Subgroups — C₂×C₁₃×#2483 #15721085

Order 3328.

4382 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal
2	C₁₃×#2483	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#397	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#385	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#381	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#379	C₂	1	1	yes	maximal, characteristic
7	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
9	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
10	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
11	C₂²×C₁₃×C₂²⋊C₄	—	2	16	no	—
12	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
13	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
14	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
15	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	16	yes	—
16	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₁₃×#397	C₂²	1	32	yes	complemented
18	C₁₃×#385	C₂²	1	32	yes	complemented
19	C₁₃×#381	C₂²	1	32	yes	complemented
20	C₁₃×#379	C₂²	1	8	yes	—
21	C₂×C₁₃×#95	C₂²	1	4	yes	complemented
22	C₂×C₁₃×#95	C₂²	1	8	yes	complemented
23	C₂⁵×C₁₃	—	2	16	no	—
24	C₂⁵×C₁₃	—	4	4	no	—
25	C₂⁵×C₁₃	D₄	1	8	yes	—
26	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
27	C₂⁵×C₁₃	C₂³	1	4	yes	—
28	C₂⁵×C₁₃	C₂³	1	2	yes	—
29	C₂³×C₄×C₁₃	—	2	8	no	—
30	C₂³×C₄×C₁₃	—	2	8	no	—
31	C₂³×C₄×C₁₃	—	2	16	no	—
32	C₂³×C₄×C₁₃	—	4	8	no	—
33	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
34	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
35	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
36	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
37	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
38	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
39	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
40	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
41	C₂×C₁₃×C₂²⋊C₄	—	2	64	no	—
42	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
43	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
44	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
45	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
46	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
47	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
48	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
49	C₁₃×#95	C₂³	1	16	yes	complemented
50	C₁₃×#95	C₂³	1	32	yes	complemented
51	C₂×#2483	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂⁴×C₁₃	—	2	8	no	—
53	C₂⁴×C₁₃	—	2	8	no	—
54	C₂⁴×C₁₃	—	2	64	no	—
55	C₂⁴×C₁₃	—	2	32	no	—
56	C₂⁴×C₁₃	—	2	8	no	—
57	C₂⁴×C₁₃	—	2	4	no	—
58	C₂⁴×C₁₃	—	4	16	no	—
59	C₂⁴×C₁₃	—	4	8	no	—
60	C₂⁴×C₁₃	—	4	64	no	—
61	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
62	C₂⁴×C₁₃	C₂×D₄	1	16	yes	—
63	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
64	C₂⁴×C₁₃	#41	1	16	yes	—
65	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
66	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
67	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	—	2	16	no	—
69	C₂²×C₄×C₁₃	—	2	16	no	—
70	C₂²×C₄×C₁₃	—	2	8	no	—
71	C₂²×C₄×C₁₃	—	2	8	no	—
72	C₂²×C₄×C₁₃	—	2	16	no	—
73	C₂²×C₄×C₁₃	—	2	32	no	—
74	C₂²×C₄×C₁₃	—	2	16	no	—
75	C₂²×C₄×C₁₃	—	2	8	no	—
76	C₂²×C₄×C₁₃	—	2	16	no	—
77	C₂²×C₄×C₁₃	—	4	16	no	—
78	C₂²×C₄×C₁₃	—	4	32	no	—
79	C₂²×C₄×C₁₃	—	4	32	no	—
80	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
81	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
82	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
83	C₁₃×C₄⋊C₄	—	4	16	no	—
84	C₁₃×C₂²⋊C₄	—	2	32	no	—
85	C₁₃×C₂²⋊C₄	—	2	32	no	—
86	C₁₃×C₂²⋊C₄	—	2	32	no	—
87	C₁₃×C₂²⋊C₄	—	4	8	no	—
88	C₂³×C₂²⋊C₄	C₂×C₁₃	1	2	yes	—
89	#2483	C₂×C₁₃	1	16	yes	direct product factor
90	C₂×#397	C₂×C₁₃	1	4	yes	complemented
91	C₂×#385	C₂×C₁₃	1	4	yes	complemented
92	C₂×#381	C₂×C₁₃	1	4	yes	complemented
93	C₂×#379	C₂×C₁₃	1	1	yes	characteristic
94	C₂³×C₁₃	—	2	16	no	—
95	C₂³×C₁₃	—	2	16	no	—
96	C₂³×C₁₃	—	2	64	no	—
97	C₂³×C₁₃	—	2	8	no	—
98	C₂³×C₁₃	—	2	8	no	—
99	C₂³×C₁₃	—	2	64	no	—
100	C₂³×C₁₃	—	2	16	no	—
101	C₂³×C₁₃	—	2	8	no	—
102	C₂³×C₁₃	—	2	8	no	—
103	C₂³×C₁₃	—	2	4	no	—
104	C₂³×C₁₃	—	4	16	no	—
105	C₂³×C₁₃	—	4	64	no	—
106	C₂³×C₁₃	—	4	128	no	—
107	C₂³×C₁₃	—	4	16	no	—
108	C₂³×C₁₃	#123	1	32	yes	—
109	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
110	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
111	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
112	C₂³×C₁₃	C₂×#41	1	16	yes	—
113	C₂³×C₁₃	C₂×#41	1	8	yes	—
114	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
115	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
116	C₂×C₄×C₁₃	—	2	8	no	—
117	C₂×C₄×C₁₃	—	2	8	no	—
118	C₂×C₄×C₁₃	—	2	16	no	—
119	C₂×C₄×C₁₃	—	2	16	no	—
120	C₂×C₄×C₁₃	—	2	8	no	—
121	C₂×C₄×C₁₃	—	2	16	no	—
122	C₂×C₄×C₁₃	—	4	32	no	—
123	C₂×C₄×C₁₃	—	4	32	no	—
124	C₂×C₄×C₁₃	—	4	16	no	—
125	C₂×C₄×C₁₃	—	4	16	no	—
126	C₂×C₄×C₁₃	—	4	16	no	—
127	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
128	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
129	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
130	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
131	C₂²×C₂²⋊C₄	—	2	16	no	—
132	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
133	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	16	yes	—
134	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
135	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
136	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
137	#397	C₂²×C₁₃	1	32	yes	complemented
138	#385	C₂²×C₁₃	1	32	yes	complemented
139	#381	C₂²×C₁₃	1	32	yes	complemented
140	#379	C₂²×C₁₃	1	8	yes	—
141	C₂×#95	C₂²×C₁₃	1	4	yes	complemented
142	C₂×#95	C₂²×C₁₃	1	8	yes	complemented
143	C₂²×C₁₃	—	2	8	no	—
144	C₂²×C₁₃	—	2	8	no	—
145	C₂²×C₁₃	—	2	32	no	—
146	C₂²×C₁₃	—	2	64	no	—
147	C₂²×C₁₃	—	2	8	no	—
148	C₂²×C₁₃	—	2	4	no	—
149	C₂²×C₁₃	—	4	64	no	—
150	C₂²×C₁₃	—	4	8	no	—
151	C₂²×C₁₃	—	4	16	no	—
152	C₂²×C₁₃	C₂×#123	1	16	yes	—
153	C₂²×C₁₃	C₂×#123	1	8	yes	—
154	C₂²×C₁₃	#534	1	4	yes	—
155	C₂²×C₁₃	#551	1	16	yes	—
156	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
157	C₂²×C₁₃	C₂²×#41	1	4	yes	—
158	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
159	C₄×C₁₃	—	4	8	no	—
160	C₄×C₁₃	—	4	8	no	—
161	C₄×C₁₃	—	4	8	no	—
162	C₂⁵	—	2	16	no	—
163	C₂⁵	—	4	4	no	—
164	C₂⁵	D₄×C₁₃	1	8	yes	—
165	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
166	C₂⁵	C₂³×C₁₃	1	4	yes	—
167	C₂⁵	C₂³×C₁₃	1	2	yes	—
168	C₂³×C₄	—	2	8	no	—
169	C₂³×C₄	—	2	8	no	—
170	C₂³×C₄	—	2	16	no	—
171	C₂³×C₄	—	4	8	no	—
172	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
173	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
174	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
175	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
176	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
177	C₂×C₄⋊C₄	—	4	8	no	—
178	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
179	C₂×C₂²⋊C₄	—	2	16	no	—
180	C₂×C₂²⋊C₄	—	2	64	no	—
181	C₂×C₂²⋊C₄	—	2	16	no	—
182	C₂×C₂²⋊C₄	—	2	16	no	—
183	C₂×C₂²⋊C₄	—	4	4	no	—
184	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
185	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
186	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
187	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
188	#95	C₂³×C₁₃	1	16	yes	complemented
189	#95	C₂³×C₁₃	1	32	yes	complemented
190	C₂×C₁₃	—	2	16	no	—
191	C₂×C₁₃	—	4	4	no	—
192	C₂×C₁₃	#2483	1	8	yes	direct product factor
193	C₂×C₁₃	C₂²×#123	1	2	yes	—
194	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
195	C₂×C₁₃	C₂×#551	1	4	yes	—
196	C₂⁴	—	2	8	no	—
197	C₂⁴	—	2	8	no	—
198	C₂⁴	—	2	64	no	—
199	C₂⁴	—	2	32	no	—
200	C₂⁴	—	2	8	no	—
201	C₂⁴	—	2	4	no	—
202	C₂⁴	—	4	16	no	—
203	C₂⁴	—	4	8	no	—
204	C₂⁴	—	4	64	no	—
205	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
206	C₂⁴	C₂×D₄×C₁₃	1	16	yes	—
207	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
208	C₂⁴	C₁₃×#41	1	16	yes	—
209	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
210	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
211	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
212	C₂²×C₄	—	2	16	no	—
213	C₂²×C₄	—	2	16	no	—
214	C₂²×C₄	—	2	8	no	—
215	C₂²×C₄	—	2	8	no	—
216	C₂²×C₄	—	2	16	no	—
217	C₂²×C₄	—	2	32	no	—
218	C₂²×C₄	—	2	16	no	—
219	C₂²×C₄	—	2	8	no	—
220	C₂²×C₄	—	2	16	no	—
221	C₂²×C₄	—	4	16	no	—
222	C₂²×C₄	—	4	32	no	—
223	C₂²×C₄	—	4	32	no	—
224	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
225	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
226	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
227	C₄⋊C₄	—	4	16	no	—
228	C₂²⋊C₄	—	2	32	no	—
229	C₂²⋊C₄	—	2	32	no	—
230	C₂²⋊C₄	—	2	32	no	—
231	C₂²⋊C₄	—	4	8	no	—
232	C₁₃	C₂×#2483	1	1	yes	characteristic, direct product factor, Sylow
233	C₂³	—	2	16	no	—
234	C₂³	—	2	16	no	—
235	C₂³	—	2	64	no	—
236	C₂³	—	2	8	no	—
237	C₂³	—	2	8	no	—
238	C₂³	—	2	64	no	—
239	C₂³	—	2	16	no	—
240	C₂³	—	2	8	no	—
241	C₂³	—	2	8	no	—
242	C₂³	—	2	4	no	—
243	C₂³	—	4	16	no	—
244	C₂³	—	4	64	no	—
245	C₂³	—	4	128	no	—
246	C₂³	—	4	16	no	—
247	C₂³	C₁₃×#123	1	32	yes	—
248	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
249	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
250	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
251	C₂³	C₂×C₁₃×#41	1	16	yes	—
252	C₂³	C₂×C₁₃×#41	1	8	yes	—
253	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
254	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
255	C₂×C₄	—	2	8	no	—
256	C₂×C₄	—	2	8	no	—
257	C₂×C₄	—	2	16	no	—
258	C₂×C₄	—	2	16	no	—
259	C₂×C₄	—	2	8	no	—
260	C₂×C₄	—	2	16	no	—
261	C₂×C₄	—	4	32	no	—
262	C₂×C₄	—	4	32	no	—
263	C₂×C₄	—	4	16	no	—
264	C₂×C₄	—	4	16	no	—
265	C₂×C₄	—	4	16	no	—
266	C₂²	—	2	8	no	—
267	C₂²	—	2	8	no	—
268	C₂²	—	2	32	no	—
269	C₂²	—	2	64	no	—
270	C₂²	—	2	8	no	—
271	C₂²	—	2	4	no	—
272	C₂²	—	4	64	no	—
273	C₂²	—	4	8	no	—
274	C₂²	—	4	16	no	—
275	C₂²	C₂×C₁₃×#123	1	16	yes	—
276	C₂²	C₂×C₁₃×#123	1	8	yes	—
277	C₂²	C₁₃×#534	1	4	yes	—
278	C₂²	C₁₃×#551	1	16	yes	—
279	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
280	C₂²	C₂²×C₁₃×#41	1	4	yes	—
281	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
282	C₄	—	4	8	no	—
283	C₄	—	4	8	no	—
284	C₄	—	4	8	no	—
285	C₂	—	2	16	no	—
286	C₂	—	4	4	no	—
287	C₂	C₁₃×#2483	1	8	yes	direct product factor
288	C₂	C₂²×C₁₃×#123	1	2	yes	—
289	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
290	C₂	C₂×C₁₃×#551	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁶×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2483	C₂	direct (N × H)
3. C₂×C₁₃×#397	C₂	semidirect
4. C₂×C₁₃×#385	C₂	semidirect
5. C₂×C₁₃×#381	C₂	semidirect
10. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
17. C₁₃×#397	C₂²	semidirect
18. C₁₃×#385	C₂²	semidirect
19. C₁₃×#381	C₂²	semidirect
21. C₂×C₁₃×#95	C₂²	semidirect
22. C₂×C₁₃×#95	C₂²	semidirect
39. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
49. C₁₃×#95	C₂³	semidirect
50. C₁₃×#95	C₂³	semidirect
51. C₂×#2483	C₁₃	direct (N × H)
89. #2483	C₂×C₁₃	direct (N × H)
90. C₂×#397	C₂×C₁₃	semidirect
91. C₂×#385	C₂×C₁₃	semidirect
92. C₂×#381	C₂×C₁₃	semidirect
130. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
137. #397	C₂²×C₁₃	semidirect
138. #385	C₂²×C₁₃	semidirect
139. #381	C₂²×C₁₃	semidirect
141. C₂×#95	C₂²×C₁₃	semidirect
142. C₂×#95	C₂²×C₁₃	semidirect
178. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
188. #95	C₂³×C₁₃	semidirect
189. #95	C₂³×C₁₃	semidirect
192. C₂×C₁₃	#2483	direct (N × H)
232. C₁₃	C₂×#2483	direct (N × H)
287. C₂	C₁₃×#2483	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×C₂²⋊C₄	2
C₁₃×#2483	2
C₂×C₁₃×#397	2
C₂×C₁₃×#385	2
C₂×C₁₃×#381	2
C₂×C₁₃×#379	2
C₂×#2483	13

Subgroups — C2×C13×#2483 #15721085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2483 #15721085