Subgroups — C₁₃×#21682 #15708021

Order 3328.

1230 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#435	C₂	1	4	yes	maximal, complemented
3	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1955	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1842	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
11	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
12	C₂×C₁₃×#127	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#436	—	2	4	no	—
17	C₁₃×#435	—	2	16	no	—
18	C₈×D₄×C₁₃	—	2	4	no	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
24	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×#97	C₂²	1	2	yes	—
27	C₂×C₁₃×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#390	C₄	1	1	yes	characteristic
31	C₁₃×#390	C₄	1	1	yes	characteristic
32	C₁₃×#390	C₄	1	4	yes	—
33	C₁₃×#384	C₄	1	1	yes	characteristic
34	C₄³×C₁₃	C₂²	1	1	yes	characteristic
35	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₃	C₂×C₄	1	4	yes	—
37	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
40	C₂×C₁₃×M₁₆	—	2	8	no	—
41	C₂×C₁₃×M₁₆	—	2	4	no	—
42	C₂²×C₈×C₁₃	—	2	4	no	—
43	C₂²×C₈×C₁₃	—	2	8	no	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×#127	—	2	4	no	—
50	C₄×D₄×C₁₃	—	2	2	no	—
51	C₄×D₄×C₁₃	—	2	8	no	—
52	C₄×D₄×C₁₃	—	2	2	no	—
53	C₄×D₄×C₁₃	—	2	2	no	—
54	C₄×D₄×C₁₃	—	2	2	no	—
55	C₄×D₄×C₁₃	—	2	8	no	—
56	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
60	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
68	C₁₃×C₄⋊C₈	—	2	2	no	—
69	C₁₃×C₄⋊C₈	—	2	8	no	—
70	C₁₃×C₄⋊C₈	—	2	2	no	—
71	C₁₃×C₂²⋊C₈	—	2	4	no	—
72	C₁₃×C₂²⋊C₈	—	2	8	no	—
73	C₁₃×C₂²⋊C₈	—	2	8	no	—
74	C₁₃×C₂²⋊C₈	—	2	4	no	—
75	C₁₃×#97	—	2	4	no	—
76	C₁₃×#97	D₄	1	8	yes	complemented
77	C₄×C₈×C₁₃	—	2	2	no	—
78	C₄×C₈×C₁₃	D₄	1	4	yes	complemented
79	#21682	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
81	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
82	C₂×D₄×C₁₃	—	2	8	no	—
83	C₂×D₄×C₁₃	—	2	2	no	—
84	C₂×D₄×C₁₃	—	2	8	no	—
85	C₂×D₄×C₁₃	—	2	2	no	—
86	C₂×D₄×C₁₃	—	2	2	no	—
87	C₂×D₄×C₁₃	—	2	2	no	—
88	C₂×D₄×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	4	4	no	—
90	C₂×D₄×C₁₃	M₁₆	1	4	yes	complemented
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₃	—	2	4	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
106	C₁₃×M₁₆	—	4	8	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	4	no	—
112	C₂×C₈×C₁₃	—	2	4	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	4	8	no	—
115	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
117	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
119	C₁₃×C₄⋊C₄	—	2	8	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₂²⋊C₄	—	2	4	no	—
123	C₁₃×C₂²⋊C₄	—	2	8	no	—
124	C₁₃×C₂²⋊C₄	—	2	8	no	—
125	C₁₃×C₂²⋊C₄	—	2	4	no	—
126	C₄²×C₁₃	—	2	2	no	—
127	C₄²×C₁₃	—	2	2	no	—
128	C₄²×C₁₃	—	4	2	no	—
129	C₄²×C₁₃	C₂×D₄	1	2	yes	—
130	C₄²×C₁₃	C₂×D₄	1	4	yes	—
131	C₄²×C₁₃	#41	1	2	yes	—
132	C₄²×C₁₃	#41	1	4	yes	—
133	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
134	C₂×#435	C₂×C₁₃	1	4	yes	complemented
135	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
136	C₄×#127	C₂×C₁₃	1	1	yes	characteristic
137	#1955	C₂×C₁₃	1	4	yes	complemented
138	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#1842	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₄×#97	C₂×C₁₃	1	1	yes	characteristic, complemented
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	—	2	4	no	—
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	—	2	4	no	—
146	C₂³×C₁₃	—	2	2	no	—
147	C₂³×C₁₃	—	2	4	no	—
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	—	2	2	no	—
150	C₂³×C₁₃	—	2	4	no	—
151	C₂³×C₁₃	C₂×M₁₆	1	4	yes	—
152	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
153	D₄×C₁₃	—	2	8	no	—
154	D₄×C₁₃	—	4	16	no	—
155	D₄×C₁₃	—	4	4	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	4	no	—
169	C₂×C₄×C₁₃	—	4	4	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
173	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
174	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
176	C₂×C₄×C₁₃	#131	1	2	yes	—
177	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
179	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
181	C₈×C₁₃	—	2	4	no	—
182	C₈×C₁₃	—	2	2	no	—
183	C₈×C₁₃	—	4	2	no	—
184	C₈×C₁₃	—	4	2	no	—
185	C₈×C₁₃	#127	1	4	yes	complemented
186	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
187	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
188	C₂×#127	C₄×C₁₃	1	1	yes	characteristic
189	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
191	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
192	#436	—	2	4	no	—
193	#435	—	2	16	no	—
194	C₈×D₄	—	2	4	no	—
195	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
197	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
199	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
200	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
201	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
202	C₂×#97	C₂²×C₁₃	1	2	yes	—
203	C₂×#97	C₂²×C₁₃	1	2	yes	—
204	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
206	#390	C₄×C₁₃	1	1	yes	characteristic
207	#390	C₄×C₁₃	1	1	yes	characteristic
208	#390	C₄×C₁₃	1	4	yes	—
209	#384	C₄×C₁₃	1	1	yes	characteristic
210	C₄³	C₂²×C₁₃	1	1	yes	characteristic
211	C₂²×C₁₃	—	2	4	no	—
212	C₂²×C₁₃	—	2	8	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	—	4	4	no	—
216	C₂²×C₁₃	—	4	2	no	—
217	C₂²×C₁₃	—	4	2	no	—
218	C₂²×C₁₃	—	4	2	no	—
219	C₂²×C₁₃	—	4	4	no	—
220	C₂²×C₁₃	—	4	4	no	—
221	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
222	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
223	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
224	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
225	C₂²×C₁₃	#568	1	2	yes	—
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	—	2	4	no	—
228	C₄×C₁₃	—	2	4	no	—
229	C₄×C₁₃	—	4	2	no	—
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	#435	1	4	yes	complemented
232	C₄×C₁₃	C₂×#127	1	1	yes	characteristic
233	C₄×C₁₃	#532	1	2	yes	—
234	C₄×C₁₃	#532	1	1	yes	characteristic
235	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
236	C₂²×D₄	C₂×C₄×C₁₃	1	4	yes	—
237	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
239	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
240	C₂×M₁₆	—	2	8	no	—
241	C₂×M₁₆	—	2	4	no	—
242	C₂²×C₈	—	2	4	no	—
243	C₂²×C₈	—	2	8	no	—
244	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
245	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
246	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
247	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
249	#127	—	2	4	no	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	—	2	8	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	—	2	8	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
260	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
263	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
264	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
265	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
266	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	8	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₂²⋊C₈	—	2	4	no	—
272	C₂²⋊C₈	—	2	8	no	—
273	C₂²⋊C₈	—	2	8	no	—
274	C₂²⋊C₈	—	2	4	no	—
275	#97	—	2	4	no	—
276	#97	D₄×C₁₃	1	8	yes	complemented
277	C₄×C₈	—	2	2	no	—
278	C₄×C₈	D₄×C₁₃	1	4	yes	complemented
279	C₂×C₁₃	—	4	4	no	—
280	C₂×C₁₃	—	8	2	no	—
281	C₂×C₁₃	C₄×#127	1	1	yes	characteristic
282	C₂×C₁₃	C₂×#435	1	1	yes	characteristic
283	C₂×C₁₃	#2932	1	1	yes	characteristic
284	C₂×C₁₃	D₄×M₁₆	1	2	yes	—
285	C₂×C₁₃	#2935	1	2	yes	—
286	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
287	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
288	C₂×D₄	—	2	8	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	4	no	—
296	C₂×D₄	C₁₃×M₁₆	1	4	yes	complemented
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
308	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
312	M₁₆	—	4	8	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	4	8	no	—
321	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
322	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
323	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
324	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	4	2	no	—
335	C₄²	C₂×D₄×C₁₃	1	2	yes	—
336	C₄²	C₂×D₄×C₁₃	1	4	yes	—
337	C₄²	C₁₃×#41	1	2	yes	—
338	C₄²	C₁₃×#41	1	4	yes	—
339	C₁₃	#21682	1	1	yes	characteristic, direct product factor, Sylow
340	C₂³	—	2	2	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	4	no	—
349	C₂³	C₂×C₁₃×M₁₆	1	4	yes	—
350	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
351	D₄	—	2	8	no	—
352	D₄	—	4	16	no	—
353	D₄	—	4	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
370	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
371	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
372	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
373	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
374	C₂×C₄	C₁₃×#131	1	2	yes	—
375	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
376	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
377	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
378	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
379	C₈	—	2	4	no	—
380	C₈	—	2	2	no	—
381	C₈	—	4	2	no	—
382	C₈	—	4	2	no	—
383	C₈	C₁₃×#127	1	4	yes	complemented
384	C₂²	—	2	4	no	—
385	C₂²	—	2	8	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
395	C₂²	C₂×C₄×D₄×C₁₃	1	2	yes	—
396	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
397	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
398	C₂²	C₁₃×#568	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	2	4	no	—
401	C₄	—	2	4	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	C₁₃×#435	1	4	yes	complemented
405	C₄	C₂×C₁₃×#127	1	1	yes	characteristic
406	C₄	C₁₃×#532	1	2	yes	—
407	C₄	C₁₃×#532	1	1	yes	characteristic
408	C₂	—	4	4	no	—
409	C₂	—	8	2	no	—
410	C₂	C₄×C₁₃×#127	1	1	yes	characteristic
411	C₂	C₂×C₁₃×#435	1	1	yes	characteristic
412	C₂	C₁₃×#2932	1	1	yes	characteristic
413	C₂	D₄×C₁₃×M₁₆	1	2	yes	—
414	C₂	C₁₃×#2935	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂×C₁₃×#127	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#436	C₂	semidirect
2. C₂×C₁₃×#435	C₂	semidirect
3. C₂×C₈×D₄×C₁₃	C₂	semidirect
5. C₁₃×#1955	C₂	semidirect
6. C₁₃×#1954	C₂	semidirect
7. C₁₃×#1954	C₂	semidirect
8. C₁₃×#1842	C₂	semidirect
9. C₄×C₁₃×#97	C₂	semidirect
76. C₁₃×#97	D₄	semidirect
78. C₄×C₈×C₁₃	D₄	semidirect
79. #21682	C₁₃	direct (N × H)
90. C₂×D₄×C₁₃	M₁₆	semidirect
133. C₂×#436	C₂×C₁₃	semidirect
134. C₂×#435	C₂×C₁₃	semidirect
135. C₂×C₈×D₄	C₂×C₁₃	semidirect
137. #1955	C₂×C₁₃	semidirect
138. #1954	C₂×C₁₃	semidirect
139. #1954	C₂×C₁₃	semidirect
140. #1842	C₂×C₁₃	semidirect
141. C₄×#97	C₂×C₁₃	semidirect
185. C₈×C₁₃	#127	semidirect
231. C₄×C₁₃	#435	semidirect
276. #97	D₄×C₁₃	semidirect
278. C₄×C₈	D₄×C₁₃	semidirect
296. C₂×D₄	C₁₃×M₁₆	semidirect
339. C₁₃	#21682	direct (N × H)
383. C₈	C₁₃×#127	semidirect
404. C₄	C₁₃×#435	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#436	2
C₂×C₁₃×#435	2
C₂×C₈×D₄×C₁₃	2
C₄×C₁₃×#127	2
C₁₃×#1955	2
C₁₃×#1954	2
C₁₃×#1842	2
C₄×C₁₃×#97	2
#21682	13

Subgroups — C13×#21682 #15708021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21682 #15708021