Finite Group Databasebeta

← C2×#11753730 #14484759

Subgroups — C2×#11753730 #14484759

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91783C211yesmaximal, characteristic, complemented
2C2×C5×#894C211yesmaximal, characteristic, complemented
3C2×C3×#4033C211yesmaximal, characteristic, complemented
4C2×#91451C211yesmaximal, characteristic
5C2×#91446C211yesmaximal, characteristic, complemented
6C2×C4×#1203C211yesmaximal, characteristic, complemented
7C2×#91433C211yesmaximal, characteristic, complemented
8C2×#91423C211yesmaximal, characteristic, complemented
9C2×#91406C211yesmaximal, characteristic, complemented
10C2×#91405C211yesmaximal, characteristic, complemented
11C2×#91350C211yesmaximal, characteristic, complemented
12C2×#91350C211yesmaximal, characteristic, complemented
13C2×#91326C211yesmaximal, characteristic, complemented
14C2×#91326C211yesmaximal, characteristic, complemented
15C2×#91323C211yesmaximal, characteristic, complemented
16#11753730C2116yesmaximal, direct product factor
17C2×#65998—31nomaximal, Hall
18C22×D60C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C5×D12C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×C3×Dic10C2211yescharacteristic
23C22×#1204C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1203C2211yescharacteristic
26C22×#1203C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1200C2211yescharacteristic
29C22×D3×Dic5C2211yescharacteristic
30C2×C3×C5×C4⋊C4C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6712C2211yescharacteristic
35#91783C2218yescomplemented
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×Dic3⋊C4C2211yescharacteristic
40C5×#894C2218yescomplemented
41C2×C3×#683C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×C4×Dic5C2211yescharacteristic
44C2×C3×C4×Dic5C2211yescharacteristic
45C2×C3×C4×Dic5C2211yescharacteristic
46C3×#4033C2218yescomplemented
47C2×#6668C2211yescharacteristic
48C2×#6667C2211yescharacteristic
49C2×#6667C2211yescharacteristic
50C2×#6667C2211yescharacteristic
51C2×(C2×D3)⋊Dic5C2211yescharacteristic
52C2×(C2×D3)⋊Dic5C2211yescharacteristic
53C2×(C2×D3)⋊Dic5C2211yescharacteristic
54C2×Dic3×Dic5C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56#91451C2218yes—
57#91446C2218yescomplemented
58C4×#1203C2218yescomplemented
59#91433C2218yescomplemented
60#91423C2218yescomplemented
61#91406C2218yescomplemented
62#91405C2218yescomplemented
63#91350C2218yescomplemented
64#91350C2218yescomplemented
65#91326C2218yescomplemented
66#91326C2218yescomplemented
67#91323C2218yescomplemented
68C2×#5585—51nomaximal, Hall
69C2×C5×#123—31no—
70C2×#4086—31no—
71C2×#4081—31no—
72C2×C4×C22⋊D5—31no—
73C2×C4×C22⋊D5—31no—
74#65998—316no—
75C2×#4040—31no—
76C2×#4040—31no—
77C2×#4033—31no—
78C2×#4033D311yescharacteristic, complemented
79C2×#4031—31no—
80C2×#4031—31no—
81C2×#4031—31no—
82C2×#4031—31no—
83C2×#4027—31no—
84C2×#4027—31no—
85C23×D15C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C2×D60—42no—
95C2×D60C2314yes—
96C2×C4×D15—42no—
97C2×C4×D15C2314yes—
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C2×C5×D12—42no—
101C2×C5×D12C2314yes—
102C2×C4×C5×D3—42no—
103C2×C4×C5×D3C2314yes—
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C2×C3×Dic10—24no—
109C2×C3×Dic10C2314yes—
110C2×#1204—24no—
111C2×#1204C2314yes—
112C2×#1203—24no—
113C2×#1203—24no—
114C2×#1203—24no—
115C2×#1203—24no—
116C2×#1203C2314yes—
117C2×#1203C2314yes—
118C2×#1203C2314yes—
119C2×#1203C2314yes—
120C2×#1200—42no—
121C2×#1200C2314yes—
122C2×D3×Dic5—42no—
123C2×D3×Dic5C2314yes—
124C3×C5×C4⋊C4C2314yes—
125#6714C2314yes—
126#6714C2314yes—
127#6714C2314yes—
128#6712C2314yes—
129C5×(C2×D3)⋊C4C2314yes—
130C5×(C2×D3)⋊C4C2314yes—
131C5×(C2×D3)⋊C4C2314yes—
132C5×Dic3⋊C4C2314yes—
133C3×#683C2314yes—
134C3×#683C2314yes—
135C3×C4×Dic5C2314yes—
136C3×C4×Dic5C2314yes—
137C3×C4×Dic5C2314yes—
138#6668C2314yes—
139#6667C2314yes—
140#6667C2314yes—
141#6667C2314yes—
142(C2×D3)⋊Dic5C2314yes—
143(C2×D3)⋊Dic5C2314yes—
144(C2×D3)⋊Dic5C2314yes—
145Dic3×Dic5C2314yes—
146Dic3×Dic5C2314yes—
147C2×C3×C4×Q8—51no—
148C2×#947—51no—
149C2×#947—51no—
150#5585—516no—
151C2×#894—51no—
152C2×#894—51no—
153C2×#894—51no—
154C2×#894D511yescharacteristic, complemented
155C2×#893—51no—
156C2×#893—51no—
157C2×#875—51no—
158C2×#875—51no—
159C2×#874—51no—
160C2×C4×D12—51no—
161C2×C4×D12—51no—
162C2×C4×Dic6—51no—
163C22×C5×D4—31no—
164C23×C4×C5—31no—
165C22×C22⋊D5—31no—
166C22×C22⋊D5—31no—
167C22×C22⋊D5—31no—
168C22×C22⋊D5—31no—
169C23×Dic5—31no—
170C22×D20—31no—
171C22×C4×D5—31no—
172C22×C4×D5—31no—
173C22×Dic10—31no—
174C22×Dic10C2×D311yescharacteristic
175C5×#123—38no—
176C2×C5×C4⋊C4—31no—
177C2×C5×C4⋊C4C2×D311yescharacteristic
178C2×C5×C22⋊C4—31no—
179C2×C5×C22⋊C4—31no—
180C2×C5×C22⋊C4—31no—
181C2×C22⋊Dic5—31no—
182C2×C22⋊Dic5—31no—
183C2×C22⋊Dic5—31no—
184#4086—38no—
185#4081—38no—
186C4×C22⋊D5—38no—
187C4×C22⋊D5—38no—
188C2×#685—31no—
189C2×#685—31no—
190C2×#685—31no—
191C2×#685—31no—
192C2×#685—31no—
193C2×#685—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683C2×D311yescharacteristic
197C2×#683C2×D311yescharacteristic
198C2×C4×Dic5—31no—
199C2×C4×Dic5—31no—
200C2×C4×Dic5C2×D311yescharacteristic
201C2×C4×Dic5C2×D311yescharacteristic
202C2×C4×Dic5C2×D311yescharacteristic
203#4040—38no—
204#4040—38no—
205#4033—38no—
206#4033C2×D318yescomplemented
207#4031—38no—
208#4031—38no—
209#4031—38no—
210#4031—38no—
211#4027—38no—
212#4027—38no—
213C2×#559—151noSylow
214C23×C3×C5C2411yescharacteristic
215C22×D15—22no—
216C22×D15—22no—
217C22×D15—22no—
218C22×D15—22no—
219C22×D15—22no—
220C22×D15—22no—
221C22×D15C2412yes—
222C22×D15C2412yes—
223C22×C5×D3—22no—
224C22×C5×D3—22no—
225C22×C5×D3—22no—
226C22×C5×D3—22no—
227C22×C5×D3—22no—
228C22×C5×D3—22no—
229C22×C5×D3C2412yes—
230C22×C5×D3C2412yes—
231C2×C3×C4×C5—22no—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5—22no—
234C2×C3×C4×C5C2412yes—
235C2×C3×C4×C5C2412yes—
236C2×C3×C4×C5C2412yes—
237C2×Dic15—22no—
238C2×Dic15—22no—
239C2×Dic15C2412yes—
240C2×Dic15C2412yes—
241D60—44no—
242C4×D15—44no—
243C2×C5×Dic3—22no—
244C2×C5×Dic3—22no—
245C2×C5×Dic3C2412yes—
246C2×C5×Dic3C2412yes—
247C5×D12—44no—
248C4×C5×D3—44no—
249C2×C3×Dic5—22no—
250C2×C3×Dic5—22no—
251C2×C3×Dic5#4114yes—
252C2×C3×Dic5#4114yes—
253C2×C3×Dic5C2412yes—
254C2×C3×Dic5C2412yes—
255C2×C3×Dic5C2412yes—
256C2×C3×Dic5C2412yes—
257C3×Dic10—28no—
258#1204—28no—
259#1203—28no—
260#1203—28no—
261#1203—28no—
262#1203—28no—
263#1200—44no—
264D3×Dic5—44no—
265C22×C3×Q8—51no—
266C22×D12—51no—
267C22×D12—51no—
268C22×D12—51no—
269C22×D12—51no—
270C22×D12—51no—
271C22×D12C2×D511yescharacteristic
272C22×C4×D3—51no—
273C22×C4×D3—51no—
274C22×C4×D3—51no—
275C22×C4×D3C2×D511yescharacteristic
276C22×Dic6—51no—
277C3×C4×Q8—58no—
278C2×C3×C4⋊C4—51no—
279C2×C3×C4⋊C4—51no—
280C2×C3×C4⋊C4C2×D511yescharacteristic
281C2×C3×C42—51no—
282C2×C3×C42—51no—
283C2×C3×C42—51no—
284#947—58no—
285#947—58no—
286C2×(C2×D3)⋊C4—51no—
287C2×(C2×D3)⋊C4—51no—
288C2×(C2×D3)⋊C4—51no—
289C2×(C2×D3)⋊C4—51no—
290C2×(C2×D3)⋊C4—51no—
291C2×(C2×D3)⋊C4—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4C2×D511yescharacteristic
296C2×(C2×D3)⋊C4C2×D511yescharacteristic
297C2×(C2×D3)⋊C4C2×D511yescharacteristic
298C2×C4⋊Dic3—51no—
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4C2×D511yescharacteristic
301C2×C4×Dic3—51no—
302C2×C4×Dic3—51no—
303#894—58no—
304#894—58no—
305#894—58no—
306#894C2×D518yescomplemented
307#893—58no—
308#893—58no—
309#875—58no—
310#875—58no—
311#874—58no—
312C4×D12—58no—
313C4×D12—58no—
314C4×Dic6—58no—
315C24×C5—31no—
316C24×C5—31no—
317C23×D5—31no—
318C23×D5—31no—
319C2×C5×D4—34no—
320C2×C5×D4—122no—
321C22×C4×C5—31no—
322C22×C4×C5—31no—
323C22×C4×C5—34no—
324C22×C4×C5—122no—
325C22×C4×C5C22×D311yescharacteristic
326C22×C4×C5C22×D311yescharacteristic
327C22×C4×C5C22×D311yescharacteristic
328C2×C22⋊D5—34no—
329C2×C22⋊D5—34no—
330C2×C22⋊D5—34no—
331C2×C22⋊D5—34no—
332C2×C22⋊D5—64no—
333C2×C22⋊D5—64no—
334C2×C22⋊D5—64no—
335C2×C22⋊D5—64no—
336C22×Dic5—31no—
337C22×Dic5—31no—
338C22×Dic5—34no—
339C22×Dic5—122no—
340C22×Dic5C22×D311yescharacteristic
341C22×Dic5C22×D311yescharacteristic
342C22×Dic5C22×D311yescharacteristic
343C22×Dic5C22×D311yescharacteristic
344C2×D20—34no—
345C2×D20—122no—
346C2×C4×D5—34no—
347C2×C4×D5—34no—
348C2×C4×D5—122no—
349C2×C4×D5—122no—
350C2×Dic10—24no—
351C2×Dic10—34no—
352C2×Dic10—64no—
353C2×Dic10C22×D314yes—
354C5×C4⋊C4—34no—
355C5×C4⋊C4C22×D314yes—
356C5×C22⋊C4—34no—
357C5×C22⋊C4—34no—
358C5×C22⋊C4—34no—
359C22⋊Dic5—34no—
360C22⋊Dic5—34no—
361C22⋊Dic5—34no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685—34no—
367#685—34no—
368#683—34no—
369#683—34no—
370#683C22×D314yes—
371#683C22×D314yes—
372C4×Dic5—34no—
373C4×Dic5—34no—
374C4×Dic5C22×D314yes—
375C4×Dic5C22×D314yes—
376C4×Dic5C22×D314yes—
377#559—1516no—
378C2×#127—151no—
379C2×#124—151no—
380C2×#124—151no—
381C2×#124—151no—
382C2×#124—151no—
383C2×#123—31no—
384C2×#123—151no—
385C2×#123—151no—
386C2×#123—151no—
387C2×C4×Q8—51no—
388C2×C4×Q8—151no—
389C2×C4×D4—151no—
390C2×C4×D4—151no—
391C2×C4×D4—151no—
392C2×C4×D4—151no—
393C22×C3×C5C2×#4112yes—
394C22×C3×C5C2×#4112yes—
395C22×C3×C5H(5,𝔽2)12yes—
396C22×C3×C5C2511yescharacteristic
397C2×D15—22no—
398C2×D15—22no—
399C2×D15—22no—
400C2×D15—22no—
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—44no—
404C2×D15—44no—
405C2×C5×D3—22no—
406C2×C5×D3—22no—
407C2×C5×D3—22no—
408C2×C5×D3—22no—
409C2×C5×D3—22no—
410C2×C5×D3—22no—
411C2×C5×D3—44no—
412C2×C5×D3—44no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—22no—
416Dic15—22no—
417Dic15—22no—
418C3×Dic5—22no—
419C3×Dic5—22no—
420C3×Dic5C2×#4114yes—
421C3×Dic5C2×#4114yes—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C23×D3—51no—
425C23×D3—51no—
426C23×D3C22×D511yescharacteristic
427C23×D3C22×D511yescharacteristic
428C2×C3×Q8—54no—
429C2×C3×Q8—104no—
430C22×C3×C4—51no—
431C22×C3×C4—51no—
432C22×C3×C4—51no—
433C22×C3×C4—51no—
434C22×C3×C4C22×D511yescharacteristic
435C22×C3×C4C22×D511yescharacteristic
436C22×C3×C4C22×D511yescharacteristic
437C22×Dic3—51no—
438C22×Dic3—51no—
439C22×Dic3C22×D511yescharacteristic
440C22×Dic3C22×D511yescharacteristic
441C2×D12—42no—
442C2×D12—54no—
443C2×D12—54no—
444C2×D12—54no—
445C2×D12—54no—
446C2×D12—54no—
447C2×D12—104no—
448C2×D12—104no—
449C2×D12—104no—
450C2×D12—104no—
451C2×D12—202no—
452C2×D12C22×D514yes—
453C2×C4×D3—42no—
454C2×C4×D3—54no—
455C2×C4×D3—54no—
456C2×C4×D3—54no—
457C2×C4×D3—202no—
458C2×C4×D3—202no—
459C2×C4×D3—202no—
460C2×C4×D3C22×D514yes—
461C2×Dic6—54no—
462C2×Dic6—104no—
463C3×C4⋊C4—54no—
464C3×C4⋊C4—54no—
465C3×C4⋊C4C22×D514yes—
466C3×C42—54no—
467C3×C42—54no—
468C3×C42—54no—
469(C2×D3)⋊C4—54no—
470(C2×D3)⋊C4—54no—
471(C2×D3)⋊C4—54no—
472(C2×D3)⋊C4—54no—
473(C2×D3)⋊C4—54no—
474(C2×D3)⋊C4—54no—
475(C2×D3)⋊C4—54no—
476(C2×D3)⋊C4—54no—
477(C2×D3)⋊C4—54no—
478(C2×D3)⋊C4C22×D514yes—
479(C2×D3)⋊C4C22×D514yes—
480(C2×D3)⋊C4C22×D514yes—
481C4⋊Dic3—54no—
482Dic3⋊C4—54no—
483Dic3⋊C4C22×D514yes—
484C4×Dic3—54no—
485C4×Dic3—54no—
486C23×C5—32no—
487C23×C5—32no—
488C23×C5—62no—
489C23×C5—62no—
490C23×C5—62no—
491C23×C5—62no—
492C23×C5—62no—
493C23×C5—62no—
494C23×C5C23×D311yescharacteristic
495C22×D5—32no—
496C22×D5—32no—
497C22×D5—62no—
498C22×D5—62no—
499C22×D5—62no—
500C22×D5—62no—
501C22×D5—62no—
502C22×D5—62no—
503C5×D4—124no—
504C2×C4×C5—22no—
505C2×C4×C5—22no—
506C2×C4×C5—22no—
507C2×C4×C5—32no—
508C2×C4×C5—32no—
509C2×C4×C5—62no—
510C2×C4×C5—62no—
511C2×C4×C5—124no—
512C2×C4×C5C23×D312yes—
513C2×C4×C5C23×D312yes—
514C2×C4×C5C23×D312yes—
515C22⋊D5—68no—
516C22⋊D5—68no—
517C22⋊D5—68no—
518C22⋊D5—68no—
519C2×Dic5—22no—
520C2×Dic5—22no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—62no—
524C2×Dic5—62no—
525C2×Dic5—124no—
526C2×Dic5#23514yes—
527C2×Dic5#23914yes—
528C2×Dic5C23×D312yes—
529C2×Dic5C23×D312yes—
530C2×Dic5C23×D312yes—
531C2×Dic5C23×D312yes—
532D20—124no—
533C4×D5—124no—
534C4×D5—124no—
535Dic10—28no—
536Dic10—68no—
537C22×Q8—51no—
538C22×Q8—151no—
539C22×D4—31no—
540C22×D4—151no—
541C22×D4—151no—
542C22×D4—151no—
543C22×D4—151no—
544C22×D4—151no—
545C23×C4—31no—
546C23×C4—151no—
547C23×C4—151no—
548C23×C4—151no—
549#127—158no—
550#124—158no—
551#124—158no—
552#124—158no—
553#124—158no—
554#123—38no—
555#123—158no—
556#123—158no—
557#123—158no—
558C4×Q8—58no—
559C4×Q8—158no—
560C4×D4—158no—
561C4×D4—158no—
562C4×D4—158no—
563C4×D4—158no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—51no—
566C2×C4⋊C4—51no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C4⋊C4D3×D511yescharacteristic
570C2×C22⋊C4—31no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—31no—
573C2×C22⋊C4—151no—
574C2×C22⋊C4—151no—
575C2×C22⋊C4—151no—
576C2×C22⋊C4—151no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C42—51no—
583C2×C42—51no—
584C2×C42—51no—
585C2×C42—151no—
586C2×C42—151no—
587C2×C3×C5#55914yescomplemented
588C2×C3×C5C22×#4111yescharacteristic
589C2×C3×C5C22×#4111yescharacteristic
590C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
591D15—42no—
592D15—42no—
593C5×D3—42no—
594C5×D3—42no—
595C23×C3C23×D511yescharacteristic
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—52no—
603C22×D3—52no—
604C22×D3—102no—
605C22×D3—102no—
606C22×D3—102no—
607C22×D3—102no—
608C22×D3—102no—
609C22×D3—102no—
610C22×D3C23×D512yes—
611C22×D3C23×D512yes—
612C3×Q8—108no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—54no—
617C2×C3×C4—54no—
618C2×C3×C4—52no—
619C2×C3×C4—52no—
620C2×C3×C4—52no—
621C2×C3×C4—52no—
622C2×C3×C4—102no—
623C2×C3×C4—102no—
624C2×C3×C4C23×D512yes—
625C2×C3×C4C23×D512yes—
626C2×C3×C4C23×D512yes—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—52no—
630C2×Dic3—52no—
631C2×Dic3—102no—
632C2×Dic3—102no—
633C2×Dic3C23×D512yes—
634C2×Dic3C23×D512yes—
635D12—44no—
636D12—108no—
637D12—108no—
638D12—108no—
639D12—108no—
640D12—204no—
641C4×D3—44no—
642C4×D3—204no—
643C4×D3—204no—
644C4×D3—204no—
645Dic6—108no—
646C22×C5—62no—
647C22×C5—62no—
648C22×C5—62no—
649C22×C5—62no—
650C22×C5—62no—
651C22×C5—62no—
652C22×C5—124no—
653C22×C5—124no—
654C22×C5C2×#23512yes—
655C22×C5C2×#23912yes—
656C22×C5#100912yes—
657C22×C5C24×D311yescharacteristic
658C2×D5—62no—
659C2×D5—62no—
660C2×D5—62no—
661C2×D5—62no—
662C2×D5—62no—
663C2×D5—62no—
664C2×D5—124no—
665C2×D5—124no—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—22no—
669C4×C5—62no—
670C4×C5—62no—
671Dic5—22no—
672Dic5—22no—
673Dic5—62no—
674Dic5—62no—
675Dic5C2×#23514yes—
676Dic5C2×#23914yes—
677C24—31no—
678C24—31no—
679C24—151no—
680C24—151no—
681C2×Q8—54no—
682C2×Q8—104no—
683C2×Q8—154no—
684C2×Q8—304no—
685C2×D4—34no—
686C2×D4—122no—
687C2×D4—154no—
688C2×D4—154no—
689C2×D4—154no—
690C2×D4—154no—
691C2×D4—154no—
692C2×D4—304no—
693C2×D4—304no—
694C2×D4—304no—
695C2×D4—304no—
696C2×D4—602no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—34no—
700C22×C4—51no—
701C22×C4—51no—
702C22×C4—51no—
703C22×C4—51no—
704C22×C4—122no—
705C22×C4—154no—
706C22×C4—154no—
707C22×C4—151no—
708C22×C4—151no—
709C22×C4—154no—
710C22×C4—602no—
711C22×C4—602no—
712C22×C4—602no—
713C22×C4C2×D3×D511yescharacteristic
714C22×C4C2×D3×D511yescharacteristic
715C22×C4C2×D3×D511yescharacteristic
716C4⋊C4—34no—
717C4⋊C4—54no—
718C4⋊C4—54no—
719C4⋊C4—154no—
720C4⋊C4—154no—
721C4⋊C4C2×D3×D514yes—
722C22⋊C4—34no—
723C22⋊C4—34no—
724C22⋊C4—34no—
725C22⋊C4—154no—
726C22⋊C4—154no—
727C22⋊C4—154no—
728C22⋊C4—154no—
729C22⋊C4—154no—
730C22⋊C4—154no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C42—54no—
735C42—54no—
736C42—54no—
737C42—154no—
738C42—154no—
739C3×C5C2×#55911yescharacteristic, complemented, Hall
740C22×C3#414412yes—
741C22×C3D5×#4112yes—
742C22×C3D5×#4112yes—
743C22×C3C24×D511yescharacteristic
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—44no—
751C2×D3—44no—
752C2×D3—102no—
753C2×D3—102no—
754C2×D3—102no—
755C2×D3—102no—
756C2×D3—102no—
757C2×D3—102no—
758C2×D3—204no—
759C2×D3—204no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—54no—
764C3×C4—54no—
765C3×C4—102no—
766C3×C4—102no—
767Dic3—22no—
768Dic3—22no—
769Dic3—102no—
770Dic3—102no—
771C2×C5—122no—
772C2×C5—122no—
773C2×C5#558514yescomplemented
774C2×C5C22×#23511yescharacteristic
775C2×C5C22×#23911yescharacteristic
776C2×C5C2×#100911yescharacteristic
777D5—122no—
778D5—122no—
779C23—32no—
780C23—32no—
781C23—62no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—152no—
788C23—152no—
789C23—302no—
790C23—302no—
791C23—302no—
792C23—302no—
793C23—302no—
794C23—302no—
795C23C22×D3×D511yescharacteristic
796Q8—108no—
797Q8—308no—
798D4—124no—
799D4—308no—
800D4—308no—
801D4—308no—
802D4—308no—
803D4—604no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—54no—
810C2×C4—54no—
811C2×C4—52no—
812C2×C4—52no—
813C2×C4—52no—
814C2×C4—52no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—102no—
818C2×C4—102no—
819C2×C4—124no—
820C2×C4—152no—
821C2×C4—152no—
822C2×C4—302no—
823C2×C4—302no—
824C2×C4—604no—
825C2×C4—604no—
826C2×C4—604no—
827C2×C4C22×D3×D512yes—
828C2×C4C22×D3×D512yes—
829C2×C4C22×D3×D512yes—
830C2×C3#6599814yescomplemented
831C2×C3C2×#414411yescharacteristic
832C2×C3C2×D5×#4111yescharacteristic
833C2×C3C2×D5×#4111yescharacteristic
834D3—42no—
835D3—42no—
836D3—202no—
837D3—202no—
838C5C2×#558511yescharacteristic, complemented, Sylow
839C22—62no—
840C22—62no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—62no—
845C22—124no—
846C22—124no—
847C22—302no—
848C22—302no—
849C22—302no—
850C22—302no—
851C22—302no—
852C22—302no—
853C22—604no—
854C22—604no—
855C22D5×#23512yes—
856C22#9202712yes—
857C22D5×#23912yes—
858C22C23×D3×D511yescharacteristic
859C4—22no—
860C4—22no—
861C4—22no—
862C4—54no—
863C4—54no—
864C4—62no—
865C4—62no—
866C4—102no—
867C4—102no—
868C4—302no—
869C4—302no—
870C3C2×#6599811yescharacteristic, complemented, Sylow
871C2—122no—
872C2—122no—
873C2—602no—
874C2—602no—
875C2#1175373014yesdirect product factor
876C2C2×D5×#23511yescharacteristic
877C2C2×#9202711yescharacteristic
878C2C2×D5×#23911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC2×#91451C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#559
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×#91783C2semidirect
2. C2×C5×#894C2semidirect
3. C2×C3×#4033C2semidirect
5. C2×#91446C2semidirect
6. C2×C4×#1203C2semidirect
7. C2×#91433C2semidirect
8. C2×#91423C2semidirect
9. C2×#91406C2semidirect
10. C2×#91405C2semidirect
11. C2×#91350C2semidirect
12. C2×#91350C2semidirect
13. C2×#91326C2semidirect
14. C2×#91326C2semidirect
15. C2×#91323C2semidirect
16. #11753730C2direct (N × H)
35. #91783C22semidirect
40. C5×#894C22semidirect
46. C3×#4033C22semidirect
57. #91446C22semidirect
58. C4×#1203C22semidirect
59. #91433C22semidirect
60. #91423C22semidirect
61. #91406C22semidirect
62. #91405C22semidirect
63. #91350C22semidirect
64. #91350C22semidirect
65. #91326C22semidirect
66. #91326C22semidirect
67. #91323C22semidirect
78. C2×#4033D3semidirect
154. C2×#894D5semidirect
206. #4033C2×D3semidirect
306. #894C2×D5semidirect
587. C2×C3×C5#559semidirect
739. C3×C5C2×#559semidirect
773. C2×C5#5585semidirect
830. C2×C3#65998semidirect
838. C5C2×#5585semidirect
870. C3C2×#65998semidirect
875. C2#11753730direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917832
C2×C5×#8942
C2×C3×#40332
C2×#914512
C2×#914462
C2×C4×#12032
C2×#914332
C2×#914232
C2×#914062
C2×#914052
C2×#913502
C2×#913262
C2×#913232
#117537302
C2×#659983
C2×#55855