Subgroups — C₁₃×#61961 #15748300

Order 3328.

2178 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3399	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3373	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3332	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3306	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3274	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3264	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3253	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3214	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3109	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3036	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	—	2	1	no	—
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
20	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
21	C₁₃×#559	—	2	1	no	—
22	C₁₃×#559	C₂²	1	2	yes	complemented
23	C₁₃×#550	—	2	1	no	—
24	C₁₃×#550	C₂²	1	2	yes	complemented
25	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
26	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#548	—	2	1	no	—
28	C₁₃×#547	C₂²	1	2	yes	—
29	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#546	—	2	2	no	—
31	C₁₃×#546	—	2	1	no	—
32	C₁₃×#546	—	2	2	no	—
33	C₁₃×#546	C₂²	1	4	yes	complemented
34	D₄²×C₁₃	C₂²	1	2	yes	—
35	D₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#540	—	2	2	no	—
37	C₁₃×#535	—	2	1	no	—
38	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₁₃×#532	C₂²	1	2	yes	complemented
41	C₁₃×#532	C₂²	1	2	yes	complemented
42	C₁₃×#532	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#525	—	2	1	no	—
45	C₁₃×#525	—	2	2	no	—
46	C₁₃×#518	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
50	C₁₃×#496	C₂²	1	4	yes	complemented
51	C₁₃×#493	C₂²	1	2	yes	complemented
52	C₁₃×#489	C₂²	1	4	yes	complemented
53	C₁₃×#486	C₂²	1	2	yes	complemented
54	C₁₃×#483	C₂²	1	2	yes	complemented
55	C₁₃×#481	C₂²	1	4	yes	complemented
56	C₁₃×#476	C₂²	1	4	yes	complemented
57	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#476	C₂²	1	2	yes	complemented
60	C₁₃×#475	C₂²	1	2	yes	complemented
61	C₁₃×#469	C₂²	1	4	yes	complemented
62	C₁₃×#469	C₂²	1	4	yes	complemented
63	C₁₃×#465	C₂²	1	4	yes	complemented
64	C₁₃×#463	C₂²	1	4	yes	complemented
65	C₁₃×#463	C₂²	1	4	yes	complemented
66	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#461	C₂²	1	2	yes	complemented
68	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#460	C₂²	1	2	yes	complemented
70	C₁₃×#459	C₂²	1	2	yes	—
71	C₁₃×#459	C₂²	1	2	yes	—
72	C₁₃×#459	C₂²	1	4	yes	complemented
73	C₁₃×#459	C₂²	1	2	yes	complemented
74	C₁₃×#459	C₂²	1	2	yes	complemented
75	C₁₃×#459	C₂²	1	2	yes	complemented
76	C₁₃×#459	C₂²	1	2	yes	complemented
77	C₁₃×#450	C₂²	1	2	yes	—
78	C₁₃×#449	C₂²	1	4	yes	complemented
79	C₁₃×#449	C₂²	1	4	yes	complemented
80	C₁₃×#447	C₂²	1	4	yes	complemented
81	C₁₃×#447	C₂²	1	4	yes	complemented
82	C₁₃×#446	C₂²	1	2	yes	complemented
83	C₁₃×#442	C₂²	1	4	yes	complemented
84	C₁₃×#442	C₂²	1	4	yes	complemented
85	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
86	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
87	C₁₃×#436	C₂²	1	2	yes	complemented
88	C₁₃×#435	C₂²	1	4	yes	complemented
89	C₁₃×#432	C₂²	1	2	yes	complemented
90	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#423	C₂²	1	2	yes	complemented
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#417	C₂²	1	4	yes	complemented
94	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	1	no	—
98	C₂×C₁₃×#41	—	2	1	no	—
99	C₂×C₁₃×#41	—	2	2	no	—
100	C₂×C₁₃×#41	—	2	2	no	—
101	C₂×C₁₃×#41	—	4	8	no	—
102	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
103	C₂×C₁₃×#41	C₂³	1	4	yes	—
104	C₂²×Q₈×C₁₃	—	2	1	no	—
105	C₂²×D₄×C₁₃	—	2	2	no	—
106	C₂²×D₄×C₁₃	—	2	1	no	—
107	C₂²×D₄×C₁₃	—	2	1	no	—
108	C₂²×D₄×C₁₃	—	2	1	no	—
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃	—	2	1	no	—
113	C₂³×C₄×C₁₃	—	2	2	no	—
114	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
115	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×D₈	—	4	4	no	—
119	C₂×C₁₃×D₈	C₂³	1	4	yes	—
120	C₂×C₁₃×D₈	C₂³	1	4	yes	—
121	C₂×C₁₃×D₈	C₂³	1	4	yes	—
122	C₂×C₁₃×D₈	C₂³	1	4	yes	—
123	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
124	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
125	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₁₃×#127	—	2	2	no	—
130	C₁₃×#127	—	2	1	no	—
131	C₁₃×#127	—	2	1	no	—
132	C₁₃×#127	C₂³	1	2	yes	—
133	C₁₃×#127	C₂³	1	2	yes	—
134	C₁₃×#127	C₂³	1	2	yes	—
135	C₁₃×#127	C₂³	1	1	yes	characteristic
136	C₁₃×#125	—	2	1	no	—
137	C₁₃×#124	—	2	2	no	—
138	C₁₃×#124	—	2	1	no	—
139	C₁₃×#124	—	2	2	no	—
140	C₁₃×#124	—	2	2	no	—
141	C₁₃×#124	C₂³	1	4	yes	—
142	C₁₃×#123	—	2	4	no	—
143	C₁₃×#123	—	2	4	no	—
144	C₁₃×#123	—	2	2	no	—
145	C₁₃×#123	—	2	2	no	—
146	C₁₃×#123	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	1	no	—
148	C₁₃×C₂²⋊Q₈	—	2	1	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	1	no	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×#121	—	2	1	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	—	2	1	no	—
160	C₁₃×#121	—	2	1	no	—
161	C₁₃×#121	—	2	2	no	—
162	C₁₃×#121	—	2	4	no	—
163	C₁₃×#121	—	2	4	no	—
164	C₁₃×#121	C₂³	1	2	yes	—
165	C₁₃×#121	C₂³	1	4	yes	—
166	C₁₃×#121	C₂³	1	2	yes	—
167	C₁₃×#121	C₂³	1	2	yes	—
168	C₁₃×#120	—	2	4	no	—
169	C₁₃×#120	—	2	2	no	—
170	C₁₃×#120	—	2	2	no	—
171	C₁₃×#120	—	2	2	no	—
172	C₄×Q₈×C₁₃	—	2	1	no	—
173	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
175	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₁₃	—	2	2	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	—	2	1	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	2	no	—
184	C₄×D₄×C₁₃	—	2	1	no	—
185	C₄×D₄×C₁₃	—	2	2	no	—
186	C₄×D₄×C₁₃	—	2	2	no	—
187	C₄×D₄×C₁₃	D₄	1	2	yes	—
188	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
189	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₁₃	C₂³	1	4	yes	—
192	C₄×D₄×C₁₃	C₂³	1	2	yes	—
193	C₄×D₄×C₁₃	C₂³	1	2	yes	—
194	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
195	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
196	C₄×D₄×C₁₃	C₂³	1	2	yes	—
197	C₄×D₄×C₁₃	C₂³	1	2	yes	—
198	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
199	C₁₃×#117	—	2	1	no	—
200	C₁₃×#117	D₄	1	1	yes	characteristic
201	C₁₃×#117	D₄	1	2	yes	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
205	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
209	C₁₃×#106	C₂³	1	2	yes	—
210	C₁₃×#106	C₂³	1	2	yes	—
211	C₁₃×#106	C₂³	1	4	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
216	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×#102	C₂³	1	4	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₁₃×#97	C₂³	1	4	yes	—
230	C₄×C₈×C₁₃	C₂³	1	2	yes	—
231	#61961	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂⁴×C₁₃	—	2	2	no	—
233	C₂⁴×C₁₃	—	2	1	no	—
234	C₂⁴×C₁₃	—	2	2	no	—
235	C₁₃×#41	—	2	4	no	—
236	C₁₃×#41	—	4	8	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₁₃×#41	—	4	4	no	—
239	C₁₃×#41	—	4	8	no	—
240	C₁₃×#41	—	4	4	no	—
241	C₁₃×#41	—	4	4	no	—
242	C₁₃×#41	—	4	4	no	—
243	C₁₃×#41	—	8	4	no	—
244	C₂×Q₈×C₁₃	—	2	1	no	—
245	C₂×Q₈×C₁₃	—	2	2	no	—
246	C₂×Q₈×C₁₃	—	2	1	no	—
247	C₂×Q₈×C₁₃	—	4	4	no	—
248	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	4	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	4	no	—
256	C₂×D₄×C₁₃	—	2	4	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	1	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	2	no	—
262	C₂×D₄×C₁₃	—	2	2	no	—
263	C₂×D₄×C₁₃	—	2	1	no	—
264	C₂×D₄×C₁₃	—	2	2	no	—
265	C₂×D₄×C₁₃	—	2	1	no	—
266	C₂×D₄×C₁₃	—	2	2	no	—
267	C₂×D₄×C₁₃	—	2	2	no	—
268	C₂×D₄×C₁₃	—	4	1	no	—
269	C₂×D₄×C₁₃	—	4	2	no	—
270	C₂×D₄×C₁₃	—	4	2	no	—
271	C₂×D₄×C₁₃	—	4	2	no	—
272	C₂×D₄×C₁₃	—	4	8	no	—
273	C₂×D₄×C₁₃	—	4	4	no	—
274	C₂×D₄×C₁₃	—	4	4	no	—
275	C₂×D₄×C₁₃	—	8	2	no	—
276	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
277	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
279	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	—	2	2	no	—
283	C₂²×C₄×C₁₃	—	2	1	no	—
284	C₂²×C₄×C₁₃	—	2	1	no	—
285	C₂²×C₄×C₁₃	—	2	1	no	—
286	C₂²×C₄×C₁₃	—	2	2	no	—
287	C₂²×C₄×C₁₃	—	2	2	no	—
288	C₂²×C₄×C₁₃	—	2	1	no	—
289	C₂²×C₄×C₁₃	—	2	2	no	—
290	C₂²×C₄×C₁₃	—	2	1	no	—
291	C₂²×C₄×C₁₃	—	2	4	no	—
292	C₂²×C₄×C₁₃	—	2	4	no	—
293	C₂²×C₄×C₁₃	—	4	8	no	—
294	C₂²×C₄×C₁₃	—	4	4	no	—
295	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
296	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₁₃×SD₁₆	—	2	4	no	—
302	C₁₃×SD₁₆	—	4	2	no	—
303	C₁₃×SD₁₆	—	4	4	no	—
304	C₁₃×D₈	—	2	8	no	—
305	C₁₃×D₈	—	4	4	no	—
306	C₁₃×D₈	—	4	4	no	—
307	C₁₃×D₈	—	4	4	no	—
308	C₁₃×M₁₆	—	4	4	no	—
309	C₂×C₈×C₁₃	—	4	2	no	—
310	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
311	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
312	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
313	C₁₃×C₄⋊C₄	—	2	2	no	—
314	C₁₃×C₄⋊C₄	—	2	1	no	—
315	C₁₃×C₄⋊C₄	—	2	1	no	—
316	C₁₃×C₄⋊C₄	—	2	1	no	—
317	C₁₃×C₄⋊C₄	—	2	1	no	—
318	C₁₃×C₄⋊C₄	—	2	2	no	—
319	C₁₃×C₄⋊C₄	—	2	1	no	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
323	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
324	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
325	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
326	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
327	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
328	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
329	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	—	2	1	no	—
332	C₁₃×C₂²⋊C₄	—	2	4	no	—
333	C₁₃×C₂²⋊C₄	—	2	4	no	—
334	C₁₃×C₂²⋊C₄	—	2	2	no	—
335	C₁₃×C₂²⋊C₄	—	2	1	no	—
336	C₁₃×C₂²⋊C₄	—	2	2	no	—
337	C₁₃×C₂²⋊C₄	—	2	1	no	—
338	C₁₃×C₂²⋊C₄	—	2	1	no	—
339	C₁₃×C₂²⋊C₄	—	2	2	no	—
340	C₁₃×C₂²⋊C₄	—	2	2	no	—
341	C₁₃×C₂²⋊C₄	—	2	2	no	—
342	C₁₃×C₂²⋊C₄	—	2	2	no	—
343	C₁₃×C₂²⋊C₄	—	2	4	no	—
344	C₁₃×C₂²⋊C₄	—	2	4	no	—
345	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
346	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
347	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
348	C₄²×C₁₃	—	2	2	no	—
349	C₄²×C₁₃	C₂×D₄	1	2	yes	—
350	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
351	C₄²×C₁₃	C₂×D₄	1	2	yes	—
352	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
353	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
354	C₄²×C₁₃	C₂⁴	1	2	yes	—
355	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
356	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
357	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3399	C₂×C₁₃	1	2	yes	complemented
359	#3373	C₂×C₁₃	1	2	yes	complemented
360	#3332	C₂×C₁₃	1	2	yes	complemented
361	#3306	C₂×C₁₃	1	4	yes	complemented
362	#3274	C₂×C₁₃	1	2	yes	complemented
363	#3264	C₂×C₁₃	1	4	yes	complemented
364	#3253	C₂×C₁₃	1	2	yes	complemented
365	#3246	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#3214	C₂×C₁₃	1	2	yes	complemented
367	#3205	C₂×C₁₃	1	1	yes	characteristic, complemented
368	#3109	C₂×C₁₃	1	2	yes	complemented
369	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
370	#3036	C₂×C₁₃	1	2	yes	complemented
371	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
372	#2989	C₂×C₁₃	1	1	yes	characteristic, complemented
373	C₂³×C₁₃	—	2	1	no	—
374	C₂³×C₁₃	—	2	4	no	—
375	C₂³×C₁₃	—	2	1	no	—
376	C₂³×C₁₃	—	2	2	no	—
377	C₂³×C₁₃	—	4	2	no	—
378	C₂³×C₁₃	—	4	4	no	—
379	C₂³×C₁₃	—	4	4	no	—
380	C₂³×C₁₃	—	4	2	no	—
381	C₂³×C₁₃	—	4	4	no	—
382	C₂³×C₁₃	—	8	1	no	—
383	C₂³×C₁₃	—	8	2	no	—
384	C₂³×C₁₃	—	8	2	no	—
385	C₂³×C₁₃	—	8	2	no	—
386	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
387	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
388	Q₈×C₁₃	—	2	2	no	—
389	Q₈×C₁₃	—	2	2	no	—
390	Q₈×C₁₃	—	2	2	no	—
391	Q₈×C₁₃	—	4	4	no	—
392	Q₈×C₁₃	—	4	2	no	—
393	Q₈×C₁₃	—	4	2	no	—
394	D₄×C₁₃	—	2	4	no	—
395	D₄×C₁₃	—	2	2	no	—
396	D₄×C₁₃	—	2	4	no	—
397	D₄×C₁₃	—	2	1	no	—
398	D₄×C₁₃	—	2	2	no	—
399	D₄×C₁₃	—	2	1	no	—
400	D₄×C₁₃	—	2	2	no	—
401	D₄×C₁₃	—	2	4	no	—
402	D₄×C₁₃	—	2	1	no	—
403	D₄×C₁₃	—	4	4	no	—
404	D₄×C₁₃	—	4	2	no	—
405	D₄×C₁₃	—	4	4	no	—
406	D₄×C₁₃	—	4	4	no	—
407	D₄×C₁₃	—	4	4	no	—
408	D₄×C₁₃	—	4	4	no	—
409	D₄×C₁₃	—	4	4	no	—
410	D₄×C₁₃	—	4	4	no	—
411	D₄×C₁₃	—	4	4	no	—
412	D₄×C₁₃	—	4	2	no	—
413	D₄×C₁₃	—	8	2	no	—
414	D₄×C₁₃	—	8	1	no	—
415	D₄×C₁₃	—	8	2	no	—
416	D₄×C₁₃	—	8	2	no	—
417	D₄×C₁₃	—	8	4	no	—
418	D₄×C₁₃	—	8	4	no	—
419	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
420	C₂×C₄×C₁₃	—	2	4	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	1	no	—
430	C₂×C₄×C₁₃	—	4	1	no	—
431	C₂×C₄×C₁₃	—	4	2	no	—
432	C₂×C₄×C₁₃	—	4	4	no	—
433	C₂×C₄×C₁₃	—	4	4	no	—
434	C₂×C₄×C₁₃	—	4	4	no	—
435	C₂×C₄×C₁₃	—	4	2	no	—
436	C₂×C₄×C₁₃	—	4	2	no	—
437	C₂×C₄×C₁₃	—	4	2	no	—
438	C₂×C₄×C₁₃	—	4	2	no	—
439	C₂×C₄×C₁₃	—	4	4	no	—
440	C₂×C₄×C₁₃	—	4	2	no	—
441	C₂×C₄×C₁₃	—	8	4	no	—
442	C₂×C₄×C₁₃	—	8	4	no	—
443	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
444	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
448	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
453	C₈×C₁₃	—	2	4	no	—
454	C₈×C₁₃	—	2	2	no	—
455	C₈×C₁₃	—	2	2	no	—
456	C₂²×#41	—	2	1	no	—
457	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
458	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
459	#559	—	2	1	no	—
460	#559	C₂²×C₁₃	1	2	yes	complemented
461	#550	—	2	1	no	—
462	#550	C₂²×C₁₃	1	2	yes	complemented
463	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
464	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
465	#548	—	2	1	no	—
466	#547	C₂²×C₁₃	1	2	yes	—
467	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
468	#546	—	2	2	no	—
469	#546	—	2	1	no	—
470	#546	—	2	2	no	—
471	#546	C₂²×C₁₃	1	4	yes	complemented
472	D₄²	C₂²×C₁₃	1	2	yes	—
473	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
474	#540	—	2	2	no	—
475	#535	—	2	1	no	—
476	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
477	#532	C₂²×C₁₃	1	1	yes	characteristic
478	#532	C₂²×C₁₃	1	2	yes	complemented
479	#532	C₂²×C₁₃	1	2	yes	complemented
480	#532	C₂²×C₁₃	1	2	yes	complemented
481	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	#525	—	2	1	no	—
483	#525	—	2	2	no	—
484	#518	—	2	1	no	—
485	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
486	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
487	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
488	#496	C₂²×C₁₃	1	4	yes	complemented
489	#493	C₂²×C₁₃	1	2	yes	complemented
490	#489	C₂²×C₁₃	1	4	yes	complemented
491	#486	C₂²×C₁₃	1	2	yes	complemented
492	#483	C₂²×C₁₃	1	2	yes	complemented
493	#481	C₂²×C₁₃	1	4	yes	complemented
494	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
495	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
496	#476	C₂²×C₁₃	1	2	yes	complemented
497	#476	C₂²×C₁₃	1	4	yes	complemented
498	#475	C₂²×C₁₃	1	2	yes	complemented
499	#469	C₂²×C₁₃	1	4	yes	complemented
500	#469	C₂²×C₁₃	1	4	yes	complemented
501	#465	C₂²×C₁₃	1	4	yes	complemented
502	#463	C₂²×C₁₃	1	4	yes	complemented
503	#463	C₂²×C₁₃	1	4	yes	complemented
504	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
505	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
506	#461	C₂²×C₁₃	1	2	yes	complemented
507	#460	C₂²×C₁₃	1	2	yes	complemented
508	#459	C₂²×C₁₃	1	2	yes	—
509	#459	C₂²×C₁₃	1	2	yes	—
510	#459	C₂²×C₁₃	1	2	yes	complemented
511	#459	C₂²×C₁₃	1	2	yes	complemented
512	#459	C₂²×C₁₃	1	4	yes	complemented
513	#459	C₂²×C₁₃	1	2	yes	complemented
514	#459	C₂²×C₁₃	1	2	yes	complemented
515	#450	C₂²×C₁₃	1	2	yes	—
516	#449	C₂²×C₁₃	1	4	yes	complemented
517	#449	C₂²×C₁₃	1	4	yes	complemented
518	#447	C₂²×C₁₃	1	4	yes	complemented
519	#447	C₂²×C₁₃	1	4	yes	complemented
520	#446	C₂²×C₁₃	1	2	yes	complemented
521	#442	C₂²×C₁₃	1	4	yes	complemented
522	#442	C₂²×C₁₃	1	4	yes	complemented
523	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
524	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
525	#436	C₂²×C₁₃	1	2	yes	complemented
526	#435	C₂²×C₁₃	1	4	yes	complemented
527	#432	C₂²×C₁₃	1	2	yes	complemented
528	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
529	#423	C₂²×C₁₃	1	2	yes	complemented
530	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
531	#417	C₂²×C₁₃	1	4	yes	complemented
532	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
533	C₂²×C₁₃	—	2	1	no	—
534	C₂²×C₁₃	—	2	1	no	—
535	C₂²×C₁₃	—	2	2	no	—
536	C₂²×C₁₃	—	2	2	no	—
537	C₂²×C₁₃	—	2	2	no	—
538	C₂²×C₁₃	—	2	2	no	—
539	C₂²×C₁₃	—	4	1	no	—
540	C₂²×C₁₃	—	4	1	no	—
541	C₂²×C₁₃	—	4	4	no	—
542	C₂²×C₁₃	—	4	1	no	—
543	C₂²×C₁₃	—	4	2	no	—
544	C₂²×C₁₃	—	4	4	no	—
545	C₂²×C₁₃	—	4	1	no	—
546	C₂²×C₁₃	—	4	2	no	—
547	C₂²×C₁₃	—	4	2	no	—
548	C₂²×C₁₃	—	4	1	no	—
549	C₂²×C₁₃	—	4	4	no	—
550	C₂²×C₁₃	—	8	4	no	—
551	C₂²×C₁₃	—	8	8	no	—
552	C₂²×C₁₃	—	16	4	no	—
553	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
554	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
555	C₄×C₁₃	—	2	1	no	—
556	C₄×C₁₃	—	2	2	no	—
557	C₄×C₁₃	—	2	1	no	—
558	C₄×C₁₃	—	2	2	no	—
559	C₄×C₁₃	—	2	1	no	—
560	C₄×C₁₃	—	2	2	no	—
561	C₄×C₁₃	—	4	2	no	—
562	C₄×C₁₃	—	4	2	no	—
563	C₄×C₁₃	—	4	1	no	—
564	C₄×C₁₃	—	4	2	no	—
565	C₄×C₁₃	—	4	1	no	—
566	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
567	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
568	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
569	C₄×C₁₃	#585	1	1	yes	characteristic
570	C₂×#41	—	2	1	no	—
571	C₂×#41	—	2	2	no	—
572	C₂×#41	—	2	1	no	—
573	C₂×#41	—	2	1	no	—
574	C₂×#41	—	2	2	no	—
575	C₂×#41	—	2	2	no	—
576	C₂×#41	—	4	8	no	—
577	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
578	C₂×#41	C₂³×C₁₃	1	4	yes	—
579	C₂²×Q₈	—	2	1	no	—
580	C₂²×D₄	—	2	2	no	—
581	C₂²×D₄	—	2	1	no	—
582	C₂²×D₄	—	2	1	no	—
583	C₂²×D₄	—	2	1	no	—
584	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
585	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
586	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
587	C₂³×C₄	—	2	1	no	—
588	C₂³×C₄	—	2	2	no	—
589	AGL(1,ℤ/8)	—	4	8	no	—
590	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
591	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
592	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
593	C₂×D₈	—	4	4	no	—
594	C₂×D₈	C₂³×C₁₃	1	4	yes	—
595	C₂×D₈	C₂³×C₁₃	1	4	yes	—
596	C₂×D₈	C₂³×C₁₃	1	4	yes	—
597	C₂×D₈	C₂³×C₁₃	1	4	yes	—
598	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
599	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
600	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
602	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
603	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
604	#127	—	2	2	no	—
605	#127	—	2	1	no	—
606	#127	—	2	1	no	—
607	#127	C₂³×C₁₃	1	2	yes	—
608	#127	C₂³×C₁₃	1	2	yes	—
609	#127	C₂³×C₁₃	1	1	yes	characteristic
610	#127	C₂³×C₁₃	1	2	yes	—
611	#125	—	2	1	no	—
612	#124	—	2	2	no	—
613	#124	—	2	1	no	—
614	#124	—	2	2	no	—
615	#124	—	2	2	no	—
616	#124	C₂³×C₁₃	1	4	yes	—
617	#123	—	2	4	no	—
618	#123	—	2	4	no	—
619	#123	—	2	2	no	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	C₂²⋊Q₈	—	2	1	no	—
623	C₂²⋊Q₈	—	2	1	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	—	2	2	no	—
626	C₂²⋊Q₈	—	2	1	no	—
627	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
628	#121	—	2	1	no	—
629	#121	—	2	2	no	—
630	#121	—	2	2	no	—
631	#121	—	2	2	no	—
632	#121	—	2	2	no	—
633	#121	—	2	2	no	—
634	#121	—	2	1	no	—
635	#121	—	2	1	no	—
636	#121	—	2	2	no	—
637	#121	—	2	4	no	—
638	#121	—	2	4	no	—
639	#121	C₂³×C₁₃	1	2	yes	—
640	#121	C₂³×C₁₃	1	2	yes	—
641	#121	C₂³×C₁₃	1	2	yes	—
642	#121	C₂³×C₁₃	1	4	yes	—
643	#120	—	2	4	no	—
644	#120	—	2	2	no	—
645	#120	—	2	2	no	—
646	#120	—	2	2	no	—
647	C₄×Q₈	—	2	1	no	—
648	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
649	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
650	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	1	no	—
654	C₄×D₄	—	2	1	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	—	2	2	no	—
657	C₄×D₄	—	2	2	no	—
658	C₄×D₄	—	2	2	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	—	2	2	no	—
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	D₄×C₁₃	1	2	yes	—
663	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
664	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
665	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
666	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
667	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
668	C₄×D₄	C₂³×C₁₃	1	2	yes	—
669	C₄×D₄	C₂³×C₁₃	1	2	yes	—
670	C₄×D₄	C₂³×C₁₃	1	2	yes	—
671	C₄×D₄	C₂³×C₁₃	1	4	yes	—
672	C₄×D₄	C₂³×C₁₃	1	2	yes	—
673	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
674	#117	—	2	1	no	—
675	#117	D₄×C₁₃	1	1	yes	characteristic
676	#117	D₄×C₁₃	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
679	C₂×C₂²⋊C₄	—	2	1	no	—
680	C₂×C₂²⋊C₄	—	2	2	no	—
681	C₂×C₂²⋊C₄	—	2	4	no	—
682	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
684	#106	C₂³×C₁₃	1	2	yes	—
685	#106	C₂³×C₁₃	1	2	yes	—
686	#106	C₂³×C₁₃	1	4	yes	—
687	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
688	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
689	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
690	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
691	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
692	#103	C₂³×C₁₃	1	2	yes	—
693	#103	C₂³×C₁₃	1	4	yes	—
694	#103	C₂³×C₁₃	1	2	yes	—
695	#102	C₂³×C₁₃	1	4	yes	—
696	#102	C₂³×C₁₃	1	4	yes	—
697	#102	C₂³×C₁₃	1	4	yes	—
698	#102	C₂³×C₁₃	1	2	yes	—
699	#102	C₂³×C₁₃	1	2	yes	—
700	#102	C₂³×C₁₃	1	4	yes	—
701	#102	C₂³×C₁₃	1	4	yes	—
702	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
703	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
704	#97	C₂³×C₁₃	1	4	yes	—
705	C₄×C₈	C₂³×C₁₃	1	2	yes	—
706	C₂×C₁₃	—	2	2	no	—
707	C₂×C₁₃	—	4	2	no	—
708	C₂×C₁₃	—	4	2	no	—
709	C₂×C₁₃	—	8	1	no	—
710	C₂×C₁₃	—	8	2	no	—
711	C₂×C₁₃	—	8	4	no	—
712	C₂×C₁₃	#3488	1	1	yes	characteristic
713	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
714	C₂×C₁₃	#3585	1	1	yes	characteristic
715	C₂⁴	—	2	2	no	—
716	C₂⁴	—	2	1	no	—
717	C₂⁴	—	2	2	no	—
718	#41	—	2	4	no	—
719	#41	—	4	8	no	—
720	#41	—	4	4	no	—
721	#41	—	4	4	no	—
722	#41	—	4	8	no	—
723	#41	—	4	4	no	—
724	#41	—	4	4	no	—
725	#41	—	4	4	no	—
726	#41	—	8	4	no	—
727	C₂×Q₈	—	2	1	no	—
728	C₂×Q₈	—	2	2	no	—
729	C₂×Q₈	—	2	1	no	—
730	C₂×Q₈	—	4	4	no	—
731	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
732	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	1	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	1	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	1	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	4	1	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	8	no	—
756	C₂×D₄	—	4	4	no	—
757	C₂×D₄	—	4	4	no	—
758	C₂×D₄	—	8	2	no	—
759	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
760	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
761	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
762	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
763	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
764	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	1	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	1	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	1	no	—
774	C₂²×C₄	—	2	4	no	—
775	C₂²×C₄	—	2	4	no	—
776	C₂²×C₄	—	4	8	no	—
777	C₂²×C₄	—	4	4	no	—
778	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
779	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
780	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
781	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
784	SD₁₆	—	2	4	no	—
785	SD₁₆	—	4	4	no	—
786	SD₁₆	—	4	2	no	—
787	D₈	—	2	8	no	—
788	D₈	—	4	4	no	—
789	D₈	—	4	4	no	—
790	D₈	—	4	4	no	—
791	M₁₆	—	4	4	no	—
792	C₂×C₈	—	4	2	no	—
793	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
794	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
795	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	1	no	—
799	C₄⋊C₄	—	2	1	no	—
800	C₄⋊C₄	—	2	1	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	1	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
806	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
807	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
808	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
809	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
810	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
812	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	1	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	1	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	1	no	—
821	C₂²⋊C₄	—	2	1	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
829	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
830	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
831	C₄²	—	2	2	no	—
832	C₄²	C₂×D₄×C₁₃	1	2	yes	—
833	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
834	C₄²	C₂×D₄×C₁₃	1	2	yes	—
835	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
836	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
837	C₄²	C₂⁴×C₁₃	1	2	yes	—
838	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
839	C₁₃	#61961	1	1	yes	characteristic, direct product factor, Sylow
840	C₂³	—	2	1	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	4	no	—
844	C₂³	—	4	2	no	—
845	C₂³	—	4	4	no	—
846	C₂³	—	4	4	no	—
847	C₂³	—	4	2	no	—
848	C₂³	—	4	4	no	—
849	C₂³	—	8	1	no	—
850	C₂³	—	8	2	no	—
851	C₂³	—	8	2	no	—
852	C₂³	—	8	2	no	—
853	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
854	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
855	Q₈	—	2	2	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	2	2	no	—
858	Q₈	—	4	4	no	—
859	Q₈	—	4	2	no	—
860	Q₈	—	4	2	no	—
861	D₄	—	2	4	no	—
862	D₄	—	2	2	no	—
863	D₄	—	2	4	no	—
864	D₄	—	2	1	no	—
865	D₄	—	2	2	no	—
866	D₄	—	2	1	no	—
867	D₄	—	2	2	no	—
868	D₄	—	2	4	no	—
869	D₄	—	2	1	no	—
870	D₄	—	4	4	no	—
871	D₄	—	4	2	no	—
872	D₄	—	4	4	no	—
873	D₄	—	4	4	no	—
874	D₄	—	4	4	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	4	no	—
879	D₄	—	4	2	no	—
880	D₄	—	8	2	no	—
881	D₄	—	8	2	no	—
882	D₄	—	8	2	no	—
883	D₄	—	8	1	no	—
884	D₄	—	8	4	no	—
885	D₄	—	8	4	no	—
886	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	4	1	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	2	no	—
903	C₂×C₄	—	4	2	no	—
904	C₂×C₄	—	4	2	no	—
905	C₂×C₄	—	4	2	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	4	2	no	—
908	C₂×C₄	—	8	4	no	—
909	C₂×C₄	—	8	4	no	—
910	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
911	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
912	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
915	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
916	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
917	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
918	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
919	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
920	C₈	—	2	4	no	—
921	C₈	—	2	2	no	—
922	C₈	—	2	2	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	1	no	—
933	C₂²	—	4	4	no	—
934	C₂²	—	4	4	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	4	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	8	4	no	—
941	C₂²	—	8	8	no	—
942	C₂²	—	16	4	no	—
943	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
944	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
945	C₄	—	2	2	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	1	no	—
951	C₄	—	4	1	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	2	no	—
956	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
957	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
958	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
959	C₄	C₁₃×#585	1	1	yes	characteristic
960	C₂	—	2	2	no	—
961	C₂	—	4	2	no	—
962	C₂	—	4	2	no	—
963	C₂	—	8	1	no	—
964	C₂	—	8	2	no	—
965	C₂	—	8	4	no	—
966	C₂	C₁₃×#3488	1	1	yes	characteristic
967	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
968	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3508	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#3399	C₂	semidirect
4. C₁₃×#3373	C₂	semidirect
5. C₁₃×#3332	C₂	semidirect
6. C₁₃×#3306	C₂	semidirect
7. C₁₃×#3274	C₂	semidirect
8. C₁₃×#3264	C₂	semidirect
9. C₁₃×#3253	C₂	semidirect
10. C₁₃×#3246	C₂	semidirect
11. C₁₃×#3214	C₂	semidirect
12. C₁₃×#3205	C₂	semidirect
13. C₁₃×#3109	C₂	semidirect
14. C₁₃×#3101	C₂	semidirect
15. C₁₃×#3036	C₂	semidirect
16. C₂×C₁₃×#459	C₂	semidirect
17. C₁₃×#2989	C₂	semidirect
19. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₁₃×#559	C₂²	semidirect
24. C₁₃×#550	C₂²	semidirect
25. C₁₃×#550	C₂²	semidirect
26. D₄×Q₈×C₁₃	C₂²	semidirect
29. C₁₃×#547	C₂²	semidirect
33. C₁₃×#546	C₂²	semidirect
35. D₄²×C₁₃	C₂²	semidirect
38. C₁₃×#533	C₂²	semidirect
40. C₁₃×#532	C₂²	semidirect
41. C₁₃×#532	C₂²	semidirect
42. C₁₃×#532	C₂²	semidirect
43. C₂×C₁₃×#127	C₂²	semidirect
49. C₂×C₄×D₄×C₁₃	C₂²	semidirect
50. C₁₃×#496	C₂²	semidirect
51. C₁₃×#493	C₂²	semidirect
52. C₁₃×#489	C₂²	semidirect
53. C₁₃×#486	C₂²	semidirect
54. C₁₃×#483	C₂²	semidirect
55. C₁₃×#481	C₂²	semidirect
56. C₁₃×#476	C₂²	semidirect
57. C₁₃×#476	C₂²	semidirect
58. C₁₃×#476	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#469	C₂²	semidirect
62. C₁₃×#469	C₂²	semidirect
63. C₁₃×#465	C₂²	semidirect
64. C₁₃×#463	C₂²	semidirect
65. C₁₃×#463	C₂²	semidirect
66. C₁₃×#461	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
68. C₁₃×#461	C₂²	semidirect
69. C₁₃×#460	C₂²	semidirect
72. C₁₃×#459	C₂²	semidirect
73. C₁₃×#459	C₂²	semidirect
74. C₁₃×#459	C₂²	semidirect
75. C₁₃×#459	C₂²	semidirect
76. C₁₃×#459	C₂²	semidirect
78. C₁₃×#449	C₂²	semidirect
79. C₁₃×#449	C₂²	semidirect
80. C₁₃×#447	C₂²	semidirect
81. C₁₃×#447	C₂²	semidirect
82. C₁₃×#446	C₂²	semidirect
83. C₁₃×#442	C₂²	semidirect
84. C₁₃×#442	C₂²	semidirect
85. C₄×C₁₃×SD₁₆	C₂²	semidirect
86. C₄×C₁₃×SD₁₆	C₂²	semidirect
87. C₁₃×#436	C₂²	semidirect
88. C₁₃×#435	C₂²	semidirect
89. C₁₃×#432	C₂²	semidirect
90. C₁₃×#431	C₂²	semidirect
91. C₁₃×#423	C₂²	semidirect
92. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
93. C₁₃×#417	C₂²	semidirect
94. C₂×C₁₃×#102	C₂²	semidirect
231. #61961	C₁₃	direct (N × H)
356. #3508	C₂×C₁₃	semidirect
357. D₄×#41	C₂×C₁₃	semidirect
358. #3399	C₂×C₁₃	semidirect
359. #3373	C₂×C₁₃	semidirect
360. #3332	C₂×C₁₃	semidirect
361. #3306	C₂×C₁₃	semidirect
362. #3274	C₂×C₁₃	semidirect
363. #3264	C₂×C₁₃	semidirect
364. #3253	C₂×C₁₃	semidirect
365. #3246	C₂×C₁₃	semidirect
366. #3214	C₂×C₁₃	semidirect
367. #3205	C₂×C₁₃	semidirect
368. #3109	C₂×C₁₃	semidirect
369. #3101	C₂×C₁₃	semidirect
370. #3036	C₂×C₁₃	semidirect
371. C₂×#459	C₂×C₁₃	semidirect
372. #2989	C₂×C₁₃	semidirect
443. C₂×C₄×C₁₃	AGL(1,ℤ/8)	semidirect
457. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
460. #559	C₂²×C₁₃	semidirect
462. #550	C₂²×C₁₃	semidirect
463. #550	C₂²×C₁₃	semidirect
464. D₄×Q₈	C₂²×C₁₃	semidirect
467. #547	C₂²×C₁₃	semidirect
471. #546	C₂²×C₁₃	semidirect
473. D₄²	C₂²×C₁₃	semidirect
476. #533	C₂²×C₁₃	semidirect
478. #532	C₂²×C₁₃	semidirect
479. #532	C₂²×C₁₃	semidirect
480. #532	C₂²×C₁₃	semidirect
481. C₂×#127	C₂²×C₁₃	semidirect
487. C₂×C₄×D₄	C₂²×C₁₃	semidirect
488. #496	C₂²×C₁₃	semidirect
489. #493	C₂²×C₁₃	semidirect
490. #489	C₂²×C₁₃	semidirect
491. #486	C₂²×C₁₃	semidirect
492. #483	C₂²×C₁₃	semidirect
493. #481	C₂²×C₁₃	semidirect
494. #476	C₂²×C₁₃	semidirect
495. #476	C₂²×C₁₃	semidirect
496. #476	C₂²×C₁₃	semidirect
497. #476	C₂²×C₁₃	semidirect
498. #475	C₂²×C₁₃	semidirect
499. #469	C₂²×C₁₃	semidirect
500. #469	C₂²×C₁₃	semidirect
501. #465	C₂²×C₁₃	semidirect
502. #463	C₂²×C₁₃	semidirect
503. #463	C₂²×C₁₃	semidirect
504. #461	C₂²×C₁₃	semidirect
505. #461	C₂²×C₁₃	semidirect
506. #461	C₂²×C₁₃	semidirect
507. #460	C₂²×C₁₃	semidirect
510. #459	C₂²×C₁₃	semidirect
511. #459	C₂²×C₁₃	semidirect
512. #459	C₂²×C₁₃	semidirect
513. #459	C₂²×C₁₃	semidirect
514. #459	C₂²×C₁₃	semidirect
516. #449	C₂²×C₁₃	semidirect
517. #449	C₂²×C₁₃	semidirect
518. #447	C₂²×C₁₃	semidirect
519. #447	C₂²×C₁₃	semidirect
520. #446	C₂²×C₁₃	semidirect
521. #442	C₂²×C₁₃	semidirect
522. #442	C₂²×C₁₃	semidirect
523. C₄×SD₁₆	C₂²×C₁₃	semidirect
524. C₄×SD₁₆	C₂²×C₁₃	semidirect
525. #436	C₂²×C₁₃	semidirect
526. #435	C₂²×C₁₃	semidirect
527. #432	C₂²×C₁₃	semidirect
528. #431	C₂²×C₁₃	semidirect
529. #423	C₂²×C₁₃	semidirect
530. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
531. #417	C₂²×C₁₃	semidirect
532. C₂×#102	C₂²×C₁₃	semidirect
839. C₁₃	#61961	direct (N × H)
910. C₂×C₄	C₁₃×AGL(1,ℤ/8)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3508	2
D₄×C₁₃×#41	2
C₁₃×#3399	2
C₁₃×#3373	2
C₁₃×#3332	2
C₁₃×#3306	2
C₁₃×#3274	2
C₁₃×#3264	2
C₁₃×#3253	2
C₁₃×#3246	2
C₁₃×#3214	2
C₁₃×#3205	2
C₁₃×#3109	2
C₁₃×#3101	2
C₁₃×#3036	2
C₂×C₁₃×#459	2
C₁₃×#2989	2
#61961	13

Subgroups — C13×#61961 #15748300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61961 #15748300