Finite Group Databasebeta

← C2×#11753303 #14495265

Subgroups — C2×#11753303 #14495265

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91771C211yesmaximal, characteristic, complemented
2C2×C5×#885C211yesmaximal, characteristic, complemented
3C2×C3×#4031C211yesmaximal, characteristic, complemented
4C2×#91577C211yesmaximal, characteristic, complemented
5C2×#91573C211yesmaximal, characteristic, complemented
6C2×#91572C211yesmaximal, characteristic, complemented
7C2×#91526C211yesmaximal, characteristic, complemented
8C2×#91476C211yesmaximal, characteristic, complemented
9C2×#91476C211yesmaximal, characteristic, complemented
10C2×#91455C211yesmaximal, characteristic, complemented
11C2×#91375C211yesmaximal, characteristic, complemented
12C2×#91374C211yesmaximal, characteristic, complemented
13C2×#91353C211yesmaximal, characteristic, complemented
14C2×#91350C211yesmaximal, characteristic, complemented
15C2×#91326C211yesmaximal, characteristic, complemented
16#11753303C2116yesmaximal, direct product factor
17C2×#66017—31nomaximal, Hall
18C24×D15C2211yescharacteristic, complemented
19C23×D3×D5C2211yescharacteristic, complemented
20C22×#1220C2211yescharacteristic
21C22×D60C2211yescharacteristic
22C22×D60C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic
24C22×C5×Dic6C2211yescharacteristic, complemented
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×Dic10C2211yescharacteristic, complemented
27C22×#1204C2211yescharacteristic, complemented
28C22×#1203C2211yescharacteristic
29C22×#1203C2211yescharacteristic
30C22×#1202C2211yescharacteristic
31C22×#1202C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
33C2×#6714C2211yescharacteristic, complemented
34C2×#6714C2211yescharacteristic, complemented
35#91771C2218yescomplemented
36C2×C5×#217C2211yescharacteristic, complemented
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C2×C4×C5×Dic3C2211yescharacteristic, complemented
40C5×#885C2218yescomplemented
41C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
42C2×C3×#685C2211yescharacteristic, complemented
43C2×C3×#685C2211yescharacteristic, complemented
44C2×C3×C4×Dic5C2211yescharacteristic, complemented
45C3×#4031C2218yescomplemented
46#91577C2218yescomplemented
47#91573C2218yescomplemented
48#91572C2218yescomplemented
49C2×#6667C2211yescharacteristic, complemented
50C2×#6667C2211yescharacteristic, complemented
51C2×#6667C2211yescharacteristic, complemented
52C2×#6667C2211yescharacteristic, complemented
53C2×#6667C2211yescharacteristic, complemented
54C2×#6667C2211yescharacteristic, complemented
55C2×#6667C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
57C2×#6665C2211yescharacteristic, complemented
58C2×Dic3×Dic5C2211yescharacteristic, complemented
59#91526C2218yescomplemented
60#91476C2218yescomplemented
61#91476C2218yescomplemented
62#91455C2218yescomplemented
63#91375C2218yescomplemented
64#91374C2218yescomplemented
65#91353C2218yescomplemented
66#91350C2218yescomplemented
67#91326C2218yescomplemented
68C2×#5683—51nomaximal, Hall
69C2×C5×#124—31no—
70C2×#4093—31no—
71C2×#4093—31no—
72C2×#4083—31no—
73C2×#4083—31no—
74#66017—316no—
75C2×#4031—31no—
76C2×#4031—31no—
77C2×#4031—31no—
78C2×#4031D311yescharacteristic, complemented
79C2×#4028—31no—
80C2×#4028—31no—
81C2×#4028—31no—
82C2×#4028—31no—
83C2×#4021—31no—
84C2×#4021—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15—42no—
87C23×D15—42no—
88C23×D15—42no—
89C23×D15C2311yescharacteristic
90C23×D15C2311yescharacteristic
91C23×D15C2311yescharacteristic
92C23×D15C2314yescomplemented
93C23×C5×D3C2311yescharacteristic
94C23×C3×D5C2311yescharacteristic
95C22×D3×D5—42no—
96C22×D3×D5—42no—
97C22×D3×D5—42no—
98C22×D3×D5C2314yescomplemented
99C22×C3×C4×C5C2311yescharacteristic
100C22×C3×C4×C5C2311yescharacteristic
101C2×#1220—42no—
102C2×#1220C2314yes—
103C22×Dic15C2311yescharacteristic
104C2×D60—42no—
105C2×D60—42no—
106C2×D60C2314yes—
107C2×D60C2314yes—
108C2×C5×#67—42no—
109C2×C5×#67C2314yes—
110C22×C5×Dic3C2311yescharacteristic
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C2×C5×Dic6—42no—
114C2×C5×Dic6C2314yescomplemented
115C2×C3×C22⋊D5—42no—
116C2×C3×C22⋊D5C2314yes—
117C22×C3×Dic5C2311yescharacteristic
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2311yescharacteristic
120C2×C3×Dic10—42no—
121C2×C3×Dic10C2314yescomplemented
122C2×#1204—42no—
123C2×#1204C2314yescomplemented
124C2×#1203—42no—
125C2×#1203—42no—
126C2×#1203C2314yes—
127C2×#1203C2314yes—
128C2×#1202—42no—
129C2×#1202—42no—
130C2×#1202C2314yes—
131C2×#1202C2314yes—
132C3×C5×C22⋊C4C2314yescomplemented
133#6714C2314yescomplemented
134#6714C2314yescomplemented
135C5×#217C2314yescomplemented
136C5×(C2×D3)⋊C4C2314yescomplemented
137C5×(C2×D3)⋊C4C2314yescomplemented
138C4×C5×Dic3C2314yescomplemented
139C3×C22⋊Dic5C2314yescomplemented
140C3×#685C2314yescomplemented
141C3×#685C2314yescomplemented
142C3×C4×Dic5C2314yescomplemented
143#6667C2314yescomplemented
144#6667C2314yescomplemented
145#6667C2314yescomplemented
146#6667C2314yescomplemented
147#6667C2314yescomplemented
148#6667C2314yescomplemented
149#6667C2314yescomplemented
150(C2×D3)⋊Dic5C2314yescomplemented
151#6665C2314yescomplemented
152Dic3×Dic5C2314yescomplemented
153C2×C3×#124—51no—
154C2×#947—51no—
155C2×#947—51no—
156C2×#937—51no—
157C2×#937—51no—
158#5683—516no—
159C2×#885—51no—
160C2×#885—51no—
161C2×#885—51no—
162C2×#885D511yescharacteristic, complemented
163C2×#882—51no—
164C2×#882—51no—
165C2×#882—51no—
166C2×#882—51no—
167C2×#875—51no—
168C2×#875—51no—
169C24×D5—31no—
170C24×D5—31no—
171C22×C5×Q8—31no—
172C22×C5×D4—31no—
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5C2×D311yescharacteristic
177C22×D20—31no—
178C22×D20—31no—
179C22×D20—31no—
180C22×D20—31no—
181C22×Dic10—31no—
182C22×Dic10C2×D311yescharacteristic, complemented
183C5×#124—38no—
184C2×C5×C22⋊C4—31no—
185C2×C5×C22⋊C4—31no—
186C2×C5×C22⋊C4—31no—
187C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
188C2×C42×C5—31no—
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5C2×D311yescharacteristic, complemented
191#4093—38no—
192#4093—38no—
193#4083—38no—
194#4083—38no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×#685—31no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×#685—31no—
204C2×#685—31no—
205C2×#685C2×D311yescharacteristic, complemented
206C2×#685C2×D311yescharacteristic, complemented
207C2×C4×Dic5—31no—
208C2×C4×Dic5C2×D311yescharacteristic, complemented
209#4031—38no—
210#4031—38no—
211#4031—38no—
212#4031C2×D318yescomplemented
213#4028—38no—
214#4028—38no—
215#4028—38no—
216#4028—38no—
217#4021—38no—
218#4021—38no—
219C2×H(3,𝔽4)—151noSylow
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5C2412yes—
224C23×C3×C5C2411yescharacteristic
225C22×D15—22no—
226C22×D15—22no—
227C22×D15—22no—
228C22×D15—22no—
229C22×D15—22no—
230C22×D15—22no—
231C22×D15—22no—
232C22×D15—22no—
233C22×D15—22no—
234C22×D15—44no—
235C22×D15—44no—
236C22×D15—44no—
237C22×D15—416no—
238C22×D15C2412yes—
239C22×D15C2412yes—
240C22×D15C2412yes—
241C22×C5×D3—22no—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3C2412yes—
245C22×C3×D5—22no—
246C22×C3×D5—22no—
247C22×C3×D5—22no—
248C22×C3×D5C2412yes—
249C2×D3×D5—44no—
250C2×D3×D5—44no—
251C2×D3×D5—44no—
252C2×D3×D5—416no—
253C2×C3×C4×C5—22no—
254C2×C3×C4×C5—22no—
255C2×C3×C4×C5C2412yes—
256C2×C3×C4×C5C2412yes—
257#1220—44no—
258C2×Dic15—22no—
259C2×Dic15C2412yes—
260D60—44no—
261D60—44no—
262C5×#67—44no—
263C2×C5×Dic3—22no—
264C2×C5×Dic3—22no—
265C2×C5×Dic3—22no—
266C2×C5×Dic3C2412yes—
267C2×C5×Dic3C2412yes—
268C2×C5×Dic3C2412yes—
269C5×Dic6—44no—
270C3×C22⋊D5—44no—
271C2×C3×Dic5—22no—
272C2×C3×Dic5—22no—
273C2×C3×Dic5—22no—
274C2×C3×Dic5C2412yes—
275C2×C3×Dic5C2412yes—
276C2×C3×Dic5C2412yes—
277C3×Dic10—44no—
278#1204—44no—
279#1203—44no—
280#1203—44no—
281#1202—44no—
282#1202—44no—
283C24×D3—51no—
284C24×D3—51no—
285C22×C3×Q8—51no—
286C22×C3×D4—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67C2×D511yescharacteristic
291C22×D12—51no—
292C22×D12—51no—
293C22×D12—51no—
294C22×D12—51no—
295C22×Dic6—51no—
296C22×Dic6C2×D511yescharacteristic, complemented
297C3×#124—58no—
298C2×C3×C22⋊C4—51no—
299C2×C3×C22⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
302C2×C3×C42—51no—
303C2×#217—51no—
304C2×#217C2×D511yescharacteristic, complemented
305#947—58no—
306#947—58no—
307#937—58no—
308#937—58no—
309C2×(C2×D3)⋊C4—51no—
310C2×(C2×D3)⋊C4—51no—
311C2×(C2×D3)⋊C4—51no—
312C2×(C2×D3)⋊C4—51no—
313C2×(C2×D3)⋊C4—51no—
314C2×(C2×D3)⋊C4—51no—
315C2×(C2×D3)⋊C4—51no—
316C2×(C2×D3)⋊C4—51no—
317C2×(C2×D3)⋊C4—51no—
318C2×(C2×D3)⋊C4—51no—
319C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
320C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
321C2×C4×Dic3—51no—
322C2×C4×Dic3C2×D511yescharacteristic, complemented
323#885—58no—
324#885—58no—
325#885—58no—
326#885C2×D518yescomplemented
327#882—58no—
328#882—58no—
329#882—58no—
330#882—58no—
331#875—58no—
332#875—58no—
333C24×C5—31no—
334C24×C5C22×D311yescharacteristic
335C23×D5—31no—
336C23×D5—31no—
337C23×D5—31no—
338C23×D5—34no—
339C23×D5—34no—
340C23×D5—122no—
341C23×D5—122no—
342C23×D5—122no—
343C23×D5—122no—
344C23×D5—122no—
345C23×D5—122no—
346C23×D5C22×D311yescharacteristic
347C2×C5×Q8—34no—
348C2×C5×Q8—122no—
349C2×C5×D4—34no—
350C2×C5×D4—122no—
351C22×C4×C5—31no—
352C22×C4×C5—31no—
353C22×C4×C5—31no—
354C22×C4×C5C22×D311yescharacteristic
355C22×C4×C5C22×D311yescharacteristic
356C2×C22⋊D5—34no—
357C2×C22⋊D5—34no—
358C2×C22⋊D5—34no—
359C2×C22⋊D5—42no—
360C2×C22⋊D5—122no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5—122no—
363C2×C22⋊D5C22×D314yes—
364C22×Dic5—31no—
365C22×Dic5C22×D311yescharacteristic
366C22×Dic5C22×D311yescharacteristic
367C22×Dic5C22×D311yescharacteristic
368C2×D20—34no—
369C2×D20—34no—
370C2×D20—34no—
371C2×D20—34no—
372C2×D20—122no—
373C2×D20—122no—
374C2×D20—122no—
375C2×D20—122no—
376C2×Dic10—34no—
377C2×Dic10—42no—
378C2×Dic10—122no—
379C2×Dic10C22×D314yescomplemented
380C5×C22⋊C4—34no—
381C5×C22⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4C22×D314yescomplemented
384C42×C5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5C22×D314yescomplemented
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685—34no—
393#685—34no—
394#685—34no—
395#685—34no—
396#685—34no—
397#685C22×D314yescomplemented
398#685C22×D314yescomplemented
399C4×Dic5—34no—
400C4×Dic5C22×D314yescomplemented
401H(3,𝔽4)—1516no—
402C2×#124—31no—
403C2×#124—51no—
404C2×#124—151no—
405C2×#124—151no—
406C2×#124—151no—
407C2×#124—151no—
408C2×#124—151no—
409C2×#124—151no—
410C2×#124—151no—
411C2×#120—151no—
412C2×#120—151no—
413C2×#120—151no—
414C2×#120—151no—
415C2×#120—151no—
416C2×#120—151no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—44no—
421C22×C3×C5H(5,𝔽2)12yes—
422C22×C3×C5H(5,𝔽2)12yes—
423C22×C3×C5H(5,𝔽2)12yes—
424C22×C3×C5C2511yescharacteristic
425C2×D15—22no—
426C2×D15—22no—
427C2×D15—22no—
428C2×D15—22no—
429C2×D15—22no—
430C2×D15—22no—
431C2×D15—22no—
432C2×D15—22no—
433C2×D15—22no—
434C2×D15—416no—
435C2×D15—44no—
436C2×D15—44no—
437C2×D15—44no—
438C2×C5×D3—22no—
439C2×C5×D3—22no—
440C2×C5×D3—22no—
441C2×C5×D3—44no—
442C2×C3×D5—22no—
443C2×C3×D5—22no—
444C2×C3×D5—22no—
445C2×C3×D5—44no—
446D3×D5—416no—
447C3×C4×C5—22no—
448C3×C4×C5—22no—
449Dic15—22no—
450C3×Dic5—22no—
451C3×Dic5—22no—
452C3×Dic5—22no—
453C5×Dic3—22no—
454C5×Dic3—22no—
455C5×Dic3—22no—
456C24×C3—51no—
457C24×C3C22×D511yescharacteristic
458C23×D3—51no—
459C23×D3—51no—
460C23×D3—51no—
461C23×D3—54no—
462C23×D3—54no—
463C23×D3—202no—
464C23×D3—202no—
465C23×D3—202no—
466C23×D3—202no—
467C23×D3—202no—
468C23×D3—202no—
469C23×D3C22×D511yescharacteristic
470C2×C3×Q8—54no—
471C2×C3×Q8—202no—
472C2×C3×D4—54no—
473C2×C3×D4—202no—
474C22×C3×C4—51no—
475C22×C3×C4—51no—
476C22×C3×C4—51no—
477C22×C3×C4C22×D511yescharacteristic
478C22×C3×C4C22×D511yescharacteristic
479C2×#67—42no—
480C2×#67—54no—
481C2×#67—54no—
482C2×#67—54no—
483C2×#67—202no—
484C2×#67—202no—
485C2×#67—202no—
486C2×#67C22×D514yes—
487C22×Dic3—51no—
488C22×Dic3C22×D511yescharacteristic
489C22×Dic3C22×D511yescharacteristic
490C22×Dic3C22×D511yescharacteristic
491C2×D12—54no—
492C2×D12—54no—
493C2×D12—54no—
494C2×D12—54no—
495C2×D12—202no—
496C2×D12—202no—
497C2×D12—202no—
498C2×D12—202no—
499C2×Dic6—42no—
500C2×Dic6—54no—
501C2×Dic6—202no—
502C2×Dic6C22×D514yescomplemented
503C3×C22⋊C4—54no—
504C3×C22⋊C4—54no—
505C3×C22⋊C4—54no—
506C3×C22⋊C4C22×D514yescomplemented
507C3×C42—54no—
508#217—54no—
509#217C22×D514yescomplemented
510(C2×D3)⋊C4—54no—
511(C2×D3)⋊C4—54no—
512(C2×D3)⋊C4—54no—
513(C2×D3)⋊C4—54no—
514(C2×D3)⋊C4—54no—
515(C2×D3)⋊C4—54no—
516(C2×D3)⋊C4—54no—
517(C2×D3)⋊C4—54no—
518(C2×D3)⋊C4—54no—
519(C2×D3)⋊C4—54no—
520(C2×D3)⋊C4C22×D514yescomplemented
521(C2×D3)⋊C4C22×D514yescomplemented
522C4×Dic3—54no—
523C4×Dic3C22×D514yescomplemented
524C23×C5—22no—
525C23×C5—22no—
526C23×C5—22no—
527C23×C5—32no—
528C23×C5—62no—
529C23×C5—62no—
530C23×C5—62no—
531C23×C5C23×D312yes—
532C23×C5C23×D311yescharacteristic
533C22×D5—22no—
534C22×D5—22no—
535C22×D5—22no—
536C22×D5—32no—
537C22×D5—32no—
538C22×D5—32no—
539C22×D5—62no—
540C22×D5—62no—
541C22×D5—62no—
542C22×D5—62no—
543C22×D5—62no—
544C22×D5—62no—
545C22×D5—62no—
546C22×D5—62no—
547C22×D5—62no—
548C22×D5—124no—
549C22×D5—124no—
550C22×D5—124no—
551C22×D5—1216no—
552C22×D5—124no—
553C22×D5—124no—
554C22×D5—124no—
555C22×D5—1216no—
556C22×D5C23×D312yes—
557C5×Q8—124no—
558C5×D4—124no—
559C2×C4×C5—22no—
560C2×C4×C5—22no—
561C2×C4×C5—32no—
562C2×C4×C5—32no—
563C2×C4×C5—32no—
564C2×C4×C5—62no—
565C2×C4×C5—62no—
566C2×C4×C5—62no—
567C2×C4×C5C23×D312yes—
568C2×C4×C5C23×D312yes—
569C22⋊D5—44no—
570C22⋊D5—124no—
571C22⋊D5—124no—
572C22⋊D5—124no—
573C2×Dic5—22no—
574C2×Dic5—22no—
575C2×Dic5—22no—
576C2×Dic5—32no—
577C2×Dic5—62no—
578C2×Dic5C23×D312yes—
579C2×Dic5C23×D312yes—
580C2×Dic5C23×D312yes—
581D20—124no—
582D20—124no—
583D20—124no—
584D20—124no—
585Dic10—44no—
586Dic10—124no—
587C25—151no—
588C25—151no—
589C22×Q8—31no—
590C22×Q8—51no—
591C22×Q8—151no—
592C22×D4—31no—
593C22×D4—51no—
594C22×D4—151no—
595C22×D4—151no—
596C22×D4—151no—
597C22×D4—151no—
598C22×D4—151no—
599C22×D4—151no—
600C22×D4—151no—
601#124—38no—
602#124—58no—
603#124—158no—
604#124—158no—
605#124—158no—
606#124—158no—
607#124—158no—
608#124—158no—
609#124—158no—
610#120—158no—
611#120—158no—
612#120—158no—
613#120—158no—
614#120—158no—
615#120—158no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—51no—
620C2×C22⋊C4—51no—
621C2×C22⋊C4—51no—
622C2×C22⋊C4—151no—
623C2×C22⋊C4—151no—
624C2×C22⋊C4—151no—
625C2×C22⋊C4—151no—
626C2×C22⋊C4—151no—
627C2×C22⋊C4—151no—
628C2×C22⋊C4—151no—
629C2×C22⋊C4—151no—
630C2×C22⋊C4—151no—
631C2×C22⋊C4—151no—
632C2×C22⋊C4—151no—
633C2×C22⋊C4D3×D511yescharacteristic, complemented
634C2×C42—31no—
635C2×C42—51no—
636C2×C42—151no—
637C2×C3×C5—42no—
638C2×C3×C5H(3,𝔽4)14yescomplemented
639C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
640C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
641C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
642D15—42no—
643D15—42no—
644D15—42no—
645C3×D5—42no—
646C5×D3—42no—
647C23×C3—22no—
648C23×C3—22no—
649C23×C3—22no—
650C23×C3—52no—
651C23×C3—102no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3C23×D512yes—
655C23×C3C23×D511yescharacteristic
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—52no—
660C22×D3—52no—
661C22×D3—52no—
662C22×D3—102no—
663C22×D3—102no—
664C22×D3—102no—
665C22×D3—102no—
666C22×D3—102no—
667C22×D3—102no—
668C22×D3—102no—
669C22×D3—102no—
670C22×D3—102no—
671C22×D3—204no—
672C22×D3—204no—
673C22×D3—204no—
674C22×D3—2016no—
675C22×D3—204no—
676C22×D3—204no—
677C22×D3—204no—
678C22×D3—2016no—
679C22×D3C23×D512yes—
680C3×Q8—204no—
681C3×D4—204no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—52no—
685C2×C3×C4—52no—
686C2×C3×C4—52no—
687C2×C3×C4—102no—
688C2×C3×C4—102no—
689C2×C3×C4—102no—
690C2×C3×C4C23×D512yes—
691C2×C3×C4C23×D512yes—
692#67—44no—
693#67—204no—
694#67—204no—
695#67—204no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—52no—
700C2×Dic3—102no—
701C2×Dic3C23×D512yes—
702C2×Dic3C23×D512yes—
703C2×Dic3C23×D512yes—
704D12—204no—
705D12—204no—
706D12—204no—
707D12—204no—
708Dic6—44no—
709Dic6—204no—
710C22×C5—22no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—44no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—62no—
717C22×C5—124no—
718C22×C5#100412yes—
719C22×C5#100912yes—
720C22×C5#100912yes—
721C22×C5C24×D311yescharacteristic
722C2×D5—22no—
723C2×D5—22no—
724C2×D5—22no—
725C2×D5—44no—
726C2×D5—62no—
727C2×D5—62no—
728C2×D5—62no—
729C2×D5—62no—
730C2×D5—62no—
731C2×D5—62no—
732C2×D5—62no—
733C2×D5—62no—
734C2×D5—62no—
735C2×D5—1216no—
736C2×D5—1216no—
737C2×D5—124no—
738C2×D5—124no—
739C2×D5—124no—
740C4×C5—22no—
741C4×C5—22no—
742C4×C5—62no—
743C4×C5—62no—
744C4×C5—62no—
745Dic5—22no—
746Dic5—22no—
747Dic5—22no—
748Dic5—62no—
749C24—31no—
750C24—51no—
751C24—154no—
752C24—151no—
753C24—151no—
754C24—151no—
755C24—154no—
756C24—602no—
757C24—602no—
758C24—602no—
759C24—602no—
760C24—602no—
761C24—602no—
762C24C2×D3×D511yescharacteristic
763C2×Q8—34no—
764C2×Q8—54no—
765C2×Q8—122no—
766C2×Q8—154no—
767C2×Q8—202no—
768C2×Q8—602no—
769C2×D4—34no—
770C2×D4—54no—
771C2×D4—122no—
772C2×D4—154no—
773C2×D4—154no—
774C2×D4—154no—
775C2×D4—154no—
776C2×D4—154no—
777C2×D4—154no—
778C2×D4—154no—
779C2×D4—202no—
780C2×D4—602no—
781C2×D4—602no—
782C2×D4—602no—
783C2×D4—602no—
784C2×D4—602no—
785C2×D4—602no—
786C2×D4—602no—
787C22×C4—31no—
788C22×C4—31no—
789C22×C4—31no—
790C22×C4—51no—
791C22×C4—51no—
792C22×C4—51no—
793C22×C4—151no—
794C22×C4C2×D3×D511yescharacteristic
795C22×C4C2×D3×D511yescharacteristic
796C22⋊C4—34no—
797C22⋊C4—34no—
798C22⋊C4—34no—
799C22⋊C4—54no—
800C22⋊C4—54no—
801C22⋊C4—54no—
802C22⋊C4—154no—
803C22⋊C4—154no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C22⋊C4C2×D3×D514yescomplemented
814C42—34no—
815C42—54no—
816C42—154no—
817C3×C5C2×H(3,𝔽4)11yescharacteristic, complemented, Hall
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—44no—
822C22×C3—102no—
823C22×C3—102no—
824C22×C3—102no—
825C22×C3—204no—
826C22×C3#414412yes—
827C22×C3#414912yes—
828C22×C3#414912yes—
829C22×C3C24×D511yescharacteristic
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—44no—
834C2×D3—102no—
835C2×D3—102no—
836C2×D3—102no—
837C2×D3—102no—
838C2×D3—102no—
839C2×D3—102no—
840C2×D3—102no—
841C2×D3—102no—
842C2×D3—102no—
843C2×D3—2016no—
844C2×D3—2016no—
845C2×D3—204no—
846C2×D3—204no—
847C2×D3—204no—
848C3×C4—22no—
849C3×C4—22no—
850C3×C4—102no—
851C3×C4—102no—
852C3×C4—102no—
853Dic3—22no—
854Dic3—22no—
855Dic3—22no—
856Dic3—102no—
857C2×C5—42no—
858C2×C5—122no—
859C2×C5#568314yescomplemented
860C2×C5C2×#100411yescharacteristic
861C2×C5C2×#100911yescharacteristic
862C2×C5C2×#100911yescharacteristic
863D5—42no—
864D5—122no—
865D5—122no—
866D5—122no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—32no—
871C23—52no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—102no—
876C23—102no—
877C23—102no—
878C23—152no—
879C23—152no—
880C23—152no—
881C23—302no—
882C23—302no—
883C23—302no—
884C23—302no—
885C23—302no—
886C23—302no—
887C23—302no—
888C23—302no—
889C23—302no—
890C23—604no—
891C23—604no—
892C23—604no—
893C23—6016no—
894C23—604no—
895C23—604no—
896C23—604no—
897C23—6016no—
898C23C22×D3×D512yes—
899C23C22×D3×D511yescharacteristic
900Q8—124no—
901Q8—204no—
902Q8—604no—
903D4—124no—
904D4—204no—
905D4—604no—
906D4—604no—
907D4—604no—
908D4—604no—
909D4—604no—
910D4—604no—
911D4—604no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—52no—
918C2×C4—52no—
919C2×C4—52no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—102no—
924C2×C4—102no—
925C2×C4—102no—
926C2×C4—152no—
927C2×C4—302no—
928C2×C4C22×D3×D512yes—
929C2×C4C22×D3×D512yes—
930C2×C3—42no—
931C2×C3—202no—
932C2×C3#6601714yescomplemented
933C2×C3C2×#414411yescharacteristic
934C2×C3C2×#414911yescharacteristic
935C2×C3C2×#414911yescharacteristic
936D3—42no—
937D3—202no—
938D3—202no—
939D3—202no—
940C5C2×#568311yescharacteristic, complemented, Sylow
941C22—22no—
942C22—22no—
943C22—22no—
944C22—44no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—102no—
949C22—102no—
950C22—102no—
951C22—124no—
952C22—204no—
953C22—302no—
954C22—302no—
955C22—302no—
956C22—302no—
957C22—302no—
958C22—302no—
959C22—302no—
960C22—302no—
961C22—302no—
962C22—6016no—
963C22—6016no—
964C22—604no—
965C22—604no—
966C22—604no—
967C22#9201912yes—
968C22#9202612yes—
969C22#9202712yes—
970C22C23×D3×D511yescharacteristic
971C4—22no—
972C4—22no—
973C4—62no—
974C4—62no—
975C4—62no—
976C4—102no—
977C4—102no—
978C4—102no—
979C4—302no—
980C3C2×#6601711yescharacteristic, complemented, Sylow
981C2—42no—
982C2—122no—
983C2—202no—
984C2—602no—
985C2—602no—
986C2—602no—
987C2#1175330314yesdirect product factor
988C2C2×#9201911yescharacteristic
989C2C2×#9202611yescharacteristic
990C2C2×#9202711yescharacteristic
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×H(3,𝔽4)
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×#91771C2semidirect
2. C2×C5×#885C2semidirect
3. C2×C3×#4031C2semidirect
4. C2×#91577C2semidirect
5. C2×#91573C2semidirect
6. C2×#91572C2semidirect
7. C2×#91526C2semidirect
8. C2×#91476C2semidirect
9. C2×#91476C2semidirect
10. C2×#91455C2semidirect
11. C2×#91375C2semidirect
12. C2×#91374C2semidirect
13. C2×#91353C2semidirect
14. C2×#91350C2semidirect
15. C2×#91326C2semidirect
16. #11753303C2direct (N × H)
18. C24×D15C22semidirect
19. C23×D3×D5C22semidirect
24. C22×C5×Dic6C22semidirect
26. C22×C3×Dic10C22semidirect
27. C22×#1204C22semidirect
32. C2×C3×C5×C22⋊C4C22semidirect
33. C2×#6714C22semidirect
34. C2×#6714C22semidirect
35. #91771C22semidirect
36. C2×C5×#217C22semidirect
37. C2×C5×(C2×D3)⋊C4C22semidirect
38. C2×C5×(C2×D3)⋊C4C22semidirect
39. C2×C4×C5×Dic3C22semidirect
40. C5×#885C22semidirect
41. C2×C3×C22⋊Dic5C22semidirect
42. C2×C3×#685C22semidirect
43. C2×C3×#685C22semidirect
44. C2×C3×C4×Dic5C22semidirect
45. C3×#4031C22semidirect
46. #91577C22semidirect
47. #91573C22semidirect
48. #91572C22semidirect
49. C2×#6667C22semidirect
50. C2×#6667C22semidirect
51. C2×#6667C22semidirect
52. C2×#6667C22semidirect
53. C2×#6667C22semidirect
54. C2×#6667C22semidirect
55. C2×#6667C22semidirect
56. C2×(C2×D3)⋊Dic5C22semidirect
57. C2×#6665C22semidirect
58. C2×Dic3×Dic5C22semidirect
59. #91526C22semidirect
60. #91476C22semidirect
61. #91476C22semidirect
62. #91455C22semidirect
63. #91375C22semidirect
64. #91374C22semidirect
65. #91353C22semidirect
66. #91350C22semidirect
67. #91326C22semidirect
78. C2×#4031D3semidirect
92. C23×D15C23semidirect
98. C22×D3×D5C23semidirect
114. C2×C5×Dic6C23semidirect
121. C2×C3×Dic10C23semidirect
123. C2×#1204C23semidirect
132. C3×C5×C22⋊C4C23semidirect
133. #6714C23semidirect
134. #6714C23semidirect
135. C5×#217C23semidirect
136. C5×(C2×D3)⋊C4C23semidirect
137. C5×(C2×D3)⋊C4C23semidirect
138. C4×C5×Dic3C23semidirect
139. C3×C22⋊Dic5C23semidirect
140. C3×#685C23semidirect
141. C3×#685C23semidirect
142. C3×C4×Dic5C23semidirect
143. #6667C23semidirect
144. #6667C23semidirect
145. #6667C23semidirect
146. #6667C23semidirect
147. #6667C23semidirect
148. #6667C23semidirect
149. #6667C23semidirect
150. (C2×D3)⋊Dic5C23semidirect
151. #6665C23semidirect
152. Dic3×Dic5C23semidirect
162. C2×#885D5semidirect
182. C22×Dic10C2×D3semidirect
187. C2×C5×C22⋊C4C2×D3semidirect
190. C2×C22⋊Dic5C2×D3semidirect
205. C2×#685C2×D3semidirect
206. C2×#685C2×D3semidirect
208. C2×C4×Dic5C2×D3semidirect
212. #4031C2×D3semidirect
296. C22×Dic6C2×D5semidirect
301. C2×C3×C22⋊C4C2×D5semidirect
304. C2×#217C2×D5semidirect
319. C2×(C2×D3)⋊C4C2×D5semidirect
320. C2×(C2×D3)⋊C4C2×D5semidirect
322. C2×C4×Dic3C2×D5semidirect
326. #885C2×D5semidirect
379. C2×Dic10C22×D3semidirect
383. C5×C22⋊C4C22×D3semidirect
386. C22⋊Dic5C22×D3semidirect
397. #685C22×D3semidirect
398. #685C22×D3semidirect
400. C4×Dic5C22×D3semidirect
502. C2×Dic6C22×D5semidirect
506. C3×C22⋊C4C22×D5semidirect
509. #217C22×D5semidirect
520. (C2×D3)⋊C4C22×D5semidirect
521. (C2×D3)⋊C4C22×D5semidirect
523. C4×Dic3C22×D5semidirect
633. C2×C22⋊C4D3×D5semidirect
638. C2×C3×C5H(3,𝔽4)semidirect
813. C22⋊C4C2×D3×D5semidirect
817. C3×C5C2×H(3,𝔽4)semidirect
859. C2×C5#5683semidirect
932. C2×C3#66017semidirect
940. C5C2×#5683semidirect
980. C3C2×#66017semidirect
987. C2#11753303direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917712
C2×C5×#8852
C2×C3×#40312
C2×#915772
C2×#915732
C2×#915722
C2×#915262
C2×#914762
C2×#914552
C2×#913752
C2×#913742
C2×#913532
C2×#913502
C2×#913262
#117533032
C2×#660173
C2×#56835