Subgroups — C₁₃×#35005 #15721344

Order 3328.

2642 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#538	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2856	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2847	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2639	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2617	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2559	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2557	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2496	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2491	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2428	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2422	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2325	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#538	—	2	16	no	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₃×#126	C₂²	1	4	yes	—
21	C₂×C₁₃×#124	C₂²	1	4	yes	—
22	C₂×C₁₃×#123	C₂²	1	4	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#121	C₂²	1	2	yes	—
25	C₂×C₁₃×#121	C₂²	1	4	yes	—
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	2	yes	—
28	C₂×C₁₃×#121	C₂²	1	2	yes	—
29	C₂×C₁₃×#121	C₂²	1	2	yes	—
30	C₂×C₁₃×#120	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#400	C₂²	1	4	yes	complemented
38	C₁₃×#397	C₂²	1	4	yes	—
39	C₁₃×#397	C₂²	1	4	yes	complemented
40	C₁₃×#394	C₂²	1	4	yes	—
41	C₁₃×#394	C₂²	1	4	yes	—
42	C₁₃×#394	C₂²	1	4	yes	complemented
43	C₁₃×#393	C₂²	1	4	yes	complemented
44	C₁₃×#392	C₂²	1	4	yes	—
45	C₁₃×#391	C₂²	1	2	yes	complemented
46	C₁₃×#390	C₂²	1	2	yes	complemented
47	C₁₃×#390	C₂²	1	2	yes	complemented
48	C₁₃×#390	C₂²	1	2	yes	complemented
49	C₁₃×#390	C₂²	1	2	yes	complemented
50	C₁₃×#389	C₂²	1	2	yes	complemented
51	C₁₃×#389	C₂²	1	2	yes	complemented
52	C₁₃×#389	C₂²	1	2	yes	complemented
53	C₁₃×#388	C₂²	1	4	yes	complemented
54	C₁₃×#388	C₂²	1	4	yes	complemented
55	C₁₃×#387	C₂²	1	4	yes	complemented
56	C₁₃×#386	C₂²	1	4	yes	—
57	C₁₃×#386	C₂²	1	4	yes	—
58	C₁₃×#386	C₂²	1	4	yes	—
59	C₁₃×#386	C₂²	1	4	yes	—
60	C₁₃×#386	C₂²	1	4	yes	complemented
61	C₁₃×#385	C₂²	1	4	yes	complemented
62	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#380	C₂²	1	2	yes	—
65	C₁₃×#380	C₂²	1	2	yes	—
66	C₁₃×#380	C₂²	1	2	yes	—
67	C₁₃×#380	C₂²	1	2	yes	—
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
69	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
70	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
71	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
73	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
74	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
76	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
79	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
81	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	—	2	4	no	—
85	C₂³×C₄×C₁₃	—	4	2	no	—
86	C₂³×C₄×C₁₃	—	4	2	no	—
87	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×C₄⋊Q₈	—	4	2	no	—
97	C₁₃×#127	—	4	2	no	—
98	C₁₃×#126	—	2	16	no	—
99	C₁₃×#124	—	2	16	no	—
100	C₁₃×#123	—	2	16	no	—
101	C₁₃×C₂²⋊Q₈	—	2	8	no	—
102	C₁₃×#121	—	2	8	no	—
103	C₁₃×#121	—	2	8	no	—
104	C₁₃×#121	—	2	8	no	—
105	C₁₃×#121	—	2	16	no	—
106	C₁₃×#121	—	4	4	no	—
107	C₁₃×#121	—	4	4	no	—
108	C₁₃×#120	—	2	16	no	—
109	C₄×D₄×C₁₃	—	2	16	no	—
110	C₄×D₄×C₁₃	—	4	4	no	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
122	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃	—	4	2	no	—
139	C₂×C₄²×C₁₃	—	4	2	no	—
140	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
144	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
147	C₁₃×#95	C₂³	1	2	yes	—
148	C₁₃×#95	C₂³	1	2	yes	—
149	C₁₃×#95	C₂³	1	2	yes	—
150	C₁₃×#95	C₂³	1	2	yes	—
151	C₁₃×#95	C₂³	1	4	yes	—
152	C₁₃×#95	C₂³	1	4	yes	—
153	C₁₃×#95	C₂³	1	4	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
156	C₁₃×#95	C₂³	1	4	yes	—
157	#35005	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂⁴×C₁₃	—	2	2	no	—
159	C₂⁴×C₁₃	—	2	2	no	—
160	C₂⁴×C₁₃	—	4	1	no	—
161	C₂⁴×C₁₃	—	4	1	no	—
162	C₂⁴×C₁₃	—	4	1	no	—
163	C₂⁴×C₁₃	—	4	1	no	—
164	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
165	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
166	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
167	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₂×Q₈×C₁₃	—	2	4	no	—
169	C₂×Q₈×C₁₃	—	4	2	no	—
170	C₂×Q₈×C₁₃	—	4	2	no	—
171	C₂×D₄×C₁₃	—	2	8	no	—
172	C₂×D₄×C₁₃	—	2	8	no	—
173	C₂×D₄×C₁₃	—	2	8	no	—
174	C₂×D₄×C₁₃	—	2	8	no	—
175	C₂×D₄×C₁₃	—	2	8	no	—
176	C₂×D₄×C₁₃	—	2	4	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	2	4	no	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	4	no	—
181	C₂×D₄×C₁₃	—	4	4	no	—
182	C₂×D₄×C₁₃	—	4	4	no	—
183	C₂×D₄×C₁₃	—	4	2	no	—
184	C₂×D₄×C₁₃	—	4	2	no	—
185	C₂×D₄×C₁₃	—	4	2	no	—
186	C₂×D₄×C₁₃	—	4	2	no	—
187	C₂×D₄×C₁₃	—	4	4	no	—
188	C₂×D₄×C₁₃	—	4	4	no	—
189	C₂²×C₄×C₁₃	—	2	2	no	—
190	C₂²×C₄×C₁₃	—	2	2	no	—
191	C₂²×C₄×C₁₃	—	2	2	no	—
192	C₂²×C₄×C₁₃	—	2	2	no	—
193	C₂²×C₄×C₁₃	—	2	4	no	—
194	C₂²×C₄×C₁₃	—	2	4	no	—
195	C₂²×C₄×C₁₃	—	2	4	no	—
196	C₂²×C₄×C₁₃	—	2	4	no	—
197	C₂²×C₄×C₁₃	—	2	8	no	—
198	C₂²×C₄×C₁₃	—	4	1	no	—
199	C₂²×C₄×C₁₃	—	4	1	no	—
200	C₂²×C₄×C₁₃	—	4	1	no	—
201	C₂²×C₄×C₁₃	—	4	1	no	—
202	C₂²×C₄×C₁₃	—	4	2	no	—
203	C₂²×C₄×C₁₃	—	4	2	no	—
204	C₂²×C₄×C₁₃	—	4	1	no	—
205	C₂²×C₄×C₁₃	—	4	1	no	—
206	C₂²×C₄×C₁₃	—	4	1	no	—
207	C₂²×C₄×C₁₃	—	4	1	no	—
208	C₂²×C₄×C₁₃	—	4	1	no	—
209	C₂²×C₄×C₁₃	—	4	1	no	—
210	C₂²×C₄×C₁₃	—	4	4	no	—
211	C₂²×C₄×C₁₃	—	4	4	no	—
212	C₂²×C₄×C₁₃	—	4	16	no	—
213	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
215	C₂²×C₄×C₁₃	#41	1	4	yes	—
216	C₂²×C₄×C₁₃	#41	1	4	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₁₃×C₄⋊C₄	—	2	8	no	—
230	C₁₃×C₄⋊C₄	—	2	8	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	4	no	—
233	C₁₃×C₄⋊C₄	—	2	4	no	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	2	4	no	—
236	C₁₃×C₄⋊C₄	—	2	4	no	—
237	C₁₃×C₄⋊C₄	—	4	2	no	—
238	C₁₃×C₄⋊C₄	—	4	2	no	—
239	C₁₃×C₂²⋊C₄	—	2	8	no	—
240	C₁₃×C₂²⋊C₄	—	2	8	no	—
241	C₁₃×C₂²⋊C₄	—	2	8	no	—
242	C₁₃×C₂²⋊C₄	—	2	8	no	—
243	C₁₃×C₂²⋊C₄	—	2	8	no	—
244	C₁₃×C₂²⋊C₄	—	2	4	no	—
245	C₁₃×C₂²⋊C₄	—	2	4	no	—
246	C₁₃×C₂²⋊C₄	—	2	8	no	—
247	C₁₃×C₂²⋊C₄	—	2	8	no	—
248	C₁₃×C₂²⋊C₄	—	4	4	no	—
249	C₁₃×C₂²⋊C₄	—	4	4	no	—
250	C₁₃×C₂²⋊C₄	—	4	4	no	—
251	C₁₃×C₂²⋊C₄	—	4	4	no	—
252	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
253	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
254	C₄²×C₁₃	—	2	8	no	—
255	C₄²×C₁₃	—	2	4	no	—
256	C₄²×C₁₃	—	2	2	no	—
257	C₄²×C₁₃	—	2	2	no	—
258	C₄²×C₁₃	—	4	1	no	—
259	C₄²×C₁₃	—	4	2	no	—
260	C₄²×C₁₃	—	4	1	no	—
261	C₂×#538	C₂×C₁₃	1	2	yes	complemented
262	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2856	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#2847	C₂×C₁₃	1	2	yes	complemented
265	#2639	C₂×C₁₃	1	2	yes	complemented
266	#2617	C₂×C₁₃	1	2	yes	complemented
267	#2559	C₂×C₁₃	1	4	yes	complemented
268	#2557	C₂×C₁₃	1	4	yes	complemented
269	#2496	C₂×C₁₃	1	2	yes	complemented
270	#2491	C₂×C₁₃	1	2	yes	complemented
271	#2428	C₂×C₁₃	1	2	yes	complemented
272	#2422	C₂×C₁₃	1	2	yes	complemented
273	#2325	C₂×C₁₃	1	2	yes	complemented
274	C₄×#121	C₂×C₁₃	1	2	yes	complemented
275	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
276	C₂³×C₁₃	—	2	1	no	—
277	C₂³×C₁₃	—	2	1	no	—
278	C₂³×C₁₃	—	2	1	no	—
279	C₂³×C₁₃	—	2	1	no	—
280	C₂³×C₁₃	—	2	8	no	—
281	C₂³×C₁₃	—	2	2	no	—
282	C₂³×C₁₃	—	2	2	no	—
283	C₂³×C₁₃	—	2	2	no	—
284	C₂³×C₁₃	—	2	2	no	—
285	C₂³×C₁₃	—	2	2	no	—
286	C₂³×C₁₃	—	2	2	no	—
287	C₂³×C₁₃	—	2	4	no	—
288	C₂³×C₁₃	—	2	4	no	—
289	C₂³×C₁₃	—	2	4	no	—
290	C₂³×C₁₃	—	2	4	no	—
291	C₂³×C₁₃	—	2	4	no	—
292	C₂³×C₁₃	—	2	4	no	—
293	C₂³×C₁₃	—	2	4	no	—
294	C₂³×C₁₃	—	4	4	no	—
295	C₂³×C₁₃	—	4	4	no	—
296	C₂³×C₁₃	—	4	4	no	—
297	C₂³×C₁₃	—	4	4	no	—
298	C₂³×C₁₃	—	4	4	no	—
299	C₂³×C₁₃	—	4	4	no	—
300	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
301	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
302	C₂³×C₁₃	C₂×#41	1	2	yes	—
303	C₂³×C₁₃	C₂×#41	1	2	yes	—
304	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
305	Q₈×C₁₃	—	8	4	no	—
306	D₄×C₁₃	—	4	16	no	—
307	D₄×C₁₃	—	4	8	no	—
308	D₄×C₁₃	—	8	4	no	—
309	D₄×C₁₃	—	8	4	no	—
310	D₄×C₁₃	—	8	8	no	—
311	D₄×C₁₃	—	8	8	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	1	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	2	1	no	—
319	C₂×C₄×C₁₃	—	2	1	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	2	1	no	—
324	C₂×C₄×C₁₃	—	2	8	no	—
325	C₂×C₄×C₁₃	—	2	4	no	—
326	C₂×C₄×C₁₃	—	2	4	no	—
327	C₂×C₄×C₁₃	—	2	4	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	4	no	—
330	C₂×C₄×C₁₃	—	2	4	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	4	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	4	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	4	no	—
339	C₂×C₄×C₁₃	—	2	4	no	—
340	C₂×C₄×C₁₃	—	4	4	no	—
341	C₂×C₄×C₁₃	—	4	4	no	—
342	C₂×C₄×C₁₃	—	4	4	no	—
343	C₂×C₄×C₁₃	—	4	8	no	—
344	C₂×C₄×C₁₃	—	4	4	no	—
345	C₂×C₄×C₁₃	—	4	4	no	—
346	C₂×C₄×C₁₃	—	4	8	no	—
347	C₂×C₄×C₁₃	—	8	8	no	—
348	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
349	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
352	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
353	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
354	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
355	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
356	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
357	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
358	#538	—	2	16	no	—
359	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
360	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
361	C₂×#126	C₂²×C₁₃	1	4	yes	—
362	C₂×#124	C₂²×C₁₃	1	4	yes	—
363	C₂×#123	C₂²×C₁₃	1	4	yes	—
364	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
365	C₂×#121	C₂²×C₁₃	1	2	yes	—
366	C₂×#121	C₂²×C₁₃	1	2	yes	—
367	C₂×#121	C₂²×C₁₃	1	2	yes	—
368	C₂×#121	C₂²×C₁₃	1	4	yes	—
369	C₂×#121	C₂²×C₁₃	1	2	yes	—
370	C₂×#121	C₂²×C₁₃	1	2	yes	—
371	C₂×#120	C₂²×C₁₃	1	4	yes	—
372	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
373	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
374	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
375	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
376	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
377	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
378	#400	C₂²×C₁₃	1	4	yes	complemented
379	#397	C₂²×C₁₃	1	4	yes	—
380	#397	C₂²×C₁₃	1	4	yes	complemented
381	#394	C₂²×C₁₃	1	4	yes	—
382	#394	C₂²×C₁₃	1	4	yes	—
383	#394	C₂²×C₁₃	1	4	yes	complemented
384	#393	C₂²×C₁₃	1	4	yes	complemented
385	#392	C₂²×C₁₃	1	4	yes	—
386	#391	C₂²×C₁₃	1	2	yes	complemented
387	#390	C₂²×C₁₃	1	2	yes	complemented
388	#390	C₂²×C₁₃	1	2	yes	complemented
389	#390	C₂²×C₁₃	1	2	yes	complemented
390	#390	C₂²×C₁₃	1	2	yes	complemented
391	#389	C₂²×C₁₃	1	2	yes	complemented
392	#389	C₂²×C₁₃	1	2	yes	complemented
393	#389	C₂²×C₁₃	1	2	yes	complemented
394	#388	C₂²×C₁₃	1	4	yes	complemented
395	#388	C₂²×C₁₃	1	4	yes	complemented
396	#387	C₂²×C₁₃	1	4	yes	complemented
397	#386	C₂²×C₁₃	1	4	yes	—
398	#386	C₂²×C₁₃	1	4	yes	—
399	#386	C₂²×C₁₃	1	4	yes	—
400	#386	C₂²×C₁₃	1	4	yes	—
401	#386	C₂²×C₁₃	1	4	yes	complemented
402	#385	C₂²×C₁₃	1	4	yes	complemented
403	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
404	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
405	#380	C₂²×C₁₃	1	2	yes	—
406	#380	C₂²×C₁₃	1	2	yes	—
407	#380	C₂²×C₁₃	1	2	yes	—
408	#380	C₂²×C₁₃	1	2	yes	—
409	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
410	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
411	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
412	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
415	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
417	C₂²×C₁₃	—	2	2	no	—
418	C₂²×C₁₃	—	2	2	no	—
419	C₂²×C₁₃	—	2	2	no	—
420	C₂²×C₁₃	—	2	2	no	—
421	C₂²×C₁₃	—	2	2	no	—
422	C₂²×C₁₃	—	2	2	no	—
423	C₂²×C₁₃	—	2	4	no	—
424	C₂²×C₁₃	—	2	4	no	—
425	C₂²×C₁₃	—	2	4	no	—
426	C₂²×C₁₃	—	4	16	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	4	2	no	—
429	C₂²×C₁₃	—	4	2	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	—	4	4	no	—
432	C₂²×C₁₃	—	4	4	no	—
433	C₂²×C₁₃	—	4	4	no	—
434	C₂²×C₁₃	—	4	4	no	—
435	C₂²×C₁₃	—	4	4	no	—
436	C₂²×C₁₃	—	4	4	no	—
437	C₂²×C₁₃	—	4	4	no	—
438	C₂²×C₁₃	#532	1	4	yes	—
439	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
440	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
441	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
442	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
443	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂²×C₁₃	#585	1	1	yes	characteristic
445	C₂²×C₁₃	#585	1	1	yes	characteristic
446	C₄×C₁₃	—	2	2	no	—
447	C₄×C₁₃	—	2	4	no	—
448	C₄×C₁₃	—	2	2	no	—
449	C₄×C₁₃	—	2	2	no	—
450	C₄×C₁₃	—	2	2	no	—
451	C₄×C₁₃	—	2	2	no	—
452	C₄×C₁₃	—	4	4	no	—
453	C₄×C₁₃	—	4	2	no	—
454	C₄×C₁₃	—	4	4	no	—
455	C₄×C₁₃	—	4	4	no	—
456	C₄×C₁₃	—	4	2	no	—
457	C₄×C₁₃	#538	1	4	yes	complemented
458	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
459	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
460	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
461	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
462	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
463	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
464	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
465	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
466	C₂³×C₄	—	2	4	no	—
467	C₂³×C₄	—	4	2	no	—
468	C₂³×C₄	—	4	2	no	—
469	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
470	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
473	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
475	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
478	C₄⋊Q₈	—	4	2	no	—
479	#127	—	4	2	no	—
480	#126	—	2	16	no	—
481	#124	—	2	16	no	—
482	#123	—	2	16	no	—
483	C₂²⋊Q₈	—	2	8	no	—
484	#121	—	2	8	no	—
485	#121	—	2	8	no	—
486	#121	—	2	8	no	—
487	#121	—	2	16	no	—
488	#121	—	4	4	no	—
489	#121	—	4	4	no	—
490	#120	—	2	16	no	—
491	C₄×D₄	—	2	16	no	—
492	C₄×D₄	—	4	4	no	—
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
503	C₂×C₂²⋊C₄	—	2	4	no	—
504	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
505	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
520	C₂×C₄²	—	4	2	no	—
521	C₂×C₄²	—	4	2	no	—
522	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
523	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
524	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
525	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
529	#95	C₂³×C₁₃	1	2	yes	—
530	#95	C₂³×C₁₃	1	2	yes	—
531	#95	C₂³×C₁₃	1	2	yes	—
532	#95	C₂³×C₁₃	1	2	yes	—
533	#95	C₂³×C₁₃	1	4	yes	—
534	#95	C₂³×C₁₃	1	4	yes	—
535	#95	C₂³×C₁₃	1	4	yes	—
536	#95	C₂³×C₁₃	1	4	yes	—
537	#95	C₂³×C₁₃	1	4	yes	—
538	#95	C₂³×C₁₃	1	4	yes	—
539	C₂×C₁₃	—	2	4	no	—
540	C₂×C₁₃	—	4	4	no	—
541	C₂×C₁₃	—	8	4	no	—
542	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
543	C₂×C₁₃	C₂×#538	1	1	yes	characteristic
544	C₂×C₁₃	#3455	1	1	yes	characteristic
545	C₂×C₁₃	#3496	1	1	yes	characteristic
546	C₂×C₁₃	#3496	1	1	yes	characteristic
547	C₂×C₁₃	#3505	1	1	yes	characteristic
548	C₂×C₁₃	#3506	1	1	yes	characteristic
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	4	1	no	—
552	C₂⁴	—	4	1	no	—
553	C₂⁴	—	4	1	no	—
554	C₂⁴	—	4	1	no	—
555	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
556	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
557	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
558	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
559	C₂×Q₈	—	2	4	no	—
560	C₂×Q₈	—	4	2	no	—
561	C₂×Q₈	—	4	2	no	—
562	C₂×D₄	—	2	8	no	—
563	C₂×D₄	—	2	8	no	—
564	C₂×D₄	—	2	8	no	—
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	2	8	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	2	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	4	2	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	8	no	—
589	C₂²×C₄	—	4	1	no	—
590	C₂²×C₄	—	4	1	no	—
591	C₂²×C₄	—	4	1	no	—
592	C₂²×C₄	—	4	1	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	4	1	no	—
596	C₂²×C₄	—	4	1	no	—
597	C₂²×C₄	—	4	1	no	—
598	C₂²×C₄	—	4	1	no	—
599	C₂²×C₄	—	4	1	no	—
600	C₂²×C₄	—	4	1	no	—
601	C₂²×C₄	—	4	4	no	—
602	C₂²×C₄	—	4	4	no	—
603	C₂²×C₄	—	4	16	no	—
604	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
605	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
606	C₂²×C₄	C₁₃×#41	1	4	yes	—
607	C₂²×C₄	C₁₃×#41	1	4	yes	—
608	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
611	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
612	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
613	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
620	C₄⋊C₄	—	2	8	no	—
621	C₄⋊C₄	—	2	8	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₂²⋊C₄	—	2	8	no	—
631	C₂²⋊C₄	—	2	8	no	—
632	C₂²⋊C₄	—	2	8	no	—
633	C₂²⋊C₄	—	2	8	no	—
634	C₂²⋊C₄	—	2	8	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	2	8	no	—
639	C₂²⋊C₄	—	4	4	no	—
640	C₂²⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	4	4	no	—
642	C₂²⋊C₄	—	4	4	no	—
643	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
644	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
645	C₄²	—	2	8	no	—
646	C₄²	—	2	4	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	4	1	no	—
650	C₄²	—	4	2	no	—
651	C₄²	—	4	1	no	—
652	C₁₃	#35005	1	1	yes	characteristic, direct product factor, Sylow
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	8	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	4	4	no	—
672	C₂³	—	4	4	no	—
673	C₂³	—	4	4	no	—
674	C₂³	—	4	4	no	—
675	C₂³	—	4	4	no	—
676	C₂³	—	4	4	no	—
677	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
678	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
679	C₂³	C₂×C₁₃×#41	1	2	yes	—
680	C₂³	C₂×C₁₃×#41	1	2	yes	—
681	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
682	Q₈	—	8	4	no	—
683	D₄	—	4	16	no	—
684	D₄	—	4	8	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	4	no	—
687	D₄	—	8	8	no	—
688	D₄	—	8	8	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	4	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	—	8	8	no	—
725	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
726	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
728	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
729	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
730	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
731	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
732	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
733	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	4	16	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	C₁₃×#532	1	4	yes	—
756	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
757	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
758	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
759	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
760	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
761	C₂²	C₁₃×#585	1	1	yes	characteristic
762	C₂²	C₁₃×#585	1	1	yes	characteristic
763	C₄	—	2	2	no	—
764	C₄	—	2	4	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	2	no	—
769	C₄	—	4	4	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	4	no	—
772	C₄	—	4	4	no	—
773	C₄	—	4	2	no	—
774	C₄	C₁₃×#538	1	4	yes	complemented
775	C₂	—	2	4	no	—
776	C₂	—	4	4	no	—
777	C₂	—	8	4	no	—
778	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
779	C₂	C₂×C₁₃×#538	1	1	yes	characteristic
780	C₂	C₁₃×#3455	1	1	yes	characteristic
781	C₂	C₁₃×#3496	1	1	yes	characteristic
782	C₂	C₁₃×#3496	1	1	yes	characteristic
783	C₂	C₁₃×#3505	1	1	yes	characteristic
784	C₂	C₁₃×#3506	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#538	C₂	semidirect
2. C₁₃×#2857	C₂	semidirect
3. C₁₃×#2856	C₂	semidirect
4. C₁₃×#2847	C₂	semidirect
5. C₁₃×#2639	C₂	semidirect
6. C₁₃×#2617	C₂	semidirect
7. C₁₃×#2559	C₂	semidirect
8. C₁₃×#2557	C₂	semidirect
9. C₁₃×#2496	C₂	semidirect
10. C₁₃×#2491	C₂	semidirect
11. C₁₃×#2428	C₂	semidirect
12. C₁₃×#2422	C₂	semidirect
13. C₁₃×#2325	C₂	semidirect
14. C₄×C₁₃×#121	C₂	semidirect
15. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
18. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₁₃×#127	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃	C₂²	semidirect
37. C₁₃×#400	C₂²	semidirect
39. C₁₃×#397	C₂²	semidirect
42. C₁₃×#394	C₂²	semidirect
43. C₁₃×#393	C₂²	semidirect
45. C₁₃×#391	C₂²	semidirect
46. C₁₃×#390	C₂²	semidirect
47. C₁₃×#390	C₂²	semidirect
48. C₁₃×#390	C₂²	semidirect
49. C₁₃×#390	C₂²	semidirect
50. C₁₃×#389	C₂²	semidirect
51. C₁₃×#389	C₂²	semidirect
52. C₁₃×#389	C₂²	semidirect
53. C₁₃×#388	C₂²	semidirect
54. C₁₃×#388	C₂²	semidirect
55. C₁₃×#387	C₂²	semidirect
60. C₁₃×#386	C₂²	semidirect
61. C₁₃×#385	C₂²	semidirect
62. C₁₃×#384	C₂²	semidirect
63. C₁₃×#384	C₂²	semidirect
68. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
73. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
122. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
157. #35005	C₁₃	direct (N × H)
261. C₂×#538	C₂×C₁₃	semidirect
262. #2857	C₂×C₁₃	semidirect
263. #2856	C₂×C₁₃	semidirect
264. #2847	C₂×C₁₃	semidirect
265. #2639	C₂×C₁₃	semidirect
266. #2617	C₂×C₁₃	semidirect
267. #2559	C₂×C₁₃	semidirect
268. #2557	C₂×C₁₃	semidirect
269. #2496	C₂×C₁₃	semidirect
270. #2491	C₂×C₁₃	semidirect
271. #2428	C₂×C₁₃	semidirect
272. #2422	C₂×C₁₃	semidirect
273. #2325	C₂×C₁₃	semidirect
274. C₄×#121	C₂×C₁₃	semidirect
275. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
359. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
360. C₂×#127	C₂²×C₁₃	semidirect
373. C₂×C₄×D₄	C₂²×C₁₃	semidirect
378. #400	C₂²×C₁₃	semidirect
380. #397	C₂²×C₁₃	semidirect
383. #394	C₂²×C₁₃	semidirect
384. #393	C₂²×C₁₃	semidirect
386. #391	C₂²×C₁₃	semidirect
387. #390	C₂²×C₁₃	semidirect
388. #390	C₂²×C₁₃	semidirect
389. #390	C₂²×C₁₃	semidirect
390. #390	C₂²×C₁₃	semidirect
391. #389	C₂²×C₁₃	semidirect
392. #389	C₂²×C₁₃	semidirect
393. #389	C₂²×C₁₃	semidirect
394. #388	C₂²×C₁₃	semidirect
395. #388	C₂²×C₁₃	semidirect
396. #387	C₂²×C₁₃	semidirect
401. #386	C₂²×C₁₃	semidirect
402. #385	C₂²×C₁₃	semidirect
403. #384	C₂²×C₁₃	semidirect
404. #384	C₂²×C₁₃	semidirect
409. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
414. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
457. C₄×C₁₃	#538	semidirect
504. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
652. C₁₃	#35005	direct (N × H)
774. C₄	C₁₃×#538	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#538	2
C₁₃×#2857	2
C₁₃×#2856	2
C₁₃×#2847	2
C₁₃×#2639	2
C₁₃×#2617	2
C₁₃×#2559	2
C₁₃×#2557	2
C₁₃×#2496	2
C₁₃×#2491	2
C₁₃×#2428	2
C₁₃×#2422	2
C₁₃×#2325	2
C₄×C₁₃×#121	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#35005	13

Subgroups — C13×#35005 #15721344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35005 #15721344