Subgroups — C₁₃×#2685 #13111743

Order 1664.

666 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#120	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁵×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#126	—	2	4	no	—
21	C₁₃×#120	—	2	4	no	—
22	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#95	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#95	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#95	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#95	C₂²	1	1	yes	characteristic, complemented
53	C₂⁴×C₁₃	—	2	2	no	—
54	C₂⁴×C₁₃	—	2	2	no	—
55	C₂⁴×C₁₃	—	2	2	no	—
56	C₂⁴×C₁₃	—	4	1	no	—
57	C₂⁴×C₁₃	—	4	1	no	—
58	C₂⁴×C₁₃	—	4	1	no	—
59	C₂⁴×C₁₃	—	4	1	no	—
60	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
61	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
62	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
63	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₁₃	—	2	2	no	—
65	C₂×D₄×C₁₃	—	2	2	no	—
66	C₂×D₄×C₁₃	—	2	2	no	—
67	C₂×D₄×C₁₃	—	2	2	no	—
68	C₂×D₄×C₁₃	—	2	2	no	—
69	C₂×D₄×C₁₃	—	4	1	no	—
70	C₂×D₄×C₁₃	—	4	1	no	—
71	C₂×D₄×C₁₃	—	4	1	no	—
72	C₂×D₄×C₁₃	—	4	1	no	—
73	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₁₃×C₄⋊C₄	—	2	2	no	—
86	C₁₃×C₄⋊C₄	—	2	2	no	—
87	C₁₃×C₄⋊C₄	—	4	1	no	—
88	C₁₃×C₄⋊C₄	—	4	1	no	—
89	C₁₃×C₄⋊C₄	—	4	1	no	—
90	C₁₃×C₂²⋊C₄	—	2	2	no	—
91	C₁₃×C₂²⋊C₄	—	2	2	no	—
92	C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₁₃×C₂²⋊C₄	—	4	1	no	—
97	C₁₃×C₂²⋊C₄	—	4	1	no	—
98	C₁₃×C₂²⋊C₄	—	4	1	no	—
99	C₁₃×C₂²⋊C₄	—	4	1	no	—
100	C₁₃×C₂²⋊C₄	—	4	1	no	—
101	C₁₃×C₂²⋊C₄	—	4	1	no	—
102	C₁₃×C₂²⋊C₄	—	4	1	no	—
103	C₁₃×C₂²⋊C₄	—	4	1	no	—
104	C₁₃×C₂²⋊C₄	—	4	1	no	—
105	C₁₃×C₂²⋊C₄	—	4	1	no	—
106	C₁₃×C₂²⋊C₄	—	4	1	no	—
107	C₁₃×C₂²⋊C₄	—	4	1	no	—
108	C₁₃×C₂²⋊C₄	D₄	1	4	yes	—
109	C₄²×C₁₃	—	2	2	no	—
110	C₄²×C₁₃	—	4	1	no	—
111	#2685	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₁₃	—	2	1	no	—
113	C₂³×C₁₃	—	2	1	no	—
114	C₂³×C₁₃	—	2	1	no	—
115	C₂³×C₁₃	—	2	1	no	—
116	C₂³×C₁₃	—	2	1	no	—
117	C₂³×C₁₃	—	2	1	no	—
118	C₂³×C₁₃	—	2	1	no	—
119	C₂³×C₁₃	—	2	1	no	—
120	C₂³×C₁₃	—	2	1	no	—
121	C₂³×C₁₃	—	2	1	no	—
122	C₂³×C₁₃	—	2	1	no	—
123	C₂³×C₁₃	—	2	1	no	—
124	C₂³×C₁₃	—	2	1	no	—
125	C₂³×C₁₃	—	2	1	no	—
126	C₂³×C₁₃	—	2	1	no	—
127	C₂³×C₁₃	—	2	1	no	—
128	C₂³×C₁₃	—	2	1	no	—
129	C₂³×C₁₃	—	2	1	no	—
130	C₂³×C₁₃	—	2	1	no	—
131	C₂³×C₁₃	—	2	1	no	—
132	C₂³×C₁₃	—	2	1	no	—
133	C₂³×C₁₃	—	2	1	no	—
134	C₂³×C₁₃	—	2	1	no	—
135	C₂³×C₁₃	—	2	1	no	—
136	C₂³×C₁₃	—	2	1	no	—
137	C₂³×C₁₃	—	4	4	no	—
138	C₂³×C₁₃	—	4	4	no	—
139	C₂³×C₁₃	—	4	4	no	—
140	C₂³×C₁₃	—	4	4	no	—
141	C₂³×C₁₃	—	4	4	no	—
142	C₂³×C₁₃	—	4	4	no	—
143	C₂³×C₁₃	—	4	4	no	—
144	C₂³×C₁₃	C₂×D₄	1	2	yes	—
145	C₂³×C₁₃	#41	1	2	yes	—
146	C₂³×C₁₃	#41	1	2	yes	—
147	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
148	D₄×C₁₃	—	4	4	no	—
149	D₄×C₁₃	—	4	4	no	—
150	D₄×C₁₃	—	4	4	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
184	C₂×#126	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#120	C₂×C₁₃	1	1	yes	characteristic
186	#399	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#396	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#394	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#394	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#394	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#394	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#390	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#390	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#388	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#388	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#388	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#379	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#379	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	2	2	no	—
201	C₂²×C₁₃	—	2	2	no	—
202	C₂²×C₁₃	—	2	2	no	—
203	C₂²×C₁₃	—	2	2	no	—
204	C₂²×C₁₃	—	2	2	no	—
205	C₂²×C₁₃	—	2	2	no	—
206	C₂²×C₁₃	—	2	2	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	4	16	no	—
209	C₂²×C₁₃	—	4	1	no	—
210	C₂²×C₁₃	—	4	1	no	—
211	C₂²×C₁₃	—	4	1	no	—
212	C₂²×C₁₃	—	4	1	no	—
213	C₂²×C₁₃	—	4	1	no	—
214	C₂²×C₁₃	—	4	1	no	—
215	C₂²×C₁₃	—	4	1	no	—
216	C₂²×C₁₃	—	4	1	no	—
217	C₂²×C₁₃	—	4	1	no	—
218	C₂²×C₁₃	—	4	1	no	—
219	C₂²×C₁₃	—	4	1	no	—
220	C₂²×C₁₃	—	4	1	no	—
221	C₂²×C₁₃	—	4	1	no	—
222	C₂²×C₁₃	—	4	1	no	—
223	C₂²×C₁₃	—	4	1	no	—
224	C₂²×C₁₃	—	4	1	no	—
225	C₂²×C₁₃	—	4	1	no	—
226	C₂²×C₁₃	—	4	1	no	—
227	C₂²×C₁₃	—	4	1	no	—
228	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
230	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
231	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	2	2	no	—
237	C₄×C₁₃	—	4	1	no	—
238	C₄×C₁₃	—	4	1	no	—
239	C₄×C₁₃	—	4	1	no	—
240	C₄×C₁₃	—	4	1	no	—
241	C₄×C₁₃	—	4	1	no	—
242	C₄×C₁₃	—	4	1	no	—
243	C₄×C₁₃	—	4	1	no	—
244	C₄×C₁₃	—	4	1	no	—
245	C₄×C₁₃	—	4	1	no	—
246	C₂⁵	C₂²×C₁₃	1	1	yes	characteristic
247	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
248	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
249	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
250	#126	—	2	4	no	—
251	#120	—	2	4	no	—
252	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
253	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
254	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
255	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
256	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
257	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
258	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
274	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
275	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
276	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
277	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
278	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
279	#95	C₂²×C₁₃	1	1	yes	characteristic, complemented
280	#95	C₂²×C₁₃	1	1	yes	characteristic, complemented
281	#95	C₂²×C₁₃	1	1	yes	characteristic, complemented
282	#95	C₂²×C₁₃	1	1	yes	characteristic, complemented
283	C₂×C₁₃	—	4	2	no	—
284	C₂×C₁₃	—	4	2	no	—
285	C₂×C₁₃	—	4	2	no	—
286	C₂×C₁₃	—	8	1	no	—
287	C₂×C₁₃	#535	1	1	yes	characteristic
288	C₂×C₁₃	#538	1	1	yes	characteristic
289	C₂×C₁₃	#538	1	1	yes	characteristic
290	C₂×C₁₃	#546	1	1	yes	characteristic
291	C₂×C₁₃	#546	1	1	yes	characteristic
292	C₂×C₁₃	#551	1	1	yes	characteristic
293	C₂×C₁₃	#560	1	1	yes	characteristic
294	C₂⁴	—	2	2	no	—
295	C₂⁴	—	2	2	no	—
296	C₂⁴	—	2	2	no	—
297	C₂⁴	—	4	1	no	—
298	C₂⁴	—	4	1	no	—
299	C₂⁴	—	4	1	no	—
300	C₂⁴	—	4	1	no	—
301	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
302	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
303	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
304	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
316	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
320	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
321	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	D₄×C₁₃	1	4	yes	—
350	C₄²	—	2	2	no	—
351	C₄²	—	4	1	no	—
352	C₁₃	#2685	1	1	yes	characteristic, direct product factor, Sylow
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	4	4	no	—
379	C₂³	—	4	4	no	—
380	C₂³	—	4	4	no	—
381	C₂³	—	4	4	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	4	4	no	—
384	C₂³	—	4	4	no	—
385	C₂³	C₂×D₄×C₁₃	1	2	yes	—
386	C₂³	C₁₃×#41	1	2	yes	—
387	C₂³	C₁₃×#41	1	2	yes	—
388	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
389	D₄	—	4	4	no	—
390	D₄	—	4	4	no	—
391	D₄	—	4	4	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
424	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	16	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
455	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
456	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
457	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	1	no	—
471	C₄	—	4	1	no	—
472	C₂	—	4	2	no	—
473	C₂	—	4	2	no	—
474	C₂	—	4	2	no	—
475	C₂	—	8	1	no	—
476	C₂	C₁₃×#535	1	1	yes	characteristic
477	C₂	C₁₃×#538	1	1	yes	characteristic
478	C₂	C₁₃×#538	1	1	yes	characteristic
479	C₂	C₁₃×#546	1	1	yes	characteristic
480	C₂	C₁₃×#546	1	1	yes	characteristic
481	C₂	C₁₃×#551	1	1	yes	characteristic
482	C₂	C₁₃×#560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#120	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#126	C₂	semidirect
3. C₁₃×#399	C₂	semidirect
4. C₁₃×#396	C₂	semidirect
5. C₁₃×#394	C₂	semidirect
6. C₁₃×#394	C₂	semidirect
7. C₁₃×#394	C₂	semidirect
8. C₁₃×#394	C₂	semidirect
9. C₁₃×#390	C₂	semidirect
10. C₁₃×#390	C₂	semidirect
11. C₁₃×#388	C₂	semidirect
12. C₁₃×#388	C₂	semidirect
13. C₁₃×#388	C₂	semidirect
14. C₁₃×#379	C₂	semidirect
15. C₁₃×#379	C₂	semidirect
22. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
23. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
24. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
25. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
26. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
27. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
43. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
44. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
45. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
46. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
47. C₂×C₄²×C₁₃	C₂²	semidirect
48. C₂×C₄²×C₁₃	C₂²	semidirect
49. C₁₃×#95	C₂²	semidirect
50. C₁₃×#95	C₂²	semidirect
51. C₁₃×#95	C₂²	semidirect
52. C₁₃×#95	C₂²	semidirect
111. #2685	C₁₃	direct (N × H)
184. C₂×#126	C₂×C₁₃	semidirect
186. #399	C₂×C₁₃	semidirect
187. #396	C₂×C₁₃	semidirect
188. #394	C₂×C₁₃	semidirect
189. #394	C₂×C₁₃	semidirect
190. #394	C₂×C₁₃	semidirect
191. #394	C₂×C₁₃	semidirect
192. #390	C₂×C₁₃	semidirect
193. #390	C₂×C₁₃	semidirect
194. #388	C₂×C₁₃	semidirect
195. #388	C₂×C₁₃	semidirect
196. #388	C₂×C₁₃	semidirect
197. #379	C₂×C₁₃	semidirect
198. #379	C₂×C₁₃	semidirect
252. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
253. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
254. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
255. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
256. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
257. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
273. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
274. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
275. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
276. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
277. C₂×C₄²	C₂²×C₁₃	semidirect
278. C₂×C₄²	C₂²×C₁₃	semidirect
279. #95	C₂²×C₁₃	semidirect
280. #95	C₂²×C₁₃	semidirect
281. #95	C₂²×C₁₃	semidirect
282. #95	C₂²×C₁₃	semidirect
352. C₁₃	#2685	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#126	2
C₂×C₁₃×#120	2
C₁₃×#399	2
C₁₃×#396	2
C₁₃×#394	2
C₁₃×#390	2
C₁₃×#388	2
C₁₃×#379	2
#2685	13

Subgroups — C13×#2685 #13111743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2685 #13111743