Subgroups — C₁₃×#34681 #15721020

Order 3328.

3700 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2472	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2464	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2461	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2452	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2424	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2416	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2392	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2388	C₂	1	2	yes	maximal, complemented
18	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₁₃×#120	C₂	1	2	yes	maximal, complemented
22	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
25	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
27	C₁₃×#532	—	2	8	no	—
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
32	C₁₃×#525	—	2	16	no	—
33	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#121	C₂²	1	2	yes	—
41	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
42	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#120	C₂²	1	2	yes	—
45	C₂×C₁₃×#120	C₂²	1	2	yes	—
46	C₂×C₁₃×#120	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₁₃	—	2	8	no	—
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
51	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
53	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
59	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
61	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
62	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
63	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
64	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
66	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
67	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#398	C₂²	1	2	yes	complemented
69	C₁₃×#397	C₂²	1	2	yes	complemented
70	C₁₃×#396	C₂²	1	2	yes	complemented
71	C₁₃×#396	C₂²	1	2	yes	complemented
72	C₁₃×#395	C₂²	1	2	yes	complemented
73	C₁₃×#394	C₂²	1	2	yes	—
74	C₁₃×#394	C₂²	1	2	yes	complemented
75	C₁₃×#394	C₂²	1	2	yes	complemented
76	C₁₃×#394	C₂²	1	2	yes	complemented
77	C₁₃×#394	C₂²	1	2	yes	complemented
78	C₁₃×#394	C₂²	1	2	yes	complemented
79	C₁₃×#393	C₂²	1	2	yes	complemented
80	C₁₃×#392	C₂²	1	2	yes	—
81	C₁₃×#392	C₂²	1	2	yes	—
82	C₁₃×#392	C₂²	1	2	yes	—
83	C₁₃×#392	C₂²	1	2	yes	complemented
84	C₁₃×#390	C₂²	1	1	yes	characteristic
85	C₁₃×#390	C₂²	1	1	yes	characteristic
86	C₁₃×#390	C₂²	1	1	yes	characteristic
87	C₁₃×#390	C₂²	1	1	yes	characteristic
88	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#390	C₂²	1	2	yes	complemented
91	C₁₃×#390	C₂²	1	2	yes	complemented
92	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#388	C₂²	1	2	yes	complemented
97	C₁₃×#388	C₂²	1	2	yes	complemented
98	C₁₃×#388	C₂²	1	2	yes	complemented
99	C₁₃×#388	C₂²	1	2	yes	complemented
100	C₁₃×#386	C₂²	1	2	yes	—
101	C₁₃×#386	C₂²	1	2	yes	—
102	C₁₃×#386	C₂²	1	2	yes	complemented
103	C₁₃×#386	C₂²	1	2	yes	complemented
104	C₁₃×#386	C₂²	1	2	yes	complemented
105	C₁₃×#385	C₂²	1	2	yes	—
106	C₁₃×#385	C₂²	1	2	yes	complemented
107	C₁₃×#385	C₂²	1	2	yes	complemented
108	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
109	C₁₃×#380	C₂²	1	1	yes	characteristic
110	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
111	C₁₃×#379	C₂²	1	2	yes	—
112	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
124	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
125	C₄³×C₁₃	C₂²	1	1	yes	characteristic, complemented
126	C₂⁵×C₁₃	C₂³	1	2	yes	—
127	C₂×C₁₃×#41	—	2	8	no	—
128	C₂×C₁₃×#41	—	2	8	no	—
129	C₂×C₁₃×#41	—	4	4	no	—
130	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
131	C₂²×D₄×C₁₃	—	2	4	no	—
132	C₂²×D₄×C₁₃	—	2	4	no	—
133	C₂²×D₄×C₁₃	—	2	4	no	—
134	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
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	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
140	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
142	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
143	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
144	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₁₃	—	2	8	no	—
148	C₂³×C₄×C₁₃	—	2	8	no	—
149	C₂³×C₄×C₁₃	—	4	4	no	—
150	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
152	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
153	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
156	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
157	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
158	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
159	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
160	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
161	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
162	C₁₃×C₄⋊Q₈	—	2	4	no	—
163	C₁₃×#127	—	2	4	no	—
164	C₁₃×#127	—	2	4	no	—
165	C₁₃×#124	—	2	8	no	—
166	C₁₃×#123	—	2	8	no	—
167	C₁₃×#123	—	2	8	no	—
168	C₁₃×C₂²⋊Q₈	—	2	8	no	—
169	C₁₃×C₂²⋊Q₈	—	2	8	no	—
170	C₁₃×#121	—	2	8	no	—
171	C₁₃×#121	—	2	4	no	—
172	C₁₃×#121	—	2	4	no	—
173	C₁₃×#121	—	2	4	no	—
174	C₁₃×#121	—	2	4	no	—
175	C₁₃×#121	—	2	8	no	—
176	C₁₃×#121	—	2	8	no	—
177	C₁₃×#120	—	2	8	no	—
178	C₁₃×#120	—	2	8	no	—
179	C₁₃×#120	—	2	8	no	—
180	C₄×D₄×C₁₃	—	2	4	no	—
181	C₄×D₄×C₁₃	—	2	8	no	—
182	C₄×D₄×C₁₃	—	2	8	no	—
183	C₄×D₄×C₁₃	—	2	8	no	—
184	C₄×D₄×C₁₃	—	2	8	no	—
185	C₄×D₄×C₁₃	—	2	4	no	—
186	C₄×D₄×C₁₃	—	2	4	no	—
187	C₄×D₄×C₁₃	—	2	8	no	—
188	C₄×D₄×C₁₃	—	2	4	no	—
189	C₄×D₄×C₁₃	—	2	4	no	—
190	C₄×D₄×C₁₃	—	2	4	no	—
191	C₄×D₄×C₁₃	—	2	8	no	—
192	C₄×D₄×C₁₃	—	4	4	no	—
193	C₄×D₄×C₁₃	D₄	1	8	yes	complemented
194	C₄×D₄×C₁₃	D₄	1	8	yes	complemented
195	C₁₃×#117	—	2	8	no	—
196	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
214	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
239	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₁₃	—	2	4	no	—
244	C₂×C₄²×C₁₃	—	2	4	no	—
245	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
246	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
247	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
248	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
249	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
250	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
251	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
252	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
253	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
254	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
255	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
256	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
257	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
258	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
259	C₁₃×#95	C₂³	1	1	yes	characteristic
260	C₁₃×#95	C₂³	1	1	yes	characteristic
261	C₁₃×#95	C₂³	1	1	yes	characteristic
262	C₁₃×#95	C₂³	1	1	yes	characteristic
263	C₁₃×#95	C₂³	1	1	yes	characteristic
264	C₁₃×#95	C₂³	1	1	yes	characteristic
265	C₁₃×#95	C₂³	1	2	yes	—
266	C₁₃×#95	C₂³	1	2	yes	—
267	C₁₃×#95	C₂³	1	2	yes	—
268	C₁₃×#95	C₂³	1	2	yes	—
269	C₁₃×#95	C₂³	1	2	yes	—
270	C₁₃×#95	C₂³	1	2	yes	—
271	C₁₃×#95	C₂³	1	2	yes	—
272	#34681	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂⁴×C₁₃	—	2	4	no	—
274	C₂⁴×C₁₃	—	2	4	no	—
275	C₂⁴×C₁₃	—	2	4	no	—
276	C₂⁴×C₁₃	—	2	4	no	—
277	C₂⁴×C₁₃	—	2	4	no	—
278	C₂⁴×C₁₃	—	4	2	no	—
279	C₂⁴×C₁₃	—	4	2	no	—
280	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
281	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
282	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
284	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₁₃×#41	—	4	32	no	—
286	C₂×Q₈×C₁₃	—	2	4	no	—
287	C₂×Q₈×C₁₃	—	2	4	no	—
288	C₂×Q₈×C₁₃	—	4	2	no	—
289	C₂×D₄×C₁₃	—	2	32	no	—
290	C₂×D₄×C₁₃	—	2	4	no	—
291	C₂×D₄×C₁₃	—	2	2	no	—
292	C₂×D₄×C₁₃	—	2	2	no	—
293	C₂×D₄×C₁₃	—	2	4	no	—
294	C₂×D₄×C₁₃	—	2	4	no	—
295	C₂×D₄×C₁₃	—	2	4	no	—
296	C₂×D₄×C₁₃	—	2	4	no	—
297	C₂×D₄×C₁₃	—	2	4	no	—
298	C₂×D₄×C₁₃	—	2	4	no	—
299	C₂×D₄×C₁₃	—	2	4	no	—
300	C₂×D₄×C₁₃	—	2	4	no	—
301	C₂×D₄×C₁₃	—	2	4	no	—
302	C₂×D₄×C₁₃	—	2	4	no	—
303	C₂×D₄×C₁₃	—	2	4	no	—
304	C₂×D₄×C₁₃	—	2	4	no	—
305	C₂×D₄×C₁₃	—	2	4	no	—
306	C₂×D₄×C₁₃	—	2	2	no	—
307	C₂×D₄×C₁₃	—	2	4	no	—
308	C₂×D₄×C₁₃	—	2	2	no	—
309	C₂×D₄×C₁₃	—	2	4	no	—
310	C₂×D₄×C₁₃	—	2	4	no	—
311	C₂×D₄×C₁₃	—	2	4	no	—
312	C₂×D₄×C₁₃	—	2	2	no	—
313	C₂×D₄×C₁₃	—	2	2	no	—
314	C₂×D₄×C₁₃	—	2	2	no	—
315	C₂×D₄×C₁₃	—	2	4	no	—
316	C₂×D₄×C₁₃	—	2	4	no	—
317	C₂×D₄×C₁₃	—	2	2	no	—
318	C₂×D₄×C₁₃	—	2	2	no	—
319	C₂×D₄×C₁₃	—	4	2	no	—
320	C₂×D₄×C₁₃	—	4	2	no	—
321	C₂×D₄×C₁₃	—	4	2	no	—
322	C₂×D₄×C₁₃	—	4	2	no	—
323	C₂×D₄×C₁₃	—	4	2	no	—
324	C₂×D₄×C₁₃	—	4	2	no	—
325	C₂×D₄×C₁₃	—	4	2	no	—
326	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
327	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
328	C₂×D₄×C₁₃	#41	1	4	yes	complemented
329	C₂²×C₄×C₁₃	—	2	2	no	—
330	C₂²×C₄×C₁₃	—	2	2	no	—
331	C₂²×C₄×C₁₃	—	2	2	no	—
332	C₂²×C₄×C₁₃	—	2	4	no	—
333	C₂²×C₄×C₁₃	—	2	2	no	—
334	C₂²×C₄×C₁₃	—	2	2	no	—
335	C₂²×C₄×C₁₃	—	2	4	no	—
336	C₂²×C₄×C₁₃	—	2	2	no	—
337	C₂²×C₄×C₁₃	—	2	4	no	—
338	C₂²×C₄×C₁₃	—	2	4	no	—
339	C₂²×C₄×C₁₃	—	2	2	no	—
340	C₂²×C₄×C₁₃	—	2	2	no	—
341	C₂²×C₄×C₁₃	—	2	2	no	—
342	C₂²×C₄×C₁₃	—	2	2	no	—
343	C₂²×C₄×C₁₃	—	2	4	no	—
344	C₂²×C₄×C₁₃	—	2	4	no	—
345	C₂²×C₄×C₁₃	—	2	4	no	—
346	C₂²×C₄×C₁₃	—	2	4	no	—
347	C₂²×C₄×C₁₃	—	2	4	no	—
348	C₂²×C₄×C₁₃	—	2	4	no	—
349	C₂²×C₄×C₁₃	—	2	4	no	—
350	C₂²×C₄×C₁₃	—	2	4	no	—
351	C₂²×C₄×C₁₃	—	2	2	no	—
352	C₂²×C₄×C₁₃	—	2	2	no	—
353	C₂²×C₄×C₁₃	—	2	2	no	—
354	C₂²×C₄×C₁₃	—	2	4	no	—
355	C₂²×C₄×C₁₃	—	2	4	no	—
356	C₂²×C₄×C₁₃	—	4	2	no	—
357	C₂²×C₄×C₁₃	—	4	2	no	—
358	C₂²×C₄×C₁₃	—	4	2	no	—
359	C₂²×C₄×C₁₃	—	4	1	no	—
360	C₂²×C₄×C₁₃	—	4	1	no	—
361	C₂²×C₄×C₁₃	—	4	32	no	—
362	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
363	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
364	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	complemented
365	C₂²×C₄×C₁₃	#41	1	4	yes	complemented
366	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
373	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
384	C₁₃×C₄⋊C₄	—	2	4	no	—
385	C₁₃×C₄⋊C₄	—	2	2	no	—
386	C₁₃×C₄⋊C₄	—	2	4	no	—
387	C₁₃×C₄⋊C₄	—	2	4	no	—
388	C₁₃×C₄⋊C₄	—	2	4	no	—
389	C₁₃×C₄⋊C₄	—	2	2	no	—
390	C₁₃×C₄⋊C₄	—	2	4	no	—
391	C₁₃×C₄⋊C₄	—	2	4	no	—
392	C₁₃×C₄⋊C₄	—	2	4	no	—
393	C₁₃×C₄⋊C₄	—	2	2	no	—
394	C₁₃×C₄⋊C₄	—	2	2	no	—
395	C₁₃×C₄⋊C₄	—	2	2	no	—
396	C₁₃×C₄⋊C₄	—	2	2	no	—
397	C₁₃×C₄⋊C₄	—	4	2	no	—
398	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
399	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
400	C₁₃×C₂²⋊C₄	—	2	4	no	—
401	C₁₃×C₂²⋊C₄	—	2	4	no	—
402	C₁₃×C₂²⋊C₄	—	2	4	no	—
403	C₁₃×C₂²⋊C₄	—	2	4	no	—
404	C₁₃×C₂²⋊C₄	—	2	2	no	—
405	C₁₃×C₂²⋊C₄	—	2	4	no	—
406	C₁₃×C₂²⋊C₄	—	2	4	no	—
407	C₁₃×C₂²⋊C₄	—	2	4	no	—
408	C₁₃×C₂²⋊C₄	—	2	4	no	—
409	C₁₃×C₂²⋊C₄	—	2	4	no	—
410	C₁₃×C₂²⋊C₄	—	2	4	no	—
411	C₁₃×C₂²⋊C₄	—	2	4	no	—
412	C₁₃×C₂²⋊C₄	—	2	4	no	—
413	C₁₃×C₂²⋊C₄	—	2	4	no	—
414	C₁₃×C₂²⋊C₄	—	2	4	no	—
415	C₁₃×C₂²⋊C₄	—	2	4	no	—
416	C₁₃×C₂²⋊C₄	—	2	2	no	—
417	C₁₃×C₂²⋊C₄	—	2	2	no	—
418	C₁₃×C₂²⋊C₄	—	2	4	no	—
419	C₁₃×C₂²⋊C₄	—	2	4	no	—
420	C₁₃×C₂²⋊C₄	—	2	4	no	—
421	C₁₃×C₂²⋊C₄	—	4	2	no	—
422	C₁₃×C₂²⋊C₄	—	4	2	no	—
423	C₁₃×C₂²⋊C₄	—	4	2	no	—
424	C₁₃×C₂²⋊C₄	—	4	2	no	—
425	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
426	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
427	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
428	C₁₃×C₂²⋊C₄	#41	1	4	yes	complemented
429	C₄²×C₁₃	—	2	2	no	—
430	C₄²×C₁₃	—	2	2	no	—
431	C₄²×C₁₃	—	2	2	no	—
432	C₄²×C₁₃	—	2	2	no	—
433	C₄²×C₁₃	—	2	2	no	—
434	C₄²×C₁₃	—	2	2	no	—
435	C₄²×C₁₃	—	2	4	no	—
436	C₄²×C₁₃	—	2	2	no	—
437	C₄²×C₁₃	—	2	2	no	—
438	C₄²×C₁₃	—	2	2	no	—
439	C₄²×C₁₃	—	2	2	no	—
440	C₄²×C₁₃	—	4	1	no	—
441	C₄²×C₁₃	C₂×D₄	1	4	yes	—
442	C₄²×C₁₃	C₂×D₄	1	4	yes	complemented
443	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
444	C₂×#525	C₂×C₁₃	1	2	yes	complemented
445	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
446	#2472	C₂×C₁₃	1	2	yes	complemented
447	#2464	C₂×C₁₃	1	2	yes	complemented
448	#2461	C₂×C₁₃	1	2	yes	complemented
449	#2452	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#2445	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#2440	C₂×C₁₃	1	1	yes	characteristic, complemented
452	#2433	C₂×C₁₃	1	1	yes	characteristic, complemented
453	#2428	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#2424	C₂×C₁₃	1	2	yes	complemented
455	#2422	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#2416	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#2408	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#2392	C₂×C₁₃	1	2	yes	complemented
459	#2388	C₂×C₁₃	1	2	yes	complemented
460	C₄×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
461	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
462	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
463	C₄×#120	C₂×C₁₃	1	2	yes	complemented
464	#2293	C₂×C₁₃	1	1	yes	characteristic, complemented
465	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
466	C₂³×C₁₃	—	2	1	no	—
467	C₂³×C₁₃	—	2	1	no	—
468	C₂³×C₁₃	—	2	1	no	—
469	C₂³×C₁₃	—	2	1	no	—
470	C₂³×C₁₃	—	2	16	no	—
471	C₂³×C₁₃	—	2	2	no	—
472	C₂³×C₁₃	—	2	2	no	—
473	C₂³×C₁₃	—	2	2	no	—
474	C₂³×C₁₃	—	2	1	no	—
475	C₂³×C₁₃	—	2	1	no	—
476	C₂³×C₁₃	—	2	1	no	—
477	C₂³×C₁₃	—	2	2	no	—
478	C₂³×C₁₃	—	2	2	no	—
479	C₂³×C₁₃	—	2	1	no	—
480	C₂³×C₁₃	—	2	2	no	—
481	C₂³×C₁₃	—	2	2	no	—
482	C₂³×C₁₃	—	2	2	no	—
483	C₂³×C₁₃	—	2	2	no	—
484	C₂³×C₁₃	—	2	2	no	—
485	C₂³×C₁₃	—	2	1	no	—
486	C₂³×C₁₃	—	2	2	no	—
487	C₂³×C₁₃	—	2	1	no	—
488	C₂³×C₁₃	—	2	2	no	—
489	C₂³×C₁₃	—	2	2	no	—
490	C₂³×C₁₃	—	2	2	no	—
491	C₂³×C₁₃	—	2	2	no	—
492	C₂³×C₁₃	—	2	2	no	—
493	C₂³×C₁₃	—	2	2	no	—
494	C₂³×C₁₃	—	2	2	no	—
495	C₂³×C₁₃	—	2	2	no	—
496	C₂³×C₁₃	—	4	8	no	—
497	C₂³×C₁₃	—	4	8	no	—
498	C₂³×C₁₃	—	4	8	no	—
499	C₂³×C₁₃	—	4	8	no	—
500	C₂³×C₁₃	—	4	8	no	—
501	C₂³×C₁₃	—	4	8	no	—
502	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
503	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
504	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
505	C₂³×C₁₃	C₂×#41	1	4	yes	—
506	C₂³×C₁₃	C₂×#41	1	2	yes	—
507	C₂³×C₁₃	C₂×#41	1	2	yes	—
508	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
509	Q₈×C₁₃	—	4	8	no	—
510	D₄×C₁₃	—	2	16	no	—
511	D₄×C₁₃	—	2	8	no	—
512	D₄×C₁₃	—	2	8	no	—
513	D₄×C₁₃	—	2	8	no	—
514	D₄×C₁₃	—	4	8	no	—
515	D₄×C₁₃	—	4	8	no	—
516	D₄×C₁₃	—	4	8	no	—
517	D₄×C₁₃	—	4	8	no	—
518	D₄×C₁₃	—	4	8	no	—
519	D₄×C₁₃	—	4	8	no	—
520	D₄×C₁₃	—	4	8	no	—
521	D₄×C₁₃	—	4	8	no	—
522	D₄×C₁₃	—	4	4	no	—
523	C₂×C₄×C₁₃	—	2	1	no	—
524	C₂×C₄×C₁₃	—	2	1	no	—
525	C₂×C₄×C₁₃	—	2	1	no	—
526	C₂×C₄×C₁₃	—	2	1	no	—
527	C₂×C₄×C₁₃	—	2	2	no	—
528	C₂×C₄×C₁₃	—	2	1	no	—
529	C₂×C₄×C₁₃	—	2	1	no	—
530	C₂×C₄×C₁₃	—	2	1	no	—
531	C₂×C₄×C₁₃	—	2	1	no	—
532	C₂×C₄×C₁₃	—	2	1	no	—
533	C₂×C₄×C₁₃	—	2	1	no	—
534	C₂×C₄×C₁₃	—	2	1	no	—
535	C₂×C₄×C₁₃	—	2	1	no	—
536	C₂×C₄×C₁₃	—	2	2	no	—
537	C₂×C₄×C₁₃	—	2	1	no	—
538	C₂×C₄×C₁₃	—	2	1	no	—
539	C₂×C₄×C₁₃	—	2	1	no	—
540	C₂×C₄×C₁₃	—	2	1	no	—
541	C₂×C₄×C₁₃	—	2	8	no	—
542	C₂×C₄×C₁₃	—	2	8	no	—
543	C₂×C₄×C₁₃	—	2	16	no	—
544	C₂×C₄×C₁₃	—	2	8	no	—
545	C₂×C₄×C₁₃	—	2	1	no	—
546	C₂×C₄×C₁₃	—	2	1	no	—
547	C₂×C₄×C₁₃	—	2	2	no	—
548	C₂×C₄×C₁₃	—	2	2	no	—
549	C₂×C₄×C₁₃	—	2	2	no	—
550	C₂×C₄×C₁₃	—	2	2	no	—
551	C₂×C₄×C₁₃	—	2	2	no	—
552	C₂×C₄×C₁₃	—	2	2	no	—
553	C₂×C₄×C₁₃	—	2	1	no	—
554	C₂×C₄×C₁₃	—	2	1	no	—
555	C₂×C₄×C₁₃	—	2	2	no	—
556	C₂×C₄×C₁₃	—	2	1	no	—
557	C₂×C₄×C₁₃	—	2	1	no	—
558	C₂×C₄×C₁₃	—	2	2	no	—
559	C₂×C₄×C₁₃	—	2	2	no	—
560	C₂×C₄×C₁₃	—	2	1	no	—
561	C₂×C₄×C₁₃	—	2	2	no	—
562	C₂×C₄×C₁₃	—	2	2	no	—
563	C₂×C₄×C₁₃	—	2	1	no	—
564	C₂×C₄×C₁₃	—	2	1	no	—
565	C₂×C₄×C₁₃	—	2	2	no	—
566	C₂×C₄×C₁₃	—	4	4	no	—
567	C₂×C₄×C₁₃	—	4	8	no	—
568	C₂×C₄×C₁₃	—	4	4	no	—
569	C₂×C₄×C₁₃	—	4	8	no	—
570	C₂×C₄×C₁₃	—	4	8	no	—
571	C₂×C₄×C₁₃	—	4	4	no	—
572	C₂×C₄×C₁₃	—	4	8	no	—
573	C₂×C₄×C₁₃	—	4	8	no	—
574	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
575	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
576	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
577	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
578	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
579	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
580	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
581	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
582	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
583	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
584	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
585	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
586	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
587	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
588	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
589	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
590	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
591	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
592	#532	—	2	8	no	—
593	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
594	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
595	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
596	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
597	#525	—	2	16	no	—
598	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
599	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
600	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
601	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
602	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
603	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
604	C₂×#121	C₂²×C₁₃	1	2	yes	—
605	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
606	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
607	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
609	C₂×#120	C₂²×C₁₃	1	2	yes	—
610	C₂×#120	C₂²×C₁₃	1	2	yes	—
611	C₂×#120	C₂²×C₁₃	1	2	yes	—
612	C₂×C₄×D₄	—	2	8	no	—
613	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
614	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
615	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
616	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
617	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
618	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
619	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
620	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
621	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
622	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
623	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
624	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
625	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
626	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
627	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
628	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
629	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
630	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
631	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
632	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
633	#398	C₂²×C₁₃	1	2	yes	complemented
634	#397	C₂²×C₁₃	1	2	yes	complemented
635	#396	C₂²×C₁₃	1	2	yes	complemented
636	#396	C₂²×C₁₃	1	2	yes	complemented
637	#395	C₂²×C₁₃	1	2	yes	complemented
638	#394	C₂²×C₁₃	1	2	yes	—
639	#394	C₂²×C₁₃	1	2	yes	complemented
640	#394	C₂²×C₁₃	1	2	yes	complemented
641	#394	C₂²×C₁₃	1	2	yes	complemented
642	#394	C₂²×C₁₃	1	2	yes	complemented
643	#394	C₂²×C₁₃	1	2	yes	complemented
644	#393	C₂²×C₁₃	1	2	yes	complemented
645	#392	C₂²×C₁₃	1	2	yes	—
646	#392	C₂²×C₁₃	1	2	yes	—
647	#392	C₂²×C₁₃	1	2	yes	—
648	#392	C₂²×C₁₃	1	2	yes	complemented
649	#390	C₂²×C₁₃	1	1	yes	characteristic
650	#390	C₂²×C₁₃	1	1	yes	characteristic
651	#390	C₂²×C₁₃	1	1	yes	characteristic
652	#390	C₂²×C₁₃	1	1	yes	characteristic
653	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
654	#390	C₂²×C₁₃	1	2	yes	complemented
655	#390	C₂²×C₁₃	1	2	yes	complemented
656	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
657	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
658	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
659	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
660	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	#388	C₂²×C₁₃	1	2	yes	complemented
662	#388	C₂²×C₁₃	1	2	yes	complemented
663	#388	C₂²×C₁₃	1	2	yes	complemented
664	#388	C₂²×C₁₃	1	2	yes	complemented
665	#386	C₂²×C₁₃	1	2	yes	—
666	#386	C₂²×C₁₃	1	2	yes	—
667	#386	C₂²×C₁₃	1	2	yes	complemented
668	#386	C₂²×C₁₃	1	2	yes	complemented
669	#386	C₂²×C₁₃	1	2	yes	complemented
670	#385	C₂²×C₁₃	1	2	yes	—
671	#385	C₂²×C₁₃	1	2	yes	complemented
672	#385	C₂²×C₁₃	1	2	yes	complemented
673	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
674	#380	C₂²×C₁₃	1	1	yes	characteristic
675	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
676	#379	C₂²×C₁₃	1	2	yes	—
677	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
678	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
679	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
680	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
681	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
682	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
683	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
684	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
685	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
686	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
687	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
688	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
689	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
690	C₄³	C₂²×C₁₃	1	1	yes	characteristic, complemented
691	C₂²×C₁₃	—	2	2	no	—
692	C₂²×C₁₃	—	2	2	no	—
693	C₂²×C₁₃	—	2	2	no	—
694	C₂²×C₁₃	—	2	2	no	—
695	C₂²×C₁₃	—	2	2	no	—
696	C₂²×C₁₃	—	2	2	no	—
697	C₂²×C₁₃	—	2	4	no	—
698	C₂²×C₁₃	—	2	4	no	—
699	C₂²×C₁₃	—	2	2	no	—
700	C₂²×C₁₃	—	2	4	no	—
701	C₂²×C₁₃	—	2	2	no	—
702	C₂²×C₁₃	—	2	4	no	—
703	C₂²×C₁₃	—	2	2	no	—
704	C₂²×C₁₃	—	2	4	no	—
705	C₂²×C₁₃	—	2	4	no	—
706	C₂²×C₁₃	—	4	32	no	—
707	C₂²×C₁₃	—	4	1	no	—
708	C₂²×C₁₃	—	4	2	no	—
709	C₂²×C₁₃	—	4	2	no	—
710	C₂²×C₁₃	—	4	1	no	—
711	C₂²×C₁₃	—	4	2	no	—
712	C₂²×C₁₃	—	4	2	no	—
713	C₂²×C₁₃	—	4	2	no	—
714	C₂²×C₁₃	—	4	1	no	—
715	C₂²×C₁₃	—	4	2	no	—
716	C₂²×C₁₃	—	4	2	no	—
717	C₂²×C₁₃	—	4	1	no	—
718	C₂²×C₁₃	—	4	2	no	—
719	C₂²×C₁₃	—	4	2	no	—
720	C₂²×C₁₃	—	4	2	no	—
721	C₂²×C₁₃	—	4	2	no	—
722	C₂²×C₁₃	—	4	2	no	—
723	C₂²×C₁₃	—	4	2	no	—
724	C₂²×C₁₃	—	4	2	no	—
725	C₂²×C₁₃	—	4	2	no	—
726	C₂²×C₁₃	#532	1	4	yes	complemented
727	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
728	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
729	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
730	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
731	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
732	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
733	C₂²×C₁₃	#585	1	1	yes	characteristic
734	C₄×C₁₃	—	2	2	no	—
735	C₄×C₁₃	—	2	2	no	—
736	C₄×C₁₃	—	2	2	no	—
737	C₄×C₁₃	—	2	4	no	—
738	C₄×C₁₃	—	2	2	no	—
739	C₄×C₁₃	—	2	2	no	—
740	C₄×C₁₃	—	2	2	no	—
741	C₄×C₁₃	—	2	2	no	—
742	C₄×C₁₃	—	2	2	no	—
743	C₄×C₁₃	—	4	1	no	—
744	C₄×C₁₃	—	4	2	no	—
745	C₄×C₁₃	—	4	1	no	—
746	C₄×C₁₃	—	4	2	no	—
747	C₄×C₁₃	—	4	2	no	—
748	C₄×C₁₃	—	4	1	no	—
749	C₄×C₁₃	—	4	2	no	—
750	C₄×C₁₃	#525	1	4	yes	complemented
751	C₄×C₁₃	D₄²	1	4	yes	—
752	C₂⁵	C₂³×C₁₃	1	2	yes	—
753	C₂×#41	—	2	8	no	—
754	C₂×#41	—	2	8	no	—
755	C₂×#41	—	4	4	no	—
756	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
757	C₂²×D₄	—	2	4	no	—
758	C₂²×D₄	—	2	4	no	—
759	C₂²×D₄	—	2	4	no	—
760	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
761	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
762	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
763	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
764	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
765	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
766	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
767	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
768	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
769	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
770	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
771	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
772	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
773	C₂³×C₄	—	2	8	no	—
774	C₂³×C₄	—	2	8	no	—
775	C₂³×C₄	—	4	4	no	—
776	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
777	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
778	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
779	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
780	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
781	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
782	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
783	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
784	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
785	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
786	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
787	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
788	C₄⋊Q₈	—	2	4	no	—
789	#127	—	2	4	no	—
790	#127	—	2	4	no	—
791	#124	—	2	8	no	—
792	#123	—	2	8	no	—
793	#123	—	2	8	no	—
794	C₂²⋊Q₈	—	2	8	no	—
795	C₂²⋊Q₈	—	2	8	no	—
796	#121	—	2	8	no	—
797	#121	—	2	4	no	—
798	#121	—	2	4	no	—
799	#121	—	2	4	no	—
800	#121	—	2	4	no	—
801	#121	—	2	8	no	—
802	#121	—	2	8	no	—
803	#120	—	2	8	no	—
804	#120	—	2	8	no	—
805	#120	—	2	8	no	—
806	C₄×D₄	—	2	4	no	—
807	C₄×D₄	—	2	8	no	—
808	C₄×D₄	—	2	8	no	—
809	C₄×D₄	—	2	8	no	—
810	C₄×D₄	—	2	8	no	—
811	C₄×D₄	—	2	4	no	—
812	C₄×D₄	—	2	4	no	—
813	C₄×D₄	—	2	8	no	—
814	C₄×D₄	—	2	4	no	—
815	C₄×D₄	—	2	4	no	—
816	C₄×D₄	—	2	4	no	—
817	C₄×D₄	—	2	8	no	—
818	C₄×D₄	—	4	4	no	—
819	C₄×D₄	D₄×C₁₃	1	8	yes	complemented
820	C₄×D₄	D₄×C₁₃	1	8	yes	complemented
821	#117	—	2	8	no	—
822	C₂×C₄⋊C₄	—	2	4	no	—
823	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
824	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
825	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
826	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
827	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
828	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
829	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
830	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
831	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
832	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
833	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
834	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
835	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
836	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
837	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
838	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
839	C₂×C₂²⋊C₄	—	2	8	no	—
840	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
841	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
842	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
843	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
844	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
845	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
846	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
847	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
848	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
849	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
850	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
851	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
852	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
853	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
854	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
855	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
856	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
857	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
858	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
859	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
860	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
861	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
862	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
863	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
864	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
865	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
866	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
867	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
868	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
869	C₂×C₄²	—	2	4	no	—
870	C₂×C₄²	—	2	4	no	—
871	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
872	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
873	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
874	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
875	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
876	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
877	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
878	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
879	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
880	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
881	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
882	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
883	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
884	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
885	#95	C₂³×C₁₃	1	1	yes	characteristic
886	#95	C₂³×C₁₃	1	1	yes	characteristic
887	#95	C₂³×C₁₃	1	1	yes	characteristic
888	#95	C₂³×C₁₃	1	1	yes	characteristic
889	#95	C₂³×C₁₃	1	1	yes	characteristic
890	#95	C₂³×C₁₃	1	1	yes	characteristic
891	#95	C₂³×C₁₃	1	2	yes	—
892	#95	C₂³×C₁₃	1	2	yes	—
893	#95	C₂³×C₁₃	1	2	yes	—
894	#95	C₂³×C₁₃	1	2	yes	—
895	#95	C₂³×C₁₃	1	2	yes	—
896	#95	C₂³×C₁₃	1	2	yes	—
897	#95	C₂³×C₁₃	1	2	yes	—
898	C₂×C₁₃	—	2	4	no	—
899	C₂×C₁₃	—	4	2	no	—
900	C₂×C₁₃	—	4	4	no	—
901	C₂×C₁₃	—	4	4	no	—
902	C₂×C₁₃	—	8	2	no	—
903	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
904	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
905	C₂×C₁₃	#3460	1	1	yes	characteristic
906	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
907	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
908	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
909	C₂×C₁₃	#3481	1	1	yes	characteristic
910	C₂⁴	—	2	4	no	—
911	C₂⁴	—	2	4	no	—
912	C₂⁴	—	2	4	no	—
913	C₂⁴	—	2	4	no	—
914	C₂⁴	—	2	4	no	—
915	C₂⁴	—	4	2	no	—
916	C₂⁴	—	4	2	no	—
917	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
918	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
919	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
920	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
921	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
922	#41	—	4	32	no	—
923	C₂×Q₈	—	2	4	no	—
924	C₂×Q₈	—	2	4	no	—
925	C₂×Q₈	—	4	2	no	—
926	C₂×D₄	—	2	32	no	—
927	C₂×D₄	—	2	4	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	4	no	—
931	C₂×D₄	—	2	4	no	—
932	C₂×D₄	—	2	4	no	—
933	C₂×D₄	—	2	4	no	—
934	C₂×D₄	—	2	4	no	—
935	C₂×D₄	—	2	4	no	—
936	C₂×D₄	—	2	4	no	—
937	C₂×D₄	—	2	4	no	—
938	C₂×D₄	—	2	4	no	—
939	C₂×D₄	—	2	4	no	—
940	C₂×D₄	—	2	4	no	—
941	C₂×D₄	—	2	4	no	—
942	C₂×D₄	—	2	4	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	4	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	4	no	—
947	C₂×D₄	—	2	4	no	—
948	C₂×D₄	—	2	4	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	4	no	—
953	C₂×D₄	—	2	4	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	4	2	no	—
957	C₂×D₄	—	4	2	no	—
958	C₂×D₄	—	4	2	no	—
959	C₂×D₄	—	4	2	no	—
960	C₂×D₄	—	4	2	no	—
961	C₂×D₄	—	4	2	no	—
962	C₂×D₄	—	4	2	no	—
963	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
964	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
965	C₂×D₄	C₁₃×#41	1	4	yes	complemented
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	4	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	4	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	4	no	—
975	C₂²×C₄	—	2	4	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	4	no	—
981	C₂²×C₄	—	2	4	no	—
982	C₂²×C₄	—	2	4	no	—
983	C₂²×C₄	—	2	4	no	—
984	C₂²×C₄	—	2	4	no	—
985	C₂²×C₄	—	2	4	no	—
986	C₂²×C₄	—	2	4	no	—
987	C₂²×C₄	—	2	4	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	4	no	—
992	C₂²×C₄	—	2	4	no	—
993	C₂²×C₄	—	4	2	no	—
994	C₂²×C₄	—	4	2	no	—
995	C₂²×C₄	—	4	2	no	—
996	C₂²×C₄	—	4	1	no	—
997	C₂²×C₄	—	4	1	no	—
998	C₂²×C₄	—	4	32	no	—
999	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
1000	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
1001	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	complemented
1002	C₂²×C₄	C₁₃×#41	1	4	yes	complemented
1003	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1004	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1006	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1007	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1008	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1009	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1010	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1011	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1015	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1016	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1017	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1019	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1021	C₄⋊C₄	—	2	4	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	4	no	—
1024	C₄⋊C₄	—	2	4	no	—
1025	C₄⋊C₄	—	2	4	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	4	no	—
1028	C₄⋊C₄	—	2	4	no	—
1029	C₄⋊C₄	—	2	4	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	4	2	no	—
1035	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
1036	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	complemented
1037	C₂²⋊C₄	—	2	4	no	—
1038	C₂²⋊C₄	—	2	4	no	—
1039	C₂²⋊C₄	—	2	4	no	—
1040	C₂²⋊C₄	—	2	4	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	4	no	—
1043	C₂²⋊C₄	—	2	4	no	—
1044	C₂²⋊C₄	—	2	4	no	—
1045	C₂²⋊C₄	—	2	4	no	—
1046	C₂²⋊C₄	—	2	4	no	—
1047	C₂²⋊C₄	—	2	4	no	—
1048	C₂²⋊C₄	—	2	4	no	—
1049	C₂²⋊C₄	—	2	4	no	—
1050	C₂²⋊C₄	—	2	4	no	—
1051	C₂²⋊C₄	—	2	4	no	—
1052	C₂²⋊C₄	—	2	4	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	4	no	—
1056	C₂²⋊C₄	—	2	4	no	—
1057	C₂²⋊C₄	—	2	4	no	—
1058	C₂²⋊C₄	—	4	2	no	—
1059	C₂²⋊C₄	—	4	2	no	—
1060	C₂²⋊C₄	—	4	2	no	—
1061	C₂²⋊C₄	—	4	2	no	—
1062	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
1063	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
1064	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	complemented
1065	C₂²⋊C₄	C₁₃×#41	1	4	yes	complemented
1066	C₄²	—	2	2	no	—
1067	C₄²	—	2	2	no	—
1068	C₄²	—	2	2	no	—
1069	C₄²	—	2	2	no	—
1070	C₄²	—	2	2	no	—
1071	C₄²	—	2	2	no	—
1072	C₄²	—	2	4	no	—
1073	C₄²	—	2	2	no	—
1074	C₄²	—	2	2	no	—
1075	C₄²	—	2	2	no	—
1076	C₄²	—	2	2	no	—
1077	C₄²	—	4	1	no	—
1078	C₄²	C₂×D₄×C₁₃	1	4	yes	—
1079	C₄²	C₂×D₄×C₁₃	1	4	yes	complemented
1080	C₁₃	#34681	1	1	yes	characteristic, direct product factor, Sylow
1081	C₂³	—	2	1	no	—
1082	C₂³	—	2	1	no	—
1083	C₂³	—	2	1	no	—
1084	C₂³	—	2	1	no	—
1085	C₂³	—	2	16	no	—
1086	C₂³	—	2	2	no	—
1087	C₂³	—	2	2	no	—
1088	C₂³	—	2	2	no	—
1089	C₂³	—	2	1	no	—
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	2	2	no	—
1094	C₂³	—	2	1	no	—
1095	C₂³	—	2	2	no	—
1096	C₂³	—	2	2	no	—
1097	C₂³	—	2	2	no	—
1098	C₂³	—	2	2	no	—
1099	C₂³	—	2	2	no	—
1100	C₂³	—	2	1	no	—
1101	C₂³	—	2	2	no	—
1102	C₂³	—	2	1	no	—
1103	C₂³	—	2	2	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	2	2	no	—
1107	C₂³	—	2	2	no	—
1108	C₂³	—	2	2	no	—
1109	C₂³	—	2	2	no	—
1110	C₂³	—	2	2	no	—
1111	C₂³	—	4	8	no	—
1112	C₂³	—	4	8	no	—
1113	C₂³	—	4	8	no	—
1114	C₂³	—	4	8	no	—
1115	C₂³	—	4	8	no	—
1116	C₂³	—	4	8	no	—
1117	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
1118	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1119	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1120	C₂³	C₂×C₁₃×#41	1	4	yes	—
1121	C₂³	C₂×C₁₃×#41	1	2	yes	—
1122	C₂³	C₂×C₁₃×#41	1	2	yes	—
1123	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
1124	Q₈	—	4	8	no	—
1125	D₄	—	2	16	no	—
1126	D₄	—	2	8	no	—
1127	D₄	—	2	8	no	—
1128	D₄	—	2	8	no	—
1129	D₄	—	4	8	no	—
1130	D₄	—	4	8	no	—
1131	D₄	—	4	8	no	—
1132	D₄	—	4	8	no	—
1133	D₄	—	4	8	no	—
1134	D₄	—	4	8	no	—
1135	D₄	—	4	8	no	—
1136	D₄	—	4	8	no	—
1137	D₄	—	4	4	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	8	no	—
1157	C₂×C₄	—	2	8	no	—
1158	C₂×C₄	—	2	16	no	—
1159	C₂×C₄	—	2	8	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	2	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	4	8	no	—
1182	C₂×C₄	—	4	4	no	—
1183	C₂×C₄	—	4	8	no	—
1184	C₂×C₄	—	4	8	no	—
1185	C₂×C₄	—	4	4	no	—
1186	C₂×C₄	—	4	4	no	—
1187	C₂×C₄	—	4	8	no	—
1188	C₂×C₄	—	4	8	no	—
1189	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1190	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1191	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1192	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
1193	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1194	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1195	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1196	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1197	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1198	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1199	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1200	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1201	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1202	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1203	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	2	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	2	no	—
1210	C₂²	—	2	4	no	—
1211	C₂²	—	2	4	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	2	4	no	—
1214	C₂²	—	2	2	no	—
1215	C₂²	—	2	4	no	—
1216	C₂²	—	2	2	no	—
1217	C₂²	—	2	4	no	—
1218	C₂²	—	2	4	no	—
1219	C₂²	—	4	32	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	2	no	—
1222	C₂²	—	4	2	no	—
1223	C₂²	—	4	1	no	—
1224	C₂²	—	4	2	no	—
1225	C₂²	—	4	2	no	—
1226	C₂²	—	4	2	no	—
1227	C₂²	—	4	1	no	—
1228	C₂²	—	4	2	no	—
1229	C₂²	—	4	2	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	2	no	—
1232	C₂²	—	4	2	no	—
1233	C₂²	—	4	2	no	—
1234	C₂²	—	4	2	no	—
1235	C₂²	—	4	2	no	—
1236	C₂²	—	4	2	no	—
1237	C₂²	—	4	2	no	—
1238	C₂²	—	4	2	no	—
1239	C₂²	C₁₃×#532	1	4	yes	complemented
1240	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1241	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1242	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1243	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1244	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1245	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1246	C₂²	C₁₃×#585	1	1	yes	characteristic
1247	C₄	—	2	2	no	—
1248	C₄	—	2	2	no	—
1249	C₄	—	2	2	no	—
1250	C₄	—	2	4	no	—
1251	C₄	—	2	2	no	—
1252	C₄	—	2	2	no	—
1253	C₄	—	2	2	no	—
1254	C₄	—	2	2	no	—
1255	C₄	—	2	2	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	2	no	—
1258	C₄	—	4	1	no	—
1259	C₄	—	4	2	no	—
1260	C₄	—	4	2	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	4	2	no	—
1263	C₄	C₁₃×#525	1	4	yes	complemented
1264	C₄	D₄²×C₁₃	1	4	yes	—
1265	C₂	—	2	4	no	—
1266	C₂	—	4	4	no	—
1267	C₂	—	4	4	no	—
1268	C₂	—	4	2	no	—
1269	C₂	—	8	2	no	—
1270	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
1271	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
1272	C₂	C₁₃×#3460	1	1	yes	characteristic
1273	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
1274	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1275	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1276	C₂	C₁₃×#3481	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#532	C₂	semidirect
2. C₂×C₁₃×#525	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃	C₂	semidirect
4. C₁₃×#2472	C₂	semidirect
5. C₁₃×#2464	C₂	semidirect
6. C₁₃×#2461	C₂	semidirect
7. C₁₃×#2452	C₂	semidirect
8. C₁₃×#2445	C₂	semidirect
9. C₁₃×#2440	C₂	semidirect
10. C₁₃×#2433	C₂	semidirect
11. C₁₃×#2428	C₂	semidirect
12. C₁₃×#2424	C₂	semidirect
13. C₁₃×#2422	C₂	semidirect
14. C₁₃×#2416	C₂	semidirect
15. C₁₃×#2408	C₂	semidirect
16. C₁₃×#2392	C₂	semidirect
17. C₁₃×#2388	C₂	semidirect
18. C₄×C₁₃×#127	C₂	semidirect
19. C₄×C₁₃×#121	C₂	semidirect
20. C₄×C₁₃×#121	C₂	semidirect
21. C₄×C₁₃×#120	C₂	semidirect
22. C₁₃×#2293	C₂	semidirect
23. C₄²×D₄×C₁₃	C₂	semidirect
24. C₂²×C₁₃×#41	C₂²	semidirect
28. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₁₃×#124	C₂²	semidirect
33. C₂×C₁₃×#123	C₂²	semidirect
34. C₂×C₁₃×#123	C₂²	semidirect
36. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
41. C₂×C₁₃×#121	C₂²	semidirect
42. C₂×C₁₃×#121	C₂²	semidirect
43. C₂×C₁₃×#121	C₂²	semidirect
58. C₂×C₄×D₄×C₁₃	C₂²	semidirect
59. C₂×C₄×D₄×C₁₃	C₂²	semidirect
60. C₂×C₄×D₄×C₁₃	C₂²	semidirect
61. C₂×C₄×D₄×C₁₃	C₂²	semidirect
62. C₂×C₄×D₄×C₁₃	C₂²	semidirect
63. C₂×C₁₃×#117	C₂²	semidirect
67. C₂²×C₄²×C₁₃	C₂²	semidirect
68. C₁₃×#398	C₂²	semidirect
69. C₁₃×#397	C₂²	semidirect
70. C₁₃×#396	C₂²	semidirect
71. C₁₃×#396	C₂²	semidirect
72. C₁₃×#395	C₂²	semidirect
74. C₁₃×#394	C₂²	semidirect
75. C₁₃×#394	C₂²	semidirect
76. C₁₃×#394	C₂²	semidirect
77. C₁₃×#394	C₂²	semidirect
78. C₁₃×#394	C₂²	semidirect
79. C₁₃×#393	C₂²	semidirect
83. C₁₃×#392	C₂²	semidirect
88. C₁₃×#390	C₂²	semidirect
89. C₁₃×#390	C₂²	semidirect
90. C₁₃×#390	C₂²	semidirect
91. C₁₃×#390	C₂²	semidirect
92. C₁₃×#389	C₂²	semidirect
93. C₁₃×#389	C₂²	semidirect
94. C₁₃×#389	C₂²	semidirect
95. C₁₃×#389	C₂²	semidirect
96. C₁₃×#388	C₂²	semidirect
97. C₁₃×#388	C₂²	semidirect
98. C₁₃×#388	C₂²	semidirect
99. C₁₃×#388	C₂²	semidirect
102. C₁₃×#386	C₂²	semidirect
103. C₁₃×#386	C₂²	semidirect
104. C₁₃×#386	C₂²	semidirect
106. C₁₃×#385	C₂²	semidirect
107. C₁₃×#385	C₂²	semidirect
108. C₁₃×#384	C₂²	semidirect
110. C₁₃×#380	C₂²	semidirect
112. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
113. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
114. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
115. C₄×C₁₃×C₄⋊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. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
124. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
125. C₄³×C₁₃	C₂²	semidirect
193. C₄×D₄×C₁₃	D₄	semidirect
194. C₄×D₄×C₁₃	D₄	semidirect
272. #34681	C₁₃	direct (N × H)
328. C₂×D₄×C₁₃	#41	semidirect
364. C₂²×C₄×C₁₃	C₂×D₄	semidirect
365. C₂²×C₄×C₁₃	#41	semidirect
399. C₁₃×C₄⋊C₄	C₂×D₄	semidirect
427. C₁₃×C₂²⋊C₄	C₂×D₄	semidirect
428. C₁₃×C₂²⋊C₄	#41	semidirect
442. C₄²×C₁₃	C₂×D₄	semidirect
443. C₂×#532	C₂×C₁₃	semidirect
444. C₂×#525	C₂×C₁₃	semidirect
445. C₂²×C₄×D₄	C₂×C₁₃	semidirect
446. #2472	C₂×C₁₃	semidirect
447. #2464	C₂×C₁₃	semidirect
448. #2461	C₂×C₁₃	semidirect
449. #2452	C₂×C₁₃	semidirect
450. #2445	C₂×C₁₃	semidirect
451. #2440	C₂×C₁₃	semidirect
452. #2433	C₂×C₁₃	semidirect
453. #2428	C₂×C₁₃	semidirect
454. #2424	C₂×C₁₃	semidirect
455. #2422	C₂×C₁₃	semidirect
456. #2416	C₂×C₁₃	semidirect
457. #2408	C₂×C₁₃	semidirect
458. #2392	C₂×C₁₃	semidirect
459. #2388	C₂×C₁₃	semidirect
460. C₄×#127	C₂×C₁₃	semidirect
461. C₄×#121	C₂×C₁₃	semidirect
462. C₄×#121	C₂×C₁₃	semidirect
463. C₄×#120	C₂×C₁₃	semidirect
464. #2293	C₂×C₁₃	semidirect
465. C₄²×D₄	C₂×C₁₃	semidirect
589. C₂²×#41	C₂²×C₁₃	semidirect
593. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
596. C₂×#124	C₂²×C₁₃	semidirect
598. C₂×#123	C₂²×C₁₃	semidirect
599. C₂×#123	C₂²×C₁₃	semidirect
601. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
606. C₂×#121	C₂²×C₁₃	semidirect
607. C₂×#121	C₂²×C₁₃	semidirect
608. C₂×#121	C₂²×C₁₃	semidirect
623. C₂×C₄×D₄	C₂²×C₁₃	semidirect
624. C₂×C₄×D₄	C₂²×C₁₃	semidirect
625. C₂×C₄×D₄	C₂²×C₁₃	semidirect
626. C₂×C₄×D₄	C₂²×C₁₃	semidirect
627. C₂×C₄×D₄	C₂²×C₁₃	semidirect
628. C₂×#117	C₂²×C₁₃	semidirect
632. C₂²×C₄²	C₂²×C₁₃	semidirect
633. #398	C₂²×C₁₃	semidirect
634. #397	C₂²×C₁₃	semidirect
635. #396	C₂²×C₁₃	semidirect
636. #396	C₂²×C₁₃	semidirect
637. #395	C₂²×C₁₃	semidirect
639. #394	C₂²×C₁₃	semidirect
640. #394	C₂²×C₁₃	semidirect
641. #394	C₂²×C₁₃	semidirect
642. #394	C₂²×C₁₃	semidirect
643. #394	C₂²×C₁₃	semidirect
644. #393	C₂²×C₁₃	semidirect
648. #392	C₂²×C₁₃	semidirect
653. #390	C₂²×C₁₃	semidirect
654. #390	C₂²×C₁₃	semidirect
655. #390	C₂²×C₁₃	semidirect
656. #390	C₂²×C₁₃	semidirect
657. #389	C₂²×C₁₃	semidirect
658. #389	C₂²×C₁₃	semidirect
659. #389	C₂²×C₁₃	semidirect
660. #389	C₂²×C₁₃	semidirect
661. #388	C₂²×C₁₃	semidirect
662. #388	C₂²×C₁₃	semidirect
663. #388	C₂²×C₁₃	semidirect
664. #388	C₂²×C₁₃	semidirect
667. #386	C₂²×C₁₃	semidirect
668. #386	C₂²×C₁₃	semidirect
669. #386	C₂²×C₁₃	semidirect
671. #385	C₂²×C₁₃	semidirect
672. #385	C₂²×C₁₃	semidirect
673. #384	C₂²×C₁₃	semidirect
675. #380	C₂²×C₁₃	semidirect
677. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
678. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
679. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
680. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
684. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
685. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
686. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
687. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
688. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
689. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
690. C₄³	C₂²×C₁₃	semidirect
726. C₂²×C₁₃	#532	semidirect
750. C₄×C₁₃	#525	semidirect
819. C₄×D₄	D₄×C₁₃	semidirect
820. C₄×D₄	D₄×C₁₃	semidirect
965. C₂×D₄	C₁₃×#41	semidirect
1001. C₂²×C₄	C₂×D₄×C₁₃	semidirect
1002. C₂²×C₄	C₁₃×#41	semidirect
1036. C₄⋊C₄	C₂×D₄×C₁₃	semidirect
1064. C₂²⋊C₄	C₂×D₄×C₁₃	semidirect
1065. C₂²⋊C₄	C₁₃×#41	semidirect
1079. C₄²	C₂×D₄×C₁₃	semidirect
1080. C₁₃	#34681	direct (N × H)
1239. C₂²	C₁₃×#532	semidirect
1263. C₄	C₁₃×#525	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#532	2
C₂×C₁₃×#525	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2472	2
C₁₃×#2464	2
C₁₃×#2461	2
C₁₃×#2452	2
C₁₃×#2445	2
C₁₃×#2440	2
C₁₃×#2433	2
C₁₃×#2428	2
C₁₃×#2424	2
C₁₃×#2422	2
C₁₃×#2416	2
C₁₃×#2408	2
C₁₃×#2392	2
C₁₃×#2388	2
C₄×C₁₃×#127	2
C₄×C₁₃×#121	2
C₄×C₁₃×#120	2
C₁₃×#2293	2
C₄²×D₄×C₁₃	2
#34681	13

Subgroups — C13×#34681 #15721020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34681 #15721020