Finite Group Databasebeta

← C59×#19300 #28431409

Subgroups — C59×#19300 #28431409

Order 15104.

648 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#487C211yesmaximal, characteristic, complemented
2C59×#3079C211yesmaximal, characteristic
3C59×#3039C211yesmaximal, characteristic
4C59×#2965C211yesmaximal, characteristic
5C59×#1700C214yesmaximal, complemented
6C59×#1699C214yesmaximal, complemented
7C59×#1567C211yesmaximal, characteristic, complemented
8C59×#1549C211yesmaximal, characteristic, complemented
9C59×#1546C211yesmaximal, characteristic, complemented
10C2×#137×C59—21no—
11C2×C4⋊Q8×C59C2211yescharacteristic
12C2×C4⋊Q8×C59C2211yescharacteristic
13C4×#41×C59C2211yescharacteristic
14C59×#487—21no—
15C59×#487—21no—
16C59×#487C2214yes—
17C59×#477—21no—
18C59×#476—21no—
19C59×#475C2212yes—
20C59×#474C2212yes—
21C59×#462—21no—
22C59×#462C2212yes—
23C59×#461—21no—
24C59×#461C2212yes—
25C59×#446C2212yes—
26C59×#436C2212yes—
27C59×#435—22no—
28C59×#431—21no—
29C59×#431C2211yescharacteristic
30C59×#428—21no—
31C59×#423C2211yescharacteristic
32C59×#423C2211yescharacteristic
33C59×#419—21no—
34C59×#417—21no—
35C2×#103×C59—22no—
36C4×M16×C59—21no—
37C2×C4×C8×C59C2211yescharacteristic
38C59×#335C2214yes—
39C59×#332C2214yes—
40C59×#332C2214yes—
41C2×#41×C59D411yescharacteristic
42C22×Q8×C59—21no—
43C22×Q8×C59—21no—
44#137×C59—44no—
45C2×Q16×C59—22no—
46C2×SD16×C59—22no—
47C2×M16×C59—21no—
48C2×M16×C59—21no—
49C2×M16×C59—22no—
50C22×C8×C59D412yes—
51C4⋊Q8×C59—21no—
52C4⋊Q8×C59—21no—
53C4⋊Q8×C59—21no—
54C4⋊Q8×C59—21no—
55C4⋊Q8×C59—21no—
56C4⋊Q8×C59—21no—
57C4⋊Q8×C59C2312yes—
58C4⋊Q8×C59C2312yes—
59C4×Q8×C59D411yescharacteristic
60C4×Q8×C59C2311yescharacteristic
61C4×D4×C59—21no—
62C4×D4×C59—21no—
63C4×D4×C59D411yescharacteristic
64C4×D4×C59C2311yescharacteristic
65#117×C59—21no—
66#117×C59D411yescharacteristic
67C2×C4⋊C4×C59—21no—
68C2×C4⋊C4×C59—21no—
69C2×C4⋊C4×C59—21no—
70C2×C4⋊C4×C59—21no—
71C2×C42×C59—21no—
72C2×C42×C59C2311yescharacteristic
73#107×C59—22no—
74#106×C59—22no—
75C4⋊C8×C59—22no—
76C4⋊C8×C59—21no—
77C4⋊C8×C59—21no—
78C4⋊C8×C59C2312yes—
79C4⋊C8×C59C2312yes—
80C4⋊C8×C59C2312yes—
81#103×C59—22no—
82#103×C59—24no—
83#103×C59—24no—
84#103×C59—22no—
85#103×C59—22no—
86#102×C59—22no—
87C22⋊C8×C59—21no—
88C22⋊C8×C59—22no—
89#97×C59—22no—
90C4×C8×C59—21no—
91C4×C8×C59D411yescharacteristic
92C4×C8×C59D411yescharacteristic
93C4×C8×C59C2312yes—
94#41×C59—22no—
95#41×C59—22no—
96C2×Q8×C59—22no—
97C2×Q8×C59—22no—
98C2×Q8×C59—44no—
99C2×Q8×C59—41no—
100C2×Q8×C59—41no—
101C2×Q8×C59—42no—
102C2×Q8×C59—42no—
103C2×Q8×C59C2×D411yescharacteristic
104C2×D4×C59—21no—
105C2×D4×C59C2×D411yescharacteristic
106C22×C4×C59—21no—
107C22×C4×C59—21no—
108C22×C4×C59—21no—
109C22×C4×C59—41no—
110C22×C4×C59—41no—
111C22×C4×C59C2×D411yescharacteristic
112C22×C4×C59C2×D411yescharacteristic
113C22×C4×C59#4111yescharacteristic
114Q16×C59—44no—
115SD16×C59—44no—
116M16×C59—44no—
117M16×C59—42no—
118M16×C59—42no—
119C2×C8×C59—22no—
120C2×C8×C59—22no—
121C2×C8×C59—22no—
122C2×C8×C59—42no—
123C2×C8×C59C2×D412yes—
124C2×C8×C59C2×D412yes—
125C4⋊C4×C59—21no—
126C4⋊C4×C59—21no—
127C4⋊C4×C59—22no—
128C4⋊C4×C59—22no—
129C4⋊C4×C59—22no—
130C4⋊C4×C59—22no—
131C4⋊C4×C59—41no—
132C4⋊C4×C59—41no—
133C4⋊C4×C59—41no—
134C4⋊C4×C59—41no—
135C4⋊C4×C59C2×D411yescharacteristic
136C4⋊C4×C59C2×D411yescharacteristic
137C22⋊C4×C59—21no—
138C22⋊C4×C59—21no—
139C22⋊C4×C59—21no—
140C42×C59—21no—
141C42×C59—21no—
142C42×C59—21no—
143C42×C59C2×D411yescharacteristic
144C42×C59C2×D411yescharacteristic
145C42×C59#4111yescharacteristic
146C42×C59C2411yescharacteristic
147C23×C59—21no—
148C23×C59#12111yescharacteristic
149Q8×C59—21no—
150Q8×C59—21no—
151Q8×C59—42no—
152Q8×C59—42no—
153Q8×C59—44no—
154Q8×C59—82no—
155Q8×C59—82no—
156D4×C59—21no—
157D4×C59—21no—
158D4×C59—42no—
159C2×C4×C59—22no—
160C2×C4×C59—22no—
161C2×C4×C59—21no—
162C2×C4×C59—21no—
163C2×C4×C59—21no—
164C2×C4×C59—42no—
165C2×C4×C59—42no—
166C2×C4×C59—42no—
167C2×C4×C59—42no—
168C2×C4×C59—42no—
169C2×C4×C59—82no—
170C2×C4×C59—82no—
171C2×C4×C59#12111yescharacteristic
172C2×C4×C59#12111yescharacteristic
173C2×C4×C59#12111yescharacteristic
174C2×C4×C59AGL(1,ℤ/8)12yes—
175C2×C4×C59#13712yes—
176C2×C4×C59C22×D411yescharacteristic
177C2×C4×C59C22×D411yescharacteristic
178C2×C4×C59C2×#4111yescharacteristic
179C8×C59—22no—
180C8×C59—22no—
181C8×C59—42no—
182C8×C59—42no—
183C8×C59—42no—
184#19300C5911yesmaximal, characteristic, direct product factor, Sylow
185C22×C59—21no—
186C22×C59—21no—
187C22×C59—41no—
188C22×C59—41no—
189C22×C59—41no—
190C22×C59#46812yes—
191C22×C59C2×#12111yescharacteristic
192C4×C59—21no—
193C4×C59—21no—
194C4×C59—41no—
195C4×C59—41no—
196C4×C59—41no—
197C4×C59—82no—
198C4×C59—82no—
199C4×C59#46812yes—
200C4×C59#47312yes—
201C4×C59C2×AGL(1,ℤ/8)11yescharacteristic
202C4×C59C2×#13711yescharacteristic
203C4×C59#57512yes—
204C2×#487C2×C5911yescharacteristic, complemented
205#3079C2×C5911yescharacteristic
206#3039C2×C5911yescharacteristic
207#2965C2×C5911yescharacteristic
208#1700C2×C5914yescomplemented
209#1699C2×C5914yescomplemented
210#1567C2×C5911yescharacteristic, complemented
211#1549C2×C5911yescharacteristic, complemented
212#1546C2×C5911yescharacteristic, complemented
213C2×C59—22no—
214C2×C59—81no—
215C2×C59#304011yescharacteristic
216C2×C59C2×#46811yescharacteristic
217C2×C59C2×#47311yescharacteristic
218C2×#137—21no—
219C2×C4⋊Q8C22×C5911yescharacteristic
220C2×C4⋊Q8C22×C5911yescharacteristic
221C4×#41C22×C5911yescharacteristic
222#487—21no—
223#487—21no—
224#487C22×C5914yes—
225#477—21no—
226#476—21no—
227#475C22×C5912yes—
228#474C22×C5912yes—
229#462—21no—
230#462C22×C5912yes—
231#461—21no—
232#461C22×C5912yes—
233#446C22×C5912yes—
234#436C22×C5912yes—
235#435—22no—
236#431—21no—
237#431C22×C5911yescharacteristic
238#428—21no—
239#423C22×C5911yescharacteristic
240#423C22×C5911yescharacteristic
241#419—21no—
242#417—21no—
243C2×#103—22no—
244C4×M16—21no—
245C2×C4×C8C22×C5911yescharacteristic
246#335C22×C5914yes—
247#332C22×C5914yes—
248#332C22×C5914yes—
249C59#1930011yescharacteristic, direct product factor, Sylow
250C2×#41D4×C5911yescharacteristic
251C22×Q8—21no—
252C22×Q8—21no—
253#137—44no—
254C2×Q16—22no—
255C2×SD16—22no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—22no—
259C22×C8D4×C5912yes—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8C23×C5912yes—
267C4⋊Q8C23×C5912yes—
268C4×Q8D4×C5911yescharacteristic
269C4×Q8C23×C5911yescharacteristic
270C4×D4—21no—
271C4×D4—21no—
272C4×D4D4×C5911yescharacteristic
273C4×D4C23×C5911yescharacteristic
274#117—21no—
275#117D4×C5911yescharacteristic
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C42—21no—
281C2×C42C23×C5911yescharacteristic
282#107—22no—
283#106—22no—
284C4⋊C8—22no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8C23×C5912yes—
288C4⋊C8C23×C5912yes—
289C4⋊C8C23×C5912yes—
290#103—22no—
291#103—24no—
292#103—24no—
293#103—22no—
294#103—22no—
295#102—22no—
296C22⋊C8—21no—
297C22⋊C8—22no—
298#97—22no—
299C4×C8—21no—
300C4×C8D4×C5911yescharacteristic
301C4×C8D4×C5911yescharacteristic
302C4×C8C23×C5912yes—
303#41—22no—
304#41—22no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—44no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—42no—
311C2×Q8—42no—
312C2×Q8C2×D4×C5911yescharacteristic
313C2×D4—21no—
314C2×D4C2×D4×C5911yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C2×D4×C5911yescharacteristic
321C22×C4C2×D4×C5911yescharacteristic
322C22×C4#41×C5911yescharacteristic
323Q16—44no—
324SD16—44no—
325M16—44no—
326M16—42no—
327M16—42no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—42no—
332C2×C8C2×D4×C5912yes—
333C2×C8C2×D4×C5912yes—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4C2×D4×C5911yescharacteristic
345C4⋊C4C2×D4×C5911yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C42—21no—
350C42—21no—
351C42—21no—
352C42C2×D4×C5911yescharacteristic
353C42C2×D4×C5911yescharacteristic
354C42#41×C5911yescharacteristic
355C42C24×C5911yescharacteristic
356C23—21no—
357C23#121×C5911yescharacteristic
358Q8—21no—
359Q8—21no—
360Q8—42no—
361Q8—42no—
362Q8—44no—
363Q8—82no—
364Q8—82no—
365D4—21no—
366D4—21no—
367D4—42no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4#121×C5911yescharacteristic
381C2×C4#121×C5911yescharacteristic
382C2×C4#121×C5911yescharacteristic
383C2×C4AGL(1,ℤ/8)×C5912yes—
384C2×C4#137×C5912yes—
385C2×C4C22×D4×C5911yescharacteristic
386C2×C4C22×D4×C5911yescharacteristic
387C2×C4C2×#41×C5911yescharacteristic
388C8—22no—
389C8—22no—
390C8—42no—
391C8—42no—
392C8—42no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22C59×#46812yes—
399C22C2×#121×C5911yescharacteristic
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—82no—
406C4—82no—
407C4C59×#46812yes—
408C4C59×#47312yes—
409C4C2×AGL(1,ℤ/8)×C5911yescharacteristic
410C4C2×#137×C5911yescharacteristic
411C4C59×#57512yes—
412C2—22no—
413C2—81no—
414C2C59×#304011yescharacteristic
415C2C2×C59×#46811yescharacteristic
416C2C2×C59×#47311yescharacteristic
subgroupG/H
center, socleC22×C59C2×#121
commutator, Frattini, cosocleC42C24×C59
prime radicalC2×#41×C59D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C59×#487C2semidirect
5. C59×#1700C2semidirect
6. C59×#1699C2semidirect
7. C59×#1567C2semidirect
8. C59×#1549C2semidirect
9. C59×#1546C2semidirect
184. #19300C59direct (N × H)
204. C2×#487C2×C59semidirect
208. #1700C2×C59semidirect
209. #1699C2×C59semidirect
210. #1567C2×C59semidirect
211. #1549C2×C59semidirect
212. #1546C2×C59semidirect
249. C59#19300direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#4872
C59×#30792
C59×#30392
C59×#29652
C59×#17002
C59×#16992
C59×#15672
C59×#15492
C59×#15462
#1930059