Subgroups — C₁₃×#61874 #15748213

Order 3328.

1654 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×#3554	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3390	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3388	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3386	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3385	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3375	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3371	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3371	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3368	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3241	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3126	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3121	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#562	—	2	2	no	—
21	C₁₃×#559	C₂²	1	1	yes	characteristic
22	C₁₃×#559	C₂²	1	2	yes	—
23	Q₈²×C₁₃	—	2	1	no	—
24	Q₈²×C₁₃	C₂²	1	2	yes	—
25	C₁₃×#557	—	2	1	no	—
26	C₁₃×#557	—	2	2	no	—
27	C₁₃×#557	C₂²	1	1	yes	characteristic
28	C₁₃×#557	C₂²	1	2	yes	—
29	C₁₃×#557	C₂²	1	2	yes	—
30	C₁₃×#557	C₂²	1	2	yes	—
31	C₁₃×#554	C₂²	1	2	yes	—
32	C₁₃×#550	C₂²	1	1	yes	characteristic
33	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#548	—	2	1	no	—
35	C₁₃×#547	—	2	1	no	—
36	C₁₃×#544	—	2	1	no	—
37	C₁₃×#544	—	2	1	no	—
38	C₁₃×#544	C₂²	1	2	yes	—
39	C₁₃×#542	—	2	1	no	—
40	C₁₃×#542	C₂²	1	2	yes	—
41	C₁₃×#540	C₂²	1	2	yes	—
42	C₁₃×#539	—	2	2	no	—
43	C₁₃×#536	—	2	1	no	—
44	C₁₃×#533	—	2	2	no	—
45	C₁₃×#533	C₂²	1	1	yes	characteristic
46	C₁₃×#533	C₂²	1	1	yes	characteristic
47	C₁₃×#532	C₂²	1	1	yes	characteristic
48	C₁₃×#529	C₂²	1	1	yes	characteristic
49	C₁₃×#519	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#501	C₂²	1	1	yes	characteristic
52	C₁₃×#501	C₂²	1	2	yes	—
53	C₁₃×#501	C₂²	1	2	yes	—
54	C₁₃×#501	C₂²	1	2	yes	—
55	C₁₃×#501	C₂²	1	1	yes	characteristic
56	C₁₃×#500	C₂²	1	2	yes	—
57	C₁₃×#499	C₂²	1	2	yes	—
58	C₁₃×#490	C₂²	1	2	yes	—
59	C₁₃×#490	C₂²	1	2	yes	—
60	C₁₃×#489	C₂²	1	1	yes	characteristic
61	C₁₃×#489	C₂²	1	2	yes	—
62	C₁₃×#489	C₂²	1	1	yes	characteristic
63	C₁₃×#488	C₂²	1	2	yes	—
64	C₁₃×#486	C₂²	1	2	yes	—
65	C₁₃×#485	C₂²	1	2	yes	—
66	C₁₃×#484	C₂²	1	1	yes	characteristic
67	C₁₃×#482	C₂²	1	2	yes	—
68	C₁₃×#482	C₂²	1	2	yes	—
69	C₁₃×#482	C₂²	1	2	yes	—
70	C₁₃×#481	C₂²	1	1	yes	characteristic
71	C₁₃×#480	C₂²	1	2	yes	—
72	C₁₃×#479	C₂²	1	2	yes	—
73	C₁₃×#479	C₂²	1	2	yes	—
74	C₁₃×#479	C₂²	1	2	yes	—
75	C₁₃×#479	C₂²	1	2	yes	—
76	C₁₃×#479	C₂²	1	2	yes	—
77	C₁₃×#478	C₂²	1	2	yes	—
78	C₁₃×#478	C₂²	1	2	yes	—
79	C₁₃×#478	C₂²	1	2	yes	—
80	C₁₃×#478	C₂²	1	2	yes	—
81	C₁₃×#477	C₂²	1	2	yes	—
82	C₁₃×#477	C₂²	1	2	yes	—
83	C₁₃×#477	C₂²	1	2	yes	—
84	C₁₃×#476	C₂²	1	2	yes	—
85	C₁₃×#476	C₂²	1	2	yes	—
86	C₁₃×#475	C₂²	1	2	yes	—
87	C₁₃×#474	C₂²	1	2	yes	—
88	C₁₃×#474	C₂²	1	2	yes	—
89	C₁₃×#474	C₂²	1	2	yes	—
90	C₁₃×#464	C₂²	1	2	yes	—
91	C₁₃×#464	C₂²	1	2	yes	—
92	C₁₃×#464	C₂²	1	2	yes	—
93	C₁₃×#460	C₂²	1	2	yes	—
94	C₁₃×#460	C₂²	1	2	yes	—
95	C₁₃×#460	C₂²	1	2	yes	—
96	C₁₃×#451	C₂²	1	1	yes	characteristic
97	C₁₃×#448	C₂²	1	2	yes	—
98	C₁₃×#448	C₂²	1	1	yes	characteristic
99	C₁₃×#446	C₂²	1	2	yes	—
100	C₁₃×#446	C₂²	1	2	yes	—
101	C₁₃×#446	C₂²	1	2	yes	—
102	C₁₃×#446	C₂²	1	2	yes	—
103	C₁₃×#441	C₂²	1	2	yes	—
104	C₁₃×#441	C₂²	1	2	yes	—
105	C₁₃×#440	C₂²	1	2	yes	—
106	C₁₃×#440	C₂²	1	2	yes	—
107	C₁₃×#440	C₂²	1	2	yes	—
108	C₁₃×#440	C₂²	1	2	yes	—
109	C₁₃×#440	C₂²	1	2	yes	—
110	C₁₃×#440	C₂²	1	2	yes	—
111	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
112	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
113	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
114	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
115	C₁₃×#433	C₂²	1	2	yes	—
116	C₁₃×#433	C₂²	1	2	yes	—
117	C₁₃×#432	C₂²	1	1	yes	characteristic
118	C₁₃×#432	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	—	2	1	no	—
120	C₂×C₁₃×#41	—	2	1	no	—
121	C₂²×Q₈×C₁₃	—	2	1	no	—
122	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
127	C₁₃×C₄⋊Q₈	—	2	2	no	—
128	C₁₃×C₄⋊Q₈	—	2	1	no	—
129	C₁₃×C₄⋊Q₈	—	2	2	no	—
130	C₁₃×C₄⋊Q₈	—	2	2	no	—
131	C₁₃×C₄⋊Q₈	—	2	2	no	—
132	C₁₃×C₄⋊Q₈	—	2	2	no	—
133	C₁₃×C₄⋊Q₈	—	2	2	no	—
134	C₁₃×C₄⋊Q₈	—	2	2	no	—
135	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
136	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
137	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₁₃×#127	C₂³	1	2	yes	—
144	C₁₃×#127	C₂³	1	1	yes	characteristic
145	C₁₃×#126	—	2	2	no	—
146	C₁₃×#126	—	2	1	no	—
147	C₁₃×#125	—	2	2	no	—
148	C₁₃×#125	—	2	2	no	—
149	C₁₃×#125	—	2	2	no	—
150	C₁₃×#125	—	2	2	no	—
151	C₁₃×#125	—	2	2	no	—
152	C₁₃×#125	—	2	2	no	—
153	C₁₃×#125	—	2	2	no	—
154	C₁₃×#125	—	2	2	no	—
155	C₁₃×#125	D₄	1	2	yes	—
156	C₁₃×#125	C₂³	1	2	yes	—
157	C₁₃×#125	C₂³	1	2	yes	—
158	C₁₃×#125	C₂³	1	2	yes	—
159	C₁₃×#125	C₂³	1	2	yes	—
160	C₁₃×#125	C₂³	1	1	yes	characteristic
161	C₁₃×#124	—	2	1	no	—
162	C₁₃×#124	—	2	2	no	—
163	C₁₃×#124	—	2	2	no	—
164	C₁₃×#124	—	2	1	no	—
165	C₁₃×#124	C₂³	1	2	yes	—
166	C₁₃×#124	C₂³	1	1	yes	characteristic
167	C₁₃×#123	—	2	1	no	—
168	C₁₃×#123	—	2	2	no	—
169	C₁₃×#123	—	2	2	no	—
170	C₁₃×#123	—	2	2	no	—
171	C₁₃×#123	—	2	2	no	—
172	C₁₃×#123	—	2	2	no	—
173	C₁₃×#123	—	2	2	no	—
174	C₁₃×C₂²⋊Q₈	—	2	2	no	—
175	C₁₃×C₂²⋊Q₈	—	2	1	no	—
176	C₁₃×C₂²⋊Q₈	—	2	1	no	—
177	C₁₃×C₂²⋊Q₈	—	2	2	no	—
178	C₁₃×C₂²⋊Q₈	—	2	2	no	—
179	C₁₃×C₂²⋊Q₈	—	2	2	no	—
180	C₁₃×C₂²⋊Q₈	—	2	2	no	—
181	C₁₃×C₂²⋊Q₈	—	2	1	no	—
182	C₁₃×C₂²⋊Q₈	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
185	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
186	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
187	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
188	C₁₃×#121	—	2	1	no	—
189	C₁₃×#121	—	2	2	no	—
190	C₁₃×#121	—	2	1	no	—
191	C₁₃×#121	—	2	2	no	—
192	C₁₃×#121	—	2	2	no	—
193	C₁₃×#121	C₂³	1	2	yes	—
194	C₁₃×#121	C₂³	1	1	yes	characteristic
195	C₄×Q₈×C₁₃	—	2	2	no	—
196	C₄×Q₈×C₁₃	—	2	2	no	—
197	C₄×Q₈×C₁₃	—	2	2	no	—
198	C₄×Q₈×C₁₃	—	2	2	no	—
199	C₄×Q₈×C₁₃	—	2	2	no	—
200	C₄×Q₈×C₁₃	—	2	2	no	—
201	C₄×Q₈×C₁₃	—	2	1	no	—
202	C₄×Q₈×C₁₃	—	2	1	no	—
203	C₄×Q₈×C₁₃	—	2	1	no	—
204	C₄×Q₈×C₁₃	—	2	1	no	—
205	C₄×Q₈×C₁₃	—	2	1	no	—
206	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
207	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
208	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
209	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
210	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
214	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
217	C₄×D₄×C₁₃	—	2	1	no	—
218	C₄×D₄×C₁₃	—	2	2	no	—
219	C₄×D₄×C₁₃	—	2	1	no	—
220	C₄×D₄×C₁₃	—	2	1	no	—
221	C₄×D₄×C₁₃	C₂³	1	2	yes	—
222	C₄×D₄×C₁₃	C₂³	1	2	yes	—
223	C₄×D₄×C₁₃	C₂³	1	2	yes	—
224	C₄×D₄×C₁₃	C₂³	1	2	yes	—
225	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
226	C₁₃×#117	—	2	2	no	—
227	C₁₃×#117	—	2	2	no	—
228	C₁₃×#117	—	2	1	no	—
229	C₁₃×#117	C₂³	1	2	yes	—
230	C₁₃×#117	C₂³	1	2	yes	—
231	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
233	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₁₃	—	2	1	no	—
235	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
236	C₁₃×#107	C₂³	1	2	yes	—
237	C₁₃×#107	C₂³	1	2	yes	—
238	C₁₃×#107	C₂³	1	2	yes	—
239	C₁₃×#107	C₂³	1	2	yes	—
240	C₁₃×#107	C₂³	1	2	yes	—
241	C₁₃×#107	C₂³	1	2	yes	—
242	C₁₃×#107	C₂³	1	2	yes	—
243	C₁₃×#106	C₂³	1	2	yes	—
244	C₁₃×#106	C₂³	1	2	yes	—
245	C₁₃×#106	C₂³	1	2	yes	—
246	C₁₃×#106	C₂³	1	2	yes	—
247	C₁₃×#106	C₂³	1	2	yes	—
248	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
251	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
252	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
253	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
254	C₁₃×#103	C₂³	1	2	yes	—
255	C₁₃×#103	C₂³	1	2	yes	—
256	C₁₃×#103	C₂³	1	2	yes	—
257	C₁₃×#103	C₂³	1	2	yes	—
258	C₁₃×#103	C₂³	1	2	yes	—
259	C₁₃×#103	C₂³	1	2	yes	—
260	C₁₃×#103	C₂³	1	2	yes	—
261	C₁₃×#102	C₂³	1	2	yes	—
262	C₁₃×#102	C₂³	1	2	yes	—
263	C₁₃×#102	C₂³	1	2	yes	—
264	C₁₃×#102	C₂³	1	2	yes	—
265	C₁₃×#102	C₂³	1	2	yes	—
266	C₁₃×#102	C₂³	1	2	yes	—
267	C₁₃×#102	C₂³	1	2	yes	—
268	C₁₃×#102	C₂³	1	2	yes	—
269	C₁₃×#102	C₂³	1	2	yes	—
270	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
271	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₁₃×#97	C₂³	1	1	yes	characteristic
274	C₁₃×#97	C₂³	1	1	yes	characteristic
275	C₁₃×#97	C₂³	1	2	yes	—
276	C₁₃×#97	C₂³	1	2	yes	—
277	C₁₃×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₁₃	C₂³	1	2	yes	—
279	C₄×C₈×C₁₃	C₂³	1	2	yes	—
280	#61874	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₁₃×#41	—	8	2	no	—
282	C₁₃×#41	—	8	2	no	—
283	C₂×Q₈×C₁₃	—	2	4	no	—
284	C₂×Q₈×C₁₃	—	2	1	no	—
285	C₂×Q₈×C₁₃	—	2	1	no	—
286	C₂×Q₈×C₁₃	—	2	1	no	—
287	C₂×Q₈×C₁₃	—	2	1	no	—
288	C₂×Q₈×C₁₃	—	2	2	no	—
289	C₂×Q₈×C₁₃	—	2	2	no	—
290	C₂×Q₈×C₁₃	—	2	2	no	—
291	C₂×Q₈×C₁₃	—	8	2	no	—
292	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
293	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
294	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
295	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
297	C₂×D₄×C₁₃	—	2	1	no	—
298	C₂×D₄×C₁₃	—	2	2	no	—
299	C₂×D₄×C₁₃	—	2	1	no	—
300	C₂×D₄×C₁₃	—	2	1	no	—
301	C₂×D₄×C₁₃	—	2	2	no	—
302	C₂×D₄×C₁₃	—	2	2	no	—
303	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
304	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₃	—	2	1	no	—
306	C₂²×C₄×C₁₃	—	2	1	no	—
307	C₂²×C₄×C₁₃	—	2	1	no	—
308	C₂²×C₄×C₁₃	—	2	2	no	—
309	C₂²×C₄×C₁₃	—	2	2	no	—
310	C₂²×C₄×C₁₃	—	2	2	no	—
311	C₂²×C₄×C₁₃	—	2	2	no	—
312	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₁₃×Q₁₆	—	2	4	no	—
316	C₁₃×SD₁₆	—	2	4	no	—
317	C₁₃×SD₁₆	—	2	4	no	—
318	C₁₃×SD₁₆	—	2	4	no	—
319	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
320	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
321	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
322	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
323	C₁₃×C₄⋊C₄	—	2	1	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	—	2	1	no	—
329	C₁₃×C₄⋊C₄	—	2	2	no	—
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	1	no	—
334	C₁₃×C₄⋊C₄	—	2	1	no	—
335	C₁₃×C₄⋊C₄	—	2	1	no	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	—	2	1	no	—
338	C₁₃×C₄⋊C₄	—	2	2	no	—
339	C₁₃×C₄⋊C₄	—	2	1	no	—
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	—	2	2	no	—
342	C₁₃×C₄⋊C₄	—	2	2	no	—
343	C₁₃×C₄⋊C₄	—	2	2	no	—
344	C₁₃×C₄⋊C₄	—	2	2	no	—
345	C₁₃×C₄⋊C₄	—	2	2	no	—
346	C₁₃×C₄⋊C₄	—	2	2	no	—
347	C₁₃×C₄⋊C₄	—	2	2	no	—
348	C₁₃×C₄⋊C₄	—	2	1	no	—
349	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
350	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
351	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
352	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
353	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
354	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
355	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
356	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
357	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
358	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
359	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
360	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
361	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
362	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
363	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
364	C₁₃×C₂²⋊C₄	—	2	2	no	—
365	C₁₃×C₂²⋊C₄	—	2	1	no	—
366	C₁₃×C₂²⋊C₄	—	2	1	no	—
367	C₁₃×C₂²⋊C₄	—	2	1	no	—
368	C₁₃×C₂²⋊C₄	—	2	1	no	—
369	C₁₃×C₂²⋊C₄	—	2	2	no	—
370	C₁₃×C₂²⋊C₄	—	2	2	no	—
371	C₁₃×C₂²⋊C₄	—	2	2	no	—
372	C₁₃×C₂²⋊C₄	—	2	1	no	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	2	no	—
375	C₁₃×C₂²⋊C₄	—	2	2	no	—
376	C₁₃×C₂²⋊C₄	—	2	2	no	—
377	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
378	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
379	C₄²×C₁₃	—	2	2	no	—
380	C₄²×C₁₃	—	2	2	no	—
381	C₄²×C₁₃	—	2	1	no	—
382	C₄²×C₁₃	—	2	2	no	—
383	C₄²×C₁₃	—	2	2	no	—
384	C₄²×C₁₃	—	2	2	no	—
385	C₄²×C₁₃	—	2	2	no	—
386	C₄²×C₁₃	—	2	2	no	—
387	C₄²×C₁₃	—	2	2	no	—
388	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₁₃	C₂⁴	1	2	yes	—
391	C₄²×C₁₃	C₂⁴	1	2	yes	—
392	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
393	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
394	#3554	C₂×C₁₃	1	1	yes	characteristic
395	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
396	#3390	C₂×C₁₃	1	2	yes	complemented
397	#3388	C₂×C₁₃	1	2	yes	complemented
398	#3386	C₂×C₁₃	1	2	yes	complemented
399	#3385	C₂×C₁₃	1	2	yes	complemented
400	#3375	C₂×C₁₃	1	2	yes	complemented
401	#3371	C₂×C₁₃	1	2	yes	complemented
402	#3371	C₂×C₁₃	1	2	yes	complemented
403	#3368	C₂×C₁₃	1	2	yes	complemented
404	#3243	C₂×C₁₃	1	2	yes	complemented
405	#3241	C₂×C₁₃	1	2	yes	complemented
406	#3240	C₂×C₁₃	1	1	yes	characteristic, complemented
407	#3235	C₂×C₁₃	1	1	yes	characteristic, complemented
408	#3126	C₂×C₁₃	1	2	yes	complemented
409	#3121	C₂×C₁₃	1	2	yes	complemented
410	#3117	C₂×C₁₃	1	1	yes	characteristic, complemented
411	#3112	C₂×C₁₃	1	1	yes	characteristic, complemented
412	#2987	C₂×C₁₃	1	1	yes	characteristic, complemented
413	C₂³×C₁₃	—	2	1	no	—
414	C₂³×C₁₃	—	2	2	no	—
415	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	Q₈×C₁₃	—	2	4	no	—
417	Q₈×C₁₃	—	2	2	no	—
418	Q₈×C₁₃	—	2	2	no	—
419	Q₈×C₁₃	—	4	1	no	—
420	Q₈×C₁₃	—	4	2	no	—
421	Q₈×C₁₃	—	4	1	no	—
422	Q₈×C₁₃	—	4	2	no	—
423	Q₈×C₁₃	—	4	2	no	—
424	Q₈×C₁₃	—	8	1	no	—
425	Q₈×C₁₃	—	8	2	no	—
426	Q₈×C₁₃	—	8	2	no	—
427	Q₈×C₁₃	—	8	2	no	—
428	Q₈×C₁₃	2₋¹⁺⁴	1	4	yes	—
429	D₄×C₁₃	—	2	2	no	—
430	D₄×C₁₃	—	2	2	no	—
431	D₄×C₁₃	—	2	2	no	—
432	D₄×C₁₃	—	4	2	no	—
433	D₄×C₁₃	—	8	1	no	—
434	D₄×C₁₃	—	8	2	no	—
435	D₄×C₁₃	—	8	2	no	—
436	D₄×C₁₃	—	8	1	no	—
437	D₄×C₁₃	—	8	2	no	—
438	C₂×C₄×C₁₃	—	2	4	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	2	1	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	1	no	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	2	1	no	—
448	C₂×C₄×C₁₃	—	4	1	no	—
449	C₂×C₄×C₁₃	—	4	1	no	—
450	C₂×C₄×C₁₃	—	4	2	no	—
451	C₂×C₄×C₁₃	—	8	2	no	—
452	C₂×C₄×C₁₃	—	8	2	no	—
453	C₂×C₄×C₁₃	—	8	2	no	—
454	C₂×C₄×C₁₃	—	8	2	no	—
455	C₂×C₄×C₁₃	—	8	1	no	—
456	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
466	C₈×C₁₃	—	2	2	no	—
467	C₈×C₁₃	—	2	2	no	—
468	C₈×C₁₃	—	2	2	no	—
469	C₈×C₁₃	—	2	2	no	—
470	#562	—	2	2	no	—
471	#559	C₂²×C₁₃	1	1	yes	characteristic
472	#559	C₂²×C₁₃	1	2	yes	—
473	Q₈²	—	2	1	no	—
474	Q₈²	C₂²×C₁₃	1	2	yes	—
475	#557	—	2	1	no	—
476	#557	—	2	2	no	—
477	#557	C₂²×C₁₃	1	2	yes	—
478	#557	C₂²×C₁₃	1	2	yes	—
479	#557	C₂²×C₁₃	1	2	yes	—
480	#557	C₂²×C₁₃	1	1	yes	characteristic
481	#554	C₂²×C₁₃	1	2	yes	—
482	#550	C₂²×C₁₃	1	1	yes	characteristic
483	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
484	#548	—	2	1	no	—
485	#547	—	2	1	no	—
486	#544	—	2	1	no	—
487	#544	—	2	1	no	—
488	#544	C₂²×C₁₃	1	2	yes	—
489	#542	—	2	1	no	—
490	#542	C₂²×C₁₃	1	2	yes	—
491	#540	C₂²×C₁₃	1	2	yes	—
492	#539	—	2	2	no	—
493	#536	—	2	1	no	—
494	#533	—	2	2	no	—
495	#533	C₂²×C₁₃	1	1	yes	characteristic
496	#533	C₂²×C₁₃	1	1	yes	characteristic
497	#532	C₂²×C₁₃	1	1	yes	characteristic
498	#529	C₂²×C₁₃	1	1	yes	characteristic
499	#519	C₂²×C₁₃	1	2	yes	—
500	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
501	#501	C₂²×C₁₃	1	1	yes	characteristic
502	#501	C₂²×C₁₃	1	2	yes	—
503	#501	C₂²×C₁₃	1	2	yes	—
504	#501	C₂²×C₁₃	1	2	yes	—
505	#501	C₂²×C₁₃	1	1	yes	characteristic
506	#500	C₂²×C₁₃	1	2	yes	—
507	#499	C₂²×C₁₃	1	2	yes	—
508	#490	C₂²×C₁₃	1	2	yes	—
509	#490	C₂²×C₁₃	1	2	yes	—
510	#489	C₂²×C₁₃	1	1	yes	characteristic
511	#489	C₂²×C₁₃	1	2	yes	—
512	#489	C₂²×C₁₃	1	1	yes	characteristic
513	#488	C₂²×C₁₃	1	2	yes	—
514	#486	C₂²×C₁₃	1	2	yes	—
515	#485	C₂²×C₁₃	1	2	yes	—
516	#484	C₂²×C₁₃	1	1	yes	characteristic
517	#482	C₂²×C₁₃	1	2	yes	—
518	#482	C₂²×C₁₃	1	2	yes	—
519	#482	C₂²×C₁₃	1	2	yes	—
520	#481	C₂²×C₁₃	1	1	yes	characteristic
521	#480	C₂²×C₁₃	1	2	yes	—
522	#479	C₂²×C₁₃	1	2	yes	—
523	#479	C₂²×C₁₃	1	2	yes	—
524	#479	C₂²×C₁₃	1	2	yes	—
525	#479	C₂²×C₁₃	1	2	yes	—
526	#479	C₂²×C₁₃	1	2	yes	—
527	#478	C₂²×C₁₃	1	2	yes	—
528	#478	C₂²×C₁₃	1	2	yes	—
529	#478	C₂²×C₁₃	1	2	yes	—
530	#478	C₂²×C₁₃	1	2	yes	—
531	#477	C₂²×C₁₃	1	2	yes	—
532	#477	C₂²×C₁₃	1	2	yes	—
533	#477	C₂²×C₁₃	1	2	yes	—
534	#476	C₂²×C₁₃	1	2	yes	—
535	#476	C₂²×C₁₃	1	2	yes	—
536	#475	C₂²×C₁₃	1	2	yes	—
537	#474	C₂²×C₁₃	1	2	yes	—
538	#474	C₂²×C₁₃	1	2	yes	—
539	#474	C₂²×C₁₃	1	2	yes	—
540	#464	C₂²×C₁₃	1	2	yes	—
541	#464	C₂²×C₁₃	1	2	yes	—
542	#464	C₂²×C₁₃	1	2	yes	—
543	#460	C₂²×C₁₃	1	2	yes	—
544	#460	C₂²×C₁₃	1	2	yes	—
545	#460	C₂²×C₁₃	1	2	yes	—
546	#451	C₂²×C₁₃	1	1	yes	characteristic
547	#448	C₂²×C₁₃	1	2	yes	—
548	#448	C₂²×C₁₃	1	1	yes	characteristic
549	#446	C₂²×C₁₃	1	2	yes	—
550	#446	C₂²×C₁₃	1	2	yes	—
551	#446	C₂²×C₁₃	1	2	yes	—
552	#446	C₂²×C₁₃	1	2	yes	—
553	#441	C₂²×C₁₃	1	2	yes	—
554	#441	C₂²×C₁₃	1	2	yes	—
555	#440	C₂²×C₁₃	1	2	yes	—
556	#440	C₂²×C₁₃	1	2	yes	—
557	#440	C₂²×C₁₃	1	2	yes	—
558	#440	C₂²×C₁₃	1	2	yes	—
559	#440	C₂²×C₁₃	1	2	yes	—
560	#440	C₂²×C₁₃	1	2	yes	—
561	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
562	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
563	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
564	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
565	#433	C₂²×C₁₃	1	2	yes	—
566	#433	C₂²×C₁₃	1	2	yes	—
567	#432	C₂²×C₁₃	1	1	yes	characteristic
568	#432	C₂²×C₁₃	1	1	yes	characteristic
569	C₂²×C₁₃	—	2	1	no	—
570	C₂²×C₁₃	—	2	1	no	—
571	C₂²×C₁₃	—	2	1	no	—
572	C₂²×C₁₃	—	4	1	no	—
573	C₂²×C₁₃	—	4	2	no	—
574	C₂²×C₁₃	—	4	2	no	—
575	C₂²×C₁₃	—	4	1	no	—
576	C₂²×C₁₃	—	4	1	no	—
577	C₂²×C₁₃	—	4	2	no	—
578	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
579	C₄×C₁₃	—	2	1	no	—
580	C₄×C₁₃	—	2	1	no	—
581	C₄×C₁₃	—	2	2	no	—
582	C₄×C₁₃	—	2	2	no	—
583	C₄×C₁₃	—	2	1	no	—
584	C₄×C₁₃	—	2	1	no	—
585	C₄×C₁₃	—	2	2	no	—
586	C₄×C₁₃	—	2	2	no	—
587	C₄×C₁₃	—	2	4	no	—
588	C₄×C₁₃	—	2	1	no	—
589	C₄×C₁₃	—	4	1	no	—
590	C₄×C₁₃	—	4	2	no	—
591	C₄×C₁₃	—	4	2	no	—
592	C₄×C₁₃	—	4	2	no	—
593	C₄×C₁₃	—	4	1	no	—
594	C₄×C₁₃	—	4	2	no	—
595	C₄×C₁₃	—	4	1	no	—
596	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
597	C₂×#41	—	2	1	no	—
598	C₂×#41	—	2	1	no	—
599	C₂²×Q₈	—	2	1	no	—
600	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
602	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
603	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
604	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
605	C₄⋊Q₈	—	2	2	no	—
606	C₄⋊Q₈	—	2	1	no	—
607	C₄⋊Q₈	—	2	2	no	—
608	C₄⋊Q₈	—	2	2	no	—
609	C₄⋊Q₈	—	2	2	no	—
610	C₄⋊Q₈	—	2	2	no	—
611	C₄⋊Q₈	—	2	2	no	—
612	C₄⋊Q₈	—	2	2	no	—
613	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
614	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
615	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
616	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
617	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
618	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
619	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
620	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
621	#127	C₂³×C₁₃	1	1	yes	characteristic
622	#127	C₂³×C₁₃	1	2	yes	—
623	#126	—	2	2	no	—
624	#126	—	2	1	no	—
625	#125	—	2	2	no	—
626	#125	—	2	2	no	—
627	#125	—	2	2	no	—
628	#125	—	2	2	no	—
629	#125	—	2	2	no	—
630	#125	—	2	2	no	—
631	#125	—	2	2	no	—
632	#125	—	2	2	no	—
633	#125	D₄×C₁₃	1	2	yes	—
634	#125	C₂³×C₁₃	1	1	yes	characteristic
635	#125	C₂³×C₁₃	1	2	yes	—
636	#125	C₂³×C₁₃	1	2	yes	—
637	#125	C₂³×C₁₃	1	2	yes	—
638	#125	C₂³×C₁₃	1	2	yes	—
639	#124	—	2	1	no	—
640	#124	—	2	2	no	—
641	#124	—	2	2	no	—
642	#124	—	2	1	no	—
643	#124	C₂³×C₁₃	1	1	yes	characteristic
644	#124	C₂³×C₁₃	1	2	yes	—
645	#123	—	2	1	no	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	C₂²⋊Q₈	—	2	2	no	—
653	C₂²⋊Q₈	—	2	1	no	—
654	C₂²⋊Q₈	—	2	1	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	2	no	—
657	C₂²⋊Q₈	—	2	2	no	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	—	2	1	no	—
660	C₂²⋊Q₈	—	2	2	no	—
661	C₂²⋊Q₈	—	2	2	no	—
662	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
663	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
664	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
665	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
666	#121	—	2	1	no	—
667	#121	—	2	2	no	—
668	#121	—	2	1	no	—
669	#121	—	2	2	no	—
670	#121	—	2	2	no	—
671	#121	C₂³×C₁₃	1	1	yes	characteristic
672	#121	C₂³×C₁₃	1	2	yes	—
673	C₄×Q₈	—	2	2	no	—
674	C₄×Q₈	—	2	2	no	—
675	C₄×Q₈	—	2	2	no	—
676	C₄×Q₈	—	2	2	no	—
677	C₄×Q₈	—	2	2	no	—
678	C₄×Q₈	—	2	2	no	—
679	C₄×Q₈	—	2	1	no	—
680	C₄×Q₈	—	2	1	no	—
681	C₄×Q₈	—	2	1	no	—
682	C₄×Q₈	—	2	1	no	—
683	C₄×Q₈	—	2	1	no	—
684	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
685	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
686	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
687	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
688	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
689	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
690	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
691	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
692	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
693	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
694	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
695	C₄×D₄	—	2	1	no	—
696	C₄×D₄	—	2	2	no	—
697	C₄×D₄	—	2	1	no	—
698	C₄×D₄	—	2	1	no	—
699	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
700	C₄×D₄	C₂³×C₁₃	1	2	yes	—
701	C₄×D₄	C₂³×C₁₃	1	2	yes	—
702	C₄×D₄	C₂³×C₁₃	1	2	yes	—
703	C₄×D₄	C₂³×C₁₃	1	2	yes	—
704	#117	—	2	2	no	—
705	#117	—	2	2	no	—
706	#117	—	2	1	no	—
707	#117	C₂³×C₁₃	1	2	yes	—
708	#117	C₂³×C₁₃	1	2	yes	—
709	C₂×C₄⋊C₄	—	2	1	no	—
710	C₂×C₄⋊C₄	—	2	2	no	—
711	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
712	C₂×C₄²	—	2	1	no	—
713	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
714	#107	C₂³×C₁₃	1	2	yes	—
715	#107	C₂³×C₁₃	1	2	yes	—
716	#107	C₂³×C₁₃	1	2	yes	—
717	#107	C₂³×C₁₃	1	2	yes	—
718	#107	C₂³×C₁₃	1	2	yes	—
719	#107	C₂³×C₁₃	1	2	yes	—
720	#107	C₂³×C₁₃	1	2	yes	—
721	#106	C₂³×C₁₃	1	2	yes	—
722	#106	C₂³×C₁₃	1	2	yes	—
723	#106	C₂³×C₁₃	1	2	yes	—
724	#106	C₂³×C₁₃	1	2	yes	—
725	#106	C₂³×C₁₃	1	2	yes	—
726	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
727	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
728	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
729	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
730	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
731	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
732	#103	C₂³×C₁₃	1	2	yes	—
733	#103	C₂³×C₁₃	1	2	yes	—
734	#103	C₂³×C₁₃	1	2	yes	—
735	#103	C₂³×C₁₃	1	2	yes	—
736	#103	C₂³×C₁₃	1	2	yes	—
737	#103	C₂³×C₁₃	1	2	yes	—
738	#103	C₂³×C₁₃	1	2	yes	—
739	#102	C₂³×C₁₃	1	2	yes	—
740	#102	C₂³×C₁₃	1	2	yes	—
741	#102	C₂³×C₁₃	1	2	yes	—
742	#102	C₂³×C₁₃	1	2	yes	—
743	#102	C₂³×C₁₃	1	2	yes	—
744	#102	C₂³×C₁₃	1	2	yes	—
745	#102	C₂³×C₁₃	1	2	yes	—
746	#102	C₂³×C₁₃	1	2	yes	—
747	#102	C₂³×C₁₃	1	2	yes	—
748	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
749	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
750	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
751	#97	C₂³×C₁₃	1	1	yes	characteristic
752	#97	C₂³×C₁₃	1	1	yes	characteristic
753	#97	C₂³×C₁₃	1	2	yes	—
754	#97	C₂³×C₁₃	1	2	yes	—
755	#97	C₂³×C₁₃	1	2	yes	—
756	C₄×C₈	C₂³×C₁₃	1	2	yes	—
757	C₄×C₈	C₂³×C₁₃	1	2	yes	—
758	C₂×C₁₃	—	4	1	no	—
759	C₂×C₁₃	—	8	1	no	—
760	C₂×C₁₃	—	8	2	no	—
761	C₂×C₁₃	#3486	1	1	yes	characteristic
762	C₂×C₁₃	#3585	1	1	yes	characteristic
763	C₂×C₁₃	#3586	1	1	yes	characteristic
764	#41	—	8	2	no	—
765	#41	—	8	2	no	—
766	C₂×Q₈	—	2	4	no	—
767	C₂×Q₈	—	2	1	no	—
768	C₂×Q₈	—	2	1	no	—
769	C₂×Q₈	—	2	1	no	—
770	C₂×Q₈	—	2	1	no	—
771	C₂×Q₈	—	2	2	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	8	2	no	—
775	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
776	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
777	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
778	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
779	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
787	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
788	C₂²×C₄	—	2	1	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
796	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
798	Q₁₆	—	2	4	no	—
799	SD₁₆	—	2	4	no	—
800	SD₁₆	—	2	4	no	—
801	SD₁₆	—	2	4	no	—
802	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
803	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
804	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
805	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
806	C₄⋊C₄	—	2	1	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	1	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
833	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
834	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
835	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
836	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
837	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
838	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
839	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
840	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
841	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
842	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
843	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
844	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
845	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
846	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	1	no	—
849	C₂²⋊C₄	—	2	1	no	—
850	C₂²⋊C₄	—	2	1	no	—
851	C₂²⋊C₄	—	2	1	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	1	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
861	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	1	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
872	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
873	C₄²	C₂⁴×C₁₃	1	2	yes	—
874	C₄²	C₂⁴×C₁₃	1	2	yes	—
875	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
876	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
877	C₁₃	#61874	1	1	yes	characteristic, direct product factor, Sylow
878	C₂³	—	2	1	no	—
879	C₂³	—	2	2	no	—
880	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
881	Q₈	—	2	4	no	—
882	Q₈	—	2	2	no	—
883	Q₈	—	2	2	no	—
884	Q₈	—	4	1	no	—
885	Q₈	—	4	1	no	—
886	Q₈	—	4	2	no	—
887	Q₈	—	4	2	no	—
888	Q₈	—	4	2	no	—
889	Q₈	—	8	2	no	—
890	Q₈	—	8	1	no	—
891	Q₈	—	8	2	no	—
892	Q₈	—	8	2	no	—
893	Q₈	C₁₃×2₋¹⁺⁴	1	4	yes	—
894	D₄	—	2	2	no	—
895	D₄	—	2	2	no	—
896	D₄	—	2	2	no	—
897	D₄	—	4	2	no	—
898	D₄	—	8	1	no	—
899	D₄	—	8	2	no	—
900	D₄	—	8	2	no	—
901	D₄	—	8	1	no	—
902	D₄	—	8	2	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	1	no	—
915	C₂×C₄	—	4	2	no	—
916	C₂×C₄	—	8	2	no	—
917	C₂×C₄	—	8	2	no	—
918	C₂×C₄	—	8	2	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	1	no	—
921	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
922	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
923	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
924	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
925	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
926	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
927	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
928	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
929	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
930	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
931	C₈	—	2	2	no	—
932	C₈	—	2	2	no	—
933	C₈	—	2	2	no	—
934	C₈	—	2	2	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	2	no	—
944	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	4	no	—
954	C₄	—	2	1	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	1	no	—
962	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
963	C₂	—	4	1	no	—
964	C₂	—	8	1	no	—
965	C₂	—	8	2	no	—
966	C₂	C₁₃×#3486	1	1	yes	characteristic
967	C₂	C₁₃×#3585	1	1	yes	characteristic
968	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3554	C₂
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
2. C₁₃×#3502	C₂	semidirect
3. C₁₃×#3390	C₂	semidirect
4. C₁₃×#3388	C₂	semidirect
5. C₁₃×#3386	C₂	semidirect
6. C₁₃×#3385	C₂	semidirect
7. C₁₃×#3375	C₂	semidirect
8. C₁₃×#3371	C₂	semidirect
9. C₁₃×#3371	C₂	semidirect
10. C₁₃×#3368	C₂	semidirect
11. C₁₃×#3243	C₂	semidirect
12. C₁₃×#3241	C₂	semidirect
13. C₁₃×#3240	C₂	semidirect
14. C₁₃×#3235	C₂	semidirect
15. C₁₃×#3126	C₂	semidirect
16. C₁₃×#3121	C₂	semidirect
17. C₁₃×#3117	C₂	semidirect
18. C₁₃×#3112	C₂	semidirect
19. C₁₃×#2987	C₂	semidirect
280. #61874	C₁₃	direct (N × H)
395. #3502	C₂×C₁₃	semidirect
396. #3390	C₂×C₁₃	semidirect
397. #3388	C₂×C₁₃	semidirect
398. #3386	C₂×C₁₃	semidirect
399. #3385	C₂×C₁₃	semidirect
400. #3375	C₂×C₁₃	semidirect
401. #3371	C₂×C₁₃	semidirect
402. #3371	C₂×C₁₃	semidirect
403. #3368	C₂×C₁₃	semidirect
404. #3243	C₂×C₁₃	semidirect
405. #3241	C₂×C₁₃	semidirect
406. #3240	C₂×C₁₃	semidirect
407. #3235	C₂×C₁₃	semidirect
408. #3126	C₂×C₁₃	semidirect
409. #3121	C₂×C₁₃	semidirect
410. #3117	C₂×C₁₃	semidirect
411. #3112	C₂×C₁₃	semidirect
412. #2987	C₂×C₁₃	semidirect
877. C₁₃	#61874	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×#3554	2
C₁₃×#3502	2
C₁₃×#3390	2
C₁₃×#3388	2
C₁₃×#3386	2
C₁₃×#3385	2
C₁₃×#3375	2
C₁₃×#3371	2
C₁₃×#3368	2
C₁₃×#3243	2
C₁₃×#3241	2
C₁₃×#3240	2
C₁₃×#3235	2
C₁₃×#3126	2
C₁₃×#3121	2
C₁₃×#3117	2
C₁₃×#3112	2
C₁₃×#2987	2
#61874	13

Subgroups — C13×#61874 #15748213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61874 #15748213