Subgroups — C₁₃×#34382 #15720721

Order 3328.

2218 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2382	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2379	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2359	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2355	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2352	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2352	C₂	1	2	yes	maximal, complemented
8	D₄×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2334	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2329	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2325	C₂	1	2	yes	maximal
12	C₁₃×#2317	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2314	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#529	C₄	1	16	yes	complemented
17	C₂×C₁₃×#126	C₂²	1	2	yes	—
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#123	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#117	C₂²	1	2	yes	—
28	C₂×C₁₃×#117	C₂²	1	2	yes	—
29	C₂×C₁₃×#117	C₂²	1	2	yes	—
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#391	C₂²	1	4	yes	—
35	C₁₃×#389	C₂²	1	4	yes	—
36	C₁₃×#389	C₂²	1	4	yes	—
37	C₁₃×#389	C₂²	1	4	yes	—
38	C₁₃×#388	C₂²	1	4	yes	—
39	C₁₃×#388	C₂²	1	4	yes	—
40	C₁₃×#388	C₂²	1	4	yes	—
41	C₁₃×#388	C₂²	1	4	yes	—
42	C₁₃×#387	C₂²	1	4	yes	—
43	C₁₃×#387	C₂²	1	4	yes	—
44	C₁₃×#387	C₂²	1	4	yes	—
45	C₁₃×#387	C₂²	1	4	yes	—
46	C₁₃×#387	C₂²	1	4	yes	—
47	C₁₃×#387	C₂²	1	4	yes	—
48	C₁₃×#386	C₂²	1	4	yes	—
49	C₁₃×#386	C₂²	1	4	yes	—
50	C₁₃×#385	C₂²	1	4	yes	—
51	C₁₃×#385	C₂²	1	4	yes	—
52	C₁₃×#385	C₂²	1	4	yes	—
53	C₁₃×#385	C₂²	1	4	yes	—
54	C₁₃×#384	C₂²	1	1	yes	characteristic
55	C₁₃×#384	C₂²	1	1	yes	characteristic
56	C₁₃×#384	C₂²	1	2	yes	—
57	C₁₃×#382	C₂²	1	2	yes	—
58	C₁₃×#382	C₂²	1	2	yes	—
59	C₁₃×#382	C₂²	1	2	yes	—
60	C₁₃×#382	C₂²	1	2	yes	—
61	C₁₃×#382	C₂²	1	2	yes	—
62	C₁₃×#382	C₂²	1	2	yes	—
63	C₁₃×#380	C₂²	1	2	yes	—
64	C₁₃×#380	C₂²	1	2	yes	—
65	C₁₃×#380	C₂²	1	2	yes	—
66	C₁₃×#380	C₂²	1	2	yes	—
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
70	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
71	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
72	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
73	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
74	C₂×C₁₃×#95	C₂²	1	2	yes	—
75	C₂×C₁₃×#95	C₂²	1	2	yes	—
76	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×#126	C₂×C₄	1	16	yes	complemented
87	C₁₃×#125	C₂×C₄	1	8	yes	complemented
88	C₁₃×#124	C₂×C₄	1	8	yes	complemented
89	C₁₃×#123	C₂×C₄	1	16	yes	complemented
90	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
91	C₁₃×#121	C₂×C₄	1	8	yes	—
92	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
93	C₄×D₄×C₁₃	—	4	8	no	—
94	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
95	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
96	C₁₃×#117	—	4	4	no	—
97	C₁₃×#117	—	4	4	no	—
98	C₁₃×#117	C₂×C₄	1	16	yes	complemented
99	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
100	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
101	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
131	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
140	C₁₃×#95	C₂³	1	4	yes	—
141	C₁₃×#95	C₂³	1	4	yes	—
142	C₁₃×#95	C₂³	1	4	yes	—
143	C₁₃×#95	C₂³	1	4	yes	—
144	C₁₃×#95	C₂³	1	4	yes	—
145	C₁₃×#95	C₂³	1	4	yes	—
146	C₁₃×#95	C₂³	1	4	yes	—
147	C₁₃×#95	C₂³	1	4	yes	—
148	C₁₃×#95	C₂³	1	4	yes	—
149	C₁₃×#95	C₂³	1	4	yes	—
150	C₁₃×#95	C₂³	1	4	yes	—
151	C₁₃×#95	C₂³	1	4	yes	—
152	#34382	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
154	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₂×Q₈×C₁₃	—	4	1	no	—
156	C₂×Q₈×C₁₃	—	4	1	no	—
157	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	4	1	no	—
161	C₂×D₄×C₁₃	—	4	1	no	—
162	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
163	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	—	2	2	no	—
166	C₂²×C₄×C₁₃	—	2	2	no	—
167	C₂²×C₄×C₁₃	—	2	4	no	—
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	—	4	1	no	—
173	C₂²×C₄×C₁₃	—	4	1	no	—
174	C₂²×C₄×C₁₃	—	4	2	no	—
175	C₂²×C₄×C₁₃	—	4	4	no	—
176	C₂²×C₄×C₁₃	—	4	2	no	—
177	C₂²×C₄×C₁₃	—	4	4	no	—
178	C₂²×C₄×C₁₃	—	4	2	no	—
179	C₂²×C₄×C₁₃	—	4	4	no	—
180	C₂²×C₄×C₁₃	—	4	2	no	—
181	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
183	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
184	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₁₃×C₄⋊C₄	—	2	4	no	—
201	C₁₃×C₄⋊C₄	—	2	4	no	—
202	C₁₃×C₄⋊C₄	—	4	4	no	—
203	C₁₃×C₄⋊C₄	—	4	2	no	—
204	C₁₃×C₄⋊C₄	—	4	2	no	—
205	C₁₃×C₄⋊C₄	—	4	2	no	—
206	C₁₃×C₄⋊C₄	—	4	2	no	—
207	C₁₃×C₄⋊C₄	—	4	4	no	—
208	C₁₃×C₄⋊C₄	—	4	2	no	—
209	C₁₃×C₄⋊C₄	—	4	2	no	—
210	C₁₃×C₄⋊C₄	—	4	4	no	—
211	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
212	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
213	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
214	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
215	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
216	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
217	C₁₃×C₂²⋊C₄	—	2	8	no	—
218	C₁₃×C₂²⋊C₄	—	4	4	no	—
219	C₁₃×C₂²⋊C₄	—	4	4	no	—
220	C₁₃×C₂²⋊C₄	—	4	4	no	—
221	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
222	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
223	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
224	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
225	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
226	C₄²×C₁₃	—	4	4	no	—
227	C₄²×C₁₃	—	4	4	no	—
228	C₄²×C₁₃	—	4	4	no	—
229	C₄²×C₁₃	—	4	4	no	—
230	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
231	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
232	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
233	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
234	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
235	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
236	#2382	C₂×C₁₃	1	2	yes	complemented
237	#2379	C₂×C₁₃	1	2	yes	complemented
238	#2359	C₂×C₁₃	1	4	yes	complemented
239	#2355	C₂×C₁₃	1	2	yes	complemented
240	#2352	C₂×C₁₃	1	2	yes	complemented
241	#2352	C₂×C₁₃	1	2	yes	complemented
242	D₄×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
243	#2334	C₂×C₁₃	1	4	yes	complemented
244	#2329	C₂×C₁₃	1	2	yes	complemented
245	#2325	C₂×C₁₃	1	2	yes	—
246	#2317	C₂×C₁₃	1	2	yes	complemented
247	#2314	C₂×C₁₃	1	2	yes	complemented
248	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
249	C₂×#382	C₂×C₁₃	1	1	yes	characteristic, complemented
250	C₂³×C₁₃	—	2	1	no	—
251	C₂³×C₁₃	—	2	1	no	—
252	C₂³×C₁₃	—	2	1	no	—
253	C₂³×C₁₃	—	2	1	no	—
254	C₂³×C₁₃	—	2	2	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	2	2	no	—
260	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
261	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
262	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
263	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
264	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
265	Q₈×C₁₃	—	4	4	no	—
266	D₄×C₁₃	—	2	16	no	—
267	D₄×C₁₃	—	4	4	no	—
268	C₂×C₄×C₁₃	—	2	8	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	8	no	—
286	C₂×C₄×C₁₃	—	2	16	no	—
287	C₂×C₄×C₁₃	—	2	4	no	—
288	C₂×C₄×C₁₃	—	2	4	no	—
289	C₂×C₄×C₁₃	—	2	4	no	—
290	C₂×C₄×C₁₃	—	2	4	no	—
291	C₂×C₄×C₁₃	—	2	4	no	—
292	C₂×C₄×C₁₃	—	2	4	no	—
293	C₂×C₄×C₁₃	—	2	4	no	—
294	C₂×C₄×C₁₃	—	2	4	no	—
295	C₂×C₄×C₁₃	—	2	4	no	—
296	C₂×C₄×C₁₃	—	2	4	no	—
297	C₂×C₄×C₁₃	—	2	4	no	—
298	C₂×C₄×C₁₃	—	2	4	no	—
299	C₂×C₄×C₁₃	—	4	4	no	—
300	C₂×C₄×C₁₃	—	8	4	no	—
301	C₂×C₄×C₁₃	—	8	4	no	—
302	C₂×C₄×C₁₃	—	8	8	no	—
303	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
304	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
305	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
306	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
307	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
308	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
309	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
310	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
311	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
312	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
313	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
314	#529	C₄×C₁₃	1	16	yes	complemented
315	C₂×#126	C₂²×C₁₃	1	2	yes	—
316	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#123	C₂²×C₁₃	1	2	yes	—
319	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
323	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
324	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#117	C₂²×C₁₃	1	2	yes	—
326	C₂×#117	C₂²×C₁₃	1	2	yes	—
327	C₂×#117	C₂²×C₁₃	1	2	yes	—
328	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
329	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
330	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
331	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
332	#391	C₂²×C₁₃	1	4	yes	—
333	#389	C₂²×C₁₃	1	4	yes	—
334	#389	C₂²×C₁₃	1	4	yes	—
335	#389	C₂²×C₁₃	1	4	yes	—
336	#388	C₂²×C₁₃	1	4	yes	—
337	#388	C₂²×C₁₃	1	4	yes	—
338	#388	C₂²×C₁₃	1	4	yes	—
339	#388	C₂²×C₁₃	1	4	yes	—
340	#387	C₂²×C₁₃	1	4	yes	—
341	#387	C₂²×C₁₃	1	4	yes	—
342	#387	C₂²×C₁₃	1	4	yes	—
343	#387	C₂²×C₁₃	1	4	yes	—
344	#387	C₂²×C₁₃	1	4	yes	—
345	#387	C₂²×C₁₃	1	4	yes	—
346	#386	C₂²×C₁₃	1	4	yes	—
347	#386	C₂²×C₁₃	1	4	yes	—
348	#385	C₂²×C₁₃	1	4	yes	—
349	#385	C₂²×C₁₃	1	4	yes	—
350	#385	C₂²×C₁₃	1	4	yes	—
351	#385	C₂²×C₁₃	1	4	yes	—
352	#384	C₂²×C₁₃	1	1	yes	characteristic
353	#384	C₂²×C₁₃	1	1	yes	characteristic
354	#384	C₂²×C₁₃	1	2	yes	—
355	#382	C₂²×C₁₃	1	2	yes	—
356	#382	C₂²×C₁₃	1	2	yes	—
357	#382	C₂²×C₁₃	1	2	yes	—
358	#382	C₂²×C₁₃	1	2	yes	—
359	#382	C₂²×C₁₃	1	2	yes	—
360	#382	C₂²×C₁₃	1	2	yes	—
361	#380	C₂²×C₁₃	1	2	yes	—
362	#380	C₂²×C₁₃	1	2	yes	—
363	#380	C₂²×C₁₃	1	2	yes	—
364	#380	C₂²×C₁₃	1	2	yes	—
365	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
366	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
367	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
368	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
369	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
370	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
371	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
372	C₂×#95	C₂²×C₁₃	1	2	yes	—
373	C₂×#95	C₂²×C₁₃	1	2	yes	—
374	C₂²×C₁₃	—	2	2	no	—
375	C₂²×C₁₃	—	2	2	no	—
376	C₂²×C₁₃	—	2	2	no	—
377	C₂²×C₁₃	—	2	2	no	—
378	C₂²×C₁₃	—	2	2	no	—
379	C₂²×C₁₃	—	2	2	no	—
380	C₂²×C₁₃	—	2	4	no	—
381	C₂²×C₁₃	—	2	4	no	—
382	C₂²×C₁₃	—	2	4	no	—
383	C₂²×C₁₃	—	4	2	no	—
384	C₂²×C₁₃	—	4	2	no	—
385	C₂²×C₁₃	—	4	2	no	—
386	C₂²×C₁₃	—	4	2	no	—
387	C₂²×C₁₃	#520	1	4	yes	—
388	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
389	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
391	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
392	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
393	C₂²×C₁₃	#585	1	1	yes	characteristic
394	C₂²×C₁₃	#585	1	1	yes	characteristic
395	C₄×C₁₃	—	2	2	no	—
396	C₄×C₁₃	—	2	2	no	—
397	C₄×C₁₃	—	2	4	no	—
398	C₄×C₁₃	—	2	2	no	—
399	C₄×C₁₃	—	2	4	no	—
400	C₄×C₁₃	—	2	2	no	—
401	C₄×C₁₃	—	2	2	no	—
402	C₄×C₁₃	—	2	4	no	—
403	C₄×C₁₃	—	4	4	no	—
404	C₄×C₁₃	—	4	4	no	—
405	C₄×C₁₃	—	4	4	no	—
406	C₄×C₁₃	—	4	4	no	—
407	C₄×C₁₃	#520	1	4	yes	—
408	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
409	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
410	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
411	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
412	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
413	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
414	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
415	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
416	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
417	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
418	#126	C₂×C₄×C₁₃	1	16	yes	complemented
419	#125	C₂×C₄×C₁₃	1	8	yes	complemented
420	#124	C₂×C₄×C₁₃	1	8	yes	complemented
421	#123	C₂×C₄×C₁₃	1	16	yes	complemented
422	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
423	#121	C₂×C₄×C₁₃	1	8	yes	—
424	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
425	C₄×D₄	—	4	8	no	—
426	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
427	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
428	#117	—	4	4	no	—
429	#117	—	4	4	no	—
430	#117	C₂×C₄×C₁₃	1	16	yes	complemented
431	C₂×C₄⋊C₄	—	4	2	no	—
432	C₂×C₄⋊C₄	—	4	4	no	—
433	C₂×C₄⋊C₄	—	4	2	no	—
434	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
462	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
463	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
464	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
465	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
466	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
467	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
469	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
472	#95	C₂³×C₁₃	1	4	yes	—
473	#95	C₂³×C₁₃	1	4	yes	—
474	#95	C₂³×C₁₃	1	4	yes	—
475	#95	C₂³×C₁₃	1	4	yes	—
476	#95	C₂³×C₁₃	1	4	yes	—
477	#95	C₂³×C₁₃	1	4	yes	—
478	#95	C₂³×C₁₃	1	4	yes	—
479	#95	C₂³×C₁₃	1	4	yes	—
480	#95	C₂³×C₁₃	1	4	yes	—
481	#95	C₂³×C₁₃	1	4	yes	—
482	#95	C₂³×C₁₃	1	4	yes	—
483	#95	C₂³×C₁₃	1	4	yes	—
484	C₂×C₁₃	—	2	4	no	—
485	C₂×C₁₃	—	4	4	no	—
486	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
487	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
488	C₂×C₁₃	#3428	1	1	yes	characteristic
489	C₂×C₁₃	#3558	1	1	yes	characteristic
490	C₂×C₁₃	#3559	1	1	yes	characteristic
491	C₂×C₁₃	#3561	1	1	yes	characteristic
492	C₂×C₁₃	#3563	1	1	yes	characteristic
493	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
494	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
495	C₂×Q₈	—	4	1	no	—
496	C₂×Q₈	—	4	1	no	—
497	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	4	1	no	—
501	C₂×D₄	—	4	1	no	—
502	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
503	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	4	1	no	—
513	C₂²×C₄	—	4	1	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	4	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	4	4	no	—
520	C₂²×C₄	—	4	2	no	—
521	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
522	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
523	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
524	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
525	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
526	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
527	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
530	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
537	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	4	4	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	4	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	4	4	no	—
551	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
552	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
553	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
554	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
555	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
556	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
557	C₂²⋊C₄	—	2	8	no	—
558	C₂²⋊C₄	—	4	4	no	—
559	C₂²⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	—	4	4	no	—
561	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
563	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
564	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
565	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
566	C₄²	—	4	4	no	—
567	C₄²	—	4	4	no	—
568	C₄²	—	4	4	no	—
569	C₄²	—	4	4	no	—
570	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
571	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
572	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
573	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
574	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
575	C₁₃	#34382	1	1	yes	characteristic, direct product factor, Sylow
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
587	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
588	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
589	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
590	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
591	Q₈	—	4	4	no	—
592	D₄	—	2	16	no	—
593	D₄	—	4	4	no	—
594	C₂×C₄	—	2	8	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	8	no	—
612	C₂×C₄	—	2	16	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	8	4	no	—
627	C₂×C₄	—	8	4	no	—
628	C₂×C₄	—	8	8	no	—
629	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
630	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
631	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
632	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
633	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
634	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
635	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
636	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
637	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
638	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
639	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	C₁₃×#520	1	4	yes	—
654	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
655	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
657	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
658	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
659	C₂²	C₁₃×#585	1	1	yes	characteristic
660	C₂²	C₁₃×#585	1	1	yes	characteristic
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	4	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	4	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	4	no	—
669	C₄	—	4	4	no	—
670	C₄	—	4	4	no	—
671	C₄	—	4	4	no	—
672	C₄	—	4	4	no	—
673	C₄	C₁₃×#520	1	4	yes	—
674	C₂	—	2	4	no	—
675	C₂	—	4	4	no	—
676	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
677	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
678	C₂	C₁₃×#3428	1	1	yes	characteristic
679	C₂	C₁₃×#3558	1	1	yes	characteristic
680	C₂	C₁₃×#3559	1	1	yes	characteristic
681	C₂	C₁₃×#3561	1	1	yes	characteristic
682	C₂	C₁₃×#3563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2382	C₂	semidirect
3. C₁₃×#2379	C₂	semidirect
4. C₁₃×#2359	C₂	semidirect
5. C₁₃×#2355	C₂	semidirect
6. C₁₃×#2352	C₂	semidirect
7. C₁₃×#2352	C₂	semidirect
8. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
9. C₁₃×#2334	C₂	semidirect
10. C₁₃×#2329	C₂	semidirect
12. C₁₃×#2317	C₂	semidirect
13. C₁₃×#2314	C₂	semidirect
14. C₁₃×#2285	C₂	semidirect
15. C₂×C₁₃×#382	C₂	semidirect
16. C₁₃×#529	C₄	semidirect
86. C₁₃×#126	C₂×C₄	semidirect
87. C₁₃×#125	C₂×C₄	semidirect
88. C₁₃×#124	C₂×C₄	semidirect
89. C₁₃×#123	C₂×C₄	semidirect
90. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
92. C₄×Q₈×C₁₃	C₂×C₄	semidirect
94. C₄×D₄×C₁₃	C₂×C₄	semidirect
95. C₄×D₄×C₁₃	C₂×C₄	semidirect
98. C₁₃×#117	C₂×C₄	semidirect
130. C₂×C₄²×C₁₃	C₂×C₄	semidirect
152. #34382	C₁₃	direct (N × H)
236. #2382	C₂×C₁₃	semidirect
237. #2379	C₂×C₁₃	semidirect
238. #2359	C₂×C₁₃	semidirect
239. #2355	C₂×C₁₃	semidirect
240. #2352	C₂×C₁₃	semidirect
241. #2352	C₂×C₁₃	semidirect
242. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
243. #2334	C₂×C₁₃	semidirect
244. #2329	C₂×C₁₃	semidirect
246. #2317	C₂×C₁₃	semidirect
247. #2314	C₂×C₁₃	semidirect
248. #2285	C₂×C₁₃	semidirect
249. C₂×#382	C₂×C₁₃	semidirect
314. #529	C₄×C₁₃	semidirect
418. #126	C₂×C₄×C₁₃	semidirect
419. #125	C₂×C₄×C₁₃	semidirect
420. #124	C₂×C₄×C₁₃	semidirect
421. #123	C₂×C₄×C₁₃	semidirect
422. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
424. C₄×Q₈	C₂×C₄×C₁₃	semidirect
426. C₄×D₄	C₂×C₄×C₁₃	semidirect
427. C₄×D₄	C₂×C₄×C₁₃	semidirect
430. #117	C₂×C₄×C₁₃	semidirect
462. C₂×C₄²	C₂×C₄×C₁₃	semidirect
575. C₁₃	#34382	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×#529	2
C₁₃×#2382	2
C₁₃×#2379	2
C₁₃×#2359	2
C₁₃×#2355	2
C₁₃×#2352	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2334	2
C₁₃×#2329	2
C₁₃×#2325	2
C₁₃×#2317	2
C₁₃×#2314	2
C₁₃×#2285	2
C₂×C₁₃×#382	2
#34382	13

Subgroups — C13×#34382 #15720721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34382 #15720721