Subgroups — #15756833

Order 3328.

552 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₅₂	C₂	1	1	yes	maximal, characteristic
2	#13115554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#88061	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718050	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11718051	C₂	1	1	yes	maximal, characteristic
6	#13112676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₁₃	—	2	1	no	—
9	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×#88061	C₄	1	1	yes	characteristic
14	C₂×#88061	C₄	1	1	yes	characteristic
15	C₂×#88060	—	2	1	no	—
16	C₂×#88054	—	2	1	no	—
17	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
20	C₈×D₅₂	—	2	2	no	—
21	C₈×D₅₂	—	2	2	no	—
22	#11718143	C₄	1	1	yes	characteristic
23	#11718143	C₄	1	1	yes	characteristic
24	#11718142	—	2	1	no	—
25	#11718051	—	2	2	no	—
26	#11718050	—	2	2	no	—
27	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₃	—	2	1	no	—
29	C₂²×C₈×C₁₃	—	2	1	no	—
30	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
35	C₂×#6103	—	2	1	no	—
36	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×Dic₁₃	—	2	1	no	—
40	C₂²×#1055	—	2	1	no	—
41	C₂²×#1055	—	2	1	no	—
42	C₂×C₈×D₁₃	—	2	4	no	—
43	C₂×C₈×D₁₃	—	4	2	no	—
44	C₂×C₈×D₁₃	—	4	2	no	—
45	C₄×D₅₂	—	2	1	no	—
46	C₄×D₅₂	—	2	1	no	—
47	C₄×D₅₂	D₄	1	2	yes	—
48	C₄×D₅₂	Q₈	1	2	yes	—
49	C₄×C₈×C₁₃	—	2	1	no	—
50	C₄×C₈×C₁₃	—	2	1	no	—
51	C₄×C₈×C₁₃	—	2	1	no	—
52	C₄×C₈×C₁₃	—	2	1	no	—
53	C₄×C₈×C₁₃	—	2	1	no	—
54	C₄×C₈×C₁₃	—	2	1	no	—
55	#88071	—	2	1	no	—
56	#88061	—	2	2	no	—
57	#88061	C₈	1	4	yes	complemented
58	#88060	—	2	4	no	—
59	#88054	—	4	2	no	—
60	C₄⋊#1055	—	2	1	no	—
61	C₄⋊#1055	—	2	1	no	—
62	C₄⋊#1055	—	2	1	no	—
63	C₄⋊#1055	D₄	1	2	yes	—
64	#8843	—	13	1	no	maximal, Sylow
65	C₂³×D₁₃	—	2	1	no	—
66	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
69	C₂²×Dic₁₃	—	2	1	no	—
70	C₂²×Dic₁₃	—	2	1	no	—
71	C₂²×Dic₁₃	—	2	1	no	—
72	C₂×D₅₂	—	2	1	no	—
73	C₂×D₅₂	—	2	1	no	—
74	C₂×D₅₂	—	2	1	no	—
75	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
76	C₂×D₅₂	C₂×C₈	1	2	yes	—
77	C₂×D₅₂	M₁₆	1	2	yes	—
78	C₂×C₄×D₁₃	—	2	2	no	—
79	C₂×C₄×D₁₃	—	2	2	no	—
80	C₂×C₄×D₁₃	—	4	1	no	—
81	C₂×C₄×D₁₃	—	4	1	no	—
82	C₂×C₄×D₁₃	—	4	1	no	—
83	C₂×C₄×D₁₃	—	4	1	no	—
84	C₂×C₈×C₁₃	—	2	1	no	—
85	C₂×C₈×C₁₃	—	2	1	no	—
86	C₂×C₈×C₁₃	—	2	1	no	—
87	C₂×C₈×C₁₃	—	2	1	no	—
88	C₂×C₈×C₁₃	—	2	2	no	—
89	C₂×C₈×C₁₃	—	2	1	no	—
90	C₂×C₈×C₁₃	—	2	1	no	—
91	C₂×C₈×C₁₃	—	2	1	no	—
92	C₂×C₈×C₁₃	—	2	1	no	—
93	C₂×C₈×C₁₃	—	2	1	no	—
94	C₂×C₈×C₁₃	—	2	1	no	—
95	C₂×C₈×C₁₃	—	4	1	no	—
96	C₂×C₈×C₁₃	—	4	1	no	—
97	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	complemented
98	C₂×C₈×C₁₃	D₈	1	2	yes	—
99	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
102	C₄²×C₁₃	#41	1	1	yes	characteristic
103	#6103	—	2	2	no	—
104	#6103	—	2	2	no	—
105	C₄⋊Dic₁₃	—	2	1	no	—
106	C₄⋊Dic₁₃	—	2	1	no	—
107	C₄⋊Dic₁₃	—	2	1	no	—
108	C₄⋊Dic₁₃	—	2	1	no	—
109	C₄⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
110	C₄⋊Dic₁₃	C₂×C₈	1	2	yes	complemented
111	C₄×Dic₁₃	—	4	1	no	—
112	C₄×Dic₁₃	—	4	1	no	—
113	C₂×#1055	—	2	2	no	—
114	C₂×#1055	—	4	1	no	—
115	C₂×#1055	—	4	1	no	—
116	C₂×#1055	—	4	1	no	—
117	C₂×#1055	—	4	1	no	—
118	C₂×#1055	—	4	1	no	—
119	C₈×D₁₃	—	4	8	no	—
120	C₂×C₈×D₄	—	13	1	no	—
121	#1939	—	13	1	no	—
122	C₄×#102	—	13	1	no	—
123	C₂×#335	—	13	1	no	—
124	C₂×D₄⋊C₈	—	13	1	no	—
125	#1279	—	13	1	no	—
126	#1273	D₁₃	1	1	yes	characteristic, complemented
127	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
128	C₂²×D₁₃	—	2	2	no	—
129	C₂²×D₁₃	—	2	2	no	—
130	C₂²×D₁₃	—	2	2	no	—
131	C₂²×D₁₃	—	4	1	no	—
132	C₂²×D₁₃	—	4	1	no	—
133	C₂²×D₁₃	—	4	1	no	—
134	C₂²×D₁₃	—	4	1	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	1	no	—
137	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
145	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
146	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
149	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
151	C₂×Dic₁₃	—	2	2	no	—
152	C₂×Dic₁₃	—	2	2	no	—
153	C₂×Dic₁₃	—	4	1	no	—
154	C₂×Dic₁₃	—	4	1	no	—
155	C₂×Dic₁₃	—	4	1	no	—
156	C₂×Dic₁₃	—	4	1	no	—
157	C₂×Dic₁₃	—	4	1	no	—
158	C₂×Dic₁₃	—	4	1	no	—
159	C₂×Dic₁₃	—	4	1	no	—
160	D₅₂	—	2	2	no	—
161	D₅₂	—	2	2	no	—
162	D₅₂	—	2	2	no	—
163	D₅₂	C₄⋊C₈	1	4	yes	complemented
164	C₄×D₁₃	—	4	2	no	—
165	C₄×D₁₃	—	4	2	no	—
166	C₄×D₁₃	—	4	2	no	—
167	C₄×D₁₃	—	4	2	no	—
168	C₈×C₁₃	—	2	2	no	—
169	C₈×C₁₃	—	2	2	no	—
170	C₈×C₁₃	—	4	2	no	—
171	C₈×C₁₃	—	4	1	no	—
172	C₈×C₁₃	—	4	1	no	—
173	#1055	—	4	2	no	—
174	#1055	—	8	1	no	—
175	C₂³×C₈	—	26	1	no	—
176	C₂×C₄×D₄	—	13	1	no	—
177	C₈×D₄	—	26	2	no	—
178	C₈×D₄	—	26	2	no	—
179	C₂×C₄⋊C₈	—	13	1	no	—
180	C₂×C₄⋊C₈	—	13	1	no	—
181	C₂×C₄⋊C₈	—	26	1	no	—
182	C₂×#102	—	13	1	no	—
183	C₂×#102	—	13	1	no	—
184	C₂×C₂²⋊C₈	—	26	1	no	—
185	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
186	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
187	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
188	C₄×C₄⋊C₄	—	13	1	no	—
189	#340	—	13	1	no	—
190	#340	—	13	1	no	—
191	#336	—	26	1	no	—
192	#335	—	26	2	no	—
193	D₄⋊C₈	—	26	2	no	—
194	C₂²×C₁₃	#385	1	1	yes	characteristic
195	C₂²×C₁₃	C₈×D₄	1	1	yes	characteristic
196	C₂²×C₁₃	#435	1	1	yes	characteristic
197	C₂²×C₁₃	C₄×D₈	1	1	yes	characteristic
198	C₂²×C₁₃	#440	1	1	yes	characteristic
199	C₂²×C₁₃	#443	1	1	yes	characteristic
200	C₂²×C₁₃	#444	1	1	yes	characteristic
201	C₂×D₁₃	—	2	4	no	—
202	C₂×D₁₃	—	4	2	no	—
203	C₂×D₁₃	—	4	2	no	—
204	C₂×D₁₃	—	4	2	no	—
205	C₂×D₁₃	—	4	2	no	—
206	C₂×D₁₃	—	4	2	no	—
207	C₂×D₁₃	—	4	2	no	—
208	C₄×C₁₃	—	2	1	no	—
209	C₄×C₁₃	—	2	1	no	—
210	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
211	C₄×C₁₃	#424	1	1	yes	characteristic
212	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
213	C₄×C₁₃	#435	1	1	yes	characteristic
214	C₄×C₁₃	#447	1	1	yes	characteristic
215	C₄×C₁₃	#452	1	1	yes	characteristic
216	C₄×C₁₃	#474	1	1	yes	characteristic
217	C₄×C₁₃	#478	1	1	yes	characteristic
218	Dic₁₃	—	4	2	no	—
219	Dic₁₃	—	4	2	no	—
220	Dic₁₃	—	8	1	no	—
221	C₂²×D₄	—	13	1	no	—
222	C₂³×C₄	—	26	1	no	—
223	C₂²×C₈	—	2	1	no	—
224	C₂²×C₈	—	26	4	no	—
225	C₂²×C₈	—	26	1	no	—
226	C₂²×C₈	—	26	1	no	—
227	C₂²×C₈	—	52	2	no	—
228	C₂²×C₈	—	52	2	no	—
229	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
230	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
231	C₂²×C₈	D₅₂	1	1	yes	characteristic
232	C₂²×C₈	D₅₂	1	1	yes	characteristic
233	C₄×D₄	—	13	2	no	—
234	C₄×D₄	—	13	2	no	—
235	C₄×D₄	—	26	1	no	—
236	C₄×D₄	—	26	1	no	—
237	C₂×C₄⋊C₄	—	13	1	no	—
238	C₂×C₄⋊C₄	—	13	1	no	—
239	C₂×C₄⋊C₄	—	13	1	no	—
240	C₂×C₂²⋊C₄	—	26	1	no	—
241	C₂×C₄²	—	26	1	no	—
242	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
243	C₄⋊C₈	—	13	2	no	—
244	C₄⋊C₈	—	26	1	no	—
245	C₄⋊C₈	—	26	1	no	—
246	C₄⋊C₈	—	26	1	no	—
247	C₄⋊C₈	—	52	2	no	—
248	#102	—	13	4	no	—
249	#102	—	26	2	no	—
250	C₂²⋊C₈	—	26	4	no	—
251	C₄×C₈	—	2	1	no	—
252	C₄×C₈	—	2	1	no	—
253	C₄×C₈	—	2	1	no	—
254	C₄×C₈	—	2	1	no	—
255	C₄×C₈	—	2	1	no	—
256	C₄×C₈	—	2	1	no	—
257	#95	—	26	1	no	—
258	C₂×C₁₃	C₈×D₈	1	1	yes	characteristic
259	C₂×C₁₃	SD₁₆⋊C₈	1	1	yes	characteristic
260	C₂×C₁₃	#1581	1	1	yes	characteristic
261	C₂×C₁₃	#1585	1	1	yes	characteristic
262	C₂×C₁₃	#1850	1	1	yes	characteristic
263	C₂×C₁₃	#1862	1	1	yes	characteristic
264	C₂×C₁₃	#1866	1	1	yes	characteristic
265	D₁₃	—	4	4	no	—
266	C₂⁴	—	26	1	no	—
267	C₂×D₄	—	13	2	no	—
268	C₂×D₄	—	13	2	no	—
269	C₂×D₄	—	13	2	no	—
270	C₂×D₄	—	26	1	no	—
271	C₂×D₄	—	26	1	no	—
272	C₂×D₄	—	26	1	no	—
273	C₂²×C₄	—	26	1	no	—
274	C₂²×C₄	—	26	1	no	—
275	C₂²×C₄	—	26	2	no	—
276	C₂²×C₄	—	26	2	no	—
277	C₂²×C₄	—	26	1	no	—
278	C₂²×C₄	—	52	1	no	—
279	C₂²×C₄	—	52	1	no	—
280	C₂²×C₄	—	52	1	no	—
281	C₂²×C₄	—	52	1	no	—
282	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
284	C₂²×C₄	#6127	1	1	yes	characteristic
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	26	2	no	—
299	C₂×C₈	—	52	8	no	—
300	C₂×C₈	—	52	1	no	—
301	C₂×C₈	—	52	1	no	—
302	C₂×C₈	—	52	1	no	—
303	C₂×C₈	—	52	1	no	—
304	C₂×C₈	—	52	1	no	—
305	C₂×C₈	C₈×D₁₃	1	2	yes	complemented
306	C₂×C₈	D₁₀₄	1	2	yes	—
307	C₄⋊C₄	—	13	2	no	—
308	C₄⋊C₄	—	13	2	no	—
309	C₄⋊C₄	—	26	1	no	—
310	C₄⋊C₄	—	26	1	no	—
311	C₄⋊C₄	—	26	1	no	—
312	C₄⋊C₄	—	26	1	no	—
313	C₂²⋊C₄	—	26	2	no	—
314	C₂²⋊C₄	—	26	2	no	—
315	C₄²	—	52	1	no	—
316	C₄²	—	52	1	no	—
317	C₄²	D₄×D₁₃	1	1	yes	characteristic
318	C₄²	D₄×D₁₃	1	1	yes	characteristic
319	C₄²	#6129	1	1	yes	characteristic
320	C₄²	Q₈×D₁₃	1	1	yes	characteristic
321	C₁₃	#8843	1	1	yes	characteristic, complemented, Sylow
322	C₂³	—	26	2	no	—
323	C₂³	—	26	2	no	—
324	C₂³	—	26	2	no	—
325	C₂³	—	52	1	no	—
326	C₂³	—	52	1	no	—
327	C₂³	—	52	1	no	—
328	C₂³	—	52	1	no	—
329	C₂³	C₄×D₅₂	1	1	yes	characteristic
330	D₄	—	13	4	no	—
331	D₄	—	26	2	no	—
332	D₄	—	26	2	no	—
333	D₄	—	26	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	26	2	no	—
337	C₂×C₄	—	26	2	no	—
338	C₂×C₄	—	52	1	no	—
339	C₂×C₄	—	52	1	no	—
340	C₂×C₄	—	52	1	no	—
341	C₂×C₄	—	52	1	no	—
342	C₂×C₄	—	52	2	no	—
343	C₂×C₄	—	52	2	no	—
344	C₂×C₄	—	52	2	no	—
345	C₂×C₄	—	52	2	no	—
346	C₂×C₄	—	52	1	no	—
347	C₂×C₄	—	52	1	no	—
348	C₂×C₄	—	52	1	no	—
349	C₂×C₄	#88135	1	1	yes	characteristic
350	C₂×C₄	#88136	1	1	yes	characteristic
351	C₂×C₄	#88137	1	1	yes	characteristic
352	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
353	C₂×C₄	#88150	1	1	yes	characteristic
354	C₂×C₄	#88151	1	1	yes	characteristic
355	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
356	C₂×C₄	#88155	1	1	yes	characteristic
357	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
358	C₂×C₄	#88158	1	1	yes	characteristic
359	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
360	C₂×C₄	#88161	1	1	yes	characteristic
361	C₂×C₄	#88162	1	1	yes	characteristic
362	C₂×C₄	#88163	1	1	yes	characteristic
363	C₈	—	2	2	no	—
364	C₈	—	2	2	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	1	no	—
367	C₈	—	4	1	no	—
368	C₈	—	52	2	no	—
369	C₈	—	104	1	no	—
370	C₂²	—	26	4	no	—
371	C₂²	—	52	2	no	—
372	C₂²	—	52	2	no	—
373	C₂²	—	52	2	no	—
374	C₂²	—	52	2	no	—
375	C₂²	—	52	2	no	—
376	C₂²	—	52	2	no	—
377	C₂²	#11718329	1	1	yes	characteristic
378	C₂²	C₈×D₅₂	1	1	yes	characteristic
379	C₂²	C₄×D₁₀₄	1	1	yes	characteristic
380	C₂²	#11718361	1	1	yes	characteristic
381	C₂²	#11718367	1	1	yes	characteristic
382	C₂²	#11718371	1	1	yes	characteristic
383	C₂²	#11718378	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	52	2	no	—
387	C₄	—	52	2	no	—
388	C₄	—	104	1	no	—
389	C₄	#11718386	1	1	yes	characteristic
390	C₄	#11718389	1	1	yes	characteristic
391	C₄	#11718393	1	1	yes	characteristic
392	C₄	#11718394	1	1	yes	characteristic
393	C₄	D₁₃×C₄⋊C₈	1	1	yes	characteristic
394	C₄	#11718500	1	1	yes	characteristic
395	C₄	#11718507	1	1	yes	characteristic
396	C₄	#11718508	1	1	yes	characteristic
397	C₂	—	52	4	no	—
398	C₂	C₈×D₁₀₄	1	1	yes	characteristic
399	C₂	#13113650	1	1	yes	characteristic
400	C₂	#13113667	1	1	yes	characteristic
401	C₂	#13113695	1	1	yes	characteristic
402	C₂	#13115015	1	1	yes	characteristic
403	C₂	#13115086	1	1	yes	characteristic
404	C₂	#13115114	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1273	C₂
socle	C₂³×C₁₃	C₄×D₄
prime radical	C₂²×D₅₂	C₂×C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1273	D₁₃
hypocenter	C₁₃	#8843
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1273

Complements

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

N	H ≅ G/N	type
2. #13115554	C₂	semidirect
4. C₂×#11718050	C₂	semidirect
6. #13112676	C₂	semidirect
7. C₁₃×#1273	C₂	semidirect
57. #88061	C₈	semidirect
97. C₂×C₈×C₁₃	C₂×C₈	semidirect
110. C₄⋊Dic₁₃	C₂×C₈	semidirect
126. #1273	D₁₃	semidirect
163. D₅₂	C₄⋊C₈	semidirect
305. C₂×C₈	C₈×D₁₃	semidirect
321. C₁₃	#8843	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₅₂	2
#13115554	2
C₄×#88061	2
C₂×#11718050	2
C₂×#11718051	2
#13112676	2
C₁₃×#1273	2
#8843	13