Subgroups — C₁₃×#24538 #15710877

Order 3328.

1156 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2499	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2073	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2071	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1825	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
25	C₁₃×#450	—	2	4	no	—
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#418	—	2	4	no	—
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₁₃×#397	—	2	1	no	—
39	C₁₃×#397	—	2	1	no	—
40	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#390	C₂²	1	1	yes	characteristic
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#387	—	2	1	no	—
45	C₁₃×#387	—	2	1	no	—
46	C₁₃×#386	—	2	1	no	—
47	C₁₃×#386	—	2	1	no	—
48	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#380	C₂²	1	1	yes	characteristic
51	C₁₃×#379	—	2	1	no	—
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
61	C₂⁵×C₁₃	—	2	1	no	—
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	—	2	2	no	—
64	C₂²×D₄×C₁₃	—	2	2	no	—
65	C₂²×D₄×C₁₃	—	2	1	no	—
66	C₂²×D₄×C₁₃	—	2	2	no	—
67	C₂²×D₄×C₁₃	—	4	1	no	—
68	C₂²×D₄×C₁₃	—	4	1	no	—
69	C₂²×D₄×C₁₃	D₄	1	4	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	—	2	1	no	—
73	C₂³×C₄×C₁₃	—	2	1	no	—
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×SD₁₆	—	2	2	no	—
76	C₂×C₁₃×SD₁₆	—	2	2	no	—
77	C₂×C₁₃×SD₁₆	—	2	2	no	—
78	C₂×C₁₃×SD₁₆	—	2	2	no	—
79	C₂×C₁₃×SD₁₆	—	4	1	no	—
80	C₂×C₁₃×SD₁₆	—	4	1	no	—
81	C₂×C₁₃×M₁₆	—	2	2	no	—
82	C₂×C₁₃×M₁₆	—	4	1	no	—
83	C₂×C₁₃×M₁₆	—	4	1	no	—
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×C₂²⋊Q₈	—	2	2	no	—
89	C₁₃×C₂²⋊Q₈	—	2	2	no	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	—	2	2	no	—
92	C₄×D₄×C₁₃	—	4	1	no	—
93	C₄×D₄×C₁₃	—	4	1	no	—
94	C₁₃×#117	—	2	2	no	—
95	C₁₃×#117	—	2	2	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	—	4	4	no	—
114	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
115	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₁₃	—	2	1	no	—
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊C₈	—	4	1	no	—
120	C₁₃×C₄⋊C₈	—	4	1	no	—
121	C₁₃×#103	—	4	1	no	—
122	C₁₃×#103	—	4	1	no	—
123	C₁₃×#102	—	2	2	no	—
124	C₁₃×#102	—	2	2	no	—
125	C₁₃×#102	—	2	2	no	—
126	C₁₃×#102	—	2	2	no	—
127	C₁₃×#102	—	2	2	no	—
128	C₁₃×#102	—	2	2	no	—
129	C₁₃×C₂²⋊C₈	—	2	2	no	—
130	C₁₃×#95	—	2	1	no	—
131	C₁₃×#95	—	2	1	no	—
132	C₁₃×#95	—	2	1	no	—
133	C₁₃×#95	—	2	1	no	—
134	C₁₃×#95	—	2	1	no	—
135	C₁₃×#95	—	2	1	no	—
136	C₁₃×#95	—	2	1	no	—
137	C₁₃×#95	D₄	1	1	yes	characteristic
138	C₁₃×#95	D₄	1	1	yes	characteristic
139	#24538	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂⁴×C₁₃	—	2	1	no	—
141	C₂⁴×C₁₃	—	2	1	no	—
142	C₂⁴×C₁₃	—	2	4	no	—
143	C₂⁴×C₁₃	—	4	2	no	—
144	C₂⁴×C₁₃	—	4	2	no	—
145	C₂⁴×C₁₃	—	4	2	no	—
146	C₂⁴×C₁₃	—	4	2	no	—
147	C₂⁴×C₁₃	—	8	1	no	—
148	C₂⁴×C₁₃	—	8	1	no	—
149	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	8	no	—
157	C₂×D₄×C₁₃	—	2	4	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	—	4	4	no	—
167	C₂×D₄×C₁₃	—	4	4	no	—
168	C₂×D₄×C₁₃	—	4	4	no	—
169	C₂×D₄×C₁₃	—	4	2	no	—
170	C₂×D₄×C₁₃	—	4	2	no	—
171	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
172	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂×D₄×C₁₃	#41	1	2	yes	—
174	C₂×D₄×C₁₃	#41	1	2	yes	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	1	no	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
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	—	4	2	no	—
186	C₂²×C₄×C₁₃	—	4	2	no	—
187	C₂²×C₄×C₁₃	—	4	2	no	—
188	C₂²×C₄×C₁₃	—	4	2	no	—
189	C₂²×C₄×C₁₃	—	8	1	no	—
190	C₂²×C₄×C₁₃	—	8	1	no	—
191	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	#41	1	2	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₁₃×SD₁₆	—	4	4	no	—
200	C₁₃×SD₁₆	—	4	4	no	—
201	C₁₃×M₁₆	—	4	4	no	—
202	C₂×C₈×C₁₃	—	2	1	no	—
203	C₂×C₈×C₁₃	—	2	1	no	—
204	C₂×C₈×C₁₃	—	2	1	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	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	2	1	no	—
218	C₁₃×C₄⋊C₄	—	2	1	no	—
219	C₁₃×C₄⋊C₄	—	2	1	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	—	4	2	no	—
225	C₁₃×C₄⋊C₄	—	4	2	no	—
226	C₁₃×C₄⋊C₄	—	4	2	no	—
227	C₁₃×C₂²⋊C₄	—	2	2	no	—
228	C₁₃×C₂²⋊C₄	—	4	1	no	—
229	C₁₃×C₂²⋊C₄	—	4	2	no	—
230	C₁₃×C₂²⋊C₄	—	4	2	no	—
231	C₁₃×C₂²⋊C₄	—	4	2	no	—
232	C₁₃×C₂²⋊C₄	—	4	2	no	—
233	C₁₃×C₂²⋊C₄	—	4	2	no	—
234	C₁₃×C₂²⋊C₄	—	4	2	no	—
235	C₁₃×C₂²⋊C₄	—	4	2	no	—
236	C₁₃×C₂²⋊C₄	—	8	1	no	—
237	C₁₃×C₂²⋊C₄	—	8	1	no	—
238	C₄²×C₁₃	—	2	1	no	—
239	C₄²×C₁₃	—	2	1	no	—
240	C₄²×C₁₃	—	2	1	no	—
241	C₄²×C₁₃	—	2	1	no	—
242	C₄²×C₁₃	—	4	2	no	—
243	C₂×#450	C₂×C₁₃	1	1	yes	characteristic
244	C₂×#418	C₂×C₁₃	1	1	yes	characteristic
245	#2499	C₂×C₁₃	1	1	yes	characteristic, complemented
246	D₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
247	#2073	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#2071	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#1894	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#1851	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#1825	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	2	2	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	1	no	—
262	C₂³×C₁₃	—	2	1	no	—
263	C₂³×C₁₃	—	2	1	no	—
264	C₂³×C₁₃	—	2	1	no	—
265	C₂³×C₁₃	—	2	1	no	—
266	C₂³×C₁₃	—	2	1	no	—
267	C₂³×C₁₃	—	2	2	no	—
268	C₂³×C₁₃	—	4	8	no	—
269	C₂³×C₁₃	—	4	8	no	—
270	C₂³×C₁₃	—	4	1	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	—	8	4	no	—
281	C₂³×C₁₃	—	8	4	no	—
282	C₂³×C₁₃	—	8	4	no	—
283	C₂³×C₁₃	—	8	4	no	—
284	C₂³×C₁₃	—	8	4	no	—
285	C₂³×C₁₃	#121	1	2	yes	—
286	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
287	Q₈×C₁₃	—	4	1	no	—
288	Q₈×C₁₃	—	4	1	no	—
289	Q₈×C₁₃	—	4	1	no	—
290	Q₈×C₁₃	—	4	1	no	—
291	D₄×C₁₃	—	2	2	no	—
292	D₄×C₁₃	—	2	2	no	—
293	D₄×C₁₃	—	2	2	no	—
294	D₄×C₁₃	—	2	2	no	—
295	D₄×C₁₃	—	2	2	no	—
296	D₄×C₁₃	—	4	8	no	—
297	D₄×C₁₃	—	4	1	no	—
298	D₄×C₁₃	—	4	1	no	—
299	D₄×C₁₃	#123	1	4	yes	—
300	C₂×C₄×C₁₃	—	2	1	no	—
301	C₂×C₄×C₁₃	—	2	1	no	—
302	C₂×C₄×C₁₃	—	2	1	no	—
303	C₂×C₄×C₁₃	—	2	1	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	1	no	—
309	C₂×C₄×C₁₃	—	2	1	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	1	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	1	no	—
326	C₂×C₄×C₁₃	—	4	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	—	8	4	no	—
336	C₂×C₄×C₁₃	—	8	4	no	—
337	C₂×C₄×C₁₃	#121	1	2	yes	—
338	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
339	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
343	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
344	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
345	C₈×C₁₃	—	4	1	no	—
346	C₈×C₁₃	—	4	1	no	—
347	C₈×C₁₃	—	4	1	no	—
348	C₈×C₁₃	—	4	1	no	—
349	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
350	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
351	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
352	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
357	C₂²×C₂²⋊C₄	—	2	1	no	—
358	#450	—	2	4	no	—
359	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
360	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
361	#418	—	2	4	no	—
362	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
363	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
364	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
371	#397	—	2	1	no	—
372	#397	—	2	1	no	—
373	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
374	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
375	#390	C₂²×C₁₃	1	1	yes	characteristic
376	#390	C₂²×C₁₃	1	1	yes	characteristic
377	#387	—	2	1	no	—
378	#387	—	2	1	no	—
379	#386	—	2	1	no	—
380	#386	—	2	1	no	—
381	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
382	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
383	#380	C₂²×C₁₃	1	1	yes	characteristic
384	#379	—	2	1	no	—
385	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
386	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
387	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
388	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
390	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
391	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
392	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
393	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
394	C₂²×C₁₃	—	2	2	no	—
395	C₂²×C₁₃	—	2	4	no	—
396	C₂²×C₁₃	—	2	2	no	—
397	C₂²×C₁₃	—	2	2	no	—
398	C₂²×C₁₃	—	4	2	no	—
399	C₂²×C₁₃	—	4	2	no	—
400	C₂²×C₁₃	—	4	2	no	—
401	C₂²×C₁₃	—	4	1	no	—
402	C₂²×C₁₃	—	4	1	no	—
403	C₂²×C₁₃	—	4	2	no	—
404	C₂²×C₁₃	—	4	1	no	—
405	C₂²×C₁₃	—	4	2	no	—
406	C₂²×C₁₃	—	4	2	no	—
407	C₂²×C₁₃	—	4	1	no	—
408	C₂²×C₁₃	—	4	2	no	—
409	C₂²×C₁₃	—	4	2	no	—
410	C₂²×C₁₃	—	4	2	no	—
411	C₂²×C₁₃	—	8	16	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	C₂×#121	1	1	yes	characteristic
417	C₂²×C₁₃	#546	1	1	yes	characteristic
418	C₂²×C₁₃	#546	1	1	yes	characteristic
419	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
420	C₂²×C₁₃	#575	1	1	yes	characteristic
421	C₂²×C₁₃	#577	1	1	yes	characteristic
422	C₂²×C₁₃	#577	1	1	yes	characteristic
423	C₄×C₁₃	—	2	2	no	—
424	C₄×C₁₃	—	2	2	no	—
425	C₄×C₁₃	—	4	1	no	—
426	C₄×C₁₃	—	4	1	no	—
427	C₄×C₁₃	—	4	1	no	—
428	C₄×C₁₃	—	8	1	no	—
429	C₄×C₁₃	—	8	1	no	—
430	C₄×C₁₃	—	8	1	no	—
431	C₄×C₁₃	—	8	1	no	—
432	C₄×C₁₃	—	8	1	no	—
433	C₄×C₁₃	—	8	1	no	—
434	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
435	C₄×C₁₃	#534	1	1	yes	characteristic
436	C₄×C₁₃	#551	1	1	yes	characteristic
437	C₄×C₁₃	#551	1	1	yes	characteristic
438	C₂⁵	—	2	1	no	—
439	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
440	C₂²×D₄	—	2	2	no	—
441	C₂²×D₄	—	2	2	no	—
442	C₂²×D₄	—	2	1	no	—
443	C₂²×D₄	—	2	2	no	—
444	C₂²×D₄	—	4	1	no	—
445	C₂²×D₄	—	4	1	no	—
446	C₂²×D₄	D₄×C₁₃	1	4	yes	—
447	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
448	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
449	C₂³×C₄	—	2	1	no	—
450	C₂³×C₄	—	2	1	no	—
451	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×SD₁₆	—	2	2	no	—
453	C₂×SD₁₆	—	2	2	no	—
454	C₂×SD₁₆	—	2	2	no	—
455	C₂×SD₁₆	—	2	2	no	—
456	C₂×SD₁₆	—	4	1	no	—
457	C₂×SD₁₆	—	4	1	no	—
458	C₂×M₁₆	—	2	2	no	—
459	C₂×M₁₆	—	4	1	no	—
460	C₂×M₁₆	—	4	1	no	—
461	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
463	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
464	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
465	C₂²⋊Q₈	—	2	2	no	—
466	C₂²⋊Q₈	—	2	2	no	—
467	C₄×D₄	—	2	2	no	—
468	C₄×D₄	—	2	2	no	—
469	C₄×D₄	—	4	1	no	—
470	C₄×D₄	—	4	1	no	—
471	#117	—	2	2	no	—
472	#117	—	2	2	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	—	2	1	no	—
484	C₂×C₂²⋊C₄	—	2	1	no	—
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	4	4	no	—
491	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
493	C₂×C₄²	—	2	1	no	—
494	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
496	C₄⋊C₈	—	4	1	no	—
497	C₄⋊C₈	—	4	1	no	—
498	#103	—	4	1	no	—
499	#103	—	4	1	no	—
500	#102	—	2	2	no	—
501	#102	—	2	2	no	—
502	#102	—	2	2	no	—
503	#102	—	2	2	no	—
504	#102	—	2	2	no	—
505	#102	—	2	2	no	—
506	C₂²⋊C₈	—	2	2	no	—
507	#95	—	2	1	no	—
508	#95	—	2	1	no	—
509	#95	—	2	1	no	—
510	#95	—	2	1	no	—
511	#95	—	2	1	no	—
512	#95	—	2	1	no	—
513	#95	—	2	1	no	—
514	#95	D₄×C₁₃	1	1	yes	characteristic
515	#95	D₄×C₁₃	1	1	yes	characteristic
516	C₂×C₁₃	—	4	2	no	—
517	C₂×C₁₃	—	4	4	no	—
518	C₂×C₁₃	—	8	2	no	—
519	C₂×C₁₃	#2412	1	1	yes	characteristic
520	C₂×C₁₃	#3036	1	1	yes	characteristic
521	C₂×C₁₃	#3042	1	1	yes	characteristic
522	C₂×C₁₃	#3310	1	1	yes	characteristic
523	C₂×C₁₃	#3311	1	1	yes	characteristic
524	C₂×C₁₃	#3323	1	1	yes	characteristic
525	C₂×C₁₃	#3324	1	1	yes	characteristic
526	C₂⁴	—	2	1	no	—
527	C₂⁴	—	2	1	no	—
528	C₂⁴	—	2	4	no	—
529	C₂⁴	—	4	2	no	—
530	C₂⁴	—	4	2	no	—
531	C₂⁴	—	4	2	no	—
532	C₂⁴	—	4	2	no	—
533	C₂⁴	—	8	1	no	—
534	C₂⁴	—	8	1	no	—
535	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×D₄	—	2	8	no	—
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	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	—	4	4	no	—
553	C₂×D₄	—	4	4	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	2	no	—
556	C₂×D₄	—	4	2	no	—
557	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
558	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
559	C₂×D₄	C₁₃×#41	1	2	yes	—
560	C₂×D₄	C₁₃×#41	1	2	yes	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	4	2	no	—
575	C₂²×C₄	—	8	1	no	—
576	C₂²×C₄	—	8	1	no	—
577	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
582	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
583	C₂²×C₄	C₁₃×#41	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
585	SD₁₆	—	4	4	no	—
586	SD₁₆	—	4	4	no	—
587	M₁₆	—	4	4	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	4	2	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	4	1	no	—
615	C₂²⋊C₄	—	4	2	no	—
616	C₂²⋊C₄	—	4	2	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	8	1	no	—
623	C₂²⋊C₄	—	8	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	4	2	no	—
629	C₁₃	#24538	1	1	yes	characteristic, direct product factor, Sylow
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	4	8	no	—
641	C₂³	—	4	8	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	8	4	no	—
653	C₂³	—	8	4	no	—
654	C₂³	—	8	4	no	—
655	C₂³	—	8	4	no	—
656	C₂³	—	8	4	no	—
657	C₂³	C₁₃×#121	1	2	yes	—
658	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
659	Q₈	—	4	1	no	—
660	Q₈	—	4	1	no	—
661	Q₈	—	4	1	no	—
662	Q₈	—	4	1	no	—
663	D₄	—	2	2	no	—
664	D₄	—	2	2	no	—
665	D₄	—	2	2	no	—
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	4	8	no	—
669	D₄	—	4	1	no	—
670	D₄	—	4	1	no	—
671	D₄	C₁₃×#123	1	4	yes	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	8	4	no	—
708	C₂×C₄	—	8	4	no	—
709	C₂×C₄	C₁₃×#121	1	2	yes	—
710	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
711	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
712	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
713	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
714	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
715	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
716	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
717	C₈	—	4	1	no	—
718	C₈	—	4	1	no	—
719	C₈	—	4	1	no	—
720	C₈	—	4	1	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	8	16	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	8	1	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	1	no	—
743	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
744	C₂²	C₁₃×#546	1	1	yes	characteristic
745	C₂²	C₁₃×#546	1	1	yes	characteristic
746	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
747	C₂²	C₁₃×#575	1	1	yes	characteristic
748	C₂²	C₁₃×#577	1	1	yes	characteristic
749	C₂²	C₁₃×#577	1	1	yes	characteristic
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	8	1	no	—
756	C₄	—	8	1	no	—
757	C₄	—	8	1	no	—
758	C₄	—	8	1	no	—
759	C₄	—	8	1	no	—
760	C₄	—	8	1	no	—
761	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
762	C₄	C₁₃×#534	1	1	yes	characteristic
763	C₄	C₁₃×#551	1	1	yes	characteristic
764	C₄	C₁₃×#551	1	1	yes	characteristic
765	C₂	—	4	2	no	—
766	C₂	—	4	4	no	—
767	C₂	—	8	2	no	—
768	C₂	C₁₃×#2412	1	1	yes	characteristic
769	C₂	C₁₃×#3036	1	1	yes	characteristic
770	C₂	C₁₃×#3042	1	1	yes	characteristic
771	C₂	C₁₃×#3310	1	1	yes	characteristic
772	C₂	C₁₃×#3311	1	1	yes	characteristic
773	C₂	C₁₃×#3323	1	1	yes	characteristic
774	C₂	C₁₃×#3324	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2499	C₂	semidirect
5. C₁₃×#2073	C₂	semidirect
6. C₁₃×#2071	C₂	semidirect
7. C₁₃×#2055	C₂	semidirect
8. C₁₃×#2055	C₂	semidirect
9. C₁₃×#1894	C₂	semidirect
10. C₁₃×#1877	C₂	semidirect
11. C₁₃×#1877	C₂	semidirect
12. C₁₃×#1851	C₂	semidirect
13. C₁₃×#1825	C₂	semidirect
14. C₁₃×#1804	C₂	semidirect
15. C₁₃×#1802	C₂	semidirect
26. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
27. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
29. C₂×C₁₃×#103	C₂²	semidirect
30. C₂×C₁₃×#103	C₂²	semidirect
40. C₁₃×#391	C₂²	semidirect
41. C₁₃×#391	C₂²	semidirect
48. C₁₃×#384	C₂²	semidirect
49. C₁₃×#382	C₂²	semidirect
53. C₁₃×#340	C₂²	semidirect
54. C₁₃×#340	C₂²	semidirect
55. C₁₃×#340	C₂²	semidirect
56. C₁₃×#340	C₂²	semidirect
57. C₁₃×#340	C₂²	semidirect
58. C₁₃×#340	C₂²	semidirect
59. C₁₃×#336	C₂²	semidirect
60. C₁₃×#336	C₂²	semidirect
139. #24538	C₁₃	direct (N × H)
245. #2499	C₂×C₁₃	semidirect
247. #2073	C₂×C₁₃	semidirect
248. #2071	C₂×C₁₃	semidirect
249. #2055	C₂×C₁₃	semidirect
250. #2055	C₂×C₁₃	semidirect
251. #1894	C₂×C₁₃	semidirect
252. #1877	C₂×C₁₃	semidirect
253. #1877	C₂×C₁₃	semidirect
254. #1851	C₂×C₁₃	semidirect
255. #1825	C₂×C₁₃	semidirect
256. #1804	C₂×C₁₃	semidirect
257. #1802	C₂×C₁₃	semidirect
359. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
360. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
362. C₂×#103	C₂²×C₁₃	semidirect
363. C₂×#103	C₂²×C₁₃	semidirect
373. #391	C₂²×C₁₃	semidirect
374. #391	C₂²×C₁₃	semidirect
381. #384	C₂²×C₁₃	semidirect
382. #382	C₂²×C₁₃	semidirect
386. #340	C₂²×C₁₃	semidirect
387. #340	C₂²×C₁₃	semidirect
388. #340	C₂²×C₁₃	semidirect
389. #340	C₂²×C₁₃	semidirect
390. #340	C₂²×C₁₃	semidirect
391. #340	C₂²×C₁₃	semidirect
392. #336	C₂²×C₁₃	semidirect
393. #336	C₂²×C₁₃	semidirect
629. C₁₃	#24538	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×#450	2
C₂×C₁₃×#418	2
C₁₃×#2499	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2073	2
C₁₃×#2071	2
C₁₃×#2055	2
C₁₃×#1894	2
C₁₃×#1877	2
C₁₃×#1851	2
C₁₃×#1825	2
C₁₃×#1804	2
C₁₃×#1802	2
#24538	13

Subgroups — C13×#24538 #15710877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24538 #15710877