Subgroups — C₁₃×#60805 #15747144

Order 3328.

2196 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3219	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3218	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3217	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3212	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3211	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3153	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3142	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3037	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3036	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3007	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3006	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	2	yes	—
16	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
18	C₁₃×#532	—	2	1	no	—
19	C₁₃×#532	—	2	1	no	—
20	C₁₃×#532	—	2	1	no	—
21	C₁₃×#532	—	2	1	no	—
22	C₁₃×#532	C₂²	1	2	yes	—
23	C₁₃×#532	C₂²	1	2	yes	—
24	C₁₃×#532	C₂²	1	2	yes	complemented
25	C₁₃×#532	C₂²	1	2	yes	complemented
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#529	—	2	1	no	—
29	C₁₃×#529	—	2	1	no	—
30	C₁₃×#529	—	2	1	no	—
31	C₁₃×#529	—	2	1	no	—
32	C₁₃×#529	C₂²	1	2	yes	—
33	C₁₃×#529	C₂²	1	2	yes	—
34	C₁₃×#529	C₂²	1	2	yes	complemented
35	C₁₃×#529	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#126	—	2	1	no	—
37	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#123	—	2	1	no	—
41	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#121	—	2	1	no	—
43	C₂×C₁₃×#121	—	2	1	no	—
44	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₁₃	—	2	1	no	—
47	C₂×C₄×D₄×C₁₃	—	2	1	no	—
48	C₂×C₄×D₄×C₁₃	—	2	1	no	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₁₃×#117	—	2	1	no	—
51	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
52	C₁₃×#497	C₂²	1	4	yes	complemented
53	C₁₃×#496	C₂²	1	4	yes	complemented
54	C₁₃×#495	C₂²	1	8	yes	complemented
55	C₁₃×#491	C₂²	1	4	yes	complemented
56	C₁₃×#490	C₂²	1	4	yes	complemented
57	C₁₃×#488	C₂²	1	8	yes	complemented
58	C₁₃×#464	C₂²	1	8	yes	complemented
59	C₁₃×#463	C₂²	1	8	yes	complemented
60	C₁₃×#462	C₂²	1	4	yes	complemented
61	C₁₃×#461	C₂²	1	4	yes	complemented
62	C₁₃×#460	C₂²	1	4	yes	complemented
63	C₁₃×#459	C₂²	1	4	yes	complemented
64	C₁₃×#452	C₂²	1	8	yes	complemented
65	C₁₃×#451	C₂²	1	4	yes	complemented
66	C₁₃×#450	C₂²	1	4	yes	complemented
67	C₁₃×#449	C₂²	1	8	yes	complemented
68	C₁₃×#448	C₂²	1	4	yes	—
69	C₁₃×#447	C₂²	1	4	yes	—
70	C₁₃×#432	C₂²	1	2	yes	complemented
71	C₁₃×#432	C₂²	1	2	yes	complemented
72	C₁₃×#431	C₂²	1	2	yes	complemented
73	C₁₃×#431	C₂²	1	2	yes	complemented
74	C₁₃×#423	C₂²	1	2	yes	complemented
75	C₁₃×#417	C₂²	1	4	yes	complemented
76	C₁₃×#417	C₂²	1	4	yes	complemented
77	C₁₃×#407	C₂²	1	2	yes	—
78	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
79	C₂×C₁₃×#41	—	2	2	no	—
80	C₂×C₁₃×#41	—	2	2	no	—
81	C₂×C₁₃×#41	—	4	8	no	—
82	C₂×C₁₃×#41	C₂³	1	4	yes	—
83	C₂×C₁₃×#41	C₂³	1	4	yes	—
84	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃	—	2	1	no	—
87	C₂²×D₄×C₁₃	—	2	2	no	—
88	C₂²×D₄×C₁₃	—	2	1	no	—
89	C₂²×D₄×C₁₃	—	2	1	no	—
90	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃	—	2	1	no	—
93	C₂³×C₄×C₁₃	—	2	2	no	—
94	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×#137	—	4	8	no	—
98	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
99	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
100	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
101	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
102	C₂×C₁₃×D₈	C₂³	1	8	yes	—
103	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
104	C₁₃×C₄⋊Q₈	—	2	1	no	—
105	C₁₃×C₄⋊Q₈	—	2	1	no	—
106	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₁₃×#127	—	2	1	no	—
109	C₁₃×#127	—	2	1	no	—
110	C₁₃×#127	C₂³	1	2	yes	—
111	C₁₃×#127	C₂³	1	2	yes	—
112	C₁₃×#126	—	2	2	no	—
113	C₁₃×#126	—	2	2	no	—
114	C₁₃×#126	—	2	2	no	—
115	C₁₃×#126	—	2	2	no	—
116	C₁₃×#125	—	2	1	no	—
117	C₁₃×#125	—	2	1	no	—
118	C₁₃×#125	C₂³	1	2	yes	—
119	C₁₃×#125	C₂³	1	2	yes	—
120	C₁₃×#124	—	2	1	no	—
121	C₁₃×#124	—	2	1	no	—
122	C₁₃×#124	—	2	2	no	—
123	C₁₃×#124	—	2	2	no	—
124	C₁₃×#124	C₂³	1	4	yes	—
125	C₁₃×#124	C₂³	1	4	yes	—
126	C₁₃×#124	C₂³	1	2	yes	—
127	C₁₃×#124	C₂³	1	2	yes	—
128	C₁₃×#123	—	2	2	no	—
129	C₁₃×#123	—	2	2	no	—
130	C₁₃×#123	—	2	2	no	—
131	C₁₃×#123	—	2	2	no	—
132	C₁₃×C₂²⋊Q₈	—	2	1	no	—
133	C₁₃×C₂²⋊Q₈	—	2	1	no	—
134	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
136	C₁₃×#121	—	2	2	no	—
137	C₁₃×#121	—	2	2	no	—
138	C₁₃×#121	—	2	2	no	—
139	C₁₃×#121	—	2	2	no	—
140	C₁₃×#121	—	2	2	no	—
141	C₁₃×#121	—	2	2	no	—
142	C₁₃×#121	—	2	2	no	—
143	C₁₃×#121	—	2	2	no	—
144	C₁₃×#121	—	2	1	no	—
145	C₁₃×#121	—	2	1	no	—
146	C₁₃×#121	C₂³	1	2	yes	—
147	C₁₃×#121	C₂³	1	2	yes	—
148	C₄×Q₈×C₁₃	—	2	1	no	—
149	C₄×Q₈×C₁₃	—	2	1	no	—
150	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₄×D₄×C₁₃	—	2	2	no	—
153	C₄×D₄×C₁₃	—	2	2	no	—
154	C₄×D₄×C₁₃	—	2	2	no	—
155	C₄×D₄×C₁₃	—	2	2	no	—
156	C₄×D₄×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	—	2	2	no	—
158	C₄×D₄×C₁₃	—	2	2	no	—
159	C₄×D₄×C₁₃	—	2	2	no	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	2	no	—
163	C₄×D₄×C₁₃	—	2	2	no	—
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	C₂³	1	2	yes	—
167	C₄×D₄×C₁₃	C₂³	1	2	yes	—
168	C₁₃×#117	—	2	2	no	—
169	C₁₃×#117	—	2	2	no	—
170	C₁₃×#117	—	2	2	no	—
171	C₁₃×#117	—	2	2	no	—
172	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
184	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
185	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
186	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
187	C₂×C₄²×C₁₃	—	2	1	no	—
188	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
201	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
202	C₁₃×#103	C₂³	1	8	yes	—
203	C₁₃×#103	C₂³	1	8	yes	—
204	C₁₃×#102	C₂³	1	8	yes	—
205	C₁₃×#102	C₂³	1	8	yes	—
206	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
207	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
208	C₁₃×#97	C₂³	1	4	yes	—
209	C₄×C₈×C₁₃	C₂³	1	4	yes	—
210	#60805	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂⁴×C₁₃	—	2	1	no	—
212	C₂⁴×C₁₃	—	2	2	no	—
213	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₁₃×#41	—	2	8	no	—
215	C₁₃×#41	—	2	8	no	—
216	C₁₃×#41	—	4	4	no	—
217	C₁₃×#41	—	4	4	no	—
218	C₁₃×#41	—	4	8	no	—
219	C₁₃×#41	—	4	8	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	2	no	—
222	C₂×Q₈×C₁₃	—	2	4	no	—
223	C₂×Q₈×C₁₃	—	4	4	no	—
224	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
225	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
226	C₂×D₄×C₁₃	—	2	2	no	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	2	4	no	—
229	C₂×D₄×C₁₃	—	2	4	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
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	—	4	4	no	—
238	C₂×D₄×C₁₃	—	4	4	no	—
239	C₂×D₄×C₁₃	—	4	4	no	—
240	C₂×D₄×C₁₃	—	4	4	no	—
241	C₂×D₄×C₁₃	—	4	8	no	—
242	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
243	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃	—	2	4	no	—
245	C₂²×C₄×C₁₃	—	2	1	no	—
246	C₂²×C₄×C₁₃	—	2	1	no	—
247	C₂²×C₄×C₁₃	—	2	1	no	—
248	C₂²×C₄×C₁₃	—	2	2	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	—	2	4	no	—
252	C₂²×C₄×C₁₃	—	2	4	no	—
253	C₂²×C₄×C₁₃	—	4	2	no	—
254	C₂²×C₄×C₁₃	—	4	2	no	—
255	C₂²×C₄×C₁₃	—	4	4	no	—
256	C₂²×C₄×C₁₃	—	4	8	no	—
257	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₁₃×Q₁₆	—	4	8	no	—
276	C₁₃×SD₁₆	—	4	8	no	—
277	C₁₃×SD₁₆	—	4	8	no	—
278	C₁₃×D₈	—	4	8	no	—
279	C₁₃×M₁₆	—	2	8	no	—
280	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
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	2	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	1	no	—
295	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
296	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
297	C₁₃×C₂²⋊C₄	—	2	2	no	—
298	C₁₃×C₂²⋊C₄	—	2	2	no	—
299	C₁₃×C₂²⋊C₄	—	2	2	no	—
300	C₁₃×C₂²⋊C₄	—	2	2	no	—
301	C₁₃×C₂²⋊C₄	—	2	2	no	—
302	C₁₃×C₂²⋊C₄	—	2	2	no	—
303	C₁₃×C₂²⋊C₄	—	2	4	no	—
304	C₁₃×C₂²⋊C₄	—	2	4	no	—
305	C₁₃×C₂²⋊C₄	—	2	4	no	—
306	C₁₃×C₂²⋊C₄	—	2	4	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	2	no	—
311	C₄²×C₁₃	—	2	2	no	—
312	C₄²×C₁₃	—	2	2	no	—
313	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
326	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
330	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
331	#3219	C₂×C₁₃	1	4	yes	complemented
332	#3218	C₂×C₁₃	1	2	yes	complemented
333	#3217	C₂×C₁₃	1	2	yes	complemented
334	#3212	C₂×C₁₃	1	4	yes	complemented
335	#3211	C₂×C₁₃	1	4	yes	complemented
336	#3153	C₂×C₁₃	1	2	yes	complemented
337	#3142	C₂×C₁₃	1	2	yes	complemented
338	#3037	C₂×C₁₃	1	2	yes	complemented
339	#3036	C₂×C₁₃	1	2	yes	complemented
340	#3007	C₂×C₁₃	1	2	yes	complemented
341	#3006	C₂×C₁₃	1	2	yes	complemented
342	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	2	2	no	—
345	C₂³×C₁₃	—	2	2	no	—
346	C₂³×C₁₃	—	2	4	no	—
347	C₂³×C₁₃	—	4	1	no	—
348	C₂³×C₁₃	—	4	4	no	—
349	C₂³×C₁₃	—	4	2	no	—
350	C₂³×C₁₃	—	4	4	no	—
351	C₂³×C₁₃	—	4	2	no	—
352	C₂³×C₁₃	—	4	2	no	—
353	C₂³×C₁₃	—	4	4	no	—
354	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
355	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
356	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₁₃	—	2	4	no	—
358	Q₈×C₁₃	—	2	4	no	—
359	Q₈×C₁₃	—	2	4	no	—
360	Q₈×C₁₃	—	4	4	no	—
361	Q₈×C₁₃	—	4	2	no	—
362	D₄×C₁₃	—	2	4	no	—
363	D₄×C₁₃	—	2	4	no	—
364	D₄×C₁₃	—	2	4	no	—
365	D₄×C₁₃	—	4	4	no	—
366	D₄×C₁₃	—	4	4	no	—
367	D₄×C₁₃	—	4	4	no	—
368	D₄×C₁₃	—	4	4	no	—
369	D₄×C₁₃	—	4	4	no	—
370	D₄×C₁₃	—	4	8	no	—
371	D₄×C₁₃	—	4	8	no	—
372	D₄×C₁₃	—	4	4	no	—
373	D₄×C₁₃	—	4	2	no	—
374	D₄×C₁₃	—	4	4	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	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	4	no	—
389	C₂×C₄×C₁₃	—	4	1	no	—
390	C₂×C₄×C₁₃	—	4	1	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	4	1	no	—
393	C₂×C₄×C₁₃	—	4	1	no	—
394	C₂×C₄×C₁₃	—	4	1	no	—
395	C₂×C₄×C₁₃	—	4	1	no	—
396	C₂×C₄×C₁₃	—	4	4	no	—
397	C₂×C₄×C₁₃	—	4	8	no	—
398	C₂×C₄×C₁₃	—	4	2	no	—
399	C₂×C₄×C₁₃	—	4	4	no	—
400	C₂×C₄×C₁₃	—	4	2	no	—
401	C₂×C₄×C₁₃	—	4	2	no	—
402	C₂×C₄×C₁₃	—	4	8	no	—
403	C₂×C₄×C₁₃	—	4	4	no	—
404	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	H(5,𝔽₂)	1	4	yes	—
416	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
417	C₈×C₁₃	—	2	8	no	—
418	C₂²×#41	C₂²×C₁₃	1	2	yes	—
419	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
420	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
421	#532	—	2	1	no	—
422	#532	—	2	1	no	—
423	#532	—	2	1	no	—
424	#532	—	2	1	no	—
425	#532	C₂²×C₁₃	1	2	yes	—
426	#532	C₂²×C₁₃	1	2	yes	—
427	#532	C₂²×C₁₃	1	2	yes	complemented
428	#532	C₂²×C₁₃	1	2	yes	complemented
429	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
430	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#529	—	2	1	no	—
432	#529	—	2	1	no	—
433	#529	—	2	1	no	—
434	#529	—	2	1	no	—
435	#529	C₂²×C₁₃	1	2	yes	—
436	#529	C₂²×C₁₃	1	2	yes	—
437	#529	C₂²×C₁₃	1	2	yes	complemented
438	#529	C₂²×C₁₃	1	2	yes	complemented
439	C₂×#126	—	2	1	no	—
440	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
442	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
443	C₂×#123	—	2	1	no	—
444	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×#121	—	2	1	no	—
446	C₂×#121	—	2	1	no	—
447	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	C₂×C₄×D₄	—	2	1	no	—
450	C₂×C₄×D₄	—	2	1	no	—
451	C₂×C₄×D₄	—	2	1	no	—
452	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	C₂×#117	—	2	1	no	—
454	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
455	#497	C₂²×C₁₃	1	4	yes	complemented
456	#496	C₂²×C₁₃	1	4	yes	complemented
457	#495	C₂²×C₁₃	1	8	yes	complemented
458	#491	C₂²×C₁₃	1	4	yes	complemented
459	#490	C₂²×C₁₃	1	4	yes	complemented
460	#488	C₂²×C₁₃	1	8	yes	complemented
461	#464	C₂²×C₁₃	1	8	yes	complemented
462	#463	C₂²×C₁₃	1	8	yes	complemented
463	#462	C₂²×C₁₃	1	4	yes	complemented
464	#461	C₂²×C₁₃	1	4	yes	complemented
465	#460	C₂²×C₁₃	1	4	yes	complemented
466	#459	C₂²×C₁₃	1	4	yes	complemented
467	#452	C₂²×C₁₃	1	8	yes	complemented
468	#451	C₂²×C₁₃	1	4	yes	complemented
469	#450	C₂²×C₁₃	1	4	yes	complemented
470	#449	C₂²×C₁₃	1	8	yes	complemented
471	#448	C₂²×C₁₃	1	4	yes	—
472	#447	C₂²×C₁₃	1	4	yes	—
473	#432	C₂²×C₁₃	1	2	yes	complemented
474	#432	C₂²×C₁₃	1	2	yes	complemented
475	#431	C₂²×C₁₃	1	2	yes	complemented
476	#431	C₂²×C₁₃	1	2	yes	complemented
477	#423	C₂²×C₁₃	1	2	yes	complemented
478	#417	C₂²×C₁₃	1	4	yes	complemented
479	#417	C₂²×C₁₃	1	4	yes	complemented
480	#407	C₂²×C₁₃	1	2	yes	—
481	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
482	C₂²×C₁₃	—	2	1	no	—
483	C₂²×C₁₃	—	2	1	no	—
484	C₂²×C₁₃	—	2	1	no	—
485	C₂²×C₁₃	—	2	1	no	—
486	C₂²×C₁₃	—	2	1	no	—
487	C₂²×C₁₃	—	2	1	no	—
488	C₂²×C₁₃	—	2	1	no	—
489	C₂²×C₁₃	—	4	4	no	—
490	C₂²×C₁₃	—	4	4	no	—
491	C₂²×C₁₃	—	4	2	no	—
492	C₂²×C₁₃	—	4	2	no	—
493	C₂²×C₁₃	—	4	4	no	—
494	C₂²×C₁₃	—	4	2	no	—
495	C₂²×C₁₃	—	4	4	no	—
496	C₂²×C₁₃	—	8	8	no	—
497	C₂²×C₁₃	—	8	4	no	—
498	C₂²×C₁₃	#535	1	2	yes	—
499	C₂²×C₁₃	#575	1	2	yes	—
500	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
501	C₄×C₁₃	—	2	1	no	—
502	C₄×C₁₃	—	2	1	no	—
503	C₄×C₁₃	—	2	1	no	—
504	C₄×C₁₃	—	2	1	no	—
505	C₄×C₁₃	—	2	1	no	—
506	C₄×C₁₃	—	2	1	no	—
507	C₄×C₁₃	—	2	1	no	—
508	C₄×C₁₃	—	2	1	no	—
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	4	4	no	—
511	C₄×C₁₃	—	4	2	no	—
512	C₄×C₁₃	—	4	2	no	—
513	C₄×C₁₃	—	4	2	no	—
514	C₄×C₁₃	#535	1	2	yes	—
515	C₄×C₁₃	#575	1	2	yes	—
516	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
517	C₂×#41	—	2	2	no	—
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	4	8	no	—
520	C₂×#41	C₂³×C₁₃	1	4	yes	—
521	C₂×#41	C₂³×C₁₃	1	4	yes	—
522	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
523	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	—	2	2	no	—
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	—	2	1	no	—
528	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
530	C₂³×C₄	—	2	1	no	—
531	C₂³×C₄	—	2	2	no	—
532	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
533	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
535	#137	—	4	8	no	—
536	AGL(1,ℤ/8)	—	4	8	no	—
537	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
538	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
539	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
540	C₂×D₈	C₂³×C₁₃	1	8	yes	—
541	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
545	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
546	#127	—	2	1	no	—
547	#127	—	2	1	no	—
548	#127	C₂³×C₁₃	1	2	yes	—
549	#127	C₂³×C₁₃	1	2	yes	—
550	#126	—	2	2	no	—
551	#126	—	2	2	no	—
552	#126	—	2	2	no	—
553	#126	—	2	2	no	—
554	#125	—	2	1	no	—
555	#125	—	2	1	no	—
556	#125	C₂³×C₁₃	1	2	yes	—
557	#125	C₂³×C₁₃	1	2	yes	—
558	#124	—	2	1	no	—
559	#124	—	2	1	no	—
560	#124	—	2	2	no	—
561	#124	—	2	2	no	—
562	#124	C₂³×C₁₃	1	2	yes	—
563	#124	C₂³×C₁₃	1	2	yes	—
564	#124	C₂³×C₁₃	1	4	yes	—
565	#124	C₂³×C₁₃	1	4	yes	—
566	#123	—	2	2	no	—
567	#123	—	2	2	no	—
568	#123	—	2	2	no	—
569	#123	—	2	2	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
573	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
574	#121	—	2	2	no	—
575	#121	—	2	2	no	—
576	#121	—	2	2	no	—
577	#121	—	2	2	no	—
578	#121	—	2	2	no	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	—	2	2	no	—
582	#121	—	2	1	no	—
583	#121	—	2	1	no	—
584	#121	C₂³×C₁₃	1	2	yes	—
585	#121	C₂³×C₁₃	1	2	yes	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
589	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	C₂³×C₁₃	1	2	yes	—
605	C₄×D₄	C₂³×C₁₃	1	2	yes	—
606	#117	—	2	2	no	—
607	#117	—	2	2	no	—
608	#117	—	2	2	no	—
609	#117	—	2	2	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	2	no	—
622	C₂×C₂²⋊C₄	—	2	2	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₄²	—	2	1	no	—
626	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
627	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
628	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
629	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
630	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
631	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
638	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
639	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
640	#103	C₂³×C₁₃	1	8	yes	—
641	#103	C₂³×C₁₃	1	8	yes	—
642	#102	C₂³×C₁₃	1	8	yes	—
643	#102	C₂³×C₁₃	1	8	yes	—
644	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
645	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
646	#97	C₂³×C₁₃	1	4	yes	—
647	C₄×C₈	C₂³×C₁₃	1	4	yes	—
648	C₂×C₁₃	—	2	2	no	—
649	C₂×C₁₃	—	2	2	no	—
650	C₂×C₁₃	—	4	1	no	—
651	C₂×C₁₃	—	8	4	no	—
652	C₂×C₁₃	—	8	2	no	—
653	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
654	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
655	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
656	C₂⁴	—	2	1	no	—
657	C₂⁴	—	2	2	no	—
658	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
659	#41	—	2	8	no	—
660	#41	—	2	8	no	—
661	#41	—	4	4	no	—
662	#41	—	4	4	no	—
663	#41	—	4	8	no	—
664	#41	—	4	8	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	4	no	—
668	C₂×Q₈	—	4	4	no	—
669	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
670	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	4	4	no	—
683	C₂×D₄	—	4	4	no	—
684	C₂×D₄	—	4	4	no	—
685	C₂×D₄	—	4	8	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
688	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	—	4	8	no	—
701	C₂²×C₄	—	4	4	no	—
702	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	C₂⁴×C₁₃	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
720	Q₁₆	—	4	8	no	—
721	SD₁₆	—	4	8	no	—
722	SD₁₆	—	4	8	no	—
723	D₈	—	4	8	no	—
724	M₁₆	—	2	8	no	—
725	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
759	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
760	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
761	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
763	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
765	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
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	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
772	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
773	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
774	C₁₃	#60805	1	1	yes	characteristic, direct product factor, Sylow
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	4	no	—
779	C₂³	—	4	1	no	—
780	C₂³	—	4	4	no	—
781	C₂³	—	4	2	no	—
782	C₂³	—	4	4	no	—
783	C₂³	—	4	2	no	—
784	C₂³	—	4	2	no	—
785	C₂³	—	4	4	no	—
786	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
787	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
788	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
789	Q₈	—	2	4	no	—
790	Q₈	—	2	4	no	—
791	Q₈	—	2	4	no	—
792	Q₈	—	4	4	no	—
793	Q₈	—	4	2	no	—
794	D₄	—	2	4	no	—
795	D₄	—	2	4	no	—
796	D₄	—	2	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	8	no	—
804	D₄	—	4	4	no	—
805	D₄	—	4	2	no	—
806	D₄	—	4	4	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	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	4	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	4	8	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	C₁₃×H(5,𝔽₂)	1	4	yes	—
848	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
849	C₈	—	2	8	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	4	4	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	4	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	4	no	—
862	C₂²	—	4	4	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	8	8	no	—
865	C₂²	—	8	4	no	—
866	C₂²	C₁₃×#535	1	2	yes	—
867	C₂²	C₁₃×#575	1	2	yes	—
868	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	1	no	—
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	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	4	no	—
881	C₄	—	4	2	no	—
882	C₄	C₁₃×#535	1	2	yes	—
883	C₄	C₁₃×#575	1	2	yes	—
884	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
885	C₂	—	2	2	no	—
886	C₂	—	2	2	no	—
887	C₂	—	4	1	no	—
888	C₂	—	8	2	no	—
889	C₂	—	8	4	no	—
890	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
891	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
892	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#532	C₂	semidirect
2. C₂×C₁₃×#529	C₂	semidirect
3. C₁₃×#3219	C₂	semidirect
4. C₁₃×#3218	C₂	semidirect
5. C₁₃×#3217	C₂	semidirect
6. C₁₃×#3212	C₂	semidirect
7. C₁₃×#3211	C₂	semidirect
8. C₁₃×#3153	C₂	semidirect
9. C₁₃×#3142	C₂	semidirect
10. C₁₃×#3037	C₂	semidirect
11. C₁₃×#3036	C₂	semidirect
12. C₁₃×#3007	C₂	semidirect
13. C₁₃×#3006	C₂	semidirect
14. C₁₃×#2920	C₂	semidirect
16. C₂×C₁₃×#137	C₂²	semidirect
17. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
24. C₁₃×#532	C₂²	semidirect
25. C₁₃×#532	C₂²	semidirect
26. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
27. C₂×C₁₃×#127	C₂²	semidirect
34. C₁₃×#529	C₂²	semidirect
35. C₁₃×#529	C₂²	semidirect
37. C₂×C₁₃×#125	C₂²	semidirect
38. C₂×C₁₃×#124	C₂²	semidirect
39. C₂×C₁₃×#124	C₂²	semidirect
45. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
49. C₂×C₄×D₄×C₁₃	C₂²	semidirect
52. C₁₃×#497	C₂²	semidirect
53. C₁₃×#496	C₂²	semidirect
54. C₁₃×#495	C₂²	semidirect
55. C₁₃×#491	C₂²	semidirect
56. C₁₃×#490	C₂²	semidirect
57. C₁₃×#488	C₂²	semidirect
58. C₁₃×#464	C₂²	semidirect
59. C₁₃×#463	C₂²	semidirect
60. C₁₃×#462	C₂²	semidirect
61. C₁₃×#461	C₂²	semidirect
62. C₁₃×#460	C₂²	semidirect
63. C₁₃×#459	C₂²	semidirect
64. C₁₃×#452	C₂²	semidirect
65. C₁₃×#451	C₂²	semidirect
66. C₁₃×#450	C₂²	semidirect
67. C₁₃×#449	C₂²	semidirect
70. C₁₃×#432	C₂²	semidirect
71. C₁₃×#432	C₂²	semidirect
72. C₁₃×#431	C₂²	semidirect
73. C₁₃×#431	C₂²	semidirect
74. C₁₃×#423	C₂²	semidirect
75. C₁₃×#417	C₂²	semidirect
76. C₁₃×#417	C₂²	semidirect
78. C₄×C₁₃×M₁₆	C₂²	semidirect
210. #60805	C₁₃	direct (N × H)
329. C₂×#532	C₂×C₁₃	semidirect
330. C₂×#529	C₂×C₁₃	semidirect
331. #3219	C₂×C₁₃	semidirect
332. #3218	C₂×C₁₃	semidirect
333. #3217	C₂×C₁₃	semidirect
334. #3212	C₂×C₁₃	semidirect
335. #3211	C₂×C₁₃	semidirect
336. #3153	C₂×C₁₃	semidirect
337. #3142	C₂×C₁₃	semidirect
338. #3037	C₂×C₁₃	semidirect
339. #3036	C₂×C₁₃	semidirect
340. #3007	C₂×C₁₃	semidirect
341. #3006	C₂×C₁₃	semidirect
342. #2920	C₂×C₁₃	semidirect
419. C₂×#137	C₂²×C₁₃	semidirect
420. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
427. #532	C₂²×C₁₃	semidirect
428. #532	C₂²×C₁₃	semidirect
429. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
430. C₂×#127	C₂²×C₁₃	semidirect
437. #529	C₂²×C₁₃	semidirect
438. #529	C₂²×C₁₃	semidirect
440. C₂×#125	C₂²×C₁₃	semidirect
441. C₂×#124	C₂²×C₁₃	semidirect
442. C₂×#124	C₂²×C₁₃	semidirect
448. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
452. C₂×C₄×D₄	C₂²×C₁₃	semidirect
455. #497	C₂²×C₁₃	semidirect
456. #496	C₂²×C₁₃	semidirect
457. #495	C₂²×C₁₃	semidirect
458. #491	C₂²×C₁₃	semidirect
459. #490	C₂²×C₁₃	semidirect
460. #488	C₂²×C₁₃	semidirect
461. #464	C₂²×C₁₃	semidirect
462. #463	C₂²×C₁₃	semidirect
463. #462	C₂²×C₁₃	semidirect
464. #461	C₂²×C₁₃	semidirect
465. #460	C₂²×C₁₃	semidirect
466. #459	C₂²×C₁₃	semidirect
467. #452	C₂²×C₁₃	semidirect
468. #451	C₂²×C₁₃	semidirect
469. #450	C₂²×C₁₃	semidirect
470. #449	C₂²×C₁₃	semidirect
473. #432	C₂²×C₁₃	semidirect
474. #432	C₂²×C₁₃	semidirect
475. #431	C₂²×C₁₃	semidirect
476. #431	C₂²×C₁₃	semidirect
477. #423	C₂²×C₁₃	semidirect
478. #417	C₂²×C₁₃	semidirect
479. #417	C₂²×C₁₃	semidirect
481. C₄×M₁₆	C₂²×C₁₃	semidirect
774. C₁₃	#60805	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₁₃×#3219	2
C₁₃×#3218	2
C₁₃×#3217	2
C₁₃×#3212	2
C₁₃×#3211	2
C₁₃×#3153	2
C₁₃×#3142	2
C₁₃×#3037	2
C₁₃×#3036	2
C₁₃×#3007	2
C₁₃×#3006	2
C₁₃×#2920	2
#60805	13

Subgroups — C13×#60805 #15747144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60805 #15747144