Subgroups — C₁₃×#61171 #15747510

Order 3328.

2174 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3319	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3318	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3309	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3308	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3305	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3301	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3297	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3294	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3006	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×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₁₃×D₈	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×#555	C₂²	1	2	yes	complemented
32	C₁₃×#553	C₂²	1	2	yes	complemented
33	C₁₃×#553	C₂²	1	2	yes	complemented
34	C₁₃×#551	—	2	2	no	—
35	C₁₃×#550	C₂²	1	2	yes	complemented
36	C₁₃×#548	C₂²	1	2	yes	complemented
37	C₁₃×#547	C₂²	1	2	yes	complemented
38	C₁₃×#546	—	2	2	no	—
39	C₁₃×#546	—	2	2	no	—
40	C₁₃×#546	C₂²	1	2	yes	complemented
41	D₄²×C₁₃	—	2	2	no	—
42	D₄²×C₁₃	C₂²	1	2	yes	complemented
43	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#542	—	2	1	no	—
45	C₁₃×#540	—	2	1	no	—
46	C₁₃×#537	—	2	1	no	—
47	C₁₃×#537	C₂²	1	1	yes	characteristic
48	C₁₃×#535	—	2	1	no	—
49	C₁₃×#535	C₂²	1	1	yes	characteristic
50	C₁₃×#535	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#532	—	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×#121	—	2	1	no	—
56	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
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, 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×#484	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×#480	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×#477	C₂²	1	2	yes	complemented
77	C₁₃×#474	C₂²	1	2	yes	complemented
78	C₁₃×#469	C₂²	1	2	yes	complemented
79	C₁₃×#468	C₂²	1	2	yes	complemented
80	C₁₃×#466	C₂²	1	2	yes	complemented
81	C₁₃×#466	C₂²	1	2	yes	complemented
82	C₁₃×#466	C₂²	1	2	yes	complemented
83	C₁₃×#466	C₂²	1	2	yes	complemented
84	C₁₃×#466	C₂²	1	2	yes	complemented
85	C₁₃×#465	C₂²	1	2	yes	complemented
86	C₁₃×#463	C₂²	1	2	yes	complemented
87	C₁₃×#463	C₂²	1	2	yes	complemented
88	C₁₃×#459	C₂²	1	2	yes	complemented
89	C₁₃×#459	C₂²	1	2	yes	complemented
90	C₁₃×#449	C₂²	1	2	yes	complemented
91	C₁₃×#449	C₂²	1	2	yes	complemented
92	C₁₃×#449	C₂²	1	2	yes	complemented
93	C₁₃×#449	C₂²	1	2	yes	complemented
94	C₁₃×#448	C₂²	1	2	yes	complemented
95	C₁₃×#447	C₂²	1	2	yes	complemented
96	C₁₃×#447	C₂²	1	2	yes	complemented
97	C₁₃×#447	C₂²	1	2	yes	complemented
98	C₁₃×#442	C₂²	1	2	yes	complemented
99	C₁₃×#440	C₂²	1	2	yes	complemented
100	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
101	C₄×C₁₃×D₈	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×#107	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×#102	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
129	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, 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	2	no	—
139	C₂×C₁₃×#41	—	2	1	no	—
140	C₂×C₁₃×#41	—	2	1	no	—
141	C₂×C₁₃×#41	—	2	4	no	—
142	C₂×C₁₃×#41	—	4	2	no	—
143	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×#41	C₂³	1	2	yes	—
147	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×#41	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	1	no	—
154	C₂²×D₄×C₁₃	—	2	2	no	—
155	C₂²×D₄×C₁₃	—	2	2	no	—
156	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
157	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
158	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
159	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
160	C₂³×C₄×C₁₃	—	2	1	no	—
161	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
162	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
163	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
164	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
165	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₁₃×D₈	—	4	2	no	—
167	C₂×C₁₃×D₈	C₂³	1	2	yes	—
168	C₂×C₁₃×D₈	C₂³	1	2	yes	—
169	C₂×C₁₃×D₈	C₂³	1	2	yes	—
170	C₂×C₁₃×D₈	C₂³	1	2	yes	—
171	C₁₃×#131	—	4	2	no	—
172	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
173	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
174	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
175	C₂²×C₈×C₁₃	—	4	2	no	—
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	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
181	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
182	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
183	C₁₃×C₄⋊Q₈	—	2	1	no	—
184	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
185	C₁₃×#127	—	2	1	no	—
186	C₁₃×#127	—	2	2	no	—
187	C₁₃×#127	C₂³	1	2	yes	—
188	C₁₃×#126	—	2	2	no	—
189	C₁₃×#126	—	2	2	no	—
190	C₁₃×#125	—	2	1	no	—
191	C₁₃×#125	C₂³	1	2	yes	—
192	C₁₃×#124	—	2	1	no	—
193	C₁₃×#124	—	2	2	no	—
194	C₁₃×#124	—	2	2	no	—
195	C₁₃×#124	—	2	2	no	—
196	C₁₃×#124	C₂³	1	2	yes	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	2	no	—
202	C₁₃×#123	D₄	1	2	yes	—
203	C₁₃×C₂²⋊Q₈	—	2	1	no	—
204	C₁₃×C₂²⋊Q₈	—	2	2	no	—
205	C₁₃×C₂²⋊Q₈	—	2	2	no	—
206	C₁₃×C₂²⋊Q₈	—	2	2	no	—
207	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₁₃×#121	—	2	1	no	—
211	C₁₃×#121	—	2	2	no	—
212	C₁₃×#121	—	2	2	no	—
213	C₁₃×#121	—	2	2	no	—
214	C₁₃×#121	—	2	2	no	—
215	C₁₃×#121	—	2	2	no	—
216	C₁₃×#121	—	2	1	no	—
217	C₁₃×#121	—	2	1	no	—
218	C₁₃×#121	—	2	1	no	—
219	C₁₃×#121	—	2	1	no	—
220	C₁₃×#121	—	2	1	no	—
221	C₁₃×#121	—	2	1	no	—
222	C₁₃×#121	—	2	2	no	—
223	C₁₃×#121	—	2	2	no	—
224	C₁₃×#121	—	2	2	no	—
225	C₁₃×#121	—	2	2	no	—
226	C₁₃×#121	D₄	1	1	yes	characteristic
227	C₁₃×#121	D₄	1	1	yes	characteristic
228	C₁₃×#121	C₂³	1	2	yes	—
229	C₁₃×#121	C₂³	1	2	yes	—
230	C₁₃×#121	C₂³	1	2	yes	—
231	C₁₃×#121	C₂³	1	2	yes	—
232	C₁₃×#121	C₂³	1	2	yes	—
233	C₁₃×#121	C₂³	1	2	yes	—
234	C₁₃×#121	C₂³	1	2	yes	—
235	C₁₃×#120	—	2	2	no	—
236	C₁₃×#120	—	2	2	no	—
237	C₁₃×#120	—	2	2	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	C₂³	1	2	yes	—
243	C₄×D₄×C₁₃	—	2	1	no	—
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	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	C₄×D₄×C₁₃	C₂³	1	2	yes	—
256	C₄×D₄×C₁₃	C₂³	1	2	yes	—
257	C₁₃×#117	—	2	1	no	—
258	C₁₃×#117	—	2	1	no	—
259	C₁₃×#117	—	2	1	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	C₂³	1	1	yes	characteristic
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	2	yes	—
272	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₁₃×C₂²⋊C₄	—	2	2	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×#107	C₂³	1	2	yes	—
282	C₁₃×#107	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×#102	C₂³	1	1	yes	characteristic
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	1	yes	characteristic
300	C₁₃×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
307	C₁₃×#102	C₂³	1	2	yes	—
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	#61171	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂⁴×C₁₃	—	2	1	no	—
323	C₂⁴×C₁₃	—	2	1	no	—
324	C₂⁴×C₁₃	—	2	2	no	—
325	C₂⁴×C₁₃	—	2	1	no	—
326	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
327	C₁₃×#41	—	2	2	no	—
328	C₁₃×#41	—	2	2	no	—
329	C₁₃×#41	—	2	2	no	—
330	C₁₃×#41	—	2	2	no	—
331	C₁₃×#41	—	2	4	no	—
332	C₁₃×#41	—	2	2	no	—
333	C₁₃×#41	—	2	2	no	—
334	C₁₃×#41	—	2	2	no	—
335	C₁₃×#41	—	4	4	no	—
336	C₁₃×#41	—	4	1	no	—
337	C₁₃×#41	—	4	1	no	—
338	C₁₃×#41	—	4	2	no	—
339	C₁₃×#41	—	4	4	no	—
340	C₁₃×#41	—	4	4	no	—
341	C₁₃×#41	—	8	4	no	—
342	C₁₃×#41	#41	1	4	yes	complemented
343	C₂×Q₈×C₁₃	—	2	1	no	—
344	C₂×Q₈×C₁₃	—	2	2	no	—
345	C₂×Q₈×C₁₃	—	2	2	no	—
346	C₂×Q₈×C₁₃	—	4	1	no	—
347	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
348	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₁₃	—	2	1	no	—
351	C₂×D₄×C₁₃	—	2	2	no	—
352	C₂×D₄×C₁₃	—	2	4	no	—
353	C₂×D₄×C₁₃	—	2	2	no	—
354	C₂×D₄×C₁₃	—	2	2	no	—
355	C₂×D₄×C₁₃	—	2	1	no	—
356	C₂×D₄×C₁₃	—	2	1	no	—
357	C₂×D₄×C₁₃	—	2	2	no	—
358	C₂×D₄×C₁₃	—	2	1	no	—
359	C₂×D₄×C₁₃	—	2	2	no	—
360	C₂×D₄×C₁₃	—	2	2	no	—
361	C₂×D₄×C₁₃	—	2	2	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	1	no	—
366	C₂×D₄×C₁₃	—	2	2	no	—
367	C₂×D₄×C₁₃	—	2	1	no	—
368	C₂×D₄×C₁₃	—	2	2	no	—
369	C₂×D₄×C₁₃	—	2	2	no	—
370	C₂×D₄×C₁₃	—	2	2	no	—
371	C₂×D₄×C₁₃	—	2	2	no	—
372	C₂×D₄×C₁₃	—	2	2	no	—
373	C₂×D₄×C₁₃	—	2	2	no	—
374	C₂×D₄×C₁₃	—	4	1	no	—
375	C₂×D₄×C₁₃	—	4	2	no	—
376	C₂×D₄×C₁₃	—	4	4	no	—
377	C₂×D₄×C₁₃	—	4	8	no	—
378	C₂×D₄×C₁₃	—	4	4	no	—
379	C₂×D₄×C₁₃	—	8	4	no	—
380	C₂×D₄×C₁₃	—	8	2	no	—
381	C₂×D₄×C₁₃	—	8	2	no	—
382	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
383	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
384	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
385	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
386	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
387	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
388	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
389	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₁₃	—	2	1	no	—
391	C₂²×C₄×C₁₃	—	2	2	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	1	no	—
396	C₂²×C₄×C₁₃	—	2	1	no	—
397	C₂²×C₄×C₁₃	—	2	1	no	—
398	C₂²×C₄×C₁₃	—	2	2	no	—
399	C₂²×C₄×C₁₃	—	2	1	no	—
400	C₂²×C₄×C₁₃	—	2	1	no	—
401	C₂²×C₄×C₁₃	—	2	2	no	—
402	C₂²×C₄×C₁₃	—	2	1	no	—
403	C₂²×C₄×C₁₃	—	2	2	no	—
404	C₂²×C₄×C₁₃	—	2	2	no	—
405	C₂²×C₄×C₁₃	—	2	2	no	—
406	C₂²×C₄×C₁₃	—	4	4	no	—
407	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
412	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
414	C₁₃×SD₁₆	—	2	4	no	—
415	C₁₃×SD₁₆	—	4	2	no	—
416	C₁₃×D₈	—	2	4	no	—
417	C₁₃×D₈	—	4	2	no	—
418	C₁₃×D₈	—	4	2	no	—
419	C₁₃×D₈	—	4	2	no	—
420	C₁₃×M₁₆	—	2	2	no	—
421	C₁₃×M₁₆	—	2	2	no	—
422	C₁₃×M₁₆	—	4	2	no	—
423	C₂×C₈×C₁₃	—	2	2	no	—
424	C₂×C₈×C₁₃	—	2	2	no	—
425	C₂×C₈×C₁₃	—	4	1	no	—
426	C₂×C₈×C₁₃	—	4	1	no	—
427	C₂×C₈×C₁₃	—	4	1	no	—
428	C₂×C₈×C₁₃	—	4	1	no	—
429	C₂×C₈×C₁₃	—	4	2	no	—
430	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
431	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
432	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
433	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
434	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
435	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
436	C₁₃×C₄⋊C₄	—	2	1	no	—
437	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
442	C₁₃×C₄⋊C₄	—	2	2	no	—
443	C₁₃×C₄⋊C₄	—	2	2	no	—
444	C₁₃×C₄⋊C₄	—	2	2	no	—
445	C₁₃×C₄⋊C₄	—	2	2	no	—
446	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
447	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
448	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
449	C₁₃×C₄⋊C₄	C₂×D₄	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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
455	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
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	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	—	2	2	no	—
471	C₁₃×C₂²⋊C₄	—	2	2	no	—
472	C₁₃×C₂²⋊C₄	—	2	2	no	—
473	C₁₃×C₂²⋊C₄	—	2	2	no	—
474	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
475	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
476	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
477	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
478	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
479	C₄²×C₁₃	—	2	1	no	—
480	C₄²×C₁₃	—	2	1	no	—
481	C₄²×C₁₃	—	2	1	no	—
482	C₄²×C₁₃	—	2	1	no	—
483	C₄²×C₁₃	—	2	2	no	—
484	C₄²×C₁₃	—	2	2	no	—
485	C₄²×C₁₃	C₂⁴	1	2	yes	—
486	#3494	C₂×C₁₃	1	1	yes	characteristic, complemented
487	#3488	C₂×C₁₃	1	1	yes	characteristic, complemented
488	#3319	C₂×C₁₃	1	2	yes	complemented
489	#3318	C₂×C₁₃	1	2	yes	complemented
490	#3309	C₂×C₁₃	1	2	yes	complemented
491	#3308	C₂×C₁₃	1	2	yes	complemented
492	#3305	C₂×C₁₃	1	2	yes	complemented
493	#3301	C₂×C₁₃	1	2	yes	complemented
494	#3297	C₂×C₁₃	1	2	yes	complemented
495	#3294	C₂×C₁₃	1	2	yes	complemented
496	#3136	C₂×C₁₃	1	1	yes	characteristic, complemented
497	#3098	C₂×C₁₃	1	1	yes	characteristic, complemented
498	#3094	C₂×C₁₃	1	1	yes	characteristic, complemented
499	#3083	C₂×C₁₃	1	1	yes	characteristic, complemented
500	#3062	C₂×C₁₃	1	1	yes	characteristic, complemented
501	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
502	#3041	C₂×C₁₃	1	1	yes	characteristic, complemented
503	#3008	C₂×C₁₃	1	1	yes	characteristic, complemented
504	#3006	C₂×C₁₃	1	1	yes	characteristic, complemented
505	#2946	C₂×C₁₃	1	1	yes	characteristic, complemented
506	#2929	C₂×C₁₃	1	1	yes	characteristic, complemented
507	#2897	C₂×C₁₃	1	1	yes	characteristic, complemented
508	C₂×#416	C₂×C₁₃	1	1	yes	characteristic, complemented
509	C₂³×C₁₃	—	2	2	no	—
510	C₂³×C₁₃	—	2	2	no	—
511	C₂³×C₁₃	—	2	1	no	—
512	C₂³×C₁₃	—	2	2	no	—
513	C₂³×C₁₃	—	2	2	no	—
514	C₂³×C₁₃	—	2	1	no	—
515	C₂³×C₁₃	—	4	1	no	—
516	C₂³×C₁₃	—	4	2	no	—
517	C₂³×C₁₃	—	4	4	no	—
518	C₂³×C₁₃	—	4	2	no	—
519	C₂³×C₁₃	—	4	2	no	—
520	C₂³×C₁₃	—	4	2	no	—
521	C₂³×C₁₃	—	8	1	no	—
522	C₂³×C₁₃	—	8	1	no	—
523	C₂³×C₁₃	—	8	1	no	—
524	C₂³×C₁₃	—	8	2	no	—
525	C₂³×C₁₃	—	8	1	no	—
526	C₂³×C₁₃	—	8	1	no	—
527	C₂³×C₁₃	—	8	2	no	—
528	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
529	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
530	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
531	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
532	Q₈×C₁₃	—	2	2	no	—
533	Q₈×C₁₃	—	2	1	no	—
534	Q₈×C₁₃	—	2	1	no	—
535	Q₈×C₁₃	—	2	1	no	—
536	Q₈×C₁₃	—	4	2	no	—
537	Q₈×C₁₃	—	8	2	no	—
538	Q₈×C₁₃	C₂×#41	1	2	yes	—
539	D₄×C₁₃	—	2	4	no	—
540	D₄×C₁₃	—	2	4	no	—
541	D₄×C₁₃	—	2	4	no	—
542	D₄×C₁₃	—	2	2	no	—
543	D₄×C₁₃	—	2	2	no	—
544	D₄×C₁₃	—	2	2	no	—
545	D₄×C₁₃	—	2	1	no	—
546	D₄×C₁₃	—	2	1	no	—
547	D₄×C₁₃	—	2	2	no	—
548	D₄×C₁₃	—	2	2	no	—
549	D₄×C₁₃	—	2	1	no	—
550	D₄×C₁₃	—	4	2	no	—
551	D₄×C₁₃	—	4	4	no	—
552	D₄×C₁₃	—	4	2	no	—
553	D₄×C₁₃	—	4	4	no	—
554	D₄×C₁₃	—	4	2	no	—
555	D₄×C₁₃	—	4	2	no	—
556	D₄×C₁₃	—	4	2	no	—
557	D₄×C₁₃	—	4	4	no	—
558	D₄×C₁₃	—	4	4	no	—
559	D₄×C₁₃	—	4	2	no	—
560	D₄×C₁₃	—	4	2	no	—
561	D₄×C₁₃	—	8	2	no	—
562	D₄×C₁₃	—	8	2	no	—
563	D₄×C₁₃	—	8	2	no	—
564	D₄×C₁₃	—	8	2	no	—
565	D₄×C₁₃	—	8	2	no	—
566	D₄×C₁₃	—	8	2	no	—
567	D₄×C₁₃	—	8	2	no	—
568	D₄×C₁₃	C₂×#41	1	2	yes	—
569	C₂×C₄×C₁₃	—	2	2	no	—
570	C₂×C₄×C₁₃	—	2	1	no	—
571	C₂×C₄×C₁₃	—	2	2	no	—
572	C₂×C₄×C₁₃	—	2	2	no	—
573	C₂×C₄×C₁₃	—	2	4	no	—
574	C₂×C₄×C₁₃	—	2	1	no	—
575	C₂×C₄×C₁₃	—	2	1	no	—
576	C₂×C₄×C₁₃	—	2	2	no	—
577	C₂×C₄×C₁₃	—	2	1	no	—
578	C₂×C₄×C₁₃	—	2	1	no	—
579	C₂×C₄×C₁₃	—	2	2	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	2	no	—
585	C₂×C₄×C₁₃	—	2	2	no	—
586	C₂×C₄×C₁₃	—	2	1	no	—
587	C₂×C₄×C₁₃	—	4	2	no	—
588	C₂×C₄×C₁₃	—	4	4	no	—
589	C₂×C₄×C₁₃	—	4	2	no	—
590	C₂×C₄×C₁₃	—	4	2	no	—
591	C₂×C₄×C₁₃	—	4	2	no	—
592	C₂×C₄×C₁₃	—	4	2	no	—
593	C₂×C₄×C₁₃	—	8	2	no	—
594	C₂×C₄×C₁₃	—	8	2	no	—
595	C₂×C₄×C₁₃	—	8	2	no	—
596	C₂×C₄×C₁₃	—	8	1	no	—
597	C₂×C₄×C₁₃	—	8	1	no	—
598	C₂×C₄×C₁₃	—	8	1	no	—
599	C₂×C₄×C₁₃	—	8	2	no	—
600	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
601	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
602	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
603	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
604	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
605	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
606	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
607	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
608	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
609	C₈×C₁₃	—	2	2	no	—
610	C₈×C₁₃	—	2	1	no	—
611	C₈×C₁₃	—	2	1	no	—
612	C₈×C₁₃	—	2	1	no	—
613	C₈×C₁₃	—	2	1	no	—
614	C₈×C₁₃	—	2	2	no	—
615	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
616	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
617	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
618	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic, complemented
619	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
620	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
621	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	#555	C₂²×C₁₃	1	2	yes	complemented
623	#553	C₂²×C₁₃	1	2	yes	complemented
624	#553	C₂²×C₁₃	1	2	yes	complemented
625	#551	—	2	2	no	—
626	#550	C₂²×C₁₃	1	2	yes	complemented
627	#548	C₂²×C₁₃	1	2	yes	complemented
628	#547	C₂²×C₁₃	1	2	yes	complemented
629	#546	—	2	2	no	—
630	#546	—	2	2	no	—
631	#546	C₂²×C₁₃	1	2	yes	complemented
632	D₄²	—	2	2	no	—
633	D₄²	C₂²×C₁₃	1	2	yes	complemented
634	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	#542	—	2	1	no	—
636	#540	—	2	1	no	—
637	#537	—	2	1	no	—
638	#537	C₂²×C₁₃	1	1	yes	characteristic
639	#535	—	2	1	no	—
640	#535	C₂²×C₁₃	1	1	yes	characteristic
641	#535	C₂²×C₁₃	1	1	yes	characteristic, complemented
642	#532	—	2	1	no	—
643	#529	—	2	1	no	—
644	#525	—	2	1	no	—
645	#525	C₂²×C₁₃	1	1	yes	characteristic
646	C₂×#121	—	2	1	no	—
647	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
648	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	#520	C₂²×C₁₃	1	1	yes	characteristic
650	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
651	#518	C₂²×C₁₃	1	1	yes	characteristic, complemented
652	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
653	#490	C₂²×C₁₃	1	2	yes	complemented
654	#489	C₂²×C₁₃	1	2	yes	complemented
655	#488	C₂²×C₁₃	1	2	yes	complemented
656	#486	C₂²×C₁₃	1	2	yes	complemented
657	#485	C₂²×C₁₃	1	2	yes	complemented
658	#484	C₂²×C₁₃	1	2	yes	complemented
659	#482	C₂²×C₁₃	1	2	yes	complemented
660	#482	C₂²×C₁₃	1	2	yes	complemented
661	#482	C₂²×C₁₃	1	2	yes	complemented
662	#481	C₂²×C₁₃	1	2	yes	complemented
663	#480	C₂²×C₁₃	1	2	yes	complemented
664	#480	C₂²×C₁₃	1	2	yes	complemented
665	#479	C₂²×C₁₃	1	2	yes	complemented
666	#478	C₂²×C₁₃	1	2	yes	complemented
667	#477	C₂²×C₁₃	1	2	yes	complemented
668	#474	C₂²×C₁₃	1	2	yes	complemented
669	#469	C₂²×C₁₃	1	2	yes	complemented
670	#468	C₂²×C₁₃	1	2	yes	complemented
671	#466	C₂²×C₁₃	1	2	yes	complemented
672	#466	C₂²×C₁₃	1	2	yes	complemented
673	#466	C₂²×C₁₃	1	2	yes	complemented
674	#466	C₂²×C₁₃	1	2	yes	complemented
675	#466	C₂²×C₁₃	1	2	yes	complemented
676	#465	C₂²×C₁₃	1	2	yes	complemented
677	#463	C₂²×C₁₃	1	2	yes	complemented
678	#463	C₂²×C₁₃	1	2	yes	complemented
679	#459	C₂²×C₁₃	1	2	yes	complemented
680	#459	C₂²×C₁₃	1	2	yes	complemented
681	#449	C₂²×C₁₃	1	2	yes	complemented
682	#449	C₂²×C₁₃	1	2	yes	complemented
683	#449	C₂²×C₁₃	1	2	yes	complemented
684	#449	C₂²×C₁₃	1	2	yes	complemented
685	#448	C₂²×C₁₃	1	2	yes	complemented
686	#447	C₂²×C₁₃	1	2	yes	complemented
687	#447	C₂²×C₁₃	1	2	yes	complemented
688	#447	C₂²×C₁₃	1	2	yes	complemented
689	#442	C₂²×C₁₃	1	2	yes	complemented
690	#440	C₂²×C₁₃	1	2	yes	complemented
691	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
692	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
693	#435	C₂²×C₁₃	1	2	yes	complemented
694	#435	C₂²×C₁₃	1	2	yes	complemented
695	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
696	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
697	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
698	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
699	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
700	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
701	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
702	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
703	#418	C₂²×C₁₃	1	2	yes	complemented
704	#417	C₂²×C₁₃	1	1	yes	characteristic
705	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
706	#417	C₂²×C₁₃	1	2	yes	complemented
707	#416	C₂²×C₁₃	1	1	yes	characteristic
708	#416	C₂²×C₁₃	1	1	yes	characteristic
709	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
710	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
711	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
712	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
713	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
714	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
715	#416	C₂²×C₁₃	1	2	yes	complemented
716	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
717	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
718	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
719	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
720	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
721	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
722	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
723	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
724	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
725	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
726	C₂²×C₁₃	—	2	1	no	—
727	C₂²×C₁₃	—	2	1	no	—
728	C₂²×C₁₃	—	2	1	no	—
729	C₂²×C₁₃	—	2	1	no	—
730	C₂²×C₁₃	—	2	1	no	—
731	C₂²×C₁₃	—	2	2	no	—
732	C₂²×C₁₃	—	2	1	no	—
733	C₂²×C₁₃	—	2	2	no	—
734	C₂²×C₁₃	—	2	2	no	—
735	C₂²×C₁₃	—	2	2	no	—
736	C₂²×C₁₃	—	2	1	no	—
737	C₂²×C₁₃	—	4	4	no	—
738	C₂²×C₁₃	—	4	1	no	—
739	C₂²×C₁₃	—	4	1	no	—
740	C₂²×C₁₃	—	4	2	no	—
741	C₂²×C₁₃	—	4	1	no	—
742	C₂²×C₁₃	—	4	2	no	—
743	C₂²×C₁₃	—	4	1	no	—
744	C₂²×C₁₃	—	4	2	no	—
745	C₂²×C₁₃	—	4	2	no	—
746	C₂²×C₁₃	—	4	2	no	—
747	C₂²×C₁₃	—	4	2	no	—
748	C₂²×C₁₃	—	4	1	no	—
749	C₂²×C₁₃	—	8	4	no	—
750	C₂²×C₁₃	—	16	2	no	—
751	C₂²×C₁₃	—	16	2	no	—
752	C₂²×C₁₃	—	16	4	no	—
753	C₂²×C₁₃	#546	1	2	yes	—
754	C₂²×C₁₃	#576	1	2	yes	—
755	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
756	C₄×C₁₃	—	2	2	no	—
757	C₄×C₁₃	—	2	1	no	—
758	C₄×C₁₃	—	2	1	no	—
759	C₄×C₁₃	—	2	2	no	—
760	C₄×C₁₃	—	2	2	no	—
761	C₄×C₁₃	—	2	2	no	—
762	C₄×C₁₃	—	4	1	no	—
763	C₄×C₁₃	—	4	1	no	—
764	C₄×C₁₃	—	4	1	no	—
765	C₄×C₁₃	—	4	1	no	—
766	C₄×C₁₃	—	4	1	no	—
767	C₄×C₁₃	—	4	2	no	—
768	C₄×C₁₃	—	4	2	no	—
769	C₄×C₁₃	#546	1	2	yes	—
770	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
771	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
772	H(5,𝔽₂)	—	2	4	no	—
773	H(5,𝔽₂)	—	4	2	no	—
774	C₂×#41	—	2	1	no	—
775	C₂×#41	—	2	2	no	—
776	C₂×#41	—	2	1	no	—
777	C₂×#41	—	2	1	no	—
778	C₂×#41	—	2	4	no	—
779	C₂×#41	—	4	2	no	—
780	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
781	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
782	C₂×#41	C₂³×C₁₃	1	2	yes	—
783	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
784	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
785	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
786	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
787	C₂²×D₄	—	2	1	no	—
788	C₂²×D₄	—	2	1	no	—
789	C₂²×D₄	—	2	1	no	—
790	C₂²×D₄	—	2	1	no	—
791	C₂²×D₄	—	2	2	no	—
792	C₂²×D₄	—	2	2	no	—
793	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
794	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
795	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
796	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
797	C₂³×C₄	—	2	1	no	—
798	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
799	AGL(1,ℤ/8)	—	2	4	no	—
800	AGL(1,ℤ/8)	—	4	2	no	—
801	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
802	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
803	C₂×D₈	—	4	2	no	—
804	C₂×D₈	C₂³×C₁₃	1	2	yes	—
805	C₂×D₈	C₂³×C₁₃	1	2	yes	—
806	C₂×D₈	C₂³×C₁₃	1	2	yes	—
807	C₂×D₈	C₂³×C₁₃	1	2	yes	—
808	#131	—	4	2	no	—
809	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
810	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
811	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
812	C₂²×C₈	—	4	2	no	—
813	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
814	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
815	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
816	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
817	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
818	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
819	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
820	C₄⋊Q₈	—	2	1	no	—
821	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
822	#127	—	2	1	no	—
823	#127	—	2	2	no	—
824	#127	C₂³×C₁₃	1	2	yes	—
825	#126	—	2	2	no	—
826	#126	—	2	2	no	—
827	#125	—	2	1	no	—
828	#125	C₂³×C₁₃	1	2	yes	—
829	#124	—	2	1	no	—
830	#124	—	2	2	no	—
831	#124	—	2	2	no	—
832	#124	—	2	2	no	—
833	#124	C₂³×C₁₃	1	2	yes	—
834	#123	—	2	2	no	—
835	#123	—	2	2	no	—
836	#123	—	2	2	no	—
837	#123	—	2	2	no	—
838	#123	—	2	2	no	—
839	#123	D₄×C₁₃	1	2	yes	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	—	2	2	no	—
842	C₂²⋊Q₈	—	2	2	no	—
843	C₂²⋊Q₈	—	2	2	no	—
844	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
845	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
846	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
847	#121	—	2	1	no	—
848	#121	—	2	2	no	—
849	#121	—	2	2	no	—
850	#121	—	2	2	no	—
851	#121	—	2	2	no	—
852	#121	—	2	2	no	—
853	#121	—	2	1	no	—
854	#121	—	2	1	no	—
855	#121	—	2	1	no	—
856	#121	—	2	1	no	—
857	#121	—	2	1	no	—
858	#121	—	2	1	no	—
859	#121	—	2	2	no	—
860	#121	—	2	2	no	—
861	#121	—	2	2	no	—
862	#121	—	2	2	no	—
863	#121	D₄×C₁₃	1	1	yes	characteristic
864	#121	D₄×C₁₃	1	1	yes	characteristic
865	#121	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
871	#121	C₂³×C₁₃	1	2	yes	—
872	#120	—	2	2	no	—
873	#120	—	2	2	no	—
874	#120	—	2	2	no	—
875	#120	—	2	2	no	—
876	#120	—	2	2	no	—
877	#120	D₄×C₁₃	1	2	yes	—
878	C₄×Q₈	—	2	1	no	—
879	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	2	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	2	no	—
885	C₄×D₄	—	2	2	no	—
886	C₄×D₄	—	2	2	no	—
887	C₄×D₄	—	2	2	no	—
888	C₄×D₄	—	2	2	no	—
889	C₄×D₄	C₂³×C₁₃	1	2	yes	—
890	C₄×D₄	C₂³×C₁₃	1	2	yes	—
891	C₄×D₄	C₂³×C₁₃	1	2	yes	—
892	C₄×D₄	C₂³×C₁₃	1	2	yes	—
893	C₄×D₄	C₂³×C₁₃	1	2	yes	—
894	#117	—	2	1	no	—
895	#117	—	2	1	no	—
896	#117	—	2	1	no	—
897	#117	—	2	2	no	—
898	#117	C₂³×C₁₃	1	1	yes	characteristic
899	#117	C₂³×C₁₃	1	1	yes	characteristic
900	#117	C₂³×C₁₃	1	1	yes	characteristic
901	#117	C₂³×C₁₃	1	1	yes	characteristic
902	#117	C₂³×C₁₃	1	2	yes	—
903	#117	C₂³×C₁₃	1	1	yes	characteristic
904	C₂×C₄⋊C₄	—	2	1	no	—
905	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
906	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
907	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
908	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
909	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
910	C₂×C₂²⋊C₄	—	2	1	no	—
911	C₂×C₂²⋊C₄	—	2	1	no	—
912	C₂×C₂²⋊C₄	—	2	1	no	—
913	C₂×C₂²⋊C₄	—	2	2	no	—
914	C₂×C₂²⋊C₄	—	2	2	no	—
915	C₂×C₄²	—	2	1	no	—
916	#107	C₂³×C₁₃	1	2	yes	—
917	#107	C₂³×C₁₃	1	2	yes	—
918	#107	C₂³×C₁₃	1	2	yes	—
919	#107	C₂³×C₁₃	1	2	yes	—
920	#106	C₂³×C₁₃	1	2	yes	—
921	#106	C₂³×C₁₃	1	2	yes	—
922	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
923	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
924	#103	C₂³×C₁₃	1	1	yes	characteristic
925	#103	C₂³×C₁₃	1	1	yes	characteristic
926	#103	C₂³×C₁₃	1	1	yes	characteristic
927	#103	C₂³×C₁₃	1	1	yes	characteristic
928	#103	C₂³×C₁₃	1	1	yes	characteristic
929	#103	C₂³×C₁₃	1	1	yes	characteristic
930	#103	C₂³×C₁₃	1	1	yes	characteristic
931	#103	C₂³×C₁₃	1	1	yes	characteristic
932	#103	C₂³×C₁₃	1	2	yes	—
933	#103	C₂³×C₁₃	1	2	yes	—
934	#102	C₂³×C₁₃	1	1	yes	characteristic
935	#102	C₂³×C₁₃	1	2	yes	—
936	#102	C₂³×C₁₃	1	1	yes	characteristic
937	#102	C₂³×C₁₃	1	1	yes	characteristic
938	#102	C₂³×C₁₃	1	1	yes	characteristic
939	#102	C₂³×C₁₃	1	1	yes	characteristic
940	#102	C₂³×C₁₃	1	1	yes	characteristic
941	#102	C₂³×C₁₃	1	1	yes	characteristic
942	#102	C₂³×C₁₃	1	1	yes	characteristic
943	#102	C₂³×C₁₃	1	2	yes	—
944	#102	C₂³×C₁₃	1	2	yes	—
945	#102	C₂³×C₁₃	1	2	yes	—
946	#102	C₂³×C₁₃	1	2	yes	—
947	#102	C₂³×C₁₃	1	2	yes	—
948	#102	C₂³×C₁₃	1	2	yes	—
949	#102	C₂³×C₁₃	1	2	yes	—
950	#102	C₂³×C₁₃	1	2	yes	—
951	#102	C₂³×C₁₃	1	2	yes	—
952	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
953	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
954	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
955	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
956	#97	C₂³×C₁₃	1	2	yes	—
957	C₄×C₈	C₂³×C₁₃	1	2	yes	—
958	C₂×C₁₃	—	2	2	no	—
959	C₂×C₁₃	—	2	2	no	—
960	C₂×C₁₃	—	4	1	no	—
961	C₂×C₁₃	—	4	2	no	—
962	C₂×C₁₃	—	4	2	no	—
963	C₂×C₁₃	—	8	1	no	—
964	C₂×C₁₃	—	8	2	no	—
965	C₂×C₁₃	—	8	2	no	—
966	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
967	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
968	C₂×C₁₃	#3584	1	1	yes	characteristic
969	C₂⁴	—	2	1	no	—
970	C₂⁴	—	2	1	no	—
971	C₂⁴	—	2	2	no	—
972	C₂⁴	—	2	1	no	—
973	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
974	#41	—	2	2	no	—
975	#41	—	2	2	no	—
976	#41	—	2	2	no	—
977	#41	—	2	2	no	—
978	#41	—	2	4	no	—
979	#41	—	2	2	no	—
980	#41	—	2	2	no	—
981	#41	—	2	2	no	—
982	#41	—	4	4	no	—
983	#41	—	4	1	no	—
984	#41	—	4	1	no	—
985	#41	—	4	2	no	—
986	#41	—	4	4	no	—
987	#41	—	4	4	no	—
988	#41	—	8	4	no	—
989	#41	C₁₃×#41	1	4	yes	complemented
990	C₂×Q₈	—	2	1	no	—
991	C₂×Q₈	—	2	2	no	—
992	C₂×Q₈	—	2	2	no	—
993	C₂×Q₈	—	4	1	no	—
994	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
995	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
996	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	4	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	2	no	—
1005	C₂×D₄	—	2	1	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	2	2	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	2	2	no	—
1010	C₂×D₄	—	2	2	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	2	1	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	2	no	—
1018	C₂×D₄	—	2	2	no	—
1019	C₂×D₄	—	2	2	no	—
1020	C₂×D₄	—	2	2	no	—
1021	C₂×D₄	—	4	1	no	—
1022	C₂×D₄	—	4	2	no	—
1023	C₂×D₄	—	4	4	no	—
1024	C₂×D₄	—	4	8	no	—
1025	C₂×D₄	—	4	4	no	—
1026	C₂×D₄	—	8	4	no	—
1027	C₂×D₄	—	8	2	no	—
1028	C₂×D₄	—	8	2	no	—
1029	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1030	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1031	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1032	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1033	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1034	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1035	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1036	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	2	no	—
1039	C₂²×C₄	—	2	2	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	1	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	2	1	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	2	2	no	—
1049	C₂²×C₄	—	2	1	no	—
1050	C₂²×C₄	—	2	2	no	—
1051	C₂²×C₄	—	2	2	no	—
1052	C₂²×C₄	—	2	2	no	—
1053	C₂²×C₄	—	4	4	no	—
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	C₂⁴×C₁₃	1	1	yes	characteristic
1058	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1059	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1060	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1061	SD₁₆	—	2	4	no	—
1062	SD₁₆	—	4	2	no	—
1063	D₈	—	2	4	no	—
1064	D₈	—	4	2	no	—
1065	D₈	—	4	2	no	—
1066	D₈	—	4	2	no	—
1067	M₁₆	—	2	2	no	—
1068	M₁₆	—	2	2	no	—
1069	M₁₆	—	4	2	no	—
1070	C₂×C₈	—	2	2	no	—
1071	C₂×C₈	—	2	2	no	—
1072	C₂×C₈	—	4	1	no	—
1073	C₂×C₈	—	4	1	no	—
1074	C₂×C₈	—	4	1	no	—
1075	C₂×C₈	—	4	1	no	—
1076	C₂×C₈	—	4	2	no	—
1077	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1078	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1079	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1080	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1081	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1082	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	1	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	—	2	2	no	—
1092	C₄⋊C₄	—	2	2	no	—
1093	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1094	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1095	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1096	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1097	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1098	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1099	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1100	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1101	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1102	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	2	no	—
1117	C₂²⋊C₄	—	2	2	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1122	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1123	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1124	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1125	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1126	C₄²	—	2	1	no	—
1127	C₄²	—	2	1	no	—
1128	C₄²	—	2	1	no	—
1129	C₄²	—	2	1	no	—
1130	C₄²	—	2	2	no	—
1131	C₄²	—	2	2	no	—
1132	C₄²	C₂⁴×C₁₃	1	2	yes	—
1133	C₁₃	#61171	1	1	yes	characteristic, direct product factor, Sylow
1134	C₂³	—	2	2	no	—
1135	C₂³	—	2	2	no	—
1136	C₂³	—	2	1	no	—
1137	C₂³	—	2	2	no	—
1138	C₂³	—	2	2	no	—
1139	C₂³	—	2	1	no	—
1140	C₂³	—	4	1	no	—
1141	C₂³	—	4	2	no	—
1142	C₂³	—	4	4	no	—
1143	C₂³	—	4	2	no	—
1144	C₂³	—	4	2	no	—
1145	C₂³	—	4	2	no	—
1146	C₂³	—	8	1	no	—
1147	C₂³	—	8	1	no	—
1148	C₂³	—	8	1	no	—
1149	C₂³	—	8	2	no	—
1150	C₂³	—	8	1	no	—
1151	C₂³	—	8	1	no	—
1152	C₂³	—	8	2	no	—
1153	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1154	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1155	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1156	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1157	Q₈	—	2	2	no	—
1158	Q₈	—	2	1	no	—
1159	Q₈	—	2	1	no	—
1160	Q₈	—	2	1	no	—
1161	Q₈	—	4	2	no	—
1162	Q₈	—	8	2	no	—
1163	Q₈	C₂×C₁₃×#41	1	2	yes	—
1164	D₄	—	2	4	no	—
1165	D₄	—	2	4	no	—
1166	D₄	—	2	4	no	—
1167	D₄	—	2	2	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	2	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	2	1	no	—
1172	D₄	—	2	2	no	—
1173	D₄	—	2	2	no	—
1174	D₄	—	2	1	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	4	no	—
1177	D₄	—	4	2	no	—
1178	D₄	—	4	4	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	4	4	no	—
1183	D₄	—	4	4	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	8	2	no	—
1187	D₄	—	8	2	no	—
1188	D₄	—	8	2	no	—
1189	D₄	—	8	2	no	—
1190	D₄	—	8	2	no	—
1191	D₄	—	8	2	no	—
1192	D₄	—	8	2	no	—
1193	D₄	C₂×C₁₃×#41	1	2	yes	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	4	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	4	2	no	—
1213	C₂×C₄	—	4	4	no	—
1214	C₂×C₄	—	4	2	no	—
1215	C₂×C₄	—	4	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	8	2	no	—
1219	C₂×C₄	—	8	2	no	—
1220	C₂×C₄	—	8	2	no	—
1221	C₂×C₄	—	8	1	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	—	8	1	no	—
1224	C₂×C₄	—	8	2	no	—
1225	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1226	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1227	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1228	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1229	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1230	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1231	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1232	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1233	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1234	C₈	—	2	2	no	—
1235	C₈	—	2	1	no	—
1236	C₈	—	2	1	no	—
1237	C₈	—	2	1	no	—
1238	C₈	—	2	1	no	—
1239	C₈	—	2	2	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	2	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	1	no	—
1247	C₂²	—	2	2	no	—
1248	C₂²	—	2	1	no	—
1249	C₂²	—	2	2	no	—
1250	C₂²	—	2	2	no	—
1251	C₂²	—	4	4	no	—
1252	C₂²	—	4	1	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	4	2	no	—
1256	C₂²	—	4	1	no	—
1257	C₂²	—	4	2	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	4	2	no	—
1260	C₂²	—	4	1	no	—
1261	C₂²	—	4	2	no	—
1262	C₂²	—	4	2	no	—
1263	C₂²	—	8	4	no	—
1264	C₂²	—	16	2	no	—
1265	C₂²	—	16	2	no	—
1266	C₂²	—	16	4	no	—
1267	C₂²	C₁₃×#546	1	2	yes	—
1268	C₂²	C₁₃×#576	1	2	yes	—
1269	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1270	C₄	—	2	2	no	—
1271	C₄	—	2	2	no	—
1272	C₄	—	2	1	no	—
1273	C₄	—	2	1	no	—
1274	C₄	—	2	2	no	—
1275	C₄	—	2	2	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	2	no	—
1279	C₄	—	4	2	no	—
1280	C₄	—	4	1	no	—
1281	C₄	—	4	1	no	—
1282	C₄	—	4	1	no	—
1283	C₄	C₁₃×#546	1	2	yes	—
1284	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1285	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1286	C₂	—	2	2	no	—
1287	C₂	—	2	2	no	—
1288	C₂	—	4	1	no	—
1289	C₂	—	4	2	no	—
1290	C₂	—	4	2	no	—
1291	C₂	—	8	1	no	—
1292	C₂	—	8	2	no	—
1293	C₂	—	8	2	no	—
1294	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
1295	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
1296	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×#3494	C₂	semidirect
2. C₁₃×#3488	C₂	semidirect
3. C₁₃×#3319	C₂	semidirect
4. C₁₃×#3318	C₂	semidirect
5. C₁₃×#3309	C₂	semidirect
6. C₁₃×#3308	C₂	semidirect
7. C₁₃×#3305	C₂	semidirect
8. C₁₃×#3301	C₂	semidirect
9. C₁₃×#3297	C₂	semidirect
10. C₁₃×#3294	C₂	semidirect
11. C₁₃×#3136	C₂	semidirect
12. C₁₃×#3098	C₂	semidirect
13. C₁₃×#3094	C₂	semidirect
14. C₁₃×#3083	C₂	semidirect
15. C₁₃×#3062	C₂	semidirect
16. C₂×C₁₃×#466	C₂	semidirect
17. C₁₃×#3041	C₂	semidirect
18. C₁₃×#3008	C₂	semidirect
19. C₁₃×#3006	C₂	semidirect
20. C₁₃×#2946	C₂	semidirect
21. C₁₃×#2929	C₂	semidirect
22. C₁₃×#2897	C₂	semidirect
23. C₂×C₁₃×#416	C₂	semidirect
27. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂²×C₁₃×D₈	C₂²	semidirect
29. C₂×C₁₃×#131	C₂²	semidirect
30. C₂³×C₈×C₁₃	C₂²	semidirect
31. C₁₃×#555	C₂²	semidirect
32. C₁₃×#553	C₂²	semidirect
33. C₁₃×#553	C₂²	semidirect
35. C₁₃×#550	C₂²	semidirect
36. C₁₃×#548	C₂²	semidirect
37. C₁₃×#547	C₂²	semidirect
40. C₁₃×#546	C₂²	semidirect
42. D₄²×C₁₃	C₂²	semidirect
43. C₁₃×#544	C₂²	semidirect
50. C₁₃×#535	C₂²	semidirect
57. C₂×C₁₃×#121	C₂²	semidirect
59. C₁₃×#520	C₂²	semidirect
60. C₁₃×#518	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×#484	C₂²	semidirect
68. C₁₃×#482	C₂²	semidirect
69. C₁₃×#482	C₂²	semidirect
70. C₁₃×#482	C₂²	semidirect
71. C₁₃×#481	C₂²	semidirect
72. C₁₃×#480	C₂²	semidirect
73. C₁₃×#480	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#477	C₂²	semidirect
77. C₁₃×#474	C₂²	semidirect
78. C₁₃×#469	C₂²	semidirect
79. C₁₃×#468	C₂²	semidirect
80. C₁₃×#466	C₂²	semidirect
81. C₁₃×#466	C₂²	semidirect
82. C₁₃×#466	C₂²	semidirect
83. C₁₃×#466	C₂²	semidirect
84. C₁₃×#466	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#463	C₂²	semidirect
87. C₁₃×#463	C₂²	semidirect
88. C₁₃×#459	C₂²	semidirect
89. C₁₃×#459	C₂²	semidirect
90. C₁₃×#449	C₂²	semidirect
91. C₁₃×#449	C₂²	semidirect
92. C₁₃×#449	C₂²	semidirect
93. C₁₃×#449	C₂²	semidirect
94. C₁₃×#448	C₂²	semidirect
95. C₁₃×#447	C₂²	semidirect
96. C₁₃×#447	C₂²	semidirect
97. C₁₃×#447	C₂²	semidirect
98. C₁₃×#442	C₂²	semidirect
99. C₁₃×#440	C₂²	semidirect
100. C₄×C₁₃×SD₁₆	C₂²	semidirect
101. C₄×C₁₃×D₈	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×#107	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×#102	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. #61171	C₁₃	direct (N × H)
342. C₁₃×#41	#41	semidirect
486. #3494	C₂×C₁₃	semidirect
487. #3488	C₂×C₁₃	semidirect
488. #3319	C₂×C₁₃	semidirect
489. #3318	C₂×C₁₃	semidirect
490. #3309	C₂×C₁₃	semidirect
491. #3308	C₂×C₁₃	semidirect
492. #3305	C₂×C₁₃	semidirect
493. #3301	C₂×C₁₃	semidirect
494. #3297	C₂×C₁₃	semidirect
495. #3294	C₂×C₁₃	semidirect
496. #3136	C₂×C₁₃	semidirect
497. #3098	C₂×C₁₃	semidirect
498. #3094	C₂×C₁₃	semidirect
499. #3083	C₂×C₁₃	semidirect
500. #3062	C₂×C₁₃	semidirect
501. C₂×#466	C₂×C₁₃	semidirect
502. #3041	C₂×C₁₃	semidirect
503. #3008	C₂×C₁₃	semidirect
504. #3006	C₂×C₁₃	semidirect
505. #2946	C₂×C₁₃	semidirect
506. #2929	C₂×C₁₃	semidirect
507. #2897	C₂×C₁₃	semidirect
508. C₂×#416	C₂×C₁₃	semidirect
618. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
619. C₂²×D₈	C₂²×C₁₃	semidirect
620. C₂×#131	C₂²×C₁₃	semidirect
621. C₂³×C₈	C₂²×C₁₃	semidirect
622. #555	C₂²×C₁₃	semidirect
623. #553	C₂²×C₁₃	semidirect
624. #553	C₂²×C₁₃	semidirect
626. #550	C₂²×C₁₃	semidirect
627. #548	C₂²×C₁₃	semidirect
628. #547	C₂²×C₁₃	semidirect
631. #546	C₂²×C₁₃	semidirect
633. D₄²	C₂²×C₁₃	semidirect
634. #544	C₂²×C₁₃	semidirect
641. #535	C₂²×C₁₃	semidirect
648. C₂×#121	C₂²×C₁₃	semidirect
650. #520	C₂²×C₁₃	semidirect
651. #518	C₂²×C₁₃	semidirect
652. C₂×#117	C₂²×C₁₃	semidirect
653. #490	C₂²×C₁₃	semidirect
654. #489	C₂²×C₁₃	semidirect
655. #488	C₂²×C₁₃	semidirect
656. #486	C₂²×C₁₃	semidirect
657. #485	C₂²×C₁₃	semidirect
658. #484	C₂²×C₁₃	semidirect
659. #482	C₂²×C₁₃	semidirect
660. #482	C₂²×C₁₃	semidirect
661. #482	C₂²×C₁₃	semidirect
662. #481	C₂²×C₁₃	semidirect
663. #480	C₂²×C₁₃	semidirect
664. #480	C₂²×C₁₃	semidirect
665. #479	C₂²×C₁₃	semidirect
666. #478	C₂²×C₁₃	semidirect
667. #477	C₂²×C₁₃	semidirect
668. #474	C₂²×C₁₃	semidirect
669. #469	C₂²×C₁₃	semidirect
670. #468	C₂²×C₁₃	semidirect
671. #466	C₂²×C₁₃	semidirect
672. #466	C₂²×C₁₃	semidirect
673. #466	C₂²×C₁₃	semidirect
674. #466	C₂²×C₁₃	semidirect
675. #466	C₂²×C₁₃	semidirect
676. #465	C₂²×C₁₃	semidirect
677. #463	C₂²×C₁₃	semidirect
678. #463	C₂²×C₁₃	semidirect
679. #459	C₂²×C₁₃	semidirect
680. #459	C₂²×C₁₃	semidirect
681. #449	C₂²×C₁₃	semidirect
682. #449	C₂²×C₁₃	semidirect
683. #449	C₂²×C₁₃	semidirect
684. #449	C₂²×C₁₃	semidirect
685. #448	C₂²×C₁₃	semidirect
686. #447	C₂²×C₁₃	semidirect
687. #447	C₂²×C₁₃	semidirect
688. #447	C₂²×C₁₃	semidirect
689. #442	C₂²×C₁₃	semidirect
690. #440	C₂²×C₁₃	semidirect
691. C₄×SD₁₆	C₂²×C₁₃	semidirect
692. C₄×D₈	C₂²×C₁₃	semidirect
693. #435	C₂²×C₁₃	semidirect
694. #435	C₂²×C₁₃	semidirect
695. C₈×D₄	C₂²×C₁₃	semidirect
696. C₈×D₄	C₂²×C₁₃	semidirect
697. #428	C₂²×C₁₃	semidirect
698. #428	C₂²×C₁₃	semidirect
699. C₂×#107	C₂²×C₁₃	semidirect
700. #424	C₂²×C₁₃	semidirect
701. #418	C₂²×C₁₃	semidirect
702. #418	C₂²×C₁₃	semidirect
703. #418	C₂²×C₁₃	semidirect
705. #417	C₂²×C₁₃	semidirect
706. #417	C₂²×C₁₃	semidirect
709. #416	C₂²×C₁₃	semidirect
710. #416	C₂²×C₁₃	semidirect
711. #416	C₂²×C₁₃	semidirect
712. #416	C₂²×C₁₃	semidirect
713. #416	C₂²×C₁₃	semidirect
714. #416	C₂²×C₁₃	semidirect
715. #416	C₂²×C₁₃	semidirect
716. C₂×#103	C₂²×C₁₃	semidirect
717. C₂×#103	C₂²×C₁₃	semidirect
718. C₂×#102	C₂²×C₁₃	semidirect
719. C₂×#102	C₂²×C₁₃	semidirect
720. C₂×#102	C₂²×C₁₃	semidirect
721. C₂×#102	C₂²×C₁₃	semidirect
722. C₂×#102	C₂²×C₁₃	semidirect
723. #408	C₂²×C₁₃	semidirect
724. #407	C₂²×C₁₃	semidirect
725. #405	C₂²×C₁₃	semidirect
989. #41	C₁₃×#41	semidirect
1133. C₁₃	#61171	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×#3494	2
C₁₃×#3488	2
C₁₃×#3319	2
C₁₃×#3318	2
C₁₃×#3309	2
C₁₃×#3308	2
C₁₃×#3305	2
C₁₃×#3301	2
C₁₃×#3297	2
C₁₃×#3294	2
C₁₃×#3136	2
C₁₃×#3098	2
C₁₃×#3094	2
C₁₃×#3083	2
C₁₃×#3062	2
C₂×C₁₃×#466	2
C₁₃×#3041	2
C₁₃×#3008	2
C₁₃×#3006	2
C₁₃×#2946	2
C₁₃×#2929	2
C₁₃×#2897	2
C₂×C₁₃×#416	2
#61171	13

Subgroups — C13×#61171 #15747510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61171 #15747510