Finite Group Databasebeta

← C2×#11753939 #14495240

Subgroups — C2×#11753939 #14495240

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×#894C211yesmaximal, characteristic, complemented
3C2×C3×#4041C211yesmaximal, characteristic, complemented
4C2×#91475C211yesmaximal, characteristic, complemented
5C2×#91474C211yesmaximal, characteristic, complemented
6C2×#91474C211yesmaximal, characteristic, complemented
7C2×#91463C211yesmaximal, characteristic, complemented
8C2×#91456C211yesmaximal, characteristic, complemented
9C2×#91454C211yesmaximal, characteristic, complemented
10C2×#91448C211yesmaximal, characteristic, complemented
11C2×#91447C211yesmaximal, characteristic, complemented
12C2×#91414C211yesmaximal, characteristic, complemented
13C2×#91409C211yesmaximal, characteristic, complemented
14C2×#91408C211yesmaximal, characteristic, complemented
15C2×#91366C211yesmaximal, characteristic, complemented
16#11753939C2116yesmaximal, direct product factor
17C2×#66000—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic, complemented
21C22×C3×D20C2211yescharacteristic
22C22×C3×D20C2211yescharacteristic
23C22×C3×D20C2211yescharacteristic, complemented
24C22×C3×C4×D5C2211yescharacteristic, complemented
25C22×#1203C2211yescharacteristic
26C22×#1202C2211yescharacteristic
27C22×#1202C2211yescharacteristic
28C22×#1201C2211yescharacteristic
29C22×#1201C2211yescharacteristic
30C22×#1201C2211yescharacteristic
31C22×#1201C2211yescharacteristic, complemented
32C22×#1201C2211yescharacteristic, complemented
33C22×D5×Dic3C2211yescharacteristic, 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
44C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
46C5×#894C2218yescomplemented
47C2×C3×#685C2211yescharacteristic
48C2×C3×#685C2211yescharacteristic, complemented
49C3×#4041C2218yescomplemented
50C2×Dic3⋊Dic5C2211yescharacteristic, complemented
51C2×#6668C2211yescharacteristic, complemented
52C2×(C2×D3)⋊Dic5C2211yescharacteristic
53C2×#6665C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55C2×#6665C2211yescharacteristic, complemented
56#91475C2218yescomplemented
57#91474C2218yescomplemented
58#91474C2218yescomplemented
59#91463C2218yescomplemented
60#91456C2218yescomplemented
61#91454C2218yescomplemented
62#91448C2218yescomplemented
63#91447C2218yescomplemented
64#91414C2218yescomplemented
65#91409C2218yescomplemented
66#91408C2218yescomplemented
67#91366C2218yescomplemented
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×#4041D311yescharacteristic, complemented
79C2×#4030—31no—
80C2×#4030—31no—
81C2×#4029—31no—
82C2×#4029—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C23×D15C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
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
102C22×C5×Dic3C2311yescharacteristic
103C2×C5×D12—42no—
104C2×C5×D12C2314yes—
105C2×C4×C5×D3—42no—
106C2×C4×C5×D3C2314yescomplemented
107C22×C3×Dic5C2311yescharacteristic
108C2×C3×D20—42no—
109C2×C3×D20—42no—
110C2×C3×D20—42no—
111C2×C3×D20C2314yes—
112C2×C3×D20C2314yes—
113C2×C3×D20C2314yescomplemented
114C2×C3×C4×D5—42no—
115C2×C3×C4×D5C2314yescomplemented
116C2×#1203—42no—
117C2×#1203C2314yes—
118C2×#1202—42no—
119C2×#1202—42no—
120C2×#1202C2314yes—
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×D5×Dic3—42no—
133C2×D5×Dic3C2314yescomplemented
134C3×C5×C4⋊C4C2314yescomplemented
135#6714C2314yes—
136#6714C2314yes—
137#6714C2314yes—
138C4⋊Dic15C2314yescomplemented
139#6712C2314yescomplemented
140C4×Dic15C2314yescomplemented
141C5×(C2×D3)⋊C4C2314yes—
142C5×(C2×D3)⋊C4C2314yes—
143C5×(C2×D3)⋊C4C2314yescomplemented
144C5×Dic3⋊C4C2314yescomplemented
145C3×#685C2314yes—
146C3×#685C2314yescomplemented
147Dic3⋊Dic5C2314yescomplemented
148#6668C2314yescomplemented
149(C2×D3)⋊Dic5C2314yes—
150#6665C2314yes—
151#6665C2314yes—
152#6665C2314yescomplemented
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×#894D511yescharacteristic, complemented
165C2×#886—51no—
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⋊D5—31no—
177C22×C22⋊D5—31no—
178C22×D20—31no—
179C22×D20—31no—
180C22×D20C2×D311yescharacteristic
181C22×D20C2×D311yescharacteristic
182C22×D20C2×D311yescharacteristic, complemented
183C22×C4×D5—31no—
184C22×C4×D5C2×D311yescharacteristic, complemented
185C5×#123—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
188C2×C5×C22⋊C4—31no—
189C2×C5×C22⋊C4—31no—
190C2×C5×C22⋊C4—31no—
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×#685C2×D311yescharacteristic
203C2×#685C2×D311yescharacteristic, complemented
204C2×C4⋊Dic5—31no—
205C2×C4⋊Dic5—31no—
206C2×#683—31no—
207C2×#683—31no—
208C2×C4×Dic5—31no—
209#4044—38no—
210#4044—38no—
211#4041—38no—
212#4041C2×D318yescomplemented
213#4030—38no—
214#4030—38no—
215#4029—38no—
216#4029—38no—
217#4028—38no—
218#4028—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×D3C2412yes—
232C22×C5×D3C2412yes—
233C22×C3×D5—22no—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5—22no—
237C22×C3×D5—22no—
238C22×C3×D5—22no—
239C22×C3×D5—22no—
240C22×C3×D5—22no—
241C22×C3×D5—22no—
242C22×C3×D5C2412yes—
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×Dic3—22no—
263C2×C5×Dic3C2412yes—
264C2×C5×Dic3C2412yes—
265C5×D12—44no—
266C4×C5×D3—44no—
267C2×C3×Dic5—22no—
268C2×C3×Dic5C2412yes—
269C3×D20—44no—
270C3×D20—44no—
271C3×D20—44no—
272C3×C4×D5—44no—
273#1203—44no—
274#1202—44no—
275#1202—44no—
276#1201—44no—
277#1201—44no—
278#1201—44no—
279#1201—44no—
280#1201—44no—
281D5×Dic3—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×#67—51no—
294C23×Dic3—51no—
295C22×D12—51no—
296C22×D12C2×D511yescharacteristic
297C22×C4×D3C2×D511yescharacteristic, complemented
298C3×#121—58no—
299C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4—51no—
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)⋊C4C2×D511yescharacteristic
318C2×(C2×D3)⋊C4C2×D511yescharacteristic
319C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
320C2×C4⋊Dic3—51no—
321C2×C4⋊Dic3—51no—
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4—51no—
324C2×Dic3⋊C4C2×D511yescharacteristic, complemented
325C2×C4×Dic3—51no—
326#898—58no—
327#894C2×D518yescomplemented
328#886—58no—
329#884—58no—
330#882—58no—
331#879—58no—
332C24×C5—31no—
333C24×C5—31no—
334C23×D5—31no—
335C23×D5—34no—
336C23×D5—122no—
337C23×D5—122no—
338C23×D5—122no—
339C23×D5C22×D311yescharacteristic
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—34no—
347C22×C4×C5—122no—
348C22×C4×C5C22×D311yescharacteristic
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—34no—
356C2×C22⋊D5—34no—
357C2×C22⋊D5—122no—
358C2×C22⋊D5—122no—
359C2×C22⋊D5—122no—
360C2×C22⋊D5—122no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5—122no—
363C22×Dic5—31no—
364C22×Dic5—31no—
365C22×Dic5—31no—
366C22×Dic5C22×D311yescharacteristic
367C2×D20—34no—
368C2×D20—34no—
369C2×D20—42no—
370C2×D20—42no—
371C2×D20—42no—
372C2×D20—122no—
373C2×D20—122no—
374C2×D20C22×D314yes—
375C2×D20C22×D314yes—
376C2×D20C22×D314yescomplemented
377C2×C4×D5—34no—
378C2×C4×D5—42no—
379C2×C4×D5—122no—
380C2×C4×D5C22×D314yescomplemented
381C5×C4⋊C4—34no—
382C5×C4⋊C4C22×D314yescomplemented
383C5×C22⋊C4—34no—
384C5×C22⋊C4—34no—
385C5×C22⋊C4—34no—
386C22⋊Dic5—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685—34no—
393#685C22×D314yes—
394#685C22×D314yescomplemented
395C4⋊Dic5—34no—
396C4⋊Dic5—34no—
397#683—34no—
398#683—34no—
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×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—44no—
431C2×C5×D3—44no—
432C2×C3×D5—22no—
433C2×C3×D5—22no—
434C2×C3×D5—22no—
435C2×C3×D5—22no—
436C2×C3×D5—22no—
437C2×C3×D5—22no—
438C2×C3×D5—22no—
439C2×C3×D5—22no—
440C2×C3×D5—22no—
441C2×C3×D5—44no—
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—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3—51no—
456C24×C3—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—54no—
466C2×C3×D4—54no—
467C2×C3×D4—202no—
468C2×C3×D4—202no—
469C2×C3×D4—202no—
470C22×C3×C4—51no—
471C22×C3×C4—54no—
472C22×C3×C4—202no—
473C22×C3×C4C22×D511yescharacteristic
474C22×C3×C4C22×D511yescharacteristic
475C22×C3×C4C22×D511yescharacteristic
476C2×#67—54no—
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×#67—202no—
490C22×Dic3—51no—
491C22×Dic3—51no—
492C22×Dic3—51no—
493C22×Dic3—54no—
494C22×Dic3—202no—
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D511yescharacteristic
497C2×D12—42no—
498C2×D12—54no—
499C2×D12—202no—
500C2×D12C22×D514yes—
501C2×C4×D3—42no—
502C2×C4×D3C22×D514yescomplemented
503C3×C4⋊C4C22×D514yescomplemented
504C3×C22⋊C4—54no—
505C3×C22⋊C4—54no—
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)⋊C4C22×D514yes—
514(C2×D3)⋊C4C22×D514yes—
515(C2×D3)⋊C4C22×D514yescomplemented
516C4⋊Dic3—54no—
517C4⋊Dic3—54no—
518Dic3⋊C4—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4C22×D514yescomplemented
521C4×Dic3—54no—
522C23×C5—32no—
523C23×C5—32no—
524C23×C5—62no—
525C23×C5—62no—
526C23×C5—62no—
527C23×C5—62no—
528C23×C5—62no—
529C23×C5—62no—
530C23×C5C23×D311yescharacteristic
531C22×D5—22no—
532C22×D5—22no—
533C22×D5—22no—
534C22×D5—22no—
535C22×D5—22no—
536C22×D5—22no—
537C22×D5—22no—
538C22×D5—22no—
539C22×D5—22no—
540C22×D5—32no—
541C22×D5—62no—
542C22×D5—62no—
543C22×D5—62no—
544C22×D5—124no—
545C22×D5—124no—
546C22×D5—124no—
547C22×D5—1216no—
548C22×D5C23×D312yes—
549C22×D5C23×D312yes—
550C22×D5C23×D312yes—
551C5×D4—124no—
552C2×C4×C5—22no—
553C2×C4×C5—22no—
554C2×C4×C5—22no—
555C2×C4×C5—32no—
556C2×C4×C5—32no—
557C2×C4×C5—62no—
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—
569C2×Dic5—22no—
570C2×Dic5—32no—
571C2×Dic5—32no—
572C2×Dic5—32no—
573C2×Dic5—62no—
574C2×Dic5—62no—
575C2×Dic5—62no—
576C2×Dic5C23×D312yes—
577D20—44no—
578D20—44no—
579D20—44no—
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—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—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#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—
641C3×D5—42no—
642C5×D3—42no—
643C5×D3—42no—
644C23×C3—52no—
645C23×C3—52no—
646C23×C3—52no—
647C23×C3—102no—
648C23×C3—102no—
649C23×C3—102no—
650C23×C3—102no—
651C23×C3—102no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3—102no—
655C23×C3—102no—
656C23×C3C23×D511yescharacteristic
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—52no—
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—
674C3×D4—204no—
675C3×D4—204no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—52no—
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—
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—44no—
704D12—204no—
705C4×D3—44no—
706C22×C5—62no—
707C22×C5—62no—
708C22×C5—62no—
709C22×C5—62no—
710C22×C5—62no—
711C22×C5—62no—
712C22×C5—124no—
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—22no—
725C2×D5—22no—
726C2×D5—22no—
727C2×D5—44no—
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—
739C4×C5—62no—
740Dic5—22no—
741Dic5—62no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—31no—
746C24—51no—
747C24—51no—
748C24—51no—
749C24—154no—
750C24—151no—
751C24—602no—
752C24—602no—
753C24—602no—
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—34no—
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—34no—
794C4⋊C4—154no—
795C4⋊C4—154no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4C2×D3×D514yescomplemented
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—102no—
814C22×C3—102no—
815C22×C3—102no—
816C22×C3—102no—
817C22×C3—102no—
818C22×C3—102no—
819C22×C3—102no—
820C22×C3—102no—
821C22×C3—102no—
822C22×C3—204no—
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—22no—
833C2×D3—22no—
834C2×D3—22no—
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—
846Dic3—22no—
847Dic3—22no—
848Dic3—102no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—122no—
852C2×C5—122no—
853C2×C5#562014yescomplemented
854C2×C5C2×#100411yescharacteristic
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#100911yescharacteristic
857D5—42no—
858D5—42no—
859D5—42no—
860D5—122no—
861C23—32no—
862C23—32no—
863C23—52no—
864C23—52no—
865C23—52no—
866C23—62no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—102no—
873C23—102no—
874C23—102no—
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—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—22no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—52no—
908C2×C4—62no—
909C2×C4—62no—
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—202no—
926C2×C3#6600014yescomplemented
927C2×C3C2×#414411yescharacteristic
928C2×C3C2×#414911yescharacteristic
929C2×C3C2×#414911yescharacteristic
930D3—42no—
931D3—42no—
932D3—202no—
933C5C2×#562011yescharacteristic, complemented, Sylow
934C22—62no—
935C22—62no—
936C22—62no—
937C22—62no—
938C22—62no—
939C22—62no—
940C22—102no—
941C22—102no—
942C22—102no—
943C22—102no—
944C22—102no—
945C22—102no—
946C22—102no—
947C22—102no—
948C22—102no—
949C22—124no—
950C22—124no—
951C22—204no—
952C22—204no—
953C22—204no—
954C22—302no—
955C22—302no—
956C22—302no—
957C22—6016no—
958C22—604no—
959C22#9201712yes—
960C22#9202512yes—
961C22#9203512yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—22no—
966C4—62no—
967C4—62no—
968C4—102no—
969C4—302no—
970C4—302no—
971C4—302no—
972C3C2×#6600011yescharacteristic, complemented, Sylow
973C2—122no—
974C2—122no—
975C2—202no—
976C2—202no—
977C2—202no—
978C2—602no—
979C2#1175393914yesdirect product factor
980C2C2×#9201711yescharacteristic
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×#894C2semidirect
3. C2×C3×#4041C2semidirect
4. C2×#91475C2semidirect
5. C2×#91474C2semidirect
6. C2×#91474C2semidirect
7. C2×#91463C2semidirect
8. C2×#91456C2semidirect
9. C2×#91454C2semidirect
10. C2×#91448C2semidirect
11. C2×#91447C2semidirect
12. C2×#91414C2semidirect
13. C2×#91409C2semidirect
14. C2×#91408C2semidirect
15. C2×#91366C2semidirect
16. #11753939C2direct (N × H)
20. C22×C4×C5×D3C22semidirect
23. C22×C3×D20C22semidirect
24. C22×C3×C4×D5C22semidirect
31. C22×#1201C22semidirect
32. C22×#1201C22semidirect
33. C22×D5×Dic3C22semidirect
34. C2×C3×C5×C4⋊C4C22semidirect
38. C2×C4⋊Dic15C22semidirect
39. C2×#6712C22semidirect
40. C2×C4×Dic15C22semidirect
41. #91787C22semidirect
44. C2×C5×(C2×D3)⋊C4C22semidirect
45. C2×C5×Dic3⋊C4C22semidirect
46. C5×#894C22semidirect
48. C2×C3×#685C22semidirect
49. C3×#4041C22semidirect
50. C2×Dic3⋊Dic5C22semidirect
51. C2×#6668C22semidirect
55. C2×#6665C22semidirect
56. #91475C22semidirect
57. #91474C22semidirect
58. #91474C22semidirect
59. #91463C22semidirect
60. #91456C22semidirect
61. #91454C22semidirect
62. #91448C22semidirect
63. #91447C22semidirect
64. #91414C22semidirect
65. #91409C22semidirect
66. #91408C22semidirect
67. #91366C22semidirect
78. C2×#4041D3semidirect
106. C2×C4×C5×D3C23semidirect
113. C2×C3×D20C23semidirect
115. C2×C3×C4×D5C23semidirect
130. C2×#1201C23semidirect
131. C2×#1201C23semidirect
133. C2×D5×Dic3C23semidirect
134. C3×C5×C4⋊C4C23semidirect
138. C4⋊Dic15C23semidirect
139. #6712C23semidirect
140. C4×Dic15C23semidirect
143. C5×(C2×D3)⋊C4C23semidirect
144. C5×Dic3⋊C4C23semidirect
146. C3×#685C23semidirect
147. Dic3⋊Dic5C23semidirect
148. #6668C23semidirect
152. #6665C23semidirect
164. C2×#894D5semidirect
182. C22×D20C2×D3semidirect
184. C22×C4×D5C2×D3semidirect
187. C2×C5×C4⋊C4C2×D3semidirect
203. C2×#685C2×D3semidirect
212. #4041C2×D3semidirect
297. C22×C4×D3C2×D5semidirect
299. C2×C3×C4⋊C4C2×D5semidirect
319. C2×(C2×D3)⋊C4C2×D5semidirect
324. C2×Dic3⋊C4C2×D5semidirect
327. #894C2×D5semidirect
376. C2×D20C22×D3semidirect
380. C2×C4×D5C22×D3semidirect
382. C5×C4⋊C4C22×D3semidirect
394. #685C22×D3semidirect
502. C2×C4×D3C22×D5semidirect
503. C3×C4⋊C4C22×D5semidirect
515. (C2×D3)⋊C4C22×D5semidirect
520. Dic3⋊C4C22×D5semidirect
620. C2×C4⋊C4D3×D5semidirect
634. C2×C3×C5#560semidirect
798. C4⋊C4C2×D3×D5semidirect
812. C3×C5C2×#560semidirect
853. C2×C5#5620semidirect
926. C2×C3#66000semidirect
933. C5C2×#5620semidirect
972. C3C2×#66000semidirect
979. C2#11753939direct (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×#8942
C2×C3×#40412
C2×#914752
C2×#914742
C2×#914632
C2×#914562
C2×#914542
C2×#914482
C2×#914472
C2×#914142
C2×#914092
C2×#914082
C2×#913662
#117539392
C2×#660003
C2×#56205