Subgroups — C₂×C₁₃×#3345 #15747576

Order 3328.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3345	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	—	2	1	no	—
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#553	—	2	4	no	—
22	C₁₃×#553	C₂²	1	8	yes	complemented
23	C₁₃×#547	—	2	4	no	—
24	C₁₃×#547	C₂²	1	8	yes	complemented
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#126	—	2	1	no	—
27	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#123	—	2	1	no	—
29	C₂×C₁₃×#123	—	2	1	no	—
30	C₂×C₁₃×#123	—	2	1	no	—
31	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
32	C₂×C₁₃×#121	—	2	1	no	—
33	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	—	2	1	no	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₁₃×#501	C₂²	1	8	yes	complemented
46	C₁₃×#482	C₂²	1	8	yes	complemented
47	C₁₃×#481	C₂²	1	8	yes	complemented
48	C₁₃×#481	C₂²	1	8	yes	complemented
49	C₁₃×#480	C₂²	1	8	yes	complemented
50	C₁₃×#478	C₂²	1	8	yes	complemented
51	C₁₃×#476	C₂²	1	8	yes	complemented
52	C₁₃×#469	C₂²	1	8	yes	complemented
53	C₁₃×#466	C₂²	1	8	yes	complemented
54	C₁₃×#442	C₂²	1	8	yes	complemented
55	C₁₃×#435	C₂²	1	8	yes	complemented
56	C₁₃×#428	C₂²	1	8	yes	complemented
57	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#106	C₂²	1	8	yes	complemented
67	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#102	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
77	C₂×C₁₃×#41	—	2	8	no	—
78	C₂×C₁₃×#41	—	4	8	no	—
79	C₂²×Q₈×C₁₃	—	2	1	no	—
80	C₂²×D₄×C₁₃	—	2	1	no	—
81	C₂²×D₄×C₁₃	—	2	1	no	—
82	C₂²×D₄×C₁₃	—	2	1	no	—
83	C₂²×D₄×C₁₃	—	2	1	no	—
84	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
85	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	—	2	1	no	—
88	C₂³×C₄×C₁₃	—	2	1	no	—
89	C₂³×C₄×C₁₃	—	2	1	no	—
90	C₂³×C₄×C₁₃	—	2	1	no	—
91	C₂³×C₄×C₁₃	—	2	1	no	—
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×D₈	—	2	4	no	—
95	C₂×C₁₃×D₈	C₂³	1	4	yes	—
96	C₂×C₁₃×M₁₆	—	2	4	no	—
97	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
98	C₂²×C₈×C₁₃	—	2	4	no	—
99	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₁₃×C₄⋊Q₈	—	2	2	no	—
105	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
106	C₁₃×#126	—	2	8	no	—
107	C₁₃×#125	—	2	2	no	—
108	C₁₃×#125	C₂³	1	4	yes	—
109	C₁₃×#123	—	2	8	no	—
110	C₁₃×#123	—	2	8	no	—
111	C₁₃×#123	—	2	8	no	—
112	C₁₃×C₂²⋊Q₈	—	2	8	no	—
113	C₁₃×#121	—	2	8	no	—
114	C₁₃×#121	—	2	2	no	—
115	C₁₃×#121	—	2	2	no	—
116	C₁₃×#121	—	2	2	no	—
117	C₁₃×#121	—	2	2	no	—
118	C₁₃×#121	C₂³	1	4	yes	—
119	C₁₃×#121	C₂³	1	4	yes	—
120	C₁₃×#121	C₂³	1	4	yes	—
121	C₁₃×#121	C₂³	1	4	yes	—
122	C₄×D₄×C₁₃	—	2	8	no	—
123	C₄×D₄×C₁₃	—	2	2	no	—
124	C₄×D₄×C₁₃	—	2	2	no	—
125	C₄×D₄×C₁₃	D₄	1	4	yes	—
126	C₄×D₄×C₁₃	C₂³	1	4	yes	—
127	C₄×D₄×C₁₃	C₂³	1	4	yes	—
128	C₄×D₄×C₁₃	C₂³	1	4	yes	—
129	C₁₃×#117	—	2	2	no	—
130	C₁₃×#117	C₂³	1	4	yes	—
131	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
150	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
151	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
152	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
157	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
158	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
159	C₂×C₄²×C₁₃	—	2	1	no	—
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₁₃×#107	C₂³	1	4	yes	—
162	C₁₃×#107	C₂³	1	4	yes	—
163	C₁₃×#107	C₂³	1	4	yes	—
164	C₁₃×#106	C₂³	1	4	yes	—
165	C₁₃×#106	C₂³	1	4	yes	—
166	C₁₃×#106	C₂³	1	4	yes	—
167	C₁₃×#106	C₂³	1	4	yes	—
168	C₁₃×#106	C₂³	1	4	yes	—
169	C₁₃×#106	C₂³	1	4	yes	—
170	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
171	C₁₃×#102	C₂³	1	4	yes	—
172	C₁₃×#102	C₂³	1	4	yes	—
173	C₁₃×#102	C₂³	1	4	yes	—
174	C₁₃×#102	C₂³	1	4	yes	—
175	C₁₃×#102	C₂³	1	4	yes	—
176	C₁₃×#102	C₂³	1	4	yes	—
177	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₁₃×#97	C₂³	1	4	yes	—
180	C₂×#3345	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂⁴×C₁₃	—	2	1	no	—
182	C₂⁴×C₁₃	—	2	1	no	—
183	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₁₃×#41	—	4	32	no	—
186	C₂×Q₈×C₁₃	—	2	4	no	—
187	C₂×Q₈×C₁₃	—	4	4	no	—
188	C₂×D₄×C₁₃	—	2	4	no	—
189	C₂×D₄×C₁₃	—	2	4	no	—
190	C₂×D₄×C₁₃	—	2	4	no	—
191	C₂×D₄×C₁₃	—	2	4	no	—
192	C₂×D₄×C₁₃	—	2	4	no	—
193	C₂×D₄×C₁₃	—	2	1	no	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	2	2	no	—
196	C₂×D₄×C₁₃	—	2	2	no	—
197	C₂×D₄×C₁₃	—	2	2	no	—
198	C₂×D₄×C₁₃	—	2	2	no	—
199	C₂×D₄×C₁₃	—	4	4	no	—
200	C₂×D₄×C₁₃	—	4	4	no	—
201	C₂×D₄×C₁₃	—	4	4	no	—
202	C₂×D₄×C₁₃	—	8	2	no	—
203	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
204	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
205	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	2	no	—
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	—	2	2	no	—
210	C₂²×C₄×C₁₃	—	2	4	no	—
211	C₂²×C₄×C₁₃	—	2	4	no	—
212	C₂²×C₄×C₁₃	—	2	1	no	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	1	no	—
215	C₂²×C₄×C₁₃	—	2	1	no	—
216	C₂²×C₄×C₁₃	—	2	1	no	—
217	C₂²×C₄×C₁₃	—	2	1	no	—
218	C₂²×C₄×C₁₃	—	2	4	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	4	4	no	—
222	C₂²×C₄×C₁₃	—	4	4	no	—
223	C₂²×C₄×C₁₃	—	4	4	no	—
224	C₂²×C₄×C₁₃	—	8	2	no	—
225	C₂²×C₄×C₁₃	—	8	2	no	—
226	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₁₃×D₈	—	2	8	no	—
236	C₁₃×M₁₆	—	2	8	no	—
237	C₂×C₈×C₁₃	—	2	2	no	—
238	C₂×C₈×C₁₃	—	2	2	no	—
239	C₂×C₈×C₁₃	—	2	2	no	—
240	C₂×C₈×C₁₃	—	2	8	no	—
241	C₂×C₈×C₁₃	#41	1	4	yes	complemented
242	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
243	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
245	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
246	C₁₃×C₄⋊C₄	—	2	1	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
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	1	no	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
259	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
260	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
261	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
263	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
264	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
273	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
274	C₄²×C₁₃	—	2	4	no	—
275	C₄²×C₁₃	C₂×D₄	1	2	yes	—
276	C₄²×C₁₃	C₂⁴	1	2	yes	—
277	C₂×#553	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#3345	C₂×C₁₃	1	16	yes	direct product factor
280	C₂×#501	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂×#481	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂×#481	C₂×C₁₃	1	1	yes	characteristic, complemented
283	C₂×#482	C₂×C₁₃	1	1	yes	characteristic, complemented
284	C₂×#480	C₂×C₁₃	1	1	yes	characteristic, complemented
285	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
286	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
291	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
292	C₂²×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	2	2	no	—
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	—	2	2	no	—
297	C₂³×C₁₃	—	2	2	no	—
298	C₂³×C₁₃	—	2	2	no	—
299	C₂³×C₁₃	—	2	2	no	—
300	C₂³×C₁₃	—	4	2	no	—
301	C₂³×C₁₃	—	4	2	no	—
302	C₂³×C₁₃	—	4	2	no	—
303	C₂³×C₁₃	—	4	2	no	—
304	C₂³×C₁₃	—	4	2	no	—
305	C₂³×C₁₃	—	4	2	no	—
306	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
307	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
308	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
309	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₁₃	—	4	8	no	—
311	D₄×C₁₃	—	2	8	no	—
312	D₄×C₁₃	—	2	2	no	—
313	D₄×C₁₃	—	2	2	no	—
314	D₄×C₁₃	—	2	2	no	—
315	D₄×C₁₃	—	2	2	no	—
316	D₄×C₁₃	—	4	8	no	—
317	D₄×C₁₃	—	4	8	no	—
318	D₄×C₁₃	—	4	8	no	—
319	D₄×C₁₃	—	4	2	no	—
320	D₄×C₁₃	—	4	2	no	—
321	D₄×C₁₃	—	8	4	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	4	no	—
327	C₂×C₄×C₁₃	—	2	4	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	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	4	8	no	—
339	C₂×C₄×C₁₃	—	4	8	no	—
340	C₂×C₄×C₁₃	—	4	2	no	—
341	C₂×C₄×C₁₃	—	4	2	no	—
342	C₂×C₄×C₁₃	—	4	2	no	—
343	C₂×C₄×C₁₃	—	4	8	no	—
344	C₂×C₄×C₁₃	—	4	2	no	—
345	C₂×C₄×C₁₃	—	4	2	no	—
346	C₂×C₄×C₁₃	—	4	2	no	—
347	C₂×C₄×C₁₃	—	8	4	no	—
348	C₂×C₄×C₁₃	—	8	4	no	—
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	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
355	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
356	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
357	C₈×C₁₃	—	2	2	no	—
358	C₈×C₁₃	—	2	2	no	—
359	C₈×C₁₃	—	2	2	no	—
360	C₈×C₁₃	C₂×#41	1	4	yes	complemented
361	C₂²×#41	—	2	1	no	—
362	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
363	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
364	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
365	#553	—	2	4	no	—
366	#553	C₂²×C₁₃	1	8	yes	complemented
367	#547	—	2	4	no	—
368	#547	C₂²×C₁₃	1	8	yes	complemented
369	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×#126	—	2	1	no	—
371	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#123	—	2	1	no	—
373	C₂×#123	—	2	1	no	—
374	C₂×#123	—	2	1	no	—
375	C₂×C₂²⋊Q₈	—	2	1	no	—
376	C₂×#121	—	2	1	no	—
377	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×C₄×D₄	—	2	1	no	—
382	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
386	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
387	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
388	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
389	#501	C₂²×C₁₃	1	8	yes	complemented
390	#482	C₂²×C₁₃	1	8	yes	complemented
391	#481	C₂²×C₁₃	1	8	yes	complemented
392	#481	C₂²×C₁₃	1	8	yes	complemented
393	#480	C₂²×C₁₃	1	8	yes	complemented
394	#478	C₂²×C₁₃	1	8	yes	complemented
395	#476	C₂²×C₁₃	1	8	yes	complemented
396	#469	C₂²×C₁₃	1	8	yes	complemented
397	#466	C₂²×C₁₃	1	8	yes	complemented
398	#442	C₂²×C₁₃	1	8	yes	complemented
399	#435	C₂²×C₁₃	1	8	yes	complemented
400	#428	C₂²×C₁₃	1	8	yes	complemented
401	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#106	C₂²×C₁₃	1	8	yes	complemented
411	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
421	C₂²×C₁₃	—	2	8	no	—
422	C₂²×C₁₃	—	2	2	no	—
423	C₂²×C₁₃	—	2	2	no	—
424	C₂²×C₁₃	—	2	2	no	—
425	C₂²×C₁₃	—	2	2	no	—
426	C₂²×C₁₃	—	2	2	no	—
427	C₂²×C₁₃	—	4	4	no	—
428	C₂²×C₁₃	—	4	2	no	—
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	—	8	4	no	—
435	C₂²×C₁₃	—	8	4	no	—
436	C₂²×C₁₃	#547	1	2	yes	—
437	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
438	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
439	C₂²×C₁₃	#577	1	2	yes	—
440	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
441	C₄×C₁₃	—	2	2	no	—
442	C₄×C₁₃	—	2	2	no	—
443	C₄×C₁₃	—	2	2	no	—
444	C₄×C₁₃	—	2	2	no	—
445	C₄×C₁₃	—	4	2	no	—
446	C₄×C₁₃	—	4	2	no	—
447	C₄×C₁₃	—	4	2	no	—
448	C₄×C₁₃	—	4	2	no	—
449	C₄×C₁₃	—	4	2	no	—
450	C₄×C₁₃	—	4	2	no	—
451	C₄×C₁₃	#547	1	2	yes	—
452	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
453	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
454	C₂×#41	—	2	8	no	—
455	C₂×#41	—	4	8	no	—
456	C₂²×Q₈	—	2	1	no	—
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
462	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
463	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
464	C₂³×C₄	—	2	1	no	—
465	C₂³×C₄	—	2	1	no	—
466	C₂³×C₄	—	2	1	no	—
467	C₂³×C₄	—	2	1	no	—
468	C₂³×C₄	—	2	1	no	—
469	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂×D₈	—	2	4	no	—
472	C₂×D₈	C₂³×C₁₃	1	4	yes	—
473	C₂×M₁₆	—	2	4	no	—
474	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
475	C₂²×C₈	—	2	4	no	—
476	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
478	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
481	C₄⋊Q₈	—	2	2	no	—
482	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
483	#126	—	2	8	no	—
484	#125	—	2	2	no	—
485	#125	C₂³×C₁₃	1	4	yes	—
486	#123	—	2	8	no	—
487	#123	—	2	8	no	—
488	#123	—	2	8	no	—
489	C₂²⋊Q₈	—	2	8	no	—
490	#121	—	2	8	no	—
491	#121	—	2	2	no	—
492	#121	—	2	2	no	—
493	#121	—	2	2	no	—
494	#121	—	2	2	no	—
495	#121	C₂³×C₁₃	1	4	yes	—
496	#121	C₂³×C₁₃	1	4	yes	—
497	#121	C₂³×C₁₃	1	4	yes	—
498	#121	C₂³×C₁₃	1	4	yes	—
499	C₄×D₄	—	2	8	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	D₄×C₁₃	1	4	yes	—
503	C₄×D₄	C₂³×C₁₃	1	4	yes	—
504	C₄×D₄	C₂³×C₁₃	1	4	yes	—
505	C₄×D₄	C₂³×C₁₃	1	4	yes	—
506	#117	—	2	2	no	—
507	#117	C₂³×C₁₃	1	4	yes	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	2	no	—
512	C₂×C₄⋊C₄	—	2	2	no	—
513	C₂×C₄⋊C₄	—	2	2	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
536	C₂×C₄²	—	2	1	no	—
537	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
538	#107	C₂³×C₁₃	1	4	yes	—
539	#107	C₂³×C₁₃	1	4	yes	—
540	#107	C₂³×C₁₃	1	4	yes	—
541	#106	C₂³×C₁₃	1	4	yes	—
542	#106	C₂³×C₁₃	1	4	yes	—
543	#106	C₂³×C₁₃	1	4	yes	—
544	#106	C₂³×C₁₃	1	4	yes	—
545	#106	C₂³×C₁₃	1	4	yes	—
546	#106	C₂³×C₁₃	1	4	yes	—
547	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
548	#102	C₂³×C₁₃	1	4	yes	—
549	#102	C₂³×C₁₃	1	4	yes	—
550	#102	C₂³×C₁₃	1	4	yes	—
551	#102	C₂³×C₁₃	1	4	yes	—
552	#102	C₂³×C₁₃	1	4	yes	—
553	#102	C₂³×C₁₃	1	4	yes	—
554	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
555	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
556	#97	C₂³×C₁₃	1	4	yes	—
557	C₂×C₁₃	—	2	4	no	—
558	C₂×C₁₃	—	4	2	no	—
559	C₂×C₁₃	—	8	2	no	—
560	C₂×C₁₃	—	8	2	no	—
561	C₂×C₁₃	#3345	1	4	yes	direct product factor
562	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
563	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
564	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
565	C₂⁴	—	2	1	no	—
566	C₂⁴	—	2	1	no	—
567	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
568	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
569	#41	—	4	32	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	—	4	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	4	4	no	—
584	C₂×D₄	—	4	4	no	—
585	C₂×D₄	—	4	4	no	—
586	C₂×D₄	—	8	2	no	—
587	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
588	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
589	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	4	4	no	—
606	C₂²×C₄	—	4	4	no	—
607	C₂²×C₄	—	4	4	no	—
608	C₂²×C₄	—	8	2	no	—
609	C₂²×C₄	—	8	2	no	—
610	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
611	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
615	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
619	D₈	—	2	8	no	—
620	M₁₆	—	2	8	no	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	8	no	—
625	C₂×C₈	C₁₃×#41	1	4	yes	complemented
626	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
627	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
628	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
629	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
643	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
645	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
646	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
647	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
648	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
657	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
658	C₄²	—	2	4	no	—
659	C₄²	C₂×D₄×C₁₃	1	2	yes	—
660	C₄²	C₂⁴×C₁₃	1	2	yes	—
661	C₁₃	C₂×#3345	1	1	yes	characteristic, direct product factor, Sylow
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	4	2	no	—
670	C₂³	—	4	2	no	—
671	C₂³	—	4	2	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	4	2	no	—
675	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
676	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
677	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
678	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
679	Q₈	—	4	8	no	—
680	D₄	—	2	8	no	—
681	D₄	—	2	2	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	4	8	no	—
686	D₄	—	4	8	no	—
687	D₄	—	4	8	no	—
688	D₄	—	4	2	no	—
689	D₄	—	4	2	no	—
690	D₄	—	8	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	4	8	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	—	4	2	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	8	4	no	—
717	C₂×C₄	—	8	4	no	—
718	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
720	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
721	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
722	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
723	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
724	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
725	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
726	C₈	—	2	2	no	—
727	C₈	—	2	2	no	—
728	C₈	—	2	2	no	—
729	C₈	C₂×C₁₃×#41	1	4	yes	complemented
730	C₂²	—	2	2	no	—
731	C₂²	—	2	8	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	8	4	no	—
744	C₂²	—	8	4	no	—
745	C₂²	C₁₃×#547	1	2	yes	—
746	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
747	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
748	C₂²	C₁₃×#577	1	2	yes	—
749	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	C₁₃×#547	1	2	yes	—
761	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
762	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
763	C₂	—	2	4	no	—
764	C₂	—	4	2	no	—
765	C₂	—	8	2	no	—
766	C₂	—	8	2	no	—
767	C₂	C₁₃×#3345	1	4	yes	direct product factor
768	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
769	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
770	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#553	C₂	semidirect
2. C₂×C₁₃×#547	C₂	semidirect
3. C₁₃×#3345	C₂	direct (N × H)
4. C₂×C₁₃×#501	C₂	semidirect
5. C₂×C₁₃×#481	C₂	semidirect
6. C₂×C₁₃×#481	C₂	semidirect
7. C₂×C₁₃×#482	C₂	semidirect
8. C₂×C₁₃×#480	C₂	semidirect
9. C₂×C₁₃×#478	C₂	semidirect
10. C₂×C₁₃×#476	C₂	semidirect
11. C₂×C₁₃×#469	C₂	semidirect
12. C₂×C₁₃×#466	C₂	semidirect
13. C₂×C₁₃×#442	C₂	semidirect
14. C₂×C₁₃×#435	C₂	semidirect
15. C₂×C₁₃×#428	C₂	semidirect
16. C₂²×C₁₃×#106	C₂	semidirect
22. C₁₃×#553	C₂²	semidirect
24. C₁₃×#547	C₂²	semidirect
45. C₁₃×#501	C₂²	semidirect
46. C₁₃×#482	C₂²	semidirect
47. C₁₃×#481	C₂²	semidirect
48. C₁₃×#481	C₂²	semidirect
49. C₁₃×#480	C₂²	semidirect
50. C₁₃×#478	C₂²	semidirect
51. C₁₃×#476	C₂²	semidirect
52. C₁₃×#469	C₂²	semidirect
53. C₁₃×#466	C₂²	semidirect
54. C₁₃×#442	C₂²	semidirect
55. C₁₃×#435	C₂²	semidirect
56. C₁₃×#428	C₂²	semidirect
66. C₂×C₁₃×#106	C₂²	semidirect
180. C₂×#3345	C₁₃	direct (N × H)
241. C₂×C₈×C₁₃	#41	semidirect
277. C₂×#553	C₂×C₁₃	semidirect
278. C₂×#547	C₂×C₁₃	semidirect
279. #3345	C₂×C₁₃	direct (N × H)
280. C₂×#501	C₂×C₁₃	semidirect
281. C₂×#481	C₂×C₁₃	semidirect
282. C₂×#481	C₂×C₁₃	semidirect
283. C₂×#482	C₂×C₁₃	semidirect
284. C₂×#480	C₂×C₁₃	semidirect
285. C₂×#478	C₂×C₁₃	semidirect
286. C₂×#476	C₂×C₁₃	semidirect
287. C₂×#469	C₂×C₁₃	semidirect
288. C₂×#466	C₂×C₁₃	semidirect
289. C₂×#442	C₂×C₁₃	semidirect
290. C₂×#435	C₂×C₁₃	semidirect
291. C₂×#428	C₂×C₁₃	semidirect
292. C₂²×#106	C₂×C₁₃	semidirect
360. C₈×C₁₃	C₂×#41	semidirect
366. #553	C₂²×C₁₃	semidirect
368. #547	C₂²×C₁₃	semidirect
389. #501	C₂²×C₁₃	semidirect
390. #482	C₂²×C₁₃	semidirect
391. #481	C₂²×C₁₃	semidirect
392. #481	C₂²×C₁₃	semidirect
393. #480	C₂²×C₁₃	semidirect
394. #478	C₂²×C₁₃	semidirect
395. #476	C₂²×C₁₃	semidirect
396. #469	C₂²×C₁₃	semidirect
397. #466	C₂²×C₁₃	semidirect
398. #442	C₂²×C₁₃	semidirect
399. #435	C₂²×C₁₃	semidirect
400. #428	C₂²×C₁₃	semidirect
410. C₂×#106	C₂²×C₁₃	semidirect
561. C₂×C₁₃	#3345	direct (N × H)
625. C₂×C₈	C₁₃×#41	semidirect
661. C₁₃	C₂×#3345	direct (N × H)
729. C₈	C₂×C₁₃×#41	semidirect
767. C₂	C₁₃×#3345	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×#553	2
C₂×C₁₃×#547	2
C₁₃×#3345	2
C₂×C₁₃×#501	2
C₂×C₁₃×#481	2
C₂×C₁₃×#482	2
C₂×C₁₃×#480	2
C₂×C₁₃×#478	2
C₂×C₁₃×#476	2
C₂×C₁₃×#469	2
C₂×C₁₃×#466	2
C₂×C₁₃×#442	2
C₂×C₁₃×#435	2
C₂×C₁₃×#428	2
C₂²×C₁₃×#106	2
C₂×#3345	13

Subgroups — C2×C13×#3345 #15747576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3345 #15747576