Finite Group Databasebeta

← C2×#11754411 #14483841

Subgroups — C2×#11754411 #14483841

Order 1920.

2400 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91813C211yesmaximal, characteristic, complemented
2C2×C4×C5×#67C211yesmaximal, characteristic
3C22×C3×#683C211yesmaximal, characteristic, complemented
4C2×#91574C211yesmaximal, characteristic, complemented
5C2×#91574C211yesmaximal, characteristic, complemented
6C2×Dic5×#67C211yesmaximal, characteristic
7C2×Dic5×#67C211yesmaximal, characteristic
8#11754411C2116yesmaximal, direct product factor
9C2×#91432C211yesmaximal, characteristic, complemented
10C2×#91417C211yesmaximal, characteristic, complemented
11C2×D3×#683C211yesmaximal, characteristic, complemented
12C2×#91379C211yesmaximal, characteristic, complemented
13C2×#91352C211yesmaximal, characteristic, complemented
14C2×#91343C211yesmaximal, characteristic, complemented
15C2×#91328C211yesmaximal, characteristic, complemented
16C2×#91324C211yesmaximal, characteristic, complemented
17C2×#65873—31nomaximal, Hall
18C23×C3×C4×C5C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C22×#1204C2211yescharacteristic
25C22×#1204C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C22×D3×Dic5C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30C2×C4⋊Dic15C2211yescharacteristic
31#91813C2218yescomplemented
32C2×#6712C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34C2×C5×#217C2211yescharacteristic
35C4×C5×#67C2218yes—
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×Dic3⋊C4C2211yescharacteristic
38C2×C4×C5×Dic3C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×#683C2218yescomplemented
44#91574C2218yescomplemented
45#91574C2218yescomplemented
46Dic5×#67C2218yes—
47Dic5×#67C2218yes—
48C2×Dic3⋊Dic5C2211yescharacteristic
49C2×Dic3⋊Dic5C2211yescharacteristic
50C2×Dic3⋊Dic5C2211yescharacteristic
51C2×Dic3⋊Dic5C2211yescharacteristic
52C2×#6669C2211yescharacteristic
53C2×#6669C2211yescharacteristic
54C2×#6668C2211yescharacteristic
55C2×#6668C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic
60#91432C2218yescomplemented
61#91417C2218yescomplemented
62D3×#683C2218yescomplemented
63#91379C2218yescomplemented
64#91352C2218yescomplemented
65#91343C2218yescomplemented
66#91328C2218yescomplemented
67#91324C2218yescomplemented
68C2×#5511—51nomaximal, Hall
69C2×C4×C5×D4—31no—
70C2×D4×Dic5—31no—
71C2×D4×Dic5—31no—
72C2×#4070—31no—
73C2×#4070—31no—
74C22×#683—31no—
75C22×#683D311yescharacteristic, complemented
76#65873—316no—
77C2×#4036—31no—
78C2×#4034—31no—
79C2×#4024—31no—
80C2×#4024—31no—
81C2×#4024—31no—
82C2×#4024—31no—
83C2×#4016—31no—
84C2×C4×Dic10—31no—
85C24×C3×C5C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C22×C3×C4×C5—42no—
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2314yes—
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C2×Dic30—42no—
96C2×Dic30C2314yes—
97C2×C5×#67Q818yescomplemented
98C2×C5×#67C2314yes—
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C2×C4×C5×D3—42no—
103C2×C4×C5×D3C2314yes—
104C22×C3×Dic5—24no—
105C22×C3×Dic5—42no—
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2314yes—
110C22×C3×Dic5C2314yes—
111C22×C3×Dic5C2311yescharacteristic
112C2×#1204—24no—
113C2×#1204—42no—
114C2×#1204C2314yes—
115C2×#1204C2314yes—
116C2×D3×Dic5—24no—
117C2×D3×Dic5—42no—
118C2×D3×Dic5C2314yes—
119C2×D3×Dic5C2314yes—
120#6719C2314yes—
121#6719C2314yes—
122C4⋊Dic15C2314yes—
123#6712C2314yes—
124#6712C2314yes—
125C5×#217C2314yes—
126C5×(C2×D3)⋊C4C2314yes—
127C5×Dic3⋊C4C2314yes—
128C4×C5×Dic3C2314yes—
129C3×#683C2314yes—
130C3×#683C2314yes—
131C3×#683C2314yes—
132C3×#683C2314yes—
133Dic3⋊Dic5C2314yes—
134Dic3⋊Dic5C2314yes—
135Dic3⋊Dic5C2314yes—
136Dic3⋊Dic5C2314yes—
137#6669C2314yes—
138#6669C2314yes—
139#6668C2314yes—
140#6668C2314yes—
141(C2×D3)⋊Dic5C2314yes—
142(C2×D3)⋊Dic5C2314yes—
143Dic3×Dic5C2314yes—
144Dic3×Dic5C2314yes—
145C22×C3×C4⋊C4—51no—
146C2×C4×#67—51no—
147C2×C4×#67—51no—
148C2×C4×#67D511yescharacteristic
149C2×#924—51no—
150C2×#924—51no—
151C2×#924—51no—
152#5511—516no—
153C2×#897—51no—
154C2×#896—51no—
155C2×#896—51no—
156C2×D3×C4⋊C4—51no—
157C2×#889—51no—
158C2×#889—51no—
159C2×#888—51no—
160C2×#887—51no—
161C22×C5×D4—31no—
162C23×C4×C5—31no—
163C23×C4×C5C2×D311yescharacteristic
164C23×Dic5—31no—
165C23×Dic5—31no—
166C23×Dic5C2×D311yescharacteristic
167C23×Dic5C2×D311yescharacteristic
168C22×Dic10—31no—
169C22×Dic10—31no—
170C22×Dic10—31no—
171C4×C5×D4—38no—
172C2×C5×C4⋊C4—31no—
173C2×C5×C22⋊C4—31no—
174C2×C5×C22⋊C4—31no—
175C2×C42×C5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5—31no—
179C2×C22⋊Dic5—31no—
180D4×Dic5—38no—
181D4×Dic5—38no—
182C2×C4⋊Dic5—31no—
183C2×C4⋊Dic5—31no—
184C2×C4⋊Dic5—31no—
185C2×C4⋊Dic5—31no—
186C2×C4⋊Dic5—31no—
187#4070—38no—
188#4070—38no—
189C2×#683—31no—
190C2×#683—31no—
191C2×#683—31no—
192C2×#683—31no—
193C2×#683—31no—
194C2×#683—31no—
195C2×#683—38no—
196C2×#683C2×D311yescharacteristic
197C2×#683C2×D311yescharacteristic
198C2×#683C2×D311yescharacteristic
199C2×#683C2×D311yescharacteristic
200C2×#683C2×D318yescomplemented
201C2×C4×Dic5—31no—
202C2×C4×Dic5—31no—
203#4036—38no—
204#4034—38no—
205#4024—38no—
206#4024—38no—
207#4024—38no—
208#4024—38no—
209#4016—38no—
210C4×Dic10—38no—
211C2×#554—151noSylow
212C23×C3×C5—22no—
213C23×C3×C5—22no—
214C23×C3×C5C2×Q814yes—
215C23×C3×C5C2412yes—
216C23×C3×C5C2411yescharacteristic
217C22×C5×D3—22no—
218C22×C5×D3—22no—
219C22×C5×D3C2×Q814yes—
220C22×C5×D3C2412yes—
221C2×C3×C4×C5—22no—
222C2×C3×C4×C5—22no—
223C2×C3×C4×C5—44no—
224C2×C3×C4×C5C2412yes—
225C2×C3×C4×C5C2412yes—
226C2×Dic15—22no—
227C2×Dic15—22no—
228C2×Dic15—22no—
229C2×Dic15—22no—
230C2×Dic15C2412yes—
231C2×Dic15C2412yes—
232C2×Dic15C2412yes—
233C2×Dic15C2412yes—
234Dic30—44no—
235C5×#67C2×Q8116yescomplemented
236C2×C5×Dic3—22no—
237C2×C5×Dic3—22no—
238C2×C5×Dic3C2×Q814yes—
239C2×C5×Dic3C2412yes—
240C2×C5×Dic3C2412yes—
241C2×C5×Dic3C2412yes—
242C4×C5×D3—44no—
243C2×C3×Dic5—22no—
244C2×C3×Dic5—22no—
245C2×C3×Dic5—22no—
246C2×C3×Dic5—28no—
247C2×C3×Dic5—44no—
248C2×C3×Dic5#4114yes—
249C2×C3×Dic5C2412yes—
250C2×C3×Dic5C2412yes—
251C2×C3×Dic5C2412yes—
252C2×C3×Dic5C2412yes—
253#1204—28no—
254#1204—44no—
255D3×Dic5—28no—
256D3×Dic5—44no—
257C23×C3×C4—51no—
258C23×C3×C4—51no—
259C23×C3×C4C2×D511yescharacteristic
260C22×#67C2×D511yescharacteristic
261C22×C4×D3—51no—
262C22×C4×D3—51no—
263C22×C4×D3C2×D511yescharacteristic
264C22×Dic6—51no—
265C22×Dic6—51no—
266C22×Dic6—51no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C4⋊C4—51no—
270C2×C3×C4⋊C4—51no—
271C2×C3×C4⋊C4—58no—
272C2×#217—51no—
273C2×#217—51no—
274C2×#217C2×D511yescharacteristic
275C4×#67—58no—
276C4×#67—58no—
277C4×#67C2×D518yes—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4C2×D511yescharacteristic
281C2×C4⋊Dic3—51no—
282C2×C4⋊Dic3—51no—
283C2×C4⋊Dic3—51no—
284#924—58no—
285#924—58no—
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×Dic3⋊C4—51no—
294C2×Dic3⋊C4—51no—
295C2×Dic3⋊C4C2×D511yescharacteristic
296C2×C4×Dic3—51no—
297C2×C4×Dic3—51no—
298C2×C4×Dic3C2×D511yescharacteristic
299#897—58no—
300#896—58no—
301#896—58no—
302D3×C4⋊C4—58no—
303#889—58no—
304#889—58no—
305#888—58no—
306#887—58no—
307C24×C5—31no—
308C24×C5C22×D311yescharacteristic
309C2×C5×D4—38no—
310C2×C5×D4—34no—
311C22×C4×C5—31no—
312C22×C4×C5—31no—
313C22×C4×C5—31no—
314C22×C4×C5—34no—
315C22×C4×C5—42no—
316C22×C4×C5—122no—
317C22×C4×C5C22×D311yescharacteristic
318C22×C4×C5C22×D311yescharacteristic
319C22×C4×C5C22×D314yes—
320C22×Dic5—24no—
321C22×Dic5—31no—
322C22×Dic5—31no—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C22×Dic5—34no—
326C22×Dic5—34no—
327C22×Dic5—42no—
328C22×Dic5—64no—
329C22×Dic5—122no—
330C22×Dic5C22×D311yescharacteristic
331C22×Dic5C22×D311yescharacteristic
332C22×Dic5C22×D311yescharacteristic
333C22×Dic5C22×D314yes—
334C22×Dic5C22×D314yes—
335C22×Dic5C22×D311yescharacteristic
336C2×Dic10—34no—
337C2×Dic10—34no—
338C2×Dic10—34no—
339C2×Dic10—64no—
340C2×Dic10—122no—
341C2×Dic10—122no—
342C5×C4⋊C4—34no—
343C5×C22⋊C4—34no—
344C5×C22⋊C4—34no—
345C42×C5—34no—
346C22⋊Dic5—34no—
347C22⋊Dic5—34no—
348C22⋊Dic5—34no—
349C22⋊Dic5—34no—
350C4⋊Dic5—34no—
351C4⋊Dic5—34no—
352C4⋊Dic5—34no—
353C4⋊Dic5—34no—
354C4⋊Dic5—34no—
355#683—34no—
356#683—34no—
357#683—34no—
358#683—34no—
359#683—34no—
360#683—34no—
361#683C22×D314yes—
362#683C22×D314yes—
363#683C22×D314yes—
364#683C22×D314yes—
365C4×Dic5—34no—
366C4×Dic5—34no—
367#554—1516no—
368C2×C4⋊Q8—151no—
369C2×#125—151no—
370C2×#125—151no—
371C2×C22⋊Q8—151no—
372C2×C22⋊Q8—151no—
373C2×C22⋊Q8—151no—
374C2×C22⋊Q8—151no—
375C2×C22⋊Q8—151no—
376C2×C22⋊Q8—151no—
377C2×C4×Q8—151no—
378C2×C4×D4—31no—
379C2×C4×D4—151no—
380C2×C4×D4—151no—
381C22×C4⋊C4—51no—
382C22×C4⋊C4—151no—
383C22×C3×C5—28no—
384C22×C3×C5—22no—
385C22×C3×C5—22no—
386C22×C3×C5C22×Q814yes—
387C22×C3×C5C22×Q812yes—
388C22×C3×C5C2×#4112yes—
389C22×C3×C5H(5,𝔽2)12yes—
390C22×C3×C5C2511yescharacteristic
391C2×C5×D3—28no—
392C2×C5×D3—22no—
393C2×C5×D3—22no—
394C2×C5×D3C22×Q814yes—
395C3×C4×C5—22no—
396C3×C4×C5—22no—
397Dic15—22no—
398Dic15—22no—
399Dic15—22no—
400Dic15—22no—
401C3×Dic5—22no—
402C3×Dic5—22no—
403C3×Dic5—22no—
404C3×Dic5C2×#4114yes—
405C5×Dic3—22no—
406C5×Dic3—22no—
407C5×Dic3C22×Q814yes—
408C24×C3C22×D511yescharacteristic
409C23×D3C22×D511yescharacteristic
410C22×C3×C4—42no—
411C22×C3×C4—51no—
412C22×C3×C4—51no—
413C22×C3×C4—51no—
414C22×C3×C4—51no—
415C22×C3×C4—54no—
416C22×C3×C4—54no—
417C22×C3×C4—104no—
418C22×C3×C4—202no—
419C22×C3×C4C22×D511yescharacteristic
420C22×C3×C4C22×D511yescharacteristic
421C22×C3×C4C22×D514yes—
422C2×#67Dic1018yescomplemented
423C2×#67C22×D514yes—
424C22×Dic3—51no—
425C22×Dic3—51no—
426C22×Dic3—51no—
427C22×Dic3—51no—
428C22×Dic3C22×D511yescharacteristic
429C22×Dic3C22×D511yescharacteristic
430C22×Dic3C22×D511yescharacteristic
431C2×C4×D3—42no—
432C2×C4×D3—54no—
433C2×C4×D3—54no—
434C2×C4×D3—104no—
435C2×C4×D3—202no—
436C2×C4×D3C22×D514yes—
437C2×Dic6—54no—
438C2×Dic6—54no—
439C2×Dic6—54no—
440C2×Dic6—104no—
441C2×Dic6—202no—
442C2×Dic6—202no—
443C3×C4⋊C4—54no—
444C3×C4⋊C4—54no—
445C3×C4⋊C4—54no—
446C3×C4⋊C4—54no—
447#217—54no—
448#217—54no—
449#217C22×D514yes—
450(C2×D3)⋊C4—54no—
451(C2×D3)⋊C4—54no—
452(C2×D3)⋊C4C22×D514yes—
453C4⋊Dic3—54no—
454C4⋊Dic3—54no—
455C4⋊Dic3—54no—
456Dic3⋊C4—54no—
457Dic3⋊C4—54no—
458Dic3⋊C4—54no—
459Dic3⋊C4—54no—
460Dic3⋊C4—54no—
461Dic3⋊C4—54no—
462Dic3⋊C4—54no—
463Dic3⋊C4—54no—
464Dic3⋊C4C22×D514yes—
465C4×Dic3—54no—
466C4×Dic3—54no—
467C4×Dic3C22×D514yes—
468C23×C5—22no—
469C23×C5—22no—
470C23×C5—34no—
471C23×C5—32no—
472C23×C5—62no—
473C23×C5—62no—
474C23×C5D3×Q814yes—
475C23×C5C23×D312yes—
476C23×C5C23×D311yescharacteristic
477C5×D4—316no—
478C2×C4×C5—22no—
479C2×C4×C5—22no—
480C2×C4×C5—34no—
481C2×C4×C5—32no—
482C2×C4×C5—32no—
483C2×C4×C5—32no—
484C2×C4×C5—44no—
485C2×C4×C5—62no—
486C2×C4×C5—62no—
487C2×C4×C5—124no—
488C2×C4×C5C23×D312yes—
489C2×C4×C5C23×D312yes—
490C2×Dic5—22no—
491C2×Dic5—22no—
492C2×Dic5—22no—
493C2×Dic5—28no—
494C2×Dic5—32no—
495C2×Dic5—32no—
496C2×Dic5—32no—
497C2×Dic5—32no—
498C2×Dic5—44no—
499C2×Dic5—62no—
500C2×Dic5—62no—
501C2×Dic5—62no—
502C2×Dic5—62no—
503C2×Dic5—68no—
504C2×Dic5—124no—
505C2×Dic5#23514yes—
506C2×Dic5C23×D312yes—
507C2×Dic5C23×D312yes—
508C2×Dic5C23×D312yes—
509C2×Dic5C23×D312yes—
510Dic10—68no—
511Dic10—124no—
512Dic10—124no—
513C22×Q8—151no—
514C22×Q8—151no—
515C22×Q8—151no—
516C22×D4—31no—
517C23×C4—31no—
518C23×C4—51no—
519C23×C4—51no—
520C23×C4—151no—
521C23×C4—151no—
522C23×C4D3×D511yescharacteristic
523C4⋊Q8—158no—
524#125—158no—
525#125—158no—
526C22⋊Q8—158no—
527C22⋊Q8—158no—
528C22⋊Q8—158no—
529C22⋊Q8—158no—
530C22⋊Q8—158no—
531C22⋊Q8—158no—
532C4×Q8—158no—
533C4×D4—38no—
534C4×D4—158no—
535C4×D4—158no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—51no—
538C2×C4⋊C4—51no—
539C2×C4⋊C4—51no—
540C2×C4⋊C4—51no—
541C2×C4⋊C4—58no—
542C2×C4⋊C4—158no—
543C2×C4⋊C4—151no—
544C2×C4⋊C4—151no—
545C2×C4⋊C4—151no—
546C2×C4⋊C4—151no—
547C2×C4⋊C4—151no—
548C2×C4⋊C4—151no—
549C2×C4⋊C4—151no—
550C2×C4⋊C4—151no—
551C2×C4⋊C4—151no—
552C2×C4⋊C4—151no—
553C2×C4⋊C4—151no—
554C2×C22⋊C4—31no—
555C2×C22⋊C4—31no—
556C2×C22⋊C4—151no—
557C2×C22⋊C4—151no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C42—31no—
561C2×C42—151no—
562C2×C42—151no—
563C2×C3×C5—24no—
564C2×C3×C5#55414yescomplemented
565C2×C3×C5C23×Q811yescharacteristic
566C2×C3×C5C22×#4111yescharacteristic
567C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
568C5×D3—24no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3C2×Dic1014yes—
572C23×C3C23×D512yes—
573C23×C3C23×D511yescharacteristic
574C22×D3—22no—
575C22×D3—22no—
576C22×D3C2×Dic1014yes—
577C22×D3C23×D512yes—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—44no—
581C2×C3×C4—54no—
582C2×C3×C4—52no—
583C2×C3×C4—52no—
584C2×C3×C4—52no—
585C2×C3×C4—52no—
586C2×C3×C4—108no—
587C2×C3×C4—102no—
588C2×C3×C4—102no—
589C2×C3×C4—102no—
590C2×C3×C4—204no—
591C2×C3×C4C23×D512yes—
592C2×C3×C4C23×D512yes—
593#67C2×Dic10116yescomplemented
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—52no—
597C2×Dic3—52no—
598C2×Dic3—52no—
599C2×Dic3—52no—
600C2×Dic3—102no—
601C2×Dic3—102no—
602C2×Dic3—102no—
603C2×Dic3—102no—
604C2×Dic3C2×Dic1014yes—
605C2×Dic3C23×D512yes—
606C2×Dic3C23×D512yes—
607C2×Dic3C23×D512yes—
608C4×D3—44no—
609C4×D3—108no—
610C4×D3—204no—
611Dic6—108no—
612Dic6—204no—
613Dic6—204no—
614C22×C5—22no—
615C22×C5—22no—
616C22×C5—28no—
617C22×C5—34no—
618C22×C5—62no—
619C22×C5—62no—
620C22×C5—68no—
621C22×C5C2×#23512yes—
622C22×C5#100412yes—
623C22×C5C2×D3×Q814yes—
624C22×C5C2×D3×Q812yes—
625C22×C5C24×D311yescharacteristic
626C4×C5—22no—
627C4×C5—22no—
628C4×C5—34no—
629C4×C5—62no—
630C4×C5—62no—
631Dic5—22no—
632Dic5—22no—
633Dic5—22no—
634Dic5—62no—
635Dic5—62no—
636Dic5—62no—
637Dic5—62no—
638Dic5C2×#23514yes—
639C24—31no—
640C24C2×D3×D511yescharacteristic
641C2×Q8—154no—
642C2×Q8—154no—
643C2×Q8—154no—
644C2×Q8—304no—
645C2×Q8—602no—
646C2×Q8—602no—
647C2×D4—38no—
648C2×D4—34no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—34no—
653C22×C4—42no—
654C22×C4—51no—
655C22×C4—54no—
656C22×C4—51no—
657C22×C4—51no—
658C22×C4—51no—
659C22×C4—54no—
660C22×C4—104no—
661C22×C4—122no—
662C22×C4—154no—
663C22×C4—154no—
664C22×C4—151no—
665C22×C4—151no—
666C22×C4—151no—
667C22×C4—151no—
668C22×C4—202no—
669C22×C4—304no—
670C22×C4—602no—
671C22×C4C2×D3×D511yescharacteristic
672C22×C4C2×D3×D511yescharacteristic
673C22×C4C2×D3×D514yes—
674C4⋊C4—34no—
675C4⋊C4—54no—
676C4⋊C4—54no—
677C4⋊C4—54no—
678C4⋊C4—54no—
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⋊C4—154no—
688C4⋊C4—154no—
689C4⋊C4—154no—
690C22⋊C4—34no—
691C22⋊C4—34no—
692C22⋊C4—154no—
693C22⋊C4—154no—
694C22⋊C4—154no—
695C22⋊C4—154no—
696C42—34no—
697C42—154no—
698C42—154no—
699C3×C5C2×#55411yescharacteristic, complemented, Hall
700C22×C3—28no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3C22×Dic1014yes—
704C22×C3C22×Dic1012yes—
705C22×C3#414412yes—
706C22×C3D5×#4112yes—
707C22×C3C24×D511yescharacteristic
708C2×D3—28no—
709C2×D3—22no—
710C2×D3—22no—
711C2×D3C22×Dic1014yes—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—54no—
715C3×C4—102no—
716C3×C4—102no—
717C3×C4—102no—
718Dic3—22no—
719Dic3—22no—
720Dic3—102no—
721Dic3—102no—
722Dic3—102no—
723Dic3—102no—
724Dic3C22×Dic1014yes—
725C2×C5—24no—
726C2×C5—64no—
727C2×C5#551114yescomplemented
728C2×C5C22×#23511yescharacteristic
729C2×C5C2×#100411yescharacteristic
730C2×C5C22×D3×Q811yescharacteristic
731C23—22no—
732C23—22no—
733C23—34no—
734C23—32no—
735C23—62no—
736C23—62no—
737C23D3×Dic1014yes—
738C23C22×D3×D512yes—
739C23C22×D3×D511yescharacteristic
740Q8—308no—
741Q8—604no—
742Q8—604no—
743D4—316no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—34no—
747C2×C4—32no—
748C2×C4—32no—
749C2×C4—32no—
750C2×C4—44no—
751C2×C4—54no—
752C2×C4—52no—
753C2×C4—52no—
754C2×C4—52no—
755C2×C4—52no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—108no—
759C2×C4—102no—
760C2×C4—102no—
761C2×C4—102no—
762C2×C4—124no—
763C2×C4—152no—
764C2×C4—152no—
765C2×C4—152no—
766C2×C4—152no—
767C2×C4—204no—
768C2×C4—308no—
769C2×C4—302no—
770C2×C4—302no—
771C2×C4—302no—
772C2×C4—302no—
773C2×C4—604no—
774C2×C4C22×D3×D512yes—
775C2×C4C22×D3×D512yes—
776C2×C3—24no—
777C2×C3#6587314yescomplemented
778C2×C3C23×Dic1011yescharacteristic
779C2×C3C2×#414411yescharacteristic
780C2×C3C2×D5×#4111yescharacteristic
781D3—24no—
782C5C2×#551111yescharacteristic, complemented, Sylow
783C22—22no—
784C22—28no—
785C22—22no—
786C22—34no—
787C22—62no—
788C22—68no—
789C22—62no—
790C22C2×D3×Dic1014yes—
791C22C2×D3×Dic1012yes—
792C22D5×#23512yes—
793C22#9204912yes—
794C22C23×D3×D511yescharacteristic
795C4—22no—
796C4—22no—
797C4—34no—
798C4—54no—
799C4—62no—
800C4—62no—
801C4—102no—
802C4—102no—
803C4—102no—
804C4—302no—
805C4—302no—
806C4—302no—
807C4—302no—
808C3C2×#6587311yescharacteristic, complemented, Sylow
809C2—24no—
810C2—64no—
811C2#1175441114yesdirect product factor
812C2C22×D3×Dic1011yescharacteristic
813C2C2×D5×#23511yescharacteristic
814C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#554
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#91813C2semidirect
3. C22×C3×#683C2semidirect
4. C2×#91574C2semidirect
5. C2×#91574C2semidirect
8. #11754411C2direct (N × H)
9. C2×#91432C2semidirect
10. C2×#91417C2semidirect
11. C2×D3×#683C2semidirect
12. C2×#91379C2semidirect
13. C2×#91352C2semidirect
14. C2×#91343C2semidirect
15. C2×#91328C2semidirect
16. C2×#91324C2semidirect
31. #91813C22semidirect
43. C2×C3×#683C22semidirect
44. #91574C22semidirect
45. #91574C22semidirect
60. #91432C22semidirect
61. #91417C22semidirect
62. D3×#683C22semidirect
63. #91379C22semidirect
64. #91352C22semidirect
65. #91343C22semidirect
66. #91328C22semidirect
67. #91324C22semidirect
75. C22×#683D3semidirect
97. C2×C5×#67Q8semidirect
200. C2×#683C2×D3semidirect
235. C5×#67C2×Q8semidirect
422. C2×#67Dic10semidirect
564. C2×C3×C5#554semidirect
593. #67C2×Dic10semidirect
699. C3×C5C2×#554semidirect
727. C2×C5#5511semidirect
777. C2×C3#65873semidirect
782. C5C2×#5511semidirect
808. C3C2×#65873semidirect
811. C2#11754411direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918132
C2×C4×C5×#672
C22×C3×#6832
C2×#915742
C2×Dic5×#672
#117544112
C2×#914322
C2×#914172
C2×D3×#6832
C2×#913792
C2×#913522
C2×#913432
C2×#913282
C2×#913242
C2×#658733
C2×#55115