Subgroups — C₁₃×#20494 #15706833

Order 3328.

1234 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×#436	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₃×M₁₆	C₂	1	2	yes	maximal, complemented
3	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₈×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1753	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1749	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×M₁₆	C₂²	1	4	yes	—
10	C₂×C₄×D₄×C₁₃	C₄	1	2	yes	—
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
13	C₁₃×#436	C₄	1	16	yes	complemented
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
16	C₄×C₁₃×M₁₆	—	2	8	no	—
17	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#97	C₂²	1	2	yes	—
19	C₂×C₁₃×#97	C₂²	1	2	yes	—
20	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃	C₂²	1	4	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
23	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
24	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₄×C₁₃×C₂²⋊C₄	C₄	1	4	yes	—
26	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₄³×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#336	C₂²	1	4	yes	—
29	C₁₃×#336	C₂²	1	2	yes	—
30	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₃	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
33	C₂×C₁₃×M₁₆	—	2	8	no	—
34	C₂×C₁₃×M₁₆	—	2	8	no	—
35	C₂×C₁₃×M₁₆	C₂×C₄	1	16	yes	complemented
36	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
38	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
39	C₄×D₄×C₁₃	—	2	8	no	—
40	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
41	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
44	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₃	—	2	4	no	—
46	C₂×C₄²×C₁₃	—	2	4	no	—
47	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	complemented
55	C₁₃×C₂²⋊C₈	C₂×C₄	1	16	yes	complemented
56	C₁₃×#97	—	2	4	no	—
57	C₁₃×#97	—	2	4	no	—
58	C₁₃×#97	—	2	2	no	—
59	C₁₃×#97	D₄	1	4	yes	complemented
60	C₄×C₈×C₁₃	—	2	8	no	—
61	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	complemented
62	C₁₃×#95	C₂×C₄	1	2	yes	—
63	C₁₃×#95	C₂×C₄	1	4	yes	—
64	#20494	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
66	C₂×D₄×C₁₃	—	2	4	no	—
67	C₂×D₄×C₁₃	C₄²	1	4	yes	—
68	C₂²×C₄×C₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₃	—	2	4	no	—
71	C₂²×C₄×C₁₃	—	2	8	no	—
72	C₂²×C₄×C₁₃	—	2	8	no	—
73	C₂²×C₄×C₁₃	—	4	4	no	—
74	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
78	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
82	C₁₃×M₁₆	—	2	32	no	—
83	C₂×C₈×C₁₃	—	2	4	no	—
84	C₂×C₈×C₁₃	—	2	2	no	—
85	C₂×C₈×C₁₃	—	2	2	no	—
86	C₂×C₈×C₁₃	—	2	4	no	—
87	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
88	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
89	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
90	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
91	C₂×C₈×C₁₃	#41	1	4	yes	—
92	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
93	C₁₃×C₄⋊C₄	M₁₆	1	8	yes	complemented
94	C₁₃×C₂²⋊C₄	—	2	8	no	—
95	C₁₃×C₂²⋊C₄	C₄²	1	8	yes	—
96	C₄²×C₁₃	—	2	8	no	—
97	C₄²×C₁₃	—	2	4	no	—
98	C₄²×C₁₃	—	2	2	no	—
99	C₄²×C₁₃	—	2	2	no	—
100	C₄²×C₁₃	—	2	2	no	—
101	C₄²×C₁₃	—	4	2	no	—
102	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
103	C₄²×C₁₃	C₂×D₄	1	2	yes	—
104	C₄²×C₁₃	#41	1	2	yes	—
105	C₂×#436	C₂×C₁₃	1	2	yes	—
106	C₂×C₄×M₁₆	C₂×C₁₃	1	2	yes	complemented
107	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic
108	C₈×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
109	#1767	C₂×C₁₃	1	1	yes	characteristic, complemented
110	#1753	C₂×C₁₃	1	4	yes	complemented
111	#1749	C₂×C₁₃	1	2	yes	complemented
112	C₄×#97	C₂×C₁₃	1	1	yes	characteristic, complemented
113	C₂³×C₁₃	—	2	2	no	—
114	C₂³×C₁₃	—	2	2	no	—
115	C₂³×C₁₃	—	2	4	no	—
116	C₂³×C₁₃	—	2	4	no	—
117	C₂³×C₁₃	C₂×C₄²	1	4	yes	—
118	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
119	D₄×C₁₃	—	2	8	no	—
120	C₂×C₄×C₁₃	—	2	4	no	—
121	C₂×C₄×C₁₃	—	2	2	no	—
122	C₂×C₄×C₁₃	—	2	2	no	—
123	C₂×C₄×C₁₃	—	2	2	no	—
124	C₂×C₄×C₁₃	—	2	2	no	—
125	C₂×C₄×C₁₃	—	2	2	no	—
126	C₂×C₄×C₁₃	—	2	4	no	—
127	C₂×C₄×C₁₃	—	2	8	no	—
128	C₂×C₄×C₁₃	—	2	8	no	—
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	2	2	no	—
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	4	16	no	—
133	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
134	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
135	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
136	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
137	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
138	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
139	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
140	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
142	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
143	C₈×C₁₃	—	2	8	no	—
144	C₈×C₁₃	—	2	4	no	—
145	C₈×C₁₃	C₄×D₄	1	8	yes	complemented
146	C₂²×M₁₆	C₂²×C₁₃	1	4	yes	—
147	C₂×C₄×D₄	C₄×C₁₃	1	2	yes	—
148	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
149	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
150	#436	C₄×C₁₃	1	16	yes	complemented
151	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
152	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
153	C₄×M₁₆	—	2	8	no	—
154	C₂×#97	C₂²×C₁₃	1	2	yes	—
155	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
156	C₂×#97	C₂²×C₁₃	1	2	yes	—
157	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
158	C₂×C₄×C₈	C₂²×C₁₃	1	4	yes	—
159	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
160	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
161	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
162	C₄×C₂²⋊C₄	C₄×C₁₃	1	4	yes	—
163	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
164	C₄³	C₂²×C₁₃	1	1	yes	characteristic
165	#336	C₂²×C₁₃	1	4	yes	—
166	#336	C₂²×C₁₃	1	2	yes	—
167	C₂²×C₁₃	—	2	4	no	—
168	C₂²×C₁₃	—	2	4	no	—
169	C₂²×C₁₃	—	2	4	no	—
170	C₂²×C₁₃	—	4	4	no	—
171	C₂²×C₁₃	—	4	4	no	—
172	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
173	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
174	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
175	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
176	C₂²×C₁₃	#568	1	2	yes	—
177	C₄×C₁₃	—	2	2	no	—
178	C₄×C₁₃	—	2	4	no	—
179	C₄×C₁₃	—	2	8	no	—
180	C₄×C₁₃	—	2	4	no	—
181	C₄×C₁₃	—	4	2	no	—
182	C₄×C₁₃	C₄×M₁₆	1	4	yes	complemented
183	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
184	C₄×C₁₃	C₄×#41	1	2	yes	—
185	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
186	C₂³×C₄	C₂×C₄×C₁₃	1	4	yes	—
187	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
188	C₂×M₁₆	—	2	8	no	—
189	C₂×M₁₆	—	2	8	no	—
190	C₂×M₁₆	C₂×C₄×C₁₃	1	16	yes	complemented
191	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
192	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
193	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
194	C₄×D₄	—	2	8	no	—
195	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
196	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
197	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
198	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
199	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
200	C₂×C₄²	—	2	4	no	—
201	C₂×C₄²	—	2	4	no	—
202	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
203	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
204	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
205	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
206	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
207	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
208	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
209	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
210	C₂²⋊C₈	C₂×C₄×C₁₃	1	16	yes	complemented
211	#97	—	2	4	no	—
212	#97	—	2	4	no	—
213	#97	—	2	2	no	—
214	#97	D₄×C₁₃	1	4	yes	complemented
215	C₄×C₈	—	2	8	no	—
216	C₄×C₈	C₂×C₄×C₁₃	1	8	yes	complemented
217	#95	C₂×C₄×C₁₃	1	2	yes	—
218	#95	C₂×C₄×C₁₃	1	4	yes	—
219	C₂×C₁₃	—	4	4	no	—
220	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
221	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
222	C₂×C₁₃	#2875	1	1	yes	characteristic
223	C₂×C₁₃	D₄×M₁₆	1	2	yes	—
224	C₂×C₁₃	#2971	1	2	yes	—
225	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
226	C₂×D₄	—	2	4	no	—
227	C₂×D₄	C₄²×C₁₃	1	4	yes	—
228	C₂²×C₄	—	2	2	no	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	8	no	—
232	C₂²×C₄	—	2	8	no	—
233	C₂²×C₄	—	4	4	no	—
234	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
235	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
236	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
237	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
238	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
239	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
240	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
241	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
242	M₁₆	—	2	32	no	—
243	C₂×C₈	—	2	4	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	2	4	no	—
247	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
248	C₂×C₈	C₂²×C₄×C₁₃	1	8	yes	—
249	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
250	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
251	C₂×C₈	C₁₃×#41	1	4	yes	—
252	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
253	C₄⋊C₄	C₁₃×M₁₆	1	8	yes	complemented
254	C₂²⋊C₄	—	2	8	no	—
255	C₂²⋊C₄	C₄²×C₁₃	1	8	yes	—
256	C₄²	—	2	8	no	—
257	C₄²	—	2	4	no	—
258	C₄²	—	2	2	no	—
259	C₄²	—	2	2	no	—
260	C₄²	—	2	2	no	—
261	C₄²	—	4	2	no	—
262	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
263	C₄²	C₂×D₄×C₁₃	1	2	yes	—
264	C₄²	C₁₃×#41	1	2	yes	—
265	C₁₃	#20494	1	1	yes	characteristic, direct product factor, Sylow
266	C₂³	—	2	2	no	—
267	C₂³	—	2	2	no	—
268	C₂³	—	2	4	no	—
269	C₂³	—	2	4	no	—
270	C₂³	C₂×C₄²×C₁₃	1	4	yes	—
271	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
272	D₄	—	2	8	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	4	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	8	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	4	16	no	—
286	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
287	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
288	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
289	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
290	C₂×C₄	C₂×C₁₃×M₁₆	1	8	yes	—
291	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
292	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
293	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
294	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
295	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
296	C₈	—	2	8	no	—
297	C₈	—	2	4	no	—
298	C₈	C₄×D₄×C₁₃	1	8	yes	complemented
299	C₂²	—	2	4	no	—
300	C₂²	—	2	4	no	—
301	C₂²	—	2	4	no	—
302	C₂²	—	4	4	no	—
303	C₂²	—	4	4	no	—
304	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
305	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
306	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
307	C₂²	C₂²×C₁₃×M₁₆	1	2	yes	—
308	C₂²	C₁₃×#568	1	2	yes	—
309	C₄	—	2	4	no	—
310	C₄	—	2	2	no	—
311	C₄	—	2	4	no	—
312	C₄	—	2	8	no	—
313	C₄	—	4	2	no	—
314	C₄	C₄×C₁₃×M₁₆	1	4	yes	complemented
315	C₄	C₂×C₄×D₄×C₁₃	1	2	yes	—
316	C₄	C₄×C₁₃×#41	1	2	yes	—
317	C₂	—	4	4	no	—
318	C₂	C₄²×D₄×C₁₃	1	1	yes	characteristic
319	C₂	C₂×C₄×C₁₃×M₁₆	1	1	yes	characteristic
320	C₂	C₁₃×#2875	1	1	yes	characteristic
321	C₂	D₄×C₁₃×M₁₆	1	2	yes	—
322	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	C₂²×D₄×C₁₃	C₂×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
2. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
4. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
5. C₁₃×#1767	C₂	semidirect
6. C₁₃×#1753	C₂	semidirect
7. C₁₃×#1749	C₂	semidirect
8. C₄×C₁₃×#97	C₂	semidirect
13. C₁₃×#436	C₄	semidirect
35. C₂×C₁₃×M₁₆	C₂×C₄	semidirect
54. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
55. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
59. C₁₃×#97	D₄	semidirect
61. C₄×C₈×C₁₃	C₂×C₄	semidirect
64. #20494	C₁₃	direct (N × H)
93. C₁₃×C₄⋊C₄	M₁₆	semidirect
106. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
108. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
109. #1767	C₂×C₁₃	semidirect
110. #1753	C₂×C₁₃	semidirect
111. #1749	C₂×C₁₃	semidirect
112. C₄×#97	C₂×C₁₃	semidirect
145. C₈×C₁₃	C₄×D₄	semidirect
150. #436	C₄×C₁₃	semidirect
182. C₄×C₁₃	C₄×M₁₆	semidirect
190. C₂×M₁₆	C₂×C₄×C₁₃	semidirect
209. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
210. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
214. #97	D₄×C₁₃	semidirect
216. C₄×C₈	C₂×C₄×C₁₃	semidirect
253. C₄⋊C₄	C₁₃×M₁₆	semidirect
265. C₁₃	#20494	direct (N × H)
298. C₈	C₄×D₄×C₁₃	semidirect
314. C₄	C₄×C₁₃×M₁₆	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×C₄×C₁₃×M₁₆	2
C₄²×D₄×C₁₃	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1767	2
C₁₃×#1753	2
C₁₃×#1749	2
C₄×C₁₃×#97	2
#20494	13

Subgroups — C13×#20494 #15706833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20494 #15706833