Subgroups — #16016138

Order 3328.

682 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718568	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123546	C₂	1	1	yes	maximal, characteristic
3	#13116666	C₂	1	2	yes	maximal, complemented
4	#13116661	C₂	1	2	yes	maximal, complemented
5	#13116659	C₂	1	2	yes	maximal, complemented
6	C₁₆×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
7	C₂×#11718093	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116450	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116449	C₂	1	1	yes	maximal, characteristic, complemented
10	M₃₂×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
13	#11719537	C₄	1	1	yes	characteristic
14	C₂×#88155	C₂²	1	1	yes	characteristic
15	C₁₃×#504	—	2	4	no	—
16	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
17	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
20	#11718895	C₄	1	1	yes	characteristic
21	#11718790	C₄	1	1	yes	characteristic
22	#11718789	C₄	1	2	yes	—
23	#11718789	C₄	1	2	yes	—
24	#11718779	C₄	1	1	yes	characteristic
25	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	—
26	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	—
27	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
28	C₂×#88052	C₂²	1	1	yes	characteristic
29	C₂²×#6090	C₂²	1	1	yes	characteristic
30	#11718568	—	2	4	no	—
31	C₂×#88038	C₂²	1	2	yes	—
32	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
33	C₂²⋊#6090	C₂²	1	2	yes	—
34	C₂²⋊#6090	C₂²	1	2	yes	—
35	#11718099	C₂²	1	2	yes	—
36	#11718099	C₂²	1	2	yes	—
37	#11718094	C₂²	1	2	yes	—
38	#11718093	C₂²	1	1	yes	characteristic
39	#11718093	C₂²	1	1	yes	characteristic
40	#11718093	C₂²	1	1	yes	characteristic
41	#11718093	C₂²	1	1	yes	characteristic
42	C₁₆×Dic₁₃	C₂²	1	2	yes	—
43	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
44	C₂×#6127	C₂×C₄	1	1	yes	characteristic
45	C₁₃×#131	—	2	2	no	—
46	C₁₃×#131	—	2	2	no	—
47	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	#88201	C₈	1	1	yes	characteristic
52	#88198	C₈	1	1	yes	characteristic
53	#88194	C₈	1	1	yes	characteristic
54	#88193	C₈	1	2	yes	—
55	#88193	C₈	1	2	yes	—
56	#88190	C₈	1	1	yes	characteristic
57	C₄×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
58	C₄×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×#6099	C₂×C₄	1	1	yes	characteristic
61	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
62	#88155	—	2	2	no	—
63	#88155	—	2	2	no	—
64	C₂×#6094	C₂×C₄	1	2	yes	—
65	C₂×C₈×D₁₃	C₂³	1	2	yes	—
66	C₁₃×M₃₂	—	2	4	no	—
67	C₁₃×M₃₂	D₄	1	4	yes	complemented
68	C₂×C₁₃×C₁₆	—	2	2	no	—
69	C₂×C₁₃×C₁₆	—	2	4	no	—
70	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
73	C₂²⋊#1055	C₂×C₄	1	2	yes	—
74	C₂²⋊#1055	C₂×C₄	1	2	yes	—
75	#88060	C₂×C₄	1	2	yes	—
76	#88060	C₂×C₄	1	2	yes	—
77	#88054	C₂×C₄	1	2	yes	—
78	#88054	C₂×C₄	1	2	yes	—
79	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
82	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
83	#88052	—	2	2	no	—
84	C₂×#6090	—	2	2	no	—
85	C₂×#6090	C₂³	1	1	yes	characteristic
86	C₂×#6090	C₂³	1	1	yes	characteristic
87	C₂×#6090	C₂³	1	2	yes	—
88	#88038	—	2	4	no	—
89	C₁₆×D₁₃	—	2	4	no	—
90	#33438	—	13	1	no	maximal, Sylow
91	C₁₃×#41	—	2	2	no	—
92	C₁₃×#41	—	2	2	no	—
93	C₂×Q₈×C₁₃	C₂×C₈	1	1	yes	characteristic
94	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
95	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊D₁₃	C₂×C₈	1	2	yes	—
99	C₂×C₂²⋊D₁₃	C₂×C₈	1	2	yes	—
100	C₂×C₂²⋊D₁₃	C₂×C₈	1	2	yes	—
101	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
102	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
103	#6127	—	2	2	no	—
104	#6127	—	2	2	no	—
105	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
107	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
108	C₁₃×M₁₆	—	2	2	no	—
109	C₁₃×M₁₆	—	2	4	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₁₃	#41	1	2	yes	—
116	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₂²⋊Dic₁₃	C₂×C₈	1	2	yes	—
118	C₂²⋊Dic₁₃	C₂×C₈	1	2	yes	—
119	#6103	C₂×C₈	1	2	yes	—
120	#6103	C₂×C₈	1	2	yes	—
121	#6101	C₂×C₈	1	2	yes	—
122	#6101	C₂×C₈	1	2	yes	—
123	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
124	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
125	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
127	#6099	—	2	2	no	—
128	C₂×#1055	—	2	2	no	—
129	C₂×#1055	C₂²×C₄	1	2	yes	—
130	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
131	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
132	#6094	—	2	4	no	—
133	C₈×D₁₃	—	2	2	no	—
134	C₈×D₁₃	—	2	2	no	—
135	C₁₃×C₁₆	—	2	1	no	—
136	C₁₃×C₁₆	—	2	1	no	—
137	C₁₃×C₁₆	C₂×D₄	1	4	yes	—
138	#6090	—	2	1	no	—
139	#6090	—	2	1	no	—
140	#6090	—	2	2	no	—
141	C₂×#504	—	13	1	no	—
142	C₂×#504	D₁₃	1	1	yes	characteristic, complemented
143	#2931	—	13	1	no	—
144	#2169	—	13	2	no	—
145	#2168	—	13	2	no	—
146	#2168	—	13	2	no	—
147	D₄×C₁₆	—	13	2	no	—
148	C₂×C₄⋊C₁₆	—	13	1	no	—
149	#2113	—	13	1	no	—
150	#2113	—	13	1	no	—
151	C₄×M₃₂	—	13	1	no	—
152	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
153	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
154	C₂²×D₁₃	C₂²×C₈	1	2	yes	—
155	Q₈×C₁₃	—	2	2	no	—
156	D₄×C₁₃	—	2	4	no	—
157	D₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
162	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
163	C₂×C₄×C₁₃	#131	1	2	yes	—
164	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
165	C₂²⋊D₁₃	—	2	4	no	—
166	C₂²⋊D₁₃	—	2	4	no	—
167	C₂²⋊D₁₃	—	4	2	no	—
168	C₂×Dic₁₃	—	2	2	no	—
169	C₂×Dic₁₃	—	4	1	no	—
170	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
171	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
172	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
173	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
174	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
175	D₅₂	—	2	2	no	—
176	C₄×D₁₃	—	2	2	no	—
177	C₄×D₁₃	—	2	2	no	—
178	Dic₂₆	—	2	2	no	—
179	C₈×C₁₃	—	2	2	no	—
180	C₈×C₁₃	C₄×D₄	1	2	yes	—
181	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
183	#1055	—	2	2	no	—
184	#1055	—	2	1	no	—
185	#1055	—	2	1	no	—
186	C₂×#131	—	13	1	no	—
187	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
188	#532	—	13	1	no	—
189	#504	—	2	4	no	—
190	#504	—	26	4	no	—
191	C₂×M₃₂	—	13	1	no	—
192	C₂×M₃₂	—	13	2	no	—
193	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
194	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
195	C₂²×C₁₆	—	13	1	no	—
196	C₂²×C₁₆	—	13	2	no	—
197	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
198	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
199	#436	—	13	2	no	—
200	#436	—	13	2	no	—
201	C₈×D₄	—	13	2	no	—
202	C₈×D₄	—	13	2	no	—
203	#423	—	13	1	no	—
204	#408	—	13	1	no	—
205	#408	—	13	1	no	—
206	C₂×C₄×C₈	—	13	1	no	—
207	C₄⋊C₁₆	—	13	1	no	—
208	C₄⋊C₁₆	—	13	1	no	—
209	C₄⋊C₁₆	—	13	1	no	—
210	C₄⋊C₁₆	—	13	1	no	—
211	C₂²⋊C₁₆	—	13	2	no	—
212	C₂²⋊C₁₆	—	13	2	no	—
213	C₂²⋊C₁₆	—	13	2	no	—
214	C₂²⋊C₁₆	—	13	2	no	—
215	#346	—	13	2	no	—
216	C₄×C₁₆	—	13	2	no	—
217	C₂²×C₁₃	—	2	1	no	—
218	C₂²×C₁₃	—	2	1	no	—
219	C₂²×C₁₃	—	2	2	no	—
220	C₂²×C₁₃	—	2	2	no	—
221	C₂²×C₁₃	—	2	2	no	—
222	C₂²×C₁₃	C₈×D₄	1	2	yes	—
223	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
224	C₂×D₁₃	—	2	2	no	—
225	C₂×D₁₃	—	2	2	no	—
226	C₂×D₁₃	—	2	2	no	—
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	C₈×D₄	1	2	yes	—
229	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
230	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
231	Dic₁₃	—	2	1	no	—
232	Dic₁₃	—	2	1	no	—
233	Dic₁₃	—	2	1	no	—
234	Dic₁₃	—	2	2	no	—
235	Dic₁₃	#504	1	2	yes	complemented
236	C₂×#41	—	13	1	no	—
237	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
238	#131	—	2	2	no	—
239	#131	—	2	2	no	—
240	#131	—	26	2	no	—
241	#131	—	26	2	no	—
242	C₂×M₁₆	—	13	1	no	—
243	C₂×M₁₆	—	13	2	no	—
244	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
245	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
246	C₂²×C₈	—	13	1	no	—
247	C₂²×C₈	—	13	2	no	—
248	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
249	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
250	C₄⋊Q₈	—	13	1	no	—
251	#127	—	13	1	no	—
252	#124	—	13	1	no	—
253	#124	—	13	1	no	—
254	#121	—	13	2	no	—
255	#121	—	13	2	no	—
256	C₄×D₄	—	13	2	no	—
257	C₄×D₄	—	13	2	no	—
258	C₂×C₄²	—	13	1	no	—
259	M₃₂	—	2	4	no	—
260	M₃₂	—	26	2	no	—
261	M₃₂	—	26	4	no	—
262	M₃₂	C₂²⋊D₁₃	1	4	yes	complemented
263	C₂×C₁₆	—	2	2	no	—
264	C₂×C₁₆	—	2	4	no	—
265	C₂×C₁₆	—	13	2	no	—
266	C₂×C₁₆	—	13	1	no	—
267	C₂×C₁₆	—	13	1	no	—
268	C₂×C₁₆	—	26	2	no	—
269	C₂×C₁₆	—	26	4	no	—
270	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
271	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
272	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
273	C₄⋊C₈	—	13	2	no	—
274	C₄⋊C₈	—	13	2	no	—
275	C₂²⋊C₈	—	13	2	no	—
276	C₂²⋊C₈	—	13	2	no	—
277	C₂²⋊C₈	—	13	2	no	—
278	C₂²⋊C₈	—	13	2	no	—
279	C₄×C₈	—	13	1	no	—
280	C₄×C₈	—	13	1	no	—
281	C₄×C₈	—	13	1	no	—
282	C₄×C₈	—	13	1	no	—
283	C₂×C₁₃	—	2	2	no	—
284	C₂×C₁₃	—	4	2	no	—
285	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
286	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
287	C₂×C₁₃	#3407	1	1	yes	characteristic
288	D₁₃	—	4	2	no	—
289	#41	—	2	2	no	—
290	#41	—	2	2	no	—
291	#41	—	26	2	no	—
292	#41	—	26	2	no	—
293	C₂×Q₈	—	13	1	no	—
294	C₂×Q₈	C₈×D₁₃	1	1	yes	characteristic
295	C₂×D₄	—	13	2	no	—
296	C₂×D₄	—	13	2	no	—
297	C₂×D₄	—	13	2	no	—
298	C₂×D₄	—	13	1	no	—
299	C₂×D₄	C₈×D₁₃	1	2	yes	—
300	C₂×D₄	C₈×D₁₃	1	1	yes	characteristic
301	C₂²×C₄	—	13	1	no	—
302	C₂²×C₄	—	13	1	no	—
303	C₂²×C₄	—	13	2	no	—
304	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
305	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
306	M₁₆	—	2	2	no	—
307	M₁₆	—	2	4	no	—
308	M₁₆	—	26	2	no	—
309	M₁₆	—	26	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	13	1	no	—
313	C₂×C₈	—	13	1	no	—
314	C₂×C₈	—	13	2	no	—
315	C₂×C₈	—	26	2	no	—
316	C₂×C₈	—	26	2	no	—
317	C₂×C₈	—	26	2	no	—
318	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
319	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
320	C₂×C₈	#6127	1	2	yes	—
321	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
322	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
323	C₄⋊C₄	—	13	2	no	—
324	C₄⋊C₄	—	13	2	no	—
325	C₂²⋊C₄	—	13	2	no	—
326	C₂²⋊C₄	—	13	2	no	—
327	C₂²⋊C₄	—	13	2	no	—
328	C₂²⋊C₄	—	13	2	no	—
329	C₄²	—	13	1	no	—
330	C₄²	—	13	1	no	—
331	C₄²	—	13	1	no	—
332	C₄²	—	13	1	no	—
333	C₁₆	—	2	1	no	—
334	C₁₆	—	2	1	no	—
335	C₁₆	—	26	2	no	—
336	C₁₆	—	26	1	no	—
337	C₁₆	—	26	1	no	—
338	C₁₆	C₂×C₂²⋊D₁₃	1	4	yes	—
339	C₁₃	#33438	1	1	yes	characteristic, complemented, Sylow
340	C₂³	—	13	2	no	—
341	C₂³	C₂×C₈×D₁₃	1	2	yes	—
342	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
343	Q₈	—	2	2	no	—
344	Q₈	—	26	2	no	—
345	D₄	—	2	4	no	—
346	D₄	—	2	2	no	—
347	D₄	—	26	4	no	—
348	D₄	—	26	4	no	—
349	D₄	—	26	2	no	—
350	D₄	—	52	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	13	1	no	—
354	C₂×C₄	—	13	1	no	—
355	C₂×C₄	—	13	1	no	—
356	C₂×C₄	—	13	1	no	—
357	C₂×C₄	—	13	2	no	—
358	C₂×C₄	—	26	2	no	—
359	C₂×C₄	—	26	2	no	—
360	C₂×C₄	—	26	2	no	—
361	C₂×C₄	—	52	1	no	—
362	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
363	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
364	C₂×C₄	#88155	1	2	yes	—
365	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
366	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
367	C₈	—	2	2	no	—
368	C₈	—	26	1	no	—
369	C₈	—	26	1	no	—
370	C₈	—	26	2	no	—
371	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
372	C₈	C₂×#6127	1	1	yes	characteristic
373	C₈	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	26	2	no	—
380	C₂²	—	26	2	no	—
381	C₂²	—	26	2	no	—
382	C₂²	C₈×C₂²⋊D₁₃	1	2	yes	—
383	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	13	2	no	—
386	C₄	—	26	1	no	—
387	C₄	—	26	1	no	—
388	C₄	—	26	2	no	—
389	C₄	—	26	1	no	—
390	C₄	C₈×C₂²⋊D₁₃	1	2	yes	—
391	C₄	C₂×#88155	1	1	yes	characteristic
392	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
393	C₂	—	2	2	no	—
394	C₂	—	4	2	no	—
395	C₂	—	52	2	no	—
396	C₂	C₂×C₈×C₂²⋊D₁₃	1	1	yes	characteristic
397	C₂	D₁₃×#504	1	1	yes	characteristic
398	C₂	#13127937	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₂×C₁₃×#504	C₂
prime radical	#11719537	C₄
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#504	D₁₃
hypocenter	C₁₃	#33438
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. C₂×#11718568	C₂	semidirect
3. #13116666	C₂	semidirect
4. #13116661	C₂	semidirect
5. #13116659	C₂	semidirect
6. C₁₆×C₂²⋊D₁₃	C₂	semidirect
7. C₂×#11718093	C₂	semidirect
8. #13116450	C₂	semidirect
9. #13116449	C₂	semidirect
10. M₃₂×Dic₁₃	C₂	semidirect
11. C₂×C₁₃×#504	C₂	semidirect
67. C₁₃×M₃₂	D₄	semidirect
142. C₂×#504	D₁₃	semidirect
235. Dic₁₃	#504	semidirect
262. M₃₂	C₂²⋊D₁₃	semidirect
339. C₁₃	#33438	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718568	2
#13123546	2
#13116666	2
#13116661	2
#13116659	2
C₁₆×C₂²⋊D₁₃	2
C₂×#11718093	2
#13116450	2
#13116449	2
M₃₂×Dic₁₃	2
C₂×C₁₃×#504	2
#33438	13