Subgroups — C₂×C₁₃×#2507 #15721109

Order 3328.

2054 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2507	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₁₃×#398	C₂	1	2	yes	maximal
3	C₂×C₁₃×#398	C₂	1	2	yes	maximal
4	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#389	C₂	1	2	yes	maximal
9	C₂×C₁₃×#387	C₂	1	2	yes	maximal
10	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#398	C₂²	1	16	yes	—
30	C₁₃×#398	C₂²	1	16	yes	—
31	C₁₃×#389	C₂²	1	16	yes	—
32	C₁₃×#389	C₂²	1	8	yes	—
33	C₁₃×#389	C₂²	1	8	yes	—
34	C₁₃×#389	C₂²	1	8	yes	—
35	C₁₃×#389	C₂²	1	8	yes	—
36	C₁₃×#387	C₂²	1	16	yes	—
37	C₁₃×#384	C₂²	1	8	yes	—
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
40	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#95	C₂²	1	2	yes	—
43	C₂×C₁₃×#95	C₂²	1	2	yes	—
44	C₂×C₁₃×#95	C₂²	1	2	yes	—
45	C₂×C₁₃×#95	C₂²	1	2	yes	—
46	C₂×C₁₃×#95	C₂²	1	2	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
63	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
64	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
65	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
66	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
67	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
68	C₂×C₁₃×C₄⋊C₄	Q₈	1	8	yes	—
69	C₂×C₁₃×C₄⋊C₄	Q₈	1	8	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
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	8	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₄²×C₁₃	—	2	4	no	—
83	C₂×C₄²×C₁₃	—	2	4	no	—
84	C₂×C₄²×C₁₃	—	2	4	no	—
85	C₂×C₄²×C₁₃	—	4	4	no	—
86	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
87	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
88	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
89	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
90	C₁₃×#95	C₂³	1	4	yes	—
91	C₁₃×#95	C₂³	1	4	yes	—
92	C₁₃×#95	C₂³	1	8	yes	—
93	C₁₃×#95	C₂³	1	8	yes	—
94	C₁₃×#95	C₂³	1	8	yes	—
95	C₁₃×#95	C₂³	1	8	yes	—
96	C₁₃×#95	C₂³	1	8	yes	—
97	C₂×#2507	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
125	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
126	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
129	C₂²×C₄×C₁₃	#41	1	4	yes	—
130	C₂²×C₄×C₁₃	#41	1	4	yes	—
131	C₂²×C₄×C₁₃	#41	1	4	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
143	C₁₃×C₄⋊C₄	—	2	8	no	—
144	C₁₃×C₄⋊C₄	—	2	16	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	8	no	—
147	C₁₃×C₄⋊C₄	—	2	8	no	—
148	C₁₃×C₄⋊C₄	—	4	8	no	—
149	C₁₃×C₄⋊C₄	—	4	8	no	—
150	C₁₃×C₄⋊C₄	—	4	8	no	—
151	C₁₃×C₄⋊C₄	—	4	8	no	—
152	C₁₃×C₄⋊C₄	—	4	8	no	—
153	C₁₃×C₄⋊C₄	C₂×Q₈	1	16	yes	—
154	C₁₃×C₄⋊C₄	C₂×Q₈	1	16	yes	—
155	C₄²×C₁₃	—	2	8	no	—
156	C₄²×C₁₃	—	2	8	no	—
157	C₄²×C₁₃	—	2	8	no	—
158	C₄²×C₁₃	—	4	8	no	—
159	#2507	C₂×C₁₃	1	16	yes	direct product factor
160	C₂×#398	C₂×C₁₃	1	2	yes	—
161	C₂×#398	C₂×C₁₃	1	2	yes	—
162	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
163	C₂×#389	C₂×C₁₃	1	2	yes	—
164	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
165	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
166	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
167	C₂×#387	C₂×C₁₃	1	2	yes	—
168	C₂×#384	C₂×C₁₃	1	1	yes	characteristic
169	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
170	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
171	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
172	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
173	C₂³×C₁₃	C₂×#41	1	2	yes	—
174	C₂³×C₁₃	C₂×#41	1	2	yes	—
175	C₂³×C₁₃	C₂×#41	1	2	yes	—
176	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
177	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
178	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
179	C₂×C₄×C₁₃	—	2	8	no	—
180	C₂×C₄×C₁₃	—	2	8	no	—
181	C₂×C₄×C₁₃	—	2	8	no	—
182	C₂×C₄×C₁₃	—	2	8	no	—
183	C₂×C₄×C₁₃	—	2	16	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	4	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	4	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	4	4	no	—
210	C₂×C₄×C₁₃	—	4	8	no	—
211	C₂×C₄×C₁₃	—	4	8	no	—
212	C₂×C₄×C₁₃	—	4	4	no	—
213	C₂×C₄×C₁₃	—	4	8	no	—
214	C₂×C₄×C₁₃	#125	1	16	yes	—
215	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
216	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
217	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
218	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
219	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
220	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
221	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
222	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
224	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
225	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
227	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
229	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
230	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
231	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
232	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
233	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
235	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
236	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
237	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
238	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
239	#398	C₂²×C₁₃	1	16	yes	—
240	#398	C₂²×C₁₃	1	16	yes	—
241	#389	C₂²×C₁₃	1	16	yes	—
242	#389	C₂²×C₁₃	1	8	yes	—
243	#389	C₂²×C₁₃	1	8	yes	—
244	#389	C₂²×C₁₃	1	8	yes	—
245	#389	C₂²×C₁₃	1	8	yes	—
246	#387	C₂²×C₁₃	1	16	yes	—
247	#384	C₂²×C₁₃	1	8	yes	—
248	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
249	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
250	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×#95	C₂²×C₁₃	1	2	yes	—
252	C₂×#95	C₂²×C₁₃	1	2	yes	—
253	C₂×#95	C₂²×C₁₃	1	2	yes	—
254	C₂×#95	C₂²×C₁₃	1	2	yes	—
255	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×#95	C₂²×C₁₃	1	2	yes	—
257	C₂²×C₁₃	C₂×#125	1	4	yes	—
258	C₂²×C₁₃	#533	1	4	yes	—
259	C₂²×C₁₃	#540	1	4	yes	—
260	C₂²×C₁₃	#553	1	4	yes	—
261	C₂²×C₁₃	#554	1	4	yes	—
262	C₂²×C₁₃	#554	1	4	yes	—
263	C₂²×C₁₃	Q₈²	1	4	yes	—
264	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
265	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
266	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
267	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
268	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
269	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
270	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
271	C₄×C₁₃	—	2	4	no	—
272	C₄×C₁₃	—	2	4	no	—
273	C₄×C₁₃	—	2	4	no	—
274	C₄×C₁₃	—	2	4	no	—
275	C₄×C₁₃	—	2	8	no	—
276	C₄×C₁₃	—	4	2	no	—
277	C₄×C₁₃	—	4	4	no	—
278	C₄×C₁₃	—	4	4	no	—
279	C₄×C₁₃	—	4	2	no	—
280	C₄×C₁₃	—	4	4	no	—
281	C₄×C₁₃	C₂×#125	1	8	yes	—
282	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
283	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
284	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
286	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
289	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	—	2	4	no	—
294	C₂×C₄⋊C₄	—	2	8	no	—
295	C₂×C₄⋊C₄	—	2	4	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	4	4	no	—
299	C₂×C₄⋊C₄	—	4	4	no	—
300	C₂×C₄⋊C₄	—	4	4	no	—
301	C₂×C₄⋊C₄	—	4	4	no	—
302	C₂×C₄⋊C₄	—	4	4	no	—
303	C₂×C₄⋊C₄	Q₈×C₁₃	1	8	yes	—
304	C₂×C₄⋊C₄	Q₈×C₁₃	1	8	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
317	C₂×C₄²	—	2	4	no	—
318	C₂×C₄²	—	2	4	no	—
319	C₂×C₄²	—	2	4	no	—
320	C₂×C₄²	—	4	4	no	—
321	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
322	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
323	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
324	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
325	#95	C₂³×C₁₃	1	4	yes	—
326	#95	C₂³×C₁₃	1	4	yes	—
327	#95	C₂³×C₁₃	1	8	yes	—
328	#95	C₂³×C₁₃	1	8	yes	—
329	#95	C₂³×C₁₃	1	8	yes	—
330	#95	C₂³×C₁₃	1	8	yes	—
331	#95	C₂³×C₁₃	1	8	yes	—
332	C₂×C₁₃	#2507	1	8	yes	direct product factor
333	C₂×C₁₃	C₂²×#125	1	1	yes	characteristic
334	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
335	C₂×C₁₃	C₂×#540	1	1	yes	characteristic
336	C₂×C₁₃	C₂×#553	1	1	yes	characteristic
337	C₂×C₁₃	C₂×#554	1	1	yes	characteristic
338	C₂×C₁₃	C₂×#554	1	1	yes	characteristic
339	C₂×C₁₃	C₂×Q₈²	1	1	yes	characteristic
340	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
367	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
368	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
369	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
370	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
371	C₂²×C₄	C₁₃×#41	1	4	yes	—
372	C₂²×C₄	C₁₃×#41	1	4	yes	—
373	C₂²×C₄	C₁₃×#41	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
376	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
378	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
379	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
382	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
383	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
385	C₄⋊C₄	—	2	8	no	—
386	C₄⋊C₄	—	2	16	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	8	no	—
389	C₄⋊C₄	—	2	8	no	—
390	C₄⋊C₄	—	4	8	no	—
391	C₄⋊C₄	—	4	8	no	—
392	C₄⋊C₄	—	4	8	no	—
393	C₄⋊C₄	—	4	8	no	—
394	C₄⋊C₄	—	4	8	no	—
395	C₄⋊C₄	C₂×Q₈×C₁₃	1	16	yes	—
396	C₄⋊C₄	C₂×Q₈×C₁₃	1	16	yes	—
397	C₄²	—	2	8	no	—
398	C₄²	—	2	8	no	—
399	C₄²	—	2	8	no	—
400	C₄²	—	4	8	no	—
401	C₁₃	C₂×#2507	1	1	yes	characteristic, direct product factor, Sylow
402	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
403	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
404	C₂³	C₂×C₁₃×#41	1	2	yes	—
405	C₂³	C₂×C₁₃×#41	1	2	yes	—
406	C₂³	C₂×C₁₃×#41	1	2	yes	—
407	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
408	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
409	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	16	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	8	no	—
442	C₂×C₄	—	4	8	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	C₁₃×#125	1	16	yes	—
446	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
447	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
448	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
449	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
450	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
451	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
452	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
453	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
454	C₂²	C₂×C₁₃×#125	1	4	yes	—
455	C₂²	C₁₃×#533	1	4	yes	—
456	C₂²	C₁₃×#540	1	4	yes	—
457	C₂²	C₁₃×#553	1	4	yes	—
458	C₂²	C₁₃×#554	1	4	yes	—
459	C₂²	C₁₃×#554	1	4	yes	—
460	C₂²	Q₈²×C₁₃	1	4	yes	—
461	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
462	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
463	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
464	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
465	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
466	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
468	C₄	—	2	4	no	—
469	C₄	—	2	4	no	—
470	C₄	—	2	4	no	—
471	C₄	—	2	4	no	—
472	C₄	—	2	8	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	4	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	4	no	—
478	C₄	C₂×C₁₃×#125	1	8	yes	—
479	C₂	C₁₃×#2507	1	8	yes	direct product factor
480	C₂	C₂²×C₁₃×#125	1	1	yes	characteristic
481	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
482	C₂	C₂×C₁₃×#540	1	1	yes	characteristic
483	C₂	C₂×C₁₃×#553	1	1	yes	characteristic
484	C₂	C₂×C₁₃×#554	1	1	yes	characteristic
485	C₂	C₂×C₁₃×#554	1	1	yes	characteristic
486	C₂	C₂×Q₈²×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	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. C₁₃×#2507	C₂	direct (N × H)
97. C₂×#2507	C₁₃	direct (N × H)
159. #2507	C₂×C₁₃	direct (N × H)
332. C₂×C₁₃	#2507	direct (N × H)
401. C₁₃	C₂×#2507	direct (N × H)
479. C₂	C₁₃×#2507	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2507	2
C₂×C₁₃×#398	2
C₂×C₁₃×#389	2
C₂×C₁₃×#387	2
C₂×C₁₃×#384	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2507	13

Subgroups — C2×C13×#2507 #15721109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2507 #15721109