Subgroups — C₂×C₁₃×#3272 #15747370

Order 3328.

3226 conjugacy classes of subgroups.

The subgroup lattice has 652 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×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3272	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#468	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#461	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×#450	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×D₈	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	2	yes	—
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
21	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
23	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	complemented
24	C₁₃×#547	—	2	4	no	—
25	C₁₃×#547	C₂²	1	8	yes	complemented
26	D₄²×C₁₃	—	2	4	no	—
27	D₄²×C₁₃	C₂²	1	8	yes	complemented
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#123	—	2	2	no	—
31	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
32	C₂×C₁₃×#121	—	2	1	no	—
33	C₂×C₁₃×#121	—	2	1	no	—
34	C₂×C₁₃×#121	C₂²	1	2	yes	—
35	C₂×C₁₃×#120	—	2	2	no	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
40	C₁₃×#492	C₂²	1	8	yes	complemented
41	C₁₃×#468	C₂²	1	16	yes	complemented
42	C₁₃×#461	C₂²	1	8	yes	complemented
43	C₁₃×#459	C₂²	1	8	yes	complemented
44	C₁₃×#450	C₂²	1	16	yes	complemented
45	C₁₃×#449	C₂²	1	16	yes	complemented
46	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
47	C₁₃×#436	C₂²	1	8	yes	complemented
48	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₁₃×#103	C₂²	1	2	yes	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	1	yes	characteristic, 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	2	yes	—
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	8	no	—
66	C₂²×D₄×C₁₃	—	2	2	no	—
67	C₂²×D₄×C₁₃	—	2	1	no	—
68	C₂²×D₄×C₁₃	—	2	4	no	—
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂²×D₄×C₁₃	—	4	4	no	—
71	C₂²×D₄×C₁₃	—	4	8	no	—
72	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
73	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
74	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	—	2	1	no	—
78	C₂³×C₄×C₁₃	—	2	2	no	—
79	C₂³×C₄×C₁₃	—	2	1	no	—
80	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
81	C₁₃×AGL(1,ℤ/8)	—	2	64	no	—
82	C₂×C₁₃×SD₁₆	—	2	8	no	—
83	C₂×C₁₃×SD₁₆	—	2	8	no	—
84	C₂×C₁₃×SD₁₆	—	4	4	no	—
85	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
86	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
87	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
88	C₂×C₁₃×D₈	—	2	8	no	—
89	C₂×C₁₃×D₈	D₄	1	8	yes	complemented
90	C₂×C₁₃×D₈	C₂³	1	4	yes	—
91	C₂×C₁₃×D₈	C₂³	1	8	yes	complemented
92	C₂×C₁₃×M₁₆	—	2	8	no	—
93	C₂×C₁₃×M₁₆	C₂³	1	8	yes	complemented
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×C₄⋊Q₈	—	2	2	no	—
98	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
99	C₁₃×#127	—	2	2	no	—
100	C₁₃×#127	C₂³	1	4	yes	—
101	C₁₃×#123	—	2	16	no	—
102	C₁₃×C₂²⋊Q₈	—	2	4	no	—
103	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
104	C₁₃×#121	—	2	8	no	—
105	C₁₃×#121	—	2	4	no	—
106	C₁₃×#121	—	2	8	no	—
107	C₁₃×#121	C₂³	1	8	yes	—
108	C₁₃×#120	—	2	16	no	—
109	C₄×D₄×C₁₃	—	2	2	no	—
110	C₄×D₄×C₁₃	—	2	2	no	—
111	C₄×D₄×C₁₃	D₄	1	4	yes	—
112	C₄×D₄×C₁₃	C₂³	1	4	yes	—
113	C₄×D₄×C₁₃	C₂³	1	4	yes	—
114	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₄⋊C₄	—	2	8	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	1	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
126	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₁₃×#107	C₂³	1	4	yes	complemented
129	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
130	C₁₃×#103	C₂³	1	8	yes	complemented
131	C₁₃×#102	C₂³	1	4	yes	—
132	C₁₃×#102	C₂³	1	4	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×#3272	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂⁴×C₁₃	—	2	1	no	—
138	C₂⁴×C₁₃	—	2	1	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	2	no	—
149	C₂×Q₈×C₁₃	—	2	4	no	—
150	C₂×Q₈×C₁₃	—	2	4	no	—
151	C₂×Q₈×C₁₃	C₂⁴	1	4	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	4	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	2	8	no	—
160	C₂×D₄×C₁₃	—	2	2	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	2	4	no	—
163	C₂×D₄×C₁₃	—	2	2	no	—
164	C₂×D₄×C₁₃	—	2	2	no	—
165	C₂×D₄×C₁₃	—	2	4	no	—
166	C₂×D₄×C₁₃	—	4	8	no	—
167	C₂×D₄×C₁₃	—	4	16	no	—
168	C₂×D₄×C₁₃	—	4	8	no	—
169	C₂×D₄×C₁₃	—	4	32	no	—
170	C₂×D₄×C₁₃	—	4	8	no	—
171	C₂×D₄×C₁₃	—	4	8	no	—
172	C₂×D₄×C₁₃	—	4	4	no	—
173	C₂×D₄×C₁₃	—	8	2	no	—
174	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
175	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
176	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	complemented
177	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
179	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃	—	2	4	no	—
181	C₂²×C₄×C₁₃	—	2	4	no	—
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	—	2	1	no	—
184	C₂²×C₄×C₁₃	—	2	2	no	—
185	C₂²×C₄×C₁₃	—	2	4	no	—
186	C₂²×C₄×C₁₃	—	2	8	no	—
187	C₂²×C₄×C₁₃	—	2	4	no	—
188	C₂²×C₄×C₁₃	—	4	8	no	—
189	C₂²×C₄×C₁₃	—	4	4	no	—
190	C₂²×C₄×C₁₃	—	4	4	no	—
191	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
192	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
194	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₁₃×SD₁₆	—	2	16	no	—
198	C₁₃×SD₁₆	—	2	16	no	—
199	C₁₃×SD₁₆	—	4	8	no	—
200	C₁₃×D₈	—	2	16	no	—
201	C₁₃×D₈	C₂×D₄	1	16	yes	complemented
202	C₁₃×M₁₆	—	2	16	no	—
203	C₂×C₈×C₁₃	—	2	4	no	—
204	C₂×C₈×C₁₃	—	2	2	no	—
205	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
206	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
207	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
208	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	2	8	no	—
211	C₁₃×C₄⋊C₄	—	2	4	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
215	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
216	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
217	C₁₃×C₂²⋊C₄	—	2	8	no	—
218	C₁₃×C₂²⋊C₄	—	2	4	no	—
219	C₁₃×C₂²⋊C₄	—	2	4	no	—
220	C₁₃×C₂²⋊C₄	—	2	8	no	—
221	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
222	C₄²×C₁₃	C₂×D₄	1	2	yes	—
223	C₄²×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
225	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#3272	C₂×C₁₃	1	16	yes	direct product factor
228	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂×#468	C₂×C₁₃	1	2	yes	complemented
230	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂×#449	C₂×C₁₃	1	2	yes	complemented
233	C₂×#450	C₂×C₁₃	1	2	yes	complemented
234	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂³×C₁₃	—	2	4	no	—
237	C₂³×C₁₃	—	2	4	no	—
238	C₂³×C₁₃	—	2	4	no	—
239	C₂³×C₁₃	—	2	4	no	—
240	C₂³×C₁₃	—	2	4	no	—
241	C₂³×C₁₃	—	2	2	no	—
242	C₂³×C₁₃	—	2	2	no	—
243	C₂³×C₁₃	—	2	4	no	—
244	C₂³×C₁₃	—	4	16	no	—
245	C₂³×C₁₃	—	4	16	no	—
246	C₂³×C₁₃	—	4	2	no	—
247	C₂³×C₁₃	—	4	2	no	—
248	C₂³×C₁₃	—	4	2	no	—
249	C₂³×C₁₃	—	4	2	no	—
250	C₂³×C₁₃	—	4	4	no	—
251	C₂³×C₁₃	—	4	4	no	—
252	C₂³×C₁₃	—	4	4	no	—
253	C₂³×C₁₃	—	8	8	no	—
254	C₂³×C₁₃	—	8	32	no	—
255	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
256	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
257	Q₈×C₁₃	—	2	4	no	—
258	Q₈×C₁₃	—	2	4	no	—
259	Q₈×C₁₃	—	4	4	no	—
260	D₄×C₁₃	—	2	4	no	—
261	D₄×C₁₃	—	2	4	no	—
262	D₄×C₁₃	—	2	8	no	—
263	D₄×C₁₃	—	2	4	no	—
264	D₄×C₁₃	—	2	2	no	—
265	D₄×C₁₃	—	2	2	no	—
266	D₄×C₁₃	—	2	4	no	—
267	D₄×C₁₃	—	4	16	no	—
268	D₄×C₁₃	—	4	16	no	—
269	D₄×C₁₃	—	4	16	no	—
270	D₄×C₁₃	—	4	4	no	—
271	D₄×C₁₃	—	4	8	no	—
272	D₄×C₁₃	—	8	4	no	—
273	D₄×C₁₃	C₂²×D₄	1	4	yes	—
274	D₄×C₁₃	C₂²×D₄	1	4	yes	complemented
275	C₂×C₄×C₁₃	—	2	4	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	8	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	2	4	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	4	no	—
283	C₂×C₄×C₁₃	—	4	16	no	—
284	C₂×C₄×C₁₃	—	4	4	no	—
285	C₂×C₄×C₁₃	—	4	2	no	—
286	C₂×C₄×C₁₃	—	4	2	no	—
287	C₂×C₄×C₁₃	—	4	8	no	—
288	C₂×C₄×C₁₃	—	4	8	no	—
289	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
290	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
292	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
296	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
297	C₈×C₁₃	—	2	4	no	—
298	C₈×C₁₃	—	2	2	no	—
299	C₈×C₁₃	C₂²×D₄	1	4	yes	complemented
300	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
301	C₂³×D₄	—	2	1	no	—
302	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
303	C₂×AGL(1,ℤ/8)	—	2	16	no	—
304	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	16	yes	complemented
305	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
306	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
307	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
308	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
310	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	complemented
311	#547	—	2	4	no	—
312	#547	C₂²×C₁₃	1	8	yes	complemented
313	D₄²	—	2	4	no	—
314	D₄²	C₂²×C₁₃	1	8	yes	complemented
315	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
316	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#123	—	2	2	no	—
318	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
319	C₂×#121	—	2	1	no	—
320	C₂×#121	—	2	1	no	—
321	C₂×#121	C₂²×C₁₃	1	2	yes	—
322	C₂×#120	—	2	2	no	—
323	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
326	C₂²×C₄⋊C₄	—	2	1	no	—
327	#492	C₂²×C₁₃	1	8	yes	complemented
328	#468	C₂²×C₁₃	1	16	yes	complemented
329	#461	C₂²×C₁₃	1	8	yes	complemented
330	#459	C₂²×C₁₃	1	8	yes	complemented
331	#450	C₂²×C₁₃	1	16	yes	complemented
332	#449	C₂²×C₁₃	1	16	yes	complemented
333	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
334	#436	C₂²×C₁₃	1	8	yes	complemented
335	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
336	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
338	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
340	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
341	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
342	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
343	C₂²×C₁₃	—	2	4	no	—
344	C₂²×C₁₃	—	2	4	no	—
345	C₂²×C₁₃	—	2	4	no	—
346	C₂²×C₁₃	—	2	4	no	—
347	C₂²×C₁₃	—	2	4	no	—
348	C₂²×C₁₃	—	4	8	no	—
349	C₂²×C₁₃	—	4	8	no	—
350	C₂²×C₁₃	—	4	8	no	—
351	C₂²×C₁₃	—	4	2	no	—
352	C₂²×C₁₃	—	4	2	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	—	8	32	no	—
359	C₂²×C₁₃	—	8	8	no	—
360	C₂²×C₁₃	D₄²	1	2	yes	—
361	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
362	C₂²×C₁₃	#577	1	2	yes	—
363	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
364	C₄×C₁₃	—	2	4	no	—
365	C₄×C₁₃	—	2	2	no	—
366	C₄×C₁₃	—	4	4	no	—
367	C₄×C₁₃	—	4	2	no	—
368	C₄×C₁₃	—	4	2	no	—
369	C₄×C₁₃	D₄²	1	2	yes	—
370	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
371	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
372	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂⁵	—	2	2	no	—
374	C₂×#41	—	2	4	no	—
375	C₂×#41	—	2	8	no	—
376	C₂×#41	—	4	4	no	—
377	C₂×#41	C₂³×C₁₃	1	8	yes	complemented
378	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
379	C₂²×D₄	—	2	8	no	—
380	C₂²×D₄	—	2	2	no	—
381	C₂²×D₄	—	2	2	no	—
382	C₂²×D₄	—	2	8	no	—
383	C₂²×D₄	—	2	2	no	—
384	C₂²×D₄	—	2	1	no	—
385	C₂²×D₄	—	2	4	no	—
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	—	4	4	no	—
388	C₂²×D₄	—	4	8	no	—
389	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
390	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
391	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
392	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
393	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₂³×C₄	—	2	1	no	—
395	C₂³×C₄	—	2	2	no	—
396	C₂³×C₄	—	2	1	no	—
397	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
398	AGL(1,ℤ/8)	—	2	64	no	—
399	C₂×SD₁₆	—	2	8	no	—
400	C₂×SD₁₆	—	2	8	no	—
401	C₂×SD₁₆	—	4	4	no	—
402	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
403	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
404	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
405	C₂×D₈	—	2	8	no	—
406	C₂×D₈	D₄×C₁₃	1	8	yes	complemented
407	C₂×D₈	C₂³×C₁₃	1	4	yes	—
408	C₂×D₈	C₂³×C₁₃	1	8	yes	complemented
409	C₂×M₁₆	—	2	8	no	—
410	C₂×M₁₆	C₂³×C₁₃	1	8	yes	complemented
411	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
412	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
414	C₄⋊Q₈	—	2	2	no	—
415	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
416	#127	—	2	2	no	—
417	#127	C₂³×C₁₃	1	4	yes	—
418	#123	—	2	16	no	—
419	C₂²⋊Q₈	—	2	4	no	—
420	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
421	#121	—	2	8	no	—
422	#121	—	2	4	no	—
423	#121	—	2	8	no	—
424	#121	C₂³×C₁₃	1	8	yes	—
425	#120	—	2	16	no	—
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	2	2	no	—
428	C₄×D₄	D₄×C₁₃	1	4	yes	—
429	C₄×D₄	C₂³×C₁₃	1	4	yes	—
430	C₄×D₄	C₂³×C₁₃	1	4	yes	—
431	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	2	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	8	no	—
436	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	—	2	2	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	2	no	—
443	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
444	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
445	#107	C₂³×C₁₃	1	4	yes	complemented
446	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
447	#103	C₂³×C₁₃	1	8	yes	complemented
448	#102	C₂³×C₁₃	1	4	yes	—
449	#102	C₂³×C₁₃	1	4	yes	complemented
450	#102	C₂³×C₁₃	1	8	yes	complemented
451	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	complemented
452	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
453	C₂×C₁₃	—	4	4	no	—
454	C₂×C₁₃	—	4	4	no	—
455	C₂×C₁₃	—	4	4	no	—
456	C₂×C₁₃	—	8	4	no	—
457	C₂×C₁₃	#3272	1	4	yes	direct product factor
458	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
459	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
460	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
461	C₂⁴	—	2	1	no	—
462	C₂⁴	—	2	1	no	—
463	C₂⁴	—	2	2	no	—
464	C₂⁴	—	2	8	no	—
465	C₂⁴	—	4	8	no	—
466	C₂⁴	—	4	8	no	—
467	C₂⁴	—	8	4	no	—
468	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
469	#41	—	2	16	no	—
470	#41	—	4	8	no	—
471	#41	—	4	16	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	—	2	4	no	—
474	C₂×Q₈	—	2	4	no	—
475	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
476	C₂×D₄	—	2	16	no	—
477	C₂×D₄	—	2	8	no	—
478	C₂×D₄	—	2	8	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	2	8	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	4	8	no	—
491	C₂×D₄	—	4	16	no	—
492	C₂×D₄	—	4	8	no	—
493	C₂×D₄	—	4	32	no	—
494	C₂×D₄	—	4	8	no	—
495	C₂×D₄	—	4	8	no	—
496	C₂×D₄	—	4	4	no	—
497	C₂×D₄	—	8	2	no	—
498	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
499	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
500	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	complemented
501	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
502	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
503	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	8	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	4	8	no	—
513	C₂²×C₄	—	4	4	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
517	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
518	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
520	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
521	SD₁₆	—	2	16	no	—
522	SD₁₆	—	2	16	no	—
523	SD₁₆	—	4	8	no	—
524	D₈	—	2	16	no	—
525	D₈	C₂×D₄×C₁₃	1	16	yes	complemented
526	M₁₆	—	2	16	no	—
527	C₂×C₈	—	2	4	no	—
528	C₂×C₈	—	2	2	no	—
529	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
530	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
531	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
532	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	8	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
539	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
540	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
541	C₂²⋊C₄	—	2	8	no	—
542	C₂²⋊C₄	—	2	4	no	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	8	no	—
545	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
546	C₄²	C₂×D₄×C₁₃	1	2	yes	—
547	C₄²	C₂⁴×C₁₃	1	2	yes	—
548	C₁₃	C₂×#3272	1	1	yes	characteristic, direct product factor, Sylow
549	C₂³	—	2	4	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	2	4	no	—
552	C₂³	—	2	4	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	4	16	no	—
558	C₂³	—	4	16	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	2	no	—
563	C₂³	—	4	4	no	—
564	C₂³	—	4	4	no	—
565	C₂³	—	4	4	no	—
566	C₂³	—	8	8	no	—
567	C₂³	—	8	32	no	—
568	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
569	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
570	Q₈	—	2	4	no	—
571	Q₈	—	2	4	no	—
572	Q₈	—	4	4	no	—
573	D₄	—	2	4	no	—
574	D₄	—	2	4	no	—
575	D₄	—	2	8	no	—
576	D₄	—	2	4	no	—
577	D₄	—	2	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	4	no	—
580	D₄	—	4	16	no	—
581	D₄	—	4	16	no	—
582	D₄	—	4	16	no	—
583	D₄	—	4	4	no	—
584	D₄	—	4	8	no	—
585	D₄	—	8	4	no	—
586	D₄	C₂²×D₄×C₁₃	1	4	yes	—
587	D₄	C₂²×D₄×C₁₃	1	4	yes	complemented
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	8	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	4	16	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	8	no	—
601	C₂×C₄	—	4	8	no	—
602	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
603	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
604	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
605	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
607	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
608	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
609	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
610	C₈	—	2	4	no	—
611	C₈	—	2	2	no	—
612	C₈	C₂²×D₄×C₁₃	1	4	yes	complemented
613	C₂²	—	2	4	no	—
614	C₂²	—	2	4	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	2	4	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	8	no	—
619	C₂²	—	4	8	no	—
620	C₂²	—	4	8	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	4	no	—
626	C₂²	—	4	4	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	8	32	no	—
629	C₂²	—	8	8	no	—
630	C₂²	D₄²×C₁₃	1	2	yes	—
631	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
632	C₂²	C₁₃×#577	1	2	yes	—
633	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
634	C₄	—	2	2	no	—
635	C₄	—	2	4	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	4	no	—
639	C₄	D₄²×C₁₃	1	2	yes	—
640	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
641	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
642	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
643	C₂	—	4	4	no	—
644	C₂	—	4	4	no	—
645	C₂	—	4	4	no	—
646	C₂	—	8	4	no	—
647	C₂	C₁₃×#3272	1	4	yes	direct product factor
648	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
649	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
650	C₂	C₂×C₁₃×#577	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×#547	C₂	semidirect
3. C₂×D₄²×C₁₃	C₂	semidirect
4. C₁₃×#3272	C₂	direct (N × H)
5. C₂×C₁₃×#492	C₂	semidirect
6. C₂×C₁₃×#468	C₂	semidirect
7. C₂×C₁₃×#461	C₂	semidirect
8. C₂×C₁₃×#459	C₂	semidirect
9. C₂×C₁₃×#449	C₂	semidirect
10. C₂×C₁₃×#450	C₂	semidirect
11. C₂×C₄×C₁₃×D₈	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
20. C₂²×C₁₃×SD₁₆	C₂²	semidirect
22. C₂²×C₁₃×D₈	C₂²	semidirect
23. C₂²×C₁₃×M₁₆	C₂²	semidirect
25. C₁₃×#547	C₂²	semidirect
27. D₄²×C₁₃	C₂²	semidirect
28. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₄×D₄×C₁₃	C₂²	semidirect
40. C₁₃×#492	C₂²	semidirect
41. C₁₃×#468	C₂²	semidirect
42. C₁₃×#461	C₂²	semidirect
43. C₁₃×#459	C₂²	semidirect
44. C₁₃×#450	C₂²	semidirect
45. C₁₃×#449	C₂²	semidirect
46. C₄×C₁₃×D₈	C₂²	semidirect
47. C₁₃×#436	C₂²	semidirect
48. C₂×C₁₃×#107	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
86. C₂×C₁₃×SD₁₆	C₂³	semidirect
87. C₂×C₁₃×SD₁₆	C₂³	semidirect
89. C₂×C₁₃×D₈	D₄	semidirect
91. C₂×C₁₃×D₈	C₂³	semidirect
93. C₂×C₁₃×M₁₆	C₂³	semidirect
98. C₁₃×C₄⋊Q₈	C₂³	semidirect
103. C₁₃×C₂²⋊Q₈	C₂³	semidirect
114. C₄×D₄×C₁₃	C₂³	semidirect
128. C₁₃×#107	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×#3272	C₁₃	direct (N × H)
176. C₂×D₄×C₁₃	C₂×D₄	semidirect
201. C₁₃×D₈	C₂×D₄	semidirect
205. C₂×C₈×C₁₃	C₂×D₄	semidirect
224. C₂²×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
225. C₂×#547	C₂×C₁₃	semidirect
226. C₂×D₄²	C₂×C₁₃	semidirect
227. #3272	C₂×C₁₃	direct (N × H)
228. C₂×#492	C₂×C₁₃	semidirect
229. C₂×#468	C₂×C₁₃	semidirect
230. C₂×#461	C₂×C₁₃	semidirect
231. C₂×#459	C₂×C₁₃	semidirect
232. C₂×#449	C₂×C₁₃	semidirect
233. C₂×#450	C₂×C₁₃	semidirect
234. C₂×C₄×D₈	C₂×C₁₃	semidirect
235. C₂×#436	C₂×C₁₃	semidirect
274. D₄×C₁₃	C₂²×D₄	semidirect
289. C₂×C₄×C₁₃	AGL(1,ℤ/8)	semidirect
299. C₈×C₁₃	C₂²×D₄	semidirect
300. C₂²×#41	C₂²×C₁₃	semidirect
304. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
306. C₂²×SD₁₆	C₂²×C₁₃	semidirect
307. C₂²×SD₁₆	C₂²×C₁₃	semidirect
309. C₂²×D₈	C₂²×C₁₃	semidirect
310. C₂²×M₁₆	C₂²×C₁₃	semidirect
312. #547	C₂²×C₁₃	semidirect
314. D₄²	C₂²×C₁₃	semidirect
315. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
318. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
325. C₂×C₄×D₄	C₂²×C₁₃	semidirect
327. #492	C₂²×C₁₃	semidirect
328. #468	C₂²×C₁₃	semidirect
329. #461	C₂²×C₁₃	semidirect
330. #459	C₂²×C₁₃	semidirect
331. #450	C₂²×C₁₃	semidirect
332. #449	C₂²×C₁₃	semidirect
333. C₄×D₈	C₂²×C₁₃	semidirect
334. #436	C₂²×C₁₃	semidirect
335. C₂×#107	C₂²×C₁₃	semidirect
336. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
337. C₂×#103	C₂²×C₁₃	semidirect
339. C₂×#102	C₂²×C₁₃	semidirect
340. C₂×#102	C₂²×C₁₃	semidirect
341. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
342. C₂×C₄×C₈	C₂²×C₁₃	semidirect
370. C₄×C₁₃	C₂×AGL(1,ℤ/8)	semidirect
377. C₂×#41	C₂³×C₁₃	semidirect
403. C₂×SD₁₆	C₂³×C₁₃	semidirect
404. C₂×SD₁₆	C₂³×C₁₃	semidirect
406. C₂×D₈	D₄×C₁₃	semidirect
408. C₂×D₈	C₂³×C₁₃	semidirect
410. C₂×M₁₆	C₂³×C₁₃	semidirect
415. C₄⋊Q₈	C₂³×C₁₃	semidirect
420. C₂²⋊Q₈	C₂³×C₁₃	semidirect
431. C₄×D₄	C₂³×C₁₃	semidirect
445. #107	C₂³×C₁₃	semidirect
446. C₄⋊C₈	C₂³×C₁₃	semidirect
447. #103	C₂³×C₁₃	semidirect
449. #102	C₂³×C₁₃	semidirect
450. #102	C₂³×C₁₃	semidirect
451. C₂²⋊C₈	C₂³×C₁₃	semidirect
452. C₄×C₈	C₂³×C₁₃	semidirect
457. C₂×C₁₃	#3272	direct (N × H)
500. C₂×D₄	C₂×D₄×C₁₃	semidirect
525. D₈	C₂×D₄×C₁₃	semidirect
529. C₂×C₈	C₂×D₄×C₁₃	semidirect
548. C₁₃	C₂×#3272	direct (N × H)
587. D₄	C₂²×D₄×C₁₃	semidirect
602. C₂×C₄	C₁₃×AGL(1,ℤ/8)	semidirect
612. C₈	C₂²×D₄×C₁₃	semidirect
640. C₄	C₂×C₁₃×AGL(1,ℤ/8)	semidirect
647. C₂	C₁₃×#3272	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×#547	2
C₂×D₄²×C₁₃	2
C₁₃×#3272	2
C₂×C₁₃×#492	2
C₂×C₁₃×#468	2
C₂×C₁₃×#461	2
C₂×C₁₃×#459	2
C₂×C₁₃×#449	2
C₂×C₁₃×#450	2
C₂×C₄×C₁₃×D₈	2
C₂×C₁₃×#436	2
C₂×#3272	13

Subgroups — C2×C13×#3272 #15747370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3272 #15747370