Subgroups — C₁₃×#34911 #15721250

Order 3328.

2570 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2604	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2603	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2602	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2592	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2584	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2562	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2540	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2415	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2414	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2395	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2388	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2293	C₂	1	4	yes	maximal, complemented
17	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₁₃×#529	—	2	8	no	—
20	C₂×C₁₃×#126	C₂²	1	2	yes	—
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₄×C₁₃×#41	—	2	8	no	—
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
39	C₂×C₁₃×#117	C₂²	1	2	yes	—
40	C₂×C₁₃×#117	C₂²	1	2	yes	—
41	C₂×C₁₃×#117	C₂²	1	2	yes	—
42	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
44	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#400	C₂²	1	2	yes	—
46	C₁₃×#399	C₂²	1	2	yes	—
47	C₁₃×#398	C₂²	1	2	yes	—
48	C₁₃×#397	C₂²	1	2	yes	—
49	C₁₃×#397	C₂²	1	4	yes	—
50	C₁₃×#395	C₂²	1	2	yes	—
51	C₁₃×#394	C₂²	1	2	yes	—
52	C₁₃×#394	C₂²	1	4	yes	—
53	C₁₃×#394	C₂²	1	4	yes	—
54	C₁₃×#393	C₂²	1	2	yes	—
55	C₁₃×#392	C₂²	1	2	yes	—
56	C₁₃×#392	C₂²	1	4	yes	—
57	C₁₃×#391	C₂²	1	2	yes	—
58	C₁₃×#390	C₂²	1	4	yes	—
59	C₁₃×#390	C₂²	1	4	yes	—
60	C₁₃×#390	C₂²	1	2	yes	—
61	C₁₃×#389	C₂²	1	4	yes	—
62	C₁₃×#389	C₂²	1	4	yes	—
63	C₁₃×#389	C₂²	1	2	yes	—
64	C₁₃×#389	C₂²	1	2	yes	—
65	C₁₃×#388	C₂²	1	4	yes	—
66	C₁₃×#388	C₂²	1	4	yes	—
67	C₁₃×#388	C₂²	1	4	yes	—
68	C₁₃×#388	C₂²	1	4	yes	—
69	C₁₃×#388	C₂²	1	4	yes	—
70	C₁₃×#387	C₂²	1	4	yes	—
71	C₁₃×#386	C₂²	1	4	yes	—
72	C₁₃×#385	C₂²	1	4	yes	—
73	C₁₃×#380	C₂²	1	2	yes	—
74	C₁₃×#380	C₂²	1	2	yes	—
75	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
77	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
82	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
83	C₁₃×#376	C₂²	1	2	yes	—
84	C₄³×C₁₃	C₂²	1	2	yes	—
85	C₂×C₁₃×#41	—	2	4	no	—
86	C₂×C₁₃×#41	—	2	8	no	—
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#126	—	2	8	no	—
102	C₁₃×#125	—	2	4	no	—
103	C₁₃×#124	—	2	4	no	—
104	C₁₃×#123	—	2	8	no	—
105	C₁₃×C₂²⋊Q₈	—	2	4	no	—
106	C₁₃×C₂²⋊Q₈	—	2	8	no	—
107	C₁₃×#121	—	2	4	no	—
108	C₁₃×#121	—	2	8	no	—
109	C₄×Q₈×C₁₃	—	2	4	no	—
110	C₄×Q₈×C₁₃	—	2	4	no	—
111	C₄×Q₈×C₁₃	—	2	4	no	—
112	C₄×D₄×C₁₃	—	2	8	no	—
113	C₄×D₄×C₁₃	—	2	8	no	—
114	C₄×D₄×C₁₃	—	2	8	no	—
115	C₄×D₄×C₁₃	—	2	16	no	—
116	C₄×D₄×C₁₃	—	2	4	no	—
117	C₄×D₄×C₁₃	—	2	4	no	—
118	C₄×D₄×C₁₃	—	2	4	no	—
119	C₁₃×#117	—	2	4	no	—
120	C₁₃×#117	—	2	8	no	—
121	C₁₃×#117	—	2	8	no	—
122	C₁₃×#117	—	2	8	no	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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	2	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₄²×C₁₃	—	2	8	no	—
154	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
155	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
157	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
159	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₁₃×#95	C₂³	1	4	yes	—
168	C₁₃×#95	C₂³	1	2	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	4	yes	—
173	C₁₃×#95	C₂³	1	4	yes	—
174	C₁₃×#95	C₂³	1	4	yes	—
175	C₁₃×#95	C₂³	1	4	yes	—
176	#34911	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
178	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
180	C₁₃×#41	—	2	32	no	—
181	C₂×Q₈×C₁₃	—	2	2	no	—
182	C₂×Q₈×C₁₃	—	2	2	no	—
183	C₂×Q₈×C₁₃	—	2	4	no	—
184	C₂×Q₈×C₁₃	—	2	4	no	—
185	C₂×D₄×C₁₃	—	2	4	no	—
186	C₂×D₄×C₁₃	—	2	4	no	—
187	C₂×D₄×C₁₃	—	2	4	no	—
188	C₂×D₄×C₁₃	—	2	4	no	—
189	C₂×D₄×C₁₃	—	2	8	no	—
190	C₂×D₄×C₁₃	—	2	2	no	—
191	C₂×D₄×C₁₃	—	2	2	no	—
192	C₂×D₄×C₁₃	—	2	4	no	—
193	C₂×D₄×C₁₃	—	2	8	no	—
194	C₂×D₄×C₁₃	—	2	4	no	—
195	C₂×D₄×C₁₃	—	4	4	no	—
196	C₂×D₄×C₁₃	—	4	2	no	—
197	C₂×D₄×C₁₃	—	4	2	no	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	—	2	4	no	—
200	C₂²×C₄×C₁₃	—	2	4	no	—
201	C₂²×C₄×C₁₃	—	2	4	no	—
202	C₂²×C₄×C₁₃	—	2	4	no	—
203	C₂²×C₄×C₁₃	—	2	4	no	—
204	C₂²×C₄×C₁₃	—	2	4	no	—
205	C₂²×C₄×C₁₃	—	2	8	no	—
206	C₂²×C₄×C₁₃	—	2	4	no	—
207	C₂²×C₄×C₁₃	—	2	4	no	—
208	C₂²×C₄×C₁₃	—	4	1	no	—
209	C₂²×C₄×C₁₃	—	4	1	no	—
210	C₂²×C₄×C₁₃	—	4	2	no	—
211	C₂²×C₄×C₁₃	—	4	2	no	—
212	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
215	C₂²×C₄×C₁₃	#41	1	8	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₁₃×C₄⋊C₄	—	2	4	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	2	no	—
233	C₁₃×C₄⋊C₄	—	2	2	no	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	2	4	no	—
236	C₁₃×C₄⋊C₄	—	2	2	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	—	2	2	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	4	no	—
241	C₁₃×C₄⋊C₄	—	2	8	no	—
242	C₁₃×C₄⋊C₄	—	2	8	no	—
243	C₁₃×C₄⋊C₄	—	4	4	no	—
244	C₁₃×C₄⋊C₄	#41	1	8	yes	complemented
245	C₁₃×C₂²⋊C₄	—	2	4	no	—
246	C₁₃×C₂²⋊C₄	—	2	4	no	—
247	C₁₃×C₂²⋊C₄	—	2	8	no	—
248	C₁₃×C₂²⋊C₄	—	2	4	no	—
249	C₁₃×C₂²⋊C₄	—	2	4	no	—
250	C₁₃×C₂²⋊C₄	—	2	4	no	—
251	C₁₃×C₂²⋊C₄	—	2	4	no	—
252	C₁₃×C₂²⋊C₄	—	2	4	no	—
253	C₁₃×C₂²⋊C₄	—	2	4	no	—
254	C₁₃×C₂²⋊C₄	—	2	8	no	—
255	C₁₃×C₂²⋊C₄	—	2	8	no	—
256	C₁₃×C₂²⋊C₄	—	2	8	no	—
257	C₁₃×C₂²⋊C₄	—	2	8	no	—
258	C₁₃×C₂²⋊C₄	—	4	4	no	—
259	C₁₃×C₂²⋊C₄	—	4	4	no	—
260	C₄²×C₁₃	—	2	4	no	—
261	C₄²×C₁₃	—	2	4	no	—
262	C₄²×C₁₃	—	2	4	no	—
263	C₄²×C₁₃	—	2	4	no	—
264	C₄²×C₁₃	—	2	8	no	—
265	C₄²×C₁₃	—	2	8	no	—
266	C₄²×C₁₃	—	4	2	no	—
267	C₄²×C₁₃	—	4	2	no	—
268	C₄²×C₁₃	C₂×D₄	1	4	yes	—
269	C₄²×C₁₃	C₂×D₄	1	4	yes	—
270	C₄²×C₁₃	C₂×D₄	1	4	yes	—
271	C₄²×C₁₃	C₂×D₄	1	4	yes	—
272	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#2604	C₂×C₁₃	1	2	yes	complemented
275	#2603	C₂×C₁₃	1	2	yes	complemented
276	#2602	C₂×C₁₃	1	4	yes	complemented
277	#2592	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2584	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#2562	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#2540	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#2415	C₂×C₁₃	1	2	yes	complemented
282	#2414	C₂×C₁₃	1	2	yes	complemented
283	#2395	C₂×C₁₃	1	2	yes	complemented
284	#2388	C₂×C₁₃	1	2	yes	complemented
285	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
286	C₄×#121	C₂×C₁₃	1	2	yes	complemented
287	#2293	C₂×C₁₃	1	4	yes	complemented
288	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	2	no	—
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	2	2	no	—
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	—	2	1	no	—
297	C₂³×C₁₃	—	2	1	no	—
298	C₂³×C₁₃	—	2	2	no	—
299	C₂³×C₁₃	—	2	2	no	—
300	C₂³×C₁₃	—	2	4	no	—
301	C₂³×C₁₃	—	2	4	no	—
302	C₂³×C₁₃	—	2	2	no	—
303	C₂³×C₁₃	—	2	2	no	—
304	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
305	C₂³×C₁₃	C₂×#41	1	4	yes	—
306	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
307	Q₈×C₁₃	—	2	8	no	—
308	Q₈×C₁₃	—	4	4	no	—
309	D₄×C₁₃	—	2	8	no	—
310	D₄×C₁₃	—	2	16	no	—
311	D₄×C₁₃	—	4	16	no	—
312	D₄×C₁₃	—	4	8	no	—
313	D₄×C₁₃	—	4	4	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	4	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	1	no	—
320	C₂×C₄×C₁₃	—	2	1	no	—
321	C₂×C₄×C₁₃	—	2	4	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	2	1	no	—
324	C₂×C₄×C₁₃	—	2	8	no	—
325	C₂×C₄×C₁₃	—	2	16	no	—
326	C₂×C₄×C₁₃	—	2	8	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	4	no	—
333	C₂×C₄×C₁₃	—	2	4	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	4	no	—
336	C₂×C₄×C₁₃	—	2	4	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	4	no	—
339	C₂×C₄×C₁₃	—	2	2	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	—	4	4	no	—
344	C₂×C₄×C₁₃	—	4	8	no	—
345	C₂×C₄×C₁₃	—	4	8	no	—
346	C₂×C₄×C₁₃	—	4	8	no	—
347	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
354	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
355	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
356	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
357	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
358	#529	—	2	8	no	—
359	C₂×#126	C₂²×C₁₃	1	2	yes	—
360	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×#123	C₂²×C₁₃	1	2	yes	—
363	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
365	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×#121	C₂²×C₁₃	1	2	yes	—
367	C₄×#41	—	2	8	no	—
368	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
373	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
375	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
376	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
377	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×#117	C₂²×C₁₃	1	2	yes	—
380	C₂×#117	C₂²×C₁₃	1	2	yes	—
381	C₂×#117	C₂²×C₁₃	1	2	yes	—
382	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
383	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
384	#400	C₂²×C₁₃	1	2	yes	—
385	#399	C₂²×C₁₃	1	2	yes	—
386	#398	C₂²×C₁₃	1	2	yes	—
387	#397	C₂²×C₁₃	1	2	yes	—
388	#397	C₂²×C₁₃	1	4	yes	—
389	#395	C₂²×C₁₃	1	2	yes	—
390	#394	C₂²×C₁₃	1	2	yes	—
391	#394	C₂²×C₁₃	1	4	yes	—
392	#394	C₂²×C₁₃	1	4	yes	—
393	#393	C₂²×C₁₃	1	2	yes	—
394	#392	C₂²×C₁₃	1	4	yes	—
395	#392	C₂²×C₁₃	1	2	yes	—
396	#391	C₂²×C₁₃	1	2	yes	—
397	#390	C₂²×C₁₃	1	2	yes	—
398	#390	C₂²×C₁₃	1	4	yes	—
399	#390	C₂²×C₁₃	1	4	yes	—
400	#389	C₂²×C₁₃	1	4	yes	—
401	#389	C₂²×C₁₃	1	2	yes	—
402	#389	C₂²×C₁₃	1	2	yes	—
403	#389	C₂²×C₁₃	1	4	yes	—
404	#388	C₂²×C₁₃	1	4	yes	—
405	#388	C₂²×C₁₃	1	4	yes	—
406	#388	C₂²×C₁₃	1	4	yes	—
407	#388	C₂²×C₁₃	1	4	yes	—
408	#388	C₂²×C₁₃	1	4	yes	—
409	#387	C₂²×C₁₃	1	4	yes	—
410	#386	C₂²×C₁₃	1	4	yes	—
411	#385	C₂²×C₁₃	1	4	yes	—
412	#380	C₂²×C₁₃	1	2	yes	—
413	#380	C₂²×C₁₃	1	2	yes	—
414	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
415	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
416	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
417	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
418	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
419	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
420	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
422	#376	C₂²×C₁₃	1	2	yes	—
423	C₄³	C₂²×C₁₃	1	2	yes	—
424	C₂²×C₁₃	—	2	2	no	—
425	C₂²×C₁₃	—	2	4	no	—
426	C₂²×C₁₃	—	2	2	no	—
427	C₂²×C₁₃	—	2	2	no	—
428	C₂²×C₁₃	—	2	4	no	—
429	C₂²×C₁₃	—	2	4	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	—	4	2	no	—
433	C₂²×C₁₃	—	4	2	no	—
434	C₂²×C₁₃	—	4	2	no	—
435	C₂²×C₁₃	—	4	2	no	—
436	C₂²×C₁₃	—	4	2	no	—
437	C₂²×C₁₃	—	4	2	no	—
438	C₂²×C₁₃	—	4	2	no	—
439	C₂²×C₁₃	—	4	4	no	—
440	C₂²×C₁₃	—	4	4	no	—
441	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
442	C₂²×C₁₃	C₂²×#41	1	2	yes	—
443	C₂²×C₁₃	C₂²×#41	1	2	yes	—
444	C₂²×C₁₃	#585	1	1	yes	characteristic
445	C₂²×C₁₃	#585	1	1	yes	characteristic
446	C₄×C₁₃	—	2	2	no	—
447	C₄×C₁₃	—	2	4	no	—
448	C₄×C₁₃	—	2	2	no	—
449	C₄×C₁₃	—	2	2	no	—
450	C₄×C₁₃	—	2	2	no	—
451	C₄×C₁₃	—	2	8	no	—
452	C₄×C₁₃	—	4	2	no	—
453	C₄×C₁₃	—	4	2	no	—
454	C₄×C₁₃	—	4	2	no	—
455	C₄×C₁₃	—	4	2	no	—
456	C₄×C₁₃	—	4	2	no	—
457	C₄×C₁₃	—	4	4	no	—
458	C₄×C₁₃	#525	1	4	yes	—
459	C₄×C₁₃	#532	1	4	yes	—
460	C₂×#41	—	2	4	no	—
461	C₂×#41	—	2	8	no	—
462	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
463	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
464	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
466	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
468	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
469	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
470	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
471	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
474	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
475	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
476	#126	—	2	8	no	—
477	#125	—	2	4	no	—
478	#124	—	2	4	no	—
479	#123	—	2	8	no	—
480	C₂²⋊Q₈	—	2	4	no	—
481	C₂²⋊Q₈	—	2	8	no	—
482	#121	—	2	4	no	—
483	#121	—	2	8	no	—
484	C₄×Q₈	—	2	4	no	—
485	C₄×Q₈	—	2	4	no	—
486	C₄×Q₈	—	2	4	no	—
487	C₄×D₄	—	2	8	no	—
488	C₄×D₄	—	2	8	no	—
489	C₄×D₄	—	2	8	no	—
490	C₄×D₄	—	2	16	no	—
491	C₄×D₄	—	2	4	no	—
492	C₄×D₄	—	2	4	no	—
493	C₄×D₄	—	2	4	no	—
494	#117	—	2	4	no	—
495	#117	—	2	8	no	—
496	#117	—	2	8	no	—
497	#117	—	2	8	no	—
498	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
528	C₂×C₄²	—	2	8	no	—
529	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
530	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
531	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
532	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
533	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
534	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
535	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
536	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
537	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
538	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
542	#95	C₂³×C₁₃	1	4	yes	—
543	#95	C₂³×C₁₃	1	2	yes	—
544	#95	C₂³×C₁₃	1	2	yes	—
545	#95	C₂³×C₁₃	1	4	yes	—
546	#95	C₂³×C₁₃	1	4	yes	—
547	#95	C₂³×C₁₃	1	4	yes	—
548	#95	C₂³×C₁₃	1	4	yes	—
549	#95	C₂³×C₁₃	1	4	yes	—
550	#95	C₂³×C₁₃	1	4	yes	—
551	C₂×C₁₃	—	4	2	no	—
552	C₂×C₁₃	—	4	4	no	—
553	C₂×C₁₃	—	8	2	no	—
554	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
555	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
556	C₂×C₁₃	#3449	1	1	yes	characteristic
557	C₂×C₁₃	#3475	1	2	yes	—
558	C₂×C₁₃	#3480	1	2	yes	—
559	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
560	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
561	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
562	#41	—	2	32	no	—
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	8	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	8	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	4	4	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	—	4	2	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	8	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	4	1	no	—
591	C₂²×C₄	—	4	1	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
595	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
596	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
597	C₂²×C₄	C₁₃×#41	1	8	yes	—
598	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
599	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
609	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	8	no	—
624	C₄⋊C₄	—	2	8	no	—
625	C₄⋊C₄	—	4	4	no	—
626	C₄⋊C₄	C₁₃×#41	1	8	yes	complemented
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	8	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	8	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	2	8	no	—
639	C₂²⋊C₄	—	2	8	no	—
640	C₂²⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	4	4	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	4	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	2	8	no	—
647	C₄²	—	2	8	no	—
648	C₄²	—	4	2	no	—
649	C₄²	—	4	2	no	—
650	C₄²	C₂×D₄×C₁₃	1	4	yes	—
651	C₄²	C₂×D₄×C₁₃	1	4	yes	—
652	C₄²	C₂×D₄×C₁₃	1	4	yes	—
653	C₄²	C₂×D₄×C₁₃	1	4	yes	—
654	C₁₃	#34911	1	1	yes	characteristic, direct product factor, Sylow
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
671	C₂³	C₂×C₁₃×#41	1	4	yes	—
672	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
673	Q₈	—	2	8	no	—
674	Q₈	—	4	4	no	—
675	D₄	—	2	8	no	—
676	D₄	—	2	16	no	—
677	D₄	—	4	16	no	—
678	D₄	—	4	8	no	—
679	D₄	—	4	4	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	8	no	—
691	C₂×C₄	—	2	16	no	—
692	C₂×C₄	—	2	8	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	8	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
714	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
719	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
720	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
721	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
722	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	4	4	no	—
740	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
741	C₂²	C₂²×C₁₃×#41	1	2	yes	—
742	C₂²	C₂²×C₁₃×#41	1	2	yes	—
743	C₂²	C₁₃×#585	1	1	yes	characteristic
744	C₂²	C₁₃×#585	1	1	yes	characteristic
745	C₄	—	2	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	8	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	4	no	—
757	C₄	C₁₃×#525	1	4	yes	—
758	C₄	C₁₃×#532	1	4	yes	—
759	C₂	—	4	2	no	—
760	C₂	—	4	4	no	—
761	C₂	—	8	2	no	—
762	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
763	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
764	C₂	C₁₃×#3449	1	1	yes	characteristic
765	C₂	C₁₃×#3475	1	2	yes	—
766	C₂	C₁₃×#3480	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
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. C₂×C₁₃×#529	C₂	semidirect
2. C₂×C₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#2604	C₂	semidirect
4. C₁₃×#2603	C₂	semidirect
5. C₁₃×#2602	C₂	semidirect
6. C₁₃×#2592	C₂	semidirect
7. C₁₃×#2584	C₂	semidirect
8. C₁₃×#2562	C₂	semidirect
9. C₁₃×#2540	C₂	semidirect
10. C₁₃×#2415	C₂	semidirect
11. C₁₃×#2414	C₂	semidirect
12. C₁₃×#2395	C₂	semidirect
13. C₁₃×#2388	C₂	semidirect
14. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
15. C₄×C₁₃×#121	C₂	semidirect
16. C₁₃×#2293	C₂	semidirect
17. C₄×C₁₃×#117	C₂	semidirect
154. C₂×C₄²×C₁₃	D₄	semidirect
176. #34911	C₁₃	direct (N × H)
244. C₁₃×C₄⋊C₄	#41	semidirect
272. C₂×#529	C₂×C₁₃	semidirect
273. C₂×C₄×#41	C₂×C₁₃	semidirect
274. #2604	C₂×C₁₃	semidirect
275. #2603	C₂×C₁₃	semidirect
276. #2602	C₂×C₁₃	semidirect
277. #2592	C₂×C₁₃	semidirect
278. #2584	C₂×C₁₃	semidirect
279. #2562	C₂×C₁₃	semidirect
280. #2540	C₂×C₁₃	semidirect
281. #2415	C₂×C₁₃	semidirect
282. #2414	C₂×C₁₃	semidirect
283. #2395	C₂×C₁₃	semidirect
284. #2388	C₂×C₁₃	semidirect
285. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
286. C₄×#121	C₂×C₁₃	semidirect
287. #2293	C₂×C₁₃	semidirect
288. C₄×#117	C₂×C₁₃	semidirect
529. C₂×C₄²	D₄×C₁₃	semidirect
626. C₄⋊C₄	C₁₃×#41	semidirect
654. C₁₃	#34911	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×#529	2
C₂×C₄×C₁₃×#41	2
C₁₃×#2604	2
C₁₃×#2603	2
C₁₃×#2602	2
C₁₃×#2592	2
C₁₃×#2584	2
C₁₃×#2562	2
C₁₃×#2540	2
C₁₃×#2415	2
C₁₃×#2414	2
C₁₃×#2395	2
C₁₃×#2388	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#121	2
C₁₃×#2293	2
C₄×C₁₃×#117	2
#34911	13

Subgroups — C13×#34911 #15721250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34911 #15721250