Finite Group Databasebeta

← C2×#11753251 #14480429

Subgroups — C2×#11753251 #14480429

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×#6790C211yesmaximal, characteristic, complemented
2C22×#6773C211yesmaximal, characteristic, complemented
3C2×#91771C211yesmaximal, characteristic, complemented
4C2×C5×#885C211yesmaximal, characteristic, complemented
5C2×C3×#4030C211yesmaximal, characteristic, complemented
6C2×#91572C211yesmaximal, characteristic, complemented
7C2×#91567C211yesmaximal, characteristic, complemented
8C2×#91533C211yesmaximal, characteristic, complemented
9C2×#91476C211yesmaximal, characteristic, complemented
10C2×#91474C211yesmaximal, characteristic, complemented
11C2×#91458C211yesmaximal, characteristic, complemented
12C2×#91455C211yesmaximal, characteristic, complemented
13C2×#91448C211yesmaximal, characteristic, complemented
14C2×#91420C211yesmaximal, characteristic, complemented
15C2×#91403C211yesmaximal, characteristic, complemented
16#11753251C2116yesmaximal, direct product factor
17C2×#66008—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic, complemented
21C22×D60C2211yescharacteristic
22C22×D60C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic
24C22×C5×Dic6C2211yescharacteristic, complemented
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×C22⋊D5C2211yescharacteristic, complemented
27C22×C3×D20C2211yescharacteristic, complemented
28C22×C3×C4×D5C2211yescharacteristic, complemented
29C2×#6790—28no—
30C2×#6790C2218yescomplemented
31C22×#1203C2211yescharacteristic
32C22×#1203C2211yescharacteristic, complemented
33C22×#1202C2211yescharacteristic
34C22×#1202C2211yescharacteristic
35C22×#1202C2211yescharacteristic, complemented
36C22×#1202C2211yescharacteristic, complemented
37C22×#1202C2211yescharacteristic, complemented
38C22×#1201C2211yescharacteristic, complemented
39C22×#1200C2211yescharacteristic
40C22×#1200C2211yescharacteristic, complemented
41C2×#6773—28no—
42C2×#6773C2218yescomplemented
43C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
44C2×#6714C2211yescharacteristic
45C2×#6714C2211yescharacteristic, complemented
46#91771C2218yescomplemented
47C2×C5×#217C2211yescharacteristic, complemented
48C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C4×C5×Dic3C2211yescharacteristic, complemented
51C5×#885C2218yescomplemented
52C2×C3×#685C2211yescharacteristic, complemented
53C2×C3×#683C2211yescharacteristic, complemented
54C3×#4030C2218yescomplemented
55#91572C2218yescomplemented
56#91567C2218yescomplemented
57C2×#6668C2211yescharacteristic, complemented
58C2×#6667C2211yescharacteristic
59C2×#6667C2211yescharacteristic, complemented
60C2×#6665C2211yescharacteristic, complemented
61#91533C2218yescomplemented
62C2×Dic3×Dic5C2211yescharacteristic, complemented
63#91476C2218yescomplemented
64#91474C2218yescomplemented
65#91458C2218yescomplemented
66#91455C2218yescomplemented
67#91448C2218yescomplemented
68#91420C2218yescomplemented
69#91403C2218yescomplemented
70C2×#5607—51nomaximal, Hall
71C22×#713—31no—
72C22×D4×D5—31no—
73C2×C5×#124—31no—
74C2×#4093—31no—
75C2×#4086—31no—
76#66008—316no—
77C2×#4030—31no—
78C2×#4030—31no—
79C2×#4030—31no—
80C2×#4030D311yescharacteristic, complemented
81C2×#4028—31no—
82C2×#4028—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C2×#4020—31no—
86C2×#4018—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15—24no—
89C23×D15—42no—
90C23×D15—42no—
91C23×D15C2311yescharacteristic
92C23×D15C2311yescharacteristic
93C23×D15C2311yescharacteristic
94C23×D15C2314yes—
95C23×C5×D3C2311yescharacteristic
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—42no—
105C2×#1220C2314yescomplemented
106C22×Dic15C2311yescharacteristic
107C2×D60—24no—
108C2×D60—42no—
109C2×D60C2314yes—
110C2×D60C2314yescomplemented
111C2×C5×#67—24no—
112C2×C5×#67C2314yes—
113C22×C5×Dic3C2311yescharacteristic
114C22×C5×Dic3C2311yescharacteristic
115C22×C5×Dic3C2311yescharacteristic
116C2×C5×Dic6—24no—
117C2×C5×Dic6C2314yescomplemented
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
128#6790—232no—
129C2×#1203—24no—
130C2×#1203—42no—
131C2×#1203C2314yes—
132C2×#1203C2314yescomplemented
133C2×#1202—24no—
134C2×#1202—24no—
135C2×#1202—24no—
136C2×#1202—42no—
137C2×#1202—42no—
138C2×#1202C2314yes—
139C2×#1202C2314yes—
140C2×#1202C2314yescomplemented
141C2×#1202C2314yescomplemented
142C2×#1202C2314yescomplemented
143C2×#1201—42no—
144C2×#1201C2314yescomplemented
145C2×#1200—24no—
146C2×#1200D418yescomplemented
147C2×#1200C2314yes—
148C2×#1200C2314yescomplemented
149#6773—232no—
150C3×C5×C22⋊C4C2314yescomplemented
151#6714C2314yes—
152#6714C2314yescomplemented
153C5×#217C2314yescomplemented
154C5×(C2×D3)⋊C4C2314yescomplemented
155C5×(C2×D3)⋊C4C2314yescomplemented
156C4×C5×Dic3C2314yescomplemented
157C3×#685C2314yescomplemented
158C3×#683C2314yescomplemented
159#6668C2314yescomplemented
160#6667C2314yes—
161#6667C2314yescomplemented
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×#885D511yescharacteristic, complemented
178C2×#882—51no—
179C2×#882—51no—
180C24×D5—31no—
181C24×D5—31no—
182C22×C5×Q8—31no—
183C22×C5×D4—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5C2×D311yescharacteristic
189C22×C22⋊D5C2×D311yescharacteristic, complemented
190C2×#713—38no—
191C2×#713—68no—
192C2×D4×D5—38no—
193C2×D4×D5—68no—
194C22×D20—31no—
195C22×D20—31no—
196C22×D20—31no—
197C22×D20—31no—
198C22×D20—31no—
199C22×D20—31no—
200C22×D20—31no—
201C22×D20C2×D311yescharacteristic, complemented
202C22×C4×D5—31no—
203C22×C4×D5—31no—
204C22×C4×D5C2×D311yescharacteristic, complemented
205C5×#124—38no—
206C2×C5×C22⋊C4—31no—
207C2×C5×C22⋊C4—31no—
208C2×C5×C22⋊C4—31no—
209C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
210C2×C42×C5—31no—
211#4093—38no—
212#4086—38no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685—31no—
218C2×#685C2×D311yescharacteristic, complemented
219C2×#683—31no—
220C2×#683C2×D311yescharacteristic, complemented
221C2×C4×Dic5—31no—
222#4030—38no—
223#4030—38no—
224#4030—38no—
225#4030C2×D318yescomplemented
226#4028—38no—
227#4028—38no—
228#4028—38no—
229#4028—38no—
230#4020—38no—
231#4018—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×D15—22no—
242C22×D15—22no—
243C22×D15—22no—
244C22×D15—22no—
245C22×D15—22no—
246C22×D15—28no—
247C22×D15—44no—
248C22×D15—44no—
249C22×D15—416no—
250C22×D15C2×D414yes—
251C22×D15C2412yes—
252C22×D15C2412yes—
253C22×D15C2412yes—
254C22×C5×D3—22no—
255C22×C5×D3—22no—
256C22×C5×D3—22no—
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—44no—
275C2×Dic15—22no—
276C2×Dic15C2412yes—
277D60—28no—
278D60—44no—
279C5×#67—28no—
280C2×C5×Dic3—22no—
281C2×C5×Dic3—22no—
282C2×C5×Dic3C2×D414yes—
283C2×C5×Dic3C2412yes—
284C2×C5×Dic3C2412yes—
285C2×C5×Dic3C2412yes—
286C5×Dic6—28no—
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—28no—
298#1202—28no—
299#1202—28no—
300#1202—44no—
301#1202—44no—
302#1201—44no—
303#1200—28no—
304#1200C2×D4116yescomplemented
305C24×D3—51no—
306C24×D3—51no—
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
319C2×D3×D4—58no—
320C2×D3×D4—108no—
321C2×#235—58no—
322C2×#235—108no—
323C22×D12—51no—
324C22×D12—51no—
325C22×D12—51no—
326C22×D12—51no—
327C22×C4×D3—51no—
328C22×C4×D3—51no—
329C22×Dic6C2×D511yescharacteristic, complemented
330C3×#121—58no—
331C2×C3×C4⋊C4—51no—
332C2×C3×C22⋊C4—51no—
333C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
334C2×#217—51no—
335C2×#217C2×D511yescharacteristic, complemented
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, complemented
347C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
348C2×C4⋊Dic3—51no—
349C2×C4×Dic3—51no—
350C2×C4×Dic3C2×D511yescharacteristic, complemented
351#895—58no—
352#892—58no—
353#885—58no—
354#885C2×D518yescomplemented
355#882—58no—
356#882—58no—
357C24×C5—31no—
358C24×C5C22×D311yescharacteristic
359C23×D5—31no—
360C23×D5—31no—
361C23×D5—31no—
362C23×D5—34no—
363C23×D5—34no—
364C23×D5—64no—
365C23×D5—64no—
366C23×D5—122no—
367C23×D5—122no—
368C23×D5—122no—
369C23×D5—122no—
370C23×D5C22×D311yescharacteristic
371C23×D5C22×D311yescharacteristic
372C2×C5×Q8—34no—
373C2×C5×Q8—64no—
374C2×C5×D4—34no—
375C2×C5×D4—64no—
376C22×C4×C5—31no—
377C22×C4×C5—31no—
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—42no—
387C2×C22⋊D5—64no—
388C2×C22⋊D5—122no—
389C2×C22⋊D5—122no—
390C2×C22⋊D5—122no—
391C2×C22⋊D5C22×D314yes—
392C2×C22⋊D5C22×D314yescomplemented
393C22×Dic5—31no—
394C22×Dic5C22×D311yescharacteristic
395C22×Dic5C22×D311yescharacteristic
396#713—632no—
397D4×D5—632no—
398C2×D20—34no—
399C2×D20—34no—
400C2×D20—34no—
401C2×D20—34no—
402C2×D20—34no—
403C2×D20—34no—
404C2×D20—34no—
405C2×D20—42no—
406C2×D20—64no—
407C2×D20—64no—
408C2×D20—64no—
409C2×D20—64no—
410C2×D20—122no—
411C2×D20—122no—
412C2×D20—122no—
413C2×D20C22×D314yescomplemented
414C2×C4×D5—24no—
415C2×C4×D5—38no—
416C2×C4×D5—34no—
417C2×C4×D5—34no—
418C2×C4×D5—64no—
419C2×C4×D5C22×D314yescomplemented
420C5×C22⋊C4—34no—
421C5×C22⋊C4—34no—
422C5×C22⋊C4—34no—
423C5×C22⋊C4C22×D314yescomplemented
424C42×C5—34no—
425#685—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685—34no—
430#685C22×D314yescomplemented
431#683—34no—
432#683C22×D314yescomplemented
433C4×Dic5—34no—
434C22×#41—151no—
435C23×D4—151no—
436#535—1516no—
437C2×#127—151no—
438C2×#127—151no—
439C2×#124—31no—
440C2×#124—151no—
441C2×#121—51no—
442C2×#121—151no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#120—151no—
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—28no—
459C2×D15—22no—
460C2×D15—22no—
461C2×D15—22no—
462C2×D15—22no—
463C2×D15—22no—
464C2×D15—22no—
465C2×D15—22no—
466C2×D15—22no—
467C2×D15—416no—
468C2×D15—44no—
469C2×D15—44no—
470C2×D15C22×D414yes—
471C2×C5×D3—22no—
472C2×C5×D3—22no—
473C2×C5×D3—22no—
474C2×C5×D3—44no—
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—
487C3×Dic5—22no—
488C3×Dic5C22×D414yes—
489C5×Dic3—22no—
490C5×Dic3—22no—
491C5×Dic3C22×D414yes—
492C24×C3—51no—
493C24×C3—51no—
494C24×C3C22×D511yescharacteristic
495C23×D3—51no—
496C23×D3—51no—
497C23×D3—51no—
498C23×D3—54no—
499C23×D3—54no—
500C23×D3—104no—
501C23×D3—104no—
502C23×D3—202no—
503C23×D3—202no—
504C23×D3—202no—
505C23×D3—202no—
506C23×D3C22×D511yescharacteristic
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—24no—
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—202no—
531C2×#67—202no—
532C2×#67—202no—
533C2×#67—202no—
534C2×#67C22×D514yes—
535C22×Dic3—51no—
536C22×Dic3C22×D511yescharacteristic
537C22×Dic3C22×D511yescharacteristic
538C22×Dic3C22×D511yescharacteristic
539D3×D4—1032no—
540#235—1032no—
541C2×D12—54no—
542C2×D12—54no—
543C2×D12—54no—
544C2×D12—54no—
545C2×D12—104no—
546C2×D12—104no—
547C2×D12—202no—
548C2×D12—202no—
549C2×C4×D3—58no—
550C2×C4×D3—54no—
551C2×C4×D3—54no—
552C2×C4×D3—104no—
553C2×Dic6—24no—
554C2×Dic6C22×D514yescomplemented
555C3×C4⋊C4—54no—
556C3×C22⋊C4—54no—
557C3×C22⋊C4C22×D514yescomplemented
558#217—54no—
559#217C22×D514yescomplemented
560(C2×D3)⋊C4—54no—
561(C2×D3)⋊C4—54no—
562(C2×D3)⋊C4—54no—
563(C2×D3)⋊C4—54no—
564(C2×D3)⋊C4C22×D514yescomplemented
565(C2×D3)⋊C4C22×D514yescomplemented
566C4⋊Dic3—54no—
567C4×Dic3—54no—
568C4×Dic3C22×D514yescomplemented
569C23×C5—22no—
570C23×C5—22no—
571C23×C5—22no—
572C23×C5—32no—
573C23×C5—62no—
574C23×C5—62no—
575C23×C5—62no—
576C23×C5C23×D312yes—
577C23×C5C23×D311yescharacteristic
578C22×D5—22no—
579C22×D5—22no—
580C22×D5—22no—
581C22×D5—22no—
582C22×D5—22no—
583C22×D5—22no—
584C22×D5—34no—
585C22×D5—32no—
586C22×D5—32no—
587C22×D5—32no—
588C22×D5—68no—
589C22×D5—68no—
590C22×D5—62no—
591C22×D5—62no—
592C22×D5—62no—
593C22×D5—62no—
594C22×D5—62no—
595C22×D5—62no—
596C22×D5—62no—
597C22×D5—62no—
598C22×D5—124no—
599C22×D5—124no—
600C22×D5—1216no—
601C22×D5—124no—
602C22×D5—124no—
603C22×D5—1216no—
604C22×D5C23×D312yes—
605C22×D5C23×D312yes—
606C5×Q8—68no—
607C5×D4—68no—
608C2×C4×C5—22no—
609C2×C4×C5—22no—
610C2×C4×C5—34no—
611C2×C4×C5—32no—
612C2×C4×C5—32no—
613C2×C4×C5—32no—
614C2×C4×C5—62no—
615C2×C4×C5—62no—
616C2×C4×C5C23×D312yes—
617C2×C4×C5C23×D312yes—
618C22⋊D5—28no—
619C22⋊D5—44no—
620C22⋊D5—68no—
621C22⋊D5—124no—
622C22⋊D5—124no—
623C22⋊D5—124no—
624C2×Dic5—22no—
625C2×Dic5—32no—
626C2×Dic5—62no—
627C2×Dic5D3×D414yes—
628C2×Dic5C23×D312yes—
629C2×Dic5C23×D312yes—
630D20—44no—
631D20—68no—
632D20—68no—
633D20—68no—
634D20—68no—
635D20—124no—
636D20—124no—
637D20—124no—
638C4×D5—28no—
639C4×D5—316no—
640C4×D5—68no—
641C25—151no—
642C25—151no—
643C2×#41—158no—
644C2×#41—308no—
645C22×Q8—31no—
646C22×D4—31no—
647C22×D4—51no—
648C22×D4—51no—
649C22×D4—51no—
650C22×D4—151no—
651C22×D4—151no—
652C22×D4—151no—
653C22×D4—151no—
654C22×D4—151no—
655C22×D4—151no—
656C22×D4—151no—
657C22×D4—158no—
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—38no—
669#124—158no—
670#121—58no—
671#121—158no—
672#121—158no—
673#121—158no—
674#120—158no—
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—31no—
684C2×C22⋊C4—51no—
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—31no—
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—24no—
699D15—42no—
700D15—42no—
701C3×D5—42no—
702C3×D5—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—54no—
721C22×D3—52no—
722C22×D3—52no—
723C22×D3—52no—
724C22×D3—108no—
725C22×D3—108no—
726C22×D3—102no—
727C22×D3—102no—
728C22×D3—102no—
729C22×D3—102no—
730C22×D3—102no—
731C22×D3—102no—
732C22×D3—102no—
733C22×D3—102no—
734C22×D3—204no—
735C22×D3—204no—
736C22×D3—2016no—
737C22×D3—204no—
738C22×D3—204no—
739C22×D3—2016no—
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—28no—
754#67—108no—
755#67—108no—
756#67—108no—
757#67—204no—
758#67—204no—
759#67—204no—
760#67—204no—
761C2×Dic3—22no—
762C2×Dic3—22no—
763C2×Dic3—52no—
764C2×Dic3—102no—
765C2×Dic3D4×D514yes—
766C2×Dic3C23×D512yes—
767C2×Dic3C23×D512yes—
768C2×Dic3C23×D512yes—
769D12—108no—
770D12—108no—
771D12—204no—
772D12—204no—
773C4×D3—516no—
774C4×D3—108no—
775Dic6—28no—
776C22×C5—22no—
777C22×C5—22no—
778C22×C5—22no—
779C22×C5—44no—
780C22×C5—62no—
781C22×C5—62no—
782C22×C5—62no—
783C22×C5—124no—
784C22×C5C2×D3×D412yes—
785C22×C5#100412yes—
786C22×C5#100912yes—
787C22×C5C24×D311yescharacteristic
788C2×D5—22no—
789C2×D5—22no—
790C2×D5—22no—
791C2×D5—22no—
792C2×D5—22no—
793C2×D5—22no—
794C2×D5—34no—
795C2×D5—44no—
796C2×D5—44no—
797C2×D5—62no—
798C2×D5—62no—
799C2×D5—68no—
800C2×D5—62no—
801C2×D5—62no—
802C2×D5—62no—
803C2×D5—62no—
804C2×D5—62no—
805C2×D5—62no—
806C2×D5—1216no—
807C2×D5—1216no—
808C2×D5—124no—
809C2×D5—124no—
810C4×C5—22no—
811C4×C5—22no—
812C4×C5—34no—
813C4×C5—62no—
814C4×C5—62no—
815Dic5—22no—
816Dic5—62no—
817Dic5C2×D3×D414yes—
818C24—31no—
819C24—51no—
820C24—51no—
821C24—154no—
822C24—151no—
823C24—151no—
824C24—151no—
825C24—154no—
826C24—304no—
827C24—304no—
828C24—602no—
829C24—602no—
830C24—602no—
831C24—602no—
832C24C2×D3×D511yescharacteristic
833#41—3032no—
834C2×Q8—34no—
835C2×Q8—64no—
836C2×D4—34no—
837C2×D4—54no—
838C2×D4—54no—
839C2×D4—54no—
840C2×D4—64no—
841C2×D4—104no—
842C2×D4—154no—
843C2×D4—154no—
844C2×D4—154no—
845C2×D4—154no—
846C2×D4—154no—
847C2×D4—154no—
848C2×D4—154no—
849C2×D4—154no—
850C2×D4—154no—
851C2×D4—154no—
852C2×D4—154no—
853C2×D4—202no—
854C2×D4—202no—
855C2×D4—304no—
856C2×D4—304no—
857C2×D4—304no—
858C2×D4—304no—
859C2×D4—304no—
860C2×D4—3032no—
861C2×D4—602no—
862C2×D4—602no—
863C2×D4—602no—
864C2×D4—602no—
865C2×D4—602no—
866C2×D4—602no—
867C22×C4—31no—
868C22×C4—31no—
869C22×C4—31no—
870C22×C4—51no—
871C22×C4—51no—
872C22×C4—54no—
873C22×C4—104no—
874C22×C4—154no—
875C22×C4—158no—
876C22×C4—154no—
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—34no—
886C22⋊C4—54no—
887C22⋊C4—154no—
888C22⋊C4—154no—
889C22⋊C4—154no—
890C22⋊C4—154no—
891C22⋊C4—154no—
892C22⋊C4C2×D3×D514yescomplemented
893C42—34no—
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#414912yes—
910C22×C3#414912yes—
911C22×C3C24×D511yescharacteristic
912C2×D3—22no—
913C2×D3—22no—
914C2×D3—22no—
915C2×D3—44no—
916C2×D3—54no—
917C2×D3—108no—
918C2×D3—102no—
919C2×D3—102no—
920C2×D3—102no—
921C2×D3—102no—
922C2×D3—102no—
923C2×D3—102no—
924C2×D3—102no—
925C2×D3—102no—
926C2×D3—2016no—
927C2×D3—2016no—
928C2×D3—204no—
929C2×D3—204no—
930C3×C4—22no—
931C3×C4—22no—
932C3×C4—54no—
933C3×C4—102no—
934Dic3—22no—
935Dic3—22no—
936Dic3—102no—
937Dic3C2×D4×D514yes—
938C2×C5—42no—
939C2×C5—122no—
940C2×C5#560714yescomplemented
941C2×C5C22×D3×D411yescharacteristic
942C2×C5C2×#100411yescharacteristic
943C2×C5C2×#100911yescharacteristic
944D5—42no—
945D5—42no—
946D5—64no—
947D5—122no—
948D5—122no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—32no—
953C23—52no—
954C23—52no—
955C23—62no—
956C23—62no—
957C23—62no—
958C23—102no—
959C23—102no—
960C23—102no—
961C23—102no—
962C23—102no—
963C23—102no—
964C23—154no—
965C23—152no—
966C23—152no—
967C23—152no—
968C23—308no—
969C23—308no—
970C23—302no—
971C23—302no—
972C23—302no—
973C23—302no—
974C23—302no—
975C23—302no—
976C23—302no—
977C23—302no—
978C23—604no—
979C23—604no—
980C23—6016no—
981C23—604no—
982C23—604no—
983C23—6016no—
984C23C22×D3×D512yes—
985C23C22×D3×D511yescharacteristic
986Q8—68no—
987D4—68no—
988D4—108no—
989D4—204no—
990D4—204no—
991D4—308no—
992D4—308no—
993D4—308no—
994D4—308no—
995D4—308no—
996D4—604no—
997D4—604no—
998D4—604no—
999D4—604no—
1000D4—604no—
1001D4—604no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—34no—
1005C2×C4—32no—
1006C2×C4—32no—
1007C2×C4—32no—
1008C2×C4—54no—
1009C2×C4—52no—
1010C2×C4—52no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—108no—
1014C2×C4—102no—
1015C2×C4—1516no—
1016C2×C4—152no—
1017C2×C4—308no—
1018C2×C4—302no—
1019C2×C4C22×D3×D512yes—
1020C2×C4C22×D3×D512yes—
1021C2×C3—42no—
1022C2×C3—202no—
1023C2×C3—202no—
1024C2×C3#6600814yescomplemented
1025C2×C3C22×D4×D511yescharacteristic
1026C2×C3C2×#414911yescharacteristic
1027C2×C3C2×#414911yescharacteristic
1028D3—42no—
1029D3—104no—
1030D3—202no—
1031D3—202no—
1032C5C2×#560711yescharacteristic, complemented, Sylow
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—44no—
1037C22—62no—
1038C22—62no—
1039C22—62no—
1040C22—102no—
1041C22—102no—
1042C22—102no—
1043C22—102no—
1044C22—102no—
1045C22—102no—
1046C22—124no—
1047C22—154no—
1048C22—204no—
1049C22—204no—
1050C22—308no—
1051C22—302no—
1052C22—302no—
1053C22—302no—
1054C22—302no—
1055C22—302no—
1056C22—302no—
1057C22—302no—
1058C22—302no—
1059C22—6016no—
1060C22—6016no—
1061C22—604no—
1062C22—604no—
1063C22#9201912yes—
1064C22D3×D4×D512yes—
1065C22#9202612yes—
1066C22C23×D3×D511yescharacteristic
1067C4—22no—
1068C4—22no—
1069C4—34no—
1070C4—54no—
1071C4—62no—
1072C4—62no—
1073C4—102no—
1074C4—302no—
1075C3C2×#6600811yescharacteristic, complemented, Sylow
1076C2—42no—
1077C2—122no—
1078C2—202no—
1079C2—202no—
1080C2—304no—
1081C2—602no—
1082C2—602no—
1083C2#1175325114yesdirect product factor
1084C2C2×#9201911yescharacteristic
1085C2C2×D3×D4×D511yescharacteristic
1086C2C2×#9202611yescharacteristic
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×#6790C2semidirect
2. C22×#6773C2semidirect
3. C2×#91771C2semidirect
4. C2×C5×#885C2semidirect
5. C2×C3×#4030C2semidirect
6. C2×#91572C2semidirect
7. C2×#91567C2semidirect
8. C2×#91533C2semidirect
9. C2×#91476C2semidirect
10. C2×#91474C2semidirect
11. C2×#91458C2semidirect
12. C2×#91455C2semidirect
13. C2×#91448C2semidirect
14. C2×#91420C2semidirect
15. C2×#91403C2semidirect
16. #11753251C2direct (N × H)
20. C22×#1220C22semidirect
22. C22×D60C22semidirect
24. C22×C5×Dic6C22semidirect
26. C22×C3×C22⋊D5C22semidirect
27. C22×C3×D20C22semidirect
28. C22×C3×C4×D5C22semidirect
30. C2×#6790C22semidirect
32. C22×#1203C22semidirect
35. C22×#1202C22semidirect
36. C22×#1202C22semidirect
37. C22×#1202C22semidirect
38. C22×#1201C22semidirect
40. C22×#1200C22semidirect
42. C2×#6773C22semidirect
43. C2×C3×C5×C22⋊C4C22semidirect
45. C2×#6714C22semidirect
46. #91771C22semidirect
47. C2×C5×#217C22semidirect
48. C2×C5×(C2×D3)⋊C4C22semidirect
49. C2×C5×(C2×D3)⋊C4C22semidirect
50. C2×C4×C5×Dic3C22semidirect
51. C5×#885C22semidirect
52. C2×C3×#685C22semidirect
53. C2×C3×#683C22semidirect
54. C3×#4030C22semidirect
55. #91572C22semidirect
56. #91567C22semidirect
57. C2×#6668C22semidirect
59. C2×#6667C22semidirect
60. C2×#6665C22semidirect
61. #91533C22semidirect
62. C2×Dic3×Dic5C22semidirect
63. #91476C22semidirect
64. #91474C22semidirect
65. #91458C22semidirect
66. #91455C22semidirect
67. #91448C22semidirect
68. #91420C22semidirect
69. #91403C22semidirect
80. C2×#4030D3semidirect
105. C2×#1220C23semidirect
110. C2×D60C23semidirect
117. C2×C5×Dic6C23semidirect
121. C2×C3×C22⋊D5C23semidirect
125. C2×C3×D20C23semidirect
127. C2×C3×C4×D5C23semidirect
132. C2×#1203C23semidirect
140. C2×#1202C23semidirect
141. C2×#1202C23semidirect
142. C2×#1202C23semidirect
144. C2×#1201C23semidirect
146. C2×#1200D4semidirect
148. C2×#1200C23semidirect
150. C3×C5×C22⋊C4C23semidirect
152. #6714C23semidirect
153. C5×#217C23semidirect
154. C5×(C2×D3)⋊C4C23semidirect
155. C5×(C2×D3)⋊C4C23semidirect
156. C4×C5×Dic3C23semidirect
157. C3×#685C23semidirect
158. C3×#683C23semidirect
159. #6668C23semidirect
161. #6667C23semidirect
162. #6665C23semidirect
163. Dic3×Dic5C23semidirect
177. C2×#885D5semidirect
189. C22×C22⋊D5C2×D3semidirect
201. C22×D20C2×D3semidirect
204. C22×C4×D5C2×D3semidirect
209. C2×C5×C22⋊C4C2×D3semidirect
218. C2×#685C2×D3semidirect
220. C2×#683C2×D3semidirect
225. #4030C2×D3semidirect
304. #1200C2×D4semidirect
329. C22×Dic6C2×D5semidirect
333. C2×C3×C22⋊C4C2×D5semidirect
335. C2×#217C2×D5semidirect
346. C2×(C2×D3)⋊C4C2×D5semidirect
347. C2×(C2×D3)⋊C4C2×D5semidirect
350. C2×C4×Dic3C2×D5semidirect
354. #885C2×D5semidirect
392. C2×C22⋊D5C22×D3semidirect
413. C2×D20C22×D3semidirect
419. C2×C4×D5C22×D3semidirect
423. C5×C22⋊C4C22×D3semidirect
430. #685C22×D3semidirect
432. #683C22×D3semidirect
554. C2×Dic6C22×D5semidirect
557. C3×C22⋊C4C22×D5semidirect
559. #217C22×D5semidirect
564. (C2×D3)⋊C4C22×D5semidirect
565. (C2×D3)⋊C4C22×D5semidirect
568. C4×Dic3C22×D5semidirect
690. C2×C22⋊C4D3×D5semidirect
694. C2×C3×C5#535semidirect
892. C22⋊C4C2×D3×D5semidirect
895. C3×C5C2×#535semidirect
940. C2×C5#5607semidirect
1024. C2×C3#66008semidirect
1032. C5C2×#5607semidirect
1075. C3C2×#66008semidirect
1083. C2#11753251direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67902
C22×#67732
C2×#917712
C2×C5×#8852
C2×C3×#40302
C2×#915722
C2×#915672
C2×#915332
C2×#914762
C2×#914742
C2×#914582
C2×#914552
C2×#914482
C2×#914202
C2×#914032
#117532512
C2×#660083
C2×#56075