Finite Group Databasebeta

← C2×#11753111 #14484730

Subgroups — C2×#11753111 #14484730

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×#91770C211yesmaximal, characteristic, complemented
2C2×C5×#883C211yesmaximal, characteristic, complemented
3C2×C3×#4031C211yesmaximal, characteristic, complemented
4C2×#91567C211yesmaximal, characteristic
5C2×#91559C211yesmaximal, characteristic, complemented
6C2×#91543C211yesmaximal, characteristic, complemented
7C2×#91526C211yesmaximal, characteristic, complemented
8C2×#91464C211yesmaximal, characteristic, complemented
9C2×C4×#1203C211yesmaximal, characteristic, complemented
10C2×#91441C211yesmaximal, characteristic, complemented
11C2×#91413C211yesmaximal, characteristic, complemented
12C2×#91354C211yesmaximal, characteristic, complemented
13C2×#91331C211yesmaximal, characteristic, complemented
14C2×#91326C211yesmaximal, characteristic, complemented
15C2×#91323C211yesmaximal, characteristic, complemented
16#11753111C2116yesmaximal, direct product factor
17C2×#65998—31nomaximal, Hall
18C22×#1220C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C22×C4×C5×D3C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×Dic10C2211yescharacteristic
25C22×#1204C2211yescharacteristic
26C22×#1203C2211yescharacteristic
27C22×#1202C2211yescharacteristic
28C22×#1201C2211yescharacteristic
29C22×D5×Dic3C2211yescharacteristic
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×#6714C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×C4×Dic15C2211yescharacteristic
34#91770C2218yescomplemented
35C2×C5×#217C2211yescharacteristic
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×C4⋊Dic3C2211yescharacteristic
38C2×C5×Dic3⋊C4C2211yescharacteristic
39C5×#883C2218yescomplemented
40C2×C3×C22⋊Dic5C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C2×C3×C4×Dic5C2211yescharacteristic
44C3×#4031C2218yescomplemented
45#91567C2218yes—
46#91559C2218yescomplemented
47#91543C2218yescomplemented
48C2×#6668C2211yescharacteristic
49C2×#6668C2211yescharacteristic
50C2×#6668C2211yescharacteristic
51C2×#6667C2211yescharacteristic
52C2×#6667C2211yescharacteristic
53C2×(C2×D3)⋊Dic5C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×#6665C2211yescharacteristic
56C2×Dic3×Dic5C2211yescharacteristic
57C2×Dic3×Dic5C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59#91526C2218yescomplemented
60#91464C2218yescomplemented
61C4×#1203C2218yescomplemented
62#91441C2218yescomplemented
63#91413C2218yescomplemented
64#91354C2218yescomplemented
65#91331C2218yescomplemented
66#91326C2218yescomplemented
67#91323C2218yescomplemented
68C2×#5681—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×#4033—31no—
79C2×#4031—31no—
80C2×#4031—31no—
81C2×#4031—31no—
82C2×#4031D311yescharacteristic, complemented
83C2×#4027—31no—
84C2×#4027—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C2×#1220—24no—
92C2×#1220C2314yes—
93C22×Dic15—42no—
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2314yes—
97C22×Dic15C2311yescharacteristic
98C2×C4×D15—42no—
99C2×C4×D15C2314yes—
100C2×C5×#67—42no—
101C2×C5×#67C2314yes—
102C22×C5×Dic3C2311yescharacteristic
103C22×C5×Dic3C2311yescharacteristic
104C22×C5×Dic3C2311yescharacteristic
105C2×C4×C5×D3—42no—
106C2×C4×C5×D3C2314yes—
107C2×C3×C22⋊D5—24no—
108C2×C3×C22⋊D5C2314yes—
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C2×C3×Dic10—24no—
113C2×C3×Dic10C2314yes—
114C2×#1204—24no—
115C2×#1204C2314yes—
116C2×#1203—24no—
117C2×#1203C2314yes—
118C2×#1202—42no—
119C2×#1202C2314yes—
120C2×#1201—24no—
121C2×#1201C2314yes—
122C2×D5×Dic3—42no—
123C2×D5×Dic3C2314yes—
124C3×C5×C22⋊C4C2314yes—
125#6714C2314yes—
126#6712C2314yes—
127C4×Dic15C2314yes—
128C5×#217C2314yes—
129C5×(C2×D3)⋊C4C2314yes—
130C5×C4⋊Dic3C2314yes—
131C5×Dic3⋊C4C2314yes—
132C3×C22⋊Dic5C2314yes—
133C3×#685C2314yes—
134C3×#685C2314yes—
135C3×C4×Dic5C2314yes—
136#6668C2314yes—
137#6668C2314yes—
138#6668C2314yes—
139#6667C2314yes—
140#6667C2314yes—
141(C2×D3)⋊Dic5C2314yes—
142(C2×D3)⋊Dic5C2314yes—
143#6665C2314yes—
144Dic3×Dic5C2314yes—
145Dic3×Dic5C2314yes—
146Dic3×Dic5C2314yes—
147C2×C3×#124—51no—
148C2×#947—51no—
149C2×Q8×Dic3—51no—
150C2×#940—51no—
151C2×D4×Dic3—51no—
152#5681—516no—
153C2×#886—51no—
154C2×#886—51no—
155C2×#885—51no—
156C2×#885—51no—
157C2×#883—51no—
158C2×#883D511yescharacteristic, complemented
159C2×#67⋊C4—51no—
160C2×#67⋊C4—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⋊D5C2×D311yescharacteristic
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⋊C4—31no—
178C2×C5×C22⋊C4—31no—
179C2×C5×C22⋊C4—31no—
180C2×C5×C22⋊C4C2×D311yescharacteristic
181C2×C22⋊Dic5—31no—
182C2×C22⋊Dic5—31no—
183C2×C22⋊Dic5C2×D311yescharacteristic
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×#685C2×D311yescharacteristic
193C2×#685C2×D311yescharacteristic
194C2×#683—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×#683—31no—
198C2×C4×Dic5—31no—
199C2×C4×Dic5—31no—
200C2×C4×Dic5—31no—
201C2×C4×Dic5—31no—
202C2×C4×Dic5C2×D311yescharacteristic
203#4040—38no—
204#4040—38no—
205#4033—38no—
206#4033—38no—
207#4031—38no—
208#4031—38no—
209#4031—38no—
210#4031C2×D318yescomplemented
211#4027—38no—
212#4027—38no—
213C2×#559—151noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5C2412yes—
218C23×C3×C5C2411yescharacteristic
219C22×D15—22no—
220C22×D15—22no—
221C22×D15—22no—
222C22×D15C2412yes—
223C22×C5×D3—22no—
224C22×C5×D3—22no—
225C22×C5×D3—22no—
226C22×C5×D3C2412yes—
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5—22no—
230C22×C3×D5C2412yes—
231C2×C3×C4×C5—22no—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5C2412yes—
234C2×C3×C4×C5C2412yes—
235#1220—28no—
236C2×Dic15—22no—
237C2×Dic15—22no—
238C2×Dic15—44no—
239C2×Dic15#4114yes—
240C2×Dic15C2412yes—
241C2×Dic15C2412yes—
242C2×Dic15C2412yes—
243C4×D15—44no—
244C5×#67—44no—
245C2×C5×Dic3—22no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3—22no—
248C2×C5×Dic3C2412yes—
249C2×C5×Dic3C2412yes—
250C2×C5×Dic3C2412yes—
251C4×C5×D3—44no—
252C3×C22⋊D5—28no—
253C2×C3×Dic5—22no—
254C2×C3×Dic5—22no—
255C2×C3×Dic5#4114yes—
256C2×C3×Dic5C2412yes—
257C2×C3×Dic5C2412yes—
258C2×C3×Dic5C2412yes—
259C3×Dic10—28no—
260#1204—28no—
261#1203—28no—
262#1202—44no—
263#1201—28no—
264D5×Dic3—44no—
265C22×C3×Q8—51no—
266C22×C3×D4—51no—
267C22×#67—51no—
268C22×#67—51no—
269C22×#67—51no—
270C22×#67C2×D511yescharacteristic
271C23×Dic3—51no—
272C23×Dic3—51no—
273C22×D12—51no—
274C22×C4×D3—51no—
275C22×C4×D3C2×D511yescharacteristic
276C22×Dic6—51no—
277C3×#124—58no—
278C2×C3×C22⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×C3×C22⋊C4—51no—
281C2×C3×C22⋊C4C2×D511yescharacteristic
282C2×C3×C42—51no—
283C2×#217—51no—
284C2×#217C2×D511yescharacteristic
285#947—58no—
286Q8×Dic3—58no—
287#940—58no—
288D4×Dic3—58no—
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)⋊C4C2×D511yescharacteristic
295C2×C4⋊Dic3—51no—
296C2×C4⋊Dic3—51no—
297C2×C4⋊Dic3—51no—
298C2×C4⋊Dic3C2×D511yescharacteristic
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4C2×D511yescharacteristic
301C2×C4×Dic3—51no—
302C2×C4×Dic3—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3—51no—
305#886—58no—
306#886—58no—
307#885—58no—
308#885—58no—
309#883—58no—
310#883C2×D518yescomplemented
311#67⋊C4—58no—
312#67⋊C4—58no—
313C4×D12—58no—
314C4×Dic6—58no—
315C24×C5—31no—
316C24×C5C22×D311yescharacteristic
317C23×D5—31no—
318C23×D5C22×D311yescharacteristic
319C2×C5×D4—34no—
320C2×C5×D4—122no—
321C22×C4×C5—31no—
322C22×C4×C5—31no—
323C22×C4×C5—31no—
324C22×C4×C5—34no—
325C22×C4×C5—122no—
326C22×C4×C5C22×D311yescharacteristic
327C22×C4×C5C22×D311yescharacteristic
328C2×C22⋊D5—24no—
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⋊D5C22×D314yes—
336C22×Dic5—31no—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—34no—
340C22×Dic5—122no—
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⋊C4—34no—
356C5×C22⋊C4—34no—
357C5×C22⋊C4—34no—
358C5×C22⋊C4C22×D314yes—
359C22⋊Dic5—34no—
360C22⋊Dic5—34no—
361C22⋊Dic5C22×D314yes—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366#685C22×D314yes—
367#685C22×D314yes—
368#683—34no—
369#683—34no—
370#683—34no—
371#683—34no—
372C4×Dic5—34no—
373C4×Dic5—34no—
374C4×Dic5—34no—
375C4×Dic5—34no—
376C4×Dic5C22×D314yes—
377#559—1516no—
378C2×#127—151no—
379C2×#124—51no—
380C2×#124—151no—
381C2×#124—151no—
382C2×#124—151no—
383C2×#123—31no—
384C2×#123—151no—
385C2×#123—151no—
386C2×#123—151no—
387C2×C4×Q8—151no—
388C2×C4×Q8—151no—
389C2×C4×D4—151no—
390C2×C4×D4—151no—
391C2×C4×D4—151no—
392C2×C4×D4—151no—
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—44no—
397C22×C3×C5C2×#4112yes—
398C22×C3×C5C2×#4112yes—
399C22×C3×C5H(5,𝔽2)12yes—
400C22×C3×C5C2511yescharacteristic
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—44no—
405C2×C5×D3—22no—
406C2×C5×D3—22no—
407C2×C5×D3—22no—
408C2×C5×D3—44no—
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—22no—
412C2×C3×D5—44no—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415Dic15—22no—
416Dic15—22no—
417Dic15C2×#4114yes—
418C3×Dic5—22no—
419C3×Dic5—22no—
420C3×Dic5C2×#4114yes—
421C5×Dic3—22no—
422C5×Dic3—22no—
423C5×Dic3—22no—
424C24×C3—51no—
425C24×C3C22×D511yescharacteristic
426C23×D3—51no—
427C23×D3C22×D511yescharacteristic
428C2×C3×Q8—54no—
429C2×C3×Q8—104no—
430C2×C3×D4—54no—
431C2×C3×D4—104no—
432C22×C3×C4—51no—
433C22×C3×C4—51no—
434C22×C3×C4—51no—
435C22×C3×C4C22×D511yescharacteristic
436C22×C3×C4C22×D511yescharacteristic
437C2×#67—42no—
438C2×#67—54no—
439C2×#67—54no—
440C2×#67—54no—
441C2×#67—104no—
442C2×#67—104no—
443C2×#67—202no—
444C2×#67C22×D514yes—
445C22×Dic3—51no—
446C22×Dic3—51no—
447C22×Dic3—51no—
448C22×Dic3—54no—
449C22×Dic3—54no—
450C22×Dic3—202no—
451C22×Dic3—202no—
452C22×Dic3C22×D511yescharacteristic
453C22×Dic3C22×D511yescharacteristic
454C22×Dic3C22×D511yescharacteristic
455C2×D12—54no—
456C2×D12—104no—
457C2×C4×D3—42no—
458C2×C4×D3—54no—
459C2×C4×D3—202no—
460C2×C4×D3C22×D514yes—
461C2×Dic6—54no—
462C2×Dic6—104no—
463C3×C22⋊C4—54no—
464C3×C22⋊C4—54no—
465C3×C22⋊C4—54no—
466C3×C22⋊C4C22×D514yes—
467C3×C42—54no—
468#217—54no—
469#217C22×D514yes—
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)⋊C4C22×D514yes—
476C4⋊Dic3—54no—
477C4⋊Dic3—54no—
478C4⋊Dic3—54no—
479C4⋊Dic3C22×D514yes—
480Dic3⋊C4—54no—
481Dic3⋊C4C22×D514yes—
482C4×Dic3—54no—
483C4×Dic3—54no—
484C4×Dic3—54no—
485C4×Dic3—54no—
486C23×C5—22no—
487C23×C5—22no—
488C23×C5—22no—
489C23×C5—32no—
490C23×C5—62no—
491C23×C5—62no—
492C23×C5—62no—
493C23×C5C23×D312yes—
494C23×C5C23×D311yescharacteristic
495C22×D5—22no—
496C22×D5—22no—
497C22×D5—22no—
498C22×D5—32no—
499C22×D5—62no—
500C22×D5—62no—
501C22×D5—62no—
502C22×D5C23×D312yes—
503C5×D4—124no—
504C2×C4×C5—22no—
505C2×C4×C5—22no—
506C2×C4×C5—32no—
507C2×C4×C5—32no—
508C2×C4×C5—32no—
509C2×C4×C5—62no—
510C2×C4×C5—62no—
511C2×C4×C5—62no—
512C2×C4×C5—124no—
513C2×C4×C5C23×D312yes—
514C2×C4×C5C23×D312yes—
515C22⋊D5—28no—
516C22⋊D5—68no—
517C22⋊D5—68no—
518C22⋊D5—68no—
519C2×Dic5—22no—
520C2×Dic5—22no—
521C2×Dic5—34no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—62no—
526C2×Dic5—62no—
527C2×Dic5—124no—
528C2×Dic5#23714yes—
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—51no—
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—58no—
551#124—158no—
552#124—158no—
553#124—158no—
554#123—38no—
555#123—158no—
556#123—158no—
557#123—158no—
558C4×Q8—158no—
559C4×Q8—158no—
560C4×D4—158no—
561C4×D4—158no—
562C4×D4—158no—
563C4×D4—158no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—31no—
566C2×C4⋊C4—151no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C4⋊C4—151no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—51no—
573C2×C22⋊C4—51no—
574C2×C22⋊C4—51no—
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⋊C4D3×D511yescharacteristic
582C2×C42—51no—
583C2×C42—151no—
584C2×C42—151no—
585C2×C42—151no—
586C2×C42—151no—
587C2×C3×C5—42no—
588C2×C3×C5#55914yescomplemented
589C2×C3×C5C22×#4111yescharacteristic
590C2×C3×C5C22×#4111yescharacteristic
591C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
592D15—42no—
593C3×D5—42no—
594C5×D3—42no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—52no—
599C23×C3—102no—
600C23×C3—102no—
601C23×C3—102no—
602C23×C3C23×D512yes—
603C23×C3C23×D511yescharacteristic
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—52no—
608C22×D3—102no—
609C22×D3—102no—
610C22×D3—102no—
611C22×D3C23×D512yes—
612C3×Q8—108no—
613C3×D4—108no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—54no—
617C2×C3×C4—52no—
618C2×C3×C4—52no—
619C2×C3×C4—52no—
620C2×C3×C4—102no—
621C2×C3×C4—102no—
622C2×C3×C4C23×D512yes—
623C2×C3×C4C23×D512yes—
624#67—44no—
625#67—108no—
626#67—108no—
627#67—204no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—54no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—52no—
635C2×Dic3—102no—
636C2×Dic3—102no—
637C2×Dic3—204no—
638C2×Dic3—204no—
639C2×Dic3C23×D512yes—
640C2×Dic3C23×D512yes—
641C2×Dic3C23×D512yes—
642D12—108no—
643C4×D3—44no—
644C4×D3—204no—
645Dic6—108no—
646C22×C5—22no—
647C22×C5—22no—
648C22×C5—22no—
649C22×C5—44no—
650C22×C5—62no—
651C22×C5—62no—
652C22×C5—62no—
653C22×C5—124no—
654C22×C5C2×#23712yes—
655C22×C5D3×#4112yes—
656C22×C5#100912yes—
657C22×C5C24×D311yescharacteristic
658C2×D5—22no—
659C2×D5—22no—
660C2×D5—22no—
661C2×D5—44no—
662C2×D5—62no—
663C2×D5—62no—
664C2×D5—62no—
665C2×D5—124no—
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—62no—
669C4×C5—62no—
670C4×C5—62no—
671Dic5—22no—
672Dic5—22no—
673Dic5—34no—
674Dic5—62no—
675Dic5—62no—
676Dic5C2×#23714yes—
677C24—31no—
678C24—51no—
679C24—151no—
680C24C2×D3×D511yescharacteristic
681C2×Q8—54no—
682C2×Q8—104no—
683C2×Q8—154no—
684C2×Q8—304no—
685C2×D4—34no—
686C2×D4—54no—
687C2×D4—104no—
688C2×D4—122no—
689C2×D4—154no—
690C2×D4—154no—
691C2×D4—154no—
692C2×D4—154no—
693C2×D4—304no—
694C2×D4—304no—
695C2×D4—304no—
696C2×D4—602no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—34no—
701C22×C4—51no—
702C22×C4—51no—
703C22×C4—51no—
704C22×C4—122no—
705C22×C4—154no—
706C22×C4—151no—
707C22×C4—151no—
708C22×C4—151no—
709C22×C4—154no—
710C22×C4—154no—
711C22×C4—602no—
712C22×C4—602no—
713C22×C4—602no—
714C22×C4C2×D3×D511yescharacteristic
715C22×C4C2×D3×D511yescharacteristic
716C4⋊C4—34no—
717C4⋊C4—34no—
718C4⋊C4—154no—
719C4⋊C4—154no—
720C4⋊C4—154no—
721C4⋊C4—154no—
722C22⋊C4—34no—
723C22⋊C4—34no—
724C22⋊C4—54no—
725C22⋊C4—54no—
726C22⋊C4—54no—
727C22⋊C4—154no—
728C22⋊C4—154no—
729C22⋊C4—154no—
730C22⋊C4—154no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4C2×D3×D514yes—
734C42—54no—
735C42—154no—
736C42—154no—
737C42—154no—
738C42—154no—
739C3×C5C2×#55911yescharacteristic, complemented, Hall
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—44no—
744C22×C3—102no—
745C22×C3—102no—
746C22×C3—102no—
747C22×C3—204no—
748C22×C3#414412yes—
749C22×C3D5×#4112yes—
750C22×C3D5×#4112yes—
751C22×C3C24×D511yescharacteristic
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—44no—
756C2×D3—102no—
757C2×D3—102no—
758C2×D3—102no—
759C2×D3—204no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—54no—
763C3×C4—102no—
764C3×C4—102no—
765Dic3—22no—
766Dic3—22no—
767Dic3—22no—
768Dic3—54no—
769Dic3—102no—
770Dic3—102no—
771C2×C5—42no—
772C2×C5—122no—
773C2×C5#568114yescomplemented
774C2×C5C22×#23711yescharacteristic
775C2×C5C2×D3×#4111yescharacteristic
776C2×C5C2×#100911yescharacteristic
777D5—42no—
778D5—122no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—32no—
783C23—52no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—102no—
788C23—102no—
789C23—102no—
790C23—152no—
791C23—302no—
792C23—302no—
793C23—302no—
794C23C22×D3×D512yes—
795C23C22×D3×D511yescharacteristic
796Q8—108no—
797Q8—308no—
798D4—108no—
799D4—124no—
800D4—308no—
801D4—308no—
802D4—308no—
803D4—604no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—54no—
810C2×C4—52no—
811C2×C4—52no—
812C2×C4—52no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—102no—
817C2×C4—102no—
818C2×C4—124no—
819C2×C4—154no—
820C2×C4—152no—
821C2×C4—152no—
822C2×C4—152no—
823C2×C4—302no—
824C2×C4—302no—
825C2×C4—604no—
826C2×C4—604no—
827C2×C4—604no—
828C2×C4C22×D3×D512yes—
829C2×C4C22×D3×D512yes—
830C2×C3—42no—
831C2×C3—202no—
832C2×C3#6599814yescomplemented
833C2×C3C2×#414411yescharacteristic
834C2×C3C2×D5×#4111yescharacteristic
835C2×C3C2×D5×#4111yescharacteristic
836D3—42no—
837D3—202no—
838C5C2×#568111yescharacteristic, complemented, Sylow
839C22—22no—
840C22—22no—
841C22—22no—
842C22—44no—
843C22—62no—
844C22—62no—
845C22—62no—
846C22—102no—
847C22—102no—
848C22—102no—
849C22—124no—
850C22—204no—
851C22—302no—
852C22—302no—
853C22—302no—
854C22—604no—
855C22#9201612yes—
856C22D5×#23712yes—
857C22#9202712yes—
858C22C23×D3×D511yescharacteristic
859C4—22no—
860C4—22no—
861C4—54no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—102no—
866C4—102no—
867C4—154no—
868C4—302no—
869C4—302no—
870C3C2×#6599811yescharacteristic, complemented, Sylow
871C2—42no—
872C2—122no—
873C2—202no—
874C2—602no—
875C2#1175311114yesdirect product factor
876C2C2×#9201611yescharacteristic
877C2C2×D5×#23711yescharacteristic
878C2C2×#9202711yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
prime radicalC2×#91567C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#559
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×#91770C2semidirect
2. C2×C5×#883C2semidirect
3. C2×C3×#4031C2semidirect
5. C2×#91559C2semidirect
6. C2×#91543C2semidirect
7. C2×#91526C2semidirect
8. C2×#91464C2semidirect
9. C2×C4×#1203C2semidirect
10. C2×#91441C2semidirect
11. C2×#91413C2semidirect
12. C2×#91354C2semidirect
13. C2×#91331C2semidirect
14. C2×#91326C2semidirect
15. C2×#91323C2semidirect
16. #11753111C2direct (N × H)
34. #91770C22semidirect
39. C5×#883C22semidirect
44. C3×#4031C22semidirect
46. #91559C22semidirect
47. #91543C22semidirect
59. #91526C22semidirect
60. #91464C22semidirect
61. C4×#1203C22semidirect
62. #91441C22semidirect
63. #91413C22semidirect
64. #91354C22semidirect
65. #91331C22semidirect
66. #91326C22semidirect
67. #91323C22semidirect
82. C2×#4031D3semidirect
158. C2×#883D5semidirect
210. #4031C2×D3semidirect
310. #883C2×D5semidirect
588. C2×C3×C5#559semidirect
739. C3×C5C2×#559semidirect
773. C2×C5#5681semidirect
832. C2×C3#65998semidirect
838. C5C2×#5681semidirect
870. C3C2×#65998semidirect
875. C2#11753111direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917702
C2×C5×#8832
C2×C3×#40312
C2×#915672
C2×#915592
C2×#915432
C2×#915262
C2×#914642
C2×C4×#12032
C2×#914412
C2×#914132
C2×#913542
C2×#913312
C2×#913262
C2×#913232
#117531112
C2×#659983
C2×#56815