Subgroups — C₁₃×#61422 #15747761

Order 3328.

1844 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3402	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3400	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3398	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3398	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3395	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3394	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3156	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3046	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3044	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic
14	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2947	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#137	C₂²	1	2	yes	—
21	C₂×C₁₃×#135	C₂²	1	2	yes	—
22	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
23	C₁₃×#559	C₂²	1	2	yes	—
24	C₁₃×#557	C₂²	1	2	yes	—
25	C₁₃×#557	C₂²	1	2	yes	—
26	C₁₃×#557	C₂²	1	2	yes	—
27	C₁₃×#556	—	2	1	no	—
28	C₁₃×#556	C₂²	1	2	yes	—
29	C₁₃×#556	C₂²	1	4	yes	—
30	C₁₃×#556	C₂²	1	2	yes	—
31	C₁₃×#554	—	2	1	no	—
32	C₁₃×#552	—	2	2	no	—
33	C₁₃×#552	—	2	2	no	—
34	C₁₃×#552	—	2	2	no	—
35	C₁₃×#541	—	2	2	no	—
36	C₁₃×#539	—	2	2	no	—
37	C₁₃×#536	C₂²	1	2	yes	—
38	C₁₃×#536	C₂²	1	2	yes	—
39	C₁₃×#533	—	2	1	no	—
40	C₁₃×#533	—	2	1	no	—
41	C₁₃×#533	C₂²	1	1	yes	characteristic
42	C₁₃×#532	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₁₃×#529	—	2	2	no	—
45	C₁₃×#520	C₂²	1	2	yes	—
46	C₁₃×#519	C₂²	1	2	yes	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#497	C₂²	1	4	yes	—
50	C₁₃×#497	C₂²	1	4	yes	—
51	C₁₃×#497	C₂²	1	4	yes	—
52	C₁₃×#495	C₂²	1	4	yes	—
53	C₁₃×#494	C₂²	1	2	yes	—
54	C₁₃×#494	C₂²	1	4	yes	—
55	C₁₃×#492	C₂²	1	2	yes	—
56	C₁₃×#464	C₂²	1	2	yes	—
57	C₁₃×#464	C₂²	1	4	yes	—
58	C₁₃×#464	C₂²	1	4	yes	—
59	C₁₃×#464	C₂²	1	4	yes	—
60	C₁₃×#463	C₂²	1	2	yes	—
61	C₁₃×#463	C₂²	1	4	yes	—
62	C₁₃×#462	C₂²	1	2	yes	—
63	C₁₃×#462	C₂²	1	2	yes	—
64	C₁₃×#462	C₂²	1	4	yes	—
65	C₁₃×#462	C₂²	1	1	yes	characteristic
66	C₁₃×#462	C₂²	1	4	yes	—
67	C₁₃×#462	C₂²	1	4	yes	—
68	C₁₃×#462	C₂²	1	4	yes	—
69	C₁₃×#461	C₂²	1	1	yes	characteristic
70	C₁₃×#461	C₂²	1	4	yes	—
71	C₁₃×#460	C₂²	1	1	yes	characteristic
72	C₁₃×#459	C₂²	1	1	yes	characteristic
73	C₁₃×#446	C₂²	1	2	yes	—
74	C₁₃×#446	C₂²	1	4	yes	—
75	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
76	C₁₃×#441	C₂²	1	2	yes	—
77	C₁₃×#441	C₂²	1	4	yes	—
78	C₁₃×#440	C₂²	1	4	yes	—
79	C₁₃×#440	C₂²	1	2	yes	—
80	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
81	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
82	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
83	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
84	C₁₃×#428	C₂²	1	1	yes	characteristic
85	C₁₃×#424	C₂²	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
87	C₁₃×#419	C₂²	1	1	yes	characteristic
88	C₁₃×#417	C₂²	1	1	yes	characteristic
89	C₁₃×#416	C₂²	1	2	yes	—
90	C₂×C₁₃×#103	C₂²	1	2	yes	—
91	C₁₃×#405	C₂²	1	2	yes	—
92	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	C₂³	1	2	yes	—
94	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
96	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×#137	—	2	8	no	—
98	C₁₃×#137	—	2	4	no	—
99	C₁₃×#137	—	4	4	no	—
100	C₁₃×#135	—	4	4	no	—
101	C₂×C₁₃×Q₁₆	—	4	4	no	—
102	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
113	C₂×C₁₃×D₈	C₂³	1	2	yes	—
114	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	—	2	1	no	—
118	C₁₃×C₄⋊Q₈	—	2	1	no	—
119	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
120	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
121	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
123	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
125	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₁₃×#127	C₂³	1	1	yes	characteristic
127	C₁₃×#126	—	2	4	no	—
128	C₁₃×#126	—	2	4	no	—
129	C₁₃×#126	—	2	4	no	—
130	C₁₃×#126	—	2	4	no	—
131	C₁₃×#125	—	2	2	no	—
132	C₁₃×#125	—	2	2	no	—
133	C₁₃×#125	—	2	2	no	—
134	C₁₃×#125	—	2	4	no	—
135	C₁₃×#125	—	2	4	no	—
136	C₁₃×#125	—	2	4	no	—
137	C₁₃×#125	D₄	1	2	yes	—
138	C₁₃×#124	—	2	2	no	—
139	C₁₃×#124	C₂³	1	4	yes	—
140	C₁₃×#124	C₂³	1	2	yes	—
141	C₁₃×#124	C₂³	1	4	yes	—
142	C₁₃×#123	—	2	4	no	—
143	C₁₃×#123	—	2	4	no	—
144	C₁₃×#123	—	2	4	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	4	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	2	no	—
152	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
153	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₄×Q₈×C₁₃	—	2	2	no	—
157	C₄×Q₈×C₁₃	—	2	2	no	—
158	C₄×Q₈×C₁₃	—	2	2	no	—
159	C₄×Q₈×C₁₃	—	2	2	no	—
160	C₄×Q₈×C₁₃	—	2	2	no	—
161	C₄×Q₈×C₁₃	—	2	1	no	—
162	C₄×Q₈×C₁₃	—	2	1	no	—
163	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
171	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	4	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₁₃	C₂³	1	4	yes	—
180	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
181	C₁₃×#117	—	2	2	no	—
182	C₁₃×#117	—	2	4	no	—
183	C₁₃×#117	—	2	2	no	—
184	C₁₃×#117	—	2	2	no	—
185	C₁₃×#117	—	2	4	no	—
186	C₁₃×#117	—	2	1	no	—
187	C₁₃×#117	C₂³	1	1	yes	characteristic
188	C₁₃×#117	C₂³	1	2	yes	—
189	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃	—	2	1	no	—
195	C₂×C₄²×C₁₃	—	2	1	no	—
196	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
197	C₁₃×#107	C₂³	1	2	yes	—
198	C₁₃×#106	C₂³	1	2	yes	—
199	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
201	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
202	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
203	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	4	yes	—
205	C₁₃×#103	C₂³	1	4	yes	—
206	C₁₃×#103	C₂³	1	2	yes	—
207	C₁₃×#103	C₂³	1	2	yes	—
208	C₁₃×#103	C₂³	1	2	yes	—
209	C₁₃×#103	C₂³	1	2	yes	—
210	C₁₃×#103	C₂³	1	2	yes	—
211	C₁₃×#102	C₂³	1	2	yes	—
212	C₁₃×#102	C₂³	1	2	yes	—
213	C₁₃×#102	C₂³	1	2	yes	—
214	C₁₃×#97	C₂³	1	2	yes	—
215	C₁₃×#97	C₂³	1	4	yes	—
216	C₄×C₈×C₁₃	C₂³	1	2	yes	—
217	C₄×C₈×C₁₃	C₂³	1	4	yes	—
218	#61422	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₁₃×#41	—	2	4	no	—
220	C₁₃×#41	—	2	2	no	—
221	C₁₃×#41	—	2	2	no	—
222	C₁₃×#41	—	2	4	no	—
223	C₂×Q₈×C₁₃	—	2	1	no	—
224	C₂×Q₈×C₁₃	—	2	2	no	—
225	C₂×Q₈×C₁₃	—	2	4	no	—
226	C₂×Q₈×C₁₃	—	2	2	no	—
227	C₂×Q₈×C₁₃	—	2	2	no	—
228	C₂×Q₈×C₁₃	—	2	4	no	—
229	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
230	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
231	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
232	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
233	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
234	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂×D₄×C₁₃	—	2	2	no	—
236	C₂×D₄×C₁₃	—	2	1	no	—
237	C₂×D₄×C₁₃	—	2	1	no	—
238	C₂×D₄×C₁₃	—	2	1	no	—
239	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃	—	2	1	no	—
242	C₂²×C₄×C₁₃	—	2	2	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	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	4	no	—
249	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₁₃×Q₁₆	—	2	4	no	—
253	C₁₃×Q₁₆	—	2	8	no	—
254	C₁₃×Q₁₆	—	4	4	no	—
255	C₁₃×Q₁₆	—	4	4	no	—
256	C₁₃×Q₁₆	—	4	2	no	—
257	C₁₃×Q₁₆	—	4	4	no	—
258	C₁₃×SD₁₆	—	2	8	no	—
259	C₁₃×SD₁₆	—	2	4	no	—
260	C₁₃×SD₁₆	—	4	2	no	—
261	C₁₃×SD₁₆	—	4	2	no	—
262	C₁₃×SD₁₆	—	4	4	no	—
263	C₁₃×D₈	—	4	2	no	—
264	C₁₃×M₁₆	—	2	2	no	—
265	C₁₃×M₁₆	#41	1	4	yes	—
266	C₂×C₈×C₁₃	—	2	4	no	—
267	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
268	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
269	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
270	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₁₃×C₄⋊C₄	—	2	4	no	—
282	C₁₃×C₄⋊C₄	—	2	4	no	—
283	C₁₃×C₄⋊C₄	—	2	4	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	4	no	—
287	C₁₃×C₄⋊C₄	—	2	4	no	—
288	C₁₃×C₄⋊C₄	—	2	4	no	—
289	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
290	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
291	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
292	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
293	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
294	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
295	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
296	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
297	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
298	C₁₃×C₂²⋊C₄	—	2	1	no	—
299	C₁₃×C₂²⋊C₄	—	2	2	no	—
300	C₁₃×C₂²⋊C₄	—	2	4	no	—
301	C₁₃×C₂²⋊C₄	—	2	1	no	—
302	C₁₃×C₂²⋊C₄	—	2	1	no	—
303	C₁₃×C₂²⋊C₄	—	2	4	no	—
304	C₁₃×C₂²⋊C₄	—	2	4	no	—
305	C₁₃×C₂²⋊C₄	—	2	4	no	—
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
309	C₄²×C₁₃	—	2	2	no	—
310	C₄²×C₁₃	—	2	1	no	—
311	C₄²×C₁₃	—	2	2	no	—
312	C₄²×C₁₃	—	2	1	no	—
313	C₄²×C₁₃	—	2	1	no	—
314	C₄²×C₁₃	—	2	4	no	—
315	C₄²×C₁₃	—	2	4	no	—
316	C₄²×C₁₃	—	2	4	no	—
317	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
320	C₄²×C₁₃	C₂⁴	1	4	yes	—
321	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
322	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
324	#3402	C₂×C₁₃	1	4	yes	complemented
325	#3400	C₂×C₁₃	1	2	yes	complemented
326	#3398	C₂×C₁₃	1	2	yes	complemented
327	#3398	C₂×C₁₃	1	4	yes	complemented
328	#3395	C₂×C₁₃	1	2	yes	complemented
329	#3394	C₂×C₁₃	1	2	yes	complemented
330	#3156	C₂×C₁₃	1	2	yes	complemented
331	#3152	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#3046	C₂×C₁₃	1	2	yes	complemented
333	#3044	C₂×C₁₃	1	2	yes	complemented
334	#3035	C₂×C₁₃	1	1	yes	characteristic
335	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#2947	C₂×C₁₃	1	2	yes	complemented
338	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
339	C₂³×C₁₃	—	2	1	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	Q₈×C₁₃	—	2	4	no	—
343	Q₈×C₁₃	—	2	2	no	—
344	Q₈×C₁₃	—	2	4	no	—
345	Q₈×C₁₃	—	2	2	no	—
346	Q₈×C₁₃	—	2	1	no	—
347	Q₈×C₁₃	—	2	1	no	—
348	Q₈×C₁₃	—	2	4	no	—
349	Q₈×C₁₃	—	2	2	no	—
350	Q₈×C₁₃	—	2	2	no	—
351	Q₈×C₁₃	—	4	2	no	—
352	Q₈×C₁₃	—	4	2	no	—
353	Q₈×C₁₃	—	4	4	no	—
354	D₄×C₁₃	—	2	1	no	—
355	D₄×C₁₃	—	2	2	no	—
356	D₄×C₁₃	—	2	1	no	—
357	D₄×C₁₃	—	2	2	no	—
358	D₄×C₁₃	—	4	4	no	—
359	D₄×C₁₃	—	4	2	no	—
360	D₄×C₁₃	—	4	2	no	—
361	D₄×C₁₃	—	8	1	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	1	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	4	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	4	1	no	—
371	C₂×C₄×C₁₃	—	4	2	no	—
372	C₂×C₄×C₁₃	—	4	2	no	—
373	C₂×C₄×C₁₃	—	4	4	no	—
374	C₂×C₄×C₁₃	—	4	2	no	—
375	C₂×C₄×C₁₃	—	4	4	no	—
376	C₂×C₄×C₁₃	—	4	2	no	—
377	C₂×C₄×C₁₃	—	8	4	no	—
378	C₂×C₄×C₁₃	—	8	1	no	—
379	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
381	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
383	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
387	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
388	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
389	C₈×C₁₃	—	2	2	no	—
390	C₈×C₁₃	—	2	2	no	—
391	C₈×C₁₃	—	2	2	no	—
392	C₈×C₁₃	C₂×#41	1	4	yes	—
393	C₂×#137	C₂²×C₁₃	1	2	yes	—
394	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×#137	C₂²×C₁₃	1	2	yes	—
396	C₂×#135	C₂²×C₁₃	1	2	yes	—
397	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
398	#559	C₂²×C₁₃	1	2	yes	—
399	#557	C₂²×C₁₃	1	2	yes	—
400	#557	C₂²×C₁₃	1	2	yes	—
401	#557	C₂²×C₁₃	1	2	yes	—
402	#556	—	2	1	no	—
403	#556	C₂²×C₁₃	1	2	yes	—
404	#556	C₂²×C₁₃	1	4	yes	—
405	#556	C₂²×C₁₃	1	2	yes	—
406	#554	—	2	1	no	—
407	#552	—	2	2	no	—
408	#552	—	2	2	no	—
409	#552	—	2	2	no	—
410	#541	—	2	2	no	—
411	#539	—	2	2	no	—
412	#536	C₂²×C₁₃	1	2	yes	—
413	#536	C₂²×C₁₃	1	2	yes	—
414	#533	—	2	1	no	—
415	#533	—	2	1	no	—
416	#533	C₂²×C₁₃	1	1	yes	characteristic
417	#532	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
419	#529	—	2	2	no	—
420	#520	C₂²×C₁₃	1	2	yes	—
421	#519	C₂²×C₁₃	1	2	yes	—
422	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
424	#497	C₂²×C₁₃	1	4	yes	—
425	#497	C₂²×C₁₃	1	4	yes	—
426	#497	C₂²×C₁₃	1	4	yes	—
427	#495	C₂²×C₁₃	1	4	yes	—
428	#494	C₂²×C₁₃	1	2	yes	—
429	#494	C₂²×C₁₃	1	4	yes	—
430	#492	C₂²×C₁₃	1	2	yes	—
431	#464	C₂²×C₁₃	1	4	yes	—
432	#464	C₂²×C₁₃	1	2	yes	—
433	#464	C₂²×C₁₃	1	4	yes	—
434	#464	C₂²×C₁₃	1	4	yes	—
435	#463	C₂²×C₁₃	1	4	yes	—
436	#463	C₂²×C₁₃	1	2	yes	—
437	#462	C₂²×C₁₃	1	2	yes	—
438	#462	C₂²×C₁₃	1	1	yes	characteristic
439	#462	C₂²×C₁₃	1	4	yes	—
440	#462	C₂²×C₁₃	1	4	yes	—
441	#462	C₂²×C₁₃	1	4	yes	—
442	#462	C₂²×C₁₃	1	2	yes	—
443	#462	C₂²×C₁₃	1	4	yes	—
444	#461	C₂²×C₁₃	1	1	yes	characteristic
445	#461	C₂²×C₁₃	1	4	yes	—
446	#460	C₂²×C₁₃	1	1	yes	characteristic
447	#459	C₂²×C₁₃	1	1	yes	characteristic
448	#446	C₂²×C₁₃	1	2	yes	—
449	#446	C₂²×C₁₃	1	4	yes	—
450	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
451	#441	C₂²×C₁₃	1	2	yes	—
452	#441	C₂²×C₁₃	1	4	yes	—
453	#440	C₂²×C₁₃	1	4	yes	—
454	#440	C₂²×C₁₃	1	2	yes	—
455	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
456	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
457	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
458	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
459	#428	C₂²×C₁₃	1	1	yes	characteristic
460	#424	C₂²×C₁₃	1	2	yes	—
461	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
462	#419	C₂²×C₁₃	1	1	yes	characteristic
463	#417	C₂²×C₁₃	1	1	yes	characteristic
464	#416	C₂²×C₁₃	1	2	yes	—
465	C₂×#103	C₂²×C₁₃	1	2	yes	—
466	#405	C₂²×C₁₃	1	2	yes	—
467	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
468	C₂²×C₁₃	—	2	1	no	—
469	C₂²×C₁₃	—	2	1	no	—
470	C₂²×C₁₃	—	4	1	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	—	4	1	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	4	1	no	—
475	C₂²×C₁₃	—	4	2	no	—
476	C₂²×C₁₃	#550	1	2	yes	—
477	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
478	C₄×C₁₃	—	2	1	no	—
479	C₄×C₁₃	—	2	1	no	—
480	C₄×C₁₃	—	2	4	no	—
481	C₄×C₁₃	—	2	1	no	—
482	C₄×C₁₃	—	2	4	no	—
483	C₄×C₁₃	—	4	1	no	—
484	C₄×C₁₃	—	4	2	no	—
485	C₄×C₁₃	—	4	2	no	—
486	C₄×C₁₃	—	4	1	no	—
487	C₄×C₁₃	—	4	2	no	—
488	C₄×C₁₃	—	4	4	no	—
489	C₄×C₁₃	—	4	1	no	—
490	C₄×C₁₃	#550	1	2	yes	—
491	C₄×C₁₃	#578	1	2	yes	—
492	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
493	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
494	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
495	C₂×#41	C₂³×C₁₃	1	2	yes	—
496	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
497	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
498	#137	—	2	8	no	—
499	#137	—	2	4	no	—
500	#137	—	4	4	no	—
501	#135	—	4	4	no	—
502	C₂×Q₁₆	—	4	4	no	—
503	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
504	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
505	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
506	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
507	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
508	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
509	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
510	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
511	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
512	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
513	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
514	C₂×D₈	C₂³×C₁₃	1	2	yes	—
515	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
516	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
517	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
518	C₄⋊Q₈	—	2	1	no	—
519	C₄⋊Q₈	—	2	1	no	—
520	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
521	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
522	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
523	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
524	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
525	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
526	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
527	#127	C₂³×C₁₃	1	1	yes	characteristic
528	#126	—	2	4	no	—
529	#126	—	2	4	no	—
530	#126	—	2	4	no	—
531	#126	—	2	4	no	—
532	#125	—	2	2	no	—
533	#125	—	2	2	no	—
534	#125	—	2	2	no	—
535	#125	—	2	4	no	—
536	#125	—	2	4	no	—
537	#125	—	2	4	no	—
538	#125	D₄×C₁₃	1	2	yes	—
539	#124	—	2	2	no	—
540	#124	C₂³×C₁₃	1	2	yes	—
541	#124	C₂³×C₁₃	1	4	yes	—
542	#124	C₂³×C₁₃	1	4	yes	—
543	#123	—	2	4	no	—
544	#123	—	2	4	no	—
545	#123	—	2	4	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	4	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
554	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
555	#121	—	2	1	no	—
556	#121	—	2	1	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	2	2	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	—	2	1	no	—
563	C₄×Q₈	—	2	1	no	—
564	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
565	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
566	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
567	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
568	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
569	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
570	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
571	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
572	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	—	2	1	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	4	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
580	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
581	C₄×D₄	C₂³×C₁₃	1	4	yes	—
582	#117	—	2	2	no	—
583	#117	—	2	4	no	—
584	#117	—	2	2	no	—
585	#117	—	2	2	no	—
586	#117	—	2	4	no	—
587	#117	—	2	1	no	—
588	#117	C₂³×C₁₃	1	1	yes	characteristic
589	#117	C₂³×C₁₃	1	2	yes	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	2	no	—
594	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×C₄²	—	2	1	no	—
596	C₂×C₄²	—	2	1	no	—
597	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
598	#107	C₂³×C₁₃	1	2	yes	—
599	#106	C₂³×C₁₃	1	2	yes	—
600	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
602	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
603	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
604	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
605	#103	C₂³×C₁₃	1	4	yes	—
606	#103	C₂³×C₁₃	1	4	yes	—
607	#103	C₂³×C₁₃	1	2	yes	—
608	#103	C₂³×C₁₃	1	2	yes	—
609	#103	C₂³×C₁₃	1	2	yes	—
610	#103	C₂³×C₁₃	1	2	yes	—
611	#103	C₂³×C₁₃	1	2	yes	—
612	#102	C₂³×C₁₃	1	2	yes	—
613	#102	C₂³×C₁₃	1	2	yes	—
614	#102	C₂³×C₁₃	1	2	yes	—
615	#97	C₂³×C₁₃	1	2	yes	—
616	#97	C₂³×C₁₃	1	4	yes	—
617	C₄×C₈	C₂³×C₁₃	1	2	yes	—
618	C₄×C₈	C₂³×C₁₃	1	4	yes	—
619	C₂×C₁₃	—	2	2	no	—
620	C₂×C₁₃	—	8	1	no	—
621	C₂×C₁₃	—	8	2	no	—
622	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
623	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
624	C₂×C₁₃	#3586	1	1	yes	characteristic
625	#41	—	2	2	no	—
626	#41	—	2	4	no	—
627	#41	—	2	2	no	—
628	#41	—	2	4	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	2	no	—
631	C₂×Q₈	—	2	2	no	—
632	C₂×Q₈	—	2	4	no	—
633	C₂×Q₈	—	2	2	no	—
634	C₂×Q₈	—	2	4	no	—
635	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
636	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
637	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
638	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
639	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
640	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
646	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
658	Q₁₆	—	2	4	no	—
659	Q₁₆	—	2	8	no	—
660	Q₁₆	—	4	4	no	—
661	Q₁₆	—	4	4	no	—
662	Q₁₆	—	4	2	no	—
663	Q₁₆	—	4	4	no	—
664	SD₁₆	—	2	8	no	—
665	SD₁₆	—	2	4	no	—
666	SD₁₆	—	4	2	no	—
667	SD₁₆	—	4	2	no	—
668	SD₁₆	—	4	4	no	—
669	D₈	—	4	2	no	—
670	M₁₆	—	2	2	no	—
671	M₁₆	C₁₃×#41	1	4	yes	—
672	C₂×C₈	—	2	4	no	—
673	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
674	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
675	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
676	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
696	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
697	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
698	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
699	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
700	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
701	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
702	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
703	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
715	C₄²	—	2	2	no	—
716	C₄²	—	2	1	no	—
717	C₄²	—	2	2	no	—
718	C₄²	—	2	1	no	—
719	C₄²	—	2	1	no	—
720	C₄²	—	2	4	no	—
721	C₄²	—	2	4	no	—
722	C₄²	—	2	4	no	—
723	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
724	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
725	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₄²	C₂⁴×C₁₃	1	4	yes	—
727	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
728	C₁₃	#61422	1	1	yes	characteristic, direct product factor, Sylow
729	C₂³	—	2	1	no	—
730	C₂³	—	2	2	no	—
731	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
732	Q₈	—	2	4	no	—
733	Q₈	—	2	2	no	—
734	Q₈	—	2	4	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	2	1	no	—
737	Q₈	—	2	1	no	—
738	Q₈	—	2	4	no	—
739	Q₈	—	2	2	no	—
740	Q₈	—	2	2	no	—
741	Q₈	—	4	2	no	—
742	Q₈	—	4	2	no	—
743	Q₈	—	4	4	no	—
744	D₄	—	2	1	no	—
745	D₄	—	2	2	no	—
746	D₄	—	2	1	no	—
747	D₄	—	2	2	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	2	no	—
750	D₄	—	4	2	no	—
751	D₄	—	8	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	8	4	no	—
768	C₂×C₄	—	8	1	no	—
769	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
771	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
773	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
776	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
777	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
778	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
779	C₈	—	2	2	no	—
780	C₈	—	2	2	no	—
781	C₈	—	2	2	no	—
782	C₈	C₂×C₁₃×#41	1	4	yes	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	2	no	—
791	C₂²	C₁₃×#550	1	2	yes	—
792	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
793	C₄	—	2	1	no	—
794	C₄	—	2	4	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	4	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	4	no	—
805	C₄	C₁₃×#550	1	2	yes	—
806	C₄	C₁₃×#578	1	2	yes	—
807	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
808	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
809	C₂	—	2	2	no	—
810	C₂	—	8	1	no	—
811	C₂	—	8	2	no	—
812	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
813	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
814	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3035	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3509	C₂	semidirect
2. C₁₃×#3507	C₂	semidirect
3. C₁₃×#3402	C₂	semidirect
4. C₁₃×#3400	C₂	semidirect
5. C₁₃×#3398	C₂	semidirect
6. C₁₃×#3398	C₂	semidirect
7. C₁₃×#3395	C₂	semidirect
8. C₁₃×#3394	C₂	semidirect
9. C₁₃×#3156	C₂	semidirect
10. C₁₃×#3152	C₂	semidirect
11. C₁₃×#3046	C₂	semidirect
12. C₁₃×#3044	C₂	semidirect
14. C₂×C₁₃×#462	C₂	semidirect
15. C₁₃×#2962	C₂	semidirect
16. C₁₃×#2947	C₂	semidirect
17. C₄×C₁₃×#137	C₂	semidirect
218. #61422	C₁₃	direct (N × H)
322. #3509	C₂×C₁₃	semidirect
323. #3507	C₂×C₁₃	semidirect
324. #3402	C₂×C₁₃	semidirect
325. #3400	C₂×C₁₃	semidirect
326. #3398	C₂×C₁₃	semidirect
327. #3398	C₂×C₁₃	semidirect
328. #3395	C₂×C₁₃	semidirect
329. #3394	C₂×C₁₃	semidirect
330. #3156	C₂×C₁₃	semidirect
331. #3152	C₂×C₁₃	semidirect
332. #3046	C₂×C₁₃	semidirect
333. #3044	C₂×C₁₃	semidirect
335. C₂×#462	C₂×C₁₃	semidirect
336. #2962	C₂×C₁₃	semidirect
337. #2947	C₂×C₁₃	semidirect
338. C₄×#137	C₂×C₁₃	semidirect
728. C₁₃	#61422	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3509	2
C₁₃×#3507	2
C₁₃×#3402	2
C₁₃×#3400	2
C₁₃×#3398	2
C₁₃×#3395	2
C₁₃×#3394	2
C₁₃×#3156	2
C₁₃×#3152	2
C₁₃×#3046	2
C₁₃×#3044	2
C₁₃×#3035	2
C₂×C₁₃×#462	2
C₁₃×#2962	2
C₁₃×#2947	2
C₄×C₁₃×#137	2
#61422	13

Subgroups — C13×#61422 #15747761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61422 #15747761