Subgroups — C₁₃×#61938 #15748277

Order 3328.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1036 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, complemented
2	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3403	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3401	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3399	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3399	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3376	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3373	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3371	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3366	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3224	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3220	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3125	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3119	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3109	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	2	yes	—
22	C₁₃×#559	C₂²	1	2	yes	—
23	C₁₃×#559	C₂²	1	2	yes	complemented
24	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#556	C₂²	1	2	yes	—
27	C₁₃×#555	—	2	1	no	—
28	C₁₃×#554	C₂²	1	2	yes	complemented
29	C₁₃×#553	—	2	2	no	—
30	C₁₃×#550	C₂²	1	2	yes	—
31	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
32	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#548	—	2	1	no	—
34	C₁₃×#547	—	2	1	no	—
35	C₁₃×#547	—	2	1	no	—
36	C₁₃×#542	—	2	1	no	—
37	C₁₃×#542	C₂²	1	2	yes	—
38	C₁₃×#540	C₂²	1	2	yes	—
39	C₁₃×#539	—	2	2	no	—
40	C₁₃×#538	—	2	1	no	—
41	C₁₃×#538	—	2	1	no	—
42	C₁₃×#536	—	2	1	no	—
43	C₁₃×#535	C₂²	1	2	yes	—
44	C₁₃×#533	C₂²	1	1	yes	characteristic
45	C₁₃×#532	C₂²	1	1	yes	characteristic
46	C₁₃×#532	C₂²	1	1	yes	characteristic
47	C₁₃×#529	C₂²	1	1	yes	characteristic
48	C₁₃×#525	—	2	2	no	—
49	C₁₃×#520	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#497	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#496	C₂²	1	2	yes	—
53	C₁₃×#496	C₂²	1	2	yes	—
54	C₁₃×#496	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#496	C₂²	1	2	yes	complemented
56	C₁₃×#495	C₂²	1	2	yes	—
57	C₁₃×#493	C₂²	1	2	yes	—
58	C₁₃×#491	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#490	C₂²	1	2	yes	—
60	C₁₃×#490	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#489	C₂²	1	2	yes	—
62	C₁₃×#489	C₂²	1	2	yes	complemented
63	C₁₃×#488	C₂²	1	2	yes	—
64	C₁₃×#486	C₂²	1	2	yes	—
65	C₁₃×#483	C₂²	1	1	yes	characteristic
66	C₁₃×#481	C₂²	1	2	yes	—
67	C₁₃×#480	C₂²	1	1	yes	characteristic
68	C₁₃×#479	C₂²	1	2	yes	complemented
69	C₁₃×#478	C₂²	1	2	yes	—
70	C₁₃×#478	C₂²	1	2	yes	complemented
71	C₁₃×#476	C₂²	1	2	yes	—
72	C₁₃×#476	C₂²	1	2	yes	complemented
73	C₁₃×#475	C₂²	1	2	yes	complemented
74	C₁₃×#464	C₂²	1	2	yes	—
75	C₁₃×#464	C₂²	1	2	yes	complemented
76	C₁₃×#464	C₂²	1	2	yes	complemented
77	C₁₃×#463	C₂²	1	2	yes	—
78	C₁₃×#463	C₂²	1	2	yes	—
79	C₁₃×#463	C₂²	1	2	yes	—
80	C₁₃×#463	C₂²	1	2	yes	—
81	C₁₃×#463	C₂²	1	2	yes	complemented
82	C₁₃×#463	C₂²	1	2	yes	complemented
83	C₁₃×#461	C₂²	1	2	yes	complemented
84	C₁₃×#460	C₂²	1	2	yes	—
85	C₁₃×#460	C₂²	1	2	yes	complemented
86	C₁₃×#459	C₂²	1	2	yes	—
87	C₁₃×#459	C₂²	1	2	yes	—
88	C₁₃×#459	C₂²	1	2	yes	—
89	C₁₃×#459	C₂²	1	2	yes	—
90	C₁₃×#459	C₂²	1	2	yes	complemented
91	C₁₃×#459	C₂²	1	2	yes	complemented
92	C₁₃×#452	C₂²	1	2	yes	—
93	C₁₃×#450	C₂²	1	1	yes	characteristic
94	C₁₃×#449	C₂²	1	2	yes	—
95	C₁₃×#449	C₂²	1	2	yes	—
96	C₁₃×#449	C₂²	1	2	yes	—
97	C₁₃×#447	C₂²	1	2	yes	—
98	C₁₃×#447	C₂²	1	1	yes	characteristic
99	C₁₃×#446	C₂²	1	2	yes	complemented
100	C₁₃×#446	C₂²	1	2	yes	complemented
101	C₁₃×#446	C₂²	1	2	yes	complemented
102	C₁₃×#446	C₂²	1	2	yes	complemented
103	C₁₃×#442	C₂²	1	2	yes	—
104	C₁₃×#442	C₂²	1	2	yes	—
105	C₁₃×#442	C₂²	1	2	yes	—
106	C₁₃×#442	C₂²	1	2	yes	complemented
107	C₁₃×#442	C₂²	1	2	yes	complemented
108	C₁₃×#441	C₂²	1	2	yes	complemented
109	C₁₃×#440	C₂²	1	2	yes	—
110	C₁₃×#440	C₂²	1	2	yes	complemented
111	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
112	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
113	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
114	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
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	2	no	—
120	C₂×C₁₃×#41	—	2	1	no	—
121	C₂×C₁₃×#41	—	2	1	no	—
122	C₂×C₁₃×#41	C₂³	1	2	yes	—
123	C₂²×Q₈×C₁₃	—	2	1	no	—
124	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₃	—	2	1	no	—
126	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
130	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
131	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
132	C₂×C₁₃×D₈	C₂³	1	2	yes	—
133	C₂×C₁₃×D₈	C₂³	1	2	yes	—
134	C₂×C₁₃×D₈	C₂³	1	2	yes	—
135	C₂×C₁₃×D₈	C₂³	1	2	yes	—
136	C₂×C₁₃×D₈	C₂³	1	2	yes	—
137	C₂×C₁₃×D₈	C₂³	1	2	yes	—
138	C₁₃×C₄⋊Q₈	—	2	1	no	—
139	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
140	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
141	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
143	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₁₃×#127	C₂³	1	2	yes	—
145	C₁₃×#127	C₂³	1	1	yes	characteristic
146	C₁₃×#127	C₂³	1	2	yes	—
147	C₁₃×#127	C₂³	1	1	yes	characteristic
148	C₁₃×#127	C₂³	1	2	yes	—
149	C₁₃×#126	—	2	2	no	—
150	C₁₃×#126	—	2	2	no	—
151	C₁₃×#126	—	2	2	no	—
152	C₁₃×#126	—	2	1	no	—
153	C₁₃×#125	—	2	2	no	—
154	C₁₃×#125	D₄	1	2	yes	—
155	C₁₃×#125	C₂³	1	1	yes	characteristic
156	C₁₃×#125	C₂³	1	2	yes	—
157	C₁₃×#124	—	2	1	no	—
158	C₁₃×#124	—	2	2	no	—
159	C₁₃×#124	—	2	2	no	—
160	C₁₃×#124	—	2	2	no	—
161	C₁₃×#124	—	2	2	no	—
162	C₁₃×#124	—	2	1	no	—
163	C₁₃×#124	C₂³	1	2	yes	—
164	C₁₃×#124	C₂³	1	1	yes	characteristic
165	C₁₃×#124	C₂³	1	2	yes	—
166	C₁₃×#124	C₂³	1	2	yes	—
167	C₁₃×#124	C₂³	1	2	yes	—
168	C₁₃×#123	—	2	1	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×#123	—	2	2	no	—
175	C₁₃×#123	—	2	2	no	—
176	C₁₃×#123	—	2	2	no	—
177	C₁₃×#123	—	2	2	no	—
178	C₁₃×#123	—	2	2	no	—
179	C₁₃×C₂²⋊Q₈	—	2	2	no	—
180	C₁₃×C₂²⋊Q₈	—	2	2	no	—
181	C₁₃×C₂²⋊Q₈	—	2	2	no	—
182	C₁₃×C₂²⋊Q₈	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	—	2	1	no	—
186	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
187	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
188	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
189	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
190	C₁₃×#121	—	2	1	no	—
191	C₁₃×#121	—	2	1	no	—
192	C₁₃×#121	—	2	1	no	—
193	C₁₃×#121	—	2	2	no	—
194	C₁₃×#121	—	2	2	no	—
195	C₁₃×#121	—	2	2	no	—
196	C₁₃×#121	—	2	2	no	—
197	C₁₃×#121	—	2	2	no	—
198	C₁₃×#121	—	2	2	no	—
199	C₁₃×#121	—	2	1	no	—
200	C₁₃×#121	—	2	2	no	—
201	C₁₃×#121	—	2	2	no	—
202	C₁₃×#121	C₂³	1	1	yes	characteristic
203	C₁₃×#121	C₂³	1	2	yes	—
204	C₁₃×#120	—	2	2	no	—
205	C₁₃×#120	—	2	2	no	—
206	C₄×Q₈×C₁₃	—	2	1	no	—
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	1	yes	characteristic
211	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₁₃	—	2	1	no	—
215	C₄×D₄×C₁₃	—	2	2	no	—
216	C₄×D₄×C₁₃	—	2	2	no	—
217	C₄×D₄×C₁₃	—	2	2	no	—
218	C₄×D₄×C₁₃	—	2	1	no	—
219	C₄×D₄×C₁₃	—	2	2	no	—
220	C₄×D₄×C₁₃	—	2	2	no	—
221	C₄×D₄×C₁₃	—	2	1	no	—
222	C₄×D₄×C₁₃	—	2	1	no	—
223	C₄×D₄×C₁₃	—	2	1	no	—
224	C₄×D₄×C₁₃	—	2	1	no	—
225	C₄×D₄×C₁₃	—	2	1	no	—
226	C₄×D₄×C₁₃	C₂³	1	2	yes	—
227	C₄×D₄×C₁₃	C₂³	1	2	yes	—
228	C₄×D₄×C₁₃	C₂³	1	2	yes	—
229	C₄×D₄×C₁₃	C₂³	1	2	yes	—
230	C₄×D₄×C₁₃	C₂³	1	2	yes	—
231	C₄×D₄×C₁₃	C₂³	1	2	yes	—
232	C₄×D₄×C₁₃	C₂³	1	2	yes	—
233	C₄×D₄×C₁₃	C₂³	1	2	yes	—
234	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
235	C₁₃×#117	—	2	2	no	—
236	C₁₃×#117	—	2	2	no	—
237	C₁₃×#117	—	2	1	no	—
238	C₁₃×#117	C₂³	1	2	yes	—
239	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
240	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
241	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
243	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
244	C₁₃×#107	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×#102	C₂³	1	2	yes	—
260	C₁₃×#102	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	1	yes	characteristic
271	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
272	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₁₃×#97	C₂³	1	2	yes	—
274	C₁₃×#97	C₂³	1	1	yes	characteristic
275	C₁₃×#97	C₂³	1	1	yes	characteristic
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	#61938	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂⁴×C₁₃	—	2	1	no	—
282	C₁₃×#41	—	4	2	no	—
283	C₁₃×#41	—	4	2	no	—
284	C₁₃×#41	—	8	2	no	—
285	C₁₃×#41	—	8	4	no	—
286	C₁₃×#41	—	8	2	no	—
287	C₂×Q₈×C₁₃	—	2	1	no	—
288	C₂×Q₈×C₁₃	—	2	2	no	—
289	C₂×Q₈×C₁₃	—	8	2	no	—
290	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
291	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
294	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₂×D₄×C₁₃	—	2	2	no	—
296	C₂×D₄×C₁₃	—	2	1	no	—
297	C₂×D₄×C₁₃	—	2	2	no	—
298	C₂×D₄×C₁₃	—	2	1	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	—	2	1	no	—
304	C₂×D₄×C₁₃	—	2	1	no	—
305	C₂×D₄×C₁₃	—	2	2	no	—
306	C₂×D₄×C₁₃	—	2	2	no	—
307	C₂×D₄×C₁₃	—	2	2	no	—
308	C₂×D₄×C₁₃	—	2	2	no	—
309	C₂×D₄×C₁₃	—	4	2	no	—
310	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
311	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
312	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
313	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₃	—	2	1	no	—
315	C₂²×C₄×C₁₃	—	2	2	no	—
316	C₂²×C₄×C₁₃	—	2	2	no	—
317	C₂²×C₄×C₁₃	—	2	1	no	—
318	C₂²×C₄×C₁₃	—	2	2	no	—
319	C₂²×C₄×C₁₃	—	2	2	no	—
320	C₂²×C₄×C₁₃	—	2	2	no	—
321	C₂²×C₄×C₁₃	—	2	2	no	—
322	C₂²×C₄×C₁₃	—	2	2	no	—
323	C₂²×C₄×C₁₃	—	2	2	no	—
324	C₂²×C₄×C₁₃	—	2	2	no	—
325	C₂²×C₄×C₁₃	—	8	2	no	—
326	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₁₃×Q₁₆	—	4	2	no	—
330	C₁₃×SD₁₆	—	4	2	no	—
331	C₁₃×SD₁₆	—	4	2	no	—
332	C₁₃×SD₁₆	—	4	2	no	—
333	C₁₃×SD₁₆	—	4	2	no	—
334	C₁₃×SD₁₆	—	4	2	no	—
335	C₁₃×D₈	—	4	2	no	—
336	C₁₃×D₈	—	4	2	no	—
337	C₁₃×D₈	—	4	2	no	—
338	C₁₃×D₈	—	4	2	no	—
339	C₁₃×D₈	—	4	2	no	—
340	C₁₃×D₈	—	4	2	no	—
341	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
342	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
343	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
344	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
345	C₁₃×C₄⋊C₄	—	2	1	no	—
346	C₁₃×C₄⋊C₄	—	2	1	no	—
347	C₁₃×C₄⋊C₄	—	2	2	no	—
348	C₁₃×C₄⋊C₄	—	2	2	no	—
349	C₁₃×C₄⋊C₄	—	2	2	no	—
350	C₁₃×C₄⋊C₄	—	2	2	no	—
351	C₁₃×C₄⋊C₄	—	2	1	no	—
352	C₁₃×C₄⋊C₄	—	2	1	no	—
353	C₁₃×C₄⋊C₄	—	2	1	no	—
354	C₁₃×C₄⋊C₄	—	2	1	no	—
355	C₁₃×C₄⋊C₄	—	2	1	no	—
356	C₁₃×C₄⋊C₄	—	2	2	no	—
357	C₁₃×C₄⋊C₄	—	2	2	no	—
358	C₁₃×C₄⋊C₄	—	2	1	no	—
359	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
360	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
361	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
362	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
363	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
364	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
365	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
366	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
367	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
368	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
369	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
370	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
371	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
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	—	2	2	no	—
378	C₁₃×C₂²⋊C₄	—	2	2	no	—
379	C₁₃×C₂²⋊C₄	—	2	1	no	—
380	C₁₃×C₂²⋊C₄	—	2	1	no	—
381	C₁₃×C₂²⋊C₄	—	2	2	no	—
382	C₁₃×C₂²⋊C₄	—	2	1	no	—
383	C₁₃×C₂²⋊C₄	—	2	2	no	—
384	C₁₃×C₂²⋊C₄	—	2	2	no	—
385	C₁₃×C₂²⋊C₄	—	2	2	no	—
386	C₁₃×C₂²⋊C₄	—	2	2	no	—
387	C₁₃×C₂²⋊C₄	—	2	2	no	—
388	C₁₃×C₂²⋊C₄	—	2	2	no	—
389	C₁₃×C₂²⋊C₄	—	2	1	no	—
390	C₁₃×C₂²⋊C₄	—	2	2	no	—
391	C₁₃×C₂²⋊C₄	—	2	2	no	—
392	C₁₃×C₂²⋊C₄	—	2	2	no	—
393	C₁₃×C₂²⋊C₄	—	2	2	no	—
394	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
395	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
396	C₄²×C₁₃	—	2	2	no	—
397	C₄²×C₁₃	—	2	2	no	—
398	C₄²×C₁₃	—	2	1	no	—
399	C₄²×C₁₃	—	2	2	no	—
400	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₁₃	C₂⁴	1	2	yes	—
403	C₄²×C₁₃	C₂⁴	1	2	yes	—
404	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
405	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
406	#3554	C₂×C₁₃	1	1	yes	characteristic, complemented
407	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
408	#3403	C₂×C₁₃	1	2	yes	complemented
409	#3401	C₂×C₁₃	1	2	yes	complemented
410	#3399	C₂×C₁₃	1	2	yes	complemented
411	#3399	C₂×C₁₃	1	2	yes	complemented
412	#3376	C₂×C₁₃	1	2	yes	complemented
413	#3373	C₂×C₁₃	1	2	yes	complemented
414	#3371	C₂×C₁₃	1	2	yes	complemented
415	#3366	C₂×C₁₃	1	2	yes	complemented
416	#3224	C₂×C₁₃	1	2	yes	complemented
417	#3220	C₂×C₁₃	1	2	yes	complemented
418	#3219	C₂×C₁₃	1	1	yes	characteristic, complemented
419	#3214	C₂×C₁₃	1	1	yes	characteristic, complemented
420	#3125	C₂×C₁₃	1	2	yes	complemented
421	#3119	C₂×C₁₃	1	2	yes	complemented
422	#3114	C₂×C₁₃	1	1	yes	characteristic, complemented
423	#3109	C₂×C₁₃	1	1	yes	characteristic, complemented
424	#2987	C₂×C₁₃	1	1	yes	characteristic, complemented
425	C₂³×C₁₃	—	2	1	no	—
426	C₂³×C₁₃	—	2	2	no	—
427	C₂³×C₁₃	—	2	2	no	—
428	C₂³×C₁₃	—	2	2	no	—
429	C₂³×C₁₃	—	4	2	no	—
430	C₂³×C₁₃	—	8	1	no	—
431	C₂³×C₁₃	—	8	1	no	—
432	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
433	Q₈×C₁₃	—	2	2	no	—
434	Q₈×C₁₃	—	2	2	no	—
435	Q₈×C₁₃	—	2	2	no	—
436	Q₈×C₁₃	—	4	1	no	—
437	Q₈×C₁₃	—	4	2	no	—
438	Q₈×C₁₃	—	4	1	no	—
439	Q₈×C₁₃	—	4	2	no	—
440	Q₈×C₁₃	—	8	2	no	—
441	D₄×C₁₃	—	2	2	no	—
442	D₄×C₁₃	—	2	2	no	—
443	D₄×C₁₃	—	2	2	no	—
444	D₄×C₁₃	—	2	2	no	—
445	D₄×C₁₃	—	2	2	no	—
446	D₄×C₁₃	—	2	2	no	—
447	D₄×C₁₃	—	2	2	no	—
448	D₄×C₁₃	—	4	2	no	—
449	D₄×C₁₃	—	4	2	no	—
450	D₄×C₁₃	—	4	2	no	—
451	D₄×C₁₃	—	4	4	no	—
452	D₄×C₁₃	—	8	1	no	—
453	D₄×C₁₃	—	8	1	no	—
454	D₄×C₁₃	—	8	2	no	—
455	D₄×C₁₃	—	8	2	no	—
456	D₄×C₁₃	—	8	2	no	—
457	D₄×C₁₃	—	8	2	no	—
458	D₄×C₁₃	—	8	2	no	—
459	D₄×C₁₃	—	8	2	no	—
460	D₄×C₁₃	—	8	1	no	—
461	D₄×C₁₃	—	8	2	no	—
462	C₂×C₄×C₁₃	—	2	2	no	—
463	C₂×C₄×C₁₃	—	2	1	no	—
464	C₂×C₄×C₁₃	—	2	2	no	—
465	C₂×C₄×C₁₃	—	2	2	no	—
466	C₂×C₄×C₁₃	—	2	1	no	—
467	C₂×C₄×C₁₃	—	2	2	no	—
468	C₂×C₄×C₁₃	—	2	1	no	—
469	C₂×C₄×C₁₃	—	4	1	no	—
470	C₂×C₄×C₁₃	—	4	1	no	—
471	C₂×C₄×C₁₃	—	4	4	no	—
472	C₂×C₄×C₁₃	—	4	2	no	—
473	C₂×C₄×C₁₃	—	4	4	no	—
474	C₂×C₄×C₁₃	—	8	2	no	—
475	C₂×C₄×C₁₃	—	8	2	no	—
476	C₂×C₄×C₁₃	—	8	2	no	—
477	C₂×C₄×C₁₃	—	8	2	no	—
478	C₂×C₄×C₁₃	—	8	2	no	—
479	C₂×C₄×C₁₃	—	8	2	no	—
480	C₂×C₄×C₁₃	—	8	2	no	—
481	C₂×C₄×C₁₃	—	8	1	no	—
482	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
492	C₈×C₁₃	—	2	2	no	—
493	C₈×C₁₃	—	2	2	no	—
494	C₈×C₁₃	—	2	2	no	—
495	C₈×C₁₃	—	2	2	no	—
496	#562	—	2	2	no	—
497	#559	C₂²×C₁₃	1	2	yes	—
498	#559	C₂²×C₁₃	1	2	yes	—
499	#559	C₂²×C₁₃	1	2	yes	complemented
500	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
501	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
502	#556	C₂²×C₁₃	1	2	yes	—
503	#555	—	2	1	no	—
504	#554	C₂²×C₁₃	1	2	yes	complemented
505	#553	—	2	2	no	—
506	#550	C₂²×C₁₃	1	2	yes	—
507	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
508	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
509	#548	—	2	1	no	—
510	#547	—	2	1	no	—
511	#547	—	2	1	no	—
512	#542	—	2	1	no	—
513	#542	C₂²×C₁₃	1	2	yes	—
514	#540	C₂²×C₁₃	1	2	yes	—
515	#539	—	2	2	no	—
516	#538	—	2	1	no	—
517	#538	—	2	1	no	—
518	#536	—	2	1	no	—
519	#535	C₂²×C₁₃	1	2	yes	—
520	#533	C₂²×C₁₃	1	1	yes	characteristic
521	#532	C₂²×C₁₃	1	1	yes	characteristic
522	#532	C₂²×C₁₃	1	1	yes	characteristic
523	#529	C₂²×C₁₃	1	1	yes	characteristic
524	#525	—	2	2	no	—
525	#520	C₂²×C₁₃	1	2	yes	—
526	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
527	#497	C₂²×C₁₃	1	1	yes	characteristic, complemented
528	#496	C₂²×C₁₃	1	2	yes	—
529	#496	C₂²×C₁₃	1	2	yes	—
530	#496	C₂²×C₁₃	1	1	yes	characteristic, complemented
531	#496	C₂²×C₁₃	1	2	yes	complemented
532	#495	C₂²×C₁₃	1	2	yes	—
533	#493	C₂²×C₁₃	1	2	yes	—
534	#491	C₂²×C₁₃	1	1	yes	characteristic, complemented
535	#490	C₂²×C₁₃	1	2	yes	—
536	#490	C₂²×C₁₃	1	1	yes	characteristic, complemented
537	#489	C₂²×C₁₃	1	2	yes	—
538	#489	C₂²×C₁₃	1	2	yes	complemented
539	#488	C₂²×C₁₃	1	2	yes	—
540	#486	C₂²×C₁₃	1	2	yes	—
541	#483	C₂²×C₁₃	1	1	yes	characteristic
542	#481	C₂²×C₁₃	1	2	yes	—
543	#480	C₂²×C₁₃	1	1	yes	characteristic
544	#479	C₂²×C₁₃	1	2	yes	complemented
545	#478	C₂²×C₁₃	1	2	yes	—
546	#478	C₂²×C₁₃	1	2	yes	complemented
547	#476	C₂²×C₁₃	1	2	yes	—
548	#476	C₂²×C₁₃	1	2	yes	complemented
549	#475	C₂²×C₁₃	1	2	yes	complemented
550	#464	C₂²×C₁₃	1	2	yes	—
551	#464	C₂²×C₁₃	1	2	yes	complemented
552	#464	C₂²×C₁₃	1	2	yes	complemented
553	#463	C₂²×C₁₃	1	2	yes	—
554	#463	C₂²×C₁₃	1	2	yes	—
555	#463	C₂²×C₁₃	1	2	yes	—
556	#463	C₂²×C₁₃	1	2	yes	—
557	#463	C₂²×C₁₃	1	2	yes	complemented
558	#463	C₂²×C₁₃	1	2	yes	complemented
559	#461	C₂²×C₁₃	1	2	yes	complemented
560	#460	C₂²×C₁₃	1	2	yes	—
561	#460	C₂²×C₁₃	1	2	yes	complemented
562	#459	C₂²×C₁₃	1	2	yes	—
563	#459	C₂²×C₁₃	1	2	yes	—
564	#459	C₂²×C₁₃	1	2	yes	—
565	#459	C₂²×C₁₃	1	2	yes	—
566	#459	C₂²×C₁₃	1	2	yes	complemented
567	#459	C₂²×C₁₃	1	2	yes	complemented
568	#452	C₂²×C₁₃	1	2	yes	—
569	#450	C₂²×C₁₃	1	1	yes	characteristic
570	#449	C₂²×C₁₃	1	2	yes	—
571	#449	C₂²×C₁₃	1	2	yes	—
572	#449	C₂²×C₁₃	1	2	yes	—
573	#447	C₂²×C₁₃	1	2	yes	—
574	#447	C₂²×C₁₃	1	1	yes	characteristic
575	#446	C₂²×C₁₃	1	2	yes	complemented
576	#446	C₂²×C₁₃	1	2	yes	complemented
577	#446	C₂²×C₁₃	1	2	yes	complemented
578	#446	C₂²×C₁₃	1	2	yes	complemented
579	#442	C₂²×C₁₃	1	2	yes	—
580	#442	C₂²×C₁₃	1	2	yes	—
581	#442	C₂²×C₁₃	1	2	yes	—
582	#442	C₂²×C₁₃	1	2	yes	complemented
583	#442	C₂²×C₁₃	1	2	yes	complemented
584	#441	C₂²×C₁₃	1	2	yes	complemented
585	#440	C₂²×C₁₃	1	2	yes	—
586	#440	C₂²×C₁₃	1	2	yes	complemented
587	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
588	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
589	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
590	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
591	#433	C₂²×C₁₃	1	2	yes	—
592	#433	C₂²×C₁₃	1	2	yes	—
593	#432	C₂²×C₁₃	1	1	yes	characteristic
594	#432	C₂²×C₁₃	1	1	yes	characteristic
595	C₂²×C₁₃	—	2	1	no	—
596	C₂²×C₁₃	—	2	1	no	—
597	C₂²×C₁₃	—	2	1	no	—
598	C₂²×C₁₃	—	4	1	no	—
599	C₂²×C₁₃	—	4	2	no	—
600	C₂²×C₁₃	—	4	2	no	—
601	C₂²×C₁₃	—	4	2	no	—
602	C₂²×C₁₃	—	4	2	no	—
603	C₂²×C₁₃	—	4	2	no	—
604	C₂²×C₁₃	—	4	1	no	—
605	C₂²×C₁₃	—	4	2	no	—
606	C₂²×C₁₃	—	4	2	no	—
607	C₂²×C₁₃	—	4	2	no	—
608	C₂²×C₁₃	—	4	2	no	—
609	C₂²×C₁₃	—	4	1	no	—
610	C₂²×C₁₃	—	8	4	no	—
611	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
612	C₄×C₁₃	—	2	1	no	—
613	C₄×C₁₃	—	2	1	no	—
614	C₄×C₁₃	—	2	1	no	—
615	C₄×C₁₃	—	2	1	no	—
616	C₄×C₁₃	—	2	2	no	—
617	C₄×C₁₃	—	2	2	no	—
618	C₄×C₁₃	—	2	2	no	—
619	C₄×C₁₃	—	2	2	no	—
620	C₄×C₁₃	—	2	1	no	—
621	C₄×C₁₃	—	4	2	no	—
622	C₄×C₁₃	—	4	1	no	—
623	C₄×C₁₃	—	4	1	no	—
624	C₄×C₁₃	—	4	2	no	—
625	C₄×C₁₃	—	4	2	no	—
626	C₄×C₁₃	—	4	1	no	—
627	C₄×C₁₃	#585	1	2	yes	—
628	C₂×#41	—	2	2	no	—
629	C₂×#41	—	2	1	no	—
630	C₂×#41	—	2	1	no	—
631	C₂×#41	C₂³×C₁₃	1	2	yes	—
632	C₂²×Q₈	—	2	1	no	—
633	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
634	C₂³×C₄	—	2	1	no	—
635	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
636	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
637	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
638	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
639	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
640	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
641	C₂×D₈	C₂³×C₁₃	1	2	yes	—
642	C₂×D₈	C₂³×C₁₃	1	2	yes	—
643	C₂×D₈	C₂³×C₁₃	1	2	yes	—
644	C₂×D₈	C₂³×C₁₃	1	2	yes	—
645	C₂×D₈	C₂³×C₁₃	1	2	yes	—
646	C₂×D₈	C₂³×C₁₃	1	2	yes	—
647	C₄⋊Q₈	—	2	1	no	—
648	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
649	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
650	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
651	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
653	#127	C₂³×C₁₃	1	1	yes	characteristic
654	#127	C₂³×C₁₃	1	1	yes	characteristic
655	#127	C₂³×C₁₃	1	2	yes	—
656	#127	C₂³×C₁₃	1	2	yes	—
657	#127	C₂³×C₁₃	1	2	yes	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	—	2	1	no	—
662	#125	—	2	2	no	—
663	#125	D₄×C₁₃	1	2	yes	—
664	#125	C₂³×C₁₃	1	1	yes	characteristic
665	#125	C₂³×C₁₃	1	2	yes	—
666	#124	—	2	1	no	—
667	#124	—	2	2	no	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	—	2	2	no	—
671	#124	—	2	1	no	—
672	#124	C₂³×C₁₃	1	1	yes	characteristic
673	#124	C₂³×C₁₃	1	2	yes	—
674	#124	C₂³×C₁₃	1	2	yes	—
675	#124	C₂³×C₁₃	1	2	yes	—
676	#124	C₂³×C₁₃	1	2	yes	—
677	#123	—	2	1	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	1	no	—
695	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
696	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
697	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
698	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
699	#121	—	2	1	no	—
700	#121	—	2	1	no	—
701	#121	—	2	1	no	—
702	#121	—	2	2	no	—
703	#121	—	2	2	no	—
704	#121	—	2	2	no	—
705	#121	—	2	2	no	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	—	2	1	no	—
709	#121	—	2	2	no	—
710	#121	—	2	2	no	—
711	#121	C₂³×C₁₃	1	1	yes	characteristic
712	#121	C₂³×C₁₃	1	2	yes	—
713	#120	—	2	2	no	—
714	#120	—	2	2	no	—
715	C₄×Q₈	—	2	1	no	—
716	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
717	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
718	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
719	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
720	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
721	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
722	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
723	C₄×D₄	—	2	1	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	2	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	2	no	—
729	C₄×D₄	—	2	2	no	—
730	C₄×D₄	—	2	1	no	—
731	C₄×D₄	—	2	1	no	—
732	C₄×D₄	—	2	1	no	—
733	C₄×D₄	—	2	1	no	—
734	C₄×D₄	—	2	1	no	—
735	C₄×D₄	C₂³×C₁₃	1	2	yes	—
736	C₄×D₄	C₂³×C₁₃	1	2	yes	—
737	C₄×D₄	C₂³×C₁₃	1	2	yes	—
738	C₄×D₄	C₂³×C₁₃	1	2	yes	—
739	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
740	C₄×D₄	C₂³×C₁₃	1	2	yes	—
741	C₄×D₄	C₂³×C₁₃	1	2	yes	—
742	C₄×D₄	C₂³×C₁₃	1	2	yes	—
743	C₄×D₄	C₂³×C₁₃	1	2	yes	—
744	#117	—	2	2	no	—
745	#117	—	2	2	no	—
746	#117	—	2	1	no	—
747	#117	C₂³×C₁₃	1	2	yes	—
748	C₂×C₄⋊C₄	—	2	2	no	—
749	C₂×C₄⋊C₄	—	2	2	no	—
750	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
751	C₂×C₂²⋊C₄	—	2	1	no	—
752	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
753	#107	C₂³×C₁₃	1	2	yes	—
754	#106	C₂³×C₁₃	1	2	yes	—
755	#106	C₂³×C₁₃	1	2	yes	—
756	#106	C₂³×C₁₃	1	2	yes	—
757	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
758	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
759	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
760	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
761	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
762	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
763	#103	C₂³×C₁₃	1	2	yes	—
764	#103	C₂³×C₁₃	1	2	yes	—
765	#103	C₂³×C₁₃	1	2	yes	—
766	#103	C₂³×C₁₃	1	2	yes	—
767	#103	C₂³×C₁₃	1	2	yes	—
768	#102	C₂³×C₁₃	1	2	yes	—
769	#102	C₂³×C₁₃	1	2	yes	—
770	#102	C₂³×C₁₃	1	2	yes	—
771	#102	C₂³×C₁₃	1	2	yes	—
772	#102	C₂³×C₁₃	1	2	yes	—
773	#102	C₂³×C₁₃	1	2	yes	—
774	#102	C₂³×C₁₃	1	2	yes	—
775	#102	C₂³×C₁₃	1	2	yes	—
776	#102	C₂³×C₁₃	1	2	yes	—
777	#102	C₂³×C₁₃	1	2	yes	—
778	#102	C₂³×C₁₃	1	2	yes	—
779	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
780	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
782	#97	C₂³×C₁₃	1	2	yes	—
783	#97	C₂³×C₁₃	1	1	yes	characteristic
784	#97	C₂³×C₁₃	1	1	yes	characteristic
785	#97	C₂³×C₁₃	1	2	yes	—
786	#97	C₂³×C₁₃	1	2	yes	—
787	C₄×C₈	C₂³×C₁₃	1	2	yes	—
788	C₄×C₈	C₂³×C₁₃	1	2	yes	—
789	C₂×C₁₃	—	4	1	no	—
790	C₂×C₁₃	—	8	1	no	—
791	C₂×C₁₃	—	8	2	no	—
792	C₂×C₁₃	—	8	2	no	—
793	C₂×C₁₃	—	8	2	no	—
794	C₂×C₁₃	#3487	1	1	yes	characteristic
795	C₂×C₁₃	#3585	1	1	yes	characteristic
796	C₂×C₁₃	#3585	1	1	yes	characteristic
797	C₂⁴	—	2	1	no	—
798	#41	—	4	2	no	—
799	#41	—	4	2	no	—
800	#41	—	8	2	no	—
801	#41	—	8	4	no	—
802	#41	—	8	2	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	8	2	no	—
806	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
807	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
808	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
809	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
810	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	1	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	2	no	—
819	C₂×D₄	—	2	1	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	4	2	no	—
826	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
827	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
828	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
829	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	8	2	no	—
842	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
843	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
845	Q₁₆	—	4	2	no	—
846	SD₁₆	—	4	2	no	—
847	SD₁₆	—	4	2	no	—
848	SD₁₆	—	4	2	no	—
849	SD₁₆	—	4	2	no	—
850	SD₁₆	—	4	2	no	—
851	D₈	—	4	2	no	—
852	D₈	—	4	2	no	—
853	D₈	—	4	2	no	—
854	D₈	—	4	2	no	—
855	D₈	—	4	2	no	—
856	D₈	—	4	2	no	—
857	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
858	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
859	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
860	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
876	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
877	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
878	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
879	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
880	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
881	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
882	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
883	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
884	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
885	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
886	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
887	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
888	C₂²⋊C₄	—	2	1	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	1	no	—
896	C₂²⋊C₄	—	2	1	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	1	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	1	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
911	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	—	2	1	no	—
915	C₄²	—	2	2	no	—
916	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
917	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
918	C₄²	C₂⁴×C₁₃	1	2	yes	—
919	C₄²	C₂⁴×C₁₃	1	2	yes	—
920	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
921	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
922	C₁₃	#61938	1	1	yes	characteristic, direct product factor, Sylow
923	C₂³	—	2	1	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	4	2	no	—
928	C₂³	—	8	1	no	—
929	C₂³	—	8	1	no	—
930	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
931	Q₈	—	2	2	no	—
932	Q₈	—	2	2	no	—
933	Q₈	—	2	2	no	—
934	Q₈	—	4	1	no	—
935	Q₈	—	4	2	no	—
936	Q₈	—	4	1	no	—
937	Q₈	—	4	2	no	—
938	Q₈	—	8	2	no	—
939	D₄	—	2	2	no	—
940	D₄	—	2	2	no	—
941	D₄	—	2	2	no	—
942	D₄	—	2	2	no	—
943	D₄	—	2	2	no	—
944	D₄	—	2	2	no	—
945	D₄	—	2	2	no	—
946	D₄	—	4	2	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	2	no	—
949	D₄	—	4	4	no	—
950	D₄	—	8	1	no	—
951	D₄	—	8	1	no	—
952	D₄	—	8	2	no	—
953	D₄	—	8	2	no	—
954	D₄	—	8	2	no	—
955	D₄	—	8	2	no	—
956	D₄	—	8	2	no	—
957	D₄	—	8	2	no	—
958	D₄	—	8	1	no	—
959	D₄	—	8	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	4	4	no	—
970	C₂×C₄	—	4	2	no	—
971	C₂×C₄	—	4	4	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	—	8	2	no	—
974	C₂×C₄	—	8	2	no	—
975	C₂×C₄	—	8	2	no	—
976	C₂×C₄	—	8	2	no	—
977	C₂×C₄	—	8	2	no	—
978	C₂×C₄	—	8	2	no	—
979	C₂×C₄	—	8	1	no	—
980	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
981	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
982	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
983	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
984	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
985	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
986	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
988	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
989	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
990	C₈	—	2	2	no	—
991	C₈	—	2	2	no	—
992	C₈	—	2	2	no	—
993	C₈	—	2	2	no	—
994	C₂²	—	2	1	no	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	1	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	8	4	no	—
1010	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	2	no	—
1016	C₄	—	2	2	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	1	no	—
1026	C₄	C₁₃×#585	1	2	yes	—
1027	C₂	—	4	1	no	—
1028	C₂	—	8	2	no	—
1029	C₂	—	8	1	no	—
1030	C₂	—	8	2	no	—
1031	C₂	—	8	2	no	—
1032	C₂	C₁₃×#3487	1	1	yes	characteristic
1033	C₂	C₁₃×#3585	1	1	yes	characteristic
1034	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 ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3554	C₂	semidirect
2. C₁₃×#3506	C₂	semidirect
3. C₁₃×#3403	C₂	semidirect
4. C₁₃×#3401	C₂	semidirect
5. C₁₃×#3399	C₂	semidirect
6. C₁₃×#3399	C₂	semidirect
7. C₁₃×#3376	C₂	semidirect
8. C₁₃×#3373	C₂	semidirect
9. C₁₃×#3371	C₂	semidirect
10. C₁₃×#3366	C₂	semidirect
11. C₁₃×#3224	C₂	semidirect
12. C₁₃×#3220	C₂	semidirect
13. C₁₃×#3219	C₂	semidirect
14. C₁₃×#3214	C₂	semidirect
15. C₁₃×#3125	C₂	semidirect
16. C₁₃×#3119	C₂	semidirect
17. C₁₃×#3114	C₂	semidirect
18. C₁₃×#3109	C₂	semidirect
19. C₁₃×#2987	C₂	semidirect
23. C₁₃×#559	C₂²	semidirect
24. C₁₃×#559	C₂²	semidirect
25. C₁₃×#557	C₂²	semidirect
28. C₁₃×#554	C₂²	semidirect
31. C₁₃×#550	C₂²	semidirect
32. D₄×Q₈×C₁₃	C₂²	semidirect
51. C₁₃×#497	C₂²	semidirect
54. C₁₃×#496	C₂²	semidirect
55. C₁₃×#496	C₂²	semidirect
58. C₁₃×#491	C₂²	semidirect
60. C₁₃×#490	C₂²	semidirect
62. C₁₃×#489	C₂²	semidirect
68. C₁₃×#479	C₂²	semidirect
70. C₁₃×#478	C₂²	semidirect
72. C₁₃×#476	C₂²	semidirect
73. C₁₃×#475	C₂²	semidirect
75. C₁₃×#464	C₂²	semidirect
76. C₁₃×#464	C₂²	semidirect
81. C₁₃×#463	C₂²	semidirect
82. C₁₃×#463	C₂²	semidirect
83. C₁₃×#461	C₂²	semidirect
85. C₁₃×#460	C₂²	semidirect
90. C₁₃×#459	C₂²	semidirect
91. C₁₃×#459	C₂²	semidirect
99. C₁₃×#446	C₂²	semidirect
100. C₁₃×#446	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₁₃×#446	C₂²	semidirect
106. C₁₃×#442	C₂²	semidirect
107. C₁₃×#442	C₂²	semidirect
108. C₁₃×#441	C₂²	semidirect
110. C₁₃×#440	C₂²	semidirect
111. C₄×C₁₃×SD₁₆	C₂²	semidirect
112. C₄×C₁₃×SD₁₆	C₂²	semidirect
113. C₄×C₁₃×SD₁₆	C₂²	semidirect
114. C₄×C₁₃×D₈	C₂²	semidirect
280. #61938	C₁₃	direct (N × H)
406. #3554	C₂×C₁₃	semidirect
407. #3506	C₂×C₁₃	semidirect
408. #3403	C₂×C₁₃	semidirect
409. #3401	C₂×C₁₃	semidirect
410. #3399	C₂×C₁₃	semidirect
411. #3399	C₂×C₁₃	semidirect
412. #3376	C₂×C₁₃	semidirect
413. #3373	C₂×C₁₃	semidirect
414. #3371	C₂×C₁₃	semidirect
415. #3366	C₂×C₁₃	semidirect
416. #3224	C₂×C₁₃	semidirect
417. #3220	C₂×C₁₃	semidirect
418. #3219	C₂×C₁₃	semidirect
419. #3214	C₂×C₁₃	semidirect
420. #3125	C₂×C₁₃	semidirect
421. #3119	C₂×C₁₃	semidirect
422. #3114	C₂×C₁₃	semidirect
423. #3109	C₂×C₁₃	semidirect
424. #2987	C₂×C₁₃	semidirect
499. #559	C₂²×C₁₃	semidirect
500. #559	C₂²×C₁₃	semidirect
501. #557	C₂²×C₁₃	semidirect
504. #554	C₂²×C₁₃	semidirect
507. #550	C₂²×C₁₃	semidirect
508. D₄×Q₈	C₂²×C₁₃	semidirect
527. #497	C₂²×C₁₃	semidirect
530. #496	C₂²×C₁₃	semidirect
531. #496	C₂²×C₁₃	semidirect
534. #491	C₂²×C₁₃	semidirect
536. #490	C₂²×C₁₃	semidirect
538. #489	C₂²×C₁₃	semidirect
544. #479	C₂²×C₁₃	semidirect
546. #478	C₂²×C₁₃	semidirect
548. #476	C₂²×C₁₃	semidirect
549. #475	C₂²×C₁₃	semidirect
551. #464	C₂²×C₁₃	semidirect
552. #464	C₂²×C₁₃	semidirect
557. #463	C₂²×C₁₃	semidirect
558. #463	C₂²×C₁₃	semidirect
559. #461	C₂²×C₁₃	semidirect
561. #460	C₂²×C₁₃	semidirect
566. #459	C₂²×C₁₃	semidirect
567. #459	C₂²×C₁₃	semidirect
575. #446	C₂²×C₁₃	semidirect
576. #446	C₂²×C₁₃	semidirect
577. #446	C₂²×C₁₃	semidirect
578. #446	C₂²×C₁₃	semidirect
582. #442	C₂²×C₁₃	semidirect
583. #442	C₂²×C₁₃	semidirect
584. #441	C₂²×C₁₃	semidirect
586. #440	C₂²×C₁₃	semidirect
587. C₄×SD₁₆	C₂²×C₁₃	semidirect
588. C₄×SD₁₆	C₂²×C₁₃	semidirect
589. C₄×SD₁₆	C₂²×C₁₃	semidirect
590. C₄×D₈	C₂²×C₁₃	semidirect
922. C₁₃	#61938	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×#3506	2
C₁₃×#3403	2
C₁₃×#3401	2
C₁₃×#3399	2
C₁₃×#3376	2
C₁₃×#3373	2
C₁₃×#3371	2
C₁₃×#3366	2
C₁₃×#3224	2
C₁₃×#3220	2
C₁₃×#3219	2
C₁₃×#3214	2
C₁₃×#3125	2
C₁₃×#3119	2
C₁₃×#3114	2
C₁₃×#3109	2
C₁₃×#2987	2
#61938	13

Subgroups — C13×#61938 #15748277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61938 #15748277