Subgroups — C₁₃×#60702 #15747041

Order 3328.

2008 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3183	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3181	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3180	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3172	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3171	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3168	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3056	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3055	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#137	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
21	C₁₃×#533	C₂²	1	1	yes	characteristic
22	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#532	C₂²	1	1	yes	characteristic
25	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#529	—	2	1	no	—
28	C₁₃×#529	—	2	1	no	—
29	C₁₃×#529	—	2	1	no	—
30	C₁₃×#529	—	2	1	no	—
31	C₁₃×#529	—	2	1	no	—
32	C₁₃×#529	—	2	1	no	—
33	C₁₃×#529	—	2	1	no	—
34	C₁₃×#529	—	2	1	no	—
35	C₁₃×#529	C₂²	1	2	yes	—
36	C₁₃×#529	C₂²	1	2	yes	—
37	C₁₃×#529	C₂²	1	2	yes	—
38	C₁₃×#529	C₂²	1	2	yes	—
39	C₁₃×#529	C₂²	1	2	yes	complemented
40	C₁₃×#529	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#126	—	2	1	no	—
42	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
44	C₁₃×#525	—	2	1	no	—
45	C₁₃×#525	—	2	1	no	—
46	C₁₃×#525	C₂²	1	2	yes	—
47	C₂×C₁₃×#123	—	2	1	no	—
48	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×#41	—	2	1	no	—
51	C₄×C₁₃×#41	—	2	1	no	—
52	C₄×C₁₃×#41	C₂²	1	2	yes	—
53	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₁₃	—	2	1	no	—
55	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#117	—	2	1	no	—
57	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
58	C₁₃×#501	C₂²	1	2	yes	complemented
59	C₁₃×#501	C₂²	1	2	yes	complemented
60	C₁₃×#499	C₂²	1	4	yes	complemented
61	C₁₃×#497	C₂²	1	2	yes	complemented
62	C₁₃×#496	C₂²	1	2	yes	complemented
63	C₁₃×#495	C₂²	1	4	yes	complemented
64	C₁₃×#491	C₂²	1	2	yes	complemented
65	C₁₃×#490	C₂²	1	2	yes	complemented
66	C₁₃×#489	C₂²	1	2	yes	complemented
67	C₁₃×#489	C₂²	1	2	yes	complemented
68	C₁₃×#488	C₂²	1	4	yes	complemented
69	C₁₃×#488	C₂²	1	4	yes	complemented
70	C₁₃×#470	C₂²	1	4	yes	complemented
71	C₁₃×#469	C₂²	1	4	yes	—
72	C₁₃×#468	C₂²	1	4	yes	—
73	C₁₃×#468	C₂²	1	4	yes	complemented
74	C₁₃×#467	C₂²	1	4	yes	complemented
75	C₁₃×#466	C₂²	1	4	yes	—
76	C₁₃×#465	C₂²	1	4	yes	—
77	C₁₃×#465	C₂²	1	4	yes	complemented
78	C₁₃×#442	C₂²	1	4	yes	complemented
79	C₁₃×#441	C₂²	1	4	yes	complemented
80	C₁₃×#440	C₂²	1	4	yes	complemented
81	C₁₃×#440	C₂²	1	4	yes	complemented
82	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
83	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
84	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
85	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
86	C₁₃×#428	C₂²	1	2	yes	—
87	C₁₃×#428	C₂²	1	2	yes	—
88	C₁₃×#419	C₂²	1	2	yes	—
89	C₁₃×#418	C₂²	1	2	yes	—
90	C₁₃×#417	C₂²	1	2	yes	—
91	C₁₃×#417	C₂²	1	2	yes	—
92	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
95	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
96	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
97	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
98	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
99	C₂×C₁₃×#41	—	2	1	no	—
100	C₂×C₁₃×#41	—	2	1	no	—
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃	—	2	1	no	—
104	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	—	2	1	no	—
106	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#137	—	2	8	no	—
110	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
111	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×D₈	C₂³	1	4	yes	—
115	C₂×C₁₃×M₁₆	—	2	8	no	—
116	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
117	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
119	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₁₃×#127	C₂³	1	1	yes	characteristic
124	C₁₃×#126	—	2	2	no	—
125	C₁₃×#126	—	2	2	no	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#126	—	2	2	no	—
128	C₁₃×#126	—	2	2	no	—
129	C₁₃×#126	—	2	2	no	—
130	C₁₃×#125	—	2	1	no	—
131	C₁₃×#125	—	2	1	no	—
132	C₁₃×#125	—	2	1	no	—
133	C₁₃×#125	—	2	1	no	—
134	C₁₃×#125	C₂³	1	2	yes	—
135	C₁₃×#125	C₂³	1	2	yes	—
136	C₁₃×#125	C₂³	1	2	yes	—
137	C₁₃×#124	—	2	1	no	—
138	C₁₃×#124	—	2	1	no	—
139	C₁₃×#124	—	2	1	no	—
140	C₁₃×#124	—	2	1	no	—
141	C₁₃×#124	C₂³	1	2	yes	—
142	C₁₃×#124	C₂³	1	2	yes	—
143	C₁₃×#124	C₂³	1	2	yes	—
144	C₁₃×#123	—	2	2	no	—
145	C₁₃×#123	—	2	2	no	—
146	C₁₃×#123	—	2	2	no	—
147	C₁₃×#123	—	2	2	no	—
148	C₁₃×#123	—	2	2	no	—
149	C₁₃×#123	—	2	2	no	—
150	C₁₃×#123	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	1	no	—
152	C₁₃×C₂²⋊Q₈	—	2	1	no	—
153	C₁₃×C₂²⋊Q₈	—	2	1	no	—
154	C₁₃×C₂²⋊Q₈	—	2	1	no	—
155	C₁₃×C₂²⋊Q₈	—	2	1	no	—
156	C₁₃×C₂²⋊Q₈	—	2	1	no	—
157	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
159	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
161	C₁₃×#121	—	2	1	no	—
162	C₁₃×#121	—	2	1	no	—
163	C₁₃×#121	—	2	1	no	—
164	C₁₃×#121	—	2	1	no	—
165	C₁₃×#121	—	2	1	no	—
166	C₁₃×#121	—	2	1	no	—
167	C₁₃×#121	C₂³	1	2	yes	—
168	C₁₃×#121	C₂³	1	2	yes	—
169	C₁₃×#121	C₂³	1	2	yes	—
170	C₁₃×#121	C₂³	1	2	yes	—
171	C₁₃×#120	—	2	2	no	—
172	C₄×Q₈×C₁₃	—	2	1	no	—
173	C₄×Q₈×C₁₃	—	2	1	no	—
174	C₄×Q₈×C₁₃	—	2	1	no	—
175	C₄×Q₈×C₁₃	—	2	1	no	—
176	C₄×Q₈×C₁₃	—	2	1	no	—
177	C₄×Q₈×C₁₃	—	2	1	no	—
178	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
179	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
180	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
181	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
182	C₄×D₄×C₁₃	—	2	2	no	—
183	C₄×D₄×C₁₃	—	2	2	no	—
184	C₄×D₄×C₁₃	—	2	2	no	—
185	C₄×D₄×C₁₃	—	2	2	no	—
186	C₄×D₄×C₁₃	—	2	2	no	—
187	C₄×D₄×C₁₃	—	2	2	no	—
188	C₄×D₄×C₁₃	—	2	2	no	—
189	C₄×D₄×C₁₃	—	2	2	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₄×D₄×C₁₃	—	2	2	no	—
192	C₄×D₄×C₁₃	—	2	1	no	—
193	C₄×D₄×C₁₃	—	2	1	no	—
194	C₄×D₄×C₁₃	—	2	1	no	—
195	C₄×D₄×C₁₃	—	2	1	no	—
196	C₄×D₄×C₁₃	—	2	1	no	—
197	C₄×D₄×C₁₃	—	2	1	no	—
198	C₄×D₄×C₁₃	C₂³	1	2	yes	—
199	C₄×D₄×C₁₃	C₂³	1	2	yes	—
200	C₄×D₄×C₁₃	C₂³	1	2	yes	—
201	C₄×D₄×C₁₃	C₂³	1	2	yes	—
202	C₁₃×#117	—	2	1	no	—
203	C₁₃×#117	—	2	1	no	—
204	C₁₃×#117	—	2	2	no	—
205	C₁₃×#117	—	2	2	no	—
206	C₁₃×#117	—	2	2	no	—
207	C₁₃×#117	—	2	2	no	—
208	C₁₃×#117	—	2	2	no	—
209	C₁₃×#117	—	2	2	no	—
210	C₁₃×#117	—	2	2	no	—
211	C₁₃×#117	C₂³	1	2	yes	—
212	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
219	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
220	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
222	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
223	C₂×C₄²×C₁₃	—	2	1	no	—
224	C₂×C₄²×C₁₃	—	2	2	no	—
225	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
226	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
227	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
228	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
229	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
230	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
231	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
237	C₁₃×#107	C₂³	1	4	yes	—
238	C₁₃×#107	C₂³	1	4	yes	—
239	C₁₃×#106	C₂³	1	4	yes	—
240	C₁₃×#106	C₂³	1	4	yes	—
241	C₁₃×#103	C₂³	1	4	yes	—
242	C₁₃×#103	C₂³	1	4	yes	—
243	C₁₃×#103	C₂³	1	4	yes	—
244	C₁₃×#103	C₂³	1	4	yes	—
245	C₁₃×#102	C₂³	1	4	yes	—
246	C₁₃×#102	C₂³	1	4	yes	—
247	C₁₃×#102	C₂³	1	4	yes	—
248	C₁₃×#102	C₂³	1	4	yes	—
249	C₁₃×#97	C₂³	1	4	yes	—
250	C₁₃×#97	C₂³	1	2	yes	—
251	C₁₃×#97	C₂³	1	2	yes	—
252	C₄×C₈×C₁₃	C₂³	1	4	yes	—
253	C₄×C₈×C₁₃	C₂³	1	2	yes	—
254	C₄×C₈×C₁₃	C₂³	1	2	yes	—
255	#60702	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂⁴×C₁₃	—	2	1	no	—
257	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₁₃×#41	—	2	4	no	—
259	C₁₃×#41	—	2	4	no	—
260	C₁₃×#41	—	4	4	no	—
261	C₁₃×#41	—	4	4	no	—
262	C₂×Q₈×C₁₃	—	2	1	no	—
263	C₂×Q₈×C₁₃	—	2	1	no	—
264	C₂×Q₈×C₁₃	—	2	1	no	—
265	C₂×Q₈×C₁₃	—	2	4	no	—
266	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
267	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
268	C₂×D₄×C₁₃	—	2	2	no	—
269	C₂×D₄×C₁₃	—	2	2	no	—
270	C₂×D₄×C₁₃	—	2	2	no	—
271	C₂×D₄×C₁₃	—	2	2	no	—
272	C₂×D₄×C₁₃	—	2	2	no	—
273	C₂×D₄×C₁₃	—	2	1	no	—
274	C₂×D₄×C₁₃	—	2	1	no	—
275	C₂×D₄×C₁₃	—	2	1	no	—
276	C₂×D₄×C₁₃	—	2	4	no	—
277	C₂×D₄×C₁₃	—	4	4	no	—
278	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃	—	2	4	no	—
281	C₂²×C₄×C₁₃	—	2	1	no	—
282	C₂²×C₄×C₁₃	—	2	1	no	—
283	C₂²×C₄×C₁₃	—	2	1	no	—
284	C₂²×C₄×C₁₃	—	2	2	no	—
285	C₂²×C₄×C₁₃	—	2	2	no	—
286	C₂²×C₄×C₁₃	—	2	2	no	—
287	C₂²×C₄×C₁₃	—	2	2	no	—
288	C₂²×C₄×C₁₃	—	2	2	no	—
289	C₂²×C₄×C₁₃	—	4	2	no	—
290	C₂²×C₄×C₁₃	—	4	2	no	—
291	C₂²×C₄×C₁₃	—	4	4	no	—
292	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₁₃×Q₁₆	—	2	8	no	—
311	C₁₃×SD₁₆	—	2	8	no	—
312	C₁₃×SD₁₆	—	2	8	no	—
313	C₁₃×D₈	—	2	8	no	—
314	C₁₃×M₁₆	—	2	4	no	—
315	C₁₃×M₁₆	—	2	8	no	—
316	C₁₃×M₁₆	#41	1	8	yes	complemented
317	C₂×C₈×C₁₃	—	2	8	no	—
318	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
319	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	—	2	1	no	—
329	C₁₃×C₄⋊C₄	—	2	1	no	—
330	C₁₃×C₄⋊C₄	—	2	1	no	—
331	C₁₃×C₄⋊C₄	—	2	1	no	—
332	C₁₃×C₄⋊C₄	—	2	1	no	—
333	C₁₃×C₄⋊C₄	—	2	1	no	—
334	C₁₃×C₄⋊C₄	—	2	2	no	—
335	C₁₃×C₄⋊C₄	—	2	2	no	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	—	2	2	no	—
338	C₁₃×C₄⋊C₄	—	2	2	no	—
339	C₁₃×C₄⋊C₄	—	2	2	no	—
340	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
341	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
342	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
343	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
344	C₁₃×C₂²⋊C₄	—	2	2	no	—
345	C₁₃×C₂²⋊C₄	—	2	2	no	—
346	C₁₃×C₂²⋊C₄	—	2	2	no	—
347	C₁₃×C₂²⋊C₄	—	2	2	no	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
349	C₁₃×C₂²⋊C₄	—	2	2	no	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	2	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	2	no	—
355	C₁₃×C₂²⋊C₄	—	2	2	no	—
356	C₁₃×C₂²⋊C₄	—	2	2	no	—
357	C₁₃×C₂²⋊C₄	—	2	2	no	—
358	C₁₃×C₂²⋊C₄	—	2	2	no	—
359	C₁₃×C₂²⋊C₄	—	2	2	no	—
360	C₁₃×C₂²⋊C₄	—	2	2	no	—
361	C₁₃×C₂²⋊C₄	—	2	2	no	—
362	C₁₃×C₂²⋊C₄	—	2	2	no	—
363	C₄²×C₁₃	—	2	2	no	—
364	C₄²×C₁₃	—	2	2	no	—
365	C₄²×C₁₃	—	2	2	no	—
366	C₄²×C₁₃	—	2	2	no	—
367	C₄²×C₁₃	—	2	2	no	—
368	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
369	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
370	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
374	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
379	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
380	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
381	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
382	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
383	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
384	#3444	C₂×C₁₃	1	1	yes	characteristic, complemented
385	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
386	#3183	C₂×C₁₃	1	4	yes	complemented
387	#3181	C₂×C₁₃	1	2	yes	complemented
388	#3180	C₂×C₁₃	1	2	yes	complemented
389	#3172	C₂×C₁₃	1	2	yes	complemented
390	#3171	C₂×C₁₃	1	2	yes	complemented
391	#3168	C₂×C₁₃	1	4	yes	complemented
392	#3166	C₂×C₁₃	1	1	yes	characteristic, complemented
393	#3153	C₂×C₁₃	1	1	yes	characteristic, complemented
394	#3142	C₂×C₁₃	1	1	yes	characteristic, complemented
395	#3140	C₂×C₁₃	1	1	yes	characteristic, complemented
396	#3056	C₂×C₁₃	1	2	yes	complemented
397	#3055	C₂×C₁₃	1	2	yes	complemented
398	C₄×#137	C₂×C₁₃	1	2	yes	complemented
399	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
400	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
401	C₂³×C₁₃	—	2	2	no	—
402	C₂³×C₁₃	—	2	2	no	—
403	C₂³×C₁₃	—	2	2	no	—
404	C₂³×C₁₃	—	2	2	no	—
405	C₂³×C₁₃	—	4	1	no	—
406	C₂³×C₁₃	—	4	2	no	—
407	C₂³×C₁₃	—	4	2	no	—
408	C₂³×C₁₃	—	4	2	no	—
409	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	Q₈×C₁₃	—	2	2	no	—
413	Q₈×C₁₃	—	2	4	no	—
414	Q₈×C₁₃	—	2	2	no	—
415	Q₈×C₁₃	—	4	2	no	—
416	Q₈×C₁₃	—	4	2	no	—
417	Q₈×C₁₃	—	4	2	no	—
418	D₄×C₁₃	—	2	2	no	—
419	D₄×C₁₃	—	2	4	no	—
420	D₄×C₁₃	—	2	2	no	—
421	D₄×C₁₃	—	4	2	no	—
422	D₄×C₁₃	—	4	2	no	—
423	D₄×C₁₃	—	4	4	no	—
424	D₄×C₁₃	—	4	4	no	—
425	D₄×C₁₃	—	4	4	no	—
426	D₄×C₁₃	—	4	4	no	—
427	D₄×C₁₃	—	4	4	no	—
428	D₄×C₁₃	—	4	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	2	2	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	4	1	no	—
446	C₂×C₄×C₁₃	—	4	1	no	—
447	C₂×C₄×C₁₃	—	4	1	no	—
448	C₂×C₄×C₁₃	—	4	1	no	—
449	C₂×C₄×C₁₃	—	4	1	no	—
450	C₂×C₄×C₁₃	—	4	1	no	—
451	C₂×C₄×C₁₃	—	4	1	no	—
452	C₂×C₄×C₁₃	—	4	4	no	—
453	C₂×C₄×C₁₃	—	4	4	no	—
454	C₂×C₄×C₁₃	—	4	2	no	—
455	C₂×C₄×C₁₃	—	4	2	no	—
456	C₂×C₄×C₁₃	—	4	2	no	—
457	C₂×C₄×C₁₃	—	4	4	no	—
458	C₂×C₄×C₁₃	—	4	4	no	—
459	C₂×C₄×C₁₃	—	4	4	no	—
460	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
472	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
473	C₈×C₁₃	—	2	4	no	—
474	C₈×C₁₃	C₂×#41	1	8	yes	—
475	C₂×#137	C₂²×C₁₃	1	2	yes	—
476	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
477	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
478	#533	C₂²×C₁₃	1	1	yes	characteristic
479	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
480	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	#532	C₂²×C₁₃	1	1	yes	characteristic
482	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
483	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	#529	—	2	1	no	—
485	#529	—	2	1	no	—
486	#529	—	2	1	no	—
487	#529	—	2	1	no	—
488	#529	—	2	1	no	—
489	#529	—	2	1	no	—
490	#529	—	2	1	no	—
491	#529	—	2	1	no	—
492	#529	C₂²×C₁₃	1	2	yes	—
493	#529	C₂²×C₁₃	1	2	yes	—
494	#529	C₂²×C₁₃	1	2	yes	—
495	#529	C₂²×C₁₃	1	2	yes	—
496	#529	C₂²×C₁₃	1	2	yes	complemented
497	#529	C₂²×C₁₃	1	2	yes	complemented
498	C₂×#126	—	2	1	no	—
499	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
500	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
501	#525	—	2	1	no	—
502	#525	—	2	1	no	—
503	#525	C₂²×C₁₃	1	2	yes	—
504	C₂×#123	—	2	1	no	—
505	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
506	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
507	C₄×#41	—	2	1	no	—
508	C₄×#41	—	2	1	no	—
509	C₄×#41	C₂²×C₁₃	1	2	yes	—
510	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
511	C₂×C₄×D₄	—	2	1	no	—
512	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
513	C₂×#117	—	2	1	no	—
514	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
515	#501	C₂²×C₁₃	1	2	yes	complemented
516	#501	C₂²×C₁₃	1	2	yes	complemented
517	#499	C₂²×C₁₃	1	4	yes	complemented
518	#497	C₂²×C₁₃	1	2	yes	complemented
519	#496	C₂²×C₁₃	1	2	yes	complemented
520	#495	C₂²×C₁₃	1	4	yes	complemented
521	#491	C₂²×C₁₃	1	2	yes	complemented
522	#490	C₂²×C₁₃	1	2	yes	complemented
523	#489	C₂²×C₁₃	1	2	yes	complemented
524	#489	C₂²×C₁₃	1	2	yes	complemented
525	#488	C₂²×C₁₃	1	4	yes	complemented
526	#488	C₂²×C₁₃	1	4	yes	complemented
527	#470	C₂²×C₁₃	1	4	yes	complemented
528	#469	C₂²×C₁₃	1	4	yes	—
529	#468	C₂²×C₁₃	1	4	yes	—
530	#468	C₂²×C₁₃	1	4	yes	complemented
531	#467	C₂²×C₁₃	1	4	yes	complemented
532	#466	C₂²×C₁₃	1	4	yes	—
533	#465	C₂²×C₁₃	1	4	yes	—
534	#465	C₂²×C₁₃	1	4	yes	complemented
535	#442	C₂²×C₁₃	1	4	yes	complemented
536	#441	C₂²×C₁₃	1	4	yes	complemented
537	#440	C₂²×C₁₃	1	4	yes	complemented
538	#440	C₂²×C₁₃	1	4	yes	complemented
539	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
540	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
541	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
542	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
543	#428	C₂²×C₁₃	1	2	yes	—
544	#428	C₂²×C₁₃	1	2	yes	—
545	#419	C₂²×C₁₃	1	2	yes	—
546	#418	C₂²×C₁₃	1	2	yes	—
547	#417	C₂²×C₁₃	1	2	yes	—
548	#417	C₂²×C₁₃	1	2	yes	—
549	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
550	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
551	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
552	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
553	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
554	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
555	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
556	C₂²×C₁₃	—	2	1	no	—
557	C₂²×C₁₃	—	2	1	no	—
558	C₂²×C₁₃	—	2	1	no	—
559	C₂²×C₁₃	—	2	1	no	—
560	C₂²×C₁₃	—	2	1	no	—
561	C₂²×C₁₃	—	2	1	no	—
562	C₂²×C₁₃	—	2	1	no	—
563	C₂²×C₁₃	—	4	4	no	—
564	C₂²×C₁₃	—	4	2	no	—
565	C₂²×C₁₃	—	4	2	no	—
566	C₂²×C₁₃	—	4	2	no	—
567	C₂²×C₁₃	—	4	2	no	—
568	C₂²×C₁₃	—	4	2	no	—
569	C₂²×C₁₃	—	4	2	no	—
570	C₂²×C₁₃	—	8	4	no	—
571	C₂²×C₁₃	#532	1	2	yes	—
572	C₂²×C₁₃	#575	1	2	yes	—
573	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
574	C₄×C₁₃	—	2	1	no	—
575	C₄×C₁₃	—	2	1	no	—
576	C₄×C₁₃	—	2	1	no	—
577	C₄×C₁₃	—	2	1	no	—
578	C₄×C₁₃	—	2	1	no	—
579	C₄×C₁₃	—	2	1	no	—
580	C₄×C₁₃	—	2	1	no	—
581	C₄×C₁₃	—	2	1	no	—
582	C₄×C₁₃	—	2	1	no	—
583	C₄×C₁₃	—	4	2	no	—
584	C₄×C₁₃	—	4	2	no	—
585	C₄×C₁₃	—	4	2	no	—
586	C₄×C₁₃	—	4	2	no	—
587	C₄×C₁₃	—	4	2	no	—
588	C₄×C₁₃	—	4	2	no	—
589	C₄×C₁₃	#532	1	2	yes	—
590	C₄×C₁₃	#575	1	2	yes	—
591	C₄×C₁₃	C₂²×#41	1	2	yes	—
592	C₂×#41	—	2	1	no	—
593	C₂×#41	—	2	1	no	—
594	C₂×#41	C₂³×C₁₃	1	2	yes	—
595	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
596	C₂²×D₄	—	2	1	no	—
597	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
598	C₂³×C₄	—	2	1	no	—
599	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
600	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
602	#137	—	2	8	no	—
603	AGL(1,ℤ/8)	—	2	8	no	—
604	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
605	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
606	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
607	C₂×D₈	C₂³×C₁₃	1	4	yes	—
608	C₂×M₁₆	—	2	8	no	—
609	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
610	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
611	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
612	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
613	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
614	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
615	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
616	#127	C₂³×C₁₃	1	1	yes	characteristic
617	#126	—	2	2	no	—
618	#126	—	2	2	no	—
619	#126	—	2	2	no	—
620	#126	—	2	2	no	—
621	#126	—	2	2	no	—
622	#126	—	2	2	no	—
623	#125	—	2	1	no	—
624	#125	—	2	1	no	—
625	#125	—	2	1	no	—
626	#125	—	2	1	no	—
627	#125	C₂³×C₁₃	1	2	yes	—
628	#125	C₂³×C₁₃	1	2	yes	—
629	#125	C₂³×C₁₃	1	2	yes	—
630	#124	—	2	1	no	—
631	#124	—	2	1	no	—
632	#124	—	2	1	no	—
633	#124	—	2	1	no	—
634	#124	C₂³×C₁₃	1	2	yes	—
635	#124	C₂³×C₁₃	1	2	yes	—
636	#124	C₂³×C₁₃	1	2	yes	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	#123	—	2	2	no	—
643	#123	—	2	2	no	—
644	C₂²⋊Q₈	—	2	1	no	—
645	C₂²⋊Q₈	—	2	1	no	—
646	C₂²⋊Q₈	—	2	1	no	—
647	C₂²⋊Q₈	—	2	1	no	—
648	C₂²⋊Q₈	—	2	1	no	—
649	C₂²⋊Q₈	—	2	1	no	—
650	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
651	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
652	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
653	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
654	#121	—	2	1	no	—
655	#121	—	2	1	no	—
656	#121	—	2	1	no	—
657	#121	—	2	1	no	—
658	#121	—	2	1	no	—
659	#121	—	2	1	no	—
660	#121	C₂³×C₁₃	1	2	yes	—
661	#121	C₂³×C₁₃	1	2	yes	—
662	#121	C₂³×C₁₃	1	2	yes	—
663	#121	C₂³×C₁₃	1	2	yes	—
664	#120	—	2	2	no	—
665	C₄×Q₈	—	2	1	no	—
666	C₄×Q₈	—	2	1	no	—
667	C₄×Q₈	—	2	1	no	—
668	C₄×Q₈	—	2	1	no	—
669	C₄×Q₈	—	2	1	no	—
670	C₄×Q₈	—	2	1	no	—
671	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
672	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
673	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
674	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	—	2	2	no	—
682	C₄×D₄	—	2	2	no	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	1	no	—
686	C₄×D₄	—	2	1	no	—
687	C₄×D₄	—	2	1	no	—
688	C₄×D₄	—	2	1	no	—
689	C₄×D₄	—	2	1	no	—
690	C₄×D₄	—	2	1	no	—
691	C₄×D₄	C₂³×C₁₃	1	2	yes	—
692	C₄×D₄	C₂³×C₁₃	1	2	yes	—
693	C₄×D₄	C₂³×C₁₃	1	2	yes	—
694	C₄×D₄	C₂³×C₁₃	1	2	yes	—
695	#117	—	2	1	no	—
696	#117	—	2	1	no	—
697	#117	—	2	2	no	—
698	#117	—	2	2	no	—
699	#117	—	2	2	no	—
700	#117	—	2	2	no	—
701	#117	—	2	2	no	—
702	#117	—	2	2	no	—
703	#117	—	2	2	no	—
704	#117	C₂³×C₁₃	1	2	yes	—
705	C₂×C₄⋊C₄	—	2	1	no	—
706	C₂×C₄⋊C₄	—	2	1	no	—
707	C₂×C₄⋊C₄	—	2	1	no	—
708	C₂×C₄⋊C₄	—	2	1	no	—
709	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
710	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
711	C₂×C₂²⋊C₄	—	2	1	no	—
712	C₂×C₂²⋊C₄	—	2	1	no	—
713	C₂×C₂²⋊C₄	—	2	1	no	—
714	C₂×C₂²⋊C₄	—	2	1	no	—
715	C₂×C₂²⋊C₄	—	2	1	no	—
716	C₂×C₄²	—	2	1	no	—
717	C₂×C₄²	—	2	2	no	—
718	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
719	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
720	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
721	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
722	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
723	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
724	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
725	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
726	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
727	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
728	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
729	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
730	#107	C₂³×C₁₃	1	4	yes	—
731	#107	C₂³×C₁₃	1	4	yes	—
732	#106	C₂³×C₁₃	1	4	yes	—
733	#106	C₂³×C₁₃	1	4	yes	—
734	#103	C₂³×C₁₃	1	4	yes	—
735	#103	C₂³×C₁₃	1	4	yes	—
736	#103	C₂³×C₁₃	1	4	yes	—
737	#103	C₂³×C₁₃	1	4	yes	—
738	#102	C₂³×C₁₃	1	4	yes	—
739	#102	C₂³×C₁₃	1	4	yes	—
740	#102	C₂³×C₁₃	1	4	yes	—
741	#102	C₂³×C₁₃	1	4	yes	—
742	#97	C₂³×C₁₃	1	4	yes	—
743	#97	C₂³×C₁₃	1	2	yes	—
744	#97	C₂³×C₁₃	1	2	yes	—
745	C₄×C₈	C₂³×C₁₃	1	4	yes	—
746	C₄×C₈	C₂³×C₁₃	1	2	yes	—
747	C₄×C₈	C₂³×C₁₃	1	2	yes	—
748	C₂×C₁₃	—	2	2	no	—
749	C₂×C₁₃	—	2	2	no	—
750	C₂×C₁₃	—	4	1	no	—
751	C₂×C₁₃	—	8	2	no	—
752	C₂×C₁₃	—	8	2	no	—
753	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
754	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
755	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
756	C₂⁴	—	2	1	no	—
757	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
758	#41	—	2	4	no	—
759	#41	—	2	4	no	—
760	#41	—	4	4	no	—
761	#41	—	4	4	no	—
762	C₂×Q₈	—	2	1	no	—
763	C₂×Q₈	—	2	1	no	—
764	C₂×Q₈	—	2	1	no	—
765	C₂×Q₈	—	2	4	no	—
766	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
767	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	1	no	—
774	C₂×D₄	—	2	1	no	—
775	C₂×D₄	—	2	1	no	—
776	C₂×D₄	—	2	4	no	—
777	C₂×D₄	—	4	4	no	—
778	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
779	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	2	1	no	—
782	C₂²×C₄	—	2	1	no	—
783	C₂²×C₄	—	2	1	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	4	2	no	—
790	C₂²×C₄	—	4	2	no	—
791	C₂²×C₄	—	4	4	no	—
792	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
793	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
794	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
796	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
798	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
799	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
800	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
801	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
802	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
803	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
804	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
805	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
806	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
810	Q₁₆	—	2	8	no	—
811	SD₁₆	—	2	8	no	—
812	SD₁₆	—	2	8	no	—
813	D₈	—	2	8	no	—
814	M₁₆	—	2	4	no	—
815	M₁₆	—	2	8	no	—
816	M₁₆	C₁₃×#41	1	8	yes	complemented
817	C₂×C₈	—	2	8	no	—
818	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
819	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	1	no	—
833	C₄⋊C₄	—	2	1	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
841	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
842	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
843	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
869	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
870	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
871	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
872	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
873	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
874	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
875	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
876	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
877	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
878	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
879	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
880	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
881	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
882	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
883	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
884	C₁₃	#60702	1	1	yes	characteristic, direct product factor, Sylow
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	4	1	no	—
890	C₂³	—	4	2	no	—
891	C₂³	—	4	2	no	—
892	C₂³	—	4	2	no	—
893	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
894	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
895	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
896	Q₈	—	2	2	no	—
897	Q₈	—	2	4	no	—
898	Q₈	—	2	2	no	—
899	Q₈	—	4	2	no	—
900	Q₈	—	4	2	no	—
901	Q₈	—	4	2	no	—
902	D₄	—	2	2	no	—
903	D₄	—	2	4	no	—
904	D₄	—	2	2	no	—
905	D₄	—	4	2	no	—
906	D₄	—	4	2	no	—
907	D₄	—	4	4	no	—
908	D₄	—	4	4	no	—
909	D₄	—	4	4	no	—
910	D₄	—	4	4	no	—
911	D₄	—	4	4	no	—
912	D₄	—	4	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	4	1	no	—
930	C₂×C₄	—	4	1	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	4	4	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	4	2	no	—
939	C₂×C₄	—	4	2	no	—
940	C₂×C₄	—	4	2	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	4	4	no	—
943	C₂×C₄	—	4	4	no	—
944	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
945	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
946	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
947	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
948	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
949	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
950	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
951	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
952	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
953	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
954	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
955	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
956	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
957	C₈	—	2	4	no	—
958	C₈	C₂×C₁₃×#41	1	8	yes	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	4	4	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	8	4	no	—
974	C₂²	C₁₃×#532	1	2	yes	—
975	C₂²	C₁₃×#575	1	2	yes	—
976	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
977	C₄	—	2	1	no	—
978	C₄	—	2	1	no	—
979	C₄	—	2	1	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	C₁₃×#532	1	2	yes	—
993	C₄	C₁₃×#575	1	2	yes	—
994	C₄	C₂²×C₁₃×#41	1	2	yes	—
995	C₂	—	2	2	no	—
996	C₂	—	2	2	no	—
997	C₂	—	4	1	no	—
998	C₂	—	8	2	no	—
999	C₂	—	8	2	no	—
1000	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
1001	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
1002	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	semidirect
2. C₂×C₁₃×#529	C₂	semidirect
3. C₁₃×#3183	C₂	semidirect
4. C₁₃×#3181	C₂	semidirect
5. C₁₃×#3180	C₂	semidirect
6. C₁₃×#3172	C₂	semidirect
7. C₁₃×#3171	C₂	semidirect
8. C₁₃×#3168	C₂	semidirect
9. C₁₃×#3166	C₂	semidirect
10. C₁₃×#3153	C₂	semidirect
11. C₁₃×#3142	C₂	semidirect
12. C₁₃×#3140	C₂	semidirect
13. C₁₃×#3056	C₂	semidirect
14. C₁₃×#3055	C₂	semidirect
15. C₄×C₁₃×#137	C₂	semidirect
16. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
17. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
22. C₁₃×#533	C₂²	semidirect
23. C₁₃×#533	C₂²	semidirect
25. C₁₃×#532	C₂²	semidirect
26. C₁₃×#532	C₂²	semidirect
39. C₁₃×#529	C₂²	semidirect
40. C₁₃×#529	C₂²	semidirect
58. C₁₃×#501	C₂²	semidirect
59. C₁₃×#501	C₂²	semidirect
60. C₁₃×#499	C₂²	semidirect
61. C₁₃×#497	C₂²	semidirect
62. C₁₃×#496	C₂²	semidirect
63. C₁₃×#495	C₂²	semidirect
64. C₁₃×#491	C₂²	semidirect
65. C₁₃×#490	C₂²	semidirect
66. C₁₃×#489	C₂²	semidirect
67. C₁₃×#489	C₂²	semidirect
68. C₁₃×#488	C₂²	semidirect
69. C₁₃×#488	C₂²	semidirect
70. C₁₃×#470	C₂²	semidirect
73. C₁₃×#468	C₂²	semidirect
74. C₁₃×#467	C₂²	semidirect
77. C₁₃×#465	C₂²	semidirect
78. C₁₃×#442	C₂²	semidirect
79. C₁₃×#441	C₂²	semidirect
80. C₁₃×#440	C₂²	semidirect
81. C₁₃×#440	C₂²	semidirect
82. C₄×C₁₃×Q₁₆	C₂²	semidirect
83. C₄×C₁₃×SD₁₆	C₂²	semidirect
84. C₄×C₁₃×SD₁₆	C₂²	semidirect
85. C₄×C₁₃×D₈	C₂²	semidirect
95. C₄×C₁₃×M₁₆	C₂²	semidirect
96. C₄×C₁₃×M₁₆	C₂²	semidirect
97. C₂×C₁₃×#97	C₂²	semidirect
98. C₂×C₄×C₈×C₁₃	C₂²	semidirect
255. #60702	C₁₃	direct (N × H)
316. C₁₃×M₁₆	#41	semidirect
384. #3444	C₂×C₁₃	semidirect
385. C₂×#529	C₂×C₁₃	semidirect
386. #3183	C₂×C₁₃	semidirect
387. #3181	C₂×C₁₃	semidirect
388. #3180	C₂×C₁₃	semidirect
389. #3172	C₂×C₁₃	semidirect
390. #3171	C₂×C₁₃	semidirect
391. #3168	C₂×C₁₃	semidirect
392. #3166	C₂×C₁₃	semidirect
393. #3153	C₂×C₁₃	semidirect
394. #3142	C₂×C₁₃	semidirect
395. #3140	C₂×C₁₃	semidirect
396. #3056	C₂×C₁₃	semidirect
397. #3055	C₂×C₁₃	semidirect
398. C₄×#137	C₂×C₁₃	semidirect
399. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
400. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
479. #533	C₂²×C₁₃	semidirect
480. #533	C₂²×C₁₃	semidirect
482. #532	C₂²×C₁₃	semidirect
483. #532	C₂²×C₁₃	semidirect
496. #529	C₂²×C₁₃	semidirect
497. #529	C₂²×C₁₃	semidirect
515. #501	C₂²×C₁₃	semidirect
516. #501	C₂²×C₁₃	semidirect
517. #499	C₂²×C₁₃	semidirect
518. #497	C₂²×C₁₃	semidirect
519. #496	C₂²×C₁₃	semidirect
520. #495	C₂²×C₁₃	semidirect
521. #491	C₂²×C₁₃	semidirect
522. #490	C₂²×C₁₃	semidirect
523. #489	C₂²×C₁₃	semidirect
524. #489	C₂²×C₁₃	semidirect
525. #488	C₂²×C₁₃	semidirect
526. #488	C₂²×C₁₃	semidirect
527. #470	C₂²×C₁₃	semidirect
530. #468	C₂²×C₁₃	semidirect
531. #467	C₂²×C₁₃	semidirect
534. #465	C₂²×C₁₃	semidirect
535. #442	C₂²×C₁₃	semidirect
536. #441	C₂²×C₁₃	semidirect
537. #440	C₂²×C₁₃	semidirect
538. #440	C₂²×C₁₃	semidirect
539. C₄×Q₁₆	C₂²×C₁₃	semidirect
540. C₄×SD₁₆	C₂²×C₁₃	semidirect
541. C₄×SD₁₆	C₂²×C₁₃	semidirect
542. C₄×D₈	C₂²×C₁₃	semidirect
552. C₄×M₁₆	C₂²×C₁₃	semidirect
553. C₄×M₁₆	C₂²×C₁₃	semidirect
554. C₂×#97	C₂²×C₁₃	semidirect
555. C₂×C₄×C₈	C₂²×C₁₃	semidirect
816. M₁₆	C₁₃×#41	semidirect
884. C₁₃	#60702	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×#3444	2
C₂×C₁₃×#529	2
C₁₃×#3183	2
C₁₃×#3181	2
C₁₃×#3180	2
C₁₃×#3172	2
C₁₃×#3171	2
C₁₃×#3168	2
C₁₃×#3166	2
C₁₃×#3153	2
C₁₃×#3142	2
C₁₃×#3140	2
C₁₃×#3056	2
C₁₃×#3055	2
C₄×C₁₃×#137	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₂×C₄×C₁₃×M₁₆	2
#60702	13

Subgroups — C13×#60702 #15747041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60702 #15747041