Subgroups — C₁₃×#36738 #15723077

Order 3328.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1002 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	2	yes	maximal, complemented
2	C₁₃×#2847	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2722	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2715	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2712	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2695	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2693	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2691	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2676	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2675	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2672	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2671	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2617	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2617	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2564	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2543	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2417	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2416	C₂	1	2	yes	maximal, complemented
19	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#538	—	2	16	no	—
22	C₂×C₁₃×#126	C₂²	1	2	yes	—
23	C₂×C₁₃×#126	C₂²	1	2	yes	—
24	C₂×C₁₃×#124	C₂²	1	2	yes	—
25	C₂×C₁₃×#124	C₂²	1	2	yes	—
26	C₂×C₁₃×#123	C₂²	1	2	yes	—
27	C₂×C₁₃×#123	C₂²	1	2	yes	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#121	C₂²	1	2	yes	—
31	C₂×C₁₃×#121	C₂²	1	2	yes	—
32	C₂×C₁₃×#121	C₂²	1	2	yes	—
33	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#121	C₂²	1	2	yes	—
35	C₂×C₁₃×#121	C₂²	1	2	yes	—
36	C₂×C₁₃×#121	C₂²	1	2	yes	—
37	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#120	C₂²	1	2	yes	—
40	C₂×C₁₃×#120	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
43	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
44	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₁₃×#400	C₂²	1	2	yes	complemented
47	C₁₃×#399	C₂²	1	2	yes	complemented
48	C₁₃×#398	C₂²	1	2	yes	complemented
49	C₁₃×#398	C₂²	1	2	yes	complemented
50	C₁₃×#398	C₂²	1	2	yes	complemented
51	C₁₃×#397	C₂²	1	1	yes	characteristic
52	C₁₃×#397	C₂²	1	1	yes	characteristic
53	C₁₃×#397	C₂²	1	1	yes	characteristic
54	C₁₃×#397	C₂²	1	1	yes	characteristic
55	C₁₃×#397	C₂²	1	2	yes	complemented
56	C₁₃×#396	C₂²	1	2	yes	complemented
57	C₁₃×#396	C₂²	1	2	yes	complemented
58	C₁₃×#396	C₂²	1	2	yes	complemented
59	C₁₃×#396	C₂²	1	2	yes	complemented
60	C₁₃×#395	C₂²	1	2	yes	complemented
61	C₁₃×#394	C₂²	1	2	yes	—
62	C₁₃×#394	C₂²	1	2	yes	—
63	C₁₃×#394	C₂²	1	2	yes	—
64	C₁₃×#394	C₂²	1	2	yes	—
65	C₁₃×#394	C₂²	1	2	yes	complemented
66	C₁₃×#394	C₂²	1	2	yes	complemented
67	C₁₃×#394	C₂²	1	2	yes	complemented
68	C₁₃×#393	C₂²	1	2	yes	complemented
69	C₁₃×#392	C₂²	1	1	yes	characteristic
70	C₁₃×#392	C₂²	1	1	yes	characteristic
71	C₁₃×#392	C₂²	1	1	yes	characteristic
72	C₁₃×#392	C₂²	1	1	yes	characteristic
73	C₁₃×#392	C₂²	1	2	yes	complemented
74	C₁₃×#391	C₂²	1	2	yes	complemented
75	C₁₃×#390	C₂²	1	2	yes	complemented
76	C₁₃×#389	C₂²	1	2	yes	complemented
77	C₁₃×#389	C₂²	1	2	yes	complemented
78	C₁₃×#388	C₂²	1	2	yes	complemented
79	C₁₃×#388	C₂²	1	2	yes	complemented
80	C₁₃×#387	C₂²	1	2	yes	complemented
81	C₁₃×#387	C₂²	1	2	yes	complemented
82	C₁₃×#386	C₂²	1	2	yes	—
83	C₁₃×#386	C₂²	1	2	yes	—
84	C₁₃×#386	C₂²	1	2	yes	—
85	C₁₃×#386	C₂²	1	2	yes	—
86	C₁₃×#386	C₂²	1	2	yes	—
87	C₁₃×#386	C₂²	1	2	yes	—
88	C₁₃×#386	C₂²	1	2	yes	—
89	C₁₃×#386	C₂²	1	2	yes	—
90	C₁₃×#386	C₂²	1	2	yes	complemented
91	C₁₃×#386	C₂²	1	2	yes	complemented
92	C₁₃×#385	C₂²	1	2	yes	—
93	C₁₃×#385	C₂²	1	1	yes	characteristic
94	C₁₃×#385	C₂²	1	1	yes	characteristic
95	C₁₃×#385	C₂²	1	2	yes	—
96	C₁₃×#385	C₂²	1	1	yes	characteristic
97	C₁₃×#385	C₂²	1	1	yes	characteristic
98	C₁₃×#385	C₂²	1	2	yes	complemented
99	C₁₃×#385	C₂²	1	2	yes	complemented
100	C₁₃×#380	C₂²	1	1	yes	characteristic
101	C₁₃×#380	C₂²	1	2	yes	—
102	C₁₃×#380	C₂²	1	2	yes	—
103	C₁₃×#380	C₂²	1	2	yes	—
104	C₁₃×#380	C₂²	1	1	yes	characteristic
105	C₁₃×#380	C₂²	1	2	yes	complemented
106	C₁₃×#380	C₂²	1	2	yes	complemented
107	C₂×C₁₃×#95	C₂²	1	2	yes	—
108	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	—	4	4	no	—
121	C₂³×C₄×C₁₃	—	4	2	no	—
122	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
131	C₁₃×#126	—	2	8	no	—
132	C₁₃×#126	—	2	8	no	—
133	C₁₃×#124	—	2	8	no	—
134	C₁₃×#124	—	2	8	no	—
135	C₁₃×#123	—	2	8	no	—
136	C₁₃×#123	—	2	8	no	—
137	C₁₃×C₂²⋊Q₈	—	2	8	no	—
138	C₁₃×C₂²⋊Q₈	—	4	4	no	—
139	C₁₃×#121	—	2	8	no	—
140	C₁₃×#121	—	2	8	no	—
141	C₁₃×#121	—	2	8	no	—
142	C₁₃×#121	—	4	4	no	—
143	C₁₃×#121	—	4	4	no	—
144	C₁₃×#121	—	4	4	no	—
145	C₁₃×#121	—	4	4	no	—
146	C₁₃×#121	—	4	2	no	—
147	C₁₃×#121	—	4	2	no	—
148	C₁₃×#120	—	2	8	no	—
149	C₁₃×#120	—	2	8	no	—
150	C₄×D₄×C₁₃	—	2	8	no	—
151	C₄×D₄×C₁₃	—	2	8	no	—
152	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
171	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₁₃×#95	C₂³	1	1	yes	characteristic
204	C₁₃×#95	C₂³	1	2	yes	—
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	1	yes	characteristic
207	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	2	yes	—
209	C₁₃×#95	C₂³	1	2	yes	—
210	C₁₃×#95	C₂³	1	2	yes	—
211	C₁₃×#95	C₂³	1	1	yes	characteristic
212	C₁₃×#95	C₂³	1	1	yes	characteristic
213	C₁₃×#95	C₂³	1	2	yes	—
214	C₁₃×#95	C₂³	1	2	yes	—
215	C₁₃×#95	C₂³	1	2	yes	—
216	C₁₃×#95	C₂³	1	2	yes	—
217	C₁₃×#95	C₂³	1	2	yes	—
218	C₁₃×#95	C₂³	1	2	yes	—
219	C₁₃×#95	C₂³	1	2	yes	—
220	C₁₃×#95	C₂³	1	2	yes	—
221	#36738	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂⁴×C₁₃	—	2	2	no	—
223	C₂⁴×C₁₃	—	2	2	no	—
224	C₂⁴×C₁₃	—	4	2	no	—
225	C₂⁴×C₁₃	—	4	2	no	—
226	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
227	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
228	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
229	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂×Q₈×C₁₃	—	2	4	no	—
233	C₂×Q₈×C₁₃	—	4	2	no	—
234	C₂×Q₈×C₁₃	—	4	2	no	—
235	C₂×D₄×C₁₃	—	2	4	no	—
236	C₂×D₄×C₁₃	—	2	4	no	—
237	C₂×D₄×C₁₃	—	2	4	no	—
238	C₂×D₄×C₁₃	—	2	4	no	—
239	C₂×D₄×C₁₃	—	2	4	no	—
240	C₂×D₄×C₁₃	—	2	4	no	—
241	C₂×D₄×C₁₃	—	2	4	no	—
242	C₂×D₄×C₁₃	—	2	4	no	—
243	C₂×D₄×C₁₃	—	2	4	no	—
244	C₂×D₄×C₁₃	—	2	4	no	—
245	C₂×D₄×C₁₃	—	2	4	no	—
246	C₂×D₄×C₁₃	—	2	4	no	—
247	C₂×D₄×C₁₃	—	4	2	no	—
248	C₂×D₄×C₁₃	—	4	2	no	—
249	C₂×D₄×C₁₃	—	4	2	no	—
250	C₂×D₄×C₁₃	—	4	2	no	—
251	C₂×D₄×C₁₃	—	4	2	no	—
252	C₂×D₄×C₁₃	—	4	2	no	—
253	C₂×D₄×C₁₃	—	4	1	no	—
254	C₂×D₄×C₁₃	—	4	1	no	—
255	C₂×D₄×C₁₃	—	4	2	no	—
256	C₂×D₄×C₁₃	—	4	2	no	—
257	C₂×D₄×C₁₃	—	4	2	no	—
258	C₂×D₄×C₁₃	—	4	2	no	—
259	C₂×D₄×C₁₃	—	4	2	no	—
260	C₂×D₄×C₁₃	—	4	2	no	—
261	C₂×D₄×C₁₃	—	4	2	no	—
262	C₂×D₄×C₁₃	—	4	2	no	—
263	C₂²×C₄×C₁₃	—	2	4	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	4	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	—	2	4	no	—
269	C₂²×C₄×C₁₃	—	2	4	no	—
270	C₂²×C₄×C₁₃	—	2	4	no	—
271	C₂²×C₄×C₁₃	—	4	2	no	—
272	C₂²×C₄×C₁₃	—	4	1	no	—
273	C₂²×C₄×C₁₃	—	4	2	no	—
274	C₂²×C₄×C₁₃	—	4	2	no	—
275	C₂²×C₄×C₁₃	—	4	2	no	—
276	C₂²×C₄×C₁₃	—	4	1	no	—
277	C₂²×C₄×C₁₃	—	4	2	no	—
278	C₂²×C₄×C₁₃	—	4	2	no	—
279	C₂²×C₄×C₁₃	—	4	2	no	—
280	C₂²×C₄×C₁₃	—	4	2	no	—
281	C₂²×C₄×C₁₃	—	4	2	no	—
282	C₂²×C₄×C₁₃	—	4	2	no	—
283	C₂²×C₄×C₁₃	—	4	2	no	—
284	C₂²×C₄×C₁₃	—	4	2	no	—
285	C₂²×C₄×C₁₃	—	4	16	no	—
286	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
301	C₁₃×C₄⋊C₄	—	2	4	no	—
302	C₁₃×C₄⋊C₄	—	2	4	no	—
303	C₁₃×C₄⋊C₄	—	2	4	no	—
304	C₁₃×C₄⋊C₄	—	2	4	no	—
305	C₁₃×C₄⋊C₄	—	2	4	no	—
306	C₁₃×C₄⋊C₄	—	2	4	no	—
307	C₁₃×C₄⋊C₄	—	2	4	no	—
308	C₁₃×C₄⋊C₄	—	2	4	no	—
309	C₁₃×C₄⋊C₄	—	2	4	no	—
310	C₁₃×C₄⋊C₄	—	4	2	no	—
311	C₁₃×C₄⋊C₄	—	4	2	no	—
312	C₁₃×C₄⋊C₄	—	4	2	no	—
313	C₁₃×C₄⋊C₄	—	4	2	no	—
314	C₁₃×C₄⋊C₄	—	4	2	no	—
315	C₁₃×C₄⋊C₄	—	4	1	no	—
316	C₁₃×C₄⋊C₄	—	4	1	no	—
317	C₁₃×C₄⋊C₄	—	4	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	—	2	4	no	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	4	no	—
323	C₁₃×C₂²⋊C₄	—	2	4	no	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	—	2	4	no	—
328	C₁₃×C₂²⋊C₄	—	2	4	no	—
329	C₁₃×C₂²⋊C₄	—	2	4	no	—
330	C₁₃×C₂²⋊C₄	—	4	1	no	—
331	C₁₃×C₂²⋊C₄	—	4	1	no	—
332	C₁₃×C₂²⋊C₄	—	4	1	no	—
333	C₁₃×C₂²⋊C₄	—	4	1	no	—
334	C₁₃×C₂²⋊C₄	—	4	2	no	—
335	C₁₃×C₂²⋊C₄	—	4	2	no	—
336	C₁₃×C₂²⋊C₄	—	4	2	no	—
337	C₁₃×C₂²⋊C₄	—	4	2	no	—
338	C₁₃×C₂²⋊C₄	—	4	2	no	—
339	C₁₃×C₂²⋊C₄	—	4	2	no	—
340	C₁₃×C₂²⋊C₄	—	4	2	no	—
341	C₁₃×C₂²⋊C₄	—	4	2	no	—
342	C₁₃×C₂²⋊C₄	—	4	2	no	—
343	C₁₃×C₂²⋊C₄	—	4	2	no	—
344	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
345	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
346	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
347	C₄²×C₁₃	—	2	4	no	—
348	C₄²×C₁₃	—	2	4	no	—
349	C₂×#538	C₂×C₁₃	1	2	yes	complemented
350	#2847	C₂×C₁₃	1	2	yes	complemented
351	#2722	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#2715	C₂×C₁₃	1	2	yes	complemented
353	#2712	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#2695	C₂×C₁₃	1	2	yes	complemented
355	#2693	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#2691	C₂×C₁₃	1	2	yes	complemented
357	#2676	C₂×C₁₃	1	2	yes	complemented
358	#2675	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#2672	C₂×C₁₃	1	2	yes	complemented
360	#2671	C₂×C₁₃	1	2	yes	complemented
361	#2617	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#2617	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#2564	C₂×C₁₃	1	2	yes	complemented
364	#2543	C₂×C₁₃	1	2	yes	complemented
365	#2417	C₂×C₁₃	1	2	yes	complemented
366	#2416	C₂×C₁₃	1	2	yes	complemented
367	C₂×#385	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₂³×C₁₃	—	2	2	no	—
369	C₂³×C₁₃	—	2	2	no	—
370	C₂³×C₁₃	—	2	8	no	—
371	C₂³×C₁₃	—	2	1	no	—
372	C₂³×C₁₃	—	2	1	no	—
373	C₂³×C₁₃	—	2	2	no	—
374	C₂³×C₁₃	—	2	2	no	—
375	C₂³×C₁₃	—	2	1	no	—
376	C₂³×C₁₃	—	2	1	no	—
377	C₂³×C₁₃	—	2	2	no	—
378	C₂³×C₁₃	—	2	2	no	—
379	C₂³×C₁₃	—	2	2	no	—
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	2	2	no	—
382	C₂³×C₁₃	—	2	2	no	—
383	C₂³×C₁₃	—	2	2	no	—
384	C₂³×C₁₃	—	2	2	no	—
385	C₂³×C₁₃	—	2	2	no	—
386	C₂³×C₁₃	—	2	2	no	—
387	C₂³×C₁₃	—	2	2	no	—
388	C₂³×C₁₃	—	2	2	no	—
389	C₂³×C₁₃	—	2	2	no	—
390	C₂³×C₁₃	—	2	2	no	—
391	C₂³×C₁₃	—	2	2	no	—
392	C₂³×C₁₃	—	2	2	no	—
393	C₂³×C₁₃	—	4	8	no	—
394	C₂³×C₁₃	—	4	4	no	—
395	C₂³×C₁₃	—	4	4	no	—
396	C₂³×C₁₃	—	4	8	no	—
397	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
398	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
399	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
400	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
401	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
402	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
403	Q₈×C₁₃	—	8	4	no	—
404	D₄×C₁₃	—	4	8	no	—
405	D₄×C₁₃	—	4	8	no	—
406	D₄×C₁₃	—	8	4	no	—
407	D₄×C₁₃	—	8	4	no	—
408	D₄×C₁₃	—	8	4	no	—
409	D₄×C₁₃	—	8	4	no	—
410	D₄×C₁₃	—	8	4	no	—
411	D₄×C₁₃	—	8	4	no	—
412	D₄×C₁₃	—	8	2	no	—
413	D₄×C₁₃	—	8	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	1	no	—
429	C₂×C₄×C₁₃	—	2	1	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	1	no	—
434	C₂×C₄×C₁₃	—	2	1	no	—
435	C₂×C₄×C₁₃	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	2	2	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	2	2	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	4	8	no	—
450	C₂×C₄×C₁₃	—	4	4	no	—
451	C₂×C₄×C₁₃	—	4	8	no	—
452	C₂×C₄×C₁₃	—	4	8	no	—
453	C₂×C₄×C₁₃	—	4	4	no	—
454	C₂×C₄×C₁₃	—	8	4	no	—
455	C₂×C₄×C₁₃	—	8	4	no	—
456	C₂×C₄×C₁₃	—	8	2	no	—
457	C₂×C₄×C₁₃	—	8	2	no	—
458	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
459	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
460	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
461	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
462	#538	—	2	16	no	—
463	C₂×#126	C₂²×C₁₃	1	2	yes	—
464	C₂×#126	C₂²×C₁₃	1	2	yes	—
465	C₂×#124	C₂²×C₁₃	1	2	yes	—
466	C₂×#124	C₂²×C₁₃	1	2	yes	—
467	C₂×#123	C₂²×C₁₃	1	2	yes	—
468	C₂×#123	C₂²×C₁₃	1	2	yes	—
469	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
470	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
471	C₂×#121	C₂²×C₁₃	1	2	yes	—
472	C₂×#121	C₂²×C₁₃	1	2	yes	—
473	C₂×#121	C₂²×C₁₃	1	2	yes	—
474	C₂×#121	C₂²×C₁₃	1	2	yes	—
475	C₂×#121	C₂²×C₁₃	1	2	yes	—
476	C₂×#121	C₂²×C₁₃	1	2	yes	—
477	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
478	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
479	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
480	C₂×#120	C₂²×C₁₃	1	2	yes	—
481	C₂×#120	C₂²×C₁₃	1	2	yes	—
482	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
483	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
484	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
485	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
486	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
487	#400	C₂²×C₁₃	1	2	yes	complemented
488	#399	C₂²×C₁₃	1	2	yes	complemented
489	#398	C₂²×C₁₃	1	2	yes	complemented
490	#398	C₂²×C₁₃	1	2	yes	complemented
491	#398	C₂²×C₁₃	1	2	yes	complemented
492	#397	C₂²×C₁₃	1	1	yes	characteristic
493	#397	C₂²×C₁₃	1	1	yes	characteristic
494	#397	C₂²×C₁₃	1	1	yes	characteristic
495	#397	C₂²×C₁₃	1	1	yes	characteristic
496	#397	C₂²×C₁₃	1	2	yes	complemented
497	#396	C₂²×C₁₃	1	2	yes	complemented
498	#396	C₂²×C₁₃	1	2	yes	complemented
499	#396	C₂²×C₁₃	1	2	yes	complemented
500	#396	C₂²×C₁₃	1	2	yes	complemented
501	#395	C₂²×C₁₃	1	2	yes	complemented
502	#394	C₂²×C₁₃	1	2	yes	—
503	#394	C₂²×C₁₃	1	2	yes	—
504	#394	C₂²×C₁₃	1	2	yes	—
505	#394	C₂²×C₁₃	1	2	yes	—
506	#394	C₂²×C₁₃	1	2	yes	complemented
507	#394	C₂²×C₁₃	1	2	yes	complemented
508	#394	C₂²×C₁₃	1	2	yes	complemented
509	#393	C₂²×C₁₃	1	2	yes	complemented
510	#392	C₂²×C₁₃	1	1	yes	characteristic
511	#392	C₂²×C₁₃	1	1	yes	characteristic
512	#392	C₂²×C₁₃	1	1	yes	characteristic
513	#392	C₂²×C₁₃	1	1	yes	characteristic
514	#392	C₂²×C₁₃	1	2	yes	complemented
515	#391	C₂²×C₁₃	1	2	yes	complemented
516	#390	C₂²×C₁₃	1	2	yes	complemented
517	#389	C₂²×C₁₃	1	2	yes	complemented
518	#389	C₂²×C₁₃	1	2	yes	complemented
519	#388	C₂²×C₁₃	1	2	yes	complemented
520	#388	C₂²×C₁₃	1	2	yes	complemented
521	#387	C₂²×C₁₃	1	2	yes	complemented
522	#387	C₂²×C₁₃	1	2	yes	complemented
523	#386	C₂²×C₁₃	1	2	yes	—
524	#386	C₂²×C₁₃	1	2	yes	—
525	#386	C₂²×C₁₃	1	2	yes	—
526	#386	C₂²×C₁₃	1	2	yes	—
527	#386	C₂²×C₁₃	1	2	yes	—
528	#386	C₂²×C₁₃	1	2	yes	—
529	#386	C₂²×C₁₃	1	2	yes	—
530	#386	C₂²×C₁₃	1	2	yes	—
531	#386	C₂²×C₁₃	1	2	yes	complemented
532	#386	C₂²×C₁₃	1	2	yes	complemented
533	#385	C₂²×C₁₃	1	2	yes	—
534	#385	C₂²×C₁₃	1	1	yes	characteristic
535	#385	C₂²×C₁₃	1	1	yes	characteristic
536	#385	C₂²×C₁₃	1	2	yes	—
537	#385	C₂²×C₁₃	1	1	yes	characteristic
538	#385	C₂²×C₁₃	1	1	yes	characteristic
539	#385	C₂²×C₁₃	1	2	yes	complemented
540	#385	C₂²×C₁₃	1	2	yes	complemented
541	#380	C₂²×C₁₃	1	1	yes	characteristic
542	#380	C₂²×C₁₃	1	2	yes	—
543	#380	C₂²×C₁₃	1	2	yes	—
544	#380	C₂²×C₁₃	1	2	yes	—
545	#380	C₂²×C₁₃	1	1	yes	characteristic
546	#380	C₂²×C₁₃	1	2	yes	complemented
547	#380	C₂²×C₁₃	1	2	yes	complemented
548	C₂×#95	C₂²×C₁₃	1	2	yes	—
549	C₂²×C₁₃	—	2	4	no	—
550	C₂²×C₁₃	—	2	2	no	—
551	C₂²×C₁₃	—	2	2	no	—
552	C₂²×C₁₃	—	2	4	no	—
553	C₂²×C₁₃	—	2	2	no	—
554	C₂²×C₁₃	—	2	2	no	—
555	C₂²×C₁₃	—	2	4	no	—
556	C₂²×C₁₃	—	2	4	no	—
557	C₂²×C₁₃	—	4	16	no	—
558	C₂²×C₁₃	—	4	1	no	—
559	C₂²×C₁₃	—	4	1	no	—
560	C₂²×C₁₃	—	4	1	no	—
561	C₂²×C₁₃	—	4	1	no	—
562	C₂²×C₁₃	—	4	2	no	—
563	C₂²×C₁₃	—	4	2	no	—
564	C₂²×C₁₃	—	4	2	no	—
565	C₂²×C₁₃	—	4	2	no	—
566	C₂²×C₁₃	—	4	2	no	—
567	C₂²×C₁₃	—	4	2	no	—
568	C₂²×C₁₃	—	4	2	no	—
569	C₂²×C₁₃	—	4	2	no	—
570	C₂²×C₁₃	—	4	2	no	—
571	C₂²×C₁₃	—	4	2	no	—
572	C₂²×C₁₃	—	4	2	no	—
573	C₂²×C₁₃	—	4	2	no	—
574	C₂²×C₁₃	—	4	2	no	—
575	C₂²×C₁₃	—	4	2	no	—
576	C₂²×C₁₃	—	4	2	no	—
577	C₂²×C₁₃	—	4	2	no	—
578	C₂²×C₁₃	#537	1	4	yes	—
579	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
580	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
582	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
583	C₂²×C₁₃	#585	1	2	yes	—
584	C₄×C₁₃	—	2	4	no	—
585	C₄×C₁₃	—	2	4	no	—
586	C₄×C₁₃	—	2	4	no	—
587	C₄×C₁₃	—	4	2	no	—
588	C₄×C₁₃	—	4	2	no	—
589	C₄×C₁₃	—	4	2	no	—
590	C₄×C₁₃	—	4	2	no	—
591	C₄×C₁₃	—	4	2	no	—
592	C₄×C₁₃	—	4	2	no	—
593	C₄×C₁₃	—	4	2	no	—
594	C₄×C₁₃	—	4	1	no	—
595	C₄×C₁₃	—	4	1	no	—
596	C₄×C₁₃	—	4	1	no	—
597	C₄×C₁₃	—	4	1	no	—
598	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
599	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
600	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
601	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
602	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
603	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
604	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
605	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
606	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
607	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
608	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
609	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₂³×C₄	—	4	4	no	—
611	C₂³×C₄	—	4	2	no	—
612	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
613	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
616	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
617	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
618	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
619	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
621	#126	—	2	8	no	—
622	#126	—	2	8	no	—
623	#124	—	2	8	no	—
624	#124	—	2	8	no	—
625	#123	—	2	8	no	—
626	#123	—	2	8	no	—
627	C₂²⋊Q₈	—	2	8	no	—
628	C₂²⋊Q₈	—	4	4	no	—
629	#121	—	2	8	no	—
630	#121	—	2	8	no	—
631	#121	—	2	8	no	—
632	#121	—	4	4	no	—
633	#121	—	4	4	no	—
634	#121	—	4	4	no	—
635	#121	—	4	4	no	—
636	#121	—	4	2	no	—
637	#121	—	4	2	no	—
638	#120	—	2	8	no	—
639	#120	—	2	8	no	—
640	C₄×D₄	—	2	8	no	—
641	C₄×D₄	—	2	8	no	—
642	C₂×C₄⋊C₄	—	4	4	no	—
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
660	C₂×C₂²⋊C₄	—	4	2	no	—
661	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
662	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
692	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
693	#95	C₂³×C₁₃	1	2	yes	—
694	#95	C₂³×C₁₃	1	2	yes	—
695	#95	C₂³×C₁₃	1	2	yes	—
696	#95	C₂³×C₁₃	1	2	yes	—
697	#95	C₂³×C₁₃	1	1	yes	characteristic
698	#95	C₂³×C₁₃	1	2	yes	—
699	#95	C₂³×C₁₃	1	2	yes	—
700	#95	C₂³×C₁₃	1	1	yes	characteristic
701	#95	C₂³×C₁₃	1	2	yes	—
702	#95	C₂³×C₁₃	1	2	yes	—
703	#95	C₂³×C₁₃	1	2	yes	—
704	#95	C₂³×C₁₃	1	2	yes	—
705	#95	C₂³×C₁₃	1	1	yes	characteristic
706	#95	C₂³×C₁₃	1	1	yes	characteristic
707	#95	C₂³×C₁₃	1	2	yes	—
708	#95	C₂³×C₁₃	1	2	yes	—
709	#95	C₂³×C₁₃	1	2	yes	—
710	#95	C₂³×C₁₃	1	2	yes	—
711	C₂×C₁₃	—	2	4	no	—
712	C₂×C₁₃	—	4	2	no	—
713	C₂×C₁₃	—	4	2	no	—
714	C₂×C₁₃	—	8	2	no	—
715	C₂×C₁₃	—	8	2	no	—
716	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
717	C₂×C₁₃	#3496	1	2	yes	—
718	C₂×C₁₃	#3532	1	1	yes	characteristic
719	C₂×C₁₃	#3533	1	1	yes	characteristic
720	C₂×C₁₃	#3541	1	2	yes	—
721	C₂⁴	—	2	2	no	—
722	C₂⁴	—	2	2	no	—
723	C₂⁴	—	4	2	no	—
724	C₂⁴	—	4	2	no	—
725	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
726	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
727	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
728	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
729	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
730	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
731	C₂×Q₈	—	2	4	no	—
732	C₂×Q₈	—	4	2	no	—
733	C₂×Q₈	—	4	2	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	4	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂×D₄	—	4	2	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	4	1	no	—
753	C₂×D₄	—	4	1	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	—	4	2	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂×D₄	—	4	2	no	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	4	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	2	4	no	—
768	C₂²×C₄	—	2	4	no	—
769	C₂²×C₄	—	2	4	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	1	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	1	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	2	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	—	4	16	no	—
785	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
786	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
799	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
800	C₄⋊C₄	—	2	4	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	4	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	1	no	—
814	C₄⋊C₄	—	4	1	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	4	1	no	—
830	C₂²⋊C₄	—	4	1	no	—
831	C₂²⋊C₄	—	4	1	no	—
832	C₂²⋊C₄	—	4	1	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	2	no	—
842	C₂²⋊C₄	—	4	2	no	—
843	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
844	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
845	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
846	C₄²	—	2	4	no	—
847	C₄²	—	2	4	no	—
848	C₁₃	#36738	1	1	yes	characteristic, direct product factor, Sylow
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	8	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	4	8	no	—
875	C₂³	—	4	4	no	—
876	C₂³	—	4	4	no	—
877	C₂³	—	4	8	no	—
878	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
879	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
880	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
881	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
882	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
883	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
884	Q₈	—	8	4	no	—
885	D₄	—	4	8	no	—
886	D₄	—	4	8	no	—
887	D₄	—	8	4	no	—
888	D₄	—	8	4	no	—
889	D₄	—	8	4	no	—
890	D₄	—	8	4	no	—
891	D₄	—	8	4	no	—
892	D₄	—	8	4	no	—
893	D₄	—	8	2	no	—
894	D₄	—	8	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	4	8	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	8	no	—
933	C₂×C₄	—	4	8	no	—
934	C₂×C₄	—	4	4	no	—
935	C₂×C₄	—	8	4	no	—
936	C₂×C₄	—	8	4	no	—
937	C₂×C₄	—	8	2	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
940	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
941	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	2	4	no	—
950	C₂²	—	4	16	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	2	no	—
971	C₂²	C₁₃×#537	1	4	yes	—
972	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
973	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
974	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
975	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
976	C₂²	C₁₃×#585	1	2	yes	—
977	C₄	—	2	4	no	—
978	C₄	—	2	4	no	—
979	C₄	—	2	4	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	1	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	1	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₂	—	2	4	no	—
992	C₂	—	4	2	no	—
993	C₂	—	4	2	no	—
994	C₂	—	8	2	no	—
995	C₂	—	8	2	no	—
996	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
997	C₂	C₁₃×#3496	1	2	yes	—
998	C₂	C₁₃×#3532	1	1	yes	characteristic
999	C₂	C₁₃×#3533	1	1	yes	characteristic
1000	C₂	C₁₃×#3541	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. C₁₃×#2847	C₂	semidirect
3. C₁₃×#2722	C₂	semidirect
4. C₁₃×#2715	C₂	semidirect
5. C₁₃×#2712	C₂	semidirect
6. C₁₃×#2695	C₂	semidirect
7. C₁₃×#2693	C₂	semidirect
8. C₁₃×#2691	C₂	semidirect
9. C₁₃×#2676	C₂	semidirect
10. C₁₃×#2675	C₂	semidirect
11. C₁₃×#2672	C₂	semidirect
12. C₁₃×#2671	C₂	semidirect
13. C₁₃×#2617	C₂	semidirect
14. C₁₃×#2617	C₂	semidirect
15. C₁₃×#2564	C₂	semidirect
16. C₁₃×#2543	C₂	semidirect
17. C₁₃×#2417	C₂	semidirect
18. C₁₃×#2416	C₂	semidirect
19. C₂×C₁₃×#385	C₂	semidirect
29. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₁₃×#121	C₂²	semidirect
46. C₁₃×#400	C₂²	semidirect
47. C₁₃×#399	C₂²	semidirect
48. C₁₃×#398	C₂²	semidirect
49. C₁₃×#398	C₂²	semidirect
50. C₁₃×#398	C₂²	semidirect
55. C₁₃×#397	C₂²	semidirect
56. C₁₃×#396	C₂²	semidirect
57. C₁₃×#396	C₂²	semidirect
58. C₁₃×#396	C₂²	semidirect
59. C₁₃×#396	C₂²	semidirect
60. C₁₃×#395	C₂²	semidirect
65. C₁₃×#394	C₂²	semidirect
66. C₁₃×#394	C₂²	semidirect
67. C₁₃×#394	C₂²	semidirect
68. C₁₃×#393	C₂²	semidirect
73. C₁₃×#392	C₂²	semidirect
74. C₁₃×#391	C₂²	semidirect
75. C₁₃×#390	C₂²	semidirect
76. C₁₃×#389	C₂²	semidirect
77. C₁₃×#389	C₂²	semidirect
78. C₁₃×#388	C₂²	semidirect
79. C₁₃×#388	C₂²	semidirect
80. C₁₃×#387	C₂²	semidirect
81. C₁₃×#387	C₂²	semidirect
90. C₁₃×#386	C₂²	semidirect
91. C₁₃×#386	C₂²	semidirect
98. C₁₃×#385	C₂²	semidirect
99. C₁₃×#385	C₂²	semidirect
105. C₁₃×#380	C₂²	semidirect
106. C₁₃×#380	C₂²	semidirect
171. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
221. #36738	C₁₃	direct (N × H)
349. C₂×#538	C₂×C₁₃	semidirect
350. #2847	C₂×C₁₃	semidirect
351. #2722	C₂×C₁₃	semidirect
352. #2715	C₂×C₁₃	semidirect
353. #2712	C₂×C₁₃	semidirect
354. #2695	C₂×C₁₃	semidirect
355. #2693	C₂×C₁₃	semidirect
356. #2691	C₂×C₁₃	semidirect
357. #2676	C₂×C₁₃	semidirect
358. #2675	C₂×C₁₃	semidirect
359. #2672	C₂×C₁₃	semidirect
360. #2671	C₂×C₁₃	semidirect
361. #2617	C₂×C₁₃	semidirect
362. #2617	C₂×C₁₃	semidirect
363. #2564	C₂×C₁₃	semidirect
364. #2543	C₂×C₁₃	semidirect
365. #2417	C₂×C₁₃	semidirect
366. #2416	C₂×C₁₃	semidirect
367. C₂×#385	C₂×C₁₃	semidirect
470. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
479. C₂×#121	C₂²×C₁₃	semidirect
487. #400	C₂²×C₁₃	semidirect
488. #399	C₂²×C₁₃	semidirect
489. #398	C₂²×C₁₃	semidirect
490. #398	C₂²×C₁₃	semidirect
491. #398	C₂²×C₁₃	semidirect
496. #397	C₂²×C₁₃	semidirect
497. #396	C₂²×C₁₃	semidirect
498. #396	C₂²×C₁₃	semidirect
499. #396	C₂²×C₁₃	semidirect
500. #396	C₂²×C₁₃	semidirect
501. #395	C₂²×C₁₃	semidirect
506. #394	C₂²×C₁₃	semidirect
507. #394	C₂²×C₁₃	semidirect
508. #394	C₂²×C₁₃	semidirect
509. #393	C₂²×C₁₃	semidirect
514. #392	C₂²×C₁₃	semidirect
515. #391	C₂²×C₁₃	semidirect
516. #390	C₂²×C₁₃	semidirect
517. #389	C₂²×C₁₃	semidirect
518. #389	C₂²×C₁₃	semidirect
519. #388	C₂²×C₁₃	semidirect
520. #388	C₂²×C₁₃	semidirect
521. #387	C₂²×C₁₃	semidirect
522. #387	C₂²×C₁₃	semidirect
531. #386	C₂²×C₁₃	semidirect
532. #386	C₂²×C₁₃	semidirect
539. #385	C₂²×C₁₃	semidirect
540. #385	C₂²×C₁₃	semidirect
546. #380	C₂²×C₁₃	semidirect
547. #380	C₂²×C₁₃	semidirect
661. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
848. C₁₃	#36738	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
C₁₃×#2847	2
C₁₃×#2722	2
C₁₃×#2715	2
C₁₃×#2712	2
C₁₃×#2695	2
C₁₃×#2693	2
C₁₃×#2691	2
C₁₃×#2676	2
C₁₃×#2675	2
C₁₃×#2672	2
C₁₃×#2671	2
C₁₃×#2617	2
C₁₃×#2564	2
C₁₃×#2543	2
C₁₃×#2417	2
C₁₃×#2416	2
C₂×C₁₃×#385	2
#36738	13

Subgroups — C13×#36738 #15723077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36738 #15723077