Subgroups — C₁₃×#61451 #15747790

Order 3328.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3345	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3318	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3306	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3180	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3114	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3109	C₂	1	2	yes	maximal, complemented
21	C₁₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₁₃×#442	C₂	1	2	yes	maximal, complemented
24	C₂²×C₁₃×#41	—	2	1	no	—
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
27	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#553	—	2	1	no	—
31	C₁₃×#553	C₂²	1	2	yes	complemented
32	C₁₃×#551	—	2	2	no	—
33	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
34	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#548	—	2	1	no	—
36	C₁₃×#547	C₂²	1	1	yes	characteristic
37	C₁₃×#547	C₂²	1	2	yes	complemented
38	C₁₃×#546	—	2	1	no	—
39	C₁₃×#546	—	2	1	no	—
40	C₁₃×#546	—	2	2	no	—
41	C₁₃×#546	C₂²	1	2	yes	complemented
42	D₄²×C₁₃	C₂²	1	1	yes	characteristic
43	D₄²×C₁₃	C₂²	1	2	yes	complemented
44	D₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#532	C₂²	1	2	yes	complemented
46	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#529	—	2	1	no	—
49	C₁₃×#529	C₂²	1	2	yes	complemented
50	C₁₃×#525	—	2	2	no	—
51	C₁₃×#525	—	2	2	no	—
52	C₁₃×#525	—	2	1	no	—
53	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
54	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₄×C₁₃	—	2	1	no	—
56	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
59	C₁₃×#501	C₂²	1	2	yes	complemented
60	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#496	C₂²	1	2	yes	complemented
62	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#490	C₂²	1	2	yes	complemented
64	C₁₃×#489	C₂²	1	2	yes	complemented
65	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#483	C₂²	1	2	yes	complemented
68	C₁₃×#482	C₂²	1	2	yes	complemented
69	C₁₃×#481	C₂²	1	2	yes	complemented
70	C₁₃×#481	C₂²	1	2	yes	complemented
71	C₁₃×#481	C₂²	1	2	yes	complemented
72	C₁₃×#480	C₂²	1	2	yes	complemented
73	C₁₃×#478	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	2	yes	complemented
75	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#476	C₂²	1	2	yes	complemented
77	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#476	C₂²	1	2	yes	complemented
79	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
80	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#469	C₂²	1	2	yes	complemented
82	C₁₃×#469	C₂²	1	2	yes	complemented
83	C₁₃×#466	C₂²	1	2	yes	complemented
84	C₁₃×#466	C₂²	1	2	yes	complemented
85	C₁₃×#465	C₂²	1	2	yes	complemented
86	C₁₃×#465	C₂²	1	2	yes	complemented
87	C₁₃×#463	C₂²	1	2	yes	complemented
88	C₁₃×#463	C₂²	1	2	yes	complemented
89	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#459	C₂²	1	1	yes	characteristic
91	C₁₃×#459	C₂²	1	2	yes	complemented
92	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#459	C₂²	1	2	yes	complemented
95	C₁₃×#450	C₂²	1	2	yes	complemented
96	C₁₃×#449	C₂²	1	2	yes	complemented
97	C₁₃×#447	C₂²	1	2	yes	—
98	C₁₃×#447	C₂²	1	2	yes	complemented
99	C₁₃×#447	C₂²	1	2	yes	complemented
100	C₁₃×#447	C₂²	1	2	yes	complemented
101	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#442	C₂²	1	2	yes	—
104	C₁₃×#442	C₂²	1	1	yes	characteristic
105	C₁₃×#442	C₂²	1	2	yes	complemented
106	C₁₃×#442	C₂²	1	2	yes	complemented
107	C₁₃×#442	C₂²	1	2	yes	complemented
108	C₁₃×#442	C₂²	1	2	yes	complemented
109	C₁₃×#442	C₂²	1	1	yes	characteristic, complemented
110	C₁₃×#442	C₂²	1	2	yes	complemented
111	C₁₃×#442	C₂²	1	2	yes	complemented
112	C₁₃×#442	C₂²	1	2	yes	complemented
113	C₁₃×#442	C₂²	1	2	yes	complemented
114	C₁₃×#440	C₂²	1	1	yes	characteristic, complemented
115	C₁₃×#440	C₂²	1	2	yes	complemented
116	C₁₃×#440	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
121	C₁₃×#435	C₂²	1	2	yes	complemented
122	C₁₃×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
125	C₁₃×#432	C₂²	1	2	yes	complemented
126	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
129	C₁₃×#418	C₂²	1	1	yes	characteristic, complemented
130	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
132	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
133	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	—	2	1	no	—
137	C₂×C₁₃×#41	—	2	2	no	—
138	C₂×C₁₃×#41	—	2	2	no	—
139	C₂×C₁₃×#41	—	2	1	no	—
140	C₂×C₁₃×#41	—	2	1	no	—
141	C₂×C₁₃×#41	—	4	8	no	—
142	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
143	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₁₃	—	2	1	no	—
145	C₂²×D₄×C₁₃	—	2	1	no	—
146	C₂²×D₄×C₁₃	—	2	1	no	—
147	C₂²×D₄×C₁₃	—	2	2	no	—
148	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
149	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
150	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₁₃	—	2	2	no	—
152	C₂³×C₄×C₁₃	—	2	1	no	—
153	C₂³×C₄×C₁₃	—	2	2	no	—
154	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
155	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
158	C₂×C₁₃×D₈	—	2	8	no	—
159	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×D₈	C₂³	1	2	yes	—
161	C₂×C₁₃×D₈	C₂³	1	2	yes	—
162	C₂×C₁₃×D₈	C₂³	1	2	yes	—
163	C₂×C₁₃×D₈	C₂³	1	2	yes	—
164	C₂×C₁₃×D₈	C₂³	1	2	yes	—
165	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
166	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
169	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
170	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₁₃×#127	C₂³	1	1	yes	characteristic
174	C₁₃×#127	C₂³	1	2	yes	—
175	C₁₃×#127	C₂³	1	1	yes	characteristic
176	C₁₃×#126	—	2	2	no	—
177	C₁₃×#126	—	2	2	no	—
178	C₁₃×#125	—	2	1	no	—
179	C₁₃×#125	C₂³	1	2	yes	—
180	C₁₃×#124	—	2	1	no	—
181	C₁₃×#124	—	2	1	no	—
182	C₁₃×#124	—	2	2	no	—
183	C₁₃×#124	—	2	1	no	—
184	C₁₃×#124	C₂³	1	2	yes	—
185	C₁₃×#123	—	2	2	no	—
186	C₁₃×#123	—	2	2	no	—
187	C₁₃×#123	—	2	2	no	—
188	C₁₃×#123	—	2	2	no	—
189	C₁₃×#123	—	2	2	no	—
190	C₁₃×#123	—	2	2	no	—
191	C₁₃×#123	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	1	no	—
193	C₁₃×C₂²⋊Q₈	—	2	1	no	—
194	C₁₃×C₂²⋊Q₈	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	1	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	C₂³	1	2	yes	—
200	C₁₃×#121	—	2	2	no	—
201	C₁₃×#121	—	2	2	no	—
202	C₁₃×#121	—	2	1	no	—
203	C₁₃×#121	—	2	1	no	—
204	C₁₃×#121	—	2	1	no	—
205	C₁₃×#121	—	2	2	no	—
206	C₁₃×#121	—	2	1	no	—
207	C₁₃×#121	—	2	2	no	—
208	C₁₃×#121	—	2	1	no	—
209	C₁₃×#121	—	2	2	no	—
210	C₁₃×#121	C₂³	1	2	yes	—
211	C₁₃×#121	C₂³	1	2	yes	—
212	C₁₃×#121	C₂³	1	2	yes	—
213	C₁₃×#121	C₂³	1	2	yes	—
214	C₁₃×#121	C₂³	1	2	yes	—
215	C₁₃×#120	—	2	2	no	—
216	C₁₃×#120	—	2	2	no	—
217	C₁₃×#120	—	2	2	no	—
218	C₁₃×#120	—	2	2	no	—
219	C₁₃×#120	—	2	2	no	—
220	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
221	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
224	C₄×D₄×C₁₃	—	2	1	no	—
225	C₄×D₄×C₁₃	—	2	2	no	—
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	2	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	1	no	—
235	C₄×D₄×C₁₃	—	2	2	no	—
236	C₄×D₄×C₁₃	—	2	2	no	—
237	C₄×D₄×C₁₃	—	2	1	no	—
238	C₄×D₄×C₁₃	—	2	2	no	—
239	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
240	C₄×D₄×C₁₃	D₄	1	2	yes	—
241	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₁₃	C₂³	1	2	yes	—
246	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₁₃	C₂³	1	2	yes	—
249	C₄×D₄×C₁₃	C₂³	1	2	yes	—
250	C₄×D₄×C₁₃	C₂³	1	2	yes	—
251	C₄×D₄×C₁₃	C₂³	1	2	yes	—
252	C₄×D₄×C₁₃	C₂³	1	2	yes	—
253	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₁₃	C₂³	1	2	yes	—
255	C₁₃×#117	—	2	1	no	—
256	C₁₃×#117	—	2	2	no	—
257	C₁₃×#117	D₄	1	2	yes	—
258	C₁₃×#117	D₄	1	1	yes	characteristic
259	C₁₃×#117	C₂³	1	1	yes	characteristic
260	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²×C₁₃	—	2	1	no	—
269	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
270	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
271	C₁₃×#107	C₂³	1	1	yes	characteristic
272	C₁₃×#107	C₂³	1	1	yes	characteristic
273	C₁₃×#107	C₂³	1	2	yes	—
274	C₁₃×#106	C₂³	1	1	yes	characteristic
275	C₁₃×#106	C₂³	1	2	yes	—
276	C₁₃×#106	C₂³	1	2	yes	—
277	C₁₃×#106	C₂³	1	2	yes	—
278	C₁₃×#106	C₂³	1	1	yes	characteristic
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×#106	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
284	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
285	C₁₃×#103	C₂³	1	1	yes	characteristic
286	C₁₃×#103	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	2	yes	—
288	C₁₃×#102	C₂³	1	1	yes	characteristic
289	C₁₃×#102	C₂³	1	1	yes	characteristic
290	C₁₃×#102	C₂³	1	2	yes	—
291	C₁₃×#102	C₂³	1	2	yes	—
292	C₁₃×#102	C₂³	1	2	yes	—
293	C₁₃×#102	C₂³	1	2	yes	—
294	C₁₃×#102	C₂³	1	2	yes	—
295	C₁₃×#102	C₂³	1	2	yes	—
296	C₁₃×#102	C₂³	1	1	yes	characteristic
297	C₁₃×#102	C₂³	1	1	yes	characteristic
298	C₁₃×#102	C₂³	1	1	yes	characteristic
299	C₁₃×#102	C₂³	1	1	yes	characteristic
300	C₁₃×#102	C₂³	1	2	yes	—
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×#102	C₂³	1	2	yes	—
305	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₁₃×#97	C₂³	1	1	yes	characteristic
309	C₁₃×#97	C₂³	1	2	yes	—
310	C₁₃×#97	C₂³	1	2	yes	—
311	C₁₃×#97	C₂³	1	2	yes	—
312	C₁₃×#97	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
315	#61451	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂⁴×C₁₃	—	2	2	no	—
317	C₂⁴×C₁₃	—	2	1	no	—
318	C₂⁴×C₁₃	—	2	2	no	—
319	C₁₃×#41	—	2	4	no	—
320	C₁₃×#41	—	2	2	no	—
321	C₁₃×#41	—	4	1	no	—
322	C₁₃×#41	—	4	8	no	—
323	C₁₃×#41	—	4	4	no	—
324	C₁₃×#41	—	4	8	no	—
325	C₁₃×#41	—	4	4	no	—
326	C₁₃×#41	—	4	4	no	—
327	C₁₃×#41	—	8	2	no	—
328	C₂×Q₈×C₁₃	—	2	2	no	—
329	C₂×Q₈×C₁₃	—	2	1	no	—
330	C₂×Q₈×C₁₃	—	2	1	no	—
331	C₂×Q₈×C₁₃	—	4	4	no	—
332	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
333	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₁₃	—	2	4	no	—
335	C₂×D₄×C₁₃	—	2	2	no	—
336	C₂×D₄×C₁₃	—	2	4	no	—
337	C₂×D₄×C₁₃	—	2	1	no	—
338	C₂×D₄×C₁₃	—	2	2	no	—
339	C₂×D₄×C₁₃	—	2	2	no	—
340	C₂×D₄×C₁₃	—	2	2	no	—
341	C₂×D₄×C₁₃	—	2	2	no	—
342	C₂×D₄×C₁₃	—	2	2	no	—
343	C₂×D₄×C₁₃	—	2	1	no	—
344	C₂×D₄×C₁₃	—	2	2	no	—
345	C₂×D₄×C₁₃	—	2	2	no	—
346	C₂×D₄×C₁₃	—	2	1	no	—
347	C₂×D₄×C₁₃	—	2	2	no	—
348	C₂×D₄×C₁₃	—	2	1	no	—
349	C₂×D₄×C₁₃	—	2	2	no	—
350	C₂×D₄×C₁₃	—	2	1	no	—
351	C₂×D₄×C₁₃	—	2	1	no	—
352	C₂×D₄×C₁₃	—	4	2	no	—
353	C₂×D₄×C₁₃	—	4	2	no	—
354	C₂×D₄×C₁₃	—	4	1	no	—
355	C₂×D₄×C₁₃	—	4	8	no	—
356	C₂×D₄×C₁₃	—	4	4	no	—
357	C₂×D₄×C₁₃	—	4	4	no	—
358	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
359	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
360	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
361	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
362	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
364	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₁₃	—	2	1	no	—
366	C₂²×C₄×C₁₃	—	2	2	no	—
367	C₂²×C₄×C₁₃	—	2	2	no	—
368	C₂²×C₄×C₁₃	—	2	1	no	—
369	C₂²×C₄×C₁₃	—	2	1	no	—
370	C₂²×C₄×C₁₃	—	2	1	no	—
371	C₂²×C₄×C₁₃	—	2	2	no	—
372	C₂²×C₄×C₁₃	—	2	1	no	—
373	C₂²×C₄×C₁₃	—	2	1	no	—
374	C₂²×C₄×C₁₃	—	2	2	no	—
375	C₂²×C₄×C₁₃	—	2	2	no	—
376	C₂²×C₄×C₁₃	—	2	1	no	—
377	C₂²×C₄×C₁₃	—	2	2	no	—
378	C₂²×C₄×C₁₃	—	2	1	no	—
379	C₂²×C₄×C₁₃	—	2	2	no	—
380	C₂²×C₄×C₁₃	—	2	2	no	—
381	C₂²×C₄×C₁₃	—	4	8	no	—
382	C₂²×C₄×C₁₃	—	4	4	no	—
383	C₂²×C₄×C₁₃	—	8	4	no	—
384	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
385	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
387	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
389	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
390	C₁₃×SD₁₆	—	2	2	no	—
391	C₁₃×SD₁₆	—	2	2	no	—
392	C₁₃×SD₁₆	—	4	2	no	—
393	C₁₃×D₈	—	2	4	no	—
394	C₁₃×D₈	—	2	4	no	—
395	C₁₃×D₈	—	2	2	no	—
396	C₁₃×D₈	—	2	4	no	—
397	C₁₃×D₈	—	4	2	no	—
398	C₁₃×D₈	—	4	2	no	—
399	C₁₃×D₈	#41	1	4	yes	complemented
400	C₁₃×M₁₆	—	2	2	no	—
401	C₁₃×M₁₆	—	4	1	no	—
402	C₂×C₈×C₁₃	—	2	4	no	—
403	C₂×C₈×C₁₃	—	4	2	no	—
404	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
408	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
409	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
410	C₁₃×C₄⋊C₄	—	2	1	no	—
411	C₁₃×C₄⋊C₄	—	2	2	no	—
412	C₁₃×C₄⋊C₄	—	2	1	no	—
413	C₁₃×C₄⋊C₄	—	2	2	no	—
414	C₁₃×C₄⋊C₄	—	2	2	no	—
415	C₁₃×C₄⋊C₄	—	2	1	no	—
416	C₁₃×C₄⋊C₄	—	2	1	no	—
417	C₁₃×C₄⋊C₄	—	2	2	no	—
418	C₁₃×C₄⋊C₄	—	2	2	no	—
419	C₁₃×C₄⋊C₄	—	2	2	no	—
420	C₁₃×C₄⋊C₄	—	2	1	no	—
421	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
422	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
423	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
424	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
425	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
426	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
427	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
428	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
429	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
430	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	—	2	1	no	—
433	C₁₃×C₂²⋊C₄	—	2	1	no	—
434	C₁₃×C₂²⋊C₄	—	2	1	no	—
435	C₁₃×C₂²⋊C₄	—	2	2	no	—
436	C₁₃×C₂²⋊C₄	—	2	2	no	—
437	C₁₃×C₂²⋊C₄	—	2	2	no	—
438	C₁₃×C₂²⋊C₄	—	2	1	no	—
439	C₁₃×C₂²⋊C₄	—	2	2	no	—
440	C₁₃×C₂²⋊C₄	—	2	2	no	—
441	C₁₃×C₂²⋊C₄	—	2	1	no	—
442	C₁₃×C₂²⋊C₄	—	2	2	no	—
443	C₁₃×C₂²⋊C₄	—	2	1	no	—
444	C₁₃×C₂²⋊C₄	—	2	2	no	—
445	C₁₃×C₂²⋊C₄	—	2	2	no	—
446	C₁₃×C₂²⋊C₄	—	2	1	no	—
447	C₁₃×C₂²⋊C₄	—	2	2	no	—
448	C₁₃×C₂²⋊C₄	—	2	2	no	—
449	C₁₃×C₂²⋊C₄	—	2	2	no	—
450	C₁₃×C₂²⋊C₄	—	2	2	no	—
451	C₁₃×C₂²⋊C₄	—	2	2	no	—
452	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
453	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
454	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
455	C₄²×C₁₃	—	2	1	no	—
456	C₄²×C₁₃	—	2	1	no	—
457	C₄²×C₁₃	—	2	1	no	—
458	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
460	C₄²×C₁₃	C₂×D₄	1	2	yes	—
461	C₄²×C₁₃	C₂×D₄	1	2	yes	—
462	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
463	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
464	C₄²×C₁₃	C₂⁴	1	2	yes	—
465	#3481	C₂×C₁₃	1	1	yes	characteristic, complemented
466	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
467	#3399	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3384	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#3373	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3366	C₂×C₁₃	1	1	yes	characteristic, complemented
471	#3345	C₂×C₁₃	1	2	yes	complemented
472	#3335	C₂×C₁₃	1	1	yes	characteristic, complemented
473	#3318	C₂×C₁₃	1	2	yes	complemented
474	#3306	C₂×C₁₃	1	2	yes	complemented
475	#3295	C₂×C₁₃	1	1	yes	characteristic, complemented
476	#3294	C₂×C₁₃	1	1	yes	characteristic, complemented
477	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
478	#3264	C₂×C₁₃	1	2	yes	complemented
479	#3184	C₂×C₁₃	1	1	yes	characteristic, complemented
480	#3180	C₂×C₁₃	1	2	yes	complemented
481	#3115	C₂×C₁₃	1	1	yes	characteristic, complemented
482	#3114	C₂×C₁₃	1	2	yes	complemented
483	#3109	C₂×C₁₃	1	1	yes	characteristic, complemented
484	#3109	C₂×C₁₃	1	2	yes	complemented
485	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
486	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
487	C₂×#442	C₂×C₁₃	1	2	yes	complemented
488	C₂³×C₁₃	—	2	1	no	—
489	C₂³×C₁₃	—	2	1	no	—
490	C₂³×C₁₃	—	2	2	no	—
491	C₂³×C₁₃	—	2	2	no	—
492	C₂³×C₁₃	—	2	1	no	—
493	C₂³×C₁₃	—	4	4	no	—
494	C₂³×C₁₃	—	4	4	no	—
495	C₂³×C₁₃	—	4	2	no	—
496	C₂³×C₁₃	—	4	2	no	—
497	C₂³×C₁₃	—	4	4	no	—
498	C₂³×C₁₃	—	4	4	no	—
499	C₂³×C₁₃	—	8	2	no	—
500	C₂³×C₁₃	—	8	2	no	—
501	C₂³×C₁₃	—	8	1	no	—
502	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
503	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
504	Q₈×C₁₃	—	2	2	no	—
505	Q₈×C₁₃	—	2	1	no	—
506	Q₈×C₁₃	—	2	1	no	—
507	Q₈×C₁₃	—	4	4	no	—
508	Q₈×C₁₃	—	4	2	no	—
509	Q₈×C₁₃	—	8	1	no	—
510	D₄×C₁₃	—	2	4	no	—
511	D₄×C₁₃	—	2	2	no	—
512	D₄×C₁₃	—	2	2	no	—
513	D₄×C₁₃	—	2	1	no	—
514	D₄×C₁₃	—	2	1	no	—
515	D₄×C₁₃	—	2	1	no	—
516	D₄×C₁₃	—	2	2	no	—
517	D₄×C₁₃	—	2	1	no	—
518	D₄×C₁₃	—	2	2	no	—
519	D₄×C₁₃	—	4	2	no	—
520	D₄×C₁₃	—	4	4	no	—
521	D₄×C₁₃	—	4	4	no	—
522	D₄×C₁₃	—	4	4	no	—
523	D₄×C₁₃	—	4	2	no	—
524	D₄×C₁₃	—	4	4	no	—
525	D₄×C₁₃	—	4	4	no	—
526	D₄×C₁₃	—	4	4	no	—
527	D₄×C₁₃	—	4	4	no	—
528	D₄×C₁₃	—	4	2	no	—
529	D₄×C₁₃	—	4	2	no	—
530	D₄×C₁₃	—	8	2	no	—
531	D₄×C₁₃	—	8	1	no	—
532	D₄×C₁₃	—	8	1	no	—
533	D₄×C₁₃	—	8	2	no	—
534	D₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
535	D₄×C₁₃	C₂×#41	1	2	yes	—
536	D₄×C₁₃	C₂×#41	1	2	yes	complemented
537	C₂×C₄×C₁₃	—	2	4	no	—
538	C₂×C₄×C₁₃	—	2	2	no	—
539	C₂×C₄×C₁₃	—	2	2	no	—
540	C₂×C₄×C₁₃	—	2	1	no	—
541	C₂×C₄×C₁₃	—	2	2	no	—
542	C₂×C₄×C₁₃	—	2	1	no	—
543	C₂×C₄×C₁₃	—	2	1	no	—
544	C₂×C₄×C₁₃	—	2	1	no	—
545	C₂×C₄×C₁₃	—	2	1	no	—
546	C₂×C₄×C₁₃	—	2	2	no	—
547	C₂×C₄×C₁₃	—	2	1	no	—
548	C₂×C₄×C₁₃	—	2	2	no	—
549	C₂×C₄×C₁₃	—	2	1	no	—
550	C₂×C₄×C₁₃	—	4	2	no	—
551	C₂×C₄×C₁₃	—	4	1	no	—
552	C₂×C₄×C₁₃	—	4	2	no	—
553	C₂×C₄×C₁₃	—	4	2	no	—
554	C₂×C₄×C₁₃	—	4	4	no	—
555	C₂×C₄×C₁₃	—	4	4	no	—
556	C₂×C₄×C₁₃	—	4	2	no	—
557	C₂×C₄×C₁₃	—	4	4	no	—
558	C₂×C₄×C₁₃	—	4	2	no	—
559	C₂×C₄×C₁₃	—	4	4	no	—
560	C₂×C₄×C₁₃	—	4	2	no	—
561	C₂×C₄×C₁₃	—	4	4	no	—
562	C₂×C₄×C₁₃	—	4	2	no	—
563	C₂×C₄×C₁₃	—	4	2	no	—
564	C₂×C₄×C₁₃	—	4	2	no	—
565	C₂×C₄×C₁₃	—	8	2	no	—
566	C₂×C₄×C₁₃	—	8	2	no	—
567	C₂×C₄×C₁₃	—	8	2	no	—
568	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
572	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
573	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
575	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
577	C₈×C₁₃	—	2	2	no	—
578	C₈×C₁₃	—	2	1	no	—
579	C₈×C₁₃	—	2	1	no	—
580	C₈×C₁₃	—	2	2	no	—
581	C₈×C₁₃	—	2	1	no	—
582	C₈×C₁₃	C₂×#41	1	2	yes	complemented
583	C₂²×#41	—	2	1	no	—
584	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
585	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
586	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
587	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
588	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
589	#553	—	2	1	no	—
590	#553	C₂²×C₁₃	1	2	yes	complemented
591	#551	—	2	2	no	—
592	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
593	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
594	#548	—	2	1	no	—
595	#547	C₂²×C₁₃	1	1	yes	characteristic
596	#547	C₂²×C₁₃	1	2	yes	complemented
597	#546	—	2	1	no	—
598	#546	—	2	1	no	—
599	#546	—	2	2	no	—
600	#546	C₂²×C₁₃	1	2	yes	complemented
601	D₄²	C₂²×C₁₃	1	1	yes	characteristic
602	D₄²	C₂²×C₁₃	1	2	yes	complemented
603	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
604	#532	C₂²×C₁₃	1	2	yes	complemented
605	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
606	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
607	#529	—	2	1	no	—
608	#529	C₂²×C₁₃	1	2	yes	complemented
609	#525	—	2	2	no	—
610	#525	—	2	2	no	—
611	#525	—	2	1	no	—
612	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
613	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
614	C₂×C₄×D₄	—	2	1	no	—
615	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
616	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
617	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
618	#501	C₂²×C₁₃	1	2	yes	complemented
619	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
620	#496	C₂²×C₁₃	1	2	yes	complemented
621	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	#490	C₂²×C₁₃	1	2	yes	complemented
623	#489	C₂²×C₁₃	1	2	yes	complemented
624	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
625	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
626	#483	C₂²×C₁₃	1	2	yes	complemented
627	#482	C₂²×C₁₃	1	2	yes	complemented
628	#481	C₂²×C₁₃	1	2	yes	complemented
629	#481	C₂²×C₁₃	1	2	yes	complemented
630	#481	C₂²×C₁₃	1	2	yes	complemented
631	#480	C₂²×C₁₃	1	2	yes	complemented
632	#478	C₂²×C₁₃	1	2	yes	complemented
633	#478	C₂²×C₁₃	1	2	yes	complemented
634	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	#476	C₂²×C₁₃	1	2	yes	complemented
636	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
637	#476	C₂²×C₁₃	1	2	yes	complemented
638	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
639	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
640	#469	C₂²×C₁₃	1	2	yes	complemented
641	#469	C₂²×C₁₃	1	2	yes	complemented
642	#466	C₂²×C₁₃	1	2	yes	complemented
643	#466	C₂²×C₁₃	1	2	yes	complemented
644	#465	C₂²×C₁₃	1	2	yes	complemented
645	#465	C₂²×C₁₃	1	2	yes	complemented
646	#463	C₂²×C₁₃	1	2	yes	complemented
647	#463	C₂²×C₁₃	1	2	yes	complemented
648	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	#459	C₂²×C₁₃	1	1	yes	characteristic
650	#459	C₂²×C₁₃	1	2	yes	complemented
651	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
652	#459	C₂²×C₁₃	1	2	yes	complemented
653	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
654	#450	C₂²×C₁₃	1	2	yes	complemented
655	#449	C₂²×C₁₃	1	2	yes	complemented
656	#447	C₂²×C₁₃	1	2	yes	—
657	#447	C₂²×C₁₃	1	2	yes	complemented
658	#447	C₂²×C₁₃	1	2	yes	complemented
659	#447	C₂²×C₁₃	1	2	yes	complemented
660	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
662	#442	C₂²×C₁₃	1	2	yes	—
663	#442	C₂²×C₁₃	1	1	yes	characteristic
664	#442	C₂²×C₁₃	1	2	yes	complemented
665	#442	C₂²×C₁₃	1	2	yes	complemented
666	#442	C₂²×C₁₃	1	1	yes	characteristic, complemented
667	#442	C₂²×C₁₃	1	2	yes	complemented
668	#442	C₂²×C₁₃	1	2	yes	complemented
669	#442	C₂²×C₁₃	1	2	yes	complemented
670	#442	C₂²×C₁₃	1	2	yes	complemented
671	#442	C₂²×C₁₃	1	2	yes	complemented
672	#442	C₂²×C₁₃	1	2	yes	complemented
673	#440	C₂²×C₁₃	1	1	yes	characteristic, complemented
674	#440	C₂²×C₁₃	1	2	yes	complemented
675	#440	C₂²×C₁₃	1	1	yes	characteristic, complemented
676	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
677	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
678	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
679	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
680	#435	C₂²×C₁₃	1	2	yes	complemented
681	#435	C₂²×C₁₃	1	2	yes	complemented
682	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
683	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
684	#432	C₂²×C₁₃	1	2	yes	complemented
685	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
686	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
687	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
688	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
689	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
690	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
691	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
692	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
693	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
694	C₂²×C₁₃	—	2	2	no	—
695	C₂²×C₁₃	—	2	2	no	—
696	C₂²×C₁₃	—	2	1	no	—
697	C₂²×C₁₃	—	2	1	no	—
698	C₂²×C₁₃	—	2	2	no	—
699	C₂²×C₁₃	—	2	2	no	—
700	C₂²×C₁₃	—	2	1	no	—
701	C₂²×C₁₃	—	4	1	no	—
702	C₂²×C₁₃	—	4	1	no	—
703	C₂²×C₁₃	—	4	1	no	—
704	C₂²×C₁₃	—	4	1	no	—
705	C₂²×C₁₃	—	4	2	no	—
706	C₂²×C₁₃	—	4	2	no	—
707	C₂²×C₁₃	—	4	1	no	—
708	C₂²×C₁₃	—	4	2	no	—
709	C₂²×C₁₃	—	4	2	no	—
710	C₂²×C₁₃	—	4	1	no	—
711	C₂²×C₁₃	—	4	2	no	—
712	C₂²×C₁₃	—	4	1	no	—
713	C₂²×C₁₃	—	4	2	no	—
714	C₂²×C₁₃	—	8	8	no	—
715	C₂²×C₁₃	—	8	8	no	—
716	C₂²×C₁₃	—	8	4	no	—
717	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
718	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
719	C₄×C₁₃	—	2	1	no	—
720	C₄×C₁₃	—	2	2	no	—
721	C₄×C₁₃	—	2	1	no	—
722	C₄×C₁₃	—	2	1	no	—
723	C₄×C₁₃	—	2	2	no	—
724	C₄×C₁₃	—	2	1	no	—
725	C₄×C₁₃	—	2	2	no	—
726	C₄×C₁₃	—	4	1	no	—
727	C₄×C₁₃	—	4	2	no	—
728	C₄×C₁₃	—	4	1	no	—
729	C₄×C₁₃	—	4	1	no	—
730	C₄×C₁₃	—	4	2	no	—
731	C₄×C₁₃	—	4	1	no	—
732	C₄×C₁₃	—	4	1	no	—
733	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
734	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
735	C₄×C₁₃	#585	1	1	yes	characteristic
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	2	2	no	—
739	C₂×#41	—	2	2	no	—
740	C₂×#41	—	2	1	no	—
741	C₂×#41	—	2	1	no	—
742	C₂×#41	—	4	8	no	—
743	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
744	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
745	C₂²×Q₈	—	2	1	no	—
746	C₂²×D₄	—	2	1	no	—
747	C₂²×D₄	—	2	1	no	—
748	C₂²×D₄	—	2	2	no	—
749	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
750	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
751	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
752	C₂³×C₄	—	2	2	no	—
753	C₂³×C₄	—	2	1	no	—
754	C₂³×C₄	—	2	2	no	—
755	AGL(1,ℤ/8)	—	2	4	no	—
756	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
757	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
758	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
759	C₂×D₈	—	2	8	no	—
760	C₂×D₈	C₂³×C₁₃	1	2	yes	—
761	C₂×D₈	C₂³×C₁₃	1	2	yes	—
762	C₂×D₈	C₂³×C₁₃	1	2	yes	—
763	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
764	C₂×D₈	C₂³×C₁₃	1	2	yes	—
765	C₂×D₈	C₂³×C₁₃	1	2	yes	—
766	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
767	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
768	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
769	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
770	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
771	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
772	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
773	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
774	#127	C₂³×C₁₃	1	1	yes	characteristic
775	#127	C₂³×C₁₃	1	2	yes	—
776	#127	C₂³×C₁₃	1	1	yes	characteristic
777	#126	—	2	2	no	—
778	#126	—	2	2	no	—
779	#125	—	2	1	no	—
780	#125	C₂³×C₁₃	1	2	yes	—
781	#124	—	2	1	no	—
782	#124	—	2	1	no	—
783	#124	—	2	2	no	—
784	#124	—	2	1	no	—
785	#124	C₂³×C₁₃	1	2	yes	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	1	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	2	no	—
807	#121	—	2	1	no	—
808	#121	—	2	2	no	—
809	#121	—	2	1	no	—
810	#121	—	2	2	no	—
811	#121	C₂³×C₁₃	1	2	yes	—
812	#121	C₂³×C₁₃	1	2	yes	—
813	#121	C₂³×C₁₃	1	2	yes	—
814	#121	C₂³×C₁₃	1	2	yes	—
815	#121	C₂³×C₁₃	1	2	yes	—
816	#120	—	2	2	no	—
817	#120	—	2	2	no	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
822	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
823	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
824	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
841	C₄×D₄	D₄×C₁₃	1	2	yes	—
842	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₁₃	1	2	yes	—
845	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₁₃	1	2	yes	—
847	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
848	C₄×D₄	C₂³×C₁₃	1	2	yes	—
849	C₄×D₄	C₂³×C₁₃	1	2	yes	—
850	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
851	C₄×D₄	C₂³×C₁₃	1	2	yes	—
852	C₄×D₄	C₂³×C₁₃	1	2	yes	—
853	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
855	C₄×D₄	C₂³×C₁₃	1	2	yes	—
856	#117	—	2	1	no	—
857	#117	—	2	2	no	—
858	#117	D₄×C₁₃	1	2	yes	—
859	#117	D₄×C₁₃	1	1	yes	characteristic
860	#117	C₂³×C₁₃	1	1	yes	characteristic
861	C₂×C₄⋊C₄	—	2	1	no	—
862	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
863	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
864	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
865	C₂×C₂²⋊C₄	—	2	2	no	—
866	C₂×C₂²⋊C₄	—	2	1	no	—
867	C₂×C₂²⋊C₄	—	2	2	no	—
868	C₂×C₂²⋊C₄	—	2	2	no	—
869	C₂×C₄²	—	2	1	no	—
870	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
871	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
872	#107	C₂³×C₁₃	1	1	yes	characteristic
873	#107	C₂³×C₁₃	1	1	yes	characteristic
874	#107	C₂³×C₁₃	1	2	yes	—
875	#106	C₂³×C₁₃	1	1	yes	characteristic
876	#106	C₂³×C₁₃	1	2	yes	—
877	#106	C₂³×C₁₃	1	2	yes	—
878	#106	C₂³×C₁₃	1	2	yes	—
879	#106	C₂³×C₁₃	1	1	yes	characteristic
880	#106	C₂³×C₁₃	1	2	yes	—
881	#106	C₂³×C₁₃	1	2	yes	—
882	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
885	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
886	#103	C₂³×C₁₃	1	1	yes	characteristic
887	#103	C₂³×C₁₃	1	1	yes	characteristic
888	#103	C₂³×C₁₃	1	2	yes	—
889	#102	C₂³×C₁₃	1	1	yes	characteristic
890	#102	C₂³×C₁₃	1	1	yes	characteristic
891	#102	C₂³×C₁₃	1	2	yes	—
892	#102	C₂³×C₁₃	1	2	yes	—
893	#102	C₂³×C₁₃	1	2	yes	—
894	#102	C₂³×C₁₃	1	2	yes	—
895	#102	C₂³×C₁₃	1	2	yes	—
896	#102	C₂³×C₁₃	1	2	yes	—
897	#102	C₂³×C₁₃	1	1	yes	characteristic
898	#102	C₂³×C₁₃	1	1	yes	characteristic
899	#102	C₂³×C₁₃	1	1	yes	characteristic
900	#102	C₂³×C₁₃	1	1	yes	characteristic
901	#102	C₂³×C₁₃	1	2	yes	—
902	#102	C₂³×C₁₃	1	2	yes	—
903	#102	C₂³×C₁₃	1	2	yes	—
904	#102	C₂³×C₁₃	1	2	yes	—
905	#102	C₂³×C₁₃	1	2	yes	—
906	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
907	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
908	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
909	#97	C₂³×C₁₃	1	1	yes	characteristic
910	#97	C₂³×C₁₃	1	2	yes	—
911	#97	C₂³×C₁₃	1	2	yes	—
912	#97	C₂³×C₁₃	1	2	yes	—
913	#97	C₂³×C₁₃	1	1	yes	characteristic
914	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
915	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
916	C₂×C₁₃	—	2	4	no	—
917	C₂×C₁₃	—	4	1	no	—
918	C₂×C₁₃	—	4	2	no	—
919	C₂×C₁₃	—	4	2	no	—
920	C₂×C₁₃	—	8	2	no	—
921	C₂×C₁₃	—	8	2	no	—
922	C₂×C₁₃	—	8	1	no	—
923	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
924	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
925	C₂×C₁₃	#3585	1	1	yes	characteristic
926	C₂⁴	—	2	2	no	—
927	C₂⁴	—	2	1	no	—
928	C₂⁴	—	2	2	no	—
929	#41	—	2	4	no	—
930	#41	—	2	2	no	—
931	#41	—	4	1	no	—
932	#41	—	4	8	no	—
933	#41	—	4	4	no	—
934	#41	—	4	8	no	—
935	#41	—	4	4	no	—
936	#41	—	4	4	no	—
937	#41	—	8	2	no	—
938	C₂×Q₈	—	2	2	no	—
939	C₂×Q₈	—	2	1	no	—
940	C₂×Q₈	—	2	1	no	—
941	C₂×Q₈	—	4	4	no	—
942	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
943	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
944	C₂×D₄	—	2	4	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	4	no	—
947	C₂×D₄	—	2	1	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	1	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	1	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	4	2	no	—
963	C₂×D₄	—	4	2	no	—
964	C₂×D₄	—	4	1	no	—
965	C₂×D₄	—	4	8	no	—
966	C₂×D₄	—	4	4	no	—
967	C₂×D₄	—	4	4	no	—
968	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
969	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
970	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
971	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
972	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
973	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
974	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
975	C₂²×C₄	—	2	1	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	4	8	no	—
992	C₂²×C₄	—	4	4	no	—
993	C₂²×C₄	—	8	4	no	—
994	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
995	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
996	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
997	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
998	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
999	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1000	SD₁₆	—	2	2	no	—
1001	SD₁₆	—	2	2	no	—
1002	SD₁₆	—	4	2	no	—
1003	D₈	—	2	4	no	—
1004	D₈	—	2	4	no	—
1005	D₈	—	2	2	no	—
1006	D₈	—	2	4	no	—
1007	D₈	—	4	2	no	—
1008	D₈	—	4	2	no	—
1009	D₈	C₁₃×#41	1	4	yes	complemented
1010	M₁₆	—	2	2	no	—
1011	M₁₆	—	4	1	no	—
1012	C₂×C₈	—	2	4	no	—
1013	C₂×C₈	—	4	2	no	—
1014	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1015	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1016	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1017	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1018	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1019	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	1	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1032	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1033	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1034	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1035	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1036	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1037	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1038	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1039	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1040	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1063	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1064	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1065	C₄²	—	2	1	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1069	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1070	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1071	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1072	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1073	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1074	C₄²	C₂⁴×C₁₃	1	2	yes	—
1075	C₁₃	#61451	1	1	yes	characteristic, direct product factor, Sylow
1076	C₂³	—	2	1	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	2	2	no	—
1079	C₂³	—	2	2	no	—
1080	C₂³	—	2	1	no	—
1081	C₂³	—	4	4	no	—
1082	C₂³	—	4	4	no	—
1083	C₂³	—	4	2	no	—
1084	C₂³	—	4	2	no	—
1085	C₂³	—	4	4	no	—
1086	C₂³	—	4	4	no	—
1087	C₂³	—	8	2	no	—
1088	C₂³	—	8	2	no	—
1089	C₂³	—	8	1	no	—
1090	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1091	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1092	Q₈	—	2	2	no	—
1093	Q₈	—	2	1	no	—
1094	Q₈	—	2	1	no	—
1095	Q₈	—	4	4	no	—
1096	Q₈	—	4	2	no	—
1097	Q₈	—	8	1	no	—
1098	D₄	—	2	4	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	2	no	—
1101	D₄	—	2	1	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	2	2	no	—
1105	D₄	—	2	1	no	—
1106	D₄	—	2	2	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	4	no	—
1109	D₄	—	4	4	no	—
1110	D₄	—	4	4	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	4	4	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	4	no	—
1115	D₄	—	4	4	no	—
1116	D₄	—	4	2	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	8	2	no	—
1119	D₄	—	8	1	no	—
1120	D₄	—	8	1	no	—
1121	D₄	—	8	2	no	—
1122	D₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
1123	D₄	C₂×C₁₃×#41	1	2	yes	—
1124	D₄	C₂×C₁₃×#41	1	2	yes	complemented
1125	C₂×C₄	—	2	4	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	4	no	—
1143	C₂×C₄	—	4	4	no	—
1144	C₂×C₄	—	4	2	no	—
1145	C₂×C₄	—	4	4	no	—
1146	C₂×C₄	—	4	2	no	—
1147	C₂×C₄	—	4	4	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	8	2	no	—
1154	C₂×C₄	—	8	2	no	—
1155	C₂×C₄	—	8	2	no	—
1156	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1157	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1158	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1159	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1160	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1161	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1162	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1164	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1165	C₈	—	2	2	no	—
1166	C₈	—	2	1	no	—
1167	C₈	—	2	1	no	—
1168	C₈	—	2	2	no	—
1169	C₈	—	2	1	no	—
1170	C₈	C₂×C₁₃×#41	1	2	yes	complemented
1171	C₂²	—	2	2	no	—
1172	C₂²	—	2	2	no	—
1173	C₂²	—	2	1	no	—
1174	C₂²	—	2	1	no	—
1175	C₂²	—	2	1	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	1	no	—
1180	C₂²	—	4	1	no	—
1181	C₂²	—	4	1	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	2	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	2	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	8	8	no	—
1192	C₂²	—	8	8	no	—
1193	C₂²	—	8	4	no	—
1194	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
1195	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1196	C₄	—	2	1	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	1	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	2	1	no	—
1201	C₄	—	2	1	no	—
1202	C₄	—	2	2	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	2	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	2	no	—
1209	C₄	—	4	1	no	—
1210	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
1211	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1212	C₄	C₁₃×#585	1	1	yes	characteristic
1213	C₂	—	2	4	no	—
1214	C₂	—	4	1	no	—
1215	C₂	—	4	2	no	—
1216	C₂	—	4	2	no	—
1217	C₂	—	8	2	no	—
1218	C₂	—	8	1	no	—
1219	C₂	—	8	2	no	—
1220	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1221	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
1222	C₂	C₁₃×#3585	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3481	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#3399	C₂	semidirect
4. C₁₃×#3384	C₂	semidirect
5. C₁₃×#3373	C₂	semidirect
6. C₁₃×#3366	C₂	semidirect
7. C₁₃×#3345	C₂	semidirect
8. C₁₃×#3335	C₂	semidirect
9. C₁₃×#3318	C₂	semidirect
10. C₁₃×#3306	C₂	semidirect
11. C₁₃×#3295	C₂	semidirect
12. C₁₃×#3294	C₂	semidirect
13. D₄×C₁₃×D₈	C₂	semidirect
14. C₁₃×#3264	C₂	semidirect
15. C₁₃×#3184	C₂	semidirect
16. C₁₃×#3180	C₂	semidirect
17. C₁₃×#3115	C₂	semidirect
18. C₁₃×#3114	C₂	semidirect
19. C₁₃×#3109	C₂	semidirect
20. C₁₃×#3109	C₂	semidirect
21. C₁₃×#2970	C₂	semidirect
22. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
23. C₂×C₁₃×#442	C₂	semidirect
27. C₁₃×#559	C₂²	semidirect
28. C₁₃×#554	C₂²	semidirect
29. C₁₃×#554	C₂²	semidirect
31. C₁₃×#553	C₂²	semidirect
33. C₁₃×#550	C₂²	semidirect
34. D₄×Q₈×C₁₃	C₂²	semidirect
37. C₁₃×#547	C₂²	semidirect
41. C₁₃×#546	C₂²	semidirect
43. D₄²×C₁₃	C₂²	semidirect
44. D₄²×C₁₃	C₂²	semidirect
45. C₁₃×#532	C₂²	semidirect
46. C₁₃×#532	C₂²	semidirect
47. C₁₃×#532	C₂²	semidirect
49. C₁₃×#529	C₂²	semidirect
54. C₄×C₁₃×#41	C₂²	semidirect
56. C₂×C₄×D₄×C₁₃	C₂²	semidirect
57. C₂×C₄×D₄×C₁₃	C₂²	semidirect
58. C₂×C₄×D₄×C₁₃	C₂²	semidirect
59. C₁₃×#501	C₂²	semidirect
60. C₁₃×#498	C₂²	semidirect
61. C₁₃×#496	C₂²	semidirect
62. C₁₃×#493	C₂²	semidirect
63. C₁₃×#490	C₂²	semidirect
64. C₁₃×#489	C₂²	semidirect
65. C₁₃×#486	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
67. C₁₃×#483	C₂²	semidirect
68. C₁₃×#482	C₂²	semidirect
69. C₁₃×#481	C₂²	semidirect
70. C₁₃×#481	C₂²	semidirect
71. C₁₃×#481	C₂²	semidirect
72. C₁₃×#480	C₂²	semidirect
73. C₁₃×#478	C₂²	semidirect
74. C₁₃×#478	C₂²	semidirect
75. C₁₃×#476	C₂²	semidirect
76. C₁₃×#476	C₂²	semidirect
77. C₁₃×#476	C₂²	semidirect
78. C₁₃×#476	C₂²	semidirect
79. C₁₃×#475	C₂²	semidirect
80. C₁₃×#474	C₂²	semidirect
81. C₁₃×#469	C₂²	semidirect
82. C₁₃×#469	C₂²	semidirect
83. C₁₃×#466	C₂²	semidirect
84. C₁₃×#466	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#465	C₂²	semidirect
87. C₁₃×#463	C₂²	semidirect
88. C₁₃×#463	C₂²	semidirect
89. C₁₃×#460	C₂²	semidirect
91. C₁₃×#459	C₂²	semidirect
92. C₁₃×#459	C₂²	semidirect
93. C₁₃×#459	C₂²	semidirect
94. C₁₃×#459	C₂²	semidirect
95. C₁₃×#450	C₂²	semidirect
96. C₁₃×#449	C₂²	semidirect
98. C₁₃×#447	C₂²	semidirect
99. C₁₃×#447	C₂²	semidirect
100. C₁₃×#447	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₁₃×#446	C₂²	semidirect
105. C₁₃×#442	C₂²	semidirect
106. C₁₃×#442	C₂²	semidirect
107. C₁₃×#442	C₂²	semidirect
108. C₁₃×#442	C₂²	semidirect
109. C₁₃×#442	C₂²	semidirect
110. C₁₃×#442	C₂²	semidirect
111. C₁₃×#442	C₂²	semidirect
112. C₁₃×#442	C₂²	semidirect
113. C₁₃×#442	C₂²	semidirect
114. C₁₃×#440	C₂²	semidirect
115. C₁₃×#440	C₂²	semidirect
116. C₁₃×#440	C₂²	semidirect
117. C₄×C₁₃×SD₁₆	C₂²	semidirect
118. C₄×C₁₃×SD₁₆	C₂²	semidirect
120. C₄×C₁₃×D₈	C₂²	semidirect
121. C₁₃×#435	C₂²	semidirect
122. C₁₃×#435	C₂²	semidirect
123. C₈×D₄×C₁₃	C₂²	semidirect
124. C₈×D₄×C₁₃	C₂²	semidirect
125. C₁₃×#432	C₂²	semidirect
126. C₁₃×#432	C₂²	semidirect
127. C₁₃×#428	C₂²	semidirect
128. C₂×C₁₃×#106	C₂²	semidirect
129. C₁₃×#418	C₂²	semidirect
130. C₁₃×#417	C₂²	semidirect
131. C₂×C₁₃×#102	C₂²	semidirect
132. C₂×C₁₃×#102	C₂²	semidirect
133. C₄×C₁₃×M₁₆	C₂²	semidirect
134. C₂×C₁₃×#97	C₂²	semidirect
315. #61451	C₁₃	direct (N × H)
399. C₁₃×D₈	#41	semidirect
465. #3481	C₂×C₁₃	semidirect
466. D₄×#41	C₂×C₁₃	semidirect
467. #3399	C₂×C₁₃	semidirect
468. #3384	C₂×C₁₃	semidirect
469. #3373	C₂×C₁₃	semidirect
470. #3366	C₂×C₁₃	semidirect
471. #3345	C₂×C₁₃	semidirect
472. #3335	C₂×C₁₃	semidirect
473. #3318	C₂×C₁₃	semidirect
474. #3306	C₂×C₁₃	semidirect
475. #3295	C₂×C₁₃	semidirect
476. #3294	C₂×C₁₃	semidirect
477. D₄×D₈	C₂×C₁₃	semidirect
478. #3264	C₂×C₁₃	semidirect
479. #3184	C₂×C₁₃	semidirect
480. #3180	C₂×C₁₃	semidirect
481. #3115	C₂×C₁₃	semidirect
482. #3114	C₂×C₁₃	semidirect
483. #3109	C₂×C₁₃	semidirect
484. #3109	C₂×C₁₃	semidirect
485. #2970	C₂×C₁₃	semidirect
486. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
487. C₂×#442	C₂×C₁₃	semidirect
534. D₄×C₁₃	AGL(1,ℤ/8)	semidirect
536. D₄×C₁₃	C₂×#41	semidirect
582. C₈×C₁₃	C₂×#41	semidirect
586. #559	C₂²×C₁₃	semidirect
587. #554	C₂²×C₁₃	semidirect
588. #554	C₂²×C₁₃	semidirect
590. #553	C₂²×C₁₃	semidirect
592. #550	C₂²×C₁₃	semidirect
593. D₄×Q₈	C₂²×C₁₃	semidirect
596. #547	C₂²×C₁₃	semidirect
600. #546	C₂²×C₁₃	semidirect
602. D₄²	C₂²×C₁₃	semidirect
603. D₄²	C₂²×C₁₃	semidirect
604. #532	C₂²×C₁₃	semidirect
605. #532	C₂²×C₁₃	semidirect
606. #532	C₂²×C₁₃	semidirect
608. #529	C₂²×C₁₃	semidirect
613. C₄×#41	C₂²×C₁₃	semidirect
615. C₂×C₄×D₄	C₂²×C₁₃	semidirect
616. C₂×C₄×D₄	C₂²×C₁₃	semidirect
617. C₂×C₄×D₄	C₂²×C₁₃	semidirect
618. #501	C₂²×C₁₃	semidirect
619. #498	C₂²×C₁₃	semidirect
620. #496	C₂²×C₁₃	semidirect
621. #493	C₂²×C₁₃	semidirect
622. #490	C₂²×C₁₃	semidirect
623. #489	C₂²×C₁₃	semidirect
624. #486	C₂²×C₁₃	semidirect
625. #486	C₂²×C₁₃	semidirect
626. #483	C₂²×C₁₃	semidirect
627. #482	C₂²×C₁₃	semidirect
628. #481	C₂²×C₁₃	semidirect
629. #481	C₂²×C₁₃	semidirect
630. #481	C₂²×C₁₃	semidirect
631. #480	C₂²×C₁₃	semidirect
632. #478	C₂²×C₁₃	semidirect
633. #478	C₂²×C₁₃	semidirect
634. #476	C₂²×C₁₃	semidirect
635. #476	C₂²×C₁₃	semidirect
636. #476	C₂²×C₁₃	semidirect
637. #476	C₂²×C₁₃	semidirect
638. #475	C₂²×C₁₃	semidirect
639. #474	C₂²×C₁₃	semidirect
640. #469	C₂²×C₁₃	semidirect
641. #469	C₂²×C₁₃	semidirect
642. #466	C₂²×C₁₃	semidirect
643. #466	C₂²×C₁₃	semidirect
644. #465	C₂²×C₁₃	semidirect
645. #465	C₂²×C₁₃	semidirect
646. #463	C₂²×C₁₃	semidirect
647. #463	C₂²×C₁₃	semidirect
648. #460	C₂²×C₁₃	semidirect
650. #459	C₂²×C₁₃	semidirect
651. #459	C₂²×C₁₃	semidirect
652. #459	C₂²×C₁₃	semidirect
653. #459	C₂²×C₁₃	semidirect
654. #450	C₂²×C₁₃	semidirect
655. #449	C₂²×C₁₃	semidirect
657. #447	C₂²×C₁₃	semidirect
658. #447	C₂²×C₁₃	semidirect
659. #447	C₂²×C₁₃	semidirect
660. #446	C₂²×C₁₃	semidirect
661. #446	C₂²×C₁₃	semidirect
664. #442	C₂²×C₁₃	semidirect
665. #442	C₂²×C₁₃	semidirect
666. #442	C₂²×C₁₃	semidirect
667. #442	C₂²×C₁₃	semidirect
668. #442	C₂²×C₁₃	semidirect
669. #442	C₂²×C₁₃	semidirect
670. #442	C₂²×C₁₃	semidirect
671. #442	C₂²×C₁₃	semidirect
672. #442	C₂²×C₁₃	semidirect
673. #440	C₂²×C₁₃	semidirect
674. #440	C₂²×C₁₃	semidirect
675. #440	C₂²×C₁₃	semidirect
676. C₄×SD₁₆	C₂²×C₁₃	semidirect
677. C₄×SD₁₆	C₂²×C₁₃	semidirect
679. C₄×D₈	C₂²×C₁₃	semidirect
680. #435	C₂²×C₁₃	semidirect
681. #435	C₂²×C₁₃	semidirect
682. C₈×D₄	C₂²×C₁₃	semidirect
683. C₈×D₄	C₂²×C₁₃	semidirect
684. #432	C₂²×C₁₃	semidirect
685. #432	C₂²×C₁₃	semidirect
686. #428	C₂²×C₁₃	semidirect
687. C₂×#106	C₂²×C₁₃	semidirect
688. #418	C₂²×C₁₃	semidirect
689. #417	C₂²×C₁₃	semidirect
690. C₂×#102	C₂²×C₁₃	semidirect
691. C₂×#102	C₂²×C₁₃	semidirect
692. C₄×M₁₆	C₂²×C₁₃	semidirect
693. C₂×#97	C₂²×C₁₃	semidirect
1009. D₈	C₁₃×#41	semidirect
1075. C₁₃	#61451	direct (N × H)
1122. D₄	C₁₃×AGL(1,ℤ/8)	semidirect
1124. D₄	C₂×C₁₃×#41	semidirect
1170. C₈	C₂×C₁₃×#41	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3481	2
D₄×C₁₃×#41	2
C₁₃×#3399	2
C₁₃×#3384	2
C₁₃×#3373	2
C₁₃×#3366	2
C₁₃×#3345	2
C₁₃×#3335	2
C₁₃×#3318	2
C₁₃×#3306	2
C₁₃×#3295	2
C₁₃×#3294	2
D₄×C₁₃×D₈	2
C₁₃×#3264	2
C₁₃×#3184	2
C₁₃×#3180	2
C₁₃×#3115	2
C₁₃×#3114	2
C₁₃×#3109	2
C₁₃×#2970	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₂×C₁₃×#442	2
#61451	13

Subgroups — C13×#61451 #15747790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61451 #15747790