Subgroups — C₁₃×#61417 #15747756

Order 3328.

1974 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3403	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3401	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3399	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3397	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2949	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
29	C₁₃×#559	C₂²	1	4	yes	complemented
30	C₁₃×#559	C₂²	1	4	yes	complemented
31	C₁₃×#556	C₂²	1	4	yes	complemented
32	C₁₃×#551	—	2	4	no	—
33	C₁₃×#550	C₂²	1	4	yes	complemented
34	C₁₃×#546	—	2	4	no	—
35	C₁₃×#542	—	2	2	no	—
36	C₁₃×#540	—	2	2	no	—
37	C₁₃×#536	C₂²	1	1	yes	characteristic
38	C₁₃×#535	C₂²	1	1	yes	characteristic
39	C₁₃×#535	C₂²	1	1	yes	characteristic
40	C₁₃×#535	C₂²	1	1	yes	characteristic
41	C₁₃×#533	C₂²	1	1	yes	characteristic
42	C₁₃×#532	—	2	2	no	—
43	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
44	C₁₃×#529	—	2	2	no	—
45	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
46	C₁₃×#519	C₂²	1	1	yes	characteristic
47	C₁₃×#518	C₂²	1	1	yes	characteristic
48	C₁₃×#518	C₂²	1	1	yes	characteristic
49	C₁₃×#518	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
52	C₁₃×#497	C₂²	1	2	yes	complemented
53	C₁₃×#496	C₂²	1	4	yes	—
54	C₁₃×#496	C₂²	1	4	yes	—
55	C₁₃×#496	C₂²	1	2	yes	complemented
56	C₁₃×#496	C₂²	1	2	yes	complemented
57	C₁₃×#496	C₂²	1	2	yes	complemented
58	C₁₃×#495	C₂²	1	2	yes	complemented
59	C₁₃×#495	C₂²	1	2	yes	complemented
60	C₁₃×#493	C₂²	1	2	yes	complemented
61	C₁₃×#492	C₂²	1	2	yes	complemented
62	C₁₃×#464	C₂²	1	4	yes	complemented
63	C₁₃×#464	C₂²	1	4	yes	complemented
64	C₁₃×#463	C₂²	1	4	yes	complemented
65	C₁₃×#463	C₂²	1	4	yes	complemented
66	C₁₃×#463	C₂²	1	4	yes	complemented
67	C₁₃×#463	C₂²	1	4	yes	complemented
68	C₁₃×#461	C₂²	1	4	yes	complemented
69	C₁₃×#460	C₂²	1	4	yes	complemented
70	C₁₃×#460	C₂²	1	4	yes	complemented
71	C₁₃×#459	C₂²	1	4	yes	complemented
72	C₁₃×#459	C₂²	1	4	yes	complemented
73	C₁₃×#459	C₂²	1	4	yes	complemented
74	C₁₃×#446	C₂²	1	4	yes	complemented
75	C₁₃×#446	C₂²	1	4	yes	complemented
76	C₁₃×#442	C₂²	1	2	yes	complemented
77	C₁₃×#442	C₂²	1	4	yes	complemented
78	C₁₃×#441	C₂²	1	2	yes	complemented
79	C₁₃×#440	C₂²	1	2	yes	complemented
80	C₁₃×#440	C₂²	1	4	yes	complemented
81	C₁₃×#440	C₂²	1	2	yes	complemented
82	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
83	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
84	C₁₃×#427	C₂²	1	1	yes	characteristic
85	C₁₃×#424	C₂²	1	1	yes	characteristic
86	C₁₃×#424	C₂²	1	1	yes	characteristic
87	C₁₃×#423	C₂²	1	1	yes	characteristic
88	C₁₃×#419	C₂²	1	1	yes	characteristic
89	C₁₃×#418	C₂²	1	1	yes	characteristic
90	C₁₃×#418	C₂²	1	1	yes	characteristic
91	C₁₃×#418	C₂²	1	1	yes	characteristic
92	C₁₃×#416	C₂²	1	1	yes	characteristic
93	C₁₃×#416	C₂²	1	1	yes	characteristic
94	C₁₃×#405	C₂²	1	1	yes	characteristic
95	C₁₃×#405	C₂²	1	1	yes	characteristic
96	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
97	C₂×C₁₃×#41	—	2	4	no	—
98	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₁₃	—	2	2	no	—
102	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#137	—	4	2	no	—
106	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
107	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
108	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
109	C₁₃×#135	—	2	4	no	—
110	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
112	C₂×C₁₃×SD₁₆	—	2	4	no	—
113	C₂×C₁₃×SD₁₆	—	4	2	no	—
114	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
115	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
119	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
120	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
121	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
122	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×D₈	—	2	4	no	—
124	C₂×C₁₃×D₈	—	4	2	no	—
125	C₂×C₁₃×D₈	C₂³	1	2	yes	—
126	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
127	C₂×C₁₃×D₈	C₂³	1	2	yes	—
128	C₂×C₁₃×D₈	C₂³	1	2	yes	—
129	C₂×C₁₃×D₈	C₂³	1	2	yes	—
130	C₂×C₁₃×D₈	C₂³	1	2	yes	—
131	C₂×C₁₃×D₈	C₂³	1	4	yes	—
132	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
136	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×#127	—	2	1	no	—
139	C₁₃×#127	—	2	1	no	—
140	C₁₃×#127	C₂³	1	2	yes	—
141	C₁₃×#127	C₂³	1	2	yes	—
142	C₁₃×#127	C₂³	1	4	yes	—
143	C₁₃×#127	C₂³	1	2	yes	—
144	C₁₃×#126	—	2	4	no	—
145	C₁₃×#126	—	2	4	no	—
146	C₁₃×#125	D₄	1	2	yes	—
147	C₁₃×#124	—	2	4	no	—
148	C₁₃×#124	—	2	4	no	—
149	C₁₃×#124	—	2	1	no	—
150	C₁₃×#124	—	2	1	no	—
151	C₁₃×#124	C₂³	1	2	yes	—
152	C₁₃×#124	C₂³	1	2	yes	—
153	C₁₃×#124	C₂³	1	2	yes	—
154	C₁₃×#124	C₂³	1	4	yes	—
155	C₁₃×#124	C₂³	1	2	yes	—
156	C₁₃×#123	—	2	4	no	—
157	C₁₃×#123	—	2	4	no	—
158	C₁₃×#123	—	2	4	no	—
159	C₁₃×#123	—	2	4	no	—
160	C₁₃×#123	—	2	2	no	—
161	C₁₃×C₂²⋊Q₈	—	2	4	no	—
162	C₁₃×C₂²⋊Q₈	—	2	2	no	—
163	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
164	C₁₃×#121	—	2	2	no	—
165	C₁₃×#121	—	2	2	no	—
166	C₁₃×#121	—	2	2	no	—
167	C₁₃×#121	—	2	4	no	—
168	C₁₃×#121	—	2	4	no	—
169	C₁₃×#121	—	2	4	no	—
170	C₁₃×#120	—	2	2	no	—
171	C₁₃×#120	—	2	2	no	—
172	C₁₃×#120	—	2	2	no	—
173	C₄×Q₈×C₁₃	—	2	2	no	—
174	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
175	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
176	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
177	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	—	2	2	no	—
183	C₄×D₄×C₁₃	—	2	4	no	—
184	C₄×D₄×C₁₃	—	2	4	no	—
185	C₄×D₄×C₁₃	C₂³	1	4	yes	—
186	C₄×D₄×C₁₃	C₂³	1	4	yes	—
187	C₄×D₄×C₁₃	C₂³	1	4	yes	—
188	C₄×D₄×C₁₃	C₂³	1	2	yes	—
189	C₄×D₄×C₁₃	C₂³	1	2	yes	—
190	C₁₃×#117	—	2	4	no	—
191	C₁₃×#117	—	2	2	no	—
192	C₁₃×#117	—	2	1	no	—
193	C₁₃×#117	—	2	1	no	—
194	C₁₃×#117	C₂³	1	1	yes	characteristic
195	C₁₃×#117	C₂³	1	1	yes	characteristic
196	C₁₃×#117	C₂³	1	1	yes	characteristic
197	C₁₃×#117	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₄²×C₁₃	—	2	1	no	—
203	C₂×C₄²×C₁₃	—	2	1	no	—
204	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
205	C₁₃×#107	C₂³	1	2	yes	—
206	C₁₃×#106	C₂³	1	2	yes	—
207	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
210	C₁₃×#103	C₂³	1	2	yes	—
211	C₁₃×#103	C₂³	1	2	yes	—
212	C₁₃×#103	C₂³	1	4	yes	—
213	C₁₃×#102	C₂³	1	2	yes	—
214	C₁₃×#102	C₂³	1	2	yes	—
215	C₁₃×#102	C₂³	1	4	yes	—
216	C₁₃×#102	C₂³	1	4	yes	—
217	C₁₃×#102	C₂³	1	4	yes	—
218	C₁₃×#97	C₂³	1	2	yes	—
219	C₁₃×#97	C₂³	1	2	yes	—
220	C₁₃×#97	C₂³	1	2	yes	—
221	C₁₃×#97	C₂³	1	2	yes	—
222	C₄×C₈×C₁₃	C₂³	1	2	yes	—
223	C₄×C₈×C₁₃	C₂³	1	2	yes	—
224	#61417	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂⁴×C₁₃	—	2	1	no	—
226	C₂⁴×C₁₃	—	2	1	no	—
227	C₂⁴×C₁₃	—	2	1	no	—
228	C₁₃×#41	—	2	2	no	—
229	C₁₃×#41	—	2	2	no	—
230	C₁₃×#41	—	2	2	no	—
231	C₁₃×#41	—	2	2	no	—
232	C₁₃×#41	—	8	8	no	—
233	C₂×Q₈×C₁₃	—	2	1	no	—
234	C₂×Q₈×C₁₃	—	2	2	no	—
235	C₂×Q₈×C₁₃	—	2	2	no	—
236	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
237	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×D₄×C₁₃	—	2	1	no	—
241	C₂×D₄×C₁₃	—	2	1	no	—
242	C₂×D₄×C₁₃	—	2	1	no	—
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	1	no	—
245	C₂×D₄×C₁₃	—	2	4	no	—
246	C₂×D₄×C₁₃	—	2	4	no	—
247	C₂×D₄×C₁₃	—	2	4	no	—
248	C₂×D₄×C₁₃	—	2	4	no	—
249	C₂×D₄×C₁₃	—	2	4	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	8	4	no	—
257	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
261	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	—	2	4	no	—
269	C₂²×C₄×C₁₃	—	2	4	no	—
270	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₁₃×Q₁₆	—	2	2	no	—
273	C₁₃×Q₁₆	—	4	2	no	—
274	C₁₃×SD₁₆	—	2	4	no	—
275	C₁₃×SD₁₆	—	2	4	no	—
276	C₁₃×SD₁₆	—	2	2	no	—
277	C₁₃×SD₁₆	—	2	2	no	—
278	C₁₃×SD₁₆	—	4	4	no	—
279	C₁₃×SD₁₆	—	4	2	no	—
280	C₁₃×SD₁₆	—	4	2	no	—
281	C₁₃×SD₁₆	—	4	2	no	—
282	C₁₃×SD₁₆	—	4	2	no	—
283	C₁₃×D₈	—	2	4	no	—
284	C₁₃×D₈	—	2	4	no	—
285	C₁₃×D₈	—	2	2	no	—
286	C₁₃×D₈	—	4	4	no	—
287	C₁₃×D₈	—	4	2	no	—
288	C₁₃×D₈	—	4	2	no	—
289	C₁₃×D₈	—	4	2	no	—
290	C₁₃×M₁₆	—	2	2	no	—
291	C₁₃×M₁₆	—	2	2	no	—
292	C₂×C₈×C₁₃	—	2	2	no	—
293	C₂×C₈×C₁₃	#41	1	4	yes	complemented
294	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
295	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
296	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
297	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
298	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	4	no	—
302	C₁₃×C₄⋊C₄	—	2	4	no	—
303	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
304	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
306	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
307	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
310	C₁₃×C₂²⋊C₄	—	2	1	no	—
311	C₁₃×C₂²⋊C₄	—	2	1	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	4	no	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	4	no	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	4	no	—
323	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
324	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
325	C₄²×C₁₃	—	2	2	no	—
326	C₄²×C₁₃	—	2	1	no	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	—	2	4	no	—
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₁₃	C₂⁴	1	2	yes	—
333	C₄²×C₁₃	C₂⁴	1	2	yes	—
334	C₄²×C₁₃	C₂⁴	1	2	yes	—
335	#3510	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#3403	C₂×C₁₃	1	4	yes	complemented
338	#3401	C₂×C₁₃	1	4	yes	complemented
339	#3399	C₂×C₁₃	1	4	yes	complemented
340	#3397	C₂×C₁₃	1	4	yes	complemented
341	#3155	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#3154	C₂×C₁₃	1	1	yes	characteristic, complemented
343	C₂×#496	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3043	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3042	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3041	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3041	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3040	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#2961	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#2949	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#2948	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#2943	C₂×C₁₃	1	1	yes	characteristic, complemented
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	2	1	no	—
356	C₂³×C₁₃	—	2	2	no	—
357	C₂³×C₁₃	—	2	2	no	—
358	C₂³×C₁₃	—	2	1	no	—
359	C₂³×C₁₃	—	4	2	no	—
360	C₂³×C₁₃	—	4	2	no	—
361	C₂³×C₁₃	—	4	2	no	—
362	C₂³×C₁₃	—	8	2	no	—
363	C₂³×C₁₃	—	8	2	no	—
364	C₂³×C₁₃	—	8	2	no	—
365	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
366	Q₈×C₁₃	—	2	2	no	—
367	Q₈×C₁₃	—	2	1	no	—
368	Q₈×C₁₃	—	2	1	no	—
369	Q₈×C₁₃	—	2	1	no	—
370	Q₈×C₁₃	—	2	2	no	—
371	Q₈×C₁₃	—	2	1	no	—
372	Q₈×C₁₃	—	4	4	no	—
373	Q₈×C₁₃	—	4	2	no	—
374	D₄×C₁₃	—	2	2	no	—
375	D₄×C₁₃	—	2	2	no	—
376	D₄×C₁₃	—	2	1	no	—
377	D₄×C₁₃	—	2	1	no	—
378	D₄×C₁₃	—	2	2	no	—
379	D₄×C₁₃	—	2	1	no	—
380	D₄×C₁₃	—	2	2	no	—
381	D₄×C₁₃	—	2	2	no	—
382	D₄×C₁₃	—	2	1	no	—
383	D₄×C₁₃	—	2	2	no	—
384	D₄×C₁₃	—	4	8	no	—
385	D₄×C₁₃	—	4	2	no	—
386	D₄×C₁₃	—	4	2	no	—
387	D₄×C₁₃	—	4	2	no	—
388	D₄×C₁₃	—	4	2	no	—
389	D₄×C₁₃	—	4	2	no	—
390	D₄×C₁₃	—	8	4	no	—
391	D₄×C₁₃	—	8	4	no	—
392	D₄×C₁₃	—	8	4	no	—
393	D₄×C₁₃	—	8	4	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	4	2	no	—
400	C₂×C₄×C₁₃	—	4	4	no	—
401	C₂×C₄×C₁₃	—	4	2	no	—
402	C₂×C₄×C₁₃	—	4	2	no	—
403	C₂×C₄×C₁₃	—	4	2	no	—
404	C₂×C₄×C₁₃	—	8	2	no	—
405	C₂×C₄×C₁₃	—	8	4	no	—
406	C₂×C₄×C₁₃	—	8	4	no	—
407	C₂×C₄×C₁₃	—	8	4	no	—
408	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
411	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
412	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
414	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
415	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
416	C₈×C₁₃	—	2	2	no	—
417	C₈×C₁₃	—	2	2	no	—
418	C₈×C₁₃	—	2	2	no	—
419	C₈×C₁₃	C₂×#41	1	2	yes	—
420	C₈×C₁₃	C₂×#41	1	2	yes	—
421	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
426	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
427	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
428	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
429	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
430	#559	C₂²×C₁₃	1	4	yes	complemented
431	#559	C₂²×C₁₃	1	4	yes	complemented
432	#556	C₂²×C₁₃	1	4	yes	complemented
433	#551	—	2	4	no	—
434	#550	C₂²×C₁₃	1	4	yes	complemented
435	#546	—	2	4	no	—
436	#542	—	2	2	no	—
437	#540	—	2	2	no	—
438	#536	C₂²×C₁₃	1	1	yes	characteristic
439	#535	C₂²×C₁₃	1	1	yes	characteristic
440	#535	C₂²×C₁₃	1	1	yes	characteristic
441	#535	C₂²×C₁₃	1	1	yes	characteristic
442	#533	C₂²×C₁₃	1	1	yes	characteristic
443	#532	—	2	2	no	—
444	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
445	#529	—	2	2	no	—
446	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
447	#519	C₂²×C₁₃	1	1	yes	characteristic
448	#518	C₂²×C₁₃	1	1	yes	characteristic
449	#518	C₂²×C₁₃	1	1	yes	characteristic
450	#518	C₂²×C₁₃	1	1	yes	characteristic
451	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
452	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
453	#497	C₂²×C₁₃	1	2	yes	complemented
454	#496	C₂²×C₁₃	1	4	yes	—
455	#496	C₂²×C₁₃	1	4	yes	—
456	#496	C₂²×C₁₃	1	2	yes	complemented
457	#496	C₂²×C₁₃	1	2	yes	complemented
458	#496	C₂²×C₁₃	1	2	yes	complemented
459	#495	C₂²×C₁₃	1	2	yes	complemented
460	#495	C₂²×C₁₃	1	2	yes	complemented
461	#493	C₂²×C₁₃	1	2	yes	complemented
462	#492	C₂²×C₁₃	1	2	yes	complemented
463	#464	C₂²×C₁₃	1	4	yes	complemented
464	#464	C₂²×C₁₃	1	4	yes	complemented
465	#463	C₂²×C₁₃	1	4	yes	complemented
466	#463	C₂²×C₁₃	1	4	yes	complemented
467	#463	C₂²×C₁₃	1	4	yes	complemented
468	#463	C₂²×C₁₃	1	4	yes	complemented
469	#461	C₂²×C₁₃	1	4	yes	complemented
470	#460	C₂²×C₁₃	1	4	yes	complemented
471	#460	C₂²×C₁₃	1	4	yes	complemented
472	#459	C₂²×C₁₃	1	4	yes	complemented
473	#459	C₂²×C₁₃	1	4	yes	complemented
474	#459	C₂²×C₁₃	1	4	yes	complemented
475	#446	C₂²×C₁₃	1	4	yes	complemented
476	#446	C₂²×C₁₃	1	4	yes	complemented
477	#442	C₂²×C₁₃	1	2	yes	complemented
478	#442	C₂²×C₁₃	1	4	yes	complemented
479	#441	C₂²×C₁₃	1	2	yes	complemented
480	#440	C₂²×C₁₃	1	2	yes	complemented
481	#440	C₂²×C₁₃	1	4	yes	complemented
482	#440	C₂²×C₁₃	1	2	yes	complemented
483	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
484	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
485	#427	C₂²×C₁₃	1	1	yes	characteristic
486	#424	C₂²×C₁₃	1	1	yes	characteristic
487	#424	C₂²×C₁₃	1	1	yes	characteristic
488	#423	C₂²×C₁₃	1	1	yes	characteristic
489	#419	C₂²×C₁₃	1	1	yes	characteristic
490	#418	C₂²×C₁₃	1	1	yes	characteristic
491	#418	C₂²×C₁₃	1	1	yes	characteristic
492	#418	C₂²×C₁₃	1	1	yes	characteristic
493	#416	C₂²×C₁₃	1	1	yes	characteristic
494	#416	C₂²×C₁₃	1	1	yes	characteristic
495	#405	C₂²×C₁₃	1	1	yes	characteristic
496	#405	C₂²×C₁₃	1	1	yes	characteristic
497	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
498	C₂²×C₁₃	—	2	2	no	—
499	C₂²×C₁₃	—	4	2	no	—
500	C₂²×C₁₃	—	4	4	no	—
501	C₂²×C₁₃	—	4	4	no	—
502	C₂²×C₁₃	—	4	2	no	—
503	C₂²×C₁₃	—	4	4	no	—
504	C₂²×C₁₃	—	4	1	no	—
505	C₂²×C₁₃	—	4	1	no	—
506	C₂²×C₁₃	—	4	2	no	—
507	C₂²×C₁₃	—	4	2	no	—
508	C₂²×C₁₃	—	4	2	no	—
509	C₂²×C₁₃	—	16	2	no	—
510	C₂²×C₁₃	—	16	2	no	—
511	C₂²×C₁₃	—	16	2	no	—
512	C₂²×C₁₃	#550	1	2	yes	—
513	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
514	C₄×C₁₃	—	2	2	no	—
515	C₄×C₁₃	—	2	2	no	—
516	C₄×C₁₃	—	2	4	no	—
517	C₄×C₁₃	—	2	4	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	—	4	2	no	—
520	C₄×C₁₃	—	4	1	no	—
521	C₄×C₁₃	—	4	1	no	—
522	C₄×C₁₃	—	4	2	no	—
523	C₄×C₁₃	#550	1	2	yes	—
524	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
525	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂×#41	—	2	4	no	—
527	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
529	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
530	C₂²×D₄	—	2	2	no	—
531	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
533	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
534	#137	—	4	2	no	—
535	AGL(1,ℤ/8)	—	4	2	no	—
536	AGL(1,ℤ/8)	—	4	2	no	—
537	AGL(1,ℤ/8)	—	4	2	no	—
538	#135	—	2	4	no	—
539	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
540	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
541	C₂×SD₁₆	—	2	4	no	—
542	C₂×SD₁₆	—	4	2	no	—
543	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
544	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
545	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
546	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
547	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
548	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
549	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
550	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
551	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
552	C₂×D₈	—	2	4	no	—
553	C₂×D₈	—	4	2	no	—
554	C₂×D₈	C₂³×C₁₃	1	2	yes	—
555	C₂×D₈	C₂³×C₁₃	1	2	yes	—
556	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×D₈	C₂³×C₁₃	1	4	yes	—
558	C₂×D₈	C₂³×C₁₃	1	2	yes	—
559	C₂×D₈	C₂³×C₁₃	1	2	yes	—
560	C₂×D₈	C₂³×C₁₃	1	2	yes	—
561	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
562	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
563	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
564	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
565	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
566	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
567	#127	—	2	1	no	—
568	#127	—	2	1	no	—
569	#127	C₂³×C₁₃	1	4	yes	—
570	#127	C₂³×C₁₃	1	2	yes	—
571	#127	C₂³×C₁₃	1	2	yes	—
572	#127	C₂³×C₁₃	1	2	yes	—
573	#126	—	2	4	no	—
574	#126	—	2	4	no	—
575	#125	D₄×C₁₃	1	2	yes	—
576	#124	—	2	4	no	—
577	#124	—	2	4	no	—
578	#124	—	2	1	no	—
579	#124	—	2	1	no	—
580	#124	C₂³×C₁₃	1	4	yes	—
581	#124	C₂³×C₁₃	1	2	yes	—
582	#124	C₂³×C₁₃	1	2	yes	—
583	#124	C₂³×C₁₃	1	2	yes	—
584	#124	C₂³×C₁₃	1	2	yes	—
585	#123	—	2	4	no	—
586	#123	—	2	4	no	—
587	#123	—	2	4	no	—
588	#123	—	2	4	no	—
589	#123	—	2	2	no	—
590	C₂²⋊Q₈	—	2	4	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	—	2	4	no	—
597	#121	—	2	4	no	—
598	#121	—	2	4	no	—
599	#120	—	2	2	no	—
600	#120	—	2	2	no	—
601	#120	—	2	2	no	—
602	C₄×Q₈	—	2	2	no	—
603	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
604	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
605	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
606	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	4	no	—
613	C₄×D₄	—	2	4	no	—
614	C₄×D₄	C₂³×C₁₃	1	2	yes	—
615	C₄×D₄	C₂³×C₁₃	1	2	yes	—
616	C₄×D₄	C₂³×C₁₃	1	4	yes	—
617	C₄×D₄	C₂³×C₁₃	1	4	yes	—
618	C₄×D₄	C₂³×C₁₃	1	4	yes	—
619	#117	—	2	4	no	—
620	#117	—	2	2	no	—
621	#117	—	2	1	no	—
622	#117	—	2	1	no	—
623	#117	C₂³×C₁₃	1	1	yes	characteristic
624	#117	C₂³×C₁₃	1	1	yes	characteristic
625	#117	C₂³×C₁₃	1	1	yes	characteristic
626	#117	C₂³×C₁₃	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	—	2	2	no	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₂²⋊C₄	—	2	2	no	—
631	C₂×C₄²	—	2	1	no	—
632	C₂×C₄²	—	2	1	no	—
633	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
634	#107	C₂³×C₁₃	1	2	yes	—
635	#106	C₂³×C₁₃	1	2	yes	—
636	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
637	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
638	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
639	#103	C₂³×C₁₃	1	2	yes	—
640	#103	C₂³×C₁₃	1	2	yes	—
641	#103	C₂³×C₁₃	1	4	yes	—
642	#102	C₂³×C₁₃	1	2	yes	—
643	#102	C₂³×C₁₃	1	2	yes	—
644	#102	C₂³×C₁₃	1	4	yes	—
645	#102	C₂³×C₁₃	1	4	yes	—
646	#102	C₂³×C₁₃	1	4	yes	—
647	#97	C₂³×C₁₃	1	2	yes	—
648	#97	C₂³×C₁₃	1	2	yes	—
649	#97	C₂³×C₁₃	1	2	yes	—
650	#97	C₂³×C₁₃	1	2	yes	—
651	C₄×C₈	C₂³×C₁₃	1	2	yes	—
652	C₄×C₈	C₂³×C₁₃	1	2	yes	—
653	C₂×C₁₃	—	2	2	no	—
654	C₂×C₁₃	—	8	1	no	—
655	C₂×C₁₃	—	8	1	no	—
656	C₂×C₁₃	—	8	2	no	—
657	C₂×C₁₃	—	8	2	no	—
658	C₂×C₁₃	—	8	2	no	—
659	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
660	C₂×C₁₃	#3585	1	2	yes	—
661	C₂⁴	—	2	1	no	—
662	C₂⁴	—	2	1	no	—
663	C₂⁴	—	2	1	no	—
664	#41	—	2	2	no	—
665	#41	—	2	2	no	—
666	#41	—	2	2	no	—
667	#41	—	2	2	no	—
668	#41	—	8	8	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
673	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
674	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	8	4	no	—
693	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
694	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
695	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
696	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
697	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
708	Q₁₆	—	2	2	no	—
709	Q₁₆	—	4	2	no	—
710	SD₁₆	—	2	4	no	—
711	SD₁₆	—	2	4	no	—
712	SD₁₆	—	2	2	no	—
713	SD₁₆	—	2	2	no	—
714	SD₁₆	—	4	4	no	—
715	SD₁₆	—	4	2	no	—
716	SD₁₆	—	4	2	no	—
717	SD₁₆	—	4	2	no	—
718	SD₁₆	—	4	2	no	—
719	D₈	—	2	4	no	—
720	D₈	—	2	4	no	—
721	D₈	—	2	2	no	—
722	D₈	—	4	4	no	—
723	D₈	—	4	2	no	—
724	D₈	—	4	2	no	—
725	D₈	—	4	2	no	—
726	M₁₆	—	2	2	no	—
727	M₁₆	—	2	2	no	—
728	C₂×C₈	—	2	2	no	—
729	C₂×C₈	C₁₃×#41	1	4	yes	complemented
730	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
731	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
732	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
733	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
734	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
740	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
741	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
742	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
743	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
744	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
745	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
760	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	4	no	—
766	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
768	C₄²	C₂⁴×C₁₃	1	2	yes	—
769	C₄²	C₂⁴×C₁₃	1	2	yes	—
770	C₄²	C₂⁴×C₁₃	1	2	yes	—
771	C₁₃	#61417	1	1	yes	characteristic, direct product factor, Sylow
772	C₂³	—	2	2	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	4	2	no	—
778	C₂³	—	4	2	no	—
779	C₂³	—	4	2	no	—
780	C₂³	—	8	2	no	—
781	C₂³	—	8	2	no	—
782	C₂³	—	8	2	no	—
783	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
784	Q₈	—	2	2	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	2	1	no	—
787	Q₈	—	2	1	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	2	1	no	—
790	Q₈	—	4	4	no	—
791	Q₈	—	4	2	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	1	no	—
795	D₄	—	2	1	no	—
796	D₄	—	2	2	no	—
797	D₄	—	2	1	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	no	—
800	D₄	—	2	1	no	—
801	D₄	—	2	2	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	2	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	8	4	no	—
809	D₄	—	8	4	no	—
810	D₄	—	8	4	no	—
811	D₄	—	8	4	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	—	8	4	no	—
825	C₂×C₄	—	8	4	no	—
826	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
827	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
828	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
829	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
830	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
831	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
832	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
833	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
834	C₈	—	2	2	no	—
835	C₈	—	2	2	no	—
836	C₈	—	2	2	no	—
837	C₈	C₂×C₁₃×#41	1	2	yes	—
838	C₈	C₂×C₁₃×#41	1	2	yes	—
839	C₂²	—	2	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	4	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	4	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	16	2	no	—
851	C₂²	—	16	2	no	—
852	C₂²	—	16	2	no	—
853	C₂²	C₁₃×#550	1	2	yes	—
854	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	4	no	—
858	C₄	—	2	4	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	2	no	—
864	C₄	C₁₃×#550	1	2	yes	—
865	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
866	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
867	C₂	—	2	2	no	—
868	C₂	—	8	2	no	—
869	C₂	—	8	2	no	—
870	C₂	—	8	2	no	—
871	C₂	—	8	1	no	—
872	C₂	—	8	1	no	—
873	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
874	C₂	C₁₃×#3585	1	2	yes	—

	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3510	C₂	semidirect
2. C₁₃×#3508	C₂	semidirect
3. C₁₃×#3403	C₂	semidirect
4. C₁₃×#3401	C₂	semidirect
5. C₁₃×#3399	C₂	semidirect
6. C₁₃×#3397	C₂	semidirect
7. C₁₃×#3155	C₂	semidirect
8. C₁₃×#3154	C₂	semidirect
9. C₂×C₁₃×#496	C₂	semidirect
10. C₁₃×#3043	C₂	semidirect
11. C₁₃×#3042	C₂	semidirect
12. C₁₃×#3041	C₂	semidirect
13. C₁₃×#3041	C₂	semidirect
14. C₁₃×#3040	C₂	semidirect
15. C₁₃×#3038	C₂	semidirect
16. C₁₃×#2961	C₂	semidirect
17. C₁₃×#2949	C₂	semidirect
18. C₁₃×#2948	C₂	semidirect
19. C₁₃×#2943	C₂	semidirect
29. C₁₃×#559	C₂²	semidirect
30. C₁₃×#559	C₂²	semidirect
31. C₁₃×#556	C₂²	semidirect
33. C₁₃×#550	C₂²	semidirect
52. C₁₃×#497	C₂²	semidirect
55. C₁₃×#496	C₂²	semidirect
56. C₁₃×#496	C₂²	semidirect
57. C₁₃×#496	C₂²	semidirect
58. C₁₃×#495	C₂²	semidirect
59. C₁₃×#495	C₂²	semidirect
60. C₁₃×#493	C₂²	semidirect
61. C₁₃×#492	C₂²	semidirect
62. C₁₃×#464	C₂²	semidirect
63. C₁₃×#464	C₂²	semidirect
64. C₁₃×#463	C₂²	semidirect
65. C₁₃×#463	C₂²	semidirect
66. C₁₃×#463	C₂²	semidirect
67. C₁₃×#463	C₂²	semidirect
68. C₁₃×#461	C₂²	semidirect
69. C₁₃×#460	C₂²	semidirect
70. C₁₃×#460	C₂²	semidirect
71. C₁₃×#459	C₂²	semidirect
72. C₁₃×#459	C₂²	semidirect
73. C₁₃×#459	C₂²	semidirect
74. C₁₃×#446	C₂²	semidirect
75. C₁₃×#446	C₂²	semidirect
76. C₁₃×#442	C₂²	semidirect
77. C₁₃×#442	C₂²	semidirect
78. C₁₃×#441	C₂²	semidirect
79. C₁₃×#440	C₂²	semidirect
80. C₁₃×#440	C₂²	semidirect
81. C₁₃×#440	C₂²	semidirect
82. C₄×C₁₃×SD₁₆	C₂²	semidirect
83. C₄×C₁₃×D₈	C₂²	semidirect
224. #61417	C₁₃	direct (N × H)
293. C₂×C₈×C₁₃	#41	semidirect
335. #3510	C₂×C₁₃	semidirect
336. #3508	C₂×C₁₃	semidirect
337. #3403	C₂×C₁₃	semidirect
338. #3401	C₂×C₁₃	semidirect
339. #3399	C₂×C₁₃	semidirect
340. #3397	C₂×C₁₃	semidirect
341. #3155	C₂×C₁₃	semidirect
342. #3154	C₂×C₁₃	semidirect
343. C₂×#496	C₂×C₁₃	semidirect
344. #3043	C₂×C₁₃	semidirect
345. #3042	C₂×C₁₃	semidirect
346. #3041	C₂×C₁₃	semidirect
347. #3041	C₂×C₁₃	semidirect
348. #3040	C₂×C₁₃	semidirect
349. #3038	C₂×C₁₃	semidirect
350. #2961	C₂×C₁₃	semidirect
351. #2949	C₂×C₁₃	semidirect
352. #2948	C₂×C₁₃	semidirect
353. #2943	C₂×C₁₃	semidirect
430. #559	C₂²×C₁₃	semidirect
431. #559	C₂²×C₁₃	semidirect
432. #556	C₂²×C₁₃	semidirect
434. #550	C₂²×C₁₃	semidirect
453. #497	C₂²×C₁₃	semidirect
456. #496	C₂²×C₁₃	semidirect
457. #496	C₂²×C₁₃	semidirect
458. #496	C₂²×C₁₃	semidirect
459. #495	C₂²×C₁₃	semidirect
460. #495	C₂²×C₁₃	semidirect
461. #493	C₂²×C₁₃	semidirect
462. #492	C₂²×C₁₃	semidirect
463. #464	C₂²×C₁₃	semidirect
464. #464	C₂²×C₁₃	semidirect
465. #463	C₂²×C₁₃	semidirect
466. #463	C₂²×C₁₃	semidirect
467. #463	C₂²×C₁₃	semidirect
468. #463	C₂²×C₁₃	semidirect
469. #461	C₂²×C₁₃	semidirect
470. #460	C₂²×C₁₃	semidirect
471. #460	C₂²×C₁₃	semidirect
472. #459	C₂²×C₁₃	semidirect
473. #459	C₂²×C₁₃	semidirect
474. #459	C₂²×C₁₃	semidirect
475. #446	C₂²×C₁₃	semidirect
476. #446	C₂²×C₁₃	semidirect
477. #442	C₂²×C₁₃	semidirect
478. #442	C₂²×C₁₃	semidirect
479. #441	C₂²×C₁₃	semidirect
480. #440	C₂²×C₁₃	semidirect
481. #440	C₂²×C₁₃	semidirect
482. #440	C₂²×C₁₃	semidirect
483. C₄×SD₁₆	C₂²×C₁₃	semidirect
484. C₄×D₈	C₂²×C₁₃	semidirect
729. C₂×C₈	C₁₃×#41	semidirect
771. C₁₃	#61417	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×#3510	2
C₁₃×#3508	2
C₁₃×#3403	2
C₁₃×#3401	2
C₁₃×#3399	2
C₁₃×#3397	2
C₁₃×#3155	2
C₁₃×#3154	2
C₂×C₁₃×#496	2
C₁₃×#3043	2
C₁₃×#3042	2
C₁₃×#3041	2
C₁₃×#3040	2
C₁₃×#3038	2
C₁₃×#2961	2
C₁₃×#2949	2
C₁₃×#2948	2
C₁₃×#2943	2
#61417	13

Subgroups — C13×#61417 #15747756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61417 #15747756