Finite Group Databasebeta

← C2×#11753246 #14480431

Subgroups — C2×#11753246 #14480431

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×#6772C211yesmaximal, characteristic, complemented
3C2×#91774C211yesmaximal, characteristic, complemented
4C2×C5×#882C211yesmaximal, characteristic, complemented
5C2×C3×#4030C211yesmaximal, characteristic, complemented
6C2×#91568C211yesmaximal, characteristic, complemented
7C2×#91567C211yesmaximal, characteristic, complemented
8C2×#91565C211yesmaximal, characteristic, complemented
9C2×#91475C211yesmaximal, characteristic, complemented
10C2×#91474C211yesmaximal, characteristic, complemented
11C2×#91463C211yesmaximal, characteristic, complemented
12C2×#91462C211yesmaximal, characteristic, complemented
13C2×#91448C211yesmaximal, characteristic, complemented
14C2×#91416C211yesmaximal, characteristic, complemented
15C2×#91400C211yesmaximal, characteristic, complemented
16#11753246C2116yesmaximal, direct product factor
17C2×#65926—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×Dic30C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic, complemented
23C22×C5×D12C2211yescharacteristic
24C22×C5×D12C2211yescharacteristic, complemented
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×C22⋊D5C2211yescharacteristic, complemented
27C22×C3×D20C2211yescharacteristic, complemented
28C22×C3×C4×D5C2211yescharacteristic, complemented
29C2×D3×C22⋊D5—28no—
30C2×D3×C22⋊D5C2218yescomplemented
31C22×#1203C2211yescharacteristic
32C22×#1203C2211yescharacteristic, complemented
33C22×#1202C2211yescharacteristic, complemented
34C22×#1201C2211yescharacteristic
35C22×#1201C2211yescharacteristic
36C22×#1201C2211yescharacteristic, complemented
37C22×#1201C2211yescharacteristic, complemented
38C22×#1201C2211yescharacteristic, complemented
39C22×D3×Dic5C2211yescharacteristic
40C22×D3×Dic5C2211yescharacteristic, complemented
41C2×#6772—28no—
42C2×#6772C2218yescomplemented
43C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
44C2×#6719C2211yescharacteristic, complemented
45C2×#6714C2211yescharacteristic, complemented
46C2×#6714C2211yescharacteristic, complemented
47C2×C4×Dic15C2211yescharacteristic, complemented
48#91774C2218yescomplemented
49C2×C5×(C2×D3)⋊C4C2211yescharacteristic
50C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C5×#882C2218yescomplemented
52C2×C3×#685C2211yescharacteristic, complemented
53C2×C3×#683C2211yescharacteristic, complemented
54C3×#4030C2218yescomplemented
55#91568C2218yescomplemented
56#91567C2218yescomplemented
57#91565C2218yescomplemented
58C2×#6668C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic5C2211yescharacteristic
60C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
61C2×#6665C2211yescharacteristic, complemented
62C2×Dic3×Dic5C2211yescharacteristic, complemented
63#91475C2218yescomplemented
64#91474C2218yescomplemented
65#91463C2218yescomplemented
66#91462C2218yescomplemented
67#91448C2218yescomplemented
68#91416C2218yescomplemented
69#91400C2218yescomplemented
70C2×#5607—51nomaximal, Hall
71C23×C22⋊D5—31no—
72C22×#711—31no—
73C2×C5×#120—31no—
74C2×#4099—31no—
75C2×#4086—31no—
76C2×#4086—31no—
77C2×#4085—31no—
78C2×#4085—31no—
79C2×#4083—31no—
80#65926—316no—
81C2×#4031—31no—
82C2×#4031—31no—
83C2×#4030—31no—
84C2×#4030D311yescharacteristic, complemented
85C2×#4028—31no—
86C2×#4023—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3—24no—
90C23×C5×D3—42no—
91C23×C5×D3—42no—
92C23×C5×D3C2311yescharacteristic
93C23×C5×D3C2311yescharacteristic
94C23×C5×D3C2311yescharacteristic
95C23×C5×D3C2314yes—
96C23×C3×D5C2311yescharacteristic
97C23×C3×D5C2311yescharacteristic
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5—42no—
101C22×D3×D5C2314yes—
102C22×C3×C4×C5C2311yescharacteristic
103C22×C3×C4×C5C2311yescharacteristic
104C2×#1220—24no—
105C2×#1220C2314yes—
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109C2×Dic30—24no—
110C2×Dic30C2314yescomplemented
111C2×C5×#67—42no—
112C2×C5×#67C2314yescomplemented
113C22×C5×Dic3C2311yescharacteristic
114C2×C5×D12—24no—
115C2×C5×D12—42no—
116C2×C5×D12C2314yes—
117C2×C5×D12C2314yescomplemented
118C2×C3×C22⋊D5—24no—
119C2×C3×C22⋊D5—42no—
120C2×C3×C22⋊D5C2314yes—
121C2×C3×C22⋊D5C2314yescomplemented
122C22×C3×Dic5C2311yescharacteristic
123C22×C3×Dic5C2311yescharacteristic
124C2×C3×D20—42no—
125C2×C3×D20C2314yescomplemented
126C2×C3×C4×D5—24no—
127C2×C3×C4×D5C2314yescomplemented
128D3×C22⋊D5—232no—
129C2×#1203—24no—
130C2×#1203—42no—
131C2×#1203C2314yes—
132C2×#1203C2314yescomplemented
133C2×#1202—42no—
134C2×#1202C2314yescomplemented
135C2×#1201—24no—
136C2×#1201—24no—
137C2×#1201—24no—
138C2×#1201—42no—
139C2×#1201—42no—
140C2×#1201C2314yes—
141C2×#1201C2314yes—
142C2×#1201C2314yescomplemented
143C2×#1201C2314yescomplemented
144C2×#1201C2314yescomplemented
145C2×D3×Dic5—24no—
146C2×D3×Dic5D418yescomplemented
147C2×D3×Dic5C2314yes—
148C2×D3×Dic5C2314yescomplemented
149#6772—232no—
150C3×C5×C22⋊C4C2314yescomplemented
151#6719C2314yescomplemented
152#6714C2314yescomplemented
153#6714C2314yescomplemented
154C4×Dic15C2314yescomplemented
155C5×(C2×D3)⋊C4C2314yes—
156C5×(C2×D3)⋊C4C2314yescomplemented
157C3×#685C2314yescomplemented
158C3×#683C2314yescomplemented
159#6668C2314yescomplemented
160(C2×D3)⋊Dic5C2314yes—
161(C2×D3)⋊Dic5C2314yescomplemented
162#6665C2314yescomplemented
163Dic3×Dic5C2314yescomplemented
164C22×D3×D4—51no—
165C22×#235—51no—
166C2×C3×#121—51no—
167C2×#940—51no—
168C2×#940—51no—
169C2×#938—51no—
170C2×#937—51no—
171C2×#937—51no—
172C2×#930—51no—
173#5607—516no—
174C2×#895—51no—
175C2×#892—51no—
176C2×#885—51no—
177C2×#885—51no—
178C2×#882—51no—
179C2×#882D511yescharacteristic, complemented
180C25×C5—31no—
181C24×D5—31no—
182C22×C5×D4—31no—
183C22×C5×D4—31no—
184C22×C5×D4—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5—31no—
190C22×C22⋊D5—31no—
191C22×C22⋊D5—38no—
192C22×C22⋊D5—31no—
193C22×C22⋊D5—31no—
194C22×C22⋊D5—68no—
195C22×C22⋊D5C2×D311yescharacteristic
196C22×C22⋊D5C2×D311yescharacteristic, complemented
197C23×Dic5—31no—
198C23×Dic5—31no—
199C2×#711—38no—
200C2×#711—68no—
201C22×D20—31no—
202C22×D20C2×D311yescharacteristic, complemented
203C22×C4×D5C2×D311yescharacteristic, complemented
204C22×Dic10—31no—
205C5×#120—38no—
206C2×C5×C22⋊C4—31no—
207C2×C5×C22⋊C4—31no—
208C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
209#4099—38no—
210C2×C22⋊Dic5—31no—
211C2×C22⋊Dic5—31no—
212C2×C22⋊Dic5—31no—
213#4086—38no—
214#4086—38no—
215#4085—38no—
216#4085—38no—
217#4083—38no—
218C2×#685—31no—
219C2×#685—31no—
220C2×#685—31no—
221C2×#685C2×D311yescharacteristic, complemented
222C2×#683—31no—
223C2×#683C2×D311yescharacteristic, complemented
224C2×C4×Dic5—31no—
225C2×C4×Dic5—31no—
226#4031—38no—
227#4031—38no—
228#4030—38no—
229#4030C2×D318yescomplemented
230#4028—38no—
231#4023—38no—
232C2×#535—151noSylow
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5C2412yes—
237C23×C3×C5C2411yescharacteristic
238C22×D15—22no—
239C22×D15—22no—
240C22×D15—22no—
241C22×D15C2412yes—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—22no—
247C22×C5×D3—22no—
248C22×C5×D3—22no—
249C22×C5×D3—22no—
250C22×C5×D3—28no—
251C22×C5×D3—44no—
252C22×C5×D3—44no—
253C22×C5×D3—416no—
254C22×C5×D3C2×D414yes—
255C22×C5×D3C2412yes—
256C22×C5×D3C2412yes—
257C22×C5×D3C2412yes—
258C22×C3×D5—22no—
259C22×C3×D5—22no—
260C22×C3×D5—22no—
261C22×C3×D5—22no—
262C22×C3×D5—22no—
263C22×C3×D5—22no—
264C22×C3×D5C2412yes—
265C22×C3×D5C2412yes—
266C2×D3×D5—28no—
267C2×D3×D5—44no—
268C2×D3×D5—44no—
269C2×D3×D5—416no—
270C2×C3×C4×C5—22no—
271C2×C3×C4×C5—22no—
272C2×C3×C4×C5C2412yes—
273C2×C3×C4×C5C2412yes—
274#1220—28no—
275C2×Dic15—22no—
276C2×Dic15—22no—
277C2×Dic15C2×D414yes—
278C2×Dic15C2412yes—
279C2×Dic15C2412yes—
280C2×Dic15C2412yes—
281Dic30—28no—
282C5×#67—44no—
283C2×C5×Dic3—22no—
284C2×C5×Dic3C2412yes—
285C5×D12—28no—
286C5×D12—44no—
287C3×C22⋊D5—28no—
288C3×C22⋊D5—44no—
289C2×C3×Dic5—22no—
290C2×C3×Dic5C2×D414yes—
291C2×C3×Dic5C2412yes—
292C2×C3×Dic5C2412yes—
293C3×D20—44no—
294C3×C4×D5—28no—
295#1203—28no—
296#1203—44no—
297#1202—44no—
298#1201—28no—
299#1201—28no—
300#1201—28no—
301#1201—44no—
302#1201—44no—
303D3×Dic5—28no—
304D3×Dic5C2×D4116yescomplemented
305C24×D3—51no—
306C24×D3C2×D511yescharacteristic
307C22×C3×D4—51no—
308C22×C3×D4—51no—
309C22×C3×D4—51no—
310C23×C3×C4—51no—
311C22×#67—51no—
312C22×#67—51no—
313C22×#67—51no—
314C22×#67—51no—
315C22×#67—51no—
316C22×#67—51no—
317C22×#67—51no—
318C22×#67C2×D511yescharacteristic, complemented
319C2×D3×D4—58no—
320C2×D3×D4—108no—
321C2×#235—58no—
322C2×#235—108no—
323C22×D12—51no—
324C22×D12—51no—
325C22×D12C2×D511yescharacteristic
326C22×D12C2×D511yescharacteristic, complemented
327C22×C4×D3—51no—
328C22×C4×D3—51no—
329C22×Dic6—51no—
330C3×#121—58no—
331C2×C3×C4⋊C4—51no—
332C2×C3×C22⋊C4—51no—
333C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
334C2×#217—51no—
335C2×#217—51no—
336#940—58no—
337#940—58no—
338#938—58no—
339#937—58no—
340#937—58no—
341#930—58no—
342C2×(C2×D3)⋊C4—51no—
343C2×(C2×D3)⋊C4—51no—
344C2×(C2×D3)⋊C4—51no—
345C2×(C2×D3)⋊C4—51no—
346C2×(C2×D3)⋊C4C2×D511yescharacteristic
347C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
348C2×C4⋊Dic3—51no—
349C2×C4×Dic3—51no—
350C2×C4×Dic3—51no—
351#895—58no—
352#892—58no—
353#885—58no—
354#885—58no—
355#882—58no—
356#882C2×D518yescomplemented
357C24×C5—31no—
358C24×C5—31no—
359C24×C5—31no—
360C24×C5—34no—
361C24×C5—64no—
362C24×C5—122no—
363C24×C5—122no—
364C24×C5C22×D311yescharacteristic
365C23×D5—31no—
366C23×D5—34no—
367C23×D5—64no—
368C23×D5—122no—
369C23×D5—122no—
370C23×D5C22×D311yescharacteristic
371C23×D5C22×D311yescharacteristic
372C2×C5×D4—34no—
373C2×C5×D4—34no—
374C2×C5×D4—34no—
375C2×C5×D4—64no—
376C2×C5×D4—122no—
377C2×C5×D4—122no—
378C22×C4×C5—31no—
379C22×C4×C5C22×D311yescharacteristic
380C22×C4×C5C22×D311yescharacteristic
381C2×C22⋊D5—24no—
382C2×C22⋊D5—34no—
383C2×C22⋊D5—34no—
384C2×C22⋊D5—34no—
385C2×C22⋊D5—34no—
386C2×C22⋊D5—34no—
387C2×C22⋊D5—34no—
388C2×C22⋊D5—34no—
389C2×C22⋊D5—34no—
390C2×C22⋊D5—42no—
391C2×C22⋊D5—632no—
392C2×C22⋊D5—64no—
393C2×C22⋊D5—64no—
394C2×C22⋊D5—64no—
395C2×C22⋊D5—64no—
396C2×C22⋊D5—64no—
397C2×C22⋊D5—122no—
398C2×C22⋊D5—122no—
399C2×C22⋊D5—122no—
400C2×C22⋊D5C22×D314yes—
401C2×C22⋊D5C22×D314yescomplemented
402C22×Dic5—31no—
403C22×Dic5—38no—
404C22×Dic5—34no—
405C22×Dic5—31no—
406C22×Dic5—31no—
407C22×Dic5—34no—
408C22×Dic5—64no—
409C22×Dic5C22×D311yescharacteristic
410C22×Dic5C22×D311yescharacteristic
411#711—632no—
412C2×D20—34no—
413C2×D20—42no—
414C2×D20—122no—
415C2×D20C22×D314yescomplemented
416C2×C4×D5—24no—
417C2×C4×D5C22×D314yescomplemented
418C2×Dic10—34no—
419C2×Dic10—64no—
420C5×C22⋊C4—34no—
421C5×C22⋊C4—34no—
422C5×C22⋊C4C22×D314yescomplemented
423C22⋊Dic5—34no—
424C22⋊Dic5—34no—
425C22⋊Dic5—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685C22×D314yescomplemented
430#683—34no—
431#683C22×D314yescomplemented
432C4×Dic5—34no—
433C4×Dic5—34no—
434C22×#41—151no—
435C23×D4—151no—
436#535—1516no—
437C2×#127—151no—
438C2×#127—151no—
439C2×#124—151no—
440C2×#124—151no—
441C2×#121—51no—
442C2×#121—151no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#120—31no—
446C2×#120—151no—
447C2×#120—151no—
448C2×#120—151no—
449C2×#117—151no—
450C22×C3×C5—22no—
451C22×C3×C5—22no—
452C22×C3×C5—22no—
453C22×C3×C5—44no—
454C22×C3×C5C22×D412yes—
455C22×C3×C5H(5,𝔽2)12yes—
456C22×C3×C5H(5,𝔽2)12yes—
457C22×C3×C5C2511yescharacteristic
458C2×D15—22no—
459C2×D15—22no—
460C2×D15—22no—
461C2×D15—44no—
462C2×C5×D3—28no—
463C2×C5×D3—22no—
464C2×C5×D3—22no—
465C2×C5×D3—22no—
466C2×C5×D3—22no—
467C2×C5×D3—22no—
468C2×C5×D3—22no—
469C2×C5×D3—22no—
470C2×C5×D3—22no—
471C2×C5×D3—416no—
472C2×C5×D3—44no—
473C2×C5×D3—44no—
474C2×C5×D3C22×D414yes—
475C2×C3×D5—22no—
476C2×C3×D5—22no—
477C2×C3×D5—22no—
478C2×C3×D5—22no—
479C2×C3×D5—22no—
480C2×C3×D5—22no—
481C2×C3×D5—44no—
482C2×C3×D5—44no—
483D3×D5—416no—
484C3×C4×C5—22no—
485C3×C4×C5—22no—
486Dic15—22no—
487Dic15—22no—
488Dic15C22×D414yes—
489C3×Dic5—22no—
490C3×Dic5C22×D414yes—
491C5×Dic3—22no—
492C24×C3—51no—
493C24×C3—51no—
494C24×C3C22×D511yescharacteristic
495C23×D3—24no—
496C23×D3—42no—
497C23×D3—42no—
498C23×D3—51no—
499C23×D3—54no—
500C23×D3—104no—
501C23×D3—202no—
502C23×D3—202no—
503C23×D3C22×D511yescharacteristic
504C23×D3C22×D511yescharacteristic
505C23×D3C22×D511yescharacteristic
506C23×D3C22×D514yes—
507C2×C3×D4—54no—
508C2×C3×D4—54no—
509C2×C3×D4—54no—
510C2×C3×D4—104no—
511C2×C3×D4—202no—
512C2×C3×D4—202no—
513C22×C3×C4—51no—
514C22×C3×C4—51no—
515C22×C3×C4—54no—
516C22×C3×C4—104no—
517C22×C3×C4C22×D511yescharacteristic
518C22×C3×C4C22×D511yescharacteristic
519C2×#67—42no—
520C2×#67—54no—
521C2×#67—54no—
522C2×#67—54no—
523C2×#67—54no—
524C2×#67—54no—
525C2×#67—54no—
526C2×#67—54no—
527C2×#67—104no—
528C2×#67—104no—
529C2×#67—104no—
530C2×#67—104no—
531C2×#67—202no—
532C2×#67—202no—
533C2×#67—202no—
534C2×#67C22×D514yescomplemented
535C22×Dic3—51no—
536C22×Dic3—51no—
537C22×Dic3—51no—
538C22×Dic3C22×D511yescharacteristic
539D3×D4—1032no—
540#235—1032no—
541C2×D12—24no—
542C2×D12—42no—
543C2×D12—54no—
544C2×D12—54no—
545C2×D12—104no—
546C2×D12—202no—
547C2×D12C22×D514yes—
548C2×D12C22×D514yescomplemented
549C2×C4×D3—58no—
550C2×C4×D3—54no—
551C2×C4×D3—54no—
552C2×C4×D3—104no—
553C2×Dic6—54no—
554C2×Dic6—104no—
555C3×C4⋊C4—54no—
556C3×C22⋊C4—54no—
557C3×C22⋊C4C22×D514yescomplemented
558#217—54no—
559#217—54no—
560(C2×D3)⋊C4—54no—
561(C2×D3)⋊C4—54no—
562(C2×D3)⋊C4—54no—
563(C2×D3)⋊C4—54no—
564(C2×D3)⋊C4C22×D514yes—
565(C2×D3)⋊C4C22×D514yescomplemented
566C4⋊Dic3—54no—
567C4×Dic3—54no—
568C4×Dic3—54no—
569C23×C5—22no—
570C23×C5—22no—
571C23×C5—22no—
572C23×C5—34no—
573C23×C5—32no—
574C23×C5—32no—
575C23×C5—32no—
576C23×C5—68no—
577C23×C5—62no—
578C23×C5—62no—
579C23×C5—62no—
580C23×C5—62no—
581C23×C5—62no—
582C23×C5—62no—
583C23×C5—62no—
584C23×C5—62no—
585C23×C5—124no—
586C23×C5—124no—
587C23×C5—1216no—
588C23×C5C23×D312yes—
589C23×C5C23×D311yescharacteristic
590C22×D5—22no—
591C22×D5—22no—
592C22×D5—22no—
593C22×D5—22no—
594C22×D5—22no—
595C22×D5—22no—
596C22×D5—32no—
597C22×D5—68no—
598C22×D5—62no—
599C22×D5—62no—
600C22×D5—62no—
601C22×D5—124no—
602C22×D5—124no—
603C22×D5—1216no—
604C22×D5C23×D312yes—
605C22×D5C23×D312yes—
606C5×D4—68no—
607C5×D4—124no—
608C5×D4—124no—
609C2×C4×C5—22no—
610C2×C4×C5—22no—
611C2×C4×C5—32no—
612C2×C4×C5—62no—
613C2×C4×C5C23×D312yes—
614C2×C4×C5C23×D312yes—
615C22⋊D5—28no—
616C22⋊D5—44no—
617C22⋊D5—68no—
618C22⋊D5—68no—
619C22⋊D5—68no—
620C22⋊D5—68no—
621C22⋊D5—68no—
622C22⋊D5—124no—
623C22⋊D5—124no—
624C22⋊D5—124no—
625C2×Dic5—22no—
626C2×Dic5—34no—
627C2×Dic5—32no—
628C2×Dic5—316no—
629C2×Dic5—32no—
630C2×Dic5—32no—
631C2×Dic5—62no—
632C2×Dic5—62no—
633C2×Dic5—68no—
634C2×Dic5D3×D414yes—
635C2×Dic5C23×D312yes—
636C2×Dic5C23×D312yes—
637D20—44no—
638D20—124no—
639C4×D5—28no—
640Dic10—68no—
641C25—31no—
642C25—151no—
643C2×#41—158no—
644C2×#41—308no—
645C22×Q8—151no—
646C22×D4—31no—
647C22×D4—31no—
648C22×D4—31no—
649C22×D4—51no—
650C22×D4—51no—
651C22×D4—51no—
652C22×D4—151no—
653C22×D4—151no—
654C22×D4—151no—
655C22×D4—158no—
656C22×D4—151no—
657C22×D4—151no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—151no—
661C22×D4—151no—
662C22×D4—308no—
663C23×C4—51no—
664C23×C4—151no—
665C23×C4—151no—
666#127—158no—
667#127—158no—
668#124—158no—
669#124—158no—
670#121—58no—
671#121—158no—
672#121—158no—
673#121—158no—
674#120—38no—
675#120—158no—
676#120—158no—
677#120—158no—
678#117—158no—
679C2×C4⋊C4—51no—
680C2×C4⋊C4—151no—
681C2×C22⋊C4—31no—
682C2×C22⋊C4—31no—
683C2×C22⋊C4—51no—
684C2×C22⋊C4—151no—
685C2×C22⋊C4—151no—
686C2×C22⋊C4—151no—
687C2×C22⋊C4—151no—
688C2×C22⋊C4—151no—
689C2×C22⋊C4—151no—
690C2×C22⋊C4D3×D511yescharacteristic, complemented
691C2×C42—151no—
692C2×C42—151no—
693C2×C3×C5—42no—
694C2×C3×C5#53514yescomplemented
695C2×C3×C5C23×D411yescharacteristic
696C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
697C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
698D15—42no—
699C3×D5—42no—
700C3×D5—42no—
701C5×D3—24no—
702C5×D3—42no—
703C5×D3—42no—
704C23×C3—22no—
705C23×C3—22no—
706C23×C3—22no—
707C23×C3—52no—
708C23×C3—52no—
709C23×C3—102no—
710C23×C3—102no—
711C23×C3—102no—
712C23×C3—102no—
713C23×C3—102no—
714C23×C3—102no—
715C23×C3C23×D512yes—
716C23×C3C23×D511yescharacteristic
717C22×D3—22no—
718C22×D3—22no—
719C22×D3—22no—
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—22no—
723C22×D3—22no—
724C22×D3—22no—
725C22×D3—28no—
726C22×D3—44no—
727C22×D3—44no—
728C22×D3—416no—
729C22×D3—52no—
730C22×D3—102no—
731C22×D3—102no—
732C22×D3—102no—
733C22×D3—108no—
734C22×D3—204no—
735C22×D3—204no—
736C22×D3—2016no—
737C22×D3D4×D514yes—
738C22×D3C23×D512yes—
739C22×D3C23×D512yes—
740C22×D3C23×D512yes—
741C3×D4—108no—
742C3×D4—204no—
743C3×D4—204no—
744C2×C3×C4—22no—
745C2×C3×C4—22no—
746C2×C3×C4—54no—
747C2×C3×C4—52no—
748C2×C3×C4—52no—
749C2×C3×C4—108no—
750C2×C3×C4—102no—
751C2×C3×C4C23×D512yes—
752C2×C3×C4C23×D512yes—
753#67—44no—
754#67—108no—
755#67—108no—
756#67—108no—
757#67—108no—
758#67—204no—
759#67—204no—
760#67—204no—
761C2×Dic3—22no—
762C2×Dic3—54no—
763C2×Dic3—52no—
764C2×Dic3—52no—
765C2×Dic3—52no—
766C2×Dic3—102no—
767C2×Dic3—102no—
768C2×Dic3C23×D512yes—
769D12—28no—
770D12—44no—
771D12—108no—
772D12—204no—
773C4×D3—516no—
774C4×D3—108no—
775Dic6—108no—
776C22×C5—22no—
777C22×C5—22no—
778C22×C5—22no—
779C22×C5—34no—
780C22×C5—44no—
781C22×C5—62no—
782C22×C5—62no—
783C22×C5—68no—
784C22×C5—62no—
785C22×C5—62no—
786C22×C5—62no—
787C22×C5—62no—
788C22×C5—62no—
789C22×C5—62no—
790C22×C5—1216no—
791C22×C5—124no—
792C22×C5—124no—
793C22×C5C2×D3×D412yes—
794C22×C5#100412yes—
795C22×C5#100912yes—
796C22×C5C24×D311yescharacteristic
797C2×D5—22no—
798C2×D5—22no—
799C2×D5—22no—
800C2×D5—22no—
801C2×D5—22no—
802C2×D5—22no—
803C2×D5—44no—
804C2×D5—44no—
805C2×D5—62no—
806C2×D5—62no—
807C2×D5—62no—
808C2×D5—1216no—
809C2×D5—124no—
810C4×C5—22no—
811C4×C5—22no—
812C4×C5—62no—
813Dic5—22no—
814Dic5—34no—
815Dic5—62no—
816Dic5—62no—
817Dic5C2×D3×D414yes—
818C24—31no—
819C24—31no—
820C24—31no—
821C24—34no—
822C24—51no—
823C24—51no—
824C24—64no—
825C24—122no—
826C24—122no—
827C24—154no—
828C24—151no—
829C24—304no—
830C24—602no—
831C24—602no—
832C24C2×D3×D511yescharacteristic
833#41—3032no—
834C2×Q8—154no—
835C2×Q8—304no—
836C2×D4—34no—
837C2×D4—34no—
838C2×D4—34no—
839C2×D4—54no—
840C2×D4—54no—
841C2×D4—54no—
842C2×D4—64no—
843C2×D4—104no—
844C2×D4—122no—
845C2×D4—122no—
846C2×D4—154no—
847C2×D4—154no—
848C2×D4—154no—
849C2×D4—154no—
850C2×D4—154no—
851C2×D4—154no—
852C2×D4—154no—
853C2×D4—154no—
854C2×D4—154no—
855C2×D4—202no—
856C2×D4—202no—
857C2×D4—304no—
858C2×D4—3032no—
859C2×D4—304no—
860C2×D4—304no—
861C2×D4—304no—
862C2×D4—304no—
863C2×D4—602no—
864C2×D4—602no—
865C2×D4—602no—
866C2×D4—602no—
867C22×C4—31no—
868C22×C4—51no—
869C22×C4—51no—
870C22×C4—54no—
871C22×C4—104no—
872C22×C4—154no—
873C22×C4—158no—
874C22×C4—154no—
875C22×C4—151no—
876C22×C4—151no—
877C22×C4—151no—
878C22×C4—304no—
879C22×C4C2×D3×D511yescharacteristic
880C22×C4C2×D3×D511yescharacteristic
881C4⋊C4—54no—
882C4⋊C4—154no—
883C22⋊C4—34no—
884C22⋊C4—34no—
885C22⋊C4—54no—
886C22⋊C4—154no—
887C22⋊C4—154no—
888C22⋊C4—154no—
889C22⋊C4—154no—
890C22⋊C4—154no—
891C22⋊C4—154no—
892C22⋊C4C2×D3×D514yescomplemented
893C42—154no—
894C42—154no—
895C3×C5C2×#53511yescharacteristic, complemented, Hall
896C22×C3—22no—
897C22×C3—22no—
898C22×C3—22no—
899C22×C3—44no—
900C22×C3—102no—
901C22×C3—102no—
902C22×C3—102no—
903C22×C3—102no—
904C22×C3—102no—
905C22×C3—102no—
906C22×C3—204no—
907C22×C3—204no—
908C22×C3C2×D4×D512yes—
909C22×C3#414412yes—
910C22×C3#414412yes—
911C22×C3C24×D511yescharacteristic
912C2×D3—28no—
913C2×D3—22no—
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—416no—
922C2×D3—44no—
923C2×D3—44no—
924C2×D3—102no—
925C2×D3—102no—
926C2×D3—102no—
927C2×D3—2016no—
928C2×D3—204no—
929C2×D3C2×D4×D514yes—
930C3×C4—22no—
931C3×C4—22no—
932C3×C4—54no—
933C3×C4—102no—
934Dic3—22no—
935Dic3—54no—
936Dic3—102no—
937Dic3—102no—
938C2×C5—42no—
939C2×C5—64no—
940C2×C5—122no—
941C2×C5—122no—
942C2×C5#560714yescomplemented
943C2×C5C22×D3×D411yescharacteristic
944C2×C5C2×#100411yescharacteristic
945C2×C5C2×#100911yescharacteristic
946D5—42no—
947D5—42no—
948D5—122no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—34no—
953C23—32no—
954C23—32no—
955C23—32no—
956C23—52no—
957C23—52no—
958C23—68no—
959C23—62no—
960C23—62no—
961C23—62no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—102no—
968C23—102no—
969C23—102no—
970C23—102no—
971C23—102no—
972C23—102no—
973C23—124no—
974C23—124no—
975C23—1216no—
976C23—152no—
977C23—308no—
978C23—302no—
979C23—302no—
980C23—302no—
981C23—604no—
982C23—604no—
983C23—6016no—
984C23C22×D3×D512yes—
985C23C22×D3×D511yescharacteristic
986Q8—308no—
987D4—68no—
988D4—108no—
989D4—124no—
990D4—124no—
991D4—204no—
992D4—204no—
993D4—308no—
994D4—308no—
995D4—308no—
996D4—308no—
997D4—308no—
998D4—604no—
999D4—604no—
1000D4—604no—
1001D4—604no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—32no—
1005C2×C4—54no—
1006C2×C4—52no—
1007C2×C4—52no—
1008C2×C4—62no—
1009C2×C4—108no—
1010C2×C4—102no—
1011C2×C4—1516no—
1012C2×C4—154no—
1013C2×C4—152no—
1014C2×C4—152no—
1015C2×C4—152no—
1016C2×C4—308no—
1017C2×C4—302no—
1018C2×C4—302no—
1019C2×C4C22×D3×D512yes—
1020C2×C4C22×D3×D512yes—
1021C2×C3—42no—
1022C2×C3—202no—
1023C2×C3—202no—
1024C2×C3#6592614yescomplemented
1025C2×C3C22×D4×D511yescharacteristic
1026C2×C3C2×#414411yescharacteristic
1027C2×C3C2×#414411yescharacteristic
1028D3—24no—
1029D3—42no—
1030D3—42no—
1031D3—202no—
1032C5C2×#560711yescharacteristic, complemented, Sylow
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—34no—
1037C22—44no—
1038C22—68no—
1039C22—62no—
1040C22—62no—
1041C22—62no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—102no—
1048C22—102no—
1049C22—102no—
1050C22—102no—
1051C22—102no—
1052C22—102no—
1053C22—1216no—
1054C22—124no—
1055C22—124no—
1056C22—204no—
1057C22—204no—
1058C22—302no—
1059C22—302no—
1060C22—302no—
1061C22—6016no—
1062C22—604no—
1063C22#9201812yes—
1064C22D3×D4×D512yes—
1065C22#9202512yes—
1066C22C23×D3×D511yescharacteristic
1067C4—22no—
1068C4—22no—
1069C4—54no—
1070C4—62no—
1071C4—102no—
1072C4—154no—
1073C4—302no—
1074C4—302no—
1075C3C2×#6592611yescharacteristic, complemented, Sylow
1076C2—42no—
1077C2—64no—
1078C2—122no—
1079C2—122no—
1080C2—202no—
1081C2—202no—
1082C2—602no—
1083C2#1175324614yesdirect product factor
1084C2C2×#9201811yescharacteristic
1085C2C2×D3×D4×D511yescharacteristic
1086C2C2×#9202511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#535
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. C22×D3×C22⋊D5C2semidirect
2. C22×#6772C2semidirect
3. C2×#91774C2semidirect
4. C2×C5×#882C2semidirect
5. C2×C3×#4030C2semidirect
6. C2×#91568C2semidirect
7. C2×#91567C2semidirect
8. C2×#91565C2semidirect
9. C2×#91475C2semidirect
10. C2×#91474C2semidirect
11. C2×#91463C2semidirect
12. C2×#91462C2semidirect
13. C2×#91448C2semidirect
14. C2×#91416C2semidirect
15. C2×#91400C2semidirect
16. #11753246C2direct (N × H)
21. C22×Dic30C22semidirect
22. C22×C5×#67C22semidirect
24. C22×C5×D12C22semidirect
26. C22×C3×C22⋊D5C22semidirect
27. C22×C3×D20C22semidirect
28. C22×C3×C4×D5C22semidirect
30. C2×D3×C22⋊D5C22semidirect
32. C22×#1203C22semidirect
33. C22×#1202C22semidirect
36. C22×#1201C22semidirect
37. C22×#1201C22semidirect
38. C22×#1201C22semidirect
40. C22×D3×Dic5C22semidirect
42. C2×#6772C22semidirect
43. C2×C3×C5×C22⋊C4C22semidirect
44. C2×#6719C22semidirect
45. C2×#6714C22semidirect
46. C2×#6714C22semidirect
47. C2×C4×Dic15C22semidirect
48. #91774C22semidirect
50. C2×C5×(C2×D3)⋊C4C22semidirect
51. C5×#882C22semidirect
52. C2×C3×#685C22semidirect
53. C2×C3×#683C22semidirect
54. C3×#4030C22semidirect
55. #91568C22semidirect
56. #91567C22semidirect
57. #91565C22semidirect
58. C2×#6668C22semidirect
60. C2×(C2×D3)⋊Dic5C22semidirect
61. C2×#6665C22semidirect
62. C2×Dic3×Dic5C22semidirect
63. #91475C22semidirect
64. #91474C22semidirect
65. #91463C22semidirect
66. #91462C22semidirect
67. #91448C22semidirect
68. #91416C22semidirect
69. #91400C22semidirect
84. C2×#4030D3semidirect
110. C2×Dic30C23semidirect
112. C2×C5×#67C23semidirect
117. C2×C5×D12C23semidirect
121. C2×C3×C22⋊D5C23semidirect
125. C2×C3×D20C23semidirect
127. C2×C3×C4×D5C23semidirect
132. C2×#1203C23semidirect
134. C2×#1202C23semidirect
142. C2×#1201C23semidirect
143. C2×#1201C23semidirect
144. C2×#1201C23semidirect
146. C2×D3×Dic5D4semidirect
148. C2×D3×Dic5C23semidirect
150. C3×C5×C22⋊C4C23semidirect
151. #6719C23semidirect
152. #6714C23semidirect
153. #6714C23semidirect
154. C4×Dic15C23semidirect
156. C5×(C2×D3)⋊C4C23semidirect
157. C3×#685C23semidirect
158. C3×#683C23semidirect
159. #6668C23semidirect
161. (C2×D3)⋊Dic5C23semidirect
162. #6665C23semidirect
163. Dic3×Dic5C23semidirect
179. C2×#882D5semidirect
196. C22×C22⋊D5C2×D3semidirect
202. C22×D20C2×D3semidirect
203. C22×C4×D5C2×D3semidirect
208. C2×C5×C22⋊C4C2×D3semidirect
221. C2×#685C2×D3semidirect
223. C2×#683C2×D3semidirect
229. #4030C2×D3semidirect
304. D3×Dic5C2×D4semidirect
318. C22×#67C2×D5semidirect
326. C22×D12C2×D5semidirect
333. C2×C3×C22⋊C4C2×D5semidirect
347. C2×(C2×D3)⋊C4C2×D5semidirect
356. #882C2×D5semidirect
401. C2×C22⋊D5C22×D3semidirect
415. C2×D20C22×D3semidirect
417. C2×C4×D5C22×D3semidirect
422. C5×C22⋊C4C22×D3semidirect
429. #685C22×D3semidirect
431. #683C22×D3semidirect
534. C2×#67C22×D5semidirect
548. C2×D12C22×D5semidirect
557. C3×C22⋊C4C22×D5semidirect
565. (C2×D3)⋊C4C22×D5semidirect
690. C2×C22⋊C4D3×D5semidirect
694. C2×C3×C5#535semidirect
892. C22⋊C4C2×D3×D5semidirect
895. C3×C5C2×#535semidirect
942. C2×C5#5607semidirect
1024. C2×C3#65926semidirect
1032. C5C2×#5607semidirect
1075. C3C2×#65926semidirect
1083. C2#11753246direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊D52
C22×#67722
C2×#917742
C2×C5×#8822
C2×C3×#40302
C2×#915682
C2×#915672
C2×#915652
C2×#914752
C2×#914742
C2×#914632
C2×#914622
C2×#914482
C2×#914162
C2×#914002
#117532462
C2×#659263
C2×#56075