Subgroups — C₁₃×#24462 #15710801

Order 3328.

1302 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#578	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#473	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#456	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2898	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2047	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2005	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1908	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1882	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1876	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1793	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
18	C₁₃×#578	—	2	4	no	—
19	C₁₃×#578	—	2	4	no	—
20	C₂×C₁₃×#137	—	2	1	no	—
21	C₂×C₁₃×#137	—	2	1	no	—
22	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#135	—	2	1	no	—
27	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×Q₁₆	—	2	1	no	—
29	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
33	C₁₃×#536	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₁₃×#520	C₂²	1	1	yes	characteristic
36	C₁₃×#473	—	2	4	no	—
37	C₁₃×#464	—	2	1	no	—
38	C₁₃×#463	—	2	1	no	—
39	C₁₃×#462	—	2	1	no	—
40	C₁₃×#461	—	2	1	no	—
41	C₁₃×#456	—	2	4	no	—
42	C₁₃×#452	—	2	1	no	—
43	C₁₃×#452	—	2	1	no	—
44	C₁₃×#451	—	2	1	no	—
45	C₁₃×#451	—	2	1	no	—
46	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
47	C₁₃×#424	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
51	C₁₃×#419	—	2	1	no	—
52	C₁₃×#419	C₂²	1	1	yes	characteristic
53	C₁₃×#419	C₂²	1	1	yes	characteristic
54	C₁₃×#417	—	2	1	no	—
55	C₁₃×#417	C₂²	1	1	yes	characteristic
56	C₁₃×#417	C₂²	1	1	yes	characteristic
57	C₁₃×#416	—	2	1	no	—
58	C₁₃×#416	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#103	—	2	1	no	—
60	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
65	C₁₃×#408	C₂²	1	1	yes	characteristic
66	C₁₃×#391	C₂²	1	1	yes	characteristic
67	C₁₃×#343	C₂²	1	1	yes	characteristic
68	C₁₃×#341	C₂²	1	1	yes	characteristic
69	C₁₃×#339	C₂²	1	1	yes	characteristic
70	C₁₃×#336	C₂²	1	1	yes	characteristic
71	C₁₃×2₋¹⁺⁴	—	2	2	no	—
72	C₁₃×2₋¹⁺⁴	—	2	2	no	—
73	C₁₃×2₋¹⁺⁴	—	2	2	no	—
74	C₁₃×2₋¹⁺⁴	—	2	2	no	—
75	C₁₃×2₋¹⁺⁴	—	2	2	no	—
76	C₁₃×2₋¹⁺⁴	—	4	1	no	—
77	C₁₃×2₋¹⁺⁴	—	4	1	no	—
78	C₁₃×2₋¹⁺⁴	D₄	1	4	yes	—
79	C₂×C₁₃×#41	—	2	1	no	—
80	C₂×C₁₃×#41	—	2	1	no	—
81	C₂×C₁₃×#41	—	2	1	no	—
82	C₂×C₁₃×#41	—	2	1	no	—
83	C₂×C₁₃×#41	—	4	1	no	—
84	C₂×C₁₃×#41	—	4	1	no	—
85	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃	—	2	1	no	—
89	C₂²×Q₈×C₁₃	—	2	1	no	—
90	C₂²×Q₈×C₁₃	—	2	1	no	—
91	C₂²×Q₈×C₁₃	—	2	1	no	—
92	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×#137	—	2	8	no	—
96	C₁₃×#137	—	2	8	no	—
97	C₁₃×#137	—	2	2	no	—
98	C₁₃×#137	—	2	2	no	—
99	C₁₃×#137	—	2	2	no	—
100	C₁₃×#137	—	2	2	no	—
101	C₁₃×#137	—	2	2	no	—
102	C₁₃×#137	—	2	2	no	—
103	C₁₃×#137	—	2	2	no	—
104	C₁₃×#137	D₄	1	4	yes	—
105	C₁₃×#135	—	2	8	no	—
106	C₁₃×#135	—	2	2	no	—
107	C₁₃×#135	—	2	2	no	—
108	C₂×C₁₃×Q₁₆	—	2	8	no	—
109	C₂×C₁₃×Q₁₆	—	2	1	no	—
110	C₂×C₁₃×Q₁₆	—	2	1	no	—
111	C₂×C₁₃×Q₁₆	—	2	2	no	—
112	C₂×C₁₃×Q₁₆	—	2	2	no	—
113	C₂×C₁₃×Q₁₆	—	2	1	no	—
114	C₂×C₁₃×Q₁₆	—	2	1	no	—
115	C₂×C₁₃×Q₁₆	—	2	2	no	—
116	C₂×C₁₃×Q₁₆	—	2	1	no	—
117	C₂×C₁₃×Q₁₆	—	2	1	no	—
118	C₂×C₁₃×Q₁₆	—	2	1	no	—
119	C₂×C₁₃×Q₁₆	—	2	1	no	—
120	C₂×C₁₃×Q₁₆	—	4	1	no	—
121	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
122	C₂×C₁₃×SD₁₆	—	2	1	no	—
123	C₂×C₁₃×SD₁₆	—	2	1	no	—
124	C₂×C₁₃×SD₁₆	—	2	1	no	—
125	C₂×C₁₃×SD₁₆	—	2	1	no	—
126	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
127	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
128	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
129	C₁₃×#131	—	2	2	no	—
130	C₁₃×#131	—	2	2	no	—
131	C₁₃×#131	—	2	2	no	—
132	C₁₃×#131	—	4	1	no	—
133	C₂×C₁₃×M₁₆	—	2	1	no	—
134	C₂×C₁₃×M₁₆	—	2	1	no	—
135	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₁₃	—	2	1	no	—
140	C₂²×C₈×C₁₃	—	2	1	no	—
141	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₁₃×C₄⋊Q₈	—	2	2	no	—
144	C₁₃×C₄⋊Q₈	—	2	1	no	—
145	C₁₃×C₄⋊Q₈	—	4	1	no	—
146	C₁₃×#124	—	2	1	no	—
147	C₁₃×#123	—	4	1	no	—
148	C₁₃×C₂²⋊Q₈	—	2	1	no	—
149	C₁₃×C₂²⋊Q₈	—	2	1	no	—
150	C₄×Q₈×C₁₃	—	2	1	no	—
151	C₄×D₄×C₁₃	—	2	1	no	—
152	C₄×D₄×C₁₃	—	4	1	no	—
153	C₁₃×#117	—	2	1	no	—
154	C₁₃×#117	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
159	C₁₃×#108	—	2	2	no	—
160	C₁₃×C₄⋊C₈	—	2	1	no	—
161	C₁₃×C₄⋊C₈	—	2	1	no	—
162	C₁₃×#104	—	2	2	no	—
163	C₁₃×#104	—	2	2	no	—
164	C₁₃×#104	—	4	1	no	—
165	C₁₃×#103	—	2	1	no	—
166	C₁₃×#103	—	2	1	no	—
167	C₁₃×#103	—	2	1	no	—
168	C₁₃×#103	—	2	1	no	—
169	C₁₃×#103	—	2	1	no	—
170	C₁₃×#103	—	2	1	no	—
171	C₁₃×#103	—	2	1	no	—
172	C₁₃×#103	—	2	1	no	—
173	C₁₃×#103	—	2	1	no	—
174	C₁₃×#103	—	2	1	no	—
175	C₁₃×#103	D₄	1	1	yes	characteristic
176	C₁₃×#103	D₄	1	1	yes	characteristic
177	C₁₃×#102	—	2	1	no	—
178	C₁₃×#102	—	2	1	no	—
179	C₁₃×#102	D₄	1	1	yes	characteristic
180	C₁₃×#102	D₄	1	1	yes	characteristic
181	C₁₃×#101	—	2	2	no	—
182	C₁₃×#101	—	2	2	no	—
183	C₁₃×#101	—	2	2	no	—
184	C₁₃×C₂²⋊C₈	—	2	1	no	—
185	C₁₃×C₂²⋊C₈	—	2	1	no	—
186	C₁₃×#95	—	4	1	no	—
187	#24462	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₁₃×#41	—	2	1	no	—
189	C₁₃×#41	—	2	1	no	—
190	C₁₃×#41	—	2	1	no	—
191	C₁₃×#41	—	2	1	no	—
192	C₁₃×#41	—	2	4	no	—
193	C₁₃×#41	—	2	4	no	—
194	C₁₃×#41	—	2	4	no	—
195	C₁₃×#41	—	2	1	no	—
196	C₁₃×#41	—	2	1	no	—
197	C₁₃×#41	—	2	1	no	—
198	C₁₃×#41	—	2	1	no	—
199	C₁₃×#41	—	4	4	no	—
200	C₁₃×#41	—	4	2	no	—
201	C₁₃×#41	—	4	2	no	—
202	C₁₃×#41	—	4	2	no	—
203	C₁₃×#41	—	4	4	no	—
204	C₁₃×#41	—	4	4	no	—
205	C₁₃×#41	—	4	2	no	—
206	C₁₃×#41	—	4	4	no	—
207	C₁₃×#41	—	4	2	no	—
208	C₁₃×#41	C₂×D₄	1	2	yes	—
209	C₁₃×#41	C₂×D₄	1	2	yes	—
210	C₁₃×#41	C₂×D₄	1	2	yes	—
211	C₁₃×#41	#41	1	2	yes	—
212	C₂×Q₈×C₁₃	—	2	1	no	—
213	C₂×Q₈×C₁₃	—	2	1	no	—
214	C₂×Q₈×C₁₃	—	2	4	no	—
215	C₂×Q₈×C₁₃	—	2	4	no	—
216	C₂×Q₈×C₁₃	—	2	4	no	—
217	C₂×Q₈×C₁₃	—	2	1	no	—
218	C₂×Q₈×C₁₃	—	2	1	no	—
219	C₂×Q₈×C₁₃	—	2	1	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	1	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	2	1	no	—
224	C₂×Q₈×C₁₃	—	2	1	no	—
225	C₂×Q₈×C₁₃	—	2	1	no	—
226	C₂×Q₈×C₁₃	—	2	1	no	—
227	C₂×Q₈×C₁₃	—	2	1	no	—
228	C₂×Q₈×C₁₃	—	2	1	no	—
229	C₂×Q₈×C₁₃	—	2	1	no	—
230	C₂×Q₈×C₁₃	—	2	1	no	—
231	C₂×Q₈×C₁₃	—	4	1	no	—
232	C₂×Q₈×C₁₃	—	4	1	no	—
233	C₂×Q₈×C₁₃	—	4	2	no	—
234	C₂×Q₈×C₁₃	—	4	2	no	—
235	C₂×Q₈×C₁₃	—	4	2	no	—
236	C₂×Q₈×C₁₃	—	4	2	no	—
237	C₂×Q₈×C₁₃	—	4	2	no	—
238	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
239	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
240	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	1	no	—
245	C₂×D₄×C₁₃	—	2	1	no	—
246	C₂×D₄×C₁₃	—	4	1	no	—
247	C₂×D₄×C₁₃	—	4	1	no	—
248	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	1	no	—
260	C₂²×C₄×C₁₃	—	4	1	no	—
261	C₂²×C₄×C₁₃	—	4	1	no	—
262	C₂²×C₄×C₁₃	—	4	1	no	—
263	C₂²×C₄×C₁₃	—	4	1	no	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₁₃×Q₁₆	—	2	4	no	—
266	C₁₃×Q₁₆	—	2	4	no	—
267	C₁₃×Q₁₆	—	2	4	no	—
268	C₁₃×Q₁₆	—	2	2	no	—
269	C₁₃×Q₁₆	—	2	4	no	—
270	C₁₃×Q₁₆	—	4	2	no	—
271	C₁₃×Q₁₆	—	4	2	no	—
272	C₁₃×Q₁₆	—	4	2	no	—
273	C₁₃×Q₁₆	—	4	2	no	—
274	C₁₃×SD₁₆	—	2	4	no	—
275	C₁₃×SD₁₆	—	2	2	no	—
276	C₁₃×SD₁₆	—	2	4	no	—
277	C₁₃×SD₁₆	—	2	2	no	—
278	C₁₃×SD₁₆	—	4	2	no	—
279	C₁₃×SD₁₆	—	4	2	no	—
280	C₁₃×D₈	—	2	2	no	—
281	C₁₃×M₁₆	—	2	4	no	—
282	C₁₃×M₁₆	—	2	1	no	—
283	C₁₃×M₁₆	—	2	1	no	—
284	C₁₃×M₁₆	—	2	1	no	—
285	C₁₃×M₁₆	—	2	1	no	—
286	C₁₃×M₁₆	—	2	1	no	—
287	C₁₃×M₁₆	—	2	1	no	—
288	C₁₃×M₁₆	—	2	1	no	—
289	C₁₃×M₁₆	—	4	2	no	—
290	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
291	C₂×C₈×C₁₃	—	2	4	no	—
292	C₂×C₈×C₁₃	—	2	1	no	—
293	C₂×C₈×C₁₃	—	2	1	no	—
294	C₂×C₈×C₁₃	—	2	1	no	—
295	C₂×C₈×C₁₃	—	2	1	no	—
296	C₂×C₈×C₁₃	—	2	1	no	—
297	C₂×C₈×C₁₃	—	2	1	no	—
298	C₂×C₈×C₁₃	—	2	1	no	—
299	C₂×C₈×C₁₃	—	2	1	no	—
300	C₂×C₈×C₁₃	—	4	2	no	—
301	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₁₃×C₄⋊C₄	—	2	1	no	—
306	C₁₃×C₄⋊C₄	—	2	1	no	—
307	C₁₃×C₄⋊C₄	—	4	1	no	—
308	C₁₃×C₄⋊C₄	—	4	1	no	—
309	C₁₃×C₄⋊C₄	—	4	1	no	—
310	C₁₃×C₄⋊C₄	—	4	4	no	—
311	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
313	C₁₃×C₂²⋊C₄	—	2	1	no	—
314	C₁₃×C₂²⋊C₄	—	4	1	no	—
315	C₁₃×C₂²⋊C₄	—	4	1	no	—
316	C₁₃×C₂²⋊C₄	—	4	1	no	—
317	C₄²×C₁₃	—	2	1	no	—
318	C₄²×C₁₃	—	2	1	no	—
319	C₄²×C₁₃	—	2	1	no	—
320	C₄²×C₁₃	—	4	1	no	—
321	C₂×#578	C₂×C₁₃	1	1	yes	characteristic
322	C₂×#473	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#3046	C₂×C₁₃	1	1	yes	characteristic, complemented
324	C₂×#456	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#3011	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#2898	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#2052	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#2047	C₂×C₁₃	1	1	yes	characteristic, complemented
329	#2016	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#2005	C₂×C₁₃	1	1	yes	characteristic, complemented
331	#1908	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#1882	C₂×C₁₃	1	1	yes	characteristic, complemented
333	#1876	C₂×C₁₃	1	1	yes	characteristic, complemented
334	#1866	C₂×C₁₃	1	1	yes	characteristic, complemented
335	#1793	C₂×C₁₃	1	1	yes	characteristic, complemented
336	C₂³×C₁₃	—	2	1	no	—
337	C₂³×C₁₃	—	2	1	no	—
338	C₂³×C₁₃	—	2	1	no	—
339	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
340	Q₈×C₁₃	—	2	1	no	—
341	Q₈×C₁₃	—	2	1	no	—
342	Q₈×C₁₃	—	2	2	no	—
343	Q₈×C₁₃	—	2	2	no	—
344	Q₈×C₁₃	—	2	1	no	—
345	Q₈×C₁₃	—	2	2	no	—
346	Q₈×C₁₃	—	2	2	no	—
347	Q₈×C₁₃	—	2	1	no	—
348	Q₈×C₁₃	—	4	4	no	—
349	Q₈×C₁₃	—	4	4	no	—
350	Q₈×C₁₃	—	4	1	no	—
351	Q₈×C₁₃	—	4	1	no	—
352	Q₈×C₁₃	—	4	1	no	—
353	Q₈×C₁₃	—	4	1	no	—
354	Q₈×C₁₃	—	4	1	no	—
355	Q₈×C₁₃	—	4	1	no	—
356	Q₈×C₁₃	—	4	1	no	—
357	Q₈×C₁₃	—	4	1	no	—
358	Q₈×C₁₃	#120	1	2	yes	—
359	Q₈×C₁₃	#121	1	2	yes	—
360	D₄×C₁₃	—	2	2	no	—
361	D₄×C₁₃	—	2	2	no	—
362	D₄×C₁₃	—	2	2	no	—
363	D₄×C₁₃	—	2	2	no	—
364	D₄×C₁₃	—	2	1	no	—
365	D₄×C₁₃	—	2	1	no	—
366	D₄×C₁₃	—	2	1	no	—
367	D₄×C₁₃	—	2	1	no	—
368	D₄×C₁₃	—	4	4	no	—
369	D₄×C₁₃	—	4	4	no	—
370	D₄×C₁₃	—	4	1	no	—
371	D₄×C₁₃	—	4	1	no	—
372	D₄×C₁₃	#120	1	2	yes	—
373	D₄×C₁₃	#121	1	2	yes	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	1	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	4	4	no	—
387	C₂×C₄×C₁₃	—	4	4	no	—
388	C₂×C₄×C₁₃	—	4	4	no	—
389	C₂×C₄×C₁₃	—	4	1	no	—
390	C₂×C₄×C₁₃	—	4	4	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	4	1	no	—
393	C₂×C₄×C₁₃	—	4	1	no	—
394	C₂×C₄×C₁₃	—	4	1	no	—
395	C₂×C₄×C₁₃	—	4	1	no	—
396	C₂×C₄×C₁₃	—	4	1	no	—
397	C₂×C₄×C₁₃	—	4	1	no	—
398	C₂×C₄×C₁₃	—	4	1	no	—
399	C₂×C₄×C₁₃	—	4	1	no	—
400	C₂×C₄×C₁₃	—	4	1	no	—
401	C₂×C₄×C₁₃	—	4	1	no	—
402	C₂×C₄×C₁₃	—	8	1	no	—
403	C₂×C₄×C₁₃	—	16	1	no	—
404	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
409	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
410	C₈×C₁₃	—	2	1	no	—
411	C₈×C₁₃	—	2	2	no	—
412	C₈×C₁₃	—	2	1	no	—
413	C₈×C₁₃	—	2	1	no	—
414	C₈×C₁₃	—	2	1	no	—
415	C₈×C₁₃	—	4	1	no	—
416	C₈×C₁₃	—	4	1	no	—
417	C₈×C₁₃	—	4	1	no	—
418	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
420	#578	—	2	4	no	—
421	#578	—	2	4	no	—
422	C₂×#137	—	2	1	no	—
423	C₂×#137	—	2	1	no	—
424	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#135	—	2	1	no	—
429	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
430	C₂²×Q₁₆	—	2	1	no	—
431	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
432	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
435	#536	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
437	#520	C₂²×C₁₃	1	1	yes	characteristic
438	#473	—	2	4	no	—
439	#464	—	2	1	no	—
440	#463	—	2	1	no	—
441	#462	—	2	1	no	—
442	#461	—	2	1	no	—
443	#456	—	2	4	no	—
444	#452	—	2	1	no	—
445	#452	—	2	1	no	—
446	#451	—	2	1	no	—
447	#451	—	2	1	no	—
448	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
449	#424	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
451	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
452	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
453	#419	—	2	1	no	—
454	#419	C₂²×C₁₃	1	1	yes	characteristic
455	#419	C₂²×C₁₃	1	1	yes	characteristic
456	#417	—	2	1	no	—
457	#417	C₂²×C₁₃	1	1	yes	characteristic
458	#417	C₂²×C₁₃	1	1	yes	characteristic
459	#416	—	2	1	no	—
460	#416	C₂²×C₁₃	1	1	yes	characteristic
461	C₂×#103	—	2	1	no	—
462	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
463	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
464	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
465	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
466	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
467	#408	C₂²×C₁₃	1	1	yes	characteristic
468	#391	C₂²×C₁₃	1	1	yes	characteristic
469	#343	C₂²×C₁₃	1	1	yes	characteristic
470	#341	C₂²×C₁₃	1	1	yes	characteristic
471	#339	C₂²×C₁₃	1	1	yes	characteristic
472	#336	C₂²×C₁₃	1	1	yes	characteristic
473	C₂²×C₁₃	—	2	1	no	—
474	C₂²×C₁₃	—	2	1	no	—
475	C₂²×C₁₃	—	2	2	no	—
476	C₂²×C₁₃	—	2	2	no	—
477	C₂²×C₁₃	—	4	1	no	—
478	C₂²×C₁₃	—	4	1	no	—
479	C₂²×C₁₃	—	4	1	no	—
480	C₂²×C₁₃	—	4	1	no	—
481	C₂²×C₁₃	—	4	1	no	—
482	C₂²×C₁₃	—	4	1	no	—
483	C₂²×C₁₃	—	4	1	no	—
484	C₂²×C₁₃	#534	1	1	yes	characteristic
485	C₂²×C₁₃	D₄²	1	1	yes	characteristic
486	C₂²×C₁₃	#546	1	1	yes	characteristic
487	C₄×C₁₃	—	2	2	no	—
488	C₄×C₁₃	—	2	2	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	—	4	2	no	—
491	C₄×C₁₃	—	4	1	no	—
492	C₄×C₁₃	—	4	2	no	—
493	C₄×C₁₃	—	4	1	no	—
494	C₄×C₁₃	—	4	1	no	—
495	C₄×C₁₃	—	8	1	no	—
496	C₄×C₁₃	—	8	1	no	—
497	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
498	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
499	C₄×C₁₃	D₄²	1	1	yes	characteristic
500	C₄×C₁₃	#546	1	1	yes	characteristic
501	2₋¹⁺⁴	—	2	2	no	—
502	2₋¹⁺⁴	—	2	2	no	—
503	2₋¹⁺⁴	—	2	2	no	—
504	2₋¹⁺⁴	—	2	2	no	—
505	2₋¹⁺⁴	—	2	2	no	—
506	2₋¹⁺⁴	—	4	1	no	—
507	2₋¹⁺⁴	—	4	1	no	—
508	2₋¹⁺⁴	D₄×C₁₃	1	4	yes	—
509	C₂×#41	—	2	1	no	—
510	C₂×#41	—	2	1	no	—
511	C₂×#41	—	2	1	no	—
512	C₂×#41	—	2	1	no	—
513	C₂×#41	—	4	1	no	—
514	C₂×#41	—	4	1	no	—
515	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
516	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
517	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
518	C₂²×Q₈	—	2	1	no	—
519	C₂²×Q₈	—	2	1	no	—
520	C₂²×Q₈	—	2	1	no	—
521	C₂²×Q₈	—	2	1	no	—
522	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
523	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
524	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
525	#137	—	2	8	no	—
526	#137	—	2	8	no	—
527	#137	—	2	2	no	—
528	#137	—	2	2	no	—
529	#137	—	2	2	no	—
530	#137	—	2	2	no	—
531	#137	—	2	2	no	—
532	#137	—	2	2	no	—
533	#137	—	2	2	no	—
534	#137	D₄×C₁₃	1	4	yes	—
535	#135	—	2	8	no	—
536	#135	—	2	2	no	—
537	#135	—	2	2	no	—
538	C₂×Q₁₆	—	2	8	no	—
539	C₂×Q₁₆	—	2	1	no	—
540	C₂×Q₁₆	—	2	1	no	—
541	C₂×Q₁₆	—	2	2	no	—
542	C₂×Q₁₆	—	2	2	no	—
543	C₂×Q₁₆	—	2	2	no	—
544	C₂×Q₁₆	—	2	1	no	—
545	C₂×Q₁₆	—	2	1	no	—
546	C₂×Q₁₆	—	2	1	no	—
547	C₂×Q₁₆	—	2	1	no	—
548	C₂×Q₁₆	—	2	1	no	—
549	C₂×Q₁₆	—	2	1	no	—
550	C₂×Q₁₆	—	4	1	no	—
551	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
552	C₂×SD₁₆	—	2	1	no	—
553	C₂×SD₁₆	—	2	1	no	—
554	C₂×SD₁₆	—	2	1	no	—
555	C₂×SD₁₆	—	2	1	no	—
556	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
557	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
558	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
559	#131	—	2	2	no	—
560	#131	—	2	2	no	—
561	#131	—	2	2	no	—
562	#131	—	4	1	no	—
563	C₂×M₁₆	—	2	1	no	—
564	C₂×M₁₆	—	2	1	no	—
565	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
566	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
567	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
568	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
569	C₂²×C₈	—	2	1	no	—
570	C₂²×C₈	—	2	1	no	—
571	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
572	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
573	C₄⋊Q₈	—	2	2	no	—
574	C₄⋊Q₈	—	2	1	no	—
575	C₄⋊Q₈	—	4	1	no	—
576	#124	—	2	1	no	—
577	#123	—	4	1	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	4	1	no	—
583	#117	—	2	1	no	—
584	#117	C₂³×C₁₃	1	1	yes	characteristic
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	4	1	no	—
587	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
588	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
589	#108	—	2	2	no	—
590	C₄⋊C₈	—	2	1	no	—
591	C₄⋊C₈	—	2	1	no	—
592	#104	—	2	2	no	—
593	#104	—	2	2	no	—
594	#104	—	4	1	no	—
595	#103	—	2	1	no	—
596	#103	—	2	1	no	—
597	#103	—	2	1	no	—
598	#103	—	2	1	no	—
599	#103	—	2	1	no	—
600	#103	—	2	1	no	—
601	#103	—	2	1	no	—
602	#103	—	2	1	no	—
603	#103	—	2	1	no	—
604	#103	—	2	1	no	—
605	#103	D₄×C₁₃	1	1	yes	characteristic
606	#103	D₄×C₁₃	1	1	yes	characteristic
607	#102	—	2	1	no	—
608	#102	—	2	1	no	—
609	#102	D₄×C₁₃	1	1	yes	characteristic
610	#102	D₄×C₁₃	1	1	yes	characteristic
611	#101	—	2	2	no	—
612	#101	—	2	2	no	—
613	#101	—	2	2	no	—
614	C₂²⋊C₈	—	2	1	no	—
615	C₂²⋊C₈	—	2	1	no	—
616	#95	—	4	1	no	—
617	C₂×C₁₃	—	2	1	no	—
618	C₂×C₁₃	—	2	1	no	—
619	C₂×C₁₃	—	4	2	no	—
620	C₂×C₁₃	—	4	2	no	—
621	C₂×C₁₃	—	8	1	no	—
622	C₂×C₁₃	#2410	1	1	yes	characteristic
623	C₂×C₁₃	#3289	1	1	yes	characteristic
624	C₂×C₁₃	#3293	1	1	yes	characteristic
625	#41	—	2	1	no	—
626	#41	—	2	1	no	—
627	#41	—	2	1	no	—
628	#41	—	2	1	no	—
629	#41	—	2	4	no	—
630	#41	—	2	4	no	—
631	#41	—	2	4	no	—
632	#41	—	2	1	no	—
633	#41	—	2	1	no	—
634	#41	—	2	1	no	—
635	#41	—	2	1	no	—
636	#41	—	4	4	no	—
637	#41	—	4	2	no	—
638	#41	—	4	2	no	—
639	#41	—	4	2	no	—
640	#41	—	4	4	no	—
641	#41	—	4	4	no	—
642	#41	—	4	2	no	—
643	#41	—	4	4	no	—
644	#41	—	4	2	no	—
645	#41	C₂×D₄×C₁₃	1	2	yes	—
646	#41	C₂×D₄×C₁₃	1	2	yes	—
647	#41	C₂×D₄×C₁₃	1	2	yes	—
648	#41	C₁₃×#41	1	2	yes	—
649	C₂×Q₈	—	2	1	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	4	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	2	1	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	1	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	1	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	4	1	no	—
669	C₂×Q₈	—	4	1	no	—
670	C₂×Q₈	—	4	2	no	—
671	C₂×Q₈	—	4	2	no	—
672	C₂×Q₈	—	4	2	no	—
673	C₂×Q₈	—	4	2	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
676	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
677	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
678	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
679	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	4	1	no	—
684	C₂×D₄	—	4	1	no	—
685	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
686	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	4	1	no	—
697	C₂²×C₄	—	4	1	no	—
698	C₂²×C₄	—	4	1	no	—
699	C₂²×C₄	—	4	1	no	—
700	C₂²×C₄	—	4	1	no	—
701	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
702	Q₁₆	—	2	4	no	—
703	Q₁₆	—	2	4	no	—
704	Q₁₆	—	2	4	no	—
705	Q₁₆	—	2	2	no	—
706	Q₁₆	—	2	4	no	—
707	Q₁₆	—	4	2	no	—
708	Q₁₆	—	4	2	no	—
709	Q₁₆	—	4	2	no	—
710	Q₁₆	—	4	2	no	—
711	SD₁₆	—	2	4	no	—
712	SD₁₆	—	2	2	no	—
713	SD₁₆	—	2	4	no	—
714	SD₁₆	—	2	2	no	—
715	SD₁₆	—	4	2	no	—
716	SD₁₆	—	4	2	no	—
717	D₈	—	2	2	no	—
718	M₁₆	—	2	4	no	—
719	M₁₆	—	2	1	no	—
720	M₁₆	—	2	1	no	—
721	M₁₆	—	2	1	no	—
722	M₁₆	—	2	1	no	—
723	M₁₆	—	2	1	no	—
724	M₁₆	—	2	1	no	—
725	M₁₆	—	2	1	no	—
726	M₁₆	—	4	2	no	—
727	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
728	C₂×C₈	—	2	4	no	—
729	C₂×C₈	—	2	1	no	—
730	C₂×C₈	—	2	1	no	—
731	C₂×C₈	—	2	1	no	—
732	C₂×C₈	—	2	1	no	—
733	C₂×C₈	—	2	1	no	—
734	C₂×C₈	—	2	1	no	—
735	C₂×C₈	—	2	1	no	—
736	C₂×C₈	—	2	1	no	—
737	C₂×C₈	—	4	2	no	—
738	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
739	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
740	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
741	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	4	1	no	—
745	C₄⋊C₄	—	4	1	no	—
746	C₄⋊C₄	—	4	1	no	—
747	C₄⋊C₄	—	4	4	no	—
748	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	4	1	no	—
752	C₂²⋊C₄	—	4	1	no	—
753	C₂²⋊C₄	—	4	1	no	—
754	C₄²	—	2	1	no	—
755	C₄²	—	2	1	no	—
756	C₄²	—	2	1	no	—
757	C₄²	—	4	1	no	—
758	C₁₃	#24462	1	1	yes	characteristic, direct product factor, Sylow
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
763	Q₈	—	2	1	no	—
764	Q₈	—	2	1	no	—
765	Q₈	—	2	2	no	—
766	Q₈	—	2	2	no	—
767	Q₈	—	2	1	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	1	no	—
771	Q₈	—	4	4	no	—
772	Q₈	—	4	4	no	—
773	Q₈	—	4	1	no	—
774	Q₈	—	4	1	no	—
775	Q₈	—	4	1	no	—
776	Q₈	—	4	1	no	—
777	Q₈	—	4	1	no	—
778	Q₈	—	4	1	no	—
779	Q₈	—	4	1	no	—
780	Q₈	—	4	1	no	—
781	Q₈	C₁₃×#120	1	2	yes	—
782	Q₈	C₁₃×#121	1	2	yes	—
783	D₄	—	2	2	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	1	no	—
788	D₄	—	2	1	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	1	no	—
794	D₄	—	4	1	no	—
795	D₄	C₁₃×#120	1	2	yes	—
796	D₄	C₁₃×#121	1	2	yes	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	4	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	—	8	1	no	—
826	C₂×C₄	—	16	1	no	—
827	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
831	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
832	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
833	C₈	—	2	1	no	—
834	C₈	—	2	2	no	—
835	C₈	—	2	1	no	—
836	C₈	—	2	1	no	—
837	C₈	—	2	1	no	—
838	C₈	—	4	1	no	—
839	C₈	—	4	1	no	—
840	C₈	—	4	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	C₁₃×#534	1	1	yes	characteristic
853	C₂²	D₄²×C₁₃	1	1	yes	characteristic
854	C₂²	C₁₃×#546	1	1	yes	characteristic
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	8	1	no	—
864	C₄	—	8	1	no	—
865	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
866	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
867	C₄	D₄²×C₁₃	1	1	yes	characteristic
868	C₄	C₁₃×#546	1	1	yes	characteristic
869	C₂	—	2	1	no	—
870	C₂	—	2	1	no	—
871	C₂	—	4	2	no	—
872	C₂	—	4	2	no	—
873	C₂	—	8	1	no	—
874	C₂	C₁₃×#2410	1	1	yes	characteristic
875	C₂	C₁₃×#3289	1	1	yes	characteristic
876	C₂	C₁₃×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#578	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#473	C₂	semidirect
3. C₁₃×#3046	C₂	semidirect
4. C₂×C₁₃×#456	C₂	semidirect
5. C₁₃×#3011	C₂	semidirect
6. C₁₃×#2898	C₂	semidirect
7. C₁₃×#2052	C₂	semidirect
8. C₁₃×#2047	C₂	semidirect
9. C₁₃×#2016	C₂	semidirect
10. C₁₃×#2005	C₂	semidirect
11. C₁₃×#1908	C₂	semidirect
12. C₁₃×#1882	C₂	semidirect
13. C₁₃×#1876	C₂	semidirect
14. C₁₃×#1866	C₂	semidirect
15. C₁₃×#1793	C₂	semidirect
187. #24462	C₁₃	direct (N × H)
322. C₂×#473	C₂×C₁₃	semidirect
323. #3046	C₂×C₁₃	semidirect
324. C₂×#456	C₂×C₁₃	semidirect
325. #3011	C₂×C₁₃	semidirect
326. #2898	C₂×C₁₃	semidirect
327. #2052	C₂×C₁₃	semidirect
328. #2047	C₂×C₁₃	semidirect
329. #2016	C₂×C₁₃	semidirect
330. #2005	C₂×C₁₃	semidirect
331. #1908	C₂×C₁₃	semidirect
332. #1882	C₂×C₁₃	semidirect
333. #1876	C₂×C₁₃	semidirect
334. #1866	C₂×C₁₃	semidirect
335. #1793	C₂×C₁₃	semidirect
758. C₁₃	#24462	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#578	2
C₂×C₁₃×#473	2
C₁₃×#3046	2
C₂×C₁₃×#456	2
C₁₃×#3011	2
C₁₃×#2898	2
C₁₃×#2052	2
C₁₃×#2047	2
C₁₃×#2016	2
C₁₃×#2005	2
C₁₃×#1908	2
C₁₃×#1882	2
C₁₃×#1876	2
C₁₃×#1866	2
C₁₃×#1793	2
#24462	13

Subgroups — C13×#24462 #15710801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24462 #15710801