Subgroups — C₁₃×#34603 #15720942

Order 3328.

1716 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2666	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2662	C₂	1	2	yes	maximal
3	C₁₃×#2654	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2651	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2651	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2650	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2637	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2632	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2398	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2396	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2396	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2395	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2392	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₃×#126	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₃×#124	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2298	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#126	C₂²	1	2	yes	—
21	C₂×C₁₃×#124	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
27	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#117	C₂²	1	2	yes	—
29	C₁₃×#400	C₂²	1	1	yes	characteristic
30	C₁₃×#400	C₂²	1	2	yes	—
31	C₁₃×#400	C₂²	1	2	yes	—
32	C₁₃×#400	C₂²	1	2	yes	—
33	C₁₃×#399	C₂²	1	2	yes	—
34	C₁₃×#399	C₂²	1	2	yes	—
35	C₁₃×#399	C₂²	1	1	yes	characteristic
36	C₁₃×#398	C₂²	1	2	yes	—
37	C₁₃×#398	C₂²	1	2	yes	—
38	C₁₃×#398	C₂²	1	2	yes	—
39	C₁₃×#398	C₂²	1	1	yes	characteristic
40	C₁₃×#398	C₂²	1	2	yes	—
41	C₁₃×#398	C₂²	1	2	yes	—
42	C₁₃×#398	C₂²	1	2	yes	—
43	C₁₃×#397	C₂²	1	2	yes	—
44	C₁₃×#397	C₂²	1	1	yes	characteristic
45	C₁₃×#397	C₂²	1	2	yes	—
46	C₁₃×#397	C₂²	1	2	yes	—
47	C₁₃×#397	C₂²	1	2	yes	—
48	C₁₃×#396	C₂²	1	2	yes	—
49	C₁₃×#396	C₂²	1	2	yes	—
50	C₁₃×#396	C₂²	1	2	yes	—
51	C₁₃×#396	C₂²	1	2	yes	—
52	C₁₃×#395	C₂²	1	2	yes	—
53	C₁₃×#395	C₂²	1	2	yes	—
54	C₁₃×#395	C₂²	1	1	yes	characteristic
55	C₁₃×#395	C₂²	1	2	yes	—
56	C₁₃×#394	C₂²	1	2	yes	—
57	C₁₃×#394	C₂²	1	2	yes	—
58	C₁₃×#394	C₂²	1	1	yes	characteristic
59	C₁₃×#394	C₂²	1	2	yes	—
60	C₁₃×#394	C₂²	1	2	yes	—
61	C₁₃×#393	C₂²	1	1	yes	characteristic
62	C₁₃×#393	C₂²	1	2	yes	—
63	C₁₃×#393	C₂²	1	2	yes	—
64	C₁₃×#392	C₂²	1	1	yes	characteristic
65	C₁₃×#391	C₂²	1	2	yes	—
66	C₁₃×#390	C₂²	1	2	yes	—
67	C₁₃×#390	C₂²	1	2	yes	—
68	C₁₃×#389	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	—
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	—
80	C₁₃×#387	C₂²	1	2	yes	—
81	C₁₃×#387	C₂²	1	2	yes	—
82	C₁₃×#387	C₂²	1	2	yes	—
83	C₁₃×#387	C₂²	1	2	yes	—
84	C₁₃×#387	C₂²	1	2	yes	—
85	C₁₃×#383	C₂²	1	2	yes	—
86	C₁₃×#382	C₂²	1	2	yes	—
87	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
88	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
89	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
90	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
91	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₁₃×#376	C₂²	1	1	yes	characteristic
105	C₄³×C₁₃	C₂²	1	1	yes	characteristic
106	C₄³×C₁₃	C₂²	1	2	yes	—
107	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
113	C₁₃×#126	—	2	8	no	—
114	C₁₃×#124	—	2	8	no	—
115	C₄×Q₈×C₁₃	—	2	4	no	—
116	C₄×Q₈×C₁₃	—	2	8	no	—
117	C₄×Q₈×C₁₃	—	4	4	no	—
118	C₄×D₄×C₁₃	—	2	4	no	—
119	C₄×D₄×C₁₃	—	4	4	no	—
120	C₁₃×#117	—	2	4	no	—
121	C₁₃×#117	—	4	4	no	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	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	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	2	yes	—
142	C₂×C₁₃×C₄⋊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	2	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	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×C₄²×C₁₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
177	C₁₃×#95	C₂³	1	2	yes	—
178	C₁₃×#95	C₂³	1	2	yes	—
179	C₁₃×#95	C₂³	1	2	yes	—
180	C₁₃×#95	C₂³	1	2	yes	—
181	C₁₃×#95	C₂³	1	2	yes	—
182	C₁₃×#95	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	1	yes	characteristic
190	C₁₃×#95	C₂³	1	2	yes	—
191	C₁₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
199	C₁₃×#95	C₂³	1	1	yes	characteristic
200	C₁₃×#95	C₂³	1	1	yes	characteristic
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	#34603	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
205	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
206	C₂×Q₈×C₁₃	—	2	2	no	—
207	C₂×Q₈×C₁₃	—	2	4	no	—
208	C₂×Q₈×C₁₃	—	2	4	no	—
209	C₂×Q₈×C₁₃	—	4	2	no	—
210	C₂×Q₈×C₁₃	—	4	2	no	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	2	4	no	—
213	C₂×D₄×C₁₃	—	4	2	no	—
214	C₂×D₄×C₁₃	—	4	2	no	—
215	C₂×D₄×C₁₃	—	4	2	no	—
216	C₂²×C₄×C₁₃	—	2	2	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	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₁₃×C₄⋊C₄	—	2	2	no	—
240	C₁₃×C₄⋊C₄	—	2	2	no	—
241	C₁₃×C₄⋊C₄	—	2	2	no	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	4	no	—
244	C₁₃×C₄⋊C₄	—	2	4	no	—
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	4	2	no	—
251	C₁₃×C₄⋊C₄	—	4	2	no	—
252	C₁₃×C₄⋊C₄	—	4	2	no	—
253	C₁₃×C₄⋊C₄	—	4	2	no	—
254	C₁₃×C₄⋊C₄	—	4	2	no	—
255	C₁₃×C₄⋊C₄	—	4	2	no	—
256	C₁₃×C₄⋊C₄	—	4	2	no	—
257	C₁₃×C₄⋊C₄	—	4	2	no	—
258	C₁₃×C₄⋊C₄	—	4	2	no	—
259	C₁₃×C₄⋊C₄	—	4	2	no	—
260	C₁₃×C₂²⋊C₄	—	2	2	no	—
261	C₁₃×C₂²⋊C₄	—	2	2	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	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	—	4	2	no	—
271	C₁₃×C₂²⋊C₄	—	4	2	no	—
272	C₁₃×C₂²⋊C₄	—	4	2	no	—
273	C₁₃×C₂²⋊C₄	—	4	2	no	—
274	C₁₃×C₂²⋊C₄	—	4	2	no	—
275	C₁₃×C₂²⋊C₄	—	4	2	no	—
276	C₁₃×C₂²⋊C₄	—	4	2	no	—
277	C₁₃×C₂²⋊C₄	—	4	2	no	—
278	C₁₃×C₂²⋊C₄	—	4	2	no	—
279	C₄²×C₁₃	—	2	2	no	—
280	C₄²×C₁₃	—	2	4	no	—
281	C₄²×C₁₃	—	2	4	no	—
282	C₄²×C₁₃	—	2	4	no	—
283	C₄²×C₁₃	—	2	2	no	—
284	C₄²×C₁₃	—	2	4	no	—
285	C₄²×C₁₃	—	2	4	no	—
286	C₄²×C₁₃	—	2	2	no	—
287	C₄²×C₁₃	—	2	2	no	—
288	C₄²×C₁₃	—	2	2	no	—
289	C₄²×C₁₃	—	4	2	no	—
290	C₄²×C₁₃	—	4	2	no	—
291	C₄²×C₁₃	—	4	2	no	—
292	C₄²×C₁₃	#41	1	4	yes	—
293	C₄²×C₁₃	#41	1	8	yes	—
294	#2666	C₂×C₁₃	1	2	yes	complemented
295	#2662	C₂×C₁₃	1	2	yes	—
296	#2654	C₂×C₁₃	1	2	yes	complemented
297	#2651	C₂×C₁₃	1	2	yes	complemented
298	#2651	C₂×C₁₃	1	2	yes	complemented
299	#2650	C₂×C₁₃	1	2	yes	complemented
300	#2637	C₂×C₁₃	1	2	yes	complemented
301	#2632	C₂×C₁₃	1	2	yes	complemented
302	#2399	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2398	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#2396	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#2396	C₂×C₁₃	1	2	yes	complemented
306	#2395	C₂×C₁₃	1	2	yes	complemented
307	#2392	C₂×C₁₃	1	1	yes	characteristic
308	C₄×#126	C₂×C₁₃	1	2	yes	complemented
309	C₄×#124	C₂×C₁₃	1	2	yes	complemented
310	#2298	C₂×C₁₃	1	1	yes	characteristic, complemented
311	#2293	C₂×C₁₃	1	1	yes	characteristic, complemented
312	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	1	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	2	no	—
319	C₂³×C₁₃	—	2	1	no	—
320	C₂³×C₁₃	—	2	1	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	—	2	2	no	—
325	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
326	Q₈×C₁₃	—	2	8	no	—
327	Q₈×C₁₃	—	4	8	no	—
328	D₄×C₁₃	—	4	4	no	—
329	D₄×C₁₃	—	4	8	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	1	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	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	2	no	—
349	C₂×C₄×C₁₃	—	2	1	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	1	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	1	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	4	4	no	—
370	C₂×C₄×C₁₃	—	4	8	no	—
371	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
372	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
373	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
374	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
375	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
376	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
377	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
378	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
379	C₂×#126	C₂²×C₁₃	1	2	yes	—
380	C₂×#124	C₂²×C₁₃	1	2	yes	—
381	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
382	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
384	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
386	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#117	C₂²×C₁₃	1	2	yes	—
388	#400	C₂²×C₁₃	1	1	yes	characteristic
389	#400	C₂²×C₁₃	1	2	yes	—
390	#400	C₂²×C₁₃	1	2	yes	—
391	#400	C₂²×C₁₃	1	2	yes	—
392	#399	C₂²×C₁₃	1	2	yes	—
393	#399	C₂²×C₁₃	1	2	yes	—
394	#399	C₂²×C₁₃	1	1	yes	characteristic
395	#398	C₂²×C₁₃	1	2	yes	—
396	#398	C₂²×C₁₃	1	2	yes	—
397	#398	C₂²×C₁₃	1	2	yes	—
398	#398	C₂²×C₁₃	1	1	yes	characteristic
399	#398	C₂²×C₁₃	1	2	yes	—
400	#398	C₂²×C₁₃	1	2	yes	—
401	#398	C₂²×C₁₃	1	2	yes	—
402	#397	C₂²×C₁₃	1	2	yes	—
403	#397	C₂²×C₁₃	1	1	yes	characteristic
404	#397	C₂²×C₁₃	1	2	yes	—
405	#397	C₂²×C₁₃	1	2	yes	—
406	#397	C₂²×C₁₃	1	2	yes	—
407	#396	C₂²×C₁₃	1	2	yes	—
408	#396	C₂²×C₁₃	1	2	yes	—
409	#396	C₂²×C₁₃	1	2	yes	—
410	#396	C₂²×C₁₃	1	2	yes	—
411	#395	C₂²×C₁₃	1	2	yes	—
412	#395	C₂²×C₁₃	1	2	yes	—
413	#395	C₂²×C₁₃	1	1	yes	characteristic
414	#395	C₂²×C₁₃	1	2	yes	—
415	#394	C₂²×C₁₃	1	2	yes	—
416	#394	C₂²×C₁₃	1	2	yes	—
417	#394	C₂²×C₁₃	1	1	yes	characteristic
418	#394	C₂²×C₁₃	1	2	yes	—
419	#394	C₂²×C₁₃	1	2	yes	—
420	#393	C₂²×C₁₃	1	1	yes	characteristic
421	#393	C₂²×C₁₃	1	2	yes	—
422	#393	C₂²×C₁₃	1	2	yes	—
423	#392	C₂²×C₁₃	1	1	yes	characteristic
424	#391	C₂²×C₁₃	1	2	yes	—
425	#390	C₂²×C₁₃	1	2	yes	—
426	#390	C₂²×C₁₃	1	2	yes	—
427	#389	C₂²×C₁₃	1	2	yes	—
428	#388	C₂²×C₁₃	1	2	yes	—
429	#388	C₂²×C₁₃	1	2	yes	—
430	#388	C₂²×C₁₃	1	2	yes	—
431	#388	C₂²×C₁₃	1	2	yes	—
432	#388	C₂²×C₁₃	1	2	yes	—
433	#388	C₂²×C₁₃	1	2	yes	—
434	#388	C₂²×C₁₃	1	2	yes	—
435	#388	C₂²×C₁₃	1	2	yes	—
436	#388	C₂²×C₁₃	1	2	yes	—
437	#388	C₂²×C₁₃	1	2	yes	—
438	#388	C₂²×C₁₃	1	2	yes	—
439	#387	C₂²×C₁₃	1	2	yes	—
440	#387	C₂²×C₁₃	1	2	yes	—
441	#387	C₂²×C₁₃	1	2	yes	—
442	#387	C₂²×C₁₃	1	2	yes	—
443	#387	C₂²×C₁₃	1	2	yes	—
444	#383	C₂²×C₁₃	1	2	yes	—
445	#382	C₂²×C₁₃	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
448	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
449	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
451	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
452	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
453	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
456	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
457	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
460	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
461	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
462	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
463	#376	C₂²×C₁₃	1	1	yes	characteristic
464	C₄³	C₂²×C₁₃	1	2	yes	—
465	C₄³	C₂²×C₁₃	1	1	yes	characteristic
466	C₂²×C₁₃	—	4	2	no	—
467	C₂²×C₁₃	—	4	1	no	—
468	C₂²×C₁₃	—	4	1	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	1	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	2	no	—
476	C₂²×C₁₃	—	4	2	no	—
477	C₂²×C₁₃	—	4	2	no	—
478	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
479	C₂²×C₁₃	C₂²×#41	1	2	yes	—
480	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
481	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
482	C₂²×C₁₃	#585	1	2	yes	—
483	C₄×C₁₃	—	2	4	no	—
484	C₄×C₁₃	—	2	2	no	—
485	C₄×C₁₃	—	2	2	no	—
486	C₄×C₁₃	—	2	4	no	—
487	C₄×C₁₃	—	2	4	no	—
488	C₄×C₁₃	—	4	1	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	—	4	1	no	—
491	C₄×C₁₃	—	4	1	no	—
492	C₄×C₁₃	—	4	2	no	—
493	C₄×C₁₃	—	4	2	no	—
494	C₄×C₁₃	—	4	2	no	—
495	C₄×C₁₃	—	4	2	no	—
496	C₄×C₁₃	—	4	2	no	—
497	C₄×C₁₃	—	4	2	no	—
498	C₄×C₁₃	—	4	2	no	—
499	C₄×C₁₃	#542	1	4	yes	—
500	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
501	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
502	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
503	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
506	#126	—	2	8	no	—
507	#124	—	2	8	no	—
508	C₄×Q₈	—	2	4	no	—
509	C₄×Q₈	—	2	8	no	—
510	C₄×Q₈	—	4	4	no	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	4	4	no	—
513	#117	—	2	4	no	—
514	#117	—	4	4	no	—
515	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
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	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×C₄²	C₂³×C₁₃	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
557	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
559	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
561	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
562	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
563	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
566	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
567	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
568	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
570	#95	C₂³×C₁₃	1	2	yes	—
571	#95	C₂³×C₁₃	1	2	yes	—
572	#95	C₂³×C₁₃	1	2	yes	—
573	#95	C₂³×C₁₃	1	2	yes	—
574	#95	C₂³×C₁₃	1	2	yes	—
575	#95	C₂³×C₁₃	1	2	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	2	yes	—
580	#95	C₂³×C₁₃	1	2	yes	—
581	#95	C₂³×C₁₃	1	2	yes	—
582	#95	C₂³×C₁₃	1	2	yes	—
583	#95	C₂³×C₁₃	1	2	yes	—
584	#95	C₂³×C₁₃	1	1	yes	characteristic
585	#95	C₂³×C₁₃	1	2	yes	—
586	#95	C₂³×C₁₃	1	1	yes	characteristic
587	#95	C₂³×C₁₃	1	2	yes	—
588	#95	C₂³×C₁₃	1	2	yes	—
589	#95	C₂³×C₁₃	1	2	yes	—
590	#95	C₂³×C₁₃	1	2	yes	—
591	#95	C₂³×C₁₃	1	2	yes	—
592	#95	C₂³×C₁₃	1	2	yes	—
593	#95	C₂³×C₁₃	1	2	yes	—
594	#95	C₂³×C₁₃	1	1	yes	characteristic
595	#95	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×C₁₃	—	8	2	no	—
597	C₂×C₁₃	—	8	1	no	—
598	C₂×C₁₃	#3444	1	1	yes	characteristic
599	C₂×C₁₃	C₂×#542	1	1	yes	characteristic
600	C₂×C₁₃	#3455	1	1	yes	characteristic
601	C₂×C₁₃	#3460	1	2	yes	—
602	C₂×C₁₃	#3461	1	2	yes	—
603	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
604	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	2	4	no	—
607	C₂×Q₈	—	2	4	no	—
608	C₂×Q₈	—	4	2	no	—
609	C₂×Q₈	—	4	2	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	4	2	no	—
613	C₂×D₄	—	4	2	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	4	2	no	—
670	C₂²⋊C₄	—	4	2	no	—
671	C₂²⋊C₄	—	4	2	no	—
672	C₂²⋊C₄	—	4	2	no	—
673	C₂²⋊C₄	—	4	2	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₂²⋊C₄	—	4	2	no	—
676	C₂²⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₄²	—	2	2	no	—
679	C₄²	—	2	4	no	—
680	C₄²	—	2	4	no	—
681	C₄²	—	2	4	no	—
682	C₄²	—	2	2	no	—
683	C₄²	—	2	4	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	2	no	—
686	C₄²	—	2	2	no	—
687	C₄²	—	2	2	no	—
688	C₄²	—	4	2	no	—
689	C₄²	—	4	2	no	—
690	C₄²	—	4	2	no	—
691	C₄²	C₁₃×#41	1	4	yes	—
692	C₄²	C₁₃×#41	1	8	yes	—
693	C₁₃	#34603	1	1	yes	characteristic, direct product factor, Sylow
694	C₂³	—	2	2	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
707	Q₈	—	2	8	no	—
708	Q₈	—	4	8	no	—
709	D₄	—	4	4	no	—
710	D₄	—	4	8	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	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	—	4	4	no	—
751	C₂×C₄	—	4	8	no	—
752	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
753	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
754	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
755	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
756	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
757	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
758	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
759	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
773	C₂²	C₂²×C₁₃×#41	1	2	yes	—
774	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
775	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
776	C₂²	C₁₃×#585	1	2	yes	—
777	C₄	—	2	4	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	2	4	no	—
781	C₄	—	2	4	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	C₁₃×#542	1	4	yes	—
794	C₂	—	8	2	no	—
795	C₂	—	8	1	no	—
796	C₂	C₁₃×#3444	1	1	yes	characteristic
797	C₂	C₂×C₁₃×#542	1	1	yes	characteristic
798	C₂	C₁₃×#3455	1	1	yes	characteristic
799	C₂	C₁₃×#3460	1	2	yes	—
800	C₂	C₁₃×#3461	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₁₃×#392	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2666	C₂	semidirect
3. C₁₃×#2654	C₂	semidirect
4. C₁₃×#2651	C₂	semidirect
5. C₁₃×#2651	C₂	semidirect
6. C₁₃×#2650	C₂	semidirect
7. C₁₃×#2637	C₂	semidirect
8. C₁₃×#2632	C₂	semidirect
9. C₁₃×#2399	C₂	semidirect
10. C₁₃×#2398	C₂	semidirect
11. C₁₃×#2396	C₂	semidirect
12. C₁₃×#2396	C₂	semidirect
13. C₁₃×#2395	C₂	semidirect
15. C₄×C₁₃×#126	C₂	semidirect
16. C₄×C₁₃×#124	C₂	semidirect
17. C₁₃×#2298	C₂	semidirect
18. C₁₃×#2293	C₂	semidirect
19. C₄²×Q₈×C₁₃	C₂	semidirect
203. #34603	C₁₃	direct (N × H)
294. #2666	C₂×C₁₃	semidirect
296. #2654	C₂×C₁₃	semidirect
297. #2651	C₂×C₁₃	semidirect
298. #2651	C₂×C₁₃	semidirect
299. #2650	C₂×C₁₃	semidirect
300. #2637	C₂×C₁₃	semidirect
301. #2632	C₂×C₁₃	semidirect
302. #2399	C₂×C₁₃	semidirect
303. #2398	C₂×C₁₃	semidirect
304. #2396	C₂×C₁₃	semidirect
305. #2396	C₂×C₁₃	semidirect
306. #2395	C₂×C₁₃	semidirect
308. C₄×#126	C₂×C₁₃	semidirect
309. C₄×#124	C₂×C₁₃	semidirect
310. #2298	C₂×C₁₃	semidirect
311. #2293	C₂×C₁₃	semidirect
312. C₄²×Q₈	C₂×C₁₃	semidirect
693. C₁₃	#34603	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×#2666	2
C₁₃×#2662	2
C₁₃×#2654	2
C₁₃×#2651	2
C₁₃×#2650	2
C₁₃×#2637	2
C₁₃×#2632	2
C₁₃×#2399	2
C₁₃×#2398	2
C₁₃×#2396	2
C₁₃×#2395	2
C₁₃×#2392	2
C₄×C₁₃×#126	2
C₄×C₁₃×#124	2
C₁₃×#2298	2
C₁₃×#2293	2
C₄²×Q₈×C₁₃	2
#34603	13

Subgroups — C13×#34603 #15720942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34603 #15720942