Finite Group Databasebeta

← C2×#11753044 #14481715

Subgroups — C2×#11753044 #14481715

Order 1920.

2592 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91767C211yesmaximal, characteristic, complemented
2C2×C5×#878C211yesmaximal, characteristic, complemented
3C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
4C2×#91576C211yesmaximal, characteristic, complemented
5C2×#91575C211yesmaximal, characteristic, complemented
6C2×D5×#217C211yesmaximal, characteristic
7C22×#6665C211yesmaximal, characteristic
8C2×#91431C211yesmaximal, characteristic, complemented
9C2×#91430C211yesmaximal, characteristic, complemented
10C2×#91422C211yesmaximal, characteristic, complemented
11C2×#91421C211yesmaximal, characteristic, complemented
12C2×#91360C211yesmaximal, characteristic, complemented
13C2×#91359C211yesmaximal, characteristic, complemented
14C2×#91349C211yesmaximal, characteristic, complemented
15C2×#91349C211yesmaximal, characteristic, complemented
16#11753044C2116yesmaximal, direct product factor
17C2×#65968—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×Dic30C2211yescharacteristic, complemented
21C23×C5×Dic3C2211yescharacteristic
22C22×C5×Dic6C2211yescharacteristic, complemented
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×#1204C2211yescharacteristic, complemented
26C22×#1204C2211yescharacteristic, complemented
27C22×D5×Dic3C2211yescharacteristic
28C22×D5×Dic3C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C2×C4⋊Dic15C2211yescharacteristic, complemented
32C2×#6712C2211yescharacteristic, complemented
33C2×#6712C2211yescharacteristic, complemented
34#91767C2218yescomplemented
35C2×C5×#217C2211yescharacteristic
36C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
37C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
38C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
39C5×#878C2218yescomplemented
40C2×C3×C22⋊Dic5C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C3×D5×C22⋊C4C2218yes—
44#91576C2218yescomplemented
45#91575C2218yescomplemented
46D5×#217C2218yes—
47C2×Dic3⋊Dic5C2211yescharacteristic, complemented
48C2×Dic3⋊Dic5C2211yescharacteristic, complemented
49C2×#6669C2211yescharacteristic, complemented
50C2×#6669C2211yescharacteristic, complemented
51C2×#6668C2211yescharacteristic, complemented
52C2×#6668C2211yescharacteristic, complemented
53C2×#6665C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55C2×#6665C2218yes—
56C2×#6665C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59C2×#6665C2211yescharacteristic
60#91431C2218yescomplemented
61#91430C2218yescomplemented
62#91422C2218yescomplemented
63#91421C2218yescomplemented
64#91360C2218yescomplemented
65#91359C2218yescomplemented
66#91349C2218yescomplemented
67#91349C2218yescomplemented
68C2×#5483—51nomaximal, Hall
69C2×C5×C22⋊Q8—31no—
70C2×#4092—31no—
71C2×#4092—31no—
72C22×#685—31no—
73C2×#4070—31no—
74#65968—316no—
75C2×#4043—31no—
76C2×#4043—31no—
77C2×#4042—31no—
78C2×#4042—31no—
79C2×#4042—31no—
80C2×#4042—31no—
81C2×D5×C22⋊C4—31no—
82C2×D5×C22⋊C4D311yescharacteristic
83C2×#4024—31no—
84C2×#4024—31no—
85C24×C3×C5C2311yescharacteristic
86C23×C3×D5—42no—
87C23×C3×D5—42no—
88C23×C3×D5Q818yescomplemented
89C23×C3×D5C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C23×C3×D5C2314yes—
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×Dic15—42no—
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2314yes—
100C2×Dic30—42no—
101C2×Dic30C2314yescomplemented
102C22×C5×Dic3—42no—
103C22×C5×Dic3C2311yescharacteristic
104C22×C5×Dic3C2311yescharacteristic
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2314yes—
108C2×C5×Dic6—42no—
109C2×C5×Dic6C2314yescomplemented
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C2×C3×C4×D5—42no—
113C2×C3×C4×D5—42no—
114C2×C3×C4×D5C2314yes—
115C2×C3×C4×D5C2314yes—
116C2×#1204—42no—
117C2×#1204—42no—
118C2×#1204C2314yescomplemented
119C2×#1204C2314yescomplemented
120C2×D5×Dic3—42no—
121C2×D5×Dic3—42no—
122C2×D5×Dic3C2314yes—
123C2×D5×Dic3C2314yes—
124C3×C5×C22⋊C4C2314yes—
125#6719C2314yes—
126C4⋊Dic15C2314yescomplemented
127#6712C2314yescomplemented
128#6712C2314yescomplemented
129C5×#217C2314yes—
130C5×C4⋊Dic3C2314yescomplemented
131C5×Dic3⋊C4C2314yescomplemented
132C5×Dic3⋊C4C2314yescomplemented
133C3×C22⋊Dic5C2314yes—
134C3×#685C2314yes—
135C3×#685C2314yes—
136Dic3⋊Dic5C2314yescomplemented
137Dic3⋊Dic5C2314yescomplemented
138#6669C2314yescomplemented
139#6669C2314yescomplemented
140#6668C2314yescomplemented
141#6668C2314yescomplemented
142#6665C2314yes—
143#6665C2314yes—
144#6665C2314yes—
145#6665C2314yes—
146#6665C2314yes—
147#6665C2314yes—
148C22×C3×C22⋊C4—51no—
149C22×#217—51no—
150C22×#217—51no—
151C2×#924—51no—
152C2×#924—51no—
153C2×#924—51no—
154C2×#924—51no—
155#5483—516no—
156C2×#878—51no—
157C2×#878—51no—
158C2×#878—51no—
159C2×#878—51no—
160C2×#878—51no—
161C2×#878—51no—
162C2×#878—51no—
163C2×#878D511yescharacteristic, complemented
164C24×D5C2×D311yescharacteristic
165C22×C5×Q8—31no—
166C23×C4×C5—31no—
167C23×Dic5—31no—
168C22×C4×D5—31no—
169C22×C4×D5—31no—
170C22×C4×D5C2×D311yescharacteristic
171C22×C4×D5C2×D311yescharacteristic
172C22×Dic10—31no—
173C22×Dic10—31no—
174C22×Dic10—31no—
175C5×C22⋊Q8—38no—
176C2×C5×C4⋊C4—31no—
177C2×C5×C4⋊C4—31no—
178C2×C5×C4⋊C4—31no—
179C2×C5×C22⋊C4—31no—
180C2×C5×C22⋊C4C2×D311yescharacteristic
181C2×C22⋊Dic5—31no—
182C2×C22⋊Dic5C2×D311yescharacteristic
183#4092—38no—
184#4092—38no—
185C2×#685—31no—
186C2×#685—31no—
187C2×#685—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—38no—
192C2×#685C2×D311yescharacteristic
193C2×#685C2×D311yescharacteristic
194C2×C4⋊Dic5—31no—
195C2×C4⋊Dic5—31no—
196C2×C4⋊Dic5—31no—
197#4070—38no—
198C2×#683—31no—
199C2×#683—31no—
200C2×#683—31no—
201C2×#683—31no—
202C2×#683—31no—
203C2×#683—31no—
204#4043—38no—
205#4043—38no—
206#4042—38no—
207#4042—38no—
208#4042—38no—
209#4042—38no—
210D5×C22⋊C4—38no—
211D5×C22⋊C4C2×D318yes—
212#4024—38no—
213#4024—38no—
214C2×#543—151noSylow
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5C2×Q814yes—
218C23×C3×C5C2412yes—
219C23×C3×C5C2411yescharacteristic
220C22×C3×D5—22no—
221C22×C3×D5—22no—
222C22×C3×D5—22no—
223C22×C3×D5—22no—
224C22×C3×D5—416no—
225C22×C3×D5—44no—
226C22×C3×D5—44no—
227C22×C3×D5C2×Q814yes—
228C22×C3×D5C2×Q814yes—
229C22×C3×D5C2×Q8116yescomplemented
230C22×C3×D5C2412yes—
231C22×C3×D5C2412yes—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5—22no—
234C2×C3×C4×C5C2412yes—
235C2×C3×C4×C5C2412yes—
236C2×Dic15—22no—
237C2×Dic15—22no—
238C2×Dic15—22no—
239C2×Dic15—22no—
240C2×Dic15—44no—
241C2×Dic15C2412yes—
242C2×Dic15C2412yes—
243C2×Dic15C2412yes—
244C2×Dic15C2412yes—
245Dic30—44no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3—22no—
248C2×C5×Dic3—22no—
249C2×C5×Dic3—22no—
250C2×C5×Dic3—44no—
251C2×C5×Dic3C2412yes—
252C2×C5×Dic3C2412yes—
253C2×C5×Dic3C2412yes—
254C2×C5×Dic3C2412yes—
255C5×Dic6—44no—
256C2×C3×Dic5—22no—
257C2×C3×Dic5—22no—
258C2×C3×Dic5C2412yes—
259C2×C3×Dic5C2412yes—
260C3×C4×D5—44no—
261C3×C4×D5—44no—
262#1204—44no—
263#1204—44no—
264D5×Dic3—44no—
265D5×Dic3—44no—
266C25×C3—51no—
267C23×C3×C4—51no—
268C23×C3×C4—51no—
269C23×Dic3—51no—
270C23×Dic3—51no—
271C23×Dic3—51no—
272C23×Dic3C2×D511yescharacteristic
273C22×Dic6—51no—
274C22×Dic6—51no—
275C22×Dic6—51no—
276C22×Dic6C2×D511yescharacteristic, complemented
277C2×C3×C22⋊C4—51no—
278C2×C3×C22⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×C3×C22⋊C4—58no—
281C2×C3×C22⋊C4C2×D511yescharacteristic
282C2×#217—51no—
283C2×#217—51no—
284C2×#217—51no—
285C2×#217—58no—
286C2×#217—51no—
287C2×#217—51no—
288C2×#217—51no—
289C2×#217—51no—
290C2×#217—58no—
291C2×#217C2×D511yescharacteristic
292C2×C4⋊Dic3—51no—
293C2×C4⋊Dic3—51no—
294C2×C4⋊Dic3—51no—
295C2×C4⋊Dic3C2×D511yescharacteristic, complemented
296#924—58no—
297#924—58no—
298#924—58no—
299#924—58no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4—51no—
305C2×Dic3⋊C4—51no—
306C2×Dic3⋊C4C2×D511yescharacteristic, complemented
307C2×Dic3⋊C4C2×D511yescharacteristic, complemented
308#878—58no—
309#878—58no—
310#878—58no—
311#878—58no—
312#878—58no—
313#878—58no—
314#878—58no—
315#878C2×D518yescomplemented
316C24×C5C22×D311yescharacteristic
317C23×D5—42no—
318C23×D5—42no—
319C23×D5Dic618yescomplemented
320C23×D5C22×D311yescharacteristic
321C23×D5C22×D311yescharacteristic
322C23×D5C22×D314yes—
323C2×C5×Q8—34no—
324C2×C5×Q8—122no—
325C22×C4×C5—31no—
326C22×C4×C5—31no—
327C22×C4×C5—31no—
328C22×C4×C5—31no—
329C22×C4×C5—34no—
330C22×C4×C5—122no—
331C22×C4×C5C22×D311yescharacteristic
332C22×C4×C5C22×D311yescharacteristic
333C22×Dic5—31no—
334C22×Dic5—31no—
335C22×Dic5—31no—
336C22×Dic5—31no—
337C22×Dic5—34no—
338C22×Dic5—122no—
339C22×Dic5C22×D311yescharacteristic
340C22×Dic5C22×D311yescharacteristic
341C2×C4×D5—34no—
342C2×C4×D5—34no—
343C2×C4×D5—42no—
344C2×C4×D5—42no—
345C2×C4×D5—122no—
346C2×C4×D5—122no—
347C2×C4×D5C22×D314yes—
348C2×C4×D5C22×D314yes—
349C2×Dic10—34no—
350C2×Dic10—34no—
351C2×Dic10—34no—
352C2×Dic10—122no—
353C2×Dic10—122no—
354C2×Dic10—122no—
355C5×C4⋊C4—34no—
356C5×C4⋊C4—34no—
357C5×C4⋊C4—34no—
358C5×C22⋊C4—34no—
359C5×C22⋊C4C22×D314yes—
360C22⋊Dic5—34no—
361C22⋊Dic5C22×D314yes—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367#685—34no—
368#685C22×D314yes—
369#685C22×D314yes—
370C4⋊Dic5—34no—
371C4⋊Dic5—34no—
372C4⋊Dic5—34no—
373#683—34no—
374#683—34no—
375#683—34no—
376#683—34no—
377#683—34no—
378#683—34no—
379#543—1516no—
380C2×C22⋊Q8—31no—
381C2×C22⋊Q8—151no—
382C2×C22⋊Q8—151no—
383C2×C22⋊Q8—151no—
384C2×C22⋊Q8—151no—
385C2×C22⋊Q8—151no—
386C2×C22⋊Q8—151no—
387C2×C22⋊Q8—151no—
388C2×C22⋊Q8—151no—
389C2×C22⋊Q8—151no—
390C2×C22⋊Q8—151no—
391C2×C22⋊Q8—151no—
392C22×C22⋊C4—51no—
393C22×C22⋊C4—151no—
394C22×C22⋊C4—151no—
395C22×C3×C5—28no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5C22×Q814yes—
399C22×C3×C5C22×Q812yes—
400C22×C3×C5H(5,𝔽2)12yes—
401C22×C3×C5H(5,𝔽2)12yes—
402C22×C3×C5C2511yescharacteristic
403C2×C3×D5—28no—
404C2×C3×D5—28no—
405C2×C3×D5—22no—
406C2×C3×D5—22no—
407C2×C3×D5—22no—
408C2×C3×D5—22no—
409C2×C3×D5—416no—
410C2×C3×D5C22×Q814yes—
411C2×C3×D5C22×Q814yes—
412C3×C4×C5—22no—
413C3×C4×C5—22no—
414Dic15—22no—
415Dic15—22no—
416Dic15—22no—
417Dic15—22no—
418C3×Dic5—22no—
419C3×Dic5—22no—
420C5×Dic3—22no—
421C5×Dic3—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C24×C3—51no—
425C24×C3—51no—
426C24×C3—58no—
427C24×C3—54no—
428C24×C3—202no—
429C24×C3—202no—
430C24×C3C22×D511yescharacteristic
431C22×C3×C4—51no—
432C22×C3×C4—51no—
433C22×C3×C4—54no—
434C22×C3×C4—54no—
435C22×C3×C4—202no—
436C22×C3×C4—202no—
437C22×C3×C4C22×D511yescharacteristic
438C22×C3×C4C22×D511yescharacteristic
439C22×Dic3—42no—
440C22×Dic3—51no—
441C22×Dic3—51no—
442C22×Dic3—51no—
443C22×Dic3—51no—
444C22×Dic3—54no—
445C22×Dic3—54no—
446C22×Dic3—54no—
447C22×Dic3—202no—
448C22×Dic3—202no—
449C22×Dic3—202no—
450C22×Dic3C22×D511yescharacteristic
451C22×Dic3C22×D511yescharacteristic
452C22×Dic3C22×D511yescharacteristic
453C22×Dic3C22×D511yescharacteristic
454C22×Dic3C22×D514yes—
455C2×Dic6—42no—
456C2×Dic6—54no—
457C2×Dic6—54no—
458C2×Dic6—54no—
459C2×Dic6—202no—
460C2×Dic6—202no—
461C2×Dic6—202no—
462C2×Dic6C22×D514yescomplemented
463C3×C22⋊C4—54no—
464C3×C22⋊C4—54no—
465C3×C22⋊C4—54no—
466C3×C22⋊C4C22×D514yes—
467#217—54no—
468#217—54no—
469#217—54no—
470#217—54no—
471#217—54no—
472#217—54no—
473#217—54no—
474#217C22×D514yes—
475C4⋊Dic3—54no—
476C4⋊Dic3—54no—
477C4⋊Dic3—54no—
478C4⋊Dic3C22×D514yescomplemented
479Dic3⋊C4—54no—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4—54no—
483Dic3⋊C4—54no—
484Dic3⋊C4—54no—
485Dic3⋊C4C22×D514yescomplemented
486Dic3⋊C4C22×D514yescomplemented
487C23×C5—22no—
488C23×C5—22no—
489C23×C5C2×Dic614yes—
490C23×C5C23×D312yes—
491C23×C5C23×D311yescharacteristic
492C22×D5—22no—
493C22×D5—22no—
494C22×D5—22no—
495C22×D5—22no—
496C22×D5—416no—
497C22×D5—44no—
498C22×D5—44no—
499C22×D5C2×Dic614yes—
500C22×D5C2×Dic614yes—
501C22×D5C2×Dic6116yescomplemented
502C22×D5C23×D312yes—
503C22×D5C23×D312yes—
504C5×Q8—124no—
505C2×C4×C5—22no—
506C2×C4×C5—22no—
507C2×C4×C5—32no—
508C2×C4×C5—32no—
509C2×C4×C5—32no—
510C2×C4×C5—32no—
511C2×C4×C5—62no—
512C2×C4×C5—62no—
513C2×C4×C5—62no—
514C2×C4×C5—62no—
515C2×C4×C5—124no—
516C2×C4×C5C23×D312yes—
517C2×C4×C5C23×D312yes—
518C2×Dic5—22no—
519C2×Dic5—22no—
520C2×Dic5—32no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—62no—
525C2×Dic5—62no—
526C2×Dic5—62no—
527C2×Dic5—62no—
528C2×Dic5—124no—
529C2×Dic5C23×D312yes—
530C2×Dic5C23×D312yes—
531C4×D5—44no—
532C4×D5—44no—
533C4×D5—124no—
534C4×D5—124no—
535Dic10—124no—
536Dic10—124no—
537Dic10—124no—
538C25—51no—
539C22×Q8—31no—
540C22×Q8—151no—
541C22×Q8—151no—
542C22×Q8—151no—
543C23×C4—31no—
544C23×C4—51no—
545C23×C4—51no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4—151no—
549C22⋊Q8—38no—
550C22⋊Q8—158no—
551C22⋊Q8—158no—
552C22⋊Q8—158no—
553C22⋊Q8—158no—
554C22⋊Q8—158no—
555C22⋊Q8—158no—
556C22⋊Q8—158no—
557C22⋊Q8—158no—
558C22⋊Q8—158no—
559C22⋊Q8—158no—
560C22⋊Q8—158no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—31no—
563C2×C4⋊C4—31no—
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⋊C4—151no—
572C2×C4⋊C4—151no—
573C2×C22⋊C4—31no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—58no—
578C2×C22⋊C4—158no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—158no—
586C2×C22⋊C4—151no—
587C2×C22⋊C4D3×D511yescharacteristic
588C2×C3×C5—24no—
589C2×C3×C5#54314yescomplemented
590C2×C3×C5C23×Q811yescharacteristic
591C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
592C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
593C3×D5—24no—
594C3×D5—24no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—54no—
598C23×C3—54no—
599C23×C3—52no—
600C23×C3—52no—
601C23×C3—516no—
602C23×C3—102no—
603C23×C3—102no—
604C23×C3—102no—
605C23×C3—102no—
606C23×C3—2016no—
607C23×C3—204no—
608C23×C3—204no—
609C23×C3Q8×D514yes—
610C23×C3C23×D512yes—
611C23×C3C23×D511yescharacteristic
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—52no—
615C2×C3×C4—52no—
616C2×C3×C4—102no—
617C2×C3×C4—102no—
618C2×C3×C4—204no—
619C2×C3×C4—204no—
620C2×C3×C4C23×D512yes—
621C2×C3×C4C23×D512yes—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—44no—
627C2×Dic3—52no—
628C2×Dic3—52no—
629C2×Dic3—52no—
630C2×Dic3—52no—
631C2×Dic3—102no—
632C2×Dic3—102no—
633C2×Dic3—102no—
634C2×Dic3—102no—
635C2×Dic3—204no—
636C2×Dic3—204no—
637C2×Dic3—204no—
638C2×Dic3C23×D512yes—
639C2×Dic3C23×D512yes—
640C2×Dic3C23×D512yes—
641C2×Dic3C23×D512yes—
642Dic6—44no—
643Dic6—204no—
644Dic6—204no—
645Dic6—204no—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5—28no—
649C22×C5C22×Dic614yes—
650C22×C5C22×Dic612yes—
651C22×C5#100412yes—
652C22×C5#100412yes—
653C22×C5C24×D311yescharacteristic
654C2×D5—22no—
655C2×D5—22no—
656C2×D5—22no—
657C2×D5—22no—
658C2×D5—28no—
659C2×D5—28no—
660C2×D5—416no—
661C2×D5C22×Dic614yes—
662C2×D5C22×Dic614yes—
663C4×C5—22no—
664C4×C5—22no—
665C4×C5—62no—
666C4×C5—62no—
667C4×C5—62no—
668C4×C5—62no—
669Dic5—22no—
670Dic5—22no—
671Dic5—62no—
672Dic5—62no—
673Dic5—62no—
674Dic5—62no—
675C24—51no—
676C24—51no—
677C24—58no—
678C24—54no—
679C24—202no—
680C24—202no—
681C24C2×D3×D511yescharacteristic
682C2×Q8—34no—
683C2×Q8—122no—
684C2×Q8—154no—
685C2×Q8—154no—
686C2×Q8—154no—
687C2×Q8—602no—
688C2×Q8—602no—
689C2×Q8—602no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—34no—
695C22×C4—51no—
696C22×C4—51no—
697C22×C4—54no—
698C22×C4—54no—
699C22×C4—122no—
700C22×C4—154no—
701C22×C4—154no—
702C22×C4—151no—
703C22×C4—151no—
704C22×C4—151no—
705C22×C4—151no—
706C22×C4—154no—
707C22×C4—202no—
708C22×C4—202no—
709C22×C4—602no—
710C22×C4—602no—
711C22×C4—602no—
712C22×C4C2×D3×D511yescharacteristic
713C22×C4C2×D3×D511yescharacteristic
714C4⋊C4—34no—
715C4⋊C4—34no—
716C4⋊C4—34no—
717C4⋊C4—154no—
718C4⋊C4—154no—
719C4⋊C4—154no—
720C4⋊C4—154no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4—154no—
726C22⋊C4—34no—
727C22⋊C4—54no—
728C22⋊C4—54no—
729C22⋊C4—54no—
730C22⋊C4—154no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C22⋊C4—154no—
736C22⋊C4—154no—
737C22⋊C4C2×D3×D514yes—
738C3×C5C2×#54311yescharacteristic, complemented, Hall
739C22×C3—28no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—54no—
743C22×C3—54no—
744C22×C3—108no—
745C22×C3—108no—
746C22×C3—102no—
747C22×C3—102no—
748C22×C3—102no—
749C22×C3—102no—
750C22×C3—2016no—
751C22×C3#414412yes—
752C22×C3C2×Q8×D514yes—
753C22×C3C2×Q8×D512yes—
754C22×C3#414912yes—
755C22×C3C24×D511yescharacteristic
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—102no—
759C3×C4—102no—
760Dic3—22no—
761Dic3—22no—
762Dic3—22no—
763Dic3—22no—
764Dic3—102no—
765Dic3—102no—
766Dic3—102no—
767Dic3—102no—
768C2×C5—24no—
769C2×C5#548314yescomplemented
770C2×C5C23×Dic611yescharacteristic
771C2×C5C2×#100411yescharacteristic
772C2×C5C2×#100411yescharacteristic
773D5—24no—
774D5—24no—
775C23—22no—
776C23—22no—
777C23—54no—
778C23—54no—
779C23—52no—
780C23—52no—
781C23—516no—
782C23—102no—
783C23—102no—
784C23—102no—
785C23—102no—
786C23—2016no—
787C23—204no—
788C23—204no—
789C23D5×Dic614yes—
790C23C22×D3×D512yes—
791C23C22×D3×D511yescharacteristic
792Q8—124no—
793Q8—604no—
794Q8—604no—
795Q8—604no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—32no—
799C2×C4—32no—
800C2×C4—32no—
801C2×C4—32no—
802C2×C4—52no—
803C2×C4—52no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—102no—
809C2×C4—102no—
810C2×C4—124no—
811C2×C4—152no—
812C2×C4—152no—
813C2×C4—152no—
814C2×C4—152no—
815C2×C4—204no—
816C2×C4—204no—
817C2×C4—302no—
818C2×C4—302no—
819C2×C4—302no—
820C2×C4—302no—
821C2×C4—604no—
822C2×C4—604no—
823C2×C4—604no—
824C2×C4C22×D3×D512yes—
825C2×C4C22×D3×D512yes—
826C2×C3—24no—
827C2×C3—104no—
828C2×C3—104no—
829C2×C3#6596814yescomplemented
830C2×C3C2×#414411yescharacteristic
831C2×C3C22×Q8×D511yescharacteristic
832C2×C3C2×#414911yescharacteristic
833C5C2×#548311yescharacteristic, complemented, Sylow
834C22—28no—
835C22—22no—
836C22—22no—
837C22—54no—
838C22—54no—
839C22—108no—
840C22—108no—
841C22—102no—
842C22—102no—
843C22—102no—
844C22—102no—
845C22—2016no—
846C22C2×D5×Dic614yes—
847C22C2×D5×Dic612yes—
848C22#9202512yes—
849C22#9202612yes—
850C22C23×D3×D511yescharacteristic
851C4—22no—
852C4—22no—
853C4—62no—
854C4—62no—
855C4—62no—
856C4—62no—
857C4—102no—
858C4—102no—
859C4—302no—
860C4—302no—
861C4—302no—
862C4—302no—
863C3C2×#6596811yescharacteristic, complemented, Sylow
864C2—24no—
865C2—104no—
866C2—104no—
867C2#1175304414yesdirect product factor
868C2C22×D5×Dic611yescharacteristic
869C2C2×#9202511yescharacteristic
870C2C2×#9202611yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
prime radicalC24×C3×D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#543
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91767C2semidirect
2. C2×C5×#878C2semidirect
4. C2×#91576C2semidirect
5. C2×#91575C2semidirect
8. C2×#91431C2semidirect
9. C2×#91430C2semidirect
10. C2×#91422C2semidirect
11. C2×#91421C2semidirect
12. C2×#91360C2semidirect
13. C2×#91359C2semidirect
14. C2×#91349C2semidirect
15. C2×#91349C2semidirect
16. #11753044C2direct (N × H)
20. C22×Dic30C22semidirect
22. C22×C5×Dic6C22semidirect
25. C22×#1204C22semidirect
26. C22×#1204C22semidirect
31. C2×C4⋊Dic15C22semidirect
32. C2×#6712C22semidirect
33. C2×#6712C22semidirect
34. #91767C22semidirect
36. C2×C5×C4⋊Dic3C22semidirect
37. C2×C5×Dic3⋊C4C22semidirect
38. C2×C5×Dic3⋊C4C22semidirect
39. C5×#878C22semidirect
44. #91576C22semidirect
45. #91575C22semidirect
47. C2×Dic3⋊Dic5C22semidirect
48. C2×Dic3⋊Dic5C22semidirect
49. C2×#6669C22semidirect
50. C2×#6669C22semidirect
51. C2×#6668C22semidirect
52. C2×#6668C22semidirect
60. #91431C22semidirect
61. #91430C22semidirect
62. #91422C22semidirect
63. #91421C22semidirect
64. #91360C22semidirect
65. #91359C22semidirect
66. #91349C22semidirect
67. #91349C22semidirect
88. C23×C3×D5Q8semidirect
101. C2×Dic30C23semidirect
109. C2×C5×Dic6C23semidirect
118. C2×#1204C23semidirect
119. C2×#1204C23semidirect
126. C4⋊Dic15C23semidirect
127. #6712C23semidirect
128. #6712C23semidirect
130. C5×C4⋊Dic3C23semidirect
131. C5×Dic3⋊C4C23semidirect
132. C5×Dic3⋊C4C23semidirect
136. Dic3⋊Dic5C23semidirect
137. Dic3⋊Dic5C23semidirect
138. #6669C23semidirect
139. #6669C23semidirect
140. #6668C23semidirect
141. #6668C23semidirect
163. C2×#878D5semidirect
229. C22×C3×D5C2×Q8semidirect
276. C22×Dic6C2×D5semidirect
295. C2×C4⋊Dic3C2×D5semidirect
306. C2×Dic3⋊C4C2×D5semidirect
307. C2×Dic3⋊C4C2×D5semidirect
315. #878C2×D5semidirect
319. C23×D5Dic6semidirect
462. C2×Dic6C22×D5semidirect
478. C4⋊Dic3C22×D5semidirect
485. Dic3⋊C4C22×D5semidirect
486. Dic3⋊C4C22×D5semidirect
501. C22×D5C2×Dic6semidirect
589. C2×C3×C5#543semidirect
738. C3×C5C2×#543semidirect
769. C2×C5#5483semidirect
829. C2×C3#65968semidirect
833. C5C2×#5483semidirect
863. C3C2×#65968semidirect
867. C2#11753044direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917672
C2×C5×#8782
C2×C3×D5×C22⋊C42
C2×#915762
C2×#915752
C2×D5×#2172
C22×#66652
C2×#914312
C2×#914302
C2×#914222
C2×#914212
C2×#913602
C2×#913592
C2×#913492
#117530442
C2×#659683
C2×#54835