Subgroups — C₁₃×#34743 #15721082

Order 3328.

3390 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2429	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2428	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2427	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2426	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2425	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2424	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2392	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₃×#121	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#532	—	2	8	no	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#525	—	2	8	no	—
25	C₁₃×#525	—	2	8	no	—
26	C₂×C₁₃×#123	C₂²	1	2	yes	—
27	C₂×C₁₃×#123	C₂²	1	2	yes	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₁₃×#121	C₂²	1	4	yes	—
31	C₂×C₁₃×#121	C₂²	1	2	yes	—
32	C₂×C₁₃×#121	C₂²	1	2	yes	—
33	C₂×C₁₃×#121	C₂²	1	4	yes	—
34	C₂×C₁₃×#120	C₂²	1	2	yes	—
35	C₂×C₁₃×#120	C₂²	1	2	yes	—
36	C₄×C₁₃×#41	—	2	8	no	—
37	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
39	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
40	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
41	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
42	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
46	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
47	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
50	C₁₃×#398	C₂²	1	4	yes	complemented
51	C₁₃×#397	C₂²	1	4	yes	complemented
52	C₁₃×#396	C₂²	1	4	yes	—
53	C₁₃×#396	C₂²	1	4	yes	complemented
54	C₁₃×#394	C₂²	1	4	yes	—
55	C₁₃×#394	C₂²	1	4	yes	—
56	C₁₃×#394	C₂²	1	4	yes	complemented
57	C₁₃×#392	C₂²	1	4	yes	—
58	C₁₃×#391	C₂²	1	2	yes	complemented
59	C₁₃×#390	C₂²	1	4	yes	—
60	C₁₃×#390	C₂²	1	2	yes	complemented
61	C₁₃×#389	C₂²	1	2	yes	complemented
62	C₁₃×#389	C₂²	1	2	yes	complemented
63	C₁₃×#389	C₂²	1	4	yes	complemented
64	C₁₃×#388	C₂²	1	4	yes	—
65	C₁₃×#388	C₂²	1	4	yes	complemented
66	C₁₃×#386	C₂²	1	4	yes	—
67	C₁₃×#386	C₂²	1	4	yes	—
68	C₁₃×#386	C₂²	1	4	yes	complemented
69	C₁₃×#385	C₂²	1	4	yes	—
70	C₁₃×#380	C₂²	1	4	yes	complemented
71	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
72	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
73	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
74	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
76	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
77	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
78	C₂×C₁₃×#95	C₂²	1	2	yes	—
79	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×#41	—	2	4	no	—
81	C₂×C₁₃×#41	—	2	4	no	—
82	C₂×C₁₃×#41	—	2	4	no	—
83	C₂×C₁₃×#41	—	2	4	no	—
84	C₂×C₁₃×#41	—	2	4	no	—
85	C₂×C₁₃×#41	D₄	1	8	yes	complemented
86	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	—	2	4	no	—
96	C₂³×C₄×C₁₃	—	2	4	no	—
97	C₂³×C₄×C₁₃	—	2	4	no	—
98	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
103	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×C₄⋊Q₈	—	2	4	no	—
108	C₁₃×#127	—	2	4	no	—
109	C₁₃×#124	—	2	4	no	—
110	C₁₃×#124	—	2	4	no	—
111	C₁₃×#123	—	2	8	no	—
112	C₁₃×#123	—	2	8	no	—
113	C₁₃×C₂²⋊Q₈	—	2	8	no	—
114	C₁₃×C₂²⋊Q₈	—	2	8	no	—
115	C₁₃×#121	—	2	8	no	—
116	C₁₃×#121	—	2	16	no	—
117	C₁₃×#121	—	2	8	no	—
118	C₁₃×#121	—	2	16	no	—
119	C₁₃×#120	—	2	8	no	—
120	C₁₃×#120	—	2	8	no	—
121	C₄×Q₈×C₁₃	—	2	8	no	—
122	C₄×D₄×C₁₃	—	2	16	no	—
123	C₄×D₄×C₁₃	—	2	16	no	—
124	C₄×D₄×C₁₃	—	2	8	no	—
125	C₄×D₄×C₁₃	—	2	16	no	—
126	C₄×D₄×C₁₃	—	2	16	no	—
127	C₁₃×#117	—	2	4	no	—
128	C₁₃×#117	—	2	8	no	—
129	C₁₃×#117	D₄	1	8	yes	complemented
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
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	4	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	4	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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×C₄²×C₁₃	—	2	4	no	—
155	C₂×C₄²×C₁₃	—	2	4	no	—
156	C₂×C₄²×C₁₃	—	2	8	no	—
157	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
161	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
166	C₁₃×#95	C₂³	1	2	yes	—
167	C₁₃×#95	C₂³	1	2	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	#34743	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂⁴×C₁₃	—	2	4	no	—
176	C₂⁴×C₁₃	—	2	2	no	—
177	C₂⁴×C₁₃	—	2	2	no	—
178	C₂⁴×C₁₃	—	2	2	no	—
179	C₂⁴×C₁₃	—	4	2	no	—
180	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
181	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
182	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
183	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₁₃×#41	—	2	32	no	—
185	C₁₃×#41	—	4	16	no	—
186	C₂×Q₈×C₁₃	—	2	2	no	—
187	C₂×Q₈×C₁₃	—	2	2	no	—
188	C₂×Q₈×C₁₃	—	2	2	no	—
189	C₂×Q₈×C₁₃	—	2	2	no	—
190	C₂×Q₈×C₁₃	—	2	2	no	—
191	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
192	C₂×D₄×C₁₃	—	2	4	no	—
193	C₂×D₄×C₁₃	—	2	4	no	—
194	C₂×D₄×C₁₃	—	2	8	no	—
195	C₂×D₄×C₁₃	—	2	8	no	—
196	C₂×D₄×C₁₃	—	2	4	no	—
197	C₂×D₄×C₁₃	—	2	4	no	—
198	C₂×D₄×C₁₃	—	2	8	no	—
199	C₂×D₄×C₁₃	—	2	8	no	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	2	no	—
202	C₂×D₄×C₁₃	—	2	8	no	—
203	C₂×D₄×C₁₃	—	2	2	no	—
204	C₂×D₄×C₁₃	—	2	2	no	—
205	C₂×D₄×C₁₃	—	2	2	no	—
206	C₂×D₄×C₁₃	—	2	8	no	—
207	C₂×D₄×C₁₃	—	2	2	no	—
208	C₂×D₄×C₁₃	—	4	4	no	—
209	C₂×D₄×C₁₃	—	4	4	no	—
210	C₂×D₄×C₁₃	—	4	4	no	—
211	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
212	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₁₃	—	2	4	no	—
214	C₂²×C₄×C₁₃	—	2	4	no	—
215	C₂²×C₄×C₁₃	—	2	4	no	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	8	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	4	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	—	2	4	no	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	—	2	4	no	—
229	C₂²×C₄×C₁₃	—	2	8	no	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	2	4	no	—
232	C₂²×C₄×C₁₃	—	2	4	no	—
233	C₂²×C₄×C₁₃	—	4	4	no	—
234	C₂²×C₄×C₁₃	—	4	2	no	—
235	C₂²×C₄×C₁₃	—	4	2	no	—
236	C₂²×C₄×C₁₃	—	4	16	no	—
237	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
238	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₁₃	#41	1	4	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	2	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	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₁₃×C₄⋊C₄	—	2	8	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	8	no	—
255	C₁₃×C₄⋊C₄	—	2	8	no	—
256	C₁₃×C₄⋊C₄	—	2	8	no	—
257	C₁₃×C₄⋊C₄	—	2	8	no	—
258	C₁₃×C₄⋊C₄	—	4	4	no	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	8	no	—
262	C₁₃×C₂²⋊C₄	—	2	8	no	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	8	no	—
265	C₁₃×C₂²⋊C₄	—	2	8	no	—
266	C₁₃×C₂²⋊C₄	—	2	8	no	—
267	C₁₃×C₂²⋊C₄	—	2	8	no	—
268	C₁₃×C₂²⋊C₄	—	2	8	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	—	4	4	no	—
273	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
274	C₁₃×C₂²⋊C₄	#41	1	8	yes	complemented
275	C₄²×C₁₃	—	2	2	no	—
276	C₄²×C₁₃	—	2	2	no	—
277	C₄²×C₁₃	—	2	4	no	—
278	C₄²×C₁₃	—	2	8	no	—
279	C₄²×C₁₃	—	2	4	no	—
280	C₄²×C₁₃	—	2	2	no	—
281	C₄²×C₁₃	—	2	2	no	—
282	C₄²×C₁₃	—	2	4	no	—
283	C₄²×C₁₃	C₂×D₄	1	8	yes	—
284	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
285	C₂×#525	C₂×C₁₃	1	1	yes	characteristic, complemented
286	C₂×#525	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#2429	C₂×C₁₃	1	2	yes	complemented
289	#2428	C₂×C₁₃	1	2	yes	complemented
290	#2427	C₂×C₁₃	1	2	yes	complemented
291	#2426	C₂×C₁₃	1	2	yes	complemented
292	#2425	C₂×C₁₃	1	4	yes	complemented
293	#2424	C₂×C₁₃	1	4	yes	complemented
294	#2392	C₂×C₁₃	1	4	yes	complemented
295	C₄×#121	C₂×C₁₃	1	4	yes	complemented
296	#2297	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂³×C₁₃	—	2	2	no	—
300	C₂³×C₁₃	—	2	2	no	—
301	C₂³×C₁₃	—	2	8	no	—
302	C₂³×C₁₃	—	2	2	no	—
303	C₂³×C₁₃	—	2	2	no	—
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	4	no	—
309	C₂³×C₁₃	—	2	4	no	—
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	4	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	4	no	—
317	C₂³×C₁₃	—	4	8	no	—
318	C₂³×C₁₃	—	4	8	no	—
319	C₂³×C₁₃	—	4	4	no	—
320	C₂³×C₁₃	—	4	4	no	—
321	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
322	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
323	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
324	C₂³×C₁₃	C₂×#41	1	4	yes	—
325	C₂³×C₁₃	C₂×#41	1	2	yes	—
326	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
327	Q₈×C₁₃	—	2	8	no	—
328	Q₈×C₁₃	—	4	4	no	—
329	D₄×C₁₃	—	2	16	no	—
330	D₄×C₁₃	—	2	8	no	—
331	D₄×C₁₃	—	4	16	no	—
332	D₄×C₁₃	—	4	16	no	—
333	D₄×C₁₃	—	4	16	no	—
334	D₄×C₁₃	—	4	8	no	—
335	D₄×C₁₃	—	4	4	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	4	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	4	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	16	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	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	4	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	4	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	4	16	no	—
361	C₂×C₄×C₁₃	—	4	8	no	—
362	C₂×C₄×C₁₃	—	4	8	no	—
363	C₂×C₄×C₁₃	—	4	4	no	—
364	C₂×C₄×C₁₃	—	4	8	no	—
365	C₂×C₄×C₁₃	—	4	8	no	—
366	C₂×C₄×C₁₃	—	4	8	no	—
367	C₂×C₄×C₁₃	#121	1	16	yes	complemented
368	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
369	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
370	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
375	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
376	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
377	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
378	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
379	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
380	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
381	#532	—	2	8	no	—
382	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
383	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
384	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
385	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	#525	—	2	8	no	—
387	#525	—	2	8	no	—
388	C₂×#123	C₂²×C₁₃	1	2	yes	—
389	C₂×#123	C₂²×C₁₃	1	2	yes	—
390	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
391	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
392	C₂×#121	C₂²×C₁₃	1	2	yes	—
393	C₂×#121	C₂²×C₁₃	1	2	yes	—
394	C₂×#121	C₂²×C₁₃	1	4	yes	—
395	C₂×#121	C₂²×C₁₃	1	4	yes	—
396	C₂×#120	C₂²×C₁₃	1	2	yes	—
397	C₂×#120	C₂²×C₁₃	1	2	yes	—
398	C₄×#41	—	2	8	no	—
399	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
400	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
401	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
402	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
403	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
404	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
405	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
408	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
409	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
410	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
411	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
412	#398	C₂²×C₁₃	1	4	yes	complemented
413	#397	C₂²×C₁₃	1	4	yes	complemented
414	#396	C₂²×C₁₃	1	4	yes	—
415	#396	C₂²×C₁₃	1	4	yes	complemented
416	#394	C₂²×C₁₃	1	4	yes	—
417	#394	C₂²×C₁₃	1	4	yes	—
418	#394	C₂²×C₁₃	1	4	yes	complemented
419	#392	C₂²×C₁₃	1	4	yes	—
420	#391	C₂²×C₁₃	1	2	yes	complemented
421	#390	C₂²×C₁₃	1	4	yes	—
422	#390	C₂²×C₁₃	1	2	yes	complemented
423	#389	C₂²×C₁₃	1	4	yes	complemented
424	#389	C₂²×C₁₃	1	2	yes	complemented
425	#389	C₂²×C₁₃	1	2	yes	complemented
426	#388	C₂²×C₁₃	1	4	yes	—
427	#388	C₂²×C₁₃	1	4	yes	complemented
428	#386	C₂²×C₁₃	1	4	yes	—
429	#386	C₂²×C₁₃	1	4	yes	—
430	#386	C₂²×C₁₃	1	4	yes	complemented
431	#385	C₂²×C₁₃	1	4	yes	—
432	#380	C₂²×C₁₃	1	4	yes	complemented
433	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
434	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
435	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
436	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
437	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
438	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
439	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
440	C₂×#95	C₂²×C₁₃	1	2	yes	—
441	C₂²×C₁₃	—	2	2	no	—
442	C₂²×C₁₃	—	2	2	no	—
443	C₂²×C₁₃	—	2	4	no	—
444	C₂²×C₁₃	—	2	4	no	—
445	C₂²×C₁₃	—	2	4	no	—
446	C₂²×C₁₃	—	2	4	no	—
447	C₂²×C₁₃	—	2	4	no	—
448	C₂²×C₁₃	—	2	4	no	—
449	C₂²×C₁₃	—	2	8	no	—
450	C₂²×C₁₃	—	4	16	no	—
451	C₂²×C₁₃	—	4	2	no	—
452	C₂²×C₁₃	—	4	2	no	—
453	C₂²×C₁₃	—	4	2	no	—
454	C₂²×C₁₃	—	4	2	no	—
455	C₂²×C₁₃	—	4	4	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	—	4	4	no	—
462	C₂²×C₁₃	—	4	4	no	—
463	C₂²×C₁₃	C₂×#121	1	4	yes	—
464	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
465	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
466	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
467	C₂²×C₁₃	C₂²×#41	1	2	yes	—
468	C₂²×C₁₃	#585	1	2	yes	—
469	C₄×C₁₃	—	2	4	no	—
470	C₄×C₁₃	—	2	4	no	—
471	C₄×C₁₃	—	2	8	no	—
472	C₄×C₁₃	—	2	4	no	—
473	C₄×C₁₃	—	4	2	no	—
474	C₄×C₁₃	—	4	2	no	—
475	C₄×C₁₃	—	4	2	no	—
476	C₄×C₁₃	—	4	2	no	—
477	C₄×C₁₃	—	4	4	no	—
478	C₄×C₁₃	C₂×#121	1	4	yes	—
479	C₄×C₁₃	C₂×#121	1	4	yes	—
480	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
481	C₂×#41	—	2	4	no	—
482	C₂×#41	—	2	4	no	—
483	C₂×#41	—	2	4	no	—
484	C₂×#41	—	2	4	no	—
485	C₂×#41	—	2	4	no	—
486	C₂×#41	D₄×C₁₃	1	8	yes	complemented
487	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
488	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
489	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
490	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
492	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
493	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
494	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
495	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂³×C₄	—	2	4	no	—
497	C₂³×C₄	—	2	4	no	—
498	C₂³×C₄	—	2	4	no	—
499	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
500	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
501	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
502	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
504	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
505	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
506	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
507	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
508	C₄⋊Q₈	—	2	4	no	—
509	#127	—	2	4	no	—
510	#124	—	2	4	no	—
511	#124	—	2	4	no	—
512	#123	—	2	8	no	—
513	#123	—	2	8	no	—
514	C₂²⋊Q₈	—	2	8	no	—
515	C₂²⋊Q₈	—	2	8	no	—
516	#121	—	2	8	no	—
517	#121	—	2	16	no	—
518	#121	—	2	8	no	—
519	#121	—	2	16	no	—
520	#120	—	2	8	no	—
521	#120	—	2	8	no	—
522	C₄×Q₈	—	2	8	no	—
523	C₄×D₄	—	2	16	no	—
524	C₄×D₄	—	2	16	no	—
525	C₄×D₄	—	2	8	no	—
526	C₄×D₄	—	2	16	no	—
527	C₄×D₄	—	2	16	no	—
528	#117	—	2	4	no	—
529	#117	—	2	8	no	—
530	#117	D₄×C₁₃	1	8	yes	complemented
531	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
539	C₂×C₂²⋊C₄	—	2	8	no	—
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	4	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
555	C₂×C₄²	—	2	4	no	—
556	C₂×C₄²	—	2	4	no	—
557	C₂×C₄²	—	2	8	no	—
558	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
559	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₁₃	1	4	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	1	yes	characteristic
566	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
567	#95	C₂³×C₁₃	1	2	yes	—
568	#95	C₂³×C₁₃	1	2	yes	—
569	#95	C₂³×C₁₃	1	2	yes	—
570	#95	C₂³×C₁₃	1	2	yes	—
571	#95	C₂³×C₁₃	1	4	yes	—
572	#95	C₂³×C₁₃	1	4	yes	—
573	#95	C₂³×C₁₃	1	4	yes	—
574	#95	C₂³×C₁₃	1	4	yes	—
575	C₂×C₁₃	—	2	4	no	—
576	C₂×C₁₃	—	4	4	no	—
577	C₂×C₁₃	—	4	4	no	—
578	C₂×C₁₃	—	8	2	no	—
579	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
580	C₂×C₁₃	#3444	1	1	yes	characteristic
581	C₂×C₁₃	#3455	1	1	yes	characteristic
582	C₂×C₁₃	D₄×#41	1	2	yes	—
583	C₂×C₁₃	D₄×#41	1	2	yes	—
584	C₂⁴	—	2	4	no	—
585	C₂⁴	—	2	2	no	—
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	4	2	no	—
589	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
590	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
591	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
592	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
593	#41	—	2	32	no	—
594	#41	—	4	16	no	—
595	C₂×Q₈	—	2	2	no	—
596	C₂×Q₈	—	2	2	no	—
597	C₂×Q₈	—	2	2	no	—
598	C₂×Q₈	—	2	2	no	—
599	C₂×Q₈	—	2	2	no	—
600	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	8	no	—
604	C₂×D₄	—	2	8	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	8	no	—
608	C₂×D₄	—	2	8	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	8	no	—
612	C₂×D₄	—	2	2	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	8	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	4	4	no	—
618	C₂×D₄	—	4	4	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
621	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	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	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	8	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	4	4	no	—
643	C₂²×C₄	—	4	2	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	—	4	16	no	—
646	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
647	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
648	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
649	C₂²×C₄	C₁₃×#41	1	4	yes	—
650	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
653	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
656	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
661	C₄⋊C₄	—	2	8	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	8	no	—
664	C₄⋊C₄	—	2	8	no	—
665	C₄⋊C₄	—	2	8	no	—
666	C₄⋊C₄	—	2	8	no	—
667	C₄⋊C₄	—	4	4	no	—
668	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	8	no	—
671	C₂²⋊C₄	—	2	8	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	8	no	—
674	C₂²⋊C₄	—	2	8	no	—
675	C₂²⋊C₄	—	2	8	no	—
676	C₂²⋊C₄	—	2	8	no	—
677	C₂²⋊C₄	—	2	8	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	8	no	—
681	C₂²⋊C₄	—	4	4	no	—
682	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
683	C₂²⋊C₄	C₁₃×#41	1	8	yes	complemented
684	C₄²	—	2	2	no	—
685	C₄²	—	2	2	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	8	no	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	4	no	—
692	C₄²	C₂×D₄×C₁₃	1	8	yes	—
693	C₁₃	#34743	1	1	yes	characteristic, direct product factor, Sylow
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	8	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	4	no	—
704	C₂³	—	2	4	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	4	no	—
712	C₂³	—	4	8	no	—
713	C₂³	—	4	8	no	—
714	C₂³	—	4	4	no	—
715	C₂³	—	4	4	no	—
716	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
717	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
718	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
719	C₂³	C₂×C₁₃×#41	1	4	yes	—
720	C₂³	C₂×C₁₃×#41	1	2	yes	—
721	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
722	Q₈	—	2	8	no	—
723	Q₈	—	4	4	no	—
724	D₄	—	2	16	no	—
725	D₄	—	2	8	no	—
726	D₄	—	4	16	no	—
727	D₄	—	4	16	no	—
728	D₄	—	4	16	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	4	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	16	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	4	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	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	4	16	no	—
756	C₂×C₄	—	4	8	no	—
757	C₂×C₄	—	4	8	no	—
758	C₂×C₄	—	4	4	no	—
759	C₂×C₄	—	4	8	no	—
760	C₂×C₄	—	4	8	no	—
761	C₂×C₄	—	4	8	no	—
762	C₂×C₄	C₁₃×#121	1	16	yes	complemented
763	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
764	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
765	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
766	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
767	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
768	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
769	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
770	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
771	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
772	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	2	4	no	—
781	C₂²	—	2	8	no	—
782	C₂²	—	4	16	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	4	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	4	no	—
794	C₂²	—	4	4	no	—
795	C₂²	C₂×C₁₃×#121	1	4	yes	—
796	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
797	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
798	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
799	C₂²	C₂²×C₁₃×#41	1	2	yes	—
800	C₂²	C₁₃×#585	1	2	yes	—
801	C₄	—	2	4	no	—
802	C₄	—	2	4	no	—
803	C₄	—	2	8	no	—
804	C₄	—	2	4	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	4	no	—
810	C₄	C₂×C₁₃×#121	1	4	yes	—
811	C₄	C₂×C₁₃×#121	1	4	yes	—
812	C₂	—	2	4	no	—
813	C₂	—	4	4	no	—
814	C₂	—	4	4	no	—
815	C₂	—	8	2	no	—
816	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
817	C₂	C₁₃×#3444	1	1	yes	characteristic
818	C₂	C₁₃×#3455	1	1	yes	characteristic
819	C₂	D₄×C₁₃×#41	1	2	yes	—
820	C₂	D₄×C₁₃×#41	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×#532	C₂	semidirect
2. C₂×C₁₃×#525	C₂	semidirect
3. C₂×C₁₃×#525	C₂	semidirect
4. C₂×C₄×C₁₃×#41	C₂	semidirect
5. C₁₃×#2429	C₂	semidirect
6. C₁₃×#2428	C₂	semidirect
7. C₁₃×#2427	C₂	semidirect
8. C₁₃×#2426	C₂	semidirect
9. C₁₃×#2425	C₂	semidirect
10. C₁₃×#2424	C₂	semidirect
11. C₁₃×#2392	C₂	semidirect
12. C₄×C₁₃×#121	C₂	semidirect
13. C₁₃×#2297	C₂	semidirect
14. C₁₃×#2296	C₂	semidirect
15. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
20. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₁₃×#127	C₂²	semidirect
22. C₂×C₁₃×#124	C₂²	semidirect
23. C₂×C₁₃×#124	C₂²	semidirect
37. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
41. C₂×C₄×D₄×C₁₃	C₂²	semidirect
42. C₂×C₄×D₄×C₁₃	C₂²	semidirect
45. C₂×C₁₃×#117	C₂²	semidirect
49. C₂²×C₄²×C₁₃	C₂²	semidirect
50. C₁₃×#398	C₂²	semidirect
51. C₁₃×#397	C₂²	semidirect
53. C₁₃×#396	C₂²	semidirect
56. C₁₃×#394	C₂²	semidirect
58. C₁₃×#391	C₂²	semidirect
60. C₁₃×#390	C₂²	semidirect
61. C₁₃×#389	C₂²	semidirect
62. C₁₃×#389	C₂²	semidirect
63. C₁₃×#389	C₂²	semidirect
65. C₁₃×#388	C₂²	semidirect
68. C₁₃×#386	C₂²	semidirect
70. C₁₃×#380	C₂²	semidirect
71. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
76. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
77. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
85. C₂×C₁₃×#41	D₄	semidirect
129. C₁₃×#117	D₄	semidirect
174. #34743	C₁₃	direct (N × H)
274. C₁₃×C₂²⋊C₄	#41	semidirect
284. C₂×#532	C₂×C₁₃	semidirect
285. C₂×#525	C₂×C₁₃	semidirect
286. C₂×#525	C₂×C₁₃	semidirect
287. C₂×C₄×#41	C₂×C₁₃	semidirect
288. #2429	C₂×C₁₃	semidirect
289. #2428	C₂×C₁₃	semidirect
290. #2427	C₂×C₁₃	semidirect
291. #2426	C₂×C₁₃	semidirect
292. #2425	C₂×C₁₃	semidirect
293. #2424	C₂×C₁₃	semidirect
294. #2392	C₂×C₁₃	semidirect
295. C₄×#121	C₂×C₁₃	semidirect
296. #2297	C₂×C₁₃	semidirect
297. #2296	C₂×C₁₃	semidirect
298. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
367. C₂×C₄×C₁₃	#121	semidirect
382. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
383. C₂×#127	C₂²×C₁₃	semidirect
384. C₂×#124	C₂²×C₁₃	semidirect
385. C₂×#124	C₂²×C₁₃	semidirect
399. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
403. C₂×C₄×D₄	C₂²×C₁₃	semidirect
404. C₂×C₄×D₄	C₂²×C₁₃	semidirect
407. C₂×#117	C₂²×C₁₃	semidirect
411. C₂²×C₄²	C₂²×C₁₃	semidirect
412. #398	C₂²×C₁₃	semidirect
413. #397	C₂²×C₁₃	semidirect
415. #396	C₂²×C₁₃	semidirect
418. #394	C₂²×C₁₃	semidirect
420. #391	C₂²×C₁₃	semidirect
422. #390	C₂²×C₁₃	semidirect
423. #389	C₂²×C₁₃	semidirect
424. #389	C₂²×C₁₃	semidirect
425. #389	C₂²×C₁₃	semidirect
427. #388	C₂²×C₁₃	semidirect
430. #386	C₂²×C₁₃	semidirect
432. #380	C₂²×C₁₃	semidirect
433. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
438. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
439. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
486. C₂×#41	D₄×C₁₃	semidirect
530. #117	D₄×C₁₃	semidirect
683. C₂²⋊C₄	C₁₃×#41	semidirect
693. C₁₃	#34743	direct (N × H)
762. C₂×C₄	C₁₃×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#532	2
C₂×C₁₃×#525	2
C₂×C₄×C₁₃×#41	2
C₁₃×#2429	2
C₁₃×#2428	2
C₁₃×#2427	2
C₁₃×#2426	2
C₁₃×#2425	2
C₁₃×#2424	2
C₁₃×#2392	2
C₄×C₁₃×#121	2
C₁₃×#2297	2
C₁₃×#2296	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#34743	13

Subgroups — C13×#34743 #15721082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34743 #15721082