Subgroups — C₁₃×#61318 #15747657

Order 3328.

1880 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3376	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3372	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3370	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3366	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3360	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3142	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3080	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3036	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#559	C₂²	1	2	yes	complemented
22	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#556	C₂²	1	2	yes	complemented
25	C₁₃×#554	—	2	1	no	—
26	C₁₃×#554	—	2	1	no	—
27	C₁₃×#554	—	2	2	no	—
28	C₁₃×#554	C₂²	1	2	yes	—
29	C₁₃×#554	C₂²	1	2	yes	—
30	C₁₃×#554	C₂²	1	4	yes	—
31	C₁₃×#553	—	2	1	no	—
32	C₁₃×#553	—	2	2	no	—
33	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#548	—	2	1	no	—
35	C₁₃×#532	C₂²	1	1	yes	characteristic
36	C₁₃×#532	C₂²	1	2	yes	—
37	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₁₃×#529	—	2	2	no	—
39	C₁₃×#529	—	2	1	no	—
40	C₂×C₁₃×#125	C₂²	1	2	yes	—
41	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
43	C₄×C₁₃×#41	—	2	1	no	—
44	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×#41	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
50	C₁₃×#491	C₂²	1	4	yes	complemented
51	C₁₃×#490	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×#487	C₂²	1	2	yes	complemented
56	C₁₃×#486	C₂²	1	2	yes	complemented
57	C₁₃×#479	C₂²	1	4	yes	complemented
58	C₁₃×#479	C₂²	1	4	yes	complemented
59	C₁₃×#478	C₂²	1	4	yes	complemented
60	C₁₃×#478	C₂²	1	4	yes	complemented
61	C₁₃×#477	C₂²	1	2	yes	complemented
62	C₁₃×#476	C₂²	1	2	yes	complemented
63	C₁₃×#475	C₂²	1	2	yes	complemented
64	C₁₃×#474	C₂²	1	2	yes	complemented
65	C₁₃×#463	C₂²	1	4	yes	—
66	C₁₃×#463	C₂²	1	4	yes	—
67	C₁₃×#463	C₂²	1	4	yes	—
68	C₁₃×#461	C₂²	1	2	yes	—
69	C₁₃×#461	C₂²	1	4	yes	—
70	C₁₃×#459	C₂²	1	2	yes	—
71	C₁₃×#459	C₂²	1	4	yes	—
72	C₁₃×#446	C₂²	1	2	yes	complemented
73	C₁₃×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
75	C₁₃×#442	C₂²	1	4	yes	—
76	C₁₃×#442	C₂²	1	2	yes	—
77	C₁₃×#440	C₂²	1	4	yes	—
78	C₁₃×#440	C₂²	1	2	yes	—
79	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
80	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
81	C₄×C₁₃×D₈	C₂²	1	2	yes	—
82	C₄×C₁₃×D₈	C₂²	1	4	yes	—
83	C₁₃×#428	C₂²	1	2	yes	—
84	C₁₃×#428	C₂²	1	1	yes	characteristic
85	C₁₃×#423	C₂²	1	1	yes	characteristic
86	C₁₃×#423	C₂²	1	2	yes	—
87	C₁₃×#418	C₂²	1	1	yes	characteristic
88	C₁₃×#417	C₂²	1	2	yes	—
89	C₁₃×#417	C₂²	1	2	yes	—
90	C₁₃×#417	C₂²	1	2	yes	—
91	C₁₃×#417	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	—	2	1	no	—
96	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₃	—	2	1	no	—
99	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
100	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃	—	2	1	no	—
102	C₂³×C₄×C₁₃	—	2	2	no	—
103	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
104	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
105	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×D₈	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	1	no	—
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×#127	C₂³	1	1	yes	characteristic
119	C₁₃×#127	C₂³	1	2	yes	—
120	C₁₃×#126	—	2	2	no	—
121	C₁₃×#126	—	2	2	no	—
122	C₁₃×#126	—	2	2	no	—
123	C₁₃×#125	—	2	1	no	—
124	C₁₃×#125	—	2	2	no	—
125	C₁₃×#125	—	2	2	no	—
126	C₁₃×#125	—	2	2	no	—
127	C₁₃×#125	C₂³	1	4	yes	—
128	C₁₃×#125	C₂³	1	4	yes	—
129	C₁₃×#124	—	2	1	no	—
130	C₁₃×#124	—	2	2	no	—
131	C₁₃×#124	C₂³	1	2	yes	—
132	C₁₃×#124	C₂³	1	2	yes	—
133	C₁₃×#124	C₂³	1	2	yes	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	2	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	4	no	—
140	C₁₃×C₂²⋊Q₈	—	2	1	no	—
141	C₁₃×C₂²⋊Q₈	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	4	no	—
143	C₁₃×C₂²⋊Q₈	—	2	4	no	—
144	C₁₃×C₂²⋊Q₈	—	2	4	no	—
145	C₁₃×C₂²⋊Q₈	—	2	4	no	—
146	C₁₃×#121	—	2	1	no	—
147	C₁₃×#121	—	2	2	no	—
148	C₁₃×#121	—	2	1	no	—
149	C₁₃×#121	—	2	2	no	—
150	C₁₃×#121	—	2	1	no	—
151	C₁₃×#121	—	2	2	no	—
152	C₄×Q₈×C₁₃	—	2	1	no	—
153	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
154	C₄×Q₈×C₁₃	D₄	1	2	yes	—
155	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
156	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	—	2	2	no	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	—	2	2	no	—
167	C₄×D₄×C₁₃	—	2	1	no	—
168	C₄×D₄×C₁₃	—	2	2	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₁₃	C₂³	1	2	yes	—
179	C₄×D₄×C₁₃	C₂³	1	2	yes	—
180	C₄×D₄×C₁₃	C₂³	1	4	yes	—
181	C₄×D₄×C₁₃	C₂³	1	4	yes	—
182	C₄×D₄×C₁₃	C₂³	1	2	yes	—
183	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₁₃×#117	—	2	1	no	—
186	C₁₃×#117	—	2	2	no	—
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	—	2	1	no	—
189	C₁₃×#117	C₂³	1	1	yes	characteristic
190	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
196	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
197	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₂²⋊C₄	—	2	2	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	4	yes	—
209	C₁₃×#106	C₂³	1	2	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#103	C₂³	1	2	yes	—
216	C₁₃×#103	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	2	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	2	yes	—
225	C₁₃×#102	C₂³	1	2	yes	—
226	C₁₃×#97	C₂³	1	2	yes	—
227	C₁₃×#97	C₂³	1	4	yes	—
228	C₄×C₈×C₁₃	C₂³	1	2	yes	—
229	C₄×C₈×C₁₃	C₂³	1	4	yes	—
230	#61318	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂⁴×C₁₃	—	2	1	no	—
232	C₁₃×#41	—	2	2	no	—
233	C₁₃×#41	—	2	4	no	—
234	C₁₃×#41	—	2	2	no	—
235	C₁₃×#41	—	2	4	no	—
236	C₁₃×#41	—	4	4	no	—
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	4	2	no	—
240	C₂×Q₈×C₁₃	—	8	2	no	—
241	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
244	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	#41	1	4	yes	complemented
255	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	2	no	—
268	C₂²×C₄×C₁₃	—	2	4	no	—
269	C₂²×C₄×C₁₃	—	2	4	no	—
270	C₂²×C₄×C₁₃	—	4	4	no	—
271	C₂²×C₄×C₁₃	—	8	4	no	—
272	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₁₃×SD₁₆	—	2	8	no	—
278	C₁₃×SD₁₆	—	2	4	no	—
279	C₁₃×D₈	—	2	4	no	—
280	C₁₃×D₈	—	2	8	no	—
281	C₁₃×M₁₆	—	2	2	no	—
282	C₁₃×M₁₆	—	2	4	no	—
283	C₁₃×M₁₆	—	2	2	no	—
284	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
285	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
287	C₁₃×C₄⋊C₄	—	2	4	no	—
288	C₁₃×C₄⋊C₄	—	2	4	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	4	no	—
292	C₁₃×C₄⋊C₄	—	2	4	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	1	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	1	no	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
304	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
305	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
313	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
314	C₁₃×C₂²⋊C₄	—	2	1	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	4	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	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	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₄²×C₁₃	—	2	1	no	—
330	C₄²×C₁₃	—	2	1	no	—
331	C₄²×C₁₃	—	2	2	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	1	yes	characteristic
341	C₄²×C₁₃	C₂⁴	1	2	yes	—
342	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
343	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3376	C₂×C₁₃	1	4	yes	complemented
345	#3372	C₂×C₁₃	1	2	yes	complemented
346	#3370	C₂×C₁₃	1	4	yes	complemented
347	#3366	C₂×C₁₃	1	2	yes	complemented
348	#3361	C₂×C₁₃	1	2	yes	complemented
349	#3360	C₂×C₁₃	1	2	yes	complemented
350	#3142	C₂×C₁₃	1	2	yes	complemented
351	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3080	C₂×C₁₃	1	2	yes	complemented
353	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3036	C₂×C₁₃	1	2	yes	complemented
356	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
357	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
359	C₂³×C₁₃	—	2	4	no	—
360	C₂³×C₁₃	—	2	2	no	—
361	C₂³×C₁₃	—	2	2	no	—
362	C₂³×C₁₃	—	2	1	no	—
363	C₂³×C₁₃	—	4	2	no	—
364	C₂³×C₁₃	—	4	2	no	—
365	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
366	Q₈×C₁₃	—	2	2	no	—
367	Q₈×C₁₃	—	2	2	no	—
368	Q₈×C₁₃	—	2	2	no	—
369	Q₈×C₁₃	—	2	1	no	—
370	Q₈×C₁₃	—	2	2	no	—
371	Q₈×C₁₃	—	2	1	no	—
372	Q₈×C₁₃	—	4	2	no	—
373	Q₈×C₁₃	—	8	2	no	—
374	Q₈×C₁₃	—	8	2	no	—
375	D₄×C₁₃	—	2	4	no	—
376	D₄×C₁₃	—	2	2	no	—
377	D₄×C₁₃	—	2	1	no	—
378	D₄×C₁₃	—	2	2	no	—
379	D₄×C₁₃	—	2	2	no	—
380	D₄×C₁₃	—	2	1	no	—
381	D₄×C₁₃	—	4	4	no	—
382	D₄×C₁₃	—	4	2	no	—
383	D₄×C₁₃	—	4	4	no	—
384	D₄×C₁₃	—	4	2	no	—
385	D₄×C₁₃	—	8	2	no	—
386	D₄×C₁₃	—	8	1	no	—
387	D₄×C₁₃	C₂×#41	1	4	yes	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	4	no	—
395	C₂×C₄×C₁₃	—	4	2	no	—
396	C₂×C₄×C₁₃	—	4	2	no	—
397	C₂×C₄×C₁₃	—	4	1	no	—
398	C₂×C₄×C₁₃	—	4	4	no	—
399	C₂×C₄×C₁₃	—	4	4	no	—
400	C₂×C₄×C₁₃	—	4	2	no	—
401	C₂×C₄×C₁₃	—	4	4	no	—
402	C₂×C₄×C₁₃	—	4	4	no	—
403	C₂×C₄×C₁₃	—	4	2	no	—
404	C₂×C₄×C₁₃	—	4	4	no	—
405	C₂×C₄×C₁₃	—	4	2	no	—
406	C₂×C₄×C₁₃	—	8	2	no	—
407	C₂×C₄×C₁₃	—	8	1	no	—
408	C₂×C₄×C₁₃	—	8	4	no	—
409	C₂×C₄×C₁₃	—	8	4	no	—
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	2	yes	—
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
420	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
421	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
422	C₈×C₁₃	—	2	2	no	—
423	C₈×C₁₃	—	2	4	no	—
424	C₈×C₁₃	—	2	2	no	—
425	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
427	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	#559	C₂²×C₁₃	1	2	yes	complemented
429	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
430	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#556	C₂²×C₁₃	1	2	yes	complemented
432	#554	—	2	1	no	—
433	#554	—	2	1	no	—
434	#554	—	2	2	no	—
435	#554	C₂²×C₁₃	1	2	yes	—
436	#554	C₂²×C₁₃	1	2	yes	—
437	#554	C₂²×C₁₃	1	4	yes	—
438	#553	—	2	1	no	—
439	#553	—	2	2	no	—
440	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	#548	—	2	1	no	—
442	#532	C₂²×C₁₃	1	1	yes	characteristic
443	#532	C₂²×C₁₃	1	2	yes	—
444	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
445	#529	—	2	2	no	—
446	#529	—	2	1	no	—
447	C₂×#125	C₂²×C₁₃	1	2	yes	—
448	C₂×C₂²⋊Q₈	—	2	1	no	—
449	C₂×C₂²⋊Q₈	—	2	2	no	—
450	C₄×#41	—	2	1	no	—
451	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
452	C₄×#41	C₂²×C₁₃	1	2	yes	—
453	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
455	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
456	C₂²×C₄⋊C₄	—	2	1	no	—
457	#491	C₂²×C₁₃	1	4	yes	complemented
458	#490	C₂²×C₁₃	1	4	yes	complemented
459	#489	C₂²×C₁₃	1	4	yes	complemented
460	#488	C₂²×C₁₃	1	4	yes	complemented
461	#488	C₂²×C₁₃	1	4	yes	complemented
462	#487	C₂²×C₁₃	1	2	yes	complemented
463	#486	C₂²×C₁₃	1	2	yes	complemented
464	#479	C₂²×C₁₃	1	4	yes	complemented
465	#479	C₂²×C₁₃	1	4	yes	complemented
466	#478	C₂²×C₁₃	1	4	yes	complemented
467	#478	C₂²×C₁₃	1	4	yes	complemented
468	#477	C₂²×C₁₃	1	2	yes	complemented
469	#476	C₂²×C₁₃	1	2	yes	complemented
470	#475	C₂²×C₁₃	1	2	yes	complemented
471	#474	C₂²×C₁₃	1	2	yes	complemented
472	#463	C₂²×C₁₃	1	4	yes	—
473	#463	C₂²×C₁₃	1	4	yes	—
474	#463	C₂²×C₁₃	1	4	yes	—
475	#461	C₂²×C₁₃	1	2	yes	—
476	#461	C₂²×C₁₃	1	4	yes	—
477	#459	C₂²×C₁₃	1	2	yes	—
478	#459	C₂²×C₁₃	1	4	yes	—
479	#446	C₂²×C₁₃	1	2	yes	complemented
480	#446	C₂²×C₁₃	1	4	yes	complemented
481	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
482	#442	C₂²×C₁₃	1	4	yes	—
483	#442	C₂²×C₁₃	1	2	yes	—
484	#440	C₂²×C₁₃	1	4	yes	—
485	#440	C₂²×C₁₃	1	2	yes	—
486	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
487	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
488	C₄×D₈	C₂²×C₁₃	1	2	yes	—
489	C₄×D₈	C₂²×C₁₃	1	4	yes	—
490	#428	C₂²×C₁₃	1	2	yes	—
491	#428	C₂²×C₁₃	1	1	yes	characteristic
492	#423	C₂²×C₁₃	1	1	yes	characteristic
493	#423	C₂²×C₁₃	1	2	yes	—
494	#418	C₂²×C₁₃	1	1	yes	characteristic
495	#417	C₂²×C₁₃	1	2	yes	—
496	#417	C₂²×C₁₃	1	2	yes	—
497	#417	C₂²×C₁₃	1	2	yes	—
498	#417	C₂²×C₁₃	1	2	yes	—
499	#417	C₂²×C₁₃	1	1	yes	characteristic
500	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
501	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
502	C₂²×C₁₃	—	2	1	no	—
503	C₂²×C₁₃	—	2	1	no	—
504	C₂²×C₁₃	—	2	4	no	—
505	C₂²×C₁₃	—	4	8	no	—
506	C₂²×C₁₃	—	4	2	no	—
507	C₂²×C₁₃	—	4	2	no	—
508	C₂²×C₁₃	—	4	2	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	—	4	2	no	—
511	C₂²×C₁₃	—	4	1	no	—
512	C₂²×C₁₃	—	4	2	no	—
513	C₂²×C₁₃	—	4	1	no	—
514	C₂²×C₁₃	#548	1	2	yes	—
515	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
516	C₄×C₁₃	—	2	2	no	—
517	C₄×C₁₃	—	2	2	no	—
518	C₄×C₁₃	—	2	1	no	—
519	C₄×C₁₃	—	2	1	no	—
520	C₄×C₁₃	—	2	1	no	—
521	C₄×C₁₃	—	2	2	no	—
522	C₄×C₁₃	—	2	2	no	—
523	C₄×C₁₃	—	4	4	no	—
524	C₄×C₁₃	—	4	1	no	—
525	C₄×C₁₃	—	4	1	no	—
526	C₄×C₁₃	—	4	2	no	—
527	C₄×C₁₃	—	4	1	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	#548	1	2	yes	—
530	C₄×C₁₃	#575	1	2	yes	—
531	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
532	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
533	C₂×#41	—	2	1	no	—
534	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
535	C₂×#41	C₂³×C₁₃	1	2	yes	—
536	C₂²×Q₈	—	2	1	no	—
537	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
539	C₂³×C₄	—	2	1	no	—
540	C₂³×C₄	—	2	2	no	—
541	AGL(1,ℤ/8)	—	2	4	no	—
542	AGL(1,ℤ/8)	—	2	8	no	—
543	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
544	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
545	C₂×D₈	C₂³×C₁₃	1	2	yes	—
546	C₂×D₈	C₂³×C₁₃	1	4	yes	—
547	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
548	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
549	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	1	no	—
552	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
553	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
554	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
555	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
556	#127	C₂³×C₁₃	1	1	yes	characteristic
557	#127	C₂³×C₁₃	1	2	yes	—
558	#126	—	2	2	no	—
559	#126	—	2	2	no	—
560	#126	—	2	2	no	—
561	#125	—	2	1	no	—
562	#125	—	2	2	no	—
563	#125	—	2	2	no	—
564	#125	—	2	2	no	—
565	#125	C₂³×C₁₃	1	4	yes	—
566	#125	C₂³×C₁₃	1	4	yes	—
567	#124	—	2	1	no	—
568	#124	—	2	2	no	—
569	#124	C₂³×C₁₃	1	2	yes	—
570	#124	C₂³×C₁₃	1	2	yes	—
571	#124	C₂³×C₁₃	1	2	yes	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	4	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	4	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₂²⋊Q₈	—	2	4	no	—
583	C₂²⋊Q₈	—	2	4	no	—
584	#121	—	2	1	no	—
585	#121	—	2	2	no	—
586	#121	—	2	1	no	—
587	#121	—	2	2	no	—
588	#121	—	2	1	no	—
589	#121	—	2	2	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
592	C₄×Q₈	D₄×C₁₃	1	2	yes	—
593	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
595	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
596	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
598	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	C₂³×C₁₃	1	2	yes	—
616	C₄×D₄	C₂³×C₁₃	1	4	yes	—
617	C₄×D₄	C₂³×C₁₃	1	4	yes	—
618	C₄×D₄	C₂³×C₁₃	1	2	yes	—
619	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₁₃	1	2	yes	—
621	C₄×D₄	C₂³×C₁₃	1	2	yes	—
622	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
623	#117	—	2	1	no	—
624	#117	—	2	2	no	—
625	#117	—	2	2	no	—
626	#117	—	2	1	no	—
627	#117	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	—	2	2	no	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	2	no	—
631	C₂×C₄⋊C₄	—	2	2	no	—
632	C₂×C₄⋊C₄	—	2	2	no	—
633	C₂×C₄⋊C₄	—	2	4	no	—
634	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	2	no	—
640	C₂×C₄²	—	2	2	no	—
641	C₂×C₄²	—	2	1	no	—
642	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
643	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
644	#107	C₂³×C₁₃	1	4	yes	—
645	#107	C₂³×C₁₃	1	2	yes	—
646	#106	C₂³×C₁₃	1	4	yes	—
647	#106	C₂³×C₁₃	1	2	yes	—
648	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
649	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
650	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
651	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
652	#103	C₂³×C₁₃	1	4	yes	—
653	#103	C₂³×C₁₃	1	2	yes	—
654	#103	C₂³×C₁₃	1	4	yes	—
655	#103	C₂³×C₁₃	1	4	yes	—
656	#103	C₂³×C₁₃	1	4	yes	—
657	#102	C₂³×C₁₃	1	4	yes	—
658	#102	C₂³×C₁₃	1	2	yes	—
659	#102	C₂³×C₁₃	1	4	yes	—
660	#102	C₂³×C₁₃	1	4	yes	—
661	#102	C₂³×C₁₃	1	4	yes	—
662	#102	C₂³×C₁₃	1	2	yes	—
663	#102	C₂³×C₁₃	1	2	yes	—
664	#97	C₂³×C₁₃	1	2	yes	—
665	#97	C₂³×C₁₃	1	4	yes	—
666	C₄×C₈	C₂³×C₁₃	1	2	yes	—
667	C₄×C₈	C₂³×C₁₃	1	4	yes	—
668	C₂×C₁₃	—	2	2	no	—
669	C₂×C₁₃	—	4	4	no	—
670	C₂×C₁₃	—	8	2	no	—
671	C₂×C₁₃	—	8	1	no	—
672	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
673	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
674	C₂×C₁₃	#3585	1	1	yes	characteristic
675	C₂⁴	—	2	1	no	—
676	#41	—	2	2	no	—
677	#41	—	2	4	no	—
678	#41	—	2	2	no	—
679	#41	—	2	4	no	—
680	#41	—	4	4	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	4	2	no	—
684	C₂×Q₈	—	8	2	no	—
685	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
686	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
688	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
689	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	C₁₃×#41	1	4	yes	complemented
699	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
700	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
701	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	4	4	no	—
715	C₂²×C₄	—	8	4	no	—
716	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
718	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
721	SD₁₆	—	2	8	no	—
722	SD₁₆	—	2	4	no	—
723	D₈	—	2	4	no	—
724	D₈	—	2	8	no	—
725	M₁₆	—	2	2	no	—
726	M₁₆	—	2	4	no	—
727	M₁₆	—	2	2	no	—
728	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
729	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
730	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
750	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
751	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
752	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
753	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
754	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
755	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
756	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
757	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₄²	—	2	1	no	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	1	no	—
778	C₄²	C₂×D₄×C₁₃	1	2	yes	—
779	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₁₃	1	2	yes	—
781	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
782	C₄²	C₂⁴×C₁₃	1	2	yes	—
783	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
784	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
785	C₄²	C₂⁴×C₁₃	1	2	yes	—
786	C₁₃	#61318	1	1	yes	characteristic, direct product factor, Sylow
787	C₂³	—	2	4	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	4	2	no	—
792	C₂³	—	4	2	no	—
793	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
794	Q₈	—	2	2	no	—
795	Q₈	—	2	2	no	—
796	Q₈	—	2	2	no	—
797	Q₈	—	2	1	no	—
798	Q₈	—	2	2	no	—
799	Q₈	—	2	1	no	—
800	Q₈	—	4	2	no	—
801	Q₈	—	8	2	no	—
802	Q₈	—	8	2	no	—
803	D₄	—	2	4	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	1	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	2	no	—
808	D₄	—	2	1	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	2	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	2	no	—
813	D₄	—	8	2	no	—
814	D₄	—	8	1	no	—
815	D₄	C₂×C₁₃×#41	1	4	yes	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	8	4	no	—
835	C₂×C₄	—	8	4	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	—	8	1	no	—
838	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
840	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
841	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
845	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
847	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
848	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
849	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
850	C₈	—	2	2	no	—
851	C₈	—	2	4	no	—
852	C₈	—	2	2	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	4	no	—
856	C₂²	—	4	8	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	1	no	—
865	C₂²	C₁₃×#548	1	2	yes	—
866	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
867	C₄	—	2	1	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	4	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	2	no	—
880	C₄	C₁₃×#548	1	2	yes	—
881	C₄	C₁₃×#575	1	2	yes	—
882	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
883	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
884	C₂	—	2	2	no	—
885	C₂	—	4	4	no	—
886	C₂	—	8	2	no	—
887	C₂	—	8	1	no	—
888	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
889	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
890	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
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. C₁₃×#3480	C₂	semidirect
2. C₂×C₁₃×#554	C₂	semidirect
3. C₁₃×#3376	C₂	semidirect
4. C₁₃×#3372	C₂	semidirect
5. C₁₃×#3370	C₂	semidirect
6. C₁₃×#3366	C₂	semidirect
7. C₁₃×#3361	C₂	semidirect
8. C₁₃×#3360	C₂	semidirect
9. C₁₃×#3142	C₂	semidirect
10. C₁₃×#3141	C₂	semidirect
11. C₁₃×#3080	C₂	semidirect
12. C₁₃×#3079	C₂	semidirect
13. C₁₃×#3036	C₂	semidirect
14. C₁₃×#3036	C₂	semidirect
15. Q₈×C₁₃×M₁₆	C₂	semidirect
16. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
17. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
20. C₁₃×#559	C₂²	semidirect
21. C₁₃×#559	C₂²	semidirect
22. C₁₃×#557	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
24. C₁₃×#556	C₂²	semidirect
33. C₁₃×#550	C₂²	semidirect
50. C₁₃×#491	C₂²	semidirect
51. C₁₃×#490	C₂²	semidirect
52. C₁₃×#489	C₂²	semidirect
53. C₁₃×#488	C₂²	semidirect
54. C₁₃×#488	C₂²	semidirect
55. C₁₃×#487	C₂²	semidirect
56. C₁₃×#486	C₂²	semidirect
57. C₁₃×#479	C₂²	semidirect
58. C₁₃×#479	C₂²	semidirect
59. C₁₃×#478	C₂²	semidirect
60. C₁₃×#478	C₂²	semidirect
61. C₁₃×#477	C₂²	semidirect
62. C₁₃×#476	C₂²	semidirect
63. C₁₃×#475	C₂²	semidirect
64. C₁₃×#474	C₂²	semidirect
72. C₁₃×#446	C₂²	semidirect
73. C₁₃×#446	C₂²	semidirect
74. C₈×Q₈×C₁₃	C₂²	semidirect
230. #61318	C₁₃	direct (N × H)
254. C₂×D₄×C₁₃	#41	semidirect
342. #3480	C₂×C₁₃	semidirect
343. C₂×#554	C₂×C₁₃	semidirect
344. #3376	C₂×C₁₃	semidirect
345. #3372	C₂×C₁₃	semidirect
346. #3370	C₂×C₁₃	semidirect
347. #3366	C₂×C₁₃	semidirect
348. #3361	C₂×C₁₃	semidirect
349. #3360	C₂×C₁₃	semidirect
350. #3142	C₂×C₁₃	semidirect
351. #3141	C₂×C₁₃	semidirect
352. #3080	C₂×C₁₃	semidirect
353. #3079	C₂×C₁₃	semidirect
354. #3036	C₂×C₁₃	semidirect
355. #3036	C₂×C₁₃	semidirect
356. Q₈×M₁₆	C₂×C₁₃	semidirect
357. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
358. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
427. #559	C₂²×C₁₃	semidirect
428. #559	C₂²×C₁₃	semidirect
429. #557	C₂²×C₁₃	semidirect
430. #556	C₂²×C₁₃	semidirect
431. #556	C₂²×C₁₃	semidirect
440. #550	C₂²×C₁₃	semidirect
457. #491	C₂²×C₁₃	semidirect
458. #490	C₂²×C₁₃	semidirect
459. #489	C₂²×C₁₃	semidirect
460. #488	C₂²×C₁₃	semidirect
461. #488	C₂²×C₁₃	semidirect
462. #487	C₂²×C₁₃	semidirect
463. #486	C₂²×C₁₃	semidirect
464. #479	C₂²×C₁₃	semidirect
465. #479	C₂²×C₁₃	semidirect
466. #478	C₂²×C₁₃	semidirect
467. #478	C₂²×C₁₃	semidirect
468. #477	C₂²×C₁₃	semidirect
469. #476	C₂²×C₁₃	semidirect
470. #475	C₂²×C₁₃	semidirect
471. #474	C₂²×C₁₃	semidirect
479. #446	C₂²×C₁₃	semidirect
480. #446	C₂²×C₁₃	semidirect
481. C₈×Q₈	C₂²×C₁₃	semidirect
698. C₂×D₄	C₁₃×#41	semidirect
786. C₁₃	#61318	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3480	2
C₂×C₁₃×#554	2
C₁₃×#3376	2
C₁₃×#3372	2
C₁₃×#3370	2
C₁₃×#3366	2
C₁₃×#3361	2
C₁₃×#3360	2
C₁₃×#3142	2
C₁₃×#3141	2
C₁₃×#3080	2
C₁₃×#3079	2
C₁₃×#3036	2
Q₈×C₁₃×M₁₆	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61318	13

Subgroups — C13×#61318 #15747657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61318 #15747657