Subgroups — C₂×C₁₃×#2416 #15721011

Order 3328.

4782 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#121	C₂	1	2	yes	maximal, complemented
2	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2416	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₁₃×#396	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#394	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#121	—	2	16	no	—
21	C₂×C₁₃×#121	—	2	8	no	—
22	C₂×C₁₃×#121	—	2	8	no	—
23	C₂×C₁₃×#121	C₂²	1	16	yes	complemented
24	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
25	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
26	C₂×C₄×D₄×C₁₃	—	2	8	no	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
28	C₂²×C₁₃×C₄⋊C₄	—	2	8	no	—
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#396	C₂²	1	16	yes	complemented
45	C₁₃×#394	C₂²	1	16	yes	complemented
46	C₁₃×#390	C₂²	1	8	yes	complemented
47	C₁₃×#389	C₂²	1	8	yes	complemented
48	C₁₃×#386	C₂²	1	16	yes	complemented
49	C₁₃×#380	C₂²	1	8	yes	complemented
50	C₂×C₁₃×#95	C₂²	1	2	yes	—
51	C₂×C₁₃×#95	C₂²	1	2	yes	—
52	C₂⁵×C₁₃	C₂³	1	2	yes	—
53	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
54	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₃	—	2	4	no	—
56	C₂²×D₄×C₁₃	—	2	4	no	—
57	C₂²×D₄×C₁₃	—	2	8	no	—
58	C₂²×D₄×C₁₃	—	2	8	no	—
59	C₂²×D₄×C₁₃	—	2	8	no	—
60	C₂²×D₄×C₁₃	—	2	8	no	—
61	C₂²×D₄×C₁₃	—	2	8	no	—
62	C₂²×D₄×C₁₃	—	2	4	no	—
63	C₂²×D₄×C₁₃	—	2	4	no	—
64	C₂²×D₄×C₁₃	—	2	4	no	—
65	C₂²×D₄×C₁₃	—	4	4	no	—
66	C₂²×D₄×C₁₃	D₄	1	8	yes	complemented
67	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₃	—	2	4	no	—
72	C₂³×C₄×C₁₃	—	2	4	no	—
73	C₂³×C₄×C₁₃	—	2	8	no	—
74	C₂³×C₄×C₁₃	—	2	8	no	—
75	C₂³×C₄×C₁₃	—	2	4	no	—
76	C₂³×C₄×C₁₃	—	2	4	no	—
77	C₂³×C₄×C₁₃	—	2	4	no	—
78	C₂³×C₄×C₁₃	—	4	4	no	—
79	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
80	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×#121	—	2	64	no	—
92	C₁₃×#121	—	2	32	no	—
93	C₁₃×#121	—	2	32	no	—
94	C₄×D₄×C₁₃	—	2	32	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	32	no	—
101	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	complemented
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
122	C₂×C₄²×C₁₃	—	2	4	no	—
123	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
124	C₁₃×#95	C₂³	1	8	yes	—
125	C₁₃×#95	C₂³	1	8	yes	—
126	C₂×#2416	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	—	2	2	no	—
128	C₂⁴×C₁₃	—	2	2	no	—
129	C₂⁴×C₁₃	—	2	2	no	—
130	C₂⁴×C₁₃	—	2	2	no	—
131	C₂⁴×C₁₃	—	2	2	no	—
132	C₂⁴×C₁₃	—	2	2	no	—
133	C₂⁴×C₁₃	—	2	2	no	—
134	C₂⁴×C₁₃	—	2	2	no	—
135	C₂⁴×C₁₃	—	2	2	no	—
136	C₂⁴×C₁₃	—	2	2	no	—
137	C₂⁴×C₁₃	—	2	4	no	—
138	C₂⁴×C₁₃	—	2	4	no	—
139	C₂⁴×C₁₃	—	2	4	no	—
140	C₂⁴×C₁₃	—	2	4	no	—
141	C₂⁴×C₁₃	—	2	4	no	—
142	C₂⁴×C₁₃	—	2	4	no	—
143	C₂⁴×C₁₃	—	2	4	no	—
144	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
145	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
146	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
147	C₂⁴×C₁₃	#41	1	4	yes	—
148	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
149	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
150	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
151	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₂×D₄×C₁₃	—	2	32	no	—
153	C₂×D₄×C₁₃	—	2	8	no	—
154	C₂×D₄×C₁₃	—	2	8	no	—
155	C₂×D₄×C₁₃	—	2	16	no	—
156	C₂×D₄×C₁₃	—	2	16	no	—
157	C₂×D₄×C₁₃	—	2	16	no	—
158	C₂×D₄×C₁₃	—	2	16	no	—
159	C₂×D₄×C₁₃	—	2	16	no	—
160	C₂×D₄×C₁₃	—	2	8	no	—
161	C₂×D₄×C₁₃	—	2	8	no	—
162	C₂×D₄×C₁₃	—	2	8	no	—
163	C₂×D₄×C₁₃	—	4	8	no	—
164	C₂×D₄×C₁₃	—	4	32	no	—
165	C₂×D₄×C₁₃	—	4	32	no	—
166	C₂×D₄×C₁₃	—	4	16	no	—
167	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	complemented
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	2	no	—
172	C₂²×C₄×C₁₃	—	2	2	no	—
173	C₂²×C₄×C₁₃	—	2	4	no	—
174	C₂²×C₄×C₁₃	—	2	32	no	—
175	C₂²×C₄×C₁₃	—	2	8	no	—
176	C₂²×C₄×C₁₃	—	2	8	no	—
177	C₂²×C₄×C₁₃	—	2	2	no	—
178	C₂²×C₄×C₁₃	—	2	2	no	—
179	C₂²×C₄×C₁₃	—	2	4	no	—
180	C₂²×C₄×C₁₃	—	2	2	no	—
181	C₂²×C₄×C₁₃	—	2	4	no	—
182	C₂²×C₄×C₁₃	—	2	4	no	—
183	C₂²×C₄×C₁₃	—	2	4	no	—
184	C₂²×C₄×C₁₃	—	2	16	no	—
185	C₂²×C₄×C₁₃	—	2	2	no	—
186	C₂²×C₄×C₁₃	—	2	4	no	—
187	C₂²×C₄×C₁₃	—	2	2	no	—
188	C₂²×C₄×C₁₃	—	2	4	no	—
189	C₂²×C₄×C₁₃	—	2	2	no	—
190	C₂²×C₄×C₁₃	—	2	16	no	—
191	C₂²×C₄×C₁₃	—	2	8	no	—
192	C₂²×C₄×C₁₃	—	2	8	no	—
193	C₂²×C₄×C₁₃	—	2	8	no	—
194	C₂²×C₄×C₁₃	—	4	8	no	—
195	C₂²×C₄×C₁₃	—	4	32	no	—
196	C₂²×C₄×C₁₃	—	4	16	no	—
197	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
198	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
200	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
201	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	complemented
203	C₂²×C₄×C₁₃	#41	1	4	yes	—
204	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
212	C₁₃×C₄⋊C₄	—	2	16	no	—
213	C₁₃×C₄⋊C₄	—	2	8	no	—
214	C₁₃×C₄⋊C₄	—	2	8	no	—
215	C₁₃×C₄⋊C₄	—	2	16	no	—
216	C₁₃×C₄⋊C₄	—	2	8	no	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	complemented
218	C₁₃×C₂²⋊C₄	—	2	8	no	—
219	C₁₃×C₂²⋊C₄	—	2	16	no	—
220	C₁₃×C₂²⋊C₄	—	2	8	no	—
221	C₁₃×C₂²⋊C₄	—	2	16	no	—
222	C₁₃×C₂²⋊C₄	—	2	16	no	—
223	C₁₃×C₂²⋊C₄	—	2	16	no	—
224	C₁₃×C₂²⋊C₄	—	4	8	no	—
225	C₄²×C₁₃	—	2	8	no	—
226	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₂²×#121	C₂×C₁₃	1	2	yes	complemented
228	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₂³×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#2416	C₂×C₁₃	1	16	yes	direct product factor
232	C₂×#396	C₂×C₁₃	1	2	yes	complemented
233	C₂×#394	C₂×C₁₃	1	2	yes	complemented
234	C₂×#390	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂×#386	C₂×C₁₃	1	2	yes	complemented
237	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
238	C₂³×C₁₃	—	2	8	no	—
239	C₂³×C₁₃	—	2	8	no	—
240	C₂³×C₁₃	—	2	8	no	—
241	C₂³×C₁₃	—	2	8	no	—
242	C₂³×C₁₃	—	2	8	no	—
243	C₂³×C₁₃	—	2	8	no	—
244	C₂³×C₁₃	—	2	2	no	—
245	C₂³×C₁₃	—	2	2	no	—
246	C₂³×C₁₃	—	2	2	no	—
247	C₂³×C₁₃	—	2	2	no	—
248	C₂³×C₁₃	—	2	8	no	—
249	C₂³×C₁₃	—	2	8	no	—
250	C₂³×C₁₃	—	2	8	no	—
251	C₂³×C₁₃	—	2	2	no	—
252	C₂³×C₁₃	—	2	2	no	—
253	C₂³×C₁₃	—	2	2	no	—
254	C₂³×C₁₃	—	2	2	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	4	no	—
258	C₂³×C₁₃	—	2	4	no	—
259	C₂³×C₁₃	—	2	4	no	—
260	C₂³×C₁₃	—	2	4	no	—
261	C₂³×C₁₃	—	2	4	no	—
262	C₂³×C₁₃	—	2	4	no	—
263	C₂³×C₁₃	—	2	4	no	—
264	C₂³×C₁₃	—	4	4	no	—
265	C₂³×C₁₃	—	4	4	no	—
266	C₂³×C₁₃	—	4	4	no	—
267	C₂³×C₁₃	—	4	4	no	—
268	C₂³×C₁₃	—	4	8	no	—
269	C₂³×C₁₃	—	4	8	no	—
270	C₂³×C₁₃	—	4	8	no	—
271	C₂³×C₁₃	—	4	8	no	—
272	C₂³×C₁₃	—	4	8	no	—
273	C₂³×C₁₃	—	4	8	no	—
274	C₂³×C₁₃	—	4	8	no	—
275	C₂³×C₁₃	#121	1	16	yes	complemented
276	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
277	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
278	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
279	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
280	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
281	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
282	C₂³×C₁₃	C₂×#41	1	4	yes	—
283	C₂³×C₁₃	C₂×#41	1	2	yes	—
284	C₂³×C₁₃	C₂×#41	1	2	yes	—
285	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
286	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
287	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
288	D₄×C₁₃	—	2	32	no	—
289	D₄×C₁₃	—	4	32	no	—
290	D₄×C₁₃	—	4	32	no	—
291	D₄×C₁₃	—	4	16	no	—
292	C₂×C₄×C₁₃	—	2	8	no	—
293	C₂×C₄×C₁₃	—	2	8	no	—
294	C₂×C₄×C₁₃	—	2	16	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	4	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	4	no	—
301	C₂×C₄×C₁₃	—	2	32	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	4	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	4	no	—
307	C₂×C₄×C₁₃	—	2	4	no	—
308	C₂×C₄×C₁₃	—	2	4	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	4	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	4	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	4	32	no	—
315	C₂×C₄×C₁₃	—	4	4	no	—
316	C₂×C₄×C₁₃	—	4	8	no	—
317	C₂×C₄×C₁₃	—	4	4	no	—
318	C₂×C₄×C₁₃	—	4	8	no	—
319	C₂×C₄×C₁₃	—	4	16	no	—
320	C₂×C₄×C₁₃	#121	1	16	yes	complemented
321	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
322	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
324	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
325	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
326	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
327	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
328	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
329	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
330	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
331	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
332	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
333	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#121	—	2	16	no	—
335	C₂×#121	—	2	8	no	—
336	C₂×#121	—	2	8	no	—
337	C₂×#121	C₂²×C₁₃	1	16	yes	complemented
338	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
339	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
340	C₂×C₄×D₄	—	2	8	no	—
341	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
342	C₂²×C₄⋊C₄	—	2	8	no	—
343	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
344	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
345	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
346	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
347	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
348	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
349	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
350	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
351	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
352	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
353	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
354	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
355	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
356	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
357	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
358	#396	C₂²×C₁₃	1	16	yes	complemented
359	#394	C₂²×C₁₃	1	16	yes	complemented
360	#390	C₂²×C₁₃	1	8	yes	complemented
361	#389	C₂²×C₁₃	1	8	yes	complemented
362	#386	C₂²×C₁₃	1	16	yes	complemented
363	#380	C₂²×C₁₃	1	8	yes	complemented
364	C₂×#95	C₂²×C₁₃	1	2	yes	—
365	C₂×#95	C₂²×C₁₃	1	2	yes	—
366	C₂²×C₁₃	—	2	4	no	—
367	C₂²×C₁₃	—	2	32	no	—
368	C₂²×C₁₃	—	2	4	no	—
369	C₂²×C₁₃	—	2	4	no	—
370	C₂²×C₁₃	—	2	4	no	—
371	C₂²×C₁₃	—	2	4	no	—
372	C₂²×C₁₃	—	2	4	no	—
373	C₂²×C₁₃	—	2	4	no	—
374	C₂²×C₁₃	—	2	4	no	—
375	C₂²×C₁₃	—	2	4	no	—
376	C₂²×C₁₃	—	4	2	no	—
377	C₂²×C₁₃	—	4	16	no	—
378	C₂²×C₁₃	—	4	2	no	—
379	C₂²×C₁₃	—	4	2	no	—
380	C₂²×C₁₃	—	4	2	no	—
381	C₂²×C₁₃	—	4	4	no	—
382	C₂²×C₁₃	—	4	4	no	—
383	C₂²×C₁₃	—	4	4	no	—
384	C₂²×C₁₃	—	4	4	no	—
385	C₂²×C₁₃	—	4	4	no	—
386	C₂²×C₁₃	—	4	4	no	—
387	C₂²×C₁₃	—	4	4	no	—
388	C₂²×C₁₃	—	8	16	no	—
389	C₂²×C₁₃	C₂×#121	1	4	yes	—
390	C₂²×C₁₃	C₂×#121	1	4	yes	—
391	C₂²×C₁₃	C₂×#121	1	8	yes	complemented
392	C₂²×C₁₃	#537	1	4	yes	—
393	C₂²×C₁₃	D₄²	1	4	yes	—
394	C₂²×C₁₃	#547	1	4	yes	—
395	C₂²×C₁₃	#548	1	4	yes	—
396	C₂²×C₁₃	#553	1	4	yes	—
397	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
398	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
399	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
400	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
401	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
402	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
404	C₄×C₁₃	—	2	4	no	—
405	C₄×C₁₃	—	2	4	no	—
406	C₄×C₁₃	—	2	8	no	—
407	C₄×C₁₃	—	4	2	no	—
408	C₄×C₁₃	—	4	4	no	—
409	C₄×C₁₃	—	4	2	no	—
410	C₄×C₁₃	—	4	4	no	—
411	C₄×C₁₃	C₂×#121	1	8	yes	complemented
412	C₂⁵	C₂³×C₁₃	1	2	yes	—
413	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
414	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
415	C₂²×D₄	—	2	4	no	—
416	C₂²×D₄	—	2	4	no	—
417	C₂²×D₄	—	2	8	no	—
418	C₂²×D₄	—	2	8	no	—
419	C₂²×D₄	—	2	8	no	—
420	C₂²×D₄	—	2	8	no	—
421	C₂²×D₄	—	2	8	no	—
422	C₂²×D₄	—	2	4	no	—
423	C₂²×D₄	—	2	4	no	—
424	C₂²×D₄	—	2	4	no	—
425	C₂²×D₄	—	4	4	no	—
426	C₂²×D₄	D₄×C₁₃	1	8	yes	complemented
427	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
428	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
429	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
430	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
431	C₂³×C₄	—	2	4	no	—
432	C₂³×C₄	—	2	4	no	—
433	C₂³×C₄	—	2	8	no	—
434	C₂³×C₄	—	2	8	no	—
435	C₂³×C₄	—	2	4	no	—
436	C₂³×C₄	—	2	4	no	—
437	C₂³×C₄	—	2	4	no	—
438	C₂³×C₄	—	4	4	no	—
439	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
440	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
442	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
444	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
445	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
446	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
449	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
450	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
451	#121	—	2	64	no	—
452	#121	—	2	32	no	—
453	#121	—	2	32	no	—
454	C₄×D₄	—	2	32	no	—
455	C₂×C₄⋊C₄	—	2	8	no	—
456	C₂×C₄⋊C₄	—	2	4	no	—
457	C₂×C₄⋊C₄	—	2	4	no	—
458	C₂×C₄⋊C₄	—	2	8	no	—
459	C₂×C₄⋊C₄	—	2	4	no	—
460	C₂×C₄⋊C₄	—	2	32	no	—
461	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	complemented
462	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
465	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
468	C₂×C₂²⋊C₄	—	2	4	no	—
469	C₂×C₂²⋊C₄	—	2	8	no	—
470	C₂×C₂²⋊C₄	—	2	4	no	—
471	C₂×C₂²⋊C₄	—	2	8	no	—
472	C₂×C₂²⋊C₄	—	2	8	no	—
473	C₂×C₂²⋊C₄	—	2	8	no	—
474	C₂×C₂²⋊C₄	—	4	4	no	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
482	C₂×C₄²	—	2	4	no	—
483	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
484	#95	C₂³×C₁₃	1	8	yes	—
485	#95	C₂³×C₁₃	1	8	yes	—
486	C₂×C₁₃	—	2	8	no	—
487	C₂×C₁₃	—	4	4	no	—
488	C₂×C₁₃	—	8	4	no	—
489	C₂×C₁₃	#2416	1	8	yes	direct product factor
490	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
491	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
492	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
493	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
494	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
495	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
496	C₂×C₁₃	C₂×#553	1	1	yes	characteristic
497	C₂⁴	—	2	2	no	—
498	C₂⁴	—	2	2	no	—
499	C₂⁴	—	2	2	no	—
500	C₂⁴	—	2	2	no	—
501	C₂⁴	—	2	2	no	—
502	C₂⁴	—	2	2	no	—
503	C₂⁴	—	2	2	no	—
504	C₂⁴	—	2	2	no	—
505	C₂⁴	—	2	2	no	—
506	C₂⁴	—	2	2	no	—
507	C₂⁴	—	2	4	no	—
508	C₂⁴	—	2	4	no	—
509	C₂⁴	—	2	4	no	—
510	C₂⁴	—	2	4	no	—
511	C₂⁴	—	2	4	no	—
512	C₂⁴	—	2	4	no	—
513	C₂⁴	—	2	4	no	—
514	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
515	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
516	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
517	C₂⁴	C₁₃×#41	1	4	yes	—
518	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
519	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
520	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
521	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
522	C₂×D₄	—	2	32	no	—
523	C₂×D₄	—	2	8	no	—
524	C₂×D₄	—	2	8	no	—
525	C₂×D₄	—	2	16	no	—
526	C₂×D₄	—	2	16	no	—
527	C₂×D₄	—	2	16	no	—
528	C₂×D₄	—	2	16	no	—
529	C₂×D₄	—	2	16	no	—
530	C₂×D₄	—	2	8	no	—
531	C₂×D₄	—	2	8	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	4	8	no	—
534	C₂×D₄	—	4	32	no	—
535	C₂×D₄	—	4	32	no	—
536	C₂×D₄	—	4	16	no	—
537	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	complemented
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	32	no	—
545	C₂²×C₄	—	2	8	no	—
546	C₂²×C₄	—	2	8	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	16	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	16	no	—
561	C₂²×C₄	—	2	8	no	—
562	C₂²×C₄	—	2	8	no	—
563	C₂²×C₄	—	2	8	no	—
564	C₂²×C₄	—	4	8	no	—
565	C₂²×C₄	—	4	32	no	—
566	C₂²×C₄	—	4	16	no	—
567	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
568	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
569	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
570	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
571	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
572	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	complemented
573	C₂²×C₄	C₁₃×#41	1	4	yes	—
574	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
577	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
578	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
579	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
582	C₄⋊C₄	—	2	16	no	—
583	C₄⋊C₄	—	2	8	no	—
584	C₄⋊C₄	—	2	8	no	—
585	C₄⋊C₄	—	2	16	no	—
586	C₄⋊C₄	—	2	8	no	—
587	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	complemented
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	16	no	—
590	C₂²⋊C₄	—	2	8	no	—
591	C₂²⋊C₄	—	2	16	no	—
592	C₂²⋊C₄	—	2	16	no	—
593	C₂²⋊C₄	—	2	16	no	—
594	C₂²⋊C₄	—	4	8	no	—
595	C₄²	—	2	8	no	—
596	C₁₃	C₂×#2416	1	1	yes	characteristic, direct product factor, Sylow
597	C₂³	—	2	8	no	—
598	C₂³	—	2	8	no	—
599	C₂³	—	2	8	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	2	8	no	—
602	C₂³	—	2	8	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	8	no	—
608	C₂³	—	2	8	no	—
609	C₂³	—	2	8	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	4	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	4	no	—
622	C₂³	—	2	4	no	—
623	C₂³	—	4	4	no	—
624	C₂³	—	4	4	no	—
625	C₂³	—	4	4	no	—
626	C₂³	—	4	4	no	—
627	C₂³	—	4	8	no	—
628	C₂³	—	4	8	no	—
629	C₂³	—	4	8	no	—
630	C₂³	—	4	8	no	—
631	C₂³	—	4	8	no	—
632	C₂³	—	4	8	no	—
633	C₂³	—	4	8	no	—
634	C₂³	C₁₃×#121	1	16	yes	complemented
635	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
636	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
637	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
638	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
639	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
640	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
641	C₂³	C₂×C₁₃×#41	1	4	yes	—
642	C₂³	C₂×C₁₃×#41	1	2	yes	—
643	C₂³	C₂×C₁₃×#41	1	2	yes	—
644	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
645	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
646	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
647	D₄	—	2	32	no	—
648	D₄	—	4	32	no	—
649	D₄	—	4	32	no	—
650	D₄	—	4	16	no	—
651	C₂×C₄	—	2	8	no	—
652	C₂×C₄	—	2	8	no	—
653	C₂×C₄	—	2	16	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	32	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	4	32	no	—
674	C₂×C₄	—	4	4	no	—
675	C₂×C₄	—	4	8	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	4	8	no	—
678	C₂×C₄	—	4	16	no	—
679	C₂×C₄	C₁₃×#121	1	16	yes	complemented
680	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
681	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
682	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
683	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
684	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
685	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	32	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	2	4	no	—
692	C₂²	—	2	4	no	—
693	C₂²	—	2	4	no	—
694	C₂²	—	2	4	no	—
695	C₂²	—	2	4	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	16	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	4	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	4	4	no	—
704	C₂²	—	4	4	no	—
705	C₂²	—	4	4	no	—
706	C₂²	—	4	4	no	—
707	C₂²	—	4	4	no	—
708	C₂²	—	8	16	no	—
709	C₂²	C₂×C₁₃×#121	1	4	yes	—
710	C₂²	C₂×C₁₃×#121	1	4	yes	—
711	C₂²	C₂×C₁₃×#121	1	8	yes	complemented
712	C₂²	C₁₃×#537	1	4	yes	—
713	C₂²	D₄²×C₁₃	1	4	yes	—
714	C₂²	C₁₃×#547	1	4	yes	—
715	C₂²	C₁₃×#548	1	4	yes	—
716	C₂²	C₁₃×#553	1	4	yes	—
717	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
718	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
719	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
720	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
721	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
722	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
723	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
724	C₄	—	2	4	no	—
725	C₄	—	2	4	no	—
726	C₄	—	2	8	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	4	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	4	no	—
731	C₄	C₂×C₁₃×#121	1	8	yes	complemented
732	C₂	—	2	8	no	—
733	C₂	—	4	4	no	—
734	C₂	—	8	4	no	—
735	C₂	C₁₃×#2416	1	8	yes	direct product factor
736	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
737	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
738	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
739	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
740	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
741	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
742	C₂	C₂×C₁₃×#553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#121	C₂	semidirect
2. C₂²×C₁₃×#121	C₂	semidirect
3. C₂²×C₁₃×#121	C₂	semidirect
4. C₂²×C₄×D₄×C₁₃	C₂	semidirect
5. C₂³×C₁₃×C₄⋊C₄	C₂	semidirect
6. C₁₃×#2416	C₂	direct (N × H)
7. C₂×C₁₃×#396	C₂	semidirect
8. C₂×C₁₃×#394	C₂	semidirect
9. C₂×C₁₃×#390	C₂	semidirect
10. C₂×C₁₃×#389	C₂	semidirect
11. C₂×C₁₃×#386	C₂	semidirect
12. C₂×C₁₃×#380	C₂	semidirect
23. C₂×C₁₃×#121	C₂²	semidirect
24. C₂×C₁₃×#121	C₂²	semidirect
25. C₂×C₁₃×#121	C₂²	semidirect
27. C₂×C₄×D₄×C₁₃	C₂²	semidirect
35. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
44. C₁₃×#396	C₂²	semidirect
45. C₁₃×#394	C₂²	semidirect
46. C₁₃×#390	C₂²	semidirect
47. C₁₃×#389	C₂²	semidirect
48. C₁₃×#386	C₂²	semidirect
49. C₁₃×#380	C₂²	semidirect
66. C₂²×D₄×C₁₃	D₄	semidirect
79. C₂³×C₄×C₁₃	D₄	semidirect
101. C₂×C₁₃×C₄⋊C₄	D₄	semidirect
126. C₂×#2416	C₁₃	direct (N × H)
167. C₂×D₄×C₁₃	C₂×D₄	semidirect
202. C₂²×C₄×C₁₃	C₂×D₄	semidirect
217. C₁₃×C₄⋊C₄	C₂×D₄	semidirect
226. C₂²×#121	C₂×C₁₃	semidirect
227. C₂²×#121	C₂×C₁₃	semidirect
228. C₂²×#121	C₂×C₁₃	semidirect
229. C₂²×C₄×D₄	C₂×C₁₃	semidirect
230. C₂³×C₄⋊C₄	C₂×C₁₃	semidirect
231. #2416	C₂×C₁₃	direct (N × H)
232. C₂×#396	C₂×C₁₃	semidirect
233. C₂×#394	C₂×C₁₃	semidirect
234. C₂×#390	C₂×C₁₃	semidirect
235. C₂×#389	C₂×C₁₃	semidirect
236. C₂×#386	C₂×C₁₃	semidirect
237. C₂×#380	C₂×C₁₃	semidirect
275. C₂³×C₁₃	#121	semidirect
320. C₂×C₄×C₁₃	#121	semidirect
337. C₂×#121	C₂²×C₁₃	semidirect
338. C₂×#121	C₂²×C₁₃	semidirect
339. C₂×#121	C₂²×C₁₃	semidirect
341. C₂×C₄×D₄	C₂²×C₁₃	semidirect
349. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
358. #396	C₂²×C₁₃	semidirect
359. #394	C₂²×C₁₃	semidirect
360. #390	C₂²×C₁₃	semidirect
361. #389	C₂²×C₁₃	semidirect
362. #386	C₂²×C₁₃	semidirect
363. #380	C₂²×C₁₃	semidirect
391. C₂²×C₁₃	C₂×#121	semidirect
411. C₄×C₁₃	C₂×#121	semidirect
426. C₂²×D₄	D₄×C₁₃	semidirect
439. C₂³×C₄	D₄×C₁₃	semidirect
461. C₂×C₄⋊C₄	D₄×C₁₃	semidirect
489. C₂×C₁₃	#2416	direct (N × H)
537. C₂×D₄	C₂×D₄×C₁₃	semidirect
572. C₂²×C₄	C₂×D₄×C₁₃	semidirect
587. C₄⋊C₄	C₂×D₄×C₁₃	semidirect
596. C₁₃	C₂×#2416	direct (N × H)
634. C₂³	C₁₃×#121	semidirect
679. C₂×C₄	C₁₃×#121	semidirect
711. C₂²	C₂×C₁₃×#121	semidirect
731. C₄	C₂×C₁₃×#121	semidirect
735. C₂	C₁₃×#2416	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×#121	2
C₂²×C₄×D₄×C₁₃	2
C₂³×C₁₃×C₄⋊C₄	2
C₁₃×#2416	2
C₂×C₁₃×#396	2
C₂×C₁₃×#394	2
C₂×C₁₃×#390	2
C₂×C₁₃×#389	2
C₂×C₁₃×#386	2
C₂×C₁₃×#380	2
C₂×#2416	13

Subgroups — C2×C13×#2416 #15721011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2416 #15721011