Subgroups — C₁₃×#20472 #15706811

Order 3328.

1050 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#431	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×#1771	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1753	C₂	1	4	yes	maximal
6	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
11	C₂×C₁₃×#117	C₄	1	2	yes	—
12	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#431	C₄	1	8	yes	complemented
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₄×C₁₃×M₁₆	C₄	1	8	yes	complemented
17	C₂×C₁₃×#97	C₂²	1	4	yes	—
18	C₂×C₁₃×#97	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₃	C₂²	1	4	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
25	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
27	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₁₃×#376	C₄	1	2	yes	—
29	C₄³×C₁₃	C₂²	1	1	yes	characteristic
30	C₄³×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#336	C₂²	1	4	yes	—
32	C₁₃×#336	C₂²	1	4	yes	—
33	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
36	C₂×C₁₃×M₁₆	—	2	8	no	—
37	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
38	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
42	C₁₃×#117	—	2	8	no	—
43	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
44	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
51	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
52	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
54	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
58	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
59	C₁₃×#97	—	2	8	no	—
60	C₁₃×#97	C₂×C₄	1	8	yes	—
61	C₄×C₈×C₁₃	—	2	8	no	—
62	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
63	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
64	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
65	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
66	C₁₃×#95	C₂×C₄	1	4	yes	—
67	C₁₃×#95	C₂×C₄	1	4	yes	—
68	#20472	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	—	2	4	no	—
71	C₂²×C₄×C₁₃	—	2	4	no	—
72	C₂²×C₄×C₁₃	—	2	4	no	—
73	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
74	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
75	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
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	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
85	C₁₃×M₁₆	—	2	16	no	—
86	C₂×C₈×C₁₃	—	2	4	no	—
87	C₂×C₈×C₁₃	—	2	4	no	—
88	C₂×C₈×C₁₃	—	2	4	no	—
89	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
90	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
91	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
92	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
93	C₂×C₈×C₁₃	#41	1	8	yes	—
94	C₁₃×C₄⋊C₄	—	2	8	no	—
95	C₁₃×C₂²⋊C₄	—	2	8	no	—
96	C₄²×C₁₃	—	2	4	no	—
97	C₄²×C₁₃	—	2	4	no	—
98	C₄²×C₁₃	—	2	4	no	—
99	C₄²×C₁₃	—	2	4	no	—
100	C₄²×C₁₃	—	2	4	no	—
101	C₄²×C₁₃	C₄²	1	4	yes	—
102	C₄²×C₁₃	C₄²	1	4	yes	—
103	C₄²×C₁₃	M₁₆	1	8	yes	complemented
104	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
105	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
106	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
107	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
108	C₂×#431	C₂×C₁₃	1	1	yes	characteristic
109	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic
110	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
111	#1771	C₂×C₁₃	1	4	yes	complemented
112	#1753	C₂×C₁₃	1	4	yes	—
113	#1744	C₂×C₁₃	1	1	yes	characteristic, complemented
114	#1744	C₂×C₁₃	1	1	yes	characteristic, complemented
115	C₄×#97	C₂×C₁₃	1	1	yes	characteristic, complemented
116	C₄²×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
117	C₂³×C₁₃	—	2	2	no	—
118	C₂³×C₁₃	—	2	2	no	—
119	C₂³×C₁₃	—	2	2	no	—
120	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
121	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₃	—	2	4	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	8	no	—
131	C₂×C₄×C₁₃	—	2	4	no	—
132	C₂×C₄×C₁₃	—	2	4	no	—
133	C₂×C₄×C₁₃	—	2	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	#131	1	4	yes	—
142	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
145	C₈×C₁₃	—	2	4	no	—
146	C₈×C₁₃	—	2	4	no	—
147	C₈×C₁₃	—	2	4	no	—
148	C₈×C₁₃	#117	1	8	yes	complemented
149	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
150	C₂×#117	C₄×C₁₃	1	2	yes	—
151	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
152	#431	C₄×C₁₃	1	8	yes	complemented
153	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
154	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
155	C₄×M₁₆	C₄×C₁₃	1	8	yes	complemented
156	C₂×#97	C₂²×C₁₃	1	4	yes	—
157	C₂×#97	C₂²×C₁₃	1	2	yes	—
158	C₂×C₄×C₈	C₂²×C₁₃	1	4	yes	—
159	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
160	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
161	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
162	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
163	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
164	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
165	C₄×C₂²⋊C₄	C₄×C₁₃	1	2	yes	—
166	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
167	#376	C₄×C₁₃	1	2	yes	—
168	C₄³	C₂²×C₁₃	1	1	yes	characteristic
169	C₄³	C₂²×C₁₃	1	1	yes	characteristic
170	#336	C₂²×C₁₃	1	4	yes	—
171	#336	C₂²×C₁₃	1	4	yes	—
172	C₂²×C₁₃	—	2	2	no	—
173	C₂²×C₁₃	—	2	2	no	—
174	C₂²×C₁₃	—	2	2	no	—
175	C₂²×C₁₃	—	4	4	no	—
176	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
177	C₂²×C₁₃	C₄×#41	1	2	yes	—
178	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
179	C₂²×C₁₃	C₂×#131	1	2	yes	—
180	C₄×C₁₃	—	2	2	no	—
181	C₄×C₁₃	—	2	2	no	—
182	C₄×C₁₃	—	2	8	no	—
183	C₄×C₁₃	—	2	2	no	—
184	C₄×C₁₃	—	4	4	no	—
185	C₄×C₁₃	C₄×M₁₆	1	4	yes	—
186	C₄×C₁₃	#405	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	8	no	—
193	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	—
194	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
195	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
196	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
197	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
198	#117	—	2	8	no	—
199	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
200	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
201	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
202	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
203	C₂×C₄²	C₂×C₄×C₁₃	1	2	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	C₂×C₄×C₁₃	1	2	yes	—
209	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
210	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
211	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
212	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
213	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
214	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
215	#97	—	2	8	no	—
216	#97	C₂×C₄×C₁₃	1	8	yes	—
217	C₄×C₈	—	2	8	no	—
218	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
219	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
220	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
221	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
222	#95	C₂×C₄×C₁₃	1	4	yes	—
223	#95	C₂×C₄×C₁₃	1	4	yes	—
224	C₂×C₁₃	—	4	2	no	—
225	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
226	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
227	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
228	C₂×C₁₃	#2965	1	4	yes	—
229	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	C₄²×C₁₃	1	4	yes	—
234	C₂²×C₄	C₄²×C₁₃	1	4	yes	—
235	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
236	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
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	2	yes	—
240	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
241	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
242	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
243	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
244	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
245	M₁₆	—	2	16	no	—
246	C₂×C₈	—	2	4	no	—
247	C₂×C₈	—	2	4	no	—
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
250	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
251	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
252	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
253	C₂×C₈	C₁₃×#41	1	8	yes	—
254	C₄⋊C₄	—	2	8	no	—
255	C₂²⋊C₄	—	2	8	no	—
256	C₄²	—	2	4	no	—
257	C₄²	—	2	4	no	—
258	C₄²	—	2	4	no	—
259	C₄²	—	2	4	no	—
260	C₄²	—	2	4	no	—
261	C₄²	C₄²×C₁₃	1	4	yes	—
262	C₄²	C₄²×C₁₃	1	4	yes	—
263	C₄²	C₁₃×M₁₆	1	8	yes	complemented
264	C₄²	C₂²×C₄×C₁₃	1	2	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	C₁₃	#20472	1	1	yes	characteristic, direct product factor, Sylow
269	C₂³	—	2	2	no	—
270	C₂³	—	2	2	no	—
271	C₂³	—	2	2	no	—
272	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
273	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
274	C₂×C₄	—	2	4	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	8	no	—
280	C₂×C₄	—	2	8	no	—
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
287	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
288	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
289	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
290	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
291	C₂×C₄	C₂×C₁₃×M₁₆	1	8	yes	—
292	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
293	C₂×C₄	C₁₃×#131	1	4	yes	—
294	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
295	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
296	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
297	C₈	—	2	4	no	—
298	C₈	—	2	4	no	—
299	C₈	—	2	4	no	—
300	C₈	C₁₃×#117	1	8	yes	complemented
301	C₂²	—	2	2	no	—
302	C₂²	—	2	2	no	—
303	C₂²	—	2	2	no	—
304	C₂²	—	4	4	no	—
305	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
306	C₂²	C₄×C₁₃×#41	1	2	yes	—
307	C₂²	C₂²×C₁₃×M₁₆	1	2	yes	—
308	C₂²	C₂×C₁₃×#131	1	2	yes	—
309	C₄	—	2	2	no	—
310	C₄	—	2	2	no	—
311	C₄	—	2	2	no	—
312	C₄	—	2	8	no	—
313	C₄	—	4	4	no	—
314	C₄	C₄×C₁₃×M₁₆	1	4	yes	—
315	C₄	C₁₃×#405	1	4	yes	—
316	C₄	C₂×C₁₃×#117	1	2	yes	—
317	C₄	C₄×C₁₃×#41	1	2	yes	—
318	C₂	—	4	2	no	—
319	C₂	C₄×C₁₃×#117	1	1	yes	characteristic
320	C₂	C₂×C₄×C₁₃×M₁₆	1	1	yes	characteristic
321	C₂	C₂×C₁₃×#405	1	1	yes	characteristic
322	C₂	C₁₃×#2965	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₃	C₂³
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 ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1771	C₂	semidirect
6. C₁₃×#1744	C₂	semidirect
7. C₁₃×#1744	C₂	semidirect
8. C₄×C₁₃×#97	C₂	semidirect
9. C₄²×C₈×C₁₃	C₂	semidirect
13. C₁₃×#431	C₄	semidirect
16. C₄×C₁₃×M₁₆	C₄	semidirect
68. #20472	C₁₃	direct (N × H)
103. C₄²×C₁₃	M₁₆	semidirect
111. #1771	C₂×C₁₃	semidirect
113. #1744	C₂×C₁₃	semidirect
114. #1744	C₂×C₁₃	semidirect
115. C₄×#97	C₂×C₁₃	semidirect
116. C₄²×C₈	C₂×C₁₃	semidirect
148. C₈×C₁₃	#117	semidirect
152. #431	C₄×C₁₃	semidirect
155. C₄×M₁₆	C₄×C₁₃	semidirect
263. C₄²	C₁₃×M₁₆	semidirect
268. C₁₃	#20472	direct (N × H)
300. 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×#431	2
C₂×C₄×C₁₃×M₁₆	2
C₄×C₁₃×#117	2
C₁₃×#1771	2
C₁₃×#1753	2
C₁₃×#1744	2
C₄×C₁₃×#97	2
C₄²×C₈×C₁₃	2
#20472	13

Subgroups — C13×#20472 #15706811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20472 #15706811