Finite Group Databasebeta

← C2×#11752604 #14483665

Subgroups — C2×#11752604 #14483665

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×#91761C211yesmaximal, characteristic, complemented
2C2×C4×C5×D12C211yesmaximal, characteristic, complemented
3C2×C3×#4022C211yesmaximal, characteristic, complemented
4C2×#91461C211yesmaximal, characteristic, complemented
5C2×#91454C211yesmaximal, characteristic, complemented
6C2×#91453C211yesmaximal, characteristic, complemented
7C2×#91442C211yesmaximal, characteristic, complemented
8C2×#91441C211yesmaximal, characteristic, complemented
9C2×#91416C211yesmaximal, characteristic, complemented
10C2×#91413C211yesmaximal, characteristic, complemented
11C2×#91406C211yesmaximal, characteristic, complemented
12C2×D3×#683C211yesmaximal, characteristic, complemented
13C2×#91367C211yesmaximal, characteristic, complemented
14C2×#91351C211yesmaximal, characteristic, complemented
15C2×#91336C211yesmaximal, characteristic, complemented
16#11752604C2116yesmaximal, direct product factor
17C2×#65874—31nomaximal, Hall
18C22×C4×D15C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×#1203C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1202C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C22×#1201C2211yescharacteristic
27C22×D3×Dic5C2211yescharacteristic
28C22×D3×Dic5C2211yescharacteristic
29C22×D5×Dic3C2211yescharacteristic
30C2×C3×C42×C5C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34C2×#6712C2211yescharacteristic
35C2×C4×Dic15C2211yescharacteristic
36#91761C2218yescomplemented
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×C4⋊Dic3C2211yescharacteristic
40C4×C5×D12C2218yescomplemented
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C2×C3×#685C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic
45C2×C3×#683C2211yescharacteristic
46C2×C3×#683C2211yescharacteristic
47C3×#4022C2218yescomplemented
48C2×Dic3⋊Dic5C2211yescharacteristic
49C2×#6669C2211yescharacteristic
50C2×#6669C2211yescharacteristic
51C2×#6668C2211yescharacteristic
52C2×#6667C2211yescharacteristic
53C2×(C2×D3)⋊Dic5C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56#91461C2218yescomplemented
57#91454C2218yescomplemented
58#91453C2218yescomplemented
59#91442C2218yescomplemented
60#91441C2218yescomplemented
61#91416C2218yescomplemented
62#91413C2218yescomplemented
63#91406C2218yescomplemented
64D3×#683C2218yescomplemented
65#91367C2218yescomplemented
66#91351C2218yescomplemented
67#91336C2218yescomplemented
68C2×#5709—51nomaximal, Hall
69C2×C4×C5×D4—31no—
70C2×#4085—31no—
71C2×#4085—31no—
72C2×#4076—31no—
73C2×#4075—31no—
74C2×C4×C22⋊D5—31no—
75C22×#683—31no—
76#65874—316no—
77C2×#4040—31no—
78C2×#4035—31no—
79C2×#4030—31no—
80C2×#4027—31no—
81C2×#4027—31no—
82C2×#4025—31no—
83C2×#4022D311yescharacteristic, complemented
84C2×#4018—31no—
85C23×D15C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C2×C4×D15—24no—
96C2×C4×D15C2314yes—
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C2×C5×D12—24no—
100C2×C5×D12C2314yes—
101C2×C4×C5×D3—42no—
102C2×C4×C5×D3—42no—
103C2×C4×C5×D3C2314yes—
104C2×C4×C5×D3C2314yes—
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C2×#1203—24no—
109C2×#1203—42no—
110C2×#1203C2314yes—
111C2×#1203C2314yes—
112C2×#1202—42no—
113C2×#1202C2314yes—
114C2×#1201—24no—
115C2×#1201—24no—
116C2×#1201C2314yes—
117C2×#1201C2314yes—
118C2×D3×Dic5—24no—
119C2×D3×Dic5—42no—
120C2×D3×Dic5C2314yes—
121C2×D3×Dic5C2314yes—
122C2×D5×Dic3—42no—
123C2×D5×Dic3C2314yes—
124C3×C42×C5C2314yes—
125#6714C2314yes—
126#6714C2314yes—
127#6712C2314yes—
128#6712C2314yes—
129C4×Dic15C2314yes—
130C5×(C2×D3)⋊C4C2314yes—
131C5×(C2×D3)⋊C4C2314yes—
132C5×C4⋊Dic3C2314yes—
133C3×#685C2314yes—
134C3×#685C2314yes—
135C3×#685C2314yes—
136C3×#683C2314yes—
137C3×#683C2314yes—
138C3×#683C2314yes—
139Dic3⋊Dic5C2314yes—
140#6669C2314yes—
141#6669C2314yes—
142#6668C2314yes—
143#6667C2314yes—
144(C2×D3)⋊Dic5C2314yes—
145(C2×D3)⋊Dic5C2314yes—
146Dic3×Dic5C2314yes—
147C2×C3×#126—51no—
148#5709—516no—
149C2×#898—51no—
150C2×#895—51no—
151C2×#894—51no—
152C2×#893—51no—
153C2×D3×C4⋊C4—51no—
154C2×#889—51no—
155C2×#886—51no—
156C2×#884—51no—
157C2×#884—51no—
158C2×#884—51no—
159C2×#67⋊C4—51no—
160C2×#67⋊C4—51no—
161C2×C4×D12D511yescharacteristic, complemented
162C2×#872—51no—
163C22×C5×D4—31no—
164C23×C4×C5—31no—
165C23×C4×C5—31no—
166C22×C22⋊D5—31no—
167C22×C22⋊D5—31no—
168C22×C22⋊D5—31no—
169C22×C22⋊D5—31no—
170C23×Dic5—31no—
171C23×Dic5—31no—
172C22×D20—31no—
173C22×C4×D5—31no—
174C22×C4×D5—31no—
175C4×C5×D4—38no—
176C2×C5×C4⋊C4—31no—
177C2×C5×C22⋊C4—31no—
178C2×C5×C22⋊C4—31no—
179C2×C42×C5C2×D311yescharacteristic
180C2×C22⋊Dic5—31no—
181C2×C22⋊Dic5—31no—
182#4085—38no—
183#4085—38no—
184#4076—38no—
185#4075—38no—
186C4×C22⋊D5—38no—
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685C2×D311yescharacteristic
191C2×#685C2×D311yescharacteristic
192C2×#685C2×D311yescharacteristic
193C2×C4⋊Dic5—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×#683—31no—
198C2×#683—31no—
199C2×#683—38no—
200C2×#683C2×D311yescharacteristic
201C2×#683C2×D311yescharacteristic
202C2×#683C2×D311yescharacteristic
203C2×C4×Dic5—31no—
204C2×C4×Dic5—31no—
205#4040—38no—
206#4035—38no—
207#4030—38no—
208#4027—38no—
209#4027—38no—
210#4025—38no—
211#4022C2×D318yescomplemented
212#4018—38no—
213C2×#553—151noSylow
214C23×C3×C5C2411yescharacteristic
215C22×D15—22no—
216C22×D15—22no—
217C22×D15—22no—
218C22×D15C2412yes—
219C22×C5×D3—22no—
220C22×C5×D3—22no—
221C22×C5×D3—22no—
222C22×C5×D3—22no—
223C22×C5×D3—22no—
224C22×C5×D3#4114yes—
225C22×C5×D3C2412yes—
226C22×C5×D3C2412yes—
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5—22no—
230C22×C3×D5C2412yes—
231C2×C3×C4×C5—22no—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5—22no—
234C2×C3×C4×C5C2412yes—
235C2×C3×C4×C5C2412yes—
236C2×C3×C4×C5C2412yes—
237C2×Dic15—22no—
238C2×Dic15—22no—
239C2×Dic15#4114yes—
240C2×Dic15C2412yes—
241C2×Dic15C2412yes—
242C2×Dic15C2412yes—
243C4×D15—28no—
244C2×C5×Dic3—22no—
245C2×C5×Dic3—22no—
246C2×C5×Dic3C2412yes—
247C2×C5×Dic3C2412yes—
248C5×D12—28no—
249C4×C5×D3—44no—
250C4×C5×D3—44no—
251C2×C3×Dic5—22no—
252C2×C3×Dic5—22no—
253C2×C3×Dic5—22no—
254C2×C3×Dic5C2412yes—
255C2×C3×Dic5C2412yes—
256C2×C3×Dic5C2412yes—
257#1203—28no—
258#1203—44no—
259#1202—44no—
260#1201—28no—
261#1201—28no—
262D3×Dic5—28no—
263D3×Dic5—44no—
264D5×Dic3—44no—
265C22×#67—51no—
266C22×#67—51no—
267C22×#67—51no—
268C23×Dic3—51no—
269C22×D12—51no—
270C22×D12—51no—
271C22×D12C2×D511yescharacteristic
272C22×C4×D3—51no—
273C22×C4×D3—51no—
274C22×C4×D3—51no—
275C22×C4×D3C2×D511yescharacteristic
276C22×C4×D3C2×D511yescharacteristic
277C3×#126—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×C3×C22⋊C4—51no—
284C2×C3×C42C2×D511yescharacteristic
285C2×(C2×D3)⋊C4—51no—
286C2×(C2×D3)⋊C4—51no—
287C2×(C2×D3)⋊C4—51no—
288C2×(C2×D3)⋊C4—51no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4C2×D511yescharacteristic
291C2×(C2×D3)⋊C4C2×D511yescharacteristic
292C2×C4⋊Dic3—51no—
293C2×C4⋊Dic3C2×D511yescharacteristic
294C2×Dic3⋊C4—51no—
295C2×Dic3⋊C4—51no—
296C2×Dic3⋊C4—51no—
297C2×Dic3⋊C4—51no—
298C2×Dic3⋊C4—51no—
299C2×C4×Dic3—51no—
300C2×C4×Dic3—51no—
301#898—58no—
302#895—58no—
303#894—58no—
304#893—58no—
305D3×C4⋊C4—58no—
306#889—58no—
307#886—58no—
308#884—58no—
309#884—58no—
310#884—58no—
311#67⋊C4—58no—
312#67⋊C4—58no—
313C4×D12C2×D518yescomplemented
314#872—58no—
315C24×C5—31no—
316C24×C5—31no—
317C23×D5—31no—
318C23×D5C22×D311yescharacteristic
319C2×C5×D4—34no—
320C2×C5×D4—64no—
321C22×C4×C5—31no—
322C22×C4×C5—31no—
323C22×C4×C5—34no—
324C22×C4×C5—34no—
325C22×C4×C5—122no—
326C22×C4×C5—122no—
327C22×C4×C5C22×D311yescharacteristic
328C22×C4×C5C22×D311yescharacteristic
329C22×C4×C5C22×D311yescharacteristic
330C2×C22⋊D5—34no—
331C2×C22⋊D5—34no—
332C2×C22⋊D5—34no—
333C2×C22⋊D5—34no—
334C2×C22⋊D5—64no—
335C2×C22⋊D5—64no—
336C2×C22⋊D5—64no—
337C2×C22⋊D5—122no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—31no—
341C22×Dic5—34no—
342C22×Dic5—34no—
343C22×Dic5—64no—
344C22×Dic5—122no—
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D311yescharacteristic
348C2×D20—34no—
349C2×D20—122no—
350C2×C4×D5—34no—
351C2×C4×D5—34no—
352C2×C4×D5—64no—
353C2×C4×D5—122no—
354C5×C4⋊C4—34no—
355C5×C22⋊C4—34no—
356C5×C22⋊C4—34no—
357C42×C5C22×D314yes—
358C22⋊Dic5—34no—
359C22⋊Dic5—34no—
360#685—34no—
361#685—34no—
362#685—34no—
363#685C22×D314yes—
364#685C22×D314yes—
365#685C22×D314yes—
366C4⋊Dic5—34no—
367#683—34no—
368#683—34no—
369#683—34no—
370#683—34no—
371#683—34no—
372#683C22×D314yes—
373#683C22×D314yes—
374#683C22×D314yes—
375C4×Dic5—34no—
376C4×Dic5—34no—
377#553—1516no—
378C2×#126—51no—
379C2×#126—151no—
380C2×#125—151no—
381C2×#123—151no—
382C2×#123—151no—
383C2×#121—151no—
384C2×#121—151no—
385C2×#121—151no—
386C2×#121—151no—
387C2×C4×D4—31no—
388C2×C4×D4—151no—
389C2×C4×D4—151no—
390C2×C4×D4—151no—
391C2×#117—151no—
392C22×C4⋊C4—151no—
393C22×C3×C5C2×#4112yes—
394C22×C3×C5C2×#4112yes—
395C22×C3×C5H(5,𝔽2)12yes—
396C22×C3×C5C2511yescharacteristic
397C2×D15—22no—
398C2×D15—22no—
399C2×D15—22no—
400C2×D15—44no—
401C2×C5×D3—28no—
402C2×C5×D3—22no—
403C2×C5×D3—22no—
404C2×C5×D3—22no—
405C2×C5×D3—22no—
406C2×C5×D3—22no—
407C2×C5×D3—44no—
408C2×C5×D3C2×#4114yes—
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—22no—
412C2×C3×D5—44no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—22no—
416Dic15—22no—
417Dic15—22no—
418Dic15C2×#4114yes—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C24×C3—51no—
425C23×D3—51no—
426C23×D3C22×D511yescharacteristic
427C23×D3C22×D511yescharacteristic
428C22×C3×C4—51no—
429C22×C3×C4—51no—
430C22×C3×C4—51no—
431C22×C3×C4C22×D511yescharacteristic
432C22×C3×C4C22×D511yescharacteristic
433C22×C3×C4C22×D511yescharacteristic
434C2×#67—54no—
435C2×#67—54no—
436C2×#67—54no—
437C2×#67—104no—
438C2×#67—104no—
439C2×#67—202no—
440C22×Dic3—51no—
441C22×Dic3—51no—
442C22×Dic3—51no—
443C22×Dic3—54no—
444C22×Dic3—202no—
445C22×Dic3C22×D511yescharacteristic
446C22×Dic3C22×D511yescharacteristic
447C2×D12—24no—
448C2×D12—54no—
449C2×D12—54no—
450C2×D12—104no—
451C2×D12—202no—
452C2×D12C22×D514yes—
453C2×C4×D3—42no—
454C2×C4×D3—42no—
455C2×C4×D3—54no—
456C2×C4×D3—54no—
457C2×C4×D3—54no—
458C2×C4×D3—104no—
459C2×C4×D3—104no—
460C2×C4×D3—202no—
461C2×C4×D3C22×D514yes—
462C2×C4×D3C22×D514yes—
463C3×C4⋊C4—54no—
464C3×C4⋊C4—54no—
465C3×C4⋊C4—54no—
466C3×C22⋊C4—54no—
467C3×C22⋊C4—54no—
468C3×C22⋊C4—54no—
469C3×C42C22×D514yes—
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⋊Dic3C22×D514yes—
479Dic3⋊C4—54no—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4—54no—
483Dic3⋊C4—54no—
484C4×Dic3—54no—
485C4×Dic3—54no—
486C23×C5—34no—
487C23×C5—32no—
488C23×C5—32no—
489C23×C5—62no—
490C23×C5—62no—
491C23×C5—62no—
492C23×C5—62no—
493C23×C5—62no—
494C23×C5C23×D311yescharacteristic
495C22×D5—22no—
496C22×D5—22no—
497C22×D5—22no—
498C22×D5—32no—
499C22×D5—62no—
500C22×D5—62no—
501C22×D5—62no—
502C22×D5C23×D312yes—
503C5×D4—68no—
504C2×C4×C5—22no—
505C2×C4×C5—22no—
506C2×C4×C5—22no—
507C2×C4×C5—32no—
508C2×C4×C5—32no—
509C2×C4×C5—62no—
510C2×C4×C5—62no—
511C2×C4×C5—124no—
512C2×C4×C5—124no—
513C2×C4×C5C23×D312yes—
514C2×C4×C5C23×D312yes—
515C2×C4×C5C23×D312yes—
516C22⋊D5—68no—
517C22⋊D5—68no—
518C22⋊D5—68no—
519C22⋊D5—124no—
520C2×Dic5—22no—
521C2×Dic5—22no—
522C2×Dic5—22no—
523C2×Dic5—34no—
524C2×Dic5—32no—
525C2×Dic5—32no—
526C2×Dic5—32no—
527C2×Dic5—68no—
528C2×Dic5—62no—
529C2×Dic5—62no—
530C2×Dic5—124no—
531C2×Dic5C23×D312yes—
532C2×Dic5C23×D312yes—
533C2×Dic5C23×D312yes—
534D20—124no—
535C4×D5—68no—
536C4×D5—124no—
537C22×D4—31no—
538C22×D4—151no—
539C22×D4—151no—
540C22×D4—151no—
541C22×D4—151no—
542C22×D4—151no—
543C23×C4—31no—
544C23×C4—31no—
545C23×C4—151no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4—151no—
549#126—58no—
550#126—158no—
551#125—158no—
552#123—158no—
553#123—158no—
554#121—158no—
555#121—158no—
556#121—158no—
557#121—158no—
558C4×D4—38no—
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—158no—
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×C42D3×D511yescharacteristic
587C2×C3×C5#55314yescomplemented
588C2×C3×C5C22×#4111yescharacteristic
589C2×C3×C5C22×#4111yescharacteristic
590C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
591D15—42no—
592C3×D5—42no—
593C5×D3—24no—
594C5×D3—42no—
595C23×C3—52no—
596C23×C3—102no—
597C23×C3—102no—
598C23×C3—102no—
599C23×C3C23×D511yescharacteristic
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—52no—
606C22×D3—102no—
607C22×D3—102no—
608C22×D3—102no—
609C22×D3#70914yes—
610C22×D3C23×D512yes—
611C22×D3C23×D512yes—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
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×C4C23×D512yes—
622C2×C3×C4C23×D512yes—
623C2×C3×C4C23×D512yes—
624#67—108no—
625#67—108no—
626#67—204no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—54no—
630C2×Dic3—52no—
631C2×Dic3—52no—
632C2×Dic3—52no—
633C2×Dic3—102no—
634C2×Dic3—102no—
635C2×Dic3—204no—
636C2×Dic3C23×D512yes—
637C2×Dic3C23×D512yes—
638D12—28no—
639D12—108no—
640D12—204no—
641C4×D3—44no—
642C4×D3—44no—
643C4×D3—108no—
644C4×D3—108no—
645C4×D3—204no—
646C22×C5—34no—
647C22×C5—62no—
648C22×C5—62no—
649C22×C5—68no—
650C22×C5—62no—
651C22×C5—62no—
652C22×C5—62no—
653C22×C5—124no—
654C22×C5D3×#4112yes—
655C22×C5D3×#4112yes—
656C22×C5#100912yes—
657C22×C5C24×D311yescharacteristic
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—44no—
662C2×D5—62no—
663C2×D5—62no—
664C2×D5—62no—
665C2×D5—124no—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—22no—
669C4×C5—62no—
670C4×C5—62no—
671Dic5—22no—
672Dic5—22no—
673Dic5—22no—
674Dic5—34no—
675Dic5—62no—
676Dic5—62no—
677C24—31no—
678C24—31no—
679C24—51no—
680C24—151no—
681C2×D4—34no—
682C2×D4—64no—
683C2×D4—154no—
684C2×D4—154no—
685C2×D4—154no—
686C2×D4—154no—
687C2×D4—154no—
688C2×D4—304no—
689C2×D4—304no—
690C2×D4—304no—
691C2×D4—602no—
692C2×D4—602no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—34no—
696C22×C4—34no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—122no—
701C22×C4—122no—
702C22×C4—154no—
703C22×C4—154no—
704C22×C4—154no—
705C22×C4—151no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—154no—
709C22×C4—304no—
710C22×C4—304no—
711C22×C4—602no—
712C22×C4—602no—
713C22×C4C2×D3×D511yescharacteristic
714C22×C4C2×D3×D511yescharacteristic
715C22×C4C2×D3×D511yescharacteristic
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—54no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C42—154no—
737C42—154no—
738C42C2×D3×D514yes—
739C3×C5C2×#55311yescharacteristic, complemented, Hall
740C22×C3—102no—
741C22×C3—102no—
742C22×C3—102no—
743C22×C3—204no—
744C22×C3C2×#70912yes—
745C22×C3#414412yes—
746C22×C3D5×#4112yes—
747C22×C3C24×D511yescharacteristic
748C2×D3—28no—
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—44no—
755C2×D3—102no—
756C2×D3—102no—
757C2×D3—102no—
758C2×D3—204no—
759C2×D3C2×#70914yes—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—102no—
764C3×C4—102no—
765C3×C4—102no—
766Dic3—22no—
767Dic3—22no—
768Dic3—54no—
769Dic3—102no—
770Dic3—102no—
771C2×C5—64no—
772C2×C5—122no—
773C2×C5#570914yescomplemented
774C2×C5C2×D3×#4111yescharacteristic
775C2×C5C2×D3×#4111yescharacteristic
776C2×C5C2×#100911yescharacteristic
777D5—42no—
778D5—122no—
779C23—34no—
780C23—32no—
781C23—32no—
782C23—52no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—102no—
789C23—102no—
790C23—102no—
791C23—152no—
792C23—302no—
793C23—302no—
794C23—302no—
795C23C22×D3×D511yescharacteristic
796D4—68no—
797D4—308no—
798D4—308no—
799D4—308no—
800D4—604no—
801D4—604no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—52no—
808C2×C4—52no—
809C2×C4—52no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—102no—
813C2×C4—102no—
814C2×C4—102no—
815C2×C4—124no—
816C2×C4—124no—
817C2×C4—154no—
818C2×C4—152no—
819C2×C4—152no—
820C2×C4—152no—
821C2×C4—308no—
822C2×C4—308no—
823C2×C4—302no—
824C2×C4—302no—
825C2×C4—604no—
826C2×C4—604no—
827C2×C4C22×D3×D512yes—
828C2×C4C22×D3×D512yes—
829C2×C4C22×D3×D512yes—
830C2×C3—202no—
831C2×C3#6587414yescomplemented
832C2×C3C22×#70911yescharacteristic
833C2×C3C2×#414411yescharacteristic
834C2×C3C2×D5×#4111yescharacteristic
835D3—24no—
836D3—42no—
837D3—202no—
838C5C2×#570911yescharacteristic, complemented, Sylow
839C22—34no—
840C22—68no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—62no—
845C22—62no—
846C22—102no—
847C22—102no—
848C22—102no—
849C22—124no—
850C22—204no—
851C22—302no—
852C22—302no—
853C22—302no—
854C22—604no—
855C22D3×#70912yes—
856C22#9201612yes—
857C22#9201812yes—
858C22C23×D3×D511yescharacteristic
859C4—22no—
860C4—22no—
861C4—22no—
862C4—62no—
863C4—62no—
864C4—102no—
865C4—102no—
866C4—102no—
867C4—154no—
868C4—302no—
869C4—302no—
870C3C2×#6587411yescharacteristic, complemented, Sylow
871C2—64no—
872C2—122no—
873C2—202no—
874C2—602no—
875C2#1175260414yesdirect product factor
876C2C2×D3×#70911yescharacteristic
877C2C2×#9201611yescharacteristic
878C2C2×#9201811yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#553
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#91761C2semidirect
2. C2×C4×C5×D12C2semidirect
3. C2×C3×#4022C2semidirect
4. C2×#91461C2semidirect
5. C2×#91454C2semidirect
6. C2×#91453C2semidirect
7. C2×#91442C2semidirect
8. C2×#91441C2semidirect
9. C2×#91416C2semidirect
10. C2×#91413C2semidirect
11. C2×#91406C2semidirect
12. C2×D3×#683C2semidirect
13. C2×#91367C2semidirect
14. C2×#91351C2semidirect
15. C2×#91336C2semidirect
16. #11752604C2direct (N × H)
36. #91761C22semidirect
40. C4×C5×D12C22semidirect
47. C3×#4022C22semidirect
56. #91461C22semidirect
57. #91454C22semidirect
58. #91453C22semidirect
59. #91442C22semidirect
60. #91441C22semidirect
61. #91416C22semidirect
62. #91413C22semidirect
63. #91406C22semidirect
64. D3×#683C22semidirect
65. #91367C22semidirect
66. #91351C22semidirect
67. #91336C22semidirect
83. C2×#4022D3semidirect
161. C2×C4×D12D5semidirect
211. #4022C2×D3semidirect
313. C4×D12C2×D5semidirect
587. C2×C3×C5#553semidirect
739. C3×C5C2×#553semidirect
773. C2×C5#5709semidirect
831. C2×C3#65874semidirect
838. C5C2×#5709semidirect
870. C3C2×#65874semidirect
875. C2#11752604direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917612
C2×C4×C5×D122
C2×C3×#40222
C2×#914612
C2×#914542
C2×#914532
C2×#914422
C2×#914412
C2×#914162
C2×#914132
C2×#914062
C2×D3×#6832
C2×#913672
C2×#913512
C2×#913362
#117526042
C2×#658743
C2×#57095