Subgroups — C₁₃×#61405 #15747744

Order 3328.

1996 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3403	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3401	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3400	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3399	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3396	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3394	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3153	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3040	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3036	C₂	1	2	yes	maximal, complemented
15	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#137	C₂²	1	2	yes	—
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
23	C₁₃×#559	—	2	1	no	—
24	C₁₃×#559	—	2	1	no	—
25	C₁₃×#559	—	2	2	no	—
26	C₁₃×#559	C₂²	1	2	yes	—
27	C₁₃×#559	C₂²	1	2	yes	—
28	C₁₃×#559	C₂²	1	4	yes	—
29	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#559	C₂²	1	2	yes	complemented
31	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#556	C₂²	1	2	yes	complemented
34	C₁₃×#553	—	2	1	no	—
35	C₁₃×#553	—	2	2	no	—
36	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#548	—	2	1	no	—
38	C₁₃×#532	C₂²	1	2	yes	—
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
41	C₁₃×#529	—	2	2	no	—
42	C₁₃×#529	—	2	1	no	—
43	C₂×C₁₃×#124	—	2	1	no	—
44	C₂×C₁₃×#124	C₂²	1	2	yes	—
45	C₂×C₁₃×#123	—	2	2	no	—
46	C₄×C₁₃×#41	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×#41	C₂²	1	2	yes	—
49	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₁₃	—	2	1	no	—
52	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
53	C₁₃×#497	C₂²	1	4	yes	complemented
54	C₁₃×#496	C₂²	1	4	yes	—
55	C₁₃×#496	C₂²	1	4	yes	complemented
56	C₁₃×#495	C₂²	1	4	yes	complemented
57	C₁₃×#495	C₂²	1	4	yes	complemented
58	C₁₃×#493	C₂²	1	2	yes	—
59	C₁₃×#492	C₂²	1	2	yes	—
60	C₁₃×#464	C₂²	1	4	yes	complemented
61	C₁₃×#464	C₂²	1	4	yes	complemented
62	C₁₃×#464	C₂²	1	4	yes	complemented
63	C₁₃×#463	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	2	yes	complemented
68	C₁₃×#461	C₂²	1	4	yes	complemented
69	C₁₃×#460	C₂²	1	2	yes	—
70	C₁₃×#460	C₂²	1	2	yes	—
71	C₁₃×#460	C₂²	1	2	yes	complemented
72	C₁₃×#459	C₂²	1	2	yes	—
73	C₁₃×#459	C₂²	1	2	yes	—
74	C₁₃×#459	C₂²	1	4	yes	complemented
75	C₁₃×#446	C₂²	1	2	yes	complemented
76	C₁₃×#446	C₂²	1	4	yes	complemented
77	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
78	C₁₃×#442	C₂²	1	4	yes	complemented
79	C₁₃×#441	C₂²	1	2	yes	complemented
80	C₁₃×#440	C₂²	1	4	yes	complemented
81	C₁₃×#440	C₂²	1	2	yes	complemented
82	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
83	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
84	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
85	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
86	C₁₃×#428	C₂²	1	1	yes	characteristic
87	C₁₃×#423	C₂²	1	2	yes	—
88	C₁₃×#423	C₂²	1	1	yes	characteristic
89	C₁₃×#419	C₂²	1	1	yes	characteristic
90	C₁₃×#418	C₂²	1	2	yes	—
91	C₁₃×#417	C₂²	1	1	yes	characteristic
92	C₁₃×#417	C₂²	1	2	yes	—
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
97	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
99	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃	—	2	2	no	—
104	C₁₃×#137	—	2	4	no	—
105	C₁₃×#137	—	4	4	no	—
106	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
107	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
108	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
109	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
110	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
113	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×D₈	C₂³	1	4	yes	—
117	C₂×C₁₃×D₈	C₂³	1	4	yes	—
118	C₂×C₁₃×D₈	C₂³	1	4	yes	—
119	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
120	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
122	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
123	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₁₃×#127	—	2	1	no	—
125	C₁₃×#127	—	2	1	no	—
126	C₁₃×#127	C₂³	1	2	yes	—
127	C₁₃×#127	C₂³	1	2	yes	—
128	C₁₃×#127	C₂³	1	2	yes	—
129	C₁₃×#127	C₂³	1	1	yes	characteristic
130	C₁₃×#126	—	2	2	no	—
131	C₁₃×#126	—	2	2	no	—
132	C₁₃×#126	—	2	2	no	—
133	C₁₃×#125	—	2	1	no	—
134	C₁₃×#125	—	2	2	no	—
135	C₁₃×#124	—	2	2	no	—
136	C₁₃×#124	—	2	2	no	—
137	C₁₃×#124	—	2	4	no	—
138	C₁₃×#124	—	2	1	no	—
139	C₁₃×#124	—	2	2	no	—
140	C₁₃×#124	—	2	2	no	—
141	C₁₃×#124	—	2	2	no	—
142	C₁₃×#124	C₂³	1	2	yes	—
143	C₁₃×#124	C₂³	1	2	yes	—
144	C₁₃×#124	C₂³	1	4	yes	—
145	C₁₃×#124	C₂³	1	4	yes	—
146	C₁₃×#124	C₂³	1	2	yes	—
147	C₁₃×#123	—	2	4	no	—
148	C₁₃×#123	—	2	4	no	—
149	C₁₃×#123	—	2	4	no	—
150	C₁₃×#123	—	2	4	no	—
151	C₁₃×#123	—	2	2	no	—
152	C₁₃×#123	—	2	2	no	—
153	C₁₃×#123	—	2	2	no	—
154	C₁₃×C₂²⋊Q₈	—	2	1	no	—
155	C₁₃×C₂²⋊Q₈	—	2	2	no	—
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	—	2	1	no	—
160	C₁₃×#121	—	2	1	no	—
161	C₁₃×#121	—	2	2	no	—
162	C₄×Q₈×C₁₃	—	2	1	no	—
163	C₄×Q₈×C₁₃	—	2	1	no	—
164	C₄×Q₈×C₁₃	—	2	1	no	—
165	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	D₄	1	2	yes	—
167	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
176	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	1	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	—	2	2	no	—
183	C₄×D₄×C₁₃	—	2	4	no	—
184	C₄×D₄×C₁₃	—	2	1	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	1	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₄×D₄×C₁₃	—	2	1	no	—
192	C₄×D₄×C₁₃	C₂³	1	2	yes	—
193	C₄×D₄×C₁₃	C₂³	1	4	yes	—
194	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
195	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
196	C₄×D₄×C₁₃	C₂³	1	4	yes	—
197	C₄×D₄×C₁₃	C₂³	1	2	yes	—
198	C₁₃×#117	—	2	1	no	—
199	C₁₃×#117	—	2	2	no	—
200	C₁₃×#117	—	2	2	no	—
201	C₁₃×#117	—	2	1	no	—
202	C₁₃×#117	C₂³	1	1	yes	characteristic
203	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
205	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
206	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
208	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
209	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₄²×C₁₃	—	2	1	no	—
211	C₂×C₄²×C₁₃	—	2	2	no	—
212	C₂×C₄²×C₁₃	—	2	1	no	—
213	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
215	C₁₃×#107	C₂³	1	2	yes	—
216	C₁₃×#106	C₂³	1	2	yes	—
217	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
219	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
220	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#103	C₂³	1	2	yes	—
223	C₁₃×#103	C₂³	1	2	yes	—
224	C₁₃×#103	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×#102	C₂³	1	2	yes	—
227	C₁₃×#102	C₂³	1	4	yes	—
228	C₁₃×#102	C₂³	1	4	yes	—
229	C₁₃×#97	C₂³	1	2	yes	—
230	C₁₃×#97	C₂³	1	4	yes	—
231	C₄×C₈×C₁₃	C₂³	1	4	yes	—
232	C₄×C₈×C₁₃	C₂³	1	2	yes	—
233	#61405	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂⁴×C₁₃	—	2	2	no	—
235	C₁₃×#41	—	2	4	no	—
236	C₁₃×#41	—	2	2	no	—
237	C₁₃×#41	—	2	2	no	—
238	C₁₃×#41	—	2	4	no	—
239	C₁₃×#41	—	4	4	no	—
240	C₂×Q₈×C₁₃	—	2	1	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	2	no	—
243	C₂×Q₈×C₁₃	—	4	2	no	—
244	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
247	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
249	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	1	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	1	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	4	no	—
262	C₂×D₄×C₁₃	—	2	4	no	—
263	C₂×D₄×C₁₃	—	4	4	no	—
264	C₂×D₄×C₁₃	—	8	2	no	—
265	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	1	no	—
272	C₂²×C₄×C₁₃	—	2	2	no	—
273	C₂²×C₄×C₁₃	—	2	1	no	—
274	C₂²×C₄×C₁₃	—	2	2	no	—
275	C₂²×C₄×C₁₃	—	2	1	no	—
276	C₂²×C₄×C₁₃	—	2	4	no	—
277	C₂²×C₄×C₁₃	—	2	4	no	—
278	C₂²×C₄×C₁₃	—	8	4	no	—
279	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₁₃×Q₁₆	—	2	4	no	—
285	C₁₃×Q₁₆	—	4	4	no	—
286	C₁₃×SD₁₆	—	2	8	no	—
287	C₁₃×SD₁₆	—	2	4	no	—
288	C₁₃×SD₁₆	—	4	4	no	—
289	C₁₃×SD₁₆	—	4	4	no	—
290	C₁₃×SD₁₆	—	4	4	no	—
291	C₁₃×D₈	—	2	8	no	—
292	C₁₃×D₈	—	4	4	no	—
293	C₁₃×D₈	—	4	4	no	—
294	C₁₃×M₁₆	—	2	2	no	—
295	C₁₃×M₁₆	—	2	4	no	—
296	C₁₃×M₁₆	#41	1	4	yes	complemented
297	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
298	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
299	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
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	—	2	1	no	—
305	C₁₃×C₄⋊C₄	—	2	1	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	—	2	1	no	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	—	2	1	no	—
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	1	yes	characteristic
314	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
315	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
316	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
317	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
319	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
320	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
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	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	—	2	4	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	—	2	2	no	—
332	C₁₃×C₂²⋊C₄	—	2	1	no	—
333	C₁₃×C₂²⋊C₄	—	2	1	no	—
334	C₁₃×C₂²⋊C₄	—	2	2	no	—
335	C₁₃×C₂²⋊C₄	—	2	2	no	—
336	C₁₃×C₂²⋊C₄	—	2	2	no	—
337	C₁₃×C₂²⋊C₄	—	2	2	no	—
338	C₄²×C₁₃	—	2	1	no	—
339	C₄²×C₁₃	—	2	2	no	—
340	C₄²×C₁₃	—	2	1	no	—
341	C₄²×C₁₃	—	2	2	no	—
342	C₄²×C₁₃	—	2	2	no	—
343	C₄²×C₁₃	—	2	2	no	—
344	C₄²×C₁₃	—	2	1	no	—
345	C₄²×C₁₃	C₂×D₄	1	2	yes	—
346	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₁₃	C₂×D₄	1	2	yes	—
348	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₁₃	C₂⁴	1	2	yes	—
350	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₄²×C₁₃	C₂⁴	1	2	yes	—
352	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
353	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
354	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3403	C₂×C₁₃	1	4	yes	complemented
356	#3401	C₂×C₁₃	1	4	yes	complemented
357	#3400	C₂×C₁₃	1	2	yes	complemented
358	#3399	C₂×C₁₃	1	2	yes	complemented
359	#3396	C₂×C₁₃	1	2	yes	complemented
360	#3394	C₂×C₁₃	1	2	yes	complemented
361	#3153	C₂×C₁₃	1	2	yes	complemented
362	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#3040	C₂×C₁₃	1	2	yes	complemented
364	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
365	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#3036	C₂×C₁₃	1	2	yes	complemented
367	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
369	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
370	C₂³×C₁₃	—	2	2	no	—
371	C₂³×C₁₃	—	2	1	no	—
372	C₂³×C₁₃	—	2	4	no	—
373	C₂³×C₁₃	—	4	4	no	—
374	C₂³×C₁₃	—	4	4	no	—
375	C₂³×C₁₃	—	4	4	no	—
376	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
377	Q₈×C₁₃	—	2	2	no	—
378	Q₈×C₁₃	—	2	2	no	—
379	Q₈×C₁₃	—	2	2	no	—
380	Q₈×C₁₃	—	2	2	no	—
381	Q₈×C₁₃	—	2	1	no	—
382	Q₈×C₁₃	—	2	1	no	—
383	Q₈×C₁₃	—	2	2	no	—
384	Q₈×C₁₃	—	2	2	no	—
385	Q₈×C₁₃	—	4	2	no	—
386	Q₈×C₁₃	—	4	2	no	—
387	D₄×C₁₃	—	2	2	no	—
388	D₄×C₁₃	—	2	4	no	—
389	D₄×C₁₃	—	2	1	no	—
390	D₄×C₁₃	—	2	1	no	—
391	D₄×C₁₃	—	2	4	no	—
392	D₄×C₁₃	—	2	2	no	—
393	D₄×C₁₃	—	4	4	no	—
394	D₄×C₁₃	—	4	4	no	—
395	D₄×C₁₃	—	4	4	no	—
396	D₄×C₁₃	—	4	2	no	—
397	D₄×C₁₃	—	4	4	no	—
398	D₄×C₁₃	—	4	4	no	—
399	D₄×C₁₃	—	4	2	no	—
400	D₄×C₁₃	—	8	2	no	—
401	D₄×C₁₃	—	8	1	no	—
402	D₄×C₁₃	—	8	2	no	—
403	D₄×C₁₃	—	8	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	4	2	no	—
412	C₂×C₄×C₁₃	—	4	1	no	—
413	C₂×C₄×C₁₃	—	4	2	no	—
414	C₂×C₄×C₁₃	—	4	4	no	—
415	C₂×C₄×C₁₃	—	4	2	no	—
416	C₂×C₄×C₁₃	—	4	2	no	—
417	C₂×C₄×C₁₃	—	4	4	no	—
418	C₂×C₄×C₁₃	—	4	2	no	—
419	C₂×C₄×C₁₃	—	4	2	no	—
420	C₂×C₄×C₁₃	—	8	2	no	—
421	C₂×C₄×C₁₃	—	8	1	no	—
422	C₂×C₄×C₁₃	—	8	4	no	—
423	C₂×C₄×C₁₃	—	8	4	no	—
424	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
434	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
435	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
436	C₈×C₁₃	—	2	2	no	—
437	C₈×C₁₃	—	2	4	no	—
438	C₈×C₁₃	C₂×#41	1	4	yes	—
439	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#137	C₂²×C₁₃	1	2	yes	—
441	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
442	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
443	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
444	#559	—	2	1	no	—
445	#559	—	2	1	no	—
446	#559	—	2	2	no	—
447	#559	C₂²×C₁₃	1	2	yes	—
448	#559	C₂²×C₁₃	1	2	yes	—
449	#559	C₂²×C₁₃	1	4	yes	—
450	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
451	#559	C₂²×C₁₃	1	2	yes	complemented
452	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
454	#556	C₂²×C₁₃	1	2	yes	complemented
455	#553	—	2	1	no	—
456	#553	—	2	2	no	—
457	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	#548	—	2	1	no	—
459	#532	C₂²×C₁₃	1	1	yes	characteristic
460	#532	C₂²×C₁₃	1	2	yes	—
461	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
462	#529	—	2	2	no	—
463	#529	—	2	1	no	—
464	C₂×#124	—	2	1	no	—
465	C₂×#124	C₂²×C₁₃	1	2	yes	—
466	C₂×#123	—	2	2	no	—
467	C₄×#41	—	2	1	no	—
468	C₄×#41	C₂²×C₁₃	1	2	yes	—
469	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
470	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
471	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
472	C₂×C₄×D₄	—	2	1	no	—
473	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
474	#497	C₂²×C₁₃	1	4	yes	complemented
475	#496	C₂²×C₁₃	1	4	yes	—
476	#496	C₂²×C₁₃	1	4	yes	complemented
477	#495	C₂²×C₁₃	1	4	yes	complemented
478	#495	C₂²×C₁₃	1	4	yes	complemented
479	#493	C₂²×C₁₃	1	2	yes	—
480	#492	C₂²×C₁₃	1	2	yes	—
481	#464	C₂²×C₁₃	1	4	yes	complemented
482	#464	C₂²×C₁₃	1	4	yes	complemented
483	#464	C₂²×C₁₃	1	4	yes	complemented
484	#463	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	2	yes	complemented
489	#461	C₂²×C₁₃	1	4	yes	complemented
490	#460	C₂²×C₁₃	1	2	yes	—
491	#460	C₂²×C₁₃	1	2	yes	—
492	#460	C₂²×C₁₃	1	2	yes	complemented
493	#459	C₂²×C₁₃	1	2	yes	—
494	#459	C₂²×C₁₃	1	2	yes	—
495	#459	C₂²×C₁₃	1	4	yes	complemented
496	#446	C₂²×C₁₃	1	2	yes	complemented
497	#446	C₂²×C₁₃	1	4	yes	complemented
498	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
499	#442	C₂²×C₁₃	1	4	yes	complemented
500	#441	C₂²×C₁₃	1	2	yes	complemented
501	#440	C₂²×C₁₃	1	4	yes	complemented
502	#440	C₂²×C₁₃	1	2	yes	complemented
503	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
504	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
505	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
506	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
507	#428	C₂²×C₁₃	1	1	yes	characteristic
508	#423	C₂²×C₁₃	1	2	yes	—
509	#423	C₂²×C₁₃	1	1	yes	characteristic
510	#419	C₂²×C₁₃	1	1	yes	characteristic
511	#418	C₂²×C₁₃	1	2	yes	—
512	#417	C₂²×C₁₃	1	2	yes	—
513	#417	C₂²×C₁₃	1	1	yes	characteristic
514	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
515	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
516	C₂²×C₁₃	—	2	1	no	—
517	C₂²×C₁₃	—	2	1	no	—
518	C₂²×C₁₃	—	4	4	no	—
519	C₂²×C₁₃	—	4	2	no	—
520	C₂²×C₁₃	—	4	1	no	—
521	C₂²×C₁₃	—	4	2	no	—
522	C₂²×C₁₃	—	4	1	no	—
523	C₂²×C₁₃	—	4	4	no	—
524	C₂²×C₁₃	—	4	2	no	—
525	C₂²×C₁₃	—	4	1	no	—
526	C₂²×C₁₃	—	4	4	no	—
527	C₂²×C₁₃	—	8	8	no	—
528	C₂²×C₁₃	#550	1	2	yes	—
529	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
530	C₄×C₁₃	—	2	2	no	—
531	C₄×C₁₃	—	2	2	no	—
532	C₄×C₁₃	—	2	1	no	—
533	C₄×C₁₃	—	2	1	no	—
534	C₄×C₁₃	—	2	1	no	—
535	C₄×C₁₃	—	2	2	no	—
536	C₄×C₁₃	—	2	2	no	—
537	C₄×C₁₃	—	4	2	no	—
538	C₄×C₁₃	—	4	1	no	—
539	C₄×C₁₃	—	4	2	no	—
540	C₄×C₁₃	—	4	1	no	—
541	C₄×C₁₃	—	4	2	no	—
542	C₄×C₁₃	—	4	1	no	—
543	C₄×C₁₃	#550	1	2	yes	—
544	C₄×C₁₃	#575	1	2	yes	—
545	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
546	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂×#41	—	2	1	no	—
548	C₂×#41	C₂³×C₁₃	1	2	yes	—
549	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
550	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
551	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
552	C₂²×D₄	—	2	1	no	—
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
555	C₂³×C₄	—	2	2	no	—
556	#137	—	2	4	no	—
557	#137	—	4	4	no	—
558	AGL(1,ℤ/8)	—	2	8	no	—
559	AGL(1,ℤ/8)	—	4	4	no	—
560	AGL(1,ℤ/8)	—	4	4	no	—
561	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
562	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
563	C₂×SD₁₆	C₂³×C₁₃	1	4	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×SD₁₆	C₂³×C₁₃	1	4	yes	—
568	C₂×D₈	C₂³×C₁₃	1	4	yes	—
569	C₂×D₈	C₂³×C₁₃	1	4	yes	—
570	C₂×D₈	C₂³×C₁₃	1	4	yes	—
571	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
572	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
573	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
574	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
575	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
581	#127	C₂³×C₁₃	1	1	yes	characteristic
582	#126	—	2	2	no	—
583	#126	—	2	2	no	—
584	#126	—	2	2	no	—
585	#125	—	2	1	no	—
586	#125	—	2	2	no	—
587	#124	—	2	2	no	—
588	#124	—	2	2	no	—
589	#124	—	2	4	no	—
590	#124	—	2	1	no	—
591	#124	—	2	2	no	—
592	#124	—	2	2	no	—
593	#124	—	2	2	no	—
594	#124	C₂³×C₁₃	1	4	yes	—
595	#124	C₂³×C₁₃	1	4	yes	—
596	#124	C₂³×C₁₃	1	2	yes	—
597	#124	C₂³×C₁₃	1	2	yes	—
598	#124	C₂³×C₁₃	1	2	yes	—
599	#123	—	2	4	no	—
600	#123	—	2	4	no	—
601	#123	—	2	4	no	—
602	#123	—	2	4	no	—
603	#123	—	2	2	no	—
604	#123	—	2	2	no	—
605	#123	—	2	2	no	—
606	C₂²⋊Q₈	—	2	1	no	—
607	C₂²⋊Q₈	—	2	2	no	—
608	#121	—	2	1	no	—
609	#121	—	2	2	no	—
610	#121	—	2	2	no	—
611	#121	—	2	1	no	—
612	#121	—	2	1	no	—
613	#121	—	2	2	no	—
614	C₄×Q₈	—	2	1	no	—
615	C₄×Q₈	—	2	1	no	—
616	C₄×Q₈	—	2	1	no	—
617	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
618	C₄×Q₈	D₄×C₁₃	1	2	yes	—
619	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
620	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
621	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
622	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
623	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
624	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
625	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
626	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
627	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
628	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	4	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	1	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	C₂³×C₁₃	1	4	yes	—
645	C₄×D₄	C₂³×C₁₃	1	4	yes	—
646	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
647	C₄×D₄	C₂³×C₁₃	1	2	yes	—
648	C₄×D₄	C₂³×C₁₃	1	2	yes	—
649	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
650	#117	—	2	1	no	—
651	#117	—	2	2	no	—
652	#117	—	2	2	no	—
653	#117	—	2	1	no	—
654	#117	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
657	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	—	2	2	no	—
660	C₂×C₂²⋊C₄	—	2	2	no	—
661	C₂×C₂²⋊C₄	—	2	2	no	—
662	C₂×C₄²	—	2	1	no	—
663	C₂×C₄²	—	2	2	no	—
664	C₂×C₄²	—	2	1	no	—
665	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
666	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
667	#107	C₂³×C₁₃	1	2	yes	—
668	#106	C₂³×C₁₃	1	2	yes	—
669	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
670	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
671	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
672	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
673	#103	C₂³×C₁₃	1	4	yes	—
674	#103	C₂³×C₁₃	1	2	yes	—
675	#103	C₂³×C₁₃	1	2	yes	—
676	#103	C₂³×C₁₃	1	2	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	#97	C₂³×C₁₃	1	2	yes	—
682	#97	C₂³×C₁₃	1	4	yes	—
683	C₄×C₈	C₂³×C₁₃	1	4	yes	—
684	C₄×C₈	C₂³×C₁₃	1	2	yes	—
685	C₂×C₁₃	—	2	2	no	—
686	C₂×C₁₃	—	8	2	no	—
687	C₂×C₁₃	—	8	1	no	—
688	C₂×C₁₃	—	8	4	no	—
689	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
690	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
691	C₂×C₁₃	#3585	1	1	yes	characteristic
692	C₂⁴	—	2	2	no	—
693	#41	—	2	4	no	—
694	#41	—	2	2	no	—
695	#41	—	2	2	no	—
696	#41	—	2	4	no	—
697	#41	—	4	4	no	—
698	C₂×Q₈	—	2	1	no	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	4	2	no	—
702	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
703	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
705	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
706	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
707	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	4	4	no	—
722	C₂×D₄	—	8	2	no	—
723	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
724	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	4	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	8	4	no	—
737	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
738	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
739	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
740	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
742	Q₁₆	—	2	4	no	—
743	Q₁₆	—	4	4	no	—
744	SD₁₆	—	2	8	no	—
745	SD₁₆	—	2	4	no	—
746	SD₁₆	—	4	4	no	—
747	SD₁₆	—	4	4	no	—
748	SD₁₆	—	4	4	no	—
749	D₈	—	2	8	no	—
750	D₈	—	4	4	no	—
751	D₈	—	4	4	no	—
752	M₁₆	—	2	2	no	—
753	M₁₆	—	2	4	no	—
754	M₁₆	C₁₃×#41	1	4	yes	complemented
755	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
756	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
757	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
770	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
771	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
772	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
773	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
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	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	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	1	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₄²	—	2	1	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	1	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	1	no	—
803	C₄²	C₂×D₄×C₁₃	1	2	yes	—
804	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
805	C₄²	C₂×D₄×C₁₃	1	2	yes	—
806	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
807	C₄²	C₂⁴×C₁₃	1	2	yes	—
808	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
809	C₄²	C₂⁴×C₁₃	1	2	yes	—
810	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₁₃	#61405	1	1	yes	characteristic, direct product factor, Sylow
812	C₂³	—	2	2	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	4	4	no	—
816	C₂³	—	4	4	no	—
817	C₂³	—	4	4	no	—
818	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
819	Q₈	—	2	2	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	2	2	no	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	1	no	—
824	Q₈	—	2	1	no	—
825	Q₈	—	2	2	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	4	2	no	—
828	Q₈	—	4	2	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	4	no	—
831	D₄	—	2	1	no	—
832	D₄	—	2	1	no	—
833	D₄	—	2	4	no	—
834	D₄	—	2	2	no	—
835	D₄	—	4	4	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	2	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	2	no	—
842	D₄	—	8	2	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	2	no	—
845	D₄	—	8	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	8	4	no	—
863	C₂×C₄	—	8	4	no	—
864	C₂×C₄	—	8	2	no	—
865	C₂×C₄	—	8	1	no	—
866	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
868	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
869	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
870	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
875	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
876	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
877	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
878	C₈	—	2	2	no	—
879	C₈	—	2	4	no	—
880	C₈	C₂×C₁₃×#41	1	4	yes	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	4	no	—
886	C₂²	—	4	4	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	4	no	—
892	C₂²	—	8	8	no	—
893	C₂²	C₁₃×#550	1	2	yes	—
894	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
895	C₄	—	2	1	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	1	no	—
901	C₄	—	2	1	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₄	C₁₃×#550	1	2	yes	—
909	C₄	C₁₃×#575	1	2	yes	—
910	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
911	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
912	C₂	—	2	2	no	—
913	C₂	—	8	4	no	—
914	C₂	—	8	2	no	—
915	C₂	—	8	1	no	—
916	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
917	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
918	C₂	C₁₃×#3585	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3480	C₂	semidirect
2. C₂×C₁₃×#559	C₂	semidirect
3. C₁₃×#3403	C₂	semidirect
4. C₁₃×#3401	C₂	semidirect
5. C₁₃×#3400	C₂	semidirect
6. C₁₃×#3399	C₂	semidirect
7. C₁₃×#3396	C₂	semidirect
8. C₁₃×#3394	C₂	semidirect
9. C₁₃×#3153	C₂	semidirect
10. C₁₃×#3151	C₂	semidirect
11. C₁₃×#3040	C₂	semidirect
12. C₁₃×#3038	C₂	semidirect
13. C₁₃×#3037	C₂	semidirect
14. C₁₃×#3036	C₂	semidirect
15. Q₈×C₁₃×M₁₆	C₂	semidirect
16. C₄×C₁₃×#137	C₂	semidirect
17. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
29. C₁₃×#559	C₂²	semidirect
30. C₁₃×#559	C₂²	semidirect
31. C₁₃×#557	C₂²	semidirect
32. C₁₃×#556	C₂²	semidirect
33. C₁₃×#556	C₂²	semidirect
36. C₁₃×#550	C₂²	semidirect
53. C₁₃×#497	C₂²	semidirect
55. C₁₃×#496	C₂²	semidirect
56. C₁₃×#495	C₂²	semidirect
57. C₁₃×#495	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#464	C₂²	semidirect
62. C₁₃×#464	C₂²	semidirect
63. C₁₃×#463	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
71. C₁₃×#460	C₂²	semidirect
74. C₁₃×#459	C₂²	semidirect
75. C₁₃×#446	C₂²	semidirect
76. C₁₃×#446	C₂²	semidirect
77. C₈×Q₈×C₁₃	C₂²	semidirect
78. C₁₃×#442	C₂²	semidirect
79. C₁₃×#441	C₂²	semidirect
80. C₁₃×#440	C₂²	semidirect
81. C₁₃×#440	C₂²	semidirect
82. C₄×C₁₃×Q₁₆	C₂²	semidirect
83. C₄×C₁₃×SD₁₆	C₂²	semidirect
84. C₄×C₁₃×SD₁₆	C₂²	semidirect
85. C₄×C₁₃×D₈	C₂²	semidirect
233. #61405	C₁₃	direct (N × H)
296. C₁₃×M₁₆	#41	semidirect
353. #3480	C₂×C₁₃	semidirect
354. C₂×#559	C₂×C₁₃	semidirect
355. #3403	C₂×C₁₃	semidirect
356. #3401	C₂×C₁₃	semidirect
357. #3400	C₂×C₁₃	semidirect
358. #3399	C₂×C₁₃	semidirect
359. #3396	C₂×C₁₃	semidirect
360. #3394	C₂×C₁₃	semidirect
361. #3153	C₂×C₁₃	semidirect
362. #3151	C₂×C₁₃	semidirect
363. #3040	C₂×C₁₃	semidirect
364. #3038	C₂×C₁₃	semidirect
365. #3037	C₂×C₁₃	semidirect
366. #3036	C₂×C₁₃	semidirect
367. Q₈×M₁₆	C₂×C₁₃	semidirect
368. C₄×#137	C₂×C₁₃	semidirect
369. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
450. #559	C₂²×C₁₃	semidirect
451. #559	C₂²×C₁₃	semidirect
452. #557	C₂²×C₁₃	semidirect
453. #556	C₂²×C₁₃	semidirect
454. #556	C₂²×C₁₃	semidirect
457. #550	C₂²×C₁₃	semidirect
474. #497	C₂²×C₁₃	semidirect
476. #496	C₂²×C₁₃	semidirect
477. #495	C₂²×C₁₃	semidirect
478. #495	C₂²×C₁₃	semidirect
481. #464	C₂²×C₁₃	semidirect
482. #464	C₂²×C₁₃	semidirect
483. #464	C₂²×C₁₃	semidirect
484. #463	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
492. #460	C₂²×C₁₃	semidirect
495. #459	C₂²×C₁₃	semidirect
496. #446	C₂²×C₁₃	semidirect
497. #446	C₂²×C₁₃	semidirect
498. C₈×Q₈	C₂²×C₁₃	semidirect
499. #442	C₂²×C₁₃	semidirect
500. #441	C₂²×C₁₃	semidirect
501. #440	C₂²×C₁₃	semidirect
502. #440	C₂²×C₁₃	semidirect
503. C₄×Q₁₆	C₂²×C₁₃	semidirect
504. C₄×SD₁₆	C₂²×C₁₃	semidirect
505. C₄×SD₁₆	C₂²×C₁₃	semidirect
506. C₄×D₈	C₂²×C₁₃	semidirect
754. M₁₆	C₁₃×#41	semidirect
811. C₁₃	#61405	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×#3480	2
C₂×C₁₃×#559	2
C₁₃×#3403	2
C₁₃×#3401	2
C₁₃×#3400	2
C₁₃×#3399	2
C₁₃×#3396	2
C₁₃×#3394	2
C₁₃×#3153	2
C₁₃×#3151	2
C₁₃×#3040	2
C₁₃×#3038	2
C₁₃×#3037	2
C₁₃×#3036	2
Q₈×C₁₃×M₁₆	2
C₄×C₁₃×#137	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61405	13

Subgroups — C13×#61405 #15747744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61405 #15747744