Subgroups — C₁₃×#61623 #15747962

Order 3328.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3332	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3316	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3306	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3295	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3282	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3275	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3271	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3264	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3224	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3204	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3192	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3125	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2976	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
26	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#562	—	2	2	no	—
29	C₁₃×#554	C₂²	1	2	yes	complemented
30	C₁₃×#550	C₂²	1	2	yes	complemented
31	C₁₃×#548	C₂²	1	2	yes	—
32	C₁₃×#548	C₂²	1	2	yes	complemented
33	C₁₃×#547	C₂²	1	2	yes	complemented
34	C₁₃×#546	—	2	2	no	—
35	C₁₃×#546	—	2	2	no	—
36	C₁₃×#546	C₂²	1	2	yes	complemented
37	C₁₃×#546	C₂²	1	2	yes	complemented
38	D₄²×C₁₃	—	2	2	no	—
39	D₄²×C₁₃	C₂²	1	2	yes	—
40	C₁₃×#543	—	2	1	no	—
41	C₁₃×#542	C₂²	1	2	yes	complemented
42	C₁₃×#539	—	2	1	no	—
43	C₁₃×#538	—	2	1	no	—
44	C₁₃×#537	—	2	1	no	—
45	C₁₃×#537	—	2	1	no	—
46	C₁₃×#537	C₂²	1	2	yes	complemented
47	C₁₃×#537	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#535	—	2	1	no	—
49	C₁₃×#535	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#525	—	2	1	no	—
51	C₁₃×#525	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₁₃×#121	—	2	1	no	—
54	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#520	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#496	C₂²	1	2	yes	complemented
58	C₁₃×#495	C₂²	1	2	yes	complemented
59	C₁₃×#489	C₂²	1	2	yes	complemented
60	C₁₃×#486	C₂²	1	2	yes	complemented
61	C₁₃×#483	C₂²	1	2	yes	complemented
62	C₁₃×#483	C₂²	1	2	yes	complemented
63	C₁₃×#481	C₂²	1	2	yes	complemented
64	C₁₃×#481	C₂²	1	2	yes	complemented
65	C₁₃×#481	C₂²	1	2	yes	complemented
66	C₁₃×#481	C₂²	1	2	yes	complemented
67	C₁₃×#476	C₂²	1	2	yes	complemented
68	C₁₃×#475	C₂²	1	2	yes	complemented
69	C₁₃×#470	C₂²	1	2	yes	complemented
70	C₁₃×#469	C₂²	1	2	yes	complemented
71	C₁₃×#469	C₂²	1	2	yes	complemented
72	C₁₃×#469	C₂²	1	2	yes	complemented
73	C₁₃×#465	C₂²	1	2	yes	complemented
74	C₁₃×#465	C₂²	1	2	yes	complemented
75	C₁₃×#465	C₂²	1	2	yes	complemented
76	C₁₃×#465	C₂²	1	2	yes	complemented
77	C₁₃×#464	C₂²	1	2	yes	complemented
78	C₁₃×#464	C₂²	1	2	yes	complemented
79	C₁₃×#463	C₂²	1	2	yes	complemented
80	C₁₃×#463	C₂²	1	2	yes	complemented
81	C₁₃×#460	C₂²	1	2	yes	complemented
82	C₁₃×#459	C₂²	1	2	yes	complemented
83	C₁₃×#452	C₂²	1	2	yes	complemented
84	C₁₃×#452	C₂²	1	2	yes	complemented
85	C₁₃×#452	C₂²	1	2	yes	complemented
86	C₁₃×#452	C₂²	1	2	yes	complemented
87	C₁₃×#451	C₂²	1	2	yes	complemented
88	C₁₃×#450	C₂²	1	2	yes	complemented
89	C₁₃×#450	C₂²	1	2	yes	complemented
90	C₁₃×#450	C₂²	1	2	yes	complemented
91	C₁₃×#449	C₂²	1	2	yes	—
92	C₁₃×#449	C₂²	1	2	yes	complemented
93	C₁₃×#449	C₂²	1	2	yes	complemented
94	C₁₃×#449	C₂²	1	2	yes	complemented
95	C₁₃×#449	C₂²	1	2	yes	complemented
96	C₁₃×#449	C₂²	1	2	yes	complemented
97	C₁₃×#448	C₂²	1	2	yes	complemented
98	C₁₃×#447	C₂²	1	2	yes	complemented
99	C₁₃×#447	C₂²	1	2	yes	complemented
100	C₁₃×#447	C₂²	1	2	yes	complemented
101	C₁₃×#442	C₂²	1	2	yes	complemented
102	C₁₃×#441	C₂²	1	2	yes	complemented
103	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
104	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
105	C₁₃×#436	C₂²	1	2	yes	complemented
106	C₁₃×#435	C₂²	1	2	yes	complemented
107	C₁₃×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
109	C₁₃×#433	C₂²	1	2	yes	complemented
110	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
111	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
112	C₁₃×#417	C₂²	1	2	yes	complemented
113	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
115	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
116	C₁₃×#408	C₂²	1	2	yes	complemented
117	C₁₃×#407	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₁₃×H(5,𝔽₂)	—	4	2	no	—
120	C₁₃×H(5,𝔽₂)	—	4	2	no	—
121	C₂×C₁₃×#41	—	2	1	no	—
122	C₂×C₁₃×#41	—	2	2	no	—
123	C₂×C₁₃×#41	—	2	1	no	—
124	C₂×C₁₃×#41	—	2	1	no	—
125	C₂×C₁₃×#41	—	4	2	no	—
126	C₂×C₁₃×#41	—	4	2	no	—
127	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
128	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
130	C₂×C₁₃×#41	C₂³	1	2	yes	—
131	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
132	C₂×C₁₃×#41	C₂³	1	2	yes	—
133	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
134	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
135	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₁₃	—	2	1	no	—
137	C₂²×D₄×C₁₃	—	2	1	no	—
138	C₂²×D₄×C₁₃	—	2	1	no	—
139	C₂²×D₄×C₁₃	—	2	1	no	—
140	C₂²×D₄×C₁₃	—	2	2	no	—
141	C₂²×D₄×C₁₃	—	2	2	no	—
142	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
143	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₁₃	—	2	1	no	—
147	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
148	C₁₃×#137	—	4	2	no	—
149	C₁₃×#137	—	4	2	no	—
150	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
151	C₁₃×#135	—	4	4	no	—
152	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
153	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
154	C₂×C₁₃×SD₁₆	—	4	2	no	—
155	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
158	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
159	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
160	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
161	C₂×C₁₃×D₈	—	4	2	no	—
162	C₂×C₁₃×D₈	C₂³	1	2	yes	—
163	C₂×C₁₃×D₈	C₂³	1	2	yes	—
164	C₂×C₁₃×D₈	C₂³	1	2	yes	—
165	C₂×C₁₃×D₈	C₂³	1	2	yes	—
166	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
168	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
169	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
170	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
172	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₁₃×#127	—	2	2	no	—
174	C₁₃×#127	C₂³	1	2	yes	—
175	C₁₃×#126	—	2	2	no	—
176	C₁₃×#125	—	2	2	no	—
177	C₁₃×#124	—	2	2	no	—
178	C₁₃×#124	—	2	2	no	—
179	C₁₃×#124	—	2	2	no	—
180	C₁₃×#124	C₂³	1	2	yes	—
181	C₁₃×#124	C₂³	1	2	yes	—
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×#123	—	2	2	no	—
184	C₁₃×#123	—	2	2	no	—
185	C₁₃×#123	—	2	2	no	—
186	C₁₃×#123	—	2	2	no	—
187	C₁₃×#123	D₄	1	2	yes	—
188	C₁₃×C₂²⋊Q₈	—	2	1	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	1	no	—
191	C₁₃×C₂²⋊Q₈	—	2	1	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	—	2	2	no	—
197	C₁₃×C₂²⋊Q₈	—	2	2	no	—
198	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
199	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
200	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₁₃×#121	—	2	1	no	—
205	C₁₃×#121	—	2	2	no	—
206	C₁₃×#121	—	2	2	no	—
207	C₁₃×#121	—	2	2	no	—
208	C₁₃×#121	—	2	2	no	—
209	C₁₃×#121	—	2	2	no	—
210	C₁₃×#121	—	2	2	no	—
211	C₁₃×#121	—	2	1	no	—
212	C₁₃×#121	—	2	1	no	—
213	C₁₃×#121	—	2	1	no	—
214	C₁₃×#121	—	2	1	no	—
215	C₁₃×#121	—	2	1	no	—
216	C₁₃×#121	—	2	1	no	—
217	C₁₃×#121	—	2	2	no	—
218	C₁₃×#121	—	2	2	no	—
219	C₁₃×#121	—	2	2	no	—
220	C₁₃×#121	—	2	2	no	—
221	C₁₃×#121	—	2	2	no	—
222	C₁₃×#121	D₄	1	1	yes	characteristic
223	C₁₃×#121	D₄	1	1	yes	characteristic
224	C₁₃×#121	C₂³	1	2	yes	—
225	C₁₃×#121	C₂³	1	2	yes	—
226	C₁₃×#121	C₂³	1	2	yes	—
227	C₁₃×#121	C₂³	1	2	yes	—
228	C₁₃×#121	C₂³	1	2	yes	—
229	C₁₃×#121	C₂³	1	2	yes	—
230	C₁₃×#120	—	2	2	no	—
231	C₁₃×#120	—	2	2	no	—
232	C₁₃×#120	—	2	2	no	—
233	C₁₃×#120	—	2	2	no	—
234	C₁₃×#120	—	2	2	no	—
235	C₁₃×#120	D₄	1	2	yes	—
236	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
237	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
238	C₄×D₄×C₁₃	—	2	2	no	—
239	C₄×D₄×C₁₃	—	2	2	no	—
240	C₄×D₄×C₁₃	—	2	2	no	—
241	C₄×D₄×C₁₃	—	2	2	no	—
242	C₄×D₄×C₁₃	—	2	2	no	—
243	C₄×D₄×C₁₃	C₂³	1	2	yes	—
244	C₄×D₄×C₁₃	C₂³	1	2	yes	—
245	C₄×D₄×C₁₃	C₂³	1	2	yes	—
246	C₄×D₄×C₁₃	C₂³	1	2	yes	—
247	C₁₃×#117	—	2	1	no	—
248	C₁₃×#117	C₂³	1	1	yes	characteristic
249	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
253	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
260	C₁₃×#106	C₂³	1	2	yes	—
261	C₁₃×#106	C₂³	1	2	yes	—
262	C₁₃×#106	C₂³	1	2	yes	—
263	C₁₃×#106	C₂³	1	2	yes	—
264	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
265	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
266	C₁₃×#103	C₂³	1	2	yes	—
267	C₁₃×#103	C₂³	1	2	yes	—
268	C₁₃×#103	C₂³	1	2	yes	—
269	C₁₃×#103	C₂³	1	2	yes	—
270	C₁₃×#103	C₂³	1	2	yes	—
271	C₁₃×#103	C₂³	1	2	yes	—
272	C₁₃×#102	C₂³	1	2	yes	—
273	C₁₃×#102	C₂³	1	2	yes	—
274	C₁₃×#102	C₂³	1	2	yes	—
275	C₁₃×#102	C₂³	1	2	yes	—
276	C₁₃×#102	C₂³	1	2	yes	—
277	C₁₃×#102	C₂³	1	2	yes	—
278	C₁₃×#102	C₂³	1	2	yes	—
279	C₁₃×#102	C₂³	1	2	yes	—
280	C₁₃×#102	C₂³	1	2	yes	—
281	C₁₃×#102	C₂³	1	2	yes	—
282	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₁₃×#97	C₂³	1	2	yes	—
289	C₄×C₈×C₁₃	C₂³	1	2	yes	—
290	#61623	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
291	C₂⁴×C₁₃	—	2	1	no	—
292	C₂⁴×C₁₃	—	2	1	no	—
293	C₂⁴×C₁₃	—	2	2	no	—
294	C₂⁴×C₁₃	—	2	1	no	—
295	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
296	C₁₃×#41	—	2	2	no	—
297	C₁₃×#41	—	2	2	no	—
298	C₁₃×#41	—	2	4	no	—
299	C₁₃×#41	—	2	2	no	—
300	C₁₃×#41	—	2	2	no	—
301	C₁₃×#41	—	4	1	no	—
302	C₁₃×#41	—	4	1	no	—
303	C₁₃×#41	—	4	1	no	—
304	C₁₃×#41	—	4	1	no	—
305	C₁₃×#41	—	4	1	no	—
306	C₁₃×#41	—	4	1	no	—
307	C₁₃×#41	—	4	2	no	—
308	C₁₃×#41	—	4	4	no	—
309	C₁₃×#41	—	4	4	no	—
310	C₁₃×#41	—	4	2	no	—
311	C₁₃×#41	—	4	2	no	—
312	C₁₃×#41	—	4	4	no	—
313	C₁₃×#41	—	8	4	no	—
314	C₂×Q₈×C₁₃	—	2	1	no	—
315	C₂×Q₈×C₁₃	—	2	1	no	—
316	C₂×Q₈×C₁₃	—	2	2	no	—
317	C₂×Q₈×C₁₃	—	2	2	no	—
318	C₂×Q₈×C₁₃	—	4	1	no	—
319	C₂×Q₈×C₁₃	—	4	1	no	—
320	C₂×Q₈×C₁₃	—	4	1	no	—
321	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₁₃	—	2	1	no	—
326	C₂×D₄×C₁₃	—	2	2	no	—
327	C₂×D₄×C₁₃	—	2	4	no	—
328	C₂×D₄×C₁₃	—	2	2	no	—
329	C₂×D₄×C₁₃	—	2	2	no	—
330	C₂×D₄×C₁₃	—	2	1	no	—
331	C₂×D₄×C₁₃	—	2	1	no	—
332	C₂×D₄×C₁₃	—	2	2	no	—
333	C₂×D₄×C₁₃	—	2	1	no	—
334	C₂×D₄×C₁₃	—	2	2	no	—
335	C₂×D₄×C₁₃	—	2	2	no	—
336	C₂×D₄×C₁₃	—	2	2	no	—
337	C₂×D₄×C₁₃	—	2	2	no	—
338	C₂×D₄×C₁₃	—	2	2	no	—
339	C₂×D₄×C₁₃	—	2	1	no	—
340	C₂×D₄×C₁₃	—	2	2	no	—
341	C₂×D₄×C₁₃	—	2	1	no	—
342	C₂×D₄×C₁₃	—	2	2	no	—
343	C₂×D₄×C₁₃	—	2	2	no	—
344	C₂×D₄×C₁₃	—	2	1	no	—
345	C₂×D₄×C₁₃	—	4	1	no	—
346	C₂×D₄×C₁₃	—	4	2	no	—
347	C₂×D₄×C₁₃	—	4	1	no	—
348	C₂×D₄×C₁₃	—	4	1	no	—
349	C₂×D₄×C₁₃	—	4	1	no	—
350	C₂×D₄×C₁₃	—	4	1	no	—
351	C₂×D₄×C₁₃	—	4	4	no	—
352	C₂×D₄×C₁₃	—	4	4	no	—
353	C₂×D₄×C₁₃	—	4	8	no	—
354	C₂×D₄×C₁₃	—	8	4	no	—
355	C₂×D₄×C₁₃	—	8	2	no	—
356	C₂×D₄×C₁₃	—	8	2	no	—
357	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
358	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
359	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
360	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
361	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
362	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
364	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₁₃	—	2	1	no	—
366	C₂²×C₄×C₁₃	—	2	1	no	—
367	C₂²×C₄×C₁₃	—	2	1	no	—
368	C₂²×C₄×C₁₃	—	2	1	no	—
369	C₂²×C₄×C₁₃	—	2	1	no	—
370	C₂²×C₄×C₁₃	—	2	1	no	—
371	C₂²×C₄×C₁₃	—	2	2	no	—
372	C₂²×C₄×C₁₃	—	2	1	no	—
373	C₂²×C₄×C₁₃	—	2	1	no	—
374	C₂²×C₄×C₁₃	—	2	2	no	—
375	C₂²×C₄×C₁₃	—	2	1	no	—
376	C₂²×C₄×C₁₃	—	2	2	no	—
377	C₂²×C₄×C₁₃	—	2	2	no	—
378	C₂²×C₄×C₁₃	—	2	2	no	—
379	C₂²×C₄×C₁₃	—	4	1	no	—
380	C₂²×C₄×C₁₃	—	4	1	no	—
381	C₂²×C₄×C₁₃	—	4	4	no	—
382	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
389	C₁₃×Q₁₆	—	2	4	no	—
390	C₁₃×Q₁₆	—	4	2	no	—
391	C₁₃×SD₁₆	—	2	4	no	—
392	C₁₃×SD₁₆	—	2	4	no	—
393	C₁₃×SD₁₆	—	4	2	no	—
394	C₁₃×SD₁₆	—	4	2	no	—
395	C₁₃×SD₁₆	—	4	2	no	—
396	C₁₃×SD₁₆	—	4	2	no	—
397	C₁₃×D₈	—	2	4	no	—
398	C₁₃×D₈	—	4	2	no	—
399	C₁₃×D₈	—	4	2	no	—
400	C₁₃×D₈	—	4	2	no	—
401	C₁₃×M₁₆	—	4	2	no	—
402	C₁₃×M₁₆	—	4	1	no	—
403	C₁₃×M₁₆	—	4	1	no	—
404	C₂×C₈×C₁₃	—	4	1	no	—
405	C₂×C₈×C₁₃	—	4	1	no	—
406	C₂×C₈×C₁₃	—	4	2	no	—
407	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
408	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
409	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
410	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
411	C₁₃×C₄⋊C₄	—	2	1	no	—
412	C₁₃×C₄⋊C₄	—	2	2	no	—
413	C₁₃×C₄⋊C₄	—	2	2	no	—
414	C₁₃×C₄⋊C₄	—	2	2	no	—
415	C₁₃×C₄⋊C₄	—	2	1	no	—
416	C₁₃×C₄⋊C₄	—	2	2	no	—
417	C₁₃×C₄⋊C₄	—	2	1	no	—
418	C₁₃×C₄⋊C₄	—	2	2	no	—
419	C₁₃×C₄⋊C₄	—	2	2	no	—
420	C₁₃×C₄⋊C₄	—	2	2	no	—
421	C₁₃×C₄⋊C₄	—	2	2	no	—
422	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
423	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
424	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
425	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
426	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
427	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
428	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
429	C₁₃×C₂²⋊C₄	—	2	2	no	—
430	C₁₃×C₂²⋊C₄	—	2	2	no	—
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	—	2	2	no	—
433	C₁₃×C₂²⋊C₄	—	2	2	no	—
434	C₁₃×C₂²⋊C₄	—	2	2	no	—
435	C₁₃×C₂²⋊C₄	—	2	2	no	—
436	C₁₃×C₂²⋊C₄	—	2	2	no	—
437	C₁₃×C₂²⋊C₄	—	2	2	no	—
438	C₁₃×C₂²⋊C₄	—	2	2	no	—
439	C₁₃×C₂²⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
446	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
447	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
448	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
449	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
450	C₄²×C₁₃	—	2	2	no	—
451	C₄²×C₁₃	—	2	2	no	—
452	C₄²×C₁₃	C₂⁴	1	2	yes	—
453	#3536	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#3488	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3332	C₂×C₁₃	1	2	yes	complemented
456	#3316	C₂×C₁₃	1	2	yes	complemented
457	#3306	C₂×C₁₃	1	2	yes	complemented
458	#3295	C₂×C₁₃	1	2	yes	complemented
459	#3282	C₂×C₁₃	1	2	yes	complemented
460	#3275	C₂×C₁₃	1	2	yes	complemented
461	#3271	C₂×C₁₃	1	2	yes	complemented
462	#3264	C₂×C₁₃	1	2	yes	complemented
463	#3224	C₂×C₁₃	1	2	yes	complemented
464	#3204	C₂×C₁₃	1	2	yes	complemented
465	#3192	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3187	C₂×C₁₃	1	1	yes	characteristic, complemented
467	#3125	C₂×C₁₃	1	2	yes	complemented
468	#3012	C₂×C₁₃	1	2	yes	complemented
469	#3007	C₂×C₁₃	1	1	yes	characteristic, complemented
470	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
471	#2976	C₂×C₁₃	1	1	yes	characteristic, complemented
472	C₂³×C₁₃	—	2	1	no	—
473	C₂³×C₁₃	—	2	2	no	—
474	C₂³×C₁₃	—	2	2	no	—
475	C₂³×C₁₃	—	2	2	no	—
476	C₂³×C₁₃	—	2	1	no	—
477	C₂³×C₁₃	—	4	1	no	—
478	C₂³×C₁₃	—	4	1	no	—
479	C₂³×C₁₃	—	4	2	no	—
480	C₂³×C₁₃	—	4	4	no	—
481	C₂³×C₁₃	—	4	2	no	—
482	C₂³×C₁₃	—	4	2	no	—
483	C₂³×C₁₃	—	4	2	no	—
484	C₂³×C₁₃	—	8	1	no	—
485	C₂³×C₁₃	—	8	1	no	—
486	C₂³×C₁₃	—	8	1	no	—
487	C₂³×C₁₃	—	8	1	no	—
488	C₂³×C₁₃	—	8	2	no	—
489	C₂³×C₁₃	—	8	2	no	—
490	C₂³×C₁₃	—	8	1	no	—
491	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
492	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
493	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
494	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
495	Q₈×C₁₃	—	2	1	no	—
496	Q₈×C₁₃	—	2	2	no	—
497	Q₈×C₁₃	—	2	2	no	—
498	Q₈×C₁₃	—	2	1	no	—
499	Q₈×C₁₃	—	2	1	no	—
500	Q₈×C₁₃	—	4	1	no	—
501	Q₈×C₁₃	—	4	2	no	—
502	Q₈×C₁₃	—	8	1	no	—
503	Q₈×C₁₃	—	8	2	no	—
504	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
505	D₄×C₁₃	—	2	4	no	—
506	D₄×C₁₃	—	2	4	no	—
507	D₄×C₁₃	—	2	1	no	—
508	D₄×C₁₃	—	2	2	no	—
509	D₄×C₁₃	—	2	1	no	—
510	D₄×C₁₃	—	2	2	no	—
511	D₄×C₁₃	—	2	2	no	—
512	D₄×C₁₃	—	2	2	no	—
513	D₄×C₁₃	—	2	1	no	—
514	D₄×C₁₃	—	4	1	no	—
515	D₄×C₁₃	—	4	2	no	—
516	D₄×C₁₃	—	4	2	no	—
517	D₄×C₁₃	—	4	4	no	—
518	D₄×C₁₃	—	4	2	no	—
519	D₄×C₁₃	—	4	4	no	—
520	D₄×C₁₃	—	4	2	no	—
521	D₄×C₁₃	—	4	2	no	—
522	D₄×C₁₃	—	4	2	no	—
523	D₄×C₁₃	—	4	2	no	—
524	D₄×C₁₃	—	4	4	no	—
525	D₄×C₁₃	—	4	4	no	—
526	D₄×C₁₃	—	8	2	no	—
527	D₄×C₁₃	—	8	1	no	—
528	D₄×C₁₃	—	8	2	no	—
529	D₄×C₁₃	—	8	2	no	—
530	D₄×C₁₃	—	8	2	no	—
531	D₄×C₁₃	—	8	2	no	—
532	D₄×C₁₃	—	8	2	no	—
533	D₄×C₁₃	—	8	2	no	—
534	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
535	C₂×C₄×C₁₃	—	2	4	no	—
536	C₂×C₄×C₁₃	—	2	1	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	1	no	—
541	C₂×C₄×C₁₃	—	2	1	no	—
542	C₂×C₄×C₁₃	—	2	2	no	—
543	C₂×C₄×C₁₃	—	2	1	no	—
544	C₂×C₄×C₁₃	—	2	1	no	—
545	C₂×C₄×C₁₃	—	2	2	no	—
546	C₂×C₄×C₁₃	—	2	2	no	—
547	C₂×C₄×C₁₃	—	2	2	no	—
548	C₂×C₄×C₁₃	—	2	1	no	—
549	C₂×C₄×C₁₃	—	2	2	no	—
550	C₂×C₄×C₁₃	—	4	1	no	—
551	C₂×C₄×C₁₃	—	4	1	no	—
552	C₂×C₄×C₁₃	—	4	1	no	—
553	C₂×C₄×C₁₃	—	4	2	no	—
554	C₂×C₄×C₁₃	—	4	4	no	—
555	C₂×C₄×C₁₃	—	4	2	no	—
556	C₂×C₄×C₁₃	—	4	2	no	—
557	C₂×C₄×C₁₃	—	4	2	no	—
558	C₂×C₄×C₁₃	—	4	2	no	—
559	C₂×C₄×C₁₃	—	8	2	no	—
560	C₂×C₄×C₁₃	—	8	2	no	—
561	C₂×C₄×C₁₃	—	8	2	no	—
562	C₂×C₄×C₁₃	—	8	1	no	—
563	C₂×C₄×C₁₃	—	8	1	no	—
564	C₂×C₄×C₁₃	—	8	1	no	—
565	C₂×C₄×C₁₃	—	8	2	no	—
566	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
567	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
568	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
570	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	2	no	—
575	C₈×C₁₃	—	2	2	no	—
576	C₈×C₁₃	—	2	2	no	—
577	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic, complemented
578	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
579	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic, complemented
580	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic, complemented
581	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
582	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
583	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
584	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
585	#562	—	2	2	no	—
586	#554	C₂²×C₁₃	1	2	yes	complemented
587	#550	C₂²×C₁₃	1	2	yes	complemented
588	#548	C₂²×C₁₃	1	2	yes	—
589	#548	C₂²×C₁₃	1	2	yes	complemented
590	#547	C₂²×C₁₃	1	2	yes	complemented
591	#546	—	2	2	no	—
592	#546	—	2	2	no	—
593	#546	C₂²×C₁₃	1	2	yes	complemented
594	#546	C₂²×C₁₃	1	2	yes	complemented
595	D₄²	—	2	2	no	—
596	D₄²	C₂²×C₁₃	1	2	yes	—
597	#543	—	2	1	no	—
598	#542	C₂²×C₁₃	1	2	yes	complemented
599	#539	—	2	1	no	—
600	#538	—	2	1	no	—
601	#537	—	2	1	no	—
602	#537	—	2	1	no	—
603	#537	C₂²×C₁₃	1	1	yes	characteristic, complemented
604	#537	C₂²×C₁₃	1	2	yes	complemented
605	#535	—	2	1	no	—
606	#535	C₂²×C₁₃	1	1	yes	characteristic, complemented
607	#525	—	2	1	no	—
608	#525	C₂²×C₁₃	1	1	yes	characteristic
609	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
610	C₂×#121	—	2	1	no	—
611	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
612	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
614	#496	C₂²×C₁₃	1	2	yes	complemented
615	#495	C₂²×C₁₃	1	2	yes	complemented
616	#489	C₂²×C₁₃	1	2	yes	complemented
617	#486	C₂²×C₁₃	1	2	yes	complemented
618	#483	C₂²×C₁₃	1	2	yes	complemented
619	#483	C₂²×C₁₃	1	2	yes	complemented
620	#481	C₂²×C₁₃	1	2	yes	complemented
621	#481	C₂²×C₁₃	1	2	yes	complemented
622	#481	C₂²×C₁₃	1	2	yes	complemented
623	#481	C₂²×C₁₃	1	2	yes	complemented
624	#476	C₂²×C₁₃	1	2	yes	complemented
625	#475	C₂²×C₁₃	1	2	yes	complemented
626	#470	C₂²×C₁₃	1	2	yes	complemented
627	#469	C₂²×C₁₃	1	2	yes	complemented
628	#469	C₂²×C₁₃	1	2	yes	complemented
629	#469	C₂²×C₁₃	1	2	yes	complemented
630	#465	C₂²×C₁₃	1	2	yes	complemented
631	#465	C₂²×C₁₃	1	2	yes	complemented
632	#465	C₂²×C₁₃	1	2	yes	complemented
633	#465	C₂²×C₁₃	1	2	yes	complemented
634	#464	C₂²×C₁₃	1	2	yes	complemented
635	#464	C₂²×C₁₃	1	2	yes	complemented
636	#463	C₂²×C₁₃	1	2	yes	complemented
637	#463	C₂²×C₁₃	1	2	yes	complemented
638	#460	C₂²×C₁₃	1	2	yes	complemented
639	#459	C₂²×C₁₃	1	2	yes	complemented
640	#452	C₂²×C₁₃	1	2	yes	complemented
641	#452	C₂²×C₁₃	1	2	yes	complemented
642	#452	C₂²×C₁₃	1	2	yes	complemented
643	#452	C₂²×C₁₃	1	2	yes	complemented
644	#451	C₂²×C₁₃	1	2	yes	complemented
645	#450	C₂²×C₁₃	1	2	yes	complemented
646	#450	C₂²×C₁₃	1	2	yes	complemented
647	#450	C₂²×C₁₃	1	2	yes	complemented
648	#449	C₂²×C₁₃	1	2	yes	—
649	#449	C₂²×C₁₃	1	2	yes	complemented
650	#449	C₂²×C₁₃	1	2	yes	complemented
651	#449	C₂²×C₁₃	1	2	yes	complemented
652	#449	C₂²×C₁₃	1	2	yes	complemented
653	#449	C₂²×C₁₃	1	2	yes	complemented
654	#448	C₂²×C₁₃	1	2	yes	complemented
655	#447	C₂²×C₁₃	1	2	yes	complemented
656	#447	C₂²×C₁₃	1	2	yes	complemented
657	#447	C₂²×C₁₃	1	2	yes	complemented
658	#442	C₂²×C₁₃	1	2	yes	complemented
659	#441	C₂²×C₁₃	1	2	yes	complemented
660	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
661	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
662	#436	C₂²×C₁₃	1	2	yes	complemented
663	#435	C₂²×C₁₃	1	2	yes	complemented
664	#435	C₂²×C₁₃	1	2	yes	complemented
665	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
666	#433	C₂²×C₁₃	1	2	yes	complemented
667	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
668	#417	C₂²×C₁₃	1	2	yes	complemented
669	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
670	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
671	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
672	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
673	#408	C₂²×C₁₃	1	2	yes	complemented
674	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
675	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
676	C₂²×C₁₃	—	2	1	no	—
677	C₂²×C₁₃	—	2	1	no	—
678	C₂²×C₁₃	—	2	1	no	—
679	C₂²×C₁₃	—	2	2	no	—
680	C₂²×C₁₃	—	2	1	no	—
681	C₂²×C₁₃	—	2	1	no	—
682	C₂²×C₁₃	—	2	1	no	—
683	C₂²×C₁₃	—	2	2	no	—
684	C₂²×C₁₃	—	2	2	no	—
685	C₂²×C₁₃	—	2	1	no	—
686	C₂²×C₁₃	—	2	2	no	—
687	C₂²×C₁₃	—	2	1	no	—
688	C₂²×C₁₃	—	4	1	no	—
689	C₂²×C₁₃	—	4	1	no	—
690	C₂²×C₁₃	—	4	2	no	—
691	C₂²×C₁₃	—	4	1	no	—
692	C₂²×C₁₃	—	4	2	no	—
693	C₂²×C₁₃	—	4	1	no	—
694	C₂²×C₁₃	—	4	2	no	—
695	C₂²×C₁₃	—	4	2	no	—
696	C₂²×C₁₃	—	4	2	no	—
697	C₂²×C₁₃	—	4	1	no	—
698	C₂²×C₁₃	—	4	2	no	—
699	C₂²×C₁₃	—	8	2	no	—
700	C₂²×C₁₃	—	8	4	no	—
701	C₂²×C₁₃	—	16	2	no	—
702	C₂²×C₁₃	—	16	4	no	—
703	C₂²×C₁₃	—	16	2	no	—
704	C₂²×C₁₃	#577	1	2	yes	—
705	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
706	C₄×C₁₃	—	2	2	no	—
707	C₄×C₁₃	—	2	1	no	—
708	C₄×C₁₃	—	2	2	no	—
709	C₄×C₁₃	—	2	1	no	—
710	C₄×C₁₃	—	2	2	no	—
711	C₄×C₁₃	—	2	1	no	—
712	C₄×C₁₃	—	2	2	no	—
713	C₄×C₁₃	—	4	2	no	—
714	C₄×C₁₃	—	4	2	no	—
715	C₄×C₁₃	—	4	1	no	—
716	C₄×C₁₃	—	4	2	no	—
717	C₄×C₁₃	—	4	2	no	—
718	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
719	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
720	H(5,𝔽₂)	—	4	2	no	—
721	H(5,𝔽₂)	—	4	2	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	2	2	no	—
724	C₂×#41	—	2	1	no	—
725	C₂×#41	—	2	1	no	—
726	C₂×#41	—	4	2	no	—
727	C₂×#41	—	4	2	no	—
728	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
729	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
730	C₂×#41	C₂³×C₁₃	1	2	yes	—
731	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
732	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
733	C₂×#41	C₂³×C₁₃	1	2	yes	—
734	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
735	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
736	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
737	C₂²×D₄	—	2	1	no	—
738	C₂²×D₄	—	2	1	no	—
739	C₂²×D₄	—	2	1	no	—
740	C₂²×D₄	—	2	1	no	—
741	C₂²×D₄	—	2	2	no	—
742	C₂²×D₄	—	2	2	no	—
743	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
744	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
745	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
746	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
747	C₂³×C₄	—	2	1	no	—
748	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
749	#137	—	4	2	no	—
750	#137	—	4	2	no	—
751	AGL(1,ℤ/8)	—	4	4	no	—
752	#135	—	4	4	no	—
753	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
754	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
755	C₂×SD₁₆	—	4	2	no	—
756	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
758	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
759	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
760	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
761	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
762	C₂×D₈	—	4	2	no	—
763	C₂×D₈	C₂³×C₁₃	1	2	yes	—
764	C₂×D₈	C₂³×C₁₃	1	2	yes	—
765	C₂×D₈	C₂³×C₁₃	1	2	yes	—
766	C₂×D₈	C₂³×C₁₃	1	2	yes	—
767	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
768	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
769	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
770	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
771	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
772	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
773	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
774	#127	—	2	2	no	—
775	#127	C₂³×C₁₃	1	2	yes	—
776	#126	—	2	2	no	—
777	#125	—	2	2	no	—
778	#124	—	2	2	no	—
779	#124	—	2	2	no	—
780	#124	—	2	2	no	—
781	#124	C₂³×C₁₃	1	2	yes	—
782	#124	C₂³×C₁₃	1	2	yes	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	D₄×C₁₃	1	2	yes	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
800	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
801	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
803	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
804	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
805	#121	—	2	1	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	1	no	—
817	#121	—	2	1	no	—
818	#121	—	2	2	no	—
819	#121	—	2	2	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	—	2	2	no	—
823	#121	D₄×C₁₃	1	1	yes	characteristic
824	#121	D₄×C₁₃	1	1	yes	characteristic
825	#121	C₂³×C₁₃	1	2	yes	—
826	#121	C₂³×C₁₃	1	2	yes	—
827	#121	C₂³×C₁₃	1	2	yes	—
828	#121	C₂³×C₁₃	1	2	yes	—
829	#121	C₂³×C₁₃	1	2	yes	—
830	#121	C₂³×C₁₃	1	2	yes	—
831	#120	—	2	2	no	—
832	#120	—	2	2	no	—
833	#120	—	2	2	no	—
834	#120	—	2	2	no	—
835	#120	—	2	2	no	—
836	#120	D₄×C₁₃	1	2	yes	—
837	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
838	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	—	2	2	no	—
842	C₄×D₄	—	2	2	no	—
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	C₂³×C₁₃	1	2	yes	—
845	C₄×D₄	C₂³×C₁₃	1	2	yes	—
846	C₄×D₄	C₂³×C₁₃	1	2	yes	—
847	C₄×D₄	C₂³×C₁₃	1	2	yes	—
848	#117	—	2	1	no	—
849	#117	C₂³×C₁₃	1	1	yes	characteristic
850	C₂×C₄⋊C₄	—	2	1	no	—
851	C₂×C₄⋊C₄	—	2	1	no	—
852	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
853	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
854	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
855	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
856	C₂×C₂²⋊C₄	—	2	1	no	—
857	C₂×C₂²⋊C₄	—	2	1	no	—
858	C₂×C₂²⋊C₄	—	2	1	no	—
859	C₂×C₂²⋊C₄	—	2	2	no	—
860	C₂×C₂²⋊C₄	—	2	2	no	—
861	#106	C₂³×C₁₃	1	2	yes	—
862	#106	C₂³×C₁₃	1	2	yes	—
863	#106	C₂³×C₁₃	1	2	yes	—
864	#106	C₂³×C₁₃	1	2	yes	—
865	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
866	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
867	#103	C₂³×C₁₃	1	2	yes	—
868	#103	C₂³×C₁₃	1	2	yes	—
869	#103	C₂³×C₁₃	1	2	yes	—
870	#103	C₂³×C₁₃	1	2	yes	—
871	#103	C₂³×C₁₃	1	2	yes	—
872	#103	C₂³×C₁₃	1	2	yes	—
873	#102	C₂³×C₁₃	1	2	yes	—
874	#102	C₂³×C₁₃	1	2	yes	—
875	#102	C₂³×C₁₃	1	2	yes	—
876	#102	C₂³×C₁₃	1	2	yes	—
877	#102	C₂³×C₁₃	1	2	yes	—
878	#102	C₂³×C₁₃	1	2	yes	—
879	#102	C₂³×C₁₃	1	2	yes	—
880	#102	C₂³×C₁₃	1	2	yes	—
881	#102	C₂³×C₁₃	1	2	yes	—
882	#102	C₂³×C₁₃	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
889	#97	C₂³×C₁₃	1	2	yes	—
890	C₄×C₈	C₂³×C₁₃	1	2	yes	—
891	C₂×C₁₃	—	2	2	no	—
892	C₂×C₁₃	—	4	1	no	—
893	C₂×C₁₃	—	4	1	no	—
894	C₂×C₁₃	—	4	2	no	—
895	C₂×C₁₃	—	4	2	no	—
896	C₂×C₁₃	—	8	1	no	—
897	C₂×C₁₃	—	8	2	no	—
898	C₂×C₁₃	—	8	2	no	—
899	C₂×C₁₃	#3484	1	1	yes	characteristic
900	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
901	C₂×C₁₃	#3585	1	1	yes	characteristic
902	C₂⁴	—	2	1	no	—
903	C₂⁴	—	2	1	no	—
904	C₂⁴	—	2	2	no	—
905	C₂⁴	—	2	1	no	—
906	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
907	#41	—	2	2	no	—
908	#41	—	2	2	no	—
909	#41	—	2	4	no	—
910	#41	—	2	2	no	—
911	#41	—	2	2	no	—
912	#41	—	4	1	no	—
913	#41	—	4	1	no	—
914	#41	—	4	1	no	—
915	#41	—	4	1	no	—
916	#41	—	4	1	no	—
917	#41	—	4	1	no	—
918	#41	—	4	2	no	—
919	#41	—	4	4	no	—
920	#41	—	4	4	no	—
921	#41	—	4	2	no	—
922	#41	—	4	2	no	—
923	#41	—	4	4	no	—
924	#41	—	8	4	no	—
925	C₂×Q₈	—	2	1	no	—
926	C₂×Q₈	—	2	1	no	—
927	C₂×Q₈	—	2	2	no	—
928	C₂×Q₈	—	2	2	no	—
929	C₂×Q₈	—	4	1	no	—
930	C₂×Q₈	—	4	1	no	—
931	C₂×Q₈	—	4	1	no	—
932	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
933	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
934	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
935	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	4	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	1	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	1	no	—
956	C₂×D₄	—	4	1	no	—
957	C₂×D₄	—	4	2	no	—
958	C₂×D₄	—	4	1	no	—
959	C₂×D₄	—	4	1	no	—
960	C₂×D₄	—	4	1	no	—
961	C₂×D₄	—	4	1	no	—
962	C₂×D₄	—	4	4	no	—
963	C₂×D₄	—	4	4	no	—
964	C₂×D₄	—	4	8	no	—
965	C₂×D₄	—	8	4	no	—
966	C₂×D₄	—	8	2	no	—
967	C₂×D₄	—	8	2	no	—
968	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
969	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
970	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
971	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
972	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
973	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
974	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
975	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	1	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	1	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	4	1	no	—
991	C₂²×C₄	—	4	1	no	—
992	C₂²×C₄	—	4	4	no	—
993	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
994	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
995	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
996	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
997	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
998	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1000	Q₁₆	—	2	4	no	—
1001	Q₁₆	—	4	2	no	—
1002	SD₁₆	—	2	4	no	—
1003	SD₁₆	—	2	4	no	—
1004	SD₁₆	—	4	2	no	—
1005	SD₁₆	—	4	2	no	—
1006	SD₁₆	—	4	2	no	—
1007	SD₁₆	—	4	2	no	—
1008	D₈	—	2	4	no	—
1009	D₈	—	4	2	no	—
1010	D₈	—	4	2	no	—
1011	D₈	—	4	2	no	—
1012	M₁₆	—	4	2	no	—
1013	M₁₆	—	4	1	no	—
1014	M₁₆	—	4	1	no	—
1015	C₂×C₈	—	4	1	no	—
1016	C₂×C₈	—	4	1	no	—
1017	C₂×C₈	—	4	2	no	—
1018	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1019	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1020	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1021	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1022	C₄⋊C₄	—	2	1	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	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1034	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1035	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1036	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1037	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1038	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1039	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
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	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1057	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1058	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1059	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1060	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1061	C₄²	—	2	2	no	—
1062	C₄²	—	2	2	no	—
1063	C₄²	C₂⁴×C₁₃	1	2	yes	—
1064	C₁₃	#61623	1	1	yes	characteristic, direct product factor, Sylow
1065	C₂³	—	2	1	no	—
1066	C₂³	—	2	2	no	—
1067	C₂³	—	2	2	no	—
1068	C₂³	—	2	2	no	—
1069	C₂³	—	2	1	no	—
1070	C₂³	—	4	1	no	—
1071	C₂³	—	4	1	no	—
1072	C₂³	—	4	2	no	—
1073	C₂³	—	4	4	no	—
1074	C₂³	—	4	2	no	—
1075	C₂³	—	4	2	no	—
1076	C₂³	—	4	2	no	—
1077	C₂³	—	8	1	no	—
1078	C₂³	—	8	1	no	—
1079	C₂³	—	8	1	no	—
1080	C₂³	—	8	1	no	—
1081	C₂³	—	8	2	no	—
1082	C₂³	—	8	2	no	—
1083	C₂³	—	8	1	no	—
1084	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1085	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1086	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1087	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1088	Q₈	—	2	1	no	—
1089	Q₈	—	2	2	no	—
1090	Q₈	—	2	2	no	—
1091	Q₈	—	2	1	no	—
1092	Q₈	—	2	1	no	—
1093	Q₈	—	4	1	no	—
1094	Q₈	—	4	2	no	—
1095	Q₈	—	8	1	no	—
1096	Q₈	—	8	2	no	—
1097	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
1098	D₄	—	2	4	no	—
1099	D₄	—	2	4	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	2	no	—
1104	D₄	—	2	2	no	—
1105	D₄	—	2	2	no	—
1106	D₄	—	2	1	no	—
1107	D₄	—	4	1	no	—
1108	D₄	—	4	2	no	—
1109	D₄	—	4	2	no	—
1110	D₄	—	4	4	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	4	4	no	—
1113	D₄	—	4	2	no	—
1114	D₄	—	4	2	no	—
1115	D₄	—	4	2	no	—
1116	D₄	—	4	2	no	—
1117	D₄	—	4	4	no	—
1118	D₄	—	4	4	no	—
1119	D₄	—	8	1	no	—
1120	D₄	—	8	2	no	—
1121	D₄	—	8	2	no	—
1122	D₄	—	8	2	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	8	2	no	—
1125	D₄	—	8	2	no	—
1126	D₄	—	8	2	no	—
1127	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1128	C₂×C₄	—	2	4	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	2	no	—
1147	C₂×C₄	—	4	4	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	2	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	8	2	no	—
1153	C₂×C₄	—	8	2	no	—
1154	C₂×C₄	—	8	2	no	—
1155	C₂×C₄	—	8	1	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1160	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1161	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1162	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1165	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1166	C₈	—	2	2	no	—
1167	C₈	—	2	2	no	—
1168	C₈	—	2	2	no	—
1169	C₈	—	2	2	no	—
1170	C₂²	—	2	1	no	—
1171	C₂²	—	2	1	no	—
1172	C₂²	—	2	1	no	—
1173	C₂²	—	2	2	no	—
1174	C₂²	—	2	1	no	—
1175	C₂²	—	2	1	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	4	1	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	2	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	4	2	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	2	no	—
1192	C₂²	—	4	2	no	—
1193	C₂²	—	8	2	no	—
1194	C₂²	—	8	4	no	—
1195	C₂²	—	16	2	no	—
1196	C₂²	—	16	4	no	—
1197	C₂²	—	16	2	no	—
1198	C₂²	C₁₃×#577	1	2	yes	—
1199	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1200	C₄	—	2	2	no	—
1201	C₄	—	2	2	no	—
1202	C₄	—	2	1	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	2	1	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	1	no	—
1207	C₄	—	4	2	no	—
1208	C₄	—	4	2	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	2	no	—
1212	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1213	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1214	C₂	—	2	2	no	—
1215	C₂	—	4	1	no	—
1216	C₂	—	4	1	no	—
1217	C₂	—	4	2	no	—
1218	C₂	—	4	2	no	—
1219	C₂	—	8	1	no	—
1220	C₂	—	8	2	no	—
1221	C₂	—	8	2	no	—
1222	C₂	C₁₃×#3484	1	1	yes	characteristic
1223	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1224	C₂	C₁₃×#3585	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3536	C₂	semidirect
2. C₁₃×#3488	C₂	semidirect
3. C₁₃×#3332	C₂	semidirect
4. C₁₃×#3316	C₂	semidirect
5. C₁₃×#3306	C₂	semidirect
6. C₁₃×#3295	C₂	semidirect
7. C₁₃×#3282	C₂	semidirect
8. C₁₃×#3275	C₂	semidirect
9. C₁₃×#3271	C₂	semidirect
10. C₁₃×#3264	C₂	semidirect
11. C₁₃×#3224	C₂	semidirect
12. C₁₃×#3204	C₂	semidirect
13. C₁₃×#3192	C₂	semidirect
14. C₁₃×#3187	C₂	semidirect
15. C₁₃×#3125	C₂	semidirect
16. C₁₃×#3012	C₂	semidirect
17. C₁₃×#3007	C₂	semidirect
18. C₂×C₁₃×#449	C₂	semidirect
19. C₁₃×#2976	C₂	semidirect
20. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
22. C₂×C₁₃×#137	C₂²	semidirect
23. C₂×C₁₃×#137	C₂²	semidirect
24. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₁₃×#135	C₂²	semidirect
26. C₂²×C₁₃×SD₁₆	C₂²	semidirect
27. C₂²×C₁₃×D₈	C₂²	semidirect
29. C₁₃×#554	C₂²	semidirect
30. C₁₃×#550	C₂²	semidirect
32. C₁₃×#548	C₂²	semidirect
33. C₁₃×#547	C₂²	semidirect
36. C₁₃×#546	C₂²	semidirect
37. C₁₃×#546	C₂²	semidirect
41. C₁₃×#542	C₂²	semidirect
46. C₁₃×#537	C₂²	semidirect
47. C₁₃×#537	C₂²	semidirect
49. C₁₃×#535	C₂²	semidirect
52. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₁₃×#121	C₂²	semidirect
56. C₁₃×#520	C₂²	semidirect
57. C₁₃×#496	C₂²	semidirect
58. C₁₃×#495	C₂²	semidirect
59. C₁₃×#489	C₂²	semidirect
60. C₁₃×#486	C₂²	semidirect
61. C₁₃×#483	C₂²	semidirect
62. C₁₃×#483	C₂²	semidirect
63. C₁₃×#481	C₂²	semidirect
64. C₁₃×#481	C₂²	semidirect
65. C₁₃×#481	C₂²	semidirect
66. C₁₃×#481	C₂²	semidirect
67. C₁₃×#476	C₂²	semidirect
68. C₁₃×#475	C₂²	semidirect
69. C₁₃×#470	C₂²	semidirect
70. C₁₃×#469	C₂²	semidirect
71. C₁₃×#469	C₂²	semidirect
72. C₁₃×#469	C₂²	semidirect
73. C₁₃×#465	C₂²	semidirect
74. C₁₃×#465	C₂²	semidirect
75. C₁₃×#465	C₂²	semidirect
76. C₁₃×#465	C₂²	semidirect
77. C₁₃×#464	C₂²	semidirect
78. C₁₃×#464	C₂²	semidirect
79. C₁₃×#463	C₂²	semidirect
80. C₁₃×#463	C₂²	semidirect
81. C₁₃×#460	C₂²	semidirect
82. C₁₃×#459	C₂²	semidirect
83. C₁₃×#452	C₂²	semidirect
84. C₁₃×#452	C₂²	semidirect
85. C₁₃×#452	C₂²	semidirect
86. C₁₃×#452	C₂²	semidirect
87. C₁₃×#451	C₂²	semidirect
88. C₁₃×#450	C₂²	semidirect
89. C₁₃×#450	C₂²	semidirect
90. C₁₃×#450	C₂²	semidirect
92. C₁₃×#449	C₂²	semidirect
93. C₁₃×#449	C₂²	semidirect
94. C₁₃×#449	C₂²	semidirect
95. C₁₃×#449	C₂²	semidirect
96. C₁₃×#449	C₂²	semidirect
97. C₁₃×#448	C₂²	semidirect
98. C₁₃×#447	C₂²	semidirect
99. C₁₃×#447	C₂²	semidirect
100. C₁₃×#447	C₂²	semidirect
101. C₁₃×#442	C₂²	semidirect
102. C₁₃×#441	C₂²	semidirect
103. C₄×C₁₃×SD₁₆	C₂²	semidirect
104. C₄×C₁₃×SD₁₆	C₂²	semidirect
105. C₁₃×#436	C₂²	semidirect
106. C₁₃×#435	C₂²	semidirect
107. C₁₃×#435	C₂²	semidirect
108. C₈×D₄×C₁₃	C₂²	semidirect
109. C₁₃×#433	C₂²	semidirect
110. C₁₃×#417	C₂²	semidirect
111. C₁₃×#417	C₂²	semidirect
112. C₁₃×#417	C₂²	semidirect
113. C₂×C₁₃×#103	C₂²	semidirect
114. C₂×C₁₃×#102	C₂²	semidirect
115. C₂×C₁₃×#102	C₂²	semidirect
116. C₁₃×#408	C₂²	semidirect
117. C₁₃×#407	C₂²	semidirect
118. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
290. #61623	C₁₃	direct (N × H)
453. #3536	C₂×C₁₃	semidirect
454. #3488	C₂×C₁₃	semidirect
455. #3332	C₂×C₁₃	semidirect
456. #3316	C₂×C₁₃	semidirect
457. #3306	C₂×C₁₃	semidirect
458. #3295	C₂×C₁₃	semidirect
459. #3282	C₂×C₁₃	semidirect
460. #3275	C₂×C₁₃	semidirect
461. #3271	C₂×C₁₃	semidirect
462. #3264	C₂×C₁₃	semidirect
463. #3224	C₂×C₁₃	semidirect
464. #3204	C₂×C₁₃	semidirect
465. #3192	C₂×C₁₃	semidirect
466. #3187	C₂×C₁₃	semidirect
467. #3125	C₂×C₁₃	semidirect
468. #3012	C₂×C₁₃	semidirect
469. #3007	C₂×C₁₃	semidirect
470. C₂×#449	C₂×C₁₃	semidirect
471. #2976	C₂×C₁₃	semidirect
577. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
579. C₂×#137	C₂²×C₁₃	semidirect
580. C₂×#137	C₂²×C₁₃	semidirect
581. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
582. C₂×#135	C₂²×C₁₃	semidirect
583. C₂²×SD₁₆	C₂²×C₁₃	semidirect
584. C₂²×D₈	C₂²×C₁₃	semidirect
586. #554	C₂²×C₁₃	semidirect
587. #550	C₂²×C₁₃	semidirect
589. #548	C₂²×C₁₃	semidirect
590. #547	C₂²×C₁₃	semidirect
593. #546	C₂²×C₁₃	semidirect
594. #546	C₂²×C₁₃	semidirect
598. #542	C₂²×C₁₃	semidirect
603. #537	C₂²×C₁₃	semidirect
604. #537	C₂²×C₁₃	semidirect
606. #535	C₂²×C₁₃	semidirect
609. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
612. C₂×#121	C₂²×C₁₃	semidirect
613. #520	C₂²×C₁₃	semidirect
614. #496	C₂²×C₁₃	semidirect
615. #495	C₂²×C₁₃	semidirect
616. #489	C₂²×C₁₃	semidirect
617. #486	C₂²×C₁₃	semidirect
618. #483	C₂²×C₁₃	semidirect
619. #483	C₂²×C₁₃	semidirect
620. #481	C₂²×C₁₃	semidirect
621. #481	C₂²×C₁₃	semidirect
622. #481	C₂²×C₁₃	semidirect
623. #481	C₂²×C₁₃	semidirect
624. #476	C₂²×C₁₃	semidirect
625. #475	C₂²×C₁₃	semidirect
626. #470	C₂²×C₁₃	semidirect
627. #469	C₂²×C₁₃	semidirect
628. #469	C₂²×C₁₃	semidirect
629. #469	C₂²×C₁₃	semidirect
630. #465	C₂²×C₁₃	semidirect
631. #465	C₂²×C₁₃	semidirect
632. #465	C₂²×C₁₃	semidirect
633. #465	C₂²×C₁₃	semidirect
634. #464	C₂²×C₁₃	semidirect
635. #464	C₂²×C₁₃	semidirect
636. #463	C₂²×C₁₃	semidirect
637. #463	C₂²×C₁₃	semidirect
638. #460	C₂²×C₁₃	semidirect
639. #459	C₂²×C₁₃	semidirect
640. #452	C₂²×C₁₃	semidirect
641. #452	C₂²×C₁₃	semidirect
642. #452	C₂²×C₁₃	semidirect
643. #452	C₂²×C₁₃	semidirect
644. #451	C₂²×C₁₃	semidirect
645. #450	C₂²×C₁₃	semidirect
646. #450	C₂²×C₁₃	semidirect
647. #450	C₂²×C₁₃	semidirect
649. #449	C₂²×C₁₃	semidirect
650. #449	C₂²×C₁₃	semidirect
651. #449	C₂²×C₁₃	semidirect
652. #449	C₂²×C₁₃	semidirect
653. #449	C₂²×C₁₃	semidirect
654. #448	C₂²×C₁₃	semidirect
655. #447	C₂²×C₁₃	semidirect
656. #447	C₂²×C₁₃	semidirect
657. #447	C₂²×C₁₃	semidirect
658. #442	C₂²×C₁₃	semidirect
659. #441	C₂²×C₁₃	semidirect
660. C₄×SD₁₆	C₂²×C₁₃	semidirect
661. C₄×SD₁₆	C₂²×C₁₃	semidirect
662. #436	C₂²×C₁₃	semidirect
663. #435	C₂²×C₁₃	semidirect
664. #435	C₂²×C₁₃	semidirect
665. C₈×D₄	C₂²×C₁₃	semidirect
666. #433	C₂²×C₁₃	semidirect
667. #417	C₂²×C₁₃	semidirect
668. #417	C₂²×C₁₃	semidirect
669. #417	C₂²×C₁₃	semidirect
670. C₂×#103	C₂²×C₁₃	semidirect
671. C₂×#102	C₂²×C₁₃	semidirect
672. C₂×#102	C₂²×C₁₃	semidirect
673. #408	C₂²×C₁₃	semidirect
674. #407	C₂²×C₁₃	semidirect
675. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
1064. C₁₃	#61623	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×#3536	2
C₁₃×#3488	2
C₁₃×#3332	2
C₁₃×#3316	2
C₁₃×#3306	2
C₁₃×#3295	2
C₁₃×#3282	2
C₁₃×#3275	2
C₁₃×#3271	2
C₁₃×#3264	2
C₁₃×#3224	2
C₁₃×#3204	2
C₁₃×#3192	2
C₁₃×#3187	2
C₁₃×#3125	2
C₁₃×#3012	2
C₁₃×#3007	2
C₂×C₁₃×#449	2
C₁₃×#2976	2
#61623	13

Subgroups — C13×#61623 #15747962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61623 #15747962