Subgroups — C₂×C₁₃×#3401 #15747737

Order 3328.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3401	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#496	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
26	C₁₃×#559	—	2	4	no	—
27	C₁₃×#559	C₂²	1	8	yes	complemented
28	C₁₃×#556	—	2	4	no	—
29	C₁₃×#556	C₂²	1	8	yes	complemented
30	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#126	—	2	1	no	—
33	C₂×C₁₃×#126	—	2	1	no	—
34	C₂×C₁₃×#124	—	2	1	no	—
35	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#123	—	2	1	no	—
40	C₂×C₁₃×#123	—	2	1	no	—
41	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	—	2	1	no	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#117	—	2	1	no	—
51	C₁₃×#497	C₂²	1	8	yes	complemented
52	C₁₃×#496	C₂²	1	8	yes	—
53	C₁₃×#495	C₂²	1	8	yes	complemented
54	C₁₃×#464	C₂²	1	8	yes	complemented
55	C₁₃×#464	C₂²	1	8	yes	complemented
56	C₁₃×#463	C₂²	1	8	yes	complemented
57	C₁₃×#463	C₂²	1	8	yes	complemented
58	C₁₃×#461	C₂²	1	8	yes	complemented
59	C₁₃×#460	C₂²	1	8	yes	complemented
60	C₁₃×#446	C₂²	1	8	yes	complemented
61	C₁₃×#442	C₂²	1	8	yes	complemented
62	C₁₃×#441	C₂²	1	8	yes	complemented
63	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
64	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₃	—	2	1	no	—
82	C₂²×D₄×C₁₃	—	2	1	no	—
83	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	—	2	1	no	—
87	C₂³×C₄×C₁₃	—	2	1	no	—
88	C₂³×C₄×C₁₃	—	2	1	no	—
89	C₂×C₁₃×Q₁₆	—	2	4	no	—
90	C₂×C₁₃×Q₁₆	—	4	2	no	—
91	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
92	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
93	C₂×C₁₃×SD₁₆	—	2	4	no	—
94	C₂×C₁₃×SD₁₆	—	4	2	no	—
95	C₂×C₁₃×SD₁₆	—	4	2	no	—
96	C₂×C₁₃×SD₁₆	—	4	2	no	—
97	C₂×C₁₃×SD₁₆	—	4	2	no	—
98	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
101	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
102	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×D₈	—	2	4	no	—
104	C₂×C₁₃×D₈	—	4	2	no	—
105	C₂×C₁₃×D₈	C₂³	1	4	yes	—
106	C₂×C₁₃×D₈	C₂³	1	4	yes	—
107	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	—	2	2	no	—
112	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
113	C₁₃×#127	—	2	2	no	—
114	C₁₃×#127	C₂³	1	4	yes	—
115	C₁₃×#126	—	2	8	no	—
116	C₁₃×#126	—	2	8	no	—
117	C₁₃×#124	—	2	8	no	—
118	C₁₃×#124	—	2	2	no	—
119	C₁₃×#124	—	2	2	no	—
120	C₁₃×#124	—	2	2	no	—
121	C₁₃×#124	—	2	2	no	—
122	C₁₃×#124	C₂³	1	4	yes	—
123	C₁₃×#124	C₂³	1	4	yes	—
124	C₁₃×#124	C₂³	1	4	yes	—
125	C₁₃×#124	C₂³	1	4	yes	—
126	C₁₃×#123	—	2	8	no	—
127	C₁₃×#123	—	2	8	no	—
128	C₁₃×C₂²⋊Q₈	—	2	8	no	—
129	C₄×Q₈×C₁₃	—	2	2	no	—
130	C₄×Q₈×C₁₃	—	2	2	no	—
131	C₄×Q₈×C₁₃	—	2	2	no	—
132	C₄×Q₈×C₁₃	D₄	1	4	yes	—
133	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
134	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
135	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
136	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
137	C₄×D₄×C₁₃	—	2	8	no	—
138	C₄×D₄×C₁₃	—	2	2	no	—
139	C₄×D₄×C₁₃	—	2	2	no	—
140	C₄×D₄×C₁₃	—	2	2	no	—
141	C₄×D₄×C₁₃	C₂³	1	4	yes	—
142	C₄×D₄×C₁₃	C₂³	1	4	yes	—
143	C₄×D₄×C₁₃	C₂³	1	4	yes	—
144	C₁₃×#117	—	2	8	no	—
145	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
157	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
158	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
160	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
162	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
163	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
164	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
165	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
166	C₂×C₄²×C₁₃	—	2	1	no	—
167	C₂×C₄²×C₁₃	—	2	1	no	—
168	C₂×C₄²×C₁₃	—	2	1	no	—
169	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
172	C₁₃×#106	C₂³	1	4	yes	—
173	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
174	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
175	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
176	C₁₃×#103	C₂³	1	4	yes	—
177	C₁₃×#103	C₂³	1	4	yes	—
178	C₁₃×#103	C₂³	1	4	yes	—
179	C₁₃×#102	C₂³	1	4	yes	—
180	C₁₃×#102	C₂³	1	4	yes	—
181	C₁₃×#102	C₂³	1	4	yes	—
182	C₁₃×#97	C₂³	1	4	yes	—
183	C₁₃×#97	C₂³	1	4	yes	—
184	C₄×C₈×C₁₃	C₂³	1	4	yes	—
185	C₂×#3401	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂⁴×C₁₃	—	2	1	no	—
187	C₂⁴×C₁₃	—	2	1	no	—
188	C₂⁴×C₁₃	—	2	1	no	—
189	C₂×Q₈×C₁₃	—	2	1	no	—
190	C₂×Q₈×C₁₃	—	2	1	no	—
191	C₂×Q₈×C₁₃	—	2	1	no	—
192	C₂×Q₈×C₁₃	—	2	2	no	—
193	C₂×Q₈×C₁₃	—	2	2	no	—
194	C₂×Q₈×C₁₃	—	2	2	no	—
195	C₂×Q₈×C₁₃	—	2	2	no	—
196	C₂×Q₈×C₁₃	—	2	2	no	—
197	C₂×Q₈×C₁₃	—	2	2	no	—
198	C₂×Q₈×C₁₃	—	4	2	no	—
199	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
200	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
201	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
202	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
203	C₂×D₄×C₁₃	—	2	1	no	—
204	C₂×D₄×C₁₃	—	2	1	no	—
205	C₂×D₄×C₁₃	—	2	1	no	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	4	no	—
208	C₂×D₄×C₁₃	—	2	2	no	—
209	C₂×D₄×C₁₃	—	2	2	no	—
210	C₂×D₄×C₁₃	—	2	2	no	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	2	2	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	4	4	no	—
215	C₂×D₄×C₁₃	—	8	2	no	—
216	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
217	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃	—	2	1	no	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	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	—	4	4	no	—
228	C₂²×C₄×C₁₃	—	8	2	no	—
229	C₂²×C₄×C₁₃	—	8	2	no	—
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₁₃×Q₁₆	—	2	8	no	—
238	C₁₃×Q₁₆	—	4	4	no	—
239	C₁₃×SD₁₆	—	2	8	no	—
240	C₁₃×SD₁₆	—	4	4	no	—
241	C₁₃×SD₁₆	—	4	4	no	—
242	C₁₃×SD₁₆	—	4	4	no	—
243	C₁₃×SD₁₆	—	4	4	no	—
244	C₁₃×D₈	—	2	8	no	—
245	C₁₃×D₈	—	4	4	no	—
246	C₂×C₈×C₁₃	—	2	2	no	—
247	C₂×C₈×C₁₃	—	2	2	no	—
248	C₂×C₈×C₁₃	—	2	2	no	—
249	C₂×C₈×C₁₃	#41	1	4	yes	—
250	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
251	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
252	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
262	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
263	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
264	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
265	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₄²×C₁₃	—	2	4	no	—
278	C₄²×C₁₃	—	2	4	no	—
279	C₄²×C₁₃	—	2	4	no	—
280	C₄²×C₁₃	C₂×D₄	1	2	yes	—
281	C₄²×C₁₃	C₂×D₄	1	2	yes	—
282	C₄²×C₁₃	C₂×D₄	1	2	yes	—
283	C₄²×C₁₃	C₂⁴	1	2	yes	—
284	C₄²×C₁₃	C₂⁴	1	2	yes	—
285	C₄²×C₁₃	C₂⁴	1	2	yes	—
286	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#3401	C₂×C₁₃	1	16	yes	direct product factor
289	C₂×#497	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂×#496	C₂×C₁₃	1	1	yes	characteristic
291	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
292	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
293	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
294	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
296	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
297	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
300	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₂³×C₁₃	—	2	2	no	—
303	C₂³×C₁₃	—	2	2	no	—
304	C₂³×C₁₃	—	2	2	no	—
305	C₂³×C₁₃	—	4	2	no	—
306	C₂³×C₁₃	—	4	2	no	—
307	C₂³×C₁₃	—	4	2	no	—
308	C₂³×C₁₃	—	4	2	no	—
309	C₂³×C₁₃	—	4	2	no	—
310	C₂³×C₁₃	—	4	2	no	—
311	C₂³×C₁₃	—	4	2	no	—
312	C₂³×C₁₃	—	4	2	no	—
313	C₂³×C₁₃	—	4	2	no	—
314	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
315	Q₈×C₁₃	—	2	2	no	—
316	Q₈×C₁₃	—	2	2	no	—
317	Q₈×C₁₃	—	2	2	no	—
318	Q₈×C₁₃	—	2	2	no	—
319	Q₈×C₁₃	—	2	2	no	—
320	Q₈×C₁₃	—	2	2	no	—
321	Q₈×C₁₃	—	4	4	no	—
322	Q₈×C₁₃	—	4	2	no	—
323	Q₈×C₁₃	—	4	2	no	—
324	Q₈×C₁₃	—	4	2	no	—
325	D₄×C₁₃	—	2	2	no	—
326	D₄×C₁₃	—	2	2	no	—
327	D₄×C₁₃	—	2	2	no	—
328	D₄×C₁₃	—	2	2	no	—
329	D₄×C₁₃	—	2	2	no	—
330	D₄×C₁₃	—	2	2	no	—
331	D₄×C₁₃	—	4	8	no	—
332	D₄×C₁₃	—	4	2	no	—
333	D₄×C₁₃	—	4	2	no	—
334	D₄×C₁₃	—	4	2	no	—
335	D₄×C₁₃	—	8	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	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	—	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	—	4	8	no	—
348	C₂×C₄×C₁₃	—	4	2	no	—
349	C₂×C₄×C₁₃	—	4	2	no	—
350	C₂×C₄×C₁₃	—	4	2	no	—
351	C₂×C₄×C₁₃	—	4	2	no	—
352	C₂×C₄×C₁₃	—	4	2	no	—
353	C₂×C₄×C₁₃	—	8	4	no	—
354	C₂×C₄×C₁₃	—	8	4	no	—
355	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₁₃	C₂²×D₄	1	2	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	2	yes	—
360	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
363	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
364	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
365	C₈×C₁₃	—	2	2	no	—
366	C₈×C₁₃	—	2	2	no	—
367	C₈×C₁₃	—	2	2	no	—
368	C₈×C₁₃	C₂×#41	1	4	yes	—
369	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
370	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
371	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
372	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
373	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
374	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
375	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
376	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
377	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
378	#559	—	2	4	no	—
379	#559	C₂²×C₁₃	1	8	yes	complemented
380	#556	—	2	4	no	—
381	#556	C₂²×C₁₃	1	8	yes	complemented
382	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×#126	—	2	1	no	—
385	C₂×#126	—	2	1	no	—
386	C₂×#124	—	2	1	no	—
387	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#123	—	2	1	no	—
392	C₂×#123	—	2	1	no	—
393	C₂×C₂²⋊Q₈	—	2	1	no	—
394	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×C₄×D₄	—	2	1	no	—
399	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×#117	—	2	1	no	—
403	#497	C₂²×C₁₃	1	8	yes	complemented
404	#496	C₂²×C₁₃	1	8	yes	—
405	#495	C₂²×C₁₃	1	8	yes	complemented
406	#464	C₂²×C₁₃	1	8	yes	complemented
407	#464	C₂²×C₁₃	1	8	yes	complemented
408	#463	C₂²×C₁₃	1	8	yes	complemented
409	#463	C₂²×C₁₃	1	8	yes	complemented
410	#461	C₂²×C₁₃	1	8	yes	complemented
411	#460	C₂²×C₁₃	1	8	yes	complemented
412	#446	C₂²×C₁₃	1	8	yes	complemented
413	#442	C₂²×C₁₃	1	8	yes	complemented
414	#441	C₂²×C₁₃	1	8	yes	complemented
415	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
416	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
429	C₂²×C₁₃	—	4	2	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	—	8	4	no	—
439	C₂²×C₁₃	—	8	4	no	—
440	C₂²×C₁₃	—	8	4	no	—
441	C₂²×C₁₃	#550	1	2	yes	—
442	C₂²×C₁₃	#575	1	2	yes	—
443	C₂²×C₁₃	#577	1	2	yes	—
444	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
445	C₄×C₁₃	—	2	2	no	—
446	C₄×C₁₃	—	2	2	no	—
447	C₄×C₁₃	—	2	2	no	—
448	C₄×C₁₃	—	2	2	no	—
449	C₄×C₁₃	—	2	2	no	—
450	C₄×C₁₃	—	2	2	no	—
451	C₄×C₁₃	—	4	2	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	#550	1	2	yes	—
457	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
458	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
460	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
461	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
462	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
468	C₂³×C₄	—	2	1	no	—
469	C₂³×C₄	—	2	1	no	—
470	C₂³×C₄	—	2	1	no	—
471	C₂×Q₁₆	—	2	4	no	—
472	C₂×Q₁₆	—	4	2	no	—
473	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
474	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
475	C₂×SD₁₆	—	2	4	no	—
476	C₂×SD₁₆	—	4	2	no	—
477	C₂×SD₁₆	—	4	2	no	—
478	C₂×SD₁₆	—	4	2	no	—
479	C₂×SD₁₆	—	4	2	no	—
480	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
481	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
482	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
483	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
484	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
485	C₂×D₈	—	2	4	no	—
486	C₂×D₈	—	4	2	no	—
487	C₂×D₈	C₂³×C₁₃	1	4	yes	—
488	C₂×D₈	C₂³×C₁₃	1	4	yes	—
489	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
490	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
493	C₄⋊Q₈	—	2	2	no	—
494	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
495	#127	—	2	2	no	—
496	#127	C₂³×C₁₃	1	4	yes	—
497	#126	—	2	8	no	—
498	#126	—	2	8	no	—
499	#124	—	2	8	no	—
500	#124	—	2	2	no	—
501	#124	—	2	2	no	—
502	#124	—	2	2	no	—
503	#124	—	2	2	no	—
504	#124	C₂³×C₁₃	1	4	yes	—
505	#124	C₂³×C₁₃	1	4	yes	—
506	#124	C₂³×C₁₃	1	4	yes	—
507	#124	C₂³×C₁₃	1	4	yes	—
508	#123	—	2	8	no	—
509	#123	—	2	8	no	—
510	C₂²⋊Q₈	—	2	8	no	—
511	C₄×Q₈	—	2	2	no	—
512	C₄×Q₈	—	2	2	no	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	D₄×C₁₃	1	4	yes	—
515	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
516	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
517	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
518	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
519	C₄×D₄	—	2	8	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	C₂³×C₁₃	1	4	yes	—
524	C₄×D₄	C₂³×C₁₃	1	4	yes	—
525	C₄×D₄	C₂³×C₁₃	1	4	yes	—
526	#117	—	2	8	no	—
527	C₂×C₄⋊C₄	—	2	1	no	—
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	—	2	1	no	—
532	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
533	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
534	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	—	2	1	no	—
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₄²	—	2	1	no	—
549	C₂×C₄²	—	2	1	no	—
550	C₂×C₄²	—	2	1	no	—
551	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
554	#106	C₂³×C₁₃	1	4	yes	—
555	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
556	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
557	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
558	#103	C₂³×C₁₃	1	4	yes	—
559	#103	C₂³×C₁₃	1	4	yes	—
560	#103	C₂³×C₁₃	1	4	yes	—
561	#102	C₂³×C₁₃	1	4	yes	—
562	#102	C₂³×C₁₃	1	4	yes	—
563	#102	C₂³×C₁₃	1	4	yes	—
564	#97	C₂³×C₁₃	1	4	yes	—
565	#97	C₂³×C₁₃	1	4	yes	—
566	C₄×C₈	C₂³×C₁₃	1	4	yes	—
567	C₂×C₁₃	—	8	2	no	—
568	C₂×C₁₃	—	8	2	no	—
569	C₂×C₁₃	—	8	2	no	—
570	C₂×C₁₃	#3401	1	4	yes	direct product factor
571	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
572	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
573	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
574	C₂⁴	—	2	1	no	—
575	C₂⁴	—	2	1	no	—
576	C₂⁴	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	4	2	no	—
587	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
588	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
589	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
590	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	4	4	no	—
603	C₂×D₄	—	8	2	no	—
604	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
605	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
606	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	4	4	no	—
616	C₂²×C₄	—	8	2	no	—
617	C₂²×C₄	—	8	2	no	—
618	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
625	Q₁₆	—	2	8	no	—
626	Q₁₆	—	4	4	no	—
627	SD₁₆	—	2	8	no	—
628	SD₁₆	—	4	4	no	—
629	SD₁₆	—	4	4	no	—
630	SD₁₆	—	4	4	no	—
631	SD₁₆	—	4	4	no	—
632	D₈	—	2	8	no	—
633	D₈	—	4	4	no	—
634	C₂×C₈	—	2	2	no	—
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	C₁₃×#41	1	4	yes	—
638	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
639	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
640	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
641	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
650	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
651	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
652	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	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	C₄²	—	2	4	no	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	4	no	—
668	C₄²	C₂×D₄×C₁₃	1	2	yes	—
669	C₄²	C₂×D₄×C₁₃	1	2	yes	—
670	C₄²	C₂×D₄×C₁₃	1	2	yes	—
671	C₄²	C₂⁴×C₁₃	1	2	yes	—
672	C₄²	C₂⁴×C₁₃	1	2	yes	—
673	C₄²	C₂⁴×C₁₃	1	2	yes	—
674	C₁₃	C₂×#3401	1	1	yes	characteristic, direct product factor, Sylow
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	4	2	no	—
685	C₂³	—	4	2	no	—
686	C₂³	—	4	2	no	—
687	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
688	Q₈	—	2	2	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	2	2	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	2	2	no	—
694	Q₈	—	4	4	no	—
695	Q₈	—	4	2	no	—
696	Q₈	—	4	2	no	—
697	Q₈	—	4	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	2	2	no	—
702	D₄	—	2	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	4	8	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	D₄	—	8	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	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	2	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	8	4	no	—
727	C₂×C₄	—	8	4	no	—
728	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
730	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
733	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
735	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
736	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
737	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	2	2	no	—
740	C₈	—	2	2	no	—
741	C₈	C₂×C₁₃×#41	1	4	yes	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	8	4	no	—
752	C₂²	—	8	4	no	—
753	C₂²	—	8	4	no	—
754	C₂²	C₁₃×#550	1	2	yes	—
755	C₂²	C₁₃×#575	1	2	yes	—
756	C₂²	C₁₃×#577	1	2	yes	—
757	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	C₁₃×#550	1	2	yes	—
770	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
771	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
772	C₂	—	8	2	no	—
773	C₂	—	8	2	no	—
774	C₂	—	8	2	no	—
775	C₂	C₁₃×#3401	1	4	yes	direct product factor
776	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
777	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
778	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#559	C₂	semidirect
2. C₂×C₁₃×#556	C₂	semidirect
3. C₁₃×#3401	C₂	direct (N × H)
4. C₂×C₁₃×#497	C₂	semidirect
6. C₂×C₁₃×#495	C₂	semidirect
7. C₂×C₁₃×#464	C₂	semidirect
8. C₂×C₁₃×#464	C₂	semidirect
9. C₂×C₁₃×#460	C₂	semidirect
10. C₂×C₁₃×#463	C₂	semidirect
11. C₂×C₁₃×#463	C₂	semidirect
12. C₂×C₁₃×#461	C₂	semidirect
13. C₂×C₁₃×#446	C₂	semidirect
14. C₂×C₁₃×#442	C₂	semidirect
15. C₂×C₁₃×#441	C₂	semidirect
16. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
27. C₁₃×#559	C₂²	semidirect
29. C₁₃×#556	C₂²	semidirect
51. C₁₃×#497	C₂²	semidirect
53. C₁₃×#495	C₂²	semidirect
54. C₁₃×#464	C₂²	semidirect
55. C₁₃×#464	C₂²	semidirect
56. C₁₃×#463	C₂²	semidirect
57. C₁₃×#463	C₂²	semidirect
58. C₁₃×#461	C₂²	semidirect
59. C₁₃×#460	C₂²	semidirect
60. C₁₃×#446	C₂²	semidirect
61. C₁₃×#442	C₂²	semidirect
62. C₁₃×#441	C₂²	semidirect
63. C₄×C₁₃×SD₁₆	C₂²	semidirect
185. C₂×#3401	C₁₃	direct (N × H)
286. C₂×#559	C₂×C₁₃	semidirect
287. C₂×#556	C₂×C₁₃	semidirect
288. #3401	C₂×C₁₃	direct (N × H)
289. C₂×#497	C₂×C₁₃	semidirect
291. C₂×#495	C₂×C₁₃	semidirect
292. C₂×#464	C₂×C₁₃	semidirect
293. C₂×#464	C₂×C₁₃	semidirect
294. C₂×#460	C₂×C₁₃	semidirect
295. C₂×#463	C₂×C₁₃	semidirect
296. C₂×#463	C₂×C₁₃	semidirect
297. C₂×#461	C₂×C₁₃	semidirect
298. C₂×#446	C₂×C₁₃	semidirect
299. C₂×#442	C₂×C₁₃	semidirect
300. C₂×#441	C₂×C₁₃	semidirect
301. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
379. #559	C₂²×C₁₃	semidirect
381. #556	C₂²×C₁₃	semidirect
403. #497	C₂²×C₁₃	semidirect
405. #495	C₂²×C₁₃	semidirect
406. #464	C₂²×C₁₃	semidirect
407. #464	C₂²×C₁₃	semidirect
408. #463	C₂²×C₁₃	semidirect
409. #463	C₂²×C₁₃	semidirect
410. #461	C₂²×C₁₃	semidirect
411. #460	C₂²×C₁₃	semidirect
412. #446	C₂²×C₁₃	semidirect
413. #442	C₂²×C₁₃	semidirect
414. #441	C₂²×C₁₃	semidirect
415. C₄×SD₁₆	C₂²×C₁₃	semidirect
570. C₂×C₁₃	#3401	direct (N × H)
674. C₁₃	C₂×#3401	direct (N × H)
775. C₂	C₁₃×#3401	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×#559	2
C₂×C₁₃×#556	2
C₁₃×#3401	2
C₂×C₁₃×#497	2
C₂×C₁₃×#496	2
C₂×C₁₃×#495	2
C₂×C₁₃×#464	2
C₂×C₁₃×#460	2
C₂×C₁₃×#463	2
C₂×C₁₃×#461	2
C₂×C₁₃×#446	2
C₂×C₁₃×#442	2
C₂×C₁₃×#441	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×#3401	13

Subgroups — C2×C13×#3401 #15747737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3401 #15747737