Subgroups — C₁₃×#60835 #15747174

Order 3328.

2040 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3225	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3224	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3223	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3222	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3219	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3215	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3210	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
34	C₁₃×#548	—	2	1	no	—
35	C₁₃×#548	—	2	1	no	—
36	C₁₃×#546	—	2	2	no	—
37	C₁₃×#546	—	2	1	no	—
38	C₁₃×#546	—	2	2	no	—
39	C₁₃×#546	—	2	1	no	—
40	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#542	—	2	1	no	—
42	C₁₃×#542	C₂²	1	2	yes	complemented
43	C₁₃×#541	—	2	1	no	—
44	C₁₃×#541	C₂²	1	2	yes	complemented
45	C₁₃×#539	—	2	2	no	—
46	C₁₃×#537	C₂²	1	1	yes	characteristic
47	C₁₃×#536	C₂²	1	1	yes	characteristic
48	C₁₃×#536	C₂²	1	2	yes	—
49	C₁₃×#536	C₂²	1	1	yes	characteristic
50	C₁₃×#536	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#535	C₂²	1	1	yes	characteristic
52	C₁₃×#535	C₂²	1	2	yes	—
53	C₁₃×#533	—	2	1	no	—
54	C₁₃×#533	C₂²	1	2	yes	complemented
55	C₁₃×#532	C₂²	1	1	yes	characteristic
56	C₁₃×#532	C₂²	1	2	yes	—
57	C₁₃×#529	—	2	2	no	—
58	C₁₃×#529	—	2	1	no	—
59	C₁₃×#529	C₂²	1	2	yes	complemented
60	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#124	C₂²	1	2	yes	—
62	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
63	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#497	C₂²	1	2	yes	complemented
66	C₁₃×#497	C₂²	1	2	yes	complemented
67	C₁₃×#497	C₂²	1	2	yes	complemented
68	C₁₃×#496	C₂²	1	2	yes	complemented
69	C₁₃×#495	C₂²	1	2	yes	complemented
70	C₁₃×#495	C₂²	1	2	yes	complemented
71	C₁₃×#494	C₂²	1	2	yes	complemented
72	C₁₃×#492	C₂²	1	2	yes	complemented
73	C₁₃×#491	C₂²	1	2	yes	complemented
74	C₁₃×#490	C₂²	1	2	yes	complemented
75	C₁₃×#489	C₂²	1	2	yes	complemented
76	C₁₃×#489	C₂²	1	2	yes	complemented
77	C₁₃×#488	C₂²	1	2	yes	complemented
78	C₁₃×#488	C₂²	1	2	yes	complemented
79	C₁₃×#487	C₂²	1	2	yes	complemented
80	C₁₃×#486	C₂²	1	2	yes	complemented
81	C₁₃×#464	C₂²	1	2	yes	complemented
82	C₁₃×#464	C₂²	1	2	yes	complemented
83	C₁₃×#464	C₂²	1	2	yes	complemented
84	C₁₃×#464	C₂²	1	2	yes	complemented
85	C₁₃×#464	C₂²	1	1	yes	characteristic, complemented
86	C₁₃×#464	C₂²	1	1	yes	characteristic, complemented
87	C₁₃×#464	C₂²	1	2	yes	complemented
88	C₁₃×#464	C₂²	1	2	yes	complemented
89	C₁₃×#464	C₂²	1	2	yes	complemented
90	C₁₃×#464	C₂²	1	2	yes	complemented
91	C₁₃×#463	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#463	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#463	C₂²	1	2	yes	complemented
94	C₁₃×#463	C₂²	1	2	yes	complemented
95	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#462	C₂²	1	2	yes	complemented
97	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
98	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
99	C₁₃×#460	C₂²	1	2	yes	complemented
100	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
101	C₁₃×#452	C₂²	1	2	yes	—
102	C₁₃×#452	C₂²	1	2	yes	—
103	C₁₃×#452	C₂²	1	2	yes	—
104	C₁₃×#452	C₂²	1	2	yes	complemented
105	C₁₃×#452	C₂²	1	2	yes	complemented
106	C₁₃×#452	C₂²	1	2	yes	complemented
107	C₁₃×#451	C₂²	1	2	yes	complemented
108	C₁₃×#451	C₂²	1	2	yes	complemented
109	C₁₃×#451	C₂²	1	2	yes	complemented
110	C₁₃×#450	C₂²	1	2	yes	—
111	C₁₃×#450	C₂²	1	2	yes	—
112	C₁₃×#450	C₂²	1	2	yes	—
113	C₁₃×#449	C₂²	1	2	yes	—
114	C₁₃×#449	C₂²	1	2	yes	complemented
115	C₁₃×#448	C₂²	1	2	yes	complemented
116	C₁₃×#447	C₂²	1	2	yes	—
117	C₁₃×#433	C₂²	1	2	yes	complemented
118	C₁₃×#433	C₂²	1	2	yes	complemented
119	C₁₃×#432	C₂²	1	2	yes	complemented
120	C₁₃×#431	C₂²	1	2	yes	complemented
121	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
123	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
124	C₁₃×#418	C₂²	1	1	yes	characteristic
125	C₁₃×#417	C₂²	1	1	yes	characteristic
126	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#416	C₂²	1	1	yes	characteristic
128	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
131	C₁₃×#408	C₂²	1	1	yes	characteristic
132	C₁₃×#408	C₂²	1	1	yes	characteristic
133	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
134	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₁₃×2₋¹⁺⁴	—	4	2	no	—
136	C₁₃×2₋¹⁺⁴	—	4	2	no	—
137	C₁₃×H(5,𝔽₂)	—	4	2	no	—
138	C₁₃×H(5,𝔽₂)	—	4	2	no	—
139	C₂×C₁₃×#41	—	2	1	no	—
140	C₂×C₁₃×#41	—	2	2	no	—
141	C₂×C₁₃×#41	—	2	1	no	—
142	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×#41	C₂³	1	2	yes	—
146	C₂×C₁₃×#41	C₂³	1	2	yes	—
147	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₁₃	—	2	1	no	—
149	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₂²×D₄×C₁₃	—	2	2	no	—
153	C₂²×D₄×C₁₃	—	2	1	no	—
154	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
155	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
156	C₁₃×#137	—	4	2	no	—
157	C₁₃×#137	—	4	2	no	—
158	C₁₃×#137	—	4	2	no	—
159	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
160	C₁₃×#135	—	4	2	no	—
161	C₁₃×#135	—	4	2	no	—
162	C₂×C₁₃×Q₁₆	—	4	2	no	—
163	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
164	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
166	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
167	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
168	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
170	C₂×C₁₃×SD₁₆	—	4	2	no	—
171	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
172	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
173	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
174	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
175	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
177	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
178	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
179	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
180	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
181	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
182	C₂×C₁₃×D₈	C₂³	1	2	yes	—
183	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
184	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
185	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
186	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
187	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
188	C₁₃×C₄⋊Q₈	—	2	1	no	—
189	C₁₃×C₄⋊Q₈	—	2	1	no	—
190	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
191	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
192	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
193	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
194	C₁₃×#127	C₂³	1	1	yes	characteristic
195	C₁₃×#127	C₂³	1	2	yes	—
196	C₁₃×#126	—	2	2	no	—
197	C₁₃×#126	—	2	2	no	—
198	C₁₃×#126	—	2	2	no	—
199	C₁₃×#126	—	2	2	no	—
200	C₁₃×#125	—	2	2	no	—
201	C₁₃×#125	—	2	1	no	—
202	C₁₃×#125	—	2	2	no	—
203	C₁₃×#125	—	2	2	no	—
204	C₁₃×#125	C₂³	1	2	yes	—
205	C₁₃×#124	—	2	1	no	—
206	C₁₃×#124	—	2	2	no	—
207	C₁₃×#124	—	2	1	no	—
208	C₁₃×#124	—	2	1	no	—
209	C₁₃×#124	—	2	2	no	—
210	C₁₃×#124	—	2	2	no	—
211	C₁₃×#124	C₂³	1	1	yes	characteristic
212	C₁₃×#124	C₂³	1	2	yes	—
213	C₁₃×#124	C₂³	1	2	yes	—
214	C₁₃×#124	C₂³	1	1	yes	characteristic
215	C₁₃×#124	C₂³	1	2	yes	—
216	C₁₃×#124	C₂³	1	2	yes	—
217	C₁₃×#124	C₂³	1	2	yes	—
218	C₁₃×#123	—	2	2	no	—
219	C₁₃×#123	—	2	2	no	—
220	C₁₃×#123	—	2	2	no	—
221	C₁₃×#123	—	2	2	no	—
222	C₁₃×#123	—	2	2	no	—
223	C₁₃×#123	—	2	2	no	—
224	C₁₃×#123	—	2	2	no	—
225	C₁₃×C₂²⋊Q₈	—	2	1	no	—
226	C₁₃×C₂²⋊Q₈	—	2	2	no	—
227	C₁₃×C₂²⋊Q₈	—	2	1	no	—
228	C₁₃×C₂²⋊Q₈	—	2	1	no	—
229	C₁₃×C₂²⋊Q₈	—	2	2	no	—
230	C₁₃×C₂²⋊Q₈	—	2	1	no	—
231	C₁₃×C₂²⋊Q₈	—	2	2	no	—
232	C₁₃×C₂²⋊Q₈	—	2	1	no	—
233	C₁₃×C₂²⋊Q₈	—	2	2	no	—
234	C₁₃×C₂²⋊Q₈	—	2	2	no	—
235	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
236	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
237	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
238	C₁₃×#121	—	2	2	no	—
239	C₁₃×#121	—	2	1	no	—
240	C₁₃×#121	—	2	1	no	—
241	C₁₃×#121	—	2	1	no	—
242	C₁₃×#121	—	2	2	no	—
243	C₁₃×#121	—	2	2	no	—
244	C₁₃×#121	—	2	1	no	—
245	C₁₃×#121	—	2	2	no	—
246	C₁₃×#121	—	2	1	no	—
247	C₁₃×#121	—	2	2	no	—
248	C₁₃×#121	C₂³	1	2	yes	—
249	C₁₃×#120	—	2	2	no	—
250	C₁₃×#120	—	2	2	no	—
251	C₁₃×#120	—	2	2	no	—
252	C₄×Q₈×C₁₃	—	2	1	no	—
253	C₄×Q₈×C₁₃	—	2	1	no	—
254	C₄×Q₈×C₁₃	—	2	2	no	—
255	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
256	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
257	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
258	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
259	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
260	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₁₃	—	2	1	no	—
262	C₄×D₄×C₁₃	—	2	1	no	—
263	C₄×D₄×C₁₃	—	2	2	no	—
264	C₄×D₄×C₁₃	—	2	1	no	—
265	C₄×D₄×C₁₃	—	2	1	no	—
266	C₄×D₄×C₁₃	—	2	2	no	—
267	C₄×D₄×C₁₃	—	2	2	no	—
268	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
269	C₄×D₄×C₁₃	D₄	1	2	yes	—
270	C₄×D₄×C₁₃	D₄	1	2	yes	—
271	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
272	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
273	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
274	C₁₃×#117	—	2	2	no	—
275	C₁₃×#117	—	2	1	no	—
276	C₁₃×#117	—	2	2	no	—
277	C₁₃×#117	C₂³	1	1	yes	characteristic
278	C₁₃×#117	C₂³	1	1	yes	characteristic
279	C₁₃×#117	C₂³	1	2	yes	—
280	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₄²×C₁₃	—	2	1	no	—
287	C₂×C₄²×C₁₃	—	2	1	no	—
288	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
290	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
293	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
294	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
295	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#103	C₂³	1	2	yes	—
298	C₁₃×#103	C₂³	1	1	yes	characteristic
299	C₁₃×#103	C₂³	1	1	yes	characteristic
300	C₁₃×#103	C₂³	1	1	yes	characteristic
301	C₁₃×#103	C₂³	1	1	yes	characteristic
302	C₁₃×#103	C₂³	1	2	yes	—
303	C₁₃×#103	C₂³	1	2	yes	—
304	C₁₃×#103	C₂³	1	2	yes	—
305	C₁₃×#103	C₂³	1	2	yes	—
306	C₁₃×#102	C₂³	1	2	yes	—
307	C₁₃×#102	C₂³	1	2	yes	—
308	C₁₃×#102	C₂³	1	1	yes	characteristic
309	C₁₃×#102	C₂³	1	1	yes	characteristic
310	C₁₃×#102	C₂³	1	1	yes	characteristic
311	C₁₃×#102	C₂³	1	1	yes	characteristic
312	C₁₃×#102	C₂³	1	2	yes	—
313	C₁₃×#102	C₂³	1	2	yes	—
314	C₁₃×#102	C₂³	1	2	yes	—
315	C₁₃×#102	C₂³	1	2	yes	—
316	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₁₃×#97	C₂³	1	2	yes	—
321	C₁₃×#97	C₂³	1	2	yes	—
322	C₄×C₈×C₁₃	C₂³	1	2	yes	—
323	C₄×C₈×C₁₃	C₂³	1	2	yes	—
324	#60835	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
325	C₂⁴×C₁₃	—	2	2	no	—
326	C₂⁴×C₁₃	—	2	1	no	—
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	—	2	2	no	—
334	C₁₃×#41	—	2	2	no	—
335	C₁₃×#41	—	4	2	no	—
336	C₁₃×#41	—	4	2	no	—
337	C₁₃×#41	—	4	2	no	—
338	C₁₃×#41	—	4	2	no	—
339	C₁₃×#41	—	4	8	no	—
340	C₁₃×#41	—	4	4	no	—
341	C₁₃×#41	—	4	4	no	—
342	C₂×Q₈×C₁₃	—	2	1	no	—
343	C₂×Q₈×C₁₃	—	2	2	no	—
344	C₂×Q₈×C₁₃	—	2	1	no	—
345	C₂×Q₈×C₁₃	—	2	2	no	—
346	C₂×Q₈×C₁₃	—	2	2	no	—
347	C₂×Q₈×C₁₃	—	2	2	no	—
348	C₂×Q₈×C₁₃	—	2	2	no	—
349	C₂×Q₈×C₁₃	—	2	2	no	—
350	C₂×Q₈×C₁₃	—	4	2	no	—
351	C₂×Q₈×C₁₃	—	4	2	no	—
352	C₂×Q₈×C₁₃	—	4	4	no	—
353	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
354	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
358	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₁₃	—	2	1	no	—
360	C₂×D₄×C₁₃	—	2	2	no	—
361	C₂×D₄×C₁₃	—	2	1	no	—
362	C₂×D₄×C₁₃	—	2	2	no	—
363	C₂×D₄×C₁₃	—	2	1	no	—
364	C₂×D₄×C₁₃	—	2	2	no	—
365	C₂×D₄×C₁₃	—	2	2	no	—
366	C₂×D₄×C₁₃	—	2	1	no	—
367	C₂×D₄×C₁₃	—	2	1	no	—
368	C₂×D₄×C₁₃	—	2	1	no	—
369	C₂×D₄×C₁₃	—	2	2	no	—
370	C₂×D₄×C₁₃	—	2	2	no	—
371	C₂×D₄×C₁₃	—	2	2	no	—
372	C₂×D₄×C₁₃	—	2	2	no	—
373	C₂×D₄×C₁₃	—	4	2	no	—
374	C₂×D₄×C₁₃	—	4	2	no	—
375	C₂×D₄×C₁₃	—	4	8	no	—
376	C₂×D₄×C₁₃	—	4	4	no	—
377	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
378	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
379	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
380	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
381	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
382	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₁₃	—	2	1	no	—
384	C₂²×C₄×C₁₃	—	2	2	no	—
385	C₂²×C₄×C₁₃	—	2	1	no	—
386	C₂²×C₄×C₁₃	—	2	1	no	—
387	C₂²×C₄×C₁₃	—	2	1	no	—
388	C₂²×C₄×C₁₃	—	2	1	no	—
389	C₂²×C₄×C₁₃	—	2	2	no	—
390	C₂²×C₄×C₁₃	—	2	1	no	—
391	C₂²×C₄×C₁₃	—	2	2	no	—
392	C₂²×C₄×C₁₃	—	2	1	no	—
393	C₂²×C₄×C₁₃	—	2	1	no	—
394	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
397	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
398	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
399	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
400	C₁₃×Q₁₆	—	4	2	no	—
401	C₁₃×Q₁₆	—	4	2	no	—
402	C₁₃×Q₁₆	—	4	1	no	—
403	C₁₃×Q₁₆	—	4	1	no	—
404	C₁₃×Q₁₆	—	4	2	no	—
405	C₁₃×Q₁₆	—	4	2	no	—
406	C₁₃×Q₁₆	—	4	2	no	—
407	C₁₃×SD₁₆	—	4	2	no	—
408	C₁₃×SD₁₆	—	4	2	no	—
409	C₁₃×SD₁₆	—	4	1	no	—
410	C₁₃×SD₁₆	—	4	1	no	—
411	C₁₃×SD₁₆	—	4	1	no	—
412	C₁₃×SD₁₆	—	4	1	no	—
413	C₁₃×SD₁₆	—	4	2	no	—
414	C₁₃×SD₁₆	—	4	2	no	—
415	C₁₃×SD₁₆	—	4	2	no	—
416	C₁₃×SD₁₆	—	4	2	no	—
417	C₁₃×D₈	—	4	1	no	—
418	C₁₃×D₈	—	4	1	no	—
419	C₁₃×D₈	—	4	2	no	—
420	C₁₃×M₁₆	—	2	2	no	—
421	C₁₃×M₁₆	—	2	2	no	—
422	C₂×C₈×C₁₃	—	2	2	no	—
423	C₂×C₈×C₁₃	—	2	2	no	—
424	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
427	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
428	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
429	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
430	C₁₃×C₄⋊C₄	—	2	2	no	—
431	C₁₃×C₄⋊C₄	—	2	2	no	—
432	C₁₃×C₄⋊C₄	—	2	1	no	—
433	C₁₃×C₄⋊C₄	—	2	1	no	—
434	C₁₃×C₄⋊C₄	—	2	1	no	—
435	C₁₃×C₄⋊C₄	—	2	2	no	—
436	C₁₃×C₄⋊C₄	—	2	2	no	—
437	C₁₃×C₄⋊C₄	—	2	2	no	—
438	C₁₃×C₄⋊C₄	—	2	2	no	—
439	C₁₃×C₄⋊C₄	—	2	1	no	—
440	C₁₃×C₄⋊C₄	—	2	1	no	—
441	C₁₃×C₄⋊C₄	—	2	2	no	—
442	C₁₃×C₄⋊C₄	—	2	2	no	—
443	C₁₃×C₄⋊C₄	—	2	2	no	—
444	C₁₃×C₄⋊C₄	—	2	2	no	—
445	C₁₃×C₄⋊C₄	—	2	2	no	—
446	C₁₃×C₄⋊C₄	—	2	2	no	—
447	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
448	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
449	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
450	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
451	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
452	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
453	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
458	C₁₃×C₂²⋊C₄	—	2	2	no	—
459	C₁₃×C₂²⋊C₄	—	2	1	no	—
460	C₁₃×C₂²⋊C₄	—	2	2	no	—
461	C₁₃×C₂²⋊C₄	—	2	1	no	—
462	C₁₃×C₂²⋊C₄	—	2	2	no	—
463	C₁₃×C₂²⋊C₄	—	2	2	no	—
464	C₁₃×C₂²⋊C₄	—	2	2	no	—
465	C₁₃×C₂²⋊C₄	—	2	2	no	—
466	C₁₃×C₂²⋊C₄	—	2	2	no	—
467	C₁₃×C₂²⋊C₄	—	2	2	no	—
468	C₁₃×C₂²⋊C₄	—	2	1	no	—
469	C₁₃×C₂²⋊C₄	—	2	1	no	—
470	C₁₃×C₂²⋊C₄	—	2	2	no	—
471	C₁₃×C₂²⋊C₄	—	2	2	no	—
472	C₁₃×C₂²⋊C₄	—	2	1	no	—
473	C₁₃×C₂²⋊C₄	—	2	1	no	—
474	C₁₃×C₂²⋊C₄	—	2	2	no	—
475	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
476	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
477	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
478	C₄²×C₁₃	—	2	2	no	—
479	C₄²×C₁₃	—	2	1	no	—
480	C₄²×C₁₃	—	2	1	no	—
481	C₄²×C₁₃	—	2	1	no	—
482	C₄²×C₁₃	—	2	2	no	—
483	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
484	C₄²×C₁₃	C₂×D₄	1	2	yes	—
485	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
486	C₄²×C₁₃	C₂×D₄	1	2	yes	—
487	C₄²×C₁₃	C₂⁴	1	2	yes	—
488	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
489	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
490	#3500	C₂×C₁₃	1	1	yes	characteristic, complemented
491	#3461	C₂×C₁₃	1	1	yes	characteristic, complemented
492	#3225	C₂×C₁₃	1	2	yes	complemented
493	#3224	C₂×C₁₃	1	2	yes	complemented
494	#3223	C₂×C₁₃	1	2	yes	complemented
495	#3222	C₂×C₁₃	1	2	yes	complemented
496	#3219	C₂×C₁₃	1	2	yes	complemented
497	#3215	C₂×C₁₃	1	2	yes	complemented
498	#3211	C₂×C₁₃	1	2	yes	complemented
499	#3210	C₂×C₁₃	1	2	yes	complemented
500	#3156	C₂×C₁₃	1	1	yes	characteristic, complemented
501	#3154	C₂×C₁₃	1	1	yes	characteristic, complemented
502	#3137	C₂×C₁₃	1	1	yes	characteristic, complemented
503	#3136	C₂×C₁₃	1	1	yes	characteristic, complemented
504	#3040	C₂×C₁₃	1	1	yes	characteristic, complemented
505	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
506	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
507	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
508	#3013	C₂×C₁₃	1	1	yes	characteristic, complemented
509	#3012	C₂×C₁₃	1	1	yes	characteristic, complemented
510	#3011	C₂×C₁₃	1	1	yes	characteristic, complemented
511	#3009	C₂×C₁₃	1	1	yes	characteristic, complemented
512	#2925	C₂×C₁₃	1	1	yes	characteristic, complemented
513	C₂³×C₁₃	—	2	1	no	—
514	C₂³×C₁₃	—	2	2	no	—
515	C₂³×C₁₃	—	2	1	no	—
516	C₂³×C₁₃	—	2	1	no	—
517	C₂³×C₁₃	—	4	4	no	—
518	C₂³×C₁₃	—	4	2	no	—
519	C₂³×C₁₃	—	8	1	no	—
520	C₂³×C₁₃	—	8	1	no	—
521	C₂³×C₁₃	—	8	2	no	—
522	C₂³×C₁₃	—	8	2	no	—
523	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
524	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
525	Q₈×C₁₃	—	2	2	no	—
526	Q₈×C₁₃	—	2	2	no	—
527	Q₈×C₁₃	—	2	2	no	—
528	Q₈×C₁₃	—	2	1	no	—
529	Q₈×C₁₃	—	2	1	no	—
530	Q₈×C₁₃	—	2	2	no	—
531	Q₈×C₁₃	—	2	1	no	—
532	Q₈×C₁₃	—	2	1	no	—
533	Q₈×C₁₃	—	2	2	no	—
534	Q₈×C₁₃	—	2	1	no	—
535	Q₈×C₁₃	—	2	1	no	—
536	Q₈×C₁₃	—	4	4	no	—
537	Q₈×C₁₃	—	4	2	no	—
538	Q₈×C₁₃	—	4	2	no	—
539	Q₈×C₁₃	—	8	2	no	—
540	D₄×C₁₃	—	2	4	no	—
541	D₄×C₁₃	—	2	2	no	—
542	D₄×C₁₃	—	2	1	no	—
543	D₄×C₁₃	—	2	1	no	—
544	D₄×C₁₃	—	2	2	no	—
545	D₄×C₁₃	—	2	1	no	—
546	D₄×C₁₃	—	2	1	no	—
547	D₄×C₁₃	—	2	2	no	—
548	D₄×C₁₃	—	2	1	no	—
549	D₄×C₁₃	—	2	1	no	—
550	D₄×C₁₃	—	4	4	no	—
551	D₄×C₁₃	—	4	4	no	—
552	D₄×C₁₃	—	4	4	no	—
553	D₄×C₁₃	—	4	2	no	—
554	D₄×C₁₃	—	4	2	no	—
555	D₄×C₁₃	—	4	2	no	—
556	D₄×C₁₃	—	4	2	no	—
557	D₄×C₁₃	—	8	1	no	—
558	D₄×C₁₃	—	8	2	no	—
559	D₄×C₁₃	—	8	1	no	—
560	D₄×C₁₃	—	8	2	no	—
561	D₄×C₁₃	—	8	2	no	—
562	C₂×C₄×C₁₃	—	2	2	no	—
563	C₂×C₄×C₁₃	—	2	2	no	—
564	C₂×C₄×C₁₃	—	2	1	no	—
565	C₂×C₄×C₁₃	—	2	2	no	—
566	C₂×C₄×C₁₃	—	2	1	no	—
567	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
573	C₂×C₄×C₁₃	—	4	2	no	—
574	C₂×C₄×C₁₃	—	4	1	no	—
575	C₂×C₄×C₁₃	—	4	2	no	—
576	C₂×C₄×C₁₃	—	4	2	no	—
577	C₂×C₄×C₁₃	—	4	4	no	—
578	C₂×C₄×C₁₃	—	4	4	no	—
579	C₂×C₄×C₁₃	—	4	4	no	—
580	C₂×C₄×C₁₃	—	4	2	no	—
581	C₂×C₄×C₁₃	—	4	2	no	—
582	C₂×C₄×C₁₃	—	4	2	no	—
583	C₂×C₄×C₁₃	—	4	2	no	—
584	C₂×C₄×C₁₃	—	4	2	no	—
585	C₂×C₄×C₁₃	—	8	1	no	—
586	C₂×C₄×C₁₃	—	8	1	no	—
587	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
592	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
593	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
594	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
595	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
596	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
597	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
598	C₈×C₁₃	—	2	1	no	—
599	C₈×C₁₃	—	2	1	no	—
600	C₈×C₁₃	—	2	1	no	—
601	C₈×C₁₃	—	2	1	no	—
602	C₈×C₁₃	—	2	2	no	—
603	C₈×C₁₃	—	2	2	no	—
604	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
605	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
606	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
607	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic, complemented
609	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
610	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
611	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
614	#548	—	2	1	no	—
615	#548	—	2	1	no	—
616	#546	—	2	2	no	—
617	#546	—	2	1	no	—
618	#546	—	2	2	no	—
619	#546	—	2	1	no	—
620	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
621	#542	—	2	1	no	—
622	#542	C₂²×C₁₃	1	2	yes	complemented
623	#541	—	2	1	no	—
624	#541	C₂²×C₁₃	1	2	yes	complemented
625	#539	—	2	2	no	—
626	#537	C₂²×C₁₃	1	1	yes	characteristic
627	#536	C₂²×C₁₃	1	1	yes	characteristic
628	#536	C₂²×C₁₃	1	2	yes	—
629	#536	C₂²×C₁₃	1	1	yes	characteristic
630	#536	C₂²×C₁₃	1	1	yes	characteristic, complemented
631	#535	C₂²×C₁₃	1	1	yes	characteristic
632	#535	C₂²×C₁₃	1	2	yes	—
633	#533	—	2	1	no	—
634	#533	C₂²×C₁₃	1	2	yes	complemented
635	#532	C₂²×C₁₃	1	2	yes	—
636	#532	C₂²×C₁₃	1	1	yes	characteristic
637	#529	—	2	2	no	—
638	#529	—	2	1	no	—
639	#529	C₂²×C₁₃	1	2	yes	complemented
640	C₂×#124	C₂²×C₁₃	1	2	yes	—
641	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
642	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
643	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
644	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
645	#497	C₂²×C₁₃	1	2	yes	complemented
646	#497	C₂²×C₁₃	1	2	yes	complemented
647	#497	C₂²×C₁₃	1	2	yes	complemented
648	#496	C₂²×C₁₃	1	2	yes	complemented
649	#495	C₂²×C₁₃	1	2	yes	complemented
650	#495	C₂²×C₁₃	1	2	yes	complemented
651	#494	C₂²×C₁₃	1	2	yes	complemented
652	#492	C₂²×C₁₃	1	2	yes	complemented
653	#491	C₂²×C₁₃	1	2	yes	complemented
654	#490	C₂²×C₁₃	1	2	yes	complemented
655	#489	C₂²×C₁₃	1	2	yes	complemented
656	#489	C₂²×C₁₃	1	2	yes	complemented
657	#488	C₂²×C₁₃	1	2	yes	complemented
658	#488	C₂²×C₁₃	1	2	yes	complemented
659	#487	C₂²×C₁₃	1	2	yes	complemented
660	#486	C₂²×C₁₃	1	2	yes	complemented
661	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
662	#464	C₂²×C₁₃	1	2	yes	complemented
663	#464	C₂²×C₁₃	1	2	yes	complemented
664	#464	C₂²×C₁₃	1	2	yes	complemented
665	#464	C₂²×C₁₃	1	2	yes	complemented
666	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
667	#464	C₂²×C₁₃	1	2	yes	complemented
668	#464	C₂²×C₁₃	1	2	yes	complemented
669	#464	C₂²×C₁₃	1	2	yes	complemented
670	#464	C₂²×C₁₃	1	2	yes	complemented
671	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
672	#463	C₂²×C₁₃	1	2	yes	complemented
673	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
674	#463	C₂²×C₁₃	1	2	yes	complemented
675	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
676	#462	C₂²×C₁₃	1	2	yes	complemented
677	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
678	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
679	#460	C₂²×C₁₃	1	2	yes	complemented
680	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
681	#452	C₂²×C₁₃	1	2	yes	—
682	#452	C₂²×C₁₃	1	2	yes	—
683	#452	C₂²×C₁₃	1	2	yes	—
684	#452	C₂²×C₁₃	1	2	yes	complemented
685	#452	C₂²×C₁₃	1	2	yes	complemented
686	#452	C₂²×C₁₃	1	2	yes	complemented
687	#451	C₂²×C₁₃	1	2	yes	complemented
688	#451	C₂²×C₁₃	1	2	yes	complemented
689	#451	C₂²×C₁₃	1	2	yes	complemented
690	#450	C₂²×C₁₃	1	2	yes	—
691	#450	C₂²×C₁₃	1	2	yes	—
692	#450	C₂²×C₁₃	1	2	yes	—
693	#449	C₂²×C₁₃	1	2	yes	—
694	#449	C₂²×C₁₃	1	2	yes	complemented
695	#448	C₂²×C₁₃	1	2	yes	complemented
696	#447	C₂²×C₁₃	1	2	yes	—
697	#433	C₂²×C₁₃	1	2	yes	complemented
698	#433	C₂²×C₁₃	1	2	yes	complemented
699	#432	C₂²×C₁₃	1	2	yes	complemented
700	#431	C₂²×C₁₃	1	2	yes	complemented
701	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
702	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
703	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
704	#418	C₂²×C₁₃	1	1	yes	characteristic
705	#417	C₂²×C₁₃	1	1	yes	characteristic
706	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
707	#416	C₂²×C₁₃	1	1	yes	characteristic
708	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
709	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
710	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
711	#408	C₂²×C₁₃	1	1	yes	characteristic
712	#408	C₂²×C₁₃	1	1	yes	characteristic
713	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
714	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
715	C₂²×C₁₃	—	2	1	no	—
716	C₂²×C₁₃	—	2	1	no	—
717	C₂²×C₁₃	—	2	2	no	—
718	C₂²×C₁₃	—	2	2	no	—
719	C₂²×C₁₃	—	2	2	no	—
720	C₂²×C₁₃	—	4	1	no	—
721	C₂²×C₁₃	—	4	1	no	—
722	C₂²×C₁₃	—	4	2	no	—
723	C₂²×C₁₃	—	4	1	no	—
724	C₂²×C₁₃	—	4	1	no	—
725	C₂²×C₁₃	—	4	1	no	—
726	C₂²×C₁₃	—	4	2	no	—
727	C₂²×C₁₃	—	4	1	no	—
728	C₂²×C₁₃	—	4	1	no	—
729	C₂²×C₁₃	—	4	2	no	—
730	C₂²×C₁₃	—	4	1	no	—
731	C₂²×C₁₃	—	4	1	no	—
732	C₂²×C₁₃	—	16	2	no	—
733	C₂²×C₁₃	—	16	4	no	—
734	C₂²×C₁₃	#535	1	2	yes	—
735	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
736	C₄×C₁₃	—	2	1	no	—
737	C₄×C₁₃	—	2	1	no	—
738	C₄×C₁₃	—	2	2	no	—
739	C₄×C₁₃	—	2	1	no	—
740	C₄×C₁₃	—	2	1	no	—
741	C₄×C₁₃	—	2	2	no	—
742	C₄×C₁₃	—	2	2	no	—
743	C₄×C₁₃	—	4	2	no	—
744	C₄×C₁₃	—	4	1	no	—
745	C₄×C₁₃	—	4	1	no	—
746	C₄×C₁₃	—	4	1	no	—
747	C₄×C₁₃	—	4	2	no	—
748	C₄×C₁₃	—	4	1	no	—
749	C₄×C₁₃	—	4	1	no	—
750	C₄×C₁₃	—	4	2	no	—
751	C₄×C₁₃	#535	1	2	yes	—
752	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
753	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
754	2₋¹⁺⁴	—	4	2	no	—
755	2₋¹⁺⁴	—	4	2	no	—
756	H(5,𝔽₂)	—	4	2	no	—
757	H(5,𝔽₂)	—	4	2	no	—
758	C₂×#41	—	2	1	no	—
759	C₂×#41	—	2	2	no	—
760	C₂×#41	—	2	1	no	—
761	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
762	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
763	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
764	C₂×#41	C₂³×C₁₃	1	2	yes	—
765	C₂×#41	C₂³×C₁₃	1	2	yes	—
766	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
767	C₂²×Q₈	—	2	1	no	—
768	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
769	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
770	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
771	C₂²×D₄	—	2	2	no	—
772	C₂²×D₄	—	2	1	no	—
773	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
774	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
775	#137	—	4	2	no	—
776	#137	—	4	2	no	—
777	#137	—	4	2	no	—
778	AGL(1,ℤ/8)	—	4	2	no	—
779	#135	—	4	2	no	—
780	#135	—	4	2	no	—
781	C₂×Q₁₆	—	4	2	no	—
782	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
783	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
784	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
785	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
786	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
787	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
788	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
789	C₂×SD₁₆	—	4	2	no	—
790	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
791	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
792	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
793	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
794	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
795	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
796	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
797	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
798	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
799	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
800	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
801	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
802	C₂×D₈	C₂³×C₁₃	1	2	yes	—
803	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
804	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
805	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
806	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
807	C₄⋊Q₈	—	2	1	no	—
808	C₄⋊Q₈	—	2	1	no	—
809	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
810	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
811	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
812	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
813	#127	C₂³×C₁₃	1	1	yes	characteristic
814	#127	C₂³×C₁₃	1	2	yes	—
815	#126	—	2	2	no	—
816	#126	—	2	2	no	—
817	#126	—	2	2	no	—
818	#126	—	2	2	no	—
819	#125	—	2	2	no	—
820	#125	—	2	1	no	—
821	#125	—	2	2	no	—
822	#125	—	2	2	no	—
823	#125	C₂³×C₁₃	1	2	yes	—
824	#124	—	2	1	no	—
825	#124	—	2	2	no	—
826	#124	—	2	1	no	—
827	#124	—	2	2	no	—
828	#124	—	2	1	no	—
829	#124	—	2	2	no	—
830	#124	C₂³×C₁₃	1	1	yes	characteristic
831	#124	C₂³×C₁₃	1	2	yes	—
832	#124	C₂³×C₁₃	1	2	yes	—
833	#124	C₂³×C₁₃	1	2	yes	—
834	#124	C₂³×C₁₃	1	2	yes	—
835	#124	C₂³×C₁₃	1	2	yes	—
836	#124	C₂³×C₁₃	1	1	yes	characteristic
837	#123	—	2	2	no	—
838	#123	—	2	2	no	—
839	#123	—	2	2	no	—
840	#123	—	2	2	no	—
841	#123	—	2	2	no	—
842	#123	—	2	2	no	—
843	#123	—	2	2	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	2	no	—
846	C₂²⋊Q₈	—	2	1	no	—
847	C₂²⋊Q₈	—	2	1	no	—
848	C₂²⋊Q₈	—	2	2	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	—	2	2	no	—
851	C₂²⋊Q₈	—	2	1	no	—
852	C₂²⋊Q₈	—	2	2	no	—
853	C₂²⋊Q₈	—	2	2	no	—
854	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
855	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
856	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
857	#121	—	2	2	no	—
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	2	no	—
862	#121	—	2	2	no	—
863	#121	—	2	1	no	—
864	#121	—	2	2	no	—
865	#121	—	2	1	no	—
866	#121	—	2	2	no	—
867	#121	C₂³×C₁₃	1	2	yes	—
868	#120	—	2	2	no	—
869	#120	—	2	2	no	—
870	#120	—	2	2	no	—
871	C₄×Q₈	—	2	1	no	—
872	C₄×Q₈	—	2	1	no	—
873	C₄×Q₈	—	2	2	no	—
874	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
875	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
876	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
877	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
878	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
879	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	2	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	2	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	2	no	—
887	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
888	C₄×D₄	D₄×C₁₃	1	2	yes	—
889	C₄×D₄	D₄×C₁₃	1	2	yes	—
890	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
891	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
892	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
893	#117	—	2	2	no	—
894	#117	—	2	1	no	—
895	#117	—	2	2	no	—
896	#117	C₂³×C₁₃	1	1	yes	characteristic
897	#117	C₂³×C₁₃	1	1	yes	characteristic
898	#117	C₂³×C₁₃	1	2	yes	—
899	C₂×C₄⋊C₄	—	2	1	no	—
900	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
901	C₂×C₂²⋊C₄	—	2	1	no	—
902	C₂×C₂²⋊C₄	—	2	1	no	—
903	C₂×C₂²⋊C₄	—	2	2	no	—
904	C₂×C₂²⋊C₄	—	2	2	no	—
905	C₂×C₄²	—	2	1	no	—
906	C₂×C₄²	—	2	1	no	—
907	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
908	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
909	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
910	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
911	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
912	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
913	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
914	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
915	#103	C₂³×C₁₃	1	2	yes	—
916	#103	C₂³×C₁₃	1	2	yes	—
917	#103	C₂³×C₁₃	1	1	yes	characteristic
918	#103	C₂³×C₁₃	1	1	yes	characteristic
919	#103	C₂³×C₁₃	1	1	yes	characteristic
920	#103	C₂³×C₁₃	1	1	yes	characteristic
921	#103	C₂³×C₁₃	1	2	yes	—
922	#103	C₂³×C₁₃	1	2	yes	—
923	#103	C₂³×C₁₃	1	2	yes	—
924	#103	C₂³×C₁₃	1	2	yes	—
925	#102	C₂³×C₁₃	1	2	yes	—
926	#102	C₂³×C₁₃	1	2	yes	—
927	#102	C₂³×C₁₃	1	1	yes	characteristic
928	#102	C₂³×C₁₃	1	1	yes	characteristic
929	#102	C₂³×C₁₃	1	1	yes	characteristic
930	#102	C₂³×C₁₃	1	1	yes	characteristic
931	#102	C₂³×C₁₃	1	2	yes	—
932	#102	C₂³×C₁₃	1	2	yes	—
933	#102	C₂³×C₁₃	1	2	yes	—
934	#102	C₂³×C₁₃	1	2	yes	—
935	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
936	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
937	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
938	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
939	#97	C₂³×C₁₃	1	2	yes	—
940	#97	C₂³×C₁₃	1	2	yes	—
941	C₄×C₈	C₂³×C₁₃	1	2	yes	—
942	C₄×C₈	C₂³×C₁₃	1	2	yes	—
943	C₂×C₁₃	—	2	2	no	—
944	C₂×C₁₃	—	4	2	no	—
945	C₂×C₁₃	—	8	1	no	—
946	C₂×C₁₃	—	8	1	no	—
947	C₂×C₁₃	—	8	2	no	—
948	C₂×C₁₃	—	8	1	no	—
949	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
950	C₂×C₁₃	#3584	1	1	yes	characteristic
951	C₂×C₁₃	#3586	1	1	yes	characteristic
952	C₂⁴	—	2	2	no	—
953	C₂⁴	—	2	1	no	—
954	#41	—	2	2	no	—
955	#41	—	2	2	no	—
956	#41	—	2	2	no	—
957	#41	—	2	2	no	—
958	#41	—	2	2	no	—
959	#41	—	2	2	no	—
960	#41	—	2	2	no	—
961	#41	—	2	2	no	—
962	#41	—	4	2	no	—
963	#41	—	4	2	no	—
964	#41	—	4	2	no	—
965	#41	—	4	2	no	—
966	#41	—	4	8	no	—
967	#41	—	4	4	no	—
968	#41	—	4	4	no	—
969	C₂×Q₈	—	2	1	no	—
970	C₂×Q₈	—	2	2	no	—
971	C₂×Q₈	—	2	1	no	—
972	C₂×Q₈	—	2	2	no	—
973	C₂×Q₈	—	2	2	no	—
974	C₂×Q₈	—	2	2	no	—
975	C₂×Q₈	—	2	2	no	—
976	C₂×Q₈	—	2	2	no	—
977	C₂×Q₈	—	4	2	no	—
978	C₂×Q₈	—	4	2	no	—
979	C₂×Q₈	—	4	4	no	—
980	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
981	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
982	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
983	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
984	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
985	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	2	no	—
992	C₂×D₄	—	2	2	no	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	4	2	no	—
1001	C₂×D₄	—	4	2	no	—
1002	C₂×D₄	—	4	8	no	—
1003	C₂×D₄	—	4	4	no	—
1004	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1005	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1006	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1007	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1008	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1009	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	2	1	no	—
1016	C₂²×C₄	—	2	2	no	—
1017	C₂²×C₄	—	2	1	no	—
1018	C₂²×C₄	—	2	2	no	—
1019	C₂²×C₄	—	2	1	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1022	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1023	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
1024	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
1025	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1026	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1027	Q₁₆	—	4	2	no	—
1028	Q₁₆	—	4	2	no	—
1029	Q₁₆	—	4	1	no	—
1030	Q₁₆	—	4	1	no	—
1031	Q₁₆	—	4	2	no	—
1032	Q₁₆	—	4	2	no	—
1033	Q₁₆	—	4	2	no	—
1034	SD₁₆	—	4	2	no	—
1035	SD₁₆	—	4	2	no	—
1036	SD₁₆	—	4	1	no	—
1037	SD₁₆	—	4	1	no	—
1038	SD₁₆	—	4	1	no	—
1039	SD₁₆	—	4	1	no	—
1040	SD₁₆	—	4	2	no	—
1041	SD₁₆	—	4	2	no	—
1042	SD₁₆	—	4	2	no	—
1043	SD₁₆	—	4	2	no	—
1044	D₈	—	4	1	no	—
1045	D₈	—	4	1	no	—
1046	D₈	—	4	2	no	—
1047	M₁₆	—	2	2	no	—
1048	M₁₆	—	2	2	no	—
1049	C₂×C₈	—	2	2	no	—
1050	C₂×C₈	—	2	2	no	—
1051	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1052	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1053	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1054	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1055	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1056	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	2	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	2	no	—
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1075	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1076	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1077	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1078	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1079	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1080	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1103	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1104	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1105	C₄²	—	2	2	no	—
1106	C₄²	—	2	1	no	—
1107	C₄²	—	2	1	no	—
1108	C₄²	—	2	1	no	—
1109	C₄²	—	2	2	no	—
1110	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1111	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1112	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1113	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1114	C₄²	C₂⁴×C₁₃	1	2	yes	—
1115	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1116	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1117	C₁₃	#60835	1	1	yes	characteristic, direct product factor, Sylow
1118	C₂³	—	2	1	no	—
1119	C₂³	—	2	2	no	—
1120	C₂³	—	2	1	no	—
1121	C₂³	—	2	1	no	—
1122	C₂³	—	4	4	no	—
1123	C₂³	—	4	2	no	—
1124	C₂³	—	8	1	no	—
1125	C₂³	—	8	1	no	—
1126	C₂³	—	8	2	no	—
1127	C₂³	—	8	2	no	—
1128	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1129	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1130	Q₈	—	2	2	no	—
1131	Q₈	—	2	2	no	—
1132	Q₈	—	2	2	no	—
1133	Q₈	—	2	1	no	—
1134	Q₈	—	2	1	no	—
1135	Q₈	—	2	2	no	—
1136	Q₈	—	2	1	no	—
1137	Q₈	—	2	1	no	—
1138	Q₈	—	2	2	no	—
1139	Q₈	—	2	1	no	—
1140	Q₈	—	2	1	no	—
1141	Q₈	—	4	4	no	—
1142	Q₈	—	4	2	no	—
1143	Q₈	—	4	2	no	—
1144	Q₈	—	8	2	no	—
1145	D₄	—	2	4	no	—
1146	D₄	—	2	2	no	—
1147	D₄	—	2	1	no	—
1148	D₄	—	2	1	no	—
1149	D₄	—	2	2	no	—
1150	D₄	—	2	1	no	—
1151	D₄	—	2	1	no	—
1152	D₄	—	2	2	no	—
1153	D₄	—	2	1	no	—
1154	D₄	—	2	1	no	—
1155	D₄	—	4	4	no	—
1156	D₄	—	4	4	no	—
1157	D₄	—	4	4	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	8	1	no	—
1163	D₄	—	8	2	no	—
1164	D₄	—	8	1	no	—
1165	D₄	—	8	2	no	—
1166	D₄	—	8	2	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	2	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	4	4	no	—
1182	C₂×C₄	—	4	2	no	—
1183	C₂×C₄	—	4	4	no	—
1184	C₂×C₄	—	4	4	no	—
1185	C₂×C₄	—	4	2	no	—
1186	C₂×C₄	—	4	2	no	—
1187	C₂×C₄	—	4	2	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	8	1	no	—
1191	C₂×C₄	—	8	1	no	—
1192	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1193	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1194	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1195	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1196	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1197	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1198	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1199	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1200	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1201	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1202	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1203	C₈	—	2	1	no	—
1204	C₈	—	2	1	no	—
1205	C₈	—	2	1	no	—
1206	C₈	—	2	1	no	—
1207	C₈	—	2	2	no	—
1208	C₈	—	2	2	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	2	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	2	2	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	2	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	2	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	16	2	no	—
1227	C₂²	—	16	4	no	—
1228	C₂²	C₁₃×#535	1	2	yes	—
1229	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1230	C₄	—	2	1	no	—
1231	C₄	—	2	1	no	—
1232	C₄	—	2	2	no	—
1233	C₄	—	2	1	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	2	no	—
1236	C₄	—	2	2	no	—
1237	C₄	—	4	2	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	2	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	2	no	—
1245	C₄	C₁₃×#535	1	2	yes	—
1246	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1247	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1248	C₂	—	2	2	no	—
1249	C₂	—	4	2	no	—
1250	C₂	—	8	2	no	—
1251	C₂	—	8	1	no	—
1252	C₂	—	8	1	no	—
1253	C₂	—	8	1	no	—
1254	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
1255	C₂	C₁₃×#3584	1	1	yes	characteristic
1256	C₂	C₁₃×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3500	C₂	semidirect
2. C₁₃×#3461	C₂	semidirect
3. C₁₃×#3225	C₂	semidirect
4. C₁₃×#3224	C₂	semidirect
5. C₁₃×#3223	C₂	semidirect
6. C₁₃×#3222	C₂	semidirect
7. C₁₃×#3219	C₂	semidirect
8. C₁₃×#3215	C₂	semidirect
9. C₁₃×#3211	C₂	semidirect
10. C₁₃×#3210	C₂	semidirect
11. C₁₃×#3156	C₂	semidirect
12. C₁₃×#3154	C₂	semidirect
13. C₁₃×#3137	C₂	semidirect
14. C₁₃×#3136	C₂	semidirect
15. C₁₃×#3040	C₂	semidirect
16. C₁₃×#3037	C₂	semidirect
17. C₁₃×#3035	C₂	semidirect
18. C₂×C₁₃×#464	C₂	semidirect
19. C₁₃×#3013	C₂	semidirect
20. C₁₃×#3012	C₂	semidirect
21. C₁₃×#3011	C₂	semidirect
22. C₁₃×#3009	C₂	semidirect
23. C₁₃×#2925	C₂	semidirect
27. C₂×C₁₃×#137	C₂²	semidirect
28. C₂×C₁₃×#137	C₂²	semidirect
31. C₂×C₁₃×#135	C₂²	semidirect
32. C₂²×C₁₃×Q₁₆	C₂²	semidirect
40. C₁₃×#544	C₂²	semidirect
42. C₁₃×#542	C₂²	semidirect
44. C₁₃×#541	C₂²	semidirect
50. C₁₃×#536	C₂²	semidirect
54. C₁₃×#533	C₂²	semidirect
59. C₁₃×#529	C₂²	semidirect
63. C₄×C₁₃×#41	C₂²	semidirect
64. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
65. C₁₃×#497	C₂²	semidirect
66. C₁₃×#497	C₂²	semidirect
67. C₁₃×#497	C₂²	semidirect
68. C₁₃×#496	C₂²	semidirect
69. C₁₃×#495	C₂²	semidirect
70. C₁₃×#495	C₂²	semidirect
71. C₁₃×#494	C₂²	semidirect
72. C₁₃×#492	C₂²	semidirect
73. C₁₃×#491	C₂²	semidirect
74. C₁₃×#490	C₂²	semidirect
75. C₁₃×#489	C₂²	semidirect
76. C₁₃×#489	C₂²	semidirect
77. C₁₃×#488	C₂²	semidirect
78. C₁₃×#488	C₂²	semidirect
79. C₁₃×#487	C₂²	semidirect
80. C₁₃×#486	C₂²	semidirect
81. C₁₃×#464	C₂²	semidirect
82. C₁₃×#464	C₂²	semidirect
83. C₁₃×#464	C₂²	semidirect
84. C₁₃×#464	C₂²	semidirect
85. C₁₃×#464	C₂²	semidirect
86. C₁₃×#464	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
88. C₁₃×#464	C₂²	semidirect
89. C₁₃×#464	C₂²	semidirect
90. C₁₃×#464	C₂²	semidirect
91. C₁₃×#463	C₂²	semidirect
92. C₁₃×#463	C₂²	semidirect
93. C₁₃×#463	C₂²	semidirect
94. C₁₃×#463	C₂²	semidirect
95. C₁₃×#462	C₂²	semidirect
96. C₁₃×#462	C₂²	semidirect
97. C₁₃×#461	C₂²	semidirect
98. C₁₃×#460	C₂²	semidirect
99. C₁₃×#460	C₂²	semidirect
100. C₁₃×#459	C₂²	semidirect
104. C₁₃×#452	C₂²	semidirect
105. C₁₃×#452	C₂²	semidirect
106. C₁₃×#452	C₂²	semidirect
107. C₁₃×#451	C₂²	semidirect
108. C₁₃×#451	C₂²	semidirect
109. C₁₃×#451	C₂²	semidirect
114. C₁₃×#449	C₂²	semidirect
115. C₁₃×#448	C₂²	semidirect
117. C₁₃×#433	C₂²	semidirect
118. C₁₃×#433	C₂²	semidirect
119. C₁₃×#432	C₂²	semidirect
120. C₁₃×#431	C₂²	semidirect
121. C₁₃×#423	C₂²	semidirect
122. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
123. C₁₃×#419	C₂²	semidirect
126. C₁₃×#417	C₂²	semidirect
128. C₁₃×#416	C₂²	semidirect
129. C₂×C₁₃×#103	C₂²	semidirect
133. C₁₃×#405	C₂²	semidirect
134. C₁₃×#405	C₂²	semidirect
324. #60835	C₁₃	direct (N × H)
490. #3500	C₂×C₁₃	semidirect
491. #3461	C₂×C₁₃	semidirect
492. #3225	C₂×C₁₃	semidirect
493. #3224	C₂×C₁₃	semidirect
494. #3223	C₂×C₁₃	semidirect
495. #3222	C₂×C₁₃	semidirect
496. #3219	C₂×C₁₃	semidirect
497. #3215	C₂×C₁₃	semidirect
498. #3211	C₂×C₁₃	semidirect
499. #3210	C₂×C₁₃	semidirect
500. #3156	C₂×C₁₃	semidirect
501. #3154	C₂×C₁₃	semidirect
502. #3137	C₂×C₁₃	semidirect
503. #3136	C₂×C₁₃	semidirect
504. #3040	C₂×C₁₃	semidirect
505. #3037	C₂×C₁₃	semidirect
506. #3035	C₂×C₁₃	semidirect
507. C₂×#464	C₂×C₁₃	semidirect
508. #3013	C₂×C₁₃	semidirect
509. #3012	C₂×C₁₃	semidirect
510. #3011	C₂×C₁₃	semidirect
511. #3009	C₂×C₁₃	semidirect
512. #2925	C₂×C₁₃	semidirect
607. C₂×#137	C₂²×C₁₃	semidirect
608. C₂×#137	C₂²×C₁₃	semidirect
611. C₂×#135	C₂²×C₁₃	semidirect
612. C₂²×Q₁₆	C₂²×C₁₃	semidirect
620. #544	C₂²×C₁₃	semidirect
622. #542	C₂²×C₁₃	semidirect
624. #541	C₂²×C₁₃	semidirect
630. #536	C₂²×C₁₃	semidirect
634. #533	C₂²×C₁₃	semidirect
639. #529	C₂²×C₁₃	semidirect
643. C₄×#41	C₂²×C₁₃	semidirect
644. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
645. #497	C₂²×C₁₃	semidirect
646. #497	C₂²×C₁₃	semidirect
647. #497	C₂²×C₁₃	semidirect
648. #496	C₂²×C₁₃	semidirect
649. #495	C₂²×C₁₃	semidirect
650. #495	C₂²×C₁₃	semidirect
651. #494	C₂²×C₁₃	semidirect
652. #492	C₂²×C₁₃	semidirect
653. #491	C₂²×C₁₃	semidirect
654. #490	C₂²×C₁₃	semidirect
655. #489	C₂²×C₁₃	semidirect
656. #489	C₂²×C₁₃	semidirect
657. #488	C₂²×C₁₃	semidirect
658. #488	C₂²×C₁₃	semidirect
659. #487	C₂²×C₁₃	semidirect
660. #486	C₂²×C₁₃	semidirect
661. #464	C₂²×C₁₃	semidirect
662. #464	C₂²×C₁₃	semidirect
663. #464	C₂²×C₁₃	semidirect
664. #464	C₂²×C₁₃	semidirect
665. #464	C₂²×C₁₃	semidirect
666. #464	C₂²×C₁₃	semidirect
667. #464	C₂²×C₁₃	semidirect
668. #464	C₂²×C₁₃	semidirect
669. #464	C₂²×C₁₃	semidirect
670. #464	C₂²×C₁₃	semidirect
671. #463	C₂²×C₁₃	semidirect
672. #463	C₂²×C₁₃	semidirect
673. #463	C₂²×C₁₃	semidirect
674. #463	C₂²×C₁₃	semidirect
675. #462	C₂²×C₁₃	semidirect
676. #462	C₂²×C₁₃	semidirect
677. #461	C₂²×C₁₃	semidirect
678. #460	C₂²×C₁₃	semidirect
679. #460	C₂²×C₁₃	semidirect
680. #459	C₂²×C₁₃	semidirect
684. #452	C₂²×C₁₃	semidirect
685. #452	C₂²×C₁₃	semidirect
686. #452	C₂²×C₁₃	semidirect
687. #451	C₂²×C₁₃	semidirect
688. #451	C₂²×C₁₃	semidirect
689. #451	C₂²×C₁₃	semidirect
694. #449	C₂²×C₁₃	semidirect
695. #448	C₂²×C₁₃	semidirect
697. #433	C₂²×C₁₃	semidirect
698. #433	C₂²×C₁₃	semidirect
699. #432	C₂²×C₁₃	semidirect
700. #431	C₂²×C₁₃	semidirect
701. #423	C₂²×C₁₃	semidirect
702. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
703. #419	C₂²×C₁₃	semidirect
706. #417	C₂²×C₁₃	semidirect
708. #416	C₂²×C₁₃	semidirect
709. C₂×#103	C₂²×C₁₃	semidirect
713. #405	C₂²×C₁₃	semidirect
714. #405	C₂²×C₁₃	semidirect
1117. C₁₃	#60835	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×#3500	2
C₁₃×#3461	2
C₁₃×#3225	2
C₁₃×#3224	2
C₁₃×#3223	2
C₁₃×#3222	2
C₁₃×#3219	2
C₁₃×#3215	2
C₁₃×#3211	2
C₁₃×#3210	2
C₁₃×#3156	2
C₁₃×#3154	2
C₁₃×#3137	2
C₁₃×#3136	2
C₁₃×#3040	2
C₁₃×#3037	2
C₁₃×#3035	2
C₂×C₁₃×#464	2
C₁₃×#3013	2
C₁₃×#3012	2
C₁₃×#3011	2
C₁₃×#3009	2
C₁₃×#2925	2
#60835	13

Subgroups — C13×#60835 #15747174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60835 #15747174