Subgroups — C₁₃×#62597 #15748936

Order 3328.

1704 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3376	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3372	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3320	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3320	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3308	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3307	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3301	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3298	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3242	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3232	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3221	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3180	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3174	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2968	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#563	—	2	2	no	—
21	C₁₃×#563	—	2	1	no	—
22	C₁₃×#562	—	2	1	no	—
23	C₁₃×#557	C₂²	1	1	yes	characteristic
24	C₁₃×#556	C₂²	1	1	yes	characteristic
25	C₁₃×#554	—	2	1	no	—
26	C₁₃×#554	C₂²	1	2	yes	—
27	C₁₃×#553	—	2	1	no	—
28	C₁₃×#553	C₂²	1	2	yes	—
29	C₁₃×#553	C₂²	1	2	yes	—
30	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#548	C₂²	1	2	yes	—
33	C₁₃×#547	—	2	2	no	—
34	C₁₃×#547	C₂²	1	1	yes	characteristic
35	C₁₃×#547	C₂²	1	2	yes	—
36	C₁₃×#544	—	2	1	no	—
37	C₁₃×#544	C₂²	1	2	yes	—
38	C₁₃×#542	—	2	1	no	—
39	C₁₃×#541	C₂²	1	2	yes	—
40	C₁₃×#540	C₂²	1	2	yes	—
41	C₁₃×#539	—	2	2	no	—
42	C₁₃×#539	—	2	2	no	—
43	C₁₃×#539	—	2	1	no	—
44	C₁₃×#537	—	2	1	no	—
45	C₁₃×#536	C₂²	1	2	yes	—
46	C₁₃×#532	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
48	C₁₃×#529	C₂²	1	1	yes	characteristic
49	C₁₃×#529	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
51	C₁₃×#501	C₂²	1	1	yes	characteristic
52	C₁₃×#499	C₂²	1	2	yes	—
53	C₁₃×#496	C₂²	1	1	yes	characteristic
54	C₁₃×#492	C₂²	1	2	yes	—
55	C₁₃×#491	C₂²	1	2	yes	—
56	C₁₃×#491	C₂²	1	2	yes	—
57	C₁₃×#491	C₂²	1	2	yes	—
58	C₁₃×#491	C₂²	1	2	yes	—
59	C₁₃×#491	C₂²	1	2	yes	—
60	C₁₃×#490	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×#488	C₂²	1	2	yes	—
65	C₁₃×#487	C₂²	1	2	yes	—
66	C₁₃×#487	C₂²	1	2	yes	—
67	C₁₃×#485	C₂²	1	2	yes	—
68	C₁₃×#485	C₂²	1	2	yes	—
69	C₁₃×#484	C₂²	1	2	yes	—
70	C₁₃×#484	C₂²	1	1	yes	characteristic
71	C₁₃×#483	C₂²	1	1	yes	characteristic
72	C₁₃×#483	C₂²	1	2	yes	—
73	C₁₃×#481	C₂²	1	1	yes	characteristic
74	C₁₃×#480	C₂²	1	1	yes	characteristic
75	C₁₃×#479	C₂²	1	2	yes	—
76	C₁₃×#479	C₂²	1	2	yes	—
77	C₁₃×#479	C₂²	1	2	yes	—
78	C₁₃×#478	C₂²	1	2	yes	—
79	C₁₃×#477	C₂²	1	2	yes	—
80	C₁₃×#475	C₂²	1	2	yes	—
81	C₁₃×#468	C₂²	1	2	yes	—
82	C₁₃×#468	C₂²	1	2	yes	—
83	C₁₃×#466	C₂²	1	2	yes	—
84	C₁₃×#465	C₂²	1	2	yes	—
85	C₁₃×#465	C₂²	1	2	yes	—
86	C₁₃×#465	C₂²	1	2	yes	—
87	C₁₃×#463	C₂²	1	2	yes	—
88	C₁₃×#463	C₂²	1	2	yes	—
89	C₁₃×#461	C₂²	1	2	yes	—
90	C₁₃×#461	C₂²	1	2	yes	—
91	C₁₃×#461	C₂²	1	2	yes	—
92	C₁₃×#461	C₂²	1	2	yes	—
93	C₁₃×#449	C₂²	1	2	yes	—
94	C₁₃×#449	C₂²	1	2	yes	—
95	C₁₃×#448	C₂²	1	2	yes	—
96	C₁₃×#448	C₂²	1	2	yes	—
97	C₁₃×#448	C₂²	1	2	yes	—
98	C₁₃×#448	C₂²	1	2	yes	—
99	C₁₃×#446	C₂²	1	2	yes	—
100	C₁₃×#442	C₂²	1	2	yes	—
101	C₁₃×#440	C₂²	1	2	yes	—
102	C₁₃×#440	C₂²	1	2	yes	—
103	C₁₃×#440	C₂²	1	2	yes	—
104	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
105	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
106	C₁₃×#435	C₂²	1	2	yes	—
107	C₁₃×#435	C₂²	1	2	yes	—
108	C₈×D₄×C₁₃	C₂²	1	2	yes	—
109	C₁₃×#433	C₂²	1	2	yes	—
110	C₁₃×#431	C₂²	1	1	yes	characteristic
111	C₁₃×#419	C₂²	1	2	yes	—
112	C₁₃×#417	C₂²	1	2	yes	—
113	C₁₃×#416	C₂²	1	2	yes	—
114	C₂×C₁₃×#103	C₂²	1	2	yes	—
115	C₂×C₁₃×#103	C₂²	1	2	yes	—
116	C₂×C₁₃×#103	C₂²	1	2	yes	—
117	C₁₃×#405	C₂²	1	2	yes	—
118	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	—	2	2	no	—
120	C₂×C₁₃×#41	—	2	1	no	—
121	C₂×C₁₃×#41	C₂³	1	2	yes	—
122	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
123	C₂²×Q₈×C₁₃	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	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×D₈	C₂³	1	2	yes	—
130	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
131	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
132	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
133	C₁₃×C₄⋊Q₈	—	2	1	no	—
134	C₁₃×C₄⋊Q₈	—	2	2	no	—
135	C₁₃×C₄⋊Q₈	—	2	2	no	—
136	C₁₃×C₄⋊Q₈	—	2	1	no	—
137	C₁₃×C₄⋊Q₈	—	2	1	no	—
138	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
143	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₁₃×#127	C₂³	1	1	yes	characteristic
145	C₁₃×#126	—	2	2	no	—
146	C₁₃×#126	—	2	2	no	—
147	C₁₃×#126	—	2	2	no	—
148	C₁₃×#126	—	2	2	no	—
149	C₁₃×#126	—	2	2	no	—
150	C₁₃×#126	—	2	1	no	—
151	C₁₃×#126	D₄	1	2	yes	—
152	C₁₃×#125	—	2	2	no	—
153	C₁₃×#125	—	2	2	no	—
154	C₁₃×#125	—	2	2	no	—
155	C₁₃×#125	—	2	2	no	—
156	C₁₃×#125	—	2	1	no	—
157	C₁₃×#125	—	2	1	no	—
158	C₁₃×#125	—	2	1	no	—
159	C₁₃×#125	D₄	1	1	yes	characteristic
160	C₁₃×#125	C₂³	1	2	yes	—
161	C₁₃×#125	C₂³	1	2	yes	—
162	C₁₃×#125	C₂³	1	2	yes	—
163	C₁₃×#125	C₂³	1	1	yes	characteristic
164	C₁₃×#124	—	2	2	no	—
165	C₁₃×#124	—	2	1	no	—
166	C₁₃×#124	D₄	1	1	yes	characteristic
167	C₁₃×#124	C₂³	1	2	yes	—
168	C₁₃×#124	C₂³	1	1	yes	characteristic
169	C₁₃×#123	—	2	1	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×#123	D₄	1	2	yes	—
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	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	—	2	2	no	—
188	C₁₃×C₂²⋊Q₈	—	2	2	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	2	no	—
191	C₁₃×C₂²⋊Q₈	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
195	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₃×#121	—	2	2	no	—
198	C₁₃×#121	—	2	2	no	—
199	C₁₃×#121	—	2	2	no	—
200	C₁₃×#121	—	2	1	no	—
201	C₁₃×#121	—	2	1	no	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	D₄	1	1	yes	characteristic
205	C₁₃×#121	C₂³	1	2	yes	—
206	C₁₃×#121	C₂³	1	2	yes	—
207	C₁₃×#121	C₂³	1	2	yes	—
208	C₁₃×#121	C₂³	1	1	yes	characteristic
209	C₄×Q₈×C₁₃	—	2	1	no	—
210	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₁₃	—	2	2	no	—
215	C₄×D₄×C₁₃	—	2	1	no	—
216	C₄×D₄×C₁₃	—	2	1	no	—
217	C₄×D₄×C₁₃	—	2	2	no	—
218	C₄×D₄×C₁₃	—	2	2	no	—
219	C₄×D₄×C₁₃	—	2	2	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	1	yes	characteristic
225	C₄×D₄×C₁₃	C₂³	1	2	yes	—
226	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
227	C₁₃×#117	—	2	1	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	1	no	—
233	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
234	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
235	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
236	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
237	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
240	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
241	C₁₃×#107	C₂³	1	2	yes	—
242	C₁₃×#107	C₂³	1	2	yes	—
243	C₁₃×#107	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×C₄⋊C₈	C₂³	1	2	yes	—
248	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₁₃×#103	C₂³	1	2	yes	—
251	C₁₃×#103	C₂³	1	2	yes	—
252	C₁₃×#103	C₂³	1	2	yes	—
253	C₁₃×#103	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×#103	C₂³	1	2	yes	—
262	C₁₃×#103	C₂³	1	2	yes	—
263	C₁₃×#103	C₂³	1	2	yes	—
264	C₁₃×#103	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	1	yes	characteristic
272	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₁₃×C₂²⋊C₈	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	#62597	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₁₃×#41	—	4	2	no	—
282	C₁₃×#41	—	4	2	no	—
283	C₁₃×#41	—	8	2	no	—
284	C₁₃×#41	—	8	4	no	—
285	C₂×Q₈×C₁₃	—	2	2	no	—
286	C₂×Q₈×C₁₃	—	2	2	no	—
287	C₂×Q₈×C₁₃	—	2	2	no	—
288	C₂×Q₈×C₁₃	—	2	1	no	—
289	C₂×Q₈×C₁₃	—	4	2	no	—
290	C₂×Q₈×C₁₃	—	4	2	no	—
291	C₂×Q₈×C₁₃	—	4	2	no	—
292	C₂×Q₈×C₁₃	—	4	2	no	—
293	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
294	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
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	2	no	—
300	C₂×D₄×C₁₃	—	2	2	no	—
301	C₂×D₄×C₁₃	—	2	2	no	—
302	C₂×D₄×C₁₃	—	2	1	no	—
303	C₂×D₄×C₁₃	—	2	1	no	—
304	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
305	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
307	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₁₃	—	2	1	no	—
309	C₂²×C₄×C₁₃	—	2	1	no	—
310	C₂²×C₄×C₁₃	—	2	2	no	—
311	C₂²×C₄×C₁₃	—	2	2	no	—
312	C₂²×C₄×C₁₃	—	2	2	no	—
313	C₂²×C₄×C₁₃	—	2	1	no	—
314	C₂²×C₄×C₁₃	—	2	2	no	—
315	C₂²×C₄×C₁₃	—	2	2	no	—
316	C₂²×C₄×C₁₃	—	2	2	no	—
317	C₂²×C₄×C₁₃	—	2	2	no	—
318	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
322	C₁₃×SD₁₆	—	4	2	no	—
323	C₁₃×SD₁₆	—	4	2	no	—
324	C₁₃×SD₁₆	—	4	2	no	—
325	C₁₃×SD₁₆	—	4	2	no	—
326	C₁₃×SD₁₆	—	4	2	no	—
327	C₁₃×D₈	—	4	2	no	—
328	C₁₃×M₁₆	—	4	2	no	—
329	C₂×C₈×C₁₃	—	4	2	no	—
330	C₂×C₈×C₁₃	—	4	2	no	—
331	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
332	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
333	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
334	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
335	C₁₃×C₄⋊C₄	—	2	2	no	—
336	C₁₃×C₄⋊C₄	—	2	1	no	—
337	C₁₃×C₄⋊C₄	—	2	1	no	—
338	C₁₃×C₄⋊C₄	—	2	2	no	—
339	C₁₃×C₄⋊C₄	—	2	2	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	1	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	1	no	—
348	C₁₃×C₄⋊C₄	—	2	1	no	—
349	C₁₃×C₄⋊C₄	—	2	2	no	—
350	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
355	C₁₃×C₄⋊C₄	—	2	2	no	—
356	C₁₃×C₄⋊C₄	—	2	2	no	—
357	C₁₃×C₄⋊C₄	—	2	1	no	—
358	C₁₃×C₄⋊C₄	—	2	2	no	—
359	C₁₃×C₄⋊C₄	—	2	2	no	—
360	C₁₃×C₄⋊C₄	—	2	2	no	—
361	C₁₃×C₄⋊C₄	—	2	1	no	—
362	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
363	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
364	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
365	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
366	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
367	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
368	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
369	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
370	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
371	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
372	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	1	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	1	no	—
379	C₁₃×C₂²⋊C₄	—	2	1	no	—
380	C₁₃×C₂²⋊C₄	—	2	2	no	—
381	C₁₃×C₂²⋊C₄	—	2	2	no	—
382	C₁₃×C₂²⋊C₄	—	2	2	no	—
383	C₁₃×C₂²⋊C₄	—	2	1	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	1	no	—
389	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
390	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
391	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
392	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
393	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
394	C₄²×C₁₃	—	2	1	no	—
395	C₄²×C₁₃	—	2	2	no	—
396	C₄²×C₁₃	—	2	2	no	—
397	C₄²×C₁₃	—	2	2	no	—
398	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
401	C₄²×C₁₃	C₂⁴	1	2	yes	—
402	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
403	#3559	C₂×C₁₃	1	1	yes	characteristic, complemented
404	#3552	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#3376	C₂×C₁₃	1	2	yes	complemented
406	#3372	C₂×C₁₃	1	2	yes	complemented
407	#3320	C₂×C₁₃	1	2	yes	complemented
408	#3320	C₂×C₁₃	1	2	yes	complemented
409	#3308	C₂×C₁₃	1	2	yes	complemented
410	#3307	C₂×C₁₃	1	2	yes	complemented
411	#3301	C₂×C₁₃	1	2	yes	complemented
412	#3298	C₂×C₁₃	1	2	yes	complemented
413	#3242	C₂×C₁₃	1	2	yes	complemented
414	#3232	C₂×C₁₃	1	1	yes	characteristic, complemented
415	#3221	C₂×C₁₃	1	2	yes	complemented
416	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
417	#3180	C₂×C₁₃	1	1	yes	characteristic, complemented
418	#3174	C₂×C₁₃	1	2	yes	complemented
419	#3137	C₂×C₁₃	1	2	yes	complemented
420	C₂×#491	C₂×C₁₃	1	1	yes	characteristic, complemented
421	#2968	C₂×C₁₃	1	1	yes	characteristic, complemented
422	C₂³×C₁₃	—	2	1	no	—
423	C₂³×C₁₃	—	2	2	no	—
424	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
425	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
426	Q₈×C₁₃	—	2	2	no	—
427	Q₈×C₁₃	—	2	2	no	—
428	Q₈×C₁₃	—	2	2	no	—
429	Q₈×C₁₃	—	2	2	no	—
430	Q₈×C₁₃	—	2	2	no	—
431	Q₈×C₁₃	—	4	1	no	—
432	Q₈×C₁₃	—	8	2	no	—
433	Q₈×C₁₃	—	8	2	no	—
434	Q₈×C₁₃	—	8	1	no	—
435	Q₈×C₁₃	—	8	2	no	—
436	D₄×C₁₃	—	2	4	no	—
437	D₄×C₁₃	—	2	2	no	—
438	D₄×C₁₃	—	2	2	no	—
439	D₄×C₁₃	—	2	2	no	—
440	D₄×C₁₃	—	4	1	no	—
441	D₄×C₁₃	—	4	2	no	—
442	D₄×C₁₃	—	4	4	no	—
443	D₄×C₁₃	—	8	1	no	—
444	D₄×C₁₃	—	8	1	no	—
445	D₄×C₁₃	—	8	2	no	—
446	D₄×C₁₃	—	8	2	no	—
447	D₄×C₁₃	—	8	2	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	2	2	no	—
450	C₂×C₄×C₁₃	—	2	2	no	—
451	C₂×C₄×C₁₃	—	2	2	no	—
452	C₂×C₄×C₁₃	—	2	1	no	—
453	C₂×C₄×C₁₃	—	2	1	no	—
454	C₂×C₄×C₁₃	—	2	2	no	—
455	C₂×C₄×C₁₃	—	2	1	no	—
456	C₂×C₄×C₁₃	—	2	2	no	—
457	C₂×C₄×C₁₃	—	2	2	no	—
458	C₂×C₄×C₁₃	—	2	2	no	—
459	C₂×C₄×C₁₃	—	2	2	no	—
460	C₂×C₄×C₁₃	—	4	1	no	—
461	C₂×C₄×C₁₃	—	4	2	no	—
462	C₂×C₄×C₁₃	—	4	2	no	—
463	C₂×C₄×C₁₃	—	8	2	no	—
464	C₂×C₄×C₁₃	—	8	2	no	—
465	C₂×C₄×C₁₃	—	8	2	no	—
466	C₂×C₄×C₁₃	—	8	2	no	—
467	C₂×C₄×C₁₃	—	8	1	no	—
468	C₂×C₄×C₁₃	—	8	2	no	—
469	C₂×C₄×C₁₃	—	8	2	no	—
470	C₂×C₄×C₁₃	—	8	2	no	—
471	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
480	C₈×C₁₃	—	2	2	no	—
481	C₈×C₁₃	—	2	2	no	—
482	C₈×C₁₃	—	2	2	no	—
483	C₈×C₁₃	—	2	2	no	—
484	#563	—	2	2	no	—
485	#563	—	2	1	no	—
486	#562	—	2	1	no	—
487	#557	C₂²×C₁₃	1	1	yes	characteristic
488	#556	C₂²×C₁₃	1	1	yes	characteristic
489	#554	—	2	1	no	—
490	#554	C₂²×C₁₃	1	2	yes	—
491	#553	—	2	1	no	—
492	#553	C₂²×C₁₃	1	2	yes	—
493	#553	C₂²×C₁₃	1	2	yes	—
494	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
495	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
496	#548	C₂²×C₁₃	1	2	yes	—
497	#547	—	2	2	no	—
498	#547	C₂²×C₁₃	1	1	yes	characteristic
499	#547	C₂²×C₁₃	1	2	yes	—
500	#544	—	2	1	no	—
501	#544	C₂²×C₁₃	1	2	yes	—
502	#542	—	2	1	no	—
503	#541	C₂²×C₁₃	1	2	yes	—
504	#540	C₂²×C₁₃	1	2	yes	—
505	#539	—	2	2	no	—
506	#539	—	2	2	no	—
507	#539	—	2	1	no	—
508	#537	—	2	1	no	—
509	#536	C₂²×C₁₃	1	2	yes	—
510	#532	C₂²×C₁₃	1	1	yes	characteristic
511	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
512	#529	C₂²×C₁₃	1	1	yes	characteristic
513	#529	C₂²×C₁₃	1	1	yes	characteristic
514	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
515	#501	C₂²×C₁₃	1	1	yes	characteristic
516	#499	C₂²×C₁₃	1	2	yes	—
517	#496	C₂²×C₁₃	1	1	yes	characteristic
518	#492	C₂²×C₁₃	1	2	yes	—
519	#491	C₂²×C₁₃	1	2	yes	—
520	#491	C₂²×C₁₃	1	2	yes	—
521	#491	C₂²×C₁₃	1	2	yes	—
522	#491	C₂²×C₁₃	1	2	yes	—
523	#491	C₂²×C₁₃	1	2	yes	—
524	#490	C₂²×C₁₃	1	1	yes	characteristic
525	#489	C₂²×C₁₃	1	2	yes	—
526	#489	C₂²×C₁₃	1	1	yes	characteristic
527	#488	C₂²×C₁₃	1	2	yes	—
528	#488	C₂²×C₁₃	1	2	yes	—
529	#487	C₂²×C₁₃	1	2	yes	—
530	#487	C₂²×C₁₃	1	2	yes	—
531	#485	C₂²×C₁₃	1	2	yes	—
532	#485	C₂²×C₁₃	1	2	yes	—
533	#484	C₂²×C₁₃	1	1	yes	characteristic
534	#484	C₂²×C₁₃	1	2	yes	—
535	#483	C₂²×C₁₃	1	1	yes	characteristic
536	#483	C₂²×C₁₃	1	2	yes	—
537	#481	C₂²×C₁₃	1	1	yes	characteristic
538	#480	C₂²×C₁₃	1	1	yes	characteristic
539	#479	C₂²×C₁₃	1	2	yes	—
540	#479	C₂²×C₁₃	1	2	yes	—
541	#479	C₂²×C₁₃	1	2	yes	—
542	#478	C₂²×C₁₃	1	2	yes	—
543	#477	C₂²×C₁₃	1	2	yes	—
544	#475	C₂²×C₁₃	1	2	yes	—
545	#468	C₂²×C₁₃	1	2	yes	—
546	#468	C₂²×C₁₃	1	2	yes	—
547	#466	C₂²×C₁₃	1	2	yes	—
548	#465	C₂²×C₁₃	1	2	yes	—
549	#465	C₂²×C₁₃	1	2	yes	—
550	#465	C₂²×C₁₃	1	2	yes	—
551	#463	C₂²×C₁₃	1	2	yes	—
552	#463	C₂²×C₁₃	1	2	yes	—
553	#461	C₂²×C₁₃	1	2	yes	—
554	#461	C₂²×C₁₃	1	2	yes	—
555	#461	C₂²×C₁₃	1	2	yes	—
556	#461	C₂²×C₁₃	1	2	yes	—
557	#449	C₂²×C₁₃	1	2	yes	—
558	#449	C₂²×C₁₃	1	2	yes	—
559	#448	C₂²×C₁₃	1	2	yes	—
560	#448	C₂²×C₁₃	1	2	yes	—
561	#448	C₂²×C₁₃	1	2	yes	—
562	#448	C₂²×C₁₃	1	2	yes	—
563	#446	C₂²×C₁₃	1	2	yes	—
564	#442	C₂²×C₁₃	1	2	yes	—
565	#440	C₂²×C₁₃	1	2	yes	—
566	#440	C₂²×C₁₃	1	2	yes	—
567	#440	C₂²×C₁₃	1	2	yes	—
568	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
569	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
570	#435	C₂²×C₁₃	1	2	yes	—
571	#435	C₂²×C₁₃	1	2	yes	—
572	C₈×D₄	C₂²×C₁₃	1	2	yes	—
573	#433	C₂²×C₁₃	1	2	yes	—
574	#431	C₂²×C₁₃	1	1	yes	characteristic
575	#419	C₂²×C₁₃	1	2	yes	—
576	#417	C₂²×C₁₃	1	2	yes	—
577	#416	C₂²×C₁₃	1	2	yes	—
578	C₂×#103	C₂²×C₁₃	1	2	yes	—
579	C₂×#103	C₂²×C₁₃	1	2	yes	—
580	C₂×#103	C₂²×C₁₃	1	2	yes	—
581	#405	C₂²×C₁₃	1	2	yes	—
582	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
583	C₂²×C₁₃	—	2	1	no	—
584	C₂²×C₁₃	—	2	1	no	—
585	C₂²×C₁₃	—	2	2	no	—
586	C₂²×C₁₃	—	2	2	no	—
587	C₂²×C₁₃	—	2	2	no	—
588	C₂²×C₁₃	—	4	1	no	—
589	C₂²×C₁₃	—	4	2	no	—
590	C₂²×C₁₃	—	4	1	no	—
591	C₂²×C₁₃	—	4	2	no	—
592	C₂²×C₁₃	—	4	2	no	—
593	C₂²×C₁₃	—	4	1	no	—
594	C₂²×C₁₃	#577	1	2	yes	—
595	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
596	C₄×C₁₃	—	2	1	no	—
597	C₄×C₁₃	—	2	1	no	—
598	C₄×C₁₃	—	2	2	no	—
599	C₄×C₁₃	—	2	2	no	—
600	C₄×C₁₃	—	2	1	no	—
601	C₄×C₁₃	—	2	1	no	—
602	C₄×C₁₃	—	2	1	no	—
603	C₄×C₁₃	—	2	2	no	—
604	C₄×C₁₃	—	4	1	no	—
605	C₄×C₁₃	—	4	2	no	—
606	C₄×C₁₃	—	4	2	no	—
607	C₄×C₁₃	—	4	1	no	—
608	C₄×C₁₃	—	4	2	no	—
609	C₄×C₁₃	—	4	2	no	—
610	C₄×C₁₃	—	4	2	no	—
611	C₄×C₁₃	—	4	1	no	—
612	C₄×C₁₃	#585	1	2	yes	—
613	C₂×#41	—	2	2	no	—
614	C₂×#41	—	2	1	no	—
615	C₂×#41	C₂³×C₁₃	1	2	yes	—
616	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
617	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
618	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
619	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
620	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
621	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
622	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
623	C₂×D₈	C₂³×C₁₃	1	2	yes	—
624	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
625	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
626	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
627	C₄⋊Q₈	—	2	1	no	—
628	C₄⋊Q₈	—	2	2	no	—
629	C₄⋊Q₈	—	2	2	no	—
630	C₄⋊Q₈	—	2	1	no	—
631	C₄⋊Q₈	—	2	1	no	—
632	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
633	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
634	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
635	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
636	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
637	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
638	#127	C₂³×C₁₃	1	1	yes	characteristic
639	#126	—	2	2	no	—
640	#126	—	2	2	no	—
641	#126	—	2	2	no	—
642	#126	—	2	2	no	—
643	#126	—	2	2	no	—
644	#126	—	2	1	no	—
645	#126	D₄×C₁₃	1	2	yes	—
646	#125	—	2	2	no	—
647	#125	—	2	2	no	—
648	#125	—	2	2	no	—
649	#125	—	2	2	no	—
650	#125	—	2	1	no	—
651	#125	—	2	1	no	—
652	#125	—	2	1	no	—
653	#125	D₄×C₁₃	1	1	yes	characteristic
654	#125	C₂³×C₁₃	1	2	yes	—
655	#125	C₂³×C₁₃	1	2	yes	—
656	#125	C₂³×C₁₃	1	1	yes	characteristic
657	#125	C₂³×C₁₃	1	2	yes	—
658	#124	—	2	2	no	—
659	#124	—	2	1	no	—
660	#124	D₄×C₁₃	1	1	yes	characteristic
661	#124	C₂³×C₁₃	1	1	yes	characteristic
662	#124	C₂³×C₁₃	1	2	yes	—
663	#123	—	2	1	no	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	#123	—	2	2	no	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	D₄×C₁₃	1	2	yes	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	1	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
688	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
689	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
690	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
691	#121	—	2	2	no	—
692	#121	—	2	2	no	—
693	#121	—	2	2	no	—
694	#121	—	2	1	no	—
695	#121	—	2	1	no	—
696	#121	—	2	2	no	—
697	#121	—	2	2	no	—
698	#121	D₄×C₁₃	1	1	yes	characteristic
699	#121	C₂³×C₁₃	1	1	yes	characteristic
700	#121	C₂³×C₁₃	1	2	yes	—
701	#121	C₂³×C₁₃	1	2	yes	—
702	#121	C₂³×C₁₃	1	2	yes	—
703	C₄×Q₈	—	2	1	no	—
704	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
705	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
706	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
707	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
708	C₄×D₄	—	2	2	no	—
709	C₄×D₄	—	2	1	no	—
710	C₄×D₄	—	2	1	no	—
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	2	no	—
713	C₄×D₄	—	2	2	no	—
714	C₄×D₄	—	2	1	no	—
715	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
716	C₄×D₄	C₂³×C₁₃	1	2	yes	—
717	C₄×D₄	C₂³×C₁₃	1	2	yes	—
718	C₄×D₄	C₂³×C₁₃	1	2	yes	—
719	C₄×D₄	C₂³×C₁₃	1	2	yes	—
720	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
721	#117	—	2	1	no	—
722	#117	—	2	1	no	—
723	#117	C₂³×C₁₃	1	2	yes	—
724	#117	C₂³×C₁₃	1	2	yes	—
725	C₂×C₄⋊C₄	—	2	1	no	—
726	C₂×C₄⋊C₄	—	2	1	no	—
727	C₂×C₄⋊C₄	—	2	1	no	—
728	C₂×C₄⋊C₄	—	2	1	no	—
729	C₂×C₄⋊C₄	—	2	2	no	—
730	C₂×C₄⋊C₄	—	2	1	no	—
731	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
734	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
735	#107	C₂³×C₁₃	1	2	yes	—
736	#107	C₂³×C₁₃	1	2	yes	—
737	#107	C₂³×C₁₃	1	2	yes	—
738	#106	C₂³×C₁₃	1	2	yes	—
739	#106	C₂³×C₁₃	1	2	yes	—
740	#106	C₂³×C₁₃	1	2	yes	—
741	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
742	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
743	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
744	#103	C₂³×C₁₃	1	2	yes	—
745	#103	C₂³×C₁₃	1	2	yes	—
746	#103	C₂³×C₁₃	1	2	yes	—
747	#103	C₂³×C₁₃	1	2	yes	—
748	#103	C₂³×C₁₃	1	2	yes	—
749	#103	C₂³×C₁₃	1	2	yes	—
750	#103	C₂³×C₁₃	1	2	yes	—
751	#103	C₂³×C₁₃	1	2	yes	—
752	#103	C₂³×C₁₃	1	2	yes	—
753	#103	C₂³×C₁₃	1	2	yes	—
754	#103	C₂³×C₁₃	1	2	yes	—
755	#103	C₂³×C₁₃	1	2	yes	—
756	#103	C₂³×C₁₃	1	2	yes	—
757	#103	C₂³×C₁₃	1	2	yes	—
758	#103	C₂³×C₁₃	1	2	yes	—
759	#102	C₂³×C₁₃	1	2	yes	—
760	#102	C₂³×C₁₃	1	2	yes	—
761	#102	C₂³×C₁₃	1	2	yes	—
762	#102	C₂³×C₁₃	1	2	yes	—
763	#102	C₂³×C₁₃	1	2	yes	—
764	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
765	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
766	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
767	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
768	#97	C₂³×C₁₃	1	1	yes	characteristic
769	#97	C₂³×C₁₃	1	1	yes	characteristic
770	#97	C₂³×C₁₃	1	2	yes	—
771	#97	C₂³×C₁₃	1	2	yes	—
772	C₄×C₈	C₂³×C₁₃	1	2	yes	—
773	C₄×C₈	C₂³×C₁₃	1	2	yes	—
774	C₂×C₁₃	—	2	2	no	—
775	C₂×C₁₃	—	4	2	no	—
776	C₂×C₁₃	—	8	1	no	—
777	C₂×C₁₃	—	8	2	no	—
778	C₂×C₁₃	#3500	1	1	yes	characteristic
779	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
780	C₂×C₁₃	#3586	1	1	yes	characteristic
781	#41	—	4	2	no	—
782	#41	—	4	2	no	—
783	#41	—	8	2	no	—
784	#41	—	8	4	no	—
785	C₂×Q₈	—	2	2	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	4	2	no	—
790	C₂×Q₈	—	4	2	no	—
791	C₂×Q₈	—	4	2	no	—
792	C₂×Q₈	—	4	2	no	—
793	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
794	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
795	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
796	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	2	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
805	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
806	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
807	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
819	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
822	SD₁₆	—	4	2	no	—
823	SD₁₆	—	4	2	no	—
824	SD₁₆	—	4	2	no	—
825	SD₁₆	—	4	2	no	—
826	SD₁₆	—	4	2	no	—
827	D₈	—	4	2	no	—
828	M₁₆	—	4	2	no	—
829	C₂×C₈	—	4	2	no	—
830	C₂×C₈	—	4	2	no	—
831	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
832	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
833	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
834	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	1	no	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
863	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
864	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
865	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
866	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
869	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
870	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
871	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
872	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	1	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	1	no	—
879	C₂²⋊C₄	—	2	1	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	1	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	1	no	—
889	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
890	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
891	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
892	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
893	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
894	C₄²	—	2	1	no	—
895	C₄²	—	2	2	no	—
896	C₄²	—	2	2	no	—
897	C₄²	—	2	2	no	—
898	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
899	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
900	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
901	C₄²	C₂⁴×C₁₃	1	2	yes	—
902	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
903	C₁₃	#62597	1	1	yes	characteristic, direct product factor, Sylow
904	C₂³	—	2	1	no	—
905	C₂³	—	2	2	no	—
906	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
907	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
908	Q₈	—	2	2	no	—
909	Q₈	—	2	2	no	—
910	Q₈	—	2	2	no	—
911	Q₈	—	2	2	no	—
912	Q₈	—	2	2	no	—
913	Q₈	—	4	1	no	—
914	Q₈	—	8	2	no	—
915	Q₈	—	8	2	no	—
916	Q₈	—	8	1	no	—
917	Q₈	—	8	2	no	—
918	D₄	—	2	4	no	—
919	D₄	—	2	2	no	—
920	D₄	—	2	2	no	—
921	D₄	—	2	2	no	—
922	D₄	—	4	1	no	—
923	D₄	—	4	2	no	—
924	D₄	—	4	4	no	—
925	D₄	—	8	1	no	—
926	D₄	—	8	1	no	—
927	D₄	—	8	2	no	—
928	D₄	—	8	2	no	—
929	D₄	—	8	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	4	1	no	—
943	C₂×C₄	—	4	2	no	—
944	C₂×C₄	—	4	2	no	—
945	C₂×C₄	—	8	2	no	—
946	C₂×C₄	—	8	2	no	—
947	C₂×C₄	—	8	2	no	—
948	C₂×C₄	—	8	2	no	—
949	C₂×C₄	—	8	1	no	—
950	C₂×C₄	—	8	2	no	—
951	C₂×C₄	—	8	2	no	—
952	C₂×C₄	—	8	2	no	—
953	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
954	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
955	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
956	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
958	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
961	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
962	C₈	—	2	2	no	—
963	C₈	—	2	2	no	—
964	C₈	—	2	2	no	—
965	C₈	—	2	2	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	1	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	2	no	—
977	C₂²	C₁₃×#577	1	2	yes	—
978	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
979	C₄	—	2	1	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	2	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	2	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	1	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	2	no	—
995	C₄	C₁₃×#585	1	2	yes	—
996	C₂	—	2	2	no	—
997	C₂	—	4	2	no	—
998	C₂	—	8	2	no	—
999	C₂	—	8	1	no	—
1000	C₂	C₁₃×#3500	1	1	yes	characteristic
1001	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1002	C₂	C₁₃×#3586	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3559	C₂	semidirect
2. C₁₃×#3552	C₂	semidirect
3. C₁₃×#3376	C₂	semidirect
4. C₁₃×#3372	C₂	semidirect
5. C₁₃×#3320	C₂	semidirect
6. C₁₃×#3320	C₂	semidirect
7. C₁₃×#3308	C₂	semidirect
8. C₁₃×#3307	C₂	semidirect
9. C₁₃×#3301	C₂	semidirect
10. C₁₃×#3298	C₂	semidirect
11. C₁₃×#3242	C₂	semidirect
12. C₁₃×#3232	C₂	semidirect
13. C₁₃×#3221	C₂	semidirect
14. C₁₃×#3206	C₂	semidirect
15. C₁₃×#3180	C₂	semidirect
16. C₁₃×#3174	C₂	semidirect
17. C₁₃×#3137	C₂	semidirect
18. C₂×C₁₃×#491	C₂	semidirect
19. C₁₃×#2968	C₂	semidirect
280. #62597	C₁₃	direct (N × H)
403. #3559	C₂×C₁₃	semidirect
404. #3552	C₂×C₁₃	semidirect
405. #3376	C₂×C₁₃	semidirect
406. #3372	C₂×C₁₃	semidirect
407. #3320	C₂×C₁₃	semidirect
408. #3320	C₂×C₁₃	semidirect
409. #3308	C₂×C₁₃	semidirect
410. #3307	C₂×C₁₃	semidirect
411. #3301	C₂×C₁₃	semidirect
412. #3298	C₂×C₁₃	semidirect
413. #3242	C₂×C₁₃	semidirect
414. #3232	C₂×C₁₃	semidirect
415. #3221	C₂×C₁₃	semidirect
416. #3206	C₂×C₁₃	semidirect
417. #3180	C₂×C₁₃	semidirect
418. #3174	C₂×C₁₃	semidirect
419. #3137	C₂×C₁₃	semidirect
420. C₂×#491	C₂×C₁₃	semidirect
421. #2968	C₂×C₁₃	semidirect
903. C₁₃	#62597	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×#3559	2
C₁₃×#3552	2
C₁₃×#3376	2
C₁₃×#3372	2
C₁₃×#3320	2
C₁₃×#3308	2
C₁₃×#3307	2
C₁₃×#3301	2
C₁₃×#3298	2
C₁₃×#3242	2
C₁₃×#3232	2
C₁₃×#3221	2
C₁₃×#3206	2
C₁₃×#3180	2
C₁₃×#3174	2
C₁₃×#3137	2
C₂×C₁₃×#491	2
C₁₃×#2968	2
#62597	13

Subgroups — C13×#62597 #15748936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62597 #15748936