Finite Group Databasebeta

← C2×#11753300 #14495266

Subgroups — C2×#11753300 #14495266

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91774C211yesmaximal, characteristic, complemented
2C2×C5×#882C211yesmaximal, characteristic, complemented
3C2×C3×#4031C211yesmaximal, characteristic, complemented
4C2×#91577C211yesmaximal, characteristic, complemented
5C2×#91570C211yesmaximal, characteristic, complemented
6C2×#91568C211yesmaximal, characteristic, complemented
7C2×#91525C211yesmaximal, characteristic, complemented
8C2×#91475C211yesmaximal, characteristic, complemented
9C2×#91475C211yesmaximal, characteristic, complemented
10C2×#91464C211yesmaximal, characteristic, complemented
11C2×#91462C211yesmaximal, characteristic, complemented
12C2×#91373C211yesmaximal, characteristic, complemented
13C2×#91370C211yesmaximal, characteristic, complemented
14C2×#91350C211yesmaximal, characteristic, complemented
15C2×#91326C211yesmaximal, characteristic, complemented
16#11753300C2116yesmaximal, direct product factor
17C2×#65928—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic, complemented
19C23×D3×D5C2211yescharacteristic, complemented
20C22×#1220C2211yescharacteristic
21C22×Dic30C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic
23C22×C5×D12C2211yescharacteristic
24C22×C5×D12C2211yescharacteristic
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×Dic10C2211yescharacteristic, complemented
27C22×#1204C2211yescharacteristic, complemented
28C22×#1203C2211yescharacteristic
29C22×#1203C2211yescharacteristic
30C22×#1201C2211yescharacteristic
31C22×#1201C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
33C2×#6719C2211yescharacteristic, complemented
34C2×#6714C2211yescharacteristic, complemented
35C2×#6714C2211yescharacteristic, complemented
36C2×C4×Dic15C2211yescharacteristic, complemented
37#91774C2218yescomplemented
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C5×#882C2218yescomplemented
41C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
42C2×C3×#685C2211yescharacteristic, complemented
43C2×C3×#685C2211yescharacteristic, complemented
44C2×C3×C4×Dic5C2211yescharacteristic, complemented
45C3×#4031C2218yescomplemented
46#91577C2218yescomplemented
47#91570C2218yescomplemented
48#91568C2218yescomplemented
49C2×#6667C2211yescharacteristic, complemented
50C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
51C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
52C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
53C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
54C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
57C2×#6665C2211yescharacteristic, complemented
58C2×Dic3×Dic5C2211yescharacteristic, complemented
59#91525C2218yescomplemented
60#91475C2218yescomplemented
61#91475C2218yescomplemented
62#91464C2218yescomplemented
63#91462C2218yescomplemented
64#91373C2218yescomplemented
65#91370C2218yescomplemented
66#91350C2218yescomplemented
67#91326C2218yescomplemented
68C2×#5683—51nomaximal, Hall
69C2×C5×#120—31no—
70C2×#4099—31no—
71C2×#4099—31no—
72C2×#4083—31no—
73C2×#4083—31no—
74C2×#4083—31no—
75C2×#4082—31no—
76C2×#4082—31no—
77C2×#4082—31no—
78#65928—316no—
79C2×#4031—31no—
80C2×#4031—31no—
81C2×#4031—31no—
82C2×#4031—31no—
83C2×#4031—31no—
84C2×#4031D311yescharacteristic, complemented
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×D3C2314yescomplemented
94C23×C3×D5C2311yescharacteristic
95C22×D3×D5—42no—
96C22×D3×D5—42no—
97C22×D3×D5—42no—
98C22×D3×D5C2314yescomplemented
99C22×C3×C4×C5C2311yescharacteristic
100C22×C3×C4×C5C2311yescharacteristic
101C2×#1220—42no—
102C2×#1220C2314yes—
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C2×Dic30—42no—
107C2×Dic30C2314yescomplemented
108C2×C5×#67—42no—
109C2×C5×#67C2314yes—
110C22×C5×Dic3C2311yescharacteristic
111C2×C5×D12—42no—
112C2×C5×D12—42no—
113C2×C5×D12C2314yes—
114C2×C5×D12C2314yes—
115C2×C3×C22⋊D5—42no—
116C2×C3×C22⋊D5C2314yes—
117C22×C3×Dic5C2311yescharacteristic
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2311yescharacteristic
120C2×C3×Dic10—42no—
121C2×C3×Dic10C2314yescomplemented
122C2×#1204—42no—
123C2×#1204C2314yescomplemented
124C2×#1203—42no—
125C2×#1203—42no—
126C2×#1203C2314yes—
127C2×#1203C2314yes—
128C2×#1201—42no—
129C2×#1201—42no—
130C2×#1201C2314yes—
131C2×#1201C2314yes—
132C3×C5×C22⋊C4C2314yescomplemented
133#6719C2314yescomplemented
134#6714C2314yescomplemented
135#6714C2314yescomplemented
136C4×Dic15C2314yescomplemented
137C5×(C2×D3)⋊C4C2314yescomplemented
138C5×(C2×D3)⋊C4C2314yescomplemented
139C3×C22⋊Dic5C2314yescomplemented
140C3×#685C2314yescomplemented
141C3×#685C2314yescomplemented
142C3×C4×Dic5C2314yescomplemented
143#6667C2314yescomplemented
144(C2×D3)⋊Dic5C2314yescomplemented
145(C2×D3)⋊Dic5C2314yescomplemented
146(C2×D3)⋊Dic5C2314yescomplemented
147(C2×D3)⋊Dic5C2314yescomplemented
148(C2×D3)⋊Dic5C2314yescomplemented
149(C2×D3)⋊Dic5C2314yescomplemented
150(C2×D3)⋊Dic5C2314yescomplemented
151#6665C2314yescomplemented
152Dic3×Dic5C2314yescomplemented
153C2×C3×#124—51no—
154C2×#947—51no—
155C2×#947—51no—
156C2×#937—51no—
157C2×#937—51no—
158#5683—516no—
159C2×#885—51no—
160C2×#885—51no—
161C2×#885—51no—
162C2×#885—51no—
163C2×#882—51no—
164C2×#882—51no—
165C2×#882—51no—
166C2×#882D511yescharacteristic, complemented
167C2×#875—51no—
168C2×#875—51no—
169C25×C5—31no—
170C24×D5—31no—
171C22×C5×D4—31no—
172C22×C5×D4—31no—
173C22×C5×D4—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C22×C22⋊D5—31no—
178C22×C22⋊D5—31no—
179C22×C22⋊D5C2×D311yescharacteristic
180C22×Dic10—31no—
181C22×Dic10—31no—
182C22×Dic10C2×D311yescharacteristic, complemented
183C5×#120—38no—
184C2×C5×C22⋊C4—31no—
185C2×C5×C22⋊C4—31no—
186C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
187#4099—38no—
188#4099—38no—
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5—31no—
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, complemented
198#4083—38no—
199#4083—38no—
200#4083—38no—
201#4082—38no—
202#4082—38no—
203#4082—38no—
204C2×#685—31no—
205C2×#685—31no—
206C2×#685—31no—
207C2×#685—31no—
208C2×#685C2×D311yescharacteristic, complemented
209C2×#685C2×D311yescharacteristic, complemented
210C2×C4×Dic5—31no—
211C2×C4×Dic5—31no—
212C2×C4×Dic5C2×D311yescharacteristic, complemented
213#4031—38no—
214#4031—38no—
215#4031—38no—
216#4031—38no—
217#4031—38no—
218#4031C2×D318yescomplemented
219C2×H(3,𝔽4)—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×D3×D5—44no—
250C2×D3×D5—44no—
251C2×D3×D5—44no—
252C2×D3×D5—416no—
253C2×C3×C4×C5—22no—
254C2×C3×C4×C5—22no—
255C2×C3×C4×C5C2412yes—
256C2×C3×C4×C5C2412yes—
257#1220—44no—
258C2×Dic15—22no—
259C2×Dic15—22no—
260C2×Dic15—22no—
261C2×Dic15C2412yes—
262C2×Dic15C2412yes—
263C2×Dic15C2412yes—
264Dic30—44no—
265C5×#67—44no—
266C2×C5×Dic3—22no—
267C2×C5×Dic3C2412yes—
268C5×D12—44no—
269C5×D12—44no—
270C3×C22⋊D5—44no—
271C2×C3×Dic5—22no—
272C2×C3×Dic5—22no—
273C2×C3×Dic5—22no—
274C2×C3×Dic5C2412yes—
275C2×C3×Dic5C2412yes—
276C2×C3×Dic5C2412yes—
277C3×Dic10—44no—
278#1204—44no—
279#1203—44no—
280#1203—44no—
281#1201—44no—
282#1201—44no—
283C24×D3—51no—
284C24×D3C2×D511yescharacteristic, complemented
285C22×C3×Q8—51no—
286C22×C3×D4—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67C2×D511yescharacteristic
291C22×D12—51no—
292C22×D12—51no—
293C22×D12C2×D511yescharacteristic
294C22×D12C2×D511yescharacteristic
295C22×Dic6—51no—
296C22×Dic6—51no—
297C3×#124—58no—
298C2×C3×C22⋊C4—51no—
299C2×C3×C22⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
302C2×C3×C42—51no—
303C2×#217—51no—
304C2×#217—51no—
305#947—58no—
306#947—58no—
307#937—58no—
308#937—58no—
309C2×(C2×D3)⋊C4—51no—
310C2×(C2×D3)⋊C4—51no—
311C2×(C2×D3)⋊C4—51no—
312C2×(C2×D3)⋊C4—51no—
313C2×(C2×D3)⋊C4—51no—
314C2×(C2×D3)⋊C4—51no—
315C2×(C2×D3)⋊C4—51no—
316C2×(C2×D3)⋊C4—51no—
317C2×(C2×D3)⋊C4—51no—
318C2×(C2×D3)⋊C4—51no—
319C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
320C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
321C2×C4×Dic3—51no—
322C2×C4×Dic3—51no—
323#885—58no—
324#885—58no—
325#885—58no—
326#885—58no—
327#882—58no—
328#882—58no—
329#882—58no—
330#882C2×D518yescomplemented
331#875—58no—
332#875—58no—
333C24×C5—31no—
334C24×C5—31no—
335C24×C5—31no—
336C24×C5—34no—
337C24×C5—122no—
338C24×C5—122no—
339C24×C5—122no—
340C24×C5C22×D311yescharacteristic
341C23×D5—31no—
342C23×D5—34no—
343C23×D5—122no—
344C23×D5—122no—
345C23×D5—122no—
346C23×D5C22×D311yescharacteristic
347C2×C5×D4—34no—
348C2×C5×D4—34no—
349C2×C5×D4—34no—
350C2×C5×D4—122no—
351C2×C5×D4—122no—
352C2×C5×D4—122no—
353C22×C4×C5—31no—
354C22×C4×C5C22×D311yescharacteristic
355C22×C4×C5C22×D311yescharacteristic
356C2×C22⋊D5—34no—
357C2×C22⋊D5—34no—
358C2×C22⋊D5—34no—
359C2×C22⋊D5—34no—
360C2×C22⋊D5—34no—
361C2×C22⋊D5—42no—
362C2×C22⋊D5—122no—
363C2×C22⋊D5—122no—
364C2×C22⋊D5—122no—
365C2×C22⋊D5—122no—
366C2×C22⋊D5—122no—
367C2×C22⋊D5C22×D314yes—
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5—31no—
371C22×Dic5C22×D311yescharacteristic
372C22×Dic5C22×D311yescharacteristic
373C22×Dic5C22×D311yescharacteristic
374C2×Dic10—34no—
375C2×Dic10—34no—
376C2×Dic10—42no—
377C2×Dic10—122no—
378C2×Dic10—122no—
379C2×Dic10C22×D314yescomplemented
380C5×C22⋊C4—34no—
381C5×C22⋊C4—34no—
382C5×C22⋊C4C22×D314yescomplemented
383C22⋊Dic5—34no—
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5—34no—
387C22⋊Dic5—34no—
388C22⋊Dic5—34no—
389C22⋊Dic5—34no—
390C22⋊Dic5—34no—
391C22⋊Dic5C22×D314yescomplemented
392#685—34no—
393#685—34no—
394#685—34no—
395#685—34no—
396#685C22×D314yescomplemented
397#685C22×D314yescomplemented
398C4×Dic5—34no—
399C4×Dic5—34no—
400C4×Dic5C22×D314yescomplemented
401H(3,𝔽4)—1516no—
402C2×#124—51no—
403C2×#124—151no—
404C2×#124—151no—
405C2×#124—151no—
406C2×#124—151no—
407C2×#124—151no—
408C2×#124—151no—
409C2×#124—151no—
410C2×#124—151no—
411C2×#120—31no—
412C2×#120—151no—
413C2×#120—151no—
414C2×#120—151no—
415C2×#120—151no—
416C2×#120—151no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—44no—
421C22×C3×C5H(5,𝔽2)12yes—
422C22×C3×C5H(5,𝔽2)12yes—
423C22×C3×C5H(5,𝔽2)12yes—
424C22×C3×C5C2511yescharacteristic
425C2×D15—22no—
426C2×D15—22no—
427C2×D15—22no—
428C2×D15—44no—
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—22no—
438C2×C5×D3—416no—
439C2×C5×D3—44no—
440C2×C5×D3—44no—
441C2×C5×D3—44no—
442C2×C3×D5—22no—
443C2×C3×D5—22no—
444C2×C3×D5—22no—
445C2×C3×D5—44no—
446D3×D5—416no—
447C3×C4×C5—22no—
448C3×C4×C5—22no—
449Dic15—22no—
450Dic15—22no—
451Dic15—22no—
452C3×Dic5—22no—
453C3×Dic5—22no—
454C3×Dic5—22no—
455C5×Dic3—22no—
456C24×C3—51no—
457C24×C3C22×D511yescharacteristic
458C23×D3—42no—
459C23×D3—42no—
460C23×D3—42no—
461C23×D3—51no—
462C23×D3—54no—
463C23×D3—202no—
464C23×D3—202no—
465C23×D3—202no—
466C23×D3C22×D511yescharacteristic
467C23×D3C22×D511yescharacteristic
468C23×D3C22×D511yescharacteristic
469C23×D3C22×D514yescomplemented
470C2×C3×Q8—54no—
471C2×C3×Q8—202no—
472C2×C3×D4—54no—
473C2×C3×D4—202no—
474C22×C3×C4—51no—
475C22×C3×C4—51no—
476C22×C3×C4—51no—
477C22×C3×C4C22×D511yescharacteristic
478C22×C3×C4C22×D511yescharacteristic
479C2×#67—42no—
480C2×#67—54no—
481C2×#67—54no—
482C2×#67—54no—
483C2×#67—202no—
484C2×#67—202no—
485C2×#67—202no—
486C2×#67C22×D514yes—
487C22×Dic3—51no—
488C22×Dic3—51no—
489C22×Dic3—51no—
490C22×Dic3C22×D511yescharacteristic
491C2×D12—42no—
492C2×D12—42no—
493C2×D12—54no—
494C2×D12—54no—
495C2×D12—202no—
496C2×D12—202no—
497C2×D12C22×D514yes—
498C2×D12C22×D514yes—
499C2×Dic6—54no—
500C2×Dic6—54no—
501C2×Dic6—202no—
502C2×Dic6—202no—
503C3×C22⋊C4—54no—
504C3×C22⋊C4—54no—
505C3×C22⋊C4—54no—
506C3×C22⋊C4C22×D514yescomplemented
507C3×C42—54no—
508#217—54no—
509#217—54no—
510(C2×D3)⋊C4—54no—
511(C2×D3)⋊C4—54no—
512(C2×D3)⋊C4—54no—
513(C2×D3)⋊C4—54no—
514(C2×D3)⋊C4—54no—
515(C2×D3)⋊C4—54no—
516(C2×D3)⋊C4—54no—
517(C2×D3)⋊C4—54no—
518(C2×D3)⋊C4—54no—
519(C2×D3)⋊C4—54no—
520(C2×D3)⋊C4C22×D514yescomplemented
521(C2×D3)⋊C4C22×D514yescomplemented
522C4×Dic3—54no—
523C4×Dic3—54no—
524C23×C5—22no—
525C23×C5—22no—
526C23×C5—22no—
527C23×C5—32no—
528C23×C5—32no—
529C23×C5—32no—
530C23×C5—62no—
531C23×C5—62no—
532C23×C5—62no—
533C23×C5—62no—
534C23×C5—62no—
535C23×C5—62no—
536C23×C5—62no—
537C23×C5—62no—
538C23×C5—62no—
539C23×C5—124no—
540C23×C5—124no—
541C23×C5—124no—
542C23×C5—1216no—
543C23×C5C23×D312yes—
544C23×C5C23×D311yescharacteristic
545C22×D5—22no—
546C22×D5—22no—
547C22×D5—22no—
548C22×D5—32no—
549C22×D5—62no—
550C22×D5—62no—
551C22×D5—62no—
552C22×D5—124no—
553C22×D5—124no—
554C22×D5—124no—
555C22×D5—1216no—
556C22×D5C23×D312yes—
557C5×D4—124no—
558C5×D4—124no—
559C5×D4—124no—
560C2×C4×C5—22no—
561C2×C4×C5—22no—
562C2×C4×C5—32no—
563C2×C4×C5—62no—
564C2×C4×C5C23×D312yes—
565C2×C4×C5C23×D312yes—
566C22⋊D5—44no—
567C22⋊D5—124no—
568C22⋊D5—124no—
569C22⋊D5—124no—
570C22⋊D5—124no—
571C22⋊D5—124no—
572C2×Dic5—22no—
573C2×Dic5—22no—
574C2×Dic5—22no—
575C2×Dic5—32no—
576C2×Dic5—32no—
577C2×Dic5—32no—
578C2×Dic5—62no—
579C2×Dic5—62no—
580C2×Dic5—62no—
581C2×Dic5C23×D312yes—
582C2×Dic5C23×D312yes—
583C2×Dic5C23×D312yes—
584Dic10—44no—
585Dic10—124no—
586Dic10—124no—
587C25—31no—
588C25—151no—
589C22×Q8—51no—
590C22×Q8—151no—
591C22×Q8—151no—
592C22×D4—31no—
593C22×D4—31no—
594C22×D4—31no—
595C22×D4—51no—
596C22×D4—151no—
597C22×D4—151no—
598C22×D4—151no—
599C22×D4—151no—
600C22×D4—151no—
601#124—58no—
602#124—158no—
603#124—158no—
604#124—158no—
605#124—158no—
606#124—158no—
607#124—158no—
608#124—158no—
609#124—158no—
610#120—38no—
611#120—158no—
612#120—158no—
613#120—158no—
614#120—158no—
615#120—158no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—51no—
619C2×C22⋊C4—51no—
620C2×C22⋊C4—51no—
621C2×C22⋊C4—151no—
622C2×C22⋊C4—151no—
623C2×C22⋊C4—151no—
624C2×C22⋊C4—151no—
625C2×C22⋊C4—151no—
626C2×C22⋊C4—151no—
627C2×C22⋊C4—151no—
628C2×C22⋊C4—151no—
629C2×C22⋊C4—151no—
630C2×C22⋊C4—151no—
631C2×C22⋊C4—151no—
632C2×C22⋊C4—151no—
633C2×C22⋊C4D3×D511yescharacteristic, complemented
634C2×C42—51no—
635C2×C42—151no—
636C2×C42—151no—
637C2×C3×C5—42no—
638C2×C3×C5H(3,𝔽4)14yescomplemented
639C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
640C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
641C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
642D15—42no—
643C3×D5—42no—
644C5×D3—42no—
645C5×D3—42no—
646C5×D3—42no—
647C23×C3—22no—
648C23×C3—22no—
649C23×C3—22no—
650C23×C3—52no—
651C23×C3—102no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3C23×D512yes—
655C23×C3C23×D511yescharacteristic
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—22no—
664C22×D3—22no—
665C22×D3—44no—
666C22×D3—44no—
667C22×D3—44no—
668C22×D3—416no—
669C22×D3—52no—
670C22×D3—102no—
671C22×D3—102no—
672C22×D3—102no—
673C22×D3—204no—
674C22×D3—204no—
675C22×D3—204no—
676C22×D3—2016no—
677C22×D3C23×D512yes—
678C22×D3C23×D512yes—
679C22×D3C23×D512yes—
680C3×Q8—204no—
681C3×D4—204no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—52no—
685C2×C3×C4—52no—
686C2×C3×C4—52no—
687C2×C3×C4—102no—
688C2×C3×C4—102no—
689C2×C3×C4—102no—
690C2×C3×C4C23×D512yes—
691C2×C3×C4C23×D512yes—
692#67—44no—
693#67—204no—
694#67—204no—
695#67—204no—
696C2×Dic3—22no—
697C2×Dic3—52no—
698C2×Dic3—52no—
699C2×Dic3—52no—
700C2×Dic3—102no—
701C2×Dic3—102no—
702C2×Dic3—102no—
703C2×Dic3C23×D512yes—
704D12—44no—
705D12—44no—
706D12—204no—
707D12—204no—
708Dic6—204no—
709Dic6—204no—
710C22×C5—22no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—44no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—62no—
717C22×C5—62no—
718C22×C5—62no—
719C22×C5—62no—
720C22×C5—62no—
721C22×C5—62no—
722C22×C5—62no—
723C22×C5—1216no—
724C22×C5—124no—
725C22×C5—124no—
726C22×C5—124no—
727C22×C5#100412yes—
728C22×C5#100912yes—
729C22×C5#100912yes—
730C22×C5C24×D311yescharacteristic
731C2×D5—22no—
732C2×D5—22no—
733C2×D5—22no—
734C2×D5—44no—
735C2×D5—62no—
736C2×D5—62no—
737C2×D5—62no—
738C2×D5—1216no—
739C2×D5—124no—
740C4×C5—22no—
741C4×C5—22no—
742C4×C5—62no—
743Dic5—22no—
744Dic5—22no—
745Dic5—22no—
746Dic5—62no—
747Dic5—62no—
748Dic5—62no—
749C24—31no—
750C24—31no—
751C24—31no—
752C24—34no—
753C24—51no—
754C24—122no—
755C24—122no—
756C24—122no—
757C24—154no—
758C24—151no—
759C24—602no—
760C24—602no—
761C24—602no—
762C24C2×D3×D511yescharacteristic
763C2×Q8—54no—
764C2×Q8—154no—
765C2×Q8—154no—
766C2×Q8—202no—
767C2×Q8—602no—
768C2×Q8—602no—
769C2×D4—34no—
770C2×D4—34no—
771C2×D4—34no—
772C2×D4—54no—
773C2×D4—122no—
774C2×D4—122no—
775C2×D4—122no—
776C2×D4—154no—
777C2×D4—154no—
778C2×D4—154no—
779C2×D4—154no—
780C2×D4—154no—
781C2×D4—202no—
782C2×D4—602no—
783C2×D4—602no—
784C2×D4—602no—
785C2×D4—602no—
786C2×D4—602no—
787C22×C4—31no—
788C22×C4—51no—
789C22×C4—51no—
790C22×C4—51no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4C2×D3×D511yescharacteristic
795C22×C4C2×D3×D511yescharacteristic
796C22⋊C4—34no—
797C22⋊C4—34no—
798C22⋊C4—54no—
799C22⋊C4—54no—
800C22⋊C4—54no—
801C22⋊C4—154no—
802C22⋊C4—154no—
803C22⋊C4—154no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C22⋊C4C2×D3×D514yescomplemented
814C42—54no—
815C42—154no—
816C42—154no—
817C3×C5C2×H(3,𝔽4)11yescharacteristic, complemented, Hall
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—44no—
822C22×C3—102no—
823C22×C3—102no—
824C22×C3—102no—
825C22×C3—204no—
826C22×C3#414412yes—
827C22×C3#414412yes—
828C22×C3#414412yes—
829C22×C3C24×D511yescharacteristic
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—416no—
840C2×D3—44no—
841C2×D3—44no—
842C2×D3—44no—
843C2×D3—102no—
844C2×D3—102no—
845C2×D3—102no—
846C2×D3—2016no—
847C2×D3—204no—
848C3×C4—22no—
849C3×C4—22no—
850C3×C4—102no—
851C3×C4—102no—
852C3×C4—102no—
853Dic3—22no—
854Dic3—102no—
855Dic3—102no—
856Dic3—102no—
857C2×C5—42no—
858C2×C5—122no—
859C2×C5—122no—
860C2×C5—122no—
861C2×C5#568314yescomplemented
862C2×C5C2×#100411yescharacteristic
863C2×C5C2×#100911yescharacteristic
864C2×C5C2×#100911yescharacteristic
865D5—42no—
866D5—122no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—32no—
871C23—32no—
872C23—32no—
873C23—52no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—102no—
884C23—102no—
885C23—102no—
886C23—124no—
887C23—124no—
888C23—124no—
889C23—1216no—
890C23—152no—
891C23—302no—
892C23—302no—
893C23—302no—
894C23—604no—
895C23—604no—
896C23—604no—
897C23—6016no—
898C23C22×D3×D512yes—
899C23C22×D3×D511yescharacteristic
900Q8—204no—
901Q8—604no—
902Q8—604no—
903D4—124no—
904D4—124no—
905D4—124no—
906D4—204no—
907D4—604no—
908D4—604no—
909D4—604no—
910D4—604no—
911D4—604no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—32no—
915C2×C4—52no—
916C2×C4—52no—
917C2×C4—52no—
918C2×C4—62no—
919C2×C4—102no—
920C2×C4—102no—
921C2×C4—102no—
922C2×C4—152no—
923C2×C4—152no—
924C2×C4—152no—
925C2×C4—302no—
926C2×C4—302no—
927C2×C4—302no—
928C2×C4C22×D3×D512yes—
929C2×C4C22×D3×D512yes—
930C2×C3—42no—
931C2×C3—202no—
932C2×C3#6592814yescomplemented
933C2×C3C2×#414411yescharacteristic
934C2×C3C2×#414411yescharacteristic
935C2×C3C2×#414411yescharacteristic
936D3—42no—
937D3—42no—
938D3—42no—
939D3—202no—
940C5C2×#568311yescharacteristic, complemented, Sylow
941C22—22no—
942C22—22no—
943C22—22no—
944C22—44no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—62no—
951C22—62no—
952C22—62no—
953C22—62no—
954C22—102no—
955C22—102no—
956C22—102no—
957C22—1216no—
958C22—124no—
959C22—124no—
960C22—124no—
961C22—204no—
962C22—302no—
963C22—302no—
964C22—302no—
965C22—6016no—
966C22—604no—
967C22#9201812yes—
968C22#9202512yes—
969C22#9202712yes—
970C22C23×D3×D511yescharacteristic
971C4—22no—
972C4—22no—
973C4—62no—
974C4—102no—
975C4—102no—
976C4—102no—
977C4—302no—
978C4—302no—
979C4—302no—
980C3C2×#6592811yescharacteristic, complemented, Sylow
981C2—42no—
982C2—122no—
983C2—122no—
984C2—122no—
985C2—202no—
986C2—602no—
987C2#1175330014yesdirect product factor
988C2C2×#9201811yescharacteristic
989C2C2×#9202511yescharacteristic
990C2C2×#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×H(3,𝔽4)
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×#91774C2semidirect
2. C2×C5×#882C2semidirect
3. C2×C3×#4031C2semidirect
4. C2×#91577C2semidirect
5. C2×#91570C2semidirect
6. C2×#91568C2semidirect
7. C2×#91525C2semidirect
8. C2×#91475C2semidirect
9. C2×#91475C2semidirect
10. C2×#91464C2semidirect
11. C2×#91462C2semidirect
12. C2×#91373C2semidirect
13. C2×#91370C2semidirect
14. C2×#91350C2semidirect
15. C2×#91326C2semidirect
16. #11753300C2direct (N × H)
18. C24×C5×D3C22semidirect
19. C23×D3×D5C22semidirect
21. C22×Dic30C22semidirect
26. C22×C3×Dic10C22semidirect
27. C22×#1204C22semidirect
32. C2×C3×C5×C22⋊C4C22semidirect
33. C2×#6719C22semidirect
34. C2×#6714C22semidirect
35. C2×#6714C22semidirect
36. C2×C4×Dic15C22semidirect
37. #91774C22semidirect
38. C2×C5×(C2×D3)⋊C4C22semidirect
39. C2×C5×(C2×D3)⋊C4C22semidirect
40. C5×#882C22semidirect
41. C2×C3×C22⋊Dic5C22semidirect
42. C2×C3×#685C22semidirect
43. C2×C3×#685C22semidirect
44. C2×C3×C4×Dic5C22semidirect
45. C3×#4031C22semidirect
46. #91577C22semidirect
47. #91570C22semidirect
48. #91568C22semidirect
49. C2×#6667C22semidirect
50. C2×(C2×D3)⋊Dic5C22semidirect
51. C2×(C2×D3)⋊Dic5C22semidirect
52. C2×(C2×D3)⋊Dic5C22semidirect
53. C2×(C2×D3)⋊Dic5C22semidirect
54. C2×(C2×D3)⋊Dic5C22semidirect
55. C2×(C2×D3)⋊Dic5C22semidirect
56. C2×(C2×D3)⋊Dic5C22semidirect
57. C2×#6665C22semidirect
58. C2×Dic3×Dic5C22semidirect
59. #91525C22semidirect
60. #91475C22semidirect
61. #91475C22semidirect
62. #91464C22semidirect
63. #91462C22semidirect
64. #91373C22semidirect
65. #91370C22semidirect
66. #91350C22semidirect
67. #91326C22semidirect
84. C2×#4031D3semidirect
93. C23×C5×D3C23semidirect
98. C22×D3×D5C23semidirect
107. C2×Dic30C23semidirect
121. C2×C3×Dic10C23semidirect
123. C2×#1204C23semidirect
132. C3×C5×C22⋊C4C23semidirect
133. #6719C23semidirect
134. #6714C23semidirect
135. #6714C23semidirect
136. C4×Dic15C23semidirect
137. C5×(C2×D3)⋊C4C23semidirect
138. C5×(C2×D3)⋊C4C23semidirect
139. C3×C22⋊Dic5C23semidirect
140. C3×#685C23semidirect
141. C3×#685C23semidirect
142. C3×C4×Dic5C23semidirect
143. #6667C23semidirect
144. (C2×D3)⋊Dic5C23semidirect
145. (C2×D3)⋊Dic5C23semidirect
146. (C2×D3)⋊Dic5C23semidirect
147. (C2×D3)⋊Dic5C23semidirect
148. (C2×D3)⋊Dic5C23semidirect
149. (C2×D3)⋊Dic5C23semidirect
150. (C2×D3)⋊Dic5C23semidirect
151. #6665C23semidirect
152. Dic3×Dic5C23semidirect
166. C2×#882D5semidirect
182. C22×Dic10C2×D3semidirect
186. C2×C5×C22⋊C4C2×D3semidirect
197. C2×C22⋊Dic5C2×D3semidirect
208. C2×#685C2×D3semidirect
209. C2×#685C2×D3semidirect
212. C2×C4×Dic5C2×D3semidirect
218. #4031C2×D3semidirect
284. C24×D3C2×D5semidirect
301. C2×C3×C22⋊C4C2×D5semidirect
319. C2×(C2×D3)⋊C4C2×D5semidirect
320. C2×(C2×D3)⋊C4C2×D5semidirect
330. #882C2×D5semidirect
379. C2×Dic10C22×D3semidirect
382. C5×C22⋊C4C22×D3semidirect
391. C22⋊Dic5C22×D3semidirect
396. #685C22×D3semidirect
397. #685C22×D3semidirect
400. C4×Dic5C22×D3semidirect
469. C23×D3C22×D5semidirect
506. C3×C22⋊C4C22×D5semidirect
520. (C2×D3)⋊C4C22×D5semidirect
521. (C2×D3)⋊C4C22×D5semidirect
633. C2×C22⋊C4D3×D5semidirect
638. C2×C3×C5H(3,𝔽4)semidirect
813. C22⋊C4C2×D3×D5semidirect
817. C3×C5C2×H(3,𝔽4)semidirect
861. C2×C5#5683semidirect
932. C2×C3#65928semidirect
940. C5C2×#5683semidirect
980. C3C2×#65928semidirect
987. C2#11753300direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917742
C2×C5×#8822
C2×C3×#40312
C2×#915772
C2×#915702
C2×#915682
C2×#915252
C2×#914752
C2×#914642
C2×#914622
C2×#913732
C2×#913702
C2×#913502
C2×#913262
#117533002
C2×#659283
C2×#56835