Subgroups — D₄×C₁₃×AGL(1,ℤ/8) #15747404

Order 3328.

3230 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
5	D₄×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3274	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3272	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3265	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3264	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3055	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3006	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3003	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₁₃	—	2	1	no	—
20	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
21	C₂×C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
28	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
29	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
30	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
31	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	complemented
32	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
33	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#548	C₂²	1	2	yes	complemented
35	C₁₃×#547	—	2	1	no	—
36	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#546	—	2	2	no	—
38	C₁₃×#546	C₂²	1	2	yes	complemented
39	D₄²×C₁₃	—	2	1	no	—
40	D₄²×C₁₃	—	2	1	no	—
41	D₄²×C₁₃	—	2	2	no	—
42	D₄²×C₁₃	—	2	1	no	—
43	D₄²×C₁₃	C₂²	1	2	yes	—
44	D₄²×C₁₃	C₂²	1	4	yes	complemented
45	D₄²×C₁₃	C₂²	1	2	yes	complemented
46	D₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#532	—	2	1	no	—
48	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#525	—	2	2	no	—
51	C₁₃×#525	C₂²	1	2	yes	complemented
52	C₂×C₁₃×#121	—	2	1	no	—
53	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
54	C₂×C₁₃×#120	—	2	2	no	—
55	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×D₄×C₁₃	—	2	1	no	—
57	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#496	C₂²	1	4	yes	complemented
60	C₁₃×#493	C₂²	1	2	yes	complemented
61	C₁₃×#492	C₂²	1	2	yes	complemented
62	C₁₃×#469	C₂²	1	4	yes	complemented
63	C₁₃×#468	C₂²	1	4	yes	complemented
64	C₁₃×#466	C₂²	1	4	yes	complemented
65	C₁₃×#465	C₂²	1	4	yes	complemented
66	C₁₃×#463	C₂²	1	4	yes	complemented
67	C₁₃×#461	C₂²	1	2	yes	complemented
68	C₁₃×#460	C₂²	1	2	yes	complemented
69	C₁₃×#460	C₂²	1	2	yes	complemented
70	C₁₃×#459	C₂²	1	2	yes	complemented
71	C₁₃×#459	C₂²	1	2	yes	complemented
72	C₁₃×#459	C₂²	1	2	yes	complemented
73	C₁₃×#450	C₂²	1	4	yes	complemented
74	C₁₃×#450	C₂²	1	4	yes	complemented
75	C₁₃×#449	C₂²	1	4	yes	complemented
76	C₁₃×#449	C₂²	1	4	yes	complemented
77	C₁₃×#448	C₂²	1	4	yes	complemented
78	C₁₃×#447	C₂²	1	4	yes	complemented
79	C₁₃×#447	C₂²	1	4	yes	complemented
80	C₁₃×#447	C₂²	1	4	yes	complemented
81	C₁₃×#442	C₂²	1	2	yes	complemented
82	C₁₃×#440	C₂²	1	2	yes	complemented
83	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
84	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
85	C₁₃×#436	C₂²	1	2	yes	complemented
86	C₁₃×#435	C₂²	1	4	yes	complemented
87	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
88	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#418	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#418	C₂²	1	2	yes	complemented
92	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#417	C₂²	1	2	yes	complemented
94	C₁₃×#407	C₂²	1	2	yes	complemented
95	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
96	C₂⁵×C₁₃	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	—	2	2	no	—
99	C₂×C₁₃×#41	—	2	8	no	—
100	C₂×C₁₃×#41	—	4	4	no	—
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×#41	C₂³	1	2	yes	complemented
104	C₂×C₁₃×#41	C₂³	1	2	yes	complemented
105	C₂²×Q₈×C₁₃	C₂³	1	2	yes	complemented
106	C₂²×D₄×C₁₃	—	2	8	no	—
107	C₂²×D₄×C₁₃	—	2	2	no	—
108	C₂²×D₄×C₁₃	—	2	2	no	—
109	C₂²×D₄×C₁₃	—	2	1	no	—
110	C₂²×D₄×C₁₃	—	2	2	no	—
111	C₂²×D₄×C₁₃	—	2	4	no	—
112	C₂²×D₄×C₁₃	—	2	2	no	—
113	C₂²×D₄×C₁₃	—	2	2	no	—
114	C₂²×D₄×C₁₃	—	2	1	no	—
115	C₂²×D₄×C₁₃	—	2	2	no	—
116	C₂²×D₄×C₁₃	—	2	2	no	—
117	C₂²×D₄×C₁₃	—	2	1	no	—
118	C₂²×D₄×C₁₃	—	4	4	no	—
119	C₂²×D₄×C₁₃	—	4	8	no	—
120	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
121	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
122	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
123	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
124	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₁₃	C₂³	1	2	yes	complemented
126	C₂³×C₄×C₁₃	—	2	2	no	—
127	C₂³×C₄×C₁₃	—	2	1	no	—
128	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
129	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
130	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
131	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
132	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
133	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
134	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
135	C₁₃×AGL(1,ℤ/8)	D₄	1	8	yes	direct product factor
136	C₂×C₁₃×SD₁₆	—	2	16	no	—
137	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
138	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
139	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
140	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
141	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
142	C₂×C₁₃×D₈	—	2	16	no	—
143	C₂×C₁₃×D₈	C₂³	1	4	yes	—
144	C₂×C₁₃×D₈	C₂³	1	2	yes	—
145	C₂×C₁₃×D₈	C₂³	1	4	yes	complemented
146	C₂×C₁₃×D₈	C₂³	1	4	yes	complemented
147	C₂×C₁₃×D₈	C₂³	1	4	yes	complemented
148	C₂×C₁₃×M₁₆	—	2	8	no	—
149	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×M₁₆	C₂³	1	4	yes	complemented
153	C₂²×C₈×C₁₃	C₂³	1	4	yes	complemented
154	C₁₃×C₄⋊Q₈	—	2	1	no	—
155	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
156	C₁₃×#127	—	2	1	no	—
157	C₁₃×#127	—	2	1	no	—
158	C₁₃×#127	—	2	1	no	—
159	C₁₃×#127	C₂³	1	2	yes	—
160	C₁₃×#127	C₂³	1	2	yes	—
161	C₁₃×#127	C₂³	1	1	yes	characteristic, complemented
162	C₁₃×#124	—	2	2	no	—
163	C₁₃×#124	C₂³	1	2	yes	complemented
164	C₁₃×#123	—	2	2	no	—
165	C₁₃×#123	—	2	2	no	—
166	C₁₃×#123	—	2	2	no	—
167	C₁₃×C₂²⋊Q₈	—	2	2	no	—
168	C₁₃×C₂²⋊Q₈	—	2	2	no	—
169	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	complemented
170	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	complemented
171	C₁₃×#121	—	2	2	no	—
172	C₁₃×#121	—	2	1	no	—
173	C₁₃×#121	—	2	2	no	—
174	C₁₃×#121	—	2	2	no	—
175	C₁₃×#121	—	2	1	no	—
176	C₁₃×#121	—	2	1	no	—
177	C₁₃×#121	—	2	2	no	—
178	C₁₃×#121	—	2	2	no	—
179	C₁₃×#121	—	2	4	no	—
180	C₁₃×#121	—	2	1	no	—
181	C₁₃×#121	—	2	2	no	—
182	C₁₃×#121	—	2	2	no	—
183	C₁₃×#121	C₂³	1	4	yes	—
184	C₁₃×#121	C₂³	1	4	yes	—
185	C₁₃×#121	C₂³	1	2	yes	complemented
186	C₁₃×#121	C₂³	1	2	yes	complemented
187	C₁₃×#120	—	2	2	no	—
188	C₁₃×#120	—	2	2	no	—
189	C₁₃×#120	—	2	4	no	—
190	C₁₃×#120	—	2	4	no	—
191	C₁₃×#120	—	2	4	no	—
192	C₁₃×#120	—	2	4	no	—
193	C₁₃×#120	—	2	2	no	—
194	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic, complemented
195	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic, complemented
196	C₄×D₄×C₁₃	—	2	1	no	—
197	C₄×D₄×C₁₃	—	2	2	no	—
198	C₄×D₄×C₁₃	—	2	1	no	—
199	C₄×D₄×C₁₃	—	2	1	no	—
200	C₄×D₄×C₁₃	—	2	2	no	—
201	C₄×D₄×C₁₃	—	2	1	no	—
202	C₄×D₄×C₁₃	—	2	2	no	—
203	C₄×D₄×C₁₃	—	2	1	no	—
204	C₄×D₄×C₁₃	—	2	1	no	—
205	C₄×D₄×C₁₃	—	2	1	no	—
206	C₄×D₄×C₁₃	—	2	1	no	—
207	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
208	C₄×D₄×C₁₃	D₄	1	2	yes	—
209	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
210	C₄×D₄×C₁₃	C₂³	1	2	yes	—
211	C₄×D₄×C₁₃	C₂³	1	2	yes	—
212	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₁₃	C₂³	1	2	yes	—
214	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
215	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
216	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
217	C₁₃×#117	—	2	1	no	—
218	C₁₃×#117	C₂³	1	1	yes	characteristic
219	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
220	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
221	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
222	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
223	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
224	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
225	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
226	C₂×C₄²×C₁₃	—	2	1	no	—
227	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
228	C₁₃×#107	C₂³	1	2	yes	complemented
229	C₁₃×#106	C₂³	1	2	yes	complemented
230	C₁₃×C₄⋊C₈	C₂³	1	2	yes	complemented
231	C₁₃×C₄⋊C₈	C₂³	1	2	yes	complemented
232	C₁₃×#103	C₂³	1	2	yes	complemented
233	C₁₃×#103	C₂³	1	4	yes	complemented
234	C₁₃×#102	C₂³	1	2	yes	—
235	C₁₃×#102	C₂³	1	2	yes	—
236	C₁₃×#102	C₂³	1	2	yes	complemented
237	C₁₃×#102	C₂³	1	4	yes	complemented
238	C₁₃×#102	C₂³	1	4	yes	complemented
239	C₁₃×#102	C₂³	1	4	yes	complemented
240	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
241	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
242	C₁₃×#97	C₂³	1	2	yes	complemented
243	C₄×C₈×C₁₃	C₂³	1	2	yes	complemented
244	D₄×AGL(1,ℤ/8)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂⁴×C₁₃	—	2	1	no	—
246	C₂⁴×C₁₃	—	2	2	no	—
247	C₂⁴×C₁₃	—	2	2	no	—
248	C₂⁴×C₁₃	—	2	4	no	—
249	C₂⁴×C₁₃	—	2	4	no	—
250	C₂⁴×C₁₃	—	4	8	no	—
251	C₂⁴×C₁₃	—	4	8	no	—
252	C₂⁴×C₁₃	—	8	4	no	—
253	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
254	C₁₃×#41	—	2	2	no	—
255	C₁₃×#41	—	2	4	no	—
256	C₁₃×#41	—	2	4	no	—
257	C₁₃×#41	—	2	4	no	—
258	C₁₃×#41	—	2	4	no	—
259	C₁₃×#41	—	4	8	no	—
260	C₁₃×#41	—	4	2	no	—
261	C₁₃×#41	—	4	2	no	—
262	C₁₃×#41	—	4	8	no	—
263	C₁₃×#41	C₂×D₄	1	4	yes	complemented
264	C₂×Q₈×C₁₃	—	2	2	no	—
265	C₂×Q₈×C₁₃	—	2	4	no	—
266	C₂×Q₈×C₁₃	—	4	2	no	—
267	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
268	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×D₄×C₁₃	—	2	1	no	—
270	C₂×D₄×C₁₃	—	2	4	no	—
271	C₂×D₄×C₁₃	—	2	8	no	—
272	C₂×D₄×C₁₃	—	2	8	no	—
273	C₂×D₄×C₁₃	—	2	4	no	—
274	C₂×D₄×C₁₃	—	2	2	no	—
275	C₂×D₄×C₁₃	—	2	4	no	—
276	C₂×D₄×C₁₃	—	2	4	no	—
277	C₂×D₄×C₁₃	—	2	2	no	—
278	C₂×D₄×C₁₃	—	2	2	no	—
279	C₂×D₄×C₁₃	—	2	2	no	—
280	C₂×D₄×C₁₃	—	2	2	no	—
281	C₂×D₄×C₁₃	—	2	1	no	—
282	C₂×D₄×C₁₃	—	2	4	no	—
283	C₂×D₄×C₁₃	—	2	1	no	—
284	C₂×D₄×C₁₃	—	2	4	no	—
285	C₂×D₄×C₁₃	—	2	4	no	—
286	C₂×D₄×C₁₃	—	2	2	no	—
287	C₂×D₄×C₁₃	—	2	2	no	—
288	C₂×D₄×C₁₃	—	2	2	no	—
289	C₂×D₄×C₁₃	—	2	2	no	—
290	C₂×D₄×C₁₃	—	2	1	no	—
291	C₂×D₄×C₁₃	—	2	2	no	—
292	C₂×D₄×C₁₃	—	2	2	no	—
293	C₂×D₄×C₁₃	—	2	2	no	—
294	C₂×D₄×C₁₃	—	2	4	no	—
295	C₂×D₄×C₁₃	—	4	4	no	—
296	C₂×D₄×C₁₃	—	4	4	no	—
297	C₂×D₄×C₁₃	—	4	2	no	—
298	C₂×D₄×C₁₃	—	4	8	no	—
299	C₂×D₄×C₁₃	—	4	8	no	—
300	C₂×D₄×C₁₃	—	4	8	no	—
301	C₂×D₄×C₁₃	—	4	4	no	—
302	C₂×D₄×C₁₃	—	4	8	no	—
303	C₂×D₄×C₁₃	—	4	16	no	—
304	C₂×D₄×C₁₃	—	4	8	no	—
305	C₂×D₄×C₁₃	—	4	8	no	—
306	C₂×D₄×C₁₃	—	4	4	no	—
307	C₂×D₄×C₁₃	—	4	8	no	—
308	C₂×D₄×C₁₃	—	8	2	no	—
309	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
310	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
311	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
312	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	complemented
313	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
314	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
315	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
316	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₁₃	—	2	1	no	—
318	C₂²×C₄×C₁₃	—	2	4	no	—
319	C₂²×C₄×C₁₃	—	2	4	no	—
320	C₂²×C₄×C₁₃	—	2	1	no	—
321	C₂²×C₄×C₁₃	—	2	2	no	—
322	C₂²×C₄×C₁₃	—	2	1	no	—
323	C₂²×C₄×C₁₃	—	2	2	no	—
324	C₂²×C₄×C₁₃	—	2	2	no	—
325	C₂²×C₄×C₁₃	—	2	2	no	—
326	C₂²×C₄×C₁₃	—	2	2	no	—
327	C₂²×C₄×C₁₃	—	2	2	no	—
328	C₂²×C₄×C₁₃	—	2	1	no	—
329	C₂²×C₄×C₁₃	—	4	8	no	—
330	C₂²×C₄×C₁₃	—	4	4	no	—
331	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
333	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
334	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
335	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₁₃×SD₁₆	—	2	8	no	—
340	C₁₃×SD₁₆	—	2	8	no	—
341	C₁₃×SD₁₆	—	2	8	no	—
342	C₁₃×SD₁₆	—	4	4	no	—
343	C₁₃×SD₁₆	C₂×D₄	1	8	yes	complemented
344	C₁₃×D₈	—	2	8	no	—
345	C₁₃×D₈	—	2	8	no	—
346	C₁₃×D₈	—	2	8	no	—
347	C₁₃×D₈	—	4	4	no	—
348	C₁₃×D₈	C₂×D₄	1	8	yes	complemented
349	C₁₃×M₁₆	—	2	4	no	—
350	C₁₃×M₁₆	—	2	2	no	—
351	C₁₃×M₁₆	—	2	8	no	—
352	C₁₃×M₁₆	C₂×D₄	1	4	yes	complemented
353	C₂×C₈×C₁₃	—	2	8	no	—
354	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
355	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
356	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
357	C₁₃×C₄⋊C₄	—	2	1	no	—
358	C₁₃×C₄⋊C₄	—	2	2	no	—
359	C₁₃×C₄⋊C₄	—	2	1	no	—
360	C₁₃×C₄⋊C₄	—	2	1	no	—
361	C₁₃×C₄⋊C₄	—	2	1	no	—
362	C₁₃×C₄⋊C₄	—	2	1	no	—
363	C₁₃×C₄⋊C₄	—	2	2	no	—
364	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
365	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
366	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
368	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
369	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
370	C₁₃×C₂²⋊C₄	—	2	2	no	—
371	C₁₃×C₂²⋊C₄	—	2	1	no	—
372	C₁₃×C₂²⋊C₄	—	2	2	no	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	2	no	—
375	C₁₃×C₂²⋊C₄	—	2	2	no	—
376	C₁₃×C₂²⋊C₄	—	2	2	no	—
377	C₁₃×C₂²⋊C₄	—	2	4	no	—
378	C₁₃×C₂²⋊C₄	—	2	4	no	—
379	C₁₃×C₂²⋊C₄	—	2	1	no	—
380	C₁₃×C₂²⋊C₄	—	2	1	no	—
381	C₁₃×C₂²⋊C₄	—	2	2	no	—
382	C₁₃×C₂²⋊C₄	—	2	2	no	—
383	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
384	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
385	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
386	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
387	C₄²×C₁₃	—	2	1	no	—
388	C₄²×C₁₃	—	2	1	no	—
389	C₄²×C₁₃	—	2	1	no	—
390	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
393	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
394	C₂²×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
395	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
396	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
397	D₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
398	D₄×D₈	C₂×C₁₃	1	2	yes	complemented
399	#3274	C₂×C₁₃	1	2	yes	complemented
400	#3272	C₂×C₁₃	1	2	yes	complemented
401	#3265	C₂×C₁₃	1	4	yes	complemented
402	#3264	C₂×C₁₃	1	4	yes	complemented
403	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
404	#3055	C₂×C₁₃	1	2	yes	complemented
405	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
406	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
407	#3006	C₂×C₁₃	1	2	yes	complemented
408	#3003	C₂×C₁₃	1	2	yes	complemented
409	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
410	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
411	C₂³×C₁₃	—	2	4	no	—
412	C₂³×C₁₃	—	2	4	no	—
413	C₂³×C₁₃	—	2	4	no	—
414	C₂³×C₁₃	—	2	1	no	—
415	C₂³×C₁₃	—	2	2	no	—
416	C₂³×C₁₃	—	2	2	no	—
417	C₂³×C₁₃	—	2	4	no	—
418	C₂³×C₁₃	—	4	2	no	—
419	C₂³×C₁₃	—	4	4	no	—
420	C₂³×C₁₃	—	4	8	no	—
421	C₂³×C₁₃	—	4	8	no	—
422	C₂³×C₁₃	—	4	2	no	—
423	C₂³×C₁₃	—	4	2	no	—
424	C₂³×C₁₃	—	4	4	no	—
425	C₂³×C₁₃	—	4	8	no	—
426	C₂³×C₁₃	—	4	4	no	—
427	C₂³×C₁₃	—	4	4	no	—
428	C₂³×C₁₃	—	4	8	no	—
429	C₂³×C₁₃	—	4	4	no	—
430	C₂³×C₁₃	—	8	2	no	—
431	C₂³×C₁₃	—	8	4	no	—
432	C₂³×C₁₃	—	8	4	no	—
433	C₂³×C₁₃	—	8	32	no	—
434	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
435	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
436	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
437	Q₈×C₁₃	—	2	1	no	—
438	Q₈×C₁₃	—	2	2	no	—
439	Q₈×C₁₃	—	2	2	no	—
440	Q₈×C₁₃	—	4	4	no	—
441	Q₈×C₁₃	C₂²×D₄	1	2	yes	complemented
442	D₄×C₁₃	—	2	4	no	—
443	D₄×C₁₃	—	2	4	no	—
444	D₄×C₁₃	—	2	4	no	—
445	D₄×C₁₃	—	2	2	no	—
446	D₄×C₁₃	—	2	2	no	—
447	D₄×C₁₃	—	2	4	no	—
448	D₄×C₁₃	—	2	2	no	—
449	D₄×C₁₃	—	2	1	no	—
450	D₄×C₁₃	—	2	2	no	—
451	D₄×C₁₃	—	2	4	no	—
452	D₄×C₁₃	—	4	8	no	—
453	D₄×C₁₃	—	4	8	no	—
454	D₄×C₁₃	—	4	4	no	—
455	D₄×C₁₃	—	4	4	no	—
456	D₄×C₁₃	—	4	4	no	—
457	D₄×C₁₃	—	4	4	no	—
458	D₄×C₁₃	—	4	8	no	—
459	D₄×C₁₃	—	4	4	no	—
460	D₄×C₁₃	—	4	4	no	—
461	D₄×C₁₃	—	4	8	no	—
462	D₄×C₁₃	—	4	4	no	—
463	D₄×C₁₃	—	4	2	no	—
464	D₄×C₁₃	—	4	4	no	—
465	D₄×C₁₃	—	8	1	no	—
466	D₄×C₁₃	—	8	2	no	—
467	D₄×C₁₃	—	8	2	no	—
468	D₄×C₁₃	—	8	2	no	—
469	D₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	direct product factor
470	D₄×C₁₃	C₂²×D₄	1	4	yes	—
471	D₄×C₁₃	C₂²×D₄	1	2	yes	complemented
472	C₂×C₄×C₁₃	—	2	4	no	—
473	C₂×C₄×C₁₃	—	2	1	no	—
474	C₂×C₄×C₁₃	—	2	4	no	—
475	C₂×C₄×C₁₃	—	2	4	no	—
476	C₂×C₄×C₁₃	—	2	4	no	—
477	C₂×C₄×C₁₃	—	2	2	no	—
478	C₂×C₄×C₁₃	—	2	2	no	—
479	C₂×C₄×C₁₃	—	2	2	no	—
480	C₂×C₄×C₁₃	—	2	2	no	—
481	C₂×C₄×C₁₃	—	2	2	no	—
482	C₂×C₄×C₁₃	—	2	1	no	—
483	C₂×C₄×C₁₃	—	2	1	no	—
484	C₂×C₄×C₁₃	—	2	2	no	—
485	C₂×C₄×C₁₃	—	2	2	no	—
486	C₂×C₄×C₁₃	—	4	1	no	—
487	C₂×C₄×C₁₃	—	4	4	no	—
488	C₂×C₄×C₁₃	—	4	4	no	—
489	C₂×C₄×C₁₃	—	4	4	no	—
490	C₂×C₄×C₁₃	—	4	4	no	—
491	C₂×C₄×C₁₃	—	4	2	no	—
492	C₂×C₄×C₁₃	—	4	4	no	—
493	C₂×C₄×C₁₃	—	4	4	no	—
494	C₂×C₄×C₁₃	—	4	2	no	—
495	C₂×C₄×C₁₃	—	8	1	no	—
496	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
505	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
506	C₈×C₁₃	—	2	4	no	—
507	C₈×C₁₃	—	2	2	no	—
508	C₈×C₁₃	C₂²×D₄	1	4	yes	complemented
509	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
510	C₂³×D₄	—	2	1	no	—
511	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
512	C₂×AGL(1,ℤ/8)	—	2	16	no	—
513	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
514	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
515	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
516	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
517	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
518	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
519	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
520	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
521	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
522	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	complemented
523	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
524	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
525	#548	C₂²×C₁₃	1	2	yes	complemented
526	#547	—	2	1	no	—
527	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
528	#546	—	2	2	no	—
529	#546	C₂²×C₁₃	1	2	yes	complemented
530	D₄²	—	2	1	no	—
531	D₄²	—	2	1	no	—
532	D₄²	—	2	2	no	—
533	D₄²	—	2	1	no	—
534	D₄²	C₂²×C₁₃	1	2	yes	—
535	D₄²	C₂²×C₁₃	1	4	yes	complemented
536	D₄²	C₂²×C₁₃	1	2	yes	complemented
537	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
538	#532	—	2	1	no	—
539	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
540	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
541	#525	—	2	2	no	—
542	#525	C₂²×C₁₃	1	2	yes	complemented
543	C₂×#121	—	2	1	no	—
544	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
545	C₂×#120	—	2	2	no	—
546	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
547	C₂×C₄×D₄	—	2	1	no	—
548	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
549	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
550	#496	C₂²×C₁₃	1	4	yes	complemented
551	#493	C₂²×C₁₃	1	2	yes	complemented
552	#492	C₂²×C₁₃	1	2	yes	complemented
553	#469	C₂²×C₁₃	1	4	yes	complemented
554	#468	C₂²×C₁₃	1	4	yes	complemented
555	#466	C₂²×C₁₃	1	4	yes	complemented
556	#465	C₂²×C₁₃	1	4	yes	complemented
557	#463	C₂²×C₁₃	1	4	yes	complemented
558	#461	C₂²×C₁₃	1	2	yes	complemented
559	#460	C₂²×C₁₃	1	2	yes	complemented
560	#460	C₂²×C₁₃	1	2	yes	complemented
561	#459	C₂²×C₁₃	1	2	yes	complemented
562	#459	C₂²×C₁₃	1	2	yes	complemented
563	#459	C₂²×C₁₃	1	2	yes	complemented
564	#450	C₂²×C₁₃	1	4	yes	complemented
565	#450	C₂²×C₁₃	1	4	yes	complemented
566	#449	C₂²×C₁₃	1	4	yes	complemented
567	#449	C₂²×C₁₃	1	4	yes	complemented
568	#448	C₂²×C₁₃	1	4	yes	complemented
569	#447	C₂²×C₁₃	1	4	yes	complemented
570	#447	C₂²×C₁₃	1	4	yes	complemented
571	#447	C₂²×C₁₃	1	4	yes	complemented
572	#442	C₂²×C₁₃	1	2	yes	complemented
573	#440	C₂²×C₁₃	1	2	yes	complemented
574	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
575	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
576	#436	C₂²×C₁₃	1	2	yes	complemented
577	#435	C₂²×C₁₃	1	4	yes	complemented
578	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
579	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
580	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
581	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
582	#418	C₂²×C₁₃	1	2	yes	complemented
583	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
584	#417	C₂²×C₁₃	1	2	yes	complemented
585	#407	C₂²×C₁₃	1	2	yes	complemented
586	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
587	C₂²×C₁₃	—	2	1	no	—
588	C₂²×C₁₃	—	2	2	no	—
589	C₂²×C₁₃	—	2	2	no	—
590	C₂²×C₁₃	—	2	1	no	—
591	C₂²×C₁₃	—	2	2	no	—
592	C₂²×C₁₃	—	2	2	no	—
593	C₂²×C₁₃	—	2	2	no	—
594	C₂²×C₁₃	—	2	4	no	—
595	C₂²×C₁₃	—	2	2	no	—
596	C₂²×C₁₃	—	4	8	no	—
597	C₂²×C₁₃	—	4	8	no	—
598	C₂²×C₁₃	—	4	1	no	—
599	C₂²×C₁₃	—	4	2	no	—
600	C₂²×C₁₃	—	4	2	no	—
601	C₂²×C₁₃	—	4	1	no	—
602	C₂²×C₁₃	—	4	4	no	—
603	C₂²×C₁₃	—	4	2	no	—
604	C₂²×C₁₃	—	4	2	no	—
605	C₂²×C₁₃	—	4	4	no	—
606	C₂²×C₁₃	—	4	4	no	—
607	C₂²×C₁₃	—	4	2	no	—
608	C₂²×C₁₃	—	8	8	no	—
609	C₂²×C₁₃	—	8	16	no	—
610	C₂²×C₁₃	—	8	8	no	—
611	C₂²×C₁₃	—	8	16	no	—
612	C₂²×C₁₃	D₄²	1	2	yes	—
613	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
614	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
615	C₄×C₁₃	—	2	1	no	—
616	C₄×C₁₃	—	2	1	no	—
617	C₄×C₁₃	—	2	2	no	—
618	C₄×C₁₃	—	2	2	no	—
619	C₄×C₁₃	—	2	2	no	—
620	C₄×C₁₃	—	2	1	no	—
621	C₄×C₁₃	—	4	1	no	—
622	C₄×C₁₃	—	4	2	no	—
623	C₄×C₁₃	—	4	2	no	—
624	C₄×C₁₃	—	4	1	no	—
625	C₄×C₁₃	D₄²	1	2	yes	—
626	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	complemented
627	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
628	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
629	C₂⁵	—	2	2	no	—
630	C₂×#41	—	2	2	no	—
631	C₂×#41	—	2	2	no	—
632	C₂×#41	—	2	8	no	—
633	C₂×#41	—	4	4	no	—
634	C₂×#41	C₂³×C₁₃	1	2	yes	—
635	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
636	C₂×#41	C₂³×C₁₃	1	2	yes	complemented
637	C₂×#41	C₂³×C₁₃	1	2	yes	complemented
638	C₂²×Q₈	C₂³×C₁₃	1	2	yes	complemented
639	C₂²×D₄	—	2	8	no	—
640	C₂²×D₄	—	2	2	no	—
641	C₂²×D₄	—	2	2	no	—
642	C₂²×D₄	—	2	1	no	—
643	C₂²×D₄	—	2	2	no	—
644	C₂²×D₄	—	2	4	no	—
645	C₂²×D₄	—	2	2	no	—
646	C₂²×D₄	—	2	2	no	—
647	C₂²×D₄	—	2	1	no	—
648	C₂²×D₄	—	2	2	no	—
649	C₂²×D₄	—	2	2	no	—
650	C₂²×D₄	—	2	1	no	—
651	C₂²×D₄	—	4	4	no	—
652	C₂²×D₄	—	4	8	no	—
653	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
654	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
655	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
656	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
657	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
658	C₂²×D₄	C₂³×C₁₃	1	2	yes	complemented
659	C₂³×C₄	—	2	2	no	—
660	C₂³×C₄	—	2	1	no	—
661	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
662	AGL(1,ℤ/8)	—	2	8	no	—
663	AGL(1,ℤ/8)	—	2	8	no	—
664	AGL(1,ℤ/8)	—	2	16	no	—
665	AGL(1,ℤ/8)	—	2	16	no	—
666	AGL(1,ℤ/8)	—	2	8	no	—
667	AGL(1,ℤ/8)	—	4	4	no	—
668	AGL(1,ℤ/8)	D₄×C₁₃	1	8	yes	direct product factor
669	C₂×SD₁₆	—	2	16	no	—
670	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
671	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
672	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
673	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
674	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
675	C₂×D₈	—	2	16	no	—
676	C₂×D₈	C₂³×C₁₃	1	4	yes	—
677	C₂×D₈	C₂³×C₁₃	1	2	yes	—
678	C₂×D₈	C₂³×C₁₃	1	4	yes	complemented
679	C₂×D₈	C₂³×C₁₃	1	4	yes	complemented
680	C₂×D₈	C₂³×C₁₃	1	4	yes	complemented
681	C₂×M₁₆	—	2	8	no	—
682	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
683	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
684	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
685	C₂×M₁₆	C₂³×C₁₃	1	4	yes	complemented
686	C₂²×C₈	C₂³×C₁₃	1	4	yes	complemented
687	C₄⋊Q₈	—	2	1	no	—
688	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
689	#127	—	2	1	no	—
690	#127	—	2	1	no	—
691	#127	—	2	1	no	—
692	#127	C₂³×C₁₃	1	2	yes	—
693	#127	C₂³×C₁₃	1	2	yes	—
694	#127	C₂³×C₁₃	1	1	yes	characteristic, complemented
695	#124	—	2	2	no	—
696	#124	C₂³×C₁₃	1	2	yes	complemented
697	#123	—	2	2	no	—
698	#123	—	2	2	no	—
699	#123	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
703	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
704	#121	—	2	2	no	—
705	#121	—	2	1	no	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	—	2	1	no	—
709	#121	—	2	1	no	—
710	#121	—	2	2	no	—
711	#121	—	2	2	no	—
712	#121	—	2	4	no	—
713	#121	—	2	1	no	—
714	#121	—	2	2	no	—
715	#121	—	2	2	no	—
716	#121	C₂³×C₁₃	1	4	yes	—
717	#121	C₂³×C₁₃	1	4	yes	—
718	#121	C₂³×C₁₃	1	2	yes	complemented
719	#121	C₂³×C₁₃	1	2	yes	complemented
720	#120	—	2	2	no	—
721	#120	—	2	2	no	—
722	#120	—	2	4	no	—
723	#120	—	2	4	no	—
724	#120	—	2	4	no	—
725	#120	—	2	4	no	—
726	#120	—	2	2	no	—
727	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
728	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	—	2	2	no	—
731	C₄×D₄	—	2	1	no	—
732	C₄×D₄	—	2	1	no	—
733	C₄×D₄	—	2	2	no	—
734	C₄×D₄	—	2	1	no	—
735	C₄×D₄	—	2	2	no	—
736	C₄×D₄	—	2	1	no	—
737	C₄×D₄	—	2	1	no	—
738	C₄×D₄	—	2	1	no	—
739	C₄×D₄	—	2	1	no	—
740	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
741	C₄×D₄	D₄×C₁₃	1	2	yes	—
742	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
743	C₄×D₄	C₂³×C₁₃	1	2	yes	—
744	C₄×D₄	C₂³×C₁₃	1	2	yes	—
745	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
746	C₄×D₄	C₂³×C₁₃	1	2	yes	—
747	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
748	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
749	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
750	#117	—	2	1	no	—
751	#117	C₂³×C₁₃	1	1	yes	characteristic
752	C₂×C₄⋊C₄	—	2	1	no	—
753	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
754	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
755	C₂×C₂²⋊C₄	—	2	1	no	—
756	C₂×C₂²⋊C₄	—	2	2	no	—
757	C₂×C₂²⋊C₄	—	2	2	no	—
758	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
759	C₂×C₄²	—	2	1	no	—
760	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
761	#107	C₂³×C₁₃	1	2	yes	complemented
762	#106	C₂³×C₁₃	1	2	yes	complemented
763	C₄⋊C₈	C₂³×C₁₃	1	2	yes	complemented
764	C₄⋊C₈	C₂³×C₁₃	1	2	yes	complemented
765	#103	C₂³×C₁₃	1	2	yes	complemented
766	#103	C₂³×C₁₃	1	4	yes	complemented
767	#102	C₂³×C₁₃	1	2	yes	—
768	#102	C₂³×C₁₃	1	2	yes	—
769	#102	C₂³×C₁₃	1	2	yes	complemented
770	#102	C₂³×C₁₃	1	4	yes	complemented
771	#102	C₂³×C₁₃	1	4	yes	complemented
772	#102	C₂³×C₁₃	1	4	yes	complemented
773	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
774	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
775	#97	C₂³×C₁₃	1	2	yes	complemented
776	C₄×C₈	C₂³×C₁₃	1	2	yes	complemented
777	C₂×C₁₃	—	2	2	no	—
778	C₂×C₁₃	—	2	4	no	—
779	C₂×C₁₃	—	4	2	no	—
780	C₂×C₁₃	—	4	4	no	—
781	C₂×C₁₃	—	4	2	no	—
782	C₂×C₁₃	—	8	2	no	—
783	C₂×C₁₃	—	8	4	no	—
784	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
785	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
786	C₂×C₁₃	#3585	1	1	yes	characteristic
787	C₂⁴	—	2	1	no	—
788	C₂⁴	—	2	2	no	—
789	C₂⁴	—	2	2	no	—
790	C₂⁴	—	2	4	no	—
791	C₂⁴	—	2	4	no	—
792	C₂⁴	—	4	8	no	—
793	C₂⁴	—	4	8	no	—
794	C₂⁴	—	8	4	no	—
795	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
796	#41	—	2	2	no	—
797	#41	—	2	4	no	—
798	#41	—	2	4	no	—
799	#41	—	2	4	no	—
800	#41	—	2	4	no	—
801	#41	—	4	8	no	—
802	#41	—	4	2	no	—
803	#41	—	4	2	no	—
804	#41	—	4	8	no	—
805	#41	C₂×D₄×C₁₃	1	4	yes	complemented
806	C₂×Q₈	—	2	2	no	—
807	C₂×Q₈	—	2	4	no	—
808	C₂×Q₈	—	4	2	no	—
809	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
810	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	4	no	—
813	C₂×D₄	—	2	8	no	—
814	C₂×D₄	—	2	8	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	4	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	1	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	1	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	2	4	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	1	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	4	no	—
837	C₂×D₄	—	4	4	no	—
838	C₂×D₄	—	4	4	no	—
839	C₂×D₄	—	4	2	no	—
840	C₂×D₄	—	4	8	no	—
841	C₂×D₄	—	4	8	no	—
842	C₂×D₄	—	4	8	no	—
843	C₂×D₄	—	4	4	no	—
844	C₂×D₄	—	4	8	no	—
845	C₂×D₄	—	4	16	no	—
846	C₂×D₄	—	4	8	no	—
847	C₂×D₄	—	4	8	no	—
848	C₂×D₄	—	4	8	no	—
849	C₂×D₄	—	4	4	no	—
850	C₂×D₄	—	8	2	no	—
851	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
852	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
853	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
854	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	complemented
855	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
856	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
857	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
858	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	4	no	—
861	C₂²×C₄	—	2	4	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	4	8	no	—
872	C₂²×C₄	—	4	4	no	—
873	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
874	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
875	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
876	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
877	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
879	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
881	SD₁₆	—	2	8	no	—
882	SD₁₆	—	2	8	no	—
883	SD₁₆	—	2	8	no	—
884	SD₁₆	—	4	4	no	—
885	SD₁₆	C₂×D₄×C₁₃	1	8	yes	complemented
886	D₈	—	2	8	no	—
887	D₈	—	2	8	no	—
888	D₈	—	2	8	no	—
889	D₈	—	4	4	no	—
890	D₈	C₂×D₄×C₁₃	1	8	yes	complemented
891	M₁₆	—	2	4	no	—
892	M₁₆	—	2	2	no	—
893	M₁₆	—	2	8	no	—
894	M₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
895	C₂×C₈	—	2	8	no	—
896	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
897	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
898	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
907	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
908	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
909	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
910	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
911	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	1	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	1	no	—
922	C₂²⋊C₄	—	2	1	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
926	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
927	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
928	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
929	C₄²	—	2	1	no	—
930	C₄²	—	2	1	no	—
931	C₄²	—	2	1	no	—
932	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
933	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
934	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
935	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
936	C₁₃	D₄×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
937	C₂³	—	2	4	no	—
938	C₂³	—	2	4	no	—
939	C₂³	—	2	4	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	4	no	—
944	C₂³	—	4	2	no	—
945	C₂³	—	4	4	no	—
946	C₂³	—	4	8	no	—
947	C₂³	—	4	8	no	—
948	C₂³	—	4	2	no	—
949	C₂³	—	4	2	no	—
950	C₂³	—	4	4	no	—
951	C₂³	—	4	8	no	—
952	C₂³	—	4	4	no	—
953	C₂³	—	4	4	no	—
954	C₂³	—	4	8	no	—
955	C₂³	—	4	4	no	—
956	C₂³	—	8	4	no	—
957	C₂³	—	8	4	no	—
958	C₂³	—	8	2	no	—
959	C₂³	—	8	32	no	—
960	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
961	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
962	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
963	Q₈	—	2	1	no	—
964	Q₈	—	2	2	no	—
965	Q₈	—	2	2	no	—
966	Q₈	—	4	4	no	—
967	Q₈	C₂²×D₄×C₁₃	1	2	yes	complemented
968	D₄	—	2	4	no	—
969	D₄	—	2	4	no	—
970	D₄	—	2	4	no	—
971	D₄	—	2	2	no	—
972	D₄	—	2	2	no	—
973	D₄	—	2	4	no	—
974	D₄	—	2	2	no	—
975	D₄	—	2	1	no	—
976	D₄	—	2	2	no	—
977	D₄	—	2	4	no	—
978	D₄	—	4	8	no	—
979	D₄	—	4	8	no	—
980	D₄	—	4	4	no	—
981	D₄	—	4	4	no	—
982	D₄	—	4	4	no	—
983	D₄	—	4	4	no	—
984	D₄	—	4	8	no	—
985	D₄	—	4	4	no	—
986	D₄	—	4	8	no	—
987	D₄	—	4	4	no	—
988	D₄	—	4	4	no	—
989	D₄	—	4	4	no	—
990	D₄	—	4	2	no	—
991	D₄	—	8	2	no	—
992	D₄	—	8	2	no	—
993	D₄	—	8	1	no	—
994	D₄	—	8	2	no	—
995	D₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	direct product factor
996	D₄	C₂²×D₄×C₁₃	1	4	yes	—
997	D₄	C₂²×D₄×C₁₃	1	2	yes	complemented
998	C₂×C₄	—	2	4	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	4	no	—
1001	C₂×C₄	—	2	4	no	—
1002	C₂×C₄	—	2	4	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	4	4	no	—
1014	C₂×C₄	—	4	4	no	—
1015	C₂×C₄	—	4	4	no	—
1016	C₂×C₄	—	4	4	no	—
1017	C₂×C₄	—	4	2	no	—
1018	C₂×C₄	—	4	4	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	2	no	—
1021	C₂×C₄	—	8	1	no	—
1022	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1026	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1027	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1028	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1029	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1030	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1031	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1032	C₈	—	2	4	no	—
1033	C₈	—	2	2	no	—
1034	C₈	C₂²×D₄×C₁₃	1	4	yes	complemented
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	2	no	—
1041	C₂²	—	2	2	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	2	4	no	—
1044	C₂²	—	4	8	no	—
1045	C₂²	—	4	8	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	4	no	—
1051	C₂²	—	4	2	no	—
1052	C₂²	—	4	4	no	—
1053	C₂²	—	4	2	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	4	no	—
1056	C₂²	—	8	8	no	—
1057	C₂²	—	8	16	no	—
1058	C₂²	—	8	8	no	—
1059	C₂²	—	8	16	no	—
1060	C₂²	D₄²×C₁₃	1	2	yes	—
1061	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
1062	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1063	C₄	—	2	1	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	2	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	2	no	—
1073	C₄	D₄²×C₁₃	1	2	yes	—
1074	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	complemented
1075	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
1076	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1077	C₂	—	2	2	no	—
1078	C₂	—	2	4	no	—
1079	C₂	—	4	2	no	—
1080	C₂	—	4	4	no	—
1081	C₂	—	4	2	no	—
1082	C₂	—	8	4	no	—
1083	C₂	—	8	2	no	—
1084	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
1085	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
1086	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×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. C₂×D₄²×C₁₃	C₂	semidirect
4. D₄×C₁₃×SD₁₆	C₂	semidirect
5. D₄×C₁₃×D₈	C₂	semidirect
6. C₁₃×#3274	C₂	semidirect
7. C₁₃×#3272	C₂	semidirect
8. C₁₃×#3265	C₂	semidirect
9. C₁₃×#3264	C₂	semidirect
10. C₁₃×#3151	C₂	semidirect
11. C₁₃×#3055	C₂	semidirect
12. C₁₃×#3038	C₂	semidirect
13. C₁₃×#3036	C₂	semidirect
14. C₁₃×#3006	C₂	semidirect
15. C₁₃×#3003	C₂	semidirect
16. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
17. D₄×C₁₃×M₁₆	C₂	semidirect
18. C₂²×C₁₃×#41	C₂²	semidirect
20. C₂³×D₄×C₁₃	C₂²	semidirect
23. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
29. C₂²×C₁₃×SD₁₆	C₂²	semidirect
30. C₂²×C₁₃×D₈	C₂²	semidirect
31. C₂²×C₁₃×M₁₆	C₂²	semidirect
32. C₁₃×#550	C₂²	semidirect
33. D₄×Q₈×C₁₃	C₂²	semidirect
34. C₁₃×#548	C₂²	semidirect
36. C₁₃×#547	C₂²	semidirect
38. C₁₃×#546	C₂²	semidirect
44. D₄²×C₁₃	C₂²	semidirect
45. D₄²×C₁₃	C₂²	semidirect
46. D₄²×C₁₃	C₂²	semidirect
48. C₁₃×#532	C₂²	semidirect
49. C₂×C₁₃×#127	C₂²	semidirect
51. C₁₃×#525	C₂²	semidirect
53. C₂×C₁₃×#121	C₂²	semidirect
55. C₄×C₁₃×#41	C₂²	semidirect
58. C₂×C₄×D₄×C₁₃	C₂²	semidirect
59. C₁₃×#496	C₂²	semidirect
60. C₁₃×#493	C₂²	semidirect
61. C₁₃×#492	C₂²	semidirect
62. C₁₃×#469	C₂²	semidirect
63. C₁₃×#468	C₂²	semidirect
64. C₁₃×#466	C₂²	semidirect
65. C₁₃×#465	C₂²	semidirect
66. C₁₃×#463	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
69. C₁₃×#460	C₂²	semidirect
70. C₁₃×#459	C₂²	semidirect
71. C₁₃×#459	C₂²	semidirect
72. C₁₃×#459	C₂²	semidirect
73. C₁₃×#450	C₂²	semidirect
74. C₁₃×#450	C₂²	semidirect
75. C₁₃×#449	C₂²	semidirect
76. C₁₃×#449	C₂²	semidirect
77. C₁₃×#448	C₂²	semidirect
78. C₁₃×#447	C₂²	semidirect
79. C₁₃×#447	C₂²	semidirect
80. C₁₃×#447	C₂²	semidirect
81. C₁₃×#442	C₂²	semidirect
82. C₁₃×#440	C₂²	semidirect
83. C₄×C₁₃×SD₁₆	C₂²	semidirect
84. C₄×C₁₃×D₈	C₂²	semidirect
85. C₁₃×#436	C₂²	semidirect
86. C₁₃×#435	C₂²	semidirect
87. C₈×D₄×C₁₃	C₂²	semidirect
88. C₁₃×#428	C₂²	semidirect
89. C₁₃×#423	C₂²	semidirect
90. C₁₃×#418	C₂²	semidirect
91. C₁₃×#418	C₂²	semidirect
92. C₁₃×#417	C₂²	semidirect
93. C₁₃×#417	C₂²	semidirect
94. C₁₃×#407	C₂²	semidirect
95. C₄×C₁₃×M₁₆	C₂²	semidirect
103. C₂×C₁₃×#41	C₂³	semidirect
104. C₂×C₁₃×#41	C₂³	semidirect
105. C₂²×Q₈×C₁₃	C₂³	semidirect
125. C₂²×D₄×C₁₃	C₂³	semidirect
135. C₁₃×AGL(1,ℤ/8)	D₄	direct (N × H)
139. C₂×C₁₃×SD₁₆	C₂³	semidirect
140. C₂×C₁₃×SD₁₆	C₂³	semidirect
141. C₂×C₁₃×SD₁₆	C₂³	semidirect
145. C₂×C₁₃×D₈	C₂³	semidirect
146. C₂×C₁₃×D₈	C₂³	semidirect
147. C₂×C₁₃×D₈	C₂³	semidirect
152. C₂×C₁₃×M₁₆	C₂³	semidirect
153. C₂²×C₈×C₁₃	C₂³	semidirect
155. C₁₃×C₄⋊Q₈	C₂³	semidirect
161. C₁₃×#127	C₂³	semidirect
163. C₁₃×#124	C₂³	semidirect
169. C₁₃×C₂²⋊Q₈	C₂³	semidirect
170. C₁₃×C₂²⋊Q₈	C₂³	semidirect
185. C₁₃×#121	C₂³	semidirect
186. C₁₃×#121	C₂³	semidirect
194. C₄×Q₈×C₁₃	C₂³	semidirect
195. C₄×Q₈×C₁₃	C₂³	semidirect
215. C₄×D₄×C₁₃	C₂³	semidirect
216. C₄×D₄×C₁₃	C₂³	semidirect
228. C₁₃×#107	C₂³	semidirect
229. C₁₃×#106	C₂³	semidirect
230. C₁₃×C₄⋊C₈	C₂³	semidirect
231. C₁₃×C₄⋊C₈	C₂³	semidirect
232. C₁₃×#103	C₂³	semidirect
233. C₁₃×#103	C₂³	semidirect
236. C₁₃×#102	C₂³	semidirect
237. C₁₃×#102	C₂³	semidirect
238. C₁₃×#102	C₂³	semidirect
239. C₁₃×#102	C₂³	semidirect
240. C₁₃×C₂²⋊C₈	C₂³	semidirect
241. C₁₃×C₂²⋊C₈	C₂³	semidirect
242. C₁₃×#97	C₂³	semidirect
243. C₄×C₈×C₁₃	C₂³	semidirect
244. D₄×AGL(1,ℤ/8)	C₁₃	direct (N × H)
263. C₁₃×#41	C₂×D₄	semidirect
312. C₂×D₄×C₁₃	C₂×D₄	semidirect
343. C₁₃×SD₁₆	C₂×D₄	semidirect
348. C₁₃×D₈	C₂×D₄	semidirect
352. C₁₃×M₁₆	C₂×D₄	semidirect
394. C₂²×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
395. D₄×#41	C₂×C₁₃	semidirect
396. C₂×D₄²	C₂×C₁₃	semidirect
397. D₄×SD₁₆	C₂×C₁₃	semidirect
398. D₄×D₈	C₂×C₁₃	semidirect
399. #3274	C₂×C₁₃	semidirect
400. #3272	C₂×C₁₃	semidirect
401. #3265	C₂×C₁₃	semidirect
402. #3264	C₂×C₁₃	semidirect
403. #3151	C₂×C₁₃	semidirect
404. #3055	C₂×C₁₃	semidirect
405. #3038	C₂×C₁₃	semidirect
406. #3036	C₂×C₁₃	semidirect
407. #3006	C₂×C₁₃	semidirect
408. #3003	C₂×C₁₃	semidirect
409. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
410. D₄×M₁₆	C₂×C₁₃	semidirect
441. Q₈×C₁₃	C₂²×D₄	semidirect
469. D₄×C₁₃	AGL(1,ℤ/8)	direct (N × H)
471. D₄×C₁₃	C₂²×D₄	semidirect
508. C₈×C₁₃	C₂²×D₄	semidirect
509. C₂²×#41	C₂²×C₁₃	semidirect
511. C₂³×D₄	C₂²×C₁₃	semidirect
514. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
515. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
516. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
517. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
518. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
519. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
520. C₂²×SD₁₆	C₂²×C₁₃	semidirect
521. C₂²×D₈	C₂²×C₁₃	semidirect
522. C₂²×M₁₆	C₂²×C₁₃	semidirect
523. #550	C₂²×C₁₃	semidirect
524. D₄×Q₈	C₂²×C₁₃	semidirect
525. #548	C₂²×C₁₃	semidirect
527. #547	C₂²×C₁₃	semidirect
529. #546	C₂²×C₁₃	semidirect
535. D₄²	C₂²×C₁₃	semidirect
536. D₄²	C₂²×C₁₃	semidirect
537. D₄²	C₂²×C₁₃	semidirect
539. #532	C₂²×C₁₃	semidirect
540. C₂×#127	C₂²×C₁₃	semidirect
542. #525	C₂²×C₁₃	semidirect
544. C₂×#121	C₂²×C₁₃	semidirect
546. C₄×#41	C₂²×C₁₃	semidirect
549. C₂×C₄×D₄	C₂²×C₁₃	semidirect
550. #496	C₂²×C₁₃	semidirect
551. #493	C₂²×C₁₃	semidirect
552. #492	C₂²×C₁₃	semidirect
553. #469	C₂²×C₁₃	semidirect
554. #468	C₂²×C₁₃	semidirect
555. #466	C₂²×C₁₃	semidirect
556. #465	C₂²×C₁₃	semidirect
557. #463	C₂²×C₁₃	semidirect
558. #461	C₂²×C₁₃	semidirect
559. #460	C₂²×C₁₃	semidirect
560. #460	C₂²×C₁₃	semidirect
561. #459	C₂²×C₁₃	semidirect
562. #459	C₂²×C₁₃	semidirect
563. #459	C₂²×C₁₃	semidirect
564. #450	C₂²×C₁₃	semidirect
565. #450	C₂²×C₁₃	semidirect
566. #449	C₂²×C₁₃	semidirect
567. #449	C₂²×C₁₃	semidirect
568. #448	C₂²×C₁₃	semidirect
569. #447	C₂²×C₁₃	semidirect
570. #447	C₂²×C₁₃	semidirect
571. #447	C₂²×C₁₃	semidirect
572. #442	C₂²×C₁₃	semidirect
573. #440	C₂²×C₁₃	semidirect
574. C₄×SD₁₆	C₂²×C₁₃	semidirect
575. C₄×D₈	C₂²×C₁₃	semidirect
576. #436	C₂²×C₁₃	semidirect
577. #435	C₂²×C₁₃	semidirect
578. C₈×D₄	C₂²×C₁₃	semidirect
579. #428	C₂²×C₁₃	semidirect
580. #423	C₂²×C₁₃	semidirect
581. #418	C₂²×C₁₃	semidirect
582. #418	C₂²×C₁₃	semidirect
583. #417	C₂²×C₁₃	semidirect
584. #417	C₂²×C₁₃	semidirect
585. #407	C₂²×C₁₃	semidirect
586. C₄×M₁₆	C₂²×C₁₃	semidirect
613. C₂²×C₁₃	C₂×AGL(1,ℤ/8)	semidirect
626. C₄×C₁₃	C₂×AGL(1,ℤ/8)	semidirect
636. C₂×#41	C₂³×C₁₃	semidirect
637. C₂×#41	C₂³×C₁₃	semidirect
638. C₂²×Q₈	C₂³×C₁₃	semidirect
658. C₂²×D₄	C₂³×C₁₃	semidirect
668. AGL(1,ℤ/8)	D₄×C₁₃	direct (N × H)
672. C₂×SD₁₆	C₂³×C₁₃	semidirect
673. C₂×SD₁₆	C₂³×C₁₃	semidirect
674. C₂×SD₁₆	C₂³×C₁₃	semidirect
678. C₂×D₈	C₂³×C₁₃	semidirect
679. C₂×D₈	C₂³×C₁₃	semidirect
680. C₂×D₈	C₂³×C₁₃	semidirect
685. C₂×M₁₆	C₂³×C₁₃	semidirect
686. C₂²×C₈	C₂³×C₁₃	semidirect
688. C₄⋊Q₈	C₂³×C₁₃	semidirect
694. #127	C₂³×C₁₃	semidirect
696. #124	C₂³×C₁₃	semidirect
702. C₂²⋊Q₈	C₂³×C₁₃	semidirect
703. C₂²⋊Q₈	C₂³×C₁₃	semidirect
718. #121	C₂³×C₁₃	semidirect
719. #121	C₂³×C₁₃	semidirect
727. C₄×Q₈	C₂³×C₁₃	semidirect
728. C₄×Q₈	C₂³×C₁₃	semidirect
748. C₄×D₄	C₂³×C₁₃	semidirect
749. C₄×D₄	C₂³×C₁₃	semidirect
761. #107	C₂³×C₁₃	semidirect
762. #106	C₂³×C₁₃	semidirect
763. C₄⋊C₈	C₂³×C₁₃	semidirect
764. C₄⋊C₈	C₂³×C₁₃	semidirect
765. #103	C₂³×C₁₃	semidirect
766. #103	C₂³×C₁₃	semidirect
769. #102	C₂³×C₁₃	semidirect
770. #102	C₂³×C₁₃	semidirect
771. #102	C₂³×C₁₃	semidirect
772. #102	C₂³×C₁₃	semidirect
773. C₂²⋊C₈	C₂³×C₁₃	semidirect
774. C₂²⋊C₈	C₂³×C₁₃	semidirect
775. #97	C₂³×C₁₃	semidirect
776. C₄×C₈	C₂³×C₁₃	semidirect
805. #41	C₂×D₄×C₁₃	semidirect
854. C₂×D₄	C₂×D₄×C₁₃	semidirect
885. SD₁₆	C₂×D₄×C₁₃	semidirect
890. D₈	C₂×D₄×C₁₃	semidirect
894. M₁₆	C₂×D₄×C₁₃	semidirect
936. C₁₃	D₄×AGL(1,ℤ/8)	direct (N × H)
967. Q₈	C₂²×D₄×C₁₃	semidirect
995. D₄	C₁₃×AGL(1,ℤ/8)	direct (N × H)
997. D₄	C₂²×D₄×C₁₃	semidirect
1034. C₈	C₂²×D₄×C₁₃	semidirect
1061. C₂²	C₂×C₁₃×AGL(1,ℤ/8)	semidirect
1074. C₄	C₂×C₁₃×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×AGL(1,ℤ/8)	2
D₄×C₁₃×#41	2
C₂×D₄²×C₁₃	2
D₄×C₁₃×SD₁₆	2
D₄×C₁₃×D₈	2
C₁₃×#3274	2
C₁₃×#3272	2
C₁₃×#3265	2
C₁₃×#3264	2
C₁₃×#3151	2
C₁₃×#3055	2
C₁₃×#3038	2
C₁₃×#3036	2
C₁₃×#3006	2
C₁₃×#3003	2
C₄×C₁₃×AGL(1,ℤ/8)	2
D₄×C₁₃×M₁₆	2
D₄×AGL(1,ℤ/8)	13

Subgroups — D4×C13×AGL(1,ℤ/8) #15747404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₃×AGL(1,ℤ/8) #15747404