Finite Group Databasebeta

← C59×#10001 #28422110

Subgroups — C59×#10001 #28422110

Order 15104.

568 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3101C211yesmaximal, characteristic
2C59×#3078C211yesmaximal, characteristic, complemented
3C59×#2536C211yesmaximal, characteristic
4C59×#1518C211yesmaximal, characteristic, complemented
5C59×#1486C211yesmaximal, characteristic
6C59×#1479C211yesmaximal, characteristic, complemented
7C59×#1286C211yesmaximal, characteristic, complemented
8C59×#533C2211yescharacteristic
9C2×C22⋊Q8×C59—21no—
10C2×C4×Q8×C59C2211yescharacteristic
11C2×C4×D4×C59C2211yescharacteristic
12C59×#483—21no—
13C59×#479—22no—
14C59×#477—21no—
15C59×#476—21no—
16C59×#475—21no—
17C59×#461—21no—
18C59×#450—21no—
19C4×SD16×C59—22no—
20C59×#431C2211yescharacteristic
21C59×#431C2211yescharacteristic
22C59×#428—21no—
23C59×#423C2211yescharacteristic
24C59×#419—21no—
25C59×#398—21no—
26C59×#394—21no—
27C59×#388—22no—
28C59×#382C2211yescharacteristic
29C59×#380—21no—
30C59×#328—22no—
31C59×Q8⋊C8—22no—
32C59×D4⋊C8—22no—
33C22×Q8×C59D411yescharacteristic
34C22×D4×C59D411yescharacteristic
35C23×C4×C59—21no—
36C2×SD16×C59—22no—
37C2×M16×C59—21no—
38C4⋊Q8×C59D411yescharacteristic
39C4⋊Q8×C59D411yescharacteristic
40#125×C59—21no—
41C22⋊Q8×C59—21no—
42C22⋊Q8×C59—21no—
43C22⋊Q8×C59—42no—
44C22⋊Q8×C59—42no—
45C4×Q8×C59—21no—
46C4×Q8×C59—21no—
47C4×Q8×C59—21no—
48C4×Q8×C59—21no—
49C4×Q8×C59—21no—
50C4×Q8×C59—21no—
51C4×D4×C59—21no—
52C4×D4×C59—21no—
53C4×D4×C59—21no—
54C4×D4×C59—21no—
55#117×C59—21no—
56C2×C4⋊C4×C59—22no—
57C2×C4⋊C4×C59—21no—
58C2×C4⋊C4×C59—21no—
59C2×C4⋊C4×C59D411yescharacteristic
60C2×C4⋊C4×C59D411yescharacteristic
61C2×C22⋊C4×C59—22no—
62C2×C22⋊C4×C59—22no—
63C2×C22⋊C4×C59—21no—
64C2×C42×C59—21no—
65C2×C42×C59C2311yescharacteristic
66#107×C59—22no—
67#106×C59—22no—
68#106×C59—22no—
69C4⋊C8×C59—21no—
70C4⋊C8×C59—21no—
71C4⋊C8×C59—21no—
72C4⋊C8×C59D412yes—
73#103×C59—22no—
74#103×C59—22no—
75#103×C59—22no—
76#102×C59—22no—
77C22⋊C8×C59—21no—
78C22⋊C8×C59—21no—
79C4×C8×C59—21no—
80C4×C8×C59D412yes—
81#95×C59—22no—
82#95×C59—21no—
83#95×C59D412yes—
84C24×C59—21no—
85C2×Q8×C59—21no—
86C2×Q8×C59—21no—
87C2×Q8×C59—21no—
88C2×Q8×C59—21no—
89C2×Q8×C59—21no—
90C2×Q8×C59—21no—
91C2×Q8×C59—21no—
92C2×Q8×C59SD1612yescomplemented
93C2×D4×C59—21no—
94C2×D4×C59—21no—
95C2×D4×C59—42no—
96C22×C4×C59—21no—
97C22×C4×C59—22no—
98C22×C4×C59—21no—
99C22×C4×C59—21no—
100C22×C4×C59—41no—
101C22×C4×C59—41no—
102C22×C4×C59—41no—
103C22×C4×C59—41no—
104C22×C4×C59—41no—
105C22×C4×C59—41no—
106C22×C4×C59C2×D411yescharacteristic
107C22×C4×C59C2×D411yescharacteristic
108C22×C4×C59C2×D411yescharacteristic
109SD16×C59—44no—
110M16×C59—41no—
111M16×C59—41no—
112C2×C8×C59—22no—
113C2×C8×C59—22no—
114C2×C8×C59—41no—
115C4⋊C4×C59—21no—
116C4⋊C4×C59—21no—
117C4⋊C4×C59—21no—
118C4⋊C4×C59—21no—
119C4⋊C4×C59—21no—
120C4⋊C4×C59—21no—
121C4⋊C4×C59—21no—
122C4⋊C4×C59—21no—
123C4⋊C4×C59—44no—
124C4⋊C4×C59—41no—
125C4⋊C4×C59—41no—
126C4⋊C4×C59—41no—
127C4⋊C4×C59—41no—
128C4⋊C4×C59—41no—
129C4⋊C4×C59—41no—
130C22⋊C4×C59—44no—
131C22⋊C4×C59—44no—
132C22⋊C4×C59—41no—
133C22⋊C4×C59—41no—
134C22⋊C4×C59—41no—
135C42×C59—41no—
136C42×C59—41no—
137C42×C59—41no—
138C42×C59C2×D411yescharacteristic
139C42×C59C2×D411yescharacteristic
140C42×C59C2×D411yescharacteristic
141C42×C59#4111yescharacteristic
142C23×C59—22no—
143C23×C59—41no—
144C23×C59—41no—
145C23×C59—41no—
146C23×C59—41no—
147C23×C59—41no—
148C23×C59—41no—
149C23×C59#12011yescharacteristic
150Q8×C59—22no—
151Q8×C59—22no—
152Q8×C59—42no—
153Q8×C59—41no—
154Q8×C59—41no—
155Q8×C59—81no—
156D4×C59—22no—
157D4×C59—22no—
158D4×C59—41no—
159D4×C59—41no—
160C2×C4×C59—22no—
161C2×C4×C59—41no—
162C2×C4×C59—41no—
163C2×C4×C59—41no—
164C2×C4×C59—41no—
165C2×C4×C59—42no—
166C2×C4×C59—42no—
167C2×C4×C59—42no—
168C2×C4×C59—41no—
169C2×C4×C59—41no—
170C2×C4×C59—41no—
171C2×C4×C59—41no—
172C2×C4×C59—42no—
173C2×C4×C59—41no—
174C2×C4×C59—41no—
175C2×C4×C59—81no—
176C2×C4×C59—81no—
177C2×C4×C59—81no—
178C2×C4×C59—81no—
179C2×C4×C59#12011yescharacteristic
180C2×C4×C59#12011yescharacteristic
181C2×C4×C59#12111yescharacteristic
182C2×C4×C59#12111yescharacteristic
183C2×C4×C59#12111yescharacteristic
184C2×C4×C59#12711yescharacteristic
185C2×C4×C59C2×SD1611yescharacteristic
186C2×C4×C59#13511yescharacteristic
187C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C59#13711yescharacteristic
189C8×C59—42no—
190C8×C59—42no—
191C8×C59—81no—
192#10001C5911yesmaximal, characteristic, direct product factor, Sylow
193C22×C59—21no—
194C22×C59—21no—
195C22×C59—42no—
196C22×C59—42no—
197C22×C59—42no—
198C22×C59—81no—
199C22×C59—81no—
200C22×C59—81no—
201C22×C59—81no—
202C22×C59#39211yescharacteristic
203C22×C59#45011yescharacteristic
204C22×C59#45211yescharacteristic
205C4×C59—21no—
206C4×C59—21no—
207C4×C59—21no—
208C4×C59—21no—
209C4×C59—42no—
210C4×C59—82no—
211C4×C59—81no—
212C4×C59—81no—
213C4×C59—81no—
214C4×C59—81no—
215C4×C59#44811yescharacteristic
216C4×C59#44911yescharacteristic
217C4×C59#46511yescharacteristic
218C4×C59#46811yescharacteristic
219#3101C2×C5911yescharacteristic
220#3078C2×C5911yescharacteristic, complemented
221#2536C2×C5911yescharacteristic
222#1518C2×C5911yescharacteristic, complemented
223#1486C2×C5911yescharacteristic
224#1479C2×C5911yescharacteristic, complemented
225#1286C2×C5911yescharacteristic, complemented
226C2×C59—21no—
227C2×C59—21no—
228C2×C59—82no—
229C2×C59#200011yescharacteristic
230C2×C59#200911yescharacteristic
231C2×C59#201011yescharacteristic
232#533C22×C5911yescharacteristic
233C2×C22⋊Q8—21no—
234C2×C4×Q8C22×C5911yescharacteristic
235C2×C4×D4C22×C5911yescharacteristic
236#483—21no—
237#479—22no—
238#477—21no—
239#476—21no—
240#475—21no—
241#461—21no—
242#450—21no—
243C4×SD16—22no—
244#431C22×C5911yescharacteristic
245#431C22×C5911yescharacteristic
246#428—21no—
247#423C22×C5911yescharacteristic
248#419—21no—
249#398—21no—
250#394—21no—
251#388—22no—
252#382C22×C5911yescharacteristic
253#380—21no—
254#328—22no—
255Q8⋊C8—22no—
256D4⋊C8—22no—
257C59#1000111yescharacteristic, direct product factor, Sylow
258C22×Q8D4×C5911yescharacteristic
259C22×D4D4×C5911yescharacteristic
260C23×C4—21no—
261C2×SD16—22no—
262C2×M16—21no—
263C4⋊Q8D4×C5911yescharacteristic
264C4⋊Q8D4×C5911yescharacteristic
265#125—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8—42no—
269C22⋊Q8—42no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280#117—21no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4D4×C5911yescharacteristic
285C2×C4⋊C4D4×C5911yescharacteristic
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C42—21no—
290C2×C42C23×C5911yescharacteristic
291#107—22no—
292#106—22no—
293#106—22no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—21no—
297C4⋊C8D4×C5912yes—
298#103—22no—
299#103—22no—
300#103—22no—
301#102—22no—
302C22⋊C8—21no—
303C22⋊C8—21no—
304C4×C8—21no—
305C4×C8D4×C5912yes—
306#95—22no—
307#95—21no—
308#95D4×C5912yes—
309C24—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8SD16×C5912yescomplemented
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—42no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4C2×D4×C5911yescharacteristic
332C22×C4C2×D4×C5911yescharacteristic
333C22×C4C2×D4×C5911yescharacteristic
334SD16—44no—
335M16—41no—
336M16—41no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—41no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—44no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C22⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C42—41no—
361C42—41no—
362C42—41no—
363C42C2×D4×C5911yescharacteristic
364C42C2×D4×C5911yescharacteristic
365C42C2×D4×C5911yescharacteristic
366C42#41×C5911yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23#120×C5911yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—42no—
378Q8—41no—
379Q8—41no—
380Q8—81no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4#120×C5911yescharacteristic
405C2×C4#120×C5911yescharacteristic
406C2×C4#121×C5911yescharacteristic
407C2×C4#121×C5911yescharacteristic
408C2×C4#121×C5911yescharacteristic
409C2×C4#127×C5911yescharacteristic
410C2×C4C2×SD16×C5911yescharacteristic
411C2×C4#135×C5911yescharacteristic
412C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
413C2×C4#137×C5911yescharacteristic
414C8—42no—
415C8—42no—
416C8—81no—
417C22—21no—
418C22—21no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22C59×#39211yescharacteristic
427C22C59×#45011yescharacteristic
428C22C59×#45211yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—82no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4C59×#44811yescharacteristic
440C4C59×#44911yescharacteristic
441C4C59×#46511yescharacteristic
442C4C59×#46811yescharacteristic
443C2—21no—
444C2—21no—
445C2—82no—
446C2C59×#200011yescharacteristic
447C2C59×#200911yescharacteristic
448C2C59×#201011yescharacteristic
subgroupG/H
center, socleC22×C59#392
commutator, Frattini, cosocleC2×C42C23×C59
prime radicalC22×D4×C59D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#3078C2semidirect
4. C59×#1518C2semidirect
6. C59×#1479C2semidirect
7. C59×#1286C2semidirect
92. C2×Q8×C59SD16semidirect
192. #10001C59direct (N × H)
220. #3078C2×C59semidirect
222. #1518C2×C59semidirect
224. #1479C2×C59semidirect
225. #1286C2×C59semidirect
257. C59#10001direct (N × H)
317. C2×Q8SD16×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#31012
C59×#30782
C59×#25362
C59×#15182
C59×#14862
C59×#14792
C59×#12862
#1000159