Finite Group Databasebeta

← C2×#11756399 #14481321

Subgroups — C2×#11756399 #14481321

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 832 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×#91833C211yesmaximal, characteristic, complemented
4C2×#91818C211yesmaximal, characteristic, complemented
5C2×C4×#1220C211yesmaximal, characteristic, complemented
6#11756399C2116yesmaximal, direct product factor
7C2×#91787C211yesmaximal, characteristic, complemented
8C2×#91785C211yesmaximal, characteristic, complemented
9C2×#91785C211yesmaximal, characteristic, complemented
10C2×#91783C211yesmaximal, characteristic, complemented
11C2×#91781C211yesmaximal, characteristic, complemented
12C2×#91776C211yesmaximal, characteristic, complemented
13C2×#91774C211yesmaximal, characteristic, complemented
14C2×#91774C211yesmaximal, characteristic, complemented
15C2×#91773C211yesmaximal, characteristic
16C2×#91768C211yesmaximal, characteristic, complemented
17C2×#65974—31nomaximal, Hall
18C22×C3×C5×Q8C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C22×D60C2211yescharacteristic
23C22×C4×D15C2211yescharacteristic
24C22×C4×D15C2211yescharacteristic
25C22×Dic30C2211yescharacteristic
26C22×Dic30C2211yescharacteristic
27C3×C5×C22⋊Q8C2218yescomplemented
28C2×C3×C5×C4⋊C4C2211yescharacteristic
29C2×C3×C5×C4⋊C4C2211yescharacteristic
30C2×C3×C5×C4⋊C4C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×#6719C2211yescharacteristic
34C2×#6719C2211yescharacteristic
35#91836C2218yescomplemented
36#91833C2218yescomplemented
37#91818C2218yescomplemented
38C4×#1220C2218yescomplemented
39C2×#6714C2211yescharacteristic
40C2×#6714C2211yescharacteristic
41C2×#6714C2211yescharacteristic
42C2×#6714C2211yescharacteristic
43C2×#6714C2211yescharacteristic
44C2×#6714C2211yescharacteristic
45C2×#6714C2211yescharacteristic
46C2×#6714C2211yescharacteristic
47C2×C4⋊Dic15C2211yescharacteristic
48C2×#6712C2211yescharacteristic
49C2×#6712C2211yescharacteristic
50C2×#6712C2211yescharacteristic
51C2×#6712C2211yescharacteristic
52C2×#6712C2211yescharacteristic
53C2×#6712C2211yescharacteristic
54C2×C4×Dic15C2211yescharacteristic
55C2×C4×Dic15C2211yescharacteristic
56C2×C4×Dic15C2211yescharacteristic
57C2×C4×Dic15C2211yescharacteristic
58#91787C2218yescomplemented
59#91785C2218yescomplemented
60#91785C2218yescomplemented
61#91783C2218yescomplemented
62#91781C2218yescomplemented
63#91776C2218yescomplemented
64#91774C2218yescomplemented
65#91774C2218yescomplemented
66#91773C2218yes—
67#91768C2218yescomplemented
68C2×#5640—51nomaximal, Hall
69C2×C5×C22⋊Q8D311yescharacteristic, complemented
70C2×#4093—31no—
71C2×#4090—31no—
72C2×#4075—31no—
73C2×C4×C22⋊D5—31no—
74#65974—316no—
75C2×#4044—31no—
76C2×#4042—31no—
77C2×#4042—31no—
78C2×#4040—31no—
79C2×#4038—31no—
80C2×#4033—31no—
81C2×#4031—31no—
82C2×#4031—31no—
83C2×#4030—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C2×C3×C5×Q8—42no—
89C2×C3×C5×Q8C2314yes—
90C22×C3×C4×C5—42no—
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2314yes—
98C2×#1220—24no—
99C2×#1220—42no—
100C2×#1220C2314yes—
101C2×#1220C2314yes—
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C2×D60—42no—
109C2×D60C2314yes—
110C2×C4×D15—24no—
111C2×C4×D15—42no—
112C2×C4×D15C2314yes—
113C2×C4×D15C2314yes—
114C2×Dic30—24no—
115C2×Dic30—42no—
116C2×Dic30C2314yes—
117C2×Dic30C2314yes—
118C3×C5×C4⋊C4C2314yes—
119C3×C5×C4⋊C4C2314yes—
120C3×C5×C4⋊C4C2314yes—
121C3×C5×C22⋊C4C2314yes—
122C3×C5×C22⋊C4C2314yes—
123#6719C2314yes—
124#6719C2314yes—
125#6714C2314yes—
126#6714C2314yes—
127#6714C2314yes—
128#6714C2314yes—
129#6714C2314yes—
130#6714C2314yes—
131#6714C2314yes—
132#6714C2314yes—
133C4⋊Dic15C2314yes—
134#6712C2314yes—
135#6712C2314yes—
136#6712C2314yes—
137#6712C2314yes—
138#6712C2314yes—
139#6712C2314yes—
140C4×Dic15C2314yes—
141C4×Dic15C2314yes—
142C4×Dic15C2314yes—
143C4×Dic15C2314yes—
144C2×C3×C22⋊Q8D511yescharacteristic, complemented
145C2×#947—51no—
146C2×#944—51no—
147C2×#929—51no—
148C2×C4×#67—51no—
149#5640—516no—
150C2×#898—51no—
151C2×#896—51no—
152C2×#896—51no—
153C2×#894—51no—
154C2×#892—51no—
155C2×#887—51no—
156C2×#885—51no—
157C2×#885—51no—
158C2×#884—51no—
159C2×#879—51no—
160C22×C5×Q8C2×D311yescharacteristic
161C23×C4×C5C2×D311yescharacteristic
162C22×C22⋊D5—31no—
163C22×C22⋊D5—31no—
164C22×D20—31no—
165C22×C4×D5—31no—
166C22×C4×D5—31no—
167C22×Dic10—31no—
168C22×Dic10—31no—
169C5×C22⋊Q8C2×D318yescomplemented
170C2×C5×C4⋊C4C2×D311yescharacteristic
171C2×C5×C4⋊C4C2×D311yescharacteristic
172C2×C5×C4⋊C4C2×D311yescharacteristic
173C2×C5×C22⋊C4C2×D311yescharacteristic
174C2×C5×C22⋊C4C2×D311yescharacteristic
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177#4093—38no—
178#4090—38no—
179#4075—38no—
180C4×C22⋊D5—38no—
181C2×#685—31no—
182C2×#685—31no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685—31no—
189C2×C4⋊Dic5—31no—
190C2×#683—31no—
191C2×#683—31no—
192C2×#683—31no—
193C2×#683—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×C4×Dic5—31no—
197C2×C4×Dic5—31no—
198C2×C4×Dic5—31no—
199C2×C4×Dic5—31no—
200#4044—38no—
201#4042—38no—
202#4042—38no—
203#4040—38no—
204#4038—38no—
205#4033—38no—
206#4031—38no—
207#4031—38no—
208#4030—38no—
209#4025—38no—
210C2×#542—151noSylow
211C23×C3×C5—22no—
212C23×C3×C5—22no—
213C23×C3×C5—22no—
214C23×C3×C5C2412yes—
215C23×C3×C5C2411yescharacteristic
216C22×D15—22no—
217C22×D15—22no—
218C22×D15—22no—
219C22×D15—22no—
220C22×D15—22no—
221C22×D15—22no—
222C22×D15C2412yes—
223C22×D15C2412yes—
224C3×C5×Q8—44no—
225C2×C3×C4×C5—22no—
226C2×C3×C4×C5—22no—
227C2×C3×C4×C5—22no—
228C2×C3×C4×C5—22no—
229C2×C3×C4×C5—22no—
230C2×C3×C4×C5—22no—
231C2×C3×C4×C5—44no—
232C2×C3×C4×C5C2412yes—
233C2×C3×C4×C5C2412yes—
234C2×C3×C4×C5C2412yes—
235C2×C3×C4×C5C2412yes—
236C2×C3×C4×C5C2412yes—
237C2×C3×C4×C5C2412yes—
238#1220—28no—
239#1220—44no—
240C2×Dic15—22no—
241C2×Dic15—22no—
242C2×Dic15—22no—
243C2×Dic15—22no—
244C2×Dic15—22no—
245C2×Dic15#4114yes—
246C2×Dic15C2412yes—
247C2×Dic15C2412yes—
248C2×Dic15C2412yes—
249C2×Dic15C2412yes—
250C2×Dic15C2412yes—
251C2×Dic15C2412yes—
252D60—44no—
253C4×D15—28no—
254C4×D15—44no—
255Dic30—28no—
256Dic30—44no—
257C22×C3×Q8C2×D511yescharacteristic
258C23×C3×C4C2×D511yescharacteristic
259C22×#67—51no—
260C22×#67—51no—
261C22×D12—51no—
262C22×C4×D3—51no—
263C22×C4×D3—51no—
264C22×Dic6—51no—
265C22×Dic6—51no—
266C3×C22⋊Q8C2×D518yescomplemented
267C2×C3×C4⋊C4C2×D511yescharacteristic
268C2×C3×C4⋊C4C2×D511yescharacteristic
269C2×C3×C4⋊C4C2×D511yescharacteristic
270C2×C3×C22⋊C4C2×D511yescharacteristic
271C2×C3×C22⋊C4C2×D511yescharacteristic
272C2×#217—51no—
273C2×#217—51no—
274#947—58no—
275#944—58no—
276#929—58no—
277C4×#67—58no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×(C2×D3)⋊C4—51no—
284C2×(C2×D3)⋊C4—51no—
285C2×(C2×D3)⋊C4—51no—
286C2×C4⋊Dic3—51no—
287C2×Dic3⋊C4—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4—51no—
290C2×Dic3⋊C4—51no—
291C2×Dic3⋊C4—51no—
292C2×Dic3⋊C4—51no—
293C2×C4×Dic3—51no—
294C2×C4×Dic3—51no—
295C2×C4×Dic3—51no—
296C2×C4×Dic3—51no—
297#898—58no—
298#896—58no—
299#896—58no—
300#894—58no—
301#892—58no—
302#887—58no—
303#885—58no—
304#885—58no—
305#884—58no—
306#879—58no—
307C24×C5C22×D311yescharacteristic
308C23×D5—31no—
309C23×D5—31no—
310C2×C5×Q8—42no—
311C2×C5×Q8C22×D314yes—
312C22×C4×C5—42no—
313C22×C4×C5C22×D311yescharacteristic
314C22×C4×C5C22×D311yescharacteristic
315C22×C4×C5C22×D311yescharacteristic
316C22×C4×C5C22×D311yescharacteristic
317C22×C4×C5C22×D311yescharacteristic
318C22×C4×C5C22×D311yescharacteristic
319C22×C4×C5C22×D314yes—
320C2×C22⋊D5—34no—
321C2×C22⋊D5—34no—
322C2×C22⋊D5—64no—
323C2×C22⋊D5—122no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—31no—
328C22×Dic5—31no—
329C22×Dic5—31no—
330C2×D20—34no—
331C2×D20—122no—
332C2×C4×D5—34no—
333C2×C4×D5—34no—
334C2×C4×D5—64no—
335C2×C4×D5—122no—
336C2×Dic10—34no—
337C2×Dic10—34no—
338C2×Dic10—64no—
339C2×Dic10—122no—
340C5×C4⋊C4C22×D314yes—
341C5×C4⋊C4C22×D314yes—
342C5×C4⋊C4C22×D314yes—
343C5×C22⋊C4C22×D314yes—
344C5×C22⋊C4C22×D314yes—
345C22⋊Dic5—34no—
346C22⋊Dic5—34no—
347#685—34no—
348#685—34no—
349#685—34no—
350#685—34no—
351#685—34no—
352#685—34no—
353#685—34no—
354#685—34no—
355C4⋊Dic5—34no—
356#683—34no—
357#683—34no—
358#683—34no—
359#683—34no—
360#683—34no—
361#683—34no—
362C4×Dic5—34no—
363C4×Dic5—34no—
364C4×Dic5—34no—
365C4×Dic5—34no—
366#542—1516no—
367C2×C4⋊Q8—151no—
368C2×#126—151no—
369C2×#126—151no—
370C2×#124—151no—
371C2×#124—151no—
372C2×#124—151no—
373C2×#123—151no—
374C2×#123—151no—
375C2×C22⋊Q8—151no—
376C2×C22⋊Q8—151no—
377C2×C22⋊Q8D1511yescharacteristic, complemented
378C2×#121—151no—
379C2×C4×Q8—151no—
380C2×C4×D4—151no—
381C2×#117—151no—
382C22×C3×C5—22no—
383C22×C3×C5—22no—
384C22×C3×C5—22no—
385C22×C3×C5—44no—
386C22×C3×C5C2×#4112yes—
387C22×C3×C5H(5,𝔽2)12yes—
388C22×C3×C52−1+412yes—
389C22×C3×C5C2511yescharacteristic
390C2×D15—22no—
391C2×D15—22no—
392C2×D15—22no—
393C2×D15—22no—
394C2×D15—22no—
395C2×D15—22no—
396C2×D15—44no—
397C2×D15—44no—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—22no—
401C3×C4×C5—22no—
402C3×C4×C5—22no—
403C3×C4×C5—22no—
404Dic15—22no—
405Dic15—22no—
406Dic15—22no—
407Dic15—22no—
408Dic15—22no—
409Dic15C2×#4114yes—
410C24×C3C22×D511yescharacteristic
411C23×D3—51no—
412C23×D3—51no—
413C2×C3×Q8—42no—
414C2×C3×Q8C22×D514yes—
415C22×C3×C4—42no—
416C22×C3×C4C22×D511yescharacteristic
417C22×C3×C4C22×D511yescharacteristic
418C22×C3×C4C22×D511yescharacteristic
419C22×C3×C4C22×D511yescharacteristic
420C22×C3×C4C22×D511yescharacteristic
421C22×C3×C4C22×D511yescharacteristic
422C22×C3×C4C22×D514yes—
423C2×#67—54no—
424C2×#67—54no—
425C2×#67—104no—
426C2×#67—202no—
427C22×Dic3—51no—
428C22×Dic3—51no—
429C22×Dic3—51no—
430C22×Dic3—51no—
431C22×Dic3—51no—
432C22×Dic3—51no—
433C2×D12—54no—
434C2×D12—202no—
435C2×C4×D3—54no—
436C2×C4×D3—54no—
437C2×C4×D3—104no—
438C2×C4×D3—202no—
439C2×Dic6—54no—
440C2×Dic6—54no—
441C2×Dic6—104no—
442C2×Dic6—202no—
443C3×C4⋊C4C22×D514yes—
444C3×C4⋊C4C22×D514yes—
445C3×C4⋊C4C22×D514yes—
446C3×C22⋊C4C22×D514yes—
447C3×C22⋊C4C22×D514yes—
448#217—54no—
449#217—54no—
450(C2×D3)⋊C4—54no—
451(C2×D3)⋊C4—54no—
452(C2×D3)⋊C4—54no—
453(C2×D3)⋊C4—54no—
454(C2×D3)⋊C4—54no—
455(C2×D3)⋊C4—54no—
456(C2×D3)⋊C4—54no—
457(C2×D3)⋊C4—54no—
458C4⋊Dic3—54no—
459Dic3⋊C4—54no—
460Dic3⋊C4—54no—
461Dic3⋊C4—54no—
462Dic3⋊C4—54no—
463Dic3⋊C4—54no—
464Dic3⋊C4—54no—
465C4×Dic3—54no—
466C4×Dic3—54no—
467C4×Dic3—54no—
468C4×Dic3—54no—
469C23×C5—22no—
470C23×C5—22no—
471C23×C5—22no—
472C23×C5C23×D312yes—
473C23×C5C23×D311yescharacteristic
474C22×D5—32no—
475C22×D5—32no—
476C22×D5—62no—
477C22×D5—62no—
478C22×D5—62no—
479C22×D5—62no—
480C22×D5—62no—
481C22×D5—62no—
482C5×Q8—44no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—22no—
486C2×C4×C5—22no—
487C2×C4×C5—22no—
488C2×C4×C5—22no—
489C2×C4×C5—44no—
490C2×C4×C5C23×D312yes—
491C2×C4×C5C23×D312yes—
492C2×C4×C5C23×D312yes—
493C2×C4×C5C23×D312yes—
494C2×C4×C5C23×D312yes—
495C2×C4×C5C23×D312yes—
496C22⋊D5—68no—
497C22⋊D5—124no—
498C2×Dic5—34no—
499C2×Dic5—32no—
500C2×Dic5—32no—
501C2×Dic5—32no—
502C2×Dic5—32no—
503C2×Dic5—32no—
504C2×Dic5—32no—
505C2×Dic5—62no—
506C2×Dic5—62no—
507C2×Dic5—62no—
508C2×Dic5—62no—
509C2×Dic5—62no—
510D20—124no—
511C4×D5—68no—
512C4×D5—124no—
513Dic10—68no—
514Dic10—124no—
515C22×Q8—151no—
516C22×Q8—151no—
517C22×Q8C2×D1511yescharacteristic
518C22×D4—151no—
519C22×D4—151no—
520C22×D4—151no—
521C23×C4—151no—
522C23×C4—151no—
523C23×C4C2×D1511yescharacteristic
524C4⋊Q8—158no—
525#126—158no—
526#126—158no—
527#124—158no—
528#124—158no—
529#124—158no—
530#123—158no—
531#123—158no—
532C22⋊Q8—158no—
533C22⋊Q8—158no—
534C22⋊Q8C2×D1518yescomplemented
535#121—158no—
536C4×Q8—158no—
537C4×D4—158no—
538#117—158no—
539C2×C4⋊C4—151no—
540C2×C4⋊C4—151no—
541C2×C4⋊C4—151no—
542C2×C4⋊C4—151no—
543C2×C4⋊C4—151no—
544C2×C4⋊C4—151no—
545C2×C4⋊C4—151no—
546C2×C4⋊C4C2×D1511yescharacteristic
547C2×C4⋊C4C2×D1511yescharacteristic
548C2×C4⋊C4C2×D1511yescharacteristic
549C2×C22⋊C4—151no—
550C2×C22⋊C4—151no—
551C2×C22⋊C4—151no—
552C2×C22⋊C4—151no—
553C2×C22⋊C4—151no—
554C2×C22⋊C4—151no—
555C2×C22⋊C4—151no—
556C2×C22⋊C4—151no—
557C2×C22⋊C4—151no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4C2×D1511yescharacteristic
560C2×C22⋊C4C2×D1511yescharacteristic
561C2×C42—151no—
562C2×C42—151no—
563C2×C42—151no—
564C2×C42—151no—
565C2×C3×C5—42no—
566C2×C3×C5#54214yescomplemented
567C2×C3×C5C22×#4111yescharacteristic
568C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
569C2×C3×C5C2×2−1+411yescharacteristic
570D15—42no—
571D15—42no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3C23×D512yes—
576C23×C3C23×D511yescharacteristic
577C22×D3—52no—
578C22×D3—52no—
579C22×D3—102no—
580C22×D3—102no—
581C22×D3—102no—
582C22×D3—102no—
583C22×D3—102no—
584C22×D3—102no—
585C3×Q8—44no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—44no—
593C2×C3×C4C23×D512yes—
594C2×C3×C4C23×D512yes—
595C2×C3×C4C23×D512yes—
596C2×C3×C4C23×D512yes—
597C2×C3×C4C23×D512yes—
598C2×C3×C4C23×D512yes—
599#67—108no—
600#67—204no—
601C2×Dic3—54no—
602C2×Dic3—52no—
603C2×Dic3—52no—
604C2×Dic3—52no—
605C2×Dic3—52no—
606C2×Dic3—52no—
607C2×Dic3—52no—
608C2×Dic3—102no—
609C2×Dic3—102no—
610C2×Dic3—102no—
611C2×Dic3—102no—
612C2×Dic3—102no—
613D12—204no—
614C4×D3—108no—
615C4×D3—204no—
616Dic6—108no—
617Dic6—204no—
618C22×C5—22no—
619C22×C5—22no—
620C22×C5—22no—
621C22×C5—44no—
622C22×C5#100412yes—
623C22×C5#100712yes—
624C22×C5D3×#4112yes—
625C22×C5C24×D311yescharacteristic
626C2×D5—62no—
627C2×D5—62no—
628C2×D5—62no—
629C2×D5—62no—
630C2×D5—62no—
631C2×D5—62no—
632C2×D5—124no—
633C2×D5—124no—
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—22no—
637C4×C5—22no—
638C4×C5—22no—
639C4×C5—22no—
640Dic5—34no—
641Dic5—62no—
642Dic5—62no—
643Dic5—62no—
644Dic5—62no—
645Dic5—62no—
646C24—151no—
647C24—151no—
648C24C22×D1511yescharacteristic
649C2×Q8—42no—
650C2×Q8—154no—
651C2×Q8—154no—
652C2×Q8—304no—
653C2×Q8—602no—
654C2×Q8C22×D1514yes—
655C2×D4—154no—
656C2×D4—154no—
657C2×D4—154no—
658C2×D4—304no—
659C2×D4—602no—
660C2×D4—602no—
661C22×C4—42no—
662C22×C4—151no—
663C22×C4—151no—
664C22×C4—151no—
665C22×C4—151no—
666C22×C4—151no—
667C22×C4—151no—
668C22×C4—154no—
669C22×C4—154no—
670C22×C4—304no—
671C22×C4—602no—
672C22×C4C22×D1511yescharacteristic
673C22×C4C22×D1511yescharacteristic
674C22×C4C22×D1511yescharacteristic
675C22×C4C22×D1511yescharacteristic
676C22×C4C22×D1511yescharacteristic
677C22×C4C22×D1511yescharacteristic
678C22×C4C22×D1514yes—
679C4⋊C4—154no—
680C4⋊C4—154no—
681C4⋊C4—154no—
682C4⋊C4—154no—
683C4⋊C4—154no—
684C4⋊C4—154no—
685C4⋊C4—154no—
686C4⋊C4C22×D1514yes—
687C4⋊C4C22×D1514yes—
688C4⋊C4C22×D1514yes—
689C22⋊C4—154no—
690C22⋊C4—154no—
691C22⋊C4—154no—
692C22⋊C4—154no—
693C22⋊C4—154no—
694C22⋊C4—154no—
695C22⋊C4—154no—
696C22⋊C4—154no—
697C22⋊C4—154no—
698C22⋊C4—154no—
699C22⋊C4C22×D1514yes—
700C22⋊C4C22×D1514yes—
701C42—154no—
702C42—154no—
703C42—154no—
704C42—154no—
705C3×C5C2×#54211yescharacteristic, complemented, Hall
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—44no—
710C22×C3#414412yes—
711C22×C3#414712yes—
712C22×C3D5×#4112yes—
713C22×C3C24×D511yescharacteristic
714C2×D3—102no—
715C2×D3—102no—
716C2×D3—102no—
717C2×D3—102no—
718C2×D3—102no—
719C2×D3—102no—
720C2×D3—204no—
721C2×D3—204no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—22no—
728Dic3—54no—
729Dic3—102no—
730Dic3—102no—
731Dic3—102no—
732Dic3—102no—
733Dic3—102no—
734C2×C5—42no—
735C2×C5#564014yescomplemented
736C2×C5C2×#100411yescharacteristic
737C2×C5C2×#100711yescharacteristic
738C2×C5C2×D3×#4111yescharacteristic
739D5—122no—
740D5—122no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—152no—
745C23—152no—
746C23—302no—
747C23—302no—
748C23—302no—
749C23—302no—
750C23—302no—
751C23—302no—
752C23C23×D1512yes—
753C23C23×D1511yescharacteristic
754Q8—44no—
755Q8—308no—
756Q8—604no—
757D4—308no—
758D4—604no—
759D4—604no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—44no—
767C2×C4—154no—
768C2×C4—152no—
769C2×C4—152no—
770C2×C4—152no—
771C2×C4—152no—
772C2×C4—152no—
773C2×C4—152no—
774C2×C4—308no—
775C2×C4—302no—
776C2×C4—302no—
777C2×C4—302no—
778C2×C4—302no—
779C2×C4—302no—
780C2×C4—604no—
781C2×C4C23×D1512yes—
782C2×C4C23×D1512yes—
783C2×C4C23×D1512yes—
784C2×C4C23×D1512yes—
785C2×C4C23×D1512yes—
786C2×C4C23×D1512yes—
787C2×C3—42no—
788C2×C3#6597414yescomplemented
789C2×C3C2×#414411yescharacteristic
790C2×C3C2×#414711yescharacteristic
791C2×C3C2×D5×#4111yescharacteristic
792D3—202no—
793D3—202no—
794C5C2×#564011yescharacteristic, complemented, Sylow
795C22—22no—
796C22—22no—
797C22—22no—
798C22—44no—
799C22—302no—
800C22—302no—
801C22—302no—
802C22—302no—
803C22—302no—
804C22—302no—
805C22—604no—
806C22—604no—
807C22#9209512yes—
808C22#9209812yes—
809C22#41×D1512yes—
810C22C24×D1511yescharacteristic
811C4—22no—
812C4—22no—
813C4—22no—
814C4—22no—
815C4—22no—
816C4—22no—
817C4—154no—
818C4—302no—
819C4—302no—
820C4—302no—
821C4—302no—
822C4—302no—
823C3C2×#6597411yescharacteristic, complemented, Sylow
824C2—42no—
825C2—602no—
826C2—602no—
827C2#1175639914yesdirect product factor
828C2C2×#9209511yescharacteristic
829C2C2×#9209811yescharacteristic
830C2C2×#41×D1511yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×C22⋊Q8C2
socleC23×C3×C5C24
prime radicalC2×#91773C2
hypercenterC2×C22⋊Q8D15
hypocenterC3×C5C2×#542
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×#91833C2semidirect
4. C2×#91818C2semidirect
5. C2×C4×#1220C2semidirect
6. #11756399C2direct (N × H)
7. C2×#91787C2semidirect
8. C2×#91785C2semidirect
9. C2×#91785C2semidirect
10. C2×#91783C2semidirect
11. C2×#91781C2semidirect
12. C2×#91776C2semidirect
13. C2×#91774C2semidirect
14. C2×#91774C2semidirect
16. C2×#91768C2semidirect
27. C3×C5×C22⋊Q8C22semidirect
35. #91836C22semidirect
36. #91833C22semidirect
37. #91818C22semidirect
38. C4×#1220C22semidirect
58. #91787C22semidirect
59. #91785C22semidirect
60. #91785C22semidirect
61. #91783C22semidirect
62. #91781C22semidirect
63. #91776C22semidirect
64. #91774C22semidirect
65. #91774C22semidirect
67. #91768C22semidirect
69. C2×C5×C22⋊Q8D3semidirect
144. C2×C3×C22⋊Q8D5semidirect
169. C5×C22⋊Q8C2×D3semidirect
266. C3×C22⋊Q8C2×D5semidirect
377. C2×C22⋊Q8D15semidirect
534. C22⋊Q8C2×D15semidirect
566. C2×C3×C5#542semidirect
705. C3×C5C2×#542semidirect
735. C2×C5#5640semidirect
788. C2×C3#65974semidirect
794. C5C2×#5640semidirect
823. C3C2×#65974semidirect
827. C2#11756399direct (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×#918332
C2×#918182
C2×C4×#12202
#117563992
C2×#917872
C2×#917852
C2×#917832
C2×#917812
C2×#917762
C2×#917742
C2×#917732
C2×#917682
C2×#659743
C2×#56405