Subgroups — C₂×C₁₃×#3274 #15747372

Order 3328.

3278 conjugacy classes of subgroups.

The subgroup lattice has 660 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	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3274	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#469	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#449	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#447	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
14	C₂³×D₄×C₁₃	—	2	1	no	—
15	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂×C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	16	yes	complemented
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
21	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
22	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
23	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	complemented
24	C₁₃×#550	—	2	4	no	—
25	C₁₃×#550	C₂²	1	8	yes	complemented
26	D₄²×C₁₃	—	2	4	no	—
27	D₄²×C₁₃	C₂²	1	8	yes	complemented
28	C₂×C₁₃×#127	—	2	1	no	—
29	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#121	—	2	1	no	—
32	C₂×C₁₃×#121	—	2	2	no	—
33	C₂×C₁₃×#121	C₂²	1	2	yes	—
34	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
35	C₂×C₁₃×#120	—	2	2	no	—
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×D₄×C₁₃	—	2	1	no	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#493	C₂²	1	8	yes	complemented
41	C₁₃×#469	C₂²	1	16	yes	complemented
42	C₁₃×#460	C₂²	1	8	yes	complemented
43	C₁₃×#459	C₂²	1	8	yes	complemented
44	C₁₃×#449	C₂²	1	16	yes	complemented
45	C₁₃×#447	C₂²	1	16	yes	complemented
46	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
47	C₁₃×#436	C₂²	1	8	yes	complemented
48	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
53	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
54	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
55	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
56	C₂⁵×C₁₃	—	2	2	no	—
57	C₂×C₁₃×#41	—	2	4	no	—
58	C₂×C₁₃×#41	—	2	8	no	—
59	C₂×C₁₃×#41	—	4	4	no	—
60	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	—	2	8	no	—
63	C₂²×D₄×C₁₃	—	2	2	no	—
64	C₂²×D₄×C₁₃	—	2	2	no	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	8	no	—
67	C₂²×D₄×C₁₃	—	2	1	no	—
68	C₂²×D₄×C₁₃	—	2	2	no	—
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂²×D₄×C₁₃	—	2	4	no	—
71	C₂²×D₄×C₁₃	—	2	1	no	—
72	C₂²×D₄×C₁₃	—	2	1	no	—
73	C₂²×D₄×C₁₃	—	4	4	no	—
74	C₂²×D₄×C₁₃	—	4	8	no	—
75	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
76	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
79	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	—	2	2	no	—
81	C₂³×C₄×C₁₃	—	2	1	no	—
82	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
83	C₁₃×AGL(1,ℤ/8)	—	2	64	no	—
84	C₂×C₁₃×SD₁₆	—	2	8	no	—
85	C₂×C₁₃×SD₁₆	D₄	1	8	yes	complemented
86	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
87	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
88	C₂×C₁₃×D₈	—	2	8	no	—
89	C₂×C₁₃×D₈	—	2	8	no	—
90	C₂×C₁₃×D₈	—	4	4	no	—
91	C₂×C₁₃×D₈	C₂³	1	8	yes	—
92	C₂×C₁₃×D₈	C₂³	1	8	yes	complemented
93	C₂×C₁₃×D₈	C₂³	1	8	yes	complemented
94	C₂×C₁₃×M₁₆	—	2	8	no	—
95	C₂×C₁₃×M₁₆	C₂³	1	8	yes	complemented
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
98	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#127	—	2	8	no	—
100	C₁₃×#127	—	2	2	no	—
101	C₁₃×#127	—	2	2	no	—
102	C₁₃×#127	C₂³	1	4	yes	—
103	C₁₃×#127	C₂³	1	4	yes	complemented
104	C₁₃×#121	—	2	4	no	—
105	C₁₃×#121	—	2	4	no	—
106	C₁₃×#121	—	2	8	no	—
107	C₁₃×#121	—	2	16	no	—
108	C₁₃×#121	C₂³	1	8	yes	—
109	C₁₃×#121	C₂³	1	8	yes	complemented
110	C₁₃×#120	—	2	16	no	—
111	C₄×Q₈×C₁₃	—	2	2	no	—
112	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
113	C₄×D₄×C₁₃	—	2	8	no	—
114	C₄×D₄×C₁₃	—	2	2	no	—
115	C₄×D₄×C₁₃	D₄	1	4	yes	—
116	C₄×D₄×C₁₃	C₂³	1	4	yes	—
117	C₄×D₄×C₁₃	C₂³	1	4	yes	—
118	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
125	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
126	C₂×C₄²×C₁₃	—	2	1	no	—
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₁₃×#106	C₂³	1	4	yes	complemented
129	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
130	C₁₃×#103	C₂³	1	4	yes	complemented
131	C₁₃×#102	C₂³	1	4	yes	—
132	C₁₃×#102	C₂³	1	8	yes	complemented
133	C₁₃×#102	C₂³	1	8	yes	complemented
134	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
135	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
136	C₂×#3274	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂⁴×C₁₃	—	2	1	no	—
138	C₂⁴×C₁₃	—	2	2	no	—
139	C₂⁴×C₁₃	—	2	2	no	—
140	C₂⁴×C₁₃	—	2	8	no	—
141	C₂⁴×C₁₃	—	4	8	no	—
142	C₂⁴×C₁₃	—	4	8	no	—
143	C₂⁴×C₁₃	—	8	4	no	—
144	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
145	C₁₃×#41	—	2	16	no	—
146	C₁₃×#41	—	4	8	no	—
147	C₁₃×#41	—	4	16	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	complemented
151	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
152	C₂×D₄×C₁₃	—	2	16	no	—
153	C₂×D₄×C₁₃	—	2	8	no	—
154	C₂×D₄×C₁₃	—	2	8	no	—
155	C₂×D₄×C₁₃	—	2	8	no	—
156	C₂×D₄×C₁₃	—	2	4	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	4	no	—
161	C₂×D₄×C₁₃	—	2	8	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	2	2	no	—
164	C₂×D₄×C₁₃	—	2	4	no	—
165	C₂×D₄×C₁₃	—	2	4	no	—
166	C₂×D₄×C₁₃	—	2	4	no	—
167	C₂×D₄×C₁₃	—	2	2	no	—
168	C₂×D₄×C₁₃	—	2	4	no	—
169	C₂×D₄×C₁₃	—	2	4	no	—
170	C₂×D₄×C₁₃	—	4	8	no	—
171	C₂×D₄×C₁₃	—	4	16	no	—
172	C₂×D₄×C₁₃	—	4	8	no	—
173	C₂×D₄×C₁₃	—	4	8	no	—
174	C₂×D₄×C₁₃	—	4	32	no	—
175	C₂×D₄×C₁₃	—	4	8	no	—
176	C₂×D₄×C₁₃	—	4	4	no	—
177	C₂×D₄×C₁₃	—	4	4	no	—
178	C₂×D₄×C₁₃	—	8	2	no	—
179	C₂×D₄×C₁₃	—	8	2	no	—
180	C₂×D₄×C₁₃	—	8	4	no	—
181	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
182	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
183	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
184	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
185	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃	—	2	1	no	—
187	C₂²×C₄×C₁₃	—	2	4	no	—
188	C₂²×C₄×C₁₃	—	2	4	no	—
189	C₂²×C₄×C₁₃	—	2	1	no	—
190	C₂²×C₄×C₁₃	—	2	1	no	—
191	C₂²×C₄×C₁₃	—	2	8	no	—
192	C₂²×C₄×C₁₃	—	2	4	no	—
193	C₂²×C₄×C₁₃	—	4	8	no	—
194	C₂²×C₄×C₁₃	—	4	4	no	—
195	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
196	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
201	C₁₃×SD₁₆	—	2	16	no	—
202	C₁₃×SD₁₆	C₂×D₄	1	16	yes	complemented
203	C₁₃×D₈	—	2	16	no	—
204	C₁₃×D₈	—	2	16	no	—
205	C₁₃×D₈	—	4	8	no	—
206	C₁₃×M₁₆	—	2	16	no	—
207	C₂×C₈×C₁₃	—	2	4	no	—
208	C₂×C₈×C₁₃	—	2	2	no	—
209	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
210	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
211	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
212	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
213	C₁₃×C₄⋊C₄	—	2	4	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
217	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
218	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
219	C₁₃×C₂²⋊C₄	—	2	8	no	—
220	C₁₃×C₂²⋊C₄	—	2	4	no	—
221	C₁₃×C₂²⋊C₄	—	2	8	no	—
222	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
223	C₄²×C₁₃	—	2	4	no	—
224	C₄²×C₁₃	C₂×D₄	1	2	yes	—
225	C₄²×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
227	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
228	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#3274	C₂×C₁₃	1	16	yes	direct product factor
230	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂×#469	C₂×C₁₃	1	2	yes	complemented
232	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
233	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
234	C₂×#449	C₂×C₁₃	1	2	yes	complemented
235	C₂×#447	C₂×C₁₃	1	2	yes	complemented
236	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
237	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
238	C₂³×C₁₃	—	2	4	no	—
239	C₂³×C₁₃	—	2	4	no	—
240	C₂³×C₁₃	—	2	4	no	—
241	C₂³×C₁₃	—	2	4	no	—
242	C₂³×C₁₃	—	2	2	no	—
243	C₂³×C₁₃	—	2	4	no	—
244	C₂³×C₁₃	—	2	4	no	—
245	C₂³×C₁₃	—	4	16	no	—
246	C₂³×C₁₃	—	4	16	no	—
247	C₂³×C₁₃	—	4	2	no	—
248	C₂³×C₁₃	—	4	2	no	—
249	C₂³×C₁₃	—	4	4	no	—
250	C₂³×C₁₃	—	4	4	no	—
251	C₂³×C₁₃	—	4	4	no	—
252	C₂³×C₁₃	—	4	4	no	—
253	C₂³×C₁₃	—	4	4	no	—
254	C₂³×C₁₃	—	4	4	no	—
255	C₂³×C₁₃	—	8	8	no	—
256	C₂³×C₁₃	—	8	32	no	—
257	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
258	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
259	Q₈×C₁₃	—	2	4	no	—
260	Q₈×C₁₃	—	2	2	no	—
261	Q₈×C₁₃	C₂²×D₄	1	4	yes	complemented
262	D₄×C₁₃	—	2	4	no	—
263	D₄×C₁₃	—	2	8	no	—
264	D₄×C₁₃	—	2	4	no	—
265	D₄×C₁₃	—	2	4	no	—
266	D₄×C₁₃	—	2	2	no	—
267	D₄×C₁₃	—	2	4	no	—
268	D₄×C₁₃	—	2	4	no	—
269	D₄×C₁₃	—	4	16	no	—
270	D₄×C₁₃	—	4	16	no	—
271	D₄×C₁₃	—	4	16	no	—
272	D₄×C₁₃	—	4	4	no	—
273	D₄×C₁₃	—	4	4	no	—
274	D₄×C₁₃	—	4	8	no	—
275	D₄×C₁₃	—	4	8	no	—
276	D₄×C₁₃	—	8	4	no	—
277	D₄×C₁₃	—	8	4	no	—
278	D₄×C₁₃	—	8	8	no	—
279	D₄×C₁₃	C₂²×D₄	1	4	yes	—
280	C₂×C₄×C₁₃	—	2	4	no	—
281	C₂×C₄×C₁₃	—	2	4	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	8	no	—
285	C₂×C₄×C₁₃	—	2	4	no	—
286	C₂×C₄×C₁₃	—	2	4	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	4	16	no	—
290	C₂×C₄×C₁₃	—	4	2	no	—
291	C₂×C₄×C₁₃	—	4	2	no	—
292	C₂×C₄×C₁₃	—	4	8	no	—
293	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
294	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
296	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
300	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
301	C₈×C₁₃	—	2	4	no	—
302	C₈×C₁₃	—	2	2	no	—
303	C₈×C₁₃	C₂²×D₄	1	4	yes	complemented
304	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
305	C₂³×D₄	—	2	1	no	—
306	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
307	C₂×AGL(1,ℤ/8)	—	2	16	no	—
308	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	16	yes	complemented
309	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
310	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
311	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
312	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
313	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
314	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	complemented
315	#550	—	2	4	no	—
316	#550	C₂²×C₁₃	1	8	yes	complemented
317	D₄²	—	2	4	no	—
318	D₄²	C₂²×C₁₃	1	8	yes	complemented
319	C₂×#127	—	2	1	no	—
320	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
322	C₂×#121	—	2	1	no	—
323	C₂×#121	—	2	2	no	—
324	C₂×#121	C₂²×C₁₃	1	2	yes	—
325	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
326	C₂×#120	—	2	2	no	—
327	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
328	C₂×C₄×D₄	—	2	1	no	—
329	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
331	#493	C₂²×C₁₃	1	8	yes	complemented
332	#469	C₂²×C₁₃	1	16	yes	complemented
333	#460	C₂²×C₁₃	1	8	yes	complemented
334	#459	C₂²×C₁₃	1	8	yes	complemented
335	#449	C₂²×C₁₃	1	16	yes	complemented
336	#447	C₂²×C₁₃	1	16	yes	complemented
337	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
338	#436	C₂²×C₁₃	1	8	yes	complemented
339	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
340	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
341	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
342	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
344	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
345	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
346	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
347	C₂²×C₁₃	—	2	4	no	—
348	C₂²×C₁₃	—	2	4	no	—
349	C₂²×C₁₃	—	2	4	no	—
350	C₂²×C₁₃	—	2	4	no	—
351	C₂²×C₁₃	—	4	8	no	—
352	C₂²×C₁₃	—	4	8	no	—
353	C₂²×C₁₃	—	4	2	no	—
354	C₂²×C₁₃	—	4	2	no	—
355	C₂²×C₁₃	—	4	4	no	—
356	C₂²×C₁₃	—	4	4	no	—
357	C₂²×C₁₃	—	4	4	no	—
358	C₂²×C₁₃	—	4	4	no	—
359	C₂²×C₁₃	—	4	4	no	—
360	C₂²×C₁₃	—	4	4	no	—
361	C₂²×C₁₃	—	8	32	no	—
362	C₂²×C₁₃	—	8	8	no	—
363	C₂²×C₁₃	—	8	8	no	—
364	C₂²×C₁₃	D₄²	1	2	yes	—
365	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
366	C₂²×C₁₃	#576	1	2	yes	—
367	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
368	C₄×C₁₃	—	2	4	no	—
369	C₄×C₁₃	—	2	4	no	—
370	C₄×C₁₃	—	2	2	no	—
371	C₄×C₁₃	—	4	2	no	—
372	C₄×C₁₃	—	4	2	no	—
373	C₄×C₁₃	D₄²	1	2	yes	—
374	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
375	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
376	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂⁵	—	2	2	no	—
378	C₂×#41	—	2	4	no	—
379	C₂×#41	—	2	8	no	—
380	C₂×#41	—	4	4	no	—
381	C₂×#41	C₂³×C₁₃	1	8	yes	complemented
382	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
383	C₂²×D₄	—	2	8	no	—
384	C₂²×D₄	—	2	2	no	—
385	C₂²×D₄	—	2	2	no	—
386	C₂²×D₄	—	2	2	no	—
387	C₂²×D₄	—	2	8	no	—
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	—	2	2	no	—
390	C₂²×D₄	—	2	1	no	—
391	C₂²×D₄	—	2	4	no	—
392	C₂²×D₄	—	2	1	no	—
393	C₂²×D₄	—	2	1	no	—
394	C₂²×D₄	—	4	4	no	—
395	C₂²×D₄	—	4	8	no	—
396	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
397	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
398	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
399	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
400	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂³×C₄	—	2	2	no	—
402	C₂³×C₄	—	2	1	no	—
403	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
404	AGL(1,ℤ/8)	—	2	64	no	—
405	C₂×SD₁₆	—	2	8	no	—
406	C₂×SD₁₆	D₄×C₁₃	1	8	yes	complemented
407	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
408	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
409	C₂×D₈	—	2	8	no	—
410	C₂×D₈	—	2	8	no	—
411	C₂×D₈	—	4	4	no	—
412	C₂×D₈	C₂³×C₁₃	1	8	yes	—
413	C₂×D₈	C₂³×C₁₃	1	8	yes	complemented
414	C₂×D₈	C₂³×C₁₃	1	8	yes	complemented
415	C₂×M₁₆	—	2	8	no	—
416	C₂×M₁₆	C₂³×C₁₃	1	8	yes	complemented
417	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
418	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
420	#127	—	2	8	no	—
421	#127	—	2	2	no	—
422	#127	—	2	2	no	—
423	#127	C₂³×C₁₃	1	4	yes	—
424	#127	C₂³×C₁₃	1	4	yes	complemented
425	#121	—	2	4	no	—
426	#121	—	2	4	no	—
427	#121	—	2	8	no	—
428	#121	—	2	16	no	—
429	#121	C₂³×C₁₃	1	8	yes	—
430	#121	C₂³×C₁₃	1	8	yes	complemented
431	#120	—	2	16	no	—
432	C₄×Q₈	—	2	2	no	—
433	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
434	C₄×D₄	—	2	8	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	D₄×C₁₃	1	4	yes	—
437	C₄×D₄	C₂³×C₁₃	1	4	yes	—
438	C₄×D₄	C₂³×C₁₃	1	4	yes	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	—	2	2	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	2	no	—
446	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
447	C₂×C₄²	—	2	1	no	—
448	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
449	#106	C₂³×C₁₃	1	4	yes	complemented
450	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
451	#103	C₂³×C₁₃	1	4	yes	complemented
452	#102	C₂³×C₁₃	1	4	yes	—
453	#102	C₂³×C₁₃	1	8	yes	complemented
454	#102	C₂³×C₁₃	1	8	yes	complemented
455	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	complemented
456	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
457	C₂×C₁₃	—	4	4	no	—
458	C₂×C₁₃	—	4	4	no	—
459	C₂×C₁₃	—	8	4	no	—
460	C₂×C₁₃	—	8	4	no	—
461	C₂×C₁₃	#3274	1	4	yes	direct product factor
462	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
463	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
464	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
465	C₂⁴	—	2	1	no	—
466	C₂⁴	—	2	2	no	—
467	C₂⁴	—	2	2	no	—
468	C₂⁴	—	2	8	no	—
469	C₂⁴	—	4	8	no	—
470	C₂⁴	—	4	8	no	—
471	C₂⁴	—	8	4	no	—
472	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
473	#41	—	2	16	no	—
474	#41	—	4	8	no	—
475	#41	—	4	16	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	2	no	—
478	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	complemented
479	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
480	C₂×D₄	—	2	16	no	—
481	C₂×D₄	—	2	8	no	—
482	C₂×D₄	—	2	8	no	—
483	C₂×D₄	—	2	8	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	8	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	4	no	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	4	8	no	—
499	C₂×D₄	—	4	16	no	—
500	C₂×D₄	—	4	8	no	—
501	C₂×D₄	—	4	8	no	—
502	C₂×D₄	—	4	32	no	—
503	C₂×D₄	—	4	8	no	—
504	C₂×D₄	—	4	4	no	—
505	C₂×D₄	—	4	4	no	—
506	C₂×D₄	—	8	2	no	—
507	C₂×D₄	—	8	2	no	—
508	C₂×D₄	—	8	4	no	—
509	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
510	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
511	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
512	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
513	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	8	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	4	8	no	—
522	C₂²×C₄	—	4	4	no	—
523	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
525	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
526	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
529	SD₁₆	—	2	16	no	—
530	SD₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
531	D₈	—	2	16	no	—
532	D₈	—	2	16	no	—
533	D₈	—	4	8	no	—
534	M₁₆	—	2	16	no	—
535	C₂×C₈	—	2	4	no	—
536	C₂×C₈	—	2	2	no	—
537	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
538	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
539	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
540	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
545	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
546	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
547	C₂²⋊C₄	—	2	8	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	8	no	—
550	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
551	C₄²	—	2	4	no	—
552	C₄²	C₂×D₄×C₁₃	1	2	yes	—
553	C₄²	C₂⁴×C₁₃	1	2	yes	—
554	C₁₃	C₂×#3274	1	1	yes	characteristic, direct product factor, Sylow
555	C₂³	—	2	4	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	2	4	no	—
562	C₂³	—	4	16	no	—
563	C₂³	—	4	16	no	—
564	C₂³	—	4	2	no	—
565	C₂³	—	4	2	no	—
566	C₂³	—	4	4	no	—
567	C₂³	—	4	4	no	—
568	C₂³	—	4	4	no	—
569	C₂³	—	4	4	no	—
570	C₂³	—	4	4	no	—
571	C₂³	—	4	4	no	—
572	C₂³	—	8	8	no	—
573	C₂³	—	8	32	no	—
574	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
575	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
576	Q₈	—	2	4	no	—
577	Q₈	—	2	2	no	—
578	Q₈	C₂²×D₄×C₁₃	1	4	yes	complemented
579	D₄	—	2	4	no	—
580	D₄	—	2	8	no	—
581	D₄	—	2	4	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	4	no	—
586	D₄	—	4	16	no	—
587	D₄	—	4	16	no	—
588	D₄	—	4	16	no	—
589	D₄	—	4	4	no	—
590	D₄	—	4	4	no	—
591	D₄	—	4	8	no	—
592	D₄	—	4	8	no	—
593	D₄	—	8	4	no	—
594	D₄	—	8	4	no	—
595	D₄	—	8	8	no	—
596	D₄	C₂²×D₄×C₁₃	1	4	yes	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	8	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	4	16	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	8	no	—
610	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
611	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
612	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
613	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
614	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
615	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
616	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
617	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
618	C₈	—	2	4	no	—
619	C₈	—	2	2	no	—
620	C₈	C₂²×D₄×C₁₃	1	4	yes	complemented
621	C₂²	—	2	4	no	—
622	C₂²	—	2	4	no	—
623	C₂²	—	2	4	no	—
624	C₂²	—	2	4	no	—
625	C₂²	—	4	8	no	—
626	C₂²	—	4	8	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	4	no	—
630	C₂²	—	4	4	no	—
631	C₂²	—	4	4	no	—
632	C₂²	—	4	4	no	—
633	C₂²	—	4	4	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	8	32	no	—
636	C₂²	—	8	8	no	—
637	C₂²	—	8	8	no	—
638	C₂²	D₄²×C₁₃	1	2	yes	—
639	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
640	C₂²	C₁₃×#576	1	2	yes	—
641	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
642	C₄	—	2	2	no	—
643	C₄	—	2	4	no	—
644	C₄	—	2	4	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	D₄²×C₁₃	1	2	yes	—
648	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
649	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
650	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
651	C₂	—	4	4	no	—
652	C₂	—	4	4	no	—
653	C₂	—	8	4	no	—
654	C₂	—	8	4	no	—
655	C₂	C₁₃×#3274	1	4	yes	direct product factor
656	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
657	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
658	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₁₃×#550	C₂	semidirect
3. C₂×D₄²×C₁₃	C₂	semidirect
4. C₁₃×#3274	C₂	direct (N × H)
5. C₂×C₁₃×#493	C₂	semidirect
6. C₂×C₁₃×#469	C₂	semidirect
7. C₂×C₁₃×#460	C₂	semidirect
8. C₂×C₁₃×#459	C₂	semidirect
9. C₂×C₁₃×#449	C₂	semidirect
10. C₂×C₁₃×#447	C₂	semidirect
11. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
12. C₂×C₁₃×#436	C₂	semidirect
13. C₂²×C₁₃×#41	C₂²	semidirect
17. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂²×C₁₃×SD₁₆	C₂²	semidirect
21. C₂²×C₁₃×D₈	C₂²	semidirect
22. C₂²×C₁₃×D₈	C₂²	semidirect
23. C₂²×C₁₃×M₁₆	C₂²	semidirect
25. C₁₃×#550	C₂²	semidirect
27. D₄²×C₁₃	C₂²	semidirect
30. C₂×C₁₃×#127	C₂²	semidirect
34. C₂×C₁₃×#121	C₂²	semidirect
36. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
40. C₁₃×#493	C₂²	semidirect
41. C₁₃×#469	C₂²	semidirect
42. C₁₃×#460	C₂²	semidirect
43. C₁₃×#459	C₂²	semidirect
44. C₁₃×#449	C₂²	semidirect
45. C₁₃×#447	C₂²	semidirect
46. C₄×C₁₃×SD₁₆	C₂²	semidirect
47. C₁₃×#436	C₂²	semidirect
48. C₂×C₁₃×#106	C₂²	semidirect
49. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
50. C₂×C₁₃×#103	C₂²	semidirect
52. C₂×C₁₃×#102	C₂²	semidirect
53. C₂×C₁₃×#102	C₂²	semidirect
54. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
55. C₂×C₄×C₈×C₁₃	C₂²	semidirect
60. C₂×C₁₃×#41	C₂³	semidirect
85. C₂×C₁₃×SD₁₆	D₄	semidirect
87. C₂×C₁₃×SD₁₆	C₂³	semidirect
92. C₂×C₁₃×D₈	C₂³	semidirect
93. C₂×C₁₃×D₈	C₂³	semidirect
95. C₂×C₁₃×M₁₆	C₂³	semidirect
103. C₁₃×#127	C₂³	semidirect
109. C₁₃×#121	C₂³	semidirect
112. C₄×Q₈×C₁₃	C₂³	semidirect
128. C₁₃×#106	C₂³	semidirect
129. C₁₃×C₄⋊C₈	C₂³	semidirect
130. C₁₃×#103	C₂³	semidirect
132. C₁₃×#102	C₂³	semidirect
133. C₁₃×#102	C₂³	semidirect
134. C₁₃×C₂²⋊C₈	C₂³	semidirect
135. C₄×C₈×C₁₃	C₂³	semidirect
136. C₂×#3274	C₁₃	direct (N × H)
150. C₂×Q₈×C₁₃	C₂×D₄	semidirect
202. C₁₃×SD₁₆	C₂×D₄	semidirect
209. C₂×C₈×C₁₃	C₂×D₄	semidirect
226. C₂²×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
227. C₂×#550	C₂×C₁₃	semidirect
228. C₂×D₄²	C₂×C₁₃	semidirect
229. #3274	C₂×C₁₃	direct (N × H)
230. C₂×#493	C₂×C₁₃	semidirect
231. C₂×#469	C₂×C₁₃	semidirect
232. C₂×#460	C₂×C₁₃	semidirect
233. C₂×#459	C₂×C₁₃	semidirect
234. C₂×#449	C₂×C₁₃	semidirect
235. C₂×#447	C₂×C₁₃	semidirect
236. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
237. C₂×#436	C₂×C₁₃	semidirect
261. Q₈×C₁₃	C₂²×D₄	semidirect
293. C₂×C₄×C₁₃	AGL(1,ℤ/8)	semidirect
303. C₈×C₁₃	C₂²×D₄	semidirect
304. C₂²×#41	C₂²×C₁₃	semidirect
308. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
310. C₂²×SD₁₆	C₂²×C₁₃	semidirect
312. C₂²×D₈	C₂²×C₁₃	semidirect
313. C₂²×D₈	C₂²×C₁₃	semidirect
314. C₂²×M₁₆	C₂²×C₁₃	semidirect
316. #550	C₂²×C₁₃	semidirect
318. D₄²	C₂²×C₁₃	semidirect
321. C₂×#127	C₂²×C₁₃	semidirect
325. C₂×#121	C₂²×C₁₃	semidirect
327. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
331. #493	C₂²×C₁₃	semidirect
332. #469	C₂²×C₁₃	semidirect
333. #460	C₂²×C₁₃	semidirect
334. #459	C₂²×C₁₃	semidirect
335. #449	C₂²×C₁₃	semidirect
336. #447	C₂²×C₁₃	semidirect
337. C₄×SD₁₆	C₂²×C₁₃	semidirect
338. #436	C₂²×C₁₃	semidirect
339. C₂×#106	C₂²×C₁₃	semidirect
340. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
341. C₂×#103	C₂²×C₁₃	semidirect
343. C₂×#102	C₂²×C₁₃	semidirect
344. C₂×#102	C₂²×C₁₃	semidirect
345. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
346. C₂×C₄×C₈	C₂²×C₁₃	semidirect
374. C₄×C₁₃	C₂×AGL(1,ℤ/8)	semidirect
381. C₂×#41	C₂³×C₁₃	semidirect
406. C₂×SD₁₆	D₄×C₁₃	semidirect
408. C₂×SD₁₆	C₂³×C₁₃	semidirect
413. C₂×D₈	C₂³×C₁₃	semidirect
414. C₂×D₈	C₂³×C₁₃	semidirect
416. C₂×M₁₆	C₂³×C₁₃	semidirect
424. #127	C₂³×C₁₃	semidirect
430. #121	C₂³×C₁₃	semidirect
433. C₄×Q₈	C₂³×C₁₃	semidirect
449. #106	C₂³×C₁₃	semidirect
450. C₄⋊C₈	C₂³×C₁₃	semidirect
451. #103	C₂³×C₁₃	semidirect
453. #102	C₂³×C₁₃	semidirect
454. #102	C₂³×C₁₃	semidirect
455. C₂²⋊C₈	C₂³×C₁₃	semidirect
456. C₄×C₈	C₂³×C₁₃	semidirect
461. C₂×C₁₃	#3274	direct (N × H)
478. C₂×Q₈	C₂×D₄×C₁₃	semidirect
530. SD₁₆	C₂×D₄×C₁₃	semidirect
537. C₂×C₈	C₂×D₄×C₁₃	semidirect
554. C₁₃	C₂×#3274	direct (N × H)
578. Q₈	C₂²×D₄×C₁₃	semidirect
610. C₂×C₄	C₁₃×AGL(1,ℤ/8)	semidirect
620. C₈	C₂²×D₄×C₁₃	semidirect
648. C₄	C₂×C₁₃×AGL(1,ℤ/8)	semidirect
655. C₂	C₁₃×#3274	direct (N × H)

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
C₂×C₁₃×#550	2
C₂×D₄²×C₁₃	2
C₁₃×#3274	2
C₂×C₁₃×#493	2
C₂×C₁₃×#469	2
C₂×C₁₃×#460	2
C₂×C₁₃×#459	2
C₂×C₁₃×#449	2
C₂×C₁₃×#447	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₁₃×#436	2
C₂×#3274	13

Subgroups — C2×C13×#3274 #15747372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3274 #15747372