Finite Group Databasebeta

← C2×#11754987 #14495225

Subgroups — C2×#11754987 #14495225

Order 1920.

2688 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91828C211yesmaximal, characteristic, complemented
2C2×C5×#937C211yesmaximal, characteristic, complemented
3C2×C3×#4084C211yesmaximal, characteristic, complemented
4C2×#91571C211yesmaximal, characteristic, complemented
5C2×#91570C211yesmaximal, characteristic, complemented
6C2×#91568C211yesmaximal, characteristic, complemented
7C2×#91567C211yesmaximal, characteristic, complemented
8C2×#91557C211yesmaximal, characteristic, complemented
9C2×#91543C211yesmaximal, characteristic, complemented
10C2×#91533C211yesmaximal, characteristic, complemented
11C2×#91531C211yesmaximal, characteristic, complemented
12#11754987C2116yesmaximal, direct product factor
13C2×#91448C211yesmaximal, characteristic, complemented
14C2×#91447C211yesmaximal, characteristic, complemented
15C2×#91438C211yesmaximal, characteristic, complemented
16C2×#91341C211yesmaximal, characteristic, complemented
17C2×#65929—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic, complemented
22C23×Dic15C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic
24C22×C5×#67C2211yescharacteristic
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×C22⋊D5C2211yescharacteristic, complemented
27C22×C3×C4×D5C2211yescharacteristic, complemented
28C22×#1203C2211yescharacteristic
29C22×#1203C2211yescharacteristic
30C22×#1202C2211yescharacteristic, complemented
31C22×#1201C2211yescharacteristic
32C22×#1201C2211yescharacteristic
33C22×#1200C2211yescharacteristic, complemented
34C2×#6719C2211yescharacteristic
35#91828C2218yescomplemented
36C2×#6714C2211yescharacteristic, complemented
37C2×#6712C2211yescharacteristic, complemented
38C2×C5×#217C2211yescharacteristic
39C5×#937C2218yescomplemented
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic
41C2×C5×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×C22⋊Dic5C2211yescharacteristic
43C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
44C3×#4084C2218yescomplemented
45C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
46#91571C2218yescomplemented
47#91570C2218yescomplemented
48#91568C2218yescomplemented
49#91567C2218yescomplemented
50#91557C2218yescomplemented
51C2×Dic3⋊Dic5C2211yescharacteristic, complemented
52C2×#6669C2211yescharacteristic, complemented
53#91543C2218yescomplemented
54C2×#6668C2211yescharacteristic, complemented
55C2×#6668C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×(C2×D3)⋊Dic5C2211yescharacteristic
59C2×(C2×D3)⋊Dic5C2211yescharacteristic
60C2×#6665C2211yescharacteristic, complemented
61#91533C2218yescomplemented
62#91531C2218yescomplemented
63C2×Dic3×Dic5C2211yescharacteristic, complemented
64#91448C2218yescomplemented
65#91447C2218yescomplemented
66#91438C2218yescomplemented
67#91341C2218yescomplemented
68C2×#5620—51nomaximal, Hall
69C2×C5×#120—31no—
70C2×#4099—31no—
71C2×#4099—31no—
72C2×#4086—31no—
73C2×#4085—31no—
74C2×#4085—31no—
75C2×#4084—31no—
76C2×#4084D311yescharacteristic, complemented
77C2×#4081—31no—
78#65929—316no—
79C2×#4030—31no—
80C2×#4030—31no—
81C2×#4029—31no—
82C2×#4029—31no—
83C2×#4025—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C5×D3—42no—
89C23×C5×D3—42no—
90C23×C5×D3—42no—
91C23×C5×D3C2311yescharacteristic
92C23×C5×D3C2311yescharacteristic
93C23×C5×D3C2314yes—
94C23×C3×D5C2311yescharacteristic
95C2×C3×C5×D4—42no—
96C2×C3×C5×D4C2314yes—
97C22×C3×C4×C5C2311yescharacteristic
98C2×#1220—42no—
99C2×#1220—42no—
100C2×#1220C2314yes—
101C2×#1220C2314yescomplemented
102C22×Dic15—42no—
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2314yescomplemented
107C2×C5×#67—42no—
108C2×C5×#67—42no—
109C2×C5×#67C2314yes—
110C2×C5×#67C2314yes—
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C2×C3×C22⋊D5—42no—
114C2×C3×C22⋊D5—42no—
115C2×C3×C22⋊D5C2314yes—
116C2×C3×C22⋊D5C2314yescomplemented
117C22×C3×Dic5C2311yescharacteristic
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2311yescharacteristic
120C2×C3×C4×D5—42no—
121C2×C3×C4×D5C2314yescomplemented
122C2×#1203—42no—
123C2×#1203—42no—
124C2×#1203C2314yes—
125C2×#1203C2314yes—
126C2×#1202—42no—
127C2×#1202C2314yescomplemented
128C2×#1201—42no—
129C2×#1201—42no—
130C2×#1201C2314yes—
131C2×#1201C2314yes—
132C2×#1200—42no—
133C2×#1200C2314yescomplemented
134#6719C2314yes—
135#6714C2314yescomplemented
136#6712C2314yescomplemented
137C5×#217C2314yes—
138C5×(C2×D3)⋊C4C2314yes—
139C5×(C2×D3)⋊C4C2314yes—
140C3×C22⋊Dic5C2314yes—
141C3×C22⋊Dic5C2314yescomplemented
142C3×C4⋊Dic5C2314yescomplemented
143Dic3⋊Dic5C2314yescomplemented
144#6669C2314yescomplemented
145#6668C2314yescomplemented
146#6668C2314yescomplemented
147(C2×D3)⋊Dic5C2314yes—
148(C2×D3)⋊Dic5C2314yes—
149(C2×D3)⋊Dic5C2314yes—
150(C2×D3)⋊Dic5C2314yes—
151#6665C2314yescomplemented
152Dic3×Dic5C2314yescomplemented
153C2×C3×#121—51no—
154C2×#940—51no—
155C2×#939—51no—
156C2×#939—51no—
157C2×#938—51no—
158C2×#937—51no—
159C2×#937D511yescharacteristic, complemented
160C2×#930—51no—
161C2×#929—51no—
162#5620—516no—
163C2×#898—51no—
164C2×#894—51no—
165C2×#886—51no—
166C2×#884—51no—
167C2×#882—51no—
168C2×#879—51no—
169C25×C5—31no—
170C22×C5×D4—31no—
171C22×C5×D4—31no—
172C22×C5×D4C2×D311yescharacteristic
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C22×C22⋊D5—31no—
178C22×C22⋊D5—31no—
179C22×C22⋊D5C2×D311yescharacteristic
180C22×C22⋊D5C2×D311yescharacteristic, complemented
181C23×Dic5—31no—
182C22×D20—31no—
183C22×C4×D5—31no—
184C22×C4×D5C2×D311yescharacteristic, complemented
185C5×#120—38no—
186C2×C5×C22⋊C4—31no—
187C2×C5×C22⋊C4—31no—
188C2×C5×C22⋊C4—31no—
189#4099—38no—
190#4099—38no—
191C2×C22⋊Dic5—31no—
192C2×C22⋊Dic5—31no—
193C2×C22⋊Dic5—31no—
194C2×C22⋊Dic5—31no—
195C2×C22⋊Dic5—31no—
196C2×C22⋊Dic5C2×D311yescharacteristic
197C2×C22⋊Dic5C2×D311yescharacteristic, complemented
198#4086—38no—
199#4085—38no—
200#4085—38no—
201#4084—38no—
202#4084C2×D318yescomplemented
203#4081—38no—
204C2×#685—31no—
205C2×#685—31no—
206C2×C4⋊Dic5—31no—
207C2×C4⋊Dic5C2×D311yescharacteristic, complemented
208C2×#683—31no—
209C2×#683—31no—
210C2×#683—31no—
211C2×#683—31no—
212C2×C4×Dic5—31no—
213#4030—38no—
214#4030—38no—
215#4029—38no—
216#4029—38no—
217#4025—38no—
218#4025—38no—
219C2×#560—151noSylow
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5—22no—
224C23×C3×C5—22no—
225C23×C3×C5—22no—
226C23×C3×C5C2412yes—
227C23×C3×C5C2412yes—
228C23×C3×C5C2411yescharacteristic
229C22×D15—22no—
230C22×D15—22no—
231C22×D15—22no—
232C22×D15C2412yes—
233C22×C5×D3—22no—
234C22×C5×D3—22no—
235C22×C5×D3—22no—
236C22×C5×D3—22no—
237C22×C5×D3—22no—
238C22×C5×D3—22no—
239C22×C5×D3—44no—
240C22×C5×D3—44no—
241C22×C5×D3—44no—
242C22×C5×D3—416no—
243C22×C5×D3C2412yes—
244C22×C5×D3C2412yes—
245C22×C3×D5—22no—
246C22×C3×D5—22no—
247C22×C3×D5—22no—
248C22×C3×D5C2412yes—
249C3×C5×D4—44no—
250C2×C3×C4×C5—22no—
251C2×C3×C4×C5C2412yes—
252#1220—44no—
253#1220—44no—
254C2×Dic15—22no—
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15—44no—
258C2×Dic15C2412yes—
259C2×Dic15C2412yes—
260C2×Dic15C2412yes—
261C5×#67—44no—
262C5×#67—44no—
263C2×C5×Dic3—22no—
264C2×C5×Dic3—22no—
265C2×C5×Dic3C2412yes—
266C2×C5×Dic3C2412yes—
267C3×C22⋊D5—44no—
268C3×C22⋊D5—44no—
269C2×C3×Dic5—22no—
270C2×C3×Dic5—22no—
271C2×C3×Dic5—22no—
272C2×C3×Dic5C2412yes—
273C2×C3×Dic5C2412yes—
274C2×C3×Dic5C2412yes—
275C3×C4×D5—44no—
276#1203—44no—
277#1203—44no—
278#1202—44no—
279#1201—44no—
280#1201—44no—
281#1200—44no—
282C24×D3C2×D511yescharacteristic
283C22×C3×D4—51no—
284C22×C3×D4—51no—
285C22×C3×D4C2×D511yescharacteristic
286C23×C3×C4—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×#67—51no—
292C22×#67C2×D511yescharacteristic
293C22×#67C2×D511yescharacteristic
294C23×Dic3—51no—
295C22×D12—51no—
296C22×D12—51no—
297C22×C4×D3—51no—
298C3×#121—58no—
299C2×C3×C4⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4—51no—
302C2×#217—51no—
303C2×#217—51no—
304C2×#217C2×D511yescharacteristic
305#940—58no—
306#939—58no—
307#939—58no—
308#938—58no—
309#937—58no—
310#937C2×D518yescomplemented
311#930—58no—
312#929—58no—
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)⋊C4C2×D511yescharacteristic
319C2×(C2×D3)⋊C4C2×D511yescharacteristic
320C2×C4⋊Dic3—51no—
321C2×C4⋊Dic3—51no—
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4—51no—
324C2×Dic3⋊C4—51no—
325C2×C4×Dic3—51no—
326#898—58no—
327#894—58no—
328#886—58no—
329#884—58no—
330#882—58no—
331#879—58no—
332C24×C5—31no—
333C24×C5—31no—
334C24×C5—34no—
335C24×C5—122no—
336C24×C5—122no—
337C24×C5—122no—
338C24×C5C22×D311yescharacteristic
339C24×C5C22×D311yescharacteristic
340C23×D5—31no—
341C23×D5C22×D311yescharacteristic
342C2×C5×D4—34no—
343C2×C5×D4—34no—
344C2×C5×D4—42no—
345C2×C5×D4—122no—
346C2×C5×D4—122no—
347C2×C5×D4C22×D314yes—
348C22×C4×C5—31no—
349C22×C4×C5—31no—
350C22×C4×C5C22×D311yescharacteristic
351C2×C22⋊D5—34no—
352C2×C22⋊D5—34no—
353C2×C22⋊D5—34no—
354C2×C22⋊D5—34no—
355C2×C22⋊D5—34no—
356C2×C22⋊D5—34no—
357C2×C22⋊D5—42no—
358C2×C22⋊D5—42no—
359C2×C22⋊D5—122no—
360C2×C22⋊D5—122no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5—122no—
363C2×C22⋊D5—122no—
364C2×C22⋊D5—122no—
365C2×C22⋊D5C22×D314yes—
366C2×C22⋊D5C22×D314yescomplemented
367C22×Dic5—31no—
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5—34no—
371C22×Dic5—122no—
372C22×Dic5C22×D311yescharacteristic
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D311yescharacteristic
375C2×D20—34no—
376C2×D20—122no—
377C2×C4×D5—34no—
378C2×C4×D5—42no—
379C2×C4×D5—122no—
380C2×C4×D5C22×D314yescomplemented
381C5×C22⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4—34no—
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5—34no—
387C22⋊Dic5—34no—
388C22⋊Dic5—34no—
389C22⋊Dic5C22×D314yes—
390C22⋊Dic5C22×D314yescomplemented
391#685—34no—
392#685—34no—
393C4⋊Dic5—34no—
394C4⋊Dic5C22×D314yescomplemented
395#683—34no—
396#683—34no—
397#683—34no—
398#683—34no—
399C4×Dic5—34no—
400#560—1516no—
401C2×#127—151no—
402C2×#126—151no—
403C2×#126—151no—
404C2×#123—151no—
405C2×#123—151no—
406C2×#123—151no—
407C2×#121—51no—
408C2×#121—151no—
409C2×#121—151no—
410C2×#121—151no—
411C2×#121—151no—
412C2×#121—151no—
413C2×#120—31no—
414C2×#120—151no—
415C2×#120—151no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—22no—
421C22×C3×C5—22no—
422C22×C3×C5—44no—
423C22×C3×C5—44no—
424C22×C3×C5H(5,𝔽2)12yes—
425C22×C3×C5H(5,𝔽2)12yes—
426C22×C3×C5H(5,𝔽2)12yes—
427C22×C3×C5C2511yescharacteristic
428C2×D15—22no—
429C2×D15—22no—
430C2×D15—22no—
431C2×D15—44no—
432C2×C5×D3—22no—
433C2×C5×D3—22no—
434C2×C5×D3—22no—
435C2×C5×D3—22no—
436C2×C5×D3—22no—
437C2×C5×D3—22no—
438C2×C5×D3—416no—
439C2×C5×D3—44no—
440C2×C5×D3—44no—
441C2×C3×D5—22no—
442C2×C3×D5—22no—
443C2×C3×D5—22no—
444C2×C3×D5—44no—
445C3×C4×C5—22no—
446Dic15—22no—
447Dic15—22no—
448Dic15—22no—
449C3×Dic5—22no—
450C3×Dic5—22no—
451C3×Dic5—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3C22×D511yescharacteristic
456C24×C3C22×D511yescharacteristic
457C23×D3—42no—
458C23×D3—42no—
459C23×D3—42no—
460C23×D3—51no—
461C23×D3C22×D511yescharacteristic
462C23×D3C22×D511yescharacteristic
463C23×D3C22×D514yes—
464C2×C3×D4—42no—
465C2×C3×D4—54no—
466C2×C3×D4—54no—
467C2×C3×D4—202no—
468C2×C3×D4—202no—
469C2×C3×D4C22×D514yes—
470C22×C3×C4—51no—
471C22×C3×C4—51no—
472C22×C3×C4—51no—
473C22×C3×C4—54no—
474C22×C3×C4—202no—
475C22×C3×C4C22×D511yescharacteristic
476C2×#67—42no—
477C2×#67—42no—
478C2×#67—54no—
479C2×#67—54no—
480C2×#67—54no—
481C2×#67—54no—
482C2×#67—54no—
483C2×#67—202no—
484C2×#67—202no—
485C2×#67—202no—
486C2×#67—202no—
487C2×#67—202no—
488C2×#67C22×D514yes—
489C2×#67C22×D514yes—
490C22×Dic3—51no—
491C22×Dic3—51no—
492C22×Dic3—51no—
493C22×Dic3—54no—
494C22×Dic3—202no—
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D511yescharacteristic
497C2×D12—54no—
498C2×D12—54no—
499C2×D12—202no—
500C2×D12—202no—
501C2×C4×D3—54no—
502C2×C4×D3—202no—
503C3×C4⋊C4—54no—
504C3×C22⋊C4—54no—
505C3×C22⋊C4—54no—
506#217—54no—
507#217—54no—
508#217C22×D514yes—
509(C2×D3)⋊C4—54no—
510(C2×D3)⋊C4—54no—
511(C2×D3)⋊C4—54no—
512(C2×D3)⋊C4—54no—
513(C2×D3)⋊C4—54no—
514(C2×D3)⋊C4C22×D514yes—
515(C2×D3)⋊C4C22×D514yes—
516C4⋊Dic3—54no—
517C4⋊Dic3—54no—
518Dic3⋊C4—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4—54no—
521C4×Dic3—54no—
522C23×C5—22no—
523C23×C5—22no—
524C23×C5—22no—
525C23×C5—22no—
526C23×C5—22no—
527C23×C5—22no—
528C23×C5—32no—
529C23×C5—32no—
530C23×C5—62no—
531C23×C5—62no—
532C23×C5—62no—
533C23×C5—62no—
534C23×C5—62no—
535C23×C5—62no—
536C23×C5—124no—
537C23×C5—124no—
538C23×C5—124no—
539C23×C5—1216no—
540C23×C5C23×D312yes—
541C23×C5C23×D312yes—
542C23×C5C23×D311yescharacteristic
543C22×D5—22no—
544C22×D5—22no—
545C22×D5—22no—
546C22×D5—32no—
547C22×D5—62no—
548C22×D5—62no—
549C22×D5—62no—
550C22×D5C23×D312yes—
551C5×D4—44no—
552C5×D4—124no—
553C5×D4—124no—
554C2×C4×C5—22no—
555C2×C4×C5—32no—
556C2×C4×C5—32no—
557C2×C4×C5—62no—
558C2×C4×C5—62no—
559C2×C4×C5C23×D312yes—
560C22⋊D5—44no—
561C22⋊D5—44no—
562C22⋊D5—124no—
563C22⋊D5—124no—
564C22⋊D5—124no—
565C22⋊D5—124no—
566C22⋊D5—124no—
567C22⋊D5—124no—
568C2×Dic5—22no—
569C2×Dic5—22no—
570C2×Dic5—22no—
571C2×Dic5—32no—
572C2×Dic5—32no—
573C2×Dic5—32no—
574C2×Dic5—62no—
575C2×Dic5—62no—
576C2×Dic5—62no—
577C2×Dic5—124no—
578C2×Dic5C23×D312yes—
579C2×Dic5C23×D312yes—
580C2×Dic5C23×D312yes—
581D20—124no—
582C4×D5—44no—
583C4×D5—124no—
584C25—31no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—51no—
588C22×D4—51no—
589C22×D4—151no—
590C22×D4—151no—
591C22×D4—151no—
592C22×D4—151no—
593C22×D4—151no—
594C22×D4—151no—
595C22×D4—151no—
596C22×D4D3×D511yescharacteristic
597C23×C4—51no—
598C23×C4—151no—
599C23×C4—151no—
600#127—158no—
601#126—158no—
602#126—158no—
603#123—158no—
604#123—158no—
605#123—158no—
606#121—58no—
607#121—158no—
608#121—158no—
609#121—158no—
610#121—158no—
611#121—158no—
612#120—38no—
613#120—158no—
614#120—158no—
615C2×C4⋊C4—51no—
616C2×C4⋊C4—151no—
617C2×C4⋊C4—151no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4—151no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—31no—
624C2×C22⋊C4—51no—
625C2×C22⋊C4—51no—
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×C42—151no—
634C2×C3×C5—42no—
635C2×C3×C5—42no—
636C2×C3×C5#56014yescomplemented
637C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
638C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
639C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
640D15—42no—
641C3×D5—42no—
642C5×D3—42no—
643C5×D3—42no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
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×D512yes—
656C23×C3C23×D511yescharacteristic
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—44no—
664C22×D3—44no—
665C22×D3—44no—
666C22×D3—416no—
667C22×D3—52no—
668C22×D3—102no—
669C22×D3—102no—
670C22×D3—102no—
671C22×D3C23×D512yes—
672C22×D3C23×D512yes—
673C3×D4—44no—
674C3×D4—204no—
675C3×D4—204no—
676C2×C3×C4—22no—
677C2×C3×C4—52no—
678C2×C3×C4—52no—
679C2×C3×C4—52no—
680C2×C3×C4—102no—
681C2×C3×C4—102no—
682C2×C3×C4—102no—
683C2×C3×C4—204no—
684C2×C3×C4C23×D512yes—
685#67—44no—
686#67—44no—
687#67—204no—
688#67—204no—
689#67—204no—
690#67—204no—
691#67—204no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—52no—
695C2×Dic3—52no—
696C2×Dic3—52no—
697C2×Dic3—102no—
698C2×Dic3—102no—
699C2×Dic3—102no—
700C2×Dic3—204no—
701C2×Dic3C23×D512yes—
702C2×Dic3C23×D512yes—
703D12—204no—
704D12—204no—
705C4×D3—204no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—22no—
709C22×C5—22no—
710C22×C5—22no—
711C22×C5—22no—
712C22×C5—44no—
713C22×C5—44no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—62no—
717C22×C5—62no—
718C22×C5—62no—
719C22×C5—62no—
720C22×C5—1216no—
721C22×C5—124no—
722C22×C5—124no—
723C22×C5#100412yes—
724C22×C5#100412yes—
725C22×C5#100912yes—
726C22×C5C24×D311yescharacteristic
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—44no—
731C2×D5—62no—
732C2×D5—62no—
733C2×D5—62no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—62no—
737C4×C5—62no—
738Dic5—22no—
739Dic5—22no—
740Dic5—22no—
741Dic5—62no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—31no—
746C24—34no—
747C24—51no—
748C24—122no—
749C24—122no—
750C24—122no—
751C24—151no—
752C24C2×D3×D511yescharacteristic
753C24C2×D3×D511yescharacteristic
754C2×D4—34no—
755C2×D4—34no—
756C2×D4—42no—
757C2×D4—54no—
758C2×D4—54no—
759C2×D4—122no—
760C2×D4—122no—
761C2×D4—154no—
762C2×D4—154no—
763C2×D4—154no—
764C2×D4—154no—
765C2×D4—154no—
766C2×D4—154no—
767C2×D4—154no—
768C2×D4—202no—
769C2×D4—202no—
770C2×D4—602no—
771C2×D4—602no—
772C2×D4—602no—
773C2×D4—602no—
774C2×D4—602no—
775C2×D4—602no—
776C2×D4—602no—
777C2×D4C2×D3×D514yes—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—54no—
784C22×C4—154no—
785C22×C4—151no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—154no—
789C22×C4—202no—
790C22×C4—602no—
791C22×C4—602no—
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—54no—
794C4⋊C4—154no—
795C4⋊C4—154no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4—154no—
799C22⋊C4—34no—
800C22⋊C4—34no—
801C22⋊C4—34no—
802C22⋊C4—54no—
803C22⋊C4—54no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C42—154no—
812C3×C5C2×#56011yescharacteristic, complemented, Hall
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—44no—
820C22×C3—44no—
821C22×C3—102no—
822C22×C3—102no—
823C22×C3—102no—
824C22×C3—204no—
825C22×C3#414412yes—
826C22×C3#414412yes—
827C22×C3#414412yes—
828C22×C3C24×D511yescharacteristic
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—416no—
836C2×D3—44no—
837C2×D3—44no—
838C2×D3—102no—
839C2×D3—102no—
840C2×D3—102no—
841C2×D3—204no—
842C3×C4—22no—
843C3×C4—102no—
844C3×C4—102no—
845C3×C4—102no—
846Dic3—22no—
847Dic3—22no—
848Dic3—102no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—42no—
853C2×C5—122no—
854C2×C5—122no—
855C2×C5#562014yescomplemented
856C2×C5C2×#100411yescharacteristic
857C2×C5C2×#100411yescharacteristic
858C2×C5C2×#100911yescharacteristic
859D5—42no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—32no—
868C23—32no—
869C23—52no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—102no—
877C23—102no—
878C23—102no—
879C23—124no—
880C23—124no—
881C23—124no—
882C23—1216no—
883C23—152no—
884C23—302no—
885C23—302no—
886C23—302no—
887C23C22×D3×D512yes—
888C23C22×D3×D512yes—
889C23C22×D3×D511yescharacteristic
890D4—44no—
891D4—124no—
892D4—124no—
893D4—204no—
894D4—204no—
895D4—604no—
896D4—604no—
897D4—604no—
898D4—604no—
899D4—604no—
900D4—604no—
901D4—604no—
902C2×C4—22no—
903C2×C4—32no—
904C2×C4—32no—
905C2×C4—52no—
906C2×C4—52no—
907C2×C4—52no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—102no—
911C2×C4—102no—
912C2×C4—102no—
913C2×C4—152no—
914C2×C4—152no—
915C2×C4—152no—
916C2×C4—204no—
917C2×C4—302no—
918C2×C4—302no—
919C2×C4—302no—
920C2×C4—604no—
921C2×C4—604no—
922C2×C4C22×D3×D512yes—
923C2×C3—42no—
924C2×C3—42no—
925C2×C3—202no—
926C2×C3#6592914yescomplemented
927C2×C3C2×#414411yescharacteristic
928C2×C3C2×#414411yescharacteristic
929C2×C3C2×#414411yescharacteristic
930D3—42no—
931D3—42no—
932D3—202no—
933C5C2×#562011yescharacteristic, complemented, Sylow
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—44no—
941C22—44no—
942C22—62no—
943C22—62no—
944C22—62no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—102no—
949C22—102no—
950C22—102no—
951C22—1216no—
952C22—124no—
953C22—124no—
954C22—204no—
955C22—302no—
956C22—302no—
957C22—302no—
958C22—604no—
959C22#9202512yes—
960C22#9202712yes—
961C22#9204912yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—62no—
965C4—62no—
966C4—102no—
967C4—102no—
968C4—102no—
969C4—302no—
970C4—302no—
971C4—302no—
972C3C2×#6592911yescharacteristic, complemented, Sylow
973C2—42no—
974C2—42no—
975C2—122no—
976C2—122no—
977C2—202no—
978C2—602no—
979C2#1175498714yesdirect product factor
980C2C2×#9202511yescharacteristic
981C2C2×#9202711yescharacteristic
982C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#560
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91828C2semidirect
2. C2×C5×#937C2semidirect
3. C2×C3×#4084C2semidirect
4. C2×#91571C2semidirect
5. C2×#91570C2semidirect
6. C2×#91568C2semidirect
7. C2×#91567C2semidirect
8. C2×#91557C2semidirect
9. C2×#91543C2semidirect
10. C2×#91533C2semidirect
11. C2×#91531C2semidirect
12. #11754987C2direct (N × H)
13. C2×#91448C2semidirect
14. C2×#91447C2semidirect
15. C2×#91438C2semidirect
16. C2×#91341C2semidirect
21. C22×#1220C22semidirect
22. C23×Dic15C22semidirect
26. C22×C3×C22⋊D5C22semidirect
27. C22×C3×C4×D5C22semidirect
30. C22×#1202C22semidirect
33. C22×#1200C22semidirect
35. #91828C22semidirect
36. C2×#6714C22semidirect
37. C2×#6712C22semidirect
39. C5×#937C22semidirect
43. C2×C3×C22⋊Dic5C22semidirect
44. C3×#4084C22semidirect
45. C2×C3×C4⋊Dic5C22semidirect
46. #91571C22semidirect
47. #91570C22semidirect
48. #91568C22semidirect
49. #91567C22semidirect
50. #91557C22semidirect
51. C2×Dic3⋊Dic5C22semidirect
52. C2×#6669C22semidirect
53. #91543C22semidirect
54. C2×#6668C22semidirect
55. C2×#6668C22semidirect
60. C2×#6665C22semidirect
61. #91533C22semidirect
62. #91531C22semidirect
63. C2×Dic3×Dic5C22semidirect
64. #91448C22semidirect
65. #91447C22semidirect
66. #91438C22semidirect
67. #91341C22semidirect
76. C2×#4084D3semidirect
101. C2×#1220C23semidirect
106. C22×Dic15C23semidirect
116. C2×C3×C22⋊D5C23semidirect
121. C2×C3×C4×D5C23semidirect
127. C2×#1202C23semidirect
133. C2×#1200C23semidirect
135. #6714C23semidirect
136. #6712C23semidirect
141. C3×C22⋊Dic5C23semidirect
142. C3×C4⋊Dic5C23semidirect
143. Dic3⋊Dic5C23semidirect
144. #6669C23semidirect
145. #6668C23semidirect
146. #6668C23semidirect
151. #6665C23semidirect
152. Dic3×Dic5C23semidirect
159. C2×#937D5semidirect
180. C22×C22⋊D5C2×D3semidirect
184. C22×C4×D5C2×D3semidirect
197. C2×C22⋊Dic5C2×D3semidirect
202. #4084C2×D3semidirect
207. C2×C4⋊Dic5C2×D3semidirect
310. #937C2×D5semidirect
366. C2×C22⋊D5C22×D3semidirect
380. C2×C4×D5C22×D3semidirect
390. C22⋊Dic5C22×D3semidirect
394. C4⋊Dic5C22×D3semidirect
636. C2×C3×C5#560semidirect
812. C3×C5C2×#560semidirect
855. C2×C5#5620semidirect
926. C2×C3#65929semidirect
933. C5C2×#5620semidirect
972. C3C2×#65929semidirect
979. C2#11754987direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918282
C2×C5×#9372
C2×C3×#40842
C2×#915712
C2×#915702
C2×#915682
C2×#915672
C2×#915572
C2×#915432
C2×#915332
C2×#915312
#117549872
C2×#914482
C2×#914472
C2×#914382
C2×#913412
C2×#659293
C2×#56205