Subgroups — C₁₃×#60823 #15747162

Order 3328.

2054 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3223	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3222	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3221	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3220	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3212	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3211	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3046	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3045	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3013	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₂×C₁₃×#135	C₂²	1	2	yes	—
23	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
24	C₁₃×#553	—	2	4	no	—
25	C₁₃×#553	—	2	2	no	—
26	C₁₃×#552	—	2	2	no	—
27	C₁₃×#548	—	2	2	no	—
28	C₁₃×#546	—	2	4	no	—
29	C₁₃×#546	—	2	2	no	—
30	C₁₃×#541	C₂²	1	2	yes	complemented
31	C₁₃×#540	C₂²	1	2	yes	complemented
32	C₁₃×#537	C₂²	1	2	yes	—
33	C₁₃×#536	C₂²	1	1	yes	characteristic
34	C₁₃×#536	C₂²	1	2	yes	—
35	C₁₃×#535	C₂²	1	1	yes	characteristic
36	C₁₃×#535	C₂²	1	2	yes	—
37	C₁₃×#532	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	2	yes	—
39	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#529	C₂²	1	4	yes	complemented
41	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#124	C₂²	1	2	yes	—
44	C₁₃×#520	C₂²	1	2	yes	complemented
45	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
46	C₁₃×#497	C₂²	1	2	yes	complemented
47	C₁₃×#496	C₂²	1	2	yes	complemented
48	C₁₃×#495	C₂²	1	2	yes	complemented
49	C₁₃×#495	C₂²	1	2	yes	complemented
50	C₁₃×#495	C₂²	1	4	yes	complemented
51	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#491	C₂²	1	2	yes	complemented
56	C₁₃×#490	C₂²	1	2	yes	complemented
57	C₁₃×#488	C₂²	1	4	yes	complemented
58	C₁₃×#488	C₂²	1	2	yes	complemented
59	C₁₃×#488	C₂²	1	2	yes	complemented
60	C₁₃×#488	C₂²	1	2	yes	complemented
61	C₁₃×#488	C₂²	1	2	yes	complemented
62	C₁₃×#464	C₂²	1	4	yes	complemented
63	C₁₃×#464	C₂²	1	4	yes	complemented
64	C₁₃×#463	C₂²	1	4	yes	complemented
65	C₁₃×#463	C₂²	1	4	yes	complemented
66	C₁₃×#462	C₂²	1	4	yes	complemented
67	C₁₃×#461	C₂²	1	4	yes	complemented
68	C₁₃×#460	C₂²	1	4	yes	complemented
69	C₁₃×#459	C₂²	1	4	yes	complemented
70	C₁₃×#452	C₂²	1	4	yes	—
71	C₁₃×#452	C₂²	1	4	yes	complemented
72	C₁₃×#451	C₂²	1	4	yes	complemented
73	C₁₃×#450	C₂²	1	4	yes	—
74	C₁₃×#449	C₂²	1	4	yes	—
75	C₁₃×#449	C₂²	1	4	yes	complemented
76	C₁₃×#448	C₂²	1	4	yes	complemented
77	C₁₃×#447	C₂²	1	4	yes	—
78	C₁₃×#433	C₂²	1	2	yes	complemented
79	C₁₃×#433	C₂²	1	2	yes	complemented
80	C₁₃×#431	C₂²	1	4	yes	complemented
81	C₁₃×#424	C₂²	1	2	yes	complemented
82	C₁₃×#417	C₂²	1	2	yes	—
83	C₁₃×#417	C₂²	1	2	yes	complemented
84	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
85	C₂×C₁₃×#102	C₂²	1	2	yes	—
86	C₁₃×#408	C₂²	1	2	yes	—
87	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×2₋¹⁺⁴	—	4	4	no	—
90	C₁₃×H(5,𝔽₂)	—	4	4	no	—
91	C₂×C₁₃×#41	—	2	1	no	—
92	C₂×C₁₃×#41	—	2	1	no	—
93	C₂×C₁₃×#41	—	2	2	no	—
94	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
97	C₂×C₁₃×#41	C₂³	1	2	yes	—
98	C₂×C₁₃×#41	C₂³	1	2	yes	—
99	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₁₃	—	2	1	no	—
101	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
103	C₂²×D₄×C₁₃	—	2	2	no	—
104	C₂²×D₄×C₁₃	—	2	1	no	—
105	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
107	C₁₃×#137	—	4	4	no	—
108	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
109	C₁₃×#135	—	4	4	no	—
110	C₁₃×#135	—	4	4	no	—
111	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
112	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
114	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
115	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
118	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
119	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
120	C₂×C₁₃×D₈	C₂³	1	2	yes	—
121	C₂×C₁₃×D₈	C₂³	1	4	yes	—
122	C₂×C₁₃×D₈	C₂³	1	2	yes	—
123	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
124	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
125	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₁₃×#127	C₂³	1	2	yes	—
129	C₁₃×#127	C₂³	1	1	yes	characteristic
130	C₁₃×#127	C₂³	1	1	yes	characteristic
131	C₁₃×#126	—	2	4	no	—
132	C₁₃×#126	—	2	4	no	—
133	C₁₃×#125	—	2	4	no	—
134	C₁₃×#125	—	2	2	no	—
135	C₁₃×#125	C₂³	1	2	yes	—
136	C₁₃×#125	C₂³	1	2	yes	—
137	C₁₃×#124	—	2	4	no	—
138	C₁₃×#124	—	2	2	no	—
139	C₁₃×#124	C₂³	1	2	yes	—
140	C₁₃×#124	C₂³	1	2	yes	—
141	C₁₃×#124	C₂³	1	2	yes	—
142	C₁₃×#124	C₂³	1	1	yes	characteristic
143	C₁₃×#124	C₂³	1	1	yes	characteristic
144	C₁₃×#124	C₂³	1	2	yes	—
145	C₁₃×#124	C₂³	1	2	yes	—
146	C₁₃×#123	—	2	4	no	—
147	C₁₃×#123	—	2	4	no	—
148	C₁₃×#123	—	2	2	no	—
149	C₁₃×#123	—	2	4	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	2	no	—
152	C₁₃×C₂²⋊Q₈	—	2	4	no	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	4	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	4	no	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	—	2	2	no	—
160	C₁₃×#121	—	2	4	no	—
161	C₁₃×#121	—	2	4	no	—
162	C₁₃×#121	C₂³	1	4	yes	—
163	C₁₃×#120	—	2	2	no	—
164	C₁₃×#120	—	2	4	no	—
165	C₄×Q₈×C₁₃	D₄	1	2	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
167	C₄×D₄×C₁₃	—	2	4	no	—
168	C₄×D₄×C₁₃	—	2	4	no	—
169	C₄×D₄×C₁₃	—	2	4	no	—
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	D₄	1	4	yes	—
173	C₄×D₄×C₁₃	D₄	1	2	yes	—
174	C₄×D₄×C₁₃	C₂³	1	4	yes	—
175	C₁₃×#117	—	2	2	no	—
176	C₁₃×#117	—	2	4	no	—
177	C₁₃×#117	C₂³	1	1	yes	characteristic
178	C₁₃×#117	C₂³	1	2	yes	—
179	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
183	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
184	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
186	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
187	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
188	C₁₃×#103	C₂³	1	4	yes	—
189	C₁₃×#103	C₂³	1	4	yes	—
190	C₁₃×#103	C₂³	1	4	yes	—
191	C₁₃×#103	C₂³	1	4	yes	—
192	C₁₃×#102	C₂³	1	4	yes	—
193	C₁₃×#102	C₂³	1	4	yes	—
194	C₁₃×#102	C₂³	1	4	yes	—
195	C₁₃×#102	C₂³	1	4	yes	—
196	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
198	C₁₃×#97	C₂³	1	2	yes	—
199	C₄×C₈×C₁₃	C₂³	1	2	yes	—
200	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
201	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
202	C₄×C₈×C₁₃	C₂³	1	2	yes	—
203	#60823	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂⁴×C₁₃	—	2	2	no	—
205	C₂⁴×C₁₃	—	2	1	no	—
206	C₁₃×#41	—	2	4	no	—
207	C₁₃×#41	—	2	4	no	—
208	C₁₃×#41	—	2	4	no	—
209	C₁₃×#41	—	2	4	no	—
210	C₁₃×#41	—	2	4	no	—
211	C₁₃×#41	—	4	4	no	—
212	C₁₃×#41	—	4	4	no	—
213	C₁₃×#41	—	4	8	no	—
214	C₁₃×#41	—	4	4	no	—
215	C₁₃×#41	—	4	4	no	—
216	C₂×Q₈×C₁₃	—	2	2	no	—
217	C₂×Q₈×C₁₃	—	2	1	no	—
218	C₂×Q₈×C₁₃	—	2	4	no	—
219	C₂×Q₈×C₁₃	—	4	4	no	—
220	C₂×Q₈×C₁₃	—	4	4	no	—
221	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
226	C₂×D₄×C₁₃	—	2	2	no	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	2	1	no	—
229	C₂×D₄×C₁₃	—	2	2	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	4	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
233	C₂×D₄×C₁₃	—	2	1	no	—
234	C₂×D₄×C₁₃	—	2	4	no	—
235	C₂×D₄×C₁₃	—	2	2	no	—
236	C₂×D₄×C₁₃	—	2	2	no	—
237	C₂×D₄×C₁₃	—	2	4	no	—
238	C₂×D₄×C₁₃	—	4	4	no	—
239	C₂×D₄×C₁₃	—	4	8	no	—
240	C₂×D₄×C₁₃	—	4	4	no	—
241	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
242	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	1	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	—	2	2	no	—
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	2	2	no	—
254	C₂²×C₄×C₁₃	—	2	1	no	—
255	C₂²×C₄×C₁₃	—	2	4	no	—
256	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₁₃×Q₁₆	—	4	2	no	—
261	C₁₃×Q₁₆	—	4	2	no	—
262	C₁₃×Q₁₆	—	4	4	no	—
263	C₁₃×SD₁₆	—	4	2	no	—
264	C₁₃×SD₁₆	—	4	2	no	—
265	C₁₃×SD₁₆	—	4	2	no	—
266	C₁₃×SD₁₆	—	4	2	no	—
267	C₁₃×SD₁₆	—	4	4	no	—
268	C₁₃×SD₁₆	—	4	4	no	—
269	C₁₃×D₈	—	4	2	no	—
270	C₁₃×D₈	—	4	2	no	—
271	C₁₃×D₈	—	4	4	no	—
272	C₁₃×M₁₆	—	2	4	no	—
273	C₂×C₈×C₁₃	—	2	4	no	—
274	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	4	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	—	2	4	no	—
281	C₁₃×C₄⋊C₄	—	2	4	no	—
282	C₁₃×C₄⋊C₄	—	2	4	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
286	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	2	2	no	—
295	C₁₃×C₂²⋊C₄	—	2	4	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	—	2	2	no	—
298	C₁₃×C₂²⋊C₄	—	2	2	no	—
299	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
300	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
301	C₄²×C₁₃	—	2	4	no	—
302	C₄²×C₁₃	C₂×D₄	1	4	yes	—
303	C₄²×C₁₃	C₂×D₄	1	2	yes	—
304	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
305	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₄²×C₁₃	C₂⁴	1	2	yes	—
307	#3512	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#3500	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#3223	C₂×C₁₃	1	2	yes	complemented
310	#3222	C₂×C₁₃	1	2	yes	complemented
311	#3221	C₂×C₁₃	1	2	yes	complemented
312	#3220	C₂×C₁₃	1	2	yes	complemented
313	#3212	C₂×C₁₃	1	4	yes	complemented
314	#3211	C₂×C₁₃	1	4	yes	complemented
315	#3153	C₂×C₁₃	1	1	yes	characteristic, complemented
316	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#3142	C₂×C₁₃	1	1	yes	characteristic, complemented
318	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
319	#3046	C₂×C₁₃	1	2	yes	complemented
320	#3045	C₂×C₁₃	1	2	yes	complemented
321	#3013	C₂×C₁₃	1	2	yes	complemented
322	#3012	C₂×C₁₃	1	2	yes	complemented
323	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
324	C₂³×C₁₃	—	2	2	no	—
325	C₂³×C₁₃	—	2	2	no	—
326	C₂³×C₁₃	—	2	1	no	—
327	C₂³×C₁₃	—	2	1	no	—
328	C₂³×C₁₃	—	4	4	no	—
329	C₂³×C₁₃	—	4	2	no	—
330	C₂³×C₁₃	—	8	2	no	—
331	C₂³×C₁₃	—	8	4	no	—
332	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
333	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
334	Q₈×C₁₃	—	2	2	no	—
335	Q₈×C₁₃	—	2	2	no	—
336	Q₈×C₁₃	—	2	2	no	—
337	Q₈×C₁₃	—	2	4	no	—
338	Q₈×C₁₃	—	2	2	no	—
339	Q₈×C₁₃	—	2	2	no	—
340	Q₈×C₁₃	—	4	4	no	—
341	Q₈×C₁₃	—	4	2	no	—
342	D₄×C₁₃	—	2	4	no	—
343	D₄×C₁₃	—	2	2	no	—
344	D₄×C₁₃	—	2	2	no	—
345	D₄×C₁₃	—	2	2	no	—
346	D₄×C₁₃	—	2	4	no	—
347	D₄×C₁₃	—	2	2	no	—
348	D₄×C₁₃	—	2	2	no	—
349	D₄×C₁₃	—	4	4	no	—
350	D₄×C₁₃	—	4	4	no	—
351	D₄×C₁₃	—	4	4	no	—
352	D₄×C₁₃	—	4	2	no	—
353	D₄×C₁₃	—	4	4	no	—
354	D₄×C₁₃	—	4	2	no	—
355	D₄×C₁₃	—	4	2	no	—
356	D₄×C₁₃	—	8	4	no	—
357	D₄×C₁₃	—	8	2	no	—
358	D₄×C₁₃	—	8	2	no	—
359	D₄×C₁₃	—	8	4	no	—
360	C₂×C₄×C₁₃	—	2	4	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	4	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	4	4	no	—
367	C₂×C₄×C₁₃	—	4	2	no	—
368	C₂×C₄×C₁₃	—	4	4	no	—
369	C₂×C₄×C₁₃	—	4	4	no	—
370	C₂×C₄×C₁₃	—	4	4	no	—
371	C₂×C₄×C₁₃	—	4	2	no	—
372	C₂×C₄×C₁₃	—	4	2	no	—
373	C₂×C₄×C₁₃	—	4	2	no	—
374	C₂×C₄×C₁₃	—	4	4	no	—
375	C₂×C₄×C₁₃	—	8	4	no	—
376	C₂×C₄×C₁₃	—	8	2	no	—
377	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
378	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
383	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
384	C₈×C₁₃	—	2	2	no	—
385	C₈×C₁₃	—	2	2	no	—
386	C₈×C₁₃	—	2	4	no	—
387	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
390	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
391	C₂×#135	C₂²×C₁₃	1	2	yes	—
392	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
393	#553	—	2	4	no	—
394	#553	—	2	2	no	—
395	#552	—	2	2	no	—
396	#548	—	2	2	no	—
397	#546	—	2	4	no	—
398	#546	—	2	2	no	—
399	#541	C₂²×C₁₃	1	2	yes	complemented
400	#540	C₂²×C₁₃	1	2	yes	complemented
401	#537	C₂²×C₁₃	1	2	yes	—
402	#536	C₂²×C₁₃	1	2	yes	—
403	#536	C₂²×C₁₃	1	1	yes	characteristic
404	#535	C₂²×C₁₃	1	2	yes	—
405	#535	C₂²×C₁₃	1	1	yes	characteristic
406	#532	C₂²×C₁₃	1	1	yes	characteristic
407	#532	C₂²×C₁₃	1	2	yes	—
408	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
409	#529	C₂²×C₁₃	1	4	yes	complemented
410	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#124	C₂²×C₁₃	1	2	yes	—
413	#520	C₂²×C₁₃	1	2	yes	complemented
414	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
415	#497	C₂²×C₁₃	1	2	yes	complemented
416	#496	C₂²×C₁₃	1	2	yes	complemented
417	#495	C₂²×C₁₃	1	2	yes	complemented
418	#495	C₂²×C₁₃	1	2	yes	complemented
419	#495	C₂²×C₁₃	1	4	yes	complemented
420	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
421	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
422	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
424	#491	C₂²×C₁₃	1	2	yes	complemented
425	#490	C₂²×C₁₃	1	2	yes	complemented
426	#488	C₂²×C₁₃	1	4	yes	complemented
427	#488	C₂²×C₁₃	1	2	yes	complemented
428	#488	C₂²×C₁₃	1	2	yes	complemented
429	#488	C₂²×C₁₃	1	2	yes	complemented
430	#488	C₂²×C₁₃	1	2	yes	complemented
431	#464	C₂²×C₁₃	1	4	yes	complemented
432	#464	C₂²×C₁₃	1	4	yes	complemented
433	#463	C₂²×C₁₃	1	4	yes	complemented
434	#463	C₂²×C₁₃	1	4	yes	complemented
435	#462	C₂²×C₁₃	1	4	yes	complemented
436	#461	C₂²×C₁₃	1	4	yes	complemented
437	#460	C₂²×C₁₃	1	4	yes	complemented
438	#459	C₂²×C₁₃	1	4	yes	complemented
439	#452	C₂²×C₁₃	1	4	yes	—
440	#452	C₂²×C₁₃	1	4	yes	complemented
441	#451	C₂²×C₁₃	1	4	yes	complemented
442	#450	C₂²×C₁₃	1	4	yes	—
443	#449	C₂²×C₁₃	1	4	yes	—
444	#449	C₂²×C₁₃	1	4	yes	complemented
445	#448	C₂²×C₁₃	1	4	yes	complemented
446	#447	C₂²×C₁₃	1	4	yes	—
447	#433	C₂²×C₁₃	1	2	yes	complemented
448	#433	C₂²×C₁₃	1	2	yes	complemented
449	#431	C₂²×C₁₃	1	4	yes	complemented
450	#424	C₂²×C₁₃	1	2	yes	complemented
451	#417	C₂²×C₁₃	1	2	yes	—
452	#417	C₂²×C₁₃	1	2	yes	complemented
453	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
454	C₂×#102	C₂²×C₁₃	1	2	yes	—
455	#408	C₂²×C₁₃	1	2	yes	—
456	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
457	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	C₂²×C₁₃	—	2	2	no	—
459	C₂²×C₁₃	—	2	4	no	—
460	C₂²×C₁₃	—	2	2	no	—
461	C₂²×C₁₃	—	4	2	no	—
462	C₂²×C₁₃	—	4	2	no	—
463	C₂²×C₁₃	—	4	2	no	—
464	C₂²×C₁₃	—	4	4	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	4	1	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	—	4	1	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	16	2	no	—
471	C₂²×C₁₃	—	16	4	no	—
472	C₂²×C₁₃	#535	1	2	yes	—
473	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
474	C₄×C₁₃	—	2	2	no	—
475	C₄×C₁₃	—	2	4	no	—
476	C₄×C₁₃	—	2	2	no	—
477	C₄×C₁₃	—	2	2	no	—
478	C₄×C₁₃	—	4	4	no	—
479	C₄×C₁₃	—	4	1	no	—
480	C₄×C₁₃	—	4	2	no	—
481	C₄×C₁₃	—	4	1	no	—
482	C₄×C₁₃	—	4	2	no	—
483	C₄×C₁₃	#535	1	2	yes	—
484	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
485	2₋¹⁺⁴	—	4	4	no	—
486	H(5,𝔽₂)	—	4	4	no	—
487	C₂×#41	—	2	1	no	—
488	C₂×#41	—	2	1	no	—
489	C₂×#41	—	2	2	no	—
490	C₂×#41	C₂³×C₁₃	1	2	yes	—
491	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
492	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
493	C₂×#41	C₂³×C₁₃	1	2	yes	—
494	C₂×#41	C₂³×C₁₃	1	2	yes	—
495	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
496	C₂²×Q₈	—	2	1	no	—
497	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
498	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
499	C₂²×D₄	—	2	2	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
503	#137	—	4	4	no	—
504	AGL(1,ℤ/8)	—	4	4	no	—
505	#135	—	4	4	no	—
506	#135	—	4	4	no	—
507	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
508	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
509	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
510	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
511	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
512	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
513	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
514	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
515	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
516	C₂×D₈	C₂³×C₁₃	1	2	yes	—
517	C₂×D₈	C₂³×C₁₃	1	2	yes	—
518	C₂×D₈	C₂³×C₁₃	1	4	yes	—
519	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
520	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
521	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
522	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
523	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
524	#127	C₂³×C₁₃	1	2	yes	—
525	#127	C₂³×C₁₃	1	1	yes	characteristic
526	#127	C₂³×C₁₃	1	1	yes	characteristic
527	#126	—	2	4	no	—
528	#126	—	2	4	no	—
529	#125	—	2	4	no	—
530	#125	—	2	2	no	—
531	#125	C₂³×C₁₃	1	2	yes	—
532	#125	C₂³×C₁₃	1	2	yes	—
533	#124	—	2	4	no	—
534	#124	—	2	2	no	—
535	#124	C₂³×C₁₃	1	2	yes	—
536	#124	C₂³×C₁₃	1	1	yes	characteristic
537	#124	C₂³×C₁₃	1	2	yes	—
538	#124	C₂³×C₁₃	1	2	yes	—
539	#124	C₂³×C₁₃	1	2	yes	—
540	#124	C₂³×C₁₃	1	2	yes	—
541	#124	C₂³×C₁₃	1	1	yes	characteristic
542	#123	—	2	4	no	—
543	#123	—	2	4	no	—
544	#123	—	2	2	no	—
545	#123	—	2	4	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	4	no	—
549	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
550	#121	—	2	2	no	—
551	#121	—	2	4	no	—
552	#121	—	2	2	no	—
553	#121	—	2	4	no	—
554	#121	—	2	2	no	—
555	#121	—	2	2	no	—
556	#121	—	2	4	no	—
557	#121	—	2	4	no	—
558	#121	C₂³×C₁₃	1	4	yes	—
559	#120	—	2	2	no	—
560	#120	—	2	4	no	—
561	C₄×Q₈	D₄×C₁₃	1	2	yes	—
562	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
563	C₄×D₄	—	2	4	no	—
564	C₄×D₄	—	2	4	no	—
565	C₄×D₄	—	2	4	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	D₄×C₁₃	1	4	yes	—
569	C₄×D₄	D₄×C₁₃	1	2	yes	—
570	C₄×D₄	C₂³×C₁₃	1	4	yes	—
571	#117	—	2	2	no	—
572	#117	—	2	4	no	—
573	#117	C₂³×C₁₃	1	1	yes	characteristic
574	#117	C₂³×C₁₃	1	2	yes	—
575	C₂×C₄⋊C₄	—	2	2	no	—
576	C₂×C₄⋊C₄	—	2	2	no	—
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
578	C₂×C₂²⋊C₄	—	2	2	no	—
579	C₂×C₂²⋊C₄	—	2	4	no	—
580	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
582	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
583	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
584	#103	C₂³×C₁₃	1	4	yes	—
585	#103	C₂³×C₁₃	1	4	yes	—
586	#103	C₂³×C₁₃	1	4	yes	—
587	#103	C₂³×C₁₃	1	4	yes	—
588	#102	C₂³×C₁₃	1	4	yes	—
589	#102	C₂³×C₁₃	1	4	yes	—
590	#102	C₂³×C₁₃	1	4	yes	—
591	#102	C₂³×C₁₃	1	4	yes	—
592	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
593	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
594	#97	C₂³×C₁₃	1	2	yes	—
595	C₄×C₈	C₂³×C₁₃	1	2	yes	—
596	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
598	C₄×C₈	C₂³×C₁₃	1	2	yes	—
599	C₂×C₁₃	—	2	2	no	—
600	C₂×C₁₃	—	4	2	no	—
601	C₂×C₁₃	—	8	2	no	—
602	C₂×C₁₃	—	8	1	no	—
603	C₂×C₁₃	—	8	2	no	—
604	C₂×C₁₃	—	8	1	no	—
605	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
606	C₂×C₁₃	#3584	1	2	yes	—
607	C₂⁴	—	2	2	no	—
608	C₂⁴	—	2	1	no	—
609	#41	—	2	4	no	—
610	#41	—	2	4	no	—
611	#41	—	2	4	no	—
612	#41	—	2	4	no	—
613	#41	—	2	4	no	—
614	#41	—	4	4	no	—
615	#41	—	4	4	no	—
616	#41	—	4	8	no	—
617	#41	—	4	4	no	—
618	#41	—	4	4	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	4	no	—
622	C₂×Q₈	—	4	4	no	—
623	C₂×Q₈	—	4	4	no	—
624	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
626	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
627	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
628	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	4	4	no	—
642	C₂×D₄	—	4	8	no	—
643	C₂×D₄	—	4	4	no	—
644	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
645	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
646	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
647	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
648	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
649	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
660	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
661	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
663	Q₁₆	—	4	2	no	—
664	Q₁₆	—	4	2	no	—
665	Q₁₆	—	4	4	no	—
666	SD₁₆	—	4	2	no	—
667	SD₁₆	—	4	2	no	—
668	SD₁₆	—	4	2	no	—
669	SD₁₆	—	4	2	no	—
670	SD₁₆	—	4	4	no	—
671	SD₁₆	—	4	4	no	—
672	D₈	—	4	2	no	—
673	D₈	—	4	2	no	—
674	D₈	—	4	4	no	—
675	M₁₆	—	2	4	no	—
676	C₂×C₈	—	2	4	no	—
677	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
678	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
679	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
689	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
690	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
703	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
704	C₄²	—	2	4	no	—
705	C₄²	C₂×D₄×C₁₃	1	4	yes	—
706	C₄²	C₂×D₄×C₁₃	1	2	yes	—
707	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
708	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
709	C₄²	C₂⁴×C₁₃	1	2	yes	—
710	C₁₃	#60823	1	1	yes	characteristic, direct product factor, Sylow
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	4	4	no	—
716	C₂³	—	4	2	no	—
717	C₂³	—	8	2	no	—
718	C₂³	—	8	4	no	—
719	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
720	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
721	Q₈	—	2	2	no	—
722	Q₈	—	2	2	no	—
723	Q₈	—	2	2	no	—
724	Q₈	—	2	4	no	—
725	Q₈	—	2	2	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	4	4	no	—
728	Q₈	—	4	2	no	—
729	D₄	—	2	4	no	—
730	D₄	—	2	2	no	—
731	D₄	—	2	2	no	—
732	D₄	—	2	2	no	—
733	D₄	—	2	4	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	4	4	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	2	no	—
740	D₄	—	4	4	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	2	no	—
743	D₄	—	8	4	no	—
744	D₄	—	8	2	no	—
745	D₄	—	8	2	no	—
746	D₄	—	8	4	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	4	4	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	4	4	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	8	4	no	—
763	C₂×C₄	—	8	2	no	—
764	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
765	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
766	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
767	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
768	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
769	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
770	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
771	C₈	—	2	2	no	—
772	C₈	—	2	2	no	—
773	C₈	—	2	4	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	4	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	16	2	no	—
787	C₂²	—	16	4	no	—
788	C₂²	C₁₃×#535	1	2	yes	—
789	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
790	C₄	—	2	2	no	—
791	C₄	—	2	4	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	4	4	no	—
795	C₄	—	4	1	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	2	no	—
799	C₄	C₁₃×#535	1	2	yes	—
800	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
801	C₂	—	2	2	no	—
802	C₂	—	4	2	no	—
803	C₂	—	8	2	no	—
804	C₂	—	8	1	no	—
805	C₂	—	8	2	no	—
806	C₂	—	8	1	no	—
807	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
808	C₂	C₁₃×#3584	1	2	yes	—

	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×#3512	C₂	semidirect
2. C₁₃×#3500	C₂	semidirect
3. C₁₃×#3223	C₂	semidirect
4. C₁₃×#3222	C₂	semidirect
5. C₁₃×#3221	C₂	semidirect
6. C₁₃×#3220	C₂	semidirect
7. C₁₃×#3212	C₂	semidirect
8. C₁₃×#3211	C₂	semidirect
9. C₁₃×#3153	C₂	semidirect
10. C₁₃×#3147	C₂	semidirect
11. C₁₃×#3142	C₂	semidirect
12. C₂×C₁₃×#488	C₂	semidirect
13. C₁₃×#3046	C₂	semidirect
14. C₁₃×#3045	C₂	semidirect
15. C₁₃×#3013	C₂	semidirect
16. C₁₃×#3012	C₂	semidirect
17. C₁₃×#2922	C₂	semidirect
20. C₂×C₁₃×#137	C₂²	semidirect
23. C₂×C₁₃×#135	C₂²	semidirect
30. C₁₃×#541	C₂²	semidirect
31. C₁₃×#540	C₂²	semidirect
39. C₁₃×#532	C₂²	semidirect
40. C₁₃×#529	C₂²	semidirect
41. C₂×C₁₃×#125	C₂²	semidirect
44. C₁₃×#520	C₂²	semidirect
46. C₁₃×#497	C₂²	semidirect
47. C₁₃×#496	C₂²	semidirect
48. C₁₃×#495	C₂²	semidirect
49. C₁₃×#495	C₂²	semidirect
50. C₁₃×#495	C₂²	semidirect
51. C₁₃×#494	C₂²	semidirect
52. C₁₃×#493	C₂²	semidirect
53. C₁₃×#492	C₂²	semidirect
54. C₁₃×#492	C₂²	semidirect
55. C₁₃×#491	C₂²	semidirect
56. C₁₃×#490	C₂²	semidirect
57. C₁₃×#488	C₂²	semidirect
58. C₁₃×#488	C₂²	semidirect
59. C₁₃×#488	C₂²	semidirect
60. C₁₃×#488	C₂²	semidirect
61. C₁₃×#488	C₂²	semidirect
62. C₁₃×#464	C₂²	semidirect
63. C₁₃×#464	C₂²	semidirect
64. C₁₃×#463	C₂²	semidirect
65. C₁₃×#463	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
69. C₁₃×#459	C₂²	semidirect
71. C₁₃×#452	C₂²	semidirect
72. C₁₃×#451	C₂²	semidirect
75. C₁₃×#449	C₂²	semidirect
76. C₁₃×#448	C₂²	semidirect
78. C₁₃×#433	C₂²	semidirect
79. C₁₃×#433	C₂²	semidirect
80. C₁₃×#431	C₂²	semidirect
81. C₁₃×#424	C₂²	semidirect
83. C₁₃×#417	C₂²	semidirect
84. C₂×C₁₃×#103	C₂²	semidirect
87. C₄×C₁₃×M₁₆	C₂²	semidirect
88. C₂×C₄×C₈×C₁₃	C₂²	semidirect
203. #60823	C₁₃	direct (N × H)
307. #3512	C₂×C₁₃	semidirect
308. #3500	C₂×C₁₃	semidirect
309. #3223	C₂×C₁₃	semidirect
310. #3222	C₂×C₁₃	semidirect
311. #3221	C₂×C₁₃	semidirect
312. #3220	C₂×C₁₃	semidirect
313. #3212	C₂×C₁₃	semidirect
314. #3211	C₂×C₁₃	semidirect
315. #3153	C₂×C₁₃	semidirect
316. #3147	C₂×C₁₃	semidirect
317. #3142	C₂×C₁₃	semidirect
318. C₂×#488	C₂×C₁₃	semidirect
319. #3046	C₂×C₁₃	semidirect
320. #3045	C₂×C₁₃	semidirect
321. #3013	C₂×C₁₃	semidirect
322. #3012	C₂×C₁₃	semidirect
323. #2922	C₂×C₁₃	semidirect
389. C₂×#137	C₂²×C₁₃	semidirect
392. C₂×#135	C₂²×C₁₃	semidirect
399. #541	C₂²×C₁₃	semidirect
400. #540	C₂²×C₁₃	semidirect
408. #532	C₂²×C₁₃	semidirect
409. #529	C₂²×C₁₃	semidirect
410. C₂×#125	C₂²×C₁₃	semidirect
413. #520	C₂²×C₁₃	semidirect
415. #497	C₂²×C₁₃	semidirect
416. #496	C₂²×C₁₃	semidirect
417. #495	C₂²×C₁₃	semidirect
418. #495	C₂²×C₁₃	semidirect
419. #495	C₂²×C₁₃	semidirect
420. #494	C₂²×C₁₃	semidirect
421. #493	C₂²×C₁₃	semidirect
422. #492	C₂²×C₁₃	semidirect
423. #492	C₂²×C₁₃	semidirect
424. #491	C₂²×C₁₃	semidirect
425. #490	C₂²×C₁₃	semidirect
426. #488	C₂²×C₁₃	semidirect
427. #488	C₂²×C₁₃	semidirect
428. #488	C₂²×C₁₃	semidirect
429. #488	C₂²×C₁₃	semidirect
430. #488	C₂²×C₁₃	semidirect
431. #464	C₂²×C₁₃	semidirect
432. #464	C₂²×C₁₃	semidirect
433. #463	C₂²×C₁₃	semidirect
434. #463	C₂²×C₁₃	semidirect
435. #462	C₂²×C₁₃	semidirect
436. #461	C₂²×C₁₃	semidirect
437. #460	C₂²×C₁₃	semidirect
438. #459	C₂²×C₁₃	semidirect
440. #452	C₂²×C₁₃	semidirect
441. #451	C₂²×C₁₃	semidirect
444. #449	C₂²×C₁₃	semidirect
445. #448	C₂²×C₁₃	semidirect
447. #433	C₂²×C₁₃	semidirect
448. #433	C₂²×C₁₃	semidirect
449. #431	C₂²×C₁₃	semidirect
450. #424	C₂²×C₁₃	semidirect
452. #417	C₂²×C₁₃	semidirect
453. C₂×#103	C₂²×C₁₃	semidirect
456. C₄×M₁₆	C₂²×C₁₃	semidirect
457. C₂×C₄×C₈	C₂²×C₁₃	semidirect
710. C₁₃	#60823	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×#3512	2
C₁₃×#3500	2
C₁₃×#3223	2
C₁₃×#3222	2
C₁₃×#3221	2
C₁₃×#3220	2
C₁₃×#3212	2
C₁₃×#3211	2
C₁₃×#3153	2
C₁₃×#3147	2
C₁₃×#3142	2
C₂×C₁₃×#488	2
C₁₃×#3046	2
C₁₃×#3045	2
C₁₃×#3013	2
C₁₃×#3012	2
C₁₃×#2922	2
#60823	13

Subgroups — C13×#60823 #15747162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60823 #15747162