Finite Group Databasebeta

← C2×#72220832 #72242488

Subgroups — C2×#72220832 #72242488

Order 6400.

7388 conjugacy classes of subgroups.

The subgroup lattice has 1145 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13107550C211yesmaximal, characteristic
2C2×#13103909C211yesmaximal, characteristic, complemented
3C22×#11716761C211yesmaximal, characteristic, complemented
4C2×#13103866C212yesmaximal, complemented
5C2×#13103842C212yesmaximal, complemented
6C2×#13104865C211yesmaximal, characteristic, complemented
7C2×#13103850C212yesmaximal, complemented
8C2×#13105798C211yesmaximal, characteristic
9C2×C8×D5⋊AGL(1,𝔽5)C212yesmaximal, complemented
10#72220832C2116yesmaximal, direct product factor
11C2×M16×#1043C211yesmaximal, characteristic, complemented
12C2×#13107559C211yesmaximal, characteristic
13C2×#11717471C2211yescharacteristic
14C2×#11717451C2211yescharacteristic
15C22×#87862C2211yescharacteristic
16C22×C4×#1043C2211yescharacteristic
17C2×#11717435C2211yescharacteristic
18C2×#11717375C414yes—
19C2×#11717373C414yescomplemented
20#13107559C418yes—
21#13107559C2218yes—
22C2×#11717363C412yes—
23C2×C4×D5⋊AGL(1,𝔽5)C2212yes—
24C2×#11717361C2212yes—
25#13107550C418yescomplemented
26#13107550C2218yes—
27C2×#11717360C414yescomplemented
28C2×D5⋊(D5⋊C8)C2212yes—
29C2×#11717356C2212yes—
30C2×#11717353C412yes—
31C2×M16×C5⋊D5C2211yescharacteristic
32C2×C5×#4053C412yescomplemented
33C22×#87767C2211yescharacteristic
34C2×#11716932C412yescomplemented
35#13105798C418yescomplemented
36#13105798C2218yes—
37C2×#11716922C414yescomplemented
38C2×#11716909C2212yes—
39C2×C8×D52C2212yes—
40#13104865C2218yescomplemented
41C2×#11716885C2212yes—
42C2×C8×#1044C2212yes—
43M16×#1043C2218yescomplemented
44C2×#11716860C2212yes—
45C2×C8×#1043C2212yes—
46C2×#11716764C2212yes—
47#13103909C2218yescomplemented
48C2×#11716762C2212yes—
49C2×#11716761C2211yescharacteristic
50C2×#11716761C2211yescharacteristic
51C2×#11716761C2211yescharacteristic
52C2×#11716761C2211yescharacteristic
53C2×#11716761C2218yescomplemented
54#13103866C22116yescomplemented
55#13103850C22116yescomplemented
56#13103842C22116yescomplemented
57C8×D5⋊AGL(1,𝔽5)C22116yescomplemented
58C2×AGL(1,𝔽5)×#131—52nomaximal
59C23×#1043C2×C412yes—
60C22×D5⋊AGL(1,𝔽5)C2×C414yes—
61C22×C4×C5⋊D5C2311yescharacteristic
62C2×C5×#709C2×C412yes—
63C2×#87886C2×C412yes—
64C2×#87880C2×C412yes—
65#11717471C2×C414yes—
66#11717471C2×C414yes—
67#11717471C2×C414yes—
68#11717471C2314yes—
69C2×#87877C2×C411yescharacteristic
70C2×C4×D52C2312yes—
71C2×#87873C2×C412yes—
72C2×#87872C2×C411yescharacteristic
73C2×#87871C2×C412yes—
74C2×C22⋊#1044C2×C412yes—
75C22×#6034C2×C412yescomplemented
76#11717451C2×C414yes—
77#11717451C2314yes—
78C2×C4⋊#1044C2×C412yes—
79C2×C4×#1044C2312yes—
80C2×#87862C2×C414yescomplemented
81C2×#87862C2×C412yescomplemented
82C2×#87862C2311yescharacteristic
83C2×#87862C2311yescharacteristic
84C2×#87862C2314yes—
85C2×#87860C2×C412yescomplemented
86C2×C4×#1043C2×C412yes—
87C2×C4×#1043C2×C414yes—
88C2×C4×#1043C2311yescharacteristic
89C2×C4×#1043C2311yescharacteristic
90C2×C4×#1043C2314yes—
91#11717435C2×C414yescomplemented
92#11717435C2314yes—
93C2×#87856C2×C412yescomplemented
94C2×#87855C2312yes—
95#11717375C2×C4132yes—
96C2×#87834C2×C418yescomplemented
97#11717373C2×C4132yescomplemented
98C2×D5⋊#170C2×C418yescomplemented
99C2×#87832C2×C414yes—
100C2×#87831C2×C414yes—
101C2×#87830C2×C414yes—
102#11717363C2×C4116yes—
103C4×D5⋊AGL(1,𝔽5)C2×C418yes—
104C4×D5⋊AGL(1,𝔽5)C2318yes—
105#11717361C2×C418yescomplemented
106#11717361C2318yes—
107#11717360C2×C4132yescomplemented
108D5⋊(D5⋊C8)C2×C418yescomplemented
109D5⋊(D5⋊C8)C2318yes—
110#11717356C2×C418yes—
111#11717356C2318yes—
112#11717353C2×C4116yes—
113C2×C52×M16C2×C411yescharacteristic, complemented
114C2×#87804C2×C411yescharacteristic, complemented
115M16×C5⋊D5C2×C414yescomplemented
116M16×C5⋊D5C2314yes—
117C2×#87799C2×C412yescomplemented
118C2×C8×C5⋊D5C2312yes—
119C22×C5×#168C2×C412yescomplemented
120C5×#4053C2×C4116yescomplemented
121C2×C5×#676C2×C414yescomplemented
122C2×C5×C8×D5C2×C414yescomplemented
123C2×#87768C2×C414yescomplemented
124C2×#87767C2×C414yescomplemented
125C2×#87767C2×C412yescomplemented
126C2×#87767C2311yescharacteristic
127C2×#87767C2311yescharacteristic
128C2×#87767C2314yes—
129#11716932C2×C4116yescomplemented
130C2×D5×#168C2×C414yescomplemented
131#11716922C2×C4132yescomplemented
132#11716909C2×C418yescomplemented
133#11716909C2318yes—
134C8×D52C2×C418yescomplemented
135C8×D52C2318yes—
136#11716885C2318yes—
137C8×#1044C2318yes—
138#11716860C2318yes—
139C8×#1043C2318yes—
140#11716764C2318yes—
141#11716762C2318yes—
142#11716761C2314yes—
143#11716761C2314yes—
144#11716761C2314yes—
145#11716761C2314yes—
146C2×#41×AGL(1,𝔽5)—52no—
147C2×D5⋊#131—52no—
148C2×D5×#131—52no—
149AGL(1,𝔽5)×#131—532no—
150C2×#65728—52no—
151C2×#65728—54no—
152C2×M16×AGL(1,𝔽5)—54no—
153C2×M16×AGL(1,𝔽5)—52no—
154C2×M16×AGL(1,𝔽5)—102no—
155C2×#65718—54no—
156C2×#65718—52no—
157C22×C8×AGL(1,𝔽5)—54no—
158C22×C8×AGL(1,𝔽5)—52no—
159C23×C5⋊D5C22×C411yescharacteristic
160C22×D52C22×C412yes—
161C22×#1044C22×C414yes—
162C22×#1043—28no—
163C22×#1043C22×C412yes—
164C22×#1043C22×C418yes—
165C22×#1043C22×C412yes—
166C2×D5⋊AGL(1,𝔽5)—216no—
167C2×D5⋊AGL(1,𝔽5)C22×C4116yes—
168C22×C4×C52C22×C411yescharacteristic
169C22×#1039C22×C411yescharacteristic
170C2×C4×C5⋊D5C22×C411yescharacteristic
171C2×C4×C5⋊D5C22×C412yes—
172C2×C4×C5⋊D5C22×C411yescharacteristic
173C2×C4×C5⋊D5C22×C412yes—
174C2×C4×C5⋊D5C22×C411yescharacteristic
175C2×C4×C5⋊D5C22×C412yes—
176C2×C4×C5⋊D5C2411yescharacteristic
177C2×C4×C5⋊D5C2412yes—
178C2×C5×C22⋊D5C4214yes—
179C5×#709C4218yes—
180C5×#709C22×C418yes—
181C2×C5×D20C4212yes—
182C2×C4×C5×D5C22×C414yes—
183C2×C5×Dic10C4212yes—
184#87886C4218yes—
185#87886C22×C418yes—
186C2×#6039C4212yes—
187C2×#6038C4214yes—
188C2×#6037C4212yes—
189C2×#6036C22×C412yes—
190#87880C4218yes—
191#87880C22×C418yes—
192C2×D5×Dic5C22×C414yes—
193#87877C4214yes—
194#87877C22×C414yes—
195C4×D52C22×C414yes—
196C4×D52C22×C414yes—
197C4×D52C22×C414yes—
198C4×D52C2414yes—
199#87873C4218yes—
200#87873C22×C418yes—
201#87872C4214yes—
202#87872C22×C414yes—
203#87871C4218yes—
204#87871C22×C418yes—
205C22⋊#1044C22×C418yes—
206C2×#6034C22×C412yes—
207C2×#6034C22×C412yes—
208C2×#6034C22×C418yescomplemented
209C4⋊#1044C22×C418yes—
210C4×#1044C22×C414yes—
211C4×#1044C2414yes—
212#87862C22×C412yes—
213#87862C22×C412yes—
214#87862C22×C418yescomplemented
215#87862C2412yes—
216#87862C2412yes—
217#87860C22×C418yescomplemented
218C2×#6033C22×C414yes—
219C4×#1043C22×C418yes—
220C4×#1043C22×C412yes—
221C4×#1043C22×C412yes—
222C4×#1043C2412yes—
223C4×#1043C2412yes—
224#87856C22×C418yescomplemented
225#87855C22×C414yes—
226#87855C2414yes—
227#87834C22×C4132yescomplemented
228D5⋊#170C22×C4132yescomplemented
229#87832C22×C4116yes—
230#87831C22×C4116yes—
231#87830C22×C4116yes—
232C52×M16C22×C414yescomplemented
233C2×C52×C8C22×C412yes—
234#87804C22×C414yescomplemented
235C2×#6029C22×C412yes—
236#87799C22×C418yescomplemented
237C8×C5⋊D5C22×C414yes—
238C8×C5⋊D5C2414yes—
239C2×C5×#168C22×C412yes—
240C2×C5×#168C22×C412yes—
241C2×C5×#168C22×C418yescomplemented
242C5×#676C22×C4116yescomplemented
243C5×C8×D5C22×C4116yescomplemented
244#87768C22×C4116yescomplemented
245#87767C22×C412yes—
246#87767C22×C412yes—
247#87767C22×C418yescomplemented
248#87767C2412yes—
249#87767C2412yes—
250D5×#168C22×C4116yescomplemented
251C2×D5×#41—52no—
252#41×AGL(1,𝔽5)—516no—
253#41×AGL(1,𝔽5)—516no—
254D5⋊#131—516no—
255D5⋊#131—516no—
256C2×Q8×AGL(1,𝔽5)—54no—
257C2×#4133—54no—
258C2×D4×AGL(1,𝔽5)—54no—
259C2×D4×AGL(1,𝔽5)—58no—
260C2×#4131—54no—
261C2×#4131—58no—
262C2×#4130—52no—
263C2×#4130—54no—
264C22×C4×AGL(1,𝔽5)—52no—
265C22×C4×AGL(1,𝔽5)—54no—
266C22×C4×AGL(1,𝔽5)—102no—
267C2×D5⋊M16—52no—
268C2×D5⋊M16—54no—
269C2×D5⋊M16—102no—
270C22×D5⋊C8—52no—
271C22×D5⋊C8—54no—
272C2×C5×#131—52no—
273C2×#4094—52no—
274D5×#131—516no—
275D5×#131—516no—
276C2×#4053—54no—
277C2×#4053AGL(1,𝔽5)12yescomplemented
278C2×D5×M16—54no—
279C2×D5×M16—52no—
280C2×D5×M16—102no—
281C2×#4047—54no—
282C2×#4047—52no—
283C22×C8×D5—52no—
284C22×C8×D5—54no—
285#65728—516no—
286#65728—532no—
287M16×AGL(1,𝔽5)—516no—
288M16×AGL(1,𝔽5)—532no—
289M16×AGL(1,𝔽5)—1016no—
290#65718—516no—
291#65718—532no—
292C2×#3992—54no—
293C2×#3992—54no—
294C2×#3992—54no—
295C2×#3992—104no—
296C2×C8×AGL(1,𝔽5)—52no—
297C2×C8×AGL(1,𝔽5)—52no—
298C2×C8×AGL(1,𝔽5)—52no—
299C2×C8×AGL(1,𝔽5)—52no—
300C2×C8×AGL(1,𝔽5)—516no—
301C2×C8×AGL(1,𝔽5)—54no—
302C2×C8×AGL(1,𝔽5)—54no—
303C2×C8×AGL(1,𝔽5)—54no—
304C2×C8×AGL(1,𝔽5)—532no—
305C2×C8×AGL(1,𝔽5)—104no—
306C2×C4×#131—251noSylow
307C23×C52C2×C4211yescharacteristic
308C22×C5⋊D5—24no—
309C22×C5⋊D5C2×C4211yescharacteristic
310C22×C5⋊D5C2×C4212yes—
311C22×C5⋊D5C23×C412yes—
312C22×C5⋊D5C23×C411yescharacteristic
313C22×C5×D5C2×C4214yes—
314C2×D52—28no—
315C2×D52C2×C4214yes—
316C2×D52C23×C414yes—
317C2×#1044—28no—
318C2×#1044C23×C418yes—
319C2×#1043—24no—
320C2×#1043—216no—
321C2×#1043#13118yescomplemented
322C2×#1043C23×C414yes—
323C2×#1043C23×C414yes—
324D5⋊AGL(1,𝔽5)—232no—
325C2×C4×C52C2×C4211yescharacteristic
326C2×C4×C52C2×C4212yes—
327C2×C4×C52C23×C411yescharacteristic
328C2×C4×C52C23×C412yes—
329C2×#1039C2×C4212yes—
330C2×#1039C2×C4211yescharacteristic
331C2×#1039C23×C411yescharacteristic
332C2×#1039C23×C412yes—
333C4×C5⋊D5C2×C4212yes—
334C4×C5⋊D5C2×C4212yes—
335C4×C5⋊D5C2×C4212yes—
336C4×C5⋊D5C23×C411yescharacteristic
337C4×C5⋊D5C23×C412yes—
338C4×C5⋊D5C23×C412yes—
339C4×C5⋊D5C23×C411yescharacteristic
340C4×C5⋊D5C23×C411yescharacteristic
341C4×C5⋊D5C23×C412yes—
342C4×C5⋊D5C2511yescharacteristic
343C5×C22⋊D5C2×C42116yes—
344C2×C5×Dic5C2×C4214yes—
345C5×D20C2×C4218yes—
346C4×C5×D5C2×C4218yes—
347C4×C5×D5C23×C418yes—
348C5×Dic10C2×C4218yes—
349#6039C2×C4218yes—
350#6038C2×C42116yes—
351#6037C2×C4218yes—
352#6036C2×C4214yes—
353#6036C23×C414yes—
354D5×Dic5C2×C4218yes—
355D5×Dic5C23×C418yes—
356#6034C23×C414yes—
357#6034C23×C414yes—
358#6033C23×C418yes—
359C52×C8C23×C414yes—
360#6029C23×C414yes—
361C5×#168C23×C414yes—
362C5×#168C23×C414yes—
363C23×AGL(1,𝔽5)—58no—
364C23×AGL(1,𝔽5)—54no—
365C23×AGL(1,𝔽5)—104no—
366C2×C5×#41—52no—
367D5×#41—58no—
368D5×#41—58no—
369D5×#41—58no—
370D5×#41—58no—
371C2×#713—52no—
372C2×Q8×D5—52no—
373C2×#711—54no—
374C2×#711—52no—
375C2×D4×D5—54no—
376C2×D4×D5—52no—
377C2×#709—54no—
378C2×#709C2×AGL(1,𝔽5)12yes—
379C22×C4×D5—52no—
380C22×C4×D5—54no—
381C22×C4×D5—102no—
382C2×C22⋊AGL(1,𝔽5)—54no—
383C2×C22⋊AGL(1,𝔽5)—58no—
384C2×#704—54no—
385C2×#704—58no—
386C2×#704—104no—
387C22×#170—54no—
388C22×#170—58no—
389Q8×AGL(1,𝔽5)—532no—
390#4133—532no—
391D4×AGL(1,𝔽5)—532no—
392D4×AGL(1,𝔽5)—564no—
393#4131—532no—
394#4131—564no—
395#4130—58no—
396#4130—58no—
397#4130—516no—
398#4130—516no—
399C2×C4⋊AGL(1,𝔽5)—54no—
400C2×C4⋊AGL(1,𝔽5)—58no—
401C2×C4×AGL(1,𝔽5)—54no—
402C2×C4×AGL(1,𝔽5)—58no—
403C2×C4×AGL(1,𝔽5)—52no—
404C2×C4×AGL(1,𝔽5)—52no—
405C2×C4×AGL(1,𝔽5)—58no—
406C2×C4×AGL(1,𝔽5)—54no—
407C2×C4×AGL(1,𝔽5)—516no—
408C2×C4×AGL(1,𝔽5)—58no—
409C2×C4×AGL(1,𝔽5)—516no—
410C2×C4×AGL(1,𝔽5)—104no—
411C2×C4×AGL(1,𝔽5)—108no—
412C2×C4×AGL(1,𝔽5)—102no—
413C2×C4×AGL(1,𝔽5)—102no—
414C2×C4×AGL(1,𝔽5)—108no—
415D5⋊M16—58no—
416D5⋊M16—58no—
417D5⋊M16—516no—
418D5⋊M16—516no—
419D5⋊M16—108no—
420D5⋊M16—108no—
421C2×#700—54no—
422C2×#700—58no—
423C2×#700—104no—
424C2×D5⋊C8—54no—
425C2×D5⋊C8—54no—
426C2×D5⋊C8—58no—
427C2×D5⋊C8—52no—
428C2×D5⋊C8—52no—
429C2×D5⋊C8—58no—
430C2×D5⋊C8—516no—
431C2×D5⋊C8—58no—
432C2×D5⋊C8—516no—
433C2×D5⋊C8—104no—
434C5×#131—516no—
435C2×C5×M16—22no—
436C2×C5×M16—54no—
437C2×C5×M16C2×AGL(1,𝔽5)12yescomplemented
438C22×C5×C8—52no—
439C22×C5×C8—54no—
440#4094—516no—
441C2×#681—52no—
442C2×#681—54no—
443C2×#681—102no—
444C22×#168—54no—
445C22×#168C2×AGL(1,𝔽5)12yescomplemented
446#4053—532no—
447#4053C2×AGL(1,𝔽5)116yescomplemented
448D5×M16—58no—
449D5×M16—58no—
450D5×M16—516no—
451D5×M16—516no—
452D5×M16—108no—
453D5×M16—108no—
454#4047—516no—
455#4047—532no—
456C2×#676—54no—
457C2×#676—54no—
458C2×#676—104no—
459C2×#676C2×AGL(1,𝔽5)14yescomplemented
460C2×C8×D5—54no—
461C2×C8×D5—54no—
462C2×C8×D5—52no—
463C2×C8×D5—52no—
464C2×C8×D5—52no—
465C2×C8×D5—52no—
466C2×C8×D5—58no—
467C2×C8×D5—58no—
468C2×C8×D5—516no—
469C2×C8×D5—516no—
470C2×C8×D5—104no—
471C2×C8×D5C2×AGL(1,𝔽5)14yescomplemented
472#3992—516no—
473#3992—516no—
474#3992—516no—
475#3992—1016no—
476C8×AGL(1,𝔽5)—516no—
477C8×AGL(1,𝔽5)—58no—
478C8×AGL(1,𝔽5)—58no—
479C8×AGL(1,𝔽5)—58no—
480C8×AGL(1,𝔽5)—58no—
481C8×AGL(1,𝔽5)—516no—
482C8×AGL(1,𝔽5)—516no—
483C8×AGL(1,𝔽5)—1016no—
484C22×#131—251no—
485C22×#131—251no—
486C2×C4×#41—251no—
487C4×#131—2516no—
488C2×#405—251no—
489C2×#405—252no—
490C2×#405—252no—
491C2×#405—251no—
492C2×C4×M16—251no—
493C2×C4×M16—252no—
494C22×C4×C8—251no—
495C22×C4×C8—252no—
496C22×C52—22no—
497C22×C52C22×C4212yes—
498C22×C52C22×C4211yescharacteristic
499C2×C5⋊D5—22no—
500C2×C5⋊D5—24no—
501C2×C5⋊D5—24no—
502C2×C5⋊D5C22×C4212yes—
503C2×C5⋊D5C22×C4211yescharacteristic
504C2×C5⋊D5C2×#13114yes—
505C2×C5⋊D5C24×C411yescharacteristic
506C2×C5×D5—28no—
507C2×C5×D5C22×C4218yes—
508D52—28no—
509D52—28no—
510#1044—28no—
511#1043—24no—
512#1043C2×#13118yescomplemented
513C4×C52C22×C4212yes—
514C4×C52C22×C4211yescharacteristic
515C4×C52C24×C411yescharacteristic
516#1039C22×C4211yescharacteristic
517#1039C22×C4212yes—
518#1039C24×C411yescharacteristic
519C5×Dic5C22×C4218yes—
520C23×D5—52no—
521C23×D5—54no—
522C23×D5—102no—
523C22×AGL(1,𝔽5)—54no—
524C22×AGL(1,𝔽5)—54no—
525C22×AGL(1,𝔽5)—58no—
526C22×AGL(1,𝔽5)—532no—
527C22×AGL(1,𝔽5)—516no—
528C22×AGL(1,𝔽5)—104no—
529C22×AGL(1,𝔽5)—104no—
530C22×AGL(1,𝔽5)—1016no—
531C22×AGL(1,𝔽5)—1032no—
532C22×AGL(1,𝔽5)—1016no—
533C22×AGL(1,𝔽5)—2016no—
534C5×#41—58no—
535C5×#41—58no—
536C2×C5×Q8—52no—
537C2×C5×D4—54no—
538C2×C5×D4—52no—
539C22×C4×C5—22no—
540C22×C4×C5—54no—
541C22×C4×C5C22×AGL(1,𝔽5)12yes—
542C2×C22⋊D5—54no—
543C2×C22⋊D5—54no—
544C2×C22⋊D5C4×AGL(1,𝔽5)14yes—
545C22×Dic5—52no—
546C22×Dic5—54no—
547C22×Dic5—102no—
548#713—58no—
549#713—58no—
550Q8×D5—58no—
551Q8×D5—58no—
552#711—516no—
553#711—516no—
554#711—58no—
555#711—58no—
556D4×D5—516no—
557D4×D5—516no—
558D4×D5—58no—
559D4×D5—58no—
560#709—516no—
561#709—516no—
562#709C4×AGL(1,𝔽5)18yes—
563#709C22×AGL(1,𝔽5)18yes—
564C2×D20—54no—
565C2×D20C4×AGL(1,𝔽5)12yes—
566C2×C4×D5—54no—
567C2×C4×D5—52no—
568C2×C4×D5—54no—
569C2×C4×D5—52no—
570C2×C4×D5—54no—
571C2×C4×D5—52no—
572C2×C4×D5—54no—
573C2×C4×D5—52no—
574C2×C4×D5—54no—
575C2×C4×D5—54no—
576C2×C4×D5—58no—
577C2×C4×D5—58no—
578C2×C4×D5—58no—
579C2×C4×D5—58no—
580C2×C4×D5—102no—
581C2×C4×D5—102no—
582C2×C4×D5—104no—
583C2×C4×D5—104no—
584C2×C4×D5—102no—
585C2×C4×D5—104no—
586C2×C4×D5—102no—
587C2×C4×D5—104no—
588C2×C4×D5C22×AGL(1,𝔽5)14yes—
589C2×Dic10—54no—
590C2×Dic10C4×AGL(1,𝔽5)12yes—
591C22⋊AGL(1,𝔽5)—532no—
592C22⋊AGL(1,𝔽5)—516no—
593#704—532no—
594#704—516no—
595#704—1016no—
596C2×#170—532no—
597C2×#170—54no—
598C2×#170—58no—
599C2×#170—54no—
600C2×#170—516no—
601C2×#170—108no—
602C4⋊AGL(1,𝔽5)—532no—
603C4⋊AGL(1,𝔽5)—516no—
604C4×AGL(1,𝔽5)—532no—
605C4×AGL(1,𝔽5)—54no—
606C4×AGL(1,𝔽5)—54no—
607C4×AGL(1,𝔽5)—54no—
608C4×AGL(1,𝔽5)—54no—
609C4×AGL(1,𝔽5)—58no—
610C4×AGL(1,𝔽5)—58no—
611C4×AGL(1,𝔽5)—516no—
612C4×AGL(1,𝔽5)—104no—
613C4×AGL(1,𝔽5)—104no—
614C4×AGL(1,𝔽5)—1016no—
615C4×AGL(1,𝔽5)—104no—
616C4×AGL(1,𝔽5)—104no—
617#700—532no—
618#700—516no—
619#700—1016no—
620D5⋊C8—532no—
621D5⋊C8—54no—
622D5⋊C8—54no—
623D5⋊C8—58no—
624D5⋊C8—58no—
625D5⋊C8—54no—
626D5⋊C8—54no—
627D5⋊C8—516no—
628D5⋊C8—108no—
629D5⋊C8—108no—
630C5×M16—28no—
631C5×M16—516no—
632C5×M16C22×AGL(1,𝔽5)18yescomplemented
633C2×C5×C8—24no—
634C2×C5×C8—52no—
635C2×C5×C8—52no—
636C2×C5×C8—58no—
637C2×C5×C8—516no—
638C2×C5×C8C22×AGL(1,𝔽5)14yes—
639#681—58no—
640#681—516no—
641#681—108no—
642C2×#168—54no—
643C2×#168—516no—
644C2×#168—104no—
645C2×#168C22×AGL(1,𝔽5)12yes—
646C2×#168C22×AGL(1,𝔽5)12yes—
647C2×#168C22×AGL(1,𝔽5)18yescomplemented
648#676—516no—
649#676—516no—
650#676—1016no—
651#676C22×AGL(1,𝔽5)116yescomplemented
652C8×D5—516no—
653C8×D5—58no—
654C8×D5—58no—
655C8×D5—54no—
656C8×D5—54no—
657C8×D5—54no—
658C8×D5—58no—
659C8×D5—54no—
660C8×D5—58no—
661C8×D5—108no—
662C8×D5—108no—
663C8×D5C22×AGL(1,𝔽5)116yescomplemented
664C22×#41—251no—
665C2×#131—52no—
666C2×#131—254no—
667C2×#131—252no—
668C2×#131—258no—
669C2×#131—258no—
670C2×#131—258no—
671C2×#131—254no—
672C2×#131—254no—
673C2×#131—258no—
674C22×M16—252no—
675C22×M16—251no—
676C22×M16—252no—
677C22×M16—251no—
678C23×C8—251no—
679C23×C8—252no—
680C23×C8—252no—
681C23×C8—251no—
682C4×#41—258no—
683C4×#41—258no—
684C2×C4×Q8—252no—
685C2×C4×D4—252no—
686C2×C4×D4—254no—
687C2×#117—252no—
688C2×#117—251no—
689C22×C42—252no—
690C22×C42—251no—
691#405—258no—
692#405—2516no—
693#405—258no—
694#405—2516no—
695C4×M16—2516no—
696C4×M16—258no—
697C2×#97—252no—
698C2×#97—252no—
699C2×#97—252no—
700C2×C4×C8—251no—
701C2×C4×C8—251no—
702C2×C4×C8—252no—
703C2×C4×C8—251no—
704C2×C4×C8—251no—
705C2×C4×C8—252no—
706C2×C4×C8—252no—
707C2×C4×C8—258no—
708C2×C4×C8—2516no—
709C2×C52—22no—
710C2×C52C4×#13112yescomplemented
711C2×C52C23×C4211yescharacteristic
712C5⋊D5—22no—
713C5⋊D5C4×#13112yescomplemented
714C5⋊D5C22×#13112yes—
715C5×D5—28no—
716C23×C5—22no—
717C23×C5—54no—
718C23×C5C2×C4×AGL(1,𝔽5)12yes—
719C22×D5—52no—
720C22×D5—52no—
721C22×D5—54no—
722C22×D5—54no—
723C22×D5—58no—
724C22×D5—58no—
725C22×D5—102no—
726C22×D5—104no—
727C22×D5—102no—
728C22×D5—104no—
729C22×D5—1016no—
730C22×D5—108no—
731C22×D5—208no—
732C22×D5C2×C4×AGL(1,𝔽5)14yes—
733C2×AGL(1,𝔽5)—516no—
734C2×AGL(1,𝔽5)—58no—
735C2×AGL(1,𝔽5)—58no—
736C2×AGL(1,𝔽5)—516no—
737C2×AGL(1,𝔽5)—1016no—
738C2×AGL(1,𝔽5)—108no—
739C2×AGL(1,𝔽5)—108no—
740C2×AGL(1,𝔽5)—1064no—
741C2×AGL(1,𝔽5)—1032no—
742C2×AGL(1,𝔽5)—108no—
743C2×AGL(1,𝔽5)—1016no—
744C2×AGL(1,𝔽5)—2032no—
745C2×AGL(1,𝔽5)—208no—
746C5×Q8—58no—
747C5×D4—516no—
748C5×D4—58no—
749C2×C4×C5—24no—
750C2×C4×C5—22no—
751C2×C4×C5—22no—
752C2×C4×C5—24no—
753C2×C4×C5—54no—
754C2×C4×C5—58no—
755C2×C4×C5—58no—
756C2×C4×C5C2×C4×AGL(1,𝔽5)12yes—
757C2×C4×C5C2×C4×AGL(1,𝔽5)14yes—
758C2×C4×C5C23×AGL(1,𝔽5)14yes—
759C2×C4×C5C23×AGL(1,𝔽5)12yes—
760C22⋊D5—516no—
761C22⋊D5—516no—
762C22⋊D5C2×C4×AGL(1,𝔽5)116yes—
763C2×Dic5—52no—
764C2×Dic5—54no—
765C2×Dic5—52no—
766C2×Dic5—54no—
767C2×Dic5—58no—
768C2×Dic5—58no—
769C2×Dic5—102no—
770C2×Dic5—104no—
771C2×Dic5—102no—
772C2×Dic5—104no—
773C2×Dic5C2×C4×AGL(1,𝔽5)14yes—
774D20—516no—
775D20C2×C4×AGL(1,𝔽5)18yes—
776C4×D5—58no—
777C4×D5—58no—
778C4×D5—54no—
779C4×D5—54no—
780C4×D5—54no—
781C4×D5—52no—
782C4×D5—54no—
783C4×D5—52no—
784C4×D5—54no—
785C4×D5—52no—
786C4×D5—54no—
787C4×D5—52no—
788C4×D5—58no—
789C4×D5—58no—
790C4×D5—104no—
791C4×D5—104no—
792C4×D5—104no—
793C4×D5—102no—
794C4×D5—104no—
795C4×D5—102no—
796C4×D5—104no—
797C4×D5—102no—
798C4×D5—104no—
799C4×D5—102no—
800C4×D5C2×C4×AGL(1,𝔽5)18yes—
801C4×D5C23×AGL(1,𝔽5)18yes—
802Dic10—516no—
803Dic10C2×C4×AGL(1,𝔽5)18yes—
804#170—516no—
805#170—58no—
806#170—58no—
807#170—1016no—
808C5×C8—28no—
809C5×C8—54no—
810C5×C8—54no—
811C5×C8C23×AGL(1,𝔽5)18yes—
812#168—58no—
813#168—108no—
814#168C23×AGL(1,𝔽5)14yes—
815#168C23×AGL(1,𝔽5)14yes—
816C2×#41—52no—
817C2×#41—252no—
818C2×#41—252no—
819C2×#41—252no—
820C2×#41—254no—
821C2×#41—254no—
822C2×#41—254no—
823C2×#41—254no—
824C22×Q8—251no—
825C22×D4—252no—
826C22×D4—251no—
827C23×C4—252no—
828C23×C4—251no—
829C23×C4—252no—
830C23×C4—254no—
831#131—516no—
832#131—2532no—
833#131—2516no—
834#131—2532no—
835#131—2532no—
836C2×M16—54no—
837C2×M16—254no—
838C2×M16—258no—
839C2×M16—258no—
840C2×M16—252no—
841C2×M16—258no—
842C2×M16—254no—
843C2×M16—254no—
844C2×M16—258no—
845C2×M16—258no—
846C2×M16—252no—
847C2×M16—251no—
848C2×M16—254no—
849C2×M16—254no—
850C2×M16—252no—
851C2×M16D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
852C22×C8—52no—
853C22×C8—54no—
854C22×C8—251no—
855C22×C8—251no—
856C22×C8—254no—
857C22×C8—258no—
858C22×C8—254no—
859C22×C8—252no—
860C22×C8—258no—
861C22×C8—254no—
862C22×C8—252no—
863C22×C8—251no—
864C22×C8—251no—
865C22×C8—254no—
866C22×C8—258no—
867C22×C8—252no—
868C22×C8—254no—
869C22×C8—258no—
870C22×C8—258no—
871C22×C8—252no—
872C22×C8—252no—
873C4×Q8—2516no—
874C4×D4—2532no—
875C4×D4—2516no—
876#117—254no—
877#117—258no—
878#117—254no—
879#117—258no—
880C2×C4⋊C4—254no—
881C2×C4⋊C4—252no—
882C2×C22⋊C4—252no—
883C2×C22⋊C4—254no—
884C2×C42—251no—
885C2×C42—252no—
886C2×C42—252no—
887C2×C42—254no—
888C2×C42—254no—
889C2×C42—254no—
890C2×C42—258no—
891C2×C42—258no—
892C2×C42—251no—
893#97—258no—
894#97—258no—
895#97—258no—
896C4×C8—254no—
897C4×C8—254no—
898C4×C8—258no—
899C4×C8—258no—
900C4×C8—258no—
901C4×C8—254no—
902C4×C8—254no—
903C52C2×C4×#13111yescharacteristic, complemented, Sylow
904C22×C5—24no—
905C22×C5—22no—
906C22×C5—24no—
907C22×C5—44no—
908C22×C5—58no—
909C22×C5—108no—
910C22×C5C22×C4×AGL(1,𝔽5)14yes—
911C22×C5C22×C4×AGL(1,𝔽5)12yes—
912C2×D5—28no—
913C2×D5—52no—
914C2×D5—52no—
915C2×D5—58no—
916C2×D5—54no—
917C2×D5—108no—
918C2×D5—102no—
919C2×D5—102no—
920C2×D5—104no—
921C2×D5—1016no—
922C2×D5—1016no—
923C2×D5—108no—
924C2×D5—108no—
925C2×D5—104no—
926C2×D5—208no—
927C2×D5—208no—
928C2×D5—204no—
929C2×D5C22×C4×AGL(1,𝔽5)18yes—
930AGL(1,𝔽5)—516no—
931AGL(1,𝔽5)—1016no—
932AGL(1,𝔽5)—108no—
933AGL(1,𝔽5)—1016no—
934AGL(1,𝔽5)—208no—
935C4×C5—22no—
936C4×C5—24no—
937C4×C5—22no—
938C4×C5—58no—
939C4×C5C22×C4×AGL(1,𝔽5)14yes—
940C4×C5C22×C4×AGL(1,𝔽5)12yes—
941C4×C5C24×AGL(1,𝔽5)12yes—
942Dic5—52no—
943Dic5—54no—
944Dic5—52no—
945Dic5—102no—
946Dic5—102no—
947Dic5—104no—
948Dic5C22×C4×AGL(1,𝔽5)18yes—
949C24—252no—
950C24—251no—
951#41—58no—
952#41—58no—
953#41—258no—
954#41—258no—
955#41—258no—
956#41—258no—
957#41—258no—
958#41—258no—
959C2×Q8—52no—
960C2×Q8—252no—
961C2×Q8—254no—
962C2×Q8—254no—
963C2×D4—54no—
964C2×D4—52no—
965C2×D4—254no—
966C2×D4—258no—
967C2×D4—254no—
968C2×D4—258no—
969C2×D4—254no—
970C2×D4—252no—
971C22×C4—54no—
972C22×C4—252no—
973C22×C4—254no—
974C22×C4—254no—
975C22×C4—254no—
976C22×C4—254no—
977C22×C4—254no—
978C22×C4—252no—
979C22×C4—251no—
980C22×C4—252no—
981C22×C4—252no—
982C22×C4—251no—
983C22×C4—251no—
984C22×C4—251no—
985C22×C4—252no—
986C22×C4—251no—
987C22×C4—252no—
988C22×C4—254no—
989C22×C4—252no—
990C22×C4—2516no—
991C22×C4—258no—
992C22×C4—5016no—
993C22×C4—508no—
994C22×C4C2×D5⋊AGL(1,𝔽5)11yescharacteristic
995M16—516no—
996M16—2516no—
997M16—258no—
998M16—2532no—
999M16—258no—
1000M16—254no—
1001M16—258no—
1002M16C2×D5⋊AGL(1,𝔽5)14yescomplemented
1003C2×C8—58no—
1004C2×C8—52no—
1005C2×C8—52no—
1006C2×C8—516no—
1007C2×C8—252no—
1008C2×C8—252no—
1009C2×C8—252no—
1010C2×C8—252no—
1011C2×C8—258no—
1012C2×C8—2516no—
1013C2×C8—252no—
1014C2×C8—252no—
1015C2×C8—254no—
1016C2×C8—252no—
1017C2×C8—252no—
1018C2×C8—252no—
1019C2×C8—254no—
1020C2×C8—252no—
1021C2×C8—254no—
1022C2×C8—258no—
1023C2×C8—2532no—
1024C2×C8—258no—
1025C2×C8—252no—
1026C2×C8—254no—
1027C2×C8—254no—
1028C2×C8C2×D5⋊AGL(1,𝔽5)12yes—
1029C4⋊C4—2516no—
1030C4⋊C4—258no—
1031C22⋊C4—258no—
1032C22⋊C4—2516no—
1033C42—252no—
1034C42—254no—
1035C42—252no—
1036C42—252no—
1037C42—254no—
1038C42—252no—
1039C42—2516no—
1040C42—258no—
1041C2×C5—24no—
1042C2×C5—24no—
1043C2×C5—22no—
1044C2×C5—44no—
1045C2×C5—108no—
1046C2×C5AGL(1,𝔽5)×#13114yescomplemented
1047C2×C5C23×C4×AGL(1,𝔽5)12yes—
1048D5—28no—
1049D5—54no—
1050D5—54no—
1051D5—104no—
1052D5—104no—
1053D5—104no—
1054D5—204no—
1055C23—54no—
1056C23—254no—
1057C23—254no—
1058C23—251no—
1059C23—252no—
1060C23—252no—
1061C23—251no—
1062C23—504no—
1063C23—508no—
1064C23C4×D5⋊AGL(1,𝔽5)11yescharacteristic
1065Q8—58no—
1066Q8—258no—
1067D4—516no—
1068D4—58no—
1069D4—2516no—
1070D4—258no—
1071C2×C4—54no—
1072C2×C4—58no—
1073C2×C4—58no—
1074C2×C4—254no—
1075C2×C4—254no—
1076C2×C4—258no—
1077C2×C4—258no—
1078C2×C4—254no—
1079C2×C4—258no—
1080C2×C4—251no—
1081C2×C4—252no—
1082C2×C4—251no—
1083C2×C4—252no—
1084C2×C4—251no—
1085C2×C4—252no—
1086C2×C4—251no—
1087C2×C4—252no—
1088C2×C4—252no—
1089C2×C4—252no—
1090C2×C4—252no—
1091C2×C4—251no—
1092C2×C4—251no—
1093C2×C4—252no—
1094C2×C4—258no—
1095C2×C4—254no—
1096C2×C4—5032no—
1097C2×C4—5016no—
1098C2×C4—508no—
1099C2×C4—504no—
1100C2×C4C4×D5⋊AGL(1,𝔽5)11yescharacteristic
1101C2×C4C4×D5⋊AGL(1,𝔽5)12yes—
1102C2×C4C22×D5⋊AGL(1,𝔽5)12yes—
1103C2×C4C22×D5⋊AGL(1,𝔽5)11yescharacteristic
1104C8—54no—
1105C8—54no—
1106C8—254no—
1107C8—254no—
1108C8—258no—
1109C8—254no—
1110C8C22×D5⋊AGL(1,𝔽5)14yes—
1111C5—22no—
1112C5C2×AGL(1,𝔽5)×#13112yescomplemented
1113C22—22no—
1114C22—58no—
1115C22—108no—
1116C22—254no—
1117C22—251no—
1118C22—251no—
1119C22—252no—
1120C22—504no—
1121C22—504no—
1122C22—508no—
1123C22—508no—
1124C22—502no—
1125C22C2×C4×D5⋊AGL(1,𝔽5)12yes—
1126C22C2×C4×D5⋊AGL(1,𝔽5)11yescharacteristic
1127C4—58no—
1128C4—258no—
1129C4—251no—
1130C4—251no—
1131C4—252no—
1132C4—508no—
1133C4—504no—
1134C4C2×C4×D5⋊AGL(1,𝔽5)11yescharacteristic
1135C4C2×C4×D5⋊AGL(1,𝔽5)12yes—
1136C4C23×D5⋊AGL(1,𝔽5)11yescharacteristic
1137C2—22no—
1138C2—108no—
1139C2—252no—
1140C2—252no—
1141C2—502no—
1142C2#7222083212yesdirect product factor
1143C2C22×C4×D5⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2×C4C22×D5⋊AGL(1,𝔽5)
commutatorC2×C52C23×C42
FrattiniC4C23×D5⋊AGL(1,𝔽5)
FittingC2×C52×M16C2×C4
socleC22×C52C22×C42
prime radicalC2×#11717471C22
cosocleC4×C5⋊D5C25
hypercenterC2×M16D5⋊AGL(1,𝔽5)
hypocenterC52C2×C4×#131
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#13103909C2semidirect
3. C22×#11716761C2semidirect
4. C2×#13103866C2semidirect
5. C2×#13103842C2semidirect
6. C2×#13104865C2semidirect
7. C2×#13103850C2semidirect
9. C2×C8×D5⋊AGL(1,𝔽5)C2semidirect
10. #72220832C2direct (N × H)
11. C2×M16×#1043C2semidirect
19. C2×#11717373C4semidirect
25. #13107550C4semidirect
27. C2×#11717360C4semidirect
32. C2×C5×#4053C4semidirect
34. C2×#11716932C4semidirect
35. #13105798C4semidirect
37. C2×#11716922C4semidirect
40. #13104865C22semidirect
43. M16×#1043C22semidirect
47. #13103909C22semidirect
53. C2×#11716761C22semidirect
54. #13103866C22semidirect
55. #13103850C22semidirect
56. #13103842C22semidirect
57. C8×D5⋊AGL(1,𝔽5)C22semidirect
75. C22×#6034C2×C4semidirect
80. C2×#87862C2×C4semidirect
81. C2×#87862C2×C4semidirect
85. C2×#87860C2×C4semidirect
91. #11717435C2×C4semidirect
93. C2×#87856C2×C4semidirect
96. C2×#87834C2×C4semidirect
97. #11717373C2×C4semidirect
98. C2×D5⋊#170C2×C4semidirect
105. #11717361C2×C4semidirect
107. #11717360C2×C4semidirect
108. D5⋊(D5⋊C8)C2×C4semidirect
113. C2×C52×M16C2×C4semidirect
114. C2×#87804C2×C4semidirect
115. M16×C5⋊D5C2×C4semidirect
117. C2×#87799C2×C4semidirect
119. C22×C5×#168C2×C4semidirect
120. C5×#4053C2×C4semidirect
121. C2×C5×#676C2×C4semidirect
122. C2×C5×C8×D5C2×C4semidirect
123. C2×#87768C2×C4semidirect
124. C2×#87767C2×C4semidirect
125. C2×#87767C2×C4semidirect
129. #11716932C2×C4semidirect
130. C2×D5×#168C2×C4semidirect
131. #11716922C2×C4semidirect
132. #11716909C2×C4semidirect
134. C8×D52C2×C4semidirect
208. C2×#6034C22×C4semidirect
214. #87862C22×C4semidirect
217. #87860C22×C4semidirect
224. #87856C22×C4semidirect
227. #87834C22×C4semidirect
228. D5⋊#170C22×C4semidirect
232. C52×M16C22×C4semidirect
234. #87804C22×C4semidirect
236. #87799C22×C4semidirect
241. C2×C5×#168C22×C4semidirect
242. C5×#676C22×C4semidirect
243. C5×C8×D5C22×C4semidirect
244. #87768C22×C4semidirect
247. #87767C22×C4semidirect
250. D5×#168C22×C4semidirect
277. C2×#4053AGL(1,𝔽5)semidirect
321. C2×#1043#131semidirect
437. C2×C5×M16C2×AGL(1,𝔽5)semidirect
445. C22×#168C2×AGL(1,𝔽5)semidirect
447. #4053C2×AGL(1,𝔽5)semidirect
459. C2×#676C2×AGL(1,𝔽5)semidirect
471. C2×C8×D5C2×AGL(1,𝔽5)semidirect
512. #1043C2×#131semidirect
632. C5×M16C22×AGL(1,𝔽5)semidirect
647. C2×#168C22×AGL(1,𝔽5)semidirect
651. #676C22×AGL(1,𝔽5)semidirect
663. C8×D5C22×AGL(1,𝔽5)semidirect
710. C2×C52C4×#131semidirect
713. C5⋊D5C4×#131semidirect
851. C2×M16D5⋊AGL(1,𝔽5)semidirect
903. C52C2×C4×#131semidirect
1002. M16C2×D5⋊AGL(1,𝔽5)semidirect
1046. C2×C5AGL(1,𝔽5)×#131semidirect
1112. C5C2×AGL(1,𝔽5)×#131semidirect
1142. C2#72220832direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#131075502
C2×#131039092
C22×#117167612
C2×#131038662
C2×#131038422
C2×#131048652
C2×#131038502
C2×#131057982
C2×C8×D5⋊AGL(1,𝔽5)2
#722208322
C2×M16×#10432
C2×#131075592
C2×AGL(1,𝔽5)×#1315