Finite Group Databasebeta

← C13×#24569 #15710908

Subgroups — C13×#24569 #15710908

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#485C211yesmaximal, characteristic, complemented
2C2×C13×#408C211yesmaximal, characteristic
3C13×#2616C211yesmaximal, characteristic
4C13×#2311C211yesmaximal, characteristic
5C13×#2077C211yesmaximal, characteristic, complemented
6C13×#2076C211yesmaximal, characteristic, complemented
7C13×#2035C211yesmaximal, characteristic, complemented
8C13×#2035C211yesmaximal, characteristic, complemented
9C13×#1894C211yesmaximal, characteristic, complemented
10C13×#1892C211yesmaximal, characteristic, complemented
11C13×#1872C211yesmaximal, characteristic, complemented
12C13×#1853C211yesmaximal, characteristic, complemented
13C13×#1825C211yesmaximal, characteristic, complemented
14C13×#1809C211yesmaximal, characteristic, complemented
15C13×#1807C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C22×C13×M16C2211yescharacteristic
18C23×C8×C13C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C13×C22⋊Q8C2211yescharacteristic
22C2×C13×#117C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C13×#485—24no—
25C2×C13×#107C2211yescharacteristic
26C2×C13×#106C2211yescharacteristic
27C2×C13×#106C2211yescharacteristic
28C2×C13×#106C2211yescharacteristic
29C2×C13×#103C2211yescharacteristic
30C2×C13×#103C2211yescharacteristic
31C2×C13×#103C2211yescharacteristic
32C2×C13×#103C2211yescharacteristic
33C13×#408—24no—
34C2×C13×C22⋊C8C2211yescharacteristic
35C2×C13×C22⋊C8C2211yescharacteristic
36C2×C13×C22⋊C8C2211yescharacteristic
37C2×C13×C22⋊C8C2211yescharacteristic
38C13×#395—21no—
39C13×#394—21no—
40C13×#394—21no—
41C13×#394—21no—
42C13×#391—21no—
43C13×#390—21no—
44C13×#386—21no—
45C13×#386—21no—
46C13×#380C2211yescharacteristic
47C13×#380C2211yescharacteristic
48C13×#380C2211yescharacteristic
49C13×#380C2211yescharacteristic
50C13×#380C2211yescharacteristic
51C13×#380C2211yescharacteristic
52C13×#380C2211yescharacteristic
53C13×#340C2211yescharacteristic
54C13×#340C2211yescharacteristic
55C13×#340C2211yescharacteristic
56C13×#340C2211yescharacteristic
57C13×#340C2211yescharacteristic
58C13×#340C2211yescharacteristic
59C13×#340C2211yescharacteristic
60C13×#340C2211yescharacteristic
61C2×C13×#41—22no—
62C2×C13×#41—22no—
63C2×C13×#41—22no—
64C2×C13×#41—22no—
65C2×C13×#41—41no—
66C2×C13×#41—41no—
67C22×Q8×C13D411yescharacteristic
68C22×Q8×C13C2311yescharacteristic
69C22×D4×C13D411yescharacteristic
70C22×D4×C13D411yescharacteristic
71C22×D4×C13D411yescharacteristic
72C23×C4×C13—21no—
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C2×C13×M16—22no—
77C2×C13×M16—22no—
78C2×C13×M16—41no—
79C22×C8×C13—22no—
80C22×C8×C13—22no—
81C22×C8×C13—41no—
82C22×C8×C13C2311yescharacteristic
83C22×C8×C13C2311yescharacteristic
84C22×C8×C13C2311yescharacteristic
85C22×C8×C13C2311yescharacteristic
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—41no—
91C13×C22⋊Q8—41no—
92C13×#117—22no—
93C13×#117—22no—
94C2×C13×C4⋊C4—21no—
95C2×C13×C4⋊C4—21no—
96C2×C13×C4⋊C4—21no—
97C2×C13×C4⋊C4—21no—
98C2×C13×C4⋊C4—41no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C13×C4⋊C4C2311yescharacteristic
105C2×C13×C4⋊C4C2311yescharacteristic
106C2×C13×C4⋊C4C2311yescharacteristic
107C2×C13×C22⋊C4—21no—
108C2×C13×C22⋊C4—21no—
109C2×C13×C22⋊C4—21no—
110C2×C13×C22⋊C4—21no—
111C2×C13×C22⋊C4—21no—
112C2×C13×C22⋊C4—21no—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4—21no—
118C2×C42×C13—21no—
119C13×#107—22no—
120C13×#106—22no—
121C13×#106—41no—
122C13×#106—41no—
123C13×#103—22no—
124C13×#103—22no—
125C13×#103—41no—
126C13×#103—41no—
127C13×C22⋊C8—22no—
128C13×C22⋊C8—22no—
129C13×C22⋊C8—22no—
130C13×C22⋊C8D414yes—
131C13×#95—21no—
132C13×#95—21no—
133C13×#95—21no—
134C13×#95—21no—
135C13×#95—21no—
136C13×#95—21no—
137C13×#95—21no—
138#24569C1311yesmaximal, characteristic, direct product factor, Sylow
139C24×C13C2×D411yescharacteristic
140C24×C13C2×D411yescharacteristic
141C24×C13C2×D411yescharacteristic
142C13×#41—44no—
143C13×#41—44no—
144C13×#41—44no—
145C13×#41—44no—
146C2×Q8×C13—22no—
147C2×Q8×C13—22no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13—21no—
151C2×Q8×C13—21no—
152C2×Q8×C13—21no—
153C2×Q8×C13—21no—
154C2×Q8×C13—41no—
155C2×D4×C13—22no—
156C2×D4×C13—22no—
157C2×D4×C13—22no—
158C2×D4×C13—22no—
159C2×D4×C13—22no—
160C2×D4×C13—22no—
161C2×D4×C13—41no—
162C2×D4×C13—41no—
163C2×D4×C13—41no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—42no—
187C22×C4×C13—81no—
188C22×C4×C13—81no—
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D412yes—
192C22×C4×C13C2×D411yescharacteristic
193C22×C4×C13#4112yes—
194C22×C4×C13#4112yes—
195C22×C4×C13#4112yes—
196C22×C4×C13C2411yescharacteristic
197C13×M16—44no—
198C2×C8×C13—21no—
199C2×C8×C13—21no—
200C2×C8×C13—21no—
201C2×C8×C13—21no—
202C2×C8×C13—21no—
203C2×C8×C13—21no—
204C2×C8×C13—21no—
205C2×C8×C13—21no—
206C2×C8×C13—21no—
207C2×C8×C13—21no—
208C2×C8×C13—44no—
209C2×C8×C13C2×D412yes—
210C2×C8×C13C2×D412yes—
211C13×C4⋊C4—21no—
212C13×C4⋊C4—21no—
213C13×C4⋊C4—21no—
214C13×C4⋊C4—21no—
215C13×C4⋊C4—21no—
216C13×C4⋊C4—21no—
217C13×C4⋊C4—21no—
218C13×C4⋊C4—21no—
219C13×C4⋊C4—21no—
220C13×C4⋊C4—21no—
221C13×C4⋊C4—21no—
222C13×C4⋊C4—21no—
223C13×C4⋊C4—21no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4—42no—
226C13×C4⋊C4—42no—
227C13×C4⋊C4—42no—
228C13×C4⋊C4—42no—
229C13×C22⋊C4—42no—
230C13×C22⋊C4—42no—
231C13×C22⋊C4—42no—
232C13×C22⋊C4—42no—
233C13×C22⋊C4—81no—
234C13×C22⋊C4—81no—
235C13×C22⋊C4—81no—
236C13×C22⋊C4—81no—
237C13×C22⋊C4—81no—
238C13×C22⋊C4—81no—
239C13×C22⋊C4—81no—
240C42×C13—42no—
241C2×#485C2×C1311yescharacteristic, complemented
242C2×#408C2×C1311yescharacteristic
243#2616C2×C1311yescharacteristic
244#2311C2×C1311yescharacteristic
245#2077C2×C1311yescharacteristic, complemented
246#2076C2×C1311yescharacteristic, complemented
247#2035C2×C1311yescharacteristic, complemented
248#2035C2×C1311yescharacteristic, complemented
249#1894C2×C1311yescharacteristic, complemented
250#1892C2×C1311yescharacteristic, complemented
251#1872C2×C1311yescharacteristic, complemented
252#1853C2×C1311yescharacteristic, complemented
253#1825C2×C1311yescharacteristic, complemented
254#1809C2×C1311yescharacteristic, complemented
255#1807C2×C1311yescharacteristic, complemented
256C23×C13—21no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13—21no—
272C23×C13—21no—
273C23×C13—21no—
274C23×C13—21no—
275C23×C13#12112yes—
276C23×C13#12312yes—
277C23×C13C22×D411yescharacteristic
278Q8×C13—44no—
279Q8×C13—41no—
280Q8×C13—41no—
281Q8×C13—41no—
282Q8×C13—41no—
283D4×C13—44no—
284D4×C13—44no—
285D4×C13—44no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—21no—
299C2×C4×C13—21no—
300C2×C4×C13—21no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13—84no—
330C2×C4×C13#12112yes—
331C2×C4×C13#12312yes—
332C2×C4×C13C22×D411yescharacteristic
333C2×C4×C13C2×#4111yescharacteristic
334C2×C4×C13C2×#4111yescharacteristic
335C2×C4×C13C2×#4111yescharacteristic
336C2×C4×C13H(5,𝔽2)11yescharacteristic
337C2×C4×C13H(5,𝔽2)11yescharacteristic
338C8×C13—22no—
339C8×C13—22no—
340C8×C13—41no—
341C8×C13—41no—
342C22×#41C22×C1311yescharacteristic
343C22×M16C22×C1311yescharacteristic
344C23×C8C22×C1311yescharacteristic
345C2×C22⋊Q8C22×C1311yescharacteristic
346C2×C22⋊Q8C22×C1311yescharacteristic
347C2×C22⋊Q8C22×C1311yescharacteristic
348C2×#117C22×C1311yescharacteristic
349C22×C4⋊C4C22×C1311yescharacteristic
350#485—24no—
351C2×#107C22×C1311yescharacteristic
352C2×#106C22×C1311yescharacteristic
353C2×#106C22×C1311yescharacteristic
354C2×#106C22×C1311yescharacteristic
355C2×#103C22×C1311yescharacteristic
356C2×#103C22×C1311yescharacteristic
357C2×#103C22×C1311yescharacteristic
358C2×#103C22×C1311yescharacteristic
359#408—24no—
360C2×C22⋊C8C22×C1311yescharacteristic
361C2×C22⋊C8C22×C1311yescharacteristic
362C2×C22⋊C8C22×C1311yescharacteristic
363C2×C22⋊C8C22×C1311yescharacteristic
364#395—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#391—21no—
369#390—21no—
370#386—21no—
371#386—21no—
372#380C22×C1311yescharacteristic
373#380C22×C1311yescharacteristic
374#380C22×C1311yescharacteristic
375#380C22×C1311yescharacteristic
376#380C22×C1311yescharacteristic
377#380C22×C1311yescharacteristic
378#380C22×C1311yescharacteristic
379#340C22×C1311yescharacteristic
380#340C22×C1311yescharacteristic
381#340C22×C1311yescharacteristic
382#340C22×C1311yescharacteristic
383#340C22×C1311yescharacteristic
384#340C22×C1311yescharacteristic
385#340C22×C1311yescharacteristic
386#340C22×C1311yescharacteristic
387C22×C13—22no—
388C22×C13—22no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—22no—
393C22×C13—41no—
394C22×C13—41no—
395C22×C13—41no—
396C22×C13—41no—
397C22×C13—41no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—41no—
401C22×C13—41no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13—41no—
405C22×C13—41no—
406C22×C13—41no—
407C22×C13—41no—
408C22×C13C2×#12111yescharacteristic
409C22×C13C2×#12311yescharacteristic
410C22×C13#53411yescharacteristic
411C22×C13#57711yescharacteristic
412C22×C13#57711yescharacteristic
413C22×C13#57711yescharacteristic
414C22×C13#57811yescharacteristic
415C4×C13—22no—
416C4×C13—22no—
417C4×C13—41no—
418C4×C13—81no—
419C4×C13—81no—
420C4×C13—81no—
421C4×C13—81no—
422C4×C13—81no—
423C4×C13—81no—
424C4×C13—81no—
425C4×C13—81no—
426C4×C13#54611yescharacteristic
427C4×C13#54611yescharacteristic
428C4×C13#55111yescharacteristic
429C4×C13#55111yescharacteristic
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—41no—
435C2×#41—41no—
436C22×Q8D4×C1311yescharacteristic
437C22×Q8C23×C1311yescharacteristic
438C22×D4D4×C1311yescharacteristic
439C22×D4D4×C1311yescharacteristic
440C22×D4D4×C1311yescharacteristic
441C23×C4—21no—
442C23×C4C23×C1311yescharacteristic
443C23×C4C23×C1311yescharacteristic
444C23×C4C23×C1311yescharacteristic
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—41no—
448C22×C8—22no—
449C22×C8—22no—
450C22×C8—41no—
451C22×C8C23×C1311yescharacteristic
452C22×C8C23×C1311yescharacteristic
453C22×C8C23×C1311yescharacteristic
454C22×C8C23×C1311yescharacteristic
455C22⋊Q8—22no—
456C22⋊Q8—22no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—41no—
460C22⋊Q8—41no—
461#117—22no—
462#117—22no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4C23×C1311yescharacteristic
470C2×C4⋊C4C23×C1311yescharacteristic
471C2×C4⋊C4C23×C1311yescharacteristic
472C2×C4⋊C4C23×C1311yescharacteristic
473C2×C4⋊C4C23×C1311yescharacteristic
474C2×C4⋊C4C23×C1311yescharacteristic
475C2×C4⋊C4C23×C1311yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C42—21no—
488#107—22no—
489#106—22no—
490#106—41no—
491#106—41no—
492#103—22no—
493#103—22no—
494#103—41no—
495#103—41no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499C22⋊C8D4×C1314yes—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507C2×C13—42no—
508C2×C13—42no—
509C2×C13—81no—
510C2×C13#241211yescharacteristic
511C2×C13#306011yescharacteristic
512C2×C13#306311yescharacteristic
513C2×C13#309711yescharacteristic
514C2×C13#309911yescharacteristic
515C2×C13#320011yescharacteristic
516C2×C13#320111yescharacteristic
517C24C2×D4×C1311yescharacteristic
518C24C2×D4×C1311yescharacteristic
519C24C2×D4×C1311yescharacteristic
520#41—44no—
521#41—44no—
522#41—44no—
523#41—44no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—41no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—41no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—81no—
566C22×C4—81no—
567C22×C4C2×D4×C1311yescharacteristic
568C22×C4C2×D4×C1311yescharacteristic
569C22×C4C2×D4×C1312yes—
570C22×C4C2×D4×C1311yescharacteristic
571C22×C4C13×#4112yes—
572C22×C4C13×#4112yes—
573C22×C4C13×#4112yes—
574C22×C4C24×C1311yescharacteristic
575M16—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—44no—
587C2×C8C2×D4×C1312yes—
588C2×C8C2×D4×C1312yes—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C22⋊C4—81no—
618C42—42no—
619C13#2456911yescharacteristic, direct product factor, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23C13×#12112yes—
640C23C13×#12312yes—
641C23C22×D4×C1311yescharacteristic
642Q8—44no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647D4—44no—
648D4—44no—
649D4—44no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—84no—
694C2×C4C13×#12112yes—
695C2×C4C13×#12312yes—
696C2×C4C22×D4×C1311yescharacteristic
697C2×C4C2×C13×#4111yescharacteristic
698C2×C4C2×C13×#4111yescharacteristic
699C2×C4C2×C13×#4111yescharacteristic
700C2×C4C13×H(5,𝔽2)11yescharacteristic
701C2×C4C13×H(5,𝔽2)11yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22C2×C13×#12111yescharacteristic
728C22C2×C13×#12311yescharacteristic
729C22C13×#53411yescharacteristic
730C22C13×#57711yescharacteristic
731C22C13×#57711yescharacteristic
732C22C13×#57711yescharacteristic
733C22C13×#57811yescharacteristic
734C4—22no—
735C4—22no—
736C4—41no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4C13×#54611yescharacteristic
746C4C13×#54611yescharacteristic
747C4C13×#55111yescharacteristic
748C4C13×#55111yescharacteristic
749C2—42no—
750C2—42no—
751C2—81no—
752C2C13×#241211yescharacteristic
753C2C13×#306011yescharacteristic
754C2C13×#306311yescharacteristic
755C2C13×#309711yescharacteristic
756C2C13×#309911yescharacteristic
757C2C13×#320011yescharacteristic
758C2C13×#320111yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC22×C13×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C22×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#485C2semidirect
5. C13×#2077C2semidirect
6. C13×#2076C2semidirect
7. C13×#2035C2semidirect
8. C13×#2035C2semidirect
9. C13×#1894C2semidirect
10. C13×#1892C2semidirect
11. C13×#1872C2semidirect
12. C13×#1853C2semidirect
13. C13×#1825C2semidirect
14. C13×#1809C2semidirect
15. C13×#1807C2semidirect
138. #24569C13direct (N × H)
241. C2×#485C2×C13semidirect
245. #2077C2×C13semidirect
246. #2076C2×C13semidirect
247. #2035C2×C13semidirect
248. #2035C2×C13semidirect
249. #1894C2×C13semidirect
250. #1892C2×C13semidirect
251. #1872C2×C13semidirect
252. #1853C2×C13semidirect
253. #1825C2×C13semidirect
254. #1809C2×C13semidirect
255. #1807C2×C13semidirect
619. C13#24569direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4852
C2×C13×#4082
C13×#26162
C13×#23112
C13×#20772
C13×#20762
C13×#20352
C13×#18942
C13×#18922
C13×#18722
C13×#18532
C13×#18252
C13×#18092
C13×#18072
#2456913