Finite Group Databasebeta

← C2×#11753302 #14495245

Subgroups — C2×#11753302 #14495245

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×#91773C211yesmaximal, characteristic, complemented
2C2×C5×#886C211yesmaximal, characteristic, complemented
3C2×C3×#4030C211yesmaximal, characteristic, complemented
4C2×#91577C211yesmaximal, characteristic, complemented
5C2×#91569C211yesmaximal, characteristic, complemented
6C2×#91569C211yesmaximal, characteristic, complemented
7C2×#91567C211yesmaximal, characteristic, complemented
8C2×#91476C211yesmaximal, characteristic, complemented
9C2×#91474C211yesmaximal, characteristic, complemented
10C2×#91465C211yesmaximal, characteristic, complemented
11C2×#91450C211yesmaximal, characteristic, complemented
12C2×#91447C211yesmaximal, characteristic, complemented
13C2×#91361C211yesmaximal, characteristic, complemented
14C2×#91355C211yesmaximal, characteristic, complemented
15C2×#91337C211yesmaximal, characteristic, complemented
16#11753302C2116yesmaximal, direct product factor
17C2×#66000—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic, complemented
21C22×D60C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic
24C23×C5×Dic3C2211yescharacteristic, complemented
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×C22⋊D5C2211yescharacteristic, complemented
27C22×C3×D20C2211yescharacteristic
28C22×C3×C4×D5C2211yescharacteristic, complemented
29C22×#1203C2211yescharacteristic
30C22×#1202C2211yescharacteristic
31C22×#1202C2211yescharacteristic
32C22×#1202C2211yescharacteristic, complemented
33C22×#1201C2211yescharacteristic
34C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
35C2×#6714C2211yescharacteristic
36C2×#6712C2211yescharacteristic, complemented
37#91773C2218yescomplemented
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×(C2×D3)⋊C4C2211yescharacteristic
40C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
41C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
42C5×#886C2218yescomplemented
43C2×C3×#685C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic, complemented
45C3×#4030C2218yescomplemented
46#91577C2218yescomplemented
47#91569C2218yescomplemented
48#91569C2218yescomplemented
49#91567C2218yescomplemented
50C2×Dic3⋊Dic5C2211yescharacteristic, complemented
51C2×Dic3⋊Dic5C2211yescharacteristic, complemented
52C2×#6667C2211yescharacteristic
53C2×#6667C2211yescharacteristic
54C2×#6667C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×#6665C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic, complemented
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91476C2218yescomplemented
61#91474C2218yescomplemented
62#91465C2218yescomplemented
63#91450C2218yescomplemented
64#91447C2218yescomplemented
65#91361C2218yescomplemented
66#91355C2218yescomplemented
67#91337C2218yescomplemented
68C2×#5620—51nomaximal, Hall
69C2×C5×#123—31no—
70C2×#4086—31no—
71C2×#4083—31no—
72C2×#4076—31no—
73C2×#4076—31no—
74#66000—316no—
75C2×#4044—31no—
76C2×#4044—31no—
77C2×#4041—31no—
78C2×#4041—31no—
79C2×#4030—31no—
80C2×#4030D311yescharacteristic, complemented
81C2×#4029—31no—
82C2×#4029—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C3×D5C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C22×D3×D5—42no—
92C22×D3×D5—42no—
93C22×D3×D5—42no—
94C22×D3×D5C2314yes—
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C2×#1220—42no—
98C2×#1220—42no—
99C2×#1220C2314yes—
100C2×#1220C2314yescomplemented
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2311yescharacteristic
103C2×D60—42no—
104C2×D60C2314yes—
105C2×C4×D15—42no—
106C2×C4×D15C2314yescomplemented
107C2×C5×#67—42no—
108C2×C5×#67C2314yes—
109C22×C5×Dic3—42no—
110C22×C5×Dic3C2311yescharacteristic
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C22×C5×Dic3C2314yescomplemented
114C2×C3×C22⋊D5—42no—
115C2×C3×C22⋊D5—42no—
116C2×C3×C22⋊D5C2314yes—
117C2×C3×C22⋊D5C2314yescomplemented
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2311yescharacteristic
120C2×C3×D20—42no—
121C2×C3×D20C2314yes—
122C2×C3×C4×D5—42no—
123C2×C3×C4×D5C2314yescomplemented
124C2×#1203—42no—
125C2×#1203C2314yes—
126C2×#1202—42no—
127C2×#1202—42no—
128C2×#1202—42no—
129C2×#1202C2314yes—
130C2×#1202C2314yes—
131C2×#1202C2314yescomplemented
132C2×#1201—42no—
133C2×#1201C2314yes—
134C3×C5×C22⋊C4C2314yescomplemented
135#6714C2314yes—
136#6712C2314yescomplemented
137C5×(C2×D3)⋊C4C2314yes—
138C5×(C2×D3)⋊C4C2314yes—
139C5×C4⋊Dic3C2314yescomplemented
140C5×C4⋊Dic3C2314yescomplemented
141C3×#685C2314yes—
142C3×#683C2314yescomplemented
143Dic3⋊Dic5C2314yescomplemented
144Dic3⋊Dic5C2314yescomplemented
145#6667C2314yes—
146#6667C2314yes—
147#6667C2314yescomplemented
148(C2×D3)⋊Dic5C2314yes—
149#6665C2314yes—
150#6665C2314yes—
151#6665C2314yescomplemented
152Dic3×Dic5C2314yescomplemented
153C2×C3×#121—51no—
154C2×#940—51no—
155C2×#939—51no—
156C2×#939—51no—
157C2×#938—51no—
158C2×#937—51no—
159C2×#937—51no—
160C2×#930—51no—
161C2×#929—51no—
162#5620—516no—
163C2×#898—51no—
164C2×#894—51no—
165C2×#886D511yescharacteristic, complemented
166C2×#884—51no—
167C2×#882—51no—
168C2×#879—51no—
169C24×D5—31no—
170C22×C5×D4—31no—
171C23×C4×C5—31no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5C2×D311yescharacteristic
177C22×C22⋊D5C2×D311yescharacteristic, complemented
178C22×D20—31no—
179C22×D20—31no—
180C22×D20—31no—
181C22×D20—31no—
182C22×D20C2×D311yescharacteristic
183C22×C4×D5—31no—
184C22×C4×D5C2×D311yescharacteristic, complemented
185C5×#123—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C4⋊C4—31no—
188C2×C5×C22⋊C4—31no—
189C2×C5×C22⋊C4—31no—
190C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
191C2×C22⋊Dic5—31no—
192#4086—38no—
193#4083—38no—
194#4076—38no—
195#4076—38no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×#685—31no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×#685C2×D311yescharacteristic
204C2×C4⋊Dic5—31no—
205C2×C4⋊Dic5—31no—
206C2×#683—31no—
207C2×#683C2×D311yescharacteristic, complemented
208C2×C4×Dic5—31no—
209#4044—38no—
210#4044—38no—
211#4041—38no—
212#4041—38no—
213#4030—38no—
214#4030C2×D318yescomplemented
215#4029—38no—
216#4029—38no—
217#4028—38no—
218#4028—38no—
219C2×#560—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×D15C2412yes—
232C22×D15C2412yes—
233C22×C5×D3—22no—
234C22×C5×D3—22no—
235C22×C5×D3—22no—
236C22×C5×D3C2412yes—
237C22×C3×D5—22no—
238C22×C3×D5—22no—
239C22×C3×D5—22no—
240C22×C3×D5—22no—
241C22×C3×D5—22no—
242C22×C3×D5—22no—
243C22×C3×D5C2412yes—
244C22×C3×D5C2412yes—
245C2×D3×D5—44no—
246C2×D3×D5—44no—
247C2×D3×D5—44no—
248C2×D3×D5—416no—
249C2×C3×C4×C5—22no—
250C2×C3×C4×C5—22no—
251C2×C3×C4×C5C2412yes—
252C2×C3×C4×C5C2412yes—
253#1220—44no—
254#1220—44no—
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15C2412yes—
258C2×Dic15C2412yes—
259D60—44no—
260C4×D15—44no—
261C5×#67—44no—
262C2×C5×Dic3—22no—
263C2×C5×Dic3—22no—
264C2×C5×Dic3—22no—
265C2×C5×Dic3—44no—
266C2×C5×Dic3C2412yes—
267C2×C5×Dic3C2412yes—
268C2×C5×Dic3C2412yes—
269C3×C22⋊D5—44no—
270C3×C22⋊D5—44no—
271C2×C3×Dic5—22no—
272C2×C3×Dic5—22no—
273C2×C3×Dic5C2412yes—
274C2×C3×Dic5C2412yes—
275C3×D20—44no—
276C3×C4×D5—44no—
277#1203—44no—
278#1202—44no—
279#1202—44no—
280#1202—44no—
281#1201—44no—
282C24×D3—51no—
283C22×C3×D4—51no—
284C22×C3×D4—51no—
285C22×C3×D4—51no—
286C23×C3×C4—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×#67—51no—
292C22×#67—51no—
293C22×#67C2×D511yescharacteristic
294C23×Dic3C2×D511yescharacteristic, complemented
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⋊C4C2×D511yescharacteristic, complemented
302C2×#217—51no—
303C2×#217—51no—
304C2×#217—51no—
305#940—58no—
306#939—58no—
307#939—58no—
308#938—58no—
309#937—58no—
310#937—58no—
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⋊Dic3C2×D511yescharacteristic, complemented
321C2×C4⋊Dic3C2×D511yescharacteristic, complemented
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4—51no—
324C2×Dic3⋊C4—51no—
325C2×C4×Dic3—51no—
326#898—58no—
327#894—58no—
328#886C2×D518yescomplemented
329#884—58no—
330#882—58no—
331#879—58no—
332C24×C5—31no—
333C24×C5C22×D311yescharacteristic
334C23×D5—31no—
335C23×D5—31no—
336C23×D5—34no—
337C23×D5—122no—
338C23×D5—122no—
339C23×D5—122no—
340C23×D5C22×D311yescharacteristic
341C23×D5C22×D311yescharacteristic
342C2×C5×D4—34no—
343C2×C5×D4—122no—
344C22×C4×C5—31no—
345C22×C4×C5—31no—
346C22×C4×C5—31no—
347C22×C4×C5—34no—
348C22×C4×C5—122no—
349C22×C4×C5C22×D311yescharacteristic
350C22×C4×C5C22×D311yescharacteristic
351C2×C22⋊D5—34no—
352C2×C22⋊D5—34no—
353C2×C22⋊D5—34no—
354C2×C22⋊D5—34no—
355C2×C22⋊D5—42no—
356C2×C22⋊D5—42no—
357C2×C22⋊D5—122no—
358C2×C22⋊D5—122no—
359C2×C22⋊D5—122no—
360C2×C22⋊D5—122no—
361C2×C22⋊D5C22×D314yes—
362C2×C22⋊D5C22×D314yescomplemented
363C22×Dic5—31no—
364C22×Dic5—31no—
365C22×Dic5C22×D311yescharacteristic
366C22×Dic5C22×D311yescharacteristic
367C2×D20—34no—
368C2×D20—34no—
369C2×D20—34no—
370C2×D20—34no—
371C2×D20—42no—
372C2×D20—122no—
373C2×D20—122no—
374C2×D20—122no—
375C2×D20—122no—
376C2×D20C22×D314yes—
377C2×C4×D5—34no—
378C2×C4×D5—42no—
379C2×C4×D5—122no—
380C2×C4×D5C22×D314yescomplemented
381C5×C4⋊C4—34no—
382C5×C4⋊C4—34no—
383C5×C22⋊C4—34no—
384C5×C22⋊C4—34no—
385C5×C22⋊C4C22×D314yescomplemented
386C22⋊Dic5—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685—34no—
393#685—34no—
394#685C22×D314yes—
395C4⋊Dic5—34no—
396C4⋊Dic5—34no—
397#683—34no—
398#683C22×D314yescomplemented
399C4×Dic5—34no—
400#560—1516no—
401C2×#127—151no—
402C2×#126—151no—
403C2×#126—151no—
404C2×#123—31no—
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—151no—
414C2×#120—151no—
415C2×#120—151no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—44no—
420C22×C3×C5H(5,𝔽2)12yes—
421C22×C3×C5H(5,𝔽2)12yes—
422C22×C3×C5H(5,𝔽2)12yes—
423C22×C3×C5C2511yescharacteristic
424C2×D15—22no—
425C2×D15—22no—
426C2×D15—22no—
427C2×D15—22no—
428C2×D15—22no—
429C2×D15—22no—
430C2×D15—44no—
431C2×D15—44no—
432C2×C5×D3—22no—
433C2×C5×D3—22no—
434C2×C5×D3—22no—
435C2×C5×D3—44no—
436C2×C3×D5—22no—
437C2×C3×D5—22no—
438C2×C3×D5—22no—
439C2×C3×D5—22no—
440C2×C3×D5—22no—
441C2×C3×D5—22no—
442C2×C3×D5—44no—
443C2×C3×D5—44no—
444D3×D5—416no—
445C3×C4×C5—22no—
446C3×C4×C5—22no—
447Dic15—22no—
448Dic15—22no—
449C3×Dic5—22no—
450C3×Dic5—22no—
451C5×Dic3—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3—51no—
456C24×C3C22×D511yescharacteristic
457C23×D3—51no—
458C23×D3—51no—
459C23×D3—54no—
460C23×D3—202no—
461C23×D3—202no—
462C23×D3—202no—
463C23×D3C22×D511yescharacteristic
464C2×C3×D4—54no—
465C2×C3×D4—54no—
466C2×C3×D4—54no—
467C2×C3×D4—202no—
468C2×C3×D4—202no—
469C2×C3×D4—202no—
470C22×C3×C4—51no—
471C22×C3×C4—51no—
472C22×C3×C4—54no—
473C22×C3×C4—202no—
474C22×C3×C4C22×D511yescharacteristic
475C22×C3×C4C22×D511yescharacteristic
476C2×#67—42no—
477C2×#67—54no—
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×#67—202no—
489C2×#67C22×D514yes—
490C22×Dic3—42no—
491C22×Dic3—51no—
492C22×Dic3—51no—
493C22×Dic3C22×D511yescharacteristic
494C22×Dic3C22×D511yescharacteristic
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D514yescomplemented
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⋊C4C22×D514yescomplemented
506#217—54no—
507#217—54no—
508#217—54no—
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⋊Dic3C22×D514yescomplemented
517C4⋊Dic3C22×D514yescomplemented
518Dic3⋊C4—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4—54no—
521C4×Dic3—54no—
522C23×C5—22no—
523C23×C5—22no—
524C23×C5—22no—
525C23×C5—32no—
526C23×C5—62no—
527C23×C5—62no—
528C23×C5—62no—
529C23×C5C23×D312yes—
530C23×C5C23×D311yescharacteristic
531C22×D5—22no—
532C22×D5—22no—
533C22×D5—22no—
534C22×D5—22no—
535C22×D5—22no—
536C22×D5—22no—
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—124no—
546C22×D5—124no—
547C22×D5—124no—
548C22×D5—1216no—
549C22×D5C23×D312yes—
550C22×D5C23×D312yes—
551C5×D4—124no—
552C2×C4×C5—22no—
553C2×C4×C5—22no—
554C2×C4×C5—32no—
555C2×C4×C5—32no—
556C2×C4×C5—32no—
557C2×C4×C5—62no—
558C2×C4×C5—62no—
559C2×C4×C5—62no—
560C2×C4×C5—124no—
561C2×C4×C5C23×D312yes—
562C2×C4×C5C23×D312yes—
563C22⋊D5—44no—
564C22⋊D5—44no—
565C22⋊D5—124no—
566C22⋊D5—124no—
567C22⋊D5—124no—
568C22⋊D5—124no—
569C2×Dic5—22no—
570C2×Dic5—22no—
571C2×Dic5—32no—
572C2×Dic5—32no—
573C2×Dic5—62no—
574C2×Dic5—62no—
575C2×Dic5C23×D312yes—
576C2×Dic5C23×D312yes—
577D20—44no—
578D20—124no—
579D20—124no—
580D20—124no—
581D20—124no—
582C4×D5—44no—
583C4×D5—124no—
584C25—151no—
585C22×D4—31no—
586C22×D4—51no—
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×D4—151no—
597C23×C4—31no—
598C23×C4—51no—
599C23×C4—151no—
600#127—158no—
601#126—158no—
602#126—158no—
603#123—38no—
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—158no—
613#120—158no—
614#120—158no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—31no—
617C2×C4⋊C4—51no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4—151no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—51no—
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⋊C4D3×D511yescharacteristic, complemented
633C2×C42—151no—
634C2×C3×C5—42no—
635C2×C3×C5#56014yescomplemented
636C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
637C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
638C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
639D15—42no—
640D15—42no—
641C3×D5—42no—
642C3×D5—42no—
643C5×D3—42no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—52no—
648C23×C3—52no—
649C23×C3—102no—
650C23×C3—102no—
651C23×C3—102no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3—102no—
655C23×C3C23×D512yes—
656C23×C3C23×D511yescharacteristic
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
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—204no—
669C22×D3—204no—
670C22×D3—204no—
671C22×D3—2016no—
672C22×D3C23×D512yes—
673C3×D4—204no—
674C3×D4—204no—
675C3×D4—204no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—52no—
679C2×C3×C4—52no—
680C2×C3×C4—102no—
681C2×C3×C4—102no—
682C2×C3×C4—204no—
683C2×C3×C4C23×D512yes—
684C2×C3×C4C23×D512yes—
685#67—44no—
686#67—204no—
687#67—204no—
688#67—204no—
689#67—204no—
690#67—204no—
691#67—204no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—44no—
696C2×Dic3—52no—
697C2×Dic3—52no—
698C2×Dic3—102no—
699C2×Dic3—102no—
700C2×Dic3C23×D512yes—
701C2×Dic3C23×D512yes—
702C2×Dic3C23×D512yes—
703D12—204no—
704D12—204no—
705C4×D3—204no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—22no—
709C22×C5—44no—
710C22×C5—62no—
711C22×C5—62no—
712C22×C5—62no—
713C22×C5—124no—
714C22×C5#100412yes—
715C22×C5#100412yes—
716C22×C5#100912yes—
717C22×C5C24×D311yescharacteristic
718C2×D5—22no—
719C2×D5—22no—
720C2×D5—22no—
721C2×D5—22no—
722C2×D5—22no—
723C2×D5—22no—
724C2×D5—44no—
725C2×D5—44no—
726C2×D5—62no—
727C2×D5—62no—
728C2×D5—62no—
729C2×D5—62no—
730C2×D5—62no—
731C2×D5—62no—
732C2×D5—1216no—
733C2×D5—124no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—22no—
737C4×C5—62no—
738C4×C5—62no—
739C4×C5—62no—
740Dic5—22no—
741Dic5—22no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—51no—
746C24—51no—
747C24—154no—
748C24—151no—
749C24—151no—
750C24—602no—
751C24—602no—
752C24—602no—
753C24C2×D3×D511yescharacteristic
754C2×D4—34no—
755C2×D4—54no—
756C2×D4—54no—
757C2×D4—54no—
758C2×D4—122no—
759C2×D4—154no—
760C2×D4—154no—
761C2×D4—154no—
762C2×D4—154no—
763C2×D4—154no—
764C2×D4—154no—
765C2×D4—154no—
766C2×D4—154no—
767C2×D4—202no—
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×D4—602no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—34no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—54no—
785C22×C4—122no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—154no—
789C22×C4—202no—
790C22×C4—602no—
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—34no—
794C4⋊C4—34no—
795C4⋊C4—54no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4—154no—
799C22⋊C4—34no—
800C22⋊C4—34no—
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⋊C4C2×D3×D514yescomplemented
811C42—154no—
812C3×C5C2×#56011yescharacteristic, complemented, Hall
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—44no—
817C22×C3—102no—
818C22×C3—102no—
819C22×C3—102no—
820C22×C3—102no—
821C22×C3—102no—
822C22×C3—102no—
823C22×C3—204no—
824C22×C3—204no—
825C22×C3#414412yes—
826C22×C3#414912yes—
827C22×C3#414912yes—
828C22×C3C24×D511yescharacteristic
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—44no—
833C2×D3—102no—
834C2×D3—102no—
835C2×D3—102no—
836C2×D3—102no—
837C2×D3—102no—
838C2×D3—102no—
839C2×D3—2016no—
840C2×D3—204no—
841C2×D3—204no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—102no—
845C3×C4—102no—
846Dic3—22no—
847Dic3—22no—
848Dic3—22no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—122no—
853C2×C5#562014yescomplemented
854C2×C5C2×#100411yescharacteristic
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#100911yescharacteristic
857D5—42no—
858D5—42no—
859D5—122no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—32no—
865C23—52no—
866C23—52no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—102no—
871C23—102no—
872C23—102no—
873C23—102no—
874C23—102no—
875C23—102no—
876C23—152no—
877C23—152no—
878C23—302no—
879C23—302no—
880C23—302no—
881C23—302no—
882C23—302no—
883C23—302no—
884C23—604no—
885C23—604no—
886C23—604no—
887C23—6016no—
888C23C22×D3×D512yes—
889C23C22×D3×D511yescharacteristic
890D4—124no—
891D4—204no—
892D4—204no—
893D4—204no—
894D4—604no—
895D4—604no—
896D4—604no—
897D4—604no—
898D4—604no—
899D4—604no—
900D4—604no—
901D4—604no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—52no—
908C2×C4—52no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—102no—
913C2×C4—102no—
914C2×C4—124no—
915C2×C4—152no—
916C2×C4—152no—
917C2×C4—204no—
918C2×C4—302no—
919C2×C4—302no—
920C2×C4—604no—
921C2×C4C22×D3×D512yes—
922C2×C4C22×D3×D512yes—
923C2×C3—42no—
924C2×C3—202no—
925C2×C3—202no—
926C2×C3#6600014yescomplemented
927C2×C3C2×#414411yescharacteristic
928C2×C3C2×#414911yescharacteristic
929C2×C3C2×#414911yescharacteristic
930D3—42no—
931D3—202no—
932D3—202no—
933C5C2×#562011yescharacteristic, complemented, Sylow
934C22—22no—
935C22—22no—
936C22—22no—
937C22—44no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—102no—
942C22—102no—
943C22—102no—
944C22—102no—
945C22—102no—
946C22—102no—
947C22—124no—
948C22—204no—
949C22—204no—
950C22—302no—
951C22—302no—
952C22—302no—
953C22—302no—
954C22—302no—
955C22—302no—
956C22—6016no—
957C22—604no—
958C22—604no—
959C22#9201812yes—
960C22#9202612yes—
961C22#9202612yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—62no—
966C4—62no—
967C4—62no—
968C4—102no—
969C4—102no—
970C4—302no—
971C4—302no—
972C3C2×#6600011yescharacteristic, complemented, Sylow
973C2—42no—
974C2—122no—
975C2—202no—
976C2—202no—
977C2—602no—
978C2—602no—
979C2#1175330214yesdirect product factor
980C2C2×#9201811yescharacteristic
981C2C2×#9202611yescharacteristic
982C2C2×#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×#560
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×#91773C2semidirect
2. C2×C5×#886C2semidirect
3. C2×C3×#4030C2semidirect
4. C2×#91577C2semidirect
5. C2×#91569C2semidirect
6. C2×#91569C2semidirect
7. C2×#91567C2semidirect
8. C2×#91476C2semidirect
9. C2×#91474C2semidirect
10. C2×#91465C2semidirect
11. C2×#91450C2semidirect
12. C2×#91447C2semidirect
13. C2×#91361C2semidirect
14. C2×#91355C2semidirect
15. C2×#91337C2semidirect
16. #11753302C2direct (N × H)
20. C22×#1220C22semidirect
22. C22×C4×D15C22semidirect
24. C23×C5×Dic3C22semidirect
26. C22×C3×C22⋊D5C22semidirect
28. C22×C3×C4×D5C22semidirect
32. C22×#1202C22semidirect
34. C2×C3×C5×C22⋊C4C22semidirect
36. C2×#6712C22semidirect
37. #91773C22semidirect
40. C2×C5×C4⋊Dic3C22semidirect
41. C2×C5×C4⋊Dic3C22semidirect
42. C5×#886C22semidirect
44. C2×C3×#683C22semidirect
45. C3×#4030C22semidirect
46. #91577C22semidirect
47. #91569C22semidirect
48. #91569C22semidirect
49. #91567C22semidirect
50. C2×Dic3⋊Dic5C22semidirect
51. C2×Dic3⋊Dic5C22semidirect
54. C2×#6667C22semidirect
58. C2×#6665C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91476C22semidirect
61. #91474C22semidirect
62. #91465C22semidirect
63. #91450C22semidirect
64. #91447C22semidirect
65. #91361C22semidirect
66. #91355C22semidirect
67. #91337C22semidirect
80. C2×#4030D3semidirect
100. C2×#1220C23semidirect
106. C2×C4×D15C23semidirect
113. C22×C5×Dic3C23semidirect
117. C2×C3×C22⋊D5C23semidirect
123. C2×C3×C4×D5C23semidirect
131. C2×#1202C23semidirect
134. C3×C5×C22⋊C4C23semidirect
136. #6712C23semidirect
139. C5×C4⋊Dic3C23semidirect
140. C5×C4⋊Dic3C23semidirect
142. C3×#683C23semidirect
143. Dic3⋊Dic5C23semidirect
144. Dic3⋊Dic5C23semidirect
147. #6667C23semidirect
151. #6665C23semidirect
152. Dic3×Dic5C23semidirect
165. C2×#886D5semidirect
177. C22×C22⋊D5C2×D3semidirect
184. C22×C4×D5C2×D3semidirect
190. C2×C5×C22⋊C4C2×D3semidirect
207. C2×#683C2×D3semidirect
214. #4030C2×D3semidirect
294. C23×Dic3C2×D5semidirect
301. C2×C3×C22⋊C4C2×D5semidirect
320. C2×C4⋊Dic3C2×D5semidirect
321. C2×C4⋊Dic3C2×D5semidirect
328. #886C2×D5semidirect
362. C2×C22⋊D5C22×D3semidirect
380. C2×C4×D5C22×D3semidirect
385. C5×C22⋊C4C22×D3semidirect
398. #683C22×D3semidirect
496. C22×Dic3C22×D5semidirect
505. C3×C22⋊C4C22×D5semidirect
516. C4⋊Dic3C22×D5semidirect
517. C4⋊Dic3C22×D5semidirect
632. C2×C22⋊C4D3×D5semidirect
635. C2×C3×C5#560semidirect
810. C22⋊C4C2×D3×D5semidirect
812. C3×C5C2×#560semidirect
853. C2×C5#5620semidirect
926. C2×C3#66000semidirect
933. C5C2×#5620semidirect
972. C3C2×#66000semidirect
979. C2#11753302direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917732
C2×C5×#8862
C2×C3×#40302
C2×#915772
C2×#915692
C2×#915672
C2×#914762
C2×#914742
C2×#914652
C2×#914502
C2×#914472
C2×#913612
C2×#913552
C2×#913372
#117533022
C2×#660003
C2×#56205