Finite Group Databasebeta

← C101×#25018 #38807169

Subgroups — C101×#25018 #38807169

Order 25856.

896 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C101C211yesmaximal, characteristic, complemented
2C2×#482×C101C211yesmaximal, characteristic, complemented
3C101×#2535C211yesmaximal, characteristic
4C101×#2352C211yesmaximal, characteristic, complemented
5C101×#2077C211yesmaximal, characteristic, complemented
6C101×#2077C211yesmaximal, characteristic, complemented
7C101×#2033C211yesmaximal, characteristic, complemented
8C101×#2033C211yesmaximal, characteristic, complemented
9C101×#1954C211yesmaximal, characteristic, complemented
10C101×#1949C211yesmaximal, characteristic, complemented
11C101×#1854C211yesmaximal, characteristic, complemented
12C101×#1852C211yesmaximal, characteristic, complemented
13C101×#1846C211yesmaximal, characteristic, complemented
14C101×#1804C211yesmaximal, characteristic, complemented
15C4×#102×C101C211yesmaximal, characteristic, complemented
16C2×#121×C101C2211yescharacteristic
17C2×#121×C101C2211yescharacteristic
18C2×C4×D4×C101C2211yescharacteristic
19C2×C4×D4×C101C2211yescharacteristic
20C2×#117×C101C2211yescharacteristic
21C22×C4⋊C4×C101C2211yescharacteristic
22#482×C101—24no—
23#481×C101—24no—
24C2×#107×C101C2211yescharacteristic
25C2×#107×C101C2211yescharacteristic
26C2×#107×C101C2211yescharacteristic
27C2×#106×C101C2211yescharacteristic
28C2×#106×C101C2211yescharacteristic
29C2×#106×C101C2211yescharacteristic
30C2×C4⋊C8×C101C2211yescharacteristic
31C2×#102×C101C2211yescharacteristic
32C2×#102×C101C2211yescharacteristic
33C2×#102×C101C2211yescharacteristic
34C2×#102×C101C2211yescharacteristic
35C2×C22⋊C8×C101C2211yescharacteristic
36C2×C22⋊C8×C101C2211yescharacteristic
37C2×C22⋊C8×C101C2211yescharacteristic
38C2×C22⋊C8×C101C2211yescharacteristic
39C2×C4×C8×C101C2211yescharacteristic
40#397×C101—21no—
41#392×C101—21no—
42#388×C101—21no—
43#387×C101—21no—
44#386×C101—21no—
45#386×C101—21no—
46#386×C101—21no—
47#382×C101C2211yescharacteristic
48#382×C101C2211yescharacteristic
49#380×C101C2211yescharacteristic
50#380×C101C2211yescharacteristic
51#380×C101C2211yescharacteristic
52#380×C101C2211yescharacteristic
53C4×C4⋊C4×C101C2211yescharacteristic
54C4×C22⋊C4×C101—21no—
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61C22×D4×C101—21no—
62C22×D4×C101—21no—
63C22×D4×C101D411yescharacteristic
64C22×D4×C101C2311yescharacteristic
65C23×C4×C101—21no—
66C23×C4×C101—21no—
67C23×C4×C101C2311yescharacteristic
68C23×C4×C101C2311yescharacteristic
69C22×C8×C101C2311yescharacteristic
70C22×C8×C101C2311yescharacteristic
71C22×C8×C101C2311yescharacteristic
72C22×C8×C101C2311yescharacteristic
73#121×C101—22no—
74#121×C101—22no—
75#121×C101—41no—
76#121×C101—41no—
77C4×D4×C101—22no—
78C4×D4×C101—22no—
79C4×D4×C101—22no—
80C4×D4×C101—22no—
81#117×C101—22no—
82#117×C101—41no—
83C2×C4⋊C4×C101—22no—
84C2×C4⋊C4×C101—21no—
85C2×C4⋊C4×C101—41no—
86C2×C4⋊C4×C101D411yescharacteristic
87C2×C4⋊C4×C101C2311yescharacteristic
88C2×C4⋊C4×C101C2311yescharacteristic
89C2×C4⋊C4×C101C2311yescharacteristic
90C2×C4⋊C4×C101C2311yescharacteristic
91C2×C4⋊C4×C101C2311yescharacteristic
92C2×C4⋊C4×C101C2311yescharacteristic
93C2×C4⋊C4×C101C2311yescharacteristic
94C2×C22⋊C4×C101—21no—
95C2×C22⋊C4×C101—21no—
96C2×C22⋊C4×C101—21no—
97C2×C22⋊C4×C101—21no—
98C2×C22⋊C4×C101—21no—
99C2×C22⋊C4×C101—21no—
100C2×C22⋊C4×C101—21no—
101C2×C22⋊C4×C101—21no—
102C2×C22⋊C4×C101D411yescharacteristic
103C2×C22⋊C4×C101D411yescharacteristic
104C2×C42×C101—21no—
105C2×C42×C101—21no—
106C2×C42×C101C2311yescharacteristic
107#107×C101—22no—
108#107×C101—41no—
109#107×C101—41no—
110#106×C101—22no—
111#106×C101—22no—
112#106×C101—22no—
113C4⋊C8×C101—22no—
114#102×C101—22no—
115#102×C101—22no—
116#102×C101—22no—
117#102×C101D414yescomplemented
118C22⋊C8×C101—22no—
119C22⋊C8×C101—22no—
120C22⋊C8×C101—22no—
121C22⋊C8×C101—22no—
122C4×C8×C101—22no—
123#95×C101—21no—
124#95×C101—21no—
125#95×C101—21no—
126#95×C101—21no—
127#95×C101—21no—
128#95×C101—21no—
129#95×C101—21no—
130#95×C101—21no—
131#95×C101—21no—
132C24×C101—21no—
133C24×C101C2×D411yescharacteristic
134C24×C101C2×D411yescharacteristic
135C2×D4×C101—22no—
136C2×D4×C101—22no—
137C2×D4×C101—21no—
138C2×D4×C101—21no—
139C2×D4×C101—21no—
140C2×D4×C101—21no—
141C2×D4×C101—21no—
142C2×D4×C101—41no—
143C2×D4×C101—42no—
144C2×D4×C101—42no—
145C2×D4×C101—42no—
146C2×D4×C101—42no—
147C2×D4×C101—81no—
148C2×D4×C101—81no—
149C2×D4×C101C2×D412yes—
150C22×C4×C101—21no—
151C22×C4×C101—21no—
152C22×C4×C101—21no—
153C22×C4×C101—21no—
154C22×C4×C101—21no—
155C22×C4×C101—21no—
156C22×C4×C101—21no—
157C22×C4×C101—21no—
158C22×C4×C101—21no—
159C22×C4×C101—21no—
160C22×C4×C101—21no—
161C22×C4×C101—21no—
162C22×C4×C101—21no—
163C22×C4×C101—21no—
164C22×C4×C101—21no—
165C22×C4×C101—21no—
166C22×C4×C101—21no—
167C22×C4×C101—21no—
168C22×C4×C101—21no—
169C22×C4×C101—42no—
170C22×C4×C101—42no—
171C22×C4×C101—42no—
172C22×C4×C101—81no—
173C22×C4×C101—81no—
174C22×C4×C101—81no—
175C22×C4×C101C2×D411yescharacteristic
176C22×C4×C101C2×D411yescharacteristic
177C22×C4×C101C2×D411yescharacteristic
178C22×C4×C101C2×D411yescharacteristic
179C22×C4×C101C2411yescharacteristic
180C2×C8×C101—21no—
181C2×C8×C101—21no—
182C2×C8×C101—21no—
183C2×C8×C101—21no—
184C2×C8×C101—21no—
185C2×C8×C101—21no—
186C2×C8×C101—21no—
187C2×C8×C101—21no—
188C2×C8×C101—21no—
189C2×C8×C101—21no—
190C2×C8×C101C2×D412yes—
191C2×C8×C101#4112yes—
192C4⋊C4×C101—22no—
193C4⋊C4×C101—21no—
194C4⋊C4×C101—21no—
195C4⋊C4×C101—21no—
196C4⋊C4×C101—21no—
197C4⋊C4×C101—21no—
198C4⋊C4×C101—21no—
199C4⋊C4×C101—21no—
200C4⋊C4×C101—21no—
201C4⋊C4×C101—21no—
202C4⋊C4×C101—21no—
203C4⋊C4×C101—21no—
204C4⋊C4×C101—21no—
205C4⋊C4×C101—21no—
206C4⋊C4×C101—42no—
207C4⋊C4×C101C2×D412yes—
208C22⋊C4×C101—22no—
209C22⋊C4×C101—22no—
210C22⋊C4×C101—42no—
211C22⋊C4×C101—42no—
212C22⋊C4×C101—42no—
213C22⋊C4×C101—42no—
214C22⋊C4×C101—42no—
215C22⋊C4×C101—81no—
216C22⋊C4×C101—81no—
217C22⋊C4×C101—81no—
218C42×C101—42no—
219C42×C101—81no—
220C42×C101#4112yes—
221C42×C101#4112yes—
222C23×C101—21no—
223C23×C101—21no—
224C23×C101—21no—
225C23×C101—21no—
226C23×C101—21no—
227C23×C101—21no—
228C23×C101—21no—
229C23×C101—21no—
230C23×C101—22no—
231C23×C101—21no—
232C23×C101—21no—
233C23×C101—21no—
234C23×C101—21no—
235C23×C101—21no—
236C23×C101—41no—
237C23×C101—41no—
238C23×C101—41no—
239C23×C101—41no—
240C23×C101—41no—
241C23×C101—41no—
242C23×C101#13512yes—
243C23×C101C22×D411yescharacteristic
244D4×C101—22no—
245D4×C101—22no—
246D4×C101—44no—
247D4×C101—41no—
248D4×C101—41no—
249D4×C101—84no—
250D4×C101—84no—
251C2×C4×C101—21no—
252C2×C4×C101—21no—
253C2×C4×C101—21no—
254C2×C4×C101—21no—
255C2×C4×C101—21no—
256C2×C4×C101—21no—
257C2×C4×C101—21no—
258C2×C4×C101—22no—
259C2×C4×C101—21no—
260C2×C4×C101—21no—
261C2×C4×C101—21no—
262C2×C4×C101—41no—
263C2×C4×C101—41no—
264C2×C4×C101—41no—
265C2×C4×C101—41no—
266C2×C4×C101—41no—
267C2×C4×C101—41no—
268C2×C4×C101—41no—
269C2×C4×C101—41no—
270C2×C4×C101—41no—
271C2×C4×C101—41no—
272C2×C4×C101—41no—
273C2×C4×C101—41no—
274C2×C4×C101—41no—
275C2×C4×C101—41no—
276C2×C4×C101—41no—
277C2×C4×C101—41no—
278C2×C4×C101—41no—
279C2×C4×C101—41no—
280C2×C4×C101—41no—
281C2×C4×C101—41no—
282C2×C4×C101—41no—
283C2×C4×C101—41no—
284C2×C4×C101—41no—
285C2×C4×C101—41no—
286C2×C4×C101—41no—
287C2×C4×C101—41no—
288C2×C4×C101—41no—
289C2×C4×C101—41no—
290C2×C4×C101—84no—
291C2×C4×C101—84no—
292C2×C4×C101#12312yes—
293C2×C4×C101#12312yes—
294C2×C4×C101C22×D411yescharacteristic
295C2×C4×C101C2×#4111yescharacteristic
296C2×C4×C101C2×#4111yescharacteristic
297C2×C4×C101C2×#4111yescharacteristic
298C2×C4×C101H(5,𝔽2)11yescharacteristic
299C2×C4×C1012−1+411yescharacteristic
300C8×C101—22no—
301C8×C101—22no—
302C8×C101—41no—
303C8×C101—41no—
304C22×C101—22no—
305C22×C101—22no—
306C22×C101—22no—
307C22×C101—41no—
308C22×C101—41no—
309C22×C101—41no—
310C22×C101—41no—
311C22×C101—41no—
312C22×C101—41no—
313C22×C101—41no—
314C22×C101—41no—
315C22×C101—41no—
316C22×C101—42no—
317C22×C101—41no—
318C22×C101—42no—
319C22×C101—42no—
320C22×C101—41no—
321C22×C101—81no—
322C22×C101—81no—
323C22×C101—81no—
324C22×C101—81no—
325C22×C101C2×#12311yescharacteristic
326C22×C101D4211yescharacteristic
327C22×C101#54711yescharacteristic
328C22×C101C2×#13511yescharacteristic
329C22×C101#57511yescharacteristic
330C22×C101#57611yescharacteristic
331C22×C101#57711yescharacteristic
332C4×C101—22no—
333C4×C101—22no—
334C4×C101—41no—
335C4×C101—41no—
336C4×C101—42no—
337C4×C101—81no—
338C4×C101—81no—
339C4×C101—81no—
340C4×C101—81no—
341C4×C101—81no—
342C4×C101—81no—
343C4×C101#53211yescharacteristic
344C4×C101#54211yescharacteristic
345C4×C101#54711yescharacteristic
346C4×C101#55311yescharacteristic
347#25018C10111yesmaximal, characteristic, direct product factor, Sylow
348C2×C101—42no—
349C2×C101—81no—
350C2×C101—82no—
351C2×C101#242211yescharacteristic
352C2×C101#309111yescharacteristic
353C2×C101#309611yescharacteristic
354C2×C101#327311yescharacteristic
355C2×C101#328211yescharacteristic
356C2×C101#333911yescharacteristic
357C2×C101#335111yescharacteristic
358C2×#481C2×C10111yescharacteristic, complemented
359C2×#482C2×C10111yescharacteristic, complemented
360#2535C2×C10111yescharacteristic
361#2352C2×C10111yescharacteristic, complemented
362#2077C2×C10111yescharacteristic, complemented
363#2077C2×C10111yescharacteristic, complemented
364#2033C2×C10111yescharacteristic, complemented
365#2033C2×C10111yescharacteristic, complemented
366#1954C2×C10111yescharacteristic, complemented
367#1949C2×C10111yescharacteristic, complemented
368#1854C2×C10111yescharacteristic, complemented
369#1852C2×C10111yescharacteristic, complemented
370#1846C2×C10111yescharacteristic, complemented
371#1804C2×C10111yescharacteristic, complemented
372C4×#102C2×C10111yescharacteristic, complemented
373C101#2501811yescharacteristic, direct product factor, Sylow
374C2×#121C22×C10111yescharacteristic
375C2×#121C22×C10111yescharacteristic
376C2×C4×D4C22×C10111yescharacteristic
377C2×C4×D4C22×C10111yescharacteristic
378C2×#117C22×C10111yescharacteristic
379C22×C4⋊C4C22×C10111yescharacteristic
380#482—24no—
381#481—24no—
382C2×#107C22×C10111yescharacteristic
383C2×#107C22×C10111yescharacteristic
384C2×#107C22×C10111yescharacteristic
385C2×#106C22×C10111yescharacteristic
386C2×#106C22×C10111yescharacteristic
387C2×#106C22×C10111yescharacteristic
388C2×C4⋊C8C22×C10111yescharacteristic
389C2×#102C22×C10111yescharacteristic
390C2×#102C22×C10111yescharacteristic
391C2×#102C22×C10111yescharacteristic
392C2×#102C22×C10111yescharacteristic
393C2×C22⋊C8C22×C10111yescharacteristic
394C2×C22⋊C8C22×C10111yescharacteristic
395C2×C22⋊C8C22×C10111yescharacteristic
396C2×C22⋊C8C22×C10111yescharacteristic
397C2×C4×C8C22×C10111yescharacteristic
398#397—21no—
399#392—21no—
400#388—21no—
401#387—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#382C22×C10111yescharacteristic
406#382C22×C10111yescharacteristic
407#380C22×C10111yescharacteristic
408#380C22×C10111yescharacteristic
409#380C22×C10111yescharacteristic
410#380C22×C10111yescharacteristic
411C4×C4⋊C4C22×C10111yescharacteristic
412C4×C22⋊C4—21no—
413#340C22×C10111yescharacteristic
414#340C22×C10111yescharacteristic
415#340C22×C10111yescharacteristic
416#340C22×C10111yescharacteristic
417#340C22×C10111yescharacteristic
418#340C22×C10111yescharacteristic
419C22×D4—21no—
420C22×D4—21no—
421C22×D4D4×C10111yescharacteristic
422C22×D4C23×C10111yescharacteristic
423C23×C4—21no—
424C23×C4—21no—
425C23×C4C23×C10111yescharacteristic
426C23×C4C23×C10111yescharacteristic
427C22×C8C23×C10111yescharacteristic
428C22×C8C23×C10111yescharacteristic
429C22×C8C23×C10111yescharacteristic
430C22×C8C23×C10111yescharacteristic
431#121—22no—
432#121—22no—
433#121—41no—
434#121—41no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439#117—22no—
440#117—41no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4D4×C10111yescharacteristic
445C2×C4⋊C4C23×C10111yescharacteristic
446C2×C4⋊C4C23×C10111yescharacteristic
447C2×C4⋊C4C23×C10111yescharacteristic
448C2×C4⋊C4C23×C10111yescharacteristic
449C2×C4⋊C4C23×C10111yescharacteristic
450C2×C4⋊C4C23×C10111yescharacteristic
451C2×C4⋊C4C23×C10111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4D4×C10111yescharacteristic
461C2×C22⋊C4D4×C10111yescharacteristic
462C2×C42—21no—
463C2×C42—21no—
464C2×C42C23×C10111yescharacteristic
465#107—22no—
466#107—41no—
467#107—41no—
468#106—22no—
469#106—22no—
470#106—22no—
471C4⋊C8—22no—
472#102—22no—
473#102—22no—
474#102—22no—
475#102D4×C10114yescomplemented
476C22⋊C8—22no—
477C22⋊C8—22no—
478C22⋊C8—22no—
479C22⋊C8—22no—
480C4×C8—22no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490C24—21no—
491C24C2×D4×C10111yescharacteristic
492C24C2×D4×C10111yescharacteristic
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—41no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—81no—
506C2×D4—81no—
507C2×D4C2×D4×C10112yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4C2×D4×C10111yescharacteristic
534C22×C4C2×D4×C10111yescharacteristic
535C22×C4C2×D4×C10111yescharacteristic
536C22×C4C2×D4×C10111yescharacteristic
537C22×C4C24×C10111yescharacteristic
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8C2×D4×C10112yes—
549C2×C8#41×C10112yes—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—42no—
565C4⋊C4C2×D4×C10112yes—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C42—42no—
577C42—81no—
578C42#41×C10112yes—
579C42#41×C10112yes—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—22no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23#135×C10112yes—
601C23C22×D4×C10111yescharacteristic
602D4—22no—
603D4—22no—
604D4—44no—
605D4—41no—
606D4—41no—
607D4—84no—
608D4—84no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4#123×C10112yes—
651C2×C4#123×C10112yes—
652C2×C4C22×D4×C10111yescharacteristic
653C2×C4C2×#41×C10111yescharacteristic
654C2×C4C2×#41×C10111yescharacteristic
655C2×C4C2×#41×C10111yescharacteristic
656C2×C4H(5,𝔽2)×C10111yescharacteristic
657C2×C42−1+4×C10111yescharacteristic
658C8—22no—
659C8—22no—
660C8—41no—
661C8—41no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—42no—
671C22—41no—
672C22—42no—
673C22—42no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C2×#123×C10111yescharacteristic
684C22D42×C10111yescharacteristic
685C22#547×C10111yescharacteristic
686C22C2×#135×C10111yescharacteristic
687C22#575×C10111yescharacteristic
688C22#576×C10111yescharacteristic
689C22#577×C10111yescharacteristic
690C4—22no—
691C4—22no—
692C4—41no—
693C4—41no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4#532×C10111yescharacteristic
702C4#542×C10111yescharacteristic
703C4#547×C10111yescharacteristic
704C4#553×C10111yescharacteristic
705C2—42no—
706C2—81no—
707C2—82no—
708C2C101×#242211yescharacteristic
709C2C101×#309111yescharacteristic
710C2C101×#309611yescharacteristic
711C2C101×#327311yescharacteristic
712C2C101×#328211yescharacteristic
713C2C101×#333911yescharacteristic
714C2C101×#335111yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#2535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C4×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#481×C101C2semidirect
2. C2×#482×C101C2semidirect
4. C101×#2352C2semidirect
5. C101×#2077C2semidirect
6. C101×#2077C2semidirect
7. C101×#2033C2semidirect
8. C101×#2033C2semidirect
9. C101×#1954C2semidirect
10. C101×#1949C2semidirect
11. C101×#1854C2semidirect
12. C101×#1852C2semidirect
13. C101×#1846C2semidirect
14. C101×#1804C2semidirect
15. C4×#102×C101C2semidirect
117. #102×C101D4semidirect
347. #25018C101direct (N × H)
358. C2×#481C2×C101semidirect
359. C2×#482C2×C101semidirect
361. #2352C2×C101semidirect
362. #2077C2×C101semidirect
363. #2077C2×C101semidirect
364. #2033C2×C101semidirect
365. #2033C2×C101semidirect
366. #1954C2×C101semidirect
367. #1949C2×C101semidirect
368. #1854C2×C101semidirect
369. #1852C2×C101semidirect
370. #1846C2×C101semidirect
371. #1804C2×C101semidirect
372. C4×#102C2×C101semidirect
373. C101#25018direct (N × H)
475. #102D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C1012
C2×#482×C1012
C101×#25352
C101×#23522
C101×#20772
C101×#20332
C101×#19542
C101×#19492
C101×#18542
C101×#18522
C101×#18462
C101×#18042
C4×#102×C1012
#25018101