Subgroups — C₁₃×#61324 #15747663

Order 3328.

1878 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×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3375	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3373	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3371	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3370	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3140	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3077	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3040	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic
15	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₁₃×#559	—	2	1	no	—
21	C₁₃×#559	—	2	2	no	—
22	C₁₃×#559	—	2	1	no	—
23	C₁₃×#559	C₂²	1	2	yes	—
24	C₁₃×#559	C₂²	1	4	yes	—
25	C₁₃×#559	C₂²	1	2	yes	—
26	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#557	C₂²	1	2	yes	complemented
29	C₁₃×#554	—	2	1	no	—
30	C₁₃×#554	—	2	2	no	—
31	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#554	C₂²	1	2	yes	complemented
33	D₄×Q₈×C₁₃	—	2	1	no	—
34	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#533	—	2	2	no	—
36	C₁₃×#533	—	2	1	no	—
37	C₁₃×#533	C₂²	1	2	yes	—
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#124	—	2	1	no	—
41	C₂×C₁₃×#124	C₂²	1	2	yes	—
42	C₂×C₁₃×#123	—	2	2	no	—
43	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×#41	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
46	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	—	2	1	no	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
50	C₁₃×#490	C₂²	1	4	yes	—
51	C₁₃×#489	C₂²	1	4	yes	complemented
52	C₁₃×#489	C₂²	1	4	yes	complemented
53	C₁₃×#488	C₂²	1	4	yes	complemented
54	C₁₃×#488	C₂²	1	4	yes	complemented
55	C₁₃×#486	C₂²	1	2	yes	—
56	C₁₃×#486	C₂²	1	2	yes	—
57	C₁₃×#479	C₂²	1	4	yes	complemented
58	C₁₃×#478	C₂²	1	4	yes	complemented
59	C₁₃×#478	C₂²	1	4	yes	complemented
60	C₁₃×#477	C₂²	1	2	yes	complemented
61	C₁₃×#476	C₂²	1	4	yes	complemented
62	C₁₃×#475	C₂²	1	2	yes	complemented
63	C₁₃×#474	C₂²	1	4	yes	complemented
64	C₁₃×#464	C₂²	1	4	yes	complemented
65	C₁₃×#464	C₂²	1	4	yes	complemented
66	C₁₃×#463	C₂²	1	4	yes	complemented
67	C₁₃×#463	C₂²	1	4	yes	complemented
68	C₁₃×#460	C₂²	1	2	yes	—
69	C₁₃×#460	C₂²	1	2	yes	—
70	C₁₃×#459	C₂²	1	2	yes	—
71	C₁₃×#459	C₂²	1	2	yes	—
72	C₁₃×#446	C₂²	1	4	yes	complemented
73	C₁₃×#446	C₂²	1	2	yes	complemented
74	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
75	C₁₃×#442	C₂²	1	4	yes	complemented
76	C₁₃×#441	C₂²	1	2	yes	complemented
77	C₁₃×#440	C₂²	1	2	yes	complemented
78	C₁₃×#440	C₂²	1	4	yes	complemented
79	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
80	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
81	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
82	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
83	C₁₃×#428	C₂²	1	1	yes	characteristic
84	C₁₃×#428	C₂²	1	2	yes	—
85	C₁₃×#423	C₂²	1	1	yes	characteristic
86	C₁₃×#423	C₂²	1	2	yes	—
87	C₁₃×#419	C₂²	1	2	yes	—
88	C₁₃×#419	C₂²	1	1	yes	characteristic
89	C₁₃×#418	C₂²	1	2	yes	—
90	C₁₃×#418	C₂²	1	2	yes	—
91	C₁₃×#418	C₂²	1	2	yes	—
92	C₁₃×#417	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	—	2	1	no	—
97	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃	—	2	2	no	—
103	C₁₃×#137	—	2	4	no	—
104	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
105	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×D₈	C₂³	1	4	yes	—
109	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	—	2	2	no	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	—	2	2	no	—
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×#127	—	2	1	no	—
121	C₁₃×#127	—	2	1	no	—
122	C₁₃×#127	C₂³	1	2	yes	—
123	C₁₃×#127	C₂³	1	2	yes	—
124	C₁₃×#125	—	2	2	no	—
125	C₁₃×#125	—	2	2	no	—
126	C₁₃×#125	—	2	2	no	—
127	C₁₃×#125	C₂³	1	2	yes	—
128	C₁₃×#125	C₂³	1	2	yes	—
129	C₁₃×#125	C₂³	1	2	yes	—
130	C₁₃×#124	—	2	2	no	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	—	2	4	no	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	—	2	2	no	—
135	C₁₃×#124	C₂³	1	4	yes	—
136	C₁₃×#124	C₂³	1	4	yes	—
137	C₁₃×#123	—	2	4	no	—
138	C₁₃×#123	—	2	4	no	—
139	C₁₃×#123	—	2	4	no	—
140	C₁₃×#123	—	2	4	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	1	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	1	no	—
147	C₁₃×C₂²⋊Q₈	—	2	1	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	2	no	—
152	C₄×Q₈×C₁₃	—	2	1	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	—	2	2	no	—
155	C₄×Q₈×C₁₃	—	2	2	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	—	2	1	no	—
158	C₄×Q₈×C₁₃	—	2	1	no	—
159	C₄×Q₈×C₁₃	—	2	2	no	—
160	C₄×Q₈×C₁₃	—	2	1	no	—
161	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
162	C₄×Q₈×C₁₃	D₄	1	2	yes	—
163	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	4	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	C₂³	1	2	yes	—
183	C₄×D₄×C₁₃	C₂³	1	4	yes	—
184	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₁₃	C₂³	1	4	yes	—
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₁₃×#117	—	2	2	no	—
189	C₁₃×#117	—	2	1	no	—
190	C₁₃×#117	C₂³	1	1	yes	characteristic
191	C₁₃×#117	C₂³	1	2	yes	—
192	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
196	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₄²×C₁₃	—	2	1	no	—
202	C₂×C₄²×C₁₃	—	2	2	no	—
203	C₂×C₄²×C₁₃	—	2	1	no	—
204	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₁₃×#107	C₂³	1	4	yes	—
207	C₁₃×#107	C₂³	1	2	yes	—
208	C₁₃×#106	C₂³	1	2	yes	—
209	C₁₃×#106	C₂³	1	4	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	C₂³	1	2	yes	—
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	2	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×#97	C₂³	1	2	yes	—
227	C₁₃×#97	C₂³	1	4	yes	—
228	C₄×C₈×C₁₃	C₂³	1	4	yes	—
229	C₄×C₈×C₁₃	C₂³	1	2	yes	—
230	#61324	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂⁴×C₁₃	—	2	2	no	—
232	C₁₃×#41	—	2	2	no	—
233	C₁₃×#41	#41	1	4	yes	—
234	C₂×Q₈×C₁₃	—	2	2	no	—
235	C₂×Q₈×C₁₃	—	2	1	no	—
236	C₂×Q₈×C₁₃	—	2	1	no	—
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	2	1	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	4	2	no	—
242	C₂×Q₈×C₁₃	—	4	4	no	—
243	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
246	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	4	no	—
256	C₂×D₄×C₁₃	—	4	4	no	—
257	C₂×D₄×C₁₃	—	8	2	no	—
258	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
259	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	2	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	—	2	4	no	—
269	C₂²×C₄×C₁₃	—	8	4	no	—
270	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₁₃×Q₁₆	—	2	4	no	—
276	C₁₃×SD₁₆	—	2	8	no	—
277	C₁₃×SD₁₆	—	2	4	no	—
278	C₁₃×D₈	—	2	8	no	—
279	C₁₃×M₁₆	—	2	4	no	—
280	C₁₃×M₁₆	—	2	2	no	—
281	C₁₃×M₁₆	—	2	2	no	—
282	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
283	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
284	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	1	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
306	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
307	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
308	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
311	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
313	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
314	C₁₃×C₂²⋊C₄	—	2	1	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	4	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	—	2	4	no	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	1	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	—	2	1	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	—	2	2	no	—
330	C₄²×C₁₃	—	2	2	no	—
331	C₄²×C₁₃	—	2	1	no	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	—	2	1	no	—
334	C₄²×C₁₃	C₂×D₄	1	2	yes	—
335	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₁₃	C₂×D₄	1	2	yes	—
337	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₁₃	C₂⁴	1	2	yes	—
339	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
340	C₄²×C₁₃	C₂⁴	1	2	yes	—
341	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
342	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
343	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3375	C₂×C₁₃	1	2	yes	complemented
345	#3373	C₂×C₁₃	1	2	yes	complemented
346	#3371	C₂×C₁₃	1	4	yes	complemented
347	#3370	C₂×C₁₃	1	4	yes	complemented
348	#3365	C₂×C₁₃	1	2	yes	complemented
349	#3361	C₂×C₁₃	1	2	yes	complemented
350	#3140	C₂×C₁₃	1	2	yes	complemented
351	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3077	C₂×C₁₃	1	2	yes	complemented
354	#3040	C₂×C₁₃	1	2	yes	complemented
355	#3038	C₂×C₁₃	1	1	yes	characteristic
356	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
357	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
359	C₂³×C₁₃	—	2	1	no	—
360	C₂³×C₁₃	—	2	4	no	—
361	C₂³×C₁₃	—	4	4	no	—
362	C₂³×C₁₃	—	4	4	no	—
363	C₂³×C₁₃	—	4	4	no	—
364	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
365	Q₈×C₁₃	—	2	2	no	—
366	Q₈×C₁₃	—	2	2	no	—
367	Q₈×C₁₃	—	2	1	no	—
368	Q₈×C₁₃	—	2	2	no	—
369	Q₈×C₁₃	—	2	2	no	—
370	Q₈×C₁₃	—	4	2	no	—
371	Q₈×C₁₃	—	4	4	no	—
372	Q₈×C₁₃	—	4	2	no	—
373	Q₈×C₁₃	—	4	2	no	—
374	Q₈×C₁₃	—	8	2	no	—
375	Q₈×C₁₃	—	8	1	no	—
376	Q₈×C₁₃	C₂×#41	1	2	yes	—
377	D₄×C₁₃	—	2	4	no	—
378	D₄×C₁₃	—	2	4	no	—
379	D₄×C₁₃	—	2	1	no	—
380	D₄×C₁₃	—	2	4	no	—
381	D₄×C₁₃	—	4	4	no	—
382	D₄×C₁₃	—	4	4	no	—
383	D₄×C₁₃	—	4	4	no	—
384	D₄×C₁₃	—	8	2	no	—
385	D₄×C₁₃	—	8	2	no	—
386	D₄×C₁₃	C₂×#41	1	2	yes	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	4	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	4	2	no	—
397	C₂×C₄×C₁₃	—	4	1	no	—
398	C₂×C₄×C₁₃	—	4	2	no	—
399	C₂×C₄×C₁₃	—	4	4	no	—
400	C₂×C₄×C₁₃	—	4	2	no	—
401	C₂×C₄×C₁₃	—	4	2	no	—
402	C₂×C₄×C₁₃	—	4	2	no	—
403	C₂×C₄×C₁₃	—	8	2	no	—
404	C₂×C₄×C₁₃	—	8	1	no	—
405	C₂×C₄×C₁₃	—	8	4	no	—
406	C₂×C₄×C₁₃	—	8	4	no	—
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
417	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
418	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
419	C₈×C₁₃	—	2	4	no	—
420	C₈×C₁₃	—	2	2	no	—
421	C₈×C₁₃	—	2	2	no	—
422	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
424	#559	—	2	1	no	—
425	#559	—	2	2	no	—
426	#559	—	2	1	no	—
427	#559	C₂²×C₁₃	1	2	yes	—
428	#559	C₂²×C₁₃	1	4	yes	—
429	#559	C₂²×C₁₃	1	2	yes	—
430	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	#557	C₂²×C₁₃	1	2	yes	complemented
433	#554	—	2	1	no	—
434	#554	—	2	2	no	—
435	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	#554	C₂²×C₁₃	1	2	yes	complemented
437	D₄×Q₈	—	2	1	no	—
438	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	#533	—	2	2	no	—
440	#533	—	2	1	no	—
441	#533	C₂²×C₁₃	1	2	yes	—
442	#533	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×#124	—	2	1	no	—
445	C₂×#124	C₂²×C₁₃	1	2	yes	—
446	C₂×#123	—	2	2	no	—
447	C₄×#41	C₂²×C₁₃	1	2	yes	—
448	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×C₄×Q₈	—	2	1	no	—
450	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
451	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
452	C₂×C₄×D₄	—	2	1	no	—
453	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
454	#490	C₂²×C₁₃	1	4	yes	—
455	#489	C₂²×C₁₃	1	4	yes	complemented
456	#489	C₂²×C₁₃	1	4	yes	complemented
457	#488	C₂²×C₁₃	1	4	yes	complemented
458	#488	C₂²×C₁₃	1	4	yes	complemented
459	#486	C₂²×C₁₃	1	2	yes	—
460	#486	C₂²×C₁₃	1	2	yes	—
461	#479	C₂²×C₁₃	1	4	yes	complemented
462	#478	C₂²×C₁₃	1	4	yes	complemented
463	#478	C₂²×C₁₃	1	4	yes	complemented
464	#477	C₂²×C₁₃	1	2	yes	complemented
465	#476	C₂²×C₁₃	1	4	yes	complemented
466	#475	C₂²×C₁₃	1	2	yes	complemented
467	#474	C₂²×C₁₃	1	4	yes	complemented
468	#464	C₂²×C₁₃	1	4	yes	complemented
469	#464	C₂²×C₁₃	1	4	yes	complemented
470	#463	C₂²×C₁₃	1	4	yes	complemented
471	#463	C₂²×C₁₃	1	4	yes	complemented
472	#460	C₂²×C₁₃	1	2	yes	—
473	#460	C₂²×C₁₃	1	2	yes	—
474	#459	C₂²×C₁₃	1	2	yes	—
475	#459	C₂²×C₁₃	1	2	yes	—
476	#446	C₂²×C₁₃	1	4	yes	complemented
477	#446	C₂²×C₁₃	1	2	yes	complemented
478	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
479	#442	C₂²×C₁₃	1	4	yes	complemented
480	#441	C₂²×C₁₃	1	2	yes	complemented
481	#440	C₂²×C₁₃	1	2	yes	complemented
482	#440	C₂²×C₁₃	1	4	yes	complemented
483	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
484	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
485	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
486	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
487	#428	C₂²×C₁₃	1	1	yes	characteristic
488	#428	C₂²×C₁₃	1	2	yes	—
489	#423	C₂²×C₁₃	1	2	yes	—
490	#423	C₂²×C₁₃	1	1	yes	characteristic
491	#419	C₂²×C₁₃	1	2	yes	—
492	#419	C₂²×C₁₃	1	1	yes	characteristic
493	#418	C₂²×C₁₃	1	2	yes	—
494	#418	C₂²×C₁₃	1	2	yes	—
495	#418	C₂²×C₁₃	1	2	yes	—
496	#417	C₂²×C₁₃	1	1	yes	characteristic
497	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
498	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
499	C₂²×C₁₃	—	2	1	no	—
500	C₂²×C₁₃	—	2	1	no	—
501	C₂²×C₁₃	—	2	2	no	—
502	C₂²×C₁₃	—	4	1	no	—
503	C₂²×C₁₃	—	4	1	no	—
504	C₂²×C₁₃	—	4	4	no	—
505	C₂²×C₁₃	—	4	4	no	—
506	C₂²×C₁₃	—	4	4	no	—
507	C₂²×C₁₃	—	8	8	no	—
508	C₂²×C₁₃	#548	1	2	yes	—
509	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
510	C₄×C₁₃	—	2	2	no	—
511	C₄×C₁₃	—	2	2	no	—
512	C₄×C₁₃	—	2	1	no	—
513	C₄×C₁₃	—	2	1	no	—
514	C₄×C₁₃	—	2	2	no	—
515	C₄×C₁₃	—	2	1	no	—
516	C₄×C₁₃	—	2	2	no	—
517	C₄×C₁₃	—	2	2	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	—	4	2	no	—
520	C₄×C₁₃	—	4	1	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	—	4	2	no	—
523	C₄×C₁₃	—	4	1	no	—
524	C₄×C₁₃	#548	1	2	yes	—
525	C₄×C₁₃	#575	1	2	yes	—
526	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
527	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
528	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
529	C₂²×Q₈	—	2	1	no	—
530	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
531	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²×D₄	—	2	1	no	—
533	C₂²×D₄	—	2	1	no	—
534	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
535	C₂³×C₄	—	2	2	no	—
536	#137	—	2	4	no	—
537	AGL(1,ℤ/8)	—	2	8	no	—
538	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
539	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
540	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
541	C₂×D₈	C₂³×C₁₃	1	4	yes	—
542	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
543	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
544	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
545	C₄⋊Q₈	—	2	1	no	—
546	C₄⋊Q₈	—	2	2	no	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	—	2	2	no	—
549	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
551	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
553	#127	—	2	1	no	—
554	#127	—	2	1	no	—
555	#127	C₂³×C₁₃	1	2	yes	—
556	#127	C₂³×C₁₃	1	2	yes	—
557	#125	—	2	2	no	—
558	#125	—	2	2	no	—
559	#125	—	2	2	no	—
560	#125	C₂³×C₁₃	1	2	yes	—
561	#125	C₂³×C₁₃	1	2	yes	—
562	#125	C₂³×C₁₃	1	2	yes	—
563	#124	—	2	2	no	—
564	#124	—	2	2	no	—
565	#124	—	2	4	no	—
566	#124	—	2	2	no	—
567	#124	—	2	2	no	—
568	#124	C₂³×C₁₃	1	4	yes	—
569	#124	C₂³×C₁₃	1	4	yes	—
570	#123	—	2	4	no	—
571	#123	—	2	4	no	—
572	#123	—	2	4	no	—
573	#123	—	2	4	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	1	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	—	2	1	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	—	2	1	no	—
594	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
595	C₄×Q₈	D₄×C₁₃	1	2	yes	—
596	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
597	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
598	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
599	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
600	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
603	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
605	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	4	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	C₂³×C₁₃	1	4	yes	—
616	C₄×D₄	C₂³×C₁₃	1	4	yes	—
617	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₁₃	1	2	yes	—
619	C₄×D₄	C₂³×C₁₃	1	2	yes	—
620	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
621	#117	—	2	2	no	—
622	#117	—	2	1	no	—
623	#117	C₂³×C₁₃	1	2	yes	—
624	#117	C₂³×C₁₃	1	1	yes	characteristic
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	2	no	—
628	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
629	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	—	2	2	no	—
632	C₂×C₂²⋊C₄	—	2	2	no	—
633	C₂×C₂²⋊C₄	—	2	2	no	—
634	C₂×C₄²	—	2	1	no	—
635	C₂×C₄²	—	2	2	no	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
639	#107	C₂³×C₁₃	1	4	yes	—
640	#107	C₂³×C₁₃	1	2	yes	—
641	#106	C₂³×C₁₃	1	2	yes	—
642	#106	C₂³×C₁₃	1	4	yes	—
643	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
644	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
645	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
646	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
647	#103	C₂³×C₁₃	1	2	yes	—
648	#103	C₂³×C₁₃	1	2	yes	—
649	#103	C₂³×C₁₃	1	2	yes	—
650	#103	C₂³×C₁₃	1	4	yes	—
651	#103	C₂³×C₁₃	1	4	yes	—
652	#102	C₂³×C₁₃	1	2	yes	—
653	#102	C₂³×C₁₃	1	4	yes	—
654	#102	C₂³×C₁₃	1	4	yes	—
655	#102	C₂³×C₁₃	1	4	yes	—
656	#102	C₂³×C₁₃	1	4	yes	—
657	#102	C₂³×C₁₃	1	4	yes	—
658	#102	C₂³×C₁₃	1	4	yes	—
659	#97	C₂³×C₁₃	1	2	yes	—
660	#97	C₂³×C₁₃	1	4	yes	—
661	C₄×C₈	C₂³×C₁₃	1	4	yes	—
662	C₄×C₈	C₂³×C₁₃	1	2	yes	—
663	C₂×C₁₃	—	2	2	no	—
664	C₂×C₁₃	—	4	2	no	—
665	C₂×C₁₃	—	8	4	no	—
666	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
667	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
668	C₂×C₁₃	#3585	1	1	yes	characteristic
669	C₂⁴	—	2	2	no	—
670	#41	—	2	2	no	—
671	#41	C₁₃×#41	1	4	yes	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	1	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	4	2	no	—
680	C₂×Q₈	—	4	4	no	—
681	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
683	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
684	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
685	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	4	4	no	—
695	C₂×D₄	—	8	2	no	—
696	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
697	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	8	4	no	—
708	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
710	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
711	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
713	Q₁₆	—	2	4	no	—
714	SD₁₆	—	2	8	no	—
715	SD₁₆	—	2	4	no	—
716	D₈	—	2	8	no	—
717	M₁₆	—	2	4	no	—
718	M₁₆	—	2	2	no	—
719	M₁₆	—	2	2	no	—
720	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
721	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
722	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
741	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
742	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
743	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
744	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
745	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
746	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
747	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
748	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
751	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	1	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	1	no	—
772	C₄²	C₂×D₄×C₁₃	1	2	yes	—
773	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₁₃	1	2	yes	—
775	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
776	C₄²	C₂⁴×C₁₃	1	2	yes	—
777	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
778	C₄²	C₂⁴×C₁₃	1	2	yes	—
779	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
780	C₁₃	#61324	1	1	yes	characteristic, direct product factor, Sylow
781	C₂³	—	2	1	no	—
782	C₂³	—	2	4	no	—
783	C₂³	—	4	4	no	—
784	C₂³	—	4	4	no	—
785	C₂³	—	4	4	no	—
786	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
787	Q₈	—	2	2	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	2	1	no	—
790	Q₈	—	2	2	no	—
791	Q₈	—	2	2	no	—
792	Q₈	—	4	2	no	—
793	Q₈	—	4	4	no	—
794	Q₈	—	4	2	no	—
795	Q₈	—	4	2	no	—
796	Q₈	—	8	2	no	—
797	Q₈	—	8	1	no	—
798	Q₈	C₂×C₁₃×#41	1	2	yes	—
799	D₄	—	2	4	no	—
800	D₄	—	2	4	no	—
801	D₄	—	2	1	no	—
802	D₄	—	2	4	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	4	no	—
805	D₄	—	4	4	no	—
806	D₄	—	8	2	no	—
807	D₄	—	8	2	no	—
808	D₄	C₂×C₁₃×#41	1	2	yes	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	4	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	8	4	no	—
826	C₂×C₄	—	8	4	no	—
827	C₂×C₄	—	8	2	no	—
828	C₂×C₄	—	8	1	no	—
829	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
831	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
832	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
834	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
835	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
838	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
839	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
840	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
841	C₈	—	2	4	no	—
842	C₈	—	2	2	no	—
843	C₈	—	2	2	no	—
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	4	no	—
850	C₂²	—	4	4	no	—
851	C₂²	—	4	4	no	—
852	C₂²	—	8	8	no	—
853	C₂²	C₁₃×#548	1	2	yes	—
854	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
855	C₄	—	2	1	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	2	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	C₁₃×#548	1	2	yes	—
870	C₄	C₁₃×#575	1	2	yes	—
871	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
872	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
873	C₂	—	2	2	no	—
874	C₂	—	4	2	no	—
875	C₂	—	8	4	no	—
876	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
877	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
878	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3038	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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. Q₈×C₁₃×#41	C₂	semidirect
3. C₁₃×#3375	C₂	semidirect
4. C₁₃×#3373	C₂	semidirect
5. C₁₃×#3371	C₂	semidirect
6. C₁₃×#3370	C₂	semidirect
7. C₁₃×#3365	C₂	semidirect
8. C₁₃×#3361	C₂	semidirect
9. C₁₃×#3140	C₂	semidirect
10. C₁₃×#3138	C₂	semidirect
11. C₁₃×#3078	C₂	semidirect
12. C₁₃×#3077	C₂	semidirect
13. C₁₃×#3040	C₂	semidirect
15. Q₈×C₁₃×M₁₆	C₂	semidirect
16. C₄×C₁₃×#137	C₂	semidirect
17. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
26. Q₈²×C₁₃	C₂²	semidirect
27. C₁₃×#557	C₂²	semidirect
28. C₁₃×#557	C₂²	semidirect
31. C₁₃×#554	C₂²	semidirect
32. C₁₃×#554	C₂²	semidirect
34. D₄×Q₈×C₁₃	C₂²	semidirect
51. C₁₃×#489	C₂²	semidirect
52. C₁₃×#489	C₂²	semidirect
53. C₁₃×#488	C₂²	semidirect
54. C₁₃×#488	C₂²	semidirect
57. C₁₃×#479	C₂²	semidirect
58. C₁₃×#478	C₂²	semidirect
59. C₁₃×#478	C₂²	semidirect
60. C₁₃×#477	C₂²	semidirect
61. C₁₃×#476	C₂²	semidirect
62. C₁₃×#475	C₂²	semidirect
63. C₁₃×#474	C₂²	semidirect
64. C₁₃×#464	C₂²	semidirect
65. C₁₃×#464	C₂²	semidirect
66. C₁₃×#463	C₂²	semidirect
67. C₁₃×#463	C₂²	semidirect
72. C₁₃×#446	C₂²	semidirect
73. C₁₃×#446	C₂²	semidirect
74. C₈×Q₈×C₁₃	C₂²	semidirect
75. C₁₃×#442	C₂²	semidirect
76. C₁₃×#441	C₂²	semidirect
77. C₁₃×#440	C₂²	semidirect
78. C₁₃×#440	C₂²	semidirect
79. C₄×C₁₃×Q₁₆	C₂²	semidirect
80. C₄×C₁₃×SD₁₆	C₂²	semidirect
81. C₄×C₁₃×SD₁₆	C₂²	semidirect
82. C₄×C₁₃×D₈	C₂²	semidirect
230. #61324	C₁₃	direct (N × H)
342. C₂×#559	C₂×C₁₃	semidirect
343. Q₈×#41	C₂×C₁₃	semidirect
344. #3375	C₂×C₁₃	semidirect
345. #3373	C₂×C₁₃	semidirect
346. #3371	C₂×C₁₃	semidirect
347. #3370	C₂×C₁₃	semidirect
348. #3365	C₂×C₁₃	semidirect
349. #3361	C₂×C₁₃	semidirect
350. #3140	C₂×C₁₃	semidirect
351. #3138	C₂×C₁₃	semidirect
352. #3078	C₂×C₁₃	semidirect
353. #3077	C₂×C₁₃	semidirect
354. #3040	C₂×C₁₃	semidirect
356. Q₈×M₁₆	C₂×C₁₃	semidirect
357. C₄×#137	C₂×C₁₃	semidirect
358. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
430. Q₈²	C₂²×C₁₃	semidirect
431. #557	C₂²×C₁₃	semidirect
432. #557	C₂²×C₁₃	semidirect
435. #554	C₂²×C₁₃	semidirect
436. #554	C₂²×C₁₃	semidirect
438. D₄×Q₈	C₂²×C₁₃	semidirect
455. #489	C₂²×C₁₃	semidirect
456. #489	C₂²×C₁₃	semidirect
457. #488	C₂²×C₁₃	semidirect
458. #488	C₂²×C₁₃	semidirect
461. #479	C₂²×C₁₃	semidirect
462. #478	C₂²×C₁₃	semidirect
463. #478	C₂²×C₁₃	semidirect
464. #477	C₂²×C₁₃	semidirect
465. #476	C₂²×C₁₃	semidirect
466. #475	C₂²×C₁₃	semidirect
467. #474	C₂²×C₁₃	semidirect
468. #464	C₂²×C₁₃	semidirect
469. #464	C₂²×C₁₃	semidirect
470. #463	C₂²×C₁₃	semidirect
471. #463	C₂²×C₁₃	semidirect
476. #446	C₂²×C₁₃	semidirect
477. #446	C₂²×C₁₃	semidirect
478. C₈×Q₈	C₂²×C₁₃	semidirect
479. #442	C₂²×C₁₃	semidirect
480. #441	C₂²×C₁₃	semidirect
481. #440	C₂²×C₁₃	semidirect
482. #440	C₂²×C₁₃	semidirect
483. C₄×Q₁₆	C₂²×C₁₃	semidirect
484. C₄×SD₁₆	C₂²×C₁₃	semidirect
485. C₄×SD₁₆	C₂²×C₁₃	semidirect
486. C₄×D₈	C₂²×C₁₃	semidirect
780. C₁₃	#61324	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
Q₈×C₁₃×#41	2
C₁₃×#3375	2
C₁₃×#3373	2
C₁₃×#3371	2
C₁₃×#3370	2
C₁₃×#3365	2
C₁₃×#3361	2
C₁₃×#3140	2
C₁₃×#3138	2
C₁₃×#3078	2
C₁₃×#3077	2
C₁₃×#3040	2
C₁₃×#3038	2
Q₈×C₁₃×M₁₆	2
C₄×C₁₃×#137	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61324	13

Subgroups — C13×#61324 #15747663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61324 #15747663