Subgroups — C₁₃×#61598 #15747937

Order 3328.

2392 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3308	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3306	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3265	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3194	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3188	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3006	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₃×#449	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
25	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
26	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
28	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
29	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
30	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
31	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#548	C₂²	1	2	yes	complemented
33	C₁₃×#547	—	2	1	no	—
34	C₁₃×#547	C₂²	1	1	yes	characteristic
35	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#547	C₂²	1	2	yes	complemented
37	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#546	—	2	1	no	—
39	C₁₃×#546	—	2	2	no	—
40	C₁₃×#546	—	2	1	no	—
41	C₁₃×#546	—	2	2	no	—
42	C₁₃×#546	C₂²	1	2	yes	complemented
43	D₄²×C₁₃	—	2	1	no	—
44	D₄²×C₁₃	C₂²	1	1	yes	characteristic
45	D₄²×C₁₃	C₂²	1	2	yes	complemented
46	D₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
47	D₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#537	—	2	1	no	—
49	C₁₃×#534	—	2	2	no	—
50	C₁₃×#532	—	2	1	no	—
51	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#525	—	2	2	no	—
55	C₁₃×#525	C₂²	1	2	yes	complemented
56	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
57	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
58	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×D₄×C₁₃	—	2	1	no	—
60	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
61	C₁₃×#496	C₂²	1	2	yes	complemented
62	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#492	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
70	C₁₃×#482	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#482	C₂²	1	2	yes	complemented
72	C₁₃×#481	C₂²	1	2	yes	complemented
73	C₁₃×#480	C₂²	1	2	yes	complemented
74	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#469	C₂²	1	2	yes	complemented
79	C₁₃×#469	C₂²	1	2	yes	complemented
80	C₁₃×#468	C₂²	1	2	yes	complemented
81	C₁₃×#468	C₂²	1	2	yes	complemented
82	C₁₃×#466	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×#463	C₂²	1	2	yes	complemented
87	C₁₃×#463	C₂²	1	2	yes	complemented
88	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#450	C₂²	1	2	yes	complemented
97	C₁₃×#450	C₂²	1	2	yes	complemented
98	C₁₃×#449	C₂²	1	1	yes	characteristic, complemented
99	C₁₃×#449	C₂²	1	2	yes	complemented
100	C₁₃×#449	C₂²	1	2	yes	complemented
101	C₁₃×#449	C₂²	1	2	yes	complemented
102	C₁₃×#449	C₂²	1	2	yes	complemented
103	C₁₃×#449	C₂²	1	2	yes	complemented
104	C₁₃×#449	C₂²	1	2	yes	complemented
105	C₁₃×#449	C₂²	1	2	yes	complemented
106	C₁₃×#449	C₂²	1	1	yes	characteristic, complemented
107	C₁₃×#449	C₂²	1	2	yes	complemented
108	C₁₃×#449	C₂²	1	2	yes	complemented
109	C₁₃×#448	C₂²	1	2	yes	complemented
110	C₁₃×#448	C₂²	1	2	yes	complemented
111	C₁₃×#447	C₂²	1	2	yes	complemented
112	C₁₃×#447	C₂²	1	2	yes	complemented
113	C₁₃×#447	C₂²	1	2	yes	complemented
114	C₁₃×#447	C₂²	1	2	yes	complemented
115	C₁₃×#442	C₂²	1	2	yes	complemented
116	C₁₃×#440	C₂²	1	2	yes	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, complemented
120	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
121	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₁₃×#435	C₂²	1	2	yes	complemented
124	C₁₃×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
128	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₁₃×#417	C₂²	1	2	yes	complemented
130	C₁₃×#417	C₂²	1	2	yes	complemented
131	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
132	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
133	C₁₃×#407	C₂²	1	2	yes	complemented
134	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	C₁₃×H(5,𝔽₂)	—	4	8	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	—	2	1	no	—
142	C₂×C₁₃×#41	—	2	2	no	—
143	C₂×C₁₃×#41	—	4	4	no	—
144	C₂×C₁₃×#41	—	4	4	no	—
145	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×#41	C₂³	1	2	yes	—
147	C₂×C₁₃×#41	C₂³	1	2	yes	—
148	C₂×C₁₃×#41	C₂³	1	2	yes	—
149	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
150	C₂²×D₄×C₁₃	—	2	2	no	—
151	C₂²×D₄×C₁₃	—	2	2	no	—
152	C₂²×D₄×C₁₃	—	2	2	no	—
153	C₂²×D₄×C₁₃	—	2	1	no	—
154	C₂²×D₄×C₁₃	—	2	1	no	—
155	C₂²×D₄×C₁₃	—	2	2	no	—
156	C₂²×D₄×C₁₃	—	2	1	no	—
157	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
158	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
159	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
160	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
161	C₂³×C₄×C₁₃	—	2	2	no	—
162	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
163	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
164	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
165	C₂×C₁₃×SD₁₆	—	4	4	no	—
166	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
168	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
169	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
170	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
171	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
172	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
173	C₂×C₁₃×D₈	—	4	4	no	—
174	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×D₈	C₂³	1	2	yes	—
177	C₂×C₁₃×D₈	C₂³	1	2	yes	—
178	C₂×C₁₃×D₈	C₂³	1	2	yes	—
179	C₂×C₁₃×D₈	C₂³	1	2	yes	—
180	C₂×C₁₃×D₈	C₂³	1	2	yes	—
181	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
182	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
183	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
184	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
185	C₁₃×C₄⋊Q₈	—	2	1	no	—
186	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
187	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
188	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
189	C₁₃×#127	—	2	1	no	—
190	C₁₃×#127	C₂³	1	1	yes	characteristic
191	C₁₃×#127	C₂³	1	1	yes	characteristic
192	C₁₃×#127	C₂³	1	1	yes	characteristic
193	C₁₃×#124	—	2	2	no	—
194	C₁₃×#124	—	2	1	no	—
195	C₁₃×#124	—	2	1	no	—
196	C₁₃×#124	C₂³	1	2	yes	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	2	no	—
202	C₁₃×#123	—	2	2	no	—
203	C₁₃×#123	—	2	2	no	—
204	C₁₃×C₂²⋊Q₈	—	2	2	no	—
205	C₁₃×C₂²⋊Q₈	—	2	1	no	—
206	C₁₃×C₂²⋊Q₈	—	2	1	no	—
207	C₁₃×C₂²⋊Q₈	—	2	2	no	—
208	C₁₃×C₂²⋊Q₈	—	2	2	no	—
209	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₁₃×#121	—	2	2	no	—
212	C₁₃×#121	—	2	1	no	—
213	C₁₃×#121	—	2	2	no	—
214	C₁₃×#121	—	2	2	no	—
215	C₁₃×#121	—	2	2	no	—
216	C₁₃×#121	—	2	2	no	—
217	C₁₃×#121	—	2	1	no	—
218	C₁₃×#121	—	2	1	no	—
219	C₁₃×#121	—	2	1	no	—
220	C₁₃×#121	—	2	1	no	—
221	C₁₃×#121	—	2	1	no	—
222	C₁₃×#121	—	2	1	no	—
223	C₁₃×#121	—	2	1	no	—
224	C₁₃×#121	—	2	2	no	—
225	C₁₃×#121	—	2	2	no	—
226	C₁₃×#121	—	2	2	no	—
227	C₁₃×#121	C₂³	1	2	yes	—
228	C₁₃×#121	C₂³	1	2	yes	—
229	C₁₃×#121	C₂³	1	2	yes	—
230	C₁₃×#121	C₂³	1	2	yes	—
231	C₁₃×#121	C₂³	1	1	yes	characteristic
232	C₁₃×#121	C₂³	1	2	yes	—
233	C₁₃×#121	C₂³	1	1	yes	characteristic
234	C₁₃×#121	C₂³	1	2	yes	—
235	C₁₃×#121	C₂³	1	2	yes	—
236	C₁₃×#120	—	2	2	no	—
237	C₁₃×#120	—	2	2	no	—
238	C₁₃×#120	—	2	2	no	—
239	C₁₃×#120	—	2	2	no	—
240	C₁₃×#120	—	2	2	no	—
241	C₁₃×#120	—	2	2	no	—
242	C₁₃×#120	—	2	2	no	—
243	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₁₃	—	2	1	no	—
246	C₄×D₄×C₁₃	—	2	2	no	—
247	C₄×D₄×C₁₃	—	2	1	no	—
248	C₄×D₄×C₁₃	—	2	1	no	—
249	C₄×D₄×C₁₃	—	2	2	no	—
250	C₄×D₄×C₁₃	—	2	1	no	—
251	C₄×D₄×C₁₃	—	2	2	no	—
252	C₄×D₄×C₁₃	—	2	1	no	—
253	C₄×D₄×C₁₃	—	2	1	no	—
254	C₄×D₄×C₁₃	—	2	1	no	—
255	C₄×D₄×C₁₃	—	2	1	no	—
256	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
257	C₄×D₄×C₁₃	D₄	1	2	yes	—
258	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
259	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₁₃	C₂³	1	2	yes	—
263	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₁₃	C₂³	1	2	yes	—
266	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
267	C₁₃×#117	—	2	1	no	—
268	C₁₃×#117	C₂³	1	1	yes	characteristic
269	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
271	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
272	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
273	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
277	C₂×C₄²×C₁₃	—	2	1	no	—
278	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
279	C₁₃×#107	C₂³	1	1	yes	characteristic
280	C₁₃×#107	C₂³	1	1	yes	characteristic
281	C₁₃×#107	C₂³	1	2	yes	—
282	C₁₃×#106	C₂³	1	1	yes	characteristic
283	C₁₃×#106	C₂³	1	1	yes	characteristic
284	C₁₃×#106	C₂³	1	2	yes	—
285	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	1	yes	characteristic
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	2	yes	—
296	C₁₃×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	1	yes	characteristic
304	C₁₃×#102	C₂³	1	1	yes	characteristic
305	C₁₃×#102	C₂³	1	1	yes	characteristic
306	C₁₃×#102	C₂³	1	1	yes	characteristic
307	C₁₃×#102	C₂³	1	2	yes	—
308	C₁₃×#102	C₂³	1	2	yes	—
309	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
314	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₁₃×#97	C₂³	1	2	yes	—
317	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
318	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
319	#61598	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
320	C₂⁴×C₁₃	—	2	2	no	—
321	C₂⁴×C₁₃	—	2	2	no	—
322	C₂⁴×C₁₃	—	2	2	no	—
323	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
324	C₁₃×#41	—	2	2	no	—
325	C₁₃×#41	—	2	2	no	—
326	C₁₃×#41	—	2	4	no	—
327	C₁₃×#41	—	2	4	no	—
328	C₁₃×#41	—	4	2	no	—
329	C₁₃×#41	—	4	2	no	—
330	C₁₃×#41	—	4	2	no	—
331	C₁₃×#41	—	4	2	no	—
332	C₁₃×#41	—	4	8	no	—
333	C₁₃×#41	—	4	4	no	—
334	C₁₃×#41	—	4	4	no	—
335	C₁₃×#41	—	4	8	no	—
336	C₁₃×#41	—	4	8	no	—
337	C₁₃×#41	—	4	4	no	—
338	C₁₃×#41	—	4	4	no	—
339	C₂×Q₈×C₁₃	—	2	2	no	—
340	C₂×Q₈×C₁₃	—	2	1	no	—
341	C₂×Q₈×C₁₃	—	2	1	no	—
342	C₂×Q₈×C₁₃	—	2	4	no	—
343	C₂×Q₈×C₁₃	—	4	2	no	—
344	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
345	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₁₃	—	2	1	no	—
347	C₂×D₄×C₁₃	—	2	4	no	—
348	C₂×D₄×C₁₃	—	2	4	no	—
349	C₂×D₄×C₁₃	—	2	2	no	—
350	C₂×D₄×C₁₃	—	2	2	no	—
351	C₂×D₄×C₁₃	—	2	2	no	—
352	C₂×D₄×C₁₃	—	2	2	no	—
353	C₂×D₄×C₁₃	—	2	2	no	—
354	C₂×D₄×C₁₃	—	2	2	no	—
355	C₂×D₄×C₁₃	—	2	2	no	—
356	C₂×D₄×C₁₃	—	2	1	no	—
357	C₂×D₄×C₁₃	—	2	2	no	—
358	C₂×D₄×C₁₃	—	2	1	no	—
359	C₂×D₄×C₁₃	—	2	2	no	—
360	C₂×D₄×C₁₃	—	2	2	no	—
361	C₂×D₄×C₁₃	—	2	1	no	—
362	C₂×D₄×C₁₃	—	2	2	no	—
363	C₂×D₄×C₁₃	—	2	1	no	—
364	C₂×D₄×C₁₃	—	2	1	no	—
365	C₂×D₄×C₁₃	—	2	1	no	—
366	C₂×D₄×C₁₃	—	2	1	no	—
367	C₂×D₄×C₁₃	—	2	1	no	—
368	C₂×D₄×C₁₃	—	2	2	no	—
369	C₂×D₄×C₁₃	—	2	2	no	—
370	C₂×D₄×C₁₃	—	4	2	no	—
371	C₂×D₄×C₁₃	—	4	2	no	—
372	C₂×D₄×C₁₃	—	4	2	no	—
373	C₂×D₄×C₁₃	—	4	2	no	—
374	C₂×D₄×C₁₃	—	4	2	no	—
375	C₂×D₄×C₁₃	—	4	8	no	—
376	C₂×D₄×C₁₃	—	4	8	no	—
377	C₂×D₄×C₁₃	—	4	4	no	—
378	C₂×D₄×C₁₃	—	4	8	no	—
379	C₂×D₄×C₁₃	—	4	8	no	—
380	C₂×D₄×C₁₃	—	4	4	no	—
381	C₂×D₄×C₁₃	—	4	4	no	—
382	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
383	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
384	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
385	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
386	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
388	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
389	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₁₃	—	2	1	no	—
391	C₂²×C₄×C₁₃	—	2	2	no	—
392	C₂²×C₄×C₁₃	—	2	2	no	—
393	C₂²×C₄×C₁₃	—	2	2	no	—
394	C₂²×C₄×C₁₃	—	2	1	no	—
395	C₂²×C₄×C₁₃	—	2	2	no	—
396	C₂²×C₄×C₁₃	—	2	2	no	—
397	C₂²×C₄×C₁₃	—	2	2	no	—
398	C₂²×C₄×C₁₃	—	2	2	no	—
399	C₂²×C₄×C₁₃	—	2	1	no	—
400	C₂²×C₄×C₁₃	—	2	1	no	—
401	C₂²×C₄×C₁₃	—	2	1	no	—
402	C₂²×C₄×C₁₃	—	4	2	no	—
403	C₂²×C₄×C₁₃	—	4	2	no	—
404	C₂²×C₄×C₁₃	—	4	8	no	—
405	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
406	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
407	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
408	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
409	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
410	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
412	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
413	C₁₃×SD₁₆	—	2	2	no	—
414	C₁₃×SD₁₆	—	2	4	no	—
415	C₁₃×SD₁₆	—	2	2	no	—
416	C₁₃×SD₁₆	—	4	2	no	—
417	C₁₃×SD₁₆	—	4	2	no	—
418	C₁₃×SD₁₆	—	4	2	no	—
419	C₁₃×SD₁₆	—	4	2	no	—
420	C₁₃×D₈	—	2	2	no	—
421	C₁₃×D₈	—	2	4	no	—
422	C₁₃×D₈	—	2	2	no	—
423	C₁₃×D₈	—	4	2	no	—
424	C₁₃×D₈	—	4	2	no	—
425	C₁₃×D₈	—	4	2	no	—
426	C₁₃×D₈	—	4	2	no	—
427	C₁₃×M₁₆	—	4	2	no	—
428	C₁₃×M₁₆	—	4	2	no	—
429	C₂×C₈×C₁₃	—	4	2	no	—
430	C₂×C₈×C₁₃	—	4	2	no	—
431	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
432	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
433	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
434	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
435	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
436	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
437	C₁₃×C₄⋊C₄	—	2	1	no	—
438	C₁₃×C₄⋊C₄	—	2	2	no	—
439	C₁₃×C₄⋊C₄	—	2	2	no	—
440	C₁₃×C₄⋊C₄	—	2	2	no	—
441	C₁₃×C₄⋊C₄	—	2	1	no	—
442	C₁₃×C₄⋊C₄	—	2	1	no	—
443	C₁₃×C₄⋊C₄	—	2	1	no	—
444	C₁₃×C₄⋊C₄	—	2	2	no	—
445	C₁₃×C₄⋊C₄	—	2	1	no	—
446	C₁₃×C₄⋊C₄	—	2	1	no	—
447	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
448	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
449	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
450	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
451	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
453	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
454	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
455	C₁₃×C₂²⋊C₄	—	2	2	no	—
456	C₁₃×C₂²⋊C₄	—	2	1	no	—
457	C₁₃×C₂²⋊C₄	—	2	2	no	—
458	C₁₃×C₂²⋊C₄	—	2	1	no	—
459	C₁₃×C₂²⋊C₄	—	2	2	no	—
460	C₁₃×C₂²⋊C₄	—	2	1	no	—
461	C₁₃×C₂²⋊C₄	—	2	2	no	—
462	C₁₃×C₂²⋊C₄	—	2	2	no	—
463	C₁₃×C₂²⋊C₄	—	2	2	no	—
464	C₁₃×C₂²⋊C₄	—	2	2	no	—
465	C₁₃×C₂²⋊C₄	—	2	2	no	—
466	C₁₃×C₂²⋊C₄	—	2	2	no	—
467	C₁₃×C₂²⋊C₄	—	2	1	no	—
468	C₁₃×C₂²⋊C₄	—	2	1	no	—
469	C₁₃×C₂²⋊C₄	—	2	2	no	—
470	C₁₃×C₂²⋊C₄	—	2	2	no	—
471	C₁₃×C₂²⋊C₄	—	2	2	no	—
472	C₁₃×C₂²⋊C₄	—	2	1	no	—
473	C₁₃×C₂²⋊C₄	—	2	1	no	—
474	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
475	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
476	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
477	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
478	C₄²×C₁₃	—	2	1	no	—
479	C₄²×C₁₃	—	2	1	no	—
480	C₄²×C₁₃	—	2	1	no	—
481	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
482	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
483	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
484	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
485	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
486	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
487	#3332	C₂×C₁₃	1	1	yes	characteristic, complemented
488	#3330	C₂×C₁₃	1	1	yes	characteristic, complemented
489	#3308	C₂×C₁₃	1	2	yes	complemented
490	#3306	C₂×C₁₃	1	2	yes	complemented
491	#3298	C₂×C₁₃	1	1	yes	characteristic, complemented
492	#3294	C₂×C₁₃	1	1	yes	characteristic, complemented
493	D₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
494	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
495	#3274	C₂×C₁₃	1	1	yes	characteristic, complemented
496	#3272	C₂×C₁₃	1	1	yes	characteristic, complemented
497	#3265	C₂×C₁₃	1	2	yes	complemented
498	#3264	C₂×C₁₃	1	2	yes	complemented
499	#3214	C₂×C₁₃	1	1	yes	characteristic, complemented
500	#3207	C₂×C₁₃	1	1	yes	characteristic, complemented
501	#3194	C₂×C₁₃	1	2	yes	complemented
502	#3188	C₂×C₁₃	1	2	yes	complemented
503	#3115	C₂×C₁₃	1	1	yes	characteristic, complemented
504	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
505	#3006	C₂×C₁₃	1	2	yes	complemented
506	C₂×#449	C₂×C₁₃	1	2	yes	complemented
507	#2974	C₂×C₁₃	1	1	yes	characteristic, complemented
508	C₂³×C₁₃	—	2	1	no	—
509	C₂³×C₁₃	—	2	4	no	—
510	C₂³×C₁₃	—	2	2	no	—
511	C₂³×C₁₃	—	2	1	no	—
512	C₂³×C₁₃	—	2	2	no	—
513	C₂³×C₁₃	—	2	1	no	—
514	C₂³×C₁₃	—	4	2	no	—
515	C₂³×C₁₃	—	4	2	no	—
516	C₂³×C₁₃	—	4	4	no	—
517	C₂³×C₁₃	—	4	4	no	—
518	C₂³×C₁₃	—	4	4	no	—
519	C₂³×C₁₃	—	4	4	no	—
520	C₂³×C₁₃	—	8	2	no	—
521	C₂³×C₁₃	—	8	2	no	—
522	C₂³×C₁₃	—	8	2	no	—
523	C₂³×C₁₃	—	8	2	no	—
524	C₂³×C₁₃	—	8	2	no	—
525	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
526	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
527	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
528	Q₈×C₁₃	—	2	1	no	—
529	Q₈×C₁₃	—	2	2	no	—
530	Q₈×C₁₃	—	2	2	no	—
531	Q₈×C₁₃	—	4	4	no	—
532	Q₈×C₁₃	—	4	2	no	—
533	Q₈×C₁₃	—	4	2	no	—
534	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	complemented
535	D₄×C₁₃	—	2	4	no	—
536	D₄×C₁₃	—	2	4	no	—
537	D₄×C₁₃	—	2	2	no	—
538	D₄×C₁₃	—	2	1	no	—
539	D₄×C₁₃	—	2	1	no	—
540	D₄×C₁₃	—	2	2	no	—
541	D₄×C₁₃	—	2	1	no	—
542	D₄×C₁₃	—	2	1	no	—
543	D₄×C₁₃	—	2	2	no	—
544	D₄×C₁₃	—	2	2	no	—
545	D₄×C₁₃	—	2	2	no	—
546	D₄×C₁₃	—	2	1	no	—
547	D₄×C₁₃	—	4	4	no	—
548	D₄×C₁₃	—	4	4	no	—
549	D₄×C₁₃	—	4	2	no	—
550	D₄×C₁₃	—	4	4	no	—
551	D₄×C₁₃	—	4	4	no	—
552	D₄×C₁₃	—	4	2	no	—
553	D₄×C₁₃	—	4	2	no	—
554	D₄×C₁₃	—	4	4	no	—
555	D₄×C₁₃	—	4	4	no	—
556	D₄×C₁₃	—	4	4	no	—
557	D₄×C₁₃	—	4	4	no	—
558	D₄×C₁₃	—	4	4	no	—
559	D₄×C₁₃	—	4	4	no	—
560	D₄×C₁₃	—	4	2	no	—
561	D₄×C₁₃	—	4	2	no	—
562	D₄×C₁₃	—	8	1	no	—
563	D₄×C₁₃	—	8	1	no	—
564	D₄×C₁₃	—	8	1	no	—
565	D₄×C₁₃	—	8	2	no	—
566	D₄×C₁₃	—	8	2	no	—
567	D₄×C₁₃	—	8	2	no	—
568	D₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
569	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	complemented
570	C₂×C₄×C₁₃	—	2	4	no	—
571	C₂×C₄×C₁₃	—	2	1	no	—
572	C₂×C₄×C₁₃	—	2	2	no	—
573	C₂×C₄×C₁₃	—	2	2	no	—
574	C₂×C₄×C₁₃	—	2	2	no	—
575	C₂×C₄×C₁₃	—	2	2	no	—
576	C₂×C₄×C₁₃	—	2	2	no	—
577	C₂×C₄×C₁₃	—	2	1	no	—
578	C₂×C₄×C₁₃	—	2	1	no	—
579	C₂×C₄×C₁₃	—	2	1	no	—
580	C₂×C₄×C₁₃	—	2	1	no	—
581	C₂×C₄×C₁₃	—	2	2	no	—
582	C₂×C₄×C₁₃	—	2	2	no	—
583	C₂×C₄×C₁₃	—	2	1	no	—
584	C₂×C₄×C₁₃	—	2	1	no	—
585	C₂×C₄×C₁₃	—	4	2	no	—
586	C₂×C₄×C₁₃	—	4	2	no	—
587	C₂×C₄×C₁₃	—	4	2	no	—
588	C₂×C₄×C₁₃	—	4	1	no	—
589	C₂×C₄×C₁₃	—	4	4	no	—
590	C₂×C₄×C₁₃	—	4	4	no	—
591	C₂×C₄×C₁₃	—	4	4	no	—
592	C₂×C₄×C₁₃	—	4	4	no	—
593	C₂×C₄×C₁₃	—	4	4	no	—
594	C₂×C₄×C₁₃	—	4	4	no	—
595	C₂×C₄×C₁₃	—	4	4	no	—
596	C₂×C₄×C₁₃	—	4	2	no	—
597	C₂×C₄×C₁₃	—	4	2	no	—
598	C₂×C₄×C₁₃	—	4	2	no	—
599	C₂×C₄×C₁₃	—	8	1	no	—
600	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
601	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
602	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
603	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
604	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
605	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
606	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
607	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
608	C₈×C₁₃	—	2	1	no	—
609	C₈×C₁₃	—	2	1	no	—
610	C₈×C₁₃	—	2	2	no	—
611	C₈×C₁₃	—	2	2	no	—
612	C₈×C₁₃	—	2	1	no	—
613	C₈×C₁₃	—	2	1	no	—
614	C₂×H(5,𝔽₂)	—	2	1	no	—
615	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
616	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
617	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
618	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
619	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
620	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
621	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	#548	C₂²×C₁₃	1	2	yes	complemented
623	#547	—	2	1	no	—
624	#547	C₂²×C₁₃	1	1	yes	characteristic
625	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
626	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
627	#547	C₂²×C₁₃	1	2	yes	complemented
628	#546	—	2	1	no	—
629	#546	—	2	2	no	—
630	#546	—	2	1	no	—
631	#546	—	2	2	no	—
632	#546	C₂²×C₁₃	1	2	yes	complemented
633	D₄²	—	2	1	no	—
634	D₄²	C₂²×C₁₃	1	1	yes	characteristic
635	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	D₄²	C₂²×C₁₃	1	2	yes	complemented
637	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
638	#537	—	2	1	no	—
639	#534	—	2	2	no	—
640	#532	—	2	1	no	—
641	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
642	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
643	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
644	#525	—	2	2	no	—
645	#525	C₂²×C₁₃	1	2	yes	complemented
646	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
647	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
648	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	C₂×C₄×D₄	—	2	1	no	—
650	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
651	#496	C₂²×C₁₃	1	2	yes	complemented
652	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
653	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
654	#489	C₂²×C₁₃	1	2	yes	complemented
655	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
656	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
657	#484	C₂²×C₁₃	1	2	yes	complemented
658	#483	C₂²×C₁₃	1	2	yes	complemented
659	#482	C₂²×C₁₃	1	1	yes	characteristic, complemented
660	#482	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	#482	C₂²×C₁₃	1	2	yes	complemented
662	#481	C₂²×C₁₃	1	2	yes	complemented
663	#480	C₂²×C₁₃	1	2	yes	complemented
664	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
665	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
666	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
667	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
668	#469	C₂²×C₁₃	1	2	yes	complemented
669	#469	C₂²×C₁₃	1	2	yes	complemented
670	#468	C₂²×C₁₃	1	2	yes	complemented
671	#468	C₂²×C₁₃	1	2	yes	complemented
672	#466	C₂²×C₁₃	1	2	yes	complemented
673	#466	C₂²×C₁₃	1	2	yes	complemented
674	#465	C₂²×C₁₃	1	2	yes	complemented
675	#465	C₂²×C₁₃	1	2	yes	complemented
676	#463	C₂²×C₁₃	1	2	yes	complemented
677	#463	C₂²×C₁₃	1	2	yes	complemented
678	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
679	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
680	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
681	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
682	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
683	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
684	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
685	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
686	#450	C₂²×C₁₃	1	2	yes	complemented
687	#450	C₂²×C₁₃	1	2	yes	complemented
688	#449	C₂²×C₁₃	1	2	yes	complemented
689	#449	C₂²×C₁₃	1	2	yes	complemented
690	#449	C₂²×C₁₃	1	1	yes	characteristic, complemented
691	#449	C₂²×C₁₃	1	1	yes	characteristic, complemented
692	#449	C₂²×C₁₃	1	2	yes	complemented
693	#449	C₂²×C₁₃	1	2	yes	complemented
694	#449	C₂²×C₁₃	1	2	yes	complemented
695	#449	C₂²×C₁₃	1	2	yes	complemented
696	#449	C₂²×C₁₃	1	2	yes	complemented
697	#449	C₂²×C₁₃	1	2	yes	complemented
698	#449	C₂²×C₁₃	1	2	yes	complemented
699	#448	C₂²×C₁₃	1	2	yes	complemented
700	#448	C₂²×C₁₃	1	2	yes	complemented
701	#447	C₂²×C₁₃	1	2	yes	complemented
702	#447	C₂²×C₁₃	1	2	yes	complemented
703	#447	C₂²×C₁₃	1	2	yes	complemented
704	#447	C₂²×C₁₃	1	2	yes	complemented
705	#442	C₂²×C₁₃	1	2	yes	complemented
706	#440	C₂²×C₁₃	1	2	yes	complemented
707	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
708	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
709	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
710	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
711	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
712	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
713	#435	C₂²×C₁₃	1	2	yes	complemented
714	#435	C₂²×C₁₃	1	2	yes	complemented
715	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
716	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
717	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
718	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
719	#417	C₂²×C₁₃	1	2	yes	complemented
720	#417	C₂²×C₁₃	1	2	yes	complemented
721	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
722	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
723	#407	C₂²×C₁₃	1	2	yes	complemented
724	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
725	C₂²×C₁₃	—	2	2	no	—
726	C₂²×C₁₃	—	2	2	no	—
727	C₂²×C₁₃	—	2	1	no	—
728	C₂²×C₁₃	—	2	2	no	—
729	C₂²×C₁₃	—	2	1	no	—
730	C₂²×C₁₃	—	2	2	no	—
731	C₂²×C₁₃	—	2	2	no	—
732	C₂²×C₁₃	—	2	1	no	—
733	C₂²×C₁₃	—	2	2	no	—
734	C₂²×C₁₃	—	4	1	no	—
735	C₂²×C₁₃	—	4	1	no	—
736	C₂²×C₁₃	—	4	2	no	—
737	C₂²×C₁₃	—	4	1	no	—
738	C₂²×C₁₃	—	4	2	no	—
739	C₂²×C₁₃	—	4	1	no	—
740	C₂²×C₁₃	—	4	2	no	—
741	C₂²×C₁₃	—	4	1	no	—
742	C₂²×C₁₃	—	4	2	no	—
743	C₂²×C₁₃	—	4	1	no	—
744	C₂²×C₁₃	—	4	2	no	—
745	C₂²×C₁₃	—	4	1	no	—
746	C₂²×C₁₃	—	4	1	no	—
747	C₂²×C₁₃	—	4	2	no	—
748	C₂²×C₁₃	—	8	4	no	—
749	C₂²×C₁₃	—	8	8	no	—
750	C₂²×C₁₃	—	16	4	no	—
751	C₂²×C₁₃	—	16	4	no	—
752	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
753	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
754	C₄×C₁₃	—	2	1	no	—
755	C₄×C₁₃	—	2	1	no	—
756	C₄×C₁₃	—	2	1	no	—
757	C₄×C₁₃	—	2	2	no	—
758	C₄×C₁₃	—	2	2	no	—
759	C₄×C₁₃	—	2	2	no	—
760	C₄×C₁₃	—	2	1	no	—
761	C₄×C₁₃	—	4	1	no	—
762	C₄×C₁₃	—	4	2	no	—
763	C₄×C₁₃	—	4	2	no	—
764	C₄×C₁₃	—	4	1	no	—
765	C₄×C₁₃	—	4	1	no	—
766	C₄×C₁₃	—	4	1	no	—
767	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
768	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
769	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
770	H(5,𝔽₂)	—	4	8	no	—
771	C₂×#41	—	2	1	no	—
772	C₂×#41	—	2	2	no	—
773	C₂×#41	—	2	1	no	—
774	C₂×#41	—	2	2	no	—
775	C₂×#41	—	2	1	no	—
776	C₂×#41	—	2	1	no	—
777	C₂×#41	—	2	2	no	—
778	C₂×#41	—	4	4	no	—
779	C₂×#41	—	4	4	no	—
780	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
781	C₂×#41	C₂³×C₁₃	1	2	yes	—
782	C₂×#41	C₂³×C₁₃	1	2	yes	—
783	C₂×#41	C₂³×C₁₃	1	2	yes	—
784	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
785	C₂²×D₄	—	2	2	no	—
786	C₂²×D₄	—	2	2	no	—
787	C₂²×D₄	—	2	2	no	—
788	C₂²×D₄	—	2	1	no	—
789	C₂²×D₄	—	2	1	no	—
790	C₂²×D₄	—	2	2	no	—
791	C₂²×D₄	—	2	1	no	—
792	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
793	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
794	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
795	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
796	C₂³×C₄	—	2	2	no	—
797	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
798	AGL(1,ℤ/8)	—	4	4	no	—
799	AGL(1,ℤ/8)	—	4	4	no	—
800	C₂×SD₁₆	—	4	4	no	—
801	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
802	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
803	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
804	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
805	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
806	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
807	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
808	C₂×D₈	—	4	4	no	—
809	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
810	C₂×D₈	C₂³×C₁₃	1	2	yes	—
811	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
812	C₂×D₈	C₂³×C₁₃	1	2	yes	—
813	C₂×D₈	C₂³×C₁₃	1	2	yes	—
814	C₂×D₈	C₂³×C₁₃	1	2	yes	—
815	C₂×D₈	C₂³×C₁₃	1	2	yes	—
816	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
817	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
818	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
819	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
820	C₄⋊Q₈	—	2	1	no	—
821	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
822	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
823	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
824	#127	—	2	1	no	—
825	#127	C₂³×C₁₃	1	1	yes	characteristic
826	#127	C₂³×C₁₃	1	1	yes	characteristic
827	#127	C₂³×C₁₃	1	1	yes	characteristic
828	#124	—	2	2	no	—
829	#124	—	2	1	no	—
830	#124	—	2	1	no	—
831	#124	C₂³×C₁₃	1	2	yes	—
832	#123	—	2	2	no	—
833	#123	—	2	2	no	—
834	#123	—	2	2	no	—
835	#123	—	2	2	no	—
836	#123	—	2	2	no	—
837	#123	—	2	2	no	—
838	#123	—	2	2	no	—
839	C₂²⋊Q₈	—	2	2	no	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	—	2	1	no	—
842	C₂²⋊Q₈	—	2	2	no	—
843	C₂²⋊Q₈	—	2	2	no	—
844	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
845	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
846	#121	—	2	2	no	—
847	#121	—	2	1	no	—
848	#121	—	2	2	no	—
849	#121	—	2	2	no	—
850	#121	—	2	2	no	—
851	#121	—	2	2	no	—
852	#121	—	2	1	no	—
853	#121	—	2	1	no	—
854	#121	—	2	1	no	—
855	#121	—	2	1	no	—
856	#121	—	2	1	no	—
857	#121	—	2	1	no	—
858	#121	—	2	1	no	—
859	#121	—	2	2	no	—
860	#121	—	2	2	no	—
861	#121	—	2	2	no	—
862	#121	C₂³×C₁₃	1	1	yes	characteristic
863	#121	C₂³×C₁₃	1	2	yes	—
864	#121	C₂³×C₁₃	1	1	yes	characteristic
865	#121	C₂³×C₁₃	1	2	yes	—
866	#121	C₂³×C₁₃	1	2	yes	—
867	#121	C₂³×C₁₃	1	2	yes	—
868	#121	C₂³×C₁₃	1	2	yes	—
869	#121	C₂³×C₁₃	1	2	yes	—
870	#121	C₂³×C₁₃	1	2	yes	—
871	#120	—	2	2	no	—
872	#120	—	2	2	no	—
873	#120	—	2	2	no	—
874	#120	—	2	2	no	—
875	#120	—	2	2	no	—
876	#120	—	2	2	no	—
877	#120	—	2	2	no	—
878	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
879	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	2	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	2	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	2	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	1	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
892	C₄×D₄	D₄×C₁₃	1	2	yes	—
893	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
894	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
895	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
896	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
897	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
898	C₄×D₄	C₂³×C₁₃	1	2	yes	—
899	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
900	C₄×D₄	C₂³×C₁₃	1	2	yes	—
901	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
902	#117	—	2	1	no	—
903	#117	C₂³×C₁₃	1	1	yes	characteristic
904	C₂×C₄⋊C₄	—	2	1	no	—
905	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
906	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
907	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
908	C₂×C₂²⋊C₄	—	2	2	no	—
909	C₂×C₂²⋊C₄	—	2	2	no	—
910	C₂×C₂²⋊C₄	—	2	2	no	—
911	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
912	C₂×C₄²	—	2	1	no	—
913	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
914	#107	C₂³×C₁₃	1	1	yes	characteristic
915	#107	C₂³×C₁₃	1	1	yes	characteristic
916	#107	C₂³×C₁₃	1	2	yes	—
917	#106	C₂³×C₁₃	1	1	yes	characteristic
918	#106	C₂³×C₁₃	1	1	yes	characteristic
919	#106	C₂³×C₁₃	1	2	yes	—
920	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
921	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
922	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
923	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
924	#103	C₂³×C₁₃	1	1	yes	characteristic
925	#103	C₂³×C₁₃	1	2	yes	—
926	#103	C₂³×C₁₃	1	2	yes	—
927	#103	C₂³×C₁₃	1	2	yes	—
928	#103	C₂³×C₁₃	1	1	yes	characteristic
929	#103	C₂³×C₁₃	1	2	yes	—
930	#103	C₂³×C₁₃	1	2	yes	—
931	#102	C₂³×C₁₃	1	1	yes	characteristic
932	#102	C₂³×C₁₃	1	2	yes	—
933	#102	C₂³×C₁₃	1	2	yes	—
934	#102	C₂³×C₁₃	1	2	yes	—
935	#102	C₂³×C₁₃	1	1	yes	characteristic
936	#102	C₂³×C₁₃	1	2	yes	—
937	#102	C₂³×C₁₃	1	2	yes	—
938	#102	C₂³×C₁₃	1	1	yes	characteristic
939	#102	C₂³×C₁₃	1	1	yes	characteristic
940	#102	C₂³×C₁₃	1	1	yes	characteristic
941	#102	C₂³×C₁₃	1	1	yes	characteristic
942	#102	C₂³×C₁₃	1	2	yes	—
943	#102	C₂³×C₁₃	1	2	yes	—
944	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
945	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
946	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
947	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
948	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
949	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
950	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
951	#97	C₂³×C₁₃	1	2	yes	—
952	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
953	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
954	C₂×C₁₃	—	2	4	no	—
955	C₂×C₁₃	—	4	1	no	—
956	C₂×C₁₃	—	4	2	no	—
957	C₂×C₁₃	—	4	2	no	—
958	C₂×C₁₃	—	8	2	no	—
959	C₂×C₁₃	—	8	1	no	—
960	C₂×C₁₃	—	8	2	no	—
961	C₂×C₁₃	—	8	1	no	—
962	C₂×C₁₃	#3484	1	1	yes	characteristic
963	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
964	C₂×C₁₃	#3584	1	1	yes	characteristic
965	C₂⁴	—	2	2	no	—
966	C₂⁴	—	2	2	no	—
967	C₂⁴	—	2	2	no	—
968	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
969	#41	—	2	2	no	—
970	#41	—	2	2	no	—
971	#41	—	2	4	no	—
972	#41	—	2	4	no	—
973	#41	—	4	2	no	—
974	#41	—	4	2	no	—
975	#41	—	4	2	no	—
976	#41	—	4	2	no	—
977	#41	—	4	8	no	—
978	#41	—	4	4	no	—
979	#41	—	4	4	no	—
980	#41	—	4	8	no	—
981	#41	—	4	8	no	—
982	#41	—	4	4	no	—
983	#41	—	4	4	no	—
984	C₂×Q₈	—	2	2	no	—
985	C₂×Q₈	—	2	1	no	—
986	C₂×Q₈	—	2	1	no	—
987	C₂×Q₈	—	2	4	no	—
988	C₂×Q₈	—	4	2	no	—
989	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
990	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	4	no	—
993	C₂×D₄	—	2	4	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	2	2	no	—
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	2	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	2	no	—
1008	C₂×D₄	—	2	1	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	4	2	no	—
1016	C₂×D₄	—	4	2	no	—
1017	C₂×D₄	—	4	2	no	—
1018	C₂×D₄	—	4	2	no	—
1019	C₂×D₄	—	4	2	no	—
1020	C₂×D₄	—	4	8	no	—
1021	C₂×D₄	—	4	8	no	—
1022	C₂×D₄	—	4	4	no	—
1023	C₂×D₄	—	4	8	no	—
1024	C₂×D₄	—	4	8	no	—
1025	C₂×D₄	—	4	4	no	—
1026	C₂×D₄	—	4	4	no	—
1027	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1028	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1029	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1030	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1031	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1032	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1033	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1034	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	1	no	—
1040	C₂²×C₄	—	2	2	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	—	2	2	no	—
1043	C₂²×C₄	—	2	2	no	—
1044	C₂²×C₄	—	2	1	no	—
1045	C₂²×C₄	—	2	1	no	—
1046	C₂²×C₄	—	2	1	no	—
1047	C₂²×C₄	—	4	2	no	—
1048	C₂²×C₄	—	4	2	no	—
1049	C₂²×C₄	—	4	8	no	—
1050	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1051	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1052	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
1053	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
1054	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
1055	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1056	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1057	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1058	SD₁₆	—	2	2	no	—
1059	SD₁₆	—	2	4	no	—
1060	SD₁₆	—	2	2	no	—
1061	SD₁₆	—	4	2	no	—
1062	SD₁₆	—	4	2	no	—
1063	SD₁₆	—	4	2	no	—
1064	SD₁₆	—	4	2	no	—
1065	D₈	—	2	2	no	—
1066	D₈	—	2	4	no	—
1067	D₈	—	2	2	no	—
1068	D₈	—	4	2	no	—
1069	D₈	—	4	2	no	—
1070	D₈	—	4	2	no	—
1071	D₈	—	4	2	no	—
1072	M₁₆	—	4	2	no	—
1073	M₁₆	—	4	2	no	—
1074	C₂×C₈	—	4	2	no	—
1075	C₂×C₈	—	4	2	no	—
1076	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1077	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1078	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1079	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1080	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1081	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1093	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1094	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1095	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1096	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1097	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1098	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1099	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	2	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1120	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1121	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1122	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1123	C₄²	—	2	1	no	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1127	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1128	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1129	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1130	C₁₃	#61598	1	1	yes	characteristic, direct product factor, Sylow
1131	C₂³	—	2	1	no	—
1132	C₂³	—	2	4	no	—
1133	C₂³	—	2	2	no	—
1134	C₂³	—	2	2	no	—
1135	C₂³	—	2	1	no	—
1136	C₂³	—	2	1	no	—
1137	C₂³	—	4	2	no	—
1138	C₂³	—	4	2	no	—
1139	C₂³	—	4	4	no	—
1140	C₂³	—	4	4	no	—
1141	C₂³	—	4	4	no	—
1142	C₂³	—	4	4	no	—
1143	C₂³	—	8	2	no	—
1144	C₂³	—	8	2	no	—
1145	C₂³	—	8	2	no	—
1146	C₂³	—	8	2	no	—
1147	C₂³	—	8	2	no	—
1148	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1149	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1150	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1151	Q₈	—	2	1	no	—
1152	Q₈	—	2	2	no	—
1153	Q₈	—	2	2	no	—
1154	Q₈	—	4	4	no	—
1155	Q₈	—	4	2	no	—
1156	Q₈	—	4	2	no	—
1157	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	complemented
1158	D₄	—	2	4	no	—
1159	D₄	—	2	4	no	—
1160	D₄	—	2	2	no	—
1161	D₄	—	2	1	no	—
1162	D₄	—	2	1	no	—
1163	D₄	—	2	2	no	—
1164	D₄	—	2	1	no	—
1165	D₄	—	2	1	no	—
1166	D₄	—	2	2	no	—
1167	D₄	—	2	2	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	4	4	no	—
1171	D₄	—	4	4	no	—
1172	D₄	—	4	2	no	—
1173	D₄	—	4	4	no	—
1174	D₄	—	4	4	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	4	4	no	—
1178	D₄	—	4	4	no	—
1179	D₄	—	4	4	no	—
1180	D₄	—	4	4	no	—
1181	D₄	—	4	4	no	—
1182	D₄	—	4	4	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	8	2	no	—
1186	D₄	—	8	2	no	—
1187	D₄	—	8	1	no	—
1188	D₄	—	8	1	no	—
1189	D₄	—	8	1	no	—
1190	D₄	—	8	2	no	—
1191	D₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
1192	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	complemented
1193	C₂×C₄	—	2	4	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	4	2	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	1	no	—
1212	C₂×C₄	—	4	4	no	—
1213	C₂×C₄	—	4	4	no	—
1214	C₂×C₄	—	4	4	no	—
1215	C₂×C₄	—	4	4	no	—
1216	C₂×C₄	—	4	4	no	—
1217	C₂×C₄	—	4	4	no	—
1218	C₂×C₄	—	4	4	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	4	2	no	—
1221	C₂×C₄	—	4	2	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1224	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1225	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1226	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1227	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1228	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1229	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1230	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1231	C₈	—	2	1	no	—
1232	C₈	—	2	1	no	—
1233	C₈	—	2	2	no	—
1234	C₈	—	2	2	no	—
1235	C₈	—	2	1	no	—
1236	C₈	—	2	1	no	—
1237	C₂²	—	2	2	no	—
1238	C₂²	—	2	2	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	2	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	2	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	2	no	—
1245	C₂²	—	2	2	no	—
1246	C₂²	—	4	1	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	2	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	2	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	2	no	—
1259	C₂²	—	4	1	no	—
1260	C₂²	—	8	4	no	—
1261	C₂²	—	8	8	no	—
1262	C₂²	—	16	4	no	—
1263	C₂²	—	16	4	no	—
1264	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
1265	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1266	C₄	—	2	1	no	—
1267	C₄	—	2	1	no	—
1268	C₄	—	2	1	no	—
1269	C₄	—	2	1	no	—
1270	C₄	—	2	2	no	—
1271	C₄	—	2	2	no	—
1272	C₄	—	2	2	no	—
1273	C₄	—	4	2	no	—
1274	C₄	—	4	1	no	—
1275	C₄	—	4	1	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	2	no	—
1279	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
1280	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1281	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1282	C₂	—	2	4	no	—
1283	C₂	—	4	1	no	—
1284	C₂	—	4	2	no	—
1285	C₂	—	4	2	no	—
1286	C₂	—	8	2	no	—
1287	C₂	—	8	1	no	—
1288	C₂	—	8	2	no	—
1289	C₂	—	8	1	no	—
1290	C₂	C₁₃×#3484	1	1	yes	characteristic
1291	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
1292	C₂	C₁₃×#3584	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3496	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#3332	C₂	semidirect
4. C₁₃×#3330	C₂	semidirect
5. C₁₃×#3308	C₂	semidirect
6. C₁₃×#3306	C₂	semidirect
7. C₁₃×#3298	C₂	semidirect
8. C₁₃×#3294	C₂	semidirect
9. D₄×C₁₃×SD₁₆	C₂	semidirect
10. D₄×C₁₃×D₈	C₂	semidirect
11. C₁₃×#3274	C₂	semidirect
12. C₁₃×#3272	C₂	semidirect
13. C₁₃×#3265	C₂	semidirect
14. C₁₃×#3264	C₂	semidirect
15. C₁₃×#3214	C₂	semidirect
16. C₁₃×#3207	C₂	semidirect
17. C₁₃×#3194	C₂	semidirect
18. C₁₃×#3188	C₂	semidirect
19. C₁₃×#3115	C₂	semidirect
20. C₁₃×#3106	C₂	semidirect
21. C₁₃×#3006	C₂	semidirect
22. C₂×C₁₃×#449	C₂	semidirect
23. C₁₃×#2974	C₂	semidirect
25. C₂²×C₁₃×#41	C₂²	semidirect
26. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂²×C₁₃×SD₁₆	C₂²	semidirect
29. C₂²×C₁₃×D₈	C₂²	semidirect
30. C₁₃×#550	C₂²	semidirect
31. D₄×Q₈×C₁₃	C₂²	semidirect
32. C₁₃×#548	C₂²	semidirect
35. C₁₃×#547	C₂²	semidirect
36. C₁₃×#547	C₂²	semidirect
37. C₁₃×#547	C₂²	semidirect
42. C₁₃×#546	C₂²	semidirect
45. D₄²×C₁₃	C₂²	semidirect
46. D₄²×C₁₃	C₂²	semidirect
47. D₄²×C₁₃	C₂²	semidirect
51. C₁₃×#532	C₂²	semidirect
52. C₁₃×#532	C₂²	semidirect
53. C₁₃×#532	C₂²	semidirect
55. C₁₃×#525	C₂²	semidirect
56. C₂×C₁₃×#121	C₂²	semidirect
57. C₂×C₁₃×#121	C₂²	semidirect
58. C₄×C₁₃×#41	C₂²	semidirect
61. C₁₃×#496	C₂²	semidirect
62. C₁₃×#493	C₂²	semidirect
63. C₁₃×#492	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×#482	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
72. C₁₃×#481	C₂²	semidirect
73. C₁₃×#480	C₂²	semidirect
74. C₁₃×#477	C₂²	semidirect
75. C₁₃×#476	C₂²	semidirect
76. C₁₃×#475	C₂²	semidirect
77. C₁₃×#474	C₂²	semidirect
78. C₁₃×#469	C₂²	semidirect
79. C₁₃×#469	C₂²	semidirect
80. C₁₃×#468	C₂²	semidirect
81. C₁₃×#468	C₂²	semidirect
82. C₁₃×#466	C₂²	semidirect
83. C₁₃×#466	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#463	C₂²	semidirect
87. C₁₃×#463	C₂²	semidirect
88. C₁₃×#461	C₂²	semidirect
89. C₁₃×#461	C₂²	semidirect
90. C₁₃×#460	C₂²	semidirect
91. C₁₃×#460	C₂²	semidirect
92. C₁₃×#459	C₂²	semidirect
93. C₁₃×#459	C₂²	semidirect
94. C₁₃×#459	C₂²	semidirect
95. C₁₃×#459	C₂²	semidirect
96. C₁₃×#450	C₂²	semidirect
97. C₁₃×#450	C₂²	semidirect
98. C₁₃×#449	C₂²	semidirect
99. C₁₃×#449	C₂²	semidirect
100. C₁₃×#449	C₂²	semidirect
101. C₁₃×#449	C₂²	semidirect
102. C₁₃×#449	C₂²	semidirect
103. C₁₃×#449	C₂²	semidirect
104. C₁₃×#449	C₂²	semidirect
105. C₁₃×#449	C₂²	semidirect
106. C₁₃×#449	C₂²	semidirect
107. C₁₃×#449	C₂²	semidirect
108. C₁₃×#449	C₂²	semidirect
109. C₁₃×#448	C₂²	semidirect
110. C₁₃×#448	C₂²	semidirect
111. C₁₃×#447	C₂²	semidirect
112. C₁₃×#447	C₂²	semidirect
113. C₁₃×#447	C₂²	semidirect
114. C₁₃×#447	C₂²	semidirect
115. C₁₃×#442	C₂²	semidirect
116. C₁₃×#440	C₂²	semidirect
117. C₄×C₁₃×SD₁₆	C₂²	semidirect
118. C₄×C₁₃×SD₁₆	C₂²	semidirect
119. C₄×C₁₃×D₈	C₂²	semidirect
120. C₄×C₁₃×D₈	C₂²	semidirect
121. C₁₃×#436	C₂²	semidirect
122. C₁₃×#436	C₂²	semidirect
123. C₁₃×#435	C₂²	semidirect
124. C₁₃×#435	C₂²	semidirect
125. C₈×D₄×C₁₃	C₂²	semidirect
126. C₈×D₄×C₁₃	C₂²	semidirect
127. C₁₃×#432	C₂²	semidirect
128. C₁₃×#431	C₂²	semidirect
129. C₁₃×#417	C₂²	semidirect
130. C₁₃×#417	C₂²	semidirect
131. C₂×C₁₃×#103	C₂²	semidirect
132. C₂×C₁₃×#102	C₂²	semidirect
133. C₁₃×#407	C₂²	semidirect
134. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
319. #61598	C₁₃	direct (N × H)
485. #3496	C₂×C₁₃	semidirect
486. D₄×#41	C₂×C₁₃	semidirect
487. #3332	C₂×C₁₃	semidirect
488. #3330	C₂×C₁₃	semidirect
489. #3308	C₂×C₁₃	semidirect
490. #3306	C₂×C₁₃	semidirect
491. #3298	C₂×C₁₃	semidirect
492. #3294	C₂×C₁₃	semidirect
493. D₄×SD₁₆	C₂×C₁₃	semidirect
494. D₄×D₈	C₂×C₁₃	semidirect
495. #3274	C₂×C₁₃	semidirect
496. #3272	C₂×C₁₃	semidirect
497. #3265	C₂×C₁₃	semidirect
498. #3264	C₂×C₁₃	semidirect
499. #3214	C₂×C₁₃	semidirect
500. #3207	C₂×C₁₃	semidirect
501. #3194	C₂×C₁₃	semidirect
502. #3188	C₂×C₁₃	semidirect
503. #3115	C₂×C₁₃	semidirect
504. #3106	C₂×C₁₃	semidirect
505. #3006	C₂×C₁₃	semidirect
506. C₂×#449	C₂×C₁₃	semidirect
507. #2974	C₂×C₁₃	semidirect
534. Q₈×C₁₃	H(5,𝔽₂)	semidirect
568. D₄×C₁₃	AGL(1,ℤ/8)	semidirect
569. D₄×C₁₃	H(5,𝔽₂)	semidirect
615. C₂²×#41	C₂²×C₁₃	semidirect
616. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
617. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
618. C₂²×SD₁₆	C₂²×C₁₃	semidirect
619. C₂²×D₈	C₂²×C₁₃	semidirect
620. #550	C₂²×C₁₃	semidirect
621. D₄×Q₈	C₂²×C₁₃	semidirect
622. #548	C₂²×C₁₃	semidirect
625. #547	C₂²×C₁₃	semidirect
626. #547	C₂²×C₁₃	semidirect
627. #547	C₂²×C₁₃	semidirect
632. #546	C₂²×C₁₃	semidirect
635. D₄²	C₂²×C₁₃	semidirect
636. D₄²	C₂²×C₁₃	semidirect
637. D₄²	C₂²×C₁₃	semidirect
641. #532	C₂²×C₁₃	semidirect
642. #532	C₂²×C₁₃	semidirect
643. #532	C₂²×C₁₃	semidirect
645. #525	C₂²×C₁₃	semidirect
646. C₂×#121	C₂²×C₁₃	semidirect
647. C₂×#121	C₂²×C₁₃	semidirect
648. C₄×#41	C₂²×C₁₃	semidirect
651. #496	C₂²×C₁₃	semidirect
652. #493	C₂²×C₁₃	semidirect
653. #492	C₂²×C₁₃	semidirect
654. #489	C₂²×C₁₃	semidirect
655. #487	C₂²×C₁₃	semidirect
656. #486	C₂²×C₁₃	semidirect
657. #484	C₂²×C₁₃	semidirect
658. #483	C₂²×C₁₃	semidirect
659. #482	C₂²×C₁₃	semidirect
660. #482	C₂²×C₁₃	semidirect
661. #482	C₂²×C₁₃	semidirect
662. #481	C₂²×C₁₃	semidirect
663. #480	C₂²×C₁₃	semidirect
664. #477	C₂²×C₁₃	semidirect
665. #476	C₂²×C₁₃	semidirect
666. #475	C₂²×C₁₃	semidirect
667. #474	C₂²×C₁₃	semidirect
668. #469	C₂²×C₁₃	semidirect
669. #469	C₂²×C₁₃	semidirect
670. #468	C₂²×C₁₃	semidirect
671. #468	C₂²×C₁₃	semidirect
672. #466	C₂²×C₁₃	semidirect
673. #466	C₂²×C₁₃	semidirect
674. #465	C₂²×C₁₃	semidirect
675. #465	C₂²×C₁₃	semidirect
676. #463	C₂²×C₁₃	semidirect
677. #463	C₂²×C₁₃	semidirect
678. #461	C₂²×C₁₃	semidirect
679. #461	C₂²×C₁₃	semidirect
680. #460	C₂²×C₁₃	semidirect
681. #460	C₂²×C₁₃	semidirect
682. #459	C₂²×C₁₃	semidirect
683. #459	C₂²×C₁₃	semidirect
684. #459	C₂²×C₁₃	semidirect
685. #459	C₂²×C₁₃	semidirect
686. #450	C₂²×C₁₃	semidirect
687. #450	C₂²×C₁₃	semidirect
688. #449	C₂²×C₁₃	semidirect
689. #449	C₂²×C₁₃	semidirect
690. #449	C₂²×C₁₃	semidirect
691. #449	C₂²×C₁₃	semidirect
692. #449	C₂²×C₁₃	semidirect
693. #449	C₂²×C₁₃	semidirect
694. #449	C₂²×C₁₃	semidirect
695. #449	C₂²×C₁₃	semidirect
696. #449	C₂²×C₁₃	semidirect
697. #449	C₂²×C₁₃	semidirect
698. #449	C₂²×C₁₃	semidirect
699. #448	C₂²×C₁₃	semidirect
700. #448	C₂²×C₁₃	semidirect
701. #447	C₂²×C₁₃	semidirect
702. #447	C₂²×C₁₃	semidirect
703. #447	C₂²×C₁₃	semidirect
704. #447	C₂²×C₁₃	semidirect
705. #442	C₂²×C₁₃	semidirect
706. #440	C₂²×C₁₃	semidirect
707. C₄×SD₁₆	C₂²×C₁₃	semidirect
708. C₄×SD₁₆	C₂²×C₁₃	semidirect
709. C₄×D₈	C₂²×C₁₃	semidirect
710. C₄×D₈	C₂²×C₁₃	semidirect
711. #436	C₂²×C₁₃	semidirect
712. #436	C₂²×C₁₃	semidirect
713. #435	C₂²×C₁₃	semidirect
714. #435	C₂²×C₁₃	semidirect
715. C₈×D₄	C₂²×C₁₃	semidirect
716. C₈×D₄	C₂²×C₁₃	semidirect
717. #432	C₂²×C₁₃	semidirect
718. #431	C₂²×C₁₃	semidirect
719. #417	C₂²×C₁₃	semidirect
720. #417	C₂²×C₁₃	semidirect
721. C₂×#103	C₂²×C₁₃	semidirect
722. C₂×#102	C₂²×C₁₃	semidirect
723. #407	C₂²×C₁₃	semidirect
724. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
1130. C₁₃	#61598	direct (N × H)
1157. Q₈	C₁₃×H(5,𝔽₂)	semidirect
1191. D₄	C₁₃×AGL(1,ℤ/8)	semidirect
1192. D₄	C₁₃×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3496	2
D₄×C₁₃×#41	2
C₁₃×#3332	2
C₁₃×#3330	2
C₁₃×#3308	2
C₁₃×#3306	2
C₁₃×#3298	2
C₁₃×#3294	2
D₄×C₁₃×SD₁₆	2
D₄×C₁₃×D₈	2
C₁₃×#3274	2
C₁₃×#3272	2
C₁₃×#3265	2
C₁₃×#3264	2
C₁₃×#3214	2
C₁₃×#3207	2
C₁₃×#3194	2
C₁₃×#3188	2
C₁₃×#3115	2
C₁₃×#3106	2
C₁₃×#3006	2
C₂×C₁₃×#449	2
C₁₃×#2974	2
#61598	13

Subgroups — C13×#61598 #15747937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61598 #15747937