Subgroups — C₁₃×#23868 #15710207

Order 3328.

1756 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2407	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2001	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#137	—	2	4	no	—
20	C₂×C₁₃×#137	—	2	4	no	—
21	C₂×C₁₃×#137	—	2	4	no	—
22	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
29	D₄×Q₈×C₁₃	—	2	4	no	—
30	D₄×Q₈×C₁₃	—	2	4	no	—
31	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
34	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃	—	2	1	no	—
41	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#452	—	2	4	no	—
43	C₁₃×#451	—	2	4	no	—
44	C₁₃×#448	—	2	4	no	—
45	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#102	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	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
56	C₁₃×#394	—	2	1	no	—
57	C₁₃×#392	—	2	1	no	—
58	C₁₃×#391	C₂²	1	1	yes	characteristic
59	C₁₃×#390	C₂²	1	1	yes	characteristic
60	C₁₃×#386	—	2	1	no	—
61	C₁₃×#385	—	2	1	no	—
62	C₁₃×#380	C₂²	1	1	yes	characteristic
63	C₁₃×#340	C₂²	1	1	yes	characteristic
64	C₁₃×#340	C₂²	1	1	yes	characteristic
65	C₁₃×#336	C₂²	1	1	yes	characteristic
66	C₁₃×#336	C₂²	1	1	yes	characteristic
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	—	2	2	no	—
71	C₂×C₁₃×#41	—	4	1	no	—
72	C₂×C₁₃×#41	—	4	1	no	—
73	C₂²×Q₈×C₁₃	—	2	2	no	—
74	C₂²×Q₈×C₁₃	—	2	2	no	—
75	C₂²×Q₈×C₁₃	—	2	1	no	—
76	C₂²×Q₈×C₁₃	—	2	1	no	—
77	C₂²×Q₈×C₁₃	—	2	2	no	—
78	C₂²×Q₈×C₁₃	—	2	2	no	—
79	C₂²×Q₈×C₁₃	—	2	2	no	—
80	C₂²×Q₈×C₁₃	—	2	2	no	—
81	C₂²×Q₈×C₁₃	—	2	2	no	—
82	C₂²×Q₈×C₁₃	—	4	1	no	—
83	C₂²×Q₈×C₁₃	—	4	1	no	—
84	C₂²×Q₈×C₁₃	—	4	1	no	—
85	C₂²×Q₈×C₁₃	—	4	1	no	—
86	C₂²×Q₈×C₁₃	D₄	1	4	yes	complemented
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃	—	2	1	no	—
92	C₂²×D₄×C₁₃	—	2	1	no	—
93	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
94	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	—	2	1	no	—
96	C₂³×C₄×C₁₃	—	2	1	no	—
97	C₂³×C₄×C₁₃	—	2	1	no	—
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#137	—	2	32	no	—
101	C₂×C₁₃×Q₁₆	—	2	2	no	—
102	C₂×C₁₃×Q₁₆	—	2	2	no	—
103	C₂×C₁₃×Q₁₆	—	2	2	no	—
104	C₂×C₁₃×Q₁₆	—	2	2	no	—
105	C₂×C₁₃×Q₁₆	—	2	2	no	—
106	C₂×C₁₃×Q₁₆	—	2	2	no	—
107	C₂×C₁₃×Q₁₆	—	2	2	no	—
108	C₂×C₁₃×Q₁₆	—	4	1	no	—
109	C₂×C₁₃×Q₁₆	D₄	1	4	yes	complemented
110	C₂×C₁₃×SD₁₆	—	2	2	no	—
111	C₂×C₁₃×SD₁₆	—	2	2	no	—
112	C₂×C₁₃×SD₁₆	—	2	2	no	—
113	C₂×C₁₃×SD₁₆	—	2	2	no	—
114	C₂×C₁₃×SD₁₆	—	2	2	no	—
115	C₂×C₁₃×SD₁₆	—	2	2	no	—
116	C₂×C₁₃×SD₁₆	—	2	2	no	—
117	C₂×C₁₃×SD₁₆	—	4	1	no	—
118	C₂×C₁₃×SD₁₆	D₄	1	4	yes	complemented
119	C₂×C₁₃×M₁₆	—	2	2	no	—
120	C₂×C₁₃×M₁₆	—	2	2	no	—
121	C₂×C₁₃×M₁₆	—	2	2	no	—
122	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₁₃×C₄⋊Q₈	—	2	8	no	—
127	C₁₃×C₄⋊Q₈	—	2	2	no	—
128	C₁₃×C₄⋊Q₈	—	2	2	no	—
129	C₁₃×C₂²⋊Q₈	—	2	8	no	—
130	C₁₃×C₂²⋊Q₈	—	2	8	no	—
131	C₁₃×C₂²⋊Q₈	—	2	2	no	—
132	C₁₃×C₂²⋊Q₈	—	2	2	no	—
133	C₁₃×C₂²⋊Q₈	—	2	2	no	—
134	C₁₃×C₂²⋊Q₈	—	2	2	no	—
135	C₁₃×C₂²⋊Q₈	—	4	1	no	—
136	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	complemented
137	C₁₃×#121	—	2	2	no	—
138	C₁₃×#121	—	4	1	no	—
139	C₄×Q₈×C₁₃	—	2	2	no	—
140	C₄×Q₈×C₁₃	—	2	2	no	—
141	C₄×D₄×C₁₃	—	2	8	no	—
142	C₄×D₄×C₁₃	—	2	2	no	—
143	C₄×D₄×C₁₃	—	2	2	no	—
144	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
157	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
158	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
160	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
162	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	—	2	1	no	—
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₁₃×#103	—	2	2	no	—
166	C₁₃×#103	—	2	2	no	—
167	C₁₃×#103	—	2	2	no	—
168	C₁₃×#103	—	2	2	no	—
169	C₁₃×#103	—	2	2	no	—
170	C₁₃×#103	—	4	1	no	—
171	C₁₃×#103	—	4	1	no	—
172	C₁₃×#102	—	2	2	no	—
173	C₁₃×C₂²⋊C₈	—	2	2	no	—
174	C₁₃×C₂²⋊C₈	—	2	2	no	—
175	C₁₃×C₂²⋊C₈	—	2	2	no	—
176	C₁₃×#95	—	2	1	no	—
177	C₁₃×#95	—	2	1	no	—
178	C₁₃×#95	—	2	1	no	—
179	#23868	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂⁴×C₁₃	—	2	1	no	—
181	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₁₃×#41	—	2	8	no	—
184	C₁₃×#41	—	4	4	no	—
185	C₁₃×#41	—	4	4	no	—
186	C₁₃×#41	—	4	4	no	—
187	C₂×Q₈×C₁₃	—	2	4	no	—
188	C₂×Q₈×C₁₃	—	2	4	no	—
189	C₂×Q₈×C₁₃	—	2	1	no	—
190	C₂×Q₈×C₁₃	—	2	1	no	—
191	C₂×Q₈×C₁₃	—	2	1	no	—
192	C₂×Q₈×C₁₃	—	2	1	no	—
193	C₂×Q₈×C₁₃	—	2	1	no	—
194	C₂×Q₈×C₁₃	—	2	1	no	—
195	C₂×Q₈×C₁₃	—	2	8	no	—
196	C₂×Q₈×C₁₃	—	2	1	no	—
197	C₂×Q₈×C₁₃	—	2	1	no	—
198	C₂×Q₈×C₁₃	—	2	1	no	—
199	C₂×Q₈×C₁₃	—	2	1	no	—
200	C₂×Q₈×C₁₃	—	2	1	no	—
201	C₂×Q₈×C₁₃	—	2	1	no	—
202	C₂×Q₈×C₁₃	—	2	1	no	—
203	C₂×Q₈×C₁₃	—	2	1	no	—
204	C₂×Q₈×C₁₃	—	2	1	no	—
205	C₂×Q₈×C₁₃	—	2	1	no	—
206	C₂×Q₈×C₁₃	—	2	1	no	—
207	C₂×Q₈×C₁₃	—	2	1	no	—
208	C₂×Q₈×C₁₃	—	4	2	no	—
209	C₂×Q₈×C₁₃	—	4	2	no	—
210	C₂×Q₈×C₁₃	—	4	2	no	—
211	C₂×Q₈×C₁₃	—	4	2	no	—
212	C₂×Q₈×C₁₃	—	4	4	no	—
213	C₂×Q₈×C₁₃	—	4	4	no	—
214	C₂×Q₈×C₁₃	—	4	4	no	—
215	C₂×Q₈×C₁₃	—	4	4	no	—
216	C₂×Q₈×C₁₃	—	4	4	no	—
217	C₂×Q₈×C₁₃	—	4	4	no	—
218	C₂×Q₈×C₁₃	—	4	4	no	—
219	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
220	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
221	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
222	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
225	C₂×D₄×C₁₃	—	2	2	no	—
226	C₂×D₄×C₁₃	—	2	2	no	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	2	1	no	—
229	C₂×D₄×C₁₃	—	2	1	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	1	no	—
232	C₂×D₄×C₁₃	—	2	1	no	—
233	C₂×D₄×C₁₃	—	4	2	no	—
234	C₂×D₄×C₁₃	—	4	2	no	—
235	C₂×D₄×C₁₃	—	4	2	no	—
236	C₂×D₄×C₁₃	—	4	2	no	—
237	C₂×D₄×C₁₃	—	4	2	no	—
238	C₂×D₄×C₁₃	—	8	1	no	—
239	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
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	4	no	—
246	C₂²×C₄×C₁₃	—	2	4	no	—
247	C₂²×C₄×C₁₃	—	2	1	no	—
248	C₂²×C₄×C₁₃	—	2	1	no	—
249	C₂²×C₄×C₁₃	—	2	1	no	—
250	C₂²×C₄×C₁₃	—	2	1	no	—
251	C₂²×C₄×C₁₃	—	2	1	no	—
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	2	1	no	—
254	C₂²×C₄×C₁₃	—	2	1	no	—
255	C₂²×C₄×C₁₃	—	2	1	no	—
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	4	2	no	—
260	C₂²×C₄×C₁₃	—	4	2	no	—
261	C₂²×C₄×C₁₃	—	4	2	no	—
262	C₂²×C₄×C₁₃	—	4	2	no	—
263	C₂²×C₄×C₁₃	—	4	2	no	—
264	C₂²×C₄×C₁₃	—	4	2	no	—
265	C₂²×C₄×C₁₃	—	4	2	no	—
266	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₁₃×Q₁₆	—	2	8	no	—
274	C₁₃×Q₁₆	—	2	8	no	—
275	C₁₃×Q₁₆	—	4	4	no	—
276	C₁₃×SD₁₆	—	2	8	no	—
277	C₁₃×SD₁₆	—	2	8	no	—
278	C₁₃×SD₁₆	—	4	4	no	—
279	C₁₃×M₁₆	—	2	8	no	—
280	C₂×C₈×C₁₃	—	2	1	no	—
281	C₂×C₈×C₁₃	—	2	1	no	—
282	C₂×C₈×C₁₃	—	2	1	no	—
283	C₂×C₈×C₁₃	—	2	1	no	—
284	C₂×C₈×C₁₃	—	2	1	no	—
285	C₂×C₈×C₁₃	—	2	1	no	—
286	C₂×C₈×C₁₃	—	2	1	no	—
287	C₂×C₈×C₁₃	—	2	1	no	—
288	C₂×C₈×C₁₃	—	2	1	no	—
289	C₂×C₈×C₁₃	—	2	1	no	—
290	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
291	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	—	2	4	no	—
294	C₁₃×C₄⋊C₄	—	2	4	no	—
295	C₁₃×C₄⋊C₄	—	2	4	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	1	no	—
299	C₁₃×C₄⋊C₄	—	2	1	no	—
300	C₁₃×C₄⋊C₄	—	2	1	no	—
301	C₁₃×C₄⋊C₄	—	2	1	no	—
302	C₁₃×C₄⋊C₄	—	2	1	no	—
303	C₁₃×C₄⋊C₄	—	4	2	no	—
304	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
305	C₁₃×C₂²⋊C₄	—	2	4	no	—
306	C₁₃×C₂²⋊C₄	—	2	4	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	4	2	no	—
310	C₁₃×C₂²⋊C₄	—	4	2	no	—
311	C₁₃×C₂²⋊C₄	—	4	2	no	—
312	C₁₃×C₂²⋊C₄	—	8	1	no	—
313	C₁₃×C₂²⋊C₄	—	8	1	no	—
314	C₄²×C₁₃	—	2	4	no	—
315	C₄²×C₁₃	—	2	1	no	—
316	C₄²×C₁₃	—	2	1	no	—
317	C₂²×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
318	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
319	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
320	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
321	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#2407	C₂×C₁₃	1	1	yes	characteristic
323	#2016	C₂×C₁₃	1	1	yes	characteristic, complemented
324	#2013	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#2001	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#2000	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#1894	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
329	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#1870	C₂×C₁₃	1	1	yes	characteristic, complemented
331	#1787	C₂×C₁₃	1	1	yes	characteristic, complemented
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	1	no	—
337	C₂³×C₁₃	—	2	1	no	—
338	C₂³×C₁₃	—	2	1	no	—
339	C₂³×C₁₃	—	2	1	no	—
340	C₂³×C₁₃	—	2	1	no	—
341	C₂³×C₁₃	—	2	1	no	—
342	C₂³×C₁₃	—	2	1	no	—
343	C₂³×C₁₃	—	2	1	no	—
344	C₂³×C₁₃	—	2	2	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	#120	1	2	yes	—
352	C₂³×C₁₃	#137	1	2	yes	complemented
353	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
354	Q₈×C₁₃	—	2	2	no	—
355	Q₈×C₁₃	—	2	2	no	—
356	Q₈×C₁₃	—	2	2	no	—
357	Q₈×C₁₃	—	2	2	no	—
358	Q₈×C₁₃	—	2	2	no	—
359	Q₈×C₁₃	—	2	2	no	—
360	Q₈×C₁₃	—	2	2	no	—
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	2	no	—
363	Q₈×C₁₃	—	4	8	no	—
364	Q₈×C₁₃	—	4	8	no	—
365	Q₈×C₁₃	—	4	1	no	—
366	Q₈×C₁₃	—	4	1	no	—
367	Q₈×C₁₃	—	4	1	no	—
368	Q₈×C₁₃	—	4	1	no	—
369	Q₈×C₁₃	—	4	1	no	—
370	Q₈×C₁₃	—	4	1	no	—
371	Q₈×C₁₃	#120	1	4	yes	—
372	D₄×C₁₃	—	2	8	no	—
373	D₄×C₁₃	—	2	2	no	—
374	D₄×C₁₃	—	2	2	no	—
375	D₄×C₁₃	—	4	8	no	—
376	D₄×C₁₃	—	4	1	no	—
377	D₄×C₁₃	—	4	1	no	—
378	D₄×C₁₃	—	8	4	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	1	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	1	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	1	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	4	8	no	—
401	C₂×C₄×C₁₃	—	4	8	no	—
402	C₂×C₄×C₁₃	—	4	8	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	#137	1	2	yes	complemented
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	C₂²×D₄	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	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
435	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×#137	—	2	4	no	—
437	C₂×#137	—	2	4	no	—
438	C₂×#137	—	2	4	no	—
439	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
440	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
441	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
442	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
443	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
444	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
445	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
446	D₄×Q₈	—	2	4	no	—
447	D₄×Q₈	—	2	4	no	—
448	C₂×C₄⋊Q₈	—	2	1	no	—
449	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×C₂²⋊Q₈	—	2	1	no	—
451	C₂×C₂²⋊Q₈	—	2	1	no	—
452	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
453	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
456	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×C₄×D₄	—	2	1	no	—
458	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
459	#452	—	2	4	no	—
460	#451	—	2	4	no	—
461	#448	—	2	4	no	—
462	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
463	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
464	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
465	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
466	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
467	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
468	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×#102	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	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
473	#394	—	2	1	no	—
474	#392	—	2	1	no	—
475	#391	C₂²×C₁₃	1	1	yes	characteristic
476	#390	C₂²×C₁₃	1	1	yes	characteristic
477	#386	—	2	1	no	—
478	#385	—	2	1	no	—
479	#380	C₂²×C₁₃	1	1	yes	characteristic
480	#340	C₂²×C₁₃	1	1	yes	characteristic
481	#340	C₂²×C₁₃	1	1	yes	characteristic
482	#336	C₂²×C₁₃	1	1	yes	characteristic
483	#336	C₂²×C₁₃	1	1	yes	characteristic
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	—	4	1	no	—
491	C₂²×C₁₃	—	4	1	no	—
492	C₂²×C₁₃	—	4	1	no	—
493	C₂²×C₁₃	—	4	1	no	—
494	C₂²×C₁₃	—	4	1	no	—
495	C₂²×C₁₃	—	4	1	no	—
496	C₂²×C₁₃	—	4	1	no	—
497	C₂²×C₁₃	—	4	1	no	—
498	C₂²×C₁₃	—	4	2	no	—
499	C₂²×C₁₃	—	4	2	no	—
500	C₂²×C₁₃	—	4	2	no	—
501	C₂²×C₁₃	—	8	1	no	—
502	C₂²×C₁₃	—	8	1	no	—
503	C₂²×C₁₃	—	8	1	no	—
504	C₂²×C₁₃	—	8	1	no	—
505	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
506	C₂²×C₁₃	D₄²	1	1	yes	characteristic
507	C₂²×C₁₃	D₄²	1	1	yes	characteristic
508	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
509	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
510	C₂²×C₁₃	#577	1	1	yes	characteristic
511	C₂²×C₁₃	#578	1	1	yes	characteristic
512	C₄×C₁₃	—	2	2	no	—
513	C₄×C₁₃	—	2	4	no	—
514	C₄×C₁₃	—	2	2	no	—
515	C₄×C₁₃	—	4	1	no	—
516	C₄×C₁₃	—	4	2	no	—
517	C₄×C₁₃	—	4	2	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	—	4	1	no	—
520	C₄×C₁₃	—	4	2	no	—
521	C₄×C₁₃	—	8	1	no	—
522	C₄×C₁₃	—	8	1	no	—
523	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
524	C₄×C₁₃	#534	1	1	yes	characteristic
525	C₄×C₁₃	D₄²	1	1	yes	characteristic
526	C₄×C₁₃	D₄²	1	1	yes	characteristic
527	C₂×#41	—	2	2	no	—
528	C₂×#41	—	2	2	no	—
529	C₂×#41	—	2	2	no	—
530	C₂×#41	—	2	2	no	—
531	C₂×#41	—	4	1	no	—
532	C₂×#41	—	4	1	no	—
533	C₂²×Q₈	—	2	2	no	—
534	C₂²×Q₈	—	2	2	no	—
535	C₂²×Q₈	—	2	1	no	—
536	C₂²×Q₈	—	2	1	no	—
537	C₂²×Q₈	—	2	2	no	—
538	C₂²×Q₈	—	2	2	no	—
539	C₂²×Q₈	—	2	2	no	—
540	C₂²×Q₈	—	2	2	no	—
541	C₂²×Q₈	—	2	2	no	—
542	C₂²×Q₈	—	4	1	no	—
543	C₂²×Q₈	—	4	1	no	—
544	C₂²×Q₈	—	4	1	no	—
545	C₂²×Q₈	—	4	1	no	—
546	C₂²×Q₈	D₄×C₁₃	1	4	yes	complemented
547	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
548	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
549	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
550	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	—	2	1	no	—
553	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
554	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
555	C₂³×C₄	—	2	1	no	—
556	C₂³×C₄	—	2	1	no	—
557	C₂³×C₄	—	2	1	no	—
558	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
560	#137	—	2	32	no	—
561	C₂×Q₁₆	—	2	2	no	—
562	C₂×Q₁₆	—	2	2	no	—
563	C₂×Q₁₆	—	2	2	no	—
564	C₂×Q₁₆	—	2	2	no	—
565	C₂×Q₁₆	—	2	2	no	—
566	C₂×Q₁₆	—	2	2	no	—
567	C₂×Q₁₆	—	2	2	no	—
568	C₂×Q₁₆	—	4	1	no	—
569	C₂×Q₁₆	D₄×C₁₃	1	4	yes	complemented
570	C₂×SD₁₆	—	2	2	no	—
571	C₂×SD₁₆	—	2	2	no	—
572	C₂×SD₁₆	—	2	2	no	—
573	C₂×SD₁₆	—	2	2	no	—
574	C₂×SD₁₆	—	2	2	no	—
575	C₂×SD₁₆	—	2	2	no	—
576	C₂×SD₁₆	—	2	2	no	—
577	C₂×SD₁₆	—	4	1	no	—
578	C₂×SD₁₆	D₄×C₁₃	1	4	yes	complemented
579	C₂×M₁₆	—	2	2	no	—
580	C₂×M₁₆	—	2	2	no	—
581	C₂×M₁₆	—	2	2	no	—
582	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
583	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
584	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
586	C₄⋊Q₈	—	2	8	no	—
587	C₄⋊Q₈	—	2	2	no	—
588	C₄⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	8	no	—
590	C₂²⋊Q₈	—	2	8	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	4	1	no	—
596	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	complemented
597	#121	—	2	2	no	—
598	#121	—	4	1	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	2	2	no	—
601	C₄×D₄	—	2	8	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	D₄×C₁₃	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
623	C₂×C₄²	—	2	1	no	—
624	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
625	#103	—	2	2	no	—
626	#103	—	2	2	no	—
627	#103	—	2	2	no	—
628	#103	—	2	2	no	—
629	#103	—	2	2	no	—
630	#103	—	4	1	no	—
631	#103	—	4	1	no	—
632	#102	—	2	2	no	—
633	C₂²⋊C₈	—	2	2	no	—
634	C₂²⋊C₈	—	2	2	no	—
635	C₂²⋊C₈	—	2	2	no	—
636	#95	—	2	1	no	—
637	#95	—	2	1	no	—
638	#95	—	2	1	no	—
639	C₂×C₁₃	—	4	2	no	—
640	C₂×C₁₃	—	4	2	no	—
641	C₂×C₁₃	—	8	2	no	—
642	C₂×C₁₃	#2403	1	1	yes	characteristic
643	C₂×C₁₃	#3004	1	1	yes	characteristic
644	C₂×C₁₃	#3013	1	1	yes	characteristic
645	C₂×C₁₃	#3266	1	1	yes	characteristic
646	C₂×C₁₃	#3270	1	1	yes	characteristic
647	C₂×C₁₃	#3276	1	1	yes	characteristic
648	C₂×C₁₃	#3278	1	1	yes	characteristic
649	C₂⁴	—	2	1	no	—
650	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
651	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
652	#41	—	2	8	no	—
653	#41	—	4	4	no	—
654	#41	—	4	4	no	—
655	#41	—	4	4	no	—
656	C₂×Q₈	—	2	4	no	—
657	C₂×Q₈	—	2	4	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	8	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	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	—	2	1	no	—
674	C₂×Q₈	—	2	1	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	—	4	2	no	—
678	C₂×Q₈	—	4	2	no	—
679	C₂×Q₈	—	4	2	no	—
680	C₂×Q₈	—	4	2	no	—
681	C₂×Q₈	—	4	4	no	—
682	C₂×Q₈	—	4	4	no	—
683	C₂×Q₈	—	4	4	no	—
684	C₂×Q₈	—	4	4	no	—
685	C₂×Q₈	—	4	4	no	—
686	C₂×Q₈	—	4	4	no	—
687	C₂×Q₈	—	4	4	no	—
688	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
689	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
690	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
691	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
692	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
693	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	8	1	no	—
708	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	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	—	4	2	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
736	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
737	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
738	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
739	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
740	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
742	Q₁₆	—	2	8	no	—
743	Q₁₆	—	2	8	no	—
744	Q₁₆	—	4	4	no	—
745	SD₁₆	—	2	8	no	—
746	SD₁₆	—	2	8	no	—
747	SD₁₆	—	4	4	no	—
748	M₁₆	—	2	8	no	—
749	C₂×C₈	—	2	1	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	C₂×D₄×C₁₃	1	2	yes	—
760	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	2	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	—	4	2	no	—
773	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	—	4	2	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	8	1	no	—
782	C₂²⋊C₄	—	8	1	no	—
783	C₄²	—	2	4	no	—
784	C₄²	—	2	1	no	—
785	C₄²	—	2	1	no	—
786	C₁₃	#23868	1	1	yes	characteristic, direct product factor, Sylow
787	C₂³	—	2	1	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	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	2	no	—
800	C₂³	—	4	1	no	—
801	C₂³	—	4	1	no	—
802	C₂³	—	4	1	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	4	1	no	—
806	C₂³	C₁₃×#120	1	2	yes	—
807	C₂³	C₁₃×#137	1	2	yes	complemented
808	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
809	Q₈	—	2	2	no	—
810	Q₈	—	2	2	no	—
811	Q₈	—	2	2	no	—
812	Q₈	—	2	2	no	—
813	Q₈	—	2	2	no	—
814	Q₈	—	2	2	no	—
815	Q₈	—	2	2	no	—
816	Q₈	—	2	2	no	—
817	Q₈	—	2	2	no	—
818	Q₈	—	4	8	no	—
819	Q₈	—	4	8	no	—
820	Q₈	—	4	1	no	—
821	Q₈	—	4	1	no	—
822	Q₈	—	4	1	no	—
823	Q₈	—	4	1	no	—
824	Q₈	—	4	1	no	—
825	Q₈	—	4	1	no	—
826	Q₈	C₁₃×#120	1	4	yes	—
827	D₄	—	2	8	no	—
828	D₄	—	2	2	no	—
829	D₄	—	2	2	no	—
830	D₄	—	4	8	no	—
831	D₄	—	4	1	no	—
832	D₄	—	4	1	no	—
833	D₄	—	8	4	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	8	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	4	1	no	—
861	C₂×C₄	—	4	1	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	—	4	1	no	—
871	C₂×C₄	—	4	1	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	C₁₃×#120	1	2	yes	—
877	C₂×C₄	C₁₃×#137	1	2	yes	complemented
878	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
880	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
881	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
882	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
883	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
884	C₈	—	2	2	no	—
885	C₈	—	2	2	no	—
886	C₈	—	4	1	no	—
887	C₈	—	4	1	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	1	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	8	1	no	—
906	C₂²	—	8	1	no	—
907	C₂²	—	8	1	no	—
908	C₂²	—	8	1	no	—
909	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
910	C₂²	D₄²×C₁₃	1	1	yes	characteristic
911	C₂²	D₄²×C₁₃	1	1	yes	characteristic
912	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
913	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
914	C₂²	C₁₃×#577	1	1	yes	characteristic
915	C₂²	C₁₃×#578	1	1	yes	characteristic
916	C₄	—	2	2	no	—
917	C₄	—	2	4	no	—
918	C₄	—	2	2	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	8	1	no	—
926	C₄	—	8	1	no	—
927	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
928	C₄	C₁₃×#534	1	1	yes	characteristic
929	C₄	D₄²×C₁₃	1	1	yes	characteristic
930	C₄	D₄²×C₁₃	1	1	yes	characteristic
931	C₂	—	4	2	no	—
932	C₂	—	4	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₁₃×#2403	1	1	yes	characteristic
935	C₂	C₁₃×#3004	1	1	yes	characteristic
936	C₂	C₁₃×#3013	1	1	yes	characteristic
937	C₂	C₁₃×#3266	1	1	yes	characteristic
938	C₂	C₁₃×#3270	1	1	yes	characteristic
939	C₂	C₁₃×#3276	1	1	yes	characteristic
940	C₂	C₁₃×#3278	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2407	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#137	C₂	semidirect
2. C₂×D₄×Q₈×C₁₃	C₂	semidirect
3. C₂×C₁₃×#452	C₂	semidirect
4. C₂×C₁₃×#451	C₂	semidirect
5. C₂×C₁₃×#448	C₂	semidirect
7. C₁₃×#2016	C₂	semidirect
8. C₁₃×#2013	C₂	semidirect
9. C₁₃×#2001	C₂	semidirect
10. C₁₃×#2000	C₂	semidirect
11. C₁₃×#1894	C₂	semidirect
12. C₁₃×#1880	C₂	semidirect
13. C₁₃×#1878	C₂	semidirect
14. C₁₃×#1870	C₂	semidirect
15. C₁₃×#1787	C₂	semidirect
86. C₂²×Q₈×C₁₃	D₄	semidirect
109. C₂×C₁₃×Q₁₆	D₄	semidirect
118. C₂×C₁₃×SD₁₆	D₄	semidirect
136. C₁₃×C₂²⋊Q₈	D₄	semidirect
179. #23868	C₁₃	direct (N × H)
317. C₂²×#137	C₂×C₁₃	semidirect
318. C₂×D₄×Q₈	C₂×C₁₃	semidirect
319. C₂×#452	C₂×C₁₃	semidirect
320. C₂×#451	C₂×C₁₃	semidirect
321. C₂×#448	C₂×C₁₃	semidirect
323. #2016	C₂×C₁₃	semidirect
324. #2013	C₂×C₁₃	semidirect
325. #2001	C₂×C₁₃	semidirect
326. #2000	C₂×C₁₃	semidirect
327. #1894	C₂×C₁₃	semidirect
328. #1880	C₂×C₁₃	semidirect
329. #1878	C₂×C₁₃	semidirect
330. #1870	C₂×C₁₃	semidirect
331. #1787	C₂×C₁₃	semidirect
352. C₂³×C₁₃	#137	semidirect
422. C₂×C₄×C₁₃	#137	semidirect
546. C₂²×Q₈	D₄×C₁₃	semidirect
569. C₂×Q₁₆	D₄×C₁₃	semidirect
578. C₂×SD₁₆	D₄×C₁₃	semidirect
596. C₂²⋊Q₈	D₄×C₁₃	semidirect
786. C₁₃	#23868	direct (N × H)
807. C₂³	C₁₃×#137	semidirect
877. C₂×C₄	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#137	2
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#452	2
C₂×C₁₃×#451	2
C₂×C₁₃×#448	2
C₁₃×#2407	2
C₁₃×#2016	2
C₁₃×#2013	2
C₁₃×#2001	2
C₁₃×#2000	2
C₁₃×#1894	2
C₁₃×#1880	2
C₁₃×#1878	2
C₁₃×#1870	2
C₁₃×#1787	2
#23868	13

Subgroups — C13×#23868 #15710207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23868 #15710207