Finite Group Databasebeta

← C61×#17290 #29520723

Subgroups — C61×#17290 #29520723

Order 15616.

1122 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#1445C211yesmaximal, characteristic, complemented
2C61×#1444C211yesmaximal, characteristic, complemented
3C61×#1443C211yesmaximal, characteristic, complemented
4C61×#1443C211yesmaximal, characteristic, complemented
5C61×#1443C211yesmaximal, characteristic, complemented
6C61×#1442C211yesmaximal, characteristic, complemented
7C61×#1442C211yesmaximal, characteristic, complemented
8C61×#1441C211yesmaximal, characteristic, complemented
9C61×#1440C211yesmaximal, characteristic
10C61×#1440C211yesmaximal, characteristic
11C61×#1440C211yesmaximal, characteristic
12C61×#1439C211yesmaximal, characteristic
13C61×#1439C211yesmaximal, characteristic
14C61×#1439C211yesmaximal, characteristic
15C61×#1439C211yesmaximal, characteristic
16C22×C4⋊C4×C61C2211yescharacteristic
17C22×C4⋊C4×C61C2211yescharacteristic
18C22×C4⋊C4×C61C2211yescharacteristic
19C22×C4⋊C4×C61C2211yescharacteristic
20C22×C22⋊C4×C61C2211yescharacteristic
21C22×C22⋊C4×C61C2211yescharacteristic
22C22×C22⋊C4×C61C2211yescharacteristic
23C22×C22⋊C4×C61C2211yescharacteristic
24C22×C22⋊C4×C61C2211yescharacteristic
25C22×C22⋊C4×C61C2211yescharacteristic
26C22×C22⋊C4×C61C2211yescharacteristic
27C2×#95×C61C2211yescharacteristic
28C2×#95×C61C2211yescharacteristic
29C2×#95×C61C2211yescharacteristic
30C2×#95×C61C2211yescharacteristic
31C2×#95×C61C2211yescharacteristic
32C2×#95×C61C2211yescharacteristic
33C2×#95×C61C2211yescharacteristic
34C2×#95×C61C2211yescharacteristic
35C2×#95×C61C2211yescharacteristic
36C2×#95×C61C2211yescharacteristic
37C2×#95×C61C2211yescharacteristic
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C2×#95×C61C2211yescharacteristic
41C2×#95×C61C2211yescharacteristic
42C2×#95×C61C2211yescharacteristic
43C2×#95×C61C2211yescharacteristic
44C2×#95×C61C2211yescharacteristic
45C2×#95×C61C2211yescharacteristic
46C2×#95×C61C2211yescharacteristic
47C2×#95×C61C2211yescharacteristic
48C2×#95×C61C2211yescharacteristic
49C2×#95×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C25×C61C2311yescharacteristic
52C23×C4×C61C2311yescharacteristic
53C23×C4×C61C2311yescharacteristic
54C23×C4×C61C2311yescharacteristic
55C23×C4×C61C2311yescharacteristic
56C23×C4×C61C2311yescharacteristic
57C23×C4×C61C2311yescharacteristic
58C23×C4×C61C2311yescharacteristic
59C23×C4×C61C2311yescharacteristic
60C23×C4×C61C2311yescharacteristic
61C23×C4×C61C2311yescharacteristic
62C23×C4×C61C2311yescharacteristic
63C23×C4×C61C2311yescharacteristic
64C23×C4×C61C2311yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C2×C4⋊C4×C61—22no—
67C2×C4⋊C4×C61—22no—
68C2×C4⋊C4×C61—41no—
69C2×C4⋊C4×C61—41no—
70C2×C4⋊C4×C61—41no—
71C2×C4⋊C4×C61—41no—
72C2×C4⋊C4×C61—41no—
73C2×C4⋊C4×C61—41no—
74C2×C4⋊C4×C61—41no—
75C2×C4⋊C4×C61—41no—
76C2×C4⋊C4×C61—41no—
77C2×C4⋊C4×C61—41no—
78C2×C22⋊C4×C61—22no—
79C2×C22⋊C4×C61—22no—
80C2×C22⋊C4×C61—22no—
81C2×C22⋊C4×C61—22no—
82C2×C22⋊C4×C61—22no—
83C2×C22⋊C4×C61—22no—
84C2×C22⋊C4×C61—22no—
85C2×C22⋊C4×C61—41no—
86C2×C22⋊C4×C61—41no—
87C2×C22⋊C4×C61—41no—
88C2×C22⋊C4×C61—41no—
89C2×C22⋊C4×C61—41no—
90C2×C22⋊C4×C61—41no—
91C2×C22⋊C4×C61—41no—
92C2×C22⋊C4×C61—41no—
93C2×C22⋊C4×C61—41no—
94C2×C22⋊C4×C61—41no—
95C2×C22⋊C4×C61—41no—
96C2×C22⋊C4×C61—41no—
97C2×C22⋊C4×C61—41no—
98C2×C22⋊C4×C61—41no—
99#95×C61—22no—
100#95×C61—22no—
101#95×C61—22no—
102#95×C61—22no—
103#95×C61—22no—
104#95×C61—22no—
105#95×C61—41no—
106#95×C61—41no—
107#95×C61—41no—
108#95×C61—41no—
109#95×C61—41no—
110#95×C61—41no—
111#95×C61—41no—
112#95×C61—41no—
113#95×C61—41no—
114#95×C61—41no—
115#95×C61—41no—
116#95×C61—41no—
117#95×C61—41no—
118#95×C61—41no—
119#95×C61—41no—
120#95×C61—41no—
121#95×C61—41no—
122#95×C61—41no—
123C24×C61—21no—
124C24×C61—21no—
125C24×C61—21no—
126C24×C61—21no—
127C24×C61—21no—
128C24×C61—21no—
129C24×C61—21no—
130C24×C61—21no—
131C24×C61—21no—
132C24×C61—21no—
133C24×C61—21no—
134C24×C61—21no—
135C24×C61—21no—
136C24×C61—21no—
137C24×C61#4112yes—
138C24×C61C2411yescharacteristic
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61#4112yes—
234C22×C4×C61#4112yes—
235C22×C4×C61#4112yes—
236C22×C4×C61#4112yes—
237C4⋊C4×C61—44no—
238C4⋊C4×C61—44no—
239C4⋊C4×C61—44no—
240C4⋊C4×C61—44no—
241C22⋊C4×C61—44no—
242C22⋊C4×C61—44no—
243C22⋊C4×C61—44no—
244C22⋊C4×C61—44no—
245C22⋊C4×C61—44no—
246C22⋊C4×C61—44no—
247C22⋊C4×C61—44no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61C2×#4111yescharacteristic
284C23×C61C2×#4111yescharacteristic
285C23×C61C2×#4111yescharacteristic
286C23×C61C2×#4111yescharacteristic
287C23×C61C2×#4111yescharacteristic
288C23×C61H(5,𝔽2)11yescharacteristic
289C23×C61H(5,𝔽2)11yescharacteristic
290C23×C61H(5,𝔽2)11yescharacteristic
291C23×C61H(5,𝔽2)11yescharacteristic
292C23×C61H(5,𝔽2)11yescharacteristic
293C23×C61H(5,𝔽2)11yescharacteristic
294C23×C61H(5,𝔽2)11yescharacteristic
295C23×C612−1+411yescharacteristic
296C23×C612−1+411yescharacteristic
297C23×C612−1+411yescharacteristic
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396#17290C6111yesmaximal, characteristic, direct product factor, Sylow
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—42no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61—81no—
407C22×C61—81no—
408C22×C61—81no—
409C22×C61—81no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61#53811yescharacteristic
413C22×C61#53811yescharacteristic
414C22×C61#53811yescharacteristic
415C22×C61#53811yescharacteristic
416C22×C61#53811yescharacteristic
417C22×C61#53911yescharacteristic
418C22×C61#53911yescharacteristic
419C22×C61#53911yescharacteristic
420C22×C61#53911yescharacteristic
421C22×C61#54011yescharacteristic
422C22×C61#54211yescharacteristic
423C22×C61#54211yescharacteristic
424C22×C61#54211yescharacteristic
425C22×C61#54211yescharacteristic
426C22×C61#54211yescharacteristic
427C22×C61#55111yescharacteristic
428C22×C61#55111yescharacteristic
429C22×C61#55211yescharacteristic
430C22×C61#55211yescharacteristic
431C22×C61#55211yescharacteristic
432C22×C61#55311yescharacteristic
433C22×C61#55311yescharacteristic
434C22×C61#55311yescharacteristic
435C22×C61#55511yescharacteristic
436C22×C61#55911yescharacteristic
437C22×C61#56011yescharacteristic
438C22×C61#56011yescharacteristic
439C22×C61#56011yescharacteristic
440C22×C61#56011yescharacteristic
441C22×C61#56211yescharacteristic
442C22×C61#56211yescharacteristic
443C22×C61#56211yescharacteristic
444C22×C61#56311yescharacteristic
445C22×C61#56311yescharacteristic
446C22×C61#56311yescharacteristic
447C4×C61—42no—
448C4×C61—42no—
449C4×C61—42no—
450C4×C61—42no—
451C4×C61—81no—
452C4×C61—81no—
453C4×C61—81no—
454C4×C61—81no—
455C4×C61—81no—
456C4×C61—81no—
457C4×C61—81no—
458C4×C61—81no—
459C4×C61—81no—
460C4×C61—81no—
461#1445C2×C6111yescharacteristic, complemented
462#1444C2×C6111yescharacteristic, complemented
463#1443C2×C6111yescharacteristic, complemented
464#1443C2×C6111yescharacteristic, complemented
465#1443C2×C6111yescharacteristic, complemented
466#1442C2×C6111yescharacteristic, complemented
467#1442C2×C6111yescharacteristic, complemented
468#1441C2×C6111yescharacteristic, complemented
469#1440C2×C6111yescharacteristic
470#1440C2×C6111yescharacteristic
471#1440C2×C6111yescharacteristic
472#1439C2×C6111yescharacteristic
473#1439C2×C6111yescharacteristic
474#1439C2×C6111yescharacteristic
475#1439C2×C6111yescharacteristic
476C2×C61—82no—
477C2×C61#273711yescharacteristic
478C2×C61#274111yescharacteristic
479C2×C61#276411yescharacteristic
480C2×C61#276511yescharacteristic
481C2×C61#277111yescharacteristic
482C2×C61#277911yescharacteristic
483C2×C61#278111yescharacteristic
484C2×C61#279511yescharacteristic
485C2×C61#279611yescharacteristic
486C2×C61#279711yescharacteristic
487C2×C61#282511yescharacteristic
488C2×C61#282711yescharacteristic
489C2×C61#283011yescharacteristic
490C2×C61#283711yescharacteristic
491C2×C61#283811yescharacteristic
492C22×C4⋊C4C22×C6111yescharacteristic
493C22×C4⋊C4C22×C6111yescharacteristic
494C22×C4⋊C4C22×C6111yescharacteristic
495C22×C4⋊C4C22×C6111yescharacteristic
496C22×C22⋊C4C22×C6111yescharacteristic
497C22×C22⋊C4C22×C6111yescharacteristic
498C22×C22⋊C4C22×C6111yescharacteristic
499C22×C22⋊C4C22×C6111yescharacteristic
500C22×C22⋊C4C22×C6111yescharacteristic
501C22×C22⋊C4C22×C6111yescharacteristic
502C22×C22⋊C4C22×C6111yescharacteristic
503C2×#95C22×C6111yescharacteristic
504C2×#95C22×C6111yescharacteristic
505C2×#95C22×C6111yescharacteristic
506C2×#95C22×C6111yescharacteristic
507C2×#95C22×C6111yescharacteristic
508C2×#95C22×C6111yescharacteristic
509C2×#95C22×C6111yescharacteristic
510C2×#95C22×C6111yescharacteristic
511C2×#95C22×C6111yescharacteristic
512C2×#95C22×C6111yescharacteristic
513C2×#95C22×C6111yescharacteristic
514C2×#95C22×C6111yescharacteristic
515C2×#95C22×C6111yescharacteristic
516C2×#95C22×C6111yescharacteristic
517C2×#95C22×C6111yescharacteristic
518C2×#95C22×C6111yescharacteristic
519C2×#95C22×C6111yescharacteristic
520C2×#95C22×C6111yescharacteristic
521C2×#95C22×C6111yescharacteristic
522C2×#95C22×C6111yescharacteristic
523C2×#95C22×C6111yescharacteristic
524C2×#95C22×C6111yescharacteristic
525C2×#95C22×C6111yescharacteristic
526C2×#95C22×C6111yescharacteristic
527C61#1729011yescharacteristic, direct product factor, Sylow
528C25C23×C6111yescharacteristic
529C23×C4C23×C6111yescharacteristic
530C23×C4C23×C6111yescharacteristic
531C23×C4C23×C6111yescharacteristic
532C23×C4C23×C6111yescharacteristic
533C23×C4C23×C6111yescharacteristic
534C23×C4C23×C6111yescharacteristic
535C23×C4C23×C6111yescharacteristic
536C23×C4C23×C6111yescharacteristic
537C23×C4C23×C6111yescharacteristic
538C23×C4C23×C6111yescharacteristic
539C23×C4C23×C6111yescharacteristic
540C23×C4C23×C6111yescharacteristic
541C23×C4C23×C6111yescharacteristic
542C23×C4C23×C6111yescharacteristic
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—41no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4—41no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—41no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—41no—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—41no—
583#95—41no—
584#95—41no—
585#95—41no—
586#95—41no—
587#95—41no—
588#95—41no—
589#95—41no—
590#95—41no—
591#95—41no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—41no—
599#95—41no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24#41×C6112yes—
615C24C24×C6111yescharacteristic
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4#41×C6112yes—
711C22×C4#41×C6112yes—
712C22×C4#41×C6112yes—
713C22×C4#41×C6112yes—
714C4⋊C4—44no—
715C4⋊C4—44no—
716C4⋊C4—44no—
717C4⋊C4—44no—
718C22⋊C4—44no—
719C22⋊C4—44no—
720C22⋊C4—44no—
721C22⋊C4—44no—
722C22⋊C4—44no—
723C22⋊C4—44no—
724C22⋊C4—44no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23C2×#41×C6111yescharacteristic
761C23C2×#41×C6111yescharacteristic
762C23C2×#41×C6111yescharacteristic
763C23C2×#41×C6111yescharacteristic
764C23C2×#41×C6111yescharacteristic
765C23H(5,𝔽2)×C6111yescharacteristic
766C23H(5,𝔽2)×C6111yescharacteristic
767C23H(5,𝔽2)×C6111yescharacteristic
768C23H(5,𝔽2)×C6111yescharacteristic
769C23H(5,𝔽2)×C6111yescharacteristic
770C23H(5,𝔽2)×C6111yescharacteristic
771C23H(5,𝔽2)×C6111yescharacteristic
772C232−1+4×C6111yescharacteristic
773C232−1+4×C6111yescharacteristic
774C232−1+4×C6111yescharacteristic
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22C61×#53811yescharacteristic
889C22C61×#53811yescharacteristic
890C22C61×#53811yescharacteristic
891C22C61×#53811yescharacteristic
892C22C61×#53811yescharacteristic
893C22C61×#53911yescharacteristic
894C22C61×#53911yescharacteristic
895C22C61×#53911yescharacteristic
896C22C61×#53911yescharacteristic
897C22C61×#54011yescharacteristic
898C22C61×#54211yescharacteristic
899C22C61×#54211yescharacteristic
900C22C61×#54211yescharacteristic
901C22C61×#54211yescharacteristic
902C22C61×#54211yescharacteristic
903C22C61×#55111yescharacteristic
904C22C61×#55111yescharacteristic
905C22C61×#55211yescharacteristic
906C22C61×#55211yescharacteristic
907C22C61×#55211yescharacteristic
908C22C61×#55311yescharacteristic
909C22C61×#55311yescharacteristic
910C22C61×#55311yescharacteristic
911C22C61×#55511yescharacteristic
912C22C61×#55911yescharacteristic
913C22C61×#56011yescharacteristic
914C22C61×#56011yescharacteristic
915C22C61×#56011yescharacteristic
916C22C61×#56011yescharacteristic
917C22C61×#56211yescharacteristic
918C22C61×#56211yescharacteristic
919C22C61×#56211yescharacteristic
920C22C61×#56311yescharacteristic
921C22C61×#56311yescharacteristic
922C22C61×#56311yescharacteristic
923C4—42no—
924C4—42no—
925C4—42no—
926C4—42no—
927C4—81no—
928C4—81no—
929C4—81no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C4—81no—
935C4—81no—
936C4—81no—
937C2—82no—
938C2C61×#273711yescharacteristic
939C2C61×#274111yescharacteristic
940C2C61×#276411yescharacteristic
941C2C61×#276511yescharacteristic
942C2C61×#277111yescharacteristic
943C2C61×#277911yescharacteristic
944C2C61×#278111yescharacteristic
945C2C61×#279511yescharacteristic
946C2C61×#279611yescharacteristic
947C2C61×#279711yescharacteristic
948C2C61×#282511yescharacteristic
949C2C61×#282711yescharacteristic
950C2C61×#283011yescharacteristic
951C2C61×#283711yescharacteristic
952C2C61×#283811yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC25×C61C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#1445C2semidirect
2. C61×#1444C2semidirect
3. C61×#1443C2semidirect
4. C61×#1443C2semidirect
5. C61×#1443C2semidirect
6. C61×#1442C2semidirect
7. C61×#1442C2semidirect
8. C61×#1441C2semidirect
396. #17290C61direct (N × H)
461. #1445C2×C61semidirect
462. #1444C2×C61semidirect
463. #1443C2×C61semidirect
464. #1443C2×C61semidirect
465. #1443C2×C61semidirect
466. #1442C2×C61semidirect
467. #1442C2×C61semidirect
468. #1441C2×C61semidirect
527. C61#17290direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#14452
C61×#14442
C61×#14432
C61×#14422
C61×#14412
C61×#14402
C61×#14392
#1729061