Finite Group Databasebeta

← C2×#11753643 #14495347

Subgroups — C2×#11753643 #14495347

Order 1920.

2304 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×#91779C211yesmaximal, characteristic, complemented
2C2×C5×#894C211yesmaximal, characteristic, complemented
3C2×C3×#4040C211yesmaximal, characteristic, complemented
4C2×#91464C211yesmaximal, characteristic, complemented
5C2×#91464C211yesmaximal, characteristic, complemented
6C2×#91457C211yesmaximal, characteristic, complemented
7C2×#91456C211yesmaximal, characteristic, complemented
8C2×#91453C211yesmaximal, characteristic, complemented
9C2×#91449C211yesmaximal, characteristic, complemented
10C2×#91422C211yesmaximal, characteristic, complemented
11C2×#91417C211yesmaximal, characteristic, complemented
12C2×#91414C211yesmaximal, characteristic, complemented
13C2×#91408C211yesmaximal, characteristic, complemented
14C2×#91352C211yesmaximal, characteristic, complemented
15C2×#91349C211yesmaximal, characteristic, complemented
16#11753643C2116yesmaximal, direct product factor
17C2×#66001—31nomaximal, Hall
18C22×C5×D12C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×#1204C2211yescharacteristic
24C22×#1201C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C22×#1201C2211yescharacteristic
27C22×#1201C2211yescharacteristic
28C22×D3×Dic5C2211yescharacteristic
29C22×D5×Dic3C2211yescharacteristic
30C2×C3×C5×C4⋊C4C2211yescharacteristic
31C2×C4⋊Dic15C2211yescharacteristic
32C2×C4⋊Dic15C2211yescharacteristic
33C2×C4⋊Dic15C2211yescharacteristic
34C2×#6712C2211yescharacteristic
35C2×#6712C2211yescharacteristic
36C2×C4×Dic15C2211yescharacteristic
37#91779C2218yescomplemented
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×(C2×D3)⋊C4C2211yescharacteristic
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic
41C2×C5×Dic3⋊C4C2211yescharacteristic
42C5×#894C2218yescomplemented
43C2×C3×#685C2211yescharacteristic
44C2×C3×#685C2211yescharacteristic
45C2×C3×#685C2211yescharacteristic
46C2×C3×#683C2211yescharacteristic
47C3×#4040C2218yescomplemented
48C2×Dic3⋊Dic5C2211yescharacteristic
49C2×#6668C2211yescharacteristic
50C2×(C2×D3)⋊Dic5C2211yescharacteristic
51C2×(C2×D3)⋊Dic5C2211yescharacteristic
52C2×(C2×D3)⋊Dic5C2211yescharacteristic
53C2×#6665C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55C2×#6665C2211yescharacteristic
56#91464C2218yescomplemented
57#91464C2218yescomplemented
58#91457C2218yescomplemented
59#91456C2218yescomplemented
60#91453C2218yescomplemented
61#91449C2218yescomplemented
62#91422C2218yescomplemented
63#91417C2218yescomplemented
64#91414C2218yescomplemented
65#91408C2218yescomplemented
66#91352C2218yescomplemented
67#91349C2218yescomplemented
68C2×#5667—51nomaximal, Hall
69C2×C5×#123—31no—
70C2×#4085—31no—
71C2×#4084—31no—
72C2×#4076—31no—
73C2×#4070—31no—
74#66001—316no—
75C2×#4043—31no—
76C2×#4042—31no—
77C2×#4040D311yescharacteristic, complemented
78C2×#4036—31no—
79C2×#4032—31no—
80C2×#4031—31no—
81C2×#4031—31no—
82C2×#4030—31no—
83C2×#4029—31no—
84C2×#4024—31no—
85C23×C5×D3C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C3×D5C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C2×C5×D12—42no—
99C2×C5×D12C2314yes—
100C2×C4×C5×D3—42no—
101C2×C4×C5×D3C2314yes—
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C2×C3×D20—42no—
105C2×C3×D20C2314yes—
106C2×C3×C4×D5—42no—
107C2×C3×C4×D5C2314yes—
108C2×#1204—42no—
109C2×#1204—42no—
110C2×#1204C2314yes—
111C2×#1204C2314yes—
112C2×#1201—42no—
113C2×#1201—42no—
114C2×#1201—42no—
115C2×#1201—42no—
116C2×#1201C2314yes—
117C2×#1201C2314yes—
118C2×#1201C2314yes—
119C2×#1201C2314yes—
120C2×D3×Dic5—42no—
121C2×D3×Dic5C2314yes—
122C2×D5×Dic3—42no—
123C2×D5×Dic3C2314yes—
124C3×C5×C4⋊C4C2314yes—
125C4⋊Dic15C2314yes—
126C4⋊Dic15C2314yes—
127C4⋊Dic15C2314yes—
128#6712C2314yes—
129#6712C2314yes—
130C4×Dic15C2314yes—
131C5×(C2×D3)⋊C4C2314yes—
132C5×(C2×D3)⋊C4C2314yes—
133C5×(C2×D3)⋊C4C2314yes—
134C5×Dic3⋊C4C2314yes—
135C3×#685C2314yes—
136C3×#685C2314yes—
137C3×#685C2314yes—
138C3×#683C2314yes—
139Dic3⋊Dic5C2314yes—
140#6668C2314yes—
141(C2×D3)⋊Dic5C2314yes—
142(C2×D3)⋊Dic5C2314yes—
143(C2×D3)⋊Dic5C2314yes—
144#6665C2314yes—
145#6665C2314yes—
146#6665C2314yes—
147C2×C3×#123—51no—
148C2×#939—51no—
149C2×#938—51no—
150C2×#930—51no—
151C2×#924—51no—
152#5667—516no—
153C2×#897—51no—
154C2×#896—51no—
155C2×#894D511yescharacteristic, complemented
156C2×#890—51no—
157C2×#886—51no—
158C2×#885—51no—
159C2×#885—51no—
160C2×#884—51no—
161C2×#883—51no—
162C2×#878—51no—
163C22×C5×D4—31no—
164C23×C4×C5—31no—
165C22×C22⋊D5—31no—
166C22×C22⋊D5—31no—
167C22×C22⋊D5—31no—
168C22×C22⋊D5—31no—
169C23×Dic5—31no—
170C22×D20C2×D311yescharacteristic
171C22×C4×D5—31no—
172C22×C4×D5C2×D311yescharacteristic
173C22×Dic10—31no—
174C22×Dic10—31no—
175C5×#123—38no—
176C2×C5×C4⋊C4—31no—
177C2×C5×C4⋊C4C2×D311yescharacteristic
178C2×C5×C22⋊C4—31no—
179C2×C5×C22⋊C4—31no—
180C2×C5×C22⋊C4—31no—
181C2×C22⋊Dic5—31no—
182C2×C22⋊Dic5—31no—
183C2×C22⋊Dic5—31no—
184#4085—38no—
185#4084—38no—
186#4076—38no—
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685C2×D311yescharacteristic
191C2×#685C2×D311yescharacteristic
192C2×#685C2×D311yescharacteristic
193C2×C4⋊Dic5—31no—
194C2×C4⋊Dic5—31no—
195C2×C4⋊Dic5—31no—
196C2×C4⋊Dic5—31no—
197#4070—38no—
198C2×#683—31no—
199C2×#683—31no—
200C2×#683—31no—
201C2×#683C2×D311yescharacteristic
202C2×C4×Dic5—31no—
203#4043—38no—
204#4042—38no—
205#4040C2×D318yescomplemented
206#4036—38no—
207#4032—38no—
208#4031—38no—
209#4031—38no—
210#4030—38no—
211#4029—38no—
212#4024—38no—
213C2×#562—151noSylow
214C23×C3×C5C2411yescharacteristic
215C22×C5×D3—22no—
216C22×C5×D3—22no—
217C22×C5×D3—22no—
218C22×C5×D3—22no—
219C22×C5×D3—22no—
220C22×C5×D3—22no—
221C22×C5×D3C2412yes—
222C22×C5×D3C2412yes—
223C22×C3×D5—22no—
224C22×C3×D5—22no—
225C22×C3×D5—22no—
226C22×C3×D5—22no—
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5C2412yes—
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—22no—
240C2×Dic15—22no—
241C2×Dic15C2412yes—
242C2×Dic15C2412yes—
243C2×Dic15C2412yes—
244C2×Dic15C2412yes—
245C2×C5×Dic3—22no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3C2412yes—
248C2×C5×Dic3C2412yes—
249C5×D12—44no—
250C4×C5×D3—44no—
251C2×C3×Dic5—22no—
252C2×C3×Dic5—22no—
253C2×C3×Dic5C2412yes—
254C2×C3×Dic5C2412yes—
255C3×D20—44no—
256C3×C4×D5—44no—
257#1204—44no—
258#1204—44no—
259#1201—44no—
260#1201—44no—
261#1201—44no—
262#1201—44no—
263D3×Dic5—44no—
264D5×Dic3—44no—
265C22×C3×D4—51no—
266C23×C3×C4—51no—
267C22×#67—51no—
268C22×#67—51no—
269C22×#67—51no—
270C22×#67—51no—
271C23×Dic3—51no—
272C22×D12C2×D511yescharacteristic
273C22×C4×D3—51no—
274C22×C4×D3C2×D511yescharacteristic
275C22×Dic6—51no—
276C22×Dic6—51no—
277C3×#123—58no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C4⋊C4C2×D511yescharacteristic
280C2×C3×C22⋊C4—51no—
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×#217—51no—
284C2×#217—51no—
285C2×#217—51no—
286#939—58no—
287#938—58no—
288#930—58no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4C2×D511yescharacteristic
293C2×(C2×D3)⋊C4C2×D511yescharacteristic
294C2×(C2×D3)⋊C4C2×D511yescharacteristic
295C2×C4⋊Dic3—51no—
296C2×C4⋊Dic3—51no—
297C2×C4⋊Dic3—51no—
298C2×C4⋊Dic3—51no—
299#924—58no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4C2×D511yescharacteristic
304C2×C4×Dic3—51no—
305#897—58no—
306#896—58no—
307#894C2×D518yescomplemented
308#890—58no—
309#886—58no—
310#885—58no—
311#885—58no—
312#884—58no—
313#883—58no—
314#878—58no—
315C24×C5—31no—
316C24×C5—31no—
317C23×D5C22×D311yescharacteristic
318C23×D5C22×D311yescharacteristic
319C2×C5×D4—34no—
320C2×C5×D4—122no—
321C22×C4×C5—31no—
322C22×C4×C5—31no—
323C22×C4×C5—34no—
324C22×C4×C5—122no—
325C22×C4×C5C22×D311yescharacteristic
326C22×C4×C5C22×D311yescharacteristic
327C22×C4×C5C22×D311yescharacteristic
328C2×C22⋊D5—34no—
329C2×C22⋊D5—34no—
330C2×C22⋊D5—34no—
331C2×C22⋊D5—34no—
332C2×C22⋊D5—122no—
333C2×C22⋊D5—122no—
334C2×C22⋊D5—122no—
335C2×C22⋊D5—122no—
336C22×Dic5—31no—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—34no—
341C22×Dic5—122no—
342C22×Dic5C22×D311yescharacteristic
343C22×Dic5C22×D311yescharacteristic
344C2×D20—42no—
345C2×D20C22×D314yes—
346C2×C4×D5—34no—
347C2×C4×D5—42no—
348C2×C4×D5—122no—
349C2×C4×D5C22×D314yes—
350C2×Dic10—34no—
351C2×Dic10—34no—
352C2×Dic10—122no—
353C2×Dic10—122no—
354C5×C4⋊C4—34no—
355C5×C4⋊C4C22×D314yes—
356C5×C22⋊C4—34no—
357C5×C22⋊C4—34no—
358C5×C22⋊C4—34no—
359C22⋊Dic5—34no—
360C22⋊Dic5—34no—
361C22⋊Dic5—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685C22×D314yes—
366#685C22×D314yes—
367#685C22×D314yes—
368C4⋊Dic5—34no—
369C4⋊Dic5—34no—
370C4⋊Dic5—34no—
371C4⋊Dic5—34no—
372#683—34no—
373#683—34no—
374#683—34no—
375#683C22×D314yes—
376C4×Dic5—34no—
377#562—1516no—
378C2×#125—151no—
379C2×#124—151no—
380C2×#124—151no—
381C2×#123—31no—
382C2×#123—51no—
383C2×#123—151no—
384C2×#123—151no—
385C2×C22⋊Q8—151no—
386C2×C22⋊Q8—151no—
387C2×C22⋊Q8—151no—
388C2×C22⋊Q8—151no—
389C2×#121—151no—
390C2×#121—151no—
391C2×#121—151no—
392C2×#121—151no—
393C22×C3×C5H(5,𝔽2)12yes—
394C22×C3×C5H(5,𝔽2)12yes—
395C22×C3×C52−1+412yes—
396C22×C3×C5C2511yescharacteristic
397C2×C5×D3—22no—
398C2×C5×D3—22no—
399C2×C5×D3—22no—
400C2×C5×D3—22no—
401C2×C5×D3—22no—
402C2×C5×D3—22no—
403C2×C5×D3—44no—
404C2×C5×D3—44no—
405C2×C3×D5—22no—
406C2×C3×D5—22no—
407C2×C3×D5—22no—
408C2×C3×D5—22no—
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—44no—
412C2×C3×D5—44no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—22no—
416Dic15—22no—
417Dic15—22no—
418Dic15—22no—
419Dic15—22no—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C24×C3—51no—
425C24×C3—51no—
426C23×D3C22×D511yescharacteristic
427C23×D3C22×D511yescharacteristic
428C2×C3×D4—54no—
429C2×C3×D4—202no—
430C22×C3×C4—51no—
431C22×C3×C4—51no—
432C22×C3×C4—54no—
433C22×C3×C4—202no—
434C22×C3×C4C22×D511yescharacteristic
435C22×C3×C4C22×D511yescharacteristic
436C22×C3×C4C22×D511yescharacteristic
437C2×#67—54no—
438C2×#67—54no—
439C2×#67—54no—
440C2×#67—54no—
441C2×#67—202no—
442C2×#67—202no—
443C2×#67—202no—
444C2×#67—202no—
445C22×Dic3—51no—
446C22×Dic3—51no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—54no—
450C22×Dic3—202no—
451C22×Dic3C22×D511yescharacteristic
452C22×Dic3C22×D511yescharacteristic
453C2×D12—42no—
454C2×D12C22×D514yes—
455C2×C4×D3—42no—
456C2×C4×D3—54no—
457C2×C4×D3—202no—
458C2×C4×D3C22×D514yes—
459C2×Dic6—54no—
460C2×Dic6—54no—
461C2×Dic6—202no—
462C2×Dic6—202no—
463C3×C4⋊C4—54no—
464C3×C4⋊C4C22×D514yes—
465C3×C22⋊C4—54no—
466C3×C22⋊C4—54no—
467C3×C22⋊C4—54no—
468#217—54no—
469#217—54no—
470#217—54no—
471(C2×D3)⋊C4—54no—
472(C2×D3)⋊C4—54no—
473(C2×D3)⋊C4—54no—
474(C2×D3)⋊C4C22×D514yes—
475(C2×D3)⋊C4C22×D514yes—
476(C2×D3)⋊C4C22×D514yes—
477C4⋊Dic3—54no—
478C4⋊Dic3—54no—
479C4⋊Dic3—54no—
480C4⋊Dic3—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4—54no—
483Dic3⋊C4—54no—
484Dic3⋊C4C22×D514yes—
485C4×Dic3—54no—
486C23×C5—32no—
487C23×C5—32no—
488C23×C5—62no—
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—22no—
499C22×D5—22no—
500C22×D5—22no—
501C22×D5C23×D312yes—
502C22×D5C23×D312yes—
503C5×D4—124no—
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×C5C23×D312yes—
513C2×C4×C5C23×D312yes—
514C2×C4×C5C23×D312yes—
515C22⋊D5—124no—
516C22⋊D5—124no—
517C22⋊D5—124no—
518C22⋊D5—124no—
519C2×Dic5—22no—
520C2×Dic5—22no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—62no—
526C2×Dic5—62no—
527C2×Dic5—62no—
528C2×Dic5—62no—
529C2×Dic5—124no—
530C2×Dic5C23×D312yes—
531C2×Dic5C23×D312yes—
532D20—44no—
533C4×D5—44no—
534C4×D5—124no—
535Dic10—124no—
536Dic10—124no—
537C22×Q8—151no—
538C22×Q8—151no—
539C22×D4—31no—
540C22×D4—51no—
541C22×D4—151no—
542C22×D4—151no—
543C22×D4—151no—
544C22×D4—151no—
545C23×C4—31no—
546C23×C4—51no—
547C23×C4—151no—
548C23×C4—151no—
549#125—158no—
550#124—158no—
551#124—158no—
552#123—38no—
553#123—58no—
554#123—158no—
555#123—158no—
556C22⋊Q8—158no—
557C22⋊Q8—158no—
558C22⋊Q8—158no—
559C22⋊Q8—158no—
560#121—158no—
561#121—158no—
562#121—158no—
563#121—158no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—51no—
566C2×C4⋊C4—151no—
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⋊C4D3×D511yescharacteristic
574C2×C22⋊C4—31no—
575C2×C22⋊C4—31no—
576C2×C22⋊C4—31no—
577C2×C22⋊C4—51no—
578C2×C22⋊C4—51no—
579C2×C22⋊C4—51no—
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×C42—151no—
587C2×C3×C5#56214yescomplemented
588C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
589C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
590C2×C3×C5C2×2−1+411yescharacteristic
591C3×D5—42no—
592C3×D5—42no—
593C5×D3—42no—
594C5×D3—42no—
595C23×C3—52no—
596C23×C3—52no—
597C23×C3—102no—
598C23×C3—102no—
599C23×C3—102no—
600C23×C3—102no—
601C23×C3—102no—
602C23×C3—102no—
603C23×C3C23×D511yescharacteristic
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3C23×D512yes—
611C22×D3C23×D512yes—
612C3×D4—204no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—52no—
617C2×C3×C4—52no—
618C2×C3×C4—102no—
619C2×C3×C4—102no—
620C2×C3×C4—204no—
621C2×C3×C4C23×D512yes—
622C2×C3×C4C23×D512yes—
623C2×C3×C4C23×D512yes—
624#67—204no—
625#67—204no—
626#67—204no—
627#67—204no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—52no—
631C2×Dic3—52no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—102no—
635C2×Dic3—102no—
636C2×Dic3—102no—
637C2×Dic3—102no—
638C2×Dic3—204no—
639C2×Dic3C23×D512yes—
640C2×Dic3C23×D512yes—
641D12—44no—
642C4×D3—44no—
643C4×D3—204no—
644Dic6—204no—
645Dic6—204no—
646C22×C5—62no—
647C22×C5—62no—
648C22×C5—62no—
649C22×C5—62no—
650C22×C5—62no—
651C22×C5—62no—
652C22×C5—124no—
653C22×C5—124no—
654C22×C5#100412yes—
655C22×C5#100912yes—
656C22×C5#101012yes—
657C22×C5C24×D311yescharacteristic
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—22no—
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—44no—
665C2×D5—44no—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—22no—
669C4×C5—62no—
670C4×C5—62no—
671Dic5—22no—
672Dic5—22no—
673Dic5—62no—
674Dic5—62no—
675Dic5—62no—
676Dic5—62no—
677C24—31no—
678C24—31no—
679C24—51no—
680C24—51no—
681C2×Q8—154no—
682C2×Q8—154no—
683C2×Q8—602no—
684C2×Q8—602no—
685C2×D4—34no—
686C2×D4—54no—
687C2×D4—122no—
688C2×D4—154no—
689C2×D4—154no—
690C2×D4—154no—
691C2×D4—154no—
692C2×D4—202no—
693C2×D4—602no—
694C2×D4—602no—
695C2×D4—602no—
696C2×D4—602no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—34no—
700C22×C4—51no—
701C22×C4—51no—
702C22×C4—54no—
703C22×C4—122no—
704C22×C4—154no—
705C22×C4—154no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—151no—
709C22×C4—151no—
710C22×C4—202no—
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—154no—
719C4⋊C4—154no—
720C4⋊C4—154no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4C2×D3×D514yes—
726C22⋊C4—34no—
727C22⋊C4—34no—
728C22⋊C4—34no—
729C22⋊C4—54no—
730C22⋊C4—54no—
731C22⋊C4—54no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C22⋊C4—154no—
737C22⋊C4—154no—
738C42—154no—
739C3×C5C2×#56211yescharacteristic, complemented, Hall
740C22×C3—102no—
741C22×C3—102no—
742C22×C3—102no—
743C22×C3—102no—
744C22×C3—102no—
745C22×C3—102no—
746C22×C3—204no—
747C22×C3—204no—
748C22×C3#414412yes—
749C22×C3#414912yes—
750C22×C3#415012yes—
751C22×C3C24×D511yescharacteristic
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—44no—
759C2×D3—44no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—102no—
764C3×C4—102no—
765Dic3—22no—
766Dic3—22no—
767Dic3—102no—
768Dic3—102no—
769Dic3—102no—
770Dic3—102no—
771C2×C5—122no—
772C2×C5—122no—
773C2×C5#566714yescomplemented
774C2×C5C2×#100411yescharacteristic
775C2×C5C2×#100911yescharacteristic
776C2×C5C2×#101011yescharacteristic
777D5—42no—
778D5—42no—
779C23—32no—
780C23—32no—
781C23—52no—
782C23—52no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—102no—
790C23—102no—
791C23—102no—
792C23—102no—
793C23—102no—
794C23—102no—
795C23C22×D3×D511yescharacteristic
796Q8—604no—
797Q8—604no—
798D4—124no—
799D4—204no—
800D4—604no—
801D4—604no—
802D4—604no—
803D4—604no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—52no—
810C2×C4—52no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—102no—
814C2×C4—102no—
815C2×C4—124no—
816C2×C4—152no—
817C2×C4—152no—
818C2×C4—152no—
819C2×C4—152no—
820C2×C4—204no—
821C2×C4—302no—
822C2×C4—302no—
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—202no—
832C2×C3#6600114yescomplemented
833C2×C3C2×#414411yescharacteristic
834C2×C3C2×#414911yescharacteristic
835C2×C3C2×#415011yescharacteristic
836D3—42no—
837D3—42no—
838C5C2×#566711yescharacteristic, complemented, Sylow
839C22—62no—
840C22—62no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—62no—
845C22—102no—
846C22—102no—
847C22—102no—
848C22—102no—
849C22—102no—
850C22—102no—
851C22—124no—
852C22—124no—
853C22—204no—
854C22—204no—
855C22#9200112yes—
856C22#9202512yes—
857C22#9203512yes—
858C22C23×D3×D511yescharacteristic
859C4—22no—
860C4—22no—
861C4—22no—
862C4—62no—
863C4—62no—
864C4—102no—
865C4—102no—
866C4—302no—
867C4—302no—
868C4—302no—
869C4—302no—
870C3C2×#6600111yescharacteristic, complemented, Sylow
871C2—122no—
872C2—122no—
873C2—202no—
874C2—202no—
875C2#1175364314yesdirect product factor
876C2C2×#9200111yescharacteristic
877C2C2×#9202511yescharacteristic
878C2C2×#9203511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#562
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91779C2semidirect
2. C2×C5×#894C2semidirect
3. C2×C3×#4040C2semidirect
4. C2×#91464C2semidirect
5. C2×#91464C2semidirect
6. C2×#91457C2semidirect
7. C2×#91456C2semidirect
8. C2×#91453C2semidirect
9. C2×#91449C2semidirect
10. C2×#91422C2semidirect
11. C2×#91417C2semidirect
12. C2×#91414C2semidirect
13. C2×#91408C2semidirect
14. C2×#91352C2semidirect
15. C2×#91349C2semidirect
16. #11753643C2direct (N × H)
37. #91779C22semidirect
42. C5×#894C22semidirect
47. C3×#4040C22semidirect
56. #91464C22semidirect
57. #91464C22semidirect
58. #91457C22semidirect
59. #91456C22semidirect
60. #91453C22semidirect
61. #91449C22semidirect
62. #91422C22semidirect
63. #91417C22semidirect
64. #91414C22semidirect
65. #91408C22semidirect
66. #91352C22semidirect
67. #91349C22semidirect
77. C2×#4040D3semidirect
155. C2×#894D5semidirect
205. #4040C2×D3semidirect
307. #894C2×D5semidirect
587. C2×C3×C5#562semidirect
739. C3×C5C2×#562semidirect
773. C2×C5#5667semidirect
832. C2×C3#66001semidirect
838. C5C2×#5667semidirect
870. C3C2×#66001semidirect
875. C2#11753643direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917792
C2×C5×#8942
C2×C3×#40402
C2×#914642
C2×#914572
C2×#914562
C2×#914532
C2×#914492
C2×#914222
C2×#914172
C2×#914142
C2×#914082
C2×#913522
C2×#913492
#117536432
C2×#660013
C2×#56675