Subgroups — C₁₃×#24762 #15711101

Order 3328.

1060 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2619	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1895	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
26	C₁₃×#469	—	2	4	no	—
27	C₁₃×#466	—	2	4	no	—
28	C₁₃×#459	—	2	4	no	—
29	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
31	C₁₃×#424	—	2	4	no	—
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
44	C₁₃×#394	—	2	1	no	—
45	C₁₃×#394	—	2	1	no	—
46	C₁₃×#392	—	2	1	no	—
47	C₁₃×#392	—	2	1	no	—
48	C₁₃×#390	—	2	1	no	—
49	C₁₃×#390	C₂²	1	1	yes	characteristic
50	C₁₃×#390	C₂²	1	1	yes	characteristic
51	C₁₃×#390	C₂²	1	1	yes	characteristic
52	C₁₃×#389	C₂²	1	1	yes	characteristic
53	C₁₃×#388	—	2	1	no	—
54	C₁₃×#386	—	2	1	no	—
55	C₁₃×#385	—	2	1	no	—
56	C₁₃×#382	C₂²	1	1	yes	characteristic
57	C₁₃×#380	C₂²	1	1	yes	characteristic
58	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	C₂²	1	1	yes	characteristic
61	C₁₃×#340	C₂²	1	1	yes	characteristic
62	C₁₃×#340	C₂²	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₂²×D₄×C₁₃	—	2	1	no	—
66	C₂²×D₄×C₁₃	—	2	1	no	—
67	C₂²×D₄×C₁₃	—	2	1	no	—
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	—	2	1	no	—
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×D₈	—	2	2	no	—
74	C₂×C₁₃×D₈	—	2	2	no	—
75	C₂×C₁₃×D₈	—	2	2	no	—
76	C₂×C₁₃×D₈	—	2	2	no	—
77	C₂×C₁₃×D₈	—	4	1	no	—
78	C₂×C₁₃×D₈	—	4	1	no	—
79	C₂×C₁₃×M₁₆	—	2	2	no	—
80	C₂×C₁₃×M₁₆	—	2	2	no	—
81	C₂×C₁₃×M₁₆	—	4	1	no	—
82	C₂²×C₈×C₁₃	—	2	2	no	—
83	C₂²×C₈×C₁₃	—	2	2	no	—
84	C₂²×C₈×C₁₃	—	4	1	no	—
85	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×#127	—	2	2	no	—
90	C₁₃×#127	—	2	2	no	—
91	C₁₃×#121	—	2	2	no	—
92	C₁₃×#121	—	2	2	no	—
93	C₁₃×#121	—	2	2	no	—
94	C₁₃×#121	—	2	2	no	—
95	C₁₃×#121	—	2	2	no	—
96	C₁₃×#121	D₄	1	4	yes	complemented
97	C₄×D₄×C₁₃	—	2	2	no	—
98	C₄×D₄×C₁₃	—	2	2	no	—
99	C₁₃×#117	—	2	2	no	—
100	C₁₃×#117	—	2	2	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
121	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
122	C₂×C₄²×C₁₃	—	2	1	no	—
123	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₁₃×#107	—	2	2	no	—
126	C₁₃×#106	—	2	2	no	—
127	C₁₃×C₄⋊C₈	—	2	2	no	—
128	C₁₃×C₄⋊C₈	—	2	2	no	—
129	C₁₃×C₄⋊C₈	—	2	2	no	—
130	C₁₃×C₄⋊C₈	D₄	1	4	yes	complemented
131	C₁₃×#102	—	2	2	no	—
132	C₁₃×#102	—	2	2	no	—
133	C₁₃×#102	—	2	2	no	—
134	C₁₃×#102	—	2	2	no	—
135	C₁₃×#102	—	2	2	no	—
136	C₁₃×#102	—	2	2	no	—
137	C₁₃×#102	—	4	1	no	—
138	C₁₃×#102	—	4	1	no	—
139	C₁₃×#95	—	2	1	no	—
140	C₁₃×#95	—	2	1	no	—
141	C₁₃×#95	—	2	1	no	—
142	C₁₃×#95	—	2	1	no	—
143	C₁₃×#95	—	2	1	no	—
144	#24762	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	—	2	1	no	—
146	C₂⁴×C₁₃	—	2	1	no	—
147	C₂⁴×C₁₃	—	2	1	no	—
148	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	2	1	no	—
163	C₂×D₄×C₁₃	—	2	1	no	—
164	C₂×D₄×C₁₃	—	2	1	no	—
165	C₂×D₄×C₁₃	—	2	1	no	—
166	C₂×D₄×C₁₃	—	2	1	no	—
167	C₂×D₄×C₁₃	—	4	2	no	—
168	C₂×D₄×C₁₃	—	4	2	no	—
169	C₂×D₄×C₁₃	—	4	2	no	—
170	C₂×D₄×C₁₃	—	4	2	no	—
171	C₂×D₄×C₁₃	—	8	1	no	—
172	C₂×D₄×C₁₃	—	8	1	no	—
173	C₂×D₄×C₁₃	—	8	1	no	—
174	C₂×D₄×C₁₃	—	8	1	no	—
175	C₂×D₄×C₁₃	—	8	1	no	—
176	C₂×D₄×C₁₃	—	8	1	no	—
177	C₂×D₄×C₁₃	—	8	1	no	—
178	C₂×D₄×C₁₃	—	8	1	no	—
179	C₂×D₄×C₁₃	—	8	1	no	—
180	C₂×D₄×C₁₃	—	8	1	no	—
181	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	—	2	1	no	—
184	C₂²×C₄×C₁₃	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	2	1	no	—
186	C₂²×C₄×C₁₃	—	2	1	no	—
187	C₂²×C₄×C₁₃	—	2	1	no	—
188	C₂²×C₄×C₁₃	—	2	1	no	—
189	C₂²×C₄×C₁₃	—	2	1	no	—
190	C₂²×C₄×C₁₃	—	2	1	no	—
191	C₂²×C₄×C₁₃	—	4	2	no	—
192	C₂²×C₄×C₁₃	—	8	1	no	—
193	C₂²×C₄×C₁₃	—	8	1	no	—
194	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₁₃	#41	1	2	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
202	C₁₃×D₈	—	4	4	no	—
203	C₁₃×D₈	—	4	4	no	—
204	C₁₃×M₁₆	—	4	4	no	—
205	C₂×C₈×C₁₃	—	2	1	no	—
206	C₂×C₈×C₁₃	—	2	1	no	—
207	C₂×C₈×C₁₃	—	2	1	no	—
208	C₂×C₈×C₁₃	—	2	1	no	—
209	C₂×C₈×C₁₃	—	2	1	no	—
210	C₂×C₈×C₁₃	—	2	1	no	—
211	C₂×C₈×C₁₃	—	2	1	no	—
212	C₂×C₈×C₁₃	—	2	1	no	—
213	C₂×C₈×C₁₃	—	2	1	no	—
214	C₂×C₈×C₁₃	—	2	1	no	—
215	C₂×C₈×C₁₃	—	4	4	no	—
216	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
217	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
218	C₁₃×C₄⋊C₄	—	2	2	no	—
219	C₁₃×C₄⋊C₄	—	2	2	no	—
220	C₁₃×C₄⋊C₄	—	2	1	no	—
221	C₁₃×C₄⋊C₄	—	2	1	no	—
222	C₁₃×C₄⋊C₄	—	2	1	no	—
223	C₁₃×C₄⋊C₄	—	2	1	no	—
224	C₁₃×C₄⋊C₄	—	2	1	no	—
225	C₁₃×C₄⋊C₄	—	2	1	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	8	1	no	—
230	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
231	C₁₃×C₂²⋊C₄	—	2	4	no	—
232	C₁₃×C₂²⋊C₄	—	2	2	no	—
233	C₁₃×C₂²⋊C₄	—	2	2	no	—
234	C₁₃×C₂²⋊C₄	—	4	2	no	—
235	C₁₃×C₂²⋊C₄	—	4	2	no	—
236	C₁₃×C₂²⋊C₄	—	4	2	no	—
237	C₁₃×C₂²⋊C₄	—	8	1	no	—
238	C₁₃×C₂²⋊C₄	—	8	1	no	—
239	C₁₃×C₂²⋊C₄	—	8	1	no	—
240	C₁₃×C₂²⋊C₄	—	8	1	no	—
241	C₁₃×C₂²⋊C₄	—	8	1	no	—
242	C₁₃×C₂²⋊C₄	—	8	1	no	—
243	C₁₃×C₂²⋊C₄	—	8	1	no	—
244	C₄²×C₁₃	—	2	1	no	—
245	C₄²×C₁₃	—	2	1	no	—
246	C₄²×C₁₃	—	8	1	no	—
247	C₄²×C₁₃	C₂×D₄	1	2	yes	—
248	C₄²×C₁₃	#41	1	2	yes	—
249	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
250	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
251	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
252	C₂×#424	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#2619	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#2324	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#2067	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#2065	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#2054	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#2054	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#1982	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#1895	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#1893	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
264	C₂³×C₁₃	—	2	1	no	—
265	C₂³×C₁₃	—	2	1	no	—
266	C₂³×C₁₃	—	2	1	no	—
267	C₂³×C₁₃	—	2	1	no	—
268	C₂³×C₁₃	—	2	1	no	—
269	C₂³×C₁₃	—	2	1	no	—
270	C₂³×C₁₃	—	2	2	no	—
271	C₂³×C₁₃	—	4	1	no	—
272	C₂³×C₁₃	—	4	1	no	—
273	C₂³×C₁₃	—	4	1	no	—
274	C₂³×C₁₃	—	4	1	no	—
275	C₂³×C₁₃	—	4	1	no	—
276	C₂³×C₁₃	—	4	1	no	—
277	C₂³×C₁₃	—	4	1	no	—
278	C₂³×C₁₃	—	4	1	no	—
279	C₂³×C₁₃	—	4	1	no	—
280	C₂³×C₁₃	—	4	1	no	—
281	C₂³×C₁₃	—	4	1	no	—
282	C₂³×C₁₃	—	4	1	no	—
283	C₂³×C₁₃	—	4	1	no	—
284	C₂³×C₁₃	—	4	1	no	—
285	C₂³×C₁₃	—	4	1	no	—
286	C₂³×C₁₃	—	4	1	no	—
287	C₂³×C₁₃	—	4	1	no	—
288	C₂³×C₁₃	—	4	1	no	—
289	C₂³×C₁₃	—	4	1	no	—
290	C₂³×C₁₃	—	4	1	no	—
291	C₂³×C₁₃	#121	1	2	yes	—
292	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
293	D₄×C₁₃	—	2	2	no	—
294	D₄×C₁₃	—	2	2	no	—
295	D₄×C₁₃	—	4	1	no	—
296	D₄×C₁₃	—	4	1	no	—
297	D₄×C₁₃	—	4	1	no	—
298	D₄×C₁₃	—	4	1	no	—
299	D₄×C₁₃	—	4	1	no	—
300	D₄×C₁₃	—	4	1	no	—
301	D₄×C₁₃	—	4	1	no	—
302	D₄×C₁₃	—	4	1	no	—
303	D₄×C₁₃	—	4	1	no	—
304	D₄×C₁₃	—	4	1	no	—
305	D₄×C₁₃	—	8	4	no	—
306	D₄×C₁₃	—	8	4	no	—
307	D₄×C₁₃	—	8	4	no	—
308	D₄×C₁₃	—	8	4	no	—
309	D₄×C₁₃	—	8	4	no	—
310	C₂×C₄×C₁₃	—	2	1	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	1	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	1	no	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	1	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	4	1	no	—
328	C₂×C₄×C₁₃	—	4	1	no	—
329	C₂×C₄×C₁₃	—	4	1	no	—
330	C₂×C₄×C₁₃	—	4	1	no	—
331	C₂×C₄×C₁₃	—	4	1	no	—
332	C₂×C₄×C₁₃	—	4	1	no	—
333	C₂×C₄×C₁₃	—	4	1	no	—
334	C₂×C₄×C₁₃	—	4	1	no	—
335	C₂×C₄×C₁₃	—	4	1	no	—
336	C₂×C₄×C₁₃	—	4	1	no	—
337	C₂×C₄×C₁₃	—	4	1	no	—
338	C₂×C₄×C₁₃	—	4	1	no	—
339	C₂×C₄×C₁₃	—	4	1	no	—
340	C₂×C₄×C₁₃	—	4	1	no	—
341	C₂×C₄×C₁₃	—	8	4	no	—
342	C₂×C₄×C₁₃	#121	1	2	yes	—
343	C₂×C₄×C₁₃	#121	1	2	yes	—
344	C₂×C₄×C₁₃	#121	1	2	yes	—
345	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
348	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
349	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
350	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
351	C₈×C₁₃	—	2	2	no	—
352	C₈×C₁₃	—	2	2	no	—
353	C₈×C₁₃	—	4	1	no	—
354	C₈×C₁₃	—	4	1	no	—
355	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
356	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
357	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
358	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
363	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
365	#469	—	2	4	no	—
366	#466	—	2	4	no	—
367	#459	—	2	4	no	—
368	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
370	#424	—	2	4	no	—
371	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
383	#394	—	2	1	no	—
384	#394	—	2	1	no	—
385	#392	—	2	1	no	—
386	#392	—	2	1	no	—
387	#390	—	2	1	no	—
388	#390	C₂²×C₁₃	1	1	yes	characteristic
389	#390	C₂²×C₁₃	1	1	yes	characteristic
390	#390	C₂²×C₁₃	1	1	yes	characteristic
391	#389	C₂²×C₁₃	1	1	yes	characteristic
392	#388	—	2	1	no	—
393	#386	—	2	1	no	—
394	#385	—	2	1	no	—
395	#382	C₂²×C₁₃	1	1	yes	characteristic
396	#380	C₂²×C₁₃	1	1	yes	characteristic
397	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
398	#340	C₂²×C₁₃	1	1	yes	characteristic
399	#340	C₂²×C₁₃	1	1	yes	characteristic
400	#340	C₂²×C₁₃	1	1	yes	characteristic
401	#340	C₂²×C₁₃	1	1	yes	characteristic
402	C₂²×C₁₃	—	2	2	no	—
403	C₂²×C₁₃	—	2	2	no	—
404	C₂²×C₁₃	—	2	2	no	—
405	C₂²×C₁₃	—	4	1	no	—
406	C₂²×C₁₃	—	4	1	no	—
407	C₂²×C₁₃	—	4	1	no	—
408	C₂²×C₁₃	—	4	1	no	—
409	C₂²×C₁₃	—	4	2	no	—
410	C₂²×C₁₃	—	4	2	no	—
411	C₂²×C₁₃	—	4	2	no	—
412	C₂²×C₁₃	—	8	1	no	—
413	C₂²×C₁₃	—	8	1	no	—
414	C₂²×C₁₃	—	8	1	no	—
415	C₂²×C₁₃	—	8	1	no	—
416	C₂²×C₁₃	—	8	1	no	—
417	C₂²×C₁₃	—	8	1	no	—
418	C₂²×C₁₃	—	8	1	no	—
419	C₂²×C₁₃	—	8	1	no	—
420	C₂²×C₁₃	—	8	1	no	—
421	C₂²×C₁₃	—	8	1	no	—
422	C₂²×C₁₃	—	8	1	no	—
423	C₂²×C₁₃	—	8	1	no	—
424	C₂²×C₁₃	—	8	1	no	—
425	C₂²×C₁₃	—	8	1	no	—
426	C₂²×C₁₃	—	8	1	no	—
427	C₂²×C₁₃	—	8	1	no	—
428	C₂²×C₁₃	—	8	1	no	—
429	C₂²×C₁₃	—	8	1	no	—
430	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
431	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
432	C₂²×C₁₃	#537	1	1	yes	characteristic
433	C₂²×C₁₃	#576	1	1	yes	characteristic
434	C₂²×C₁₃	#576	1	1	yes	characteristic
435	C₂²×C₁₃	#576	1	1	yes	characteristic
436	C₂²×C₁₃	#577	1	1	yes	characteristic
437	C₄×C₁₃	—	2	2	no	—
438	C₄×C₁₃	—	2	2	no	—
439	C₄×C₁₃	—	2	2	no	—
440	C₄×C₁₃	—	4	2	no	—
441	C₄×C₁₃	—	4	1	no	—
442	C₄×C₁₃	—	4	1	no	—
443	C₄×C₁₃	—	8	1	no	—
444	C₄×C₁₃	—	8	1	no	—
445	C₄×C₁₃	—	8	1	no	—
446	C₄×C₁₃	—	8	1	no	—
447	C₄×C₁₃	D₄²	1	1	yes	characteristic
448	C₄×C₁₃	#547	1	1	yes	characteristic
449	C₄×C₁₃	#548	1	1	yes	characteristic
450	C₄×C₁₃	#553	1	1	yes	characteristic
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	—	2	1	no	—
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
459	C₂³×C₄	—	2	1	no	—
460	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
461	C₂×D₈	—	2	2	no	—
462	C₂×D₈	—	2	2	no	—
463	C₂×D₈	—	2	2	no	—
464	C₂×D₈	—	2	2	no	—
465	C₂×D₈	—	4	1	no	—
466	C₂×D₈	—	4	1	no	—
467	C₂×M₁₆	—	2	2	no	—
468	C₂×M₁₆	—	2	2	no	—
469	C₂×M₁₆	—	4	1	no	—
470	C₂²×C₈	—	2	2	no	—
471	C₂²×C₈	—	2	2	no	—
472	C₂²×C₈	—	4	1	no	—
473	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
477	#127	—	2	2	no	—
478	#127	—	2	2	no	—
479	#121	—	2	2	no	—
480	#121	—	2	2	no	—
481	#121	—	2	2	no	—
482	#121	—	2	2	no	—
483	#121	—	2	2	no	—
484	#121	D₄×C₁₃	1	4	yes	complemented
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	2	no	—
487	#117	—	2	2	no	—
488	#117	—	2	2	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
510	C₂×C₄²	—	2	1	no	—
511	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
512	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
513	#107	—	2	2	no	—
514	#106	—	2	2	no	—
515	C₄⋊C₈	—	2	2	no	—
516	C₄⋊C₈	—	2	2	no	—
517	C₄⋊C₈	—	2	2	no	—
518	C₄⋊C₈	D₄×C₁₃	1	4	yes	complemented
519	#102	—	2	2	no	—
520	#102	—	2	2	no	—
521	#102	—	2	2	no	—
522	#102	—	2	2	no	—
523	#102	—	2	2	no	—
524	#102	—	2	2	no	—
525	#102	—	4	1	no	—
526	#102	—	4	1	no	—
527	#95	—	2	1	no	—
528	#95	—	2	1	no	—
529	#95	—	2	1	no	—
530	#95	—	2	1	no	—
531	#95	—	2	1	no	—
532	C₂×C₁₃	—	4	2	no	—
533	C₂×C₁₃	—	8	2	no	—
534	C₂×C₁₃	—	16	1	no	—
535	C₂×C₁₃	—	16	1	no	—
536	C₂×C₁₃	#2416	1	1	yes	characteristic
537	C₂×C₁₃	#3041	1	1	yes	characteristic
538	C₂×C₁₃	#3045	1	1	yes	characteristic
539	C₂×C₁₃	#3058	1	1	yes	characteristic
540	C₂×C₁₃	#3062	1	1	yes	characteristic
541	C₂×C₁₃	#3257	1	1	yes	characteristic
542	C₂×C₁₃	#3259	1	1	yes	characteristic
543	C₂⁴	—	2	1	no	—
544	C₂⁴	—	2	1	no	—
545	C₂⁴	—	2	1	no	—
546	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	—	4	2	no	—
569	C₂×D₄	—	8	1	no	—
570	C₂×D₄	—	8	1	no	—
571	C₂×D₄	—	8	1	no	—
572	C₂×D₄	—	8	1	no	—
573	C₂×D₄	—	8	1	no	—
574	C₂×D₄	—	8	1	no	—
575	C₂×D₄	—	8	1	no	—
576	C₂×D₄	—	8	1	no	—
577	C₂×D₄	—	8	1	no	—
578	C₂×D₄	—	8	1	no	—
579	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	8	1	no	—
591	C₂²×C₄	—	8	1	no	—
592	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
598	C₂²×C₄	C₁₃×#41	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
600	D₈	—	4	4	no	—
601	D₈	—	4	4	no	—
602	M₁₆	—	4	4	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	4	4	no	—
614	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
615	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	8	1	no	—
628	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	4	2	no	—
633	C₂²⋊C₄	—	4	2	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	8	1	no	—
636	C₂²⋊C₄	—	8	1	no	—
637	C₂²⋊C₄	—	8	1	no	—
638	C₂²⋊C₄	—	8	1	no	—
639	C₂²⋊C₄	—	8	1	no	—
640	C₂²⋊C₄	—	8	1	no	—
641	C₂²⋊C₄	—	8	1	no	—
642	C₄²	—	2	1	no	—
643	C₄²	—	2	1	no	—
644	C₄²	—	8	1	no	—
645	C₄²	C₂×D₄×C₁₃	1	2	yes	—
646	C₄²	C₁₃×#41	1	2	yes	—
647	C₁₃	#24762	1	1	yes	characteristic, direct product factor, Sylow
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	C₁₃×#121	1	2	yes	—
676	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
677	D₄	—	2	2	no	—
678	D₄	—	2	2	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	1	no	—
685	D₄	—	4	1	no	—
686	D₄	—	4	1	no	—
687	D₄	—	4	1	no	—
688	D₄	—	4	1	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	4	no	—
691	D₄	—	8	4	no	—
692	D₄	—	8	4	no	—
693	D₄	—	8	4	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	C₁₃×#121	1	2	yes	—
727	C₂×C₄	C₁₃×#121	1	2	yes	—
728	C₂×C₄	C₁₃×#121	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
731	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
732	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
733	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
734	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
735	C₈	—	2	2	no	—
736	C₈	—	2	2	no	—
737	C₈	—	4	1	no	—
738	C₈	—	4	1	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	8	1	no	—
750	C₂²	—	8	1	no	—
751	C₂²	—	8	1	no	—
752	C₂²	—	8	1	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	—	8	1	no	—
756	C₂²	—	8	1	no	—
757	C₂²	—	8	1	no	—
758	C₂²	—	8	1	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	—	8	1	no	—
764	C₂²	—	8	1	no	—
765	C₂²	—	8	1	no	—
766	C₂²	—	8	1	no	—
767	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
768	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
769	C₂²	C₁₃×#537	1	1	yes	characteristic
770	C₂²	C₁₃×#576	1	1	yes	characteristic
771	C₂²	C₁₃×#576	1	1	yes	characteristic
772	C₂²	C₁₃×#576	1	1	yes	characteristic
773	C₂²	C₁₃×#577	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	1	no	—
780	C₄	—	8	1	no	—
781	C₄	—	8	1	no	—
782	C₄	—	8	1	no	—
783	C₄	—	8	1	no	—
784	C₄	D₄²×C₁₃	1	1	yes	characteristic
785	C₄	C₁₃×#547	1	1	yes	characteristic
786	C₄	C₁₃×#548	1	1	yes	characteristic
787	C₄	C₁₃×#553	1	1	yes	characteristic
788	C₂	—	4	2	no	—
789	C₂	—	8	2	no	—
790	C₂	—	16	1	no	—
791	C₂	—	16	1	no	—
792	C₂	C₁₃×#2416	1	1	yes	characteristic
793	C₂	C₁₃×#3041	1	1	yes	characteristic
794	C₂	C₁₃×#3045	1	1	yes	characteristic
795	C₂	C₁₃×#3058	1	1	yes	characteristic
796	C₂	C₁₃×#3062	1	1	yes	characteristic
797	C₂	C₁₃×#3257	1	1	yes	characteristic
798	C₂	C₁₃×#3259	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#469	C₂	semidirect
2. C₂×C₁₃×#466	C₂	semidirect
3. C₂×C₁₃×#459	C₂	semidirect
4. C₂×C₁₃×#424	C₂	semidirect
5. C₁₃×#2619	C₂	semidirect
6. C₁₃×#2324	C₂	semidirect
7. C₁₃×#2067	C₂	semidirect
8. C₁₃×#2065	C₂	semidirect
9. C₁₃×#2054	C₂	semidirect
10. C₁₃×#2054	C₂	semidirect
11. C₁₃×#1982	C₂	semidirect
12. C₁₃×#1949	C₂	semidirect
13. C₁₃×#1895	C₂	semidirect
14. C₁₃×#1893	C₂	semidirect
15. C₁₃×#1804	C₂	semidirect
96. C₁₃×#121	D₄	semidirect
130. C₁₃×C₄⋊C₈	D₄	semidirect
144. #24762	C₁₃	direct (N × H)
249. C₂×#469	C₂×C₁₃	semidirect
250. C₂×#466	C₂×C₁₃	semidirect
251. C₂×#459	C₂×C₁₃	semidirect
252. C₂×#424	C₂×C₁₃	semidirect
253. #2619	C₂×C₁₃	semidirect
254. #2324	C₂×C₁₃	semidirect
255. #2067	C₂×C₁₃	semidirect
256. #2065	C₂×C₁₃	semidirect
257. #2054	C₂×C₁₃	semidirect
258. #2054	C₂×C₁₃	semidirect
259. #1982	C₂×C₁₃	semidirect
260. #1949	C₂×C₁₃	semidirect
261. #1895	C₂×C₁₃	semidirect
262. #1893	C₂×C₁₃	semidirect
263. #1804	C₂×C₁₃	semidirect
484. #121	D₄×C₁₃	semidirect
518. C₄⋊C₈	D₄×C₁₃	semidirect
647. C₁₃	#24762	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×#469	2
C₂×C₁₃×#466	2
C₂×C₁₃×#459	2
C₂×C₁₃×#424	2
C₁₃×#2619	2
C₁₃×#2324	2
C₁₃×#2067	2
C₁₃×#2065	2
C₁₃×#2054	2
C₁₃×#1982	2
C₁₃×#1949	2
C₁₃×#1895	2
C₁₃×#1893	2
C₁₃×#1804	2
#24762	13

Subgroups — C13×#24762 #15711101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24762 #15711101