Subgroups — C₁₃×#10056 #15696395

Order 3328.

646 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2563	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×Q₁₆	—	2	2	no	—
9	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#494	—	2	2	no	—
13	C₁₃×#494	—	2	2	no	—
14	C₁₃×#476	—	2	2	no	—
15	C₁₃×#476	—	2	2	no	—
16	C₂×C₁₃×#106	—	2	1	no	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#102	—	2	1	no	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#393	—	2	2	no	—
22	C₁₃×#390	—	2	1	no	—
23	C₁₃×#382	—	2	1	no	—
24	C₁₃×#380	—	2	2	no	—
25	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₁₃×#340	—	2	2	no	—
27	C₁₃×#333	—	2	2	no	—
28	C₁₃×D₄⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₁₃	—	2	1	no	—
30	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
31	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	—	2	1	no	—
33	C₂×C₁₃×Q₁₆	—	2	8	no	—
34	C₂×C₁₃×Q₁₆	—	4	8	no	—
35	C₂²×C₈×C₁₃	—	2	1	no	—
36	C₂²×C₈×C₁₃	—	2	1	no	—
37	C₂²×C₈×C₁₃	—	2	1	no	—
38	C₁₃×C₄⋊Q₈	—	2	1	no	—
39	C₁₃×C₄⋊Q₈	—	2	1	no	—
40	C₁₃×C₄⋊Q₈	—	2	1	no	—
41	C₁₃×C₄⋊Q₈	—	2	1	no	—
42	C₁₃×C₄⋊Q₈	—	2	1	no	—
43	C₁₃×C₄⋊Q₈	—	2	1	no	—
44	C₁₃×C₄⋊Q₈	—	2	1	no	—
45	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
46	C₄×D₄×C₁₃	—	2	1	no	—
47	C₄×D₄×C₁₃	—	2	1	no	—
48	C₄×D₄×C₁₃	—	2	1	no	—
49	C₄×D₄×C₁₃	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
55	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
56	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
58	C₂×C₄²×C₁₃	—	2	1	no	—
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×#106	—	2	4	no	—
61	C₁₃×C₄⋊C₈	—	2	1	no	—
62	C₁₃×C₄⋊C₈	—	2	1	no	—
63	C₁₃×C₄⋊C₈	—	2	1	no	—
64	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
65	C₁₃×#102	—	2	4	no	—
66	C₄×C₈×C₁₃	—	2	1	no	—
67	C₄×C₈×C₁₃	D₄	1	2	yes	—
68	C₁₃×#95	—	2	4	no	—
69	C₁₃×#95	—	2	1	no	—
70	#10056	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁴×C₁₃	—	2	1	no	—
72	C₂×Q₈×C₁₃	—	2	2	no	—
73	C₂×Q₈×C₁₃	—	2	2	no	—
74	C₂×Q₈×C₁₃	—	2	2	no	—
75	C₂×Q₈×C₁₃	—	4	4	no	—
76	C₂×Q₈×C₁₃	—	4	4	no	—
77	C₂×Q₈×C₁₃	—	4	1	no	—
78	C₂×D₄×C₁₃	—	2	1	no	—
79	C₂×D₄×C₁₃	—	2	1	no	—
80	C₂×D₄×C₁₃	—	2	1	no	—
81	C₂×D₄×C₁₃	—	2	1	no	—
82	C₂×D₄×C₁₃	—	2	1	no	—
83	C₂×D₄×C₁₃	Q₁₆	1	2	yes	complemented
84	C₂²×C₄×C₁₃	—	2	1	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	4	1	no	—
88	C₂²×C₄×C₁₃	—	4	1	no	—
89	C₂²×C₄×C₁₃	—	4	1	no	—
90	C₂²×C₄×C₁₃	—	4	2	no	—
91	C₂²×C₄×C₁₃	—	4	2	no	—
92	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₁₃×Q₁₆	—	4	16	no	—
96	C₂×C₈×C₁₃	—	2	4	no	—
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₂×C₈×C₁₃	—	4	1	no	—
100	C₂×C₈×C₁₃	—	4	1	no	—
101	C₂×C₈×C₁₃	—	4	1	no	—
102	C₂×C₈×C₁₃	—	4	2	no	—
103	C₁₃×C₄⋊C₄	—	2	2	no	—
104	C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₁₃×C₄⋊C₄	—	4	1	no	—
110	C₁₃×C₄⋊C₄	—	4	1	no	—
111	C₁₃×C₄⋊C₄	—	4	1	no	—
112	C₁₃×C₄⋊C₄	—	4	1	no	—
113	C₁₃×C₄⋊C₄	—	4	1	no	—
114	C₁₃×C₄⋊C₄	—	4	1	no	—
115	C₁₃×C₂²⋊C₄	—	4	1	no	—
116	C₁₃×C₂²⋊C₄	—	4	1	no	—
117	C₁₃×C₂²⋊C₄	—	8	4	no	—
118	C₄²×C₁₃	—	4	1	no	—
119	C₄²×C₁₃	—	4	1	no	—
120	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₃	#41	1	1	yes	characteristic
124	C₂×#494	C₂×C₁₃	1	1	yes	characteristic, complemented
125	C₂×#476	C₂×C₁₃	1	1	yes	characteristic
126	#2563	C₂×C₁₃	1	1	yes	characteristic
127	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
128	C₂×#333	C₂×C₁₃	1	1	yes	characteristic, complemented
129	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
130	#1279	C₂×C₁₃	1	1	yes	characteristic, complemented
131	C₂³×C₁₃	—	2	2	no	—
132	C₂³×C₁₃	—	4	1	no	—
133	C₂³×C₁₃	—	4	2	no	—
134	C₂³×C₁₃	—	4	1	no	—
135	C₂³×C₁₃	—	4	2	no	—
136	C₂³×C₁₃	#120	1	1	yes	characteristic
137	Q₈×C₁₃	—	4	4	no	—
138	Q₈×C₁₃	—	4	4	no	—
139	Q₈×C₁₃	—	8	2	no	—
140	Q₈×C₁₃	—	8	2	no	—
141	D₄×C₁₃	—	2	2	no	—
142	D₄×C₁₃	—	2	2	no	—
143	D₄×C₁₃	—	4	1	no	—
144	D₄×C₁₃	—	4	1	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	4	1	no	—
147	C₂×C₄×C₁₃	—	4	2	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	4	2	no	—
152	C₂×C₄×C₁₃	—	4	2	no	—
153	C₂×C₄×C₁₃	—	4	4	no	—
154	C₂×C₄×C₁₃	—	8	2	no	—
155	C₂×C₄×C₁₃	—	8	2	no	—
156	C₂×C₄×C₁₃	—	8	1	no	—
157	C₂×C₄×C₁₃	—	8	1	no	—
158	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
159	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
160	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
161	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
165	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
166	C₂×C₄×C₁₃	#135	1	2	yes	—
167	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
168	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
169	C₂×C₄×C₁₃	#137	1	2	yes	—
170	C₈×C₁₃	—	2	4	no	—
171	C₈×C₁₃	—	4	2	no	—
172	C₈×C₁₃	—	8	1	no	—
173	C₂²×Q₁₆	—	2	2	no	—
174	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
175	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
176	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
177	#494	—	2	2	no	—
178	#494	—	2	2	no	—
179	#476	—	2	2	no	—
180	#476	—	2	2	no	—
181	C₂×#106	—	2	1	no	—
182	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
183	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×#102	—	2	1	no	—
185	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
186	#393	—	2	2	no	—
187	#390	—	2	1	no	—
188	#382	—	2	1	no	—
189	#380	—	2	2	no	—
190	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
191	#340	—	2	2	no	—
192	#333	—	2	2	no	—
193	D₄⋊C₈	—	2	2	no	—
194	C₂²×C₁₃	—	4	4	no	—
195	C₂²×C₁₃	—	4	2	no	—
196	C₂²×C₁₃	—	8	2	no	—
197	C₂²×C₁₃	—	8	1	no	—
198	C₂²×C₁₃	—	8	1	no	—
199	C₂²×C₁₃	#392	1	1	yes	characteristic
200	C₂²×C₁₃	#451	1	1	yes	characteristic
201	C₂²×C₁₃	#452	1	2	yes	—
202	C₂²×C₁₃	#452	1	1	yes	characteristic
203	C₂²×C₁₃	#453	1	2	yes	—
204	C₄×C₁₃	—	2	1	no	—
205	C₄×C₁₃	—	2	1	no	—
206	C₄×C₁₃	—	8	2	no	—
207	C₄×C₁₃	—	8	2	no	—
208	C₄×C₁₃	—	8	2	no	—
209	C₄×C₁₃	—	8	1	no	—
210	C₄×C₁₃	#451	1	1	yes	characteristic
211	C₄×C₁₃	#452	1	1	yes	characteristic
212	C₄×C₁₃	#464	1	2	yes	—
213	C₄×C₁₃	#467	1	1	yes	characteristic
214	C₄×C₁₃	#470	1	1	yes	characteristic
215	C₄×C₁₃	#495	1	1	yes	characteristic
216	C₄×C₁₃	#497	1	1	yes	characteristic
217	C₂²×Q₈	—	2	1	no	—
218	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
219	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
220	C₂³×C₄	—	2	1	no	—
221	C₂×Q₁₆	—	2	8	no	—
222	C₂×Q₁₆	—	4	8	no	—
223	C₂²×C₈	—	2	1	no	—
224	C₂²×C₈	—	2	1	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₄⋊Q₈	—	2	1	no	—
227	C₄⋊Q₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
243	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₂²⋊C₄	—	2	4	no	—
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
248	#106	—	2	4	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	—	2	1	no	—
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
253	#102	—	2	4	no	—
254	C₄×C₈	—	2	1	no	—
255	C₄×C₈	D₄×C₁₃	1	2	yes	—
256	#95	—	2	4	no	—
257	#95	—	2	1	no	—
258	C₂×C₁₃	—	8	2	no	—
259	C₂×C₁₃	#1632	1	2	yes	—
260	C₂×C₁₃	#1634	1	2	yes	—
261	C₂×C₁₃	#2001	1	1	yes	characteristic
262	C₂×C₁₃	#2002	1	1	yes	characteristic
263	C₂×C₁₃	#2015	1	1	yes	characteristic
264	C₂⁴	—	2	1	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	4	4	no	—
269	C₂×Q₈	—	4	4	no	—
270	C₂×Q₈	—	4	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	C₁₃×Q₁₆	1	2	yes	complemented
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
288	Q₁₆	—	4	16	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	8	4	no	—
311	C₄²	—	4	1	no	—
312	C₄²	—	4	1	no	—
313	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₄²	C₁₃×#41	1	1	yes	characteristic
317	C₁₃	#10056	1	1	yes	characteristic, direct product factor, Sylow
318	C₂³	—	2	2	no	—
319	C₂³	—	4	1	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	4	1	no	—
322	C₂³	—	4	2	no	—
323	C₂³	C₁₃×#120	1	1	yes	characteristic
324	Q₈	—	4	4	no	—
325	Q₈	—	4	4	no	—
326	Q₈	—	8	2	no	—
327	Q₈	—	8	2	no	—
328	D₄	—	2	2	no	—
329	D₄	—	2	2	no	—
330	D₄	—	4	1	no	—
331	D₄	—	4	1	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	8	2	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	—	8	1	no	—
344	C₂×C₄	—	8	1	no	—
345	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
346	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
347	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
348	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
349	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
350	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
351	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
352	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
353	C₂×C₄	C₁₃×#135	1	2	yes	—
354	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
355	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
356	C₂×C₄	C₁₃×#137	1	2	yes	—
357	C₈	—	2	4	no	—
358	C₈	—	4	2	no	—
359	C₈	—	8	1	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	8	1	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	2	no	—
365	C₂²	C₁₃×#392	1	1	yes	characteristic
366	C₂²	C₁₃×#451	1	1	yes	characteristic
367	C₂²	C₁₃×#452	1	1	yes	characteristic
368	C₂²	C₁₃×#452	1	2	yes	—
369	C₂²	C₁₃×#453	1	2	yes	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	8	2	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	1	no	—
375	C₄	—	8	2	no	—
376	C₄	C₁₃×#451	1	1	yes	characteristic
377	C₄	C₁₃×#452	1	1	yes	characteristic
378	C₄	C₁₃×#464	1	2	yes	—
379	C₄	C₁₃×#467	1	1	yes	characteristic
380	C₄	C₁₃×#470	1	1	yes	characteristic
381	C₄	C₁₃×#495	1	1	yes	characteristic
382	C₄	C₁₃×#497	1	1	yes	characteristic
383	C₂	—	8	2	no	—
384	C₂	C₁₃×#1632	1	2	yes	—
385	C₂	C₁₃×#1634	1	2	yes	—
386	C₂	C₁₃×#2001	1	1	yes	characteristic
387	C₂	C₁₃×#2002	1	1	yes	characteristic
388	C₂	C₁₃×#2015	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#494	C₂	semidirect
4. C₁₃×#1987	C₂	semidirect
5. C₂×C₁₃×#333	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
70. #10056	C₁₃	direct (N × H)
83. C₂×D₄×C₁₃	Q₁₆	semidirect
124. C₂×#494	C₂×C₁₃	semidirect
127. #1987	C₂×C₁₃	semidirect
128. C₂×#333	C₂×C₁₃	semidirect
130. #1279	C₂×C₁₃	semidirect
276. C₂×D₄	C₁₃×Q₁₆	semidirect
317. C₁₃	#10056	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#494	2
C₂×C₁₃×#476	2
C₁₃×#2563	2
C₁₃×#1987	2
C₂×C₁₃×#333	2
C₂×C₁₃×D₄⋊C₈	2
C₁₃×#1279	2
#10056	13

Subgroups — C13×#10056 #15696395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10056 #15696395