Finite Group Databasebeta

← C2×#11753298 #14495246

Subgroups — C2×#11753298 #14495246

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×#884C211yesmaximal, characteristic, complemented
3C2×C3×#4032C211yesmaximal, characteristic, complemented
4C2×#91577C211yesmaximal, characteristic, complemented
5C2×#91567C211yesmaximal, characteristic, complemented
6C2×#91566C211yesmaximal, characteristic, complemented
7C2×#91566C211yesmaximal, characteristic, complemented
8C2×#91476C211yesmaximal, characteristic, complemented
9C2×#91475C211yesmaximal, characteristic, complemented
10C2×#91466C211yesmaximal, characteristic, complemented
11C2×#91460C211yesmaximal, characteristic, complemented
12C2×#91452C211yesmaximal, characteristic, complemented
13C2×#91354C211yesmaximal, characteristic, complemented
14C2×#91345C211yesmaximal, characteristic, complemented
15C2×#91341C211yesmaximal, characteristic, complemented
16#11753298C2116yesmaximal, direct product factor
17C2×#65954—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic, complemented
21C22×D60C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic
24C22×C5×#67C2211yescharacteristic, complemented
25C22×C5×D12C2211yescharacteristic
26C22×C4×C5×D3C2211yescharacteristic, complemented
27C22×C3×C22⋊D5C2211yescharacteristic
28C23×C3×Dic5C2211yescharacteristic, complemented
29C22×#1203C2211yescharacteristic
30C22×#1203C2211yescharacteristic
31C22×#1203C2211yescharacteristic, complemented
32C22×#1202C2211yescharacteristic
33C22×#1201C2211yescharacteristic
34C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
35C2×#6714C2211yescharacteristic
36C2×#6712C2211yescharacteristic, complemented
37#91773C2218yescomplemented
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
40C5×#884C2218yescomplemented
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
44C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
45C3×#4032C2218yescomplemented
46#91577C2218yescomplemented
47#91567C2218yescomplemented
48#91566C2218yescomplemented
49#91566C2218yescomplemented
50C2×#6668C2211yescharacteristic, complemented
51C2×#6668C2211yescharacteristic, complemented
52C2×#6667C2211yescharacteristic
53C2×#6667C2211yescharacteristic
54C2×#6667C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
58C2×#6665C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91476C2218yescomplemented
61#91475C2218yescomplemented
62#91466C2218yescomplemented
63#91460C2218yescomplemented
64#91452C2218yescomplemented
65#91354C2218yescomplemented
66#91345C2218yescomplemented
67#91341C2218yescomplemented
68C2×#5666—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4086—31no—
71C2×#4085—31no—
72C2×#4085—31no—
73C2×#4084—31no—
74C2×#4083—31no—
75C2×#4083—31no—
76C2×#4076—31no—
77C2×#4075—31no—
78#65954—316no—
79C2×#4044—31no—
80C2×#4040—31no—
81C2×#4032D311yescharacteristic, complemented
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
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×#67—42no—
109C2×C5×#67C2314yes—
110C2×C5×#67C2314yescomplemented
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C2×C5×D12—42no—
114C2×C5×D12C2314yes—
115C2×C4×C5×D3—42no—
116C2×C4×C5×D3C2314yescomplemented
117C2×C3×C22⋊D5—42no—
118C2×C3×C22⋊D5C2314yes—
119C22×C3×Dic5—42no—
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C22×C3×Dic5C2311yescharacteristic
123C22×C3×Dic5C2314yescomplemented
124C2×#1203—42no—
125C2×#1203—42no—
126C2×#1203—42no—
127C2×#1203C2314yes—
128C2×#1203C2314yes—
129C2×#1203C2314yescomplemented
130C2×#1202—42no—
131C2×#1202C2314yes—
132C2×#1201—42no—
133C2×#1201C2314yes—
134C3×C5×C22⋊C4C2314yescomplemented
135#6714C2314yes—
136#6712C2314yescomplemented
137C5×(C2×D3)⋊C4C2314yes—
138C5×Dic3⋊C4C2314yescomplemented
139C3×#685C2314yes—
140C3×#685C2314yes—
141C3×C4⋊Dic5C2314yescomplemented
142C3×C4⋊Dic5C2314yescomplemented
143#6668C2314yescomplemented
144#6668C2314yescomplemented
145#6667C2314yes—
146#6667C2314yes—
147#6667C2314yescomplemented
148(C2×D3)⋊Dic5C2314yes—
149(C2×D3)⋊Dic5C2314yes—
150(C2×D3)⋊Dic5C2314yescomplemented
151#6665C2314yes—
152Dic3×Dic5C2314yescomplemented
153C2×C3×#123—51no—
154C2×#940—51no—
155C2×#937—51no—
156C2×#930—51no—
157C2×#930—51no—
158#5666—516no—
159C2×#898—51no—
160C2×#898—51no—
161C2×#895—51no—
162C2×#895—51no—
163C2×#884—51no—
164C2×#884D511yescharacteristic, complemented
165C2×#883—51no—
166C2×#883—51no—
167C2×#882—51no—
168C2×#882—51no—
169C24×D5—31no—
170C22×C5×D4—31no—
171C22×C5×D4—31no—
172C22×C5×D4—31no—
173C23×C4×C5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C22×C22⋊D5—31no—
178C22×C22⋊D5—31no—
179C22×C22⋊D5—31no—
180C22×C22⋊D5C2×D311yescharacteristic
181C23×Dic5C2×D311yescharacteristic, complemented
182C22×D20—31no—
183C22×D20—31no—
184C22×C4×D5—31no—
185C5×#121—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C22⋊C4—31no—
188C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5—31no—
191C2×C22⋊Dic5—31no—
192#4086—38no—
193#4085—38no—
194#4085—38no—
195#4084—38no—
196#4083—38no—
197#4083—38no—
198#4076—38no—
199#4075—38no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×#685—31no—
204C2×#685—31no—
205C2×#685C2×D311yescharacteristic
206C2×#685C2×D311yescharacteristic
207C2×C4⋊Dic5C2×D311yescharacteristic, complemented
208C2×C4⋊Dic5C2×D311yescharacteristic, complemented
209C2×#683—31no—
210C2×#683—31no—
211C2×#683—31no—
212C2×C4×Dic5—31no—
213#4044—38no—
214#4040—38no—
215#4032C2×D318yescomplemented
216#4030—38no—
217#4028—38no—
218#4025—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×D3—22no—
237C22×C5×D3—22no—
238C22×C5×D3—22no—
239C22×C5×D3C2412yes—
240C22×C5×D3C2412yes—
241C22×C3×D5—22no—
242C22×C3×D5—22no—
243C22×C3×D5—22no—
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—
262C5×#67—44no—
263C2×C5×Dic3—22no—
264C2×C5×Dic3—22no—
265C2×C5×Dic3C2412yes—
266C2×C5×Dic3C2412yes—
267C5×D12—44no—
268C4×C5×D3—44no—
269C3×C22⋊D5—44no—
270C2×C3×Dic5—22no—
271C2×C3×Dic5—22no—
272C2×C3×Dic5—22no—
273C2×C3×Dic5—44no—
274C2×C3×Dic5C2412yes—
275C2×C3×Dic5C2412yes—
276C2×C3×Dic5C2412yes—
277#1203—44no—
278#1203—44no—
279#1203—44no—
280#1202—44no—
281#1201—44no—
282C24×D3—51no—
283C22×C3×D4—51no—
284C23×C3×C4—51no—
285C22×#67—51no—
286C22×#67—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67C2×D511yescharacteristic
290C22×#67C2×D511yescharacteristic, complemented
291C22×D12—51no—
292C22×D12—51no—
293C22×D12—51no—
294C22×D12—51no—
295C22×D12C2×D511yescharacteristic
296C22×C4×D3—51no—
297C22×C4×D3C2×D511yescharacteristic, complemented
298C3×#123—58no—
299C2×C3×C4⋊C4—51no—
300C2×C3×C4⋊C4—51no—
301C2×C3×C22⋊C4—51no—
302C2×C3×C22⋊C4—51no—
303C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
304C2×#217—51no—
305#940—58no—
306#937—58no—
307#930—58no—
308#930—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)⋊C4C2×D511yescharacteristic
317C2×C4⋊Dic3—51no—
318C2×C4⋊Dic3—51no—
319C2×Dic3⋊C4—51no—
320C2×Dic3⋊C4C2×D511yescharacteristic, complemented
321C2×C4×Dic3—51no—
322#898—58no—
323#898—58no—
324#895—58no—
325#895—58no—
326#884—58no—
327#884C2×D518yescomplemented
328#883—58no—
329#883—58no—
330#882—58no—
331#882—58no—
332C24×C5—31no—
333C24×C5—31no—
334C24×C5C22×D311yescharacteristic
335C23×D5—31no—
336C23×D5—31no—
337C23×D5—34no—
338C23×D5—122no—
339C23×D5—122no—
340C23×D5—122no—
341C23×D5C22×D311yescharacteristic
342C2×C5×D4—34no—
343C2×C5×D4—34no—
344C2×C5×D4—34no—
345C2×C5×D4—122no—
346C2×C5×D4—122no—
347C2×C5×D4—122no—
348C22×C4×C5—31no—
349C22×C4×C5—31no—
350C22×C4×C5—34no—
351C22×C4×C5—122no—
352C22×C4×C5C22×D311yescharacteristic
353C22×C4×C5C22×D311yescharacteristic
354C2×C22⋊D5—34no—
355C2×C22⋊D5—34no—
356C2×C22⋊D5—34no—
357C2×C22⋊D5—34no—
358C2×C22⋊D5—34no—
359C2×C22⋊D5—34no—
360C2×C22⋊D5—42no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5—122no—
363C2×C22⋊D5—122no—
364C2×C22⋊D5—122no—
365C2×C22⋊D5—122no—
366C2×C22⋊D5—122no—
367C2×C22⋊D5C22×D314yes—
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5—42no—
371C22×Dic5C22×D311yescharacteristic
372C22×Dic5C22×D311yescharacteristic
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D314yescomplemented
375C2×D20—34no—
376C2×D20—34no—
377C2×D20—122no—
378C2×D20—122no—
379C2×C4×D5—34no—
380C2×C4×D5—122no—
381C5×C4⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4C22×D314yescomplemented
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685C22×D314yes—
393#685C22×D314yes—
394C4⋊Dic5C22×D314yescomplemented
395C4⋊Dic5C22×D314yescomplemented
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—51no—
405C2×#123—151no—
406C2×#123—151no—
407C2×#121—31no—
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—22no—
436C2×C5×D3—22no—
437C2×C5×D3—22no—
438C2×C5×D3—44no—
439C2×C5×D3—44no—
440C2×C3×D5—22no—
441C2×C3×D5—22no—
442C2×C3×D5—22no—
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—
451C3×Dic5—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3C22×D511yescharacteristic
456C23×D3—51no—
457C23×D3—51no—
458C23×D3—54no—
459C23×D3—202no—
460C23×D3—202no—
461C23×D3—202no—
462C23×D3C22×D511yescharacteristic
463C23×D3C22×D511yescharacteristic
464C2×C3×D4—54no—
465C2×C3×D4—202no—
466C22×C3×C4—51no—
467C22×C3×C4—51no—
468C22×C3×C4—51no—
469C22×C3×C4—54no—
470C22×C3×C4—202no—
471C22×C3×C4C22×D511yescharacteristic
472C22×C3×C4C22×D511yescharacteristic
473C2×#67—42no—
474C2×#67—42no—
475C2×#67—54no—
476C2×#67—54no—
477C2×#67—54no—
478C2×#67—54no—
479C2×#67—202no—
480C2×#67—202no—
481C2×#67—202no—
482C2×#67—202no—
483C2×#67C22×D514yes—
484C2×#67C22×D514yescomplemented
485C22×Dic3—51no—
486C22×Dic3—51no—
487C22×Dic3C22×D511yescharacteristic
488C22×Dic3C22×D511yescharacteristic
489C2×D12—42no—
490C2×D12—54no—
491C2×D12—54no—
492C2×D12—54no—
493C2×D12—54no—
494C2×D12—202no—
495C2×D12—202no—
496C2×D12—202no—
497C2×D12—202no—
498C2×D12C22×D514yes—
499C2×C4×D3—42no—
500C2×C4×D3—54no—
501C2×C4×D3—202no—
502C2×C4×D3C22×D514yescomplemented
503C3×C4⋊C4—54no—
504C3×C4⋊C4—54no—
505C3×C22⋊C4—54no—
506C3×C22⋊C4—54no—
507C3×C22⋊C4C22×D514yescomplemented
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)⋊C4—54no—
515(C2×D3)⋊C4—54no—
516(C2×D3)⋊C4C22×D514yes—
517C4⋊Dic3—54no—
518C4⋊Dic3—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4C22×D514yescomplemented
521C4×Dic3—54no—
522C23×C5—22no—
523C23×C5—22no—
524C23×C5—22no—
525C23×C5—32no—
526C23×C5—32no—
527C23×C5—62no—
528C23×C5—62no—
529C23×C5—62no—
530C23×C5—62no—
531C23×C5—62no—
532C23×C5—62no—
533C23×C5C23×D312yes—
534C23×C5C23×D311yescharacteristic
535C22×D5—22no—
536C22×D5—22no—
537C22×D5—22no—
538C22×D5—32no—
539C22×D5—32no—
540C22×D5—62no—
541C22×D5—62no—
542C22×D5—62no—
543C22×D5—62no—
544C22×D5—62no—
545C22×D5—62no—
546C22×D5—124no—
547C22×D5—124no—
548C22×D5—124no—
549C22×D5—1216no—
550C22×D5C23×D312yes—
551C5×D4—124no—
552C5×D4—124no—
553C5×D4—124no—
554C2×C4×C5—22no—
555C2×C4×C5—22no—
556C2×C4×C5—32no—
557C2×C4×C5—32no—
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—124no—
565C22⋊D5—124no—
566C22⋊D5—124no—
567C22⋊D5—124no—
568C22⋊D5—124no—
569C22⋊D5—124no—
570C2×Dic5—22no—
571C2×Dic5—22no—
572C2×Dic5—22no—
573C2×Dic5—32no—
574C2×Dic5—32no—
575C2×Dic5—44no—
576C2×Dic5—62no—
577C2×Dic5—62no—
578C2×Dic5C23×D312yes—
579C2×Dic5C23×D312yes—
580C2×Dic5C23×D312yes—
581D20—124no—
582D20—124no—
583C4×D5—124no—
584C25—151no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
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—58no—
604#123—158no—
605#123—158no—
606#121—38no—
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—51no—
617C2×C4⋊C4—51no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4—151no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—51no—
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—
642C5×D3—42no—
643C5×D3—42no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—52no—
648C23×C3—102no—
649C23×C3—102no—
650C23×C3—102no—
651C23×C3C23×D512yes—
652C23×C3C23×D511yescharacteristic
653C22×D3—22no—
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—52no—
660C22×D3—52no—
661C22×D3—102no—
662C22×D3—102no—
663C22×D3—102no—
664C22×D3—102no—
665C22×D3—102no—
666C22×D3—102no—
667C22×D3—204no—
668C22×D3—204no—
669C22×D3—204no—
670C22×D3—2016no—
671C22×D3C23×D512yes—
672C22×D3C23×D512yes—
673C3×D4—204no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—52no—
677C2×C3×C4—52no—
678C2×C3×C4—52no—
679C2×C3×C4—102no—
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—44no—
687#67—204no—
688#67—204no—
689#67—204no—
690#67—204no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—52no—
694C2×Dic3—52no—
695C2×Dic3—102no—
696C2×Dic3—102no—
697C2×Dic3C23×D512yes—
698C2×Dic3C23×D512yes—
699D12—44no—
700D12—204no—
701D12—204no—
702D12—204no—
703D12—204no—
704C4×D3—44no—
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—62no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—124no—
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—1216no—
733C2×D5—124no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—22no—
737C4×C5—62no—
738C4×C5—62no—
739Dic5—22no—
740Dic5—22no—
741Dic5—22no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—31no—
746C24—51no—
747C24—154no—
748C24—151no—
749C24—151no—
750C24—602no—
751C24—602no—
752C24—602no—
753C24C2×D3×D511yescharacteristic
754C2×D4—34no—
755C2×D4—34no—
756C2×D4—34no—
757C2×D4—54no—
758C2×D4—122no—
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—154no—
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—34no—
781C22×C4—51no—
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—54no—
795C4⋊C4—54no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4—154no—
799C22⋊C4—34no—
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⋊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—204no—
821C22×C3#414412yes—
822C22×C3#414412yes—
823C22×C3#414912yes—
824C22×C3C24×D511yescharacteristic
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—44no—
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—
846C3×C4—102no—
847Dic3—22no—
848Dic3—22no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—122no—
853C2×C5—122no—
854C2×C5#566614yescomplemented
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#100911yescharacteristic
857C2×C5C2×#100911yescharacteristic
858D5—42no—
859D5—122no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—32no—
865C23—32no—
866C23—52no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
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—124no—
892D4—124no—
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—52no—
907C2×C4—52no—
908C2×C4—52no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—102no—
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#6595414yescomplemented
926C2×C3C2×#414411yescharacteristic
927C2×C3C2×#414411yescharacteristic
928C2×C3C2×#414911yescharacteristic
929D3—42no—
930D3—42no—
931D3—202no—
932D3—202no—
933C5C2×#566611yescharacteristic, complemented, Sylow
934C22—22no—
935C22—22no—
936C22—22no—
937C22—44no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—62no—
943C22—62no—
944C22—102no—
945C22—102no—
946C22—102no—
947C22—124no—
948C22—124no—
949C22—204no—
950C22—302no—
951C22—302no—
952C22—302no—
953C22—302no—
954C22—302no—
955C22—302no—
956C22—6016no—
957C22—604no—
958C22—604no—
959C22#9201712yes—
960C22#9202712yes—
961C22#9202712yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—62no—
966C4—62no—
967C4—102no—
968C4—102no—
969C4—102no—
970C4—302no—
971C4—302no—
972C3C2×#6595411yescharacteristic, complemented, Sylow
973C2—42no—
974C2—122no—
975C2—122no—
976C2—202no—
977C2—602no—
978C2—602no—
979C2#1175329814yesdirect product factor
980C2C2×#9201711yescharacteristic
981C2C2×#9202711yescharacteristic
982C2C2×#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×#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×#884C2semidirect
3. C2×C3×#4032C2semidirect
4. C2×#91577C2semidirect
5. C2×#91567C2semidirect
6. C2×#91566C2semidirect
7. C2×#91566C2semidirect
8. C2×#91476C2semidirect
9. C2×#91475C2semidirect
10. C2×#91466C2semidirect
11. C2×#91460C2semidirect
12. C2×#91452C2semidirect
13. C2×#91354C2semidirect
14. C2×#91345C2semidirect
15. C2×#91341C2semidirect
16. #11753298C2direct (N × H)
20. C22×#1220C22semidirect
22. C22×C4×D15C22semidirect
24. C22×C5×#67C22semidirect
26. C22×C4×C5×D3C22semidirect
28. C23×C3×Dic5C22semidirect
31. C22×#1203C22semidirect
34. C2×C3×C5×C22⋊C4C22semidirect
36. C2×#6712C22semidirect
37. #91773C22semidirect
39. C2×C5×Dic3⋊C4C22semidirect
40. C5×#884C22semidirect
43. C2×C3×C4⋊Dic5C22semidirect
44. C2×C3×C4⋊Dic5C22semidirect
45. C3×#4032C22semidirect
46. #91577C22semidirect
47. #91567C22semidirect
48. #91566C22semidirect
49. #91566C22semidirect
50. C2×#6668C22semidirect
51. C2×#6668C22semidirect
54. C2×#6667C22semidirect
57. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91476C22semidirect
61. #91475C22semidirect
62. #91466C22semidirect
63. #91460C22semidirect
64. #91452C22semidirect
65. #91354C22semidirect
66. #91345C22semidirect
67. #91341C22semidirect
81. C2×#4032D3semidirect
100. C2×#1220C23semidirect
106. C2×C4×D15C23semidirect
110. C2×C5×#67C23semidirect
116. C2×C4×C5×D3C23semidirect
123. C22×C3×Dic5C23semidirect
129. C2×#1203C23semidirect
134. C3×C5×C22⋊C4C23semidirect
136. #6712C23semidirect
138. C5×Dic3⋊C4C23semidirect
141. C3×C4⋊Dic5C23semidirect
142. C3×C4⋊Dic5C23semidirect
143. #6668C23semidirect
144. #6668C23semidirect
147. #6667C23semidirect
150. (C2×D3)⋊Dic5C23semidirect
152. Dic3×Dic5C23semidirect
164. C2×#884D5semidirect
181. C23×Dic5C2×D3semidirect
188. C2×C5×C22⋊C4C2×D3semidirect
207. C2×C4⋊Dic5C2×D3semidirect
208. C2×C4⋊Dic5C2×D3semidirect
215. #4032C2×D3semidirect
290. C22×#67C2×D5semidirect
297. C22×C4×D3C2×D5semidirect
303. C2×C3×C22⋊C4C2×D5semidirect
320. C2×Dic3⋊C4C2×D5semidirect
327. #884C2×D5semidirect
374. C22×Dic5C22×D3semidirect
383. C5×C22⋊C4C22×D3semidirect
394. C4⋊Dic5C22×D3semidirect
395. C4⋊Dic5C22×D3semidirect
484. C2×#67C22×D5semidirect
502. C2×C4×D3C22×D5semidirect
507. C3×C22⋊C4C22×D5semidirect
520. Dic3⋊C4C22×D5semidirect
632. C2×C22⋊C4D3×D5semidirect
635. C2×C3×C5#560semidirect
810. C22⋊C4C2×D3×D5semidirect
812. C3×C5C2×#560semidirect
854. C2×C5#5666semidirect
925. C2×C3#65954semidirect
933. C5C2×#5666semidirect
972. C3C2×#65954semidirect
979. C2#11753298direct (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×#8842
C2×C3×#40322
C2×#915772
C2×#915672
C2×#915662
C2×#914762
C2×#914752
C2×#914662
C2×#914602
C2×#914522
C2×#913542
C2×#913452
C2×#913412
#117532982
C2×#659543
C2×#56665