Subgroups — C₁₃×#61452 #15747791

Order 3328.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3343	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3310	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3308	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3265	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3182	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×#3112	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3110	C₂	1	1	yes	maximal, characteristic, 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×#440	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×SD₁₆	C₂²	1	2	yes	—
27	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#556	—	2	1	no	—
29	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#552	—	2	2	no	—
31	C₁₃×#552	C₂²	1	2	yes	complemented
32	C₁₃×#550	C₂²	1	1	yes	characteristic
33	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#548	—	2	1	no	—
36	C₁₃×#548	C₂²	1	2	yes	complemented
37	C₁₃×#547	—	2	1	no	—
38	C₁₃×#547	C₂²	1	1	yes	characteristic
39	C₁₃×#547	C₂²	1	2	yes	—
40	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#546	—	2	1	no	—
42	C₁₃×#546	—	2	2	no	—
43	D₄²×C₁₃	C₂²	1	2	yes	—
44	D₄²×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#533	—	2	1	no	—
46	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#532	C₂²	1	2	yes	—
48	C₁₃×#532	C₂²	1	1	yes	characteristic
49	C₁₃×#529	—	2	2	no	—
50	C₁₃×#529	C₂²	1	2	yes	complemented
51	C₁₃×#525	—	2	2	no	—
52	C₁₃×#525	—	2	1	no	—
53	C₄×C₁₃×#41	—	2	1	no	—
54	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
55	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
59	C₁₃×#501	C₂²	1	2	yes	complemented
60	C₁₃×#500	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×#490	C₂²	1	2	yes	complemented
64	C₁₃×#489	C₂²	1	2	yes	complemented
65	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#484	C₂²	1	2	yes	complemented
68	C₁₃×#483	C₂²	1	2	yes	complemented
69	C₁₃×#482	C₂²	1	2	yes	complemented
70	C₁₃×#480	C₂²	1	2	yes	complemented
71	C₁₃×#480	C₂²	1	2	yes	complemented
72	C₁₃×#480	C₂²	1	2	yes	complemented
73	C₁₃×#478	C₂²	1	2	yes	—
74	C₁₃×#478	C₂²	1	2	yes	complemented
75	C₁₃×#477	C₂²	1	2	yes	complemented
76	C₁₃×#477	C₂²	1	2	yes	complemented
77	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#474	C₂²	1	1	yes	characteristic
79	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
80	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#468	C₂²	1	2	yes	complemented
82	C₁₃×#468	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	—
88	C₁₃×#463	C₂²	1	2	yes	complemented
89	C₁₃×#461	C₂²	1	1	yes	characteristic
90	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#460	C₂²	1	2	yes	complemented
92	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#460	C₂²	1	2	yes	complemented
94	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#450	C₂²	1	2	yes	—
96	C₁₃×#450	C₂²	1	2	yes	—
97	C₁₃×#449	C₂²	1	2	yes	complemented
98	C₁₃×#448	C₂²	1	2	yes	complemented
99	C₁₃×#448	C₂²	1	2	yes	complemented
100	C₁₃×#447	C₂²	1	2	yes	—
101	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#442	C₂²	1	1	yes	characteristic
104	C₁₃×#442	C₂²	1	2	yes	complemented
105	C₁₃×#442	C₂²	1	1	yes	characteristic, complemented
106	C₁₃×#440	C₂²	1	2	yes	—
107	C₁₃×#440	C₂²	1	2	yes	—
108	C₁₃×#440	C₂²	1	2	yes	—
109	C₁₃×#440	C₂²	1	1	yes	characteristic
110	C₁₃×#440	C₂²	1	2	yes	complemented
111	C₁₃×#440	C₂²	1	2	yes	complemented
112	C₁₃×#440	C₂²	1	2	yes	complemented
113	C₁₃×#440	C₂²	1	1	yes	characteristic, complemented
114	C₁₃×#440	C₂²	1	2	yes	complemented
115	C₁₃×#440	C₂²	1	2	yes	complemented
116	C₁₃×#440	C₂²	1	2	yes	complemented
117	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
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	1	yes	characteristic, complemented
126	C₁₃×#432	C₂²	1	2	yes	complemented
127	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
129	C₁₃×#418	C₂²	1	1	yes	characteristic
130	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
132	C₂×C₁₃×#102	C₂²	1	2	yes	—
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	1	no	—
139	C₂×C₁₃×#41	—	2	2	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×Q₈×C₁₃	C₂³	1	2	yes	—
146	C₂²×D₄×C₁₃	—	2	2	no	—
147	C₂²×D₄×C₁₃	—	2	1	no	—
148	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
149	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₁₃	—	2	2	no	—
151	C₂³×C₄×C₁₃	—	2	1	no	—
152	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
153	C₂×C₁₃×SD₁₆	—	2	8	no	—
154	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
158	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
159	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
160	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×D₈	C₂³	1	2	yes	—
164	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
167	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
168	C₁₃×C₄⋊Q₈	—	2	1	no	—
169	C₁₃×C₄⋊Q₈	—	2	1	no	—
170	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
174	C₁₃×#127	C₂³	1	1	yes	characteristic
175	C₁₃×#127	C₂³	1	2	yes	—
176	C₁₃×#126	—	2	2	no	—
177	C₁₃×#126	—	2	2	no	—
178	C₁₃×#126	—	2	2	no	—
179	C₁₃×#125	—	2	2	no	—
180	C₁₃×#125	—	2	2	no	—
181	C₁₃×#125	—	2	1	no	—
182	C₁₃×#125	C₂³	1	2	yes	—
183	C₁₃×#124	—	2	2	no	—
184	C₁₃×#124	—	2	1	no	—
185	C₁₃×#124	—	2	2	no	—
186	C₁₃×#124	C₂³	1	2	yes	—
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×#123	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	—	2	1	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	1	no	—
199	C₁₃×C₂²⋊Q₈	—	2	1	no	—
200	C₁₃×C₂²⋊Q₈	—	2	2	no	—
201	C₁₃×C₂²⋊Q₈	—	2	2	no	—
202	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₁₃×#121	—	2	2	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	1	no	—
210	C₁₃×#121	—	2	2	no	—
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	C₄×Q₈×C₁₃	—	2	1	no	—
219	C₄×Q₈×C₁₃	—	2	2	no	—
220	C₄×Q₈×C₁₃	—	2	2	no	—
221	C₄×Q₈×C₁₃	—	2	1	no	—
222	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
223	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
227	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
228	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₁₃	—	2	1	no	—
230	C₄×D₄×C₁₃	—	2	2	no	—
231	C₄×D₄×C₁₃	—	2	1	no	—
232	C₄×D₄×C₁₃	—	2	1	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	1	no	—
237	C₄×D₄×C₁₃	—	2	2	no	—
238	C₄×D₄×C₁₃	—	2	1	no	—
239	C₄×D₄×C₁₃	—	2	2	no	—
240	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
241	C₄×D₄×C₁₃	D₄	1	2	yes	—
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	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	1	yes	characteristic
251	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₃	C₂³	1	2	yes	—
253	C₁₃×#117	—	2	1	no	—
254	C₁₃×#117	—	2	1	no	—
255	C₁₃×#117	—	2	2	no	—
256	C₁₃×#117	—	2	1	no	—
257	C₁₃×#117	—	2	2	no	—
258	C₁₃×#117	D₄	1	2	yes	—
259	C₁₃×#117	D₄	1	1	yes	characteristic
260	C₁₃×#117	C₂³	1	1	yes	characteristic
261	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₄²×C₁₃	—	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	2	yes	—
273	C₁₃×#107	C₂³	1	2	yes	—
274	C₁₃×#107	C₂³	1	2	yes	—
275	C₁₃×#107	C₂³	1	1	yes	characteristic
276	C₁₃×#107	C₂³	1	2	yes	—
277	C₁₃×#107	C₂³	1	2	yes	—
278	C₁₃×#106	C₂³	1	1	yes	characteristic
279	C₁₃×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
287	C₁₃×#103	C₂³	1	2	yes	—
288	C₁₃×#103	C₂³	1	2	yes	—
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	#61452	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂⁴×C₁₃	—	2	1	no	—
317	C₂⁴×C₁₃	—	2	2	no	—
318	C₁₃×#41	—	2	4	no	—
319	C₁₃×#41	—	2	2	no	—
320	C₁₃×#41	—	4	1	no	—
321	C₁₃×#41	—	4	8	no	—
322	C₁₃×#41	—	4	4	no	—
323	C₁₃×#41	—	4	8	no	—
324	C₁₃×#41	—	4	4	no	—
325	C₁₃×#41	—	4	4	no	—
326	C₁₃×#41	—	4	4	no	—
327	C₂×Q₈×C₁₃	—	2	2	no	—
328	C₂×Q₈×C₁₃	—	2	1	no	—
329	C₂×Q₈×C₁₃	—	2	2	no	—
330	C₂×Q₈×C₁₃	—	2	1	no	—
331	C₂×Q₈×C₁₃	—	2	4	no	—
332	C₂×Q₈×C₁₃	—	4	2	no	—
333	C₂×Q₈×C₁₃	—	4	4	no	—
334	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
335	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
336	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₁₃	—	2	4	no	—
338	C₂×D₄×C₁₃	—	2	2	no	—
339	C₂×D₄×C₁₃	—	2	1	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	2	no	—
344	C₂×D₄×C₁₃	—	2	1	no	—
345	C₂×D₄×C₁₃	—	2	2	no	—
346	C₂×D₄×C₁₃	—	2	2	no	—
347	C₂×D₄×C₁₃	—	2	1	no	—
348	C₂×D₄×C₁₃	—	2	2	no	—
349	C₂×D₄×C₁₃	—	2	1	no	—
350	C₂×D₄×C₁₃	—	4	2	no	—
351	C₂×D₄×C₁₃	—	4	1	no	—
352	C₂×D₄×C₁₃	—	4	8	no	—
353	C₂×D₄×C₁₃	—	4	4	no	—
354	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
355	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
356	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
359	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₁₃	—	2	2	no	—
361	C₂²×C₄×C₁₃	—	2	2	no	—
362	C₂²×C₄×C₁₃	—	2	1	no	—
363	C₂²×C₄×C₁₃	—	2	2	no	—
364	C₂²×C₄×C₁₃	—	2	1	no	—
365	C₂²×C₄×C₁₃	—	2	1	no	—
366	C₂²×C₄×C₁₃	—	2	1	no	—
367	C₂²×C₄×C₁₃	—	2	1	no	—
368	C₂²×C₄×C₁₃	—	2	1	no	—
369	C₂²×C₄×C₁₃	—	2	2	no	—
370	C₂²×C₄×C₁₃	—	2	2	no	—
371	C₂²×C₄×C₁₃	—	2	1	no	—
372	C₂²×C₄×C₁₃	—	2	2	no	—
373	C₂²×C₄×C₁₃	—	2	1	no	—
374	C₂²×C₄×C₁₃	—	4	8	no	—
375	C₂²×C₄×C₁₃	—	4	4	no	—
376	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
377	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
379	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
382	C₁₃×SD₁₆	—	2	4	no	—
383	C₁₃×SD₁₆	—	2	2	no	—
384	C₁₃×SD₁₆	—	2	4	no	—
385	C₁₃×SD₁₆	—	2	4	no	—
386	C₁₃×SD₁₆	—	4	2	no	—
387	C₁₃×SD₁₆	—	4	2	no	—
388	C₁₃×SD₁₆	#41	1	4	yes	complemented
389	C₁₃×D₈	—	2	2	no	—
390	C₁₃×D₈	—	2	2	no	—
391	C₁₃×D₈	—	4	2	no	—
392	C₁₃×M₁₆	—	2	2	no	—
393	C₁₃×M₁₆	—	4	1	no	—
394	C₂×C₈×C₁₃	—	2	4	no	—
395	C₂×C₈×C₁₃	—	4	2	no	—
396	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
398	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
400	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
401	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
402	C₁₃×C₄⋊C₄	—	2	1	no	—
403	C₁₃×C₄⋊C₄	—	2	2	no	—
404	C₁₃×C₄⋊C₄	—	2	2	no	—
405	C₁₃×C₄⋊C₄	—	2	2	no	—
406	C₁₃×C₄⋊C₄	—	2	1	no	—
407	C₁₃×C₄⋊C₄	—	2	2	no	—
408	C₁₃×C₄⋊C₄	—	2	2	no	—
409	C₁₃×C₄⋊C₄	—	2	1	no	—
410	C₁₃×C₄⋊C₄	—	2	2	no	—
411	C₁₃×C₄⋊C₄	—	2	2	no	—
412	C₁₃×C₄⋊C₄	—	2	1	no	—
413	C₁₃×C₄⋊C₄	—	2	1	no	—
414	C₁₃×C₄⋊C₄	—	2	2	no	—
415	C₁₃×C₄⋊C₄	—	2	1	no	—
416	C₁₃×C₄⋊C₄	—	2	2	no	—
417	C₁₃×C₄⋊C₄	—	2	2	no	—
418	C₁₃×C₄⋊C₄	—	2	1	no	—
419	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
420	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
421	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
422	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
423	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
424	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
425	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
426	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
427	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
428	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
429	C₁₃×C₂²⋊C₄	—	2	2	no	—
430	C₁₃×C₂²⋊C₄	—	2	2	no	—
431	C₁₃×C₂²⋊C₄	—	2	1	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	2	no	—
436	C₁₃×C₂²⋊C₄	—	2	1	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	1	no	—
441	C₁₃×C₂²⋊C₄	—	2	1	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	—	2	2	no	—
446	C₁₃×C₂²⋊C₄	—	2	2	no	—
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	1	no	—
451	C₄²×C₁₃	—	2	1	no	—
452	C₄²×C₁₃	—	2	2	no	—
453	C₄²×C₁₃	—	2	2	no	—
454	C₄²×C₁₃	—	2	1	no	—
455	C₄²×C₁₃	—	2	2	no	—
456	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₁₃	C₂×D₄	1	2	yes	—
459	C₄²×C₁₃	C₂×D₄	1	2	yes	—
460	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
461	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
462	C₄²×C₁₃	C₂⁴	1	2	yes	—
463	#3482	C₂×C₁₃	1	1	yes	characteristic, complemented
464	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3397	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3386	C₂×C₁₃	1	1	yes	characteristic, complemented
467	#3368	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3367	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#3343	C₂×C₁₃	1	2	yes	complemented
470	#3334	C₂×C₁₃	1	1	yes	characteristic, complemented
471	#3310	C₂×C₁₃	1	2	yes	complemented
472	#3308	C₂×C₁₃	1	2	yes	complemented
473	#3298	C₂×C₁₃	1	1	yes	characteristic, complemented
474	#3294	C₂×C₁₃	1	1	yes	characteristic, complemented
475	D₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
476	#3265	C₂×C₁₃	1	2	yes	complemented
477	#3182	C₂×C₁₃	1	1	yes	characteristic, complemented
478	#3180	C₂×C₁₃	1	2	yes	complemented
479	#3115	C₂×C₁₃	1	1	yes	characteristic, complemented
480	#3114	C₂×C₁₃	1	2	yes	complemented
481	#3112	C₂×C₁₃	1	2	yes	complemented
482	#3110	C₂×C₁₃	1	1	yes	characteristic, complemented
483	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
484	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
485	C₂×#440	C₂×C₁₃	1	2	yes	complemented
486	C₂³×C₁₃	—	2	1	no	—
487	C₂³×C₁₃	—	2	1	no	—
488	C₂³×C₁₃	—	2	1	no	—
489	C₂³×C₁₃	—	2	2	no	—
490	C₂³×C₁₃	—	4	4	no	—
491	C₂³×C₁₃	—	4	2	no	—
492	C₂³×C₁₃	—	4	2	no	—
493	C₂³×C₁₃	—	4	4	no	—
494	C₂³×C₁₃	—	8	2	no	—
495	C₂³×C₁₃	—	8	1	no	—
496	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
497	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
498	Q₈×C₁₃	—	2	2	no	—
499	Q₈×C₁₃	—	2	1	no	—
500	Q₈×C₁₃	—	2	2	no	—
501	Q₈×C₁₃	—	2	2	no	—
502	Q₈×C₁₃	—	4	4	no	—
503	Q₈×C₁₃	—	4	4	no	—
504	Q₈×C₁₃	—	4	2	no	—
505	Q₈×C₁₃	—	4	2	no	—
506	Q₈×C₁₃	C₂×#41	1	2	yes	complemented
507	D₄×C₁₃	—	2	4	no	—
508	D₄×C₁₃	—	2	1	no	—
509	D₄×C₁₃	—	2	1	no	—
510	D₄×C₁₃	—	2	2	no	—
511	D₄×C₁₃	—	2	1	no	—
512	D₄×C₁₃	—	2	1	no	—
513	D₄×C₁₃	—	2	2	no	—
514	D₄×C₁₃	—	2	1	no	—
515	D₄×C₁₃	—	4	2	no	—
516	D₄×C₁₃	—	4	4	no	—
517	D₄×C₁₃	—	4	2	no	—
518	D₄×C₁₃	—	4	4	no	—
519	D₄×C₁₃	—	4	4	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	—	8	2	no	—
525	D₄×C₁₃	—	8	1	no	—
526	D₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
527	D₄×C₁₃	C₂×#41	1	2	yes	—
528	C₂×C₄×C₁₃	—	2	4	no	—
529	C₂×C₄×C₁₃	—	2	1	no	—
530	C₂×C₄×C₁₃	—	2	2	no	—
531	C₂×C₄×C₁₃	—	2	2	no	—
532	C₂×C₄×C₁₃	—	2	1	no	—
533	C₂×C₄×C₁₃	—	2	2	no	—
534	C₂×C₄×C₁₃	—	2	1	no	—
535	C₂×C₄×C₁₃	—	2	1	no	—
536	C₂×C₄×C₁₃	—	2	1	no	—
537	C₂×C₄×C₁₃	—	2	2	no	—
538	C₂×C₄×C₁₃	—	2	2	no	—
539	C₂×C₄×C₁₃	—	2	1	no	—
540	C₂×C₄×C₁₃	—	2	2	no	—
541	C₂×C₄×C₁₃	—	2	1	no	—
542	C₂×C₄×C₁₃	—	4	2	no	—
543	C₂×C₄×C₁₃	—	4	1	no	—
544	C₂×C₄×C₁₃	—	4	2	no	—
545	C₂×C₄×C₁₃	—	4	4	no	—
546	C₂×C₄×C₁₃	—	4	2	no	—
547	C₂×C₄×C₁₃	—	4	2	no	—
548	C₂×C₄×C₁₃	—	4	4	no	—
549	C₂×C₄×C₁₃	—	4	4	no	—
550	C₂×C₄×C₁₃	—	4	2	no	—
551	C₂×C₄×C₁₃	—	4	4	no	—
552	C₂×C₄×C₁₃	—	4	2	no	—
553	C₂×C₄×C₁₃	—	4	4	no	—
554	C₂×C₄×C₁₃	—	4	4	no	—
555	C₂×C₄×C₁₃	—	4	2	no	—
556	C₂×C₄×C₁₃	—	4	2	no	—
557	C₂×C₄×C₁₃	—	4	2	no	—
558	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
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	C₂²×D₄	1	2	yes	—
565	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
567	C₈×C₁₃	—	2	2	no	—
568	C₈×C₁₃	—	2	1	no	—
569	C₈×C₁₃	—	2	1	no	—
570	C₈×C₁₃	—	2	2	no	—
571	C₈×C₁₃	—	2	1	no	—
572	C₈×C₁₃	C₂×#41	1	2	yes	complemented
573	C₂²×#41	—	2	1	no	—
574	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
575	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
576	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
577	#556	—	2	1	no	—
578	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
579	#552	—	2	2	no	—
580	#552	C₂²×C₁₃	1	2	yes	complemented
581	#550	C₂²×C₁₃	1	1	yes	characteristic
582	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
583	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
584	#548	—	2	1	no	—
585	#548	C₂²×C₁₃	1	2	yes	complemented
586	#547	—	2	1	no	—
587	#547	C₂²×C₁₃	1	1	yes	characteristic
588	#547	C₂²×C₁₃	1	2	yes	—
589	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
590	#546	—	2	1	no	—
591	#546	—	2	2	no	—
592	D₄²	C₂²×C₁₃	1	2	yes	—
593	D₄²	C₂²×C₁₃	1	1	yes	characteristic
594	#533	—	2	1	no	—
595	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
596	#532	C₂²×C₁₃	1	2	yes	—
597	#532	C₂²×C₁₃	1	1	yes	characteristic
598	#529	—	2	2	no	—
599	#529	C₂²×C₁₃	1	2	yes	complemented
600	#525	—	2	2	no	—
601	#525	—	2	1	no	—
602	C₄×#41	—	2	1	no	—
603	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
604	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
605	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
606	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
607	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
608	#501	C₂²×C₁₃	1	2	yes	complemented
609	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
610	#496	C₂²×C₁₃	1	2	yes	complemented
611	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	#490	C₂²×C₁₃	1	2	yes	complemented
613	#489	C₂²×C₁₃	1	2	yes	complemented
614	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
615	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
616	#484	C₂²×C₁₃	1	2	yes	complemented
617	#483	C₂²×C₁₃	1	2	yes	complemented
618	#482	C₂²×C₁₃	1	2	yes	complemented
619	#480	C₂²×C₁₃	1	2	yes	complemented
620	#480	C₂²×C₁₃	1	2	yes	complemented
621	#480	C₂²×C₁₃	1	2	yes	complemented
622	#478	C₂²×C₁₃	1	2	yes	—
623	#478	C₂²×C₁₃	1	2	yes	complemented
624	#477	C₂²×C₁₃	1	2	yes	complemented
625	#477	C₂²×C₁₃	1	2	yes	complemented
626	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
627	#474	C₂²×C₁₃	1	1	yes	characteristic
628	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
629	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
630	#468	C₂²×C₁₃	1	2	yes	complemented
631	#468	C₂²×C₁₃	1	2	yes	complemented
632	#466	C₂²×C₁₃	1	2	yes	complemented
633	#466	C₂²×C₁₃	1	2	yes	complemented
634	#465	C₂²×C₁₃	1	2	yes	complemented
635	#465	C₂²×C₁₃	1	2	yes	complemented
636	#463	C₂²×C₁₃	1	2	yes	—
637	#463	C₂²×C₁₃	1	2	yes	complemented
638	#461	C₂²×C₁₃	1	1	yes	characteristic
639	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
640	#460	C₂²×C₁₃	1	2	yes	complemented
641	#460	C₂²×C₁₃	1	2	yes	complemented
642	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
643	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
644	#450	C₂²×C₁₃	1	2	yes	—
645	#450	C₂²×C₁₃	1	2	yes	—
646	#449	C₂²×C₁₃	1	2	yes	complemented
647	#448	C₂²×C₁₃	1	2	yes	complemented
648	#448	C₂²×C₁₃	1	2	yes	complemented
649	#447	C₂²×C₁₃	1	2	yes	—
650	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
651	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
652	#442	C₂²×C₁₃	1	1	yes	characteristic
653	#442	C₂²×C₁₃	1	2	yes	complemented
654	#442	C₂²×C₁₃	1	1	yes	characteristic, complemented
655	#440	C₂²×C₁₃	1	2	yes	—
656	#440	C₂²×C₁₃	1	2	yes	—
657	#440	C₂²×C₁₃	1	2	yes	—
658	#440	C₂²×C₁₃	1	1	yes	characteristic
659	#440	C₂²×C₁₃	1	2	yes	complemented
660	#440	C₂²×C₁₃	1	2	yes	complemented
661	#440	C₂²×C₁₃	1	1	yes	characteristic, complemented
662	#440	C₂²×C₁₃	1	2	yes	complemented
663	#440	C₂²×C₁₃	1	2	yes	complemented
664	#440	C₂²×C₁₃	1	2	yes	complemented
665	#440	C₂²×C₁₃	1	2	yes	complemented
666	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
667	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
668	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
669	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
670	#435	C₂²×C₁₃	1	2	yes	complemented
671	#435	C₂²×C₁₃	1	2	yes	complemented
672	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
673	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
674	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
675	#432	C₂²×C₁₃	1	2	yes	complemented
676	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
677	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
678	#418	C₂²×C₁₃	1	1	yes	characteristic
679	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
680	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
681	C₂×#102	C₂²×C₁₃	1	2	yes	—
682	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
683	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
684	C₂²×C₁₃	—	2	2	no	—
685	C₂²×C₁₃	—	2	2	no	—
686	C₂²×C₁₃	—	2	1	no	—
687	C₂²×C₁₃	—	2	1	no	—
688	C₂²×C₁₃	—	2	2	no	—
689	C₂²×C₁₃	—	2	1	no	—
690	C₂²×C₁₃	—	4	1	no	—
691	C₂²×C₁₃	—	4	1	no	—
692	C₂²×C₁₃	—	4	1	no	—
693	C₂²×C₁₃	—	4	2	no	—
694	C₂²×C₁₃	—	4	1	no	—
695	C₂²×C₁₃	—	4	1	no	—
696	C₂²×C₁₃	—	4	1	no	—
697	C₂²×C₁₃	—	4	2	no	—
698	C₂²×C₁₃	—	4	2	no	—
699	C₂²×C₁₃	—	4	1	no	—
700	C₂²×C₁₃	—	4	1	no	—
701	C₂²×C₁₃	—	8	8	no	—
702	C₂²×C₁₃	—	8	4	no	—
703	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
704	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
705	C₄×C₁₃	—	2	1	no	—
706	C₄×C₁₃	—	2	2	no	—
707	C₄×C₁₃	—	2	1	no	—
708	C₄×C₁₃	—	2	1	no	—
709	C₄×C₁₃	—	2	2	no	—
710	C₄×C₁₃	—	2	2	no	—
711	C₄×C₁₃	—	2	1	no	—
712	C₄×C₁₃	—	2	2	no	—
713	C₄×C₁₃	—	4	1	no	—
714	C₄×C₁₃	—	4	2	no	—
715	C₄×C₁₃	—	4	1	no	—
716	C₄×C₁₃	—	4	1	no	—
717	C₄×C₁₃	—	4	2	no	—
718	C₄×C₁₃	—	4	1	no	—
719	C₄×C₁₃	—	4	2	no	—
720	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
721	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
722	C₄×C₁₃	#585	1	1	yes	characteristic
723	C₂×#41	—	2	1	no	—
724	C₂×#41	—	2	1	no	—
725	C₂×#41	—	2	2	no	—
726	C₂×#41	—	2	1	no	—
727	C₂×#41	—	2	2	no	—
728	C₂×#41	—	2	1	no	—
729	C₂×#41	—	4	8	no	—
730	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
731	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
732	C₂²×Q₈	—	2	1	no	—
733	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
734	C₂²×D₄	—	2	2	no	—
735	C₂²×D₄	—	2	1	no	—
736	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
737	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
738	C₂³×C₄	—	2	2	no	—
739	C₂³×C₄	—	2	1	no	—
740	AGL(1,ℤ/8)	—	2	4	no	—
741	C₂×SD₁₆	—	2	8	no	—
742	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
746	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
749	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
750	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
751	C₂×D₈	C₂³×C₁₃	1	2	yes	—
752	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
753	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
754	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
755	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
756	C₄⋊Q₈	—	2	1	no	—
757	C₄⋊Q₈	—	2	1	no	—
758	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
759	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
760	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
761	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
762	#127	C₂³×C₁₃	1	1	yes	characteristic
763	#127	C₂³×C₁₃	1	2	yes	—
764	#126	—	2	2	no	—
765	#126	—	2	2	no	—
766	#126	—	2	2	no	—
767	#125	—	2	2	no	—
768	#125	—	2	2	no	—
769	#125	—	2	1	no	—
770	#125	C₂³×C₁₃	1	2	yes	—
771	#124	—	2	2	no	—
772	#124	—	2	1	no	—
773	#124	—	2	2	no	—
774	#124	C₂³×C₁₃	1	2	yes	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
791	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
792	#121	—	2	2	no	—
793	#121	—	2	2	no	—
794	#121	—	2	1	no	—
795	#121	—	2	2	no	—
796	#121	—	2	1	no	—
797	#121	—	2	1	no	—
798	#121	—	2	2	no	—
799	#121	C₂³×C₁₃	1	2	yes	—
800	#121	C₂³×C₁₃	1	2	yes	—
801	#121	C₂³×C₁₃	1	2	yes	—
802	#121	C₂³×C₁₃	1	2	yes	—
803	#120	—	2	2	no	—
804	#120	—	2	2	no	—
805	#120	—	2	2	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	2	no	—
808	C₄×Q₈	—	2	2	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
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×Q₈	C₂³×C₁₃	1	1	yes	characteristic
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
829	C₄×D₄	D₄×C₁₃	1	2	yes	—
830	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₁₃	1	2	yes	—
833	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₁₃	1	2	yes	—
835	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₁₃	1	2	yes	—
837	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₁₃	1	2	yes	—
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	—	2	2	no	—
844	#117	—	2	1	no	—
845	#117	—	2	2	no	—
846	#117	D₄×C₁₃	1	2	yes	—
847	#117	D₄×C₁₃	1	1	yes	characteristic
848	#117	C₂³×C₁₃	1	1	yes	characteristic
849	C₂×C₄⋊C₄	—	2	2	no	—
850	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
851	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
852	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
853	C₂×C₂²⋊C₄	—	2	2	no	—
854	C₂×C₂²⋊C₄	—	2	1	no	—
855	C₂×C₄²	—	2	2	no	—
856	C₂×C₄²	—	2	1	no	—
857	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
858	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
859	#107	C₂³×C₁₃	1	1	yes	characteristic
860	#107	C₂³×C₁₃	1	2	yes	—
861	#107	C₂³×C₁₃	1	2	yes	—
862	#107	C₂³×C₁₃	1	2	yes	—
863	#107	C₂³×C₁₃	1	1	yes	characteristic
864	#107	C₂³×C₁₃	1	2	yes	—
865	#107	C₂³×C₁₃	1	2	yes	—
866	#106	C₂³×C₁₃	1	1	yes	characteristic
867	#106	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
874	#103	C₂³×C₁₃	1	2	yes	—
875	#103	C₂³×C₁₃	1	2	yes	—
876	#103	C₂³×C₁₃	1	2	yes	—
877	#103	C₂³×C₁₃	1	1	yes	characteristic
878	#103	C₂³×C₁₃	1	2	yes	—
879	#103	C₂³×C₁₃	1	2	yes	—
880	#102	C₂³×C₁₃	1	1	yes	characteristic
881	#102	C₂³×C₁₃	1	2	yes	—
882	#102	C₂³×C₁₃	1	2	yes	—
883	#102	C₂³×C₁₃	1	2	yes	—
884	#102	C₂³×C₁₃	1	1	yes	characteristic
885	#102	C₂³×C₁₃	1	1	yes	characteristic
886	#102	C₂³×C₁₃	1	1	yes	characteristic
887	#102	C₂³×C₁₃	1	1	yes	characteristic
888	#102	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
897	#97	C₂³×C₁₃	1	2	yes	—
898	#97	C₂³×C₁₃	1	2	yes	—
899	#97	C₂³×C₁₃	1	2	yes	—
900	#97	C₂³×C₁₃	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
902	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
903	C₂×C₁₃	—	2	4	no	—
904	C₂×C₁₃	—	4	1	no	—
905	C₂×C₁₃	—	4	2	no	—
906	C₂×C₁₃	—	8	1	no	—
907	C₂×C₁₃	—	8	2	no	—
908	C₂×C₁₃	—	8	1	no	—
909	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
910	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
911	C₂×C₁₃	#3586	1	1	yes	characteristic
912	C₂⁴	—	2	1	no	—
913	C₂⁴	—	2	2	no	—
914	#41	—	2	4	no	—
915	#41	—	2	2	no	—
916	#41	—	4	1	no	—
917	#41	—	4	8	no	—
918	#41	—	4	4	no	—
919	#41	—	4	8	no	—
920	#41	—	4	4	no	—
921	#41	—	4	4	no	—
922	#41	—	4	4	no	—
923	C₂×Q₈	—	2	2	no	—
924	C₂×Q₈	—	2	1	no	—
925	C₂×Q₈	—	2	2	no	—
926	C₂×Q₈	—	2	1	no	—
927	C₂×Q₈	—	2	4	no	—
928	C₂×Q₈	—	4	2	no	—
929	C₂×Q₈	—	4	4	no	—
930	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
931	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
932	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
933	C₂×D₄	—	2	4	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	4	2	no	—
947	C₂×D₄	—	4	1	no	—
948	C₂×D₄	—	4	8	no	—
949	C₂×D₄	—	4	4	no	—
950	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
951	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
952	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
953	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
954	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
955	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	4	8	no	—
971	C₂²×C₄	—	4	4	no	—
972	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
973	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
974	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
975	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
976	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
977	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
978	SD₁₆	—	2	4	no	—
979	SD₁₆	—	2	2	no	—
980	SD₁₆	—	2	4	no	—
981	SD₁₆	—	2	4	no	—
982	SD₁₆	—	4	2	no	—
983	SD₁₆	—	4	2	no	—
984	SD₁₆	C₁₃×#41	1	4	yes	complemented
985	D₈	—	2	2	no	—
986	D₈	—	2	2	no	—
987	D₈	—	4	2	no	—
988	M₁₆	—	2	2	no	—
989	M₁₆	—	4	1	no	—
990	C₂×C₈	—	2	4	no	—
991	C₂×C₈	—	4	2	no	—
992	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
993	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
994	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
995	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
996	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
997	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
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	1	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1016	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1017	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1018	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1021	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1022	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1023	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1024	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	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	2	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	1	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	C₄²	—	2	1	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	2	no	—
1049	C₄²	—	2	2	no	—
1050	C₄²	—	2	1	no	—
1051	C₄²	—	2	2	no	—
1052	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1053	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1054	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1055	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1056	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1057	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1058	C₄²	C₂⁴×C₁₃	1	2	yes	—
1059	C₁₃	#61452	1	1	yes	characteristic, direct product factor, Sylow
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	2	no	—
1063	C₂³	—	2	1	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	2	no	—
1066	C₂³	—	4	2	no	—
1067	C₂³	—	4	4	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	—	8	1	no	—
1070	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1071	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1072	Q₈	—	2	2	no	—
1073	Q₈	—	2	1	no	—
1074	Q₈	—	2	2	no	—
1075	Q₈	—	2	2	no	—
1076	Q₈	—	4	4	no	—
1077	Q₈	—	4	4	no	—
1078	Q₈	—	4	2	no	—
1079	Q₈	—	4	2	no	—
1080	Q₈	C₂×C₁₃×#41	1	2	yes	complemented
1081	D₄	—	2	4	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	4	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	4	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	4	4	no	—
1095	D₄	—	4	4	no	—
1096	D₄	—	4	4	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	1	no	—
1100	D₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
1101	D₄	C₂×C₁₃×#41	1	2	yes	—
1102	C₂×C₄	—	2	4	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	4	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	4	4	no	—
1122	C₂×C₄	—	4	4	no	—
1123	C₂×C₄	—	4	2	no	—
1124	C₂×C₄	—	4	4	no	—
1125	C₂×C₄	—	4	2	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	4	4	no	—
1128	C₂×C₄	—	4	4	no	—
1129	C₂×C₄	—	4	2	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	4	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	1	yes	characteristic
1135	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1136	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
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	2	no	—
1142	C₈	—	2	1	no	—
1143	C₈	—	2	1	no	—
1144	C₈	—	2	2	no	—
1145	C₈	—	2	1	no	—
1146	C₈	C₂×C₁₃×#41	1	2	yes	complemented
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	2	no	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	1	no	—
1151	C₂²	—	2	1	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	2	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	2	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	8	8	no	—
1165	C₂²	—	8	4	no	—
1166	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
1167	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1168	C₄	—	2	1	no	—
1169	C₄	—	2	2	no	—
1170	C₄	—	2	1	no	—
1171	C₄	—	2	2	no	—
1172	C₄	—	2	1	no	—
1173	C₄	—	2	1	no	—
1174	C₄	—	2	2	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	4	1	no	—
1177	C₄	—	4	1	no	—
1178	C₄	—	4	2	no	—
1179	C₄	—	4	1	no	—
1180	C₄	—	4	2	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	2	no	—
1183	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
1184	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1185	C₄	C₁₃×#585	1	1	yes	characteristic
1186	C₂	—	2	4	no	—
1187	C₂	—	4	1	no	—
1188	C₂	—	4	2	no	—
1189	C₂	—	8	2	no	—
1190	C₂	—	8	1	no	—
1191	C₂	—	8	1	no	—
1192	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1193	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
1194	C₂	C₁₃×#3586	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×#3482	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#3397	C₂	semidirect
4. C₁₃×#3386	C₂	semidirect
5. C₁₃×#3368	C₂	semidirect
6. C₁₃×#3367	C₂	semidirect
7. C₁₃×#3343	C₂	semidirect
8. C₁₃×#3334	C₂	semidirect
9. C₁₃×#3310	C₂	semidirect
10. C₁₃×#3308	C₂	semidirect
11. C₁₃×#3298	C₂	semidirect
12. C₁₃×#3294	C₂	semidirect
13. D₄×C₁₃×SD₁₆	C₂	semidirect
14. C₁₃×#3265	C₂	semidirect
15. C₁₃×#3182	C₂	semidirect
16. C₁₃×#3180	C₂	semidirect
17. C₁₃×#3115	C₂	semidirect
18. C₁₃×#3114	C₂	semidirect
19. C₁₃×#3112	C₂	semidirect
20. C₁₃×#3110	C₂	semidirect
21. C₁₃×#2970	C₂	semidirect
22. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
23. C₂×C₁₃×#440	C₂	semidirect
27. C₁₃×#557	C₂²	semidirect
29. C₁₃×#556	C₂²	semidirect
31. C₁₃×#552	C₂²	semidirect
34. D₄×Q₈×C₁₃	C₂²	semidirect
36. C₁₃×#548	C₂²	semidirect
40. C₁₃×#547	C₂²	semidirect
46. C₁₃×#533	C₂²	semidirect
50. C₁₃×#529	C₂²	semidirect
55. C₄×C₁₃×#41	C₂²	semidirect
56. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
59. C₁₃×#501	C₂²	semidirect
60. C₁₃×#500	C₂²	semidirect
61. C₁₃×#496	C₂²	semidirect
62. C₁₃×#492	C₂²	semidirect
63. C₁₃×#490	C₂²	semidirect
64. C₁₃×#489	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
67. C₁₃×#484	C₂²	semidirect
68. C₁₃×#483	C₂²	semidirect
69. C₁₃×#482	C₂²	semidirect
70. C₁₃×#480	C₂²	semidirect
71. C₁₃×#480	C₂²	semidirect
72. C₁₃×#480	C₂²	semidirect
74. C₁₃×#478	C₂²	semidirect
75. C₁₃×#477	C₂²	semidirect
76. C₁₃×#477	C₂²	semidirect
77. C₁₃×#475	C₂²	semidirect
79. C₁₃×#474	C₂²	semidirect
80. C₁₃×#474	C₂²	semidirect
81. C₁₃×#468	C₂²	semidirect
82. C₁₃×#468	C₂²	semidirect
83. C₁₃×#466	C₂²	semidirect
84. C₁₃×#466	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#465	C₂²	semidirect
88. C₁₃×#463	C₂²	semidirect
90. C₁₃×#461	C₂²	semidirect
91. C₁₃×#460	C₂²	semidirect
92. C₁₃×#460	C₂²	semidirect
93. C₁₃×#460	C₂²	semidirect
94. C₁₃×#459	C₂²	semidirect
97. C₁₃×#449	C₂²	semidirect
98. C₁₃×#448	C₂²	semidirect
99. C₁₃×#448	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₁₃×#446	C₂²	semidirect
104. C₁₃×#442	C₂²	semidirect
105. C₁₃×#442	C₂²	semidirect
110. C₁₃×#440	C₂²	semidirect
111. C₁₃×#440	C₂²	semidirect
112. C₁₃×#440	C₂²	semidirect
113. C₁₃×#440	C₂²	semidirect
114. C₁₃×#440	C₂²	semidirect
115. C₁₃×#440	C₂²	semidirect
116. C₁₃×#440	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×#107	C₂²	semidirect
130. C₁₃×#417	C₂²	semidirect
131. C₂×C₁₃×#103	C₂²	semidirect
133. C₄×C₁₃×M₁₆	C₂²	semidirect
134. C₂×C₁₃×#97	C₂²	semidirect
315. #61452	C₁₃	direct (N × H)
388. C₁₃×SD₁₆	#41	semidirect
463. #3482	C₂×C₁₃	semidirect
464. D₄×#41	C₂×C₁₃	semidirect
465. #3397	C₂×C₁₃	semidirect
466. #3386	C₂×C₁₃	semidirect
467. #3368	C₂×C₁₃	semidirect
468. #3367	C₂×C₁₃	semidirect
469. #3343	C₂×C₁₃	semidirect
470. #3334	C₂×C₁₃	semidirect
471. #3310	C₂×C₁₃	semidirect
472. #3308	C₂×C₁₃	semidirect
473. #3298	C₂×C₁₃	semidirect
474. #3294	C₂×C₁₃	semidirect
475. D₄×SD₁₆	C₂×C₁₃	semidirect
476. #3265	C₂×C₁₃	semidirect
477. #3182	C₂×C₁₃	semidirect
478. #3180	C₂×C₁₃	semidirect
479. #3115	C₂×C₁₃	semidirect
480. #3114	C₂×C₁₃	semidirect
481. #3112	C₂×C₁₃	semidirect
482. #3110	C₂×C₁₃	semidirect
483. #2970	C₂×C₁₃	semidirect
484. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
485. C₂×#440	C₂×C₁₃	semidirect
506. Q₈×C₁₃	C₂×#41	semidirect
526. D₄×C₁₃	AGL(1,ℤ/8)	semidirect
572. C₈×C₁₃	C₂×#41	semidirect
576. #557	C₂²×C₁₃	semidirect
578. #556	C₂²×C₁₃	semidirect
580. #552	C₂²×C₁₃	semidirect
583. D₄×Q₈	C₂²×C₁₃	semidirect
585. #548	C₂²×C₁₃	semidirect
589. #547	C₂²×C₁₃	semidirect
595. #533	C₂²×C₁₃	semidirect
599. #529	C₂²×C₁₃	semidirect
604. C₄×#41	C₂²×C₁₃	semidirect
605. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
608. #501	C₂²×C₁₃	semidirect
609. #500	C₂²×C₁₃	semidirect
610. #496	C₂²×C₁₃	semidirect
611. #492	C₂²×C₁₃	semidirect
612. #490	C₂²×C₁₃	semidirect
613. #489	C₂²×C₁₃	semidirect
614. #487	C₂²×C₁₃	semidirect
615. #486	C₂²×C₁₃	semidirect
616. #484	C₂²×C₁₃	semidirect
617. #483	C₂²×C₁₃	semidirect
618. #482	C₂²×C₁₃	semidirect
619. #480	C₂²×C₁₃	semidirect
620. #480	C₂²×C₁₃	semidirect
621. #480	C₂²×C₁₃	semidirect
623. #478	C₂²×C₁₃	semidirect
624. #477	C₂²×C₁₃	semidirect
625. #477	C₂²×C₁₃	semidirect
626. #475	C₂²×C₁₃	semidirect
628. #474	C₂²×C₁₃	semidirect
629. #474	C₂²×C₁₃	semidirect
630. #468	C₂²×C₁₃	semidirect
631. #468	C₂²×C₁₃	semidirect
632. #466	C₂²×C₁₃	semidirect
633. #466	C₂²×C₁₃	semidirect
634. #465	C₂²×C₁₃	semidirect
635. #465	C₂²×C₁₃	semidirect
637. #463	C₂²×C₁₃	semidirect
639. #461	C₂²×C₁₃	semidirect
640. #460	C₂²×C₁₃	semidirect
641. #460	C₂²×C₁₃	semidirect
642. #460	C₂²×C₁₃	semidirect
643. #459	C₂²×C₁₃	semidirect
646. #449	C₂²×C₁₃	semidirect
647. #448	C₂²×C₁₃	semidirect
648. #448	C₂²×C₁₃	semidirect
650. #446	C₂²×C₁₃	semidirect
651. #446	C₂²×C₁₃	semidirect
653. #442	C₂²×C₁₃	semidirect
654. #442	C₂²×C₁₃	semidirect
659. #440	C₂²×C₁₃	semidirect
660. #440	C₂²×C₁₃	semidirect
661. #440	C₂²×C₁₃	semidirect
662. #440	C₂²×C₁₃	semidirect
663. #440	C₂²×C₁₃	semidirect
664. #440	C₂²×C₁₃	semidirect
665. #440	C₂²×C₁₃	semidirect
667. C₄×SD₁₆	C₂²×C₁₃	semidirect
669. C₄×D₈	C₂²×C₁₃	semidirect
670. #435	C₂²×C₁₃	semidirect
671. #435	C₂²×C₁₃	semidirect
672. C₈×D₄	C₂²×C₁₃	semidirect
673. C₈×D₄	C₂²×C₁₃	semidirect
674. #432	C₂²×C₁₃	semidirect
675. #432	C₂²×C₁₃	semidirect
676. #428	C₂²×C₁₃	semidirect
677. C₂×#107	C₂²×C₁₃	semidirect
679. #417	C₂²×C₁₃	semidirect
680. C₂×#103	C₂²×C₁₃	semidirect
682. C₄×M₁₆	C₂²×C₁₃	semidirect
683. C₂×#97	C₂²×C₁₃	semidirect
984. SD₁₆	C₁₃×#41	semidirect
1059. C₁₃	#61452	direct (N × H)
1080. Q₈	C₂×C₁₃×#41	semidirect
1100. D₄	C₁₃×AGL(1,ℤ/8)	semidirect
1146. 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×#3482	2
D₄×C₁₃×#41	2
C₁₃×#3397	2
C₁₃×#3386	2
C₁₃×#3368	2
C₁₃×#3367	2
C₁₃×#3343	2
C₁₃×#3334	2
C₁₃×#3310	2
C₁₃×#3308	2
C₁₃×#3298	2
C₁₃×#3294	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3265	2
C₁₃×#3182	2
C₁₃×#3180	2
C₁₃×#3115	2
C₁₃×#3114	2
C₁₃×#3112	2
C₁₃×#3110	2
C₁₃×#2970	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₂×C₁₃×#440	2
#61452	13

Subgroups — C13×#61452 #15747791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61452 #15747791