Subgroups — C₁₃×#25159 #15711498

Order 3328.

1212 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2011	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	—	2	1	no	—
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#460	—	2	4	no	—
29	C₁₃×#449	—	2	4	no	—
30	C₁₃×#449	—	2	4	no	—
31	C₄×C₁₃×SD₁₆	—	2	4	no	—
32	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₁₃×#394	—	2	1	no	—
47	C₁₃×#392	—	2	1	no	—
48	C₁₃×#390	—	2	1	no	—
49	C₁₃×#390	—	2	1	no	—
50	C₁₃×#390	C₂²	1	1	yes	characteristic
51	C₁₃×#390	C₂²	1	1	yes	characteristic
52	C₁₃×#390	C₂²	1	1	yes	characteristic
53	C₁₃×#389	C₂²	1	1	yes	characteristic
54	C₁₃×#386	—	2	1	no	—
55	C₁₃×#380	—	2	1	no	—
56	C₁₃×#380	C₂²	1	1	yes	characteristic
57	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	C₂²	1	1	yes	characteristic
61	C₁₃×#336	C₂²	1	1	yes	characteristic
62	C₁₃×#336	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	—	2	2	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	4	1	no	—
68	C₂×C₁₃×#41	—	4	1	no	—
69	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	—	2	1	no	—
71	C₂²×D₄×C₁₃	—	2	1	no	—
72	C₂²×D₄×C₁₃	—	2	1	no	—
73	C₂²×D₄×C₁₃	—	2	1	no	—
74	C₂²×D₄×C₁₃	—	2	1	no	—
75	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	—	2	1	no	—
79	C₂³×C₄×C₁₃	—	2	1	no	—
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×SD₁₆	—	2	2	no	—
82	C₂×C₁₃×SD₁₆	—	2	2	no	—
83	C₂×C₁₃×SD₁₆	—	2	2	no	—
84	C₂×C₁₃×SD₁₆	—	2	2	no	—
85	C₂×C₁₃×SD₁₆	—	2	2	no	—
86	C₂×C₁₃×SD₁₆	D₄	1	4	yes	complemented
87	C₂×C₁₃×D₈	—	2	2	no	—
88	C₂×C₁₃×D₈	—	2	2	no	—
89	C₂×C₁₃×D₈	—	2	2	no	—
90	C₂×C₁₃×D₈	—	2	2	no	—
91	C₂×C₁₃×D₈	—	4	1	no	—
92	C₂×C₁₃×D₈	—	4	1	no	—
93	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×#127	—	2	2	no	—
98	C₁₃×#127	—	4	1	no	—
99	C₁₃×#121	—	2	2	no	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#121	—	4	4	no	—
102	C₁₃×#121	—	4	1	no	—
103	C₁₃×#121	—	4	1	no	—
104	C₄×Q₈×C₁₃	—	2	2	no	—
105	C₄×Q₈×C₁₃	—	2	2	no	—
106	C₄×Q₈×C₁₃	—	4	1	no	—
107	C₄×Q₈×C₁₃	—	4	1	no	—
108	C₄×D₄×C₁₃	—	2	2	no	—
109	C₄×D₄×C₁₃	—	4	1	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
128	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	—	2	1	no	—
130	C₂×C₄²×C₁₃	—	2	1	no	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₁₃×#107	—	4	1	no	—
134	C₁₃×#106	—	2	2	no	—
135	C₁₃×C₄⋊C₈	—	2	2	no	—
136	C₁₃×#103	—	2	2	no	—
137	C₁₃×#103	D₄	1	4	yes	complemented
138	C₁₃×#102	—	2	2	no	—
139	C₁₃×#102	—	2	2	no	—
140	C₁₃×#102	—	2	2	no	—
141	C₁₃×#102	—	2	2	no	—
142	C₁₃×#102	—	2	2	no	—
143	C₁₃×#102	—	4	1	no	—
144	C₁₃×C₂²⋊C₈	—	2	2	no	—
145	C₁₃×C₂²⋊C₈	—	2	2	no	—
146	C₄×C₈×C₁₃	—	2	2	no	—
147	C₁₃×#95	—	2	1	no	—
148	C₁₃×#95	—	2	1	no	—
149	C₁₃×#95	D₄	1	1	yes	characteristic
150	C₁₃×#95	D₄	1	1	yes	characteristic
151	#25159	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂⁴×C₁₃	—	2	1	no	—
153	C₂⁴×C₁₃	—	2	1	no	—
154	C₂⁴×C₁₃	—	2	1	no	—
155	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₁₃×#41	—	4	4	no	—
157	C₁₃×#41	—	4	4	no	—
158	C₁₃×#41	—	4	4	no	—
159	C₁₃×#41	—	4	4	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	—	2	1	no	—
162	C₂×Q₈×C₁₃	—	2	1	no	—
163	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
164	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
165	C₂×Q₈×C₁₃	#41	1	2	yes	—
166	C₂×D₄×C₁₃	—	2	4	no	—
167	C₂×D₄×C₁₃	—	2	1	no	—
168	C₂×D₄×C₁₃	—	2	1	no	—
169	C₂×D₄×C₁₃	—	2	1	no	—
170	C₂×D₄×C₁₃	—	2	1	no	—
171	C₂×D₄×C₁₃	—	2	1	no	—
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	—	2	1	no	—
174	C₂×D₄×C₁₃	—	2	1	no	—
175	C₂×D₄×C₁₃	—	2	1	no	—
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	1	no	—
178	C₂×D₄×C₁₃	—	2	1	no	—
179	C₂×D₄×C₁₃	—	2	1	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	4	2	no	—
184	C₂×D₄×C₁₃	—	4	2	no	—
185	C₂×D₄×C₁₃	—	4	2	no	—
186	C₂×D₄×C₁₃	—	4	2	no	—
187	C₂×D₄×C₁₃	—	4	2	no	—
188	C₂×D₄×C₁₃	—	4	2	no	—
189	C₂×D₄×C₁₃	—	4	2	no	—
190	C₂×D₄×C₁₃	—	4	2	no	—
191	C₂×D₄×C₁₃	—	4	2	no	—
192	C₂×D₄×C₁₃	—	4	2	no	—
193	C₂×D₄×C₁₃	—	8	1	no	—
194	C₂×D₄×C₁₃	—	8	1	no	—
195	C₂×D₄×C₁₃	—	8	1	no	—
196	C₂×D₄×C₁₃	—	8	1	no	—
197	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
198	C₂×D₄×C₁₃	#41	1	2	yes	—
199	C₂²×C₄×C₁₃	—	2	1	no	—
200	C₂²×C₄×C₁₃	—	2	4	no	—
201	C₂²×C₄×C₁₃	—	2	1	no	—
202	C₂²×C₄×C₁₃	—	2	1	no	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	2	1	no	—
205	C₂²×C₄×C₁₃	—	2	1	no	—
206	C₂²×C₄×C₁₃	—	2	1	no	—
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	2	1	no	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	2	1	no	—
211	C₂²×C₄×C₁₃	—	4	2	no	—
212	C₂²×C₄×C₁₃	—	4	2	no	—
213	C₂²×C₄×C₁₃	—	4	2	no	—
214	C₂²×C₄×C₁₃	—	4	2	no	—
215	C₂²×C₄×C₁₃	—	8	1	no	—
216	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
222	C₁₃×SD₁₆	—	2	8	no	—
223	C₁₃×SD₁₆	—	4	4	no	—
224	C₁₃×D₈	—	4	4	no	—
225	C₁₃×D₈	—	4	4	no	—
226	C₂×C₈×C₁₃	—	2	1	no	—
227	C₂×C₈×C₁₃	—	2	1	no	—
228	C₂×C₈×C₁₃	—	2	1	no	—
229	C₂×C₈×C₁₃	—	2	1	no	—
230	C₂×C₈×C₁₃	—	2	1	no	—
231	C₂×C₈×C₁₃	—	2	1	no	—
232	C₂×C₈×C₁₃	—	2	1	no	—
233	C₂×C₈×C₁₃	—	2	1	no	—
234	C₂×C₈×C₁₃	—	2	1	no	—
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
237	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	1	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	2	1	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	4	2	no	—
246	C₁₃×C₄⋊C₄	—	4	2	no	—
247	C₁₃×C₄⋊C₄	—	4	2	no	—
248	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
249	C₁₃×C₂²⋊C₄	—	2	2	no	—
250	C₁₃×C₂²⋊C₄	—	2	2	no	—
251	C₁₃×C₂²⋊C₄	—	4	2	no	—
252	C₁₃×C₂²⋊C₄	—	4	2	no	—
253	C₁₃×C₂²⋊C₄	—	4	2	no	—
254	C₁₃×C₂²⋊C₄	—	4	2	no	—
255	C₁₃×C₂²⋊C₄	—	4	2	no	—
256	C₁₃×C₂²⋊C₄	—	4	2	no	—
257	C₁₃×C₂²⋊C₄	—	8	1	no	—
258	C₁₃×C₂²⋊C₄	—	8	1	no	—
259	C₁₃×C₂²⋊C₄	—	8	1	no	—
260	C₁₃×C₂²⋊C₄	—	8	1	no	—
261	C₄²×C₁₃	—	2	1	no	—
262	C₄²×C₁₃	—	2	1	no	—
263	C₄²×C₁₃	—	2	1	no	—
264	C₄²×C₁₃	—	2	1	no	—
265	C₄²×C₁₃	—	4	2	no	—
266	C₄²×C₁₃	—	4	2	no	—
267	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
268	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
269	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
270	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#2428	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#2341	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#2065	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#2011	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#1923	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂³×C₁₃	—	2	1	no	—
283	C₂³×C₁₃	—	2	2	no	—
284	C₂³×C₁₃	—	2	2	no	—
285	C₂³×C₁₃	—	2	1	no	—
286	C₂³×C₁₃	—	2	1	no	—
287	C₂³×C₁₃	—	2	1	no	—
288	C₂³×C₁₃	—	2	1	no	—
289	C₂³×C₁₃	—	2	1	no	—
290	C₂³×C₁₃	—	2	1	no	—
291	C₂³×C₁₃	—	4	1	no	—
292	C₂³×C₁₃	—	4	1	no	—
293	C₂³×C₁₃	—	4	1	no	—
294	C₂³×C₁₃	—	4	1	no	—
295	C₂³×C₁₃	—	4	1	no	—
296	C₂³×C₁₃	—	4	1	no	—
297	C₂³×C₁₃	—	4	1	no	—
298	C₂³×C₁₃	—	4	1	no	—
299	C₂³×C₁₃	—	4	1	no	—
300	C₂³×C₁₃	—	4	1	no	—
301	C₂³×C₁₃	—	4	1	no	—
302	C₂³×C₁₃	—	4	1	no	—
303	C₂³×C₁₃	—	4	1	no	—
304	C₂³×C₁₃	—	4	1	no	—
305	C₂³×C₁₃	—	4	1	no	—
306	C₂³×C₁₃	—	4	1	no	—
307	C₂³×C₁₃	—	4	1	no	—
308	C₂³×C₁₃	—	4	1	no	—
309	C₂³×C₁₃	—	4	1	no	—
310	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
311	Q₈×C₁₃	—	2	2	no	—
312	Q₈×C₁₃	—	2	2	no	—
313	Q₈×C₁₃	—	2	2	no	—
314	Q₈×C₁₃	#121	1	4	yes	complemented
315	D₄×C₁₃	—	2	2	no	—
316	D₄×C₁₃	—	2	2	no	—
317	D₄×C₁₃	—	2	2	no	—
318	D₄×C₁₃	—	2	2	no	—
319	D₄×C₁₃	—	4	8	no	—
320	D₄×C₁₃	—	4	1	no	—
321	D₄×C₁₃	—	4	1	no	—
322	D₄×C₁₃	—	4	1	no	—
323	D₄×C₁₃	—	4	1	no	—
324	D₄×C₁₃	—	4	1	no	—
325	D₄×C₁₃	—	4	1	no	—
326	D₄×C₁₃	—	4	1	no	—
327	D₄×C₁₃	—	4	1	no	—
328	D₄×C₁₃	—	8	4	no	—
329	D₄×C₁₃	—	8	4	no	—
330	D₄×C₁₃	—	8	4	no	—
331	D₄×C₁₃	—	8	4	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	1	no	—
334	C₂×C₄×C₁₃	—	2	1	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	1	no	—
338	C₂×C₄×C₁₃	—	2	1	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	2	1	no	—
341	C₂×C₄×C₁₃	—	2	1	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	1	no	—
344	C₂×C₄×C₁₃	—	2	1	no	—
345	C₂×C₄×C₁₃	—	2	1	no	—
346	C₂×C₄×C₁₃	—	2	1	no	—
347	C₂×C₄×C₁₃	—	2	1	no	—
348	C₂×C₄×C₁₃	—	2	1	no	—
349	C₂×C₄×C₁₃	—	4	8	no	—
350	C₂×C₄×C₁₃	—	4	1	no	—
351	C₂×C₄×C₁₃	—	4	1	no	—
352	C₂×C₄×C₁₃	—	4	1	no	—
353	C₂×C₄×C₁₃	—	4	1	no	—
354	C₂×C₄×C₁₃	—	4	1	no	—
355	C₂×C₄×C₁₃	—	4	1	no	—
356	C₂×C₄×C₁₃	—	4	1	no	—
357	C₂×C₄×C₁₃	—	4	1	no	—
358	C₂×C₄×C₁₃	—	4	1	no	—
359	C₂×C₄×C₁₃	—	4	1	no	—
360	C₂×C₄×C₁₃	—	4	1	no	—
361	C₂×C₄×C₁₃	—	4	1	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
365	C₂×C₄×C₁₃	—	8	4	no	—
366	C₂×C₄×C₁₃	#135	1	2	yes	—
367	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
368	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
371	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
372	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
374	C₈×C₁₃	—	2	2	no	—
375	C₈×C₁₃	—	2	2	no	—
376	C₈×C₁₃	—	4	1	no	—
377	C₈×C₁₃	—	4	1	no	—
378	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
379	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
380	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
381	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
382	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×#121	—	2	1	no	—
385	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
390	#460	—	2	4	no	—
391	#449	—	2	4	no	—
392	#449	—	2	4	no	—
393	C₄×SD₁₆	—	2	4	no	—
394	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
408	#394	—	2	1	no	—
409	#392	—	2	1	no	—
410	#390	—	2	1	no	—
411	#390	—	2	1	no	—
412	#390	C₂²×C₁₃	1	1	yes	characteristic
413	#390	C₂²×C₁₃	1	1	yes	characteristic
414	#390	C₂²×C₁₃	1	1	yes	characteristic
415	#389	C₂²×C₁₃	1	1	yes	characteristic
416	#386	—	2	1	no	—
417	#380	—	2	1	no	—
418	#380	C₂²×C₁₃	1	1	yes	characteristic
419	C₄×C₂²⋊C₄	—	2	1	no	—
420	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
421	#340	C₂²×C₁₃	1	1	yes	characteristic
422	#340	C₂²×C₁₃	1	1	yes	characteristic
423	#336	C₂²×C₁₃	1	1	yes	characteristic
424	#336	C₂²×C₁₃	1	1	yes	characteristic
425	C₂²×C₁₃	—	4	1	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	1	no	—
428	C₂²×C₁₃	—	4	2	no	—
429	C₂²×C₁₃	—	4	2	no	—
430	C₂²×C₁₃	—	4	1	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	—	4	1	no	—
433	C₂²×C₁₃	—	4	1	no	—
434	C₂²×C₁₃	—	4	2	no	—
435	C₂²×C₁₃	—	4	2	no	—
436	C₂²×C₁₃	—	4	1	no	—
437	C₂²×C₁₃	—	4	1	no	—
438	C₂²×C₁₃	—	8	1	no	—
439	C₂²×C₁₃	—	8	1	no	—
440	C₂²×C₁₃	—	8	1	no	—
441	C₂²×C₁₃	—	8	1	no	—
442	C₂²×C₁₃	—	8	1	no	—
443	C₂²×C₁₃	—	8	1	no	—
444	C₂²×C₁₃	—	8	1	no	—
445	C₂²×C₁₃	—	8	1	no	—
446	C₂²×C₁₃	—	8	1	no	—
447	C₂²×C₁₃	—	8	1	no	—
448	C₂²×C₁₃	—	8	1	no	—
449	C₂²×C₁₃	—	8	1	no	—
450	C₂²×C₁₃	—	8	1	no	—
451	C₂²×C₁₃	—	8	1	no	—
452	C₂²×C₁₃	—	8	1	no	—
453	C₂²×C₁₃	#525	1	1	yes	characteristic
454	C₂²×C₁₃	D₄²	1	1	yes	characteristic
455	C₂²×C₁₃	D₄²	1	1	yes	characteristic
456	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
457	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
458	C₂²×C₁₃	#576	1	1	yes	characteristic
459	C₂²×C₁₃	#577	1	1	yes	characteristic
460	C₄×C₁₃	—	2	4	no	—
461	C₄×C₁₃	—	2	2	no	—
462	C₄×C₁₃	—	2	2	no	—
463	C₄×C₁₃	—	4	1	no	—
464	C₄×C₁₃	—	4	2	no	—
465	C₄×C₁₃	—	4	1	no	—
466	C₄×C₁₃	—	4	1	no	—
467	C₄×C₁₃	—	8	1	no	—
468	C₄×C₁₃	—	8	1	no	—
469	C₄×C₁₃	—	8	1	no	—
470	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
471	C₄×C₁₃	#538	1	1	yes	characteristic
472	C₄×C₁₃	#546	1	1	yes	characteristic
473	C₄×C₁₃	#546	1	1	yes	characteristic
474	C₂×#41	—	2	2	no	—
475	C₂×#41	—	2	2	no	—
476	C₂×#41	—	2	2	no	—
477	C₂×#41	—	2	2	no	—
478	C₂×#41	—	4	1	no	—
479	C₂×#41	—	4	1	no	—
480	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	—	2	1	no	—
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	—	2	1	no	—
485	C₂²×D₄	—	2	1	no	—
486	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
487	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
488	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
489	C₂³×C₄	—	2	1	no	—
490	C₂³×C₄	—	2	1	no	—
491	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
492	C₂×SD₁₆	—	2	2	no	—
493	C₂×SD₁₆	—	2	2	no	—
494	C₂×SD₁₆	—	2	2	no	—
495	C₂×SD₁₆	—	2	2	no	—
496	C₂×SD₁₆	—	2	2	no	—
497	C₂×SD₁₆	D₄×C₁₃	1	4	yes	complemented
498	C₂×D₈	—	2	2	no	—
499	C₂×D₈	—	2	2	no	—
500	C₂×D₈	—	2	2	no	—
501	C₂×D₈	—	2	2	no	—
502	C₂×D₈	—	4	1	no	—
503	C₂×D₈	—	4	1	no	—
504	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
505	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
506	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
508	#127	—	2	2	no	—
509	#127	—	4	1	no	—
510	#121	—	2	2	no	—
511	#121	—	2	2	no	—
512	#121	—	4	4	no	—
513	#121	—	4	1	no	—
514	#121	—	4	1	no	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	—	4	1	no	—
518	C₄×Q₈	—	4	1	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	4	1	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
540	C₂×C₄²	—	2	1	no	—
541	C₂×C₄²	—	2	1	no	—
542	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
544	#107	—	4	1	no	—
545	#106	—	2	2	no	—
546	C₄⋊C₈	—	2	2	no	—
547	#103	—	2	2	no	—
548	#103	D₄×C₁₃	1	4	yes	complemented
549	#102	—	2	2	no	—
550	#102	—	2	2	no	—
551	#102	—	2	2	no	—
552	#102	—	2	2	no	—
553	#102	—	2	2	no	—
554	#102	—	4	1	no	—
555	C₂²⋊C₈	—	2	2	no	—
556	C₂²⋊C₈	—	2	2	no	—
557	C₄×C₈	—	2	2	no	—
558	#95	—	2	1	no	—
559	#95	—	2	1	no	—
560	#95	D₄×C₁₃	1	1	yes	characteristic
561	#95	D₄×C₁₃	1	1	yes	characteristic
562	C₂×C₁₃	—	8	1	no	—
563	C₂×C₁₃	—	8	2	no	—
564	C₂×C₁₃	—	8	2	no	—
565	C₂×C₁₃	—	16	1	no	—
566	C₂×C₁₃	#2424	1	1	yes	characteristic
567	C₂×C₁₃	#3106	1	1	yes	characteristic
568	C₂×C₁₃	#3119	1	1	yes	characteristic
569	C₂×C₁₃	#3265	1	1	yes	characteristic
570	C₂×C₁₃	#3274	1	1	yes	characteristic
571	C₂×C₁₃	#3282	1	1	yes	characteristic
572	C₂×C₁₃	#3287	1	1	yes	characteristic
573	C₂⁴	—	2	1	no	—
574	C₂⁴	—	2	1	no	—
575	C₂⁴	—	2	1	no	—
576	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
577	#41	—	4	4	no	—
578	#41	—	4	4	no	—
579	#41	—	4	4	no	—
580	#41	—	4	4	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
585	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
586	C₂×Q₈	C₁₃×#41	1	2	yes	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	1	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	2	no	—
608	C₂×D₄	—	4	2	no	—
609	C₂×D₄	—	4	2	no	—
610	C₂×D₄	—	4	2	no	—
611	C₂×D₄	—	4	2	no	—
612	C₂×D₄	—	4	2	no	—
613	C₂×D₄	—	4	2	no	—
614	C₂×D₄	—	8	1	no	—
615	C₂×D₄	—	8	1	no	—
616	C₂×D₄	—	8	1	no	—
617	C₂×D₄	—	8	1	no	—
618	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
619	C₂×D₄	C₁₃×#41	1	2	yes	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	—	4	2	no	—
635	C₂²×C₄	—	4	2	no	—
636	C₂²×C₄	—	8	1	no	—
637	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
643	SD₁₆	—	2	8	no	—
644	SD₁₆	—	4	4	no	—
645	D₈	—	4	4	no	—
646	D₈	—	4	4	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	2	1	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
658	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	4	2	no	—
673	C₂²⋊C₄	—	4	2	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₂²⋊C₄	—	4	2	no	—
676	C₂²⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	—	8	1	no	—
679	C₂²⋊C₄	—	8	1	no	—
680	C₂²⋊C₄	—	8	1	no	—
681	C₂²⋊C₄	—	8	1	no	—
682	C₄²	—	2	1	no	—
683	C₄²	—	2	1	no	—
684	C₄²	—	2	1	no	—
685	C₄²	—	2	1	no	—
686	C₄²	—	4	2	no	—
687	C₄²	—	4	2	no	—
688	C₁₃	#25159	1	1	yes	characteristic, direct product factor, Sylow
689	C₂³	—	2	1	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	4	1	no	—
699	C₂³	—	4	1	no	—
700	C₂³	—	4	1	no	—
701	C₂³	—	4	1	no	—
702	C₂³	—	4	1	no	—
703	C₂³	—	4	1	no	—
704	C₂³	—	4	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	—	4	1	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	1	no	—
717	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	C₁₃×#121	1	4	yes	complemented
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	4	8	no	—
727	D₄	—	4	1	no	—
728	D₄	—	4	1	no	—
729	D₄	—	4	1	no	—
730	D₄	—	4	1	no	—
731	D₄	—	4	1	no	—
732	D₄	—	4	1	no	—
733	D₄	—	4	1	no	—
734	D₄	—	4	1	no	—
735	D₄	—	8	4	no	—
736	D₄	—	8	4	no	—
737	D₄	—	8	4	no	—
738	D₄	—	8	4	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	4	8	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	8	4	no	—
773	C₂×C₄	C₁₃×#135	1	2	yes	—
774	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
775	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
777	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
778	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
779	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
780	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
781	C₈	—	2	2	no	—
782	C₈	—	2	2	no	—
783	C₈	—	4	1	no	—
784	C₈	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	8	1	no	—
799	C₂²	—	8	1	no	—
800	C₂²	—	8	1	no	—
801	C₂²	—	8	1	no	—
802	C₂²	—	8	1	no	—
803	C₂²	—	8	1	no	—
804	C₂²	—	8	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	—	8	1	no	—
808	C₂²	—	8	1	no	—
809	C₂²	—	8	1	no	—
810	C₂²	—	8	1	no	—
811	C₂²	—	8	1	no	—
812	C₂²	—	8	1	no	—
813	C₂²	C₁₃×#525	1	1	yes	characteristic
814	C₂²	D₄²×C₁₃	1	1	yes	characteristic
815	C₂²	D₄²×C₁₃	1	1	yes	characteristic
816	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
817	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
818	C₂²	C₁₃×#576	1	1	yes	characteristic
819	C₂²	C₁₃×#577	1	1	yes	characteristic
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	4	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	8	1	no	—
828	C₄	—	8	1	no	—
829	C₄	—	8	1	no	—
830	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
831	C₄	C₁₃×#538	1	1	yes	characteristic
832	C₄	C₁₃×#546	1	1	yes	characteristic
833	C₄	C₁₃×#546	1	1	yes	characteristic
834	C₂	—	8	1	no	—
835	C₂	—	8	2	no	—
836	C₂	—	8	2	no	—
837	C₂	—	16	1	no	—
838	C₂	C₁₃×#2424	1	1	yes	characteristic
839	C₂	C₁₃×#3106	1	1	yes	characteristic
840	C₂	C₁₃×#3119	1	1	yes	characteristic
841	C₂	C₁₃×#3265	1	1	yes	characteristic
842	C₂	C₁₃×#3274	1	1	yes	characteristic
843	C₂	C₁₃×#3282	1	1	yes	characteristic
844	C₂	C₁₃×#3287	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#460	C₂	semidirect
2. C₂×C₁₃×#449	C₂	semidirect
3. C₂×C₁₃×#449	C₂	semidirect
4. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
5. C₁₃×#2428	C₂	semidirect
6. C₁₃×#2341	C₂	semidirect
7. C₁₃×#2065	C₂	semidirect
8. C₁₃×#2034	C₂	semidirect
9. C₁₃×#2033	C₂	semidirect
10. C₁₃×#2011	C₂	semidirect
11. C₁₃×#1970	C₂	semidirect
12. C₁₃×#1923	C₂	semidirect
13. C₁₃×#1880	C₂	semidirect
14. C₁₃×#1879	C₂	semidirect
15. C₁₃×#1863	C₂	semidirect
86. C₂×C₁₃×SD₁₆	D₄	semidirect
137. C₁₃×#103	D₄	semidirect
151. #25159	C₁₃	direct (N × H)
267. C₂×#460	C₂×C₁₃	semidirect
268. C₂×#449	C₂×C₁₃	semidirect
269. C₂×#449	C₂×C₁₃	semidirect
270. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
271. #2428	C₂×C₁₃	semidirect
272. #2341	C₂×C₁₃	semidirect
273. #2065	C₂×C₁₃	semidirect
274. #2034	C₂×C₁₃	semidirect
275. #2033	C₂×C₁₃	semidirect
276. #2011	C₂×C₁₃	semidirect
277. #1970	C₂×C₁₃	semidirect
278. #1923	C₂×C₁₃	semidirect
279. #1880	C₂×C₁₃	semidirect
280. #1879	C₂×C₁₃	semidirect
281. #1863	C₂×C₁₃	semidirect
314. Q₈×C₁₃	#121	semidirect
497. C₂×SD₁₆	D₄×C₁₃	semidirect
548. #103	D₄×C₁₃	semidirect
688. C₁₃	#25159	direct (N × H)
721. Q₈	C₁₃×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#460	2
C₂×C₁₃×#449	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2428	2
C₁₃×#2341	2
C₁₃×#2065	2
C₁₃×#2034	2
C₁₃×#2033	2
C₁₃×#2011	2
C₁₃×#1970	2
C₁₃×#1923	2
C₁₃×#1880	2
C₁₃×#1879	2
C₁₃×#1863	2
#25159	13

Subgroups — C13×#25159 #15711498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25159 #15711498