Finite Group Databasebeta

← C2×#11756421 #14481315

Subgroups — C2×#11756421 #14481315

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×#123C211yesmaximal, characteristic, complemented
2C2×#91828C211yesmaximal, characteristic
3C2×#91825C211yesmaximal, characteristic, complemented
4C2×C4×#1220C211yesmaximal, characteristic, complemented
5C2×#91813C211yesmaximal, characteristic, complemented
6#11756421C2116yesmaximal, direct product factor
7C2×#91787C211yesmaximal, characteristic, complemented
8C2×#91785C211yesmaximal, characteristic, complemented
9C2×#91777C211yesmaximal, characteristic, complemented
10C2×#91776C211yesmaximal, characteristic, complemented
11C2×#91774C211yesmaximal, characteristic, complemented
12C2×#91774C211yesmaximal, characteristic, complemented
13C2×#91772C211yesmaximal, characteristic, complemented
14C2×#91768C211yesmaximal, characteristic, complemented
15C2×#91767C211yesmaximal, characteristic, complemented
16C2×#91766C211yesmaximal, characteristic, complemented
17C2×#65996—31nomaximal, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C23×Dic15C2211yescharacteristic
23C22×C4×D15C2211yescharacteristic
24C22×Dic30C2211yescharacteristic
25C22×Dic30C2211yescharacteristic
26C22×Dic30C2211yescharacteristic
27C3×C5×#123C2218yescomplemented
28C2×C3×C5×C4⋊C4C2211yescharacteristic
29C2×C3×C5×C4⋊C4C2211yescharacteristic
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×#6719C2211yescharacteristic
34C2×#6719C2211yescharacteristic
35C2×#6719C2211yescharacteristic
36C2×#6719C2211yescharacteristic
37C2×#6719C2211yescharacteristic
38#91828C2218yes—
39#91825C2218yescomplemented
40C4×#1220C2218yescomplemented
41C2×#6714C2211yescharacteristic
42C2×#6714C2211yescharacteristic
43C2×#6714C2211yescharacteristic
44C2×#6714C2211yescharacteristic
45C2×C4⋊Dic15C2211yescharacteristic
46C2×C4⋊Dic15C2211yescharacteristic
47#91813C2218yescomplemented
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#91777C2218yescomplemented
61#91776C2218yescomplemented
62#91774C2218yescomplemented
63#91774C2218yescomplemented
64#91772C2218yescomplemented
65#91768C2218yescomplemented
66#91767C2218yescomplemented
67#91766C2218yescomplemented
68C2×#5662—51nomaximal, Hall
69C2×C5×#123D311yescharacteristic, complemented
70C2×#4085—31no—
71C2×#4082—31no—
72C2×C4×C22⋊D5—31no—
73C2×#4070—31no—
74#65996—316no—
75C2×#4044—31no—
76C2×#4042—31no—
77C2×#4034—31no—
78C2×#4033—31no—
79C2×#4031—31no—
80C2×#4031—31no—
81C2×#4029—31no—
82C2×#4025—31no—
83C2×#4024—31no—
84C2×#4023—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C2×C3×C5×D4—42no—
89C2×C3×C5×D4C2314yes—
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×C5C2314yes—
97C2×#1220—24no—
98C2×#1220—42no—
99C2×#1220C2314yes—
100C2×#1220C2314yes—
101C22×Dic15—24no—
102C22×Dic15C2314yes—
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109C22×Dic15C2311yescharacteristic
110C2×C4×D15—42no—
111C2×C4×D15C2314yes—
112C2×Dic30—24no—
113C2×Dic30—42no—
114C2×Dic30—42no—
115C2×Dic30C2314yes—
116C2×Dic30C2314yes—
117C2×Dic30C2314yes—
118C3×C5×C4⋊C4C2314yes—
119C3×C5×C4⋊C4C2314yes—
120C3×C5×C22⋊C4C2314yes—
121C3×C5×C22⋊C4C2314yes—
122C3×C5×C22⋊C4C2314yes—
123#6719C2314yes—
124#6719C2314yes—
125#6719C2314yes—
126#6719C2314yes—
127#6719C2314yes—
128#6714C2314yes—
129#6714C2314yes—
130#6714C2314yes—
131#6714C2314yes—
132C4⋊Dic15C2314yes—
133C4⋊Dic15C2314yes—
134#6712C2314yes—
135#6712C2314yes—
136#6712C2314yes—
137#6712C2314yes—
138#6712C2314yes—
139#6712C2314yes—
140C4×Dic15C2314yes—
141C4×Dic15C2314yes—
142C4×Dic15C2314yes—
143C4×Dic15C2314yes—
144C2×C3×#123D511yescharacteristic, complemented
145C2×#939—51no—
146C2×#936—51no—
147C2×C4×#67—51no—
148C2×#924—51no—
149#5662—516no—
150C2×#898—51no—
151C2×#896—51no—
152C2×#888—51no—
153C2×#887—51no—
154C2×#885—51no—
155C2×#885—51no—
156C2×#883—51no—
157C2×#879—51no—
158C2×#878—51no—
159C2×#877—51no—
160C22×C5×D4C2×D311yescharacteristic
161C23×C4×C5C2×D311yescharacteristic
162C22×C22⋊D5—31no—
163C22×C22⋊D5—31no—
164C23×Dic5—31no—
165C22×C4×D5—31no—
166C22×Dic10—31no—
167C22×Dic10—31no—
168C22×Dic10—31no—
169C5×#123C2×D318yescomplemented
170C2×C5×C4⋊C4C2×D311yescharacteristic
171C2×C5×C4⋊C4C2×D311yescharacteristic
172C2×C5×C22⋊C4C2×D311yescharacteristic
173C2×C5×C22⋊C4C2×D311yescharacteristic
174C2×C5×C22⋊C4C2×D311yescharacteristic
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5—31no—
179C2×C22⋊Dic5—31no—
180#4085—38no—
181#4082—38no—
182C4×C22⋊D5—38no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×C4⋊Dic5—31no—
188C2×C4⋊Dic5—31no—
189#4070—38no—
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#4034—38no—
203#4033—38no—
204#4031—38no—
205#4031—38no—
206#4029—38no—
207#4025—38no—
208#4024—38no—
209#4023—38no—
210C2×#542—151noSylow
211C23×C3×C5—22no—
212C23×C3×C5—22no—
213C23×C3×C5—22no—
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5C2412yes—
218C23×C3×C5C2412yes—
219C23×C3×C5C2411yescharacteristic
220C22×D15—22no—
221C22×D15—22no—
222C22×D15—22no—
223C22×D15C2412yes—
224C3×C5×D4—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—44no—
231C2×C3×C4×C5C2412yes—
232C2×C3×C4×C5C2412yes—
233C2×C3×C4×C5C2412yes—
234C2×C3×C4×C5C2412yes—
235C2×C3×C4×C5C2412yes—
236#1220—28no—
237#1220—44no—
238C2×Dic15—22no—
239C2×Dic15—22no—
240C2×Dic15—22no—
241C2×Dic15—22no—
242C2×Dic15—22no—
243C2×Dic15—22no—
244C2×Dic15—28no—
245C2×Dic15#4114yes—
246C2×Dic15C2412yes—
247C2×Dic15C2412yes—
248C2×Dic15C2412yes—
249C2×Dic15C2412yes—
250C2×Dic15C2412yes—
251C2×Dic15C2412yes—
252C2×Dic15C2412yes—
253C4×D15—44no—
254Dic30—28no—
255Dic30—44no—
256Dic30—44no—
257C22×C3×D4C2×D511yescharacteristic
258C23×C3×C4C2×D511yescharacteristic
259C22×#67—51no—
260C22×#67—51no—
261C23×Dic3—51no—
262C22×C4×D3—51no—
263C22×Dic6—51no—
264C22×Dic6—51no—
265C22×Dic6—51no—
266C3×#123C2×D518yescomplemented
267C2×C3×C4⋊C4C2×D511yescharacteristic
268C2×C3×C4⋊C4C2×D511yescharacteristic
269C2×C3×C22⋊C4C2×D511yescharacteristic
270C2×C3×C22⋊C4C2×D511yescharacteristic
271C2×C3×C22⋊C4C2×D511yescharacteristic
272C2×#217—51no—
273C2×#217—51no—
274C2×#217—51no—
275C2×#217—51no—
276C2×#217—51no—
277#939—58no—
278#936—58no—
279C4×#67—58no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×(C2×D3)⋊C4—51no—
284C2×C4⋊Dic3—51no—
285C2×C4⋊Dic3—51no—
286#924—58no—
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#888—58no—
300#887—58no—
301#885—58no—
302#885—58no—
303#883—58no—
304#879—58no—
305#878—58no—
306#877—58no—
307C24×C5C22×D311yescharacteristic
308C24×C5C22×D311yescharacteristic
309C23×D5—31no—
310C2×C5×D4—42no—
311C2×C5×D4C22×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×D314yes—
319C2×C22⋊D5—34no—
320C2×C22⋊D5—34no—
321C2×C22⋊D5—64no—
322C2×C22⋊D5—122no—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—31no—
328C22×Dic5—31no—
329C22×Dic5—31no—
330C22×Dic5—34no—
331C22×Dic5—64no—
332C2×C4×D5—34no—
333C2×C4×D5—122no—
334C2×Dic10—34no—
335C2×Dic10—34no—
336C2×Dic10—34no—
337C2×Dic10—64no—
338C2×Dic10—122no—
339C2×Dic10—122no—
340C5×C4⋊C4C22×D314yes—
341C5×C4⋊C4C22×D314yes—
342C5×C22⋊C4C22×D314yes—
343C5×C22⋊C4C22×D314yes—
344C5×C22⋊C4C22×D314yes—
345C22⋊Dic5—34no—
346C22⋊Dic5—34no—
347C22⋊Dic5—34no—
348C22⋊Dic5—34no—
349C22⋊Dic5—34no—
350#685—34no—
351#685—34no—
352#685—34no—
353#685—34no—
354C4⋊Dic5—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×#123D1511yescharacteristic, complemented
375C2×C22⋊Q8—151no—
376C2×C22⋊Q8—151no—
377C2×C22⋊Q8—151no—
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—22no—
386C22×C3×C5—22no—
387C22×C3×C5—22no—
388C22×C3×C5—44no—
389C22×C3×C5—44no—
390C22×C3×C5C2×#4112yes—
391C22×C3×C5H(5,𝔽2)12yes—
392C22×C3×C52−1+412yes—
393C22×C3×C5C2511yescharacteristic
394C2×D15—22no—
395C2×D15—22no—
396C2×D15—22no—
397C2×D15—44no—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—22no—
401C3×C4×C5—22no—
402C3×C4×C5—22no—
403Dic15—22no—
404Dic15—22no—
405Dic15—22no—
406Dic15—22no—
407Dic15—22no—
408Dic15—22no—
409Dic15C2×#4114yes—
410C24×C3C22×D511yescharacteristic
411C24×C3C22×D511yescharacteristic
412C23×D3—51no—
413C2×C3×D4—42no—
414C2×C3×D4C22×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×D514yes—
422C2×#67—54no—
423C2×#67—54no—
424C2×#67—104no—
425C2×#67—202no—
426C22×Dic3—51no—
427C22×Dic3—54no—
428C22×Dic3—51no—
429C22×Dic3—51no—
430C22×Dic3—51no—
431C22×Dic3—51no—
432C22×Dic3—51no—
433C22×Dic3—51no—
434C22×Dic3—104no—
435C2×C4×D3—54no—
436C2×C4×D3—202no—
437C2×Dic6—54no—
438C2×Dic6—54no—
439C2×Dic6—54no—
440C2×Dic6—104no—
441C2×Dic6—202no—
442C2×Dic6—202no—
443C3×C4⋊C4C22×D514yes—
444C3×C4⋊C4C22×D514yes—
445C3×C22⋊C4C22×D514yes—
446C3×C22⋊C4C22×D514yes—
447C3×C22⋊C4C22×D514yes—
448#217—54no—
449#217—54no—
450#217—54no—
451#217—54no—
452#217—54no—
453(C2×D3)⋊C4—54no—
454(C2×D3)⋊C4—54no—
455(C2×D3)⋊C4—54no—
456(C2×D3)⋊C4—54no—
457C4⋊Dic3—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×C5—22no—
473C23×C5—22no—
474C23×C5—22no—
475C23×C5C23×D312yes—
476C23×C5C23×D312yes—
477C23×C5C23×D311yescharacteristic
478C22×D5—32no—
479C22×D5—62no—
480C22×D5—62no—
481C22×D5—62no—
482C5×D4—44no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—22no—
486C2×C4×C5—22no—
487C2×C4×C5—22no—
488C2×C4×C5—44no—
489C2×C4×C5C23×D312yes—
490C2×C4×C5C23×D312yes—
491C2×C4×C5C23×D312yes—
492C2×C4×C5C23×D312yes—
493C2×C4×C5C23×D312yes—
494C22⋊D5—68no—
495C22⋊D5—124no—
496C2×Dic5—34no—
497C2×Dic5—32no—
498C2×Dic5—32no—
499C2×Dic5—32no—
500C2×Dic5—32no—
501C2×Dic5—32no—
502C2×Dic5—32no—
503C2×Dic5—32no—
504C2×Dic5—68no—
505C2×Dic5—62no—
506C2×Dic5—62no—
507C2×Dic5—62no—
508C2×Dic5—62no—
509C2×Dic5—62no—
510C2×Dic5—62no—
511C4×D5—124no—
512Dic10—68no—
513Dic10—124no—
514Dic10—124no—
515C22×Q8—151no—
516C22×Q8—151no—
517C22×Q8—151no—
518C22×D4—151no—
519C22×D4—151no—
520C22×D4C2×D1511yescharacteristic
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#123C2×D1518yescomplemented
532C22⋊Q8—158no—
533C22⋊Q8—158no—
534C22⋊Q8—158no—
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⋊C4—151no—
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⋊C4C2×D1511yescharacteristic
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—42no—
567C2×C3×C5#54214yescomplemented
568C2×C3×C5C22×#4111yescharacteristic
569C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
570C2×C3×C5C2×2−1+411yescharacteristic
571D15—42no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3C23×D512yes—
579C23×C3C23×D512yes—
580C23×C3C23×D511yescharacteristic
581C22×D3—52no—
582C22×D3—102no—
583C22×D3—102no—
584C22×D3—102no—
585C3×D4—44no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—44no—
592C2×C3×C4C23×D512yes—
593C2×C3×C4C23×D512yes—
594C2×C3×C4C23×D512yes—
595C2×C3×C4C23×D512yes—
596C2×C3×C4C23×D512yes—
597#67—108no—
598#67—204no—
599C2×Dic3—54no—
600C2×Dic3—52no—
601C2×Dic3—52no—
602C2×Dic3—52no—
603C2×Dic3—52no—
604C2×Dic3—52no—
605C2×Dic3—52no—
606C2×Dic3—52no—
607C2×Dic3—108no—
608C2×Dic3—102no—
609C2×Dic3—102no—
610C2×Dic3—102no—
611C2×Dic3—102no—
612C2×Dic3—102no—
613C2×Dic3—102no—
614C4×D3—204no—
615Dic6—108no—
616Dic6—204no—
617Dic6—204no—
618C22×C5—22no—
619C22×C5—22no—
620C22×C5—22no—
621C22×C5—22no—
622C22×C5—22no—
623C22×C5—22no—
624C22×C5—44no—
625C22×C5—44no—
626C22×C5#100412yes—
627C22×C5D3×#4112yes—
628C22×C5#101012yes—
629C22×C5C24×D311yescharacteristic
630C2×D5—62no—
631C2×D5—62no—
632C2×D5—62no—
633C2×D5—124no—
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—22no—
637C4×C5—22no—
638C4×C5—22no—
639Dic5—34no—
640Dic5—62no—
641Dic5—62no—
642Dic5—62no—
643Dic5—62no—
644Dic5—62no—
645Dic5—62no—
646C24—151no—
647C24C22×D1511yescharacteristic
648C24C22×D1511yescharacteristic
649C2×Q8—154no—
650C2×Q8—154no—
651C2×Q8—154no—
652C2×Q8—304no—
653C2×Q8—602no—
654C2×Q8—602no—
655C2×D4—42no—
656C2×D4—154no—
657C2×D4—154no—
658C2×D4—304no—
659C2×D4—602no—
660C2×D4C22×D1514yes—
661C22×C4—42no—
662C22×C4—151no—
663C22×C4—154no—
664C22×C4—151no—
665C22×C4—151no—
666C22×C4—151no—
667C22×C4—151no—
668C22×C4—151no—
669C22×C4—151no—
670C22×C4—154no—
671C22×C4—304no—
672C22×C4—602no—
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⋊C4—154no—
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⋊C4C22×D1514yes—
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—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—44no—
713C22×C3—44no—
714C22×C3#414412yes—
715C22×C3D5×#4112yes—
716C22×C3#415012yes—
717C22×C3C24×D511yescharacteristic
718C2×D3—102no—
719C2×D3—102no—
720C2×D3—102no—
721C2×D3—204no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—22no—
727Dic3—54no—
728Dic3—102no—
729Dic3—102no—
730Dic3—102no—
731Dic3—102no—
732Dic3—102no—
733Dic3—102no—
734C2×C5—42no—
735C2×C5—42no—
736C2×C5#566214yescomplemented
737C2×C5C2×#100411yescharacteristic
738C2×C5C2×D3×#4111yescharacteristic
739C2×C5C2×#101011yescharacteristic
740D5—122no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—152no—
748C23—302no—
749C23—302no—
750C23—302no—
751C23C23×D1512yes—
752C23C23×D1512yes—
753C23C23×D1511yescharacteristic
754Q8—308no—
755Q8—604no—
756Q8—604no—
757D4—44no—
758D4—308no—
759D4—604no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—44no—
766C2×C4—154no—
767C2×C4—152no—
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—302no—
781C2×C4—604no—
782C2×C4C23×D1512yes—
783C2×C4C23×D1512yes—
784C2×C4C23×D1512yes—
785C2×C4C23×D1512yes—
786C2×C4C23×D1512yes—
787C2×C3—42no—
788C2×C3—42no—
789C2×C3#6599614yescomplemented
790C2×C3C2×#414411yescharacteristic
791C2×C3C2×D5×#4111yescharacteristic
792C2×C3C2×#415011yescharacteristic
793D3—202no—
794C5C2×#566211yescharacteristic, complemented, Sylow
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—44no—
803C22—302no—
804C22—302no—
805C22—302no—
806C22—604no—
807C22#9209512yes—
808C22#41×D1512yes—
809C22#9210112yes—
810C22C24×D1511yescharacteristic
811C4—22no—
812C4—22no—
813C4—22no—
814C4—22no—
815C4—22no—
816C4—154no—
817C4—302no—
818C4—302no—
819C4—302no—
820C4—302no—
821C4—302no—
822C4—302no—
823C3C2×#6599611yescharacteristic, complemented, Sylow
824C2—42no—
825C2—42no—
826C2—602no—
827C2#1175642114yesdirect product factor
828C2C2×#9209511yescharacteristic
829C2C2×#41×D1511yescharacteristic
830C2C2×#9210111yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#123C2
socleC23×C3×C5C24
prime radicalC2×#91828C2
hypercenterC2×#123D15
hypocenterC3×C5C2×#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#123C2semidirect
3. C2×#91825C2semidirect
4. C2×C4×#1220C2semidirect
5. C2×#91813C2semidirect
6. #11756421C2direct (N × H)
7. C2×#91787C2semidirect
8. C2×#91785C2semidirect
9. C2×#91777C2semidirect
10. C2×#91776C2semidirect
11. C2×#91774C2semidirect
12. C2×#91774C2semidirect
13. C2×#91772C2semidirect
14. C2×#91768C2semidirect
15. C2×#91767C2semidirect
16. C2×#91766C2semidirect
27. C3×C5×#123C22semidirect
39. #91825C22semidirect
40. C4×#1220C22semidirect
47. #91813C22semidirect
58. #91787C22semidirect
59. #91785C22semidirect
60. #91777C22semidirect
61. #91776C22semidirect
62. #91774C22semidirect
63. #91774C22semidirect
64. #91772C22semidirect
65. #91768C22semidirect
66. #91767C22semidirect
67. #91766C22semidirect
69. C2×C5×#123D3semidirect
144. C2×C3×#123D5semidirect
169. C5×#123C2×D3semidirect
266. C3×#123C2×D5semidirect
374. C2×#123D15semidirect
531. #123C2×D15semidirect
567. C2×C3×C5#542semidirect
705. C3×C5C2×#542semidirect
736. C2×C5#5662semidirect
789. C2×C3#65996semidirect
794. C5C2×#5662semidirect
823. C3C2×#65996semidirect
827. C2#11756421direct (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×#1232
C2×#918282
C2×#918252
C2×C4×#12202
C2×#918132
#117564212
C2×#917872
C2×#917852
C2×#917772
C2×#917762
C2×#917742
C2×#917722
C2×#917682
C2×#917672
C2×#917662
C2×#659963
C2×#56625