Subgroups — #16016169

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13127937	C₂	1	2	yes	maximal, complemented
2	D₁₃×#443	C₂	1	1	yes	maximal, characteristic
3	#13116676	C₂	1	2	yes	maximal, complemented
4	#13116675	C₂	1	2	yes	maximal, complemented
5	#13116674	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116673	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116672	C₂	1	1	yes	maximal, characteristic, complemented
8	D₁₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116462	C₂	1	2	yes	maximal, complemented
10	C₄×#88038	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₃×#135	C₄	1	1	yes	characteristic
13	D₁₃×#131	C₂²	1	2	yes	—
14	C₁₃×#504	C₂²	1	2	yes	complemented
15	C₁₃×#443	C₂²	1	1	yes	characteristic
16	#11718857	C₄	1	1	yes	characteristic
17	#11718805	C₂²	1	2	yes	—
18	#11718801	C₂²	1	2	yes	complemented
19	#11718568	—	2	2	no	—
20	#11718568	C₂²	1	2	yes	complemented
21	D₁₃×M₃₂	—	2	2	no	—
22	D₁₃×M₃₂	C₂²	1	2	yes	—
23	#11718562	—	2	2	no	—
24	#11718562	C₂²	1	2	yes	complemented
25	C₂×#88038	—	2	2	no	—
26	C₂×#88038	C₂²	1	1	yes	characteristic
27	C₂×#88038	C₂²	1	1	yes	characteristic
28	#11718556	C₄	1	1	yes	characteristic
29	D₁₃×#108	C₄	1	1	yes	characteristic
30	#11718485	C₄	1	2	yes	—
31	D₁₃×#104	C₄	1	2	yes	—
32	#11718361	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#364	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#350	C₂²	1	2	yes	complemented
36	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
37	#11718153	C₂²	1	2	yes	complemented
38	#11718107	C₂²	1	2	yes	complemented
39	#11718103	C₂²	1	2	yes	complemented
40	#11718100	C₂²	1	2	yes	complemented
41	#11718094	C₂²	1	1	yes	characteristic, complemented
42	#11718094	C₂²	1	1	yes	characteristic, complemented
43	#11718055	C₂²	1	1	yes	characteristic, complemented
44	C₄×#6090	C₂²	1	1	yes	characteristic, complemented
45	#41×D₁₃	C₂×C₄	1	2	yes	—
46	C₁₃×#135	C₂×C₄	1	1	yes	characteristic
47	C₁₃×#131	C₂³	1	2	yes	—
48	#88204	C₂×C₄	1	2	yes	—
49	#88202	C₂×C₄	1	2	yes	—
50	#88173	C₈	1	1	yes	characteristic
51	Q₁₆×D₁₃	C₈	1	1	yes	characteristic
52	#88170	C₈	1	2	yes	—
53	SD₁₆×D₁₃	C₈	1	2	yes	—
54	#88166	C₈	1	1	yes	characteristic
55	D₈×D₁₃	C₈	1	1	yes	characteristic
56	#88161	—	2	2	no	—
57	#88161	C₂×C₄	1	2	yes	—
58	M₁₆×D₁₃	—	2	2	no	—
59	M₁₆×D₁₃	C₂×C₄	1	2	yes	—
60	#88158	C₂×C₄	1	1	yes	characteristic
61	#88155	—	2	2	no	—
62	#88155	C₂³	1	2	yes	—
63	C₂×C₈×D₁₃	—	2	2	no	—
64	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
66	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
67	C₁₃×M₃₂	—	2	2	no	—
68	C₁₃×M₃₂	C₂³	1	2	yes	—
69	C₂×C₁₃×C₁₆	—	2	2	no	—
70	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
72	C₁₃×#108	C₂×C₄	1	1	yes	characteristic
73	C₁₃×#104	C₂×C₄	1	2	yes	—
74	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	#88077	C₂×C₄	1	2	yes	—
76	#88065	C₂×C₄	1	2	yes	—
77	#88062	C₂×C₄	1	2	yes	—
78	#88059	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
81	#88052	—	2	2	no	—
82	#88052	C₂³	1	2	yes	—
83	C₂×#6090	—	2	2	no	—
84	C₂×#6090	C₂³	1	1	yes	characteristic
85	C₂×#6090	C₂³	1	1	yes	characteristic
86	#88045	C₂×C₄	1	2	yes	—
87	C₄×#1055	C₂×C₄	1	1	yes	characteristic
88	#88038	—	2	2	no	—
89	#88038	—	2	1	no	—
90	#88038	—	2	1	no	—
91	#88038	—	2	2	no	—
92	#88038	—	2	2	no	—
93	#88038	D₄	1	1	yes	characteristic
94	#88038	D₄	1	1	yes	characteristic
95	#88038	D₄	1	1	yes	characteristic
96	#88038	D₄	1	1	yes	characteristic
97	C₁₆×D₁₃	—	2	2	no	—
98	C₁₆×D₁₃	—	2	2	no	—
99	C₁₆×D₁₃	—	2	2	no	—
100	#33443	—	13	1	no	maximal, Sylow
101	C₁₃×#41	C₂²×C₄	1	2	yes	—
102	#6131	C₂×C₈	1	2	yes	—
103	Q₈×D₁₃	C₂×C₈	1	2	yes	—
104	#6129	—	2	2	no	—
105	#6129	C₂×C₈	1	2	yes	—
106	D₄×D₁₃	—	2	2	no	—
107	D₄×D₁₃	C₂×C₈	1	2	yes	—
108	#6127	—	2	2	no	—
109	#6127	C₂²×C₄	1	2	yes	—
110	C₂×C₄×D₁₃	—	2	2	no	—
111	C₂×C₄×D₁₃	—	2	1	no	—
112	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₁₃×Q₁₆	C₂×C₈	1	1	yes	characteristic
114	C₁₃×SD₁₆	C₂×C₈	1	2	yes	—
115	C₁₃×D₈	C₂×C₈	1	1	yes	characteristic
116	C₁₃×M₁₆	—	2	2	no	—
117	C₁₃×M₁₆	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	#6107	C₂×C₈	1	2	yes	—
123	#6106	C₂×C₈	1	2	yes	—
124	#6105	C₂×C₈	1	2	yes	—
125	#6104	C₂×C₈	1	2	yes	—
126	C₄×Dic₁₃	—	2	1	no	—
127	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
128	#6099	—	2	2	no	—
129	#6099	C₂²×C₄	1	2	yes	—
130	C₂×#1055	—	2	2	no	—
131	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
132	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
133	Dic₅₂	C₂×C₈	1	1	yes	characteristic
134	D₁₀₄	C₂×C₈	1	1	yes	characteristic
135	#6095	C₂×C₈	1	2	yes	—
136	#6094	—	2	2	no	—
137	#6094	—	2	2	no	—
138	#6094	—	2	2	no	—
139	C₈×D₁₃	—	2	2	no	—
140	C₈×D₁₃	—	2	2	no	—
141	C₈×D₁₃	—	2	2	no	—
142	C₈×D₁₃	C₂×C₈	1	1	yes	characteristic
143	C₈×D₁₃	C₂×C₈	1	1	yes	characteristic
144	C₈×D₁₃	C₂×C₈	1	1	yes	characteristic
145	C₈×D₁₃	C₂×C₈	1	1	yes	characteristic
146	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
147	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
148	C₈×D₁₃	#41	1	1	yes	characteristic
149	C₈×D₁₃	#41	1	1	yes	characteristic
150	C₁₃×C₁₆	—	2	2	no	—
151	C₁₃×C₁₆	—	2	1	no	—
152	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
153	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
154	#6090	—	2	2	no	—
155	#6090	—	2	1	no	—
156	#6090	C₂×D₄	1	1	yes	characteristic
157	#6090	C₂×D₄	1	1	yes	characteristic
158	#3407	—	13	2	no	—
159	C₂×#443	—	13	1	no	—
160	#2171	—	13	2	no	—
161	#2171	—	13	2	no	—
162	#2170	—	13	1	no	—
163	#2170	—	13	1	no	—
164	#2170	—	13	1	no	—
165	#2170	D₁₃	1	1	yes	characteristic, complemented
166	C₂×#364	—	13	1	no	—
167	#2117	—	13	2	no	—
168	C₄×M₃₂	—	13	1	no	—
169	C₂²×D₁₃	—	2	2	no	—
170	C₂²×D₁₃	#131	1	1	yes	characteristic
171	Q₈×C₁₃	C₂²×C₈	1	2	yes	—
172	D₄×C₁₃	—	2	2	no	—
173	D₄×C₁₃	C₂²×C₈	1	2	yes	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
177	C₂²⋊D₁₃	—	2	2	no	—
178	C₂²⋊D₁₃	—	2	2	no	—
179	C₂²⋊D₁₃	—	2	2	no	—
180	C₂×Dic₁₃	—	2	2	no	—
181	C₂×Dic₁₃	—	2	1	no	—
182	C₂×Dic₁₃	#131	1	1	yes	characteristic
183	D₅₂	—	2	2	no	—
184	D₅₂	C₂²×C₈	1	2	yes	—
185	C₄×D₁₃	—	2	2	no	—
186	C₄×D₁₃	—	2	2	no	—
187	C₄×D₁₃	—	2	2	no	—
188	C₄×D₁₃	—	4	2	no	—
189	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
190	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
191	C₄×D₁₃	C₂²×C₈	1	1	yes	characteristic
192	C₄×D₁₃	C₂²×C₈	1	1	yes	characteristic
193	Dic₂₆	—	2	2	no	—
194	Dic₂₆	C₂²×C₈	1	2	yes	—
195	C₈×C₁₃	—	2	2	no	—
196	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
197	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
198	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
200	#1055	—	2	2	no	—
201	#1055	C₄×D₄	1	1	yes	characteristic
202	#1055	C₄×D₄	1	1	yes	characteristic
203	#1055	C₂²×C₈	1	1	yes	characteristic
204	#1055	C₂²×C₈	1	1	yes	characteristic
205	C₂×#135	—	13	1	no	—
206	C₂×#131	—	13	2	no	—
207	#504	—	13	2	no	—
208	#504	—	13	2	no	—
209	#504	—	13	2	no	—
210	#504	—	26	2	no	—
211	#504	—	26	2	no	—
212	#504	C₂×D₁₃	1	2	yes	complemented
213	C₂×M₃₂	—	13	1	no	—
214	C₂×M₃₂	—	13	1	no	—
215	C₂×M₃₂	—	13	2	no	—
216	C₂×M₃₂	—	26	2	no	—
217	C₂×M₃₂	—	26	2	no	—
218	#443	—	13	1	no	—
219	#443	—	13	2	no	—
220	#443	—	13	1	no	—
221	#443	—	13	2	no	—
222	#443	—	13	1	no	—
223	#443	C₂×D₁₃	1	1	yes	characteristic
224	C₂×#108	—	13	1	no	—
225	C₂×#104	—	13	2	no	—
226	C₂×C₄×C₈	—	13	1	no	—
227	#364	—	13	2	no	—
228	#364	—	13	1	no	—
229	#364	C₂×D₁₃	1	1	yes	characteristic, complemented
230	#350	—	13	2	no	—
231	#350	—	13	2	no	—
232	#350	—	13	2	no	—
233	#350	C₂×D₁₃	1	2	yes	complemented
234	#346	—	13	1	no	—
235	#346	—	13	1	no	—
236	C₄×C₁₆	—	13	1	no	—
237	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
240	C₂×D₁₃	—	2	2	no	—
241	C₂×D₁₃	—	4	1	no	—
242	C₂×D₁₃	—	8	2	no	—
243	C₂×D₁₃	C₈×D₄	1	1	yes	characteristic
244	C₂×D₁₃	C₈×D₄	1	1	yes	characteristic
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
248	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
249	Dic₁₃	—	2	2	no	—
250	Dic₁₃	—	4	1	no	—
251	Dic₁₃	C₈×D₄	1	1	yes	characteristic
252	Dic₁₃	C₈×D₄	1	1	yes	characteristic
253	C₂×#41	—	13	2	no	—
254	#135	—	13	2	no	—
255	#135	—	13	1	no	—
256	#135	—	13	2	no	—
257	#135	—	13	1	no	—
258	#135	—	13	1	no	—
259	#135	C₄×D₁₃	1	1	yes	characteristic
260	C₂×Q₁₆	—	13	1	no	—
261	C₂×SD₁₆	—	13	2	no	—
262	C₂×D₈	—	13	1	no	—
263	#131	—	13	2	no	—
264	#131	—	13	2	no	—
265	#131	—	13	2	no	—
266	#131	—	26	2	no	—
267	#131	—	26	2	no	—
268	#131	C₂²×D₁₃	1	2	yes	—
269	C₂×M₁₆	—	13	2	no	—
270	C₂×M₁₆	—	26	2	no	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	—	13	1	no	—
273	C₂²×C₈	—	26	2	no	—
274	C₂×C₄²	—	13	1	no	—
275	M₃₂	—	2	2	no	—
276	M₃₂	—	13	1	no	—
277	M₃₂	—	13	1	no	—
278	M₃₂	—	13	1	no	—
279	M₃₂	—	13	1	no	—
280	M₃₂	—	13	2	no	—
281	M₃₂	—	26	2	no	—
282	M₃₂	—	26	1	no	—
283	M₃₂	—	26	1	no	—
284	M₃₂	—	26	2	no	—
285	M₃₂	—	26	2	no	—
286	M₃₂	—	26	2	no	—
287	M₃₂	C₂²×D₁₃	1	2	yes	—
288	C₂×C₁₆	—	2	2	no	—
289	C₂×C₁₆	—	13	1	no	—
290	C₂×C₁₆	—	13	1	no	—
291	C₂×C₁₆	—	26	2	no	—
292	C₂×C₁₆	—	26	2	no	—
293	C₂×C₁₆	—	26	2	no	—
294	C₂×C₁₆	—	26	2	no	—
295	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
296	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
297	#108	—	13	2	no	—
298	#108	—	13	1	no	—
299	#108	C₄×D₁₃	1	1	yes	characteristic
300	#104	—	13	2	no	—
301	#104	—	13	2	no	—
302	#104	—	13	2	no	—
303	#104	C₄×D₁₃	1	2	yes	—
304	C₄×C₈	—	13	1	no	—
305	C₄×C₈	—	13	1	no	—
306	C₄×C₈	—	13	1	no	—
307	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
308	C₂×C₁₃	—	2	1	no	—
309	C₂×C₁₃	—	4	2	no	—
310	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
311	D₁₃	—	2	1	no	—
312	D₁₃	—	2	1	no	—
313	D₁₃	—	4	2	no	—
314	#41	—	13	2	no	—
315	#41	—	13	2	no	—
316	#41	—	13	2	no	—
317	#41	—	26	2	no	—
318	#41	—	26	2	no	—
319	#41	C₂×C₄×D₁₃	1	2	yes	—
320	C₂×Q₈	—	13	2	no	—
321	C₂×D₄	—	13	2	no	—
322	C₂×D₄	—	26	2	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	26	2	no	—
325	C₂²×C₄	—	26	1	no	—
326	Q₁₆	—	13	2	no	—
327	Q₁₆	—	13	1	no	—
328	Q₁₆	C₈×D₁₃	1	1	yes	characteristic
329	SD₁₆	—	13	2	no	—
330	SD₁₆	—	13	2	no	—
331	SD₁₆	—	13	2	no	—
332	SD₁₆	C₈×D₁₃	1	2	yes	—
333	D₈	—	13	2	no	—
334	D₈	—	13	1	no	—
335	D₈	C₈×D₁₃	1	1	yes	characteristic
336	M₁₆	—	2	2	no	—
337	M₁₆	—	13	2	no	—
338	M₁₆	—	26	2	no	—
339	M₁₆	—	26	2	no	—
340	M₁₆	—	26	2	no	—
341	M₁₆	—	26	2	no	—
342	M₁₆	C₂×C₄×D₁₃	1	2	yes	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	13	1	no	—
345	C₂×C₈	—	13	1	no	—
346	C₂×C₈	—	13	1	no	—
347	C₂×C₈	—	13	1	no	—
348	C₂×C₈	—	13	1	no	—
349	C₂×C₈	—	13	1	no	—
350	C₂×C₈	—	13	1	no	—
351	C₂×C₈	—	13	1	no	—
352	C₂×C₈	—	13	1	no	—
353	C₂×C₈	—	13	1	no	—
354	C₂×C₈	—	26	2	no	—
355	C₂×C₈	—	26	2	no	—
356	C₂×C₈	—	26	2	no	—
357	C₂×C₈	—	26	2	no	—
358	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
359	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
360	C₄²	—	13	1	no	—
361	C₄²	—	26	1	no	—
362	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
363	C₁₆	—	2	2	no	—
364	C₁₆	—	2	1	no	—
365	C₁₆	—	13	1	no	—
366	C₁₆	—	13	1	no	—
367	C₁₆	—	26	2	no	—
368	C₁₆	—	26	1	no	—
369	C₁₆	D₄×D₁₃	1	1	yes	characteristic
370	C₁₆	D₄×D₁₃	1	1	yes	characteristic
371	C₁₃	#33443	1	1	yes	characteristic, complemented, Sylow
372	C₂³	—	13	1	no	—
373	C₂³	—	26	2	no	—
374	Q₈	—	13	2	no	—
375	Q₈	—	26	2	no	—
376	Q₈	C₂×C₈×D₁₃	1	2	yes	—
377	D₄	—	2	2	no	—
378	D₄	—	13	2	no	—
379	D₄	—	26	2	no	—
380	D₄	—	26	2	no	—
381	D₄	—	26	2	no	—
382	D₄	—	26	2	no	—
383	D₄	C₂×C₈×D₁₃	1	2	yes	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	13	1	no	—
387	C₂×C₄	—	13	1	no	—
388	C₂×C₄	—	13	1	no	—
389	C₂×C₄	—	13	1	no	—
390	C₂×C₄	—	13	1	no	—
391	C₂×C₄	—	26	2	no	—
392	C₂×C₄	—	26	2	no	—
393	C₂×C₄	—	26	2	no	—
394	C₂×C₄	—	26	2	no	—
395	C₂×C₄	—	26	1	no	—
396	C₂×C₄	—	52	2	no	—
397	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	13	1	no	—
400	C₈	—	13	1	no	—
401	C₈	—	13	1	no	—
402	C₈	—	13	1	no	—
403	C₈	—	26	2	no	—
404	C₈	C₂×C₈×D₁₃	1	1	yes	characteristic
405	C₈	C₂×C₈×D₁₃	1	1	yes	characteristic
406	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
407	C₈	#41×D₁₃	1	1	yes	characteristic
408	C₂²	—	2	2	no	—
409	C₂²	—	13	1	no	—
410	C₂²	—	13	1	no	—
411	C₂²	—	26	2	no	—
412	C₂²	—	52	1	no	—
413	C₂²	—	104	2	no	—
414	C₂²	D₁₃×#131	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	13	1	no	—
418	C₄	—	13	1	no	—
419	C₄	—	26	2	no	—
420	C₄	—	52	1	no	—
421	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
422	C₄	C₂²×C₈×D₁₃	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	26	1	no	—
426	C₂	—	26	1	no	—
427	C₂	—	52	2	no	—
428	C₂	C₈×D₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₁₃
commutator	C₄×C₁₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2170	C₂
socle	C₂×C₁₃	C₂×C₈×D₄
prime radical	D₁₃×#135	C₄
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2170	D₁₃
hypocenter	C₁₃	#33443
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #2170

Complements

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

N	H ≅ G/N	type
1. #13127937	C₂	semidirect
3. #13116676	C₂	semidirect
4. #13116675	C₂	semidirect
5. #13116674	C₂	semidirect
6. #13116673	C₂	semidirect
7. #13116672	C₂	semidirect
8. D₁₃×#364	C₂	semidirect
9. #13116462	C₂	semidirect
10. C₄×#88038	C₂	semidirect
11. C₁₃×#2170	C₂	semidirect
14. C₁₃×#504	C₂²	semidirect
18. #11718801	C₂²	semidirect
20. #11718568	C₂²	semidirect
24. #11718562	C₂²	semidirect
34. C₁₃×#364	C₂²	semidirect
35. C₁₃×#350	C₂²	semidirect
36. C₄×C₁₃×C₁₆	C₂²	semidirect
37. #11718153	C₂²	semidirect
38. #11718107	C₂²	semidirect
39. #11718103	C₂²	semidirect
40. #11718100	C₂²	semidirect
41. #11718094	C₂²	semidirect
42. #11718094	C₂²	semidirect
43. #11718055	C₂²	semidirect
44. C₄×#6090	C₂²	semidirect
165. #2170	D₁₃	semidirect
212. #504	C₂×D₁₃	semidirect
229. #364	C₂×D₁₃	semidirect
233. #350	C₂×D₁₃	semidirect
237. C₄×C₁₆	C₂×D₁₃	semidirect
371. C₁₃	#33443	semidirect

Maximal subgroups

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

subgroup	index
#13127937	2
D₁₃×#443	2
#13116676	2
#13116675	2
#13116674	2
#13116673	2
#13116672	2
D₁₃×#364	2
#13116462	2
C₄×#88038	2
C₁₃×#2170	2
#33443	13