Finite Group Databasebeta

← C2×#11753141 #14481177

Subgroups — C2×#11753141 #14481177

Order 1920.

2520 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91775C211yesmaximal, characteristic, complemented
2C2×C5×#884C211yesmaximal, characteristic, complemented
3C2×C3×#4029C211yesmaximal, characteristic, complemented
4C2×#91571C211yesmaximal, characteristic, complemented
5C2×#91567C211yesmaximal, characteristic, complemented
6C2×#67⋊Dic5C211yesmaximal, characteristic, complemented
7C2×#91557C211yesmaximal, characteristic, complemented
8C2×#91457C211yesmaximal, characteristic, complemented
9C2×#91454C211yesmaximal, characteristic, complemented
10C2×#91449C211yesmaximal, characteristic, complemented
11C2×#91444C211yesmaximal, characteristic, complemented
12C2×#91438C211yesmaximal, characteristic, complemented
13C2×#91416C211yesmaximal, characteristic, complemented
14C2×#91343C211yesmaximal, characteristic, complemented
15C2×#91338C211yesmaximal, characteristic, complemented
16#11753141C2116yesmaximal, direct product factor
17C2×#65953—31nomaximal, Hall
18C22×#1220C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C22×C5×D12C2211yescharacteristic
23C22×C4×C5×D3C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic
26C22×#1203C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1202C2211yescharacteristic
29C22×#1201C2211yescharacteristic
30C22×#1201C2211yescharacteristic
31C22×#1200C2211yescharacteristic
32C22×D3×Dic5C2211yescharacteristic
33C2×C3×C5×C22⋊C4C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6714C2211yescharacteristic
36C2×C4⋊Dic15C2211yescharacteristic
37C2×C4⋊Dic15C2211yescharacteristic
38#91775C2218yescomplemented
39C2×C5×(C2×D3)⋊C4C2211yescharacteristic
40C2×C5×Dic3⋊C4C2211yescharacteristic
41C5×#884C2218yescomplemented
42C2×C3×C22⋊Dic5C2211yescharacteristic
43C2×C3×#685C2211yescharacteristic
44C2×C3×C4⋊Dic5C2211yescharacteristic
45C2×C3×#683C2211yescharacteristic
46C3×#4029C2218yescomplemented
47#91571C2218yescomplemented
48#91567C2218yescomplemented
49#67⋊Dic5C2218yescomplemented
50#91557C2218yescomplemented
51C2×Dic3⋊Dic5C2211yescharacteristic
52C2×Dic3⋊Dic5C2211yescharacteristic
53C2×#6669C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic
60#91457C2218yescomplemented
61#91454C2218yescomplemented
62#91449C2218yescomplemented
63#91444C2218yescomplemented
64#91438C2218yescomplemented
65#91416C2218yescomplemented
66#91343C2218yescomplemented
67#91338C2218yescomplemented
68C2×#5663—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4086—31no—
71C2×#4085—31no—
72C2×#4085—31no—
73C2×#4084—31no—
74C2×#4084—31no—
75C2×D4×Dic5—31no—
76C2×#4076—31no—
77C2×#4072—31no—
78#65953—316no—
79C2×#4039—31no—
80C2×#4036—31no—
81C2×#4032—31no—
82C2×#4032—31no—
83C2×#4029—31no—
84C2×#4029D311yescharacteristic, complemented
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C3×D5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C2×#1220—42no—
93C2×#1220C2314yes—
94C22×Dic15—42no—
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2314yes—
99C2×C5×#67—24no—
100C2×C5×#67—42no—
101C2×C5×#67C2314yes—
102C2×C5×#67C2314yes—
103C22×C5×Dic3C2311yescharacteristic
104C22×C5×Dic3C2311yescharacteristic
105C2×C5×D12—42no—
106C2×C5×D12C2314yes—
107C2×C4×C5×D3—24no—
108C2×C4×C5×D3C2314yes—
109C2×C3×C22⋊D5—42no—
110C2×C3×C22⋊D5C2314yes—
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C2×C3×C4×D5—42no—
115C2×C3×C4×D5C2314yes—
116C2×#1203—42no—
117C2×#1203—42no—
118C2×#1203C2314yes—
119C2×#1203C2314yes—
120C2×#1202—24no—
121C2×#1202C2314yes—
122C2×#1201—42no—
123C2×#1201—42no—
124C2×#1201C2314yes—
125C2×#1201C2314yes—
126C2×#1200—42no—
127C2×#1200C2314yes—
128C2×D3×Dic5—42no—
129C2×D3×Dic5C2314yes—
130C3×C5×C22⋊C4C2314yes—
131#6714C2314yes—
132#6714C2314yes—
133C4⋊Dic15C2314yes—
134C4⋊Dic15C2314yes—
135C5×(C2×D3)⋊C4C2314yes—
136C5×Dic3⋊C4C2314yes—
137C3×C22⋊Dic5C2314yes—
138C3×#685C2314yes—
139C3×C4⋊Dic5C2314yes—
140C3×#683C2314yes—
141Dic3⋊Dic5C2314yes—
142Dic3⋊Dic5C2314yes—
143#6669C2314yes—
144(C2×D3)⋊Dic5C2314yes—
145(C2×D3)⋊Dic5C2314yes—
146(C2×D3)⋊Dic5C2314yes—
147#6665C2314yes—
148Dic3×Dic5C2314yes—
149Dic3×Dic5C2314yes—
150C2×C3×#123—51no—
151C2×#940—51no—
152C2×#939—51no—
153C2×#930—51no—
154C2×C4×#67—51no—
155#5663—516no—
156C2×#895—51no—
157C2×#894—51no—
158C2×#892—51no—
159C2×#889—51no—
160C2×#886—51no—
161C2×#884—51no—
162C2×#884—51no—
163C2×#884D511yescharacteristic, complemented
164C2×#883—51no—
165C2×#67⋊C4—51no—
166C22×C5×D4—31no—
167C22×C5×D4—31no—
168C22×C5×D4—31no—
169C23×C4×C5—31no—
170C22×C22⋊D5—31no—
171C22×C22⋊D5—31no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5C2×D311yescharacteristic
176C23×Dic5—31no—
177C23×Dic5—31no—
178C22×D20—31no—
179C22×C4×D5—31no—
180C22×C4×D5C2×D311yescharacteristic
181C5×#121—38no—
182C2×C5×C4⋊C4—31no—
183C2×C5×C22⋊C4—31no—
184C2×C5×C22⋊C4C2×D311yescharacteristic
185C2×C22⋊Dic5—31no—
186C2×C22⋊Dic5—31no—
187C2×C22⋊Dic5—31no—
188C2×C22⋊Dic5C2×D311yescharacteristic
189#4086—38no—
190#4085—38no—
191#4085—38no—
192#4084—38no—
193#4084—38no—
194D4×Dic5—38no—
195#4076—38no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×#685C2×D311yescharacteristic
200#4072—38no—
201C2×C4⋊Dic5—31no—
202C2×C4⋊Dic5—31no—
203C2×C4⋊Dic5—31no—
204C2×C4⋊Dic5—31no—
205C2×C4⋊Dic5C2×D311yescharacteristic
206C2×#683—31no—
207C2×#683C2×D311yescharacteristic
208C2×C4×Dic5—31no—
209C2×C4×Dic5—31no—
210#4039—38no—
211#4036—38no—
212#4032—38no—
213#4032—38no—
214#4029—38no—
215#4029C2×D318yescomplemented
216C2×#540—151noSylow
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5—22no—
220C23×C3×C5C2412yes—
221C23×C3×C5C2411yescharacteristic
222C22×D15—22no—
223C22×D15—22no—
224C22×D15—22no—
225C22×D15C2412yes—
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×D3C2412yes—
233C22×C5×D3C2412yes—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5—22no—
237C22×C3×D5C2412yes—
238C2×C3×C4×C5—22no—
239C2×C3×C4×C5—22no—
240C2×C3×C4×C5C2412yes—
241C2×C3×C4×C5C2412yes—
242#1220—44no—
243C2×Dic15—22no—
244C2×Dic15—22no—
245C2×Dic15—22no—
246C2×Dic15—44no—
247C2×Dic15C2412yes—
248C2×Dic15C2412yes—
249C2×Dic15C2412yes—
250C5×#67—28no—
251C5×#67—44no—
252C2×C5×Dic3—22no—
253C2×C5×Dic3#4114yes—
254C2×C5×Dic3C2412yes—
255C2×C5×Dic3C2412yes—
256C5×D12—44no—
257C4×C5×D3—28no—
258C3×C22⋊D5—44no—
259C2×C3×Dic5—22no—
260C2×C3×Dic5—22no—
261C2×C3×Dic5—22no—
262C2×C3×Dic5C2412yes—
263C2×C3×Dic5C2412yes—
264C2×C3×Dic5C2412yes—
265C3×C4×D5—44no—
266#1203—44no—
267#1203—44no—
268#1202—28no—
269#1201—44no—
270#1201—44no—
271#1200—44no—
272D3×Dic5—44no—
273C22×C3×D4—51no—
274C23×C3×C4—51no—
275C22×#67—51no—
276C22×#67—51no—
277C22×#67—51no—
278C22×#67—51no—
279C22×#67C2×D511yescharacteristic
280C22×#67C2×D511yescharacteristic
281C23×Dic3—51no—
282C22×D12—51no—
283C22×D12—51no—
284C22×D12C2×D511yescharacteristic
285C22×C4×D3—51no—
286C22×C4×D3—51no—
287C22×C4×D3C2×D511yescharacteristic
288C3×#123—58no—
289C2×C3×C4⋊C4—51no—
290C2×C3×C4⋊C4—51no—
291C2×C3×C22⋊C4—51no—
292C2×C3×C22⋊C4—51no—
293C2×C3×C22⋊C4C2×D511yescharacteristic
294C2×#217—51no—
295#940—58no—
296#939—58no—
297#930—58no—
298C4×#67—58no—
299C2×(C2×D3)⋊C4—51no—
300C2×(C2×D3)⋊C4—51no—
301C2×(C2×D3)⋊C4—51no—
302C2×(C2×D3)⋊C4—51no—
303C2×(C2×D3)⋊C4—51no—
304C2×(C2×D3)⋊C4C2×D511yescharacteristic
305C2×C4⋊Dic3—51no—
306C2×C4⋊Dic3—51no—
307C2×Dic3⋊C4—51no—
308C2×Dic3⋊C4—51no—
309C2×Dic3⋊C4—51no—
310C2×Dic3⋊C4C2×D511yescharacteristic
311C2×C4×Dic3—51no—
312C2×C4×Dic3—51no—
313#895—58no—
314#894—58no—
315#892—58no—
316#889—58no—
317#886—58no—
318#884—58no—
319#884—58no—
320#884C2×D518yescomplemented
321#883—58no—
322#67⋊C4—58no—
323C24×C5—31no—
324C24×C5—31no—
325C24×C5C22×D311yescharacteristic
326C23×D5—31no—
327C23×D5C22×D311yescharacteristic
328C2×C5×D4—34no—
329C2×C5×D4—34no—
330C2×C5×D4—34no—
331C2×C5×D4—64no—
332C2×C5×D4—122no—
333C2×C5×D4—122no—
334C22×C4×C5—31no—
335C22×C4×C5—31no—
336C22×C4×C5—34no—
337C22×C4×C5—64no—
338C22×C4×C5C22×D311yescharacteristic
339C22×C4×C5C22×D311yescharacteristic
340C2×C22⋊D5—34no—
341C2×C22⋊D5—34no—
342C2×C22⋊D5—34no—
343C2×C22⋊D5—34no—
344C2×C22⋊D5—34no—
345C2×C22⋊D5—42no—
346C2×C22⋊D5—122no—
347C2×C22⋊D5—122no—
348C2×C22⋊D5—122no—
349C2×C22⋊D5—122no—
350C2×C22⋊D5—122no—
351C2×C22⋊D5C22×D314yes—
352C22×Dic5—31no—
353C22×Dic5—31no—
354C22×Dic5—31no—
355C22×Dic5—34no—
356C22×Dic5—34no—
357C22×Dic5—122no—
358C22×Dic5—122no—
359C22×Dic5C22×D311yescharacteristic
360C22×Dic5C22×D311yescharacteristic
361C22×Dic5C22×D311yescharacteristic
362C2×D20—34no—
363C2×D20—64no—
364C2×C4×D5—34no—
365C2×C4×D5—42no—
366C2×C4×D5—122no—
367C2×C4×D5C22×D314yes—
368C5×C4⋊C4—34no—
369C5×C22⋊C4—34no—
370C5×C22⋊C4C22×D314yes—
371C22⋊Dic5—34no—
372C22⋊Dic5—34no—
373C22⋊Dic5—34no—
374C22⋊Dic5C22×D314yes—
375#685—34no—
376#685—34no—
377#685—34no—
378#685C22×D314yes—
379C4⋊Dic5—34no—
380C4⋊Dic5—34no—
381C4⋊Dic5—34no—
382C4⋊Dic5—34no—
383C4⋊Dic5C22×D314yes—
384#683—34no—
385#683C22×D314yes—
386C4×Dic5—34no—
387C4×Dic5—34no—
388#540—1516no—
389C2×#127—151no—
390C2×#125—151no—
391C2×#123—51no—
392C2×#123—151no—
393C2×#123—151no—
394C2×#123—151no—
395C2×#121—31no—
396C2×#121—151no—
397C2×#121—151no—
398C2×#121—151no—
399C2×#121—151no—
400C2×#121—151no—
401C2×C4×D4—151no—
402C2×C4×D4—151no—
403C2×#117—151no—
404C22×C3×C5—22no—
405C22×C3×C5—22no—
406C22×C3×C5—22no—
407C22×C3×C5—44no—
408C22×C3×C5C2×#4112yes—
409C22×C3×C5H(5,𝔽2)12yes—
410C22×C3×C5H(5,𝔽2)12yes—
411C22×C3×C5C2511yescharacteristic
412C2×D15—22no—
413C2×D15—22no—
414C2×D15—22no—
415C2×D15—44no—
416C2×C5×D3—22no—
417C2×C5×D3—22no—
418C2×C5×D3—22no—
419C2×C5×D3—22no—
420C2×C5×D3—22no—
421C2×C5×D3—22no—
422C2×C5×D3—44no—
423C2×C5×D3—44no—
424C2×C3×D5—22no—
425C2×C3×D5—22no—
426C2×C3×D5—22no—
427C2×C3×D5—44no—
428C3×C4×C5—22no—
429C3×C4×C5—22no—
430Dic15—22no—
431Dic15—22no—
432Dic15—22no—
433C3×Dic5—22no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C5×Dic3—22no—
437C5×Dic3C2×#4114yes—
438C24×C3—51no—
439C24×C3C22×D511yescharacteristic
440C23×D3—51no—
441C23×D3C22×D511yescharacteristic
442C23×D3C22×D511yescharacteristic
443C2×C3×D4—54no—
444C2×C3×D4—202no—
445C22×C3×C4—51no—
446C22×C3×C4—51no—
447C22×C3×C4—51no—
448C22×C3×C4—54no—
449C22×C3×C4—202no—
450C22×C3×C4C22×D511yescharacteristic
451C22×C3×C4C22×D511yescharacteristic
452C2×#67—24no—
453C2×#67—42no—
454C2×#67—54no—
455C2×#67—54no—
456C2×#67—54no—
457C2×#67—54no—
458C2×#67—104no—
459C2×#67—202no—
460C2×#67—202no—
461C2×#67—202no—
462C2×#67C22×D514yes—
463C2×#67C22×D514yes—
464C22×Dic3—51no—
465C22×Dic3—51no—
466C22×Dic3—51no—
467C22×Dic3—54no—
468C22×Dic3—202no—
469C22×Dic3C22×D511yescharacteristic
470C22×Dic3C22×D511yescharacteristic
471C2×D12—42no—
472C2×D12—54no—
473C2×D12—54no—
474C2×D12—202no—
475C2×D12—202no—
476C2×D12C22×D514yes—
477C2×C4×D3—24no—
478C2×C4×D3—54no—
479C2×C4×D3—54no—
480C2×C4×D3—202no—
481C2×C4×D3—202no—
482C2×C4×D3C22×D514yes—
483C3×C4⋊C4—54no—
484C3×C4⋊C4—54no—
485C3×C22⋊C4—54no—
486C3×C22⋊C4—54no—
487C3×C22⋊C4C22×D514yes—
488#217—54no—
489(C2×D3)⋊C4—54no—
490(C2×D3)⋊C4—54no—
491(C2×D3)⋊C4—54no—
492(C2×D3)⋊C4—54no—
493(C2×D3)⋊C4—54no—
494(C2×D3)⋊C4C22×D514yes—
495C4⋊Dic3—54no—
496C4⋊Dic3—54no—
497Dic3⋊C4—54no—
498Dic3⋊C4—54no—
499Dic3⋊C4—54no—
500Dic3⋊C4C22×D514yes—
501C4×Dic3—54no—
502C4×Dic3—54no—
503C23×C5—22no—
504C23×C5—22no—
505C23×C5—22no—
506C23×C5—32no—
507C23×C5—32no—
508C23×C5—62no—
509C23×C5—62no—
510C23×C5—62no—
511C23×C5—62no—
512C23×C5—62no—
513C23×C5—62no—
514C23×C5C23×D312yes—
515C23×C5C23×D311yescharacteristic
516C22×D5—22no—
517C22×D5—22no—
518C22×D5—22no—
519C22×D5—32no—
520C22×D5—62no—
521C22×D5—62no—
522C22×D5—62no—
523C22×D5C23×D312yes—
524C5×D4—68no—
525C5×D4—124no—
526C5×D4—124no—
527C2×C4×C5—22no—
528C2×C4×C5—22no—
529C2×C4×C5—34no—
530C2×C4×C5—32no—
531C2×C4×C5—32no—
532C2×C4×C5—68no—
533C2×C4×C5—62no—
534C2×C4×C5C23×D312yes—
535C2×C4×C5C23×D312yes—
536C22⋊D5—44no—
537C22⋊D5—124no—
538C22⋊D5—124no—
539C22⋊D5—124no—
540C22⋊D5—124no—
541C22⋊D5—124no—
542C2×Dic5—22no—
543C2×Dic5—22no—
544C2×Dic5—22no—
545C2×Dic5—32no—
546C2×Dic5—32no—
547C2×Dic5—32no—
548C2×Dic5—62no—
549C2×Dic5—62no—
550C2×Dic5—62no—
551C2×Dic5—124no—
552C2×Dic5—124no—
553C2×Dic5C23×D312yes—
554C2×Dic5C23×D312yes—
555C2×Dic5C23×D312yes—
556D20—68no—
557C4×D5—44no—
558C4×D5—124no—
559C22×D4—31no—
560C22×D4—31no—
561C22×D4—31no—
562C22×D4—51no—
563C22×D4—151no—
564C22×D4—151no—
565C22×D4—151no—
566C22×D4—151no—
567C22×D4—151no—
568C22×D4—151no—
569C23×C4—31no—
570C23×C4—51no—
571C23×C4—151no—
572C23×C4—151no—
573C23×C4—151no—
574#127—158no—
575#125—158no—
576#123—58no—
577#123—158no—
578#123—158no—
579#123—158no—
580#121—38no—
581#121—158no—
582#121—158no—
583#121—158no—
584#121—158no—
585#121—158no—
586C4×D4—158no—
587C4×D4—158no—
588#117—158no—
589C2×C4⋊C4—31no—
590C2×C4⋊C4—51no—
591C2×C4⋊C4—51no—
592C2×C4⋊C4—151no—
593C2×C4⋊C4—151no—
594C2×C4⋊C4—151no—
595C2×C4⋊C4—151no—
596C2×C4⋊C4—151no—
597C2×C22⋊C4—31no—
598C2×C22⋊C4—51no—
599C2×C22⋊C4—51no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4D3×D511yescharacteristic
607C2×C42—151no—
608C2×C42—151no—
609C2×C3×C5—42no—
610C2×C3×C5#54014yescomplemented
611C2×C3×C5C22×#4111yescharacteristic
612C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
613C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
614D15—42no—
615C3×D5—42no—
616C5×D3—42no—
617C5×D3—42no—
618C23×C3—22no—
619C23×C3—22no—
620C23×C3—22no—
621C23×C3—52no—
622C23×C3—102no—
623C23×C3—102no—
624C23×C3—102no—
625C23×C3C23×D512yes—
626C23×C3C23×D511yescharacteristic
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—52no—
634C22×D3—102no—
635C22×D3—102no—
636C22×D3—102no—
637C22×D3C23×D512yes—
638C22×D3C23×D512yes—
639C3×D4—204no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—52no—
643C2×C3×C4—52no—
644C2×C3×C4—52no—
645C2×C3×C4—102no—
646C2×C3×C4—102no—
647C2×C3×C4—102no—
648C2×C3×C4—204no—
649C2×C3×C4C23×D512yes—
650C2×C3×C4C23×D512yes—
651#67—28no—
652#67—44no—
653#67—108no—
654#67—204no—
655#67—204no—
656#67—204no—
657C2×Dic3—22no—
658C2×Dic3—52no—
659C2×Dic3—52no—
660C2×Dic3—52no—
661C2×Dic3—102no—
662C2×Dic3—102no—
663C2×Dic3—102no—
664C2×Dic3—204no—
665C2×Dic3#71114yes—
666C2×Dic3C23×D512yes—
667C2×Dic3C23×D512yes—
668D12—44no—
669D12—204no—
670D12—204no—
671C4×D3—28no—
672C4×D3—204no—
673C4×D3—204no—
674C22×C5—22no—
675C22×C5—22no—
676C22×C5—22no—
677C22×C5—44no—
678C22×C5—62no—
679C22×C5—62no—
680C22×C5—62no—
681C22×C5—62no—
682C22×C5—62no—
683C22×C5—62no—
684C22×C5—124no—
685C22×C5—124no—
686C22×C5#100412yes—
687C22×C5D3×#4112yes—
688C22×C5#100912yes—
689C22×C5C24×D311yescharacteristic
690C2×D5—22no—
691C2×D5—22no—
692C2×D5—22no—
693C2×D5—44no—
694C2×D5—62no—
695C2×D5—62no—
696C2×D5—62no—
697C2×D5—124no—
698C4×C5—22no—
699C4×C5—22no—
700C4×C5—34no—
701C4×C5—62no—
702Dic5—22no—
703Dic5—22no—
704Dic5—22no—
705Dic5—62no—
706Dic5—62no—
707Dic5—62no—
708C24—31no—
709C24—31no—
710C24—51no—
711C24—151no—
712C24C2×D3×D511yescharacteristic
713C2×D4—34no—
714C2×D4—34no—
715C2×D4—34no—
716C2×D4—54no—
717C2×D4—64no—
718C2×D4—122no—
719C2×D4—122no—
720C2×D4—154no—
721C2×D4—154no—
722C2×D4—154no—
723C2×D4—154no—
724C2×D4—154no—
725C2×D4—154no—
726C2×D4—202no—
727C2×D4—304no—
728C2×D4—602no—
729C2×D4—602no—
730C2×D4—602no—
731C2×D4—602no—
732C2×D4—602no—
733C22×C4—31no—
734C22×C4—31no—
735C22×C4—34no—
736C22×C4—51no—
737C22×C4—51no—
738C22×C4—51no—
739C22×C4—54no—
740C22×C4—64no—
741C22×C4—154no—
742C22×C4—154no—
743C22×C4—151no—
744C22×C4—151no—
745C22×C4—151no—
746C22×C4—154no—
747C22×C4—202no—
748C22×C4—602no—
749C22×C4—602no—
750C22×C4—602no—
751C22×C4C2×D3×D511yescharacteristic
752C22×C4C2×D3×D511yescharacteristic
753C4⋊C4—34no—
754C4⋊C4—54no—
755C4⋊C4—54no—
756C4⋊C4—154no—
757C4⋊C4—154no—
758C4⋊C4—154no—
759C4⋊C4—154no—
760C4⋊C4—154no—
761C22⋊C4—34no—
762C22⋊C4—54no—
763C22⋊C4—54no—
764C22⋊C4—154no—
765C22⋊C4—154no—
766C22⋊C4—154no—
767C22⋊C4—154no—
768C22⋊C4—154no—
769C22⋊C4—154no—
770C22⋊C4C2×D3×D514yes—
771C42—154no—
772C42—154no—
773C3×C5C2×#54011yescharacteristic, complemented, Hall
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—44no—
778C22×C3—102no—
779C22×C3—102no—
780C22×C3—102no—
781C22×C3—204no—
782C22×C3C2×#71112yes—
783C22×C3#414412yes—
784C22×C3#414912yes—
785C22×C3C24×D511yescharacteristic
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—44no—
793C2×D3—44no—
794C2×D3—102no—
795C2×D3—102no—
796C2×D3—102no—
797C2×D3—204no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—102no—
801C3×C4—102no—
802C3×C4—102no—
803Dic3—22no—
804Dic3—102no—
805Dic3—102no—
806Dic3—102no—
807Dic3C2×#71114yes—
808C2×C5—42no—
809C2×C5—122no—
810C2×C5—122no—
811C2×C5#566314yescomplemented
812C2×C5C2×#100411yescharacteristic
813C2×C5C2×D3×#4111yescharacteristic
814C2×C5C2×#100911yescharacteristic
815D5—42no—
816D5—122no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—32no—
821C23—32no—
822C23—52no—
823C23—62no—
824C23—62no—
825C23—62no—
826C23—62no—
827C23—62no—
828C23—62no—
829C23—102no—
830C23—102no—
831C23—102no—
832C23—152no—
833C23—302no—
834C23—302no—
835C23—302no—
836C23C22×D3×D512yes—
837C23C22×D3×D511yescharacteristic
838D4—68no—
839D4—124no—
840D4—124no—
841D4—204no—
842D4—308no—
843D4—604no—
844D4—604no—
845D4—604no—
846D4—604no—
847D4—604no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—34no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—52no—
854C2×C4—52no—
855C2×C4—52no—
856C2×C4—68no—
857C2×C4—62no—
858C2×C4—102no—
859C2×C4—102no—
860C2×C4—102no—
861C2×C4—152no—
862C2×C4—152no—
863C2×C4—152no—
864C2×C4—204no—
865C2×C4—302no—
866C2×C4—302no—
867C2×C4—302no—
868C2×C4—604no—
869C2×C4—604no—
870C2×C4—604no—
871C2×C4C22×D3×D512yes—
872C2×C4C22×D3×D512yes—
873C2×C3—42no—
874C2×C3—202no—
875C2×C3#6595314yescomplemented
876C2×C3C22×#71111yescharacteristic
877C2×C3C2×#414411yescharacteristic
878C2×C3C2×#414911yescharacteristic
879D3—42no—
880D3—42no—
881D3—202no—
882C5C2×#566311yescharacteristic, complemented, Sylow
883C22—22no—
884C22—22no—
885C22—22no—
886C22—44no—
887C22—62no—
888C22—62no—
889C22—62no—
890C22—62no—
891C22—62no—
892C22—62no—
893C22—102no—
894C22—102no—
895C22—102no—
896C22—124no—
897C22—124no—
898C22—204no—
899C22—302no—
900C22—302no—
901C22—302no—
902C22—604no—
903C22#9201912yes—
904C22D3×#71112yes—
905C22#9202512yes—
906C22C23×D3×D511yescharacteristic
907C4—22no—
908C4—22no—
909C4—34no—
910C4—62no—
911C4—102no—
912C4—102no—
913C4—102no—
914C4—302no—
915C4—302no—
916C4—302no—
917C3C2×#6595311yescharacteristic, complemented, Sylow
918C2—42no—
919C2—122no—
920C2—122no—
921C2—202no—
922C2—602no—
923C2#1175314114yesdirect product factor
924C2C2×#9201911yescharacteristic
925C2C2×D3×#71111yescharacteristic
926C2C2×#9202511yescharacteristic
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×#540
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×#91775C2semidirect
2. C2×C5×#884C2semidirect
3. C2×C3×#4029C2semidirect
4. C2×#91571C2semidirect
5. C2×#91567C2semidirect
6. C2×#67⋊Dic5C2semidirect
7. C2×#91557C2semidirect
8. C2×#91457C2semidirect
9. C2×#91454C2semidirect
10. C2×#91449C2semidirect
11. C2×#91444C2semidirect
12. C2×#91438C2semidirect
13. C2×#91416C2semidirect
14. C2×#91343C2semidirect
15. C2×#91338C2semidirect
16. #11753141C2direct (N × H)
38. #91775C22semidirect
41. C5×#884C22semidirect
46. C3×#4029C22semidirect
47. #91571C22semidirect
48. #91567C22semidirect
49. #67⋊Dic5C22semidirect
50. #91557C22semidirect
60. #91457C22semidirect
61. #91454C22semidirect
62. #91449C22semidirect
63. #91444C22semidirect
64. #91438C22semidirect
65. #91416C22semidirect
66. #91343C22semidirect
67. #91338C22semidirect
84. C2×#4029D3semidirect
163. C2×#884D5semidirect
215. #4029C2×D3semidirect
320. #884C2×D5semidirect
610. C2×C3×C5#540semidirect
773. C3×C5C2×#540semidirect
811. C2×C5#5663semidirect
875. C2×C3#65953semidirect
882. C5C2×#5663semidirect
917. C3C2×#65953semidirect
923. C2#11753141direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917752
C2×C5×#8842
C2×C3×#40292
C2×#915712
C2×#915672
C2×#67⋊Dic52
C2×#915572
C2×#914572
C2×#914542
C2×#914492
C2×#914442
C2×#914382
C2×#914162
C2×#913432
C2×#913382
#117531412
C2×#659533
C2×#56635