Subgroups — C₁₃×#36742 #15723081

Order 3328.

2038 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#539	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2850	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2721	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2719	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2716	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2713	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2694	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2690	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2677	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2674	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2639	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#2564	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2498	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2498	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2417	C₂	1	2	yes	maximal, complemented
19	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#544	—	2	8	no	—
21	C₁₃×#539	—	2	8	no	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#126	C₂²	1	2	yes	—
26	C₂×C₁₃×#125	C₂²	1	2	yes	—
27	C₂×C₁₃×#125	C₂²	1	2	yes	—
28	C₂×C₁₃×#125	C₂²	1	2	yes	—
29	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#123	C₂²	1	2	yes	—
31	C₂×C₁₃×#123	C₂²	1	2	yes	—
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
40	C₂×C₁₃×#117	C₂²	1	2	yes	—
41	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#400	C₂²	1	2	yes	—
45	C₁₃×#400	C₂²	1	2	yes	—
46	C₁₃×#400	C₂²	1	2	yes	—
47	C₁₃×#400	C₂²	1	2	yes	—
48	C₁₃×#399	C₂²	1	2	yes	—
49	C₁₃×#399	C₂²	1	2	yes	—
50	C₁₃×#399	C₂²	1	2	yes	—
51	C₁₃×#398	C₂²	1	2	yes	—
52	C₁₃×#398	C₂²	1	2	yes	—
53	C₁₃×#398	C₂²	1	2	yes	—
54	C₁₃×#398	C₂²	1	2	yes	—
55	C₁₃×#398	C₂²	1	2	yes	—
56	C₁₃×#398	C₂²	1	2	yes	—
57	C₁₃×#397	C₂²	1	2	yes	—
58	C₁₃×#397	C₂²	1	2	yes	—
59	C₁₃×#397	C₂²	1	2	yes	—
60	C₁₃×#396	C₂²	1	2	yes	—
61	C₁₃×#396	C₂²	1	2	yes	—
62	C₁₃×#395	C₂²	1	2	yes	—
63	C₁₃×#395	C₂²	1	2	yes	—
64	C₁₃×#395	C₂²	1	2	yes	—
65	C₁₃×#394	C₂²	1	2	yes	—
66	C₁₃×#393	C₂²	1	2	yes	—
67	C₁₃×#393	C₂²	1	2	yes	—
68	C₁₃×#391	C₂²	1	1	yes	characteristic
69	C₁₃×#391	C₂²	1	1	yes	characteristic
70	C₁₃×#391	C₂²	1	1	yes	characteristic
71	C₁₃×#391	C₂²	1	2	yes	—
72	C₁₃×#390	C₂²	1	1	yes	characteristic
73	C₁₃×#389	C₂²	1	2	yes	—
74	C₁₃×#389	C₂²	1	2	yes	—
75	C₁₃×#389	C₂²	1	2	yes	—
76	C₁₃×#388	C₂²	1	2	yes	—
77	C₁₃×#388	C₂²	1	2	yes	—
78	C₁₃×#388	C₂²	1	2	yes	—
79	C₁₃×#388	C₂²	1	2	yes	—
80	C₁₃×#388	C₂²	1	2	yes	—
81	C₁₃×#388	C₂²	1	2	yes	—
82	C₁₃×#387	C₂²	1	2	yes	—
83	C₁₃×#387	C₂²	1	2	yes	—
84	C₁₃×#387	C₂²	1	2	yes	—
85	C₁₃×#387	C₂²	1	2	yes	—
86	C₁₃×#387	C₂²	1	2	yes	—
87	C₁₃×#387	C₂²	1	2	yes	—
88	C₁₃×#387	C₂²	1	2	yes	—
89	C₁₃×#387	C₂²	1	2	yes	—
90	C₁₃×#387	C₂²	1	2	yes	—
91	C₁₃×#387	C₂²	1	2	yes	—
92	C₁₃×#386	C₂²	1	2	yes	—
93	C₁₃×#386	C₂²	1	2	yes	—
94	C₁₃×#386	C₂²	1	2	yes	—
95	C₁₃×#386	C₂²	1	2	yes	—
96	C₁₃×#385	C₂²	1	2	yes	—
97	C₁₃×#385	C₂²	1	2	yes	—
98	C₁₃×#384	C₂²	1	1	yes	characteristic
99	C₁₃×#382	C₂²	1	1	yes	characteristic
100	C₁₃×#380	C₂²	1	2	yes	—
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	2	yes	—
105	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
106	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
107	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
108	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
111	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊Q₈	—	2	8	no	—
124	C₁₃×C₄⋊Q₈	—	2	8	no	—
125	C₁₃×C₄⋊Q₈	—	4	2	no	—
126	C₁₃×#126	—	2	8	no	—
127	C₁₃×#125	—	2	8	no	—
128	C₁₃×#125	—	2	8	no	—
129	C₁₃×#125	—	2	8	no	—
130	C₁₃×#124	—	4	2	no	—
131	C₁₃×#123	—	2	8	no	—
132	C₁₃×#123	—	2	8	no	—
133	C₁₃×C₂²⋊Q₈	—	2	4	no	—
134	C₁₃×C₂²⋊Q₈	—	2	8	no	—
135	C₁₃×C₂²⋊Q₈	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	—	2	8	no	—
138	C₁₃×C₂²⋊Q₈	—	4	4	no	—
139	C₁₃×#121	—	2	4	no	—
140	C₄×D₄×C₁₃	—	2	8	no	—
141	C₁₃×#117	—	2	8	no	—
142	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₄²×C₁₃	—	4	2	no	—
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
192	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
194	C₁₃×#95	C₂³	1	2	yes	—
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	2	yes	—
200	C₁₃×#95	C₂³	1	2	yes	—
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	C₁₃×#95	C₂³	1	2	yes	—
204	C₁₃×#95	C₂³	1	2	yes	—
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
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	2	yes	—
212	C₁₃×#95	C₂³	1	2	yes	—
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	#36742	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
220	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
221	C₂×Q₈×C₁₃	—	2	2	no	—
222	C₂×Q₈×C₁₃	—	2	4	no	—
223	C₂×Q₈×C₁₃	—	2	2	no	—
224	C₂×Q₈×C₁₃	—	2	2	no	—
225	C₂×Q₈×C₁₃	—	4	2	no	—
226	C₂×Q₈×C₁₃	—	4	1	no	—
227	C₂×Q₈×C₁₃	—	4	1	no	—
228	C₂×Q₈×C₁₃	—	4	1	no	—
229	C₂×Q₈×C₁₃	—	4	2	no	—
230	C₂×Q₈×C₁₃	—	4	1	no	—
231	C₂×Q₈×C₁₃	—	4	1	no	—
232	C₂×Q₈×C₁₃	—	4	1	no	—
233	C₂×D₄×C₁₃	—	2	4	no	—
234	C₂×D₄×C₁₃	—	2	4	no	—
235	C₂×D₄×C₁₃	—	2	4	no	—
236	C₂×D₄×C₁₃	—	2	2	no	—
237	C₂×D₄×C₁₃	—	4	1	no	—
238	C₂×D₄×C₁₃	—	4	1	no	—
239	C₂²×C₄×C₁₃	—	2	2	no	—
240	C₂²×C₄×C₁₃	—	2	2	no	—
241	C₂²×C₄×C₁₃	—	2	2	no	—
242	C₂²×C₄×C₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₃	—	2	2	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	2	4	no	—
248	C₂²×C₄×C₁₃	—	4	1	no	—
249	C₂²×C₄×C₁₃	—	4	1	no	—
250	C₂²×C₄×C₁₃	—	4	1	no	—
251	C₂²×C₄×C₁₃	—	4	1	no	—
252	C₂²×C₄×C₁₃	—	4	1	no	—
253	C₂²×C₄×C₁₃	—	4	1	no	—
254	C₂²×C₄×C₁₃	—	4	1	no	—
255	C₂²×C₄×C₁₃	—	4	2	no	—
256	C₂²×C₄×C₁₃	—	4	2	no	—
257	C₂²×C₄×C₁₃	—	4	1	no	—
258	C₂²×C₄×C₁₃	—	4	1	no	—
259	C₂²×C₄×C₁₃	—	4	1	no	—
260	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
261	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
262	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₁₃×C₄⋊C₄	—	2	4	no	—
281	C₁₃×C₄⋊C₄	—	2	4	no	—
282	C₁₃×C₄⋊C₄	—	2	4	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	4	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	2	4	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	4	no	—
290	C₁₃×C₄⋊C₄	—	2	4	no	—
291	C₁₃×C₄⋊C₄	—	2	4	no	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	4	no	—
295	C₁₃×C₄⋊C₄	—	2	4	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	2	4	no	—
298	C₁₃×C₄⋊C₄	—	4	2	no	—
299	C₁₃×C₄⋊C₄	—	4	2	no	—
300	C₁₃×C₄⋊C₄	—	4	2	no	—
301	C₁₃×C₄⋊C₄	—	4	2	no	—
302	C₁₃×C₄⋊C₄	—	4	2	no	—
303	C₁₃×C₄⋊C₄	—	4	2	no	—
304	C₁₃×C₄⋊C₄	—	4	2	no	—
305	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
306	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	4	no	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	4	2	no	—
317	C₁₃×C₂²⋊C₄	—	4	2	no	—
318	C₁₃×C₂²⋊C₄	—	4	2	no	—
319	C₁₃×C₂²⋊C₄	—	4	2	no	—
320	C₁₃×C₂²⋊C₄	—	4	2	no	—
321	C₁₃×C₂²⋊C₄	—	4	2	no	—
322	C₄²×C₁₃	—	2	4	no	—
323	C₄²×C₁₃	—	2	4	no	—
324	C₄²×C₁₃	—	2	4	no	—
325	C₄²×C₁₃	—	2	2	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	4	1	no	—
328	C₄²×C₁₃	—	4	1	no	—
329	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
330	C₂×#539	C₂×C₁₃	1	1	yes	characteristic
331	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#2850	C₂×C₁₃	1	1	yes	characteristic
333	#2721	C₂×C₁₃	1	2	yes	complemented
334	#2719	C₂×C₁₃	1	2	yes	complemented
335	#2716	C₂×C₁₃	1	2	yes	complemented
336	#2713	C₂×C₁₃	1	2	yes	complemented
337	#2694	C₂×C₁₃	1	2	yes	complemented
338	#2690	C₂×C₁₃	1	2	yes	complemented
339	#2677	C₂×C₁₃	1	2	yes	complemented
340	#2674	C₂×C₁₃	1	2	yes	complemented
341	#2659	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#2639	C₂×C₁₃	1	1	yes	characteristic
343	#2564	C₂×C₁₃	1	2	yes	complemented
344	#2498	C₂×C₁₃	1	2	yes	complemented
345	#2498	C₂×C₁₃	1	2	yes	complemented
346	#2417	C₂×C₁₃	1	2	yes	complemented
347	C₂×#387	C₂×C₁₃	1	1	yes	characteristic, complemented
348	C₂³×C₁₃	—	2	1	no	—
349	C₂³×C₁₃	—	2	1	no	—
350	C₂³×C₁₃	—	2	1	no	—
351	C₂³×C₁₃	—	2	1	no	—
352	C₂³×C₁₃	—	2	2	no	—
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	2	2	no	—
356	C₂³×C₁₃	—	2	2	no	—
357	C₂³×C₁₃	—	2	2	no	—
358	C₂³×C₁₃	—	2	2	no	—
359	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
360	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
361	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
362	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
363	Q₈×C₁₃	—	8	4	no	—
364	Q₈×C₁₃	—	8	2	no	—
365	Q₈×C₁₃	—	8	2	no	—
366	Q₈×C₁₃	—	8	2	no	—
367	D₄×C₁₃	—	4	8	no	—
368	D₄×C₁₃	—	8	2	no	—
369	C₂×C₄×C₁₃	—	2	8	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	1	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	4	4	no	—
416	C₂×C₄×C₁₃	—	4	4	no	—
417	C₂×C₄×C₁₃	—	4	4	no	—
418	C₂×C₄×C₁₃	—	4	4	no	—
419	C₂×C₄×C₁₃	—	8	4	no	—
420	C₂×C₄×C₁₃	—	8	2	no	—
421	C₂×C₄×C₁₃	—	8	2	no	—
422	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
423	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
424	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
427	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
428	#544	—	2	8	no	—
429	#539	—	2	8	no	—
430	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
431	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
432	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#126	C₂²×C₁₃	1	2	yes	—
434	C₂×#125	C₂²×C₁₃	1	2	yes	—
435	C₂×#125	C₂²×C₁₃	1	2	yes	—
436	C₂×#125	C₂²×C₁₃	1	2	yes	—
437	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#123	C₂²×C₁₃	1	2	yes	—
439	C₂×#123	C₂²×C₁₃	1	2	yes	—
440	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
441	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
445	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
446	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
448	C₂×#117	C₂²×C₁₃	1	2	yes	—
449	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
450	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
451	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
452	#400	C₂²×C₁₃	1	2	yes	—
453	#400	C₂²×C₁₃	1	2	yes	—
454	#400	C₂²×C₁₃	1	2	yes	—
455	#400	C₂²×C₁₃	1	2	yes	—
456	#399	C₂²×C₁₃	1	2	yes	—
457	#399	C₂²×C₁₃	1	2	yes	—
458	#399	C₂²×C₁₃	1	2	yes	—
459	#398	C₂²×C₁₃	1	2	yes	—
460	#398	C₂²×C₁₃	1	2	yes	—
461	#398	C₂²×C₁₃	1	2	yes	—
462	#398	C₂²×C₁₃	1	2	yes	—
463	#398	C₂²×C₁₃	1	2	yes	—
464	#398	C₂²×C₁₃	1	2	yes	—
465	#397	C₂²×C₁₃	1	2	yes	—
466	#397	C₂²×C₁₃	1	2	yes	—
467	#397	C₂²×C₁₃	1	2	yes	—
468	#396	C₂²×C₁₃	1	2	yes	—
469	#396	C₂²×C₁₃	1	2	yes	—
470	#395	C₂²×C₁₃	1	2	yes	—
471	#395	C₂²×C₁₃	1	2	yes	—
472	#395	C₂²×C₁₃	1	2	yes	—
473	#394	C₂²×C₁₃	1	2	yes	—
474	#393	C₂²×C₁₃	1	2	yes	—
475	#393	C₂²×C₁₃	1	2	yes	—
476	#391	C₂²×C₁₃	1	1	yes	characteristic
477	#391	C₂²×C₁₃	1	1	yes	characteristic
478	#391	C₂²×C₁₃	1	1	yes	characteristic
479	#391	C₂²×C₁₃	1	2	yes	—
480	#390	C₂²×C₁₃	1	1	yes	characteristic
481	#389	C₂²×C₁₃	1	2	yes	—
482	#389	C₂²×C₁₃	1	2	yes	—
483	#389	C₂²×C₁₃	1	2	yes	—
484	#388	C₂²×C₁₃	1	2	yes	—
485	#388	C₂²×C₁₃	1	2	yes	—
486	#388	C₂²×C₁₃	1	2	yes	—
487	#388	C₂²×C₁₃	1	2	yes	—
488	#388	C₂²×C₁₃	1	2	yes	—
489	#388	C₂²×C₁₃	1	2	yes	—
490	#387	C₂²×C₁₃	1	2	yes	—
491	#387	C₂²×C₁₃	1	2	yes	—
492	#387	C₂²×C₁₃	1	2	yes	—
493	#387	C₂²×C₁₃	1	2	yes	—
494	#387	C₂²×C₁₃	1	2	yes	—
495	#387	C₂²×C₁₃	1	2	yes	—
496	#387	C₂²×C₁₃	1	2	yes	—
497	#387	C₂²×C₁₃	1	2	yes	—
498	#387	C₂²×C₁₃	1	2	yes	—
499	#387	C₂²×C₁₃	1	2	yes	—
500	#386	C₂²×C₁₃	1	2	yes	—
501	#386	C₂²×C₁₃	1	2	yes	—
502	#386	C₂²×C₁₃	1	2	yes	—
503	#386	C₂²×C₁₃	1	2	yes	—
504	#385	C₂²×C₁₃	1	2	yes	—
505	#385	C₂²×C₁₃	1	2	yes	—
506	#384	C₂²×C₁₃	1	1	yes	characteristic
507	#382	C₂²×C₁₃	1	1	yes	characteristic
508	#380	C₂²×C₁₃	1	2	yes	—
509	#380	C₂²×C₁₃	1	2	yes	—
510	#380	C₂²×C₁₃	1	2	yes	—
511	#380	C₂²×C₁₃	1	2	yes	—
512	#380	C₂²×C₁₃	1	2	yes	—
513	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
514	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
515	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
516	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
517	C₂²×C₁₃	—	2	2	no	—
518	C₂²×C₁₃	—	2	2	no	—
519	C₂²×C₁₃	—	2	2	no	—
520	C₂²×C₁₃	—	2	2	no	—
521	C₂²×C₁₃	—	2	2	no	—
522	C₂²×C₁₃	—	2	2	no	—
523	C₂²×C₁₃	—	4	2	no	—
524	C₂²×C₁₃	—	4	2	no	—
525	C₂²×C₁₃	—	4	2	no	—
526	C₂²×C₁₃	—	4	2	no	—
527	C₂²×C₁₃	—	4	2	no	—
528	C₂²×C₁₃	—	4	2	no	—
529	C₂²×C₁₃	—	4	2	no	—
530	C₂²×C₁₃	#536	1	4	yes	—
531	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
532	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
533	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
534	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
535	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
536	C₂²×C₁₃	#585	1	1	yes	characteristic
537	C₂²×C₁₃	#585	1	1	yes	characteristic
538	C₄×C₁₃	—	2	4	no	—
539	C₄×C₁₃	—	2	4	no	—
540	C₄×C₁₃	—	2	2	no	—
541	C₄×C₁₃	—	2	2	no	—
542	C₄×C₁₃	—	2	2	no	—
543	C₄×C₁₃	—	2	2	no	—
544	C₄×C₁₃	—	4	2	no	—
545	C₄×C₁₃	—	4	2	no	—
546	C₄×C₁₃	—	4	2	no	—
547	C₄×C₁₃	—	4	2	no	—
548	C₄×C₁₃	—	4	2	no	—
549	C₄×C₁₃	—	4	2	no	—
550	C₄×C₁₃	—	4	2	no	—
551	C₄×C₁₃	—	4	1	no	—
552	C₄×C₁₃	—	4	2	no	—
553	C₄×C₁₃	—	4	1	no	—
554	C₄×C₁₃	—	4	2	no	—
555	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
556	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
557	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
558	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
559	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
560	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
561	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
564	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
566	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₄⋊Q₈	—	2	8	no	—
570	C₄⋊Q₈	—	2	8	no	—
571	C₄⋊Q₈	—	4	2	no	—
572	#126	—	2	8	no	—
573	#125	—	2	8	no	—
574	#125	—	2	8	no	—
575	#125	—	2	8	no	—
576	#124	—	4	2	no	—
577	#123	—	2	8	no	—
578	#123	—	2	8	no	—
579	C₂²⋊Q₈	—	2	4	no	—
580	C₂²⋊Q₈	—	2	8	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₂²⋊Q₈	—	2	4	no	—
583	C₂²⋊Q₈	—	2	8	no	—
584	C₂²⋊Q₈	—	4	4	no	—
585	#121	—	2	4	no	—
586	C₄×D₄	—	2	8	no	—
587	#117	—	2	8	no	—
588	C₂×C₄⋊C₄	—	4	2	no	—
589	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
632	C₂×C₄²	—	4	2	no	—
633	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
634	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
635	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
636	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
640	#95	C₂³×C₁₃	1	2	yes	—
641	#95	C₂³×C₁₃	1	2	yes	—
642	#95	C₂³×C₁₃	1	2	yes	—
643	#95	C₂³×C₁₃	1	2	yes	—
644	#95	C₂³×C₁₃	1	2	yes	—
645	#95	C₂³×C₁₃	1	2	yes	—
646	#95	C₂³×C₁₃	1	2	yes	—
647	#95	C₂³×C₁₃	1	2	yes	—
648	#95	C₂³×C₁₃	1	2	yes	—
649	#95	C₂³×C₁₃	1	2	yes	—
650	#95	C₂³×C₁₃	1	2	yes	—
651	#95	C₂³×C₁₃	1	2	yes	—
652	#95	C₂³×C₁₃	1	2	yes	—
653	#95	C₂³×C₁₃	1	2	yes	—
654	#95	C₂³×C₁₃	1	2	yes	—
655	#95	C₂³×C₁₃	1	2	yes	—
656	#95	C₂³×C₁₃	1	2	yes	—
657	#95	C₂³×C₁₃	1	2	yes	—
658	#95	C₂³×C₁₃	1	2	yes	—
659	#95	C₂³×C₁₃	1	2	yes	—
660	#95	C₂³×C₁₃	1	2	yes	—
661	#95	C₂³×C₁₃	1	2	yes	—
662	#95	C₂³×C₁₃	1	2	yes	—
663	#95	C₂³×C₁₃	1	2	yes	—
664	C₂×C₁₃	—	2	4	no	—
665	C₂×C₁₃	—	8	2	no	—
666	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
667	C₂×C₁₃	#3496	1	1	yes	characteristic
668	C₂×C₁₃	#3497	1	1	yes	characteristic
669	C₂×C₁₃	#3535	1	1	yes	characteristic
670	C₂×C₁₃	#3538	1	1	yes	characteristic
671	C₂×C₁₃	#3563	1	1	yes	characteristic
672	C₂×C₁₃	#3564	1	1	yes	characteristic
673	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
674	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	4	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	4	2	no	—
680	C₂×Q₈	—	4	1	no	—
681	C₂×Q₈	—	4	1	no	—
682	C₂×Q₈	—	4	1	no	—
683	C₂×Q₈	—	4	2	no	—
684	C₂×Q₈	—	4	1	no	—
685	C₂×Q₈	—	4	1	no	—
686	C₂×Q₈	—	4	1	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	4	1	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	4	1	no	—
703	C₂²×C₄	—	4	1	no	—
704	C₂²×C₄	—	4	1	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	—	4	1	no	—
707	C₂²×C₄	—	4	1	no	—
708	C₂²×C₄	—	4	1	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	1	no	—
712	C₂²×C₄	—	4	1	no	—
713	C₂²×C₄	—	4	1	no	—
714	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
715	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
716	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
717	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
760	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	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	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	4	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	4	1	no	—
782	C₄²	—	4	1	no	—
783	C₁₃	#36742	1	1	yes	characteristic, direct product factor, Sylow
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
796	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
797	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
798	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
799	Q₈	—	8	4	no	—
800	Q₈	—	8	2	no	—
801	Q₈	—	8	2	no	—
802	Q₈	—	8	2	no	—
803	D₄	—	4	8	no	—
804	D₄	—	8	2	no	—
805	C₂×C₄	—	2	8	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	4	4	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	8	4	no	—
856	C₂×C₄	—	8	2	no	—
857	C₂×C₄	—	8	2	no	—
858	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
859	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
860	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
861	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
862	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
863	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	C₁₃×#536	1	4	yes	—
878	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
879	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
880	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
881	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
882	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
883	C₂²	C₁₃×#585	1	1	yes	characteristic
884	C₂²	C₁₃×#585	1	1	yes	characteristic
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₂	—	2	4	no	—
903	C₂	—	8	2	no	—
904	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
905	C₂	C₁₃×#3496	1	1	yes	characteristic
906	C₂	C₁₃×#3497	1	1	yes	characteristic
907	C₂	C₁₃×#3535	1	1	yes	characteristic
908	C₂	C₁₃×#3538	1	1	yes	characteristic
909	C₂	C₁₃×#3563	1	1	yes	characteristic
910	C₂	C₁₃×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
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×#544	C₂	semidirect
3. C₁₃×#2857	C₂	semidirect
5. C₁₃×#2721	C₂	semidirect
6. C₁₃×#2719	C₂	semidirect
7. C₁₃×#2716	C₂	semidirect
8. C₁₃×#2713	C₂	semidirect
9. C₁₃×#2694	C₂	semidirect
10. C₁₃×#2690	C₂	semidirect
11. C₁₃×#2677	C₂	semidirect
12. C₁₃×#2674	C₂	semidirect
13. C₁₃×#2659	C₂	semidirect
15. C₁₃×#2564	C₂	semidirect
16. C₁₃×#2498	C₂	semidirect
17. C₁₃×#2498	C₂	semidirect
18. C₁₃×#2417	C₂	semidirect
19. C₂×C₁₃×#387	C₂	semidirect
218. #36742	C₁₃	direct (N × H)
329. C₂×#544	C₂×C₁₃	semidirect
331. #2857	C₂×C₁₃	semidirect
333. #2721	C₂×C₁₃	semidirect
334. #2719	C₂×C₁₃	semidirect
335. #2716	C₂×C₁₃	semidirect
336. #2713	C₂×C₁₃	semidirect
337. #2694	C₂×C₁₃	semidirect
338. #2690	C₂×C₁₃	semidirect
339. #2677	C₂×C₁₃	semidirect
340. #2674	C₂×C₁₃	semidirect
341. #2659	C₂×C₁₃	semidirect
343. #2564	C₂×C₁₃	semidirect
344. #2498	C₂×C₁₃	semidirect
345. #2498	C₂×C₁₃	semidirect
346. #2417	C₂×C₁₃	semidirect
347. C₂×#387	C₂×C₁₃	semidirect
783. C₁₃	#36742	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×#544	2
C₂×C₁₃×#539	2
C₁₃×#2857	2
C₁₃×#2850	2
C₁₃×#2721	2
C₁₃×#2719	2
C₁₃×#2716	2
C₁₃×#2713	2
C₁₃×#2694	2
C₁₃×#2690	2
C₁₃×#2677	2
C₁₃×#2674	2
C₁₃×#2659	2
C₁₃×#2639	2
C₁₃×#2564	2
C₁₃×#2498	2
C₁₃×#2417	2
C₂×C₁₃×#387	2
#36742	13

Subgroups — C13×#36742 #15723081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36742 #15723081