Subgroups — C₂×C₁₃×#3376 #15747652

Order 3328.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3376	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic
15	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₁₃×#556	—	2	4	no	—
21	C₁₃×#556	C₂²	1	8	yes	complemented
22	C₁₃×#554	—	2	4	no	—
23	C₁₃×#554	C₂²	1	8	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#126	—	2	1	no	—
27	C₂×C₁₃×#126	—	2	1	no	—
28	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
33	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
34	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
35	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#117	—	2	1	no	—
44	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
45	C₁₃×#491	C₂²	1	8	yes	complemented
46	C₁₃×#489	C₂²	1	8	yes	complemented
47	C₁₃×#488	C₂²	1	8	yes	complemented
48	C₁₃×#479	C₂²	1	8	yes	complemented
49	C₁₃×#478	C₂²	1	8	yes	complemented
50	C₁₃×#475	C₂²	1	8	yes	complemented
51	C₁₃×#463	C₂²	1	8	yes	—
52	C₁₃×#463	C₂²	1	8	yes	—
53	C₁₃×#461	C₂²	1	8	yes	complemented
54	C₁₃×#446	C₂²	1	8	yes	complemented
55	C₁₃×#442	C₂²	1	8	yes	—
56	C₁₃×#440	C₂²	1	8	yes	complemented
57	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₁₃	—	2	1	no	—
78	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	—	2	1	no	—
84	C₂³×C₄×C₁₃	—	2	1	no	—
85	C₂³×C₄×C₁₃	—	2	1	no	—
86	C₂³×C₄×C₁₃	—	2	1	no	—
87	C₂×C₁₃×SD₁₆	—	2	4	no	—
88	C₂×C₁₃×SD₁₆	—	2	4	no	—
89	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
90	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
91	C₂×C₁₃×D₈	—	2	4	no	—
92	C₂×C₁₃×D₈	C₂³	1	4	yes	—
93	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×C₄⋊Q₈	—	2	2	no	—
98	C₁₃×C₄⋊Q₈	—	2	2	no	—
99	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
100	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
101	C₁₃×#126	—	2	8	no	—
102	C₁₃×#126	—	2	8	no	—
103	C₁₃×#125	—	2	2	no	—
104	C₁₃×#125	—	2	2	no	—
105	C₁₃×#125	C₂³	1	4	yes	—
106	C₁₃×#125	C₂³	1	4	yes	—
107	C₁₃×#124	—	2	2	no	—
108	C₁₃×#124	—	2	2	no	—
109	C₁₃×#124	C₂³	1	4	yes	—
110	C₁₃×#124	C₂³	1	4	yes	—
111	C₁₃×C₂²⋊Q₈	—	2	8	no	—
112	C₁₃×C₂²⋊Q₈	—	2	8	no	—
113	C₁₃×C₂²⋊Q₈	—	2	8	no	—
114	C₁₃×C₂²⋊Q₈	—	2	8	no	—
115	C₄×Q₈×C₁₃	—	2	2	no	—
116	C₄×Q₈×C₁₃	—	2	2	no	—
117	C₄×Q₈×C₁₃	D₄	1	4	yes	—
118	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
119	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
120	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
121	C₄×D₄×C₁₃	—	2	2	no	—
122	C₄×D₄×C₁₃	—	2	2	no	—
123	C₄×D₄×C₁₃	—	2	2	no	—
124	C₄×D₄×C₁₃	—	2	2	no	—
125	C₄×D₄×C₁₃	C₂³	1	4	yes	—
126	C₄×D₄×C₁₃	C₂³	1	4	yes	—
127	C₄×D₄×C₁₃	C₂³	1	4	yes	—
128	C₄×D₄×C₁₃	C₂³	1	4	yes	—
129	C₁₃×#117	—	2	8	no	—
130	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
140	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
149	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
150	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
151	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
152	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₄²×C₁₃	—	2	1	no	—
156	C₂×C₄²×C₁₃	—	2	1	no	—
157	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
160	C₁₃×#107	C₂³	1	4	yes	—
161	C₁₃×#106	C₂³	1	4	yes	—
162	C₁₃×#106	C₂³	1	4	yes	—
163	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
164	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
165	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
166	C₁₃×#103	C₂³	1	4	yes	—
167	C₁₃×#103	C₂³	1	4	yes	—
168	C₁₃×#103	C₂³	1	4	yes	—
169	C₁₃×#103	C₂³	1	4	yes	—
170	C₁₃×#103	C₂³	1	4	yes	—
171	C₁₃×#103	C₂³	1	4	yes	—
172	C₁₃×#102	C₂³	1	4	yes	—
173	C₁₃×#102	C₂³	1	4	yes	—
174	C₁₃×#102	C₂³	1	4	yes	—
175	C₁₃×#102	C₂³	1	4	yes	—
176	C₁₃×#97	C₂³	1	4	yes	—
177	C₁₃×#97	C₂³	1	4	yes	—
178	C₄×C₈×C₁₃	C₂³	1	4	yes	—
179	C₂×#3376	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂⁴×C₁₃	—	2	1	no	—
181	C₂⁴×C₁₃	—	2	1	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	4	no	—
185	C₂×Q₈×C₁₃	—	2	2	no	—
186	C₂×Q₈×C₁₃	—	2	2	no	—
187	C₂×Q₈×C₁₃	—	2	2	no	—
188	C₂×Q₈×C₁₃	—	2	2	no	—
189	C₂×Q₈×C₁₃	—	4	2	no	—
190	C₂×Q₈×C₁₃	—	8	2	no	—
191	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
192	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
193	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	2	1	no	—
196	C₂×D₄×C₁₃	—	2	2	no	—
197	C₂×D₄×C₁₃	—	2	2	no	—
198	C₂×D₄×C₁₃	—	2	2	no	—
199	C₂×D₄×C₁₃	#41	1	4	yes	—
200	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃	—	2	1	no	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	2	1	no	—
205	C₂²×C₄×C₁₃	—	2	1	no	—
206	C₂²×C₄×C₁₃	—	2	1	no	—
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	2	4	no	—
209	C₂²×C₄×C₁₃	—	2	4	no	—
210	C₂²×C₄×C₁₃	—	2	4	no	—
211	C₂²×C₄×C₁₃	—	2	4	no	—
212	C₂²×C₄×C₁₃	—	4	4	no	—
213	C₂²×C₄×C₁₃	—	4	4	no	—
214	C₂²×C₄×C₁₃	—	8	2	no	—
215	C₂²×C₄×C₁₃	—	8	2	no	—
216	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₁₃×SD₁₆	—	2	8	no	—
224	C₁₃×SD₁₆	—	2	8	no	—
225	C₁₃×D₈	—	2	8	no	—
226	C₂×C₈×C₁₃	—	2	2	no	—
227	C₂×C₈×C₁₃	—	2	2	no	—
228	C₂×C₈×C₁₃	—	2	2	no	—
229	C₂×C₈×C₁₃	—	2	2	no	—
230	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
231	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
232	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
233	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	2	4	no	—
236	C₁₃×C₄⋊C₄	—	2	4	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	4	no	—
241	C₁₃×C₄⋊C₄	—	2	4	no	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	2	1	no	—
246	C₁₃×C₄⋊C₄	—	2	1	no	—
247	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
248	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
249	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
250	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
251	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
252	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
253	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
254	C₁₃×C₂²⋊C₄	—	2	4	no	—
255	C₁₃×C₂²⋊C₄	—	2	4	no	—
256	C₁₃×C₂²⋊C₄	—	2	4	no	—
257	C₁₃×C₂²⋊C₄	—	2	4	no	—
258	C₁₃×C₂²⋊C₄	—	2	4	no	—
259	C₁₃×C₂²⋊C₄	—	2	4	no	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	4	no	—
262	C₄²×C₁₃	—	2	4	no	—
263	C₄²×C₁₃	—	2	4	no	—
264	C₄²×C₁₃	C₂×D₄	1	2	yes	—
265	C₄²×C₁₃	C₂×D₄	1	2	yes	—
266	C₄²×C₁₃	C₂×D₄	1	2	yes	—
267	C₄²×C₁₃	C₂⁴	1	2	yes	—
268	C₄²×C₁₃	C₂⁴	1	2	yes	—
269	C₄²×C₁₃	C₂⁴	1	2	yes	—
270	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
271	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#3376	C₂×C₁₃	1	16	yes	direct product factor
273	C₂×#491	C₂×C₁₃	1	1	yes	characteristic, complemented
274	C₂×#489	C₂×C₁₃	1	1	yes	characteristic, complemented
275	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
276	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
277	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
279	C₂×#463	C₂×C₁₃	1	1	yes	characteristic
280	C₂×#463	C₂×C₁₃	1	1	yes	characteristic
281	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
283	C₂×#442	C₂×C₁₃	1	1	yes	characteristic
284	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
285	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
286	C₂³×C₁₃	—	2	4	no	—
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	4	2	no	—
290	C₂³×C₁₃	—	4	2	no	—
291	C₂³×C₁₃	—	4	2	no	—
292	C₂³×C₁₃	—	4	2	no	—
293	C₂³×C₁₃	—	4	2	no	—
294	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₁₃	—	2	2	no	—
296	Q₈×C₁₃	—	2	2	no	—
297	Q₈×C₁₃	—	2	2	no	—
298	Q₈×C₁₃	—	2	2	no	—
299	Q₈×C₁₃	—	4	4	no	—
300	Q₈×C₁₃	—	4	2	no	—
301	Q₈×C₁₃	—	4	2	no	—
302	Q₈×C₁₃	—	8	4	no	—
303	D₄×C₁₃	—	2	4	no	—
304	D₄×C₁₃	—	2	2	no	—
305	D₄×C₁₃	—	2	2	no	—
306	D₄×C₁₃	—	2	2	no	—
307	D₄×C₁₃	—	4	2	no	—
308	D₄×C₁₃	C₂×#41	1	4	yes	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	2	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	4	8	no	—
322	C₂×C₄×C₁₃	—	4	8	no	—
323	C₂×C₄×C₁₃	—	4	2	no	—
324	C₂×C₄×C₁₃	—	4	2	no	—
325	C₂×C₄×C₁₃	—	4	2	no	—
326	C₂×C₄×C₁₃	—	4	2	no	—
327	C₂×C₄×C₁₃	—	4	2	no	—
328	C₂×C₄×C₁₃	—	4	2	no	—
329	C₂×C₄×C₁₃	—	8	4	no	—
330	C₂×C₄×C₁₃	—	8	4	no	—
331	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
339	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
340	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
341	C₈×C₁₃	—	2	2	no	—
342	C₈×C₁₃	—	2	2	no	—
343	C₈×C₁₃	—	2	2	no	—
344	C₈×C₁₃	—	2	2	no	—
345	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
346	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
347	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
348	#556	—	2	4	no	—
349	#556	C₂²×C₁₃	1	8	yes	complemented
350	#554	—	2	4	no	—
351	#554	C₂²×C₁₃	1	8	yes	complemented
352	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×#126	—	2	1	no	—
355	C₂×#126	—	2	1	no	—
356	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×C₂²⋊Q₈	—	2	1	no	—
361	C₂×C₂²⋊Q₈	—	2	1	no	—
362	C₂×C₂²⋊Q₈	—	2	1	no	—
363	C₂×C₂²⋊Q₈	—	2	1	no	—
364	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#117	—	2	1	no	—
372	C₂²×C₄⋊C₄	—	2	1	no	—
373	#491	C₂²×C₁₃	1	8	yes	complemented
374	#489	C₂²×C₁₃	1	8	yes	complemented
375	#488	C₂²×C₁₃	1	8	yes	complemented
376	#479	C₂²×C₁₃	1	8	yes	complemented
377	#478	C₂²×C₁₃	1	8	yes	complemented
378	#475	C₂²×C₁₃	1	8	yes	complemented
379	#463	C₂²×C₁₃	1	8	yes	—
380	#463	C₂²×C₁₃	1	8	yes	—
381	#461	C₂²×C₁₃	1	8	yes	complemented
382	#446	C₂²×C₁₃	1	8	yes	complemented
383	#442	C₂²×C₁₃	1	8	yes	—
384	#440	C₂²×C₁₃	1	8	yes	complemented
385	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
386	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
405	C₂²×C₁₃	—	2	4	no	—
406	C₂²×C₁₃	—	4	8	no	—
407	C₂²×C₁₃	—	4	2	no	—
408	C₂²×C₁₃	—	4	2	no	—
409	C₂²×C₁₃	—	4	2	no	—
410	C₂²×C₁₃	—	4	2	no	—
411	C₂²×C₁₃	—	4	2	no	—
412	C₂²×C₁₃	—	8	4	no	—
413	C₂²×C₁₃	#548	1	2	yes	—
414	C₂²×C₁₃	#575	1	2	yes	—
415	C₂²×C₁₃	#577	1	2	yes	—
416	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
417	C₄×C₁₃	—	2	2	no	—
418	C₄×C₁₃	—	2	2	no	—
419	C₄×C₁₃	—	2	2	no	—
420	C₄×C₁₃	—	2	2	no	—
421	C₄×C₁₃	—	2	2	no	—
422	C₄×C₁₃	—	2	2	no	—
423	C₄×C₁₃	—	4	2	no	—
424	C₄×C₁₃	—	4	2	no	—
425	C₄×C₁₃	—	4	2	no	—
426	C₄×C₁₃	—	4	2	no	—
427	C₄×C₁₃	—	4	2	no	—
428	C₄×C₁₃	—	4	2	no	—
429	C₄×C₁₃	#548	1	2	yes	—
430	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
431	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
432	C₂²×Q₈	—	2	1	no	—
433	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
434	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
435	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
436	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	—	2	1	no	—
440	C₂³×C₄	—	2	1	no	—
441	C₂³×C₄	—	2	1	no	—
442	C₂×SD₁₆	—	2	4	no	—
443	C₂×SD₁₆	—	2	4	no	—
444	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
445	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
446	C₂×D₈	—	2	4	no	—
447	C₂×D₈	C₂³×C₁₃	1	4	yes	—
448	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
450	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
452	C₄⋊Q₈	—	2	2	no	—
453	C₄⋊Q₈	—	2	2	no	—
454	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
455	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
456	#126	—	2	8	no	—
457	#126	—	2	8	no	—
458	#125	—	2	2	no	—
459	#125	—	2	2	no	—
460	#125	C₂³×C₁₃	1	4	yes	—
461	#125	C₂³×C₁₃	1	4	yes	—
462	#124	—	2	2	no	—
463	#124	—	2	2	no	—
464	#124	C₂³×C₁₃	1	4	yes	—
465	#124	C₂³×C₁₃	1	4	yes	—
466	C₂²⋊Q₈	—	2	8	no	—
467	C₂²⋊Q₈	—	2	8	no	—
468	C₂²⋊Q₈	—	2	8	no	—
469	C₂²⋊Q₈	—	2	8	no	—
470	C₄×Q₈	—	2	2	no	—
471	C₄×Q₈	—	2	2	no	—
472	C₄×Q₈	D₄×C₁₃	1	4	yes	—
473	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
474	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
475	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
476	C₄×D₄	—	2	2	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	C₂³×C₁₃	1	4	yes	—
481	C₄×D₄	C₂³×C₁₃	1	4	yes	—
482	C₄×D₄	C₂³×C₁₃	1	4	yes	—
483	C₄×D₄	C₂³×C₁₃	1	4	yes	—
484	#117	—	2	8	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	—	2	1	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	8	no	—
495	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
497	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₄²	—	2	1	no	—
511	C₂×C₄²	—	2	1	no	—
512	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
513	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
515	#107	C₂³×C₁₃	1	4	yes	—
516	#106	C₂³×C₁₃	1	4	yes	—
517	#106	C₂³×C₁₃	1	4	yes	—
518	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
519	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
520	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
521	#103	C₂³×C₁₃	1	4	yes	—
522	#103	C₂³×C₁₃	1	4	yes	—
523	#103	C₂³×C₁₃	1	4	yes	—
524	#103	C₂³×C₁₃	1	4	yes	—
525	#103	C₂³×C₁₃	1	4	yes	—
526	#103	C₂³×C₁₃	1	4	yes	—
527	#102	C₂³×C₁₃	1	4	yes	—
528	#102	C₂³×C₁₃	1	4	yes	—
529	#102	C₂³×C₁₃	1	4	yes	—
530	#102	C₂³×C₁₃	1	4	yes	—
531	#97	C₂³×C₁₃	1	4	yes	—
532	#97	C₂³×C₁₃	1	4	yes	—
533	C₄×C₈	C₂³×C₁₃	1	4	yes	—
534	C₂×C₁₃	—	4	4	no	—
535	C₂×C₁₃	—	8	2	no	—
536	C₂×C₁₃	#3376	1	4	yes	direct product factor
537	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
538	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
539	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
540	C₂⁴	—	2	1	no	—
541	C₂⁴	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	4	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	4	2	no	—
550	C₂×Q₈	—	8	2	no	—
551	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
552	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
553	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	C₁₃×#41	1	4	yes	—
560	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
561	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	4	4	no	—
573	C₂²×C₄	—	4	4	no	—
574	C₂²×C₄	—	8	2	no	—
575	C₂²×C₄	—	8	2	no	—
576	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
583	SD₁₆	—	2	8	no	—
584	SD₁₆	—	2	8	no	—
585	D₈	—	2	8	no	—
586	C₂×C₈	—	2	2	no	—
587	C₂×C₈	—	2	2	no	—
588	C₂×C₈	—	2	2	no	—
589	C₂×C₈	—	2	2	no	—
590	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
591	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
592	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
593	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
608	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
609	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
610	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
611	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
612	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
613	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	4	no	—
624	C₄²	C₂×D₄×C₁₃	1	2	yes	—
625	C₄²	C₂×D₄×C₁₃	1	2	yes	—
626	C₄²	C₂×D₄×C₁₃	1	2	yes	—
627	C₄²	C₂⁴×C₁₃	1	2	yes	—
628	C₄²	C₂⁴×C₁₃	1	2	yes	—
629	C₄²	C₂⁴×C₁₃	1	2	yes	—
630	C₁₃	C₂×#3376	1	1	yes	characteristic, direct product factor, Sylow
631	C₂³	—	2	4	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	4	2	no	—
635	C₂³	—	4	2	no	—
636	C₂³	—	4	2	no	—
637	C₂³	—	4	2	no	—
638	C₂³	—	4	2	no	—
639	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
640	Q₈	—	2	2	no	—
641	Q₈	—	2	2	no	—
642	Q₈	—	2	2	no	—
643	Q₈	—	2	2	no	—
644	Q₈	—	4	4	no	—
645	Q₈	—	4	2	no	—
646	Q₈	—	4	2	no	—
647	Q₈	—	8	4	no	—
648	D₄	—	2	4	no	—
649	D₄	—	2	2	no	—
650	D₄	—	2	2	no	—
651	D₄	—	2	2	no	—
652	D₄	—	4	2	no	—
653	D₄	C₂×C₁₃×#41	1	4	yes	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	4	8	no	—
667	C₂×C₄	—	4	8	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	4	2	no	—
673	C₂×C₄	—	4	2	no	—
674	C₂×C₄	—	8	4	no	—
675	C₂×C₄	—	8	4	no	—
676	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
677	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
678	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
679	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
680	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
681	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
682	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
683	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
684	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
685	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
686	C₈	—	2	2	no	—
687	C₈	—	2	2	no	—
688	C₈	—	2	2	no	—
689	C₈	—	2	2	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	8	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	8	4	no	—
698	C₂²	C₁₃×#548	1	2	yes	—
699	C₂²	C₁₃×#575	1	2	yes	—
700	C₂²	C₁₃×#577	1	2	yes	—
701	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	C₁₃×#548	1	2	yes	—
715	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
716	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
717	C₂	—	4	4	no	—
718	C₂	—	8	2	no	—
719	C₂	C₁₃×#3376	1	4	yes	direct product factor
720	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
721	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
722	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#556	C₂	semidirect
2. C₂×C₁₃×#554	C₂	semidirect
3. C₁₃×#3376	C₂	direct (N × H)
4. C₂×C₁₃×#491	C₂	semidirect
5. C₂×C₁₃×#489	C₂	semidirect
6. C₂×C₁₃×#488	C₂	semidirect
7. C₂×C₁₃×#479	C₂	semidirect
8. C₂×C₁₃×#475	C₂	semidirect
9. C₂×C₁₃×#478	C₂	semidirect
12. C₂×C₁₃×#461	C₂	semidirect
13. C₂×C₁₃×#446	C₂	semidirect
15. C₂×C₁₃×#440	C₂	semidirect
16. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
21. C₁₃×#556	C₂²	semidirect
23. C₁₃×#554	C₂²	semidirect
45. C₁₃×#491	C₂²	semidirect
46. C₁₃×#489	C₂²	semidirect
47. C₁₃×#488	C₂²	semidirect
48. C₁₃×#479	C₂²	semidirect
49. C₁₃×#478	C₂²	semidirect
50. C₁₃×#475	C₂²	semidirect
53. C₁₃×#461	C₂²	semidirect
54. C₁₃×#446	C₂²	semidirect
56. C₁₃×#440	C₂²	semidirect
57. C₄×C₁₃×SD₁₆	C₂²	semidirect
179. C₂×#3376	C₁₃	direct (N × H)
270. C₂×#556	C₂×C₁₃	semidirect
271. C₂×#554	C₂×C₁₃	semidirect
272. #3376	C₂×C₁₃	direct (N × H)
273. C₂×#491	C₂×C₁₃	semidirect
274. C₂×#489	C₂×C₁₃	semidirect
275. C₂×#488	C₂×C₁₃	semidirect
276. C₂×#479	C₂×C₁₃	semidirect
277. C₂×#475	C₂×C₁₃	semidirect
278. C₂×#478	C₂×C₁₃	semidirect
281. C₂×#461	C₂×C₁₃	semidirect
282. C₂×#446	C₂×C₁₃	semidirect
284. C₂×#440	C₂×C₁₃	semidirect
285. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
349. #556	C₂²×C₁₃	semidirect
351. #554	C₂²×C₁₃	semidirect
373. #491	C₂²×C₁₃	semidirect
374. #489	C₂²×C₁₃	semidirect
375. #488	C₂²×C₁₃	semidirect
376. #479	C₂²×C₁₃	semidirect
377. #478	C₂²×C₁₃	semidirect
378. #475	C₂²×C₁₃	semidirect
381. #461	C₂²×C₁₃	semidirect
382. #446	C₂²×C₁₃	semidirect
384. #440	C₂²×C₁₃	semidirect
385. C₄×SD₁₆	C₂²×C₁₃	semidirect
536. C₂×C₁₃	#3376	direct (N × H)
630. C₁₃	C₂×#3376	direct (N × H)
719. C₂	C₁₃×#3376	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#556	2
C₂×C₁₃×#554	2
C₁₃×#3376	2
C₂×C₁₃×#491	2
C₂×C₁₃×#489	2
C₂×C₁₃×#488	2
C₂×C₁₃×#479	2
C₂×C₁₃×#475	2
C₂×C₁₃×#478	2
C₂×C₁₃×#463	2
C₂×C₁₃×#461	2
C₂×C₁₃×#446	2
C₂×C₁₃×#442	2
C₂×C₁₃×#440	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×#3376	13

Subgroups — C2×C13×#3376 #15747652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3376 #15747652