Subgroups — C₁₃×#60955 #15747294

Order 3328.

1804 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3460	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3262	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3259	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3257	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3241	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3224	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3220	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3203	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3199	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3198	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3171	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3106	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3105	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3102	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3100	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#544	C₂²	1	2	yes	complemented
21	C₁₃×#542	—	2	2	no	—
22	C₁₃×#542	C₂²	1	2	yes	—
23	C₁₃×#542	C₂²	1	2	yes	complemented
24	C₁₃×#540	—	2	2	no	—
25	C₁₃×#540	C₂²	1	2	yes	—
26	C₁₃×#540	C₂²	1	2	yes	complemented
27	C₁₃×#538	—	2	2	no	—
28	C₁₃×#538	—	2	2	no	—
29	C₁₃×#537	C₂²	1	2	yes	—
30	C₁₃×#535	C₂²	1	2	yes	—
31	C₁₃×#535	C₂²	1	2	yes	complemented
32	C₁₃×#532	—	2	2	no	—
33	C₁₃×#532	C₂²	1	2	yes	—
34	C₁₃×#532	C₂²	1	2	yes	complemented
35	C₁₃×#529	—	2	2	no	—
36	C₁₃×#529	C₂²	1	2	yes	—
37	C₁₃×#529	C₂²	1	2	yes	complemented
38	C₁₃×#525	—	2	2	no	—
39	C₁₃×#525	—	2	2	no	—
40	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
41	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
43	C₁₃×#501	C₂²	1	2	yes	complemented
44	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#499	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#496	C₂²	1	2	yes	—
47	C₁₃×#495	C₂²	1	1	yes	characteristic
48	C₁₃×#493	C₂²	1	1	yes	characteristic
49	C₁₃×#490	C₂²	1	2	yes	complemented
50	C₁₃×#489	C₂²	1	2	yes	complemented
51	C₁₃×#488	C₂²	1	2	yes	complemented
52	C₁₃×#486	C₂²	1	2	yes	complemented
53	C₁₃×#485	C₂²	1	2	yes	complemented
54	C₁₃×#484	C₂²	1	2	yes	complemented
55	C₁₃×#482	C₂²	1	2	yes	—
56	C₁₃×#482	C₂²	1	2	yes	—
57	C₁₃×#482	C₂²	1	2	yes	complemented
58	C₁₃×#481	C₂²	1	2	yes	—
59	C₁₃×#480	C₂²	1	2	yes	—
60	C₁₃×#480	C₂²	1	2	yes	complemented
61	C₁₃×#479	C₂²	1	2	yes	complemented
62	C₁₃×#478	C₂²	1	2	yes	complemented
63	C₁₃×#478	C₂²	1	2	yes	complemented
64	C₁₃×#478	C₂²	1	2	yes	complemented
65	C₁₃×#477	C₂²	1	2	yes	complemented
66	C₁₃×#476	C₂²	1	2	yes	complemented
67	C₁₃×#474	C₂²	1	2	yes	complemented
68	C₁₃×#474	C₂²	1	2	yes	complemented
69	C₁₃×#469	C₂²	1	2	yes	—
70	C₁₃×#469	C₂²	1	2	yes	complemented
71	C₁₃×#468	C₂²	1	2	yes	complemented
72	C₁₃×#468	C₂²	1	2	yes	complemented
73	C₁₃×#467	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#466	C₂²	1	1	yes	characteristic
75	C₁₃×#466	C₂²	1	1	yes	characteristic
76	C₁₃×#466	C₂²	1	2	yes	complemented
77	C₁₃×#466	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#465	C₂²	1	2	yes	complemented
79	C₁₃×#464	C₂²	1	2	yes	complemented
80	C₁₃×#463	C₂²	1	2	yes	—
81	C₁₃×#463	C₂²	1	2	yes	—
82	C₁₃×#463	C₂²	1	2	yes	complemented
83	C₁₃×#460	C₂²	1	2	yes	complemented
84	C₁₃×#459	C₂²	1	2	yes	—
85	C₁₃×#459	C₂²	1	2	yes	—
86	C₁₃×#459	C₂²	1	2	yes	complemented
87	C₁₃×#452	C₂²	1	2	yes	complemented
88	C₁₃×#450	C₂²	1	2	yes	complemented
89	C₁₃×#449	C₂²	1	2	yes	—
90	C₁₃×#449	C₂²	1	2	yes	—
91	C₁₃×#449	C₂²	1	2	yes	complemented
92	C₁₃×#447	C₂²	1	2	yes	—
93	C₁₃×#447	C₂²	1	2	yes	—
94	C₁₃×#447	C₂²	1	2	yes	complemented
95	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
97	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
98	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
99	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
100	C₄×C₁₃×D₈	C₂²	1	2	yes	—
101	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
102	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
103	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
104	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
105	C₁₃×#433	C₂²	1	2	yes	complemented
106	C₁₃×#433	C₂²	1	2	yes	complemented
107	C₁₃×#431	C₂²	1	2	yes	complemented
108	C₁₃×#431	C₂²	1	2	yes	complemented
109	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
110	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
111	C₁₃×#408	C₂²	1	1	yes	characteristic
112	C₁₃×#408	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₁₃×#41	—	2	2	no	—
116	C₂×C₁₃×#41	—	2	2	no	—
117	C₂×C₁₃×#41	C₂³	1	2	yes	—
118	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃	—	2	2	no	—
121	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×D₈	C₂³	1	2	yes	—
127	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
128	C₂×C₁₃×D₈	C₂³	1	2	yes	—
129	C₂×C₁₃×D₈	C₂³	1	2	yes	—
130	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
132	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
135	C₁₃×C₄⋊Q₈	—	2	2	no	—
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×#127	—	2	2	no	—
139	C₁₃×#127	C₂³	1	2	yes	—
140	C₁₃×#127	C₂³	1	2	yes	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#126	—	2	2	no	—
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#126	—	2	2	no	—
145	C₁₃×#125	—	2	2	no	—
146	C₁₃×#125	C₂³	1	2	yes	—
147	C₁₃×#125	C₂³	1	2	yes	—
148	C₁₃×#124	—	2	2	no	—
149	C₁₃×#124	—	2	2	no	—
150	C₁₃×#124	—	2	2	no	—
151	C₁₃×#124	—	2	2	no	—
152	C₁₃×#124	—	2	2	no	—
153	C₁₃×#124	C₂³	1	2	yes	—
154	C₁₃×#124	C₂³	1	2	yes	—
155	C₁₃×#123	—	2	2	no	—
156	C₁₃×#123	—	2	2	no	—
157	C₁₃×#123	—	2	2	no	—
158	C₁₃×#123	—	2	2	no	—
159	C₁₃×#123	—	2	2	no	—
160	C₁₃×#123	—	2	2	no	—
161	C₁₃×#123	—	2	2	no	—
162	C₁₃×#123	—	2	2	no	—
163	C₁₃×C₂²⋊Q₈	—	2	2	no	—
164	C₁₃×C₂²⋊Q₈	—	2	2	no	—
165	C₁₃×C₂²⋊Q₈	—	2	2	no	—
166	C₁₃×C₂²⋊Q₈	—	2	2	no	—
167	C₁₃×C₂²⋊Q₈	—	2	2	no	—
168	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
170	C₁₃×#121	—	2	2	no	—
171	C₁₃×#121	—	2	2	no	—
172	C₁₃×#121	—	2	2	no	—
173	C₁₃×#121	—	2	2	no	—
174	C₁₃×#121	—	2	2	no	—
175	C₁₃×#121	—	2	2	no	—
176	C₁₃×#121	—	2	2	no	—
177	C₁₃×#121	—	2	2	no	—
178	C₁₃×#121	—	2	2	no	—
179	C₁₃×#121	—	2	2	no	—
180	C₁₃×#121	—	2	2	no	—
181	C₁₃×#121	C₂³	1	2	yes	—
182	C₁₃×#121	C₂³	1	2	yes	—
183	C₁₃×#121	C₂³	1	2	yes	—
184	C₁₃×#121	C₂³	1	2	yes	—
185	C₁₃×#121	C₂³	1	2	yes	—
186	C₁₃×#121	C₂³	1	2	yes	—
187	C₁₃×#120	—	2	2	no	—
188	C₁₃×#120	—	2	2	no	—
189	C₁₃×#120	—	2	2	no	—
190	C₁₃×#120	—	2	2	no	—
191	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
192	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
193	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
194	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
195	C₄×D₄×C₁₃	—	2	2	no	—
196	C₄×D₄×C₁₃	—	2	2	no	—
197	C₄×D₄×C₁₃	—	2	2	no	—
198	C₄×D₄×C₁₃	—	2	2	no	—
199	C₄×D₄×C₁₃	—	2	2	no	—
200	C₄×D₄×C₁₃	—	2	2	no	—
201	C₄×D₄×C₁₃	—	2	2	no	—
202	C₄×D₄×C₁₃	—	2	2	no	—
203	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
204	C₄×D₄×C₁₃	D₄	1	2	yes	—
205	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
206	C₄×D₄×C₁₃	D₄	1	2	yes	—
207	C₄×D₄×C₁₃	C₂³	1	2	yes	—
208	C₄×D₄×C₁₃	C₂³	1	2	yes	—
209	C₄×D₄×C₁₃	C₂³	1	2	yes	—
210	C₄×D₄×C₁₃	C₂³	1	2	yes	—
211	C₄×D₄×C₁₃	C₂³	1	2	yes	—
212	C₄×D₄×C₁₃	C₂³	1	2	yes	—
213	C₁₃×#117	—	2	2	no	—
214	C₁₃×#117	—	2	2	no	—
215	C₁₃×#117	—	2	2	no	—
216	C₁₃×#117	C₂³	1	2	yes	—
217	C₁₃×#117	C₂³	1	1	yes	characteristic
218	C₁₃×#117	C₂³	1	2	yes	—
219	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
220	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₄²×C₁₃	—	2	2	no	—
222	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
224	C₁₃×#107	C₂³	1	1	yes	characteristic
225	C₁₃×#107	C₂³	1	1	yes	characteristic
226	C₁₃×#107	C₂³	1	2	yes	—
227	C₁₃×#107	C₂³	1	1	yes	characteristic
228	C₁₃×#107	C₂³	1	2	yes	—
229	C₁₃×#107	C₂³	1	2	yes	—
230	C₁₃×#107	C₂³	1	1	yes	characteristic
231	C₁₃×#106	C₂³	1	2	yes	—
232	C₁₃×#106	C₂³	1	2	yes	—
233	C₁₃×#106	C₂³	1	2	yes	—
234	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
235	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
238	C₁₃×#103	C₂³	1	2	yes	—
239	C₁₃×#103	C₂³	1	2	yes	—
240	C₁₃×#103	C₂³	1	2	yes	—
241	C₁₃×#103	C₂³	1	2	yes	—
242	C₁₃×#102	C₂³	1	2	yes	—
243	C₁₃×#102	C₂³	1	2	yes	—
244	C₁₃×#102	C₂³	1	2	yes	—
245	C₁₃×#102	C₂³	1	2	yes	—
246	C₁₃×#102	C₂³	1	2	yes	—
247	C₁₃×#102	C₂³	1	2	yes	—
248	C₁₃×#102	C₂³	1	2	yes	—
249	C₁₃×#102	C₂³	1	2	yes	—
250	C₁₃×#102	C₂³	1	2	yes	—
251	C₁₃×#102	C₂³	1	2	yes	—
252	C₁₃×#102	C₂³	1	2	yes	—
253	C₁₃×#102	C₂³	1	2	yes	—
254	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₁₃×#97	C₂³	1	2	yes	—
259	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
260	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₁₃	C₂³	1	2	yes	—
264	#60955	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂⁴×C₁₃	—	2	2	no	—
266	C₁₃×#41	—	4	1	no	—
267	C₁₃×#41	—	4	1	no	—
268	C₁₃×#41	—	4	2	no	—
269	C₁₃×#41	—	4	2	no	—
270	C₁₃×#41	—	8	4	no	—
271	C₁₃×#41	—	8	4	no	—
272	C₂×Q₈×C₁₃	—	2	2	no	—
273	C₂×Q₈×C₁₃	—	2	2	no	—
274	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
276	C₂×D₄×C₁₃	—	2	2	no	—
277	C₂×D₄×C₁₃	—	2	2	no	—
278	C₂×D₄×C₁₃	—	2	2	no	—
279	C₂×D₄×C₁₃	—	2	2	no	—
280	C₂×D₄×C₁₃	—	2	2	no	—
281	C₂×D₄×C₁₃	—	2	2	no	—
282	C₂×D₄×C₁₃	—	2	2	no	—
283	C₂×D₄×C₁₃	—	2	2	no	—
284	C₂×D₄×C₁₃	—	2	2	no	—
285	C₂×D₄×C₁₃	—	2	2	no	—
286	C₂×D₄×C₁₃	—	2	2	no	—
287	C₂×D₄×C₁₃	—	2	2	no	—
288	C₂×D₄×C₁₃	—	4	2	no	—
289	C₂×D₄×C₁₃	—	4	2	no	—
290	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
291	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
292	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
293	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
294	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₁₃	—	2	2	no	—
296	C₂²×C₄×C₁₃	—	2	2	no	—
297	C₂²×C₄×C₁₃	—	2	2	no	—
298	C₂²×C₄×C₁₃	—	2	2	no	—
299	C₂²×C₄×C₁₃	—	2	2	no	—
300	C₂²×C₄×C₁₃	—	2	2	no	—
301	C₂²×C₄×C₁₃	—	2	2	no	—
302	C₂²×C₄×C₁₃	—	2	2	no	—
303	C₂²×C₄×C₁₃	—	8	4	no	—
304	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
305	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
307	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₁₃×Q₁₆	—	4	1	no	—
311	C₁₃×SD₁₆	—	4	2	no	—
312	C₁₃×SD₁₆	—	4	2	no	—
313	C₁₃×SD₁₆	—	4	2	no	—
314	C₁₃×D₈	—	4	2	no	—
315	C₁₃×D₈	—	4	1	no	—
316	C₁₃×D₈	—	4	1	no	—
317	C₁₃×D₈	—	4	1	no	—
318	C₁₃×D₈	—	4	2	no	—
319	C₁₃×D₈	—	4	2	no	—
320	C₁₃×M₁₆	—	4	1	no	—
321	C₁₃×M₁₆	—	4	1	no	—
322	C₂×C₈×C₁₃	—	4	1	no	—
323	C₂×C₈×C₁₃	—	4	1	no	—
324	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
329	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
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	2	no	—
334	C₁₃×C₄⋊C₄	—	2	2	no	—
335	C₁₃×C₄⋊C₄	—	2	2	no	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
342	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
343	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
344	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
345	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
346	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
347	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
348	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
349	C₁₃×C₂²⋊C₄	—	2	2	no	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	2	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	2	no	—
355	C₁₃×C₂²⋊C₄	—	2	2	no	—
356	C₁₃×C₂²⋊C₄	—	2	2	no	—
357	C₁₃×C₂²⋊C₄	—	2	2	no	—
358	C₁₃×C₂²⋊C₄	—	2	2	no	—
359	C₁₃×C₂²⋊C₄	—	2	2	no	—
360	C₁₃×C₂²⋊C₄	—	2	2	no	—
361	C₁₃×C₂²⋊C₄	—	2	2	no	—
362	C₁₃×C₂²⋊C₄	—	2	2	no	—
363	C₁₃×C₂²⋊C₄	—	2	2	no	—
364	C₁₃×C₂²⋊C₄	—	2	2	no	—
365	C₁₃×C₂²⋊C₄	—	2	2	no	—
366	C₁₃×C₂²⋊C₄	—	2	2	no	—
367	C₁₃×C₂²⋊C₄	—	2	2	no	—
368	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
369	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
370	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
371	C₄²×C₁₃	—	2	2	no	—
372	C₄²×C₁₃	—	2	2	no	—
373	C₄²×C₁₃	—	2	2	no	—
374	C₄²×C₁₃	C₂×D₄	1	2	yes	—
375	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₁₃	C₂×D₄	1	2	yes	—
377	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
379	C₄²×C₁₃	C₂⁴	1	2	yes	—
380	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
381	#3460	C₂×C₁₃	1	2	yes	complemented
382	#3262	C₂×C₁₃	1	1	yes	characteristic, complemented
383	#3259	C₂×C₁₃	1	1	yes	characteristic, complemented
384	#3257	C₂×C₁₃	1	2	yes	complemented
385	#3243	C₂×C₁₃	1	2	yes	complemented
386	#3241	C₂×C₁₃	1	2	yes	complemented
387	#3224	C₂×C₁₃	1	2	yes	complemented
388	#3220	C₂×C₁₃	1	2	yes	complemented
389	#3203	C₂×C₁₃	1	1	yes	characteristic, complemented
390	#3199	C₂×C₁₃	1	1	yes	characteristic, complemented
391	#3198	C₂×C₁₃	1	2	yes	complemented
392	#3171	C₂×C₁₃	1	2	yes	complemented
393	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
394	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
395	#3106	C₂×C₁₃	1	2	yes	complemented
396	#3105	C₂×C₁₃	1	2	yes	complemented
397	#3102	C₂×C₁₃	1	2	yes	complemented
398	#3100	C₂×C₁₃	1	2	yes	complemented
399	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
400	C₂³×C₁₃	—	2	2	no	—
401	C₂³×C₁₃	—	2	2	no	—
402	C₂³×C₁₃	—	2	2	no	—
403	C₂³×C₁₃	—	4	4	no	—
404	C₂³×C₁₃	—	8	2	no	—
405	C₂³×C₁₃	—	8	2	no	—
406	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
407	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	Q₈×C₁₃	—	2	2	no	—
409	Q₈×C₁₃	—	2	2	no	—
410	Q₈×C₁₃	—	4	1	no	—
411	Q₈×C₁₃	—	8	2	no	—
412	Q₈×C₁₃	—	8	2	no	—
413	D₄×C₁₃	—	2	2	no	—
414	D₄×C₁₃	—	2	2	no	—
415	D₄×C₁₃	—	2	2	no	—
416	D₄×C₁₃	—	2	2	no	—
417	D₄×C₁₃	—	2	2	no	—
418	D₄×C₁₃	—	2	2	no	—
419	D₄×C₁₃	—	4	2	no	—
420	D₄×C₁₃	—	4	1	no	—
421	D₄×C₁₃	—	4	4	no	—
422	D₄×C₁₃	—	4	4	no	—
423	D₄×C₁₃	—	8	2	no	—
424	D₄×C₁₃	—	8	2	no	—
425	D₄×C₁₃	—	8	2	no	—
426	D₄×C₁₃	—	8	2	no	—
427	D₄×C₁₃	—	8	2	no	—
428	D₄×C₁₃	—	8	2	no	—
429	D₄×C₁₃	—	8	2	no	—
430	D₄×C₁₃	—	8	2	no	—
431	D₄×C₁₃	—	8	2	no	—
432	D₄×C₁₃	—	8	2	no	—
433	C₂×C₄×C₁₃	—	2	4	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	1	no	—
436	C₂×C₄×C₁₃	—	2	1	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	2	2	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	4	2	no	—
445	C₂×C₄×C₁₃	—	4	1	no	—
446	C₂×C₄×C₁₃	—	4	4	no	—
447	C₂×C₄×C₁₃	—	4	4	no	—
448	C₂×C₄×C₁₃	—	4	4	no	—
449	C₂×C₄×C₁₃	—	4	4	no	—
450	C₂×C₄×C₁₃	—	8	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	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
462	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
463	C₈×C₁₃	—	2	1	no	—
464	C₈×C₁₃	—	2	1	no	—
465	C₈×C₁₃	—	2	1	no	—
466	C₈×C₁₃	—	2	1	no	—
467	C₈×C₁₃	—	2	2	no	—
468	C₈×C₁₃	—	2	2	no	—
469	#544	C₂²×C₁₃	1	2	yes	complemented
470	#542	—	2	2	no	—
471	#542	C₂²×C₁₃	1	2	yes	—
472	#542	C₂²×C₁₃	1	2	yes	complemented
473	#540	—	2	2	no	—
474	#540	C₂²×C₁₃	1	2	yes	—
475	#540	C₂²×C₁₃	1	2	yes	complemented
476	#538	—	2	2	no	—
477	#538	—	2	2	no	—
478	#537	C₂²×C₁₃	1	2	yes	—
479	#535	C₂²×C₁₃	1	2	yes	—
480	#535	C₂²×C₁₃	1	2	yes	complemented
481	#532	—	2	2	no	—
482	#532	C₂²×C₁₃	1	2	yes	—
483	#532	C₂²×C₁₃	1	2	yes	complemented
484	#529	—	2	2	no	—
485	#529	C₂²×C₁₃	1	2	yes	—
486	#529	C₂²×C₁₃	1	2	yes	complemented
487	#525	—	2	2	no	—
488	#525	—	2	2	no	—
489	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
490	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
491	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
492	#501	C₂²×C₁₃	1	2	yes	complemented
493	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
494	#499	C₂²×C₁₃	1	1	yes	characteristic, complemented
495	#496	C₂²×C₁₃	1	2	yes	—
496	#495	C₂²×C₁₃	1	1	yes	characteristic
497	#493	C₂²×C₁₃	1	1	yes	characteristic
498	#490	C₂²×C₁₃	1	2	yes	complemented
499	#489	C₂²×C₁₃	1	2	yes	complemented
500	#488	C₂²×C₁₃	1	2	yes	complemented
501	#486	C₂²×C₁₃	1	2	yes	complemented
502	#485	C₂²×C₁₃	1	2	yes	complemented
503	#484	C₂²×C₁₃	1	2	yes	complemented
504	#482	C₂²×C₁₃	1	2	yes	—
505	#482	C₂²×C₁₃	1	2	yes	—
506	#482	C₂²×C₁₃	1	2	yes	complemented
507	#481	C₂²×C₁₃	1	2	yes	—
508	#480	C₂²×C₁₃	1	2	yes	—
509	#480	C₂²×C₁₃	1	2	yes	complemented
510	#479	C₂²×C₁₃	1	2	yes	complemented
511	#478	C₂²×C₁₃	1	2	yes	complemented
512	#478	C₂²×C₁₃	1	2	yes	complemented
513	#478	C₂²×C₁₃	1	2	yes	complemented
514	#477	C₂²×C₁₃	1	2	yes	complemented
515	#476	C₂²×C₁₃	1	2	yes	complemented
516	#474	C₂²×C₁₃	1	2	yes	complemented
517	#474	C₂²×C₁₃	1	2	yes	complemented
518	#469	C₂²×C₁₃	1	2	yes	—
519	#469	C₂²×C₁₃	1	2	yes	complemented
520	#468	C₂²×C₁₃	1	2	yes	complemented
521	#468	C₂²×C₁₃	1	2	yes	complemented
522	#467	C₂²×C₁₃	1	1	yes	characteristic, complemented
523	#466	C₂²×C₁₃	1	1	yes	characteristic
524	#466	C₂²×C₁₃	1	1	yes	characteristic
525	#466	C₂²×C₁₃	1	2	yes	complemented
526	#466	C₂²×C₁₃	1	1	yes	characteristic, complemented
527	#465	C₂²×C₁₃	1	2	yes	complemented
528	#464	C₂²×C₁₃	1	2	yes	complemented
529	#463	C₂²×C₁₃	1	2	yes	—
530	#463	C₂²×C₁₃	1	2	yes	—
531	#463	C₂²×C₁₃	1	2	yes	complemented
532	#460	C₂²×C₁₃	1	2	yes	complemented
533	#459	C₂²×C₁₃	1	2	yes	—
534	#459	C₂²×C₁₃	1	2	yes	—
535	#459	C₂²×C₁₃	1	2	yes	complemented
536	#452	C₂²×C₁₃	1	2	yes	complemented
537	#450	C₂²×C₁₃	1	2	yes	complemented
538	#449	C₂²×C₁₃	1	2	yes	—
539	#449	C₂²×C₁₃	1	2	yes	—
540	#449	C₂²×C₁₃	1	2	yes	complemented
541	#447	C₂²×C₁₃	1	2	yes	—
542	#447	C₂²×C₁₃	1	2	yes	—
543	#447	C₂²×C₁₃	1	2	yes	complemented
544	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
545	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
546	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
547	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
548	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
549	C₄×D₈	C₂²×C₁₃	1	2	yes	—
550	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
551	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
552	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
553	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
554	#433	C₂²×C₁₃	1	2	yes	complemented
555	#433	C₂²×C₁₃	1	2	yes	complemented
556	#431	C₂²×C₁₃	1	2	yes	complemented
557	#431	C₂²×C₁₃	1	2	yes	complemented
558	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
559	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
560	#408	C₂²×C₁₃	1	1	yes	characteristic
561	#408	C₂²×C₁₃	1	1	yes	characteristic
562	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
563	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
564	C₂²×C₁₃	—	2	1	no	—
565	C₂²×C₁₃	—	2	2	no	—
566	C₂²×C₁₃	—	2	2	no	—
567	C₂²×C₁₃	—	2	1	no	—
568	C₂²×C₁₃	—	2	2	no	—
569	C₂²×C₁₃	—	2	1	no	—
570	C₂²×C₁₃	—	4	2	no	—
571	C₂²×C₁₃	—	4	2	no	—
572	C₂²×C₁₃	—	4	2	no	—
573	C₂²×C₁₃	—	4	2	no	—
574	C₂²×C₁₃	—	4	2	no	—
575	C₂²×C₁₃	—	4	2	no	—
576	C₂²×C₁₃	—	4	2	no	—
577	C₂²×C₁₃	—	4	2	no	—
578	C₂²×C₁₃	—	4	2	no	—
579	C₂²×C₁₃	—	8	8	no	—
580	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
581	C₄×C₁₃	—	2	1	no	—
582	C₄×C₁₃	—	2	2	no	—
583	C₄×C₁₃	—	2	1	no	—
584	C₄×C₁₃	—	2	2	no	—
585	C₄×C₁₃	—	2	1	no	—
586	C₄×C₁₃	—	2	2	no	—
587	C₄×C₁₃	—	2	1	no	—
588	C₄×C₁₃	—	4	2	no	—
589	C₄×C₁₃	—	4	2	no	—
590	C₄×C₁₃	—	4	2	no	—
591	C₄×C₁₃	—	4	2	no	—
592	C₄×C₁₃	—	4	2	no	—
593	C₄×C₁₃	#576	1	2	yes	—
594	C₄×C₁₃	#585	1	1	yes	characteristic
595	C₄×C₁₃	#585	1	1	yes	characteristic
596	C₂×#41	—	2	2	no	—
597	C₂×#41	—	2	2	no	—
598	C₂×#41	C₂³×C₁₃	1	2	yes	—
599	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
600	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
601	C₂³×C₄	—	2	2	no	—
602	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
603	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
604	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
605	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
606	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
607	C₂×D₈	C₂³×C₁₃	1	2	yes	—
608	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
609	C₂×D₈	C₂³×C₁₃	1	2	yes	—
610	C₂×D₈	C₂³×C₁₃	1	2	yes	—
611	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
612	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
614	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
615	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
616	C₄⋊Q₈	—	2	2	no	—
617	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
618	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
619	#127	—	2	2	no	—
620	#127	C₂³×C₁₃	1	2	yes	—
621	#127	C₂³×C₁₃	1	2	yes	—
622	#126	—	2	2	no	—
623	#126	—	2	2	no	—
624	#126	—	2	2	no	—
625	#126	—	2	2	no	—
626	#125	—	2	2	no	—
627	#125	C₂³×C₁₃	1	2	yes	—
628	#125	C₂³×C₁₃	1	2	yes	—
629	#124	—	2	2	no	—
630	#124	—	2	2	no	—
631	#124	—	2	2	no	—
632	#124	—	2	2	no	—
633	#124	—	2	2	no	—
634	#124	C₂³×C₁₃	1	2	yes	—
635	#124	C₂³×C₁₃	1	2	yes	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	#123	—	2	2	no	—
643	#123	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	—	2	2	no	—
648	C₂²⋊Q₈	—	2	2	no	—
649	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
650	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	2	no	—
656	#121	—	2	2	no	—
657	#121	—	2	2	no	—
658	#121	—	2	2	no	—
659	#121	—	2	2	no	—
660	#121	—	2	2	no	—
661	#121	—	2	2	no	—
662	#121	C₂³×C₁₃	1	2	yes	—
663	#121	C₂³×C₁₃	1	2	yes	—
664	#121	C₂³×C₁₃	1	2	yes	—
665	#121	C₂³×C₁₃	1	2	yes	—
666	#121	C₂³×C₁₃	1	2	yes	—
667	#121	C₂³×C₁₃	1	2	yes	—
668	#120	—	2	2	no	—
669	#120	—	2	2	no	—
670	#120	—	2	2	no	—
671	#120	—	2	2	no	—
672	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
673	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
674	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
675	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	—	2	2	no	—
682	C₄×D₄	—	2	2	no	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
685	C₄×D₄	D₄×C₁₃	1	2	yes	—
686	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
687	C₄×D₄	D₄×C₁₃	1	2	yes	—
688	C₄×D₄	C₂³×C₁₃	1	2	yes	—
689	C₄×D₄	C₂³×C₁₃	1	2	yes	—
690	C₄×D₄	C₂³×C₁₃	1	2	yes	—
691	C₄×D₄	C₂³×C₁₃	1	2	yes	—
692	C₄×D₄	C₂³×C₁₃	1	2	yes	—
693	C₄×D₄	C₂³×C₁₃	1	2	yes	—
694	#117	—	2	2	no	—
695	#117	—	2	2	no	—
696	#117	—	2	2	no	—
697	#117	C₂³×C₁₃	1	2	yes	—
698	#117	C₂³×C₁₃	1	2	yes	—
699	#117	C₂³×C₁₃	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
701	C₂×C₂²⋊C₄	—	2	2	no	—
702	C₂×C₄²	—	2	2	no	—
703	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
704	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
705	#107	C₂³×C₁₃	1	1	yes	characteristic
706	#107	C₂³×C₁₃	1	1	yes	characteristic
707	#107	C₂³×C₁₃	1	2	yes	—
708	#107	C₂³×C₁₃	1	1	yes	characteristic
709	#107	C₂³×C₁₃	1	2	yes	—
710	#107	C₂³×C₁₃	1	2	yes	—
711	#107	C₂³×C₁₃	1	1	yes	characteristic
712	#106	C₂³×C₁₃	1	2	yes	—
713	#106	C₂³×C₁₃	1	2	yes	—
714	#106	C₂³×C₁₃	1	2	yes	—
715	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
716	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
717	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
718	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
719	#103	C₂³×C₁₃	1	2	yes	—
720	#103	C₂³×C₁₃	1	2	yes	—
721	#103	C₂³×C₁₃	1	2	yes	—
722	#103	C₂³×C₁₃	1	2	yes	—
723	#102	C₂³×C₁₃	1	2	yes	—
724	#102	C₂³×C₁₃	1	2	yes	—
725	#102	C₂³×C₁₃	1	2	yes	—
726	#102	C₂³×C₁₃	1	2	yes	—
727	#102	C₂³×C₁₃	1	2	yes	—
728	#102	C₂³×C₁₃	1	2	yes	—
729	#102	C₂³×C₁₃	1	2	yes	—
730	#102	C₂³×C₁₃	1	2	yes	—
731	#102	C₂³×C₁₃	1	2	yes	—
732	#102	C₂³×C₁₃	1	2	yes	—
733	#102	C₂³×C₁₃	1	2	yes	—
734	#102	C₂³×C₁₃	1	2	yes	—
735	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
736	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
737	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
738	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
739	#97	C₂³×C₁₃	1	2	yes	—
740	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
741	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
742	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
743	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
744	C₄×C₈	C₂³×C₁₃	1	2	yes	—
745	C₂×C₁₃	—	4	1	no	—
746	C₂×C₁₃	—	4	2	no	—
747	C₂×C₁₃	—	8	2	no	—
748	C₂×C₁₃	—	8	2	no	—
749	C₂×C₁₃	—	8	2	no	—
750	C₂×C₁₃	#3449	1	1	yes	characteristic
751	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
752	C₂×C₁₃	#3584	1	1	yes	characteristic
753	C₂⁴	—	2	2	no	—
754	#41	—	4	1	no	—
755	#41	—	4	1	no	—
756	#41	—	4	2	no	—
757	#41	—	4	2	no	—
758	#41	—	8	4	no	—
759	#41	—	8	4	no	—
760	C₂×Q₈	—	2	2	no	—
761	C₂×Q₈	—	2	2	no	—
762	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
763	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	4	2	no	—
777	C₂×D₄	—	4	2	no	—
778	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
779	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
780	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
781	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
782	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	8	4	no	—
792	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
793	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
794	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
795	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
798	Q₁₆	—	4	1	no	—
799	SD₁₆	—	4	2	no	—
800	SD₁₆	—	4	2	no	—
801	SD₁₆	—	4	2	no	—
802	D₈	—	4	2	no	—
803	D₈	—	4	1	no	—
804	D₈	—	4	1	no	—
805	D₈	—	4	1	no	—
806	D₈	—	4	2	no	—
807	D₈	—	4	2	no	—
808	M₁₆	—	4	1	no	—
809	M₁₆	—	4	1	no	—
810	C₂×C₈	—	4	1	no	—
811	C₂×C₈	—	4	1	no	—
812	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
813	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
814	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
815	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
816	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
817	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	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	C₂×D₄×C₁₃	1	2	yes	—
830	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
831	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
832	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
833	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
834	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
835	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
836	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
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	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
857	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
858	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
859	C₄²	—	2	2	no	—
860	C₄²	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	C₂×D₄×C₁₃	1	2	yes	—
863	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
864	C₄²	C₂×D₄×C₁₃	1	2	yes	—
865	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
866	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
867	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
868	C₄²	C₂⁴×C₁₃	1	2	yes	—
869	C₁₃	#60955	1	1	yes	characteristic, direct product factor, Sylow
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	4	4	no	—
874	C₂³	—	8	2	no	—
875	C₂³	—	8	2	no	—
876	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
877	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
878	Q₈	—	2	2	no	—
879	Q₈	—	2	2	no	—
880	Q₈	—	4	1	no	—
881	Q₈	—	8	2	no	—
882	Q₈	—	8	2	no	—
883	D₄	—	2	2	no	—
884	D₄	—	2	2	no	—
885	D₄	—	2	2	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	2	no	—
888	D₄	—	2	2	no	—
889	D₄	—	4	2	no	—
890	D₄	—	4	1	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	8	2	no	—
894	D₄	—	8	2	no	—
895	D₄	—	8	2	no	—
896	D₄	—	8	2	no	—
897	D₄	—	8	2	no	—
898	D₄	—	8	2	no	—
899	D₄	—	8	2	no	—
900	D₄	—	8	2	no	—
901	D₄	—	8	2	no	—
902	D₄	—	8	2	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	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	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	4	2	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	4	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	—	8	2	no	—
922	C₂×C₄	—	8	2	no	—
923	C₂×C₄	—	8	2	no	—
924	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
925	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
926	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
927	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
929	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
930	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
932	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
933	C₈	—	2	1	no	—
934	C₈	—	2	1	no	—
935	C₈	—	2	1	no	—
936	C₈	—	2	1	no	—
937	C₈	—	2	2	no	—
938	C₈	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	8	8	no	—
955	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
956	C₄	—	2	2	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	1	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	1	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	C₁₃×#576	1	2	yes	—
969	C₄	C₁₃×#585	1	1	yes	characteristic
970	C₄	C₁₃×#585	1	1	yes	characteristic
971	C₂	—	4	2	no	—
972	C₂	—	4	1	no	—
973	C₂	—	8	2	no	—
974	C₂	—	8	2	no	—
975	C₂	—	8	2	no	—
976	C₂	C₁₃×#3449	1	1	yes	characteristic
977	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
978	C₂	C₁₃×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3460	C₂	semidirect
2. C₁₃×#3262	C₂	semidirect
3. C₁₃×#3259	C₂	semidirect
4. C₁₃×#3257	C₂	semidirect
5. C₁₃×#3243	C₂	semidirect
6. C₁₃×#3241	C₂	semidirect
7. C₁₃×#3224	C₂	semidirect
8. C₁₃×#3220	C₂	semidirect
9. C₁₃×#3203	C₂	semidirect
10. C₁₃×#3199	C₂	semidirect
11. C₁₃×#3198	C₂	semidirect
12. C₁₃×#3171	C₂	semidirect
13. C₁₃×#3169	C₂	semidirect
14. C₁₃×#3168	C₂	semidirect
15. C₁₃×#3106	C₂	semidirect
16. C₁₃×#3105	C₂	semidirect
17. C₁₃×#3102	C₂	semidirect
18. C₁₃×#3100	C₂	semidirect
19. C₁₃×#2922	C₂	semidirect
20. C₁₃×#544	C₂²	semidirect
23. C₁₃×#542	C₂²	semidirect
26. C₁₃×#540	C₂²	semidirect
31. C₁₃×#535	C₂²	semidirect
34. C₁₃×#532	C₂²	semidirect
37. C₁₃×#529	C₂²	semidirect
41. C₄×C₁₃×#41	C₂²	semidirect
42. C₂×C₄×D₄×C₁₃	C₂²	semidirect
43. C₁₃×#501	C₂²	semidirect
44. C₁₃×#500	C₂²	semidirect
45. C₁₃×#499	C₂²	semidirect
49. C₁₃×#490	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
51. C₁₃×#488	C₂²	semidirect
52. C₁₃×#486	C₂²	semidirect
53. C₁₃×#485	C₂²	semidirect
54. C₁₃×#484	C₂²	semidirect
57. C₁₃×#482	C₂²	semidirect
60. C₁₃×#480	C₂²	semidirect
61. C₁₃×#479	C₂²	semidirect
62. C₁₃×#478	C₂²	semidirect
63. C₁₃×#478	C₂²	semidirect
64. C₁₃×#478	C₂²	semidirect
65. C₁₃×#477	C₂²	semidirect
66. C₁₃×#476	C₂²	semidirect
67. C₁₃×#474	C₂²	semidirect
68. C₁₃×#474	C₂²	semidirect
70. C₁₃×#469	C₂²	semidirect
71. C₁₃×#468	C₂²	semidirect
72. C₁₃×#468	C₂²	semidirect
73. C₁₃×#467	C₂²	semidirect
76. C₁₃×#466	C₂²	semidirect
77. C₁₃×#466	C₂²	semidirect
78. C₁₃×#465	C₂²	semidirect
79. C₁₃×#464	C₂²	semidirect
82. C₁₃×#463	C₂²	semidirect
83. C₁₃×#460	C₂²	semidirect
86. C₁₃×#459	C₂²	semidirect
87. C₁₃×#452	C₂²	semidirect
88. C₁₃×#450	C₂²	semidirect
91. C₁₃×#449	C₂²	semidirect
94. C₁₃×#447	C₂²	semidirect
95. C₄×C₁₃×Q₁₆	C₂²	semidirect
96. C₄×C₁₃×SD₁₆	C₂²	semidirect
97. C₄×C₁₃×SD₁₆	C₂²	semidirect
98. C₄×C₁₃×SD₁₆	C₂²	semidirect
102. C₄×C₁₃×D₈	C₂²	semidirect
103. C₄×C₁₃×D₈	C₂²	semidirect
104. C₄×C₁₃×D₈	C₂²	semidirect
105. C₁₃×#433	C₂²	semidirect
106. C₁₃×#433	C₂²	semidirect
107. C₁₃×#431	C₂²	semidirect
108. C₁₃×#431	C₂²	semidirect
109. C₁₃×#424	C₂²	semidirect
110. C₁₃×#424	C₂²	semidirect
113. C₄×C₁₃×M₁₆	C₂²	semidirect
114. C₂×C₄×C₈×C₁₃	C₂²	semidirect
264. #60955	C₁₃	direct (N × H)
381. #3460	C₂×C₁₃	semidirect
382. #3262	C₂×C₁₃	semidirect
383. #3259	C₂×C₁₃	semidirect
384. #3257	C₂×C₁₃	semidirect
385. #3243	C₂×C₁₃	semidirect
386. #3241	C₂×C₁₃	semidirect
387. #3224	C₂×C₁₃	semidirect
388. #3220	C₂×C₁₃	semidirect
389. #3203	C₂×C₁₃	semidirect
390. #3199	C₂×C₁₃	semidirect
391. #3198	C₂×C₁₃	semidirect
392. #3171	C₂×C₁₃	semidirect
393. #3169	C₂×C₁₃	semidirect
394. #3168	C₂×C₁₃	semidirect
395. #3106	C₂×C₁₃	semidirect
396. #3105	C₂×C₁₃	semidirect
397. #3102	C₂×C₁₃	semidirect
398. #3100	C₂×C₁₃	semidirect
399. #2922	C₂×C₁₃	semidirect
469. #544	C₂²×C₁₃	semidirect
472. #542	C₂²×C₁₃	semidirect
475. #540	C₂²×C₁₃	semidirect
480. #535	C₂²×C₁₃	semidirect
483. #532	C₂²×C₁₃	semidirect
486. #529	C₂²×C₁₃	semidirect
490. C₄×#41	C₂²×C₁₃	semidirect
491. C₂×C₄×D₄	C₂²×C₁₃	semidirect
492. #501	C₂²×C₁₃	semidirect
493. #500	C₂²×C₁₃	semidirect
494. #499	C₂²×C₁₃	semidirect
498. #490	C₂²×C₁₃	semidirect
499. #489	C₂²×C₁₃	semidirect
500. #488	C₂²×C₁₃	semidirect
501. #486	C₂²×C₁₃	semidirect
502. #485	C₂²×C₁₃	semidirect
503. #484	C₂²×C₁₃	semidirect
506. #482	C₂²×C₁₃	semidirect
509. #480	C₂²×C₁₃	semidirect
510. #479	C₂²×C₁₃	semidirect
511. #478	C₂²×C₁₃	semidirect
512. #478	C₂²×C₁₃	semidirect
513. #478	C₂²×C₁₃	semidirect
514. #477	C₂²×C₁₃	semidirect
515. #476	C₂²×C₁₃	semidirect
516. #474	C₂²×C₁₃	semidirect
517. #474	C₂²×C₁₃	semidirect
519. #469	C₂²×C₁₃	semidirect
520. #468	C₂²×C₁₃	semidirect
521. #468	C₂²×C₁₃	semidirect
522. #467	C₂²×C₁₃	semidirect
525. #466	C₂²×C₁₃	semidirect
526. #466	C₂²×C₁₃	semidirect
527. #465	C₂²×C₁₃	semidirect
528. #464	C₂²×C₁₃	semidirect
531. #463	C₂²×C₁₃	semidirect
532. #460	C₂²×C₁₃	semidirect
535. #459	C₂²×C₁₃	semidirect
536. #452	C₂²×C₁₃	semidirect
537. #450	C₂²×C₁₃	semidirect
540. #449	C₂²×C₁₃	semidirect
543. #447	C₂²×C₁₃	semidirect
544. C₄×Q₁₆	C₂²×C₁₃	semidirect
545. C₄×SD₁₆	C₂²×C₁₃	semidirect
546. C₄×SD₁₆	C₂²×C₁₃	semidirect
547. C₄×SD₁₆	C₂²×C₁₃	semidirect
551. C₄×D₈	C₂²×C₁₃	semidirect
552. C₄×D₈	C₂²×C₁₃	semidirect
553. C₄×D₈	C₂²×C₁₃	semidirect
554. #433	C₂²×C₁₃	semidirect
555. #433	C₂²×C₁₃	semidirect
556. #431	C₂²×C₁₃	semidirect
557. #431	C₂²×C₁₃	semidirect
558. #424	C₂²×C₁₃	semidirect
559. #424	C₂²×C₁₃	semidirect
562. C₄×M₁₆	C₂²×C₁₃	semidirect
563. C₂×C₄×C₈	C₂²×C₁₃	semidirect
869. C₁₃	#60955	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×#3460	2
C₁₃×#3262	2
C₁₃×#3259	2
C₁₃×#3257	2
C₁₃×#3243	2
C₁₃×#3241	2
C₁₃×#3224	2
C₁₃×#3220	2
C₁₃×#3203	2
C₁₃×#3199	2
C₁₃×#3198	2
C₁₃×#3171	2
C₁₃×#3169	2
C₁₃×#3168	2
C₁₃×#3106	2
C₁₃×#3105	2
C₁₃×#3102	2
C₁₃×#3100	2
C₁₃×#2922	2
#60955	13

Subgroups — C13×#60955 #15747294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60955 #15747294