Finite Group Databasebeta

← C101×#22158 #38804309

Subgroups — C101×#22158 #38804309

Order 25856.

928 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C101C211yesmaximal, characteristic
2C101×#2328C211yesmaximal, characteristic, complemented
3C101×#2319C211yesmaximal, characteristic, complemented
4C101×#1982C211yesmaximal, characteristic, complemented
5C101×#1972C211yesmaximal, characteristic, complemented
6C101×#1970C211yesmaximal, characteristic, complemented
7C101×#1949C211yesmaximal, characteristic, complemented
8C101×#1936C211yesmaximal, characteristic, complemented
9C101×#1934C211yesmaximal, characteristic, complemented
10C101×#1879C211yesmaximal, characteristic, complemented
11C101×#1879C211yesmaximal, characteristic, complemented
12C101×#1864C211yesmaximal, characteristic, complemented
13C101×#1862C211yesmaximal, characteristic, complemented
14C101×#1804C211yesmaximal, characteristic, complemented
15C101×#1768C211yesmaximal, characteristic, complemented
16C22×D8×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C2×#127×C101C2211yescharacteristic
19C2×C4×D4×C101C2211yescharacteristic
20C2×C4×D4×C101C2211yescharacteristic
21C2×C4×D4×C101C2211yescharacteristic
22#459×C101C418yescomplemented
23C2×#107×C101C2211yescharacteristic
24C2×#106×C101C2211yescharacteristic
25C2×C4⋊C8×C101C2211yescharacteristic
26C2×C4⋊C8×C101C2211yescharacteristic
27C2×#102×C101C2211yescharacteristic
28C2×#102×C101C2211yescharacteristic
29C2×#102×C101C2211yescharacteristic
30C2×#102×C101C2211yescharacteristic
31C2×#102×C101C2211yescharacteristic
32C2×#102×C101C2211yescharacteristic
33C2×#102×C101C2211yescharacteristic
34C2×#102×C101C2211yescharacteristic
35C2×#97×C101C2211yescharacteristic
36C2×C4×C8×C101C2211yescharacteristic
37#390×C101C2211yescharacteristic
38#390×C101C2211yescharacteristic
39#390×C101C2211yescharacteristic
40#390×C101C2211yescharacteristic
41#389×C101C2211yescharacteristic
42#389×C101C2211yescharacteristic
43#388×C101—21no—
44#388×C101—21no—
45#386×C101—21no—
46#386×C101—21no—
47#386×C101—21no—
48#386×C101—21no—
49#382×C101C2211yescharacteristic
50#381×C101—21no—
51#380×C101—21no—
52C4×C4⋊C4×C101C2211yescharacteristic
53#376×C101C2211yescharacteristic
54#340×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#336×C101C2211yescharacteristic
59#336×C101C2211yescharacteristic
60C22×D4×C101—21no—
61C22×D4×C101—21no—
62C22×D4×C101C2311yescharacteristic
63C22×D4×C101C2311yescharacteristic
64C22×D4×C101C2311yescharacteristic
65C23×C4×C101—21no—
66C23×C4×C101—21no—
67C23×C4×C101—21no—
68C2×D8×C101—41no—
69C2×D8×C101—41no—
70C2×D8×C101—41no—
71C2×D8×C101—41no—
72C2×D8×C101C2×C414yescomplemented
73C2×D8×C101C2×C414yescomplemented
74C22×C8×C101C2311yescharacteristic
75C22×C8×C101C2311yescharacteristic
76C22×C8×C101C2311yescharacteristic
77C22×C8×C101C2311yescharacteristic
78#127×C101—22no—
79#127×C101C2×C414yes—
80C4×D4×C101—22no—
81C4×D4×C101—41no—
82C4×D4×C101—41no—
83C4×D4×C101—41no—
84C4×D4×C101—41no—
85C4×D4×C101C2×C414yescomplemented
86C2×C4⋊C4×C101—21no—
87C2×C4⋊C4×C101—21no—
88C2×C4⋊C4×C101C2311yescharacteristic
89C2×C4⋊C4×C101C2311yescharacteristic
90C2×C4⋊C4×C101C2311yescharacteristic
91C2×C4⋊C4×C101C2311yescharacteristic
92C2×C4⋊C4×C101C2311yescharacteristic
93C2×C22⋊C4×C101—21no—
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×C101—21no—
103C2×C22⋊C4×C101—21no—
104C2×C42×C101—21no—
105C2×C42×C101C2311yescharacteristic
106C2×C42×C101C2311yescharacteristic
107C2×C42×C101C2311yescharacteristic
108#107×C101—41no—
109#106×C101—41no—
110C4⋊C8×C101—22no—
111C4⋊C8×C101C2×C414yescomplemented
112#102×C101—41no—
113#102×C101—41no—
114#102×C101—41no—
115#102×C101—41no—
116#102×C101—41no—
117#102×C101—41no—
118#102×C101C2×C414yescomplemented
119#102×C101C2×C414yescomplemented
120#97×C101—41no—
121C4×C8×C101—41no—
122#95×C101—21no—
123#95×C101—21no—
124#95×C101—21no—
125#95×C101—21no—
126#95×C101—21no—
127#95×C101D411yescharacteristic
128#95×C101D411yescharacteristic
129#95×C101D411yescharacteristic
130#95×C101D411yescharacteristic
131C24×C101—21no—
132C24×C101—21no—
133C24×C101—21no—
134C2×D4×C101—24no—
135C2×D4×C101—24no—
136C2×D4×C101—21no—
137C2×D4×C101—21no—
138C2×D4×C101—21no—
139C2×D4×C101—21no—
140C2×D4×C101—21no—
141C2×D4×C101—21no—
142C2×D4×C101—21no—
143C2×D4×C101—21no—
144C2×D4×C101—21no—
145C2×D4×C101—21no—
146C2×D4×C101—21no—
147C2×D4×C101—21no—
148C2×D4×C101—21no—
149C2×D4×C101—21no—
150C2×D4×C101—21no—
151C2×D4×C101—81no—
152C2×D4×C101—81no—
153C2×D4×C101—81no—
154C2×D4×C101—81no—
155C2×D4×C101C22×C412yes—
156C2×D4×C101C22×C412yes—
157C2×D4×C101C22×C412yes—
158C22×C4×C101—21no—
159C22×C4×C101—24no—
160C22×C4×C101—21no—
161C22×C4×C101—21no—
162C22×C4×C101—21no—
163C22×C4×C101—21no—
164C22×C4×C101—42no—
165C22×C4×C101—42no—
166C22×C4×C101—81no—
167C22×C4×C101—81no—
168C22×C4×C101—81no—
169C22×C4×C101—81no—
170C22×C4×C101—81no—
171C22×C4×C101—81no—
172C22×C4×C101C2×D411yescharacteristic
173C22×C4×C101C2×D411yescharacteristic
174C22×C4×C101C2×D411yescharacteristic
175C22×C4×C101C2×D411yescharacteristic
176C22×C4×C101C2×D411yescharacteristic
177C22×C4×C101C2×D411yescharacteristic
178C22×C4×C101C2411yescharacteristic
179D8×C101—44no—
180D8×C101—44no—
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×C101—21no—
191C2×C8×C101C22×C412yes—
192C2×C8×C101C22×C412yes—
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—81no—
203C4⋊C4×C101—81no—
204C4⋊C4×C101C22×C412yes—
205C22⋊C4×C101—24no—
206C22⋊C4×C101—42no—
207C22⋊C4×C101—42no—
208C22⋊C4×C101—81no—
209C22⋊C4×C101—81no—
210C22⋊C4×C101—81no—
211C22⋊C4×C101—81no—
212C22⋊C4×C101—81no—
213C22⋊C4×C101—81no—
214C22⋊C4×C101—81no—
215C22⋊C4×C101—81no—
216C42×C101—21no—
217C42×C101—21no—
218C42×C101—21no—
219C42×C101—21no—
220C42×C101—81no—
221C42×C101C22×C412yes—
222C42×C101#4112yes—
223C23×C101—22no—
224C23×C101—22no—
225C23×C101—22no—
226C23×C101—41no—
227C23×C101—41no—
228C23×C101—41no—
229C23×C101—41no—
230C23×C101—41no—
231C23×C101—41no—
232C23×C101—41no—
233C23×C101—41no—
234C23×C101—41no—
235C23×C101—41no—
236C23×C101—41no—
237C23×C101—41no—
238C23×C101—41no—
239C23×C101—41no—
240C23×C101—41no—
241C23×C101—41no—
242C23×C101—41no—
243C23×C101—41no—
244C23×C101C22×D411yescharacteristic
245D4×C101—22no—
246D4×C101—22no—
247D4×C101—22no—
248D4×C101—22no—
249D4×C101—22no—
250D4×C101—22no—
251D4×C101—41no—
252D4×C101—41no—
253D4×C101—41no—
254D4×C101—41no—
255D4×C101—41no—
256D4×C101—41no—
257D4×C101—84no—
258D4×C101—84no—
259C2×C4×C101—21no—
260C2×C4×C101—21no—
261C2×C4×C101—21no—
262C2×C4×C101—21no—
263C2×C4×C101—22no—
264C2×C4×C101—21no—
265C2×C4×C101—21no—
266C2×C4×C101—21no—
267C2×C4×C101—21no—
268C2×C4×C101—21no—
269C2×C4×C101—21no—
270C2×C4×C101—21no—
271C2×C4×C101—21no—
272C2×C4×C101—21no—
273C2×C4×C101—21no—
274C2×C4×C101—21no—
275C2×C4×C101—21no—
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—84no—
293C2×C4×C101C4×D412yes—
294C2×C4×C101C4×D412yes—
295C2×C4×C101C23×C411yescharacteristic
296C2×C4×C101C2×#4111yescharacteristic
297C2×C4×C101H(5,𝔽2)11yescharacteristic
298C2×C4×C101H(5,𝔽2)11yescharacteristic
299C2×C4×C101H(5,𝔽2)11yescharacteristic
300C2×C4×C1012−1+411yescharacteristic
301C8×C101—22no—
302C8×C101—22no—
303C8×C101—41no—
304C8×C101—41no—
305C22×C101—42no—
306C22×C101—42no—
307C22×C101—42no—
308C22×C101—42no—
309C22×C101—42no—
310C22×C101—42no—
311C22×C101—42no—
312C22×C101—42no—
313C22×C101—42no—
314C22×C101—81no—
315C22×C101—81no—
316C22×C101—81no—
317C22×C101—81no—
318C22×C101—81no—
319C22×C101—81no—
320C22×C101—81no—
321C22×C101—81no—
322C22×C101—81no—
323C22×C101—81no—
324C22×C101—81no—
325C22×C101—81no—
326C22×C101C2×C4×D411yescharacteristic
327C22×C101#53511yescharacteristic
328C22×C101#53711yescharacteristic
329C22×C101#57611yescharacteristic
330C22×C101#57611yescharacteristic
331C22×C101#57611yescharacteristic
332C22×C101#57711yescharacteristic
333C4×C101—22no—
334C4×C101—22no—
335C4×C101—42no—
336C4×C101—41no—
337C4×C101—41no—
338C4×C101—41no—
339C4×C101—41no—
340C4×C101—81no—
341C4×C101—81no—
342C4×C101—81no—
343C4×C101—81no—
344C4×C101#51811yescharacteristic
345C4×C101#52011yescharacteristic
346C4×C101#54011yescharacteristic
347C4×C101#54211yescharacteristic
348#22158C10111yesmaximal, characteristic, direct product factor, Sylow
349C2×C101—82no—
350C2×C101—82no—
351C2×C101—82no—
352C2×C101#232411yescharacteristic
353C2×C101#294611yescharacteristic
354C2×C101#294811yescharacteristic
355C2×C101#322011yescharacteristic
356C2×C101#322411yescharacteristic
357C2×C101#325711yescharacteristic
358C2×C101#325911yescharacteristic
359C2×#459C2×C10111yescharacteristic
360#2328C2×C10111yescharacteristic, complemented
361#2319C2×C10111yescharacteristic, complemented
362#1982C2×C10111yescharacteristic, complemented
363#1972C2×C10111yescharacteristic, complemented
364#1970C2×C10111yescharacteristic, complemented
365#1949C2×C10111yescharacteristic, complemented
366#1936C2×C10111yescharacteristic, complemented
367#1934C2×C10111yescharacteristic, complemented
368#1879C2×C10111yescharacteristic, complemented
369#1879C2×C10111yescharacteristic, complemented
370#1864C2×C10111yescharacteristic, complemented
371#1862C2×C10111yescharacteristic, complemented
372#1804C2×C10111yescharacteristic, complemented
373#1768C2×C10111yescharacteristic, complemented
374C101#2215811yescharacteristic, direct product factor, Sylow
375C22×D8C22×C10111yescharacteristic
376C22×D8C22×C10111yescharacteristic
377C2×#127C22×C10111yescharacteristic
378C2×C4×D4C22×C10111yescharacteristic
379C2×C4×D4C22×C10111yescharacteristic
380C2×C4×D4C22×C10111yescharacteristic
381#459C4×C10118yescomplemented
382C2×#107C22×C10111yescharacteristic
383C2×#106C22×C10111yescharacteristic
384C2×C4⋊C8C22×C10111yescharacteristic
385C2×C4⋊C8C22×C10111yescharacteristic
386C2×#102C22×C10111yescharacteristic
387C2×#102C22×C10111yescharacteristic
388C2×#102C22×C10111yescharacteristic
389C2×#102C22×C10111yescharacteristic
390C2×#102C22×C10111yescharacteristic
391C2×#102C22×C10111yescharacteristic
392C2×#102C22×C10111yescharacteristic
393C2×#102C22×C10111yescharacteristic
394C2×#97C22×C10111yescharacteristic
395C2×C4×C8C22×C10111yescharacteristic
396#390C22×C10111yescharacteristic
397#390C22×C10111yescharacteristic
398#390C22×C10111yescharacteristic
399#390C22×C10111yescharacteristic
400#389C22×C10111yescharacteristic
401#389C22×C10111yescharacteristic
402#388—21no—
403#388—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#382C22×C10111yescharacteristic
409#381—21no—
410#380—21no—
411C4×C4⋊C4C22×C10111yescharacteristic
412#376C22×C10111yescharacteristic
413#340C22×C10111yescharacteristic
414#340C22×C10111yescharacteristic
415#340C22×C10111yescharacteristic
416#340C22×C10111yescharacteristic
417#336C22×C10111yescharacteristic
418#336C22×C10111yescharacteristic
419C22×D4—21no—
420C22×D4—21no—
421C22×D4C23×C10111yescharacteristic
422C22×D4C23×C10111yescharacteristic
423C22×D4C23×C10111yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C2×D8—41no—
428C2×D8—41no—
429C2×D8—41no—
430C2×D8—41no—
431C2×D8C2×C4×C10114yescomplemented
432C2×D8C2×C4×C10114yescomplemented
433C22×C8C23×C10111yescharacteristic
434C22×C8C23×C10111yescharacteristic
435C22×C8C23×C10111yescharacteristic
436C22×C8C23×C10111yescharacteristic
437#127—22no—
438#127C2×C4×C10114yes—
439C4×D4—22no—
440C4×D4—41no—
441C4×D4—41no—
442C4×D4—41no—
443C4×D4—41no—
444C4×D4C2×C4×C10114yescomplemented
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
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⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C42—21no—
464C2×C42C23×C10111yescharacteristic
465C2×C42C23×C10111yescharacteristic
466C2×C42C23×C10111yescharacteristic
467#107—41no—
468#106—41no—
469C4⋊C8—22no—
470C4⋊C8C2×C4×C10114yescomplemented
471#102—41no—
472#102—41no—
473#102—41no—
474#102—41no—
475#102—41no—
476#102—41no—
477#102C2×C4×C10114yescomplemented
478#102C2×C4×C10114yescomplemented
479#97—41no—
480C4×C8—41no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95D4×C10111yescharacteristic
487#95D4×C10111yescharacteristic
488#95D4×C10111yescharacteristic
489#95D4×C10111yescharacteristic
490C24—21no—
491C24—21no—
492C24—21no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—81no—
511C2×D4—81no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4C22×C4×C10112yes—
515C2×D4C22×C4×C10112yes—
516C2×D4C22×C4×C10112yes—
517C22×C4—21no—
518C22×C4—24no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4C2×D4×C10111yescharacteristic
532C22×C4C2×D4×C10111yescharacteristic
533C22×C4C2×D4×C10111yescharacteristic
534C22×C4C2×D4×C10111yescharacteristic
535C22×C4C2×D4×C10111yescharacteristic
536C22×C4C2×D4×C10111yescharacteristic
537C22×C4C24×C10111yescharacteristic
538D8—44no—
539D8—44no—
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×C8—21no—
549C2×C8—21no—
550C2×C8C22×C4×C10112yes—
551C2×C8C22×C4×C10112yes—
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—81no—
562C4⋊C4—81no—
563C4⋊C4C22×C4×C10112yes—
564C22⋊C4—24no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—81no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—81no—
580C42C22×C4×C10112yes—
581C42#41×C10112yes—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23C22×D4×C10111yescharacteristic
604D4—22no—
605D4—22no—
606D4—22no—
607D4—22no—
608D4—22no—
609D4—22no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—84no—
617D4—84no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
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—41no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—84no—
652C2×C4C4×D4×C10112yes—
653C2×C4C4×D4×C10112yes—
654C2×C4C23×C4×C10111yescharacteristic
655C2×C4C2×#41×C10111yescharacteristic
656C2×C4H(5,𝔽2)×C10111yescharacteristic
657C2×C4H(5,𝔽2)×C10111yescharacteristic
658C2×C4H(5,𝔽2)×C10111yescharacteristic
659C2×C42−1+4×C10111yescharacteristic
660C8—22no—
661C8—22no—
662C8—41no—
663C8—41no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×C4×D4×C10111yescharacteristic
686C22#535×C10111yescharacteristic
687C22#537×C10111yescharacteristic
688C22#576×C10111yescharacteristic
689C22#576×C10111yescharacteristic
690C22#576×C10111yescharacteristic
691C22#577×C10111yescharacteristic
692C4—22no—
693C4—22no—
694C4—42no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4#518×C10111yescharacteristic
704C4#520×C10111yescharacteristic
705C4#540×C10111yescharacteristic
706C4#542×C10111yescharacteristic
707C2—82no—
708C2—82no—
709C2—82no—
710C2C101×#232411yescharacteristic
711C2C101×#294611yescharacteristic
712C2C101×#294811yescharacteristic
713C2C101×#322011yescharacteristic
714C2C101×#322411yescharacteristic
715C2C101×#325711yescharacteristic
716C2C101×#325911yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC2×#459×C101C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ #376×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2328C2semidirect
3. C101×#2319C2semidirect
4. C101×#1982C2semidirect
5. C101×#1972C2semidirect
6. C101×#1970C2semidirect
7. C101×#1949C2semidirect
8. C101×#1936C2semidirect
9. C101×#1934C2semidirect
10. C101×#1879C2semidirect
11. C101×#1879C2semidirect
12. C101×#1864C2semidirect
13. C101×#1862C2semidirect
14. C101×#1804C2semidirect
15. C101×#1768C2semidirect
22. #459×C101C4semidirect
72. C2×D8×C101C2×C4semidirect
73. C2×D8×C101C2×C4semidirect
85. C4×D4×C101C2×C4semidirect
111. C4⋊C8×C101C2×C4semidirect
118. #102×C101C2×C4semidirect
119. #102×C101C2×C4semidirect
348. #22158C101direct (N × H)
360. #2328C2×C101semidirect
361. #2319C2×C101semidirect
362. #1982C2×C101semidirect
363. #1972C2×C101semidirect
364. #1970C2×C101semidirect
365. #1949C2×C101semidirect
366. #1936C2×C101semidirect
367. #1934C2×C101semidirect
368. #1879C2×C101semidirect
369. #1879C2×C101semidirect
370. #1864C2×C101semidirect
371. #1862C2×C101semidirect
372. #1804C2×C101semidirect
373. #1768C2×C101semidirect
374. C101#22158direct (N × H)
381. #459C4×C101semidirect
431. C2×D8C2×C4×C101semidirect
432. C2×D8C2×C4×C101semidirect
444. C4×D4C2×C4×C101semidirect
470. C4⋊C8C2×C4×C101semidirect
477. #102C2×C4×C101semidirect
478. #102C2×C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1012
C101×#23282
C101×#23192
C101×#19822
C101×#19722
C101×#19702
C101×#19492
C101×#19362
C101×#19342
C101×#18792
C101×#18642
C101×#18622
C101×#18042
C101×#17682
#22158101