Subgroups — C₁₃×#24174 #15710513

Order 3328.

1078 conjugacy classes of subgroups.

The subgroup lattice has 870 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×#3036	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2566	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2040	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2039	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2006	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2006	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1998	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1980	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1883	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1859	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1806	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₁₃×#553	—	2	1	no	—
20	C₁₃×#553	—	2	1	no	—
21	C₁₃×#553	—	2	2	no	—
22	C₁₃×#553	—	2	2	no	—
23	C₁₃×#552	—	2	1	no	—
24	C₁₃×#552	—	2	1	no	—
25	C₁₃×#541	—	2	1	no	—
26	C₁₃×#540	—	2	1	no	—
27	C₁₃×#537	C₂²	1	1	yes	characteristic
28	C₁₃×#537	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₁₃×#529	—	2	1	no	—
31	C₁₃×#529	—	2	1	no	—
32	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
33	C₁₃×#520	C₂²	1	1	yes	characteristic
34	C₁₃×#520	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#463	—	2	1	no	—
38	C₁₃×#463	—	2	1	no	—
39	C₁₃×#461	—	2	1	no	—
40	C₁₃×#459	—	2	1	no	—
41	C₁₃×#442	—	2	1	no	—
42	C₁₃×#440	—	2	1	no	—
43	C₄×C₁₃×SD₁₆	—	2	1	no	—
44	C₄×C₁₃×D₈	—	2	1	no	—
45	C₁₃×#428	C₂²	1	1	yes	characteristic
46	C₁₃×#423	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
53	C₁₃×#418	C₂²	1	1	yes	characteristic
54	C₁₃×#417	C₂²	1	1	yes	characteristic
55	C₁₃×#417	C₂²	1	1	yes	characteristic
56	C₁₃×#417	C₂²	1	1	yes	characteristic
57	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
58	C₁₃×#396	—	2	2	no	—
59	C₁₃×#390	C₂²	1	1	yes	characteristic
60	C₁₃×#390	C₂²	1	1	yes	characteristic
61	C₁₃×#385	—	2	2	no	—
62	C₁₃×#384	C₂²	1	1	yes	characteristic
63	C₁₃×#382	C₂²	1	1	yes	characteristic
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₁₃×#343	C₂²	1	1	yes	characteristic
66	C₁₃×#343	C₂²	1	1	yes	characteristic
67	C₁₃×#343	C₂²	1	1	yes	characteristic
68	C₁₃×#343	C₂²	1	1	yes	characteristic
69	C₁₃×#339	C₂²	1	1	yes	characteristic
70	C₁₃×#339	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	—	2	1	no	—
76	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
77	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
78	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
79	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
80	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
81	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
82	C₂×C₁₃×SD₁₆	—	2	1	no	—
83	C₂×C₁₃×SD₁₆	—	2	1	no	—
84	C₂×C₁₃×SD₁₆	—	2	1	no	—
85	C₂×C₁₃×D₈	—	2	1	no	—
86	C₂×C₁₃×D₈	—	2	1	no	—
87	C₂×C₁₃×D₈	—	2	1	no	—
88	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
92	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
93	C₁₃×#127	D₄	1	1	yes	characteristic
94	C₁₃×#126	—	2	2	no	—
95	C₁₃×#126	—	2	2	no	—
96	C₁₃×#126	—	2	2	no	—
97	C₁₃×#126	—	2	2	no	—
98	C₁₃×#125	—	2	2	no	—
99	C₁₃×#125	—	2	2	no	—
100	C₁₃×#125	—	2	1	no	—
101	C₁₃×#125	—	2	1	no	—
102	C₁₃×#125	—	2	1	no	—
103	C₁₃×#125	—	2	1	no	—
104	C₁₃×#124	D₄	1	1	yes	characteristic
105	C₁₃×#124	D₄	1	1	yes	characteristic
106	C₁₃×#123	—	2	2	no	—
107	C₁₃×#123	—	2	2	no	—
108	C₁₃×#123	—	2	2	no	—
109	C₁₃×#123	—	2	2	no	—
110	C₁₃×C₂²⋊Q₈	—	2	1	no	—
111	C₁₃×C₂²⋊Q₈	—	2	1	no	—
112	C₁₃×C₂²⋊Q₈	—	2	1	no	—
113	C₁₃×C₂²⋊Q₈	—	2	1	no	—
114	C₁₃×#121	—	2	2	no	—
115	C₁₃×#121	—	2	2	no	—
116	C₁₃×#121	—	2	1	no	—
117	C₁₃×#121	—	2	1	no	—
118	C₁₃×#121	—	2	1	no	—
119	C₁₃×#121	—	2	1	no	—
120	C₁₃×#121	—	2	1	no	—
121	C₁₃×#121	—	2	1	no	—
122	C₁₃×#121	—	2	2	no	—
123	C₁₃×#121	—	2	2	no	—
124	C₄×Q₈×C₁₃	—	2	1	no	—
125	C₄×Q₈×C₁₃	—	2	1	no	—
126	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
127	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
128	C₄×D₄×C₁₃	—	2	2	no	—
129	C₄×D₄×C₁₃	—	2	2	no	—
130	C₄×D₄×C₁₃	—	2	1	no	—
131	C₄×D₄×C₁₃	—	2	1	no	—
132	C₄×D₄×C₁₃	—	2	1	no	—
133	C₄×D₄×C₁₃	—	2	1	no	—
134	C₄×D₄×C₁₃	—	2	2	no	—
135	C₄×D₄×C₁₃	—	2	2	no	—
136	C₄×D₄×C₁₃	—	2	1	no	—
137	C₄×D₄×C₁₃	—	2	1	no	—
138	C₄×D₄×C₁₃	—	2	1	no	—
139	C₄×D₄×C₁₃	—	2	1	no	—
140	C₄×D₄×C₁₃	—	2	1	no	—
141	C₄×D₄×C₁₃	—	2	1	no	—
142	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
143	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
144	C₁₃×#117	—	2	2	no	—
145	C₁₃×#117	—	2	2	no	—
146	C₁₃×#117	—	2	1	no	—
147	C₁₃×#117	—	2	1	no	—
148	C₁₃×#117	—	2	1	no	—
149	C₁₃×#117	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
162	C₂×C₄²×C₁₃	—	2	1	no	—
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₁₃×#107	—	2	1	no	—
167	C₁₃×#106	—	2	1	no	—
168	C₁₃×C₄⋊C₈	—	2	1	no	—
169	C₁₃×C₄⋊C₈	—	2	1	no	—
170	C₁₃×#104	—	2	2	no	—
171	C₁₃×#104	—	2	2	no	—
172	C₁₃×#104	—	4	1	no	—
173	C₁₃×#104	—	4	1	no	—
174	C₁₃×#104	—	4	1	no	—
175	C₁₃×#104	—	4	1	no	—
176	C₁₃×#103	—	2	1	no	—
177	C₁₃×#103	—	2	1	no	—
178	C₁₃×#103	—	2	1	no	—
179	C₁₃×#102	—	2	1	no	—
180	C₁₃×#102	—	2	1	no	—
181	C₁₃×#102	—	2	1	no	—
182	C₁₃×#102	—	2	1	no	—
183	C₁₃×#102	—	2	1	no	—
184	C₁₃×#97	—	2	1	no	—
185	C₄×C₈×C₁₃	—	2	1	no	—
186	C₁₃×#95	—	2	1	no	—
187	C₁₃×#95	—	2	2	no	—
188	#24174	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂⁴×C₁₃	—	2	1	no	—
190	C₁₃×#41	—	2	1	no	—
191	C₁₃×#41	—	2	1	no	—
192	C₁₃×#41	—	2	1	no	—
193	C₁₃×#41	—	2	1	no	—
194	C₁₃×#41	—	2	1	no	—
195	C₁₃×#41	—	2	1	no	—
196	C₁₃×#41	—	2	1	no	—
197	C₁₃×#41	—	2	1	no	—
198	C₁₃×#41	—	2	1	no	—
199	C₁₃×#41	—	2	1	no	—
200	C₁₃×#41	—	2	1	no	—
201	C₁₃×#41	—	2	1	no	—
202	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂×D₄×C₁₃	—	2	1	no	—
206	C₂×D₄×C₁₃	—	2	1	no	—
207	C₂×D₄×C₁₃	—	2	1	no	—
208	C₂×D₄×C₁₃	—	2	2	no	—
209	C₂×D₄×C₁₃	—	2	2	no	—
210	C₂×D₄×C₁₃	—	2	1	no	—
211	C₂×D₄×C₁₃	—	2	1	no	—
212	C₂×D₄×C₁₃	—	2	1	no	—
213	C₂×D₄×C₁₃	—	2	1	no	—
214	C₂×D₄×C₁₃	—	2	1	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	2	1	no	—
217	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂×D₄×C₁₃	#41	1	2	yes	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	—	2	1	no	—
231	C₂²×C₄×C₁₃	—	4	1	no	—
232	C₂²×C₄×C₁₃	—	4	1	no	—
233	C₂²×C₄×C₁₃	—	8	2	no	—
234	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₁₃×SD₁₆	—	2	4	no	—
240	C₁₃×SD₁₆	—	4	2	no	—
241	C₁₃×SD₁₆	—	4	2	no	—
242	C₁₃×D₈	—	2	4	no	—
243	C₁₃×D₈	—	4	2	no	—
244	C₁₃×D₈	—	4	2	no	—
245	C₁₃×M₁₆	—	2	1	no	—
246	C₁₃×M₁₆	—	2	1	no	—
247	C₁₃×M₁₆	—	2	1	no	—
248	C₁₃×M₁₆	—	2	1	no	—
249	C₁₃×M₁₆	—	2	1	no	—
250	C₁₃×M₁₆	—	2	1	no	—
251	C₁₃×M₁₆	—	2	1	no	—
252	C₁₃×M₁₆	#41	1	2	yes	—
253	C₂×C₈×C₁₃	—	2	1	no	—
254	C₂×C₈×C₁₃	—	2	1	no	—
255	C₂×C₈×C₁₃	—	2	1	no	—
256	C₂×C₈×C₁₃	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₁₃×C₄⋊C₄	—	2	2	no	—
260	C₁₃×C₄⋊C₄	—	2	2	no	—
261	C₁₃×C₄⋊C₄	—	2	2	no	—
262	C₁₃×C₄⋊C₄	—	2	2	no	—
263	C₁₃×C₄⋊C₄	—	2	2	no	—
264	C₁₃×C₄⋊C₄	—	2	2	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	4	2	no	—
276	C₁₃×C₄⋊C₄	—	8	2	no	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
278	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
279	C₁₃×C₂²⋊C₄	—	2	2	no	—
280	C₁₃×C₂²⋊C₄	—	2	2	no	—
281	C₁₃×C₂²⋊C₄	—	2	2	no	—
282	C₁₃×C₂²⋊C₄	—	2	2	no	—
283	C₁₃×C₂²⋊C₄	—	2	2	no	—
284	C₁₃×C₂²⋊C₄	—	2	2	no	—
285	C₁₃×C₂²⋊C₄	—	2	1	no	—
286	C₁₃×C₂²⋊C₄	—	2	1	no	—
287	C₁₃×C₂²⋊C₄	—	2	1	no	—
288	C₁₃×C₂²⋊C₄	—	2	1	no	—
289	C₁₃×C₂²⋊C₄	—	2	1	no	—
290	C₁₃×C₂²⋊C₄	—	2	1	no	—
291	C₁₃×C₂²⋊C₄	—	2	1	no	—
292	C₁₃×C₂²⋊C₄	—	4	4	no	—
293	C₁₃×C₂²⋊C₄	—	4	1	no	—
294	C₁₃×C₂²⋊C₄	—	4	1	no	—
295	C₁₃×C₂²⋊C₄	—	8	2	no	—
296	C₄²×C₁₃	—	2	2	no	—
297	C₄²×C₁₃	—	2	2	no	—
298	C₄²×C₁₃	—	2	1	no	—
299	C₄²×C₁₃	—	2	1	no	—
300	C₄²×C₁₃	—	2	1	no	—
301	C₄²×C₁₃	—	2	1	no	—
302	C₄²×C₁₃	—	2	1	no	—
303	C₄²×C₁₃	—	2	1	no	—
304	C₄²×C₁₃	—	2	1	no	—
305	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
309	#3512	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#2566	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#2040	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#2039	C₂×C₁₃	1	1	yes	characteristic, complemented
315	#2006	C₂×C₁₃	1	1	yes	characteristic, complemented
316	#2006	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#1998	C₂×C₁₃	1	1	yes	characteristic, complemented
318	#1980	C₂×C₁₃	1	1	yes	characteristic, complemented
319	#1883	C₂×C₁₃	1	1	yes	characteristic, complemented
320	#1883	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#1860	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#1859	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#1806	C₂×C₁₃	1	1	yes	characteristic, complemented
324	C₂³×C₁₃	—	2	1	no	—
325	C₂³×C₁₃	—	2	1	no	—
326	C₂³×C₁₃	—	2	1	no	—
327	C₂³×C₁₃	—	2	2	no	—
328	C₂³×C₁₃	—	4	2	no	—
329	C₂³×C₁₃	—	4	2	no	—
330	C₂³×C₁₃	—	4	1	no	—
331	C₂³×C₁₃	—	4	1	no	—
332	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
333	Q₈×C₁₃	—	2	1	no	—
334	Q₈×C₁₃	—	2	1	no	—
335	Q₈×C₁₃	—	2	1	no	—
336	Q₈×C₁₃	—	2	1	no	—
337	Q₈×C₁₃	—	2	1	no	—
338	Q₈×C₁₃	—	2	1	no	—
339	D₄×C₁₃	—	2	1	no	—
340	D₄×C₁₃	—	2	2	no	—
341	D₄×C₁₃	—	2	1	no	—
342	D₄×C₁₃	—	2	2	no	—
343	D₄×C₁₃	—	2	1	no	—
344	D₄×C₁₃	—	2	1	no	—
345	D₄×C₁₃	—	2	1	no	—
346	D₄×C₁₃	—	2	1	no	—
347	D₄×C₁₃	—	4	1	no	—
348	D₄×C₁₃	—	4	1	no	—
349	D₄×C₁₃	—	4	1	no	—
350	D₄×C₁₃	—	4	1	no	—
351	D₄×C₁₃	—	4	1	no	—
352	D₄×C₁₃	—	4	1	no	—
353	D₄×C₁₃	—	4	1	no	—
354	D₄×C₁₃	—	4	1	no	—
355	D₄×C₁₃	—	8	1	no	—
356	D₄×C₁₃	—	8	1	no	—
357	D₄×C₁₃	—	8	2	no	—
358	D₄×C₁₃	—	8	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	1	no	—
362	C₂×C₄×C₁₃	—	2	1	no	—
363	C₂×C₄×C₁₃	—	2	1	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	4	1	no	—
368	C₂×C₄×C₁₃	—	4	1	no	—
369	C₂×C₄×C₁₃	—	4	1	no	—
370	C₂×C₄×C₁₃	—	4	1	no	—
371	C₂×C₄×C₁₃	—	4	1	no	—
372	C₂×C₄×C₁₃	—	4	1	no	—
373	C₂×C₄×C₁₃	—	4	1	no	—
374	C₂×C₄×C₁₃	—	4	1	no	—
375	C₂×C₄×C₁₃	—	4	1	no	—
376	C₂×C₄×C₁₃	—	4	1	no	—
377	C₂×C₄×C₁₃	—	4	2	no	—
378	C₂×C₄×C₁₃	—	4	2	no	—
379	C₂×C₄×C₁₃	—	4	1	no	—
380	C₂×C₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	—	4	2	no	—
382	C₂×C₄×C₁₃	—	4	1	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	8	1	no	—
385	C₂×C₄×C₁₃	—	8	1	no	—
386	C₂×C₄×C₁₃	—	8	2	no	—
387	C₂×C₄×C₁₃	—	8	2	no	—
388	C₂×C₄×C₁₃	—	8	2	no	—
389	C₂×C₄×C₁₃	—	8	2	no	—
390	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
391	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
392	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
393	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
394	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
397	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
398	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
399	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
400	C₈×C₁₃	—	2	2	no	—
401	C₈×C₁₃	—	4	1	no	—
402	C₈×C₁₃	—	4	1	no	—
403	C₈×C₁₃	—	4	1	no	—
404	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
407	#553	—	2	1	no	—
408	#553	—	2	1	no	—
409	#553	—	2	2	no	—
410	#553	—	2	2	no	—
411	#552	—	2	1	no	—
412	#552	—	2	1	no	—
413	#541	—	2	1	no	—
414	#540	—	2	1	no	—
415	#537	C₂²×C₁₃	1	1	yes	characteristic
416	#537	C₂²×C₁₃	1	1	yes	characteristic
417	#532	C₂²×C₁₃	1	1	yes	characteristic
418	#529	—	2	1	no	—
419	#529	—	2	1	no	—
420	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
421	#520	C₂²×C₁₃	1	1	yes	characteristic
422	#520	C₂²×C₁₃	1	1	yes	characteristic
423	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
425	#463	—	2	1	no	—
426	#463	—	2	1	no	—
427	#461	—	2	1	no	—
428	#459	—	2	1	no	—
429	#442	—	2	1	no	—
430	#440	—	2	1	no	—
431	C₄×SD₁₆	—	2	1	no	—
432	C₄×D₈	—	2	1	no	—
433	#428	C₂²×C₁₃	1	1	yes	characteristic
434	#423	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
441	#418	C₂²×C₁₃	1	1	yes	characteristic
442	#417	C₂²×C₁₃	1	1	yes	characteristic
443	#417	C₂²×C₁₃	1	1	yes	characteristic
444	#417	C₂²×C₁₃	1	1	yes	characteristic
445	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
446	#396	—	2	2	no	—
447	#390	C₂²×C₁₃	1	1	yes	characteristic
448	#390	C₂²×C₁₃	1	1	yes	characteristic
449	#385	—	2	2	no	—
450	#384	C₂²×C₁₃	1	1	yes	characteristic
451	#382	C₂²×C₁₃	1	1	yes	characteristic
452	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
453	#343	C₂²×C₁₃	1	1	yes	characteristic
454	#343	C₂²×C₁₃	1	1	yes	characteristic
455	#343	C₂²×C₁₃	1	1	yes	characteristic
456	#343	C₂²×C₁₃	1	1	yes	characteristic
457	#339	C₂²×C₁₃	1	1	yes	characteristic
458	#339	C₂²×C₁₃	1	1	yes	characteristic
459	C₂²×C₁₃	—	2	1	no	—
460	C₂²×C₁₃	—	2	1	no	—
461	C₂²×C₁₃	—	4	4	no	—
462	C₂²×C₁₃	—	4	1	no	—
463	C₂²×C₁₃	—	4	1	no	—
464	C₂²×C₁₃	—	4	1	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	4	1	no	—
467	C₂²×C₁₃	—	4	1	no	—
468	C₂²×C₁₃	—	4	1	no	—
469	C₂²×C₁₃	—	4	1	no	—
470	C₂²×C₁₃	—	4	1	no	—
471	C₂²×C₁₃	—	4	1	no	—
472	C₂²×C₁₃	—	8	2	no	—
473	C₂²×C₁₃	—	8	1	no	—
474	C₂²×C₁₃	—	8	1	no	—
475	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
476	C₂²×C₁₃	#548	1	1	yes	characteristic
477	C₂²×C₁₃	#550	1	1	yes	characteristic
478	C₄×C₁₃	—	2	1	no	—
479	C₄×C₁₃	—	2	1	no	—
480	C₄×C₁₃	—	2	1	no	—
481	C₄×C₁₃	—	2	1	no	—
482	C₄×C₁₃	—	4	2	no	—
483	C₄×C₁₃	—	4	1	no	—
484	C₄×C₁₃	—	4	1	no	—
485	C₄×C₁₃	—	4	1	no	—
486	C₄×C₁₃	—	4	2	no	—
487	C₄×C₁₃	—	4	1	no	—
488	C₄×C₁₃	—	4	2	no	—
489	C₄×C₁₃	—	4	1	no	—
490	C₄×C₁₃	—	8	1	no	—
491	C₄×C₁₃	—	8	1	no	—
492	C₄×C₁₃	#525	1	1	yes	characteristic
493	C₄×C₁₃	#537	1	1	yes	characteristic
494	C₄×C₁₃	#546	1	1	yes	characteristic
495	C₄×C₁₃	#547	1	1	yes	characteristic
496	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
497	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
498	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
499	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
500	C₂³×C₄	—	2	1	no	—
501	AGL(1,ℤ/8)	—	2	2	no	—
502	AGL(1,ℤ/8)	—	2	2	no	—
503	AGL(1,ℤ/8)	—	2	2	no	—
504	AGL(1,ℤ/8)	—	2	2	no	—
505	AGL(1,ℤ/8)	—	4	1	no	—
506	AGL(1,ℤ/8)	—	4	1	no	—
507	C₂×SD₁₆	—	2	1	no	—
508	C₂×SD₁₆	—	2	1	no	—
509	C₂×SD₁₆	—	2	1	no	—
510	C₂×D₈	—	2	1	no	—
511	C₂×D₈	—	2	1	no	—
512	C₂×D₈	—	2	1	no	—
513	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
514	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
515	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
516	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
517	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
518	#127	D₄×C₁₃	1	1	yes	characteristic
519	#126	—	2	2	no	—
520	#126	—	2	2	no	—
521	#126	—	2	2	no	—
522	#126	—	2	2	no	—
523	#125	—	2	2	no	—
524	#125	—	2	2	no	—
525	#125	—	2	1	no	—
526	#125	—	2	1	no	—
527	#125	—	2	1	no	—
528	#125	—	2	1	no	—
529	#124	D₄×C₁₃	1	1	yes	characteristic
530	#124	D₄×C₁₃	1	1	yes	characteristic
531	#123	—	2	2	no	—
532	#123	—	2	2	no	—
533	#123	—	2	2	no	—
534	#123	—	2	2	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	—	2	1	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	#121	—	2	2	no	—
540	#121	—	2	2	no	—
541	#121	—	2	1	no	—
542	#121	—	2	1	no	—
543	#121	—	2	1	no	—
544	#121	—	2	1	no	—
545	#121	—	2	1	no	—
546	#121	—	2	1	no	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	C₄×Q₈	—	2	1	no	—
550	C₄×Q₈	—	2	1	no	—
551	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
552	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	1	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
568	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
569	#117	—	2	2	no	—
570	#117	—	2	2	no	—
571	#117	—	2	1	no	—
572	#117	—	2	1	no	—
573	#117	—	2	1	no	—
574	#117	C₂³×C₁₃	1	1	yes	characteristic
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	2	no	—
579	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
580	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	2	no	—
586	C₂×C₂²⋊C₄	—	2	2	no	—
587	C₂×C₄²	—	2	1	no	—
588	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
589	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
591	#107	—	2	1	no	—
592	#106	—	2	1	no	—
593	C₄⋊C₈	—	2	1	no	—
594	C₄⋊C₈	—	2	1	no	—
595	#104	—	2	2	no	—
596	#104	—	2	2	no	—
597	#104	—	4	1	no	—
598	#104	—	4	1	no	—
599	#104	—	4	1	no	—
600	#104	—	4	1	no	—
601	#103	—	2	1	no	—
602	#103	—	2	1	no	—
603	#103	—	2	1	no	—
604	#102	—	2	1	no	—
605	#102	—	2	1	no	—
606	#102	—	2	1	no	—
607	#102	—	2	1	no	—
608	#102	—	2	1	no	—
609	#97	—	2	1	no	—
610	C₄×C₈	—	2	1	no	—
611	#95	—	2	1	no	—
612	#95	—	2	2	no	—
613	C₂×C₁₃	—	2	1	no	—
614	C₂×C₁₃	—	2	1	no	—
615	C₂×C₁₃	—	8	1	no	—
616	C₂×C₁₃	—	8	1	no	—
617	C₂×C₁₃	—	8	1	no	—
618	C₂×C₁₃	—	8	2	no	—
619	C₂×C₁₃	#2407	1	1	yes	characteristic
620	C₂×C₁₃	#3018	1	1	yes	characteristic
621	C₂×C₁₃	#3021	1	1	yes	characteristic
622	C₂⁴	—	2	1	no	—
623	#41	—	2	1	no	—
624	#41	—	2	1	no	—
625	#41	—	2	1	no	—
626	#41	—	2	1	no	—
627	#41	—	2	1	no	—
628	#41	—	2	1	no	—
629	#41	—	2	1	no	—
630	#41	—	2	1	no	—
631	#41	—	2	1	no	—
632	#41	—	2	1	no	—
633	#41	—	2	1	no	—
634	#41	—	2	1	no	—
635	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
636	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
637	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
651	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
652	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
653	C₂×D₄	C₁₃×#41	1	2	yes	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	4	1	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	—	8	2	no	—
667	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
668	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
669	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
672	SD₁₆	—	2	4	no	—
673	SD₁₆	—	4	2	no	—
674	SD₁₆	—	4	2	no	—
675	D₈	—	2	4	no	—
676	D₈	—	4	2	no	—
677	D₈	—	4	2	no	—
678	M₁₆	—	2	1	no	—
679	M₁₆	—	2	1	no	—
680	M₁₆	—	2	1	no	—
681	M₁₆	—	2	1	no	—
682	M₁₆	—	2	1	no	—
683	M₁₆	—	2	1	no	—
684	M₁₆	—	2	1	no	—
685	M₁₆	C₁₃×#41	1	2	yes	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	2	1	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	8	2	no	—
710	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
711	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	1	no	—
720	C₂²⋊C₄	—	2	1	no	—
721	C₂²⋊C₄	—	2	1	no	—
722	C₂²⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	4	4	no	—
726	C₂²⋊C₄	—	4	1	no	—
727	C₂²⋊C₄	—	4	1	no	—
728	C₂²⋊C₄	—	8	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	1	no	—
732	C₄²	—	2	1	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	1	no	—
735	C₄²	—	2	1	no	—
736	C₄²	—	2	1	no	—
737	C₄²	—	2	1	no	—
738	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
739	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
740	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
741	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
742	C₁₃	#24174	1	1	yes	characteristic, direct product factor, Sylow
743	C₂³	—	2	1	no	—
744	C₂³	—	2	1	no	—
745	C₂³	—	2	1	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	4	2	no	—
748	C₂³	—	4	2	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
752	Q₈	—	2	1	no	—
753	Q₈	—	2	1	no	—
754	Q₈	—	2	1	no	—
755	Q₈	—	2	1	no	—
756	Q₈	—	2	1	no	—
757	Q₈	—	2	1	no	—
758	D₄	—	2	1	no	—
759	D₄	—	2	2	no	—
760	D₄	—	2	1	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	1	no	—
763	D₄	—	2	1	no	—
764	D₄	—	2	1	no	—
765	D₄	—	2	1	no	—
766	D₄	—	4	1	no	—
767	D₄	—	4	1	no	—
768	D₄	—	4	1	no	—
769	D₄	—	4	1	no	—
770	D₄	—	4	1	no	—
771	D₄	—	4	1	no	—
772	D₄	—	4	1	no	—
773	D₄	—	4	1	no	—
774	D₄	—	8	1	no	—
775	D₄	—	8	1	no	—
776	D₄	—	8	2	no	—
777	D₄	—	8	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	8	1	no	—
804	C₂×C₄	—	8	1	no	—
805	C₂×C₄	—	8	2	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
810	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
811	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
812	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
815	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
816	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
817	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
818	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
819	C₈	—	2	2	no	—
820	C₈	—	4	1	no	—
821	C₈	—	4	1	no	—
822	C₈	—	4	1	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	4	4	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	8	2	no	—
837	C₂²	—	8	1	no	—
838	C₂²	—	8	1	no	—
839	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
840	C₂²	C₁₃×#548	1	1	yes	characteristic
841	C₂²	C₁₃×#550	1	1	yes	characteristic
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	1	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	1	no	—
854	C₄	—	8	1	no	—
855	C₄	—	8	1	no	—
856	C₄	C₁₃×#525	1	1	yes	characteristic
857	C₄	C₁₃×#537	1	1	yes	characteristic
858	C₄	C₁₃×#546	1	1	yes	characteristic
859	C₄	C₁₃×#547	1	1	yes	characteristic
860	C₂	—	2	1	no	—
861	C₂	—	2	1	no	—
862	C₂	—	8	2	no	—
863	C₂	—	8	1	no	—
864	C₂	—	8	1	no	—
865	C₂	—	8	1	no	—
866	C₂	C₁₃×#2407	1	1	yes	characteristic
867	C₂	C₁₃×#3018	1	1	yes	characteristic
868	C₂	C₁₃×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3512	C₂	semidirect
2. C₁₃×#3036	C₂	semidirect
3. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
4. C₁₃×#2566	C₂	semidirect
5. C₁₃×#2040	C₂	semidirect
6. C₁₃×#2039	C₂	semidirect
7. C₁₃×#2006	C₂	semidirect
8. C₁₃×#2006	C₂	semidirect
9. C₁₃×#1998	C₂	semidirect
10. C₁₃×#1980	C₂	semidirect
11. C₁₃×#1883	C₂	semidirect
12. C₁₃×#1883	C₂	semidirect
13. C₁₃×#1860	C₂	semidirect
14. C₁₃×#1859	C₂	semidirect
15. C₁₃×#1806	C₂	semidirect
188. #24174	C₁₃	direct (N × H)
309. #3512	C₂×C₁₃	semidirect
310. #3036	C₂×C₁₃	semidirect
311. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
312. #2566	C₂×C₁₃	semidirect
313. #2040	C₂×C₁₃	semidirect
314. #2039	C₂×C₁₃	semidirect
315. #2006	C₂×C₁₃	semidirect
316. #2006	C₂×C₁₃	semidirect
317. #1998	C₂×C₁₃	semidirect
318. #1980	C₂×C₁₃	semidirect
319. #1883	C₂×C₁₃	semidirect
320. #1883	C₂×C₁₃	semidirect
321. #1860	C₂×C₁₃	semidirect
322. #1859	C₂×C₁₃	semidirect
323. #1806	C₂×C₁₃	semidirect
742. C₁₃	#24174	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×#3036	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2566	2
C₁₃×#2040	2
C₁₃×#2039	2
C₁₃×#2006	2
C₁₃×#1998	2
C₁₃×#1980	2
C₁₃×#1883	2
C₁₃×#1860	2
C₁₃×#1859	2
C₁₃×#1806	2
#24174	13

Subgroups — C13×#24174 #15710513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24174 #15710513