Finite Group Databasebeta

← C2×#11753936 #14480894

Subgroups — C2×#11753936 #14480894

Order 1920.

2672 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91785C211yesmaximal, characteristic, complemented
2C2×C5×#898C211yesmaximal, characteristic, complemented
3C2×C3×#4041C211yesmaximal, characteristic, complemented
4C2×#91474C211yesmaximal, characteristic, complemented
5C2×#91474C211yesmaximal, characteristic, complemented
6C2×#91473C211yesmaximal, characteristic, complemented
7C2×#91465C211yesmaximal, characteristic, complemented
8C2×#91462C211yesmaximal, characteristic, complemented
9C2×#91447C211yesmaximal, characteristic, complemented
10C2×#91444C211yesmaximal, characteristic, complemented
11C2×#91408C211yesmaximal, characteristic, complemented
12C2×#91407C211yesmaximal, characteristic, complemented
13C2×#91395C211yesmaximal, characteristic, complemented
14C2×#91364C211yesmaximal, characteristic, complemented
15C2×#91361C211yesmaximal, characteristic, complemented
16#11753936C2116yesmaximal, direct product factor
17C2×#66038—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×Dic30C2211yescharacteristic, complemented
21C22×C3×D20C2211yescharacteristic
22C22×C3×D20C2211yescharacteristic
23C22×C3×D20C2211yescharacteristic, complemented
24C22×C3×C4×D5C2211yescharacteristic, complemented
25C22×#1202C2211yescharacteristic
26C22×#1202C2211yescharacteristic
27C22×#1201C2211yescharacteristic
28C22×#1201C2211yescharacteristic
29C22×#1200C2211yescharacteristic
30C22×D5×Dic3C2211yescharacteristic, complemented
31C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6712C2211yescharacteristic, complemented
35C2×#6712C2211yescharacteristic, complemented
36#91785C2218yescomplemented
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×(C2×D3)⋊C4C2211yescharacteristic
40C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
41C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
42C2×C4×C5×Dic3C2211yescharacteristic, complemented
43C5×#898C2218yescomplemented
44C2×C3×#685C2211yescharacteristic
45C2×C3×#685C2211yescharacteristic, complemented
46C3×#4041C2218yescomplemented
47C2×Dic3⋊Dic5C2211yescharacteristic, complemented
48C2×(C2×D3)⋊Dic5C2211yescharacteristic
49C2×#6665C2211yescharacteristic
50C2×#6665C2211yescharacteristic
51C2×#6665C2211yescharacteristic
52C2×#6665C2211yescharacteristic, complemented
53C2×#6665C2211yescharacteristic, complemented
54C2×#6665C2211yescharacteristic, complemented
55C2×Dic3×Dic5C2211yescharacteristic, complemented
56#91474C2218yescomplemented
57#91474C2218yescomplemented
58#91473C2218yescomplemented
59#91465C2218yescomplemented
60#91462C2218yescomplemented
61#91447C2218yescomplemented
62#91444C2218yescomplemented
63#91408C2218yescomplemented
64#91407C2218yescomplemented
65#91395C2218yescomplemented
66#91364C2218yescomplemented
67#91361C2218yescomplemented
68C2×#5613—51nomaximal, Hall
69C2×C5×#126—31no—
70#66038—316no—
71C2×#4044—31no—
72C2×#4042—31no—
73C2×#4041—31no—
74C2×#4041D311yescharacteristic, complemented
75C2×#4040—31no—
76C2×#4039—31no—
77C2×#4031—31no—
78C2×#4030—31no—
79C2×#4029—31no—
80C2×#4028—31no—
81C2×#4028—31no—
82C2×D5×C22⋊C4—31no—
83C2×#4021—31no—
84C2×C4×D20—31no—
85C23×D15C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C3×D5C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C23×C3×D5C2311yescharacteristic
90C22×D3×D5—24no—
91C22×D3×D5—42no—
92C22×D3×D5—42no—
93C22×D3×D5C2314yes—
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C2×C4×D15—42no—
101C2×C4×D15C2314yes—
102C2×Dic30—42no—
103C2×Dic30C2314yescomplemented
104C22×C5×Dic3C2311yescharacteristic
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C2×C3×D20—42no—
109C2×C3×D20—42no—
110C2×C3×D20—42no—
111C2×C3×D20C2314yes—
112C2×C3×D20C2314yes—
113C2×C3×D20C2314yescomplemented
114C2×C3×C4×D5—42no—
115C2×C3×C4×D5C2314yescomplemented
116C2×#1202—24no—
117C2×#1202—24no—
118C2×#1202C2314yes—
119C2×#1202C2314yes—
120C2×#1201—42no—
121C2×#1201—42no—
122C2×#1201C2314yes—
123C2×#1201C2314yes—
124C2×#1200—42no—
125C2×#1200C2314yes—
126C2×D5×Dic3—42no—
127C2×D5×Dic3C2314yescomplemented
128C3×C5×C4⋊C4C2314yescomplemented
129#6714C2314yes—
130#6714C2314yes—
131#6712C2314yescomplemented
132#6712C2314yescomplemented
133C5×(C2×D3)⋊C4C2314yes—
134C5×(C2×D3)⋊C4C2314yes—
135C5×(C2×D3)⋊C4C2314yes—
136C5×C4⋊Dic3C2314yescomplemented
137C5×Dic3⋊C4C2314yescomplemented
138C4×C5×Dic3C2314yescomplemented
139C3×#685C2314yes—
140C3×#685C2314yescomplemented
141Dic3⋊Dic5C2314yescomplemented
142(C2×D3)⋊Dic5C2314yes—
143#6665C2314yes—
144#6665C2314yes—
145#6665C2314yes—
146#6665C2314yescomplemented
147#6665C2314yescomplemented
148#6665C2314yescomplemented
149Dic3×Dic5C2314yescomplemented
150C2×C3×#121—51no—
151C2×#939—51no—
152C2×#938—51no—
153C2×#937—51no—
154C2×#937—51no—
155C2×#936—51no—
156C2×#935—51no—
157C2×#929—51no—
158C2×C4×#67—51no—
159#5613—516no—
160C2×#898D511yescharacteristic, complemented
161C2×#896—51no—
162C2×#885—51no—
163C2×#67⋊C4—51no—
164C2×D3×C22⋊C4—51no—
165C2×#879—51no—
166C24×D5—31no—
167C22×C22⋊D5—31no—
168C22×C22⋊D5—31no—
169C22×D20—31no—
170C22×D20—31no—
171C22×D20C2×D311yescharacteristic
172C22×D20C2×D311yescharacteristic
173C22×D20C2×D311yescharacteristic, complemented
174C22×C4×D5—31no—
175C22×C4×D5—31no—
176C22×C4×D5—31no—
177C22×C4×D5C2×D311yescharacteristic, complemented
178C22×Dic10—31no—
179C5×#126—38no—
180C2×C5×C4⋊C4—31no—
181C2×C5×C4⋊C4—31no—
182C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
183C2×C5×C22⋊C4—31no—
184C2×C5×C22⋊C4—31no—
185C2×C5×C22⋊C4—31no—
186C2×C42×C5—31no—
187C2×C22⋊Dic5—31no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685—31no—
196C2×#685C2×D311yescharacteristic
197C2×#685C2×D311yescharacteristic, complemented
198C2×C4⋊Dic5—31no—
199C2×#683—31no—
200C2×#683—31no—
201C2×C4×Dic5—31no—
202#4044—38no—
203#4042—38no—
204#4041—38no—
205#4041C2×D318yescomplemented
206#4040—38no—
207#4039—38no—
208#4031—38no—
209#4030—38no—
210#4029—38no—
211#4028—38no—
212#4028—38no—
213D5×C22⋊C4—38no—
214#4021—38no—
215C4×D20—38no—
216C2×#538—151noSylow
217C23×C3×C5C2411yescharacteristic
218C22×D15—22no—
219C22×D15—22no—
220C22×D15#4114yes—
221C22×D15C2412yes—
222C22×C5×D3—22no—
223C22×C5×D3—22no—
224C22×C5×D3—22no—
225C22×C5×D3C2412yes—
226C22×C3×D5—22no—
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5—22no—
230C22×C3×D5—22no—
231C22×C3×D5—22no—
232C22×C3×D5—22no—
233C22×C3×D5—22no—
234C22×C3×D5—22no—
235C22×C3×D5C2412yes—
236C22×C3×D5C2412yes—
237C22×C3×D5C2412yes—
238C2×D3×D5—28no—
239C2×D3×D5—44no—
240C2×D3×D5—44no—
241C2×D3×D5—416no—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5—22no—
245C2×C3×C4×C5C2412yes—
246C2×C3×C4×C5C2412yes—
247C2×C3×C4×C5C2412yes—
248C2×Dic15—22no—
249C2×Dic15—22no—
250C2×Dic15—22no—
251C2×Dic15C2412yes—
252C2×Dic15C2412yes—
253C2×Dic15C2412yes—
254C4×D15—44no—
255Dic30—44no—
256C2×C5×Dic3—22no—
257C2×C5×Dic3—22no—
258C2×C5×Dic3—22no—
259C2×C5×Dic3C2412yes—
260C2×C5×Dic3C2412yes—
261C2×C5×Dic3C2412yes—
262C2×C3×Dic5—22no—
263C2×C3×Dic5C2412yes—
264C3×D20—44no—
265C3×D20—44no—
266C3×D20—44no—
267C3×C4×D5—44no—
268#1202—28no—
269#1202—28no—
270#1201—44no—
271#1201—44no—
272#1200—44no—
273D5×Dic3—44no—
274C24×D3—51no—
275C22×C3×D4—51no—
276C22×C3×D4—51no—
277C22×C3×D4—51no—
278C23×C3×C4—51no—
279C22×#67—51no—
280C22×#67—51no—
281C22×#67—51no—
282C22×#67—51no—
283C23×Dic3—51no—
284C22×C4×D3—51no—
285C22×C4×D3—51no—
286C22×Dic6—51no—
287C3×#121—58no—
288C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
289C2×C3×C22⋊C4—51no—
290C2×C3×C22⋊C4—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217—51no—
294C2×#217—51no—
295C2×#217—51no—
296C2×#217—51no—
297#939—58no—
298#938—58no—
299#937—58no—
300#937—58no—
301#936—58no—
302#935—58no—
303#929—58no—
304C4×#67—58no—
305C2×(C2×D3)⋊C4—51no—
306C2×(C2×D3)⋊C4—51no—
307C2×(C2×D3)⋊C4—51no—
308C2×(C2×D3)⋊C4C2×D511yescharacteristic
309C2×(C2×D3)⋊C4C2×D511yescharacteristic
310C2×(C2×D3)⋊C4C2×D511yescharacteristic
311C2×C4⋊Dic3C2×D511yescharacteristic, complemented
312C2×Dic3⋊C4—51no—
313C2×Dic3⋊C4—51no—
314C2×Dic3⋊C4—51no—
315C2×Dic3⋊C4C2×D511yescharacteristic, complemented
316C2×C4×Dic3—51no—
317C2×C4×Dic3C2×D511yescharacteristic, complemented
318#898C2×D518yescomplemented
319#896—58no—
320#885—58no—
321#67⋊C4—58no—
322D3×C22⋊C4—58no—
323#879—58no—
324C24×C5—31no—
325C23×D5—31no—
326C23×D5—34no—
327C23×D5—64no—
328C23×D5—122no—
329C23×D5—122no—
330C23×D5C22×D311yescharacteristic
331C23×D5C22×D311yescharacteristic
332C23×D5C22×D311yescharacteristic
333C22×C4×C5—31no—
334C22×C4×C5—31no—
335C22×C4×C5—31no—
336C22×C4×C5C22×D311yescharacteristic
337C22×C4×C5C22×D311yescharacteristic
338C22×C4×C5C22×D311yescharacteristic
339C2×C22⋊D5—34no—
340C2×C22⋊D5—34no—
341C2×C22⋊D5—122no—
342C2×C22⋊D5—122no—
343C22×Dic5—31no—
344C22×Dic5—31no—
345C22×Dic5—31no—
346C22×Dic5C22×D311yescharacteristic
347C2×D20—34no—
348C2×D20—34no—
349C2×D20—42no—
350C2×D20—42no—
351C2×D20—42no—
352C2×D20—64no—
353C2×D20—64no—
354C2×D20C22×D314yes—
355C2×D20C22×D314yes—
356C2×D20C22×D314yescomplemented
357C2×C4×D5—34no—
358C2×C4×D5—34no—
359C2×C4×D5—34no—
360C2×C4×D5—42no—
361C2×C4×D5—122no—
362C2×C4×D5—122no—
363C2×C4×D5—122no—
364C2×C4×D5C22×D314yescomplemented
365C2×Dic10—34no—
366C2×Dic10—122no—
367C5×C4⋊C4—34no—
368C5×C4⋊C4—34no—
369C5×C4⋊C4C22×D314yescomplemented
370C5×C22⋊C4—34no—
371C5×C22⋊C4—34no—
372C5×C22⋊C4—34no—
373C42×C5—34no—
374C22⋊Dic5—34no—
375#685—34no—
376#685—34no—
377#685—34no—
378#685—34no—
379#685—34no—
380#685—34no—
381#685—34no—
382#685—34no—
383#685C22×D314yes—
384#685C22×D314yescomplemented
385C4⋊Dic5—34no—
386#683—34no—
387#683—34no—
388C4×Dic5—34no—
389#538—1516no—
390C2×#126—31no—
391C2×#126—151no—
392C2×#124—151no—
393C2×#124—151no—
394C2×#123—151no—
395C2×#123—151no—
396C2×C22⋊Q8—151no—
397C2×#121—51no—
398C2×#121—151no—
399C2×#121—151no—
400C2×#120—151no—
401C2×#120—151no—
402C2×C4×D4—151no—
403C2×C4×D4—151no—
404C22×C22⋊C4—151no—
405C22×C3×C5C2×#4112yes—
406C22×C3×C5H(5,𝔽2)12yes—
407C22×C3×C5H(5,𝔽2)12yes—
408C22×C3×C5C2511yescharacteristic
409C2×D15—28no—
410C2×D15—22no—
411C2×D15—22no—
412C2×D15C2×#4114yes—
413C2×C5×D3—22no—
414C2×C5×D3—22no—
415C2×C5×D3—22no—
416C2×C5×D3—44no—
417C2×C3×D5—22no—
418C2×C3×D5—22no—
419C2×C3×D5—22no—
420C2×C3×D5—22no—
421C2×C3×D5—22no—
422C2×C3×D5—22no—
423C2×C3×D5—22no—
424C2×C3×D5—22no—
425C2×C3×D5—22no—
426C2×C3×D5—44no—
427C2×C3×D5—44no—
428C2×C3×D5—44no—
429D3×D5—416no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432C3×C4×C5—22no—
433Dic15—22no—
434Dic15—22no—
435Dic15—22no—
436C3×Dic5—22no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—22no—
440C24×C3—51no—
441C24×C3—51no—
442C24×C3—51no—
443C23×D3—51no—
444C23×D3—54no—
445C23×D3—104no—
446C23×D3—202no—
447C23×D3—202no—
448C23×D3C22×D511yescharacteristic
449C2×C3×D4—54no—
450C2×C3×D4—54no—
451C2×C3×D4—54no—
452C2×C3×D4—202no—
453C2×C3×D4—202no—
454C2×C3×D4—202no—
455C22×C3×C4—51no—
456C22×C3×C4—54no—
457C22×C3×C4—202no—
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C22×C3×C4C22×D511yescharacteristic
461C2×#67—54no—
462C2×#67—54no—
463C2×#67—54no—
464C2×#67—54no—
465C2×#67—104no—
466C2×#67—104no—
467C2×#67—202no—
468C2×#67—202no—
469C22×Dic3—51no—
470C22×Dic3—51no—
471C22×Dic3—51no—
472C22×Dic3—54no—
473C22×Dic3—202no—
474C22×Dic3C22×D511yescharacteristic
475C22×Dic3C22×D511yescharacteristic
476C22×Dic3C22×D511yescharacteristic
477C2×C4×D3—54no—
478C2×C4×D3—54no—
479C2×C4×D3—202no—
480C2×C4×D3—202no—
481C2×Dic6—54no—
482C2×Dic6—202no—
483C3×C4⋊C4C22×D514yescomplemented
484C3×C22⋊C4—54no—
485C3×C22⋊C4—54no—
486#217—54no—
487#217—54no—
488#217—54no—
489#217—54no—
490#217—54no—
491#217—54no—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4—54no—
495(C2×D3)⋊C4C22×D514yes—
496(C2×D3)⋊C4C22×D514yes—
497(C2×D3)⋊C4C22×D514yes—
498C4⋊Dic3C22×D514yescomplemented
499Dic3⋊C4—54no—
500Dic3⋊C4—54no—
501Dic3⋊C4—54no—
502Dic3⋊C4C22×D514yescomplemented
503C4×Dic3—54no—
504C4×Dic3C22×D514yescomplemented
505C23×C5—32no—
506C23×C5—62no—
507C23×C5—62no—
508C23×C5—62no—
509C23×C5C23×D311yescharacteristic
510C22×D5—22no—
511C22×D5—22no—
512C22×D5—22no—
513C22×D5—22no—
514C22×D5—22no—
515C22×D5—22no—
516C22×D5—22no—
517C22×D5—22no—
518C22×D5—22no—
519C22×D5—34no—
520C22×D5—32no—
521C22×D5—68no—
522C22×D5—62no—
523C22×D5—62no—
524C22×D5—124no—
525C22×D5—124no—
526C22×D5—1216no—
527C22×D5C23×D312yes—
528C22×D5C23×D312yes—
529C22×D5C23×D312yes—
530C2×C4×C5—22no—
531C2×C4×C5—22no—
532C2×C4×C5—22no—
533C2×C4×C5—32no—
534C2×C4×C5—32no—
535C2×C4×C5—32no—
536C2×C4×C5—62no—
537C2×C4×C5—62no—
538C2×C4×C5—62no—
539C2×C4×C5C23×D312yes—
540C2×C4×C5C23×D312yes—
541C2×C4×C5C23×D312yes—
542C22⋊D5—124no—
543C22⋊D5—124no—
544C2×Dic5—22no—
545C2×Dic5—32no—
546C2×Dic5—32no—
547C2×Dic5—32no—
548C2×Dic5—62no—
549C2×Dic5—62no—
550C2×Dic5—62no—
551C2×Dic5C23×D312yes—
552D20—44no—
553D20—44no—
554D20—44no—
555D20—68no—
556D20—68no—
557C4×D5—44no—
558C4×D5—124no—
559C4×D5—124no—
560C4×D5—124no—
561Dic10—124no—
562C25—151no—
563C22×Q8—151no—
564C22×D4—51no—
565C22×D4—51no—
566C22×D4—51no—
567C22×D4—151no—
568C22×D4—151no—
569C22×D4—151no—
570C22×D4—151no—
571C23×C4—51no—
572C23×C4—151no—
573C23×C4—151no—
574C23×C4—151no—
575#126—38no—
576#126—158no—
577#124—158no—
578#124—158no—
579#123—158no—
580#123—158no—
581C22⋊Q8—158no—
582#121—58no—
583#121—158no—
584#121—158no—
585#120—158no—
586#120—158no—
587C4×D4—158no—
588C4×D4—158no—
589C2×C4⋊C4—31no—
590C2×C4⋊C4—31no—
591C2×C4⋊C4—151no—
592C2×C4⋊C4—151no—
593C2×C4⋊C4—151no—
594C2×C4⋊C4D3×D511yescharacteristic, complemented
595C2×C22⋊C4—31no—
596C2×C22⋊C4—31no—
597C2×C22⋊C4—31no—
598C2×C22⋊C4—51no—
599C2×C22⋊C4—51no—
600C2×C22⋊C4—158no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4—151no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4—151no—
610C2×C42—31no—
611C2×C42—151no—
612C2×C3×C5#53814yescomplemented
613C2×C3×C5C22×#4111yescharacteristic
614C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
615C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
616D15—24no—
617C3×D5—42no—
618C3×D5—42no—
619C3×D5—42no—
620C5×D3—42no—
621C23×C3—52no—
622C23×C3—52no—
623C23×C3—52no—
624C23×C3—102no—
625C23×C3—102no—
626C23×C3—102no—
627C23×C3—102no—
628C23×C3—102no—
629C23×C3—102no—
630C23×C3—102no—
631C23×C3—102no—
632C23×C3—102no—
633C23×C3C23×D511yescharacteristic
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—22no—
637C22×D3—54no—
638C22×D3—52no—
639C22×D3—108no—
640C22×D3—102no—
641C22×D3—102no—
642C22×D3—204no—
643C22×D3—204no—
644C22×D3—2016no—
645C22×D3C23×D512yes—
646C3×D4—204no—
647C3×D4—204no—
648C3×D4—204no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—52no—
653C2×C3×C4—102no—
654C2×C3×C4—204no—
655C2×C3×C4C23×D512yes—
656C2×C3×C4C23×D512yes—
657C2×C3×C4C23×D512yes—
658#67—108no—
659#67—108no—
660#67—204no—
661#67—204no—
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3—52no—
666C2×Dic3—52no—
667C2×Dic3—52no—
668C2×Dic3—102no—
669C2×Dic3—102no—
670C2×Dic3—102no—
671C2×Dic3—204no—
672C2×Dic3C23×D512yes—
673C2×Dic3C23×D512yes—
674C2×Dic3C23×D512yes—
675C4×D3—204no—
676C4×D3—204no—
677Dic6—204no—
678C22×C5—62no—
679C22×C5—62no—
680C22×C5—62no—
681C22×C5—124no—
682C22×C5#100412yes—
683C22×C5#100412yes—
684C22×C5D3×#4112yes—
685C22×C5C24×D311yescharacteristic
686C2×D5—22no—
687C2×D5—22no—
688C2×D5—22no—
689C2×D5—22no—
690C2×D5—22no—
691C2×D5—22no—
692C2×D5—22no—
693C2×D5—22no—
694C2×D5—22no—
695C2×D5—34no—
696C2×D5—44no—
697C2×D5—44no—
698C2×D5—44no—
699C2×D5—62no—
700C2×D5—62no—
701C2×D5—68no—
702C2×D5—1216no—
703C4×C5—22no—
704C4×C5—22no—
705C4×C5—22no—
706C4×C5—62no—
707C4×C5—62no—
708C4×C5—62no—
709Dic5—22no—
710Dic5—62no—
711Dic5—62no—
712Dic5—62no—
713C24—31no—
714C24—51no—
715C24—51no—
716C24—51no—
717C24—154no—
718C24—151no—
719C24—304no—
720C24—602no—
721C24—602no—
722C2×Q8—154no—
723C2×Q8—602no—
724C2×D4—54no—
725C2×D4—54no—
726C2×D4—54no—
727C2×D4—154no—
728C2×D4—154no—
729C2×D4—154no—
730C2×D4—154no—
731C2×D4—202no—
732C2×D4—202no—
733C2×D4—202no—
734C2×D4—304no—
735C2×D4—304no—
736C2×D4—602no—
737C2×D4—602no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—31no—
741C22×C4—51no—
742C22×C4—54no—
743C22×C4—154no—
744C22×C4—154no—
745C22×C4—151no—
746C22×C4—151no—
747C22×C4—151no—
748C22×C4—154no—
749C22×C4—202no—
750C22×C4—602no—
751C22×C4—602no—
752C22×C4—602no—
753C22×C4C2×D3×D511yescharacteristic
754C22×C4C2×D3×D511yescharacteristic
755C22×C4C2×D3×D511yescharacteristic
756C4⋊C4—34no—
757C4⋊C4—34no—
758C4⋊C4—154no—
759C4⋊C4—154no—
760C4⋊C4—154no—
761C4⋊C4C2×D3×D514yescomplemented
762C22⋊C4—34no—
763C22⋊C4—34no—
764C22⋊C4—34no—
765C22⋊C4—54no—
766C22⋊C4—54no—
767C22⋊C4—154no—
768C22⋊C4—154no—
769C22⋊C4—154no—
770C22⋊C4—154no—
771C22⋊C4—154no—
772C22⋊C4—154no—
773C22⋊C4—154no—
774C22⋊C4—154no—
775C22⋊C4—154no—
776C42—34no—
777C42—154no—
778C3×C5C2×#53811yescharacteristic, complemented, Hall
779C22×C3—102no—
780C22×C3—102no—
781C22×C3—102no—
782C22×C3—102no—
783C22×C3—102no—
784C22×C3—102no—
785C22×C3—102no—
786C22×C3—102no—
787C22×C3—102no—
788C22×C3—204no—
789C22×C3—204no—
790C22×C3—204no—
791C22×C3D5×#4112yes—
792C22×C3#414912yes—
793C22×C3#414912yes—
794C22×C3C24×D511yescharacteristic
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—44no—
799C2×D3—54no—
800C2×D3—102no—
801C2×D3—102no—
802C2×D3—108no—
803C2×D3—2016no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—102no—
808Dic3—22no—
809Dic3—22no—
810Dic3—22no—
811Dic3—102no—
812Dic3—102no—
813Dic3—102no—
814C2×C5—122no—
815C2×C5#561314yescomplemented
816C2×C5C2×#100411yescharacteristic
817C2×C5C2×#100411yescharacteristic
818C2×C5C2×D3×#4111yescharacteristic
819D5—42no—
820D5—42no—
821D5—42no—
822D5—64no—
823C23—32no—
824C23—52no—
825C23—52no—
826C23—52no—
827C23—62no—
828C23—62no—
829C23—62no—
830C23—102no—
831C23—102no—
832C23—102no—
833C23—102no—
834C23—102no—
835C23—102no—
836C23—102no—
837C23—102no—
838C23—102no—
839C23—154no—
840C23—152no—
841C23—308no—
842C23—302no—
843C23—302no—
844C23—604no—
845C23—604no—
846C23—6016no—
847C23C22×D3×D511yescharacteristic
848Q8—604no—
849D4—204no—
850D4—204no—
851D4—204no—
852D4—308no—
853D4—308no—
854D4—604no—
855D4—604no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—32no—
862C2×C4—52no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—102no—
867C2×C4—152no—
868C2×C4—152no—
869C2×C4—152no—
870C2×C4—204no—
871C2×C4—302no—
872C2×C4—302no—
873C2×C4—302no—
874C2×C4—604no—
875C2×C4—604no—
876C2×C4—604no—
877C2×C4C22×D3×D512yes—
878C2×C4C22×D3×D512yes—
879C2×C4C22×D3×D512yes—
880C2×C3—202no—
881C2×C3—202no—
882C2×C3—202no—
883C2×C3#6603814yescomplemented
884C2×C3C2×D5×#4111yescharacteristic
885C2×C3C2×#414911yescharacteristic
886C2×C3C2×#414911yescharacteristic
887D3—42no—
888D3—104no—
889C5C2×#561311yescharacteristic, complemented, Sylow
890C22—62no—
891C22—62no—
892C22—62no—
893C22—102no—
894C22—102no—
895C22—102no—
896C22—102no—
897C22—102no—
898C22—102no—
899C22—102no—
900C22—102no—
901C22—102no—
902C22—124no—
903C22—154no—
904C22—204no—
905C22—204no—
906C22—204no—
907C22—308no—
908C22—302no—
909C22—302no—
910C22—6016no—
911C22#9201712yes—
912C22#9202612yes—
913C22#9203412yes—
914C22C23×D3×D511yescharacteristic
915C4—22no—
916C4—22no—
917C4—22no—
918C4—62no—
919C4—62no—
920C4—62no—
921C4—102no—
922C4—302no—
923C4—302no—
924C4—302no—
925C3C2×#6603811yescharacteristic, complemented, Sylow
926C2—122no—
927C2—202no—
928C2—202no—
929C2—202no—
930C2—304no—
931C2#1175393614yesdirect product factor
932C2C2×#9201711yescharacteristic
933C2C2×#9202611yescharacteristic
934C2C2×#9203411yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#538
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91785C2semidirect
2. C2×C5×#898C2semidirect
3. C2×C3×#4041C2semidirect
4. C2×#91474C2semidirect
5. C2×#91474C2semidirect
6. C2×#91473C2semidirect
7. C2×#91465C2semidirect
8. C2×#91462C2semidirect
9. C2×#91447C2semidirect
10. C2×#91444C2semidirect
11. C2×#91408C2semidirect
12. C2×#91407C2semidirect
13. C2×#91395C2semidirect
14. C2×#91364C2semidirect
15. C2×#91361C2semidirect
16. #11753936C2direct (N × H)
20. C22×Dic30C22semidirect
23. C22×C3×D20C22semidirect
24. C22×C3×C4×D5C22semidirect
30. C22×D5×Dic3C22semidirect
31. C2×C3×C5×C4⋊C4C22semidirect
34. C2×#6712C22semidirect
35. C2×#6712C22semidirect
36. #91785C22semidirect
40. C2×C5×C4⋊Dic3C22semidirect
41. C2×C5×Dic3⋊C4C22semidirect
42. C2×C4×C5×Dic3C22semidirect
43. C5×#898C22semidirect
45. C2×C3×#685C22semidirect
46. C3×#4041C22semidirect
47. C2×Dic3⋊Dic5C22semidirect
52. C2×#6665C22semidirect
53. C2×#6665C22semidirect
54. C2×#6665C22semidirect
55. C2×Dic3×Dic5C22semidirect
56. #91474C22semidirect
57. #91474C22semidirect
58. #91473C22semidirect
59. #91465C22semidirect
60. #91462C22semidirect
61. #91447C22semidirect
62. #91444C22semidirect
63. #91408C22semidirect
64. #91407C22semidirect
65. #91395C22semidirect
66. #91364C22semidirect
67. #91361C22semidirect
74. C2×#4041D3semidirect
103. C2×Dic30C23semidirect
113. C2×C3×D20C23semidirect
115. C2×C3×C4×D5C23semidirect
127. C2×D5×Dic3C23semidirect
128. C3×C5×C4⋊C4C23semidirect
131. #6712C23semidirect
132. #6712C23semidirect
136. C5×C4⋊Dic3C23semidirect
137. C5×Dic3⋊C4C23semidirect
138. C4×C5×Dic3C23semidirect
140. C3×#685C23semidirect
141. Dic3⋊Dic5C23semidirect
146. #6665C23semidirect
147. #6665C23semidirect
148. #6665C23semidirect
149. Dic3×Dic5C23semidirect
160. C2×#898D5semidirect
173. C22×D20C2×D3semidirect
177. C22×C4×D5C2×D3semidirect
182. C2×C5×C4⋊C4C2×D3semidirect
197. C2×#685C2×D3semidirect
205. #4041C2×D3semidirect
288. C2×C3×C4⋊C4C2×D5semidirect
311. C2×C4⋊Dic3C2×D5semidirect
315. C2×Dic3⋊C4C2×D5semidirect
317. C2×C4×Dic3C2×D5semidirect
318. #898C2×D5semidirect
356. C2×D20C22×D3semidirect
364. C2×C4×D5C22×D3semidirect
369. C5×C4⋊C4C22×D3semidirect
384. #685C22×D3semidirect
483. C3×C4⋊C4C22×D5semidirect
498. C4⋊Dic3C22×D5semidirect
502. Dic3⋊C4C22×D5semidirect
504. C4×Dic3C22×D5semidirect
594. C2×C4⋊C4D3×D5semidirect
612. C2×C3×C5#538semidirect
761. C4⋊C4C2×D3×D5semidirect
778. C3×C5C2×#538semidirect
815. C2×C5#5613semidirect
883. C2×C3#66038semidirect
889. C5C2×#5613semidirect
925. C3C2×#66038semidirect
931. C2#11753936direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917852
C2×C5×#8982
C2×C3×#40412
C2×#914742
C2×#914732
C2×#914652
C2×#914622
C2×#914472
C2×#914442
C2×#914082
C2×#914072
C2×#913952
C2×#913642
C2×#913612
#117539362
C2×#660383
C2×#56135