Finite Group Databasebeta

← C2×#11754419 #14483843

Subgroups — C2×#11754419 #14483843

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
2C22×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
4C2×#91575C211yesmaximal, characteristic, complemented
5C2×#91575C211yesmaximal, characteristic, complemented
6C2×Dic3×C22⋊D5C211yesmaximal, characteristic
7C2×Dic3×C22⋊D5C211yesmaximal, characteristic
8#11754419C2116yesmaximal, direct product factor
9C2×#91431C211yesmaximal, characteristic, complemented
10C2×#91422C211yesmaximal, characteristic, complemented
11C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
12C2×#91378C211yesmaximal, characteristic, complemented
13C2×#91349C211yesmaximal, characteristic, complemented
14C2×#91334C211yesmaximal, characteristic, complemented
15C2×#91328C211yesmaximal, characteristic, complemented
16C2×#91323C211yesmaximal, characteristic, complemented
17C2×#65845—31nomaximal, Hall
18C23×C3×C4×C5C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C23×C5×Dic3C2211yescharacteristic
21C23×C5×Dic3C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×#1204C2211yescharacteristic
25C22×#1204C2211yescharacteristic
26C22×D5×Dic3C2211yescharacteristic
27C22×D5×Dic3C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30C2×C4⋊Dic15C2211yescharacteristic
31#91813C2218yescomplemented
32C2×#6712C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic
35C2×C5×Dic3⋊C4C2211yescharacteristic
36C2×C5×Dic3⋊C4C2211yescharacteristic
37C2×C5×Dic3⋊C4C2211yescharacteristic
38C2×C5×Dic3⋊C4C2218yescomplemented
39C2×C3×C22⋊Dic5C2211yescharacteristic
40C3×C4×C22⋊D5C2218yes—
41C2×C3×#685C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×C4×Dic5C2211yescharacteristic
44#91575C2218yescomplemented
45#91575C2218yescomplemented
46Dic3×C22⋊D5C2218yes—
47Dic3×C22⋊D5C2218yes—
48C2×Dic3⋊Dic5C2211yescharacteristic
49C2×Dic3⋊Dic5C2211yescharacteristic
50C2×#6669C2211yescharacteristic
51C2×#6669C2211yescharacteristic
52C2×#6668C2211yescharacteristic
53C2×#6668C2211yescharacteristic
54C2×#6668C2211yescharacteristic
55C2×#6668C2211yescharacteristic
56C2×#6665C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic
60#91431C2218yescomplemented
61#91422C2218yescomplemented
62D5×Dic3⋊C4C2218yescomplemented
63#91378C2218yescomplemented
64#91349C2218yescomplemented
65#91334C2218yescomplemented
66#91328C2218yescomplemented
67#91323C2218yescomplemented
68C2×#5539—51nomaximal, Hall
69C22×C5×C4⋊C4—31no—
70C2×C4×C22⋊D5—31no—
71C2×C4×C22⋊D5—31no—
72C2×C4×C22⋊D5D311yescharacteristic
73C2×#4070—31no—
74C2×#4070—31no—
75C2×#4070—31no—
76#65845—316no—
77C2×#4043—31no—
78C2×#4042—31no—
79C2×#4042—31no—
80C2×D5×C4⋊C4—31no—
81C2×#4035—31no—
82C2×#4035—31no—
83C2×#4034—31no—
84C2×#4033—31no—
85C24×C3×C5C2311yescharacteristic
86C23×C3×D5C2311yescharacteristic
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—
97C22×C5×Dic3—24no—
98C22×C5×Dic3—42no—
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C22×C5×Dic3C2314yes—
103C22×C5×Dic3C2314yes—
104C22×C5×Dic3C2311yescharacteristic
105C2×C3×C22⋊D5Q818yescomplemented
106C2×C3×C22⋊D5C2314yes—
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C2×C3×C4×D5—42no—
111C2×C3×C4×D5C2314yes—
112C2×#1204—24no—
113C2×#1204—42no—
114C2×#1204C2314yes—
115C2×#1204C2314yes—
116C2×D5×Dic3—24no—
117C2×D5×Dic3—42no—
118C2×D5×Dic3C2314yes—
119C2×D5×Dic3C2314yes—
120#6719C2314yes—
121#6719C2314yes—
122C4⋊Dic15C2314yes—
123#6712C2314yes—
124#6712C2314yes—
125C5×Dic3⋊C4C2314yes—
126C5×Dic3⋊C4C2314yes—
127C5×Dic3⋊C4C2314yes—
128C5×Dic3⋊C4C2314yes—
129C3×C22⋊Dic5C2314yes—
130C3×#685C2314yes—
131C3×#683C2314yes—
132C3×C4×Dic5C2314yes—
133Dic3⋊Dic5C2314yes—
134Dic3⋊Dic5C2314yes—
135#6669C2314yes—
136#6669C2314yes—
137#6668C2314yes—
138#6668C2314yes—
139#6668C2314yes—
140#6668C2314yes—
141#6665C2314yes—
142#6665C2314yes—
143Dic3×Dic5C2314yes—
144Dic3×Dic5C2314yes—
145C2×C3×C4×D4—51no—
146C2×D4×Dic3—51no—
147C2×D4×Dic3—51no—
148C2×#924—51no—
149C2×#924—51no—
150C22×Dic3⋊C4—51no—
151C22×Dic3⋊C4D511yescharacteristic, complemented
152#5539—516no—
153C2×#890—51no—
154C2×#888—51no—
155C2×#878—51no—
156C2×#878—51no—
157C2×#878—51no—
158C2×#878—51no—
159C2×#870—51no—
160C2×C4×Dic6—51no—
161C23×C4×C5—31no—
162C23×C4×C5—31no—
163C23×C4×C5C2×D311yescharacteristic
164C22×C22⋊D5C2×D311yescharacteristic
165C22×C4×D5—31no—
166C22×C4×D5—31no—
167C22×C4×D5C2×D311yescharacteristic
168C22×Dic10—31no—
169C22×Dic10—31no—
170C22×Dic10—31no—
171C2×C5×C4⋊C4—31no—
172C2×C5×C4⋊C4—31no—
173C2×C5×C4⋊C4—31no—
174C2×C5×C4⋊C4—31no—
175C2×C5×C4⋊C4—38no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5C2×D311yescharacteristic
179C4×C22⋊D5—38no—
180C4×C22⋊D5—38no—
181C4×C22⋊D5C2×D318yes—
182C2×#685—31no—
183C2×#685—31no—
184C2×#685C2×D311yescharacteristic
185C2×C4⋊Dic5—31no—
186C2×C4⋊Dic5—31no—
187C2×C4⋊Dic5—31no—
188#4070—38no—
189#4070—38no—
190#4070—38no—
191C2×#683—31no—
192C2×#683—31no—
193C2×#683—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×#683—31no—
198C2×#683—31no—
199C2×#683C2×D311yescharacteristic
200C2×C4×Dic5—31no—
201C2×C4×Dic5—31no—
202C2×C4×Dic5C2×D311yescharacteristic
203#4043—38no—
204#4042—38no—
205#4042—38no—
206D5×C4⋊C4—38no—
207#4035—38no—
208#4035—38no—
209#4034—38no—
210#4033—38no—
211C2×#554—151noSylow
212C23×C3×C5—22no—
213C23×C3×C5—22no—
214C23×C3×C5C2×Q814yes—
215C23×C3×C5C2412yes—
216C23×C3×C5C2411yescharacteristic
217C22×C3×D5—22no—
218C22×C3×D5—22no—
219C22×C3×D5C2×Q814yes—
220C22×C3×D5C2412yes—
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—
235C2×C5×Dic3—22no—
236C2×C5×Dic3—22no—
237C2×C5×Dic3—22no—
238C2×C5×Dic3—28no—
239C2×C5×Dic3—44no—
240C2×C5×Dic3#4114yes—
241C2×C5×Dic3C2412yes—
242C2×C5×Dic3C2412yes—
243C2×C5×Dic3C2412yes—
244C2×C5×Dic3C2412yes—
245C3×C22⋊D5C2×Q8116yescomplemented
246C2×C3×Dic5—22no—
247C2×C3×Dic5—22no—
248C2×C3×Dic5C2×Q814yes—
249C2×C3×Dic5C2412yes—
250C2×C3×Dic5C2412yes—
251C2×C3×Dic5C2412yes—
252C3×C4×D5—44no—
253#1204—28no—
254#1204—44no—
255D5×Dic3—28no—
256D5×Dic3—44no—
257C22×C3×D4—51no—
258C23×C3×C4—51no—
259C23×C3×C4C2×D511yescharacteristic
260C23×Dic3—51no—
261C23×Dic3—51no—
262C23×Dic3C2×D511yescharacteristic
263C23×Dic3C2×D511yescharacteristic
264C22×Dic6—51no—
265C22×Dic6—51no—
266C22×Dic6—51no—
267C3×C4×D4—58no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C42—51no—
272C2×#217—51no—
273C2×#217—51no—
274C2×#217—51no—
275C2×#217—51no—
276D4×Dic3—58no—
277D4×Dic3—58no—
278C2×C4⋊Dic3—51no—
279C2×C4⋊Dic3—51no—
280C2×C4⋊Dic3—51no—
281C2×C4⋊Dic3—51no—
282C2×C4⋊Dic3—51no—
283#924—58no—
284#924—58no—
285C2×Dic3⋊C4—51no—
286C2×Dic3⋊C4—51no—
287C2×Dic3⋊C4—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4—51no—
290C2×Dic3⋊C4—51no—
291C2×Dic3⋊C4—58no—
292C2×Dic3⋊C4C2×D511yescharacteristic
293C2×Dic3⋊C4C2×D511yescharacteristic
294C2×Dic3⋊C4C2×D511yescharacteristic
295C2×Dic3⋊C4C2×D511yescharacteristic
296C2×Dic3⋊C4C2×D518yescomplemented
297C2×C4×Dic3—51no—
298C2×C4×Dic3—51no—
299#890—58no—
300#888—58no—
301#878—58no—
302#878—58no—
303#878—58no—
304#878—58no—
305#870—58no—
306C4×Dic6—58no—
307C24×C5C22×D311yescharacteristic
308C23×D5C22×D311yescharacteristic
309C22×C4×C5—31no—
310C22×C4×C5—31no—
311C22×C4×C5—31no—
312C22×C4×C5—31no—
313C22×C4×C5—34no—
314C22×C4×C5—34no—
315C22×C4×C5—42no—
316C22×C4×C5—64no—
317C22×C4×C5—122no—
318C22×C4×C5C22×D311yescharacteristic
319C22×C4×C5C22×D311yescharacteristic
320C22×C4×C5C22×D314yes—
321C2×C22⋊D5Dic618yescomplemented
322C2×C22⋊D5C22×D314yes—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5C22×D311yescharacteristic
328C22×Dic5C22×D311yescharacteristic
329C22×Dic5C22×D311yescharacteristic
330C2×C4×D5—34no—
331C2×C4×D5—34no—
332C2×C4×D5—42no—
333C2×C4×D5—64no—
334C2×C4×D5—122no—
335C2×C4×D5C22×D314yes—
336C2×Dic10—34no—
337C2×Dic10—34no—
338C2×Dic10—34no—
339C2×Dic10—64no—
340C2×Dic10—122no—
341C2×Dic10—122no—
342C5×C4⋊C4—34no—
343C5×C4⋊C4—34no—
344C5×C4⋊C4—34no—
345C5×C4⋊C4—34no—
346C22⋊Dic5—34no—
347C22⋊Dic5—34no—
348C22⋊Dic5C22×D314yes—
349#685—34no—
350#685—34no—
351#685C22×D314yes—
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#683—34no—
362#683—34no—
363#683C22×D314yes—
364C4×Dic5—34no—
365C4×Dic5—34no—
366C4×Dic5C22×D314yes—
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—51no—
379C2×C4×D4—151no—
380C2×C4×D4—151no—
381C22×C4⋊C4—31no—
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×C3×D5—28no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5C22×Q814yes—
395C3×C4×C5—22no—
396C3×C4×C5—22no—
397Dic15—22no—
398Dic15—22no—
399Dic15—22no—
400Dic15—22no—
401C3×Dic5—22no—
402C3×Dic5—22no—
403C3×Dic5C22×Q814yes—
404C5×Dic3—22no—
405C5×Dic3—22no—
406C5×Dic3—22no—
407C5×Dic3C2×#4114yes—
408C24×C3—51no—
409C24×C3C22×D511yescharacteristic
410C2×C3×D4—58no—
411C2×C3×D4—54no—
412C22×C3×C4—42no—
413C22×C3×C4—51no—
414C22×C3×C4—51no—
415C22×C3×C4—51no—
416C22×C3×C4—54no—
417C22×C3×C4—202no—
418C22×C3×C4C22×D511yescharacteristic
419C22×C3×C4C22×D511yescharacteristic
420C22×C3×C4C22×D514yes—
421C22×Dic3—24no—
422C22×Dic3—42no—
423C22×Dic3—51no—
424C22×Dic3—51no—
425C22×Dic3—51no—
426C22×Dic3—51no—
427C22×Dic3—54no—
428C22×Dic3—54no—
429C22×Dic3—104no—
430C22×Dic3—202no—
431C22×Dic3C22×D514yes—
432C22×Dic3C22×D511yescharacteristic
433C22×Dic3C22×D511yescharacteristic
434C22×Dic3C22×D511yescharacteristic
435C22×Dic3C22×D514yes—
436C22×Dic3C22×D511yescharacteristic
437C2×Dic6—54no—
438C2×Dic6—54no—
439C2×Dic6—54no—
440C2×Dic6—104no—
441C2×Dic6—202no—
442C2×Dic6—202no—
443C3×C4⋊C4—54no—
444C3×C22⋊C4—54no—
445C3×C22⋊C4—54no—
446C3×C42—54no—
447#217—54no—
448#217—54no—
449#217—54no—
450#217—54no—
451C4⋊Dic3—54no—
452C4⋊Dic3—54no—
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⋊C4C22×D514yes—
463Dic3⋊C4C22×D514yes—
464Dic3⋊C4C22×D514yes—
465Dic3⋊C4C22×D514yes—
466C4×Dic3—54no—
467C4×Dic3—54no—
468C23×C5—22no—
469C23×C5—22no—
470C23×C5C2×Dic614yes—
471C23×C5C23×D312yes—
472C23×C5C23×D311yescharacteristic
473C22×D5—22no—
474C22×D5—22no—
475C22×D5C2×Dic614yes—
476C22×D5C23×D312yes—
477C2×C4×C5—22no—
478C2×C4×C5—22no—
479C2×C4×C5—34no—
480C2×C4×C5—32no—
481C2×C4×C5—32no—
482C2×C4×C5—32no—
483C2×C4×C5—32no—
484C2×C4×C5—44no—
485C2×C4×C5—68no—
486C2×C4×C5—62no—
487C2×C4×C5—62no—
488C2×C4×C5—62no—
489C2×C4×C5—124no—
490C2×C4×C5C23×D312yes—
491C2×C4×C5C23×D312yes—
492C22⋊D5C2×Dic6116yescomplemented
493C2×Dic5—22no—
494C2×Dic5—22no—
495C2×Dic5—32no—
496C2×Dic5—32no—
497C2×Dic5—32no—
498C2×Dic5—32no—
499C2×Dic5—62no—
500C2×Dic5—62no—
501C2×Dic5—62no—
502C2×Dic5—62no—
503C2×Dic5C2×Dic614yes—
504C2×Dic5C23×D312yes—
505C2×Dic5C23×D312yes—
506C2×Dic5C23×D312yes—
507C4×D5—44no—
508C4×D5—68no—
509C4×D5—124no—
510Dic10—68no—
511Dic10—124no—
512Dic10—124no—
513C22×Q8—151no—
514C22×Q8—151no—
515C22×Q8—151no—
516C22×D4—51no—
517C23×C4—31no—
518C23×C4—31no—
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—58no—
534C4×D4—158no—
535C4×D4—158no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—38no—
541C2×C4⋊C4—51no—
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—51no—
555C2×C22⋊C4—51no—
556C2×C22⋊C4—151no—
557C2×C22⋊C4—151no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C42—51no—
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
568C3×D5—24no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—54no—
572C23×C3—52no—
573C23×C3—102no—
574C23×C3—102no—
575C23×C3Q8×D514yes—
576C23×C3C23×D512yes—
577C23×C3C23×D511yescharacteristic
578C3×D4—516no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—44no—
582C2×C3×C4—54no—
583C2×C3×C4—52no—
584C2×C3×C4—52no—
585C2×C3×C4—52no—
586C2×C3×C4—102no—
587C2×C3×C4—102no—
588C2×C3×C4—204no—
589C2×C3×C4C23×D512yes—
590C2×C3×C4C23×D512yes—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—28no—
595C2×Dic3—44no—
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×Dic3—108no—
605C2×Dic3—204no—
606C2×Dic3#70914yes—
607C2×Dic3C23×D512yes—
608C2×Dic3C23×D512yes—
609C2×Dic3C23×D512yes—
610C2×Dic3C23×D512yes—
611Dic6—108no—
612Dic6—204no—
613Dic6—204no—
614C22×C5—22no—
615C22×C5—22no—
616C22×C5—28no—
617C22×C5C22×Dic614yes—
618C22×C5C22×Dic612yes—
619C22×C5#100412yes—
620C22×C5D3×#4112yes—
621C22×C5C24×D311yescharacteristic
622C2×D5—22no—
623C2×D5—22no—
624C2×D5—28no—
625C2×D5C22×Dic614yes—
626C4×C5—22no—
627C4×C5—22no—
628C4×C5—34no—
629C4×C5—62no—
630C4×C5—62no—
631C4×C5—62no—
632Dic5—22no—
633Dic5—22no—
634Dic5—62no—
635Dic5—62no—
636Dic5—62no—
637Dic5—62no—
638Dic5C22×Dic614yes—
639C24—51no—
640C24C2×D3×D511yescharacteristic
641C2×Q8—154no—
642C2×Q8—154no—
643C2×Q8—154no—
644C2×Q8—304no—
645C2×Q8—602no—
646C2×Q8—602no—
647C2×D4—58no—
648C2×D4—54no—
649C22×C4—31no—
650C22×C4—34no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—34no—
655C22×C4—42no—
656C22×C4—51no—
657C22×C4—51no—
658C22×C4—51no—
659C22×C4—54no—
660C22×C4—64no—
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—34no—
676C4⋊C4—34no—
677C4⋊C4—34no—
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—54no—
691C22⋊C4—54no—
692C22⋊C4—154no—
693C22⋊C4—154no—
694C22⋊C4—154no—
695C22⋊C4—154no—
696C42—54no—
697C42—154no—
698C42—154no—
699C3×C5C2×#55411yescharacteristic, complemented, Hall
700C22×C3—28no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—54no—
704C22×C3—108no—
705C22×C3—102no—
706C22×C3—102no—
707C22×C3C2×#70912yes—
708C22×C3#414412yes—
709C22×C3C2×Q8×D514yes—
710C22×C3C2×Q8×D512yes—
711C22×C3C24×D511yescharacteristic
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—54no—
715C3×C4—102no—
716C3×C4—102no—
717Dic3—22no—
718Dic3—22no—
719Dic3—22no—
720Dic3—102no—
721Dic3—102no—
722Dic3—102no—
723Dic3—102no—
724Dic3C2×#70914yes—
725C2×C5—24no—
726C2×C5#553914yescomplemented
727C2×C5C23×Dic611yescharacteristic
728C2×C5C2×#100411yescharacteristic
729C2×C5C2×D3×#4111yescharacteristic
730D5—24no—
731C23—22no—
732C23—22no—
733C23—54no—
734C23—52no—
735C23—102no—
736C23—102no—
737C23D5×Dic614yes—
738C23C22×D3×D512yes—
739C23C22×D3×D511yescharacteristic
740Q8—308no—
741Q8—604no—
742Q8—604no—
743D4—516no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—34no—
747C2×C4—32no—
748C2×C4—32no—
749C2×C4—32no—
750C2×C4—32no—
751C2×C4—44no—
752C2×C4—54no—
753C2×C4—52no—
754C2×C4—52no—
755C2×C4—52no—
756C2×C4—68no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
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—104no—
778C2×C3#6584514yescomplemented
779C2×C3C22×#70911yescharacteristic
780C2×C3C2×#414411yescharacteristic
781C2×C3C22×Q8×D511yescharacteristic
782C5C2×#553911yescharacteristic, complemented, Sylow
783C22—22no—
784C22—28no—
785C22—22no—
786C22—54no—
787C22—102no—
788C22—108no—
789C22—102no—
790C22C2×D5×Dic614yes—
791C22C2×D5×Dic612yes—
792C22D3×#70912yes—
793C22#9204912yes—
794C22C23×D3×D511yescharacteristic
795C4—22no—
796C4—22no—
797C4—34no—
798C4—54no—
799C4—62no—
800C4—62no—
801C4—62no—
802C4—102no—
803C4—102no—
804C4—302no—
805C4—302no—
806C4—302no—
807C4—302no—
808C3C2×#6584511yescharacteristic, complemented, Sylow
809C2—24no—
810C2—104no—
811C2#1175441914yesdirect product factor
812C2C22×D5×Dic611yescharacteristic
813C2C2×D3×#70911yescharacteristic
814C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
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
2. C22×C5×Dic3⋊C4C2semidirect
4. C2×#91575C2semidirect
5. C2×#91575C2semidirect
8. #11754419C2direct (N × H)
9. C2×#91431C2semidirect
10. C2×#91422C2semidirect
11. C2×D5×Dic3⋊C4C2semidirect
12. C2×#91378C2semidirect
13. C2×#91349C2semidirect
14. C2×#91334C2semidirect
15. C2×#91328C2semidirect
16. C2×#91323C2semidirect
31. #91813C22semidirect
38. C2×C5×Dic3⋊C4C22semidirect
44. #91575C22semidirect
45. #91575C22semidirect
60. #91431C22semidirect
61. #91422C22semidirect
62. D5×Dic3⋊C4C22semidirect
63. #91378C22semidirect
64. #91349C22semidirect
65. #91334C22semidirect
66. #91328C22semidirect
67. #91323C22semidirect
105. C2×C3×C22⋊D5Q8semidirect
151. C22×Dic3⋊C4D5semidirect
245. C3×C22⋊D5C2×Q8semidirect
296. C2×Dic3⋊C4C2×D5semidirect
321. C2×C22⋊D5Dic6semidirect
492. C22⋊D5C2×Dic6semidirect
564. C2×C3×C5#554semidirect
699. C3×C5C2×#554semidirect
726. C2×C5#5539semidirect
778. C2×C3#65845semidirect
782. C5C2×#5539semidirect
808. C3C2×#65845semidirect
811. C2#11754419direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918132
C22×C5×Dic3⋊C42
C2×C3×C4×C22⋊D52
C2×#915752
C2×Dic3×C22⋊D52
#117544192
C2×#914312
C2×#914222
C2×D5×Dic3⋊C42
C2×#913782
C2×#913492
C2×#913342
C2×#913282
C2×#913232
C2×#658453
C2×#55395