Subgroups — C₁₃×#34320 #15720659

Order 3328.

2840 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#546	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2374	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2363	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2358	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2342	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2335	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2333	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2321	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2273	C₂	1	2	yes	maximal, complemented
23	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#546	C₄	1	16	yes	complemented
27	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#123	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×#120	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
42	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
46	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
47	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
48	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
49	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
50	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
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	1	yes	characteristic
58	C₁₃×#390	C₂²	1	2	yes	—
59	C₁₃×#390	C₂²	1	1	yes	characteristic
60	C₁₃×#390	C₂²	1	1	yes	characteristic
61	C₁₃×#390	C₂²	1	2	yes	complemented
62	C₁₃×#390	C₂²	1	2	yes	complemented
63	C₁₃×#390	C₂²	1	2	yes	complemented
64	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#389	C₂²	1	2	yes	complemented
67	C₁₃×#388	C₂²	1	2	yes	complemented
68	C₁₃×#388	C₂²	1	2	yes	complemented
69	C₁₃×#388	C₂²	1	2	yes	complemented
70	C₁₃×#388	C₂²	1	2	yes	complemented
71	C₁₃×#388	C₂²	1	2	yes	complemented
72	C₁₃×#388	C₂²	1	2	yes	complemented
73	C₁₃×#388	C₂²	1	2	yes	complemented
74	C₁₃×#388	C₂²	1	2	yes	complemented
75	C₁₃×#388	C₂²	1	2	yes	complemented
76	C₁₃×#388	C₂²	1	2	yes	complemented
77	C₁₃×#388	C₂²	1	2	yes	complemented
78	C₁₃×#387	C₂²	1	2	yes	complemented
79	C₁₃×#387	C₂²	1	2	yes	complemented
80	C₁₃×#387	C₂²	1	2	yes	complemented
81	C₁₃×#386	C₂²	1	2	yes	—
82	C₁₃×#386	C₂²	1	2	yes	—
83	C₁₃×#386	C₂²	1	2	yes	—
84	C₁₃×#386	C₂²	1	2	yes	complemented
85	C₁₃×#386	C₂²	1	2	yes	complemented
86	C₁₃×#386	C₂²	1	2	yes	complemented
87	C₁₃×#386	C₂²	1	2	yes	complemented
88	C₁₃×#385	C₂²	1	2	yes	—
89	C₁₃×#385	C₂²	1	2	yes	—
90	C₁₃×#385	C₂²	1	2	yes	complemented
91	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#381	C₂²	1	2	yes	complemented
93	C₁₃×#380	C₂²	1	1	yes	characteristic
94	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#380	C₂²	1	2	yes	complemented
96	C₁₃×#379	C₂²	1	2	yes	—
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
108	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
109	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
110	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
114	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
117	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
120	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₄³×C₁₃	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₁₃	C₂³	1	2	yes	—
125	C₂×C₁₃×#41	—	4	2	no	—
126	C₂×C₁₃×#41	—	4	2	no	—
127	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
128	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₁₃	—	4	2	no	—
130	C₂²×D₄×C₁₃	—	4	2	no	—
131	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
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	2	yes	—
136	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
149	C₁₃×#124	C₂×C₄	1	8	yes	complemented
150	C₁₃×#123	C₂×C₄	1	16	yes	complemented
151	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
152	C₁₃×#121	C₂×C₄	1	8	yes	complemented
153	C₁₃×#121	C₂×C₄	1	16	yes	complemented
154	C₁₃×#120	C₂×C₄	1	16	yes	complemented
155	C₄×Q₈×C₁₃	—	4	2	no	—
156	C₄×Q₈×C₁₃	—	4	2	no	—
157	C₄×D₄×C₁₃	—	2	4	no	—
158	C₄×D₄×C₁₃	—	2	4	no	—
159	C₄×D₄×C₁₃	—	4	2	no	—
160	C₄×D₄×C₁₃	—	4	2	no	—
161	C₄×D₄×C₁₃	—	4	4	no	—
162	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
163	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
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	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
180	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
182	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
183	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
184	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
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	2	yes	—
205	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
210	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₁₃	—	4	2	no	—
214	C₂×C₄²×C₁₃	—	4	2	no	—
215	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
225	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
227	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
229	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
230	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
231	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
234	C₁₃×#95	C₂³	1	1	yes	characteristic
235	C₁₃×#95	C₂³	1	1	yes	characteristic
236	C₁₃×#95	C₂³	1	2	yes	—
237	C₁₃×#95	C₂³	1	2	yes	—
238	C₁₃×#95	C₂³	1	2	yes	—
239	C₁₃×#95	C₂³	1	2	yes	—
240	C₁₃×#95	C₂³	1	2	yes	—
241	C₁₃×#95	C₂³	1	2	yes	—
242	C₁₃×#95	C₂³	1	1	yes	characteristic
243	C₁₃×#95	C₂³	1	1	yes	characteristic
244	C₁₃×#95	C₂³	1	1	yes	characteristic
245	C₁₃×#95	C₂³	1	1	yes	characteristic
246	C₁₃×#95	C₂³	1	2	yes	—
247	C₁₃×#95	C₂³	1	2	yes	—
248	C₁₃×#95	C₂³	1	2	yes	—
249	C₁₃×#95	C₂³	1	2	yes	—
250	C₁₃×#95	C₂³	1	2	yes	—
251	C₁₃×#95	C₂³	1	2	yes	—
252	C₁₃×#95	C₂³	1	2	yes	—
253	#34320	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂⁴×C₁₃	—	2	4	no	—
255	C₂⁴×C₁₃	—	2	4	no	—
256	C₂⁴×C₁₃	—	4	2	no	—
257	C₂⁴×C₁₃	—	4	2	no	—
258	C₂⁴×C₁₃	—	4	2	no	—
259	C₂⁴×C₁₃	—	4	2	no	—
260	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
261	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
262	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
263	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₁₃×#41	—	4	16	no	—
266	C₂×Q₈×C₁₃	—	2	2	no	—
267	C₂×Q₈×C₁₃	—	2	2	no	—
268	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
269	C₂×D₄×C₁₃	—	2	2	no	—
270	C₂×D₄×C₁₃	—	2	2	no	—
271	C₂×D₄×C₁₃	—	2	2	no	—
272	C₂×D₄×C₁₃	—	2	2	no	—
273	C₂×D₄×C₁₃	—	2	2	no	—
274	C₂×D₄×C₁₃	—	2	2	no	—
275	C₂×D₄×C₁₃	—	4	16	no	—
276	C₂×D₄×C₁₃	—	4	2	no	—
277	C₂×D₄×C₁₃	—	4	2	no	—
278	C₂×D₄×C₁₃	—	4	2	no	—
279	C₂×D₄×C₁₃	—	4	2	no	—
280	C₂×D₄×C₁₃	—	4	2	no	—
281	C₂×D₄×C₁₃	—	4	2	no	—
282	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
283	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
284	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
285	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
286	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
287	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
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	2	no	—
292	C₂²×C₄×C₁₃	—	2	2	no	—
293	C₂²×C₄×C₁₃	—	2	4	no	—
294	C₂²×C₄×C₁₃	—	2	2	no	—
295	C₂²×C₄×C₁₃	—	2	2	no	—
296	C₂²×C₄×C₁₃	—	2	2	no	—
297	C₂²×C₄×C₁₃	—	2	2	no	—
298	C₂²×C₄×C₁₃	—	2	4	no	—
299	C₂²×C₄×C₁₃	—	2	4	no	—
300	C₂²×C₄×C₁₃	—	4	1	no	—
301	C₂²×C₄×C₁₃	—	4	1	no	—
302	C₂²×C₄×C₁₃	—	4	1	no	—
303	C₂²×C₄×C₁₃	—	4	1	no	—
304	C₂²×C₄×C₁₃	—	4	2	no	—
305	C₂²×C₄×C₁₃	—	4	1	no	—
306	C₂²×C₄×C₁₃	—	4	2	no	—
307	C₂²×C₄×C₁₃	—	4	1	no	—
308	C₂²×C₄×C₁₃	—	4	2	no	—
309	C₂²×C₄×C₁₃	—	4	2	no	—
310	C₂²×C₄×C₁₃	—	4	2	no	—
311	C₂²×C₄×C₁₃	—	4	2	no	—
312	C₂²×C₄×C₁₃	—	4	2	no	—
313	C₂²×C₄×C₁₃	—	4	2	no	—
314	C₂²×C₄×C₁₃	—	4	2	no	—
315	C₂²×C₄×C₁₃	—	4	2	no	—
316	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
317	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
318	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
319	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
320	C₂²×C₄×C₁₃	#41	1	4	yes	complemented
321	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
329	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	—	2	2	no	—
342	C₁₃×C₄⋊C₄	—	2	2	no	—
343	C₁₃×C₄⋊C₄	—	2	2	no	—
344	C₁₃×C₄⋊C₄	—	2	4	no	—
345	C₁₃×C₄⋊C₄	—	2	2	no	—
346	C₁₃×C₄⋊C₄	—	2	2	no	—
347	C₁₃×C₄⋊C₄	—	4	2	no	—
348	C₁₃×C₄⋊C₄	—	4	2	no	—
349	C₁₃×C₄⋊C₄	—	4	2	no	—
350	C₁₃×C₄⋊C₄	—	4	2	no	—
351	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
352	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
353	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
354	C₁₃×C₂²⋊C₄	—	2	4	no	—
355	C₁₃×C₂²⋊C₄	—	2	2	no	—
356	C₁₃×C₂²⋊C₄	—	2	4	no	—
357	C₁₃×C₂²⋊C₄	—	2	4	no	—
358	C₁₃×C₂²⋊C₄	—	2	4	no	—
359	C₁₃×C₂²⋊C₄	—	2	4	no	—
360	C₁₃×C₂²⋊C₄	—	2	4	no	—
361	C₁₃×C₂²⋊C₄	—	2	4	no	—
362	C₁₃×C₂²⋊C₄	—	2	2	no	—
363	C₁₃×C₂²⋊C₄	—	2	2	no	—
364	C₁₃×C₂²⋊C₄	—	2	4	no	—
365	C₁₃×C₂²⋊C₄	—	2	4	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	—	4	2	no	—
372	C₁₃×C₂²⋊C₄	—	4	2	no	—
373	C₁₃×C₂²⋊C₄	—	4	2	no	—
374	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
375	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
376	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
377	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
378	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
379	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
380	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
381	C₁₃×C₂²⋊C₄	#41	1	4	yes	complemented
382	C₄²×C₁₃	—	2	2	no	—
383	C₄²×C₁₃	—	2	2	no	—
384	C₄²×C₁₃	—	2	2	no	—
385	C₄²×C₁₃	—	2	2	no	—
386	C₄²×C₁₃	—	2	2	no	—
387	C₄²×C₁₃	—	2	2	no	—
388	C₄²×C₁₃	—	2	2	no	—
389	C₄²×C₁₃	—	4	1	no	—
390	C₄²×C₁₃	—	4	1	no	—
391	C₄²×C₁₃	—	4	1	no	—
392	C₄²×C₁₃	—	4	1	no	—
393	C₄²×C₁₃	—	4	2	no	—
394	C₄²×C₁₃	—	4	1	no	—
395	C₄²×C₁₃	—	4	2	no	—
396	C₄²×C₁₃	—	4	2	no	—
397	C₄²×C₁₃	—	4	2	no	—
398	C₄²×C₁₃	—	4	2	no	—
399	C₄²×C₁₃	—	4	2	no	—
400	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
401	C₂×#546	C₂×C₁₃	1	1	yes	characteristic
402	#2374	C₂×C₁₃	1	2	yes	complemented
403	#2367	C₂×C₁₃	1	1	yes	characteristic, complemented
404	#2363	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#2363	C₂×C₁₃	1	2	yes	complemented
406	#2360	C₂×C₁₃	1	1	yes	characteristic, complemented
407	#2358	C₂×C₁₃	1	2	yes	complemented
408	#2357	C₂×C₁₃	1	1	yes	characteristic, complemented
409	#2352	C₂×C₁₃	1	1	yes	characteristic, complemented
410	#2342	C₂×C₁₃	1	2	yes	complemented
411	#2341	C₂×C₁₃	1	1	yes	characteristic, complemented
412	D₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
413	#2335	C₂×C₁₃	1	2	yes	complemented
414	#2333	C₂×C₁₃	1	2	yes	complemented
415	#2321	C₂×C₁₃	1	2	yes	complemented
416	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
417	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
418	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
419	#2297	C₂×C₁₃	1	1	yes	characteristic, complemented
420	#2293	C₂×C₁₃	1	1	yes	characteristic, complemented
421	C₂×#390	C₂×C₁₃	1	1	yes	characteristic, complemented
422	#2273	C₂×C₁₃	1	2	yes	complemented
423	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
424	C₂³×C₁₃	—	2	1	no	—
425	C₂³×C₁₃	—	2	1	no	—
426	C₂³×C₁₃	—	2	1	no	—
427	C₂³×C₁₃	—	2	1	no	—
428	C₂³×C₁₃	—	2	2	no	—
429	C₂³×C₁₃	—	2	2	no	—
430	C₂³×C₁₃	—	2	2	no	—
431	C₂³×C₁₃	—	2	1	no	—
432	C₂³×C₁₃	—	2	1	no	—
433	C₂³×C₁₃	—	2	2	no	—
434	C₂³×C₁₃	—	2	2	no	—
435	C₂³×C₁₃	—	2	2	no	—
436	C₂³×C₁₃	—	2	1	no	—
437	C₂³×C₁₃	—	2	1	no	—
438	C₂³×C₁₃	—	2	2	no	—
439	C₂³×C₁₃	—	2	2	no	—
440	C₂³×C₁₃	—	2	1	no	—
441	C₂³×C₁₃	—	2	2	no	—
442	C₂³×C₁₃	—	2	2	no	—
443	C₂³×C₁₃	—	2	2	no	—
444	C₂³×C₁₃	—	2	1	no	—
445	C₂³×C₁₃	—	2	2	no	—
446	C₂³×C₁₃	—	2	16	no	—
447	C₂³×C₁₃	—	4	8	no	—
448	C₂³×C₁₃	—	4	8	no	—
449	C₂³×C₁₃	—	8	4	no	—
450	C₂³×C₁₃	—	8	4	no	—
451	C₂³×C₁₃	—	8	4	no	—
452	C₂³×C₁₃	—	8	4	no	—
453	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
454	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
455	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
456	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
457	C₂³×C₁₃	C₂×#41	1	2	yes	—
458	C₂³×C₁₃	C₂×#41	1	2	yes	—
459	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
460	Q₈×C₁₃	—	2	8	no	—
461	D₄×C₁₃	—	2	8	no	—
462	D₄×C₁₃	—	2	8	no	—
463	D₄×C₁₃	—	2	8	no	—
464	D₄×C₁₃	—	4	8	no	—
465	D₄×C₁₃	—	4	8	no	—
466	D₄×C₁₃	—	4	8	no	—
467	C₂×C₄×C₁₃	—	2	1	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	1	no	—
475	C₂×C₄×C₁₃	—	2	1	no	—
476	C₂×C₄×C₁₃	—	2	1	no	—
477	C₂×C₄×C₁₃	—	2	1	no	—
478	C₂×C₄×C₁₃	—	2	1	no	—
479	C₂×C₄×C₁₃	—	2	1	no	—
480	C₂×C₄×C₁₃	—	2	2	no	—
481	C₂×C₄×C₁₃	—	2	2	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	1	no	—
486	C₂×C₄×C₁₃	—	2	1	no	—
487	C₂×C₄×C₁₃	—	2	1	no	—
488	C₂×C₄×C₁₃	—	2	2	no	—
489	C₂×C₄×C₁₃	—	2	8	no	—
490	C₂×C₄×C₁₃	—	2	8	no	—
491	C₂×C₄×C₁₃	—	2	1	no	—
492	C₂×C₄×C₁₃	—	2	2	no	—
493	C₂×C₄×C₁₃	—	2	2	no	—
494	C₂×C₄×C₁₃	—	2	2	no	—
495	C₂×C₄×C₁₃	—	2	2	no	—
496	C₂×C₄×C₁₃	—	2	1	no	—
497	C₂×C₄×C₁₃	—	2	1	no	—
498	C₂×C₄×C₁₃	—	2	1	no	—
499	C₂×C₄×C₁₃	—	2	1	no	—
500	C₂×C₄×C₁₃	—	2	1	no	—
501	C₂×C₄×C₁₃	—	2	1	no	—
502	C₂×C₄×C₁₃	—	2	2	no	—
503	C₂×C₄×C₁₃	—	2	2	no	—
504	C₂×C₄×C₁₃	—	2	2	no	—
505	C₂×C₄×C₁₃	—	2	2	no	—
506	C₂×C₄×C₁₃	—	2	2	no	—
507	C₂×C₄×C₁₃	—	2	2	no	—
508	C₂×C₄×C₁₃	—	2	2	no	—
509	C₂×C₄×C₁₃	—	2	1	no	—
510	C₂×C₄×C₁₃	—	2	2	no	—
511	C₂×C₄×C₁₃	—	2	1	no	—
512	C₂×C₄×C₁₃	—	4	8	no	—
513	C₂×C₄×C₁₃	—	4	8	no	—
514	C₂×C₄×C₁₃	—	4	4	no	—
515	C₂×C₄×C₁₃	—	4	4	no	—
516	C₂×C₄×C₁₃	—	4	4	no	—
517	C₂×C₄×C₁₃	—	4	4	no	—
518	C₂×C₄×C₁₃	—	8	4	no	—
519	C₂×C₄×C₁₃	—	8	4	no	—
520	C₂×C₄×C₁₃	—	8	4	no	—
521	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
522	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
523	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
524	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
525	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
526	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
527	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
528	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
529	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
530	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
531	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
532	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
533	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
534	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
535	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
536	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
537	#546	C₄×C₁₃	1	16	yes	complemented
538	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
539	C₂×#123	C₂²×C₁₃	1	2	yes	—
540	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
541	C₂×#121	C₂²×C₁₃	1	2	yes	—
542	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
543	C₂×#120	C₂²×C₁₃	1	2	yes	—
544	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
545	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
546	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
547	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
548	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
549	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
550	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
551	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
552	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
553	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
554	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
555	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
556	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
557	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
558	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
559	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
560	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
561	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
562	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
563	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
564	#390	C₂²×C₁₃	1	2	yes	—
565	#390	C₂²×C₁₃	1	1	yes	characteristic
566	#390	C₂²×C₁₃	1	1	yes	characteristic
567	#390	C₂²×C₁₃	1	1	yes	characteristic
568	#390	C₂²×C₁₃	1	1	yes	characteristic
569	#390	C₂²×C₁₃	1	2	yes	—
570	#390	C₂²×C₁₃	1	1	yes	characteristic
571	#390	C₂²×C₁₃	1	1	yes	characteristic
572	#390	C₂²×C₁₃	1	2	yes	complemented
573	#390	C₂²×C₁₃	1	2	yes	complemented
574	#390	C₂²×C₁₃	1	2	yes	complemented
575	#389	C₂²×C₁₃	1	2	yes	complemented
576	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
577	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
578	#388	C₂²×C₁₃	1	2	yes	complemented
579	#388	C₂²×C₁₃	1	2	yes	complemented
580	#388	C₂²×C₁₃	1	2	yes	complemented
581	#388	C₂²×C₁₃	1	2	yes	complemented
582	#388	C₂²×C₁₃	1	2	yes	complemented
583	#388	C₂²×C₁₃	1	2	yes	complemented
584	#388	C₂²×C₁₃	1	2	yes	complemented
585	#388	C₂²×C₁₃	1	2	yes	complemented
586	#388	C₂²×C₁₃	1	2	yes	complemented
587	#388	C₂²×C₁₃	1	2	yes	complemented
588	#388	C₂²×C₁₃	1	2	yes	complemented
589	#387	C₂²×C₁₃	1	2	yes	complemented
590	#387	C₂²×C₁₃	1	2	yes	complemented
591	#387	C₂²×C₁₃	1	2	yes	complemented
592	#386	C₂²×C₁₃	1	2	yes	—
593	#386	C₂²×C₁₃	1	2	yes	—
594	#386	C₂²×C₁₃	1	2	yes	—
595	#386	C₂²×C₁₃	1	2	yes	complemented
596	#386	C₂²×C₁₃	1	2	yes	complemented
597	#386	C₂²×C₁₃	1	2	yes	complemented
598	#386	C₂²×C₁₃	1	2	yes	complemented
599	#385	C₂²×C₁₃	1	2	yes	—
600	#385	C₂²×C₁₃	1	2	yes	—
601	#385	C₂²×C₁₃	1	2	yes	complemented
602	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
603	#381	C₂²×C₁₃	1	2	yes	complemented
604	#380	C₂²×C₁₃	1	1	yes	characteristic
605	#380	C₂²×C₁₃	1	2	yes	complemented
606	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
607	#379	C₂²×C₁₃	1	2	yes	—
608	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
609	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
610	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
611	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
614	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
615	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
616	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
617	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
618	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
619	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
620	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
621	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
623	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
624	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
625	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
626	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
627	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
628	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
629	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
630	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
631	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
633	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
634	C₄³	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	C₂²×C₁₃	—	2	2	no	—
636	C₂²×C₁₃	—	2	2	no	—
637	C₂²×C₁₃	—	2	2	no	—
638	C₂²×C₁₃	—	2	2	no	—
639	C₂²×C₁₃	—	2	2	no	—
640	C₂²×C₁₃	—	2	2	no	—
641	C₂²×C₁₃	—	2	2	no	—
642	C₂²×C₁₃	—	2	4	no	—
643	C₂²×C₁₃	—	2	4	no	—
644	C₂²×C₁₃	—	2	2	no	—
645	C₂²×C₁₃	—	2	4	no	—
646	C₂²×C₁₃	—	2	4	no	—
647	C₂²×C₁₃	—	2	4	no	—
648	C₂²×C₁₃	—	2	2	no	—
649	C₂²×C₁₃	—	2	4	no	—
650	C₂²×C₁₃	—	4	1	no	—
651	C₂²×C₁₃	—	4	2	no	—
652	C₂²×C₁₃	—	4	2	no	—
653	C₂²×C₁₃	—	4	1	no	—
654	C₂²×C₁₃	—	4	2	no	—
655	C₂²×C₁₃	—	4	2	no	—
656	C₂²×C₁₃	—	4	2	no	—
657	C₂²×C₁₃	—	4	1	no	—
658	C₂²×C₁₃	—	4	2	no	—
659	C₂²×C₁₃	—	4	1	no	—
660	C₂²×C₁₃	—	4	2	no	—
661	C₂²×C₁₃	—	4	2	no	—
662	C₂²×C₁₃	—	8	16	no	—
663	C₂²×C₁₃	C₄×#41	1	4	yes	—
664	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
665	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
666	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
667	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
668	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
669	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
670	C₂²×C₁₃	#585	1	1	yes	characteristic
671	C₄×C₁₃	—	2	2	no	—
672	C₄×C₁₃	—	2	2	no	—
673	C₄×C₁₃	—	2	2	no	—
674	C₄×C₁₃	—	2	4	no	—
675	C₄×C₁₃	—	2	2	no	—
676	C₄×C₁₃	—	2	4	no	—
677	C₄×C₁₃	—	2	2	no	—
678	C₄×C₁₃	—	2	2	no	—
679	C₄×C₁₃	—	2	2	no	—
680	C₄×C₁₃	—	2	2	no	—
681	C₄×C₁₃	—	2	2	no	—
682	C₄×C₁₃	—	4	1	no	—
683	C₄×C₁₃	—	4	1	no	—
684	C₄×C₁₃	—	4	2	no	—
685	C₄×C₁₃	—	4	2	no	—
686	C₄×C₁₃	—	4	2	no	—
687	C₄×C₁₃	—	4	1	no	—
688	C₄×C₁₃	—	4	2	no	—
689	C₄×C₁₃	#518	1	4	yes	—
690	C₂⁵	C₂³×C₁₃	1	2	yes	—
691	C₂×#41	—	4	2	no	—
692	C₂×#41	—	4	2	no	—
693	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
694	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
695	C₂²×D₄	—	4	2	no	—
696	C₂²×D₄	—	4	2	no	—
697	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
698	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
699	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
700	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
701	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
702	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
703	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
704	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
705	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
706	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
707	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
708	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
709	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
710	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
711	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
712	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
713	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
714	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
715	#124	C₂×C₄×C₁₃	1	8	yes	complemented
716	#123	C₂×C₄×C₁₃	1	16	yes	complemented
717	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
718	#121	C₂×C₄×C₁₃	1	8	yes	complemented
719	#121	C₂×C₄×C₁₃	1	16	yes	complemented
720	#120	C₂×C₄×C₁₃	1	16	yes	complemented
721	C₄×Q₈	—	4	2	no	—
722	C₄×Q₈	—	4	2	no	—
723	C₄×D₄	—	2	4	no	—
724	C₄×D₄	—	2	4	no	—
725	C₄×D₄	—	4	2	no	—
726	C₄×D₄	—	4	2	no	—
727	C₄×D₄	—	4	4	no	—
728	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
729	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
730	#117	—	4	4	no	—
731	#117	—	4	2	no	—
732	C₂×C₄⋊C₄	—	4	2	no	—
733	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
737	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
741	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
747	C₂×C₂²⋊C₄	—	2	8	no	—
748	C₂×C₂²⋊C₄	—	2	8	no	—
749	C₂×C₂²⋊C₄	—	4	4	no	—
750	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
751	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
763	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
772	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
779	C₂×C₄²	—	4	2	no	—
780	C₂×C₄²	—	4	2	no	—
781	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
782	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
783	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
784	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
785	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
786	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
787	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
788	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
789	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
790	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
791	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
792	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
793	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
794	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
795	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
796	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
797	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
798	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
799	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
800	#95	C₂³×C₁₃	1	1	yes	characteristic
801	#95	C₂³×C₁₃	1	1	yes	characteristic
802	#95	C₂³×C₁₃	1	2	yes	—
803	#95	C₂³×C₁₃	1	2	yes	—
804	#95	C₂³×C₁₃	1	2	yes	—
805	#95	C₂³×C₁₃	1	2	yes	—
806	#95	C₂³×C₁₃	1	2	yes	—
807	#95	C₂³×C₁₃	1	2	yes	—
808	#95	C₂³×C₁₃	1	1	yes	characteristic
809	#95	C₂³×C₁₃	1	1	yes	characteristic
810	#95	C₂³×C₁₃	1	1	yes	characteristic
811	#95	C₂³×C₁₃	1	1	yes	characteristic
812	#95	C₂³×C₁₃	1	2	yes	—
813	#95	C₂³×C₁₃	1	2	yes	—
814	#95	C₂³×C₁₃	1	2	yes	—
815	#95	C₂³×C₁₃	1	2	yes	—
816	#95	C₂³×C₁₃	1	2	yes	—
817	#95	C₂³×C₁₃	1	2	yes	—
818	#95	C₂³×C₁₃	1	2	yes	—
819	C₂×C₁₃	—	2	4	no	—
820	C₂×C₁₃	—	4	2	no	—
821	C₂×C₁₃	—	4	4	no	—
822	C₂×C₁₃	—	4	4	no	—
823	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
824	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
825	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
826	C₂×C₁₃	#3505	1	1	yes	characteristic
827	C₂×C₁₃	#3508	1	1	yes	characteristic
828	C₂×C₁₃	#3514	1	1	yes	characteristic
829	C₂×C₁₃	#3519	1	1	yes	characteristic
830	C₂⁴	—	2	4	no	—
831	C₂⁴	—	2	4	no	—
832	C₂⁴	—	4	2	no	—
833	C₂⁴	—	4	2	no	—
834	C₂⁴	—	4	2	no	—
835	C₂⁴	—	4	2	no	—
836	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
837	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
838	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
839	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
840	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
841	#41	—	4	16	no	—
842	C₂×Q₈	—	2	2	no	—
843	C₂×Q₈	—	2	2	no	—
844	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	4	16	no	—
852	C₂×D₄	—	4	2	no	—
853	C₂×D₄	—	4	2	no	—
854	C₂×D₄	—	4	2	no	—
855	C₂×D₄	—	4	2	no	—
856	C₂×D₄	—	4	2	no	—
857	C₂×D₄	—	4	2	no	—
858	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
859	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
860	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
861	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
862	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
863	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	4	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	4	no	—
875	C₂²×C₄	—	2	4	no	—
876	C₂²×C₄	—	4	1	no	—
877	C₂²×C₄	—	4	1	no	—
878	C₂²×C₄	—	4	1	no	—
879	C₂²×C₄	—	4	1	no	—
880	C₂²×C₄	—	4	2	no	—
881	C₂²×C₄	—	4	2	no	—
882	C₂²×C₄	—	4	2	no	—
883	C₂²×C₄	—	4	1	no	—
884	C₂²×C₄	—	4	2	no	—
885	C₂²×C₄	—	4	1	no	—
886	C₂²×C₄	—	4	2	no	—
887	C₂²×C₄	—	4	2	no	—
888	C₂²×C₄	—	4	2	no	—
889	C₂²×C₄	—	4	2	no	—
890	C₂²×C₄	—	4	2	no	—
891	C₂²×C₄	—	4	2	no	—
892	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
893	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
894	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
895	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
896	C₂²×C₄	C₁₃×#41	1	4	yes	complemented
897	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
899	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
900	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
901	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
902	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
906	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
907	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
908	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	4	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	4	2	no	—
924	C₄⋊C₄	—	4	2	no	—
925	C₄⋊C₄	—	4	2	no	—
926	C₄⋊C₄	—	4	2	no	—
927	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
928	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
929	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
930	C₂²⋊C₄	—	2	4	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	4	no	—
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	4	no	—
936	C₂²⋊C₄	—	2	4	no	—
937	C₂²⋊C₄	—	2	4	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	4	no	—
941	C₂²⋊C₄	—	2	4	no	—
942	C₂²⋊C₄	—	4	2	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	4	2	no	—
947	C₂²⋊C₄	—	4	2	no	—
948	C₂²⋊C₄	—	4	2	no	—
949	C₂²⋊C₄	—	4	2	no	—
950	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
951	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
952	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
953	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
954	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
955	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
956	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
957	C₂²⋊C₄	C₁₃×#41	1	4	yes	complemented
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	4	1	no	—
966	C₄²	—	4	1	no	—
967	C₄²	—	4	1	no	—
968	C₄²	—	4	1	no	—
969	C₄²	—	4	2	no	—
970	C₄²	—	4	2	no	—
971	C₄²	—	4	2	no	—
972	C₄²	—	4	2	no	—
973	C₄²	—	4	2	no	—
974	C₄²	—	4	2	no	—
975	C₄²	—	4	1	no	—
976	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
977	C₁₃	#34320	1	1	yes	characteristic, direct product factor, Sylow
978	C₂³	—	2	1	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	1	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	2	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	2	1	no	—
987	C₂³	—	2	2	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	2	1	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	2	no	—
998	C₂³	—	2	1	no	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	16	no	—
1001	C₂³	—	4	8	no	—
1002	C₂³	—	4	8	no	—
1003	C₂³	—	8	4	no	—
1004	C₂³	—	8	4	no	—
1005	C₂³	—	8	4	no	—
1006	C₂³	—	8	4	no	—
1007	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
1008	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
1009	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
1010	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
1011	C₂³	C₂×C₁₃×#41	1	2	yes	—
1012	C₂³	C₂×C₁₃×#41	1	2	yes	—
1013	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
1014	Q₈	—	2	8	no	—
1015	D₄	—	2	8	no	—
1016	D₄	—	2	8	no	—
1017	D₄	—	2	8	no	—
1018	D₄	—	4	8	no	—
1019	D₄	—	4	8	no	—
1020	D₄	—	4	8	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	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	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	8	no	—
1044	C₂×C₄	—	2	8	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	4	8	no	—
1067	C₂×C₄	—	4	8	no	—
1068	C₂×C₄	—	4	4	no	—
1069	C₂×C₄	—	4	4	no	—
1070	C₂×C₄	—	4	4	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	8	4	no	—
1073	C₂×C₄	—	8	4	no	—
1074	C₂×C₄	—	8	4	no	—
1075	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1076	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1077	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1078	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1079	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1080	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1081	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1082	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1083	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1084	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1085	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1086	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1087	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1088	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	4	no	—
1097	C₂²	—	2	4	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	4	no	—
1100	C₂²	—	2	4	no	—
1101	C₂²	—	2	4	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	4	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	8	16	no	—
1117	C₂²	C₄×C₁₃×#41	1	4	yes	—
1118	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
1119	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1120	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1121	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1122	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1123	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1124	C₂²	C₁₃×#585	1	1	yes	characteristic
1125	C₄	—	2	2	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	4	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	4	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	2	no	—
1143	C₄	C₁₃×#518	1	4	yes	—
1144	C₂	—	2	4	no	—
1145	C₂	—	4	4	no	—
1146	C₂	—	4	4	no	—
1147	C₂	—	4	2	no	—
1148	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
1149	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
1150	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1151	C₂	C₁₃×#3505	1	1	yes	characteristic
1152	C₂	C₁₃×#3508	1	1	yes	characteristic
1153	C₂	C₁₃×#3514	1	1	yes	characteristic
1154	C₂	C₁₃×#3519	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×#546	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×#2374	C₂	semidirect
3. C₁₃×#2367	C₂	semidirect
4. C₁₃×#2363	C₂	semidirect
5. C₁₃×#2363	C₂	semidirect
6. C₁₃×#2360	C₂	semidirect
7. C₁₃×#2358	C₂	semidirect
8. C₁₃×#2357	C₂	semidirect
9. C₁₃×#2352	C₂	semidirect
10. C₁₃×#2342	C₂	semidirect
11. C₁₃×#2341	C₂	semidirect
12. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
13. C₁₃×#2335	C₂	semidirect
14. C₁₃×#2333	C₂	semidirect
15. C₁₃×#2321	C₂	semidirect
16. C₄×C₁₃×#124	C₂	semidirect
17. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₁₃×#121	C₂	semidirect
19. C₁₃×#2297	C₂	semidirect
20. C₁₃×#2293	C₂	semidirect
21. C₂×C₁₃×#390	C₂	semidirect
22. C₁₃×#2273	C₂	semidirect
23. C₄²×D₄×C₁₃	C₂	semidirect
26. C₁₃×#546	C₄	semidirect
33. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
34. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
41. C₂×C₄×D₄×C₁₃	C₂²	semidirect
42. C₂×C₁₃×#117	C₂²	semidirect
43. C₂×C₁₃×#117	C₂²	semidirect
50. C₂²×C₄²×C₁₃	C₂²	semidirect
51. C₁₃×#391	C₂²	semidirect
52. C₁₃×#391	C₂²	semidirect
61. C₁₃×#390	C₂²	semidirect
62. C₁₃×#390	C₂²	semidirect
63. C₁₃×#390	C₂²	semidirect
64. C₁₃×#389	C₂²	semidirect
65. C₁₃×#389	C₂²	semidirect
66. C₁₃×#389	C₂²	semidirect
67. C₁₃×#388	C₂²	semidirect
68. C₁₃×#388	C₂²	semidirect
69. C₁₃×#388	C₂²	semidirect
70. C₁₃×#388	C₂²	semidirect
71. C₁₃×#388	C₂²	semidirect
72. C₁₃×#388	C₂²	semidirect
73. C₁₃×#388	C₂²	semidirect
74. C₁₃×#388	C₂²	semidirect
75. C₁₃×#388	C₂²	semidirect
76. C₁₃×#388	C₂²	semidirect
77. C₁₃×#388	C₂²	semidirect
78. C₁₃×#387	C₂²	semidirect
79. C₁₃×#387	C₂²	semidirect
80. C₁₃×#387	C₂²	semidirect
84. C₁₃×#386	C₂²	semidirect
85. C₁₃×#386	C₂²	semidirect
86. C₁₃×#386	C₂²	semidirect
87. C₁₃×#386	C₂²	semidirect
90. C₁₃×#385	C₂²	semidirect
91. C₁₃×#382	C₂²	semidirect
92. C₁₃×#381	C₂²	semidirect
94. C₁₃×#380	C₂²	semidirect
95. C₁₃×#380	C₂²	semidirect
97. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
98. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
99. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
100. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
101. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
102. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
103. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
110. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
111. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
112. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
113. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
114. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
115. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
116. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
117. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
118. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
119. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
120. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
121. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
122. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
123. C₄³×C₁₃	C₂²	semidirect
127. C₂×C₁₃×#41	C₂×C₄	semidirect
131. C₂²×D₄×C₁₃	C₂×C₄	semidirect
149. C₁₃×#124	C₂×C₄	semidirect
150. C₁₃×#123	C₂×C₄	semidirect
151. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
152. C₁₃×#121	C₂×C₄	semidirect
153. C₁₃×#121	C₂×C₄	semidirect
154. C₁₃×#120	C₂×C₄	semidirect
162. C₄×D₄×C₁₃	C₂×C₄	semidirect
163. C₄×D₄×C₁₃	C₂×C₄	semidirect
184. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
253. #34320	C₁₃	direct (N × H)
320. C₂²×C₄×C₁₃	#41	semidirect
381. C₁₃×C₂²⋊C₄	#41	semidirect
402. #2374	C₂×C₁₃	semidirect
403. #2367	C₂×C₁₃	semidirect
404. #2363	C₂×C₁₃	semidirect
405. #2363	C₂×C₁₃	semidirect
406. #2360	C₂×C₁₃	semidirect
407. #2358	C₂×C₁₃	semidirect
408. #2357	C₂×C₁₃	semidirect
409. #2352	C₂×C₁₃	semidirect
410. #2342	C₂×C₁₃	semidirect
411. #2341	C₂×C₁₃	semidirect
412. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
413. #2335	C₂×C₁₃	semidirect
414. #2333	C₂×C₁₃	semidirect
415. #2321	C₂×C₁₃	semidirect
416. C₄×#124	C₂×C₁₃	semidirect
417. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
418. C₄×#121	C₂×C₁₃	semidirect
419. #2297	C₂×C₁₃	semidirect
420. #2293	C₂×C₁₃	semidirect
421. C₂×#390	C₂×C₁₃	semidirect
422. #2273	C₂×C₁₃	semidirect
423. C₄²×D₄	C₂×C₁₃	semidirect
537. #546	C₄×C₁₃	semidirect
544. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
545. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
552. C₂×C₄×D₄	C₂²×C₁₃	semidirect
553. C₂×#117	C₂²×C₁₃	semidirect
554. C₂×#117	C₂²×C₁₃	semidirect
561. C₂²×C₄²	C₂²×C₁₃	semidirect
562. #391	C₂²×C₁₃	semidirect
563. #391	C₂²×C₁₃	semidirect
572. #390	C₂²×C₁₃	semidirect
573. #390	C₂²×C₁₃	semidirect
574. #390	C₂²×C₁₃	semidirect
575. #389	C₂²×C₁₃	semidirect
576. #389	C₂²×C₁₃	semidirect
577. #389	C₂²×C₁₃	semidirect
578. #388	C₂²×C₁₃	semidirect
579. #388	C₂²×C₁₃	semidirect
580. #388	C₂²×C₁₃	semidirect
581. #388	C₂²×C₁₃	semidirect
582. #388	C₂²×C₁₃	semidirect
583. #388	C₂²×C₁₃	semidirect
584. #388	C₂²×C₁₃	semidirect
585. #388	C₂²×C₁₃	semidirect
586. #388	C₂²×C₁₃	semidirect
587. #388	C₂²×C₁₃	semidirect
588. #388	C₂²×C₁₃	semidirect
589. #387	C₂²×C₁₃	semidirect
590. #387	C₂²×C₁₃	semidirect
591. #387	C₂²×C₁₃	semidirect
595. #386	C₂²×C₁₃	semidirect
596. #386	C₂²×C₁₃	semidirect
597. #386	C₂²×C₁₃	semidirect
598. #386	C₂²×C₁₃	semidirect
601. #385	C₂²×C₁₃	semidirect
602. #382	C₂²×C₁₃	semidirect
603. #381	C₂²×C₁₃	semidirect
605. #380	C₂²×C₁₃	semidirect
606. #380	C₂²×C₁₃	semidirect
608. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
609. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
610. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
611. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
612. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
613. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
614. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
621. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
622. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
623. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
624. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
625. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
626. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
627. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
628. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
629. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
630. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
631. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
632. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
633. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
634. C₄³	C₂²×C₁₃	semidirect
693. C₂×#41	C₂×C₄×C₁₃	semidirect
697. C₂²×D₄	C₂×C₄×C₁₃	semidirect
715. #124	C₂×C₄×C₁₃	semidirect
716. #123	C₂×C₄×C₁₃	semidirect
717. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
718. #121	C₂×C₄×C₁₃	semidirect
719. #121	C₂×C₄×C₁₃	semidirect
720. #120	C₂×C₄×C₁₃	semidirect
728. C₄×D₄	C₂×C₄×C₁₃	semidirect
729. C₄×D₄	C₂×C₄×C₁₃	semidirect
750. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
896. C₂²×C₄	C₁₃×#41	semidirect
957. C₂²⋊C₄	C₁₃×#41	semidirect
977. C₁₃	#34320	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×#546	2
C₁₃×#2374	2
C₁₃×#2367	2
C₁₃×#2363	2
C₁₃×#2360	2
C₁₃×#2358	2
C₁₃×#2357	2
C₁₃×#2352	2
C₁₃×#2342	2
C₁₃×#2341	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2335	2
C₁₃×#2333	2
C₁₃×#2321	2
C₄×C₁₃×#124	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#121	2
C₁₃×#2297	2
C₁₃×#2293	2
C₂×C₁₃×#390	2
C₁₃×#2273	2
C₄²×D₄×C₁₃	2
#34320	13

Subgroups — C13×#34320 #15720659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34320 #15720659