Subgroups — C₁₃×#61255 #15747594

Order 3328.

1898 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3355	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3351	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3350	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3347	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3346	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3345	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3339	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3337	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
27	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#555	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#553	—	2	1	no	—
31	C₁₃×#553	—	2	1	no	—
32	C₁₃×#553	—	2	1	no	—
33	C₁₃×#553	—	2	1	no	—
34	C₁₃×#553	C₂²	1	2	yes	—
35	C₁₃×#553	C₂²	1	2	yes	—
36	C₁₃×#553	C₂²	1	2	yes	—
37	C₁₃×#553	C₂²	1	2	yes	—
38	C₁₃×#553	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#553	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#552	—	2	1	no	—
41	C₁₃×#552	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#552	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#551	—	2	1	no	—
44	C₁₃×#551	—	2	1	no	—
45	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#546	—	2	1	no	—
47	C₁₃×#533	C₂²	1	1	yes	characteristic
48	C₁₃×#529	—	2	1	no	—
49	C₁₃×#529	—	2	1	no	—
50	C₁₃×#529	—	2	1	no	—
51	C₂×C₁₃×#126	—	2	1	no	—
52	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
53	C₁₃×#525	C₂²	1	1	yes	characteristic
54	C₁₃×#525	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#123	—	2	1	no	—
56	C₂×C₁₃×#121	—	2	1	no	—
57	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
59	C₄×C₁₃×#41	—	2	1	no	—
60	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₄×C₁₃	—	2	1	no	—
62	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
67	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₁₃×#501	C₂²	1	2	yes	complemented
69	C₁₃×#501	C₂²	1	2	yes	complemented
70	C₁₃×#499	C₂²	1	2	yes	complemented
71	C₁₃×#499	C₂²	1	2	yes	complemented
72	C₁₃×#485	C₂²	1	2	yes	complemented
73	C₁₃×#485	C₂²	1	2	yes	complemented
74	C₁₃×#484	C₂²	1	2	yes	complemented
75	C₁₃×#483	C₂²	1	2	yes	complemented
76	C₁₃×#482	C₂²	1	2	yes	complemented
77	C₁₃×#482	C₂²	1	2	yes	complemented
78	C₁₃×#482	C₂²	1	2	yes	complemented
79	C₁₃×#482	C₂²	1	2	yes	complemented
80	C₁₃×#482	C₂²	1	2	yes	complemented
81	C₁₃×#482	C₂²	1	2	yes	complemented
82	C₁₃×#481	C₂²	1	2	yes	complemented
83	C₁₃×#481	C₂²	1	2	yes	complemented
84	C₁₃×#481	C₂²	1	2	yes	complemented
85	C₁₃×#480	C₂²	1	2	yes	complemented
86	C₁₃×#480	C₂²	1	2	yes	complemented
87	C₁₃×#480	C₂²	1	2	yes	complemented
88	C₁₃×#479	C₂²	1	2	yes	complemented
89	C₁₃×#479	C₂²	1	2	yes	complemented
90	C₁₃×#478	C₂²	1	2	yes	complemented
91	C₁₃×#478	C₂²	1	2	yes	complemented
92	C₁₃×#478	C₂²	1	2	yes	complemented
93	C₁₃×#478	C₂²	1	2	yes	complemented
94	C₁₃×#476	C₂²	1	2	yes	complemented
95	C₁₃×#474	C₂²	1	2	yes	complemented
96	C₁₃×#469	C₂²	1	2	yes	complemented
97	C₁₃×#469	C₂²	1	2	yes	complemented
98	C₁₃×#468	C₂²	1	2	yes	complemented
99	C₁₃×#468	C₂²	1	2	yes	complemented
100	C₁₃×#466	C₂²	1	2	yes	complemented
101	C₁₃×#466	C₂²	1	2	yes	complemented
102	C₁₃×#465	C₂²	1	2	yes	complemented
103	C₁₃×#465	C₂²	1	2	yes	complemented
104	C₁₃×#442	C₂²	1	2	yes	complemented
105	C₁₃×#440	C₂²	1	2	yes	complemented
106	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
107	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
108	C₁₃×#436	C₂²	1	2	yes	complemented
109	C₁₃×#435	C₂²	1	2	yes	complemented
110	C₁₃×#435	C₂²	1	2	yes	complemented
111	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
112	C₁₃×#428	C₂²	1	1	yes	characteristic
113	C₁₃×#428	C₂²	1	1	yes	characteristic
114	C₁₃×#428	C₂²	1	1	yes	characteristic
115	C₁₃×#428	C₂²	1	1	yes	characteristic
116	C₁₃×#428	C₂²	1	1	yes	characteristic
117	C₁₃×#428	C₂²	1	1	yes	characteristic
118	C₁₃×#428	C₂²	1	1	yes	characteristic
119	C₁₃×#428	C₂²	1	1	yes	characteristic
120	C₁₃×#428	C₂²	1	1	yes	characteristic
121	C₁₃×#428	C₂²	1	2	yes	complemented
122	C₁₃×#428	C₂²	1	2	yes	complemented
123	C₁₃×#428	C₂²	1	2	yes	complemented
124	C₁₃×#428	C₂²	1	2	yes	complemented
125	C₁₃×#427	C₂²	1	2	yes	complemented
126	C₁₃×#427	C₂²	1	2	yes	complemented
127	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
128	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
129	C₁₃×#423	C₂²	1	1	yes	characteristic
130	C₁₃×#418	C₂²	1	1	yes	characteristic
131	C₁₃×#418	C₂²	1	1	yes	characteristic
132	C₁₃×#418	C₂²	1	1	yes	characteristic
133	C₁₃×#417	C₂²	1	1	yes	characteristic
134	C₁₃×#417	C₂²	1	1	yes	characteristic
135	C₁₃×#417	C₂²	1	1	yes	characteristic
136	C₁₃×#407	C₂²	1	1	yes	characteristic
137	C₁₃×#407	C₂²	1	1	yes	characteristic
138	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
139	C₂×C₁₃×#41	—	2	1	no	—
140	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₁₃	—	2	1	no	—
142	C₂²×D₄×C₁₃	—	2	1	no	—
143	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
144	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₁₃	—	2	1	no	—
146	C₂³×C₄×C₁₃	—	2	1	no	—
147	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
149	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
150	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×D₈	C₂³	1	2	yes	—
152	C₂×C₁₃×M₁₆	—	2	4	no	—
153	C₂×C₁₃×M₁₆	—	2	4	no	—
154	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
158	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
159	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
161	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
162	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#126	—	2	2	no	—
166	C₁₃×#126	—	2	2	no	—
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#126	—	2	1	no	—
169	C₁₃×#126	—	2	1	no	—
170	C₁₃×#126	—	2	1	no	—
171	C₁₃×#126	—	2	1	no	—
172	C₁₃×#126	—	2	1	no	—
173	C₁₃×#126	—	2	1	no	—
174	C₁₃×#125	—	2	1	no	—
175	C₁₃×#125	—	2	1	no	—
176	C₁₃×#125	—	2	1	no	—
177	C₁₃×#125	—	2	1	no	—
178	C₁₃×#125	—	2	1	no	—
179	C₁₃×#125	C₂³	1	1	yes	characteristic
180	C₁₃×#125	C₂³	1	1	yes	characteristic
181	C₁₃×#125	C₂³	1	2	yes	—
182	C₁₃×#125	C₂³	1	2	yes	—
183	C₁₃×#124	—	2	1	no	—
184	C₁₃×#124	—	2	1	no	—
185	C₁₃×#124	—	2	1	no	—
186	C₁₃×#123	—	2	1	no	—
187	C₁₃×#123	—	2	1	no	—
188	C₁₃×#123	—	2	1	no	—
189	C₁₃×#123	—	2	1	no	—
190	C₁₃×#123	—	2	2	no	—
191	C₁₃×#123	—	2	2	no	—
192	C₁₃×#123	—	2	2	no	—
193	C₁₃×#123	—	2	2	no	—
194	C₁₃×#123	—	2	1	no	—
195	C₁₃×#123	—	2	1	no	—
196	C₁₃×#123	—	2	1	no	—
197	C₁₃×#123	—	2	1	no	—
198	C₁₃×C₂²⋊Q₈	—	2	1	no	—
199	C₁₃×C₂²⋊Q₈	—	2	1	no	—
200	C₁₃×C₂²⋊Q₈	—	2	1	no	—
201	C₁₃×C₂²⋊Q₈	—	2	1	no	—
202	C₁₃×C₂²⋊Q₈	—	2	1	no	—
203	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
204	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
205	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
206	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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	1	no	—
218	C₁₃×#121	C₂³	1	2	yes	—
219	C₁₃×#121	C₂³	1	2	yes	—
220	C₁₃×#121	C₂³	1	1	yes	characteristic
221	C₁₃×#121	C₂³	1	1	yes	characteristic
222	C₁₃×#121	C₂³	1	2	yes	—
223	C₁₃×#121	C₂³	1	2	yes	—
224	C₁₃×#121	C₂³	1	1	yes	characteristic
225	C₁₃×#121	C₂³	1	1	yes	characteristic
226	C₁₃×#120	—	2	1	no	—
227	C₁₃×#120	—	2	1	no	—
228	C₄×Q₈×C₁₃	—	2	1	no	—
229	C₄×Q₈×C₁₃	—	2	1	no	—
230	C₄×Q₈×C₁₃	—	2	1	no	—
231	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₁₃	—	2	1	no	—
234	C₄×D₄×C₁₃	—	2	1	no	—
235	C₄×D₄×C₁₃	—	2	1	no	—
236	C₄×D₄×C₁₃	—	2	1	no	—
237	C₄×D₄×C₁₃	—	2	1	no	—
238	C₄×D₄×C₁₃	—	2	1	no	—
239	C₄×D₄×C₁₃	—	2	1	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	—	2	2	no	—
244	C₄×D₄×C₁₃	—	2	1	no	—
245	C₄×D₄×C₁₃	—	2	1	no	—
246	C₄×D₄×C₁₃	—	2	1	no	—
247	C₄×D₄×C₁₃	—	2	1	no	—
248	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
249	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
250	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
251	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
252	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₁₃	C₂³	1	2	yes	—
254	C₄×D₄×C₁₃	C₂³	1	2	yes	—
255	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
260	C₁₃×#117	—	2	1	no	—
261	C₁₃×#117	—	2	1	no	—
262	C₁₃×#117	—	2	1	no	—
263	C₁₃×#117	—	2	1	no	—
264	C₁₃×#117	—	2	1	no	—
265	C₁₃×#117	—	2	1	no	—
266	C₁₃×#117	—	2	1	no	—
267	C₁₃×#117	—	2	1	no	—
268	C₁₃×#117	—	2	1	no	—
269	C₁₃×#117	—	2	1	no	—
270	C₁₃×#117	C₂³	1	1	yes	characteristic
271	C₁₃×#117	C₂³	1	1	yes	characteristic
272	C₁₃×#117	C₂³	1	1	yes	characteristic
273	C₁₃×#117	C₂³	1	1	yes	characteristic
274	C₁₃×#117	C₂³	1	1	yes	characteristic
275	C₁₃×#117	C₂³	1	2	yes	—
276	C₁₃×#117	C₂³	1	1	yes	characteristic
277	C₁₃×#117	C₂³	1	1	yes	characteristic
278	C₁₃×#117	C₂³	1	2	yes	—
279	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
285	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
289	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
290	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
293	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
301	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
302	C₂×C₄²×C₁₃	—	2	1	no	—
303	C₂×C₄²×C₁₃	—	2	1	no	—
304	C₂×C₄²×C₁₃	—	2	1	no	—
305	C₂×C₄²×C₁₃	—	2	1	no	—
306	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
307	C₁₃×#107	C₂³	1	2	yes	—
308	C₁₃×#107	C₂³	1	2	yes	—
309	C₁₃×#107	C₂³	1	2	yes	—
310	C₁₃×#107	C₂³	1	2	yes	—
311	C₁₃×#107	C₂³	1	2	yes	—
312	C₁₃×#107	C₂³	1	2	yes	—
313	C₁₃×#107	C₂³	1	2	yes	—
314	C₁₃×#107	C₂³	1	2	yes	—
315	C₁₃×#107	C₂³	1	2	yes	—
316	C₁₃×#106	C₂³	1	2	yes	—
317	C₁₃×#106	C₂³	1	2	yes	—
318	C₁₃×#106	C₂³	1	2	yes	—
319	C₁₃×#106	C₂³	1	2	yes	—
320	C₁₃×#106	C₂³	1	2	yes	—
321	C₁₃×#106	C₂³	1	2	yes	—
322	C₁₃×#106	C₂³	1	2	yes	—
323	C₁₃×#106	C₂³	1	2	yes	—
324	C₁₃×#106	C₂³	1	2	yes	—
325	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
326	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
327	C₁₃×#103	C₂³	1	2	yes	—
328	C₁₃×#103	C₂³	1	2	yes	—
329	C₁₃×#103	C₂³	1	2	yes	—
330	C₁₃×#102	C₂³	1	2	yes	—
331	C₁₃×#102	C₂³	1	2	yes	—
332	C₁₃×#102	C₂³	1	2	yes	—
333	C₁₃×#102	C₂³	1	2	yes	—
334	C₁₃×#102	C₂³	1	2	yes	—
335	C₁₃×#102	C₂³	1	2	yes	—
336	C₁₃×#102	C₂³	1	2	yes	—
337	C₁₃×#102	C₂³	1	2	yes	—
338	C₁₃×#102	C₂³	1	2	yes	—
339	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
340	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
341	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
342	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
343	C₁₃×#97	C₂³	1	2	yes	—
344	C₄×C₈×C₁₃	C₂³	1	2	yes	—
345	#61255	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂⁴×C₁₃	—	2	1	no	—
347	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
348	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
349	C₁₃×#41	—	2	2	no	—
350	C₁₃×#41	—	2	2	no	—
351	C₁₃×#41	—	4	4	no	—
352	C₂×Q₈×C₁₃	—	2	1	no	—
353	C₂×Q₈×C₁₃	—	2	1	no	—
354	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₁₃	—	2	1	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	2	no	—
360	C₂×D₄×C₁₃	—	2	1	no	—
361	C₂×D₄×C₁₃	—	2	1	no	—
362	C₂×D₄×C₁₃	—	2	2	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	—	4	2	no	—
368	C₂×D₄×C₁₃	—	4	4	no	—
369	C₂×D₄×C₁₃	—	8	2	no	—
370	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
372	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
380	C₂²×C₄×C₁₃	—	2	1	no	—
381	C₂²×C₄×C₁₃	—	2	1	no	—
382	C₂²×C₄×C₁₃	—	2	1	no	—
383	C₂²×C₄×C₁₃	—	2	1	no	—
384	C₂²×C₄×C₁₃	—	2	1	no	—
385	C₂²×C₄×C₁₃	—	2	1	no	—
386	C₂²×C₄×C₁₃	—	2	1	no	—
387	C₂²×C₄×C₁₃	—	2	2	no	—
388	C₂²×C₄×C₁₃	—	2	2	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	2	no	—
394	C₂²×C₄×C₁₃	—	8	2	no	—
395	C₂²×C₄×C₁₃	—	8	2	no	—
396	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
409	C₁₃×SD₁₆	—	2	4	no	—
410	C₁₃×D₈	—	2	4	no	—
411	C₁₃×M₁₆	—	2	2	no	—
412	C₁₃×M₁₆	—	2	2	no	—
413	C₁₃×M₁₆	—	2	2	no	—
414	C₁₃×M₁₆	—	2	4	no	—
415	C₁₃×M₁₆	—	2	4	no	—
416	C₁₃×M₁₆	#41	1	4	yes	complemented
417	C₂×C₈×C₁₃	—	2	4	no	—
418	C₂×C₈×C₁₃	—	2	4	no	—
419	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
420	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
421	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
422	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
423	C₁₃×C₄⋊C₄	—	2	1	no	—
424	C₁₃×C₄⋊C₄	—	2	1	no	—
425	C₁₃×C₄⋊C₄	—	2	2	no	—
426	C₁₃×C₄⋊C₄	—	2	2	no	—
427	C₁₃×C₄⋊C₄	—	2	2	no	—
428	C₁₃×C₄⋊C₄	—	2	2	no	—
429	C₁₃×C₄⋊C₄	—	2	2	no	—
430	C₁₃×C₄⋊C₄	—	2	2	no	—
431	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
436	C₁₃×C₄⋊C₄	—	2	1	no	—
437	C₁₃×C₄⋊C₄	—	2	1	no	—
438	C₁₃×C₄⋊C₄	—	2	1	no	—
439	C₁₃×C₄⋊C₄	—	2	1	no	—
440	C₁₃×C₄⋊C₄	—	2	1	no	—
441	C₁₃×C₄⋊C₄	—	2	1	no	—
442	C₁₃×C₄⋊C₄	—	2	1	no	—
443	C₁₃×C₄⋊C₄	—	2	1	no	—
444	C₁₃×C₄⋊C₄	—	2	1	no	—
445	C₁₃×C₄⋊C₄	—	2	1	no	—
446	C₁₃×C₄⋊C₄	—	2	1	no	—
447	C₁₃×C₄⋊C₄	—	2	1	no	—
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	1	yes	characteristic
451	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
452	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
453	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
454	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
455	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
456	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
457	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
458	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
459	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
460	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
461	C₁₃×C₂²⋊C₄	—	2	1	no	—
462	C₁₃×C₂²⋊C₄	—	2	1	no	—
463	C₁₃×C₂²⋊C₄	—	2	1	no	—
464	C₁₃×C₂²⋊C₄	—	2	2	no	—
465	C₁₃×C₂²⋊C₄	—	2	2	no	—
466	C₁₃×C₂²⋊C₄	—	2	1	no	—
467	C₁₃×C₂²⋊C₄	—	2	1	no	—
468	C₁₃×C₂²⋊C₄	—	2	1	no	—
469	C₁₃×C₂²⋊C₄	—	2	1	no	—
470	C₁₃×C₂²⋊C₄	—	2	1	no	—
471	C₁₃×C₂²⋊C₄	—	2	1	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	—	2	2	no	—
476	C₁₃×C₂²⋊C₄	—	2	2	no	—
477	C₁₃×C₂²⋊C₄	—	2	2	no	—
478	C₁₃×C₂²⋊C₄	—	2	2	no	—
479	C₁₃×C₂²⋊C₄	—	2	2	no	—
480	C₁₃×C₂²⋊C₄	—	2	1	no	—
481	C₁₃×C₂²⋊C₄	—	2	1	no	—
482	C₁₃×C₂²⋊C₄	—	2	1	no	—
483	C₁₃×C₂²⋊C₄	—	2	1	no	—
484	C₁₃×C₂²⋊C₄	—	2	1	no	—
485	C₁₃×C₂²⋊C₄	—	2	1	no	—
486	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
487	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
488	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
489	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
490	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
491	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
492	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
493	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₁₃	—	2	1	no	—
495	C₄²×C₁₃	—	2	1	no	—
496	C₄²×C₁₃	—	2	1	no	—
497	C₄²×C₁₃	—	2	1	no	—
498	C₄²×C₁₃	—	2	1	no	—
499	C₄²×C₁₃	—	2	1	no	—
500	C₄²×C₁₃	—	2	2	no	—
501	C₄²×C₁₃	—	2	2	no	—
502	C₄²×C₁₃	—	2	1	no	—
503	C₄²×C₁₃	—	2	1	no	—
504	C₄²×C₁₃	—	2	1	no	—
505	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
506	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
507	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
508	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
509	#3475	C₂×C₁₃	1	1	yes	characteristic, complemented
510	C₂×#553	C₂×C₁₃	1	1	yes	characteristic, complemented
511	#3355	C₂×C₁₃	1	2	yes	complemented
512	#3351	C₂×C₁₃	1	2	yes	complemented
513	#3350	C₂×C₁₃	1	2	yes	complemented
514	#3347	C₂×C₁₃	1	2	yes	complemented
515	#3346	C₂×C₁₃	1	2	yes	complemented
516	#3345	C₂×C₁₃	1	2	yes	complemented
517	#3339	C₂×C₁₃	1	2	yes	complemented
518	#3337	C₂×C₁₃	1	2	yes	complemented
519	#3166	C₂×C₁₃	1	1	yes	characteristic, complemented
520	#3094	C₂×C₁₃	1	1	yes	characteristic, complemented
521	#3094	C₂×C₁₃	1	1	yes	characteristic, complemented
522	#3093	C₂×C₁₃	1	1	yes	characteristic, complemented
523	#3092	C₂×C₁₃	1	1	yes	characteristic, complemented
524	#3080	C₂×C₁₃	1	1	yes	characteristic, complemented
525	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
526	#3055	C₂×C₁₃	1	1	yes	characteristic, complemented
527	#3055	C₂×C₁₃	1	1	yes	characteristic, complemented
528	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
529	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
530	#2911	C₂×C₁₃	1	1	yes	characteristic, complemented
531	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
532	C₂³×C₁₃	—	2	2	no	—
533	C₂³×C₁₃	—	2	2	no	—
534	C₂³×C₁₃	—	2	2	no	—
535	C₂³×C₁₃	—	2	1	no	—
536	C₂³×C₁₃	—	2	2	no	—
537	C₂³×C₁₃	—	4	1	no	—
538	C₂³×C₁₃	—	4	1	no	—
539	C₂³×C₁₃	—	4	1	no	—
540	C₂³×C₁₃	—	4	2	no	—
541	C₂³×C₁₃	—	4	2	no	—
542	C₂³×C₁₃	—	4	2	no	—
543	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
544	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
545	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
546	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
547	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
548	Q₈×C₁₃	—	2	1	no	—
549	Q₈×C₁₃	—	2	1	no	—
550	Q₈×C₁₃	—	4	2	no	—
551	Q₈×C₁₃	—	8	1	no	—
552	D₄×C₁₃	—	2	2	no	—
553	D₄×C₁₃	—	2	2	no	—
554	D₄×C₁₃	—	2	1	no	—
555	D₄×C₁₃	—	2	2	no	—
556	D₄×C₁₃	—	2	2	no	—
557	D₄×C₁₃	—	2	1	no	—
558	D₄×C₁₃	—	4	1	no	—
559	D₄×C₁₃	—	4	1	no	—
560	D₄×C₁₃	—	4	4	no	—
561	D₄×C₁₃	—	4	2	no	—
562	D₄×C₁₃	—	4	2	no	—
563	D₄×C₁₃	—	4	4	no	—
564	D₄×C₁₃	—	4	2	no	—
565	D₄×C₁₃	—	4	2	no	—
566	D₄×C₁₃	—	8	1	no	—
567	D₄×C₁₃	—	8	1	no	—
568	D₄×C₁₃	—	8	2	no	—
569	D₄×C₁₃	—	8	2	no	—
570	C₂×C₄×C₁₃	—	2	2	no	—
571	C₂×C₄×C₁₃	—	2	2	no	—
572	C₂×C₄×C₁₃	—	2	2	no	—
573	C₂×C₄×C₁₃	—	2	2	no	—
574	C₂×C₄×C₁₃	—	2	2	no	—
575	C₂×C₄×C₁₃	—	2	2	no	—
576	C₂×C₄×C₁₃	—	2	1	no	—
577	C₂×C₄×C₁₃	—	2	1	no	—
578	C₂×C₄×C₁₃	—	2	1	no	—
579	C₂×C₄×C₁₃	—	2	1	no	—
580	C₂×C₄×C₁₃	—	2	1	no	—
581	C₂×C₄×C₁₃	—	2	1	no	—
582	C₂×C₄×C₁₃	—	2	1	no	—
583	C₂×C₄×C₁₃	—	2	1	no	—
584	C₂×C₄×C₁₃	—	2	1	no	—
585	C₂×C₄×C₁₃	—	2	1	no	—
586	C₂×C₄×C₁₃	—	2	1	no	—
587	C₂×C₄×C₁₃	—	2	2	no	—
588	C₂×C₄×C₁₃	—	2	1	no	—
589	C₂×C₄×C₁₃	—	2	1	no	—
590	C₂×C₄×C₁₃	—	2	1	no	—
591	C₂×C₄×C₁₃	—	2	1	no	—
592	C₂×C₄×C₁₃	—	2	2	no	—
593	C₂×C₄×C₁₃	—	2	2	no	—
594	C₂×C₄×C₁₃	—	4	1	no	—
595	C₂×C₄×C₁₃	—	4	1	no	—
596	C₂×C₄×C₁₃	—	4	2	no	—
597	C₂×C₄×C₁₃	—	4	2	no	—
598	C₂×C₄×C₁₃	—	4	2	no	—
599	C₂×C₄×C₁₃	—	4	2	no	—
600	C₂×C₄×C₁₃	—	4	2	no	—
601	C₂×C₄×C₁₃	—	4	2	no	—
602	C₂×C₄×C₁₃	—	4	2	no	—
603	C₂×C₄×C₁₃	—	8	1	no	—
604	C₂×C₄×C₁₃	—	8	2	no	—
605	C₂×C₄×C₁₃	—	8	2	no	—
606	C₂×C₄×C₁₃	—	8	1	no	—
607	C₂×C₄×C₁₃	—	8	1	no	—
608	C₂×C₄×C₁₃	—	8	2	no	—
609	C₂×C₄×C₁₃	—	8	2	no	—
610	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
611	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
612	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
613	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
614	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
615	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
616	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
617	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
618	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
619	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
620	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
621	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
622	C₈×C₁₃	—	2	2	no	—
623	C₈×C₁₃	—	2	2	no	—
624	C₈×C₁₃	—	2	2	no	—
625	C₈×C₁₃	C₂×#41	1	4	yes	—
626	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
627	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
628	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
629	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
630	#555	C₂²×C₁₃	1	1	yes	characteristic, complemented
631	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	#553	—	2	1	no	—
633	#553	—	2	1	no	—
634	#553	—	2	1	no	—
635	#553	—	2	1	no	—
636	#553	C₂²×C₁₃	1	2	yes	—
637	#553	C₂²×C₁₃	1	2	yes	—
638	#553	C₂²×C₁₃	1	2	yes	—
639	#553	C₂²×C₁₃	1	2	yes	—
640	#553	C₂²×C₁₃	1	1	yes	characteristic, complemented
641	#553	C₂²×C₁₃	1	1	yes	characteristic, complemented
642	#552	—	2	1	no	—
643	#552	C₂²×C₁₃	1	1	yes	characteristic, complemented
644	#552	C₂²×C₁₃	1	1	yes	characteristic, complemented
645	#551	—	2	1	no	—
646	#551	—	2	1	no	—
647	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
648	#546	—	2	1	no	—
649	#533	C₂²×C₁₃	1	1	yes	characteristic
650	#529	—	2	1	no	—
651	#529	—	2	1	no	—
652	#529	—	2	1	no	—
653	C₂×#126	—	2	1	no	—
654	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
655	#525	C₂²×C₁₃	1	1	yes	characteristic
656	#525	C₂²×C₁₃	1	1	yes	characteristic
657	C₂×#123	—	2	1	no	—
658	C₂×#121	—	2	1	no	—
659	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
660	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
661	C₄×#41	—	2	1	no	—
662	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
663	C₂×C₄×D₄	—	2	1	no	—
664	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
665	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
666	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
667	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
668	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
669	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
670	#501	C₂²×C₁₃	1	2	yes	complemented
671	#501	C₂²×C₁₃	1	2	yes	complemented
672	#499	C₂²×C₁₃	1	2	yes	complemented
673	#499	C₂²×C₁₃	1	2	yes	complemented
674	#485	C₂²×C₁₃	1	2	yes	complemented
675	#485	C₂²×C₁₃	1	2	yes	complemented
676	#484	C₂²×C₁₃	1	2	yes	complemented
677	#483	C₂²×C₁₃	1	2	yes	complemented
678	#482	C₂²×C₁₃	1	2	yes	complemented
679	#482	C₂²×C₁₃	1	2	yes	complemented
680	#482	C₂²×C₁₃	1	2	yes	complemented
681	#482	C₂²×C₁₃	1	2	yes	complemented
682	#482	C₂²×C₁₃	1	2	yes	complemented
683	#482	C₂²×C₁₃	1	2	yes	complemented
684	#481	C₂²×C₁₃	1	2	yes	complemented
685	#481	C₂²×C₁₃	1	2	yes	complemented
686	#481	C₂²×C₁₃	1	2	yes	complemented
687	#480	C₂²×C₁₃	1	2	yes	complemented
688	#480	C₂²×C₁₃	1	2	yes	complemented
689	#480	C₂²×C₁₃	1	2	yes	complemented
690	#479	C₂²×C₁₃	1	2	yes	complemented
691	#479	C₂²×C₁₃	1	2	yes	complemented
692	#478	C₂²×C₁₃	1	2	yes	complemented
693	#478	C₂²×C₁₃	1	2	yes	complemented
694	#478	C₂²×C₁₃	1	2	yes	complemented
695	#478	C₂²×C₁₃	1	2	yes	complemented
696	#476	C₂²×C₁₃	1	2	yes	complemented
697	#474	C₂²×C₁₃	1	2	yes	complemented
698	#469	C₂²×C₁₃	1	2	yes	complemented
699	#469	C₂²×C₁₃	1	2	yes	complemented
700	#468	C₂²×C₁₃	1	2	yes	complemented
701	#468	C₂²×C₁₃	1	2	yes	complemented
702	#466	C₂²×C₁₃	1	2	yes	complemented
703	#466	C₂²×C₁₃	1	2	yes	complemented
704	#465	C₂²×C₁₃	1	2	yes	complemented
705	#465	C₂²×C₁₃	1	2	yes	complemented
706	#442	C₂²×C₁₃	1	2	yes	complemented
707	#440	C₂²×C₁₃	1	2	yes	complemented
708	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
709	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
710	#436	C₂²×C₁₃	1	2	yes	complemented
711	#435	C₂²×C₁₃	1	2	yes	complemented
712	#435	C₂²×C₁₃	1	2	yes	complemented
713	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
714	#428	C₂²×C₁₃	1	1	yes	characteristic
715	#428	C₂²×C₁₃	1	1	yes	characteristic
716	#428	C₂²×C₁₃	1	1	yes	characteristic
717	#428	C₂²×C₁₃	1	1	yes	characteristic
718	#428	C₂²×C₁₃	1	1	yes	characteristic
719	#428	C₂²×C₁₃	1	1	yes	characteristic
720	#428	C₂²×C₁₃	1	1	yes	characteristic
721	#428	C₂²×C₁₃	1	1	yes	characteristic
722	#428	C₂²×C₁₃	1	1	yes	characteristic
723	#428	C₂²×C₁₃	1	2	yes	complemented
724	#428	C₂²×C₁₃	1	2	yes	complemented
725	#428	C₂²×C₁₃	1	2	yes	complemented
726	#428	C₂²×C₁₃	1	2	yes	complemented
727	#427	C₂²×C₁₃	1	2	yes	complemented
728	#427	C₂²×C₁₃	1	2	yes	complemented
729	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
730	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
731	#423	C₂²×C₁₃	1	1	yes	characteristic
732	#418	C₂²×C₁₃	1	1	yes	characteristic
733	#418	C₂²×C₁₃	1	1	yes	characteristic
734	#418	C₂²×C₁₃	1	1	yes	characteristic
735	#417	C₂²×C₁₃	1	1	yes	characteristic
736	#417	C₂²×C₁₃	1	1	yes	characteristic
737	#417	C₂²×C₁₃	1	1	yes	characteristic
738	#407	C₂²×C₁₃	1	1	yes	characteristic
739	#407	C₂²×C₁₃	1	1	yes	characteristic
740	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
741	C₂²×C₁₃	—	2	1	no	—
742	C₂²×C₁₃	—	2	1	no	—
743	C₂²×C₁₃	—	2	1	no	—
744	C₂²×C₁₃	—	2	1	no	—
745	C₂²×C₁₃	—	2	1	no	—
746	C₂²×C₁₃	—	2	1	no	—
747	C₂²×C₁₃	—	2	1	no	—
748	C₂²×C₁₃	—	2	1	no	—
749	C₂²×C₁₃	—	2	1	no	—
750	C₂²×C₁₃	—	2	1	no	—
751	C₂²×C₁₃	—	2	1	no	—
752	C₂²×C₁₃	—	2	1	no	—
753	C₂²×C₁₃	—	2	1	no	—
754	C₂²×C₁₃	—	4	4	no	—
755	C₂²×C₁₃	—	4	2	no	—
756	C₂²×C₁₃	—	4	1	no	—
757	C₂²×C₁₃	—	4	1	no	—
758	C₂²×C₁₃	—	4	2	no	—
759	C₂²×C₁₃	—	4	1	no	—
760	C₂²×C₁₃	—	4	2	no	—
761	C₂²×C₁₃	—	8	2	no	—
762	C₂²×C₁₃	—	8	4	no	—
763	C₂²×C₁₃	#547	1	2	yes	—
764	C₂²×C₁₃	#575	1	2	yes	—
765	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
766	C₄×C₁₃	—	2	1	no	—
767	C₄×C₁₃	—	2	1	no	—
768	C₄×C₁₃	—	2	1	no	—
769	C₄×C₁₃	—	2	1	no	—
770	C₄×C₁₃	—	2	1	no	—
771	C₄×C₁₃	—	2	1	no	—
772	C₄×C₁₃	—	2	1	no	—
773	C₄×C₁₃	—	2	1	no	—
774	C₄×C₁₃	—	4	2	no	—
775	C₄×C₁₃	—	4	2	no	—
776	C₄×C₁₃	—	4	1	no	—
777	C₄×C₁₃	—	4	1	no	—
778	C₄×C₁₃	—	4	1	no	—
779	C₄×C₁₃	—	4	1	no	—
780	C₄×C₁₃	—	4	1	no	—
781	C₄×C₁₃	—	4	2	no	—
782	C₄×C₁₃	—	4	1	no	—
783	C₄×C₁₃	—	4	1	no	—
784	C₄×C₁₃	#547	1	2	yes	—
785	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
786	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
787	C₂×#41	—	2	1	no	—
788	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
789	C₂²×D₄	—	2	1	no	—
790	C₂²×D₄	—	2	1	no	—
791	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
792	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
793	C₂³×C₄	—	2	1	no	—
794	C₂³×C₄	—	2	1	no	—
795	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
796	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
797	AGL(1,ℤ/8)	—	2	4	no	—
798	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
799	C₂×D₈	C₂³×C₁₃	1	2	yes	—
800	C₂×M₁₆	—	2	4	no	—
801	C₂×M₁₆	—	2	4	no	—
802	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
803	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
804	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
805	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
806	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
807	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
808	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
809	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
810	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
811	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
812	#126	—	2	2	no	—
813	#126	—	2	2	no	—
814	#126	—	2	2	no	—
815	#126	—	2	2	no	—
816	#126	—	2	1	no	—
817	#126	—	2	1	no	—
818	#126	—	2	1	no	—
819	#126	—	2	1	no	—
820	#126	—	2	1	no	—
821	#126	—	2	1	no	—
822	#125	—	2	1	no	—
823	#125	—	2	1	no	—
824	#125	—	2	1	no	—
825	#125	—	2	1	no	—
826	#125	—	2	1	no	—
827	#125	C₂³×C₁₃	1	2	yes	—
828	#125	C₂³×C₁₃	1	2	yes	—
829	#125	C₂³×C₁₃	1	1	yes	characteristic
830	#125	C₂³×C₁₃	1	1	yes	characteristic
831	#124	—	2	1	no	—
832	#124	—	2	1	no	—
833	#124	—	2	1	no	—
834	#123	—	2	1	no	—
835	#123	—	2	1	no	—
836	#123	—	2	1	no	—
837	#123	—	2	1	no	—
838	#123	—	2	2	no	—
839	#123	—	2	2	no	—
840	#123	—	2	2	no	—
841	#123	—	2	2	no	—
842	#123	—	2	1	no	—
843	#123	—	2	1	no	—
844	#123	—	2	1	no	—
845	#123	—	2	1	no	—
846	C₂²⋊Q₈	—	2	1	no	—
847	C₂²⋊Q₈	—	2	1	no	—
848	C₂²⋊Q₈	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	—	2	1	no	—
851	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
852	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
853	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
854	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
855	#121	—	2	2	no	—
856	#121	—	2	2	no	—
857	#121	—	2	2	no	—
858	#121	—	2	2	no	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	1	no	—
862	#121	—	2	1	no	—
863	#121	—	2	1	no	—
864	#121	—	2	1	no	—
865	#121	—	2	1	no	—
866	#121	C₂³×C₁₃	1	2	yes	—
867	#121	C₂³×C₁₃	1	2	yes	—
868	#121	C₂³×C₁₃	1	2	yes	—
869	#121	C₂³×C₁₃	1	2	yes	—
870	#121	C₂³×C₁₃	1	1	yes	characteristic
871	#121	C₂³×C₁₃	1	1	yes	characteristic
872	#121	C₂³×C₁₃	1	1	yes	characteristic
873	#121	C₂³×C₁₃	1	1	yes	characteristic
874	#120	—	2	1	no	—
875	#120	—	2	1	no	—
876	C₄×Q₈	—	2	1	no	—
877	C₄×Q₈	—	2	1	no	—
878	C₄×Q₈	—	2	1	no	—
879	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
880	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	2	no	—
889	C₄×D₄	—	2	2	no	—
890	C₄×D₄	—	2	2	no	—
891	C₄×D₄	—	2	2	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
897	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
898	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
899	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
900	C₄×D₄	C₂³×C₁₃	1	2	yes	—
901	C₄×D₄	C₂³×C₁₃	1	2	yes	—
902	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
903	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
904	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
905	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
906	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
907	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
908	#117	—	2	1	no	—
909	#117	—	2	1	no	—
910	#117	—	2	1	no	—
911	#117	—	2	1	no	—
912	#117	—	2	1	no	—
913	#117	—	2	1	no	—
914	#117	—	2	1	no	—
915	#117	—	2	1	no	—
916	#117	—	2	1	no	—
917	#117	—	2	1	no	—
918	#117	C₂³×C₁₃	1	1	yes	characteristic
919	#117	C₂³×C₁₃	1	1	yes	characteristic
920	#117	C₂³×C₁₃	1	1	yes	characteristic
921	#117	C₂³×C₁₃	1	1	yes	characteristic
922	#117	C₂³×C₁₃	1	1	yes	characteristic
923	#117	C₂³×C₁₃	1	2	yes	—
924	#117	C₂³×C₁₃	1	2	yes	—
925	#117	C₂³×C₁₃	1	1	yes	characteristic
926	#117	C₂³×C₁₃	1	1	yes	characteristic
927	C₂×C₄⋊C₄	—	2	1	no	—
928	C₂×C₄⋊C₄	—	2	1	no	—
929	C₂×C₄⋊C₄	—	2	1	no	—
930	C₂×C₄⋊C₄	—	2	1	no	—
931	C₂×C₄⋊C₄	—	2	1	no	—
932	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
934	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
935	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
936	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
937	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
938	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
939	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
940	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
942	C₂×C₂²⋊C₄	—	2	1	no	—
943	C₂×C₂²⋊C₄	—	2	1	no	—
944	C₂×C₂²⋊C₄	—	2	1	no	—
945	C₂×C₂²⋊C₄	—	2	1	no	—
946	C₂×C₂²⋊C₄	—	2	1	no	—
947	C₂×C₂²⋊C₄	—	2	1	no	—
948	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
949	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
950	C₂×C₄²	—	2	1	no	—
951	C₂×C₄²	—	2	1	no	—
952	C₂×C₄²	—	2	1	no	—
953	C₂×C₄²	—	2	1	no	—
954	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
955	#107	C₂³×C₁₃	1	2	yes	—
956	#107	C₂³×C₁₃	1	2	yes	—
957	#107	C₂³×C₁₃	1	2	yes	—
958	#107	C₂³×C₁₃	1	2	yes	—
959	#107	C₂³×C₁₃	1	2	yes	—
960	#107	C₂³×C₁₃	1	2	yes	—
961	#107	C₂³×C₁₃	1	2	yes	—
962	#107	C₂³×C₁₃	1	2	yes	—
963	#107	C₂³×C₁₃	1	2	yes	—
964	#106	C₂³×C₁₃	1	2	yes	—
965	#106	C₂³×C₁₃	1	2	yes	—
966	#106	C₂³×C₁₃	1	2	yes	—
967	#106	C₂³×C₁₃	1	2	yes	—
968	#106	C₂³×C₁₃	1	2	yes	—
969	#106	C₂³×C₁₃	1	2	yes	—
970	#106	C₂³×C₁₃	1	2	yes	—
971	#106	C₂³×C₁₃	1	2	yes	—
972	#106	C₂³×C₁₃	1	2	yes	—
973	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
974	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
975	#103	C₂³×C₁₃	1	2	yes	—
976	#103	C₂³×C₁₃	1	2	yes	—
977	#103	C₂³×C₁₃	1	2	yes	—
978	#102	C₂³×C₁₃	1	2	yes	—
979	#102	C₂³×C₁₃	1	2	yes	—
980	#102	C₂³×C₁₃	1	2	yes	—
981	#102	C₂³×C₁₃	1	2	yes	—
982	#102	C₂³×C₁₃	1	2	yes	—
983	#102	C₂³×C₁₃	1	2	yes	—
984	#102	C₂³×C₁₃	1	2	yes	—
985	#102	C₂³×C₁₃	1	2	yes	—
986	#102	C₂³×C₁₃	1	2	yes	—
987	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
988	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
989	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
990	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
991	#97	C₂³×C₁₃	1	2	yes	—
992	C₄×C₈	C₂³×C₁₃	1	2	yes	—
993	C₂×C₁₃	—	2	2	no	—
994	C₂×C₁₃	—	2	2	no	—
995	C₂×C₁₃	—	4	1	no	—
996	C₂×C₁₃	—	4	1	no	—
997	C₂×C₁₃	—	4	1	no	—
998	C₂×C₁₃	—	8	1	no	—
999	C₂×C₁₃	—	8	2	no	—
1000	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
1001	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
1002	C₂×C₁₃	#3585	1	1	yes	characteristic
1003	C₂⁴	—	2	1	no	—
1004	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
1005	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
1006	#41	—	2	2	no	—
1007	#41	—	2	2	no	—
1008	#41	—	4	4	no	—
1009	C₂×Q₈	—	2	1	no	—
1010	C₂×Q₈	—	2	1	no	—
1011	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	2	1	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	1	no	—
1018	C₂×D₄	—	2	1	no	—
1019	C₂×D₄	—	2	2	no	—
1020	C₂×D₄	—	2	2	no	—
1021	C₂×D₄	—	2	1	no	—
1022	C₂×D₄	—	2	2	no	—
1023	C₂×D₄	—	2	2	no	—
1024	C₂×D₄	—	4	2	no	—
1025	C₂×D₄	—	4	4	no	—
1026	C₂×D₄	—	8	2	no	—
1027	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1028	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1029	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1030	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1031	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1032	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1033	C₂²×C₄	—	2	2	no	—
1034	C₂²×C₄	—	2	2	no	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	1	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	1	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	1	no	—
1044	C₂²×C₄	—	2	2	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	2	1	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	2	1	no	—
1049	C₂²×C₄	—	2	2	no	—
1050	C₂²×C₄	—	2	2	no	—
1051	C₂²×C₄	—	8	2	no	—
1052	C₂²×C₄	—	8	2	no	—
1053	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1054	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1055	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1056	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1057	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1058	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1059	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1060	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1061	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1062	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1063	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1064	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1065	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1066	SD₁₆	—	2	4	no	—
1067	D₈	—	2	4	no	—
1068	M₁₆	—	2	2	no	—
1069	M₁₆	—	2	2	no	—
1070	M₁₆	—	2	2	no	—
1071	M₁₆	—	2	4	no	—
1072	M₁₆	—	2	4	no	—
1073	M₁₆	C₁₃×#41	1	4	yes	complemented
1074	C₂×C₈	—	2	4	no	—
1075	C₂×C₈	—	2	4	no	—
1076	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1077	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1078	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1079	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	—	2	1	no	—
1096	C₄⋊C₄	—	2	1	no	—
1097	C₄⋊C₄	—	2	1	no	—
1098	C₄⋊C₄	—	2	1	no	—
1099	C₄⋊C₄	—	2	1	no	—
1100	C₄⋊C₄	—	2	1	no	—
1101	C₄⋊C₄	—	2	1	no	—
1102	C₄⋊C₄	—	2	1	no	—
1103	C₄⋊C₄	—	2	1	no	—
1104	C₄⋊C₄	—	2	1	no	—
1105	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1106	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1107	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1108	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1109	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1110	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1111	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1112	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1113	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1114	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1115	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1116	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1117	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	—	2	1	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	1	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	1	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	1	no	—
1129	C₂²⋊C₄	—	2	1	no	—
1130	C₂²⋊C₄	—	2	1	no	—
1131	C₂²⋊C₄	—	2	2	no	—
1132	C₂²⋊C₄	—	2	2	no	—
1133	C₂²⋊C₄	—	2	2	no	—
1134	C₂²⋊C₄	—	2	2	no	—
1135	C₂²⋊C₄	—	2	2	no	—
1136	C₂²⋊C₄	—	2	2	no	—
1137	C₂²⋊C₄	—	2	1	no	—
1138	C₂²⋊C₄	—	2	1	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	1	no	—
1141	C₂²⋊C₄	—	2	1	no	—
1142	C₂²⋊C₄	—	2	1	no	—
1143	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1144	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1145	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1146	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1147	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1148	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1149	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1150	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1151	C₄²	—	2	1	no	—
1152	C₄²	—	2	1	no	—
1153	C₄²	—	2	1	no	—
1154	C₄²	—	2	1	no	—
1155	C₄²	—	2	1	no	—
1156	C₄²	—	2	1	no	—
1157	C₄²	—	2	2	no	—
1158	C₄²	—	2	2	no	—
1159	C₄²	—	2	1	no	—
1160	C₄²	—	2	1	no	—
1161	C₄²	—	2	1	no	—
1162	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1163	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1164	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1165	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1166	C₁₃	#61255	1	1	yes	characteristic, direct product factor, Sylow
1167	C₂³	—	2	2	no	—
1168	C₂³	—	2	2	no	—
1169	C₂³	—	2	2	no	—
1170	C₂³	—	2	1	no	—
1171	C₂³	—	2	2	no	—
1172	C₂³	—	4	1	no	—
1173	C₂³	—	4	1	no	—
1174	C₂³	—	4	1	no	—
1175	C₂³	—	4	2	no	—
1176	C₂³	—	4	2	no	—
1177	C₂³	—	4	2	no	—
1178	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1179	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1180	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1181	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1182	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1183	Q₈	—	2	1	no	—
1184	Q₈	—	2	1	no	—
1185	Q₈	—	4	2	no	—
1186	Q₈	—	8	1	no	—
1187	D₄	—	2	2	no	—
1188	D₄	—	2	2	no	—
1189	D₄	—	2	1	no	—
1190	D₄	—	2	2	no	—
1191	D₄	—	2	2	no	—
1192	D₄	—	2	1	no	—
1193	D₄	—	4	1	no	—
1194	D₄	—	4	1	no	—
1195	D₄	—	4	4	no	—
1196	D₄	—	4	2	no	—
1197	D₄	—	4	2	no	—
1198	D₄	—	4	4	no	—
1199	D₄	—	4	2	no	—
1200	D₄	—	4	2	no	—
1201	D₄	—	8	2	no	—
1202	D₄	—	8	2	no	—
1203	D₄	—	8	1	no	—
1204	D₄	—	8	1	no	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	1	no	—
1216	C₂×C₄	—	2	1	no	—
1217	C₂×C₄	—	2	1	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	1	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	2	1	no	—
1227	C₂×C₄	—	2	2	no	—
1228	C₂×C₄	—	2	2	no	—
1229	C₂×C₄	—	4	1	no	—
1230	C₂×C₄	—	4	1	no	—
1231	C₂×C₄	—	4	2	no	—
1232	C₂×C₄	—	4	2	no	—
1233	C₂×C₄	—	4	2	no	—
1234	C₂×C₄	—	4	2	no	—
1235	C₂×C₄	—	4	2	no	—
1236	C₂×C₄	—	4	2	no	—
1237	C₂×C₄	—	4	2	no	—
1238	C₂×C₄	—	8	2	no	—
1239	C₂×C₄	—	8	2	no	—
1240	C₂×C₄	—	8	1	no	—
1241	C₂×C₄	—	8	2	no	—
1242	C₂×C₄	—	8	2	no	—
1243	C₂×C₄	—	8	1	no	—
1244	C₂×C₄	—	8	1	no	—
1245	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1246	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1247	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1248	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1249	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1250	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1251	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1252	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1253	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1254	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1255	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
1256	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1257	C₈	—	2	2	no	—
1258	C₈	—	2	2	no	—
1259	C₈	—	2	2	no	—
1260	C₈	C₂×C₁₃×#41	1	4	yes	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	1	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	1	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	1	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	4	4	no	—
1275	C₂²	—	4	1	no	—
1276	C₂²	—	4	2	no	—
1277	C₂²	—	4	2	no	—
1278	C₂²	—	4	1	no	—
1279	C₂²	—	4	1	no	—
1280	C₂²	—	4	2	no	—
1281	C₂²	—	8	2	no	—
1282	C₂²	—	8	4	no	—
1283	C₂²	C₁₃×#547	1	2	yes	—
1284	C₂²	C₁₃×#575	1	2	yes	—
1285	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1286	C₄	—	2	1	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	1	no	—
1290	C₄	—	2	1	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	1	no	—
1294	C₄	—	4	1	no	—
1295	C₄	—	4	2	no	—
1296	C₄	—	4	1	no	—
1297	C₄	—	4	1	no	—
1298	C₄	—	4	2	no	—
1299	C₄	—	4	2	no	—
1300	C₄	—	4	1	no	—
1301	C₄	—	4	1	no	—
1302	C₄	—	4	1	no	—
1303	C₄	—	4	1	no	—
1304	C₄	C₁₃×#547	1	2	yes	—
1305	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1306	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1307	C₂	—	2	2	no	—
1308	C₂	—	2	2	no	—
1309	C₂	—	4	1	no	—
1310	C₂	—	4	1	no	—
1311	C₂	—	4	1	no	—
1312	C₂	—	8	2	no	—
1313	C₂	—	8	1	no	—
1314	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
1315	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
1316	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3475	C₂	semidirect
2. C₂×C₁₃×#553	C₂	semidirect
3. C₁₃×#3355	C₂	semidirect
4. C₁₃×#3351	C₂	semidirect
5. C₁₃×#3350	C₂	semidirect
6. C₁₃×#3347	C₂	semidirect
7. C₁₃×#3346	C₂	semidirect
8. C₁₃×#3345	C₂	semidirect
9. C₁₃×#3339	C₂	semidirect
10. C₁₃×#3337	C₂	semidirect
11. C₁₃×#3166	C₂	semidirect
12. C₁₃×#3094	C₂	semidirect
13. C₁₃×#3094	C₂	semidirect
14. C₁₃×#3093	C₂	semidirect
15. C₁₃×#3092	C₂	semidirect
16. C₁₃×#3080	C₂	semidirect
17. C₁₃×#3077	C₂	semidirect
18. C₁₃×#3055	C₂	semidirect
19. C₁₃×#3055	C₂	semidirect
20. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
21. D₄×C₁₃×M₁₆	C₂	semidirect
22. C₁₃×#2911	C₂	semidirect
23. C₂×C₁₃×#428	C₂	semidirect
27. C₁₃×#556	C₂²	semidirect
28. C₁₃×#555	C₂²	semidirect
29. C₁₃×#554	C₂²	semidirect
38. C₁₃×#553	C₂²	semidirect
39. C₁₃×#553	C₂²	semidirect
41. C₁₃×#552	C₂²	semidirect
42. C₁₃×#552	C₂²	semidirect
45. C₁₃×#547	C₂²	semidirect
68. C₁₃×#501	C₂²	semidirect
69. C₁₃×#501	C₂²	semidirect
70. C₁₃×#499	C₂²	semidirect
71. C₁₃×#499	C₂²	semidirect
72. C₁₃×#485	C₂²	semidirect
73. C₁₃×#485	C₂²	semidirect
74. C₁₃×#484	C₂²	semidirect
75. C₁₃×#483	C₂²	semidirect
76. C₁₃×#482	C₂²	semidirect
77. C₁₃×#482	C₂²	semidirect
78. C₁₃×#482	C₂²	semidirect
79. C₁₃×#482	C₂²	semidirect
80. C₁₃×#482	C₂²	semidirect
81. C₁₃×#482	C₂²	semidirect
82. C₁₃×#481	C₂²	semidirect
83. C₁₃×#481	C₂²	semidirect
84. C₁₃×#481	C₂²	semidirect
85. C₁₃×#480	C₂²	semidirect
86. C₁₃×#480	C₂²	semidirect
87. C₁₃×#480	C₂²	semidirect
88. C₁₃×#479	C₂²	semidirect
89. C₁₃×#479	C₂²	semidirect
90. C₁₃×#478	C₂²	semidirect
91. C₁₃×#478	C₂²	semidirect
92. C₁₃×#478	C₂²	semidirect
93. C₁₃×#478	C₂²	semidirect
94. C₁₃×#476	C₂²	semidirect
95. C₁₃×#474	C₂²	semidirect
96. C₁₃×#469	C₂²	semidirect
97. C₁₃×#469	C₂²	semidirect
98. C₁₃×#468	C₂²	semidirect
99. C₁₃×#468	C₂²	semidirect
100. C₁₃×#466	C₂²	semidirect
101. C₁₃×#466	C₂²	semidirect
102. C₁₃×#465	C₂²	semidirect
103. C₁₃×#465	C₂²	semidirect
104. C₁₃×#442	C₂²	semidirect
105. C₁₃×#440	C₂²	semidirect
106. C₄×C₁₃×SD₁₆	C₂²	semidirect
107. C₄×C₁₃×D₈	C₂²	semidirect
108. C₁₃×#436	C₂²	semidirect
109. C₁₃×#435	C₂²	semidirect
110. C₁₃×#435	C₂²	semidirect
111. C₈×D₄×C₁₃	C₂²	semidirect
121. C₁₃×#428	C₂²	semidirect
122. C₁₃×#428	C₂²	semidirect
123. C₁₃×#428	C₂²	semidirect
124. C₁₃×#428	C₂²	semidirect
125. C₁₃×#427	C₂²	semidirect
126. C₁₃×#427	C₂²	semidirect
127. C₂×C₁₃×#107	C₂²	semidirect
128. C₂×C₁₃×#106	C₂²	semidirect
345. #61255	C₁₃	direct (N × H)
416. C₁₃×M₁₆	#41	semidirect
509. #3475	C₂×C₁₃	semidirect
510. C₂×#553	C₂×C₁₃	semidirect
511. #3355	C₂×C₁₃	semidirect
512. #3351	C₂×C₁₃	semidirect
513. #3350	C₂×C₁₃	semidirect
514. #3347	C₂×C₁₃	semidirect
515. #3346	C₂×C₁₃	semidirect
516. #3345	C₂×C₁₃	semidirect
517. #3339	C₂×C₁₃	semidirect
518. #3337	C₂×C₁₃	semidirect
519. #3166	C₂×C₁₃	semidirect
520. #3094	C₂×C₁₃	semidirect
521. #3094	C₂×C₁₃	semidirect
522. #3093	C₂×C₁₃	semidirect
523. #3092	C₂×C₁₃	semidirect
524. #3080	C₂×C₁₃	semidirect
525. #3077	C₂×C₁₃	semidirect
526. #3055	C₂×C₁₃	semidirect
527. #3055	C₂×C₁₃	semidirect
528. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
529. D₄×M₁₆	C₂×C₁₃	semidirect
530. #2911	C₂×C₁₃	semidirect
531. C₂×#428	C₂×C₁₃	semidirect
629. #556	C₂²×C₁₃	semidirect
630. #555	C₂²×C₁₃	semidirect
631. #554	C₂²×C₁₃	semidirect
640. #553	C₂²×C₁₃	semidirect
641. #553	C₂²×C₁₃	semidirect
643. #552	C₂²×C₁₃	semidirect
644. #552	C₂²×C₁₃	semidirect
647. #547	C₂²×C₁₃	semidirect
670. #501	C₂²×C₁₃	semidirect
671. #501	C₂²×C₁₃	semidirect
672. #499	C₂²×C₁₃	semidirect
673. #499	C₂²×C₁₃	semidirect
674. #485	C₂²×C₁₃	semidirect
675. #485	C₂²×C₁₃	semidirect
676. #484	C₂²×C₁₃	semidirect
677. #483	C₂²×C₁₃	semidirect
678. #482	C₂²×C₁₃	semidirect
679. #482	C₂²×C₁₃	semidirect
680. #482	C₂²×C₁₃	semidirect
681. #482	C₂²×C₁₃	semidirect
682. #482	C₂²×C₁₃	semidirect
683. #482	C₂²×C₁₃	semidirect
684. #481	C₂²×C₁₃	semidirect
685. #481	C₂²×C₁₃	semidirect
686. #481	C₂²×C₁₃	semidirect
687. #480	C₂²×C₁₃	semidirect
688. #480	C₂²×C₁₃	semidirect
689. #480	C₂²×C₁₃	semidirect
690. #479	C₂²×C₁₃	semidirect
691. #479	C₂²×C₁₃	semidirect
692. #478	C₂²×C₁₃	semidirect
693. #478	C₂²×C₁₃	semidirect
694. #478	C₂²×C₁₃	semidirect
695. #478	C₂²×C₁₃	semidirect
696. #476	C₂²×C₁₃	semidirect
697. #474	C₂²×C₁₃	semidirect
698. #469	C₂²×C₁₃	semidirect
699. #469	C₂²×C₁₃	semidirect
700. #468	C₂²×C₁₃	semidirect
701. #468	C₂²×C₁₃	semidirect
702. #466	C₂²×C₁₃	semidirect
703. #466	C₂²×C₁₃	semidirect
704. #465	C₂²×C₁₃	semidirect
705. #465	C₂²×C₁₃	semidirect
706. #442	C₂²×C₁₃	semidirect
707. #440	C₂²×C₁₃	semidirect
708. C₄×SD₁₆	C₂²×C₁₃	semidirect
709. C₄×D₈	C₂²×C₁₃	semidirect
710. #436	C₂²×C₁₃	semidirect
711. #435	C₂²×C₁₃	semidirect
712. #435	C₂²×C₁₃	semidirect
713. C₈×D₄	C₂²×C₁₃	semidirect
723. #428	C₂²×C₁₃	semidirect
724. #428	C₂²×C₁₃	semidirect
725. #428	C₂²×C₁₃	semidirect
726. #428	C₂²×C₁₃	semidirect
727. #427	C₂²×C₁₃	semidirect
728. #427	C₂²×C₁₃	semidirect
729. C₂×#107	C₂²×C₁₃	semidirect
730. C₂×#106	C₂²×C₁₃	semidirect
1073. M₁₆	C₁₃×#41	semidirect
1166. C₁₃	#61255	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×#3475	2
C₂×C₁₃×#553	2
C₁₃×#3355	2
C₁₃×#3351	2
C₁₃×#3350	2
C₁₃×#3347	2
C₁₃×#3346	2
C₁₃×#3345	2
C₁₃×#3339	2
C₁₃×#3337	2
C₁₃×#3166	2
C₁₃×#3094	2
C₁₃×#3093	2
C₁₃×#3092	2
C₁₃×#3080	2
C₁₃×#3077	2
C₁₃×#3055	2
C₄×C₁₃×AGL(1,ℤ/8)	2
D₄×C₁₃×M₁₆	2
C₁₃×#2911	2
C₂×C₁₃×#428	2
#61255	13

Subgroups — C13×#61255 #15747594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61255 #15747594