Subgroups — C₁₃×#20480 #15706819

Order 3328.

1022 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1770	C₂	1	2	yes	maximal, complemented
5	C₈×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1753	C₂	1	4	yes	maximal
7	C₁₃×#1745	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×#97	C₂	1	2	yes	maximal, complemented
9	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
10	C₂×C₁₃×#117	C₄	1	2	yes	—
11	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#432	C₄	1	8	yes	complemented
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
15	C₄×C₁₃×M₁₆	C₄	1	8	yes	complemented
16	C₂×C₁₃×#97	C₂²	1	4	yes	—
17	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#97	C₂²	1	2	yes	—
19	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃	C₂²	1	4	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
22	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
23	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
26	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₁₃×#376	C₄	1	2	yes	—
28	C₄³×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#336	C₂²	1	4	yes	—
30	C₁₃×#336	C₂²	1	4	yes	—
31	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
34	C₂×C₁₃×M₁₆	—	2	4	no	—
35	C₂×C₁₃×M₁₆	—	2	4	no	—
36	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
37	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
38	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
40	C₁₃×#117	—	2	8	no	—
41	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
42	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
49	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
50	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
55	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
56	C₁₃×#97	—	2	8	no	—
57	C₁₃×#97	C₂×C₄	1	4	yes	—
58	C₁₃×#97	C₂×C₄	1	4	yes	—
59	C₁₃×#97	C₂×C₄	1	8	yes	—
60	C₄×C₈×C₁₃	—	2	8	no	—
61	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
62	C₁₃×#95	C₂×C₄	1	2	yes	—
63	C₁₃×#95	C₂×C₄	1	2	yes	—
64	C₁₃×#95	C₂×C₄	1	4	yes	—
65	#20480	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	—	2	4	no	—
68	C₂²×C₄×C₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₃	—	4	2	no	—
71	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
72	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
73	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
74	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
83	C₁₃×M₁₆	—	2	16	no	—
84	C₂×C₈×C₁₃	—	2	4	no	—
85	C₂×C₈×C₁₃	—	2	4	no	—
86	C₂×C₈×C₁₃	—	2	2	no	—
87	C₂×C₈×C₁₃	—	2	2	no	—
88	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
89	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
90	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
91	C₂×C₈×C₁₃	#41	1	4	yes	—
92	C₂×C₈×C₁₃	#41	1	4	yes	—
93	C₁₃×C₄⋊C₄	—	2	4	no	—
94	C₁₃×C₄⋊C₄	M₁₆	1	8	yes	complemented
95	C₁₃×C₂²⋊C₄	—	2	8	no	—
96	C₄²×C₁₃	—	2	8	no	—
97	C₄²×C₁₃	—	2	4	no	—
98	C₄²×C₁₃	—	2	4	no	—
99	C₄²×C₁₃	—	4	4	no	—
100	C₄²×C₁₃	C₄²	1	4	yes	—
101	C₄²×C₁₃	C₄²	1	4	yes	—
102	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
103	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
104	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
105	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂×#432	C₂×C₁₃	1	1	yes	characteristic
107	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic
108	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
109	#1770	C₂×C₁₃	1	2	yes	complemented
110	C₈×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
111	#1753	C₂×C₁₃	1	4	yes	—
112	#1745	C₂×C₁₃	1	2	yes	complemented
113	C₄×#97	C₂×C₁₃	1	2	yes	complemented
114	C₂³×C₁₃	—	2	1	no	—
115	C₂³×C₁₃	—	2	1	no	—
116	C₂³×C₁₃	—	2	2	no	—
117	C₂³×C₁₃	—	2	2	no	—
118	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
119	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
120	C₂×C₄×C₁₃	—	2	4	no	—
121	C₂×C₄×C₁₃	—	2	1	no	—
122	C₂×C₄×C₁₃	—	2	1	no	—
123	C₂×C₄×C₁₃	—	2	2	no	—
124	C₂×C₄×C₁₃	—	2	2	no	—
125	C₂×C₄×C₁₃	—	2	4	no	—
126	C₂×C₄×C₁₃	—	2	2	no	—
127	C₂×C₄×C₁₃	—	2	4	no	—
128	C₂×C₄×C₁₃	—	2	4	no	—
129	C₂×C₄×C₁₃	—	2	8	no	—
130	C₂×C₄×C₁₃	—	2	4	no	—
131	C₂×C₄×C₁₃	—	2	4	no	—
132	C₂×C₄×C₁₃	—	2	4	no	—
133	C₂×C₄×C₁₃	—	4	4	no	—
134	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
135	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
136	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
137	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
138	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
139	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
140	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
141	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
144	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
145	C₈×C₁₃	—	2	4	no	—
146	C₈×C₁₃	—	2	8	no	—
147	C₈×C₁₃	#117	1	8	yes	complemented
148	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
149	C₂×#117	C₄×C₁₃	1	2	yes	—
150	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
151	#432	C₄×C₁₃	1	8	yes	complemented
152	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
153	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
154	C₄×M₁₆	C₄×C₁₃	1	8	yes	complemented
155	C₂×#97	C₂²×C₁₃	1	4	yes	—
156	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
157	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
158	C₂×#97	C₂²×C₁₃	1	2	yes	—
159	C₂×C₄×C₈	C₂²×C₁₃	1	4	yes	—
160	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
161	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
162	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
163	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
164	C₄×C₂²⋊C₄	C₄×C₁₃	1	2	yes	—
165	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
166	#376	C₄×C₁₃	1	2	yes	—
167	C₄³	C₂²×C₁₃	1	2	yes	—
168	#336	C₂²×C₁₃	1	4	yes	—
169	#336	C₂²×C₁₃	1	4	yes	—
170	C₂²×C₁₃	—	2	2	no	—
171	C₂²×C₁₃	—	2	2	no	—
172	C₂²×C₁₃	—	2	2	no	—
173	C₂²×C₁₃	—	4	2	no	—
174	C₂²×C₁₃	—	4	2	no	—
175	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
176	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
177	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
178	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
179	C₂²×C₁₃	#568	1	2	yes	—
180	C₄×C₁₃	—	2	2	no	—
181	C₄×C₁₃	—	2	2	no	—
182	C₄×C₁₃	—	2	2	no	—
183	C₄×C₁₃	—	2	8	no	—
184	C₄×C₁₃	—	2	2	no	—
185	C₄×C₁₃	—	4	4	no	—
186	C₄×C₁₃	C₄×M₁₆	1	4	yes	—
187	C₄×C₁₃	C₂×#117	1	2	yes	—
188	C₄×C₁₃	C₄×#41	1	2	yes	—
189	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
190	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
191	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
192	C₂×M₁₆	—	2	4	no	—
193	C₂×M₁₆	—	2	4	no	—
194	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	—
195	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
196	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
197	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
198	#117	—	2	8	no	—
199	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
200	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
201	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
202	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
203	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
204	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
205	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
206	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
207	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
208	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
209	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
210	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
211	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
212	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
213	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
214	#97	—	2	8	no	—
215	#97	C₂×C₄×C₁₃	1	4	yes	—
216	#97	C₂×C₄×C₁₃	1	4	yes	—
217	#97	C₂×C₄×C₁₃	1	8	yes	—
218	C₄×C₈	—	2	8	no	—
219	C₄×C₈	C₂×C₄×C₁₃	1	8	yes	—
220	#95	C₂×C₄×C₁₃	1	2	yes	—
221	#95	C₂×C₄×C₁₃	1	2	yes	—
222	#95	C₂×C₄×C₁₃	1	4	yes	—
223	C₂×C₁₃	—	4	2	no	—
224	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
225	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
226	C₂×C₁₃	#2873	1	1	yes	characteristic
227	C₂×C₁₃	#2970	1	2	yes	—
228	C₂×C₁₃	#2971	1	2	yes	—
229	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	4	2	no	—
234	C₂²×C₄	C₄²×C₁₃	1	4	yes	—
235	C₂²×C₄	C₄²×C₁₃	1	4	yes	—
236	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
237	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
240	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
242	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
243	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
244	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
245	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
246	M₁₆	—	2	16	no	—
247	C₂×C₈	—	2	4	no	—
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	—	2	2	no	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
252	C₂×C₈	C₂²×C₄×C₁₃	1	8	yes	—
253	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
254	C₂×C₈	C₁₃×#41	1	4	yes	—
255	C₂×C₈	C₁₃×#41	1	4	yes	—
256	C₄⋊C₄	—	2	4	no	—
257	C₄⋊C₄	C₁₃×M₁₆	1	8	yes	complemented
258	C₂²⋊C₄	—	2	8	no	—
259	C₄²	—	2	8	no	—
260	C₄²	—	2	4	no	—
261	C₄²	—	2	4	no	—
262	C₄²	—	4	4	no	—
263	C₄²	C₄²×C₁₃	1	4	yes	—
264	C₄²	C₄²×C₁₃	1	4	yes	—
265	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
266	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
267	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
268	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
269	C₁₃	#20480	1	1	yes	characteristic, direct product factor, Sylow
270	C₂³	—	2	1	no	—
271	C₂³	—	2	1	no	—
272	C₂³	—	2	2	no	—
273	C₂³	—	2	2	no	—
274	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
275	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
291	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
292	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
293	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
294	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
295	C₂×C₄	C₂×C₁₃×M₁₆	1	8	yes	—
296	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
297	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
298	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
299	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
300	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
301	C₈	—	2	4	no	—
302	C₈	—	2	8	no	—
303	C₈	C₁₃×#117	1	8	yes	complemented
304	C₂²	—	2	2	no	—
305	C₂²	—	2	2	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	4	2	no	—
308	C₂²	—	4	2	no	—
309	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
310	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
311	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
312	C₂²	C₂²×C₁₃×M₁₆	1	2	yes	—
313	C₂²	C₁₃×#568	1	2	yes	—
314	C₄	—	2	2	no	—
315	C₄	—	2	2	no	—
316	C₄	—	2	2	no	—
317	C₄	—	2	2	no	—
318	C₄	—	2	8	no	—
319	C₄	—	4	4	no	—
320	C₄	C₄×C₁₃×M₁₆	1	4	yes	—
321	C₄	C₂×C₁₃×#117	1	2	yes	—
322	C₄	C₄×C₁₃×#41	1	2	yes	—
323	C₂	—	4	2	no	—
324	C₂	C₄×C₁₃×#117	1	1	yes	characteristic
325	C₂	C₂×C₄×C₁₃×M₁₆	1	1	yes	characteristic
326	C₂	C₁₃×#2873	1	1	yes	characteristic
327	C₂	C₁₃×#2970	1	2	yes	—
328	C₂	C₁₃×#2971	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1770	C₂	semidirect
5. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
7. C₁₃×#1745	C₂	semidirect
8. C₄×C₁₃×#97	C₂	semidirect
12. C₁₃×#432	C₄	semidirect
15. C₄×C₁₃×M₁₆	C₄	semidirect
65. #20480	C₁₃	direct (N × H)
94. C₁₃×C₄⋊C₄	M₁₆	semidirect
109. #1770	C₂×C₁₃	semidirect
110. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
112. #1745	C₂×C₁₃	semidirect
113. C₄×#97	C₂×C₁₃	semidirect
147. C₈×C₁₃	#117	semidirect
151. #432	C₄×C₁₃	semidirect
154. C₄×M₁₆	C₄×C₁₃	semidirect
257. C₄⋊C₄	C₁₃×M₁₆	semidirect
269. C₁₃	#20480	direct (N × H)
303. C₈	C₁₃×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#432	2
C₂×C₄×C₁₃×M₁₆	2
C₄×C₁₃×#117	2
C₁₃×#1770	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1753	2
C₁₃×#1745	2
C₄×C₁₃×#97	2
#20480	13

Subgroups — C13×#20480 #15706819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20480 #15706819