Subgroups — C₁₃×#35011 #15721350

Order 3328.

2650 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal
2	C₁₃×#2857	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2659	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2583	C₂	1	8	yes	maximal, complemented
5	C₁₃×#2502	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2434	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2315	C₂	1	4	yes	maximal
8	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	complemented
12	C₂×C₁₃×C₂²⋊Q₈	—	2	16	no	—
13	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
19	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#398	C₂²	1	16	yes	complemented
23	C₁₃×#395	C₂²	1	16	yes	complemented
24	C₁₃×#391	C₂²	1	8	yes	complemented
25	C₁₃×#389	C₂²	1	16	yes	complemented
26	C₁₃×#385	C₂²	1	16	yes	—
27	C₁₃×#385	C₂²	1	16	yes	—
28	C₁₃×#384	C₂²	1	4	yes	complemented
29	C₁₃×#380	C₂²	1	16	yes	—
30	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
31	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
32	C₂×C₁₃×#95	C₂²	1	2	yes	—
33	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
34	C₂²×Q₈×C₁₃	—	2	8	no	—
35	C₂²×Q₈×C₁₃	—	4	8	no	—
36	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
37	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
38	C₂³×C₄×C₁₃	—	4	4	no	—
39	C₂³×C₄×C₁₃	D₄	1	8	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
47	C₁₃×C₄⋊Q₈	—	4	8	no	—
48	C₁₃×C₂²⋊Q₈	—	2	16	no	—
49	C₁₃×C₂²⋊Q₈	—	2	16	no	—
50	C₁₃×C₂²⋊Q₈	—	2	16	no	—
51	C₁₃×C₂²⋊Q₈	—	2	16	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
61	C₂×C₁₃×C₂²⋊C₄	Q₈	1	16	yes	complemented
62	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
63	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
64	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
65	C₂×C₄²×C₁₃	—	4	4	no	—
66	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
67	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
68	C₁₃×#95	C₂³	1	8	yes	—
69	C₁₃×#95	C₂³	1	32	yes	—
70	#35011	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁴×C₁₃	—	4	2	no	—
72	C₂⁴×C₁₃	—	4	2	no	—
73	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
74	C₂⁴×C₁₃	C₂×Q₈	1	8	yes	—
75	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
76	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
77	C₂×Q₈×C₁₃	—	2	8	no	—
78	C₂×Q₈×C₁₃	—	2	8	no	—
79	C₂×Q₈×C₁₃	—	2	16	no	—
80	C₂×Q₈×C₁₃	—	4	8	no	—
81	C₂×Q₈×C₁₃	—	4	32	no	—
82	C₂²×C₄×C₁₃	—	2	4	no	—
83	C₂²×C₄×C₁₃	—	2	8	no	—
84	C₂²×C₄×C₁₃	—	2	8	no	—
85	C₂²×C₄×C₁₃	—	2	8	no	—
86	C₂²×C₄×C₁₃	—	4	16	no	—
87	C₂²×C₄×C₁₃	—	4	4	no	—
88	C₂²×C₄×C₁₃	—	4	4	no	—
89	C₂²×C₄×C₁₃	—	4	2	no	—
90	C₂²×C₄×C₁₃	—	4	4	no	—
91	C₂²×C₄×C₁₃	—	4	8	no	—
92	C₂²×C₄×C₁₃	—	4	8	no	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂×Q₈	1	16	yes	complemented
98	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
103	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
104	C₁₃×C₄⋊C₄	—	2	8	no	—
105	C₁₃×C₄⋊C₄	—	2	8	no	—
106	C₁₃×C₄⋊C₄	—	2	16	no	—
107	C₁₃×C₄⋊C₄	—	2	16	no	—
108	C₁₃×C₄⋊C₄	—	4	16	no	—
109	C₁₃×C₄⋊C₄	—	4	16	no	—
110	C₁₃×C₂²⋊C₄	—	2	16	no	—
111	C₁₃×C₂²⋊C₄	—	2	16	no	—
112	C₁₃×C₂²⋊C₄	C₂×Q₈	1	32	yes	complemented
113	C₄²×C₁₃	—	2	8	no	—
114	C₄²×C₁₃	—	4	4	no	—
115	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	—
116	#2857	C₂×C₁₃	1	4	yes	complemented
117	#2659	C₂×C₁₃	1	4	yes	complemented
118	#2583	C₂×C₁₃	1	8	yes	complemented
119	#2502	C₂×C₁₃	1	4	yes	complemented
120	#2434	C₂×C₁₃	1	4	yes	complemented
121	#2315	C₂×C₁₃	1	4	yes	—
122	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
123	C₂³×C₁₃	—	2	4	no	—
124	C₂³×C₁₃	—	2	2	no	—
125	C₂³×C₁₃	—	2	4	no	—
126	C₂³×C₁₃	—	2	2	no	—
127	C₂³×C₁₃	—	4	4	no	—
128	C₂³×C₁₃	—	4	4	no	—
129	C₂³×C₁₃	—	4	16	no	—
130	C₂³×C₁₃	C₄⋊Q₈	1	16	yes	complemented
131	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
132	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
133	C₂³×C₁₃	C₂²×Q₈	1	8	yes	—
134	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
135	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
136	Q₈×C₁₃	—	4	16	no	—
137	Q₈×C₁₃	—	4	16	no	—
138	C₂×C₄×C₁₃	—	2	8	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	4	no	—
141	C₂×C₄×C₁₃	—	2	8	no	—
142	C₂×C₄×C₁₃	—	2	8	no	—
143	C₂×C₄×C₁₃	—	2	16	no	—
144	C₂×C₄×C₁₃	—	2	8	no	—
145	C₂×C₄×C₁₃	—	2	8	no	—
146	C₂×C₄×C₁₃	—	2	16	no	—
147	C₂×C₄×C₁₃	—	2	16	no	—
148	C₂×C₄×C₁₃	—	4	8	no	—
149	C₂×C₄×C₁₃	—	4	4	no	—
150	C₂×C₄×C₁₃	—	4	16	no	—
151	C₂×C₄×C₁₃	—	4	16	no	—
152	C₂×C₄×C₁₃	—	4	16	no	—
153	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
154	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
155	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
156	C₂×C₄×C₁₃	C₂²×Q₈	1	16	yes	—
157	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
158	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
159	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
160	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
161	C₂×C₂²⋊Q₈	—	2	16	no	—
162	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
163	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
164	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
165	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
166	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
167	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
168	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
169	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
170	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
171	#398	C₂²×C₁₃	1	16	yes	complemented
172	#395	C₂²×C₁₃	1	16	yes	complemented
173	#391	C₂²×C₁₃	1	8	yes	complemented
174	#389	C₂²×C₁₃	1	16	yes	complemented
175	#385	C₂²×C₁₃	1	16	yes	—
176	#385	C₂²×C₁₃	1	16	yes	—
177	#384	C₂²×C₁₃	1	4	yes	complemented
178	#380	C₂²×C₁₃	1	16	yes	—
179	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
180	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
181	C₂×#95	C₂²×C₁₃	1	2	yes	—
182	C₂²×C₁₃	—	2	4	no	—
183	C₂²×C₁₃	—	2	2	no	—
184	C₂²×C₁₃	—	2	4	no	—
185	C₂²×C₁₃	—	2	2	no	—
186	C₂²×C₁₃	—	2	8	no	—
187	C₂²×C₁₃	—	2	16	no	—
188	C₂²×C₁₃	—	4	16	no	—
189	C₂²×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
190	C₂²×C₁₃	C₂×C₄⋊Q₈	1	8	yes	—
191	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
192	C₂²×C₁₃	C₂³×Q₈	1	2	yes	—
193	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
194	C₂²×C₁₃	#585	1	2	yes	—
195	C₄×C₁₃	—	2	2	no	—
196	C₄×C₁₃	—	2	4	no	—
197	C₄×C₁₃	—	2	16	no	—
198	C₄×C₁₃	—	4	8	no	—
199	C₄×C₁₃	—	4	8	no	—
200	C₄×C₁₃	#534	1	4	yes	—
201	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
202	C₂²×Q₈	—	2	8	no	—
203	C₂²×Q₈	—	4	8	no	—
204	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
205	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
206	C₂³×C₄	—	4	4	no	—
207	C₂³×C₄	D₄×C₁₃	1	8	yes	—
208	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
209	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
210	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
211	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
212	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
213	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
214	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
215	C₄⋊Q₈	—	4	8	no	—
216	C₂²⋊Q₈	—	2	16	no	—
217	C₂²⋊Q₈	—	2	16	no	—
218	C₂²⋊Q₈	—	2	16	no	—
219	C₂²⋊Q₈	—	2	16	no	—
220	C₂×C₄⋊C₄	—	2	8	no	—
221	C₂×C₄⋊C₄	—	2	16	no	—
222	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
223	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
224	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
225	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
226	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
227	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
228	C₂×C₂²⋊C₄	—	2	16	no	—
229	C₂×C₂²⋊C₄	Q₈×C₁₃	1	16	yes	complemented
230	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
231	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
232	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
233	C₂×C₄²	—	4	4	no	—
234	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
235	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
236	#95	C₂³×C₁₃	1	8	yes	—
237	#95	C₂³×C₁₃	1	32	yes	—
238	C₂×C₁₃	—	2	8	no	—
239	C₂×C₁₃	—	2	4	no	—
240	C₂×C₁₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
241	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
242	C₂×C₁₃	#3449	1	1	yes	characteristic
243	C₂×C₁₃	#3501	1	4	yes	—
244	C₂⁴	—	4	2	no	—
245	C₂⁴	—	4	2	no	—
246	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
247	C₂⁴	C₂×Q₈×C₁₃	1	8	yes	—
248	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
249	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
250	C₂×Q₈	—	2	8	no	—
251	C₂×Q₈	—	2	8	no	—
252	C₂×Q₈	—	2	16	no	—
253	C₂×Q₈	—	4	8	no	—
254	C₂×Q₈	—	4	32	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	4	16	no	—
260	C₂²×C₄	—	4	4	no	—
261	C₂²×C₄	—	4	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	8	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	—	4	8	no	—
266	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
267	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
268	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
269	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
270	C₂²×C₄	C₂×Q₈×C₁₃	1	16	yes	complemented
271	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
272	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
273	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
274	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
276	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
277	C₄⋊C₄	—	2	8	no	—
278	C₄⋊C₄	—	2	8	no	—
279	C₄⋊C₄	—	2	16	no	—
280	C₄⋊C₄	—	2	16	no	—
281	C₄⋊C₄	—	4	16	no	—
282	C₄⋊C₄	—	4	16	no	—
283	C₂²⋊C₄	—	2	16	no	—
284	C₂²⋊C₄	—	2	16	no	—
285	C₂²⋊C₄	C₂×Q₈×C₁₃	1	32	yes	complemented
286	C₄²	—	2	8	no	—
287	C₄²	—	4	4	no	—
288	C₁₃	#35011	1	1	yes	characteristic, direct product factor, Sylow
289	C₂³	—	2	4	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	4	no	—
292	C₂³	—	2	2	no	—
293	C₂³	—	4	4	no	—
294	C₂³	—	4	4	no	—
295	C₂³	—	4	16	no	—
296	C₂³	C₁₃×C₄⋊Q₈	1	16	yes	complemented
297	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
298	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
299	C₂³	C₂²×Q₈×C₁₃	1	8	yes	—
300	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
301	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
302	Q₈	—	4	16	no	—
303	Q₈	—	4	16	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	16	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	2	16	no	—
313	C₂×C₄	—	2	16	no	—
314	C₂×C₄	—	4	8	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	16	no	—
317	C₂×C₄	—	4	16	no	—
318	C₂×C₄	—	4	16	no	—
319	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
320	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
321	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
322	C₂×C₄	C₂²×Q₈×C₁₃	1	16	yes	—
323	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	4	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	8	no	—
329	C₂²	—	2	16	no	—
330	C₂²	—	4	16	no	—
331	C₂²	C₂×C₁₃×C₄⋊Q₈	1	4	yes	—
332	C₂²	C₂×C₁₃×C₄⋊Q₈	1	8	yes	—
333	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
334	C₂²	C₂³×Q₈×C₁₃	1	2	yes	—
335	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
336	C₂²	C₁₃×#585	1	2	yes	—
337	C₄	—	2	2	no	—
338	C₄	—	2	4	no	—
339	C₄	—	2	16	no	—
340	C₄	—	4	8	no	—
341	C₄	—	4	8	no	—
342	C₄	C₁₃×#534	1	4	yes	—
343	C₂	—	2	8	no	—
344	C₂	—	2	4	no	—
345	C₂	C₂²×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
346	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
347	C₂	C₁₃×#3449	1	1	yes	characteristic
348	C₂	C₁₃×#3501	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2857	C₂	semidirect
3. C₁₃×#2659	C₂	semidirect
4. C₁₃×#2583	C₂	semidirect
5. C₁₃×#2502	C₂	semidirect
6. C₁₃×#2434	C₂	semidirect
11. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
22. C₁₃×#398	C₂²	semidirect
23. C₁₃×#395	C₂²	semidirect
24. C₁₃×#391	C₂²	semidirect
25. C₁₃×#389	C₂²	semidirect
28. C₁₃×#384	C₂²	semidirect
61. C₂×C₁₃×C₂²⋊C₄	Q₈	semidirect
70. #35011	C₁₃	direct (N × H)
97. C₂²×C₄×C₁₃	C₂×Q₈	semidirect
112. C₁₃×C₂²⋊C₄	C₂×Q₈	semidirect
116. #2857	C₂×C₁₃	semidirect
117. #2659	C₂×C₁₃	semidirect
118. #2583	C₂×C₁₃	semidirect
119. #2502	C₂×C₁₃	semidirect
120. #2434	C₂×C₁₃	semidirect
130. C₂³×C₁₃	C₄⋊Q₈	semidirect
160. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
171. #398	C₂²×C₁₃	semidirect
172. #395	C₂²×C₁₃	semidirect
173. #391	C₂²×C₁₃	semidirect
174. #389	C₂²×C₁₃	semidirect
177. #384	C₂²×C₁₃	semidirect
229. C₂×C₂²⋊C₄	Q₈×C₁₃	semidirect
270. C₂²×C₄	C₂×Q₈×C₁₃	semidirect
285. C₂²⋊C₄	C₂×Q₈×C₁₃	semidirect
288. C₁₃	#35011	direct (N × H)
296. C₂³	C₁₃×C₄⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₂²⋊Q₈	2
C₁₃×#2857	2
C₁₃×#2659	2
C₁₃×#2583	2
C₁₃×#2502	2
C₁₃×#2434	2
C₁₃×#2315	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#35011	13

Subgroups — C13×#35011 #15721350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35011 #15721350