Finite Group Databasebeta

← C2×#11756406 #14495283

Subgroups — C2×#11756406 #14495283

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×C3×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#91836C211yesmaximal, characteristic, complemented
3C2×#91835C211yesmaximal, characteristic, complemented
4C2×#91819C211yesmaximal, characteristic, complemented
5C2×#91818C211yesmaximal, characteristic, complemented
6#11756406C2116yesmaximal, direct product factor
7C2×#91786C211yesmaximal, characteristic, complemented
8C2×#91785C211yesmaximal, characteristic, complemented
9C2×#91784C211yesmaximal, characteristic, complemented
10C2×#91783C211yesmaximal, characteristic, complemented
11C2×#91783C211yesmaximal, characteristic, complemented
12C2×#91778C211yesmaximal, characteristic, complemented
13C2×#91774C211yesmaximal, characteristic, complemented
14C2×#91773C211yesmaximal, characteristic, complemented
15C2×#91773C211yesmaximal, characteristic, complemented
16C2×#91772C211yesmaximal, characteristic, complemented
17C2×#65981—31nomaximal, Hall
18C22×C3×C5×Q8C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic
23C22×D60C2211yescharacteristic
24C22×D60C2211yescharacteristic
25C22×D60C2211yescharacteristic
26C22×C4×D15C2211yescharacteristic
27C22×C4×D15C2211yescharacteristic
28C22×C4×D15C2211yescharacteristic
29C22×Dic30C2211yescharacteristic
30C3×C5×C22⋊Q8C2218yescomplemented
31C2×C3×C5×C4⋊C4C2211yescharacteristic
32C2×C3×C5×C4⋊C4C2211yescharacteristic
33C2×C3×C5×C4⋊C4C2211yescharacteristic
34C2×C3×C5×C22⋊C4C2211yescharacteristic
35C2×C3×C5×C22⋊C4C2211yescharacteristic
36C2×#6719C2211yescharacteristic
37#91836C2218yescomplemented
38#91835C2218yescomplemented
39#91819C2218yescomplemented
40#91818C2218yescomplemented
41C2×#6714C2211yescharacteristic
42C2×#6714C2211yescharacteristic
43C2×#6714C2211yescharacteristic
44C2×#6714C2211yescharacteristic
45C2×#6714C2211yescharacteristic
46C2×#6714C2211yescharacteristic
47C2×#6714C2211yescharacteristic
48C2×#6714C2211yescharacteristic
49C2×#6714C2211yescharacteristic
50C2×C4⋊Dic15C2211yescharacteristic
51C2×C4⋊Dic15C2211yescharacteristic
52C2×#6712C2211yescharacteristic
53C2×#6712C2211yescharacteristic
54C2×#6712C2211yescharacteristic
55C2×#6712C2211yescharacteristic
56C2×#6712C2211yescharacteristic
57C2×C4×Dic15C2211yescharacteristic
58#91786C2218yescomplemented
59#91785C2218yescomplemented
60#91784C2218yescomplemented
61#91783C2218yescomplemented
62#91783C2218yescomplemented
63#91778C2218yescomplemented
64#91774C2218yescomplemented
65#91773C2218yescomplemented
66#91773C2218yescomplemented
67#91772C2218yescomplemented
68C2×#5647—51nomaximal, Hall
69C2×C5×C22⋊Q8D311yescharacteristic, complemented
70C2×#4093—31no—
71C2×#4092—31no—
72C2×#4076—31no—
73C2×#4075—31no—
74#65981—316no—
75C2×#4043—31no—
76C2×#4042—31no—
77C2×#4041—31no—
78C2×#4040—31no—
79C2×#4040—31no—
80C2×#4035—31no—
81C2×#4031—31no—
82C2×#4030—31no—
83C2×#4030—31no—
84C2×#4029—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C2×C3×C5×Q8—42no—
90C2×C3×C5×Q8C2314yes—
91C22×C3×C4×C5—42no—
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2314yes—
99C2×#1220—42no—
100C2×#1220—42no—
101C2×#1220—42no—
102C2×#1220C2314yes—
103C2×#1220C2314yes—
104C2×#1220C2314yes—
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109C22×Dic15C2311yescharacteristic
110C2×D60—42no—
111C2×D60—42no—
112C2×D60—42no—
113C2×D60C2314yes—
114C2×D60C2314yes—
115C2×D60C2314yes—
116C2×C4×D15—42no—
117C2×C4×D15—42no—
118C2×C4×D15—42no—
119C2×C4×D15C2314yes—
120C2×C4×D15C2314yes—
121C2×C4×D15C2314yes—
122C2×Dic30—42no—
123C2×Dic30C2314yes—
124C3×C5×C4⋊C4C2314yes—
125C3×C5×C4⋊C4C2314yes—
126C3×C5×C4⋊C4C2314yes—
127C3×C5×C22⋊C4C2314yes—
128C3×C5×C22⋊C4C2314yes—
129#6719C2314yes—
130#6714C2314yes—
131#6714C2314yes—
132#6714C2314yes—
133#6714C2314yes—
134#6714C2314yes—
135#6714C2314yes—
136#6714C2314yes—
137#6714C2314yes—
138#6714C2314yes—
139C4⋊Dic15C2314yes—
140C4⋊Dic15C2314yes—
141#6712C2314yes—
142#6712C2314yes—
143#6712C2314yes—
144#6712C2314yes—
145#6712C2314yes—
146C4×Dic15C2314yes—
147C2×C3×C22⋊Q8D511yescharacteristic, complemented
148C2×#947—51no—
149C2×#946—51no—
150C2×#930—51no—
151C2×#929—51no—
152#5647—516no—
153C2×#897—51no—
154C2×#896—51no—
155C2×#895—51no—
156C2×#894—51no—
157C2×#894—51no—
158C2×#889—51no—
159C2×#885—51no—
160C2×#884—51no—
161C2×#884—51no—
162C2×#883—51no—
163C22×C5×Q8C2×D311yescharacteristic
164C23×C4×C5C2×D311yescharacteristic
165C22×C22⋊D5—31no—
166C22×C22⋊D5—31no—
167C22×C22⋊D5—31no—
168C22×D20—31no—
169C22×D20—31no—
170C22×D20—31no—
171C22×C4×D5—31no—
172C22×C4×D5—31no—
173C22×C4×D5—31no—
174C22×Dic10—31no—
175C5×C22⋊Q8C2×D318yescomplemented
176C2×C5×C4⋊C4C2×D311yescharacteristic
177C2×C5×C4⋊C4C2×D311yescharacteristic
178C2×C5×C4⋊C4C2×D311yescharacteristic
179C2×C5×C22⋊C4C2×D311yescharacteristic
180C2×C5×C22⋊C4C2×D311yescharacteristic
181C2×C22⋊Dic5—31no—
182#4093—38no—
183#4092—38no—
184#4076—38no—
185#4075—38no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×C4⋊Dic5—31no—
196C2×C4⋊Dic5—31no—
197C2×#683—31no—
198C2×#683—31no—
199C2×#683—31no—
200C2×#683—31no—
201C2×#683—31no—
202C2×C4×Dic5—31no—
203#4043—38no—
204#4042—38no—
205#4041—38no—
206#4040—38no—
207#4040—38no—
208#4035—38no—
209#4031—38no—
210#4030—38no—
211#4030—38no—
212#4029—38no—
213C2×#562—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5C2412yes—
218C23×C3×C5C2411yescharacteristic
219C22×D15—22no—
220C22×D15—22no—
221C22×D15—22no—
222C22×D15—22no—
223C22×D15—22no—
224C22×D15—22no—
225C22×D15—22no—
226C22×D15—22no—
227C22×D15—22no—
228C22×D15C2412yes—
229C22×D15C2412yes—
230C22×D15C2412yes—
231C3×C5×Q8—44no—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5—22no—
234C2×C3×C4×C5—22no—
235C2×C3×C4×C5—22no—
236C2×C3×C4×C5—22no—
237C2×C3×C4×C5—22no—
238C2×C3×C4×C5—44no—
239C2×C3×C4×C5C2412yes—
240C2×C3×C4×C5C2412yes—
241C2×C3×C4×C5C2412yes—
242C2×C3×C4×C5C2412yes—
243C2×C3×C4×C5C2412yes—
244C2×C3×C4×C5C2412yes—
245#1220—44no—
246#1220—44no—
247#1220—44no—
248C2×Dic15—22no—
249C2×Dic15—22no—
250C2×Dic15—22no—
251C2×Dic15—22no—
252C2×Dic15—22no—
253C2×Dic15C2412yes—
254C2×Dic15C2412yes—
255C2×Dic15C2412yes—
256C2×Dic15C2412yes—
257C2×Dic15C2412yes—
258D60—44no—
259D60—44no—
260D60—44no—
261C4×D15—44no—
262C4×D15—44no—
263C4×D15—44no—
264Dic30—44no—
265C22×C3×Q8C2×D511yescharacteristic
266C23×C3×C4C2×D511yescharacteristic
267C22×#67—51no—
268C22×#67—51no—
269C22×#67—51no—
270C22×D12—51no—
271C22×D12—51no—
272C22×D12—51no—
273C22×C4×D3—51no—
274C22×C4×D3—51no—
275C22×C4×D3—51no—
276C22×Dic6—51no—
277C3×C22⋊Q8C2×D518yescomplemented
278C2×C3×C4⋊C4C2×D511yescharacteristic
279C2×C3×C4⋊C4C2×D511yescharacteristic
280C2×C3×C4⋊C4C2×D511yescharacteristic
281C2×C3×C22⋊C4C2×D511yescharacteristic
282C2×C3×C22⋊C4C2×D511yescharacteristic
283C2×#217—51no—
284#947—58no—
285#946—58no—
286#930—58no—
287#929—58no—
288C2×(C2×D3)⋊C4—51no—
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)⋊C4—51no—
297C2×C4⋊Dic3—51no—
298C2×C4⋊Dic3—51no—
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×C4×Dic3—51no—
305#897—58no—
306#896—58no—
307#895—58no—
308#894—58no—
309#894—58no—
310#889—58no—
311#885—58no—
312#884—58no—
313#884—58no—
314#883—58no—
315C24×C5C22×D311yescharacteristic
316C23×D5—31no—
317C23×D5—31no—
318C23×D5—31no—
319C2×C5×Q8—42no—
320C2×C5×Q8C22×D314yes—
321C22×C4×C5—42no—
322C22×C4×C5C22×D311yescharacteristic
323C22×C4×C5C22×D311yescharacteristic
324C22×C4×C5C22×D311yescharacteristic
325C22×C4×C5C22×D311yescharacteristic
326C22×C4×C5C22×D311yescharacteristic
327C22×C4×C5C22×D311yescharacteristic
328C22×C4×C5C22×D314yes—
329C2×C22⋊D5—34no—
330C2×C22⋊D5—34no—
331C2×C22⋊D5—34no—
332C2×C22⋊D5—122no—
333C2×C22⋊D5—122no—
334C2×C22⋊D5—122no—
335C22×Dic5—31no—
336C22×Dic5—31no—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C2×D20—34no—
341C2×D20—34no—
342C2×D20—34no—
343C2×D20—122no—
344C2×D20—122no—
345C2×D20—122no—
346C2×C4×D5—34no—
347C2×C4×D5—34no—
348C2×C4×D5—34no—
349C2×C4×D5—122no—
350C2×C4×D5—122no—
351C2×C4×D5—122no—
352C2×Dic10—34no—
353C2×Dic10—122no—
354C5×C4⋊C4C22×D314yes—
355C5×C4⋊C4C22×D314yes—
356C5×C4⋊C4C22×D314yes—
357C5×C22⋊C4C22×D314yes—
358C5×C22⋊C4C22×D314yes—
359C22⋊Dic5—34no—
360#685—34no—
361#685—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367#685—34no—
368#685—34no—
369C4⋊Dic5—34no—
370C4⋊Dic5—34no—
371#683—34no—
372#683—34no—
373#683—34no—
374#683—34no—
375#683—34no—
376C4×Dic5—34no—
377#562—1516no—
378C2×#125—151no—
379C2×#124—151no—
380C2×#124—151no—
381C2×#123—151no—
382C2×#123—151no—
383C2×#123—151no—
384C2×#123—151no—
385C2×C22⋊Q8—151no—
386C2×C22⋊Q8—151no—
387C2×C22⋊Q8—151no—
388C2×C22⋊Q8D1511yescharacteristic, complemented
389C2×#121—151no—
390C2×#121—151no—
391C2×#121—151no—
392C2×#121—151no—
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—44no—
397C22×C3×C5H(5,𝔽2)12yes—
398C22×C3×C5H(5,𝔽2)12yes—
399C22×C3×C52−1+412yes—
400C22×C3×C5C2511yescharacteristic
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—22no—
405C2×D15—22no—
406C2×D15—22no—
407C2×D15—22no—
408C2×D15—22no—
409C2×D15—22no—
410C2×D15—44no—
411C2×D15—44no—
412C2×D15—44no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—22no—
416C3×C4×C5—22no—
417C3×C4×C5—22no—
418C3×C4×C5—22no—
419Dic15—22no—
420Dic15—22no—
421Dic15—22no—
422Dic15—22no—
423Dic15—22no—
424C24×C3C22×D511yescharacteristic
425C23×D3—51no—
426C23×D3—51no—
427C23×D3—51no—
428C2×C3×Q8—42no—
429C2×C3×Q8C22×D514yes—
430C22×C3×C4—42no—
431C22×C3×C4C22×D511yescharacteristic
432C22×C3×C4C22×D511yescharacteristic
433C22×C3×C4C22×D511yescharacteristic
434C22×C3×C4C22×D511yescharacteristic
435C22×C3×C4C22×D511yescharacteristic
436C22×C3×C4C22×D511yescharacteristic
437C22×C3×C4C22×D514yes—
438C2×#67—54no—
439C2×#67—54no—
440C2×#67—54no—
441C2×#67—202no—
442C2×#67—202no—
443C2×#67—202no—
444C22×Dic3—51no—
445C22×Dic3—51no—
446C22×Dic3—51no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C2×D12—54no—
450C2×D12—54no—
451C2×D12—54no—
452C2×D12—202no—
453C2×D12—202no—
454C2×D12—202no—
455C2×C4×D3—54no—
456C2×C4×D3—54no—
457C2×C4×D3—54no—
458C2×C4×D3—202no—
459C2×C4×D3—202no—
460C2×C4×D3—202no—
461C2×Dic6—54no—
462C2×Dic6—202no—
463C3×C4⋊C4C22×D514yes—
464C3×C4⋊C4C22×D514yes—
465C3×C4⋊C4C22×D514yes—
466C3×C22⋊C4C22×D514yes—
467C3×C22⋊C4C22×D514yes—
468#217—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)⋊C4—54no—
476(C2×D3)⋊C4—54no—
477(C2×D3)⋊C4—54no—
478C4⋊Dic3—54no—
479C4⋊Dic3—54no—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4—54no—
483Dic3⋊C4—54no—
484Dic3⋊C4—54no—
485C4×Dic3—54no—
486C23×C5—22no—
487C23×C5—22no—
488C23×C5—22no—
489C23×C5C23×D312yes—
490C23×C5C23×D311yescharacteristic
491C22×D5—32no—
492C22×D5—32no—
493C22×D5—32no—
494C22×D5—62no—
495C22×D5—62no—
496C22×D5—62no—
497C22×D5—62no—
498C22×D5—62no—
499C22×D5—62no—
500C22×D5—62no—
501C22×D5—62no—
502C22×D5—62no—
503C5×Q8—44no—
504C2×C4×C5—22no—
505C2×C4×C5—22no—
506C2×C4×C5—22no—
507C2×C4×C5—22no—
508C2×C4×C5—22no—
509C2×C4×C5—22no—
510C2×C4×C5—44no—
511C2×C4×C5C23×D312yes—
512C2×C4×C5C23×D312yes—
513C2×C4×C5C23×D312yes—
514C2×C4×C5C23×D312yes—
515C2×C4×C5C23×D312yes—
516C2×C4×C5C23×D312yes—
517C22⋊D5—124no—
518C22⋊D5—124no—
519C22⋊D5—124no—
520C2×Dic5—32no—
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—62no—
530D20—124no—
531D20—124no—
532D20—124no—
533C4×D5—124no—
534C4×D5—124no—
535C4×D5—124no—
536Dic10—124no—
537C22×Q8—151no—
538C22×Q8C2×D1511yescharacteristic
539C22×D4—151no—
540C22×D4—151no—
541C22×D4—151no—
542C22×D4—151no—
543C22×D4—151no—
544C22×D4—151no—
545C23×C4—151no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4C2×D1511yescharacteristic
549#125—158no—
550#124—158no—
551#124—158no—
552#123—158no—
553#123—158no—
554#123—158no—
555#123—158no—
556C22⋊Q8—158no—
557C22⋊Q8—158no—
558C22⋊Q8—158no—
559C22⋊Q8C2×D1518yescomplemented
560#121—158no—
561#121—158no—
562#121—158no—
563#121—158no—
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×C4⋊C4C2×D1511yescharacteristic
572C2×C4⋊C4C2×D1511yescharacteristic
573C2×C4⋊C4C2×D1511yescharacteristic
574C2×C22⋊C4—151no—
575C2×C22⋊C4—151no—
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×C22⋊C4C2×D1511yescharacteristic
585C2×C22⋊C4C2×D1511yescharacteristic
586C2×C42—151no—
587C2×C3×C5—42no—
588C2×C3×C5#56214yescomplemented
589C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
590C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
591C2×C3×C5C2×2−1+411yescharacteristic
592D15—42no—
593D15—42no—
594D15—42no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3C23×D512yes—
599C23×C3C23×D511yescharacteristic
600C22×D3—52no—
601C22×D3—52no—
602C22×D3—52no—
603C22×D3—102no—
604C22×D3—102no—
605C22×D3—102no—
606C22×D3—102no—
607C22×D3—102no—
608C22×D3—102no—
609C22×D3—102no—
610C22×D3—102no—
611C22×D3—102no—
612C3×Q8—44no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—44no—
620C2×C3×C4C23×D512yes—
621C2×C3×C4C23×D512yes—
622C2×C3×C4C23×D512yes—
623C2×C3×C4C23×D512yes—
624C2×C3×C4C23×D512yes—
625C2×C3×C4C23×D512yes—
626#67—204no—
627#67—204no—
628#67—204no—
629C2×Dic3—52no—
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—102no—
639D12—204no—
640D12—204no—
641D12—204no—
642C4×D3—204no—
643C4×D3—204no—
644C4×D3—204no—
645Dic6—204no—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5—22no—
649C22×C5—44no—
650C22×C5#100412yes—
651C22×C5#100712yes—
652C22×C5#100912yes—
653C22×C5C24×D311yescharacteristic
654C2×D5—62no—
655C2×D5—62no—
656C2×D5—62no—
657C2×D5—62no—
658C2×D5—62no—
659C2×D5—62no—
660C2×D5—62no—
661C2×D5—62no—
662C2×D5—62no—
663C2×D5—124no—
664C2×D5—124no—
665C2×D5—124no—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—22no—
669C4×C5—22no—
670C4×C5—22no—
671C4×C5—22no—
672Dic5—62no—
673Dic5—62no—
674Dic5—62no—
675Dic5—62no—
676Dic5—62no—
677C24—151no—
678C24—151no—
679C24—151no—
680C24C22×D1511yescharacteristic
681C2×Q8—42no—
682C2×Q8—154no—
683C2×Q8—602no—
684C2×Q8C22×D1514yes—
685C2×D4—154no—
686C2×D4—154no—
687C2×D4—154no—
688C2×D4—154no—
689C2×D4—154no—
690C2×D4—154no—
691C2×D4—602no—
692C2×D4—602no—
693C2×D4—602no—
694C2×D4—602no—
695C2×D4—602no—
696C2×D4—602no—
697C22×C4—42no—
698C22×C4—151no—
699C22×C4—151no—
700C22×C4—151no—
701C22×C4—151no—
702C22×C4—151no—
703C22×C4—154no—
704C22×C4—154no—
705C22×C4—154no—
706C22×C4—602no—
707C22×C4—602no—
708C22×C4—602no—
709C22×C4C22×D1511yescharacteristic
710C22×C4C22×D1511yescharacteristic
711C22×C4C22×D1511yescharacteristic
712C22×C4C22×D1511yescharacteristic
713C22×C4C22×D1511yescharacteristic
714C22×C4C22×D1511yescharacteristic
715C22×C4C22×D1514yes—
716C4⋊C4—154no—
717C4⋊C4—154no—
718C4⋊C4—154no—
719C4⋊C4—154no—
720C4⋊C4—154no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4C22×D1514yes—
724C4⋊C4C22×D1514yes—
725C4⋊C4C22×D1514yes—
726C22⋊C4—154no—
727C22⋊C4—154no—
728C22⋊C4—154no—
729C22⋊C4—154no—
730C22⋊C4—154no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C22⋊C4C22×D1514yes—
737C22⋊C4C22×D1514yes—
738C42—154no—
739C3×C5C2×#56211yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—44no—
744C22×C3#414412yes—
745C22×C3#414712yes—
746C22×C3#414912yes—
747C22×C3C24×D511yescharacteristic
748C2×D3—102no—
749C2×D3—102no—
750C2×D3—102no—
751C2×D3—102no—
752C2×D3—102no—
753C2×D3—102no—
754C2×D3—102no—
755C2×D3—102no—
756C2×D3—102no—
757C2×D3—204no—
758C2×D3—204no—
759C2×D3—204no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—22no—
766Dic3—102no—
767Dic3—102no—
768Dic3—102no—
769Dic3—102no—
770Dic3—102no—
771C2×C5—42no—
772C2×C5#564714yescomplemented
773C2×C5C2×#100411yescharacteristic
774C2×C5C2×#100711yescharacteristic
775C2×C5C2×#100911yescharacteristic
776D5—122no—
777D5—122no—
778D5—122no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—152no—
783C23—152no—
784C23—152no—
785C23—302no—
786C23—302no—
787C23—302no—
788C23—302no—
789C23—302no—
790C23—302no—
791C23—302no—
792C23—302no—
793C23—302no—
794C23C23×D1512yes—
795C23C23×D1511yescharacteristic
796Q8—44no—
797Q8—604no—
798D4—604no—
799D4—604no—
800D4—604no—
801D4—604no—
802D4—604no—
803D4—604no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—44no—
811C2×C4—152no—
812C2×C4—152no—
813C2×C4—152no—
814C2×C4—152no—
815C2×C4—152no—
816C2×C4—302no—
817C2×C4—302no—
818C2×C4—302no—
819C2×C4—302no—
820C2×C4—302no—
821C2×C4—604no—
822C2×C4—604no—
823C2×C4—604no—
824C2×C4C23×D1512yes—
825C2×C4C23×D1512yes—
826C2×C4C23×D1512yes—
827C2×C4C23×D1512yes—
828C2×C4C23×D1512yes—
829C2×C4C23×D1512yes—
830C2×C3—42no—
831C2×C3#6598114yescomplemented
832C2×C3C2×#414411yescharacteristic
833C2×C3C2×#414711yescharacteristic
834C2×C3C2×#414911yescharacteristic
835D3—202no—
836D3—202no—
837D3—202no—
838C5C2×#564711yescharacteristic, complemented, Sylow
839C22—22no—
840C22—22no—
841C22—22no—
842C22—44no—
843C22—302no—
844C22—302no—
845C22—302no—
846C22—302no—
847C22—302no—
848C22—302no—
849C22—302no—
850C22—302no—
851C22—302no—
852C22—604no—
853C22—604no—
854C22—604no—
855C22#9209512yes—
856C22#9209812yes—
857C22#9210012yes—
858C22C24×D1511yescharacteristic
859C4—22no—
860C4—22no—
861C4—22no—
862C4—22no—
863C4—22no—
864C4—22no—
865C4—302no—
866C4—302no—
867C4—302no—
868C4—302no—
869C4—302no—
870C3C2×#6598111yescharacteristic, complemented, Sylow
871C2—42no—
872C2—602no—
873C2—602no—
874C2—602no—
875C2#1175640614yesdirect product factor
876C2C2×#9209511yescharacteristic
877C2C2×#9209811yescharacteristic
878C2C2×#9210011yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×C22⋊Q8C2
socleC23×C3×C5C24
hypercenterC2×C22⋊Q8D15
hypocenterC3×C5C2×#562
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C22⋊Q8C2semidirect
2. C2×#91836C2semidirect
3. C2×#91835C2semidirect
4. C2×#91819C2semidirect
5. C2×#91818C2semidirect
6. #11756406C2direct (N × H)
7. C2×#91786C2semidirect
8. C2×#91785C2semidirect
9. C2×#91784C2semidirect
10. C2×#91783C2semidirect
11. C2×#91783C2semidirect
12. C2×#91778C2semidirect
13. C2×#91774C2semidirect
14. C2×#91773C2semidirect
15. C2×#91773C2semidirect
16. C2×#91772C2semidirect
30. C3×C5×C22⋊Q8C22semidirect
37. #91836C22semidirect
38. #91835C22semidirect
39. #91819C22semidirect
40. #91818C22semidirect
58. #91786C22semidirect
59. #91785C22semidirect
60. #91784C22semidirect
61. #91783C22semidirect
62. #91783C22semidirect
63. #91778C22semidirect
64. #91774C22semidirect
65. #91773C22semidirect
66. #91773C22semidirect
67. #91772C22semidirect
69. C2×C5×C22⋊Q8D3semidirect
147. C2×C3×C22⋊Q8D5semidirect
175. C5×C22⋊Q8C2×D3semidirect
277. C3×C22⋊Q8C2×D5semidirect
388. C2×C22⋊Q8D15semidirect
559. C22⋊Q8C2×D15semidirect
588. C2×C3×C5#562semidirect
739. C3×C5C2×#562semidirect
772. C2×C5#5647semidirect
831. C2×C3#65981semidirect
838. C5C2×#5647semidirect
870. C3C2×#65981semidirect
875. C2#11756406direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C22⋊Q82
C2×#918362
C2×#918352
C2×#918192
C2×#918182
#117564062
C2×#917862
C2×#917852
C2×#917842
C2×#917832
C2×#917782
C2×#917742
C2×#917732
C2×#917722
C2×#659813
C2×#56475