Subgroups — C₁₃×#10855 #15697194

Order 3328.

802 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#344	C₂	1	4	yes	maximal
5	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
6	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂×C₁₃×#117	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#423	—	2	1	no	—
10	C₁₃×#423	—	2	1	no	—
11	C₁₃×#423	—	2	2	no	—
12	C₂×C₁₃×C₄⋊C₈	C₄	1	4	yes	complemented
13	C₄×C₁₃×M₁₆	—	2	1	no	—
14	C₄×C₁₃×M₁₆	—	2	1	no	—
15	C₄×C₁₃×M₁₆	C₄	1	2	yes	complemented
16	C₄×C₁₃×M₁₆	C₄	1	2	yes	complemented
17	C₂×C₁₃×#97	—	2	1	no	—
18	C₂×C₄×C₈×C₁₃	—	2	1	no	—
19	C₁₃×#384	—	2	1	no	—
20	C₁₃×#382	—	2	1	no	—
21	C₁₃×#380	C₄	1	4	yes	—
22	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₁₃×#344	—	2	8	no	—
24	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
26	C₂×C₁₃×M₁₆	—	2	2	no	—
27	C₂×C₁₃×M₁₆	—	2	2	no	—
28	C₂×C₁₃×M₁₆	—	2	2	no	—
29	C₂×C₁₃×M₁₆	—	2	4	no	—
30	C₂×C₁₃×M₁₆	—	2	2	no	—
31	C₂×C₁₃×M₁₆	—	2	2	no	—
32	C₂×C₁₃×M₁₆	—	2	4	no	—
33	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
34	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
35	C₂×C₁₃×M₁₆	Q₈	1	4	yes	—
36	C₂²×C₈×C₁₃	—	2	2	no	—
37	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
38	C₁₃×#117	—	2	4	no	—
39	C₁₃×#117	—	2	4	no	—
40	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
41	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
42	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₁₃	—	2	2	no	—
44	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	D₄	1	2	yes	—
50	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
53	C₁₃×C₄⋊C₈	—	2	4	no	—
54	C₁₃×C₄⋊C₈	—	2	4	no	—
55	C₁₃×#97	—	2	2	no	—
56	C₁₃×#97	—	2	2	no	—
57	C₄×C₈×C₁₃	—	2	2	no	—
58	C₄×C₈×C₁₃	—	2	2	no	—
59	C₁₃×#95	—	2	4	no	—
60	#10855	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	—	2	4	no	—
63	C₂²×C₄×C₁₃	—	4	4	no	—
64	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
65	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
66	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
70	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
78	C₂²×C₄×C₁₃	#41	1	2	yes	—
79	C₂²×C₄×C₁₃	#41	1	2	yes	—
80	C₁₃×M₁₆	—	2	4	no	—
81	C₁₃×M₁₆	—	2	4	no	—
82	C₁₃×M₁₆	—	2	4	no	—
83	C₁₃×M₁₆	—	4	4	no	—
84	C₁₃×M₁₆	—	4	2	no	—
85	C₁₃×M₁₆	—	4	2	no	—
86	C₁₃×M₁₆	C₄⋊C₄	1	8	yes	complemented
87	C₂×C₈×C₁₃	—	2	4	no	—
88	C₂×C₈×C₁₃	—	2	4	no	—
89	C₂×C₈×C₁₃	—	2	4	no	—
90	C₂×C₈×C₁₃	—	2	4	no	—
91	C₂×C₈×C₁₃	—	2	8	no	—
92	C₁₃×C₄⋊C₄	—	4	8	no	—
93	C₁₃×C₄⋊C₄	—	4	4	no	—
94	C₁₃×C₂²⋊C₄	—	2	8	no	—
95	C₄²×C₁₃	—	4	2	no	—
96	C₄²×C₁₃	—	4	2	no	—
97	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
102	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
103	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
104	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
105	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
106	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
107	C₂×#423	C₂×C₁₃	1	1	yes	characteristic
108	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic
109	#2285	C₂×C₁₃	1	1	yes	characteristic
110	C₂×#344	C₂×C₁₃	1	4	yes	—
111	C₂³×C₁₃	—	4	2	no	—
112	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
113	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
114	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₂³×C₁₃	C₄×D₄	1	2	yes	—
116	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
117	C₂×C₄×C₁₃	—	2	4	no	—
118	C₂×C₄×C₁₃	—	2	4	no	—
119	C₂×C₄×C₁₃	—	2	4	no	—
120	C₂×C₄×C₁₃	—	4	2	no	—
121	C₂×C₄×C₁₃	—	4	2	no	—
122	C₂×C₄×C₁₃	—	4	2	no	—
123	C₂×C₄×C₁₃	—	4	8	no	—
124	C₂×C₄×C₁₃	—	4	4	no	—
125	C₂×C₄×C₁₃	#95	1	2	yes	—
126	C₂×C₄×C₁₃	#95	1	2	yes	—
127	C₂×C₄×C₁₃	#95	1	2	yes	—
128	C₂×C₄×C₁₃	#95	1	2	yes	—
129	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
132	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₃	#117	1	2	yes	—
135	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
136	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
137	C₂×C₄×C₁₃	#121	1	2	yes	—
138	C₂×C₄×C₁₃	#121	1	2	yes	—
139	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
140	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
141	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
142	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
143	C₂×C₄×C₁₃	#125	1	2	yes	—
144	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
146	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
147	C₈×C₁₃	—	2	8	no	—
148	C₈×C₁₃	—	4	4	no	—
149	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
150	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
151	C₂×#117	C₂²×C₁₃	1	2	yes	—
152	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
153	#423	—	2	1	no	—
154	#423	—	2	1	no	—
155	#423	—	2	2	no	—
156	C₂×C₄⋊C₈	C₄×C₁₃	1	4	yes	complemented
157	C₄×M₁₆	—	2	1	no	—
158	C₄×M₁₆	—	2	1	no	—
159	C₄×M₁₆	C₄×C₁₃	1	2	yes	complemented
160	C₄×M₁₆	C₄×C₁₃	1	2	yes	complemented
161	C₂×#97	—	2	1	no	—
162	C₂×C₄×C₈	—	2	1	no	—
163	#384	—	2	1	no	—
164	#382	—	2	1	no	—
165	#380	C₄×C₁₃	1	4	yes	—
166	C₄×C₄⋊C₄	—	2	2	no	—
167	#344	—	2	8	no	—
168	C₂²×C₁₃	—	2	2	no	—
169	C₂²×C₁₃	—	2	2	no	—
170	C₂²×C₁₃	—	2	2	no	—
171	C₂²×C₁₃	—	4	2	no	—
172	C₂²×C₁₃	—	4	2	no	—
173	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
174	C₂²×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
175	C₂²×C₁₃	#389	1	2	yes	—
176	C₂²×C₁₃	#390	1	1	yes	characteristic
177	C₂²×C₁₃	#391	1	1	yes	characteristic
178	C₄×C₁₃	—	2	2	no	—
179	C₄×C₁₃	—	2	2	no	—
180	C₄×C₁₃	—	2	2	no	—
181	C₄×C₁₃	—	8	4	no	—
182	C₄×C₁₃	#344	1	4	yes	complemented
183	C₄×C₁₃	#380	1	2	yes	—
184	C₄×C₁₃	#382	1	1	yes	characteristic
185	C₄×C₁₃	#384	1	1	yes	characteristic
186	C₄×C₁₃	#389	1	2	yes	—
187	C₄×C₁₃	#390	1	1	yes	characteristic
188	C₄×C₁₃	#391	1	1	yes	characteristic
189	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
190	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
191	C₂×M₁₆	—	2	2	no	—
192	C₂×M₁₆	—	2	2	no	—
193	C₂×M₁₆	—	2	2	no	—
194	C₂×M₁₆	—	2	4	no	—
195	C₂×M₁₆	—	2	2	no	—
196	C₂×M₁₆	—	2	2	no	—
197	C₂×M₁₆	—	2	4	no	—
198	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
199	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
200	C₂×M₁₆	Q₈×C₁₃	1	4	yes	—
201	C₂²×C₈	—	2	2	no	—
202	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
203	#117	—	2	4	no	—
204	#117	—	2	4	no	—
205	C₂×C₄⋊C₄	—	2	4	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
208	C₂×C₄²	—	2	2	no	—
209	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
210	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
211	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
212	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
213	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
214	C₂×C₄²	D₄×C₁₃	1	2	yes	—
215	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
216	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
217	C₂×C₄²	Q₈×C₁₃	1	2	yes	—
218	C₄⋊C₈	—	2	4	no	—
219	C₄⋊C₈	—	2	4	no	—
220	#97	—	2	2	no	—
221	#97	—	2	2	no	—
222	C₄×C₈	—	2	2	no	—
223	C₄×C₈	—	2	2	no	—
224	#95	—	2	4	no	—
225	C₂×C₁₃	—	2	1	no	—
226	C₂×C₁₃	—	2	2	no	—
227	C₂×C₁₃	—	2	2	no	—
228	C₂×C₁₃	—	2	1	no	—
229	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
230	C₂×C₁₃	C₂×#344	1	2	yes	—
231	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	4	4	no	—
234	C₂²×C₄	C₄²×C₁₃	1	2	yes	—
235	C₂²×C₄	C₄²×C₁₃	1	2	yes	—
236	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
237	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
238	C₂²×C₄	C₁₃×C₄⋊C₄	1	2	yes	—
239	C₂²×C₄	C₁₃×C₄⋊C₄	1	2	yes	—
240	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
242	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
243	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
244	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
245	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
246	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
247	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
248	C₂²×C₄	C₁₃×#41	1	2	yes	—
249	C₂²×C₄	C₁₃×#41	1	2	yes	—
250	M₁₆	—	2	4	no	—
251	M₁₆	—	2	4	no	—
252	M₁₆	—	2	4	no	—
253	M₁₆	—	4	4	no	—
254	M₁₆	—	4	2	no	—
255	M₁₆	—	4	2	no	—
256	M₁₆	C₁₃×C₄⋊C₄	1	8	yes	complemented
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	8	no	—
262	C₄⋊C₄	—	4	8	no	—
263	C₄⋊C₄	—	4	4	no	—
264	C₂²⋊C₄	—	2	8	no	—
265	C₄²	—	4	2	no	—
266	C₄²	—	4	2	no	—
267	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
268	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
269	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
270	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
271	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
272	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
273	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
274	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
275	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
276	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
277	C₁₃	#10855	1	1	yes	characteristic, direct product factor, Sylow
278	C₂³	—	4	2	no	—
279	C₂³	C₂×C₄²×C₁₃	1	1	yes	characteristic
280	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
281	C₂³	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
282	C₂³	C₄×D₄×C₁₃	1	2	yes	—
283	C₂³	C₄×Q₈×C₁₃	1	2	yes	—
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	4	2	no	—
288	C₂×C₄	—	4	2	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	4	8	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	C₁₃×#95	1	2	yes	—
293	C₂×C₄	C₁₃×#95	1	2	yes	—
294	C₂×C₄	C₁₃×#95	1	2	yes	—
295	C₂×C₄	C₁₃×#95	1	2	yes	—
296	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
299	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
300	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
301	C₂×C₄	C₁₃×#117	1	2	yes	—
302	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
303	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
304	C₂×C₄	C₁₃×#121	1	2	yes	—
305	C₂×C₄	C₁₃×#121	1	2	yes	—
306	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
307	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
308	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
309	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
310	C₂×C₄	C₁₃×#125	1	2	yes	—
311	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
312	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
313	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
314	C₈	—	2	8	no	—
315	C₈	—	4	4	no	—
316	C₂²	—	2	2	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	C₂×C₁₃×#95	1	1	yes	characteristic
322	C₂²	C₄×C₁₃×C₄⋊C₄	1	2	yes	—
323	C₂²	C₁₃×#389	1	2	yes	—
324	C₂²	C₁₃×#390	1	1	yes	characteristic
325	C₂²	C₁₃×#391	1	1	yes	characteristic
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	—	2	2	no	—
329	C₄	—	8	4	no	—
330	C₄	C₁₃×#344	1	4	yes	complemented
331	C₄	C₁₃×#380	1	2	yes	—
332	C₄	C₁₃×#382	1	1	yes	characteristic
333	C₄	C₁₃×#384	1	1	yes	characteristic
334	C₄	C₁₃×#389	1	2	yes	—
335	C₄	C₁₃×#390	1	1	yes	characteristic
336	C₄	C₁₃×#391	1	1	yes	characteristic
337	C₂	—	2	1	no	—
338	C₂	—	2	2	no	—
339	C₂	—	2	2	no	—
340	C₂	—	2	1	no	—
341	C₂	C₁₃×C₄⋊#95	1	1	yes	characteristic
342	C₂	C₂×C₁₃×#344	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#95
prime radical	C₂⁴×C₁₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₂×C₁₃×C₄⋊C₈	C₄	semidirect
15. C₄×C₁₃×M₁₆	C₄	semidirect
16. C₄×C₁₃×M₁₆	C₄	semidirect
60. #10855	C₁₃	direct (N × H)
86. C₁₃×M₁₆	C₄⋊C₄	semidirect
156. C₂×C₄⋊C₈	C₄×C₁₃	semidirect
159. C₄×M₁₆	C₄×C₁₃	semidirect
160. C₄×M₁₆	C₄×C₁₃	semidirect
182. C₄×C₁₃	#344	semidirect
256. M₁₆	C₁₃×C₄⋊C₄	semidirect
277. C₁₃	#10855	direct (N × H)
330. C₄	C₁₃×#344	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#423	2
C₂×C₄×C₁₃×M₁₆	2
C₁₃×#2285	2
C₂×C₁₃×#344	2
#10855	13

Subgroups — C13×#10855 #15697194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10855 #15697194