Subgroups — C₁₃×#61169 #15747508

Order 3328.

2074 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3319	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3315	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3311	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3307	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3303	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3302	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3297	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3296	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3005	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2946	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, complemented
27	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
30	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#556	—	2	1	no	—
32	C₁₃×#556	C₂²	1	2	yes	complemented
33	C₁₃×#555	—	2	1	no	—
34	C₁₃×#555	C₂²	1	2	yes	complemented
35	C₁₃×#553	—	2	1	no	—
36	C₁₃×#553	C₂²	1	2	yes	complemented
37	C₁₃×#552	—	2	1	no	—
38	C₁₃×#552	C₂²	1	2	yes	complemented
39	C₁₃×#547	—	2	1	no	—
40	C₁₃×#547	—	2	1	no	—
41	C₁₃×#547	C₂²	1	2	yes	—
42	C₁₃×#547	C₂²	1	2	yes	—
43	C₁₃×#546	—	2	1	no	—
44	C₁₃×#546	—	2	1	no	—
45	C₁₃×#546	C₂²	1	2	yes	—
46	C₁₃×#546	C₂²	1	2	yes	—
47	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#538	—	2	2	no	—
49	C₁₃×#537	C₂²	1	1	yes	characteristic
50	C₁₃×#536	C₂²	1	1	yes	characteristic
51	C₁₃×#536	C₂²	1	1	yes	characteristic
52	C₁₃×#534	—	2	2	no	—
53	C₁₃×#529	—	2	2	no	—
54	C₁₃×#525	C₂²	1	1	yes	characteristic
55	C₁₃×#525	C₂²	1	1	yes	characteristic
56	C₁₃×#525	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₁₃×#123	—	2	2	no	—
58	C₁₃×#520	C₂²	1	1	yes	characteristic
59	C₁₃×#520	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#518	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#491	C₂²	1	2	yes	complemented
63	C₁₃×#489	C₂²	1	2	yes	complemented
64	C₁₃×#488	C₂²	1	2	yes	complemented
65	C₁₃×#487	C₂²	1	2	yes	complemented
66	C₁₃×#485	C₂²	1	2	yes	complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#485	C₂²	1	2	yes	complemented
69	C₁₃×#485	C₂²	1	2	yes	complemented
70	C₁₃×#484	C₂²	1	2	yes	complemented
71	C₁₃×#483	C₂²	1	2	yes	complemented
72	C₁₃×#482	C₂²	1	2	yes	complemented
73	C₁₃×#482	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	2	yes	complemented
75	C₁₃×#478	C₂²	1	2	yes	complemented
76	C₁₃×#476	C₂²	1	2	yes	complemented
77	C₁₃×#474	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×#467	C₂²	1	1	yes	characteristic, complemented
82	C₁₃×#467	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×#466	C₂²	1	1	yes	characteristic, complemented
84	C₁₃×#466	C₂²	1	1	yes	characteristic, complemented
85	C₁₃×#465	C₂²	1	1	yes	characteristic, complemented
86	C₁₃×#465	C₂²	1	2	yes	complemented
87	C₁₃×#465	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#465	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#465	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#464	C₂²	1	2	yes	complemented
91	C₁₃×#463	C₂²	1	2	yes	complemented
92	C₁₃×#462	C₂²	1	2	yes	complemented
93	C₁₃×#461	C₂²	1	2	yes	complemented
94	C₁₃×#452	C₂²	1	2	yes	complemented
95	C₁₃×#452	C₂²	1	2	yes	complemented
96	C₁₃×#452	C₂²	1	2	yes	complemented
97	C₁₃×#450	C₂²	1	2	yes	complemented
98	C₁₃×#449	C₂²	1	2	yes	complemented
99	C₁₃×#449	C₂²	1	2	yes	complemented
100	C₁₃×#449	C₂²	1	2	yes	complemented
101	C₁₃×#447	C₂²	1	2	yes	complemented
102	C₁₃×#442	C₂²	1	2	yes	complemented
103	C₁₃×#440	C₂²	1	2	yes	complemented
104	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
105	C₄×C₁₃×D₈	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	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
110	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
111	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
112	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
113	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
114	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
115	C₁₃×#418	C₂²	1	1	yes	characteristic
116	C₁₃×#418	C₂²	1	2	yes	complemented
117	C₁₃×#417	C₂²	1	1	yes	characteristic
118	C₁₃×#417	C₂²	1	1	yes	characteristic
119	C₁₃×#417	C₂²	1	2	yes	complemented
120	C₁₃×#416	C₂²	1	1	yes	characteristic
121	C₁₃×#416	C₂²	1	2	yes	complemented
122	C₁₃×#416	C₂²	1	2	yes	complemented
123	C₁₃×#416	C₂²	1	2	yes	complemented
124	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
125	C₁₃×#416	C₂²	1	2	yes	complemented
126	C₁₃×#416	C₂²	1	2	yes	complemented
127	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
130	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
131	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
132	C₁₃×#408	C₂²	1	1	yes	characteristic
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	2	yes	—
145	C₂×C₁₃×#41	C₂³	1	2	yes	—
146	C₂×C₁₃×#41	C₂³	1	2	yes	—
147	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₁₃	—	2	1	no	—
150	C₂²×D₄×C₁₃	—	2	2	no	—
151	C₂²×D₄×C₁₃	—	2	1	no	—
152	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
153	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₁₃	—	2	1	no	—
155	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
156	C₁₃×#137	—	4	2	no	—
157	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
158	C₁₃×#135	—	4	2	no	—
159	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
161	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
162	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×D₈	C₂³	1	2	yes	—
166	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
167	C₁₃×#131	—	4	2	no	—
168	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
171	C₂²×C₈×C₁₃	—	4	2	no	—
172	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
179	C₁₃×C₄⋊Q₈	—	2	1	no	—
180	C₁₃×C₄⋊Q₈	—	2	1	no	—
181	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
182	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
183	C₁₃×#126	—	2	2	no	—
184	C₁₃×#126	—	2	2	no	—
185	C₁₃×#126	—	2	2	no	—
186	C₁₃×#126	—	2	2	no	—
187	C₁₃×#125	—	2	2	no	—
188	C₁₃×#125	—	2	1	no	—
189	C₁₃×#125	C₂³	1	2	yes	—
190	C₁₃×#124	—	2	1	no	—
191	C₁₃×#124	—	2	2	no	—
192	C₁₃×#124	—	2	2	no	—
193	C₁₃×#124	—	2	2	no	—
194	C₁₃×#124	C₂³	1	2	yes	—
195	C₁₃×#123	—	2	2	no	—
196	C₁₃×#123	—	2	2	no	—
197	C₁₃×#123	—	2	1	no	—
198	C₁₃×#123	—	2	1	no	—
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	—	2	2	no	—
204	C₁₃×#123	—	2	2	no	—
205	C₁₃×#123	—	2	2	no	—
206	C₁₃×#123	—	2	2	no	—
207	C₁₃×#123	D₄	1	2	yes	—
208	C₁₃×C₂²⋊Q₈	—	2	1	no	—
209	C₁₃×C₂²⋊Q₈	—	2	1	no	—
210	C₁₃×C₂²⋊Q₈	—	2	1	no	—
211	C₁₃×C₂²⋊Q₈	—	2	2	no	—
212	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
213	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
214	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₁₃×#121	—	2	2	no	—
222	C₁₃×#121	—	2	2	no	—
223	C₁₃×#121	—	2	2	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	1	yes	characteristic
233	C₁₃×#121	C₂³	1	1	yes	characteristic
234	C₁₃×#121	C₂³	1	1	yes	characteristic
235	C₁₃×#121	C₂³	1	1	yes	characteristic
236	C₁₃×#120	—	2	1	no	—
237	C₁₃×#120	—	2	1	no	—
238	C₁₃×#120	—	2	2	no	—
239	C₁₃×#120	—	2	2	no	—
240	C₁₃×#120	D₄	1	2	yes	—
241	C₄×Q₈×C₁₃	—	2	1	no	—
242	C₄×Q₈×C₁₃	—	2	2	no	—
243	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
244	C₄×D₄×C₁₃	—	2	2	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	—	2	1	no	—
249	C₄×D₄×C₁₃	—	2	1	no	—
250	C₄×D₄×C₁₃	—	2	1	no	—
251	C₄×D₄×C₁₃	—	2	1	no	—
252	C₄×D₄×C₁₃	—	2	2	no	—
253	C₄×D₄×C₁₃	—	2	2	no	—
254	C₄×D₄×C₁₃	C₂³	1	2	yes	—
255	C₄×D₄×C₁₃	C₂³	1	2	yes	—
256	C₄×D₄×C₁₃	C₂³	1	2	yes	—
257	C₄×D₄×C₁₃	C₂³	1	2	yes	—
258	C₄×D₄×C₁₃	C₂³	1	2	yes	—
259	C₁₃×#117	—	2	1	no	—
260	C₁₃×#117	—	2	1	no	—
261	C₁₃×#117	—	2	1	no	—
262	C₁₃×#117	—	2	2	no	—
263	C₁₃×#117	—	2	2	no	—
264	C₁₃×#117	C₂³	1	1	yes	characteristic
265	C₁₃×#117	C₂³	1	2	yes	—
266	C₁₃×#117	C₂³	1	2	yes	—
267	C₁₃×#117	C₂³	1	2	yes	—
268	C₁₃×#117	C₂³	1	1	yes	characteristic
269	C₁₃×#117	C₂³	1	1	yes	characteristic
270	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
272	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
276	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₄²×C₁₃	—	2	1	no	—
281	C₁₃×#107	C₂³	1	1	yes	characteristic
282	C₁₃×#107	C₂³	1	1	yes	characteristic
283	C₁₃×#107	C₂³	1	2	yes	—
284	C₁₃×#107	C₂³	1	2	yes	—
285	C₁₃×#106	C₂³	1	1	yes	characteristic
286	C₁₃×#106	C₂³	1	1	yes	characteristic
287	C₁₃×#106	C₂³	1	2	yes	—
288	C₁₃×#106	C₂³	1	2	yes	—
289	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
290	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	1	yes	characteristic
296	C₁₃×#103	C₂³	1	1	yes	characteristic
297	C₁₃×#103	C₂³	1	2	yes	—
298	C₁₃×#103	C₂³	1	1	yes	characteristic
299	C₁₃×#103	C₂³	1	1	yes	characteristic
300	C₁₃×#103	C₂³	1	2	yes	—
301	C₁₃×#103	C₂³	1	2	yes	—
302	C₁₃×#103	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×#102	C₂³	1	2	yes	—
305	C₁₃×#102	C₂³	1	2	yes	—
306	C₁₃×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
311	C₁₃×#102	C₂³	1	2	yes	—
312	C₁₃×#102	C₂³	1	1	yes	characteristic
313	C₁₃×#102	C₂³	1	1	yes	characteristic
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	#61169	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	C₂×D₄	1	1	yes	characteristic
325	C₁₃×#41	—	2	2	no	—
326	C₁₃×#41	—	2	2	no	—
327	C₁₃×#41	—	2	4	no	—
328	C₁₃×#41	—	2	4	no	—
329	C₁₃×#41	—	2	4	no	—
330	C₁₃×#41	—	2	2	no	—
331	C₁₃×#41	—	2	2	no	—
332	C₁₃×#41	—	2	2	no	—
333	C₁₃×#41	—	2	2	no	—
334	C₁₃×#41	—	4	2	no	—
335	C₁₃×#41	—	4	2	no	—
336	C₁₃×#41	—	4	2	no	—
337	C₁₃×#41	—	4	4	no	—
338	C₁₃×#41	—	4	4	no	—
339	C₁₃×#41	—	4	4	no	—
340	C₂×Q₈×C₁₃	—	2	1	no	—
341	C₂×Q₈×C₁₃	—	2	2	no	—
342	C₂×Q₈×C₁₃	—	2	2	no	—
343	C₂×Q₈×C₁₃	—	2	2	no	—
344	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
345	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
346	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₁₃	—	2	4	no	—
349	C₂×D₄×C₁₃	—	2	1	no	—
350	C₂×D₄×C₁₃	—	2	2	no	—
351	C₂×D₄×C₁₃	—	2	2	no	—
352	C₂×D₄×C₁₃	—	2	1	no	—
353	C₂×D₄×C₁₃	—	2	2	no	—
354	C₂×D₄×C₁₃	—	2	1	no	—
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	1	no	—
360	C₂×D₄×C₁₃	—	2	2	no	—
361	C₂×D₄×C₁₃	—	2	2	no	—
362	C₂×D₄×C₁₃	—	4	2	no	—
363	C₂×D₄×C₁₃	—	4	4	no	—
364	C₂×D₄×C₁₃	—	4	8	no	—
365	C₂×D₄×C₁₃	—	4	4	no	—
366	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
368	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₁₃	#41	1	4	yes	—
371	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₁₃	—	2	2	no	—
375	C₂²×C₄×C₁₃	—	2	2	no	—
376	C₂²×C₄×C₁₃	—	2	1	no	—
377	C₂²×C₄×C₁₃	—	2	1	no	—
378	C₂²×C₄×C₁₃	—	2	1	no	—
379	C₂²×C₄×C₁₃	—	2	2	no	—
380	C₂²×C₄×C₁₃	—	2	2	no	—
381	C₂²×C₄×C₁₃	—	2	2	no	—
382	C₂²×C₄×C₁₃	—	2	2	no	—
383	C₂²×C₄×C₁₃	—	2	1	no	—
384	C₂²×C₄×C₁₃	—	2	1	no	—
385	C₂²×C₄×C₁₃	—	2	2	no	—
386	C₂²×C₄×C₁₃	—	2	2	no	—
387	C₂²×C₄×C₁₃	—	2	2	no	—
388	C₂²×C₄×C₁₃	—	4	4	no	—
389	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
393	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
396	C₁₃×Q₁₆	—	4	1	no	—
397	C₁₃×Q₁₆	—	4	2	no	—
398	C₁₃×SD₁₆	—	2	4	no	—
399	C₁₃×SD₁₆	—	4	1	no	—
400	C₁₃×SD₁₆	—	4	1	no	—
401	C₁₃×SD₁₆	—	4	2	no	—
402	C₁₃×D₈	—	2	4	no	—
403	C₁₃×D₈	—	4	1	no	—
404	C₁₃×M₁₆	—	2	2	no	—
405	C₁₃×M₁₆	—	2	2	no	—
406	C₁₃×M₁₆	—	4	2	no	—
407	C₂×C₈×C₁₃	—	2	2	no	—
408	C₂×C₈×C₁₃	—	2	2	no	—
409	C₂×C₈×C₁₃	—	4	1	no	—
410	C₂×C₈×C₁₃	—	4	1	no	—
411	C₂×C₈×C₁₃	—	4	1	no	—
412	C₂×C₈×C₁₃	—	4	1	no	—
413	C₂×C₈×C₁₃	—	4	2	no	—
414	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
416	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
418	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
420	C₁₃×C₄⋊C₄	—	2	1	no	—
421	C₁₃×C₄⋊C₄	—	2	1	no	—
422	C₁₃×C₄⋊C₄	—	2	1	no	—
423	C₁₃×C₄⋊C₄	—	2	2	no	—
424	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
429	C₁₃×C₄⋊C₄	—	2	2	no	—
430	C₁₃×C₄⋊C₄	—	2	1	no	—
431	C₁₃×C₄⋊C₄	—	2	2	no	—
432	C₁₃×C₄⋊C₄	—	2	2	no	—
433	C₁₃×C₄⋊C₄	—	2	1	no	—
434	C₁₃×C₄⋊C₄	—	2	2	no	—
435	C₁₃×C₄⋊C₄	—	2	2	no	—
436	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
437	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
438	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
439	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
440	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
441	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
442	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
443	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
444	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
445	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
446	C₁₃×C₂²⋊C₄	—	2	1	no	—
447	C₁₃×C₂²⋊C₄	—	2	2	no	—
448	C₁₃×C₂²⋊C₄	—	2	2	no	—
449	C₁₃×C₂²⋊C₄	—	2	2	no	—
450	C₁₃×C₂²⋊C₄	—	2	2	no	—
451	C₁₃×C₂²⋊C₄	—	2	2	no	—
452	C₁₃×C₂²⋊C₄	—	2	1	no	—
453	C₁₃×C₂²⋊C₄	—	2	2	no	—
454	C₁₃×C₂²⋊C₄	—	2	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	1	no	—
459	C₁₃×C₂²⋊C₄	—	2	1	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	1	no	—
465	C₁₃×C₂²⋊C₄	—	2	2	no	—
466	C₁₃×C₂²⋊C₄	—	2	2	no	—
467	C₁₃×C₂²⋊C₄	—	2	1	no	—
468	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
469	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
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	C₄²×C₁₃	—	2	2	no	—
474	C₄²×C₁₃	—	2	2	no	—
475	C₄²×C₁₃	—	2	2	no	—
476	C₄²×C₁₃	—	2	2	no	—
477	C₄²×C₁₃	—	2	1	no	—
478	C₄²×C₁₃	—	2	1	no	—
479	C₄²×C₁₃	C₂⁴	1	2	yes	—
480	#3493	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#3485	C₂×C₁₃	1	1	yes	characteristic, complemented
482	#3319	C₂×C₁₃	1	2	yes	complemented
483	#3315	C₂×C₁₃	1	2	yes	complemented
484	#3311	C₂×C₁₃	1	2	yes	complemented
485	#3307	C₂×C₁₃	1	2	yes	complemented
486	#3303	C₂×C₁₃	1	2	yes	complemented
487	#3302	C₂×C₁₃	1	2	yes	complemented
488	#3297	C₂×C₁₃	1	2	yes	complemented
489	#3296	C₂×C₁₃	1	2	yes	complemented
490	#3137	C₂×C₁₃	1	1	yes	characteristic, complemented
491	#3097	C₂×C₁₃	1	1	yes	characteristic, complemented
492	#3093	C₂×C₁₃	1	1	yes	characteristic, complemented
493	#3081	C₂×C₁₃	1	1	yes	characteristic, complemented
494	#3063	C₂×C₁₃	1	1	yes	characteristic, complemented
495	#3050	C₂×C₁₃	1	1	yes	characteristic, complemented
496	#3046	C₂×C₁₃	1	1	yes	characteristic, complemented
497	#3012	C₂×C₁₃	1	1	yes	characteristic, complemented
498	#3005	C₂×C₁₃	1	1	yes	characteristic, complemented
499	#2946	C₂×C₁₃	1	1	yes	characteristic, complemented
500	#2929	C₂×C₁₃	1	1	yes	characteristic, complemented
501	#2897	C₂×C₁₃	1	1	yes	characteristic, complemented
502	C₂×#416	C₂×C₁₃	1	1	yes	characteristic, complemented
503	C₂³×C₁₃	—	2	2	no	—
504	C₂³×C₁₃	—	2	2	no	—
505	C₂³×C₁₃	—	2	4	no	—
506	C₂³×C₁₃	—	2	1	no	—
507	C₂³×C₁₃	—	2	1	no	—
508	C₂³×C₁₃	—	4	1	no	—
509	C₂³×C₁₃	—	4	1	no	—
510	C₂³×C₁₃	—	4	4	no	—
511	C₂³×C₁₃	—	8	1	no	—
512	C₂³×C₁₃	—	8	1	no	—
513	C₂³×C₁₃	—	8	2	no	—
514	C₂³×C₁₃	—	8	2	no	—
515	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
516	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
517	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
518	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
519	Q₈×C₁₃	—	2	2	no	—
520	Q₈×C₁₃	—	2	1	no	—
521	Q₈×C₁₃	—	2	2	no	—
522	Q₈×C₁₃	—	2	1	no	—
523	Q₈×C₁₃	—	2	1	no	—
524	Q₈×C₁₃	—	2	2	no	—
525	Q₈×C₁₃	—	2	1	no	—
526	Q₈×C₁₃	—	4	2	no	—
527	Q₈×C₁₃	—	8	2	no	—
528	D₄×C₁₃	—	2	4	no	—
529	D₄×C₁₃	—	2	4	no	—
530	D₄×C₁₃	—	2	2	no	—
531	D₄×C₁₃	—	2	1	no	—
532	D₄×C₁₃	—	2	1	no	—
533	D₄×C₁₃	—	2	2	no	—
534	D₄×C₁₃	—	2	1	no	—
535	D₄×C₁₃	—	2	1	no	—
536	D₄×C₁₃	—	4	2	no	—
537	D₄×C₁₃	—	4	2	no	—
538	D₄×C₁₃	—	4	4	no	—
539	D₄×C₁₃	—	4	4	no	—
540	D₄×C₁₃	—	4	4	no	—
541	D₄×C₁₃	—	4	4	no	—
542	D₄×C₁₃	—	4	2	no	—
543	D₄×C₁₃	—	4	2	no	—
544	D₄×C₁₃	—	8	1	no	—
545	D₄×C₁₃	—	8	1	no	—
546	D₄×C₁₃	—	8	1	no	—
547	D₄×C₁₃	—	8	2	no	—
548	D₄×C₁₃	—	8	1	no	—
549	D₄×C₁₃	C₂×#41	1	4	yes	—
550	C₂×C₄×C₁₃	—	2	2	no	—
551	C₂×C₄×C₁₃	—	2	2	no	—
552	C₂×C₄×C₁₃	—	2	2	no	—
553	C₂×C₄×C₁₃	—	2	1	no	—
554	C₂×C₄×C₁₃	—	2	1	no	—
555	C₂×C₄×C₁₃	—	2	2	no	—
556	C₂×C₄×C₁₃	—	2	1	no	—
557	C₂×C₄×C₁₃	—	2	1	no	—
558	C₂×C₄×C₁₃	—	2	2	no	—
559	C₂×C₄×C₁₃	—	2	2	no	—
560	C₂×C₄×C₁₃	—	2	1	no	—
561	C₂×C₄×C₁₃	—	2	1	no	—
562	C₂×C₄×C₁₃	—	2	2	no	—
563	C₂×C₄×C₁₃	—	2	1	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	—	4	4	no	—
569	C₂×C₄×C₁₃	—	4	4	no	—
570	C₂×C₄×C₁₃	—	4	4	no	—
571	C₂×C₄×C₁₃	—	4	2	no	—
572	C₂×C₄×C₁₃	—	4	2	no	—
573	C₂×C₄×C₁₃	—	4	2	no	—
574	C₂×C₄×C₁₃	—	8	2	no	—
575	C₂×C₄×C₁₃	—	8	2	no	—
576	C₂×C₄×C₁₃	—	8	2	no	—
577	C₂×C₄×C₁₃	—	8	1	no	—
578	C₂×C₄×C₁₃	—	8	2	no	—
579	C₂×C₄×C₁₃	—	8	1	no	—
580	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
583	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
584	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
585	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
587	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
588	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
589	C₈×C₁₃	—	2	2	no	—
590	C₈×C₁₃	—	2	1	no	—
591	C₈×C₁₃	—	2	1	no	—
592	C₈×C₁₃	—	2	1	no	—
593	C₈×C₁₃	—	2	1	no	—
594	C₈×C₁₃	—	2	2	no	—
595	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
596	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
597	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic, complemented
598	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
599	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
600	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
601	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
602	#556	—	2	1	no	—
603	#556	C₂²×C₁₃	1	2	yes	complemented
604	#555	—	2	1	no	—
605	#555	C₂²×C₁₃	1	2	yes	complemented
606	#553	—	2	1	no	—
607	#553	C₂²×C₁₃	1	2	yes	complemented
608	#552	—	2	1	no	—
609	#552	C₂²×C₁₃	1	2	yes	complemented
610	#547	—	2	1	no	—
611	#547	—	2	1	no	—
612	#547	C₂²×C₁₃	1	2	yes	—
613	#547	C₂²×C₁₃	1	2	yes	—
614	#546	—	2	1	no	—
615	#546	—	2	1	no	—
616	#546	C₂²×C₁₃	1	2	yes	—
617	#546	C₂²×C₁₃	1	2	yes	—
618	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
619	#538	—	2	2	no	—
620	#537	C₂²×C₁₃	1	1	yes	characteristic
621	#536	C₂²×C₁₃	1	1	yes	characteristic
622	#536	C₂²×C₁₃	1	1	yes	characteristic
623	#534	—	2	2	no	—
624	#529	—	2	2	no	—
625	#525	C₂²×C₁₃	1	1	yes	characteristic
626	#525	C₂²×C₁₃	1	1	yes	characteristic
627	#525	C₂²×C₁₃	1	1	yes	characteristic, complemented
628	C₂×#123	—	2	2	no	—
629	#520	C₂²×C₁₃	1	1	yes	characteristic
630	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
631	#518	C₂²×C₁₃	1	1	yes	characteristic
632	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
633	#491	C₂²×C₁₃	1	2	yes	complemented
634	#489	C₂²×C₁₃	1	2	yes	complemented
635	#488	C₂²×C₁₃	1	2	yes	complemented
636	#487	C₂²×C₁₃	1	2	yes	complemented
637	#485	C₂²×C₁₃	1	2	yes	complemented
638	#485	C₂²×C₁₃	1	2	yes	complemented
639	#485	C₂²×C₁₃	1	2	yes	complemented
640	#485	C₂²×C₁₃	1	2	yes	complemented
641	#484	C₂²×C₁₃	1	2	yes	complemented
642	#483	C₂²×C₁₃	1	2	yes	complemented
643	#482	C₂²×C₁₃	1	2	yes	complemented
644	#482	C₂²×C₁₃	1	2	yes	complemented
645	#478	C₂²×C₁₃	1	2	yes	complemented
646	#478	C₂²×C₁₃	1	2	yes	complemented
647	#476	C₂²×C₁₃	1	2	yes	complemented
648	#474	C₂²×C₁₃	1	2	yes	complemented
649	#470	C₂²×C₁₃	1	2	yes	complemented
650	#468	C₂²×C₁₃	1	2	yes	complemented
651	#467	C₂²×C₁₃	1	2	yes	complemented
652	#467	C₂²×C₁₃	1	1	yes	characteristic, complemented
653	#467	C₂²×C₁₃	1	1	yes	characteristic, complemented
654	#466	C₂²×C₁₃	1	1	yes	characteristic, complemented
655	#466	C₂²×C₁₃	1	1	yes	characteristic, complemented
656	#465	C₂²×C₁₃	1	1	yes	characteristic, complemented
657	#465	C₂²×C₁₃	1	2	yes	complemented
658	#465	C₂²×C₁₃	1	1	yes	characteristic, complemented
659	#465	C₂²×C₁₃	1	1	yes	characteristic, complemented
660	#465	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	#464	C₂²×C₁₃	1	2	yes	complemented
662	#463	C₂²×C₁₃	1	2	yes	complemented
663	#462	C₂²×C₁₃	1	2	yes	complemented
664	#461	C₂²×C₁₃	1	2	yes	complemented
665	#452	C₂²×C₁₃	1	2	yes	complemented
666	#452	C₂²×C₁₃	1	2	yes	complemented
667	#452	C₂²×C₁₃	1	2	yes	complemented
668	#450	C₂²×C₁₃	1	2	yes	complemented
669	#449	C₂²×C₁₃	1	2	yes	complemented
670	#449	C₂²×C₁₃	1	2	yes	complemented
671	#449	C₂²×C₁₃	1	2	yes	complemented
672	#447	C₂²×C₁₃	1	2	yes	complemented
673	#442	C₂²×C₁₃	1	2	yes	complemented
674	#440	C₂²×C₁₃	1	2	yes	complemented
675	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
676	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
677	#435	C₂²×C₁₃	1	2	yes	complemented
678	#435	C₂²×C₁₃	1	2	yes	complemented
679	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
680	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
681	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
682	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
683	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
684	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
685	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
686	#418	C₂²×C₁₃	1	1	yes	characteristic
687	#418	C₂²×C₁₃	1	2	yes	complemented
688	#417	C₂²×C₁₃	1	1	yes	characteristic
689	#417	C₂²×C₁₃	1	1	yes	characteristic
690	#417	C₂²×C₁₃	1	2	yes	complemented
691	#416	C₂²×C₁₃	1	1	yes	characteristic
692	#416	C₂²×C₁₃	1	2	yes	complemented
693	#416	C₂²×C₁₃	1	2	yes	complemented
694	#416	C₂²×C₁₃	1	2	yes	complemented
695	#416	C₂²×C₁₃	1	2	yes	complemented
696	#416	C₂²×C₁₃	1	2	yes	complemented
697	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
698	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
699	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
700	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
701	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
702	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
703	#408	C₂²×C₁₃	1	1	yes	characteristic
704	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
705	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
706	C₂²×C₁₃	—	2	1	no	—
707	C₂²×C₁₃	—	2	1	no	—
708	C₂²×C₁₃	—	2	2	no	—
709	C₂²×C₁₃	—	2	1	no	—
710	C₂²×C₁₃	—	2	1	no	—
711	C₂²×C₁₃	—	2	2	no	—
712	C₂²×C₁₃	—	2	1	no	—
713	C₂²×C₁₃	—	2	1	no	—
714	C₂²×C₁₃	—	2	1	no	—
715	C₂²×C₁₃	—	2	1	no	—
716	C₂²×C₁₃	—	2	2	no	—
717	C₂²×C₁₃	—	2	4	no	—
718	C₂²×C₁₃	—	4	4	no	—
719	C₂²×C₁₃	—	4	2	no	—
720	C₂²×C₁₃	—	4	2	no	—
721	C₂²×C₁₃	—	4	1	no	—
722	C₂²×C₁₃	—	4	1	no	—
723	C₂²×C₁₃	—	4	1	no	—
724	C₂²×C₁₃	—	4	1	no	—
725	C₂²×C₁₃	—	4	1	no	—
726	C₂²×C₁₃	—	4	1	no	—
727	C₂²×C₁₃	—	8	4	no	—
728	C₂²×C₁₃	—	16	4	no	—
729	C₂²×C₁₃	#546	1	2	yes	—
730	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
731	C₄×C₁₃	—	2	2	no	—
732	C₄×C₁₃	—	2	2	no	—
733	C₄×C₁₃	—	2	1	no	—
734	C₄×C₁₃	—	2	1	no	—
735	C₄×C₁₃	—	2	2	no	—
736	C₄×C₁₃	—	4	2	no	—
737	C₄×C₁₃	—	4	1	no	—
738	C₄×C₁₃	—	4	1	no	—
739	C₄×C₁₃	—	4	1	no	—
740	C₄×C₁₃	—	4	2	no	—
741	C₄×C₁₃	—	4	1	no	—
742	C₄×C₁₃	—	4	1	no	—
743	C₄×C₁₃	—	4	2	no	—
744	C₄×C₁₃	—	4	1	no	—
745	C₄×C₁₃	#546	1	2	yes	—
746	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
747	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
748	H(5,𝔽₂)	—	2	4	no	—
749	H(5,𝔽₂)	—	4	2	no	—
750	C₂×#41	—	2	1	no	—
751	C₂×#41	—	2	1	no	—
752	C₂×#41	—	2	1	no	—
753	C₂×#41	—	2	4	no	—
754	C₂×#41	—	4	2	no	—
755	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
756	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
757	C₂×#41	C₂³×C₁₃	1	2	yes	—
758	C₂×#41	C₂³×C₁₃	1	2	yes	—
759	C₂×#41	C₂³×C₁₃	1	2	yes	—
760	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
761	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
762	C₂²×D₄	—	2	1	no	—
763	C₂²×D₄	—	2	2	no	—
764	C₂²×D₄	—	2	1	no	—
765	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
766	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
767	C₂³×C₄	—	2	1	no	—
768	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
769	#137	—	4	2	no	—
770	AGL(1,ℤ/8)	—	2	4	no	—
771	#135	—	4	2	no	—
772	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
773	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
776	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
777	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
778	C₂×D₈	C₂³×C₁₃	1	2	yes	—
779	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
780	#131	—	4	2	no	—
781	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
782	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
783	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
784	C₂²×C₈	—	4	2	no	—
785	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
786	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
787	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
788	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
789	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
790	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
791	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
792	C₄⋊Q₈	—	2	1	no	—
793	C₄⋊Q₈	—	2	1	no	—
794	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
795	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
796	#126	—	2	2	no	—
797	#126	—	2	2	no	—
798	#126	—	2	2	no	—
799	#126	—	2	2	no	—
800	#125	—	2	2	no	—
801	#125	—	2	1	no	—
802	#125	C₂³×C₁₃	1	2	yes	—
803	#124	—	2	1	no	—
804	#124	—	2	2	no	—
805	#124	—	2	2	no	—
806	#124	—	2	2	no	—
807	#124	C₂³×C₁₃	1	2	yes	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	—	2	1	no	—
811	#123	—	2	1	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	D₄×C₁₃	1	2	yes	—
821	C₂²⋊Q₈	—	2	1	no	—
822	C₂²⋊Q₈	—	2	1	no	—
823	C₂²⋊Q₈	—	2	1	no	—
824	C₂²⋊Q₈	—	2	2	no	—
825	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
826	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
827	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
828	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
829	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
830	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
831	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
832	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
833	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	1	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	—	2	2	no	—
842	#121	D₄×C₁₃	1	1	yes	characteristic
843	#121	D₄×C₁₃	1	1	yes	characteristic
844	#121	C₂³×C₁₃	1	1	yes	characteristic
845	#121	C₂³×C₁₃	1	1	yes	characteristic
846	#121	C₂³×C₁₃	1	1	yes	characteristic
847	#121	C₂³×C₁₃	1	1	yes	characteristic
848	#121	C₂³×C₁₃	1	2	yes	—
849	#120	—	2	1	no	—
850	#120	—	2	1	no	—
851	#120	—	2	2	no	—
852	#120	—	2	2	no	—
853	#120	D₄×C₁₃	1	2	yes	—
854	C₄×Q₈	—	2	1	no	—
855	C₄×Q₈	—	2	2	no	—
856	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	C₂³×C₁₃	1	2	yes	—
868	C₄×D₄	C₂³×C₁₃	1	2	yes	—
869	C₄×D₄	C₂³×C₁₃	1	2	yes	—
870	C₄×D₄	C₂³×C₁₃	1	2	yes	—
871	C₄×D₄	C₂³×C₁₃	1	2	yes	—
872	#117	—	2	1	no	—
873	#117	—	2	1	no	—
874	#117	—	2	1	no	—
875	#117	—	2	2	no	—
876	#117	—	2	2	no	—
877	#117	C₂³×C₁₃	1	2	yes	—
878	#117	C₂³×C₁₃	1	2	yes	—
879	#117	C₂³×C₁₃	1	1	yes	characteristic
880	#117	C₂³×C₁₃	1	1	yes	characteristic
881	#117	C₂³×C₁₃	1	2	yes	—
882	#117	C₂³×C₁₃	1	1	yes	characteristic
883	C₂×C₄⋊C₄	—	2	1	no	—
884	C₂×C₄⋊C₄	—	2	2	no	—
885	C₂×C₄⋊C₄	—	2	2	no	—
886	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
888	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
889	C₂×C₂²⋊C₄	—	2	1	no	—
890	C₂×C₂²⋊C₄	—	2	2	no	—
891	C₂×C₂²⋊C₄	—	2	2	no	—
892	C₂×C₂²⋊C₄	—	2	2	no	—
893	C₂×C₄²	—	2	1	no	—
894	#107	C₂³×C₁₃	1	1	yes	characteristic
895	#107	C₂³×C₁₃	1	1	yes	characteristic
896	#107	C₂³×C₁₃	1	2	yes	—
897	#107	C₂³×C₁₃	1	2	yes	—
898	#106	C₂³×C₁₃	1	1	yes	characteristic
899	#106	C₂³×C₁₃	1	1	yes	characteristic
900	#106	C₂³×C₁₃	1	2	yes	—
901	#106	C₂³×C₁₃	1	2	yes	—
902	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
903	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
904	#103	C₂³×C₁₃	1	2	yes	—
905	#103	C₂³×C₁₃	1	2	yes	—
906	#103	C₂³×C₁₃	1	2	yes	—
907	#103	C₂³×C₁₃	1	2	yes	—
908	#103	C₂³×C₁₃	1	1	yes	characteristic
909	#103	C₂³×C₁₃	1	1	yes	characteristic
910	#103	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	2	yes	—
914	#103	C₂³×C₁₃	1	2	yes	—
915	#103	C₂³×C₁₃	1	2	yes	—
916	#102	C₂³×C₁₃	1	2	yes	—
917	#102	C₂³×C₁₃	1	2	yes	—
918	#102	C₂³×C₁₃	1	2	yes	—
919	#102	C₂³×C₁₃	1	2	yes	—
920	#102	C₂³×C₁₃	1	1	yes	characteristic
921	#102	C₂³×C₁₃	1	2	yes	—
922	#102	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	2	yes	—
928	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
930	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
931	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
932	#97	C₂³×C₁₃	1	2	yes	—
933	C₄×C₈	C₂³×C₁₃	1	2	yes	—
934	C₂×C₁₃	—	2	2	no	—
935	C₂×C₁₃	—	4	1	no	—
936	C₂×C₁₃	—	4	1	no	—
937	C₂×C₁₃	—	4	2	no	—
938	C₂×C₁₃	—	4	4	no	—
939	C₂×C₁₃	—	8	1	no	—
940	C₂×C₁₃	—	8	1	no	—
941	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
942	C₂×C₁₃	#3584	1	1	yes	characteristic
943	C₂×C₁₃	#3584	1	1	yes	characteristic
944	C₂⁴	—	2	1	no	—
945	C₂⁴	—	2	2	no	—
946	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
947	#41	—	2	2	no	—
948	#41	—	2	2	no	—
949	#41	—	2	4	no	—
950	#41	—	2	4	no	—
951	#41	—	2	4	no	—
952	#41	—	2	2	no	—
953	#41	—	2	2	no	—
954	#41	—	2	2	no	—
955	#41	—	2	2	no	—
956	#41	—	4	2	no	—
957	#41	—	4	2	no	—
958	#41	—	4	2	no	—
959	#41	—	4	4	no	—
960	#41	—	4	4	no	—
961	#41	—	4	4	no	—
962	C₂×Q₈	—	2	1	no	—
963	C₂×Q₈	—	2	2	no	—
964	C₂×Q₈	—	2	2	no	—
965	C₂×Q₈	—	2	2	no	—
966	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
967	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
968	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
969	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
970	C₂×D₄	—	2	4	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	1	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	2	1	no	—
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	4	2	no	—
985	C₂×D₄	—	4	4	no	—
986	C₂×D₄	—	4	8	no	—
987	C₂×D₄	—	4	4	no	—
988	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
989	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
990	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
991	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
992	C₂×D₄	C₁₃×#41	1	4	yes	—
993	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
994	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
995	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	2	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	4	4	no	—
1011	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1012	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1013	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1015	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1016	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1017	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1018	Q₁₆	—	4	1	no	—
1019	Q₁₆	—	4	2	no	—
1020	SD₁₆	—	2	4	no	—
1021	SD₁₆	—	4	1	no	—
1022	SD₁₆	—	4	1	no	—
1023	SD₁₆	—	4	2	no	—
1024	D₈	—	2	4	no	—
1025	D₈	—	4	1	no	—
1026	M₁₆	—	2	2	no	—
1027	M₁₆	—	2	2	no	—
1028	M₁₆	—	4	2	no	—
1029	C₂×C₈	—	2	2	no	—
1030	C₂×C₈	—	2	2	no	—
1031	C₂×C₈	—	4	1	no	—
1032	C₂×C₈	—	4	1	no	—
1033	C₂×C₈	—	4	1	no	—
1034	C₂×C₈	—	4	1	no	—
1035	C₂×C₈	—	4	2	no	—
1036	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1037	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1038	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1039	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1040	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1041	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1059	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1060	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1061	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1062	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1063	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1064	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1065	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1091	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1092	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1093	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1094	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1095	C₄²	—	2	2	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	2	no	—
1098	C₄²	—	2	2	no	—
1099	C₄²	—	2	1	no	—
1100	C₄²	—	2	1	no	—
1101	C₄²	C₂⁴×C₁₃	1	2	yes	—
1102	C₁₃	#61169	1	1	yes	characteristic, direct product factor, Sylow
1103	C₂³	—	2	2	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	4	no	—
1106	C₂³	—	2	1	no	—
1107	C₂³	—	2	1	no	—
1108	C₂³	—	4	1	no	—
1109	C₂³	—	4	1	no	—
1110	C₂³	—	4	4	no	—
1111	C₂³	—	8	1	no	—
1112	C₂³	—	8	1	no	—
1113	C₂³	—	8	2	no	—
1114	C₂³	—	8	2	no	—
1115	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1116	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1117	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1118	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1119	Q₈	—	2	2	no	—
1120	Q₈	—	2	1	no	—
1121	Q₈	—	2	2	no	—
1122	Q₈	—	2	1	no	—
1123	Q₈	—	2	1	no	—
1124	Q₈	—	2	2	no	—
1125	Q₈	—	2	1	no	—
1126	Q₈	—	4	2	no	—
1127	Q₈	—	8	2	no	—
1128	D₄	—	2	4	no	—
1129	D₄	—	2	4	no	—
1130	D₄	—	2	2	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	2	2	no	—
1134	D₄	—	2	1	no	—
1135	D₄	—	2	1	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	4	no	—
1139	D₄	—	4	4	no	—
1140	D₄	—	4	4	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	4	2	no	—
1143	D₄	—	4	2	no	—
1144	D₄	—	8	1	no	—
1145	D₄	—	8	1	no	—
1146	D₄	—	8	1	no	—
1147	D₄	—	8	2	no	—
1148	D₄	—	8	1	no	—
1149	D₄	C₂×C₁₃×#41	1	4	yes	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	4	4	no	—
1169	C₂×C₄	—	4	4	no	—
1170	C₂×C₄	—	4	4	no	—
1171	C₂×C₄	—	4	2	no	—
1172	C₂×C₄	—	4	2	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	8	2	no	—
1175	C₂×C₄	—	8	2	no	—
1176	C₂×C₄	—	8	2	no	—
1177	C₂×C₄	—	8	1	no	—
1178	C₂×C₄	—	8	2	no	—
1179	C₂×C₄	—	8	1	no	—
1180	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1181	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1182	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1183	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1184	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1185	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1186	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1187	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1188	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1189	C₈	—	2	2	no	—
1190	C₈	—	2	1	no	—
1191	C₈	—	2	1	no	—
1192	C₈	—	2	1	no	—
1193	C₈	—	2	1	no	—
1194	C₈	—	2	2	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	1	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	4	no	—
1207	C₂²	—	4	4	no	—
1208	C₂²	—	4	2	no	—
1209	C₂²	—	4	2	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	1	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	8	4	no	—
1217	C₂²	—	16	4	no	—
1218	C₂²	C₁₃×#546	1	2	yes	—
1219	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1220	C₄	—	2	2	no	—
1221	C₄	—	2	2	no	—
1222	C₄	—	2	1	no	—
1223	C₄	—	2	1	no	—
1224	C₄	—	2	2	no	—
1225	C₄	—	4	2	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	2	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	2	no	—
1233	C₄	—	4	1	no	—
1234	C₄	C₁₃×#546	1	2	yes	—
1235	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1236	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1237	C₂	—	2	2	no	—
1238	C₂	—	4	1	no	—
1239	C₂	—	4	1	no	—
1240	C₂	—	4	2	no	—
1241	C₂	—	4	4	no	—
1242	C₂	—	8	1	no	—
1243	C₂	—	8	1	no	—
1244	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
1245	C₂	C₁₃×#3584	1	1	yes	characteristic
1246	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3493	C₂	semidirect
2. C₁₃×#3485	C₂	semidirect
3. C₁₃×#3319	C₂	semidirect
4. C₁₃×#3315	C₂	semidirect
5. C₁₃×#3311	C₂	semidirect
6. C₁₃×#3307	C₂	semidirect
7. C₁₃×#3303	C₂	semidirect
8. C₁₃×#3302	C₂	semidirect
9. C₁₃×#3297	C₂	semidirect
10. C₁₃×#3296	C₂	semidirect
11. C₁₃×#3137	C₂	semidirect
12. C₁₃×#3097	C₂	semidirect
13. C₁₃×#3093	C₂	semidirect
14. C₁₃×#3081	C₂	semidirect
15. C₁₃×#3063	C₂	semidirect
16. C₁₃×#3050	C₂	semidirect
17. C₁₃×#3046	C₂	semidirect
18. C₁₃×#3012	C₂	semidirect
19. C₁₃×#3005	C₂	semidirect
20. C₁₃×#2946	C₂	semidirect
21. C₁₃×#2929	C₂	semidirect
22. C₁₃×#2897	C₂	semidirect
23. C₂×C₁₃×#416	C₂	semidirect
26. C₂×C₁₃×#137	C₂²	semidirect
30. C₂³×C₈×C₁₃	C₂²	semidirect
32. C₁₃×#556	C₂²	semidirect
34. C₁₃×#555	C₂²	semidirect
36. C₁₃×#553	C₂²	semidirect
38. C₁₃×#552	C₂²	semidirect
47. C₁₃×#544	C₂²	semidirect
56. C₁₃×#525	C₂²	semidirect
59. C₁₃×#520	C₂²	semidirect
61. C₂×C₁₃×#117	C₂²	semidirect
62. C₁₃×#491	C₂²	semidirect
63. C₁₃×#489	C₂²	semidirect
64. C₁₃×#488	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#485	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
69. C₁₃×#485	C₂²	semidirect
70. C₁₃×#484	C₂²	semidirect
71. C₁₃×#483	C₂²	semidirect
72. C₁₃×#482	C₂²	semidirect
73. C₁₃×#482	C₂²	semidirect
74. C₁₃×#478	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#476	C₂²	semidirect
77. C₁₃×#474	C₂²	semidirect
78. C₁₃×#470	C₂²	semidirect
79. C₁₃×#468	C₂²	semidirect
80. C₁₃×#467	C₂²	semidirect
81. C₁₃×#467	C₂²	semidirect
82. C₁₃×#467	C₂²	semidirect
83. C₁₃×#466	C₂²	semidirect
84. C₁₃×#466	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#465	C₂²	semidirect
87. C₁₃×#465	C₂²	semidirect
88. C₁₃×#465	C₂²	semidirect
89. C₁₃×#465	C₂²	semidirect
90. C₁₃×#464	C₂²	semidirect
91. C₁₃×#463	C₂²	semidirect
92. C₁₃×#462	C₂²	semidirect
93. C₁₃×#461	C₂²	semidirect
94. C₁₃×#452	C₂²	semidirect
95. C₁₃×#452	C₂²	semidirect
96. C₁₃×#452	C₂²	semidirect
97. C₁₃×#450	C₂²	semidirect
98. C₁₃×#449	C₂²	semidirect
99. C₁₃×#449	C₂²	semidirect
100. C₁₃×#449	C₂²	semidirect
101. C₁₃×#447	C₂²	semidirect
102. C₁₃×#442	C₂²	semidirect
103. C₁₃×#440	C₂²	semidirect
104. C₄×C₁₃×SD₁₆	C₂²	semidirect
105. C₄×C₁₃×D₈	C₂²	semidirect
106. C₁₃×#435	C₂²	semidirect
107. C₁₃×#435	C₂²	semidirect
108. C₈×D₄×C₁₃	C₂²	semidirect
109. C₈×D₄×C₁₃	C₂²	semidirect
110. C₁₃×#428	C₂²	semidirect
111. C₁₃×#428	C₂²	semidirect
112. C₁₃×#427	C₂²	semidirect
113. C₁₃×#424	C₂²	semidirect
114. C₁₃×#419	C₂²	semidirect
116. C₁₃×#418	C₂²	semidirect
119. C₁₃×#417	C₂²	semidirect
121. C₁₃×#416	C₂²	semidirect
122. C₁₃×#416	C₂²	semidirect
123. C₁₃×#416	C₂²	semidirect
124. C₁₃×#416	C₂²	semidirect
125. C₁₃×#416	C₂²	semidirect
126. C₁₃×#416	C₂²	semidirect
127. C₂×C₁₃×#103	C₂²	semidirect
128. C₂×C₁₃×#103	C₂²	semidirect
131. C₂×C₁₃×#102	C₂²	semidirect
133. C₁₃×#407	C₂²	semidirect
134. C₁₃×#405	C₂²	semidirect
321. #61169	C₁₃	direct (N × H)
480. #3493	C₂×C₁₃	semidirect
481. #3485	C₂×C₁₃	semidirect
482. #3319	C₂×C₁₃	semidirect
483. #3315	C₂×C₁₃	semidirect
484. #3311	C₂×C₁₃	semidirect
485. #3307	C₂×C₁₃	semidirect
486. #3303	C₂×C₁₃	semidirect
487. #3302	C₂×C₁₃	semidirect
488. #3297	C₂×C₁₃	semidirect
489. #3296	C₂×C₁₃	semidirect
490. #3137	C₂×C₁₃	semidirect
491. #3097	C₂×C₁₃	semidirect
492. #3093	C₂×C₁₃	semidirect
493. #3081	C₂×C₁₃	semidirect
494. #3063	C₂×C₁₃	semidirect
495. #3050	C₂×C₁₃	semidirect
496. #3046	C₂×C₁₃	semidirect
497. #3012	C₂×C₁₃	semidirect
498. #3005	C₂×C₁₃	semidirect
499. #2946	C₂×C₁₃	semidirect
500. #2929	C₂×C₁₃	semidirect
501. #2897	C₂×C₁₃	semidirect
502. C₂×#416	C₂×C₁₃	semidirect
597. C₂×#137	C₂²×C₁₃	semidirect
601. C₂³×C₈	C₂²×C₁₃	semidirect
603. #556	C₂²×C₁₃	semidirect
605. #555	C₂²×C₁₃	semidirect
607. #553	C₂²×C₁₃	semidirect
609. #552	C₂²×C₁₃	semidirect
618. #544	C₂²×C₁₃	semidirect
627. #525	C₂²×C₁₃	semidirect
630. #520	C₂²×C₁₃	semidirect
632. C₂×#117	C₂²×C₁₃	semidirect
633. #491	C₂²×C₁₃	semidirect
634. #489	C₂²×C₁₃	semidirect
635. #488	C₂²×C₁₃	semidirect
636. #487	C₂²×C₁₃	semidirect
637. #485	C₂²×C₁₃	semidirect
638. #485	C₂²×C₁₃	semidirect
639. #485	C₂²×C₁₃	semidirect
640. #485	C₂²×C₁₃	semidirect
641. #484	C₂²×C₁₃	semidirect
642. #483	C₂²×C₁₃	semidirect
643. #482	C₂²×C₁₃	semidirect
644. #482	C₂²×C₁₃	semidirect
645. #478	C₂²×C₁₃	semidirect
646. #478	C₂²×C₁₃	semidirect
647. #476	C₂²×C₁₃	semidirect
648. #474	C₂²×C₁₃	semidirect
649. #470	C₂²×C₁₃	semidirect
650. #468	C₂²×C₁₃	semidirect
651. #467	C₂²×C₁₃	semidirect
652. #467	C₂²×C₁₃	semidirect
653. #467	C₂²×C₁₃	semidirect
654. #466	C₂²×C₁₃	semidirect
655. #466	C₂²×C₁₃	semidirect
656. #465	C₂²×C₁₃	semidirect
657. #465	C₂²×C₁₃	semidirect
658. #465	C₂²×C₁₃	semidirect
659. #465	C₂²×C₁₃	semidirect
660. #465	C₂²×C₁₃	semidirect
661. #464	C₂²×C₁₃	semidirect
662. #463	C₂²×C₁₃	semidirect
663. #462	C₂²×C₁₃	semidirect
664. #461	C₂²×C₁₃	semidirect
665. #452	C₂²×C₁₃	semidirect
666. #452	C₂²×C₁₃	semidirect
667. #452	C₂²×C₁₃	semidirect
668. #450	C₂²×C₁₃	semidirect
669. #449	C₂²×C₁₃	semidirect
670. #449	C₂²×C₁₃	semidirect
671. #449	C₂²×C₁₃	semidirect
672. #447	C₂²×C₁₃	semidirect
673. #442	C₂²×C₁₃	semidirect
674. #440	C₂²×C₁₃	semidirect
675. C₄×SD₁₆	C₂²×C₁₃	semidirect
676. C₄×D₈	C₂²×C₁₃	semidirect
677. #435	C₂²×C₁₃	semidirect
678. #435	C₂²×C₁₃	semidirect
679. C₈×D₄	C₂²×C₁₃	semidirect
680. C₈×D₄	C₂²×C₁₃	semidirect
681. #428	C₂²×C₁₃	semidirect
682. #428	C₂²×C₁₃	semidirect
683. #427	C₂²×C₁₃	semidirect
684. #424	C₂²×C₁₃	semidirect
685. #419	C₂²×C₁₃	semidirect
687. #418	C₂²×C₁₃	semidirect
690. #417	C₂²×C₁₃	semidirect
692. #416	C₂²×C₁₃	semidirect
693. #416	C₂²×C₁₃	semidirect
694. #416	C₂²×C₁₃	semidirect
695. #416	C₂²×C₁₃	semidirect
696. #416	C₂²×C₁₃	semidirect
697. #416	C₂²×C₁₃	semidirect
698. C₂×#103	C₂²×C₁₃	semidirect
699. C₂×#103	C₂²×C₁₃	semidirect
702. C₂×#102	C₂²×C₁₃	semidirect
704. #407	C₂²×C₁₃	semidirect
705. #405	C₂²×C₁₃	semidirect
1102. C₁₃	#61169	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×#3493	2
C₁₃×#3485	2
C₁₃×#3319	2
C₁₃×#3315	2
C₁₃×#3311	2
C₁₃×#3307	2
C₁₃×#3303	2
C₁₃×#3302	2
C₁₃×#3297	2
C₁₃×#3296	2
C₁₃×#3137	2
C₁₃×#3097	2
C₁₃×#3093	2
C₁₃×#3081	2
C₁₃×#3063	2
C₁₃×#3050	2
C₁₃×#3046	2
C₁₃×#3012	2
C₁₃×#3005	2
C₁₃×#2946	2
C₁₃×#2929	2
C₁₃×#2897	2
C₂×C₁₃×#416	2
#61169	13

Subgroups — C13×#61169 #15747508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61169 #15747508