Subgroups — C₁₃×#34738 #15721077

Order 3328.

5570 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#532	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2432	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2431	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2430	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2410	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2388	C₂	1	4	yes	maximal, complemented
13	C₄×C₁₃×#120	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2297	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	—	2	16	no	—
17	C₂²×C₁₃×#41	—	2	8	no	—
18	C₂²×C₁₃×#41	C₂²	1	2	yes	—
19	C₂²×C₁₃×#41	C₂²	1	2	yes	—
20	C₂²×C₁₃×#41	C₂²	1	2	yes	—
21	C₂²×C₁₃×#41	C₂²	1	2	yes	—
22	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
23	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
25	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
27	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#532	—	2	16	no	—
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
32	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
33	C₁₃×#525	—	2	8	no	—
34	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
39	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#120	C₂²	1	4	yes	—
41	C₂×C₁₃×#120	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
44	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
45	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
47	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
48	C₁₃×#395	C₂²	1	4	yes	complemented
49	C₁₃×#394	C₂²	1	8	yes	complemented
50	C₁₃×#394	C₂²	1	4	yes	complemented
51	C₁₃×#393	C₂²	1	4	yes	complemented
52	C₁₃×#392	C₂²	1	8	yes	complemented
53	C₁₃×#392	C₂²	1	4	yes	complemented
54	C₁₃×#391	C₂²	1	2	yes	complemented
55	C₁₃×#391	C₂²	1	2	yes	complemented
56	C₁₃×#390	C₂²	1	2	yes	complemented
57	C₁₃×#390	C₂²	1	2	yes	complemented
58	C₁₃×#386	C₂²	1	4	yes	—
59	C₁₃×#386	C₂²	1	8	yes	complemented
60	C₁₃×#386	C₂²	1	8	yes	complemented
61	C₁₃×#385	C₂²	1	4	yes	—
62	C₁₃×#385	C₂²	1	8	yes	complemented
63	C₁₃×#379	C₂²	1	4	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
68	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
69	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
70	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
71	C₂⁵×C₁₃	C₂³	1	2	yes	—
72	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×#41	—	2	128	no	—
74	C₂×C₁₃×#41	—	2	8	no	—
75	C₂×C₁₃×#41	—	2	16	no	—
76	C₂×C₁₃×#41	—	2	8	no	—
77	C₂×C₁₃×#41	—	2	16	no	—
78	C₂×C₁₃×#41	—	2	8	no	—
79	C₂×C₁₃×#41	—	2	8	no	—
80	C₂×C₁₃×#41	—	2	8	no	—
81	C₂×C₁₃×#41	—	2	8	no	—
82	C₂×C₁₃×#41	—	2	8	no	—
83	C₂×C₁₃×#41	—	2	4	no	—
84	C₂×C₁₃×#41	—	2	8	no	—
85	C₂×C₁₃×#41	D₄	1	16	yes	complemented
86	C₂²×Q₈×C₁₃	—	2	8	no	—
87	C₂²×Q₈×C₁₃	—	2	4	no	—
88	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃	—	2	8	no	—
92	C₂²×D₄×C₁₃	—	2	16	no	—
93	C₂²×D₄×C₁₃	—	2	8	no	—
94	C₂²×D₄×C₁₃	—	2	4	no	—
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	2	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
101	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
102	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
103	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃	—	2	8	no	—
105	C₂³×C₄×C₁₃	—	2	16	no	—
106	C₂³×C₄×C₁₃	—	2	8	no	—
107	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
108	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
110	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃	C₂³	1	4	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	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	—	2	8	no	—
120	C₁₃×#127	—	2	8	no	—
121	C₁₃×#124	—	2	8	no	—
122	C₁₃×#124	—	2	8	no	—
123	C₁₃×#123	—	2	8	no	—
124	C₁₃×C₂²⋊Q₈	—	2	4	no	—
125	C₁₃×C₂²⋊Q₈	—	2	4	no	—
126	C₁₃×#121	—	2	32	no	—
127	C₁₃×#121	—	2	4	no	—
128	C₁₃×#121	—	2	4	no	—
129	C₁₃×#120	—	2	8	no	—
130	C₁₃×#120	—	2	16	no	—
131	C₄×D₄×C₁₃	—	2	8	no	—
132	C₄×D₄×C₁₃	—	2	8	no	—
133	C₄×D₄×C₁₃	—	2	32	no	—
134	C₁₃×#117	—	2	4	no	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	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	8	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃	—	2	8	no	—
154	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
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	C₁₃×#95	C₂³	1	4	yes	—
159	C₁₃×#95	C₂³	1	2	yes	—
160	C₁₃×#95	C₂³	1	2	yes	—
161	C₁₃×#95	C₂³	1	8	yes	—
162	C₁₃×#95	C₂³	1	8	yes	—
163	#34738	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂⁴×C₁₃	—	2	8	no	—
165	C₂⁴×C₁₃	—	2	4	no	—
166	C₂⁴×C₁₃	—	2	4	no	—
167	C₂⁴×C₁₃	—	2	4	no	—
168	C₂⁴×C₁₃	—	2	8	no	—
169	C₂⁴×C₁₃	—	4	2	no	—
170	C₂⁴×C₁₃	—	4	4	no	—
171	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
172	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
173	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
175	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₁₃×#41	—	2	64	no	—
178	C₁₃×#41	—	2	64	no	—
179	C₁₃×#41	—	2	64	no	—
180	C₁₃×#41	—	2	64	no	—
181	C₁₃×#41	—	4	16	no	—
182	C₂×Q₈×C₁₃	—	2	32	no	—
183	C₂×Q₈×C₁₃	—	2	8	no	—
184	C₂×Q₈×C₁₃	—	2	4	no	—
185	C₂×Q₈×C₁₃	—	2	4	no	—
186	C₂×Q₈×C₁₃	—	2	4	no	—
187	C₂×Q₈×C₁₃	—	2	2	no	—
188	C₂×Q₈×C₁₃	—	2	4	no	—
189	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
190	C₂×D₄×C₁₃	—	2	64	no	—
191	C₂×D₄×C₁₃	—	2	32	no	—
192	C₂×D₄×C₁₃	—	2	8	no	—
193	C₂×D₄×C₁₃	—	2	8	no	—
194	C₂×D₄×C₁₃	—	2	8	no	—
195	C₂×D₄×C₁₃	—	2	8	no	—
196	C₂×D₄×C₁₃	—	2	8	no	—
197	C₂×D₄×C₁₃	—	2	4	no	—
198	C₂×D₄×C₁₃	—	2	4	no	—
199	C₂×D₄×C₁₃	—	2	16	no	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	8	no	—
202	C₂×D₄×C₁₃	—	2	8	no	—
203	C₂×D₄×C₁₃	—	2	8	no	—
204	C₂×D₄×C₁₃	—	2	4	no	—
205	C₂×D₄×C₁₃	—	2	4	no	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	2	no	—
208	C₂×D₄×C₁₃	—	2	4	no	—
209	C₂×D₄×C₁₃	—	2	16	no	—
210	C₂×D₄×C₁₃	—	4	8	no	—
211	C₂×D₄×C₁₃	—	4	4	no	—
212	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	—
213	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
214	C₂²×C₄×C₁₃	—	2	64	no	—
215	C₂²×C₄×C₁₃	—	2	4	no	—
216	C₂²×C₄×C₁₃	—	2	8	no	—
217	C₂²×C₄×C₁₃	—	2	4	no	—
218	C₂²×C₄×C₁₃	—	2	32	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	8	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	8	no	—
223	C₂²×C₄×C₁₃	—	2	8	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	2	8	no	—
226	C₂²×C₄×C₁₃	—	2	8	no	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	—	2	8	no	—
229	C₂²×C₄×C₁₃	—	2	4	no	—
230	C₂²×C₄×C₁₃	—	2	8	no	—
231	C₂²×C₄×C₁₃	—	2	8	no	—
232	C₂²×C₄×C₁₃	—	4	4	no	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
234	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
235	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
236	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
237	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
238	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
240	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₁₃×C₄⋊C₄	—	2	2	no	—
252	C₁₃×C₄⋊C₄	—	2	2	no	—
253	C₁₃×C₄⋊C₄	—	2	16	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₂²⋊C₄	—	2	4	no	—
257	C₁₃×C₂²⋊C₄	—	2	4	no	—
258	C₁₃×C₂²⋊C₄	—	2	4	no	—
259	C₁₃×C₂²⋊C₄	—	2	16	no	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	4	no	—
262	C₁₃×C₂²⋊C₄	—	2	4	no	—
263	C₁₃×C₂²⋊C₄	—	2	16	no	—
264	C₁₃×C₂²⋊C₄	—	2	8	no	—
265	C₁₃×C₂²⋊C₄	—	2	16	no	—
266	C₁₃×C₂²⋊C₄	—	4	8	no	—
267	C₁₃×C₂²⋊C₄	#41	1	8	yes	complemented
268	C₄²×C₁₃	—	2	8	no	—
269	C₄²×C₁₃	—	2	4	no	—
270	C₄²×C₁₃	—	2	4	no	—
271	C₄²×C₁₃	—	2	4	no	—
272	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₂×#532	C₂×C₁₃	1	2	yes	complemented
274	C₂×#525	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#2436	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#2435	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#2434	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2433	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#2432	C₂×C₁₃	1	2	yes	complemented
280	#2431	C₂×C₁₃	1	2	yes	complemented
281	#2430	C₂×C₁₃	1	4	yes	complemented
282	#2410	C₂×C₁₃	1	4	yes	complemented
283	#2388	C₂×C₁₃	1	4	yes	complemented
284	C₄×#120	C₂×C₁₃	1	4	yes	complemented
285	#2297	C₂×C₁₃	1	2	yes	complemented
286	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	2	no	—
291	C₂³×C₁₃	—	2	16	no	—
292	C₂³×C₁₃	—	2	8	no	—
293	C₂³×C₁₃	—	2	8	no	—
294	C₂³×C₁₃	—	2	4	no	—
295	C₂³×C₁₃	—	2	4	no	—
296	C₂³×C₁₃	—	2	2	no	—
297	C₂³×C₁₃	—	2	2	no	—
298	C₂³×C₁₃	—	2	8	no	—
299	C₂³×C₁₃	—	2	8	no	—
300	C₂³×C₁₃	—	2	2	no	—
301	C₂³×C₁₃	—	2	2	no	—
302	C₂³×C₁₃	—	2	4	no	—
303	C₂³×C₁₃	—	2	4	no	—
304	C₂³×C₁₃	—	2	4	no	—
305	C₂³×C₁₃	—	4	4	no	—
306	C₂³×C₁₃	—	4	16	no	—
307	C₂³×C₁₃	—	4	32	no	—
308	C₂³×C₁₃	—	4	8	no	—
309	C₂³×C₁₃	—	4	8	no	—
310	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
311	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
312	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
313	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
314	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
315	C₂³×C₁₃	C₂×#41	1	4	yes	—
316	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
317	Q₈×C₁₃	—	2	16	no	—
318	Q₈×C₁₃	—	2	16	no	—
319	Q₈×C₁₃	—	4	4	no	—
320	D₄×C₁₃	—	2	32	no	—
321	D₄×C₁₃	—	2	16	no	—
322	D₄×C₁₃	—	2	32	no	—
323	D₄×C₁₃	—	2	16	no	—
324	D₄×C₁₃	—	4	32	no	—
325	D₄×C₁₃	—	4	8	no	—
326	D₄×C₁₃	—	4	8	no	—
327	D₄×C₁₃	—	4	8	no	—
328	D₄×C₁₃	—	4	4	no	—
329	C₂×C₄×C₁₃	—	2	16	no	—
330	C₂×C₄×C₁₃	—	2	32	no	—
331	C₂×C₄×C₁₃	—	2	8	no	—
332	C₂×C₄×C₁₃	—	2	4	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	4	no	—
335	C₂×C₄×C₁₃	—	2	4	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	4	no	—
338	C₂×C₄×C₁₃	—	2	8	no	—
339	C₂×C₄×C₁₃	—	2	8	no	—
340	C₂×C₄×C₁₃	—	2	8	no	—
341	C₂×C₄×C₁₃	—	2	32	no	—
342	C₂×C₄×C₁₃	—	2	8	no	—
343	C₂×C₄×C₁₃	—	2	4	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	4	no	—
348	C₂×C₄×C₁₃	—	2	4	no	—
349	C₂×C₄×C₁₃	—	2	4	no	—
350	C₂×C₄×C₁₃	—	2	4	no	—
351	C₂×C₄×C₁₃	—	2	4	no	—
352	C₂×C₄×C₁₃	—	4	16	no	—
353	C₂×C₄×C₁₃	—	4	8	no	—
354	C₂×C₄×C₁₃	#120	1	16	yes	complemented
355	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
357	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
360	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
361	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₁₃	C₂×#41	1	8	yes	complemented
363	C₂²×#41	—	2	16	no	—
364	C₂²×#41	—	2	8	no	—
365	C₂²×#41	C₂²×C₁₃	1	2	yes	—
366	C₂²×#41	C₂²×C₁₃	1	2	yes	—
367	C₂²×#41	C₂²×C₁₃	1	2	yes	—
368	C₂²×#41	C₂²×C₁₃	1	2	yes	—
369	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
370	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
371	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
372	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
373	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
374	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
375	#532	—	2	16	no	—
376	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
377	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
378	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
379	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
380	#525	—	2	8	no	—
381	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
382	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
384	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
386	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
387	C₂×#120	C₂²×C₁₃	1	2	yes	—
388	C₂×#120	C₂²×C₁₃	1	4	yes	—
389	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
390	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
391	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
392	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
393	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
394	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
395	#395	C₂²×C₁₃	1	4	yes	complemented
396	#394	C₂²×C₁₃	1	8	yes	complemented
397	#394	C₂²×C₁₃	1	4	yes	complemented
398	#393	C₂²×C₁₃	1	4	yes	complemented
399	#392	C₂²×C₁₃	1	8	yes	complemented
400	#392	C₂²×C₁₃	1	4	yes	complemented
401	#391	C₂²×C₁₃	1	2	yes	complemented
402	#391	C₂²×C₁₃	1	2	yes	complemented
403	#390	C₂²×C₁₃	1	2	yes	complemented
404	#390	C₂²×C₁₃	1	2	yes	complemented
405	#386	C₂²×C₁₃	1	4	yes	—
406	#386	C₂²×C₁₃	1	8	yes	complemented
407	#386	C₂²×C₁₃	1	8	yes	complemented
408	#385	C₂²×C₁₃	1	4	yes	—
409	#385	C₂²×C₁₃	1	8	yes	complemented
410	#379	C₂²×C₁₃	1	4	yes	—
411	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
412	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
413	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
415	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
416	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
417	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
418	C₂²×C₁₃	—	2	2	no	—
419	C₂²×C₁₃	—	2	2	no	—
420	C₂²×C₁₃	—	2	2	no	—
421	C₂²×C₁₃	—	2	2	no	—
422	C₂²×C₁₃	—	2	8	no	—
423	C₂²×C₁₃	—	2	8	no	—
424	C₂²×C₁₃	—	2	8	no	—
425	C₂²×C₁₃	—	2	2	no	—
426	C₂²×C₁₃	—	2	2	no	—
427	C₂²×C₁₃	—	2	2	no	—
428	C₂²×C₁₃	—	2	16	no	—
429	C₂²×C₁₃	—	4	16	no	—
430	C₂²×C₁₃	—	4	32	no	—
431	C₂²×C₁₃	—	4	4	no	—
432	C₂²×C₁₃	—	4	4	no	—
433	C₂²×C₁₃	—	4	4	no	—
434	C₂²×C₁₃	—	4	8	no	—
435	C₂²×C₁₃	—	4	2	no	—
436	C₂²×C₁₃	—	4	2	no	—
437	C₂²×C₁₃	—	4	2	no	—
438	C₂²×C₁₃	—	4	8	no	—
439	C₂²×C₁₃	C₂×#120	1	4	yes	—
440	C₂²×C₁₃	#532	1	4	yes	complemented
441	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
442	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
443	C₂²×C₁₃	C₂²×#41	1	2	yes	—
444	C₂²×C₁₃	#585	1	2	yes	—
445	C₄×C₁₃	—	2	2	no	—
446	C₄×C₁₃	—	2	8	no	—
447	C₄×C₁₃	—	2	2	no	—
448	C₄×C₁₃	—	2	8	no	—
449	C₄×C₁₃	—	4	2	no	—
450	C₄×C₁₃	—	4	2	no	—
451	C₄×C₁₃	—	4	2	no	—
452	C₄×C₁₃	—	4	4	no	—
453	C₄×C₁₃	C₂×#120	1	4	yes	—
454	C₄×C₁₃	C₂×#120	1	4	yes	—
455	C₂⁵	C₂³×C₁₃	1	2	yes	—
456	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
457	C₂×#41	—	2	128	no	—
458	C₂×#41	—	2	8	no	—
459	C₂×#41	—	2	16	no	—
460	C₂×#41	—	2	8	no	—
461	C₂×#41	—	2	16	no	—
462	C₂×#41	—	2	8	no	—
463	C₂×#41	—	2	8	no	—
464	C₂×#41	—	2	8	no	—
465	C₂×#41	—	2	8	no	—
466	C₂×#41	—	2	8	no	—
467	C₂×#41	—	2	4	no	—
468	C₂×#41	—	2	8	no	—
469	C₂×#41	D₄×C₁₃	1	16	yes	complemented
470	C₂²×Q₈	—	2	8	no	—
471	C₂²×Q₈	—	2	4	no	—
472	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
473	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
474	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
475	C₂²×D₄	—	2	8	no	—
476	C₂²×D₄	—	2	16	no	—
477	C₂²×D₄	—	2	8	no	—
478	C₂²×D₄	—	2	4	no	—
479	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
480	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
481	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
483	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
484	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
485	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
486	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
487	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
488	C₂³×C₄	—	2	8	no	—
489	C₂³×C₄	—	2	16	no	—
490	C₂³×C₄	—	2	8	no	—
491	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
492	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
493	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
494	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
495	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
496	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
498	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₄⋊Q₈	—	2	8	no	—
504	#127	—	2	8	no	—
505	#124	—	2	8	no	—
506	#124	—	2	8	no	—
507	#123	—	2	8	no	—
508	C₂²⋊Q₈	—	2	4	no	—
509	C₂²⋊Q₈	—	2	4	no	—
510	#121	—	2	32	no	—
511	#121	—	2	4	no	—
512	#121	—	2	4	no	—
513	#120	—	2	8	no	—
514	#120	—	2	16	no	—
515	C₄×D₄	—	2	8	no	—
516	C₄×D₄	—	2	8	no	—
517	C₄×D₄	—	2	32	no	—
518	#117	—	2	4	no	—
519	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
524	C₂×C₂²⋊C₄	—	2	8	no	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
537	C₂×C₄²	—	2	8	no	—
538	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
539	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
540	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
541	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
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	8	yes	—
546	#95	C₂³×C₁₃	1	8	yes	—
547	C₂×C₁₃	—	2	4	no	—
548	C₂×C₁₃	—	2	4	no	—
549	C₂×C₁₃	—	4	2	no	—
550	C₂×C₁₃	—	4	8	no	—
551	C₂×C₁₃	—	8	2	no	—
552	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
553	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
554	C₂×C₁₃	#3449	1	1	yes	characteristic
555	C₂×C₁₃	D₄×#41	1	4	yes	—
556	C₂⁴	—	2	8	no	—
557	C₂⁴	—	2	4	no	—
558	C₂⁴	—	2	4	no	—
559	C₂⁴	—	2	4	no	—
560	C₂⁴	—	2	8	no	—
561	C₂⁴	—	4	2	no	—
562	C₂⁴	—	4	4	no	—
563	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
564	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
565	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
566	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
567	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
568	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
569	#41	—	2	64	no	—
570	#41	—	2	64	no	—
571	#41	—	2	64	no	—
572	#41	—	2	64	no	—
573	#41	—	4	16	no	—
574	C₂×Q₈	—	2	32	no	—
575	C₂×Q₈	—	2	8	no	—
576	C₂×Q₈	—	2	4	no	—
577	C₂×Q₈	—	2	4	no	—
578	C₂×Q₈	—	2	4	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
582	C₂×D₄	—	2	64	no	—
583	C₂×D₄	—	2	32	no	—
584	C₂×D₄	—	2	8	no	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	8	no	—
587	C₂×D₄	—	2	8	no	—
588	C₂×D₄	—	2	8	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	16	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	8	no	—
594	C₂×D₄	—	2	8	no	—
595	C₂×D₄	—	2	8	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	16	no	—
602	C₂×D₄	—	4	8	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	—
605	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
606	C₂²×C₄	—	2	64	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	8	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	32	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	8	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	8	no	—
615	C₂²×C₄	—	2	8	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	8	no	—
618	C₂²×C₄	—	2	8	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	8	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	8	no	—
623	C₂²×C₄	—	2	8	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
626	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
627	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
628	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
629	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
630	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
631	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
632	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
633	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
634	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
639	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
641	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	16	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	16	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	16	no	—
656	C₂²⋊C₄	—	2	8	no	—
657	C₂²⋊C₄	—	2	16	no	—
658	C₂²⋊C₄	—	4	8	no	—
659	C₂²⋊C₄	C₁₃×#41	1	8	yes	complemented
660	C₄²	—	2	8	no	—
661	C₄²	—	2	4	no	—
662	C₄²	—	2	4	no	—
663	C₄²	—	2	4	no	—
664	C₁₃	#34738	1	1	yes	characteristic, direct product factor, Sylow
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	16	no	—
670	C₂³	—	2	8	no	—
671	C₂³	—	2	8	no	—
672	C₂³	—	2	4	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	8	no	—
677	C₂³	—	2	8	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	2	4	no	—
682	C₂³	—	2	4	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	4	16	no	—
685	C₂³	—	4	32	no	—
686	C₂³	—	4	8	no	—
687	C₂³	—	4	8	no	—
688	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
689	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
690	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
691	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
692	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
693	C₂³	C₂×C₁₃×#41	1	4	yes	—
694	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
695	Q₈	—	2	16	no	—
696	Q₈	—	2	16	no	—
697	Q₈	—	4	4	no	—
698	D₄	—	2	32	no	—
699	D₄	—	2	16	no	—
700	D₄	—	2	32	no	—
701	D₄	—	2	16	no	—
702	D₄	—	4	32	no	—
703	D₄	—	4	8	no	—
704	D₄	—	4	8	no	—
705	D₄	—	4	8	no	—
706	D₄	—	4	4	no	—
707	C₂×C₄	—	2	16	no	—
708	C₂×C₄	—	2	32	no	—
709	C₂×C₄	—	2	8	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	8	no	—
717	C₂×C₄	—	2	8	no	—
718	C₂×C₄	—	2	8	no	—
719	C₂×C₄	—	2	32	no	—
720	C₂×C₄	—	2	8	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	4	16	no	—
731	C₂×C₄	—	4	8	no	—
732	C₂×C₄	C₁₃×#120	1	16	yes	complemented
733	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
735	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
736	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
737	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
738	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
739	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
740	C₂×C₄	C₂×C₁₃×#41	1	8	yes	complemented
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	8	no	—
746	C₂²	—	2	8	no	—
747	C₂²	—	2	8	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	16	no	—
752	C₂²	—	4	16	no	—
753	C₂²	—	4	32	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	8	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	8	no	—
762	C₂²	C₂×C₁₃×#120	1	4	yes	—
763	C₂²	C₁₃×#532	1	4	yes	complemented
764	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
765	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
766	C₂²	C₂²×C₁₃×#41	1	2	yes	—
767	C₂²	C₁₃×#585	1	2	yes	—
768	C₄	—	2	2	no	—
769	C₄	—	2	8	no	—
770	C₄	—	2	2	no	—
771	C₄	—	2	8	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	4	no	—
776	C₄	C₂×C₁₃×#120	1	4	yes	—
777	C₄	C₂×C₁₃×#120	1	4	yes	—
778	C₂	—	2	4	no	—
779	C₂	—	2	4	no	—
780	C₂	—	4	2	no	—
781	C₂	—	4	8	no	—
782	C₂	—	8	2	no	—
783	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic
784	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
785	C₂	C₁₃×#3449	1	1	yes	characteristic
786	C₂	D₄×C₁₃×#41	1	4	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. C₂³×C₁₃×#41	C₂	semidirect
2. C₂×C₁₃×#532	C₂	semidirect
3. C₂×C₁₃×#525	C₂	semidirect
4. C₁₃×#2436	C₂	semidirect
5. C₁₃×#2435	C₂	semidirect
6. C₁₃×#2434	C₂	semidirect
7. C₁₃×#2433	C₂	semidirect
8. C₁₃×#2432	C₂	semidirect
9. C₁₃×#2431	C₂	semidirect
10. C₁₃×#2430	C₂	semidirect
11. C₁₃×#2410	C₂	semidirect
12. C₁₃×#2388	C₂	semidirect
13. C₄×C₁₃×#120	C₂	semidirect
14. C₁₃×#2297	C₂	semidirect
15. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
22. C₂²×C₁₃×#41	C₂²	semidirect
29. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₁₃×#127	C₂²	semidirect
31. C₂×C₁₃×#124	C₂²	semidirect
32. C₂×C₁₃×#124	C₂²	semidirect
34. C₂×C₁₃×#123	C₂²	semidirect
36. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₁₃×#121	C₂²	semidirect
39. C₂×C₁₃×#121	C₂²	semidirect
43. C₂×C₄×D₄×C₁₃	C₂²	semidirect
44. C₂×C₄×D₄×C₁₃	C₂²	semidirect
45. C₂×C₁₃×#117	C₂²	semidirect
47. C₂²×C₄²×C₁₃	C₂²	semidirect
48. C₁₃×#395	C₂²	semidirect
49. C₁₃×#394	C₂²	semidirect
50. C₁₃×#394	C₂²	semidirect
51. C₁₃×#393	C₂²	semidirect
52. C₁₃×#392	C₂²	semidirect
53. C₁₃×#392	C₂²	semidirect
54. C₁₃×#391	C₂²	semidirect
55. C₁₃×#391	C₂²	semidirect
56. C₁₃×#390	C₂²	semidirect
57. C₁₃×#390	C₂²	semidirect
59. C₁₃×#386	C₂²	semidirect
60. C₁₃×#386	C₂²	semidirect
62. C₁₃×#385	C₂²	semidirect
67. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
68. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
69. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
70. C₂×C₁₃×#95	C₂²	semidirect
85. C₂×C₁₃×#41	D₄	semidirect
107. C₂³×C₄×C₁₃	D₄	semidirect
163. #34738	C₁₃	direct (N × H)
267. C₁₃×C₂²⋊C₄	#41	semidirect
272. C₂³×#41	C₂×C₁₃	semidirect
273. C₂×#532	C₂×C₁₃	semidirect
274. C₂×#525	C₂×C₁₃	semidirect
275. #2436	C₂×C₁₃	semidirect
276. #2435	C₂×C₁₃	semidirect
277. #2434	C₂×C₁₃	semidirect
278. #2433	C₂×C₁₃	semidirect
279. #2432	C₂×C₁₃	semidirect
280. #2431	C₂×C₁₃	semidirect
281. #2430	C₂×C₁₃	semidirect
282. #2410	C₂×C₁₃	semidirect
283. #2388	C₂×C₁₃	semidirect
284. C₄×#120	C₂×C₁₃	semidirect
285. #2297	C₂×C₁₃	semidirect
286. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
354. C₂×C₄×C₁₃	#120	semidirect
362. C₂×C₄×C₁₃	C₂×#41	semidirect
369. C₂²×#41	C₂²×C₁₃	semidirect
376. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
377. C₂×#127	C₂²×C₁₃	semidirect
378. C₂×#124	C₂²×C₁₃	semidirect
379. C₂×#124	C₂²×C₁₃	semidirect
381. C₂×#123	C₂²×C₁₃	semidirect
383. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
385. C₂×#121	C₂²×C₁₃	semidirect
386. C₂×#121	C₂²×C₁₃	semidirect
390. C₂×C₄×D₄	C₂²×C₁₃	semidirect
391. C₂×C₄×D₄	C₂²×C₁₃	semidirect
392. C₂×#117	C₂²×C₁₃	semidirect
394. C₂²×C₄²	C₂²×C₁₃	semidirect
395. #395	C₂²×C₁₃	semidirect
396. #394	C₂²×C₁₃	semidirect
397. #394	C₂²×C₁₃	semidirect
398. #393	C₂²×C₁₃	semidirect
399. #392	C₂²×C₁₃	semidirect
400. #392	C₂²×C₁₃	semidirect
401. #391	C₂²×C₁₃	semidirect
402. #391	C₂²×C₁₃	semidirect
403. #390	C₂²×C₁₃	semidirect
404. #390	C₂²×C₁₃	semidirect
406. #386	C₂²×C₁₃	semidirect
407. #386	C₂²×C₁₃	semidirect
409. #385	C₂²×C₁₃	semidirect
414. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
415. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
416. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
417. C₂×#95	C₂²×C₁₃	semidirect
440. C₂²×C₁₃	#532	semidirect
469. C₂×#41	D₄×C₁₃	semidirect
491. C₂³×C₄	D₄×C₁₃	semidirect
659. C₂²⋊C₄	C₁₃×#41	semidirect
664. C₁₃	#34738	direct (N × H)
732. C₂×C₄	C₁₃×#120	semidirect
740. C₂×C₄	C₂×C₁₃×#41	semidirect
763. C₂²	C₁₃×#532	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₁₃×#41	2
C₂×C₁₃×#532	2
C₂×C₁₃×#525	2
C₁₃×#2436	2
C₁₃×#2435	2
C₁₃×#2434	2
C₁₃×#2433	2
C₁₃×#2432	2
C₁₃×#2431	2
C₁₃×#2430	2
C₁₃×#2410	2
C₁₃×#2388	2
C₄×C₁₃×#120	2
C₁₃×#2297	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#34738	13

Subgroups — C13×#34738 #15721077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34738 #15721077