Finite Group Databasebeta

← C2×#11753177 #14495222

Subgroups — C2×#11753177 #14495222

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×#91772C211yesmaximal, characteristic, complemented
2C2×C5×#882C211yesmaximal, characteristic, complemented
3C2×C3×#4029C211yesmaximal, characteristic, complemented
4C2×#91570C211yesmaximal, characteristic, complemented
5C2×#91568C211yesmaximal, characteristic, complemented
6C2×#91567C211yesmaximal, characteristic, complemented
7C2×#91555C211yesmaximal, characteristic, complemented
8C2×#91466C211yesmaximal, characteristic, complemented
9C2×#91461C211yesmaximal, characteristic, complemented
10C2×#91453C211yesmaximal, characteristic, complemented
11C2×#91449C211yesmaximal, characteristic, complemented
12C2×#91448C211yesmaximal, characteristic, complemented
13C2×#91416C211yesmaximal, characteristic, complemented
14C2×#91342C211yesmaximal, characteristic, complemented
15C2×#91341C211yesmaximal, characteristic, complemented
16#11753177C2116yesmaximal, direct product factor
17C2×#65929—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic, complemented
21C22×C5×#67C2211yescharacteristic
22C22×C5×D12C2211yescharacteristic
23C22×C5×D12C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic, complemented
26C22×#1203C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1203C2211yescharacteristic, complemented
29C22×#1202C2211yescharacteristic, complemented
30C22×#1201C2211yescharacteristic
31C22×#1201C2211yescharacteristic
32C22×#1201C2211yescharacteristic, complemented
33C22×D3×Dic5C2211yescharacteristic, complemented
34C2×C3×C5×C22⋊C4C2211yescharacteristic
35C2×#6719C2211yescharacteristic
36C2×#6714C2211yescharacteristic, complemented
37C2×C4⋊Dic15C2211yescharacteristic, complemented
38C2×#6712C2211yescharacteristic, complemented
39#91772C2218yescomplemented
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic
41C2×C5×(C2×D3)⋊C4C2211yescharacteristic
42C5×#882C2218yescomplemented
43C2×C3×C22⋊Dic5C2211yescharacteristic
44C2×C3×#685C2211yescharacteristic, complemented
45C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
46C2×C3×#683C2211yescharacteristic, complemented
47C3×#4029C2218yescomplemented
48#91570C2218yescomplemented
49#91568C2218yescomplemented
50#91567C2218yescomplemented
51#91555C2218yescomplemented
52C2×#6669C2211yescharacteristic, complemented
53C2×#6668C2211yescharacteristic, complemented
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91466C2218yescomplemented
61#91461C2218yescomplemented
62#91453C2218yescomplemented
63#91449C2218yescomplemented
64#91448C2218yescomplemented
65#91416C2218yescomplemented
66#91342C2218yescomplemented
67#91341C2218yescomplemented
68C2×#5666—51nomaximal, Hall
69C2×C5×#120—31no—
70C2×#4099—31no—
71C2×#4099—31no—
72C2×#4086—31no—
73C2×#4085—31no—
74C2×#4085—31no—
75C2×#4084—31no—
76C2×#4084—31no—
77C2×#4081—31no—
78#65929—316no—
79C2×#4030—31no—
80C2×#4030—31no—
81C2×#4029—31no—
82C2×#4029D311yescharacteristic, complemented
83C2×#4025—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3—42no—
88C23×C5×D3—42no—
89C23×C5×D3—42no—
90C23×C5×D3C2311yescharacteristic
91C23×C5×D3C2311yescharacteristic
92C23×C5×D3C2311yescharacteristic
93C23×C5×D3C2314yes—
94C23×C3×D5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C2×#1220—42no—
98C2×#1220C2314yes—
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C2×C4×D15—42no—
103C2×C4×D15C2314yescomplemented
104C2×C5×#67—42no—
105C2×C5×#67C2314yes—
106C22×C5×Dic3C2311yescharacteristic
107C2×C5×D12—42no—
108C2×C5×D12—42no—
109C2×C5×D12C2314yes—
110C2×C5×D12C2314yes—
111C2×C3×C22⋊D5—42no—
112C2×C3×C22⋊D5C2314yes—
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C2×C3×C4×D5—42no—
117C2×C3×C4×D5C2314yescomplemented
118C2×#1203—42no—
119C2×#1203—42no—
120C2×#1203—42no—
121C2×#1203C2314yes—
122C2×#1203C2314yes—
123C2×#1203C2314yescomplemented
124C2×#1202—42no—
125C2×#1202C2314yescomplemented
126C2×#1201—42no—
127C2×#1201—42no—
128C2×#1201—42no—
129C2×#1201C2314yes—
130C2×#1201C2314yes—
131C2×#1201C2314yescomplemented
132C2×D3×Dic5—42no—
133C2×D3×Dic5C2314yescomplemented
134C3×C5×C22⋊C4C2314yes—
135#6719C2314yes—
136#6714C2314yescomplemented
137C4⋊Dic15C2314yescomplemented
138#6712C2314yescomplemented
139C5×(C2×D3)⋊C4C2314yes—
140C5×(C2×D3)⋊C4C2314yes—
141C3×C22⋊Dic5C2314yes—
142C3×#685C2314yescomplemented
143C3×C4⋊Dic5C2314yescomplemented
144C3×#683C2314yescomplemented
145#6669C2314yescomplemented
146#6668C2314yescomplemented
147(C2×D3)⋊Dic5C2314yes—
148(C2×D3)⋊Dic5C2314yes—
149(C2×D3)⋊Dic5C2314yes—
150(C2×D3)⋊Dic5C2314yes—
151(C2×D3)⋊Dic5C2314yescomplemented
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×#884—51no—
165C2×#883—51no—
166C2×#883—51no—
167C2×#882—51no—
168C2×#882D511yescharacteristic, complemented
169C25×C5—31no—
170C22×C5×D4—31no—
171C22×C5×D4—31no—
172C22×C5×D4—31no—
173C22×C22⋊D5—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×Dic5—31no—
182C22×D20—31no—
183C22×C4×D5—31no—
184C22×C4×D5C2×D311yescharacteristic, complemented
185C5×#120—38no—
186C2×C5×C22⋊C4—31no—
187C2×C5×C22⋊C4—31no—
188C2×C5×C22⋊C4C2×D311yescharacteristic
189#4099—38no—
190#4099—38no—
191C2×C22⋊Dic5—31no—
192C2×C22⋊Dic5—31no—
193C2×C22⋊Dic5—31no—
194C2×C22⋊Dic5—31no—
195C2×C22⋊Dic5—31no—
196C2×C22⋊Dic5—31no—
197C2×C22⋊Dic5C2×D311yescharacteristic
198#4086—38no—
199#4085—38no—
200#4085—38no—
201#4084—38no—
202#4084—38no—
203#4081—38no—
204C2×#685—31no—
205C2×#685C2×D311yescharacteristic, complemented
206C2×C4⋊Dic5—31no—
207C2×C4⋊Dic5C2×D311yescharacteristic, complemented
208C2×#683—31no—
209C2×#683—31no—
210C2×#683—31no—
211C2×#683C2×D311yescharacteristic, complemented
212C2×C4×Dic5—31no—
213#4030—38no—
214#4030—38no—
215#4029—38no—
216#4029C2×D318yescomplemented
217#4025—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×D15C2412yes—
229C22×C5×D3—22no—
230C22×C5×D3—22no—
231C22×C5×D3—22no—
232C22×C5×D3—22no—
233C22×C5×D3—22no—
234C22×C5×D3—22no—
235C22×C5×D3—22no—
236C22×C5×D3—22no—
237C22×C5×D3—22no—
238C22×C5×D3—44no—
239C22×C5×D3—44no—
240C22×C5×D3—44no—
241C22×C5×D3—416no—
242C22×C5×D3C2412yes—
243C22×C5×D3C2412yes—
244C22×C5×D3C2412yes—
245C22×C3×D5—22no—
246C22×C3×D5—22no—
247C22×C3×D5—22no—
248C22×C3×D5C2412yes—
249C2×C3×C4×C5—22no—
250C2×C3×C4×C5—22no—
251C2×C3×C4×C5C2412yes—
252C2×C3×C4×C5C2412yes—
253#1220—44no—
254C2×Dic15—22no—
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15C2412yes—
258C2×Dic15C2412yes—
259C2×Dic15C2412yes—
260C4×D15—44no—
261C5×#67—44no—
262C2×C5×Dic3—22no—
263C2×C5×Dic3C2412yes—
264C5×D12—44no—
265C5×D12—44no—
266C3×C22⋊D5—44no—
267C2×C3×Dic5—22no—
268C2×C3×Dic5—22no—
269C2×C3×Dic5—22no—
270C2×C3×Dic5C2412yes—
271C2×C3×Dic5C2412yes—
272C2×C3×Dic5C2412yes—
273C3×C4×D5—44no—
274#1203—44no—
275#1203—44no—
276#1203—44no—
277#1202—44no—
278#1201—44no—
279#1201—44no—
280#1201—44no—
281D3×Dic5—44no—
282C24×D3C2×D511yescharacteristic
283C22×C3×D4—51no—
284C23×C3×C4—51no—
285C22×#67—51no—
286C22×#67—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67C2×D511yescharacteristic
291C22×D12—51no—
292C22×D12—51no—
293C22×D12—51no—
294C22×D12C2×D511yescharacteristic
295C22×D12C2×D511yescharacteristic
296C22×C4×D3—51no—
297C22×C4×D3—51no—
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
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
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#895—58no—
326#884—58no—
327#884—58no—
328#883—58no—
329#883—58no—
330#882—58no—
331#882C2×D518yescomplemented
332C24×C5—31no—
333C24×C5—31no—
334C24×C5—31no—
335C24×C5—34no—
336C24×C5—122no—
337C24×C5—122no—
338C24×C5—122no—
339C24×C5C22×D311yescharacteristic
340C23×D5—31no—
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×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—34no—
358C2×C22⋊D5—42no—
359C2×C22⋊D5—122no—
360C2×C22⋊D5—122no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5—122no—
363C2×C22⋊D5—122no—
364C2×C22⋊D5—122no—
365C2×C22⋊D5—122no—
366C2×C22⋊D5C22×D314yes—
367C22×Dic5—31no—
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5—34no—
371C22×Dic5—122no—
372C22×Dic5C22×D311yescharacteristic
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D311yescharacteristic
375C2×D20—34no—
376C2×D20—122no—
377C2×C4×D5—34no—
378C2×C4×D5—42no—
379C2×C4×D5—122no—
380C2×C4×D5C22×D314yescomplemented
381C5×C22⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4C22×D314yes—
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5—34no—
387C22⋊Dic5—34no—
388C22⋊Dic5—34no—
389C22⋊Dic5—34no—
390C22⋊Dic5C22×D314yes—
391#685—34no—
392#685C22×D314yescomplemented
393C4⋊Dic5—34no—
394C4⋊Dic5C22×D314yescomplemented
395#683—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—151no—
408C2×#121—151no—
409C2×#121—151no—
410C2×#121—151no—
411C2×#121—151no—
412C2×#121—151no—
413C2×#120—31no—
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—44no—
428C2×C5×D3—22no—
429C2×C5×D3—22no—
430C2×C5×D3—22no—
431C2×C5×D3—22no—
432C2×C5×D3—22no—
433C2×C5×D3—22no—
434C2×C5×D3—22no—
435C2×C5×D3—22no—
436C2×C5×D3—22no—
437C2×C5×D3—416no—
438C2×C5×D3—44no—
439C2×C5×D3—44no—
440C2×C5×D3—44no—
441C2×C3×D5—22no—
442C2×C3×D5—22no—
443C2×C3×D5—22no—
444C2×C3×D5—44no—
445C3×C4×C5—22no—
446C3×C4×C5—22no—
447Dic15—22no—
448Dic15—22no—
449Dic15—22no—
450C3×Dic5—22no—
451C3×Dic5—22no—
452C3×Dic5—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3C22×D511yescharacteristic
456C23×D3—42no—
457C23×D3—42no—
458C23×D3—42no—
459C23×D3—51no—
460C23×D3C22×D511yescharacteristic
461C23×D3C22×D511yescharacteristic
462C23×D3C22×D511yescharacteristic
463C23×D3C22×D514yes—
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—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×#67C22×D514yes—
485C22×Dic3—51no—
486C22×Dic3—51no—
487C22×Dic3—51no—
488C22×Dic3C22×D511yescharacteristic
489C2×D12—42no—
490C2×D12—42no—
491C2×D12—54no—
492C2×D12—54no—
493C2×D12—54no—
494C2×D12—202no—
495C2×D12—202no—
496C2×D12—202no—
497C2×D12C22×D514yes—
498C2×D12C22×D514yes—
499C2×C4×D3—54no—
500C2×C4×D3—54no—
501C2×C4×D3—202no—
502C2×C4×D3—202no—
503C3×C4⋊C4—54no—
504C3×C4⋊C4—54no—
505C3×C22⋊C4—54no—
506C3×C22⋊C4—54no—
507C3×C22⋊C4C22×D514yes—
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×D514yes—
517C4⋊Dic3—54no—
518C4⋊Dic3—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4—54no—
521C4×Dic3—54no—
522C23×C5—22no—
523C23×C5—22no—
524C23×C5—22no—
525C23×C5—32no—
526C23×C5—32no—
527C23×C5—32no—
528C23×C5—62no—
529C23×C5—62no—
530C23×C5—62no—
531C23×C5—62no—
532C23×C5—62no—
533C23×C5—62no—
534C23×C5—62no—
535C23×C5—62no—
536C23×C5—62no—
537C23×C5—124no—
538C23×C5—124no—
539C23×C5—124no—
540C23×C5—1216no—
541C23×C5C23×D312yes—
542C23×C5C23×D311yescharacteristic
543C22×D5—22no—
544C22×D5—22no—
545C22×D5—22no—
546C22×D5—32no—
547C22×D5—62no—
548C22×D5—62no—
549C22×D5—62no—
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—62no—
558C2×C4×C5C23×D312yes—
559C2×C4×C5C23×D312yes—
560C22⋊D5—44no—
561C22⋊D5—124no—
562C22⋊D5—124no—
563C22⋊D5—124no—
564C22⋊D5—124no—
565C22⋊D5—124no—
566C22⋊D5—124no—
567C22⋊D5—124no—
568C2×Dic5—22no—
569C2×Dic5—22no—
570C2×Dic5—22no—
571C2×Dic5—32no—
572C2×Dic5—32no—
573C2×Dic5—32no—
574C2×Dic5—62no—
575C2×Dic5—62no—
576C2×Dic5—62no—
577C2×Dic5—124no—
578C2×Dic5C23×D312yes—
579C2×Dic5C23×D312yes—
580C2×Dic5C23×D312yes—
581D20—124no—
582C4×D5—44no—
583C4×D5—124no—
584C25—31no—
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—51no—
598C23×C4—151no—
599C23×C4—151no—
600#127—158no—
601#126—158no—
602#126—158no—
603#123—58no—
604#123—158no—
605#123—158no—
606#121—158no—
607#121—158no—
608#121—158no—
609#121—158no—
610#121—158no—
611#121—158no—
612#120—38no—
613#120—158no—
614#120—158no—
615C2×C4⋊C4—51no—
616C2×C4⋊C4—51no—
617C2×C4⋊C4—151no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4—151no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—51no—
624C2×C22⋊C4—51no—
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
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—
640C3×D5—42no—
641C5×D3—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—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—44no—
663C22×D3—44no—
664C22×D3—44no—
665C22×D3—416no—
666C22×D3—52no—
667C22×D3—102no—
668C22×D3—102no—
669C22×D3—102no—
670C22×D3C23×D512yes—
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—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—204no—
702D12—204no—
703D12—204no—
704C4×D3—204no—
705C4×D3—204no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—22no—
709C22×C5—44no—
710C22×C5—62no—
711C22×C5—62no—
712C22×C5—62no—
713C22×C5—62no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—62no—
717C22×C5—62no—
718C22×C5—62no—
719C22×C5—1216no—
720C22×C5—124no—
721C22×C5—124no—
722C22×C5—124no—
723C22×C5#100412yes—
724C22×C5#100912yes—
725C22×C5#100912yes—
726C22×C5C24×D311yescharacteristic
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—44no—
731C2×D5—62no—
732C2×D5—62no—
733C2×D5—62no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—22no—
737C4×C5—62no—
738Dic5—22no—
739Dic5—22no—
740Dic5—22no—
741Dic5—62no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—31no—
746C24—31no—
747C24—34no—
748C24—51no—
749C24—122no—
750C24—122no—
751C24—122no—
752C24—151no—
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—51no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—54no—
783C22×C4—154no—
784C22×C4—151no—
785C22×C4—151no—
786C22×C4—151no—
787C22×C4—154no—
788C22×C4—202no—
789C22×C4—602no—
790C22×C4—602no—
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—54no—
794C4⋊C4—54no—
795C4⋊C4—154no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4—154no—
799C22⋊C4—34no—
800C22⋊C4—34no—
801C22⋊C4—54no—
802C22⋊C4—54no—
803C22⋊C4—154no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4C2×D3×D514yes—
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#414412yes—
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—416no—
835C2×D3—44no—
836C2×D3—44no—
837C2×D3—44no—
838C2×D3—102no—
839C2×D3—102no—
840C2×D3—102no—
841C2×D3—204no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—102no—
845C3×C4—102no—
846C3×C4—102no—
847Dic3—22no—
848Dic3—102no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—122no—
853C2×C5—122no—
854C2×C5—122no—
855C2×C5#566614yescomplemented
856C2×C5C2×#100411yescharacteristic
857C2×C5C2×#100911yescharacteristic
858C2×C5C2×#100911yescharacteristic
859D5—42no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—32no—
865C23—32no—
866C23—32no—
867C23—52no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—102no—
878C23—102no—
879C23—102no—
880C23—124no—
881C23—124no—
882C23—124no—
883C23—1216no—
884C23—152no—
885C23—302no—
886C23—302no—
887C23—302no—
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—52no—
906C2×C4—52no—
907C2×C4—52no—
908C2×C4—62no—
909C2×C4—102no—
910C2×C4—102no—
911C2×C4—102no—
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×C4—604no—
921C2×C4C22×D3×D512yes—
922C2×C4C22×D3×D512yes—
923C2×C3—42no—
924C2×C3—202no—
925C2×C3#6592914yescomplemented
926C2×C3C2×#414411yescharacteristic
927C2×C3C2×#414411yescharacteristic
928C2×C3C2×#414411yescharacteristic
929D3—42no—
930D3—42no—
931D3—42no—
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—62no—
945C22—62no—
946C22—62no—
947C22—102no—
948C22—102no—
949C22—102no—
950C22—1216no—
951C22—124no—
952C22—124no—
953C22—124no—
954C22—204no—
955C22—302no—
956C22—302no—
957C22—302no—
958C22—604no—
959C22#9201812yes—
960C22#9202512yes—
961C22#9202712yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—62no—
966C4—102no—
967C4—102no—
968C4—102no—
969C4—302no—
970C4—302no—
971C4—302no—
972C3C2×#6592911yescharacteristic, complemented, Sylow
973C2—42no—
974C2—122no—
975C2—122no—
976C2—122no—
977C2—202no—
978C2—602no—
979C2#1175317714yesdirect product factor
980C2C2×#9201811yescharacteristic
981C2C2×#9202511yescharacteristic
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×#91772C2semidirect
2. C2×C5×#882C2semidirect
3. C2×C3×#4029C2semidirect
4. C2×#91570C2semidirect
5. C2×#91568C2semidirect
6. C2×#91567C2semidirect
7. C2×#91555C2semidirect
8. C2×#91466C2semidirect
9. C2×#91461C2semidirect
10. C2×#91453C2semidirect
11. C2×#91449C2semidirect
12. C2×#91448C2semidirect
13. C2×#91416C2semidirect
14. C2×#91342C2semidirect
15. C2×#91341C2semidirect
16. #11753177C2direct (N × H)
20. C22×C4×D15C22semidirect
25. C22×C3×C4×D5C22semidirect
28. C22×#1203C22semidirect
29. C22×#1202C22semidirect
32. C22×#1201C22semidirect
33. C22×D3×Dic5C22semidirect
36. C2×#6714C22semidirect
37. C2×C4⋊Dic15C22semidirect
38. C2×#6712C22semidirect
39. #91772C22semidirect
42. C5×#882C22semidirect
44. C2×C3×#685C22semidirect
45. C2×C3×C4⋊Dic5C22semidirect
46. C2×C3×#683C22semidirect
47. C3×#4029C22semidirect
48. #91570C22semidirect
49. #91568C22semidirect
50. #91567C22semidirect
51. #91555C22semidirect
52. C2×#6669C22semidirect
53. C2×#6668C22semidirect
58. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91466C22semidirect
61. #91461C22semidirect
62. #91453C22semidirect
63. #91449C22semidirect
64. #91448C22semidirect
65. #91416C22semidirect
66. #91342C22semidirect
67. #91341C22semidirect
82. C2×#4029D3semidirect
103. C2×C4×D15C23semidirect
117. C2×C3×C4×D5C23semidirect
123. C2×#1203C23semidirect
125. C2×#1202C23semidirect
131. C2×#1201C23semidirect
133. C2×D3×Dic5C23semidirect
136. #6714C23semidirect
137. C4⋊Dic15C23semidirect
138. #6712C23semidirect
142. C3×#685C23semidirect
143. C3×C4⋊Dic5C23semidirect
144. C3×#683C23semidirect
145. #6669C23semidirect
146. #6668C23semidirect
151. (C2×D3)⋊Dic5C23semidirect
152. Dic3×Dic5C23semidirect
168. C2×#882D5semidirect
184. C22×C4×D5C2×D3semidirect
205. C2×#685C2×D3semidirect
207. C2×C4⋊Dic5C2×D3semidirect
211. C2×#683C2×D3semidirect
216. #4029C2×D3semidirect
331. #882C2×D5semidirect
380. C2×C4×D5C22×D3semidirect
392. #685C22×D3semidirect
394. C4⋊Dic5C22×D3semidirect
398. #683C22×D3semidirect
635. C2×C3×C5#560semidirect
812. C3×C5C2×#560semidirect
855. C2×C5#5666semidirect
925. C2×C3#65929semidirect
933. C5C2×#5666semidirect
972. C3C2×#65929semidirect
979. C2#11753177direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917722
C2×C5×#8822
C2×C3×#40292
C2×#915702
C2×#915682
C2×#915672
C2×#915552
C2×#914662
C2×#914612
C2×#914532
C2×#914492
C2×#914482
C2×#914162
C2×#913422
C2×#913412
#117531772
C2×#659293
C2×#56665