Finite Group Databasebeta

← C2×#11754413 #14483679

Subgroups — C2×#11754413 #14483679

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×C4×#1220C211yesmaximal, characteristic, complemented
2C2×C5×#930C211yesmaximal, characteristic, complemented
3C22×C3×#683C211yesmaximal, characteristic, complemented
4C2×#91566C211yesmaximal, characteristic, complemented
5C2×#91566C211yesmaximal, characteristic, complemented
6C2×Dic5×#67C211yesmaximal, characteristic, complemented
7C2×Dic5×#67C211yesmaximal, characteristic, complemented
8#11754413C2116yesmaximal, direct product factor
9C2×#91423C211yesmaximal, characteristic, complemented
10C2×#91416C211yesmaximal, characteristic, complemented
11C2×#91406C211yesmaximal, characteristic, complemented
12C2×#91400C211yesmaximal, characteristic, complemented
13C2×#91367C211yesmaximal, characteristic, complemented
14C2×#91355C211yesmaximal, characteristic, complemented
15C2×#91337C211yesmaximal, characteristic, complemented
16C2×#91335C211yesmaximal, characteristic, complemented
17C2×#65935—31nomaximal, Hall
18C23×C3×C4×C5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic
23C22×C5×D12C2211yescharacteristic
24C23×C3×Dic5C2211yescharacteristic
25C23×C3×Dic5C2211yescharacteristic
26C22×#1203C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×D3×Dic5C2211yescharacteristic
29C22×D3×Dic5C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C4×#1220C2218yescomplemented
32C2×#6714C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34C2×C4×Dic15C2211yescharacteristic
35C5×#930C2218yescomplemented
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C5×C4⋊Dic3C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×#683C2218yescomplemented
44#91566C2218yescomplemented
45#91566C2218yescomplemented
46Dic5×#67C2218yescomplemented
47Dic5×#67C2218yescomplemented
48C2×Dic3⋊Dic5C2211yescharacteristic
49C2×Dic3⋊Dic5C2211yescharacteristic
50C2×#6668C2211yescharacteristic
51C2×#6668C2211yescharacteristic
52C2×#6667C2211yescharacteristic
53C2×#6667C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic
60#91423C2218yescomplemented
61#91416C2218yescomplemented
62#91406C2218yescomplemented
63#91400C2218yescomplemented
64#91367C2218yescomplemented
65#91355C2218yescomplemented
66#91337C2218yescomplemented
67#91335C2218yescomplemented
68C2×#5514—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4085—31no—
71C2×#4085—31no—
72C2×#4085—31no—
73C2×#4081—31no—
74C2×D4×Dic5—31no—
75C2×D4×Dic5—31no—
76C2×C4×C22⋊D5—31no—
77C22×#683D311yescharacteristic, complemented
78#65935—316no—
79C2×#4044—31no—
80C2×#4035—31no—
81C2×#4029—31no—
82C2×#4027—31no—
83C2×#4025—31no—
84C2×#4023—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C22×C3×C4×C5—42no—
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2314yes—
93C2×#1220—24no—
94C2×#1220C2314yes—
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C2×C4×D15—42no—
99C2×C4×D15C2314yes—
100C2×C5×#67—24no—
101C2×C5×#67—24no—
102C2×C5×#67C2314yes—
103C2×C5×#67C2314yes—
104C22×C5×Dic3C2311yescharacteristic
105C22×C5×Dic3C2311yescharacteristic
106C2×C5×D12—42no—
107C2×C5×D12C2314yes—
108C22×C3×Dic5—24no—
109C22×C3×Dic5—42no—
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2314yes—
114C22×C3×Dic5C2314yes—
115C22×C3×Dic5C2311yescharacteristic
116C2×#1203—24no—
117C2×#1203—42no—
118C2×#1203C2314yes—
119C2×#1203C2314yes—
120C2×D3×Dic5—24no—
121C2×D3×Dic5—42no—
122C2×D3×Dic5C2314yes—
123C2×D3×Dic5C2314yes—
124#6719C2314yes—
125#6714C2314yes—
126#6712C2314yes—
127C4×Dic15C2314yes—
128C5×(C2×D3)⋊C4C2314yes—
129C5×(C2×D3)⋊C4C2314yes—
130C5×C4⋊Dic3C2314yes—
131C3×#683C2314yes—
132C3×#683C2314yes—
133C3×#683C2314yes—
134C3×#683C2314yes—
135Dic3⋊Dic5C2314yes—
136Dic3⋊Dic5C2314yes—
137#6668C2314yes—
138#6668C2314yes—
139#6667C2314yes—
140#6667C2314yes—
141(C2×D3)⋊Dic5C2314yes—
142(C2×D3)⋊Dic5C2314yes—
143(C2×D3)⋊Dic5C2314yes—
144(C2×D3)⋊Dic5C2314yes—
145Dic3×Dic5C2314yes—
146Dic3×Dic5C2314yes—
147C22×C3×C4⋊C4—51no—
148C2×#930—51no—
149C2×#930—51no—
150C2×#930D511yescharacteristic, complemented
151C2×C4×#67—51no—
152C2×C4×#67—51no—
153C2×C4×#67—51no—
154#5514—516no—
155C2×#898—51no—
156C2×#898—51no—
157C2×#895—51no—
158C2×#894—51no—
159C2×#894—51no—
160C2×#893—51no—
161C2×#892—51no—
162C2×#890—51no—
163C22×C5×D4—31no—
164C22×C5×D4—31no—
165C22×C5×D4—31no—
166C23×C4×C5C2×D311yescharacteristic
167C22×C22⋊D5—31no—
168C22×C22⋊D5—31no—
169C22×C22⋊D5—31no—
170C23×Dic5—31no—
171C23×Dic5—31no—
172C23×Dic5C2×D311yescharacteristic
173C23×Dic5C2×D311yescharacteristic
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⋊Dic5—31no—
184#4085—38no—
185#4085—38no—
186#4085—38no—
187#4081—38no—
188D4×Dic5—38no—
189D4×Dic5—38no—
190C4×C22⋊D5—38no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×C4⋊Dic5—31no—
195C2×C4⋊Dic5—31no—
196C2×#683—31no—
197C2×#683—31no—
198C2×#683—31no—
199C2×#683C2×D311yescharacteristic
200C2×#683C2×D311yescharacteristic
201C2×#683C2×D311yescharacteristic
202C2×#683C2×D311yescharacteristic
203C2×#683C2×D318yescomplemented
204C2×C4×Dic5—31no—
205C2×C4×Dic5—31no—
206C2×C4×Dic5—31no—
207#4044—38no—
208#4035—38no—
209#4029—38no—
210#4027—38no—
211#4025—38no—
212#4023—38no—
213C2×#553—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5#4114yes—
217C23×C3×C5C2412yes—
218C23×C3×C5C2411yescharacteristic
219C22×D15—22no—
220C22×D15—22no—
221C22×D15—22no—
222C22×D15C2412yes—
223C22×C5×D3—22no—
224C22×C5×D3—22no—
225C22×C5×D3—22no—
226C22×C5×D3—22no—
227C22×C5×D3—22no—
228C22×C5×D3—22no—
229C22×C5×D3C2412yes—
230C22×C5×D3C2412yes—
231C2×C3×C4×C5—22no—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5—44no—
234C2×C3×C4×C5C2412yes—
235C2×C3×C4×C5C2412yes—
236#1220—28no—
237C2×Dic15—22no—
238C2×Dic15—22no—
239C2×Dic15—22no—
240C2×Dic15C2412yes—
241C2×Dic15C2412yes—
242C2×Dic15C2412yes—
243C4×D15—44no—
244C5×#67—28no—
245C5×#67—28no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3—22no—
248C2×C5×Dic3C2412yes—
249C2×C5×Dic3C2412yes—
250C5×D12—44no—
251C2×C3×Dic5—22no—
252C2×C3×Dic5—22no—
253C2×C3×Dic5—22no—
254C2×C3×Dic5—28no—
255C2×C3×Dic5—44no—
256C2×C3×Dic5#4114yes—
257C2×C3×Dic5C2412yes—
258C2×C3×Dic5C2412yes—
259C2×C3×Dic5C2412yes—
260C2×C3×Dic5C2412yes—
261#1203—28no—
262#1203—44no—
263D3×Dic5—28no—
264D3×Dic5—44no—
265C23×C3×C4—51no—
266C23×C3×C4—51no—
267C23×C3×C4C2×D511yescharacteristic
268C22×#67—51no—
269C22×#67C2×D511yescharacteristic
270C22×#67C2×D511yescharacteristic
271C22×D12—51no—
272C22×D12—51no—
273C22×D12C2×D511yescharacteristic
274C22×C4×D3—51no—
275C22×C4×D3—51no—
276C22×C4×D3—51no—
277C2×C3×C4⋊C4—51no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C4⋊C4—51no—
280C2×C3×C4⋊C4—51no—
281C2×C3×C4⋊C4—58no—
282C2×#217—51no—
283#930—58no—
284#930—58no—
285#930C2×D518yescomplemented
286C4×#67—58no—
287C4×#67—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—51no—
296C2×(C2×D3)⋊C4C2×D511yescharacteristic
297C2×(C2×D3)⋊C4C2×D511yescharacteristic
298C2×C4⋊Dic3—51no—
299C2×C4⋊Dic3—51no—
300C2×C4⋊Dic3C2×D511yescharacteristic
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×C4×Dic3—51no—
305C2×C4×Dic3—51no—
306C2×C4×Dic3—51no—
307#898—58no—
308#898—58no—
309#895—58no—
310#894—58no—
311#894—58no—
312#893—58no—
313#892—58no—
314#890—58no—
315C24×C5—31no—
316C24×C5—31no—
317C24×C5C22×D311yescharacteristic
318C23×D5—31no—
319C2×C5×D4—34no—
320C2×C5×D4—34no—
321C2×C5×D4—34no—
322C2×C5×D4—64no—
323C2×C5×D4—64no—
324C2×C5×D4—122no—
325C22×C4×C5—31no—
326C22×C4×C5—31no—
327C22×C4×C5—42no—
328C22×C4×C5C22×D311yescharacteristic
329C22×C4×C5C22×D311yescharacteristic
330C22×C4×C5C22×D314yes—
331C2×C22⋊D5—34no—
332C2×C22⋊D5—34no—
333C2×C22⋊D5—34no—
334C2×C22⋊D5—64no—
335C2×C22⋊D5—64no—
336C2×C22⋊D5—122no—
337C22×Dic5—24no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—31no—
341C22×Dic5—34no—
342C22×Dic5—34no—
343C22×Dic5—42no—
344C22×Dic5—64no—
345C22×Dic5—122no—
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D311yescharacteristic
348C22×Dic5C22×D311yescharacteristic
349C22×Dic5C22×D314yes—
350C22×Dic5C22×D314yes—
351C22×Dic5C22×D311yescharacteristic
352C2×C4×D5—34no—
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⋊Dic5—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365C4⋊Dic5—34no—
366C4⋊Dic5—34no—
367#683—34no—
368#683—34no—
369#683—34no—
370#683C22×D314yes—
371#683C22×D314yes—
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—151no—
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—51no—
393C22×C3×C5—28no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5C2×#4114yes—
397C22×C3×C5C2×#4112yes—
398C22×C3×C5C2×#4112yes—
399C22×C3×C5H(5,𝔽2)12yes—
400C22×C3×C5C2511yescharacteristic
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—44no—
405C2×C5×D3—22no—
406C2×C5×D3—22no—
407C2×C5×D3—22no—
408C2×C5×D3—22no—
409C2×C5×D3—22no—
410C2×C5×D3—22no—
411C2×C5×D3—44no—
412C2×C5×D3—44no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415Dic15—22no—
416Dic15—22no—
417Dic15—22no—
418C3×Dic5—22no—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C3×Dic5C2×#4114yes—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C24×C3C22×D511yescharacteristic
425C23×D3—51no—
426C23×D3C22×D511yescharacteristic
427C23×D3C22×D511yescharacteristic
428C22×C3×C4—42no—
429C22×C3×C4—51no—
430C22×C3×C4—51no—
431C22×C3×C4—51no—
432C22×C3×C4—51no—
433C22×C3×C4—54no—
434C22×C3×C4—54no—
435C22×C3×C4—104no—
436C22×C3×C4—202no—
437C22×C3×C4C22×D511yescharacteristic
438C22×C3×C4C22×D511yescharacteristic
439C22×C3×C4C22×D514yes—
440C2×#67—24no—
441C2×#67—24no—
442C2×#67—54no—
443C2×#67—104no—
444C2×#67C22×D514yes—
445C2×#67C22×D514yes—
446C22×Dic3—51no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3C22×D511yescharacteristic
450C22×Dic3C22×D511yescharacteristic
451C2×D12—42no—
452C2×D12—54no—
453C2×D12—54no—
454C2×D12—104no—
455C2×D12—202no—
456C2×D12C22×D514yes—
457C2×C4×D3—54no—
458C2×C4×D3—54no—
459C2×C4×D3—54no—
460C2×C4×D3—104no—
461C2×C4×D3—202no—
462C2×C4×D3—202no—
463C3×C4⋊C4—54no—
464C3×C4⋊C4—54no—
465C3×C4⋊C4—54no—
466C3×C4⋊C4—54no—
467#217—54no—
468(C2×D3)⋊C4—54no—
469(C2×D3)⋊C4—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)⋊C4C22×D514yes—
476(C2×D3)⋊C4C22×D514yes—
477C4⋊Dic3—54no—
478C4⋊Dic3—54no—
479C4⋊Dic3C22×D514yes—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4—54no—
483C4×Dic3—54no—
484C4×Dic3—54no—
485C4×Dic3—54no—
486C23×C5—22no—
487C23×C5—22no—
488C23×C5—32no—
489C23×C5—32no—
490C23×C5—62no—
491C23×C5—62no—
492C23×C5—62no—
493C23×C5—62no—
494C23×C5—62no—
495C23×C5—62no—
496C23×C5#23914yes—
497C23×C5C23×D312yes—
498C23×C5C23×D311yescharacteristic
499C22×D5—32no—
500C22×D5—62no—
501C22×D5—62no—
502C22×D5—62no—
503C5×D4—68no—
504C5×D4—68no—
505C5×D4—124no—
506C2×C4×C5—22no—
507C2×C4×C5—22no—
508C2×C4×C5—32no—
509C2×C4×C5—32no—
510C2×C4×C5—44no—
511C2×C4×C5—62no—
512C2×C4×C5—62no—
513C2×C4×C5C23×D312yes—
514C2×C4×C5C23×D312yes—
515C22⋊D5—68no—
516C22⋊D5—68no—
517C22⋊D5—124no—
518C2×Dic5—22no—
519C2×Dic5—22no—
520C2×Dic5—22no—
521C2×Dic5—28no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—44no—
526C2×Dic5—62no—
527C2×Dic5—62no—
528C2×Dic5—62no—
529C2×Dic5—68no—
530C2×Dic5—124no—
531C2×Dic5#23514yes—
532C2×Dic5C23×D312yes—
533C2×Dic5C23×D312yes—
534C2×Dic5C23×D312yes—
535C2×Dic5C23×D312yes—
536C4×D5—124no—
537C22×D4—31no—
538C22×D4—31no—
539C22×D4—31no—
540C22×D4—151no—
541C22×D4—151no—
542C22×D4—151no—
543C23×C4—51no—
544C23×C4—51no—
545C23×C4—151no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4D3×D511yescharacteristic
549#126—158no—
550#126—158no—
551#125—158no—
552#123—158no—
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—51no—
567C2×C4⋊C4—51no—
568C2×C4⋊C4—58no—
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—151no—
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—151no—
584C2×C42—151no—
585C2×C42—151no—
586C2×C42—151no—
587C2×C3×C5—24no—
588C2×C3×C5#55314yescomplemented
589C2×C3×C5C22×#4111yescharacteristic
590C2×C3×C5C22×#4111yescharacteristic
591C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
592D15—42no—
593C5×D3—42no—
594C5×D3—42no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3#71114yes—
598C23×C3C23×D512yes—
599C23×C3C23×D511yescharacteristic
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—52no—
607C22×D3—102no—
608C22×D3—102no—
609C22×D3—102no—
610C22×D3C23×D512yes—
611C22×D3C23×D512yes—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—44no—
615C2×C3×C4—54no—
616C2×C3×C4—52no—
617C2×C3×C4—52no—
618C2×C3×C4—52no—
619C2×C3×C4—52no—
620C2×C3×C4—108no—
621C2×C3×C4—102no—
622C2×C3×C4—102no—
623C2×C3×C4—102no—
624C2×C3×C4—204no—
625C2×C3×C4C23×D512yes—
626C2×C3×C4C23×D512yes—
627#67—28no—
628#67—28no—
629#67—108no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—52no—
635C2×Dic3—102no—
636C2×Dic3—102no—
637C2×Dic3—102no—
638C2×Dic3C23×D512yes—
639C2×Dic3C23×D512yes—
640D12—44no—
641D12—108no—
642D12—204no—
643C4×D3—108no—
644C4×D3—204no—
645C4×D3—204no—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5—28no—
649C22×C5—62no—
650C22×C5—62no—
651C22×C5—62no—
652C22×C5—62no—
653C22×C5—62no—
654C22×C5—62no—
655C22×C5—124no—
656C22×C5—124no—
657C22×C5C2×#23512yes—
658C22×C5#100412yes—
659C22×C5C2×#23914yes—
660C22×C5C2×#23912yes—
661C22×C5C24×D311yescharacteristic
662C2×D5—62no—
663C2×D5—62no—
664C2×D5—62no—
665C2×D5—124no—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—62no—
669C4×C5—62no—
670Dic5—22no—
671Dic5—22no—
672Dic5—22no—
673Dic5—62no—
674Dic5—62no—
675Dic5—62no—
676Dic5C2×#23514yes—
677C24—31no—
678C24—31no—
679C24—151no—
680C24C2×D3×D511yescharacteristic
681C2×D4—34no—
682C2×D4—34no—
683C2×D4—34no—
684C2×D4—64no—
685C2×D4—64no—
686C2×D4—122no—
687C2×D4—154no—
688C2×D4—154no—
689C2×D4—154no—
690C2×D4—304no—
691C2×D4—304no—
692C2×D4—602no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—42no—
696C22×C4—51no—
697C22×C4—54no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—51no—
701C22×C4—54no—
702C22×C4—104no—
703C22×C4—154no—
704C22×C4—154no—
705C22×C4—151no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—154no—
709C22×C4—202no—
710C22×C4—304no—
711C22×C4—602no—
712C22×C4—602no—
713C22×C4C2×D3×D511yescharacteristic
714C22×C4C2×D3×D511yescharacteristic
715C22×C4C2×D3×D514yes—
716C4⋊C4—34no—
717C4⋊C4—54no—
718C4⋊C4—54no—
719C4⋊C4—54no—
720C4⋊C4—54no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4—154no—
726C22⋊C4—34no—
727C22⋊C4—34no—
728C22⋊C4—154no—
729C22⋊C4—154no—
730C22⋊C4—154no—
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—28no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3C2×#71114yes—
744C22×C3C2×#71112yes—
745C22×C3#414412yes—
746C22×C3D5×#4112yes—
747C22×C3C24×D511yescharacteristic
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—44no—
755C2×D3—44no—
756C2×D3—102no—
757C2×D3—102no—
758C2×D3—102no—
759C2×D3—204no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—54no—
763C3×C4—102no—
764C3×C4—102no—
765C3×C4—102no—
766Dic3—22no—
767Dic3—22no—
768Dic3—102no—
769Dic3—102no—
770Dic3—102no—
771C2×C5—24no—
772C2×C5—122no—
773C2×C5—122no—
774C2×C5#551414yescomplemented
775C2×C5C22×#23511yescharacteristic
776C2×C5C2×#100411yescharacteristic
777C2×C5C22×#23911yescharacteristic
778D5—122no—
779C23—22no—
780C23—22no—
781C23—32no—
782C23—32no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—152no—
790C23—302no—
791C23—302no—
792C23—302no—
793C23#676814yes—
794C23C22×D3×D512yes—
795C23C22×D3×D511yescharacteristic
796D4—68no—
797D4—68no—
798D4—124no—
799D4—308no—
800D4—308no—
801D4—604no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—44no—
807C2×C4—54no—
808C2×C4—52no—
809C2×C4—52no—
810C2×C4—52no—
811C2×C4—52no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—108no—
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×C4C22×D3×D512yes—
829C2×C4C22×D3×D512yes—
830C2×C3—24no—
831C2×C3#6593514yescomplemented
832C2×C3C22×#71111yescharacteristic
833C2×C3C2×#414411yescharacteristic
834C2×C3C2×D5×#4111yescharacteristic
835D3—42no—
836D3—42no—
837D3—202no—
838C5C2×#551411yescharacteristic, complemented, Sylow
839C22—22no—
840C22—28no—
841C22—22no—
842C22—62no—
843C22—62no—
844C22—62no—
845C22—62no—
846C22—62no—
847C22—62no—
848C22—124no—
849C22—124no—
850C22—302no—
851C22—302no—
852C22—302no—
853C22—604no—
854C22C2×#676814yes—
855C22C2×#676812yes—
856C22D5×#23512yes—
857C22#9204912yes—
858C22C23×D3×D511yescharacteristic
859C4—22no—
860C4—22no—
861C4—54no—
862C4—62no—
863C4—62no—
864C4—102no—
865C4—102no—
866C4—102no—
867C4—302no—
868C4—302no—
869C4—302no—
870C3C2×#6593511yescharacteristic, complemented, Sylow
871C2—24no—
872C2—122no—
873C2—122no—
874C2—602no—
875C2#1175441314yesdirect product factor
876C2C22×#676811yescharacteristic
877C2C2×D5×#23511yescharacteristic
878C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#553
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#1220C2semidirect
2. C2×C5×#930C2semidirect
3. C22×C3×#683C2semidirect
4. C2×#91566C2semidirect
5. C2×#91566C2semidirect
6. C2×Dic5×#67C2semidirect
7. C2×Dic5×#67C2semidirect
8. #11754413C2direct (N × H)
9. C2×#91423C2semidirect
10. C2×#91416C2semidirect
11. C2×#91406C2semidirect
12. C2×#91400C2semidirect
13. C2×#91367C2semidirect
14. C2×#91355C2semidirect
15. C2×#91337C2semidirect
16. C2×#91335C2semidirect
31. C4×#1220C22semidirect
35. C5×#930C22semidirect
43. C2×C3×#683C22semidirect
44. #91566C22semidirect
45. #91566C22semidirect
46. Dic5×#67C22semidirect
47. Dic5×#67C22semidirect
60. #91423C22semidirect
61. #91416C22semidirect
62. #91406C22semidirect
63. #91400C22semidirect
64. #91367C22semidirect
65. #91355C22semidirect
66. #91337C22semidirect
67. #91335C22semidirect
77. C22×#683D3semidirect
150. C2×#930D5semidirect
203. C2×#683C2×D3semidirect
285. #930C2×D5semidirect
588. C2×C3×C5#553semidirect
739. C3×C5C2×#553semidirect
774. C2×C5#5514semidirect
831. C2×C3#65935semidirect
838. C5C2×#5514semidirect
870. C3C2×#65935semidirect
875. C2#11754413direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C2×C5×#9302
C22×C3×#6832
C2×#915662
C2×Dic5×#672
#117544132
C2×#914232
C2×#914162
C2×#914062
C2×#914002
C2×#913672
C2×#913552
C2×#913372
C2×#913352
C2×#659353
C2×#55145