Subgroups — C₁₃×#60953 #15747292

Order 3328.

1824 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3252	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3251	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3240	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3219	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3197	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3172	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3171	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3107	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3106	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3102	C₂	1	4	yes	maximal, complemented
17	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#533	C₂²	1	1	yes	characteristic
19	C₁₃×#533	C₂²	1	1	yes	characteristic
20	C₁₃×#533	C₂²	1	1	yes	characteristic
21	C₁₃×#533	C₂²	1	1	yes	characteristic
22	C₁₃×#533	C₂²	1	1	yes	characteristic
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₁₃×#532	C₂²	1	1	yes	characteristic
25	C₁₃×#532	C₂²	1	1	yes	characteristic
26	C₁₃×#532	C₂²	1	1	yes	characteristic
27	C₁₃×#532	C₂²	1	1	yes	characteristic
28	C₁₃×#532	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₁₃×#529	—	2	1	no	—
31	C₁₃×#529	—	2	1	no	—
32	C₁₃×#529	—	2	1	no	—
33	C₁₃×#529	—	2	1	no	—
34	C₁₃×#529	—	2	1	no	—
35	C₁₃×#529	—	2	1	no	—
36	C₁₃×#529	—	2	1	no	—
37	C₁₃×#529	—	2	1	no	—
38	C₁₃×#529	C₂²	1	2	yes	—
39	C₁₃×#529	C₂²	1	2	yes	—
40	C₁₃×#529	C₂²	1	2	yes	—
41	C₁₃×#529	C₂²	1	2	yes	—
42	C₁₃×#525	—	2	1	no	—
43	C₁₃×#525	—	2	1	no	—
44	C₁₃×#525	—	2	1	no	—
45	C₁₃×#525	—	2	1	no	—
46	C₁₃×#525	C₂²	1	2	yes	—
47	C₁₃×#525	C₂²	1	2	yes	—
48	C₄×C₁₃×#41	—	2	1	no	—
49	C₄×C₁₃×#41	—	2	1	no	—
50	C₄×C₁₃×#41	—	2	1	no	—
51	C₄×C₁₃×#41	—	2	1	no	—
52	C₄×C₁₃×#41	C₂²	1	2	yes	—
53	C₄×C₁₃×#41	C₂²	1	2	yes	—
54	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
55	C₁₃×#501	C₂²	1	2	yes	complemented
56	C₁₃×#501	C₂²	1	2	yes	complemented
57	C₁₃×#497	C₂²	1	2	yes	complemented
58	C₁₃×#496	C₂²	1	2	yes	complemented
59	C₁₃×#491	C₂²	1	2	yes	complemented
60	C₁₃×#490	C₂²	1	2	yes	complemented
61	C₁₃×#489	C₂²	1	2	yes	complemented
62	C₁₃×#489	C₂²	1	2	yes	complemented
63	C₁₃×#485	C₂²	1	4	yes	—
64	C₁₃×#485	C₂²	1	4	yes	—
65	C₁₃×#482	C₂²	1	4	yes	—
66	C₁₃×#482	C₂²	1	4	yes	—
67	C₁₃×#479	C₂²	1	4	yes	complemented
68	C₁₃×#478	C₂²	1	4	yes	complemented
69	C₁₃×#477	C₂²	1	2	yes	complemented
70	C₁₃×#476	C₂²	1	2	yes	complemented
71	C₁₃×#475	C₂²	1	2	yes	complemented
72	C₁₃×#474	C₂²	1	2	yes	complemented
73	C₁₃×#470	C₂²	1	4	yes	—
74	C₁₃×#469	C₂²	1	4	yes	—
75	C₁₃×#468	C₂²	1	4	yes	—
76	C₁₃×#468	C₂²	1	4	yes	—
77	C₁₃×#464	C₂²	1	4	yes	complemented
78	C₁₃×#463	C₂²	1	4	yes	complemented
79	C₁₃×#462	C₂²	1	2	yes	complemented
80	C₁₃×#461	C₂²	1	2	yes	complemented
81	C₁₃×#460	C₂²	1	2	yes	complemented
82	C₁₃×#459	C₂²	1	2	yes	complemented
83	C₁₃×#452	C₂²	1	4	yes	—
84	C₁₃×#452	C₂²	1	4	yes	—
85	C₁₃×#449	C₂²	1	4	yes	—
86	C₁₃×#449	C₂²	1	4	yes	—
87	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
88	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
89	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
90	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
91	C₁₃×#432	C₂²	1	1	yes	characteristic
92	C₁₃×#432	C₂²	1	1	yes	characteristic
93	C₁₃×#432	C₂²	1	2	yes	—
94	C₁₃×#431	C₂²	1	2	yes	—
95	C₁₃×#431	C₂²	1	2	yes	—
96	C₁₃×#423	C₂²	1	2	yes	—
97	C₁₃×#407	C₂²	1	2	yes	—
98	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
99	C₂×C₁₃×#41	—	2	1	no	—
100	C₂×C₁₃×#41	—	2	1	no	—
101	C₂×C₁₃×#41	—	2	1	no	—
102	C₂×C₁₃×#41	—	2	1	no	—
103	C₂×C₁₃×#41	C₂³	1	2	yes	—
104	C₂×C₁₃×#41	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×D₈	C₂³	1	4	yes	—
112	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×#127	C₂³	1	1	yes	characteristic
120	C₁₃×#127	C₂³	1	1	yes	characteristic
121	C₁₃×#126	—	2	2	no	—
122	C₁₃×#126	—	2	2	no	—
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#126	—	2	2	no	—
125	C₁₃×#125	—	2	1	no	—
126	C₁₃×#125	—	2	1	no	—
127	C₁₃×#125	—	2	1	no	—
128	C₁₃×#125	—	2	1	no	—
129	C₁₃×#125	C₂³	1	2	yes	—
130	C₁₃×#125	C₂³	1	2	yes	—
131	C₁₃×#124	—	2	1	no	—
132	C₁₃×#124	—	2	1	no	—
133	C₁₃×#124	—	2	1	no	—
134	C₁₃×#124	—	2	1	no	—
135	C₁₃×#124	C₂³	1	2	yes	—
136	C₁₃×#124	C₂³	1	2	yes	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	1	no	—
144	C₁₃×C₂²⋊Q₈	—	2	1	no	—
145	C₁₃×C₂²⋊Q₈	—	2	1	no	—
146	C₁₃×C₂²⋊Q₈	—	2	1	no	—
147	C₁₃×C₂²⋊Q₈	—	2	1	no	—
148	C₁₃×C₂²⋊Q₈	—	2	1	no	—
149	C₁₃×C₂²⋊Q₈	—	2	1	no	—
150	C₁₃×C₂²⋊Q₈	—	2	1	no	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	1	no	—
158	C₁₃×#121	—	2	1	no	—
159	C₁₃×#121	—	2	1	no	—
160	C₁₃×#121	—	2	1	no	—
161	C₁₃×#121	—	2	1	no	—
162	C₁₃×#121	—	2	1	no	—
163	C₁₃×#121	C₂³	1	2	yes	—
164	C₁₃×#121	C₂³	1	2	yes	—
165	C₁₃×#121	C₂³	1	2	yes	—
166	C₁₃×#121	C₂³	1	2	yes	—
167	C₁₃×#120	—	2	2	no	—
168	C₁₃×#120	—	2	2	no	—
169	C₄×Q₈×C₁₃	—	2	1	no	—
170	C₄×Q₈×C₁₃	—	2	1	no	—
171	C₄×Q₈×C₁₃	—	2	1	no	—
172	C₄×Q₈×C₁₃	—	2	1	no	—
173	C₄×Q₈×C₁₃	—	2	1	no	—
174	C₄×Q₈×C₁₃	—	2	1	no	—
175	C₄×Q₈×C₁₃	—	2	1	no	—
176	C₄×Q₈×C₁₃	—	2	1	no	—
177	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
178	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
179	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
180	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	—	2	2	no	—
183	C₄×D₄×C₁₃	—	2	2	no	—
184	C₄×D₄×C₁₃	—	2	2	no	—
185	C₄×D₄×C₁₃	—	2	2	no	—
186	C₄×D₄×C₁₃	—	2	2	no	—
187	C₄×D₄×C₁₃	—	2	2	no	—
188	C₄×D₄×C₁₃	—	2	2	no	—
189	C₄×D₄×C₁₃	—	2	2	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₄×D₄×C₁₃	—	2	2	no	—
192	C₄×D₄×C₁₃	—	2	2	no	—
193	C₄×D₄×C₁₃	—	2	1	no	—
194	C₄×D₄×C₁₃	—	2	1	no	—
195	C₄×D₄×C₁₃	—	2	1	no	—
196	C₄×D₄×C₁₃	—	2	1	no	—
197	C₄×D₄×C₁₃	—	2	1	no	—
198	C₄×D₄×C₁₃	—	2	1	no	—
199	C₄×D₄×C₁₃	—	2	1	no	—
200	C₄×D₄×C₁₃	—	2	1	no	—
201	C₄×D₄×C₁₃	C₂³	1	2	yes	—
202	C₄×D₄×C₁₃	C₂³	1	2	yes	—
203	C₄×D₄×C₁₃	C₂³	1	2	yes	—
204	C₄×D₄×C₁₃	C₂³	1	2	yes	—
205	C₁₃×#117	—	2	1	no	—
206	C₁₃×#117	—	2	1	no	—
207	C₁₃×#117	—	2	1	no	—
208	C₁₃×#117	—	2	1	no	—
209	C₁₃×#117	—	2	2	no	—
210	C₁₃×#117	—	2	2	no	—
211	C₁₃×#117	—	2	2	no	—
212	C₁₃×#117	—	2	2	no	—
213	C₁₃×#117	—	2	2	no	—
214	C₁₃×#117	—	2	2	no	—
215	C₁₃×#117	C₂³	1	2	yes	—
216	C₁₃×#117	C₂³	1	2	yes	—
217	C₂×C₄²×C₁₃	—	2	2	no	—
218	C₂×C₄²×C₁₃	—	2	2	no	—
219	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
220	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
221	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
223	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
224	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
225	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
231	C₁₃×#107	C₂³	1	4	yes	—
232	C₁₃×#107	C₂³	1	4	yes	—
233	C₁₃×#106	C₂³	1	4	yes	—
234	C₁₃×#106	C₂³	1	4	yes	—
235	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
238	C₁₃×#103	C₂³	1	4	yes	—
239	C₁₃×#103	C₂³	1	4	yes	—
240	C₁₃×#103	C₂³	1	4	yes	—
241	C₁₃×#103	C₂³	1	4	yes	—
242	C₁₃×#102	C₂³	1	4	yes	—
243	C₁₃×#102	C₂³	1	4	yes	—
244	C₁₃×#102	C₂³	1	4	yes	—
245	C₁₃×#102	C₂³	1	4	yes	—
246	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
248	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
249	C₁₃×#97	C₂³	1	2	yes	—
250	C₁₃×#97	C₂³	1	2	yes	—
251	C₄×C₈×C₁₃	C₂³	1	4	yes	—
252	#60953	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₁₃×#41	—	4	2	no	—
255	C₁₃×#41	—	4	4	no	—
256	C₁₃×#41	—	4	2	no	—
257	C₁₃×#41	—	4	4	no	—
258	C₁₃×#41	—	4	4	no	—
259	C₁₃×#41	—	4	4	no	—
260	C₁₃×#41	—	4	4	no	—
261	C₂×Q₈×C₁₃	—	2	1	no	—
262	C₂×Q₈×C₁₃	—	2	1	no	—
263	C₂×Q₈×C₁₃	—	2	1	no	—
264	C₂×Q₈×C₁₃	—	2	1	no	—
265	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
266	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
267	C₂×D₄×C₁₃	—	2	2	no	—
268	C₂×D₄×C₁₃	—	2	2	no	—
269	C₂×D₄×C₁₃	—	2	2	no	—
270	C₂×D₄×C₁₃	—	2	2	no	—
271	C₂×D₄×C₁₃	—	2	2	no	—
272	C₂×D₄×C₁₃	—	2	2	no	—
273	C₂×D₄×C₁₃	—	2	1	no	—
274	C₂×D₄×C₁₃	—	2	1	no	—
275	C₂×D₄×C₁₃	—	2	1	no	—
276	C₂×D₄×C₁₃	—	2	1	no	—
277	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
278	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₃	—	2	2	no	—
280	C₂²×C₄×C₁₃	—	2	2	no	—
281	C₂²×C₄×C₁₃	—	2	2	no	—
282	C₂²×C₄×C₁₃	—	2	2	no	—
283	C₂²×C₄×C₁₃	—	2	2	no	—
284	C₂²×C₄×C₁₃	—	2	2	no	—
285	C₂²×C₄×C₁₃	—	4	2	no	—
286	C₂²×C₄×C₁₃	—	4	2	no	—
287	C₂²×C₄×C₁₃	—	4	2	no	—
288	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₁₃×Q₁₆	—	4	4	no	—
307	C₁₃×SD₁₆	—	4	4	no	—
308	C₁₃×SD₁₆	—	4	4	no	—
309	C₁₃×D₈	—	4	4	no	—
310	C₁₃×M₁₆	—	4	4	no	—
311	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
312	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
313	C₁₃×C₄⋊C₄	—	2	1	no	—
314	C₁₃×C₄⋊C₄	—	2	1	no	—
315	C₁₃×C₄⋊C₄	—	2	1	no	—
316	C₁₃×C₄⋊C₄	—	2	1	no	—
317	C₁₃×C₄⋊C₄	—	2	1	no	—
318	C₁₃×C₄⋊C₄	—	2	1	no	—
319	C₁₃×C₄⋊C₄	—	2	1	no	—
320	C₁₃×C₄⋊C₄	—	2	1	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	—	2	2	no	—
329	C₁₃×C₄⋊C₄	—	2	2	no	—
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
334	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
335	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
336	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
337	C₁₃×C₂²⋊C₄	—	2	2	no	—
338	C₁₃×C₂²⋊C₄	—	2	2	no	—
339	C₁₃×C₂²⋊C₄	—	2	2	no	—
340	C₁₃×C₂²⋊C₄	—	2	2	no	—
341	C₁₃×C₂²⋊C₄	—	2	2	no	—
342	C₁₃×C₂²⋊C₄	—	2	2	no	—
343	C₁₃×C₂²⋊C₄	—	2	2	no	—
344	C₁₃×C₂²⋊C₄	—	2	2	no	—
345	C₁₃×C₂²⋊C₄	—	2	2	no	—
346	C₁₃×C₂²⋊C₄	—	2	2	no	—
347	C₁₃×C₂²⋊C₄	—	2	2	no	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
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	C₄²×C₁₃	—	2	2	no	—
356	C₄²×C₁₃	—	2	2	no	—
357	C₄²×C₁₃	—	2	2	no	—
358	C₄²×C₁₃	—	2	2	no	—
359	C₄²×C₁₃	—	2	2	no	—
360	C₄²×C₁₃	—	2	2	no	—
361	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
362	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
363	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
364	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
365	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
366	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
367	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
369	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
370	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
374	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
377	#3444	C₂×C₁₃	1	1	yes	characteristic, complemented
378	#3444	C₂×C₁₃	1	1	yes	characteristic, complemented
379	#3252	C₂×C₁₃	1	2	yes	complemented
380	#3251	C₂×C₁₃	1	2	yes	complemented
381	#3240	C₂×C₁₃	1	2	yes	complemented
382	#3237	C₂×C₁₃	1	1	yes	characteristic, complemented
383	#3235	C₂×C₁₃	1	1	yes	characteristic, complemented
384	#3219	C₂×C₁₃	1	2	yes	complemented
385	#3216	C₂×C₁₃	1	1	yes	characteristic, complemented
386	#3214	C₂×C₁₃	1	1	yes	characteristic, complemented
387	#3197	C₂×C₁₃	1	4	yes	complemented
388	#3172	C₂×C₁₃	1	2	yes	complemented
389	#3171	C₂×C₁₃	1	2	yes	complemented
390	#3107	C₂×C₁₃	1	2	yes	complemented
391	#3106	C₂×C₁₃	1	2	yes	complemented
392	#3102	C₂×C₁₃	1	4	yes	complemented
393	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
394	C₂³×C₁₃	—	2	2	no	—
395	C₂³×C₁₃	—	2	2	no	—
396	C₂³×C₁₃	—	4	1	no	—
397	C₂³×C₁₃	—	4	1	no	—
398	C₂³×C₁₃	—	4	1	no	—
399	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
401	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
402	Q₈×C₁₃	—	2	2	no	—
403	Q₈×C₁₃	—	2	4	no	—
404	Q₈×C₁₃	—	2	2	no	—
405	Q₈×C₁₃	—	4	2	no	—
406	Q₈×C₁₃	—	4	2	no	—
407	Q₈×C₁₃	—	4	2	no	—
408	Q₈×C₁₃	—	4	2	no	—
409	D₄×C₁₃	—	2	2	no	—
410	D₄×C₁₃	—	2	4	no	—
411	D₄×C₁₃	—	2	2	no	—
412	D₄×C₁₃	—	4	2	no	—
413	D₄×C₁₃	—	4	2	no	—
414	D₄×C₁₃	—	4	2	no	—
415	D₄×C₁₃	—	4	4	no	—
416	D₄×C₁₃	—	4	4	no	—
417	D₄×C₁₃	—	4	4	no	—
418	D₄×C₁₃	—	4	4	no	—
419	D₄×C₁₃	—	4	4	no	—
420	D₄×C₁₃	—	4	4	no	—
421	D₄×C₁₃	—	4	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	4	1	no	—
438	C₂×C₄×C₁₃	—	4	1	no	—
439	C₂×C₄×C₁₃	—	4	1	no	—
440	C₂×C₄×C₁₃	—	4	1	no	—
441	C₂×C₄×C₁₃	—	4	1	no	—
442	C₂×C₄×C₁₃	—	4	1	no	—
443	C₂×C₄×C₁₃	—	4	1	no	—
444	C₂×C₄×C₁₃	—	4	1	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	—	4	4	no	—
451	C₂×C₄×C₁₃	—	4	4	no	—
452	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
460	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
464	C₈×C₁₃	—	2	4	no	—
465	C₈×C₁₃	—	2	4	no	—
466	#533	C₂²×C₁₃	1	1	yes	characteristic
467	#533	C₂²×C₁₃	1	1	yes	characteristic
468	#533	C₂²×C₁₃	1	1	yes	characteristic
469	#533	C₂²×C₁₃	1	1	yes	characteristic
470	#533	C₂²×C₁₃	1	1	yes	characteristic
471	#533	C₂²×C₁₃	1	1	yes	characteristic
472	#532	C₂²×C₁₃	1	1	yes	characteristic
473	#532	C₂²×C₁₃	1	1	yes	characteristic
474	#532	C₂²×C₁₃	1	1	yes	characteristic
475	#532	C₂²×C₁₃	1	1	yes	characteristic
476	#532	C₂²×C₁₃	1	1	yes	characteristic
477	#532	C₂²×C₁₃	1	1	yes	characteristic
478	#529	—	2	1	no	—
479	#529	—	2	1	no	—
480	#529	—	2	1	no	—
481	#529	—	2	1	no	—
482	#529	—	2	1	no	—
483	#529	—	2	1	no	—
484	#529	—	2	1	no	—
485	#529	—	2	1	no	—
486	#529	C₂²×C₁₃	1	2	yes	—
487	#529	C₂²×C₁₃	1	2	yes	—
488	#529	C₂²×C₁₃	1	2	yes	—
489	#529	C₂²×C₁₃	1	2	yes	—
490	#525	—	2	1	no	—
491	#525	—	2	1	no	—
492	#525	—	2	1	no	—
493	#525	—	2	1	no	—
494	#525	C₂²×C₁₃	1	2	yes	—
495	#525	C₂²×C₁₃	1	2	yes	—
496	C₄×#41	—	2	1	no	—
497	C₄×#41	—	2	1	no	—
498	C₄×#41	—	2	1	no	—
499	C₄×#41	—	2	1	no	—
500	C₄×#41	C₂²×C₁₃	1	2	yes	—
501	C₄×#41	C₂²×C₁₃	1	2	yes	—
502	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
503	#501	C₂²×C₁₃	1	2	yes	complemented
504	#501	C₂²×C₁₃	1	2	yes	complemented
505	#497	C₂²×C₁₃	1	2	yes	complemented
506	#496	C₂²×C₁₃	1	2	yes	complemented
507	#491	C₂²×C₁₃	1	2	yes	complemented
508	#490	C₂²×C₁₃	1	2	yes	complemented
509	#489	C₂²×C₁₃	1	2	yes	complemented
510	#489	C₂²×C₁₃	1	2	yes	complemented
511	#485	C₂²×C₁₃	1	4	yes	—
512	#485	C₂²×C₁₃	1	4	yes	—
513	#482	C₂²×C₁₃	1	4	yes	—
514	#482	C₂²×C₁₃	1	4	yes	—
515	#479	C₂²×C₁₃	1	4	yes	complemented
516	#478	C₂²×C₁₃	1	4	yes	complemented
517	#477	C₂²×C₁₃	1	2	yes	complemented
518	#476	C₂²×C₁₃	1	2	yes	complemented
519	#475	C₂²×C₁₃	1	2	yes	complemented
520	#474	C₂²×C₁₃	1	2	yes	complemented
521	#470	C₂²×C₁₃	1	4	yes	—
522	#469	C₂²×C₁₃	1	4	yes	—
523	#468	C₂²×C₁₃	1	4	yes	—
524	#468	C₂²×C₁₃	1	4	yes	—
525	#464	C₂²×C₁₃	1	4	yes	complemented
526	#463	C₂²×C₁₃	1	4	yes	complemented
527	#462	C₂²×C₁₃	1	2	yes	complemented
528	#461	C₂²×C₁₃	1	2	yes	complemented
529	#460	C₂²×C₁₃	1	2	yes	complemented
530	#459	C₂²×C₁₃	1	2	yes	complemented
531	#452	C₂²×C₁₃	1	4	yes	—
532	#452	C₂²×C₁₃	1	4	yes	—
533	#449	C₂²×C₁₃	1	4	yes	—
534	#449	C₂²×C₁₃	1	4	yes	—
535	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
536	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
537	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
538	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
539	#432	C₂²×C₁₃	1	1	yes	characteristic
540	#432	C₂²×C₁₃	1	1	yes	characteristic
541	#432	C₂²×C₁₃	1	2	yes	—
542	#431	C₂²×C₁₃	1	2	yes	—
543	#431	C₂²×C₁₃	1	2	yes	—
544	#423	C₂²×C₁₃	1	2	yes	—
545	#407	C₂²×C₁₃	1	2	yes	—
546	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
547	C₂²×C₁₃	—	2	1	no	—
548	C₂²×C₁₃	—	2	1	no	—
549	C₂²×C₁₃	—	2	1	no	—
550	C₂²×C₁₃	—	2	1	no	—
551	C₂²×C₁₃	—	2	1	no	—
552	C₂²×C₁₃	—	2	1	no	—
553	C₂²×C₁₃	—	2	1	no	—
554	C₂²×C₁₃	—	2	1	no	—
555	C₂²×C₁₃	—	2	1	no	—
556	C₂²×C₁₃	—	4	4	no	—
557	C₂²×C₁₃	—	4	2	no	—
558	C₂²×C₁₃	—	4	2	no	—
559	C₂²×C₁₃	—	4	2	no	—
560	C₂²×C₁₃	—	4	2	no	—
561	C₂²×C₁₃	—	4	2	no	—
562	C₂²×C₁₃	—	4	2	no	—
563	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
564	C₄×C₁₃	—	2	1	no	—
565	C₄×C₁₃	—	2	1	no	—
566	C₄×C₁₃	—	2	1	no	—
567	C₄×C₁₃	—	2	1	no	—
568	C₄×C₁₃	—	2	1	no	—
569	C₄×C₁₃	—	2	1	no	—
570	C₄×C₁₃	—	2	1	no	—
571	C₄×C₁₃	—	2	1	no	—
572	C₄×C₁₃	—	2	1	no	—
573	C₄×C₁₃	—	4	2	no	—
574	C₄×C₁₃	—	4	2	no	—
575	C₄×C₁₃	—	4	2	no	—
576	C₄×C₁₃	—	4	2	no	—
577	C₄×C₁₃	—	4	2	no	—
578	C₄×C₁₃	—	4	2	no	—
579	C₄×C₁₃	#575	1	2	yes	—
580	C₄×C₁₃	#575	1	2	yes	—
581	C₄×C₁₃	#585	1	2	yes	—
582	C₂×#41	—	2	1	no	—
583	C₂×#41	—	2	1	no	—
584	C₂×#41	—	2	1	no	—
585	C₂×#41	—	2	1	no	—
586	C₂×#41	C₂³×C₁₃	1	2	yes	—
587	C₂×#41	C₂³×C₁₃	1	2	yes	—
588	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
589	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
591	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
592	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
593	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
594	C₂×D₈	C₂³×C₁₃	1	4	yes	—
595	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
596	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
598	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
599	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
600	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
602	#127	C₂³×C₁₃	1	1	yes	characteristic
603	#127	C₂³×C₁₃	1	1	yes	characteristic
604	#126	—	2	2	no	—
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#126	—	2	2	no	—
608	#125	—	2	1	no	—
609	#125	—	2	1	no	—
610	#125	—	2	1	no	—
611	#125	—	2	1	no	—
612	#125	C₂³×C₁₃	1	2	yes	—
613	#125	C₂³×C₁₃	1	2	yes	—
614	#124	—	2	1	no	—
615	#124	—	2	1	no	—
616	#124	—	2	1	no	—
617	#124	—	2	1	no	—
618	#124	C₂³×C₁₃	1	2	yes	—
619	#124	C₂³×C₁₃	1	2	yes	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	#123	—	2	2	no	—
623	#123	—	2	2	no	—
624	#123	—	2	2	no	—
625	#123	—	2	2	no	—
626	C₂²⋊Q₈	—	2	1	no	—
627	C₂²⋊Q₈	—	2	1	no	—
628	C₂²⋊Q₈	—	2	1	no	—
629	C₂²⋊Q₈	—	2	1	no	—
630	C₂²⋊Q₈	—	2	1	no	—
631	C₂²⋊Q₈	—	2	1	no	—
632	C₂²⋊Q₈	—	2	1	no	—
633	C₂²⋊Q₈	—	2	1	no	—
634	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
635	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
636	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
637	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
638	#121	—	2	1	no	—
639	#121	—	2	1	no	—
640	#121	—	2	1	no	—
641	#121	—	2	1	no	—
642	#121	—	2	1	no	—
643	#121	—	2	1	no	—
644	#121	—	2	1	no	—
645	#121	—	2	1	no	—
646	#121	C₂³×C₁₃	1	2	yes	—
647	#121	C₂³×C₁₃	1	2	yes	—
648	#121	C₂³×C₁₃	1	2	yes	—
649	#121	C₂³×C₁₃	1	2	yes	—
650	#120	—	2	2	no	—
651	#120	—	2	2	no	—
652	C₄×Q₈	—	2	1	no	—
653	C₄×Q₈	—	2	1	no	—
654	C₄×Q₈	—	2	1	no	—
655	C₄×Q₈	—	2	1	no	—
656	C₄×Q₈	—	2	1	no	—
657	C₄×Q₈	—	2	1	no	—
658	C₄×Q₈	—	2	1	no	—
659	C₄×Q₈	—	2	1	no	—
660	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
661	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
662	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
663	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	1	no	—
677	C₄×D₄	—	2	1	no	—
678	C₄×D₄	—	2	1	no	—
679	C₄×D₄	—	2	1	no	—
680	C₄×D₄	—	2	1	no	—
681	C₄×D₄	—	2	1	no	—
682	C₄×D₄	—	2	1	no	—
683	C₄×D₄	—	2	1	no	—
684	C₄×D₄	C₂³×C₁₃	1	2	yes	—
685	C₄×D₄	C₂³×C₁₃	1	2	yes	—
686	C₄×D₄	C₂³×C₁₃	1	2	yes	—
687	C₄×D₄	C₂³×C₁₃	1	2	yes	—
688	#117	—	2	1	no	—
689	#117	—	2	1	no	—
690	#117	—	2	1	no	—
691	#117	—	2	1	no	—
692	#117	—	2	2	no	—
693	#117	—	2	2	no	—
694	#117	—	2	2	no	—
695	#117	—	2	2	no	—
696	#117	—	2	2	no	—
697	#117	—	2	2	no	—
698	#117	C₂³×C₁₃	1	2	yes	—
699	#117	C₂³×C₁₃	1	2	yes	—
700	C₂×C₄²	—	2	2	no	—
701	C₂×C₄²	—	2	2	no	—
702	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
703	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
704	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
705	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
706	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
707	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
709	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
714	#107	C₂³×C₁₃	1	4	yes	—
715	#107	C₂³×C₁₃	1	4	yes	—
716	#106	C₂³×C₁₃	1	4	yes	—
717	#106	C₂³×C₁₃	1	4	yes	—
718	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
719	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
720	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
721	#103	C₂³×C₁₃	1	4	yes	—
722	#103	C₂³×C₁₃	1	4	yes	—
723	#103	C₂³×C₁₃	1	4	yes	—
724	#103	C₂³×C₁₃	1	4	yes	—
725	#102	C₂³×C₁₃	1	4	yes	—
726	#102	C₂³×C₁₃	1	4	yes	—
727	#102	C₂³×C₁₃	1	4	yes	—
728	#102	C₂³×C₁₃	1	4	yes	—
729	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
730	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
731	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
732	#97	C₂³×C₁₃	1	2	yes	—
733	#97	C₂³×C₁₃	1	2	yes	—
734	C₄×C₈	C₂³×C₁₃	1	4	yes	—
735	C₂×C₁₃	—	4	1	no	—
736	C₂×C₁₃	—	4	1	no	—
737	C₂×C₁₃	—	4	1	no	—
738	C₂×C₁₃	—	8	2	no	—
739	C₂×C₁₃	—	8	2	no	—
740	C₂×C₁₃	#3449	1	1	yes	characteristic
741	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
742	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
743	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
744	#41	—	4	2	no	—
745	#41	—	4	4	no	—
746	#41	—	4	2	no	—
747	#41	—	4	4	no	—
748	#41	—	4	4	no	—
749	#41	—	4	4	no	—
750	#41	—	4	4	no	—
751	C₂×Q₈	—	2	1	no	—
752	C₂×Q₈	—	2	1	no	—
753	C₂×Q₈	—	2	1	no	—
754	C₂×Q₈	—	2	1	no	—
755	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
756	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	1	no	—
764	C₂×D₄	—	2	1	no	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	2	1	no	—
767	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
768	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
779	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
780	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
781	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
782	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
783	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
784	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
785	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
790	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
791	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
792	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
796	Q₁₆	—	4	4	no	—
797	SD₁₆	—	4	4	no	—
798	SD₁₆	—	4	4	no	—
799	D₈	—	4	4	no	—
800	M₁₆	—	4	4	no	—
801	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
802	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
803	C₄⋊C₄	—	2	1	no	—
804	C₄⋊C₄	—	2	1	no	—
805	C₄⋊C₄	—	2	1	no	—
806	C₄⋊C₄	—	2	1	no	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
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	C₂⁴×C₁₃	1	2	yes	—
824	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
825	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	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	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
852	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
853	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
854	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
855	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
856	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
857	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
858	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
859	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
860	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
861	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
862	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
863	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
864	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
865	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
866	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
867	C₁₃	#60953	1	1	yes	characteristic, direct product factor, Sylow
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	4	1	no	—
871	C₂³	—	4	1	no	—
872	C₂³	—	4	1	no	—
873	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
874	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
875	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
876	Q₈	—	2	2	no	—
877	Q₈	—	2	4	no	—
878	Q₈	—	2	2	no	—
879	Q₈	—	4	2	no	—
880	Q₈	—	4	2	no	—
881	Q₈	—	4	2	no	—
882	Q₈	—	4	2	no	—
883	D₄	—	2	2	no	—
884	D₄	—	2	4	no	—
885	D₄	—	2	2	no	—
886	D₄	—	4	2	no	—
887	D₄	—	4	2	no	—
888	D₄	—	4	2	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	4	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	4	no	—
894	D₄	—	4	4	no	—
895	D₄	—	4	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	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	—	4	1	no	—
912	C₂×C₄	—	4	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	1	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	4	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	4	no	—
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	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
932	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
936	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
937	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
938	C₈	—	2	4	no	—
939	C₈	—	2	4	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	2	1	no	—
949	C₂²	—	4	4	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	1	no	—
960	C₄	—	2	1	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	C₁₃×#575	1	2	yes	—
973	C₄	C₁₃×#575	1	2	yes	—
974	C₄	C₁₃×#585	1	2	yes	—
975	C₂	—	4	1	no	—
976	C₂	—	4	1	no	—
977	C₂	—	4	1	no	—
978	C₂	—	8	2	no	—
979	C₂	—	8	2	no	—
980	C₂	C₁₃×#3449	1	1	yes	characteristic
981	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
982	C₂	C₂×C₁₃×#575	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	semidirect
2. C₁₃×#3444	C₂	semidirect
3. C₁₃×#3252	C₂	semidirect
4. C₁₃×#3251	C₂	semidirect
5. C₁₃×#3240	C₂	semidirect
6. C₁₃×#3237	C₂	semidirect
7. C₁₃×#3235	C₂	semidirect
8. C₁₃×#3219	C₂	semidirect
9. C₁₃×#3216	C₂	semidirect
10. C₁₃×#3214	C₂	semidirect
11. C₁₃×#3197	C₂	semidirect
12. C₁₃×#3172	C₂	semidirect
13. C₁₃×#3171	C₂	semidirect
14. C₁₃×#3107	C₂	semidirect
15. C₁₃×#3106	C₂	semidirect
16. C₁₃×#3102	C₂	semidirect
17. C₁₃×#2920	C₂	semidirect
55. C₁₃×#501	C₂²	semidirect
56. C₁₃×#501	C₂²	semidirect
57. C₁₃×#497	C₂²	semidirect
58. C₁₃×#496	C₂²	semidirect
59. C₁₃×#491	C₂²	semidirect
60. C₁₃×#490	C₂²	semidirect
61. C₁₃×#489	C₂²	semidirect
62. C₁₃×#489	C₂²	semidirect
67. C₁₃×#479	C₂²	semidirect
68. C₁₃×#478	C₂²	semidirect
69. C₁₃×#477	C₂²	semidirect
70. C₁₃×#476	C₂²	semidirect
71. C₁₃×#475	C₂²	semidirect
72. C₁₃×#474	C₂²	semidirect
77. C₁₃×#464	C₂²	semidirect
78. C₁₃×#463	C₂²	semidirect
79. C₁₃×#462	C₂²	semidirect
80. C₁₃×#461	C₂²	semidirect
81. C₁₃×#460	C₂²	semidirect
82. C₁₃×#459	C₂²	semidirect
87. C₄×C₁₃×Q₁₆	C₂²	semidirect
88. C₄×C₁₃×SD₁₆	C₂²	semidirect
89. C₄×C₁₃×SD₁₆	C₂²	semidirect
90. C₄×C₁₃×D₈	C₂²	semidirect
252. #60953	C₁₃	direct (N × H)
377. #3444	C₂×C₁₃	semidirect
378. #3444	C₂×C₁₃	semidirect
379. #3252	C₂×C₁₃	semidirect
380. #3251	C₂×C₁₃	semidirect
381. #3240	C₂×C₁₃	semidirect
382. #3237	C₂×C₁₃	semidirect
383. #3235	C₂×C₁₃	semidirect
384. #3219	C₂×C₁₃	semidirect
385. #3216	C₂×C₁₃	semidirect
386. #3214	C₂×C₁₃	semidirect
387. #3197	C₂×C₁₃	semidirect
388. #3172	C₂×C₁₃	semidirect
389. #3171	C₂×C₁₃	semidirect
390. #3107	C₂×C₁₃	semidirect
391. #3106	C₂×C₁₃	semidirect
392. #3102	C₂×C₁₃	semidirect
393. #2920	C₂×C₁₃	semidirect
503. #501	C₂²×C₁₃	semidirect
504. #501	C₂²×C₁₃	semidirect
505. #497	C₂²×C₁₃	semidirect
506. #496	C₂²×C₁₃	semidirect
507. #491	C₂²×C₁₃	semidirect
508. #490	C₂²×C₁₃	semidirect
509. #489	C₂²×C₁₃	semidirect
510. #489	C₂²×C₁₃	semidirect
515. #479	C₂²×C₁₃	semidirect
516. #478	C₂²×C₁₃	semidirect
517. #477	C₂²×C₁₃	semidirect
518. #476	C₂²×C₁₃	semidirect
519. #475	C₂²×C₁₃	semidirect
520. #474	C₂²×C₁₃	semidirect
525. #464	C₂²×C₁₃	semidirect
526. #463	C₂²×C₁₃	semidirect
527. #462	C₂²×C₁₃	semidirect
528. #461	C₂²×C₁₃	semidirect
529. #460	C₂²×C₁₃	semidirect
530. #459	C₂²×C₁₃	semidirect
535. C₄×Q₁₆	C₂²×C₁₃	semidirect
536. C₄×SD₁₆	C₂²×C₁₃	semidirect
537. C₄×SD₁₆	C₂²×C₁₃	semidirect
538. C₄×D₈	C₂²×C₁₃	semidirect
867. C₁₃	#60953	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×#3444	2
C₁₃×#3252	2
C₁₃×#3251	2
C₁₃×#3240	2
C₁₃×#3237	2
C₁₃×#3235	2
C₁₃×#3219	2
C₁₃×#3216	2
C₁₃×#3214	2
C₁₃×#3197	2
C₁₃×#3172	2
C₁₃×#3171	2
C₁₃×#3107	2
C₁₃×#3106	2
C₁₃×#3102	2
C₁₃×#2920	2
#60953	13

Subgroups — C13×#60953 #15747292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60953 #15747292