Subgroups — C₁₃×#60700 #15747039

Order 3328.

2256 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3184	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3182	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3180	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3171	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3169	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3167	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3055	C₂	1	4	yes	maximal, complemented
14	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	4	yes	maximal, complemented
15	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	—	2	1	no	—
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
18	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
19	C₁₃×#533	C₂²	1	1	yes	characteristic
20	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#532	—	2	1	no	—
23	C₁₃×#532	—	2	1	no	—
24	C₁₃×#532	—	2	1	no	—
25	C₁₃×#532	—	2	1	no	—
26	C₁₃×#532	C₂²	1	1	yes	characteristic
27	C₁₃×#532	C₂²	1	2	yes	—
28	C₁₃×#532	C₂²	1	2	yes	—
29	C₁₃×#532	C₂²	1	2	yes	—
30	C₁₃×#532	C₂²	1	2	yes	—
31	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
35	C₁₃×#529	—	2	1	no	—
36	C₁₃×#529	—	2	1	no	—
37	C₁₃×#529	—	2	1	no	—
38	C₁₃×#529	—	2	1	no	—
39	C₁₃×#529	C₂²	1	2	yes	complemented
40	C₁₃×#529	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#124	—	2	1	no	—
42	C₁₃×#525	—	2	1	no	—
43	C₁₃×#525	—	2	1	no	—
44	C₁₃×#525	C₂²	1	2	yes	—
45	C₂×C₁₃×#121	—	2	1	no	—
46	C₂×C₁₃×#121	C₂²	1	2	yes	—
47	C₄×C₁₃×#41	—	2	1	no	—
48	C₄×C₁₃×#41	—	2	1	no	—
49	C₄×C₁₃×#41	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₁₃	—	2	1	no	—
51	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
52	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
53	C₁₃×#501	C₂²	1	4	yes	complemented
54	C₁₃×#500	C₂²	1	2	yes	complemented
55	C₁₃×#498	C₂²	1	2	yes	complemented
56	C₁₃×#496	C₂²	1	4	yes	complemented
57	C₁₃×#493	C₂²	1	2	yes	complemented
58	C₁₃×#492	C₂²	1	2	yes	complemented
59	C₁₃×#490	C₂²	1	4	yes	complemented
60	C₁₃×#489	C₂²	1	4	yes	complemented
61	C₁₃×#487	C₂²	1	2	yes	complemented
62	C₁₃×#486	C₂²	1	2	yes	complemented
63	C₁₃×#486	C₂²	1	2	yes	complemented
64	C₁₃×#486	C₂²	1	2	yes	complemented
65	C₁₃×#469	C₂²	1	8	yes	complemented
66	C₁₃×#468	C₂²	1	8	yes	complemented
67	C₁₃×#466	C₂²	1	8	yes	complemented
68	C₁₃×#465	C₂²	1	8	yes	complemented
69	C₁₃×#442	C₂²	1	8	yes	complemented
70	C₁₃×#440	C₂²	1	8	yes	complemented
71	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
72	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
73	C₁₃×#428	C₂²	1	4	yes	—
74	C₁₃×#418	C₂²	1	4	yes	—
75	C₁₃×#417	C₂²	1	4	yes	—
76	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
77	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
78	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
79	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
80	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
81	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
82	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
83	C₂×C₁₃×#41	—	2	1	no	—
84	C₂×C₁₃×#41	—	2	1	no	—
85	C₂×C₁₃×#41	—	2	2	no	—
86	C₂×C₁₃×#41	—	2	2	no	—
87	C₂×C₁₃×#41	—	2	2	no	—
88	C₂×C₁₃×#41	—	2	2	no	—
89	C₂×C₁₃×#41	—	4	8	no	—
90	C₂×C₁₃×#41	C₂³	1	2	yes	—
91	C₂²×Q₈×C₁₃	—	2	1	no	—
92	C₂²×D₄×C₁₃	—	2	2	no	—
93	C₂²×D₄×C₁₃	—	2	1	no	—
94	C₂²×D₄×C₁₃	—	2	1	no	—
95	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃	—	2	2	no	—
97	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
101	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
102	C₂×C₁₃×D₈	C₂³	1	8	yes	—
103	C₂×C₁₃×M₁₆	—	2	8	no	—
104	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
107	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
108	C₁₃×C₄⋊Q₈	—	2	1	no	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₃×#127	—	2	1	no	—
116	C₁₃×#127	—	2	1	no	—
117	C₁₃×#127	C₂³	1	2	yes	—
118	C₁₃×#127	C₂³	1	1	yes	characteristic
119	C₁₃×#127	C₂³	1	2	yes	—
120	C₁₃×#126	—	2	2	no	—
121	C₁₃×#126	—	2	2	no	—
122	C₁₃×#125	—	2	1	no	—
123	C₁₃×#125	—	2	1	no	—
124	C₁₃×#125	C₂³	1	2	yes	—
125	C₁₃×#124	—	2	2	no	—
126	C₁₃×#124	—	2	2	no	—
127	C₁₃×#124	—	2	2	no	—
128	C₁₃×#124	—	2	2	no	—
129	C₁₃×#124	—	2	1	no	—
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	C₂³	1	2	yes	—
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×C₂²⋊Q₈	—	2	1	no	—
136	C₁₃×C₂²⋊Q₈	—	2	1	no	—
137	C₁₃×C₂²⋊Q₈	—	2	1	no	—
138	C₁₃×C₂²⋊Q₈	—	2	1	no	—
139	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
140	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₁₃×#121	—	2	2	no	—
142	C₁₃×#121	—	2	2	no	—
143	C₁₃×#121	—	2	2	no	—
144	C₁₃×#121	—	2	2	no	—
145	C₁₃×#121	—	2	2	no	—
146	C₁₃×#121	—	2	2	no	—
147	C₁₃×#121	—	2	1	no	—
148	C₁₃×#121	—	2	1	no	—
149	C₁₃×#121	—	2	1	no	—
150	C₁₃×#121	—	2	1	no	—
151	C₁₃×#121	C₂³	1	4	yes	—
152	C₁₃×#121	C₂³	1	2	yes	—
153	C₁₃×#121	C₂³	1	4	yes	—
154	C₁₃×#121	C₂³	1	2	yes	—
155	C₁₃×#120	—	2	2	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	—	2	1	no	—
158	C₄×Q₈×C₁₃	—	2	1	no	—
159	C₄×Q₈×C₁₃	—	2	1	no	—
160	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
161	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
162	C₄×D₄×C₁₃	—	2	2	no	—
163	C₄×D₄×C₁₃	—	2	2	no	—
164	C₄×D₄×C₁₃	—	2	2	no	—
165	C₄×D₄×C₁₃	—	2	2	no	—
166	C₄×D₄×C₁₃	—	2	2	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	2	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	C₂³	1	2	yes	—
179	C₄×D₄×C₁₃	C₂³	1	4	yes	—
180	C₄×D₄×C₁₃	C₂³	1	4	yes	—
181	C₄×D₄×C₁₃	C₂³	1	2	yes	—
182	C₁₃×#117	—	2	1	no	—
183	C₁₃×#117	—	2	1	no	—
184	C₁₃×#117	—	2	2	no	—
185	C₁₃×#117	—	2	2	no	—
186	C₁₃×#117	—	2	2	no	—
187	C₁₃×#117	C₂³	1	2	yes	—
188	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
191	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
192	C₂×C₄²×C₁₃	—	2	2	no	—
193	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
195	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
196	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
197	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
205	C₁₃×#107	C₂³	1	8	yes	—
206	C₁₃×#106	C₂³	1	8	yes	—
207	C₁₃×#103	C₂³	1	8	yes	—
208	C₁₃×#102	C₂³	1	8	yes	—
209	C₁₃×#102	C₂³	1	8	yes	—
210	C₁₃×#102	C₂³	1	8	yes	—
211	C₁₃×#97	C₂³	1	4	yes	—
212	C₁₃×#97	C₂³	1	2	yes	—
213	C₁₃×#97	C₂³	1	2	yes	—
214	C₄×C₈×C₁₃	C₂³	1	4	yes	—
215	C₄×C₈×C₁₃	C₂³	1	2	yes	—
216	C₄×C₈×C₁₃	C₂³	1	2	yes	—
217	#60700	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂⁴×C₁₃	—	2	2	no	—
219	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₁₃×#41	—	2	8	no	—
221	C₁₃×#41	—	4	4	no	—
222	C₁₃×#41	—	4	8	no	—
223	C₁₃×#41	—	4	8	no	—
224	C₁₃×#41	—	4	8	no	—
225	C₁₃×#41	—	4	4	no	—
226	C₁₃×#41	—	4	8	no	—
227	C₂×Q₈×C₁₃	—	2	1	no	—
228	C₂×Q₈×C₁₃	—	2	1	no	—
229	C₂×Q₈×C₁₃	—	2	2	no	—
230	C₂×Q₈×C₁₃	—	2	2	no	—
231	C₂×Q₈×C₁₃	—	4	4	no	—
232	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
233	C₂×D₄×C₁₃	—	2	2	no	—
234	C₂×D₄×C₁₃	—	2	2	no	—
235	C₂×D₄×C₁₃	—	2	2	no	—
236	C₂×D₄×C₁₃	—	2	4	no	—
237	C₂×D₄×C₁₃	—	2	4	no	—
238	C₂×D₄×C₁₃	—	2	1	no	—
239	C₂×D₄×C₁₃	—	2	1	no	—
240	C₂×D₄×C₁₃	—	2	2	no	—
241	C₂×D₄×C₁₃	—	2	2	no	—
242	C₂×D₄×C₁₃	—	2	2	no	—
243	C₂×D₄×C₁₃	—	2	2	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	8	no	—
246	C₂×D₄×C₁₃	—	4	4	no	—
247	C₂×D₄×C₁₃	—	4	4	no	—
248	C₂×D₄×C₁₃	—	4	8	no	—
249	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₁₃	—	2	4	no	—
252	C₂²×C₄×C₁₃	—	2	4	no	—
253	C₂²×C₄×C₁₃	—	2	2	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	4	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	4	no	—
259	C₂²×C₄×C₁₃	—	4	2	no	—
260	C₂²×C₄×C₁₃	—	4	8	no	—
261	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₁₃×SD₁₆	—	2	16	no	—
280	C₁₃×D₈	—	2	16	no	—
281	C₁₃×M₁₆	—	2	4	no	—
282	C₁₃×M₁₆	—	2	8	no	—
283	C₁₃×M₁₆	#41	1	8	yes	complemented
284	C₂×C₈×C₁₃	—	2	8	no	—
285	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
286	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
303	C₁₃×C₂²⋊C₄	—	2	2	no	—
304	C₁₃×C₂²⋊C₄	—	2	2	no	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	4	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	2	no	—
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₄²×C₁₃	—	2	2	no	—
317	C₄²×C₁₃	—	2	2	no	—
318	C₄²×C₁₃	—	2	2	no	—
319	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
332	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
334	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
335	#3444	C₂×C₁₃	1	1	yes	characteristic, complemented
336	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#3184	C₂×C₁₃	1	2	yes	complemented
338	#3182	C₂×C₁₃	1	2	yes	complemented
339	#3180	C₂×C₁₃	1	4	yes	complemented
340	#3171	C₂×C₁₃	1	4	yes	complemented
341	#3169	C₂×C₁₃	1	2	yes	complemented
342	#3167	C₂×C₁₃	1	2	yes	complemented
343	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3055	C₂×C₁₃	1	4	yes	complemented
348	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	4	yes	complemented
349	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
350	C₂³×C₁₃	—	2	2	no	—
351	C₂³×C₁₃	—	2	2	no	—
352	C₂³×C₁₃	—	2	2	no	—
353	C₂³×C₁₃	—	2	4	no	—
354	C₂³×C₁₃	—	4	1	no	—
355	C₂³×C₁₃	—	4	4	no	—
356	C₂³×C₁₃	—	4	4	no	—
357	C₂³×C₁₃	—	4	4	no	—
358	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
360	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	Q₈×C₁₃	—	2	4	no	—
362	Q₈×C₁₃	—	4	4	no	—
363	Q₈×C₁₃	—	4	4	no	—
364	Q₈×C₁₃	—	4	2	no	—
365	Q₈×C₁₃	—	4	2	no	—
366	D₄×C₁₃	—	2	4	no	—
367	D₄×C₁₃	—	2	8	no	—
368	D₄×C₁₃	—	4	4	no	—
369	D₄×C₁₃	—	4	4	no	—
370	D₄×C₁₃	—	4	8	no	—
371	D₄×C₁₃	—	4	4	no	—
372	D₄×C₁₃	—	4	4	no	—
373	D₄×C₁₃	—	4	8	no	—
374	D₄×C₁₃	—	4	4	no	—
375	D₄×C₁₃	—	4	4	no	—
376	D₄×C₁₃	—	4	4	no	—
377	D₄×C₁₃	—	4	2	no	—
378	D₄×C₁₃	—	4	4	no	—
379	D₄×C₁₃	—	4	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	4	no	—
397	C₂×C₄×C₁₃	—	4	1	no	—
398	C₂×C₄×C₁₃	—	4	1	no	—
399	C₂×C₄×C₁₃	—	4	1	no	—
400	C₂×C₄×C₁₃	—	4	8	no	—
401	C₂×C₄×C₁₃	—	4	4	no	—
402	C₂×C₄×C₁₃	—	4	4	no	—
403	C₂×C₄×C₁₃	—	4	4	no	—
404	C₂×C₄×C₁₃	—	4	8	no	—
405	C₂×C₄×C₁₃	—	4	4	no	—
406	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
419	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
420	C₈×C₁₃	—	2	4	no	—
421	C₈×C₁₃	C₂×#41	1	8	yes	complemented
422	C₂²×#41	—	2	1	no	—
423	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
424	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
425	#533	C₂²×C₁₃	1	1	yes	characteristic
426	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	#532	—	2	1	no	—
429	#532	—	2	1	no	—
430	#532	—	2	1	no	—
431	#532	—	2	1	no	—
432	#532	C₂²×C₁₃	1	1	yes	characteristic
433	#532	C₂²×C₁₃	1	2	yes	—
434	#532	C₂²×C₁₃	1	2	yes	—
435	#532	C₂²×C₁₃	1	2	yes	—
436	#532	C₂²×C₁₃	1	2	yes	—
437	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
441	#529	—	2	1	no	—
442	#529	—	2	1	no	—
443	#529	—	2	1	no	—
444	#529	—	2	1	no	—
445	#529	C₂²×C₁₃	1	2	yes	complemented
446	#529	C₂²×C₁₃	1	2	yes	complemented
447	C₂×#124	—	2	1	no	—
448	#525	—	2	1	no	—
449	#525	—	2	1	no	—
450	#525	C₂²×C₁₃	1	2	yes	—
451	C₂×#121	—	2	1	no	—
452	C₂×#121	C₂²×C₁₃	1	2	yes	—
453	C₄×#41	—	2	1	no	—
454	C₄×#41	—	2	1	no	—
455	C₄×#41	C₂²×C₁₃	1	2	yes	—
456	C₂×C₄×D₄	—	2	1	no	—
457	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
458	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
459	#501	C₂²×C₁₃	1	4	yes	complemented
460	#500	C₂²×C₁₃	1	2	yes	complemented
461	#498	C₂²×C₁₃	1	2	yes	complemented
462	#496	C₂²×C₁₃	1	4	yes	complemented
463	#493	C₂²×C₁₃	1	2	yes	complemented
464	#492	C₂²×C₁₃	1	2	yes	complemented
465	#490	C₂²×C₁₃	1	4	yes	complemented
466	#489	C₂²×C₁₃	1	4	yes	complemented
467	#487	C₂²×C₁₃	1	2	yes	complemented
468	#486	C₂²×C₁₃	1	2	yes	complemented
469	#486	C₂²×C₁₃	1	2	yes	complemented
470	#486	C₂²×C₁₃	1	2	yes	complemented
471	#469	C₂²×C₁₃	1	8	yes	complemented
472	#468	C₂²×C₁₃	1	8	yes	complemented
473	#466	C₂²×C₁₃	1	8	yes	complemented
474	#465	C₂²×C₁₃	1	8	yes	complemented
475	#442	C₂²×C₁₃	1	8	yes	complemented
476	#440	C₂²×C₁₃	1	8	yes	complemented
477	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
478	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
479	#428	C₂²×C₁₃	1	4	yes	—
480	#418	C₂²×C₁₃	1	4	yes	—
481	#417	C₂²×C₁₃	1	4	yes	—
482	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
483	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
484	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
485	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
486	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
487	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
488	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
489	C₂²×C₁₃	—	2	1	no	—
490	C₂²×C₁₃	—	2	1	no	—
491	C₂²×C₁₃	—	2	1	no	—
492	C₂²×C₁₃	—	2	1	no	—
493	C₂²×C₁₃	—	2	1	no	—
494	C₂²×C₁₃	—	2	1	no	—
495	C₂²×C₁₃	—	2	1	no	—
496	C₂²×C₁₃	—	4	4	no	—
497	C₂²×C₁₃	—	4	2	no	—
498	C₂²×C₁₃	—	4	4	no	—
499	C₂²×C₁₃	—	4	4	no	—
500	C₂²×C₁₃	—	4	2	no	—
501	C₂²×C₁₃	—	4	2	no	—
502	C₂²×C₁₃	—	4	4	no	—
503	C₂²×C₁₃	—	8	8	no	—
504	C₂²×C₁₃	#532	1	2	yes	—
505	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
506	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
507	C₄×C₁₃	—	2	1	no	—
508	C₄×C₁₃	—	2	1	no	—
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	1	no	—
511	C₄×C₁₃	—	2	1	no	—
512	C₄×C₁₃	—	2	1	no	—
513	C₄×C₁₃	—	2	1	no	—
514	C₄×C₁₃	—	4	2	no	—
515	C₄×C₁₃	—	4	4	no	—
516	C₄×C₁₃	—	4	2	no	—
517	C₄×C₁₃	—	4	2	no	—
518	C₄×C₁₃	#532	1	2	yes	—
519	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
520	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
521	C₄×C₁₃	#575	1	2	yes	—
522	C₄×C₁₃	C₂²×#41	1	2	yes	—
523	C₂×#41	—	2	1	no	—
524	C₂×#41	—	2	1	no	—
525	C₂×#41	—	2	2	no	—
526	C₂×#41	—	2	2	no	—
527	C₂×#41	—	2	2	no	—
528	C₂×#41	—	2	2	no	—
529	C₂×#41	—	4	8	no	—
530	C₂×#41	C₂³×C₁₃	1	2	yes	—
531	C₂²×Q₈	—	2	1	no	—
532	C₂²×D₄	—	2	2	no	—
533	C₂²×D₄	—	2	1	no	—
534	C₂²×D₄	—	2	1	no	—
535	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
536	C₂³×C₄	—	2	2	no	—
537	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
538	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
540	AGL(1,ℤ/8)	—	2	16	no	—
541	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
542	C₂×D₈	C₂³×C₁₃	1	8	yes	—
543	C₂×M₁₆	—	2	8	no	—
544	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
545	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
546	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
547	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
551	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
554	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
555	#127	—	2	1	no	—
556	#127	—	2	1	no	—
557	#127	C₂³×C₁₃	1	2	yes	—
558	#127	C₂³×C₁₃	1	2	yes	—
559	#127	C₂³×C₁₃	1	1	yes	characteristic
560	#126	—	2	2	no	—
561	#126	—	2	2	no	—
562	#125	—	2	1	no	—
563	#125	—	2	1	no	—
564	#125	C₂³×C₁₃	1	2	yes	—
565	#124	—	2	2	no	—
566	#124	—	2	2	no	—
567	#124	—	2	2	no	—
568	#124	—	2	2	no	—
569	#124	—	2	1	no	—
570	#124	—	2	1	no	—
571	#124	C₂³×C₁₃	1	2	yes	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
580	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
581	#121	—	2	2	no	—
582	#121	—	2	2	no	—
583	#121	—	2	2	no	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	1	no	—
588	#121	—	2	1	no	—
589	#121	—	2	1	no	—
590	#121	—	2	1	no	—
591	#121	C₂³×C₁₃	1	4	yes	—
592	#121	C₂³×C₁₃	1	4	yes	—
593	#121	C₂³×C₁₃	1	2	yes	—
594	#121	C₂³×C₁₃	1	2	yes	—
595	#120	—	2	2	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	—	2	1	no	—
600	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
601	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	C₂³×C₁₃	1	4	yes	—
619	C₄×D₄	C₂³×C₁₃	1	4	yes	—
620	C₄×D₄	C₂³×C₁₃	1	2	yes	—
621	C₄×D₄	C₂³×C₁₃	1	2	yes	—
622	#117	—	2	1	no	—
623	#117	—	2	1	no	—
624	#117	—	2	2	no	—
625	#117	—	2	2	no	—
626	#117	—	2	2	no	—
627	#117	C₂³×C₁₃	1	2	yes	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₂²⋊C₄	—	2	2	no	—
631	C₂×C₂²⋊C₄	—	2	2	no	—
632	C₂×C₄²	—	2	2	no	—
633	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
634	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
635	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
636	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
637	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
638	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
645	#107	C₂³×C₁₃	1	8	yes	—
646	#106	C₂³×C₁₃	1	8	yes	—
647	#103	C₂³×C₁₃	1	8	yes	—
648	#102	C₂³×C₁₃	1	8	yes	—
649	#102	C₂³×C₁₃	1	8	yes	—
650	#102	C₂³×C₁₃	1	8	yes	—
651	#97	C₂³×C₁₃	1	4	yes	—
652	#97	C₂³×C₁₃	1	2	yes	—
653	#97	C₂³×C₁₃	1	2	yes	—
654	C₄×C₈	C₂³×C₁₃	1	4	yes	—
655	C₄×C₈	C₂³×C₁₃	1	2	yes	—
656	C₄×C₈	C₂³×C₁₃	1	2	yes	—
657	C₂×C₁₃	—	2	2	no	—
658	C₂×C₁₃	—	2	2	no	—
659	C₂×C₁₃	—	4	1	no	—
660	C₂×C₁₃	—	8	2	no	—
661	C₂×C₁₃	—	8	4	no	—
662	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
663	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
664	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
665	C₂⁴	—	2	2	no	—
666	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
667	#41	—	2	8	no	—
668	#41	—	4	8	no	—
669	#41	—	4	8	no	—
670	#41	—	4	8	no	—
671	#41	—	4	4	no	—
672	#41	—	4	8	no	—
673	#41	—	4	4	no	—
674	C₂×Q₈	—	2	1	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	4	4	no	—
679	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	8	no	—
693	C₂×D₄	—	4	4	no	—
694	C₂×D₄	—	4	4	no	—
695	C₂×D₄	—	4	8	no	—
696	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
697	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
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	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	4	2	no	—
707	C₂²×C₄	—	4	8	no	—
708	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
726	SD₁₆	—	2	16	no	—
727	D₈	—	2	16	no	—
728	M₁₆	—	2	4	no	—
729	M₁₆	—	2	8	no	—
730	M₁₆	C₁₃×#41	1	8	yes	complemented
731	C₂×C₈	—	2	8	no	—
732	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
733	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
748	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
749	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
772	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
773	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
775	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
776	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
777	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
778	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
779	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
780	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
781	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
782	C₁₃	#60700	1	1	yes	characteristic, direct product factor, Sylow
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	4	no	—
787	C₂³	—	4	1	no	—
788	C₂³	—	4	4	no	—
789	C₂³	—	4	4	no	—
790	C₂³	—	4	4	no	—
791	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
792	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
793	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
794	Q₈	—	2	4	no	—
795	Q₈	—	4	4	no	—
796	Q₈	—	4	4	no	—
797	Q₈	—	4	2	no	—
798	Q₈	—	4	2	no	—
799	D₄	—	2	4	no	—
800	D₄	—	2	8	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	8	no	—
804	D₄	—	4	4	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	8	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	2	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	8	no	—
838	C₂×C₄	—	4	4	no	—
839	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
840	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
847	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
851	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
852	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
853	C₈	—	2	4	no	—
854	C₈	C₂×C₁₃×#41	1	8	yes	complemented
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	4	4	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	4	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	4	no	—
869	C₂²	—	8	8	no	—
870	C₂²	C₁₃×#532	1	2	yes	—
871	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
872	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	1	no	—
878	C₄	—	2	1	no	—
879	C₄	—	2	1	no	—
880	C₄	—	4	4	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₄	C₁₃×#532	1	2	yes	—
885	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
886	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
887	C₄	C₁₃×#575	1	2	yes	—
888	C₄	C₂²×C₁₃×#41	1	2	yes	—
889	C₂	—	2	2	no	—
890	C₂	—	2	2	no	—
891	C₂	—	4	1	no	—
892	C₂	—	8	4	no	—
893	C₂	—	8	2	no	—
894	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
895	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
896	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	semidirect
2. C₂×C₁₃×#532	C₂	semidirect
3. C₁₃×#3184	C₂	semidirect
4. C₁₃×#3182	C₂	semidirect
5. C₁₃×#3180	C₂	semidirect
6. C₁₃×#3171	C₂	semidirect
7. C₁₃×#3169	C₂	semidirect
8. C₁₃×#3167	C₂	semidirect
9. C₁₃×#3165	C₂	semidirect
10. C₁₃×#3151	C₂	semidirect
11. C₁₃×#3141	C₂	semidirect
12. C₁₃×#3138	C₂	semidirect
13. C₁₃×#3055	C₂	semidirect
14. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
15. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
20. C₁₃×#533	C₂²	semidirect
21. C₁₃×#533	C₂²	semidirect
31. C₁₃×#532	C₂²	semidirect
32. C₁₃×#532	C₂²	semidirect
39. C₁₃×#529	C₂²	semidirect
40. C₁₃×#529	C₂²	semidirect
53. C₁₃×#501	C₂²	semidirect
54. C₁₃×#500	C₂²	semidirect
55. C₁₃×#498	C₂²	semidirect
56. C₁₃×#496	C₂²	semidirect
57. C₁₃×#493	C₂²	semidirect
58. C₁₃×#492	C₂²	semidirect
59. C₁₃×#490	C₂²	semidirect
60. C₁₃×#489	C₂²	semidirect
61. C₁₃×#487	C₂²	semidirect
62. C₁₃×#486	C₂²	semidirect
63. C₁₃×#486	C₂²	semidirect
64. C₁₃×#486	C₂²	semidirect
65. C₁₃×#469	C₂²	semidirect
66. C₁₃×#468	C₂²	semidirect
67. C₁₃×#466	C₂²	semidirect
68. C₁₃×#465	C₂²	semidirect
69. C₁₃×#442	C₂²	semidirect
70. C₁₃×#440	C₂²	semidirect
71. C₄×C₁₃×SD₁₆	C₂²	semidirect
72. C₄×C₁₃×D₈	C₂²	semidirect
79. C₄×C₁₃×M₁₆	C₂²	semidirect
80. C₄×C₁₃×M₁₆	C₂²	semidirect
81. C₂×C₁₃×#97	C₂²	semidirect
82. C₂×C₄×C₈×C₁₃	C₂²	semidirect
217. #60700	C₁₃	direct (N × H)
283. C₁₃×M₁₆	#41	semidirect
335. #3444	C₂×C₁₃	semidirect
336. C₂×#532	C₂×C₁₃	semidirect
337. #3184	C₂×C₁₃	semidirect
338. #3182	C₂×C₁₃	semidirect
339. #3180	C₂×C₁₃	semidirect
340. #3171	C₂×C₁₃	semidirect
341. #3169	C₂×C₁₃	semidirect
342. #3167	C₂×C₁₃	semidirect
343. #3165	C₂×C₁₃	semidirect
344. #3151	C₂×C₁₃	semidirect
345. #3141	C₂×C₁₃	semidirect
346. #3138	C₂×C₁₃	semidirect
347. #3055	C₂×C₁₃	semidirect
348. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
349. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
406. C₂×C₄×C₁₃	AGL(1,ℤ/8)	semidirect
421. C₈×C₁₃	C₂×#41	semidirect
426. #533	C₂²×C₁₃	semidirect
427. #533	C₂²×C₁₃	semidirect
437. #532	C₂²×C₁₃	semidirect
438. #532	C₂²×C₁₃	semidirect
445. #529	C₂²×C₁₃	semidirect
446. #529	C₂²×C₁₃	semidirect
459. #501	C₂²×C₁₃	semidirect
460. #500	C₂²×C₁₃	semidirect
461. #498	C₂²×C₁₃	semidirect
462. #496	C₂²×C₁₃	semidirect
463. #493	C₂²×C₁₃	semidirect
464. #492	C₂²×C₁₃	semidirect
465. #490	C₂²×C₁₃	semidirect
466. #489	C₂²×C₁₃	semidirect
467. #487	C₂²×C₁₃	semidirect
468. #486	C₂²×C₁₃	semidirect
469. #486	C₂²×C₁₃	semidirect
470. #486	C₂²×C₁₃	semidirect
471. #469	C₂²×C₁₃	semidirect
472. #468	C₂²×C₁₃	semidirect
473. #466	C₂²×C₁₃	semidirect
474. #465	C₂²×C₁₃	semidirect
475. #442	C₂²×C₁₃	semidirect
476. #440	C₂²×C₁₃	semidirect
477. C₄×SD₁₆	C₂²×C₁₃	semidirect
478. C₄×D₈	C₂²×C₁₃	semidirect
485. C₄×M₁₆	C₂²×C₁₃	semidirect
486. C₄×M₁₆	C₂²×C₁₃	semidirect
487. C₂×#97	C₂²×C₁₃	semidirect
488. C₂×C₄×C₈	C₂²×C₁₃	semidirect
730. M₁₆	C₁₃×#41	semidirect
782. C₁₃	#60700	direct (N × H)
839. C₂×C₄	C₁₃×AGL(1,ℤ/8)	semidirect
854. C₈	C₂×C₁₃×#41	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3444	2
C₂×C₁₃×#532	2
C₁₃×#3184	2
C₁₃×#3182	2
C₁₃×#3180	2
C₁₃×#3171	2
C₁₃×#3169	2
C₁₃×#3167	2
C₁₃×#3165	2
C₁₃×#3151	2
C₁₃×#3141	2
C₁₃×#3138	2
C₁₃×#3055	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₂×C₄×C₁₃×M₁₆	2
#60700	13

Subgroups — C13×#60700 #15747039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60700 #15747039