋊C4—151no—
570C2×C4⋊C4—151no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—31no—
573C2×C22⋊C4—31no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—158no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—158no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4—151no—
587C2×C42—51no—
588C2×C42—151no—
589C2×C42—151no—
590C2×C3×C5—24no—
591C2×C3×C5—42no—
592C2×C3×C5#55114yescomplemented
593C2×C3×C5C22×#4111yescharacteristic
594C2×C3×C5C22×#4111yescharacteristic
595C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
596C5×D3—24no—
597C5×D3—42no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3#71114yes—
604C23×C3C23×D512yes—
605C23×C3C23×D512yes—
606C23×C3C23×D511yescharacteristic
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—28no—
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—28no—
614C22×D3—44no—
615C22×D3—416no—
616C22×D3#71114yes—
617C22×D3C23×D512yes—
618C22×D3C23×D512yes—
619C3×D4—28no—
620C2×C3×C4—22no—
621C2×C3×C4—52no—
622C2×C3×C4—52no—
623C2×C3×C4—52no—
624C2×C3×C4—52no—
625C2×C3×C4—102no—
626C2×C3×C4—102no—
627C2×C3×C4—102no—
628C2×C3×C4—102no—
629C2×C3×C4—204no—
630C2×C3×C4—204no—
631C2×C3×C4C23×D512yes—
632#67—28no—
633#67—44no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—52no—
637C2×Dic3—52no—
638C2×Dic3—52no—
639C2×Dic3—52no—
640C2×Dic3—102no—
641C2×Dic3—108no—
642C2×Dic3—102no—
643C2×Dic3—102no—
644C2×Dic3—102no—
645C2×Dic3C23×D512yes—
646C2×Dic3C23×D512yes—
647C4×D3—108no—
648C4×D3—204no—
649Dic6—204no—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—28no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—22no—
656C22×C5—34no—
657C22×C5—44no—
658C22×C5—62no—
659C22×C5—62no—
660C22×C5—68no—
661C22×C5—62no—
662C22×C5—62no—
663C22×C5—62no—
664C22×C5—1216no—
665C22×C5—124no—
666C22×C5C2×#23514yes—
667C22×C5C2×#23512yes—
668C22×C5#100412yes—
669C22×C5D3×#4112yes—
670C22×C5C24×D311yescharacteristic
671C4×C5—22no—
672C4×C5—62no—
673C4×C5—62no—
674Dic5—22no—
675Dic5—22no—
676Dic5—22no—
677Dic5—22no—
678Dic5—62no—
679Dic5—62no—
680Dic5—62no—
681Dic5—62no—
682C24—31no—
683C24—31no—
684C24—34no—
685C24—64no—
686C24—64no—
687C24—122no—
688C24C2×D3×D511yescharacteristic
689C24C2×D3×D511yescharacteristic
690C2×Q8—154no—
691C2×Q8—602no—
692C2×D4—24no—
693C2×D4—34no—
694C2×D4—34no—
695C2×D4—64no—
696C2×D4—122no—
697C2×D4C2×D3×D514yes—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—51no—
701C22×C4—51no—
702C22×C4—51no—
703C22×C4—51no—
704C22×C4—54no—
705C22×C4—54no—
706C22×C4—154no—
707C22×C4—154no—
708C22×C4—154no—
709C22×C4—151no—
710C22×C4—151no—
711C22×C4—151no—
712C22×C4—151no—
713C22×C4—202no—
714C22×C4—202no—
715C22×C4—304no—
716C22×C4—304no—
717C22×C4—602no—
718C22×C4C2×D3×D511yescharacteristic
719C4⋊C4—54no—
720C4⋊C4—154no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4—154no—
726C4⋊C4—154no—
727C22⋊C4—34no—
728C22⋊C4—34no—
729C22⋊C4—34no—
730C22⋊C4—54no—
731C22⋊C4—54no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C22⋊C4—154no—
737C22⋊C4—154no—
738C22⋊C4—154no—
739C22⋊C4—154no—
740C22⋊C4—154no—
741C42—54no—
742C42—154no—
743C42—154no—
744C3×C5C2×#55111yescharacteristic, complemented, Hall
745C22×C3—28no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—44no—
752C22×C3C2×#71112yes—
753C22×C3C2×#71114yes—
754C22×C3C2×#71112yes—
755C22×C3#414412yes—
756C22×C3C24×D511yescharacteristic
757C2×D3—28no—
758C2×D3—22no—
759C2×D3—22no—
760C2×D3—22no—
761C2×D3—22no—
762C2×D3—22no—
763C2×D3—416no—
764C2×D3—44no—
765C2×D3C2×#71114yes—
766C3×C4—22no—
767C3×C4—102no—
768C3×C4—102no—
769C3×C4—102no—
770C3×C4—102no—
771Dic3—22no—
772Dic3—22no—
773Dic3—102no—
774Dic3—102no—
775Dic3—102no—
776Dic3—102no—
777C2×C5—24no—
778C2×C5—42no—
779C2×C5—64no—
780C2×C5—122no—
781C2×C5#555614yescomplemented
782C2×C5C22×#23511yescharacteristic
783C2×C5C2×#100411yescharacteristic
784C2×C5C2×D3×#4111yescharacteristic
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—34no—
791C23—32no—
792C23—32no—
793C23—68no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—68no—
799C23—62no—
800C23—124no—
801C23—1216no—
802C23#678214yes—
803C23C22×D3×D512yes—
804C23C22×D3×D512yes—
805C23C22×D3×D511yescharacteristic
806Q8—604no—
807D4—28no—
808D4—68no—
809D4—124no—
810C2×C4—22no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—52no—
814C2×C4—52no—
815C2×C4—52no—
816C2×C4—52no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—152no—
824C2×C4—152no—
825C2×C4—152no—
826C2×C4—152no—
827C2×C4—204no—
828C2×C4—204no—
829C2×C4—308no—
830C2×C4—302no—
831C2×C4—302no—
832C2×C4—308no—
833C2×C4—302no—
834C2×C4—302no—
835C2×C4—604no—
836C2×C4C22×D3×D512yes—
837C2×C3—24no—
838C2×C3—42no—
839C2×C3#6592114yescomplemented
840C2×C3C22×#71111yescharacteristic
841C2×C3C22×#71111yescharacteristic
842C2×C3C2×#414411yescharacteristic
843D3—24no—
844D3—42no—
845C5C2×#555611yescharacteristic, complemented, Sylow
846C22—28no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—34no—
853C22—44no—
854C22—62no—
855C22—68no—
856C22—62no—
857C22—62no—
858C22—62no—
859C22—62no—
860C22—1216no—
861C22—124no—
862C22D3×#71112yes—
863C22#9202512yes—
864C22C2×#678214yes—
865C22C2×#678212yes—
866C22C23×D3×D511yescharacteristic
867C4—22no—
868C4—62no—
869C4—62no—
870C4—102no—
871C4—102no—
872C4—102no—
873C4—102no—
874C4—302no—
875C4—302no—
876C4—302no—
877C4—302no—
878C3C2×#6592111yescharacteristic, complemented, Sylow
879C2—24no—
880C2—42no—
881C2—64no—
882C2—122no—
883C2#1175487414yesdirect product factor
884C2C2×D3×#71111yescharacteristic
885C2C2×#9202511yescharacteristic
886C2C22×#678211yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
prime radicalC2×C5×#937C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#551
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91824C2semidirect
3. C2×C3×D4×Dic5C2semidirect
4. C2×#91574C2semidirect
5. C2×#91555C2semidirect
6. C2×D3×C22⋊Dic5C2semidirect
7. C2×Dic5×#67C2semidirect
8. C2×#91539C2semidirect
9. C22×(C2×D3)⋊Dic5C2semidirect
10. C2×#91532C2semidirect
11. C2×#91525C2semidirect
12. #11754874C2direct (N × H)
13. C2×#91436C2semidirect
14. C2×#91398C2semidirect
15. C2×#91372C2semidirect
16. C2×#91341C2semidirect
24. C23×C3×Dic5C22semidirect
25. C22×#1204C22semidirect
29. C2×#6719C22semidirect
30. C2×#6719C22semidirect
31. #91824C22semidirect
32. C2×#6712C22semidirect
33. C2×#6712C22semidirect
39. C2×C3×C22⋊Dic5C22semidirect
40. C3×D4×Dic5C22semidirect
41. C2×C3×C4⋊Dic5C22semidirect
42. C2×C3×C4×Dic5C22semidirect
43. #91574C22semidirect
44. #91555C22semidirect
45. D3×C22⋊Dic5C22semidirect
46. Dic5×#67C22semidirect
47. C2×Dic3⋊Dic5C22semidirect
48. C2×#6669C22semidirect
49. C2×#6669C22semidirect
50. C2×#6669C22semidirect
51. C2×#6668C22semidirect
52. #91539C22semidirect
59. C2×(C2×D3)⋊Dic5C22semidirect
60. #91532C22semidirect
61. C2×Dic3×Dic5C22semidirect
62. C2×Dic3×Dic5C22semidirect
63. #91525C22semidirect
64. #91436C22semidirect
65. #91398C22semidirect
66. #91372C22semidirect
67. #91341C22semidirect
77. C2×D4×Dic5D3semidirect
115. C22×C3×Dic5C23semidirect
117. C2×#1204C23semidirect
123. #6719C23semidirect
124. #6719C23semidirect
125. #6712C23semidirect
126. #6712C23semidirect
131. C3×C22⋊Dic5C23semidirect
132. C3×C4⋊Dic5C23semidirect
133. C3×C4×Dic5C23semidirect
134. Dic3⋊Dic5C23semidirect
135. #6669C23semidirect
136. #6669C23semidirect
137. #6669C23semidirect
138. #6668C23semidirect
145. Dic3×Dic5C23semidirect
146. Dic3×Dic5C23semidirect
171. C23×Dic5C2×D3semidirect
189. C2×C22⋊Dic5C2×D3semidirect
195. D4×Dic5C2×D3semidirect
197. C2×C4⋊Dic5C2×D3semidirect
206. C2×C4×Dic5C2×D3semidirect
350. C22×Dic5C22×D3semidirect
366. C22⋊Dic5C22×D3semidirect
368. C4⋊Dic5C22×D3semidirect
377. C4×Dic5C22×D3semidirect
592. C2×C3×C5#551semidirect
744. C3×C5C2×#551semidirect
781. C2×C5#5556semidirect
839. C2×C3#65921semidirect
845. C5C2×#5556semidirect
878. C3C2×#65921semidirect
883. C2#11754874direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918242
C2×C5×#9372
C2×C3×D4×Dic52
C2×#915742
C2×#915552
C2×D3×C22⋊Dic52
C2×Dic5×#672
C2×#915392
C22×(C2×D3)⋊Dic52
C2×#915322
C2×#915252
#117548742
C2×#914362
C2×#913982
C2×#913722
C2×#913412
C2×#659213
C2×#55565