Subgroups — C₁₃×#36812 #15723151

Order 3328.

2048 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2854	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2798	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2710	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2705	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2705	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2693	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2678	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2678	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2673	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2648	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2608	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2559	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2539	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2471	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2431	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2404	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2333	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×#123	C₂²	1	2	yes	—
26	C₂×C₁₃×#123	C₂²	1	2	yes	—
27	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#121	C₂²	1	2	yes	—
30	C₂×C₁₃×#121	C₂²	1	2	yes	—
31	C₂×C₁₃×#120	C₂²	1	2	yes	—
32	C₂×C₁₃×#120	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#120	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#400	C₂²	1	2	yes	complemented
38	C₁₃×#400	C₂²	1	2	yes	complemented
39	C₁₃×#399	C₂²	1	2	yes	—
40	C₁₃×#399	C₂²	1	2	yes	complemented
41	C₁₃×#397	C₂²	1	2	yes	—
42	C₁₃×#397	C₂²	1	2	yes	—
43	C₁₃×#397	C₂²	1	2	yes	complemented
44	C₁₃×#396	C₂²	1	2	yes	—
45	C₁₃×#396	C₂²	1	2	yes	—
46	C₁₃×#396	C₂²	1	2	yes	complemented
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	2	yes	—
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×#392	C₂²	1	2	yes	—
56	C₁₃×#392	C₂²	1	2	yes	—
57	C₁₃×#392	C₂²	1	2	yes	—
58	C₁₃×#392	C₂²	1	2	yes	—
59	C₁₃×#392	C₂²	1	2	yes	—
60	C₁₃×#392	C₂²	1	2	yes	—
61	C₁₃×#391	C₂²	1	1	yes	characteristic, 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	—
66	C₁₃×#390	C₂²	1	2	yes	—
67	C₁₃×#390	C₂²	1	2	yes	—
68	C₁₃×#390	C₂²	1	2	yes	—
69	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#389	C₂²	1	2	yes	complemented
71	C₁₃×#389	C₂²	1	2	yes	complemented
72	C₁₃×#389	C₂²	1	2	yes	complemented
73	C₁₃×#388	C₂²	1	2	yes	—
74	C₁₃×#388	C₂²	1	2	yes	—
75	C₁₃×#388	C₂²	1	2	yes	—
76	C₁₃×#388	C₂²	1	2	yes	—
77	C₁₃×#388	C₂²	1	2	yes	—
78	C₁₃×#388	C₂²	1	2	yes	—
79	C₁₃×#388	C₂²	1	2	yes	complemented
80	C₁₃×#388	C₂²	1	2	yes	complemented
81	C₁₃×#387	C₂²	1	2	yes	complemented
82	C₁₃×#387	C₂²	1	2	yes	complemented
83	C₁₃×#387	C₂²	1	2	yes	complemented
84	C₁₃×#387	C₂²	1	2	yes	complemented
85	C₁₃×#386	C₂²	1	2	yes	—
86	C₁₃×#386	C₂²	1	2	yes	—
87	C₁₃×#386	C₂²	1	2	yes	—
88	C₁₃×#386	C₂²	1	2	yes	—
89	C₁₃×#386	C₂²	1	1	yes	characteristic
90	C₁₃×#386	C₂²	1	1	yes	characteristic
91	C₁₃×#386	C₂²	1	2	yes	complemented
92	C₁₃×#386	C₂²	1	2	yes	complemented
93	C₁₃×#386	C₂²	1	2	yes	complemented
94	C₁₃×#386	C₂²	1	2	yes	complemented
95	C₁₃×#386	C₂²	1	2	yes	complemented
96	C₁₃×#385	C₂²	1	2	yes	complemented
97	C₁₃×#381	C₂²	1	1	yes	characteristic
98	C₁₃×#380	C₂²	1	2	yes	—
99	C₁₃×#380	C₂²	1	2	yes	complemented
100	C₁₃×#379	C₂²	1	2	yes	—
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×#41	—	2	4	no	—
109	C₂×C₁₃×#41	—	4	2	no	—
110	C₂×C₁₃×#41	—	4	2	no	—
111	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
120	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
121	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
122	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₁₃×#127	—	4	2	no	—
130	C₁₃×#126	—	4	4	no	—
131	C₁₃×#124	—	4	2	no	—
132	C₁₃×#123	—	4	4	no	—
133	C₁₃×#123	—	4	4	no	—
134	C₁₃×#123	—	4	4	no	—
135	C₁₃×#123	—	4	4	no	—
136	C₁₃×#121	—	2	4	no	—
137	C₁₃×#121	—	4	4	no	—
138	C₁₃×#121	—	4	4	no	—
139	C₁₃×#120	—	4	2	no	—
140	C₁₃×#120	—	4	4	no	—
141	C₁₃×#120	—	4	2	no	—
142	C₁₃×#117	—	4	2	no	—
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	2	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃	—	4	2	no	—
188	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
195	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	2	yes	—
200	C₁₃×#95	C₂³	1	2	yes	—
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	C₁₃×#95	C₂³	1	2	yes	—
204	C₁₃×#95	C₂³	1	2	yes	—
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	2	yes	—
209	C₁₃×#95	C₂³	1	2	yes	—
210	C₁₃×#95	C₂³	1	2	yes	—
211	C₁₃×#95	C₂³	1	2	yes	—
212	C₁₃×#95	C₂³	1	2	yes	—
213	#36812	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂⁴×C₁₃	—	2	2	no	—
215	C₂⁴×C₁₃	—	4	2	no	—
216	C₂⁴×C₁₃	—	4	2	no	—
217	C₂⁴×C₁₃	—	4	1	no	—
218	C₂⁴×C₁₃	—	4	1	no	—
219	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
220	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
221	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₁₃×#41	—	4	16	no	—
225	C₂×Q₈×C₁₃	—	2	2	no	—
226	C₂×Q₈×C₁₃	—	2	2	no	—
227	C₂×Q₈×C₁₃	—	4	1	no	—
228	C₂×D₄×C₁₃	—	2	2	no	—
229	C₂×D₄×C₁₃	—	2	2	no	—
230	C₂×D₄×C₁₃	—	2	2	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	4	no	—
233	C₂×D₄×C₁₃	—	2	4	no	—
234	C₂×D₄×C₁₃	—	2	4	no	—
235	C₂×D₄×C₁₃	—	2	2	no	—
236	C₂×D₄×C₁₃	—	2	2	no	—
237	C₂×D₄×C₁₃	—	2	2	no	—
238	C₂×D₄×C₁₃	—	2	4	no	—
239	C₂×D₄×C₁₃	—	4	1	no	—
240	C₂×D₄×C₁₃	—	4	1	no	—
241	C₂×D₄×C₁₃	—	4	1	no	—
242	C₂×D₄×C₁₃	—	4	2	no	—
243	C₂×D₄×C₁₃	—	4	2	no	—
244	C₂×D₄×C₁₃	—	4	2	no	—
245	C₂×D₄×C₁₃	—	4	2	no	—
246	C₂×D₄×C₁₃	—	4	2	no	—
247	C₂×D₄×C₁₃	—	4	2	no	—
248	C₂×D₄×C₁₃	—	4	2	no	—
249	C₂×D₄×C₁₃	—	4	2	no	—
250	C₂×D₄×C₁₃	—	4	2	no	—
251	C₂×D₄×C₁₃	—	4	2	no	—
252	C₂×D₄×C₁₃	—	4	1	no	—
253	C₂×D₄×C₁₃	—	4	1	no	—
254	C₂×D₄×C₁₃	—	4	2	no	—
255	C₂×D₄×C₁₃	—	4	2	no	—
256	C₂×D₄×C₁₃	—	4	2	no	—
257	C₂×D₄×C₁₃	—	4	2	no	—
258	C₂×D₄×C₁₃	—	4	2	no	—
259	C₂×D₄×C₁₃	—	4	2	no	—
260	C₂×D₄×C₁₃	—	4	2	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	2	no	—
264	C₂²×C₄×C₁₃	—	2	4	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	—	4	2	no	—
269	C₂²×C₄×C₁₃	—	4	1	no	—
270	C₂²×C₄×C₁₃	—	4	1	no	—
271	C₂²×C₄×C₁₃	—	4	1	no	—
272	C₂²×C₄×C₁₃	—	4	1	no	—
273	C₂²×C₄×C₁₃	—	4	2	no	—
274	C₂²×C₄×C₁₃	—	4	2	no	—
275	C₂²×C₄×C₁₃	—	4	2	no	—
276	C₂²×C₄×C₁₃	—	4	2	no	—
277	C₂²×C₄×C₁₃	#41	1	4	yes	—
278	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	4	no	—
294	C₁₃×C₄⋊C₄	—	2	4	no	—
295	C₁₃×C₄⋊C₄	—	2	4	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	4	2	no	—
298	C₁₃×C₄⋊C₄	—	4	2	no	—
299	C₁₃×C₄⋊C₄	—	4	2	no	—
300	C₁₃×C₄⋊C₄	—	4	2	no	—
301	C₁₃×C₄⋊C₄	—	4	2	no	—
302	C₁₃×C₄⋊C₄	—	4	2	no	—
303	C₁₃×C₄⋊C₄	—	4	2	no	—
304	C₁₃×C₄⋊C₄	—	4	2	no	—
305	C₁₃×C₂²⋊C₄	—	2	4	no	—
306	C₁₃×C₂²⋊C₄	—	2	4	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	4	no	—
314	C₁₃×C₂²⋊C₄	—	4	2	no	—
315	C₁₃×C₂²⋊C₄	—	4	2	no	—
316	C₁₃×C₂²⋊C₄	—	4	2	no	—
317	C₁₃×C₂²⋊C₄	—	4	2	no	—
318	C₁₃×C₂²⋊C₄	—	4	2	no	—
319	C₁₃×C₂²⋊C₄	—	4	2	no	—
320	C₁₃×C₂²⋊C₄	—	4	1	no	—
321	C₁₃×C₂²⋊C₄	—	4	1	no	—
322	C₁₃×C₂²⋊C₄	—	4	2	no	—
323	C₁₃×C₂²⋊C₄	—	4	2	no	—
324	C₁₃×C₂²⋊C₄	—	4	2	no	—
325	C₁₃×C₂²⋊C₄	—	4	2	no	—
326	C₁₃×C₂²⋊C₄	—	4	2	no	—
327	C₁₃×C₂²⋊C₄	—	4	2	no	—
328	C₁₃×C₂²⋊C₄	—	4	2	no	—
329	C₁₃×C₂²⋊C₄	—	4	2	no	—
330	C₁₃×C₂²⋊C₄	—	4	2	no	—
331	C₁₃×C₂²⋊C₄	—	4	2	no	—
332	C₁₃×C₂²⋊C₄	—	4	2	no	—
333	C₁₃×C₂²⋊C₄	—	4	2	no	—
334	C₁₃×C₂²⋊C₄	—	4	2	no	—
335	C₄²×C₁₃	—	4	1	no	—
336	C₄²×C₁₃	—	4	2	no	—
337	C₄²×C₁₃	—	4	1	no	—
338	C₄²×C₁₃	—	4	1	no	—
339	C₄²×C₁₃	—	4	1	no	—
340	C₄²×C₁₃	—	4	1	no	—
341	C₄²×C₁₃	—	4	2	no	—
342	C₄²×C₁₃	—	4	1	no	—
343	#2854	C₂×C₁₃	1	2	yes	complemented
344	#2798	C₂×C₁₃	1	2	yes	complemented
345	#2710	C₂×C₁₃	1	2	yes	complemented
346	#2705	C₂×C₁₃	1	2	yes	complemented
347	#2705	C₂×C₁₃	1	2	yes	complemented
348	#2693	C₂×C₁₃	1	2	yes	complemented
349	#2678	C₂×C₁₃	1	2	yes	complemented
350	#2678	C₂×C₁₃	1	2	yes	complemented
351	#2673	C₂×C₁₃	1	2	yes	complemented
352	#2648	C₂×C₁₃	1	2	yes	complemented
353	#2608	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#2559	C₂×C₁₃	1	2	yes	complemented
355	#2539	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#2471	C₂×C₁₃	1	2	yes	complemented
357	#2431	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#2404	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#2333	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#2312	C₂×C₁₃	1	1	yes	characteristic, complemented
361	#2297	C₂×C₁₃	1	1	yes	characteristic, complemented
362	C₂³×C₁₃	—	2	1	no	—
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	—	2	1	no	—
365	C₂³×C₁₃	—	2	2	no	—
366	C₂³×C₁₃	—	2	1	no	—
367	C₂³×C₁₃	—	2	1	no	—
368	C₂³×C₁₃	—	2	2	no	—
369	C₂³×C₁₃	—	2	2	no	—
370	C₂³×C₁₃	—	2	2	no	—
371	C₂³×C₁₃	—	2	2	no	—
372	C₂³×C₁₃	—	2	1	no	—
373	C₂³×C₁₃	—	2	2	no	—
374	C₂³×C₁₃	—	2	2	no	—
375	C₂³×C₁₃	—	2	2	no	—
376	C₂³×C₁₃	—	2	2	no	—
377	C₂³×C₁₃	—	2	2	no	—
378	C₂³×C₁₃	—	2	2	no	—
379	C₂³×C₁₃	—	2	2	no	—
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	2	1	no	—
382	C₂³×C₁₃	—	2	1	no	—
383	C₂³×C₁₃	—	2	2	no	—
384	C₂³×C₁₃	—	2	2	no	—
385	C₂³×C₁₃	—	2	2	no	—
386	C₂³×C₁₃	—	2	2	no	—
387	C₂³×C₁₃	—	2	2	no	—
388	C₂³×C₁₃	—	2	2	no	—
389	C₂³×C₁₃	—	4	4	no	—
390	C₂³×C₁₃	—	8	2	no	—
391	C₂³×C₁₃	—	8	2	no	—
392	C₂³×C₁₃	—	8	4	no	—
393	C₂³×C₁₃	—	8	4	no	—
394	C₂³×C₁₃	C₂×#41	1	2	yes	—
395	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
396	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
397	Q₈×C₁₃	—	4	4	no	—
398	D₄×C₁₃	—	4	4	no	—
399	D₄×C₁₃	—	4	4	no	—
400	D₄×C₁₃	—	4	4	no	—
401	D₄×C₁₃	—	8	2	no	—
402	D₄×C₁₃	—	8	4	no	—
403	D₄×C₁₃	—	8	4	no	—
404	D₄×C₁₃	—	8	4	no	—
405	D₄×C₁₃	—	8	4	no	—
406	D₄×C₁₃	—	8	4	no	—
407	D₄×C₁₃	—	8	4	no	—
408	D₄×C₁₃	—	8	4	no	—
409	C₂×C₄×C₁₃	—	2	8	no	—
410	C₂×C₄×C₁₃	—	2	1	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	1	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	1	no	—
439	C₂×C₄×C₁₃	—	2	1	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	2	2	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	2	2	no	—
448	C₂×C₄×C₁₃	—	4	4	no	—
449	C₂×C₄×C₁₃	—	4	8	no	—
450	C₂×C₄×C₁₃	—	4	4	no	—
451	C₂×C₄×C₁₃	—	8	2	no	—
452	C₂×C₄×C₁₃	—	8	4	no	—
453	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
454	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
455	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
456	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
457	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
460	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
461	C₂×#123	C₂²×C₁₃	1	2	yes	—
462	C₂×#123	C₂²×C₁₃	1	2	yes	—
463	C₂×#123	C₂²×C₁₃	1	2	yes	—
464	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
465	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
466	C₂×#121	C₂²×C₁₃	1	2	yes	—
467	C₂×#121	C₂²×C₁₃	1	2	yes	—
468	C₂×#120	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×#120	C₂²×C₁₃	1	1	yes	characteristic
470	C₂×#120	C₂²×C₁₃	1	2	yes	—
471	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
472	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
473	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
474	#400	C₂²×C₁₃	1	2	yes	complemented
475	#400	C₂²×C₁₃	1	2	yes	complemented
476	#399	C₂²×C₁₃	1	2	yes	—
477	#399	C₂²×C₁₃	1	2	yes	complemented
478	#397	C₂²×C₁₃	1	2	yes	—
479	#397	C₂²×C₁₃	1	2	yes	—
480	#397	C₂²×C₁₃	1	2	yes	complemented
481	#396	C₂²×C₁₃	1	2	yes	—
482	#396	C₂²×C₁₃	1	2	yes	—
483	#396	C₂²×C₁₃	1	2	yes	complemented
484	#396	C₂²×C₁₃	1	2	yes	complemented
485	#394	C₂²×C₁₃	1	2	yes	—
486	#394	C₂²×C₁₃	1	2	yes	—
487	#394	C₂²×C₁₃	1	2	yes	—
488	#394	C₂²×C₁₃	1	2	yes	—
489	#394	C₂²×C₁₃	1	2	yes	complemented
490	#394	C₂²×C₁₃	1	2	yes	complemented
491	#393	C₂²×C₁₃	1	2	yes	—
492	#392	C₂²×C₁₃	1	2	yes	—
493	#392	C₂²×C₁₃	1	2	yes	—
494	#392	C₂²×C₁₃	1	2	yes	—
495	#392	C₂²×C₁₃	1	2	yes	—
496	#392	C₂²×C₁₃	1	2	yes	—
497	#392	C₂²×C₁₃	1	2	yes	—
498	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
499	#391	C₂²×C₁₃	1	2	yes	complemented
500	#390	C₂²×C₁₃	1	2	yes	—
501	#390	C₂²×C₁₃	1	2	yes	—
502	#390	C₂²×C₁₃	1	2	yes	—
503	#390	C₂²×C₁₃	1	2	yes	—
504	#390	C₂²×C₁₃	1	2	yes	—
505	#390	C₂²×C₁₃	1	2	yes	—
506	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
507	#389	C₂²×C₁₃	1	2	yes	complemented
508	#389	C₂²×C₁₃	1	2	yes	complemented
509	#389	C₂²×C₁₃	1	2	yes	complemented
510	#388	C₂²×C₁₃	1	2	yes	—
511	#388	C₂²×C₁₃	1	2	yes	—
512	#388	C₂²×C₁₃	1	2	yes	—
513	#388	C₂²×C₁₃	1	2	yes	—
514	#388	C₂²×C₁₃	1	2	yes	—
515	#388	C₂²×C₁₃	1	2	yes	—
516	#388	C₂²×C₁₃	1	2	yes	complemented
517	#388	C₂²×C₁₃	1	2	yes	complemented
518	#387	C₂²×C₁₃	1	2	yes	complemented
519	#387	C₂²×C₁₃	1	2	yes	complemented
520	#387	C₂²×C₁₃	1	2	yes	complemented
521	#387	C₂²×C₁₃	1	2	yes	complemented
522	#386	C₂²×C₁₃	1	2	yes	—
523	#386	C₂²×C₁₃	1	2	yes	—
524	#386	C₂²×C₁₃	1	2	yes	—
525	#386	C₂²×C₁₃	1	1	yes	characteristic
526	#386	C₂²×C₁₃	1	1	yes	characteristic
527	#386	C₂²×C₁₃	1	2	yes	—
528	#386	C₂²×C₁₃	1	2	yes	complemented
529	#386	C₂²×C₁₃	1	2	yes	complemented
530	#386	C₂²×C₁₃	1	2	yes	complemented
531	#386	C₂²×C₁₃	1	2	yes	complemented
532	#386	C₂²×C₁₃	1	2	yes	complemented
533	#385	C₂²×C₁₃	1	2	yes	complemented
534	#381	C₂²×C₁₃	1	1	yes	characteristic
535	#380	C₂²×C₁₃	1	2	yes	—
536	#380	C₂²×C₁₃	1	2	yes	complemented
537	#379	C₂²×C₁₃	1	2	yes	—
538	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
539	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
540	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
541	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
542	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
543	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
544	C₂²×C₁₃	—	2	2	no	—
545	C₂²×C₁₃	—	2	2	no	—
546	C₂²×C₁₃	—	2	2	no	—
547	C₂²×C₁₃	—	2	2	no	—
548	C₂²×C₁₃	—	2	4	no	—
549	C₂²×C₁₃	—	4	1	no	—
550	C₂²×C₁₃	—	4	1	no	—
551	C₂²×C₁₃	—	4	2	no	—
552	C₂²×C₁₃	—	4	2	no	—
553	C₂²×C₁₃	—	4	2	no	—
554	C₂²×C₁₃	—	4	2	no	—
555	C₂²×C₁₃	—	4	1	no	—
556	C₂²×C₁₃	—	4	2	no	—
557	C₂²×C₁₃	—	4	1	no	—
558	C₂²×C₁₃	—	4	2	no	—
559	C₂²×C₁₃	—	4	2	no	—
560	C₂²×C₁₃	—	4	2	no	—
561	C₂²×C₁₃	—	4	1	no	—
562	C₂²×C₁₃	—	4	2	no	—
563	C₂²×C₁₃	—	4	2	no	—
564	C₂²×C₁₃	—	4	2	no	—
565	C₂²×C₁₃	—	4	2	no	—
566	C₂²×C₁₃	—	4	2	no	—
567	C₂²×C₁₃	—	4	2	no	—
568	C₂²×C₁₃	—	4	2	no	—
569	C₂²×C₁₃	—	4	2	no	—
570	C₂²×C₁₃	—	4	2	no	—
571	C₂²×C₁₃	—	4	2	no	—
572	C₂²×C₁₃	—	4	2	no	—
573	C₂²×C₁₃	—	8	8	no	—
574	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
575	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
578	C₂²×C₁₃	#585	1	2	yes	—
579	C₄×C₁₃	—	2	2	no	—
580	C₄×C₁₃	—	2	2	no	—
581	C₄×C₁₃	—	2	2	no	—
582	C₄×C₁₃	—	2	4	no	—
583	C₄×C₁₃	—	4	1	no	—
584	C₄×C₁₃	—	4	2	no	—
585	C₄×C₁₃	—	4	2	no	—
586	C₄×C₁₃	—	4	2	no	—
587	C₄×C₁₃	—	4	2	no	—
588	C₄×C₁₃	—	4	2	no	—
589	C₄×C₁₃	—	4	2	no	—
590	C₄×C₁₃	—	4	2	no	—
591	C₄×C₁₃	—	4	2	no	—
592	C₄×C₁₃	—	4	2	no	—
593	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
594	C₂×#41	—	2	4	no	—
595	C₂×#41	—	4	2	no	—
596	C₂×#41	—	4	2	no	—
597	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
598	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
599	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
601	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
602	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
603	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
604	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
605	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
606	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
607	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
608	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
609	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
611	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
614	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
615	#127	—	4	2	no	—
616	#126	—	4	4	no	—
617	#124	—	4	2	no	—
618	#123	—	4	4	no	—
619	#123	—	4	4	no	—
620	#123	—	4	4	no	—
621	#123	—	4	4	no	—
622	#121	—	2	4	no	—
623	#121	—	4	4	no	—
624	#121	—	4	4	no	—
625	#120	—	4	2	no	—
626	#120	—	4	4	no	—
627	#120	—	4	2	no	—
628	#117	—	4	2	no	—
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
642	C₂×C₂²⋊C₄	—	2	4	no	—
643	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
673	C₂×C₄²	—	4	2	no	—
674	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
678	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
682	#95	C₂³×C₁₃	1	2	yes	—
683	#95	C₂³×C₁₃	1	2	yes	—
684	#95	C₂³×C₁₃	1	2	yes	—
685	#95	C₂³×C₁₃	1	2	yes	—
686	#95	C₂³×C₁₃	1	2	yes	—
687	#95	C₂³×C₁₃	1	2	yes	—
688	#95	C₂³×C₁₃	1	2	yes	—
689	#95	C₂³×C₁₃	1	2	yes	—
690	#95	C₂³×C₁₃	1	2	yes	—
691	#95	C₂³×C₁₃	1	2	yes	—
692	#95	C₂³×C₁₃	1	2	yes	—
693	#95	C₂³×C₁₃	1	2	yes	—
694	#95	C₂³×C₁₃	1	2	yes	—
695	#95	C₂³×C₁₃	1	2	yes	—
696	#95	C₂³×C₁₃	1	2	yes	—
697	#95	C₂³×C₁₃	1	2	yes	—
698	#95	C₂³×C₁₃	1	2	yes	—
699	C₂×C₁₃	—	4	2	no	—
700	C₂×C₁₃	—	4	2	no	—
701	C₂×C₁₃	—	8	1	no	—
702	C₂×C₁₃	—	8	2	no	—
703	C₂×C₁₃	—	8	2	no	—
704	C₂×C₁₃	#3455	1	1	yes	characteristic
705	C₂×C₁₃	#3490	1	1	yes	characteristic
706	C₂×C₁₃	#3508	1	1	yes	characteristic
707	C₂×C₁₃	#3534	1	2	yes	—
708	C₂×C₁₃	#3546	1	2	yes	—
709	C₂⁴	—	2	2	no	—
710	C₂⁴	—	4	2	no	—
711	C₂⁴	—	4	2	no	—
712	C₂⁴	—	4	1	no	—
713	C₂⁴	—	4	1	no	—
714	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
715	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
716	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
717	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
718	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
719	#41	—	4	16	no	—
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	4	1	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	4	1	no	—
735	C₂×D₄	—	4	1	no	—
736	C₂×D₄	—	4	1	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	2	no	—
744	C₂×D₄	—	4	2	no	—
745	C₂×D₄	—	4	2	no	—
746	C₂×D₄	—	4	2	no	—
747	C₂×D₄	—	4	1	no	—
748	C₂×D₄	—	4	1	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂×D₄	—	4	2	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	4	1	no	—
764	C₂²×C₄	—	4	1	no	—
765	C₂²×C₄	—	4	1	no	—
766	C₂²×C₄	—	4	1	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	C₁₃×#41	1	4	yes	—
773	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	4	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	2	4	no	—
791	C₄⋊C₄	—	2	4	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	1	no	—
812	C₂²⋊C₄	—	4	1	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₂²⋊C₄	—	4	2	no	—
823	C₂²⋊C₄	—	4	2	no	—
824	C₂²⋊C₄	—	4	2	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₄²	—	4	1	no	—
831	C₄²	—	4	2	no	—
832	C₄²	—	4	1	no	—
833	C₄²	—	4	1	no	—
834	C₄²	—	4	1	no	—
835	C₄²	—	4	1	no	—
836	C₄²	—	4	2	no	—
837	C₄²	—	4	1	no	—
838	C₁₃	#36812	1	1	yes	characteristic, direct product factor, Sylow
839	C₂³	—	2	1	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	4	4	no	—
867	C₂³	—	8	2	no	—
868	C₂³	—	8	2	no	—
869	C₂³	—	8	4	no	—
870	C₂³	—	8	4	no	—
871	C₂³	C₂×C₁₃×#41	1	2	yes	—
872	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
873	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
874	Q₈	—	4	4	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	4	no	—
878	D₄	—	8	4	no	—
879	D₄	—	8	2	no	—
880	D₄	—	8	4	no	—
881	D₄	—	8	4	no	—
882	D₄	—	8	4	no	—
883	D₄	—	8	4	no	—
884	D₄	—	8	4	no	—
885	D₄	—	8	4	no	—
886	C₂×C₄	—	2	8	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	8	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	—	8	4	no	—
930	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
931	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
932	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
933	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
934	C₂²	—	2	4	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	8	8	no	—
964	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
965	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
966	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
967	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
968	C₂²	C₁₃×#585	1	2	yes	—
969	C₄	—	2	4	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	1	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₂	—	4	2	no	—
984	C₂	—	4	2	no	—
985	C₂	—	8	2	no	—
986	C₂	—	8	2	no	—
987	C₂	—	8	1	no	—
988	C₂	C₁₃×#3455	1	1	yes	characteristic
989	C₂	C₁₃×#3490	1	1	yes	characteristic
990	C₂	C₁₃×#3508	1	1	yes	characteristic
991	C₂	C₁₃×#3534	1	2	yes	—
992	C₂	C₁₃×#3546	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. C₁₃×#2854	C₂	semidirect
2. C₁₃×#2798	C₂	semidirect
3. C₁₃×#2710	C₂	semidirect
4. C₁₃×#2705	C₂	semidirect
5. C₁₃×#2705	C₂	semidirect
6. C₁₃×#2693	C₂	semidirect
7. C₁₃×#2678	C₂	semidirect
8. C₁₃×#2678	C₂	semidirect
9. C₁₃×#2673	C₂	semidirect
10. C₁₃×#2648	C₂	semidirect
11. C₁₃×#2608	C₂	semidirect
12. C₁₃×#2559	C₂	semidirect
13. C₁₃×#2539	C₂	semidirect
14. C₁₃×#2471	C₂	semidirect
15. C₁₃×#2431	C₂	semidirect
16. C₁₃×#2404	C₂	semidirect
17. C₁₃×#2333	C₂	semidirect
18. C₁₃×#2312	C₂	semidirect
19. C₁₃×#2297	C₂	semidirect
21. C₂×C₁₃×#127	C₂²	semidirect
22. C₂×C₁₃×#126	C₂²	semidirect
23. C₂×C₁₃×#124	C₂²	semidirect
27. C₂×C₁₃×#123	C₂²	semidirect
34. C₂×C₁₃×#117	C₂²	semidirect
36. C₂²×C₄²×C₁₃	C₂²	semidirect
37. C₁₃×#400	C₂²	semidirect
38. C₁₃×#400	C₂²	semidirect
40. C₁₃×#399	C₂²	semidirect
43. C₁₃×#397	C₂²	semidirect
46. C₁₃×#396	C₂²	semidirect
47. C₁₃×#396	C₂²	semidirect
52. C₁₃×#394	C₂²	semidirect
53. C₁₃×#394	C₂²	semidirect
61. C₁₃×#391	C₂²	semidirect
62. C₁₃×#391	C₂²	semidirect
69. C₁₃×#390	C₂²	semidirect
70. C₁₃×#389	C₂²	semidirect
71. C₁₃×#389	C₂²	semidirect
72. C₁₃×#389	C₂²	semidirect
79. C₁₃×#388	C₂²	semidirect
80. C₁₃×#388	C₂²	semidirect
81. C₁₃×#387	C₂²	semidirect
82. C₁₃×#387	C₂²	semidirect
83. C₁₃×#387	C₂²	semidirect
84. C₁₃×#387	C₂²	semidirect
91. C₁₃×#386	C₂²	semidirect
92. C₁₃×#386	C₂²	semidirect
93. C₁₃×#386	C₂²	semidirect
94. C₁₃×#386	C₂²	semidirect
95. C₁₃×#386	C₂²	semidirect
96. C₁₃×#385	C₂²	semidirect
99. C₁₃×#380	C₂²	semidirect
104. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
105. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
106. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
213. #36812	C₁₃	direct (N × H)
343. #2854	C₂×C₁₃	semidirect
344. #2798	C₂×C₁₃	semidirect
345. #2710	C₂×C₁₃	semidirect
346. #2705	C₂×C₁₃	semidirect
347. #2705	C₂×C₁₃	semidirect
348. #2693	C₂×C₁₃	semidirect
349. #2678	C₂×C₁₃	semidirect
350. #2678	C₂×C₁₃	semidirect
351. #2673	C₂×C₁₃	semidirect
352. #2648	C₂×C₁₃	semidirect
353. #2608	C₂×C₁₃	semidirect
354. #2559	C₂×C₁₃	semidirect
355. #2539	C₂×C₁₃	semidirect
356. #2471	C₂×C₁₃	semidirect
357. #2431	C₂×C₁₃	semidirect
358. #2404	C₂×C₁₃	semidirect
359. #2333	C₂×C₁₃	semidirect
360. #2312	C₂×C₁₃	semidirect
361. #2297	C₂×C₁₃	semidirect
458. C₂×#127	C₂²×C₁₃	semidirect
459. C₂×#126	C₂²×C₁₃	semidirect
460. C₂×#124	C₂²×C₁₃	semidirect
464. C₂×#123	C₂²×C₁₃	semidirect
471. C₂×#117	C₂²×C₁₃	semidirect
473. C₂²×C₄²	C₂²×C₁₃	semidirect
474. #400	C₂²×C₁₃	semidirect
475. #400	C₂²×C₁₃	semidirect
477. #399	C₂²×C₁₃	semidirect
480. #397	C₂²×C₁₃	semidirect
483. #396	C₂²×C₁₃	semidirect
484. #396	C₂²×C₁₃	semidirect
489. #394	C₂²×C₁₃	semidirect
490. #394	C₂²×C₁₃	semidirect
498. #391	C₂²×C₁₃	semidirect
499. #391	C₂²×C₁₃	semidirect
506. #390	C₂²×C₁₃	semidirect
507. #389	C₂²×C₁₃	semidirect
508. #389	C₂²×C₁₃	semidirect
509. #389	C₂²×C₁₃	semidirect
516. #388	C₂²×C₁₃	semidirect
517. #388	C₂²×C₁₃	semidirect
518. #387	C₂²×C₁₃	semidirect
519. #387	C₂²×C₁₃	semidirect
520. #387	C₂²×C₁₃	semidirect
521. #387	C₂²×C₁₃	semidirect
528. #386	C₂²×C₁₃	semidirect
529. #386	C₂²×C₁₃	semidirect
530. #386	C₂²×C₁₃	semidirect
531. #386	C₂²×C₁₃	semidirect
532. #386	C₂²×C₁₃	semidirect
533. #385	C₂²×C₁₃	semidirect
536. #380	C₂²×C₁₃	semidirect
541. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
542. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
543. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
838. C₁₃	#36812	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×#2854	2
C₁₃×#2798	2
C₁₃×#2710	2
C₁₃×#2705	2
C₁₃×#2693	2
C₁₃×#2678	2
C₁₃×#2673	2
C₁₃×#2648	2
C₁₃×#2608	2
C₁₃×#2559	2
C₁₃×#2539	2
C₁₃×#2471	2
C₁₃×#2431	2
C₁₃×#2404	2
C₁₃×#2333	2
C₁₃×#2312	2
C₁₃×#2297	2
#36812	13

Subgroups — C13×#36812 #15723151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36812 #15723151