Subgroups — C₁₃×#34986 #15721325

Order 3328.

2902 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2849	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2626	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2617	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2613	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2466	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2459	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2456	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2455	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2322	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#120	C₂	1	2	yes	maximal, complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#538	—	2	8	no	—
20	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#123	C₂²	1	2	yes	—
23	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#120	C₂²	1	2	yes	—
29	C₂×C₁₃×#120	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	—	2	8	no	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
33	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
35	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#399	C₂²	1	2	yes	complemented
40	C₁₃×#397	C₂²	1	2	yes	complemented
41	C₁₃×#396	C₂²	1	4	yes	complemented
42	C₁₃×#394	C₂²	1	4	yes	—
43	C₁₃×#394	C₂²	1	4	yes	—
44	C₁₃×#394	C₂²	1	4	yes	complemented
45	C₁₃×#393	C₂²	1	2	yes	complemented
46	C₁₃×#392	C₂²	1	4	yes	—
47	C₁₃×#392	C₂²	1	4	yes	—
48	C₁₃×#392	C₂²	1	2	yes	complemented
49	C₁₃×#391	C₂²	1	2	yes	complemented
50	C₁₃×#390	C₂²	1	2	yes	complemented
51	C₁₃×#389	C₂²	1	4	yes	complemented
52	C₁₃×#389	C₂²	1	2	yes	complemented
53	C₁₃×#389	C₂²	1	2	yes	complemented
54	C₁₃×#388	C₂²	1	4	yes	complemented
55	C₁₃×#388	C₂²	1	4	yes	complemented
56	C₁₃×#388	C₂²	1	4	yes	complemented
57	C₁₃×#388	C₂²	1	4	yes	complemented
58	C₁₃×#387	C₂²	1	4	yes	complemented
59	C₁₃×#387	C₂²	1	4	yes	complemented
60	C₁₃×#386	C₂²	1	2	yes	—
61	C₁₃×#386	C₂²	1	2	yes	—
62	C₁₃×#386	C₂²	1	4	yes	complemented
63	C₁₃×#386	C₂²	1	4	yes	complemented
64	C₁₃×#385	C₂²	1	2	yes	—
65	C₁₃×#385	C₂²	1	2	yes	—
66	C₁₃×#385	C₂²	1	4	yes	complemented
67	C₁₃×#385	C₂²	1	4	yes	complemented
68	C₁₃×#385	C₂²	1	4	yes	complemented
69	C₁₃×#381	C₂²	1	2	yes	—
70	C₁₃×#381	C₂²	1	4	yes	complemented
71	C₁₃×#380	C₂²	1	1	yes	characteristic
72	C₁₃×#380	C₂²	1	1	yes	characteristic
73	C₁₃×#379	C₂²	1	2	yes	—
74	C₁₃×#379	C₂²	1	2	yes	—
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
76	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
77	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
78	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃	—	2	4	no	—
81	C₂²×D₄×C₁₃	—	2	4	no	—
82	C₂²×D₄×C₁₃	—	2	4	no	—
83	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
87	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃	—	2	4	no	—
90	C₂³×C₄×C₁₃	—	2	4	no	—
91	C₂³×C₄×C₁₃	—	4	4	no	—
92	C₂³×C₄×C₁₃	—	4	4	no	—
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
95	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#126	—	2	8	no	—
102	C₁₃×#124	—	2	8	no	—
103	C₁₃×#123	—	2	8	no	—
104	C₁₃×#123	—	2	8	no	—
105	C₁₃×#123	—	4	8	no	—
106	C₁₃×C₂²⋊Q₈	—	2	4	no	—
107	C₁₃×#121	—	2	4	no	—
108	C₁₃×#121	—	2	8	no	—
109	C₁₃×#120	—	2	8	no	—
110	C₁₃×#120	—	2	8	no	—
111	C₄×D₄×C₁₃	—	2	8	no	—
112	C₄×D₄×C₁₃	—	2	16	no	—
113	C₄×D₄×C₁₃	—	2	16	no	—
114	C₄×D₄×C₁₃	—	4	8	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
127	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₄²×C₁₃	—	2	4	no	—
148	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
150	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
152	C₁₃×#95	C₂³	1	4	yes	—
153	C₁₃×#95	C₂³	1	4	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	2	yes	—
156	C₁₃×#95	C₂³	1	2	yes	—
157	C₁₃×#95	C₂³	1	4	yes	—
158	C₁₃×#95	C₂³	1	4	yes	—
159	C₁₃×#95	C₂³	1	4	yes	—
160	C₁₃×#95	C₂³	1	4	yes	—
161	#34986	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂⁴×C₁₃	—	2	2	no	—
163	C₂⁴×C₁₃	—	2	2	no	—
164	C₂⁴×C₁₃	—	2	2	no	—
165	C₂⁴×C₁₃	—	2	2	no	—
166	C₂⁴×C₁₃	—	4	2	no	—
167	C₂⁴×C₁₃	—	4	2	no	—
168	C₂⁴×C₁₃	—	4	2	no	—
169	C₂⁴×C₁₃	—	4	2	no	—
170	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
171	C₂⁴×C₁₃	#41	1	4	yes	—
172	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
173	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
174	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
175	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×Q₈×C₁₃	—	2	2	no	—
177	C₂×Q₈×C₁₃	—	4	2	no	—
178	C₂×D₄×C₁₃	—	2	32	no	—
179	C₂×D₄×C₁₃	—	2	8	no	—
180	C₂×D₄×C₁₃	—	2	8	no	—
181	C₂×D₄×C₁₃	—	2	4	no	—
182	C₂×D₄×C₁₃	—	2	8	no	—
183	C₂×D₄×C₁₃	—	2	4	no	—
184	C₂×D₄×C₁₃	—	2	4	no	—
185	C₂×D₄×C₁₃	—	2	4	no	—
186	C₂×D₄×C₁₃	—	2	4	no	—
187	C₂×D₄×C₁₃	—	2	2	no	—
188	C₂×D₄×C₁₃	—	2	8	no	—
189	C₂×D₄×C₁₃	—	4	4	no	—
190	C₂×D₄×C₁₃	—	4	4	no	—
191	C₂×D₄×C₁₃	—	4	4	no	—
192	C₂×D₄×C₁₃	—	4	2	no	—
193	C₂×D₄×C₁₃	—	4	4	no	—
194	C₂²×C₄×C₁₃	—	2	2	no	—
195	C₂²×C₄×C₁₃	—	2	2	no	—
196	C₂²×C₄×C₁₃	—	2	2	no	—
197	C₂²×C₄×C₁₃	—	2	4	no	—
198	C₂²×C₄×C₁₃	—	2	2	no	—
199	C₂²×C₄×C₁₃	—	2	8	no	—
200	C₂²×C₄×C₁₃	—	2	8	no	—
201	C₂²×C₄×C₁₃	—	2	8	no	—
202	C₂²×C₄×C₁₃	—	2	8	no	—
203	C₂²×C₄×C₁₃	—	2	4	no	—
204	C₂²×C₄×C₁₃	—	4	2	no	—
205	C₂²×C₄×C₁₃	—	4	4	no	—
206	C₂²×C₄×C₁₃	—	4	4	no	—
207	C₂²×C₄×C₁₃	—	4	2	no	—
208	C₂²×C₄×C₁₃	—	4	2	no	—
209	C₂²×C₄×C₁₃	—	4	4	no	—
210	C₂²×C₄×C₁₃	—	4	16	no	—
211	C₂²×C₄×C₁₃	—	4	16	no	—
212	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₁₃	#41	1	4	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
226	C₁₃×C₄⋊C₄	—	2	8	no	—
227	C₁₃×C₄⋊C₄	—	2	4	no	—
228	C₁₃×C₄⋊C₄	—	2	4	no	—
229	C₁₃×C₄⋊C₄	—	2	2	no	—
230	C₁₃×C₄⋊C₄	—	2	2	no	—
231	C₁₃×C₄⋊C₄	—	2	8	no	—
232	C₁₃×C₄⋊C₄	—	2	8	no	—
233	C₁₃×C₄⋊C₄	—	4	2	no	—
234	C₁₃×C₄⋊C₄	—	4	2	no	—
235	C₁₃×C₄⋊C₄	—	4	4	no	—
236	C₁₃×C₂²⋊C₄	—	2	4	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	—	2	4	no	—
239	C₁₃×C₂²⋊C₄	—	2	8	no	—
240	C₁₃×C₂²⋊C₄	—	2	4	no	—
241	C₁₃×C₂²⋊C₄	—	2	4	no	—
242	C₁₃×C₂²⋊C₄	—	2	4	no	—
243	C₁₃×C₂²⋊C₄	—	2	4	no	—
244	C₁₃×C₂²⋊C₄	—	2	4	no	—
245	C₁₃×C₂²⋊C₄	—	2	4	no	—
246	C₁₃×C₂²⋊C₄	—	2	8	no	—
247	C₁₃×C₂²⋊C₄	—	2	8	no	—
248	C₁₃×C₂²⋊C₄	—	4	4	no	—
249	C₁₃×C₂²⋊C₄	—	4	4	no	—
250	C₁₃×C₂²⋊C₄	—	4	4	no	—
251	C₁₃×C₂²⋊C₄	—	4	4	no	—
252	C₁₃×C₂²⋊C₄	—	4	4	no	—
253	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
254	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
255	C₄²×C₁₃	—	2	4	no	—
256	C₄²×C₁₃	—	2	4	no	—
257	C₄²×C₁₃	—	2	4	no	—
258	C₄²×C₁₃	—	4	4	no	—
259	C₂×#538	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#2855	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#2854	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2849	C₂×C₁₃	1	2	yes	complemented
264	#2626	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#2617	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#2613	C₂×C₁₃	1	2	yes	complemented
267	#2466	C₂×C₁₃	1	4	yes	complemented
268	#2459	C₂×C₁₃	1	4	yes	complemented
269	#2456	C₂×C₁₃	1	4	yes	complemented
270	#2455	C₂×C₁₃	1	4	yes	complemented
271	#2322	C₂×C₁₃	1	2	yes	complemented
272	#2312	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₄×#120	C₂×C₁₃	1	2	yes	complemented
274	C₂³×C₁₃	—	2	2	no	—
275	C₂³×C₁₃	—	2	2	no	—
276	C₂³×C₁₃	—	2	8	no	—
277	C₂³×C₁₃	—	2	8	no	—
278	C₂³×C₁₃	—	2	2	no	—
279	C₂³×C₁₃	—	2	2	no	—
280	C₂³×C₁₃	—	2	2	no	—
281	C₂³×C₁₃	—	2	2	no	—
282	C₂³×C₁₃	—	2	4	no	—
283	C₂³×C₁₃	—	2	4	no	—
284	C₂³×C₁₃	—	2	4	no	—
285	C₂³×C₁₃	—	2	4	no	—
286	C₂³×C₁₃	—	2	2	no	—
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	2	4	no	—
290	C₂³×C₁₃	—	2	4	no	—
291	C₂³×C₁₃	—	4	4	no	—
292	C₂³×C₁₃	—	4	4	no	—
293	C₂³×C₁₃	—	4	8	no	—
294	C₂³×C₁₃	—	4	4	no	—
295	C₂³×C₁₃	—	4	8	no	—
296	C₂³×C₁₃	—	4	4	no	—
297	C₂³×C₁₃	—	4	8	no	—
298	C₂³×C₁₃	—	4	8	no	—
299	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
300	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
301	C₂³×C₁₃	C₂×#41	1	4	yes	—
302	C₂³×C₁₃	C₂×#41	1	2	yes	—
303	C₂³×C₁₃	C₂×#41	1	2	yes	—
304	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
305	Q₈×C₁₃	—	8	2	no	—
306	D₄×C₁₃	—	2	32	no	—
307	D₄×C₁₃	—	4	16	no	—
308	D₄×C₁₃	—	4	8	no	—
309	D₄×C₁₃	—	8	2	no	—
310	D₄×C₁₃	—	8	4	no	—
311	D₄×C₁₃	—	8	4	no	—
312	C₂×C₄×C₁₃	—	2	8	no	—
313	C₂×C₄×C₁₃	—	2	8	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	4	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	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	4	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	4	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	4	no	—
330	C₂×C₄×C₁₃	—	2	4	no	—
331	C₂×C₄×C₁₃	—	2	4	no	—
332	C₂×C₄×C₁₃	—	2	4	no	—
333	C₂×C₄×C₁₃	—	2	4	no	—
334	C₂×C₄×C₁₃	—	2	4	no	—
335	C₂×C₄×C₁₃	—	2	4	no	—
336	C₂×C₄×C₁₃	—	4	4	no	—
337	C₂×C₄×C₁₃	—	4	4	no	—
338	C₂×C₄×C₁₃	—	4	16	no	—
339	C₂×C₄×C₁₃	—	4	16	no	—
340	C₂×C₄×C₁₃	—	4	4	no	—
341	C₂×C₄×C₁₃	—	8	4	no	—
342	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
346	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
347	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
348	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
349	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
350	#538	—	2	8	no	—
351	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
352	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
353	C₂×#123	C₂²×C₁₃	1	2	yes	—
354	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
355	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
356	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
359	C₂×#120	C₂²×C₁₃	1	2	yes	—
360	C₂×#120	C₂²×C₁₃	1	2	yes	—
361	C₂×C₄×D₄	—	2	8	no	—
362	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
363	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
364	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
365	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
366	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
367	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
368	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
369	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
370	#399	C₂²×C₁₃	1	2	yes	complemented
371	#397	C₂²×C₁₃	1	2	yes	complemented
372	#396	C₂²×C₁₃	1	4	yes	complemented
373	#394	C₂²×C₁₃	1	4	yes	—
374	#394	C₂²×C₁₃	1	4	yes	—
375	#394	C₂²×C₁₃	1	4	yes	complemented
376	#393	C₂²×C₁₃	1	2	yes	complemented
377	#392	C₂²×C₁₃	1	4	yes	—
378	#392	C₂²×C₁₃	1	4	yes	—
379	#392	C₂²×C₁₃	1	2	yes	complemented
380	#391	C₂²×C₁₃	1	2	yes	complemented
381	#390	C₂²×C₁₃	1	2	yes	complemented
382	#389	C₂²×C₁₃	1	4	yes	complemented
383	#389	C₂²×C₁₃	1	2	yes	complemented
384	#389	C₂²×C₁₃	1	2	yes	complemented
385	#388	C₂²×C₁₃	1	4	yes	complemented
386	#388	C₂²×C₁₃	1	4	yes	complemented
387	#388	C₂²×C₁₃	1	4	yes	complemented
388	#388	C₂²×C₁₃	1	4	yes	complemented
389	#387	C₂²×C₁₃	1	4	yes	complemented
390	#387	C₂²×C₁₃	1	4	yes	complemented
391	#386	C₂²×C₁₃	1	2	yes	—
392	#386	C₂²×C₁₃	1	2	yes	—
393	#386	C₂²×C₁₃	1	4	yes	complemented
394	#386	C₂²×C₁₃	1	4	yes	complemented
395	#385	C₂²×C₁₃	1	2	yes	—
396	#385	C₂²×C₁₃	1	2	yes	—
397	#385	C₂²×C₁₃	1	4	yes	complemented
398	#385	C₂²×C₁₃	1	4	yes	complemented
399	#385	C₂²×C₁₃	1	4	yes	complemented
400	#381	C₂²×C₁₃	1	2	yes	—
401	#381	C₂²×C₁₃	1	4	yes	complemented
402	#380	C₂²×C₁₃	1	1	yes	characteristic
403	#380	C₂²×C₁₃	1	1	yes	characteristic
404	#379	C₂²×C₁₃	1	2	yes	—
405	#379	C₂²×C₁₃	1	2	yes	—
406	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
407	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
408	C₂²×C₁₃	—	2	4	no	—
409	C₂²×C₁₃	—	2	2	no	—
410	C₂²×C₁₃	—	2	2	no	—
411	C₂²×C₁₃	—	2	4	no	—
412	C₂²×C₁₃	—	2	4	no	—
413	C₂²×C₁₃	—	2	4	no	—
414	C₂²×C₁₃	—	2	8	no	—
415	C₂²×C₁₃	—	2	4	no	—
416	C₂²×C₁₃	—	2	4	no	—
417	C₂²×C₁₃	—	4	16	no	—
418	C₂²×C₁₃	—	4	16	no	—
419	C₂²×C₁₃	—	4	4	no	—
420	C₂²×C₁₃	—	4	2	no	—
421	C₂²×C₁₃	—	4	2	no	—
422	C₂²×C₁₃	—	4	4	no	—
423	C₂²×C₁₃	—	4	4	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	—	4	4	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	4	4	no	—
429	C₂²×C₁₃	#525	1	4	yes	—
430	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
431	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
432	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
433	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
434	C₂²×C₁₃	#585	1	2	yes	—
435	C₄×C₁₃	—	2	4	no	—
436	C₄×C₁₃	—	2	4	no	—
437	C₄×C₁₃	—	2	4	no	—
438	C₄×C₁₃	—	2	2	no	—
439	C₄×C₁₃	—	2	2	no	—
440	C₄×C₁₃	—	4	2	no	—
441	C₄×C₁₃	—	4	4	no	—
442	C₄×C₁₃	—	4	2	no	—
443	C₄×C₁₃	—	4	2	no	—
444	C₄×C₁₃	—	4	2	no	—
445	C₄×C₁₃	—	4	4	no	—
446	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
447	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
448	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
449	C₂²×D₄	—	2	4	no	—
450	C₂²×D₄	—	2	4	no	—
451	C₂²×D₄	—	2	4	no	—
452	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
453	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
454	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
455	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
456	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
457	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₂³×C₄	—	2	4	no	—
459	C₂³×C₄	—	2	4	no	—
460	C₂³×C₄	—	4	4	no	—
461	C₂³×C₄	—	4	4	no	—
462	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
464	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
465	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
468	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
470	#126	—	2	8	no	—
471	#124	—	2	8	no	—
472	#123	—	2	8	no	—
473	#123	—	2	8	no	—
474	#123	—	4	8	no	—
475	C₂²⋊Q₈	—	2	4	no	—
476	#121	—	2	4	no	—
477	#121	—	2	8	no	—
478	#120	—	2	8	no	—
479	#120	—	2	8	no	—
480	C₄×D₄	—	2	8	no	—
481	C₄×D₄	—	2	16	no	—
482	C₄×D₄	—	2	16	no	—
483	C₄×D₄	—	4	8	no	—
484	C₂×C₄⋊C₄	—	2	4	no	—
485	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
495	C₂×C₂²⋊C₄	—	2	4	no	—
496	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
497	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
516	C₂×C₄²	—	2	4	no	—
517	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
518	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
519	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
520	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
521	#95	C₂³×C₁₃	1	4	yes	—
522	#95	C₂³×C₁₃	1	4	yes	—
523	#95	C₂³×C₁₃	1	4	yes	—
524	#95	C₂³×C₁₃	1	2	yes	—
525	#95	C₂³×C₁₃	1	2	yes	—
526	#95	C₂³×C₁₃	1	4	yes	—
527	#95	C₂³×C₁₃	1	4	yes	—
528	#95	C₂³×C₁₃	1	4	yes	—
529	#95	C₂³×C₁₃	1	4	yes	—
530	C₂×C₁₃	—	2	4	no	—
531	C₂×C₁₃	—	4	4	no	—
532	C₂×C₁₃	—	4	4	no	—
533	C₂×C₁₃	—	8	2	no	—
534	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
535	C₂×C₁₃	#3459	1	2	yes	—
536	C₂×C₁₃	#3484	1	1	yes	characteristic
537	C₂×C₁₃	#3485	1	1	yes	characteristic
538	C₂×C₁₃	#3506	1	2	yes	—
539	C₂⁴	—	2	2	no	—
540	C₂⁴	—	2	2	no	—
541	C₂⁴	—	2	2	no	—
542	C₂⁴	—	2	2	no	—
543	C₂⁴	—	4	2	no	—
544	C₂⁴	—	4	2	no	—
545	C₂⁴	—	4	2	no	—
546	C₂⁴	—	4	2	no	—
547	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
548	C₂⁴	C₁₃×#41	1	4	yes	—
549	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
550	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
551	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
552	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	4	2	no	—
555	C₂×D₄	—	2	32	no	—
556	C₂×D₄	—	2	8	no	—
557	C₂×D₄	—	2	8	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	8	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	4	2	no	—
570	C₂×D₄	—	4	4	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	8	no	—
577	C₂²×C₄	—	2	8	no	—
578	C₂²×C₄	—	2	8	no	—
579	C₂²×C₄	—	2	8	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	4	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	—	4	16	no	—
588	C₂²×C₄	—	4	16	no	—
589	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
590	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
591	C₂²×C₄	C₁₃×#41	1	4	yes	—
592	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
593	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
595	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
603	C₄⋊C₄	—	2	8	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	8	no	—
609	C₄⋊C₄	—	2	8	no	—
610	C₄⋊C₄	—	4	4	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	8	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	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	8	no	—
624	C₂²⋊C₄	—	2	8	no	—
625	C₂²⋊C₄	—	4	4	no	—
626	C₂²⋊C₄	—	4	4	no	—
627	C₂²⋊C₄	—	4	4	no	—
628	C₂²⋊C₄	—	4	4	no	—
629	C₂²⋊C₄	—	4	4	no	—
630	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
631	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	4	4	no	—
636	C₁₃	#34986	1	1	yes	characteristic, direct product factor, Sylow
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	8	no	—
640	C₂³	—	2	8	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	4	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	2	4	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	4	no	—
653	C₂³	—	2	4	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	4	4	no	—
656	C₂³	—	4	8	no	—
657	C₂³	—	4	4	no	—
658	C₂³	—	4	8	no	—
659	C₂³	—	4	4	no	—
660	C₂³	—	4	8	no	—
661	C₂³	—	4	8	no	—
662	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
663	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
664	C₂³	C₂×C₁₃×#41	1	4	yes	—
665	C₂³	C₂×C₁₃×#41	1	2	yes	—
666	C₂³	C₂×C₁₃×#41	1	2	yes	—
667	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
668	Q₈	—	8	2	no	—
669	D₄	—	2	32	no	—
670	D₄	—	4	16	no	—
671	D₄	—	4	8	no	—
672	D₄	—	8	2	no	—
673	D₄	—	8	4	no	—
674	D₄	—	8	4	no	—
675	C₂×C₄	—	2	8	no	—
676	C₂×C₄	—	2	8	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	16	no	—
702	C₂×C₄	—	4	16	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	8	4	no	—
705	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
706	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
707	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
708	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
709	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
710	C₂²	—	2	4	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	4	no	—
714	C₂²	—	2	4	no	—
715	C₂²	—	2	4	no	—
716	C₂²	—	2	8	no	—
717	C₂²	—	2	4	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	4	16	no	—
720	C₂²	—	4	16	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	4	no	—
731	C₂²	C₁₃×#525	1	4	yes	—
732	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
733	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
734	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
735	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
736	C₂²	C₁₃×#585	1	2	yes	—
737	C₄	—	2	4	no	—
738	C₄	—	2	4	no	—
739	C₄	—	2	4	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	4	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	4	no	—
748	C₂	—	2	4	no	—
749	C₂	—	4	4	no	—
750	C₂	—	4	4	no	—
751	C₂	—	8	2	no	—
752	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
753	C₂	C₁₃×#3459	1	2	yes	—
754	C₂	C₁₃×#3484	1	1	yes	characteristic
755	C₂	C₁₃×#3485	1	1	yes	characteristic
756	C₂	C₁₃×#3506	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#538	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃	C₂	semidirect
3. C₁₃×#2855	C₂	semidirect
4. C₁₃×#2854	C₂	semidirect
5. C₁₃×#2849	C₂	semidirect
6. C₁₃×#2626	C₂	semidirect
7. C₁₃×#2617	C₂	semidirect
8. C₁₃×#2613	C₂	semidirect
9. C₁₃×#2466	C₂	semidirect
10. C₁₃×#2459	C₂	semidirect
11. C₁₃×#2456	C₂	semidirect
12. C₁₃×#2455	C₂	semidirect
13. C₁₃×#2322	C₂	semidirect
14. C₁₃×#2312	C₂	semidirect
15. C₄×C₁₃×#120	C₂	semidirect
20. C₂×C₁₃×#126	C₂²	semidirect
21. C₂×C₁₃×#124	C₂²	semidirect
23. C₂×C₁₃×#123	C₂²	semidirect
24. C₂×C₁₃×#123	C₂²	semidirect
27. C₂×C₁₃×#121	C₂²	semidirect
34. C₂×C₄×D₄×C₁₃	C₂²	semidirect
39. C₁₃×#399	C₂²	semidirect
40. C₁₃×#397	C₂²	semidirect
41. C₁₃×#396	C₂²	semidirect
44. C₁₃×#394	C₂²	semidirect
45. C₁₃×#393	C₂²	semidirect
48. C₁₃×#392	C₂²	semidirect
49. C₁₃×#391	C₂²	semidirect
50. C₁₃×#390	C₂²	semidirect
51. C₁₃×#389	C₂²	semidirect
52. C₁₃×#389	C₂²	semidirect
53. C₁₃×#389	C₂²	semidirect
54. C₁₃×#388	C₂²	semidirect
55. C₁₃×#388	C₂²	semidirect
56. C₁₃×#388	C₂²	semidirect
57. C₁₃×#388	C₂²	semidirect
58. C₁₃×#387	C₂²	semidirect
59. C₁₃×#387	C₂²	semidirect
62. C₁₃×#386	C₂²	semidirect
63. C₁₃×#386	C₂²	semidirect
66. C₁₃×#385	C₂²	semidirect
67. C₁₃×#385	C₂²	semidirect
68. C₁₃×#385	C₂²	semidirect
70. C₁₃×#381	C₂²	semidirect
76. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
127. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
161. #34986	C₁₃	direct (N × H)
259. C₂×#538	C₂×C₁₃	semidirect
260. C₂²×C₄×D₄	C₂×C₁₃	semidirect
261. #2855	C₂×C₁₃	semidirect
262. #2854	C₂×C₁₃	semidirect
263. #2849	C₂×C₁₃	semidirect
264. #2626	C₂×C₁₃	semidirect
265. #2617	C₂×C₁₃	semidirect
266. #2613	C₂×C₁₃	semidirect
267. #2466	C₂×C₁₃	semidirect
268. #2459	C₂×C₁₃	semidirect
269. #2456	C₂×C₁₃	semidirect
270. #2455	C₂×C₁₃	semidirect
271. #2322	C₂×C₁₃	semidirect
272. #2312	C₂×C₁₃	semidirect
273. C₄×#120	C₂×C₁₃	semidirect
351. C₂×#126	C₂²×C₁₃	semidirect
352. C₂×#124	C₂²×C₁₃	semidirect
354. C₂×#123	C₂²×C₁₃	semidirect
355. C₂×#123	C₂²×C₁₃	semidirect
358. C₂×#121	C₂²×C₁₃	semidirect
365. C₂×C₄×D₄	C₂²×C₁₃	semidirect
370. #399	C₂²×C₁₃	semidirect
371. #397	C₂²×C₁₃	semidirect
372. #396	C₂²×C₁₃	semidirect
375. #394	C₂²×C₁₃	semidirect
376. #393	C₂²×C₁₃	semidirect
379. #392	C₂²×C₁₃	semidirect
380. #391	C₂²×C₁₃	semidirect
381. #390	C₂²×C₁₃	semidirect
382. #389	C₂²×C₁₃	semidirect
383. #389	C₂²×C₁₃	semidirect
384. #389	C₂²×C₁₃	semidirect
385. #388	C₂²×C₁₃	semidirect
386. #388	C₂²×C₁₃	semidirect
387. #388	C₂²×C₁₃	semidirect
388. #388	C₂²×C₁₃	semidirect
389. #387	C₂²×C₁₃	semidirect
390. #387	C₂²×C₁₃	semidirect
393. #386	C₂²×C₁₃	semidirect
394. #386	C₂²×C₁₃	semidirect
397. #385	C₂²×C₁₃	semidirect
398. #385	C₂²×C₁₃	semidirect
399. #385	C₂²×C₁₃	semidirect
401. #381	C₂²×C₁₃	semidirect
407. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
496. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
636. C₁₃	#34986	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×#538	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2855	2
C₁₃×#2854	2
C₁₃×#2849	2
C₁₃×#2626	2
C₁₃×#2617	2
C₁₃×#2613	2
C₁₃×#2466	2
C₁₃×#2459	2
C₁₃×#2456	2
C₁₃×#2455	2
C₁₃×#2322	2
C₁₃×#2312	2
C₄×C₁₃×#120	2
#34986	13

Subgroups — C13×#34986 #15721325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34986 #15721325