Subgroups — C₁₃×#61995 #15748334

Order 3328.

1978 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3396	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3333	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3322	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3274	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3273	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3251	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3212	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3100	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3036	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
20	C₁₃×#559	—	2	1	no	—
21	C₁₃×#559	C₂²	1	2	yes	complemented
22	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#553	—	2	1	no	—
26	C₁₃×#553	C₂²	1	2	yes	—
27	C₁₃×#551	—	2	2	no	—
28	C₁₃×#550	—	2	1	no	—
29	C₁₃×#550	C₂²	1	2	yes	—
30	C₁₃×#546	—	2	1	no	—
31	C₁₃×#546	—	2	2	no	—
32	C₁₃×#546	C₂²	1	2	yes	—
33	C₁₃×#546	C₂²	1	4	yes	complemented
34	D₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#540	—	2	2	no	—
36	C₁₃×#535	—	2	1	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₁₃×#532	C₂²	1	2	yes	complemented
40	C₁₃×#532	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#529	—	2	1	no	—
43	C₁₃×#529	C₂²	1	2	yes	complemented
44	C₁₃×#525	—	2	2	no	—
45	C₁₃×#518	—	2	1	no	—
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	—	2	1	no	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
50	C₁₃×#495	C₂²	1	4	yes	complemented
51	C₁₃×#493	C₂²	1	2	yes	—
52	C₁₃×#488	C₂²	1	4	yes	complemented
53	C₁₃×#486	C₂²	1	2	yes	complemented
54	C₁₃×#485	C₂²	1	2	yes	complemented
55	C₁₃×#480	C₂²	1	4	yes	complemented
56	C₁₃×#478	C₂²	1	4	yes	complemented
57	C₁₃×#477	C₂²	1	2	yes	complemented
58	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#474	C₂²	1	2	yes	complemented
61	C₁₃×#469	C₂²	1	4	yes	complemented
62	C₁₃×#468	C₂²	1	4	yes	complemented
63	C₁₃×#468	C₂²	1	4	yes	complemented
64	C₁₃×#463	C₂²	1	4	yes	complemented
65	C₁₃×#463	C₂²	1	4	yes	complemented
66	C₁₃×#463	C₂²	1	4	yes	complemented
67	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#461	C₂²	1	2	yes	complemented
70	C₁₃×#460	C₂²	1	2	yes	complemented
71	C₁₃×#460	C₂²	1	2	yes	complemented
72	C₁₃×#460	C₂²	1	2	yes	complemented
73	C₁₃×#459	C₂²	1	2	yes	—
74	C₁₃×#459	C₂²	1	2	yes	—
75	C₁₃×#459	C₂²	1	2	yes	complemented
76	C₁₃×#459	C₂²	1	2	yes	complemented
77	C₁₃×#452	C₂²	1	2	yes	—
78	C₁₃×#452	C₂²	1	4	yes	complemented
79	C₁₃×#449	C₂²	1	4	yes	complemented
80	C₁₃×#447	C₂²	1	4	yes	complemented
81	C₁₃×#447	C₂²	1	4	yes	complemented
82	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
83	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
84	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
85	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
86	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
87	C₁₃×#436	C₂²	1	4	yes	complemented
88	C₁₃×#436	C₂²	1	2	yes	complemented
89	C₁₃×#431	C₂²	1	2	yes	complemented
90	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#423	C₂²	1	2	yes	complemented
92	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#418	C₂²	1	2	yes	complemented
94	C₁₃×#417	C₂²	1	4	yes	complemented
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
98	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×#41	C₂³	1	4	yes	—
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	—	2	1	no	—
103	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
104	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃	—	2	2	no	—
106	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
107	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
108	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×D₈	C₂³	1	4	yes	—
113	C₂×C₁₃×D₈	C₂³	1	4	yes	—
114	C₂×C₁₃×D₈	C₂³	1	4	yes	—
115	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×#127	—	2	2	no	—
121	C₁₃×#127	—	2	1	no	—
122	C₁₃×#127	—	2	1	no	—
123	C₁₃×#127	C₂³	1	2	yes	—
124	C₁₃×#127	C₂³	1	2	yes	—
125	C₁₃×#127	C₂³	1	1	yes	characteristic
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#126	—	2	2	no	—
128	C₁₃×#125	—	2	1	no	—
129	C₁₃×#125	—	2	1	no	—
130	C₁₃×#125	C₂³	1	2	yes	—
131	C₁₃×#124	—	2	1	no	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	—	2	1	no	—
134	C₁₃×#124	—	2	2	no	—
135	C₁₃×#124	C₂³	1	4	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	4	no	—
141	C₁₃×#123	—	2	4	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	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₃×#121	—	2	2	no	—
150	C₁₃×#121	—	2	1	no	—
151	C₁₃×#121	—	2	2	no	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	4	no	—
157	C₁₃×#121	—	2	4	no	—
158	C₁₃×#121	C₂³	1	2	yes	—
159	C₁₃×#121	C₂³	1	4	yes	—
160	C₁₃×#121	C₂³	1	2	yes	—
161	C₁₃×#120	—	2	2	no	—
162	C₁₃×#120	—	2	4	no	—
163	C₁₃×#120	—	2	2	no	—
164	C₄×Q₈×C₁₃	—	2	1	no	—
165	C₄×Q₈×C₁₃	D₄	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	1	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	1	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	2	no	—
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
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	D₄	1	1	yes	characteristic
185	C₄×D₄×C₁₃	D₄	1	2	yes	—
186	C₄×D₄×C₁₃	C₂³	1	2	yes	—
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₄×D₄×C₁₃	C₂³	1	4	yes	—
189	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₁₃	C₂³	1	2	yes	—
192	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₁₃	C₂³	1	2	yes	—
194	C₁₃×#117	—	2	1	no	—
195	C₁₃×#117	—	2	1	no	—
196	C₁₃×#117	—	2	2	no	—
197	C₁₃×#117	D₄	1	1	yes	characteristic
198	C₁₃×#117	D₄	1	2	yes	—
199	C₁₃×#117	C₂³	1	1	yes	characteristic
200	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₂×C₄²×C₁₃	—	2	1	no	—
206	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₁₃×#107	C₂³	1	2	yes	—
209	C₁₃×#107	C₂³	1	4	yes	—
210	C₁₃×#106	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	2	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₄×C₈×C₁₃	C₂³	1	4	yes	—
229	C₄×C₈×C₁₃	C₂³	1	2	yes	—
230	#61995	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂⁴×C₁₃	—	2	2	no	—
232	C₂⁴×C₁₃	—	2	2	no	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	4	2	no	—
235	C₁₃×#41	—	4	1	no	—
236	C₁₃×#41	—	4	4	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₁₃×#41	—	8	2	no	—
239	C₁₃×#41	—	8	4	no	—
240	C₂×Q₈×C₁₃	—	2	1	no	—
241	C₂×Q₈×C₁₃	—	2	1	no	—
242	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₁₃	—	2	4	no	—
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	4	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	4	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	1	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	1	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	—	4	2	no	—
260	C₂×D₄×C₁₃	—	4	2	no	—
261	C₂×D₄×C₁₃	—	4	2	no	—
262	C₂×D₄×C₁₃	—	4	4	no	—
263	C₂×D₄×C₁₃	—	4	4	no	—
264	C₂×D₄×C₁₃	—	8	2	no	—
265	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
267	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
268	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
269	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	1	no	—
272	C₂²×C₄×C₁₃	—	2	1	no	—
273	C₂²×C₄×C₁₃	—	2	1	no	—
274	C₂²×C₄×C₁₃	—	2	2	no	—
275	C₂²×C₄×C₁₃	—	2	2	no	—
276	C₂²×C₄×C₁₃	—	2	4	no	—
277	C₂²×C₄×C₁₃	—	2	4	no	—
278	C₂²×C₄×C₁₃	—	2	2	no	—
279	C₂²×C₄×C₁₃	—	8	4	no	—
280	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₁₃×Q₁₆	—	4	2	no	—
287	C₁₃×SD₁₆	—	2	4	no	—
288	C₁₃×SD₁₆	—	4	4	no	—
289	C₁₃×SD₁₆	—	4	4	no	—
290	C₁₃×D₈	—	2	8	no	—
291	C₁₃×D₈	—	4	4	no	—
292	C₁₃×D₈	—	4	4	no	—
293	C₁₃×M₁₆	—	4	2	no	—
294	C₁₃×M₁₆	—	4	4	no	—
295	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
296	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
297	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
298	C₁₃×C₄⋊C₄	—	2	1	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	1	no	—
302	C₁₃×C₄⋊C₄	—	2	1	no	—
303	C₁₃×C₄⋊C₄	—	2	1	no	—
304	C₁₃×C₄⋊C₄	—	2	1	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	1	no	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
311	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
313	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
315	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
316	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	1	no	—
321	C₁₃×C₂²⋊C₄	—	2	1	no	—
322	C₁₃×C₂²⋊C₄	—	2	4	no	—
323	C₁₃×C₂²⋊C₄	—	2	4	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	1	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	—	2	2	no	—
332	C₁₃×C₂²⋊C₄	—	2	4	no	—
333	C₁₃×C₂²⋊C₄	—	2	4	no	—
334	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
335	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
336	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
337	C₄²×C₁₃	—	2	1	no	—
338	C₄²×C₁₃	—	2	1	no	—
339	C₄²×C₁₃	—	2	1	no	—
340	C₄²×C₁₃	—	2	2	no	—
341	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₁₃	C₂×D₄	1	2	yes	—
344	C₄²×C₁₃	C₂×D₄	1	2	yes	—
345	C₄²×C₁₃	C₂⁴	1	2	yes	—
346	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
348	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3481	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3396	C₂×C₁₃	1	2	yes	complemented
351	#3361	C₂×C₁₃	1	2	yes	complemented
352	#3333	C₂×C₁₃	1	2	yes	complemented
353	#3322	C₂×C₁₃	1	4	yes	complemented
354	#3274	C₂×C₁₃	1	2	yes	complemented
355	#3273	C₂×C₁₃	1	4	yes	complemented
356	#3254	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#3251	C₂×C₁₃	1	2	yes	complemented
358	#3212	C₂×C₁₃	1	2	yes	complemented
359	#3205	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
361	#3100	C₂×C₁₃	1	2	yes	complemented
362	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#3036	C₂×C₁₃	1	2	yes	complemented
364	#2991	C₂×C₁₃	1	1	yes	characteristic, complemented
365	C₂³×C₁₃	—	2	1	no	—
366	C₂³×C₁₃	—	2	2	no	—
367	C₂³×C₁₃	—	2	4	no	—
368	C₂³×C₁₃	—	4	4	no	—
369	C₂³×C₁₃	—	4	4	no	—
370	C₂³×C₁₃	—	4	4	no	—
371	C₂³×C₁₃	—	8	2	no	—
372	C₂³×C₁₃	—	8	2	no	—
373	C₂³×C₁₃	—	8	2	no	—
374	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
376	Q₈×C₁₃	—	2	2	no	—
377	Q₈×C₁₃	—	2	2	no	—
378	Q₈×C₁₃	—	2	1	no	—
379	Q₈×C₁₃	—	2	1	no	—
380	Q₈×C₁₃	—	2	2	no	—
381	Q₈×C₁₃	—	4	2	no	—
382	Q₈×C₁₃	—	8	1	no	—
383	D₄×C₁₃	—	2	2	no	—
384	D₄×C₁₃	—	2	4	no	—
385	D₄×C₁₃	—	2	2	no	—
386	D₄×C₁₃	—	2	1	no	—
387	D₄×C₁₃	—	2	2	no	—
388	D₄×C₁₃	—	2	4	no	—
389	D₄×C₁₃	—	4	2	no	—
390	D₄×C₁₃	—	4	4	no	—
391	D₄×C₁₃	—	4	4	no	—
392	D₄×C₁₃	—	4	2	no	—
393	D₄×C₁₃	—	4	4	no	—
394	D₄×C₁₃	—	4	2	no	—
395	D₄×C₁₃	—	4	4	no	—
396	D₄×C₁₃	—	4	4	no	—
397	D₄×C₁₃	—	8	2	no	—
398	D₄×C₁₃	—	8	2	no	—
399	D₄×C₁₃	—	8	1	no	—
400	D₄×C₁₃	—	8	4	no	—
401	D₄×C₁₃	—	8	2	no	—
402	D₄×C₁₃	—	8	4	no	—
403	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	4	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	1	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	4	2	no	—
418	C₂×C₄×C₁₃	—	4	2	no	—
419	C₂×C₄×C₁₃	—	4	2	no	—
420	C₂×C₄×C₁₃	—	4	2	no	—
421	C₂×C₄×C₁₃	—	4	4	no	—
422	C₂×C₄×C₁₃	—	8	2	no	—
423	C₂×C₄×C₁₃	—	8	2	no	—
424	C₂×C₄×C₁₃	—	8	4	no	—
425	C₂×C₄×C₁₃	—	8	4	no	—
426	C₂×C₄×C₁₃	—	8	2	no	—
427	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
436	C₈×C₁₃	—	2	4	no	—
437	C₈×C₁₃	—	2	2	no	—
438	C₈×C₁₃	—	2	2	no	—
439	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
440	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
441	#559	—	2	1	no	—
442	#559	C₂²×C₁₃	1	2	yes	complemented
443	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
445	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
446	#553	—	2	1	no	—
447	#553	C₂²×C₁₃	1	2	yes	—
448	#551	—	2	2	no	—
449	#550	—	2	1	no	—
450	#550	C₂²×C₁₃	1	2	yes	—
451	#546	—	2	1	no	—
452	#546	—	2	2	no	—
453	#546	C₂²×C₁₃	1	2	yes	—
454	#546	C₂²×C₁₃	1	4	yes	complemented
455	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	#540	—	2	2	no	—
457	#535	—	2	1	no	—
458	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	#532	C₂²×C₁₃	1	1	yes	characteristic
460	#532	C₂²×C₁₃	1	2	yes	complemented
461	#532	C₂²×C₁₃	1	2	yes	complemented
462	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	#529	—	2	1	no	—
464	#529	C₂²×C₁₃	1	2	yes	complemented
465	#525	—	2	2	no	—
466	#518	—	2	1	no	—
467	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
468	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×C₄×D₄	—	2	1	no	—
470	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
471	#495	C₂²×C₁₃	1	4	yes	complemented
472	#493	C₂²×C₁₃	1	2	yes	—
473	#488	C₂²×C₁₃	1	4	yes	complemented
474	#486	C₂²×C₁₃	1	2	yes	complemented
475	#485	C₂²×C₁₃	1	2	yes	complemented
476	#480	C₂²×C₁₃	1	4	yes	complemented
477	#478	C₂²×C₁₃	1	4	yes	complemented
478	#477	C₂²×C₁₃	1	2	yes	complemented
479	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
480	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	#474	C₂²×C₁₃	1	2	yes	complemented
482	#469	C₂²×C₁₃	1	4	yes	complemented
483	#468	C₂²×C₁₃	1	4	yes	complemented
484	#468	C₂²×C₁₃	1	4	yes	complemented
485	#463	C₂²×C₁₃	1	4	yes	complemented
486	#463	C₂²×C₁₃	1	4	yes	complemented
487	#463	C₂²×C₁₃	1	4	yes	complemented
488	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
489	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	#461	C₂²×C₁₃	1	2	yes	complemented
491	#460	C₂²×C₁₃	1	2	yes	complemented
492	#460	C₂²×C₁₃	1	2	yes	complemented
493	#460	C₂²×C₁₃	1	2	yes	complemented
494	#459	C₂²×C₁₃	1	2	yes	—
495	#459	C₂²×C₁₃	1	2	yes	—
496	#459	C₂²×C₁₃	1	2	yes	complemented
497	#459	C₂²×C₁₃	1	2	yes	complemented
498	#452	C₂²×C₁₃	1	2	yes	—
499	#452	C₂²×C₁₃	1	4	yes	complemented
500	#449	C₂²×C₁₃	1	4	yes	complemented
501	#447	C₂²×C₁₃	1	4	yes	complemented
502	#447	C₂²×C₁₃	1	4	yes	complemented
503	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
504	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
505	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
506	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
507	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
508	#436	C₂²×C₁₃	1	2	yes	complemented
509	#436	C₂²×C₁₃	1	4	yes	complemented
510	#431	C₂²×C₁₃	1	2	yes	complemented
511	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
512	#423	C₂²×C₁₃	1	2	yes	complemented
513	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
514	#418	C₂²×C₁₃	1	2	yes	complemented
515	#417	C₂²×C₁₃	1	4	yes	complemented
516	C₂²×C₁₃	—	2	1	no	—
517	C₂²×C₁₃	—	2	2	no	—
518	C₂²×C₁₃	—	2	2	no	—
519	C₂²×C₁₃	—	2	1	no	—
520	C₂²×C₁₃	—	2	2	no	—
521	C₂²×C₁₃	—	2	2	no	—
522	C₂²×C₁₃	—	2	1	no	—
523	C₂²×C₁₃	—	4	1	no	—
524	C₂²×C₁₃	—	4	1	no	—
525	C₂²×C₁₃	—	4	4	no	—
526	C₂²×C₁₃	—	4	2	no	—
527	C₂²×C₁₃	—	4	2	no	—
528	C₂²×C₁₃	—	4	4	no	—
529	C₂²×C₁₃	—	4	2	no	—
530	C₂²×C₁₃	—	4	4	no	—
531	C₂²×C₁₃	—	8	8	no	—
532	C₂²×C₁₃	—	16	4	no	—
533	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
534	C₄×C₁₃	—	2	1	no	—
535	C₄×C₁₃	—	2	2	no	—
536	C₄×C₁₃	—	2	1	no	—
537	C₄×C₁₃	—	2	2	no	—
538	C₄×C₁₃	—	2	2	no	—
539	C₄×C₁₃	—	2	1	no	—
540	C₄×C₁₃	—	4	1	no	—
541	C₄×C₁₃	—	4	2	no	—
542	C₄×C₁₃	—	4	1	no	—
543	C₄×C₁₃	—	4	1	no	—
544	C₄×C₁₃	—	4	2	no	—
545	C₄×C₁₃	—	4	2	no	—
546	C₄×C₁₃	#575	1	2	yes	—
547	C₄×C₁₃	#576	1	2	yes	—
548	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
549	C₄×C₁₃	#585	1	1	yes	characteristic
550	C₂×#41	—	2	1	no	—
551	C₂×#41	—	2	2	no	—
552	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
553	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
554	C₂×#41	C₂³×C₁₃	1	4	yes	—
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
559	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
560	C₂³×C₄	—	2	2	no	—
561	AGL(1,ℤ/8)	—	4	4	no	—
562	AGL(1,ℤ/8)	—	4	8	no	—
563	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
564	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
565	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
566	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
567	C₂×D₈	C₂³×C₁₃	1	4	yes	—
568	C₂×D₈	C₂³×C₁₃	1	4	yes	—
569	C₂×D₈	C₂³×C₁₃	1	4	yes	—
570	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
571	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
572	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
573	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
574	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
575	#127	—	2	2	no	—
576	#127	—	2	1	no	—
577	#127	—	2	1	no	—
578	#127	C₂³×C₁₃	1	2	yes	—
579	#127	C₂³×C₁₃	1	2	yes	—
580	#127	C₂³×C₁₃	1	1	yes	characteristic
581	#126	—	2	2	no	—
582	#126	—	2	2	no	—
583	#125	—	2	1	no	—
584	#125	—	2	1	no	—
585	#125	C₂³×C₁₃	1	2	yes	—
586	#124	—	2	1	no	—
587	#124	—	2	2	no	—
588	#124	—	2	1	no	—
589	#124	—	2	2	no	—
590	#124	C₂³×C₁₃	1	2	yes	—
591	#124	C₂³×C₁₃	1	4	yes	—
592	#123	—	2	2	no	—
593	#123	—	2	2	no	—
594	#123	—	2	2	no	—
595	#123	—	2	4	no	—
596	#123	—	2	4	no	—
597	#123	—	2	2	no	—
598	C₂²⋊Q₈	—	2	1	no	—
599	C₂²⋊Q₈	—	2	1	no	—
600	C₂²⋊Q₈	—	2	2	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
603	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
604	#121	—	2	2	no	—
605	#121	—	2	1	no	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	1	no	—
610	#121	—	2	2	no	—
611	#121	—	2	4	no	—
612	#121	—	2	4	no	—
613	#121	C₂³×C₁₃	1	2	yes	—
614	#121	C₂³×C₁₃	1	2	yes	—
615	#121	C₂³×C₁₃	1	4	yes	—
616	#120	—	2	2	no	—
617	#120	—	2	4	no	—
618	#120	—	2	2	no	—
619	C₄×Q₈	—	2	1	no	—
620	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
621	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
622	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
623	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
624	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	1	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
640	C₄×D₄	D₄×C₁₃	1	2	yes	—
641	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₄×D₄	C₂³×C₁₃	1	2	yes	—
643	C₄×D₄	C₂³×C₁₃	1	2	yes	—
644	C₄×D₄	C₂³×C₁₃	1	2	yes	—
645	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
646	C₄×D₄	C₂³×C₁₃	1	4	yes	—
647	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
648	C₄×D₄	C₂³×C₁₃	1	2	yes	—
649	#117	—	2	1	no	—
650	#117	—	2	1	no	—
651	#117	—	2	2	no	—
652	#117	D₄×C₁₃	1	1	yes	characteristic
653	#117	D₄×C₁₃	1	2	yes	—
654	#117	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
657	C₂×C₂²⋊C₄	—	2	2	no	—
658	C₂×C₂²⋊C₄	—	2	2	no	—
659	C₂×C₂²⋊C₄	—	2	4	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
662	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
663	#107	C₂³×C₁₃	1	2	yes	—
664	#107	C₂³×C₁₃	1	4	yes	—
665	#106	C₂³×C₁₃	1	2	yes	—
666	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
667	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
668	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
669	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
670	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
671	#103	C₂³×C₁₃	1	2	yes	—
672	#103	C₂³×C₁₃	1	4	yes	—
673	#103	C₂³×C₁₃	1	2	yes	—
674	#103	C₂³×C₁₃	1	2	yes	—
675	#102	C₂³×C₁₃	1	4	yes	—
676	#102	C₂³×C₁₃	1	4	yes	—
677	#102	C₂³×C₁₃	1	4	yes	—
678	#102	C₂³×C₁₃	1	2	yes	—
679	#102	C₂³×C₁₃	1	4	yes	—
680	#102	C₂³×C₁₃	1	4	yes	—
681	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
682	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
683	C₄×C₈	C₂³×C₁₃	1	4	yes	—
684	C₄×C₈	C₂³×C₁₃	1	2	yes	—
685	C₂×C₁₃	—	4	2	no	—
686	C₂×C₁₃	—	4	1	no	—
687	C₂×C₁₃	—	4	2	no	—
688	C₂×C₁₃	—	8	2	no	—
689	C₂×C₁₃	—	8	4	no	—
690	C₂×C₁₃	#3488	1	1	yes	characteristic
691	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
692	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
693	C₂⁴	—	2	2	no	—
694	C₂⁴	—	2	2	no	—
695	#41	—	2	2	no	—
696	#41	—	4	2	no	—
697	#41	—	4	1	no	—
698	#41	—	4	4	no	—
699	#41	—	4	4	no	—
700	#41	—	8	2	no	—
701	#41	—	8	4	no	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	2	1	no	—
704	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
705	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
706	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	4	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	4	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	4	2	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂×D₄	—	4	4	no	—
726	C₂×D₄	—	8	2	no	—
727	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
728	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
729	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
730	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
731	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	4	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	8	4	no	—
742	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
744	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
748	Q₁₆	—	4	2	no	—
749	SD₁₆	—	2	4	no	—
750	SD₁₆	—	4	4	no	—
751	SD₁₆	—	4	4	no	—
752	D₈	—	2	8	no	—
753	D₈	—	4	4	no	—
754	D₈	—	4	4	no	—
755	M₁₆	—	4	2	no	—
756	M₁₆	—	4	4	no	—
757	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
758	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
759	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
773	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
774	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
775	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
776	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
777	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
778	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
779	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	1	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	4	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	—	2	1	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
797	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
798	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
799	C₄²	—	2	1	no	—
800	C₄²	—	2	1	no	—
801	C₄²	—	2	1	no	—
802	C₄²	—	2	2	no	—
803	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
804	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
805	C₄²	C₂×D₄×C₁₃	1	2	yes	—
806	C₄²	C₂×D₄×C₁₃	1	2	yes	—
807	C₄²	C₂⁴×C₁₃	1	2	yes	—
808	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
809	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
810	C₁₃	#61995	1	1	yes	characteristic, direct product factor, Sylow
811	C₂³	—	2	1	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	4	4	no	—
815	C₂³	—	4	4	no	—
816	C₂³	—	4	4	no	—
817	C₂³	—	8	2	no	—
818	C₂³	—	8	2	no	—
819	C₂³	—	8	2	no	—
820	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
821	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	2	no	—
824	Q₈	—	2	1	no	—
825	Q₈	—	2	1	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	4	2	no	—
828	Q₈	—	8	1	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	4	no	—
831	D₄	—	2	2	no	—
832	D₄	—	2	1	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	4	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	2	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	2	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	4	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	2	no	—
845	D₄	—	8	1	no	—
846	D₄	—	8	4	no	—
847	D₄	—	8	2	no	—
848	D₄	—	8	4	no	—
849	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	2	no	—
870	C₂×C₄	—	8	4	no	—
871	C₂×C₄	—	8	4	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
876	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
878	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
880	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
881	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
882	C₈	—	2	4	no	—
883	C₈	—	2	2	no	—
884	C₈	—	2	2	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	1	no	—
889	C₂²	—	2	1	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	4	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	4	no	—
898	C₂²	—	4	4	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	8	8	no	—
901	C₂²	—	16	4	no	—
902	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
903	C₄	—	2	1	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	1	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	2	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	2	no	—
915	C₄	C₁₃×#575	1	2	yes	—
916	C₄	C₁₃×#576	1	2	yes	—
917	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
918	C₄	C₁₃×#585	1	1	yes	characteristic
919	C₂	—	4	2	no	—
920	C₂	—	4	1	no	—
921	C₂	—	4	2	no	—
922	C₂	—	8	2	no	—
923	C₂	—	8	4	no	—
924	C₂	C₁₃×#3488	1	1	yes	characteristic
925	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
926	C₂	C₂×C₁₃×#576	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×#3508	C₂	semidirect
2. C₁₃×#3481	C₂	semidirect
3. C₁₃×#3396	C₂	semidirect
4. C₁₃×#3361	C₂	semidirect
5. C₁₃×#3333	C₂	semidirect
6. C₁₃×#3322	C₂	semidirect
7. C₁₃×#3274	C₂	semidirect
8. C₁₃×#3273	C₂	semidirect
9. C₁₃×#3254	C₂	semidirect
10. C₁₃×#3251	C₂	semidirect
11. C₁₃×#3212	C₂	semidirect
12. C₁₃×#3205	C₂	semidirect
13. C₁₃×#3107	C₂	semidirect
14. C₁₃×#3100	C₂	semidirect
15. C₁₃×#3038	C₂	semidirect
16. C₁₃×#3036	C₂	semidirect
17. C₁₃×#2991	C₂	semidirect
19. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₁₃×#559	C₂²	semidirect
22. C₁₃×#559	C₂²	semidirect
23. C₁₃×#554	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
33. C₁₃×#546	C₂²	semidirect
34. D₄²×C₁₃	C₂²	semidirect
37. C₁₃×#533	C₂²	semidirect
39. C₁₃×#532	C₂²	semidirect
40. C₁₃×#532	C₂²	semidirect
41. C₂×C₁₃×#127	C₂²	semidirect
43. C₁₃×#529	C₂²	semidirect
49. C₂×C₄×D₄×C₁₃	C₂²	semidirect
50. C₁₃×#495	C₂²	semidirect
52. C₁₃×#488	C₂²	semidirect
53. C₁₃×#486	C₂²	semidirect
54. C₁₃×#485	C₂²	semidirect
55. C₁₃×#480	C₂²	semidirect
56. C₁₃×#478	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
58. C₁₃×#475	C₂²	semidirect
59. C₁₃×#474	C₂²	semidirect
60. C₁₃×#474	C₂²	semidirect
61. C₁₃×#469	C₂²	semidirect
62. C₁₃×#468	C₂²	semidirect
63. C₁₃×#468	C₂²	semidirect
64. C₁₃×#463	C₂²	semidirect
65. C₁₃×#463	C₂²	semidirect
66. C₁₃×#463	C₂²	semidirect
67. C₁₃×#462	C₂²	semidirect
68. C₁₃×#461	C₂²	semidirect
69. C₁₃×#461	C₂²	semidirect
70. C₁₃×#460	C₂²	semidirect
71. C₁₃×#460	C₂²	semidirect
72. C₁₃×#460	C₂²	semidirect
75. C₁₃×#459	C₂²	semidirect
76. C₁₃×#459	C₂²	semidirect
78. C₁₃×#452	C₂²	semidirect
79. C₁₃×#449	C₂²	semidirect
80. C₁₃×#447	C₂²	semidirect
81. C₁₃×#447	C₂²	semidirect
82. C₈×Q₈×C₁₃	C₂²	semidirect
83. C₄×C₁₃×Q₁₆	C₂²	semidirect
84. C₄×C₁₃×SD₁₆	C₂²	semidirect
85. C₄×C₁₃×D₈	C₂²	semidirect
86. C₄×C₁₃×D₈	C₂²	semidirect
87. C₁₃×#436	C₂²	semidirect
88. C₁₃×#436	C₂²	semidirect
89. C₁₃×#431	C₂²	semidirect
90. C₁₃×#431	C₂²	semidirect
91. C₁₃×#423	C₂²	semidirect
92. C₁₃×#423	C₂²	semidirect
93. C₁₃×#418	C₂²	semidirect
94. C₁₃×#417	C₂²	semidirect
230. #61995	C₁₃	direct (N × H)
348. #3508	C₂×C₁₃	semidirect
349. #3481	C₂×C₁₃	semidirect
350. #3396	C₂×C₁₃	semidirect
351. #3361	C₂×C₁₃	semidirect
352. #3333	C₂×C₁₃	semidirect
353. #3322	C₂×C₁₃	semidirect
354. #3274	C₂×C₁₃	semidirect
355. #3273	C₂×C₁₃	semidirect
356. #3254	C₂×C₁₃	semidirect
357. #3251	C₂×C₁₃	semidirect
358. #3212	C₂×C₁₃	semidirect
359. #3205	C₂×C₁₃	semidirect
360. #3107	C₂×C₁₃	semidirect
361. #3100	C₂×C₁₃	semidirect
362. #3038	C₂×C₁₃	semidirect
363. #3036	C₂×C₁₃	semidirect
364. #2991	C₂×C₁₃	semidirect
440. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
442. #559	C₂²×C₁₃	semidirect
443. #559	C₂²×C₁₃	semidirect
444. #554	C₂²×C₁₃	semidirect
445. #554	C₂²×C₁₃	semidirect
454. #546	C₂²×C₁₃	semidirect
455. D₄²	C₂²×C₁₃	semidirect
458. #533	C₂²×C₁₃	semidirect
460. #532	C₂²×C₁₃	semidirect
461. #532	C₂²×C₁₃	semidirect
462. C₂×#127	C₂²×C₁₃	semidirect
464. #529	C₂²×C₁₃	semidirect
470. C₂×C₄×D₄	C₂²×C₁₃	semidirect
471. #495	C₂²×C₁₃	semidirect
473. #488	C₂²×C₁₃	semidirect
474. #486	C₂²×C₁₃	semidirect
475. #485	C₂²×C₁₃	semidirect
476. #480	C₂²×C₁₃	semidirect
477. #478	C₂²×C₁₃	semidirect
478. #477	C₂²×C₁₃	semidirect
479. #475	C₂²×C₁₃	semidirect
480. #474	C₂²×C₁₃	semidirect
481. #474	C₂²×C₁₃	semidirect
482. #469	C₂²×C₁₃	semidirect
483. #468	C₂²×C₁₃	semidirect
484. #468	C₂²×C₁₃	semidirect
485. #463	C₂²×C₁₃	semidirect
486. #463	C₂²×C₁₃	semidirect
487. #463	C₂²×C₁₃	semidirect
488. #462	C₂²×C₁₃	semidirect
489. #461	C₂²×C₁₃	semidirect
490. #461	C₂²×C₁₃	semidirect
491. #460	C₂²×C₁₃	semidirect
492. #460	C₂²×C₁₃	semidirect
493. #460	C₂²×C₁₃	semidirect
496. #459	C₂²×C₁₃	semidirect
497. #459	C₂²×C₁₃	semidirect
499. #452	C₂²×C₁₃	semidirect
500. #449	C₂²×C₁₃	semidirect
501. #447	C₂²×C₁₃	semidirect
502. #447	C₂²×C₁₃	semidirect
503. C₈×Q₈	C₂²×C₁₃	semidirect
504. C₄×Q₁₆	C₂²×C₁₃	semidirect
505. C₄×SD₁₆	C₂²×C₁₃	semidirect
506. C₄×D₈	C₂²×C₁₃	semidirect
507. C₄×D₈	C₂²×C₁₃	semidirect
508. #436	C₂²×C₁₃	semidirect
509. #436	C₂²×C₁₃	semidirect
510. #431	C₂²×C₁₃	semidirect
511. #431	C₂²×C₁₃	semidirect
512. #423	C₂²×C₁₃	semidirect
513. #423	C₂²×C₁₃	semidirect
514. #418	C₂²×C₁₃	semidirect
515. #417	C₂²×C₁₃	semidirect
810. C₁₃	#61995	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×#3508	2
C₁₃×#3481	2
C₁₃×#3396	2
C₁₃×#3361	2
C₁₃×#3333	2
C₁₃×#3322	2
C₁₃×#3274	2
C₁₃×#3273	2
C₁₃×#3254	2
C₁₃×#3251	2
C₁₃×#3212	2
C₁₃×#3205	2
C₁₃×#3107	2
C₁₃×#3100	2
C₁₃×#3038	2
C₁₃×#3036	2
C₁₃×#2991	2
#61995	13

Subgroups — C13×#61995 #15748334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61995 #15748334