Subgroups — C₂×C₁₃×#2637 #15720940

Order 3328.

2482 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#126	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2637	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#398	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#397	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#396	C₂	1	2	yes	maximal
8	C₂×C₁₃×#395	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#393	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#388	C₂	1	2	yes	maximal
11	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#126	—	2	8	no	—
15	C₂×C₁₃×#126	C₂²	1	8	yes	—
16	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#398	C₂²	1	8	yes	complemented
34	C₁₃×#398	C₂²	1	16	yes	complemented
35	C₁₃×#397	C₂²	1	8	yes	—
36	C₁₃×#396	C₂²	1	16	yes	—
37	C₁₃×#395	C₂²	1	8	yes	complemented
38	C₁₃×#393	C₂²	1	8	yes	—
39	C₁₃×#388	C₂²	1	16	yes	—
40	C₁₃×#387	C₂²	1	16	yes	complemented
41	C₁₃×#382	C₂²	1	8	yes	complemented
42	C₂×C₁₃×#95	C₂²	1	2	yes	—
43	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#95	C₂²	1	2	yes	—
46	C₂×C₁₃×#95	C₂²	1	2	yes	—
47	C₂×C₁₃×#95	C₂²	1	2	yes	—
48	C₂×C₁₃×#95	C₂²	1	2	yes	—
49	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃	—	2	4	no	—
51	C₂²×Q₈×C₁₃	—	2	8	no	—
52	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₁₃×#126	—	2	32	no	—
64	C₄×Q₈×C₁₃	—	2	32	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
71	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
72	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₂×C₄²×C₁₃	—	2	8	no	—
92	C₂×C₄²×C₁₃	D₄	1	8	yes	—
93	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
94	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
95	C₁₃×#95	C₂³	1	8	yes	—
96	C₁₃×#95	C₂³	1	4	yes	—
97	C₁₃×#95	C₂³	1	4	yes	—
98	C₁₃×#95	C₂³	1	8	yes	—
99	C₁₃×#95	C₂³	1	8	yes	—
100	C₁₃×#95	C₂³	1	8	yes	—
101	C₁₃×#95	C₂³	1	8	yes	—
102	C₂×#2637	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	—	2	2	no	—
104	C₂⁴×C₁₃	—	2	4	no	—
105	C₂⁴×C₁₃	—	2	2	no	—
106	C₂⁴×C₁₃	—	2	4	no	—
107	C₂⁴×C₁₃	—	2	2	no	—
108	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
109	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₂×Q₈×C₁₃	—	2	32	no	—
111	C₂×Q₈×C₁₃	—	2	8	no	—
112	C₂×Q₈×C₁₃	—	2	16	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₁₃	#41	1	8	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
149	C₁₃×C₄⋊C₄	—	2	16	no	—
150	C₁₃×C₄⋊C₄	—	2	8	no	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	8	no	—
153	C₁₃×C₄⋊C₄	—	2	8	no	—
154	C₁₃×C₄⋊C₄	—	2	16	no	—
155	C₁₃×C₄⋊C₄	—	4	8	no	—
156	C₁₃×C₄⋊C₄	—	4	8	no	—
157	C₁₃×C₂²⋊C₄	—	2	8	no	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	2	8	no	—
160	C₁₃×C₂²⋊C₄	—	2	16	no	—
161	C₁₃×C₂²⋊C₄	—	4	8	no	—
162	C₄²×C₁₃	—	2	16	no	—
163	C₄²×C₁₃	C₂×D₄	1	16	yes	—
164	C₂²×#126	C₂×C₁₃	1	1	yes	characteristic
165	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#2637	C₂×C₁₃	1	16	yes	direct product factor
167	C₂×#398	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂×#398	C₂×C₁₃	1	2	yes	complemented
169	C₂×#397	C₂×C₁₃	1	1	yes	characteristic
170	C₂×#396	C₂×C₁₃	1	2	yes	—
171	C₂×#395	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂×#393	C₂×C₁₃	1	1	yes	characteristic
173	C₂×#388	C₂×C₁₃	1	2	yes	—
174	C₂×#387	C₂×C₁₃	1	2	yes	complemented
175	C₂×#382	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	2	4	no	—
178	C₂³×C₁₃	—	2	2	no	—
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	4	4	no	—
182	C₂³×C₁₃	—	4	4	no	—
183	C₂³×C₁₃	—	4	4	no	—
184	C₂³×C₁₃	—	4	8	no	—
185	C₂³×C₁₃	—	4	8	no	—
186	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
187	C₂³×C₁₃	C₂×#41	1	4	yes	—
188	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
189	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
190	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
191	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
192	Q₈×C₁₃	—	2	32	no	—
193	C₂×C₄×C₁₃	—	2	8	no	—
194	C₂×C₄×C₁₃	—	2	16	no	—
195	C₂×C₄×C₁₃	—	2	8	no	—
196	C₂×C₄×C₁₃	—	2	8	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	4	4	no	—
220	C₂×C₄×C₁₃	—	4	4	no	—
221	C₂×C₄×C₁₃	—	4	8	no	—
222	C₂×C₄×C₁₃	—	4	4	no	—
223	C₂×C₄×C₁₃	—	4	8	no	—
224	C₂×C₄×C₁₃	—	4	8	no	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
228	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
229	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×#126	—	2	8	no	—
231	C₂×#126	C₂²×C₁₃	1	8	yes	—
232	C₂×C₄×Q₈	—	2	8	no	—
233	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
234	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
235	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
237	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
241	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
242	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
243	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
244	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
247	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
248	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
249	#398	C₂²×C₁₃	1	8	yes	complemented
250	#398	C₂²×C₁₃	1	16	yes	complemented
251	#397	C₂²×C₁₃	1	8	yes	—
252	#396	C₂²×C₁₃	1	16	yes	—
253	#395	C₂²×C₁₃	1	8	yes	complemented
254	#393	C₂²×C₁₃	1	8	yes	—
255	#388	C₂²×C₁₃	1	16	yes	—
256	#387	C₂²×C₁₃	1	16	yes	complemented
257	#382	C₂²×C₁₃	1	8	yes	complemented
258	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×#95	C₂²×C₁₃	1	2	yes	—
260	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#95	C₂²×C₁₃	1	2	yes	—
262	C₂×#95	C₂²×C₁₃	1	2	yes	—
263	C₂×#95	C₂²×C₁₃	1	2	yes	—
264	C₂×#95	C₂²×C₁₃	1	2	yes	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	4	no	—
269	C₂²×C₁₃	—	4	4	no	—
270	C₂²×C₁₃	—	8	8	no	—
271	C₂²×C₁₃	#525	1	4	yes	—
272	C₂²×C₁₃	#536	1	4	yes	—
273	C₂²×C₁₃	#537	1	4	yes	—
274	C₂²×C₁₃	#541	1	8	yes	—
275	C₂²×C₁₃	#542	1	8	yes	—
276	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
277	C₂²×C₁₃	C₂²×#41	1	2	yes	—
278	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
279	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
280	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
281	C₄×C₁₃	—	2	4	no	—
282	C₄×C₁₃	—	2	8	no	—
283	C₄×C₁₃	—	2	4	no	—
284	C₄×C₁₃	—	2	4	no	—
285	C₄×C₁₃	—	4	2	no	—
286	C₄×C₁₃	—	4	2	no	—
287	C₄×C₁₃	—	4	4	no	—
288	C₄×C₁₃	—	4	2	no	—
289	C₄×C₁₃	—	4	4	no	—
290	C₄×C₁₃	—	4	4	no	—
291	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×Q₈	—	2	4	no	—
293	C₂²×Q₈	—	2	8	no	—
294	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
295	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
297	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
298	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
300	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
301	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
302	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
305	#126	—	2	32	no	—
306	C₄×Q₈	—	2	32	no	—
307	C₂×C₄⋊C₄	—	2	8	no	—
308	C₂×C₄⋊C₄	—	2	4	no	—
309	C₂×C₄⋊C₄	—	2	4	no	—
310	C₂×C₄⋊C₄	—	2	4	no	—
311	C₂×C₄⋊C₄	—	2	4	no	—
312	C₂×C₄⋊C₄	—	2	8	no	—
313	C₂×C₄⋊C₄	—	4	4	no	—
314	C₂×C₄⋊C₄	—	4	4	no	—
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
323	C₂×C₂²⋊C₄	—	2	4	no	—
324	C₂×C₂²⋊C₄	—	2	4	no	—
325	C₂×C₂²⋊C₄	—	2	4	no	—
326	C₂×C₂²⋊C₄	—	2	8	no	—
327	C₂×C₂²⋊C₄	—	4	4	no	—
328	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
333	C₂×C₄²	—	2	8	no	—
334	C₂×C₄²	D₄×C₁₃	1	8	yes	—
335	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
336	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
337	#95	C₂³×C₁₃	1	8	yes	—
338	#95	C₂³×C₁₃	1	4	yes	—
339	#95	C₂³×C₁₃	1	4	yes	—
340	#95	C₂³×C₁₃	1	8	yes	—
341	#95	C₂³×C₁₃	1	8	yes	—
342	#95	C₂³×C₁₃	1	8	yes	—
343	#95	C₂³×C₁₃	1	8	yes	—
344	C₂×C₁₃	—	8	2	no	—
345	C₂×C₁₃	#2637	1	8	yes	direct product factor
346	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
347	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
348	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
349	C₂×C₁₃	C₂×#541	1	2	yes	—
350	C₂×C₁₃	C₂×#542	1	2	yes	—
351	C₂⁴	—	2	2	no	—
352	C₂⁴	—	2	4	no	—
353	C₂⁴	—	2	2	no	—
354	C₂⁴	—	2	4	no	—
355	C₂⁴	—	2	2	no	—
356	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
357	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
358	C₂×Q₈	—	2	32	no	—
359	C₂×Q₈	—	2	8	no	—
360	C₂×Q₈	—	2	16	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
384	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
385	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
386	C₂²×C₄	C₁₃×#41	1	8	yes	—
387	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
388	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
389	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
390	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
391	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
392	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
393	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
394	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
396	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
397	C₄⋊C₄	—	2	16	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	8	no	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	16	no	—
403	C₄⋊C₄	—	4	8	no	—
404	C₄⋊C₄	—	4	8	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	—	2	16	no	—
409	C₂²⋊C₄	—	4	8	no	—
410	C₄²	—	2	16	no	—
411	C₄²	C₂×D₄×C₁₃	1	16	yes	—
412	C₁₃	C₂×#2637	1	1	yes	characteristic, direct product factor, Sylow
413	C₂³	—	2	2	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	4	8	no	—
422	C₂³	—	4	8	no	—
423	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
424	C₂³	C₂×C₁₃×#41	1	4	yes	—
425	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
426	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
427	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
428	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
429	Q₈	—	2	32	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	16	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	8	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	4	8	no	—
462	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
463	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
464	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
465	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	8	8	no	—
472	C₂²	C₁₃×#525	1	4	yes	—
473	C₂²	C₁₃×#536	1	4	yes	—
474	C₂²	C₁₃×#537	1	4	yes	—
475	C₂²	C₁₃×#541	1	8	yes	—
476	C₂²	C₁₃×#542	1	8	yes	—
477	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
478	C₂²	C₂²×C₁₃×#41	1	2	yes	—
479	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
481	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
482	C₄	—	2	4	no	—
483	C₄	—	2	8	no	—
484	C₄	—	2	4	no	—
485	C₄	—	2	4	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	4	no	—
491	C₄	—	4	4	no	—
492	C₂	—	8	2	no	—
493	C₂	C₁₃×#2637	1	8	yes	direct product factor
494	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
495	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
496	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
497	C₂	C₂×C₁₃×#541	1	2	yes	—
498	C₂	C₂×C₁₃×#542	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
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
2. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#2637	C₂	direct (N × H)
4. C₂×C₁₃×#398	C₂	semidirect
5. C₂×C₁₃×#398	C₂	semidirect
8. C₂×C₁₃×#395	C₂	semidirect
11. C₂×C₁₃×#387	C₂	semidirect
12. C₂×C₁₃×#382	C₂	semidirect
17. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
33. C₁₃×#398	C₂²	semidirect
34. C₁₃×#398	C₂²	semidirect
37. C₁₃×#395	C₂²	semidirect
40. C₁₃×#387	C₂²	semidirect
41. C₁₃×#382	C₂²	semidirect
102. C₂×#2637	C₁₃	direct (N × H)
165. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
166. #2637	C₂×C₁₃	direct (N × H)
167. C₂×#398	C₂×C₁₃	semidirect
168. C₂×#398	C₂×C₁₃	semidirect
171. C₂×#395	C₂×C₁₃	semidirect
174. C₂×#387	C₂×C₁₃	semidirect
175. C₂×#382	C₂×C₁₃	semidirect
233. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
249. #398	C₂²×C₁₃	semidirect
250. #398	C₂²×C₁₃	semidirect
253. #395	C₂²×C₁₃	semidirect
256. #387	C₂²×C₁₃	semidirect
257. #382	C₂²×C₁₃	semidirect
345. C₂×C₁₃	#2637	direct (N × H)
412. C₁₃	C₂×#2637	direct (N × H)
493. C₂	C₁₃×#2637	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×#126	2
C₂²×C₄×Q₈×C₁₃	2
C₁₃×#2637	2
C₂×C₁₃×#398	2
C₂×C₁₃×#397	2
C₂×C₁₃×#396	2
C₂×C₁₃×#395	2
C₂×C₁₃×#393	2
C₂×C₁₃×#388	2
C₂×C₁₃×#387	2
C₂×C₁₃×#382	2
C₂×#2637	13

Subgroups — C2×C13×#2637 #15720940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2637 #15720940