Subgroups — C₁₃×#35063 #15721402

Order 3328.

2994 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×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2853	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2849	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2638	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2635	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2600	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2564	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2543	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2484	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2482	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2412	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2410	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2406	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2404	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2325	C₂	1	4	yes	maximal, complemented
17	C₂×C₁₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#525	—	2	8	no	—
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#121	C₂²	1	4	yes	—
28	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#120	C₂²	1	2	yes	—
31	C₂×C₁₃×#120	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	—	2	8	no	—
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
44	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#400	C₂²	1	2	yes	complemented
46	C₁₃×#399	C₂²	1	2	yes	complemented
47	C₁₃×#398	C₂²	1	2	yes	complemented
48	C₁₃×#397	C₂²	1	2	yes	complemented
49	C₁₃×#397	C₂²	1	4	yes	complemented
50	C₁₃×#395	C₂²	1	2	yes	complemented
51	C₁₃×#394	C₂²	1	4	yes	—
52	C₁₃×#394	C₂²	1	2	yes	complemented
53	C₁₃×#394	C₂²	1	4	yes	complemented
54	C₁₃×#393	C₂²	1	2	yes	complemented
55	C₁₃×#392	C₂²	1	4	yes	—
56	C₁₃×#392	C₂²	1	2	yes	complemented
57	C₁₃×#388	C₂²	1	4	yes	complemented
58	C₁₃×#388	C₂²	1	4	yes	complemented
59	C₁₃×#388	C₂²	1	4	yes	complemented
60	C₁₃×#387	C₂²	1	4	yes	complemented
61	C₁₃×#387	C₂²	1	4	yes	complemented
62	C₁₃×#387	C₂²	1	4	yes	complemented
63	C₁₃×#386	C₂²	1	4	yes	—
64	C₁₃×#386	C₂²	1	2	yes	—
65	C₁₃×#386	C₂²	1	2	yes	—
66	C₁₃×#386	C₂²	1	4	yes	complemented
67	C₁₃×#386	C₂²	1	4	yes	complemented
68	C₁₃×#386	C₂²	1	4	yes	complemented
69	C₁₃×#386	C₂²	1	4	yes	complemented
70	C₁₃×#385	C₂²	1	2	yes	—
71	C₁₃×#385	C₂²	1	2	yes	—
72	C₁₃×#385	C₂²	1	4	yes	complemented
73	C₁₃×#385	C₂²	1	4	yes	complemented
74	C₁₃×#385	C₂²	1	4	yes	complemented
75	C₁₃×#381	C₂²	1	2	yes	—
76	C₁₃×#381	C₂²	1	1	yes	characteristic
77	C₁₃×#381	C₂²	1	1	yes	characteristic
78	C₁₃×#381	C₂²	1	2	yes	—
79	C₁₃×#381	C₂²	1	2	yes	complemented
80	C₁₃×#381	C₂²	1	2	yes	complemented
81	C₁₃×#380	C₂²	1	4	yes	complemented
82	C₁₃×#379	C₂²	1	2	yes	—
83	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
84	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
86	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×#41	—	2	4	no	—
88	C₂×C₁₃×#41	—	4	4	no	—
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	—	2	4	no	—
91	C₂²×D₄×C₁₃	—	2	8	no	—
92	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	—	2	4	no	—
100	C₂³×C₄×C₁₃	—	4	4	no	—
101	C₂³×C₄×C₁₃	—	4	4	no	—
102	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×#123	—	2	8	no	—
117	C₁₃×#123	—	4	4	no	—
118	C₁₃×C₂²⋊Q₈	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	—	2	4	no	—
120	C₁₃×#121	—	2	16	no	—
121	C₁₃×#121	—	2	4	no	—
122	C₁₃×#121	—	2	4	no	—
123	C₁₃×#120	—	2	8	no	—
124	C₁₃×#120	—	4	4	no	—
125	C₄×D₄×C₁₃	—	2	8	no	—
126	C₄×D₄×C₁₃	—	2	8	no	—
127	C₄×D₄×C₁₃	—	2	8	no	—
128	C₄×D₄×C₁₃	—	2	8	no	—
129	C₄×D₄×C₁₃	—	2	8	no	—
130	C₄×D₄×C₁₃	—	2	8	no	—
131	C₁₃×#117	—	2	4	no	—
132	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
144	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
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	4	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	4	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	2	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
163	C₂×C₄²×C₁₃	—	2	4	no	—
164	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
167	C₁₃×#95	C₂³	1	4	yes	—
168	C₁₃×#95	C₂³	1	4	yes	—
169	C₁₃×#95	C₂³	1	2	yes	—
170	C₁₃×#95	C₂³	1	4	yes	—
171	C₁₃×#95	C₂³	1	4	yes	—
172	C₁₃×#95	C₂³	1	2	yes	—
173	C₁₃×#95	C₂³	1	2	yes	—
174	C₁₃×#95	C₂³	1	2	yes	—
175	C₁₃×#95	C₂³	1	4	yes	—
176	C₁₃×#95	C₂³	1	4	yes	—
177	C₁₃×#95	C₂³	1	4	yes	—
178	C₁₃×#95	C₂³	1	4	yes	—
179	#35063	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂⁴×C₁₃	—	2	2	no	—
181	C₂⁴×C₁₃	—	2	4	no	—
182	C₂⁴×C₁₃	—	2	4	no	—
183	C₂⁴×C₁₃	—	2	4	no	—
184	C₂⁴×C₁₃	—	2	4	no	—
185	C₂⁴×C₁₃	—	4	2	no	—
186	C₂⁴×C₁₃	—	4	2	no	—
187	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
188	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
189	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
191	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₁₃×#41	—	4	16	no	—
194	C₂×Q₈×C₁₃	—	2	2	no	—
195	C₂×Q₈×C₁₃	—	4	2	no	—
196	C₂×D₄×C₁₃	—	2	32	no	—
197	C₂×D₄×C₁₃	—	2	4	no	—
198	C₂×D₄×C₁₃	—	2	4	no	—
199	C₂×D₄×C₁₃	—	2	4	no	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	4	no	—
202	C₂×D₄×C₁₃	—	2	4	no	—
203	C₂×D₄×C₁₃	—	2	4	no	—
204	C₂×D₄×C₁₃	—	2	8	no	—
205	C₂×D₄×C₁₃	—	2	4	no	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	8	no	—
208	C₂×D₄×C₁₃	—	2	2	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	4	4	no	—
211	C₂×D₄×C₁₃	—	4	2	no	—
212	C₂×D₄×C₁₃	—	4	4	no	—
213	C₂×D₄×C₁₃	—	4	4	no	—
214	C₂×D₄×C₁₃	#41	1	8	yes	complemented
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
217	C₂²×C₄×C₁₃	—	2	4	no	—
218	C₂²×C₄×C₁₃	—	2	4	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	2	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	8	no	—
223	C₂²×C₄×C₁₃	—	2	4	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	2	4	no	—
226	C₂²×C₄×C₁₃	—	4	16	no	—
227	C₂²×C₄×C₁₃	—	4	2	no	—
228	C₂²×C₄×C₁₃	—	4	2	no	—
229	C₂²×C₄×C₁₃	—	4	2	no	—
230	C₂²×C₄×C₁₃	—	4	2	no	—
231	C₂²×C₄×C₁₃	—	4	4	no	—
232	C₂²×C₄×C₁₃	—	4	4	no	—
233	C₂²×C₄×C₁₃	—	4	2	no	—
234	C₂²×C₄×C₁₃	—	4	2	no	—
235	C₂²×C₄×C₁₃	—	4	2	no	—
236	C₂²×C₄×C₁₃	—	4	4	no	—
237	C₂²×C₄×C₁₃	—	4	4	no	—
238	C₂²×C₄×C₁₃	—	4	16	no	—
239	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
243	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
244	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	—	2	2	no	—
260	C₁₃×C₄⋊C₄	—	2	2	no	—
261	C₁₃×C₄⋊C₄	—	2	4	no	—
262	C₁₃×C₄⋊C₄	—	2	4	no	—
263	C₁₃×C₄⋊C₄	—	2	8	no	—
264	C₁₃×C₄⋊C₄	—	4	4	no	—
265	C₁₃×C₄⋊C₄	—	4	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	8	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₁₃×C₂²⋊C₄	—	2	4	no	—
278	C₁₃×C₂²⋊C₄	—	2	8	no	—
279	C₁₃×C₂²⋊C₄	—	4	4	no	—
280	C₁₃×C₂²⋊C₄	—	4	4	no	—
281	C₁₃×C₂²⋊C₄	—	4	4	no	—
282	C₁₃×C₂²⋊C₄	—	4	4	no	—
283	C₁₃×C₂²⋊C₄	—	4	4	no	—
284	C₄²×C₁₃	—	2	4	no	—
285	C₄²×C₁₃	—	2	4	no	—
286	C₄²×C₁₃	—	2	4	no	—
287	C₂×#525	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#2853	C₂×C₁₃	1	2	yes	complemented
290	#2849	C₂×C₁₃	1	2	yes	complemented
291	#2638	C₂×C₁₃	1	2	yes	complemented
292	#2635	C₂×C₁₃	1	2	yes	complemented
293	#2600	C₂×C₁₃	1	4	yes	complemented
294	#2564	C₂×C₁₃	1	2	yes	complemented
295	#2543	C₂×C₁₃	1	2	yes	complemented
296	#2484	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#2482	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#2412	C₂×C₁₃	1	2	yes	complemented
299	#2410	C₂×C₁₃	1	2	yes	complemented
300	#2406	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#2404	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#2325	C₂×C₁₃	1	4	yes	complemented
303	C₂×#381	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂³×C₁₃	—	2	2	no	—
305	C₂³×C₁₃	—	2	2	no	—
306	C₂³×C₁₃	—	2	2	no	—
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	2	8	no	—
309	C₂³×C₁₃	—	2	8	no	—
310	C₂³×C₁₃	—	2	8	no	—
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	2	4	no	—
316	C₂³×C₁₃	—	2	4	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	2	no	—
319	C₂³×C₁₃	—	2	4	no	—
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	4	no	—
323	C₂³×C₁₃	—	4	4	no	—
324	C₂³×C₁₃	—	4	16	no	—
325	C₂³×C₁₃	—	4	16	no	—
326	C₂³×C₁₃	—	4	4	no	—
327	C₂³×C₁₃	—	4	4	no	—
328	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
329	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
330	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
331	C₂³×C₁₃	C₂×#41	1	4	yes	—
332	C₂³×C₁₃	C₂×#41	1	4	yes	—
333	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
334	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
335	Q₈×C₁₃	—	4	4	no	—
336	D₄×C₁₃	—	2	16	no	—
337	D₄×C₁₃	—	2	16	no	—
338	D₄×C₁₃	—	4	4	no	—
339	D₄×C₁₃	—	4	8	no	—
340	D₄×C₁₃	—	4	8	no	—
341	D₄×C₁₃	—	4	8	no	—
342	D₄×C₁₃	—	8	8	no	—
343	C₂×C₄×C₁₃	—	2	8	no	—
344	C₂×C₄×C₁₃	—	2	8	no	—
345	C₂×C₄×C₁₃	—	2	8	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	2	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	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	4	no	—
358	C₂×C₄×C₁₃	—	2	4	no	—
359	C₂×C₄×C₁₃	—	2	4	no	—
360	C₂×C₄×C₁₃	—	2	4	no	—
361	C₂×C₄×C₁₃	—	2	4	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	4	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	4	no	—
366	C₂×C₄×C₁₃	—	2	4	no	—
367	C₂×C₄×C₁₃	—	2	4	no	—
368	C₂×C₄×C₁₃	—	2	4	no	—
369	C₂×C₄×C₁₃	—	4	4	no	—
370	C₂×C₄×C₁₃	—	4	4	no	—
371	C₂×C₄×C₁₃	—	4	4	no	—
372	C₂×C₄×C₁₃	—	4	4	no	—
373	C₂×C₄×C₁₃	—	4	8	no	—
374	C₂×C₄×C₁₃	—	4	8	no	—
375	C₂×C₄×C₁₃	—	4	8	no	—
376	C₂×C₄×C₁₃	—	4	4	no	—
377	C₂×C₄×C₁₃	—	4	4	no	—
378	C₂×C₄×C₁₃	—	8	8	no	—
379	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
384	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
385	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
386	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
387	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
388	#525	—	2	8	no	—
389	C₂×#123	C₂²×C₁₃	1	2	yes	—
390	C₂×#123	C₂²×C₁₃	1	2	yes	—
391	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
392	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
393	C₂×#121	C₂²×C₁₃	1	4	yes	—
394	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
395	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
396	C₂×#120	C₂²×C₁₃	1	2	yes	—
397	C₂×#120	C₂²×C₁₃	1	2	yes	—
398	C₂×C₄×D₄	—	2	8	no	—
399	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
400	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
401	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
402	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
403	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
404	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
405	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
406	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
407	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
410	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
411	#400	C₂²×C₁₃	1	2	yes	complemented
412	#399	C₂²×C₁₃	1	2	yes	complemented
413	#398	C₂²×C₁₃	1	2	yes	complemented
414	#397	C₂²×C₁₃	1	4	yes	complemented
415	#397	C₂²×C₁₃	1	2	yes	complemented
416	#395	C₂²×C₁₃	1	2	yes	complemented
417	#394	C₂²×C₁₃	1	4	yes	—
418	#394	C₂²×C₁₃	1	4	yes	complemented
419	#394	C₂²×C₁₃	1	2	yes	complemented
420	#393	C₂²×C₁₃	1	2	yes	complemented
421	#392	C₂²×C₁₃	1	4	yes	—
422	#392	C₂²×C₁₃	1	2	yes	complemented
423	#388	C₂²×C₁₃	1	4	yes	complemented
424	#388	C₂²×C₁₃	1	4	yes	complemented
425	#388	C₂²×C₁₃	1	4	yes	complemented
426	#387	C₂²×C₁₃	1	4	yes	complemented
427	#387	C₂²×C₁₃	1	4	yes	complemented
428	#387	C₂²×C₁₃	1	4	yes	complemented
429	#386	C₂²×C₁₃	1	4	yes	—
430	#386	C₂²×C₁₃	1	2	yes	—
431	#386	C₂²×C₁₃	1	2	yes	—
432	#386	C₂²×C₁₃	1	4	yes	complemented
433	#386	C₂²×C₁₃	1	4	yes	complemented
434	#386	C₂²×C₁₃	1	4	yes	complemented
435	#386	C₂²×C₁₃	1	4	yes	complemented
436	#385	C₂²×C₁₃	1	2	yes	—
437	#385	C₂²×C₁₃	1	2	yes	—
438	#385	C₂²×C₁₃	1	4	yes	complemented
439	#385	C₂²×C₁₃	1	4	yes	complemented
440	#385	C₂²×C₁₃	1	4	yes	complemented
441	#381	C₂²×C₁₃	1	2	yes	—
442	#381	C₂²×C₁₃	1	2	yes	—
443	#381	C₂²×C₁₃	1	1	yes	characteristic
444	#381	C₂²×C₁₃	1	1	yes	characteristic
445	#381	C₂²×C₁₃	1	2	yes	complemented
446	#381	C₂²×C₁₃	1	2	yes	complemented
447	#380	C₂²×C₁₃	1	4	yes	complemented
448	#379	C₂²×C₁₃	1	2	yes	—
449	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
450	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
451	C₂²×C₁₃	—	2	2	no	—
452	C₂²×C₁₃	—	2	2	no	—
453	C₂²×C₁₃	—	2	2	no	—
454	C₂²×C₁₃	—	2	2	no	—
455	C₂²×C₁₃	—	2	8	no	—
456	C₂²×C₁₃	—	2	8	no	—
457	C₂²×C₁₃	—	2	2	no	—
458	C₂²×C₁₃	—	2	4	no	—
459	C₂²×C₁₃	—	2	2	no	—
460	C₂²×C₁₃	—	2	2	no	—
461	C₂²×C₁₃	—	2	8	no	—
462	C₂²×C₁₃	—	4	16	no	—
463	C₂²×C₁₃	—	4	16	no	—
464	C₂²×C₁₃	—	4	2	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	4	4	no	—
467	C₂²×C₁₃	—	4	4	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	4	no	—
472	C₂²×C₁₃	—	4	4	no	—
473	C₂²×C₁₃	#525	1	4	yes	—
474	C₂²×C₁₃	#534	1	4	yes	—
475	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
476	C₂²×C₁₃	C₂²×#41	1	2	yes	—
477	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
478	C₂²×C₁₃	#585	1	2	yes	—
479	C₄×C₁₃	—	2	4	no	—
480	C₄×C₁₃	—	2	2	no	—
481	C₄×C₁₃	—	2	2	no	—
482	C₄×C₁₃	—	2	2	no	—
483	C₄×C₁₃	—	2	2	no	—
484	C₄×C₁₃	—	4	2	no	—
485	C₄×C₁₃	—	4	2	no	—
486	C₄×C₁₃	—	4	2	no	—
487	C₄×C₁₃	—	4	2	no	—
488	C₄×C₁₃	—	4	2	no	—
489	C₄×C₁₃	—	4	4	no	—
490	C₄×C₁₃	—	4	4	no	—
491	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
492	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
493	C₂×#41	—	2	4	no	—
494	C₂×#41	—	4	4	no	—
495	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
496	C₂²×D₄	—	2	4	no	—
497	C₂²×D₄	—	2	8	no	—
498	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
499	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
500	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
501	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
502	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
503	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
504	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
505	C₂³×C₄	—	2	4	no	—
506	C₂³×C₄	—	4	4	no	—
507	C₂³×C₄	—	4	4	no	—
508	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
509	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
515	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
516	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
517	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
518	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
522	#123	—	2	8	no	—
523	#123	—	4	4	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	—	2	4	no	—
526	#121	—	2	16	no	—
527	#121	—	2	4	no	—
528	#121	—	2	4	no	—
529	#120	—	2	8	no	—
530	#120	—	4	4	no	—
531	C₄×D₄	—	2	8	no	—
532	C₄×D₄	—	2	8	no	—
533	C₄×D₄	—	2	8	no	—
534	C₄×D₄	—	2	8	no	—
535	C₄×D₄	—	2	8	no	—
536	C₄×D₄	—	2	8	no	—
537	#117	—	2	4	no	—
538	C₂×C₄⋊C₄	—	2	4	no	—
539	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
548	C₂×C₂²⋊C₄	—	2	4	no	—
549	C₂×C₂²⋊C₄	—	2	4	no	—
550	C₂×C₂²⋊C₄	—	4	4	no	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
569	C₂×C₄²	—	2	4	no	—
570	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
572	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
573	#95	C₂³×C₁₃	1	2	yes	—
574	#95	C₂³×C₁₃	1	4	yes	—
575	#95	C₂³×C₁₃	1	4	yes	—
576	#95	C₂³×C₁₃	1	2	yes	—
577	#95	C₂³×C₁₃	1	2	yes	—
578	#95	C₂³×C₁₃	1	2	yes	—
579	#95	C₂³×C₁₃	1	4	yes	—
580	#95	C₂³×C₁₃	1	4	yes	—
581	#95	C₂³×C₁₃	1	4	yes	—
582	#95	C₂³×C₁₃	1	4	yes	—
583	#95	C₂³×C₁₃	1	4	yes	—
584	#95	C₂³×C₁₃	1	4	yes	—
585	C₂×C₁₃	—	2	4	no	—
586	C₂×C₁₃	—	2	4	no	—
587	C₂×C₁₃	—	4	2	no	—
588	C₂×C₁₃	—	4	4	no	—
589	C₂×C₁₃	—	8	2	no	—
590	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
591	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
592	C₂×C₁₃	#3449	1	1	yes	characteristic
593	C₂×C₁₃	#3513	1	4	yes	—
594	C₂⁴	—	2	2	no	—
595	C₂⁴	—	2	4	no	—
596	C₂⁴	—	2	4	no	—
597	C₂⁴	—	2	4	no	—
598	C₂⁴	—	2	4	no	—
599	C₂⁴	—	4	2	no	—
600	C₂⁴	—	4	2	no	—
601	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
602	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
603	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
604	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
605	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
606	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
607	#41	—	4	16	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	4	2	no	—
610	C₂×D₄	—	2	32	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	8	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	8	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	4	2	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	—	4	4	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	C₁₃×#41	1	8	yes	complemented
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	8	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	4	16	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	—	4	2	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	—	4	4	no	—
646	C₂²×C₄	—	4	4	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	4	no	—
651	C₂²×C₄	—	4	4	no	—
652	C₂²×C₄	—	4	16	no	—
653	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
654	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
655	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
656	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
657	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
658	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
659	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
660	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
661	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	8	no	—
678	C₄⋊C₄	—	4	4	no	—
679	C₄⋊C₄	—	4	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	8	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	8	no	—
693	C₂²⋊C₄	—	4	4	no	—
694	C₂²⋊C₄	—	4	4	no	—
695	C₂²⋊C₄	—	4	4	no	—
696	C₂²⋊C₄	—	4	4	no	—
697	C₂²⋊C₄	—	4	4	no	—
698	C₄²	—	2	4	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	4	no	—
701	C₁₃	#35063	1	1	yes	characteristic, direct product factor, Sylow
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	8	no	—
707	C₂³	—	2	8	no	—
708	C₂³	—	2	8	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	4	no	—
714	C₂³	—	2	4	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	4	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	4	no	—
721	C₂³	—	4	4	no	—
722	C₂³	—	4	16	no	—
723	C₂³	—	4	16	no	—
724	C₂³	—	4	4	no	—
725	C₂³	—	4	4	no	—
726	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
727	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
728	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
729	C₂³	C₂×C₁₃×#41	1	4	yes	—
730	C₂³	C₂×C₁₃×#41	1	4	yes	—
731	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
732	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
733	Q₈	—	4	4	no	—
734	D₄	—	2	16	no	—
735	D₄	—	2	16	no	—
736	D₄	—	4	4	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	8	no	—
739	D₄	—	4	8	no	—
740	D₄	—	8	8	no	—
741	C₂×C₄	—	2	8	no	—
742	C₂×C₄	—	2	8	no	—
743	C₂×C₄	—	2	8	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	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	2	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	4	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	4	4	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	—	4	4	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	8	no	—
772	C₂×C₄	—	4	8	no	—
773	C₂×C₄	—	4	8	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	8	8	no	—
777	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
778	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
779	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
780	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
781	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	8	no	—
787	C₂²	—	2	8	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	4	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	8	no	—
793	C₂²	—	4	16	no	—
794	C₂²	—	4	16	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	4	no	—
798	C₂²	—	4	4	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	4	no	—
803	C₂²	—	4	4	no	—
804	C₂²	C₁₃×#525	1	4	yes	—
805	C₂²	C₁₃×#534	1	4	yes	—
806	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
807	C₂²	C₂²×C₁₃×#41	1	2	yes	—
808	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
809	C₂²	C₁₃×#585	1	2	yes	—
810	C₄	—	2	4	no	—
811	C₄	—	2	2	no	—
812	C₄	—	2	2	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	4	no	—
821	C₄	—	4	4	no	—
822	C₂	—	2	4	no	—
823	C₂	—	2	4	no	—
824	C₂	—	4	2	no	—
825	C₂	—	4	4	no	—
826	C₂	—	8	2	no	—
827	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
828	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
829	C₂	C₁₃×#3449	1	1	yes	characteristic
830	C₂	C₁₃×#3513	1	4	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×#525	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃	C₂	semidirect
3. C₁₃×#2853	C₂	semidirect
4. C₁₃×#2849	C₂	semidirect
5. C₁₃×#2638	C₂	semidirect
6. C₁₃×#2635	C₂	semidirect
7. C₁₃×#2600	C₂	semidirect
8. C₁₃×#2564	C₂	semidirect
9. C₁₃×#2543	C₂	semidirect
10. C₁₃×#2484	C₂	semidirect
11. C₁₃×#2482	C₂	semidirect
12. C₁₃×#2412	C₂	semidirect
13. C₁₃×#2410	C₂	semidirect
14. C₁₃×#2406	C₂	semidirect
15. C₁₃×#2404	C₂	semidirect
16. C₁₃×#2325	C₂	semidirect
17. C₂×C₁₃×#381	C₂	semidirect
25. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₁₃×#121	C₂²	semidirect
29. C₂×C₁₃×#121	C₂²	semidirect
37. C₂×C₄×D₄×C₁₃	C₂²	semidirect
38. C₂×C₄×D₄×C₁₃	C₂²	semidirect
45. C₁₃×#400	C₂²	semidirect
46. C₁₃×#399	C₂²	semidirect
47. C₁₃×#398	C₂²	semidirect
48. C₁₃×#397	C₂²	semidirect
49. C₁₃×#397	C₂²	semidirect
50. C₁₃×#395	C₂²	semidirect
52. C₁₃×#394	C₂²	semidirect
53. C₁₃×#394	C₂²	semidirect
54. C₁₃×#393	C₂²	semidirect
56. C₁₃×#392	C₂²	semidirect
57. C₁₃×#388	C₂²	semidirect
58. C₁₃×#388	C₂²	semidirect
59. C₁₃×#388	C₂²	semidirect
60. C₁₃×#387	C₂²	semidirect
61. C₁₃×#387	C₂²	semidirect
62. C₁₃×#387	C₂²	semidirect
66. C₁₃×#386	C₂²	semidirect
67. C₁₃×#386	C₂²	semidirect
68. C₁₃×#386	C₂²	semidirect
69. C₁₃×#386	C₂²	semidirect
72. C₁₃×#385	C₂²	semidirect
73. C₁₃×#385	C₂²	semidirect
74. C₁₃×#385	C₂²	semidirect
79. C₁₃×#381	C₂²	semidirect
80. C₁₃×#381	C₂²	semidirect
81. C₁₃×#380	C₂²	semidirect
83. C₂×C₁₃×#95	C₂²	semidirect
84. C₂×C₁₃×#95	C₂²	semidirect
102. C₂³×C₄×C₁₃	D₄	semidirect
179. #35063	C₁₃	direct (N × H)
214. C₂×D₄×C₁₃	#41	semidirect
287. C₂×#525	C₂×C₁₃	semidirect
288. C₂²×C₄×D₄	C₂×C₁₃	semidirect
289. #2853	C₂×C₁₃	semidirect
290. #2849	C₂×C₁₃	semidirect
291. #2638	C₂×C₁₃	semidirect
292. #2635	C₂×C₁₃	semidirect
293. #2600	C₂×C₁₃	semidirect
294. #2564	C₂×C₁₃	semidirect
295. #2543	C₂×C₁₃	semidirect
296. #2484	C₂×C₁₃	semidirect
297. #2482	C₂×C₁₃	semidirect
298. #2412	C₂×C₁₃	semidirect
299. #2410	C₂×C₁₃	semidirect
300. #2406	C₂×C₁₃	semidirect
301. #2404	C₂×C₁₃	semidirect
302. #2325	C₂×C₁₃	semidirect
303. C₂×#381	C₂×C₁₃	semidirect
391. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
392. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
394. C₂×#121	C₂²×C₁₃	semidirect
395. C₂×#121	C₂²×C₁₃	semidirect
403. C₂×C₄×D₄	C₂²×C₁₃	semidirect
404. C₂×C₄×D₄	C₂²×C₁₃	semidirect
411. #400	C₂²×C₁₃	semidirect
412. #399	C₂²×C₁₃	semidirect
413. #398	C₂²×C₁₃	semidirect
414. #397	C₂²×C₁₃	semidirect
415. #397	C₂²×C₁₃	semidirect
416. #395	C₂²×C₁₃	semidirect
418. #394	C₂²×C₁₃	semidirect
419. #394	C₂²×C₁₃	semidirect
420. #393	C₂²×C₁₃	semidirect
422. #392	C₂²×C₁₃	semidirect
423. #388	C₂²×C₁₃	semidirect
424. #388	C₂²×C₁₃	semidirect
425. #388	C₂²×C₁₃	semidirect
426. #387	C₂²×C₁₃	semidirect
427. #387	C₂²×C₁₃	semidirect
428. #387	C₂²×C₁₃	semidirect
432. #386	C₂²×C₁₃	semidirect
433. #386	C₂²×C₁₃	semidirect
434. #386	C₂²×C₁₃	semidirect
435. #386	C₂²×C₁₃	semidirect
438. #385	C₂²×C₁₃	semidirect
439. #385	C₂²×C₁₃	semidirect
440. #385	C₂²×C₁₃	semidirect
445. #381	C₂²×C₁₃	semidirect
446. #381	C₂²×C₁₃	semidirect
447. #380	C₂²×C₁₃	semidirect
449. C₂×#95	C₂²×C₁₃	semidirect
450. C₂×#95	C₂²×C₁₃	semidirect
508. C₂³×C₄	D₄×C₁₃	semidirect
628. C₂×D₄	C₁₃×#41	semidirect
701. C₁₃	#35063	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×#525	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2853	2
C₁₃×#2849	2
C₁₃×#2638	2
C₁₃×#2635	2
C₁₃×#2600	2
C₁₃×#2564	2
C₁₃×#2543	2
C₁₃×#2484	2
C₁₃×#2482	2
C₁₃×#2412	2
C₁₃×#2410	2
C₁₃×#2406	2
C₁₃×#2404	2
C₁₃×#2325	2
C₂×C₁₃×#381	2
#35063	13

Subgroups — C13×#35063 #15721402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35063 #15721402