Subgroups — C₂×C₁₃×#3318 #15747467

Order 3328.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 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×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3318	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#447	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×#418	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₄×C₁₃	—	2	1	no	—
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#553	—	2	4	no	—
26	C₁₃×#553	C₂²	1	8	yes	complemented
27	D₄²×C₁₃	—	2	4	no	—
28	D₄²×C₁₃	C₂²	1	8	yes	complemented
29	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#126	—	2	1	no	—
31	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×#123	—	2	1	no	—
33	C₂×C₁₃×#121	—	2	1	no	—
34	C₂×C₁₃×#121	—	2	1	no	—
35	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×#120	—	2	1	no	—
40	C₂×C₁₃×#120	—	2	1	no	—
41	C₂×C₄×D₄×C₁₃	—	2	1	no	—
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#490	C₂²	1	8	yes	complemented
48	C₁₃×#482	C₂²	1	8	yes	complemented
49	C₁₃×#481	C₂²	1	8	yes	complemented
50	C₁₃×#478	C₂²	1	8	yes	complemented
51	C₁₃×#469	C₂²	1	8	yes	complemented
52	C₁₃×#466	C₂²	1	8	yes	complemented
53	C₁₃×#459	C₂²	1	8	yes	complemented
54	C₁₃×#447	C₂²	1	8	yes	complemented
55	C₁₃×#447	C₂²	1	8	yes	complemented
56	C₁₃×#442	C₂²	1	8	yes	complemented
57	C₁₃×#435	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#418	C₂²	1	8	yes	complemented
63	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#102	C₂²	1	8	yes	complemented
67	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₁₃	—	2	1	no	—
78	C₂⁵×C₁₃	—	2	1	no	—
79	C₂²×D₄×C₁₃	—	2	4	no	—
80	C₂²×D₄×C₁₃	—	2	4	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	—	2	1	no	—
85	C₂²×D₄×C₁₃	—	2	8	no	—
86	C₂²×D₄×C₁₃	—	2	1	no	—
87	C₂²×D₄×C₁₃	—	2	1	no	—
88	C₂²×D₄×C₁₃	—	2	1	no	—
89	C₂²×D₄×C₁₃	—	2	2	no	—
90	C₂²×D₄×C₁₃	—	2	2	no	—
91	C₂²×D₄×C₁₃	—	2	1	no	—
92	C₂²×D₄×C₁₃	—	4	2	no	—
93	C₂²×D₄×C₁₃	—	4	2	no	—
94	C₂²×D₄×C₁₃	—	4	8	no	—
95	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
96	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
100	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
101	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	—	2	1	no	—
103	C₂³×C₄×C₁₃	—	2	1	no	—
104	C₂³×C₄×C₁₃	—	2	1	no	—
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×D₈	—	2	4	no	—
108	C₂×C₁₃×D₈	—	4	2	no	—
109	C₂×C₁₃×D₈	—	4	2	no	—
110	C₂×C₁₃×D₈	C₂³	1	4	yes	—
111	C₂×C₁₃×D₈	C₂³	1	4	yes	complemented
112	C₂×C₁₃×D₈	C₂³	1	4	yes	complemented
113	C₂×C₁₃×M₁₆	—	4	2	no	—
114	C₂×C₁₃×M₁₆	C₂³	1	4	yes	complemented
115	C₂²×C₈×C₁₃	—	4	2	no	—
116	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₁₃	C₂³	1	4	yes	complemented
121	C₁₃×#127	—	2	2	no	—
122	C₁₃×#127	C₂³	1	4	yes	—
123	C₁₃×#126	—	2	8	no	—
124	C₁₃×#125	—	2	2	no	—
125	C₁₃×#125	C₂³	1	4	yes	complemented
126	C₁₃×#123	—	2	8	no	—
127	C₁₃×#121	—	2	8	no	—
128	C₁₃×#121	—	2	2	no	—
129	C₁₃×#121	—	2	2	no	—
130	C₁₃×#121	—	2	2	no	—
131	C₁₃×#121	—	2	2	no	—
132	C₁₃×#121	—	2	8	no	—
133	C₁₃×#121	C₂³	1	4	yes	—
134	C₁₃×#121	C₂³	1	4	yes	—
135	C₁₃×#121	C₂³	1	4	yes	complemented
136	C₁₃×#121	C₂³	1	4	yes	complemented
137	C₁₃×#120	—	2	8	no	—
138	C₁₃×#120	—	2	8	no	—
139	C₄×D₄×C₁₃	—	2	8	no	—
140	C₄×D₄×C₁₃	—	2	2	no	—
141	C₄×D₄×C₁₃	—	2	2	no	—
142	C₄×D₄×C₁₃	D₄	1	4	yes	—
143	C₄×D₄×C₁₃	C₂³	1	4	yes	—
144	C₄×D₄×C₁₃	C₂³	1	4	yes	—
145	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
146	C₁₃×#117	—	2	2	no	—
147	C₁₃×#117	C₂³	1	4	yes	complemented
148	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
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	D₄	1	1	yes	characteristic
166	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
167	C₂×C₄²×C₁₃	—	2	1	no	—
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₁₃×#107	C₂³	1	4	yes	complemented
170	C₁₃×#106	C₂³	1	4	yes	complemented
171	C₁₃×#106	C₂³	1	4	yes	complemented
172	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
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	complemented
177	C₁₃×#102	C₂³	1	4	yes	complemented
178	C₁₃×#102	C₂³	1	4	yes	complemented
179	C₁₃×#102	C₂³	1	4	yes	complemented
180	C₁₃×#102	C₂³	1	4	yes	complemented
181	C₁₃×#102	C₂³	1	4	yes	complemented
182	C₁₃×#102	C₂³	1	4	yes	complemented
183	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
184	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
185	C₁₃×#97	C₂³	1	4	yes	complemented
186	C₂×#3318	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂⁴×C₁₃	—	2	1	no	—
188	C₂⁴×C₁₃	—	2	1	no	—
189	C₂⁴×C₁₃	—	2	1	no	—
190	C₂⁴×C₁₃	—	2	1	no	—
191	C₂⁴×C₁₃	—	2	4	no	—
192	C₂⁴×C₁₃	—	2	4	no	—
193	C₂⁴×C₁₃	—	4	4	no	—
194	C₂⁴×C₁₃	—	4	4	no	—
195	C₂⁴×C₁₃	—	4	4	no	—
196	C₂⁴×C₁₃	—	4	4	no	—
197	C₂⁴×C₁₃	—	8	2	no	—
198	C₂⁴×C₁₃	—	8	2	no	—
199	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₂×D₄×C₁₃	—	2	4	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	4	no	—
208	C₂×D₄×C₁₃	—	2	1	no	—
209	C₂×D₄×C₁₃	—	2	1	no	—
210	C₂×D₄×C₁₃	—	2	4	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	1	no	—
213	C₂×D₄×C₁₃	—	2	1	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	—	2	4	no	—
216	C₂×D₄×C₁₃	—	2	2	no	—
217	C₂×D₄×C₁₃	—	2	2	no	—
218	C₂×D₄×C₁₃	—	2	2	no	—
219	C₂×D₄×C₁₃	—	2	2	no	—
220	C₂×D₄×C₁₃	—	2	2	no	—
221	C₂×D₄×C₁₃	—	2	2	no	—
222	C₂×D₄×C₁₃	—	2	2	no	—
223	C₂×D₄×C₁₃	—	4	4	no	—
224	C₂×D₄×C₁₃	—	4	4	no	—
225	C₂×D₄×C₁₃	—	4	8	no	—
226	C₂×D₄×C₁₃	—	4	8	no	—
227	C₂×D₄×C₁₃	—	4	4	no	—
228	C₂×D₄×C₁₃	—	4	4	no	—
229	C₂×D₄×C₁₃	—	4	4	no	—
230	C₂×D₄×C₁₃	—	4	32	no	—
231	C₂×D₄×C₁₃	—	4	4	no	—
232	C₂×D₄×C₁₃	—	4	4	no	—
233	C₂×D₄×C₁₃	—	4	4	no	—
234	C₂×D₄×C₁₃	—	8	2	no	—
235	C₂×D₄×C₁₃	—	8	2	no	—
236	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
237	C₂×D₄×C₁₃	#41	1	4	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₃	—	2	2	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	1	no	—
247	C₂²×C₄×C₁₃	—	2	1	no	—
248	C₂²×C₄×C₁₃	—	2	1	no	—
249	C₂²×C₄×C₁₃	—	2	1	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	2	4	no	—
252	C₂²×C₄×C₁₃	—	2	4	no	—
253	C₂²×C₄×C₁₃	—	4	4	no	—
254	C₂²×C₄×C₁₃	—	8	2	no	—
255	C₂²×C₄×C₁₃	—	8	2	no	—
256	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₁₃×D₈	—	2	8	no	—
266	C₁₃×D₈	—	4	4	no	—
267	C₁₃×D₈	—	4	4	no	—
268	C₁₃×M₁₆	—	4	4	no	—
269	C₂×C₈×C₁₃	—	2	2	no	—
270	C₂×C₈×C₁₃	—	2	2	no	—
271	C₂×C₈×C₁₃	—	2	2	no	—
272	C₂×C₈×C₁₃	—	2	2	no	—
273	C₂×C₈×C₁₃	—	4	4	no	—
274	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
277	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	2	4	no	—
281	C₁₃×C₄⋊C₄	—	2	4	no	—
282	C₁₃×C₄⋊C₄	—	2	4	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
288	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
289	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	—	2	4	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
298	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
299	C₄²×C₁₃	—	2	4	no	—
300	C₄²×C₁₃	C₂×D₄	1	2	yes	—
301	C₄²×C₁₃	C₂⁴	1	2	yes	—
302	C₂×#553	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#3318	C₂×C₁₃	1	16	yes	direct product factor
305	C₂×#490	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₂×#481	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂×#482	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
309	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
310	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
312	C₂×#447	C₂×C₁₃	1	1	yes	characteristic, complemented
313	C₂×#447	C₂×C₁₃	1	1	yes	characteristic, complemented
314	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
315	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
316	C₂×#418	C₂×C₁₃	1	1	yes	characteristic, complemented
317	C₂²×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
318	C₂³×C₁₃	—	2	2	no	—
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	4	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	—	2	2	no	—
325	C₂³×C₁₃	—	2	2	no	—
326	C₂³×C₁₃	—	2	2	no	—
327	C₂³×C₁₃	—	2	2	no	—
328	C₂³×C₁₃	—	4	8	no	—
329	C₂³×C₁₃	—	4	8	no	—
330	C₂³×C₁₃	—	4	8	no	—
331	C₂³×C₁₃	—	4	2	no	—
332	C₂³×C₁₃	—	4	2	no	—
333	C₂³×C₁₃	—	4	2	no	—
334	C₂³×C₁₃	—	4	2	no	—
335	C₂³×C₁₃	—	4	2	no	—
336	C₂³×C₁₃	—	4	8	no	—
337	C₂³×C₁₃	—	4	2	no	—
338	C₂³×C₁₃	—	4	2	no	—
339	C₂³×C₁₃	—	4	2	no	—
340	C₂³×C₁₃	—	4	2	no	—
341	C₂³×C₁₃	—	4	2	no	—
342	C₂³×C₁₃	—	4	2	no	—
343	C₂³×C₁₃	—	8	4	no	—
344	C₂³×C₁₃	—	8	4	no	—
345	C₂³×C₁₃	—	8	16	no	—
346	C₂³×C₁₃	—	8	16	no	—
347	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
348	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
349	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
350	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
351	D₄×C₁₃	—	2	8	no	—
352	D₄×C₁₃	—	2	4	no	—
353	D₄×C₁₃	—	2	2	no	—
354	D₄×C₁₃	—	2	2	no	—
355	D₄×C₁₃	—	2	2	no	—
356	D₄×C₁₃	—	2	2	no	—
357	D₄×C₁₃	—	2	2	no	—
358	D₄×C₁₃	—	2	2	no	—
359	D₄×C₁₃	—	2	2	no	—
360	D₄×C₁₃	—	4	8	no	—
361	D₄×C₁₃	—	4	8	no	—
362	D₄×C₁₃	—	4	8	no	—
363	D₄×C₁₃	—	4	8	no	—
364	D₄×C₁₃	—	4	8	no	—
365	D₄×C₁₃	—	4	8	no	—
366	D₄×C₁₃	—	4	2	no	—
367	D₄×C₁₃	—	4	2	no	—
368	D₄×C₁₃	—	4	2	no	—
369	D₄×C₁₃	—	8	4	no	—
370	D₄×C₁₃	—	8	4	no	—
371	D₄×C₁₃	C₂×#41	1	4	yes	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	4	no	—
377	C₂×C₄×C₁₃	—	2	4	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	4	8	no	—
387	C₂×C₄×C₁₃	—	4	2	no	—
388	C₂×C₄×C₁₃	—	4	2	no	—
389	C₂×C₄×C₁₃	—	4	2	no	—
390	C₂×C₄×C₁₃	—	4	2	no	—
391	C₂×C₄×C₁₃	—	8	4	no	—
392	C₂×C₄×C₁₃	—	8	4	no	—
393	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
399	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
400	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
401	C₈×C₁₃	—	2	2	no	—
402	C₈×C₁₃	—	2	2	no	—
403	C₈×C₁₃	—	2	2	no	—
404	C₈×C₁₃	—	2	2	no	—
405	C₂³×D₄	—	2	1	no	—
406	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
407	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
408	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
409	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
412	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	#553	—	2	4	no	—
414	#553	C₂²×C₁₃	1	8	yes	complemented
415	D₄²	—	2	4	no	—
416	D₄²	C₂²×C₁₃	1	8	yes	complemented
417	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×#126	—	2	1	no	—
419	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	C₂×#123	—	2	1	no	—
421	C₂×#121	—	2	1	no	—
422	C₂×#121	—	2	1	no	—
423	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	C₂×#120	—	2	1	no	—
428	C₂×#120	—	2	1	no	—
429	C₂×C₄×D₄	—	2	1	no	—
430	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
433	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	#490	C₂²×C₁₃	1	8	yes	complemented
436	#482	C₂²×C₁₃	1	8	yes	complemented
437	#481	C₂²×C₁₃	1	8	yes	complemented
438	#478	C₂²×C₁₃	1	8	yes	complemented
439	#469	C₂²×C₁₃	1	8	yes	complemented
440	#466	C₂²×C₁₃	1	8	yes	complemented
441	#459	C₂²×C₁₃	1	8	yes	complemented
442	#447	C₂²×C₁₃	1	8	yes	complemented
443	#447	C₂²×C₁₃	1	8	yes	complemented
444	#442	C₂²×C₁₃	1	8	yes	complemented
445	#435	C₂²×C₁₃	1	8	yes	complemented
446	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
447	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	#418	C₂²×C₁₃	1	8	yes	complemented
451	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
452	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
453	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×#102	C₂²×C₁₃	1	8	yes	complemented
455	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
457	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
461	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
462	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
464	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
465	C₂²×C₁₃	—	2	2	no	—
466	C₂²×C₁₃	—	2	8	no	—
467	C₂²×C₁₃	—	2	2	no	—
468	C₂²×C₁₃	—	2	2	no	—
469	C₂²×C₁₃	—	2	4	no	—
470	C₂²×C₁₃	—	2	2	no	—
471	C₂²×C₁₃	—	2	2	no	—
472	C₂²×C₁₃	—	4	4	no	—
473	C₂²×C₁₃	—	4	8	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	2	no	—
476	C₂²×C₁₃	—	4	2	no	—
477	C₂²×C₁₃	—	4	2	no	—
478	C₂²×C₁₃	—	4	2	no	—
479	C₂²×C₁₃	—	4	2	no	—
480	C₂²×C₁₃	—	4	2	no	—
481	C₂²×C₁₃	—	4	2	no	—
482	C₂²×C₁₃	—	4	2	no	—
483	C₂²×C₁₃	—	4	2	no	—
484	C₂²×C₁₃	—	4	2	no	—
485	C₂²×C₁₃	—	8	16	no	—
486	C₂²×C₁₃	—	8	16	no	—
487	C₂²×C₁₃	—	8	4	no	—
488	C₂²×C₁₃	—	8	4	no	—
489	C₂²×C₁₃	—	8	4	no	—
490	C₂²×C₁₃	#546	1	2	yes	—
491	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
492	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
493	C₂²×C₁₃	#576	1	2	yes	—
494	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
495	C₄×C₁₃	—	2	2	no	—
496	C₄×C₁₃	—	2	2	no	—
497	C₄×C₁₃	—	2	2	no	—
498	C₄×C₁₃	—	2	2	no	—
499	C₄×C₁₃	—	4	2	no	—
500	C₄×C₁₃	—	4	2	no	—
501	C₄×C₁₃	—	4	2	no	—
502	C₄×C₁₃	—	4	2	no	—
503	C₄×C₁₃	#546	1	2	yes	—
504	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
505	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
506	C₂⁵	—	2	1	no	—
507	C₂⁵	—	2	1	no	—
508	C₂²×D₄	—	2	4	no	—
509	C₂²×D₄	—	2	4	no	—
510	C₂²×D₄	—	2	1	no	—
511	C₂²×D₄	—	2	1	no	—
512	C₂²×D₄	—	2	1	no	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	—	2	8	no	—
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	—	2	1	no	—
517	C₂²×D₄	—	2	1	no	—
518	C₂²×D₄	—	2	2	no	—
519	C₂²×D₄	—	2	2	no	—
520	C₂²×D₄	—	2	1	no	—
521	C₂²×D₄	—	4	2	no	—
522	C₂²×D₄	—	4	2	no	—
523	C₂²×D₄	—	4	8	no	—
524	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
525	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
526	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
529	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
530	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
531	C₂³×C₄	—	2	1	no	—
532	C₂³×C₄	—	2	1	no	—
533	C₂³×C₄	—	2	1	no	—
534	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂×D₈	—	2	4	no	—
537	C₂×D₈	—	4	2	no	—
538	C₂×D₈	—	4	2	no	—
539	C₂×D₈	C₂³×C₁₃	1	4	yes	—
540	C₂×D₈	C₂³×C₁₃	1	4	yes	complemented
541	C₂×D₈	C₂³×C₁₃	1	4	yes	complemented
542	C₂×M₁₆	—	4	2	no	—
543	C₂×M₁₆	C₂³×C₁₃	1	4	yes	complemented
544	C₂²×C₈	—	4	2	no	—
545	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
546	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
547	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
548	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
549	C₂²×C₈	C₂³×C₁₃	1	4	yes	complemented
550	#127	—	2	2	no	—
551	#127	C₂³×C₁₃	1	4	yes	—
552	#126	—	2	8	no	—
553	#125	—	2	2	no	—
554	#125	C₂³×C₁₃	1	4	yes	complemented
555	#123	—	2	8	no	—
556	#121	—	2	8	no	—
557	#121	—	2	2	no	—
558	#121	—	2	2	no	—
559	#121	—	2	2	no	—
560	#121	—	2	2	no	—
561	#121	—	2	8	no	—
562	#121	C₂³×C₁₃	1	4	yes	—
563	#121	C₂³×C₁₃	1	4	yes	—
564	#121	C₂³×C₁₃	1	4	yes	complemented
565	#121	C₂³×C₁₃	1	4	yes	complemented
566	#120	—	2	8	no	—
567	#120	—	2	8	no	—
568	C₄×D₄	—	2	8	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	D₄×C₁₃	1	4	yes	—
572	C₄×D₄	C₂³×C₁₃	1	4	yes	—
573	C₄×D₄	C₂³×C₁₃	1	4	yes	—
574	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
575	#117	—	2	2	no	—
576	#117	C₂³×C₁₃	1	4	yes	complemented
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	2	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
596	C₂×C₄²	—	2	1	no	—
597	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
598	#107	C₂³×C₁₃	1	4	yes	complemented
599	#106	C₂³×C₁₃	1	4	yes	complemented
600	#106	C₂³×C₁₃	1	4	yes	complemented
601	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
602	#102	C₂³×C₁₃	1	4	yes	—
603	#102	C₂³×C₁₃	1	4	yes	—
604	#102	C₂³×C₁₃	1	4	yes	—
605	#102	C₂³×C₁₃	1	4	yes	complemented
606	#102	C₂³×C₁₃	1	4	yes	complemented
607	#102	C₂³×C₁₃	1	4	yes	complemented
608	#102	C₂³×C₁₃	1	4	yes	complemented
609	#102	C₂³×C₁₃	1	4	yes	complemented
610	#102	C₂³×C₁₃	1	4	yes	complemented
611	#102	C₂³×C₁₃	1	4	yes	complemented
612	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
613	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
614	#97	C₂³×C₁₃	1	4	yes	complemented
615	C₂×C₁₃	—	2	4	no	—
616	C₂×C₁₃	—	4	2	no	—
617	C₂×C₁₃	—	4	4	no	—
618	C₂×C₁₃	—	8	2	no	—
619	C₂×C₁₃	—	8	2	no	—
620	C₂×C₁₃	—	8	2	no	—
621	C₂×C₁₃	#3318	1	4	yes	direct product factor
622	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
623	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
624	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
625	C₂⁴	—	2	1	no	—
626	C₂⁴	—	2	1	no	—
627	C₂⁴	—	2	1	no	—
628	C₂⁴	—	2	1	no	—
629	C₂⁴	—	2	4	no	—
630	C₂⁴	—	2	4	no	—
631	C₂⁴	—	4	4	no	—
632	C₂⁴	—	4	4	no	—
633	C₂⁴	—	4	4	no	—
634	C₂⁴	—	4	4	no	—
635	C₂⁴	—	8	2	no	—
636	C₂⁴	—	8	2	no	—
637	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	8	no	—
641	C₂×D₄	—	2	8	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	4	4	no	—
662	C₂×D₄	—	4	4	no	—
663	C₂×D₄	—	4	8	no	—
664	C₂×D₄	—	4	8	no	—
665	C₂×D₄	—	4	4	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	—	4	4	no	—
668	C₂×D₄	—	4	32	no	—
669	C₂×D₄	—	4	4	no	—
670	C₂×D₄	—	4	4	no	—
671	C₂×D₄	—	4	4	no	—
672	C₂×D₄	—	8	2	no	—
673	C₂×D₄	—	8	2	no	—
674	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
675	C₂×D₄	C₁₃×#41	1	4	yes	—
676	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
677	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
678	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
679	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	4	4	no	—
692	C₂²×C₄	—	8	2	no	—
693	C₂²×C₄	—	8	2	no	—
694	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
699	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
703	D₈	—	2	8	no	—
704	D₈	—	4	4	no	—
705	D₈	—	4	4	no	—
706	M₁₆	—	4	4	no	—
707	C₂×C₈	—	2	2	no	—
708	C₂×C₈	—	2	2	no	—
709	C₂×C₈	—	2	2	no	—
710	C₂×C₈	—	2	2	no	—
711	C₂×C₈	—	4	4	no	—
712	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
713	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
714	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
715	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
724	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
736	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
737	C₄²	—	2	4	no	—
738	C₄²	C₂×D₄×C₁₃	1	2	yes	—
739	C₄²	C₂⁴×C₁₃	1	2	yes	—
740	C₁₃	C₂×#3318	1	1	yes	characteristic, direct product factor, Sylow
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	4	8	no	—
752	C₂³	—	4	8	no	—
753	C₂³	—	4	8	no	—
754	C₂³	—	4	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	2	no	—
757	C₂³	—	4	2	no	—
758	C₂³	—	4	2	no	—
759	C₂³	—	4	8	no	—
760	C₂³	—	4	2	no	—
761	C₂³	—	4	2	no	—
762	C₂³	—	4	2	no	—
763	C₂³	—	4	2	no	—
764	C₂³	—	4	2	no	—
765	C₂³	—	4	2	no	—
766	C₂³	—	8	4	no	—
767	C₂³	—	8	4	no	—
768	C₂³	—	8	16	no	—
769	C₂³	—	8	16	no	—
770	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
771	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
772	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
773	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
774	D₄	—	2	8	no	—
775	D₄	—	2	4	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	2	2	no	—
782	D₄	—	2	2	no	—
783	D₄	—	4	8	no	—
784	D₄	—	4	8	no	—
785	D₄	—	4	8	no	—
786	D₄	—	4	8	no	—
787	D₄	—	4	8	no	—
788	D₄	—	4	8	no	—
789	D₄	—	4	2	no	—
790	D₄	—	4	2	no	—
791	D₄	—	4	2	no	—
792	D₄	—	8	4	no	—
793	D₄	—	8	4	no	—
794	D₄	C₂×C₁₃×#41	1	4	yes	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	4	8	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	8	4	no	—
815	C₂×C₄	—	8	4	no	—
816	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
821	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
822	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
823	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
824	C₈	—	2	2	no	—
825	C₈	—	2	2	no	—
826	C₈	—	2	2	no	—
827	C₈	—	2	2	no	—
828	C₂²	—	2	8	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	8	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	8	16	no	—
849	C₂²	—	8	16	no	—
850	C₂²	—	8	4	no	—
851	C₂²	—	8	4	no	—
852	C₂²	—	8	4	no	—
853	C₂²	C₁₃×#546	1	2	yes	—
854	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
855	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
856	C₂²	C₁₃×#576	1	2	yes	—
857	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	C₁₃×#546	1	2	yes	—
867	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
868	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
869	C₂	—	2	4	no	—
870	C₂	—	4	2	no	—
871	C₂	—	4	4	no	—
872	C₂	—	8	2	no	—
873	C₂	—	8	2	no	—
874	C₂	—	8	2	no	—
875	C₂	C₁₃×#3318	1	4	yes	direct product factor
876	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
877	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
878	C₂	C₂×C₁₃×#576	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×D₄²×C₁₃	C₂	semidirect
3. C₁₃×#3318	C₂	direct (N × H)
4. C₂×C₁₃×#490	C₂	semidirect
5. C₂×C₁₃×#481	C₂	semidirect
6. C₂×C₁₃×#482	C₂	semidirect
7. C₂×C₁₃×#478	C₂	semidirect
8. C₂×C₁₃×#469	C₂	semidirect
9. C₂×C₁₃×#466	C₂	semidirect
10. C₂×C₁₃×#459	C₂	semidirect
11. C₂×C₁₃×#447	C₂	semidirect
12. C₂×C₁₃×#447	C₂	semidirect
13. C₂×C₁₃×#442	C₂	semidirect
14. C₂×C₁₃×#435	C₂	semidirect
15. C₂×C₁₃×#418	C₂	semidirect
16. C₂²×C₁₃×#102	C₂	semidirect
21. C₂²×C₁₃×D₈	C₂²	semidirect
22. C₂²×C₁₃×D₈	C₂²	semidirect
23. C₂²×C₁₃×M₁₆	C₂²	semidirect
24. C₂³×C₈×C₁₃	C₂²	semidirect
26. C₁₃×#553	C₂²	semidirect
28. D₄²×C₁₃	C₂²	semidirect
31. C₂×C₁₃×#125	C₂²	semidirect
37. C₂×C₁₃×#121	C₂²	semidirect
38. C₂×C₁₃×#121	C₂²	semidirect
44. C₂×C₄×D₄×C₁₃	C₂²	semidirect
45. C₂×C₁₃×#117	C₂²	semidirect
46. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
47. C₁₃×#490	C₂²	semidirect
48. C₁₃×#482	C₂²	semidirect
49. C₁₃×#481	C₂²	semidirect
50. C₁₃×#478	C₂²	semidirect
51. C₁₃×#469	C₂²	semidirect
52. C₁₃×#466	C₂²	semidirect
53. C₁₃×#459	C₂²	semidirect
54. C₁₃×#447	C₂²	semidirect
55. C₁₃×#447	C₂²	semidirect
56. C₁₃×#442	C₂²	semidirect
57. C₁₃×#435	C₂²	semidirect
58. C₂×C₁₃×#107	C₂²	semidirect
59. C₂×C₁₃×#106	C₂²	semidirect
60. C₂×C₁₃×#106	C₂²	semidirect
61. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
62. C₁₃×#418	C₂²	semidirect
66. C₂×C₁₃×#102	C₂²	semidirect
67. C₂×C₁₃×#102	C₂²	semidirect
68. C₂×C₁₃×#102	C₂²	semidirect
69. C₂×C₁₃×#102	C₂²	semidirect
70. C₂×C₁₃×#102	C₂²	semidirect
71. C₂×C₁₃×#102	C₂²	semidirect
72. C₂×C₁₃×#102	C₂²	semidirect
73. C₂×C₁₃×#102	C₂²	semidirect
74. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
75. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₁₃×#97	C₂²	semidirect
111. C₂×C₁₃×D₈	C₂³	semidirect
112. C₂×C₁₃×D₈	C₂³	semidirect
114. C₂×C₁₃×M₁₆	C₂³	semidirect
120. C₂²×C₈×C₁₃	C₂³	semidirect
125. C₁₃×#125	C₂³	semidirect
135. C₁₃×#121	C₂³	semidirect
136. C₁₃×#121	C₂³	semidirect
145. C₄×D₄×C₁₃	C₂³	semidirect
147. C₁₃×#117	C₂³	semidirect
157. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
169. C₁₃×#107	C₂³	semidirect
170. C₁₃×#106	C₂³	semidirect
171. C₁₃×#106	C₂³	semidirect
172. C₁₃×C₄⋊C₈	C₂³	semidirect
176. C₁₃×#102	C₂³	semidirect
177. C₁₃×#102	C₂³	semidirect
178. C₁₃×#102	C₂³	semidirect
179. C₁₃×#102	C₂³	semidirect
180. C₁₃×#102	C₂³	semidirect
181. C₁₃×#102	C₂³	semidirect
182. C₁₃×#102	C₂³	semidirect
183. C₁₃×C₂²⋊C₈	C₂³	semidirect
184. C₁₃×C₂²⋊C₈	C₂³	semidirect
185. C₁₃×#97	C₂³	semidirect
186. C₂×#3318	C₁₃	direct (N × H)
302. C₂×#553	C₂×C₁₃	semidirect
303. C₂×D₄²	C₂×C₁₃	semidirect
304. #3318	C₂×C₁₃	direct (N × H)
305. C₂×#490	C₂×C₁₃	semidirect
306. C₂×#481	C₂×C₁₃	semidirect
307. C₂×#482	C₂×C₁₃	semidirect
308. C₂×#478	C₂×C₁₃	semidirect
309. C₂×#469	C₂×C₁₃	semidirect
310. C₂×#466	C₂×C₁₃	semidirect
311. C₂×#459	C₂×C₁₃	semidirect
312. C₂×#447	C₂×C₁₃	semidirect
313. C₂×#447	C₂×C₁₃	semidirect
314. C₂×#442	C₂×C₁₃	semidirect
315. C₂×#435	C₂×C₁₃	semidirect
316. C₂×#418	C₂×C₁₃	semidirect
317. C₂²×#102	C₂×C₁₃	semidirect
409. C₂²×D₈	C₂²×C₁₃	semidirect
410. C₂²×D₈	C₂²×C₁₃	semidirect
411. C₂²×M₁₆	C₂²×C₁₃	semidirect
412. C₂³×C₈	C₂²×C₁₃	semidirect
414. #553	C₂²×C₁₃	semidirect
416. D₄²	C₂²×C₁₃	semidirect
419. C₂×#125	C₂²×C₁₃	semidirect
425. C₂×#121	C₂²×C₁₃	semidirect
426. C₂×#121	C₂²×C₁₃	semidirect
432. C₂×C₄×D₄	C₂²×C₁₃	semidirect
433. C₂×#117	C₂²×C₁₃	semidirect
434. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
435. #490	C₂²×C₁₃	semidirect
436. #482	C₂²×C₁₃	semidirect
437. #481	C₂²×C₁₃	semidirect
438. #478	C₂²×C₁₃	semidirect
439. #469	C₂²×C₁₃	semidirect
440. #466	C₂²×C₁₃	semidirect
441. #459	C₂²×C₁₃	semidirect
442. #447	C₂²×C₁₃	semidirect
443. #447	C₂²×C₁₃	semidirect
444. #442	C₂²×C₁₃	semidirect
445. #435	C₂²×C₁₃	semidirect
446. C₂×#107	C₂²×C₁₃	semidirect
447. C₂×#106	C₂²×C₁₃	semidirect
448. C₂×#106	C₂²×C₁₃	semidirect
449. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
450. #418	C₂²×C₁₃	semidirect
454. C₂×#102	C₂²×C₁₃	semidirect
455. C₂×#102	C₂²×C₁₃	semidirect
456. C₂×#102	C₂²×C₁₃	semidirect
457. C₂×#102	C₂²×C₁₃	semidirect
458. C₂×#102	C₂²×C₁₃	semidirect
459. C₂×#102	C₂²×C₁₃	semidirect
460. C₂×#102	C₂²×C₁₃	semidirect
461. C₂×#102	C₂²×C₁₃	semidirect
462. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
463. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
464. C₂×#97	C₂²×C₁₃	semidirect
540. C₂×D₈	C₂³×C₁₃	semidirect
541. C₂×D₈	C₂³×C₁₃	semidirect
543. C₂×M₁₆	C₂³×C₁₃	semidirect
549. C₂²×C₈	C₂³×C₁₃	semidirect
554. #125	C₂³×C₁₃	semidirect
564. #121	C₂³×C₁₃	semidirect
565. #121	C₂³×C₁₃	semidirect
574. C₄×D₄	C₂³×C₁₃	semidirect
576. #117	C₂³×C₁₃	semidirect
586. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
598. #107	C₂³×C₁₃	semidirect
599. #106	C₂³×C₁₃	semidirect
600. #106	C₂³×C₁₃	semidirect
601. C₄⋊C₈	C₂³×C₁₃	semidirect
605. #102	C₂³×C₁₃	semidirect
606. #102	C₂³×C₁₃	semidirect
607. #102	C₂³×C₁₃	semidirect
608. #102	C₂³×C₁₃	semidirect
609. #102	C₂³×C₁₃	semidirect
610. #102	C₂³×C₁₃	semidirect
611. #102	C₂³×C₁₃	semidirect
612. C₂²⋊C₈	C₂³×C₁₃	semidirect
613. C₂²⋊C₈	C₂³×C₁₃	semidirect
614. #97	C₂³×C₁₃	semidirect
621. C₂×C₁₃	#3318	direct (N × H)
740. C₁₃	C₂×#3318	direct (N × H)
875. C₂	C₁₃×#3318	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×D₄²×C₁₃	2
C₁₃×#3318	2
C₂×C₁₃×#490	2
C₂×C₁₃×#481	2
C₂×C₁₃×#482	2
C₂×C₁₃×#478	2
C₂×C₁₃×#469	2
C₂×C₁₃×#466	2
C₂×C₁₃×#459	2
C₂×C₁₃×#447	2
C₂×C₁₃×#442	2
C₂×C₁₃×#435	2
C₂×C₁₃×#418	2
C₂²×C₁₃×#102	2
C₂×#3318	13

Subgroups — C2×C13×#3318 #15747467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3318 #15747467