Subgroups — C₁₃×#25140 #15711479

Order 3328.

1140 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₃×#100	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2045	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2018	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1978	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1900	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃	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	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
25	C₁₃×#525	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
27	C₁₃×#472	—	2	4	no	—
28	C₁₃×#469	—	2	1	no	—
29	C₁₃×#468	—	2	1	no	—
30	C₁₃×#466	—	2	1	no	—
31	C₁₃×#465	—	2	1	no	—
32	C₁₃×#450	—	2	1	no	—
33	C₁₃×#450	—	2	1	no	—
34	C₁₃×#447	—	2	1	no	—
35	C₁₃×#447	—	2	1	no	—
36	C₁₃×#447	—	2	1	no	—
37	C₁₃×#447	—	2	1	no	—
38	C₁₃×#447	—	2	1	no	—
39	C₁₃×#447	—	2	1	no	—
40	C₁₃×#436	—	2	1	no	—
41	C₁₃×#435	—	2	1	no	—
42	C₁₃×#435	—	2	1	no	—
43	C₈×D₄×C₁₃	—	2	1	no	—
44	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#418	C₂²	1	1	yes	characteristic
49	C₁₃×#418	C₂²	1	1	yes	characteristic
50	C₁₃×#418	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#100	—	2	4	no	—
55	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#408	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#407	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#341	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#341	C₂²	1	1	yes	characteristic, complemented
69	C₂⁵×C₁₃	—	2	1	no	—
70	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃	—	2	2	no	—
72	C₂²×D₄×C₁₃	—	2	2	no	—
73	C₂²×D₄×C₁₃	—	2	1	no	—
74	C₂²×D₄×C₁₃	—	2	1	no	—
75	C₂²×D₄×C₁₃	—	2	1	no	—
76	C₂²×D₄×C₁₃	—	2	1	no	—
77	C₂²×D₄×C₁₃	—	2	1	no	—
78	C₂²×D₄×C₁₃	—	2	1	no	—
79	C₂²×D₄×C₁₃	—	4	1	no	—
80	C₂²×D₄×C₁₃	—	4	1	no	—
81	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
86	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
87	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
88	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
89	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
90	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
91	C₂×C₁₃×SD₁₆	—	2	1	no	—
92	C₂×C₁₃×SD₁₆	—	2	1	no	—
93	C₂×C₁₃×SD₁₆	—	2	1	no	—
94	C₂×C₁₃×D₈	—	2	1	no	—
95	C₂×C₁₃×D₈	—	2	1	no	—
96	C₂×C₁₃×D₈	—	2	1	no	—
97	C₂×C₁₃×D₈	—	2	2	no	—
98	C₂×C₁₃×D₈	—	2	2	no	—
99	C₂×C₁₃×D₈	—	2	1	no	—
100	C₂×C₁₃×D₈	—	2	1	no	—
101	C₂×C₁₃×D₈	—	2	1	no	—
102	C₂×C₁₃×D₈	—	2	1	no	—
103	C₂×C₁₃×D₈	—	4	1	no	—
104	C₂×C₁₃×D₈	—	4	1	no	—
105	C₁₃×#131	—	2	2	no	—
106	C₁₃×#131	—	4	1	no	—
107	C₂×C₁₃×M₁₆	—	2	1	no	—
108	C₂×C₁₃×M₁₆	—	2	1	no	—
109	C₂×C₁₃×M₁₆	—	2	1	no	—
110	C₂×C₁₃×M₁₆	—	2	2	no	—
111	C₂×C₁₃×M₁₆	—	2	2	no	—
112	C₂×C₁₃×M₁₆	—	4	1	no	—
113	C₂×C₁₃×M₁₆	—	4	1	no	—
114	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₁₃	—	2	1	no	—
121	C₂²×C₈×C₁₃	—	2	1	no	—
122	C₂²×C₈×C₁₃	—	2	1	no	—
123	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₁₃×#123	—	2	1	no	—
126	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
127	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
128	C₁₃×#121	—	2	1	no	—
129	C₁₃×#121	—	2	1	no	—
130	C₁₃×#121	—	2	1	no	—
131	C₁₃×#121	—	2	1	no	—
132	C₁₃×#121	D₄	1	1	yes	characteristic
133	C₁₃×#121	D₄	1	1	yes	characteristic
134	C₁₃×#120	—	2	1	no	—
135	C₄×D₄×C₁₃	—	2	1	no	—
136	C₄×D₄×C₁₃	—	2	1	no	—
137	C₁₃×#117	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
140	C₁₃×#108	—	2	2	no	—
141	C₁₃×#108	—	4	1	no	—
142	C₁₃×#107	—	2	1	no	—
143	C₁₃×#106	—	2	1	no	—
144	C₁₃×C₄⋊C₈	—	2	1	no	—
145	C₁₃×C₄⋊C₈	—	2	1	no	—
146	C₁₃×#103	—	2	1	no	—
147	C₁₃×#102	—	2	1	no	—
148	C₁₃×#102	—	2	1	no	—
149	C₁₃×#102	—	2	1	no	—
150	C₁₃×#102	—	2	1	no	—
151	C₁₃×#102	—	2	1	no	—
152	C₁₃×#102	—	2	1	no	—
153	C₁₃×#102	—	2	1	no	—
154	C₁₃×#102	—	2	1	no	—
155	C₁₃×#102	—	2	1	no	—
156	C₁₃×#102	—	2	1	no	—
157	C₁₃×#102	—	2	1	no	—
158	C₁₃×#100	—	2	2	no	—
159	C₁₃×#100	—	2	2	no	—
160	C₁₃×#100	—	2	2	no	—
161	C₁₃×#100	—	2	2	no	—
162	C₁₃×#100	—	4	1	no	—
163	C₁₃×#100	D₄	1	4	yes	complemented
164	C₁₃×C₂²⋊C₈	—	2	1	no	—
165	C₁₃×C₂²⋊C₈	—	2	1	no	—
166	C₁₃×C₂²⋊C₈	—	2	1	no	—
167	C₁₃×C₂²⋊C₈	—	2	1	no	—
168	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
169	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
170	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
171	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
172	C₁₃×#97	—	2	1	no	—
173	C₄×C₈×C₁₃	—	2	1	no	—
174	#25140	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂⁴×C₁₃	—	2	4	no	—
176	C₂⁴×C₁₃	—	2	1	no	—
177	C₂⁴×C₁₃	—	2	1	no	—
178	C₂⁴×C₁₃	—	2	1	no	—
179	C₂⁴×C₁₃	—	4	2	no	—
180	C₂⁴×C₁₃	—	4	1	no	—
181	C₂⁴×C₁₃	—	4	1	no	—
182	C₂⁴×C₁₃	—	8	2	no	—
183	C₂⁴×C₁₃	—	8	2	no	—
184	C₂⁴×C₁₃	#41	1	1	yes	characteristic
185	C₁₃×#41	—	2	1	no	—
186	C₁₃×#41	—	2	1	no	—
187	C₁₃×#41	—	2	1	no	—
188	C₁₃×#41	—	2	1	no	—
189	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₁₃	—	2	4	no	—
191	C₂×D₄×C₁₃	—	2	1	no	—
192	C₂×D₄×C₁₃	—	2	1	no	—
193	C₂×D₄×C₁₃	—	2	1	no	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	2	1	no	—
196	C₂×D₄×C₁₃	—	2	1	no	—
197	C₂×D₄×C₁₃	—	2	1	no	—
198	C₂×D₄×C₁₃	—	2	1	no	—
199	C₂×D₄×C₁₃	—	2	1	no	—
200	C₂×D₄×C₁₃	—	2	1	no	—
201	C₂×D₄×C₁₃	—	2	1	no	—
202	C₂×D₄×C₁₃	—	2	1	no	—
203	C₂×D₄×C₁₃	—	2	1	no	—
204	C₂×D₄×C₁₃	—	2	1	no	—
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	1	no	—
209	C₂×D₄×C₁₃	—	2	1	no	—
210	C₂×D₄×C₁₃	—	4	2	no	—
211	C₂×D₄×C₁₃	—	4	2	no	—
212	C₂×D₄×C₁₃	—	4	2	no	—
213	C₂×D₄×C₁₃	—	4	2	no	—
214	C₂×D₄×C₁₃	—	4	2	no	—
215	C₂×D₄×C₁₃	—	4	2	no	—
216	C₂×D₄×C₁₃	—	4	2	no	—
217	C₂×D₄×C₁₃	—	4	2	no	—
218	C₂×D₄×C₁₃	—	4	2	no	—
219	C₂×D₄×C₁₃	—	4	1	no	—
220	C₂×D₄×C₁₃	—	4	1	no	—
221	C₂×D₄×C₁₃	—	4	1	no	—
222	C₂×D₄×C₁₃	—	4	1	no	—
223	C₂×D₄×C₁₃	—	8	2	no	—
224	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
225	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂×D₄×C₁₃	#41	1	2	yes	—
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	—	2	1	no	—
232	C₂²×C₄×C₁₃	—	2	1	no	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
238	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₁₃×SD₁₆	—	4	2	no	—
240	C₁₃×SD₁₆	—	4	2	no	—
241	C₁₃×SD₁₆	—	4	2	no	—
242	C₁₃×D₈	—	4	2	no	—
243	C₁₃×D₈	—	4	2	no	—
244	C₁₃×D₈	—	4	2	no	—
245	C₁₃×D₈	—	4	2	no	—
246	C₁₃×D₈	—	4	2	no	—
247	C₁₃×D₈	—	4	2	no	—
248	C₁₃×D₈	—	4	2	no	—
249	C₁₃×M₁₆	—	2	1	no	—
250	C₁₃×M₁₆	—	2	1	no	—
251	C₁₃×M₁₆	—	2	1	no	—
252	C₁₃×M₁₆	—	2	1	no	—
253	C₁₃×M₁₆	—	2	1	no	—
254	C₁₃×M₁₆	—	2	1	no	—
255	C₁₃×M₁₆	—	2	1	no	—
256	C₁₃×M₁₆	—	2	1	no	—
257	C₁₃×M₁₆	—	2	1	no	—
258	C₁₃×M₁₆	—	2	1	no	—
259	C₁₃×M₁₆	—	4	2	no	—
260	C₁₃×M₁₆	—	4	2	no	—
261	C₁₃×M₁₆	—	4	2	no	—
262	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
263	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
264	C₂×C₈×C₁₃	—	2	1	no	—
265	C₂×C₈×C₁₃	—	2	1	no	—
266	C₂×C₈×C₁₃	—	2	1	no	—
267	C₂×C₈×C₁₃	—	2	1	no	—
268	C₂×C₈×C₁₃	—	2	1	no	—
269	C₂×C₈×C₁₃	—	2	1	no	—
270	C₂×C₈×C₁₃	—	2	1	no	—
271	C₂×C₈×C₁₃	—	2	1	no	—
272	C₂×C₈×C₁₃	—	2	1	no	—
273	C₂×C₈×C₁₃	—	2	1	no	—
274	C₂×C₈×C₁₃	—	4	2	no	—
275	C₂×C₈×C₁₃	—	4	2	no	—
276	C₂×C₈×C₁₃	—	4	2	no	—
277	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
286	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	1	no	—
293	C₁₃×C₂²⋊C₄	—	4	1	no	—
294	C₄²×C₁₃	—	2	1	no	—
295	C₂×#472	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#3055	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#3003	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×#447	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#2933	C₂×C₁₃	1	1	yes	characteristic, complemented
300	C₂²×#100	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#2051	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2045	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#2018	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#1978	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#1931	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#1907	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#1900	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#1855	C₂×C₁₃	1	1	yes	characteristic, complemented
310	C₂³×C₁₃	—	2	1	no	—
311	C₂³×C₁₃	—	2	1	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	1	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	4	1	no	—
317	C₂³×C₁₃	—	4	4	no	—
318	C₂³×C₁₃	—	4	4	no	—
319	C₂³×C₁₃	—	4	1	no	—
320	C₂³×C₁₃	—	4	1	no	—
321	C₂³×C₁₃	—	4	1	no	—
322	C₂³×C₁₃	—	4	1	no	—
323	C₂³×C₁₃	—	4	1	no	—
324	C₂³×C₁₃	—	4	1	no	—
325	C₂³×C₁₃	—	4	1	no	—
326	C₂³×C₁₃	—	8	2	no	—
327	C₂³×C₁₃	—	8	2	no	—
328	C₂³×C₁₃	—	8	2	no	—
329	C₂³×C₁₃	—	8	1	no	—
330	C₂³×C₁₃	—	8	1	no	—
331	C₂³×C₁₃	—	8	1	no	—
332	C₂³×C₁₃	—	8	1	no	—
333	C₂³×C₁₃	—	8	1	no	—
334	C₂³×C₁₃	—	8	1	no	—
335	C₂³×C₁₃	—	8	8	no	—
336	C₂³×C₁₃	—	8	8	no	—
337	C₂³×C₁₃	—	8	2	no	—
338	C₂³×C₁₃	#121	1	1	yes	characteristic
339	C₂³×C₁₃	#121	1	1	yes	characteristic
340	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
341	Q₈×C₁₃	—	2	1	no	—
342	Q₈×C₁₃	—	2	1	no	—
343	D₄×C₁₃	—	2	1	no	—
344	D₄×C₁₃	—	2	2	no	—
345	D₄×C₁₃	—	2	2	no	—
346	D₄×C₁₃	—	2	2	no	—
347	D₄×C₁₃	—	2	1	no	—
348	D₄×C₁₃	—	2	2	no	—
349	D₄×C₁₃	—	4	4	no	—
350	D₄×C₁₃	—	4	4	no	—
351	D₄×C₁₃	—	4	1	no	—
352	D₄×C₁₃	—	4	1	no	—
353	D₄×C₁₃	—	4	2	no	—
354	D₄×C₁₃	—	4	1	no	—
355	D₄×C₁₃	—	4	1	no	—
356	D₄×C₁₃	—	4	1	no	—
357	D₄×C₁₃	—	4	1	no	—
358	D₄×C₁₃	—	4	1	no	—
359	D₄×C₁₃	—	4	1	no	—
360	D₄×C₁₃	—	4	1	no	—
361	D₄×C₁₃	—	4	1	no	—
362	D₄×C₁₃	—	8	1	no	—
363	D₄×C₁₃	—	8	2	no	—
364	D₄×C₁₃	—	8	2	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	1	no	—
367	C₂×C₄×C₁₃	—	2	1	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	1	no	—
376	C₂×C₄×C₁₃	—	2	1	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	—	4	1	no	—
379	C₂×C₄×C₁₃	—	4	1	no	—
380	C₂×C₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	—	8	1	no	—
382	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
383	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
384	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
388	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
389	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
390	C₈×C₁₃	—	2	1	no	—
391	C₈×C₁₃	—	2	1	no	—
392	C₈×C₁₃	—	2	2	no	—
393	C₈×C₁₃	—	2	2	no	—
394	C₈×C₁₃	—	2	1	no	—
395	C₈×C₁₃	—	2	1	no	—
396	C₈×C₁₃	—	4	1	no	—
397	C₈×C₁₃	—	4	1	no	—
398	C₈×C₁₃	—	4	1	no	—
399	C₈×C₁₃	—	4	1	no	—
400	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic, complemented
404	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
405	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
407	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
408	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
409	#525	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
411	#472	—	2	4	no	—
412	#469	—	2	1	no	—
413	#468	—	2	1	no	—
414	#466	—	2	1	no	—
415	#465	—	2	1	no	—
416	#450	—	2	1	no	—
417	#450	—	2	1	no	—
418	#447	—	2	1	no	—
419	#447	—	2	1	no	—
420	#447	—	2	1	no	—
421	#447	—	2	1	no	—
422	#447	—	2	1	no	—
423	#447	—	2	1	no	—
424	#436	—	2	1	no	—
425	#435	—	2	1	no	—
426	#435	—	2	1	no	—
427	C₈×D₄	—	2	1	no	—
428	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
429	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
430	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	#418	C₂²×C₁₃	1	1	yes	characteristic
433	#418	C₂²×C₁₃	1	1	yes	characteristic
434	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#100	—	2	4	no	—
439	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
445	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
446	#407	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
448	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
451	#341	C₂²×C₁₃	1	1	yes	characteristic, complemented
452	#341	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	C₂²×C₁₃	—	2	1	no	—
454	C₂²×C₁₃	—	2	1	no	—
455	C₂²×C₁₃	—	2	1	no	—
456	C₂²×C₁₃	—	2	1	no	—
457	C₂²×C₁₃	—	2	1	no	—
458	C₂²×C₁₃	—	2	1	no	—
459	C₂²×C₁₃	—	2	1	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	—	4	2	no	—
462	C₂²×C₁₃	—	4	1	no	—
463	C₂²×C₁₃	—	4	2	no	—
464	C₂²×C₁₃	—	4	2	no	—
465	C₂²×C₁₃	—	4	1	no	—
466	C₂²×C₁₃	—	4	1	no	—
467	C₂²×C₁₃	—	8	2	no	—
468	C₂²×C₁₃	—	8	2	no	—
469	C₂²×C₁₃	—	8	8	no	—
470	C₂²×C₁₃	—	8	2	no	—
471	C₂²×C₁₃	—	8	2	no	—
472	C₂²×C₁₃	—	8	8	no	—
473	C₂²×C₁₃	—	8	1	no	—
474	C₂²×C₁₃	—	8	1	no	—
475	C₂²×C₁₃	—	8	1	no	—
476	C₂²×C₁₃	—	8	1	no	—
477	C₂²×C₁₃	—	8	1	no	—
478	C₂²×C₁₃	—	8	1	no	—
479	C₂²×C₁₃	—	8	1	no	—
480	C₂²×C₁₃	—	16	1	no	—
481	C₂²×C₁₃	—	16	1	no	—
482	C₂²×C₁₃	#472	1	2	yes	complemented
483	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
484	C₂²×C₁₃	#525	1	1	yes	characteristic
485	C₂²×C₁₃	#538	1	1	yes	characteristic
486	C₄×C₁₃	—	2	1	no	—
487	C₄×C₁₃	—	2	1	no	—
488	C₄×C₁₃	—	4	1	no	—
489	C₄×C₁₃	—	4	1	no	—
490	C₄×C₁₃	—	4	1	no	—
491	C₄×C₁₃	—	8	1	no	—
492	C₄×C₁₃	D₄²	1	1	yes	characteristic
493	C₄×C₁₃	D₄²	1	1	yes	characteristic
494	C₄×C₁₃	#546	1	1	yes	characteristic
495	C₄×C₁₃	#546	1	1	yes	characteristic
496	C₂⁵	—	2	1	no	—
497	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
498	C₂²×D₄	—	2	2	no	—
499	C₂²×D₄	—	2	2	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	—	2	1	no	—
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	4	1	no	—
507	C₂²×D₄	—	4	1	no	—
508	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
512	AGL(1,ℤ/8)	—	2	2	no	—
513	AGL(1,ℤ/8)	—	2	2	no	—
514	AGL(1,ℤ/8)	—	2	2	no	—
515	AGL(1,ℤ/8)	—	4	1	no	—
516	AGL(1,ℤ/8)	—	4	1	no	—
517	AGL(1,ℤ/8)	—	4	1	no	—
518	C₂×SD₁₆	—	2	1	no	—
519	C₂×SD₁₆	—	2	1	no	—
520	C₂×SD₁₆	—	2	1	no	—
521	C₂×D₈	—	2	2	no	—
522	C₂×D₈	—	2	1	no	—
523	C₂×D₈	—	2	1	no	—
524	C₂×D₈	—	2	1	no	—
525	C₂×D₈	—	2	2	no	—
526	C₂×D₈	—	2	1	no	—
527	C₂×D₈	—	2	1	no	—
528	C₂×D₈	—	2	1	no	—
529	C₂×D₈	—	2	1	no	—
530	C₂×D₈	—	4	1	no	—
531	C₂×D₈	—	4	1	no	—
532	#131	—	2	2	no	—
533	#131	—	4	1	no	—
534	C₂×M₁₆	—	2	1	no	—
535	C₂×M₁₆	—	2	1	no	—
536	C₂×M₁₆	—	2	1	no	—
537	C₂×M₁₆	—	2	2	no	—
538	C₂×M₁₆	—	2	2	no	—
539	C₂×M₁₆	—	4	1	no	—
540	C₂×M₁₆	—	4	1	no	—
541	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
542	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
544	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
545	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
546	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
547	C₂²×C₈	—	2	1	no	—
548	C₂²×C₈	—	2	1	no	—
549	C₂²×C₈	—	2	1	no	—
550	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
551	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
552	#123	—	2	1	no	—
553	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
554	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
555	#121	—	2	1	no	—
556	#121	—	2	1	no	—
557	#121	—	2	1	no	—
558	#121	—	2	1	no	—
559	#121	D₄×C₁₃	1	1	yes	characteristic
560	#121	D₄×C₁₃	1	1	yes	characteristic
561	#120	—	2	1	no	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	—	2	1	no	—
564	#117	C₂³×C₁₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	#108	—	2	2	no	—
568	#108	—	4	1	no	—
569	#107	—	2	1	no	—
570	#106	—	2	1	no	—
571	C₄⋊C₈	—	2	1	no	—
572	C₄⋊C₈	—	2	1	no	—
573	#103	—	2	1	no	—
574	#102	—	2	1	no	—
575	#102	—	2	1	no	—
576	#102	—	2	1	no	—
577	#102	—	2	1	no	—
578	#102	—	2	1	no	—
579	#102	—	2	1	no	—
580	#102	—	2	1	no	—
581	#102	—	2	1	no	—
582	#102	—	2	1	no	—
583	#102	—	2	1	no	—
584	#102	—	2	1	no	—
585	#100	—	2	2	no	—
586	#100	—	2	2	no	—
587	#100	—	2	2	no	—
588	#100	—	2	2	no	—
589	#100	—	4	1	no	—
590	#100	D₄×C₁₃	1	4	yes	complemented
591	C₂²⋊C₈	—	2	1	no	—
592	C₂²⋊C₈	—	2	1	no	—
593	C₂²⋊C₈	—	2	1	no	—
594	C₂²⋊C₈	—	2	1	no	—
595	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
596	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
597	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
598	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
599	#97	—	2	1	no	—
600	C₄×C₈	—	2	1	no	—
601	C₂×C₁₃	—	2	1	no	—
602	C₂×C₁₃	—	2	1	no	—
603	C₂×C₁₃	—	2	2	no	—
604	C₂×C₁₃	—	4	1	no	—
605	C₂×C₁₃	—	8	1	no	—
606	C₂×C₁₃	—	8	2	no	—
607	C₂×C₁₃	—	8	2	no	—
608	C₂×C₁₃	—	16	1	no	—
609	C₂×C₁₃	#2424	1	1	yes	characteristic
610	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
611	C₂×C₁₃	#3068	1	1	yes	characteristic
612	C₂⁴	—	2	4	no	—
613	C₂⁴	—	2	1	no	—
614	C₂⁴	—	2	1	no	—
615	C₂⁴	—	2	1	no	—
616	C₂⁴	—	4	2	no	—
617	C₂⁴	—	4	1	no	—
618	C₂⁴	—	4	1	no	—
619	C₂⁴	—	8	2	no	—
620	C₂⁴	—	8	2	no	—
621	C₂⁴	C₁₃×#41	1	1	yes	characteristic
622	#41	—	2	1	no	—
623	#41	—	2	1	no	—
624	#41	—	2	1	no	—
625	#41	—	2	1	no	—
626	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	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	—	4	2	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	—	4	2	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	1	no	—
657	C₂×D₄	—	4	1	no	—
658	C₂×D₄	—	4	1	no	—
659	C₂×D₄	—	4	1	no	—
660	C₂×D₄	—	8	2	no	—
661	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
662	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
663	C₂×D₄	C₁₃×#41	1	2	yes	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
671	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
676	SD₁₆	—	4	2	no	—
677	SD₁₆	—	4	2	no	—
678	SD₁₆	—	4	2	no	—
679	D₈	—	4	2	no	—
680	D₈	—	4	2	no	—
681	D₈	—	4	2	no	—
682	D₈	—	4	2	no	—
683	D₈	—	4	2	no	—
684	D₈	—	4	2	no	—
685	D₈	—	4	2	no	—
686	M₁₆	—	2	1	no	—
687	M₁₆	—	2	1	no	—
688	M₁₆	—	2	1	no	—
689	M₁₆	—	2	1	no	—
690	M₁₆	—	2	1	no	—
691	M₁₆	—	2	1	no	—
692	M₁₆	—	2	1	no	—
693	M₁₆	—	2	1	no	—
694	M₁₆	—	2	1	no	—
695	M₁₆	—	2	1	no	—
696	M₁₆	—	4	2	no	—
697	M₁₆	—	4	2	no	—
698	M₁₆	—	4	2	no	—
699	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
700	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
701	C₂×C₈	—	2	1	no	—
702	C₂×C₈	—	2	1	no	—
703	C₂×C₈	—	2	1	no	—
704	C₂×C₈	—	2	1	no	—
705	C₂×C₈	—	2	1	no	—
706	C₂×C₈	—	2	1	no	—
707	C₂×C₈	—	2	1	no	—
708	C₂×C₈	—	2	1	no	—
709	C₂×C₈	—	2	1	no	—
710	C₂×C₈	—	2	1	no	—
711	C₂×C₈	—	4	2	no	—
712	C₂×C₈	—	4	2	no	—
713	C₂×C₈	—	4	2	no	—
714	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
715	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
723	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	4	1	no	—
730	C₂²⋊C₄	—	4	1	no	—
731	C₄²	—	2	1	no	—
732	C₁₃	#25140	1	1	yes	characteristic, direct product factor, Sylow
733	C₂³	—	2	2	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	4	1	no	—
740	C₂³	—	4	4	no	—
741	C₂³	—	4	4	no	—
742	C₂³	—	4	1	no	—
743	C₂³	—	4	1	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	—	4	1	no	—
749	C₂³	—	8	1	no	—
750	C₂³	—	8	1	no	—
751	C₂³	—	8	1	no	—
752	C₂³	—	8	1	no	—
753	C₂³	—	8	2	no	—
754	C₂³	—	8	2	no	—
755	C₂³	—	8	2	no	—
756	C₂³	—	8	1	no	—
757	C₂³	—	8	1	no	—
758	C₂³	—	8	8	no	—
759	C₂³	—	8	8	no	—
760	C₂³	—	8	2	no	—
761	C₂³	C₁₃×#121	1	1	yes	characteristic
762	C₂³	C₁₃×#121	1	1	yes	characteristic
763	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
764	Q₈	—	2	1	no	—
765	Q₈	—	2	1	no	—
766	D₄	—	2	1	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	1	no	—
771	D₄	—	2	2	no	—
772	D₄	—	4	4	no	—
773	D₄	—	4	4	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	1	no	—
776	D₄	—	4	1	no	—
777	D₄	—	4	1	no	—
778	D₄	—	4	1	no	—
779	D₄	—	4	1	no	—
780	D₄	—	4	1	no	—
781	D₄	—	4	1	no	—
782	D₄	—	4	1	no	—
783	D₄	—	4	1	no	—
784	D₄	—	4	1	no	—
785	D₄	—	8	1	no	—
786	D₄	—	8	2	no	—
787	D₄	—	8	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	8	1	no	—
805	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
806	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
810	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
811	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
812	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
813	C₈	—	2	1	no	—
814	C₈	—	2	1	no	—
815	C₈	—	2	2	no	—
816	C₈	—	2	2	no	—
817	C₈	—	2	1	no	—
818	C₈	—	2	1	no	—
819	C₈	—	4	1	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	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	8	2	no	—
838	C₂²	—	8	2	no	—
839	C₂²	—	8	8	no	—
840	C₂²	—	8	2	no	—
841	C₂²	—	8	2	no	—
842	C₂²	—	8	8	no	—
843	C₂²	—	8	1	no	—
844	C₂²	—	8	1	no	—
845	C₂²	—	8	1	no	—
846	C₂²	—	8	1	no	—
847	C₂²	—	8	1	no	—
848	C₂²	—	8	1	no	—
849	C₂²	—	8	1	no	—
850	C₂²	—	16	1	no	—
851	C₂²	—	16	1	no	—
852	C₂²	C₁₃×#472	1	2	yes	complemented
853	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
854	C₂²	C₁₃×#525	1	1	yes	characteristic
855	C₂²	C₁₃×#538	1	1	yes	characteristic
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	8	1	no	—
862	C₄	D₄²×C₁₃	1	1	yes	characteristic
863	C₄	D₄²×C₁₃	1	1	yes	characteristic
864	C₄	C₁₃×#546	1	1	yes	characteristic
865	C₄	C₁₃×#546	1	1	yes	characteristic
866	C₂	—	2	1	no	—
867	C₂	—	2	1	no	—
868	C₂	—	2	2	no	—
869	C₂	—	4	1	no	—
870	C₂	—	8	1	no	—
871	C₂	—	8	2	no	—
872	C₂	—	8	2	no	—
873	C₂	—	16	1	no	—
874	C₂	C₁₃×#2424	1	1	yes	characteristic
875	C₂	C₂×C₁₃×#472	1	1	yes	characteristic
876	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#472	C₂	semidirect
2. C₁₃×#3055	C₂	semidirect
3. C₁₃×#3003	C₂	semidirect
4. C₂×C₁₃×#447	C₂	semidirect
5. C₁₃×#2933	C₂	semidirect
6. C₂²×C₁₃×#100	C₂	semidirect
7. C₁₃×#2063	C₂	semidirect
8. C₁₃×#2051	C₂	semidirect
9. C₁₃×#2045	C₂	semidirect
10. C₁₃×#2018	C₂	semidirect
11. C₁₃×#1978	C₂	semidirect
12. C₁₃×#1931	C₂	semidirect
13. C₁₃×#1907	C₂	semidirect
14. C₁₃×#1900	C₂	semidirect
15. C₁₃×#1855	C₂	semidirect
19. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₁₃×#131	C₂²	semidirect
44. C₂×C₁₃×#108	C₂²	semidirect
45. C₂×C₁₃×#108	C₂²	semidirect
46. C₁₃×#428	C₂²	semidirect
47. C₁₃×#424	C₂²	semidirect
50. C₁₃×#418	C₂²	semidirect
51. C₁₃×#417	C₂²	semidirect
59. C₂×C₁₃×#100	C₂²	semidirect
60. C₂×C₁₃×#100	C₂²	semidirect
61. C₁₃×#408	C₂²	semidirect
64. C₁₃×#405	C₂²	semidirect
65. C₁₃×#343	C₂²	semidirect
66. C₁₃×#343	C₂²	semidirect
67. C₁₃×#341	C₂²	semidirect
68. C₁₃×#341	C₂²	semidirect
163. C₁₃×#100	D₄	semidirect
174. #25140	C₁₃	direct (N × H)
295. C₂×#472	C₂×C₁₃	semidirect
296. #3055	C₂×C₁₃	semidirect
297. #3003	C₂×C₁₃	semidirect
298. C₂×#447	C₂×C₁₃	semidirect
299. #2933	C₂×C₁₃	semidirect
300. C₂²×#100	C₂×C₁₃	semidirect
301. #2063	C₂×C₁₃	semidirect
302. #2051	C₂×C₁₃	semidirect
303. #2045	C₂×C₁₃	semidirect
304. #2018	C₂×C₁₃	semidirect
305. #1978	C₂×C₁₃	semidirect
306. #1931	C₂×C₁₃	semidirect
307. #1907	C₂×C₁₃	semidirect
308. #1900	C₂×C₁₃	semidirect
309. #1855	C₂×C₁₃	semidirect
403. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
406. C₂×#131	C₂²×C₁₃	semidirect
428. C₂×#108	C₂²×C₁₃	semidirect
429. C₂×#108	C₂²×C₁₃	semidirect
430. #428	C₂²×C₁₃	semidirect
431. #424	C₂²×C₁₃	semidirect
434. #418	C₂²×C₁₃	semidirect
435. #417	C₂²×C₁₃	semidirect
443. C₂×#100	C₂²×C₁₃	semidirect
444. C₂×#100	C₂²×C₁₃	semidirect
445. #408	C₂²×C₁₃	semidirect
448. #405	C₂²×C₁₃	semidirect
449. #343	C₂²×C₁₃	semidirect
450. #343	C₂²×C₁₃	semidirect
451. #341	C₂²×C₁₃	semidirect
452. #341	C₂²×C₁₃	semidirect
482. C₂²×C₁₃	#472	semidirect
590. #100	D₄×C₁₃	semidirect
732. C₁₃	#25140	direct (N × H)
852. C₂²	C₁₃×#472	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#472	2
C₁₃×#3055	2
C₁₃×#3003	2
C₂×C₁₃×#447	2
C₁₃×#2933	2
C₂²×C₁₃×#100	2
C₁₃×#2063	2
C₁₃×#2051	2
C₁₃×#2045	2
C₁₃×#2018	2
C₁₃×#1978	2
C₁₃×#1931	2
C₁₃×#1907	2
C₁₃×#1900	2
C₁₃×#1855	2
#25140	13

Subgroups — C13×#25140 #15711479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25140 #15711479