Finite Group Databasebeta

← C103×#25548 #39930823

Subgroups — C103×#25548 #39930823

Order 26368.

1172 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C103C211yesmaximal, characteristic
2C2×#485×C103C211yesmaximal, characteristic, complemented
3C2×#468×C103C211yesmaximal, characteristic, complemented
4C103×#2417C211yesmaximal, characteristic, complemented
5C103×#2059C211yesmaximal, characteristic, complemented
6C103×#2034C211yesmaximal, characteristic, complemented
7C103×#2026C211yesmaximal, characteristic, complemented
8C103×#2000C211yesmaximal, characteristic, complemented
9C103×#1877C211yesmaximal, characteristic, complemented
10C103×#1874C211yesmaximal, characteristic, complemented
11C103×#1872C211yesmaximal, characteristic, complemented
12C103×#1870C211yesmaximal, characteristic, complemented
13C103×#1862C211yesmaximal, characteristic, complemented
14C103×#1852C211yesmaximal, characteristic, complemented
15C103×#1736C211yesmaximal, characteristic, complemented
16C22×SD16×C103C2211yescharacteristic
17C22×M16×C103C2211yescharacteristic
18#553×C103—24no—
19#553×C103—24no—
20C2×#126×C103—21no—
21C2×#125×C103C2211yescharacteristic
22C2×#123×C103—21no—
23C2×C22⋊Q8×C103C2211yescharacteristic
24C2×C22⋊Q8×C103C2211yescharacteristic
25C2×#121×C103—21no—
26C2×#121×C103C2211yescharacteristic
27C2×#121×C103C2211yescharacteristic
28C2×C4×D4×C103—21no—
29C2×C4×D4×C103C2211yescharacteristic
30C2×C4×D4×C103C2211yescharacteristic
31C2×#117×C103C2211yescharacteristic
32C22×C4⋊C4×C103C2211yescharacteristic
33C22×C4⋊C4×C103C2211yescharacteristic
34#485×C103—24no—
35#468×C103—24no—
36C2×#107×C103C2211yescharacteristic
37C2×#107×C103C2211yescharacteristic
38C2×#106×C103C2211yescharacteristic
39C2×#103×C103C2211yescharacteristic
40C2×#103×C103C2211yescharacteristic
41C2×#103×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#102×C103C2211yescharacteristic
45C2×C22⋊C8×C103C2211yescharacteristic
46C2×C22⋊C8×C103C2211yescharacteristic
47C2×C22⋊C8×C103C2211yescharacteristic
48#398×C103—21no—
49#396×C103—21no—
50#391×C103C2211yescharacteristic
51#389×C103C2211yescharacteristic
52#386×C103—21no—
53#380×C103—21no—
54#380×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#340×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61#336×C103C2211yescharacteristic
62#336×C103C2211yescharacteristic
63C22×Q8×C103C2311yescharacteristic
64C22×D4×C103—21no—
65C22×D4×C103—21no—
66C22×D4×C103D411yescharacteristic
67C22×D4×C103C2311yescharacteristic
68C23×C4×C103—21no—
69C23×C4×C103—21no—
70C23×C4×C103—21no—
71C23×C4×C103C2311yescharacteristic
72C23×C4×C103C2311yescharacteristic
73C2×SD16×C103—22no—
74C2×SD16×C103—22no—
75C2×SD16×C103—41no—
76C2×M16×C103—22no—
77C2×M16×C103—22no—
78C2×M16×C103—41no—
79C22×C8×C103C2311yescharacteristic
80C22×C8×C103C2311yescharacteristic
81C22×C8×C103C2311yescharacteristic
82C22×C8×C103C2311yescharacteristic
83#126×C103—28no—
84#125×C103—22no—
85#125×C103—22no—
86#123×C103—28no—
87C22⋊Q8×C103—22no—
88C22⋊Q8×C103—22no—
89C22⋊Q8×C103—22no—
90C22⋊Q8×C103—41no—
91#121×C103—28no—
92#121×C103—22no—
93#121×C103—22no—
94#121×C103—22no—
95#121×C103D414yes—
96C4×D4×C103—28no—
97C4×D4×C103—22no—
98C4×D4×C103—22no—
99C4×D4×C103—22no—
100C4×D4×C103—22no—
101#117×C103—22no—
102#117×C103D414yes—
103C2×C4⋊C4×C103—21no—
104C2×C4⋊C4×C103—21no—
105C2×C4⋊C4×C103—21no—
106C2×C4⋊C4×C103—22no—
107C2×C4⋊C4×C103—22no—
108C2×C4⋊C4×C103—22no—
109C2×C4⋊C4×C103—21no—
110C2×C4⋊C4×C103—21no—
111C2×C4⋊C4×C103—21no—
112C2×C4⋊C4×C103—21no—
113C2×C4⋊C4×C103—41no—
114C2×C4⋊C4×C103D411yescharacteristic
115C2×C4⋊C4×C103C2311yescharacteristic
116C2×C4⋊C4×C103C2311yescharacteristic
117C2×C4⋊C4×C103C2311yescharacteristic
118C2×C4⋊C4×C103C2311yescharacteristic
119C2×C4⋊C4×C103C2311yescharacteristic
120C2×C4⋊C4×C103C2311yescharacteristic
121C2×C22⋊C4×C103—21no—
122C2×C22⋊C4×C103—21no—
123C2×C22⋊C4×C103—21no—
124C2×C22⋊C4×C103—21no—
125C2×C22⋊C4×C103—21no—
126C2×C22⋊C4×C103—21no—
127C2×C22⋊C4×C103—21no—
128C2×C22⋊C4×C103D411yescharacteristic
129C2×C22⋊C4×C103D411yescharacteristic
130C2×C42×C103—21no—
131C2×C42×C103C2311yescharacteristic
132#107×C103—22no—
133#107×C103—22no—
134#106×C103—22no—
135#103×C103—22no—
136#103×C103—22no—
137#103×C103—22no—
138#102×C103—22no—
139#102×C103—22no—
140#102×C103—41no—
141C22⋊C8×C103—22no—
142C22⋊C8×C103—22no—
143C22⋊C8×C103—41no—
144#95×C103—21no—
145#95×C103—21no—
146#95×C103—21no—
147#95×C103—21no—
148C24×C103—21no—
149C24×C103C2×D411yescharacteristic
150C24×C103C2×D411yescharacteristic
151C2×Q8×C103—21no—
152C2×Q8×C103—21no—
153C2×Q8×C103—21no—
154C2×Q8×C103—21no—
155C2×Q8×C103—21no—
156C2×Q8×C103—21no—
157C2×D4×C103—24no—
158C2×D4×C103—22no—
159C2×D4×C103—22no—
160C2×D4×C103—24no—
161C2×D4×C103—21no—
162C2×D4×C103—21no—
163C2×D4×C103—21no—
164C2×D4×C103—21no—
165C2×D4×C103—21no—
166C2×D4×C103—41no—
167C2×D4×C103—42no—
168C2×D4×C103—42no—
169C2×D4×C103—81no—
170C2×D4×C103—81no—
171C2×D4×C103C2×D412yes—
172C22×C4×C103—21no—
173C22×C4×C103—21no—
174C22×C4×C103—21no—
175C22×C4×C103—21no—
176C22×C4×C103—21no—
177C22×C4×C103—21no—
178C22×C4×C103—21no—
179C22×C4×C103—21no—
180C22×C4×C103—24no—
181C22×C4×C103—24no—
182C22×C4×C103—21no—
183C22×C4×C103—21no—
184C22×C4×C103—21no—
185C22×C4×C103—21no—
186C22×C4×C103—21no—
187C22×C4×C103—21no—
188C22×C4×C103—21no—
189C22×C4×C103—21no—
190C22×C4×C103—21no—
191C22×C4×C103—42no—
192C22×C4×C103—42no—
193C22×C4×C103—81no—
194C22×C4×C103—81no—
195C22×C4×C103—81no—
196C22×C4×C103—81no—
197C22×C4×C103—81no—
198C22×C4×C103C2×D411yescharacteristic
199C22×C4×C103C2×D411yescharacteristic
200C22×C4×C103C2×D411yescharacteristic
201C22×C4×C103C2×D411yescharacteristic
202C22×C4×C103C2×D412yes—
203C22×C4×C103C2×D412yes—
204C22×C4×C103C2411yescharacteristic
205SD16×C103—44no—
206M16×C103—44no—
207C2×C8×C103—21no—
208C2×C8×C103—21no—
209C2×C8×C103—21no—
210C2×C8×C103—21no—
211C2×C8×C103—21no—
212C2×C8×C103—21no—
213C2×C8×C103—21no—
214C2×C8×C103—21no—
215C2×C8×C103—21no—
216C2×C8×C103—21no—
217C2×C8×C103—21no—
218C2×C8×C103#4112yes—
219C4⋊C4×C103—24no—
220C4⋊C4×C103—24no—
221C4⋊C4×C103—24no—
222C4⋊C4×C103—22no—
223C4⋊C4×C103—21no—
224C4⋊C4×C103—21no—
225C4⋊C4×C103—21no—
226C4⋊C4×C103—21no—
227C4⋊C4×C103—21no—
228C4⋊C4×C103—21no—
229C4⋊C4×C103—21no—
230C4⋊C4×C103—21no—
231C4⋊C4×C103—42no—
232C4⋊C4×C103—42no—
233C4⋊C4×C103—42no—
234C4⋊C4×C103—81no—
235C4⋊C4×C103C2×D412yes—
236C4⋊C4×C103C2×D412yes—
237C4⋊C4×C103C2×D412yes—
238C4⋊C4×C103#4112yes—
239C22⋊C4×C103—24no—
240C22⋊C4×C103—24no—
241C22⋊C4×C103—24no—
242C22⋊C4×C103—22no—
243C22⋊C4×C103—24no—
244C22⋊C4×C103—22no—
245C22⋊C4×C103—42no—
246C22⋊C4×C103—42no—
247C22⋊C4×C103—81no—
248C42×C103—24no—
249C42×C103—21no—
250C42×C103—21no—
251C23×C103—21no—
252C23×C103—21no—
253C23×C103—21no—
254C23×C103—21no—
255C23×C103—21no—
256C23×C103—21no—
257C23×C103—21no—
258C23×C103—21no—
259C23×C103—21no—
260C23×C103—21no—
261C23×C103—21no—
262C23×C103—21no—
263C23×C103—22no—
264C23×C103—41no—
265C23×C103—41no—
266C23×C103—41no—
267C23×C103—41no—
268C23×C103—41no—
269C23×C103—41no—
270C23×C103#12012yes—
271C23×C103#13712yes—
272C23×C103C22×D411yescharacteristic
273Q8×C103—41no—
274Q8×C103—41no—
275Q8×C103—41no—
276Q8×C103—41no—
277D4×C103—22no—
278D4×C103—22no—
279D4×C103—44no—
280D4×C103—48no—
281D4×C103—41no—
282D4×C103—41no—
283D4×C103—84no—
284C2×C4×C103—21no—
285C2×C4×C103—21no—
286C2×C4×C103—22no—
287C2×C4×C103—22no—
288C2×C4×C103—22no—
289C2×C4×C103—22no—
290C2×C4×C103—21no—
291C2×C4×C103—22no—
292C2×C4×C103—21no—
293C2×C4×C103—22no—
294C2×C4×C103—21no—
295C2×C4×C103—22no—
296C2×C4×C103—22no—
297C2×C4×C103—21no—
298C2×C4×C103—21no—
299C2×C4×C103—21no—
300C2×C4×C103—21no—
301C2×C4×C103—21no—
302C2×C4×C103—21no—
303C2×C4×C103—41no—
304C2×C4×C103—41no—
305C2×C4×C103—41no—
306C2×C4×C103—41no—
307C2×C4×C103—41no—
308C2×C4×C103—41no—
309C2×C4×C103—41no—
310C2×C4×C103—41no—
311C2×C4×C103—41no—
312C2×C4×C103—41no—
313C2×C4×C103—41no—
314C2×C4×C103—41no—
315C2×C4×C103—41no—
316C2×C4×C103—41no—
317C2×C4×C103—41no—
318C2×C4×C103—41no—
319C2×C4×C103—41no—
320C2×C4×C103—41no—
321C2×C4×C103—41no—
322C2×C4×C103—41no—
323C2×C4×C103—41no—
324C2×C4×C103—84no—
325C2×C4×C103—84no—
326C2×C4×C103—84no—
327C2×C4×C103#12012yes—
328C2×C4×C103C22×D411yescharacteristic
329C2×C4×C103C22×D411yescharacteristic
330C2×C4×C103C2×#4111yescharacteristic
331C2×C4×C103C2×#4111yescharacteristic
332C2×C4×C103H(5,𝔽2)11yescharacteristic
333C2×C4×C1032−1+411yescharacteristic
334C8×C103—22no—
335C8×C103—41no—
336C8×C103—41no—
337C8×C103—41no—
338C22×C103—22no—
339C22×C103—22no—
340C22×C103—22no—
341C22×C103—22no—
342C22×C103—22no—
343C22×C103—22no—
344C22×C103—41no—
345C22×C103—41no—
346C22×C103—41no—
347C22×C103—41no—
348C22×C103—41no—
349C22×C103—41no—
350C22×C103—41no—
351C22×C103—41no—
352C22×C103—42no—
353C22×C103—42no—
354C22×C103—42no—
355C22×C103—81no—
356C22×C103—81no—
357C22×C103—81no—
358C22×C103—81no—
359C22×C103C2×#12011yescharacteristic
360C22×C103#54611yescharacteristic
361C22×C103#54711yescharacteristic
362C22×C103C2×#13711yescharacteristic
363C22×C103#57511yescharacteristic
364C22×C103#57611yescharacteristic
365C22×C103#57711yescharacteristic
366C4×C103—22no—
367C4×C103—41no—
368C4×C103—41no—
369C4×C103—42no—
370C4×C103—41no—
371C4×C103—42no—
372C4×C103—42no—
373C4×C103—42no—
374C4×C103—81no—
375C4×C103—81no—
376C4×C103—81no—
377C4×C103#53211yescharacteristic
378C4×C103#53711yescharacteristic
379C4×C103#54611yescharacteristic
380C4×C103#54711yescharacteristic
381#25548C10311yesmaximal, characteristic, direct product factor, Sylow
382C2×C103—42no—
383C2×C103—42no—
384C2×C103—82no—
385C2×C103#243011yescharacteristic
386C2×C103#300711yescharacteristic
387C2×C103#301211yescharacteristic
388C2×C103#332011yescharacteristic
389C2×C103#332211yescharacteristic
390C2×C103#334611yescharacteristic
391C2×C103#335111yescharacteristic
392C2×#553C2×C10311yescharacteristic
393C2×#485C2×C10311yescharacteristic, complemented
394C2×#468C2×C10311yescharacteristic, complemented
395#2417C2×C10311yescharacteristic, complemented
396#2059C2×C10311yescharacteristic, complemented
397#2034C2×C10311yescharacteristic, complemented
398#2026C2×C10311yescharacteristic, complemented
399#2000C2×C10311yescharacteristic, complemented
400#1877C2×C10311yescharacteristic, complemented
401#1874C2×C10311yescharacteristic, complemented
402#1872C2×C10311yescharacteristic, complemented
403#1870C2×C10311yescharacteristic, complemented
404#1862C2×C10311yescharacteristic, complemented
405#1852C2×C10311yescharacteristic, complemented
406#1736C2×C10311yescharacteristic, complemented
407C103#2554811yescharacteristic, direct product factor, Sylow
408C22×SD16C22×C10311yescharacteristic
409C22×M16C22×C10311yescharacteristic
410#553—24no—
411#553—24no—
412C2×#126—21no—
413C2×#125C22×C10311yescharacteristic
414C2×#123—21no—
415C2×C22⋊Q8C22×C10311yescharacteristic
416C2×C22⋊Q8C22×C10311yescharacteristic
417C2×#121—21no—
418C2×#121C22×C10311yescharacteristic
419C2×#121C22×C10311yescharacteristic
420C2×C4×D4—21no—
421C2×C4×D4C22×C10311yescharacteristic
422C2×C4×D4C22×C10311yescharacteristic
423C2×#117C22×C10311yescharacteristic
424C22×C4⋊C4C22×C10311yescharacteristic
425C22×C4⋊C4C22×C10311yescharacteristic
426#485—24no—
427#468—24no—
428C2×#107C22×C10311yescharacteristic
429C2×#107C22×C10311yescharacteristic
430C2×#106C22×C10311yescharacteristic
431C2×#103C22×C10311yescharacteristic
432C2×#103C22×C10311yescharacteristic
433C2×#103C22×C10311yescharacteristic
434C2×#102C22×C10311yescharacteristic
435C2×#102C22×C10311yescharacteristic
436C2×#102C22×C10311yescharacteristic
437C2×C22⋊C8C22×C10311yescharacteristic
438C2×C22⋊C8C22×C10311yescharacteristic
439C2×C22⋊C8C22×C10311yescharacteristic
440#398—21no—
441#396—21no—
442#391C22×C10311yescharacteristic
443#389C22×C10311yescharacteristic
444#386—21no—
445#380—21no—
446#380C22×C10311yescharacteristic
447#340C22×C10311yescharacteristic
448#340C22×C10311yescharacteristic
449#340C22×C10311yescharacteristic
450#340C22×C10311yescharacteristic
451#340C22×C10311yescharacteristic
452#340C22×C10311yescharacteristic
453#336C22×C10311yescharacteristic
454#336C22×C10311yescharacteristic
455C22×Q8C23×C10311yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4D4×C10311yescharacteristic
459C22×D4C23×C10311yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C23×C10311yescharacteristic
464C23×C4C23×C10311yescharacteristic
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—41no—
468C2×M16—22no—
469C2×M16—22no—
470C2×M16—41no—
471C22×C8C23×C10311yescharacteristic
472C22×C8C23×C10311yescharacteristic
473C22×C8C23×C10311yescharacteristic
474C22×C8C23×C10311yescharacteristic
475#126—28no—
476#125—22no—
477#125—22no—
478#123—28no—
479C22⋊Q8—22no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8—41no—
483#121—28no—
484#121—22no—
485#121—22no—
486#121—22no—
487#121D4×C10314yes—
488C4×D4—28no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493#117—22no—
494#117D4×C10314yes—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—41no—
506C2×C4⋊C4D4×C10311yescharacteristic
507C2×C4⋊C4C23×C10311yescharacteristic
508C2×C4⋊C4C23×C10311yescharacteristic
509C2×C4⋊C4C23×C10311yescharacteristic
510C2×C4⋊C4C23×C10311yescharacteristic
511C2×C4⋊C4C23×C10311yescharacteristic
512C2×C4⋊C4C23×C10311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4D4×C10311yescharacteristic
521C2×C22⋊C4D4×C10311yescharacteristic
522C2×C42—21no—
523C2×C42C23×C10311yescharacteristic
524#107—22no—
525#107—22no—
526#106—22no—
527#103—22no—
528#103—22no—
529#103—22no—
530#102—22no—
531#102—22no—
532#102—41no—
533C22⋊C8—22no—
534C22⋊C8—22no—
535C22⋊C8—41no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540C24—21no—
541C24C2×D4×C10311yescharacteristic
542C24C2×D4×C10311yescharacteristic
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×D4—24no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—24no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—41no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4C2×D4×C10312yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4C2×D4×C10311yescharacteristic
591C22×C4C2×D4×C10311yescharacteristic
592C22×C4C2×D4×C10311yescharacteristic
593C22×C4C2×D4×C10311yescharacteristic
594C22×C4C2×D4×C10312yes—
595C22×C4C2×D4×C10312yes—
596C22×C4C24×C10311yescharacteristic
597SD16—44no—
598M16—44no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8#41×C10312yes—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—81no—
627C4⋊C4C2×D4×C10312yes—
628C4⋊C4C2×D4×C10312yes—
629C4⋊C4C2×D4×C10312yes—
630C4⋊C4#41×C10312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—22no—
635C22⋊C4—24no—
636C22⋊C4—22no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—81no—
640C42—24no—
641C42—21no—
642C42—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—22no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23#120×C10312yes—
663C23#137×C10312yes—
664C23C22×D4×C10311yescharacteristic
665Q8—41no—
666Q8—41no—
667Q8—41no—
668Q8—41no—
669D4—22no—
670D4—22no—
671D4—44no—
672D4—48no—
673D4—41no—
674D4—41no—
675D4—84no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4#120×C10312yes—
720C2×C4C22×D4×C10311yescharacteristic
721C2×C4C22×D4×C10311yescharacteristic
722C2×C4C2×#41×C10311yescharacteristic
723C2×C4C2×#41×C10311yescharacteristic
724C2×C4H(5,𝔽2)×C10311yescharacteristic
725C2×C42−1+4×C10311yescharacteristic
726C8—22no—
727C8—41no—
728C8—41no—
729C8—41no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×#120×C10311yescharacteristic
752C22#546×C10311yescharacteristic
753C22#547×C10311yescharacteristic
754C22C2×#137×C10311yescharacteristic
755C22#575×C10311yescharacteristic
756C22#576×C10311yescharacteristic
757C22#577×C10311yescharacteristic
758C4—22no—
759C4—41no—
760C4—42no—
761C4—41no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—41no—
766C4—81no—
767C4—81no—
768C4—81no—
769C4#532×C10311yescharacteristic
770C4#537×C10311yescharacteristic
771C4#546×C10311yescharacteristic
772C4#547×C10311yescharacteristic
773C2—42no—
774C2—42no—
775C2—82no—
776C2C103×#243011yescharacteristic
777C2C103×#300711yescharacteristic
778C2C103×#301211yescharacteristic
779C2C103×#332011yescharacteristic
780C2C103×#332211yescharacteristic
781C2C103×#334611yescharacteristic
782C2C103×#335111yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#553×C103C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C4×D4×C103 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#485×C103C2semidirect
3. C2×#468×C103C2semidirect
4. C103×#2417C2semidirect
5. C103×#2059C2semidirect
6. C103×#2034C2semidirect
7. C103×#2026C2semidirect
8. C103×#2000C2semidirect
9. C103×#1877C2semidirect
10. C103×#1874C2semidirect
11. C103×#1872C2semidirect
12. C103×#1870C2semidirect
13. C103×#1862C2semidirect
14. C103×#1852C2semidirect
15. C103×#1736C2semidirect
381. #25548C103direct (N × H)
393. C2×#485C2×C103semidirect
394. C2×#468C2×C103semidirect
395. #2417C2×C103semidirect
396. #2059C2×C103semidirect
397. #2034C2×C103semidirect
398. #2026C2×C103semidirect
399. #2000C2×C103semidirect
400. #1877C2×C103semidirect
401. #1874C2×C103semidirect
402. #1872C2×C103semidirect
403. #1870C2×C103semidirect
404. #1862C2×C103semidirect
405. #1852C2×C103semidirect
406. #1736C2×C103semidirect
407. C103#25548direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#553×C1032
C2×#485×C1032
C2×#468×C1032
C103×#24172
C103×#20592
C103×#20342
C103×#20262
C103×#20002
C103×#18772
C103×#18742
C103×#18722
C103×#18702
C103×#18622
C103×#18522
C103×#17362
#25548103