Subgroups — C₁₃×#61172 #15747511

Order 3328.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3488	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3317	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3316	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3311	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3310	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3304	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3300	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3296	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3295	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×#41	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	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#556	C₂²	1	2	yes	complemented
32	C₁₃×#554	C₂²	1	2	yes	complemented
33	C₁₃×#552	—	2	2	no	—
34	C₁₃×#552	C₂²	1	2	yes	complemented
35	C₁₃×#552	C₂²	1	2	yes	complemented
36	C₁₃×#551	—	2	2	no	—
37	C₁₃×#550	C₂²	1	2	yes	—
38	C₁₃×#548	C₂²	1	2	yes	—
39	C₁₃×#546	—	2	2	no	—
40	C₁₃×#546	C₂²	1	2	yes	—
41	D₄²×C₁₃	—	2	2	no	—
42	D₄²×C₁₃	C₂²	1	2	yes	—
43	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#542	—	2	1	no	—
45	C₁₃×#541	—	2	1	no	—
46	C₁₃×#537	—	2	1	no	—
47	C₁₃×#537	C₂²	1	1	yes	characteristic
48	C₁₃×#536	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#535	—	2	1	no	—
50	C₁₃×#535	C₂²	1	1	yes	characteristic
51	C₁₃×#533	—	2	1	no	—
52	C₁₃×#529	—	2	1	no	—
53	C₁₃×#525	—	2	1	no	—
54	C₁₃×#525	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₁₃×#121	—	2	1	no	—
57	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
58	C₁₃×#520	C₂²	1	1	yes	characteristic
59	C₁₃×#520	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#519	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#490	C₂²	1	2	yes	complemented
63	C₁₃×#489	C₂²	1	2	yes	complemented
64	C₁₃×#488	C₂²	1	2	yes	complemented
65	C₁₃×#486	C₂²	1	2	yes	complemented
66	C₁₃×#485	C₂²	1	2	yes	complemented
67	C₁₃×#483	C₂²	1	2	yes	complemented
68	C₁₃×#482	C₂²	1	2	yes	complemented
69	C₁₃×#482	C₂²	1	2	yes	complemented
70	C₁₃×#482	C₂²	1	2	yes	complemented
71	C₁₃×#481	C₂²	1	2	yes	complemented
72	C₁₃×#481	C₂²	1	2	yes	complemented
73	C₁₃×#480	C₂²	1	2	yes	complemented
74	C₁₃×#479	C₂²	1	2	yes	complemented
75	C₁₃×#478	C₂²	1	2	yes	complemented
76	C₁₃×#476	C₂²	1	2	yes	complemented
77	C₁₃×#475	C₂²	1	2	yes	complemented
78	C₁₃×#470	C₂²	1	2	yes	complemented
79	C₁₃×#468	C₂²	1	2	yes	complemented
80	C₁₃×#467	C₂²	1	2	yes	complemented
81	C₁₃×#465	C₂²	1	2	yes	complemented
82	C₁₃×#465	C₂²	1	2	yes	complemented
83	C₁₃×#465	C₂²	1	2	yes	complemented
84	C₁₃×#465	C₂²	1	2	yes	complemented
85	C₁₃×#465	C₂²	1	2	yes	complemented
86	C₁₃×#464	C₂²	1	2	yes	complemented
87	C₁₃×#464	C₂²	1	2	yes	complemented
88	C₁₃×#460	C₂²	1	2	yes	complemented
89	C₁₃×#460	C₂²	1	2	yes	complemented
90	C₁₃×#452	C₂²	1	2	yes	complemented
91	C₁₃×#452	C₂²	1	2	yes	complemented
92	C₁₃×#452	C₂²	1	2	yes	complemented
93	C₁₃×#452	C₂²	1	2	yes	complemented
94	C₁₃×#451	C₂²	1	2	yes	complemented
95	C₁₃×#450	C₂²	1	2	yes	complemented
96	C₁₃×#450	C₂²	1	2	yes	complemented
97	C₁₃×#450	C₂²	1	2	yes	complemented
98	C₁₃×#441	C₂²	1	2	yes	complemented
99	C₁₃×#440	C₂²	1	2	yes	complemented
100	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
101	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
102	C₁₃×#435	C₂²	1	2	yes	complemented
103	C₁₃×#435	C₂²	1	2	yes	complemented
104	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
105	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
106	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
107	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
109	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
110	C₁₃×#418	C₂²	1	1	yes	characteristic, complemented
111	C₁₃×#418	C₂²	1	1	yes	characteristic, complemented
112	C₁₃×#418	C₂²	1	2	yes	complemented
113	C₁₃×#417	C₂²	1	1	yes	characteristic
114	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
115	C₁₃×#417	C₂²	1	2	yes	complemented
116	C₁₃×#416	C₂²	1	1	yes	characteristic
117	C₁₃×#416	C₂²	1	1	yes	characteristic
118	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
119	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
120	C₁₃×#416	C₂²	1	2	yes	complemented
121	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
122	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
123	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
124	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
130	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
132	C₁₃×#408	C₂²	1	1	yes	characteristic, complemented
133	C₁₃×#407	C₂²	1	1	yes	characteristic, complemented
134	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₁₃×H(5,𝔽₂)	—	2	4	no	—
136	C₁₃×H(5,𝔽₂)	—	4	2	no	—
137	C₂×C₁₃×#41	—	2	1	no	—
138	C₂×C₁₃×#41	—	2	1	no	—
139	C₂×C₁₃×#41	—	2	1	no	—
140	C₂×C₁₃×#41	—	2	4	no	—
141	C₂×C₁₃×#41	—	4	2	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	1	yes	characteristic
147	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₁₃	—	2	1	no	—
151	C₂²×D₄×C₁₃	—	2	1	no	—
152	C₂²×D₄×C₁₃	—	2	1	no	—
153	C₂²×D₄×C₁₃	—	2	2	no	—
154	C₂²×D₄×C₁₃	—	2	2	no	—
155	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
156	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
157	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
158	C₂³×C₄×C₁₃	—	2	1	no	—
159	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
160	C₁₃×#137	—	2	4	no	—
161	C₁₃×#137	—	4	2	no	—
162	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
163	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
164	C₂×C₁₃×SD₁₆	—	4	2	no	—
165	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
168	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
169	C₁₃×#131	—	4	2	no	—
170	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
172	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
173	C₂²×C₈×C₁₃	—	4	2	no	—
174	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
179	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
181	C₁₃×C₄⋊Q₈	—	2	1	no	—
182	C₁₃×C₄⋊Q₈	—	2	1	no	—
183	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
184	C₁₃×#127	—	2	2	no	—
185	C₁₃×#127	C₂³	1	2	yes	—
186	C₁₃×#126	—	2	2	no	—
187	C₁₃×#126	—	2	2	no	—
188	C₁₃×#126	—	2	2	no	—
189	C₁₃×#126	—	2	2	no	—
190	C₁₃×#125	—	2	1	no	—
191	C₁₃×#125	—	2	2	no	—
192	C₁₃×#125	—	2	2	no	—
193	C₁₃×#125	—	2	2	no	—
194	C₁₃×#125	C₂³	1	2	yes	—
195	C₁₃×#124	—	2	1	no	—
196	C₁₃×#124	—	2	2	no	—
197	C₁₃×#124	—	2	2	no	—
198	C₁₃×#124	C₂³	1	2	yes	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	2	no	—
202	C₁₃×#123	—	2	2	no	—
203	C₁₃×#123	D₄	1	2	yes	—
204	C₁₃×C₂²⋊Q₈	—	2	1	no	—
205	C₁₃×C₂²⋊Q₈	—	2	1	no	—
206	C₁₃×C₂²⋊Q₈	—	2	1	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	D₄	1	1	yes	characteristic
212	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
213	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
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×#121	—	2	1	no	—
219	C₁₃×#121	—	2	2	no	—
220	C₁₃×#121	—	2	2	no	—
221	C₁₃×#121	—	2	1	no	—
222	C₁₃×#121	—	2	1	no	—
223	C₁₃×#121	—	2	1	no	—
224	C₁₃×#121	—	2	1	no	—
225	C₁₃×#121	—	2	2	no	—
226	C₁₃×#121	—	2	2	no	—
227	C₁₃×#121	—	2	2	no	—
228	C₁₃×#121	—	2	2	no	—
229	C₁₃×#121	D₄	1	1	yes	characteristic
230	C₁₃×#121	D₄	1	1	yes	characteristic
231	C₁₃×#121	C₂³	1	2	yes	—
232	C₁₃×#121	C₂³	1	2	yes	—
233	C₁₃×#121	C₂³	1	2	yes	—
234	C₁₃×#120	—	2	2	no	—
235	C₁₃×#120	—	2	2	no	—
236	C₁₃×#120	—	2	2	no	—
237	C₁₃×#120	—	2	2	no	—
238	C₁₃×#120	D₄	1	2	yes	—
239	C₄×Q₈×C₁₃	—	2	1	no	—
240	C₄×Q₈×C₁₃	—	2	1	no	—
241	C₄×Q₈×C₁₃	—	2	1	no	—
242	C₄×Q₈×C₁₃	—	2	2	no	—
243	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
244	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
245	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
246	C₄×D₄×C₁₃	—	2	1	no	—
247	C₄×D₄×C₁₃	—	2	2	no	—
248	C₄×D₄×C₁₃	—	2	2	no	—
249	C₄×D₄×C₁₃	—	2	2	no	—
250	C₄×D₄×C₁₃	—	2	2	no	—
251	C₄×D₄×C₁₃	—	2	2	no	—
252	C₄×D₄×C₁₃	C₂³	1	2	yes	—
253	C₄×D₄×C₁₃	C₂³	1	2	yes	—
254	C₄×D₄×C₁₃	C₂³	1	2	yes	—
255	C₁₃×#117	—	2	1	no	—
256	C₁₃×#117	—	2	1	no	—
257	C₁₃×#117	—	2	1	no	—
258	C₁₃×#117	—	2	2	no	—
259	C₁₃×#117	—	2	2	no	—
260	C₁₃×#117	—	2	2	no	—
261	C₁₃×#117	C₂³	1	1	yes	characteristic
262	C₁₃×#117	C₂³	1	1	yes	characteristic
263	C₁₃×#117	C₂³	1	1	yes	characteristic
264	C₁₃×#117	C₂³	1	1	yes	characteristic
265	C₁₃×#117	C₂³	1	2	yes	—
266	C₁₃×#117	C₂³	1	1	yes	characteristic
267	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
273	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²×C₁₃	—	2	1	no	—
279	C₁₃×#107	C₂³	1	2	yes	—
280	C₁₃×#107	C₂³	1	2	yes	—
281	C₁₃×#106	C₂³	1	2	yes	—
282	C₁₃×#106	C₂³	1	2	yes	—
283	C₁₃×#106	C₂³	1	2	yes	—
284	C₁₃×#106	C₂³	1	2	yes	—
285	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
286	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
287	C₁₃×#103	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	1	yes	characteristic
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	1	yes	characteristic
291	C₁₃×#103	C₂³	1	1	yes	characteristic
292	C₁₃×#103	C₂³	1	1	yes	characteristic
293	C₁₃×#103	C₂³	1	1	yes	characteristic
294	C₁₃×#103	C₂³	1	1	yes	characteristic
295	C₁₃×#103	C₂³	1	2	yes	—
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#103	C₂³	1	2	yes	—
298	C₁₃×#103	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	1	yes	characteristic
300	C₁₃×#102	C₂³	1	2	yes	—
301	C₁₃×#102	C₂³	1	1	yes	characteristic
302	C₁₃×#102	C₂³	1	1	yes	characteristic
303	C₁₃×#102	C₂³	1	1	yes	characteristic
304	C₁₃×#102	C₂³	1	1	yes	characteristic
305	C₁₃×#102	C₂³	1	1	yes	characteristic
306	C₁₃×#102	C₂³	1	1	yes	characteristic
307	C₁₃×#102	C₂³	1	1	yes	characteristic
308	C₁₃×#102	C₂³	1	2	yes	—
309	C₁₃×#102	C₂³	1	2	yes	—
310	C₁₃×#102	C₂³	1	2	yes	—
311	C₁₃×#102	C₂³	1	2	yes	—
312	C₁₃×#102	C₂³	1	2	yes	—
313	C₁₃×#102	C₂³	1	2	yes	—
314	C₁₃×#102	C₂³	1	2	yes	—
315	C₁₃×C₂²⋊C₈	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×#97	C₂³	1	2	yes	—
320	C₄×C₈×C₁₃	C₂³	1	2	yes	—
321	#61172	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂⁴×C₁₃	—	2	1	no	—
323	C₂⁴×C₁₃	—	2	2	no	—
324	C₂⁴×C₁₃	—	2	1	no	—
325	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₁₃×#41	—	2	2	no	—
327	C₁₃×#41	—	2	2	no	—
328	C₁₃×#41	—	2	2	no	—
329	C₁₃×#41	—	2	2	no	—
330	C₁₃×#41	—	2	4	no	—
331	C₁₃×#41	—	2	2	no	—
332	C₁₃×#41	—	2	2	no	—
333	C₁₃×#41	—	2	2	no	—
334	C₁₃×#41	—	4	4	no	—
335	C₁₃×#41	—	4	1	no	—
336	C₁₃×#41	—	4	1	no	—
337	C₁₃×#41	—	4	2	no	—
338	C₁₃×#41	—	4	4	no	—
339	C₁₃×#41	—	4	4	no	—
340	C₁₃×#41	#41	1	4	yes	—
341	C₂×Q₈×C₁₃	—	2	1	no	—
342	C₂×Q₈×C₁₃	—	2	1	no	—
343	C₂×Q₈×C₁₃	—	2	2	no	—
344	C₂×Q₈×C₁₃	—	2	2	no	—
345	C₂×Q₈×C₁₃	—	2	2	no	—
346	C₂×Q₈×C₁₃	—	2	2	no	—
347	C₂×Q₈×C₁₃	—	4	1	no	—
348	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
349	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
350	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
351	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₁₃	—	2	1	no	—
353	C₂×D₄×C₁₃	—	2	2	no	—
354	C₂×D₄×C₁₃	—	2	4	no	—
355	C₂×D₄×C₁₃	—	2	2	no	—
356	C₂×D₄×C₁₃	—	2	1	no	—
357	C₂×D₄×C₁₃	—	2	1	no	—
358	C₂×D₄×C₁₃	—	2	2	no	—
359	C₂×D₄×C₁₃	—	2	1	no	—
360	C₂×D₄×C₁₃	—	2	2	no	—
361	C₂×D₄×C₁₃	—	2	2	no	—
362	C₂×D₄×C₁₃	—	2	1	no	—
363	C₂×D₄×C₁₃	—	2	2	no	—
364	C₂×D₄×C₁₃	—	2	1	no	—
365	C₂×D₄×C₁₃	—	2	2	no	—
366	C₂×D₄×C₁₃	—	2	2	no	—
367	C₂×D₄×C₁₃	—	2	2	no	—
368	C₂×D₄×C₁₃	—	2	2	no	—
369	C₂×D₄×C₁₃	—	4	1	no	—
370	C₂×D₄×C₁₃	—	4	2	no	—
371	C₂×D₄×C₁₃	—	4	4	no	—
372	C₂×D₄×C₁₃	—	4	8	no	—
373	C₂×D₄×C₁₃	—	4	4	no	—
374	C₂×D₄×C₁₃	—	8	4	no	—
375	C₂×D₄×C₁₃	—	8	2	no	—
376	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
377	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
378	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
379	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
380	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
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	2	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	1	no	—
390	C₂²×C₄×C₁₃	—	2	1	no	—
391	C₂²×C₄×C₁₃	—	2	1	no	—
392	C₂²×C₄×C₁₃	—	2	2	no	—
393	C₂²×C₄×C₁₃	—	2	1	no	—
394	C₂²×C₄×C₁₃	—	2	1	no	—
395	C₂²×C₄×C₁₃	—	2	2	no	—
396	C₂²×C₄×C₁₃	—	2	1	no	—
397	C₂²×C₄×C₁₃	—	2	2	no	—
398	C₂²×C₄×C₁₃	—	4	4	no	—
399	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
404	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
406	C₁₃×Q₁₆	—	2	4	no	—
407	C₁₃×Q₁₆	—	4	2	no	—
408	C₁₃×SD₁₆	—	2	4	no	—
409	C₁₃×SD₁₆	—	4	2	no	—
410	C₁₃×SD₁₆	—	4	2	no	—
411	C₁₃×SD₁₆	—	4	2	no	—
412	C₁₃×M₁₆	—	2	2	no	—
413	C₁₃×M₁₆	—	2	2	no	—
414	C₁₃×M₁₆	—	4	2	no	—
415	C₂×C₈×C₁₃	—	2	2	no	—
416	C₂×C₈×C₁₃	—	2	2	no	—
417	C₂×C₈×C₁₃	—	4	1	no	—
418	C₂×C₈×C₁₃	—	4	1	no	—
419	C₂×C₈×C₁₃	—	4	1	no	—
420	C₂×C₈×C₁₃	—	4	1	no	—
421	C₂×C₈×C₁₃	—	4	2	no	—
422	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
423	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
424	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
426	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
427	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
428	C₁₃×C₄⋊C₄	—	2	1	no	—
429	C₁₃×C₄⋊C₄	—	2	2	no	—
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	2	no	—
440	C₁₃×C₄⋊C₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
445	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
446	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
447	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
448	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
450	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
451	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
453	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
454	C₁₃×C₂²⋊C₄	—	2	1	no	—
455	C₁₃×C₂²⋊C₄	—	2	1	no	—
456	C₁₃×C₂²⋊C₄	—	2	1	no	—
457	C₁₃×C₂²⋊C₄	—	2	1	no	—
458	C₁₃×C₂²⋊C₄	—	2	2	no	—
459	C₁₃×C₂²⋊C₄	—	2	2	no	—
460	C₁₃×C₂²⋊C₄	—	2	2	no	—
461	C₁₃×C₂²⋊C₄	—	2	2	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	2	no	—
469	C₁₃×C₂²⋊C₄	—	2	2	no	—
470	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
471	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
472	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
473	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
474	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
475	C₄²×C₁₃	—	2	1	no	—
476	C₄²×C₁₃	—	2	1	no	—
477	C₄²×C₁₃	—	2	1	no	—
478	C₄²×C₁₃	—	2	1	no	—
479	C₄²×C₁₃	—	2	2	no	—
480	C₄²×C₁₃	—	2	2	no	—
481	C₄²×C₁₃	—	2	2	no	—
482	C₄²×C₁₃	—	2	2	no	—
483	C₄²×C₁₃	C₂⁴	1	2	yes	—
484	#3495	C₂×C₁₃	1	1	yes	characteristic, complemented
485	#3488	C₂×C₁₃	1	1	yes	characteristic
486	#3317	C₂×C₁₃	1	2	yes	complemented
487	#3316	C₂×C₁₃	1	2	yes	complemented
488	#3311	C₂×C₁₃	1	2	yes	complemented
489	#3310	C₂×C₁₃	1	2	yes	complemented
490	#3304	C₂×C₁₃	1	2	yes	complemented
491	#3300	C₂×C₁₃	1	2	yes	complemented
492	#3296	C₂×C₁₃	1	2	yes	complemented
493	#3295	C₂×C₁₃	1	2	yes	complemented
494	#3136	C₂×C₁₃	1	1	yes	characteristic, complemented
495	#3099	C₂×C₁₃	1	1	yes	characteristic, complemented
496	#3094	C₂×C₁₃	1	1	yes	characteristic, complemented
497	#3084	C₂×C₁₃	1	1	yes	characteristic, complemented
498	#3063	C₂×C₁₃	1	1	yes	characteristic, complemented
499	C₂×#465	C₂×C₁₃	1	1	yes	characteristic, complemented
500	#3043	C₂×C₁₃	1	1	yes	characteristic, complemented
501	#3009	C₂×C₁₃	1	1	yes	characteristic, complemented
502	#3007	C₂×C₁₃	1	1	yes	characteristic, complemented
503	#2947	C₂×C₁₃	1	1	yes	characteristic, complemented
504	#2929	C₂×C₁₃	1	1	yes	characteristic, complemented
505	#2897	C₂×C₁₃	1	1	yes	characteristic, complemented
506	C₂×#416	C₂×C₁₃	1	1	yes	characteristic, complemented
507	C₂³×C₁₃	—	2	2	no	—
508	C₂³×C₁₃	—	2	2	no	—
509	C₂³×C₁₃	—	2	1	no	—
510	C₂³×C₁₃	—	2	2	no	—
511	C₂³×C₁₃	—	2	1	no	—
512	C₂³×C₁₃	—	4	1	no	—
513	C₂³×C₁₃	—	4	2	no	—
514	C₂³×C₁₃	—	4	4	no	—
515	C₂³×C₁₃	—	4	2	no	—
516	C₂³×C₁₃	—	4	2	no	—
517	C₂³×C₁₃	—	8	1	no	—
518	C₂³×C₁₃	—	8	1	no	—
519	C₂³×C₁₃	—	8	2	no	—
520	C₂³×C₁₃	—	8	1	no	—
521	C₂³×C₁₃	—	8	2	no	—
522	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
523	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
524	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
525	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
526	Q₈×C₁₃	—	2	2	no	—
527	Q₈×C₁₃	—	2	1	no	—
528	Q₈×C₁₃	—	2	2	no	—
529	Q₈×C₁₃	—	2	1	no	—
530	Q₈×C₁₃	—	2	2	no	—
531	Q₈×C₁₃	—	2	1	no	—
532	Q₈×C₁₃	—	4	2	no	—
533	Q₈×C₁₃	—	4	2	no	—
534	Q₈×C₁₃	—	8	2	no	—
535	Q₈×C₁₃	C₂×#41	1	2	yes	—
536	D₄×C₁₃	—	2	4	no	—
537	D₄×C₁₃	—	2	4	no	—
538	D₄×C₁₃	—	2	4	no	—
539	D₄×C₁₃	—	2	2	no	—
540	D₄×C₁₃	—	2	2	no	—
541	D₄×C₁₃	—	2	1	no	—
542	D₄×C₁₃	—	2	1	no	—
543	D₄×C₁₃	—	2	2	no	—
544	D₄×C₁₃	—	2	1	no	—
545	D₄×C₁₃	—	4	2	no	—
546	D₄×C₁₃	—	4	4	no	—
547	D₄×C₁₃	—	4	2	no	—
548	D₄×C₁₃	—	4	4	no	—
549	D₄×C₁₃	—	4	2	no	—
550	D₄×C₁₃	—	4	2	no	—
551	D₄×C₁₃	—	4	2	no	—
552	D₄×C₁₃	—	4	4	no	—
553	D₄×C₁₃	—	4	2	no	—
554	D₄×C₁₃	—	8	2	no	—
555	D₄×C₁₃	—	8	2	no	—
556	D₄×C₁₃	—	8	2	no	—
557	D₄×C₁₃	—	8	2	no	—
558	D₄×C₁₃	C₂×#41	1	2	yes	—
559	C₂×C₄×C₁₃	—	2	2	no	—
560	C₂×C₄×C₁₃	—	2	1	no	—
561	C₂×C₄×C₁₃	—	2	2	no	—
562	C₂×C₄×C₁₃	—	2	2	no	—
563	C₂×C₄×C₁₃	—	2	4	no	—
564	C₂×C₄×C₁₃	—	2	1	no	—
565	C₂×C₄×C₁₃	—	2	1	no	—
566	C₂×C₄×C₁₃	—	2	2	no	—
567	C₂×C₄×C₁₃	—	2	1	no	—
568	C₂×C₄×C₁₃	—	2	1	no	—
569	C₂×C₄×C₁₃	—	2	2	no	—
570	C₂×C₄×C₁₃	—	2	1	no	—
571	C₂×C₄×C₁₃	—	2	1	no	—
572	C₂×C₄×C₁₃	—	2	1	no	—
573	C₂×C₄×C₁₃	—	2	2	no	—
574	C₂×C₄×C₁₃	—	2	1	no	—
575	C₂×C₄×C₁₃	—	2	2	no	—
576	C₂×C₄×C₁₃	—	2	2	no	—
577	C₂×C₄×C₁₃	—	2	1	no	—
578	C₂×C₄×C₁₃	—	4	2	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	2	no	—
586	C₂×C₄×C₁₃	—	8	2	no	—
587	C₂×C₄×C₁₃	—	8	1	no	—
588	C₂×C₄×C₁₃	—	8	1	no	—
589	C₂×C₄×C₁₃	—	8	1	no	—
590	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
591	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
597	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
598	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
599	C₈×C₁₃	—	2	2	no	—
600	C₈×C₁₃	—	2	1	no	—
601	C₈×C₁₃	—	2	1	no	—
602	C₈×C₁₃	—	2	1	no	—
603	C₈×C₁₃	—	2	1	no	—
604	C₈×C₁₃	—	2	2	no	—
605	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
606	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
607	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
608	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic, complemented
609	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
610	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
611	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	#556	C₂²×C₁₃	1	2	yes	complemented
613	#554	C₂²×C₁₃	1	2	yes	complemented
614	#552	—	2	2	no	—
615	#552	C₂²×C₁₃	1	2	yes	complemented
616	#552	C₂²×C₁₃	1	2	yes	complemented
617	#551	—	2	2	no	—
618	#550	C₂²×C₁₃	1	2	yes	—
619	#548	C₂²×C₁₃	1	2	yes	—
620	#546	—	2	2	no	—
621	#546	C₂²×C₁₃	1	2	yes	—
622	D₄²	—	2	2	no	—
623	D₄²	C₂²×C₁₃	1	2	yes	—
624	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
625	#542	—	2	1	no	—
626	#541	—	2	1	no	—
627	#537	—	2	1	no	—
628	#537	C₂²×C₁₃	1	1	yes	characteristic
629	#536	C₂²×C₁₃	1	1	yes	characteristic, complemented
630	#535	—	2	1	no	—
631	#535	C₂²×C₁₃	1	1	yes	characteristic
632	#533	—	2	1	no	—
633	#529	—	2	1	no	—
634	#525	—	2	1	no	—
635	#525	C₂²×C₁₃	1	1	yes	characteristic
636	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
637	C₂×#121	—	2	1	no	—
638	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
639	#520	C₂²×C₁₃	1	1	yes	characteristic
640	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
641	#519	C₂²×C₁₃	1	1	yes	characteristic, complemented
642	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
643	#490	C₂²×C₁₃	1	2	yes	complemented
644	#489	C₂²×C₁₃	1	2	yes	complemented
645	#488	C₂²×C₁₃	1	2	yes	complemented
646	#486	C₂²×C₁₃	1	2	yes	complemented
647	#485	C₂²×C₁₃	1	2	yes	complemented
648	#483	C₂²×C₁₃	1	2	yes	complemented
649	#482	C₂²×C₁₃	1	2	yes	complemented
650	#482	C₂²×C₁₃	1	2	yes	complemented
651	#482	C₂²×C₁₃	1	2	yes	complemented
652	#481	C₂²×C₁₃	1	2	yes	complemented
653	#481	C₂²×C₁₃	1	2	yes	complemented
654	#480	C₂²×C₁₃	1	2	yes	complemented
655	#479	C₂²×C₁₃	1	2	yes	complemented
656	#478	C₂²×C₁₃	1	2	yes	complemented
657	#476	C₂²×C₁₃	1	2	yes	complemented
658	#475	C₂²×C₁₃	1	2	yes	complemented
659	#470	C₂²×C₁₃	1	2	yes	complemented
660	#468	C₂²×C₁₃	1	2	yes	complemented
661	#467	C₂²×C₁₃	1	2	yes	complemented
662	#465	C₂²×C₁₃	1	2	yes	complemented
663	#465	C₂²×C₁₃	1	2	yes	complemented
664	#465	C₂²×C₁₃	1	2	yes	complemented
665	#465	C₂²×C₁₃	1	2	yes	complemented
666	#465	C₂²×C₁₃	1	2	yes	complemented
667	#464	C₂²×C₁₃	1	2	yes	complemented
668	#464	C₂²×C₁₃	1	2	yes	complemented
669	#460	C₂²×C₁₃	1	2	yes	complemented
670	#460	C₂²×C₁₃	1	2	yes	complemented
671	#452	C₂²×C₁₃	1	2	yes	complemented
672	#452	C₂²×C₁₃	1	2	yes	complemented
673	#452	C₂²×C₁₃	1	2	yes	complemented
674	#452	C₂²×C₁₃	1	2	yes	complemented
675	#451	C₂²×C₁₃	1	2	yes	complemented
676	#450	C₂²×C₁₃	1	2	yes	complemented
677	#450	C₂²×C₁₃	1	2	yes	complemented
678	#450	C₂²×C₁₃	1	2	yes	complemented
679	#441	C₂²×C₁₃	1	2	yes	complemented
680	#440	C₂²×C₁₃	1	2	yes	complemented
681	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
682	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
683	#435	C₂²×C₁₃	1	2	yes	complemented
684	#435	C₂²×C₁₃	1	2	yes	complemented
685	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
686	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
687	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
688	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
689	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
690	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
691	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
692	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
693	#418	C₂²×C₁₃	1	2	yes	complemented
694	#417	C₂²×C₁₃	1	1	yes	characteristic
695	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
696	#417	C₂²×C₁₃	1	2	yes	complemented
697	#416	C₂²×C₁₃	1	1	yes	characteristic
698	#416	C₂²×C₁₃	1	1	yes	characteristic
699	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
700	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
701	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
702	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
703	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
704	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
705	#416	C₂²×C₁₃	1	2	yes	complemented
706	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
707	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
708	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
709	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
710	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
711	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
712	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
713	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
714	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
715	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
716	C₂²×C₁₃	—	2	1	no	—
717	C₂²×C₁₃	—	2	1	no	—
718	C₂²×C₁₃	—	2	1	no	—
719	C₂²×C₁₃	—	2	1	no	—
720	C₂²×C₁₃	—	2	2	no	—
721	C₂²×C₁₃	—	2	1	no	—
722	C₂²×C₁₃	—	2	1	no	—
723	C₂²×C₁₃	—	2	2	no	—
724	C₂²×C₁₃	—	2	2	no	—
725	C₂²×C₁₃	—	2	2	no	—
726	C₂²×C₁₃	—	2	1	no	—
727	C₂²×C₁₃	—	4	4	no	—
728	C₂²×C₁₃	—	4	1	no	—
729	C₂²×C₁₃	—	4	1	no	—
730	C₂²×C₁₃	—	4	1	no	—
731	C₂²×C₁₃	—	4	2	no	—
732	C₂²×C₁₃	—	4	1	no	—
733	C₂²×C₁₃	—	4	2	no	—
734	C₂²×C₁₃	—	4	2	no	—
735	C₂²×C₁₃	—	4	1	no	—
736	C₂²×C₁₃	—	8	4	no	—
737	C₂²×C₁₃	—	16	2	no	—
738	C₂²×C₁₃	—	16	4	no	—
739	C₂²×C₁₃	#546	1	2	yes	—
740	C₂²×C₁₃	#577	1	2	yes	—
741	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
742	C₄×C₁₃	—	2	2	no	—
743	C₄×C₁₃	—	2	1	no	—
744	C₄×C₁₃	—	2	1	no	—
745	C₄×C₁₃	—	2	2	no	—
746	C₄×C₁₃	—	2	2	no	—
747	C₄×C₁₃	—	2	2	no	—
748	C₄×C₁₃	—	4	1	no	—
749	C₄×C₁₃	—	4	2	no	—
750	C₄×C₁₃	—	4	1	no	—
751	C₄×C₁₃	—	4	1	no	—
752	C₄×C₁₃	—	4	2	no	—
753	C₄×C₁₃	—	4	1	no	—
754	C₄×C₁₃	—	4	1	no	—
755	C₄×C₁₃	—	4	2	no	—
756	C₄×C₁₃	#546	1	2	yes	—
757	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
758	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
759	H(5,𝔽₂)	—	2	4	no	—
760	H(5,𝔽₂)	—	4	2	no	—
761	C₂×#41	—	2	1	no	—
762	C₂×#41	—	2	1	no	—
763	C₂×#41	—	2	1	no	—
764	C₂×#41	—	2	4	no	—
765	C₂×#41	—	4	2	no	—
766	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
767	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
768	C₂×#41	C₂³×C₁₃	1	2	yes	—
769	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
770	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
771	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
772	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
773	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
774	C₂²×D₄	—	2	1	no	—
775	C₂²×D₄	—	2	1	no	—
776	C₂²×D₄	—	2	1	no	—
777	C₂²×D₄	—	2	2	no	—
778	C₂²×D₄	—	2	2	no	—
779	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
780	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
781	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
782	C₂³×C₄	—	2	1	no	—
783	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
784	#137	—	2	4	no	—
785	#137	—	4	2	no	—
786	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
787	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
788	C₂×SD₁₆	—	4	2	no	—
789	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
790	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
791	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
792	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
793	#131	—	4	2	no	—
794	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
795	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
796	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
797	C₂²×C₈	—	4	2	no	—
798	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
799	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
800	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
801	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
802	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
803	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
804	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
805	C₄⋊Q₈	—	2	1	no	—
806	C₄⋊Q₈	—	2	1	no	—
807	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
808	#127	—	2	2	no	—
809	#127	C₂³×C₁₃	1	2	yes	—
810	#126	—	2	2	no	—
811	#126	—	2	2	no	—
812	#126	—	2	2	no	—
813	#126	—	2	2	no	—
814	#125	—	2	1	no	—
815	#125	—	2	2	no	—
816	#125	—	2	2	no	—
817	#125	—	2	2	no	—
818	#125	C₂³×C₁₃	1	2	yes	—
819	#124	—	2	1	no	—
820	#124	—	2	2	no	—
821	#124	—	2	2	no	—
822	#124	C₂³×C₁₃	1	2	yes	—
823	#123	—	2	2	no	—
824	#123	—	2	2	no	—
825	#123	—	2	2	no	—
826	#123	—	2	2	no	—
827	#123	D₄×C₁₃	1	2	yes	—
828	C₂²⋊Q₈	—	2	1	no	—
829	C₂²⋊Q₈	—	2	1	no	—
830	C₂²⋊Q₈	—	2	1	no	—
831	C₂²⋊Q₈	—	2	2	no	—
832	C₂²⋊Q₈	—	2	2	no	—
833	C₂²⋊Q₈	—	2	2	no	—
834	C₂²⋊Q₈	—	2	2	no	—
835	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
836	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
837	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
838	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
839	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
840	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
841	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
842	#121	—	2	1	no	—
843	#121	—	2	2	no	—
844	#121	—	2	2	no	—
845	#121	—	2	1	no	—
846	#121	—	2	1	no	—
847	#121	—	2	1	no	—
848	#121	—	2	1	no	—
849	#121	—	2	2	no	—
850	#121	—	2	2	no	—
851	#121	—	2	2	no	—
852	#121	—	2	2	no	—
853	#121	D₄×C₁₃	1	1	yes	characteristic
854	#121	D₄×C₁₃	1	1	yes	characteristic
855	#121	C₂³×C₁₃	1	2	yes	—
856	#121	C₂³×C₁₃	1	2	yes	—
857	#121	C₂³×C₁₃	1	2	yes	—
858	#120	—	2	2	no	—
859	#120	—	2	2	no	—
860	#120	—	2	2	no	—
861	#120	—	2	2	no	—
862	#120	D₄×C₁₃	1	2	yes	—
863	C₄×Q₈	—	2	1	no	—
864	C₄×Q₈	—	2	1	no	—
865	C₄×Q₈	—	2	1	no	—
866	C₄×Q₈	—	2	2	no	—
867	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
868	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
869	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	2	no	—
872	C₄×D₄	—	2	2	no	—
873	C₄×D₄	—	2	2	no	—
874	C₄×D₄	—	2	2	no	—
875	C₄×D₄	—	2	2	no	—
876	C₄×D₄	C₂³×C₁₃	1	2	yes	—
877	C₄×D₄	C₂³×C₁₃	1	2	yes	—
878	C₄×D₄	C₂³×C₁₃	1	2	yes	—
879	#117	—	2	1	no	—
880	#117	—	2	1	no	—
881	#117	—	2	1	no	—
882	#117	—	2	2	no	—
883	#117	—	2	2	no	—
884	#117	—	2	2	no	—
885	#117	C₂³×C₁₃	1	1	yes	characteristic
886	#117	C₂³×C₁₃	1	1	yes	characteristic
887	#117	C₂³×C₁₃	1	1	yes	characteristic
888	#117	C₂³×C₁₃	1	1	yes	characteristic
889	#117	C₂³×C₁₃	1	2	yes	—
890	#117	C₂³×C₁₃	1	1	yes	characteristic
891	C₂×C₄⋊C₄	—	2	1	no	—
892	C₂×C₄⋊C₄	—	2	1	no	—
893	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
894	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
895	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
896	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
897	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
898	C₂×C₂²⋊C₄	—	2	1	no	—
899	C₂×C₂²⋊C₄	—	2	1	no	—
900	C₂×C₂²⋊C₄	—	2	1	no	—
901	C₂×C₂²⋊C₄	—	2	2	no	—
902	C₂×C₄²	—	2	1	no	—
903	#107	C₂³×C₁₃	1	2	yes	—
904	#107	C₂³×C₁₃	1	2	yes	—
905	#106	C₂³×C₁₃	1	2	yes	—
906	#106	C₂³×C₁₃	1	2	yes	—
907	#106	C₂³×C₁₃	1	2	yes	—
908	#106	C₂³×C₁₃	1	2	yes	—
909	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
910	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
911	#103	C₂³×C₁₃	1	1	yes	characteristic
912	#103	C₂³×C₁₃	1	1	yes	characteristic
913	#103	C₂³×C₁₃	1	1	yes	characteristic
914	#103	C₂³×C₁₃	1	1	yes	characteristic
915	#103	C₂³×C₁₃	1	1	yes	characteristic
916	#103	C₂³×C₁₃	1	1	yes	characteristic
917	#103	C₂³×C₁₃	1	1	yes	characteristic
918	#103	C₂³×C₁₃	1	1	yes	characteristic
919	#103	C₂³×C₁₃	1	2	yes	—
920	#103	C₂³×C₁₃	1	2	yes	—
921	#103	C₂³×C₁₃	1	2	yes	—
922	#103	C₂³×C₁₃	1	2	yes	—
923	#102	C₂³×C₁₃	1	1	yes	characteristic
924	#102	C₂³×C₁₃	1	2	yes	—
925	#102	C₂³×C₁₃	1	1	yes	characteristic
926	#102	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
932	#102	C₂³×C₁₃	1	2	yes	—
933	#102	C₂³×C₁₃	1	2	yes	—
934	#102	C₂³×C₁₃	1	2	yes	—
935	#102	C₂³×C₁₃	1	2	yes	—
936	#102	C₂³×C₁₃	1	2	yes	—
937	#102	C₂³×C₁₃	1	2	yes	—
938	#102	C₂³×C₁₃	1	2	yes	—
939	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
940	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
941	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
942	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
943	#97	C₂³×C₁₃	1	2	yes	—
944	C₄×C₈	C₂³×C₁₃	1	2	yes	—
945	C₂×C₁₃	—	2	2	no	—
946	C₂×C₁₃	—	2	2	no	—
947	C₂×C₁₃	—	4	1	no	—
948	C₂×C₁₃	—	4	2	no	—
949	C₂×C₁₃	—	4	2	no	—
950	C₂×C₁₃	—	8	1	no	—
951	C₂×C₁₃	—	8	2	no	—
952	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
953	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
954	C₂×C₁₃	#3584	1	1	yes	characteristic
955	C₂⁴	—	2	1	no	—
956	C₂⁴	—	2	2	no	—
957	C₂⁴	—	2	1	no	—
958	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
959	#41	—	2	2	no	—
960	#41	—	2	2	no	—
961	#41	—	2	2	no	—
962	#41	—	2	2	no	—
963	#41	—	2	4	no	—
964	#41	—	2	2	no	—
965	#41	—	2	2	no	—
966	#41	—	2	2	no	—
967	#41	—	4	4	no	—
968	#41	—	4	1	no	—
969	#41	—	4	1	no	—
970	#41	—	4	2	no	—
971	#41	—	4	4	no	—
972	#41	—	4	4	no	—
973	#41	C₁₃×#41	1	4	yes	—
974	C₂×Q₈	—	2	1	no	—
975	C₂×Q₈	—	2	1	no	—
976	C₂×Q₈	—	2	2	no	—
977	C₂×Q₈	—	2	2	no	—
978	C₂×Q₈	—	2	2	no	—
979	C₂×Q₈	—	2	2	no	—
980	C₂×Q₈	—	4	1	no	—
981	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
982	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
983	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
984	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	4	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	2	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	4	1	no	—
1003	C₂×D₄	—	4	2	no	—
1004	C₂×D₄	—	4	4	no	—
1005	C₂×D₄	—	4	8	no	—
1006	C₂×D₄	—	4	4	no	—
1007	C₂×D₄	—	8	4	no	—
1008	C₂×D₄	—	8	2	no	—
1009	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1010	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1011	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1012	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1013	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1014	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1015	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	2	no	—
1018	C₂²×C₄	—	2	2	no	—
1019	C₂²×C₄	—	2	1	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	1	no	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	2	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	2	no	—
1029	C₂²×C₄	—	2	1	no	—
1030	C₂²×C₄	—	2	2	no	—
1031	C₂²×C₄	—	4	4	no	—
1032	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1033	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1034	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1035	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1036	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1037	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1038	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1039	Q₁₆	—	2	4	no	—
1040	Q₁₆	—	4	2	no	—
1041	SD₁₆	—	2	4	no	—
1042	SD₁₆	—	4	2	no	—
1043	SD₁₆	—	4	2	no	—
1044	SD₁₆	—	4	2	no	—
1045	M₁₆	—	2	2	no	—
1046	M₁₆	—	2	2	no	—
1047	M₁₆	—	4	2	no	—
1048	C₂×C₈	—	2	2	no	—
1049	C₂×C₈	—	2	2	no	—
1050	C₂×C₈	—	4	1	no	—
1051	C₂×C₈	—	4	1	no	—
1052	C₂×C₈	—	4	1	no	—
1053	C₂×C₈	—	4	1	no	—
1054	C₂×C₈	—	4	2	no	—
1055	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1056	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1057	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1058	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1059	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1060	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
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	1	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	—	2	2	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1078	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1079	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1080	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1081	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1082	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1083	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1084	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1085	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1086	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	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	2	no	—
1096	C₂²⋊C₄	—	2	2	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1104	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1105	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1106	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1107	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1108	C₄²	—	2	1	no	—
1109	C₄²	—	2	1	no	—
1110	C₄²	—	2	1	no	—
1111	C₄²	—	2	1	no	—
1112	C₄²	—	2	2	no	—
1113	C₄²	—	2	2	no	—
1114	C₄²	—	2	2	no	—
1115	C₄²	—	2	2	no	—
1116	C₄²	C₂⁴×C₁₃	1	2	yes	—
1117	C₁₃	#61172	1	1	yes	characteristic, direct product factor, Sylow
1118	C₂³	—	2	2	no	—
1119	C₂³	—	2	2	no	—
1120	C₂³	—	2	1	no	—
1121	C₂³	—	2	2	no	—
1122	C₂³	—	2	1	no	—
1123	C₂³	—	4	1	no	—
1124	C₂³	—	4	2	no	—
1125	C₂³	—	4	4	no	—
1126	C₂³	—	4	2	no	—
1127	C₂³	—	4	2	no	—
1128	C₂³	—	8	1	no	—
1129	C₂³	—	8	1	no	—
1130	C₂³	—	8	2	no	—
1131	C₂³	—	8	1	no	—
1132	C₂³	—	8	2	no	—
1133	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1134	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1135	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1136	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1137	Q₈	—	2	2	no	—
1138	Q₈	—	2	1	no	—
1139	Q₈	—	2	2	no	—
1140	Q₈	—	2	1	no	—
1141	Q₈	—	2	2	no	—
1142	Q₈	—	2	1	no	—
1143	Q₈	—	4	2	no	—
1144	Q₈	—	4	2	no	—
1145	Q₈	—	8	2	no	—
1146	Q₈	C₂×C₁₃×#41	1	2	yes	—
1147	D₄	—	2	4	no	—
1148	D₄	—	2	4	no	—
1149	D₄	—	2	4	no	—
1150	D₄	—	2	2	no	—
1151	D₄	—	2	2	no	—
1152	D₄	—	2	1	no	—
1153	D₄	—	2	1	no	—
1154	D₄	—	2	2	no	—
1155	D₄	—	2	1	no	—
1156	D₄	—	4	2	no	—
1157	D₄	—	4	4	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	4	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	4	2	no	—
1163	D₄	—	4	4	no	—
1164	D₄	—	4	2	no	—
1165	D₄	—	8	2	no	—
1166	D₄	—	8	2	no	—
1167	D₄	—	8	2	no	—
1168	D₄	—	8	2	no	—
1169	D₄	C₂×C₁₃×#41	1	2	yes	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	4	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	2	no	—
1187	C₂×C₄	—	2	2	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	4	4	no	—
1191	C₂×C₄	—	4	2	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	4	2	no	—
1194	C₂×C₄	—	4	2	no	—
1195	C₂×C₄	—	4	2	no	—
1196	C₂×C₄	—	8	2	no	—
1197	C₂×C₄	—	8	1	no	—
1198	C₂×C₄	—	8	2	no	—
1199	C₂×C₄	—	8	1	no	—
1200	C₂×C₄	—	8	1	no	—
1201	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1202	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1203	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1204	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1205	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1207	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1208	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1209	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1210	C₈	—	2	2	no	—
1211	C₈	—	2	1	no	—
1212	C₈	—	2	1	no	—
1213	C₈	—	2	1	no	—
1214	C₈	—	2	1	no	—
1215	C₈	—	2	2	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	2	no	—
1221	C₂²	—	2	1	no	—
1222	C₂²	—	2	2	no	—
1223	C₂²	—	2	1	no	—
1224	C₂²	—	2	1	no	—
1225	C₂²	—	2	2	no	—
1226	C₂²	—	2	2	no	—
1227	C₂²	—	4	4	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	2	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	4	1	no	—
1233	C₂²	—	4	2	no	—
1234	C₂²	—	4	1	no	—
1235	C₂²	—	4	2	no	—
1236	C₂²	—	8	4	no	—
1237	C₂²	—	16	2	no	—
1238	C₂²	—	16	4	no	—
1239	C₂²	C₁₃×#546	1	2	yes	—
1240	C₂²	C₁₃×#577	1	2	yes	—
1241	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1242	C₄	—	2	2	no	—
1243	C₄	—	2	2	no	—
1244	C₄	—	2	1	no	—
1245	C₄	—	2	1	no	—
1246	C₄	—	2	2	no	—
1247	C₄	—	2	2	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	2	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	2	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	2	no	—
1256	C₄	C₁₃×#546	1	2	yes	—
1257	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1258	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1259	C₂	—	2	2	no	—
1260	C₂	—	2	2	no	—
1261	C₂	—	4	1	no	—
1262	C₂	—	4	2	no	—
1263	C₂	—	4	2	no	—
1264	C₂	—	8	1	no	—
1265	C₂	—	8	2	no	—
1266	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
1267	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1268	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3488	C₂
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×#3495	C₂	semidirect
3. C₁₃×#3317	C₂	semidirect
4. C₁₃×#3316	C₂	semidirect
5. C₁₃×#3311	C₂	semidirect
6. C₁₃×#3310	C₂	semidirect
7. C₁₃×#3304	C₂	semidirect
8. C₁₃×#3300	C₂	semidirect
9. C₁₃×#3296	C₂	semidirect
10. C₁₃×#3295	C₂	semidirect
11. C₁₃×#3136	C₂	semidirect
12. C₁₃×#3099	C₂	semidirect
13. C₁₃×#3094	C₂	semidirect
14. C₁₃×#3084	C₂	semidirect
15. C₁₃×#3063	C₂	semidirect
16. C₂×C₁₃×#465	C₂	semidirect
17. C₁₃×#3043	C₂	semidirect
18. C₁₃×#3009	C₂	semidirect
19. C₁₃×#3007	C₂	semidirect
20. C₁₃×#2947	C₂	semidirect
21. C₁₃×#2929	C₂	semidirect
22. C₁₃×#2897	C₂	semidirect
23. C₂×C₁₃×#416	C₂	semidirect
27. C₂×C₁₃×#137	C₂²	semidirect
28. C₂²×C₁₃×SD₁₆	C₂²	semidirect
29. C₂×C₁₃×#131	C₂²	semidirect
30. C₂³×C₈×C₁₃	C₂²	semidirect
31. C₁₃×#556	C₂²	semidirect
32. C₁₃×#554	C₂²	semidirect
34. C₁₃×#552	C₂²	semidirect
35. C₁₃×#552	C₂²	semidirect
43. C₁₃×#544	C₂²	semidirect
48. C₁₃×#536	C₂²	semidirect
55. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
59. C₁₃×#520	C₂²	semidirect
60. C₁₃×#519	C₂²	semidirect
61. C₂×C₁₃×#117	C₂²	semidirect
62. C₁₃×#490	C₂²	semidirect
63. C₁₃×#489	C₂²	semidirect
64. C₁₃×#488	C₂²	semidirect
65. C₁₃×#486	C₂²	semidirect
66. C₁₃×#485	C₂²	semidirect
67. C₁₃×#483	C₂²	semidirect
68. C₁₃×#482	C₂²	semidirect
69. C₁₃×#482	C₂²	semidirect
70. C₁₃×#482	C₂²	semidirect
71. C₁₃×#481	C₂²	semidirect
72. C₁₃×#481	C₂²	semidirect
73. C₁₃×#480	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#476	C₂²	semidirect
77. C₁₃×#475	C₂²	semidirect
78. C₁₃×#470	C₂²	semidirect
79. C₁₃×#468	C₂²	semidirect
80. C₁₃×#467	C₂²	semidirect
81. C₁₃×#465	C₂²	semidirect
82. C₁₃×#465	C₂²	semidirect
83. C₁₃×#465	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#464	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
88. C₁₃×#460	C₂²	semidirect
89. C₁₃×#460	C₂²	semidirect
90. C₁₃×#452	C₂²	semidirect
91. C₁₃×#452	C₂²	semidirect
92. C₁₃×#452	C₂²	semidirect
93. C₁₃×#452	C₂²	semidirect
94. C₁₃×#451	C₂²	semidirect
95. C₁₃×#450	C₂²	semidirect
96. C₁₃×#450	C₂²	semidirect
97. C₁₃×#450	C₂²	semidirect
98. C₁₃×#441	C₂²	semidirect
99. C₁₃×#440	C₂²	semidirect
100. C₄×C₁₃×Q₁₆	C₂²	semidirect
101. C₄×C₁₃×SD₁₆	C₂²	semidirect
102. C₁₃×#435	C₂²	semidirect
103. C₁₃×#435	C₂²	semidirect
104. C₈×D₄×C₁₃	C₂²	semidirect
105. C₈×D₄×C₁₃	C₂²	semidirect
106. C₁₃×#428	C₂²	semidirect
107. C₁₃×#428	C₂²	semidirect
108. C₂×C₁₃×#106	C₂²	semidirect
109. C₁₃×#424	C₂²	semidirect
110. C₁₃×#418	C₂²	semidirect
111. C₁₃×#418	C₂²	semidirect
112. C₁₃×#418	C₂²	semidirect
114. C₁₃×#417	C₂²	semidirect
115. C₁₃×#417	C₂²	semidirect
118. C₁₃×#416	C₂²	semidirect
119. C₁₃×#416	C₂²	semidirect
120. C₁₃×#416	C₂²	semidirect
121. C₁₃×#416	C₂²	semidirect
122. C₁₃×#416	C₂²	semidirect
123. C₁₃×#416	C₂²	semidirect
124. C₁₃×#416	C₂²	semidirect
125. C₂×C₁₃×#103	C₂²	semidirect
126. C₂×C₁₃×#103	C₂²	semidirect
127. C₂×C₁₃×#103	C₂²	semidirect
128. C₂×C₁₃×#102	C₂²	semidirect
129. C₂×C₁₃×#102	C₂²	semidirect
130. C₂×C₁₃×#102	C₂²	semidirect
131. C₂×C₁₃×#102	C₂²	semidirect
132. C₁₃×#408	C₂²	semidirect
133. C₁₃×#407	C₂²	semidirect
134. C₁₃×#405	C₂²	semidirect
321. #61172	C₁₃	direct (N × H)
484. #3495	C₂×C₁₃	semidirect
486. #3317	C₂×C₁₃	semidirect
487. #3316	C₂×C₁₃	semidirect
488. #3311	C₂×C₁₃	semidirect
489. #3310	C₂×C₁₃	semidirect
490. #3304	C₂×C₁₃	semidirect
491. #3300	C₂×C₁₃	semidirect
492. #3296	C₂×C₁₃	semidirect
493. #3295	C₂×C₁₃	semidirect
494. #3136	C₂×C₁₃	semidirect
495. #3099	C₂×C₁₃	semidirect
496. #3094	C₂×C₁₃	semidirect
497. #3084	C₂×C₁₃	semidirect
498. #3063	C₂×C₁₃	semidirect
499. C₂×#465	C₂×C₁₃	semidirect
500. #3043	C₂×C₁₃	semidirect
501. #3009	C₂×C₁₃	semidirect
502. #3007	C₂×C₁₃	semidirect
503. #2947	C₂×C₁₃	semidirect
504. #2929	C₂×C₁₃	semidirect
505. #2897	C₂×C₁₃	semidirect
506. C₂×#416	C₂×C₁₃	semidirect
608. C₂×#137	C₂²×C₁₃	semidirect
609. C₂²×SD₁₆	C₂²×C₁₃	semidirect
610. C₂×#131	C₂²×C₁₃	semidirect
611. C₂³×C₈	C₂²×C₁₃	semidirect
612. #556	C₂²×C₁₃	semidirect
613. #554	C₂²×C₁₃	semidirect
615. #552	C₂²×C₁₃	semidirect
616. #552	C₂²×C₁₃	semidirect
624. #544	C₂²×C₁₃	semidirect
629. #536	C₂²×C₁₃	semidirect
636. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
640. #520	C₂²×C₁₃	semidirect
641. #519	C₂²×C₁₃	semidirect
642. C₂×#117	C₂²×C₁₃	semidirect
643. #490	C₂²×C₁₃	semidirect
644. #489	C₂²×C₁₃	semidirect
645. #488	C₂²×C₁₃	semidirect
646. #486	C₂²×C₁₃	semidirect
647. #485	C₂²×C₁₃	semidirect
648. #483	C₂²×C₁₃	semidirect
649. #482	C₂²×C₁₃	semidirect
650. #482	C₂²×C₁₃	semidirect
651. #482	C₂²×C₁₃	semidirect
652. #481	C₂²×C₁₃	semidirect
653. #481	C₂²×C₁₃	semidirect
654. #480	C₂²×C₁₃	semidirect
655. #479	C₂²×C₁₃	semidirect
656. #478	C₂²×C₁₃	semidirect
657. #476	C₂²×C₁₃	semidirect
658. #475	C₂²×C₁₃	semidirect
659. #470	C₂²×C₁₃	semidirect
660. #468	C₂²×C₁₃	semidirect
661. #467	C₂²×C₁₃	semidirect
662. #465	C₂²×C₁₃	semidirect
663. #465	C₂²×C₁₃	semidirect
664. #465	C₂²×C₁₃	semidirect
665. #465	C₂²×C₁₃	semidirect
666. #465	C₂²×C₁₃	semidirect
667. #464	C₂²×C₁₃	semidirect
668. #464	C₂²×C₁₃	semidirect
669. #460	C₂²×C₁₃	semidirect
670. #460	C₂²×C₁₃	semidirect
671. #452	C₂²×C₁₃	semidirect
672. #452	C₂²×C₁₃	semidirect
673. #452	C₂²×C₁₃	semidirect
674. #452	C₂²×C₁₃	semidirect
675. #451	C₂²×C₁₃	semidirect
676. #450	C₂²×C₁₃	semidirect
677. #450	C₂²×C₁₃	semidirect
678. #450	C₂²×C₁₃	semidirect
679. #441	C₂²×C₁₃	semidirect
680. #440	C₂²×C₁₃	semidirect
681. C₄×Q₁₆	C₂²×C₁₃	semidirect
682. C₄×SD₁₆	C₂²×C₁₃	semidirect
683. #435	C₂²×C₁₃	semidirect
684. #435	C₂²×C₁₃	semidirect
685. C₈×D₄	C₂²×C₁₃	semidirect
686. C₈×D₄	C₂²×C₁₃	semidirect
687. #428	C₂²×C₁₃	semidirect
688. #428	C₂²×C₁₃	semidirect
689. C₂×#106	C₂²×C₁₃	semidirect
690. #424	C₂²×C₁₃	semidirect
691. #418	C₂²×C₁₃	semidirect
692. #418	C₂²×C₁₃	semidirect
693. #418	C₂²×C₁₃	semidirect
695. #417	C₂²×C₁₃	semidirect
696. #417	C₂²×C₁₃	semidirect
699. #416	C₂²×C₁₃	semidirect
700. #416	C₂²×C₁₃	semidirect
701. #416	C₂²×C₁₃	semidirect
702. #416	C₂²×C₁₃	semidirect
703. #416	C₂²×C₁₃	semidirect
704. #416	C₂²×C₁₃	semidirect
705. #416	C₂²×C₁₃	semidirect
706. C₂×#103	C₂²×C₁₃	semidirect
707. C₂×#103	C₂²×C₁₃	semidirect
708. C₂×#103	C₂²×C₁₃	semidirect
709. C₂×#102	C₂²×C₁₃	semidirect
710. C₂×#102	C₂²×C₁₃	semidirect
711. C₂×#102	C₂²×C₁₃	semidirect
712. C₂×#102	C₂²×C₁₃	semidirect
713. #408	C₂²×C₁₃	semidirect
714. #407	C₂²×C₁₃	semidirect
715. #405	C₂²×C₁₃	semidirect
1117. C₁₃	#61172	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×#3495	2
C₁₃×#3488	2
C₁₃×#3317	2
C₁₃×#3316	2
C₁₃×#3311	2
C₁₃×#3310	2
C₁₃×#3304	2
C₁₃×#3300	2
C₁₃×#3296	2
C₁₃×#3295	2
C₁₃×#3136	2
C₁₃×#3099	2
C₁₃×#3094	2
C₁₃×#3084	2
C₁₃×#3063	2
C₂×C₁₃×#465	2
C₁₃×#3043	2
C₁₃×#3009	2
C₁₃×#3007	2
C₁₃×#2947	2
C₁₃×#2929	2
C₁₃×#2897	2
C₂×C₁₃×#416	2
#61172	13

Subgroups — C13×#61172 #15747511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61172 #15747511