Subgroups — C₁₃×#24382 #15710721

Order 3328.

1678 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2847	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1892	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#525	—	2	4	no	—
23	C₁₃×#525	—	2	4	no	—
24	C₂×C₁₃×#123	—	2	1	no	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#120	—	2	1	no	—
33	C₂×C₁₃×#120	—	2	1	no	—
34	C₂×C₄×D₄×C₁₃	—	2	1	no	—
35	C₂×C₄×D₄×C₁₃	—	2	1	no	—
36	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
37	C₁₃×#466	—	2	4	no	—
38	C₁₃×#465	—	2	4	no	—
39	C₁₃×#449	—	2	4	no	—
40	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₁₃×C₂²⋊C₈	—	2	4	no	—
51	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
55	C₁₃×#386	—	2	1	no	—
56	C₁₃×#386	—	2	1	no	—
57	C₁₃×#386	—	2	1	no	—
58	C₁₃×#380	C₂²	1	1	yes	characteristic
59	C₁₃×#380	C₂²	1	1	yes	characteristic
60	C₁₃×#380	C₂²	1	1	yes	characteristic
61	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
65	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	2	2	no	—
69	C₂×C₁₃×#41	—	2	2	no	—
70	C₂×C₁₃×#41	—	4	1	no	—
71	C₂×C₁₃×#41	—	4	1	no	—
72	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₃	—	2	1	no	—
74	C₂²×D₄×C₁₃	—	2	1	no	—
75	C₂²×D₄×C₁₃	—	2	1	no	—
76	C₂²×D₄×C₁₃	—	2	1	no	—
77	C₂²×D₄×C₁₃	—	2	1	no	—
78	C₂²×D₄×C₁₃	—	2	1	no	—
79	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	—	2	2	no	—
82	C₂³×C₄×C₁₃	—	2	1	no	—
83	C₂³×C₄×C₁₃	—	2	2	no	—
84	C₂³×C₄×C₁₃	—	2	2	no	—
85	C₂³×C₄×C₁₃	—	2	2	no	—
86	C₂³×C₄×C₁₃	—	4	1	no	—
87	C₂³×C₄×C₁₃	—	4	1	no	—
88	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×SD₁₆	—	2	2	no	—
95	C₂×C₁₃×SD₁₆	—	2	2	no	—
96	C₂×C₁₃×SD₁₆	—	4	1	no	—
97	C₂×C₁₃×D₈	—	2	2	no	—
98	C₂×C₁₃×D₈	—	2	2	no	—
99	C₂×C₁₃×D₈	—	4	1	no	—
100	C₂²×C₈×C₁₃	—	2	2	no	—
101	C₂²×C₈×C₁₃	—	2	2	no	—
102	C₂²×C₈×C₁₃	—	2	2	no	—
103	C₂²×C₈×C₁₃	—	2	2	no	—
104	C₂²×C₈×C₁₃	—	4	1	no	—
105	C₂²×C₈×C₁₃	—	4	1	no	—
106	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#123	—	2	8	no	—
111	C₁₃×C₂²⋊Q₈	—	2	2	no	—
112	C₁₃×C₂²⋊Q₈	—	2	2	no	—
113	C₁₃×C₂²⋊Q₈	—	2	2	no	—
114	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	complemented
115	C₁₃×#121	—	2	2	no	—
116	C₁₃×#121	—	2	2	no	—
117	C₁₃×#121	—	2	2	no	—
118	C₁₃×#121	—	2	2	no	—
119	C₁₃×#121	—	2	2	no	—
120	C₁₃×#121	—	2	2	no	—
121	C₁₃×#121	—	2	2	no	—
122	C₁₃×#121	—	4	1	no	—
123	C₁₃×#121	—	4	1	no	—
124	C₁₃×#121	D₄	1	4	yes	complemented
125	C₁₃×#120	—	2	8	no	—
126	C₁₃×#120	—	4	4	no	—
127	C₄×D₄×C₁₃	—	2	8	no	—
128	C₄×D₄×C₁₃	—	2	8	no	—
129	C₁₃×#117	—	2	2	no	—
130	C₁₃×#117	—	2	2	no	—
131	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
139	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
140	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
144	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
146	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
147	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
149	C₂×C₄²×C₁₃	—	2	1	no	—
150	C₁₃×#107	—	2	2	no	—
151	C₁₃×#106	—	2	2	no	—
152	C₁₃×#103	—	2	2	no	—
153	C₁₃×#103	—	2	2	no	—
154	C₁₃×#103	—	4	1	no	—
155	C₁₃×#102	—	2	2	no	—
156	C₁₃×#102	—	2	2	no	—
157	C₁₃×#102	—	2	2	no	—
158	C₁₃×#102	—	2	2	no	—
159	C₁₃×#102	—	4	1	no	—
160	C₁₃×C₂²⋊C₈	—	2	2	no	—
161	C₁₃×C₂²⋊C₈	—	2	2	no	—
162	C₁₃×C₂²⋊C₈	—	2	2	no	—
163	C₁₃×C₂²⋊C₈	D₄	1	4	yes	complemented
164	C₁₃×#95	—	2	1	no	—
165	C₁₃×#95	—	2	1	no	—
166	C₁₃×#95	—	2	1	no	—
167	#24382	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂⁴×C₁₃	—	2	2	no	—
169	C₂⁴×C₁₃	—	2	2	no	—
170	C₂⁴×C₁₃	—	2	2	no	—
171	C₂⁴×C₁₃	—	2	2	no	—
172	C₂⁴×C₁₃	—	2	2	no	—
173	C₂⁴×C₁₃	—	2	1	no	—
174	C₂⁴×C₁₃	—	2	1	no	—
175	C₂⁴×C₁₃	—	4	1	no	—
176	C₂⁴×C₁₃	—	4	1	no	—
177	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₁₃×#41	—	4	4	no	—
181	C₁₃×#41	—	4	4	no	—
182	C₁₃×#41	—	4	4	no	—
183	C₁₃×#41	—	4	4	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	—	2	1	no	—
187	C₂×Q₈×C₁₃	—	2	1	no	—
188	C₂×Q₈×C₁₃	—	2	1	no	—
189	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
190	C₂×D₄×C₁₃	—	2	4	no	—
191	C₂×D₄×C₁₃	—	2	4	no	—
192	C₂×D₄×C₁₃	—	2	4	no	—
193	C₂×D₄×C₁₃	—	2	1	no	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	2	1	no	—
196	C₂×D₄×C₁₃	—	2	1	no	—
197	C₂×D₄×C₁₃	—	2	1	no	—
198	C₂×D₄×C₁₃	—	2	1	no	—
199	C₂×D₄×C₁₃	—	2	1	no	—
200	C₂×D₄×C₁₃	—	2	1	no	—
201	C₂×D₄×C₁₃	—	2	1	no	—
202	C₂×D₄×C₁₃	—	2	1	no	—
203	C₂×D₄×C₁₃	—	2	1	no	—
204	C₂×D₄×C₁₃	—	4	2	no	—
205	C₂×D₄×C₁₃	—	4	2	no	—
206	C₂×D₄×C₁₃	—	4	2	no	—
207	C₂×D₄×C₁₃	—	4	2	no	—
208	C₂×D₄×C₁₃	—	4	2	no	—
209	C₂×D₄×C₁₃	—	4	2	no	—
210	C₂×D₄×C₁₃	—	4	2	no	—
211	C₂×D₄×C₁₃	—	4	2	no	—
212	C₂×D₄×C₁₃	—	4	2	no	—
213	C₂×D₄×C₁₃	—	4	2	no	—
214	C₂×D₄×C₁₃	—	4	2	no	—
215	C₂×D₄×C₁₃	—	4	2	no	—
216	C₂×D₄×C₁₃	—	4	2	no	—
217	C₂×D₄×C₁₃	—	4	2	no	—
218	C₂×D₄×C₁₃	—	4	2	no	—
219	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	4	no	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	2	1	no	—
232	C₂²×C₄×C₁₃	—	2	1	no	—
233	C₂²×C₄×C₁₃	—	2	1	no	—
234	C₂²×C₄×C₁₃	—	2	2	no	—
235	C₂²×C₄×C₁₃	—	2	2	no	—
236	C₂²×C₄×C₁₃	—	2	2	no	—
237	C₂²×C₄×C₁₃	—	2	2	no	—
238	C₂²×C₄×C₁₃	—	2	1	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	2	1	no	—
241	C₂²×C₄×C₁₃	—	2	1	no	—
242	C₂²×C₄×C₁₃	—	2	1	no	—
243	C₂²×C₄×C₁₃	—	2	1	no	—
244	C₂²×C₄×C₁₃	—	2	1	no	—
245	C₂²×C₄×C₁₃	—	2	1	no	—
246	C₂²×C₄×C₁₃	—	2	1	no	—
247	C₂²×C₄×C₁₃	—	4	1	no	—
248	C₂²×C₄×C₁₃	—	4	1	no	—
249	C₂²×C₄×C₁₃	—	4	1	no	—
250	C₂²×C₄×C₁₃	—	4	4	no	—
251	C₂²×C₄×C₁₃	—	4	4	no	—
252	C₂²×C₄×C₁₃	—	4	4	no	—
253	C₂²×C₄×C₁₃	—	4	4	no	—
254	C₂²×C₄×C₁₃	—	4	2	no	—
255	C₂²×C₄×C₁₃	—	4	2	no	—
256	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₁₃	#41	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₁₃×SD₁₆	—	4	4	no	—
265	C₁₃×D₈	—	4	4	no	—
266	C₂×C₈×C₁₃	—	2	1	no	—
267	C₂×C₈×C₁₃	—	2	1	no	—
268	C₂×C₈×C₁₃	—	2	1	no	—
269	C₂×C₈×C₁₃	—	2	1	no	—
270	C₂×C₈×C₁₃	—	2	1	no	—
271	C₂×C₈×C₁₃	—	2	1	no	—
272	C₂×C₈×C₁₃	—	2	1	no	—
273	C₂×C₈×C₁₃	—	2	1	no	—
274	C₂×C₈×C₁₃	—	2	1	no	—
275	C₂×C₈×C₁₃	—	2	1	no	—
276	C₂×C₈×C₁₃	—	4	4	no	—
277	C₂×C₈×C₁₃	—	4	4	no	—
278	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
279	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
280	C₁₃×C₄⋊C₄	—	2	4	no	—
281	C₁₃×C₄⋊C₄	—	2	4	no	—
282	C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	1	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
291	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	—	2	4	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	—	4	2	no	—
298	C₁₃×C₂²⋊C₄	—	4	2	no	—
299	C₁₃×C₂²⋊C₄	—	4	2	no	—
300	C₁₃×C₂²⋊C₄	—	4	2	no	—
301	C₁₃×C₂²⋊C₄	—	4	2	no	—
302	C₁₃×C₂²⋊C₄	—	4	2	no	—
303	C₄²×C₁₃	—	2	4	no	—
304	C₂×#525	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₂×#465	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂²×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#2847	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
311	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#2000	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#1999	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#1893	C₂×C₁₃	1	1	yes	characteristic, complemented
315	#1892	C₂×C₁₃	1	1	yes	characteristic, complemented
316	#1875	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
318	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
319	C₂³×C₁₃	—	2	1	no	—
320	C₂³×C₁₃	—	2	1	no	—
321	C₂³×C₁₃	—	2	1	no	—
322	C₂³×C₁₃	—	2	1	no	—
323	C₂³×C₁₃	—	2	8	no	—
324	C₂³×C₁₃	—	2	1	no	—
325	C₂³×C₁₃	—	2	1	no	—
326	C₂³×C₁₃	—	2	1	no	—
327	C₂³×C₁₃	—	2	1	no	—
328	C₂³×C₁₃	—	2	1	no	—
329	C₂³×C₁₃	—	2	1	no	—
330	C₂³×C₁₃	—	2	1	no	—
331	C₂³×C₁₃	—	2	1	no	—
332	C₂³×C₁₃	—	2	1	no	—
333	C₂³×C₁₃	—	2	1	no	—
334	C₂³×C₁₃	—	2	1	no	—
335	C₂³×C₁₃	—	2	1	no	—
336	C₂³×C₁₃	—	2	2	no	—
337	C₂³×C₁₃	—	4	4	no	—
338	C₂³×C₁₃	—	4	4	no	—
339	C₂³×C₁₃	—	4	4	no	—
340	C₂³×C₁₃	—	4	4	no	—
341	C₂³×C₁₃	—	4	4	no	—
342	C₂³×C₁₃	—	4	4	no	—
343	C₂³×C₁₃	—	4	1	no	—
344	C₂³×C₁₃	—	4	1	no	—
345	C₂³×C₁₃	—	4	1	no	—
346	C₂³×C₁₃	—	4	1	no	—
347	C₂³×C₁₃	—	4	1	no	—
348	C₂³×C₁₃	—	4	1	no	—
349	C₂³×C₁₃	—	4	1	no	—
350	C₂³×C₁₃	—	4	1	no	—
351	C₂³×C₁₃	—	4	1	no	—
352	C₂³×C₁₃	—	4	1	no	—
353	C₂³×C₁₃	—	4	1	no	—
354	C₂³×C₁₃	—	4	1	no	—
355	C₂³×C₁₃	—	4	1	no	—
356	C₂³×C₁₃	#120	1	2	yes	—
357	C₂³×C₁₃	#121	1	2	yes	—
358	C₂³×C₁₃	#135	1	2	yes	—
359	C₂³×C₁₃	#135	1	2	yes	—
360	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
361	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
362	Q₈×C₁₃	—	2	2	no	—
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	4	1	no	—
365	Q₈×C₁₃	—	4	1	no	—
366	D₄×C₁₃	—	2	2	no	—
367	D₄×C₁₃	—	2	2	no	—
368	D₄×C₁₃	—	4	8	no	—
369	D₄×C₁₃	—	4	8	no	—
370	D₄×C₁₃	—	4	8	no	—
371	D₄×C₁₃	—	4	1	no	—
372	D₄×C₁₃	—	4	1	no	—
373	D₄×C₁₃	—	4	1	no	—
374	D₄×C₁₃	—	4	1	no	—
375	D₄×C₁₃	—	4	1	no	—
376	D₄×C₁₃	—	4	1	no	—
377	D₄×C₁₃	—	8	4	no	—
378	D₄×C₁₃	—	8	4	no	—
379	D₄×C₁₃	—	8	4	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	4	4	no	—
399	C₂×C₄×C₁₃	—	4	4	no	—
400	C₂×C₄×C₁₃	—	4	4	no	—
401	C₂×C₄×C₁₃	—	4	8	no	—
402	C₂×C₄×C₁₃	—	4	1	no	—
403	C₂×C₄×C₁₃	—	4	1	no	—
404	C₂×C₄×C₁₃	—	4	1	no	—
405	C₂×C₄×C₁₃	—	4	1	no	—
406	C₂×C₄×C₁₃	—	4	1	no	—
407	C₂×C₄×C₁₃	—	4	1	no	—
408	C₂×C₄×C₁₃	—	4	1	no	—
409	C₂×C₄×C₁₃	—	4	1	no	—
410	C₂×C₄×C₁₃	—	4	1	no	—
411	C₂×C₄×C₁₃	—	4	1	no	—
412	C₂×C₄×C₁₃	—	4	1	no	—
413	C₂×C₄×C₁₃	—	4	1	no	—
414	C₂×C₄×C₁₃	—	4	1	no	—
415	C₂×C₄×C₁₃	—	4	1	no	—
416	C₂×C₄×C₁₃	—	4	1	no	—
417	C₂×C₄×C₁₃	—	4	1	no	—
418	C₂×C₄×C₁₃	—	4	1	no	—
419	C₂×C₄×C₁₃	—	4	1	no	—
420	C₂×C₄×C₁₃	—	4	1	no	—
421	C₂×C₄×C₁₃	#120	1	2	yes	—
422	C₂×C₄×C₁₃	#121	1	2	yes	—
423	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
427	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
428	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
429	C₈×C₁₃	—	2	2	no	—
430	C₈×C₁₃	—	2	2	no	—
431	C₈×C₁₃	—	4	1	no	—
432	C₈×C₁₃	—	4	1	no	—
433	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
434	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
435	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
438	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
439	#525	—	2	4	no	—
440	#525	—	2	4	no	—
441	C₂×#123	—	2	1	no	—
442	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×#120	—	2	1	no	—
450	C₂×#120	—	2	1	no	—
451	C₂×C₄×D₄	—	2	1	no	—
452	C₂×C₄×D₄	—	2	1	no	—
453	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
454	#466	—	2	4	no	—
455	#465	—	2	4	no	—
456	#449	—	2	4	no	—
457	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
461	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
462	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
464	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
465	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
466	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
467	C₂×C₂²⋊C₈	—	2	4	no	—
468	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
470	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
471	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
472	#386	—	2	1	no	—
473	#386	—	2	1	no	—
474	#386	—	2	1	no	—
475	#380	C₂²×C₁₃	1	1	yes	characteristic
476	#380	C₂²×C₁₃	1	1	yes	characteristic
477	#380	C₂²×C₁₃	1	1	yes	characteristic
478	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
479	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
480	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	C₂²×C₁₃	—	2	2	no	—
483	C₂²×C₁₃	—	2	2	no	—
484	C₂²×C₁₃	—	2	2	no	—
485	C₂²×C₁₃	—	2	2	no	—
486	C₂²×C₁₃	—	2	2	no	—
487	C₂²×C₁₃	—	2	2	no	—
488	C₂²×C₁₃	—	2	2	no	—
489	C₂²×C₁₃	—	2	2	no	—
490	C₂²×C₁₃	—	2	2	no	—
491	C₂²×C₁₃	—	2	2	no	—
492	C₂²×C₁₃	—	2	2	no	—
493	C₂²×C₁₃	—	2	2	no	—
494	C₂²×C₁₃	—	4	16	no	—
495	C₂²×C₁₃	—	4	1	no	—
496	C₂²×C₁₃	—	4	1	no	—
497	C₂²×C₁₃	—	4	1	no	—
498	C₂²×C₁₃	—	4	1	no	—
499	C₂²×C₁₃	—	4	1	no	—
500	C₂²×C₁₃	—	4	1	no	—
501	C₂²×C₁₃	—	4	1	no	—
502	C₂²×C₁₃	—	4	1	no	—
503	C₂²×C₁₃	—	4	2	no	—
504	C₂²×C₁₃	—	4	2	no	—
505	C₂²×C₁₃	—	4	2	no	—
506	C₂²×C₁₃	—	8	1	no	—
507	C₂²×C₁₃	—	8	1	no	—
508	C₂²×C₁₃	—	8	1	no	—
509	C₂²×C₁₃	—	8	1	no	—
510	C₂²×C₁₃	—	8	1	no	—
511	C₂²×C₁₃	—	8	1	no	—
512	C₂²×C₁₃	—	8	1	no	—
513	C₂²×C₁₃	—	8	1	no	—
514	C₂²×C₁₃	—	8	1	no	—
515	C₂²×C₁₃	—	8	1	no	—
516	C₂²×C₁₃	—	8	1	no	—
517	C₂²×C₁₃	#449	1	4	yes	complemented
518	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
519	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
520	C₂²×C₁₃	#534	1	1	yes	characteristic
521	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
522	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
523	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
524	C₂²×C₁₃	#575	1	1	yes	characteristic
525	C₄×C₁₃	—	2	2	no	—
526	C₄×C₁₃	—	2	2	no	—
527	C₄×C₁₃	—	4	1	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	—	4	2	no	—
530	C₄×C₁₃	—	4	2	no	—
531	C₄×C₁₃	—	8	1	no	—
532	C₄×C₁₃	—	8	1	no	—
533	C₄×C₁₃	—	8	1	no	—
534	C₄×C₁₃	D₄²	1	1	yes	characteristic
535	C₄×C₁₃	D₄²	1	1	yes	characteristic
536	C₄×C₁₃	#546	1	1	yes	characteristic
537	C₄×C₁₃	#546	1	1	yes	characteristic
538	C₂⁵	D₄×C₁₃	1	1	yes	characteristic
539	C₂×#41	—	2	2	no	—
540	C₂×#41	—	2	2	no	—
541	C₂×#41	—	2	2	no	—
542	C₂×#41	—	2	2	no	—
543	C₂×#41	—	4	1	no	—
544	C₂×#41	—	4	1	no	—
545	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
546	C₂²×D₄	—	2	1	no	—
547	C₂²×D₄	—	2	1	no	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
553	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
554	C₂³×C₄	—	2	1	no	—
555	C₂³×C₄	—	2	2	no	—
556	C₂³×C₄	—	2	2	no	—
557	C₂³×C₄	—	2	2	no	—
558	C₂³×C₄	—	2	2	no	—
559	C₂³×C₄	—	4	1	no	—
560	C₂³×C₄	—	4	1	no	—
561	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
562	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
563	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
564	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
567	C₂×SD₁₆	—	2	2	no	—
568	C₂×SD₁₆	—	2	2	no	—
569	C₂×SD₁₆	—	4	1	no	—
570	C₂×D₈	—	2	2	no	—
571	C₂×D₈	—	2	2	no	—
572	C₂×D₈	—	4	1	no	—
573	C₂²×C₈	—	2	2	no	—
574	C₂²×C₈	—	2	2	no	—
575	C₂²×C₈	—	2	2	no	—
576	C₂²×C₈	—	2	2	no	—
577	C₂²×C₈	—	4	1	no	—
578	C₂²×C₈	—	4	1	no	—
579	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
580	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
581	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
582	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
583	#123	—	2	8	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	complemented
588	#121	—	2	2	no	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	4	1	no	—
596	#121	—	4	1	no	—
597	#121	D₄×C₁₃	1	4	yes	complemented
598	#120	—	2	8	no	—
599	#120	—	4	4	no	—
600	C₄×D₄	—	2	8	no	—
601	C₄×D₄	—	2	8	no	—
602	#117	—	2	2	no	—
603	#117	—	2	2	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₄²	—	2	1	no	—
623	#107	—	2	2	no	—
624	#106	—	2	2	no	—
625	#103	—	2	2	no	—
626	#103	—	2	2	no	—
627	#103	—	4	1	no	—
628	#102	—	2	2	no	—
629	#102	—	2	2	no	—
630	#102	—	2	2	no	—
631	#102	—	2	2	no	—
632	#102	—	4	1	no	—
633	C₂²⋊C₈	—	2	2	no	—
634	C₂²⋊C₈	—	2	2	no	—
635	C₂²⋊C₈	—	2	2	no	—
636	C₂²⋊C₈	D₄×C₁₃	1	4	yes	complemented
637	#95	—	2	1	no	—
638	#95	—	2	1	no	—
639	#95	—	2	1	no	—
640	C₂×C₁₃	—	2	4	no	—
641	C₂×C₁₃	—	4	2	no	—
642	C₂×C₁₃	—	4	2	no	—
643	C₂×C₁₃	—	8	2	no	—
644	C₂×C₁₃	—	16	1	no	—
645	C₂×C₁₃	#2410	1	1	yes	characteristic
646	C₂×C₁₃	C₂×#449	1	1	yes	characteristic
647	C₂×C₁₃	#3002	1	1	yes	characteristic
648	C₂×C₁₃	#3050	1	1	yes	characteristic
649	C₂×C₁₃	#3055	1	1	yes	characteristic
650	C₂×C₁₃	#3188	1	1	yes	characteristic
651	C₂×C₁₃	#3191	1	1	yes	characteristic
652	C₂⁴	—	2	2	no	—
653	C₂⁴	—	2	2	no	—
654	C₂⁴	—	2	2	no	—
655	C₂⁴	—	2	2	no	—
656	C₂⁴	—	2	2	no	—
657	C₂⁴	—	2	1	no	—
658	C₂⁴	—	2	1	no	—
659	C₂⁴	—	4	1	no	—
660	C₂⁴	—	4	1	no	—
661	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
662	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
663	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
664	#41	—	4	4	no	—
665	#41	—	4	4	no	—
666	#41	—	4	4	no	—
667	#41	—	4	4	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	4	2	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	4	1	no	—
732	C₂²×C₄	—	4	1	no	—
733	C₂²×C₄	—	4	1	no	—
734	C₂²×C₄	—	4	4	no	—
735	C₂²×C₄	—	4	4	no	—
736	C₂²×C₄	—	4	4	no	—
737	C₂²×C₄	—	4	4	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
741	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
742	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
743	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
744	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
746	C₂²×C₄	C₁₃×#41	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
748	SD₁₆	—	4	4	no	—
749	D₈	—	4	4	no	—
750	C₂×C₈	—	2	1	no	—
751	C₂×C₈	—	2	1	no	—
752	C₂×C₈	—	2	1	no	—
753	C₂×C₈	—	2	1	no	—
754	C₂×C₈	—	2	1	no	—
755	C₂×C₈	—	2	1	no	—
756	C₂×C₈	—	2	1	no	—
757	C₂×C₈	—	2	1	no	—
758	C₂×C₈	—	2	1	no	—
759	C₂×C₈	—	2	1	no	—
760	C₂×C₈	—	4	4	no	—
761	C₂×C₈	—	4	4	no	—
762	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
763	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
775	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₄²	—	2	4	no	—
788	C₁₃	#24382	1	1	yes	characteristic, direct product factor, Sylow
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	8	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	4	4	no	—
808	C₂³	—	4	4	no	—
809	C₂³	—	4	4	no	—
810	C₂³	—	4	4	no	—
811	C₂³	—	4	4	no	—
812	C₂³	—	4	4	no	—
813	C₂³	—	4	1	no	—
814	C₂³	—	4	1	no	—
815	C₂³	—	4	1	no	—
816	C₂³	—	4	1	no	—
817	C₂³	—	4	1	no	—
818	C₂³	—	4	1	no	—
819	C₂³	—	4	1	no	—
820	C₂³	—	4	1	no	—
821	C₂³	—	4	1	no	—
822	C₂³	—	4	1	no	—
823	C₂³	—	4	1	no	—
824	C₂³	—	4	1	no	—
825	C₂³	—	4	1	no	—
826	C₂³	C₁₃×#120	1	2	yes	—
827	C₂³	C₁₃×#121	1	2	yes	—
828	C₂³	C₁₃×#135	1	2	yes	—
829	C₂³	C₁₃×#135	1	2	yes	—
830	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
831	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
832	Q₈	—	2	2	no	—
833	Q₈	—	2	2	no	—
834	Q₈	—	4	1	no	—
835	Q₈	—	4	1	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	2	no	—
838	D₄	—	4	8	no	—
839	D₄	—	4	8	no	—
840	D₄	—	4	8	no	—
841	D₄	—	4	1	no	—
842	D₄	—	4	1	no	—
843	D₄	—	4	1	no	—
844	D₄	—	4	1	no	—
845	D₄	—	4	1	no	—
846	D₄	—	4	1	no	—
847	D₄	—	8	4	no	—
848	D₄	—	8	4	no	—
849	D₄	—	8	4	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	—	4	8	no	—
872	C₂×C₄	—	4	1	no	—
873	C₂×C₄	—	4	1	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	4	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	4	1	no	—
885	C₂×C₄	—	4	1	no	—
886	C₂×C₄	—	4	1	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	1	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	C₁₃×#120	1	2	yes	—
892	C₂×C₄	C₁₃×#121	1	2	yes	—
893	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
894	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
896	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
897	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
898	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
899	C₈	—	2	2	no	—
900	C₈	—	2	2	no	—
901	C₈	—	4	1	no	—
902	C₈	—	4	1	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	4	16	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	8	1	no	—
928	C₂²	—	8	1	no	—
929	C₂²	—	8	1	no	—
930	C₂²	—	8	1	no	—
931	C₂²	—	8	1	no	—
932	C₂²	—	8	1	no	—
933	C₂²	—	8	1	no	—
934	C₂²	—	8	1	no	—
935	C₂²	—	8	1	no	—
936	C₂²	—	8	1	no	—
937	C₂²	—	8	1	no	—
938	C₂²	C₁₃×#449	1	4	yes	complemented
939	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
940	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
941	C₂²	C₁₃×#534	1	1	yes	characteristic
942	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
943	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
944	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
945	C₂²	C₁₃×#575	1	1	yes	characteristic
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	8	1	no	—
953	C₄	—	8	1	no	—
954	C₄	—	8	1	no	—
955	C₄	D₄²×C₁₃	1	1	yes	characteristic
956	C₄	D₄²×C₁₃	1	1	yes	characteristic
957	C₄	C₁₃×#546	1	1	yes	characteristic
958	C₄	C₁₃×#546	1	1	yes	characteristic
959	C₂	—	2	4	no	—
960	C₂	—	4	2	no	—
961	C₂	—	4	2	no	—
962	C₂	—	8	2	no	—
963	C₂	—	16	1	no	—
964	C₂	C₁₃×#2410	1	1	yes	characteristic
965	C₂	C₂×C₁₃×#449	1	1	yes	characteristic
966	C₂	C₁₃×#3002	1	1	yes	characteristic
967	C₂	C₁₃×#3050	1	1	yes	characteristic
968	C₂	C₁₃×#3055	1	1	yes	characteristic
969	C₂	C₁₃×#3188	1	1	yes	characteristic
970	C₂	C₁₃×#3191	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂⁴×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#525	C₂	semidirect
2. C₂×C₁₃×#466	C₂	semidirect
3. C₂×C₁₃×#465	C₂	semidirect
4. C₂×C₁₃×#449	C₂	semidirect
5. C₂²×C₁₃×C₂²⋊C₈	C₂	semidirect
6. C₁₃×#2847	C₂	semidirect
7. C₁₃×#2036	C₂	semidirect
8. C₁₃×#2034	C₂	semidirect
9. C₁₃×#2000	C₂	semidirect
10. C₁₃×#1999	C₂	semidirect
11. C₁₃×#1893	C₂	semidirect
12. C₁₃×#1892	C₂	semidirect
13. C₁₃×#1875	C₂	semidirect
14. C₁₃×#1854	C₂	semidirect
15. C₁₃×#1788	C₂	semidirect
18. C₂²×C₁₃×SD₁₆	C₂²	semidirect
19. C₂²×C₁₃×D₈	C₂²	semidirect
40. C₂×C₁₃×#107	C₂²	semidirect
41. C₂×C₁₃×#106	C₂²	semidirect
42. C₂×C₁₃×#103	C₂²	semidirect
43. C₂×C₁₃×#103	C₂²	semidirect
44. C₂×C₁₃×#103	C₂²	semidirect
45. C₂×C₁₃×#102	C₂²	semidirect
46. C₂×C₁₃×#102	C₂²	semidirect
47. C₂×C₁₃×#102	C₂²	semidirect
48. C₂×C₁₃×#102	C₂²	semidirect
49. C₂×C₁₃×#102	C₂²	semidirect
61. C₁₃×#340	C₂²	semidirect
62. C₁₃×#340	C₂²	semidirect
63. C₁₃×#340	C₂²	semidirect
64. C₁₃×#340	C₂²	semidirect
114. C₁₃×C₂²⋊Q₈	D₄	semidirect
124. C₁₃×#121	D₄	semidirect
163. C₁₃×C₂²⋊C₈	D₄	semidirect
167. #24382	C₁₃	direct (N × H)
304. C₂×#525	C₂×C₁₃	semidirect
305. C₂×#466	C₂×C₁₃	semidirect
306. C₂×#465	C₂×C₁₃	semidirect
307. C₂×#449	C₂×C₁₃	semidirect
308. C₂²×C₂²⋊C₈	C₂×C₁₃	semidirect
309. #2847	C₂×C₁₃	semidirect
310. #2036	C₂×C₁₃	semidirect
311. #2034	C₂×C₁₃	semidirect
312. #2000	C₂×C₁₃	semidirect
313. #1999	C₂×C₁₃	semidirect
314. #1893	C₂×C₁₃	semidirect
315. #1892	C₂×C₁₃	semidirect
316. #1875	C₂×C₁₃	semidirect
317. #1854	C₂×C₁₃	semidirect
318. #1788	C₂×C₁₃	semidirect
435. C₂²×SD₁₆	C₂²×C₁₃	semidirect
436. C₂²×D₈	C₂²×C₁₃	semidirect
457. C₂×#107	C₂²×C₁₃	semidirect
458. C₂×#106	C₂²×C₁₃	semidirect
459. C₂×#103	C₂²×C₁₃	semidirect
460. C₂×#103	C₂²×C₁₃	semidirect
461. C₂×#103	C₂²×C₁₃	semidirect
462. C₂×#102	C₂²×C₁₃	semidirect
463. C₂×#102	C₂²×C₁₃	semidirect
464. C₂×#102	C₂²×C₁₃	semidirect
465. C₂×#102	C₂²×C₁₃	semidirect
466. C₂×#102	C₂²×C₁₃	semidirect
478. #340	C₂²×C₁₃	semidirect
479. #340	C₂²×C₁₃	semidirect
480. #340	C₂²×C₁₃	semidirect
481. #340	C₂²×C₁₃	semidirect
517. C₂²×C₁₃	#449	semidirect
587. C₂²⋊Q₈	D₄×C₁₃	semidirect
597. #121	D₄×C₁₃	semidirect
636. C₂²⋊C₈	D₄×C₁₃	semidirect
788. C₁₃	#24382	direct (N × H)
938. C₂²	C₁₃×#449	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#525	2
C₂×C₁₃×#466	2
C₂×C₁₃×#465	2
C₂×C₁₃×#449	2
C₂²×C₁₃×C₂²⋊C₈	2
C₁₃×#2847	2
C₁₃×#2036	2
C₁₃×#2034	2
C₁₃×#2000	2
C₁₃×#1999	2
C₁₃×#1893	2
C₁₃×#1892	2
C₁₃×#1875	2
C₁₃×#1854	2
C₁₃×#1788	2
#24382	13

Subgroups — C13×#24382 #15710721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24382 #15710721