Subgroups — C₁₃×#62111 #15748450

Order 3328.

1948 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3386	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3373	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3353	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3345	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3332	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3308	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3251	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3239	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3115	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3079	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
19	C₁₃×#559	—	2	1	no	—
20	C₁₃×#559	C₂²	1	1	yes	characteristic
21	C₁₃×#557	C₂²	1	1	yes	characteristic
22	C₁₃×#556	—	2	1	no	—
23	C₁₃×#556	C₂²	1	1	yes	characteristic
24	C₁₃×#553	—	2	2	no	—
25	C₁₃×#553	C₂²	1	2	yes	—
26	C₁₃×#550	C₂²	1	1	yes	characteristic
27	D₄×Q₈×C₁₃	—	2	1	no	—
28	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#548	C₂²	1	2	yes	—
30	C₁₃×#547	—	2	2	no	—
31	C₁₃×#547	—	2	1	no	—
32	C₁₃×#547	C₂²	1	4	yes	—
33	C₁₃×#547	C₂²	1	2	yes	—
34	C₁₃×#536	—	2	1	no	—
35	C₁₃×#536	—	2	2	no	—
36	C₁₃×#532	—	2	1	no	—
37	C₁₃×#532	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	2	yes	—
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
42	C₁₃×#529	—	2	2	no	—
43	C₁₃×#529	C₂²	1	2	yes	—
44	C₄×C₁₃×#41	—	2	1	no	—
45	C₄×C₁₃×#41	C₂²	1	2	yes	—
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	4	yes	—
49	C₁₃×#500	C₂²	1	2	yes	—
50	C₁₃×#489	C₂²	1	4	yes	—
51	C₁₃×#486	C₂²	1	2	yes	—
52	C₁₃×#484	C₂²	1	4	yes	—
53	C₁₃×#482	C₂²	1	4	yes	—
54	C₁₃×#481	C₂²	1	4	yes	—
55	C₁₃×#481	C₂²	1	2	yes	—
56	C₁₃×#480	C₂²	1	4	yes	—
57	C₁₃×#478	C₂²	1	4	yes	—
58	C₁₃×#477	C₂²	1	4	yes	—
59	C₁₃×#476	C₂²	1	4	yes	—
60	C₁₃×#475	C₂²	1	2	yes	—
61	C₁₃×#475	C₂²	1	2	yes	—
62	C₁₃×#475	C₂²	1	2	yes	—
63	C₁₃×#475	C₂²	1	2	yes	—
64	C₁₃×#475	C₂²	1	1	yes	characteristic
65	C₁₃×#475	C₂²	1	1	yes	characteristic
66	C₁₃×#474	C₂²	1	2	yes	—
67	C₁₃×#474	C₂²	1	2	yes	—
68	C₁₃×#474	C₂²	1	2	yes	—
69	C₁₃×#474	C₂²	1	2	yes	—
70	C₁₃×#469	C₂²	1	4	yes	—
71	C₁₃×#468	C₂²	1	4	yes	—
72	C₁₃×#466	C₂²	1	4	yes	—
73	C₁₃×#463	C₂²	1	4	yes	—
74	C₁₃×#460	C₂²	1	1	yes	characteristic
75	C₁₃×#460	C₂²	1	1	yes	characteristic
76	C₁₃×#459	C₂²	1	2	yes	—
77	C₁₃×#459	C₂²	1	2	yes	—
78	C₁₃×#449	C₂²	1	4	yes	—
79	C₁₃×#448	C₂²	1	2	yes	—
80	C₁₃×#446	C₂²	1	2	yes	—
81	C₁₃×#442	C₂²	1	4	yes	—
82	C₁₃×#440	C₂²	1	4	yes	—
83	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
84	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
85	C₁₃×#436	C₂²	1	2	yes	—
86	C₁₃×#435	C₂²	1	4	yes	—
87	C₁₃×#432	C₂²	1	2	yes	—
88	C₁₃×#431	C₂²	1	1	yes	characteristic
89	C₁₃×#428	C₂²	1	4	yes	—
90	C₂×C₁₃×#106	C₂²	1	2	yes	—
91	C₁₃×#423	C₂²	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
93	C₁₃×#417	C₂²	1	4	yes	—
94	C₂×C₁₃×#103	C₂²	1	2	yes	—
95	C₁₃×2₋¹⁺⁴	—	4	8	no	—
96	C₂×C₁₃×#41	—	2	4	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	—	2	1	no	—
99	C₂×C₁₃×#41	—	2	2	no	—
100	C₂×C₁₃×#41	—	2	1	no	—
101	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
102	C₂×C₁₃×#41	C₂³	1	2	yes	—
103	C₂²×Q₈×C₁₃	—	2	2	no	—
104	C₂²×Q₈×C₁₃	—	2	2	no	—
105	C₂²×Q₈×C₁₃	—	2	1	no	—
106	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×D₈	C₂³	1	4	yes	—
110	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
111	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	—	2	2	no	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	—	2	2	no	—
116	C₁₃×C₄⋊Q₈	—	2	1	no	—
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
122	C₁₃×#127	—	2	1	no	—
123	C₁₃×#127	C₂³	1	1	yes	characteristic
124	C₁₃×#127	C₂³	1	1	yes	characteristic
125	C₁₃×#126	—	2	2	no	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#126	—	2	2	no	—
128	C₁₃×#125	—	2	2	no	—
129	C₁₃×#125	C₂³	1	2	yes	—
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	—	2	1	no	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	—	2	1	no	—
135	C₁₃×#124	—	2	1	no	—
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	4	no	—
141	C₁₃×#123	—	2	4	no	—
142	C₁₃×#123	—	2	4	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	4	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	4	no	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₃×#121	—	2	2	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	—	2	1	no	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	—	2	1	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	C₂³	1	2	yes	—
156	C₁₃×#121	C₂³	1	4	yes	—
157	C₁₃×#121	C₂³	1	2	yes	—
158	C₁₃×#121	C₂³	1	2	yes	—
159	C₄×Q₈×C₁₃	—	2	1	no	—
160	C₄×Q₈×C₁₃	—	2	1	no	—
161	C₄×Q₈×C₁₃	—	2	1	no	—
162	C₄×Q₈×C₁₃	—	2	1	no	—
163	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	2	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	D₄	1	2	yes	—
181	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
182	C₄×D₄×C₁₃	C₂³	1	2	yes	—
183	C₄×D₄×C₁₃	C₂³	1	4	yes	—
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₄×D₄×C₁₃	C₂³	1	2	yes	—
186	C₄×D₄×C₁₃	C₂³	1	2	yes	—
187	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
188	C₁₃×#117	—	2	2	no	—
189	C₁₃×#117	—	2	2	no	—
190	C₁₃×#117	D₄	1	1	yes	characteristic
191	C₁₃×#117	D₄	1	2	yes	—
192	C₁₃×#117	C₂³	1	2	yes	—
193	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃	—	2	1	no	—
200	C₂×C₄²×C₁₃	—	2	2	no	—
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₁₃×#107	C₂³	1	4	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#107	C₂³	1	4	yes	—
206	C₁₃×#106	C₂³	1	4	yes	—
207	C₁₃×#106	C₂³	1	4	yes	—
208	C₁₃×#106	C₂³	1	2	yes	—
209	C₁₃×#106	C₂³	1	2	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	2	yes	—
222	C₁₃×#102	C₂³	1	2	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₁₃×#97	C₂³	1	4	yes	—
228	C₄×C₈×C₁₃	C₂³	1	2	yes	—
229	#62111	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₁₃×#41	—	2	4	no	—
231	C₁₃×#41	—	2	4	no	—
232	C₁₃×#41	—	4	2	no	—
233	C₁₃×#41	—	4	8	no	—
234	C₁₃×#41	—	4	16	no	—
235	C₁₃×#41	—	4	8	no	—
236	C₁₃×#41	—	4	4	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₂×Q₈×C₁₃	—	2	1	no	—
239	C₂×Q₈×C₁₃	—	2	1	no	—
240	C₂×Q₈×C₁₃	—	2	4	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	1	no	—
243	C₂×Q₈×C₁₃	—	2	2	no	—
244	C₂×Q₈×C₁₃	—	2	2	no	—
245	C₂×Q₈×C₁₃	—	4	1	no	—
246	C₂×Q₈×C₁₃	—	4	8	no	—
247	C₂×Q₈×C₁₃	—	4	8	no	—
248	C₂×Q₈×C₁₃	—	4	4	no	—
249	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	1	no	—
258	C₂×D₄×C₁₃	—	2	1	no	—
259	C₂×D₄×C₁₃	—	2	1	no	—
260	C₂×D₄×C₁₃	—	2	1	no	—
261	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	4	no	—
267	C₂²×C₄×C₁₃	—	2	2	no	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	2	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	4	no	—
272	C₂²×C₄×C₁₃	—	2	2	no	—
273	C₂²×C₄×C₁₃	—	2	2	no	—
274	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
280	C₁₃×SD₁₆	—	2	4	no	—
281	C₁₃×SD₁₆	—	4	2	no	—
282	C₁₃×D₈	—	4	4	no	—
283	C₁₃×M₁₆	—	4	4	no	—
284	C₂×C₈×C₁₃	—	4	2	no	—
285	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	4	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	4	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	1	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
305	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
306	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
307	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
311	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	4	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
326	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
327	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
328	C₄²×C₁₃	—	2	1	no	—
329	C₄²×C₁₃	—	2	1	no	—
330	C₄²×C₁₃	—	2	2	no	—
331	C₄²×C₁₃	—	2	2	no	—
332	C₄²×C₁₃	—	2	1	no	—
333	C₄²×C₁₃	—	2	1	no	—
334	C₄²×C₁₃	C₂×D₄	1	2	yes	—
335	C₄²×C₁₃	C₂×D₄	1	2	yes	—
336	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₄²×C₁₃	C₂⁴	1	2	yes	—
340	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
341	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#3386	C₂×C₁₃	1	2	yes	complemented
344	#3373	C₂×C₁₃	1	2	yes	complemented
345	#3353	C₂×C₁₃	1	2	yes	complemented
346	#3345	C₂×C₁₃	1	4	yes	complemented
347	#3332	C₂×C₁₃	1	2	yes	complemented
348	#3308	C₂×C₁₃	1	4	yes	complemented
349	#3251	C₂×C₁₃	1	2	yes	complemented
350	#3245	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3239	C₂×C₁₃	1	2	yes	complemented
352	#3226	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3115	C₂×C₁₃	1	2	yes	complemented
354	#3103	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3079	C₂×C₁₃	1	2	yes	complemented
356	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#2989	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂³×C₁₃	—	2	2	no	—
359	C₂³×C₁₃	—	2	2	no	—
360	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
361	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
362	Q₈×C₁₃	—	2	2	no	—
363	Q₈×C₁₃	—	2	1	no	—
364	Q₈×C₁₃	—	2	1	no	—
365	Q₈×C₁₃	—	2	1	no	—
366	Q₈×C₁₃	—	4	2	no	—
367	Q₈×C₁₃	—	4	8	no	—
368	Q₈×C₁₃	—	4	2	no	—
369	Q₈×C₁₃	—	4	4	no	—
370	Q₈×C₁₃	—	4	4	no	—
371	Q₈×C₁₃	—	4	2	no	—
372	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	complemented
373	D₄×C₁₃	—	2	4	no	—
374	D₄×C₁₃	—	2	2	no	—
375	D₄×C₁₃	—	2	2	no	—
376	D₄×C₁₃	—	2	2	no	—
377	D₄×C₁₃	—	2	2	no	—
378	D₄×C₁₃	—	2	2	no	—
379	D₄×C₁₃	—	4	4	no	—
380	D₄×C₁₃	—	4	2	no	—
381	D₄×C₁₃	—	4	8	no	—
382	D₄×C₁₃	—	4	4	no	—
383	D₄×C₁₃	—	4	4	no	—
384	D₄×C₁₃	—	4	2	no	—
385	D₄×C₁₃	—	4	2	no	—
386	D₄×C₁₃	—	8	1	no	—
387	D₄×C₁₃	—	8	2	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	4	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	4	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	4	2	no	—
401	C₂×C₄×C₁₃	—	4	1	no	—
402	C₂×C₄×C₁₃	—	4	4	no	—
403	C₂×C₄×C₁₃	—	4	2	no	—
404	C₂×C₄×C₁₃	—	4	8	no	—
405	C₂×C₄×C₁₃	—	4	8	no	—
406	C₂×C₄×C₁₃	—	4	4	no	—
407	C₂×C₄×C₁₃	—	4	4	no	—
408	C₂×C₄×C₁₃	—	4	4	no	—
409	C₂×C₄×C₁₃	—	8	2	no	—
410	C₂×C₄×C₁₃	—	8	1	no	—
411	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
412	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
421	C₈×C₁₃	—	2	2	no	—
422	C₈×C₁₃	—	2	4	no	—
423	C₈×C₁₃	—	2	2	no	—
424	C₂×2₋¹⁺⁴	—	2	1	no	—
425	#559	—	2	1	no	—
426	#559	C₂²×C₁₃	1	1	yes	characteristic
427	#557	C₂²×C₁₃	1	1	yes	characteristic
428	#556	—	2	1	no	—
429	#556	C₂²×C₁₃	1	1	yes	characteristic
430	#553	—	2	2	no	—
431	#553	C₂²×C₁₃	1	2	yes	—
432	#550	C₂²×C₁₃	1	1	yes	characteristic
433	D₄×Q₈	—	2	1	no	—
434	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
435	#548	C₂²×C₁₃	1	2	yes	—
436	#547	—	2	2	no	—
437	#547	—	2	1	no	—
438	#547	C₂²×C₁₃	1	2	yes	—
439	#547	C₂²×C₁₃	1	4	yes	—
440	#536	—	2	1	no	—
441	#536	—	2	2	no	—
442	#532	—	2	1	no	—
443	#532	C₂²×C₁₃	1	1	yes	characteristic
444	#532	C₂²×C₁₃	1	2	yes	—
445	#532	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
448	#529	—	2	2	no	—
449	#529	C₂²×C₁₃	1	2	yes	—
450	C₄×#41	—	2	1	no	—
451	C₄×#41	C₂²×C₁₃	1	2	yes	—
452	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
453	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
454	#501	C₂²×C₁₃	1	4	yes	—
455	#500	C₂²×C₁₃	1	2	yes	—
456	#489	C₂²×C₁₃	1	4	yes	—
457	#486	C₂²×C₁₃	1	2	yes	—
458	#484	C₂²×C₁₃	1	4	yes	—
459	#482	C₂²×C₁₃	1	4	yes	—
460	#481	C₂²×C₁₃	1	4	yes	—
461	#481	C₂²×C₁₃	1	2	yes	—
462	#480	C₂²×C₁₃	1	4	yes	—
463	#478	C₂²×C₁₃	1	4	yes	—
464	#477	C₂²×C₁₃	1	4	yes	—
465	#476	C₂²×C₁₃	1	4	yes	—
466	#475	C₂²×C₁₃	1	2	yes	—
467	#475	C₂²×C₁₃	1	2	yes	—
468	#475	C₂²×C₁₃	1	2	yes	—
469	#475	C₂²×C₁₃	1	2	yes	—
470	#475	C₂²×C₁₃	1	1	yes	characteristic
471	#475	C₂²×C₁₃	1	1	yes	characteristic
472	#474	C₂²×C₁₃	1	2	yes	—
473	#474	C₂²×C₁₃	1	2	yes	—
474	#474	C₂²×C₁₃	1	2	yes	—
475	#474	C₂²×C₁₃	1	2	yes	—
476	#469	C₂²×C₁₃	1	4	yes	—
477	#468	C₂²×C₁₃	1	4	yes	—
478	#466	C₂²×C₁₃	1	4	yes	—
479	#463	C₂²×C₁₃	1	4	yes	—
480	#460	C₂²×C₁₃	1	1	yes	characteristic
481	#460	C₂²×C₁₃	1	1	yes	characteristic
482	#459	C₂²×C₁₃	1	2	yes	—
483	#459	C₂²×C₁₃	1	2	yes	—
484	#449	C₂²×C₁₃	1	4	yes	—
485	#448	C₂²×C₁₃	1	2	yes	—
486	#446	C₂²×C₁₃	1	2	yes	—
487	#442	C₂²×C₁₃	1	4	yes	—
488	#440	C₂²×C₁₃	1	4	yes	—
489	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
490	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
491	#436	C₂²×C₁₃	1	2	yes	—
492	#435	C₂²×C₁₃	1	4	yes	—
493	#432	C₂²×C₁₃	1	2	yes	—
494	#431	C₂²×C₁₃	1	1	yes	characteristic
495	#428	C₂²×C₁₃	1	4	yes	—
496	C₂×#106	C₂²×C₁₃	1	2	yes	—
497	#423	C₂²×C₁₃	1	2	yes	—
498	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
499	#417	C₂²×C₁₃	1	4	yes	—
500	C₂×#103	C₂²×C₁₃	1	2	yes	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	2	1	no	—
503	C₂²×C₁₃	—	2	2	no	—
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	2	2	no	—
506	C₂²×C₁₃	—	4	2	no	—
507	C₂²×C₁₃	—	4	2	no	—
508	C₂²×C₁₃	—	4	2	no	—
509	C₂²×C₁₃	—	4	2	no	—
510	C₂²×C₁₃	—	4	2	no	—
511	C₂²×C₁₃	—	4	2	no	—
512	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
513	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
514	C₄×C₁₃	—	2	1	no	—
515	C₄×C₁₃	—	2	2	no	—
516	C₄×C₁₃	—	2	1	no	—
517	C₄×C₁₃	—	2	2	no	—
518	C₄×C₁₃	—	2	1	no	—
519	C₄×C₁₃	—	2	2	no	—
520	C₄×C₁₃	—	2	2	no	—
521	C₄×C₁₃	—	4	1	no	—
522	C₄×C₁₃	—	4	1	no	—
523	C₄×C₁₃	—	4	1	no	—
524	C₄×C₁₃	—	4	4	no	—
525	C₄×C₁₃	—	4	2	no	—
526	C₄×C₁₃	—	4	2	no	—
527	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
528	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
529	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	C₄×C₁₃	#585	1	1	yes	characteristic
531	2₋¹⁺⁴	—	4	8	no	—
532	C₂×#41	—	2	4	no	—
533	C₂×#41	—	2	2	no	—
534	C₂×#41	—	2	1	no	—
535	C₂×#41	—	2	2	no	—
536	C₂×#41	—	2	1	no	—
537	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
538	C₂×#41	C₂³×C₁₃	1	2	yes	—
539	C₂²×Q₈	—	2	2	no	—
540	C₂²×Q₈	—	2	2	no	—
541	C₂²×Q₈	—	2	1	no	—
542	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
544	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
545	C₂×D₈	C₂³×C₁₃	1	4	yes	—
546	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
547	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	—	2	2	no	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	2	no	—
552	C₄⋊Q₈	—	2	1	no	—
553	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
554	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
555	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
556	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
557	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
558	#127	—	2	1	no	—
559	#127	C₂³×C₁₃	1	1	yes	characteristic
560	#127	C₂³×C₁₃	1	1	yes	characteristic
561	#126	—	2	2	no	—
562	#126	—	2	2	no	—
563	#126	—	2	2	no	—
564	#125	—	2	2	no	—
565	#125	C₂³×C₁₃	1	2	yes	—
566	#124	—	2	1	no	—
567	#124	—	2	1	no	—
568	#124	—	2	2	no	—
569	#124	—	2	2	no	—
570	#124	—	2	1	no	—
571	#124	—	2	1	no	—
572	#124	C₂³×C₁₃	1	2	yes	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	#123	—	2	2	no	—
576	#123	—	2	4	no	—
577	#123	—	2	4	no	—
578	#123	—	2	4	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	4	no	—
584	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	1	no	—
588	#121	—	2	2	no	—
589	#121	—	2	1	no	—
590	#121	—	2	2	no	—
591	#121	C₂³×C₁₃	1	2	yes	—
592	#121	C₂³×C₁₃	1	2	yes	—
593	#121	C₂³×C₁₃	1	4	yes	—
594	#121	C₂³×C₁₃	1	2	yes	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
603	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
605	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	D₄×C₁₃	1	2	yes	—
617	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₁₃	1	2	yes	—
619	C₄×D₄	C₂³×C₁₃	1	2	yes	—
620	C₄×D₄	C₂³×C₁₃	1	2	yes	—
621	C₄×D₄	C₂³×C₁₃	1	4	yes	—
622	C₄×D₄	C₂³×C₁₃	1	2	yes	—
623	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
624	#117	—	2	2	no	—
625	#117	—	2	2	no	—
626	#117	D₄×C₁₃	1	1	yes	characteristic
627	#117	D₄×C₁₃	1	2	yes	—
628	#117	C₂³×C₁₃	1	2	yes	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	2	no	—
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	—	2	2	no	—
637	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
639	#107	C₂³×C₁₃	1	4	yes	—
640	#107	C₂³×C₁₃	1	4	yes	—
641	#107	C₂³×C₁₃	1	4	yes	—
642	#106	C₂³×C₁₃	1	4	yes	—
643	#106	C₂³×C₁₃	1	4	yes	—
644	#106	C₂³×C₁₃	1	2	yes	—
645	#106	C₂³×C₁₃	1	2	yes	—
646	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
647	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
648	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
649	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
650	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
651	#103	C₂³×C₁₃	1	4	yes	—
652	#103	C₂³×C₁₃	1	4	yes	—
653	#103	C₂³×C₁₃	1	2	yes	—
654	#103	C₂³×C₁₃	1	2	yes	—
655	#102	C₂³×C₁₃	1	4	yes	—
656	#102	C₂³×C₁₃	1	4	yes	—
657	#102	C₂³×C₁₃	1	2	yes	—
658	#102	C₂³×C₁₃	1	2	yes	—
659	#102	C₂³×C₁₃	1	4	yes	—
660	#102	C₂³×C₁₃	1	4	yes	—
661	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
662	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
663	#97	C₂³×C₁₃	1	4	yes	—
664	C₄×C₈	C₂³×C₁₃	1	2	yes	—
665	C₂×C₁₃	—	2	2	no	—
666	C₂×C₁₃	—	4	2	no	—
667	C₂×C₁₃	—	8	2	no	—
668	C₂×C₁₃	—	8	2	no	—
669	C₂×C₁₃	#3489	1	1	yes	characteristic
670	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
671	C₂×C₁₃	#3586	1	1	yes	characteristic
672	#41	—	2	4	no	—
673	#41	—	2	4	no	—
674	#41	—	4	2	no	—
675	#41	—	4	8	no	—
676	#41	—	4	16	no	—
677	#41	—	4	8	no	—
678	#41	—	4	4	no	—
679	#41	—	4	4	no	—
680	C₂×Q₈	—	2	1	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	4	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	4	1	no	—
688	C₂×Q₈	—	4	8	no	—
689	C₂×Q₈	—	4	8	no	—
690	C₂×Q₈	—	4	4	no	—
691	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
692	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
693	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
704	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
705	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
706	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
717	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
719	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
722	SD₁₆	—	2	4	no	—
723	SD₁₆	—	4	2	no	—
724	D₈	—	4	4	no	—
725	M₁₆	—	4	4	no	—
726	C₂×C₈	—	4	2	no	—
727	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
728	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
729	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
749	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
752	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
768	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
769	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
770	C₄²	—	2	1	no	—
771	C₄²	—	2	1	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	1	no	—
776	C₄²	C₂×D₄×C₁₃	1	2	yes	—
777	C₄²	C₂×D₄×C₁₃	1	2	yes	—
778	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
779	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
780	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
781	C₄²	C₂⁴×C₁₃	1	2	yes	—
782	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
783	C₁₃	#62111	1	1	yes	characteristic, direct product factor, Sylow
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
787	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
788	Q₈	—	2	2	no	—
789	Q₈	—	2	1	no	—
790	Q₈	—	2	1	no	—
791	Q₈	—	2	1	no	—
792	Q₈	—	4	2	no	—
793	Q₈	—	4	8	no	—
794	Q₈	—	4	2	no	—
795	Q₈	—	4	4	no	—
796	Q₈	—	4	4	no	—
797	Q₈	—	4	2	no	—
798	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	complemented
799	D₄	—	2	4	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	8	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	2	no	—
811	D₄	—	4	2	no	—
812	D₄	—	8	1	no	—
813	D₄	—	8	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	8	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	8	2	no	—
836	C₂×C₄	—	8	1	no	—
837	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
838	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
839	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
840	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
844	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
846	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
847	C₈	—	2	2	no	—
848	C₈	—	2	4	no	—
849	C₈	—	2	2	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
862	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
863	C₄	—	2	2	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	2	no	—
866	C₄	—	2	1	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	2	no	—
870	C₄	—	4	4	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	1	no	—
876	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
877	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
878	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
879	C₄	C₁₃×#585	1	1	yes	characteristic
880	C₂	—	2	2	no	—
881	C₂	—	4	2	no	—
882	C₂	—	8	2	no	—
883	C₂	—	8	2	no	—
884	C₂	C₁₃×#3489	1	1	yes	characteristic
885	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
886	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3499	C₂	semidirect
2. C₁₃×#3480	C₂	semidirect
3. C₁₃×#3386	C₂	semidirect
4. C₁₃×#3373	C₂	semidirect
5. C₁₃×#3353	C₂	semidirect
6. C₁₃×#3345	C₂	semidirect
7. C₁₃×#3332	C₂	semidirect
8. C₁₃×#3308	C₂	semidirect
9. C₁₃×#3251	C₂	semidirect
10. C₁₃×#3245	C₂	semidirect
11. C₁₃×#3239	C₂	semidirect
12. C₁₃×#3226	C₂	semidirect
13. C₁₃×#3115	C₂	semidirect
14. C₁₃×#3103	C₂	semidirect
15. C₁₃×#3079	C₂	semidirect
16. C₂×C₁₃×#475	C₂	semidirect
17. C₁₃×#2989	C₂	semidirect
229. #62111	C₁₃	direct (N × H)
341. #3499	C₂×C₁₃	semidirect
342. #3480	C₂×C₁₃	semidirect
343. #3386	C₂×C₁₃	semidirect
344. #3373	C₂×C₁₃	semidirect
345. #3353	C₂×C₁₃	semidirect
346. #3345	C₂×C₁₃	semidirect
347. #3332	C₂×C₁₃	semidirect
348. #3308	C₂×C₁₃	semidirect
349. #3251	C₂×C₁₃	semidirect
350. #3245	C₂×C₁₃	semidirect
351. #3239	C₂×C₁₃	semidirect
352. #3226	C₂×C₁₃	semidirect
353. #3115	C₂×C₁₃	semidirect
354. #3103	C₂×C₁₃	semidirect
355. #3079	C₂×C₁₃	semidirect
356. C₂×#475	C₂×C₁₃	semidirect
357. #2989	C₂×C₁₃	semidirect
372. Q₈×C₁₃	2₋¹⁺⁴	semidirect
783. C₁₃	#62111	direct (N × H)
798. Q₈	C₁₃×2₋¹⁺⁴	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3499	2
C₁₃×#3480	2
C₁₃×#3386	2
C₁₃×#3373	2
C₁₃×#3353	2
C₁₃×#3345	2
C₁₃×#3332	2
C₁₃×#3308	2
C₁₃×#3251	2
C₁₃×#3245	2
C₁₃×#3239	2
C₁₃×#3226	2
C₁₃×#3115	2
C₁₃×#3103	2
C₁₃×#3079	2
C₂×C₁₃×#475	2
C₁₃×#2989	2
#62111	13

Subgroups — C13×#62111 #15748450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62111 #15748450