Subgroups — C₁₃×#36709 #15723048

Order 3328.

2630 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2847	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2695	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2693	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2672	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2671	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2627	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2618	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2534	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2487	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2412	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2410	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#538	—	2	8	no	—
19	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
20	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#123	—	2	8	no	—
22	C₂×C₁₃×#123	C₂²	1	4	yes	—
23	C₂×C₁₃×#123	C₂²	1	4	yes	—
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#121	C₂²	1	4	yes	—
30	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
32	C₂×C₁₃×#120	C₂²	1	2	yes	—
33	C₂×C₁₃×#120	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₃×#400	C₂²	1	2	yes	complemented
42	C₁₃×#400	C₂²	1	4	yes	complemented
43	C₁₃×#399	C₂²	1	4	yes	complemented
44	C₁₃×#398	C₂²	1	2	yes	complemented
45	C₁₃×#398	C₂²	1	4	yes	complemented
46	C₁₃×#397	C₂²	1	4	yes	complemented
47	C₁₃×#396	C₂²	1	4	yes	complemented
48	C₁₃×#396	C₂²	1	4	yes	complemented
49	C₁₃×#395	C₂²	1	2	yes	complemented
50	C₁₃×#394	C₂²	1	4	yes	—
51	C₁₃×#394	C₂²	1	4	yes	complemented
52	C₁₃×#394	C₂²	1	2	yes	complemented
53	C₁₃×#394	C₂²	1	4	yes	complemented
54	C₁₃×#392	C₂²	1	4	yes	—
55	C₁₃×#389	C₂²	1	4	yes	complemented
56	C₁₃×#388	C₂²	1	4	yes	complemented
57	C₁₃×#386	C₂²	1	2	yes	—
58	C₁₃×#386	C₂²	1	2	yes	—
59	C₁₃×#386	C₂²	1	4	yes	—
60	C₁₃×#386	C₂²	1	4	yes	complemented
61	C₁₃×#386	C₂²	1	4	yes	complemented
62	C₁₃×#386	C₂²	1	4	yes	complemented
63	C₁₃×#385	C₂²	1	2	yes	—
64	C₁₃×#385	C₂²	1	2	yes	—
65	C₁₃×#385	C₂²	1	4	yes	complemented
66	C₁₃×#385	C₂²	1	4	yes	complemented
67	C₁₃×#385	C₂²	1	4	yes	complemented
68	C₁₃×#381	C₂²	1	2	yes	—
69	C₁₃×#380	C₂²	1	2	yes	—
70	C₁₃×#380	C₂²	1	1	yes	characteristic
71	C₁₃×#380	C₂²	1	1	yes	characteristic
72	C₁₃×#380	C₂²	1	2	yes	complemented
73	C₁₃×#380	C₂²	1	2	yes	complemented
74	C₁₃×#380	C₂²	1	4	yes	complemented
75	C₁₃×#380	C₂²	1	4	yes	complemented
76	C₁₃×#379	C₂²	1	2	yes	—
77	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
78	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃	—	2	4	no	—
81	C₂²×D₄×C₁₃	—	4	4	no	—
82	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	—	2	4	no	—
89	C₂³×C₄×C₁₃	—	4	4	no	—
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
97	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#126	—	2	8	no	—
100	C₁₃×#124	—	2	8	no	—
101	C₁₃×#123	—	2	16	no	—
102	C₁₃×#123	—	2	16	no	—
103	C₁₃×#123	—	2	8	no	—
104	C₁₃×#123	—	4	4	no	—
105	C₁₃×C₂²⋊Q₈	—	2	4	no	—
106	C₁₃×C₂²⋊Q₈	—	4	4	no	—
107	C₁₃×#121	—	2	4	no	—
108	C₁₃×#121	—	2	8	no	—
109	C₁₃×#121	—	4	8	no	—
110	C₁₃×#121	—	4	4	no	—
111	C₁₃×#120	—	2	8	no	—
112	C₁₃×#120	—	4	4	no	—
113	C₄×D₄×C₁₃	—	2	8	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
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	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
130	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
131	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
132	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
152	C₁₃×#95	C₂³	1	2	yes	—
153	C₁₃×#95	C₂³	1	2	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
156	C₁₃×#95	C₂³	1	4	yes	—
157	C₁₃×#95	C₂³	1	4	yes	—
158	C₁₃×#95	C₂³	1	4	yes	—
159	C₁₃×#95	C₂³	1	4	yes	—
160	C₁₃×#95	C₂³	1	4	yes	—
161	#36709	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂⁴×C₁₃	—	2	2	no	—
163	C₂⁴×C₁₃	—	2	4	no	—
164	C₂⁴×C₁₃	—	2	2	no	—
165	C₂⁴×C₁₃	—	2	2	no	—
166	C₂⁴×C₁₃	—	2	2	no	—
167	C₂⁴×C₁₃	—	2	2	no	—
168	C₂⁴×C₁₃	—	4	2	no	—
169	C₂⁴×C₁₃	—	4	2	no	—
170	C₂⁴×C₁₃	—	4	2	no	—
171	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
172	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
173	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
174	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
175	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×Q₈×C₁₃	—	2	2	no	—
177	C₂×Q₈×C₁₃	—	4	2	no	—
178	C₂×D₄×C₁₃	—	2	4	no	—
179	C₂×D₄×C₁₃	—	2	8	no	—
180	C₂×D₄×C₁₃	—	2	4	no	—
181	C₂×D₄×C₁₃	—	2	8	no	—
182	C₂×D₄×C₁₃	—	2	4	no	—
183	C₂×D₄×C₁₃	—	2	4	no	—
184	C₂×D₄×C₁₃	—	2	4	no	—
185	C₂×D₄×C₁₃	—	2	8	no	—
186	C₂×D₄×C₁₃	—	2	2	no	—
187	C₂×D₄×C₁₃	—	4	4	no	—
188	C₂×D₄×C₁₃	—	4	4	no	—
189	C₂×D₄×C₁₃	—	4	2	no	—
190	C₂×D₄×C₁₃	—	4	4	no	—
191	C₂×D₄×C₁₃	—	4	4	no	—
192	C₂×D₄×C₁₃	—	4	4	no	—
193	C₂×D₄×C₁₃	—	4	16	no	—
194	C₂²×C₄×C₁₃	—	2	2	no	—
195	C₂²×C₄×C₁₃	—	2	2	no	—
196	C₂²×C₄×C₁₃	—	2	2	no	—
197	C₂²×C₄×C₁₃	—	2	4	no	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	—	2	2	no	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	4	no	—
202	C₂²×C₄×C₁₃	—	2	4	no	—
203	C₂²×C₄×C₁₃	—	2	4	no	—
204	C₂²×C₄×C₁₃	—	4	2	no	—
205	C₂²×C₄×C₁₃	—	4	2	no	—
206	C₂²×C₄×C₁₃	—	4	2	no	—
207	C₂²×C₄×C₁₃	—	4	2	no	—
208	C₂²×C₄×C₁₃	—	4	2	no	—
209	C₂²×C₄×C₁₃	—	4	2	no	—
210	C₂²×C₄×C₁₃	—	4	4	no	—
211	C₂²×C₄×C₁₃	—	4	4	no	—
212	C₂²×C₄×C₁₃	—	4	4	no	—
213	C₂²×C₄×C₁₃	—	4	4	no	—
214	C₂²×C₄×C₁₃	—	4	16	no	—
215	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
216	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₁₃×C₄⋊C₄	—	2	4	no	—
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	2	8	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	4	no	—
233	C₁₃×C₄⋊C₄	—	2	2	no	—
234	C₁₃×C₄⋊C₄	—	2	2	no	—
235	C₁₃×C₄⋊C₄	—	4	4	no	—
236	C₁₃×C₄⋊C₄	—	4	2	no	—
237	C₁₃×C₄⋊C₄	—	4	4	no	—
238	C₁₃×C₄⋊C₄	—	4	2	no	—
239	C₁₃×C₄⋊C₄	—	4	4	no	—
240	C₁₃×C₄⋊C₄	—	4	4	no	—
241	C₁₃×C₂²⋊C₄	—	2	8	no	—
242	C₁₃×C₂²⋊C₄	—	2	4	no	—
243	C₁₃×C₂²⋊C₄	—	2	4	no	—
244	C₁₃×C₂²⋊C₄	—	2	4	no	—
245	C₁₃×C₂²⋊C₄	—	2	4	no	—
246	C₁₃×C₂²⋊C₄	—	2	4	no	—
247	C₁₃×C₂²⋊C₄	—	2	8	no	—
248	C₁₃×C₂²⋊C₄	—	2	8	no	—
249	C₁₃×C₂²⋊C₄	—	2	4	no	—
250	C₁₃×C₂²⋊C₄	—	2	4	no	—
251	C₁₃×C₂²⋊C₄	—	4	4	no	—
252	C₁₃×C₂²⋊C₄	—	4	4	no	—
253	C₁₃×C₂²⋊C₄	—	4	4	no	—
254	C₁₃×C₂²⋊C₄	—	4	4	no	—
255	C₁₃×C₂²⋊C₄	—	4	4	no	—
256	C₁₃×C₂²⋊C₄	—	4	4	no	—
257	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
258	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
259	C₄²×C₁₃	—	2	4	no	—
260	C₂×#538	C₂×C₁₃	1	1	yes	characteristic, complemented
261	C₂²×#123	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#2848	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2847	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#2695	C₂×C₁₃	1	4	yes	complemented
265	#2693	C₂×C₁₃	1	4	yes	complemented
266	#2672	C₂×C₁₃	1	4	yes	complemented
267	#2671	C₂×C₁₃	1	4	yes	complemented
268	#2627	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#2618	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#2534	C₂×C₁₃	1	2	yes	complemented
271	#2487	C₂×C₁₃	1	2	yes	complemented
272	#2412	C₂×C₁₃	1	2	yes	complemented
273	#2410	C₂×C₁₃	1	2	yes	complemented
274	#2315	C₂×C₁₃	1	1	yes	characteristic, complemented
275	C₂³×C₁₃	—	2	2	no	—
276	C₂³×C₁₃	—	2	2	no	—
277	C₂³×C₁₃	—	2	8	no	—
278	C₂³×C₁₃	—	2	2	no	—
279	C₂³×C₁₃	—	2	2	no	—
280	C₂³×C₁₃	—	2	2	no	—
281	C₂³×C₁₃	—	2	2	no	—
282	C₂³×C₁₃	—	2	4	no	—
283	C₂³×C₁₃	—	2	2	no	—
284	C₂³×C₁₃	—	2	2	no	—
285	C₂³×C₁₃	—	2	2	no	—
286	C₂³×C₁₃	—	2	4	no	—
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	2	8	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	2	no	—
291	C₂³×C₁₃	—	2	4	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	4	no	—
294	C₂³×C₁₃	—	4	4	no	—
295	C₂³×C₁₃	—	4	4	no	—
296	C₂³×C₁₃	—	4	8	no	—
297	C₂³×C₁₃	—	4	8	no	—
298	C₂³×C₁₃	—	4	4	no	—
299	C₂³×C₁₃	—	4	4	no	—
300	C₂³×C₁₃	—	8	4	no	—
301	C₂³×C₁₃	—	8	4	no	—
302	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
303	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
304	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
305	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
306	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
307	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
308	Q₈×C₁₃	—	8	2	no	—
309	D₄×C₁₃	—	4	16	no	—
310	D₄×C₁₃	—	4	8	no	—
311	D₄×C₁₃	—	8	2	no	—
312	D₄×C₁₃	—	8	4	no	—
313	D₄×C₁₃	—	8	4	no	—
314	D₄×C₁₃	—	8	8	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	4	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	4	no	—
325	C₂×C₄×C₁₃	—	2	4	no	—
326	C₂×C₄×C₁₃	—	2	4	no	—
327	C₂×C₄×C₁₃	—	2	4	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	4	no	—
332	C₂×C₄×C₁₃	—	2	4	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	4	no	—
337	C₂×C₄×C₁₃	—	2	4	no	—
338	C₂×C₄×C₁₃	—	2	4	no	—
339	C₂×C₄×C₁₃	—	4	4	no	—
340	C₂×C₄×C₁₃	—	4	4	no	—
341	C₂×C₄×C₁₃	—	4	8	no	—
342	C₂×C₄×C₁₃	—	4	8	no	—
343	C₂×C₄×C₁₃	—	4	4	no	—
344	C₂×C₄×C₁₃	—	4	4	no	—
345	C₂×C₄×C₁₃	—	4	4	no	—
346	C₂×C₄×C₁₃	—	8	4	no	—
347	C₂×C₄×C₁₃	—	8	8	no	—
348	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
349	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
351	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
352	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
353	#538	—	2	8	no	—
354	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
355	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
356	C₂×#123	—	2	8	no	—
357	C₂×#123	C₂²×C₁₃	1	4	yes	—
358	C₂×#123	C₂²×C₁₃	1	4	yes	—
359	C₂×#123	C₂²×C₁₃	1	2	yes	—
360	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
361	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
363	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×#121	C₂²×C₁₃	1	4	yes	—
365	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
366	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
367	C₂×#120	C₂²×C₁₃	1	2	yes	—
368	C₂×#120	C₂²×C₁₃	1	2	yes	—
369	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
370	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
371	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
372	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
373	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
374	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
375	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
376	#400	C₂²×C₁₃	1	2	yes	complemented
377	#400	C₂²×C₁₃	1	4	yes	complemented
378	#399	C₂²×C₁₃	1	4	yes	complemented
379	#398	C₂²×C₁₃	1	2	yes	complemented
380	#398	C₂²×C₁₃	1	4	yes	complemented
381	#397	C₂²×C₁₃	1	4	yes	complemented
382	#396	C₂²×C₁₃	1	4	yes	complemented
383	#396	C₂²×C₁₃	1	4	yes	complemented
384	#395	C₂²×C₁₃	1	2	yes	complemented
385	#394	C₂²×C₁₃	1	4	yes	—
386	#394	C₂²×C₁₃	1	2	yes	complemented
387	#394	C₂²×C₁₃	1	4	yes	complemented
388	#394	C₂²×C₁₃	1	4	yes	complemented
389	#392	C₂²×C₁₃	1	4	yes	—
390	#389	C₂²×C₁₃	1	4	yes	complemented
391	#388	C₂²×C₁₃	1	4	yes	complemented
392	#386	C₂²×C₁₃	1	2	yes	—
393	#386	C₂²×C₁₃	1	2	yes	—
394	#386	C₂²×C₁₃	1	4	yes	—
395	#386	C₂²×C₁₃	1	4	yes	complemented
396	#386	C₂²×C₁₃	1	4	yes	complemented
397	#386	C₂²×C₁₃	1	4	yes	complemented
398	#385	C₂²×C₁₃	1	2	yes	—
399	#385	C₂²×C₁₃	1	2	yes	—
400	#385	C₂²×C₁₃	1	4	yes	complemented
401	#385	C₂²×C₁₃	1	4	yes	complemented
402	#385	C₂²×C₁₃	1	4	yes	complemented
403	#381	C₂²×C₁₃	1	2	yes	—
404	#380	C₂²×C₁₃	1	1	yes	characteristic
405	#380	C₂²×C₁₃	1	1	yes	characteristic
406	#380	C₂²×C₁₃	1	2	yes	—
407	#380	C₂²×C₁₃	1	2	yes	complemented
408	#380	C₂²×C₁₃	1	2	yes	complemented
409	#380	C₂²×C₁₃	1	4	yes	complemented
410	#380	C₂²×C₁₃	1	4	yes	complemented
411	#379	C₂²×C₁₃	1	2	yes	—
412	C₂²×C₁₃	—	2	2	no	—
413	C₂²×C₁₃	—	2	2	no	—
414	C₂²×C₁₃	—	2	4	no	—
415	C₂²×C₁₃	—	2	4	no	—
416	C₂²×C₁₃	—	2	4	no	—
417	C₂²×C₁₃	—	2	4	no	—
418	C₂²×C₁₃	—	2	4	no	—
419	C₂²×C₁₃	—	2	4	no	—
420	C₂²×C₁₃	—	2	4	no	—
421	C₂²×C₁₃	—	2	4	no	—
422	C₂²×C₁₃	—	4	16	no	—
423	C₂²×C₁₃	—	4	2	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	—	4	4	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	4	4	no	—
429	C₂²×C₁₃	—	4	2	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	—	4	4	no	—
433	C₂²×C₁₃	—	4	4	no	—
434	C₂²×C₁₃	—	8	8	no	—
435	C₂²×C₁₃	#537	1	4	yes	—
436	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
437	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
439	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
440	C₂²×C₁₃	#585	1	2	yes	—
441	C₄×C₁₃	—	2	2	no	—
442	C₄×C₁₃	—	2	2	no	—
443	C₄×C₁₃	—	2	4	no	—
444	C₄×C₁₃	—	4	2	no	—
445	C₄×C₁₃	—	4	2	no	—
446	C₄×C₁₃	—	4	2	no	—
447	C₄×C₁₃	—	4	2	no	—
448	C₄×C₁₃	—	4	2	no	—
449	C₄×C₁₃	—	4	2	no	—
450	C₄×C₁₃	—	4	4	no	—
451	C₄×C₁₃	—	4	4	no	—
452	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
453	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
454	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
455	C₂²×D₄	—	2	4	no	—
456	C₂²×D₄	—	4	4	no	—
457	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
458	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
459	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
460	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
461	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
462	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
463	C₂³×C₄	—	2	4	no	—
464	C₂³×C₄	—	4	4	no	—
465	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
467	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
468	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
471	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
472	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
474	#126	—	2	8	no	—
475	#124	—	2	8	no	—
476	#123	—	2	16	no	—
477	#123	—	2	16	no	—
478	#123	—	2	8	no	—
479	#123	—	4	4	no	—
480	C₂²⋊Q₈	—	2	4	no	—
481	C₂²⋊Q₈	—	4	4	no	—
482	#121	—	2	4	no	—
483	#121	—	2	8	no	—
484	#121	—	4	8	no	—
485	#121	—	4	4	no	—
486	#120	—	2	8	no	—
487	#120	—	4	4	no	—
488	C₄×D₄	—	2	8	no	—
489	C₂×C₄⋊C₄	—	2	4	no	—
490	C₂×C₄⋊C₄	—	2	4	no	—
491	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
504	C₂×C₂²⋊C₄	—	2	4	no	—
505	C₂×C₂²⋊C₄	—	2	4	no	—
506	C₂×C₂²⋊C₄	—	4	4	no	—
507	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
508	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
526	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
527	#95	C₂³×C₁₃	1	2	yes	—
528	#95	C₂³×C₁₃	1	2	yes	—
529	#95	C₂³×C₁₃	1	4	yes	—
530	#95	C₂³×C₁₃	1	4	yes	—
531	#95	C₂³×C₁₃	1	4	yes	—
532	#95	C₂³×C₁₃	1	4	yes	—
533	#95	C₂³×C₁₃	1	4	yes	—
534	#95	C₂³×C₁₃	1	4	yes	—
535	#95	C₂³×C₁₃	1	4	yes	—
536	C₂×C₁₃	—	2	4	no	—
537	C₂×C₁₃	—	4	4	no	—
538	C₂×C₁₃	—	4	4	no	—
539	C₂×C₁₃	—	8	2	no	—
540	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
541	C₂×C₁₃	#3484	1	1	yes	characteristic
542	C₂×C₁₃	#3485	1	1	yes	characteristic
543	C₂×C₁₃	#3534	1	2	yes	—
544	C₂×C₁₃	#3535	1	2	yes	—
545	C₂⁴	—	2	2	no	—
546	C₂⁴	—	2	4	no	—
547	C₂⁴	—	2	2	no	—
548	C₂⁴	—	2	2	no	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	4	2	no	—
552	C₂⁴	—	4	2	no	—
553	C₂⁴	—	4	2	no	—
554	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
555	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
556	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
557	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
558	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	4	2	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	8	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	8	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	8	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	4	4	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	4	2	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	—	4	16	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	4	no	—
594	C₂²×C₄	—	4	4	no	—
595	C₂²×C₄	—	4	4	no	—
596	C₂²×C₄	—	4	4	no	—
597	C₂²×C₄	—	4	16	no	—
598	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
599	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
602	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
605	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	8	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	4	4	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	4	no	—
622	C₄⋊C₄	—	4	4	no	—
623	C₄⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	2	8	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	8	no	—
631	C₂²⋊C₄	—	2	8	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	4	4	no	—
635	C₂²⋊C₄	—	4	4	no	—
636	C₂²⋊C₄	—	4	4	no	—
637	C₂²⋊C₄	—	4	4	no	—
638	C₂²⋊C₄	—	4	4	no	—
639	C₂²⋊C₄	—	4	4	no	—
640	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
641	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
642	C₄²	—	2	4	no	—
643	C₁₃	#36709	1	1	yes	characteristic, direct product factor, Sylow
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	8	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	8	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	4	no	—
663	C₂³	—	4	4	no	—
664	C₂³	—	4	4	no	—
665	C₂³	—	4	8	no	—
666	C₂³	—	4	8	no	—
667	C₂³	—	4	4	no	—
668	C₂³	—	4	4	no	—
669	C₂³	—	8	4	no	—
670	C₂³	—	8	4	no	—
671	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
672	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
673	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
674	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
675	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
676	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
677	Q₈	—	8	2	no	—
678	D₄	—	4	16	no	—
679	D₄	—	4	8	no	—
680	D₄	—	8	2	no	—
681	D₄	—	8	8	no	—
682	D₄	—	8	4	no	—
683	D₄	—	8	4	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	8	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	8	4	no	—
716	C₂×C₄	—	8	8	no	—
717	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
718	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
720	C₂²	—	2	4	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	4	16	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	8	8	no	—
743	C₂²	C₁₃×#537	1	4	yes	—
744	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
745	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
746	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
747	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
748	C₂²	C₁₃×#585	1	2	yes	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	4	no	—
752	C₄	—	4	4	no	—
753	C₄	—	4	4	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₂	—	2	4	no	—
761	C₂	—	4	4	no	—
762	C₂	—	4	4	no	—
763	C₂	—	8	2	no	—
764	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
765	C₂	C₁₃×#3484	1	1	yes	characteristic
766	C₂	C₁₃×#3485	1	1	yes	characteristic
767	C₂	C₁₃×#3534	1	2	yes	—
768	C₂	C₁₃×#3535	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
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
1. C₂×C₁₃×#538	C₂	semidirect
2. C₂²×C₁₃×#123	C₂	semidirect
3. C₁₃×#2848	C₂	semidirect
4. C₁₃×#2847	C₂	semidirect
5. C₁₃×#2695	C₂	semidirect
6. C₁₃×#2693	C₂	semidirect
7. C₁₃×#2672	C₂	semidirect
8. C₁₃×#2671	C₂	semidirect
9. C₁₃×#2627	C₂	semidirect
10. C₁₃×#2618	C₂	semidirect
11. C₁₃×#2534	C₂	semidirect
12. C₁₃×#2487	C₂	semidirect
13. C₁₃×#2412	C₂	semidirect
14. C₁₃×#2410	C₂	semidirect
15. C₁₃×#2315	C₂	semidirect
19. C₂×C₁₃×#126	C₂²	semidirect
20. C₂×C₁₃×#124	C₂²	semidirect
25. C₂×C₁₃×#123	C₂²	semidirect
27. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₁₃×#121	C₂²	semidirect
31. C₂×C₁₃×#121	C₂²	semidirect
41. C₁₃×#400	C₂²	semidirect
42. C₁₃×#400	C₂²	semidirect
43. C₁₃×#399	C₂²	semidirect
44. C₁₃×#398	C₂²	semidirect
45. C₁₃×#398	C₂²	semidirect
46. C₁₃×#397	C₂²	semidirect
47. C₁₃×#396	C₂²	semidirect
48. C₁₃×#396	C₂²	semidirect
49. C₁₃×#395	C₂²	semidirect
51. C₁₃×#394	C₂²	semidirect
52. C₁₃×#394	C₂²	semidirect
53. C₁₃×#394	C₂²	semidirect
55. C₁₃×#389	C₂²	semidirect
56. C₁₃×#388	C₂²	semidirect
60. C₁₃×#386	C₂²	semidirect
61. C₁₃×#386	C₂²	semidirect
62. C₁₃×#386	C₂²	semidirect
65. C₁₃×#385	C₂²	semidirect
66. C₁₃×#385	C₂²	semidirect
67. C₁₃×#385	C₂²	semidirect
72. C₁₃×#380	C₂²	semidirect
73. C₁₃×#380	C₂²	semidirect
74. C₁₃×#380	C₂²	semidirect
75. C₁₃×#380	C₂²	semidirect
132. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
161. #36709	C₁₃	direct (N × H)
260. C₂×#538	C₂×C₁₃	semidirect
261. C₂²×#123	C₂×C₁₃	semidirect
262. #2848	C₂×C₁₃	semidirect
263. #2847	C₂×C₁₃	semidirect
264. #2695	C₂×C₁₃	semidirect
265. #2693	C₂×C₁₃	semidirect
266. #2672	C₂×C₁₃	semidirect
267. #2671	C₂×C₁₃	semidirect
268. #2627	C₂×C₁₃	semidirect
269. #2618	C₂×C₁₃	semidirect
270. #2534	C₂×C₁₃	semidirect
271. #2487	C₂×C₁₃	semidirect
272. #2412	C₂×C₁₃	semidirect
273. #2410	C₂×C₁₃	semidirect
274. #2315	C₂×C₁₃	semidirect
354. C₂×#126	C₂²×C₁₃	semidirect
355. C₂×#124	C₂²×C₁₃	semidirect
360. C₂×#123	C₂²×C₁₃	semidirect
362. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
365. C₂×#121	C₂²×C₁₃	semidirect
366. C₂×#121	C₂²×C₁₃	semidirect
376. #400	C₂²×C₁₃	semidirect
377. #400	C₂²×C₁₃	semidirect
378. #399	C₂²×C₁₃	semidirect
379. #398	C₂²×C₁₃	semidirect
380. #398	C₂²×C₁₃	semidirect
381. #397	C₂²×C₁₃	semidirect
382. #396	C₂²×C₁₃	semidirect
383. #396	C₂²×C₁₃	semidirect
384. #395	C₂²×C₁₃	semidirect
386. #394	C₂²×C₁₃	semidirect
387. #394	C₂²×C₁₃	semidirect
388. #394	C₂²×C₁₃	semidirect
390. #389	C₂²×C₁₃	semidirect
391. #388	C₂²×C₁₃	semidirect
395. #386	C₂²×C₁₃	semidirect
396. #386	C₂²×C₁₃	semidirect
397. #386	C₂²×C₁₃	semidirect
400. #385	C₂²×C₁₃	semidirect
401. #385	C₂²×C₁₃	semidirect
402. #385	C₂²×C₁₃	semidirect
407. #380	C₂²×C₁₃	semidirect
408. #380	C₂²×C₁₃	semidirect
409. #380	C₂²×C₁₃	semidirect
410. #380	C₂²×C₁₃	semidirect
507. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
643. C₁₃	#36709	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×#538	2
C₂²×C₁₃×#123	2
C₁₃×#2848	2
C₁₃×#2847	2
C₁₃×#2695	2
C₁₃×#2693	2
C₁₃×#2672	2
C₁₃×#2671	2
C₁₃×#2627	2
C₁₃×#2618	2
C₁₃×#2534	2
C₁₃×#2487	2
C₁₃×#2412	2
C₁₃×#2410	2
C₁₃×#2315	2
#36709	13

Subgroups — C13×#36709 #15723048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36709 #15723048