Finite Group Databasebeta

← C2×#11754882 #14483739

Subgroups — C2×#11754882 #14483739

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91827C211yesmaximal, characteristic, complemented
2C2×C5×#939C211yesmaximal, characteristic, complemented
3C2×C3×#4081C211yesmaximal, characteristic, complemented
4C2×#91557C211yesmaximal, characteristic, complemented
5C2×#91557C211yesmaximal, characteristic, complemented
6C2×#91556C211yesmaximal, characteristic, complemented
7C2×#91555C211yesmaximal, characteristic, complemented
8C2×#91552C211yesmaximal, characteristic, complemented
9C2×Dic5×#67C211yesmaximal, characteristic, complemented
10C2×#91530C211yesmaximal, characteristic, complemented
11C2×#91529C211yesmaximal, characteristic, complemented
12#11754882C2116yesmaximal, direct product factor
13C2×#91406C211yesmaximal, characteristic, complemented
14C2×#91404C211yesmaximal, characteristic, complemented
15C2×#91343C211yesmaximal, characteristic, complemented
16C2×#91342C211yesmaximal, characteristic, complemented
17C2×#65948—31nomaximal, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic
24C23×C5×Dic3C2211yescharacteristic
25C23×C3×Dic5C2211yescharacteristic
26C22×#1203C2211yescharacteristic
27C22×#1200C2211yescharacteristic
28C22×#1200C2211yescharacteristic
29C22×D3×Dic5C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C2×#6719C2211yescharacteristic
32#91827C2218yescomplemented
33C2×C4⋊Dic15C2211yescharacteristic
34C2×C5×#217C2211yescharacteristic
35C5×#939C2218yescomplemented
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×Dic3⋊C4C2211yescharacteristic
38C2×C3×C22⋊Dic5C2211yescharacteristic
39C2×C3×C22⋊Dic5C2211yescharacteristic
40C2×C3×C22⋊Dic5C2211yescharacteristic
41C3×#4081C2218yescomplemented
42C2×C3×#683C2211yescharacteristic
43C2×C3×#683C2211yescharacteristic
44#91557C2218yescomplemented
45#91557C2218yescomplemented
46#91556C2218yescomplemented
47#91555C2218yescomplemented
48#91552C2218yescomplemented
49Dic5×#67C2218yescomplemented
50C2×Dic3⋊Dic5C2211yescharacteristic
51C2×Dic3⋊Dic5C2211yescharacteristic
52C2×Dic3⋊Dic5C2211yescharacteristic
53C2×#6669C2211yescharacteristic
54C2×#6669C2211yescharacteristic
55C2×#6668C2211yescharacteristic
56C2×#6667C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×(C2×D3)⋊Dic5C2211yescharacteristic
59#91530C2218yescomplemented
60#91529C2218yescomplemented
61C2×Dic3×Dic5C2211yescharacteristic
62C2×Dic3×Dic5C2211yescharacteristic
63C2×Dic3×Dic5C2211yescharacteristic
64#91406C2218yescomplemented
65#91404C2218yescomplemented
66#91343C2218yescomplemented
67#91342C2218yescomplemented
68C2×#5661—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4084—31no—
71C2×#4084—31no—
72C2×#4084—31no—
73C2×#4081—31no—
74C2×#4081D311yescharacteristic, complemented
75C2×D4×Dic5—31no—
76C2×C4×C22⋊D5—31no—
77C2×#4072—31no—
78#65948—316no—
79C2×D5×C4⋊C4—31no—
80C2×#4036—31no—
81C2×#4027—31no—
82C2×#4027—31no—
83C2×#4025—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C2×C3×C5×D4—42no—
90C2×C3×C5×D4C2314yes—
91C22×C3×C4×C5C2311yescharacteristic
92C2×#1220—24no—
93C2×#1220—24no—
94C2×#1220C2314yes—
95C2×#1220C2314yes—
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C2×C4×D15—42no—
100C2×C4×D15C2314yes—
101C2×C5×#67—24no—
102C2×C5×#67—42no—
103C2×C5×#67C2314yes—
104C2×C5×#67C2314yes—
105C22×C5×Dic3—24no—
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2314yes—
109C22×C5×Dic3C2311yescharacteristic
110C22×C3×Dic5—42no—
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2314yes—
116C2×#1203—24no—
117C2×#1203C2314yes—
118C2×#1200—24no—
119C2×#1200—42no—
120C2×#1200C2314yes—
121C2×#1200C2314yes—
122C2×D3×Dic5—42no—
123C2×D3×Dic5C2314yes—
124#6719C2314yes—
125#6719C2314yes—
126C4⋊Dic15C2314yes—
127C5×#217C2314yes—
128C5×(C2×D3)⋊C4C2314yes—
129C5×Dic3⋊C4C2314yes—
130C3×C22⋊Dic5C2314yes—
131C3×C22⋊Dic5C2314yes—
132C3×C22⋊Dic5C2314yes—
133C3×#683C2314yes—
134C3×#683C2314yes—
135Dic3⋊Dic5C2314yes—
136Dic3⋊Dic5C2314yes—
137Dic3⋊Dic5C2314yes—
138#6669C2314yes—
139#6669C2314yes—
140#6668C2314yes—
141#6667C2314yes—
142(C2×D3)⋊Dic5C2314yes—
143(C2×D3)⋊Dic5C2314yes—
144Dic3×Dic5C2314yes—
145Dic3×Dic5C2314yes—
146Dic3×Dic5C2314yes—
147C2×C3×#123—51no—
148C2×#939D511yescharacteristic, complemented
149C2×#938—51no—
150C2×C4×#67—51no—
151C2×C4×#67—51no—
152#5661—516no—
153C2×#898—51no—
154C2×#893—51no—
155C2×D3×C4⋊C4—51no—
156C2×#889—51no—
157C2×#884—51no—
158C2×#884—51no—
159C2×#883—51no—
160C2×#67⋊C4—51no—
161C2×#879—51no—
162C2×#877—51no—
163C22×C5×D4—31no—
164C22×C5×D4—31no—
165C22×C5×D4C2×D311yescharacteristic
166C23×C4×C5—31no—
167C22×C22⋊D5—31no—
168C22×C22⋊D5—31no—
169C22×C22⋊D5—31no—
170C23×Dic5—31no—
171C23×Dic5C2×D311yescharacteristic
172C22×C4×D5—31no—
173C22×C4×D5—31no—
174C22×C4×D5—31no—
175C5×#121—38no—
176C2×C5×C4⋊C4—31no—
177C2×C5×C22⋊C4—31no—
178C2×C5×C22⋊C4—31no—
179C2×C22⋊Dic5—31no—
180C2×C22⋊Dic5—31no—
181C2×C22⋊Dic5—31no—
182C2×C22⋊Dic5—31no—
183C2×C22⋊Dic5C2×D311yescharacteristic
184C2×C22⋊Dic5C2×D311yescharacteristic
185C2×C22⋊Dic5C2×D311yescharacteristic
186#4084—38no—
187#4084—38no—
188#4084—38no—
189#4081—38no—
190#4081C2×D318yescomplemented
191D4×Dic5—38no—
192C4×C22⋊D5—38no—
193C2×#685—31no—
194#4072—38no—
195C2×C4⋊Dic5—31no—
196C2×C4⋊Dic5—31no—
197C2×C4⋊Dic5—31no—
198C2×C4⋊Dic5—31no—
199C2×#683—31no—
200C2×#683—31no—
201C2×#683—31no—
202C2×#683C2×D311yescharacteristic
203C2×#683C2×D311yescharacteristic
204C2×C4×Dic5—31no—
205C2×C4×Dic5—31no—
206C2×C4×Dic5—31no—
207D5×C4⋊C4—38no—
208#4036—38no—
209#4027—38no—
210#4027—38no—
211#4025—38no—
212#4025—38no—
213C2×#553—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5—22no—
220C23×C3×C5C2412yes—
221C23×C3×C5C2412yes—
222C23×C3×C5C2411yescharacteristic
223C22×D15—22no—
224C22×D15—22no—
225C22×D15#4114yes—
226C22×D15C2412yes—
227C22×C5×D3—22no—
228C22×C5×D3—22no—
229C22×C5×D3—22no—
230C22×C5×D3C2412yes—
231C3×C5×D4—44no—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5C2412yes—
234#1220—28no—
235#1220—28no—
236C2×Dic15—22no—
237C2×Dic15—22no—
238C2×Dic15—22no—
239C2×Dic15C2412yes—
240C2×Dic15C2412yes—
241C2×Dic15C2412yes—
242C4×D15—44no—
243C5×#67—28no—
244C5×#67—44no—
245C2×C5×Dic3—22no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3—28no—
248C2×C5×Dic3#4114yes—
249C2×C5×Dic3C2412yes—
250C2×C5×Dic3C2412yes—
251C2×C5×Dic3C2412yes—
252C2×C3×Dic5—22no—
253C2×C3×Dic5—22no—
254C2×C3×Dic5—22no—
255C2×C3×Dic5—22no—
256C2×C3×Dic5—44no—
257C2×C3×Dic5C2412yes—
258C2×C3×Dic5C2412yes—
259C2×C3×Dic5C2412yes—
260C2×C3×Dic5C2412yes—
261#1203—28no—
262#1200—28no—
263#1200—44no—
264D3×Dic5—44no—
265C22×C3×D4C2×D511yescharacteristic
266C23×C3×C4—51no—
267C22×#67—51no—
268C22×#67—51no—
269C22×#67C2×D511yescharacteristic
270C22×#67C2×D511yescharacteristic
271C23×Dic3C2×D511yescharacteristic
272C22×D12—51no—
273C22×C4×D3—51no—
274C22×C4×D3—51no—
275C22×C4×D3—51no—
276C22×C4×D3—51no—
277C3×#123—58no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C4⋊C4—51no—
280C2×C3×C22⋊C4—51no—
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×#217—51no—
284C2×#217—51no—
285C2×#217C2×D511yescharacteristic
286#939C2×D518yescomplemented
287#938—58no—
288C4×#67—58no—
289C4×#67—58no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4C2×D511yescharacteristic
294C2×C4⋊Dic3—51no—
295C2×C4⋊Dic3—51no—
296C2×Dic3⋊C4—51no—
297C2×Dic3⋊C4—51no—
298C2×Dic3⋊C4—51no—
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4C2×D511yescharacteristic
302C2×C4×Dic3—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3—51no—
305#898—58no—
306#893—58no—
307D3×C4⋊C4—58no—
308#889—58no—
309#884—58no—
310#884—58no—
311#883—58no—
312#67⋊C4—58no—
313#879—58no—
314#877—58no—
315C24×C5—31no—
316C24×C5C22×D311yescharacteristic
317C24×C5C22×D311yescharacteristic
318C23×D5—31no—
319C2×C5×D4—34no—
320C2×C5×D4—34no—
321C2×C5×D4—42no—
322C2×C5×D4—64no—
323C2×C5×D4—122no—
324C2×C5×D4C22×D314yes—
325C22×C4×C5—31no—
326C22×C4×C5—31no—
327C22×C4×C5—31no—
328C22×C4×C5—34no—
329C22×C4×C5—64no—
330C22×C4×C5C22×D311yescharacteristic
331C2×C22⋊D5—34no—
332C2×C22⋊D5—34no—
333C2×C22⋊D5—34no—
334C2×C22⋊D5—64no—
335C2×C22⋊D5—64no—
336C2×C22⋊D5—64no—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—34no—
341C22×Dic5—42no—
342C22×Dic5—122no—
343C22×Dic5C22×D311yescharacteristic
344C22×Dic5C22×D311yescharacteristic
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D314yes—
348C2×C4×D5—34no—
349C2×C4×D5—34no—
350C2×C4×D5—34no—
351C2×C4×D5—64no—
352C2×C4×D5—122no—
353C2×C4×D5—122no—
354C5×C4⋊C4—34no—
355C5×C22⋊C4—34no—
356C5×C22⋊C4—34no—
357C22⋊Dic5—34no—
358C22⋊Dic5—34no—
359C22⋊Dic5—34no—
360C22⋊Dic5—34no—
361C22⋊Dic5C22×D314yes—
362C22⋊Dic5C22×D314yes—
363C22⋊Dic5C22×D314yes—
364#685—34no—
365C4⋊Dic5—34no—
366C4⋊Dic5—34no—
367C4⋊Dic5—34no—
368C4⋊Dic5—34no—
369#683—34no—
370#683—34no—
371#683—34no—
372#683C22×D314yes—
373#683C22×D314yes—
374C4×Dic5—34no—
375C4×Dic5—34no—
376C4×Dic5—34no—
377#553—1516no—
378C2×#126—151no—
379C2×#126—151no—
380C2×#125—151no—
381C2×#123—51no—
382C2×#123—151no—
383C2×#121—31no—
384C2×#121—151no—
385C2×#121—151no—
386C2×#121—151no—
387C2×C4×D4—151no—
388C2×C4×D4—151no—
389C2×C4×D4—151no—
390C2×C4×D4—151no—
391C2×#117—151no—
392C22×C4⋊C4—151no—
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5—44no—
400C22×C3×C5—44no—
401C22×C3×C5C2×#4112yes—
402C22×C3×C5C2×#4112yes—
403C22×C3×C5H(5,𝔽2)12yes—
404C22×C3×C5C2511yescharacteristic
405C2×D15—28no—
406C2×D15—22no—
407C2×D15—22no—
408C2×D15C2×#4114yes—
409C2×C5×D3—22no—
410C2×C5×D3—22no—
411C2×C5×D3—22no—
412C2×C5×D3—44no—
413C3×C4×C5—22no—
414Dic15—22no—
415Dic15—22no—
416Dic15—22no—
417C3×Dic5—22no—
418C3×Dic5—22no—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C5×Dic3—22no—
422C5×Dic3—22no—
423C5×Dic3C2×#4114yes—
424C24×C3C22×D511yescharacteristic
425C24×C3C22×D511yescharacteristic
426C23×D3—51no—
427C23×D3C22×D511yescharacteristic
428C2×C3×D4—42no—
429C2×C3×D4C22×D514yes—
430C22×C3×C4—51no—
431C22×C3×C4—51no—
432C22×C3×C4—51no—
433C22×C3×C4—51no—
434C22×C3×C4—54no—
435C22×C3×C4—202no—
436C22×C3×C4C22×D511yescharacteristic
437C2×#67—24no—
438C2×#67—42no—
439C2×#67—54no—
440C2×#67—54no—
441C2×#67—104no—
442C2×#67—104no—
443C2×#67C22×D514yes—
444C2×#67C22×D514yes—
445C22×Dic3—24no—
446C22×Dic3—51no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3C22×D514yes—
450C22×Dic3C22×D511yescharacteristic
451C22×Dic3C22×D511yescharacteristic
452C22×Dic3C22×D511yescharacteristic
453C2×D12—54no—
454C2×D12—104no—
455C2×C4×D3—54no—
456C2×C4×D3—54no—
457C2×C4×D3—54no—
458C2×C4×D3—54no—
459C2×C4×D3—104no—
460C2×C4×D3—202no—
461C2×C4×D3—202no—
462C2×C4×D3—202no—
463C3×C4⋊C4—54no—
464C3×C4⋊C4—54no—
465C3×C22⋊C4—54no—
466C3×C22⋊C4—54no—
467C3×C22⋊C4—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)⋊C4C22×D514yes—
475C4⋊Dic3—54no—
476C4⋊Dic3—54no—
477Dic3⋊C4—54no—
478Dic3⋊C4—54no—
479Dic3⋊C4—54no—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4C22×D514yes—
483C4×Dic3—54no—
484C4×Dic3—54no—
485C4×Dic3—54no—
486C23×C5—22no—
487C23×C5—22no—
488C23×C5—22no—
489C23×C5—22no—
490C23×C5—22no—
491C23×C5—22no—
492C23×C5—32no—
493C23×C5—62no—
494C23×C5—62no—
495C23×C5—62no—
496C23×C5C23×D312yes—
497C23×C5C23×D312yes—
498C23×C5C23×D311yescharacteristic
499C22×D5—34no—
500C22×D5—32no—
501C22×D5—62no—
502C22×D5—62no—
503C5×D4—44no—
504C5×D4—68no—
505C5×D4—124no—
506C2×C4×C5—22no—
507C2×C4×C5—34no—
508C2×C4×C5—32no—
509C2×C4×C5—32no—
510C2×C4×C5—32no—
511C2×C4×C5—68no—
512C2×C4×C5—62no—
513C2×C4×C5—62no—
514C2×C4×C5C23×D312yes—
515C22⋊D5—68no—
516C22⋊D5—68no—
517C22⋊D5—68no—
518C2×Dic5—22no—
519C2×Dic5—22no—
520C2×Dic5—22no—
521C2×Dic5—22no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—44no—
526C2×Dic5—62no—
527C2×Dic5—62no—
528C2×Dic5—62no—
529C2×Dic5—124no—
530C2×Dic5C23×D312yes—
531C2×Dic5C23×D312yes—
532C2×Dic5C23×D312yes—
533C2×Dic5C23×D312yes—
534C4×D5—68no—
535C4×D5—124no—
536C4×D5—124no—
537C22×D4—31no—
538C22×D4—31no—
539C22×D4—151no—
540C22×D4—151no—
541C22×D4—151no—
542C22×D4D3×D511yescharacteristic
543C23×C4—31no—
544C23×C4—51no—
545C23×C4—151no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4—151no—
549#126—158no—
550#126—158no—
551#125—158no—
552#123—58no—
553#123—158no—
554#121—38no—
555#121—158no—
556#121—158no—
557#121—158no—
558C4×D4—158no—
559C4×D4—158no—
560C4×D4—158no—
561C4×D4—158no—
562#117—158no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—51no—
565C2×C4⋊C4—51no—
566C2×C4⋊C4—158no—
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×C4⋊C4—151no—
574C2×C22⋊C4—31no—
575C2×C22⋊C4—31no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—51no—
578C2×C22⋊C4—51no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C42—151no—
585C2×C42—151no—
586C2×C42—151no—
587C2×C3×C5—42no—
588C2×C3×C5—42no—
589C2×C3×C5#55314yescomplemented
590C2×C3×C5C22×#4111yescharacteristic
591C2×C3×C5C22×#4111yescharacteristic
592C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
593D15—24no—
594C5×D3—42no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3C23×D512yes—
602C23×C3C23×D512yes—
603C23×C3C23×D511yescharacteristic
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—54no—
608C22×D3—52no—
609C22×D3—102no—
610C22×D3—102no—
611C22×D3C23×D512yes—
612C3×D4—44no—
613C2×C3×C4—22no—
614C2×C3×C4—52no—
615C2×C3×C4—52no—
616C2×C3×C4—52no—
617C2×C3×C4—52no—
618C2×C3×C4—102no—
619C2×C3×C4—102no—
620C2×C3×C4—102no—
621C2×C3×C4—102no—
622C2×C3×C4—204no—
623C2×C3×C4C23×D512yes—
624#67—28no—
625#67—44no—
626#67—108no—
627#67—108no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—28no—
631C2×Dic3—52no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—102no—
635C2×Dic3—102no—
636C2×Dic3—102no—
637C2×Dic3#71114yes—
638C2×Dic3C23×D512yes—
639C2×Dic3C23×D512yes—
640C2×Dic3C23×D512yes—
641D12—108no—
642C4×D3—108no—
643C4×D3—204no—
644C4×D3—204no—
645C4×D3—204no—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5—22no—
649C22×C5—22no—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—44no—
653C22×C5—44no—
654C22×C5—62no—
655C22×C5—62no—
656C22×C5—62no—
657C22×C5—124no—
658C22×C5#100412yes—
659C22×C5D3×#4112yes—
660C22×C5D3×#4112yes—
661C22×C5C24×D311yescharacteristic
662C2×D5—34no—
663C2×D5—68no—
664C2×D5—62no—
665C2×D5—62no—
666C4×C5—22no—
667C4×C5—34no—
668C4×C5—62no—
669C4×C5—62no—
670Dic5—22no—
671Dic5—22no—
672Dic5—22no—
673Dic5—22no—
674Dic5—62no—
675Dic5—62no—
676Dic5—62no—
677C24—31no—
678C24—151no—
679C24C2×D3×D511yescharacteristic
680C24C2×D3×D511yescharacteristic
681C2×D4—34no—
682C2×D4—34no—
683C2×D4—42no—
684C2×D4—64no—
685C2×D4—122no—
686C2×D4—154no—
687C2×D4—154no—
688C2×D4—154no—
689C2×D4—304no—
690C2×D4—304no—
691C2×D4—304no—
692C2×D4C2×D3×D514yes—
693C22×C4—31no—
694C22×C4—34no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—51no—
701C22×C4—54no—
702C22×C4—64no—
703C22×C4—154no—
704C22×C4—154no—
705C22×C4—154no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—151no—
709C22×C4—154no—
710C22×C4—202no—
711C22×C4—304no—
712C22×C4—602no—
713C22×C4—602no—
714C22×C4—602no—
715C22×C4C2×D3×D511yescharacteristic
716C4⋊C4—34no—
717C4⋊C4—54no—
718C4⋊C4—54no—
719C4⋊C4—154no—
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—54no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C42—154no—
737C42—154no—
738C42—154no—
739C3×C5C2×#55311yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—44no—
747C22×C3—44no—
748C22×C3C2×#71112yes—
749C22×C3#414412yes—
750C22×C3D5×#4112yes—
751C22×C3C24×D511yescharacteristic
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—44no—
756C2×D3—54no—
757C2×D3—108no—
758C2×D3—102no—
759C2×D3—102no—
760C3×C4—22no—
761C3×C4—102no—
762C3×C4—102no—
763C3×C4—102no—
764C3×C4—102no—
765Dic3—22no—
766Dic3—22no—
767Dic3—102no—
768Dic3—102no—
769Dic3—102no—
770Dic3C2×#71114yes—
771C2×C5—42no—
772C2×C5—42no—
773C2×C5—122no—
774C2×C5#566114yescomplemented
775C2×C5C2×#100411yescharacteristic
776C2×C5C2×D3×#4111yescharacteristic
777C2×C5C2×D3×#4111yescharacteristic
778D5—64no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—32no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—154no—
790C23—152no—
791C23—302no—
792C23—302no—
793C23C22×D3×D512yes—
794C23C22×D3×D512yes—
795C23C22×D3×D511yescharacteristic
796D4—44no—
797D4—68no—
798D4—124no—
799D4—308no—
800D4—308no—
801D4—308no—
802C2×C4—22no—
803C2×C4—34no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—52no—
808C2×C4—52no—
809C2×C4—52no—
810C2×C4—52no—
811C2×C4—68no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—102no—
815C2×C4—102no—
816C2×C4—102no—
817C2×C4—102no—
818C2×C4—152no—
819C2×C4—152no—
820C2×C4—152no—
821C2×C4—204no—
822C2×C4—308no—
823C2×C4—302no—
824C2×C4—302no—
825C2×C4—302no—
826C2×C4—604no—
827C2×C4—604no—
828C2×C4—604no—
829C2×C4C22×D3×D512yes—
830C2×C3—42no—
831C2×C3—42no—
832C2×C3#6594814yescomplemented
833C2×C3C22×#71111yescharacteristic
834C2×C3C2×#414411yescharacteristic
835C2×C3C2×D5×#4111yescharacteristic
836D3—42no—
837D3—104no—
838C5C2×#566111yescharacteristic, complemented, Sylow
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—44no—
846C22—44no—
847C22—62no—
848C22—62no—
849C22—62no—
850C22—124no—
851C22—154no—
852C22—302no—
853C22—308no—
854C22—302no—
855C22D3×#71112yes—
856C22#9202412yes—
857C22#9204912yes—
858C22C23×D3×D511yescharacteristic
859C4—22no—
860C4—34no—
861C4—62no—
862C4—62no—
863C4—102no—
864C4—102no—
865C4—102no—
866C4—102no—
867C4—302no—
868C4—302no—
869C4—302no—
870C3C2×#6594811yescharacteristic, complemented, Sylow
871C2—42no—
872C2—42no—
873C2—122no—
874C2—304no—
875C2#1175488214yesdirect product factor
876C2C2×D3×#71111yescharacteristic
877C2C2×#9202411yescharacteristic
878C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#553
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×#91827C2semidirect
2. C2×C5×#939C2semidirect
3. C2×C3×#4081C2semidirect
4. C2×#91557C2semidirect
5. C2×#91557C2semidirect
6. C2×#91556C2semidirect
7. C2×#91555C2semidirect
8. C2×#91552C2semidirect
9. C2×Dic5×#67C2semidirect
10. C2×#91530C2semidirect
11. C2×#91529C2semidirect
12. #11754882C2direct (N × H)
13. C2×#91406C2semidirect
14. C2×#91404C2semidirect
15. C2×#91343C2semidirect
16. C2×#91342C2semidirect
32. #91827C22semidirect
35. C5×#939C22semidirect
41. C3×#4081C22semidirect
44. #91557C22semidirect
45. #91557C22semidirect
46. #91556C22semidirect
47. #91555C22semidirect
48. #91552C22semidirect
49. Dic5×#67C22semidirect
59. #91530C22semidirect
60. #91529C22semidirect
64. #91406C22semidirect
65. #91404C22semidirect
66. #91343C22semidirect
67. #91342C22semidirect
74. C2×#4081D3semidirect
148. C2×#939D5semidirect
190. #4081C2×D3semidirect
286. #939C2×D5semidirect
589. C2×C3×C5#553semidirect
739. C3×C5C2×#553semidirect
774. C2×C5#5661semidirect
832. C2×C3#65948semidirect
838. C5C2×#5661semidirect
870. C3C2×#65948semidirect
875. C2#11754882direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918272
C2×C5×#9392
C2×C3×#40812
C2×#915572
C2×#915562
C2×#915552
C2×#915522
C2×Dic5×#672
C2×#915302
C2×#915292
#117548822
C2×#914062
C2×#914042
C2×#913432
C2×#913422
C2×#659483
C2×#56615