Subgroups — C₁₃×#61496 #15747835

Order 3328.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3346	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3297	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3295	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3179	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3119	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3118	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2946	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
26	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#555	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#554	C₂²	1	2	yes	complemented
30	C₁₃×#553	—	2	1	no	—
31	C₁₃×#553	C₂²	1	2	yes	—
32	C₁₃×#552	—	2	1	no	—
33	C₁₃×#551	—	2	2	no	—
34	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#548	—	2	1	no	—
37	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
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	2	yes	—
43	D₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#542	C₂²	1	2	yes	complemented
45	C₁₃×#540	C₂²	1	2	yes	complemented
46	C₁₃×#539	—	2	2	no	—
47	C₁₃×#538	—	2	2	no	—
48	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#532	C₂²	1	1	yes	characteristic
50	C₁₃×#529	C₂²	1	1	yes	characteristic
51	C₁₃×#525	—	2	1	no	—
52	C₁₃×#525	—	2	1	no	—
53	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
54	C₂×C₁₃×#121	—	2	1	no	—
55	C₁₃×#520	C₂²	1	2	yes	complemented
56	C₁₃×#518	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, 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×#492	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#488	C₂²	1	2	yes	complemented
64	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#486	C₂²	1	2	yes	complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#484	C₂²	1	2	yes	complemented
69	C₁₃×#482	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×#479	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	2	yes	complemented
75	C₁₃×#476	C₂²	1	2	yes	complemented
76	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
79	C₁₃×#474	C₂²	1	2	yes	complemented
80	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#469	C₂²	1	2	yes	complemented
82	C₁₃×#468	C₂²	1	2	yes	complemented
83	C₁₃×#466	C₂²	1	2	yes	complemented
84	C₁₃×#465	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	—
88	C₁₃×#463	C₂²	1	2	yes	complemented
89	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#460	C₂²	1	2	yes	complemented
92	C₁₃×#459	C₂²	1	2	yes	complemented
93	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#450	C₂²	1	2	yes	—
96	C₁₃×#450	C₂²	1	2	yes	complemented
97	C₁₃×#449	C₂²	1	2	yes	complemented
98	C₁₃×#449	C₂²	1	2	yes	complemented
99	C₁₃×#447	C₂²	1	2	yes	—
100	C₁₃×#447	C₂²	1	2	yes	complemented
101	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#442	C₂²	1	2	yes	—
104	C₁₃×#442	C₂²	1	2	yes	complemented
105	C₁₃×#442	C₂²	1	2	yes	complemented
106	C₁₃×#440	C₂²	1	2	yes	complemented
107	C₁₃×#440	C₂²	1	2	yes	complemented
108	C₁₃×#440	C₂²	1	2	yes	complemented
109	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
110	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
111	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
112	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
114	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
115	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
116	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
117	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
121	C₁₃×#436	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
125	C₁₃×#433	C₂²	1	2	yes	complemented
126	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#428	C₂²	1	2	yes	complemented
128	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
129	C₁₃×#416	C₂²	1	2	yes	complemented
130	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
131	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
132	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
133	C₁₃×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	—	2	1	no	—
137	C₂×C₁₃×#41	—	2	1	no	—
138	C₂×C₁₃×#41	C₂³	1	2	yes	—
139	C₂²×Q₈×C₁₃	—	2	1	no	—
140	C₂²×D₄×C₁₃	—	2	2	no	—
141	C₂²×D₄×C₁₃	—	2	1	no	—
142	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
144	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₁₃	—	2	1	no	—
146	C₂³×C₄×C₁₃	—	2	1	no	—
147	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
148	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₁₃×D₈	—	2	4	no	—
153	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×D₈	C₂³	1	2	yes	—
157	C₂×C₁₃×D₈	C₂³	1	2	yes	—
158	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
160	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
163	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₁₃×#127	C₂³	1	1	yes	characteristic
168	C₁₃×#127	C₂³	1	2	yes	—
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#126	—	2	2	no	—
171	C₁₃×#126	—	2	2	no	—
172	C₁₃×#126	D₄	1	2	yes	—
173	C₁₃×#125	—	2	2	no	—
174	C₁₃×#125	—	2	1	no	—
175	C₁₃×#125	D₄	1	1	yes	characteristic
176	C₁₃×#125	C₂³	1	2	yes	—
177	C₁₃×#124	—	2	2	no	—
178	C₁₃×#124	—	2	2	no	—
179	C₁₃×#124	—	2	1	no	—
180	C₁₃×#124	D₄	1	1	yes	characteristic
181	C₁₃×#124	C₂³	1	2	yes	—
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×#123	—	2	2	no	—
184	C₁₃×#123	—	2	2	no	—
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	D₄	1	2	yes	—
190	C₁₃×C₂²⋊Q₈	—	2	1	no	—
191	C₁₃×C₂²⋊Q₈	—	2	1	no	—
192	C₁₃×C₂²⋊Q₈	—	2	1	no	—
193	C₁₃×C₂²⋊Q₈	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
200	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
201	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	—	2	1	no	—
205	C₁₃×#121	—	2	1	no	—
206	C₁₃×#121	—	2	1	no	—
207	C₁₃×#121	—	2	1	no	—
208	C₁₃×#121	—	2	1	no	—
209	C₁₃×#121	—	2	2	no	—
210	C₁₃×#121	—	2	2	no	—
211	C₁₃×#121	—	2	2	no	—
212	C₁₃×#121	—	2	2	no	—
213	C₁₃×#121	—	2	2	no	—
214	C₁₃×#121	D₄	1	1	yes	characteristic
215	C₁₃×#121	C₂³	1	2	yes	—
216	C₁₃×#121	C₂³	1	2	yes	—
217	C₁₃×#121	C₂³	1	2	yes	—
218	C₁₃×#121	C₂³	1	2	yes	—
219	C₁₃×#120	—	2	2	no	—
220	C₁₃×#120	—	2	2	no	—
221	C₁₃×#120	—	2	2	no	—
222	C₁₃×#120	—	2	2	no	—
223	C₄×Q₈×C₁₃	—	2	1	no	—
224	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
225	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₁₃	—	2	2	no	—
228	C₄×D₄×C₁₃	—	2	2	no	—
229	C₄×D₄×C₁₃	—	2	2	no	—
230	C₄×D₄×C₁₃	—	2	2	no	—
231	C₄×D₄×C₁₃	—	2	2	no	—
232	C₄×D₄×C₁₃	—	2	2	no	—
233	C₄×D₄×C₁₃	—	2	1	no	—
234	C₄×D₄×C₁₃	—	2	1	no	—
235	C₄×D₄×C₁₃	—	2	1	no	—
236	C₄×D₄×C₁₃	—	2	1	no	—
237	C₄×D₄×C₁₃	—	2	1	no	—
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	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	1	yes	characteristic
246	C₄×D₄×C₁₃	C₂³	1	2	yes	—
247	C₄×D₄×C₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
252	C₁₃×#117	—	2	1	no	—
253	C₁₃×#117	—	2	2	no	—
254	C₁₃×#117	—	2	1	no	—
255	C₁₃×#117	—	2	1	no	—
256	C₁₃×#117	C₂³	1	2	yes	—
257	C₁₃×#117	C₂³	1	2	yes	—
258	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₁₃×C₂²⋊C₄	—	2	1	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×C₁₃×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
270	C₁₃×#107	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	1	yes	characteristic
274	C₁₃×#107	C₂³	1	2	yes	—
275	C₁₃×#107	C₂³	1	2	yes	—
276	C₁₃×#106	C₂³	1	2	yes	—
277	C₁₃×#106	C₂³	1	2	yes	—
278	C₁₃×#106	C₂³	1	2	yes	—
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₃×C₄⋊C₈	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	2	yes	—
288	C₁₃×#102	C₂³	1	1	yes	characteristic
289	C₁₃×#102	C₂³	1	1	yes	characteristic
290	C₁₃×#102	C₂³	1	1	yes	characteristic
291	C₁₃×#102	C₂³	1	1	yes	characteristic
292	C₁₃×#102	C₂³	1	1	yes	characteristic
293	C₁₃×#102	C₂³	1	1	yes	characteristic
294	C₁₃×#102	C₂³	1	1	yes	characteristic
295	C₁₃×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
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×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₁₃×C₂²⋊C₈	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	#61496	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂⁴×C₁₃	—	2	1	no	—
316	C₂⁴×C₁₃	—	2	1	no	—
317	C₂⁴×C₁₃	—	2	2	no	—
318	C₁₃×#41	—	2	4	no	—
319	C₁₃×#41	—	4	2	no	—
320	C₁₃×#41	—	8	2	no	—
321	C₁₃×#41	—	8	2	no	—
322	C₁₃×#41	—	8	2	no	—
323	C₂×Q₈×C₁₃	—	2	1	no	—
324	C₂×Q₈×C₁₃	—	2	2	no	—
325	C₂×Q₈×C₁₃	—	2	1	no	—
326	C₂×Q₈×C₁₃	—	8	2	no	—
327	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
329	C₂×D₄×C₁₃	—	2	2	no	—
330	C₂×D₄×C₁₃	—	2	2	no	—
331	C₂×D₄×C₁₃	—	2	4	no	—
332	C₂×D₄×C₁₃	—	2	2	no	—
333	C₂×D₄×C₁₃	—	2	2	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	—	2	1	no	—
339	C₂×D₄×C₁₃	—	2	1	no	—
340	C₂×D₄×C₁₃	—	2	1	no	—
341	C₂×D₄×C₁₃	—	2	2	no	—
342	C₂×D₄×C₁₃	—	2	1	no	—
343	C₂×D₄×C₁₃	—	2	2	no	—
344	C₂×D₄×C₁₃	—	4	1	no	—
345	C₂×D₄×C₁₃	—	4	1	no	—
346	C₂×D₄×C₁₃	—	4	2	no	—
347	C₂×D₄×C₁₃	—	8	2	no	—
348	C₂×D₄×C₁₃	—	8	4	no	—
349	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
354	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₁₃	—	2	1	no	—
357	C₂²×C₄×C₁₃	—	2	1	no	—
358	C₂²×C₄×C₁₃	—	2	2	no	—
359	C₂²×C₄×C₁₃	—	2	2	no	—
360	C₂²×C₄×C₁₃	—	2	1	no	—
361	C₂²×C₄×C₁₃	—	2	1	no	—
362	C₂²×C₄×C₁₃	—	2	1	no	—
363	C₂²×C₄×C₁₃	—	2	1	no	—
364	C₂²×C₄×C₁₃	—	2	1	no	—
365	C₂²×C₄×C₁₃	—	2	2	no	—
366	C₂²×C₄×C₁₃	—	2	2	no	—
367	C₂²×C₄×C₁₃	—	2	2	no	—
368	C₂²×C₄×C₁₃	—	2	2	no	—
369	C₂²×C₄×C₁₃	—	2	1	no	—
370	C₂²×C₄×C₁₃	—	2	1	no	—
371	C₂²×C₄×C₁₃	—	2	1	no	—
372	C₂²×C₄×C₁₃	—	8	2	no	—
373	C₂²×C₄×C₁₃	—	8	2	no	—
374	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
378	C₁₃×SD₁₆	—	2	4	no	—
379	C₁₃×SD₁₆	—	2	4	no	—
380	C₁₃×SD₁₆	—	4	2	no	—
381	C₁₃×SD₁₆	—	4	2	no	—
382	C₁₃×D₈	—	2	2	no	—
383	C₁₃×D₈	—	2	2	no	—
384	C₁₃×D₈	—	2	4	no	—
385	C₁₃×D₈	—	2	2	no	—
386	C₁₃×D₈	—	4	2	no	—
387	C₁₃×D₈	#41	1	4	yes	complemented
388	C₁₃×M₁₆	—	2	4	no	—
389	C₂×C₈×C₁₃	—	2	2	no	—
390	C₂×C₈×C₁₃	—	4	2	no	—
391	C₂×C₈×C₁₃	—	4	1	no	—
392	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
396	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
397	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
398	C₁₃×C₄⋊C₄	—	2	2	no	—
399	C₁₃×C₄⋊C₄	—	2	1	no	—
400	C₁₃×C₄⋊C₄	—	2	1	no	—
401	C₁₃×C₄⋊C₄	—	2	2	no	—
402	C₁₃×C₄⋊C₄	—	2	2	no	—
403	C₁₃×C₄⋊C₄	—	2	2	no	—
404	C₁₃×C₄⋊C₄	—	2	2	no	—
405	C₁₃×C₄⋊C₄	—	2	1	no	—
406	C₁₃×C₄⋊C₄	—	2	1	no	—
407	C₁₃×C₄⋊C₄	—	2	1	no	—
408	C₁₃×C₄⋊C₄	—	2	1	no	—
409	C₁₃×C₄⋊C₄	—	2	2	no	—
410	C₁₃×C₄⋊C₄	—	2	2	no	—
411	C₁₃×C₄⋊C₄	—	2	2	no	—
412	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
413	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
414	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
415	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
416	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
417	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
418	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
419	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
420	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
421	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
422	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
423	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
424	C₁₃×C₂²⋊C₄	—	2	2	no	—
425	C₁₃×C₂²⋊C₄	—	2	2	no	—
426	C₁₃×C₂²⋊C₄	—	2	2	no	—
427	C₁₃×C₂²⋊C₄	—	2	1	no	—
428	C₁₃×C₂²⋊C₄	—	2	1	no	—
429	C₁₃×C₂²⋊C₄	—	2	2	no	—
430	C₁₃×C₂²⋊C₄	—	2	1	no	—
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	—	2	1	no	—
433	C₁₃×C₂²⋊C₄	—	2	2	no	—
434	C₁₃×C₂²⋊C₄	—	2	1	no	—
435	C₁₃×C₂²⋊C₄	—	2	1	no	—
436	C₁₃×C₂²⋊C₄	—	2	1	no	—
437	C₁₃×C₂²⋊C₄	—	2	1	no	—
438	C₁₃×C₂²⋊C₄	—	2	2	no	—
439	C₁₃×C₂²⋊C₄	—	2	2	no	—
440	C₁₃×C₂²⋊C₄	—	2	2	no	—
441	C₁₃×C₂²⋊C₄	—	2	2	no	—
442	C₁₃×C₂²⋊C₄	—	2	2	no	—
443	C₁₃×C₂²⋊C₄	—	2	2	no	—
444	C₁₃×C₂²⋊C₄	—	2	2	no	—
445	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
446	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
447	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
448	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
449	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
450	C₄²×C₁₃	—	2	2	no	—
451	C₄²×C₁₃	—	2	2	no	—
452	C₄²×C₁₃	—	2	2	no	—
453	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
456	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
457	C₄²×C₁₃	C₂⁴	1	2	yes	—
458	#3520	C₂×C₁₃	1	1	yes	characteristic, complemented
459	#3519	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3397	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3384	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3360	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3358	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3354	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3346	C₂×C₁₃	1	2	yes	complemented
466	#3303	C₂×C₁₃	1	1	yes	characteristic, complemented
467	#3297	C₂×C₁₃	1	2	yes	complemented
468	#3295	C₂×C₁₃	1	2	yes	complemented
469	#3294	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3272	C₂×C₁₃	1	1	yes	characteristic, complemented
471	#3264	C₂×C₁₃	1	2	yes	complemented
472	#3179	C₂×C₁₃	1	2	yes	complemented
473	#3167	C₂×C₁₃	1	1	yes	characteristic, complemented
474	#3119	C₂×C₁₃	1	2	yes	complemented
475	#3118	C₂×C₁₃	1	2	yes	complemented
476	#3110	C₂×C₁₃	1	1	yes	characteristic, complemented
477	#3109	C₂×C₁₃	1	1	yes	characteristic, complemented
478	#2966	C₂×C₁₃	1	1	yes	characteristic, complemented
479	#2946	C₂×C₁₃	1	2	yes	complemented
480	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
481	C₂³×C₁₃	—	2	1	no	—
482	C₂³×C₁₃	—	2	1	no	—
483	C₂³×C₁₃	—	2	1	no	—
484	C₂³×C₁₃	—	2	1	no	—
485	C₂³×C₁₃	—	2	2	no	—
486	C₂³×C₁₃	—	4	2	no	—
487	C₂³×C₁₃	—	4	2	no	—
488	C₂³×C₁₃	—	4	4	no	—
489	C₂³×C₁₃	—	4	2	no	—
490	C₂³×C₁₃	—	4	2	no	—
491	C₂³×C₁₃	—	8	1	no	—
492	C₂³×C₁₃	—	8	1	no	—
493	C₂³×C₁₃	—	8	2	no	—
494	C₂³×C₁₃	—	8	2	no	—
495	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
496	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
497	Q₈×C₁₃	—	2	2	no	—
498	Q₈×C₁₃	—	2	2	no	—
499	Q₈×C₁₃	—	2	2	no	—
500	Q₈×C₁₃	—	4	2	no	—
501	Q₈×C₁₃	—	8	2	no	—
502	Q₈×C₁₃	—	8	1	no	—
503	D₄×C₁₃	—	2	4	no	—
504	D₄×C₁₃	—	2	2	no	—
505	D₄×C₁₃	—	2	1	no	—
506	D₄×C₁₃	—	2	1	no	—
507	D₄×C₁₃	—	2	2	no	—
508	D₄×C₁₃	—	2	1	no	—
509	D₄×C₁₃	—	2	1	no	—
510	D₄×C₁₃	—	2	1	no	—
511	D₄×C₁₃	—	2	2	no	—
512	D₄×C₁₃	—	2	1	no	—
513	D₄×C₁₃	—	4	4	no	—
514	D₄×C₁₃	—	4	2	no	—
515	D₄×C₁₃	—	4	2	no	—
516	D₄×C₁₃	—	4	4	no	—
517	D₄×C₁₃	—	4	4	no	—
518	D₄×C₁₃	—	4	2	no	—
519	D₄×C₁₃	—	8	2	no	—
520	D₄×C₁₃	—	8	2	no	—
521	D₄×C₁₃	—	8	1	no	—
522	D₄×C₁₃	—	8	2	no	—
523	D₄×C₁₃	—	8	2	no	—
524	D₄×C₁₃	—	8	2	no	—
525	D₄×C₁₃	C₂×#41	1	2	yes	—
526	D₄×C₁₃	C₂×#41	1	2	yes	—
527	C₂×C₄×C₁₃	—	2	2	no	—
528	C₂×C₄×C₁₃	—	2	2	no	—
529	C₂×C₄×C₁₃	—	2	1	no	—
530	C₂×C₄×C₁₃	—	2	2	no	—
531	C₂×C₄×C₁₃	—	2	1	no	—
532	C₂×C₄×C₁₃	—	2	2	no	—
533	C₂×C₄×C₁₃	—	2	1	no	—
534	C₂×C₄×C₁₃	—	2	2	no	—
535	C₂×C₄×C₁₃	—	2	1	no	—
536	C₂×C₄×C₁₃	—	2	2	no	—
537	C₂×C₄×C₁₃	—	2	2	no	—
538	C₂×C₄×C₁₃	—	2	1	no	—
539	C₂×C₄×C₁₃	—	2	1	no	—
540	C₂×C₄×C₁₃	—	4	4	no	—
541	C₂×C₄×C₁₃	—	4	2	no	—
542	C₂×C₄×C₁₃	—	4	2	no	—
543	C₂×C₄×C₁₃	—	4	2	no	—
544	C₂×C₄×C₁₃	—	4	2	no	—
545	C₂×C₄×C₁₃	—	8	1	no	—
546	C₂×C₄×C₁₃	—	8	1	no	—
547	C₂×C₄×C₁₃	—	8	1	no	—
548	C₂×C₄×C₁₃	—	8	1	no	—
549	C₂×C₄×C₁₃	—	8	2	no	—
550	C₂×C₄×C₁₃	—	8	2	no	—
551	C₂×C₄×C₁₃	—	8	2	no	—
552	C₂×C₄×C₁₃	—	8	2	no	—
553	C₂×C₄×C₁₃	—	8	1	no	—
554	C₂×C₄×C₁₃	—	8	1	no	—
555	C₂×C₄×C₁₃	—	8	2	no	—
556	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
558	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
559	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
563	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
565	C₈×C₁₃	—	2	1	no	—
566	C₈×C₁₃	—	2	2	no	—
567	C₈×C₁₃	—	2	1	no	—
568	C₈×C₁₃	—	2	2	no	—
569	C₈×C₁₃	—	2	1	no	—
570	C₈×C₁₃	C₂×#41	1	2	yes	—
571	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
572	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
573	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
574	#555	C₂²×C₁₃	1	1	yes	characteristic, complemented
575	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
576	#554	C₂²×C₁₃	1	2	yes	complemented
577	#553	—	2	1	no	—
578	#553	C₂²×C₁₃	1	2	yes	—
579	#552	—	2	1	no	—
580	#551	—	2	2	no	—
581	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
582	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
583	#548	—	2	1	no	—
584	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
585	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
586	#546	—	2	1	no	—
587	#546	—	2	2	no	—
588	#546	C₂²×C₁₃	1	2	yes	complemented
589	D₄²	C₂²×C₁₃	1	2	yes	—
590	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
591	#542	C₂²×C₁₃	1	2	yes	complemented
592	#540	C₂²×C₁₃	1	2	yes	complemented
593	#539	—	2	2	no	—
594	#538	—	2	2	no	—
595	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
596	#532	C₂²×C₁₃	1	1	yes	characteristic
597	#529	C₂²×C₁₃	1	1	yes	characteristic
598	#525	—	2	1	no	—
599	#525	—	2	1	no	—
600	C₂×C₂²⋊Q₈	—	2	1	no	—
601	C₂×#121	—	2	1	no	—
602	#520	C₂²×C₁₃	1	2	yes	complemented
603	#518	C₂²×C₁₃	1	2	yes	complemented
604	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
605	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
606	#501	C₂²×C₁₃	1	2	yes	complemented
607	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	#496	C₂²×C₁₃	1	2	yes	complemented
609	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
610	#488	C₂²×C₁₃	1	2	yes	complemented
611	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	#486	C₂²×C₁₃	1	2	yes	complemented
614	#485	C₂²×C₁₃	1	2	yes	complemented
615	#484	C₂²×C₁₃	1	2	yes	complemented
616	#482	C₂²×C₁₃	1	2	yes	complemented
617	#481	C₂²×C₁₃	1	2	yes	complemented
618	#481	C₂²×C₁₃	1	2	yes	complemented
619	#480	C₂²×C₁₃	1	2	yes	complemented
620	#479	C₂²×C₁₃	1	2	yes	complemented
621	#478	C₂²×C₁₃	1	2	yes	complemented
622	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
623	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
624	#476	C₂²×C₁₃	1	2	yes	complemented
625	#474	C₂²×C₁₃	1	2	yes	complemented
626	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
627	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
628	#469	C₂²×C₁₃	1	2	yes	complemented
629	#468	C₂²×C₁₃	1	2	yes	complemented
630	#466	C₂²×C₁₃	1	2	yes	complemented
631	#465	C₂²×C₁₃	1	2	yes	complemented
632	#465	C₂²×C₁₃	1	2	yes	complemented
633	#465	C₂²×C₁₃	1	2	yes	complemented
634	#463	C₂²×C₁₃	1	2	yes	—
635	#463	C₂²×C₁₃	1	2	yes	complemented
636	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
637	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
638	#460	C₂²×C₁₃	1	2	yes	complemented
639	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
640	#459	C₂²×C₁₃	1	2	yes	complemented
641	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
642	#450	C₂²×C₁₃	1	2	yes	—
643	#450	C₂²×C₁₃	1	2	yes	complemented
644	#449	C₂²×C₁₃	1	2	yes	complemented
645	#449	C₂²×C₁₃	1	2	yes	complemented
646	#447	C₂²×C₁₃	1	2	yes	—
647	#447	C₂²×C₁₃	1	2	yes	complemented
648	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
650	#442	C₂²×C₁₃	1	2	yes	—
651	#442	C₂²×C₁₃	1	2	yes	complemented
652	#442	C₂²×C₁₃	1	2	yes	complemented
653	#440	C₂²×C₁₃	1	2	yes	complemented
654	#440	C₂²×C₁₃	1	2	yes	complemented
655	#440	C₂²×C₁₃	1	2	yes	complemented
656	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
657	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
658	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
659	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
660	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
661	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
662	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
663	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
664	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
665	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
666	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
667	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
668	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
669	#435	C₂²×C₁₃	1	2	yes	complemented
670	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
671	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
672	#433	C₂²×C₁₃	1	2	yes	complemented
673	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
674	#428	C₂²×C₁₃	1	2	yes	complemented
675	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
676	#416	C₂²×C₁₃	1	2	yes	complemented
677	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
678	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
679	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
680	#405	C₂²×C₁₃	1	2	yes	complemented
681	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
682	C₂²×C₁₃	—	2	1	no	—
683	C₂²×C₁₃	—	2	1	no	—
684	C₂²×C₁₃	—	2	2	no	—
685	C₂²×C₁₃	—	2	2	no	—
686	C₂²×C₁₃	—	2	2	no	—
687	C₂²×C₁₃	—	2	2	no	—
688	C₂²×C₁₃	—	2	2	no	—
689	C₂²×C₁₃	—	4	1	no	—
690	C₂²×C₁₃	—	4	1	no	—
691	C₂²×C₁₃	—	4	1	no	—
692	C₂²×C₁₃	—	4	1	no	—
693	C₂²×C₁₃	—	4	1	no	—
694	C₂²×C₁₃	—	4	1	no	—
695	C₂²×C₁₃	—	4	2	no	—
696	C₂²×C₁₃	—	4	1	no	—
697	C₂²×C₁₃	—	4	1	no	—
698	C₂²×C₁₃	—	4	2	no	—
699	C₂²×C₁₃	—	4	2	no	—
700	C₂²×C₁₃	—	4	1	no	—
701	C₂²×C₁₃	—	4	1	no	—
702	C₂²×C₁₃	—	8	4	no	—
703	C₂²×C₁₃	—	8	4	no	—
704	C₂²×C₁₃	—	16	4	no	—
705	C₂²×C₁₃	#577	1	2	yes	—
706	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
707	C₄×C₁₃	—	2	2	no	—
708	C₄×C₁₃	—	2	1	no	—
709	C₄×C₁₃	—	2	1	no	—
710	C₄×C₁₃	—	2	2	no	—
711	C₄×C₁₃	—	2	1	no	—
712	C₄×C₁₃	—	2	1	no	—
713	C₄×C₁₃	—	2	2	no	—
714	C₄×C₁₃	—	4	2	no	—
715	C₄×C₁₃	—	4	1	no	—
716	C₄×C₁₃	—	4	1	no	—
717	C₄×C₁₃	—	4	1	no	—
718	C₄×C₁₃	—	4	1	no	—
719	C₄×C₁₃	—	4	2	no	—
720	C₄×C₁₃	—	4	2	no	—
721	C₄×C₁₃	#576	1	2	yes	—
722	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
723	C₄×C₁₃	#585	1	1	yes	characteristic
724	C₂×#41	—	2	1	no	—
725	C₂×#41	—	2	1	no	—
726	C₂×#41	—	2	1	no	—
727	C₂×#41	C₂³×C₁₃	1	2	yes	—
728	C₂²×Q₈	—	2	1	no	—
729	C₂²×D₄	—	2	2	no	—
730	C₂²×D₄	—	2	1	no	—
731	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
732	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
733	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
734	C₂³×C₄	—	2	1	no	—
735	C₂³×C₄	—	2	1	no	—
736	AGL(1,ℤ/8)	—	2	8	no	—
737	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
739	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
741	C₂×D₈	—	2	4	no	—
742	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
743	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
744	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
745	C₂×D₈	C₂³×C₁₃	1	2	yes	—
746	C₂×D₈	C₂³×C₁₃	1	2	yes	—
747	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
748	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
749	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
750	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
751	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
752	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
753	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
754	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
755	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
756	#127	C₂³×C₁₃	1	1	yes	characteristic
757	#127	C₂³×C₁₃	1	2	yes	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#126	D₄×C₁₃	1	2	yes	—
762	#125	—	2	2	no	—
763	#125	—	2	1	no	—
764	#125	D₄×C₁₃	1	1	yes	characteristic
765	#125	C₂³×C₁₃	1	2	yes	—
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	1	no	—
769	#124	D₄×C₁₃	1	1	yes	characteristic
770	#124	C₂³×C₁₃	1	2	yes	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	D₄×C₁₃	1	2	yes	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
790	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
791	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
792	#121	—	2	2	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	1	no	—
796	#121	—	2	1	no	—
797	#121	—	2	1	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	D₄×C₁₃	1	1	yes	characteristic
804	#121	C₂³×C₁₃	1	2	yes	—
805	#121	C₂³×C₁₃	1	2	yes	—
806	#121	C₂³×C₁₃	1	2	yes	—
807	#121	C₂³×C₁₃	1	2	yes	—
808	#120	—	2	2	no	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	#120	—	2	2	no	—
812	C₄×Q₈	—	2	1	no	—
813	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
814	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
815	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₁₃	1	2	yes	—
836	C₄×D₄	C₂³×C₁₃	1	2	yes	—
837	C₄×D₄	C₂³×C₁₃	1	2	yes	—
838	C₄×D₄	C₂³×C₁₃	1	2	yes	—
839	C₄×D₄	C₂³×C₁₃	1	2	yes	—
840	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
841	#117	—	2	1	no	—
842	#117	—	2	2	no	—
843	#117	—	2	1	no	—
844	#117	—	2	1	no	—
845	#117	C₂³×C₁₃	1	2	yes	—
846	#117	C₂³×C₁₃	1	2	yes	—
847	C₂×C₄⋊C₄	—	2	2	no	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
851	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
852	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
853	C₂×C₂²⋊C₄	—	2	1	no	—
854	C₂×C₂²⋊C₄	—	2	1	no	—
855	C₂×C₂²⋊C₄	—	2	2	no	—
856	C₂×C₂²⋊C₄	—	2	2	no	—
857	C₂×C₂²⋊C₄	—	2	2	no	—
858	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
859	#107	C₂³×C₁₃	1	1	yes	characteristic
860	#107	C₂³×C₁₃	1	1	yes	characteristic
861	#107	C₂³×C₁₃	1	1	yes	characteristic
862	#107	C₂³×C₁₃	1	1	yes	characteristic
863	#107	C₂³×C₁₃	1	2	yes	—
864	#107	C₂³×C₁₃	1	2	yes	—
865	#106	C₂³×C₁₃	1	2	yes	—
866	#106	C₂³×C₁₃	1	2	yes	—
867	#106	C₂³×C₁₃	1	2	yes	—
868	#106	C₂³×C₁₃	1	2	yes	—
869	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
870	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
871	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
872	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
873	#103	C₂³×C₁₃	1	2	yes	—
874	#103	C₂³×C₁₃	1	2	yes	—
875	#103	C₂³×C₁₃	1	2	yes	—
876	#103	C₂³×C₁₃	1	2	yes	—
877	#102	C₂³×C₁₃	1	1	yes	characteristic
878	#102	C₂³×C₁₃	1	1	yes	characteristic
879	#102	C₂³×C₁₃	1	1	yes	characteristic
880	#102	C₂³×C₁₃	1	1	yes	characteristic
881	#102	C₂³×C₁₃	1	1	yes	characteristic
882	#102	C₂³×C₁₃	1	1	yes	characteristic
883	#102	C₂³×C₁₃	1	1	yes	characteristic
884	#102	C₂³×C₁₃	1	1	yes	characteristic
885	#102	C₂³×C₁₃	1	2	yes	—
886	#102	C₂³×C₁₃	1	2	yes	—
887	#102	C₂³×C₁₃	1	2	yes	—
888	#102	C₂³×C₁₃	1	2	yes	—
889	#102	C₂³×C₁₃	1	2	yes	—
890	#102	C₂³×C₁₃	1	2	yes	—
891	#102	C₂³×C₁₃	1	2	yes	—
892	#102	C₂³×C₁₃	1	2	yes	—
893	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
894	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
896	#97	C₂³×C₁₃	1	2	yes	—
897	#97	C₂³×C₁₃	1	2	yes	—
898	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
899	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
900	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
902	C₄×C₈	C₂³×C₁₃	1	2	yes	—
903	C₂×C₁₃	—	2	2	no	—
904	C₂×C₁₃	—	4	2	no	—
905	C₂×C₁₃	—	4	2	no	—
906	C₂×C₁₃	—	4	2	no	—
907	C₂×C₁₃	—	8	1	no	—
908	C₂×C₁₃	—	8	1	no	—
909	C₂×C₁₃	—	8	2	no	—
910	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
911	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
912	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
913	C₂⁴	—	2	1	no	—
914	C₂⁴	—	2	1	no	—
915	C₂⁴	—	2	2	no	—
916	#41	—	2	4	no	—
917	#41	—	4	2	no	—
918	#41	—	8	2	no	—
919	#41	—	8	2	no	—
920	#41	—	8	2	no	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	2	2	no	—
923	C₂×Q₈	—	2	1	no	—
924	C₂×Q₈	—	8	2	no	—
925	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	4	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	4	1	no	—
943	C₂×D₄	—	4	1	no	—
944	C₂×D₄	—	4	2	no	—
945	C₂×D₄	—	8	2	no	—
946	C₂×D₄	—	8	4	no	—
947	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
948	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
949	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
950	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
951	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
952	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
953	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	8	2	no	—
971	C₂²×C₄	—	8	2	no	—
972	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
973	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
974	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
975	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
976	SD₁₆	—	2	4	no	—
977	SD₁₆	—	2	4	no	—
978	SD₁₆	—	4	2	no	—
979	SD₁₆	—	4	2	no	—
980	D₈	—	2	2	no	—
981	D₈	—	2	2	no	—
982	D₈	—	2	4	no	—
983	D₈	—	2	2	no	—
984	D₈	—	4	2	no	—
985	D₈	C₁₃×#41	1	4	yes	complemented
986	M₁₆	—	2	4	no	—
987	C₂×C₈	—	2	2	no	—
988	C₂×C₈	—	4	2	no	—
989	C₂×C₈	—	4	1	no	—
990	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
991	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
992	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
993	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
994	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
995	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1011	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1012	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1013	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1014	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1015	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1018	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1019	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1020	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1021	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1044	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1047	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1048	C₄²	—	2	2	no	—
1049	C₄²	—	2	2	no	—
1050	C₄²	—	2	2	no	—
1051	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1052	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1053	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1054	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₁₃	1	2	yes	—
1056	C₁₃	#61496	1	1	yes	characteristic, direct product factor, Sylow
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	2	no	—
1062	C₂³	—	4	2	no	—
1063	C₂³	—	4	2	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	2	no	—
1066	C₂³	—	4	2	no	—
1067	C₂³	—	8	1	no	—
1068	C₂³	—	8	1	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	—	8	2	no	—
1071	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1072	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1073	Q₈	—	2	2	no	—
1074	Q₈	—	2	2	no	—
1075	Q₈	—	2	2	no	—
1076	Q₈	—	4	2	no	—
1077	Q₈	—	8	2	no	—
1078	Q₈	—	8	1	no	—
1079	D₄	—	2	4	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	4	4	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	4	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	no	—
1097	D₄	—	8	1	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	2	no	—
1100	D₄	—	8	2	no	—
1101	D₄	C₂×C₁₃×#41	1	2	yes	—
1102	D₄	C₂×C₁₃×#41	1	2	yes	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	4	4	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	2	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	8	1	no	—
1122	C₂×C₄	—	8	1	no	—
1123	C₂×C₄	—	8	1	no	—
1124	C₂×C₄	—	8	1	no	—
1125	C₂×C₄	—	8	2	no	—
1126	C₂×C₄	—	8	2	no	—
1127	C₂×C₄	—	8	2	no	—
1128	C₂×C₄	—	8	2	no	—
1129	C₂×C₄	—	8	1	no	—
1130	C₂×C₄	—	8	1	no	—
1131	C₂×C₄	—	8	2	no	—
1132	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1133	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1134	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1135	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1136	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1137	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1140	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1141	C₈	—	2	1	no	—
1142	C₈	—	2	2	no	—
1143	C₈	—	2	1	no	—
1144	C₈	—	2	2	no	—
1145	C₈	—	2	1	no	—
1146	C₈	C₂×C₁₃×#41	1	2	yes	—
1147	C₂²	—	2	1	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	2	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	8	4	no	—
1168	C₂²	—	8	4	no	—
1169	C₂²	—	16	4	no	—
1170	C₂²	C₁₃×#577	1	2	yes	—
1171	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1172	C₄	—	2	1	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	2	1	no	—
1175	C₄	—	2	1	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	4	1	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	2	no	—
1184	C₄	—	4	2	no	—
1185	C₄	—	4	2	no	—
1186	C₄	C₁₃×#576	1	2	yes	—
1187	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1188	C₄	C₁₃×#585	1	1	yes	characteristic
1189	C₂	—	2	2	no	—
1190	C₂	—	4	2	no	—
1191	C₂	—	4	2	no	—
1192	C₂	—	4	2	no	—
1193	C₂	—	8	1	no	—
1194	C₂	—	8	1	no	—
1195	C₂	—	8	2	no	—
1196	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1197	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
1198	C₂	C₂×C₁₃×#577	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 ◁ C₁₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3520	C₂	semidirect
2. C₁₃×#3519	C₂	semidirect
3. C₁₃×#3397	C₂	semidirect
4. C₁₃×#3384	C₂	semidirect
5. C₁₃×#3360	C₂	semidirect
6. C₁₃×#3358	C₂	semidirect
7. C₁₃×#3354	C₂	semidirect
8. C₁₃×#3346	C₂	semidirect
9. C₁₃×#3303	C₂	semidirect
10. C₁₃×#3297	C₂	semidirect
11. C₁₃×#3295	C₂	semidirect
12. C₁₃×#3294	C₂	semidirect
13. C₁₃×#3272	C₂	semidirect
14. C₁₃×#3264	C₂	semidirect
15. C₁₃×#3179	C₂	semidirect
16. C₁₃×#3167	C₂	semidirect
17. C₁₃×#3119	C₂	semidirect
18. C₁₃×#3118	C₂	semidirect
19. C₁₃×#3110	C₂	semidirect
20. C₁₃×#3109	C₂	semidirect
21. C₁₃×#2966	C₂	semidirect
22. C₁₃×#2946	C₂	semidirect
23. C₂×C₄×C₁₃×D₈	C₂	semidirect
26. C₁₃×#556	C₂²	semidirect
27. C₁₃×#555	C₂²	semidirect
28. C₁₃×#554	C₂²	semidirect
29. C₁₃×#554	C₂²	semidirect
34. C₁₃×#550	C₂²	semidirect
35. D₄×Q₈×C₁₃	C₂²	semidirect
37. C₁₃×#547	C₂²	semidirect
38. C₁₃×#547	C₂²	semidirect
41. C₁₃×#546	C₂²	semidirect
43. D₄²×C₁₃	C₂²	semidirect
44. C₁₃×#542	C₂²	semidirect
45. C₁₃×#540	C₂²	semidirect
48. C₁₃×#533	C₂²	semidirect
55. C₁₃×#520	C₂²	semidirect
56. C₁₃×#518	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×#492	C₂²	semidirect
63. C₁₃×#488	C₂²	semidirect
64. C₁₃×#487	C₂²	semidirect
65. C₁₃×#486	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#484	C₂²	semidirect
69. C₁₃×#482	C₂²	semidirect
70. C₁₃×#481	C₂²	semidirect
71. C₁₃×#481	C₂²	semidirect
72. C₁₃×#480	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
74. C₁₃×#478	C₂²	semidirect
75. C₁₃×#476	C₂²	semidirect
76. C₁₃×#476	C₂²	semidirect
77. C₁₃×#476	C₂²	semidirect
78. C₁₃×#474	C₂²	semidirect
79. C₁₃×#474	C₂²	semidirect
80. C₁₃×#474	C₂²	semidirect
81. C₁₃×#469	C₂²	semidirect
82. C₁₃×#468	C₂²	semidirect
83. C₁₃×#466	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#465	C₂²	semidirect
88. C₁₃×#463	C₂²	semidirect
89. C₁₃×#461	C₂²	semidirect
90. C₁₃×#461	C₂²	semidirect
91. C₁₃×#460	C₂²	semidirect
92. C₁₃×#459	C₂²	semidirect
93. C₁₃×#459	C₂²	semidirect
94. C₁₃×#459	C₂²	semidirect
96. C₁₃×#450	C₂²	semidirect
97. C₁₃×#449	C₂²	semidirect
98. C₁₃×#449	C₂²	semidirect
100. C₁₃×#447	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₈×Q₈×C₁₃	C₂²	semidirect
104. C₁₃×#442	C₂²	semidirect
105. C₁₃×#442	C₂²	semidirect
106. C₁₃×#440	C₂²	semidirect
107. C₁₃×#440	C₂²	semidirect
108. C₁₃×#440	C₂²	semidirect
109. C₄×C₁₃×SD₁₆	C₂²	semidirect
110. C₄×C₁₃×SD₁₆	C₂²	semidirect
111. C₄×C₁₃×SD₁₆	C₂²	semidirect
116. C₄×C₁₃×D₈	C₂²	semidirect
117. C₄×C₁₃×D₈	C₂²	semidirect
118. C₄×C₁₃×D₈	C₂²	semidirect
119. C₄×C₁₃×D₈	C₂²	semidirect
120. C₄×C₁₃×D₈	C₂²	semidirect
121. C₁₃×#436	C₂²	semidirect
122. C₁₃×#435	C₂²	semidirect
123. C₈×D₄×C₁₃	C₂²	semidirect
124. C₈×D₄×C₁₃	C₂²	semidirect
125. C₁₃×#433	C₂²	semidirect
126. C₁₃×#432	C₂²	semidirect
127. C₁₃×#428	C₂²	semidirect
128. C₂×C₁₃×#107	C₂²	semidirect
129. C₁₃×#416	C₂²	semidirect
131. C₂×C₁₃×#102	C₂²	semidirect
132. C₂×C₁₃×#102	C₂²	semidirect
133. C₁₃×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₁₃	C₂²	semidirect
314. #61496	C₁₃	direct (N × H)
387. C₁₃×D₈	#41	semidirect
458. #3520	C₂×C₁₃	semidirect
459. #3519	C₂×C₁₃	semidirect
460. #3397	C₂×C₁₃	semidirect
461. #3384	C₂×C₁₃	semidirect
462. #3360	C₂×C₁₃	semidirect
463. #3358	C₂×C₁₃	semidirect
464. #3354	C₂×C₁₃	semidirect
465. #3346	C₂×C₁₃	semidirect
466. #3303	C₂×C₁₃	semidirect
467. #3297	C₂×C₁₃	semidirect
468. #3295	C₂×C₁₃	semidirect
469. #3294	C₂×C₁₃	semidirect
470. #3272	C₂×C₁₃	semidirect
471. #3264	C₂×C₁₃	semidirect
472. #3179	C₂×C₁₃	semidirect
473. #3167	C₂×C₁₃	semidirect
474. #3119	C₂×C₁₃	semidirect
475. #3118	C₂×C₁₃	semidirect
476. #3110	C₂×C₁₃	semidirect
477. #3109	C₂×C₁₃	semidirect
478. #2966	C₂×C₁₃	semidirect
479. #2946	C₂×C₁₃	semidirect
480. C₂×C₄×D₈	C₂×C₁₃	semidirect
573. #556	C₂²×C₁₃	semidirect
574. #555	C₂²×C₁₃	semidirect
575. #554	C₂²×C₁₃	semidirect
576. #554	C₂²×C₁₃	semidirect
581. #550	C₂²×C₁₃	semidirect
582. D₄×Q₈	C₂²×C₁₃	semidirect
584. #547	C₂²×C₁₃	semidirect
585. #547	C₂²×C₁₃	semidirect
588. #546	C₂²×C₁₃	semidirect
590. D₄²	C₂²×C₁₃	semidirect
591. #542	C₂²×C₁₃	semidirect
592. #540	C₂²×C₁₃	semidirect
595. #533	C₂²×C₁₃	semidirect
602. #520	C₂²×C₁₃	semidirect
603. #518	C₂²×C₁₃	semidirect
605. C₂×C₄×D₄	C₂²×C₁₃	semidirect
606. #501	C₂²×C₁₃	semidirect
607. #498	C₂²×C₁₃	semidirect
608. #496	C₂²×C₁₃	semidirect
609. #492	C₂²×C₁₃	semidirect
610. #488	C₂²×C₁₃	semidirect
611. #487	C₂²×C₁₃	semidirect
612. #486	C₂²×C₁₃	semidirect
613. #486	C₂²×C₁₃	semidirect
614. #485	C₂²×C₁₃	semidirect
615. #484	C₂²×C₁₃	semidirect
616. #482	C₂²×C₁₃	semidirect
617. #481	C₂²×C₁₃	semidirect
618. #481	C₂²×C₁₃	semidirect
619. #480	C₂²×C₁₃	semidirect
620. #479	C₂²×C₁₃	semidirect
621. #478	C₂²×C₁₃	semidirect
622. #476	C₂²×C₁₃	semidirect
623. #476	C₂²×C₁₃	semidirect
624. #476	C₂²×C₁₃	semidirect
625. #474	C₂²×C₁₃	semidirect
626. #474	C₂²×C₁₃	semidirect
627. #474	C₂²×C₁₃	semidirect
628. #469	C₂²×C₁₃	semidirect
629. #468	C₂²×C₁₃	semidirect
630. #466	C₂²×C₁₃	semidirect
631. #465	C₂²×C₁₃	semidirect
632. #465	C₂²×C₁₃	semidirect
633. #465	C₂²×C₁₃	semidirect
635. #463	C₂²×C₁₃	semidirect
636. #461	C₂²×C₁₃	semidirect
637. #461	C₂²×C₁₃	semidirect
638. #460	C₂²×C₁₃	semidirect
639. #459	C₂²×C₁₃	semidirect
640. #459	C₂²×C₁₃	semidirect
641. #459	C₂²×C₁₃	semidirect
643. #450	C₂²×C₁₃	semidirect
644. #449	C₂²×C₁₃	semidirect
645. #449	C₂²×C₁₃	semidirect
647. #447	C₂²×C₁₃	semidirect
648. #446	C₂²×C₁₃	semidirect
649. C₈×Q₈	C₂²×C₁₃	semidirect
651. #442	C₂²×C₁₃	semidirect
652. #442	C₂²×C₁₃	semidirect
653. #440	C₂²×C₁₃	semidirect
654. #440	C₂²×C₁₃	semidirect
655. #440	C₂²×C₁₃	semidirect
656. C₄×SD₁₆	C₂²×C₁₃	semidirect
657. C₄×SD₁₆	C₂²×C₁₃	semidirect
658. C₄×SD₁₆	C₂²×C₁₃	semidirect
663. C₄×D₈	C₂²×C₁₃	semidirect
664. C₄×D₈	C₂²×C₁₃	semidirect
665. C₄×D₈	C₂²×C₁₃	semidirect
666. C₄×D₈	C₂²×C₁₃	semidirect
667. C₄×D₈	C₂²×C₁₃	semidirect
668. #436	C₂²×C₁₃	semidirect
669. #435	C₂²×C₁₃	semidirect
670. C₈×D₄	C₂²×C₁₃	semidirect
671. C₈×D₄	C₂²×C₁₃	semidirect
672. #433	C₂²×C₁₃	semidirect
673. #432	C₂²×C₁₃	semidirect
674. #428	C₂²×C₁₃	semidirect
675. C₂×#107	C₂²×C₁₃	semidirect
676. #416	C₂²×C₁₃	semidirect
678. C₂×#102	C₂²×C₁₃	semidirect
679. C₂×#102	C₂²×C₁₃	semidirect
680. #405	C₂²×C₁₃	semidirect
681. C₂×C₄×C₈	C₂²×C₁₃	semidirect
985. D₈	C₁₃×#41	semidirect
1056. C₁₃	#61496	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×#3520	2
C₁₃×#3519	2
C₁₃×#3397	2
C₁₃×#3384	2
C₁₃×#3360	2
C₁₃×#3358	2
C₁₃×#3354	2
C₁₃×#3346	2
C₁₃×#3303	2
C₁₃×#3297	2
C₁₃×#3295	2
C₁₃×#3294	2
C₁₃×#3272	2
C₁₃×#3264	2
C₁₃×#3179	2
C₁₃×#3167	2
C₁₃×#3119	2
C₁₃×#3118	2
C₁₃×#3110	2
C₁₃×#3109	2
C₁₃×#2966	2
C₁₃×#2946	2
C₂×C₄×C₁₃×D₈	2
#61496	13

Subgroups — C13×#61496 #15747835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61496 #15747835