Finite Group Databasebeta

← C2×#519×D59 #29495271

Subgroups — C2×#519×D59 #29495271

Order 15104.

11230 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q8×D59C211yesmaximal, characteristic
2C2×#16837880C211yesmaximal, characteristic, complemented
3C2×#16837879C216yesmaximal, complemented
4C2×#16837878C218yesmaximal, complemented
5#519×D59C2132yesmaximal, direct product factor
6C2×C4×Q8×D59C218yesmaximal, complemented
7C2×#117×D59C216yesmaximal
8C2×C59×#519C211yesmaximal, characteristic, complemented
9C23×Dic118C2213yes—
10C22×Q8×D59C4132yescomplemented
11C22×Q8×D59C2214yes—
12C22×Q8×D59C22116yes—
13C22×Q8×D59C2214yes—
14C23×C4×D59C2213yes—
15#16837880C22116yescomplemented
16#16837879C22196yescomplemented
17#16837878C221128yescomplemented
18C2×Q8×Dic59C2218yescomplemented
19C2×C4×Dic118C22124yescomplemented
20C2×#14273692C22124yescomplemented
21C4×Q8×D59C221128yescomplemented
22C2×#14273686C2216yes—
23C2×#14273685C22112yes—
24C2×#14273684C22112yes—
25C2×#14273683C22112yes—
26#117×D59C22196yes—
27C2×C4⋊C4×D59C22112yes—
28C2×C22⋊C4×D59C2214yes—
29C2×C42×D59C22112yes—
30C23×Q8×C59C2211yescharacteristic
31C59×#519C22116yescomplemented
32C2×C4×Q8×C59C2218yescomplemented
33C2×#117×C59C2216yes—
34C24×D59C2311yescharacteristic
35C22×Dic118C2×C4148yescomplemented
36C22×Dic118C23112yes—
37C22×Dic118C23124yes—
38C2×Q8×D59C2×C4164yes—
39C2×Q8×D59C2×C4164yescomplemented
40C2×Q8×D59C2×C41256yescomplemented
41C2×Q8×D59C23132yes—
42C2×Q8×D59C23132yes—
43C23×Dic59C2313yes—
44C22×C4×D59C2×C4148yes—
45C22×C4×D59C2318yes—
46C22×C4×D59C2316yes—
47C22×C4×D59C23124yes—
48C22×C4×D59C2316yes—
49Q8×Dic59C23164yescomplemented
50C4×Dic118C231192yescomplemented
51#14273692C231192yescomplemented
52#14273686C23148yes—
53#14273685C23196yes—
54#14273684C23196yes—
55#14273683C23196yes—
56C2×C4⋊Dic59C23112yes—
57C2×Dic59⋊C4C23124yes—
58C4⋊C4×D59C23196yes—
59C2×C22⋊Dic59C2314yes—
60C2×(C2×D59)⋊C4C2318yes—
61C22⋊C4×D59C23132yes—
62C2×C4×Dic59C23124yes—
63C2×C4×Dic59C23112yes—
64C42×D59C23196yes—
65C22×Q8×C59C2×C4116yescomplemented
66C22×Q8×C59C2314yes—
67C22×Q8×C59C2318yes—
68C23×C4×C59C2313yes—
69C4×Q8×C59C23164yescomplemented
70#117×C59C23148yes—
71C2×C4⋊C4×C59C23112yes—
72C2×C22⋊C4×C59C2314yes—
73C2×C42×C59C23112yes—
74C24×C59C2411yescharacteristic
75C23×D59—28no—
76C23×D59C22×C418yes—
77C23×D59C2414yes—
78C23×D59C2411yescharacteristic
79C23×D59C2411yescharacteristic
80C2×Q8×C59C22×C4132yes—
81C2×Q8×C59C22×C4164yescomplemented
82C2×Q8×C59C24116yes—
83C22×C4×C59C22×C4124yes—
84C22×C4×C59C2418yes—
85C22×C4×C59C2416yes—
86C22×C4×C59C24112yes—
87C22×Dic59C22×C4124yes—
88C22×Dic59C2418yes—
89C22×Dic59C2416yes—
90C22×Dic59C24112yes—
91Q8×D59C22×C41256yes—
92Q8×D59C22×C41256yescomplemented
93C2×C4×D59—232no—
94C2×C4×D59C22×C4148yes—
95C2×C4×D59C22×C41192yes—
96C2×C4×D59C22×C4148yes—
97C2×C4×D59C24132yes—
98C2×C4×D59C24124yes—
99C2×C4×D59C24124yes—
100C2×Dic118C22×C4196yes—
101C2×Dic118C22×C41192yescomplemented
102C2×Dic118C24148yes—
103C4⋊C4×C59C24148yes—
104C22⋊C4×C59C24116yes—
105C42×C59C24148yes—
106C22⋊Dic59C24116yes—
107(C2×D59)⋊C4C24132yes—
108C4⋊Dic59C24148yes—
109Dic59⋊C4C24196yes—
110C4×Dic59C24196yes—
111C4×Dic59C24148yes—
112C23×C59—24no—
113C23×C59C23×C414yes—
114C23×C59C2512yes—
115C23×C59C2511yescharacteristic
116C22×D59—24no—
117C22×D59—232no—
118C22×D59—216no—
119C22×D59C23×C414yes—
120C22×D59C23×C4116yes—
121C22×D59C23×C414yes—
122C22×D592−1+418yes—
123C22×D59C2512yes—
124C22×D59C2512yes—
125Q8×C59C23×C4164yes—
126C2×C4×C59—216no—
127C2×C4×C59C23×C4124yes—
128C2×C4×C59C23×C4148yes—
129C2×C4×C59C25116yes—
130C2×C4×C59C25112yes—
131C2×Dic59—216no—
132C2×Dic59C23×C4124yes—
133C2×Dic59C23×C4148yes—
134C2×Dic59C25116yes—
135C2×Dic59C25112yes—
136C4×D59—264no—
137C4×D59C23×C4196yes—
138C4×D59C23×C4196yes—
139Dic118C23×C41192yes—
140C22×#519—591nomaximal, Sylow
141C22×C59—24no—
142C22×C59—28no—
143C22×C59C24×C414yes—
144C22×C59C24×C412yes—
145C22×C59C2×2−1+414yes—
146C22×C59C2611yescharacteristic
147C2×D59—24no—
148C2×D59—28no—
149C2×D59—232no—
150C2×D59#519116yesdirect product factor
151C2×D59C24×C414yes—
152C2×D59C24×C414yes—
153C2×D59C2×2−1+418yes—
154C4×C59—216no—
155C4×C59C24×C4124yes—
156Dic59—216no—
157Dic59C24×C4124yes—
158C24×Q8—591no—
159C2×#519—591no—
160C2×#519—5932no—
161C2×#519—598no—
162C2×#519—596no—
163C2×#519D5911yescharacteristic, direct product factor
164C22×C4×Q8—598no—
165C22×#117—596no—
166C2×C59—24no—
167C2×C59C2×#51914yescomplemented
168C2×C59C25×C411yescharacteristic
169C2×C59C22×2−1+412yes—
170D59—24no—
171D59C2×#51918yesdirect product factor
172C23×Q8—5932no—
173C23×Q8—594no—
174C23×Q8—594no—
175C23×Q8—5916no—
176C23×Q8—593no—
177C23×Q8C2×D5911yescharacteristic
178C24×C4—593no—
179#519—5916no—
180#519—59128no—
181#519—5996no—
182#519C2×D59116yesdirect product factor
183C2×C4×Q8—598no—
184C2×C4×Q8—59128no—
185C2×C4×Q8—5924no—
186C2×C4×Q8—5924no—
187C2×C4×Q8C2×D5918yescomplemented
188C2×#117—596no—
189C2×#117—5996no—
190C2×#117—5912no—
191C2×#117—5912no—
192C2×#117—5912no—
193C2×#117C2×D5916yes—
194C22×C4⋊C4—5912no—
195C22×C22⋊C4—594no—
196C22×C42—5912no—
197C59C22×#51911yescharacteristic, complemented, Sylow
198C25—591no—
199C22×Q8—5964no—
200C22×Q8—5964no—
201C22×Q8—59256no—
202C22×Q8—5932no—
203C22×Q8—5932no—
204C22×Q8—5948no—
205C22×Q8—5912no—
206C22×Q8—5924no—
207C22×Q8C4×D59116yescomplemented
208C22×Q8C22×D5914yes—
209C22×Q8C22×D5918yes—
210C23×C4—593no—
211C23×C4—5948no—
212C23×C4—596no—
213C23×C4—5924no—
214C23×C4—596no—
215C23×C4—598no—
216C23×C4C22×D5913yes—
217C4×Q8—5964no—
218C4×Q8—59192no—
219C4×Q8—59192no—
220C4×Q8C22×D59164yescomplemented
221#117—5948no—
222#117—5996no—
223#117—5996no—
224#117—5996no—
225#117C22×D59148yes—
226C2×C4⋊C4—5924no—
227C2×C4⋊C4—5912no—
228C2×C4⋊C4—5996no—
229C2×C4⋊C4C22×D59112yes—
230C2×C22⋊C4—594no—
231C2×C22⋊C4—598no—
232C2×C22⋊C4—5932no—
233C2×C22⋊C4C22×D5914yes—
234C2×C42—5924no—
235C2×C42—5912no—
236C2×C42—5996no—
237C2×C42C22×D59112yes—
238C24—591no—
239C24—598no—
240C24—594no—
241C24—591no—
242C24—1188no—
243C24C23×D5911yescharacteristic
244C2×Q8—59256no—
245C2×Q8—59256no—
246C2×Q8—5996no—
247C2×Q8—59192no—
248C2×Q8—5948no—
249C2×Q8C2×C4×D59132yes—
250C2×Q8C2×C4×D59164yescomplemented
251C2×Q8C23×D59116yes—
252C22×C4—5924no—
253C22×C4—5912no—
254C22×C4—596no—
255C22×C4—5948no—
256C22×C4—5948no—
257C22×C4—59192no—
258C22×C4—5924no—
259C22×C4—5924no—
260C22×C4—598no—
261C22×C4—5932no—
262C22×C4—11832no—
263C22×C4C2×C4×D59124yes—
264C22×C4C23×D5918yes—
265C22×C4C23×D59112yes—
266C22×C4C23×D5916yes—
267C4⋊C4—5996no—
268C4⋊C4—5948no—
269C4⋊C4C23×D59148yes—
270C22⋊C4—5916no—
271C22⋊C4—5932no—
272C22⋊C4C23×D59116yes—
273C42—5996no—
274C42—5948no—
275C42C23×D59148yes—
276C23—24no—
277C23—594no—
278C23—598no—
279C23—592no—
280C23—5916no—
281C23—594no—
282C23—592no—
283C23—11832no—
284C23—11816no—
285C23—1184no—
286C23C22×C4×D5914yes—
287C23C24×D5912yes—
288C23C24×D5911yescharacteristic
289Q8—59192no—
290Q8C22×C4×D59164yes—
291C2×C4—216no—
292C2×C4—5948no—
293C2×C4—5924no—
294C2×C4—5912no—
295C2×C4—5996no—
296C2×C4—5996no—
297C2×C4—5916no—
298C2×C4—11864no—
299C2×C4—11816no—
300C2×C4C22×C4×D59124yes—
301C2×C4C22×C4×D59148yes—
302C2×C4C24×D59116yes—
303C2×C4C24×D59112yes—
304C22—28no—
305C22—24no—
306C22—5916no—
307C22—594no—
308C22—598no—
309C22—594no—
310C22—11832no—
311C22—1188no—
312C22—1184no—
313C22C23×C4×D5914yes—
314C22C23×C4×D5912yes—
315C222−1+4×D5914yes—
316C22C25×D5911yescharacteristic
317C4—216no—
318C4—5924no—
319C4—11816no—
320C4C23×C4×D59124yes—
321C2—24no—
322C2—598no—
323C2—1184no—
324C2#519×D5914yesdirect product factor
325C2C24×C4×D5911yescharacteristic
326C2C2×2−1+4×D5912yes—
subgroupG/H
centerC23C24×D59
commutatorC2×C59C25×C4
FrattiniC22C25×D59
FittingC2×C59×#519C2
socleC23×C59C25
prime radicalC24×D59C23
cosocleC22×C59C26
hypercenterC2×#519D59
hypocenterC59C22×#519
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. C2×#16837880C2semidirect
3. C2×#16837879C2semidirect
4. C2×#16837878C2semidirect
5. #519×D59C2direct (N × H)
6. C2×C4×Q8×D59C2semidirect
8. C2×C59×#519C2semidirect
10. C22×Q8×D59C4semidirect
15. #16837880C22semidirect
16. #16837879C22semidirect
17. #16837878C22semidirect
18. C2×Q8×Dic59C22semidirect
19. C2×C4×Dic118C22semidirect
20. C2×#14273692C22semidirect
21. C4×Q8×D59C22semidirect
31. C59×#519C22semidirect
32. C2×C4×Q8×C59C22semidirect
35. C22×Dic118C2×C4semidirect
39. C2×Q8×D59C2×C4semidirect
40. C2×Q8×D59C2×C4semidirect
49. Q8×Dic59C23semidirect
50. C4×Dic118C23semidirect
51. #14273692C23semidirect
65. C22×Q8×C59C2×C4semidirect
69. C4×Q8×C59C23semidirect
81. C2×Q8×C59C22×C4semidirect
92. Q8×D59C22×C4semidirect
101. C2×Dic118C22×C4semidirect
150. C2×D59#519direct (N × H)
163. C2×#519D59direct (N × H)
167. C2×C59C2×#519semidirect
171. D59C2×#519direct (N × H)
182. #519C2×D59direct (N × H)
187. C2×C4×Q8C2×D59semidirect
197. C59C22×#519semidirect
207. C22×Q8C4×D59semidirect
220. C4×Q8C22×D59semidirect
250. C2×Q8C2×C4×D59semidirect
324. C2#519×D59direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q8×D592
C2×#168378802
C2×#168378792
C2×#168378782
#519×D592
C2×C4×Q8×D592
C2×#117×D592
C2×C59×#5192
C22×#51959