Subgroups — C₁₃×#2691 #13111749

Order 1664.

554 conjugacy classes of subgroups.

The subgroup lattice has 438 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×#121	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#396	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×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×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	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#126	—	2	4	no	—
22	C₁₃×#121	—	2	4	no	—
23	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊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
44	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#95	C₂²	1	1	yes	characteristic
46	C₁₃×#95	C₂²	1	1	yes	characteristic
47	C₁₃×#95	C₂²	1	1	yes	characteristic
48	C₁₃×#95	C₂²	1	1	yes	characteristic
49	C₁₃×#95	C₂²	1	1	yes	characteristic
50	C₁₃×#95	C₂²	1	1	yes	characteristic
51	C₁₃×#95	C₂²	1	1	yes	characteristic
52	C₁₃×#95	C₂²	1	1	yes	characteristic
53	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
54	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
55	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×D₄×C₁₃	—	2	2	no	—
57	C₂×D₄×C₁₃	—	2	2	no	—
58	C₂×D₄×C₁₃	—	2	2	no	—
59	C₂×D₄×C₁₃	—	2	2	no	—
60	C₂×D₄×C₁₃	—	2	2	no	—
61	C₂×D₄×C₁₃	—	2	2	no	—
62	C₂×D₄×C₁₃	—	4	1	no	—
63	C₂×D₄×C₁₃	—	4	1	no	—
64	C₂×D₄×C₁₃	—	4	1	no	—
65	C₂²×C₄×C₁₃	—	2	2	no	—
66	C₂²×C₄×C₁₃	—	2	2	no	—
67	C₂²×C₄×C₁₃	—	4	1	no	—
68	C₂²×C₄×C₁₃	—	4	1	no	—
69	C₂²×C₄×C₁₃	—	4	1	no	—
70	C₂²×C₄×C₁₃	—	4	1	no	—
71	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×C₄⋊C₄	—	2	2	no	—
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	—	2	2	no	—
88	C₁₃×C₄⋊C₄	—	4	1	no	—
89	C₁₃×C₄⋊C₄	—	4	1	no	—
90	C₁₃×C₄⋊C₄	—	4	1	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	—	4	1	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	D₄	1	4	yes	—
104	C₄²×C₁₃	—	2	2	no	—
105	#2691	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₁₃	—	2	1	no	—
107	C₂³×C₁₃	—	2	1	no	—
108	C₂³×C₁₃	—	2	1	no	—
109	C₂³×C₁₃	—	2	1	no	—
110	C₂³×C₁₃	—	2	1	no	—
111	C₂³×C₁₃	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
126	C₂³×C₁₃	#41	1	2	yes	—
127	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
128	D₄×C₁₃	—	4	4	no	—
129	D₄×C₁₃	—	4	4	no	—
130	D₄×C₁₃	—	4	4	no	—
131	C₂×C₄×C₁₃	—	2	1	no	—
132	C₂×C₄×C₁₃	—	2	1	no	—
133	C₂×C₄×C₁₃	—	2	1	no	—
134	C₂×C₄×C₁₃	—	2	1	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	1	no	—
137	C₂×C₄×C₁₃	—	2	1	no	—
138	C₂×C₄×C₁₃	—	2	1	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	1	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	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	—	4	4	no	—
165	C₂×C₄×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
167	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂×C₄×C₁₃	#41	1	2	yes	—
169	C₂×#126	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂×#121	C₂×C₁₃	1	1	yes	characteristic
171	#398	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#397	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#396	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#394	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#394	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#394	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#390	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#387	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#386	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#386	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#385	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#385	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#380	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂²×C₁₃	—	2	2	no	—
185	C₂²×C₁₃	—	2	2	no	—
186	C₂²×C₁₃	—	2	2	no	—
187	C₂²×C₁₃	—	2	2	no	—
188	C₂²×C₁₃	—	2	2	no	—
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	4	1	no	—
191	C₂²×C₁₃	—	4	1	no	—
192	C₂²×C₁₃	—	4	1	no	—
193	C₂²×C₁₃	—	4	1	no	—
194	C₂²×C₁₃	—	4	1	no	—
195	C₂²×C₁₃	—	4	1	no	—
196	C₂²×C₁₃	—	4	1	no	—
197	C₂²×C₁₃	—	4	1	no	—
198	C₂²×C₁₃	—	4	1	no	—
199	C₂²×C₁₃	—	4	1	no	—
200	C₂²×C₁₃	—	4	1	no	—
201	C₂²×C₁₃	—	4	1	no	—
202	C₂²×C₁₃	—	4	1	no	—
203	C₂²×C₁₃	—	4	1	no	—
204	C₂²×C₁₃	—	4	1	no	—
205	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
207	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
212	C₄×C₁₃	—	2	2	no	—
213	C₄×C₁₃	—	2	2	no	—
214	C₄×C₁₃	—	2	2	no	—
215	C₄×C₁₃	—	4	1	no	—
216	C₄×C₁₃	—	4	1	no	—
217	C₄×C₁₃	—	4	1	no	—
218	C₄×C₁₃	—	4	1	no	—
219	C₄×C₁₃	—	4	1	no	—
220	C₄×C₁₃	—	4	1	no	—
221	C₄×C₁₃	—	4	1	no	—
222	C₄×C₁₃	—	4	1	no	—
223	C₄×C₁₃	—	4	1	no	—
224	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
225	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
226	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
227	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
228	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
229	#126	—	2	4	no	—
230	#121	—	2	4	no	—
231	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
253	#95	C₂²×C₁₃	1	1	yes	characteristic
254	#95	C₂²×C₁₃	1	1	yes	characteristic
255	#95	C₂²×C₁₃	1	1	yes	characteristic
256	#95	C₂²×C₁₃	1	1	yes	characteristic
257	#95	C₂²×C₁₃	1	1	yes	characteristic
258	#95	C₂²×C₁₃	1	1	yes	characteristic
259	#95	C₂²×C₁₃	1	1	yes	characteristic
260	#95	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₁₃	—	4	2	no	—
262	C₂×C₁₃	—	4	2	no	—
263	C₂×C₁₃	—	8	1	no	—
264	C₂×C₁₃	#537	1	1	yes	characteristic
265	C₂×C₁₃	#539	1	1	yes	characteristic
266	C₂×C₁₃	#542	1	1	yes	characteristic
267	C₂×C₁₃	#546	1	1	yes	characteristic
268	C₂×C₁₃	#546	1	1	yes	characteristic
269	C₂×C₁₃	#553	1	1	yes	characteristic
270	C₂×C₁₃	#560	1	1	yes	characteristic
271	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
272	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
273	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	1	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	4	1	no	—
314	C₂²⋊C₄	—	4	1	no	—
315	C₂²⋊C₄	—	4	1	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	D₄×C₁₃	1	4	yes	—
322	C₄²	—	2	2	no	—
323	C₁₃	#2691	1	1	yes	characteristic, direct product factor, Sylow
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	C₂×D₄×C₁₃	1	2	yes	—
344	C₂³	C₁₃×#41	1	2	yes	—
345	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
346	D₄	—	4	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	4	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
385	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
386	C₂×C₄	C₁₃×#41	1	2	yes	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
409	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
410	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
411	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
412	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂²	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₂	—	4	2	no	—
428	C₂	—	4	2	no	—
429	C₂	—	8	1	no	—
430	C₂	C₁₃×#537	1	1	yes	characteristic
431	C₂	C₁₃×#539	1	1	yes	characteristic
432	C₂	C₁₃×#542	1	1	yes	characteristic
433	C₂	C₁₃×#546	1	1	yes	characteristic
434	C₂	C₁₃×#546	1	1	yes	characteristic
435	C₂	C₁₃×#553	1	1	yes	characteristic
436	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×#121	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×#398	C₂	semidirect
4. C₁₃×#397	C₂	semidirect
5. C₁₃×#396	C₂	semidirect
6. C₁₃×#394	C₂	semidirect
7. C₁₃×#394	C₂	semidirect
8. C₁₃×#394	C₂	semidirect
9. C₁₃×#390	C₂	semidirect
10. C₁₃×#387	C₂	semidirect
11. C₁₃×#386	C₂	semidirect
12. C₁₃×#386	C₂	semidirect
13. C₁₃×#385	C₂	semidirect
14. C₁₃×#385	C₂	semidirect
15. C₁₃×#380	C₂	semidirect
105. #2691	C₁₃	direct (N × H)
169. C₂×#126	C₂×C₁₃	semidirect
171. #398	C₂×C₁₃	semidirect
172. #397	C₂×C₁₃	semidirect
173. #396	C₂×C₁₃	semidirect
174. #394	C₂×C₁₃	semidirect
175. #394	C₂×C₁₃	semidirect
176. #394	C₂×C₁₃	semidirect
177. #390	C₂×C₁₃	semidirect
178. #387	C₂×C₁₃	semidirect
179. #386	C₂×C₁₃	semidirect
180. #386	C₂×C₁₃	semidirect
181. #385	C₂×C₁₃	semidirect
182. #385	C₂×C₁₃	semidirect
183. #380	C₂×C₁₃	semidirect
323. C₁₃	#2691	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×#121	2
C₁₃×#398	2
C₁₃×#397	2
C₁₃×#396	2
C₁₃×#394	2
C₁₃×#390	2
C₁₃×#387	2
C₁₃×#386	2
C₁₃×#385	2
C₁₃×#380	2
#2691	13

Subgroups — C13×#2691 #13111749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2691 #13111749