Subgroups — C₁₃×#24364 #15710703

Order 3328.

1512 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2431	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2015	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1850	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	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#135	—	2	4	no	—
19	C₂×C₁₃×#135	—	2	4	no	—
20	C₂×C₁₃×#135	—	2	4	no	—
21	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
27	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#463	—	2	4	no	—
34	C₁₃×#459	—	2	4	no	—
35	C₁₃×#449	—	2	4	no	—
36	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₁₃×#392	—	2	1	no	—
48	C₁₃×#392	—	2	1	no	—
49	C₁₃×#391	C₂²	1	1	yes	characteristic
50	C₁₃×#391	C₂²	1	1	yes	characteristic
51	C₁₃×#391	C₂²	1	1	yes	characteristic
52	C₁₃×#390	C₂²	1	1	yes	characteristic
53	C₁₃×#386	—	2	1	no	—
54	C₁₃×#386	—	2	1	no	—
55	C₁₃×#386	—	2	1	no	—
56	C₁₃×#386	—	2	1	no	—
57	C₁₃×#381	—	2	1	no	—
58	C₁₃×#380	C₂²	1	1	yes	characteristic
59	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#95	—	2	1	no	—
61	C₁₃×#340	C₂²	1	1	yes	characteristic
62	C₁₃×#340	C₂²	1	1	yes	characteristic
63	C₁₃×#336	C₂²	1	1	yes	characteristic
64	C₁₃×#336	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#41	—	2	2	no	—
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	—	2	2	no	—
71	C₂×C₁₃×#41	—	2	2	no	—
72	C₂×C₁₃×#41	—	4	1	no	—
73	C₂×C₁₃×#41	—	4	1	no	—
74	C₂×C₁₃×#41	—	4	1	no	—
75	C₂×C₁₃×#41	—	4	1	no	—
76	C₂×C₁₃×#41	D₄	1	4	yes	complemented
77	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₃	—	2	1	no	—
80	C₂²×D₄×C₁₃	—	2	1	no	—
81	C₂²×D₄×C₁₃	—	2	1	no	—
82	C₂²×D₄×C₁₃	—	2	1	no	—
83	C₂²×D₄×C₁₃	—	2	1	no	—
84	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	—	2	1	no	—
88	C₂³×C₄×C₁₃	—	2	1	no	—
89	C₂³×C₄×C₁₃	—	2	1	no	—
90	C₂³×C₄×C₁₃	—	2	1	no	—
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#135	—	2	32	no	—
93	C₂×C₁₃×Q₁₆	—	2	2	no	—
94	C₂×C₁₃×Q₁₆	—	2	2	no	—
95	C₂×C₁₃×Q₁₆	—	2	2	no	—
96	C₂×C₁₃×SD₁₆	—	2	2	no	—
97	C₂×C₁₃×SD₁₆	—	2	2	no	—
98	C₂×C₁₃×SD₁₆	—	2	2	no	—
99	C₂×C₁₃×SD₁₆	—	2	2	no	—
100	C₂×C₁₃×SD₁₆	—	2	2	no	—
101	C₂×C₁₃×SD₁₆	—	2	2	no	—
102	C₂×C₁₃×SD₁₆	—	4	1	no	—
103	C₂×C₁₃×SD₁₆	—	4	1	no	—
104	C₂×C₁₃×SD₁₆	D₄	1	4	yes	complemented
105	C₂×C₁₃×D₈	—	2	2	no	—
106	C₂×C₁₃×D₈	—	2	2	no	—
107	C₂×C₁₃×D₈	—	2	2	no	—
108	C₂×C₁₃×D₈	—	2	2	no	—
109	C₂×C₁₃×D₈	—	2	2	no	—
110	C₂×C₁₃×D₈	D₄	1	4	yes	complemented
111	C₂²×C₈×C₁₃	—	2	2	no	—
112	C₂²×C₈×C₁₃	—	2	2	no	—
113	C₂²×C₈×C₁₃	—	2	2	no	—
114	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×#127	—	2	2	no	—
119	C₁₃×#127	—	4	1	no	—
120	C₁₃×#124	—	2	2	no	—
121	C₁₃×#124	—	4	1	no	—
122	C₁₃×#121	—	2	2	no	—
123	C₁₃×#121	—	2	2	no	—
124	C₄×D₄×C₁₃	—	2	2	no	—
125	C₄×D₄×C₁₃	—	2	2	no	—
126	C₄×D₄×C₁₃	—	4	1	no	—
127	C₄×D₄×C₁₃	—	4	1	no	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
136	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
137	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
138	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
139	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
140	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
143	C₁₃×C₄⋊C₈	—	2	2	no	—
144	C₁₃×C₄⋊C₈	—	2	2	no	—
145	C₁₃×#103	—	2	2	no	—
146	C₁₃×#103	—	2	2	no	—
147	C₁₃×#103	—	4	1	no	—
148	C₁₃×#102	—	2	2	no	—
149	C₁₃×#102	—	2	2	no	—
150	C₁₃×#102	—	2	2	no	—
151	C₁₃×#102	—	2	2	no	—
152	C₁₃×#102	—	4	1	no	—
153	C₁₃×C₂²⋊C₈	—	2	2	no	—
154	C₁₃×#95	—	2	1	no	—
155	C₁₃×#95	—	2	1	no	—
156	C₁₃×#95	—	2	1	no	—
157	C₁₃×#95	—	2	1	no	—
158	C₁₃×#95	—	2	1	no	—
159	C₁₃×#95	—	2	1	no	—
160	C₁₃×#95	—	2	1	no	—
161	C₁₃×#95	D₄	1	1	yes	characteristic
162	C₁₃×#95	D₄	1	1	yes	characteristic
163	#24364	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂⁴×C₁₃	—	2	1	no	—
165	C₂⁴×C₁₃	—	2	1	no	—
166	C₂⁴×C₁₃	—	2	1	no	—
167	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₁₃×#41	—	2	8	no	—
169	C₁₃×#41	—	2	8	no	—
170	C₁₃×#41	—	4	4	no	—
171	C₁₃×#41	—	4	4	no	—
172	C₁₃×#41	—	4	4	no	—
173	C₁₃×#41	—	4	4	no	—
174	C₁₃×#41	—	4	4	no	—
175	C₁₃×#41	—	4	4	no	—
176	C₂×Q₈×C₁₃	—	2	1	no	—
177	C₂×Q₈×C₁₃	—	2	1	no	—
178	C₂×Q₈×C₁₃	—	2	1	no	—
179	C₂×Q₈×C₁₃	—	2	1	no	—
180	C₂×Q₈×C₁₃	—	2	1	no	—
181	C₂×Q₈×C₁₃	—	2	1	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
187	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
188	C₂×D₄×C₁₃	—	2	4	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	2	1	no	—
192	C₂×D₄×C₁₃	—	2	1	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	—	4	2	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	—	8	1	no	—
214	C₂×D₄×C₁₃	—	8	1	no	—
215	C₂×D₄×C₁₃	—	8	1	no	—
216	C₂×D₄×C₁₃	—	8	1	no	—
217	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
219	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
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	4	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	—	2	1	no	—
231	C₂²×C₄×C₁₃	—	4	2	no	—
232	C₂²×C₄×C₁₃	—	4	2	no	—
233	C₂²×C₄×C₁₃	—	4	2	no	—
234	C₂²×C₄×C₁₃	—	4	2	no	—
235	C₂²×C₄×C₁₃	—	4	2	no	—
236	C₂²×C₄×C₁₃	—	4	2	no	—
237	C₂²×C₄×C₁₃	—	4	2	no	—
238	C₂²×C₄×C₁₃	—	4	2	no	—
239	C₂²×C₄×C₁₃	—	4	2	no	—
240	C₂²×C₄×C₁₃	—	8	1	no	—
241	C₂²×C₄×C₁₃	—	8	1	no	—
242	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	#41	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₁₃×Q₁₆	—	2	8	no	—
251	C₁₃×SD₁₆	—	2	8	no	—
252	C₁₃×SD₁₆	—	2	8	no	—
253	C₁₃×SD₁₆	—	4	4	no	—
254	C₁₃×D₈	—	2	8	no	—
255	C₁₃×D₈	—	4	4	no	—
256	C₂×C₈×C₁₃	—	2	8	no	—
257	C₂×C₈×C₁₃	—	2	1	no	—
258	C₂×C₈×C₁₃	—	2	1	no	—
259	C₂×C₈×C₁₃	—	2	1	no	—
260	C₂×C₈×C₁₃	—	2	1	no	—
261	C₂×C₈×C₁₃	—	2	1	no	—
262	C₂×C₈×C₁₃	—	2	1	no	—
263	C₂×C₈×C₁₃	—	2	1	no	—
264	C₂×C₈×C₁₃	—	2	1	no	—
265	C₂×C₈×C₁₃	—	2	1	no	—
266	C₂×C₈×C₁₃	—	2	1	no	—
267	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
268	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₁₃×C₂²⋊C₄	—	4	1	no	—
277	C₁₃×C₂²⋊C₄	—	4	2	no	—
278	C₁₃×C₂²⋊C₄	—	4	2	no	—
279	C₁₃×C₂²⋊C₄	—	4	2	no	—
280	C₁₃×C₂²⋊C₄	—	4	2	no	—
281	C₁₃×C₂²⋊C₄	—	4	2	no	—
282	C₁₃×C₂²⋊C₄	—	8	1	no	—
283	C₁₃×C₂²⋊C₄	—	8	1	no	—
284	C₁₃×C₂²⋊C₄	—	8	1	no	—
285	C₄²×C₁₃	—	2	1	no	—
286	C₄²×C₁₃	—	2	1	no	—
287	C₄²×C₁₃	—	2	1	no	—
288	C₄²×C₁₃	—	2	1	no	—
289	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
291	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
292	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#2431	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#2339	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#2056	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#2015	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#2014	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#1893	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#1850	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂³×C₁₃	—	2	2	no	—
305	C₂³×C₁₃	—	2	2	no	—
306	C₂³×C₁₃	—	2	2	no	—
307	C₂³×C₁₃	—	2	1	no	—
308	C₂³×C₁₃	—	2	1	no	—
309	C₂³×C₁₃	—	2	1	no	—
310	C₂³×C₁₃	—	2	1	no	—
311	C₂³×C₁₃	—	2	1	no	—
312	C₂³×C₁₃	—	2	1	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	4	1	no	—
315	C₂³×C₁₃	—	4	1	no	—
316	C₂³×C₁₃	—	4	1	no	—
317	C₂³×C₁₃	—	4	1	no	—
318	C₂³×C₁₃	—	4	1	no	—
319	C₂³×C₁₃	—	4	1	no	—
320	C₂³×C₁₃	—	4	1	no	—
321	C₂³×C₁₃	—	4	1	no	—
322	C₂³×C₁₃	—	4	1	no	—
323	C₂³×C₁₃	—	4	1	no	—
324	C₂³×C₁₃	—	4	1	no	—
325	C₂³×C₁₃	—	4	1	no	—
326	C₂³×C₁₃	—	4	1	no	—
327	C₂³×C₁₃	—	4	1	no	—
328	C₂³×C₁₃	—	4	1	no	—
329	C₂³×C₁₃	—	4	1	no	—
330	C₂³×C₁₃	—	4	1	no	—
331	C₂³×C₁₃	#121	1	2	yes	—
332	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
333	Q₈×C₁₃	—	2	2	no	—
334	Q₈×C₁₃	—	2	2	no	—
335	Q₈×C₁₃	—	2	2	no	—
336	Q₈×C₁₃	—	2	2	no	—
337	Q₈×C₁₃	—	4	1	no	—
338	Q₈×C₁₃	—	4	1	no	—
339	Q₈×C₁₃	—	4	1	no	—
340	Q₈×C₁₃	—	4	1	no	—
341	D₄×C₁₃	—	2	2	no	—
342	D₄×C₁₃	—	2	2	no	—
343	D₄×C₁₃	—	2	2	no	—
344	D₄×C₁₃	—	2	2	no	—
345	D₄×C₁₃	—	2	2	no	—
346	D₄×C₁₃	—	4	8	no	—
347	D₄×C₁₃	—	4	8	no	—
348	D₄×C₁₃	—	4	1	no	—
349	D₄×C₁₃	—	4	1	no	—
350	D₄×C₁₃	—	4	1	no	—
351	D₄×C₁₃	—	4	1	no	—
352	D₄×C₁₃	—	4	1	no	—
353	D₄×C₁₃	—	4	1	no	—
354	D₄×C₁₃	—	8	4	no	—
355	D₄×C₁₃	—	8	4	no	—
356	D₄×C₁₃	—	8	4	no	—
357	D₄×C₁₃	#120	1	4	yes	—
358	C₂×C₄×C₁₃	—	2	1	no	—
359	C₂×C₄×C₁₃	—	2	1	no	—
360	C₂×C₄×C₁₃	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	1	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	1	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	1	no	—
376	C₂×C₄×C₁₃	—	2	1	no	—
377	C₂×C₄×C₁₃	—	4	8	no	—
378	C₂×C₄×C₁₃	—	4	8	no	—
379	C₂×C₄×C₁₃	—	4	1	no	—
380	C₂×C₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	—	4	1	no	—
382	C₂×C₄×C₁₃	—	4	1	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	4	1	no	—
385	C₂×C₄×C₁₃	—	4	1	no	—
386	C₂×C₄×C₁₃	—	4	1	no	—
387	C₂×C₄×C₁₃	—	4	1	no	—
388	C₂×C₄×C₁₃	—	4	1	no	—
389	C₂×C₄×C₁₃	—	4	1	no	—
390	C₂×C₄×C₁₃	—	4	1	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	8	4	no	—
393	C₂×C₄×C₁₃	—	8	4	no	—
394	C₂×C₄×C₁₃	#121	1	2	yes	—
395	C₂×C₄×C₁₃	#135	1	2	yes	complemented
396	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
400	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
401	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
402	C₈×C₁₃	—	2	2	no	—
403	C₈×C₁₃	—	2	2	no	—
404	C₈×C₁₃	—	4	1	no	—
405	C₈×C₁₃	—	4	1	no	—
406	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
407	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×#135	—	2	4	no	—
409	C₂×#135	—	2	4	no	—
410	C₂×#135	—	2	4	no	—
411	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
412	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
413	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
414	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
415	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
416	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
417	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
423	#463	—	2	4	no	—
424	#459	—	2	4	no	—
425	#449	—	2	4	no	—
426	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
437	#392	—	2	1	no	—
438	#392	—	2	1	no	—
439	#391	C₂²×C₁₃	1	1	yes	characteristic
440	#391	C₂²×C₁₃	1	1	yes	characteristic
441	#391	C₂²×C₁₃	1	1	yes	characteristic
442	#390	C₂²×C₁₃	1	1	yes	characteristic
443	#386	—	2	1	no	—
444	#386	—	2	1	no	—
445	#386	—	2	1	no	—
446	#386	—	2	1	no	—
447	#381	—	2	1	no	—
448	#380	C₂²×C₁₃	1	1	yes	characteristic
449	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×#95	—	2	1	no	—
451	#340	C₂²×C₁₃	1	1	yes	characteristic
452	#340	C₂²×C₁₃	1	1	yes	characteristic
453	#336	C₂²×C₁₃	1	1	yes	characteristic
454	#336	C₂²×C₁₃	1	1	yes	characteristic
455	C₂²×C₁₃	—	2	2	no	—
456	C₂²×C₁₃	—	2	4	no	—
457	C₂²×C₁₃	—	2	2	no	—
458	C₂²×C₁₃	—	2	2	no	—
459	C₂²×C₁₃	—	4	1	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	—	4	2	no	—
462	C₂²×C₁₃	—	4	1	no	—
463	C₂²×C₁₃	—	4	2	no	—
464	C₂²×C₁₃	—	4	1	no	—
465	C₂²×C₁₃	—	4	1	no	—
466	C₂²×C₁₃	—	4	2	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	—	8	1	no	—
473	C₂²×C₁₃	—	8	1	no	—
474	C₂²×C₁₃	—	8	1	no	—
475	C₂²×C₁₃	—	8	1	no	—
476	C₂²×C₁₃	—	8	1	no	—
477	C₂²×C₁₃	—	8	1	no	—
478	C₂²×C₁₃	—	8	1	no	—
479	C₂²×C₁₃	—	8	1	no	—
480	C₂²×C₁₃	—	8	1	no	—
481	C₂²×C₁₃	—	8	1	no	—
482	C₂²×C₁₃	—	8	1	no	—
483	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
484	C₂²×C₁₃	D₄²	1	1	yes	characteristic
485	C₂²×C₁₃	D₄²	1	1	yes	characteristic
486	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
487	C₂²×C₁₃	#575	1	1	yes	characteristic
488	C₂²×C₁₃	#576	1	1	yes	characteristic
489	C₂²×C₁₃	#577	1	1	yes	characteristic
490	C₄×C₁₃	—	2	2	no	—
491	C₄×C₁₃	—	2	2	no	—
492	C₄×C₁₃	—	4	2	no	—
493	C₄×C₁₃	—	4	2	no	—
494	C₄×C₁₃	—	4	1	no	—
495	C₄×C₁₃	—	4	1	no	—
496	C₄×C₁₃	—	4	1	no	—
497	C₄×C₁₃	—	8	1	no	—
498	C₄×C₁₃	—	8	1	no	—
499	C₄×C₁₃	—	8	1	no	—
500	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
501	C₄×C₁₃	#534	1	1	yes	characteristic
502	C₄×C₁₃	#546	1	1	yes	characteristic
503	C₄×C₁₃	#546	1	1	yes	characteristic
504	C₂×#41	—	2	2	no	—
505	C₂×#41	—	2	2	no	—
506	C₂×#41	—	2	2	no	—
507	C₂×#41	—	2	2	no	—
508	C₂×#41	—	2	2	no	—
509	C₂×#41	—	2	2	no	—
510	C₂×#41	—	2	2	no	—
511	C₂×#41	—	4	1	no	—
512	C₂×#41	—	4	1	no	—
513	C₂×#41	—	4	1	no	—
514	C₂×#41	—	4	1	no	—
515	C₂×#41	D₄×C₁₃	1	4	yes	complemented
516	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
517	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	—	2	1	no	—
520	C₂²×D₄	—	2	1	no	—
521	C₂²×D₄	—	2	1	no	—
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
524	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
525	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
526	C₂³×C₄	—	2	1	no	—
527	C₂³×C₄	—	2	1	no	—
528	C₂³×C₄	—	2	1	no	—
529	C₂³×C₄	—	2	1	no	—
530	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
531	#135	—	2	32	no	—
532	C₂×Q₁₆	—	2	2	no	—
533	C₂×Q₁₆	—	2	2	no	—
534	C₂×Q₁₆	—	2	2	no	—
535	C₂×SD₁₆	—	2	2	no	—
536	C₂×SD₁₆	—	2	2	no	—
537	C₂×SD₁₆	—	2	2	no	—
538	C₂×SD₁₆	—	2	2	no	—
539	C₂×SD₁₆	—	2	2	no	—
540	C₂×SD₁₆	—	2	2	no	—
541	C₂×SD₁₆	—	4	1	no	—
542	C₂×SD₁₆	—	4	1	no	—
543	C₂×SD₁₆	D₄×C₁₃	1	4	yes	complemented
544	C₂×D₈	—	2	2	no	—
545	C₂×D₈	—	2	2	no	—
546	C₂×D₈	—	2	2	no	—
547	C₂×D₈	—	2	2	no	—
548	C₂×D₈	—	2	2	no	—
549	C₂×D₈	D₄×C₁₃	1	4	yes	complemented
550	C₂²×C₈	—	2	2	no	—
551	C₂²×C₈	—	2	2	no	—
552	C₂²×C₈	—	2	2	no	—
553	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
554	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
555	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
556	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
557	#127	—	2	2	no	—
558	#127	—	4	1	no	—
559	#124	—	2	2	no	—
560	#124	—	4	1	no	—
561	#121	—	2	2	no	—
562	#121	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	4	1	no	—
566	C₄×D₄	—	4	1	no	—
567	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	—	2	1	no	—
571	C₂×C₂²⋊C₄	—	2	1	no	—
572	C₂×C₂²⋊C₄	—	2	1	no	—
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
582	C₄⋊C₈	—	2	2	no	—
583	C₄⋊C₈	—	2	2	no	—
584	#103	—	2	2	no	—
585	#103	—	2	2	no	—
586	#103	—	4	1	no	—
587	#102	—	2	2	no	—
588	#102	—	2	2	no	—
589	#102	—	2	2	no	—
590	#102	—	2	2	no	—
591	#102	—	4	1	no	—
592	C₂²⋊C₈	—	2	2	no	—
593	#95	—	2	1	no	—
594	#95	—	2	1	no	—
595	#95	—	2	1	no	—
596	#95	—	2	1	no	—
597	#95	—	2	1	no	—
598	#95	—	2	1	no	—
599	#95	—	2	1	no	—
600	#95	D₄×C₁₃	1	1	yes	characteristic
601	#95	D₄×C₁₃	1	1	yes	characteristic
602	C₂×C₁₃	—	4	2	no	—
603	C₂×C₁₃	—	4	4	no	—
604	C₂×C₁₃	—	8	2	no	—
605	C₂×C₁₃	—	16	1	no	—
606	C₂×C₁₃	#2410	1	1	yes	characteristic
607	C₂×C₁₃	#3035	1	1	yes	characteristic
608	C₂×C₁₃	#3045	1	1	yes	characteristic
609	C₂×C₁₃	#3267	1	1	yes	characteristic
610	C₂×C₁₃	#3268	1	1	yes	characteristic
611	C₂×C₁₃	#3280	1	1	yes	characteristic
612	C₂×C₁₃	#3284	1	1	yes	characteristic
613	C₂⁴	—	2	1	no	—
614	C₂⁴	—	2	1	no	—
615	C₂⁴	—	2	1	no	—
616	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
617	#41	—	2	8	no	—
618	#41	—	2	8	no	—
619	#41	—	4	4	no	—
620	#41	—	4	4	no	—
621	#41	—	4	4	no	—
622	#41	—	4	4	no	—
623	#41	—	4	4	no	—
624	#41	—	4	4	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	2	1	no	—
633	C₂×Q₈	—	2	1	no	—
634	C₂×Q₈	—	2	1	no	—
635	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
636	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂×D₄	—	4	2	no	—
660	C₂×D₄	—	4	2	no	—
661	C₂×D₄	—	4	2	no	—
662	C₂×D₄	—	8	1	no	—
663	C₂×D₄	—	8	1	no	—
664	C₂×D₄	—	8	1	no	—
665	C₂×D₄	—	8	1	no	—
666	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
667	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
668	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
669	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	8	1	no	—
690	C₂²×C₄	—	8	1	no	—
691	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₂²×C₄	C₁₃×#41	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
699	Q₁₆	—	2	8	no	—
700	SD₁₆	—	2	8	no	—
701	SD₁₆	—	2	8	no	—
702	SD₁₆	—	4	4	no	—
703	D₈	—	2	8	no	—
704	D₈	—	4	4	no	—
705	C₂×C₈	—	2	8	no	—
706	C₂×C₈	—	2	1	no	—
707	C₂×C₈	—	2	1	no	—
708	C₂×C₈	—	2	1	no	—
709	C₂×C₈	—	2	1	no	—
710	C₂×C₈	—	2	1	no	—
711	C₂×C₈	—	2	1	no	—
712	C₂×C₈	—	2	1	no	—
713	C₂×C₈	—	2	1	no	—
714	C₂×C₈	—	2	1	no	—
715	C₂×C₈	—	2	1	no	—
716	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
717	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	4	1	no	—
726	C₂²⋊C₄	—	4	2	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	—	4	2	no	—
729	C₂²⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₂²⋊C₄	—	8	1	no	—
732	C₂²⋊C₄	—	8	1	no	—
733	C₂²⋊C₄	—	8	1	no	—
734	C₄²	—	2	1	no	—
735	C₄²	—	2	1	no	—
736	C₄²	—	2	1	no	—
737	C₄²	—	2	1	no	—
738	C₁₃	#24364	1	1	yes	characteristic, direct product factor, Sylow
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	1	no	—
745	C₂³	—	2	1	no	—
746	C₂³	—	2	1	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	—	4	1	no	—
752	C₂³	—	4	1	no	—
753	C₂³	—	4	1	no	—
754	C₂³	—	4	1	no	—
755	C₂³	—	4	1	no	—
756	C₂³	—	4	1	no	—
757	C₂³	—	4	1	no	—
758	C₂³	—	4	1	no	—
759	C₂³	—	4	1	no	—
760	C₂³	—	4	1	no	—
761	C₂³	—	4	1	no	—
762	C₂³	—	4	1	no	—
763	C₂³	—	4	1	no	—
764	C₂³	—	4	1	no	—
765	C₂³	—	4	1	no	—
766	C₂³	C₁₃×#121	1	2	yes	—
767	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	4	1	no	—
773	Q₈	—	4	1	no	—
774	Q₈	—	4	1	no	—
775	Q₈	—	4	1	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	4	8	no	—
782	D₄	—	4	8	no	—
783	D₄	—	4	1	no	—
784	D₄	—	4	1	no	—
785	D₄	—	4	1	no	—
786	D₄	—	4	1	no	—
787	D₄	—	4	1	no	—
788	D₄	—	4	1	no	—
789	D₄	—	8	4	no	—
790	D₄	—	8	4	no	—
791	D₄	—	8	4	no	—
792	D₄	C₁₃×#120	1	4	yes	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	4	8	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	8	4	no	—
828	C₂×C₄	—	8	4	no	—
829	C₂×C₄	C₁₃×#121	1	2	yes	—
830	C₂×C₄	C₁₃×#135	1	2	yes	complemented
831	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
834	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
835	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
836	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
837	C₈	—	2	2	no	—
838	C₈	—	2	2	no	—
839	C₈	—	4	1	no	—
840	C₈	—	4	1	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	8	1	no	—
859	C₂²	—	8	1	no	—
860	C₂²	—	8	1	no	—
861	C₂²	—	8	1	no	—
862	C₂²	—	8	1	no	—
863	C₂²	—	8	1	no	—
864	C₂²	—	8	1	no	—
865	C₂²	—	8	1	no	—
866	C₂²	—	8	1	no	—
867	C₂²	—	8	1	no	—
868	C₂²	—	8	1	no	—
869	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
870	C₂²	D₄²×C₁₃	1	1	yes	characteristic
871	C₂²	D₄²×C₁₃	1	1	yes	characteristic
872	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
873	C₂²	C₁₃×#575	1	1	yes	characteristic
874	C₂²	C₁₃×#576	1	1	yes	characteristic
875	C₂²	C₁₃×#577	1	1	yes	characteristic
876	C₄	—	2	2	no	—
877	C₄	—	2	2	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	8	1	no	—
884	C₄	—	8	1	no	—
885	C₄	—	8	1	no	—
886	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
887	C₄	C₁₃×#534	1	1	yes	characteristic
888	C₄	C₁₃×#546	1	1	yes	characteristic
889	C₄	C₁₃×#546	1	1	yes	characteristic
890	C₂	—	4	2	no	—
891	C₂	—	4	4	no	—
892	C₂	—	8	2	no	—
893	C₂	—	16	1	no	—
894	C₂	C₁₃×#2410	1	1	yes	characteristic
895	C₂	C₁₃×#3035	1	1	yes	characteristic
896	C₂	C₁₃×#3045	1	1	yes	characteristic
897	C₂	C₁₃×#3267	1	1	yes	characteristic
898	C₂	C₁₃×#3268	1	1	yes	characteristic
899	C₂	C₁₃×#3280	1	1	yes	characteristic
900	C₂	C₁₃×#3284	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 ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#135	C₂	semidirect
2. C₂×C₁₃×#463	C₂	semidirect
3. C₂×C₁₃×#459	C₂	semidirect
4. C₂×C₁₃×#449	C₂	semidirect
5. C₁₃×#2431	C₂	semidirect
6. C₁₃×#2339	C₂	semidirect
7. C₁₃×#2056	C₂	semidirect
8. C₁₃×#2055	C₂	semidirect
9. C₁₃×#2015	C₂	semidirect
10. C₁₃×#2014	C₂	semidirect
11. C₁₃×#1893	C₂	semidirect
12. C₁₃×#1879	C₂	semidirect
13. C₁₃×#1877	C₂	semidirect
14. C₁₃×#1850	C₂	semidirect
15. C₁₃×#1788	C₂	semidirect
76. C₂×C₁₃×#41	D₄	semidirect
104. C₂×C₁₃×SD₁₆	D₄	semidirect
110. C₂×C₁₃×D₈	D₄	semidirect
163. #24364	C₁₃	direct (N × H)
289. C₂²×#135	C₂×C₁₃	semidirect
290. C₂×#463	C₂×C₁₃	semidirect
291. C₂×#459	C₂×C₁₃	semidirect
292. C₂×#449	C₂×C₁₃	semidirect
293. #2431	C₂×C₁₃	semidirect
294. #2339	C₂×C₁₃	semidirect
295. #2056	C₂×C₁₃	semidirect
296. #2055	C₂×C₁₃	semidirect
297. #2015	C₂×C₁₃	semidirect
298. #2014	C₂×C₁₃	semidirect
299. #1893	C₂×C₁₃	semidirect
300. #1879	C₂×C₁₃	semidirect
301. #1877	C₂×C₁₃	semidirect
302. #1850	C₂×C₁₃	semidirect
303. #1788	C₂×C₁₃	semidirect
395. C₂×C₄×C₁₃	#135	semidirect
515. C₂×#41	D₄×C₁₃	semidirect
543. C₂×SD₁₆	D₄×C₁₃	semidirect
549. C₂×D₈	D₄×C₁₃	semidirect
738. C₁₃	#24364	direct (N × H)
830. C₂×C₄	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#135	2
C₂×C₁₃×#463	2
C₂×C₁₃×#459	2
C₂×C₁₃×#449	2
C₁₃×#2431	2
C₁₃×#2339	2
C₁₃×#2056	2
C₁₃×#2055	2
C₁₃×#2015	2
C₁₃×#2014	2
C₁₃×#1893	2
C₁₃×#1879	2
C₁₃×#1877	2
C₁₃×#1850	2
C₁₃×#1788	2
#24364	13

Subgroups — C13×#24364 #15710703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24364 #15710703