Subgroups — C₁₃×#61331 #15747670

Order 3328.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3376	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3371	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3370	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3360	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3045	C₂	1	1	yes	maximal, characteristic
19	C₁₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
27	C₁₃×#559	C₂²	1	2	yes	—
28	C₁₃×#559	C₂²	1	2	yes	—
29	C₁₃×#557	C₂²	1	2	yes	complemented
30	C₁₃×#557	C₂²	1	2	yes	complemented
31	C₁₃×#556	C₂²	1	2	yes	—
32	C₁₃×#556	C₂²	1	2	yes	—
33	C₁₃×#554	—	2	2	no	—
34	C₁₃×#554	—	2	2	no	—
35	C₁₃×#554	C₂²	1	2	yes	complemented
36	C₁₃×#554	C₂²	1	2	yes	complemented
37	C₁₃×#551	—	2	2	no	—
38	C₁₃×#551	—	2	2	no	—
39	C₁₃×#544	—	2	1	no	—
40	C₁₃×#544	—	2	1	no	—
41	C₁₃×#544	C₂²	1	1	yes	characteristic
42	C₁₃×#544	C₂²	1	1	yes	characteristic
43	C₁₃×#542	—	2	1	no	—
44	C₁₃×#542	—	2	1	no	—
45	C₁₃×#536	C₂²	1	1	yes	characteristic
46	C₁₃×#535	C₂²	1	1	yes	characteristic
47	C₁₃×#533	—	2	1	no	—
48	C₁₃×#533	C₂²	1	1	yes	characteristic
49	C₁₃×#529	—	2	1	no	—
50	C₁₃×#529	—	2	1	no	—
51	C₂×C₁₃×#125	—	2	1	no	—
52	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
54	C₁₃×#520	C₂²	1	1	yes	characteristic
55	C₁₃×#520	C₂²	1	1	yes	characteristic
56	C₁₃×#519	C₂²	1	1	yes	characteristic
57	C₁₃×#518	C₂²	1	1	yes	characteristic
58	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
59	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
60	C₁₃×#491	C₂²	1	2	yes	complemented
61	C₁₃×#490	C₂²	1	2	yes	—
62	C₁₃×#489	C₂²	1	2	yes	—
63	C₁₃×#489	C₂²	1	2	yes	complemented
64	C₁₃×#488	C₂²	1	2	yes	—
65	C₁₃×#488	C₂²	1	2	yes	—
66	C₁₃×#488	C₂²	1	2	yes	—
67	C₁₃×#488	C₂²	1	2	yes	—
68	C₁₃×#488	C₂²	1	2	yes	—
69	C₁₃×#488	C₂²	1	2	yes	complemented
70	C₁₃×#487	C₂²	1	2	yes	complemented
71	C₁₃×#486	C₂²	1	2	yes	—
72	C₁₃×#479	C₂²	1	2	yes	complemented
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#479	C₂²	1	2	yes	complemented
75	C₁₃×#479	C₂²	1	2	yes	complemented
76	C₁₃×#478	C₂²	1	2	yes	—
77	C₁₃×#478	C₂²	1	2	yes	—
78	C₁₃×#478	C₂²	1	2	yes	complemented
79	C₁₃×#478	C₂²	1	2	yes	complemented
80	C₁₃×#477	C₂²	1	2	yes	complemented
81	C₁₃×#476	C₂²	1	2	yes	—
82	C₁₃×#475	C₂²	1	2	yes	complemented
83	C₁₃×#474	C₂²	1	2	yes	—
84	C₁₃×#464	C₂²	1	2	yes	—
85	C₁₃×#464	C₂²	1	2	yes	—
86	C₁₃×#464	C₂²	1	2	yes	—
87	C₁₃×#464	C₂²	1	2	yes	complemented
88	C₁₃×#463	C₂²	1	2	yes	—
89	C₁₃×#463	C₂²	1	2	yes	—
90	C₁₃×#463	C₂²	1	2	yes	—
91	C₁₃×#463	C₂²	1	2	yes	complemented
92	C₁₃×#462	C₂²	1	2	yes	complemented
93	C₁₃×#461	C₂²	1	2	yes	complemented
94	C₁₃×#460	C₂²	1	2	yes	—
95	C₁₃×#459	C₂²	1	2	yes	—
96	C₁₃×#446	C₂²	1	2	yes	complemented
97	C₁₃×#446	C₂²	1	2	yes	complemented
98	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
99	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
100	C₁₃×#442	C₂²	1	2	yes	—
101	C₁₃×#441	C₂²	1	2	yes	complemented
102	C₁₃×#440	C₂²	1	2	yes	—
103	C₁₃×#440	C₂²	1	2	yes	complemented
104	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
106	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
107	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
108	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
109	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
110	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₁₃×D₈	C₂²	1	2	yes	—
114	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
116	C₁₃×#428	C₂²	1	1	yes	characteristic
117	C₁₃×#428	C₂²	1	1	yes	characteristic
118	C₁₃×#427	C₂²	1	1	yes	characteristic
119	C₁₃×#424	C₂²	1	1	yes	characteristic
120	C₁₃×#424	C₂²	1	1	yes	characteristic
121	C₁₃×#423	C₂²	1	1	yes	characteristic
122	C₁₃×#419	C₂²	1	1	yes	characteristic
123	C₁₃×#418	C₂²	1	1	yes	characteristic
124	C₁₃×#417	C₂²	1	1	yes	characteristic
125	C₁₃×#417	C₂²	1	1	yes	characteristic
126	C₁₃×#416	C₂²	1	1	yes	characteristic
127	C₁₃×#416	C₂²	1	1	yes	characteristic
128	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
129	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
130	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
131	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
132	C₁₃×#405	C₂²	1	1	yes	characteristic
133	C₁₃×#405	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₁₃×#137	—	2	4	no	—
140	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
141	C₁₃×#135	—	2	4	no	—
142	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
144	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×D₈	C₂³	1	2	yes	—
149	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
154	C₁₃×C₄⋊Q₈	—	2	2	no	—
155	C₁₃×C₄⋊Q₈	—	2	2	no	—
156	C₁₃×C₄⋊Q₈	—	2	1	no	—
157	C₁₃×C₄⋊Q₈	—	2	1	no	—
158	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
159	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
160	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₁₃×#127	C₂³	1	2	yes	—
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#126	—	2	2	no	—
166	C₁₃×#126	—	2	2	no	—
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#125	—	2	1	no	—
169	C₁₃×#125	—	2	1	no	—
170	C₁₃×#125	—	2	2	no	—
171	C₁₃×#125	—	2	2	no	—
172	C₁₃×#125	—	2	2	no	—
173	C₁₃×#125	—	2	2	no	—
174	C₁₃×#125	—	2	1	no	—
175	C₁₃×#125	—	2	1	no	—
176	C₁₃×#125	D₄	1	1	yes	characteristic
177	C₁₃×#125	D₄	1	1	yes	characteristic
178	C₁₃×#125	C₂³	1	2	yes	—
179	C₁₃×#125	C₂³	1	2	yes	—
180	C₁₃×#125	C₂³	1	2	yes	—
181	C₁₃×#125	C₂³	1	2	yes	—
182	C₁₃×#124	—	2	2	no	—
183	C₁₃×#124	—	2	2	no	—
184	C₁₃×#124	—	2	1	no	—
185	C₁₃×#124	—	2	1	no	—
186	C₁₃×#124	C₂³	1	2	yes	—
187	C₁₃×#124	C₂³	1	2	yes	—
188	C₁₃×#124	C₂³	1	2	yes	—
189	C₁₃×#124	C₂³	1	2	yes	—
190	C₁₃×#123	—	2	2	no	—
191	C₁₃×#123	—	2	2	no	—
192	C₁₃×#123	—	2	2	no	—
193	C₁₃×#123	—	2	2	no	—
194	C₁₃×#123	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	—	2	2	no	—
197	C₁₃×C₂²⋊Q₈	—	2	2	no	—
198	C₁₃×C₂²⋊Q₈	—	2	2	no	—
199	C₁₃×C₂²⋊Q₈	—	2	1	no	—
200	C₁₃×C₂²⋊Q₈	—	2	1	no	—
201	C₁₃×C₂²⋊Q₈	—	2	2	no	—
202	C₁₃×C₂²⋊Q₈	—	2	2	no	—
203	C₁₃×C₂²⋊Q₈	—	2	2	no	—
204	C₁₃×C₂²⋊Q₈	—	2	2	no	—
205	C₁₃×C₂²⋊Q₈	—	2	2	no	—
206	C₁₃×C₂²⋊Q₈	—	2	2	no	—
207	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
208	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
209	C₁₃×#121	—	2	1	no	—
210	C₁₃×#121	—	2	1	no	—
211	C₁₃×#120	—	2	2	no	—
212	C₄×Q₈×C₁₃	—	2	1	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	—	2	2	no	—
215	C₄×Q₈×C₁₃	—	2	2	no	—
216	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
225	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
226	C₄×D₄×C₁₃	—	2	1	no	—
227	C₄×D₄×C₁₃	—	2	1	no	—
228	C₄×D₄×C₁₃	—	2	1	no	—
229	C₄×D₄×C₁₃	—	2	1	no	—
230	C₄×D₄×C₁₃	—	2	1	no	—
231	C₄×D₄×C₁₃	—	2	1	no	—
232	C₄×D₄×C₁₃	—	2	2	no	—
233	C₄×D₄×C₁₃	—	2	2	no	—
234	C₄×D₄×C₁₃	—	2	2	no	—
235	C₄×D₄×C₁₃	—	2	2	no	—
236	C₄×D₄×C₁₃	C₂³	1	2	yes	—
237	C₄×D₄×C₁₃	C₂³	1	2	yes	—
238	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₁₃	C₂³	1	2	yes	—
243	C₄×D₄×C₁₃	C₂³	1	2	yes	—
244	C₁₃×#117	—	2	1	no	—
245	C₁₃×#117	—	2	1	no	—
246	C₁₃×#117	—	2	2	no	—
247	C₁₃×#117	—	2	2	no	—
248	C₁₃×#117	—	2	2	no	—
249	C₁₃×#117	—	2	1	no	—
250	C₁₃×#117	—	2	1	no	—
251	C₁₃×#117	C₂³	1	1	yes	characteristic
252	C₁₃×#117	C₂³	1	1	yes	characteristic
253	C₁₃×#117	C₂³	1	1	yes	characteristic
254	C₁₃×#117	C₂³	1	1	yes	characteristic
255	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
260	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₄²×C₁₃	—	2	1	no	—
267	C₂×C₄²×C₁₃	—	2	1	no	—
268	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
269	C₁₃×#107	C₂³	1	1	yes	characteristic
270	C₁₃×#107	C₂³	1	1	yes	characteristic
271	C₁₃×#107	C₂³	1	2	yes	—
272	C₁₃×#107	C₂³	1	2	yes	—
273	C₁₃×#106	C₂³	1	1	yes	characteristic
274	C₁₃×#106	C₂³	1	1	yes	characteristic
275	C₁₃×#106	C₂³	1	2	yes	—
276	C₁₃×#106	C₂³	1	2	yes	—
277	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
278	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
279	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₃×#103	C₂³	1	2	yes	—
284	C₁₃×#103	C₂³	1	2	yes	—
285	C₁₃×#103	C₂³	1	2	yes	—
286	C₁₃×#103	C₂³	1	2	yes	—
287	C₁₃×#103	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	1	yes	characteristic
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	1	yes	characteristic
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#102	C₂³	1	2	yes	—
296	C₁₃×#102	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	1	yes	characteristic
300	C₁₃×#102	C₂³	1	1	yes	characteristic
301	C₁₃×#102	C₂³	1	1	yes	characteristic
302	C₁₃×#102	C₂³	1	1	yes	characteristic
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×#102	C₂³	1	2	yes	—
305	C₁₃×#102	C₂³	1	2	yes	—
306	C₁₃×#102	C₂³	1	2	yes	—
307	C₁₃×#97	C₂³	1	2	yes	—
308	C₁₃×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₃	C₂³	1	2	yes	—
314	C₄×C₈×C₁₃	C₂³	1	2	yes	—
315	#61331	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂⁴×C₁₃	—	2	1	no	—
317	C₁₃×#41	—	2	2	no	—
318	C₁₃×#41	—	2	2	no	—
319	C₁₃×#41	—	2	2	no	—
320	C₁₃×#41	#41	1	4	yes	—
321	C₂×Q₈×C₁₃	—	2	1	no	—
322	C₂×Q₈×C₁₃	—	2	2	no	—
323	C₂×Q₈×C₁₃	—	2	2	no	—
324	C₂×Q₈×C₁₃	—	2	2	no	—
325	C₂×Q₈×C₁₃	—	2	2	no	—
326	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
327	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
328	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₁₃	—	2	1	no	—
332	C₂×D₄×C₁₃	—	2	1	no	—
333	C₂×D₄×C₁₃	—	2	1	no	—
334	C₂×D₄×C₁₃	—	2	2	no	—
335	C₂×D₄×C₁₃	—	2	2	no	—
336	C₂×D₄×C₁₃	—	2	2	no	—
337	C₂×D₄×C₁₃	—	2	2	no	—
338	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
339	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₁₃	—	2	1	no	—
342	C₂²×C₄×C₁₃	—	2	1	no	—
343	C₂²×C₄×C₁₃	—	2	1	no	—
344	C₂²×C₄×C₁₃	—	2	1	no	—
345	C₂²×C₄×C₁₃	—	2	1	no	—
346	C₂²×C₄×C₁₃	—	2	1	no	—
347	C₂²×C₄×C₁₃	—	2	1	no	—
348	C₂²×C₄×C₁₃	—	2	1	no	—
349	C₂²×C₄×C₁₃	—	2	1	no	—
350	C₂²×C₄×C₁₃	—	2	2	no	—
351	C₂²×C₄×C₁₃	—	2	2	no	—
352	C₂²×C₄×C₁₃	—	2	2	no	—
353	C₂²×C₄×C₁₃	—	2	2	no	—
354	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₁₃×Q₁₆	—	2	2	no	—
358	C₁₃×Q₁₆	—	2	4	no	—
359	C₁₃×SD₁₆	—	2	2	no	—
360	C₁₃×SD₁₆	—	2	4	no	—
361	C₁₃×SD₁₆	—	2	2	no	—
362	C₁₃×SD₁₆	—	2	4	no	—
363	C₁₃×D₈	—	2	2	no	—
364	C₁₃×D₈	—	2	4	no	—
365	C₁₃×M₁₆	—	2	2	no	—
366	C₁₃×M₁₆	—	2	2	no	—
367	C₂×C₈×C₁₃	—	2	2	no	—
368	C₂×C₈×C₁₃	—	2	2	no	—
369	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
374	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
375	C₁₃×C₄⋊C₄	—	2	2	no	—
376	C₁₃×C₄⋊C₄	—	2	2	no	—
377	C₁₃×C₄⋊C₄	—	2	1	no	—
378	C₁₃×C₄⋊C₄	—	2	1	no	—
379	C₁₃×C₄⋊C₄	—	2	2	no	—
380	C₁₃×C₄⋊C₄	—	2	2	no	—
381	C₁₃×C₄⋊C₄	—	2	2	no	—
382	C₁₃×C₄⋊C₄	—	2	2	no	—
383	C₁₃×C₄⋊C₄	—	2	2	no	—
384	C₁₃×C₄⋊C₄	—	2	2	no	—
385	C₁₃×C₄⋊C₄	—	2	2	no	—
386	C₁₃×C₄⋊C₄	—	2	2	no	—
387	C₁₃×C₄⋊C₄	—	2	1	no	—
388	C₁₃×C₄⋊C₄	—	2	1	no	—
389	C₁₃×C₄⋊C₄	—	2	1	no	—
390	C₁₃×C₄⋊C₄	—	2	1	no	—
391	C₁₃×C₄⋊C₄	—	2	2	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	2	no	—
394	C₁₃×C₄⋊C₄	—	2	2	no	—
395	C₁₃×C₄⋊C₄	—	2	2	no	—
396	C₁₃×C₄⋊C₄	—	2	2	no	—
397	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
401	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
402	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
403	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
405	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
406	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
407	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
408	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
409	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
410	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
411	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₁₃×C₂²⋊C₄	—	2	1	no	—
414	C₁₃×C₂²⋊C₄	—	2	1	no	—
415	C₁₃×C₂²⋊C₄	—	2	2	no	—
416	C₁₃×C₂²⋊C₄	—	2	2	no	—
417	C₁₃×C₂²⋊C₄	—	2	2	no	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	2	no	—
421	C₁₃×C₂²⋊C₄	—	2	1	no	—
422	C₁₃×C₂²⋊C₄	—	2	1	no	—
423	C₁₃×C₂²⋊C₄	—	2	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	2	no	—
425	C₁₃×C₂²⋊C₄	—	2	1	no	—
426	C₁₃×C₂²⋊C₄	—	2	1	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	—	2	2	no	—
429	C₁₃×C₂²⋊C₄	—	2	2	no	—
430	C₁₃×C₂²⋊C₄	—	2	2	no	—
431	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
432	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₄²×C₁₃	—	2	1	no	—
434	C₄²×C₁₃	—	2	1	no	—
435	C₄²×C₁₃	—	2	1	no	—
436	C₄²×C₁₃	—	2	1	no	—
437	C₄²×C₁₃	—	2	1	no	—
438	C₄²×C₁₃	—	2	1	no	—
439	C₄²×C₁₃	—	2	2	no	—
440	C₄²×C₁₃	—	2	2	no	—
441	C₄²×C₁₃	—	2	2	no	—
442	C₄²×C₁₃	—	2	2	no	—
443	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
446	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
447	C₄²×C₁₃	C₂⁴	1	2	yes	—
448	C₄²×C₁₃	C₂⁴	1	2	yes	—
449	#3510	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#3377	C₂×C₁₃	1	2	yes	complemented
452	#3376	C₂×C₁₃	1	2	yes	complemented
453	#3371	C₂×C₁₃	1	2	yes	complemented
454	#3370	C₂×C₁₃	1	2	yes	complemented
455	#3365	C₂×C₁₃	1	2	yes	complemented
456	#3364	C₂×C₁₃	1	2	yes	complemented
457	#3361	C₂×C₁₃	1	2	yes	complemented
458	#3360	C₂×C₁₃	1	2	yes	complemented
459	#3137	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3136	C₂×C₁₃	1	1	yes	characteristic, complemented
461	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3082	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3081	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3080	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3046	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3045	C₂×C₁₃	1	1	yes	characteristic
467	#3040	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#2947	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#2946	C₂×C₁₃	1	1	yes	characteristic, complemented
471	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
472	C₂³×C₁₃	—	2	1	no	—
473	C₂³×C₁₃	—	2	2	no	—
474	C₂³×C₁₃	—	2	1	no	—
475	C₂³×C₁₃	—	4	2	no	—
476	C₂³×C₁₃	—	8	1	no	—
477	C₂³×C₁₃	—	8	1	no	—
478	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
479	Q₈×C₁₃	—	2	1	no	—
480	Q₈×C₁₃	—	2	2	no	—
481	Q₈×C₁₃	—	2	1	no	—
482	Q₈×C₁₃	—	2	2	no	—
483	Q₈×C₁₃	—	2	1	no	—
484	Q₈×C₁₃	—	4	2	no	—
485	Q₈×C₁₃	—	4	2	no	—
486	Q₈×C₁₃	—	4	2	no	—
487	Q₈×C₁₃	—	8	2	no	—
488	Q₈×C₁₃	—	8	2	no	—
489	Q₈×C₁₃	C₂×#41	1	2	yes	—
490	D₄×C₁₃	—	2	4	no	—
491	D₄×C₁₃	—	2	2	no	—
492	D₄×C₁₃	—	2	1	no	—
493	D₄×C₁₃	—	2	1	no	—
494	D₄×C₁₃	—	2	2	no	—
495	D₄×C₁₃	—	2	1	no	—
496	D₄×C₁₃	—	4	2	no	—
497	D₄×C₁₃	—	4	2	no	—
498	D₄×C₁₃	—	8	2	no	—
499	D₄×C₁₃	—	8	2	no	—
500	D₄×C₁₃	C₂×#41	1	2	yes	—
501	C₂×C₄×C₁₃	—	2	1	no	—
502	C₂×C₄×C₁₃	—	2	4	no	—
503	C₂×C₄×C₁₃	—	2	1	no	—
504	C₂×C₄×C₁₃	—	2	1	no	—
505	C₂×C₄×C₁₃	—	2	2	no	—
506	C₂×C₄×C₁₃	—	2	1	no	—
507	C₂×C₄×C₁₃	—	2	1	no	—
508	C₂×C₄×C₁₃	—	2	1	no	—
509	C₂×C₄×C₁₃	—	2	2	no	—
510	C₂×C₄×C₁₃	—	2	2	no	—
511	C₂×C₄×C₁₃	—	4	1	no	—
512	C₂×C₄×C₁₃	—	4	1	no	—
513	C₂×C₄×C₁₃	—	4	2	no	—
514	C₂×C₄×C₁₃	—	4	2	no	—
515	C₂×C₄×C₁₃	—	8	1	no	—
516	C₂×C₄×C₁₃	—	8	1	no	—
517	C₂×C₄×C₁₃	—	8	1	no	—
518	C₂×C₄×C₁₃	—	8	1	no	—
519	C₂×C₄×C₁₃	—	8	2	no	—
520	C₂×C₄×C₁₃	—	8	2	no	—
521	C₂×C₄×C₁₃	—	8	2	no	—
522	C₂×C₄×C₁₃	—	8	2	no	—
523	C₂×C₄×C₁₃	—	8	1	no	—
524	C₂×C₄×C₁₃	—	8	1	no	—
525	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
535	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
536	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
537	C₈×C₁₃	—	2	1	no	—
538	C₈×C₁₃	—	2	1	no	—
539	C₈×C₁₃	—	2	2	no	—
540	C₈×C₁₃	—	2	2	no	—
541	C₈×C₁₃	—	2	1	no	—
542	C₈×C₁₃	—	2	1	no	—
543	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
544	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
545	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
546	#559	C₂²×C₁₃	1	2	yes	—
547	#559	C₂²×C₁₃	1	2	yes	—
548	#557	C₂²×C₁₃	1	2	yes	complemented
549	#557	C₂²×C₁₃	1	2	yes	complemented
550	#556	C₂²×C₁₃	1	2	yes	—
551	#556	C₂²×C₁₃	1	2	yes	—
552	#554	—	2	2	no	—
553	#554	—	2	2	no	—
554	#554	C₂²×C₁₃	1	2	yes	complemented
555	#554	C₂²×C₁₃	1	2	yes	complemented
556	#551	—	2	2	no	—
557	#551	—	2	2	no	—
558	#544	—	2	1	no	—
559	#544	—	2	1	no	—
560	#544	C₂²×C₁₃	1	1	yes	characteristic
561	#544	C₂²×C₁₃	1	1	yes	characteristic
562	#542	—	2	1	no	—
563	#542	—	2	1	no	—
564	#536	C₂²×C₁₃	1	1	yes	characteristic
565	#535	C₂²×C₁₃	1	1	yes	characteristic
566	#533	—	2	1	no	—
567	#533	C₂²×C₁₃	1	1	yes	characteristic
568	#529	—	2	1	no	—
569	#529	—	2	1	no	—
570	C₂×#125	—	2	1	no	—
571	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
572	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
573	#520	C₂²×C₁₃	1	1	yes	characteristic
574	#520	C₂²×C₁₃	1	1	yes	characteristic
575	#519	C₂²×C₁₃	1	1	yes	characteristic
576	#518	C₂²×C₁₃	1	1	yes	characteristic
577	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
578	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
579	#491	C₂²×C₁₃	1	2	yes	complemented
580	#490	C₂²×C₁₃	1	2	yes	—
581	#489	C₂²×C₁₃	1	2	yes	—
582	#489	C₂²×C₁₃	1	2	yes	complemented
583	#488	C₂²×C₁₃	1	2	yes	—
584	#488	C₂²×C₁₃	1	2	yes	—
585	#488	C₂²×C₁₃	1	2	yes	—
586	#488	C₂²×C₁₃	1	2	yes	—
587	#488	C₂²×C₁₃	1	2	yes	—
588	#488	C₂²×C₁₃	1	2	yes	complemented
589	#487	C₂²×C₁₃	1	2	yes	complemented
590	#486	C₂²×C₁₃	1	2	yes	—
591	#479	C₂²×C₁₃	1	2	yes	complemented
592	#479	C₂²×C₁₃	1	2	yes	complemented
593	#479	C₂²×C₁₃	1	2	yes	complemented
594	#479	C₂²×C₁₃	1	2	yes	complemented
595	#478	C₂²×C₁₃	1	2	yes	—
596	#478	C₂²×C₁₃	1	2	yes	—
597	#478	C₂²×C₁₃	1	2	yes	complemented
598	#478	C₂²×C₁₃	1	2	yes	complemented
599	#477	C₂²×C₁₃	1	2	yes	complemented
600	#476	C₂²×C₁₃	1	2	yes	—
601	#475	C₂²×C₁₃	1	2	yes	complemented
602	#474	C₂²×C₁₃	1	2	yes	—
603	#464	C₂²×C₁₃	1	2	yes	—
604	#464	C₂²×C₁₃	1	2	yes	—
605	#464	C₂²×C₁₃	1	2	yes	—
606	#464	C₂²×C₁₃	1	2	yes	complemented
607	#463	C₂²×C₁₃	1	2	yes	—
608	#463	C₂²×C₁₃	1	2	yes	—
609	#463	C₂²×C₁₃	1	2	yes	—
610	#463	C₂²×C₁₃	1	2	yes	complemented
611	#462	C₂²×C₁₃	1	2	yes	complemented
612	#461	C₂²×C₁₃	1	2	yes	complemented
613	#460	C₂²×C₁₃	1	2	yes	—
614	#459	C₂²×C₁₃	1	2	yes	—
615	#446	C₂²×C₁₃	1	2	yes	complemented
616	#446	C₂²×C₁₃	1	2	yes	complemented
617	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
618	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
619	#442	C₂²×C₁₃	1	2	yes	—
620	#441	C₂²×C₁₃	1	2	yes	complemented
621	#440	C₂²×C₁₃	1	2	yes	—
622	#440	C₂²×C₁₃	1	2	yes	complemented
623	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
624	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
625	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
626	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
627	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
628	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
629	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
630	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
631	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	C₄×D₈	C₂²×C₁₃	1	2	yes	—
633	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
634	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	#428	C₂²×C₁₃	1	1	yes	characteristic
636	#428	C₂²×C₁₃	1	1	yes	characteristic
637	#427	C₂²×C₁₃	1	1	yes	characteristic
638	#424	C₂²×C₁₃	1	1	yes	characteristic
639	#424	C₂²×C₁₃	1	1	yes	characteristic
640	#423	C₂²×C₁₃	1	1	yes	characteristic
641	#419	C₂²×C₁₃	1	1	yes	characteristic
642	#418	C₂²×C₁₃	1	1	yes	characteristic
643	#417	C₂²×C₁₃	1	1	yes	characteristic
644	#417	C₂²×C₁₃	1	1	yes	characteristic
645	#416	C₂²×C₁₃	1	1	yes	characteristic
646	#416	C₂²×C₁₃	1	1	yes	characteristic
647	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
648	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
649	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
650	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
651	#405	C₂²×C₁₃	1	1	yes	characteristic
652	#405	C₂²×C₁₃	1	1	yes	characteristic
653	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
654	C₂²×C₁₃	—	2	1	no	—
655	C₂²×C₁₃	—	2	1	no	—
656	C₂²×C₁₃	—	2	2	no	—
657	C₂²×C₁₃	—	4	1	no	—
658	C₂²×C₁₃	—	4	1	no	—
659	C₂²×C₁₃	—	4	1	no	—
660	C₂²×C₁₃	—	4	1	no	—
661	C₂²×C₁₃	—	4	2	no	—
662	C₂²×C₁₃	—	4	2	no	—
663	C₂²×C₁₃	—	4	1	no	—
664	C₂²×C₁₃	—	4	2	no	—
665	C₂²×C₁₃	—	16	2	no	—
666	C₂²×C₁₃	#548	1	2	yes	—
667	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
668	C₄×C₁₃	—	2	1	no	—
669	C₄×C₁₃	—	2	1	no	—
670	C₄×C₁₃	—	2	1	no	—
671	C₄×C₁₃	—	2	1	no	—
672	C₄×C₁₃	—	2	2	no	—
673	C₄×C₁₃	—	2	2	no	—
674	C₄×C₁₃	—	2	2	no	—
675	C₄×C₁₃	—	2	2	no	—
676	C₄×C₁₃	—	2	2	no	—
677	C₄×C₁₃	—	4	1	no	—
678	C₄×C₁₃	—	4	1	no	—
679	C₄×C₁₃	—	4	2	no	—
680	C₄×C₁₃	—	4	2	no	—
681	C₄×C₁₃	—	4	1	no	—
682	C₄×C₁₃	—	4	1	no	—
683	C₄×C₁₃	—	4	1	no	—
684	C₄×C₁₃	—	4	2	no	—
685	C₄×C₁₃	#548	1	2	yes	—
686	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
687	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
688	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
689	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
690	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
691	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
692	#137	—	2	4	no	—
693	AGL(1,ℤ/8)	—	2	4	no	—
694	#135	—	2	4	no	—
695	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
696	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
697	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
698	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
699	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
700	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
701	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
702	C₂×D₈	C₂³×C₁₃	1	2	yes	—
703	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
704	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
705	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
706	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
707	C₄⋊Q₈	—	2	2	no	—
708	C₄⋊Q₈	—	2	2	no	—
709	C₄⋊Q₈	—	2	1	no	—
710	C₄⋊Q₈	—	2	1	no	—
711	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
712	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
713	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
714	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
715	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
716	#127	C₂³×C₁₃	1	2	yes	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#125	—	2	1	no	—
722	#125	—	2	1	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	1	no	—
728	#125	—	2	1	no	—
729	#125	D₄×C₁₃	1	1	yes	characteristic
730	#125	D₄×C₁₃	1	1	yes	characteristic
731	#125	C₂³×C₁₃	1	2	yes	—
732	#125	C₂³×C₁₃	1	2	yes	—
733	#125	C₂³×C₁₃	1	2	yes	—
734	#125	C₂³×C₁₃	1	2	yes	—
735	#124	—	2	2	no	—
736	#124	—	2	2	no	—
737	#124	—	2	1	no	—
738	#124	—	2	1	no	—
739	#124	C₂³×C₁₃	1	2	yes	—
740	#124	C₂³×C₁₃	1	2	yes	—
741	#124	C₂³×C₁₃	1	2	yes	—
742	#124	C₂³×C₁₃	1	2	yes	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
761	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
762	#121	—	2	1	no	—
763	#121	—	2	1	no	—
764	#120	—	2	2	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	2	no	—
768	C₄×Q₈	—	2	2	no	—
769	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
774	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
775	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
776	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
777	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
778	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
791	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
792	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
793	C₄×D₄	C₂³×C₁₃	1	2	yes	—
794	C₄×D₄	C₂³×C₁₃	1	2	yes	—
795	C₄×D₄	C₂³×C₁₃	1	2	yes	—
796	C₄×D₄	C₂³×C₁₃	1	2	yes	—
797	#117	—	2	1	no	—
798	#117	—	2	1	no	—
799	#117	—	2	2	no	—
800	#117	—	2	2	no	—
801	#117	—	2	2	no	—
802	#117	—	2	1	no	—
803	#117	—	2	1	no	—
804	#117	C₂³×C₁₃	1	1	yes	characteristic
805	#117	C₂³×C₁₃	1	1	yes	characteristic
806	#117	C₂³×C₁₃	1	1	yes	characteristic
807	#117	C₂³×C₁₃	1	1	yes	characteristic
808	C₂×C₄⋊C₄	—	2	1	no	—
809	C₂×C₄⋊C₄	—	2	1	no	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	—	2	1	no	—
812	C₂×C₄⋊C₄	—	2	2	no	—
813	C₂×C₄⋊C₄	—	2	2	no	—
814	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
815	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	—	2	1	no	—
817	C₂×C₂²⋊C₄	—	2	1	no	—
818	C₂×C₂²⋊C₄	—	2	2	no	—
819	C₂×C₄²	—	2	1	no	—
820	C₂×C₄²	—	2	1	no	—
821	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
822	#107	C₂³×C₁₃	1	1	yes	characteristic
823	#107	C₂³×C₁₃	1	1	yes	characteristic
824	#107	C₂³×C₁₃	1	2	yes	—
825	#107	C₂³×C₁₃	1	2	yes	—
826	#106	C₂³×C₁₃	1	1	yes	characteristic
827	#106	C₂³×C₁₃	1	1	yes	characteristic
828	#106	C₂³×C₁₃	1	2	yes	—
829	#106	C₂³×C₁₃	1	2	yes	—
830	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
831	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
832	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
833	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
834	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
835	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
836	#103	C₂³×C₁₃	1	2	yes	—
837	#103	C₂³×C₁₃	1	2	yes	—
838	#103	C₂³×C₁₃	1	2	yes	—
839	#103	C₂³×C₁₃	1	2	yes	—
840	#103	C₂³×C₁₃	1	1	yes	characteristic
841	#103	C₂³×C₁₃	1	1	yes	characteristic
842	#103	C₂³×C₁₃	1	1	yes	characteristic
843	#103	C₂³×C₁₃	1	1	yes	characteristic
844	#103	C₂³×C₁₃	1	2	yes	—
845	#103	C₂³×C₁₃	1	2	yes	—
846	#103	C₂³×C₁₃	1	2	yes	—
847	#103	C₂³×C₁₃	1	2	yes	—
848	#102	C₂³×C₁₃	1	2	yes	—
849	#102	C₂³×C₁₃	1	2	yes	—
850	#102	C₂³×C₁₃	1	2	yes	—
851	#102	C₂³×C₁₃	1	2	yes	—
852	#102	C₂³×C₁₃	1	1	yes	characteristic
853	#102	C₂³×C₁₃	1	1	yes	characteristic
854	#102	C₂³×C₁₃	1	1	yes	characteristic
855	#102	C₂³×C₁₃	1	1	yes	characteristic
856	#102	C₂³×C₁₃	1	2	yes	—
857	#102	C₂³×C₁₃	1	2	yes	—
858	#102	C₂³×C₁₃	1	2	yes	—
859	#102	C₂³×C₁₃	1	2	yes	—
860	#97	C₂³×C₁₃	1	2	yes	—
861	#97	C₂³×C₁₃	1	2	yes	—
862	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
865	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
866	C₄×C₈	C₂³×C₁₃	1	2	yes	—
867	C₄×C₈	C₂³×C₁₃	1	2	yes	—
868	C₂×C₁₃	—	2	2	no	—
869	C₂×C₁₃	—	4	2	no	—
870	C₂×C₁₃	—	8	1	no	—
871	C₂×C₁₃	—	8	2	no	—
872	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
873	C₂×C₁₃	#3584	1	1	yes	characteristic
874	C₂×C₁₃	#3584	1	1	yes	characteristic
875	C₂⁴	—	2	1	no	—
876	#41	—	2	2	no	—
877	#41	—	2	2	no	—
878	#41	—	2	2	no	—
879	#41	C₁₃×#41	1	4	yes	—
880	C₂×Q₈	—	2	1	no	—
881	C₂×Q₈	—	2	2	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
886	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
887	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
888	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
898	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
899	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
914	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
916	Q₁₆	—	2	2	no	—
917	Q₁₆	—	2	4	no	—
918	SD₁₆	—	2	2	no	—
919	SD₁₆	—	2	4	no	—
920	SD₁₆	—	2	2	no	—
921	SD₁₆	—	2	4	no	—
922	D₈	—	2	2	no	—
923	D₈	—	2	4	no	—
924	M₁₆	—	2	2	no	—
925	M₁₆	—	2	2	no	—
926	C₂×C₈	—	2	2	no	—
927	C₂×C₈	—	2	2	no	—
928	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
933	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
957	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
960	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
961	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
963	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
964	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
965	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
968	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1003	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1004	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₁₃	1	2	yes	—
1007	C₄²	C₂⁴×C₁₃	1	2	yes	—
1008	C₁₃	#61331	1	1	yes	characteristic, direct product factor, Sylow
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	4	2	no	—
1013	C₂³	—	8	1	no	—
1014	C₂³	—	8	1	no	—
1015	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	4	2	no	—
1023	Q₈	—	4	2	no	—
1024	Q₈	—	8	2	no	—
1025	Q₈	—	8	2	no	—
1026	Q₈	C₂×C₁₃×#41	1	2	yes	—
1027	D₄	—	2	4	no	—
1028	D₄	—	2	2	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	2	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	4	2	no	—
1035	D₄	—	8	2	no	—
1036	D₄	—	8	2	no	—
1037	D₄	C₂×C₁₃×#41	1	2	yes	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	4	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	4	1	no	—
1049	C₂×C₄	—	4	1	no	—
1050	C₂×C₄	—	4	2	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	8	1	no	—
1053	C₂×C₄	—	8	1	no	—
1054	C₂×C₄	—	8	1	no	—
1055	C₂×C₄	—	8	1	no	—
1056	C₂×C₄	—	8	2	no	—
1057	C₂×C₄	—	8	2	no	—
1058	C₂×C₄	—	8	2	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	1	no	—
1062	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1064	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1065	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1067	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1069	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1071	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1072	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
1073	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	16	2	no	—
1092	C₂²	C₁₃×#548	1	2	yes	—
1093	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1094	C₄	—	2	1	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	C₁₃×#548	1	2	yes	—
1112	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1113	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1114	C₂	—	2	2	no	—
1115	C₂	—	4	2	no	—
1116	C₂	—	8	2	no	—
1117	C₂	—	8	1	no	—
1118	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
1119	C₂	C₁₃×#3584	1	1	yes	characteristic
1120	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3045	C₂
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×#3510	C₂	semidirect
2. C₁₃×#3504	C₂	semidirect
3. C₁₃×#3377	C₂	semidirect
4. C₁₃×#3376	C₂	semidirect
5. C₁₃×#3371	C₂	semidirect
6. C₁₃×#3370	C₂	semidirect
7. C₁₃×#3365	C₂	semidirect
8. C₁₃×#3364	C₂	semidirect
9. C₁₃×#3361	C₂	semidirect
10. C₁₃×#3360	C₂	semidirect
11. C₁₃×#3137	C₂	semidirect
12. C₁₃×#3136	C₂	semidirect
13. C₂×C₁₃×#488	C₂	semidirect
14. C₁₃×#3082	C₂	semidirect
15. C₁₃×#3081	C₂	semidirect
16. C₁₃×#3080	C₂	semidirect
17. C₁₃×#3046	C₂	semidirect
19. C₁₃×#3040	C₂	semidirect
20. C₁₃×#2960	C₂	semidirect
21. C₁₃×#2947	C₂	semidirect
22. C₁₃×#2946	C₂	semidirect
23. C₄×C₁₃×#135	C₂	semidirect
29. C₁₃×#557	C₂²	semidirect
30. C₁₃×#557	C₂²	semidirect
35. C₁₃×#554	C₂²	semidirect
36. C₁₃×#554	C₂²	semidirect
60. C₁₃×#491	C₂²	semidirect
63. C₁₃×#489	C₂²	semidirect
69. C₁₃×#488	C₂²	semidirect
70. C₁₃×#487	C₂²	semidirect
72. C₁₃×#479	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#479	C₂²	semidirect
78. C₁₃×#478	C₂²	semidirect
79. C₁₃×#478	C₂²	semidirect
80. C₁₃×#477	C₂²	semidirect
82. C₁₃×#475	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
91. C₁₃×#463	C₂²	semidirect
92. C₁₃×#462	C₂²	semidirect
93. C₁₃×#461	C₂²	semidirect
96. C₁₃×#446	C₂²	semidirect
97. C₁₃×#446	C₂²	semidirect
98. C₈×Q₈×C₁₃	C₂²	semidirect
99. C₈×Q₈×C₁₃	C₂²	semidirect
101. C₁₃×#441	C₂²	semidirect
103. C₁₃×#440	C₂²	semidirect
104. C₄×C₁₃×Q₁₆	C₂²	semidirect
105. C₄×C₁₃×Q₁₆	C₂²	semidirect
106. C₄×C₁₃×Q₁₆	C₂²	semidirect
108. C₄×C₁₃×SD₁₆	C₂²	semidirect
109. C₄×C₁₃×SD₁₆	C₂²	semidirect
110. C₄×C₁₃×SD₁₆	C₂²	semidirect
111. C₄×C₁₃×SD₁₆	C₂²	semidirect
112. C₄×C₁₃×SD₁₆	C₂²	semidirect
114. C₄×C₁₃×D₈	C₂²	semidirect
115. C₄×C₁₃×D₈	C₂²	semidirect
315. #61331	C₁₃	direct (N × H)
449. #3510	C₂×C₁₃	semidirect
450. #3504	C₂×C₁₃	semidirect
451. #3377	C₂×C₁₃	semidirect
452. #3376	C₂×C₁₃	semidirect
453. #3371	C₂×C₁₃	semidirect
454. #3370	C₂×C₁₃	semidirect
455. #3365	C₂×C₁₃	semidirect
456. #3364	C₂×C₁₃	semidirect
457. #3361	C₂×C₁₃	semidirect
458. #3360	C₂×C₁₃	semidirect
459. #3137	C₂×C₁₃	semidirect
460. #3136	C₂×C₁₃	semidirect
461. C₂×#488	C₂×C₁₃	semidirect
462. #3082	C₂×C₁₃	semidirect
463. #3081	C₂×C₁₃	semidirect
464. #3080	C₂×C₁₃	semidirect
465. #3046	C₂×C₁₃	semidirect
467. #3040	C₂×C₁₃	semidirect
468. #2960	C₂×C₁₃	semidirect
469. #2947	C₂×C₁₃	semidirect
470. #2946	C₂×C₁₃	semidirect
471. C₄×#135	C₂×C₁₃	semidirect
548. #557	C₂²×C₁₃	semidirect
549. #557	C₂²×C₁₃	semidirect
554. #554	C₂²×C₁₃	semidirect
555. #554	C₂²×C₁₃	semidirect
579. #491	C₂²×C₁₃	semidirect
582. #489	C₂²×C₁₃	semidirect
588. #488	C₂²×C₁₃	semidirect
589. #487	C₂²×C₁₃	semidirect
591. #479	C₂²×C₁₃	semidirect
592. #479	C₂²×C₁₃	semidirect
593. #479	C₂²×C₁₃	semidirect
594. #479	C₂²×C₁₃	semidirect
597. #478	C₂²×C₁₃	semidirect
598. #478	C₂²×C₁₃	semidirect
599. #477	C₂²×C₁₃	semidirect
601. #475	C₂²×C₁₃	semidirect
606. #464	C₂²×C₁₃	semidirect
610. #463	C₂²×C₁₃	semidirect
611. #462	C₂²×C₁₃	semidirect
612. #461	C₂²×C₁₃	semidirect
615. #446	C₂²×C₁₃	semidirect
616. #446	C₂²×C₁₃	semidirect
617. C₈×Q₈	C₂²×C₁₃	semidirect
618. C₈×Q₈	C₂²×C₁₃	semidirect
620. #441	C₂²×C₁₃	semidirect
622. #440	C₂²×C₁₃	semidirect
623. C₄×Q₁₆	C₂²×C₁₃	semidirect
624. C₄×Q₁₆	C₂²×C₁₃	semidirect
625. C₄×Q₁₆	C₂²×C₁₃	semidirect
627. C₄×SD₁₆	C₂²×C₁₃	semidirect
628. C₄×SD₁₆	C₂²×C₁₃	semidirect
629. C₄×SD₁₆	C₂²×C₁₃	semidirect
630. C₄×SD₁₆	C₂²×C₁₃	semidirect
631. C₄×SD₁₆	C₂²×C₁₃	semidirect
633. C₄×D₈	C₂²×C₁₃	semidirect
634. C₄×D₈	C₂²×C₁₃	semidirect
1008. C₁₃	#61331	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×#3510	2
C₁₃×#3504	2
C₁₃×#3377	2
C₁₃×#3376	2
C₁₃×#3371	2
C₁₃×#3370	2
C₁₃×#3365	2
C₁₃×#3364	2
C₁₃×#3361	2
C₁₃×#3360	2
C₁₃×#3137	2
C₁₃×#3136	2
C₂×C₁₃×#488	2
C₁₃×#3082	2
C₁₃×#3081	2
C₁₃×#3080	2
C₁₃×#3046	2
C₁₃×#3045	2
C₁₃×#3040	2
C₁₃×#2960	2
C₁₃×#2947	2
C₁₃×#2946	2
C₄×C₁₃×#135	2
#61331	13

Subgroups — C13×#61331 #15747670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61331 #15747670