Subgroups — C₁₃×#34410 #15720749

Order 3328.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#537	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2377	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2377	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2364	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2363	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2345	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2333	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2332	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2329	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2324	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₁₃×#537	C₄	1	16	yes	complemented
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#121	C₂²	1	2	yes	—
32	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#121	C₂²	1	2	yes	—
34	C₂×C₁₃×#121	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
41	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#117	C₂²	1	2	yes	—
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
47	C₁₃×#391	C₂²	1	1	yes	characteristic
48	C₁₃×#391	C₂²	1	1	yes	characteristic
49	C₁₃×#391	C₂²	1	1	yes	characteristic
50	C₁₃×#391	C₂²	1	2	yes	—
51	C₁₃×#391	C₂²	1	1	yes	characteristic
52	C₁₃×#390	C₂²	1	1	yes	characteristic
53	C₁₃×#390	C₂²	1	1	yes	characteristic
54	C₁₃×#390	C₂²	1	1	yes	characteristic
55	C₁₃×#390	C₂²	1	2	yes	—
56	C₁₃×#390	C₂²	1	1	yes	characteristic
57	C₁₃×#390	C₂²	1	2	yes	—
58	C₁₃×#390	C₂²	1	2	yes	—
59	C₁₃×#390	C₂²	1	2	yes	—
60	C₁₃×#390	C₂²	1	2	yes	—
61	C₁₃×#389	C₂²	1	1	yes	characteristic
62	C₁₃×#389	C₂²	1	1	yes	characteristic
63	C₁₃×#389	C₂²	1	2	yes	—
64	C₁₃×#389	C₂²	1	1	yes	characteristic
65	C₁₃×#389	C₂²	1	1	yes	characteristic
66	C₁₃×#389	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#388	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#388	C₂²	1	2	yes	—
72	C₁₃×#388	C₂²	1	2	yes	—
73	C₁₃×#388	C₂²	1	2	yes	—
74	C₁₃×#388	C₂²	1	2	yes	—
75	C₁₃×#387	C₂²	1	2	yes	—
76	C₁₃×#387	C₂²	1	2	yes	—
77	C₁₃×#387	C₂²	1	2	yes	—
78	C₁₃×#387	C₂²	1	2	yes	—
79	C₁₃×#387	C₂²	1	2	yes	—
80	C₁₃×#387	C₂²	1	2	yes	—
81	C₁₃×#387	C₂²	1	2	yes	—
82	C₁₃×#387	C₂²	1	2	yes	—
83	C₁₃×#386	C₂²	1	1	yes	characteristic
84	C₁₃×#386	C₂²	1	1	yes	characteristic
85	C₁₃×#386	C₂²	1	1	yes	characteristic
86	C₁₃×#386	C₂²	1	1	yes	characteristic
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	—
91	C₁₃×#386	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×#385	C₂²	1	2	yes	—
96	C₁₃×#385	C₂²	1	2	yes	—
97	C₁₃×#385	C₂²	1	2	yes	—
98	C₁₃×#385	C₂²	1	2	yes	—
99	C₁₃×#381	C₂²	1	2	yes	—
100	C₁₃×#381	C₂²	1	2	yes	—
101	C₁₃×#380	C₂²	1	1	yes	characteristic
102	C₁₃×#380	C₂²	1	1	yes	characteristic
103	C₁₃×#380	C₂²	1	1	yes	characteristic
104	C₁₃×#380	C₂²	1	1	yes	characteristic
105	C₁₃×#380	C₂²	1	2	yes	—
106	C₁₃×#380	C₂²	1	2	yes	—
107	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
113	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₂×C₁₃×#95	C₂²	1	2	yes	—
124	C₂×C₁₃×#41	—	4	2	no	—
125	C₂×C₁₃×#41	—	4	2	no	—
126	C₂×C₁₃×#41	—	4	2	no	—
127	C₂×C₁₃×#41	—	4	2	no	—
128	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
129	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
138	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
139	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
145	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
148	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
149	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
150	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
151	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
152	C₁₃×#121	C₂×C₄	1	8	yes	complemented
153	C₁₃×#121	C₂×C₄	1	8	yes	complemented
154	C₁₃×#121	C₂×C₄	1	16	yes	complemented
155	C₁₃×#121	C₂×C₄	1	16	yes	complemented
156	C₁₃×#121	C₂×C₄	1	16	yes	complemented
157	C₄×Q₈×C₁₃	—	4	2	no	—
158	C₄×Q₈×C₁₃	—	4	2	no	—
159	C₄×D₄×C₁₃	—	4	4	no	—
160	C₄×D₄×C₁₃	—	4	2	no	—
161	C₄×D₄×C₁₃	—	4	2	no	—
162	C₄×D₄×C₁₃	—	4	4	no	—
163	C₁₃×#117	—	4	2	no	—
164	C₁₃×#117	—	4	4	no	—
165	C₁₃×#117	—	4	2	no	—
166	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
167	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
197	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
201	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₄²×C₁₃	—	4	2	no	—
212	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
217	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
218	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
219	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
220	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
222	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
223	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
224	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
225	C₁₃×#95	C₂³	1	2	yes	—
226	C₁₃×#95	C₂³	1	1	yes	characteristic
227	C₁₃×#95	C₂³	1	1	yes	characteristic
228	C₁₃×#95	C₂³	1	2	yes	—
229	C₁₃×#95	C₂³	1	1	yes	characteristic
230	C₁₃×#95	C₂³	1	1	yes	characteristic
231	C₁₃×#95	C₂³	1	2	yes	—
232	C₁₃×#95	C₂³	1	2	yes	—
233	C₁₃×#95	C₂³	1	1	yes	characteristic
234	C₁₃×#95	C₂³	1	2	yes	—
235	C₁₃×#95	C₂³	1	2	yes	—
236	C₁₃×#95	C₂³	1	1	yes	characteristic
237	C₁₃×#95	C₂³	1	2	yes	—
238	C₁₃×#95	C₂³	1	1	yes	characteristic
239	C₁₃×#95	C₂³	1	1	yes	characteristic
240	C₁₃×#95	C₂³	1	2	yes	—
241	C₁₃×#95	C₂³	1	2	yes	—
242	C₁₃×#95	C₂³	1	2	yes	—
243	C₁₃×#95	C₂³	1	2	yes	—
244	C₁₃×#95	C₂³	1	2	yes	—
245	C₁₃×#95	C₂³	1	2	yes	—
246	C₁₃×#95	C₂³	1	2	yes	—
247	C₁₃×#95	C₂³	1	2	yes	—
248	C₁₃×#95	C₂³	1	2	yes	—
249	#34410	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
253	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₁₃×#41	—	4	16	no	—
255	C₁₃×#41	—	4	16	no	—
256	C₂×Q₈×C₁₃	—	2	2	no	—
257	C₂×Q₈×C₁₃	—	2	2	no	—
258	C₂×Q₈×C₁₃	—	4	1	no	—
259	C₂×Q₈×C₁₃	—	4	1	no	—
260	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
261	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
262	C₂×D₄×C₁₃	—	2	2	no	—
263	C₂×D₄×C₁₃	—	2	2	no	—
264	C₂×D₄×C₁₃	—	4	2	no	—
265	C₂×D₄×C₁₃	—	4	2	no	—
266	C₂×D₄×C₁₃	—	4	2	no	—
267	C₂×D₄×C₁₃	—	4	2	no	—
268	C₂×D₄×C₁₃	—	4	1	no	—
269	C₂×D₄×C₁₃	—	4	1	no	—
270	C₂×D₄×C₁₃	—	4	2	no	—
271	C₂×D₄×C₁₃	—	4	2	no	—
272	C₂×D₄×C₁₃	—	4	1	no	—
273	C₂×D₄×C₁₃	—	4	1	no	—
274	C₂×D₄×C₁₃	—	4	1	no	—
275	C₂×D₄×C₁₃	—	4	1	no	—
276	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
277	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
278	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
279	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
280	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
281	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
282	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
283	C₂²×C₄×C₁₃	—	2	2	no	—
284	C₂²×C₄×C₁₃	—	2	2	no	—
285	C₂²×C₄×C₁₃	—	2	2	no	—
286	C₂²×C₄×C₁₃	—	2	2	no	—
287	C₂²×C₄×C₁₃	—	2	2	no	—
288	C₂²×C₄×C₁₃	—	2	2	no	—
289	C₂²×C₄×C₁₃	—	2	2	no	—
290	C₂²×C₄×C₁₃	—	2	2	no	—
291	C₂²×C₄×C₁₃	—	2	4	no	—
292	C₂²×C₄×C₁₃	—	4	1	no	—
293	C₂²×C₄×C₁₃	—	4	1	no	—
294	C₂²×C₄×C₁₃	—	4	2	no	—
295	C₂²×C₄×C₁₃	—	4	2	no	—
296	C₂²×C₄×C₁₃	—	4	1	no	—
297	C₂²×C₄×C₁₃	—	4	1	no	—
298	C₂²×C₄×C₁₃	—	4	2	no	—
299	C₂²×C₄×C₁₃	—	4	2	no	—
300	C₂²×C₄×C₁₃	—	4	2	no	—
301	C₂²×C₄×C₁₃	—	4	2	no	—
302	C₂²×C₄×C₁₃	—	4	2	no	—
303	C₂²×C₄×C₁₃	—	4	2	no	—
304	C₂²×C₄×C₁₃	—	4	2	no	—
305	C₂²×C₄×C₁₃	—	4	2	no	—
306	C₂²×C₄×C₁₃	—	4	2	no	—
307	C₂²×C₄×C₁₃	—	4	2	no	—
308	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
309	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
310	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
311	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
312	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
313	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	2	no	—
334	C₁₃×C₄⋊C₄	—	2	4	no	—
335	C₁₃×C₄⋊C₄	—	2	2	no	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	—	4	2	no	—
338	C₁₃×C₄⋊C₄	—	4	2	no	—
339	C₁₃×C₄⋊C₄	—	4	2	no	—
340	C₁₃×C₄⋊C₄	—	4	1	no	—
341	C₁₃×C₄⋊C₄	—	4	1	no	—
342	C₁₃×C₄⋊C₄	—	4	2	no	—
343	C₁₃×C₄⋊C₄	—	4	2	no	—
344	C₁₃×C₄⋊C₄	—	4	2	no	—
345	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
346	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
347	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
348	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
349	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	4	no	—
352	C₁₃×C₂²⋊C₄	—	2	2	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	2	no	—
355	C₁₃×C₂²⋊C₄	—	4	1	no	—
356	C₁₃×C₂²⋊C₄	—	4	2	no	—
357	C₁₃×C₂²⋊C₄	—	4	2	no	—
358	C₁₃×C₂²⋊C₄	—	4	2	no	—
359	C₁₃×C₂²⋊C₄	—	4	1	no	—
360	C₁₃×C₂²⋊C₄	—	4	1	no	—
361	C₁₃×C₂²⋊C₄	—	4	2	no	—
362	C₁₃×C₂²⋊C₄	—	4	2	no	—
363	C₁₃×C₂²⋊C₄	—	4	1	no	—
364	C₁₃×C₂²⋊C₄	—	4	1	no	—
365	C₁₃×C₂²⋊C₄	—	4	1	no	—
366	C₁₃×C₂²⋊C₄	—	4	2	no	—
367	C₁₃×C₂²⋊C₄	—	4	2	no	—
368	C₁₃×C₂²⋊C₄	—	4	2	no	—
369	C₁₃×C₂²⋊C₄	—	4	2	no	—
370	C₁₃×C₂²⋊C₄	—	4	2	no	—
371	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
372	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
373	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
374	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
375	C₄²×C₁₃	—	2	2	no	—
376	C₄²×C₁₃	—	2	2	no	—
377	C₄²×C₁₃	—	2	4	no	—
378	C₄²×C₁₃	—	2	2	no	—
379	C₄²×C₁₃	—	2	2	no	—
380	C₄²×C₁₃	—	4	1	no	—
381	C₄²×C₁₃	—	4	1	no	—
382	C₄²×C₁₃	—	4	2	no	—
383	C₄²×C₁₃	—	4	2	no	—
384	C₄²×C₁₃	—	4	2	no	—
385	C₄²×C₁₃	—	4	2	no	—
386	C₄²×C₁₃	—	4	2	no	—
387	C₄²×C₁₃	—	4	2	no	—
388	C₂×#537	C₂×C₁₃	1	1	yes	characteristic
389	#2377	C₂×C₁₃	1	2	yes	complemented
390	#2377	C₂×C₁₃	1	2	yes	complemented
391	#2364	C₂×C₁₃	1	2	yes	complemented
392	#2363	C₂×C₁₃	1	1	yes	characteristic, complemented
393	#2363	C₂×C₁₃	1	2	yes	complemented
394	#2362	C₂×C₁₃	1	1	yes	characteristic, complemented
395	#2361	C₂×C₁₃	1	1	yes	characteristic, complemented
396	#2360	C₂×C₁₃	1	1	yes	characteristic, complemented
397	#2345	C₂×C₁₃	1	1	yes	characteristic, complemented
398	#2344	C₂×C₁₃	1	1	yes	characteristic, complemented
399	#2341	C₂×C₁₃	1	1	yes	characteristic, complemented
400	#2339	C₂×C₁₃	1	1	yes	characteristic, complemented
401	#2333	C₂×C₁₃	1	2	yes	complemented
402	#2332	C₂×C₁₃	1	2	yes	complemented
403	#2329	C₂×C₁₃	1	2	yes	complemented
404	#2324	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#2324	C₂×C₁₃	1	2	yes	complemented
406	#2323	C₂×C₁₃	1	1	yes	characteristic, complemented
407	#2311	C₂×C₁₃	1	1	yes	characteristic, complemented
408	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
409	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
410	#2297	C₂×C₁₃	1	1	yes	characteristic, complemented
411	C₂³×C₁₃	—	2	1	no	—
412	C₂³×C₁₃	—	2	2	no	—
413	C₂³×C₁₃	—	2	1	no	—
414	C₂³×C₁₃	—	2	1	no	—
415	C₂³×C₁₃	—	2	1	no	—
416	C₂³×C₁₃	—	2	1	no	—
417	C₂³×C₁₃	—	2	2	no	—
418	C₂³×C₁₃	—	2	2	no	—
419	C₂³×C₁₃	—	2	1	no	—
420	C₂³×C₁₃	—	2	1	no	—
421	C₂³×C₁₃	—	2	1	no	—
422	C₂³×C₁₃	—	2	1	no	—
423	C₂³×C₁₃	—	2	1	no	—
424	C₂³×C₁₃	—	2	1	no	—
425	C₂³×C₁₃	—	2	1	no	—
426	C₂³×C₁₃	—	2	2	no	—
427	C₂³×C₁₃	—	2	1	no	—
428	C₂³×C₁₃	—	2	1	no	—
429	C₂³×C₁₃	—	2	2	no	—
430	C₂³×C₁₃	—	2	1	no	—
431	C₂³×C₁₃	—	2	1	no	—
432	C₂³×C₁₃	—	2	1	no	—
433	C₂³×C₁₃	—	2	2	no	—
434	C₂³×C₁₃	—	2	1	no	—
435	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
436	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
437	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
438	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
439	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
440	Q₈×C₁₃	—	2	8	no	—
441	Q₈×C₁₃	—	4	4	no	—
442	D₄×C₁₃	—	2	8	no	—
443	D₄×C₁₃	—	4	8	no	—
444	D₄×C₁₃	—	4	8	no	—
445	D₄×C₁₃	—	4	4	no	—
446	D₄×C₁₃	—	4	4	no	—
447	D₄×C₁₃	—	4	4	no	—
448	D₄×C₁₃	—	4	8	no	—
449	C₂×C₄×C₁₃	—	2	1	no	—
450	C₂×C₄×C₁₃	—	2	2	no	—
451	C₂×C₄×C₁₃	—	2	1	no	—
452	C₂×C₄×C₁₃	—	2	1	no	—
453	C₂×C₄×C₁₃	—	2	1	no	—
454	C₂×C₄×C₁₃	—	2	1	no	—
455	C₂×C₄×C₁₃	—	2	2	no	—
456	C₂×C₄×C₁₃	—	2	2	no	—
457	C₂×C₄×C₁₃	—	2	2	no	—
458	C₂×C₄×C₁₃	—	2	1	no	—
459	C₂×C₄×C₁₃	—	2	1	no	—
460	C₂×C₄×C₁₃	—	2	1	no	—
461	C₂×C₄×C₁₃	—	2	1	no	—
462	C₂×C₄×C₁₃	—	2	1	no	—
463	C₂×C₄×C₁₃	—	2	2	no	—
464	C₂×C₄×C₁₃	—	2	2	no	—
465	C₂×C₄×C₁₃	—	2	8	no	—
466	C₂×C₄×C₁₃	—	2	8	no	—
467	C₂×C₄×C₁₃	—	2	8	no	—
468	C₂×C₄×C₁₃	—	2	1	no	—
469	C₂×C₄×C₁₃	—	2	1	no	—
470	C₂×C₄×C₁₃	—	2	1	no	—
471	C₂×C₄×C₁₃	—	2	1	no	—
472	C₂×C₄×C₁₃	—	2	1	no	—
473	C₂×C₄×C₁₃	—	2	1	no	—
474	C₂×C₄×C₁₃	—	2	2	no	—
475	C₂×C₄×C₁₃	—	2	1	no	—
476	C₂×C₄×C₁₃	—	2	2	no	—
477	C₂×C₄×C₁₃	—	2	2	no	—
478	C₂×C₄×C₁₃	—	2	2	no	—
479	C₂×C₄×C₁₃	—	2	2	no	—
480	C₂×C₄×C₁₃	—	2	2	no	—
481	C₂×C₄×C₁₃	—	2	1	no	—
482	C₂×C₄×C₁₃	—	2	2	no	—
483	C₂×C₄×C₁₃	—	2	1	no	—
484	C₂×C₄×C₁₃	—	2	1	no	—
485	C₂×C₄×C₁₃	—	2	2	no	—
486	C₂×C₄×C₁₃	—	2	1	no	—
487	C₂×C₄×C₁₃	—	2	2	no	—
488	C₂×C₄×C₁₃	—	2	2	no	—
489	C₂×C₄×C₁₃	—	2	1	no	—
490	C₂×C₄×C₁₃	—	2	1	no	—
491	C₂×C₄×C₁₃	—	2	1	no	—
492	C₂×C₄×C₁₃	—	2	1	no	—
493	C₂×C₄×C₁₃	—	2	1	no	—
494	C₂×C₄×C₁₃	—	2	2	no	—
495	C₂×C₄×C₁₃	—	2	1	no	—
496	C₂×C₄×C₁₃	—	2	2	no	—
497	C₂×C₄×C₁₃	—	2	1	no	—
498	C₂×C₄×C₁₃	—	4	8	no	—
499	C₂×C₄×C₁₃	—	4	8	no	—
500	C₂×C₄×C₁₃	—	4	4	no	—
501	C₂×C₄×C₁₃	—	4	4	no	—
502	C₂×C₄×C₁₃	—	8	4	no	—
503	C₂×C₄×C₁₃	—	8	4	no	—
504	C₂×C₄×C₁₃	—	8	4	no	—
505	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
506	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
507	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
508	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
509	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
510	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
511	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
512	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
513	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
514	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
515	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
516	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
517	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
518	#537	C₄×C₁₃	1	16	yes	complemented
519	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
520	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
521	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
522	C₂×#121	C₂²×C₁₃	1	2	yes	—
523	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
524	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
525	C₂×#121	C₂²×C₁₃	1	2	yes	—
526	C₂×#121	C₂²×C₁₃	1	2	yes	—
527	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
528	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
529	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
530	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
531	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
532	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
533	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
534	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
535	C₂×#117	C₂²×C₁₃	1	2	yes	—
536	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
537	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
538	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
539	#391	C₂²×C₁₃	1	2	yes	—
540	#391	C₂²×C₁₃	1	1	yes	characteristic
541	#391	C₂²×C₁₃	1	1	yes	characteristic
542	#391	C₂²×C₁₃	1	1	yes	characteristic
543	#391	C₂²×C₁₃	1	1	yes	characteristic
544	#390	C₂²×C₁₃	1	2	yes	—
545	#390	C₂²×C₁₃	1	1	yes	characteristic
546	#390	C₂²×C₁₃	1	1	yes	characteristic
547	#390	C₂²×C₁₃	1	2	yes	—
548	#390	C₂²×C₁₃	1	2	yes	—
549	#390	C₂²×C₁₃	1	2	yes	—
550	#390	C₂²×C₁₃	1	1	yes	characteristic
551	#390	C₂²×C₁₃	1	2	yes	—
552	#390	C₂²×C₁₃	1	1	yes	characteristic
553	#389	C₂²×C₁₃	1	2	yes	—
554	#389	C₂²×C₁₃	1	1	yes	characteristic
555	#389	C₂²×C₁₃	1	1	yes	characteristic
556	#389	C₂²×C₁₃	1	2	yes	—
557	#389	C₂²×C₁₃	1	1	yes	characteristic
558	#389	C₂²×C₁₃	1	1	yes	characteristic
559	#388	C₂²×C₁₃	1	2	yes	—
560	#388	C₂²×C₁₃	1	2	yes	—
561	#388	C₂²×C₁₃	1	2	yes	—
562	#388	C₂²×C₁₃	1	2	yes	—
563	#388	C₂²×C₁₃	1	2	yes	—
564	#388	C₂²×C₁₃	1	2	yes	—
565	#388	C₂²×C₁₃	1	2	yes	—
566	#388	C₂²×C₁₃	1	2	yes	—
567	#387	C₂²×C₁₃	1	2	yes	—
568	#387	C₂²×C₁₃	1	2	yes	—
569	#387	C₂²×C₁₃	1	2	yes	—
570	#387	C₂²×C₁₃	1	2	yes	—
571	#387	C₂²×C₁₃	1	2	yes	—
572	#387	C₂²×C₁₃	1	2	yes	—
573	#387	C₂²×C₁₃	1	2	yes	—
574	#387	C₂²×C₁₃	1	2	yes	—
575	#386	C₂²×C₁₃	1	2	yes	—
576	#386	C₂²×C₁₃	1	2	yes	—
577	#386	C₂²×C₁₃	1	2	yes	—
578	#386	C₂²×C₁₃	1	2	yes	—
579	#386	C₂²×C₁₃	1	2	yes	—
580	#386	C₂²×C₁₃	1	2	yes	—
581	#386	C₂²×C₁₃	1	2	yes	—
582	#386	C₂²×C₁₃	1	1	yes	characteristic
583	#386	C₂²×C₁₃	1	1	yes	characteristic
584	#386	C₂²×C₁₃	1	1	yes	characteristic
585	#386	C₂²×C₁₃	1	1	yes	characteristic
586	#386	C₂²×C₁₃	1	2	yes	—
587	#385	C₂²×C₁₃	1	2	yes	—
588	#385	C₂²×C₁₃	1	2	yes	—
589	#385	C₂²×C₁₃	1	2	yes	—
590	#385	C₂²×C₁₃	1	2	yes	—
591	#381	C₂²×C₁₃	1	2	yes	—
592	#381	C₂²×C₁₃	1	2	yes	—
593	#380	C₂²×C₁₃	1	1	yes	characteristic
594	#380	C₂²×C₁₃	1	1	yes	characteristic
595	#380	C₂²×C₁₃	1	1	yes	characteristic
596	#380	C₂²×C₁₃	1	1	yes	characteristic
597	#380	C₂²×C₁₃	1	2	yes	—
598	#380	C₂²×C₁₃	1	2	yes	—
599	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
600	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
601	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
602	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
603	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
604	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
605	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
606	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
607	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
608	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
609	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
610	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
611	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
612	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
613	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
614	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
615	C₂×#95	C₂²×C₁₃	1	2	yes	—
616	C₂²×C₁₃	—	2	2	no	—
617	C₂²×C₁₃	—	2	2	no	—
618	C₂²×C₁₃	—	2	2	no	—
619	C₂²×C₁₃	—	2	4	no	—
620	C₂²×C₁₃	—	2	2	no	—
621	C₂²×C₁₃	—	2	2	no	—
622	C₂²×C₁₃	—	2	4	no	—
623	C₂²×C₁₃	—	2	2	no	—
624	C₂²×C₁₃	—	2	2	no	—
625	C₂²×C₁₃	—	2	2	no	—
626	C₂²×C₁₃	—	2	2	no	—
627	C₂²×C₁₃	—	2	4	no	—
628	C₂²×C₁₃	—	4	1	no	—
629	C₂²×C₁₃	—	4	2	no	—
630	C₂²×C₁₃	—	4	1	no	—
631	C₂²×C₁₃	—	4	1	no	—
632	C₂²×C₁₃	—	4	1	no	—
633	C₂²×C₁₃	—	4	1	no	—
634	C₂²×C₁₃	—	4	2	no	—
635	C₂²×C₁₃	—	4	1	no	—
636	C₂²×C₁₃	—	4	1	no	—
637	C₂²×C₁₃	—	4	2	no	—
638	C₂²×C₁₃	—	4	1	no	—
639	C₂²×C₁₃	—	4	1	no	—
640	C₂²×C₁₃	—	4	1	no	—
641	C₂²×C₁₃	—	4	2	no	—
642	C₂²×C₁₃	—	4	1	no	—
643	C₂²×C₁₃	—	4	1	no	—
644	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
645	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
646	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
647	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
648	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
649	C₂²×C₁₃	#585	1	1	yes	characteristic
650	C₂²×C₁₃	#585	1	1	yes	characteristic
651	C₄×C₁₃	—	2	2	no	—
652	C₄×C₁₃	—	2	2	no	—
653	C₄×C₁₃	—	2	2	no	—
654	C₄×C₁₃	—	2	4	no	—
655	C₄×C₁₃	—	2	4	no	—
656	C₄×C₁₃	—	2	4	no	—
657	C₄×C₁₃	—	2	2	no	—
658	C₄×C₁₃	—	2	2	no	—
659	C₄×C₁₃	—	4	2	no	—
660	C₄×C₁₃	—	4	2	no	—
661	C₄×C₁₃	—	4	1	no	—
662	C₄×C₁₃	—	4	1	no	—
663	C₄×C₁₃	—	4	1	no	—
664	C₄×C₁₃	—	4	2	no	—
665	C₄×C₁₃	—	4	1	no	—
666	C₄×C₁₃	—	4	2	no	—
667	C₄×C₁₃	—	4	1	no	—
668	C₄×C₁₃	—	4	1	no	—
669	C₄×C₁₃	#518	1	4	yes	—
670	C₂×#41	—	4	2	no	—
671	C₂×#41	—	4	2	no	—
672	C₂×#41	—	4	2	no	—
673	C₂×#41	—	4	2	no	—
674	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
675	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
676	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
677	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
678	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
679	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
680	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
681	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
682	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
683	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
684	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
685	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
686	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
687	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
688	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
689	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
690	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
691	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
692	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
693	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
694	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
695	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
696	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
697	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
698	#121	C₂×C₄×C₁₃	1	8	yes	complemented
699	#121	C₂×C₄×C₁₃	1	8	yes	complemented
700	#121	C₂×C₄×C₁₃	1	16	yes	complemented
701	#121	C₂×C₄×C₁₃	1	16	yes	complemented
702	#121	C₂×C₄×C₁₃	1	16	yes	complemented
703	C₄×Q₈	—	4	2	no	—
704	C₄×Q₈	—	4	2	no	—
705	C₄×D₄	—	4	4	no	—
706	C₄×D₄	—	4	2	no	—
707	C₄×D₄	—	4	2	no	—
708	C₄×D₄	—	4	4	no	—
709	#117	—	4	2	no	—
710	#117	—	4	4	no	—
711	#117	—	4	2	no	—
712	C₂×C₄⋊C₄	—	4	2	no	—
713	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
714	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
718	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
722	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
729	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
733	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
734	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
739	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
745	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
750	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
751	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
752	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
757	C₂×C₄²	—	4	2	no	—
758	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
759	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
760	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
761	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
762	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
764	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
765	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
766	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
767	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
768	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
770	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
771	#95	C₂³×C₁₃	1	1	yes	characteristic
772	#95	C₂³×C₁₃	1	2	yes	—
773	#95	C₂³×C₁₃	1	2	yes	—
774	#95	C₂³×C₁₃	1	2	yes	—
775	#95	C₂³×C₁₃	1	2	yes	—
776	#95	C₂³×C₁₃	1	1	yes	characteristic
777	#95	C₂³×C₁₃	1	1	yes	characteristic
778	#95	C₂³×C₁₃	1	1	yes	characteristic
779	#95	C₂³×C₁₃	1	1	yes	characteristic
780	#95	C₂³×C₁₃	1	2	yes	—
781	#95	C₂³×C₁₃	1	2	yes	—
782	#95	C₂³×C₁₃	1	1	yes	characteristic
783	#95	C₂³×C₁₃	1	2	yes	—
784	#95	C₂³×C₁₃	1	2	yes	—
785	#95	C₂³×C₁₃	1	1	yes	characteristic
786	#95	C₂³×C₁₃	1	2	yes	—
787	#95	C₂³×C₁₃	1	1	yes	characteristic
788	#95	C₂³×C₁₃	1	2	yes	—
789	#95	C₂³×C₁₃	1	2	yes	—
790	#95	C₂³×C₁₃	1	2	yes	—
791	#95	C₂³×C₁₃	1	2	yes	—
792	#95	C₂³×C₁₃	1	2	yes	—
793	#95	C₂³×C₁₃	1	2	yes	—
794	#95	C₂³×C₁₃	1	2	yes	—
795	C₂×C₁₃	—	4	2	no	—
796	C₂×C₁₃	—	4	2	no	—
797	C₂×C₁₃	—	4	2	no	—
798	C₂×C₁₃	—	4	4	no	—
799	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
800	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
801	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
802	C₂×C₁₃	#3536	1	1	yes	characteristic
803	C₂×C₁₃	#3539	1	1	yes	characteristic
804	C₂×C₁₃	#3546	1	1	yes	characteristic
805	C₂×C₁₃	#3547	1	1	yes	characteristic
806	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
807	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
808	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
809	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
810	#41	—	4	16	no	—
811	#41	—	4	16	no	—
812	C₂×Q₈	—	2	2	no	—
813	C₂×Q₈	—	2	2	no	—
814	C₂×Q₈	—	4	1	no	—
815	C₂×Q₈	—	4	1	no	—
816	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
817	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
818	C₂×D₄	—	2	2	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	4	2	no	—
821	C₂×D₄	—	4	2	no	—
822	C₂×D₄	—	4	1	no	—
823	C₂×D₄	—	4	1	no	—
824	C₂×D₄	—	4	2	no	—
825	C₂×D₄	—	4	2	no	—
826	C₂×D₄	—	4	1	no	—
827	C₂×D₄	—	4	1	no	—
828	C₂×D₄	—	4	1	no	—
829	C₂×D₄	—	4	1	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
833	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
834	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
835	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
836	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
837	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
838	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	4	no	—
848	C₂²×C₄	—	4	1	no	—
849	C₂²×C₄	—	4	1	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	4	2	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	1	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
865	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
866	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
867	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
868	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
869	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
873	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
882	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	4	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	4	2	no	—
894	C₄⋊C₄	—	4	2	no	—
895	C₄⋊C₄	—	4	1	no	—
896	C₄⋊C₄	—	4	1	no	—
897	C₄⋊C₄	—	4	2	no	—
898	C₄⋊C₄	—	4	2	no	—
899	C₄⋊C₄	—	4	2	no	—
900	C₄⋊C₄	—	4	2	no	—
901	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
902	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
903	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
904	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
905	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	4	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	4	1	no	—
912	C₂²⋊C₄	—	4	1	no	—
913	C₂²⋊C₄	—	4	2	no	—
914	C₂²⋊C₄	—	4	2	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	1	no	—
919	C₂²⋊C₄	—	4	2	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	2	no	—
922	C₂²⋊C₄	—	4	1	no	—
923	C₂²⋊C₄	—	4	1	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	1	no	—
927	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
928	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
929	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
930	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
931	C₄²	—	2	2	no	—
932	C₄²	—	2	2	no	—
933	C₄²	—	2	4	no	—
934	C₄²	—	2	2	no	—
935	C₄²	—	2	2	no	—
936	C₄²	—	4	1	no	—
937	C₄²	—	4	1	no	—
938	C₄²	—	4	2	no	—
939	C₄²	—	4	2	no	—
940	C₄²	—	4	2	no	—
941	C₄²	—	4	2	no	—
942	C₄²	—	4	2	no	—
943	C₄²	—	4	2	no	—
944	C₁₃	#34410	1	1	yes	characteristic, direct product factor, Sylow
945	C₂³	—	2	1	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	1	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	1	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	1	no	—
963	C₂³	—	2	2	no	—
964	C₂³	—	2	1	no	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	1	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	1	no	—
969	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
970	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
971	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
972	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
973	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
974	Q₈	—	2	8	no	—
975	Q₈	—	4	4	no	—
976	D₄	—	2	8	no	—
977	D₄	—	4	8	no	—
978	D₄	—	4	8	no	—
979	D₄	—	4	4	no	—
980	D₄	—	4	4	no	—
981	D₄	—	4	4	no	—
982	D₄	—	4	8	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	8	no	—
1000	C₂×C₄	—	2	8	no	—
1001	C₂×C₄	—	2	8	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	4	8	no	—
1033	C₂×C₄	—	4	8	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	4	4	no	—
1036	C₂×C₄	—	8	4	no	—
1037	C₂×C₄	—	8	4	no	—
1038	C₂×C₄	—	8	4	no	—
1039	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1040	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1041	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1042	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1043	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1044	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1045	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1046	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1047	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1048	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1049	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	4	no	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	4	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	4	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	1	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
1079	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1080	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1081	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1082	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1083	C₂²	C₁₃×#585	1	1	yes	characteristic
1084	C₂²	C₁₃×#585	1	1	yes	characteristic
1085	C₄	—	2	2	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	4	no	—
1091	C₄	—	2	4	no	—
1092	C₄	—	2	4	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	2	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	C₁₃×#518	1	4	yes	—
1104	C₂	—	4	2	no	—
1105	C₂	—	4	2	no	—
1106	C₂	—	4	2	no	—
1107	C₂	—	4	4	no	—
1108	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
1109	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1110	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1111	C₂	C₁₃×#3536	1	1	yes	characteristic
1112	C₂	C₁₃×#3539	1	1	yes	characteristic
1113	C₂	C₁₃×#3546	1	1	yes	characteristic
1114	C₂	C₁₃×#3547	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#537	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2377	C₂	semidirect
3. C₁₃×#2377	C₂	semidirect
4. C₁₃×#2364	C₂	semidirect
5. C₁₃×#2363	C₂	semidirect
6. C₁₃×#2363	C₂	semidirect
7. C₁₃×#2362	C₂	semidirect
8. C₁₃×#2361	C₂	semidirect
9. C₁₃×#2360	C₂	semidirect
10. C₁₃×#2345	C₂	semidirect
11. C₁₃×#2344	C₂	semidirect
12. C₁₃×#2341	C₂	semidirect
13. C₁₃×#2339	C₂	semidirect
14. C₁₃×#2333	C₂	semidirect
15. C₁₃×#2332	C₂	semidirect
16. C₁₃×#2329	C₂	semidirect
17. C₁₃×#2324	C₂	semidirect
18. C₁₃×#2324	C₂	semidirect
19. C₁₃×#2323	C₂	semidirect
20. C₁₃×#2311	C₂	semidirect
21. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
22. C₄×C₁₃×#121	C₂	semidirect
23. C₁₃×#2297	C₂	semidirect
26. C₁₃×#537	C₄	semidirect
128. C₂×C₁₃×#41	C₂×C₄	semidirect
129. C₂×C₁₃×#41	C₂×C₄	semidirect
149. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
150. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
151. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
152. C₁₃×#121	C₂×C₄	semidirect
153. C₁₃×#121	C₂×C₄	semidirect
154. C₁₃×#121	C₂×C₄	semidirect
155. C₁₃×#121	C₂×C₄	semidirect
156. C₁₃×#121	C₂×C₄	semidirect
167. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
249. #34410	C₁₃	direct (N × H)
389. #2377	C₂×C₁₃	semidirect
390. #2377	C₂×C₁₃	semidirect
391. #2364	C₂×C₁₃	semidirect
392. #2363	C₂×C₁₃	semidirect
393. #2363	C₂×C₁₃	semidirect
394. #2362	C₂×C₁₃	semidirect
395. #2361	C₂×C₁₃	semidirect
396. #2360	C₂×C₁₃	semidirect
397. #2345	C₂×C₁₃	semidirect
398. #2344	C₂×C₁₃	semidirect
399. #2341	C₂×C₁₃	semidirect
400. #2339	C₂×C₁₃	semidirect
401. #2333	C₂×C₁₃	semidirect
402. #2332	C₂×C₁₃	semidirect
403. #2329	C₂×C₁₃	semidirect
404. #2324	C₂×C₁₃	semidirect
405. #2324	C₂×C₁₃	semidirect
406. #2323	C₂×C₁₃	semidirect
407. #2311	C₂×C₁₃	semidirect
408. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
409. C₄×#121	C₂×C₁₃	semidirect
410. #2297	C₂×C₁₃	semidirect
518. #537	C₄×C₁₃	semidirect
674. C₂×#41	C₂×C₄×C₁₃	semidirect
675. C₂×#41	C₂×C₄×C₁₃	semidirect
695. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
696. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
697. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
698. #121	C₂×C₄×C₁₃	semidirect
699. #121	C₂×C₄×C₁₃	semidirect
700. #121	C₂×C₄×C₁₃	semidirect
701. #121	C₂×C₄×C₁₃	semidirect
702. #121	C₂×C₄×C₁₃	semidirect
713. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
944. C₁₃	#34410	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×#537	2
C₁₃×#2377	2
C₁₃×#2364	2
C₁₃×#2363	2
C₁₃×#2362	2
C₁₃×#2361	2
C₁₃×#2360	2
C₁₃×#2345	2
C₁₃×#2344	2
C₁₃×#2341	2
C₁₃×#2339	2
C₁₃×#2333	2
C₁₃×#2332	2
C₁₃×#2329	2
C₁₃×#2324	2
C₁₃×#2323	2
C₁₃×#2311	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#121	2
C₁₃×#2297	2
#34410	13

Subgroups — C13×#34410 #15720749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34410 #15720749