Subgroups — C₁₃×#61382 #15747721

Order 3328.

1794 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3388	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3385	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3384	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3384	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3380	C₂	1	2	yes	maximal, complemented
8	Q₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3163	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3084	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3081	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2946	C₂	1	2	yes	maximal
17	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	Q₈²×C₁₃	C₂²	1	2	yes	complemented
20	C₁₃×#557	C₂²	1	2	yes	complemented
21	C₁₃×#554	—	2	1	no	—
22	C₁₃×#554	—	2	2	no	—
23	C₁₃×#554	—	2	2	no	—
24	C₁₃×#554	C₂²	1	2	yes	—
25	C₁₃×#554	C₂²	1	4	yes	—
26	C₁₃×#554	C₂²	1	2	yes	complemented
27	D₄×Q₈×C₁₃	—	2	1	no	—
28	D₄×Q₈×C₁₃	—	2	2	no	—
29	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
30	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
31	C₁₃×#544	—	2	2	no	—
32	C₁₃×#544	C₂²	1	2	yes	—
33	C₁₃×#544	C₂²	1	2	yes	—
34	C₁₃×#543	—	2	2	no	—
35	C₁₃×#533	—	2	1	no	—
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
41	C₁₃×#520	C₂²	1	2	yes	—
42	C₁₃×#518	C₂²	1	2	yes	—
43	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#501	C₂²	1	4	yes	complemented
46	C₁₃×#501	C₂²	1	4	yes	complemented
47	C₁₃×#501	C₂²	1	4	yes	complemented
48	C₁₃×#500	C₂²	1	2	yes	complemented
49	C₁₃×#499	C₂²	1	4	yes	complemented
50	C₁₃×#498	C₂²	1	4	yes	complemented
51	C₁₃×#498	C₂²	1	2	yes	complemented
52	C₁₃×#479	C₂²	1	2	yes	complemented
53	C₁₃×#479	C₂²	1	4	yes	complemented
54	C₁₃×#478	C₂²	1	4	yes	—
55	C₁₃×#478	C₂²	1	4	yes	—
56	C₁₃×#478	C₂²	1	2	yes	complemented
57	C₁₃×#478	C₂²	1	4	yes	complemented
58	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#476	C₂²	1	2	yes	—
60	C₁₃×#476	C₂²	1	2	yes	—
61	C₁₃×#476	C₂²	1	4	yes	—
62	C₁₃×#476	C₂²	1	4	yes	—
63	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#476	C₂²	1	4	yes	complemented
65	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#475	C₂²	1	4	yes	complemented
67	C₁₃×#474	C₂²	1	4	yes	—
68	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#446	C₂²	1	2	yes	complemented
70	C₁₃×#446	C₂²	1	4	yes	complemented
71	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
72	C₁₃×#442	C₂²	1	2	yes	—
73	C₁₃×#442	C₂²	1	4	yes	—
74	C₁₃×#440	C₂²	1	4	yes	—
75	C₁₃×#440	C₂²	1	2	yes	—
76	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
77	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
78	C₄×C₁₃×D₈	C₂²	1	2	yes	—
79	C₄×C₁₃×D₈	C₂²	1	4	yes	—
80	C₁₃×#428	C₂²	1	2	yes	—
81	C₁₃×#428	C₂²	1	1	yes	characteristic
82	C₁₃×#428	C₂²	1	2	yes	—
83	C₁₃×#427	C₂²	1	2	yes	—
84	C₂×C₁₃×#106	C₂²	1	2	yes	—
85	C₁₃×#424	C₂²	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
87	C₁₃×#418	C₂²	1	1	yes	characteristic
88	C₁₃×#417	C₂²	1	1	yes	characteristic
89	C₁₃×#416	C₂²	1	2	yes	—
90	C₂×C₁₃×#102	C₂²	1	2	yes	—
91	C₁₃×#405	C₂²	1	2	yes	—
92	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₁₃	—	2	2	no	—
95	C₂²×Q₈×C₁₃	—	2	2	no	—
96	C₂²×Q₈×C₁₃	—	2	1	no	—
97	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	—	2	1	no	—
99	C₁₃×AGL(1,ℤ/8)	Q₈	1	8	yes	complemented
100	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
101	C₂×C₁₃×D₈	C₂³	1	2	yes	—
102	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
105	C₁₃×C₄⋊Q₈	—	2	2	no	—
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	—	2	4	no	—
109	C₁₃×C₄⋊Q₈	—	2	2	no	—
110	C₁₃×C₄⋊Q₈	—	2	1	no	—
111	C₁₃×C₄⋊Q₈	—	2	1	no	—
112	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×#125	—	2	2	no	—
121	C₁₃×#125	—	2	4	no	—
122	C₁₃×#125	—	2	2	no	—
123	C₁₃×#125	D₄	1	2	yes	—
124	C₁₃×#125	C₂³	1	4	yes	—
125	C₁₃×#125	C₂³	1	4	yes	—
126	C₁₃×#125	C₂³	1	2	yes	—
127	C₁₃×C₂²⋊Q₈	—	2	2	no	—
128	C₁₃×C₂²⋊Q₈	—	2	2	no	—
129	C₁₃×C₂²⋊Q₈	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	—	2	1	no	—
131	C₁₃×C₂²⋊Q₈	—	2	1	no	—
132	C₁₃×C₂²⋊Q₈	—	2	2	no	—
133	C₁₃×C₂²⋊Q₈	—	2	4	no	—
134	C₁₃×C₂²⋊Q₈	—	2	2	no	—
135	C₁₃×C₂²⋊Q₈	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	—	2	4	no	—
139	C₁₃×C₂²⋊Q₈	—	2	4	no	—
140	C₁₃×C₂²⋊Q₈	—	2	4	no	—
141	C₁₃×C₂²⋊Q₈	—	2	4	no	—
142	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
143	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
144	C₄×Q₈×C₁₃	—	2	2	no	—
145	C₄×Q₈×C₁₃	—	2	2	no	—
146	C₄×Q₈×C₁₃	—	2	1	no	—
147	C₄×Q₈×C₁₃	—	2	1	no	—
148	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
149	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
150	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
151	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
153	C₄×D₄×C₁₃	—	2	1	no	—
154	C₄×D₄×C₁₃	—	2	1	no	—
155	C₄×D₄×C₁₃	—	2	2	no	—
156	C₄×D₄×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	—	2	4	no	—
158	C₄×D₄×C₁₃	—	2	1	no	—
159	C₄×D₄×C₁₃	—	2	1	no	—
160	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
161	C₄×D₄×C₁₃	C₂³	1	2	yes	—
162	C₄×D₄×C₁₃	C₂³	1	4	yes	—
163	C₄×D₄×C₁₃	C₂³	1	4	yes	—
164	C₄×D₄×C₁₃	C₂³	1	4	yes	—
165	C₄×D₄×C₁₃	C₂³	1	2	yes	—
166	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
167	C₁₃×#117	—	2	2	no	—
168	C₁₃×#117	—	2	1	no	—
169	C₁₃×#117	C₂³	1	2	yes	—
170	C₁₃×#117	C₂³	1	1	yes	characteristic
171	C₁₃×#117	C₂³	1	2	yes	—
172	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
180	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
181	C₂×C₄²×C₁₃	—	2	1	no	—
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₁₃×#107	C₂³	1	2	yes	—
184	C₁₃×#107	C₂³	1	2	yes	—
185	C₁₃×#107	C₂³	1	2	yes	—
186	C₁₃×#107	C₂³	1	4	yes	—
187	C₁₃×#107	C₂³	1	4	yes	—
188	C₁₃×#106	C₂³	1	4	yes	—
189	C₁₃×#106	C₂³	1	4	yes	—
190	C₁₃×#106	C₂³	1	2	yes	—
191	C₁₃×#106	C₂³	1	2	yes	—
192	C₁₃×#106	C₂³	1	4	yes	—
193	C₁₃×#106	C₂³	1	2	yes	—
194	C₁₃×#106	C₂³	1	4	yes	—
195	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
196	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
197	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
198	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
199	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
200	C₁₃×#103	C₂³	1	2	yes	—
201	C₁₃×#103	C₂³	1	2	yes	—
202	C₁₃×#103	C₂³	1	2	yes	—
203	C₁₃×#102	C₂³	1	4	yes	—
204	C₁₃×#102	C₂³	1	4	yes	—
205	C₁₃×#102	C₂³	1	2	yes	—
206	C₁₃×#102	C₂³	1	2	yes	—
207	C₁₃×#102	C₂³	1	2	yes	—
208	C₁₃×#102	C₂³	1	2	yes	—
209	C₁₃×#102	C₂³	1	2	yes	—
210	C₁₃×#97	C₂³	1	2	yes	—
211	C₁₃×#97	C₂³	1	4	yes	—
212	C₄×C₈×C₁₃	C₂³	1	2	yes	—
213	C₄×C₈×C₁₃	C₂³	1	4	yes	—
214	#61382	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂⁴×C₁₃	—	2	1	no	—
216	C₁₃×#41	—	2	2	no	—
217	C₁₃×#41	C₂×Q₈	1	4	yes	complemented
218	C₂×Q₈×C₁₃	—	2	1	no	—
219	C₂×Q₈×C₁₃	—	2	2	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	4	no	—
222	C₂×Q₈×C₁₃	—	2	4	no	—
223	C₂×Q₈×C₁₃	—	2	2	no	—
224	C₂×Q₈×C₁₃	—	8	4	no	—
225	C₂×Q₈×C₁₃	—	8	2	no	—
226	C₂×Q₈×C₁₃	—	8	4	no	—
227	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	1	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
233	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	complemented
234	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	2	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	2	1	no	—
241	C₂²×C₄×C₁₃	—	2	2	no	—
242	C₂²×C₄×C₁₃	—	2	4	no	—
243	C₂²×C₄×C₁₃	—	2	4	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	2	4	no	—
246	C₂²×C₄×C₁₃	—	8	2	no	—
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₁₃×SD₁₆	C₂×Q₈	1	8	yes	complemented
251	C₁₃×D₈	C₂×Q₈	1	8	yes	complemented
252	C₁₃×M₁₆	—	2	2	no	—
253	C₁₃×M₁₆	C₂×Q₈	1	4	yes	complemented
254	C₂×C₈×C₁₃	—	2	4	no	—
255	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
256	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
257	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
258	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
259	C₁₃×C₄⋊C₄	—	2	2	no	—
260	C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₁₃×C₄⋊C₄	—	2	2	no	—
262	C₁₃×C₄⋊C₄	—	2	2	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	4	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	2	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
284	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
285	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
288	C₁₃×C₂²⋊C₄	—	2	2	no	—
289	C₁₃×C₂²⋊C₄	—	2	1	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	2	no	—
293	C₁₃×C₂²⋊C₄	—	2	2	no	—
294	C₁₃×C₂²⋊C₄	—	2	1	no	—
295	C₁₃×C₂²⋊C₄	—	2	1	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
298	C₄²×C₁₃	—	2	1	no	—
299	C₄²×C₁₃	—	2	1	no	—
300	C₄²×C₁₃	—	2	1	no	—
301	C₄²×C₁₃	—	2	4	no	—
302	C₄²×C₁₃	—	2	2	no	—
303	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₄²×C₁₃	C₂⁴	1	4	yes	—
307	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
308	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#3388	C₂×C₁₃	1	4	yes	complemented
311	#3385	C₂×C₁₃	1	2	yes	complemented
312	#3384	C₂×C₁₃	1	2	yes	complemented
313	#3384	C₂×C₁₃	1	4	yes	complemented
314	#3380	C₂×C₁₃	1	2	yes	complemented
315	Q₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
316	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#3163	C₂×C₁₃	1	2	yes	complemented
318	#3084	C₂×C₁₃	1	2	yes	complemented
319	#3081	C₂×C₁₃	1	2	yes	complemented
320	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
321	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#2946	C₂×C₁₃	1	2	yes	—
324	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic
325	C₂³×C₁₃	—	2	1	no	—
326	C₂³×C₁₃	—	2	2	no	—
327	C₂³×C₁₃	—	2	4	no	—
328	C₂³×C₁₃	—	8	1	no	—
329	C₂³×C₁₃	—	8	1	no	—
330	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
331	Q₈×C₁₃	—	2	4	no	—
332	Q₈×C₁₃	—	2	1	no	—
333	Q₈×C₁₃	—	4	2	no	—
334	Q₈×C₁₃	—	4	4	no	—
335	Q₈×C₁₃	—	4	2	no	—
336	Q₈×C₁₃	—	8	1	no	—
337	Q₈×C₁₃	—	8	2	no	—
338	Q₈×C₁₃	—	8	4	no	—
339	Q₈×C₁₃	—	8	4	no	—
340	Q₈×C₁₃	C₂²×Q₈	1	2	yes	—
341	D₄×C₁₃	—	2	4	no	—
342	D₄×C₁₃	—	2	4	no	—
343	D₄×C₁₃	—	2	2	no	—
344	D₄×C₁₃	—	2	1	no	—
345	D₄×C₁₃	C₂²×Q₈	1	2	yes	—
346	D₄×C₁₃	C₂²×Q₈	1	4	yes	—
347	C₂×C₄×C₁₃	—	2	1	no	—
348	C₂×C₄×C₁₃	—	2	4	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	1	no	—
351	C₂×C₄×C₁₃	—	2	1	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	4	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	4	1	no	—
357	C₂×C₄×C₁₃	—	4	2	no	—
358	C₂×C₄×C₁₃	—	4	2	no	—
359	C₂×C₄×C₁₃	—	4	4	no	—
360	C₂×C₄×C₁₃	—	8	4	no	—
361	C₂×C₄×C₁₃	—	8	2	no	—
362	C₂×C₄×C₁₃	—	8	4	no	—
363	C₂×C₄×C₁₃	—	8	4	no	—
364	C₂×C₄×C₁₃	—	8	1	no	—
365	C₂×C₄×C₁₃	—	8	2	no	—
366	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
368	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
371	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
374	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
375	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
376	C₈×C₁₃	—	2	2	no	—
377	C₈×C₁₃	—	2	2	no	—
378	C₈×C₁₃	—	2	2	no	—
379	C₈×C₁₃	C₂²×Q₈	1	4	yes	—
380	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
381	Q₈²	C₂²×C₁₃	1	2	yes	complemented
382	#557	C₂²×C₁₃	1	2	yes	complemented
383	#554	—	2	1	no	—
384	#554	—	2	2	no	—
385	#554	—	2	2	no	—
386	#554	C₂²×C₁₃	1	2	yes	—
387	#554	C₂²×C₁₃	1	4	yes	—
388	#554	C₂²×C₁₃	1	2	yes	complemented
389	D₄×Q₈	—	2	1	no	—
390	D₄×Q₈	—	2	2	no	—
391	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
392	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
393	#544	—	2	2	no	—
394	#544	C₂²×C₁₃	1	2	yes	—
395	#544	C₂²×C₁₃	1	2	yes	—
396	#543	—	2	2	no	—
397	#533	—	2	1	no	—
398	#533	C₂²×C₁₃	1	1	yes	characteristic
399	#533	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊Q₈	—	2	1	no	—
401	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×C₂²⋊Q₈	—	2	2	no	—
403	#520	C₂²×C₁₃	1	2	yes	—
404	#518	C₂²×C₁₃	1	2	yes	—
405	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
407	#501	C₂²×C₁₃	1	4	yes	complemented
408	#501	C₂²×C₁₃	1	4	yes	complemented
409	#501	C₂²×C₁₃	1	4	yes	complemented
410	#500	C₂²×C₁₃	1	2	yes	complemented
411	#499	C₂²×C₁₃	1	4	yes	complemented
412	#498	C₂²×C₁₃	1	4	yes	complemented
413	#498	C₂²×C₁₃	1	2	yes	complemented
414	#479	C₂²×C₁₃	1	2	yes	complemented
415	#479	C₂²×C₁₃	1	4	yes	complemented
416	#478	C₂²×C₁₃	1	4	yes	—
417	#478	C₂²×C₁₃	1	4	yes	—
418	#478	C₂²×C₁₃	1	2	yes	complemented
419	#478	C₂²×C₁₃	1	4	yes	complemented
420	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
421	#476	C₂²×C₁₃	1	4	yes	—
422	#476	C₂²×C₁₃	1	2	yes	—
423	#476	C₂²×C₁₃	1	2	yes	—
424	#476	C₂²×C₁₃	1	4	yes	—
425	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	#476	C₂²×C₁₃	1	4	yes	complemented
427	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	#475	C₂²×C₁₃	1	4	yes	complemented
429	#474	C₂²×C₁₃	1	4	yes	—
430	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#446	C₂²×C₁₃	1	2	yes	complemented
432	#446	C₂²×C₁₃	1	4	yes	complemented
433	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
434	#442	C₂²×C₁₃	1	2	yes	—
435	#442	C₂²×C₁₃	1	4	yes	—
436	#440	C₂²×C₁₃	1	4	yes	—
437	#440	C₂²×C₁₃	1	2	yes	—
438	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
439	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
440	C₄×D₈	C₂²×C₁₃	1	2	yes	—
441	C₄×D₈	C₂²×C₁₃	1	4	yes	—
442	#428	C₂²×C₁₃	1	2	yes	—
443	#428	C₂²×C₁₃	1	1	yes	characteristic
444	#428	C₂²×C₁₃	1	2	yes	—
445	#427	C₂²×C₁₃	1	2	yes	—
446	C₂×#106	C₂²×C₁₃	1	2	yes	—
447	#424	C₂²×C₁₃	1	2	yes	—
448	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
449	#418	C₂²×C₁₃	1	1	yes	characteristic
450	#417	C₂²×C₁₃	1	1	yes	characteristic
451	#416	C₂²×C₁₃	1	2	yes	—
452	C₂×#102	C₂²×C₁₃	1	2	yes	—
453	#405	C₂²×C₁₃	1	2	yes	—
454	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
455	C₂²×C₁₃	—	2	1	no	—
456	C₂²×C₁₃	—	2	1	no	—
457	C₂²×C₁₃	—	2	2	no	—
458	C₂²×C₁₃	—	2	4	no	—
459	C₂²×C₁₃	—	4	1	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	—	4	2	no	—
462	C₂²×C₁₃	—	4	1	no	—
463	C₂²×C₁₃	—	8	4	no	—
464	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
465	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
466	C₄×C₁₃	—	2	1	no	—
467	C₄×C₁₃	—	2	1	no	—
468	C₄×C₁₃	—	2	4	no	—
469	C₄×C₁₃	—	2	2	no	—
470	C₄×C₁₃	—	2	1	no	—
471	C₄×C₁₃	—	2	4	no	—
472	C₄×C₁₃	—	4	1	no	—
473	C₄×C₁₃	—	4	4	no	—
474	C₄×C₁₃	—	4	2	no	—
475	C₄×C₁₃	—	4	1	no	—
476	C₄×C₁₃	—	4	2	no	—
477	C₄×C₁₃	—	4	2	no	—
478	C₄×C₁₃	D₄×Q₈	1	2	yes	—
479	C₄×C₁₃	#577	1	2	yes	—
480	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
481	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
482	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
483	C₂²×Q₈	—	2	2	no	—
484	C₂²×Q₈	—	2	2	no	—
485	C₂²×Q₈	—	2	1	no	—
486	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
487	C₂³×C₄	—	2	1	no	—
488	AGL(1,ℤ/8)	Q₈×C₁₃	1	8	yes	complemented
489	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
490	C₂×D₈	C₂³×C₁₃	1	2	yes	—
491	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
492	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	—	2	2	no	—
496	C₄⋊Q₈	—	2	2	no	—
497	C₄⋊Q₈	—	2	4	no	—
498	C₄⋊Q₈	—	2	2	no	—
499	C₄⋊Q₈	—	2	1	no	—
500	C₄⋊Q₈	—	2	1	no	—
501	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
502	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
503	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
504	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
505	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
508	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
509	#125	—	2	2	no	—
510	#125	—	2	4	no	—
511	#125	—	2	2	no	—
512	#125	D₄×C₁₃	1	2	yes	—
513	#125	C₂³×C₁₃	1	2	yes	—
514	#125	C₂³×C₁₃	1	4	yes	—
515	#125	C₂³×C₁₃	1	4	yes	—
516	C₂²⋊Q₈	—	2	2	no	—
517	C₂²⋊Q₈	—	2	2	no	—
518	C₂²⋊Q₈	—	2	4	no	—
519	C₂²⋊Q₈	—	2	1	no	—
520	C₂²⋊Q₈	—	2	1	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	4	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	—	2	4	no	—
526	C₂²⋊Q₈	—	2	4	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
532	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
533	C₄×Q₈	—	2	2	no	—
534	C₄×Q₈	—	2	2	no	—
535	C₄×Q₈	—	2	1	no	—
536	C₄×Q₈	—	2	1	no	—
537	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
538	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
539	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
540	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
541	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	4	no	—
547	C₄×D₄	—	2	1	no	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	C₂³×C₁₃	1	2	yes	—
550	C₄×D₄	C₂³×C₁₃	1	2	yes	—
551	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
552	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
553	C₄×D₄	C₂³×C₁₃	1	4	yes	—
554	C₄×D₄	C₂³×C₁₃	1	4	yes	—
555	C₄×D₄	C₂³×C₁₃	1	4	yes	—
556	#117	—	2	2	no	—
557	#117	—	2	1	no	—
558	#117	C₂³×C₁₃	1	1	yes	characteristic
559	#117	C₂³×C₁₃	1	2	yes	—
560	#117	C₂³×C₁₃	1	2	yes	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	2	no	—
563	C₂×C₄⋊C₄	—	2	4	no	—
564	C₂×C₄⋊C₄	—	2	2	no	—
565	C₂×C₄⋊C₄	—	2	2	no	—
566	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	4	no	—
570	C₂×C₄²	—	2	1	no	—
571	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
572	#107	C₂³×C₁₃	1	2	yes	—
573	#107	C₂³×C₁₃	1	2	yes	—
574	#107	C₂³×C₁₃	1	2	yes	—
575	#107	C₂³×C₁₃	1	4	yes	—
576	#107	C₂³×C₁₃	1	4	yes	—
577	#106	C₂³×C₁₃	1	4	yes	—
578	#106	C₂³×C₁₃	1	4	yes	—
579	#106	C₂³×C₁₃	1	2	yes	—
580	#106	C₂³×C₁₃	1	2	yes	—
581	#106	C₂³×C₁₃	1	4	yes	—
582	#106	C₂³×C₁₃	1	2	yes	—
583	#106	C₂³×C₁₃	1	4	yes	—
584	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
586	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
587	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
588	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
589	#103	C₂³×C₁₃	1	2	yes	—
590	#103	C₂³×C₁₃	1	2	yes	—
591	#103	C₂³×C₁₃	1	2	yes	—
592	#102	C₂³×C₁₃	1	4	yes	—
593	#102	C₂³×C₁₃	1	4	yes	—
594	#102	C₂³×C₁₃	1	2	yes	—
595	#102	C₂³×C₁₃	1	2	yes	—
596	#102	C₂³×C₁₃	1	2	yes	—
597	#102	C₂³×C₁₃	1	2	yes	—
598	#102	C₂³×C₁₃	1	2	yes	—
599	#97	C₂³×C₁₃	1	2	yes	—
600	#97	C₂³×C₁₃	1	4	yes	—
601	C₄×C₈	C₂³×C₁₃	1	2	yes	—
602	C₄×C₈	C₂³×C₁₃	1	4	yes	—
603	C₂×C₁₃	—	2	2	no	—
604	C₂×C₁₃	—	4	2	no	—
605	C₂×C₁₃	—	4	4	no	—
606	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
607	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
608	C₂×C₁₃	#3585	1	1	yes	characteristic
609	C₂⁴	—	2	1	no	—
610	#41	—	2	2	no	—
611	#41	C₂×Q₈×C₁₃	1	4	yes	complemented
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	2	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	4	no	—
616	C₂×Q₈	—	2	4	no	—
617	C₂×Q₈	—	2	2	no	—
618	C₂×Q₈	—	8	4	no	—
619	C₂×Q₈	—	8	2	no	—
620	C₂×Q₈	—	8	4	no	—
621	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
622	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
623	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	complemented
628	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
629	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	8	2	no	—
641	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
644	SD₁₆	C₂×Q₈×C₁₃	1	8	yes	complemented
645	D₈	C₂×Q₈×C₁₃	1	8	yes	complemented
646	M₁₆	—	2	2	no	—
647	M₁₆	C₂×Q₈×C₁₃	1	4	yes	complemented
648	C₂×C₈	—	2	4	no	—
649	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
650	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
651	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
652	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
671	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
672	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
673	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
674	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
676	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
677	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
678	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
679	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
681	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	1	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	1	no	—
689	C₂²⋊C₄	—	2	1	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
692	C₄²	—	2	1	no	—
693	C₄²	—	2	1	no	—
694	C₄²	—	2	1	no	—
695	C₄²	—	2	4	no	—
696	C₄²	—	2	2	no	—
697	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
699	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
700	C₄²	C₂⁴×C₁₃	1	4	yes	—
701	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
702	C₁₃	#61382	1	1	yes	characteristic, direct product factor, Sylow
703	C₂³	—	2	1	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	4	no	—
706	C₂³	—	8	1	no	—
707	C₂³	—	8	1	no	—
708	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
709	Q₈	—	2	4	no	—
710	Q₈	—	2	1	no	—
711	Q₈	—	4	2	no	—
712	Q₈	—	4	4	no	—
713	Q₈	—	4	2	no	—
714	Q₈	—	8	4	no	—
715	Q₈	—	8	2	no	—
716	Q₈	—	8	4	no	—
717	Q₈	—	8	1	no	—
718	Q₈	C₂²×Q₈×C₁₃	1	2	yes	—
719	D₄	—	2	4	no	—
720	D₄	—	2	4	no	—
721	D₄	—	2	2	no	—
722	D₄	—	2	1	no	—
723	D₄	C₂²×Q₈×C₁₃	1	2	yes	—
724	D₄	C₂²×Q₈×C₁₃	1	4	yes	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	8	2	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	—	8	4	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	—	8	1	no	—
743	C₂×C₄	—	8	2	no	—
744	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
746	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
749	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
750	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
751	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
752	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
753	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
754	C₈	—	2	2	no	—
755	C₈	—	2	2	no	—
756	C₈	—	2	2	no	—
757	C₈	C₂²×Q₈×C₁₃	1	4	yes	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	4	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	8	4	no	—
767	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
768	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
769	C₄	—	2	1	no	—
770	C₄	—	2	4	no	—
771	C₄	—	2	1	no	—
772	C₄	—	2	1	no	—
773	C₄	—	2	4	no	—
774	C₄	—	2	2	no	—
775	C₄	—	4	1	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	4	no	—
780	C₄	—	4	2	no	—
781	C₄	D₄×Q₈×C₁₃	1	2	yes	—
782	C₄	C₁₃×#577	1	2	yes	—
783	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
784	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
785	C₂	—	2	2	no	—
786	C₂	—	4	4	no	—
787	C₂	—	4	2	no	—
788	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
789	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
790	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3503	C₂	semidirect
2. C₁₃×#3501	C₂	semidirect
3. C₁₃×#3388	C₂	semidirect
4. C₁₃×#3385	C₂	semidirect
5. C₁₃×#3384	C₂	semidirect
6. C₁₃×#3384	C₂	semidirect
7. C₁₃×#3380	C₂	semidirect
8. Q₈×C₁₃×SD₁₆	C₂	semidirect
9. C₁₃×#3165	C₂	semidirect
10. C₁₃×#3163	C₂	semidirect
11. C₁₃×#3084	C₂	semidirect
12. C₁₃×#3081	C₂	semidirect
13. C₁₃×#3076	C₂	semidirect
14. C₂×C₁₃×#476	C₂	semidirect
15. C₁₃×#2962	C₂	semidirect
19. Q₈²×C₁₃	C₂²	semidirect
20. C₁₃×#557	C₂²	semidirect
26. C₁₃×#554	C₂²	semidirect
30. D₄×Q₈×C₁₃	C₂²	semidirect
45. C₁₃×#501	C₂²	semidirect
46. C₁₃×#501	C₂²	semidirect
47. C₁₃×#501	C₂²	semidirect
48. C₁₃×#500	C₂²	semidirect
49. C₁₃×#499	C₂²	semidirect
50. C₁₃×#498	C₂²	semidirect
51. C₁₃×#498	C₂²	semidirect
52. C₁₃×#479	C₂²	semidirect
53. C₁₃×#479	C₂²	semidirect
56. C₁₃×#478	C₂²	semidirect
57. C₁₃×#478	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
63. C₁₃×#476	C₂²	semidirect
64. C₁₃×#476	C₂²	semidirect
65. C₁₃×#475	C₂²	semidirect
66. C₁₃×#475	C₂²	semidirect
68. C₁₃×#474	C₂²	semidirect
69. C₁₃×#446	C₂²	semidirect
70. C₁₃×#446	C₂²	semidirect
71. C₈×Q₈×C₁₃	C₂²	semidirect
99. C₁₃×AGL(1,ℤ/8)	Q₈	semidirect
214. #61382	C₁₃	direct (N × H)
217. C₁₃×#41	C₂×Q₈	semidirect
233. C₂×D₄×C₁₃	C₂×Q₈	semidirect
250. C₁₃×SD₁₆	C₂×Q₈	semidirect
251. C₁₃×D₈	C₂×Q₈	semidirect
253. C₁₃×M₁₆	C₂×Q₈	semidirect
308. #3503	C₂×C₁₃	semidirect
309. #3501	C₂×C₁₃	semidirect
310. #3388	C₂×C₁₃	semidirect
311. #3385	C₂×C₁₃	semidirect
312. #3384	C₂×C₁₃	semidirect
313. #3384	C₂×C₁₃	semidirect
314. #3380	C₂×C₁₃	semidirect
315. Q₈×SD₁₆	C₂×C₁₃	semidirect
316. #3165	C₂×C₁₃	semidirect
317. #3163	C₂×C₁₃	semidirect
318. #3084	C₂×C₁₃	semidirect
319. #3081	C₂×C₁₃	semidirect
320. #3076	C₂×C₁₃	semidirect
321. C₂×#476	C₂×C₁₃	semidirect
322. #2962	C₂×C₁₃	semidirect
381. Q₈²	C₂²×C₁₃	semidirect
382. #557	C₂²×C₁₃	semidirect
388. #554	C₂²×C₁₃	semidirect
392. D₄×Q₈	C₂²×C₁₃	semidirect
407. #501	C₂²×C₁₃	semidirect
408. #501	C₂²×C₁₃	semidirect
409. #501	C₂²×C₁₃	semidirect
410. #500	C₂²×C₁₃	semidirect
411. #499	C₂²×C₁₃	semidirect
412. #498	C₂²×C₁₃	semidirect
413. #498	C₂²×C₁₃	semidirect
414. #479	C₂²×C₁₃	semidirect
415. #479	C₂²×C₁₃	semidirect
418. #478	C₂²×C₁₃	semidirect
419. #478	C₂²×C₁₃	semidirect
420. #477	C₂²×C₁₃	semidirect
425. #476	C₂²×C₁₃	semidirect
426. #476	C₂²×C₁₃	semidirect
427. #475	C₂²×C₁₃	semidirect
428. #475	C₂²×C₁₃	semidirect
430. #474	C₂²×C₁₃	semidirect
431. #446	C₂²×C₁₃	semidirect
432. #446	C₂²×C₁₃	semidirect
433. C₈×Q₈	C₂²×C₁₃	semidirect
488. AGL(1,ℤ/8)	Q₈×C₁₃	semidirect
611. #41	C₂×Q₈×C₁₃	semidirect
627. C₂×D₄	C₂×Q₈×C₁₃	semidirect
644. SD₁₆	C₂×Q₈×C₁₃	semidirect
645. D₈	C₂×Q₈×C₁₃	semidirect
647. M₁₆	C₂×Q₈×C₁₃	semidirect
702. C₁₃	#61382	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×#3503	2
C₁₃×#3501	2
C₁₃×#3388	2
C₁₃×#3385	2
C₁₃×#3384	2
C₁₃×#3380	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3165	2
C₁₃×#3163	2
C₁₃×#3084	2
C₁₃×#3081	2
C₁₃×#3076	2
C₂×C₁₃×#476	2
C₁₃×#2962	2
C₁₃×#2946	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61382	13

Subgroups — C13×#61382 #15747721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61382 #15747721