Subgroups — C₁₃×#36842 #15723181

Order 3328.

1966 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2849	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2807	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2764	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2749	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2749	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2735	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2712	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2710	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2701	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2670	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2668	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2635	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2633	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2572	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2558	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2464	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2447	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2337	C₂	1	2	yes	maximal, complemented
19	C₄×C₁₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×#124	C₂²	1	2	yes	—
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×#123	C₂²	1	2	yes	—
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×#120	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#120	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₁₃×#400	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#400	C₂²	1	2	yes	complemented
34	C₁₃×#400	C₂²	1	2	yes	complemented
35	C₁₃×#399	C₂²	1	1	yes	characteristic
36	C₁₃×#399	C₂²	1	1	yes	characteristic
37	C₁₃×#399	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#398	C₂²	1	2	yes	complemented
39	C₁₃×#398	C₂²	1	2	yes	complemented
40	C₁₃×#397	C₂²	1	2	yes	—
41	C₁₃×#397	C₂²	1	1	yes	characteristic
42	C₁₃×#397	C₂²	1	2	yes	—
43	C₁₃×#397	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#397	C₂²	1	2	yes	complemented
45	C₁₃×#397	C₂²	1	2	yes	complemented
46	C₁₃×#396	C₂²	1	2	yes	—
47	C₁₃×#396	C₂²	1	2	yes	complemented
48	C₁₃×#394	C₂²	1	2	yes	—
49	C₁₃×#394	C₂²	1	2	yes	—
50	C₁₃×#394	C₂²	1	2	yes	—
51	C₁₃×#394	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#394	C₂²	1	2	yes	complemented
53	C₁₃×#394	C₂²	1	2	yes	complemented
54	C₁₃×#393	C₂²	1	2	yes	—
55	C₁₃×#393	C₂²	1	2	yes	complemented
56	C₁₃×#392	C₂²	1	1	yes	characteristic
57	C₁₃×#392	C₂²	1	2	yes	—
58	C₁₃×#392	C₂²	1	2	yes	—
59	C₁₃×#392	C₂²	1	2	yes	—
60	C₁₃×#391	C₂²	1	2	yes	complemented
61	C₁₃×#391	C₂²	1	2	yes	complemented
62	C₁₃×#391	C₂²	1	2	yes	complemented
63	C₁₃×#390	C₂²	1	2	yes	—
64	C₁₃×#390	C₂²	1	2	yes	—
65	C₁₃×#390	C₂²	1	2	yes	complemented
66	C₁₃×#389	C₂²	1	2	yes	complemented
67	C₁₃×#389	C₂²	1	2	yes	complemented
68	C₁₃×#388	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#388	C₂²	1	2	yes	—
72	C₁₃×#388	C₂²	1	2	yes	—
73	C₁₃×#388	C₂²	1	2	yes	complemented
74	C₁₃×#388	C₂²	1	2	yes	complemented
75	C₁₃×#388	C₂²	1	2	yes	complemented
76	C₁₃×#388	C₂²	1	2	yes	complemented
77	C₁₃×#386	C₂²	1	2	yes	—
78	C₁₃×#386	C₂²	1	1	yes	characteristic
79	C₁₃×#386	C₂²	1	2	yes	—
80	C₁₃×#386	C₂²	1	2	yes	—
81	C₁₃×#386	C₂²	1	2	yes	—
82	C₁₃×#386	C₂²	1	2	yes	—
83	C₁₃×#386	C₂²	1	2	yes	—
84	C₁₃×#386	C₂²	1	2	yes	—
85	C₁₃×#386	C₂²	1	2	yes	complemented
86	C₁₃×#385	C₂²	1	2	yes	—
87	C₁₃×#385	C₂²	1	2	yes	—
88	C₁₃×#385	C₂²	1	1	yes	characteristic
89	C₁₃×#385	C₂²	1	2	yes	—
90	C₁₃×#385	C₂²	1	2	yes	—
91	C₁₃×#385	C₂²	1	2	yes	—
92	C₁₃×#385	C₂²	1	2	yes	complemented
93	C₁₃×#385	C₂²	1	2	yes	complemented
94	C₁₃×#383	C₂²	1	2	yes	complemented
95	C₁₃×#383	C₂²	1	2	yes	complemented
96	C₁₃×#383	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#381	C₂²	1	2	yes	—
98	C₁₃×#381	C₂²	1	2	yes	—
99	C₁₃×#381	C₂²	1	2	yes	complemented
100	C₁₃×#381	C₂²	1	1	yes	characteristic, complemented
101	C₁₃×#379	C₂²	1	1	yes	characteristic
102	C₁₃×#379	C₂²	1	2	yes	—
103	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	—	4	2	no	—
117	C₂³×C₄×C₁₃	—	4	4	no	—
118	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×#125	—	4	2	no	—
125	C₁₃×#124	—	2	8	no	—
126	C₁₃×#124	—	4	4	no	—
127	C₁₃×#123	—	4	4	no	—
128	C₁₃×#123	—	4	4	no	—
129	C₁₃×#121	—	4	2	no	—
130	C₁₃×#121	—	4	4	no	—
131	C₁₃×#120	—	2	4	no	—
132	C₁₃×#120	—	4	4	no	—
133	C₄×D₄×C₁₃	—	4	2	no	—
134	C₄×D₄×C₁₃	—	4	4	no	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
183	C₁₃×#95	C₂³	1	2	yes	—
184	C₁₃×#95	C₂³	1	2	yes	—
185	C₁₃×#95	C₂³	1	2	yes	—
186	C₁₃×#95	C₂³	1	2	yes	—
187	C₁₃×#95	C₂³	1	2	yes	—
188	C₁₃×#95	C₂³	1	2	yes	—
189	C₁₃×#95	C₂³	1	2	yes	—
190	C₁₃×#95	C₂³	1	2	yes	—
191	C₁₃×#95	C₂³	1	2	yes	—
192	C₁₃×#95	C₂³	1	2	yes	—
193	C₁₃×#95	C₂³	1	2	yes	—
194	C₁₃×#95	C₂³	1	2	yes	—
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	1	yes	characteristic
199	C₁₃×#95	C₂³	1	1	yes	characteristic
200	C₁₃×#95	C₂³	1	2	yes	—
201	C₁₃×#95	C₂³	1	1	yes	characteristic
202	C₁₃×#95	C₂³	1	2	yes	—
203	C₁₃×#95	C₂³	1	1	yes	characteristic
204	C₁₃×#95	C₂³	1	2	yes	—
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	#36842	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂⁴×C₁₃	—	2	2	no	—
209	C₂⁴×C₁₃	—	2	4	no	—
210	C₂⁴×C₁₃	—	4	1	no	—
211	C₂⁴×C₁₃	—	4	2	no	—
212	C₂⁴×C₁₃	—	4	1	no	—
213	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
214	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
217	C₂×Q₈×C₁₃	—	2	4	no	—
218	C₂×Q₈×C₁₃	—	4	2	no	—
219	C₂×Q₈×C₁₃	—	4	2	no	—
220	C₂×D₄×C₁₃	—	2	2	no	—
221	C₂×D₄×C₁₃	—	2	4	no	—
222	C₂×D₄×C₁₃	—	2	4	no	—
223	C₂×D₄×C₁₃	—	2	4	no	—
224	C₂×D₄×C₁₃	—	2	4	no	—
225	C₂×D₄×C₁₃	—	2	4	no	—
226	C₂×D₄×C₁₃	—	4	1	no	—
227	C₂×D₄×C₁₃	—	4	2	no	—
228	C₂×D₄×C₁₃	—	4	1	no	—
229	C₂×D₄×C₁₃	—	4	2	no	—
230	C₂×D₄×C₁₃	—	4	2	no	—
231	C₂×D₄×C₁₃	—	4	2	no	—
232	C₂×D₄×C₁₃	—	4	2	no	—
233	C₂×D₄×C₁₃	—	4	1	no	—
234	C₂×D₄×C₁₃	—	4	2	no	—
235	C₂×D₄×C₁₃	—	4	2	no	—
236	C₂×D₄×C₁₃	—	4	2	no	—
237	C₂×D₄×C₁₃	—	4	2	no	—
238	C₂×D₄×C₁₃	—	4	2	no	—
239	C₂×D₄×C₁₃	—	4	2	no	—
240	C₂²×C₄×C₁₃	—	2	4	no	—
241	C₂²×C₄×C₁₃	—	2	4	no	—
242	C₂²×C₄×C₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₃	—	2	4	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	4	2	no	—
246	C₂²×C₄×C₁₃	—	4	2	no	—
247	C₂²×C₄×C₁₃	—	4	2	no	—
248	C₂²×C₄×C₁₃	—	4	2	no	—
249	C₂²×C₄×C₁₃	—	4	1	no	—
250	C₂²×C₄×C₁₃	—	4	2	no	—
251	C₂²×C₄×C₁₃	—	4	2	no	—
252	C₂²×C₄×C₁₃	—	4	2	no	—
253	C₂²×C₄×C₁₃	—	4	2	no	—
254	C₂²×C₄×C₁₃	—	4	2	no	—
255	C₂²×C₄×C₁₃	—	4	16	no	—
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	4	2	no	—
273	C₁₃×C₄⋊C₄	—	4	2	no	—
274	C₁₃×C₄⋊C₄	—	4	2	no	—
275	C₁₃×C₄⋊C₄	—	4	2	no	—
276	C₁₃×C₄⋊C₄	—	4	1	no	—
277	C₁₃×C₄⋊C₄	—	4	1	no	—
278	C₁₃×C₄⋊C₄	—	4	2	no	—
279	C₁₃×C₄⋊C₄	—	4	2	no	—
280	C₁₃×C₄⋊C₄	—	4	2	no	—
281	C₁₃×C₄⋊C₄	—	4	2	no	—
282	C₁₃×C₄⋊C₄	—	4	1	no	—
283	C₁₃×C₄⋊C₄	—	4	1	no	—
284	C₁₃×C₄⋊C₄	—	4	2	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	4	2	no	—
294	C₁₃×C₂²⋊C₄	—	4	2	no	—
295	C₁₃×C₂²⋊C₄	—	4	2	no	—
296	C₁₃×C₂²⋊C₄	—	4	2	no	—
297	C₁₃×C₂²⋊C₄	—	4	2	no	—
298	C₁₃×C₂²⋊C₄	—	4	2	no	—
299	C₁₃×C₂²⋊C₄	—	4	2	no	—
300	C₁₃×C₂²⋊C₄	—	4	1	no	—
301	C₁₃×C₂²⋊C₄	—	4	1	no	—
302	C₁₃×C₂²⋊C₄	—	4	1	no	—
303	C₁₃×C₂²⋊C₄	—	4	2	no	—
304	C₁₃×C₂²⋊C₄	—	4	2	no	—
305	C₁₃×C₂²⋊C₄	—	4	2	no	—
306	C₁₃×C₂²⋊C₄	—	4	2	no	—
307	C₁₃×C₂²⋊C₄	—	4	2	no	—
308	C₁₃×C₂²⋊C₄	—	4	2	no	—
309	C₁₃×C₂²⋊C₄	—	4	2	no	—
310	C₁₃×C₂²⋊C₄	—	4	2	no	—
311	C₁₃×C₂²⋊C₄	—	4	2	no	—
312	C₁₃×C₂²⋊C₄	—	4	2	no	—
313	C₁₃×C₂²⋊C₄	#41	1	4	yes	—
314	C₄²×C₁₃	—	2	4	no	—
315	C₄²×C₁₃	—	2	2	no	—
316	C₄²×C₁₃	—	4	2	no	—
317	C₄²×C₁₃	—	4	2	no	—
318	C₄²×C₁₃	—	4	2	no	—
319	#2849	C₂×C₁₃	1	2	yes	complemented
320	#2807	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#2764	C₂×C₁₃	1	2	yes	complemented
322	#2749	C₂×C₁₃	1	2	yes	complemented
323	#2749	C₂×C₁₃	1	2	yes	complemented
324	#2735	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#2712	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#2710	C₂×C₁₃	1	2	yes	complemented
327	#2701	C₂×C₁₃	1	2	yes	complemented
328	#2670	C₂×C₁₃	1	2	yes	complemented
329	#2668	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#2635	C₂×C₁₃	1	1	yes	characteristic, complemented
331	#2633	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#2572	C₂×C₁₃	1	2	yes	complemented
333	#2558	C₂×C₁₃	1	2	yes	complemented
334	#2464	C₂×C₁₃	1	2	yes	complemented
335	#2447	C₂×C₁₃	1	2	yes	complemented
336	#2337	C₂×C₁₃	1	2	yes	complemented
337	C₄×#120	C₂×C₁₃	1	1	yes	characteristic, complemented
338	C₂³×C₁₃	—	2	2	no	—
339	C₂³×C₁₃	—	2	1	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	2	2	no	—
343	C₂³×C₁₃	—	2	1	no	—
344	C₂³×C₁₃	—	2	2	no	—
345	C₂³×C₁₃	—	2	2	no	—
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	—	2	2	no	—
348	C₂³×C₁₃	—	2	2	no	—
349	C₂³×C₁₃	—	2	1	no	—
350	C₂³×C₁₃	—	2	2	no	—
351	C₂³×C₁₃	—	2	2	no	—
352	C₂³×C₁₃	—	2	2	no	—
353	C₂³×C₁₃	—	2	1	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	2	1	no	—
356	C₂³×C₁₃	—	2	2	no	—
357	C₂³×C₁₃	—	2	2	no	—
358	C₂³×C₁₃	—	2	2	no	—
359	C₂³×C₁₃	—	2	2	no	—
360	C₂³×C₁₃	—	4	4	no	—
361	C₂³×C₁₃	—	4	8	no	—
362	C₂³×C₁₃	—	4	4	no	—
363	C₂³×C₁₃	—	4	8	no	—
364	C₂³×C₁₃	—	4	4	no	—
365	C₂³×C₁₃	C₂×#41	1	2	yes	—
366	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
367	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
368	Q₈×C₁₃	—	8	4	no	—
369	D₄×C₁₃	—	4	8	no	—
370	D₄×C₁₃	—	4	4	no	—
371	D₄×C₁₃	—	8	4	no	—
372	D₄×C₁₃	—	8	4	no	—
373	D₄×C₁₃	—	8	4	no	—
374	D₄×C₁₃	—	8	2	no	—
375	D₄×C₁₃	—	8	4	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	1	no	—
382	C₂×C₄×C₁₃	—	2	2	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	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	4	8	no	—
416	C₂×C₄×C₁₃	—	4	4	no	—
417	C₂×C₄×C₁₃	—	4	8	no	—
418	C₂×C₄×C₁₃	—	4	4	no	—
419	C₂×C₄×C₁₃	—	8	2	no	—
420	C₂×C₄×C₁₃	—	8	4	no	—
421	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
422	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
423	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	C₂×#124	C₂²×C₁₃	1	2	yes	—
426	C₂×#124	C₂²×C₁₃	1	2	yes	—
427	C₂×#123	C₂²×C₁₃	1	2	yes	—
428	C₂×#123	C₂²×C₁₃	1	2	yes	—
429	C₂×#121	C₂²×C₁₃	1	2	yes	—
430	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	C₂×#120	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#120	C₂²×C₁₃	1	2	yes	—
433	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
435	#400	C₂²×C₁₃	1	2	yes	complemented
436	#400	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	#400	C₂²×C₁₃	1	2	yes	complemented
438	#399	C₂²×C₁₃	1	1	yes	characteristic
439	#399	C₂²×C₁₃	1	1	yes	characteristic
440	#399	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	#398	C₂²×C₁₃	1	2	yes	complemented
442	#398	C₂²×C₁₃	1	2	yes	complemented
443	#397	C₂²×C₁₃	1	1	yes	characteristic
444	#397	C₂²×C₁₃	1	2	yes	—
445	#397	C₂²×C₁₃	1	2	yes	—
446	#397	C₂²×C₁₃	1	1	yes	characteristic, complemented
447	#397	C₂²×C₁₃	1	2	yes	complemented
448	#397	C₂²×C₁₃	1	2	yes	complemented
449	#396	C₂²×C₁₃	1	2	yes	—
450	#396	C₂²×C₁₃	1	2	yes	complemented
451	#394	C₂²×C₁₃	1	2	yes	—
452	#394	C₂²×C₁₃	1	2	yes	—
453	#394	C₂²×C₁₃	1	2	yes	—
454	#394	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	#394	C₂²×C₁₃	1	2	yes	complemented
456	#394	C₂²×C₁₃	1	2	yes	complemented
457	#393	C₂²×C₁₃	1	2	yes	—
458	#393	C₂²×C₁₃	1	2	yes	complemented
459	#392	C₂²×C₁₃	1	1	yes	characteristic
460	#392	C₂²×C₁₃	1	2	yes	—
461	#392	C₂²×C₁₃	1	2	yes	—
462	#392	C₂²×C₁₃	1	2	yes	—
463	#391	C₂²×C₁₃	1	2	yes	complemented
464	#391	C₂²×C₁₃	1	2	yes	complemented
465	#391	C₂²×C₁₃	1	2	yes	complemented
466	#390	C₂²×C₁₃	1	2	yes	—
467	#390	C₂²×C₁₃	1	2	yes	—
468	#390	C₂²×C₁₃	1	2	yes	complemented
469	#389	C₂²×C₁₃	1	2	yes	complemented
470	#389	C₂²×C₁₃	1	2	yes	complemented
471	#388	C₂²×C₁₃	1	2	yes	—
472	#388	C₂²×C₁₃	1	2	yes	—
473	#388	C₂²×C₁₃	1	2	yes	—
474	#388	C₂²×C₁₃	1	2	yes	—
475	#388	C₂²×C₁₃	1	2	yes	—
476	#388	C₂²×C₁₃	1	2	yes	complemented
477	#388	C₂²×C₁₃	1	2	yes	complemented
478	#388	C₂²×C₁₃	1	2	yes	complemented
479	#388	C₂²×C₁₃	1	2	yes	complemented
480	#386	C₂²×C₁₃	1	2	yes	—
481	#386	C₂²×C₁₃	1	2	yes	—
482	#386	C₂²×C₁₃	1	2	yes	—
483	#386	C₂²×C₁₃	1	2	yes	—
484	#386	C₂²×C₁₃	1	2	yes	—
485	#386	C₂²×C₁₃	1	2	yes	—
486	#386	C₂²×C₁₃	1	2	yes	—
487	#386	C₂²×C₁₃	1	1	yes	characteristic
488	#386	C₂²×C₁₃	1	2	yes	complemented
489	#385	C₂²×C₁₃	1	2	yes	—
490	#385	C₂²×C₁₃	1	2	yes	—
491	#385	C₂²×C₁₃	1	2	yes	—
492	#385	C₂²×C₁₃	1	2	yes	—
493	#385	C₂²×C₁₃	1	2	yes	—
494	#385	C₂²×C₁₃	1	1	yes	characteristic
495	#385	C₂²×C₁₃	1	2	yes	complemented
496	#385	C₂²×C₁₃	1	2	yes	complemented
497	#383	C₂²×C₁₃	1	1	yes	characteristic, complemented
498	#383	C₂²×C₁₃	1	2	yes	complemented
499	#383	C₂²×C₁₃	1	2	yes	complemented
500	#381	C₂²×C₁₃	1	2	yes	—
501	#381	C₂²×C₁₃	1	2	yes	—
502	#381	C₂²×C₁₃	1	2	yes	complemented
503	#381	C₂²×C₁₃	1	1	yes	characteristic, complemented
504	#379	C₂²×C₁₃	1	2	yes	—
505	#379	C₂²×C₁₃	1	1	yes	characteristic
506	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
507	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
508	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
509	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
510	C₂²×C₁₃	—	2	2	no	—
511	C₂²×C₁₃	—	2	4	no	—
512	C₂²×C₁₃	—	2	4	no	—
513	C₂²×C₁₃	—	2	4	no	—
514	C₂²×C₁₃	—	2	4	no	—
515	C₂²×C₁₃	—	4	16	no	—
516	C₂²×C₁₃	—	4	2	no	—
517	C₂²×C₁₃	—	4	2	no	—
518	C₂²×C₁₃	—	4	1	no	—
519	C₂²×C₁₃	—	4	2	no	—
520	C₂²×C₁₃	—	4	2	no	—
521	C₂²×C₁₃	—	4	1	no	—
522	C₂²×C₁₃	—	4	2	no	—
523	C₂²×C₁₃	—	4	1	no	—
524	C₂²×C₁₃	—	4	2	no	—
525	C₂²×C₁₃	—	4	2	no	—
526	C₂²×C₁₃	—	4	2	no	—
527	C₂²×C₁₃	—	4	2	no	—
528	C₂²×C₁₃	—	4	1	no	—
529	C₂²×C₁₃	—	4	2	no	—
530	C₂²×C₁₃	—	4	2	no	—
531	C₂²×C₁₃	—	4	2	no	—
532	C₂²×C₁₃	—	4	2	no	—
533	C₂²×C₁₃	—	4	1	no	—
534	C₂²×C₁₃	—	4	2	no	—
535	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
536	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
537	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
538	C₂²×C₁₃	#585	1	1	yes	characteristic
539	C₂²×C₁₃	#585	1	2	yes	—
540	C₄×C₁₃	—	2	4	no	—
541	C₄×C₁₃	—	2	2	no	—
542	C₄×C₁₃	—	4	2	no	—
543	C₄×C₁₃	—	4	1	no	—
544	C₄×C₁₃	—	4	2	no	—
545	C₄×C₁₃	—	4	2	no	—
546	C₄×C₁₃	—	4	2	no	—
547	C₄×C₁₃	—	4	1	no	—
548	C₄×C₁₃	—	4	1	no	—
549	C₄×C₁₃	—	4	2	no	—
550	C₄×C₁₃	—	4	2	no	—
551	C₄×C₁₃	—	4	2	no	—
552	C₄×C₁₃	—	4	2	no	—
553	C₄×C₁₃	—	4	1	no	—
554	C₄×C₁₃	—	4	2	no	—
555	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
556	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
557	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
558	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
559	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
560	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
561	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
562	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
563	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
564	C₂³×C₄	—	4	2	no	—
565	C₂³×C₄	—	4	4	no	—
566	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
567	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
570	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
571	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
572	#125	—	4	2	no	—
573	#124	—	2	8	no	—
574	#124	—	4	4	no	—
575	#123	—	4	4	no	—
576	#123	—	4	4	no	—
577	#121	—	4	2	no	—
578	#121	—	4	4	no	—
579	#120	—	2	4	no	—
580	#120	—	4	4	no	—
581	C₄×D₄	—	4	2	no	—
582	C₄×D₄	—	4	4	no	—
583	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
628	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
629	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
630	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
631	#95	C₂³×C₁₃	1	2	yes	—
632	#95	C₂³×C₁₃	1	2	yes	—
633	#95	C₂³×C₁₃	1	2	yes	—
634	#95	C₂³×C₁₃	1	2	yes	—
635	#95	C₂³×C₁₃	1	2	yes	—
636	#95	C₂³×C₁₃	1	2	yes	—
637	#95	C₂³×C₁₃	1	2	yes	—
638	#95	C₂³×C₁₃	1	2	yes	—
639	#95	C₂³×C₁₃	1	2	yes	—
640	#95	C₂³×C₁₃	1	2	yes	—
641	#95	C₂³×C₁₃	1	2	yes	—
642	#95	C₂³×C₁₃	1	2	yes	—
643	#95	C₂³×C₁₃	1	2	yes	—
644	#95	C₂³×C₁₃	1	2	yes	—
645	#95	C₂³×C₁₃	1	2	yes	—
646	#95	C₂³×C₁₃	1	1	yes	characteristic
647	#95	C₂³×C₁₃	1	1	yes	characteristic
648	#95	C₂³×C₁₃	1	2	yes	—
649	#95	C₂³×C₁₃	1	1	yes	characteristic
650	#95	C₂³×C₁₃	1	2	yes	—
651	#95	C₂³×C₁₃	1	1	yes	characteristic
652	#95	C₂³×C₁₃	1	2	yes	—
653	#95	C₂³×C₁₃	1	2	yes	—
654	#95	C₂³×C₁₃	1	2	yes	—
655	C₂×C₁₃	—	4	2	no	—
656	C₂×C₁₃	—	4	4	no	—
657	C₂×C₁₃	—	8	1	no	—
658	C₂×C₁₃	—	8	2	no	—
659	C₂×C₁₃	#3460	1	1	yes	characteristic
660	C₂×C₁₃	#3513	1	2	yes	—
661	C₂×C₁₃	#3532	1	1	yes	characteristic
662	C₂×C₁₃	#3533	1	2	yes	—
663	C₂×C₁₃	#3540	1	1	yes	characteristic
664	C₂⁴	—	2	2	no	—
665	C₂⁴	—	2	4	no	—
666	C₂⁴	—	4	1	no	—
667	C₂⁴	—	4	2	no	—
668	C₂⁴	—	4	1	no	—
669	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
670	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
672	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	—	4	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	4	1	no	—
683	C₂×D₄	—	4	2	no	—
684	C₂×D₄	—	4	1	no	—
685	C₂×D₄	—	4	2	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	2	no	—
688	C₂×D₄	—	4	2	no	—
689	C₂×D₄	—	4	1	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	—	4	2	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	16	no	—
712	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	1	no	—
730	C₄⋊C₄	—	4	1	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	1	no	—
736	C₄⋊C₄	—	4	1	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	4	1	no	—
750	C₂²⋊C₄	—	4	1	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	1	no	—
769	C₂²⋊C₄	C₁₃×#41	1	4	yes	—
770	C₄²	—	2	4	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	4	2	no	—
773	C₄²	—	4	2	no	—
774	C₄²	—	4	2	no	—
775	C₁₃	#36842	1	1	yes	characteristic, direct product factor, Sylow
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	4	4	no	—
799	C₂³	—	4	8	no	—
800	C₂³	—	4	8	no	—
801	C₂³	—	4	4	no	—
802	C₂³	—	4	4	no	—
803	C₂³	C₂×C₁₃×#41	1	2	yes	—
804	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
805	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
806	Q₈	—	8	4	no	—
807	D₄	—	4	8	no	—
808	D₄	—	4	4	no	—
809	D₄	—	8	4	no	—
810	D₄	—	8	4	no	—
811	D₄	—	8	4	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	4	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	4	8	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	8	2	no	—
858	C₂×C₄	—	8	4	no	—
859	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
860	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
861	C₂²	—	2	4	no	—
862	C₂²	—	2	4	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	4	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	4	16	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
887	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
888	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
889	C₂²	C₁₃×#585	1	1	yes	characteristic
890	C₂²	C₁₃×#585	1	2	yes	—
891	C₄	—	2	2	no	—
892	C₄	—	2	4	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₂	—	4	4	no	—
907	C₂	—	4	2	no	—
908	C₂	—	8	1	no	—
909	C₂	—	8	2	no	—
910	C₂	C₁₃×#3460	1	1	yes	characteristic
911	C₂	C₁₃×#3513	1	2	yes	—
912	C₂	C₁₃×#3532	1	1	yes	characteristic
913	C₂	C₁₃×#3533	1	2	yes	—
914	C₂	C₁₃×#3540	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. C₁₃×#2849	C₂	semidirect
2. C₁₃×#2807	C₂	semidirect
3. C₁₃×#2764	C₂	semidirect
4. C₁₃×#2749	C₂	semidirect
5. C₁₃×#2749	C₂	semidirect
6. C₁₃×#2735	C₂	semidirect
7. C₁₃×#2712	C₂	semidirect
8. C₁₃×#2710	C₂	semidirect
9. C₁₃×#2701	C₂	semidirect
10. C₁₃×#2670	C₂	semidirect
11. C₁₃×#2668	C₂	semidirect
12. C₁₃×#2635	C₂	semidirect
13. C₁₃×#2633	C₂	semidirect
14. C₁₃×#2572	C₂	semidirect
15. C₁₃×#2558	C₂	semidirect
16. C₁₃×#2464	C₂	semidirect
17. C₁₃×#2447	C₂	semidirect
18. C₁₃×#2337	C₂	semidirect
19. C₄×C₁₃×#120	C₂	semidirect
21. C₂×C₁₃×#125	C₂²	semidirect
27. C₂×C₁₃×#121	C₂²	semidirect
32. C₁₃×#400	C₂²	semidirect
33. C₁₃×#400	C₂²	semidirect
34. C₁₃×#400	C₂²	semidirect
37. C₁₃×#399	C₂²	semidirect
38. C₁₃×#398	C₂²	semidirect
39. C₁₃×#398	C₂²	semidirect
43. C₁₃×#397	C₂²	semidirect
44. C₁₃×#397	C₂²	semidirect
45. C₁₃×#397	C₂²	semidirect
47. C₁₃×#396	C₂²	semidirect
51. C₁₃×#394	C₂²	semidirect
52. C₁₃×#394	C₂²	semidirect
53. C₁₃×#394	C₂²	semidirect
55. C₁₃×#393	C₂²	semidirect
60. C₁₃×#391	C₂²	semidirect
61. C₁₃×#391	C₂²	semidirect
62. C₁₃×#391	C₂²	semidirect
65. C₁₃×#390	C₂²	semidirect
66. C₁₃×#389	C₂²	semidirect
67. C₁₃×#389	C₂²	semidirect
73. C₁₃×#388	C₂²	semidirect
74. C₁₃×#388	C₂²	semidirect
75. C₁₃×#388	C₂²	semidirect
76. C₁₃×#388	C₂²	semidirect
85. C₁₃×#386	C₂²	semidirect
92. C₁₃×#385	C₂²	semidirect
93. C₁₃×#385	C₂²	semidirect
94. C₁₃×#383	C₂²	semidirect
95. C₁₃×#383	C₂²	semidirect
96. C₁₃×#383	C₂²	semidirect
99. C₁₃×#381	C₂²	semidirect
100. C₁₃×#381	C₂²	semidirect
103. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
106. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
207. #36842	C₁₃	direct (N × H)
319. #2849	C₂×C₁₃	semidirect
320. #2807	C₂×C₁₃	semidirect
321. #2764	C₂×C₁₃	semidirect
322. #2749	C₂×C₁₃	semidirect
323. #2749	C₂×C₁₃	semidirect
324. #2735	C₂×C₁₃	semidirect
325. #2712	C₂×C₁₃	semidirect
326. #2710	C₂×C₁₃	semidirect
327. #2701	C₂×C₁₃	semidirect
328. #2670	C₂×C₁₃	semidirect
329. #2668	C₂×C₁₃	semidirect
330. #2635	C₂×C₁₃	semidirect
331. #2633	C₂×C₁₃	semidirect
332. #2572	C₂×C₁₃	semidirect
333. #2558	C₂×C₁₃	semidirect
334. #2464	C₂×C₁₃	semidirect
335. #2447	C₂×C₁₃	semidirect
336. #2337	C₂×C₁₃	semidirect
337. C₄×#120	C₂×C₁₃	semidirect
424. C₂×#125	C₂²×C₁₃	semidirect
430. C₂×#121	C₂²×C₁₃	semidirect
435. #400	C₂²×C₁₃	semidirect
436. #400	C₂²×C₁₃	semidirect
437. #400	C₂²×C₁₃	semidirect
440. #399	C₂²×C₁₃	semidirect
441. #398	C₂²×C₁₃	semidirect
442. #398	C₂²×C₁₃	semidirect
446. #397	C₂²×C₁₃	semidirect
447. #397	C₂²×C₁₃	semidirect
448. #397	C₂²×C₁₃	semidirect
450. #396	C₂²×C₁₃	semidirect
454. #394	C₂²×C₁₃	semidirect
455. #394	C₂²×C₁₃	semidirect
456. #394	C₂²×C₁₃	semidirect
458. #393	C₂²×C₁₃	semidirect
463. #391	C₂²×C₁₃	semidirect
464. #391	C₂²×C₁₃	semidirect
465. #391	C₂²×C₁₃	semidirect
468. #390	C₂²×C₁₃	semidirect
469. #389	C₂²×C₁₃	semidirect
470. #389	C₂²×C₁₃	semidirect
476. #388	C₂²×C₁₃	semidirect
477. #388	C₂²×C₁₃	semidirect
478. #388	C₂²×C₁₃	semidirect
479. #388	C₂²×C₁₃	semidirect
488. #386	C₂²×C₁₃	semidirect
495. #385	C₂²×C₁₃	semidirect
496. #385	C₂²×C₁₃	semidirect
497. #383	C₂²×C₁₃	semidirect
498. #383	C₂²×C₁₃	semidirect
499. #383	C₂²×C₁₃	semidirect
502. #381	C₂²×C₁₃	semidirect
503. #381	C₂²×C₁₃	semidirect
506. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
509. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
775. C₁₃	#36842	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×#2849	2
C₁₃×#2807	2
C₁₃×#2764	2
C₁₃×#2749	2
C₁₃×#2735	2
C₁₃×#2712	2
C₁₃×#2710	2
C₁₃×#2701	2
C₁₃×#2670	2
C₁₃×#2668	2
C₁₃×#2635	2
C₁₃×#2633	2
C₁₃×#2572	2
C₁₃×#2558	2
C₁₃×#2464	2
C₁₃×#2447	2
C₁₃×#2337	2
C₄×C₁₃×#120	2
#36842	13

Subgroups — C13×#36842 #15723181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36842 #15723181