Subgroups — C₁₃×#36706 #15723045

Order 3328.

3038 conjugacy classes of subgroups.

The subgroup lattice has 832 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	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2847	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2691	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2676	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2675	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2671	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2626	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2617	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2579	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2410	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2410	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2408	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#538	—	2	8	no	—
21	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#121	—	2	8	no	—
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#121	C₂²	1	4	yes	—
29	C₂×C₁₃×#121	C₂²	1	4	yes	—
30	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
32	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
33	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
34	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
35	C₂×C₁₃×#120	C₂²	1	2	yes	—
36	C₂×C₁₃×#120	C₂²	1	2	yes	—
37	C₂×C₁₃×#120	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
39	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₁₃×#399	C₂²	1	2	yes	complemented
44	C₁₃×#398	C₂²	1	4	yes	complemented
45	C₁₃×#397	C₂²	1	2	yes	complemented
46	C₁₃×#396	C₂²	1	4	yes	complemented
47	C₁₃×#396	C₂²	1	4	yes	complemented
48	C₁₃×#394	C₂²	1	4	yes	complemented
49	C₁₃×#394	C₂²	1	4	yes	complemented
50	C₁₃×#394	C₂²	1	4	yes	complemented
51	C₁₃×#394	C₂²	1	4	yes	complemented
52	C₁₃×#393	C₂²	1	2	yes	complemented
53	C₁₃×#392	C₂²	1	2	yes	complemented
54	C₁₃×#392	C₂²	1	4	yes	complemented
55	C₁₃×#392	C₂²	1	4	yes	complemented
56	C₁₃×#392	C₂²	1	4	yes	complemented
57	C₁₃×#390	C₂²	1	4	yes	complemented
58	C₁₃×#387	C₂²	1	4	yes	complemented
59	C₁₃×#386	C₂²	1	2	yes	—
60	C₁₃×#386	C₂²	1	2	yes	—
61	C₁₃×#386	C₂²	1	4	yes	complemented
62	C₁₃×#386	C₂²	1	4	yes	complemented
63	C₁₃×#386	C₂²	1	4	yes	complemented
64	C₁₃×#385	C₂²	1	2	yes	—
65	C₁₃×#385	C₂²	1	2	yes	—
66	C₁₃×#385	C₂²	1	4	yes	complemented
67	C₁₃×#385	C₂²	1	4	yes	complemented
68	C₁₃×#385	C₂²	1	4	yes	complemented
69	C₁₃×#385	C₂²	1	4	yes	complemented
70	C₁₃×#380	C₂²	1	2	yes	—
71	C₁₃×#380	C₂²	1	1	yes	characteristic
72	C₁₃×#380	C₂²	1	1	yes	characteristic
73	C₁₃×#380	C₂²	1	2	yes	complemented
74	C₁₃×#380	C₂²	1	2	yes	complemented
75	C₁₃×#379	C₂²	1	2	yes	—
76	C₁₃×#379	C₂²	1	2	yes	—
77	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
78	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
79	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₃	—	2	4	no	—
82	C₂²×D₄×C₁₃	—	2	4	no	—
83	C₂²×D₄×C₁₃	—	2	4	no	—
84	C₂²×D₄×C₁₃	—	4	4	no	—
85	C₂²×D₄×C₁₃	—	4	4	no	—
86	C₂²×D₄×C₁₃	—	4	4	no	—
87	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
89	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
96	C₂³×C₄×C₁₃	—	2	4	no	—
97	C₂³×C₄×C₁₃	—	4	4	no	—
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×#126	—	2	8	no	—
107	C₁₃×#124	—	2	8	no	—
108	C₁₃×#123	—	2	8	no	—
109	C₁₃×C₂²⋊Q₈	—	2	4	no	—
110	C₁₃×C₂²⋊Q₈	—	4	4	no	—
111	C₁₃×#121	—	2	4	no	—
112	C₁₃×#121	—	2	16	no	—
113	C₁₃×#121	—	2	16	no	—
114	C₁₃×#121	—	2	8	no	—
115	C₁₃×#121	—	4	4	no	—
116	C₁₃×#121	—	4	8	no	—
117	C₁₃×#121	—	4	8	no	—
118	C₁₃×#121	—	4	8	no	—
119	C₁₃×#120	—	2	8	no	—
120	C₁₃×#120	—	4	4	no	—
121	C₁₃×#120	—	4	4	no	—
122	C₄×D₄×C₁₃	—	2	8	no	—
123	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
136	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
158	C₁₃×#95	C₂³	1	2	yes	—
159	C₁₃×#95	C₂³	1	4	yes	—
160	C₁₃×#95	C₂³	1	2	yes	—
161	C₁₃×#95	C₂³	1	4	yes	—
162	C₁₃×#95	C₂³	1	4	yes	—
163	C₁₃×#95	C₂³	1	4	yes	—
164	C₁₃×#95	C₂³	1	4	yes	—
165	#36706	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂⁴×C₁₃	—	2	2	no	—
167	C₂⁴×C₁₃	—	2	4	no	—
168	C₂⁴×C₁₃	—	2	2	no	—
169	C₂⁴×C₁₃	—	2	2	no	—
170	C₂⁴×C₁₃	—	2	2	no	—
171	C₂⁴×C₁₃	—	2	2	no	—
172	C₂⁴×C₁₃	—	2	2	no	—
173	C₂⁴×C₁₃	—	2	2	no	—
174	C₂⁴×C₁₃	—	2	2	no	—
175	C₂⁴×C₁₃	—	4	2	no	—
176	C₂⁴×C₁₃	—	4	2	no	—
177	C₂⁴×C₁₃	—	4	2	no	—
178	C₂⁴×C₁₃	—	4	2	no	—
179	C₂⁴×C₁₃	—	4	2	no	—
180	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
181	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
182	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
183	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
184	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
185	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂×Q₈×C₁₃	—	2	2	no	—
187	C₂×Q₈×C₁₃	—	4	2	no	—
188	C₂×D₄×C₁₃	—	2	4	no	—
189	C₂×D₄×C₁₃	—	2	8	no	—
190	C₂×D₄×C₁₃	—	2	8	no	—
191	C₂×D₄×C₁₃	—	2	4	no	—
192	C₂×D₄×C₁₃	—	2	8	no	—
193	C₂×D₄×C₁₃	—	2	8	no	—
194	C₂×D₄×C₁₃	—	2	4	no	—
195	C₂×D₄×C₁₃	—	2	4	no	—
196	C₂×D₄×C₁₃	—	2	4	no	—
197	C₂×D₄×C₁₃	—	2	8	no	—
198	C₂×D₄×C₁₃	—	2	8	no	—
199	C₂×D₄×C₁₃	—	2	2	no	—
200	C₂×D₄×C₁₃	—	2	8	no	—
201	C₂×D₄×C₁₃	—	4	4	no	—
202	C₂×D₄×C₁₃	—	4	4	no	—
203	C₂×D₄×C₁₃	—	4	4	no	—
204	C₂×D₄×C₁₃	—	4	16	no	—
205	C₂×D₄×C₁₃	—	4	4	no	—
206	C₂×D₄×C₁₃	—	4	4	no	—
207	C₂×D₄×C₁₃	—	4	2	no	—
208	C₂×D₄×C₁₃	—	4	4	no	—
209	C₂×D₄×C₁₃	—	4	4	no	—
210	C₂×D₄×C₁₃	—	4	4	no	—
211	C₂×D₄×C₁₃	—	4	4	no	—
212	C₂×D₄×C₁₃	—	4	4	no	—
213	C₂×D₄×C₁₃	—	4	16	no	—
214	C₂×D₄×C₁₃	—	4	16	no	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	4	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	—	4	2	no	—
224	C₂²×C₄×C₁₃	—	4	2	no	—
225	C₂²×C₄×C₁₃	—	4	2	no	—
226	C₂²×C₄×C₁₃	—	4	2	no	—
227	C₂²×C₄×C₁₃	—	4	2	no	—
228	C₂²×C₄×C₁₃	—	4	4	no	—
229	C₂²×C₄×C₁₃	—	4	4	no	—
230	C₂²×C₄×C₁₃	—	4	4	no	—
231	C₂²×C₄×C₁₃	—	4	4	no	—
232	C₂²×C₄×C₁₃	—	4	16	no	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
234	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
235	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
238	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₁₃×C₄⋊C₄	—	2	8	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	2	no	—
249	C₁₃×C₄⋊C₄	—	2	2	no	—
250	C₁₃×C₄⋊C₄	—	2	8	no	—
251	C₁₃×C₄⋊C₄	—	4	2	no	—
252	C₁₃×C₄⋊C₄	—	4	4	no	—
253	C₁₃×C₄⋊C₄	—	4	4	no	—
254	C₁₃×C₄⋊C₄	—	4	2	no	—
255	C₁₃×C₂²⋊C₄	—	2	4	no	—
256	C₁₃×C₂²⋊C₄	—	2	4	no	—
257	C₁₃×C₂²⋊C₄	—	2	4	no	—
258	C₁₃×C₂²⋊C₄	—	2	4	no	—
259	C₁₃×C₂²⋊C₄	—	2	4	no	—
260	C₁₃×C₂²⋊C₄	—	2	8	no	—
261	C₁₃×C₂²⋊C₄	—	2	4	no	—
262	C₁₃×C₂²⋊C₄	—	2	4	no	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	8	no	—
266	C₁₃×C₂²⋊C₄	—	4	4	no	—
267	C₁₃×C₂²⋊C₄	—	4	4	no	—
268	C₁₃×C₂²⋊C₄	—	4	4	no	—
269	C₁₃×C₂²⋊C₄	—	4	4	no	—
270	C₁₃×C₂²⋊C₄	—	4	4	no	—
271	C₁₃×C₂²⋊C₄	—	4	4	no	—
272	C₁₃×C₂²⋊C₄	—	4	4	no	—
273	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
274	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
275	C₄²×C₁₃	—	2	4	no	—
276	C₂×#538	C₂×C₁₃	1	1	yes	characteristic, complemented
277	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2848	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#2847	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#2691	C₂×C₁₃	1	4	yes	complemented
281	#2676	C₂×C₁₃	1	4	yes	complemented
282	#2675	C₂×C₁₃	1	4	yes	complemented
283	#2671	C₂×C₁₃	1	4	yes	complemented
284	#2626	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#2617	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#2579	C₂×C₁₃	1	2	yes	complemented
287	#2410	C₂×C₁₃	1	2	yes	complemented
288	#2410	C₂×C₁₃	1	2	yes	complemented
289	#2408	C₂×C₁₃	1	2	yes	complemented
290	#2315	C₂×C₁₃	1	1	yes	characteristic, complemented
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	8	no	—
294	C₂³×C₁₃	—	2	2	no	—
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	—	2	2	no	—
297	C₂³×C₁₃	—	2	2	no	—
298	C₂³×C₁₃	—	2	2	no	—
299	C₂³×C₁₃	—	2	4	no	—
300	C₂³×C₁₃	—	2	4	no	—
301	C₂³×C₁₃	—	2	2	no	—
302	C₂³×C₁₃	—	2	2	no	—
303	C₂³×C₁₃	—	2	2	no	—
304	C₂³×C₁₃	—	2	8	no	—
305	C₂³×C₁₃	—	2	2	no	—
306	C₂³×C₁₃	—	2	2	no	—
307	C₂³×C₁₃	—	2	4	no	—
308	C₂³×C₁₃	—	2	2	no	—
309	C₂³×C₁₃	—	2	4	no	—
310	C₂³×C₁₃	—	2	4	no	—
311	C₂³×C₁₃	—	2	4	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	4	4	no	—
316	C₂³×C₁₃	—	4	4	no	—
317	C₂³×C₁₃	—	4	8	no	—
318	C₂³×C₁₃	—	4	8	no	—
319	C₂³×C₁₃	—	4	4	no	—
320	C₂³×C₁₃	—	4	4	no	—
321	C₂³×C₁₃	—	4	4	no	—
322	C₂³×C₁₃	—	4	4	no	—
323	C₂³×C₁₃	—	4	4	no	—
324	C₂³×C₁₃	—	8	4	no	—
325	C₂³×C₁₃	—	8	4	no	—
326	C₂³×C₁₃	—	8	4	no	—
327	C₂³×C₁₃	—	8	4	no	—
328	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
329	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
330	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
331	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
332	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
333	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
334	Q₈×C₁₃	—	8	2	no	—
335	D₄×C₁₃	—	4	16	no	—
336	D₄×C₁₃	—	4	16	no	—
337	D₄×C₁₃	—	4	16	no	—
338	D₄×C₁₃	—	4	8	no	—
339	D₄×C₁₃	—	8	2	no	—
340	D₄×C₁₃	—	8	4	no	—
341	D₄×C₁₃	—	8	4	no	—
342	D₄×C₁₃	—	8	8	no	—
343	D₄×C₁₃	—	8	8	no	—
344	C₂×C₄×C₁₃	—	2	8	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	4	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	4	no	—
355	C₂×C₄×C₁₃	—	2	4	no	—
356	C₂×C₄×C₁₃	—	2	4	no	—
357	C₂×C₄×C₁₃	—	2	4	no	—
358	C₂×C₄×C₁₃	—	2	4	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	4	no	—
361	C₂×C₄×C₁₃	—	2	4	no	—
362	C₂×C₄×C₁₃	—	2	4	no	—
363	C₂×C₄×C₁₃	—	2	4	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	4	4	no	—
366	C₂×C₄×C₁₃	—	4	4	no	—
367	C₂×C₄×C₁₃	—	4	8	no	—
368	C₂×C₄×C₁₃	—	4	8	no	—
369	C₂×C₄×C₁₃	—	4	4	no	—
370	C₂×C₄×C₁₃	—	8	4	no	—
371	C₂×C₄×C₁₃	—	8	8	no	—
372	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
373	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
376	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
377	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
378	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
379	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
380	#538	—	2	8	no	—
381	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
382	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
383	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
384	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
386	C₂×#121	—	2	8	no	—
387	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#121	C₂²×C₁₃	1	4	yes	—
389	C₂×#121	C₂²×C₁₃	1	4	yes	—
390	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
391	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
392	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
393	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
394	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
395	C₂×#120	C₂²×C₁₃	1	2	yes	—
396	C₂×#120	C₂²×C₁₃	1	2	yes	—
397	C₂×#120	C₂²×C₁₃	1	2	yes	—
398	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
399	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
400	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
401	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
402	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
403	#399	C₂²×C₁₃	1	2	yes	complemented
404	#398	C₂²×C₁₃	1	4	yes	complemented
405	#397	C₂²×C₁₃	1	2	yes	complemented
406	#396	C₂²×C₁₃	1	4	yes	complemented
407	#396	C₂²×C₁₃	1	4	yes	complemented
408	#394	C₂²×C₁₃	1	4	yes	complemented
409	#394	C₂²×C₁₃	1	4	yes	complemented
410	#394	C₂²×C₁₃	1	4	yes	complemented
411	#394	C₂²×C₁₃	1	4	yes	complemented
412	#393	C₂²×C₁₃	1	2	yes	complemented
413	#392	C₂²×C₁₃	1	2	yes	complemented
414	#392	C₂²×C₁₃	1	4	yes	complemented
415	#392	C₂²×C₁₃	1	4	yes	complemented
416	#392	C₂²×C₁₃	1	4	yes	complemented
417	#390	C₂²×C₁₃	1	4	yes	complemented
418	#387	C₂²×C₁₃	1	4	yes	complemented
419	#386	C₂²×C₁₃	1	2	yes	—
420	#386	C₂²×C₁₃	1	2	yes	—
421	#386	C₂²×C₁₃	1	4	yes	complemented
422	#386	C₂²×C₁₃	1	4	yes	complemented
423	#386	C₂²×C₁₃	1	4	yes	complemented
424	#385	C₂²×C₁₃	1	2	yes	—
425	#385	C₂²×C₁₃	1	2	yes	—
426	#385	C₂²×C₁₃	1	4	yes	complemented
427	#385	C₂²×C₁₃	1	4	yes	complemented
428	#385	C₂²×C₁₃	1	4	yes	complemented
429	#385	C₂²×C₁₃	1	4	yes	complemented
430	#380	C₂²×C₁₃	1	2	yes	—
431	#380	C₂²×C₁₃	1	1	yes	characteristic
432	#380	C₂²×C₁₃	1	1	yes	characteristic
433	#380	C₂²×C₁₃	1	2	yes	complemented
434	#380	C₂²×C₁₃	1	2	yes	complemented
435	#379	C₂²×C₁₃	1	2	yes	—
436	#379	C₂²×C₁₃	1	2	yes	—
437	C₂²×C₁₃	—	2	2	no	—
438	C₂²×C₁₃	—	2	2	no	—
439	C₂²×C₁₃	—	2	4	no	—
440	C₂²×C₁₃	—	2	4	no	—
441	C₂²×C₁₃	—	2	4	no	—
442	C₂²×C₁₃	—	2	4	no	—
443	C₂²×C₁₃	—	2	4	no	—
444	C₂²×C₁₃	—	2	4	no	—
445	C₂²×C₁₃	—	2	4	no	—
446	C₂²×C₁₃	—	2	4	no	—
447	C₂²×C₁₃	—	4	16	no	—
448	C₂²×C₁₃	—	4	2	no	—
449	C₂²×C₁₃	—	4	2	no	—
450	C₂²×C₁₃	—	4	2	no	—
451	C₂²×C₁₃	—	4	4	no	—
452	C₂²×C₁₃	—	4	4	no	—
453	C₂²×C₁₃	—	4	2	no	—
454	C₂²×C₁₃	—	4	2	no	—
455	C₂²×C₁₃	—	4	2	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	4	4	no	—
461	C₂²×C₁₃	—	4	4	no	—
462	C₂²×C₁₃	—	4	4	no	—
463	C₂²×C₁₃	—	4	4	no	—
464	C₂²×C₁₃	—	8	8	no	—
465	C₂²×C₁₃	—	8	8	no	—
466	C₂²×C₁₃	#537	1	4	yes	—
467	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
468	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
469	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
470	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
471	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
472	C₄×C₁₃	—	2	4	no	—
473	C₄×C₁₃	—	2	2	no	—
474	C₄×C₁₃	—	2	2	no	—
475	C₄×C₁₃	—	2	4	no	—
476	C₄×C₁₃	—	4	2	no	—
477	C₄×C₁₃	—	4	2	no	—
478	C₄×C₁₃	—	4	2	no	—
479	C₄×C₁₃	—	4	2	no	—
480	C₄×C₁₃	—	4	4	no	—
481	C₄×C₁₃	—	4	4	no	—
482	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
483	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
484	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
486	C₂²×D₄	—	2	4	no	—
487	C₂²×D₄	—	2	4	no	—
488	C₂²×D₄	—	2	4	no	—
489	C₂²×D₄	—	4	4	no	—
490	C₂²×D₄	—	4	4	no	—
491	C₂²×D₄	—	4	4	no	—
492	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
493	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
494	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
495	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
496	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
497	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
498	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
499	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
501	C₂³×C₄	—	2	4	no	—
502	C₂³×C₄	—	4	4	no	—
503	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
505	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
506	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
508	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
509	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
511	#126	—	2	8	no	—
512	#124	—	2	8	no	—
513	#123	—	2	8	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	4	4	no	—
516	#121	—	2	4	no	—
517	#121	—	2	16	no	—
518	#121	—	2	16	no	—
519	#121	—	2	8	no	—
520	#121	—	4	4	no	—
521	#121	—	4	8	no	—
522	#121	—	4	8	no	—
523	#121	—	4	8	no	—
524	#120	—	2	8	no	—
525	#120	—	4	4	no	—
526	#120	—	4	4	no	—
527	C₄×D₄	—	2	8	no	—
528	C₂×C₄⋊C₄	—	2	4	no	—
529	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
539	C₂×C₂²⋊C₄	—	2	4	no	—
540	C₂×C₂²⋊C₄	—	4	4	no	—
541	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
542	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
562	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
563	#95	C₂³×C₁₃	1	2	yes	—
564	#95	C₂³×C₁₃	1	4	yes	—
565	#95	C₂³×C₁₃	1	2	yes	—
566	#95	C₂³×C₁₃	1	4	yes	—
567	#95	C₂³×C₁₃	1	4	yes	—
568	#95	C₂³×C₁₃	1	4	yes	—
569	#95	C₂³×C₁₃	1	4	yes	—
570	C₂×C₁₃	—	2	4	no	—
571	C₂×C₁₃	—	4	4	no	—
572	C₂×C₁₃	—	4	4	no	—
573	C₂×C₁₃	—	8	2	no	—
574	C₂×C₁₃	—	8	2	no	—
575	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
576	C₂×C₁₃	#3484	1	1	yes	characteristic
577	C₂×C₁₃	#3484	1	1	yes	characteristic
578	C₂×C₁₃	#3536	1	2	yes	—
579	C₂×C₁₃	#3537	1	2	yes	—
580	C₂⁴	—	2	2	no	—
581	C₂⁴	—	2	4	no	—
582	C₂⁴	—	2	2	no	—
583	C₂⁴	—	2	2	no	—
584	C₂⁴	—	2	2	no	—
585	C₂⁴	—	2	2	no	—
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	2	2	no	—
589	C₂⁴	—	4	2	no	—
590	C₂⁴	—	4	2	no	—
591	C₂⁴	—	4	2	no	—
592	C₂⁴	—	4	2	no	—
593	C₂⁴	—	4	2	no	—
594	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
595	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
596	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
597	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
598	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
599	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	—	4	2	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	8	no	—
604	C₂×D₄	—	2	8	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	8	no	—
607	C₂×D₄	—	2	8	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	8	no	—
612	C₂×D₄	—	2	8	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	8	no	—
615	C₂×D₄	—	4	4	no	—
616	C₂×D₄	—	4	4	no	—
617	C₂×D₄	—	4	4	no	—
618	C₂×D₄	—	4	16	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	—	4	4	no	—
621	C₂×D₄	—	4	2	no	—
622	C₂×D₄	—	4	4	no	—
623	C₂×D₄	—	4	4	no	—
624	C₂×D₄	—	4	4	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	—	4	4	no	—
627	C₂×D₄	—	4	16	no	—
628	C₂×D₄	—	4	16	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	4	2	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	4	no	—
643	C₂²×C₄	—	4	4	no	—
644	C₂²×C₄	—	4	4	no	—
645	C₂²×C₄	—	4	4	no	—
646	C₂²×C₄	—	4	16	no	—
647	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
648	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
649	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
651	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
652	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
659	C₄⋊C₄	—	2	8	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	8	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	4	no	—
667	C₄⋊C₄	—	4	4	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	8	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	8	no	—
680	C₂²⋊C₄	—	4	4	no	—
681	C₂²⋊C₄	—	4	4	no	—
682	C₂²⋊C₄	—	4	4	no	—
683	C₂²⋊C₄	—	4	4	no	—
684	C₂²⋊C₄	—	4	4	no	—
685	C₂²⋊C₄	—	4	4	no	—
686	C₂²⋊C₄	—	4	4	no	—
687	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
688	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
689	C₄²	—	2	4	no	—
690	C₁₃	#36706	1	1	yes	characteristic, direct product factor, Sylow
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	8	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	4	no	—
700	C₂³	—	2	4	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	8	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	4	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	4	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	4	4	no	—
716	C₂³	—	4	4	no	—
717	C₂³	—	4	8	no	—
718	C₂³	—	4	8	no	—
719	C₂³	—	4	4	no	—
720	C₂³	—	4	4	no	—
721	C₂³	—	4	4	no	—
722	C₂³	—	4	4	no	—
723	C₂³	—	4	4	no	—
724	C₂³	—	8	4	no	—
725	C₂³	—	8	4	no	—
726	C₂³	—	8	4	no	—
727	C₂³	—	8	4	no	—
728	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
729	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
730	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
731	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
732	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
733	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
734	Q₈	—	8	2	no	—
735	D₄	—	4	16	no	—
736	D₄	—	4	16	no	—
737	D₄	—	4	16	no	—
738	D₄	—	4	8	no	—
739	D₄	—	8	2	no	—
740	D₄	—	8	8	no	—
741	D₄	—	8	4	no	—
742	D₄	—	8	4	no	—
743	D₄	—	8	8	no	—
744	C₂×C₄	—	2	8	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	4	8	no	—
768	C₂×C₄	—	4	8	no	—
769	C₂×C₄	—	4	4	no	—
770	C₂×C₄	—	8	4	no	—
771	C₂×C₄	—	8	8	no	—
772	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
773	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
774	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
775	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	4	no	—
781	C₂²	—	2	4	no	—
782	C₂²	—	2	4	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	4	16	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	4	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	4	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	4	4	no	—
796	C₂²	—	4	4	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	8	8	no	—
804	C₂²	—	8	8	no	—
805	C₂²	C₁₃×#537	1	4	yes	—
806	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
807	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
808	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
809	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
810	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
811	C₄	—	2	4	no	—
812	C₄	—	2	2	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	4	no	—
815	C₄	—	4	4	no	—
816	C₄	—	4	4	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₂	—	2	4	no	—
822	C₂	—	4	4	no	—
823	C₂	—	4	4	no	—
824	C₂	—	8	2	no	—
825	C₂	—	8	2	no	—
826	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
827	C₂	C₁₃×#3484	1	1	yes	characteristic
828	C₂	C₁₃×#3484	1	1	yes	characteristic
829	C₂	C₁₃×#3536	1	2	yes	—
830	C₂	C₁₃×#3537	1	2	yes	—

	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. C₂²×C₁₃×#121	C₂	semidirect
3. C₁₃×#2848	C₂	semidirect
4. C₁₃×#2847	C₂	semidirect
5. C₁₃×#2691	C₂	semidirect
6. C₁₃×#2676	C₂	semidirect
7. C₁₃×#2675	C₂	semidirect
8. C₁₃×#2671	C₂	semidirect
9. C₁₃×#2626	C₂	semidirect
10. C₁₃×#2617	C₂	semidirect
11. C₁₃×#2579	C₂	semidirect
12. C₁₃×#2410	C₂	semidirect
13. C₁₃×#2410	C₂	semidirect
14. C₁₃×#2408	C₂	semidirect
15. C₁₃×#2315	C₂	semidirect
21. C₂×C₁₃×#126	C₂²	semidirect
22. C₂×C₁₃×#124	C₂²	semidirect
23. C₂×C₁₃×#123	C₂²	semidirect
25. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₁₃×#121	C₂²	semidirect
31. C₂×C₁₃×#121	C₂²	semidirect
32. C₂×C₁₃×#121	C₂²	semidirect
33. C₂×C₁₃×#121	C₂²	semidirect
34. C₂×C₁₃×#121	C₂²	semidirect
43. C₁₃×#399	C₂²	semidirect
44. C₁₃×#398	C₂²	semidirect
45. C₁₃×#397	C₂²	semidirect
46. C₁₃×#396	C₂²	semidirect
47. C₁₃×#396	C₂²	semidirect
48. C₁₃×#394	C₂²	semidirect
49. C₁₃×#394	C₂²	semidirect
50. C₁₃×#394	C₂²	semidirect
51. C₁₃×#394	C₂²	semidirect
52. C₁₃×#393	C₂²	semidirect
53. C₁₃×#392	C₂²	semidirect
54. C₁₃×#392	C₂²	semidirect
55. C₁₃×#392	C₂²	semidirect
56. C₁₃×#392	C₂²	semidirect
57. C₁₃×#390	C₂²	semidirect
58. C₁₃×#387	C₂²	semidirect
61. C₁₃×#386	C₂²	semidirect
62. C₁₃×#386	C₂²	semidirect
63. C₁₃×#386	C₂²	semidirect
66. C₁₃×#385	C₂²	semidirect
67. C₁₃×#385	C₂²	semidirect
68. C₁₃×#385	C₂²	semidirect
69. C₁₃×#385	C₂²	semidirect
73. C₁₃×#380	C₂²	semidirect
74. C₁₃×#380	C₂²	semidirect
136. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
165. #36706	C₁₃	direct (N × H)
276. C₂×#538	C₂×C₁₃	semidirect
277. C₂²×#121	C₂×C₁₃	semidirect
278. #2848	C₂×C₁₃	semidirect
279. #2847	C₂×C₁₃	semidirect
280. #2691	C₂×C₁₃	semidirect
281. #2676	C₂×C₁₃	semidirect
282. #2675	C₂×C₁₃	semidirect
283. #2671	C₂×C₁₃	semidirect
284. #2626	C₂×C₁₃	semidirect
285. #2617	C₂×C₁₃	semidirect
286. #2579	C₂×C₁₃	semidirect
287. #2410	C₂×C₁₃	semidirect
288. #2410	C₂×C₁₃	semidirect
289. #2408	C₂×C₁₃	semidirect
290. #2315	C₂×C₁₃	semidirect
381. C₂×#126	C₂²×C₁₃	semidirect
382. C₂×#124	C₂²×C₁₃	semidirect
383. C₂×#123	C₂²×C₁₃	semidirect
385. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
390. C₂×#121	C₂²×C₁₃	semidirect
391. C₂×#121	C₂²×C₁₃	semidirect
392. C₂×#121	C₂²×C₁₃	semidirect
393. C₂×#121	C₂²×C₁₃	semidirect
394. C₂×#121	C₂²×C₁₃	semidirect
403. #399	C₂²×C₁₃	semidirect
404. #398	C₂²×C₁₃	semidirect
405. #397	C₂²×C₁₃	semidirect
406. #396	C₂²×C₁₃	semidirect
407. #396	C₂²×C₁₃	semidirect
408. #394	C₂²×C₁₃	semidirect
409. #394	C₂²×C₁₃	semidirect
410. #394	C₂²×C₁₃	semidirect
411. #394	C₂²×C₁₃	semidirect
412. #393	C₂²×C₁₃	semidirect
413. #392	C₂²×C₁₃	semidirect
414. #392	C₂²×C₁₃	semidirect
415. #392	C₂²×C₁₃	semidirect
416. #392	C₂²×C₁₃	semidirect
417. #390	C₂²×C₁₃	semidirect
418. #387	C₂²×C₁₃	semidirect
421. #386	C₂²×C₁₃	semidirect
422. #386	C₂²×C₁₃	semidirect
423. #386	C₂²×C₁₃	semidirect
426. #385	C₂²×C₁₃	semidirect
427. #385	C₂²×C₁₃	semidirect
428. #385	C₂²×C₁₃	semidirect
429. #385	C₂²×C₁₃	semidirect
433. #380	C₂²×C₁₃	semidirect
434. #380	C₂²×C₁₃	semidirect
541. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
690. C₁₃	#36706	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×#538	2
C₂²×C₁₃×#121	2
C₁₃×#2848	2
C₁₃×#2847	2
C₁₃×#2691	2
C₁₃×#2676	2
C₁₃×#2675	2
C₁₃×#2671	2
C₁₃×#2626	2
C₁₃×#2617	2
C₁₃×#2579	2
C₁₃×#2410	2
C₁₃×#2408	2
C₁₃×#2315	2
#36706	13

Subgroups — C13×#36706 #15723045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36706 #15723045