Subgroups — C₁₃×#61660 #15747999

Order 3328.

2026 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3327	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3305	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3300	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3285	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3277	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3276	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3203	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3201	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3013	C₂	1	2	yes	maximal, complemented
22	C₁₃×#3011	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
25	C₂×C₁₃×#137	C₂²	1	2	yes	—
26	C₂×C₁₃×#137	C₂²	1	2	yes	—
27	C₂×C₁₃×#135	C₂²	1	2	yes	—
28	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
29	C₁₃×#562	—	2	2	no	—
30	C₁₃×#555	—	2	1	no	—
31	C₁₃×#555	C₂²	1	1	yes	characteristic
32	C₁₃×#554	C₂²	1	1	yes	characteristic
33	C₁₃×#553	—	2	1	no	—
34	C₁₃×#552	C₂²	1	2	yes	—
35	C₁₃×#550	—	2	1	no	—
36	C₁₃×#550	C₂²	1	1	yes	characteristic
37	C₁₃×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₁₃	—	2	1	no	—
39	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#548	—	2	2	no	—
43	C₁₃×#548	C₂²	1	2	yes	—
44	C₁₃×#548	C₂²	1	2	yes	—
45	C₁₃×#548	C₂²	1	2	yes	—
46	C₁₃×#547	C₂²	1	1	yes	characteristic
47	C₁₃×#544	—	2	1	no	—
48	C₁₃×#542	—	2	2	no	—
49	C₁₃×#540	—	2	1	no	—
50	C₁₃×#537	—	2	2	no	—
51	C₁₃×#537	C₂²	1	2	yes	—
52	C₁₃×#537	C₂²	1	2	yes	—
53	C₁₃×#536	C₂²	1	2	yes	—
54	C₁₃×#533	C₂²	1	1	yes	characteristic
55	C₁₃×#532	—	2	1	no	—
56	C₁₃×#532	—	2	1	no	—
57	C₁₃×#532	C₂²	1	1	yes	characteristic
58	C₁₃×#532	C₂²	1	1	yes	characteristic
59	C₁₃×#529	C₂²	1	1	yes	characteristic
60	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
61	C₁₃×#495	C₂²	1	2	yes	—
62	C₁₃×#494	C₂²	1	1	yes	characteristic
63	C₁₃×#492	C₂²	1	1	yes	characteristic
64	C₁₃×#488	C₂²	1	2	yes	—
65	C₁₃×#487	C₂²	1	1	yes	characteristic
66	C₁₃×#486	C₂²	1	1	yes	characteristic
67	C₁₃×#485	C₂²	1	2	yes	—
68	C₁₃×#484	C₂²	1	2	yes	—
69	C₁₃×#484	C₂²	1	2	yes	—
70	C₁₃×#483	C₂²	1	1	yes	characteristic
71	C₁₃×#482	C₂²	1	2	yes	—
72	C₁₃×#480	C₂²	1	2	yes	—
73	C₁₃×#480	C₂²	1	1	yes	characteristic
74	C₁₃×#479	C₂²	1	1	yes	characteristic
75	C₁₃×#479	C₂²	1	1	yes	characteristic
76	C₁₃×#477	C₂²	1	1	yes	characteristic
77	C₁₃×#477	C₂²	1	1	yes	characteristic
78	C₁₃×#470	C₂²	1	2	yes	—
79	C₁₃×#468	C₂²	1	2	yes	—
80	C₁₃×#468	C₂²	1	2	yes	—
81	C₁₃×#468	C₂²	1	2	yes	—
82	C₁₃×#467	C₂²	1	2	yes	—
83	C₁₃×#467	C₂²	1	2	yes	—
84	C₁₃×#466	C₂²	1	2	yes	—
85	C₁₃×#465	C₂²	1	2	yes	—
86	C₁₃×#464	C₂²	1	1	yes	characteristic
87	C₁₃×#464	C₂²	1	2	yes	—
88	C₁₃×#464	C₂²	1	1	yes	characteristic
89	C₁₃×#464	C₂²	1	2	yes	—
90	C₁₃×#462	C₂²	1	1	yes	characteristic
91	C₁₃×#462	C₂²	1	1	yes	characteristic
92	C₁₃×#462	C₂²	1	1	yes	characteristic
93	C₁₃×#461	C₂²	1	1	yes	characteristic
94	C₁₃×#460	C₂²	1	1	yes	characteristic
95	C₁₃×#459	C₂²	1	1	yes	characteristic
96	C₁₃×#452	C₂²	1	2	yes	—
97	C₁₃×#452	C₂²	1	2	yes	—
98	C₁₃×#452	C₂²	1	2	yes	—
99	C₁₃×#452	C₂²	1	2	yes	—
100	C₁₃×#452	C₂²	1	2	yes	—
101	C₁₃×#452	C₂²	1	2	yes	—
102	C₁₃×#452	C₂²	1	2	yes	—
103	C₁₃×#451	C₂²	1	1	yes	characteristic
104	C₁₃×#451	C₂²	1	2	yes	—
105	C₁₃×#451	C₂²	1	2	yes	—
106	C₁₃×#451	C₂²	1	2	yes	—
107	C₁₃×#451	C₂²	1	2	yes	—
108	C₁₃×#451	C₂²	1	2	yes	—
109	C₁₃×#449	C₂²	1	2	yes	—
110	C₁₃×#449	C₂²	1	2	yes	—
111	C₁₃×#449	C₂²	1	2	yes	—
112	C₁₃×#448	C₂²	1	1	yes	characteristic
113	C₁₃×#448	C₂²	1	2	yes	—
114	C₁₃×#448	C₂²	1	2	yes	—
115	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
116	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
117	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
118	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
121	C₁₃×#436	C₂²	1	1	yes	characteristic
122	C₁₃×#436	C₂²	1	2	yes	—
123	C₁₃×#436	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
125	C₈×D₄×C₁₃	C₂²	1	2	yes	—
126	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
127	C₁₃×#431	C₂²	1	1	yes	characteristic
128	C₁₃×#431	C₂²	1	1	yes	characteristic
129	C₁₃×#419	C₂²	1	2	yes	—
130	C₁₃×#417	C₂²	1	2	yes	—
131	C₁₃×#416	C₂²	1	2	yes	—
132	C₂×C₁₃×#103	C₂²	1	2	yes	—
133	C₁₃×#408	C₂²	1	2	yes	—
134	C₁₃×#408	C₂²	1	2	yes	—
135	C₁₃×2₋¹⁺⁴	—	4	4	no	—
136	C₁₃×2₋¹⁺⁴	—	4	4	no	—
137	C₂×C₁₃×#41	—	2	2	no	—
138	C₂×C₁₃×#41	—	2	2	no	—
139	C₂×C₁₃×#41	—	2	2	no	—
140	C₂×C₁₃×#41	C₂³	1	2	yes	—
141	C₂×C₁₃×#41	C₂³	1	2	yes	—
142	C₂×C₁₃×#41	C₂³	1	2	yes	—
143	C₂×C₁₃×#41	C₂³	1	2	yes	—
144	C₂×C₁₃×#41	C₂³	1	2	yes	—
145	C₂²×Q₈×C₁₃	—	2	2	no	—
146	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
147	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
148	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
149	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
150	C₁₃×#137	—	4	4	no	—
151	C₁₃×#137	—	4	4	no	—
152	C₁₃×#135	—	4	4	no	—
153	C₂×C₁₃×Q₁₆	—	4	4	no	—
154	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
156	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
157	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
159	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
160	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
161	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
165	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₁₃×D₈	C₂³	1	2	yes	—
168	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
169	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
170	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
171	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
172	C₁₃×C₄⋊Q₈	—	2	2	no	—
173	C₁₃×C₄⋊Q₈	—	2	1	no	—
174	C₁₃×C₄⋊Q₈	—	2	1	no	—
175	C₁₃×C₄⋊Q₈	—	2	1	no	—
176	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
177	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
178	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₁₃×#127	—	2	1	no	—
181	C₁₃×#127	—	2	1	no	—
182	C₁₃×#127	D₄	1	1	yes	characteristic
183	C₁₃×#127	C₂³	1	1	yes	characteristic
184	C₁₃×#126	—	2	2	no	—
185	C₁₃×#126	—	2	1	no	—
186	C₁₃×#125	—	2	2	no	—
187	C₁₃×#125	—	2	1	no	—
188	C₁₃×#125	—	2	1	no	—
189	C₁₃×#125	C₂³	1	1	yes	characteristic
190	C₁₃×#124	—	2	2	no	—
191	C₁₃×#124	—	2	2	no	—
192	C₁₃×#124	—	2	2	no	—
193	C₁₃×#124	—	2	2	no	—
194	C₁₃×#124	—	2	2	no	—
195	C₁₃×#124	D₄	1	2	yes	—
196	C₁₃×#124	C₂³	1	2	yes	—
197	C₁₃×#124	C₂³	1	1	yes	characteristic
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	1	no	—
202	C₁₃×#123	—	2	2	no	—
203	C₁₃×C₂²⋊Q₈	—	2	2	no	—
204	C₁₃×C₂²⋊Q₈	—	2	2	no	—
205	C₁₃×C₂²⋊Q₈	—	2	1	no	—
206	C₁₃×C₂²⋊Q₈	—	2	2	no	—
207	C₁₃×C₂²⋊Q₈	—	2	2	no	—
208	C₁₃×C₂²⋊Q₈	—	2	2	no	—
209	C₁₃×C₂²⋊Q₈	—	2	2	no	—
210	C₁₃×C₂²⋊Q₈	—	2	2	no	—
211	C₁₃×C₂²⋊Q₈	—	2	2	no	—
212	C₁₃×C₂²⋊Q₈	—	2	2	no	—
213	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₁₃×#121	—	2	2	no	—
221	C₁₃×#121	—	2	2	no	—
222	C₁₃×#121	—	2	2	no	—
223	C₁₃×#121	—	2	2	no	—
224	C₁₃×#121	—	2	2	no	—
225	C₁₃×#121	—	2	2	no	—
226	C₁₃×#121	—	2	2	no	—
227	C₁₃×#121	—	2	2	no	—
228	C₁₃×#121	—	2	1	no	—
229	C₁₃×#121	—	2	2	no	—
230	C₁₃×#121	—	2	1	no	—
231	C₁₃×#121	—	2	1	no	—
232	C₁₃×#121	—	2	1	no	—
233	C₁₃×#121	—	2	2	no	—
234	C₁₃×#121	—	2	2	no	—
235	C₁₃×#121	D₄	1	1	yes	characteristic
236	C₁₃×#121	D₄	1	1	yes	characteristic
237	C₁₃×#121	D₄	1	2	yes	—
238	C₁₃×#121	C₂³	1	1	yes	characteristic
239	C₁₃×#121	C₂³	1	2	yes	—
240	C₁₃×#121	C₂³	1	2	yes	—
241	C₁₃×#121	C₂³	1	2	yes	—
242	C₄×Q₈×C₁₃	—	2	1	no	—
243	C₄×Q₈×C₁₃	—	2	1	no	—
244	C₄×Q₈×C₁₃	—	2	1	no	—
245	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
249	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₁₃	—	2	1	no	—
252	C₄×D₄×C₁₃	—	2	1	no	—
253	C₄×D₄×C₁₃	—	2	1	no	—
254	C₄×D₄×C₁₃	—	2	1	no	—
255	C₄×D₄×C₁₃	—	2	1	no	—
256	C₄×D₄×C₁₃	—	2	1	no	—
257	C₄×D₄×C₁₃	—	2	1	no	—
258	C₄×D₄×C₁₃	—	2	2	no	—
259	C₄×D₄×C₁₃	—	2	2	no	—
260	C₄×D₄×C₁₃	—	2	2	no	—
261	C₄×D₄×C₁₃	—	2	1	no	—
262	C₄×D₄×C₁₃	—	2	1	no	—
263	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₁₃	C₂³	1	2	yes	—
266	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
267	C₁₃×#117	—	2	1	no	—
268	C₁₃×#117	—	2	1	no	—
269	C₁₃×#117	—	2	2	no	—
270	C₁₃×#117	—	2	1	no	—
271	C₁₃×#117	C₂³	1	2	yes	—
272	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
275	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₄²×C₁₃	—	2	1	no	—
277	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
278	C₁₃×#107	C₂³	1	2	yes	—
279	C₁₃×#107	C₂³	1	1	yes	characteristic
280	C₁₃×#107	C₂³	1	2	yes	—
281	C₁₃×#107	C₂³	1	1	yes	characteristic
282	C₁₃×#106	C₂³	1	1	yes	characteristic
283	C₁₃×#106	C₂³	1	1	yes	characteristic
284	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	1	yes	characteristic
289	C₁₃×#103	C₂³	1	2	yes	—
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	1	yes	characteristic
293	C₁₃×#103	C₂³	1	1	yes	characteristic
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	1	yes	characteristic
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	2	yes	—
300	C₁₃×#103	C₂³	1	2	yes	—
301	C₁₃×#103	C₂³	1	1	yes	characteristic
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×#102	C₂³	1	2	yes	—
305	C₁₃×#102	C₂³	1	2	yes	—
306	C₁₃×#102	C₂³	1	1	yes	characteristic
307	C₁₃×#102	C₂³	1	1	yes	characteristic
308	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₁₃	C₂³	1	2	yes	—
318	#61660	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₁₃×#41	—	2	4	no	—
320	C₁₃×#41	—	2	4	no	—
321	C₁₃×#41	—	4	2	no	—
322	C₁₃×#41	—	4	2	no	—
323	C₁₃×#41	—	4	2	no	—
324	C₁₃×#41	—	4	2	no	—
325	C₁₃×#41	—	4	2	no	—
326	C₁₃×#41	—	4	2	no	—
327	C₁₃×#41	—	4	8	no	—
328	C₁₃×#41	—	4	8	no	—
329	C₁₃×#41	—	4	2	no	—
330	C₁₃×#41	—	4	2	no	—
331	C₁₃×#41	—	4	8	no	—
332	C₂×Q₈×C₁₃	—	2	2	no	—
333	C₂×Q₈×C₁₃	—	2	2	no	—
334	C₂×Q₈×C₁₃	—	2	1	no	—
335	C₂×Q₈×C₁₃	—	2	2	no	—
336	C₂×Q₈×C₁₃	—	2	2	no	—
337	C₂×Q₈×C₁₃	—	2	1	no	—
338	C₂×Q₈×C₁₃	—	2	2	no	—
339	C₂×Q₈×C₁₃	—	2	4	no	—
340	C₂×Q₈×C₁₃	—	2	4	no	—
341	C₂×Q₈×C₁₃	—	4	2	no	—
342	C₂×Q₈×C₁₃	—	4	2	no	—
343	C₂×Q₈×C₁₃	—	4	2	no	—
344	C₂×Q₈×C₁₃	—	4	2	no	—
345	C₂×Q₈×C₁₃	—	4	8	no	—
346	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
347	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
348	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
350	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₁₃	—	2	2	no	—
353	C₂×D₄×C₁₃	—	2	2	no	—
354	C₂×D₄×C₁₃	—	2	2	no	—
355	C₂×D₄×C₁₃	—	2	1	no	—
356	C₂×D₄×C₁₃	—	2	2	no	—
357	C₂×D₄×C₁₃	—	2	2	no	—
358	C₂×D₄×C₁₃	—	2	2	no	—
359	C₂×D₄×C₁₃	—	2	2	no	—
360	C₂×D₄×C₁₃	—	2	1	no	—
361	C₂×D₄×C₁₃	—	2	1	no	—
362	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
364	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
365	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
366	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
369	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₁₃	—	2	1	no	—
371	C₂²×C₄×C₁₃	—	2	2	no	—
372	C₂²×C₄×C₁₃	—	2	2	no	—
373	C₂²×C₄×C₁₃	—	2	1	no	—
374	C₂²×C₄×C₁₃	—	2	2	no	—
375	C₂²×C₄×C₁₃	—	2	2	no	—
376	C₂²×C₄×C₁₃	—	2	1	no	—
377	C₂²×C₄×C₁₃	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
386	C₁₃×Q₁₆	—	2	2	no	—
387	C₁₃×Q₁₆	—	2	4	no	—
388	C₁₃×Q₁₆	—	2	2	no	—
389	C₁₃×Q₁₆	—	2	4	no	—
390	C₁₃×Q₁₆	—	4	2	no	—
391	C₁₃×Q₁₆	—	4	2	no	—
392	C₁₃×Q₁₆	—	4	2	no	—
393	C₁₃×SD₁₆	—	2	2	no	—
394	C₁₃×SD₁₆	—	2	2	no	—
395	C₁₃×SD₁₆	—	4	2	no	—
396	C₁₃×SD₁₆	—	4	2	no	—
397	C₁₃×SD₁₆	—	4	2	no	—
398	C₁₃×SD₁₆	—	4	2	no	—
399	C₁₃×D₈	—	4	2	no	—
400	C₁₃×M₁₆	—	4	2	no	—
401	C₁₃×M₁₆	—	4	2	no	—
402	C₂×C₈×C₁₃	—	4	2	no	—
403	C₂×C₈×C₁₃	—	4	2	no	—
404	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
407	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
409	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
410	C₁₃×C₄⋊C₄	—	2	1	no	—
411	C₁₃×C₄⋊C₄	—	2	1	no	—
412	C₁₃×C₄⋊C₄	—	2	1	no	—
413	C₁₃×C₄⋊C₄	—	2	1	no	—
414	C₁₃×C₄⋊C₄	—	2	1	no	—
415	C₁₃×C₄⋊C₄	—	2	2	no	—
416	C₁₃×C₄⋊C₄	—	2	1	no	—
417	C₁₃×C₄⋊C₄	—	2	2	no	—
418	C₁₃×C₄⋊C₄	—	2	1	no	—
419	C₁₃×C₄⋊C₄	—	2	1	no	—
420	C₁₃×C₄⋊C₄	—	2	2	no	—
421	C₁₃×C₄⋊C₄	—	2	1	no	—
422	C₁₃×C₄⋊C₄	—	2	1	no	—
423	C₁₃×C₄⋊C₄	—	2	1	no	—
424	C₁₃×C₄⋊C₄	—	2	1	no	—
425	C₁₃×C₄⋊C₄	—	2	2	no	—
426	C₁₃×C₄⋊C₄	—	2	2	no	—
427	C₁₃×C₄⋊C₄	—	2	2	no	—
428	C₁₃×C₄⋊C₄	—	2	2	no	—
429	C₁₃×C₄⋊C₄	—	2	1	no	—
430	C₁₃×C₄⋊C₄	—	2	2	no	—
431	C₁₃×C₄⋊C₄	—	2	1	no	—
432	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
433	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
434	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
435	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
436	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
437	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
438	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
439	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
440	C₁₃×C₂²⋊C₄	—	2	2	no	—
441	C₁₃×C₂²⋊C₄	—	2	2	no	—
442	C₁₃×C₂²⋊C₄	—	2	2	no	—
443	C₁₃×C₂²⋊C₄	—	2	2	no	—
444	C₁₃×C₂²⋊C₄	—	2	2	no	—
445	C₁₃×C₂²⋊C₄	—	2	2	no	—
446	C₁₃×C₂²⋊C₄	—	2	2	no	—
447	C₁₃×C₂²⋊C₄	—	2	1	no	—
448	C₁₃×C₂²⋊C₄	—	2	1	no	—
449	C₁₃×C₂²⋊C₄	—	2	1	no	—
450	C₁₃×C₂²⋊C₄	—	2	2	no	—
451	C₁₃×C₂²⋊C₄	—	2	2	no	—
452	C₁₃×C₂²⋊C₄	—	2	1	no	—
453	C₁₃×C₂²⋊C₄	—	2	2	no	—
454	C₁₃×C₂²⋊C₄	—	2	2	no	—
455	C₁₃×C₂²⋊C₄	—	2	2	no	—
456	C₁₃×C₂²⋊C₄	—	2	1	no	—
457	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
458	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
459	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
460	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
461	C₄²×C₁₃	—	2	1	no	—
462	C₄²×C₁₃	—	2	1	no	—
463	C₄²×C₁₃	—	2	1	no	—
464	C₄²×C₁₃	—	2	1	no	—
465	C₄²×C₁₃	—	2	2	no	—
466	C₄²×C₁₃	—	2	2	no	—
467	C₄²×C₁₃	—	2	1	no	—
468	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
469	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
470	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
471	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
472	#3547	C₂×C₁₃	1	1	yes	characteristic, complemented
473	#3497	C₂×C₁₃	1	1	yes	characteristic, complemented
474	#3333	C₂×C₁₃	1	1	yes	characteristic, complemented
475	#3329	C₂×C₁₃	1	1	yes	characteristic, complemented
476	#3327	C₂×C₁₃	1	2	yes	complemented
477	#3305	C₂×C₁₃	1	1	yes	characteristic, complemented
478	#3300	C₂×C₁₃	1	2	yes	complemented
479	#3299	C₂×C₁₃	1	1	yes	characteristic, complemented
480	D₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#3285	C₂×C₁₃	1	2	yes	complemented
482	#3284	C₂×C₁₃	1	1	yes	characteristic, complemented
483	#3278	C₂×C₁₃	1	1	yes	characteristic, complemented
484	#3277	C₂×C₁₃	1	2	yes	complemented
485	#3276	C₂×C₁₃	1	1	yes	characteristic, complemented
486	#3212	C₂×C₁₃	1	1	yes	characteristic, complemented
487	#3210	C₂×C₁₃	1	1	yes	characteristic, complemented
488	#3203	C₂×C₁₃	1	2	yes	complemented
489	#3201	C₂×C₁₃	1	2	yes	complemented
490	#3108	C₂×C₁₃	1	1	yes	characteristic, complemented
491	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
492	#3013	C₂×C₁₃	1	2	yes	complemented
493	#3011	C₂×C₁₃	1	2	yes	complemented
494	#2979	C₂×C₁₃	1	1	yes	characteristic, complemented
495	C₂³×C₁₃	—	2	1	no	—
496	C₂³×C₁₃	—	2	2	no	—
497	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
498	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
499	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
500	Q₈×C₁₃	—	2	4	no	—
501	Q₈×C₁₃	—	2	1	no	—
502	Q₈×C₁₃	—	2	1	no	—
503	Q₈×C₁₃	—	2	1	no	—
504	Q₈×C₁₃	—	2	2	no	—
505	Q₈×C₁₃	—	2	2	no	—
506	Q₈×C₁₃	—	2	2	no	—
507	Q₈×C₁₃	—	2	1	no	—
508	Q₈×C₁₃	—	2	2	no	—
509	Q₈×C₁₃	—	4	2	no	—
510	Q₈×C₁₃	—	4	4	no	—
511	Q₈×C₁₃	—	4	4	no	—
512	Q₈×C₁₃	—	8	1	no	—
513	Q₈×C₁₃	—	8	2	no	—
514	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
515	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
516	D₄×C₁₃	—	2	2	no	—
517	D₄×C₁₃	—	2	2	no	—
518	D₄×C₁₃	—	2	1	no	—
519	D₄×C₁₃	—	2	2	no	—
520	D₄×C₁₃	—	2	1	no	—
521	D₄×C₁₃	—	2	2	no	—
522	D₄×C₁₃	—	4	2	no	—
523	D₄×C₁₃	—	4	2	no	—
524	D₄×C₁₃	—	4	2	no	—
525	D₄×C₁₃	—	4	2	no	—
526	D₄×C₁₃	—	4	4	no	—
527	D₄×C₁₃	—	4	4	no	—
528	D₄×C₁₃	—	4	4	no	—
529	D₄×C₁₃	—	4	2	no	—
530	D₄×C₁₃	—	8	1	no	—
531	D₄×C₁₃	—	8	1	no	—
532	D₄×C₁₃	—	8	2	no	—
533	D₄×C₁₃	—	8	2	no	—
534	D₄×C₁₃	—	8	2	no	—
535	D₄×C₁₃	—	8	2	no	—
536	C₂×C₄×C₁₃	—	2	4	no	—
537	C₂×C₄×C₁₃	—	2	1	no	—
538	C₂×C₄×C₁₃	—	2	1	no	—
539	C₂×C₄×C₁₃	—	2	2	no	—
540	C₂×C₄×C₁₃	—	2	2	no	—
541	C₂×C₄×C₁₃	—	2	2	no	—
542	C₂×C₄×C₁₃	—	2	2	no	—
543	C₂×C₄×C₁₃	—	2	2	no	—
544	C₂×C₄×C₁₃	—	2	1	no	—
545	C₂×C₄×C₁₃	—	2	1	no	—
546	C₂×C₄×C₁₃	—	2	1	no	—
547	C₂×C₄×C₁₃	—	2	1	no	—
548	C₂×C₄×C₁₃	—	2	1	no	—
549	C₂×C₄×C₁₃	—	2	2	no	—
550	C₂×C₄×C₁₃	—	2	1	no	—
551	C₂×C₄×C₁₃	—	2	1	no	—
552	C₂×C₄×C₁₃	—	2	2	no	—
553	C₂×C₄×C₁₃	—	2	2	no	—
554	C₂×C₄×C₁₃	—	4	1	no	—
555	C₂×C₄×C₁₃	—	4	4	no	—
556	C₂×C₄×C₁₃	—	4	4	no	—
557	C₂×C₄×C₁₃	—	4	4	no	—
558	C₂×C₄×C₁₃	—	4	4	no	—
559	C₂×C₄×C₁₃	—	4	4	no	—
560	C₂×C₄×C₁₃	—	4	2	no	—
561	C₂×C₄×C₁₃	—	8	2	no	—
562	C₂×C₄×C₁₃	—	8	2	no	—
563	C₂×C₄×C₁₃	—	8	1	no	—
564	C₂×C₄×C₁₃	—	8	2	no	—
565	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
567	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
571	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
573	C₈×C₁₃	—	2	2	no	—
574	C₈×C₁₃	—	2	1	no	—
575	C₈×C₁₃	—	2	1	no	—
576	C₈×C₁₃	—	2	1	no	—
577	C₈×C₁₃	—	2	1	no	—
578	C₈×C₁₃	—	2	2	no	—
579	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
580	C₂×#137	C₂²×C₁₃	1	2	yes	—
581	C₂×#137	C₂²×C₁₃	1	2	yes	—
582	C₂×#135	C₂²×C₁₃	1	2	yes	—
583	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
584	#562	—	2	2	no	—
585	#555	—	2	1	no	—
586	#555	C₂²×C₁₃	1	1	yes	characteristic
587	#554	C₂²×C₁₃	1	1	yes	characteristic
588	#553	—	2	1	no	—
589	#552	C₂²×C₁₃	1	2	yes	—
590	#550	—	2	1	no	—
591	#550	C₂²×C₁₃	1	1	yes	characteristic
592	#550	C₂²×C₁₃	1	1	yes	characteristic
593	D₄×Q₈	—	2	1	no	—
594	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
595	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
596	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
597	#548	—	2	2	no	—
598	#548	C₂²×C₁₃	1	2	yes	—
599	#548	C₂²×C₁₃	1	2	yes	—
600	#548	C₂²×C₁₃	1	2	yes	—
601	#547	C₂²×C₁₃	1	1	yes	characteristic
602	#544	—	2	1	no	—
603	#542	—	2	2	no	—
604	#540	—	2	1	no	—
605	#537	—	2	2	no	—
606	#537	C₂²×C₁₃	1	2	yes	—
607	#537	C₂²×C₁₃	1	2	yes	—
608	#536	C₂²×C₁₃	1	2	yes	—
609	#533	C₂²×C₁₃	1	1	yes	characteristic
610	#532	—	2	1	no	—
611	#532	—	2	1	no	—
612	#532	C₂²×C₁₃	1	1	yes	characteristic
613	#532	C₂²×C₁₃	1	1	yes	characteristic
614	#529	C₂²×C₁₃	1	1	yes	characteristic
615	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
616	#495	C₂²×C₁₃	1	2	yes	—
617	#494	C₂²×C₁₃	1	1	yes	characteristic
618	#492	C₂²×C₁₃	1	1	yes	characteristic
619	#488	C₂²×C₁₃	1	2	yes	—
620	#487	C₂²×C₁₃	1	1	yes	characteristic
621	#486	C₂²×C₁₃	1	1	yes	characteristic
622	#485	C₂²×C₁₃	1	2	yes	—
623	#484	C₂²×C₁₃	1	2	yes	—
624	#484	C₂²×C₁₃	1	2	yes	—
625	#483	C₂²×C₁₃	1	1	yes	characteristic
626	#482	C₂²×C₁₃	1	2	yes	—
627	#480	C₂²×C₁₃	1	2	yes	—
628	#480	C₂²×C₁₃	1	1	yes	characteristic
629	#479	C₂²×C₁₃	1	1	yes	characteristic
630	#479	C₂²×C₁₃	1	1	yes	characteristic
631	#477	C₂²×C₁₃	1	1	yes	characteristic
632	#477	C₂²×C₁₃	1	1	yes	characteristic
633	#470	C₂²×C₁₃	1	2	yes	—
634	#468	C₂²×C₁₃	1	2	yes	—
635	#468	C₂²×C₁₃	1	2	yes	—
636	#468	C₂²×C₁₃	1	2	yes	—
637	#467	C₂²×C₁₃	1	2	yes	—
638	#467	C₂²×C₁₃	1	2	yes	—
639	#466	C₂²×C₁₃	1	2	yes	—
640	#465	C₂²×C₁₃	1	2	yes	—
641	#464	C₂²×C₁₃	1	1	yes	characteristic
642	#464	C₂²×C₁₃	1	1	yes	characteristic
643	#464	C₂²×C₁₃	1	2	yes	—
644	#464	C₂²×C₁₃	1	2	yes	—
645	#462	C₂²×C₁₃	1	1	yes	characteristic
646	#462	C₂²×C₁₃	1	1	yes	characteristic
647	#462	C₂²×C₁₃	1	1	yes	characteristic
648	#461	C₂²×C₁₃	1	1	yes	characteristic
649	#460	C₂²×C₁₃	1	1	yes	characteristic
650	#459	C₂²×C₁₃	1	1	yes	characteristic
651	#452	C₂²×C₁₃	1	2	yes	—
652	#452	C₂²×C₁₃	1	2	yes	—
653	#452	C₂²×C₁₃	1	2	yes	—
654	#452	C₂²×C₁₃	1	2	yes	—
655	#452	C₂²×C₁₃	1	2	yes	—
656	#452	C₂²×C₁₃	1	2	yes	—
657	#452	C₂²×C₁₃	1	2	yes	—
658	#451	C₂²×C₁₃	1	2	yes	—
659	#451	C₂²×C₁₃	1	1	yes	characteristic
660	#451	C₂²×C₁₃	1	2	yes	—
661	#451	C₂²×C₁₃	1	2	yes	—
662	#451	C₂²×C₁₃	1	2	yes	—
663	#451	C₂²×C₁₃	1	2	yes	—
664	#449	C₂²×C₁₃	1	2	yes	—
665	#449	C₂²×C₁₃	1	2	yes	—
666	#449	C₂²×C₁₃	1	2	yes	—
667	#448	C₂²×C₁₃	1	2	yes	—
668	#448	C₂²×C₁₃	1	1	yes	characteristic
669	#448	C₂²×C₁₃	1	2	yes	—
670	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
671	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
672	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
673	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
674	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
675	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
676	#436	C₂²×C₁₃	1	1	yes	characteristic
677	#436	C₂²×C₁₃	1	1	yes	characteristic
678	#436	C₂²×C₁₃	1	2	yes	—
679	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
680	C₈×D₄	C₂²×C₁₃	1	2	yes	—
681	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
682	#431	C₂²×C₁₃	1	1	yes	characteristic
683	#431	C₂²×C₁₃	1	1	yes	characteristic
684	#419	C₂²×C₁₃	1	2	yes	—
685	#417	C₂²×C₁₃	1	2	yes	—
686	#416	C₂²×C₁₃	1	2	yes	—
687	C₂×#103	C₂²×C₁₃	1	2	yes	—
688	#408	C₂²×C₁₃	1	2	yes	—
689	#408	C₂²×C₁₃	1	2	yes	—
690	C₂²×C₁₃	—	2	1	no	—
691	C₂²×C₁₃	—	2	2	no	—
692	C₂²×C₁₃	—	2	2	no	—
693	C₂²×C₁₃	—	2	1	no	—
694	C₂²×C₁₃	—	2	2	no	—
695	C₂²×C₁₃	—	2	2	no	—
696	C₂²×C₁₃	—	2	1	no	—
697	C₂²×C₁₃	—	2	2	no	—
698	C₂²×C₁₃	—	2	2	no	—
699	C₂²×C₁₃	—	4	2	no	—
700	C₂²×C₁₃	—	4	1	no	—
701	C₂²×C₁₃	—	4	2	no	—
702	C₂²×C₁₃	—	4	1	no	—
703	C₂²×C₁₃	—	4	1	no	—
704	C₂²×C₁₃	—	4	2	no	—
705	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
706	C₄×C₁₃	—	2	1	no	—
707	C₄×C₁₃	—	2	1	no	—
708	C₄×C₁₃	—	2	2	no	—
709	C₄×C₁₃	—	2	2	no	—
710	C₄×C₁₃	—	2	1	no	—
711	C₄×C₁₃	—	2	2	no	—
712	C₄×C₁₃	—	2	2	no	—
713	C₄×C₁₃	—	2	1	no	—
714	C₄×C₁₃	—	4	1	no	—
715	C₄×C₁₃	—	4	1	no	—
716	C₄×C₁₃	—	4	1	no	—
717	C₄×C₁₃	—	4	2	no	—
718	C₄×C₁₃	—	4	2	no	—
719	C₄×C₁₃	—	4	2	no	—
720	C₄×C₁₃	—	4	1	no	—
721	C₄×C₁₃	—	4	1	no	—
722	C₄×C₁₃	#578	1	2	yes	—
723	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
724	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
725	2₋¹⁺⁴	—	4	4	no	—
726	2₋¹⁺⁴	—	4	4	no	—
727	C₂×#41	—	2	2	no	—
728	C₂×#41	—	2	2	no	—
729	C₂×#41	—	2	2	no	—
730	C₂×#41	C₂³×C₁₃	1	2	yes	—
731	C₂×#41	C₂³×C₁₃	1	2	yes	—
732	C₂×#41	C₂³×C₁₃	1	2	yes	—
733	C₂×#41	C₂³×C₁₃	1	2	yes	—
734	C₂×#41	C₂³×C₁₃	1	2	yes	—
735	C₂²×Q₈	—	2	2	no	—
736	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
737	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
738	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
739	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
740	#137	—	4	4	no	—
741	#137	—	4	4	no	—
742	#135	—	4	4	no	—
743	C₂×Q₁₆	—	4	4	no	—
744	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
745	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
746	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
747	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
748	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
749	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
750	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
751	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
752	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
753	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
754	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
755	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
757	C₂×D₈	C₂³×C₁₃	1	2	yes	—
758	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
759	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
760	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
761	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
762	C₄⋊Q₈	—	2	2	no	—
763	C₄⋊Q₈	—	2	1	no	—
764	C₄⋊Q₈	—	2	1	no	—
765	C₄⋊Q₈	—	2	1	no	—
766	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
767	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
768	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
769	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
770	#127	—	2	1	no	—
771	#127	—	2	1	no	—
772	#127	D₄×C₁₃	1	1	yes	characteristic
773	#127	C₂³×C₁₃	1	1	yes	characteristic
774	#126	—	2	2	no	—
775	#126	—	2	1	no	—
776	#125	—	2	2	no	—
777	#125	—	2	1	no	—
778	#125	—	2	1	no	—
779	#125	C₂³×C₁₃	1	1	yes	characteristic
780	#124	—	2	2	no	—
781	#124	—	2	2	no	—
782	#124	—	2	2	no	—
783	#124	—	2	2	no	—
784	#124	—	2	2	no	—
785	#124	D₄×C₁₃	1	2	yes	—
786	#124	C₂³×C₁₃	1	1	yes	characteristic
787	#124	C₂³×C₁₃	1	2	yes	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	1	no	—
792	#123	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	1	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
804	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
805	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
806	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
807	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
808	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
809	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	—	2	1	no	—
819	#121	—	2	2	no	—
820	#121	—	2	1	no	—
821	#121	—	2	1	no	—
822	#121	—	2	1	no	—
823	#121	—	2	2	no	—
824	#121	—	2	2	no	—
825	#121	D₄×C₁₃	1	1	yes	characteristic
826	#121	D₄×C₁₃	1	1	yes	characteristic
827	#121	D₄×C₁₃	1	2	yes	—
828	#121	C₂³×C₁₃	1	1	yes	characteristic
829	#121	C₂³×C₁₃	1	2	yes	—
830	#121	C₂³×C₁₃	1	2	yes	—
831	#121	C₂³×C₁₃	1	2	yes	—
832	C₄×Q₈	—	2	1	no	—
833	C₄×Q₈	—	2	1	no	—
834	C₄×Q₈	—	2	1	no	—
835	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
836	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
837	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
838	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
839	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
840	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	2	no	—
849	C₄×D₄	—	2	2	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
855	C₄×D₄	C₂³×C₁₃	1	2	yes	—
856	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
857	#117	—	2	1	no	—
858	#117	—	2	1	no	—
859	#117	—	2	2	no	—
860	#117	—	2	1	no	—
861	#117	C₂³×C₁₃	1	2	yes	—
862	C₂×C₄⋊C₄	—	2	1	no	—
863	C₂×C₄⋊C₄	—	2	1	no	—
864	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
865	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
866	C₂×C₄²	—	2	1	no	—
867	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
868	#107	C₂³×C₁₃	1	2	yes	—
869	#107	C₂³×C₁₃	1	1	yes	characteristic
870	#107	C₂³×C₁₃	1	2	yes	—
871	#107	C₂³×C₁₃	1	1	yes	characteristic
872	#106	C₂³×C₁₃	1	1	yes	characteristic
873	#106	C₂³×C₁₃	1	1	yes	characteristic
874	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
875	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
877	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
878	#103	C₂³×C₁₃	1	1	yes	characteristic
879	#103	C₂³×C₁₃	1	2	yes	—
880	#103	C₂³×C₁₃	1	2	yes	—
881	#103	C₂³×C₁₃	1	2	yes	—
882	#103	C₂³×C₁₃	1	1	yes	characteristic
883	#103	C₂³×C₁₃	1	1	yes	characteristic
884	#103	C₂³×C₁₃	1	2	yes	—
885	#103	C₂³×C₁₃	1	1	yes	characteristic
886	#103	C₂³×C₁₃	1	2	yes	—
887	#103	C₂³×C₁₃	1	2	yes	—
888	#103	C₂³×C₁₃	1	1	yes	characteristic
889	#103	C₂³×C₁₃	1	2	yes	—
890	#103	C₂³×C₁₃	1	2	yes	—
891	#103	C₂³×C₁₃	1	1	yes	characteristic
892	#102	C₂³×C₁₃	1	2	yes	—
893	#102	C₂³×C₁₃	1	2	yes	—
894	#102	C₂³×C₁₃	1	2	yes	—
895	#102	C₂³×C₁₃	1	2	yes	—
896	#102	C₂³×C₁₃	1	1	yes	characteristic
897	#102	C₂³×C₁₃	1	1	yes	characteristic
898	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
899	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
901	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
904	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
905	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
906	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
907	C₄×C₈	C₂³×C₁₃	1	2	yes	—
908	C₂×C₁₃	—	4	1	no	—
909	C₂×C₁₃	—	4	2	no	—
910	C₂×C₁₃	—	4	2	no	—
911	C₂×C₁₃	—	8	2	no	—
912	C₂×C₁₃	—	8	1	no	—
913	C₂×C₁₃	#3484	1	1	yes	characteristic
914	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
915	C₂×C₁₃	#3584	1	1	yes	characteristic
916	#41	—	2	4	no	—
917	#41	—	2	4	no	—
918	#41	—	4	2	no	—
919	#41	—	4	2	no	—
920	#41	—	4	2	no	—
921	#41	—	4	2	no	—
922	#41	—	4	2	no	—
923	#41	—	4	2	no	—
924	#41	—	4	8	no	—
925	#41	—	4	8	no	—
926	#41	—	4	2	no	—
927	#41	—	4	2	no	—
928	#41	—	4	8	no	—
929	C₂×Q₈	—	2	2	no	—
930	C₂×Q₈	—	2	2	no	—
931	C₂×Q₈	—	2	1	no	—
932	C₂×Q₈	—	2	2	no	—
933	C₂×Q₈	—	2	2	no	—
934	C₂×Q₈	—	2	1	no	—
935	C₂×Q₈	—	2	2	no	—
936	C₂×Q₈	—	2	4	no	—
937	C₂×Q₈	—	2	4	no	—
938	C₂×Q₈	—	4	2	no	—
939	C₂×Q₈	—	4	2	no	—
940	C₂×Q₈	—	4	2	no	—
941	C₂×Q₈	—	4	2	no	—
942	C₂×Q₈	—	4	8	no	—
943	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
944	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
945	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
946	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
947	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
948	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	1	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	2	1	no	—
959	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
960	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
961	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
962	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
963	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
964	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
965	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
966	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
979	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
980	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
981	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
982	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
983	Q₁₆	—	2	2	no	—
984	Q₁₆	—	2	4	no	—
985	Q₁₆	—	2	2	no	—
986	Q₁₆	—	2	4	no	—
987	Q₁₆	—	4	2	no	—
988	Q₁₆	—	4	2	no	—
989	Q₁₆	—	4	2	no	—
990	SD₁₆	—	2	2	no	—
991	SD₁₆	—	2	2	no	—
992	SD₁₆	—	4	2	no	—
993	SD₁₆	—	4	2	no	—
994	SD₁₆	—	4	2	no	—
995	SD₁₆	—	4	2	no	—
996	D₈	—	4	2	no	—
997	M₁₆	—	4	2	no	—
998	M₁₆	—	4	2	no	—
999	C₂×C₈	—	4	2	no	—
1000	C₂×C₈	—	4	2	no	—
1001	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1002	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1003	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1004	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1005	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1006	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1030	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1031	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1032	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1033	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1034	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1035	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1036	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1055	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1056	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1057	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1058	C₄²	—	2	1	no	—
1059	C₄²	—	2	1	no	—
1060	C₄²	—	2	1	no	—
1061	C₄²	—	2	1	no	—
1062	C₄²	—	2	2	no	—
1063	C₄²	—	2	2	no	—
1064	C₄²	—	2	1	no	—
1065	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1066	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1067	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1068	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1069	C₁₃	#61660	1	1	yes	characteristic, direct product factor, Sylow
1070	C₂³	—	2	1	no	—
1071	C₂³	—	2	2	no	—
1072	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1073	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1074	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1075	Q₈	—	2	4	no	—
1076	Q₈	—	2	1	no	—
1077	Q₈	—	2	1	no	—
1078	Q₈	—	2	1	no	—
1079	Q₈	—	2	2	no	—
1080	Q₈	—	2	2	no	—
1081	Q₈	—	2	2	no	—
1082	Q₈	—	2	1	no	—
1083	Q₈	—	2	2	no	—
1084	Q₈	—	4	2	no	—
1085	Q₈	—	4	4	no	—
1086	Q₈	—	4	4	no	—
1087	Q₈	—	8	2	no	—
1088	Q₈	—	8	1	no	—
1089	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
1090	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
1091	D₄	—	2	2	no	—
1092	D₄	—	2	2	no	—
1093	D₄	—	2	1	no	—
1094	D₄	—	2	2	no	—
1095	D₄	—	2	1	no	—
1096	D₄	—	2	2	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	4	2	no	—
1099	D₄	—	4	2	no	—
1100	D₄	—	4	2	no	—
1101	D₄	—	4	4	no	—
1102	D₄	—	4	4	no	—
1103	D₄	—	4	4	no	—
1104	D₄	—	4	2	no	—
1105	D₄	—	8	1	no	—
1106	D₄	—	8	1	no	—
1107	D₄	—	8	2	no	—
1108	D₄	—	8	2	no	—
1109	D₄	—	8	2	no	—
1110	D₄	—	8	2	no	—
1111	C₂×C₄	—	2	4	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	4	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	4	4	no	—
1135	C₂×C₄	—	4	2	no	—
1136	C₂×C₄	—	8	2	no	—
1137	C₂×C₄	—	8	2	no	—
1138	C₂×C₄	—	8	1	no	—
1139	C₂×C₄	—	8	2	no	—
1140	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1141	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1142	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1143	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1144	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1145	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1146	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1147	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1148	C₈	—	2	2	no	—
1149	C₈	—	2	1	no	—
1150	C₈	—	2	1	no	—
1151	C₈	—	2	1	no	—
1152	C₈	—	2	1	no	—
1153	C₈	—	2	2	no	—
1154	C₂²	—	2	1	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	1	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	2	1	no	—
1161	C₂²	—	2	2	no	—
1162	C₂²	—	2	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1170	C₄	—	2	1	no	—
1171	C₄	—	2	1	no	—
1172	C₄	—	2	1	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	2	2	no	—
1175	C₄	—	2	1	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	4	1	no	—
1179	C₄	—	4	1	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	2	no	—
1183	C₄	—	4	2	no	—
1184	C₄	—	4	2	no	—
1185	C₄	—	4	1	no	—
1186	C₄	C₁₃×#578	1	2	yes	—
1187	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1188	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1189	C₂	—	4	1	no	—
1190	C₂	—	4	2	no	—
1191	C₂	—	4	2	no	—
1192	C₂	—	8	1	no	—
1193	C₂	—	8	2	no	—
1194	C₂	C₁₃×#3484	1	1	yes	characteristic
1195	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
1196	C₂	C₁₃×#3584	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 ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3547	C₂	semidirect
2. C₁₃×#3497	C₂	semidirect
3. C₁₃×#3333	C₂	semidirect
4. C₁₃×#3329	C₂	semidirect
5. C₁₃×#3327	C₂	semidirect
6. C₁₃×#3305	C₂	semidirect
7. C₁₃×#3300	C₂	semidirect
8. C₁₃×#3299	C₂	semidirect
9. D₄×C₁₃×Q₁₆	C₂	semidirect
10. C₁₃×#3285	C₂	semidirect
11. C₁₃×#3284	C₂	semidirect
12. C₁₃×#3278	C₂	semidirect
13. C₁₃×#3277	C₂	semidirect
14. C₁₃×#3276	C₂	semidirect
15. C₁₃×#3212	C₂	semidirect
16. C₁₃×#3210	C₂	semidirect
17. C₁₃×#3203	C₂	semidirect
18. C₁₃×#3201	C₂	semidirect
19. C₁₃×#3108	C₂	semidirect
20. C₁₃×#3104	C₂	semidirect
21. C₁₃×#3013	C₂	semidirect
22. C₁₃×#3011	C₂	semidirect
23. C₁₃×#2979	C₂	semidirect
318. #61660	C₁₃	direct (N × H)
472. #3547	C₂×C₁₃	semidirect
473. #3497	C₂×C₁₃	semidirect
474. #3333	C₂×C₁₃	semidirect
475. #3329	C₂×C₁₃	semidirect
476. #3327	C₂×C₁₃	semidirect
477. #3305	C₂×C₁₃	semidirect
478. #3300	C₂×C₁₃	semidirect
479. #3299	C₂×C₁₃	semidirect
480. D₄×Q₁₆	C₂×C₁₃	semidirect
481. #3285	C₂×C₁₃	semidirect
482. #3284	C₂×C₁₃	semidirect
483. #3278	C₂×C₁₃	semidirect
484. #3277	C₂×C₁₃	semidirect
485. #3276	C₂×C₁₃	semidirect
486. #3212	C₂×C₁₃	semidirect
487. #3210	C₂×C₁₃	semidirect
488. #3203	C₂×C₁₃	semidirect
489. #3201	C₂×C₁₃	semidirect
490. #3108	C₂×C₁₃	semidirect
491. #3104	C₂×C₁₃	semidirect
492. #3013	C₂×C₁₃	semidirect
493. #3011	C₂×C₁₃	semidirect
494. #2979	C₂×C₁₃	semidirect
1069. C₁₃	#61660	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×#3547	2
C₁₃×#3497	2
C₁₃×#3333	2
C₁₃×#3329	2
C₁₃×#3327	2
C₁₃×#3305	2
C₁₃×#3300	2
C₁₃×#3299	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3285	2
C₁₃×#3284	2
C₁₃×#3278	2
C₁₃×#3277	2
C₁₃×#3276	2
C₁₃×#3212	2
C₁₃×#3210	2
C₁₃×#3203	2
C₁₃×#3201	2
C₁₃×#3108	2
C₁₃×#3104	2
C₁₃×#3013	2
C₁₃×#3011	2
C₁₃×#2979	2
#61660	13

Subgroups — C13×#61660 #15747999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61660 #15747999