Subgroups — #16727826

Order 3328.

2136 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123912	C₂	1	2	yes	maximal, complemented
2	#13123907	C₂	1	2	yes	maximal, complemented
3	#13123898	C₂	1	2	yes	maximal, complemented
4	#13123892	C₂	1	2	yes	maximal, complemented
5	#13123884	C₂	1	2	yes	maximal, complemented
6	#13123884	C₂	1	2	yes	maximal, complemented
7	#13123871	C₂	1	2	yes	maximal, complemented
8	#13123865	C₂	1	2	yes	maximal, complemented
9	#13123580	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×#6099	C₂	1	1	yes	maximal, characteristic, complemented
11	#13123563	C₂	1	1	yes	maximal, characteristic, complemented
12	#13123563	C₂	1	1	yes	maximal, characteristic, complemented
13	#13123554	C₂	1	1	yes	maximal, characteristic, complemented
14	#13123540	C₂	1	1	yes	maximal, characteristic, complemented
15	#13123531	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11718672	C₂	1	1	yes	maximal, characteristic, complemented
17	#13123502	C₂	1	1	yes	maximal, characteristic, complemented
18	#13123487	C₂	1	1	yes	maximal, characteristic, complemented
19	#13123285	C₂	1	1	yes	maximal, characteristic, complemented
20	#13123285	C₂	1	1	yes	maximal, characteristic, complemented
21	#13123281	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#11718895	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
24	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₁₃×#550	C₄	1	1	yes	characteristic
27	D₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
28	C₁₃×#548	C₄	1	1	yes	characteristic
29	C₁₃×#548	C₄	1	1	yes	characteristic
30	C₁₃×#547	C₄	1	2	yes	—
31	C₁₃×#547	C₄	1	1	yes	characteristic
32	C₁₃×#546	C₄	1	2	yes	—
33	C₁₃×#546	C₄	1	2	yes	—
34	C₁₃×#546	C₄	1	1	yes	characteristic
35	C₁₃×#546	C₄	1	1	yes	characteristic
36	D₄²×C₁₃	C₄	1	1	yes	characteristic
37	D₄²×C₁₃	C₄	1	2	yes	—
38	C₁₃×#532	C₂²	1	2	yes	—
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₁₃×#525	C₂²	1	2	yes	—
41	C₁₃×#525	C₂²	1	2	yes	—
42	C₁₃×#525	C₂²	1	1	yes	characteristic
43	C₁₃×#525	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×#88202	C₂²	1	1	yes	characteristic, complemented
48	C₂×#88202	C₂²	1	1	yes	characteristic, complemented
49	C₂×#88202	C₂²	1	1	yes	characteristic, complemented
50	C₂×#88202	C₂²	1	1	yes	characteristic, complemented
51	C₂²×#6099	C₂²	1	1	yes	characteristic, complemented
52	C₂²×#6099	C₂²	1	1	yes	characteristic, complemented
53	C₂²×#6099	C₂²	1	1	yes	characteristic, complemented
54	C₂³×#1055	C₂²	1	1	yes	characteristic, complemented
55	#11718895	C₂²	1	1	yes	characteristic
56	#11718895	C₂²	1	1	yes	characteristic
57	#11718895	C₂²	1	1	yes	characteristic
58	#11718895	C₂²	1	1	yes	characteristic
59	#11718895	C₂²	1	2	yes	complemented
60	#11718895	C₂²	1	2	yes	complemented
61	#11718895	C₂²	1	2	yes	complemented
62	#11718895	C₂²	1	2	yes	complemented
63	#11718895	C₂²	1	2	yes	complemented
64	#11718895	C₂²	1	2	yes	complemented
65	#11718895	C₂²	1	2	yes	complemented
66	#11718895	C₂²	1	2	yes	complemented
67	#11718895	C₂²	1	1	yes	characteristic, complemented
68	#11718895	C₂²	1	1	yes	characteristic, complemented
69	#11718895	C₂²	1	1	yes	characteristic, complemented
70	#11718895	C₂²	1	1	yes	characteristic, complemented
71	#11718868	C₂²	1	2	yes	complemented
72	#11718868	C₂²	1	2	yes	complemented
73	#11718868	C₂²	1	2	yes	complemented
74	#11718868	C₂²	1	2	yes	complemented
75	#11718868	C₂²	1	1	yes	characteristic, complemented
76	#11718868	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₂²⋊#1055	C₂²	1	2	yes	complemented
78	C₂×C₂²⋊#1055	C₂²	1	2	yes	complemented
79	C₂×C₂²⋊#1055	C₂²	1	2	yes	complemented
80	C₂×C₂²⋊#1055	C₂²	1	2	yes	complemented
81	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic, complemented
83	#11718673	C₂²	1	2	yes	complemented
84	#11718673	C₂²	1	2	yes	complemented
85	#11718673	C₂²	1	2	yes	complemented
86	#11718673	C₂²	1	2	yes	complemented
87	#11718673	C₂²	1	2	yes	complemented
88	#11718673	C₂²	1	2	yes	complemented
89	#11718672	C₂²	1	1	yes	characteristic
90	#11718672	C₂²	1	2	yes	—
91	#11718672	C₂²	1	1	yes	characteristic
92	#11718672	C₂²	1	2	yes	complemented
93	#11718672	C₂²	1	2	yes	complemented
94	#11718672	C₂²	1	2	yes	complemented
95	#11718672	C₂²	1	2	yes	complemented
96	#11718672	C₂²	1	2	yes	complemented
97	#11718672	C₂²	1	2	yes	complemented
98	#11718672	C₂²	1	2	yes	complemented
99	#11718672	C₂²	1	2	yes	complemented
100	#11718672	C₂²	1	1	yes	characteristic, complemented
101	#11718672	C₂²	1	1	yes	characteristic, complemented
102	#11718672	C₂²	1	2	yes	complemented
103	#11718672	C₂²	1	2	yes	complemented
104	#11718672	C₂²	1	2	yes	complemented
105	#11718672	C₂²	1	1	yes	characteristic, complemented
106	#11718672	C₂²	1	2	yes	complemented
107	#11718672	C₂²	1	2	yes	complemented
108	#11718672	C₂²	1	1	yes	characteristic, complemented
109	#11718672	C₂²	1	2	yes	complemented
110	#11718672	C₂²	1	1	yes	characteristic, complemented
111	#11718672	C₂²	1	2	yes	complemented
112	#11718672	C₂²	1	1	yes	characteristic, complemented
113	D₄×#1055	C₂²	1	2	yes	complemented
114	D₄×#1055	C₂²	1	2	yes	complemented
115	D₄×#1055	C₂²	1	2	yes	complemented
116	D₄×#1055	C₂²	1	2	yes	complemented
117	D₄×#1055	C₂²	1	2	yes	complemented
118	D₄×#1055	C₂²	1	2	yes	complemented
119	#11718661	C₂²	1	2	yes	complemented
120	#11718661	C₂²	1	2	yes	complemented
121	#11718661	C₂²	1	2	yes	complemented
122	#11718661	C₂²	1	2	yes	complemented
123	#11718660	C₂²	1	1	yes	characteristic, complemented
124	#11718660	C₂²	1	1	yes	characteristic, complemented
125	#11718658	C₂²	1	1	yes	characteristic, complemented
126	#11718658	C₂²	1	1	yes	characteristic, complemented
127	#11718587	C₂²	1	2	yes	complemented
128	#11718587	C₂²	1	2	yes	complemented
129	#11718587	C₂²	1	2	yes	complemented
130	#11718586	C₂²	1	2	yes	complemented
131	#11718585	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
133	C₄×#6099	C₂²	1	1	yes	characteristic, complemented
134	C₂×#88043	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₁₃×#41	—	4	2	no	—
136	C₂×C₁₃×#41	—	4	2	no	—
137	C₂×C₁₃×#41	—	4	2	no	—
138	C₂×C₁₃×#41	—	4	2	no	—
139	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
140	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
141	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
142	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
143	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
144	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
145	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×#41	C₂³	1	2	yes	—
149	C₂×C₁₃×#41	C₂³	1	2	yes	—
150	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
151	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
152	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
153	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
154	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
155	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
156	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
157	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
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	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
163	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
164	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
165	C₁₃×#127	C₂×C₄	1	2	yes	—
166	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
167	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
168	C₁₃×#124	C₂×C₄	1	2	yes	—
169	C₁₃×#124	C₂×C₄	1	2	yes	—
170	C₁₃×#123	C₂×C₄	1	2	yes	—
171	C₁₃×#123	C₂×C₄	1	2	yes	—
172	C₁₃×#123	C₂×C₄	1	2	yes	—
173	C₁₃×#123	C₂×C₄	1	2	yes	—
174	C₁₃×#123	C₂×C₄	1	2	yes	—
175	C₁₃×#123	C₂×C₄	1	2	yes	—
176	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
177	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
178	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
179	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
180	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
181	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
182	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
183	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
184	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
185	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
186	C₁₃×#121	C₂×C₄	1	2	yes	—
187	C₁₃×#121	C₂×C₄	1	2	yes	—
188	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
189	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
190	C₁₃×#121	C₂×C₄	1	2	yes	—
191	C₁₃×#121	C₂×C₄	1	2	yes	—
192	C₁₃×#121	C₂×C₄	1	2	yes	—
193	C₁₃×#121	C₂×C₄	1	2	yes	—
194	C₁₃×#121	C₂×C₄	1	2	yes	—
195	C₁₃×#121	C₂×C₄	1	2	yes	—
196	C₁₃×#121	C₂×C₄	1	2	yes	—
197	C₁₃×#121	C₂×C₄	1	2	yes	—
198	C₁₃×#120	C₂×C₄	1	2	yes	—
199	C₁₃×#120	C₂×C₄	1	2	yes	—
200	C₁₃×#120	C₂×C₄	1	2	yes	—
201	C₁₃×#120	C₂×C₄	1	2	yes	—
202	C₁₃×#120	C₂×C₄	1	2	yes	—
203	C₁₃×#120	C₂×C₄	1	2	yes	—
204	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
205	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
206	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
207	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
208	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
209	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
210	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
211	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
212	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
213	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
214	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
215	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
216	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
217	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
218	C₄×D₄×C₁₃	C₂³	1	2	yes	—
219	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₁₃	C₂³	1	2	yes	—
221	C₄×D₄×C₁₃	C₂³	1	2	yes	—
222	C₄×D₄×C₁₃	C₂³	1	2	yes	—
223	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
224	C₄×D₄×C₁₃	C₂³	1	2	yes	—
225	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
226	C₄×D₄×C₁₃	C₂³	1	2	yes	—
227	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
228	C₁₃×#117	C₂³	1	1	yes	characteristic
229	C₁₃×#117	C₂³	1	2	yes	—
230	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
231	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
232	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
233	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
234	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
235	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
236	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
238	#88202	—	4	2	no	—
239	#88202	—	4	2	no	—
240	#88202	—	4	2	no	—
241	#88202	—	4	2	no	—
242	C₂×#6099	—	4	2	no	—
243	C₂×#6099	—	4	2	no	—
244	C₂×#6099	—	4	2	no	—
245	C₂×#6099	C₂³	1	1	yes	characteristic
246	C₂×#6099	C₂³	1	1	yes	characteristic
247	C₂×#6099	C₂³	1	1	yes	characteristic
248	C₂×#6099	C₂³	1	1	yes	characteristic
249	C₂×#6099	C₂³	1	1	yes	characteristic
250	C₂×#6099	C₂³	1	1	yes	characteristic
251	C₂×#6099	C₂³	1	2	yes	—
252	C₂×#6099	C₂³	1	1	yes	characteristic
253	C₂×#6099	C₂³	1	2	yes	—
254	C₂×#6099	C₂³	1	2	yes	—
255	C₂×#6099	C₂³	1	2	yes	—
256	C₂×#6099	C₂³	1	1	yes	characteristic
257	C₂×#6099	C₂³	1	2	yes	—
258	C₂×#6099	C₂³	1	2	yes	—
259	C₂²×#1055	—	4	2	no	—
260	C₂²×#1055	C₂³	1	1	yes	characteristic
261	C₂²×#1055	C₂³	1	1	yes	characteristic
262	C₂²×#1055	C₂³	1	1	yes	characteristic
263	C₂²×#1055	C₂³	1	1	yes	characteristic
264	C₂²×#1055	C₂³	1	2	yes	—
265	C₂²×#1055	C₂³	1	1	yes	characteristic
266	C₂²×#1055	C₂³	1	2	yes	—
267	C₂²×#1055	C₂³	1	1	yes	characteristic
268	C₂²×#1055	C₂³	1	2	yes	—
269	C₂²×#1055	C₂³	1	2	yes	—
270	C₂²×#1055	C₂³	1	2	yes	—
271	C₂²×#1055	C₂³	1	2	yes	—
272	C₂²×#1055	C₂³	1	1	yes	characteristic
273	C₂²×#1055	C₂³	1	1	yes	characteristic
274	C₂²⋊#1055	C₂³	1	2	yes	—
275	C₂²⋊#1055	C₂³	1	2	yes	—
276	C₂²⋊#1055	C₂³	1	2	yes	—
277	C₂²⋊#1055	C₂³	1	2	yes	—
278	C₂²⋊#1055	C₂³	1	2	yes	—
279	C₂²⋊#1055	C₂³	1	2	yes	—
280	C₂²⋊#1055	C₂³	1	2	yes	—
281	C₂²⋊#1055	C₂³	1	2	yes	—
282	C₂²⋊#1055	C₂³	1	1	yes	characteristic
283	C₂²⋊#1055	C₂³	1	2	yes	—
284	C₂²⋊#1055	C₂³	1	1	yes	characteristic
285	C₂²⋊#1055	C₂³	1	2	yes	—
286	C₂²⋊#1055	C₂³	1	2	yes	—
287	C₂²⋊#1055	C₂³	1	2	yes	—
288	C₂²⋊#1055	C₂³	1	2	yes	—
289	C₂²⋊#1055	C₂³	1	2	yes	—
290	C₂²⋊#1055	C₂³	1	2	yes	—
291	C₂²⋊#1055	C₂³	1	2	yes	—
292	C₂²⋊#1055	C₂³	1	1	yes	characteristic
293	C₂²⋊#1055	C₂³	1	1	yes	characteristic
294	C₂²⋊#1055	C₂³	1	1	yes	characteristic
295	C₂²⋊#1055	C₂³	1	2	yes	—
296	C₂²⋊#1055	C₂³	1	1	yes	characteristic
297	C₂²⋊#1055	C₂³	1	1	yes	characteristic
298	C₂²⋊#1055	C₂³	1	2	yes	—
299	C₂²⋊#1055	C₂³	1	2	yes	—
300	C₂²⋊#1055	C₂³	1	2	yes	—
301	C₂²⋊#1055	C₂³	1	1	yes	characteristic
302	C₄⋊#1055	C₂³	1	2	yes	—
303	C₄⋊#1055	C₂³	1	2	yes	—
304	C₄⋊#1055	C₂³	1	2	yes	—
305	C₄⋊#1055	C₂³	1	2	yes	—
306	C₄⋊#1055	C₂³	1	1	yes	characteristic
307	C₄⋊#1055	C₂³	1	2	yes	—
308	C₄⋊#1055	C₂³	1	1	yes	characteristic
309	C₄⋊#1055	C₂³	1	1	yes	characteristic
310	C₄⋊#1055	C₂³	1	1	yes	characteristic
311	C₄⋊#1055	C₂³	1	2	yes	—
312	#88043	C₂³	1	2	yes	—
313	#88043	C₂³	1	2	yes	—
314	#88043	C₂³	1	1	yes	characteristic
315	#88043	C₂³	1	1	yes	characteristic
316	#88043	C₂³	1	1	yes	characteristic
317	#88043	C₂³	1	1	yes	characteristic
318	#88043	C₂³	1	2	yes	—
319	C₄×#1055	C₂³	1	2	yes	—
320	C₄×#1055	C₂³	1	2	yes	—
321	C₄×#1055	C₂³	1	2	yes	—
322	#60240	—	13	1	no	maximal, Sylow
323	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
324	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
325	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
326	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
327	C₁₃×#41	—	2	2	no	—
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	—	4	2	no	—
334	C₁₃×#41	—	4	2	no	—
335	C₁₃×#41	—	4	2	no	—
336	C₁₃×#41	—	4	2	no	—
337	C₁₃×#41	—	4	4	no	—
338	C₁₃×#41	—	4	4	no	—
339	C₁₃×#41	—	4	2	no	—
340	C₁₃×#41	—	4	2	no	—
341	C₁₃×#41	—	4	2	no	—
342	C₁₃×#41	—	4	2	no	—
343	C₂×Q₈×C₁₃	—	4	2	no	—
344	C₂×Q₈×C₁₃	—	4	2	no	—
345	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
346	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
347	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
348	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
349	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
350	C₂×D₄×C₁₃	—	4	2	no	—
351	C₂×D₄×C₁₃	—	4	2	no	—
352	C₂×D₄×C₁₃	—	4	2	no	—
353	C₂×D₄×C₁₃	—	4	4	no	—
354	C₂×D₄×C₁₃	—	4	4	no	—
355	C₂×D₄×C₁₃	—	4	4	no	—
356	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
357	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
358	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
359	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
360	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
361	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
362	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
363	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
364	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
365	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
366	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
367	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
368	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
369	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
370	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
371	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
372	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
373	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
374	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
375	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
376	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
377	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
378	C₂²×C₄×C₁₃	—	2	2	no	—
379	C₂²×C₄×C₁₃	—	2	2	no	—
380	C₂²×C₄×C₁₃	—	2	2	no	—
381	C₂²×C₄×C₁₃	—	2	2	no	—
382	C₂²×C₄×C₁₃	—	4	2	no	—
383	C₂²×C₄×C₁₃	—	4	2	no	—
384	C₂²×C₄×C₁₃	—	4	2	no	—
385	C₂²×C₄×C₁₃	—	4	2	no	—
386	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
387	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
388	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
389	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
390	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
391	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
392	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
393	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
394	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
395	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
396	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
397	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
398	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
399	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
400	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
401	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
402	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
403	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
408	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
410	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
411	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
412	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
413	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
414	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
415	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
416	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
417	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
418	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
419	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
420	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
421	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
422	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
423	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
424	C₁₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
425	C₁₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
426	C₁₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
427	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
428	C₁₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
429	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
430	C₁₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
431	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
432	C₁₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
433	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
434	C₁₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
435	C₁₃×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
436	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
437	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
438	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
439	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
440	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
441	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
442	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
443	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
444	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
445	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
446	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
447	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
448	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
449	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
450	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
451	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
452	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₁₃	C₂⁴	1	2	yes	—
454	#6099	—	2	2	no	—
455	#6099	—	2	2	no	—
456	#6099	—	2	2	no	—
457	#6099	—	2	2	no	—
458	#6099	—	4	1	no	—
459	#6099	—	4	1	no	—
460	#6099	—	4	1	no	—
461	#6099	—	4	1	no	—
462	#6099	—	4	2	no	—
463	#6099	—	4	2	no	—
464	#6099	—	4	2	no	—
465	#6099	—	4	2	no	—
466	#6099	—	4	2	no	—
467	#6099	—	4	2	no	—
468	C₂×#1055	—	2	2	no	—
469	C₂×#1055	—	2	2	no	—
470	C₂×#1055	—	2	2	no	—
471	C₂×#1055	—	2	2	no	—
472	C₂×#1055	—	4	1	no	—
473	C₂×#1055	—	4	1	no	—
474	C₂×#1055	—	4	1	no	—
475	C₂×#1055	—	4	1	no	—
476	C₂×#1055	—	4	2	no	—
477	C₂×#1055	—	4	2	no	—
478	C₂×#1055	—	4	2	no	—
479	C₂×#1055	—	4	2	no	—
480	C₂×#1055	—	4	2	no	—
481	C₂×#1055	—	4	2	no	—
482	C₂×#1055	C₂⁴	1	1	yes	characteristic
483	C₂×#1055	C₂⁴	1	1	yes	characteristic
484	C₂×#1055	C₂⁴	1	1	yes	characteristic
485	C₂×#1055	C₂⁴	1	1	yes	characteristic
486	C₂×#1055	C₂⁴	1	1	yes	characteristic
487	C₂×#1055	C₂⁴	1	1	yes	characteristic
488	C₂×#1055	C₂⁴	1	1	yes	characteristic
489	C₂×#1055	C₂⁴	1	2	yes	—
490	C₂×#1055	C₂⁴	1	2	yes	—
491	C₂×#1055	C₂⁴	1	2	yes	—
492	C₂×#1055	C₂⁴	1	2	yes	—
493	C₂×#1055	C₂⁴	1	1	yes	characteristic
494	D₄×#41	D₁₃	1	1	yes	characteristic
495	#2981	—	13	2	no	—
496	#2980	—	13	2	no	—
497	#2978	—	13	2	no	—
498	#2977	—	13	2	no	—
499	#2976	—	13	2	no	—
500	#2976	—	13	2	no	—
501	#2974	—	13	2	no	—
502	#2973	—	13	2	no	—
503	#2935	—	13	1	no	—
504	D₄×M₁₆	—	13	1	no	—
505	#2933	—	13	1	no	—
506	#2933	—	13	1	no	—
507	#2932	—	13	1	no	—
508	#2930	—	13	1	no	—
509	#2929	—	13	1	no	—
510	C₂×#435	—	13	1	no	—
511	#2925	—	13	1	no	—
512	#2923	—	13	1	no	—
513	#2880	—	13	1	no	—
514	#2880	—	13	1	no	—
515	#2879	—	13	1	no	—
516	C₂×#408	—	13	1	no	—
517	C₂³×C₁₃	—	2	2	no	—
518	C₂³×C₁₃	—	2	2	no	—
519	C₂³×C₁₃	—	2	2	no	—
520	C₂³×C₁₃	—	2	4	no	—
521	C₂³×C₁₃	—	4	1	no	—
522	C₂³×C₁₃	—	4	2	no	—
523	C₂³×C₁₃	—	4	2	no	—
524	C₂³×C₁₃	—	4	1	no	—
525	C₂³×C₁₃	—	4	2	no	—
526	C₂³×C₁₃	—	4	1	no	—
527	C₂³×C₁₃	—	4	2	no	—
528	C₂³×C₁₃	—	4	2	no	—
529	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
530	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
531	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
532	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
533	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
534	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
535	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
536	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
537	Q₈×C₁₃	—	2	2	no	—
538	Q₈×C₁₃	—	2	2	no	—
539	Q₈×C₁₃	—	2	2	no	—
540	Q₈×C₁₃	—	4	2	no	—
541	Q₈×C₁₃	—	4	2	no	—
542	D₄×C₁₃	—	2	4	no	—
543	D₄×C₁₃	—	2	4	no	—
544	D₄×C₁₃	—	2	4	no	—
545	D₄×C₁₃	—	2	2	no	—
546	D₄×C₁₃	—	2	2	no	—
547	D₄×C₁₃	—	2	4	no	—
548	D₄×C₁₃	—	2	2	no	—
549	D₄×C₁₃	—	2	2	no	—
550	D₄×C₁₃	—	2	2	no	—
551	D₄×C₁₃	—	4	1	no	—
552	D₄×C₁₃	—	4	2	no	—
553	D₄×C₁₃	—	4	1	no	—
554	D₄×C₁₃	—	4	2	no	—
555	D₄×C₁₃	—	4	2	no	—
556	D₄×C₁₃	—	4	2	no	—
557	D₄×C₁₃	—	4	2	no	—
558	D₄×C₁₃	—	4	2	no	—
559	D₄×C₁₃	—	4	2	no	—
560	D₄×C₁₃	—	4	2	no	—
561	D₄×C₁₃	—	4	2	no	—
562	D₄×C₁₃	—	4	2	no	—
563	D₄×C₁₃	—	4	2	no	—
564	C₂×C₄×C₁₃	—	2	2	no	—
565	C₂×C₄×C₁₃	—	2	2	no	—
566	C₂×C₄×C₁₃	—	2	2	no	—
567	C₂×C₄×C₁₃	—	2	2	no	—
568	C₂×C₄×C₁₃	—	2	2	no	—
569	C₂×C₄×C₁₃	—	2	2	no	—
570	C₂×C₄×C₁₃	—	2	1	no	—
571	C₂×C₄×C₁₃	—	2	1	no	—
572	C₂×C₄×C₁₃	—	2	1	no	—
573	C₂×C₄×C₁₃	—	2	1	no	—
574	C₂×C₄×C₁₃	—	2	2	no	—
575	C₂×C₄×C₁₃	—	2	2	no	—
576	C₂×C₄×C₁₃	—	2	2	no	—
577	C₂×C₄×C₁₃	—	2	2	no	—
578	C₂×C₄×C₁₃	—	2	1	no	—
579	C₂×C₄×C₁₃	—	2	1	no	—
580	C₂×C₄×C₁₃	—	2	1	no	—
581	C₂×C₄×C₁₃	—	2	1	no	—
582	C₂×C₄×C₁₃	—	2	2	no	—
583	C₂×C₄×C₁₃	—	2	2	no	—
584	C₂×C₄×C₁₃	—	4	2	no	—
585	C₂×C₄×C₁₃	—	4	2	no	—
586	C₂×C₄×C₁₃	—	4	2	no	—
587	C₂×C₄×C₁₃	—	4	2	no	—
588	C₂×C₄×C₁₃	—	4	2	no	—
589	C₂×C₄×C₁₃	—	4	2	no	—
590	C₂×C₄×C₁₃	—	4	1	no	—
591	C₂×C₄×C₁₃	—	4	2	no	—
592	C₂×C₄×C₁₃	—	4	1	no	—
593	C₂×C₄×C₁₃	—	4	2	no	—
594	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
595	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
596	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
597	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
598	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
599	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
600	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
601	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
602	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
603	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
604	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
605	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
606	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
607	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
608	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
609	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
610	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
611	#1055	—	2	1	no	—
612	#1055	—	2	1	no	—
613	#1055	—	2	1	no	—
614	#1055	—	2	1	no	—
615	#1055	—	2	1	no	—
616	#1055	—	2	1	no	—
617	#1055	—	2	1	no	—
618	#1055	—	2	1	no	—
619	#1055	—	2	2	no	—
620	#1055	—	2	2	no	—
621	#1055	—	2	2	no	—
622	#1055	—	2	2	no	—
623	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
624	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
625	C₂×#131	—	13	1	no	—
626	C₂×#131	—	13	1	no	—
627	C₂×#131	—	13	1	no	—
628	C₂×#131	—	13	1	no	—
629	C₂²×M₁₆	—	13	1	no	—
630	C₂²×M₁₆	—	13	1	no	—
631	C₂²×M₁₆	—	13	1	no	—
632	C₂³×C₈	—	13	1	no	—
633	#550	Dic₁₃	1	1	yes	characteristic
634	D₄×Q₈	Dic₁₃	1	1	yes	characteristic
635	#548	Dic₁₃	1	1	yes	characteristic
636	#548	Dic₁₃	1	1	yes	characteristic
637	#547	Dic₁₃	1	2	yes	—
638	#547	Dic₁₃	1	1	yes	characteristic
639	#546	Dic₁₃	1	2	yes	—
640	#546	Dic₁₃	1	2	yes	—
641	#546	Dic₁₃	1	1	yes	characteristic
642	#546	Dic₁₃	1	1	yes	characteristic
643	D₄²	Dic₁₃	1	1	yes	characteristic
644	D₄²	Dic₁₃	1	2	yes	—
645	#532	C₂×D₁₃	1	1	yes	characteristic
646	#532	C₂×D₁₃	1	2	yes	—
647	#525	C₂×D₁₃	1	1	yes	characteristic
648	#525	C₂×D₁₃	1	1	yes	characteristic
649	#525	C₂×D₁₃	1	2	yes	—
650	#525	C₂×D₁₃	1	2	yes	—
651	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
652	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
653	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
654	#436	—	13	2	no	—
655	#436	—	13	2	no	—
656	#436	—	13	2	no	—
657	#436	—	13	2	no	—
658	#436	—	13	2	no	—
659	#436	—	13	2	no	—
660	#435	—	13	1	no	—
661	#435	—	13	1	no	—
662	#435	—	13	2	no	—
663	#435	—	13	1	no	—
664	#435	—	13	1	no	—
665	#435	—	13	1	no	—
666	#435	—	13	1	no	—
667	#435	—	13	1	no	—
668	#435	—	13	1	no	—
669	#435	—	13	2	no	—
670	#435	—	13	2	no	—
671	#435	—	13	2	no	—
672	#435	—	13	2	no	—
673	#435	—	13	2	no	—
674	#435	—	13	2	no	—
675	#435	—	13	2	no	—
676	#435	—	13	2	no	—
677	#435	—	13	2	no	—
678	#435	—	13	2	no	—
679	#435	—	13	2	no	—
680	#435	—	13	2	no	—
681	#435	—	13	2	no	—
682	#435	—	13	2	no	—
683	#435	—	13	2	no	—
684	C₈×D₄	—	13	2	no	—
685	C₈×D₄	—	13	2	no	—
686	C₈×D₄	—	13	2	no	—
687	C₈×D₄	—	13	2	no	—
688	C₈×D₄	—	13	2	no	—
689	C₈×D₄	—	13	2	no	—
690	#433	—	13	2	no	—
691	#433	—	13	2	no	—
692	#433	—	13	2	no	—
693	#433	—	13	2	no	—
694	#432	—	13	2	no	—
695	#432	—	13	2	no	—
696	#432	—	13	2	no	—
697	#431	—	13	2	no	—
698	#424	—	13	1	no	—
699	#424	—	13	1	no	—
700	#423	—	13	1	no	—
701	C₂×C₄⋊C₈	—	13	1	no	—
702	#408	—	13	1	no	—
703	#408	—	13	1	no	—
704	#408	—	13	1	no	—
705	#408	—	13	1	no	—
706	#408	—	13	2	no	—
707	#408	—	13	2	no	—
708	#408	—	13	1	no	—
709	#408	—	13	1	no	—
710	#408	—	13	1	no	—
711	#408	—	13	2	no	—
712	#408	—	13	2	no	—
713	#408	—	13	1	no	—
714	#408	—	13	2	no	—
715	#408	—	13	2	no	—
716	#408	—	13	2	no	—
717	#408	—	13	2	no	—
718	#407	—	13	2	no	—
719	#407	—	13	2	no	—
720	#407	—	13	1	no	—
721	#407	—	13	1	no	—
722	#407	—	13	2	no	—
723	#407	—	13	2	no	—
724	C₂×C₂²⋊C₈	—	13	2	no	—
725	C₂×C₂²⋊C₈	—	13	2	no	—
726	C₂×C₂²⋊C₈	—	13	1	no	—
727	C₂×C₂²⋊C₈	—	13	1	no	—
728	C₂×C₂²⋊C₈	—	13	2	no	—
729	C₂×C₂²⋊C₈	—	13	2	no	—
730	#405	—	13	1	no	—
731	#405	—	13	1	no	—
732	C₄×M₁₆	—	13	1	no	—
733	C₂×#97	—	13	1	no	—
734	C₂²×C₁₃	—	2	1	no	—
735	C₂²×C₁₃	—	2	1	no	—
736	C₂²×C₁₃	—	2	1	no	—
737	C₂²×C₁₃	—	2	1	no	—
738	C₂²×C₁₃	—	2	1	no	—
739	C₂²×C₁₃	—	2	1	no	—
740	C₂²×C₁₃	—	2	1	no	—
741	C₂²×C₁₃	—	2	2	no	—
742	C₂²×C₁₃	—	2	2	no	—
743	C₂²×C₁₃	—	2	2	no	—
744	C₂²×C₁₃	—	2	2	no	—
745	C₂²×C₁₃	—	2	1	no	—
746	C₂²×C₁₃	—	2	1	no	—
747	C₂²×C₁₃	—	2	2	no	—
748	C₂²×C₁₃	—	2	1	no	—
749	C₂²×C₁₃	—	2	2	no	—
750	C₂²×C₁₃	—	2	2	no	—
751	C₂²×C₁₃	—	2	1	no	—
752	C₂²×C₁₃	—	2	1	no	—
753	C₂²×C₁₃	—	2	2	no	—
754	C₂²×C₁₃	—	2	2	no	—
755	C₂²×C₁₃	—	2	1	no	—
756	C₂²×C₁₃	—	4	4	no	—
757	C₂²×C₁₃	—	8	4	no	—
758	C₂²×C₁₃	—	8	2	no	—
759	C₂²×C₁₃	—	8	4	no	—
760	C₂²×C₁₃	#518	1	2	yes	—
761	C₂²×C₁₃	#568	1	2	yes	—
762	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
763	C₄×C₁₃	—	2	1	no	—
764	C₄×C₁₃	—	2	1	no	—
765	C₄×C₁₃	—	2	1	no	—
766	C₄×C₁₃	—	2	1	no	—
767	C₄×C₁₃	—	2	2	no	—
768	C₄×C₁₃	—	2	2	no	—
769	C₄×C₁₃	—	2	2	no	—
770	C₄×C₁₃	—	2	1	no	—
771	C₄×C₁₃	—	2	1	no	—
772	C₄×C₁₃	—	2	2	no	—
773	C₄×C₁₃	—	2	1	no	—
774	C₄×C₁₃	—	2	1	no	—
775	C₄×C₁₃	—	2	2	no	—
776	C₄×C₁₃	#518	1	2	yes	—
777	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
778	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
779	C₂×#41	—	4	2	no	—
780	C₂×#41	—	4	2	no	—
781	C₂×#41	—	4	2	no	—
782	C₂×#41	—	4	2	no	—
783	C₂×#41	C₂×Dic₁₃	1	2	yes	—
784	C₂×#41	C₂×Dic₁₃	1	2	yes	—
785	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
786	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
787	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
788	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
789	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
790	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
791	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
792	C₂×#41	C₂²×D₁₃	1	2	yes	—
793	C₂×#41	C₂²×D₁₃	1	2	yes	—
794	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
795	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
796	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
797	C₂²×D₄	C₂×Dic₁₃	1	2	yes	—
798	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
799	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
800	C₂²×D₄	C₂×Dic₁₃	1	2	yes	—
801	C₂²×D₄	C₂×Dic₁₃	1	2	yes	—
802	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
803	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
804	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
805	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
806	#131	—	52	2	no	—
807	#131	—	52	2	no	—
808	#131	—	52	2	no	—
809	#131	—	52	2	no	—
810	C₂×M₁₆	—	13	1	no	—
811	C₂×M₁₆	—	13	1	no	—
812	C₂×M₁₆	—	13	1	no	—
813	C₂×M₁₆	—	13	1	no	—
814	C₂×M₁₆	—	13	1	no	—
815	C₂×M₁₆	—	13	1	no	—
816	C₂×M₁₆	—	13	2	no	—
817	C₂×M₁₆	—	13	1	no	—
818	C₂×M₁₆	—	13	1	no	—
819	C₂×M₁₆	—	13	2	no	—
820	C₂×M₁₆	—	13	2	no	—
821	C₂×M₁₆	—	13	2	no	—
822	C₂×M₁₆	—	13	2	no	—
823	C₂×M₁₆	—	13	2	no	—
824	C₂×M₁₆	—	52	2	no	—
825	C₂×M₁₆	—	52	2	no	—
826	C₂×M₁₆	—	52	2	no	—
827	C₂²×C₈	—	13	1	no	—
828	C₂²×C₈	—	13	1	no	—
829	C₂²×C₈	—	13	1	no	—
830	C₂²×C₈	—	13	1	no	—
831	C₂²×C₈	—	13	1	no	—
832	C₂²×C₈	—	13	1	no	—
833	C₂²×C₈	—	13	1	no	—
834	C₂²×C₈	—	13	1	no	—
835	C₂²×C₈	—	13	2	no	—
836	C₂²×C₈	—	13	2	no	—
837	C₂²×C₈	—	13	2	no	—
838	C₂²×C₈	—	13	2	no	—
839	C₂²×C₈	—	13	2	no	—
840	C₂²×C₈	—	13	2	no	—
841	C₂²×C₈	—	52	2	no	—
842	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
843	C₄⋊Q₈	C₂×Dic₁₃	1	2	yes	—
844	#127	C₂×Dic₁₃	1	1	yes	characteristic
845	#127	C₂×Dic₁₃	1	2	yes	—
846	#124	C₂×Dic₁₃	1	1	yes	characteristic
847	#124	C₂×Dic₁₃	1	1	yes	characteristic
848	#124	C₂×Dic₁₃	1	2	yes	—
849	#124	C₂×Dic₁₃	1	2	yes	—
850	#123	C₂×Dic₁₃	1	2	yes	—
851	#123	C₂×Dic₁₃	1	2	yes	—
852	#123	C₂×Dic₁₃	1	2	yes	—
853	#123	C₂×Dic₁₃	1	2	yes	—
854	#123	C₂×Dic₁₃	1	2	yes	—
855	#123	C₂×Dic₁₃	1	2	yes	—
856	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
857	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
858	C₂²⋊Q₈	C₂×Dic₁₃	1	2	yes	—
859	C₂²⋊Q₈	C₂×Dic₁₃	1	2	yes	—
860	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
861	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
862	C₂²⋊Q₈	C₂×Dic₁₃	1	2	yes	—
863	C₂²⋊Q₈	C₂×Dic₁₃	1	2	yes	—
864	#121	C₂×Dic₁₃	1	1	yes	characteristic
865	#121	C₂×Dic₁₃	1	1	yes	characteristic
866	#121	C₂×Dic₁₃	1	2	yes	—
867	#121	C₂×Dic₁₃	1	2	yes	—
868	#121	C₂×Dic₁₃	1	1	yes	characteristic
869	#121	C₂×Dic₁₃	1	1	yes	characteristic
870	#121	C₂×Dic₁₃	1	2	yes	—
871	#121	C₂×Dic₁₃	1	2	yes	—
872	#121	C₂×Dic₁₃	1	2	yes	—
873	#121	C₂×Dic₁₃	1	2	yes	—
874	#121	C₂×Dic₁₃	1	2	yes	—
875	#121	C₂×Dic₁₃	1	2	yes	—
876	#121	C₂×Dic₁₃	1	2	yes	—
877	#121	C₂×Dic₁₃	1	2	yes	—
878	#120	C₂×Dic₁₃	1	2	yes	—
879	#120	C₂×Dic₁₃	1	2	yes	—
880	#120	C₂×Dic₁₃	1	2	yes	—
881	#120	C₂×Dic₁₃	1	2	yes	—
882	#120	C₂×Dic₁₃	1	2	yes	—
883	#120	C₂×Dic₁₃	1	2	yes	—
884	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
885	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
886	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
887	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
888	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
889	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
890	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
891	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
892	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
893	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
894	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
895	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
896	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
897	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
898	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
899	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
900	C₄×D₄	C₂²×D₁₃	1	2	yes	—
901	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
902	C₄×D₄	C₂²×D₁₃	1	2	yes	—
903	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
904	C₄×D₄	C₂²×D₁₃	1	2	yes	—
905	C₄×D₄	C₂²×D₁₃	1	2	yes	—
906	C₄×D₄	C₂²×D₁₃	1	2	yes	—
907	C₄×D₄	C₂²×D₁₃	1	2	yes	—
908	#117	C₂²×D₁₃	1	1	yes	characteristic
909	#117	C₂²×D₁₃	1	2	yes	—
910	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
911	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
912	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
913	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
914	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
915	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
916	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
917	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
918	C₄⋊C₈	—	13	1	no	—
919	C₄⋊C₈	—	13	1	no	—
920	C₄⋊C₈	—	13	1	no	—
921	C₄⋊C₈	—	13	1	no	—
922	C₄⋊C₈	—	13	2	no	—
923	C₄⋊C₈	—	13	2	no	—
924	C₄⋊C₈	—	13	2	no	—
925	C₄⋊C₈	—	13	2	no	—
926	C₄⋊C₈	—	13	2	no	—
927	C₄⋊C₈	—	13	2	no	—
928	C₂²⋊C₈	—	13	1	no	—
929	C₂²⋊C₈	—	13	1	no	—
930	C₂²⋊C₈	—	13	2	no	—
931	C₂²⋊C₈	—	13	1	no	—
932	C₂²⋊C₈	—	13	2	no	—
933	C₂²⋊C₈	—	13	1	no	—
934	C₂²⋊C₈	—	13	2	no	—
935	C₂²⋊C₈	—	13	2	no	—
936	C₂²⋊C₈	—	13	2	no	—
937	C₂²⋊C₈	—	13	2	no	—
938	C₂²⋊C₈	—	13	2	no	—
939	C₂²⋊C₈	—	13	2	no	—
940	C₂²⋊C₈	—	13	2	no	—
941	C₂²⋊C₈	—	13	1	no	—
942	C₂²⋊C₈	—	13	2	no	—
943	C₂²⋊C₈	—	13	1	no	—
944	C₂²⋊C₈	—	13	1	no	—
945	C₂²⋊C₈	—	13	2	no	—
946	C₂²⋊C₈	—	13	2	no	—
947	C₂²⋊C₈	—	13	2	no	—
948	C₂²⋊C₈	—	13	1	no	—
949	C₂²⋊C₈	—	13	2	no	—
950	C₂²⋊C₈	—	13	2	no	—
951	C₂²⋊C₈	—	13	2	no	—
952	C₂²⋊C₈	—	13	2	no	—
953	C₂²⋊C₈	—	13	2	no	—
954	C₂²⋊C₈	—	13	2	no	—
955	C₂²⋊C₈	—	13	2	no	—
956	#97	—	13	1	no	—
957	#97	—	13	1	no	—
958	#97	—	13	1	no	—
959	#97	—	13	1	no	—
960	#97	—	13	2	no	—
961	#97	—	13	2	no	—
962	#97	—	13	2	no	—
963	C₄×C₈	—	13	2	no	—
964	C₄×C₈	—	13	2	no	—
965	C₄×C₈	—	13	2	no	—
966	C₂×C₁₃	—	2	2	no	—
967	C₂×C₁₃	—	2	2	no	—
968	C₂×C₁₃	—	4	1	no	—
969	C₂×C₁₃	—	4	1	no	—
970	C₂×C₁₃	—	4	2	no	—
971	C₂×C₁₃	—	4	2	no	—
972	C₂×C₁₃	—	4	2	no	—
973	C₂×C₁₃	—	4	1	no	—
974	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
975	C₂×C₁₃	C₂×#568	1	1	yes	characteristic
976	C₂×C₁₃	#3573	1	1	yes	characteristic
977	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
978	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
979	C₂⁴	C₂²×Dic₁₃	1	2	yes	—
980	C₂⁴	C₂²×Dic₁₃	1	2	yes	—
981	#41	—	2	2	no	—
982	#41	—	2	2	no	—
983	#41	—	2	2	no	—
984	#41	—	2	2	no	—
985	#41	—	2	2	no	—
986	#41	—	2	2	no	—
987	#41	—	4	2	no	—
988	#41	—	4	2	no	—
989	#41	—	4	2	no	—
990	#41	—	4	2	no	—
991	#41	—	4	4	no	—
992	#41	—	4	4	no	—
993	#41	—	4	2	no	—
994	#41	—	4	2	no	—
995	#41	—	4	2	no	—
996	#41	—	4	2	no	—
997	C₂×Q₈	—	4	2	no	—
998	C₂×Q₈	—	4	2	no	—
999	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
1000	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
1001	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
1002	C₂×Q₈	C₂²×Dic₁₃	1	2	yes	—
1003	C₂×Q₈	C₂²×Dic₁₃	1	2	yes	—
1004	C₂×D₄	—	4	2	no	—
1005	C₂×D₄	—	4	2	no	—
1006	C₂×D₄	—	4	4	no	—
1007	C₂×D₄	—	4	4	no	—
1008	C₂×D₄	—	4	2	no	—
1009	C₂×D₄	—	4	4	no	—
1010	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
1011	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1012	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
1013	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
1014	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1015	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1016	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1017	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
1018	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
1019	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
1020	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1021	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
1022	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1023	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1024	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1025	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1026	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1027	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1028	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1029	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1030	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1031	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
1032	C₂²×C₄	—	2	2	no	—
1033	C₂²×C₄	—	2	2	no	—
1034	C₂²×C₄	—	2	2	no	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	4	2	no	—
1037	C₂²×C₄	—	4	2	no	—
1038	C₂²×C₄	—	4	2	no	—
1039	C₂²×C₄	—	4	2	no	—
1040	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1041	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1042	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1043	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1044	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1045	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1046	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
1047	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1048	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
1049	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1050	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
1051	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
1052	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
1053	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
1054	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
1055	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
1056	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
1057	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1058	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1059	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1060	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
1061	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
1062	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1063	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
1064	M₁₆	—	26	2	no	—
1065	M₁₆	—	26	2	no	—
1066	M₁₆	—	26	2	no	—
1067	M₁₆	—	26	2	no	—
1068	M₁₆	—	52	1	no	—
1069	M₁₆	—	52	1	no	—
1070	M₁₆	—	52	1	no	—
1071	M₁₆	—	52	1	no	—
1072	M₁₆	—	52	2	no	—
1073	M₁₆	—	52	2	no	—
1074	M₁₆	—	52	2	no	—
1075	M₁₆	—	52	2	no	—
1076	M₁₆	—	52	2	no	—
1077	M₁₆	—	52	2	no	—
1078	C₂×C₈	—	13	1	no	—
1079	C₂×C₈	—	13	1	no	—
1080	C₂×C₈	—	13	2	no	—
1081	C₂×C₈	—	13	2	no	—
1082	C₂×C₈	—	13	2	no	—
1083	C₂×C₈	—	13	2	no	—
1084	C₂×C₈	—	13	1	no	—
1085	C₂×C₈	—	13	1	no	—
1086	C₂×C₈	—	13	1	no	—
1087	C₂×C₈	—	13	1	no	—
1088	C₂×C₈	—	13	1	no	—
1089	C₂×C₈	—	13	1	no	—
1090	C₂×C₈	—	26	2	no	—
1091	C₂×C₈	—	26	2	no	—
1092	C₂×C₈	—	26	2	no	—
1093	C₂×C₈	—	26	2	no	—
1094	C₂×C₈	—	52	1	no	—
1095	C₂×C₈	—	52	1	no	—
1096	C₂×C₈	—	52	1	no	—
1097	C₂×C₈	—	52	1	no	—
1098	C₂×C₈	—	52	2	no	—
1099	C₂×C₈	—	52	2	no	—
1100	C₂×C₈	—	52	2	no	—
1101	C₂×C₈	—	52	2	no	—
1102	C₂×C₈	—	52	2	no	—
1103	C₂×C₈	—	52	2	no	—
1104	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1105	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1106	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1107	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1108	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1109	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1110	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1111	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1112	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1113	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1114	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1115	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1116	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1117	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1118	C₂²⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1119	C₂²⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1120	C₂²⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1122	C₂²⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1123	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1124	C₂²⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1125	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1126	C₂²⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1127	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1128	C₂²⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1129	C₂²⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
1130	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1131	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1132	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1133	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1134	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1135	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1136	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1137	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1138	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1139	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1140	C₂²⋊C₄	C₂²×Dic₁₃	1	2	yes	—
1141	C₄²	C₂²×Dic₁₃	1	2	yes	—
1142	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
1143	C₄²	C₂²×Dic₁₃	1	2	yes	—
1144	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
1145	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1146	C₄²	C₂³×D₁₃	1	2	yes	—
1147	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1148	C₁₃	#60240	1	1	yes	characteristic, complemented, Sylow
1149	C₂³	—	2	2	no	—
1150	C₂³	—	2	2	no	—
1151	C₂³	—	2	2	no	—
1152	C₂³	—	2	4	no	—
1153	C₂³	—	4	1	no	—
1154	C₂³	—	4	2	no	—
1155	C₂³	—	4	2	no	—
1156	C₂³	—	4	1	no	—
1157	C₂³	—	4	2	no	—
1158	C₂³	—	4	1	no	—
1159	C₂³	—	4	2	no	—
1160	C₂³	—	4	2	no	—
1161	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
1162	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
1163	C₂³	C₂³×Dic₁₃	1	2	yes	—
1164	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
1165	C₂³	C₂³×Dic₁₃	1	2	yes	—
1166	C₂³	C₂³×Dic₁₃	1	2	yes	—
1167	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
1168	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
1169	Q₈	—	2	2	no	—
1170	Q₈	—	2	2	no	—
1171	Q₈	—	2	2	no	—
1172	Q₈	—	4	2	no	—
1173	Q₈	—	4	2	no	—
1174	D₄	—	2	4	no	—
1175	D₄	—	2	4	no	—
1176	D₄	—	2	4	no	—
1177	D₄	—	2	2	no	—
1178	D₄	—	2	2	no	—
1179	D₄	—	2	4	no	—
1180	D₄	—	2	2	no	—
1181	D₄	—	2	2	no	—
1182	D₄	—	2	2	no	—
1183	D₄	—	4	1	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	1	no	—
1186	D₄	—	4	2	no	—
1187	D₄	—	4	2	no	—
1188	D₄	—	4	2	no	—
1189	D₄	—	4	2	no	—
1190	D₄	—	4	2	no	—
1191	D₄	—	4	2	no	—
1192	D₄	—	4	2	no	—
1193	D₄	—	4	2	no	—
1194	D₄	—	4	2	no	—
1195	D₄	—	4	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	2	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	2	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	4	2	no	—
1221	C₂×C₄	—	4	2	no	—
1222	C₂×C₄	—	4	1	no	—
1223	C₂×C₄	—	4	2	no	—
1224	C₂×C₄	—	4	1	no	—
1225	C₂×C₄	—	4	2	no	—
1226	C₂×C₄	#88251	1	2	yes	—
1227	C₂×C₄	#88251	1	2	yes	—
1228	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
1229	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
1230	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
1231	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
1232	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
1233	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
1234	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
1235	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
1236	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
1237	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
1238	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
1239	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
1240	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
1241	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
1242	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
1243	C₈	—	26	1	no	—
1244	C₈	—	26	1	no	—
1245	C₈	—	26	1	no	—
1246	C₈	—	26	1	no	—
1247	C₈	—	26	1	no	—
1248	C₈	—	26	1	no	—
1249	C₈	—	26	1	no	—
1250	C₈	—	26	1	no	—
1251	C₈	—	26	2	no	—
1252	C₈	—	26	2	no	—
1253	C₈	—	26	2	no	—
1254	C₈	—	26	2	no	—
1255	C₂²	—	2	1	no	—
1256	C₂²	—	2	1	no	—
1257	C₂²	—	2	1	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	2	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	2	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	2	no	—
1265	C₂²	—	2	2	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	2	no	—
1269	C₂²	—	2	2	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	2	no	—
1275	C₂²	—	2	2	no	—
1276	C₂²	—	2	2	no	—
1277	C₂²	—	4	4	no	—
1278	C₂²	—	8	4	no	—
1279	C₂²	—	8	2	no	—
1280	C₂²	—	8	4	no	—
1281	C₂²	#11719503	1	2	yes	—
1282	C₂²	#11719524	1	2	yes	—
1283	C₂²	C₂⁴×Dic₁₃	1	1	yes	characteristic
1284	C₄	—	2	1	no	—
1285	C₄	—	2	1	no	—
1286	C₄	—	2	2	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	2	no	—
1290	C₄	—	2	1	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	1	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	2	no	—
1296	C₄	—	2	2	no	—
1297	C₄	#11719503	1	2	yes	—
1298	C₄	C₂×#88251	1	1	yes	characteristic
1299	C₄	C₂×#88251	1	1	yes	characteristic
1300	C₂	—	2	2	no	—
1301	C₂	—	2	2	no	—
1302	C₂	—	4	1	no	—
1303	C₂	—	4	1	no	—
1304	C₂	—	4	2	no	—
1305	C₂	—	4	1	no	—
1306	C₂	—	4	2	no	—
1307	C₂	—	4	2	no	—
1308	C₂	C₂×#11719503	1	1	yes	characteristic
1309	C₂	C₂×#11719524	1	1	yes	characteristic
1310	C₂	#13129548	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₁₃
commutator, socle	C₂²×C₁₃	C₂⁴×C₄
Fitting, prime radical	D₄×C₁₃×#41	C₂
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	D₄×#41	D₁₃
hypocenter	C₁₃	#60240
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ D₄×#41

Complements

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

N	H ≅ G/N	type
1. #13123912	C₂	semidirect
2. #13123907	C₂	semidirect
3. #13123898	C₂	semidirect
4. #13123892	C₂	semidirect
5. #13123884	C₂	semidirect
6. #13123884	C₂	semidirect
7. #13123871	C₂	semidirect
8. #13123865	C₂	semidirect
9. #13123580	C₂	semidirect
10. D₄×#6099	C₂	semidirect
11. #13123563	C₂	semidirect
12. #13123563	C₂	semidirect
13. #13123554	C₂	semidirect
14. #13123540	C₂	semidirect
15. #13123531	C₂	semidirect
16. C₂×#11718672	C₂	semidirect
17. #13123502	C₂	semidirect
18. #13123487	C₂	semidirect
19. #13123285	C₂	semidirect
20. #13123285	C₂	semidirect
21. #13123281	C₂	semidirect
22. C₂×#11718895	C₂	semidirect
47. C₂×#88202	C₂²	semidirect
48. C₂×#88202	C₂²	semidirect
49. C₂×#88202	C₂²	semidirect
50. C₂×#88202	C₂²	semidirect
51. C₂²×#6099	C₂²	semidirect
52. C₂²×#6099	C₂²	semidirect
53. C₂²×#6099	C₂²	semidirect
54. C₂³×#1055	C₂²	semidirect
59. #11718895	C₂²	semidirect
60. #11718895	C₂²	semidirect
61. #11718895	C₂²	semidirect
62. #11718895	C₂²	semidirect
63. #11718895	C₂²	semidirect
64. #11718895	C₂²	semidirect
65. #11718895	C₂²	semidirect
66. #11718895	C₂²	semidirect
67. #11718895	C₂²	semidirect
68. #11718895	C₂²	semidirect
69. #11718895	C₂²	semidirect
70. #11718895	C₂²	semidirect
71. #11718868	C₂²	semidirect
72. #11718868	C₂²	semidirect
73. #11718868	C₂²	semidirect
74. #11718868	C₂²	semidirect
75. #11718868	C₂²	semidirect
76. #11718868	C₂²	semidirect
77. C₂×C₂²⋊#1055	C₂²	semidirect
78. C₂×C₂²⋊#1055	C₂²	semidirect
79. C₂×C₂²⋊#1055	C₂²	semidirect
80. C₂×C₂²⋊#1055	C₂²	semidirect
81. C₂×C₂²⋊#1055	C₂²	semidirect
82. C₂×C₂²⋊#1055	C₂²	semidirect
83. #11718673	C₂²	semidirect
84. #11718673	C₂²	semidirect
85. #11718673	C₂²	semidirect
86. #11718673	C₂²	semidirect
87. #11718673	C₂²	semidirect
88. #11718673	C₂²	semidirect
92. #11718672	C₂²	semidirect
93. #11718672	C₂²	semidirect
94. #11718672	C₂²	semidirect
95. #11718672	C₂²	semidirect
96. #11718672	C₂²	semidirect
97. #11718672	C₂²	semidirect
98. #11718672	C₂²	semidirect
99. #11718672	C₂²	semidirect
100. #11718672	C₂²	semidirect
101. #11718672	C₂²	semidirect
102. #11718672	C₂²	semidirect
103. #11718672	C₂²	semidirect
104. #11718672	C₂²	semidirect
105. #11718672	C₂²	semidirect
106. #11718672	C₂²	semidirect
107. #11718672	C₂²	semidirect
108. #11718672	C₂²	semidirect
109. #11718672	C₂²	semidirect
110. #11718672	C₂²	semidirect
111. #11718672	C₂²	semidirect
112. #11718672	C₂²	semidirect
113. D₄×#1055	C₂²	semidirect
114. D₄×#1055	C₂²	semidirect
115. D₄×#1055	C₂²	semidirect
116. D₄×#1055	C₂²	semidirect
117. D₄×#1055	C₂²	semidirect
118. D₄×#1055	C₂²	semidirect
119. #11718661	C₂²	semidirect
120. #11718661	C₂²	semidirect
121. #11718661	C₂²	semidirect
122. #11718661	C₂²	semidirect
123. #11718660	C₂²	semidirect
124. #11718660	C₂²	semidirect
125. #11718658	C₂²	semidirect
126. #11718658	C₂²	semidirect
127. #11718587	C₂²	semidirect
128. #11718587	C₂²	semidirect
129. #11718587	C₂²	semidirect
130. #11718586	C₂²	semidirect
131. #11718585	C₂²	semidirect
132. C₂×C₄⋊#1055	C₂²	semidirect
133. C₄×#6099	C₂²	semidirect
134. C₂×#88043	C₂²	semidirect
1148. C₁₃	#60240	semidirect

Maximal subgroups

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

subgroup	index
#13123912	2
#13123907	2
#13123898	2
#13123892	2
#13123884	2
#13123871	2
#13123865	2
#13123580	2
D₄×#6099	2
#13123563	2
#13123554	2
#13123540	2
#13123531	2
C₂×#11718672	2
#13123502	2
#13123487	2
#13123285	2
#13123281	2
C₂×#11718895	2
D₄×C₁₃×#41	2
#60240	13