Finite Group Databasebeta

← C2×#11753940 #14495243

Subgroups — C2×#11753940 #14495243

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×#91787C211yesmaximal, characteristic, complemented
2C2×C5×#895C211yesmaximal, characteristic, complemented
3C2×C3×#4040C211yesmaximal, characteristic, complemented
4C2×#91475C211yesmaximal, characteristic, complemented
5C2×#91475C211yesmaximal, characteristic, complemented
6C2×#91474C211yesmaximal, characteristic, complemented
7C2×#91463C211yesmaximal, characteristic, complemented
8C2×#91457C211yesmaximal, characteristic, complemented
9C2×#91454C211yesmaximal, characteristic, complemented
10C2×#91453C211yesmaximal, characteristic, complemented
11C2×#91452C211yesmaximal, characteristic, complemented
12C2×#91449C211yesmaximal, characteristic, complemented
13C2×#91448C211yesmaximal, characteristic, complemented
14C2×#91416C211yesmaximal, characteristic, complemented
15C2×#91367C211yesmaximal, characteristic, complemented
16#11753940C2116yesmaximal, direct product factor
17C2×#65954—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C22×C5×D12C2211yescharacteristic
21C22×C5×D12C2211yescharacteristic, complemented
22C22×C4×C5×D3C2211yescharacteristic, complemented
23C22×C3×D20C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic, complemented
25C22×#1203C2211yescharacteristic
26C22×#1203C2211yescharacteristic
27C22×#1202C2211yescharacteristic
28C22×#1201C2211yescharacteristic
29C22×#1201C2211yescharacteristic
30C22×#1201C2211yescharacteristic
31C22×#1201C2211yescharacteristic, complemented
32C22×#1201C2211yescharacteristic, complemented
33C22×D3×Dic5C2211yescharacteristic, complemented
34C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×C4⋊Dic15C2211yescharacteristic, complemented
39C2×#6712C2211yescharacteristic, complemented
40C2×C4×Dic15C2211yescharacteristic, complemented
41#91787C2218yescomplemented
42C2×C5×(C2×D3)⋊C4C2211yescharacteristic
43C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C5×#895C2218yescomplemented
45C2×C3×#685C2211yescharacteristic
46C2×C3×#685C2211yescharacteristic
47C2×C3×#685C2211yescharacteristic, complemented
48C2×C3×#683C2211yescharacteristic, complemented
49C3×#4040C2218yescomplemented
50C2×Dic3⋊Dic5C2211yescharacteristic, complemented
51C2×#6668C2211yescharacteristic, complemented
52C2×(C2×D3)⋊Dic5C2211yescharacteristic
53C2×(C2×D3)⋊Dic5C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
55C2×#6665C2211yescharacteristic
56#91475C2218yescomplemented
57#91475C2218yescomplemented
58#91474C2218yescomplemented
59#91463C2218yescomplemented
60#91457C2218yescomplemented
61#91454C2218yescomplemented
62#91453C2218yescomplemented
63#91452C2218yescomplemented
64#91449C2218yescomplemented
65#91448C2218yescomplemented
66#91416C2218yescomplemented
67#91367C2218yescomplemented
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×#4040D311yescharacteristic, complemented
81C2×#4032—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4025—31no—
85C23×D15C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
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
97C22×C3×C4×C5C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C2×C5×D12—42no—
103C2×C5×D12—42no—
104C2×C5×D12—42no—
105C2×C5×D12C2314yes—
106C2×C5×D12C2314yes—
107C2×C5×D12C2314yescomplemented
108C2×C4×C5×D3—42no—
109C2×C4×C5×D3C2314yescomplemented
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C2×C3×D20—42no—
113C2×C3×D20C2314yes—
114C2×C3×C4×D5—42no—
115C2×C3×C4×D5C2314yescomplemented
116C2×#1203—42no—
117C2×#1203—42no—
118C2×#1203C2314yes—
119C2×#1203C2314yes—
120C2×#1202—42no—
121C2×#1202C2314yes—
122C2×#1201—42no—
123C2×#1201—42no—
124C2×#1201—42no—
125C2×#1201—42no—
126C2×#1201—42no—
127C2×#1201C2314yes—
128C2×#1201C2314yes—
129C2×#1201C2314yes—
130C2×#1201C2314yescomplemented
131C2×#1201C2314yescomplemented
132C2×D3×Dic5—42no—
133C2×D3×Dic5C2314yescomplemented
134C3×C5×C4⋊C4C2314yescomplemented
135#6714C2314yes—
136#6714C2314yes—
137#6714C2314yes—
138C4⋊Dic15C2314yescomplemented
139#6712C2314yescomplemented
140C4×Dic15C2314yescomplemented
141C5×(C2×D3)⋊C4C2314yes—
142C5×(C2×D3)⋊C4C2314yescomplemented
143C3×#685C2314yes—
144C3×#685C2314yes—
145C3×#685C2314yescomplemented
146C3×#683C2314yescomplemented
147Dic3⋊Dic5C2314yescomplemented
148#6668C2314yescomplemented
149(C2×D3)⋊Dic5C2314yes—
150(C2×D3)⋊Dic5C2314yes—
151(C2×D3)⋊Dic5C2314yescomplemented
152#6665C2314yes—
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×#895D511yescharacteristic, complemented
163C2×#884—51no—
164C2×#884—51no—
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⋊D5—31no—
181C23×Dic5—31no—
182C22×D20—31no—
183C22×D20C2×D311yescharacteristic
184C22×C4×D5C2×D311yescharacteristic, complemented
185C5×#121—38no—
186C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
187C2×C5×C22⋊C4—31no—
188C2×C5×C22⋊C4—31no—
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×#685C2×D311yescharacteristic
205C2×#685C2×D311yescharacteristic
206C2×#685C2×D311yescharacteristic, complemented
207C2×C4⋊Dic5—31no—
208C2×C4⋊Dic5—31no—
209C2×#683—31no—
210C2×#683—31no—
211C2×#683C2×D311yescharacteristic, complemented
212C2×C4×Dic5—31no—
213#4044—38no—
214#4040C2×D318yescomplemented
215#4032—38no—
216#4030—38no—
217#4028—38no—
218#4025—38no—
219C2×#560—151noSylow
220C23×C3×C5C2411yescharacteristic
221C22×D15—22no—
222C22×D15—22no—
223C22×D15—22no—
224C22×D15C2412yes—
225C22×C5×D3—22no—
226C22×C5×D3—22no—
227C22×C5×D3—22no—
228C22×C5×D3—22no—
229C22×C5×D3—22no—
230C22×C5×D3—22no—
231C22×C5×D3—22no—
232C22×C5×D3—22no—
233C22×C5×D3—22no—
234C22×C5×D3C2412yes—
235C22×C5×D3C2412yes—
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×C5—22no—
252C2×C3×C4×C5C2412yes—
253C2×C3×C4×C5C2412yes—
254C2×C3×C4×C5C2412yes—
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15—22no—
258C2×Dic15C2412yes—
259C2×Dic15C2412yes—
260C2×Dic15C2412yes—
261C2×C5×Dic3—22no—
262C2×C5×Dic3C2412yes—
263C5×D12—44no—
264C5×D12—44no—
265C5×D12—44no—
266C4×C5×D3—44no—
267C2×C3×Dic5—22no—
268C2×C3×Dic5—22no—
269C2×C3×Dic5C2412yes—
270C2×C3×Dic5C2412yes—
271C3×D20—44no—
272C3×C4×D5—44no—
273#1203—44no—
274#1203—44no—
275#1202—44no—
276#1201—44no—
277#1201—44no—
278#1201—44no—
279#1201—44no—
280#1201—44no—
281D3×Dic5—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×#67—51no—
290C22×#67—51no—
291C22×D12—51no—
292C22×D12—51no—
293C22×D12C2×D511yescharacteristic
294C22×D12C2×D511yescharacteristic
295C22×D12C2×D511yescharacteristic, complemented
296C22×C4×D3—51no—
297C22×C4×D3C2×D511yescharacteristic, complemented
298C3×#123—58no—
299C2×C3×C4⋊C4—51no—
300C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
301C2×C3×C22⋊C4—51no—
302C2×C3×C22⋊C4—51no—
303C2×C3×C22⋊C4—51no—
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)⋊C4C2×D511yescharacteristic
316C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
317C2×C4⋊Dic3—51no—
318C2×C4⋊Dic3—51no—
319C2×Dic3⋊C4—51no—
320C2×Dic3⋊C4—51no—
321C2×C4×Dic3—51no—
322#898—58no—
323#898—58no—
324#895—58no—
325#895C2×D518yescomplemented
326#884—58no—
327#884—58no—
328#883—58no—
329#883—58no—
330#882—58no—
331#882—58no—
332C24×C5—31no—
333C24×C5—31no—
334C24×C5—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—34no—
344C2×C5×D4—34no—
345C2×C5×D4—122no—
346C2×C5×D4—122no—
347C2×C5×D4—122no—
348C22×C4×C5—31no—
349C22×C4×C5—34no—
350C22×C4×C5—122no—
351C22×C4×C5C22×D311yescharacteristic
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—34no—
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⋊D5—122no—
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5—31no—
371C22×Dic5—34no—
372C22×Dic5—122no—
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D311yescharacteristic
375C2×D20—34no—
376C2×D20—42no—
377C2×D20—122no—
378C2×D20C22×D314yes—
379C2×C4×D5—42no—
380C2×C4×D5C22×D314yescomplemented
381C5×C4⋊C4C22×D314yescomplemented
382C5×C22⋊C4—34no—
383C5×C22⋊C4—34no—
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685C22×D314yes—
392#685C22×D314yes—
393#685C22×D314yescomplemented
394C4⋊Dic5—34no—
395C4⋊Dic5—34no—
396#683—34no—
397#683—34no—
398#683C22×D314yescomplemented
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×C5H(5,𝔽2)12yes—
417C22×C3×C5H(5,𝔽2)12yes—
418C22×C3×C5H(5,𝔽2)12yes—
419C22×C3×C5C2511yescharacteristic
420C2×D15—22no—
421C2×D15—22no—
422C2×D15—22no—
423C2×D15—44no—
424C2×C5×D3—22no—
425C2×C5×D3—22no—
426C2×C5×D3—22no—
427C2×C5×D3—22no—
428C2×C5×D3—22no—
429C2×C5×D3—22no—
430C2×C5×D3—22no—
431C2×C5×D3—22no—
432C2×C5×D3—22no—
433C2×C5×D3—44no—
434C2×C5×D3—44no—
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—
447C3×C4×C5—22no—
448Dic15—22no—
449Dic15—22no—
450Dic15—22no—
451C3×Dic5—22no—
452C3×Dic5—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3—51no—
456C23×D3—51no—
457C23×D3—54no—
458C23×D3—202no—
459C23×D3—202no—
460C23×D3—202no—
461C23×D3C22×D511yescharacteristic
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—54no—
469C22×C3×C4—202no—
470C22×C3×C4C22×D511yescharacteristic
471C22×C3×C4C22×D511yescharacteristic
472C22×C3×C4C22×D511yescharacteristic
473C2×#67—54no—
474C2×#67—54no—
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×#67—202no—
484C2×#67—202no—
485C22×Dic3—51no—
486C22×Dic3—51no—
487C22×Dic3—51no—
488C22×Dic3C22×D511yescharacteristic
489C2×D12—42no—
490C2×D12—42no—
491C2×D12—42no—
492C2×D12—54no—
493C2×D12—54no—
494C2×D12—202no—
495C2×D12—202no—
496C2×D12C22×D514yes—
497C2×D12C22×D514yes—
498C2×D12C22×D514yescomplemented
499C2×C4×D3—42no—
500C2×C4×D3—54no—
501C2×C4×D3—202no—
502C2×C4×D3C22×D514yescomplemented
503C3×C4⋊C4—54no—
504C3×C4⋊C4C22×D514yescomplemented
505C3×C22⋊C4—54no—
506C3×C22⋊C4—54no—
507C3×C22⋊C4—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)⋊C4—54no—
515(C2×D3)⋊C4C22×D514yes—
516(C2×D3)⋊C4C22×D514yescomplemented
517C4⋊Dic3—54no—
518C4⋊Dic3—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4—54no—
521C4×Dic3—54no—
522C23×C5—32no—
523C23×C5—32no—
524C23×C5—32no—
525C23×C5—62no—
526C23×C5—62no—
527C23×C5—62no—
528C23×C5—62no—
529C23×C5—62no—
530C23×C5—62no—
531C23×C5—62no—
532C23×C5—62no—
533C23×C5—62no—
534C23×C5C23×D311yescharacteristic
535C22×D5—22no—
536C22×D5—22no—
537C22×D5—22no—
538C22×D5—22no—
539C22×D5—22no—
540C22×D5—22no—
541C22×D5—32no—
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—
552C5×D4—124no—
553C5×D4—124no—
554C2×C4×C5—22no—
555C2×C4×C5—22no—
556C2×C4×C5—22no—
557C2×C4×C5—32no—
558C2×C4×C5—62no—
559C2×C4×C5—124no—
560C2×C4×C5C23×D312yes—
561C2×C4×C5C23×D312yes—
562C2×C4×C5C23×D312yes—
563C22⋊D5—124no—
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—32no—
573C2×Dic5—32no—
574C2×Dic5—32no—
575C2×Dic5—62no—
576C2×Dic5—62no—
577C2×Dic5—62no—
578C2×Dic5—124no—
579C2×Dic5C23×D312yes—
580C2×Dic5C23×D312yes—
581D20—44no—
582D20—124no—
583C4×D5—44no—
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—51no—
616C2×C4⋊C4—151no—
617C2×C4⋊C4—151no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4D3×D511yescharacteristic, complemented
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—51no—
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#56014yescomplemented
635C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
636C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
637C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
638D15—42no—
639C3×D5—42no—
640C3×D5—42no—
641C5×D3—42no—
642C5×D3—42no—
643C5×D3—42no—
644C23×C3—52no—
645C23×C3—52no—
646C23×C3—102no—
647C23×C3—102no—
648C23×C3—102no—
649C23×C3—102no—
650C23×C3—102no—
651C23×C3—102no—
652C23×C3C23×D511yescharacteristic
653C22×D3—22no—
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—52no—
663C22×D3—102no—
664C22×D3—102no—
665C22×D3—102no—
666C22×D3—204no—
667C22×D3—204no—
668C22×D3—204no—
669C22×D3—2016no—
670C22×D3C23×D512yes—
671C22×D3C23×D512yes—
672C22×D3C23×D512yes—
673C3×D4—204no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—52no—
678C2×C3×C4—52no—
679C2×C3×C4—102no—
680C2×C3×C4—102no—
681C2×C3×C4—204no—
682C2×C3×C4C23×D512yes—
683C2×C3×C4C23×D512yes—
684C2×C3×C4C23×D512yes—
685#67—204no—
686#67—204no—
687#67—204no—
688#67—204no—
689#67—204no—
690#67—204no—
691C2×Dic3—22no—
692C2×Dic3—52no—
693C2×Dic3—52no—
694C2×Dic3—52no—
695C2×Dic3—102no—
696C2×Dic3—102no—
697C2×Dic3—102no—
698C2×Dic3C23×D512yes—
699D12—44no—
700D12—44no—
701D12—44no—
702D12—204no—
703D12—204no—
704C4×D3—44no—
705C4×D3—204no—
706C22×C5—62no—
707C22×C5—62no—
708C22×C5—62no—
709C22×C5—62no—
710C22×C5—62no—
711C22×C5—62no—
712C22×C5—62no—
713C22×C5—62no—
714C22×C5—62no—
715C22×C5—124no—
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—22no—
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—44no—
729C2×D5—44no—
730C2×D5—62no—
731C2×D5—62no—
732C2×D5—62no—
733C2×D5—1216no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—22no—
737C4×C5—22no—
738C4×C5—62no—
739Dic5—22no—
740Dic5—22no—
741Dic5—62no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—31no—
746C24—31no—
747C24—51no—
748C24—51no—
749C24—154no—
750C24—151no—
751C24—602no—
752C24—602no—
753C24—602no—
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—34no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—54no—
783C22×C4—122no—
784C22×C4—154no—
785C22×C4—151no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—202no—
789C22×C4—602no—
790C22×C4C2×D3×D511yescharacteristic
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—54no—
794C4⋊C4—154no—
795C4⋊C4—154no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4C2×D3×D514yescomplemented
799C22⋊C4—34no—
800C22⋊C4—34no—
801C22⋊C4—54no—
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—102no—
814C22×C3—102no—
815C22×C3—102no—
816C22×C3—102no—
817C22×C3—102no—
818C22×C3—102no—
819C22×C3—204no—
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—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—44no—
835C2×D3—44no—
836C2×D3—44no—
837C2×D3—102no—
838C2×D3—102no—
839C2×D3—102no—
840C2×D3—2016no—
841C2×D3—204no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—22no—
845C3×C4—102no—
846C3×C4—102no—
847Dic3—22no—
848Dic3—102no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—122no—
852C2×C5—122no—
853C2×C5—122no—
854C2×C5#566614yescomplemented
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#100911yescharacteristic
857C2×C5C2×#100911yescharacteristic
858D5—42no—
859D5—42no—
860D5—122no—
861C23—32no—
862C23—32no—
863C23—32no—
864C23—52no—
865C23—52no—
866C23—62no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—102no—
876C23—102no—
877C23—102no—
878C23—102no—
879C23—102no—
880C23—102no—
881C23—152no—
882C23—302no—
883C23—302no—
884C23—302no—
885C23—604no—
886C23—604no—
887C23—604no—
888C23—6016no—
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—22no—
905C2×C4—32no—
906C2×C4—52no—
907C2×C4—52no—
908C2×C4—62no—
909C2×C4—102no—
910C2×C4—102no—
911C2×C4—124no—
912C2×C4—152no—
913C2×C4—152no—
914C2×C4—152no—
915C2×C4—204no—
916C2×C4—302no—
917C2×C4—302no—
918C2×C4—302no—
919C2×C4—604no—
920C2×C4C22×D3×D512yes—
921C2×C4C22×D3×D512yes—
922C2×C4C22×D3×D512yes—
923C2×C3—202no—
924C2×C3—202no—
925C2×C3#6595414yescomplemented
926C2×C3C2×#414411yescharacteristic
927C2×C3C2×#414411yescharacteristic
928C2×C3C2×#414911yescharacteristic
929D3—42no—
930D3—42no—
931D3—42no—
932D3—202no—
933C5C2×#566611yescharacteristic, complemented, Sylow
934C22—62no—
935C22—62no—
936C22—62no—
937C22—62no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—62no—
943C22—102no—
944C22—102no—
945C22—102no—
946C22—102no—
947C22—102no—
948C22—102no—
949C22—124no—
950C22—124no—
951C22—124no—
952C22—204no—
953C22—204no—
954C22—302no—
955C22—302no—
956C22—302no—
957C22—6016no—
958C22—604no—
959C22#9201812yes—
960C22#9202512yes—
961C22#9203512yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—22no—
966C4—62no—
967C4—102no—
968C4—102no—
969C4—302no—
970C4—302no—
971C4—302no—
972C3C2×#6595411yescharacteristic, complemented, Sylow
973C2—122no—
974C2—122no—
975C2—122no—
976C2—202no—
977C2—202no—
978C2—602no—
979C2#1175394014yesdirect product factor
980C2C2×#9201811yescharacteristic
981C2C2×#9202511yescharacteristic
982C2C2×#9203511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#560
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91787C2semidirect
2. C2×C5×#895C2semidirect
3. C2×C3×#4040C2semidirect
4. C2×#91475C2semidirect
5. C2×#91475C2semidirect
6. C2×#91474C2semidirect
7. C2×#91463C2semidirect
8. C2×#91457C2semidirect
9. C2×#91454C2semidirect
10. C2×#91453C2semidirect
11. C2×#91452C2semidirect
12. C2×#91449C2semidirect
13. C2×#91448C2semidirect
14. C2×#91416C2semidirect
15. C2×#91367C2semidirect
16. #11753940C2direct (N × H)
21. C22×C5×D12C22semidirect
22. C22×C4×C5×D3C22semidirect
24. C22×C3×C4×D5C22semidirect
31. C22×#1201C22semidirect
32. C22×#1201C22semidirect
33. C22×D3×Dic5C22semidirect
34. C2×C3×C5×C4⋊C4C22semidirect
38. C2×C4⋊Dic15C22semidirect
39. C2×#6712C22semidirect
40. C2×C4×Dic15C22semidirect
41. #91787C22semidirect
43. C2×C5×(C2×D3)⋊C4C22semidirect
44. C5×#895C22semidirect
47. C2×C3×#685C22semidirect
48. C2×C3×#683C22semidirect
49. C3×#4040C22semidirect
50. C2×Dic3⋊Dic5C22semidirect
51. C2×#6668C22semidirect
54. C2×(C2×D3)⋊Dic5C22semidirect
56. #91475C22semidirect
57. #91475C22semidirect
58. #91474C22semidirect
59. #91463C22semidirect
60. #91457C22semidirect
61. #91454C22semidirect
62. #91453C22semidirect
63. #91452C22semidirect
64. #91449C22semidirect
65. #91448C22semidirect
66. #91416C22semidirect
67. #91367C22semidirect
80. C2×#4040D3semidirect
107. C2×C5×D12C23semidirect
109. C2×C4×C5×D3C23semidirect
115. C2×C3×C4×D5C23semidirect
130. C2×#1201C23semidirect
131. C2×#1201C23semidirect
133. C2×D3×Dic5C23semidirect
134. C3×C5×C4⋊C4C23semidirect
138. C4⋊Dic15C23semidirect
139. #6712C23semidirect
140. C4×Dic15C23semidirect
142. C5×(C2×D3)⋊C4C23semidirect
145. C3×#685C23semidirect
146. C3×#683C23semidirect
147. Dic3⋊Dic5C23semidirect
148. #6668C23semidirect
151. (C2×D3)⋊Dic5C23semidirect
162. C2×#895D5semidirect
184. C22×C4×D5C2×D3semidirect
186. C2×C5×C4⋊C4C2×D3semidirect
206. C2×#685C2×D3semidirect
211. C2×#683C2×D3semidirect
214. #4040C2×D3semidirect
295. C22×D12C2×D5semidirect
297. C22×C4×D3C2×D5semidirect
300. C2×C3×C4⋊C4C2×D5semidirect
316. C2×(C2×D3)⋊C4C2×D5semidirect
325. #895C2×D5semidirect
380. C2×C4×D5C22×D3semidirect
381. C5×C4⋊C4C22×D3semidirect
393. #685C22×D3semidirect
398. #683C22×D3semidirect
498. C2×D12C22×D5semidirect
502. C2×C4×D3C22×D5semidirect
504. C3×C4⋊C4C22×D5semidirect
516. (C2×D3)⋊C4C22×D5semidirect
620. C2×C4⋊C4D3×D5semidirect
634. C2×C3×C5#560semidirect
798. C4⋊C4C2×D3×D5semidirect
812. C3×C5C2×#560semidirect
854. C2×C5#5666semidirect
925. C2×C3#65954semidirect
933. C5C2×#5666semidirect
972. C3C2×#65954semidirect
979. C2#11753940direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917872
C2×C5×#8952
C2×C3×#40402
C2×#914752
C2×#914742
C2×#914632
C2×#914572
C2×#914542
C2×#914532
C2×#914522
C2×#914492
C2×#914482
C2×#914162
C2×#913672
#117539402
C2×#659543
C2×#56665