Subgroups — C₁₃×#60766 #15747105

Order 3328.

2140 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3202	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3201	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3200	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3198	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3197	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3196	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3191	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3190	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
33	D₄×Q₈×C₁₃	—	2	1	no	—
34	C₁₃×#548	—	2	1	no	—
35	C₁₃×#547	—	2	2	no	—
36	C₁₃×#547	—	2	1	no	—
37	C₁₃×#546	—	2	2	no	—
38	C₁₃×#546	—	2	1	no	—
39	C₁₃×#537	C₂²	1	1	yes	characteristic
40	C₁₃×#537	C₂²	1	1	yes	characteristic
41	C₁₃×#537	C₂²	1	1	yes	characteristic
42	C₁₃×#537	C₂²	1	1	yes	characteristic
43	C₁₃×#537	C₂²	1	2	yes	—
44	C₁₃×#537	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#536	—	2	1	no	—
46	C₁₃×#536	C₂²	1	2	yes	—
47	C₁₃×#536	C₂²	1	2	yes	—
48	C₁₃×#536	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#535	—	2	1	no	—
50	C₁₃×#535	C₂²	1	2	yes	—
51	C₁₃×#534	—	2	2	no	—
52	C₁₃×#532	—	2	2	no	—
53	C₁₃×#525	—	2	1	no	—
54	C₁₃×#525	—	2	1	no	—
55	C₁₃×#525	C₂²	1	1	yes	characteristic
56	C₁₃×#525	C₂²	1	2	yes	—
57	C₁₃×#525	C₂²	1	2	yes	—
58	C₁₃×#525	C₂²	1	2	yes	complemented
59	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₁₃×#520	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
63	C₁₃×#485	C₂²	1	2	yes	complemented
64	C₁₃×#485	C₂²	1	2	yes	complemented
65	C₁₃×#485	C₂²	1	2	yes	complemented
66	C₁₃×#485	C₂²	1	2	yes	complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#485	C₂²	1	2	yes	complemented
69	C₁₃×#485	C₂²	1	2	yes	complemented
70	C₁₃×#485	C₂²	1	2	yes	complemented
71	C₁₃×#484	C₂²	1	2	yes	complemented
72	C₁₃×#483	C₂²	1	2	yes	complemented
73	C₁₃×#482	C₂²	1	2	yes	complemented
74	C₁₃×#482	C₂²	1	2	yes	complemented
75	C₁₃×#482	C₂²	1	2	yes	complemented
76	C₁₃×#482	C₂²	1	2	yes	complemented
77	C₁₃×#481	C₂²	1	2	yes	complemented
78	C₁₃×#480	C₂²	1	2	yes	complemented
79	C₁₃×#470	C₂²	1	2	yes	complemented
80	C₁₃×#470	C₂²	1	2	yes	complemented
81	C₁₃×#470	C₂²	1	2	yes	complemented
82	C₁₃×#469	C₂²	1	2	yes	complemented
83	C₁₃×#468	C₂²	1	2	yes	complemented
84	C₁₃×#468	C₂²	1	2	yes	complemented
85	C₁₃×#468	C₂²	1	2	yes	complemented
86	C₁₃×#468	C₂²	1	2	yes	complemented
87	C₁₃×#467	C₂²	1	2	yes	complemented
88	C₁₃×#467	C₂²	1	2	yes	complemented
89	C₁₃×#467	C₂²	1	2	yes	complemented
90	C₁₃×#466	C₂²	1	2	yes	complemented
91	C₁₃×#465	C₂²	1	2	yes	complemented
92	C₁₃×#465	C₂²	1	2	yes	complemented
93	C₁₃×#465	C₂²	1	2	yes	complemented
94	C₁₃×#465	C₂²	1	2	yes	complemented
95	C₁₃×#452	C₂²	1	2	yes	—
96	C₁₃×#452	C₂²	1	2	yes	—
97	C₁₃×#452	C₂²	1	1	yes	characteristic
98	C₁₃×#452	C₂²	1	1	yes	characteristic
99	C₁₃×#452	C₂²	1	2	yes	complemented
100	C₁₃×#452	C₂²	1	2	yes	complemented
101	C₁₃×#451	C₂²	1	2	yes	complemented
102	C₁₃×#451	C₂²	1	2	yes	complemented
103	C₁₃×#451	C₂²	1	2	yes	complemented
104	C₁₃×#451	C₂²	1	1	yes	characteristic, complemented
105	C₁₃×#450	C₂²	1	2	yes	complemented
106	C₁₃×#450	C₂²	1	1	yes	characteristic, complemented
107	C₁₃×#449	C₂²	1	1	yes	characteristic
108	C₁₃×#449	C₂²	1	1	yes	characteristic
109	C₁₃×#449	C₂²	1	2	yes	complemented
110	C₁₃×#449	C₂²	1	2	yes	complemented
111	C₁₃×#448	C₂²	1	2	yes	complemented
112	C₁₃×#448	C₂²	1	2	yes	complemented
113	C₁₃×#448	C₂²	1	1	yes	characteristic, complemented
114	C₁₃×#447	C₂²	1	1	yes	characteristic, complemented
115	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
116	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
119	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
120	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
121	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
122	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
123	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
124	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#408	C₂²	1	2	yes	—
128	C₁₃×#408	C₂²	1	2	yes	—
129	C₁₃×#408	C₂²	1	1	yes	characteristic, complemented
130	C₁₃×#408	C₂²	1	1	yes	characteristic, complemented
131	C₁₃×#407	C₂²	1	1	yes	characteristic
132	C₁₃×#407	C₂²	1	2	yes	complemented
133	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	C₁₃×2₋¹⁺⁴	—	4	2	no	—
136	C₁₃×2₋¹⁺⁴	—	4	2	no	—
137	C₂×C₁₃×#41	—	2	1	no	—
138	C₂×C₁₃×#41	—	2	2	no	—
139	C₂×C₁₃×#41	—	2	1	no	—
140	C₂×C₁₃×#41	—	2	1	no	—
141	C₂×C₁₃×#41	—	4	2	no	—
142	C₂×C₁₃×#41	—	4	2	no	—
143	C₂×C₁₃×#41	—	4	2	no	—
144	C₂×C₁₃×#41	—	4	2	no	—
145	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
146	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
147	C₂×C₁₃×#41	D₄	1	2	yes	—
148	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×#41	C₂³	1	2	yes	—
154	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×#41	C₂³	1	2	yes	—
157	C₂²×Q₈×C₁₃	—	2	1	no	—
158	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
159	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
160	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
161	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
162	C₂²×D₄×C₁₃	—	2	1	no	—
163	C₂²×D₄×C₁₃	D₄	1	2	yes	—
164	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
165	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
166	C₂³×C₄×C₁₃	—	2	1	no	—
167	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
168	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
169	C₁₃×#137	—	4	2	no	—
170	C₁₃×#137	—	4	2	no	—
171	C₁₃×#135	—	4	2	no	—
172	C₁₃×#135	—	4	2	no	—
173	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
174	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
176	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
177	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
178	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
179	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
180	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
181	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
182	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
183	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
184	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
185	C₁₃×#131	—	4	2	no	—
186	C₁₃×#131	—	4	2	no	—
187	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
188	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
189	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
190	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
191	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
192	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
193	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
194	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
195	C₁₃×C₄⋊Q₈	—	2	2	no	—
196	C₁₃×C₄⋊Q₈	—	2	2	no	—
197	C₁₃×C₄⋊Q₈	—	2	1	no	—
198	C₁₃×#127	—	2	2	no	—
199	C₁₃×#124	—	2	2	no	—
200	C₁₃×#124	—	2	2	no	—
201	C₁₃×#124	—	2	2	no	—
202	C₁₃×#124	—	2	1	no	—
203	C₁₃×#123	—	2	2	no	—
204	C₁₃×#123	—	2	2	no	—
205	C₁₃×#123	—	2	2	no	—
206	C₁₃×#123	—	2	2	no	—
207	C₁₃×#123	—	2	2	no	—
208	C₁₃×#123	—	2	2	no	—
209	C₁₃×#123	—	2	2	no	—
210	C₁₃×#123	—	2	1	no	—
211	C₁₃×#123	—	2	2	no	—
212	C₁₃×C₂²⋊Q₈	—	2	1	no	—
213	C₁₃×C₂²⋊Q₈	—	2	1	no	—
214	C₁₃×C₂²⋊Q₈	—	2	1	no	—
215	C₁₃×C₂²⋊Q₈	—	2	1	no	—
216	C₁₃×C₂²⋊Q₈	—	2	2	no	—
217	C₁₃×C₂²⋊Q₈	—	2	1	no	—
218	C₁₃×C₂²⋊Q₈	—	2	1	no	—
219	C₁₃×C₂²⋊Q₈	—	2	1	no	—
220	C₁₃×C₂²⋊Q₈	—	2	2	no	—
221	C₁₃×C₂²⋊Q₈	—	2	2	no	—
222	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
227	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
229	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
230	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
231	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
232	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
233	C₁₃×#121	—	2	1	no	—
234	C₁₃×#121	—	2	1	no	—
235	C₁₃×#121	—	2	1	no	—
236	C₁₃×#121	—	2	1	no	—
237	C₁₃×#121	—	2	2	no	—
238	C₁₃×#121	—	2	2	no	—
239	C₁₃×#121	—	2	2	no	—
240	C₁₃×#121	—	2	2	no	—
241	C₁₃×#121	—	2	2	no	—
242	C₁₃×#121	—	2	2	no	—
243	C₁₃×#121	—	2	2	no	—
244	C₁₃×#121	—	2	2	no	—
245	C₁₃×#121	—	2	1	no	—
246	C₁₃×#121	C₂³	1	1	yes	characteristic
247	C₁₃×#121	C₂³	1	2	yes	—
248	C₁₃×#121	C₂³	1	2	yes	—
249	C₁₃×#121	C₂³	1	1	yes	characteristic
250	C₁₃×#121	C₂³	1	2	yes	—
251	C₁₃×#121	C₂³	1	2	yes	—
252	C₁₃×#121	C₂³	1	2	yes	—
253	C₁₃×#120	—	2	2	no	—
254	C₁₃×#120	—	2	2	no	—
255	C₁₃×#120	—	2	1	no	—
256	C₁₃×#120	—	2	2	no	—
257	C₁₃×#120	—	2	2	no	—
258	C₁₃×#120	—	2	2	no	—
259	C₄×Q₈×C₁₃	—	2	1	no	—
260	C₄×D₄×C₁₃	—	2	2	no	—
261	C₄×D₄×C₁₃	—	2	1	no	—
262	C₄×D₄×C₁₃	—	2	2	no	—
263	C₄×D₄×C₁₃	—	2	2	no	—
264	C₄×D₄×C₁₃	—	2	2	no	—
265	C₄×D₄×C₁₃	—	2	2	no	—
266	C₄×D₄×C₁₃	—	2	1	no	—
267	C₄×D₄×C₁₃	—	2	1	no	—
268	C₄×D₄×C₁₃	—	2	2	no	—
269	C₄×D₄×C₁₃	—	2	2	no	—
270	C₁₃×#117	—	2	1	no	—
271	C₁₃×#117	—	2	1	no	—
272	C₁₃×#117	C₂³	1	1	yes	characteristic
273	C₁₃×#117	C₂³	1	2	yes	—
274	C₁₃×#117	C₂³	1	2	yes	—
275	C₁₃×#117	C₂³	1	2	yes	—
276	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
282	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₄²×C₁₃	—	2	1	no	—
286	C₁₃×#107	C₂³	1	2	yes	—
287	C₁₃×#107	C₂³	1	2	yes	—
288	C₁₃×#107	C₂³	1	2	yes	—
289	C₁₃×#107	C₂³	1	2	yes	—
290	C₁₃×#106	C₂³	1	2	yes	—
291	C₁₃×#106	C₂³	1	2	yes	—
292	C₁₃×#106	C₂³	1	2	yes	—
293	C₁₃×#106	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	2	yes	—
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#103	C₂³	1	2	yes	—
298	C₁₃×#103	C₂³	1	1	yes	characteristic
299	C₁₃×#103	C₂³	1	1	yes	characteristic
300	C₁₃×#103	C₂³	1	1	yes	characteristic
301	C₁₃×#103	C₂³	1	1	yes	characteristic
302	C₁₃×#103	C₂³	1	2	yes	—
303	C₁₃×#103	C₂³	1	2	yes	—
304	C₁₃×#103	C₂³	1	2	yes	—
305	C₁₃×#103	C₂³	1	2	yes	—
306	C₁₃×#102	C₂³	1	1	yes	characteristic
307	C₁₃×#102	C₂³	1	1	yes	characteristic
308	C₁₃×#102	C₂³	1	1	yes	characteristic
309	C₁₃×#102	C₂³	1	1	yes	characteristic
310	C₁₃×#102	C₂³	1	2	yes	—
311	C₁₃×#102	C₂³	1	2	yes	—
312	C₁₃×#102	C₂³	1	2	yes	—
313	C₁₃×#102	C₂³	1	2	yes	—
314	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
315	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
316	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
317	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
318	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
321	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
322	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
323	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
324	#60766	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
325	C₂⁴×C₁₃	—	2	1	no	—
326	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
327	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
328	C₁₃×#41	—	2	2	no	—
329	C₁₃×#41	—	2	2	no	—
330	C₁₃×#41	—	2	2	no	—
331	C₁₃×#41	—	2	2	no	—
332	C₁₃×#41	—	2	2	no	—
333	C₁₃×#41	—	2	2	no	—
334	C₁₃×#41	—	2	2	no	—
335	C₁₃×#41	—	2	2	no	—
336	C₁₃×#41	—	2	2	no	—
337	C₁₃×#41	—	2	2	no	—
338	C₁₃×#41	—	4	2	no	—
339	C₁₃×#41	—	4	2	no	—
340	C₁₃×#41	—	4	4	no	—
341	C₁₃×#41	—	4	2	no	—
342	C₁₃×#41	—	4	2	no	—
343	C₁₃×#41	—	4	1	no	—
344	C₁₃×#41	—	4	1	no	—
345	C₁₃×#41	—	4	1	no	—
346	C₁₃×#41	—	4	1	no	—
347	C₁₃×#41	—	4	2	no	—
348	C₁₃×#41	—	4	2	no	—
349	C₁₃×#41	—	4	4	no	—
350	C₁₃×#41	—	4	4	no	—
351	C₁₃×#41	—	4	8	no	—
352	C₁₃×#41	—	4	4	no	—
353	C₂×Q₈×C₁₃	—	2	2	no	—
354	C₂×Q₈×C₁₃	—	2	1	no	—
355	C₂×Q₈×C₁₃	—	2	1	no	—
356	C₂×Q₈×C₁₃	—	2	2	no	—
357	C₂×Q₈×C₁₃	—	2	2	no	—
358	C₂×Q₈×C₁₃	—	4	2	no	—
359	C₂×Q₈×C₁₃	—	4	1	no	—
360	C₂×Q₈×C₁₃	—	4	1	no	—
361	C₂×Q₈×C₁₃	—	4	2	no	—
362	C₂×Q₈×C₁₃	—	4	2	no	—
363	C₂×Q₈×C₁₃	—	4	4	no	—
364	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
365	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
366	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
367	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
368	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
369	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
370	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₂×D₄×C₁₃	—	2	1	no	—
372	C₂×D₄×C₁₃	—	2	1	no	—
373	C₂×D₄×C₁₃	—	2	1	no	—
374	C₂×D₄×C₁₃	—	2	2	no	—
375	C₂×D₄×C₁₃	—	2	1	no	—
376	C₂×D₄×C₁₃	—	2	1	no	—
377	C₂×D₄×C₁₃	—	2	1	no	—
378	C₂×D₄×C₁₃	—	2	2	no	—
379	C₂×D₄×C₁₃	—	2	2	no	—
380	C₂×D₄×C₁₃	—	2	2	no	—
381	C₂×D₄×C₁₃	—	2	2	no	—
382	C₂×D₄×C₁₃	—	2	1	no	—
383	C₂×D₄×C₁₃	—	2	2	no	—
384	C₂×D₄×C₁₃	—	2	1	no	—
385	C₂×D₄×C₁₃	—	4	2	no	—
386	C₂×D₄×C₁₃	—	4	1	no	—
387	C₂×D₄×C₁₃	—	4	1	no	—
388	C₂×D₄×C₁₃	—	4	4	no	—
389	C₂×D₄×C₁₃	—	4	4	no	—
390	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
391	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
392	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
393	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
394	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
395	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
396	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
397	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
398	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
399	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₁₃	—	2	2	no	—
401	C₂²×C₄×C₁₃	—	2	2	no	—
402	C₂²×C₄×C₁₃	—	2	2	no	—
403	C₂²×C₄×C₁₃	—	2	1	no	—
404	C₂²×C₄×C₁₃	—	2	1	no	—
405	C₂²×C₄×C₁₃	—	2	1	no	—
406	C₂²×C₄×C₁₃	—	2	1	no	—
407	C₂²×C₄×C₁₃	—	2	2	no	—
408	C₂²×C₄×C₁₃	—	2	1	no	—
409	C₂²×C₄×C₁₃	—	2	1	no	—
410	C₂²×C₄×C₁₃	—	2	1	no	—
411	C₂²×C₄×C₁₃	—	2	2	no	—
412	C₂²×C₄×C₁₃	—	2	1	no	—
413	C₂²×C₄×C₁₃	—	2	1	no	—
414	C₂²×C₄×C₁₃	—	2	1	no	—
415	C₂²×C₄×C₁₃	—	4	2	no	—
416	C₂²×C₄×C₁₃	—	4	2	no	—
417	C₂²×C₄×C₁₃	—	4	4	no	—
418	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
419	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
420	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
421	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
422	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
423	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
424	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
425	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
428	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
429	C₁₃×Q₁₆	—	4	1	no	—
430	C₁₃×Q₁₆	—	4	1	no	—
431	C₁₃×Q₁₆	—	4	2	no	—
432	C₁₃×Q₁₆	—	4	2	no	—
433	C₁₃×SD₁₆	—	4	1	no	—
434	C₁₃×SD₁₆	—	4	1	no	—
435	C₁₃×SD₁₆	—	4	1	no	—
436	C₁₃×SD₁₆	—	4	1	no	—
437	C₁₃×SD₁₆	—	4	2	no	—
438	C₁₃×SD₁₆	—	4	2	no	—
439	C₁₃×D₈	—	4	1	no	—
440	C₁₃×D₈	—	4	1	no	—
441	C₁₃×M₁₆	—	2	2	no	—
442	C₁₃×M₁₆	—	2	2	no	—
443	C₁₃×M₁₆	—	4	2	no	—
444	C₁₃×M₁₆	—	4	2	no	—
445	C₂×C₈×C₁₃	—	2	2	no	—
446	C₂×C₈×C₁₃	—	2	2	no	—
447	C₂×C₈×C₁₃	—	4	2	no	—
448	C₂×C₈×C₁₃	—	4	2	no	—
449	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
450	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
451	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
452	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
453	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
454	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
455	C₁₃×C₄⋊C₄	—	2	2	no	—
456	C₁₃×C₄⋊C₄	—	2	1	no	—
457	C₁₃×C₄⋊C₄	—	2	2	no	—
458	C₁₃×C₄⋊C₄	—	2	2	no	—
459	C₁₃×C₄⋊C₄	—	2	2	no	—
460	C₁₃×C₄⋊C₄	—	2	1	no	—
461	C₁₃×C₄⋊C₄	—	2	1	no	—
462	C₁₃×C₄⋊C₄	—	2	2	no	—
463	C₁₃×C₄⋊C₄	—	2	1	no	—
464	C₁₃×C₄⋊C₄	—	2	2	no	—
465	C₁₃×C₄⋊C₄	—	2	2	no	—
466	C₁₃×C₄⋊C₄	—	2	2	no	—
467	C₁₃×C₄⋊C₄	—	2	2	no	—
468	C₁₃×C₄⋊C₄	—	2	1	no	—
469	C₁₃×C₄⋊C₄	—	2	2	no	—
470	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
471	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
472	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
473	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
474	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
475	C₁₃×C₂²⋊C₄	—	2	2	no	—
476	C₁₃×C₂²⋊C₄	—	2	1	no	—
477	C₁₃×C₂²⋊C₄	—	2	2	no	—
478	C₁₃×C₂²⋊C₄	—	2	2	no	—
479	C₁₃×C₂²⋊C₄	—	2	2	no	—
480	C₁₃×C₂²⋊C₄	—	2	2	no	—
481	C₁₃×C₂²⋊C₄	—	2	2	no	—
482	C₁₃×C₂²⋊C₄	—	2	2	no	—
483	C₁₃×C₂²⋊C₄	—	2	1	no	—
484	C₁₃×C₂²⋊C₄	—	2	2	no	—
485	C₁₃×C₂²⋊C₄	—	2	2	no	—
486	C₁₃×C₂²⋊C₄	—	2	2	no	—
487	C₁₃×C₂²⋊C₄	—	2	2	no	—
488	C₁₃×C₂²⋊C₄	—	2	1	no	—
489	C₁₃×C₂²⋊C₄	—	2	2	no	—
490	C₁₃×C₂²⋊C₄	—	2	1	no	—
491	C₁₃×C₂²⋊C₄	—	2	2	no	—
492	C₁₃×C₂²⋊C₄	—	2	2	no	—
493	C₁₃×C₂²⋊C₄	—	2	2	no	—
494	C₁₃×C₂²⋊C₄	—	2	2	no	—
495	C₁₃×C₂²⋊C₄	—	2	1	no	—
496	C₁₃×C₂²⋊C₄	—	2	2	no	—
497	C₄²×C₁₃	—	2	2	no	—
498	C₄²×C₁₃	—	2	2	no	—
499	C₄²×C₁₃	—	2	2	no	—
500	C₄²×C₁₃	—	2	1	no	—
501	#3489	C₂×C₁₃	1	1	yes	characteristic, complemented
502	#3449	C₂×C₁₃	1	1	yes	characteristic, complemented
503	#3202	C₂×C₁₃	1	2	yes	complemented
504	#3201	C₂×C₁₃	1	2	yes	complemented
505	#3200	C₂×C₁₃	1	2	yes	complemented
506	#3198	C₂×C₁₃	1	2	yes	complemented
507	#3197	C₂×C₁₃	1	2	yes	complemented
508	#3196	C₂×C₁₃	1	2	yes	complemented
509	#3191	C₂×C₁₃	1	2	yes	complemented
510	#3190	C₂×C₁₃	1	2	yes	complemented
511	#3099	C₂×C₁₃	1	1	yes	characteristic, complemented
512	#3098	C₂×C₁₃	1	1	yes	characteristic, complemented
513	#3093	C₂×C₁₃	1	1	yes	characteristic, complemented
514	C₂×#485	C₂×C₁₃	1	1	yes	characteristic, complemented
515	#3063	C₂×C₁₃	1	1	yes	characteristic, complemented
516	#3063	C₂×C₁₃	1	1	yes	characteristic, complemented
517	#3061	C₂×C₁₃	1	1	yes	characteristic, complemented
518	#3060	C₂×C₁₃	1	1	yes	characteristic, complemented
519	#3013	C₂×C₁₃	1	1	yes	characteristic, complemented
520	#3013	C₂×C₁₃	1	1	yes	characteristic, complemented
521	#3007	C₂×C₁₃	1	1	yes	characteristic, complemented
522	#3002	C₂×C₁₃	1	1	yes	characteristic, complemented
523	#2880	C₂×C₁₃	1	1	yes	characteristic, complemented
524	C₂³×C₁₃	—	2	2	no	—
525	C₂³×C₁₃	—	2	1	no	—
526	C₂³×C₁₃	—	2	1	no	—
527	C₂³×C₁₃	—	2	1	no	—
528	C₂³×C₁₃	—	4	2	no	—
529	C₂³×C₁₃	—	4	1	no	—
530	C₂³×C₁₃	—	4	1	no	—
531	C₂³×C₁₃	—	4	2	no	—
532	C₂³×C₁₃	—	4	2	no	—
533	C₂³×C₁₃	—	4	2	no	—
534	C₂³×C₁₃	—	8	1	no	—
535	C₂³×C₁₃	—	8	1	no	—
536	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
537	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
538	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
539	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
540	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
541	Q₈×C₁₃	—	2	2	no	—
542	Q₈×C₁₃	—	2	2	no	—
543	Q₈×C₁₃	—	2	2	no	—
544	Q₈×C₁₃	—	2	2	no	—
545	Q₈×C₁₃	—	2	1	no	—
546	Q₈×C₁₃	—	2	1	no	—
547	Q₈×C₁₃	—	2	1	no	—
548	Q₈×C₁₃	—	2	1	no	—
549	Q₈×C₁₃	—	2	1	no	—
550	Q₈×C₁₃	—	2	1	no	—
551	Q₈×C₁₃	—	4	2	no	—
552	Q₈×C₁₃	—	4	4	no	—
553	Q₈×C₁₃	—	4	2	no	—
554	Q₈×C₁₃	—	4	2	no	—
555	D₄×C₁₃	—	2	4	no	—
556	D₄×C₁₃	—	2	4	no	—
557	D₄×C₁₃	—	2	2	no	—
558	D₄×C₁₃	—	2	2	no	—
559	D₄×C₁₃	—	2	1	no	—
560	D₄×C₁₃	—	2	1	no	—
561	D₄×C₁₃	—	2	1	no	—
562	D₄×C₁₃	—	2	1	no	—
563	D₄×C₁₃	—	2	1	no	—
564	D₄×C₁₃	—	2	1	no	—
565	D₄×C₁₃	—	4	2	no	—
566	D₄×C₁₃	—	4	2	no	—
567	D₄×C₁₃	—	4	2	no	—
568	D₄×C₁₃	—	4	2	no	—
569	D₄×C₁₃	—	4	2	no	—
570	D₄×C₁₃	—	4	2	no	—
571	D₄×C₁₃	—	4	2	no	—
572	D₄×C₁₃	—	4	4	no	—
573	D₄×C₁₃	—	4	2	no	—
574	D₄×C₁₃	—	4	2	no	—
575	D₄×C₁₃	—	4	2	no	—
576	D₄×C₁₃	—	8	2	no	—
577	D₄×C₁₃	—	8	1	no	—
578	D₄×C₁₃	—	8	2	no	—
579	D₄×C₁₃	—	8	2	no	—
580	D₄×C₁₃	—	8	2	no	—
581	D₄×C₁₃	—	8	2	no	—
582	C₂×C₄×C₁₃	—	2	2	no	—
583	C₂×C₄×C₁₃	—	2	2	no	—
584	C₂×C₄×C₁₃	—	2	2	no	—
585	C₂×C₄×C₁₃	—	2	2	no	—
586	C₂×C₄×C₁₃	—	2	2	no	—
587	C₂×C₄×C₁₃	—	2	1	no	—
588	C₂×C₄×C₁₃	—	2	1	no	—
589	C₂×C₄×C₁₃	—	2	1	no	—
590	C₂×C₄×C₁₃	—	2	1	no	—
591	C₂×C₄×C₁₃	—	2	2	no	—
592	C₂×C₄×C₁₃	—	2	2	no	—
593	C₂×C₄×C₁₃	—	2	1	no	—
594	C₂×C₄×C₁₃	—	2	2	no	—
595	C₂×C₄×C₁₃	—	2	2	no	—
596	C₂×C₄×C₁₃	—	2	2	no	—
597	C₂×C₄×C₁₃	—	2	1	no	—
598	C₂×C₄×C₁₃	—	2	1	no	—
599	C₂×C₄×C₁₃	—	2	1	no	—
600	C₂×C₄×C₁₃	—	2	2	no	—
601	C₂×C₄×C₁₃	—	2	1	no	—
602	C₂×C₄×C₁₃	—	4	2	no	—
603	C₂×C₄×C₁₃	—	4	2	no	—
604	C₂×C₄×C₁₃	—	4	2	no	—
605	C₂×C₄×C₁₃	—	4	2	no	—
606	C₂×C₄×C₁₃	—	4	2	no	—
607	C₂×C₄×C₁₃	—	4	4	no	—
608	C₂×C₄×C₁₃	—	4	2	no	—
609	C₂×C₄×C₁₃	—	4	4	no	—
610	C₂×C₄×C₁₃	—	4	2	no	—
611	C₂×C₄×C₁₃	—	4	2	no	—
612	C₂×C₄×C₁₃	—	4	2	no	—
613	C₂×C₄×C₁₃	—	4	2	no	—
614	C₂×C₄×C₁₃	—	8	1	no	—
615	C₂×C₄×C₁₃	—	8	2	no	—
616	C₂×C₄×C₁₃	—	8	1	no	—
617	C₂×C₄×C₁₃	—	8	1	no	—
618	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
619	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
620	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
621	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
622	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
623	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
624	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
625	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
626	C₈×C₁₃	—	2	1	no	—
627	C₈×C₁₃	—	2	1	no	—
628	C₈×C₁₃	—	2	1	no	—
629	C₈×C₁₃	—	2	1	no	—
630	C₈×C₁₃	—	2	2	no	—
631	C₈×C₁₃	—	2	2	no	—
632	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic, complemented
633	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
634	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
635	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic, complemented
637	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
638	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
639	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
640	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
641	D₄×Q₈	—	2	1	no	—
642	#548	—	2	1	no	—
643	#547	—	2	2	no	—
644	#547	—	2	1	no	—
645	#546	—	2	2	no	—
646	#546	—	2	1	no	—
647	#537	C₂²×C₁₃	1	1	yes	characteristic
648	#537	C₂²×C₁₃	1	1	yes	characteristic
649	#537	C₂²×C₁₃	1	1	yes	characteristic
650	#537	C₂²×C₁₃	1	1	yes	characteristic
651	#537	C₂²×C₁₃	1	2	yes	—
652	#537	C₂²×C₁₃	1	1	yes	characteristic, complemented
653	#536	—	2	1	no	—
654	#536	C₂²×C₁₃	1	2	yes	—
655	#536	C₂²×C₁₃	1	2	yes	—
656	#536	C₂²×C₁₃	1	1	yes	characteristic, complemented
657	#535	—	2	1	no	—
658	#535	C₂²×C₁₃	1	2	yes	—
659	#534	—	2	2	no	—
660	#532	—	2	2	no	—
661	#525	—	2	1	no	—
662	#525	—	2	1	no	—
663	#525	C₂²×C₁₃	1	1	yes	characteristic
664	#525	C₂²×C₁₃	1	2	yes	—
665	#525	C₂²×C₁₃	1	2	yes	—
666	#525	C₂²×C₁₃	1	2	yes	complemented
667	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
668	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
669	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
670	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
671	#485	C₂²×C₁₃	1	2	yes	complemented
672	#485	C₂²×C₁₃	1	2	yes	complemented
673	#485	C₂²×C₁₃	1	2	yes	complemented
674	#485	C₂²×C₁₃	1	2	yes	complemented
675	#485	C₂²×C₁₃	1	2	yes	complemented
676	#485	C₂²×C₁₃	1	2	yes	complemented
677	#485	C₂²×C₁₃	1	2	yes	complemented
678	#485	C₂²×C₁₃	1	2	yes	complemented
679	#484	C₂²×C₁₃	1	2	yes	complemented
680	#483	C₂²×C₁₃	1	2	yes	complemented
681	#482	C₂²×C₁₃	1	2	yes	complemented
682	#482	C₂²×C₁₃	1	2	yes	complemented
683	#482	C₂²×C₁₃	1	2	yes	complemented
684	#482	C₂²×C₁₃	1	2	yes	complemented
685	#481	C₂²×C₁₃	1	2	yes	complemented
686	#480	C₂²×C₁₃	1	2	yes	complemented
687	#470	C₂²×C₁₃	1	2	yes	complemented
688	#470	C₂²×C₁₃	1	2	yes	complemented
689	#470	C₂²×C₁₃	1	2	yes	complemented
690	#469	C₂²×C₁₃	1	2	yes	complemented
691	#468	C₂²×C₁₃	1	2	yes	complemented
692	#468	C₂²×C₁₃	1	2	yes	complemented
693	#468	C₂²×C₁₃	1	2	yes	complemented
694	#468	C₂²×C₁₃	1	2	yes	complemented
695	#467	C₂²×C₁₃	1	2	yes	complemented
696	#467	C₂²×C₁₃	1	2	yes	complemented
697	#467	C₂²×C₁₃	1	2	yes	complemented
698	#466	C₂²×C₁₃	1	2	yes	complemented
699	#465	C₂²×C₁₃	1	2	yes	complemented
700	#465	C₂²×C₁₃	1	2	yes	complemented
701	#465	C₂²×C₁₃	1	2	yes	complemented
702	#465	C₂²×C₁₃	1	2	yes	complemented
703	#452	C₂²×C₁₃	1	1	yes	characteristic
704	#452	C₂²×C₁₃	1	2	yes	—
705	#452	C₂²×C₁₃	1	2	yes	—
706	#452	C₂²×C₁₃	1	1	yes	characteristic
707	#452	C₂²×C₁₃	1	2	yes	complemented
708	#452	C₂²×C₁₃	1	2	yes	complemented
709	#451	C₂²×C₁₃	1	2	yes	complemented
710	#451	C₂²×C₁₃	1	2	yes	complemented
711	#451	C₂²×C₁₃	1	2	yes	complemented
712	#451	C₂²×C₁₃	1	1	yes	characteristic, complemented
713	#450	C₂²×C₁₃	1	2	yes	complemented
714	#450	C₂²×C₁₃	1	1	yes	characteristic, complemented
715	#449	C₂²×C₁₃	1	1	yes	characteristic
716	#449	C₂²×C₁₃	1	1	yes	characteristic
717	#449	C₂²×C₁₃	1	2	yes	complemented
718	#449	C₂²×C₁₃	1	2	yes	complemented
719	#448	C₂²×C₁₃	1	2	yes	complemented
720	#448	C₂²×C₁₃	1	2	yes	complemented
721	#448	C₂²×C₁₃	1	1	yes	characteristic, complemented
722	#447	C₂²×C₁₃	1	1	yes	characteristic, complemented
723	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
724	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
725	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
726	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
727	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
728	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
729	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
730	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
731	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
732	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
733	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
734	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
735	#408	C₂²×C₁₃	1	2	yes	—
736	#408	C₂²×C₁₃	1	2	yes	—
737	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
738	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
739	#407	C₂²×C₁₃	1	1	yes	characteristic
740	#407	C₂²×C₁₃	1	2	yes	complemented
741	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
742	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
743	C₂²×C₁₃	—	2	1	no	—
744	C₂²×C₁₃	—	2	1	no	—
745	C₂²×C₁₃	—	2	2	no	—
746	C₂²×C₁₃	—	2	2	no	—
747	C₂²×C₁₃	—	2	1	no	—
748	C₂²×C₁₃	—	2	1	no	—
749	C₂²×C₁₃	—	2	1	no	—
750	C₂²×C₁₃	—	2	2	no	—
751	C₂²×C₁₃	—	2	2	no	—
752	C₂²×C₁₃	—	2	1	no	—
753	C₂²×C₁₃	—	2	1	no	—
754	C₂²×C₁₃	—	2	1	no	—
755	C₂²×C₁₃	—	2	2	no	—
756	C₂²×C₁₃	—	2	2	no	—
757	C₂²×C₁₃	—	4	1	no	—
758	C₂²×C₁₃	—	4	1	no	—
759	C₂²×C₁₃	—	4	1	no	—
760	C₂²×C₁₃	—	4	1	no	—
761	C₂²×C₁₃	—	4	1	no	—
762	C₂²×C₁₃	—	4	1	no	—
763	C₂²×C₁₃	—	4	1	no	—
764	C₂²×C₁₃	—	4	1	no	—
765	C₂²×C₁₃	—	4	1	no	—
766	C₂²×C₁₃	—	8	2	no	—
767	C₂²×C₁₃	—	8	4	no	—
768	C₂²×C₁₃	—	8	4	no	—
769	C₂²×C₁₃	#534	1	2	yes	—
770	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
771	C₄×C₁₃	—	2	1	no	—
772	C₄×C₁₃	—	2	1	no	—
773	C₄×C₁₃	—	2	2	no	—
774	C₄×C₁₃	—	2	2	no	—
775	C₄×C₁₃	—	4	2	no	—
776	C₄×C₁₃	—	4	1	no	—
777	C₄×C₁₃	—	4	2	no	—
778	C₄×C₁₃	—	4	2	no	—
779	C₄×C₁₃	—	4	1	no	—
780	C₄×C₁₃	—	4	1	no	—
781	C₄×C₁₃	—	4	1	no	—
782	C₄×C₁₃	—	4	2	no	—
783	C₄×C₁₃	—	4	1	no	—
784	C₄×C₁₃	#534	1	2	yes	—
785	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
786	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
787	2₋¹⁺⁴	—	4	2	no	—
788	2₋¹⁺⁴	—	4	2	no	—
789	C₂×#41	—	2	1	no	—
790	C₂×#41	—	2	2	no	—
791	C₂×#41	—	2	1	no	—
792	C₂×#41	—	2	1	no	—
793	C₂×#41	—	4	2	no	—
794	C₂×#41	—	4	2	no	—
795	C₂×#41	—	4	2	no	—
796	C₂×#41	—	4	2	no	—
797	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
798	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
799	C₂×#41	D₄×C₁₃	1	2	yes	—
800	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
801	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
802	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
803	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
804	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
805	C₂×#41	C₂³×C₁₃	1	2	yes	—
806	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
807	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
808	C₂×#41	C₂³×C₁₃	1	2	yes	—
809	C₂²×Q₈	—	2	1	no	—
810	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
811	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
812	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
813	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
814	C₂²×D₄	—	2	1	no	—
815	C₂²×D₄	D₄×C₁₃	1	2	yes	—
816	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
817	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
818	C₂³×C₄	—	2	1	no	—
819	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
820	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
821	#137	—	4	2	no	—
822	#137	—	4	2	no	—
823	#135	—	4	2	no	—
824	#135	—	4	2	no	—
825	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
826	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
827	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
828	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
829	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
830	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
831	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
832	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
833	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
834	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
835	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
836	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
837	#131	—	4	2	no	—
838	#131	—	4	2	no	—
839	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
840	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
841	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
842	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
843	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
844	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
845	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
846	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
847	C₄⋊Q₈	—	2	2	no	—
848	C₄⋊Q₈	—	2	2	no	—
849	C₄⋊Q₈	—	2	1	no	—
850	#127	—	2	2	no	—
851	#124	—	2	2	no	—
852	#124	—	2	2	no	—
853	#124	—	2	2	no	—
854	#124	—	2	1	no	—
855	#123	—	2	2	no	—
856	#123	—	2	2	no	—
857	#123	—	2	2	no	—
858	#123	—	2	2	no	—
859	#123	—	2	2	no	—
860	#123	—	2	2	no	—
861	#123	—	2	2	no	—
862	#123	—	2	1	no	—
863	#123	—	2	2	no	—
864	C₂²⋊Q₈	—	2	1	no	—
865	C₂²⋊Q₈	—	2	1	no	—
866	C₂²⋊Q₈	—	2	1	no	—
867	C₂²⋊Q₈	—	2	1	no	—
868	C₂²⋊Q₈	—	2	2	no	—
869	C₂²⋊Q₈	—	2	1	no	—
870	C₂²⋊Q₈	—	2	1	no	—
871	C₂²⋊Q₈	—	2	1	no	—
872	C₂²⋊Q₈	—	2	2	no	—
873	C₂²⋊Q₈	—	2	2	no	—
874	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
875	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
876	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
877	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
878	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
879	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
880	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
881	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
882	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
883	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
884	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
885	#121	—	2	1	no	—
886	#121	—	2	1	no	—
887	#121	—	2	1	no	—
888	#121	—	2	1	no	—
889	#121	—	2	2	no	—
890	#121	—	2	2	no	—
891	#121	—	2	2	no	—
892	#121	—	2	2	no	—
893	#121	—	2	2	no	—
894	#121	—	2	2	no	—
895	#121	—	2	2	no	—
896	#121	—	2	2	no	—
897	#121	—	2	1	no	—
898	#121	C₂³×C₁₃	1	1	yes	characteristic
899	#121	C₂³×C₁₃	1	2	yes	—
900	#121	C₂³×C₁₃	1	2	yes	—
901	#121	C₂³×C₁₃	1	2	yes	—
902	#121	C₂³×C₁₃	1	2	yes	—
903	#121	C₂³×C₁₃	1	1	yes	characteristic
904	#121	C₂³×C₁₃	1	2	yes	—
905	#120	—	2	2	no	—
906	#120	—	2	2	no	—
907	#120	—	2	1	no	—
908	#120	—	2	2	no	—
909	#120	—	2	2	no	—
910	#120	—	2	2	no	—
911	C₄×Q₈	—	2	1	no	—
912	C₄×D₄	—	2	2	no	—
913	C₄×D₄	—	2	1	no	—
914	C₄×D₄	—	2	2	no	—
915	C₄×D₄	—	2	2	no	—
916	C₄×D₄	—	2	2	no	—
917	C₄×D₄	—	2	2	no	—
918	C₄×D₄	—	2	1	no	—
919	C₄×D₄	—	2	1	no	—
920	C₄×D₄	—	2	2	no	—
921	C₄×D₄	—	2	2	no	—
922	#117	—	2	1	no	—
923	#117	—	2	1	no	—
924	#117	C₂³×C₁₃	1	2	yes	—
925	#117	C₂³×C₁₃	1	2	yes	—
926	#117	C₂³×C₁₃	1	1	yes	characteristic
927	#117	C₂³×C₁₃	1	2	yes	—
928	C₂×C₄⋊C₄	—	2	1	no	—
929	C₂×C₄⋊C₄	—	2	2	no	—
930	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
931	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
932	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
934	C₂×C₂²⋊C₄	—	2	1	no	—
935	C₂×C₂²⋊C₄	—	2	1	no	—
936	C₂×C₂²⋊C₄	—	2	2	no	—
937	C₂×C₄²	—	2	1	no	—
938	#107	C₂³×C₁₃	1	2	yes	—
939	#107	C₂³×C₁₃	1	2	yes	—
940	#107	C₂³×C₁₃	1	2	yes	—
941	#107	C₂³×C₁₃	1	2	yes	—
942	#106	C₂³×C₁₃	1	2	yes	—
943	#106	C₂³×C₁₃	1	2	yes	—
944	#106	C₂³×C₁₃	1	2	yes	—
945	#106	C₂³×C₁₃	1	2	yes	—
946	#103	C₂³×C₁₃	1	2	yes	—
947	#103	C₂³×C₁₃	1	2	yes	—
948	#103	C₂³×C₁₃	1	2	yes	—
949	#103	C₂³×C₁₃	1	2	yes	—
950	#103	C₂³×C₁₃	1	1	yes	characteristic
951	#103	C₂³×C₁₃	1	1	yes	characteristic
952	#103	C₂³×C₁₃	1	1	yes	characteristic
953	#103	C₂³×C₁₃	1	1	yes	characteristic
954	#103	C₂³×C₁₃	1	2	yes	—
955	#103	C₂³×C₁₃	1	2	yes	—
956	#103	C₂³×C₁₃	1	2	yes	—
957	#103	C₂³×C₁₃	1	2	yes	—
958	#102	C₂³×C₁₃	1	1	yes	characteristic
959	#102	C₂³×C₁₃	1	1	yes	characteristic
960	#102	C₂³×C₁₃	1	1	yes	characteristic
961	#102	C₂³×C₁₃	1	1	yes	characteristic
962	#102	C₂³×C₁₃	1	2	yes	—
963	#102	C₂³×C₁₃	1	2	yes	—
964	#102	C₂³×C₁₃	1	2	yes	—
965	#102	C₂³×C₁₃	1	2	yes	—
966	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
967	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
968	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
969	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
970	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
971	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
972	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
973	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
974	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
975	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
976	C₂×C₁₃	—	2	2	no	—
977	C₂×C₁₃	—	4	2	no	—
978	C₂×C₁₃	—	4	2	no	—
979	C₂×C₁₃	—	4	1	no	—
980	C₂×C₁₃	—	4	1	no	—
981	C₂×C₁₃	—	8	1	no	—
982	C₂×C₁₃	—	8	1	no	—
983	C₂×C₁₃	—	8	1	no	—
984	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
985	C₂×C₁₃	#3584	1	1	yes	characteristic
986	C₂×C₁₃	#3586	1	1	yes	characteristic
987	C₂⁴	—	2	1	no	—
988	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
989	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
990	#41	—	2	2	no	—
991	#41	—	2	2	no	—
992	#41	—	2	2	no	—
993	#41	—	2	2	no	—
994	#41	—	2	2	no	—
995	#41	—	2	2	no	—
996	#41	—	2	2	no	—
997	#41	—	2	2	no	—
998	#41	—	2	2	no	—
999	#41	—	2	2	no	—
1000	#41	—	4	2	no	—
1001	#41	—	4	2	no	—
1002	#41	—	4	4	no	—
1003	#41	—	4	2	no	—
1004	#41	—	4	2	no	—
1005	#41	—	4	1	no	—
1006	#41	—	4	1	no	—
1007	#41	—	4	1	no	—
1008	#41	—	4	1	no	—
1009	#41	—	4	2	no	—
1010	#41	—	4	2	no	—
1011	#41	—	4	4	no	—
1012	#41	—	4	4	no	—
1013	#41	—	4	8	no	—
1014	#41	—	4	4	no	—
1015	C₂×Q₈	—	2	2	no	—
1016	C₂×Q₈	—	2	1	no	—
1017	C₂×Q₈	—	2	1	no	—
1018	C₂×Q₈	—	2	2	no	—
1019	C₂×Q₈	—	2	2	no	—
1020	C₂×Q₈	—	4	2	no	—
1021	C₂×Q₈	—	4	1	no	—
1022	C₂×Q₈	—	4	1	no	—
1023	C₂×Q₈	—	4	2	no	—
1024	C₂×Q₈	—	4	2	no	—
1025	C₂×Q₈	—	4	4	no	—
1026	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
1027	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
1028	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
1029	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
1030	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
1031	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
1032	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
1033	C₂×D₄	—	2	1	no	—
1034	C₂×D₄	—	2	1	no	—
1035	C₂×D₄	—	2	1	no	—
1036	C₂×D₄	—	2	2	no	—
1037	C₂×D₄	—	2	1	no	—
1038	C₂×D₄	—	2	1	no	—
1039	C₂×D₄	—	2	1	no	—
1040	C₂×D₄	—	2	2	no	—
1041	C₂×D₄	—	2	2	no	—
1042	C₂×D₄	—	2	2	no	—
1043	C₂×D₄	—	2	2	no	—
1044	C₂×D₄	—	2	1	no	—
1045	C₂×D₄	—	2	2	no	—
1046	C₂×D₄	—	2	1	no	—
1047	C₂×D₄	—	4	2	no	—
1048	C₂×D₄	—	4	1	no	—
1049	C₂×D₄	—	4	1	no	—
1050	C₂×D₄	—	4	4	no	—
1051	C₂×D₄	—	4	4	no	—
1052	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1053	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1054	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1055	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1056	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1057	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1058	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1059	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1060	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1061	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1062	C₂²×C₄	—	2	2	no	—
1063	C₂²×C₄	—	2	2	no	—
1064	C₂²×C₄	—	2	2	no	—
1065	C₂²×C₄	—	2	1	no	—
1066	C₂²×C₄	—	2	1	no	—
1067	C₂²×C₄	—	2	1	no	—
1068	C₂²×C₄	—	2	1	no	—
1069	C₂²×C₄	—	2	2	no	—
1070	C₂²×C₄	—	2	1	no	—
1071	C₂²×C₄	—	2	1	no	—
1072	C₂²×C₄	—	2	1	no	—
1073	C₂²×C₄	—	2	2	no	—
1074	C₂²×C₄	—	2	1	no	—
1075	C₂²×C₄	—	2	1	no	—
1076	C₂²×C₄	—	2	1	no	—
1077	C₂²×C₄	—	4	2	no	—
1078	C₂²×C₄	—	4	2	no	—
1079	C₂²×C₄	—	4	4	no	—
1080	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1081	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1082	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1083	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
1084	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
1085	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
1086	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1087	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1088	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1089	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1090	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1091	Q₁₆	—	4	1	no	—
1092	Q₁₆	—	4	1	no	—
1093	Q₁₆	—	4	2	no	—
1094	Q₁₆	—	4	2	no	—
1095	SD₁₆	—	4	1	no	—
1096	SD₁₆	—	4	1	no	—
1097	SD₁₆	—	4	1	no	—
1098	SD₁₆	—	4	1	no	—
1099	SD₁₆	—	4	2	no	—
1100	SD₁₆	—	4	2	no	—
1101	D₈	—	4	1	no	—
1102	D₈	—	4	1	no	—
1103	M₁₆	—	2	2	no	—
1104	M₁₆	—	2	2	no	—
1105	M₁₆	—	4	2	no	—
1106	M₁₆	—	4	2	no	—
1107	C₂×C₈	—	2	2	no	—
1108	C₂×C₈	—	2	2	no	—
1109	C₂×C₈	—	4	2	no	—
1110	C₂×C₈	—	4	2	no	—
1111	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1112	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1113	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1114	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1115	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1116	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1117	C₄⋊C₄	—	2	2	no	—
1118	C₄⋊C₄	—	2	1	no	—
1119	C₄⋊C₄	—	2	2	no	—
1120	C₄⋊C₄	—	2	2	no	—
1121	C₄⋊C₄	—	2	2	no	—
1122	C₄⋊C₄	—	2	1	no	—
1123	C₄⋊C₄	—	2	1	no	—
1124	C₄⋊C₄	—	2	2	no	—
1125	C₄⋊C₄	—	2	1	no	—
1126	C₄⋊C₄	—	2	2	no	—
1127	C₄⋊C₄	—	2	2	no	—
1128	C₄⋊C₄	—	2	2	no	—
1129	C₄⋊C₄	—	2	2	no	—
1130	C₄⋊C₄	—	2	1	no	—
1131	C₄⋊C₄	—	2	2	no	—
1132	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1133	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1134	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1135	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1136	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1137	C₂²⋊C₄	—	2	2	no	—
1138	C₂²⋊C₄	—	2	1	no	—
1139	C₂²⋊C₄	—	2	2	no	—
1140	C₂²⋊C₄	—	2	2	no	—
1141	C₂²⋊C₄	—	2	2	no	—
1142	C₂²⋊C₄	—	2	2	no	—
1143	C₂²⋊C₄	—	2	2	no	—
1144	C₂²⋊C₄	—	2	2	no	—
1145	C₂²⋊C₄	—	2	1	no	—
1146	C₂²⋊C₄	—	2	2	no	—
1147	C₂²⋊C₄	—	2	2	no	—
1148	C₂²⋊C₄	—	2	2	no	—
1149	C₂²⋊C₄	—	2	2	no	—
1150	C₂²⋊C₄	—	2	1	no	—
1151	C₂²⋊C₄	—	2	2	no	—
1152	C₂²⋊C₄	—	2	1	no	—
1153	C₂²⋊C₄	—	2	2	no	—
1154	C₂²⋊C₄	—	2	2	no	—
1155	C₂²⋊C₄	—	2	2	no	—
1156	C₂²⋊C₄	—	2	2	no	—
1157	C₂²⋊C₄	—	2	1	no	—
1158	C₂²⋊C₄	—	2	2	no	—
1159	C₄²	—	2	2	no	—
1160	C₄²	—	2	2	no	—
1161	C₄²	—	2	2	no	—
1162	C₄²	—	2	1	no	—
1163	C₁₃	#60766	1	1	yes	characteristic, direct product factor, Sylow
1164	C₂³	—	2	2	no	—
1165	C₂³	—	2	1	no	—
1166	C₂³	—	2	1	no	—
1167	C₂³	—	2	1	no	—
1168	C₂³	—	4	2	no	—
1169	C₂³	—	4	1	no	—
1170	C₂³	—	4	1	no	—
1171	C₂³	—	4	2	no	—
1172	C₂³	—	4	2	no	—
1173	C₂³	—	4	2	no	—
1174	C₂³	—	8	1	no	—
1175	C₂³	—	8	1	no	—
1176	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1177	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1178	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1179	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1180	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1181	Q₈	—	2	2	no	—
1182	Q₈	—	2	2	no	—
1183	Q₈	—	2	2	no	—
1184	Q₈	—	2	2	no	—
1185	Q₈	—	2	1	no	—
1186	Q₈	—	2	1	no	—
1187	Q₈	—	2	1	no	—
1188	Q₈	—	2	1	no	—
1189	Q₈	—	2	1	no	—
1190	Q₈	—	2	1	no	—
1191	Q₈	—	4	2	no	—
1192	Q₈	—	4	4	no	—
1193	Q₈	—	4	2	no	—
1194	Q₈	—	4	2	no	—
1195	D₄	—	2	4	no	—
1196	D₄	—	2	4	no	—
1197	D₄	—	2	2	no	—
1198	D₄	—	2	2	no	—
1199	D₄	—	2	1	no	—
1200	D₄	—	2	1	no	—
1201	D₄	—	2	1	no	—
1202	D₄	—	2	1	no	—
1203	D₄	—	2	1	no	—
1204	D₄	—	2	1	no	—
1205	D₄	—	4	2	no	—
1206	D₄	—	4	2	no	—
1207	D₄	—	4	2	no	—
1208	D₄	—	4	2	no	—
1209	D₄	—	4	2	no	—
1210	D₄	—	4	2	no	—
1211	D₄	—	4	2	no	—
1212	D₄	—	4	4	no	—
1213	D₄	—	4	2	no	—
1214	D₄	—	4	2	no	—
1215	D₄	—	4	2	no	—
1216	D₄	—	8	2	no	—
1217	D₄	—	8	1	no	—
1218	D₄	—	8	2	no	—
1219	D₄	—	8	2	no	—
1220	D₄	—	8	2	no	—
1221	D₄	—	8	2	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	2	no	—
1224	C₂×C₄	—	2	2	no	—
1225	C₂×C₄	—	2	2	no	—
1226	C₂×C₄	—	2	2	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	1	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	2	no	—
1232	C₂×C₄	—	2	2	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	2	no	—
1235	C₂×C₄	—	2	2	no	—
1236	C₂×C₄	—	2	2	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	2	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	4	2	no	—
1243	C₂×C₄	—	4	2	no	—
1244	C₂×C₄	—	4	2	no	—
1245	C₂×C₄	—	4	2	no	—
1246	C₂×C₄	—	4	2	no	—
1247	C₂×C₄	—	4	4	no	—
1248	C₂×C₄	—	4	2	no	—
1249	C₂×C₄	—	4	4	no	—
1250	C₂×C₄	—	4	2	no	—
1251	C₂×C₄	—	4	2	no	—
1252	C₂×C₄	—	4	2	no	—
1253	C₂×C₄	—	4	2	no	—
1254	C₂×C₄	—	8	1	no	—
1255	C₂×C₄	—	8	2	no	—
1256	C₂×C₄	—	8	1	no	—
1257	C₂×C₄	—	8	1	no	—
1258	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1259	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1260	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1261	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1262	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1263	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1264	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1265	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1266	C₈	—	2	1	no	—
1267	C₈	—	2	1	no	—
1268	C₈	—	2	1	no	—
1269	C₈	—	2	1	no	—
1270	C₈	—	2	2	no	—
1271	C₈	—	2	2	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	2	no	—
1275	C₂²	—	2	2	no	—
1276	C₂²	—	2	1	no	—
1277	C₂²	—	2	1	no	—
1278	C₂²	—	2	1	no	—
1279	C₂²	—	2	2	no	—
1280	C₂²	—	2	2	no	—
1281	C₂²	—	2	1	no	—
1282	C₂²	—	2	1	no	—
1283	C₂²	—	2	1	no	—
1284	C₂²	—	2	2	no	—
1285	C₂²	—	2	2	no	—
1286	C₂²	—	4	1	no	—
1287	C₂²	—	4	1	no	—
1288	C₂²	—	4	1	no	—
1289	C₂²	—	4	1	no	—
1290	C₂²	—	4	1	no	—
1291	C₂²	—	4	1	no	—
1292	C₂²	—	4	1	no	—
1293	C₂²	—	4	1	no	—
1294	C₂²	—	4	1	no	—
1295	C₂²	—	8	2	no	—
1296	C₂²	—	8	4	no	—
1297	C₂²	—	8	4	no	—
1298	C₂²	C₁₃×#534	1	2	yes	—
1299	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1300	C₄	—	2	1	no	—
1301	C₄	—	2	1	no	—
1302	C₄	—	2	2	no	—
1303	C₄	—	2	2	no	—
1304	C₄	—	4	2	no	—
1305	C₄	—	4	1	no	—
1306	C₄	—	4	2	no	—
1307	C₄	—	4	2	no	—
1308	C₄	—	4	1	no	—
1309	C₄	—	4	1	no	—
1310	C₄	—	4	1	no	—
1311	C₄	—	4	2	no	—
1312	C₄	—	4	1	no	—
1313	C₄	C₁₃×#534	1	2	yes	—
1314	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1315	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1316	C₂	—	2	2	no	—
1317	C₂	—	4	1	no	—
1318	C₂	—	4	1	no	—
1319	C₂	—	4	2	no	—
1320	C₂	—	4	2	no	—
1321	C₂	—	8	1	no	—
1322	C₂	—	8	1	no	—
1323	C₂	—	8	1	no	—
1324	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
1325	C₂	C₁₃×#3584	1	1	yes	characteristic
1326	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3489	C₂	semidirect
2. C₁₃×#3449	C₂	semidirect
3. C₁₃×#3202	C₂	semidirect
4. C₁₃×#3201	C₂	semidirect
5. C₁₃×#3200	C₂	semidirect
6. C₁₃×#3198	C₂	semidirect
7. C₁₃×#3197	C₂	semidirect
8. C₁₃×#3196	C₂	semidirect
9. C₁₃×#3191	C₂	semidirect
10. C₁₃×#3190	C₂	semidirect
11. C₁₃×#3099	C₂	semidirect
12. C₁₃×#3098	C₂	semidirect
13. C₁₃×#3093	C₂	semidirect
14. C₂×C₁₃×#485	C₂	semidirect
15. C₁₃×#3063	C₂	semidirect
16. C₁₃×#3063	C₂	semidirect
17. C₁₃×#3061	C₂	semidirect
18. C₁₃×#3060	C₂	semidirect
19. C₁₃×#3013	C₂	semidirect
20. C₁₃×#3013	C₂	semidirect
21. C₁₃×#3007	C₂	semidirect
22. C₁₃×#3002	C₂	semidirect
23. C₁₃×#2880	C₂	semidirect
24. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
27. C₂×C₁₃×#137	C₂²	semidirect
28. C₂×C₁₃×#137	C₂²	semidirect
29. C₂×C₁₃×#135	C₂²	semidirect
30. C₂×C₁₃×#135	C₂²	semidirect
31. C₂×C₁₃×#131	C₂²	semidirect
32. C₂×C₁₃×#131	C₂²	semidirect
44. C₁₃×#537	C₂²	semidirect
48. C₁₃×#536	C₂²	semidirect
58. C₁₃×#525	C₂²	semidirect
60. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
61. C₁₃×#520	C₂²	semidirect
63. C₁₃×#485	C₂²	semidirect
64. C₁₃×#485	C₂²	semidirect
65. C₁₃×#485	C₂²	semidirect
66. C₁₃×#485	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
69. C₁₃×#485	C₂²	semidirect
70. C₁₃×#485	C₂²	semidirect
71. C₁₃×#484	C₂²	semidirect
72. C₁₃×#483	C₂²	semidirect
73. C₁₃×#482	C₂²	semidirect
74. C₁₃×#482	C₂²	semidirect
75. C₁₃×#482	C₂²	semidirect
76. C₁₃×#482	C₂²	semidirect
77. C₁₃×#481	C₂²	semidirect
78. C₁₃×#480	C₂²	semidirect
79. C₁₃×#470	C₂²	semidirect
80. C₁₃×#470	C₂²	semidirect
81. C₁₃×#470	C₂²	semidirect
82. C₁₃×#469	C₂²	semidirect
83. C₁₃×#468	C₂²	semidirect
84. C₁₃×#468	C₂²	semidirect
85. C₁₃×#468	C₂²	semidirect
86. C₁₃×#468	C₂²	semidirect
87. C₁₃×#467	C₂²	semidirect
88. C₁₃×#467	C₂²	semidirect
89. C₁₃×#467	C₂²	semidirect
90. C₁₃×#466	C₂²	semidirect
91. C₁₃×#465	C₂²	semidirect
92. C₁₃×#465	C₂²	semidirect
93. C₁₃×#465	C₂²	semidirect
94. C₁₃×#465	C₂²	semidirect
99. C₁₃×#452	C₂²	semidirect
100. C₁₃×#452	C₂²	semidirect
101. C₁₃×#451	C₂²	semidirect
102. C₁₃×#451	C₂²	semidirect
103. C₁₃×#451	C₂²	semidirect
104. C₁₃×#451	C₂²	semidirect
105. C₁₃×#450	C₂²	semidirect
106. C₁₃×#450	C₂²	semidirect
109. C₁₃×#449	C₂²	semidirect
110. C₁₃×#449	C₂²	semidirect
111. C₁₃×#448	C₂²	semidirect
112. C₁₃×#448	C₂²	semidirect
113. C₁₃×#448	C₂²	semidirect
114. C₁₃×#447	C₂²	semidirect
115. C₁₃×#428	C₂²	semidirect
116. C₁₃×#428	C₂²	semidirect
117. C₂×C₁₃×#107	C₂²	semidirect
118. C₂×C₁₃×#106	C₂²	semidirect
119. C₁₃×#417	C₂²	semidirect
120. C₁₃×#417	C₂²	semidirect
121. C₁₃×#417	C₂²	semidirect
122. C₁₃×#417	C₂²	semidirect
123. C₁₃×#416	C₂²	semidirect
124. C₁₃×#416	C₂²	semidirect
125. C₂×C₁₃×#103	C₂²	semidirect
126. C₂×C₁₃×#103	C₂²	semidirect
129. C₁₃×#408	C₂²	semidirect
130. C₁₃×#408	C₂²	semidirect
132. C₁₃×#407	C₂²	semidirect
134. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
324. #60766	C₁₃	direct (N × H)
501. #3489	C₂×C₁₃	semidirect
502. #3449	C₂×C₁₃	semidirect
503. #3202	C₂×C₁₃	semidirect
504. #3201	C₂×C₁₃	semidirect
505. #3200	C₂×C₁₃	semidirect
506. #3198	C₂×C₁₃	semidirect
507. #3197	C₂×C₁₃	semidirect
508. #3196	C₂×C₁₃	semidirect
509. #3191	C₂×C₁₃	semidirect
510. #3190	C₂×C₁₃	semidirect
511. #3099	C₂×C₁₃	semidirect
512. #3098	C₂×C₁₃	semidirect
513. #3093	C₂×C₁₃	semidirect
514. C₂×#485	C₂×C₁₃	semidirect
515. #3063	C₂×C₁₃	semidirect
516. #3063	C₂×C₁₃	semidirect
517. #3061	C₂×C₁₃	semidirect
518. #3060	C₂×C₁₃	semidirect
519. #3013	C₂×C₁₃	semidirect
520. #3013	C₂×C₁₃	semidirect
521. #3007	C₂×C₁₃	semidirect
522. #3002	C₂×C₁₃	semidirect
523. #2880	C₂×C₁₃	semidirect
632. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
635. C₂×#137	C₂²×C₁₃	semidirect
636. C₂×#137	C₂²×C₁₃	semidirect
637. C₂×#135	C₂²×C₁₃	semidirect
638. C₂×#135	C₂²×C₁₃	semidirect
639. C₂×#131	C₂²×C₁₃	semidirect
640. C₂×#131	C₂²×C₁₃	semidirect
652. #537	C₂²×C₁₃	semidirect
656. #536	C₂²×C₁₃	semidirect
666. #525	C₂²×C₁₃	semidirect
668. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
669. #520	C₂²×C₁₃	semidirect
671. #485	C₂²×C₁₃	semidirect
672. #485	C₂²×C₁₃	semidirect
673. #485	C₂²×C₁₃	semidirect
674. #485	C₂²×C₁₃	semidirect
675. #485	C₂²×C₁₃	semidirect
676. #485	C₂²×C₁₃	semidirect
677. #485	C₂²×C₁₃	semidirect
678. #485	C₂²×C₁₃	semidirect
679. #484	C₂²×C₁₃	semidirect
680. #483	C₂²×C₁₃	semidirect
681. #482	C₂²×C₁₃	semidirect
682. #482	C₂²×C₁₃	semidirect
683. #482	C₂²×C₁₃	semidirect
684. #482	C₂²×C₁₃	semidirect
685. #481	C₂²×C₁₃	semidirect
686. #480	C₂²×C₁₃	semidirect
687. #470	C₂²×C₁₃	semidirect
688. #470	C₂²×C₁₃	semidirect
689. #470	C₂²×C₁₃	semidirect
690. #469	C₂²×C₁₃	semidirect
691. #468	C₂²×C₁₃	semidirect
692. #468	C₂²×C₁₃	semidirect
693. #468	C₂²×C₁₃	semidirect
694. #468	C₂²×C₁₃	semidirect
695. #467	C₂²×C₁₃	semidirect
696. #467	C₂²×C₁₃	semidirect
697. #467	C₂²×C₁₃	semidirect
698. #466	C₂²×C₁₃	semidirect
699. #465	C₂²×C₁₃	semidirect
700. #465	C₂²×C₁₃	semidirect
701. #465	C₂²×C₁₃	semidirect
702. #465	C₂²×C₁₃	semidirect
707. #452	C₂²×C₁₃	semidirect
708. #452	C₂²×C₁₃	semidirect
709. #451	C₂²×C₁₃	semidirect
710. #451	C₂²×C₁₃	semidirect
711. #451	C₂²×C₁₃	semidirect
712. #451	C₂²×C₁₃	semidirect
713. #450	C₂²×C₁₃	semidirect
714. #450	C₂²×C₁₃	semidirect
717. #449	C₂²×C₁₃	semidirect
718. #449	C₂²×C₁₃	semidirect
719. #448	C₂²×C₁₃	semidirect
720. #448	C₂²×C₁₃	semidirect
721. #448	C₂²×C₁₃	semidirect
722. #447	C₂²×C₁₃	semidirect
723. #428	C₂²×C₁₃	semidirect
724. #428	C₂²×C₁₃	semidirect
725. C₂×#107	C₂²×C₁₃	semidirect
726. C₂×#106	C₂²×C₁₃	semidirect
727. #417	C₂²×C₁₃	semidirect
728. #417	C₂²×C₁₃	semidirect
729. #417	C₂²×C₁₃	semidirect
730. #417	C₂²×C₁₃	semidirect
731. #416	C₂²×C₁₃	semidirect
732. #416	C₂²×C₁₃	semidirect
733. C₂×#103	C₂²×C₁₃	semidirect
734. C₂×#103	C₂²×C₁₃	semidirect
737. #408	C₂²×C₁₃	semidirect
738. #408	C₂²×C₁₃	semidirect
740. #407	C₂²×C₁₃	semidirect
742. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
1163. C₁₃	#60766	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3489	2
C₁₃×#3449	2
C₁₃×#3202	2
C₁₃×#3201	2
C₁₃×#3200	2
C₁₃×#3198	2
C₁₃×#3197	2
C₁₃×#3196	2
C₁₃×#3191	2
C₁₃×#3190	2
C₁₃×#3099	2
C₁₃×#3098	2
C₁₃×#3093	2
C₂×C₁₃×#485	2
C₁₃×#3063	2
C₁₃×#3061	2
C₁₃×#3060	2
C₁₃×#3013	2
C₁₃×#3007	2
C₁₃×#3002	2
C₁₃×#2880	2
#60766	13

Subgroups — C13×#60766 #15747105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60766 #15747105