Subgroups — #15860918

Order 3328.

1138 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718783	C₂	1	2	yes	maximal
3	#13117243	C₂	1	1	yes	maximal, characteristic
4	#13114708	C₂	1	4	yes	maximal, complemented
5	#13114703	C₂	1	2	yes	maximal, complemented
6	C₈×C₄⋊Dic₁₃	C₂	1	2	yes	maximal, complemented
7	#13114534	C₂	1	2	yes	maximal
8	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×#88180	C₂²	1	2	yes	—
13	C₂³×#1055	C₂²	1	2	yes	—
14	C₄×C₁₃×M₁₆	C₄	1	8	yes	complemented
15	C₂×C₁₃×#97	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
17	#11718873	C₄	1	2	yes	—
18	#11718873	C₄	1	2	yes	—
19	#11718783	—	2	8	no	—
20	C₂×#88055	C₂²	1	4	yes	—
21	C₂×C₈×Dic₁₃	C₂²	1	4	yes	—
22	#11718597	C₄	1	2	yes	—
23	#11718596	C₄	1	2	yes	—
24	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
25	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
26	C₂×C₄⋊#1055	C₄	1	8	yes	complemented
27	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊#1055	C₂²	1	2	yes	—
30	#11718142	C₂²	1	4	yes	—
31	#11718142	C₂²	1	4	yes	—
32	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
35	C₂×C₁₃×M₁₆	—	2	2	no	—
36	C₂×C₁₃×M₁₆	—	2	2	no	—
37	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
38	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
39	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
40	C₂×C₁₃×M₁₆	Q₈	1	4	yes	—
41	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	4	yes	—
50	#88180	—	2	4	no	—
51	#88180	—	2	4	no	—
52	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
55	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
56	C₂²×#1055	—	2	4	no	—
57	C₂²×#1055	—	2	4	no	—
58	C₂²×#1055	C₂×C₄	1	8	yes	—
59	C₂²×#1055	C₂³	1	2	yes	—
60	C₂²×#1055	C₂³	1	2	yes	—
61	C₁₃×#97	C₂×C₄	1	8	yes	—
62	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
63	#88071	C₂×C₄	1	4	yes	—
64	#88071	C₂×C₄	1	4	yes	—
65	#88055	—	2	8	no	—
66	C₈×Dic₁₃	—	2	8	no	—
67	C₄⋊#1055	C₂×C₄	1	4	yes	—
68	C₄⋊#1055	C₂×C₄	1	4	yes	—
69	C₄⋊#1055	C₂×C₄	1	8	yes	—
70	#20441	—	13	1	no	maximal, Sylow
71	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	—	2	4	no	—
73	C₂²×C₄×C₁₃	—	4	2	no	—
74	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
75	C₂²×C₄×C₁₃	C₄²	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	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₁₃	#41	1	2	yes	—
86	C₂²×C₄×C₁₃	#41	1	2	yes	—
87	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
88	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
89	C₁₃×M₁₆	—	2	8	no	—
90	C₁₃×M₁₆	C₄⋊C₄	1	16	yes	complemented
91	C₂×C₈×C₁₃	—	2	2	no	—
92	C₂×C₈×C₁₃	—	2	2	no	—
93	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
94	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
95	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
96	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
97	C₄²×C₁₃	C₄²	1	4	yes	—
98	C₄²×C₁₃	C₄²	1	4	yes	—
99	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
100	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
101	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
102	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
103	C₂²⋊Dic₁₃	—	2	8	no	—
104	C₄⋊Dic₁₃	—	2	8	no	—
105	C₄⋊Dic₁₃	—	2	8	no	—
106	C₄⋊Dic₁₃	—	4	4	no	—
107	C₄×Dic₁₃	—	2	4	no	—
108	C₄×Dic₁₃	—	2	4	no	—
109	C₂×#1055	—	2	16	no	—
110	C₂×#1055	—	2	2	no	—
111	C₂×#1055	—	2	2	no	—
112	C₂×#1055	—	2	2	no	—
113	C₂×#1055	—	2	2	no	—
114	C₂×#1055	C₂²×C₄	1	4	yes	—
115	C₂×#1055	C₂²×C₄	1	4	yes	—
116	C₂²×C₄⋊C₈	—	13	1	no	—
117	C₂×#405	—	13	2	no	—
118	C₂×C₄×M₁₆	D₁₃	1	1	yes	characteristic
119	#2285	—	13	1	no	—
120	#1771	—	13	4	no	—
121	#1770	—	13	2	no	—
122	C₈×C₄⋊C₄	—	13	2	no	—
123	#1729	—	13	2	no	—
124	C₂³×C₁₃	—	2	2	no	—
125	C₂³×C₁₃	—	2	2	no	—
126	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
127	C₂³×C₁₃	C₄×D₄	1	2	yes	—
128	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
129	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃	—	2	2	no	—
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	8	no	—
134	C₂×C₄×C₁₃	—	4	4	no	—
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×C₄²	1	2	yes	—
140	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
141	C₂×C₄×C₁₃	#117	1	4	yes	—
142	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
143	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
144	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
145	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
146	C₂×C₄×C₁₃	#131	1	4	yes	—
147	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
153	C₂×Dic₁₃	—	2	8	no	—
154	C₂×Dic₁₃	—	2	8	no	—
155	C₂×Dic₁₃	—	2	8	no	—
156	C₈×C₁₃	—	2	4	no	—
157	C₈×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
158	#1055	—	2	4	no	—
159	#1055	—	2	4	no	—
160	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
161	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
162	C₂³×C₈	—	13	2	no	—
163	C₂×#117	—	13	2	no	—
164	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
165	C₂×C₄⋊C₈	—	13	8	no	—
166	C₂×C₄⋊C₈	—	13	1	no	—
167	C₂×C₄⋊C₈	—	13	1	no	—
168	C₂×C₄⋊C₈	—	13	2	no	—
169	#405	—	26	8	no	—
170	C₄×M₁₆	Dic₁₃	1	8	yes	complemented
171	C₂×#97	—	13	4	no	—
172	C₂×#97	C₂×D₁₃	1	2	yes	—
173	C₂×C₄×C₈	—	13	4	no	—
174	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
175	#384	—	13	2	no	—
176	#382	—	13	2	no	—
177	#380	—	13	2	no	—
178	#380	—	13	2	no	—
179	C₄×C₄⋊C₄	—	13	2	no	—
180	C₄×C₄⋊C₄	—	13	2	no	—
181	#336	—	13	4	no	—
182	#336	—	13	4	no	—
183	C₂²×C₁₃	—	2	2	no	—
184	C₂²×C₁₃	—	2	2	no	—
185	C₂²×C₁₃	—	2	4	no	—
186	C₂²×C₁₃	—	2	4	no	—
187	C₂²×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
188	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
189	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
191	C₂²×C₁₃	C₂×#131	1	2	yes	—
192	C₂²×C₁₃	#568	1	2	yes	—
193	C₄×C₁₃	—	2	2	no	—
194	C₄×C₁₃	—	2	2	no	—
195	C₄×C₁₃	—	2	2	no	—
196	C₄×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
197	C₄×C₁₃	#405	1	4	yes	complemented
198	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
199	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
200	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
201	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
202	Dic₁₃	—	4	8	no	—
203	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
204	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
205	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
206	C₂×M₁₆	—	2	2	no	—
207	C₂×M₁₆	—	2	2	no	—
208	C₂×M₁₆	Dic₂₆	1	4	yes	—
209	C₂×M₁₆	D₅₂	1	4	yes	—
210	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
211	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
212	C₂²×C₈	—	13	8	no	—
213	C₂²×C₈	—	13	2	no	—
214	C₂²×C₈	—	13	2	no	—
215	C₂²×C₈	—	26	4	no	—
216	C₂²×C₈	—	26	4	no	—
217	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
218	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
219	#117	—	26	4	no	—
220	#117	—	26	4	no	—
221	C₂×C₄⋊C₄	—	13	4	no	—
222	C₂×C₄⋊C₄	—	13	4	no	—
223	C₂×C₄⋊C₄	—	13	4	no	—
224	C₂×C₂²⋊C₄	—	13	4	no	—
225	C₂×C₄²	—	13	4	no	—
226	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
228	C₂×C₄²	C₄×D₁₃	1	4	yes	—
229	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
230	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
231	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
232	C₄⋊C₈	—	13	4	no	—
233	C₄⋊C₈	—	13	4	no	—
234	C₄⋊C₈	—	13	8	no	—
235	#97	—	26	8	no	—
236	#97	C₂×Dic₁₃	1	8	yes	—
237	C₄×C₈	—	26	8	no	—
238	C₄×C₈	C₂×Dic₁₃	1	8	yes	—
239	#95	—	13	4	no	—
240	#95	—	13	4	no	—
241	C₂×C₁₃	—	2	4	no	—
242	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
243	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
244	C₂×C₁₃	#2873	1	1	yes	characteristic
245	C₂×C₁₃	#2935	1	2	yes	—
246	C₂×C₁₃	#2962	1	2	yes	—
247	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	4	2	no	—
250	C₂²×C₄	—	13	8	no	—
251	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
252	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
253	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
254	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
255	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
258	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
259	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
260	C₂²×C₄	C₂×D₅₂	1	2	yes	—
261	C₂²×C₄	#6127	1	2	yes	—
262	C₂²×C₄	#6127	1	2	yes	—
263	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
264	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
265	M₁₆	—	2	8	no	—
266	M₁₆	C₄⋊Dic₁₃	1	16	yes	complemented
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	13	4	no	—
270	C₂×C₈	—	13	4	no	—
271	C₂×C₈	—	26	16	no	—
272	C₂×C₈	—	26	2	no	—
273	C₂×C₈	—	26	2	no	—
274	C₂×C₈	—	26	2	no	—
275	C₂×C₈	—	26	2	no	—
276	C₂×C₈	C₂×Dic₂₆	1	4	yes	—
277	C₂×C₈	C₂×D₅₂	1	4	yes	—
278	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
279	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
280	C₄⋊C₄	—	26	8	no	—
281	C₄⋊C₄	—	26	8	no	—
282	C₄⋊C₄	—	52	4	no	—
283	C₂²⋊C₄	—	26	8	no	—
284	C₄²	—	26	4	no	—
285	C₄²	—	26	4	no	—
286	C₄²	C₄×Dic₁₃	1	4	yes	—
287	C₄²	C₄×Dic₁₃	1	4	yes	—
288	C₄²	C₂×C₄×D₁₃	1	2	yes	—
289	C₄²	C₂×C₄×D₁₃	1	2	yes	—
290	C₄²	C₂²×Dic₁₃	1	2	yes	—
291	C₄²	C₂²×Dic₁₃	1	2	yes	—
292	C₁₃	#20441	1	1	yes	characteristic, complemented, Sylow
293	C₂³	—	2	2	no	—
294	C₂³	—	2	2	no	—
295	C₂³	C₄×Dic₂₆	1	2	yes	—
296	C₂³	C₄×D₅₂	1	2	yes	—
297	C₂³	C₂×C₄×Dic₁₃	1	2	yes	—
298	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	26	8	no	—
305	C₂×C₄	—	26	8	no	—
306	C₂×C₄	—	26	8	no	—
307	C₂×C₄	C₄×Dic₂₆	1	4	yes	—
308	C₂×C₄	C₄×Dic₂₆	1	2	yes	—
309	C₂×C₄	C₄×D₅₂	1	4	yes	—
310	C₂×C₄	C₄×D₅₂	1	2	yes	—
311	C₂×C₄	#88161	1	4	yes	—
312	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
313	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
314	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
315	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
316	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
317	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
318	C₂×C₄	#88180	1	4	yes	—
319	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
320	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
321	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
322	C₂×C₄	C₂×#6127	1	1	yes	characteristic
323	C₂×C₄	C₂×#6127	1	1	yes	characteristic
324	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
325	C₈	—	2	4	no	—
326	C₈	—	26	4	no	—
327	C₈	—	26	4	no	—
328	C₈	C₂×C₄⋊Dic₁₃	1	8	yes	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	4	no	—
333	C₂²	C₄×C₄⋊Dic₁₃	1	4	yes	—
334	C₂²	C₂×C₄×Dic₂₆	1	1	yes	characteristic
335	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
336	C₂²	C₂×#88161	1	2	yes	—
337	C₂²	#11719450	1	2	yes	—
338	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
339	C₄	—	2	2	no	—
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	52	8	no	—
343	C₄	C₄×C₄⋊Dic₁₃	1	4	yes	—
344	C₄	#11718783	1	4	yes	complemented
345	C₄	C₂×C₄×Dic₂₆	1	1	yes	characteristic
346	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
347	C₄	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
348	C₄	C₂×#88180	1	1	yes	characteristic
349	C₂	—	2	4	no	—
350	C₂	C₂×C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
351	C₂	C₂×#11718783	1	1	yes	characteristic
352	C₂	#13123254	1	1	yes	characteristic
353	C₂	#13123582	1	2	yes	—
354	C₂	#13123783	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Fitting	C₂×C₄×C₁₃×M₁₆	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₁₃
hypocenter	C₁₃	#20441
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
4. #13114708	C₂	semidirect
5. #13114703	C₂	semidirect
6. C₈×C₄⋊Dic₁₃	C₂	semidirect
14. C₄×C₁₃×M₁₆	C₄	semidirect
26. C₂×C₄⋊#1055	C₄	semidirect
90. C₁₃×M₁₆	C₄⋊C₄	semidirect
170. C₄×M₁₆	Dic₁₃	semidirect
197. C₄×C₁₃	#405	semidirect
266. M₁₆	C₄⋊Dic₁₃	semidirect
292. C₁₃	#20441	semidirect
344. C₄	#11718783	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊#1055	2
C₂×#11718783	2
#13117243	2
#13114708	2
#13114703	2
C₈×C₄⋊Dic₁₃	2
#13114534	2
C₂×C₄×C₁₃×M₁₆	2
#20441	13