Subgroups — C₂×#13129402 #16770268

Order 3328.

7258 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129402	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719440	C₂	1	2	yes	maximal, complemented
3	C₂×#11719352	C₂	1	2	yes	maximal, complemented
4	C₂×#11719437	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11719273	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11719261	C₂	1	2	yes	maximal, complemented
7	C₂×#11719342	C₂	1	2	yes	maximal, complemented
8	C₂×Q₈×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11719522	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11719338	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#11719255	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11719335	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#11719339	C₂	1	2	yes	maximal, complemented
14	C₂×#11719438	C₂	1	2	yes	maximal, complemented
15	C₂×#11719348	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11719287	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#11719345	C₂	1	2	yes	maximal, complemented
18	C₂×#11719265	C₂	1	2	yes	maximal, complemented
19	C₂×#11719429	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11719521	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#11719327	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#11719243	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂²×#88201	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#6131	C₂²	1	1	yes	characteristic
28	C₂²×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#6127	C₂²	1	1	yes	characteristic
30	C₂³×D₅₂	C₂²	1	1	yes	characteristic
31	D₄×Q₈×C₁₃	C₂²	1	16	yes	complemented
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
33	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
41	#11719522	C₂²	1	16	yes	complemented
42	#11719521	C₂²	1	16	yes	complemented
43	Q₈×C₂²⋊D₁₃	C₂²	1	16	yes	complemented
44	C₂×#88201	C₂²	1	2	yes	—
45	C₂×#88201	C₂²	1	2	yes	—
46	C₂×#88201	C₂²	1	1	yes	characteristic
47	C₂×#88201	C₂²	1	1	yes	characteristic
48	C₂×#88201	C₂²	1	1	yes	characteristic
49	C₂×#88201	C₂²	1	1	yes	characteristic
50	C₂×#88201	C₂²	1	1	yes	characteristic
51	C₂×#88201	C₂²	1	16	yes	complemented
52	C₂×#88201	C₂²	1	2	yes	complemented
53	C₂×#88200	C₂²	1	2	yes	complemented
54	C₂×#88200	C₂²	1	2	yes	complemented
55	C₂×#88200	C₂²	1	2	yes	complemented
56	C₂×#88200	C₂²	1	1	yes	characteristic, complemented
57	C₂×#88200	C₂²	1	2	yes	complemented
58	C₂×Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×#88198	C₂²	1	2	yes	complemented
61	C₂×#88198	C₂²	1	1	yes	characteristic, complemented
62	C₂×#88198	C₂²	1	1	yes	characteristic, complemented
63	C₂×#88193	C₂²	1	1	yes	characteristic
64	C₂×#88191	C₂²	1	2	yes	—
65	C₂×#88189	C₂²	1	1	yes	characteristic
66	C₂×#88184	C₂²	1	1	yes	characteristic
67	C₂×#88184	C₂²	1	2	yes	complemented
68	C₂×#88183	C₂²	1	2	yes	complemented
69	C₂×#88183	C₂²	1	2	yes	complemented
70	C₂×C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
71	C₂×C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
72	C₂×C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
73	C₂×C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
74	C₂²×#6103	C₂²	1	2	yes	—
75	C₂²×#6103	C₂²	1	2	yes	—
76	C₂×#88180	C₂²	1	1	yes	characteristic, complemented
77	C₂×#88178	C₂²	1	2	yes	—
78	C₂×#88178	C₂²	1	1	yes	characteristic
79	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
80	#11719440	C₂²	1	32	yes	complemented
81	#11719438	C₂²	1	32	yes	complemented
82	#11719437	C₂²	1	16	yes	complemented
83	#11719429	C₂²	1	16	yes	complemented
84	#11719352	C₂²	1	32	yes	complemented
85	#11719348	C₂²	1	16	yes	complemented
86	#11719345	C₂²	1	32	yes	complemented
87	#11719342	C₂²	1	32	yes	complemented
88	#11719339	C₂²	1	32	yes	complemented
89	#11719338	C₂²	1	16	yes	complemented
90	#11719335	C₂²	1	16	yes	complemented
91	#11719327	C₂²	1	16	yes	complemented
92	#11719287	C₂²	1	16	yes	complemented
93	#11719273	C₂²	1	16	yes	complemented
94	#11719265	C₂²	1	32	yes	complemented
95	#11719261	C₂²	1	32	yes	complemented
96	#11719255	C₂²	1	16	yes	complemented
97	#11719243	C₂²	1	16	yes	complemented
98	C₂×#88152	C₂²	1	2	yes	complemented
99	C₂×#88152	C₂²	1	2	yes	complemented
100	C₂×#88152	C₂²	1	2	yes	complemented
101	C₂×#88152	C₂²	1	1	yes	characteristic, complemented
102	C₂×#88152	C₂²	1	2	yes	complemented
103	C₂×#88151	C₂²	1	2	yes	complemented
104	C₂×#88151	C₂²	1	2	yes	complemented
105	C₂×#88150	C₂²	1	2	yes	complemented
106	C₂×#88150	C₂²	1	2	yes	complemented
107	C₂×#88150	C₂²	1	2	yes	complemented
108	C₂×#88150	C₂²	1	2	yes	complemented
109	C₂×#88150	C₂²	1	2	yes	complemented
110	C₂×#88149	C₂²	1	2	yes	—
111	C₂×#88149	C₂²	1	1	yes	characteristic
112	C₂×#88148	C₂²	1	2	yes	—
113	C₂×#88148	C₂²	1	2	yes	—
114	C₂×#88148	C₂²	1	2	yes	complemented
115	C₂×#88148	C₂²	1	2	yes	complemented
116	C₂×#88148	C₂²	1	2	yes	complemented
117	C₂×#88147	C₂²	1	1	yes	characteristic
118	C₂×#88147	C₂²	1	2	yes	complemented
119	C₂×#88146	C₂²	1	2	yes	complemented
120	C₂×#88143	C₂²	1	2	yes	complemented
121	C₂×#88143	C₂²	1	1	yes	characteristic, complemented
122	C₂×#88142	C₂²	1	1	yes	characteristic, complemented
123	C₂×#88141	C₂²	1	2	yes	complemented
124	C₂×#88141	C₂²	1	1	yes	characteristic, complemented
125	C₂×#88140	C₂²	1	1	yes	characteristic
126	C₂×#88139	C₂²	1	1	yes	characteristic, complemented
127	C₂×#88139	C₂²	1	2	yes	complemented
128	C₂×#88139	C₂²	1	2	yes	complemented
129	C₂×#88138	C₂²	1	2	yes	—
130	C₂×#88138	C₂²	1	2	yes	complemented
131	C₂×#88137	C₂²	1	2	yes	complemented
132	C₂×#88136	C₂²	1	2	yes	—
133	C₂×C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
134	C₂×C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
135	C₂×#88133	C₂²	1	1	yes	characteristic, complemented
136	C₂×#88132	C₂²	1	1	yes	characteristic
137	C₂×#88132	C₂²	1	2	yes	—
138	C₂×#88131	C₂²	1	2	yes	—
139	C₂×#88130	C₂²	1	2	yes	complemented
140	C₂×#88130	C₂²	1	2	yes	complemented
141	C₂×#88129	C₂²	1	1	yes	characteristic
142	C₂×#88129	C₂²	1	2	yes	complemented
143	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
144	C₂×#88126	C₂²	1	1	yes	characteristic, complemented
145	C₂×#88126	C₂²	1	2	yes	complemented
146	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₁₃	C₂³	1	2	yes	—
148	C₂²×Q₈×C₁₃	—	4	4	no	—
149	C₂²×Q₈×C₁₃	—	4	4	no	—
150	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
152	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
153	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
154	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
155	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
156	C₂²×Q₈×C₁₃	C₂³	1	8	yes	complemented
157	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
159	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
160	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
161	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
162	C₂²×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
163	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
164	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
165	C₂²×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
166	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
167	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
168	C₂×#6131	—	4	4	no	—
169	C₂×#6131	C₂³	1	8	yes	—
170	C₂×Q₈×D₁₃	—	4	4	no	—
171	C₂×Q₈×D₁₃	C₂³	1	8	yes	complemented
172	C₂×#6127	—	4	4	no	—
173	C₂×#6127	C₂³	1	8	yes	—
174	C₂²×D₅₂	—	4	4	no	—
175	C₂²×D₅₂	C₂³	1	1	yes	characteristic
176	C₂²×D₅₂	C₂³	1	1	yes	characteristic
177	C₂²×D₅₂	C₂³	1	2	yes	—
178	C₂²×D₅₂	C₂³	1	2	yes	—
179	C₂²×D₅₂	C₂³	1	2	yes	—
180	C₂²×D₅₂	C₂³	1	8	yes	—
181	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
182	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
183	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
184	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
185	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
186	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
187	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
188	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
189	C₂²×Dic₂₆	C₂³	1	2	yes	—
190	C₂²×Dic₂₆	C₂³	1	2	yes	—
191	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
192	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
193	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
195	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
196	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
197	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
198	C₄×D₄×C₁₃	C₂³	1	8	yes	—
199	C₄×D₄×C₁₃	C₂³	1	16	yes	—
200	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
213	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
214	C₂×C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
218	#88201	C₂³	1	8	yes	—
219	#88201	C₂³	1	8	yes	—
220	#88201	C₂³	1	8	yes	—
221	#88201	C₂³	1	16	yes	—
222	#88201	C₂³	1	16	yes	—
223	#88201	C₂³	1	8	yes	—
224	#88201	C₂³	1	8	yes	—
225	#88201	C₂³	1	16	yes	complemented
226	#88200	C₂³	1	16	yes	complemented
227	#88200	C₂³	1	16	yes	complemented
228	#88200	C₂³	1	16	yes	complemented
229	#88200	C₂³	1	16	yes	complemented
230	#88200	C₂³	1	8	yes	complemented
231	Q₈×Dic₁₃	C₂³	1	8	yes	complemented
232	Q₈×Dic₁₃	C₂³	1	8	yes	complemented
233	#88198	C₂³	1	8	yes	complemented
234	#88198	C₂³	1	16	yes	complemented
235	#88198	C₂³	1	8	yes	complemented
236	#88193	C₂³	1	8	yes	—
237	#88191	C₂³	1	16	yes	—
238	#88189	C₂³	1	8	yes	—
239	#88184	C₂³	1	8	yes	—
240	#88184	C₂³	1	16	yes	complemented
241	#88183	C₂³	1	16	yes	complemented
242	#88183	C₂³	1	16	yes	complemented
243	C₄×C₂²⋊D₁₃	C₂³	1	8	yes	—
244	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	—
245	C₄×C₂²⋊D₁₃	C₂³	1	8	yes	complemented
246	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	complemented
247	C₂×#6103	C₂³	1	2	yes	—
248	C₂×#6103	C₂³	1	1	yes	characteristic
249	C₂×#6103	C₂³	1	1	yes	characteristic
250	C₂×#6103	C₂³	1	2	yes	—
251	C₂×#6103	C₂³	1	2	yes	—
252	C₂×#6103	C₂³	1	2	yes	—
253	C₂×#6103	C₂³	1	2	yes	—
254	C₂×#6103	C₂³	1	2	yes	—
255	C₂×#6103	C₂³	1	2	yes	—
256	C₂×#6103	C₂³	1	2	yes	—
257	C₂×#6103	C₂³	1	2	yes	—
258	C₂×#6103	C₂³	1	2	yes	—
259	C₂×#6103	C₂³	1	2	yes	—
260	C₂×#6103	C₂³	1	2	yes	—
261	C₂×#6103	C₂³	1	2	yes	—
262	C₂×#6103	C₂³	1	2	yes	—
263	C₂×#6103	C₂³	1	2	yes	—
264	C₂×#6103	C₂³	1	2	yes	—
265	C₂×#6103	C₂³	1	2	yes	—
266	C₂×#6103	C₂³	1	1	yes	characteristic
267	C₂×#6103	C₂³	1	1	yes	characteristic
268	C₂×#6103	C₂³	1	16	yes	—
269	C₂×#6103	C₂³	1	16	yes	—
270	#88180	C₂³	1	8	yes	complemented
271	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
274	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
276	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
277	#88178	C₂³	1	8	yes	—
278	#88178	C₂³	1	16	yes	—
279	C₂×#6101	C₂³	1	1	yes	characteristic
280	C₂×#6101	C₂³	1	1	yes	characteristic
281	C₂×#6101	C₂³	1	1	yes	characteristic
282	C₂×#6101	C₂³	1	1	yes	characteristic
283	C₂×#6101	C₂³	1	2	yes	—
284	C₂×#6101	C₂³	1	2	yes	—
285	C₂×#6101	C₂³	1	2	yes	—
286	C₂×#6101	C₂³	1	2	yes	—
287	C₂×#6101	C₂³	1	2	yes	—
288	C₂×#6101	C₂³	1	2	yes	—
289	C₂×#6101	C₂³	1	2	yes	—
290	C₂×#6101	C₂³	1	1	yes	characteristic
291	C₂×#6101	C₂³	1	1	yes	characteristic
292	C₂×#6101	C₂³	1	2	yes	—
293	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
294	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
295	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
296	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
297	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
298	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
299	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
300	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
301	C₂×C₄×Dic₁₃	C₂³	1	8	yes	—
302	#88152	C₂³	1	16	yes	complemented
303	#88152	C₂³	1	16	yes	complemented
304	#88152	C₂³	1	8	yes	complemented
305	#88152	C₂³	1	16	yes	complemented
306	#88152	C₂³	1	16	yes	complemented
307	#88151	C₂³	1	16	yes	complemented
308	#88151	C₂³	1	16	yes	complemented
309	#88150	C₂³	1	16	yes	complemented
310	#88150	C₂³	1	16	yes	complemented
311	#88150	C₂³	1	16	yes	complemented
312	#88150	C₂³	1	16	yes	complemented
313	#88150	C₂³	1	16	yes	complemented
314	#88149	C₂³	1	16	yes	—
315	#88149	C₂³	1	8	yes	—
316	#88148	C₂³	1	16	yes	—
317	#88148	C₂³	1	16	yes	—
318	#88148	C₂³	1	16	yes	complemented
319	#88148	C₂³	1	16	yes	complemented
320	#88148	C₂³	1	16	yes	complemented
321	#88147	C₂³	1	8	yes	—
322	#88147	C₂³	1	16	yes	complemented
323	#88146	C₂³	1	16	yes	complemented
324	#88143	C₂³	1	8	yes	complemented
325	#88143	C₂³	1	16	yes	complemented
326	#88142	C₂³	1	8	yes	complemented
327	#88141	C₂³	1	16	yes	complemented
328	#88141	C₂³	1	8	yes	complemented
329	#88140	C₂³	1	8	yes	—
330	#88139	C₂³	1	8	yes	complemented
331	#88139	C₂³	1	16	yes	complemented
332	#88139	C₂³	1	16	yes	complemented
333	#88138	C₂³	1	16	yes	—
334	#88138	C₂³	1	16	yes	complemented
335	#88137	C₂³	1	16	yes	complemented
336	#88136	C₂³	1	16	yes	—
337	C₂²⋊C₄×D₁₃	C₂³	1	16	yes	—
338	C₂²⋊C₄×D₁₃	C₂³	1	16	yes	—
339	#88133	C₂³	1	8	yes	complemented
340	#88132	C₂³	1	8	yes	—
341	#88132	C₂³	1	16	yes	—
342	#88131	C₂³	1	16	yes	—
343	#88130	C₂³	1	16	yes	complemented
344	#88130	C₂³	1	16	yes	complemented
345	#88129	C₂³	1	8	yes	—
346	#88129	C₂³	1	16	yes	complemented
347	C₄×D₅₂	C₂³	1	8	yes	—
348	#88126	C₂³	1	8	yes	complemented
349	#88126	C₂³	1	16	yes	complemented
350	C₄×Dic₂₆	C₂³	1	8	yes	complemented
351	C₂×#3561	—	13	1	no	maximal, Sylow
352	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
354	C₂³×D₁₃	—	2	8	no	—
355	C₂³×D₁₃	—	4	4	no	—
356	C₂³×D₁₃	—	4	4	no	—
357	C₂³×D₁₃	C₂⁴	1	2	yes	—
358	C₂³×D₁₃	C₂⁴	1	2	yes	—
359	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
360	C₂³×D₁₃	C₂⁴	1	8	yes	—
361	C₂×Q₈×C₁₃	—	2	4	no	—
362	C₂×Q₈×C₁₃	—	2	4	no	—
363	C₂×Q₈×C₁₃	—	2	4	no	—
364	C₂×Q₈×C₁₃	—	4	4	no	—
365	C₂×Q₈×C₁₃	—	4	4	no	—
366	C₂×Q₈×C₁₃	—	4	16	no	—
367	C₂×Q₈×C₁₃	—	4	16	no	—
368	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
369	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
370	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
371	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
372	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
373	C₂×D₄×C₁₃	—	2	4	no	—
374	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
375	C₂²×C₄×C₁₃	—	2	4	no	—
376	C₂²×C₄×C₁₃	—	2	4	no	—
377	C₂²×C₄×C₁₃	—	4	4	no	—
378	C₂²×C₄×C₁₃	—	4	4	no	—
379	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
381	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
382	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
383	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
384	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
386	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
389	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
390	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
391	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₂²⋊D₁₃	—	2	4	no	—
393	C₂×C₂²⋊D₁₃	—	4	4	no	—
394	C₂×C₂²⋊D₁₃	—	4	4	no	—
395	C₂×C₂²⋊D₁₃	—	4	2	no	—
396	C₂×C₂²⋊D₁₃	C₂⁴	1	4	yes	—
397	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
398	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
399	C₂×C₂²⋊D₁₃	C₂⁴	1	4	yes	—
400	C₂²×Dic₁₃	—	2	4	no	—
401	C₂²×Dic₁₃	—	4	2	no	—
402	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
403	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
408	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
410	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
413	#6131	—	4	16	no	—
414	Q₈×D₁₃	—	4	16	no	—
415	#6127	—	4	16	no	—
416	C₂×D₅₂	—	2	4	no	—
417	C₂×D₅₂	—	2	4	no	—
418	C₂×D₅₂	—	4	16	no	—
419	C₂×D₅₂	—	4	4	no	—
420	C₂×D₅₂	—	4	4	no	—
421	C₂×D₅₂	—	4	4	no	—
422	C₂×D₅₂	C₂⁴	1	4	yes	—
423	C₂×D₅₂	C₂⁴	1	4	yes	—
424	C₂×D₅₂	C₂⁴	1	8	yes	—
425	C₂×D₅₂	C₂⁴	1	8	yes	—
426	C₂×D₅₂	C₂⁴	1	8	yes	—
427	C₂×C₄×D₁₃	—	2	4	no	—
428	C₂×C₄×D₁₃	—	4	4	no	—
429	C₂×C₄×D₁₃	—	4	4	no	—
430	C₂×C₄×D₁₃	—	4	4	no	—
431	C₂×C₄×D₁₃	—	4	4	no	—
432	C₂×C₄×D₁₃	—	4	4	no	—
433	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
434	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
435	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
436	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
437	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
438	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
439	C₂×Dic₂₆	—	2	4	no	—
440	C₂×Dic₂₆	—	4	4	no	—
441	C₂×Dic₂₆	—	4	2	no	—
442	C₂×Dic₂₆	—	4	4	no	—
443	C₂×Dic₂₆	C₂⁴	1	4	yes	—
444	C₂×Dic₂₆	C₂⁴	1	4	yes	—
445	C₂×Dic₂₆	C₂⁴	1	8	yes	—
446	C₂×Dic₂₆	C₂⁴	1	8	yes	—
447	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
448	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
449	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
450	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
451	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
452	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
453	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
454	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
455	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
456	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
457	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
458	C₄²×C₁₃	C₂⁴	1	4	yes	—
459	C₄²×C₁₃	C₂⁴	1	8	yes	—
460	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
461	C₂²⋊Dic₁₃	C₂⁴	1	4	yes	—
462	C₂²⋊Dic₁₃	C₂⁴	1	4	yes	—
463	C₂²⋊Dic₁₃	C₂⁴	1	4	yes	—
464	C₂²⋊Dic₁₃	C₂⁴	1	4	yes	—
465	#6103	C₂⁴	1	8	yes	—
466	#6103	C₂⁴	1	4	yes	—
467	#6103	C₂⁴	1	4	yes	—
468	#6103	C₂⁴	1	8	yes	—
469	#6103	C₂⁴	1	8	yes	—
470	#6103	C₂⁴	1	8	yes	—
471	#6103	C₂⁴	1	8	yes	—
472	#6103	C₂⁴	1	8	yes	—
473	#6103	C₂⁴	1	8	yes	—
474	#6103	C₂⁴	1	8	yes	—
475	#6103	C₂⁴	1	8	yes	—
476	#6103	C₂⁴	1	8	yes	—
477	#6103	C₂⁴	1	8	yes	—
478	#6103	C₂⁴	1	8	yes	—
479	#6103	C₂⁴	1	8	yes	—
480	#6103	C₂⁴	1	8	yes	—
481	#6103	C₂⁴	1	8	yes	—
482	#6103	C₂⁴	1	8	yes	—
483	#6103	C₂⁴	1	8	yes	—
484	#6103	C₂⁴	1	4	yes	—
485	#6103	C₂⁴	1	4	yes	—
486	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
487	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
488	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
489	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
490	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
491	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
492	#6101	C₂⁴	1	4	yes	—
493	#6101	C₂⁴	1	4	yes	—
494	#6101	C₂⁴	1	4	yes	—
495	#6101	C₂⁴	1	4	yes	—
496	#6101	C₂⁴	1	8	yes	—
497	#6101	C₂⁴	1	8	yes	—
498	#6101	C₂⁴	1	8	yes	—
499	#6101	C₂⁴	1	8	yes	—
500	#6101	C₂⁴	1	8	yes	—
501	#6101	C₂⁴	1	8	yes	—
502	#6101	C₂⁴	1	8	yes	—
503	#6101	C₂⁴	1	4	yes	—
504	#6101	C₂⁴	1	4	yes	—
505	#6101	C₂⁴	1	8	yes	—
506	C₄×Dic₁₃	C₂⁴	1	4	yes	—
507	C₄×Dic₁₃	C₂⁴	1	4	yes	—
508	C₄×Dic₁₃	C₂⁴	1	8	yes	—
509	C₄×Dic₁₃	C₂⁴	1	4	yes	—
510	C₄×Dic₁₃	C₂⁴	1	8	yes	—
511	C₄×Dic₁₃	C₂⁴	1	4	yes	—
512	C₄×Dic₁₃	C₂⁴	1	4	yes	—
513	C₄×Dic₁₃	C₂⁴	1	8	yes	—
514	#3561	—	13	32	no	—
515	C₂×#563	—	13	2	no	—
516	C₂×#562	—	13	2	no	—
517	C₂×#556	—	13	1	no	—
518	C₂×#556	—	13	1	no	—
519	C₂×#551	—	13	2	no	—
520	C₂×#551	—	13	2	no	—
521	C₂×D₄×Q₈	—	13	1	no	—
522	C₂×D₄×Q₈	D₁₃	1	1	yes	characteristic, complemented
523	C₂×#548	—	13	1	no	—
524	C₂×#548	—	13	1	no	—
525	C₂×#546	—	13	1	no	—
526	C₂×#546	—	13	1	no	—
527	C₂×#543	—	13	2	no	—
528	C₂×#542	—	13	2	no	—
529	C₂×#542	—	13	2	no	—
530	C₂×#542	—	13	1	no	—
531	C₂×#542	—	13	1	no	—
532	C₂×#538	—	13	2	no	—
533	C₂×#536	—	13	1	no	—
534	C₂×#536	—	13	1	no	—
535	C₂×#533	—	13	1	no	—
536	C₂×#529	—	13	1	no	—
537	C₂²×#124	—	13	1	no	—
538	C₂³×C₁₃	—	2	2	no	—
539	C₂³×C₁₃	—	2	2	no	—
540	C₂³×C₁₃	—	2	2	no	—
541	C₂³×C₁₃	—	2	2	no	—
542	C₂³×C₁₃	—	2	2	no	—
543	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
544	C₂³×C₁₃	C₂⁵	1	2	yes	—
545	C₂³×C₁₃	C₂⁵	1	2	yes	—
546	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
547	C₂²×D₁₃	—	2	2	no	—
548	C₂²×D₁₃	—	2	4	no	—
549	C₂²×D₁₃	—	2	4	no	—
550	C₂²×D₁₃	—	2	2	no	—
551	C₂²×D₁₃	—	2	4	no	—
552	C₂²×D₁₃	—	2	4	no	—
553	C₂²×D₁₃	—	2	4	no	—
554	C₂²×D₁₃	—	2	4	no	—
555	C₂²×D₁₃	—	2	2	no	—
556	C₂²×D₁₃	—	2	16	no	—
557	C₂²×D₁₃	—	4	8	no	—
558	C₂²×D₁₃	—	4	8	no	—
559	C₂²×D₁₃	—	8	16	no	—
560	C₂²×D₁₃	C₂⁵	1	4	yes	—
561	C₂²×D₁₃	C₂⁵	1	4	yes	—
562	C₂²×D₁₃	C₂⁵	1	2	yes	—
563	Q₈×C₁₃	—	2	8	no	—
564	Q₈×C₁₃	—	2	8	no	—
565	Q₈×C₁₃	—	2	8	no	—
566	Q₈×C₁₃	—	4	8	no	—
567	Q₈×C₁₃	—	4	8	no	—
568	D₄×C₁₃	—	2	8	no	—
569	C₂×C₄×C₁₃	—	2	4	no	—
570	C₂×C₄×C₁₃	—	2	2	no	—
571	C₂×C₄×C₁₃	—	2	4	no	—
572	C₂×C₄×C₁₃	—	2	2	no	—
573	C₂×C₄×C₁₃	—	2	4	no	—
574	C₂×C₄×C₁₃	—	2	2	no	—
575	C₂×C₄×C₁₃	—	2	2	no	—
576	C₂×C₄×C₁₃	—	2	4	no	—
577	C₂×C₄×C₁₃	—	2	8	no	—
578	C₂×C₄×C₁₃	—	2	8	no	—
579	C₂×C₄×C₁₃	—	4	8	no	—
580	C₂×C₄×C₁₃	—	4	8	no	—
581	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
582	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
583	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
584	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
585	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
586	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
587	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
588	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
589	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
590	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
591	C₂²⋊D₁₃	—	2	8	no	—
592	C₂²⋊D₁₃	—	4	8	no	—
593	C₂²⋊D₁₃	—	4	8	no	—
594	C₂²⋊D₁₃	—	4	4	no	—
595	C₂×Dic₁₃	—	2	4	no	—
596	C₂×Dic₁₃	—	2	2	no	—
597	C₂×Dic₁₃	—	2	8	no	—
598	C₂×Dic₁₃	—	2	2	no	—
599	C₂×Dic₁₃	—	2	2	no	—
600	C₂×Dic₁₃	—	2	2	no	—
601	C₂×Dic₁₃	—	2	2	no	—
602	C₂×Dic₁₃	—	2	2	no	—
603	C₂×Dic₁₃	—	2	4	no	—
604	C₂×Dic₁₃	—	2	2	no	—
605	C₂×Dic₁₃	—	4	4	no	—
606	C₂×Dic₁₃	C₂⁵	1	2	yes	—
607	C₂×Dic₁₃	C₂⁵	1	2	yes	—
608	C₂×Dic₁₃	C₂⁵	1	2	yes	—
609	C₂×Dic₁₃	C₂⁵	1	2	yes	—
610	C₂×Dic₁₃	C₂⁵	1	4	yes	—
611	C₂×Dic₁₃	C₂⁵	1	2	yes	—
612	C₂×Dic₁₃	C₂⁵	1	4	yes	—
613	C₂×Dic₁₃	C₂⁵	1	2	yes	—
614	C₂×Dic₁₃	C₂⁵	1	2	yes	—
615	D₅₂	—	2	8	no	—
616	D₅₂	—	2	8	no	—
617	D₅₂	—	4	8	no	—
618	D₅₂	—	4	8	no	—
619	D₅₂	—	4	8	no	—
620	C₄×D₁₃	—	2	8	no	—
621	C₄×D₁₃	—	4	8	no	—
622	C₄×D₁₃	—	4	8	no	—
623	C₄×D₁₃	—	4	8	no	—
624	C₄×D₁₃	—	4	8	no	—
625	C₄×D₁₃	—	4	8	no	—
626	Dic₂₆	—	2	8	no	—
627	Dic₂₆	—	4	8	no	—
628	Dic₂₆	—	4	4	no	—
629	Dic₂₆	—	4	8	no	—
630	C₂²×#41	—	13	1	no	—
631	C₂²×#41	—	13	1	no	—
632	C₂³×Q₈	—	13	1	no	—
633	C₂³×Q₈	C₂×D₁₃	1	1	yes	characteristic
634	C₂³×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
635	C₂³×D₄	—	13	1	no	—
636	#563	—	13	32	no	—
637	#562	—	13	32	no	—
638	#556	—	13	16	no	—
639	#556	—	13	16	no	—
640	#551	—	13	32	no	—
641	#551	—	13	32	no	—
642	D₄×Q₈	—	13	16	no	—
643	D₄×Q₈	C₂×D₁₃	1	16	yes	complemented
644	#548	—	13	16	no	—
645	#548	—	13	16	no	—
646	#546	—	13	16	no	—
647	#546	—	13	16	no	—
648	#543	—	13	32	no	—
649	#542	—	13	32	no	—
650	#542	—	13	32	no	—
651	#542	—	13	16	no	—
652	#542	—	13	16	no	—
653	#538	—	13	32	no	—
654	#536	—	13	16	no	—
655	#536	—	13	16	no	—
656	#533	—	13	16	no	—
657	C₂×C₄⋊Q₈	—	13	1	no	—
658	C₂×C₄⋊Q₈	—	13	1	no	—
659	C₂×C₄⋊Q₈	—	13	2	no	—
660	C₂×C₄⋊Q₈	—	13	1	no	—
661	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
662	C₂×C₄⋊Q₈	C₂×D₁₃	1	2	yes	complemented
663	#529	—	13	16	no	—
664	C₂×#126	—	13	1	no	—
665	C₂×#126	—	13	2	no	—
666	C₂×#126	—	13	2	no	—
667	C₂×#126	—	13	2	no	—
668	C₂×#126	—	13	2	no	—
669	C₂×#126	—	13	1	no	—
670	C₂×#126	—	13	2	no	—
671	C₂×#126	—	13	2	no	—
672	C₂×#125	—	13	1	no	—
673	C₂×#125	—	13	2	no	—
674	C₂×#124	—	13	1	no	—
675	C₂×#124	—	13	1	no	—
676	C₂×#124	—	13	2	no	—
677	C₂×#124	—	13	1	no	—
678	C₂×#124	—	13	1	no	—
679	C₂×#124	—	13	2	no	—
680	C₂×#124	—	13	1	no	—
681	C₂×#124	—	13	16	no	—
682	C₂×#124	—	13	2	no	—
683	C₂×#124	—	13	1	no	—
684	C₂×#124	—	13	2	no	—
685	C₂×#124	—	13	2	no	—
686	C₂×#124	—	13	1	no	—
687	C₂×#124	—	13	2	no	—
688	C₂×#123	—	13	1	no	—
689	C₂×#123	—	13	2	no	—
690	C₂×#123	—	13	2	no	—
691	C₂×#123	—	13	2	no	—
692	C₂×#123	—	13	2	no	—
693	C₂×#123	—	13	2	no	—
694	C₂×#123	—	13	2	no	—
695	C₂×#123	—	13	2	no	—
696	C₂×#123	—	13	2	no	—
697	C₂×#123	—	13	1	no	—
698	C₂×C₂²⋊Q₈	—	13	2	no	—
699	C₂×C₂²⋊Q₈	—	13	2	no	—
700	C₂×C₂²⋊Q₈	—	13	1	no	—
701	C₂×C₂²⋊Q₈	—	13	2	no	—
702	C₂×C₂²⋊Q₈	—	13	2	no	—
703	C₂×C₂²⋊Q₈	—	13	1	no	—
704	C₂×C₂²⋊Q₈	—	13	2	no	—
705	C₂×C₂²⋊Q₈	—	13	2	no	—
706	C₂×C₂²⋊Q₈	—	13	2	no	—
707	C₂×C₂²⋊Q₈	—	13	2	no	—
708	C₂×C₂²⋊Q₈	—	13	2	no	—
709	C₂×C₂²⋊Q₈	—	13	2	no	—
710	C₂×C₂²⋊Q₈	—	13	2	no	—
711	C₂×C₂²⋊Q₈	—	13	2	no	—
712	C₂×C₂²⋊Q₈	—	13	1	no	—
713	C₂×C₂²⋊Q₈	—	13	2	no	—
714	C₂×C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
715	C₂×C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
716	C₂×C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
717	C₂×C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
718	C₂×#121	—	13	1	no	—
719	C₂×#121	—	13	1	no	—
720	C₂×#121	—	13	2	no	—
721	C₂×#121	—	13	1	no	—
722	C₂×#121	—	13	2	no	—
723	C₂×#121	—	13	2	no	—
724	C₂×#121	—	13	2	no	—
725	C₂×#120	—	13	2	no	—
726	C₂×#120	—	13	2	no	—
727	C₂×C₄×Q₈	—	13	1	no	—
728	C₂×C₄×Q₈	—	13	1	no	—
729	C₂×C₄×Q₈	—	13	2	no	—
730	C₂×C₄×Q₈	—	13	1	no	—
731	C₂×C₄×Q₈	—	13	1	no	—
732	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
733	C₂×C₄×D₄	—	13	1	no	—
734	C₂×C₄×D₄	—	13	2	no	—
735	C₂×C₄×D₄	—	13	1	no	—
736	C₂×C₄×D₄	—	13	2	no	—
737	C₂×C₄×D₄	—	13	1	no	—
738	C₂×C₄×D₄	—	13	2	no	—
739	C₂×C₄×D₄	—	13	1	no	—
740	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
741	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
742	C₂×#117	—	13	1	no	—
743	C₂×#117	—	13	2	no	—
744	C₂×#117	—	13	2	no	—
745	C₂×#117	—	13	1	no	—
746	C₂×#117	—	13	2	no	—
747	C₂²×C₂²⋊C₄	—	13	2	no	—
748	C₂²×C₂²⋊C₄	—	13	2	no	—
749	C₂²×C₂²⋊C₄	—	13	2	no	—
750	C₂²×C₂²⋊C₄	—	13	2	no	—
751	C₂²×C₄²	—	13	1	no	—
752	C₂²×C₁₃	—	2	2	no	—
753	C₂²×C₁₃	—	2	2	no	—
754	C₂²×C₁₃	—	2	8	no	—
755	C₂²×C₁₃	—	2	2	no	—
756	C₂²×C₁₃	—	2	2	no	—
757	C₂²×C₁₃	—	2	2	no	—
758	C₂²×C₁₃	—	4	4	no	—
759	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
760	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
761	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
762	C₂²×C₁₃	#585	1	2	yes	—
763	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
764	C₂×D₁₃	—	2	2	no	—
765	C₂×D₁₃	—	2	4	no	—
766	C₂×D₁₃	—	2	4	no	—
767	C₂×D₁₃	—	2	2	no	—
768	C₂×D₁₃	—	2	4	no	—
769	C₂×D₁₃	—	2	4	no	—
770	C₂×D₁₃	—	2	4	no	—
771	C₂×D₁₃	—	2	4	no	—
772	C₂×D₁₃	—	2	2	no	—
773	C₂×D₁₃	—	4	4	no	—
774	C₂×D₁₃	—	4	8	no	—
775	C₂×D₁₃	—	4	8	no	—
776	C₂×D₁₃	—	8	16	no	—
777	C₄×C₁₃	—	2	4	no	—
778	C₄×C₁₃	—	2	2	no	—
779	C₄×C₁₃	—	2	4	no	—
780	C₄×C₁₃	—	2	2	no	—
781	C₄×C₁₃	—	2	4	no	—
782	C₄×C₁₃	—	2	2	no	—
783	C₄×C₁₃	—	2	2	no	—
784	C₄×C₁₃	—	2	4	no	—
785	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
786	Dic₁₃	—	2	4	no	—
787	Dic₁₃	—	2	2	no	—
788	Dic₁₃	—	2	2	no	—
789	Dic₁₃	—	2	2	no	—
790	Dic₁₃	—	2	2	no	—
791	Dic₁₃	—	2	2	no	—
792	Dic₁₃	—	2	2	no	—
793	Dic₁₃	—	2	4	no	—
794	Dic₁₃	—	2	2	no	—
795	C₂⁵	—	13	2	no	—
796	C₂×#41	—	13	8	no	—
797	C₂×#41	—	13	8	no	—
798	C₂×#41	—	52	4	no	—
799	C₂×#41	—	52	4	no	—
800	C₂²×Q₈	—	4	4	no	—
801	C₂²×Q₈	—	4	4	no	—
802	C₂²×Q₈	—	13	8	no	—
803	C₂²×Q₈	—	13	1	no	—
804	C₂²×Q₈	—	13	1	no	—
805	C₂²×Q₈	—	13	2	no	—
806	C₂²×Q₈	—	13	2	no	—
807	C₂²×Q₈	—	52	4	no	—
808	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
809	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
810	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
811	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
812	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
813	C₂²×Q₈	C₂²×D₁₃	1	8	yes	—
814	C₂²×Q₈	C₂²×D₁₃	1	8	yes	complemented
815	C₂²×D₄	—	13	1	no	—
816	C₂²×D₄	—	13	2	no	—
817	C₂²×D₄	—	13	1	no	—
818	C₂²×D₄	—	13	2	no	—
819	C₂²×D₄	—	13	1	no	—
820	C₂²×D₄	—	13	1	no	—
821	C₂²×D₄	—	13	2	no	—
822	C₂²×D₄	—	13	2	no	—
823	C₂²×D₄	—	13	2	no	—
824	C₂²×D₄	—	13	8	no	—
825	C₂²×D₄	—	52	4	no	—
826	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
827	C₂³×C₄	—	13	1	no	—
828	C₂³×C₄	—	13	1	no	—
829	C₂³×C₄	—	13	1	no	—
830	C₂³×C₄	—	13	2	no	—
831	C₂³×C₄	—	13	2	no	—
832	C₂³×C₄	—	13	2	no	—
833	C₂³×C₄	—	13	2	no	—
834	C₂³×C₄	—	13	2	no	—
835	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
836	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
837	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
838	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
839	C₄⋊Q₈	—	13	8	no	—
840	C₄⋊Q₈	—	13	8	no	—
841	C₄⋊Q₈	—	13	16	no	—
842	C₄⋊Q₈	—	13	8	no	—
843	C₄⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
844	C₄⋊Q₈	C₂²×D₁₃	1	16	yes	complemented
845	#126	—	13	8	no	—
846	#126	—	13	16	no	—
847	#126	—	13	16	no	—
848	#126	—	13	16	no	—
849	#126	—	13	16	no	—
850	#126	—	13	8	no	—
851	#126	—	13	16	no	—
852	#126	—	13	16	no	—
853	#125	—	13	8	no	—
854	#125	—	13	16	no	—
855	#124	—	13	8	no	—
856	#124	—	13	8	no	—
857	#124	—	13	16	no	—
858	#124	—	13	8	no	—
859	#124	—	13	8	no	—
860	#124	—	13	16	no	—
861	#124	—	13	8	no	—
862	#124	—	13	16	no	—
863	#124	—	13	8	no	—
864	#124	—	13	16	no	—
865	#124	—	13	16	no	—
866	#124	—	13	8	no	—
867	#124	—	13	16	no	—
868	#123	—	13	8	no	—
869	#123	—	13	16	no	—
870	#123	—	13	16	no	—
871	#123	—	13	16	no	—
872	#123	—	13	16	no	—
873	#123	—	13	16	no	—
874	#123	—	13	16	no	—
875	#123	—	13	16	no	—
876	#123	—	13	8	no	—
877	#123	—	13	16	no	—
878	C₂²⋊Q₈	—	13	16	no	—
879	C₂²⋊Q₈	—	13	16	no	—
880	C₂²⋊Q₈	—	13	8	no	—
881	C₂²⋊Q₈	—	13	16	no	—
882	C₂²⋊Q₈	—	13	16	no	—
883	C₂²⋊Q₈	—	13	8	no	—
884	C₂²⋊Q₈	—	13	16	no	—
885	C₂²⋊Q₈	—	13	16	no	—
886	C₂²⋊Q₈	—	13	16	no	—
887	C₂²⋊Q₈	—	13	16	no	—
888	C₂²⋊Q₈	—	13	16	no	—
889	C₂²⋊Q₈	—	13	16	no	—
890	C₂²⋊Q₈	—	13	16	no	—
891	C₂²⋊Q₈	—	13	16	no	—
892	C₂²⋊Q₈	—	13	8	no	—
893	C₂²⋊Q₈	—	13	16	no	—
894	C₂²⋊Q₈	C₂²×D₁₃	1	8	yes	—
895	C₂²⋊Q₈	C₂²×D₁₃	1	16	yes	—
896	C₂²⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
897	C₂²⋊Q₈	C₂²×D₁₃	1	16	yes	complemented
898	#121	—	13	8	no	—
899	#121	—	13	16	no	—
900	#121	—	13	8	no	—
901	#121	—	13	8	no	—
902	#121	—	13	16	no	—
903	#121	—	13	16	no	—
904	#121	—	13	16	no	—
905	#120	—	13	16	no	—
906	#120	—	13	16	no	—
907	C₄×Q₈	—	13	8	no	—
908	C₄×Q₈	—	13	8	no	—
909	C₄×Q₈	—	13	16	no	—
910	C₄×Q₈	—	13	8	no	—
911	C₄×Q₈	—	13	8	no	—
912	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
913	C₄×D₄	—	13	8	no	—
914	C₄×D₄	—	13	8	no	—
915	C₄×D₄	—	13	16	no	—
916	C₄×D₄	—	13	16	no	—
917	C₄×D₄	—	13	8	no	—
918	C₄×D₄	—	13	16	no	—
919	C₄×D₄	—	13	8	no	—
920	C₄×D₄	C₂²×D₁₃	1	8	yes	—
921	C₄×D₄	C₂²×D₁₃	1	16	yes	—
922	#117	—	13	8	no	—
923	#117	—	13	16	no	—
924	#117	—	13	16	no	—
925	#117	—	13	8	no	—
926	#117	—	13	16	no	—
927	C₂×C₄⋊C₄	—	13	1	no	—
928	C₂×C₄⋊C₄	—	13	1	no	—
929	C₂×C₄⋊C₄	—	13	1	no	—
930	C₂×C₄⋊C₄	—	13	1	no	—
931	C₂×C₄⋊C₄	—	13	2	no	—
932	C₂×C₄⋊C₄	—	13	2	no	—
933	C₂×C₄⋊C₄	—	13	1	no	—
934	C₂×C₄⋊C₄	—	13	1	no	—
935	C₂×C₄⋊C₄	—	13	2	no	—
936	C₂×C₄⋊C₄	—	13	1	no	—
937	C₂×C₄⋊C₄	—	13	1	no	—
938	C₂×C₄⋊C₄	—	13	2	no	—
939	C₂×C₄⋊C₄	—	13	2	no	—
940	C₂×C₄⋊C₄	—	13	1	no	—
941	C₂×C₄⋊C₄	—	13	2	no	—
942	C₂×C₄⋊C₄	—	13	2	no	—
943	C₂×C₄⋊C₄	—	13	2	no	—
944	C₂×C₄⋊C₄	—	13	1	no	—
945	C₂×C₄⋊C₄	—	13	2	no	—
946	C₂×C₄⋊C₄	—	13	2	no	—
947	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
948	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
949	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
950	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
951	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
952	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
953	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
954	C₂×C₂²⋊C₄	—	13	1	no	—
955	C₂×C₂²⋊C₄	—	13	2	no	—
956	C₂×C₂²⋊C₄	—	13	1	no	—
957	C₂×C₂²⋊C₄	—	13	1	no	—
958	C₂×C₂²⋊C₄	—	13	1	no	—
959	C₂×C₂²⋊C₄	—	13	2	no	—
960	C₂×C₂²⋊C₄	—	13	2	no	—
961	C₂×C₂²⋊C₄	—	13	2	no	—
962	C₂×C₂²⋊C₄	—	13	2	no	—
963	C₂×C₂²⋊C₄	—	13	2	no	—
964	C₂×C₂²⋊C₄	—	13	2	no	—
965	C₂×C₂²⋊C₄	—	13	2	no	—
966	C₂×C₂²⋊C₄	—	13	2	no	—
967	C₂×C₂²⋊C₄	—	13	2	no	—
968	C₂×C₂²⋊C₄	—	13	2	no	—
969	C₂×C₂²⋊C₄	—	13	2	no	—
970	C₂×C₂²⋊C₄	—	13	2	no	—
971	C₂×C₂²⋊C₄	—	13	16	no	—
972	C₂×C₂²⋊C₄	—	13	16	no	—
973	C₂×C₂²⋊C₄	—	13	2	no	—
974	C₂×C₂²⋊C₄	—	13	2	no	—
975	C₂×C₂²⋊C₄	—	13	1	no	—
976	C₂×C₂²⋊C₄	—	13	1	no	—
977	C₂×C₂²⋊C₄	—	13	1	no	—
978	C₂×C₂²⋊C₄	—	13	2	no	—
979	C₂×C₂²⋊C₄	—	13	2	no	—
980	C₂×C₂²⋊C₄	—	13	1	no	—
981	C₂×C₂²⋊C₄	—	13	2	no	—
982	C₂×C₂²⋊C₄	—	13	16	no	—
983	C₂×C₂²⋊C₄	—	13	16	no	—
984	C₂×C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
985	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
986	C₂×C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
987	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
988	C₂×C₄²	—	13	2	no	—
989	C₂×C₄²	—	13	2	no	—
990	C₂×C₄²	—	13	1	no	—
991	C₂×C₄²	—	13	1	no	—
992	C₂×C₄²	—	13	2	no	—
993	C₂×C₄²	—	13	1	no	—
994	C₂×C₄²	—	13	1	no	—
995	C₂×C₄²	—	13	1	no	—
996	C₂×C₄²	—	13	8	no	—
997	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
998	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
999	C₂×C₁₃	—	2	4	no	—
1000	C₂×C₁₃	—	4	2	no	—
1001	C₂×C₁₃	#3561	1	4	yes	complemented
1002	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1003	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
1004	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
1005	D₁₃	—	4	2	no	—
1006	D₁₃	—	4	4	no	—
1007	D₁₃	—	4	4	no	—
1008	C₂⁴	—	13	2	no	—
1009	C₂⁴	—	13	2	no	—
1010	C₂⁴	—	13	1	no	—
1011	C₂⁴	—	13	8	no	—
1012	C₂⁴	—	26	8	no	—
1013	C₂⁴	—	52	4	no	—
1014	C₂⁴	—	52	4	no	—
1015	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
1016	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
1017	#41	—	52	16	no	—
1018	#41	—	52	16	no	—
1019	C₂×Q₈	—	2	4	no	—
1020	C₂×Q₈	—	2	4	no	—
1021	C₂×Q₈	—	2	4	no	—
1022	C₂×Q₈	—	4	4	no	—
1023	C₂×Q₈	—	4	4	no	—
1024	C₂×Q₈	—	4	16	no	—
1025	C₂×Q₈	—	4	16	no	—
1026	C₂×Q₈	—	13	4	no	—
1027	C₂×Q₈	—	13	4	no	—
1028	C₂×Q₈	—	13	8	no	—
1029	C₂×Q₈	—	13	8	no	—
1030	C₂×Q₈	—	26	4	no	—
1031	C₂×Q₈	—	52	4	no	—
1032	C₂×Q₈	—	52	2	no	—
1033	C₂×Q₈	—	52	4	no	—
1034	C₂×Q₈	—	52	16	no	—
1035	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
1036	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
1037	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
1038	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
1039	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
1040	C₂×D₄	—	2	4	no	—
1041	C₂×D₄	—	13	4	no	—
1042	C₂×D₄	—	13	8	no	—
1043	C₂×D₄	—	13	4	no	—
1044	C₂×D₄	—	13	8	no	—
1045	C₂×D₄	—	13	4	no	—
1046	C₂×D₄	—	13	4	no	—
1047	C₂×D₄	—	13	8	no	—
1048	C₂×D₄	—	13	8	no	—
1049	C₂×D₄	—	13	8	no	—
1050	C₂×D₄	—	26	4	no	—
1051	C₂×D₄	—	26	4	no	—
1052	C₂×D₄	—	26	4	no	—
1053	C₂×D₄	—	52	16	no	—
1054	C₂×D₄	—	52	4	no	—
1055	C₂×D₄	—	52	4	no	—
1056	C₂×D₄	—	52	4	no	—
1057	C₂×D₄	—	52	4	no	—
1058	C₂×D₄	—	52	4	no	—
1059	C₂×D₄	—	52	2	no	—
1060	C₂×D₄	C₂³×D₁₃	1	4	yes	—
1061	C₂²×C₄	—	2	4	no	—
1062	C₂²×C₄	—	2	4	no	—
1063	C₂²×C₄	—	4	4	no	—
1064	C₂²×C₄	—	4	4	no	—
1065	C₂²×C₄	—	13	4	no	—
1066	C₂²×C₄	—	13	1	no	—
1067	C₂²×C₄	—	13	1	no	—
1068	C₂²×C₄	—	13	1	no	—
1069	C₂²×C₄	—	13	1	no	—
1070	C₂²×C₄	—	13	2	no	—
1071	C₂²×C₄	—	13	1	no	—
1072	C₂²×C₄	—	13	1	no	—
1073	C₂²×C₄	—	13	2	no	—
1074	C₂²×C₄	—	13	1	no	—
1075	C₂²×C₄	—	13	4	no	—
1076	C₂²×C₄	—	13	4	no	—
1077	C₂²×C₄	—	13	8	no	—
1078	C₂²×C₄	—	13	8	no	—
1079	C₂²×C₄	—	13	8	no	—
1080	C₂²×C₄	—	13	8	no	—
1081	C₂²×C₄	—	13	8	no	—
1082	C₂²×C₄	—	26	4	no	—
1083	C₂²×C₄	—	26	4	no	—
1084	C₂²×C₄	—	52	4	no	—
1085	C₂²×C₄	—	52	4	no	—
1086	C₂²×C₄	—	52	4	no	—
1087	C₂²×C₄	—	52	4	no	—
1088	C₂²×C₄	—	52	4	no	—
1089	C₂²×C₄	—	52	2	no	—
1090	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
1091	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
1092	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1093	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
1094	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
1095	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
1096	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1097	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
1098	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1099	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1100	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
1101	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
1102	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1103	C₄⋊C₄	—	13	4	no	—
1104	C₄⋊C₄	—	13	4	no	—
1105	C₄⋊C₄	—	13	4	no	—
1106	C₄⋊C₄	—	13	4	no	—
1107	C₄⋊C₄	—	13	8	no	—
1108	C₄⋊C₄	—	13	8	no	—
1109	C₄⋊C₄	—	13	4	no	—
1110	C₄⋊C₄	—	13	4	no	—
1111	C₄⋊C₄	—	13	8	no	—
1112	C₄⋊C₄	—	13	4	no	—
1113	C₄⋊C₄	—	13	4	no	—
1114	C₄⋊C₄	—	13	8	no	—
1115	C₄⋊C₄	—	13	8	no	—
1116	C₄⋊C₄	—	13	4	no	—
1117	C₄⋊C₄	—	13	8	no	—
1118	C₄⋊C₄	—	13	8	no	—
1119	C₄⋊C₄	—	13	8	no	—
1120	C₄⋊C₄	—	13	4	no	—
1121	C₄⋊C₄	—	13	8	no	—
1122	C₄⋊C₄	—	13	8	no	—
1123	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
1124	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
1125	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
1126	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
1127	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
1128	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
1129	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
1130	C₂²⋊C₄	—	13	4	no	—
1131	C₂²⋊C₄	—	13	8	no	—
1132	C₂²⋊C₄	—	13	4	no	—
1133	C₂²⋊C₄	—	13	4	no	—
1134	C₂²⋊C₄	—	13	4	no	—
1135	C₂²⋊C₄	—	13	8	no	—
1136	C₂²⋊C₄	—	13	8	no	—
1137	C₂²⋊C₄	—	13	8	no	—
1138	C₂²⋊C₄	—	13	8	no	—
1139	C₂²⋊C₄	—	13	8	no	—
1140	C₂²⋊C₄	—	13	8	no	—
1141	C₂²⋊C₄	—	13	8	no	—
1142	C₂²⋊C₄	—	13	8	no	—
1143	C₂²⋊C₄	—	13	8	no	—
1144	C₂²⋊C₄	—	13	8	no	—
1145	C₂²⋊C₄	—	13	8	no	—
1146	C₂²⋊C₄	—	13	8	no	—
1147	C₂²⋊C₄	—	13	8	no	—
1148	C₂²⋊C₄	—	13	8	no	—
1149	C₂²⋊C₄	—	13	4	no	—
1150	C₂²⋊C₄	—	13	4	no	—
1151	C₂²⋊C₄	—	13	4	no	—
1152	C₂²⋊C₄	—	13	8	no	—
1153	C₂²⋊C₄	—	13	8	no	—
1154	C₂²⋊C₄	—	13	4	no	—
1155	C₂²⋊C₄	—	13	8	no	—
1156	C₂²⋊C₄	C₂³×D₁₃	1	4	yes	—
1157	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
1158	C₂²⋊C₄	C₂³×D₁₃	1	4	yes	—
1159	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
1160	C₄²	—	13	4	no	—
1161	C₄²	—	13	4	no	—
1162	C₄²	—	13	4	no	—
1163	C₄²	—	13	4	no	—
1164	C₄²	—	13	8	no	—
1165	C₄²	—	13	8	no	—
1166	C₄²	—	13	4	no	—
1167	C₄²	—	13	8	no	—
1168	C₄²	C₂³×D₁₃	1	4	yes	—
1169	C₄²	C₂³×D₁₃	1	8	yes	—
1170	C₁₃	C₂×#3561	1	1	yes	characteristic, complemented, Sylow
1171	C₂³	—	2	2	no	—
1172	C₂³	—	2	2	no	—
1173	C₂³	—	2	2	no	—
1174	C₂³	—	2	2	no	—
1175	C₂³	—	2	2	no	—
1176	C₂³	—	13	4	no	—
1177	C₂³	—	13	4	no	—
1178	C₂³	—	13	2	no	—
1179	C₂³	—	26	2	no	—
1180	C₂³	—	26	4	no	—
1181	C₂³	—	26	4	no	—
1182	C₂³	—	26	2	no	—
1183	C₂³	—	26	4	no	—
1184	C₂³	—	26	4	no	—
1185	C₂³	—	26	4	no	—
1186	C₂³	—	26	4	no	—
1187	C₂³	—	26	2	no	—
1188	C₂³	—	26	16	no	—
1189	C₂³	—	52	8	no	—
1190	C₂³	—	52	8	no	—
1191	C₂³	—	104	16	no	—
1192	C₂³	#88254	1	4	yes	—
1193	C₂³	C₂⁴×D₁₃	1	2	yes	—
1194	C₂³	C₂⁴×D₁₃	1	2	yes	—
1195	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
1196	Q₈	—	2	8	no	—
1197	Q₈	—	2	8	no	—
1198	Q₈	—	2	8	no	—
1199	Q₈	—	4	8	no	—
1200	Q₈	—	4	8	no	—
1201	Q₈	—	26	8	no	—
1202	Q₈	—	52	4	no	—
1203	Q₈	—	52	8	no	—
1204	Q₈	—	52	8	no	—
1205	D₄	—	2	8	no	—
1206	D₄	—	26	8	no	—
1207	D₄	—	26	8	no	—
1208	D₄	—	26	8	no	—
1209	D₄	—	52	8	no	—
1210	D₄	—	52	8	no	—
1211	D₄	—	52	8	no	—
1212	D₄	—	52	8	no	—
1213	D₄	—	52	4	no	—
1214	D₄	—	52	8	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	2	2	no	—
1217	C₂×C₄	—	2	4	no	—
1218	C₂×C₄	—	2	4	no	—
1219	C₂×C₄	—	2	4	no	—
1220	C₂×C₄	—	2	2	no	—
1221	C₂×C₄	—	2	2	no	—
1222	C₂×C₄	—	2	4	no	—
1223	C₂×C₄	—	2	8	no	—
1224	C₂×C₄	—	2	8	no	—
1225	C₂×C₄	—	4	8	no	—
1226	C₂×C₄	—	4	8	no	—
1227	C₂×C₄	—	13	2	no	—
1228	C₂×C₄	—	13	2	no	—
1229	C₂×C₄	—	13	2	no	—
1230	C₂×C₄	—	13	2	no	—
1231	C₂×C₄	—	13	2	no	—
1232	C₂×C₄	—	13	4	no	—
1233	C₂×C₄	—	13	2	no	—
1234	C₂×C₄	—	13	4	no	—
1235	C₂×C₄	—	13	2	no	—
1236	C₂×C₄	—	26	2	no	—
1237	C₂×C₄	—	26	4	no	—
1238	C₂×C₄	—	26	8	no	—
1239	C₂×C₄	—	26	2	no	—
1240	C₂×C₄	—	26	2	no	—
1241	C₂×C₄	—	26	2	no	—
1242	C₂×C₄	—	26	2	no	—
1243	C₂×C₄	—	26	4	no	—
1244	C₂×C₄	—	26	2	no	—
1245	C₂×C₄	—	26	2	no	—
1246	C₂×C₄	—	26	8	no	—
1247	C₂×C₄	—	52	8	no	—
1248	C₂×C₄	—	52	8	no	—
1249	C₂×C₄	—	52	8	no	—
1250	C₂×C₄	—	52	8	no	—
1251	C₂×C₄	—	52	8	no	—
1252	C₂×C₄	—	52	4	no	—
1253	C₂×C₄	#88251	1	4	yes	—
1254	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1255	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
1256	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
1257	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
1258	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1259	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
1260	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1261	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1262	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
1263	C₂²	—	2	2	no	—
1264	C₂²	—	2	2	no	—
1265	C₂²	—	2	8	no	—
1266	C₂²	—	2	2	no	—
1267	C₂²	—	2	2	no	—
1268	C₂²	—	2	2	no	—
1269	C₂²	—	4	4	no	—
1270	C₂²	—	26	2	no	—
1271	C₂²	—	26	4	no	—
1272	C₂²	—	26	4	no	—
1273	C₂²	—	26	2	no	—
1274	C₂²	—	26	4	no	—
1275	C₂²	—	26	4	no	—
1276	C₂²	—	26	4	no	—
1277	C₂²	—	26	4	no	—
1278	C₂²	—	26	2	no	—
1279	C₂²	—	52	4	no	—
1280	C₂²	—	52	8	no	—
1281	C₂²	—	52	8	no	—
1282	C₂²	—	104	16	no	—
1283	C₂²	C₂×#88251	1	2	yes	—
1284	C₂²	C₂×#88254	1	4	yes	—
1285	C₂²	C₂×#88254	1	2	yes	—
1286	C₂²	#11719652	1	2	yes	—
1287	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
1288	C₄	—	2	2	no	—
1289	C₄	—	2	2	no	—
1290	C₄	—	2	4	no	—
1291	C₄	—	2	4	no	—
1292	C₄	—	2	4	no	—
1293	C₄	—	2	2	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	4	no	—
1296	C₄	—	26	2	no	—
1297	C₄	—	26	4	no	—
1298	C₄	—	26	2	no	—
1299	C₄	—	26	2	no	—
1300	C₄	—	26	2	no	—
1301	C₄	—	26	2	no	—
1302	C₄	—	26	4	no	—
1303	C₄	—	26	2	no	—
1304	C₄	—	26	2	no	—
1305	C₄	C₂×#88251	1	4	yes	—
1306	C₂	—	2	4	no	—
1307	C₂	—	4	2	no	—
1308	C₂	—	52	4	no	—
1309	C₂	—	52	4	no	—
1310	C₂	—	52	2	no	—
1311	C₂	#13129402	1	4	yes	direct product factor
1312	C₂	C₂²×#88251	1	1	yes	characteristic
1313	C₂	C₂²×#88254	1	1	yes	characteristic
1314	C₂	C₂×#11719652	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×D₄×Q₈×C₁₃	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×D₄×Q₈	D₁₃
hypocenter	C₁₃	C₂×#3561
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #13129402	C₂	direct (N × H)
2. C₂×#11719440	C₂	semidirect
3. C₂×#11719352	C₂	semidirect
4. C₂×#11719437	C₂	semidirect
5. C₂×#11719273	C₂	semidirect
6. C₂×#11719261	C₂	semidirect
7. C₂×#11719342	C₂	semidirect
8. C₂×Q₈×C₂²⋊D₁₃	C₂	semidirect
9. C₂×#11719522	C₂	semidirect
10. C₂×#11719338	C₂	semidirect
11. C₂×#11719255	C₂	semidirect
12. C₂×#11719335	C₂	semidirect
13. C₂×#11719339	C₂	semidirect
14. C₂×#11719438	C₂	semidirect
15. C₂×#11719348	C₂	semidirect
16. C₂×#11719287	C₂	semidirect
17. C₂×#11719345	C₂	semidirect
18. C₂×#11719265	C₂	semidirect
19. C₂×#11719429	C₂	semidirect
20. C₂×#11719521	C₂	semidirect
21. C₂×#11719327	C₂	semidirect
22. C₂×#11719243	C₂	semidirect
23. C₂²×#88201	C₂	semidirect
24. C₂×D₄×Q₈×C₁₃	C₂	semidirect
26. C₂³×Q₈×C₁₃	C₂²	semidirect
28. C₂²×Q₈×D₁₃	C₂²	semidirect
31. D₄×Q₈×C₁₃	C₂²	semidirect
32. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
36. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
37. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
41. #11719522	C₂²	semidirect
42. #11719521	C₂²	semidirect
43. Q₈×C₂²⋊D₁₃	C₂²	semidirect
51. C₂×#88201	C₂²	semidirect
52. C₂×#88201	C₂²	semidirect
53. C₂×#88200	C₂²	semidirect
54. C₂×#88200	C₂²	semidirect
55. C₂×#88200	C₂²	semidirect
56. C₂×#88200	C₂²	semidirect
57. C₂×#88200	C₂²	semidirect
58. C₂×Q₈×Dic₁₃	C₂²	semidirect
59. C₂×Q₈×Dic₁₃	C₂²	semidirect
60. C₂×#88198	C₂²	semidirect
61. C₂×#88198	C₂²	semidirect
62. C₂×#88198	C₂²	semidirect
67. C₂×#88184	C₂²	semidirect
68. C₂×#88183	C₂²	semidirect
69. C₂×#88183	C₂²	semidirect
72. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
73. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
76. C₂×#88180	C₂²	semidirect
80. #11719440	C₂²	semidirect
81. #11719438	C₂²	semidirect
82. #11719437	C₂²	semidirect
83. #11719429	C₂²	semidirect
84. #11719352	C₂²	semidirect
85. #11719348	C₂²	semidirect
86. #11719345	C₂²	semidirect
87. #11719342	C₂²	semidirect
88. #11719339	C₂²	semidirect
89. #11719338	C₂²	semidirect
90. #11719335	C₂²	semidirect
91. #11719327	C₂²	semidirect
92. #11719287	C₂²	semidirect
93. #11719273	C₂²	semidirect
94. #11719265	C₂²	semidirect
95. #11719261	C₂²	semidirect
96. #11719255	C₂²	semidirect
97. #11719243	C₂²	semidirect
98. C₂×#88152	C₂²	semidirect
99. C₂×#88152	C₂²	semidirect
100. C₂×#88152	C₂²	semidirect
101. C₂×#88152	C₂²	semidirect
102. C₂×#88152	C₂²	semidirect
103. C₂×#88151	C₂²	semidirect
104. C₂×#88151	C₂²	semidirect
105. C₂×#88150	C₂²	semidirect
106. C₂×#88150	C₂²	semidirect
107. C₂×#88150	C₂²	semidirect
108. C₂×#88150	C₂²	semidirect
109. C₂×#88150	C₂²	semidirect
114. C₂×#88148	C₂²	semidirect
115. C₂×#88148	C₂²	semidirect
116. C₂×#88148	C₂²	semidirect
118. C₂×#88147	C₂²	semidirect
119. C₂×#88146	C₂²	semidirect
120. C₂×#88143	C₂²	semidirect
121. C₂×#88143	C₂²	semidirect
122. C₂×#88142	C₂²	semidirect
123. C₂×#88141	C₂²	semidirect
124. C₂×#88141	C₂²	semidirect
126. C₂×#88139	C₂²	semidirect
127. C₂×#88139	C₂²	semidirect
128. C₂×#88139	C₂²	semidirect
130. C₂×#88138	C₂²	semidirect
131. C₂×#88137	C₂²	semidirect
135. C₂×#88133	C₂²	semidirect
139. C₂×#88130	C₂²	semidirect
140. C₂×#88130	C₂²	semidirect
142. C₂×#88129	C₂²	semidirect
144. C₂×#88126	C₂²	semidirect
145. C₂×#88126	C₂²	semidirect
146. C₂×C₄×Dic₂₆	C₂²	semidirect
156. C₂²×Q₈×C₁₃	C₂³	semidirect
171. C₂×Q₈×D₁₃	C₂³	semidirect
191. C₁₃×C₄⋊Q₈	C₂³	semidirect
192. C₁₃×C₄⋊Q₈	C₂³	semidirect
195. C₁₃×C₂²⋊Q₈	C₂³	semidirect
196. C₁₃×C₂²⋊Q₈	C₂³	semidirect
197. C₄×Q₈×C₁₃	C₂³	semidirect
225. #88201	C₂³	semidirect
226. #88200	C₂³	semidirect
227. #88200	C₂³	semidirect
228. #88200	C₂³	semidirect
229. #88200	C₂³	semidirect
230. #88200	C₂³	semidirect
231. Q₈×Dic₁₃	C₂³	semidirect
232. Q₈×Dic₁₃	C₂³	semidirect
233. #88198	C₂³	semidirect
234. #88198	C₂³	semidirect
235. #88198	C₂³	semidirect
240. #88184	C₂³	semidirect
241. #88183	C₂³	semidirect
242. #88183	C₂³	semidirect
245. C₄×C₂²⋊D₁₃	C₂³	semidirect
246. C₄×C₂²⋊D₁₃	C₂³	semidirect
270. #88180	C₂³	semidirect
302. #88152	C₂³	semidirect
303. #88152	C₂³	semidirect
304. #88152	C₂³	semidirect
305. #88152	C₂³	semidirect
306. #88152	C₂³	semidirect
307. #88151	C₂³	semidirect
308. #88151	C₂³	semidirect
309. #88150	C₂³	semidirect
310. #88150	C₂³	semidirect
311. #88150	C₂³	semidirect
312. #88150	C₂³	semidirect
313. #88150	C₂³	semidirect
318. #88148	C₂³	semidirect
319. #88148	C₂³	semidirect
320. #88148	C₂³	semidirect
322. #88147	C₂³	semidirect
323. #88146	C₂³	semidirect
324. #88143	C₂³	semidirect
325. #88143	C₂³	semidirect
326. #88142	C₂³	semidirect
327. #88141	C₂³	semidirect
328. #88141	C₂³	semidirect
330. #88139	C₂³	semidirect
331. #88139	C₂³	semidirect
332. #88139	C₂³	semidirect
334. #88138	C₂³	semidirect
335. #88137	C₂³	semidirect
339. #88133	C₂³	semidirect
343. #88130	C₂³	semidirect
344. #88130	C₂³	semidirect
346. #88129	C₂³	semidirect
348. #88126	C₂³	semidirect
349. #88126	C₂³	semidirect
350. C₄×Dic₂₆	C₂³	semidirect
522. C₂×D₄×Q₈	D₁₃	semidirect
634. C₂³×Q₈	C₂×D₁₃	semidirect
643. D₄×Q₈	C₂×D₁₃	semidirect
661. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
662. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
716. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
717. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
732. C₂×C₄×Q₈	C₂×D₁₃	semidirect
814. C₂²×Q₈	C₂²×D₁₃	semidirect
843. C₄⋊Q₈	C₂²×D₁₃	semidirect
844. C₄⋊Q₈	C₂²×D₁₃	semidirect
896. C₂²⋊Q₈	C₂²×D₁₃	semidirect
897. C₂²⋊Q₈	C₂²×D₁₃	semidirect
912. C₄×Q₈	C₂²×D₁₃	semidirect
1001. C₂×C₁₃	#3561	semidirect
1170. C₁₃	C₂×#3561	semidirect
1311. C₂	#13129402	direct (N × H)

Maximal subgroups

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

subgroup	index
#13129402	2
C₂×#11719440	2
C₂×#11719352	2
C₂×#11719437	2
C₂×#11719273	2
C₂×#11719261	2
C₂×#11719342	2
C₂×Q₈×C₂²⋊D₁₃	2
C₂×#11719522	2
C₂×#11719338	2
C₂×#11719255	2
C₂×#11719335	2
C₂×#11719339	2
C₂×#11719438	2
C₂×#11719348	2
C₂×#11719287	2
C₂×#11719345	2
C₂×#11719265	2
C₂×#11719429	2
C₂×#11719521	2
C₂×#11719327	2
C₂×#11719243	2
C₂²×#88201	2
C₂×D₄×Q₈×C₁₃	2
C₂×#3561	13

Subgroups — C2×#13129402 #16770268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129402 #16770268